Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,14,Mod(5,8)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.5");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.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: | \(8.57847431615\) |
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: | \( x^{10} - 5 x^{9} + 752 x^{8} + 708 x^{7} - 743866 x^{6} + 96647426 x^{5} + 2540283092 x^{4} + \cdots + 31\!\cdots\!68 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{48}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5.8 | ||
Root | \(27.9424 + 31.0290i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.5 |
Dual form | 8.14.b.b.5.7 |
$q$-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 \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 65.8848 | + | 62.0580i | 0.727931 | + | 0.685650i | ||||
\(3\) | − | 1231.41i | − | 0.975247i | −0.873054 | − | 0.487624i | \(-0.837864\pi\) | ||
0.873054 | − | 0.487624i | \(-0.162136\pi\) | |||||||
\(4\) | 489.620 | + | 8177.36i | 0.0597680 | + | 0.998212i | ||||
\(5\) | 25270.7i | 0.723288i | 0.932316 | + | 0.361644i | \(0.117784\pi\) | ||||
−0.932316 | + | 0.361644i | \(0.882216\pi\) | |||||||
\(6\) | 76418.8 | − | 81131.3i | 0.668678 | − | 0.709913i | ||||
\(7\) | 608245. | 1.95408 | 0.977038 | − | 0.213064i | \(-0.0683442\pi\) | ||||
0.977038 | + | 0.213064i | \(0.0683442\pi\) | |||||||
\(8\) | −475211. | + | 569148.i | −0.640917 | + | 0.767610i | ||||
\(9\) | 77950.5 | 0.0488925 | ||||||||
\(10\) | −1.56825e6 | + | 1.66495e6i | −0.495923 | + | 0.526504i | ||||
\(11\) | 7.12288e6i | 1.21228i | 0.795358 | + | 0.606140i | \(0.207283\pi\) | ||||
−0.795358 | + | 0.606140i | \(0.792717\pi\) | |||||||
\(12\) | 1.00697e7 | − | 602923.i | 0.973504 | − | 0.0582886i | ||||
\(13\) | − | 1.12887e7i | − | 0.648652i | −0.945945 | − | 0.324326i | \(-0.894863\pi\) | ||
0.945945 | − | 0.324326i | \(-0.105137\pi\) | |||||||
\(14\) | 4.00741e7 | + | 3.77465e7i | 1.42243 | + | 1.33981i | ||||
\(15\) | 3.11186e7 | 0.705385 | ||||||||
\(16\) | −6.66294e7 | + | 8.00759e6i | −0.992856 | + | 0.119322i | ||||
\(17\) | −5.09178e7 | −0.511625 | −0.255812 | − | 0.966726i | \(-0.582343\pi\) | ||||
−0.255812 | + | 0.966726i | \(0.582343\pi\) | |||||||
\(18\) | 5.13575e6 | + | 4.83745e6i | 0.0355904 | + | 0.0335232i | ||||
\(19\) | − | 1.86178e8i | − | 0.907881i | −0.891032 | − | 0.453941i | \(-0.850018\pi\) | ||
0.891032 | − | 0.453941i | \(-0.149982\pi\) | |||||||
\(20\) | −2.06647e8 | + | 1.23730e7i | −0.721995 | + | 0.0432295i | ||||
\(21\) | − | 7.49000e8i | − | 1.90571i | ||||||
\(22\) | −4.42031e8 | + | 4.69289e8i | −0.831200 | + | 0.882457i | ||||
\(23\) | −3.07644e8 | −0.433328 | −0.216664 | − | 0.976246i | \(-0.569518\pi\) | ||||
−0.216664 | + | 0.976246i | \(0.569518\pi\) | |||||||
\(24\) | 7.00855e8 | + | 5.85181e8i | 0.748610 | + | 0.625053i | ||||
\(25\) | 5.82097e8 | 0.476854 | ||||||||
\(26\) | 7.00553e8 | − | 7.43753e8i | 0.444748 | − | 0.472174i | ||||
\(27\) | − | 2.05926e9i | − | 1.02293i | ||||||
\(28\) | 2.97809e8 | + | 4.97384e9i | 0.116791 | + | 1.95058i | ||||
\(29\) | 4.74147e8i | 0.148022i | 0.997257 | + | 0.0740110i | \(0.0235800\pi\) | ||||
−0.997257 | + | 0.0740110i | \(0.976420\pi\) | |||||||
\(30\) | 2.05024e9 | + | 1.93115e9i | 0.513472 | + | 0.483647i | ||||
\(31\) | −2.41919e9 | −0.489574 | −0.244787 | − | 0.969577i | \(-0.578718\pi\) | ||||
−0.244787 | + | 0.969577i | \(0.578718\pi\) | |||||||
\(32\) | −4.88680e9 | − | 3.60731e9i | −0.804544 | − | 0.593893i | ||||
\(33\) | 8.77119e9 | 1.18227 | ||||||||
\(34\) | −3.35471e9 | − | 3.15985e9i | −0.372427 | − | 0.350795i | ||||
\(35\) | 1.53708e10i | 1.41336i | ||||||||
\(36\) | 3.81661e7 | + | 6.37429e8i | 0.00292221 | + | 0.0488051i | ||||
\(37\) | − | 1.55589e10i | − | 0.996939i | −0.866907 | − | 0.498470i | \(-0.833896\pi\) | ||
0.866907 | − | 0.498470i | \(-0.166104\pi\) | |||||||
\(38\) | 1.15538e10 | − | 1.22663e10i | 0.622489 | − | 0.660875i | ||||
\(39\) | −1.39010e10 | −0.632596 | ||||||||
\(40\) | −1.43828e10 | − | 1.20089e10i | −0.555203 | − | 0.463568i | ||||
\(41\) | −2.32986e10 | −0.766009 | −0.383005 | − | 0.923746i | \(-0.625111\pi\) | ||||
−0.383005 | + | 0.923746i | \(0.625111\pi\) | |||||||
\(42\) | 4.64814e10 | − | 4.93477e10i | 1.30665 | − | 1.38722i | ||||
\(43\) | 6.55713e10i | 1.58186i | 0.611905 | + | 0.790932i | \(0.290404\pi\) | ||||
−0.611905 | + | 0.790932i | \(0.709596\pi\) | |||||||
\(44\) | −5.82463e10 | + | 3.48750e9i | −1.21011 | + | 0.0724556i | ||||
\(45\) | 1.96986e9i | 0.0353634i | ||||||||
\(46\) | −2.02691e10 | − | 1.90917e10i | −0.315433 | − | 0.297112i | ||||
\(47\) | −6.84950e10 | −0.926879 | −0.463440 | − | 0.886129i | \(-0.653385\pi\) | ||||
−0.463440 | + | 0.886129i | \(0.653385\pi\) | |||||||
\(48\) | 9.86063e9 | + | 8.20482e10i | 0.116369 | + | 0.968280i | ||||
\(49\) | 2.73073e11 | 2.81842 | ||||||||
\(50\) | 3.83514e10 | + | 3.61237e10i | 0.347117 | + | 0.326955i | ||||
\(51\) | 6.27007e10i | 0.498960i | ||||||||
\(52\) | 9.23116e10 | − | 5.52716e9i | 0.647492 | − | 0.0387686i | ||||
\(53\) | − | 9.64859e10i | − | 0.597958i | −0.954260 | − | 0.298979i | \(-0.903354\pi\) | ||
0.954260 | − | 0.298979i | \(-0.0966460\pi\) | |||||||
\(54\) | 1.27793e11 | − | 1.35674e11i | 0.701372 | − | 0.744623i | ||||
\(55\) | −1.80000e11 | −0.876828 | ||||||||
\(56\) | −2.89045e11 | + | 3.46182e11i | −1.25240 | + | 1.49997i | ||||
\(57\) | −2.29261e11 | −0.885409 | ||||||||
\(58\) | −2.94246e10 | + | 3.12391e10i | −0.101491 | + | 0.107750i | ||||
\(59\) | − | 3.22470e11i | − | 0.995295i | −0.867379 | − | 0.497647i | \(-0.834197\pi\) | ||
0.867379 | − | 0.497647i | \(-0.165803\pi\) | |||||||
\(60\) | 1.52363e10 | + | 2.54468e11i | 0.0421595 | + | 0.704124i | ||||
\(61\) | − | 6.66785e11i | − | 1.65707i | −0.559934 | − | 0.828537i | \(-0.689174\pi\) | ||
0.559934 | − | 0.828537i | \(-0.310826\pi\) | |||||||
\(62\) | −1.59388e11 | − | 1.50130e11i | −0.356377 | − | 0.335677i | ||||
\(63\) | 4.74130e10 | 0.0955397 | ||||||||
\(64\) | −9.81039e10 | − | 5.40932e11i | −0.178450 | − | 0.983949i | ||||
\(65\) | 2.85273e11 | 0.469162 | ||||||||
\(66\) | 5.77888e11 | + | 5.44322e11i | 0.860614 | + | 0.810626i | ||||
\(67\) | 5.91556e11i | 0.798932i | 0.916748 | + | 0.399466i | \(0.130804\pi\) | ||||
−0.916748 | + | 0.399466i | \(0.869196\pi\) | |||||||
\(68\) | −2.49303e10 | − | 4.16373e11i | −0.0305788 | − | 0.510710i | ||||
\(69\) | 3.78836e11i | 0.422602i | ||||||||
\(70\) | −9.53878e11 | + | 1.01270e12i | −0.969071 | + | 1.02883i | ||||
\(71\) | 8.43664e11 | 0.781610 | 0.390805 | − | 0.920473i | \(-0.372197\pi\) | ||||
0.390805 | + | 0.920473i | \(0.372197\pi\) | |||||||
\(72\) | −3.70430e10 | + | 4.43654e10i | −0.0313361 | + | 0.0375304i | ||||
\(73\) | −7.21901e11 | −0.558315 | −0.279158 | − | 0.960245i | \(-0.590055\pi\) | ||||
−0.279158 | + | 0.960245i | \(0.590055\pi\) | |||||||
\(74\) | 9.65556e11 | − | 1.02510e12i | 0.683552 | − | 0.725703i | ||||
\(75\) | − | 7.16800e11i | − | 0.465050i | ||||||
\(76\) | 1.52244e12 | − | 9.11562e10i | 0.906258 | − | 0.0542622i | ||||
\(77\) | 4.33246e12i | 2.36889i | ||||||||
\(78\) | −9.15866e11 | − | 8.62668e11i | −0.460486 | − | 0.433739i | ||||
\(79\) | 5.78664e11 | 0.267824 | 0.133912 | − | 0.990993i | \(-0.457246\pi\) | ||||
0.133912 | + | 0.990993i | \(0.457246\pi\) | |||||||
\(80\) | −2.02357e11 | − | 1.68377e12i | −0.0863045 | − | 0.718121i | ||||
\(81\) | −2.41151e12 | −0.948717 | ||||||||
\(82\) | −1.53502e12 | − | 1.44586e12i | −0.557602 | − | 0.525214i | ||||
\(83\) | − | 1.54397e11i | − | 0.0518361i | −0.999664 | − | 0.0259180i | \(-0.991749\pi\) | ||
0.999664 | − | 0.0259180i | \(-0.00825089\pi\) | |||||||
\(84\) | 6.12484e12 | − | 3.66725e11i | 1.90230 | − | 0.113900i | ||||
\(85\) | − | 1.28673e12i | − | 0.370052i | ||||||
\(86\) | −4.06922e12 | + | 4.32015e12i | −1.08460 | + | 1.15149i | ||||
\(87\) | 5.83870e11 | 0.144358 | ||||||||
\(88\) | −4.05397e12 | − | 3.38487e12i | −0.930558 | − | 0.776971i | ||||
\(89\) | 2.38527e12 | 0.508749 | 0.254374 | − | 0.967106i | \(-0.418130\pi\) | ||||
0.254374 | + | 0.967106i | \(0.418130\pi\) | |||||||
\(90\) | −1.22245e11 | + | 1.29784e11i | −0.0242469 | + | 0.0257421i | ||||
\(91\) | − | 6.86629e12i | − | 1.26752i | ||||||
\(92\) | −1.50628e11 | − | 2.51571e12i | −0.0258992 | − | 0.432554i | ||||
\(93\) | 2.97901e12i | 0.477456i | ||||||||
\(94\) | −4.51278e12 | − | 4.25066e12i | −0.674704 | − | 0.635515i | ||||
\(95\) | 4.70483e12 | 0.656660 | ||||||||
\(96\) | −4.44208e12 | + | 6.01766e12i | −0.579193 | + | 0.784629i | ||||
\(97\) | −1.26695e13 | −1.54435 | −0.772173 | − | 0.635412i | \(-0.780830\pi\) | ||||
−0.772173 | + | 0.635412i | \(0.780830\pi\) | |||||||
\(98\) | 1.79914e13 | + | 1.69464e13i | 2.05161 | + | 1.93245i | ||||
\(99\) | 5.55232e11i | 0.0592714i | ||||||||
\(100\) | 2.85006e11 | + | 4.76001e12i | 0.0285006 | + | 0.476001i | ||||
\(101\) | − | 1.38377e13i | − | 1.29710i | −0.761170 | − | 0.648552i | \(-0.775375\pi\) | ||
0.761170 | − | 0.648552i | \(-0.224625\pi\) | |||||||
\(102\) | −3.89108e12 | + | 4.13102e12i | −0.342112 | + | 0.363209i | ||||
\(103\) | 1.67913e12 | 0.138561 | 0.0692806 | − | 0.997597i | \(-0.477930\pi\) | ||||
0.0692806 | + | 0.997597i | \(0.477930\pi\) | |||||||
\(104\) | 6.42494e12 | + | 5.36451e12i | 0.497912 | + | 0.415732i | ||||
\(105\) | 1.89277e13 | 1.37838 | ||||||||
\(106\) | 5.98772e12 | − | 6.35695e12i | 0.409990 | − | 0.435272i | ||||
\(107\) | 1.44249e13i | 0.929217i | 0.885516 | + | 0.464608i | \(0.153805\pi\) | ||||
−0.885516 | + | 0.464608i | \(0.846195\pi\) | |||||||
\(108\) | 1.68393e13 | − | 1.00825e12i | 1.02110 | − | 0.0611385i | ||||
