Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [387,3,Mod(343,387)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(387, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("387.343");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 387 = 3^{2} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 387.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: | \(10.5449862307\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 20x^{4} + 121x^{2} + 214 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 43) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 343.5 | ||
Root | \(2.58315i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 387.343 |
Dual form | 387.3.b.c.343.2 |
$q$-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 \(\left(\mathbb{Z}/387\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(173\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.58315i | 1.29158i | 0.763517 | + | 0.645788i | \(0.223471\pi\) | ||||
−0.763517 | + | 0.645788i | \(0.776529\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.67267 | −0.668168 | ||||||||
\(5\) | − | 7.02284i | − | 1.40457i | −0.711897 | − | 0.702284i | \(-0.752164\pi\) | ||
0.711897 | − | 0.702284i | \(-0.247836\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.845536i | − | 0.120791i | −0.998175 | − | 0.0603954i | \(-0.980764\pi\) | ||
0.998175 | − | 0.0603954i | \(-0.0192362\pi\) | |||||||
\(8\) | 3.42869i | 0.428586i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 18.1411 | 1.81411 | ||||||||
\(11\) | −14.5475 | −1.32250 | −0.661251 | − | 0.750165i | \(-0.729974\pi\) | ||||
−0.661251 | + | 0.750165i | \(0.729974\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −15.5505 | −1.19619 | −0.598095 | − | 0.801425i | \(-0.704075\pi\) | ||||
−0.598095 | + | 0.801425i | \(0.704075\pi\) | |||||||
\(14\) | 2.18415 | 0.156011 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −19.5475 | −1.22172 | ||||||||
\(17\) | −6.95691 | −0.409230 | −0.204615 | − | 0.978843i | \(-0.565594\pi\) | ||||
−0.204615 | + | 0.978843i | \(0.565594\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 30.8865i | 1.62561i | 0.582539 | + | 0.812803i | \(0.302060\pi\) | ||||
−0.582539 | + | 0.812803i | \(0.697940\pi\) | |||||||
\(20\) | 18.7698i | 0.938488i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 37.5784i | − | 1.70811i | ||||||
\(23\) | −17.5074 | −0.761190 | −0.380595 | − | 0.924742i | \(-0.624281\pi\) | ||||
−0.380595 | + | 0.924742i | \(0.624281\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −24.3203 | −0.972811 | ||||||||
\(26\) | − | 40.1692i | − | 1.54497i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.25984i | 0.0807086i | ||||||||
\(29\) | − | 7.86076i | − | 0.271061i | −0.990773 | − | 0.135530i | \(-0.956726\pi\) | ||
0.990773 | − | 0.135530i | \(-0.0432738\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −57.7456 | −1.86276 | −0.931380 | − | 0.364048i | \(-0.881394\pi\) | ||||
−0.931380 | + | 0.364048i | \(0.881394\pi\) | |||||||
\(32\) | − | 36.7794i | − | 1.14936i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 17.9708i | − | 0.528552i | ||||||
\(35\) | −5.93806 | −0.169659 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 32.5310i | 0.879217i | 0.898189 | + | 0.439609i | \(0.144883\pi\) | ||||
−0.898189 | + | 0.439609i | \(0.855117\pi\) | |||||||
\(38\) | −79.7846 | −2.09959 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 24.0791 | 0.601978 | ||||||||
\(41\) | 18.4425 | 0.449817 | 0.224908 | − | 0.974380i | \(-0.427792\pi\) | ||||
0.224908 | + | 0.974380i | \(0.427792\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 22.2772 | − | 36.7794i | 0.518074 | − | 0.855336i | ||||
\(44\) | 38.8807 | 0.883653 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 45.2242i | − | 0.983135i | ||||||
\(47\) | 25.7806 | 0.548524 | 0.274262 | − | 0.961655i | \(-0.411566\pi\) | ||||
0.274262 | + | 0.961655i | \(0.411566\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 48.2851 | 0.985410 | ||||||||
\(50\) | − | 62.8230i | − | 1.25646i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 41.5613 | 0.799256 | ||||||||
\(53\) | 79.9247 | 1.50801 | 0.754006 | − | 0.656867i | \(-0.228119\pi\) | ||||
0.754006 | + | 0.656867i | \(0.228119\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 102.165i | 1.85754i | ||||||||
\(56\) | 2.89908 | 0.0517693 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 20.3055 | 0.350095 | ||||||||
\(59\) | −18.4243 | −0.312277 | −0.156138 | − | 0.987735i | \(-0.549905\pi\) | ||||
−0.156138 | + | 0.987735i | \(0.549905\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 76.1107i | − | 1.24772i | −0.781537 | − | 0.623858i | \(-0.785564\pi\) | ||
0.781537 | − | 0.623858i | \(-0.214436\pi\) | |||||||
\(62\) | − | 149.166i | − | 2.40590i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 16.8168 | 0.262763 | ||||||||
\(65\) | 109.208i | 1.68013i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.00391 | 0.134387 | 0.0671934 | − | 0.997740i | \(-0.478596\pi\) | ||||
0.0671934 | + | 0.997740i | \(0.478596\pi\) | |||||||
\(68\) | 18.5935 | 0.273435 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | − | 15.3389i | − | 0.219127i | ||||||
\(71\) | 51.6630i | 0.727648i | 0.931468 | + | 0.363824i | \(0.118529\pi\) | ||||
−0.931468 | + | 0.363824i | \(0.881471\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 77.4556i | − | 1.06104i | −0.847674 | − | 0.530518i | \(-0.821997\pi\) | ||
0.847674 | − | 0.530518i | \(-0.178003\pi\) | |||||||
\(74\) | −84.0326 | −1.13558 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 82.5496i | − | 1.08618i | ||||||
\(77\) | 12.3004i | 0.159746i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.04014 | 0.0891157 | 0.0445578 | − | 0.999007i | \(-0.485812\pi\) | ||||
0.0445578 | + | 0.999007i | \(0.485812\pi\) | |||||||
\(80\) | 137.279i | 1.71599i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 47.6397i | 0.580972i | ||||||||
\(83\) | −83.8385 | −1.01010 | −0.505051 | − | 0.863089i | \(-0.668526\pi\) | ||||
−0.505051 | + | 0.863089i | \(0.668526\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 48.8573i | 0.574791i | ||||||||
\(86\) | 95.0069 | + | 57.5454i | 1.10473 | + | 0.669132i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 49.8789i | − | 0.566805i | ||||||
\(89\) | − | 91.8322i | − | 1.03182i | −0.856642 | − | 0.515911i | \(-0.827453\pi\) | ||
