Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [27,11,Mod(26,27)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(27, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("27.26");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 27 = 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 27.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(17.1546458222\) |
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: |
\( x^{4} + 188x^{2} + 756 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{9} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 26.3 | ||
Root | \(13.5606i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 27.26 |
Dual form | 27.11.b.c.26.2 |
$q$-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 \(\left(\mathbb{Z}/27\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 23.5425i | 0.735704i | 0.929884 | + | 0.367852i | \(0.119907\pi\) | ||||
−0.929884 | + | 0.367852i | \(0.880093\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 469.750 | 0.458740 | ||||||||
\(5\) | − 4424.52i | − 1.41585i | −0.706289 | − | 0.707923i | \(-0.749632\pi\) | ||||
0.706289 | − | 0.707923i | \(-0.250368\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −21568.0 | −1.28327 | −0.641637 | − | 0.767009i | \(-0.721744\pi\) | ||||
−0.641637 | + | 0.767009i | \(0.721744\pi\) | |||||||
\(8\) | 35166.6i | 1.07320i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 104164. | 1.04164 | ||||||||
\(11\) | 242828.i | 1.50777i | 0.657007 | + | 0.753885i | \(0.271822\pi\) | ||||
−0.657007 | + | 0.753885i | \(0.728178\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −398104. | −1.07221 | −0.536105 | − | 0.844152i | \(-0.680105\pi\) | ||||
−0.536105 | + | 0.844152i | \(0.680105\pi\) | |||||||
\(14\) | − 507765.i | − 0.944109i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −346888. | −0.330818 | ||||||||
\(17\) | 2.02619e6i | 1.42704i | 0.700634 | + | 0.713520i | \(0.252900\pi\) | ||||
−0.700634 | + | 0.713520i | \(0.747100\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.77192e6 | −1.11947 | −0.559735 | − | 0.828672i | \(-0.689097\pi\) | ||||
−0.559735 | + | 0.828672i | \(0.689097\pi\) | |||||||
\(20\) | − 2.07842e6i | − 0.649505i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.71678e6 | −1.10927 | ||||||||
\(23\) | − 2.47900e6i | − 0.385157i | −0.981282 | − | 0.192579i | \(-0.938315\pi\) | ||||
0.981282 | − | 0.192579i | \(-0.0616850\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −9.81076e6 | −1.00462 | ||||||||
\(26\) | − 9.37237e6i | − 0.788828i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.01315e7 | −0.588689 | ||||||||
\(29\) | − 9.13358e6i | − 0.445298i | −0.974899 | − | 0.222649i | \(-0.928530\pi\) | ||||
0.974899 | − | 0.222649i | \(-0.0714704\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.81463e7 | −0.633840 | −0.316920 | − | 0.948452i | \(-0.602649\pi\) | ||||
−0.316920 | + | 0.948452i | \(0.602649\pi\) | |||||||
\(32\) | 2.78440e7i | 0.829816i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.77017e7 | −1.04988 | ||||||||
\(35\) | 9.54280e7i | 1.81692i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.14330e7 | 0.164874 | 0.0824369 | − | 0.996596i | \(-0.473730\pi\) | ||||
0.0824369 | + | 0.996596i | \(0.473730\pi\) | |||||||
\(38\) | − 6.52579e7i | − 0.823598i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.55595e8 | 1.51949 | ||||||||
\(41\) | − 1.37099e8i | − 1.18336i | −0.806174 | − | 0.591678i | \(-0.798466\pi\) | ||||
0.806174 | − | 0.591678i | \(-0.201534\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.87897e7 | 0.672000 | 0.336000 | − | 0.941862i | \(-0.390926\pi\) | ||||
0.336000 | + | 0.941862i | \(0.390926\pi\) | |||||||
\(44\) | 1.14068e8i | 0.691674i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.83620e7 | 0.283362 | ||||||||
\(47\) | 1.41804e8i | 0.618302i | 0.951013 | + | 0.309151i | \(0.100045\pi\) | ||||
−0.951013 | + | 0.309151i | \(0.899955\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.82702e8 | 0.646791 | ||||||||
\(50\) | − 2.30970e8i | − 0.739104i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.87009e8 | −0.491865 | ||||||||
\(53\) | − 1.39084e8i | − 0.332582i | −0.986077 | − | 0.166291i | \(-0.946821\pi\) | ||||
0.986077 | − | 0.166291i | \(-0.0531792\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.07440e9 | 2.13477 | ||||||||
\(56\) | − 7.58473e8i | − 1.37721i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.15027e8 | 0.327608 | ||||||||
\(59\) | 1.06798e9i | 1.49384i | 0.664916 | + | 0.746918i | \(0.268467\pi\) | ||||
−0.664916 | + | 0.746918i | \(0.731533\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.44976e9 | −1.71651 | −0.858256 | − | 0.513222i | \(-0.828452\pi\) | ||||
−0.858256 | + | 0.513222i | \(0.828452\pi\) | |||||||
\(62\) | − 4.27210e8i | − 0.466318i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.01073e9 | −0.941317 | ||||||||
\(65\) | 1.76142e9i | 1.51808i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.44613e9 | 1.07111 | 0.535556 | − | 0.844500i | \(-0.320102\pi\) | ||||
0.535556 | + | 0.844500i | \(0.320102\pi\) | |||||||
\(68\) | 9.51804e8i | 0.654640i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.24662e9 | −1.33671 | ||||||||
\(71\) | − 1.33807e9i | − 0.741630i | −0.928707 | − | 0.370815i | \(-0.879078\pi\) | ||||
0.928707 | − | 0.370815i | \(-0.120922\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.46812e9 | −0.708187 | −0.354094 | − | 0.935210i | \(-0.615211\pi\) | ||||
−0.354094 | + | 0.935210i | \(0.615211\pi\) | |||||||
\(74\) | 2.69162e8i | 0.121298i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.30211e9 | −0.513545 | ||||||||
\(77\) | − 5.23731e9i | − 1.93488i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.95381e9 | −1.60992 | −0.804959 | − | 0.593331i | \(-0.797813\pi\) | ||||
−0.804959 | + | 0.593331i | \(0.797813\pi\) | |||||||
\(80\) | 1.53481e9i | 0.468388i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.22766e9 | 0.870600 | ||||||||
\(83\) | 5.60643e8i | 0.142330i | 0.997465 | + | 0.0711650i | \(0.0226717\pi\) | ||||
−0.997465 | + | 0.0711650i | \(0.977328\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.96494e9 | 2.02047 | ||||||||
\(86\) | 2.32576e9i | 0.494393i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −8.53944e9 | −1.61814 | ||||||||
\(89\) | − 4.73263e9i | − 0.847524i | −0.905774 | − | 0.423762i | \(-0.860709\pi\) | ||||
0.905774 | − | 0.423762i | \(-0.139291\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.58629e9 | 1.37594 | ||||||||
\(92\) | − 1.16451e9i | − 0.176687i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.33843e9 | −0.454887 | ||||||||
\(95\) | 1.22644e10i | 1.58500i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.21701e10 | 1.41722 | 0.708609 | − | 0.705601i | \(-0.249323\pi\) | ||||
0.708609 | + | 0.705601i | \(0.249323\pi\) | |||||||
\(98\) | 4.30128e9i | 0.475847i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.60860e9 | −0.460860 | ||||||||
\(101\) | − 1.19970e10i | − 1.14148i | −0.821132 | − | 0.570738i | \(-0.806657\pi\) | ||||
0.821132 | − | 0.570738i | \(-0.193343\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.17848e10 | 1.01657 | 0.508286 | − | 0.861188i | \(-0.330279\pi\) | ||||