\(109\) | − | 4.17643e12i | − | 0.238524i | −0.992863 | − | 0.119262i | \(-0.961947\pi\) | ||
0.992863 | − | 0.119262i | \(-0.0380529\pi\) | |||||||
\(110\) | −1.18593e13 | − | 1.11704e13i | −0.638271 | − | 0.601197i | ||||
\(111\) | −1.91594e13 | −0.972263 | ||||||||
\(112\) | −4.05270e13 | + | 4.87058e12i | −1.94012 | + | 0.233165i | ||||
\(113\) | 1.63143e13 | 0.737156 | 0.368578 | − | 0.929597i | \(-0.379845\pi\) | ||||
0.368578 | + | 0.929597i | \(0.379845\pi\) | |||||||
\(114\) | −1.51048e13 | − | 1.42275e13i | −0.644517 | − | 0.607080i | ||||
\(115\) | − | 7.77436e12i | − | 0.313421i | ||||||
\(116\) | −3.87727e12 | + | 2.32152e11i | −0.147757 | + | 0.00884698i | ||||
\(117\) | − | 8.79958e11i | − | 0.0317142i | ||||||
\(118\) | 2.00119e13 | − | 2.12459e13i | 0.682424 | − | 0.724506i | ||||
\(119\) | −3.09705e13 | −0.999753 | ||||||||
\(120\) | −1.47879e13 | + | 1.77111e13i | −0.452094 | + | 0.541461i | ||||
\(121\) | −1.62127e13 | −0.469623 | ||||||||
\(122\) | 4.13793e13 | − | 4.39310e13i | 1.13617 | − | 1.20624i | ||||
\(123\) | 2.86901e13i | 0.747048i | ||||||||
\(124\) | −1.18448e12 | − | 1.97826e13i | −0.0292609 | − | 0.488699i | ||||
\(125\) | 4.55579e13i | 1.06819i | ||||||||
\(126\) | 3.12380e12 | + | 2.94235e12i | 0.0695464 | + | 0.0655068i | ||||
\(127\) | −1.28760e13 | −0.272306 | −0.136153 | − | 0.990688i | \(-0.543474\pi\) | ||||
−0.136153 | + | 0.990688i | \(0.543474\pi\) | |||||||
\(128\) | 2.71056e13 | − | 4.17273e13i | 0.544745 | − | 0.838602i | ||||
\(129\) | 8.07452e13 | 1.54271 | ||||||||
\(130\) | 1.87951e13 | + | 1.77034e13i | 0.341518 | + | 0.321681i | ||||
\(131\) | 7.97301e13i | 1.37835i | 0.724596 | + | 0.689174i | \(0.242027\pi\) | ||||
−0.724596 | + | 0.689174i | \(0.757973\pi\) | |||||||
\(132\) | 4.29454e12 | + | 7.17251e13i | 0.0706621 | + | 1.18016i | ||||
\(133\) | − | 1.13242e14i | − | 1.77407i | ||||||
\(134\) | −3.67108e13 | + | 3.89746e13i | −0.547788 | + | 0.581567i | ||||
\(135\) | 5.20387e13 | 0.739873 | ||||||||
\(136\) | 2.41967e13 | − | 2.89798e13i | 0.327909 | − | 0.392728i | ||||
\(137\) | −1.07364e14 | −1.38732 | −0.693660 | − | 0.720303i | \(-0.744003\pi\) | ||||
−0.693660 | + | 0.720303i | \(0.744003\pi\) | |||||||
\(138\) | −2.35098e13 | + | 2.49595e13i | −0.289757 | + | 0.307626i | ||||
\(139\) | 1.57684e12i | 0.0185435i | 0.999957 | + | 0.00927176i | \(0.00295134\pi\) | ||||
−0.999957 | + | 0.00927176i | \(0.997049\pi\) | |||||||
\(140\) | −1.25692e14 | + | 7.52583e12i | −1.41083 | + | 0.0844738i | ||||
\(141\) | 8.43455e13i | 0.903936i | ||||||||
\(142\) | 5.55847e13 | + | 5.23561e13i | 0.568959 | + | 0.535911i | ||||
\(143\) | 8.04079e13 | 0.786348 | ||||||||
\(144\) | −5.19379e12 | + | 6.24195e11i | −0.0485432 | + | 0.00583397i | ||||
\(145\) | −1.19820e13 | −0.107063 | ||||||||
\(146\) | −4.75623e13 | − | 4.47997e13i | −0.406415 | − | 0.382809i | ||||
\(147\) | − | 3.36266e14i | − | 2.74865i | ||||||
\(148\) | 1.27231e14 | − | 7.61796e12i | 0.995157 | − | 0.0595851i | ||||
\(149\) | − | 6.35045e13i | − | 0.475438i | −0.971334 | − | 0.237719i | \(-0.923600\pi\) | ||
0.971334 | − | 0.237719i | \(-0.0763998\pi\) | |||||||
\(150\) | 4.44832e13 | − | 4.72263e13i | 0.318862 | − | 0.338525i | ||||
\(151\) | −5.05899e13 | −0.347307 | −0.173654 | − | 0.984807i | \(-0.555557\pi\) | ||||
−0.173654 | + | 0.984807i | \(0.555557\pi\) | |||||||
\(152\) | 1.05963e14 | + | 8.84737e13i | 0.696899 | + | 0.581877i | ||||
\(153\) | −3.96906e12 | −0.0250146 | ||||||||
\(154\) | −2.68863e14 | + | 2.85443e14i | −1.62423 | + | 1.72439i | ||||
\(155\) | − | 6.11345e13i | − | 0.354104i | ||||||
\(156\) | −6.80621e12 | − | 1.13673e14i | −0.0378090 | − | 0.631465i | ||||
\(157\) | 1.02755e14i | 0.547587i | 0.961788 | + | 0.273794i | \(0.0882786\pi\) | ||||
−0.961788 | + | 0.273794i | \(0.911721\pi\) | |||||||
\(158\) | 3.81251e13 | + | 3.59107e13i | 0.194958 | + | 0.183634i | ||||
\(159\) | −1.18814e14 | −0.583157 | ||||||||
\(160\) | 9.11590e13 | − | 1.23493e14i | 0.429556 | − | 0.581917i | ||||
\(161\) | −1.87123e14 | −0.846757 | ||||||||
\(162\) | −1.58882e14 | − | 1.49653e14i | −0.690601 | − | 0.650488i | ||||
\(163\) | 1.15948e14i | 0.484221i | 0.970249 | + | 0.242111i | \(0.0778397\pi\) | ||||
−0.970249 | + | 0.242111i | \(0.922160\pi\) | |||||||
\(164\) | −1.14074e13 | − | 1.90521e14i | −0.0457828 | − | 0.764640i | ||||
\(165\) | 2.21654e14i | 0.855124i | ||||||||
\(166\) | 9.58158e12 | − | 1.01724e13i | 0.0355414 | − | 0.0377331i | ||||
\(167\) | 4.53080e14 | 1.61628 | 0.808142 | − | 0.588988i | \(-0.200474\pi\) | ||||
0.808142 | + | 0.588988i | \(0.200474\pi\) | |||||||
\(168\) | 4.26292e14 | + | 3.55933e14i | 1.46284 | + | 1.22140i | ||||
\(169\) | 1.75441e14 | 0.579251 | ||||||||
\(170\) | 7.98516e13 | − | 8.47757e13i | 0.253726 | − | 0.269373i | ||||
\(171\) | − | 1.45126e13i | − | 0.0443886i | ||||||
\(172\) | −5.36200e14 | + | 3.21050e13i | −1.57904 | + | 0.0945448i | ||||
\(173\) | 2.54255e14i | 0.721058i | 0.932748 | + | 0.360529i | \(0.117404\pi\) | ||||
−0.932748 | + | 0.360529i | \(0.882596\pi\) | |||||||
\(174\) | 3.84682e13 | + | 3.62338e13i | 0.105083 | + | 0.0989792i | ||||
\(175\) | 3.54058e14 | 0.931809 | ||||||||
\(176\) | −5.70370e13 | − | 4.74593e14i | −0.144652 | − | 1.20362i | ||||
\(177\) | −3.97094e14 | −0.970659 | ||||||||
\(178\) | 1.57153e14 | + | 1.48025e14i | 0.370334 | + | 0.348823i | ||||
\(179\) | 7.88234e14i | 1.79106i | 0.445000 | + | 0.895531i | \(0.353204\pi\) | ||||
−0.445000 | + | 0.895531i | \(0.646796\pi\) | |||||||
\(180\) | −1.61082e13 | + | 9.64482e11i | −0.0353002 | + | 0.00211360i | ||||
\(181\) | − | 4.57640e13i | − | 0.0967417i | −0.998829 | − | 0.0483708i | \(-0.984597\pi\) | ||
0.998829 | − | 0.0483708i | \(-0.0154029\pi\) | |||||||
\(182\) | 4.26108e14 | − | 4.52384e14i | 0.869072 | − | 0.922664i | ||||
\(183\) | −8.21086e14 | −1.61606 | ||||||||
\(184\) | 1.46196e14 | − | 1.75095e14i | 0.277728 | − | 0.332627i | ||||
\(185\) | 3.93185e14 | 0.721075 | ||||||||
\(186\) | −1.84872e14 | + | 1.96272e14i | −0.327368 | + | 0.347555i | ||||
\(187\) | − | 3.62681e14i | − | 0.620232i | ||||||
\(188\) | −3.35365e13 | − | 5.60108e14i | −0.0553977 | − | 0.925222i | ||||
\(189\) | − | 1.25253e15i | − | 1.99888i | ||||||
\(190\) | 3.09977e14 | + | 2.91972e14i | 0.478003 | + | 0.450239i | ||||
\(191\) | −1.01606e15 | −1.51426 | −0.757131 | − | 0.653263i | \(-0.773400\pi\) | ||||
−0.757131 | + | 0.653263i | \(0.773400\pi\) | |||||||
\(192\) | −6.66109e14 | + | 1.20806e14i | −0.959594 | + | 0.174033i | ||||
\(193\) | 1.86151e14 | 0.259265 | 0.129632 | − | 0.991562i | \(-0.458620\pi\) | ||||
0.129632 | + | 0.991562i | \(0.458620\pi\) | |||||||
\(194\) | −8.34731e14 | − | 7.86246e14i | −1.12418 | − | 1.05888i | ||||
\(195\) | − | 3.51288e14i | − | 0.457549i | ||||||
\(196\) | 1.33702e14 | + | 2.23302e15i | 0.168451 | + | 2.81338i | ||||
\(197\) | 4.84912e14i | 0.591061i | 0.955333 | + | 0.295530i | \(0.0954963\pi\) | ||||
−0.955333 | + | 0.295530i | \(0.904504\pi\) | |||||||
\(198\) | −3.44565e13 | + | 3.65813e13i | −0.0406395 | + | 0.0431455i | ||||
\(199\) | 9.85926e14 | 1.12538 | 0.562690 | − | 0.826668i | \(-0.309766\pi\) | ||||
0.562690 | + | 0.826668i | \(0.309766\pi\) | |||||||
\(200\) | −2.76619e14 | + | 3.31300e14i | −0.305624 | + | 0.366038i | ||||
\(201\) | 7.28448e14 | 0.779156 | ||||||||
\(202\) | 8.58740e14 | − | 9.11695e14i | 0.889360 | − | 0.944203i | ||||
\(203\) | 2.88398e14i | 0.289246i | ||||||||
\(204\) | −5.12726e14 | + | 3.06995e13i | −0.498068 | + | 0.0298219i | ||||
\(205\) | − | 5.88770e14i | − | 0.554046i | ||||||
\(206\) | 1.10629e14 | + | 1.04203e14i | 0.100863 | + | 0.0950045i | ||||
\(207\) | −2.39810e13 | −0.0211865 | ||||||||
\(208\) | 9.03951e13 | + | 7.52158e14i | 0.0773986 | + | 0.644018i | ||||
\(209\) | 1.32612e15 | 1.10061 | ||||||||
\(210\) | 1.24705e15 | + | 1.17462e15i | 1.00336 | + | 0.945084i | ||||
\(211\) | − | 1.22592e14i | − | 0.0956368i | −0.998856 | − | 0.0478184i | \(-0.984773\pi\) | ||
0.998856 | − | 0.0478184i | \(-0.0152269\pi\) | |||||||
\(212\) | 7.88999e14 | − | 4.72414e13i | 0.596889 | − | 0.0357388i | ||||
\(213\) | − | 1.03890e15i | − | 0.762263i | ||||||
\(214\) | −8.95177e14 | + | 9.50379e14i | −0.637118 | + | 0.676406i | ||||
\(215\) | −1.65703e15 | −1.14414 | ||||||||
\(216\) | 1.17202e15 | + | 9.78582e14i | 0.785211 | + | 0.655613i | ||||
\(217\) | −1.47146e15 | −0.956666 | ||||||||
\(218\) | 2.59181e14 | − | 2.75163e14i | 0.163544 | − | 0.173629i | ||||
\(219\) | 8.88957e14i | 0.544495i | ||||||||
\(220\) | −8.81314e13 | − | 1.47192e15i | −0.0524063 | − | 0.875261i | ||||
\(221\) | 5.74795e14i | 0.331866i | ||||||||
\(222\) | −1.26232e15 | − | 1.18900e15i | −0.707740 | − | 0.666632i | ||||
\(223\) | −8.05170e14 | −0.438436 | −0.219218 | − | 0.975676i | \(-0.570351\pi\) | ||||
−0.219218 | + | 0.975676i | \(0.570351\pi\) | |||||||
\(224\) | −2.97237e15 | − | 2.19413e15i | −1.57214 | − | 1.16051i | ||||
\(225\) | 4.53747e13 | 0.0233146 | ||||||||
\(226\) | 1.07487e15 | + | 1.01243e15i | 0.536599 | + | 0.505431i | ||||
\(227\) | 5.78017e14i | 0.280396i | 0.990123 | + | 0.140198i | \(0.0447740\pi\) | ||||
−0.990123 | + | 0.140198i | \(0.955226\pi\) | |||||||
\(228\) | −1.12251e14 | − | 1.87475e15i | −0.0529191 | − | 0.883826i | ||||
\(229\) | 1.90351e15i | 0.872219i | 0.899894 | + | 0.436110i | \(0.143644\pi\) | ||||
−0.899894 | + | 0.436110i | \(0.856356\pi\) | |||||||
\(230\) | 4.82461e14 | − | 5.12212e14i | 0.214897 | − | 0.228149i | ||||
\(231\) | 5.33503e15 | 2.31025 | ||||||||
\(232\) | −2.69860e14 | − | 2.25320e14i | −0.113623 | − | 0.0948699i | ||||
\(233\) | −3.29786e15 | −1.35026 | −0.675132 | − | 0.737697i | \(-0.735913\pi\) | ||||