0.856642 | − | 0.515911i | \(-0.172547\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.1485i | 0.144489i | ||||||||
\(92\) | 46.7915 | 0.508603 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 66.5953i | 0.708461i | ||||||||
\(95\) | 216.911 | 2.28327 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −155.976 | −1.60800 | −0.803998 | − | 0.594632i | \(-0.797298\pi\) | ||||
−0.803998 | + | 0.594632i | \(0.797298\pi\) | |||||||
\(98\) | 124.728i | 1.27273i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 65.0001 | 0.650001 | ||||||||
\(101\) | −61.9489 | −0.613355 | −0.306678 | − | 0.951813i | \(-0.599217\pi\) | ||||
−0.306678 | + | 0.951813i | \(0.599217\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −19.2194 | −0.186596 | −0.0932978 | − | 0.995638i | \(-0.529741\pi\) | ||||
−0.0932978 | + | 0.995638i | \(0.529741\pi\) | |||||||
\(104\) | − | 53.3177i | − | 0.512670i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 206.458i | 1.94771i | ||||||||
\(107\) | −151.561 | −1.41646 | −0.708230 | − | 0.705981i | \(-0.750506\pi\) | ||||
−0.708230 | + | 0.705981i | \(0.750506\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 43.6904 | 0.400829 | 0.200415 | − | 0.979711i | \(-0.435771\pi\) | ||||
0.200415 | + | 0.979711i | \(0.435771\pi\) | |||||||
\(110\) | −263.907 | −2.39916 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 16.5281i | 0.147573i | ||||||||
\(113\) | 30.9047i | 0.273493i | 0.990606 | + | 0.136747i | \(0.0436646\pi\) | ||||
−0.990606 | + | 0.136747i | \(0.956335\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 122.951i | 1.06914i | ||||||||
\(116\) | 21.0092i | 0.181114i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 47.5928i | − | 0.403329i | ||||||
\(119\) | 5.88232i | 0.0494313i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 90.6301 | 0.749009 | ||||||||
\(122\) | 196.606 | 1.61152 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 154.335 | 1.24464 | ||||||||
\(125\) | − | 4.77360i | − | 0.0381888i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.3094 | 0.152043 | 0.0760214 | − | 0.997106i | \(-0.475778\pi\) | ||||
0.0760214 | + | 0.997106i | \(0.475778\pi\) | |||||||
\(128\) | − | 103.677i | − | 0.809979i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −282.102 | −2.17001 | ||||||||
\(131\) | 19.3546i | 0.147745i | 0.997268 | + | 0.0738725i | \(0.0235358\pi\) | ||||
−0.997268 | + | 0.0738725i | \(0.976464\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 26.1157 | 0.196358 | ||||||||
\(134\) | 23.2585i | 0.173571i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 23.8531i | − | 0.175390i | ||||||
\(137\) | 74.8826i | 0.546588i | 0.961931 | + | 0.273294i | \(0.0881132\pi\) | ||||
−0.961931 | + | 0.273294i | \(0.911887\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 48.3195 | 0.347622 | 0.173811 | − | 0.984779i | \(-0.444392\pi\) | ||||
0.173811 | + | 0.984779i | \(0.444392\pi\) | |||||||
\(140\) | 15.8705 | 0.113361 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −133.453 | −0.939813 | ||||||||
\(143\) | 226.221 | 1.58196 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −55.2048 | −0.380723 | ||||||||
\(146\) | 200.080 | 1.37041 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 86.9448i | − | 0.587465i | ||||||
\(149\) | − | 56.9508i | − | 0.382220i | −0.981569 | − | 0.191110i | \(-0.938791\pi\) | ||
0.981569 | − | 0.191110i | \(-0.0612087\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 133.385i | − | 0.883346i | −0.897176 | − | 0.441673i | \(-0.854385\pi\) | ||
0.897176 | − | 0.441673i | \(-0.145615\pi\) | |||||||
\(152\) | −105.900 | −0.696712 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −31.7739 | −0.206324 | ||||||||
\(155\) | 405.538i | 2.61637i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 172.766i | 1.10042i | 0.835026 | + | 0.550210i | \(0.185452\pi\) | ||||
−0.835026 | + | 0.550210i | \(0.814548\pi\) | |||||||
\(158\) | 18.1857i | 0.115100i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −258.296 | −1.61435 | ||||||||
\(161\) | 14.8031i | 0.0919448i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 243.720i | 1.49521i | 0.664142 | + | 0.747607i | \(0.268797\pi\) | ||||
−0.664142 | + | 0.747607i | \(0.731203\pi\) | |||||||
\(164\) | −49.2907 | −0.300553 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 216.568i | − | 1.30462i | ||||||
\(167\) | −246.040 | −1.47330 | −0.736648 | − | 0.676277i | \(-0.763592\pi\) | ||||
−0.736648 | + | 0.676277i | \(0.763592\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 72.8168 | 0.430869 | ||||||||
\(170\) | −126.206 | −0.742387 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −59.5396 | + | 98.2994i | −0.346161 | + | 0.571508i | ||||
\(173\) | 137.397 | 0.794201 | 0.397100 | − | 0.917775i | \(-0.370016\pi\) | ||||
0.397100 | + | 0.917775i | \(0.370016\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 20.5637i | 0.117507i | ||||||||
\(176\) | 284.368 | 1.61573 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 237.217 | 1.33268 | ||||||||
\(179\) | 131.174i | 0.732816i | 0.930454 | + | 0.366408i | \(0.119413\pi\) | ||||
−0.930454 | + | 0.366408i | \(0.880587\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 229.555 | 1.26826 | 0.634129 | − | 0.773227i | \(-0.281359\pi\) | ||||
0.634129 | + | 0.773227i | \(0.281359\pi\) | |||||||
\(182\) | −33.9645 | −0.186618 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 60.0273i | − | 0.326235i | ||||||
\(185\) | 228.460 | 1.23492 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 101.206 | 0.541207 | ||||||||
\(188\) | −68.9032 | −0.366507 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 560.314i | 2.94902i | ||||||||
\(191\) | 209.496i | 1.09684i | 0.836204 | + | 0.548419i | \(0.184770\pi\) | ||||
−0.836204 | + | 0.548419i | \(0.815230\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −261.300 | −1.35389 | −0.676943 | − | 0.736035i | \(-0.736696\pi\) | ||||
−0.676943 | + | 0.736035i | \(0.736696\pi\) | |||||||
\(194\) | − | 402.909i | − | 2.07685i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −129.050 | −0.658419 | ||||||||
\(197\) | −94.0645 | −0.477485 | −0.238742 | − | 0.971083i | \(-0.576735\pi\) | ||||
−0.238742 | + | 0.971083i | \(0.576735\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 28.5992i | 0.143715i | 0.997415 | + | 0.0718573i | \(0.0228926\pi\) | ||||
−0.997415 | + | 0.0718573i | \(0.977107\pi\) | |||||||