0.508286 | + | 0.861188i | \(0.330279\pi\) | |||||||
\(104\) | − 1.40000e10i | − 1.15070i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.27440e9 | 0.244682 | ||||||||
\(107\) | 1.67650e10i | 1.19532i | 0.801749 | + | 0.597661i | \(0.203903\pi\) | ||||
−0.801749 | + | 0.597661i | \(0.796097\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.39867e10 | 0.909040 | 0.454520 | − | 0.890736i | \(-0.349811\pi\) | ||||
0.454520 | + | 0.890736i | \(0.349811\pi\) | |||||||
\(110\) | 2.52940e10i | 1.57056i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 7.48167e9 | 0.424530 | ||||||||
\(113\) | 1.66178e9i | 0.0901948i | 0.998983 | + | 0.0450974i | \(0.0143598\pi\) | ||||
−0.998983 | + | 0.0450974i | \(0.985640\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.09684e10 | −0.545323 | ||||||||
\(116\) | − 4.29049e9i | − 0.204276i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.51430e10 | −1.09902 | ||||||||
\(119\) | − 4.37009e10i | − 1.83128i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.30279e10 | −1.27337 | ||||||||
\(122\) | − 3.41310e10i | − 1.26284i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −8.52421e9 | −0.290768 | ||||||||
\(125\) | 1.99685e8i | 0.00654329i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.55071e9 | 0.0772045 | 0.0386022 | − | 0.999255i | \(-0.487709\pi\) | ||||
0.0386022 | + | 0.999255i | \(0.487709\pi\) | |||||||
\(128\) | 4.71710e9i | 0.137286i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.14682e10 | −1.11686 | ||||||||
\(131\) | 1.62753e10i | 0.421863i | 0.977501 | + | 0.210932i | \(0.0676498\pi\) | ||||
−0.977501 | + | 0.210932i | \(0.932350\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.97846e10 | 1.43659 | ||||||||
\(134\) | 3.40457e10i | 0.788021i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.12544e10 | −1.53150 | ||||||||
\(137\) | 6.54848e10i | 1.35687i | 0.734661 | + | 0.678434i | \(0.237341\pi\) | ||||
−0.734661 | + | 0.678434i | \(0.762659\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.01191e10 | −0.580454 | −0.290227 | − | 0.956958i | \(-0.593731\pi\) | ||||
−0.290227 | + | 0.956958i | \(0.593731\pi\) | |||||||
\(140\) | 4.48272e10i | 0.833493i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.15015e10 | 0.545620 | ||||||||
\(143\) | − 9.66707e10i | − 1.61664i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.04117e10 | −0.630474 | ||||||||
\(146\) | − 3.45633e10i | − 0.521016i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.37065e9 | 0.0756342 | ||||||||
\(149\) | 9.88459e10i | 1.34595i | 0.739667 | + | 0.672973i | \(0.234983\pi\) | ||||
−0.739667 | + | 0.672973i | \(0.765017\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.33061e10 | 1.06119 | 0.530594 | − | 0.847626i | \(-0.321969\pi\) | ||||
0.530594 | + | 0.847626i | \(0.321969\pi\) | |||||||
\(152\) | − 9.74790e10i | − 1.20141i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.23299e11 | 1.42350 | ||||||||
\(155\) | 8.02887e10i | 0.897420i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.89160e10 | −0.827307 | −0.413653 | − | 0.910434i | \(-0.635747\pi\) | ||||
−0.413653 | + | 0.910434i | \(0.635747\pi\) | |||||||
\(158\) | − 1.16625e11i | − 1.18442i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.23196e11 | 1.17489 | ||||||||
\(161\) | 5.34671e10i | 0.494262i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.98358e10 | 0.172390 | 0.0861951 | − | 0.996278i | \(-0.472529\pi\) | ||||
0.0861951 | + | 0.996278i | \(0.472529\pi\) | |||||||
\(164\) | − 6.44023e10i | − 0.542853i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.31990e10 | −0.104713 | ||||||||
\(167\) | − 4.31117e10i | − 0.331905i | −0.986134 | − | 0.165952i | \(-0.946930\pi\) | ||||
0.986134 | − | 0.165952i | \(-0.0530698\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.06281e10 | 0.149632 | ||||||||
\(170\) | 2.11057e11i | 1.48647i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.64064e10 | 0.308273 | ||||||||
\(173\) | − 1.26896e11i | − 0.818875i | −0.912338 | − | 0.409438i | \(-0.865725\pi\) | ||||
0.912338 | − | 0.409438i | \(-0.134275\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.11598e11 | 1.28920 | ||||||||
\(176\) | − 8.42340e10i | − 0.498797i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.11418e11 | 0.623527 | ||||||||
\(179\) | − 1.71735e11i | − 0.934531i | −0.884117 | − | 0.467265i | \(-0.845239\pi\) | ||||
0.884117 | − | 0.467265i | \(-0.154761\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.76637e10 | −0.502737 | −0.251368 | − | 0.967892i | \(-0.580881\pi\) | ||||
−0.251368 | + | 0.967892i | \(0.580881\pi\) | |||||||
\(182\) | 2.02143e11i | 1.01228i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.71782e10 | 0.413351 | ||||||||
\(185\) | − 5.05856e10i | − 0.233436i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.92016e11 | −2.15165 | ||||||||
\(188\) | 6.66126e10i | 0.283640i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.88735e11 | −1.16609 | ||||||||
\(191\) | 1.00665e11i | 0.396015i | 0.980201 | + | 0.198007i | \(0.0634470\pi\) | ||||
−0.980201 | + | 0.198007i | \(0.936553\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.28449e11 | −1.22654 | −0.613270 | − | 0.789873i | \(-0.710146\pi\) | ||||
−0.613270 | + | 0.789873i | \(0.710146\pi\) | |||||||
\(194\) | 2.86516e11i | 1.04265i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 8.58244e10 | 0.296709 | ||||||||
\(197\) | 2.22370e11i | 0.749453i | 0.927135 | + | 0.374727i | \(0.122263\pi\) | ||||
−0.927135 | + | 0.374727i | \(0.877737\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.76697e11 | 0.566191 | 0.283095 | − | 0.959092i | \(-0.408639\pi\) | ||||
0.283095 | + | 0.959092i | \(0.408639\pi\) | |||||||
\(200\) | − 3.45011e11i | − 1.07816i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.82440e11 | 0.839788 | ||||||||
\(203\) | 1.96993e11i | 0.571439i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.06598e11 | −1.67545 | ||||||||
\(206\) | 2.77445e11i | 0.747896i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.38097e11 | 0.354706 | ||||||||
\(209\) | − 6.73098e11i | − 1.68790i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.67258e11 | −0.639027 | −0.319513 | − | 0.947582i | \(-0.603519\pi\) | ||||
−0.319513 | + | 0.947582i | \(0.603519\pi\) | |||||||
\(212\) | − 6.53349e10i | − 0.152569i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.94691e11 | −0.879403 | ||||||||
\(215\) | − 4.37097e11i | − 0.951449i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.91379e11 | 0.813390 | ||||||||
\(218\) | 3.29283e11i | 0.668785i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 5.04697e11 | 0.979304 | ||||||||
\(221\) | − 8.06635e11i | − 1.53009i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.07380e11 | −0.920046 | −0.460023 | − | 0.887907i | \(-0.652159\pi\) | ||||
−0.460023 | + | 0.887907i | \(0.652159\pi\) | |||||||
\(224\) | − 6.00539e11i | − 1.06488i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.91225e10 | −0.0663566 | ||||||||
\(227\) | 9.61037e11i | 1.59445i | 0.603682 | + | 0.797225i | \(0.293700\pi\) | ||||
