Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [272,12,Mod(33,272)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(272, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("272.33");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 272 = 2^{4} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 272.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: | \(208.989345112\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{16} + 2012924 x^{14} + 1580196076372 x^{12} + \cdots + 11\!\cdots\!16 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{59}\cdot 3^{4}\cdot 17^{2} \) |
Twist minimal: | no (minimal twist has level 17) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 33.8 | ||
Root | \(-37.5132i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 272.33 |
Dual form | 272.12.b.c.33.9 |
$q$-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 \(\left(\mathbb{Z}/272\mathbb{Z}\right)^\times\).
\(n\) | \(69\) | \(239\) | \(241\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 37.5132i | − | 0.0891287i | −0.999007 | − | 0.0445643i | \(-0.985810\pi\) | ||
0.999007 | − | 0.0445643i | \(-0.0141900\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 7015.33i | 1.00395i | 0.864881 | + | 0.501976i | \(0.167394\pi\) | ||||
−0.864881 | + | 0.501976i | \(0.832606\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 40939.8i | − | 0.920675i | −0.887744 | − | 0.460338i | \(-0.847728\pi\) | ||
0.887744 | − | 0.460338i | \(-0.152272\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 175740. | 0.992056 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 436092.i | − | 0.816429i | −0.912886 | − | 0.408214i | \(-0.866152\pi\) | ||
0.912886 | − | 0.408214i | \(-0.133848\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 954432. | 0.712946 | 0.356473 | − | 0.934306i | \(-0.383979\pi\) | ||||
0.356473 | + | 0.934306i | \(0.383979\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 263168. | 0.0894810 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.84007e6 | − | 5.55752e6i | 0.314316 | − | 0.949319i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.78988e6 | 0.258489 | 0.129244 | − | 0.991613i | \(-0.458745\pi\) | ||||
0.129244 | + | 0.991613i | \(0.458745\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.53578e6 | −0.0820586 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 4.14357e7i | − | 1.34237i | −0.741291 | − | 0.671184i | \(-0.765786\pi\) | ||
0.741291 | − | 0.671184i | \(-0.234214\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −386743. | −0.00792050 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.32379e7i | − | 0.177549i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1.18734e8i | − | 1.07495i | −0.843281 | − | 0.537473i | \(-0.819379\pi\) | ||
0.843281 | − | 0.537473i | \(-0.180621\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.77240e8i | 1.11192i | 0.831210 | + | 0.555959i | \(0.187649\pi\) | ||||
−0.831210 | + | 0.555959i | \(0.812351\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.63592e7 | −0.0727672 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.87206e8 | 0.924314 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 5.80565e8i | − | 1.37639i | −0.725526 | − | 0.688195i | \(-0.758404\pi\) | ||
0.725526 | − | 0.688195i | \(-0.241596\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 3.58038e7i | − | 0.0635439i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.07835e8i | − | 0.145361i | −0.997355 | − | 0.0726804i | \(-0.976845\pi\) | ||
0.997355 | − | 0.0726804i | \(-0.0231553\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.42735e7 | 0.0148065 | 0.00740326 | − | 0.999973i | \(-0.497643\pi\) | ||||
0.00740326 | + | 0.999973i | \(0.497643\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.23287e9i | 0.995977i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.65181e9 | −1.05056 | −0.525281 | − | 0.850929i | \(-0.676040\pi\) | ||||
−0.525281 | + | 0.850929i | \(0.676040\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.01260e8 | 0.152357 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.08480e8 | − | 6.90271e7i | −0.0846115 | − | 0.0280145i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.69980e9 | −0.558318 | −0.279159 | − | 0.960245i | \(-0.590056\pi\) | ||||
−0.279159 | + | 0.960245i | \(0.590056\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.05933e9 | 0.819656 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 1.04658e8i | − | 0.0230387i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.97623e9 | −0.359876 | −0.179938 | − | 0.983678i | \(-0.557590\pi\) | ||||
−0.179938 | + | 0.983678i | \(0.557590\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.84931e9i | 1.18992i | 0.803756 | + | 0.594960i | \(0.202832\pi\) | ||||
−0.803756 | + | 0.594960i | \(0.797168\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 7.19475e9i | − | 0.913361i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.69565e9i | 0.715763i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.92771e10 | −1.74434 | −0.872169 | − | 0.489205i | \(-0.837287\pi\) | ||||
−0.872169 | + | 0.489205i | \(0.837287\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.55439e9 | −0.119643 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.81174e9i | 0.316505i | 0.987399 | + | 0.158253i | \(0.0505860\pi\) | ||||
−0.987399 | + | 0.158253i | \(0.949414\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.24976e10i | 0.705586i | 0.935701 | + | 0.352793i | \(0.114768\pi\) | ||||
−0.935701 | + | 0.352793i | \(0.885232\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.45080e7i | 0.000705944i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.78535e10 | −0.751666 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 2.94120e10i | − | 1.07541i | −0.843132 | − | 0.537706i | \(-0.819291\pi\) | ||
0.843132 | − | 0.537706i | \(-0.180709\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.06352e10 | 0.976231 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.55654e9 | −0.0712399 | −0.0356199 | − | 0.999365i | \(-0.511341\pi\) | ||||
−0.0356199 | + | 0.999365i | \(0.511341\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.89878e10 | + | 1.29087e10i | 0.953071 | + | 0.315558i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.45410e9 | −0.0958085 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.01332e10 | −1.71096 | −0.855480 | − | 0.517837i | \(-0.826738\pi\) | ||||
−0.855480 | + | 0.517837i | \(0.826738\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 3.90742e10i | − | 0.656391i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.64885e9 | 0.0991038 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.95720e10i | 0.259510i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.01766e10i | 0.120325i | 0.998189 | + | 0.0601626i | \(0.0191619\pi\) | ||||
−0.998189 | + | 0.0601626i | \(0.980838\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 7.66387e10i | − | 0.809943i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.71725e10 | 0.635951 | 0.317976 | − | 0.948099i | \(-0.396997\pi\) | ||||