\(200\) | − | 83.3866i | − | 0.416933i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 160.023i | − | 0.792195i | ||||||
\(203\) | −6.64655 | −0.0327416 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 129.519i | − | 0.631798i | ||||||
\(206\) | − | 49.6465i | − | 0.241002i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 303.973 | 1.46141 | ||||||||
\(209\) | − | 449.322i | − | 2.14987i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 22.6639i | − | 0.107412i | −0.998557 | − | 0.0537059i | \(-0.982897\pi\) | ||
0.998557 | − | 0.0537059i | \(-0.0171033\pi\) | |||||||
\(212\) | −213.612 | −1.00761 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 391.506i | − | 1.82947i | ||||||
\(215\) | −258.296 | − | 156.449i | −1.20138 | − | 0.727670i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 48.8260i | 0.225004i | ||||||||
\(218\) | 112.859i | 0.517701i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 273.053i | − | 1.24115i | ||||||
\(221\) | 108.183 | 0.489517 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 263.106i | − | 1.17985i | −0.807460 | − | 0.589923i | \(-0.799158\pi\) | ||
0.807460 | − | 0.589923i | \(-0.200842\pi\) | |||||||
\(224\) | −31.0983 | −0.138832 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −79.8316 | −0.353237 | ||||||||
\(227\) | − | 54.4887i | − | 0.240038i | −0.992772 | − | 0.120019i | \(-0.961704\pi\) | ||
0.992772 | − | 0.120019i | \(-0.0382956\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 189.993 | 0.829664 | 0.414832 | − | 0.909898i | \(-0.363840\pi\) | ||||
0.414832 | + | 0.909898i | \(0.363840\pi\) | |||||||
\(230\) | −317.602 | −1.38088 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 26.9521 | 0.116173 | ||||||||
\(233\) | 209.186i | 0.897795i | 0.893583 | + | 0.448898i | \(0.148183\pi\) | ||||
−0.893583 | + | 0.448898i | \(0.851817\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 181.053i | − | 0.770440i | ||||||
\(236\) | 49.2422 | 0.208653 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −15.1949 | −0.0638442 | ||||||||
\(239\) | 68.1912 | 0.285319 | 0.142659 | − | 0.989772i | \(-0.454435\pi\) | ||||
0.142659 | + | 0.989772i | \(0.454435\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 380.930i | 1.58062i | 0.612705 | + | 0.790312i | \(0.290082\pi\) | ||||
−0.612705 | + | 0.790312i | \(0.709918\pi\) | |||||||
\(242\) | 234.111i | 0.967402i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 203.419i | 0.833685i | ||||||||
\(245\) | − | 339.098i | − | 1.38407i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 480.300i | − | 1.94453i | ||||||
\(248\) | − | 197.992i | − | 0.798353i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 12.3309 | 0.0493237 | ||||||||
\(251\) | 175.752 | 0.700208 | 0.350104 | − | 0.936711i | \(-0.386146\pi\) | ||||
0.350104 | + | 0.936711i | \(0.386146\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 254.689 | 1.00667 | ||||||||
\(254\) | 49.8792i | 0.196375i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 335.082 | 1.30891 | ||||||||
\(257\) | − | 162.749i | − | 0.633263i | −0.948549 | − | 0.316632i | \(-0.897448\pi\) | ||
0.948549 | − | 0.316632i | \(-0.102552\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 27.5062 | 0.106201 | ||||||||
\(260\) | − | 291.878i | − | 1.12261i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −49.9959 | −0.190824 | ||||||||
\(263\) | 78.4612i | 0.298331i | 0.988812 | + | 0.149166i | \(0.0476588\pi\) | ||||
−0.988812 | + | 0.149166i | \(0.952341\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 561.298i | − | 2.11811i | ||||||
\(266\) | 67.4607i | 0.253612i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −24.0645 | −0.0897930 | ||||||||
\(269\) | 48.1852 | 0.179127 | 0.0895636 | − | 0.995981i | \(-0.471453\pi\) | ||||
0.0895636 | + | 0.995981i | \(0.471453\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 81.9474 | 0.302389 | 0.151194 | − | 0.988504i | \(-0.451688\pi\) | ||||
0.151194 | + | 0.988504i | \(0.451688\pi\) | |||||||
\(272\) | 135.990 | 0.499964 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −193.433 | −0.705960 | ||||||||
\(275\) | 353.799 | 1.28654 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 1.40205i | − | 0.00506156i | −0.999997 | − | 0.00253078i | \(-0.999194\pi\) | ||
0.999997 | − | 0.00253078i | \(-0.000805573\pi\) | |||||||
\(278\) | 124.817i | 0.448981i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | − | 20.3598i | − | 0.0727135i | ||||||
\(281\) | −248.005 | −0.882580 | −0.441290 | − | 0.897364i | \(-0.645479\pi\) | ||||
−0.441290 | + | 0.897364i | \(0.645479\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −138.544 | −0.489553 | −0.244777 | − | 0.969580i | \(-0.578715\pi\) | ||||
−0.244777 | + | 0.969580i | \(0.578715\pi\) | |||||||
\(284\) | − | 138.078i | − | 0.486191i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 584.362i | 2.04322i | ||||||||
\(287\) | − | 15.5938i | − | 0.0543338i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −240.601 | −0.832531 | ||||||||
\(290\) | − | 142.602i | − | 0.491733i | ||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 207.014i | 0.708950i | ||||||||
\(293\) | −493.442 | −1.68410 | −0.842051 | − | 0.539398i | \(-0.818652\pi\) | ||||
−0.842051 | + | 0.539398i | \(0.818652\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 129.391i | 0.438614i | ||||||||
\(296\) | −111.539 | −0.376820 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 147.112 | 0.493666 | ||||||||
\(299\) | 272.248 | 0.910527 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −31.0983 | − | 18.8362i | −0.103317 | − | 0.0625786i | ||||
\(302\) | 344.554 | 1.14091 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 603.755i | − | 1.98603i | ||||||
\(305\) | −534.513 | −1.75250 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 74.5297 | 0.242768 | 0.121384 | − | 0.992606i | \(-0.461267\pi\) | ||||
0.121384 | + | 0.992606i | \(0.461267\pi\) | |||||||
\(308\) | − | 32.8751i | − | 0.106737i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1047.57 | −3.37924 | ||||||||
\(311\) | −21.3831 | −0.0687560 | −0.0343780 | − | 0.999409i | \(-0.510945\pi\) | ||||
−0.0343780 | + | 0.999409i | \(0.510945\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 231.173i | 0.738571i | 0.929316 | + | 0.369285i | \(0.120398\pi\) | ||||
−0.929316 | + | 0.369285i | \(0.879602\pi\) | |||||||
