Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [25,34,Mod(24,25)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 34, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("25.24");
S:= CuspForms(chi, 34);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 34 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.b (of order \(2\), degree \(1\), not 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: | \(172.457072203\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1178101x^{2} + 346979902500 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{4}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 1) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 24.3 | ||
Root | \(766.996i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 25.24 |
Dual form | 25.34.b.a.24.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/25\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 49679.4i | 0.536021i | 0.963416 | + | 0.268010i | \(0.0863662\pi\) | ||||
−0.963416 | + | 0.268010i | \(0.913634\pi\) | |||||||
\(3\) | 1.55221e7i | 0.208185i | 0.994568 | + | 0.104093i | \(0.0331939\pi\) | ||||
−0.994568 | + | 0.104093i | \(0.966806\pi\) | |||||||
\(4\) | 6.12189e9 | 0.712682 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −7.71130e11 | −0.111592 | ||||||||
\(7\) | − 1.22168e14i | − 1.38944i | −0.719278 | − | 0.694722i | \(-0.755527\pi\) | ||||
0.719278 | − | 0.694722i | \(-0.244473\pi\) | |||||||
\(8\) | 7.30875e14i | 0.918033i | ||||||||
\(9\) | 5.31812e15 | 0.956659 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.15763e17 | 1.41578 | 0.707892 | − | 0.706321i | \(-0.249646\pi\) | ||||
0.707892 | + | 0.706321i | \(0.249646\pi\) | |||||||
\(12\) | 9.50247e16i | 0.148370i | ||||||||
\(13\) | 1.07762e18i | 0.449158i | 0.974456 | + | 0.224579i | \(0.0721007\pi\) | ||||
−0.974456 | + | 0.224579i | \(0.927899\pi\) | |||||||
\(14\) | 6.06926e18 | 0.744771 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.62772e19 | 0.220597 | ||||||||
\(17\) | 2.54532e20i | 1.26863i | 0.773074 | + | 0.634316i | \(0.218718\pi\) | ||||
−0.773074 | + | 0.634316i | \(0.781282\pi\) | |||||||
\(18\) | 2.64201e20i | 0.512789i | ||||||||
\(19\) | 1.22020e21 | 0.970505 | 0.485252 | − | 0.874374i | \(-0.338728\pi\) | ||||
0.485252 | + | 0.874374i | \(0.338728\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.89631e21 | 0.289262 | ||||||||
\(22\) | 1.07190e22i | 0.758890i | ||||||||
\(23\) | 5.11280e21i | 0.173840i | 0.996215 | + | 0.0869199i | \(0.0277024\pi\) | ||||
−0.996215 | + | 0.0869199i | \(0.972298\pi\) | |||||||
\(24\) | −1.13447e22 | −0.191121 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5.35354e22 | −0.240758 | ||||||||
\(27\) | 1.68837e23i | 0.407348i | ||||||||
\(28\) | − 7.47901e23i | − 0.990231i | ||||||||
\(29\) | 1.64733e23 | 0.122240 | 0.0611201 | − | 0.998130i | \(-0.480533\pi\) | ||||
0.0611201 | + | 0.998130i | \(0.480533\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.75706e24 | −1.66836 | −0.834181 | − | 0.551491i | \(-0.814059\pi\) | ||||
−0.834181 | + | 0.551491i | \(0.814059\pi\) | |||||||
\(32\) | 7.08681e24i | 1.03628i | ||||||||
\(33\) | 3.34910e24i | 0.294746i | ||||||||
\(34\) | −1.26450e25 | −0.680013 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.25570e25 | 0.681793 | ||||||||
\(37\) | − 7.46520e25i | − 0.994748i | −0.867536 | − | 0.497374i | \(-0.834298\pi\) | ||||
0.867536 | − | 0.497374i | \(-0.165702\pi\) | |||||||
\(38\) | 6.06190e25i | 0.520211i | ||||||||
\(39\) | −1.67269e25 | −0.0935082 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.96453e26 | 1.21603 | 0.608016 | − | 0.793925i | \(-0.291966\pi\) | ||||
0.608016 | + | 0.793925i | \(0.291966\pi\) | |||||||
\(42\) | 9.42077e25i | 0.155051i | ||||||||
\(43\) | 1.99347e26i | 0.222525i | 0.993791 | + | 0.111263i | \(0.0354895\pi\) | ||||
−0.993791 | + | 0.111263i | \(0.964511\pi\) | |||||||
\(44\) | 1.32088e27 | 1.00900 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.54001e26 | −0.0931818 | ||||||||
\(47\) | 2.16452e27i | 0.556862i | 0.960456 | + | 0.278431i | \(0.0898143\pi\) | ||||
−0.960456 | + | 0.278431i | \(0.910186\pi\) | |||||||
\(48\) | 2.52656e26i | 0.0459250i | ||||||||
\(49\) | −7.19411e27 | −0.930555 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.95088e27 | −0.264111 | ||||||||
\(52\) | 6.59706e27i | 0.320107i | ||||||||
\(53\) | 3.60439e28i | 1.27726i | 0.769513 | + | 0.638631i | \(0.220499\pi\) | ||||
−0.769513 | + | 0.638631i | \(0.779501\pi\) | |||||||
\(54\) | −8.38773e27 | −0.218347 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 8.92898e28 | 1.27556 | ||||||||
\(57\) | 1.89401e28i | 0.202045i | ||||||||
\(58\) | 8.18385e27i | 0.0655233i | ||||||||
\(59\) | 1.87520e29 | 1.13237 | 0.566186 | − | 0.824278i | \(-0.308418\pi\) | ||||
0.566186 | + | 0.824278i | \(0.308418\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.18340e27 | 0.0145743 | 0.00728715 | − | 0.999973i | \(-0.497680\pi\) | ||||
0.00728715 | + | 0.999973i | \(0.497680\pi\) | |||||||
\(62\) | − 3.35687e29i | − 0.894276i | ||||||||
\(63\) | − 6.49706e29i | − 1.32922i | ||||||||
\(64\) | −2.12249e29 | −0.334870 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.66381e29 | −0.157990 | ||||||||
\(67\) | 4.85975e29i | 0.360064i | 0.983661 | + | 0.180032i | \(0.0576201\pi\) | ||||
−0.983661 | + | 0.180032i | \(0.942380\pi\) | |||||||
\(68\) | 1.55822e30i | 0.904130i | ||||||||
\(69\) | −7.93615e28 | −0.0361909 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.42819e30 | −0.975667 | −0.487834 | − | 0.872937i | \(-0.662213\pi\) | ||||
−0.487834 | + | 0.872937i | \(0.662213\pi\) | |||||||
\(72\) | 3.88688e30i | 0.878244i | ||||||||
\(73\) | − 7.01467e30i | − 1.26235i | −0.775640 | − | 0.631175i | \(-0.782573\pi\) | ||||
0.775640 | − | 0.631175i | \(-0.217427\pi\) | |||||||
\(74\) | 3.70867e30 | 0.533206 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.46995e30 | 0.691661 | ||||||||
\(77\) | − 2.63594e31i | − 1.96715i | ||||||||
\(78\) | − 8.30984e29i | − 0.0501224i | ||||||||
\(79\) | 2.95630e30 | 0.144511 | 0.0722555 | − | 0.997386i | \(-0.476980\pi\) | ||||
0.0722555 | + | 0.997386i | \(0.476980\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.69431e31 | 0.871855 | ||||||||
\(82\) | 2.46635e31i | 0.651818i | ||||||||
\(83\) | 1.23020e31i | 0.266187i | 0.991103 | + | 0.133094i | \(0.0424911\pi\) | ||||
−0.991103 | + | 0.133094i | \(0.957509\pi\) | |||||||
\(84\) | 1.16090e31 | 0.206152 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −9.90343e30 | −0.119278 | ||||||||
\(87\) | 2.55701e30i | 0.0254486i | ||||||||
\(88\) | 1.57696e32i | 1.29974i | ||||||||
\(89\) | −7.05623e31 | −0.482656 | −0.241328 | − | 0.970444i | \(-0.577583\pi\) | ||||
−0.241328 | + | 0.970444i | \(0.577583\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.31651e32 | 0.624080 | ||||||||
\(92\) | 3.13000e31i | 0.123892i | ||||||||
\(93\) | − 1.04884e32i | − 0.347329i | ||||||||
\(94\) | −1.07532e32 | −0.298490 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.10002e32 | −0.215738 | ||||||||
\(97\) | − 7.71791e32i | − 1.27575i | −0.770140 | − | 0.637875i | \(-0.779813\pi\) | ||||
0.770140 | − | 0.637875i | \(-0.220187\pi\) | |||||||
\(98\) | − 3.57399e32i | − 0.498797i | ||||||||
\(99\) | 1.14745e33 | 1.35442 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.88601e33 | 1.60045 | 0.800224 | − | 0.599701i | \(-0.204714\pi\) | ||||
0.800224 | + | 0.599701i | \(0.204714\pi\) | |||||||
\(102\) | − 1.96278e32i | − 0.141569i | ||||||||