−0.603682 | + | 0.797225i | \(0.706300\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.08272e11 | 0.330715 | 0.165357 | − | 0.986234i | \(-0.447122\pi\) | ||||
0.165357 | + | 0.986234i | \(0.447122\pi\) | |||||||
\(230\) | − 2.58224e11i | − 0.401197i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.21197e11 | 0.477894 | ||||||||
\(233\) | 1.26797e12i | 1.84642i | 0.384296 | + | 0.923210i | \(0.374444\pi\) | ||||
−0.384296 | + | 0.923210i | \(0.625556\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.27417e11 | 0.875420 | ||||||||
\(236\) | 5.01683e11i | 0.685282i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.02883e12 | 1.34728 | ||||||||
\(239\) | 9.98539e11i | 1.28049i | 0.768171 | + | 0.640244i | \(0.221167\pi\) | ||||
−0.768171 | + | 0.640244i | \(0.778833\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.61004e11 | 0.690050 | 0.345025 | − | 0.938594i | \(-0.387870\pi\) | ||||
0.345025 | + | 0.938594i | \(0.387870\pi\) | |||||||
\(242\) | − 7.77561e11i | − 0.936823i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.81024e11 | −0.787432 | ||||||||
\(245\) | − 8.08371e11i | − 0.915757i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.10351e12 | 1.20031 | ||||||||
\(248\) | − 6.38144e11i | − 0.680237i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4.70110e9 | −0.00481392 | ||||||||
\(251\) | − 1.09342e12i | − 1.09753i | −0.835975 | − | 0.548767i | \(-0.815097\pi\) | ||||
0.835975 | − | 0.548767i | \(-0.184903\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.01971e11 | 0.580728 | ||||||||
\(254\) | 6.00502e10i | 0.0567996i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.14604e12 | −1.04232 | ||||||||
\(257\) | 1.74563e12i | 1.55699i | 0.627648 | + | 0.778497i | \(0.284018\pi\) | ||||
−0.627648 | + | 0.778497i | \(0.715982\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.46587e11 | −0.211578 | ||||||||
\(260\) | 8.27425e11i | 0.696405i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.83161e11 | −0.310367 | ||||||||
\(263\) | 3.82099e11i | 0.303667i | 0.988406 | + | 0.151833i | \(0.0485177\pi\) | ||||
−0.988406 | + | 0.151833i | \(0.951482\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.15382e11 | −0.470886 | ||||||||
\(266\) | 1.40748e12i | 1.05690i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.79321e11 | 0.491361 | ||||||||
\(269\) | − 1.54623e12i | − 1.09777i | −0.835896 | − | 0.548887i | \(-0.815052\pi\) | ||||
0.835896 | − | 0.548887i | \(-0.184948\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.85954e12 | 1.27221 | 0.636104 | − | 0.771603i | \(-0.280545\pi\) | ||||
0.636104 | + | 0.771603i | \(0.280545\pi\) | |||||||
\(272\) | − 7.02862e11i | − 0.472091i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.54168e12 | −0.998253 | ||||||||
\(275\) | − 2.38232e12i | − 1.51474i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.96780e12 | −1.20665 | −0.603326 | − | 0.797495i | \(-0.706158\pi\) | ||||
−0.603326 | + | 0.797495i | \(0.706158\pi\) | |||||||
\(278\) | − 7.09079e11i | − 0.427042i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.35588e12 | −1.94992 | ||||||||
\(281\) | 3.53773e11i | 0.201926i | 0.994890 | + | 0.100963i | \(0.0321924\pi\) | ||||
−0.994890 | + | 0.100963i | \(0.967808\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.55446e12 | −0.856341 | −0.428170 | − | 0.903698i | \(-0.640842\pi\) | ||||
−0.428170 | + | 0.903698i | \(0.640842\pi\) | |||||||
\(284\) | − 6.28558e11i | − 0.340215i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.27587e12 | 1.18937 | ||||||||
\(287\) | 2.95695e12i | 1.51857i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.08947e12 | −1.03645 | ||||||||
\(290\) | − 9.51393e11i | − 0.463842i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.89650e11 | −0.324874 | ||||||||
\(293\) | − 3.65602e12i | − 1.69305i | −0.532347 | − | 0.846526i | \(-0.678690\pi\) | ||||
0.532347 | − | 0.846526i | \(-0.321310\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.72530e12 | 2.11504 | ||||||||
\(296\) | 4.02060e11i | 0.176943i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.32708e12 | −0.990217 | ||||||||
\(299\) | 9.86901e11i | 0.412969i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.13069e12 | −0.862360 | ||||||||
\(302\) | 1.96124e12i | 0.780719i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 9.61544e11 | 0.370341 | ||||||||
\(305\) | 6.41449e12i | 2.43032i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.14571e12 | 1.52022 | 0.760111 | − | 0.649793i | \(-0.225144\pi\) | ||||
0.760111 | + | 0.649793i | \(0.225144\pi\) | |||||||
\(308\) | − 2.46022e12i | − 0.887607i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.89020e12 | −0.660235 | ||||||||
\(311\) | 7.41396e11i | 0.254829i | 0.991850 | + | 0.127414i | \(0.0406678\pi\) | ||||
−0.991850 | + | 0.127414i | \(0.959332\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.19855e12 | −0.398966 | −0.199483 | − | 0.979901i | \(-0.563926\pi\) | ||||
−0.199483 | + | 0.979901i | \(0.563926\pi\) | |||||||
\(314\) | − 1.85788e12i | − 0.608653i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.32705e12 | −0.738533 | ||||||||
\(317\) | 2.08772e12i | 0.652191i | 0.945337 | + | 0.326096i | \(0.105733\pi\) | ||||
−0.945337 | + | 0.326096i | \(0.894267\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.21789e12 | 0.671407 | ||||||||
\(320\) | 4.47200e12i | 1.33276i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.25875e12 | −0.363631 | ||||||||
\(323\) | − 5.61644e12i | − 1.59753i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.90570e12 | 1.07716 | ||||||||
\(326\) | 4.66986e11i | 0.126828i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.82132e12 | 1.26998 | ||||||||
\(329\) | − 3.05843e12i | − 0.793450i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.73492e12 | 1.44340 | 0.721701 | − | 0.692204i | \(-0.243360\pi\) | ||||
0.721701 | + | 0.692204i | \(0.243360\pi\) | |||||||
\(332\) | 2.63362e11i | 0.0652924i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.01496e12 | 0.244184 | ||||||||
\(335\) | − 6.39845e12i | − 1.51653i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.80990e11 | −0.0876524 | −0.0438262 | − | 0.999039i | \(-0.513955\pi\) | ||||
−0.0438262 | + | 0.999039i | \(0.513955\pi\) | |||||||
\(338\) | 4.85638e11i | 0.110085i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.21127e12 | 0.926870 | ||||||||
\(341\) | − 4.40643e12i | − 0.955685i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.15190e12 | 0.453264 | ||||||||
\(344\) | 3.47410e12i | 0.721191i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.98745e12 | 0.602450 | ||||||||
\(347\) | 3.54684e11i | 0.0705009i | 0.999379 | + | 0.0352505i | \(0.0112229\pi\) | ||||
−0.999379 | + | 0.0352505i | \(0.988777\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.67975e12 | −1.48327 | −0.741634 | − | 0.670805i | \(-0.765949\pi\) | ||||
−0.741634 | + | 0.670805i | \(0.765949\pi\) | |||||||
\(350\) | 4.98156e12i | 0.948473i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.76130e12 | −1.25117 | ||||||||
\(353\) | 6.58216e12i | 1.20087i | 0.799674 | + | 0.600434i | \(0.205005\pi\) | ||||