\(314\) | −446.281 | −1.42128 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −18.8160 | −0.0595443 | ||||||||
\(317\) | 160.636 | 0.506737 | 0.253369 | − | 0.967370i | \(-0.418461\pi\) | ||||
0.253369 | + | 0.967370i | \(0.418461\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 114.354i | 0.358478i | ||||||||
\(320\) | − | 118.102i | − | 0.369068i | ||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −38.2387 | −0.118754 | ||||||||
\(323\) | − | 214.875i | − | 0.665247i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 378.191 | 1.16367 | ||||||||
\(326\) | −629.565 | −1.93118 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 63.2335i | 0.192785i | ||||||||
\(329\) | − | 21.7985i | − | 0.0662567i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 409.618i | 1.23752i | 0.785581 | + | 0.618759i | \(0.212364\pi\) | ||||
−0.785581 | + | 0.618759i | \(0.787636\pi\) | |||||||
\(332\) | 224.073 | 0.674918 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 635.559i | − | 1.90287i | ||||||
\(335\) | − | 63.2330i | − | 0.188755i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −476.795 | −1.41482 | −0.707411 | − | 0.706803i | \(-0.750137\pi\) | ||||
−0.707411 | + | 0.706803i | \(0.750137\pi\) | |||||||
\(338\) | 188.097i | 0.556500i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | − | 130.580i | − | 0.384057i | ||||||
\(341\) | 840.054 | 2.46350 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 82.2580i | − | 0.239819i | ||||||
\(344\) | 126.105 | + | 76.3815i | 0.366585 | + | 0.222039i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 354.917i | 1.02577i | ||||||||
\(347\) | 180.778i | 0.520973i | 0.965477 | + | 0.260487i | \(0.0838830\pi\) | ||||
−0.965477 | + | 0.260487i | \(0.916117\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 280.319i | 0.803206i | 0.915814 | + | 0.401603i | \(0.131547\pi\) | ||||
−0.915814 | + | 0.401603i | \(0.868453\pi\) | |||||||
\(350\) | −53.1191 | −0.151769 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 535.049i | 1.52003i | ||||||||
\(353\) | 117.502 | 0.332866 | 0.166433 | − | 0.986053i | \(-0.446775\pi\) | ||||
0.166433 | + | 0.986053i | \(0.446775\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 362.821 | 1.02203 | ||||||||
\(356\) | 245.437i | 0.689431i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −338.843 | −0.946488 | ||||||||
\(359\) | 208.289 | 0.580193 | 0.290096 | − | 0.956997i | \(-0.406313\pi\) | ||||
0.290096 | + | 0.956997i | \(0.406313\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −592.977 | −1.64260 | ||||||||
\(362\) | 592.975i | 1.63805i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 35.1416i | − | 0.0965428i | ||||||
\(365\) | −543.958 | −1.49030 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −444.860 | −1.21215 | −0.606076 | − | 0.795407i | \(-0.707257\pi\) | ||||
−0.606076 | + | 0.795407i | \(0.707257\pi\) | |||||||
\(368\) | 342.226 | 0.929961 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 590.148i | 1.59499i | ||||||||
\(371\) | − | 67.5792i | − | 0.182154i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 71.8648i | 0.192667i | 0.995349 | + | 0.0963335i | \(0.0307115\pi\) | ||||
−0.995349 | + | 0.0963335i | \(0.969288\pi\) | |||||||
\(374\) | 261.430i | 0.699010i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 88.3938i | 0.235090i | ||||||||
\(377\) | 122.238i | 0.324240i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 146.399 | 0.386276 | 0.193138 | − | 0.981172i | \(-0.438133\pi\) | ||||
0.193138 | + | 0.981172i | \(0.438133\pi\) | |||||||
\(380\) | −579.732 | −1.52561 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −541.160 | −1.41665 | ||||||||
\(383\) | 698.948i | 1.82493i | 0.409155 | + | 0.912465i | \(0.365824\pi\) | ||||
−0.409155 | + | 0.912465i | \(0.634176\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 86.3841 | 0.224374 | ||||||||
\(386\) | − | 674.978i | − | 1.74865i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 416.872 | 1.07441 | ||||||||
\(389\) | − | 500.337i | − | 1.28621i | −0.765776 | − | 0.643107i | \(-0.777645\pi\) | ||
0.765776 | − | 0.643107i | \(-0.222355\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 121.797 | 0.311502 | ||||||||
\(392\) | 165.554i | 0.422333i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 242.983i | − | 0.616708i | ||||||
\(395\) | − | 49.4418i | − | 0.125169i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −546.245 | −1.37593 | −0.687966 | − | 0.725743i | \(-0.741496\pi\) | ||||
−0.687966 | + | 0.725743i | \(0.741496\pi\) | |||||||
\(398\) | −73.8760 | −0.185618 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 475.401 | 1.18850 | ||||||||
\(401\) | −393.142 | −0.980405 | −0.490203 | − | 0.871609i | \(-0.663077\pi\) | ||||
−0.490203 | + | 0.871609i | \(0.663077\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 897.970 | 2.22821 | ||||||||
\(404\) | 165.569 | 0.409825 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 17.1691i | − | 0.0422883i | ||||||
\(407\) | − | 473.246i | − | 1.16277i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 788.894i | − | 1.92884i | −0.264382 | − | 0.964418i | \(-0.585168\pi\) | ||
0.264382 | − | 0.964418i | \(-0.414832\pi\) | |||||||
\(410\) | 334.566 | 0.816015 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 51.3670 | 0.124677 | ||||||||
\(413\) | 15.5784i | 0.0377202i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 588.784i | 1.41876i | ||||||||
\(416\) | 571.937i | 1.37485i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1160.67 | 2.77671 | ||||||||
\(419\) | 221.714i | 0.529149i | 0.964365 | + | 0.264575i | \(0.0852316\pi\) | ||||
−0.964365 | + | 0.264575i | \(0.914768\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 253.802i | − | 0.602855i | −0.953489 | − | 0.301427i | \(-0.902537\pi\) | ||
0.953489 | − | 0.301427i | \(-0.0974631\pi\) | |||||||
\(422\) | 58.5442 | 0.138730 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 274.037i | 0.646313i | ||||||||
\(425\) | 169.194 | 0.398104 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −64.3544 | −0.150713 | ||||||||
\(428\) | 405.074 | 0.946434 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 404.132 | − | 667.218i | 0.939841 | − | 1.55167i | ||||
\(431\) | −455.340 | −1.05647 | −0.528237 | − | 0.849097i | \(-0.677147\pi\) | ||||
−0.528237 | + | 0.849097i | \(0.677147\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 611.084i | − | 1.41128i | −0.708571 | − | 0.705640i | \(-0.750660\pi\) | ||