−0.675132 | + | 0.737697i | \(0.735913\pi\) | |||||||
\(234\) | 5.46084e13 | − | 5.79759e13i | 0.0217449 | − | 0.0230858i | ||||
\(235\) | − | 1.73091e15i | − | 0.670401i | ||||||
\(236\) | 2.63695e15 | − | 1.57888e14i | 0.993516 | − | 0.0594868i | ||||
\(237\) | − | 7.12573e14i | − | 0.261195i | ||||||
\(238\) | −2.04049e15 | − | 1.92197e15i | −0.727752 | − | 0.685481i | ||||
\(239\) | 4.02617e14 | 0.139735 | 0.0698675 | − | 0.997556i | \(-0.477742\pi\) | ||||
0.0698675 | + | 0.997556i | \(0.477742\pi\) | |||||||
\(240\) | −2.07341e15 | + | 2.49185e14i | −0.700346 | + | 0.0841682i | ||||
\(241\) | 3.60468e14 | 0.118510 | 0.0592551 | − | 0.998243i | \(-0.481127\pi\) | ||||
0.0592551 | + | 0.998243i | \(0.481127\pi\) | |||||||
\(242\) | −1.06817e15 | − | 1.00612e15i | −0.341853 | − | 0.321997i | ||||
\(243\) | − | 3.13557e14i | − | 0.0976959i | ||||||
\(244\) | 5.45254e15 | − | 3.26471e14i | 1.65411 | − | 0.0990400i | ||||
\(245\) | 6.90075e15i | 2.03853i | ||||||||
\(246\) | −1.78045e15 | + | 1.89024e15i | −0.512214 | + | 0.543800i | ||||
\(247\) | −2.10170e15 | −0.588899 | ||||||||
\(248\) | 1.14963e15 | − | 1.37688e15i | 0.313777 | − | 0.375802i | ||||
\(249\) | −1.90127e14 | −0.0505530 | ||||||||
\(250\) | −2.82723e15 | + | 3.00158e15i | −0.732405 | + | 0.777570i | ||||
\(251\) | 2.41736e15i | 0.610187i | 0.952322 | + | 0.305093i | \(0.0986876\pi\) | ||||
−0.952322 | + | 0.305093i | \(0.901312\pi\) | |||||||
\(252\) | 2.32143e13 | + | 3.87713e14i | 0.00571022 | + | 0.0953689i | ||||
\(253\) | − | 2.19131e15i | − | 0.525315i | ||||||
\(254\) | −8.48333e14 | − | 7.99058e14i | −0.198220 | − | 0.186706i | ||||
\(255\) | −1.58449e15 | −0.360892 | ||||||||
\(256\) | 4.37536e15 | − | 1.06708e15i | 0.971524 | − | 0.236940i | ||||
\(257\) | 4.22633e14 | 0.0914952 | 0.0457476 | − | 0.998953i | \(-0.485433\pi\) | ||||
0.0457476 | + | 0.998953i | \(0.485433\pi\) | |||||||
\(258\) | 5.31988e15 | + | 5.01088e15i | 1.12299 | + | 1.05776i | ||||
\(259\) | − | 9.46365e15i | − | 1.94810i | ||||||
\(260\) | 1.39675e14 | + | 2.33277e15i | 0.0280409 | + | 0.468324i | ||||
\(261\) | 3.69600e13i | 0.00723717i | ||||||||
\(262\) | −4.94789e15 | + | 5.25301e15i | −0.945065 | + | 1.00334i | ||||
\(263\) | 7.16704e15 | 1.33545 | 0.667725 | − | 0.744408i | \(-0.267268\pi\) | ||||
0.667725 | + | 0.744408i | \(0.267268\pi\) | |||||||
\(264\) | −4.16817e15 | + | 4.99211e15i | −0.757739 | + | 0.907524i | ||||
\(265\) | 2.43826e15 | 0.432496 | ||||||||
\(266\) | 7.02755e15 | − | 7.46091e15i | 1.21639 | − | 1.29140i | ||||
\(267\) | − | 2.93725e15i | − | 0.496156i | ||||||
\(268\) | −4.83736e15 | + | 2.89637e14i | −0.797503 | + | 0.0477506i | ||||
\(269\) | 3.89871e14i | 0.0627381i | 0.999508 | + | 0.0313690i | \(0.00998671\pi\) | ||||
−0.999508 | + | 0.0313690i | \(0.990013\pi\) | |||||||
\(270\) | 3.42856e15 | + | 3.22942e15i | 0.538577 | + | 0.507294i | ||||
\(271\) | −2.03497e15 | −0.312073 | −0.156037 | − | 0.987751i | \(-0.549872\pi\) | ||||
−0.156037 | + | 0.987751i | \(0.549872\pi\) | |||||||
\(272\) | 3.39262e15 | − | 4.07728e14i | 0.507969 | − | 0.0610482i | ||||
\(273\) | −8.45523e15 | −1.23614 | ||||||||
\(274\) | −7.07368e15 | − | 6.66281e15i | −1.00987 | − | 0.951216i | ||||
\(275\) | 4.14620e15i | 0.578080i | ||||||||
\(276\) | −3.09788e15 | + | 1.85485e14i | −0.421847 | + | 0.0252581i | ||||
\(277\) | − | 1.40387e16i | − | 1.86728i | −0.358215 | − | 0.933639i | \(-0.616614\pi\) | ||
0.358215 | − | 0.933639i | \(-0.383386\pi\) | |||||||
\(278\) | −9.78557e13 | + | 1.03890e14i | −0.0127144 | + | 0.0134984i | ||||
\(279\) | −1.88577e14 | −0.0239365 | ||||||||
\(280\) | −8.74824e15 | − | 7.30436e15i | −1.08491 | − | 0.905848i | ||||
\(281\) | 9.81872e15 | 1.18977 | 0.594886 | − | 0.803810i | \(-0.297197\pi\) | ||||
0.594886 | + | 0.803810i | \(0.297197\pi\) | |||||||
\(282\) | −5.23431e15 | + | 5.55709e15i | −0.619784 | + | 0.658004i | ||||
\(283\) | 4.93395e15i | 0.570930i | 0.958389 | + | 0.285465i | \(0.0921480\pi\) | ||||
−0.958389 | + | 0.285465i | \(0.907852\pi\) | |||||||
\(284\) | 4.13074e14 | + | 6.89894e15i | 0.0467153 | + | 0.780213i | ||||
\(285\) | − | 5.79358e15i | − | 0.640406i | ||||||
\(286\) | 5.29766e15 | + | 4.98995e15i | 0.572407 | + | 0.539159i | ||||
\(287\) | −1.41712e16 | −1.49684 | ||||||||
\(288\) | −3.80928e14 | − | 2.81191e14i | −0.0393362 | − | 0.0290369i | ||||
\(289\) | −7.31196e15 | −0.738240 | ||||||||
\(290\) | −7.89433e14 | − | 7.43580e14i | −0.0779343 | − | 0.0734075i | ||||
\(291\) | 1.56014e16i | 1.50612i | ||||||||
\(292\) | −3.53457e14 | − | 5.90324e15i | −0.0333694 | − | 0.557317i | ||||
\(293\) | − | 5.77550e15i | − | 0.533274i | −0.963797 | − | 0.266637i | \(-0.914088\pi\) | ||
0.963797 | − | 0.266637i | \(-0.0859124\pi\) | |||||||
\(294\) | 2.08680e16 | − | 2.21548e16i | 1.88461 | − | 2.00083i | ||||
\(295\) | 8.14904e15 | 0.719885 | ||||||||
\(296\) | 8.85534e15 | + | 7.39379e15i | 0.765261 | + | 0.638956i | ||||
\(297\) | 1.46678e16 | 1.24008 | ||||||||
\(298\) | 3.94096e15 | − | 4.18399e15i | 0.325984 | − | 0.346086i | ||||
\(299\) | 3.47289e15i | 0.281079i | ||||||||
\(300\) | 5.86153e15 | − | 3.50960e14i | 0.464219 | − | 0.0277951i | ||||
\(301\) | 3.98835e16i | 3.09108i | ||||||||
\(302\) | −3.33311e15 | − | 3.13951e15i | −0.252816 | − | 0.238131i | ||||
\(303\) | −1.70399e16 | −1.26500 | ||||||||
\(304\) | 1.49083e15 | + | 1.24049e16i | 0.108330 | + | 0.901395i | ||||
\(305\) | 1.68501e16 | 1.19854 | ||||||||
\(306\) | −2.61501e14 | − | 2.46312e14i | −0.0182089 | − | 0.0171513i | ||||
\(307\) | − | 4.46483e15i | − | 0.304373i | −0.988352 | − | 0.152186i | \(-0.951369\pi\) | ||
0.988352 | − | 0.152186i | \(-0.0486314\pi\) | |||||||
\(308\) | −3.54280e16 | + | 2.12126e15i | −2.36465 | + | 0.141584i | ||||
\(309\) | − | 2.06770e15i | − | 0.135132i | ||||||
\(310\) | 3.79388e15 | − | 4.02783e15i | 0.242791 | − | 0.257763i | ||||
\(311\) | 9.38805e15 | 0.588346 | 0.294173 | − | 0.955752i | \(-0.404956\pi\) | ||||
0.294173 | + | 0.955752i | \(0.404956\pi\) | |||||||
\(312\) | 6.60592e15 | − | 7.91174e15i | 0.405442 | − | 0.485587i | ||||
\(313\) | −1.26946e16 | −0.763100 | −0.381550 | − | 0.924348i | \(-0.624610\pi\) | ||||
−0.381550 | + | 0.924348i | \(0.624610\pi\) | |||||||
\(314\) | −6.37674e15 | + | 6.76997e15i | −0.375453 | + | 0.398606i | ||||
\(315\) | 1.19816e15i | 0.0691028i | ||||||||
\(316\) | 2.83325e14 | + | 4.73194e15i | 0.0160073 | + | 0.267346i | ||||
\(317\) | − | 2.54168e16i | − | 1.40681i | −0.710789 | − | 0.703405i | \(-0.751662\pi\) | ||
0.710789 | − | 0.703405i | \(-0.248338\pi\) | |||||||
\(318\) | −7.82802e15 | − | 7.37334e15i | −0.424498 | − | 0.399841i | ||||
\(319\) | −3.37729e15 | −0.179444 | ||||||||
\(320\) | 1.36697e16 | − | 2.47915e15i | 0.711679 | − | 0.129071i | ||||
\(321\) | 1.77629e16 | 0.906216 | ||||||||
\(322\) | −1.23286e16 | − | 1.16125e16i | −0.616381 | − | 0.580579i | ||||
\(323\) | 9.47975e15i | 0.464494i | ||||||||
\(324\) | −1.18072e15 | − | 1.97198e16i | −0.0567029 | − | 0.947021i | ||||
\(325\) | − | 6.57111e15i | − | 0.309312i | ||||||
\(326\) | −7.19550e15 | + | 7.63921e15i | −0.332006 | + | 0.352480i | ||||
\(327\) | −5.14290e15 | −0.232620 | ||||||||
\(328\) | 1.10717e16 | − | 1.32603e16i | 0.490949 | − | 0.587996i | ||||
\(329\) | −4.16618e16 | −1.81119 | ||||||||
\(330\) | −1.37554e16 | + | 1.46036e16i | −0.586316 | + | 0.622472i | ||||
\(331\) | − | 2.60098e16i | − | 1.08706i | −0.839389 | − | 0.543531i | \(-0.817087\pi\) | ||
0.839389 | − | 0.543531i | \(-0.182913\pi\) | |||||||
\(332\) | 1.26256e15 | − | 7.55960e13i | 0.0517434 | − | 0.00309814i | ||||
\(333\) | − | 1.21283e15i | − | 0.0487429i | ||||||
\(334\) | 2.98511e16 | + | 2.81172e16i | 1.17654 | + | 1.10820i | ||||
\(335\) | −1.49490e16 | −0.577858 | ||||||||
\(336\) | 5.99768e15 | + | 4.99054e16i | 0.227394 | + | 1.89209i | ||||
\(337\) | −1.68977e16 | −0.628395 | −0.314197 | − | 0.949358i | \(-0.601735\pi\) | ||||
−0.314197 | + | 0.949358i | \(0.601735\pi\) | |||||||
\(338\) | 1.15589e16 | + | 1.08875e16i | 0.421655 | + | 0.397163i | ||||
\(339\) | − | 2.00897e16i | − | 0.718910i | ||||||
\(340\) | 1.05220e16 | − | 6.30006e14i | 0.369391 | − | 0.0221173i | ||||
\(341\) | − | 1.72316e16i | − | 0.593501i | ||||||
\(342\) | 9.00624e14 | − | 9.56162e14i | 0.0304350 | − | 0.0323118i | ||||
\(343\) | 1.07163e17 | 3.55332 | ||||||||
\(344\) | −3.73198e16 | − | 3.11602e16i | −1.21425 | − | 1.01384i | ||||
\(345\) | −9.57343e15 | −0.305663 | ||||||||
\(346\) | −1.57786e16 | + | 1.67516e16i | −0.494394 | + | 0.524881i | ||||
\(347\) | − | 3.24877e16i | − | 0.999027i | −0.866306 | − | 0.499513i | \(-0.833512\pi\) | ||
0.866306 | − | 0.499513i | \(-0.166488\pi\) | |||||||
\(348\) | 2.85874e14 | + | 4.77451e15i | 0.00862800 | + | 0.144100i | ||||
\(349\) | 4.20305e16i | 1.24509i | 0.782586 | + | 0.622543i | \(0.213900\pi\) | ||||
−0.782586 | + | 0.622543i | \(0.786100\pi\) | |||||||
\(350\) | 2.33270e16 | + | 2.19721e16i | 0.678293 | + | 0.638895i | ||||
\(351\) | −2.32463e16 | −0.663525 | ||||||||
\(352\) | 2.56944e16 | − | 3.48081e16i | 0.719965 | − | 0.975333i | ||||
\(353\) | 1.92556e16 | 0.529691 | 0.264845 | − | 0.964291i | \(-0.414679\pi\) | ||||
0.264845 | + | 0.964291i | \(0.414679\pi\) | |||||||
\(354\) | −2.61624e16 | − | 2.46428e16i | −0.706573 | − | 0.665532i | ||||
\(355\) | 2.13199e16i | 0.565330i | ||||||||
\(356\) | 1.16788e15 | + | 1.95052e16i | 0.0304069 | + | 0.507839i | ||||
\(357\) | 3.81374e16i | 0.975007i | ||||||||
\(358\) | −4.89162e16 | + | 5.19327e16i | −1.22804 | + | 1.30377i | ||||
\(359\) | −1.57860e16 | −0.389186 | −0.194593 | − | 0.980884i | \(-0.562339\pi\) | ||||
−0.194593 | + | 0.980884i | \(0.562339\pi\) | |||||||