−0.799674 | + | 0.600434i | \(0.794995\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.92032e12 | −1.05003 | ||||||||
\(356\) | − 2.22315e12i | − 0.388793i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.04307e12 | 0.687538 | ||||||||
\(359\) | − 6.68773e12i | − 1.12152i | −0.827979 | − | 0.560760i | \(-0.810509\pi\) | ||||
0.827979 | − | 0.560760i | \(-0.189491\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.55245e12 | 0.253211 | ||||||||
\(362\) | − 2.29925e12i | − 0.369865i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.03341e12 | 0.631197 | ||||||||
\(365\) | 6.49574e12i | 1.00268i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.31180e12 | −1.39863 | −0.699316 | − | 0.714813i | \(-0.746512\pi\) | ||||
−0.699316 | + | 0.714813i | \(0.746512\pi\) | |||||||
\(368\) | 8.59936e11i | 0.127417i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.19091e12 | 0.171740 | ||||||||
\(371\) | 2.99977e12i | 0.426794i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.18448e11 | 0.0856562 | 0.0428281 | − | 0.999082i | \(-0.486363\pi\) | ||||
0.0428281 | + | 0.999082i | \(0.486363\pi\) | |||||||
\(374\) | − 1.15833e13i | − 1.58298i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.98678e12 | −0.663562 | ||||||||
\(377\) | 3.63611e12i | 0.477453i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.79881e11 | 0.0869435 | 0.0434717 | − | 0.999055i | \(-0.486158\pi\) | ||||
0.0434717 | + | 0.999055i | \(0.486158\pi\) | |||||||
\(380\) | 5.76120e12i | 0.727101i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.36991e12 | −0.291350 | ||||||||
\(383\) | 5.62340e12i | 0.682346i | 0.940000 | + | 0.341173i | \(0.110824\pi\) | ||||
−0.940000 | + | 0.341173i | \(0.889176\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.31726e13 | −2.73949 | ||||||||
\(386\) | − 7.73252e12i | − 0.902370i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.71692e12 | 0.650135 | ||||||||
\(389\) | − 9.64393e12i | − 1.08270i | −0.840799 | − | 0.541348i | \(-0.817914\pi\) | ||||
0.840799 | − | 0.541348i | \(-0.182086\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.02294e12 | 0.549635 | ||||||||
\(392\) | 6.42503e12i | 0.694137i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.23515e12 | −0.551376 | ||||||||
\(395\) | 2.19182e13i | 2.27940i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.48431e11 | −0.0150512 | −0.00752561 | − | 0.999972i | \(-0.502395\pi\) | ||||
−0.00752561 | + | 0.999972i | \(0.502395\pi\) | |||||||
\(398\) | 4.15988e12i | 0.416549i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.40323e12 | 0.332347 | ||||||||
\(401\) | 2.15508e11i | 0.0207846i | 0.999946 | + | 0.0103923i | \(0.00330803\pi\) | ||||
−0.999946 | + | 0.0103923i | \(0.996692\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.22411e12 | 0.679609 | ||||||||
\(404\) | − 5.63560e12i | − 0.523640i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.63771e12 | −0.420410 | ||||||||
\(407\) | 2.77625e12i | 0.248592i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.10585e13 | −0.966228 | −0.483114 | − | 0.875557i | \(-0.660494\pi\) | ||||
−0.483114 | + | 0.875557i | \(0.660494\pi\) | |||||||
\(410\) | − 1.42809e13i | − 1.23264i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.53593e12 | 0.466342 | ||||||||
\(413\) | − 2.30342e13i | − 1.91700i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.48058e12 | 0.201517 | ||||||||
\(416\) | − 1.10848e13i | − 0.889737i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.58464e13 | 1.24180 | ||||||||
\(419\) | 7.75836e12i | 0.600758i | 0.953820 | + | 0.300379i | \(0.0971132\pi\) | ||||
−0.953820 | + | 0.300379i | \(0.902887\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.44013e12 | −0.713785 | −0.356893 | − | 0.934145i | \(-0.616164\pi\) | ||||
−0.356893 | + | 0.934145i | \(0.616164\pi\) | |||||||
\(422\) | − 6.29194e12i | − 0.470135i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.89113e12 | 0.356928 | ||||||||
\(425\) | − 1.98785e13i | − 1.43364i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.12684e13 | 2.20275 | ||||||||
\(428\) | 7.87535e12i | 0.548342i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.02904e13 | 0.699985 | ||||||||
\(431\) | 1.56255e13i | 1.05063i | 0.850909 | + | 0.525313i | \(0.176052\pi\) | ||||
−0.850909 | + | 0.525313i | \(0.823948\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.68288e13 | −1.10564 | −0.552820 | − | 0.833301i | \(-0.686448\pi\) | ||||
−0.552820 | + | 0.833301i | \(0.686448\pi\) | |||||||
\(434\) | 9.21405e12i | 0.598414i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.57025e12 | 0.417013 | ||||||||
\(437\) | 6.87159e12i | 0.431172i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.14121e12 | −0.376644 | −0.188322 | − | 0.982107i | \(-0.560305\pi\) | ||||
−0.188322 | + | 0.982107i | \(0.560305\pi\) | |||||||
\(440\) | 3.77829e13i | 2.29104i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.89902e13 | 1.12569 | ||||||||
\(443\) | − 1.37391e12i | − 0.0805265i | −0.999189 | − | 0.0402633i | \(-0.987180\pi\) | ||||
0.999189 | − | 0.0402633i | \(-0.0128197\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.09396e13 | −1.19996 | ||||||||
\(446\) | − 1.19450e13i | − 0.676881i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.17994e13 | 1.20797 | ||||||||
\(449\) | 1.04566e13i | 0.573004i | 0.958080 | + | 0.286502i | \(0.0924925\pi\) | ||||
−0.958080 | + | 0.286502i | \(0.907508\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.32915e13 | 1.78423 | ||||||||
\(452\) | 7.80621e11i | 0.0413759i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.26252e13 | −1.17304 | ||||||||
\(455\) | − 3.79902e13i | − 1.94812i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.39247e13 | 1.70190 | 0.850951 | − | 0.525245i | \(-0.176026\pi\) | ||||
0.850951 | + | 0.525245i | \(0.176026\pi\) | |||||||
\(458\) | 4.90325e12i | 0.243308i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −5.15240e12 | −0.250162 | ||||||||
\(461\) | 2.28758e13i | 1.09868i | 0.835599 | + | 0.549340i | \(0.185121\pi\) | ||||
−0.835599 | + | 0.549340i | \(0.814879\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.66690e12 | −0.172343 | −0.0861716 | − | 0.996280i | \(-0.527463\pi\) | ||||
−0.0861716 | + | 0.996280i | \(0.527463\pi\) | |||||||
\(464\) | 3.16833e12i | 0.147313i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.98513e13 | −1.35842 | ||||||||
\(467\) | − 2.48699e13i | − 1.11967i | −0.828605 | − | 0.559834i | \(-0.810865\pi\) | ||||
0.828605 | − | 0.559834i | \(-0.189135\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.11902e13 | −1.37453 | ||||||||
\(470\) | 1.47710e13i | 0.644050i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.75573e13 | −1.60319 | ||||||||
\(473\) | 2.39889e13i | 1.01322i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.71946e13 | 1.12464 | ||||||||
\(476\) | − 2.05285e13i | − 0.840083i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.35081e13 | −0.942060 | ||||||||
\(479\) | 4.40756e12i | 0.174792i | 0.996174 | + | 0.0873959i | \(0.0278545\pi\) | ||||
−0.996174 | + | 0.0873959i | \(0.972145\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.55152e12 | −0.176779 | ||||||||