0.317976 | + | 0.948099i | \(0.396997\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.26906e10 | 0.447846 | 0.223923 | − | 0.974607i | \(-0.428114\pi\) | ||||
0.223923 | + | 0.974607i | \(0.428114\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 1.07740e10i | − | 0.0823829i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.30745e11i | 1.59046i | 0.606309 | + | 0.795229i | \(0.292650\pi\) | ||||
−0.606309 | + | 0.795229i | \(0.707350\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 2.37657e11i | − | 1.47946i | −0.672901 | − | 0.739732i | \(-0.734952\pi\) | ||
0.672901 | − | 0.739732i | \(-0.265048\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.17789e10 | −0.122676 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1.18308e11i | − | 0.604062i | −0.953298 | − | 0.302031i | \(-0.902335\pi\) | ||
0.953298 | − | 0.302031i | \(-0.0976646\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.90685e11 | 1.34767 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.67732e11 | 0.707282 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.27524e11 | − | 7.53322e10i | −0.874014 | − | 0.289383i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.51354e10 | 0.333444 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.04523e9 | −0.0129558 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.39832e11i | 0.996001i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.94266e11 | 1.59610 | 0.798050 | − | 0.602591i | \(-0.205865\pi\) | ||||
0.798050 | + | 0.602591i | \(0.205865\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 5.35444e8i | − | 0.00131969i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 3.66561e11i | − | 0.830145i | −0.909788 | − | 0.415073i | \(-0.863756\pi\) | ||
0.909788 | − | 0.415073i | \(-0.136244\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 1.14217e11i | − | 0.237984i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.28684e10 | 0.178251 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.59466e11 | 0.282297 | 0.141148 | − | 0.989988i | \(-0.454921\pi\) | ||||
0.141148 | + | 0.989988i | \(0.454921\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.52929e11i | 1.23076i | 0.788231 | + | 0.615379i | \(0.210997\pi\) | ||||
−0.788231 | + | 0.615379i | \(0.789003\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.19647e10i | 0.0936352i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 4.16220e11i | − | 0.582069i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.32959e11 | 1.07919 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 1.13012e10i | − | 0.0135794i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.63907e12 | −1.82840 | −0.914202 | − | 0.405259i | \(-0.867181\pi\) | ||||
−0.914202 | + | 0.405259i | \(0.867181\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.57160e12 | −1.62917 | −0.814587 | − | 0.580041i | \(-0.803037\pi\) | ||||
−0.814587 | + | 0.580041i | \(0.803037\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.23374e11 | − | 9.76677e11i | 0.311819 | − | 0.941777i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.24340e12 | −1.11631 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.24309e12 | −1.04005 | −0.520027 | − | 0.854150i | \(-0.674078\pi\) | ||||
−0.520027 | + | 0.854150i | \(0.674078\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.37651e10i | 0.0497621i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.69637e12 | −1.23588 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.76482e12i | 1.20135i | 0.799494 | + | 0.600675i | \(0.205101\pi\) | ||||
−0.799494 | + | 0.600675i | \(0.794899\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 1.14765e11i | − | 0.0730548i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 2.00184e12i | − | 1.19258i | −0.802768 | − | 0.596292i | \(-0.796640\pi\) | ||
0.802768 | − | 0.596292i | \(-0.203360\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.81221e11 | −0.491709 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.90293e11 | 0.256435 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 3.54453e11i | − | 0.173902i | −0.996213 | − | 0.0869511i | \(-0.972288\pi\) | ||
0.996213 | − | 0.0869511i | \(-0.0277124\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.58332e10i | 0.00729221i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.41349e10i | 0.0320752i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.84094e11 | −0.156223 | −0.0781116 | − | 0.996945i | \(-0.524889\pi\) | ||||
−0.0781116 | + | 0.996945i | \(0.524889\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 3.59801e12i | − | 1.37667i | −0.725392 | − | 0.688336i | \(-0.758341\pi\) | ||
0.725392 | − | 0.688336i | \(-0.241659\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.94453e11 | 0.106056 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.07285e12 | 1.38183 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.42359e12 | − | 8.02441e11i | −0.775051 | − | 0.256616i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.41958e11 | −0.163465 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.54417e12 | 1.57817 | 0.789084 | − | 0.614285i | \(-0.210556\pi\) | ||||
0.789084 | + | 0.614285i | \(0.210556\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 6.31838e11i | − | 0.169840i | −0.996388 | − | 0.0849202i | \(-0.972936\pi\) | ||
0.996388 | − | 0.0849202i | \(-0.0270635\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.51176e11 | 0.0637951 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.74159e12i | 1.85894i | 0.368895 | + | 0.929471i | \(0.379736\pi\) | ||||
−0.368895 | + | 0.929471i | \(0.620264\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1.47357e12i | − | 0.334718i | −0.985896 | − | 0.167359i | \(-0.946476\pi\) | ||
0.985896 | − | 0.167359i | \(-0.0535239\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.23147e11i | 0.155471i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.86095e12 | −0.989676 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.56496e11 | 0.145935 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 7.28190e12i | − | 1.33170i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 1.21665e12i | − | 0.211038i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 1.93592e11i | − | 0.0318664i | −0.999873 | − | 0.0159332i | \(-0.994928\pi\) | ||
0.999873 | − | 0.0159332i | \(-0.00507191\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.80504e11 | 0.0282097 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.00133e11i | 0.0148650i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.25617e12 | 1.02372 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.68825e11 | 0.0628880 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.75622e12 | − | 5.30427e12i | 0.224090 | − | 0.676812i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.10132e12 | 0.983737 | 0.491869 | − | 0.870669i | \(-0.336314\pi\) | ||||
0.491869 | + | 0.870669i | \(0.336314\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.79661e10 | −0.00785758 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 1.47294e13i | − | 1.62197i | −0.585065 | − | 0.810987i | \(-0.698931\pi\) | ||