\(103\) | 4.05317e32i | 0.248874i | 0.992227 | + | 0.124437i | \(0.0397125\pi\) | ||||
−0.992227 | + | 0.124437i | \(0.960287\pi\) | |||||||
\(104\) | −7.87604e32 | −0.412342 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.79064e33 | −0.684640 | ||||||||
\(107\) | − 1.13905e33i | − 0.373003i | −0.982455 | − | 0.186501i | \(-0.940285\pi\) | ||||
0.982455 | − | 0.186501i | \(-0.0597149\pi\) | |||||||
\(108\) | 1.03360e33i | 0.290309i | ||||||||
\(109\) | −5.47789e32 | −0.132153 | −0.0660764 | − | 0.997815i | \(-0.521048\pi\) | ||||
−0.0660764 | + | 0.997815i | \(0.521048\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.15876e33 | 0.207092 | ||||||||
\(112\) | − 1.98855e33i | − 0.306507i | ||||||||
\(113\) | − 7.05689e33i | − 0.939332i | −0.882844 | − | 0.469666i | \(-0.844374\pi\) | ||||
0.882844 | − | 0.469666i | \(-0.155626\pi\) | |||||||
\(114\) | −9.40936e32 | −0.108300 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.00848e33 | 0.0871183 | ||||||||
\(117\) | 5.73090e33i | 0.429691i | ||||||||
\(118\) | 9.31588e33i | 0.606975i | ||||||||
\(119\) | 3.10958e34 | 1.76269 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.33284e34 | 1.00444 | ||||||||
\(122\) | 2.07829e32i | 0.00781213i | ||||||||
\(123\) | 7.70601e33i | 0.253160i | ||||||||
\(124\) | −4.13660e34 | −1.18901 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.22771e34 | 0.712492 | ||||||||
\(127\) | − 1.88228e34i | − 0.364689i | −0.983235 | − | 0.182344i | \(-0.941631\pi\) | ||||
0.983235 | − | 0.182344i | \(-0.0583685\pi\) | |||||||
\(128\) | 5.03308e34i | 0.856780i | ||||||||
\(129\) | −3.09428e33 | −0.0463265 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.26378e35 | −1.46790 | −0.733949 | − | 0.679204i | \(-0.762325\pi\) | ||||
−0.733949 | + | 0.679204i | \(0.762325\pi\) | |||||||
\(132\) | 2.05028e34i | 0.210060i | ||||||||
\(133\) | − 1.49070e35i | − 1.34846i | ||||||||
\(134\) | −2.41430e34 | −0.193002 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.86031e35 | −1.16465 | ||||||||
\(137\) | 2.95759e35i | 1.64077i | 0.571809 | + | 0.820387i | \(0.306242\pi\) | ||||
−0.571809 | + | 0.820387i | \(0.693758\pi\) | |||||||
\(138\) | − 3.94263e33i | − 0.0193991i | ||||||||
\(139\) | 8.22498e34 | 0.359245 | 0.179622 | − | 0.983736i | \(-0.442512\pi\) | ||||
0.179622 | + | 0.983736i | \(0.442512\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.35980e34 | −0.115931 | ||||||||
\(142\) | − 1.70310e35i | − 0.522978i | ||||||||
\(143\) | 2.32510e35i | 0.635911i | ||||||||
\(144\) | 8.65639e34 | 0.211036 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.48485e35 | 0.676646 | ||||||||
\(147\) | − 1.11668e35i | − 0.193728i | ||||||||
\(148\) | − 4.57011e35i | − 0.708939i | ||||||||
\(149\) | −5.29045e35 | −0.734378 | −0.367189 | − | 0.930146i | \(-0.619680\pi\) | ||||
−0.367189 | + | 0.930146i | \(0.619680\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.18728e35 | −0.577856 | −0.288928 | − | 0.957351i | \(-0.593299\pi\) | ||||
−0.288928 | + | 0.957351i | \(0.593299\pi\) | |||||||
\(152\) | 8.91816e35i | 0.890955i | ||||||||
\(153\) | 1.35363e36i | 1.21365i | ||||||||
\(154\) | 1.30952e36 | 1.05444 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.02400e35 | −0.0666416 | ||||||||
\(157\) | 1.31075e36i | 0.767669i | 0.923402 | + | 0.383835i | \(0.125397\pi\) | ||||
−0.923402 | + | 0.383835i | \(0.874603\pi\) | |||||||
\(158\) | 1.46867e35i | 0.0774609i | ||||||||
\(159\) | −5.59478e35 | −0.265908 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.24622e35 | 0.241541 | ||||||||
\(162\) | 1.33852e36i | 0.467332i | ||||||||
\(163\) | − 1.61518e36i | − 0.509478i | −0.967010 | − | 0.254739i | \(-0.918010\pi\) | ||||
0.967010 | − | 0.254739i | \(-0.0819896\pi\) | |||||||
\(164\) | 3.03923e36 | 0.866643 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.11157e35 | −0.142682 | ||||||||
\(167\) | − 6.45682e35i | − 0.136520i | −0.997668 | − | 0.0682601i | \(-0.978255\pi\) | ||||
0.997668 | − | 0.0682601i | \(-0.0217448\pi\) | |||||||
\(168\) | 1.38597e36i | 0.265552i | ||||||||
\(169\) | 4.59487e36 | 0.798257 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.48919e36 | 0.928442 | ||||||||
\(172\) | 1.22038e36i | 0.158590i | ||||||||
\(173\) | 6.58049e36i | 0.777137i | 0.921420 | + | 0.388569i | \(0.127030\pi\) | ||||
−0.921420 | + | 0.388569i | \(0.872970\pi\) | |||||||
\(174\) | −1.27031e35 | −0.0136410 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.51200e36 | 0.312317 | ||||||||
\(177\) | 2.91071e36i | 0.235743i | ||||||||
\(178\) | − 3.50549e36i | − 0.258714i | ||||||||
\(179\) | 2.08823e37 | 1.40508 | 0.702542 | − | 0.711642i | \(-0.252048\pi\) | ||||
0.702542 | + | 0.711642i | \(0.252048\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.42658e37 | −1.35925 | −0.679624 | − | 0.733561i | \(-0.737857\pi\) | ||||
−0.679624 | + | 0.733561i | \(0.737857\pi\) | |||||||
\(182\) | 6.54034e36i | 0.334520i | ||||||||
\(183\) | 6.49353e34i | 0.00303416i | ||||||||
\(184\) | −3.73682e36 | −0.159591 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 5.21058e36 | 0.186175 | ||||||||
\(187\) | 5.49185e37i | 1.79611i | ||||||||
\(188\) | 1.32510e37i | 0.396865i | ||||||||
\(189\) | 2.06265e37 | 0.565987 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.06968e37 | 0.938664 | 0.469332 | − | 0.883022i | \(-0.344495\pi\) | ||||
0.469332 | + | 0.883022i | \(0.344495\pi\) | |||||||
\(192\) | − 3.29455e36i | − 0.0697150i | ||||||||
\(193\) | 5.23242e37i | 1.01627i | 0.861279 | + | 0.508133i | \(0.169664\pi\) | ||||
−0.861279 | + | 0.508133i | \(0.830336\pi\) | |||||||
\(194\) | 3.83421e37 | 0.683829 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.40416e37 | −0.663189 | ||||||||
\(197\) | 1.35006e38i | 1.86922i | 0.355672 | + | 0.934611i | \(0.384252\pi\) | ||||
−0.355672 | + | 0.934611i | \(0.615748\pi\) | |||||||
\(198\) | 5.70048e37i | 0.725999i | ||||||||
\(199\) | 9.91562e37 | 1.16210 | 0.581051 | − | 0.813867i | \(-0.302642\pi\) | ||||
0.581051 | + | 0.813867i | \(0.302642\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.54336e36 | −0.0749601 | ||||||||
\(202\) | 9.36960e37i | 0.857874i | ||||||||
\(203\) | − 2.01252e37i | − 0.169846i | ||||||||
\(204\) | −2.41868e37 | −0.188227 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.01359e37 | −0.133402 | ||||||||
\(207\) | 2.71905e37i | 0.166305i | ||||||||
\(208\) | 1.75406e37i | 0.0990828i | ||||||||
\(209\) | 2.63274e38 | 1.37403 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.07128e38 | −0.923802 | −0.461901 | − | 0.886931i | \(-0.652832\pi\) | ||||
−0.461901 | + | 0.886931i | \(0.652832\pi\) | |||||||
\(212\) | 2.20657e38i | 0.910282i | ||||||||
\(213\) | − 5.32127e37i | − 0.203120i | ||||||||
\(214\) | 5.65876e37 | 0.199937 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.23399e38 | −0.373959 | ||||||||
\(217\) | 8.25499e38i | 2.31809i | ||||||||
\(218\) | − 2.72139e37i | − 0.0708367i | ||||||||
\(219\) | 1.08883e38 | 0.262803 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.74288e38 | −0.569816 | ||||||||
\(222\) | 5.75665e37i | 0.111006i | ||||||||
\(223\) | 4.51334e38i | 0.808106i | 0.914736 | + | 0.404053i | \(0.132399\pi\) | ||||
−0.914736 | + | 0.404053i | \(0.867601\pi\) | |||||||
\(224\) | 8.65784e38 | 1.43985 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.50582e38 | 0.503501 | ||||||||
\(227\) | − 2.43217e38i | − 0.324764i | −0.986728 | − | 0.162382i | \(-0.948082\pi\) | ||||
0.986728 | − | 0.162382i | \(-0.0519176\pi\) | |||||||