\(360\) | −1.12114e15 | − | 9.36100e14i | −0.0271453 | − | 0.0226650i | ||||
\(361\) | 7.39089e15 | 0.175752 | ||||||||
\(362\) | 2.84002e15 | − | 3.01516e15i | 0.0663309 | − | 0.0704213i | ||||
\(363\) | 1.99644e16i | 0.457999i | ||||||||
\(364\) | 5.61481e16 | − | 3.36187e15i | 1.26525 | − | 0.0757569i | ||||
\(365\) | − | 1.82429e16i | − | 0.403823i | ||||||
\(366\) | −5.40971e16 | − | 5.09549e16i | −1.17638 | − | 1.10805i | ||||
\(367\) | −4.63823e16 | −0.990885 | −0.495442 | − | 0.868641i | \(-0.664994\pi\) | ||||
−0.495442 | + | 0.868641i | \(0.664994\pi\) | |||||||
\(368\) | 2.04981e16 | − | 2.46348e15i | 0.430233 | − | 0.0517058i | ||||
\(369\) | −1.81613e15 | −0.0374521 | ||||||||
\(370\) | 2.59049e16 | + | 2.44002e16i | 0.524893 | + | 0.494405i | ||||
\(371\) | − | 5.86871e16i | − | 1.16846i | ||||||
\(372\) | −2.43605e16 | + | 1.45858e15i | −0.476603 | + | 0.0285366i | ||||
\(373\) | 3.24323e16i | 0.623548i | 0.950156 | + | 0.311774i | \(0.100923\pi\) | ||||
−0.950156 | + | 0.311774i | \(0.899077\pi\) | |||||||
\(374\) | 2.25072e16 | − | 2.38952e16i | 0.425262 | − | 0.451486i | ||||
\(375\) | 5.61005e16 | 1.04175 | ||||||||
\(376\) | 3.25496e16 | − | 3.89838e16i | 0.594053 | − | 0.711482i | ||||
\(377\) | 5.35250e15 | 0.0960148 | ||||||||
\(378\) | 7.77296e16 | − | 8.25229e16i | 1.37053 | − | 1.45505i | ||||
\(379\) | 7.89922e16i | 1.36908i | 0.728975 | + | 0.684541i | \(0.239997\pi\) | ||||
−0.728975 | + | 0.684541i | \(0.760003\pi\) | |||||||
\(380\) | 2.30358e15 | + | 3.84731e16i | 0.0392473 | + | 0.655486i | ||||
\(381\) | 1.58556e16i | 0.265565i | ||||||||
\(382\) | −6.69427e16 | − | 6.30544e16i | −1.10228 | − | 1.03825i | ||||
\(383\) | −3.96583e16 | −0.642010 | −0.321005 | − | 0.947078i | \(-0.604021\pi\) | ||||
−0.321005 | + | 0.947078i | \(0.604021\pi\) | |||||||
\(384\) | −5.13835e16 | − | 3.33781e16i | −0.817844 | − | 0.531261i | ||||
\(385\) | −1.09484e17 | −1.71339 | ||||||||
\(386\) | 1.22645e16 | + | 1.15522e16i | 0.188727 | + | 0.177765i | ||||
\(387\) | 5.11131e15i | 0.0773413i | ||||||||
\(388\) | −6.20326e15 | − | 1.03603e17i | −0.0923025 | − | 1.54159i | ||||
\(389\) | − | 3.70327e16i | − | 0.541892i | −0.962595 | − | 0.270946i | \(-0.912663\pi\) | ||
0.962595 | − | 0.270946i | \(-0.0873365\pi\) | |||||||
\(390\) | 2.18002e16 | − | 2.31445e16i | 0.313719 | − | 0.333064i | ||||
\(391\) | 1.56645e16 | 0.221701 | ||||||||
\(392\) | −1.29768e17 | + | 1.55419e17i | −1.80637 | + | 2.16344i | ||||
\(393\) | 9.81805e16 | 1.34423 | ||||||||
\(394\) | −3.00926e16 | + | 3.19483e16i | −0.405261 | + | 0.430252i | ||||
\(395\) | 1.46232e16i | 0.193714i | ||||||||
\(396\) | −4.54033e15 | + | 2.71852e14i | −0.0591655 | + | 0.00354254i | ||||
\(397\) | − | 1.88759e16i | − | 0.241974i | −0.992654 | − | 0.120987i | \(-0.961394\pi\) | ||
0.992654 | − | 0.120987i | \(-0.0386060\pi\) | |||||||
\(398\) | 6.49576e16 | + | 6.11846e16i | 0.819200 | + | 0.771617i | ||||
\(399\) | −1.39447e17 | −1.73016 | ||||||||
\(400\) | −3.87848e16 | + | 4.66119e15i | −0.473447 | + | 0.0568993i | ||||
\(401\) | 8.64929e16 | 1.03882 | 0.519412 | − | 0.854524i | \(-0.326151\pi\) | ||||
0.519412 | + | 0.854524i | \(0.326151\pi\) | |||||||
\(402\) | 4.79937e16 | + | 4.52060e16i | 0.567172 | + | 0.534228i | ||||
\(403\) | 2.73095e16i | 0.317563i | ||||||||
\(404\) | 1.13156e17 | − | 6.77521e15i | 1.29479 | − | 0.0775254i | ||||
\(405\) | − | 6.09405e16i | − | 0.686196i | ||||||
\(406\) | −1.78974e16 | + | 1.90011e16i | −0.198322 | + | 0.210552i | ||||
\(407\) | 1.10824e17 | 1.20857 | ||||||||
\(408\) | −3.56860e16 | − | 2.97961e16i | −0.383007 | − | 0.319792i | ||||
\(409\) | 6.70383e16 | 0.708144 | 0.354072 | − | 0.935218i | \(-0.384797\pi\) | ||||
0.354072 | + | 0.935218i | \(0.384797\pi\) | |||||||
\(410\) | 3.65379e16 | − | 3.87910e16i | 0.379881 | − | 0.403307i | ||||
\(411\) | 1.32210e17i | 1.35298i | ||||||||
\(412\) | 8.22134e14 | + | 1.37308e16i | 0.00828153 | + | 0.138314i | ||||
\(413\) | − | 1.96141e17i | − | 1.94488i | ||||||
\(414\) | −1.57998e15 | − | 1.48821e15i | −0.0154223 | − | 0.0145265i | ||||
\(415\) | 3.90172e15 | 0.0374924 | ||||||||
\(416\) | −4.07218e16 | + | 5.51656e16i | −0.385230 | + | 0.521869i | ||||
\(417\) | 1.94174e15 | 0.0180845 | ||||||||
\(418\) | 8.73712e16 | + | 8.22963e16i | 0.801166 | + | 0.754631i | ||||
\(419\) | 4.36873e16i | 0.394425i | 0.980361 | + | 0.197212i | \(0.0631889\pi\) | ||||
−0.980361 | + | 0.197212i | \(0.936811\pi\) | |||||||
\(420\) | 9.26738e15 | + | 1.54779e17i | 0.0823828 | + | 1.37591i | ||||
\(421\) | 1.39165e17i | 1.21814i | 0.793116 | + | 0.609071i | \(0.208457\pi\) | ||||
−0.793116 | + | 0.609071i | \(0.791543\pi\) | |||||||
\(422\) | 7.60779e15 | − | 8.07693e15i | 0.0655734 | − | 0.0696170i | ||||
\(423\) | −5.33922e15 | −0.0453175 | ||||||||
\(424\) | 5.49148e16 | + | 4.58512e16i | 0.458998 | + | 0.383242i | ||||
\(425\) | −2.96391e16 | −0.243970 | ||||||||
\(426\) | 6.44718e16 | − | 6.84475e16i | 0.522646 | − | 0.554875i | ||||
\(427\) | − | 4.05569e17i | − | 3.23805i | ||||||
\(428\) | −1.17957e17 | + | 7.06269e15i | −0.927556 | + | 0.0555375i | ||||
\(429\) | − | 9.90152e16i | − | 0.766883i | ||||||
\(430\) | −1.09173e17 | − | 1.02832e17i | −0.832858 | − | 0.784482i | ||||
\(431\) | −2.36158e17 | −1.77460 | −0.887299 | − | 0.461195i | \(-0.847421\pi\) | ||||
−0.887299 | + | 0.461195i | \(0.847421\pi\) | |||||||
\(432\) | 1.64897e16 | + | 1.37207e17i | 0.122058 | + | 1.01562i | ||||
\(433\) | −1.55171e17 | −1.13146 | −0.565730 | − | 0.824590i | \(-0.691406\pi\) | ||||
−0.565730 | + | 0.824590i | \(0.691406\pi\) | |||||||
\(434\) | −9.69469e16 | − | 9.13158e16i | −0.696387 | − | 0.655938i | ||||
\(435\) | 1.47548e16i | 0.104413i | ||||||||
\(436\) | 3.41521e16 | − | 2.04486e15i | 0.238098 | − | 0.0142561i | ||||
\(437\) | 5.72764e16i | 0.393411i | ||||||||
\(438\) | −5.51669e16 | + | 5.85688e16i | −0.373333 | + | 0.396355i | ||||
\(439\) | 1.35637e17 | 0.904398 | 0.452199 | − | 0.891917i | \(-0.350640\pi\) | ||||
0.452199 | + | 0.891917i | \(0.350640\pi\) | |||||||
\(440\) | 8.55380e16 | − | 1.02447e17i | 0.561974 | − | 0.673062i | ||||
\(441\) | 2.12862e16 | 0.137799 | ||||||||
\(442\) | −3.56706e16 | + | 3.78702e16i | −0.227544 | + | 0.241576i | ||||
\(443\) | 2.37606e17i | 1.49360i | 0.665050 | + | 0.746799i | \(0.268410\pi\) | ||||
−0.665050 | + | 0.746799i | \(0.731590\pi\) | |||||||
\(444\) | −9.38084e15 | − | 1.56674e17i | −0.0581102 | − | 0.970524i | ||||
\(445\) | 6.02774e16i | 0.367972i | ||||||||
\(446\) | −5.30485e16 | − | 4.99672e16i | −0.319151 | − | 0.300614i | ||||
\(447\) | −7.82002e16 | −0.463670 | ||||||||
\(448\) | −5.96713e16 | − | 3.29019e17i | −0.348705 | − | 1.92271i | ||||
\(449\) | 3.25912e17 | 1.87715 | 0.938576 | − | 0.345074i | \(-0.112146\pi\) | ||||
0.938576 | + | 0.345074i | \(0.112146\pi\) | |||||||
\(450\) | 2.98951e15 | + | 2.81586e15i | 0.0169714 | + | 0.0159856i | ||||
\(451\) | − | 1.65953e17i | − | 0.928618i | ||||||
\(452\) | 7.98782e15 | + | 1.33408e17i | 0.0440584 | + | 0.735839i | ||||
\(453\) | 6.22970e16i | 0.338710i | ||||||||
\(454\) | −3.58705e16 | + | 3.80825e16i | −0.192254 | + | 0.204109i | ||||
\(455\) | 1.73516e17 | 0.916779 | ||||||||
\(456\) | 1.08947e17 | − | 1.30484e17i | 0.567474 | − | 0.679648i | ||||
\(457\) | −2.28623e17 | −1.17399 | −0.586995 | − | 0.809591i | \(-0.699689\pi\) | ||||
−0.586995 | + | 0.809591i | \(0.699689\pi\) | |||||||
\(458\) | −1.18128e17 | + | 1.25413e17i | −0.598037 | + | 0.634916i | ||||
\(459\) | 1.04853e17i | 0.523356i | ||||||||
\(460\) | 6.35737e16 | − | 3.80648e15i | 0.312861 | − | 0.0187326i | ||||
\(461\) | 1.78032e17i | 0.863857i | 0.901908 | + | 0.431928i | \(0.142167\pi\) | ||||
−0.901908 | + | 0.431928i | \(0.857833\pi\) | |||||||
\(462\) | 3.51498e17 | + | 3.31081e17i | 1.68170 | + | 1.58402i | ||||
\(463\) | 2.15010e17 | 1.01434 | 0.507168 | − | 0.861847i | \(-0.330692\pi\) | ||||
0.507168 | + | 0.861847i | \(0.330692\pi\) | |||||||
\(464\) | −3.79678e15 | − | 3.15922e16i | −0.0176623 | − | 0.146965i | ||||
\(465\) | −7.52817e16 | −0.345339 | ||||||||
\(466\) | −2.17279e17 | − | 2.04658e17i | −0.982899 | − | 0.925808i | ||||
\(467\) | 9.62373e16i | 0.429322i | 0.976689 | + | 0.214661i | \(0.0688647\pi\) | ||||
−0.976689 | + | 0.214661i | \(0.931135\pi\) | |||||||
\(468\) | 7.19573e15 | − | 4.30845e14i | 0.0316575 | − | 0.00189550i | ||||
\(469\) | 3.59811e17i | 1.56117i | ||||||||
\(470\) | 1.07417e17 | − | 1.14041e17i | 0.459660 | − | 0.488006i | ||||
\(471\) | 1.26533e17 | 0.534033 | ||||||||
\(472\) | 1.83533e17 | + | 1.53242e17i | 0.763998 | + | 0.637902i | ||||
\(473\) | −4.67056e17 | −1.91766 | ||||||||
\(474\) | 4.42208e16 | − | 4.69477e16i | 0.179088 | − | 0.190132i | ||||
\(475\) | − | 1.08373e17i | − | 0.432927i | ||||||
\(476\) | −1.51638e16 | − | 2.53257e17i | −0.0597533 | − | 0.997966i | ||||
\(477\) | − | 7.52112e15i | − | 0.0292357i | ||||||
\(478\) | 2.65263e16 | + | 2.49856e16i | 0.101718 | + | 0.0958093i | ||||
\(479\) | −1.07139e17 | −0.405290 | −0.202645 | − | 0.979252i | \(-0.564954\pi\) | ||||
−0.202645 | + | 0.979252i | \(0.564954\pi\) | |||||||
\(480\) | −1.52070e17 | − | 1.12254e17i | −0.567513 | − | 0.418923i | ||||
\(481\) | −1.75640e17 | −0.646666 | ||||||||
\(482\) | 2.37494e16 | + | 2.23699e16i | 0.0862674 | + | 0.0812566i | ||||
\(483\) | 2.30425e17i | 0.825798i | ||||||||
\(484\) | −7.93804e15 | − | 1.32577e17i | −0.0280684 | − | 0.468783i | ||||
\(485\) | − | 3.20168e17i | − | 1.11701i | ||||||
\(486\) | 1.94587e16 | − | 2.06587e16i | 0.0669852 | − | 0.0711159i | ||||
\(487\) | 2.87139e17 | 0.975337 | 0.487668 | − | 0.873029i | \(-0.337848\pi\) | ||||
0.487668 | + | 0.873029i | \(0.337848\pi\) | |||||||