0.585065 | − | 0.810987i | \(-0.301069\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.60411e12 | −0.692977 | −0.346489 | − | 0.938054i | \(-0.612626\pi\) | ||||
−0.346489 | + | 0.938054i | \(0.612626\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.69743e11i | 0.0669950i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 1.89377e13i | − | 1.80663i | −0.428979 | − | 0.903314i | \(-0.641127\pi\) | ||
0.428979 | − | 0.903314i | \(-0.358873\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 1.15880e13i | − | 1.05471i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.10334e12 | −0.0958501 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.13918e12 | −0.675138 | −0.337569 | − | 0.941301i | \(-0.609605\pi\) | ||||
−0.337569 | + | 0.941301i | \(0.609605\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.41957e12i | 0.429409i | 0.976679 | + | 0.214704i | \(0.0688788\pi\) | ||||
−0.976679 | + | 0.214704i | \(0.931121\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 3.49428e12i | − | 0.264560i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.11344e12i | 0.152960i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.66275e12 | 0.184288 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.59041e10i | 0.00634952i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.61292e13 | −1.02190 | −0.510950 | − | 0.859610i | \(-0.670706\pi\) | ||||
−0.510950 | + | 0.859610i | \(0.670706\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.80698e13 | −1.09595 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.84248e11 | − | 1.46256e12i | 0.0281253 | − | 0.0849459i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.15196e12 | −0.286642 | −0.143321 | − | 0.989676i | \(-0.545778\pi\) | ||||
−0.143321 | + | 0.989676i | \(0.545778\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.37682e13 | −1.26721 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 2.08663e13i | − | 1.06641i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.77857e12 | −0.0871592 | −0.0435796 | − | 0.999050i | \(-0.513876\pi\) | ||||
−0.0435796 | + | 0.999050i | \(0.513876\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 1.19247e13i | − | 0.560525i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.38119e12i | 0.152496i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 1.78034e13i | − | 0.770663i | −0.922778 | − | 0.385331i | \(-0.874087\pi\) | ||
0.922778 | − | 0.385331i | \(-0.125913\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.26277e13 | 1.35599 | 0.677993 | − | 0.735069i | \(-0.262850\pi\) | ||||
0.677993 | + | 0.735069i | \(0.262850\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.46580e12 | −0.0585033 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.68656e11i | 0.00646652i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 2.71764e13i | − | 1.00128i | −0.865657 | − | 0.500638i | \(-0.833099\pi\) | ||
0.865657 | − | 0.500638i | \(-0.166901\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.11481e13i | 1.10309i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.57016e13 | −1.21563 | −0.607817 | − | 0.794077i | \(-0.707954\pi\) | ||||
−0.607817 | + | 0.794077i | \(0.707954\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.04843e13i | 0.343333i | 0.985155 | + | 0.171666i | \(0.0549151\pi\) | ||||
−0.985155 | + | 0.171666i | \(0.945085\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.34207e11 | 0.0231298 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.41473e12 | −0.133830 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.75002e13 | − | 2.04525e13i | −0.802411 | − | 0.596771i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.81756e11 | 0.0107244 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.03512e13 | 1.90327 | 0.951633 | − | 0.307238i | \(-0.0994047\pi\) | ||||
0.951633 | + | 0.307238i | \(0.0994047\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 1.38639e13i | − | 0.361298i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.77295e12 | −0.144956 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 3.95475e13i | − | 0.957035i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 5.84353e11i | − | 0.0136320i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 2.51986e12i | − | 0.0566815i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.50655e13 | −1.19462 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.93815e13 | −0.824197 | −0.412099 | − | 0.911139i | \(-0.635204\pi\) | ||||
−0.412099 | + | 0.911139i | \(0.635204\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 1.97659e12i | − | 0.0399159i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 8.38957e13i | − | 1.63515i | −0.575823 | − | 0.817575i | \(-0.695318\pi\) | ||
0.575823 | − | 0.817575i | \(-0.304682\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 5.07613e13i | − | 0.955078i | −0.878610 | − | 0.477539i | \(-0.841529\pi\) | ||
0.878610 | − | 0.477539i | \(-0.158471\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.04735e13 | 0.916971 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 7.52575e12i | − | 0.132046i | −0.997818 | − | 0.0660228i | \(-0.978969\pi\) | ||
0.997818 | − | 0.0660228i | \(-0.0210310\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.17790e13 | −0.877617 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.65600e12 | 0.141755 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.13359e12 | − | 1.55048e13i | 0.0812470 | − | 0.245388i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.69120e11 | −0.00564689 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.91527e12 | −0.131863 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.76247e13i | 0.967226i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.92457e13 | −0.681262 | −0.340631 | − | 0.940197i | \(-0.610641\pi\) | ||||
−0.340631 | + | 0.940197i | \(0.610641\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 1.02028e14i | − | 1.36546i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 1.35235e14i | − | 1.75123i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.20199e13i | 0.150638i | 0.997159 | + | 0.0753190i | \(0.0239975\pi\) | ||||
−0.997159 | + | 0.0753190i | \(0.976002\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.43810e12 | −0.0538393 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.72930e13 | 0.907802 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 9.32849e13i | − | 1.06095i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 1.09045e13i | − | 0.120116i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 3.76384e13i | − | 0.401624i | −0.979630 | − | 0.200812i | \(-0.935642\pi\) | ||
0.979630 | − | 0.200812i | \(-0.0643580\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.41594e13 | −0.456545 | −0.228273 | − | 0.973597i | \(-0.573308\pi\) | ||||
−0.228273 | + | 0.973597i | \(0.573308\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 1.26347e13i | − | 0.126583i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.03528e14 | 1.00530 | 0.502652 | − | 0.864489i | \(-0.332358\pi\) | ||||