0.708571 | − | 0.705640i | \(-0.249340\pi\) | |||||||
\(434\) | −126.125 | −0.290610 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −116.770 | −0.267821 | ||||||||
\(437\) | − | 540.742i | − | 1.23740i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 598.936 | 1.36432 | 0.682159 | − | 0.731204i | \(-0.261041\pi\) | ||||
0.682159 | + | 0.731204i | \(0.261041\pi\) | |||||||
\(440\) | −350.291 | −0.796117 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 279.454i | 0.632248i | ||||||||
\(443\) | 379.068 | 0.855683 | 0.427842 | − | 0.903854i | \(-0.359274\pi\) | ||||
0.427842 | + | 0.903854i | \(0.359274\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −644.923 | −1.44927 | ||||||||
\(446\) | 679.642 | 1.52386 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 14.2192i | − | 0.0317393i | ||||||
\(449\) | − | 260.317i | − | 0.579770i | −0.957061 | − | 0.289885i | \(-0.906383\pi\) | ||
0.957061 | − | 0.289885i | \(-0.0936171\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −268.292 | −0.594883 | ||||||||
\(452\) | − | 82.5982i | − | 0.182739i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 140.752 | 0.310027 | ||||||||
\(455\) | 92.3396 | 0.202944 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 670.232i | 1.46659i | 0.679910 | + | 0.733296i | \(0.262019\pi\) | ||||
−0.679910 | + | 0.733296i | \(0.737981\pi\) | |||||||
\(458\) | 490.781i | 1.07157i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 328.609i | − | 0.714367i | ||||||
\(461\) | 557.387 | 1.20908 | 0.604541 | − | 0.796574i | \(-0.293356\pi\) | ||||
0.604541 | + | 0.796574i | \(0.293356\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 116.501i | 0.251622i | 0.992054 | + | 0.125811i | \(0.0401533\pi\) | ||||
−0.992054 | + | 0.125811i | \(0.959847\pi\) | |||||||
\(464\) | 153.658i | 0.331160i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −540.360 | −1.15957 | ||||||||
\(467\) | 465.465i | 0.996712i | 0.866972 | + | 0.498356i | \(0.166063\pi\) | ||||
−0.866972 | + | 0.498356i | \(0.833937\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 7.61313i | − | 0.0162327i | ||||||
\(470\) | 467.688 | 0.995081 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 63.1713i | − | 0.133837i | ||||||
\(473\) | −324.078 | + | 535.049i | −0.685154 | + | 1.13118i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 751.169i | − | 1.58141i | ||||||
\(476\) | − | 15.7215i | − | 0.0330284i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 176.148i | 0.368511i | ||||||||
\(479\) | −24.7759 | −0.0517241 | −0.0258621 | − | 0.999666i | \(-0.508233\pi\) | ||||
−0.0258621 | + | 0.999666i | \(0.508233\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 505.873i | − | 1.05171i | ||||||
\(482\) | −984.001 | −2.04150 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −242.225 | −0.500464 | ||||||||
\(485\) | 1095.39i | 2.25854i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 356.159 | 0.731333 | 0.365667 | − | 0.930746i | \(-0.380841\pi\) | ||||
0.365667 | + | 0.930746i | \(0.380841\pi\) | |||||||
\(488\) | 260.960 | 0.534754 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 875.942 | 1.78764 | ||||||||
\(491\) | − | 498.114i | − | 1.01449i | −0.861802 | − | 0.507244i | \(-0.830664\pi\) | ||
0.861802 | − | 0.507244i | \(-0.169336\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 54.6866i | 0.110926i | ||||||||
\(494\) | 1240.69 | 2.51151 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1128.78 | 2.27577 | ||||||||
\(497\) | 43.6830 | 0.0878933 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 0.670777i | − | 0.00134424i | −1.00000 | 0.000672122i | \(-0.999786\pi\) | |||
1.00000 | 0.000672122i | \(-0.000213943\pi\) | ||||||||
\(500\) | 12.7583i | 0.0255165i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 453.995i | 0.904372i | ||||||||
\(503\) | − | 775.171i | − | 1.54109i | −0.637383 | − | 0.770547i | \(-0.719983\pi\) | ||
0.637383 | − | 0.770547i | \(-0.280017\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 435.057i | 0.861499i | ||||||||
\(506\) | 657.900i | 1.30020i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −51.6078 | −0.101590 | ||||||||
\(509\) | −825.181 | −1.62118 | −0.810591 | − | 0.585613i | \(-0.800854\pi\) | ||||
−0.810591 | + | 0.585613i | \(0.800854\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −65.4915 | −0.128163 | ||||||||
\(512\) | 450.857i | 0.880580i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 420.404 | 0.817908 | ||||||||
\(515\) | 134.974i | 0.262086i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −375.044 | −0.725424 | ||||||||
\(518\) | 71.0526i | 0.137167i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −374.441 | −0.720080 | ||||||||
\(521\) | − | 801.382i | − | 1.53816i | −0.639151 | − | 0.769081i | \(-0.720714\pi\) | ||
0.639151 | − | 0.769081i | \(-0.279286\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 274.667i | − | 0.525176i | −0.964908 | − | 0.262588i | \(-0.915424\pi\) | ||
0.964908 | − | 0.262588i | \(-0.0845760\pi\) | |||||||
\(524\) | − | 51.7285i | − | 0.0987185i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −202.677 | −0.385318 | ||||||||
\(527\) | 401.731 | 0.762298 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −222.492 | −0.420590 | ||||||||
\(530\) | 1449.92 | 2.73569 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −69.7986 | −0.131200 | ||||||||
\(533\) | −286.789 | −0.538066 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1064.39i | 1.98952i | ||||||||
\(536\) | 30.8716i | 0.0575963i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 124.470i | 0.231356i | ||||||||
\(539\) | −702.428 | −1.30321 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 361.835 | 0.668826 | 0.334413 | − | 0.942427i | \(-0.391462\pi\) | ||||
0.334413 | + | 0.942427i | \(0.391462\pi\) | |||||||
\(542\) | 211.682i | 0.390558i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 255.871i | 0.470352i | ||||||||
\(545\) | − | 306.830i | − | 0.562992i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −281.855 | −0.515273 | −0.257637 | − | 0.966242i | \(-0.582944\pi\) | ||||
−0.257637 | + | 0.966242i | \(0.582944\pi\) | |||||||
\(548\) | − | 200.137i | − | 0.365213i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 913.918i | 1.66167i | ||||||||
\(551\) | 242.791 | 0.440638 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 5.95269i | − | 0.0107644i | ||||||