\(488\) | 3.79500e17 | + | 3.16864e17i | 1.27199 | + | 1.06205i | ||||
\(489\) | 1.42780e17 | 0.472235 | ||||||||
\(490\) | −4.28246e17 | + | 4.54654e17i | −1.39772 | + | 1.48391i | ||||
\(491\) | − | 4.18123e17i | − | 1.34671i | −0.739319 | − | 0.673355i | \(-0.764853\pi\) | ||
0.739319 | − | 0.673355i | \(-0.235147\pi\) | |||||||
\(492\) | −2.34609e17 | + | 1.40472e16i | −0.745713 | + | 0.0446496i | ||||
\(493\) | − | 2.41425e16i | − | 0.0757317i | ||||||
\(494\) | −1.38470e17 | − | 1.30427e17i | −0.428678 | − | 0.403778i | ||||
\(495\) | −1.40311e16 | −0.0428703 | ||||||||
\(496\) | 1.61189e17 | − | 1.93719e16i | 0.486077 | − | 0.0584172i | ||||
\(497\) | 5.13155e17 | 1.52733 | ||||||||
\(498\) | −1.25265e16 | − | 1.17989e16i | −0.0367991 | − | 0.0346617i | ||||
\(499\) | − | 2.23370e17i | − | 0.647695i | −0.946109 | − | 0.323847i | \(-0.895024\pi\) | ||
0.946109 | − | 0.323847i | \(-0.104976\pi\) | |||||||
\(500\) | −3.72543e17 | + | 2.23061e16i | −1.06628 | + | 0.0638437i | ||||
\(501\) | − | 5.57927e17i | − | 1.57628i | ||||||
\(502\) | −1.50017e17 | + | 1.59268e17i | −0.418374 | + | 0.444174i | ||||
\(503\) | −5.16254e17 | −1.42125 | −0.710626 | − | 0.703570i | \(-0.751588\pi\) | ||||
−0.710626 | + | 0.703570i | \(0.751588\pi\) | |||||||
\(504\) | −2.25312e16 | + | 2.69850e16i | −0.0612331 | + | 0.0733372i | ||||
\(505\) | 3.49688e17 | 0.938181 | ||||||||
\(506\) | 1.35988e17 | − | 1.44374e17i | 0.360183 | − | 0.382394i | ||||
\(507\) | − | 2.16040e17i | − | 0.564913i | ||||||
\(508\) | −6.30434e15 | − | 1.05292e17i | −0.0162752 | − | 0.271819i | ||||
\(509\) | 7.65587e17i | 1.95132i | 0.219284 | + | 0.975661i | \(0.429628\pi\) | ||||
−0.219284 | + | 0.975661i | \(0.570372\pi\) | |||||||
\(510\) | −1.04394e17 | − | 9.83301e16i | −0.262705 | − | 0.247446i | ||||
\(511\) | −4.39093e17 | −1.09099 | ||||||||
\(512\) | 3.54491e17 | + | 2.01221e17i | 0.869661 | + | 0.493650i | ||||
\(513\) | −3.83387e17 | −0.928699 | ||||||||
\(514\) | 2.78451e16 | + | 2.62278e16i | 0.0666022 | + | 0.0627337i | ||||
\(515\) | 4.24327e16i | 0.100220i | ||||||||
\(516\) | 3.95344e16 | + | 6.60282e17i | 0.0922046 | + | 1.53995i | ||||
\(517\) | − | 4.87882e17i | − | 1.12364i | ||||||
\(518\) | 5.87295e17 | − | 6.23511e17i | 1.33571 | − | 1.41808i | ||||
\(519\) | 3.13093e17 | 0.703210 | ||||||||
\(520\) | −1.35565e17 | + | 1.62362e17i | −0.300694 | + | 0.360134i | ||||
\(521\) | 1.10381e17 | 0.241796 | 0.120898 | − | 0.992665i | \(-0.461423\pi\) | ||||
0.120898 | + | 0.992665i | \(0.461423\pi\) | |||||||
\(522\) | −2.29366e15 | + | 2.43510e15i | −0.00496217 | + | 0.00526816i | ||||
\(523\) | 6.91731e15i | 0.0147801i | 0.999973 | + | 0.00739003i | \(0.00235234\pi\) | ||||
−0.999973 | + | 0.00739003i | \(0.997648\pi\) | |||||||
\(524\) | −6.51982e17 | + | 3.90374e16i | −1.37588 | + | 0.0823812i | ||||
\(525\) | − | 4.35991e17i | − | 0.908744i | ||||||
\(526\) | 4.72199e17 | + | 4.44772e17i | 0.972116 | + | 0.915651i | ||||
\(527\) | 1.23180e17 | 0.250478 | ||||||||
\(528\) | −5.84419e17 | + | 7.02360e16i | −1.17383 | + | 0.141072i | ||||
\(529\) | −4.09392e17 | −0.812226 | ||||||||
\(530\) | 1.60644e17 | + | 1.51314e17i | 0.314827 | + | 0.296541i | ||||
\(531\) | − | 2.51367e16i | − | 0.0486625i | ||||||
\(532\) | 9.26017e17 | − | 5.54453e16i | 1.77090 | − | 0.106033i | ||||
\(533\) | 2.63010e17i | 0.496873i | ||||||||
\(534\) | 1.82280e17 | − | 1.93520e17i | 0.340189 | − | 0.361167i | ||||
\(535\) | −3.64526e17 | −0.672092 | ||||||||
\(536\) | −3.36683e17 | − | 2.81114e17i | −0.613268 | − | 0.512049i | ||||
\(537\) | 9.70640e17 | 1.74673 | ||||||||
\(538\) | −2.41946e16 | + | 2.56866e16i | −0.0430164 | + | 0.0456690i | ||||
\(539\) | 1.94507e18i | 3.41671i | ||||||||
\(540\) | 2.54792e16 | + | 4.25539e17i | 0.0442208 | + | 0.738551i | ||||
\(541\) | − | 1.19723e17i | − | 0.205304i | −0.994717 | − | 0.102652i | \(-0.967267\pi\) | ||
0.994717 | − | 0.102652i | \(-0.0327327\pi\) | |||||||
\(542\) | −1.34073e17 | − | 1.26286e17i | −0.227168 | − | 0.213973i | ||||
\(543\) | −5.63543e16 | −0.0943471 | ||||||||
\(544\) | 2.48825e17 | + | 1.83676e17i | 0.411624 | + | 0.303850i | ||||
\(545\) | 1.05541e17 | 0.172522 | ||||||||
\(546\) | −5.57071e17 | − | 5.24714e17i | −0.899826 | − | 0.847560i | ||||
\(547\) | 6.30037e17i | 1.00565i | 0.864387 | + | 0.502827i | \(0.167707\pi\) | ||||
−0.864387 | + | 0.502827i | \(0.832293\pi\) | |||||||
\(548\) | −5.25677e16 | − | 8.77957e17i | −0.0829173 | − | 1.38484i | ||||
\(549\) | − | 5.19762e16i | − | 0.0810185i | ||||||
\(550\) | −2.57305e17 | + | 2.73172e17i | −0.396361 | + | 0.420803i | ||||
\(551\) | 8.82756e16 | 0.134386 | ||||||||
\(552\) | −2.15614e17 | − | 1.80027e17i | −0.324394 | − | 0.270853i | ||||
\(553\) | 3.51969e17 | 0.523349 | ||||||||
\(554\) | 8.71214e17 | − | 9.24939e17i | 1.28030 | − | 1.35925i | ||||
\(555\) | − | 4.84172e17i | − | 0.703226i | ||||||
\(556\) | −1.28944e16 | + | 7.72053e14i | −0.0185104 | + | 0.00110831i | ||||
\(557\) | − | 5.28413e17i | − | 0.749747i | −0.927076 | − | 0.374873i | \(-0.877686\pi\) | ||
0.927076 | − | 0.374873i | \(-0.122314\pi\) | |||||||
\(558\) | −1.24244e16 | − | 1.17027e16i | −0.0174241 | − | 0.0164121i | ||||
\(559\) | 7.40214e17 | 1.02608 | ||||||||
\(560\) | −1.23083e17 | − | 1.02414e18i | −0.168646 | − | 1.40326i | ||||
\(561\) | −4.46609e17 | −0.604880 | ||||||||
\(562\) | 6.46905e17 | + | 6.09330e17i | 0.866073 | + | 0.815768i | ||||
\(563\) | − | 7.95577e17i | − | 1.05288i | −0.850213 | − | 0.526439i | \(-0.823527\pi\) | ||
0.850213 | − | 0.526439i | \(-0.176473\pi\) | |||||||
\(564\) | −6.89723e17 | + | 4.12972e16i | −0.902320 | + | 0.0540265i | ||||
\(565\) | 4.12274e17i | 0.533177i | ||||||||
\(566\) | −3.06191e17 | + | 3.25072e17i | −0.391458 | + | 0.415598i | ||||
\(567\) | −1.46679e18 | −1.85387 | ||||||||
\(568\) | −4.00919e17 | + | 4.80170e17i | −0.500948 | + | 0.599972i | ||||
\(569\) | −1.05443e18 | −1.30253 | −0.651264 | − | 0.758851i | \(-0.725761\pi\) | ||||
−0.651264 | + | 0.758851i | \(0.725761\pi\) | |||||||
\(570\) | 3.59538e17 | − | 3.81709e17i | 0.439094 | − | 0.466171i | ||||
\(571\) | − | 2.04900e17i | − | 0.247405i | −0.992319 | − | 0.123702i | \(-0.960523\pi\) | ||
0.992319 | − | 0.123702i | \(-0.0394768\pi\) | |||||||
\(572\) | 3.93693e16 | + | 6.57524e17i | 0.0469984 | + | 0.784942i | ||||
\(573\) | 1.25118e18i | 1.47678i | ||||||||
\(574\) | −9.33670e17 | − | 8.79438e17i | −1.08960 | − | 1.02631i | ||||
\(575\) | −1.79079e17 | −0.206634 | ||||||||
\(576\) | −7.64725e15 | − | 4.21659e16i | −0.00872487 | − | 0.0481077i | ||||
\(577\) | 4.21685e16 | 0.0475714 | 0.0237857 | − | 0.999717i | \(-0.492428\pi\) | ||||
0.0237857 | + | 0.999717i | \(0.492428\pi\) | |||||||
\(578\) | −4.81747e17 | − | 4.53765e17i | −0.537388 | − | 0.506175i | ||||
\(579\) | − | 2.29229e17i | − | 0.252847i | ||||||
\(580\) | −5.86663e15 | − | 9.79812e16i | −0.00639892 | − | 0.106871i | ||||
\(581\) | − | 9.39115e16i | − | 0.101292i | ||||||
\(582\) | −9.68192e17 | + | 1.02790e18i | −1.03267 | + | 1.09635i | ||||
\(583\) | 6.87257e17 | 0.724892 | ||||||||
\(584\) | 3.43056e17 | − | 4.10869e17i | 0.357834 | − | 0.428568i | ||||
\(585\) | 2.22371e16 | 0.0229385 | ||||||||
\(586\) | 3.58416e17 | − | 3.80518e17i | 0.365639 | − | 0.388187i | ||||
\(587\) | − | 7.61315e17i | − | 0.768099i | −0.923313 | − | 0.384049i | \(-0.874529\pi\) | ||
0.923313 | − | 0.384049i | \(-0.125471\pi\) | |||||||
\(588\) | 2.74976e18 | − | 1.64642e17i | 2.74374 | − | 0.164281i | ||||
\(589\) | 4.50399e17i | 0.444475i | ||||||||
\(590\) | 5.36898e17 | + | 5.05713e17i | 0.524027 | + | 0.493589i | ||||
\(591\) | 5.97125e17 | 0.576430 | ||||||||
\(592\) | 1.24590e17 | + | 1.03668e18i | 0.118957 | + | 0.989817i | ||||
\(593\) | 1.40229e18 | 1.32428 | 0.662142 | − | 0.749378i | \(-0.269647\pi\) | ||||
0.662142 | + | 0.749378i | \(0.269647\pi\) | |||||||
\(594\) | 9.66387e17 | + | 9.10255e17i | 0.902691 | + | 0.850259i | ||||
\(595\) | − | 7.82645e17i | − | 0.723110i | ||||||
\(596\) | 5.19299e17 | − | 3.10931e16i | 0.474588 | − | 0.0284160i | ||||
\(597\) | − | 1.21408e18i | − | 1.09752i | ||||||
\(598\) | −2.15521e17 | + | 2.28811e17i | −0.192722 | + | 0.204606i | ||||
\(599\) | −5.57093e16 | −0.0492780 | −0.0246390 | − | 0.999696i | \(-0.507844\pi\) | ||||
−0.0246390 | + | 0.999696i | \(0.507844\pi\) | |||||||
\(600\) | 4.07966e17 | + | 3.40632e17i | 0.356977 | + | 0.298059i | ||||
\(601\) | −1.05450e18 | −0.912769 | −0.456384 | − | 0.889783i | \(-0.650856\pi\) | ||||
−0.456384 | + | 0.889783i | \(0.650856\pi\) | |||||||
\(602\) | −2.47509e18 | + | 2.62771e18i | −2.11940 | + | 2.25010i | ||||
\(603\) | 4.61121e16i | 0.0390618i | ||||||||
\(604\) | −2.47698e16 | − | 4.13692e17i | −0.0207579 | − | 0.346686i | ||||
\(605\) | − | 4.09705e17i | − | 0.339673i | ||||||
\(606\) | −1.12267e18 | − | 1.05746e18i | −0.920832 | − | 0.867346i | ||||
\(607\) | 2.20475e18 | 1.78910 | 0.894548 | − | 0.446971i | \(-0.147497\pi\) | ||||
0.894548 | + | 0.446971i | \(0.147497\pi\) | |||||||
\(608\) | −6.71600e17 | + | 9.09813e17i | −0.539184 | + | 0.730430i | ||||
\(609\) | 3.55136e17 | 0.282087 | ||||||||
\(610\) | 1.11017e18 | + | 1.04568e18i | 0.872457 | + | 0.821781i | ||||
\(611\) | 7.73219e17i | 0.601222i | ||||||||
\(612\) | −1.94333e15 | − | 3.24564e16i | −0.00149507 | − | 0.0249699i | ||||
\(613\) | 9.76001e17i | 0.742946i | 0.928444 | + | 0.371473i | \(0.121147\pi\) | ||||
−0.928444 | + | 0.371473i | \(0.878853\pi\) | |||||||
\(614\) | 2.77078e17 | − | 2.94165e17i | 0.208693 | − | 0.221562i | ||||
\(615\) | −7.25018e17 | −0.540331 | ||||||||
\(616\) | −2.46581e18 | − | 2.05883e18i | −1.81838 | − | 1.51826i | ||||