0.502652 | + | 0.864489i | \(0.332358\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.37559e13 | −0.317756 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.82595e12 | + | 8.53515e12i | −0.0257923 | + | 0.0778997i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.07192e13 | 0.625918 | 0.312959 | − | 0.949767i | \(-0.398680\pi\) | ||||
0.312959 | + | 0.949767i | \(0.398680\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.08707e14 | −0.933184 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 3.56884e12i | − | 0.0297194i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.76747e13 | −0.708375 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.59083e13i | 0.124727i | 0.998053 | + | 0.0623636i | \(0.0198639\pi\) | ||||
−0.998053 | + | 0.0623636i | \(0.980136\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 1.89508e13i | − | 0.144206i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.95896e13i | 0.514029i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.58474e13 | −0.113647 | −0.0568237 | − | 0.998384i | \(-0.518097\pi\) | ||||
−0.0568237 | + | 0.998384i | \(0.518097\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.27482e13 | 0.0887722 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 1.13324e14i | − | 0.766378i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 6.78416e12i | − | 0.0445636i | −0.999752 | − | 0.0222818i | \(-0.992907\pi\) | ||
0.999752 | − | 0.0222818i | \(-0.00709311\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 2.22928e13i | − | 0.142258i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.16812e13 | 0.506441 | 0.253221 | − | 0.967409i | \(-0.418510\pi\) | ||||
0.253221 | + | 0.967409i | \(0.418510\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 1.25248e14i | − | 0.754637i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.50842e12 | 0.0146889 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.02293e14 | 0.582270 | 0.291135 | − | 0.956682i | \(-0.405967\pi\) | ||||
0.291135 | + | 0.956682i | \(0.405967\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.30280e14 | − | 7.62447e13i | −1.27433 | − | 0.421927i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.37509e13 | −0.0739897 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.06335e14 | 1.07966 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 4.33650e13i | − | 0.220694i | −0.993893 | − | 0.110347i | \(-0.964804\pi\) | ||
0.993893 | − | 0.110347i | \(-0.0351963\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.28466e12 | −0.0212112 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.20106e13i | 0.0578459i | 0.999582 | + | 0.0289229i | \(0.00920774\pi\) | ||||
−0.999582 | + | 0.0289229i | \(0.990792\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.69164e14i | 0.792737i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.14916e14i | 0.980090i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.53180e14 | −1.12372 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.37591e14 | 1.02648 | 0.513242 | − | 0.858244i | \(-0.328444\pi\) | ||||
0.513242 | + | 0.858244i | \(0.328444\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 5.98209e12i | − | 0.0251607i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.09066e13i | 0.331328i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 1.79350e13i | − | 0.0715215i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.82448e13 | 0.109696 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 4.63527e14i | − | 1.75347i | −0.480974 | − | 0.876735i | \(-0.659717\pi\) | ||
0.480974 | − | 0.876735i | \(-0.340283\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.04223e14 | −1.85811 | −0.929055 | − | 0.369942i | \(-0.879378\pi\) | ||||
−0.929055 | + | 0.369942i | \(0.879378\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.90288e14 | −1.04222 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.11636e11 | + | 2.14933e12i | −0.00248954 | + | 0.00751908i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.21349e14 | 1.09553 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.56138e13 | −0.0518791 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.94622e14i | 1.27807i | 0.769176 | + | 0.639037i | \(0.220667\pi\) | ||||
−0.769176 | + | 0.639037i | \(0.779333\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.14797e14 | −1.30964 | −0.654820 | − | 0.755785i | \(-0.727256\pi\) | ||||
−0.654820 | + | 0.755785i | \(0.727256\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 3.12470e13i | − | 0.0961872i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 1.15601e14i | − | 0.346987i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.31859e14i | 0.971402i | 0.874125 | + | 0.485701i | \(0.161436\pi\) | ||||
−0.874125 | + | 0.485701i | \(0.838564\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.29434e13 | 0.151147 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.44788e13 | −0.0960135 | −0.0480067 | − | 0.998847i | \(-0.515287\pi\) | ||||
−0.0480067 | + | 0.998847i | \(0.515287\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 6.32314e14i | − | 1.71772i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.14867e13i | 0.162963i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.93233e14i | 0.758329i | 0.925329 | + | 0.379164i | \(0.123789\pi\) | ||||
−0.925329 | + | 0.379164i | \(0.876211\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.70258e13 | −0.118677 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.89556e13i | 0.145206i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.74119e14 | 0.658986 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.64192e14 | 1.08933 | 0.544664 | − | 0.838654i | \(-0.316657\pi\) | ||||
0.544664 | + | 0.838654i | \(0.316657\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.35700e13 | − | 2.43587e13i | −0.168551 | − | 0.0558065i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.23883e14 | 1.39556 | 0.697779 | − | 0.716313i | \(-0.254172\pi\) | ||||
0.697779 | + | 0.716313i | \(0.254172\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.75054e14 | −0.600790 | −0.300395 | − | 0.953815i | \(-0.597119\pi\) | ||||
−0.300395 | + | 0.953815i | \(0.597119\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.66439e13i | 0.0994955i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.49799e14 | 1.14541 | 0.572705 | − | 0.819761i | \(-0.305894\pi\) | ||||
0.572705 | + | 0.819761i | \(0.305894\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.89201e14i | 1.60597i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.66325e13i | 0.0926987i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 6.22454e12i | − | 0.0120885i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.07897e12 | −0.00204736 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.98723e14 | −0.553883 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 8.02043e14i | − | 1.45329i | −0.687013 | − | 0.726645i | \(-0.741078\pi\) | ||