\(482\) | 1.32074e13i | 0.507672i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.55149e13 | −0.584145 | ||||||||
\(485\) | − 5.38470e13i | − 2.00656i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.42862e12 | −0.344194 | −0.172097 | − | 0.985080i | \(-0.555054\pi\) | ||||
−0.172097 | + | 0.985080i | \(0.555054\pi\) | |||||||
\(488\) | − 5.09831e13i | − 1.84216i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.90311e13 | 0.673726 | ||||||||
\(491\) | 1.40743e13i | 0.493195i | 0.969118 | + | 0.246597i | \(0.0793125\pi\) | ||||
−0.969118 | + | 0.246597i | \(0.920688\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.85064e13 | 0.635459 | ||||||||
\(494\) | 2.59794e13i | 0.883069i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.29473e12 | 0.209686 | ||||||||
\(497\) | 2.88595e13i | 0.951714i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.37708e13 | −1.09154 | −0.545769 | − | 0.837935i | \(-0.683763\pi\) | ||||
−0.545769 | + | 0.837935i | \(0.683763\pi\) | |||||||
\(500\) | 9.38021e10i | 0.00300167i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.57418e13 | 0.807460 | ||||||||
\(503\) | 4.24460e12i | 0.131825i | 0.997825 | + | 0.0659124i | \(0.0209958\pi\) | ||||
−0.997825 | + | 0.0659124i | \(0.979004\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.30811e13 | −1.61615 | ||||||||
\(506\) | 1.41719e13i | 0.427244i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.19819e12 | 0.0354168 | ||||||||
\(509\) | 2.01121e13i | 0.588664i | 0.955703 | + | 0.294332i | \(0.0950972\pi\) | ||||
−0.955703 | + | 0.294332i | \(0.904903\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.16644e13 | 0.908798 | ||||||||
\(512\) | − 2.21504e13i | − 0.629552i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.10966e13 | −1.14549 | ||||||||
\(515\) | − 5.21423e13i | − 1.43931i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.44341e13 | −0.932257 | ||||||||
\(518\) | − 5.80527e12i | − 0.155659i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.19432e13 | −1.62921 | ||||||||
\(521\) | 1.35570e12i | 0.0353163i | 0.999844 | + | 0.0176581i | \(0.00562105\pi\) | ||||
−0.999844 | + | 0.0176581i | \(0.994379\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.72383e13 | 1.46278 | 0.731389 | − | 0.681961i | \(-0.238872\pi\) | ||||
0.731389 | + | 0.681961i | \(0.238872\pi\) | |||||||
\(524\) | 7.64530e12i | 0.193526i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.99557e12 | −0.223409 | ||||||||
\(527\) | − 3.67679e13i | − 0.904515i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.52811e13 | 0.851654 | ||||||||
\(530\) | − 1.44877e13i | − 0.346432i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.80838e13 | 0.659019 | ||||||||
\(533\) | 5.45797e13i | 1.26881i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.41771e13 | 1.69239 | ||||||||
\(536\) | 5.08557e13i | 1.14952i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.64022e13 | 0.807637 | ||||||||
\(539\) | 4.43653e13i | 0.975212i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.34478e13 | 0.505961 | 0.252980 | − | 0.967471i | \(-0.418589\pi\) | ||||
0.252980 | + | 0.967471i | \(0.418589\pi\) | |||||||
\(542\) | 4.37782e13i | 0.935969i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.64174e13 | −1.18418 | ||||||||
\(545\) | − 6.18845e13i | − 1.28706i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.36836e13 | −0.279424 | −0.139712 | − | 0.990192i | \(-0.544618\pi\) | ||||
−0.139712 | + | 0.990192i | \(0.544618\pi\) | |||||||
\(548\) | 3.07615e13i | 0.622449i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 5.60859e13 | 1.11440 | ||||||||
\(551\) | 2.53175e13i | 0.498498i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.06844e14 | 2.06597 | ||||||||
\(554\) | − 4.63269e13i | − 0.887738i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.41484e13 | −0.266277 | ||||||||
\(557\) | 6.54044e13i | 1.21992i | 0.792432 | + | 0.609960i | \(0.208814\pi\) | ||||
−0.792432 | + | 0.609960i | \(0.791186\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.93285e13 | −0.720525 | ||||||||
\(560\) | − 3.31028e13i | − 0.601069i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8.32871e12 | −0.148558 | ||||||||
\(563\) | 3.14419e13i | 0.555862i | 0.960601 | + | 0.277931i | \(0.0896486\pi\) | ||||
−0.960601 | + | 0.277931i | \(0.910351\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.35258e12 | 0.127702 | ||||||||
\(566\) | − 3.65959e13i | − 0.630013i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.70554e13 | 0.795917 | ||||||||
\(569\) | − 1.01433e14i | − 1.70066i | −0.526247 | − | 0.850332i | \(-0.676401\pi\) | ||||
0.526247 | − | 0.850332i | \(-0.323599\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.86156e13 | 0.471435 | 0.235718 | − | 0.971822i | \(-0.424256\pi\) | ||||
0.235718 | + | 0.971822i | \(0.424256\pi\) | |||||||
\(572\) | − 4.54110e13i | − 0.741619i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6.96141e13 | −1.11722 | ||||||||
\(575\) | 2.43209e13i | 0.386937i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.60161e13 | −0.250425 | −0.125212 | − | 0.992130i | \(-0.539961\pi\) | ||||
−0.125212 | + | 0.992130i | \(0.539961\pi\) | |||||||
\(578\) | − 4.91913e13i | − 0.762517i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.89834e13 | −0.289223 | ||||||||
\(581\) | − 1.20919e13i | − 0.182648i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.37736e13 | 0.501458 | ||||||||
\(584\) | − 5.16289e13i | − 0.760027i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.60719e13 | 1.24559 | ||||||||
\(587\) | − 1.31766e14i | − 1.89066i | −0.326115 | − | 0.945330i | \(-0.605740\pi\) | ||||
0.326115 | − | 0.945330i | \(-0.394260\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.03000e13 | 0.709564 | ||||||||
\(590\) | 1.11246e14i | 1.55605i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.96597e12 | −0.0545432 | ||||||||
\(593\) | 4.28136e13i | 0.583859i | 0.956440 | + | 0.291930i | \(0.0942973\pi\) | ||||
−0.956440 | + | 0.291930i | \(0.905703\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.93356e14 | −2.59282 | ||||||||
\(596\) | 4.64328e13i | 0.617439i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.32341e13 | −0.303823 | ||||||||
\(599\) | 1.26813e14i | 1.64448i | 0.569141 | + | 0.822240i | \(0.307276\pi\) | ||||
−0.569141 | + | 0.822240i | \(0.692724\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.25899e14 | −1.60565 | −0.802823 | − | 0.596217i | \(-0.796670\pi\) | ||||
−0.802823 | + | 0.596217i | \(0.796670\pi\) | |||||||
\(602\) | − 5.01619e13i | − 0.634442i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.91330e13 | 0.486809 | ||||||||
\(605\) | 1.46133e14i | 1.80290i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.15751e13 | −0.625889 | −0.312944 | − | 0.949771i | \(-0.601315\pi\) | ||||
−0.312944 | + | 0.949771i | \(0.601315\pi\) | |||||||
\(608\) | − 7.71813e13i | − 0.928954i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.51013e14 | −1.78799 | ||||||||
\(611\) | − 5.64529e13i | − 0.662949i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.86500e13 | 0.793119 | 0.396560 | − | 0.918009i | \(-0.370204\pi\) | ||||
0.396560 | + | 0.918009i | \(0.370204\pi\) | |||||||