\(617\) | −2.29244e18 | −1.67280 | −0.836402 | − | 0.548117i | \(-0.815345\pi\) | ||||
−0.836402 | + | 0.548117i | \(0.815345\pi\) | |||||||
\(618\) | 1.28317e17 | − | 1.36230e17i | 0.0926529 | − | 0.0983665i | ||||
\(619\) | − | 1.01339e18i | − | 0.724084i | −0.932162 | − | 0.362042i | \(-0.882080\pi\) | ||
0.932162 | − | 0.362042i | \(-0.117920\pi\) | |||||||
\(620\) | 4.99918e17 | − | 2.99326e16i | 0.353470 | − | 0.0211641i | ||||
\(621\) | 6.33517e17i | 0.443265i | ||||||||
\(622\) | 6.18530e17 | + | 5.82603e17i | 0.428276 | + | 0.403400i | ||||
\(623\) | 1.45083e18 | 0.994134 | ||||||||
\(624\) | 9.26216e17 | − | 1.11314e17i | 0.628076 | − | 0.0754828i | ||||
\(625\) | −4.40712e17 | −0.295757 | ||||||||
\(626\) | −8.36382e17 | − | 7.87802e17i | −0.555484 | − | 0.523219i | ||||
\(627\) | − | 1.63300e18i | − | 1.07336i | ||||||
\(628\) | −8.40261e17 | + | 5.03107e16i | −0.546609 | + | 0.0327282i | ||||
\(629\) | 7.92226e17i | 0.510059i | ||||||||
\(630\) | −7.43552e16 | + | 7.89404e16i | −0.0473803 | + | 0.0503021i | ||||
\(631\) | −1.25814e18 | −0.793485 | −0.396742 | − | 0.917930i | \(-0.629859\pi\) | ||||
−0.396742 | + | 0.917930i | \(0.629859\pi\) | |||||||
\(632\) | −2.74988e17 | + | 3.29345e17i | −0.171653 | + | 0.205585i | ||||
\(633\) | −1.50961e17 | −0.0932695 | ||||||||
\(634\) | 1.57731e18 | − | 1.67458e18i | 0.964580 | − | 1.02406i | ||||
\(635\) | − | 3.25385e17i | − | 0.196956i | ||||||
\(636\) | −5.81735e16 | − | 9.71582e17i | −0.0348541 | − | 0.582114i | ||||
\(637\) | − | 3.08264e18i | − | 1.82817i | ||||||
\(638\) | −2.22512e17 | − | 2.09588e17i | −0.130623 | − | 0.123036i | ||||
\(639\) | 6.57640e16 | 0.0382149 | ||||||||
\(640\) | 1.05448e18 | + | 6.84975e17i | 0.606551 | + | 0.394008i | ||||
\(641\) | −4.20462e17 | −0.239414 | −0.119707 | − | 0.992809i | \(-0.538196\pi\) | ||||
−0.119707 | + | 0.992809i | \(0.538196\pi\) | |||||||
\(642\) | 1.17031e18 | + | 1.10233e18i | 0.659663 | + | 0.621347i | ||||
\(643\) | 2.53475e18i | 1.41437i | 0.707026 | + | 0.707187i | \(0.250036\pi\) | ||||
−0.707026 | + | 0.707187i | \(0.749964\pi\) | |||||||
\(644\) | −9.16190e16 | − | 1.53017e18i | −0.0506090 | − | 0.845243i | ||||
\(645\) | 2.04049e18i | 1.11582i | ||||||||
\(646\) | −5.88294e17 | + | 6.24571e17i | −0.318480 | + | 0.338120i | ||||
\(647\) | −1.77278e18 | −0.950119 | −0.475059 | − | 0.879954i | \(-0.657573\pi\) | ||||
−0.475059 | + | 0.879954i | \(0.657573\pi\) | |||||||
\(648\) | 1.14598e18 | − | 1.37251e18i | 0.608049 | − | 0.728245i | ||||
\(649\) | 2.29692e18 | 1.20658 | ||||||||
\(650\) | 4.07790e17 | − | 4.32936e17i | 0.212080 | − | 0.225158i | ||||
\(651\) | 1.81197e18i | 0.932986i | ||||||||
\(652\) | −9.48148e17 | + | 5.67704e16i | −0.483356 | + | 0.0289409i | ||||
\(653\) | − | 4.81484e17i | − | 0.243022i | −0.992590 | − | 0.121511i | \(-0.961226\pi\) | ||
0.992590 | − | 0.121511i | \(-0.0387740\pi\) | |||||||
\(654\) | −3.38839e17 | − | 3.19158e17i | −0.169332 | − | 0.159496i | ||||
\(655\) | −2.01483e18 | −0.996944 | ||||||||
\(656\) | 1.55237e18 | − | 1.86565e17i | 0.760536 | − | 0.0914020i | ||||
\(657\) | −5.62726e16 | −0.0272974 | ||||||||
\(658\) | −2.74488e18 | − | 2.58545e18i | −1.31842 | − | 1.24184i | ||||
\(659\) | 2.71767e18i | 1.29253i | 0.763113 | + | 0.646266i | \(0.223670\pi\) | ||||
−0.763113 | + | 0.646266i | \(0.776330\pi\) | |||||||
\(660\) | −1.81254e18 | + | 1.08526e17i | −0.853596 | + | 0.0511091i | ||||
\(661\) | 8.55628e17i | 0.399002i | 0.979898 | + | 0.199501i | \(0.0639322\pi\) | ||||
−0.979898 | + | 0.199501i | \(0.936068\pi\) | |||||||
\(662\) | 1.61411e18 | − | 1.71365e18i | 0.745345 | − | 0.791307i | ||||
\(663\) | 7.07808e17 | 0.323652 | ||||||||
\(664\) | 8.78750e16 | + | 7.33714e16i | 0.0397899 | + | 0.0332226i | ||||
\(665\) | 2.86169e18 | 1.28316 | ||||||||
\(666\) | 7.52655e16 | − | 7.99069e16i | 0.0334206 | − | 0.0354815i | ||||
\(667\) | − | 1.45869e17i | − | 0.0641422i | ||||||
\(668\) | 2.21837e17 | + | 3.70499e18i | 0.0966020 | + | 1.61339i | ||||
\(669\) | 9.91495e17i | 0.427583i | ||||||||
\(670\) | −9.84913e17 | − | 9.27705e17i | −0.420641 | − | 0.396208i | ||||
\(671\) | 4.74943e18 | 2.00884 | ||||||||
\(672\) | −2.70187e18 | + | 3.66021e18i | −1.13179 | + | 1.53323i | ||||
\(673\) | 7.38036e17 | 0.306182 | 0.153091 | − | 0.988212i | \(-0.451077\pi\) | ||||
0.153091 | + | 0.988212i | \(0.451077\pi\) | |||||||
\(674\) | −1.11330e18 | − | 1.04863e18i | −0.457428 | − | 0.430859i | ||||
\(675\) | − | 1.19869e18i | − | 0.487788i | ||||||
\(676\) | 8.58992e16 | + | 1.43464e18i | 0.0346207 | + | 0.578215i | ||||
\(677\) | 3.87097e17i | 0.154523i | 0.997011 | + | 0.0772615i | \(0.0246176\pi\) | ||||
−0.997011 | + | 0.0772615i | \(0.975382\pi\) | |||||||
\(678\) | 1.24672e18 | − | 1.32360e18i | 0.492921 | − | 0.523317i | ||||
\(679\) | −7.70619e18 | −3.01777 | ||||||||
\(680\) | 7.32338e17 | + | 6.11467e17i | 0.284056 | + | 0.237173i | ||||
\(681\) | 7.11776e17 | 0.273456 | ||||||||
\(682\) | 1.06936e18 | − | 1.13530e18i | 0.406934 | − | 0.432028i | ||||
\(683\) | − | 3.15274e18i | − | 1.18838i | −0.804326 | − | 0.594188i | \(-0.797474\pi\) | ||
0.804326 | − | 0.594188i | \(-0.202526\pi\) | |||||||
\(684\) | 1.18675e17 | − | 7.10567e15i | 0.0443092 | − | 0.00265302i | ||||
\(685\) | − | 2.71317e18i | − | 1.00343i | ||||||
\(686\) | 7.06044e18 | + | 6.65034e18i | 2.58657 | + | 2.43634i | ||||
\(687\) | 2.34401e18 | 0.850629 | ||||||||
\(688\) | −5.25068e17 | − | 4.36898e18i | −0.188752 | − | 1.57056i | ||||
\(689\) | −1.08920e18 | −0.387866 | ||||||||
\(690\) | −6.30744e17 | − | 5.94108e17i | −0.222502 | − | 0.209578i | ||||
\(691\) | 3.51153e18i | 1.22712i | 0.789646 | + | 0.613562i | \(0.210264\pi\) | ||||
−0.789646 | + | 0.613562i | \(0.789736\pi\) | |||||||
\(692\) | −2.07914e18 | + | 1.24488e17i | −0.719769 | + | 0.0430962i | ||||
\(693\) | 3.37717e17i | 0.115821i | ||||||||
\(694\) | 2.01612e18 | − | 2.14045e18i | 0.684983 | − | 0.727223i | ||||
\(695\) | −3.98479e16 | −0.0134123 | ||||||||
\(696\) | −2.77462e17 | + | 3.32309e17i | −0.0925216 | + | 0.110811i | ||||
\(697\) | 1.18631e18 | 0.391909 | ||||||||
\(698\) | −2.60833e18 | + | 2.76917e18i | −0.853693 | + | 0.906337i | ||||
\(699\) | 4.06102e18i | 1.31684i | ||||||||
\(700\) | 1.73354e17 | + | 2.89526e18i | 0.0556924 | + | 0.930143i | ||||
\(701\) | − | 3.88716e18i | − | 1.23727i | −0.785678 | − | 0.618636i | \(-0.787686\pi\) | ||
0.785678 | − | 0.618636i | \(-0.212314\pi\) | |||||||
\(702\) | −1.53158e18 | − | 1.44262e18i | −0.483001 | − | 0.454946i | ||||
\(703\) | −2.89673e18 | −0.905102 | ||||||||
\(704\) | 3.85299e18 | − | 6.98782e17i | 1.19282 | − | 0.216331i | ||||
\(705\) | −2.13147e18 | −0.653807 | ||||||||
\(706\) | 1.26865e18 | + | 1.19497e18i | 0.385578 | + | 0.363182i | ||||
\(707\) | − | 8.41672e18i | − | 2.53464i | ||||||
\(708\) | −1.94425e17 | − | 3.24717e18i | −0.0580143 | − | 0.968923i | ||||
\(709\) | − | 5.71982e18i | − | 1.69115i | −0.533857 | − | 0.845575i | \(-0.679258\pi\) | ||
0.533857 | − | 0.845575i | \(-0.320742\pi\) | |||||||
\(710\) | −1.32307e18 | + | 1.40466e18i | −0.387618 | + | 0.411521i | ||||
\(711\) | 4.51071e16 | 0.0130946 | ||||||||
\(712\) | −1.13351e18 | + | 1.35757e18i | −0.326066 | + | 0.390520i | ||||
\(713\) | 7.44248e17 | 0.212147 | ||||||||
\(714\) | −2.36673e18 | + | 2.51268e18i | −0.668514 | + | 0.709738i | ||||
\(715\) | 2.03196e18i | 0.568756i | ||||||||
\(716\) | −6.44567e18 | + | 3.85935e17i | −1.78786 | + | 0.107048i | ||||
\(717\) | − | 4.95786e17i | − | 0.136276i | ||||||
\(718\) | −1.04005e18 | − | 9.79644e17i | −0.283300 | − | 0.266845i | ||||
\(719\) | −1.87126e17 | −0.0505121 | −0.0252560 | − | 0.999681i | \(-0.508040\pi\) | ||||
−0.0252560 | + | 0.999681i | \(0.508040\pi\) | |||||||
\(720\) | −1.57738e16 | − | 1.31251e17i | −0.00421964 | − | 0.0351107i | ||||
\(721\) | 1.02132e18 | 0.270759 | ||||||||
\(722\) | 4.86948e17 | + | 4.58664e17i | 0.127935 | + | 0.120504i | ||||
\(723\) | − | 4.43884e17i | − | 0.115577i | ||||||
\(724\) | 3.74229e17 | − | 2.24070e16i | 0.0965687 | − | 0.00578206i | ||||
\(725\) | 2.76000e17i | 0.0705849i | ||||||||
\(726\) | −1.23895e18 | + | 1.31535e18i | −0.314027 | + | 0.333392i | ||||
\(727\) | 4.51258e18 | 1.13358 | 0.566789 | − | 0.823863i | \(-0.308186\pi\) | ||||
0.566789 | + | 0.823863i | \(0.308186\pi\) | |||||||
\(728\) | 3.90794e18 | + | 3.26294e18i | 0.972957 | + | 0.812372i | ||||
\(729\) | −4.23085e18 | −1.04399 | ||||||||
\(730\) | 1.13212e18 | − | 1.20193e18i | 0.276881 | − | 0.293955i | ||||
\(731\) | − | 3.33874e18i | − | 0.809320i | ||||||
\(732\) | −4.02020e17 | − | 6.71431e18i | −0.0965885 | − | 1.61317i | ||||
\(733\) | 7.21224e18i | 1.71749i | 0.512403 | + | 0.858745i | \(0.328755\pi\) | ||||
−0.512403 | + | 0.858745i | \(0.671245\pi\) | |||||||
\(734\) | −3.05589e18 | − | 2.87839e18i | −0.721296 | − | 0.679400i | ||||
\(735\) | 8.49765e18 | 1.98807 | ||||||||
\(736\) | 1.50339e18 | + | 1.10977e18i | 0.348632 | + | 0.257351i | ||||
\(737\) | −4.21358e18 | −0.968529 | ||||||||
\(738\) | −1.19656e17 | − | 1.12706e17i | −0.0272626 | − | 0.0256790i | ||||
\(739\) | 3.50368e18i | 0.791289i | 0.918404 | + | 0.395644i | \(0.129479\pi\) | ||||
−0.918404 | + | 0.395644i | \(0.870521\pi\) | |||||||
\(740\) | 1.92511e17 | + | 3.21521e18i | 0.0430972 | + | 0.719786i | ||||
\(741\) | 2.58806e18i | 0.574322i | ||||||||
\(742\) | 3.64200e18 | − | 3.86659e18i | 0.801151 | − | 0.850555i | ||||
\(743\) | −5.28199e18 | −1.15178 | −0.575891 | − | 0.817526i | \(-0.695345\pi\) | ||||
−0.575891 | + | 0.817526i | \(0.695345\pi\) | |||||||
\(744\) | −1.69550e18 | − | 1.41566e18i | −0.366500 | − | 0.306010i | ||||
\(745\) | 1.60480e18 | 0.343879 | ||||||||