0.687013 | − | 0.726645i | \(-0.258922\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 5.54109e14i | − | 0.981291i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.36362e13i | 0.110153i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.13920e13 | −0.120801 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.07735e15i | 1.78216i | 0.453843 | + | 0.891082i | \(0.350053\pi\) | ||||
−0.453843 | + | 0.891082i | \(0.649947\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.62042e13 | 0.107075 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.30247e14 | −0.838552 | −0.419276 | − | 0.907859i | \(-0.637716\pi\) | ||||
−0.419276 | + | 0.907859i | \(0.637716\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.59867e14 | − | 2.18480e14i | −1.02047 | − | 0.337872i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.37646e14 | 0.813144 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.96991e14 | 0.291398 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.36944e14i | 0.632227i | 0.948721 | + | 0.316113i | \(0.102378\pi\) | ||||
−0.948721 | + | 0.316113i | \(0.897622\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.50955e13 | −0.106293 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.09919e14i | 0.567642i | 0.958877 | + | 0.283821i | \(0.0916022\pi\) | ||||
−0.958877 | + | 0.283821i | \(0.908398\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.71237e14i | 0.638465i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.30574e13i | 0.0438253i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.07378e15 | 1.39305 | 0.696524 | − | 0.717533i | \(-0.254729\pi\) | ||||
0.696524 | + | 0.717533i | \(0.254729\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.11648e14 | 0.649616 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 3.69323e13i | − | 0.0458945i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.69642e14i | 0.449616i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.20341e14i | 0.857709i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.32967e13 | −0.0154997 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.25271e15i | 1.42970i | 0.699278 | + | 0.714849i | \(0.253505\pi\) | ||||
−0.699278 | + | 0.714849i | \(0.746495\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.63073e14 | 0.517476 | 0.258738 | − | 0.965948i | \(-0.416693\pi\) | ||||
0.258738 | + | 0.965948i | \(0.416693\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.93954e11 | 0.000649945 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.85016e14 | + | 3.26135e14i | 1.05556 | + | 0.349493i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.64106e14 | −0.801951 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.47303e14 | −0.357017 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 1.02921e14i | − | 0.103634i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.61876e15 | −1.59674 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.44086e13i | 0.0139240i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 1.31377e14i | − | 0.124389i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.93255e14i | 0.364829i | 0.983222 | + | 0.182415i | \(0.0583913\pi\) | ||||
−0.983222 | + | 0.182415i | \(0.941609\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.34973e14 | −0.122701 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.66724e15 | 1.48531 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.15470e15i | 1.00818i | 0.863652 | + | 0.504089i | \(0.168172\pi\) | ||||
−0.863652 | + | 0.504089i | \(0.831828\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.37944e15i | 1.18047i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 3.31254e14i | − | 0.277861i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.20412e15 | −0.990105 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 1.52786e14i | − | 0.123161i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.77959e14 | 0.535796 | 0.267898 | − | 0.963447i | \(-0.413671\pi\) | ||||
0.267898 | + | 0.963447i | \(0.413671\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.36230e13 | 0.0105562 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.01022e13 | + | 9.09167e13i | −0.0228719 | + | 0.0690793i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.64475e15 | 1.22547 | 0.612735 | − | 0.790289i | \(-0.290069\pi\) | ||||
0.612735 | + | 0.790289i | \(0.290069\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.29968e14 | 0.606450 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 1.25420e15i | − | 0.898792i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.00657e14 | 0.422191 | 0.211096 | − | 0.977465i | \(-0.432297\pi\) | ||||
0.211096 | + | 0.977465i | \(0.432297\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.83687e14i | 0.471367i | 0.971830 | + | 0.235683i | \(0.0757328\pi\) | ||||
−0.971830 | + | 0.235683i | \(0.924267\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 2.07980e14i | − | 0.140660i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.60250e13i | 0.0106322i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.27361e15 | 1.47995 | 0.739977 | − | 0.672632i | \(-0.234836\pi\) | ||||
0.739977 | + | 0.672632i | \(0.234836\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.37023e13 | −0.0151376 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.04664e14i | 0.0655888i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.41271e14i | 0.455827i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.17669e15i | 0.710078i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.59694e15 | 0.945755 | 0.472877 | − | 0.881128i | \(-0.343215\pi\) | ||||
0.472877 | + | 0.881128i | \(0.343215\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.94479e14i | 0.287418i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.90412e14 | 0.165685 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.87894e15 | −1.61225 | −0.806123 | − | 0.591748i | \(-0.798438\pi\) | ||||
−0.806123 | + | 0.591748i | \(0.798438\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.28480e14 | − | 1.59615e15i | 0.290526 | − | 0.877468i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.52783e13 | −0.0298330 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.13434e14 | −0.219058 | −0.109529 | − | 0.993984i | \(-0.534934\pi\) | ||||
−0.109529 | + | 0.993984i | \(0.534934\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.17849e15i | 1.13330i | 0.823958 | + | 0.566652i | \(0.191761\pi\) | ||||
−0.823958 | + | 0.566652i | \(0.808239\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.38776e15 | −1.73048 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.67407e14i | 0.334762i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 3.25356e15i | − | 1.60258i | −0.598273 | − | 0.801292i | \(-0.704146\pi\) | ||
0.598273 | − | 0.801292i | \(-0.295854\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.82350e14i | 0.0882085i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.57654e15 | −0.748993 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.72107e15 | 0.803095 | 0.401547 | − | 0.915838i | \(-0.368472\pi\) | ||||