\(614\) | 9.76005e13i | 1.11843i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.84178e14 | 2.07652 | ||||||||
\(617\) | − 9.31549e13i | − 1.04179i | −0.853621 | − | 0.520895i | \(-0.825598\pi\) | ||||
0.853621 | − | 0.520895i | \(-0.174402\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.30635e13 | −1.02406 | −0.512031 | − | 0.858967i | \(-0.671107\pi\) | ||||
−0.512031 | + | 0.858967i | \(0.671107\pi\) | |||||||
\(620\) | 3.77156e13i | 0.411682i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.74543e13 | −0.187478 | ||||||||
\(623\) | 1.02073e14i | 1.08761i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.49247e13 | −0.995357 | ||||||||
\(626\) | − 2.82170e13i | − 0.293521i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.70707e13 | −0.379519 | ||||||||
\(629\) | 2.31655e13i | 0.235282i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.95590e13 | 0.895288 | 0.447644 | − | 0.894212i | \(-0.352263\pi\) | ||||
0.447644 | + | 0.894212i | \(0.352263\pi\) | |||||||
\(632\) | − 1.74209e14i | − 1.72776i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.91501e13 | −0.479820 | ||||||||
\(635\) | − 1.12857e13i | − 0.109310i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.27345e13 | −0.693495 | ||||||||
\(638\) | 5.22147e13i | 0.493957i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.08709e13 | 0.194375 | ||||||||
\(641\) | − 1.07669e14i | − 0.994946i | −0.867480 | − | 0.497473i | \(-0.834261\pi\) | ||||
0.867480 | − | 0.497473i | \(-0.165739\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.75748e13 | 0.432835 | 0.216417 | − | 0.976301i | \(-0.430563\pi\) | ||||
0.216417 | + | 0.976301i | \(0.430563\pi\) | |||||||
\(644\) | 2.51161e13i | 0.226738i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.32225e14 | 1.17531 | ||||||||
\(647\) | 1.19789e13i | 0.105656i | 0.998604 | + | 0.0528280i | \(0.0168235\pi\) | ||||
−0.998604 | + | 0.0528280i | \(0.983176\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.59335e14 | −2.25236 | ||||||||
\(650\) | 9.19500e13i | 0.792474i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.31788e12 | 0.0790823 | ||||||||
\(653\) | 1.60289e13i | 0.135001i | 0.997719 | + | 0.0675007i | \(0.0215025\pi\) | ||||
−0.997719 | + | 0.0675007i | \(0.978498\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.20103e13 | 0.597294 | ||||||||
\(656\) | 4.75580e13i | 0.391476i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 7.20033e13 | 0.583744 | ||||||||
\(659\) | 2.23451e14i | 1.79786i | 0.438093 | + | 0.898930i | \(0.355654\pi\) | ||||
−0.438093 | + | 0.898930i | \(0.644346\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.81957e13 | 0.144198 | 0.0720992 | − | 0.997397i | \(-0.477030\pi\) | ||||
0.0720992 | + | 0.997397i | \(0.477030\pi\) | |||||||
\(662\) | 1.35015e14i | 1.06192i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.97159e13 | −0.152749 | ||||||||
\(665\) | − 2.64518e14i | − 2.03398i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.26422e13 | −0.171510 | ||||||||
\(668\) | − 2.02517e13i | − 0.152258i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.50636e14 | 1.11572 | ||||||||
\(671\) | − 3.52042e14i | − 2.58810i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.39243e14 | 1.73286 | 0.866432 | − | 0.499294i | \(-0.166407\pi\) | ||||
0.866432 | + | 0.499294i | \(0.166407\pi\) | |||||||
\(674\) | − 8.96946e12i | − 0.0644862i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.69004e12 | 0.0686423 | ||||||||
\(677\) | − 2.31720e14i | − 1.62937i | −0.579902 | − | 0.814686i | \(-0.696909\pi\) | ||||
0.579902 | − | 0.814686i | \(-0.303091\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.62485e14 | −1.81868 | ||||||||
\(680\) | 3.15267e14i | 2.16837i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.03738e14 | 0.703101 | ||||||||
\(683\) | − 1.67561e14i | − 1.12738i | −0.825986 | − | 0.563690i | \(-0.809381\pi\) | ||||
0.825986 | − | 0.563690i | \(-0.190619\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.89739e14 | 1.92112 | ||||||||
\(686\) | 5.06611e13i | 0.333468i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.42689e13 | −0.222310 | ||||||||
\(689\) | 5.53701e13i | 0.356598i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.92427e14 | 1.22145 | 0.610725 | − | 0.791843i | \(-0.290878\pi\) | ||||
0.610725 | + | 0.791843i | \(0.290878\pi\) | |||||||
\(692\) | − 5.96094e13i | − 0.375651i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.35017e12 | −0.0518678 | ||||||||
\(695\) | 1.33262e14i | 0.821833i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.77790e14 | 1.68870 | ||||||||
\(698\) | − 1.80801e14i | − 1.09125i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 9.93982e13 | 0.591409 | ||||||||
\(701\) | 3.26565e14i | 1.92921i | 0.263702 | + | 0.964604i | \(0.415057\pi\) | ||||
−0.263702 | + | 0.964604i | \(0.584943\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.16913e13 | −0.184571 | ||||||||
\(704\) | − 2.45434e14i | − 1.41929i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.54961e14 | −0.883483 | ||||||||
\(707\) | 2.58752e14i | 1.46483i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.21622e14 | −1.79521 | −0.897604 | − | 0.440804i | \(-0.854694\pi\) | ||||
−0.897604 | + | 0.440804i | \(0.854694\pi\) | |||||||
\(710\) | − 1.39379e14i | − 0.772514i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.66431e14 | 0.909563 | ||||||||
\(713\) | 4.49847e13i | 0.244128i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.27721e14 | −2.28892 | ||||||||
\(716\) | − 8.06724e13i | − 0.428706i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.57446e14 | 0.825106 | ||||||||
\(719\) | 2.74758e13i | 0.142990i | 0.997441 | + | 0.0714950i | \(0.0227770\pi\) | ||||
−0.997441 | + | 0.0714950i | \(0.977223\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.54175e14 | −1.30454 | ||||||||
\(722\) | 3.65487e13i | 0.186288i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4.58775e13 | −0.230625 | ||||||||
\(725\) | 8.96073e13i | 0.447356i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.42042e13 | 0.414631 | 0.207316 | − | 0.978274i | \(-0.433527\pi\) | ||||
0.207316 | + | 0.978274i | \(0.433527\pi\) | |||||||
\(728\) | 3.01951e14i | 1.47666i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.52926e14 | −0.737679 | ||||||||
\(731\) | 2.00167e14i | 0.958971i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.62014e14 | 1.71082 | 0.855412 | − | 0.517947i | \(-0.173304\pi\) | ||||
0.855412 | + | 0.517947i | \(0.173304\pi\) | |||||||
\(734\) | − 2.19223e14i | − 1.02898i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.90254e13 | 0.319610 | ||||||||
\(737\) | 3.51162e14i | 1.61499i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.44206e14 | −1.10799 | −0.553993 | − | 0.832522i | \(-0.686896\pi\) | ||||
−0.553993 | + | 0.832522i | \(0.686896\pi\) | |||||||
\(740\) | − 2.37625e13i | − 0.107086i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.06222e13 | −0.313994 | ||||||||
\(743\) | − 6.89118e13i | − 0.304333i | −0.988355 | − | 0.152167i | \(-0.951375\pi\) | ||||
0.988355 | − | 0.152167i | \(-0.0486250\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.37346e14 | 1.90565 | ||||||||