\(228\) | 1.15949e38i | 0.143994i | ||||||||
\(229\) | −3.41418e38 | −0.394458 | −0.197229 | − | 0.980357i | \(-0.563194\pi\) | ||||
−0.197229 | + | 0.980357i | \(0.563194\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.09153e38 | 0.409533 | ||||||||
\(232\) | 1.20399e38i | 0.112221i | ||||||||
\(233\) | 6.99608e37i | 0.0607410i | 0.999539 | + | 0.0303705i | \(0.00966871\pi\) | ||||
−0.999539 | + | 0.0303705i | \(0.990331\pi\) | |||||||
\(234\) | −2.84708e38 | −0.230323 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.14798e39 | 0.807020 | ||||||||
\(237\) | 4.58880e37i | 0.0300851i | ||||||||
\(238\) | 1.54482e39i | 0.944840i | ||||||||
\(239\) | 1.63523e39 | 0.933282 | 0.466641 | − | 0.884447i | \(-0.345464\pi\) | ||||
0.466641 | + | 0.884447i | \(0.345464\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.64560e38 | −0.181338 | −0.0906689 | − | 0.995881i | \(-0.528900\pi\) | ||||
−0.0906689 | + | 0.995881i | \(0.528900\pi\) | |||||||
\(242\) | 1.15894e39i | 0.538403i | ||||||||
\(243\) | 1.35679e39i | 0.588856i | ||||||||
\(244\) | 2.56103e37 | 0.0103868 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.82830e38 | −0.135699 | ||||||||
\(247\) | 1.31491e39i | 0.435910i | ||||||||
\(248\) | − 4.93857e39i | − 1.53161i | ||||||||
\(249\) | −1.90953e38 | −0.0554164 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.94693e39 | 0.495147 | 0.247573 | − | 0.968869i | \(-0.420367\pi\) | ||||
0.247573 | + | 0.968869i | \(0.420367\pi\) | |||||||
\(252\) | − 3.97743e39i | − 0.947313i | ||||||||
\(253\) | 1.10315e39i | 0.246120i | ||||||||
\(254\) | 9.35105e38 | 0.195481 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.32361e39 | −0.794122 | ||||||||
\(257\) | − 5.64464e39i | − 0.972164i | −0.873913 | − | 0.486082i | \(-0.838426\pi\) | ||||
0.873913 | − | 0.486082i | \(-0.161574\pi\) | |||||||
\(258\) | − 1.53722e38i | − 0.0248320i | ||||||||
\(259\) | −9.12012e39 | −1.38215 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.76071e38 | 0.116942 | ||||||||
\(262\) | − 6.27840e39i | − 0.786824i | ||||||||
\(263\) | − 9.75930e39i | − 1.14855i | −0.818663 | − | 0.574274i | \(-0.805285\pi\) | ||||
0.818663 | − | 0.574274i | \(-0.194715\pi\) | |||||||
\(264\) | −2.44777e39 | −0.270586 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 7.40572e39 | 0.722804 | ||||||||
\(267\) | − 1.09528e39i | − 0.100482i | ||||||||
\(268\) | 2.97508e39i | 0.256611i | ||||||||
\(269\) | 1.08142e40 | 0.877168 | 0.438584 | − | 0.898690i | \(-0.355480\pi\) | ||||
0.438584 | + | 0.898690i | \(0.355480\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.19121e39 | −0.444408 | −0.222204 | − | 0.975000i | \(-0.571325\pi\) | ||||
−0.222204 | + | 0.975000i | \(0.571325\pi\) | |||||||
\(272\) | 4.14306e39i | 0.279856i | ||||||||
\(273\) | 2.04350e39i | 0.129924i | ||||||||
\(274\) | −1.46931e40 | −0.879489 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.85842e38 | −0.0257926 | ||||||||
\(277\) | − 5.15662e39i | − 0.257898i | −0.991651 | − | 0.128949i | \(-0.958840\pi\) | ||||
0.991651 | − | 0.128949i | \(-0.0411604\pi\) | |||||||
\(278\) | 4.08612e39i | 0.192563i | ||||||||
\(279\) | −3.59349e40 | −1.59605 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.28386e40 | −0.506832 | −0.253416 | − | 0.967357i | \(-0.581554\pi\) | ||||
−0.253416 | + | 0.967357i | \(0.581554\pi\) | |||||||
\(282\) | − 1.66913e39i | − 0.0621412i | ||||||||
\(283\) | − 3.83806e40i | − 1.34783i | −0.738809 | − | 0.673915i | \(-0.764611\pi\) | ||||
0.738809 | − | 0.673915i | \(-0.235389\pi\) | |||||||
\(284\) | −2.09870e40 | −0.695340 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.15510e40 | −0.340862 | ||||||||
\(287\) | − 6.06509e40i | − 1.68961i | ||||||||
\(288\) | 3.76885e40i | 0.991364i | ||||||||
\(289\) | −2.45321e40 | −0.609426 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.19798e40 | 0.265593 | ||||||||
\(292\) | − 4.29430e40i | − 0.899654i | ||||||||
\(293\) | − 1.90344e40i | − 0.376897i | −0.982083 | − | 0.188449i | \(-0.939654\pi\) | ||||
0.982083 | − | 0.188449i | \(-0.0603459\pi\) | |||||||
\(294\) | 5.54760e39 | 0.103842 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.45613e40 | 0.913212 | ||||||||
\(297\) | 3.64287e40i | 0.576717i | ||||||||
\(298\) | − 2.62827e40i | − 0.393642i | ||||||||
\(299\) | −5.50964e39 | −0.0780816 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.43538e40 | 0.309186 | ||||||||
\(302\) | − 2.57701e40i | − 0.309743i | ||||||||
\(303\) | 2.92749e40i | 0.333190i | ||||||||
\(304\) | 1.98614e40 | 0.214090 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −6.72478e40 | −0.650540 | ||||||||
\(307\) | − 1.48955e41i | − 1.36544i | −0.730682 | − | 0.682718i | \(-0.760798\pi\) | ||||
0.730682 | − | 0.682718i | \(-0.239202\pi\) | |||||||
\(308\) | − 1.61369e41i | − 1.40195i | ||||||||
\(309\) | −6.29138e39 | −0.0518121 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.37928e39 | −0.0546345 | −0.0273173 | − | 0.999627i | \(-0.508696\pi\) | ||||
−0.0273173 | + | 0.999627i | \(0.508696\pi\) | |||||||
\(312\) | − 1.22253e40i | − 0.0858437i | ||||||||
\(313\) | 2.63324e40i | 0.175391i | 0.996147 | + | 0.0876957i | \(0.0279503\pi\) | ||||
−0.996147 | + | 0.0876957i | \(0.972050\pi\) | |||||||
\(314\) | −6.51171e40 | −0.411487 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.80981e40 | 0.102990 | ||||||||
\(317\) | 1.79226e41i | 0.968109i | 0.875038 | + | 0.484054i | \(0.160836\pi\) | ||||
−0.875038 | + | 0.484054i | \(0.839164\pi\) | |||||||
\(318\) | − 2.77946e40i | − 0.142532i | ||||||||
\(319\) | 3.55433e40 | 0.173066 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.76805e40 | 0.0776538 | ||||||||
\(322\) | 3.10309e40i | 0.129471i | ||||||||
\(323\) | 3.10581e41i | 1.23121i | ||||||||
\(324\) | 1.64942e41 | 0.621355 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8.02413e40 | 0.273091 | ||||||||
\(327\) | − 8.50285e39i | − 0.0275123i | ||||||||
\(328\) | 3.62845e41i | 1.11636i | ||||||||
\(329\) | 2.64436e41 | 0.773728 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.16181e41 | 1.63135 | 0.815674 | − | 0.578512i | \(-0.196366\pi\) | ||||
0.815674 | + | 0.578512i | \(0.196366\pi\) | |||||||
\(332\) | 7.53115e40i | 0.189707i | ||||||||
\(333\) | − 3.97009e41i | − 0.951635i | ||||||||
\(334\) | 3.20771e40 | 0.0731777 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.08666e40 | 0.0638102 | ||||||||
\(337\) | 4.51357e41i | 0.888437i | 0.895919 | + | 0.444218i | \(0.146519\pi\) | ||||
−0.895919 | + | 0.444218i | \(0.853481\pi\) | |||||||
\(338\) | 2.28271e41i | 0.427882i | ||||||||
\(339\) | 1.09538e41 | 0.195555 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.45792e42 | −2.36204 | ||||||||
\(342\) | 3.22379e41i | 0.497664i | ||||||||
\(343\) | − 6.55899e40i | − 0.0964903i | ||||||||
\(344\) | −1.45697e41 | −0.204286 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.26915e41 | −0.416562 | ||||||||
\(347\) | 8.17900e41i | 0.993720i | 0.867831 | + | 0.496860i | \(0.165514\pi\) | ||||
−0.867831 | + | 0.496860i | \(0.834486\pi\) | |||||||
\(348\) | 1.56537e40i | 0.0181368i | ||||||||
\(349\) | 1.22969e42 | 1.35886 | 0.679432 | − | 0.733739i | \(-0.262226\pi\) | ||||
0.679432 | + | 0.733739i | \(0.262226\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.81942e41 | −0.182964 | ||||||||
\(352\) | 1.52907e42i | 1.46715i | ||||||||
\(353\) | − 1.62570e41i | − 0.148853i | −0.997226 | − | 0.0744266i | \(-0.976287\pi\) | ||||
0.997226 | − | 0.0744266i | \(-0.0237126\pi\) | |||||||