0.401547 | + | 0.915838i | \(0.368472\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 2.83786e13i | − | 0.0130070i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 4.72457e14i | − | 0.212713i | −0.994328 | − | 0.106357i | \(-0.966082\pi\) | ||
0.994328 | − | 0.106357i | \(-0.0339185\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.90001e15i | 1.72491i | 0.506131 | + | 0.862456i | \(0.331075\pi\) | ||||
−0.506131 | + | 0.862456i | \(0.668925\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.48522e14 | −0.238336 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.69003e15i | 1.57524i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.40292e15 | −1.00786 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.56403e13 | −0.0188095 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.22650e15 | − | 1.06828e15i | −1.30663 | − | 0.432621i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.31182e15 | 0.920011 | 0.460006 | − | 0.887916i | \(-0.347847\pi\) | ||||
0.460006 | + | 0.887916i | \(0.347847\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.26225e12 | −0.00284021 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.16897e15i | 1.60241i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.87532e14 | 0.108622 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.45613e14i | 0.313991i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 3.34975e15i | − | 1.22263i | −0.791389 | − | 0.611313i | \(-0.790642\pi\) | ||
0.791389 | − | 0.611313i | \(-0.209358\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.23818e15i | 1.16182i | 0.813966 | + | 0.580912i | \(0.197304\pi\) | ||||
−0.813966 | + | 0.580912i | \(0.802696\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.75631e12 | 0.00132490 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.93334e15 | −0.670401 | −0.335201 | − | 0.942147i | \(-0.608804\pi\) | ||||
−0.335201 | + | 0.942147i | \(0.608804\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.61820e14i | 0.293813i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 2.72202e14i | − | 0.0912424i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 3.67243e15i | − | 1.21041i | −0.796071 | − | 0.605203i | \(-0.793092\pi\) | ||
0.796071 | − | 0.605203i | \(-0.206908\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.57155e15 | 0.833426 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.19632e15i | 0.699981i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.41018e15 | 1.06883 | 0.534414 | − | 0.845223i | \(-0.320532\pi\) | ||||
0.534414 | + | 0.845223i | \(0.320532\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.62601e15 | 1.11769 | 0.558845 | − | 0.829272i | \(-0.311245\pi\) | ||||
0.558845 | + | 0.829272i | \(0.311245\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.98980e14 | − | 6.58816e13i | −0.0603234 | − | 0.0199728i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.01272e14 | 0.238925 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.91983e15 | −1.44297 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 3.03907e14i | − | 0.0876792i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.42302e15 | 0.971484 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 2.54005e15i | − | 0.709184i | −0.935021 | − | 0.354592i | \(-0.884620\pi\) | ||
0.935021 | − | 0.354592i | \(-0.115380\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.11967e12i | 0.00140628i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.36364e15i | 1.44951i | 0.689005 | + | 0.724757i | \(0.258048\pi\) | ||||
−0.689005 | + | 0.724757i | \(0.741952\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.16627e14 | 0.110780 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.52548e14 | −0.144564 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 1.42743e15i | − | 0.367486i | −0.982974 | − | 0.183743i | \(-0.941179\pi\) | ||
0.982974 | − | 0.183743i | \(-0.0588214\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.11871e15i | 0.283412i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.47741e14i | 0.0617641i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.62235e15 | −0.398050 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.20192e15i | 0.290233i | 0.989415 | + | 0.145117i | \(0.0463558\pi\) | ||||
−0.989415 | + | 0.145117i | \(0.953644\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.13757e15 | −0.745695 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.28205e15 | −1.23562 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.99293e14 | − | 1.98424e14i | −0.137994 | − | 0.0456892i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.10413e14 | −0.161022 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.33740e15 | −0.298409 | −0.149205 | − | 0.988806i | \(-0.547671\pi\) | ||||
−0.149205 | + | 0.988806i | \(0.547671\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.61971e15i | − | 0.355781i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.34703e14 | −0.0940053 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 2.75003e15i | − | 0.585504i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 6.70214e15i | − | 1.40494i | −0.711711 | − | 0.702472i | \(-0.752079\pi\) | ||
0.711711 | − | 0.702472i | \(-0.247921\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 5.16885e15i | − | 1.06687i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.34407e15 | 1.49260 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.91992e15 | 0.584370 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.05327e14i | 0.0601741i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 5.55050e15i | − | 1.07727i | −0.842540 | − | 0.538633i | \(-0.818941\pi\) | ||
0.842540 | − | 0.538633i | \(-0.181059\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 2.15714e15i | − | 0.412320i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.03306e14 | 0.0382726 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.59196e13i | 0.00851411i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.21071e15 | 1.31686 | 0.658428 | − | 0.752643i | \(-0.271222\pi\) | ||||
0.658428 | + | 0.752643i | \(0.271222\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.29585e15 | 0.952652 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.62642e13 | − | 7.93251e13i | 0.00465392 | − | 0.0140561i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.98314e15 | −0.346163 | −0.173082 | − | 0.984907i | \(-0.555372\pi\) | ||||
−0.173082 | + | 0.984907i | \(0.555372\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.92820e13 | 0.0136331 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.40660e15i | 1.42413i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.59631e15 | 0.433323 | 0.216662 | − | 0.976247i | \(-0.430483\pi\) | ||||
0.216662 | + | 0.976247i | \(0.430483\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 9.98885e13i | − | 0.0164254i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1.13755e15i | − | 0.184304i | −0.995745 | − | 0.0921518i | \(-0.970625\pi\) | ||