\(746\) | 1.45598e13i | 0.0630176i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.31124e14 | −0.987047 | ||||||||
\(749\) | − 3.61587e14i | − 1.53392i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.44541e14 | −1.02365 | −0.511825 | − | 0.859090i | \(-0.671030\pi\) | ||||
−0.511825 | + | 0.859090i | \(0.671030\pi\) | |||||||
\(752\) | − 4.91902e13i | − 0.204545i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −8.56032e13 | −0.351264 | ||||||||
\(755\) | − 3.68589e14i | − 1.50248i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.72001e13 | −0.149646 | −0.0748230 | − | 0.997197i | \(-0.523839\pi\) | ||||
−0.0748230 | + | 0.997197i | \(0.523839\pi\) | |||||||
\(758\) | 1.60061e13i | 0.0639646i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.31298e14 | −1.70102 | ||||||||
\(761\) | − 5.57377e13i | − 0.218386i | −0.994021 | − | 0.109193i | \(-0.965173\pi\) | ||||
0.994021 | − | 0.109193i | \(-0.0348267\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.01665e14 | −1.16655 | ||||||||
\(764\) | 4.72873e13i | 0.181668i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.32389e14 | −0.502005 | ||||||||
\(767\) | − 4.25167e14i | − 1.60171i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.18923e13 | 0.155777 | 0.0778883 | − | 0.996962i | \(-0.475182\pi\) | ||||
0.0778883 | + | 0.996962i | \(0.475182\pi\) | |||||||
\(770\) | − 5.45541e14i | − 2.01546i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.54289e14 | −0.562663 | ||||||||
\(773\) | 4.44998e13i | 0.161236i | 0.996745 | + | 0.0806178i | \(0.0256893\pi\) | ||||
−0.996745 | + | 0.0806178i | \(0.974311\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.78029e14 | 0.636769 | ||||||||
\(776\) | 4.27983e14i | 1.52096i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.27043e14 | 0.796543 | ||||||||
\(779\) | 3.80027e14i | 1.32473i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.24921e14 | 1.11821 | ||||||||
\(782\) | 1.18253e14i | 0.404369i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.33773e13 | −0.213970 | ||||||||
\(785\) | 3.49165e14i | 1.17134i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.29172e12 | −0.0175276 | −0.00876381 | − | 0.999962i | \(-0.502790\pi\) | ||||
−0.00876381 | + | 0.999962i | \(0.502790\pi\) | |||||||
\(788\) | 1.04458e14i | 0.343804i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5.16010e14 | −1.67696 | ||||||||
\(791\) | − 3.58412e13i | − 0.115745i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.77155e14 | 1.84046 | ||||||||
\(794\) | − 3.49444e12i | − 0.0110732i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.30031e13 | 0.259734 | ||||||||
\(797\) | 2.29589e14i | 0.713936i | 0.934117 | + | 0.356968i | \(0.116190\pi\) | ||||
−0.934117 | + | 0.356968i | \(0.883810\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.87323e14 | −0.882342 | ||||||||
\(800\) | − 2.73171e14i | − 0.833651i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −5.07360e12 | −0.0152913 | ||||||||
\(803\) | − 3.56501e14i | − 1.06778i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.36566e14 | 0.699799 | ||||||||
\(806\) | 1.70074e14i | 0.499991i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.21895e14 | 1.22503 | ||||||||
\(809\) | − 2.21639e14i | − 0.639594i | −0.947486 | − | 0.319797i | \(-0.896385\pi\) | ||||
0.947486 | − | 0.319797i | \(-0.103615\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.70111e14 | 0.769907 | 0.384953 | − | 0.922936i | \(-0.374218\pi\) | ||||
0.384953 | + | 0.922936i | \(0.374218\pi\) | |||||||
\(812\) | 9.25373e13i | 0.262142i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6.53600e13 | −0.182890 | ||||||||
\(815\) | − 8.77641e13i | − 0.244078i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.73837e14 | −0.752283 | ||||||||
\(818\) | − 2.60345e14i | − 0.710858i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.84949e14 | −0.768596 | ||||||||
\(821\) | 1.46064e14i | 0.391586i | 0.980645 | + | 0.195793i | \(0.0627281\pi\) | ||||
−0.980645 | + | 0.195793i | \(0.937272\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.82425e13 | −0.101286 | −0.0506428 | − | 0.998717i | \(-0.516127\pi\) | ||||
−0.0506428 | + | 0.998717i | \(0.516127\pi\) | |||||||
\(824\) | 4.14434e14i | 1.09099i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.42283e14 | 1.41035 | ||||||||
\(827\) | 3.49746e13i | 0.0904119i | 0.998978 | + | 0.0452060i | \(0.0143944\pi\) | ||||
−0.998978 | + | 0.0452060i | \(0.985606\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.43554e14 | 1.64366 | 0.821831 | − | 0.569732i | \(-0.192953\pi\) | ||||
0.821831 | + | 0.569732i | \(0.192953\pi\) | |||||||
\(830\) | 5.83991e13i | 0.148257i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.02376e14 | 1.00929 | ||||||||
\(833\) | 3.70191e14i | 0.922997i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.90749e14 | −0.469926 | ||||||||
\(836\) | − 3.16188e14i | − 0.774308i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.82651e14 | −0.441980 | ||||||||
\(839\) | 7.76705e13i | 0.186830i | 0.995627 | + | 0.0934149i | \(0.0297783\pi\) | ||||
−0.995627 | + | 0.0934149i | \(0.970222\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.37285e14 | 0.801710 | ||||||||
\(842\) | − 2.22245e14i | − 0.525135i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.25545e14 | −0.293147 | ||||||||
\(845\) | − 9.12695e13i | − 0.211857i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.12346e14 | 1.63408 | ||||||||
\(848\) | 4.82467e13i | 0.110024i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.67990e14 | 1.05473 | ||||||||
\(851\) | − 2.83425e13i | − 0.0635023i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.53687e14 | −0.783202 | −0.391601 | − | 0.920135i | \(-0.628079\pi\) | ||||
−0.391601 | + | 0.920135i | \(0.628079\pi\) | |||||||
\(854\) | 7.36136e14i | 1.62057i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.89569e14 | −1.28282 | ||||||||
\(857\) | 5.53847e14i | 1.19808i | 0.800719 | + | 0.599040i | \(0.204451\pi\) | ||||
−0.800719 | + | 0.599040i | \(0.795549\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.82091e14 | 1.03077 | 0.515387 | − | 0.856958i | \(-0.327648\pi\) | ||||
0.515387 | + | 0.856958i | \(0.327648\pi\) | |||||||
\(860\) | − 2.05326e14i | − 0.436467i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.67864e14 | −0.772950 | ||||||||
\(863\) | 2.02122e14i | 0.422240i | 0.977460 | + | 0.211120i | \(0.0677111\pi\) | ||||
−0.977460 | + | 0.211120i | \(0.932289\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.61454e14 | −1.15940 | ||||||||
\(866\) | − 3.96193e14i | − 0.813424i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.83850e14 | 0.373134 | ||||||||
\(869\) | − 1.20292e15i | − 2.42739i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.75712e14 | −1.14846 | ||||||||
\(872\) | 4.91866e14i | 0.975583i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.61775e14 | −0.317215 | ||||||||
\(875\) | − 4.30681e12i | − 0.00839683i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.83664e14 | −0.546771 | −0.273386 | − | 0.961905i | \(-0.588143\pi\) | ||||
−0.273386 | + | 0.961905i | \(0.588143\pi\) | |||||||