\(354\) | −1.44602e41 | −0.126363 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.31974e41 | −0.343980 | ||||||||
\(357\) | 4.82673e41i | 0.366967i | ||||||||
\(358\) | 1.03742e42i | 0.753155i | ||||||||
\(359\) | −3.64036e41 | −0.252398 | −0.126199 | − | 0.992005i | \(-0.540278\pi\) | ||||
−0.126199 | + | 0.992005i | \(0.540278\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.18755e40 | −0.0581207 | ||||||||
\(362\) | − 1.20551e42i | − 0.728585i | ||||||||
\(363\) | 3.62106e41i | 0.209111i | ||||||||
\(364\) | 8.05951e41 | 0.444771 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.22595e39 | −0.00162637 | ||||||||
\(367\) | 1.35581e42i | 0.653442i | 0.945121 | + | 0.326721i | \(0.105944\pi\) | ||||
−0.945121 | + | 0.326721i | \(0.894056\pi\) | |||||||
\(368\) | 8.32218e40i | 0.0383485i | ||||||||
\(369\) | 2.64020e42 | 1.16333 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.40343e42 | 1.77469 | ||||||||
\(372\) | − 6.42088e41i | − 0.247535i | ||||||||
\(373\) | − 1.93457e42i | − 0.713493i | −0.934201 | − | 0.356746i | \(-0.883886\pi\) | ||||
0.934201 | − | 0.356746i | \(-0.116114\pi\) | |||||||
\(374\) | −2.72832e42 | −0.962752 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.58200e42 | −0.511218 | ||||||||
\(377\) | 1.77519e41i | 0.0549052i | ||||||||
\(378\) | 1.02471e42i | 0.303381i | ||||||||
\(379\) | 5.45789e42 | 1.54696 | 0.773478 | − | 0.633823i | \(-0.218515\pi\) | ||||
0.773478 | + | 0.633823i | \(0.218515\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.92169e41 | 0.0759229 | ||||||||
\(382\) | 2.02180e42i | 0.503143i | ||||||||
\(383\) | 5.06942e42i | 1.20831i | 0.796867 | + | 0.604155i | \(0.206489\pi\) | ||||
−0.796867 | + | 0.604155i | \(0.793511\pi\) | |||||||
\(384\) | −7.81241e41 | −0.178369 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.59944e42 | −0.544740 | ||||||||
\(387\) | 1.06015e42i | 0.212881i | ||||||||
\(388\) | − 4.72482e42i | − 0.909204i | ||||||||
\(389\) | −7.51028e42 | −1.38512 | −0.692560 | − | 0.721360i | \(-0.743517\pi\) | ||||
−0.692560 | + | 0.721360i | \(0.743517\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.30137e42 | −0.220539 | ||||||||
\(392\) | − 5.25800e42i | − 0.854280i | ||||||||
\(393\) | − 1.96166e42i | − 0.305595i | ||||||||
\(394\) | −6.70703e42 | −1.00194 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 7.02458e42 | 0.965272 | ||||||||
\(397\) | − 1.26926e43i | − 1.67304i | −0.547938 | − | 0.836519i | \(-0.684587\pi\) | ||||
0.547938 | − | 0.836519i | \(-0.315413\pi\) | |||||||
\(398\) | 4.92603e42i | 0.622911i | ||||||||
\(399\) | 2.31389e42 | 0.280730 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.29553e42 | 0.591598 | 0.295799 | − | 0.955250i | \(-0.404414\pi\) | ||||
0.295799 | + | 0.955250i | \(0.404414\pi\) | |||||||
\(402\) | − 3.74750e41i | − 0.0401802i | ||||||||
\(403\) | − 7.28153e42i | − 0.749358i | ||||||||
\(404\) | 1.15459e43 | 1.14061 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9.99807e41 | 0.0910410 | ||||||||
\(407\) | − 1.61071e43i | − 1.40835i | ||||||||
\(408\) | − 2.88760e42i | − 0.242462i | ||||||||
\(409\) | −1.80907e43 | −1.45888 | −0.729442 | − | 0.684042i | \(-0.760220\pi\) | ||||
−0.729442 | + | 0.684042i | \(0.760220\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.59081e42 | −0.341585 | ||||||||
\(412\) | 2.48130e42i | 0.177368i | ||||||||
\(413\) | − 2.29090e43i | − 1.57337i | ||||||||
\(414\) | −1.35081e42 | −0.0891432 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −7.63687e42 | −0.465453 | ||||||||
\(417\) | 1.27669e42i | 0.0747896i | ||||||||
\(418\) | 1.30793e43i | 0.736506i | ||||||||
\(419\) | −9.59306e42 | −0.519309 | −0.259654 | − | 0.965702i | \(-0.583609\pi\) | ||||
−0.259654 | + | 0.965702i | \(0.583609\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.95406e43 | −0.977875 | −0.488938 | − | 0.872319i | \(-0.662615\pi\) | ||||
−0.488938 | + | 0.872319i | \(0.662615\pi\) | |||||||
\(422\) | − 1.02900e43i | − 0.495177i | ||||||||
\(423\) | 1.15112e43i | 0.532727i | ||||||||
\(424\) | −2.63436e43 | −1.17257 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.64358e42 | 0.108876 | ||||||||
\(427\) | − 5.11080e41i | − 0.0202502i | ||||||||
\(428\) | − 6.97316e42i | − 0.265832i | ||||||||
\(429\) | −3.60904e42 | −0.132387 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.01382e43 | 1.36359 | 0.681794 | − | 0.731544i | \(-0.261200\pi\) | ||||
0.681794 | + | 0.731544i | \(0.261200\pi\) | |||||||
\(432\) | 2.74819e42i | 0.0898596i | ||||||||
\(433\) | 1.24146e43i | 0.390735i | 0.980730 | + | 0.195367i | \(0.0625899\pi\) | ||||
−0.980730 | + | 0.195367i | \(0.937410\pi\) | |||||||
\(434\) | −4.10103e43 | −1.24255 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.35350e42 | −0.0941829 | ||||||||
\(437\) | 6.23865e42i | 0.168712i | ||||||||
\(438\) | 5.40922e42i | 0.140868i | ||||||||
\(439\) | 6.07044e43 | 1.52249 | 0.761247 | − | 0.648462i | \(-0.224587\pi\) | ||||
0.761247 | + | 0.648462i | \(0.224587\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.82592e43 | −0.890223 | ||||||||
\(442\) | − 1.36265e43i | − 0.305433i | ||||||||
\(443\) | − 6.61294e43i | − 1.42802i | −0.700137 | − | 0.714009i | \(-0.746878\pi\) | ||||
0.700137 | − | 0.714009i | \(-0.253122\pi\) | |||||||
\(444\) | 7.09379e42 | 0.147591 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.24220e43 | −0.433162 | ||||||||
\(447\) | − 8.21191e42i | − 0.152887i | ||||||||
\(448\) | 2.59301e43i | 0.465283i | ||||||||
\(449\) | 1.54504e43 | 0.267225 | 0.133612 | − | 0.991034i | \(-0.457342\pi\) | ||||
0.133612 | + | 0.991034i | \(0.457342\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.07116e44 | 1.72164 | ||||||||
\(452\) | − 4.32015e43i | − 0.669444i | ||||||||
\(453\) | − 8.05175e42i | − 0.120301i | ||||||||
\(454\) | 1.20829e43 | 0.174080 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.38429e43 | −0.185484 | ||||||||
\(457\) | 7.12331e43i | 0.920586i | 0.887767 | + | 0.460293i | \(0.152256\pi\) | ||||
−0.887767 | + | 0.460293i | \(0.847744\pi\) | |||||||
\(458\) | − 1.69615e43i | − 0.211438i | ||||||||
\(459\) | −4.29745e43 | −0.516774 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.34004e44 | −1.49986 | −0.749932 | − | 0.661515i | \(-0.769914\pi\) | ||||
−0.749932 | + | 0.661515i | \(0.769914\pi\) | |||||||
\(462\) | 2.03265e43i | 0.219518i | ||||||||
\(463\) | 5.53073e43i | 0.576363i | 0.957576 | + | 0.288182i | \(0.0930507\pi\) | ||||
−0.957576 | + | 0.288182i | \(0.906949\pi\) | |||||||
\(464\) | 2.68139e42 | 0.0269658 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.47561e42 | −0.0325584 | ||||||||
\(467\) | − 3.51798e43i | − 0.318101i | −0.987270 | − | 0.159050i | \(-0.949157\pi\) | ||||
0.987270 | − | 0.159050i | \(-0.0508432\pi\) | |||||||
\(468\) | 3.50840e43i | 0.306233i | ||||||||
\(469\) | 5.93707e43 | 0.500288 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.03456e43 | −0.159818 | ||||||||
\(472\) | 1.37054e44i | 1.03955i | ||||||||
\(473\) | 4.30116e43i | 0.315048i | ||||||||
\(474\) | −2.27969e42 | −0.0161262 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.90365e44 | 1.25624 | ||||||||
\(477\) | 1.91686e44i | 1.22190i | ||||||||
\(478\) | 8.12372e43i | 0.500258i | ||||||||
\(479\) | 2.90520e44 | 1.72838 | 0.864192 | − | 0.503162i | \(-0.167830\pi\) | ||||
0.864192 | + | 0.503162i | \(0.167830\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.04464e43 | 0.446799 | ||||||||
\(482\) | − 1.81112e43i | − 0.0972008i | ||||||||