0.995745 | − | 0.0921518i | \(-0.0293745\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 1.14986e16i | − | 1.83563i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.49286e14 | −0.0706740 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.44667e15 | 1.46430 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1.21818e16i | − | 1.86077i | −0.366586 | − | 0.930384i | \(-0.619473\pi\) | ||
0.366586 | − | 0.930384i | \(-0.380527\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.05060e14i | 0.0910806i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 1.10253e16i | − | 1.63561i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.32645e15 | −0.193938 | −0.0969689 | − | 0.995287i | \(-0.530915\pi\) | ||||
−0.0969689 | + | 0.995287i | \(0.530915\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.77855e14i | 0.0976804i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.04705e15 | 0.432777 | 0.216389 | − | 0.976307i | \(-0.430572\pi\) | ||||
0.216389 | + | 0.976307i | \(0.430572\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.72962e15 | −1.36211 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.85171e15 | + | 2.26858e15i | 0.945500 | + | 0.313051i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.88618e15 | −0.256572 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.94860e15 | −0.797664 | −0.398832 | − | 0.917024i | \(-0.630584\pi\) | ||||
−0.398832 | + | 0.917024i | \(0.630584\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.93267e14i | 0.0255481i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.28250e16 | −1.67136 | −0.835679 | − | 0.549218i | \(-0.814926\pi\) | ||||
−0.835679 | + | 0.549218i | \(0.814926\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 6.85464e13i | − | 0.00880695i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.91622e14i | 0.112945i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 3.00846e14i | − | 0.0375741i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.09836e15 | 0.258404 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.57179e15 | −0.190856 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 8.72072e15i | − | 1.04417i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.44859e16i | 1.71035i | 0.518337 | + | 0.855177i | \(0.326551\pi\) | ||||
−0.518337 | + | 0.855177i | \(0.673449\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.67197e13i | 0.00776839i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.84349e15 | −0.556145 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.49163e15i | 0.848348i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.47333e14 | −0.0499588 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.71817e15 | −0.850146 | −0.425073 | − | 0.905159i | \(-0.639752\pi\) | ||||
−0.425073 | + | 0.905159i | \(0.639752\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.03945e15 | + | 9.17996e15i | −0.330208 | + | 0.997318i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.58400e16 | −1.69737 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.45010e15 | 0.576061 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 1.19006e16i | − | 1.24077i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.67861e14 | −0.0686882 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.64116e15i | 0.166508i | 0.996528 | + | 0.0832540i | \(0.0265313\pi\) | ||||
−0.996528 | + | 0.0832540i | \(0.973469\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 9.52939e15i | − | 0.953784i | −0.878962 | − | 0.476892i | \(-0.841763\pi\) | ||
0.878962 | − | 0.476892i | \(-0.158237\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 1.22397e15i | − | 0.120857i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.23808e16 | −1.20610 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.98213e13 | 0.00382731 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 6.86690e15i | − | 0.651177i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.50797e16i | 1.41093i | 0.708746 | + | 0.705464i | \(0.249261\pi\) | ||||
−0.708746 | + | 0.705464i | \(0.750739\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1.05599e16i | − | 0.974902i | −0.873150 | − | 0.487451i | \(-0.837927\pi\) | ||
0.873150 | − | 0.487451i | \(-0.162073\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.32681e12 | 0.000576353 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.10007e16i | 0.988871i | 0.869214 | + | 0.494435i | \(0.164625\pi\) | ||||
−0.869214 | + | 0.494435i | \(0.835375\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.29931e15 | −0.292667 | −0.146334 | − | 0.989235i | \(-0.546747\pi\) | ||||
−0.146334 | + | 0.989235i | \(0.546747\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.01948e15 | −0.0892424 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.54341e14 | − | 1.67426e15i | 0.0478883 | − | 0.144636i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.40436e16 | 1.19730 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.34629e15 | 0.197420 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 7.12405e15i | − | 0.591611i | −0.955248 | − | 0.295806i | \(-0.904412\pi\) | ||
0.955248 | − | 0.295806i | \(-0.0955881\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.89729e15 | −0.155509 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.33928e15i | 0.108348i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 6.18205e15i | − | 0.493652i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 3.89482e15i | − | 0.306993i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.93301e14 | 0.0306008 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.40561e16 | −1.84762 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 2.31162e16i | − | 1.75266i | −0.481713 | − | 0.876329i | \(-0.659985\pi\) | ||
0.481713 | − | 0.876329i | \(-0.340015\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.43957e15i | 0.257449i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 2.55454e16i | − | 1.88764i | −0.330466 | − | 0.943818i | \(-0.607206\pi\) | ||
0.330466 | − | 0.943818i | \(-0.392794\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.70194e14 | 0.0634825 | 0.0317412 | − | 0.999496i | \(-0.489895\pi\) | ||||
0.0317412 | + | 0.999496i | \(0.489895\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.65611e14i | 0.0119281i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.24118e15 | −0.514932 | −0.257466 | − | 0.966287i | \(-0.582888\pi\) | ||||
−0.257466 | + | 0.966287i | \(0.582888\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.48661e15 | 0.174590 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.67239e14 | + | 1.03162e15i | −0.0531894 | + | 0.0715179i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.28263e16 | −0.877998 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.83987e16 | −1.24362 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.78843e15i | 0.119369i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.39127e16 | 0.916993 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 4.70621e15i | − | 0.306319i | −0.988202 | − | 0.153159i | \(-0.951055\pi\) | ||