\(554\) | 3.62171 | 0.00653739 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −129.142 | −0.232270 | ||||||||
\(557\) | −227.271 | −0.408026 | −0.204013 | − | 0.978968i | \(-0.565399\pi\) | ||||
−0.204013 | + | 0.978968i | \(0.565399\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −346.421 | + | 571.937i | −0.619715 | + | 1.02314i | ||||
\(560\) | 116.074 | 0.207276 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 640.635i | − | 1.13992i | ||||||
\(563\) | −789.251 | −1.40187 | −0.700934 | − | 0.713226i | \(-0.747233\pi\) | ||||
−0.700934 | + | 0.713226i | \(0.747233\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 217.039 | 0.384140 | ||||||||
\(566\) | − | 357.879i | − | 0.632295i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −177.136 | −0.311860 | ||||||||
\(569\) | −581.996 | −1.02284 | −0.511420 | − | 0.859331i | \(-0.670880\pi\) | ||||
−0.511420 | + | 0.859331i | \(0.670880\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 761.473i | 1.33358i | 0.745246 | + | 0.666789i | \(0.232332\pi\) | ||||
−0.745246 | + | 0.666789i | \(0.767668\pi\) | |||||||
\(572\) | −604.613 | −1.05702 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 40.2811 | 0.0701762 | ||||||||
\(575\) | 425.784 | 0.740494 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 570.663i | 0.989017i | 0.869173 | + | 0.494509i | \(0.164652\pi\) | ||||
−0.869173 | + | 0.494509i | \(0.835348\pi\) | |||||||
\(578\) | − | 621.510i | − | 1.07528i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 147.544 | 0.254387 | ||||||||
\(581\) | 70.8885i | 0.122011i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1162.70 | −1.99435 | ||||||||
\(584\) | 265.571 | 0.454745 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 1274.64i | − | 2.17515i | ||||||
\(587\) | 188.120i | 0.320477i | 0.987078 | + | 0.160238i | \(0.0512263\pi\) | ||||
−0.987078 | + | 0.160238i | \(0.948774\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 1783.56i | − | 3.02811i | ||||||
\(590\) | −334.237 | −0.566503 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 635.901i | − | 1.07416i | ||||||
\(593\) | 527.123i | 0.888909i | 0.895801 | + | 0.444455i | \(0.146602\pi\) | ||||
−0.895801 | + | 0.444455i | \(0.853398\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 41.3106 | 0.0694296 | ||||||||
\(596\) | 152.211i | 0.255387i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 703.257i | 1.17602i | ||||||||
\(599\) | 1156.58 | 1.93085 | 0.965427 | − | 0.260675i | \(-0.0839451\pi\) | ||||
0.965427 | + | 0.260675i | \(0.0839451\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 119.619i | − | 0.199033i | −0.995036 | − | 0.0995166i | \(-0.968270\pi\) | ||
0.995036 | − | 0.0995166i | \(-0.0317297\pi\) | |||||||
\(602\) | 48.6567 | − | 80.3317i | 0.0808250 | − | 0.133441i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 356.495i | 0.590224i | ||||||||
\(605\) | − | 636.481i | − | 1.05203i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 295.289i | − | 0.486472i | −0.969967 | − | 0.243236i | \(-0.921791\pi\) | ||
0.969967 | − | 0.243236i | \(-0.0782090\pi\) | |||||||
\(608\) | 1135.99 | 1.86840 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 1380.73i | − | 2.26349i | ||||||
\(611\) | −400.901 | −0.656139 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 846.563 | 1.38102 | 0.690508 | − | 0.723324i | \(-0.257387\pi\) | ||||
0.690508 | + | 0.723324i | \(0.257387\pi\) | |||||||
\(614\) | 192.522i | 0.313553i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −42.1744 | −0.0684649 | ||||||||
\(617\) | −495.684 | −0.803377 | −0.401689 | − | 0.915776i | \(-0.631577\pi\) | ||||
−0.401689 | + | 0.915776i | \(0.631577\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 228.258 | 0.368753 | 0.184376 | − | 0.982856i | \(-0.440973\pi\) | ||||
0.184376 | + | 0.982856i | \(0.440973\pi\) | |||||||
\(620\) | − | 1083.87i | − | 1.74818i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 55.2358i | − | 0.0888035i | ||||||
\(623\) | −77.6475 | −0.124635 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −641.531 | −1.02645 | ||||||||
\(626\) | −597.154 | −0.953920 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 461.747i | − | 0.735266i | ||||||
\(629\) | − | 226.316i | − | 0.359802i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 702.132i | 1.11273i | 0.830939 | + | 0.556364i | \(0.187804\pi\) | ||||
−0.830939 | + | 0.556364i | \(0.812196\pi\) | |||||||
\(632\) | 24.1384i | 0.0381937i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 414.946i | 0.654490i | ||||||||
\(635\) | − | 135.607i | − | 0.213555i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −750.855 | −1.17874 | ||||||||
\(638\) | −295.395 | −0.463001 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −728.109 | −1.13767 | ||||||||
\(641\) | − | 897.002i | − | 1.39938i | −0.714447 | − | 0.699689i | \(-0.753322\pi\) | ||
0.714447 | − | 0.699689i | \(-0.246678\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1054.92 | −1.64062 | −0.820311 | − | 0.571918i | \(-0.806200\pi\) | ||||
−0.820311 | + | 0.571918i | \(0.806200\pi\) | |||||||
\(644\) | − | 39.5639i | − | 0.0614346i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 555.054 | 0.859217 | ||||||||
\(647\) | 1230.50i | 1.90185i | 0.309414 | + | 0.950927i | \(0.399867\pi\) | ||||
−0.309414 | + | 0.950927i | \(0.600133\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 268.028 | 0.412986 | ||||||||
\(650\) | 976.926i | 1.50296i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 651.383i | − | 0.999054i | ||||||
\(653\) | 234.774i | 0.359532i | 0.983709 | + | 0.179766i | \(0.0575340\pi\) | ||||
−0.983709 | + | 0.179766i | \(0.942466\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 135.924 | 0.207518 | ||||||||
\(656\) | −360.505 | −0.549550 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 56.3087 | 0.0855756 | ||||||||
\(659\) | 493.253 | 0.748488 | 0.374244 | − | 0.927330i | \(-0.377902\pi\) | ||||
0.374244 | + | 0.927330i | \(0.377902\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 429.533 | 0.649823 | 0.324911 | − | 0.945744i | \(-0.394666\pi\) | ||||
0.324911 | + | 0.945744i | \(0.394666\pi\) | |||||||
\(662\) | −1058.11 | −1.59835 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 287.456i | − | 0.432916i | ||||||
\(665\) | − | 183.406i | − | 0.275799i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 137.621i | 0.206329i | ||||||||