\(483\) | 9.69546e42i | 0.0502853i | ||||||||
\(484\) | 1.42814e44 | 0.715849 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −6.74045e43 | −0.315639 | ||||||||
\(487\) | − 1.45706e44i | − 0.659551i | −0.944059 | − | 0.329776i | \(-0.893027\pi\) | ||||
0.944059 | − | 0.329776i | \(-0.106973\pi\) | |||||||
\(488\) | 3.05755e42i | 0.0133797i | ||||||||
\(489\) | 2.50710e43 | 0.106066 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.43984e44 | 0.569469 | 0.284735 | − | 0.958606i | \(-0.408095\pi\) | ||||
0.284735 | + | 0.958606i | \(0.408095\pi\) | |||||||
\(492\) | 4.71753e43i | 0.180423i | ||||||||
\(493\) | 4.19299e43i | 0.155078i | ||||||||
\(494\) | −6.53241e43 | −0.233657 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.09986e44 | −0.368035 | ||||||||
\(497\) | 4.18816e44i | 1.35564i | ||||||||
\(498\) | − 9.48646e42i | − 0.0297043i | ||||||||
\(499\) | −1.76176e44 | −0.533687 | −0.266843 | − | 0.963740i | \(-0.585981\pi\) | ||||
−0.266843 | + | 0.963740i | \(0.585981\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.00224e43 | 0.0284215 | ||||||||
\(502\) | 9.67224e43i | 0.265409i | ||||||||
\(503\) | 2.43829e44i | 0.647460i | 0.946149 | + | 0.323730i | \(0.104937\pi\) | ||||
−0.946149 | + | 0.323730i | \(0.895063\pi\) | |||||||
\(504\) | 4.74854e44 | 1.22027 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5.48039e43 | −0.131925 | ||||||||
\(507\) | 7.13222e43i | 0.166185i | ||||||||
\(508\) | − 1.15231e44i | − 0.259907i | ||||||||
\(509\) | −3.49786e44 | −0.763763 | −0.381882 | − | 0.924211i | \(-0.624724\pi\) | ||||
−0.381882 | + | 0.924211i | \(0.624724\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.56970e44 | −1.75396 | ||||||||
\(512\) | 2.17544e44i | 0.431114i | ||||||||
\(513\) | 2.06015e44i | 0.395333i | ||||||||
\(514\) | 2.80422e44 | 0.521100 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.89429e43 | −0.0330161 | ||||||||
\(517\) | 4.67023e44i | 0.788396i | ||||||||
\(518\) | − 4.53082e44i | − 0.740860i | ||||||||
\(519\) | −1.02143e44 | −0.161789 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.31981e44 | −0.493505 | −0.246752 | − | 0.969079i | \(-0.579363\pi\) | ||||
−0.246752 | + | 0.969079i | \(0.579363\pi\) | |||||||
\(522\) | 4.35227e43i | 0.0626834i | ||||||||
\(523\) | − 1.02645e45i | − 1.43238i | −0.697905 | − | 0.716190i | \(-0.745884\pi\) | ||||
0.697905 | − | 0.716190i | \(-0.254116\pi\) | |||||||
\(524\) | −7.73674e44 | −1.04614 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.84837e44 | 0.615645 | ||||||||
\(527\) | − 1.71989e45i | − 2.11654i | ||||||||
\(528\) | 5.45137e43i | 0.0650199i | ||||||||
\(529\) | 8.38864e44 | 0.969780 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.97254e44 | 1.08329 | ||||||||
\(532\) | − 9.12591e44i | − 0.961024i | ||||||||
\(533\) | 5.34987e44i | 0.546191i | ||||||||
\(534\) | 5.44127e43 | 0.0538604 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.55187e44 | −0.330550 | ||||||||
\(537\) | 3.24137e44i | 0.292518i | ||||||||
\(538\) | 5.37245e44i | 0.470180i | ||||||||
\(539\) | −1.55222e45 | −1.31746 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.08746e44 | 0.326361 | 0.163180 | − | 0.986596i | \(-0.447825\pi\) | ||||
0.163180 | + | 0.986596i | \(0.447825\pi\) | |||||||
\(542\) | − 3.07576e44i | − 0.238212i | ||||||||
\(543\) | − 3.76657e44i | − 0.282976i | ||||||||
\(544\) | −1.80382e45 | −1.31465 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.01520e44 | −0.0696422 | ||||||||
\(547\) | 7.54748e44i | 0.502355i | 0.967941 | + | 0.251178i | \(0.0808178\pi\) | ||||
−0.967941 | + | 0.251178i | \(0.919182\pi\) | |||||||
\(548\) | 1.81060e45i | 1.16935i | ||||||||
\(549\) | 2.22479e43 | 0.0139426 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.01008e44 | 0.118635 | ||||||||
\(552\) | − 5.80033e43i | − 0.0332245i | ||||||||
\(553\) | − 3.61166e44i | − 0.200790i | ||||||||
\(554\) | 2.56178e44 | 0.138239 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.03524e44 | 0.256027 | ||||||||
\(557\) | − 3.77046e45i | − 1.86116i | −0.366087 | − | 0.930581i | \(-0.619303\pi\) | ||||
0.366087 | − | 0.930581i | \(-0.380697\pi\) | |||||||
\(558\) | − 1.78523e45i | − 0.855517i | ||||||||
\(559\) | −2.14819e44 | −0.0999491 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.52453e44 | −0.373924 | ||||||||
\(562\) | − 6.37816e44i | − 0.271673i | ||||||||
\(563\) | − 1.99523e45i | − 0.825284i | −0.910893 | − | 0.412642i | \(-0.864606\pi\) | ||||
0.910893 | − | 0.412642i | \(-0.135394\pi\) | |||||||
\(564\) | −2.05683e44 | −0.0826216 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.90672e45 | 0.722465 | ||||||||
\(567\) | − 3.29159e45i | − 1.21139i | ||||||||
\(568\) | − 2.50558e45i | − 0.895695i | ||||||||
\(569\) | −2.38895e45 | −0.829574 | −0.414787 | − | 0.909919i | \(-0.636144\pi\) | ||||
−0.414787 | + | 0.909919i | \(0.636144\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.25875e44 | 0.303429 | 0.151714 | − | 0.988424i | \(-0.451521\pi\) | ||||
0.151714 | + | 0.988424i | \(0.451521\pi\) | |||||||
\(572\) | 1.42340e45i | 0.453202i | ||||||||
\(573\) | 6.31701e44i | 0.195416i | ||||||||
\(574\) | 3.01310e45 | 0.905665 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.12877e45 | −0.320356 | ||||||||
\(577\) | − 3.73598e45i | − 1.03040i | −0.857071 | − | 0.515198i | \(-0.827719\pi\) | ||||
0.857071 | − | 0.515198i | \(-0.172281\pi\) | |||||||
\(578\) | − 1.21874e45i | − 0.326665i | ||||||||
\(579\) | −8.12183e44 | −0.211572 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.50292e45 | 0.369853 | ||||||||
\(582\) | 5.95151e44i | 0.142363i | ||||||||
\(583\) | 7.77694e45i | 1.80833i | ||||||||
\(584\) | 5.12684e45 | 1.15888 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.45617e44 | 0.202025 | ||||||||
\(587\) | 6.35230e45i | 1.31948i | 0.751495 | + | 0.659739i | \(0.229333\pi\) | ||||
−0.751495 | + | 0.659739i | \(0.770667\pi\) | |||||||
\(588\) | − 6.83618e44i | − 0.138066i | ||||||||
\(589\) | −8.24499e45 | −1.61915 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.09558e45 | −0.389145 | ||||||||
\(592\) | − 1.21512e45i | − 0.219438i | ||||||||
\(593\) | − 7.20521e45i | − 1.26545i | −0.774378 | − | 0.632724i | \(-0.781937\pi\) | ||||
0.774378 | − | 0.632724i | \(-0.218063\pi\) | |||||||
\(594\) | −1.80976e45 | −0.309132 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.23876e45 | −0.523377 | ||||||||
\(597\) | 1.53912e45i | 0.241933i | ||||||||
\(598\) | − 2.73716e44i | − 0.0418534i | ||||||||
\(599\) | 6.37291e45 | 0.947971 | 0.473985 | − | 0.880533i | \(-0.342815\pi\) | ||||
0.473985 | + | 0.880533i | \(0.342815\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.13523e45 | −1.14536 | −0.572679 | − | 0.819780i | \(-0.694096\pi\) | ||||
−0.572679 | + | 0.819780i | \(0.694096\pi\) | |||||||
\(602\) | 1.20989e45i | 0.165730i | ||||||||
\(603\) | 2.58447e45i | 0.344458i | ||||||||
\(604\) | −3.17559e45 | −0.411827 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.45436e45 | −0.178597 | ||||||||
\(607\) | 8.31211e45i | 0.993339i | 0.867940 | + | 0.496670i | \(0.165444\pi\) | ||||
−0.867940 | + | 0.496670i | \(0.834556\pi\) | |||||||
\(608\) | 8.64734e45i | 1.00571i | ||||||||
\(609\) | 3.12386e44 | 0.0353595 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.33253e45 | −0.250119 | ||||||||
\(612\) | 8.28679e45i | 0.864944i | ||||||||
\(613\) | 2.99559e44i | 0.0304358i | 0.999884 | + | 0.0152179i | \(0.00484420\pi\) | ||||