\(746\) | −2.01268e18 | + | 2.13680e18i | −0.427536 | + | 0.453900i | ||||
\(747\) | − | 1.20353e16i | − | 0.00253440i | ||||||
\(748\) | 2.96577e18 | − | 1.77576e17i | 0.619123 | − | 0.0370700i | ||||
\(749\) | 8.77386e18i | 1.81576i | ||||||||
\(750\) | 3.69617e18 | + | 3.48149e18i | 0.758323 | + | 0.714276i | ||||
\(751\) | 3.18060e18 | 0.646917 | 0.323459 | − | 0.946242i | \(-0.395154\pi\) | ||||
0.323459 | + | 0.946242i | \(0.395154\pi\) | |||||||
\(752\) | 4.56378e18 | − | 5.48480e17i | 0.920257 | − | 0.110597i | ||||
\(753\) | 2.97677e18 | 0.595083 | ||||||||
\(754\) | 3.52649e17 | + | 3.32165e17i | 0.0698922 | + | 0.0658325i | ||||
\(755\) | − | 1.27844e18i | − | 0.251203i | ||||||
\(756\) | 1.02424e19 | − | 6.13265e17i | 1.99531 | − | 0.119469i | ||||
\(757\) | 1.08578e18i | 0.209710i | 0.994488 | + | 0.104855i | \(0.0334378\pi\) | ||||
−0.994488 | + | 0.104855i | \(0.966562\pi\) | |||||||
\(758\) | −4.90209e18 | + | 5.20439e18i | −0.938711 | + | 0.996597i | ||||
\(759\) | −2.69840e18 | −0.512313 | ||||||||
\(760\) | −2.23579e18 | + | 2.67775e18i | −0.420865 | + | 0.504059i | ||||
\(761\) | −7.22568e17 | −0.134859 | −0.0674293 | − | 0.997724i | \(-0.521480\pi\) | ||||
−0.0674293 | + | 0.997724i | \(0.521480\pi\) | |||||||
\(762\) | −9.83969e17 | + | 1.04465e18i | −0.182085 | + | 0.193313i | ||||
\(763\) | − | 2.54029e18i | − | 0.466095i | ||||||
\(764\) | −4.97481e17 | − | 8.30866e18i | −0.0905045 | − | 1.51156i | ||||
\(765\) | − | 1.00301e17i | − | 0.0180928i | ||||||
\(766\) | −2.61288e18 | − | 2.46111e18i | −0.467339 | − | 0.440194i | ||||
\(767\) | −3.64027e18 | −0.645600 | ||||||||
\(768\) | −1.31402e18 | − | 5.38786e18i | −0.231075 | − | 0.947477i | ||||
\(769\) | 7.37979e18 | 1.28684 | 0.643418 | − | 0.765515i | \(-0.277516\pi\) | ||||
0.643418 | + | 0.765515i | \(0.277516\pi\) | |||||||
\(770\) | −7.21334e18 | − | 6.79436e18i | −1.24723 | − | 1.17479i | ||||
\(771\) | − | 5.20435e17i | − | 0.0892305i | ||||||
\(772\) | 9.11432e16 | + | 1.52222e18i | 0.0154957 | + | 0.258801i | ||||
\(773\) | 1.85746e18i | 0.313150i | 0.987666 | + | 0.156575i | \(0.0500453\pi\) | ||||
−0.987666 | + | 0.156575i | \(0.949955\pi\) | |||||||
\(774\) | −3.17198e17 | + | 3.36758e17i | −0.0530291 | + | 0.0562991i | ||||
\(775\) | −1.40820e18 | −0.233455 | ||||||||
\(776\) | 6.02071e18 | − | 7.21085e18i | 0.989798 | − | 1.18546i | ||||
\(777\) | −1.16536e19 | −1.89988 | ||||||||
\(778\) | 2.29817e18 | − | 2.43989e18i | 0.371548 | − | 0.394460i | ||||
\(779\) | 4.33767e18i | 0.695445i | ||||||||
\(780\) | 2.87260e18 | − | 1.71997e17i | 0.456731 | − | 0.0273468i | ||||
\(781\) | 6.00931e18i | 0.947531i | ||||||||
\(782\) | 1.03205e18 | + | 9.72109e17i | 0.161383 | + | 0.152010i | ||||
\(783\) | 9.76391e17 | 0.151416 | ||||||||
\(784\) | −1.81947e19 | + | 2.18666e18i | −2.79828 | + | 0.336300i | ||||
\(785\) | −2.59668e18 | −0.396064 | ||||||||
\(786\) | 6.46861e18 | + | 6.09288e18i | 0.978508 | + | 0.921672i | ||||
\(787\) | − | 1.68643e18i | − | 0.253007i | −0.991966 | − | 0.126503i | \(-0.959625\pi\) | ||
0.991966 | − | 0.126503i | \(-0.0403754\pi\) | |||||||
\(788\) | −3.96529e18 | + | 2.37422e17i | −0.590004 | + | 0.0353265i | ||||
\(789\) | − | 8.82557e18i | − | 1.30239i | ||||||
\(790\) | −9.07486e17 | + | 9.63448e17i | −0.132820 | + | 0.141011i | ||||
\(791\) | 9.92312e18 | 1.44046 | ||||||||
\(792\) | −3.16009e17 | − | 2.63852e17i | −0.0454973 | − | 0.0379881i | ||||
\(793\) | −7.52713e18 | −1.07486 | ||||||||
\(794\) | 1.17140e18 | − | 1.24364e18i | 0.165910 | − | 0.176141i | ||||
\(795\) | − | 3.00250e18i | − | 0.421791i | ||||||
\(796\) | 4.82729e17 | + | 8.06227e18i | 0.0672617 | + | 1.12337i | ||||
\(797\) | − | 9.80081e18i | − | 1.35451i | −0.735747 | − | 0.677256i | \(-0.763169\pi\) | ||
0.735747 | − | 0.677256i | \(-0.236831\pi\) | |||||||
\(798\) | −9.18744e18 | − | 8.65380e18i | −1.25943 | − | 1.18628i | ||||
\(799\) | 3.48761e18 | 0.474214 | ||||||||
\(800\) | −2.84459e18 | − | 2.09980e18i | −0.383650 | − | 0.283200i | ||||
\(801\) | 1.85933e17 | 0.0248740 | ||||||||
\(802\) | 5.69857e18 | + | 5.36758e18i | 0.756193 | + | 0.712270i | ||||
\(803\) | − | 5.14201e18i | − | 0.676834i | ||||||
\(804\) | 3.56663e17 | + | 5.95678e18i | 0.0465686 | + | 0.777763i | ||||
\(805\) | − | 4.72872e18i | − | 0.612450i | ||||||
\(806\) | −1.69477e18 | + | 1.79928e18i | −0.217737 | + | 0.231164i | ||||
\(807\) | 4.80091e17 | 0.0611851 | ||||||||
\(808\) | 7.87571e18 | + | 6.57584e18i | 0.995671 | + | 0.831337i | ||||
\(809\) | 9.57224e18 | 1.20046 | 0.600231 | − | 0.799827i | \(-0.295075\pi\) | ||||
0.600231 | + | 0.799827i | \(0.295075\pi\) | |||||||
\(810\) | 3.78184e18 | − | 4.01505e18i | 0.470490 | − | 0.499504i | ||||
\(811\) | 9.21325e18i | 1.13704i | 0.822668 | + | 0.568522i | \(0.192485\pi\) | ||||
−0.822668 | + | 0.568522i | \(0.807515\pi\) | |||||||
\(812\) | −2.35833e18 | + | 1.41205e17i | −0.288729 | + | 0.0172877i | ||||
\(813\) | 2.50588e18i | 0.304349i | ||||||||
\(814\) | 7.30165e18 | + | 6.87754e18i | 0.879756 | + | 0.828656i | ||||
\(815\) | −2.93008e18 | −0.350232 | ||||||||
\(816\) | −5.02081e17 | − | 4.17771e18i | −0.0595371 | − | 0.495396i | ||||
\(817\) | 1.22079e19 | 1.43614 | ||||||||
\(818\) | 4.41681e18 | + | 4.16026e18i | 0.515480 | + | 0.485539i | ||||
\(819\) | − | 5.35231e17i | − | 0.0619720i | ||||||
\(820\) | 4.81458e18 | − | 2.88273e17i | 0.553055 | − | 0.0331142i | ||||
\(821\) | − | 3.41203e18i | − | 0.388850i | −0.980917 | − | 0.194425i | \(-0.937716\pi\) | ||
0.980917 | − | 0.194425i | \(-0.0622840\pi\) | |||||||
\(822\) | −8.20466e18 | + | 8.71061e18i | −0.927671 | + | 0.984876i | ||||
\(823\) | −1.10180e19 | −1.23596 | −0.617980 | − | 0.786194i | \(-0.712049\pi\) | ||||
−0.617980 | + | 0.786194i | \(0.712049\pi\) | |||||||
\(824\) | −7.97941e17 | + | 9.55673e17i | −0.0888063 | + | 0.106361i | ||||
\(825\) | 5.10568e18 | 0.563771 | ||||||||
\(826\) | 1.21721e19 | − | 1.29227e19i | 1.33351 | − | 1.41574i | ||||
\(827\) | 1.97457e18i | 0.214628i | 0.994225 | + | 0.107314i | \(0.0342251\pi\) | ||||
−0.994225 | + | 0.107314i | \(0.965775\pi\) | |||||||
\(828\) | −1.17416e16 | − | 1.96101e17i | −0.00126628 | − | 0.0211486i | ||||
\(829\) | − | 1.22147e19i | − | 1.30701i | −0.756921 | − | 0.653506i | \(-0.773297\pi\) | ||
0.756921 | − | 0.653506i | \(-0.226703\pi\) | |||||||
\(830\) | 2.57064e17 | + | 2.42133e17i | 0.0272919 | + | 0.0257067i | ||||
\(831\) | −1.72874e19 | −1.82106 | ||||||||
\(832\) | −6.10641e18 | + | 1.10746e18i | −0.638240 | + | 0.115752i | ||||
\(833\) | −1.39043e19 | −1.44197 | ||||||||
\(834\) | 1.27931e17 | + | 1.20501e17i | 0.0131643 | + | 0.0123997i | ||||
\(835\) | 1.14496e19i | 1.16904i | ||||||||
\(836\) | 6.49294e17 | + | 1.08442e19i | 0.0657810 | + | 1.09864i | ||||
\(837\) | 4.98173e18i | 0.500800i | ||||||||
\(838\) | −2.71115e18 | + | 2.87833e18i | −0.270437 | + | 0.287114i | ||||
\(839\) | 9.89468e18 | 0.979375 | 0.489688 | − | 0.871898i | \(-0.337111\pi\) | ||||
0.489688 | + | 0.871898i | \(0.337111\pi\) | |||||||
\(840\) | −8.99467e18 | + | 1.07727e19i | −0.883425 | + | 1.05806i | ||||
\(841\) | 1.00358e19 | 0.978089 | ||||||||
\(842\) | −8.63632e18 | + | 9.16889e18i | −0.835219 | + | 0.886723i | ||||
\(843\) | − | 1.20909e19i | − | 1.16032i | ||||||
\(844\) | 1.00248e18 | − | 6.00233e16i | 0.0954658 | − | 0.00571602i | ||||
\(845\) | 4.43350e18i | 0.418965i | ||||||||
\(846\) | −3.51774e17 | − | 3.31341e17i | −0.0329880 | − | 0.0310719i | ||||
\(847\) | −9.86128e18 | −0.917679 | ||||||||
\(848\) | 7.72619e17 | + | 6.42880e18i | 0.0713497 | + | 0.593686i | ||||
\(849\) | 6.07572e18 | 0.556798 | ||||||||
\(850\) | −1.95277e18 | − | 1.83934e18i | −0.177593 | − | 0.167278i | ||||
\(851\) | 4.78661e18i | 0.432002i | ||||||||
\(852\) | 8.49543e18 | − | 5.08664e17i | 0.760901 | − | 0.0455590i | ||||
\(853\) | − | 3.91840e18i | − | 0.348289i | −0.984720 | − | 0.174145i | \(-0.944284\pi\) | ||
0.984720 | − | 0.174145i | \(-0.0557160\pi\) | |||||||
\(854\) | 2.51688e19 | − | 2.67208e19i | 2.22017 | − | 2.35708i | ||||
\(855\) | 3.66744e17 | 0.0321058 | ||||||||
\(856\) | −8.20989e18 | − | 6.85486e18i | −0.713276 | − | 0.595551i | ||||
\(857\) | 1.50331e19 | 1.29621 | 0.648104 | − | 0.761552i | \(-0.275562\pi\) | ||||
0.648104 | + | 0.761552i | \(0.275562\pi\) | |||||||
\(858\) | 6.14468e18 | − | 6.52360e18i | 0.525814 | − | 0.558238i | ||||
\(859\) | − | 1.77260e19i | − | 1.50541i | −0.658357 | − | 0.752706i | \(-0.728748\pi\) | ||
0.658357 | − | 0.752706i | \(-0.271252\pi\) | |||||||
\(860\) | −8.11314e17 | − | 1.35501e19i | −0.0683832 | − | 1.14210i | ||||
\(861\) | 1.74506e19i | 1.45979i | ||||||||
\(862\) | −1.55592e19 | − | 1.46555e19i | −1.29179 | − | 1.21675i | ||||
\(863\) | 1.17921e19 | 0.971678 | 0.485839 | − | 0.874048i | \(-0.338514\pi\) | ||||
0.485839 | + | 0.874048i | \(0.338514\pi\) | |||||||
\(864\) | −7.42837e18 | + | 1.00632e19i | −0.607511 | + | 0.822992i | ||||
\(865\) | −6.42520e18 | −0.521533 | ||||||||
\(866\) | −1.02234e19 | − | 9.62960e18i | −0.823625 | − | 0.775786i | ||||
\(867\) | 9.00403e18i | 0.719967i | ||||||||
\(868\) | −7.20456e17 | − | 1.20327e19i | −0.0571780 | − | 0.954956i | ||||
\(869\) | 4.12175e18i | 0.324678i | ||||||||
\(870\) | −9.15652e17 | + | 9.72117e17i | −0.0715905 | + | 0.0760052i | ||||
\(871\) | 6.67789e18 | 0.518228 | ||||||||
\(872\) | 2.37701e18 | + | 1.98469e18i | 0.183094 | + | 0.152874i | ||||
\(873\) | −9.87597e17 | −0.0755070 | ||||||||
\(874\) | −3.55445e18 | + | 3.77364e18i | −0.269742 | + | 0.286376i | ||||
\(875\) | 2.77104e19i | 2.08733i | ||||||||
\(876\) | −7.26932e18 | + | 4.35251e17i | −0.543522 | + | 0.0325434i | ||||