0.988202 | − | 0.153159i | \(-0.0489448\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 2.63910e15i | − | 0.169636i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.34030e15i | 0.402478i | 0.979542 | + | 0.201239i | \(0.0644968\pi\) | ||||
−0.979542 | + | 0.201239i | \(0.935503\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.54085e16 | 1.59292 | 0.796461 | − | 0.604690i | \(-0.206703\pi\) | ||||
0.796461 | + | 0.604690i | \(0.206703\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.20081e14 | −0.0322020 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 4.30148e15i | − | 0.263050i | −0.991313 | − | 0.131525i | \(-0.958013\pi\) | ||
0.991313 | − | 0.131525i | \(-0.0419874\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 2.43291e16i | − | 1.46949i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 1.33598e16i | − | 0.797023i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.60835e15 | −0.271558 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 2.69455e15i | − | 0.156841i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.48356e15 | −0.0852993 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.10445e16 | 1.19525 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.12776e15 | + | 9.44669e15i | −0.175488 | + | 0.530022i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.19209e13 | −0.00121500 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.52413e16 | 1.38211 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.06988e15i | 0.436543i | 0.975888 | + | 0.218272i | \(0.0700419\pi\) | ||||
−0.975888 | + | 0.218272i | \(0.929958\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.18049e16 | 0.630899 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 2.04923e16i | − | 1.08203i | −0.841013 | − | 0.541016i | \(-0.818040\pi\) | ||
0.841013 | − | 0.541016i | \(-0.181960\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.11489e15i | 0.0581623i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.06568e15i | 0.106475i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.50069e16 | −0.764294 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.55836e16 | −0.784210 | −0.392105 | − | 0.919921i | \(-0.628253\pi\) | ||||
−0.392105 | + | 0.919921i | \(0.628253\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.47733e15i | 0.0734596i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.59247e15i | 0.225651i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.24529e14i | 0.0109017i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.25984e15 | 0.444288 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.26357e16i | 1.07327i | 0.843816 | + | 0.536633i | \(0.180304\pi\) | ||||
−0.843816 | + | 0.536633i | \(0.819696\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.40481e14 | 0.0393826 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.14720e15 | −0.145739 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.62939e15 | − | 1.70023e16i | 0.257631 | − | 0.778114i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.85278e16 | 1.29033 | 0.645164 | − | 0.764044i | \(-0.276789\pi\) | ||||
0.645164 | + | 0.764044i | \(0.276789\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.90422e15 | −0.0851249 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1.88306e15i | − | 0.0831995i | −0.999134 | − | 0.0415997i | \(-0.986755\pi\) | ||
0.999134 | − | 0.0415997i | \(-0.0132454\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.46820e15 | −0.195128 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 3.80201e15i | − | 0.164111i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 1.78705e16i | − | 0.762451i | −0.924482 | − | 0.381226i | \(-0.875502\pi\) | ||
0.924482 | − | 0.381226i | \(-0.124498\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.19281e16i | 0.503045i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.82315e14 | −0.0117691 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.70042e15 | 0.0700721 | 0.0350361 | − | 0.999386i | \(-0.488845\pi\) | ||||
0.0350361 | + | 0.999386i | \(0.488845\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.88942e16i | 1.58441i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.94240e15i | 0.0782208i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 6.52852e15i | − | 0.259904i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.00559e15 | −0.236362 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.05511e16i | 1.57782i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.43256e15 | 0.170512 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.07223e16 | 0.788121 | 0.394060 | − | 0.919085i | \(-0.371070\pi\) | ||||
0.394060 | + | 0.919085i | \(0.371070\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.81636e14 | − | 1.92578e14i | −0.0218711 | − | 0.00724144i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.81060e15 | −0.290388 | −0.145194 | − | 0.989403i | \(-0.546381\pi\) | ||||
−0.145194 | + | 0.989403i | \(0.546381\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.08248e16 | 1.13313 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.38469e13i | 0.000503299i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.83369e16 | 0.659031 | 0.329516 | − | 0.944150i | \(-0.393115\pi\) | ||||
0.329516 | + | 0.944150i | \(0.393115\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.93064e16i | 1.39688i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 4.17657e16i | − | 1.46771i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.01380e15i | 0.0699797i | 0.999388 | + | 0.0349898i | \(0.0111399\pi\) | ||||
−0.999388 | + | 0.0349898i | \(0.988860\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.43098e16 | −1.86629 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.53682e15 | 0.0862076 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 5.91431e14i | − | 0.0198758i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 3.19132e16i | − | 1.06063i | −0.847800 | − | 0.530317i | \(-0.822073\pi\) | ||
0.847800 | − | 0.530317i | \(-0.177927\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.84736e15i | 0.0607200i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.03376e16 | 0.336041 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.30322e16i | 1.38347i | 0.722150 | + | 0.691736i | \(0.243154\pi\) | ||||
−0.722150 | + | 0.691736i | \(0.756846\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.68547e15 | −0.244377 |
(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 | 272.12.b.c.33.8 | 16 | ||
4.3 | odd | 2 | 17.12.b.a.16.14 | yes | 16 | ||
12.11 | even | 2 | 153.12.d.b.118.3 | 16 | |||
17.16 | even | 2 | inner | 272.12.b.c.33.9 | 16 | ||
68.67 | odd | 2 | 17.12.b.a.16.13 | ✓ | 16 | ||
204.203 | even | 2 | 153.12.d.b.118.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.12.b.a.16.13 | ✓ | 16 | 68.67 | odd | 2 | ||
17.12.b.a.16.14 | yes | 16 | 4.3 | odd | 2 | ||
153.12.d.b.118.3 | 16 | 12.11 | even | 2 | |||
153.12.d.b.118.4 | 16 | 204.203 | even | 2 | |||
272.12.b.c.33.8 | 16 | 1.1 | even | 1 | trivial | ||
272.12.b.c.33.9 | 16 | 17.16 | even | 2 | inner |