−0.999884 | + | 0.0152179i | \(0.995156\pi\) | |||||||
\(614\) | 7.40000e45 | 0.731903 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.92654e46 | 1.80591 | ||||||||
\(617\) | 9.03503e45i | 0.824564i | 0.911056 | + | 0.412282i | \(0.135268\pi\) | ||||
−0.911056 | + | 0.412282i | \(0.864732\pi\) | |||||||
\(618\) | − 3.12552e44i | − 0.0277723i | ||||||||
\(619\) | 1.15706e46 | 1.00106 | 0.500528 | − | 0.865720i | \(-0.333139\pi\) | ||||
0.500528 | + | 0.865720i | \(0.333139\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.63230e44 | −0.0708133 | ||||||||
\(622\) | − 3.66598e44i | − 0.0292853i | ||||||||
\(623\) | 8.62048e45i | 0.670623i | ||||||||
\(624\) | −2.72267e44 | −0.0206276 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.30818e45 | −0.0940135 | ||||||||
\(627\) | 4.08658e45i | 0.286052i | ||||||||
\(628\) | 8.02424e45i | 0.547104i | ||||||||
\(629\) | 1.90013e46 | 1.26197 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.43742e46 | −0.905939 | −0.452970 | − | 0.891526i | \(-0.649635\pi\) | ||||
−0.452970 | + | 0.891526i | \(0.649635\pi\) | |||||||
\(632\) | 2.16068e45i | 0.132666i | ||||||||
\(633\) | − 3.21507e45i | − 0.192322i | ||||||||
\(634\) | −8.90387e45 | −0.518927 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3.42506e45 | −0.189507 | ||||||||
\(637\) | − 7.75250e45i | − 0.417966i | ||||||||
\(638\) | 1.76577e45i | 0.0927668i | ||||||||
\(639\) | −1.82315e46 | −0.933381 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.34213e46 | 0.652586 | 0.326293 | − | 0.945269i | \(-0.394200\pi\) | ||||
0.326293 | + | 0.945269i | \(0.394200\pi\) | |||||||
\(642\) | 8.78360e44i | 0.0416241i | ||||||||
\(643\) | − 3.48572e46i | − 1.60995i | −0.593312 | − | 0.804973i | \(-0.702180\pi\) | ||||
0.593312 | − | 0.804973i | \(-0.297820\pi\) | |||||||
\(644\) | 3.82387e45 | 0.172142 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.54295e46 | −0.659956 | ||||||||
\(647\) | 3.47978e46i | 1.45088i | 0.688285 | + | 0.725440i | \(0.258364\pi\) | ||||
−0.688285 | + | 0.725440i | \(0.741636\pi\) | |||||||
\(648\) | 1.96920e46i | 0.800392i | ||||||||
\(649\) | 4.04598e46 | 1.60319 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.28135e46 | −0.482594 | ||||||||
\(652\) | − 9.88796e45i | − 0.363096i | ||||||||
\(653\) | − 1.19815e46i | − 0.428986i | −0.976726 | − | 0.214493i | \(-0.931190\pi\) | ||||
0.976726 | − | 0.214493i | \(-0.0688099\pi\) | |||||||
\(654\) | 4.22417e44 | 0.0147472 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 8.08085e45 | 0.268252 | ||||||||
\(657\) | − 3.73049e46i | − 1.20764i | ||||||||
\(658\) | 1.31370e46i | 0.414735i | ||||||||
\(659\) | 2.00047e46 | 0.615918 | 0.307959 | − | 0.951400i | \(-0.400354\pi\) | ||||
0.307959 | + | 0.951400i | \(0.400354\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.80588e46 | 1.11463 | 0.557316 | − | 0.830301i | \(-0.311831\pi\) | ||||
0.557316 | + | 0.830301i | \(0.311831\pi\) | |||||||
\(662\) | 3.06115e46i | 0.874437i | ||||||||
\(663\) | − 4.25754e45i | − 0.118628i | ||||||||
\(664\) | −8.99123e45 | −0.244369 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.97232e46 | 0.510096 | ||||||||
\(667\) | 8.42247e44i | 0.0212502i | ||||||||
\(668\) | − 3.95279e45i | − 0.0972954i | ||||||||
\(669\) | −7.00567e45 | −0.168236 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.02622e44 | 0.0206341 | ||||||||
\(672\) | 1.34388e46i | 0.299756i | ||||||||
\(673\) | 5.38328e46i | 1.17165i | 0.810437 | + | 0.585825i | \(0.199230\pi\) | ||||
−0.810437 | + | 0.585825i | \(0.800770\pi\) | |||||||
\(674\) | −2.24231e46 | −0.476221 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.81293e46 | 0.568903 | ||||||||
\(677\) | − 9.38585e46i | − 1.85251i | −0.376898 | − | 0.926255i | \(-0.623009\pi\) | ||||
0.376898 | − | 0.926255i | \(-0.376991\pi\) | |||||||
\(678\) | 5.44178e45i | 0.104822i | ||||||||
\(679\) | −9.42884e46 | −1.77258 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.77525e45 | 0.0676111 | ||||||||
\(682\) | − 7.24288e46i | − 1.26610i | ||||||||
\(683\) | − 1.22152e46i | − 0.208430i | −0.994555 | − | 0.104215i | \(-0.966767\pi\) | ||||
0.994555 | − | 0.104215i | \(-0.0332329\pi\) | |||||||
\(684\) | 3.97261e46 | 0.661683 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3.25847e45 | 0.0517208 | ||||||||
\(687\) | − 5.29953e45i | − 0.0821205i | ||||||||
\(688\) | 3.24480e45i | 0.0490883i | ||||||||
\(689\) | −3.88416e46 | −0.573693 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.01396e47 | −1.42768 | −0.713841 | − | 0.700308i | \(-0.753046\pi\) | ||||
−0.713841 | + | 0.700308i | \(0.753046\pi\) | |||||||
\(692\) | 4.02850e46i | 0.553851i | ||||||||
\(693\) | − 1.40182e47i | − 1.88189i | ||||||||
\(694\) | −4.06328e46 | −0.532655 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.86885e45 | −0.0233627 | ||||||||
\(697\) | 1.26363e47i | 1.54270i | ||||||||
\(698\) | 6.10903e46i | 0.728379i | ||||||||
\(699\) | −1.08594e45 | −0.0126454 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.07227e47 | −1.19112 | −0.595560 | − | 0.803311i | \(-0.703070\pi\) | ||||
−0.595560 | + | 0.803311i | \(0.703070\pi\) | |||||||
\(702\) | − 9.03876e45i | − 0.0980724i | ||||||||
\(703\) | − 9.10906e46i | − 0.965408i | ||||||||
\(704\) | −4.57954e46 | −0.474103 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.07639e45 | 0.0797884 | ||||||||
\(707\) | − 2.30411e47i | − 2.22373i | ||||||||
\(708\) | 1.78190e46i | 0.168010i | ||||||||
\(709\) | 3.54939e45 | 0.0326957 | 0.0163478 | − | 0.999866i | \(-0.494796\pi\) | ||||
0.0163478 | + | 0.999866i | \(0.494796\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.57219e46 | 0.138248 | ||||||||
\(712\) | − 5.15722e46i | − 0.443094i | ||||||||
\(713\) | − 3.45475e46i | − 0.290028i | ||||||||
\(714\) | −2.39789e46 | −0.196702 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.27839e47 | 1.00138 | ||||||||
\(717\) | 2.53822e46i | 0.194296i | ||||||||
\(718\) | − 1.80851e46i | − 0.135290i | ||||||||
\(719\) | −6.94896e46 | −0.508035 | −0.254017 | − | 0.967200i | \(-0.581752\pi\) | ||||
−0.254017 | + | 0.967200i | \(0.581752\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.95169e46 | 0.345797 | ||||||||
\(722\) | − 4.56432e45i | − 0.0311539i | ||||||||
\(723\) | − 5.65875e45i | − 0.0377519i | ||||||||
\(724\) | −1.48553e47 | −0.968711 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.79892e46 | −0.112088 | ||||||||
\(727\) | − 1.73359e47i | − 1.05592i | −0.849270 | − | 0.527958i | \(-0.822958\pi\) | ||||
0.849270 | − | 0.527958i | \(-0.177042\pi\) | |||||||
\(728\) | 9.62203e46i | 0.572926i | ||||||||
\(729\) | 1.28718e47 | 0.749264 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.07401e46 | −0.282303 | ||||||||
\(732\) | 3.97527e44i | 0.00216239i | ||||||||
\(733\) | − 4.59301e46i | − 0.244277i | −0.992513 | − | 0.122138i | \(-0.961025\pi\) | ||||
0.992513 | − | 0.122138i | \(-0.0389752\pi\) | |||||||
\(734\) | −6.73556e46 | −0.350259 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.62334e46 | −0.180146 | ||||||||
\(737\) | 1.04855e47i | 0.509773i | ||||||||
\(738\) | 1.31164e47i | 0.623568i | ||||||||
\(739\) | 3.24514e47 | 1.50869 | 0.754346 | − | 0.656477i | \(-0.227954\pi\) | ||||
0.754346 | + | 0.656477i | \(0.227954\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.04102e46 | −0.0907502 | ||||||||
\(742\) | 2.18760e47i | 0.951268i | ||||||||
\(743\) | − 3.63726e47i | − 1.54689i | −0.633866 | − | 0.773443i | \(-0.718533\pi\) | ||||
0.633866 | − | 0.773443i | \(-0.281467\pi\) | |||||||