\(877\) | − | 1.76021e19i | − | 1.30637i | −0.757197 | − | 0.653187i | \(-0.773432\pi\) | ||
0.757197 | − | 0.653187i | \(-0.226568\pi\) | |||||||
\(878\) | 8.93644e18 | + | 8.41737e18i | 0.658340 | + | 0.620101i | ||||
\(879\) | −7.11202e18 | −0.520074 | ||||||||
\(880\) | 1.19933e19 | − | 1.44136e18i | 0.870564 | − | 0.104625i | ||||
\(881\) | −2.52269e19 | −1.81770 | −0.908848 | − | 0.417127i | \(-0.863037\pi\) | ||||
−0.908848 | + | 0.417127i | \(0.863037\pi\) | |||||||
\(882\) | 1.40244e18 | + | 1.32098e18i | 0.100309 | + | 0.0944822i | ||||
\(883\) | 1.05758e19i | 0.750878i | 0.926847 | + | 0.375439i | \(0.122508\pi\) | ||||
−0.926847 | + | 0.375439i | \(0.877492\pi\) | |||||||
\(884\) | −4.70030e18 | + | 2.81431e17i | −0.331273 | + | 0.0198350i | ||||
\(885\) | − | 1.00348e19i | − | 0.702066i | ||||||
\(886\) | −1.47454e19 | + | 1.56547e19i | −1.02409 | + | 1.08724i | ||||
\(887\) | −1.38265e19 | −0.953255 | −0.476628 | − | 0.879105i | \(-0.658141\pi\) | ||||
−0.476628 | + | 0.879105i | \(0.658141\pi\) | |||||||
\(888\) | 9.10479e18 | − | 1.09046e19i | 0.623140 | − | 0.746318i | ||||
\(889\) | −7.83177e18 | −0.532106 | ||||||||
\(890\) | −3.74069e18 | + | 3.97137e18i | −0.252300 | + | 0.267858i | ||||
\(891\) | − | 1.71769e19i | − | 1.15011i | ||||||
\(892\) | −3.94227e17 | − | 6.58416e18i | −0.0262044 | − | 0.437652i | ||||
\(893\) | 1.27522e19i | 0.841496i | ||||||||
\(894\) | −5.15221e18 | − | 4.85294e18i | −0.337520 | − | 0.317915i | ||||
\(895\) | −1.99192e19 | −1.29545 | ||||||||
\(896\) | 1.64868e19 | − | 2.53804e19i | 1.06447 | − | 1.63869i | ||||
\(897\) | 4.27656e18 | 0.274122 | ||||||||
\(898\) | 2.14727e19 | + | 2.02254e19i | 1.36644 | + | 1.28707i | ||||
\(899\) | − | 1.14705e18i | − | 0.0724678i | ||||||
\(900\) | 2.22164e16 | + | 3.71045e17i | 0.00139347 | + | 0.0232729i | ||||
\(901\) | 4.91284e18i | 0.305930i | ||||||||
\(902\) | 1.02987e19 | − | 1.09338e19i | 0.636707 | − | 0.675970i | ||||
\(903\) | 4.91129e19 | 3.01457 | ||||||||
\(904\) | −7.75276e18 | + | 9.28528e18i | −0.472456 | + | 0.565849i | ||||
\(905\) | 1.15649e18 | 0.0699721 | ||||||||
\(906\) | −3.86602e18 | + | 4.10442e18i | −0.232237 | + | 0.246558i | ||||
\(907\) | 1.03159e19i | 0.615263i | 0.951506 | + | 0.307631i | \(0.0995363\pi\) | ||||
−0.951506 | + | 0.307631i | \(0.900464\pi\) | |||||||
\(908\) | −4.72665e18 | + | 2.83008e17i | −0.279895 | + | 0.0167587i | ||||
\(909\) | − | 1.07866e18i | − | 0.0634187i | ||||||
\(910\) | 1.14321e19 | + | 1.07680e19i | 0.667352 | + | 0.628590i | ||||
\(911\) | 4.56605e18 | 0.264650 | 0.132325 | − | 0.991206i | \(-0.457756\pi\) | ||||
0.132325 | + | 0.991206i | \(0.457756\pi\) | |||||||
\(912\) | 1.52755e19 | − | 1.83583e18i | 0.879083 | − | 0.105649i | ||||
\(913\) | 1.09975e18 | 0.0628399 | ||||||||
\(914\) | −1.50628e19 | − | 1.41879e19i | −0.854584 | − | 0.804946i | ||||
\(915\) | − | 2.07494e19i | − | 1.16888i | ||||||
\(916\) | −1.55657e19 | + | 9.31998e17i | −0.870660 | + | 0.0521308i | ||||
\(917\) | 4.84955e19i | 2.69340i | ||||||||
\(918\) | −6.50694e18 | + | 6.90820e18i | −0.358839 | + | 0.380967i | ||||
\(919\) | 1.83999e19 | 1.00755 | 0.503774 | − | 0.863836i | \(-0.331945\pi\) | ||||
0.503774 | + | 0.863836i | \(0.331945\pi\) | |||||||
\(920\) | 4.42476e18 | + | 3.69447e18i | 0.240585 | + | 0.200877i | ||||
\(921\) | −5.49804e18 | −0.296839 | ||||||||
\(922\) | −1.10483e19 | + | 1.17296e19i | −0.592304 | + | 0.628829i | ||||
\(923\) | − | 9.52386e18i | − | 0.506993i | ||||||
\(924\) | 2.61214e18 | + | 4.36265e19i | 0.138079 | + | 2.30612i | ||||
\(925\) | − | 9.05681e18i | − | 0.475394i | ||||||
\(926\) | 1.41659e19 | + | 1.33431e19i | 0.738367 | + | 0.695479i | ||||
\(927\) | 1.30889e17 | 0.00677461 | ||||||||
\(928\) | 1.71040e18 | − | 2.31706e18i | 0.0879093 | − | 0.119090i | ||||
\(929\) | 1.02573e19 | 0.523515 | 0.261757 | − | 0.965134i | \(-0.415698\pi\) | ||||
0.261757 | + | 0.965134i | \(0.415698\pi\) | |||||||
\(930\) | −4.95992e18 | − | 4.67183e18i | −0.251383 | − | 0.236781i | ||||
\(931\) | − | 5.08402e19i | − | 2.55879i | ||||||
\(932\) | −1.61470e18 | − | 2.69678e19i | −0.0807025 | − | 1.34785i | ||||
\(933\) | − | 1.15605e19i | − | 0.573783i | ||||||
\(934\) | −5.97229e18 | + | 6.34057e18i | −0.294365 | + | 0.312517i | ||||
\(935\) | 9.16519e18 | 0.448607 | ||||||||
\(936\) | 5.00827e17 | + | 4.18166e17i | 0.0243441 | + | 0.0203262i | ||||
\(937\) | −2.98943e19 | −1.44305 | −0.721525 | − | 0.692388i | \(-0.756559\pi\) | ||||
−0.721525 | + | 0.692388i | \(0.756559\pi\) | |||||||
\(938\) | −2.23291e19 | + | 2.37061e19i | −1.07042 | + | 1.13643i | ||||
\(939\) | 1.56323e19i | 0.744211i | ||||||||
\(940\) | 1.41543e19 | − | 8.47490e17i | 0.669202 | − | 0.0400685i | ||||
\(941\) | − | 3.86590e19i | − | 1.81517i | −0.419867 | − | 0.907586i | \(-0.637923\pi\) | ||
0.419867 | − | 0.907586i | \(-0.362077\pi\) | |||||||
\(942\) | 8.33661e18 | + | 7.85239e18i | 0.388740 | + | 0.366160i | ||||
\(943\) | 7.16766e18 | 0.331934 | ||||||||
\(944\) | 2.58221e18 | + | 2.14860e19i | 0.118761 | + | 0.988184i | ||||
\(945\) | 3.16523e19 | 1.44577 | ||||||||
\(946\) | −3.07719e19 | − | 2.89846e19i | −1.39593 | − | 1.31484i | ||||
\(947\) | 1.48690e19i | 0.669896i | 0.942237 | + | 0.334948i | \(0.108719\pi\) | ||||
−0.942237 | + | 0.334948i | \(0.891281\pi\) | |||||||
\(948\) | 5.82696e18 | − | 3.48889e17i | 0.260728 | − | 0.0156111i | ||||
\(949\) | 8.14932e18i | 0.362152i | ||||||||
\(950\) | 6.72543e18 | − | 7.14016e18i | 0.296836 | − | 0.315141i | ||||
\(951\) | −3.12985e19 | −1.37199 | ||||||||
\(952\) | 1.47175e19 | − | 1.76268e19i | 0.640759 | − | 0.767421i | ||||
\(953\) | −2.39907e19 | −1.03738 | −0.518691 | − | 0.854962i | \(-0.673580\pi\) | ||||
−0.518691 | + | 0.854962i | \(0.673580\pi\) | |||||||
\(954\) | 4.66745e17 | − | 4.95528e17i | 0.0200454 | − | 0.0212816i | ||||
\(955\) | − | 2.56764e19i | − | 1.09525i | ||||||
\(956\) | 1.97129e17 | + | 3.29234e18i | 0.00835169 | + | 0.139485i | ||||
\(957\) | 4.15884e18i | 0.175002i | ||||||||
\(958\) | −7.05882e18 | − | 6.64881e18i | −0.295023 | − | 0.277887i | ||||
\(959\) | −6.53039e19 | −2.71093 | ||||||||
\(960\) | −3.05285e18 | − | 1.68330e19i | −0.125876 | − | 0.694063i | ||||
\(961\) | −1.85651e19 | −0.760317 | ||||||||
\(962\) | −1.15720e19 | − | 1.08999e19i | −0.470729 | − | 0.443387i | ||||
\(963\) | 1.12442e18i | 0.0454318i | ||||||||
\(964\) | 1.76492e17 | + | 2.94768e18i | 0.00708312 | + | 0.118298i | ||||
\(965\) | 4.70416e18i | 0.187523i | ||||||||
\(966\) | −1.42997e19 | + | 1.51815e19i | −0.566208 | + | 0.601124i | ||||
\(967\) | 4.01216e19 | 1.57800 | 0.788999 | − | 0.614394i | \(-0.210600\pi\) | ||||
0.788999 | + | 0.614394i | \(0.210600\pi\) | |||||||
\(968\) | 7.70444e18 | − | 9.22741e18i | 0.300989 | − | 0.360487i | ||||
\(969\) | 1.16735e19 | 0.452997 | ||||||||
\(970\) | 1.98690e19 | − | 2.10942e19i | 0.765877 | − | 0.813105i | ||||
\(971\) | − | 1.31013e19i | − | 0.501639i | −0.968034 | − | 0.250819i | \(-0.919300\pi\) | ||
0.968034 | − | 0.250819i | \(-0.0807000\pi\) | |||||||
\(972\) | 2.56407e18 | − | 1.53524e17i | 0.0975213 | − | 0.00583909i | ||||
\(973\) | 9.59108e17i | 0.0362355i | ||||||||
\(974\) | 1.89181e19 | + | 1.78193e19i | 0.709978 | + | 0.668740i | ||||
\(975\) | −8.09174e18 | −0.301656 | ||||||||
\(976\) | 5.33934e18 | + | 4.44275e19i | 0.197726 | + | 1.64524i | ||||
\(977\) | 3.73291e19 | 1.37320 | 0.686598 | − | 0.727037i | \(-0.259103\pi\) | ||||
0.686598 | + | 0.727037i | \(0.259103\pi\) | |||||||
\(978\) | 9.40701e18 | + | 8.86061e18i | 0.343755 | + | 0.323788i | ||||
\(979\) | 1.69900e19i | 0.616746i | ||||||||
\(980\) | −5.64298e19 | + | 3.37874e18i | −2.03488 | + | 0.121839i | ||||
\(981\) | − | 3.25555e17i | − | 0.0116621i | ||||||
\(982\) | 2.59478e19 | − | 2.75479e19i | 0.923372 | − | 0.980313i | ||||
\(983\) | 4.66140e19 | 1.64785 | 0.823926 | − | 0.566697i | \(-0.191779\pi\) | ||||
0.823926 | + | 0.566697i | \(0.191779\pi\) | |||||||
\(984\) | −1.63289e19 | − | 1.36339e19i | −0.573442 | − | 0.478796i | ||||
\(985\) | −1.22540e19 | −0.427507 | ||||||||
\(986\) | 1.49824e18 | − | 1.59063e18i | 0.0519255 | − | 0.0551275i | ||||
\(987\) | 5.13028e19i | 1.76636i | ||||||||
\(988\) | −1.02903e18 | − | 1.71863e19i | −0.0351973 | − | 0.587846i | ||||
\(989\) | − | 2.01726e19i | − | 0.685466i | ||||||
\(990\) | −9.24434e17 | − | 8.70739e17i | −0.0312067 | − | 0.0293940i | ||||
\(991\) | 1.76475e19 | 0.591840 | 0.295920 | − | 0.955213i | \(-0.404374\pi\) | ||||
0.295920 | + | 0.955213i | \(0.404374\pi\) | |||||||
\(992\) | 1.18221e19 | + | 8.72675e18i | 0.393884 | + | 0.290755i | ||||
\(993\) | −3.20287e19 | −1.06016 | ||||||||
\(994\) | 3.38091e19 | + | 3.18453e19i | 1.11179 | + | 1.04721i | ||||
\(995\) | 2.49150e19i | 0.813975i | ||||||||
\(996\) | −9.30897e16 | − | 1.55473e18i | −0.00302145 | − | 0.0504626i | ||||
\(997\) | 4.89441e19i | 1.57827i | 0.614219 | + | 0.789135i | \(0.289471\pi\) | ||||
−0.614219 | + | 0.789135i | \(0.710529\pi\) | |||||||
\(998\) | 1.38619e19 | − | 1.47167e19i | 0.444092 | − | 0.471477i | ||||
\(999\) | −3.20398e19 | −1.01980 |
(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 | 8.14.b.b.5.8 | yes | 10 | |
3.2 | odd | 2 | 72.14.d.c.37.3 | 10 | |||
4.3 | odd | 2 | 32.14.b.b.17.8 | 10 | |||
8.3 | odd | 2 | 32.14.b.b.17.3 | 10 | |||
8.5 | even | 2 | inner | 8.14.b.b.5.7 | ✓ | 10 | |
24.5 | odd | 2 | 72.14.d.c.37.4 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.14.b.b.5.7 | ✓ | 10 | 8.5 | even | 2 | inner | |
8.14.b.b.5.8 | yes | 10 | 1.1 | even | 1 | trivial | |
32.14.b.b.17.3 | 10 | 8.3 | odd | 2 | |||
32.14.b.b.17.8 | 10 | 4.3 | odd | 2 | |||
72.14.d.c.37.3 | 10 | 3.2 | odd | 2 | |||
72.14.d.c.37.4 | 10 | 24.5 | odd | 2 |