\(668\) | 657.585 | 0.984409 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 163.341 | 0.243792 | ||||||||
\(671\) | 1107.22i | 1.65011i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 349.722i | 0.519647i | 0.965656 | + | 0.259823i | \(0.0836644\pi\) | ||||
−0.965656 | + | 0.259823i | \(0.916336\pi\) | |||||||
\(674\) | − | 1231.63i | − | 1.82735i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −194.616 | −0.287893 | ||||||||
\(677\) | − | 788.649i | − | 1.16492i | −0.812861 | − | 0.582458i | \(-0.802091\pi\) | ||
0.812861 | − | 0.582458i | \(-0.197909\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 131.883i | 0.194231i | ||||||||
\(680\) | −167.516 | −0.246348 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2169.99i | 3.18180i | ||||||||
\(683\) | 94.5265 | 0.138399 | 0.0691995 | − | 0.997603i | \(-0.477956\pi\) | ||||
0.0691995 | + | 0.997603i | \(0.477956\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 525.888 | 0.767720 | ||||||||
\(686\) | 212.485 | 0.309745 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −435.464 | + | 718.946i | −0.632941 | + | 1.04498i | ||||
\(689\) | −1242.87 | −1.80387 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 942.228i | − | 1.36357i | −0.731552 | − | 0.681786i | \(-0.761203\pi\) | ||
0.731552 | − | 0.681786i | \(-0.238797\pi\) | |||||||
\(692\) | −367.217 | −0.530660 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −466.976 | −0.672877 | ||||||||
\(695\) | − | 339.340i | − | 0.488259i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −128.303 | −0.184079 | ||||||||
\(698\) | −724.106 | −1.03740 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | − | 54.9600i | − | 0.0785142i | ||||||
\(701\) | −568.235 | −0.810607 | −0.405303 | − | 0.914182i | \(-0.632834\pi\) | ||||
−0.405303 | + | 0.914182i | \(0.632834\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1004.77 | −1.42926 | ||||||||
\(704\) | −244.643 | −0.347504 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 303.524i | 0.429921i | ||||||||
\(707\) | 52.3800i | 0.0740877i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1211.96 | 1.70939 | 0.854696 | − | 0.519128i | \(-0.173743\pi\) | ||||
0.854696 | + | 0.519128i | \(0.173743\pi\) | |||||||
\(710\) | 937.222i | 1.32003i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 314.864 | 0.442225 | ||||||||
\(713\) | 1010.97 | 1.41791 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 1588.71i | − | 2.22197i | ||||||
\(716\) | − | 350.585i | − | 0.489645i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 538.043i | 0.749363i | ||||||||
\(719\) | −692.271 | −0.962825 | −0.481413 | − | 0.876494i | \(-0.659876\pi\) | ||||
−0.481413 | + | 0.876494i | \(0.659876\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.2507i | 0.0225391i | ||||||||
\(722\) | − | 1531.75i | − | 2.12154i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −613.525 | −0.847410 | ||||||||
\(725\) | 191.176i | 0.263691i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 441.195i | 0.606871i | 0.952852 | + | 0.303435i | \(0.0981337\pi\) | ||||
−0.952852 | + | 0.303435i | \(0.901866\pi\) | |||||||
\(728\) | −45.0820 | −0.0619258 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | − | 1405.13i | − | 1.92483i | ||||||
\(731\) | −154.980 | + | 255.871i | −0.212012 | + | 0.350029i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 251.039i | 0.342481i | 0.985229 | + | 0.171240i | \(0.0547775\pi\) | ||||
−0.985229 | + | 0.171240i | \(0.945222\pi\) | |||||||
\(734\) | − | 1149.14i | − | 1.56559i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 643.911i | 0.874879i | ||||||||
\(737\) | −130.985 | −0.177727 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 635.071i | − | 0.859365i | −0.902980 | − | 0.429683i | \(-0.858625\pi\) | ||
0.902980 | − | 0.429683i | \(-0.141375\pi\) | |||||||
\(740\) | −610.600 | −0.825135 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 174.567 | 0.235266 | ||||||||
\(743\) | − | 899.136i | − | 1.21014i | −0.796171 | − | 0.605071i | \(-0.793145\pi\) | ||
0.796171 | − | 0.605071i | \(-0.206855\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −399.956 | −0.536854 | ||||||||
\(746\) | −185.638 | −0.248844 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −270.490 | −0.361617 | ||||||||
\(749\) | 128.151i | 0.171096i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 597.422i | − | 0.795502i | −0.917493 | − | 0.397751i | \(-0.869791\pi\) | ||
0.917493 | − | 0.397751i | \(-0.130209\pi\) | |||||||
\(752\) | −503.947 | −0.670143 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −315.760 | −0.418780 | ||||||||
\(755\) | −936.743 | −1.24072 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 392.757i | 0.518834i | 0.965765 | + | 0.259417i | \(0.0835304\pi\) | ||||
−0.965765 | + | 0.259417i | \(0.916470\pi\) | |||||||
\(758\) | 378.170i | 0.498905i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 743.720i | 0.978579i | ||||||||
\(761\) | 472.103i | 0.620371i | 0.950676 | + | 0.310186i | \(0.100391\pi\) | ||||
−0.950676 | + | 0.310186i | \(0.899609\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 36.9418i | − | 0.0484165i | ||||||
\(764\) | − | 559.914i | − | 0.732872i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1805.49 | −2.35704 | ||||||||
\(767\) | 286.507 | 0.373542 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −591.892 | −0.769690 | −0.384845 | − | 0.922981i | \(-0.625745\pi\) | ||||
−0.384845 | + | 0.922981i | \(0.625745\pi\) | |||||||
\(770\) | 223.143i | 0.289796i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 698.369 | 0.904624 | ||||||||
\(773\) | − | 632.541i | − | 0.818293i | −0.912469 | − | 0.409147i | \(-0.865826\pi\) | ||
0.912469 | − | 0.409147i | \(-0.134174\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1404.39 | 1.81211 | ||||||||
\(776\) | − | 534.792i | − | 0.689164i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1292.45 | 1.66124 | ||||||||
\(779\) | 569.624i | 0.731225i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 751.569i | − | 0.962316i | ||||||
\(782\) | 314.621i | 0.402328i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −943.853 | −1.20389 | ||||||||
\(785\) | 1213.31 | 1.54562 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.7235 | 0.0339561 | 0.0169781 | − | 0.999856i | \(-0.494595\pi\) | ||||
0.0169781 | + | 0.999856i | \(0.494595\pi\) | |||||||