\(744\) | 7.66571e46 | 0.318859 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 9.61085e46 | 0.382447 | ||||||||
\(747\) | 6.54236e46i | 0.254651i | ||||||||
\(748\) | 3.36205e47i | 1.28005i | ||||||||
\(749\) | −1.39156e47 | −0.518267 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.28361e47 | 0.813885 | 0.406943 | − | 0.913454i | \(-0.366595\pi\) | ||||
0.406943 | + | 0.913454i | \(0.366595\pi\) | |||||||
\(752\) | 3.52323e46i | 0.122842i | ||||||||
\(753\) | 3.02205e46i | 0.103082i | ||||||||
\(754\) | −8.81906e45 | −0.0294303 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.26273e47 | 0.403369 | ||||||||
\(757\) | − 1.23646e47i | − 0.386453i | −0.981154 | − | 0.193226i | \(-0.938105\pi\) | ||||
0.981154 | − | 0.193226i | \(-0.0618952\pi\) | |||||||
\(758\) | 2.71145e47i | 0.829201i | ||||||||
\(759\) | −1.71233e46 | −0.0512386 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.65073e47 | −0.472966 | −0.236483 | − | 0.971636i | \(-0.575995\pi\) | ||||
−0.236483 | + | 0.971636i | \(0.575995\pi\) | |||||||
\(762\) | 1.45148e46i | 0.0406962i | ||||||||
\(763\) | 6.69225e46i | 0.183619i | ||||||||
\(764\) | 2.49141e47 | 0.668968 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.51846e47 | −0.647679 | ||||||||
\(767\) | 2.02075e47i | 0.508614i | ||||||||
\(768\) | − 6.71116e46i | − 0.165325i | ||||||||
\(769\) | 2.15810e47 | 0.520339 | 0.260170 | − | 0.965563i | \(-0.416222\pi\) | ||||
0.260170 | + | 0.965563i | \(0.416222\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.76167e46 | 0.202390 | ||||||||
\(772\) | 3.20323e47i | 0.724274i | ||||||||
\(773\) | − 5.97126e46i | − 0.132161i | −0.997814 | − | 0.0660806i | \(-0.978951\pi\) | ||||
0.997814 | − | 0.0660806i | \(-0.0210495\pi\) | |||||||
\(774\) | −5.26677e46 | −0.114109 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 5.64083e47 | 1.17118 | ||||||||
\(777\) | − 1.41564e47i | − 0.287743i | ||||||||
\(778\) | − 3.73106e47i | − 0.742453i | ||||||||
\(779\) | 6.05774e47 | 1.18016 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.39675e47 | −1.38133 | ||||||||
\(782\) | − 6.46514e46i | − 0.118213i | ||||||||
\(783\) | 2.78131e46i | 0.0497943i | ||||||||
\(784\) | −1.17100e47 | −0.205277 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 9.74541e46 | 0.163805 | ||||||||
\(787\) | 2.40999e47i | 0.396673i | 0.980134 | + | 0.198336i | \(0.0635539\pi\) | ||||
−0.980134 | + | 0.198336i | \(0.936446\pi\) | |||||||
\(788\) | 8.26493e47i | 1.33216i | ||||||||
\(789\) | 1.51485e47 | 0.239111 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.62128e47 | −1.30515 | ||||||||
\(792\) | 8.38645e47i | 1.24340i | ||||||||
\(793\) | 4.50811e45i | 0.00654616i | ||||||||
\(794\) | 6.30559e47 | 0.896783 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.07023e47 | 0.828209 | ||||||||
\(797\) | 5.30320e47i | 0.708722i | 0.935109 | + | 0.354361i | \(0.115302\pi\) | ||||
−0.935109 | + | 0.354361i | \(0.884698\pi\) | |||||||
\(798\) | 1.14953e47i | 0.150477i | ||||||||
\(799\) | −5.50941e47 | −0.706452 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.75259e47 | −0.461737 | ||||||||
\(802\) | 2.63079e47i | 0.317109i | ||||||||
\(803\) | − 1.51350e48i | − 1.78722i | ||||||||
\(804\) | −4.61796e46 | −0.0534226 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.61742e47 | 0.401672 | ||||||||
\(807\) | 1.67860e47i | 0.182614i | ||||||||
\(808\) | 1.37844e48i | 1.46926i | ||||||||
\(809\) | −6.52623e47 | −0.681572 | −0.340786 | − | 0.940141i | \(-0.610693\pi\) | ||||
−0.340786 | + | 0.940141i | \(0.610693\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.54256e47 | −0.455466 | −0.227733 | − | 0.973724i | \(-0.573131\pi\) | ||||
−0.227733 | + | 0.973724i | \(0.573131\pi\) | |||||||
\(812\) | − 1.23204e47i | − 0.121046i | ||||||||
\(813\) | − 9.61007e46i | − 0.0925194i | ||||||||
\(814\) | 8.00193e47 | 0.754904 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −6.43091e46 | −0.0582619 | ||||||||
\(817\) | 2.43243e47i | 0.215962i | ||||||||
\(818\) | − 8.98736e47i | − 0.781993i | ||||||||
\(819\) | 7.00135e47 | 0.597032 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.88660e47 | −0.318352 | −0.159176 | − | 0.987250i | \(-0.550884\pi\) | ||||
−0.159176 | + | 0.987250i | \(0.550884\pi\) | |||||||
\(822\) | − 2.28069e47i | − 0.183097i | ||||||||
\(823\) | 2.16262e48i | 1.70170i | 0.525410 | + | 0.850849i | \(0.323912\pi\) | ||||
−0.525410 | + | 0.850849i | \(0.676088\pi\) | |||||||
\(824\) | −2.96236e47 | −0.228475 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.13811e48 | 0.843358 | ||||||||
\(827\) | − 5.70292e47i | − 0.414244i | −0.978315 | − | 0.207122i | \(-0.933590\pi\) | ||||
0.978315 | − | 0.207122i | \(-0.0664097\pi\) | |||||||
\(828\) | 1.66457e47i | 0.118523i | ||||||||
\(829\) | −1.81254e48 | −1.26514 | −0.632569 | − | 0.774504i | \(-0.717999\pi\) | ||||
−0.632569 | + | 0.774504i | \(0.717999\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.00417e46 | 0.0536907 | ||||||||
\(832\) | − 2.28723e47i | − 0.150410i | ||||||||
\(833\) | − 1.83113e48i | − 1.18053i | ||||||||
\(834\) | −6.34253e46 | −0.0400888 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.61174e48 | 0.979242 | ||||||||
\(837\) | − 1.14084e48i | − 0.679603i | ||||||||
\(838\) | − 4.76578e47i | − 0.278360i | ||||||||
\(839\) | 1.88483e47 | 0.107945 | 0.0539723 | − | 0.998542i | \(-0.482812\pi\) | ||||
0.0539723 | + | 0.998542i | \(0.482812\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.78894e48 | −0.985057 | ||||||||
\(842\) | − 9.70766e47i | − 0.524162i | ||||||||
\(843\) | − 1.99283e47i | − 0.105515i | ||||||||
\(844\) | −1.26802e48 | −0.658377 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −5.71870e47 | −0.285553 | ||||||||
\(847\) | − 2.84999e48i | − 1.39562i | ||||||||
\(848\) | 5.86693e47i | 0.281760i | ||||||||
\(849\) | 5.95748e47 | 0.280599 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.81681e47 | 0.172927 | ||||||||
\(852\) | − 3.25762e47i | − 0.144760i | ||||||||
\(853\) | − 3.65000e48i | − 1.59087i | −0.606040 | − | 0.795434i | \(-0.707243\pi\) | ||||
0.606040 | − | 0.795434i | \(-0.292757\pi\) | |||||||
\(854\) | 2.53901e46 | 0.0108545 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.32507e47 | 0.342429 | ||||||||
\(857\) | − 1.58574e48i | − 0.639807i | −0.947450 | − | 0.319903i | \(-0.896350\pi\) | ||||
0.947450 | − | 0.319903i | \(-0.103650\pi\) | |||||||
\(858\) | − 1.79295e47i | − 0.0709625i | ||||||||
\(859\) | −2.88906e48 | −1.12168 | −0.560840 | − | 0.827924i | \(-0.689522\pi\) | ||||
−0.560840 | + | 0.827924i | \(0.689522\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.41431e47 | 0.351752 | ||||||||
\(862\) | 1.99404e48i | 0.730912i | ||||||||
\(863\) | − 3.38580e46i | − 0.0121754i | −0.999981 | − | 0.00608770i | \(-0.998062\pi\) | ||||
0.999981 | − | 0.00608770i | \(-0.00193779\pi\) | |||||||
\(864\) | −1.19652e48 | −0.422126 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −6.16750e47 | −0.209442 | ||||||||
\(867\) | − 3.80791e47i | − 0.126874i | ||||||||
\(868\) | 5.05361e48i | 1.65206i | ||||||||
\(869\) | 6.37858e47 | 0.204596 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.23695e47 | −0.161726 | ||||||||
\(872\) | − 4.00366e47i | − 0.121321i | ||||||||
\(873\) | − 4.10448e48i | − 1.22046i | ||||||||
\(874\) | −3.09933e47 | −0.0904334 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.66567e47 | 0.187295 | ||||||||
\(877\) | − 4.24252e48i | − 1.16985i | −0.811087 | − | 0.584925i | \(-0.801124\pi\) | ||||