\(878\) | − 1.44580e14i | − 0.277099i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.72695e14 | −0.706221 | ||||||||
\(881\) | − 7.92783e14i | − 1.49374i | −0.664970 | − | 0.746870i | \(-0.731556\pi\) | ||||
0.664970 | − | 0.746870i | \(-0.268444\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.58732e14 | 1.04088 | 0.520439 | − | 0.853899i | \(-0.325768\pi\) | ||||
0.520439 | + | 0.853899i | \(0.325768\pi\) | |||||||
\(884\) | − 3.78917e14i | − 0.701911i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.23453e13 | 0.0592437 | ||||||||
\(887\) | 5.60792e13i | 0.102137i | 0.998695 | + | 0.0510685i | \(0.0162627\pi\) | ||||
−0.998695 | + | 0.0510685i | \(0.983737\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.50137e13 | −0.0990745 | ||||||||
\(890\) | − 4.92971e14i | − 0.882818i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.38342e14 | −0.422062 | ||||||||
\(893\) | − 3.93070e14i | − 0.692170i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.59845e14 | −1.32315 | ||||||||
\(896\) | − 1.01738e14i | − 0.176175i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.46174e14 | −0.421561 | ||||||||
\(899\) | 1.65741e14i | 0.282248i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.81812e14 | 0.474609 | ||||||||
\(902\) | 7.83766e14i | 1.31266i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.84392e13 | −0.0967971 | ||||||||
\(905\) | 4.32115e14i | 0.711798i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.02359e14 | −0.166759 | −0.0833795 | − | 0.996518i | \(-0.526571\pi\) | ||||
−0.0833795 | + | 0.996518i | \(0.526571\pi\) | |||||||
\(908\) | 4.51447e14i | 0.731438i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 8.94386e14 | 1.43324 | ||||||||
\(911\) | 2.03072e14i | 0.323637i | 0.986821 | + | 0.161818i | \(0.0517358\pi\) | ||||
−0.986821 | + | 0.161818i | \(0.948264\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.36140e14 | −0.214601 | ||||||||
\(914\) | 7.98672e14i | 1.25210i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.78357e13 | 0.151712 | ||||||||
\(917\) | − 3.51025e14i | − 0.541366i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.21378e15 | −1.85167 | −0.925835 | − | 0.377929i | \(-0.876636\pi\) | ||||
−0.925835 | + | 0.377929i | \(0.876636\pi\) | |||||||
\(920\) | − 3.85722e14i | − 0.585241i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5.38554e14 | −0.808304 | ||||||||
\(923\) | 5.32691e14i | 0.795182i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.12166e14 | −0.165636 | ||||||||
\(926\) | − 8.63281e13i | − 0.126794i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.54315e14 | 0.369516 | ||||||||
\(929\) | − 7.35885e14i | − 1.06348i | −0.846906 | − | 0.531742i | \(-0.821537\pi\) | ||||
0.846906 | − | 0.531742i | \(-0.178463\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.06436e14 | −0.724063 | ||||||||
\(932\) | 5.95630e14i | 0.847026i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5.85499e14 | 0.823744 | ||||||||
\(935\) | 2.17694e15i | 3.04640i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.68431e14 | −1.34082 | −0.670410 | − | 0.741991i | \(-0.733882\pi\) | ||||
−0.670410 | + | 0.741991i | \(0.733882\pi\) | |||||||
\(938\) | − 7.34296e14i | − 1.01125i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.94729e14 | 0.401590 | ||||||||
\(941\) | − 5.71203e14i | − 0.774180i | −0.922042 | − | 0.387090i | \(-0.873480\pi\) | ||||
0.922042 | − | 0.387090i | \(-0.126520\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.39869e14 | −0.455778 | ||||||||
\(944\) | − 3.70469e14i | − 0.494188i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.64759e14 | −0.745431 | ||||||||
\(947\) | − 5.06129e14i | − 0.664525i | −0.943187 | − | 0.332263i | \(-0.892188\pi\) | ||||
0.943187 | − | 0.332263i | \(-0.107812\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.84465e14 | 0.759325 | ||||||||
\(950\) | 6.40229e14i | 0.827404i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.53681e15 | 1.96533 | ||||||||
\(953\) | − 1.56038e14i | − 0.198503i | −0.995062 | − | 0.0992515i | \(-0.968355\pi\) | ||||
0.995062 | − | 0.0992515i | \(-0.0316448\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.45394e14 | 0.560696 | ||||||||
\(956\) | 4.69063e14i | 0.587411i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.03765e14 | −0.128595 | ||||||||
\(959\) | − 1.41237e15i | − 1.74123i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.90340e14 | −0.598247 | ||||||||
\(962\) | − 1.07154e14i | − 0.130057i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.63531e14 | 0.316553 | ||||||||
\(965\) | 1.45323e15i | 1.73659i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.20480e14 | −0.970366 | −0.485183 | − | 0.874413i | \(-0.661247\pi\) | ||||
−0.485183 | + | 0.874413i | \(0.661247\pi\) | |||||||
\(968\) | − 1.16148e15i | − 1.36658i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.26769e15 | 1.47624 | ||||||||
\(971\) | − 3.49738e14i | − 0.405179i | −0.979264 | − | 0.202590i | \(-0.935064\pi\) | ||||
0.979264 | − | 0.202590i | \(-0.0649357\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.49608e14 | 0.744881 | ||||||||
\(974\) | − 2.21974e14i | − 0.253225i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.02904e14 | 0.567853 | ||||||||
\(977\) | 4.03993e13i | 0.0453838i | 0.999743 | + | 0.0226919i | \(0.00722368\pi\) | ||||
−0.999743 | + | 0.0226919i | \(0.992776\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.14921e15 | 1.27787 | ||||||||
\(980\) | − 3.79732e14i | − 0.420094i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.31344e14 | −0.362845 | ||||||||
\(983\) | 3.08888e14i | 0.336537i | 0.985741 | + | 0.168269i | \(0.0538176\pi\) | ||||
−0.985741 | + | 0.168269i | \(0.946182\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.83880e14 | 1.06111 | ||||||||
\(986\) | 4.35687e14i | 0.467509i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.18373e14 | 0.550628 | ||||||||
\(989\) | − 2.44900e14i | − 0.258826i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.06886e15 | 1.11828 | 0.559140 | − | 0.829073i | \(-0.311131\pi\) | ||||
0.559140 | + | 0.829073i | \(0.311131\pi\) | |||||||
\(992\) | − 5.05266e14i | − 0.525971i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6.79425e14 | −0.700179 | ||||||||
\(995\) | − 7.81798e14i | − 0.801639i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.25262e14 | 0.939267 | 0.469633 | − | 0.882862i | \(-0.344386\pi\) | ||||
0.469633 | + | 0.882862i | \(0.344386\pi\) | |||||||
\(998\) | − 7.95051e14i | − 0.803049i | ||||||||
\(999\) | 0 | 0 |
(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 | 27.11.b.c.26.3 | yes | 4 | |
3.2 | odd | 2 | inner | 27.11.b.c.26.2 | ✓ | 4 | |
9.2 | odd | 6 | 81.11.d.e.53.2 | 8 | |||
9.4 | even | 3 | 81.11.d.e.26.2 | 8 | |||
9.5 | odd | 6 | 81.11.d.e.26.3 | 8 | |||
9.7 | even | 3 | 81.11.d.e.53.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.11.b.c.26.2 | ✓ | 4 | 3.2 | odd | 2 | inner | |
27.11.b.c.26.3 | yes | 4 | 1.1 | even | 1 | trivial | |
81.11.d.e.26.2 | 8 | 9.4 | even | 3 | |||
81.11.d.e.26.3 | 8 | 9.5 | odd | 6 | |||
81.11.d.e.53.2 | 8 | 9.2 | odd | 6 | |||
81.11.d.e.53.3 | 8 | 9.7 | even | 3 |