0.811087 | − | 0.584925i | \(-0.198876\pi\) | |||||||
\(878\) | 3.01576e48i | 0.816089i | ||||||||
\(879\) | 2.95454e47 | 0.0784646 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.17405e48 | −0.556119 | −0.278059 | − | 0.960564i | \(-0.589691\pi\) | ||||
−0.278059 | + | 0.960564i | \(0.589691\pi\) | |||||||
\(882\) | − 1.90069e48i | − 0.477178i | ||||||||
\(883\) | − 4.77705e48i | − 1.17708i | −0.808466 | − | 0.588542i | \(-0.799702\pi\) | ||||
0.808466 | − | 0.588542i | \(-0.200298\pi\) | |||||||
\(884\) | −1.67916e48 | −0.406098 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.28527e48 | 0.765447 | ||||||||
\(887\) | − 5.12275e48i | − 1.17156i | −0.810471 | − | 0.585779i | \(-0.800789\pi\) | ||||
0.810471 | − | 0.585779i | \(-0.199211\pi\) | |||||||
\(888\) | 8.46907e47i | 0.190117i | ||||||||
\(889\) | −2.29955e48 | −0.506714 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.81331e48 | 1.23436 | ||||||||
\(892\) | 2.76302e48i | 0.575922i | ||||||||
\(893\) | 2.64116e48i | 0.540437i | ||||||||
\(894\) | 4.07963e47 | 0.0819505 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 6.14883e48 | 1.19045 | ||||||||
\(897\) | − 8.55214e46i | − 0.0162555i | ||||||||
\(898\) | 7.67570e47i | 0.143238i | ||||||||
\(899\) | −1.11311e48 | −0.203941 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.17434e48 | −1.62038 | ||||||||
\(902\) | 5.32147e48i | 0.922834i | ||||||||
\(903\) | 3.78023e47i | 0.0643681i | ||||||||
\(904\) | 5.15770e48 | 0.862338 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 4.00007e47 | 0.0644840 | ||||||||
\(907\) | 7.71888e48i | 1.22190i | 0.791671 | + | 0.610948i | \(0.209211\pi\) | ||||
−0.791671 | + | 0.610948i | \(0.790789\pi\) | |||||||
\(908\) | − 1.48895e48i | − 0.231453i | ||||||||
\(909\) | 1.00300e49 | 1.53108 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.06274e49 | −1.56450 | −0.782250 | − | 0.622964i | \(-0.785928\pi\) | ||||
−0.782250 | + | 0.622964i | \(0.785928\pi\) | |||||||
\(912\) | 3.08292e47i | 0.0445704i | ||||||||
\(913\) | 2.65432e48i | 0.376864i | ||||||||
\(914\) | −3.53882e48 | −0.493454 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.09012e48 | −0.281123 | ||||||||
\(917\) | 1.54394e49i | 2.03956i | ||||||||
\(918\) | − 2.13495e48i | − 0.277002i | ||||||||
\(919\) | −8.89051e48 | −1.13298 | −0.566488 | − | 0.824070i | \(-0.691698\pi\) | ||||
−0.566488 | + | 0.824070i | \(0.691698\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.31210e48 | 0.284264 | ||||||||
\(922\) | − 6.65723e48i | − 0.803959i | ||||||||
\(923\) | − 3.69428e48i | − 0.438229i | ||||||||
\(924\) | 2.50479e48 | 0.291866 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2.74764e48 | −0.308943 | ||||||||
\(927\) | 2.15552e48i | 0.238088i | ||||||||
\(928\) | 1.16743e48i | 0.126675i | ||||||||
\(929\) | 7.35883e48 | 0.784422 | 0.392211 | − | 0.919875i | \(-0.371710\pi\) | ||||
0.392211 | + | 0.919875i | \(0.371710\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.77828e48 | −0.903108 | ||||||||
\(932\) | 4.28292e47i | 0.0432890i | ||||||||
\(933\) | − 1.14542e47i | − 0.0113741i | ||||||||
\(934\) | 1.74771e48 | 0.170509 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.18858e48 | −0.394471 | ||||||||
\(937\) | − 7.92924e48i | − 0.733717i | −0.930277 | − | 0.366858i | \(-0.880433\pi\) | ||||
0.930277 | − | 0.366858i | \(-0.119567\pi\) | |||||||
\(938\) | 2.94950e48i | 0.268165i | ||||||||
\(939\) | −4.08734e47 | −0.0365140 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.44230e49 | 1.24402 | 0.622008 | − | 0.783011i | \(-0.286317\pi\) | ||||
0.622008 | + | 0.783011i | \(0.286317\pi\) | |||||||
\(942\) | − 1.01076e48i | − 0.0856656i | ||||||||
\(943\) | 2.53827e48i | 0.211395i | ||||||||
\(944\) | 3.05229e48 | 0.249797 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.13679e48 | −0.168872 | ||||||||
\(947\) | 9.83625e48i | 0.763932i | 0.924176 | + | 0.381966i | \(0.124753\pi\) | ||||
−0.924176 | + | 0.381966i | \(0.875247\pi\) | |||||||
\(948\) | 2.80921e47i | 0.0214411i | ||||||||
\(949\) | 7.55913e48 | 0.566995 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.78198e48 | −0.201546 | ||||||||
\(952\) | 2.27271e49i | 1.61821i | ||||||||
\(953\) | 8.19274e48i | 0.573319i | 0.958033 | + | 0.286660i | \(0.0925449\pi\) | ||||
−0.958033 | + | 0.286660i | \(0.907455\pi\) | |||||||
\(954\) | −9.52286e48 | −0.654967 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.00107e49 | 0.665133 | ||||||||
\(957\) | 5.51707e47i | 0.0360298i | ||||||||
\(958\) | 1.44329e49i | 0.926450i | ||||||||
\(959\) | 3.61324e49 | 2.27976 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.92544e49 | 1.78343 | ||||||||
\(962\) | 3.99653e48i | 0.239494i | ||||||||
\(963\) | − 6.05763e48i | − 0.356837i | ||||||||
\(964\) | −2.23180e48 | −0.129236 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.81665e47 | −0.0269540 | ||||||||
\(967\) | − 1.65015e49i | − 0.907791i | −0.891055 | − | 0.453895i | \(-0.850034\pi\) | ||||
0.891055 | − | 0.453895i | \(-0.149966\pi\) | |||||||
\(968\) | 1.70501e49i | 0.922113i | ||||||||
\(969\) | −4.82088e48 | −0.256321 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.28602e49 | −1.68870 | −0.844352 | − | 0.535789i | \(-0.820014\pi\) | ||||
−0.844352 | + | 0.535789i | \(0.820014\pi\) | |||||||
\(972\) | 8.30611e48i | 0.419666i | ||||||||
\(973\) | − 1.00483e49i | − 0.499151i | ||||||||
\(974\) | 7.23857e48 | 0.353533 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.80939e46 | 0.00321504 | ||||||||
\(977\) | 1.17177e49i | 0.543977i | 0.962300 | + | 0.271989i | \(0.0876813\pi\) | ||||
−0.962300 | + | 0.271989i | \(0.912319\pi\) | |||||||
\(978\) | 1.24552e48i | 0.0568536i | ||||||||
\(979\) | −1.52247e49 | −0.683336 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.91321e48 | −0.126425 | ||||||||
\(982\) | 7.15306e48i | 0.305247i | ||||||||
\(983\) | − 3.61572e49i | − 1.51726i | −0.651519 | − | 0.758632i | \(-0.725868\pi\) | ||||
0.651519 | − | 0.758632i | \(-0.274132\pi\) | |||||||
\(984\) | −5.63213e48 | −0.232409 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.08305e48 | −0.0831249 | ||||||||
\(987\) | 4.10461e48i | 0.161079i | ||||||||
\(988\) | 8.04975e48i | 0.310665i | ||||||||
\(989\) | −1.01922e48 | −0.0386838 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.27623e49 | 0.835603 | 0.417802 | − | 0.908538i | \(-0.362801\pi\) | ||||
0.417802 | + | 0.908538i | \(0.362801\pi\) | |||||||
\(992\) | − 4.78860e49i | − 1.72889i | ||||||||
\(993\) | 9.56445e48i | 0.339623i | ||||||||
\(994\) | −2.08065e49 | −0.726649 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.16900e48 | −0.0394942 | ||||||||
\(997\) | − 5.01160e49i | − 1.66535i | −0.553761 | − | 0.832676i | \(-0.686808\pi\) | ||||
0.553761 | − | 0.832676i | \(-0.313192\pi\) | |||||||
\(998\) | − 8.75230e48i | − 0.286067i | ||||||||
\(999\) | 1.26040e49 | 0.405209 |
(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 | 25.34.b.a.24.3 | 4 | ||
5.2 | odd | 4 | 25.34.a.a.1.1 | 2 | |||
5.3 | odd | 4 | 1.34.a.a.1.2 | ✓ | 2 | ||
5.4 | even | 2 | inner | 25.34.b.a.24.2 | 4 | ||
15.8 | even | 4 | 9.34.a.b.1.1 | 2 | |||
20.3 | even | 4 | 16.34.a.b.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.34.a.a.1.2 | ✓ | 2 | 5.3 | odd | 4 | ||
9.34.a.b.1.1 | 2 | 15.8 | even | 4 | |||
16.34.a.b.1.2 | 2 | 20.3 | even | 4 | |||
25.34.a.a.1.1 | 2 | 5.2 | odd | 4 | |||
25.34.b.a.24.2 | 4 | 5.4 | even | 2 | inner | ||
25.34.b.a.24.3 | 4 | 1.1 | even | 1 | trivial |