\(788\) | 251.404 | 0.319040 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 127.716 | 0.161665 | ||||||||
\(791\) | 26.1311 | 0.0330355 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1183.56i | 1.49251i | ||||||||
\(794\) | − | 1411.03i | − | 1.77712i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 76.4363i | − | 0.0960255i | ||||||
\(797\) | 638.409 | 0.801015 | 0.400508 | − | 0.916293i | \(-0.368834\pi\) | ||||
0.400508 | + | 0.916293i | \(0.368834\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −179.354 | −0.224473 | ||||||||
\(800\) | 894.486i | 1.11811i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 1015.55i | − | 1.26627i | ||||||
\(803\) | 1126.79i | 1.40322i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 103.960 | 0.129143 | ||||||||
\(806\) | 2319.59i | 2.87791i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 212.403i | − | 0.262876i | ||||||
\(809\) | −996.366 | −1.23160 | −0.615801 | − | 0.787902i | \(-0.711167\pi\) | ||||
−0.615801 | + | 0.787902i | \(0.711167\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1348.22i | − | 1.66242i | −0.555959 | − | 0.831209i | \(-0.687649\pi\) | ||
0.555959 | − | 0.831209i | \(-0.312351\pi\) | |||||||
\(812\) | 17.7641 | 0.0218769 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1222.47 | 1.50180 | ||||||||
\(815\) | 1711.60 | 2.10013 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1135.99 | + | 688.065i | 1.39044 | + | 0.842184i | ||||
\(818\) | 2037.83 | 2.49124 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 346.161i | 0.422147i | ||||||||
\(821\) | 1363.54 | 1.66083 | 0.830417 | − | 0.557142i | \(-0.188102\pi\) | ||||
0.830417 | + | 0.557142i | \(0.188102\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 590.955 | 0.718050 | 0.359025 | − | 0.933328i | \(-0.383109\pi\) | ||||
0.359025 | + | 0.933328i | \(0.383109\pi\) | |||||||
\(824\) | − | 65.8972i | − | 0.0799723i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −40.2415 | −0.0487185 | ||||||||
\(827\) | 1422.73 | 1.72035 | 0.860175 | − | 0.509999i | \(-0.170354\pi\) | ||||
0.860175 | + | 0.509999i | \(0.170354\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 873.419i | − | 1.05358i | −0.849995 | − | 0.526791i | \(-0.823395\pi\) | ||
0.849995 | − | 0.526791i | \(-0.176605\pi\) | |||||||
\(830\) | −1520.92 | −1.83243 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −261.509 | −0.314314 | ||||||||
\(833\) | −335.915 | −0.403259 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1727.90i | 2.06934i | ||||||||
\(836\) | 1200.89i | 1.43647i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −572.720 | −0.683437 | ||||||||
\(839\) | − | 1155.58i | − | 1.37732i | −0.725082 | − | 0.688662i | \(-0.758198\pi\) | ||
0.725082 | − | 0.688662i | \(-0.241802\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 779.208 | 0.926526 | ||||||||
\(842\) | 655.608 | 0.778632 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 60.5731i | 0.0717691i | ||||||||
\(845\) | − | 511.381i | − | 0.605184i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 76.6310i | − | 0.0904734i | ||||||
\(848\) | −1562.33 | −1.84237 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 437.054i | 0.514181i | ||||||||
\(851\) | − | 569.533i | − | 0.669252i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 86.1596 | 0.101008 | 0.0505039 | − | 0.998724i | \(-0.483917\pi\) | ||||
0.0505039 | + | 0.998724i | \(0.483917\pi\) | |||||||
\(854\) | − | 166.237i | − | 0.194657i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 519.656i | − | 0.607075i | ||||||
\(857\) | 813.017 | 0.948678 | 0.474339 | − | 0.880342i | \(-0.342687\pi\) | ||||
0.474339 | + | 0.880342i | \(0.342687\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 282.918i | 0.329357i | 0.986347 | + | 0.164678i | \(0.0526587\pi\) | ||||
−0.986347 | + | 0.164678i | \(0.947341\pi\) | |||||||
\(860\) | 690.341 | + | 418.137i | 0.802722 | + | 0.486206i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 1176.21i | − | 1.36452i | ||||||
\(863\) | 579.879i | 0.671934i | 0.941874 | + | 0.335967i | \(0.109063\pi\) | ||||
−0.941874 | + | 0.335967i | \(0.890937\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 964.915i | − | 1.11551i | ||||||
\(866\) | 1578.52 | 1.82277 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 130.496i | − | 0.150341i | ||||||
\(869\) | −102.417 | −0.117856 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −140.015 | −0.160752 | ||||||||
\(872\) | 149.801i | 0.171790i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1396.82 | 1.59819 | ||||||||
\(875\) | −4.03625 | −0.00461286 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 305.763 | 0.348647 | 0.174323 | − | 0.984688i | \(-0.444226\pi\) | ||||
0.174323 | + | 0.984688i | \(0.444226\pi\) | |||||||
\(878\) | 1547.14i | 1.76212i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 1997.07i | − | 2.26940i | ||||||
\(881\) | −911.059 | −1.03412 | −0.517059 | − | 0.855950i | \(-0.672973\pi\) | ||||
−0.517059 | + | 0.855950i | \(0.672973\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 396.432 | 0.448960 | 0.224480 | − | 0.974479i | \(-0.427932\pi\) | ||||
0.224480 | + | 0.974479i | \(0.427932\pi\) | |||||||
\(884\) | −289.138 | −0.327079 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 979.189i | 1.10518i | ||||||||
\(887\) | − | 266.284i | − | 0.300207i | −0.988670 | − | 0.150104i | \(-0.952039\pi\) | ||
0.988670 | − | 0.150104i | \(-0.0479607\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 16.3268i | − | 0.0183654i | ||||||
\(890\) | − | 1665.93i | − | 1.87184i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 703.195i | 0.788336i | ||||||||
\(893\) | 796.274i | 0.891685i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 921.215 | 1.02929 | ||||||||
\(896\) | −87.6629 | −0.0978381 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 672.438 | 0.748817 | ||||||||
\(899\) | 453.924i | 0.504921i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −556.029 | −0.617124 | ||||||||
\(902\) | − | 693.040i | − | 0.768337i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −105.963 | −0.117215 | ||||||||
\(905\) | − | 1612.13i | − | 1.78135i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1168.24 | −1.28802 | −0.644012 | − | 0.765015i | \(-0.722731\pi\) | ||||
−0.644012 | + | 0.765015i | \(0.722731\pi\) | |||||||
\(908\) | 145.630i | 0.160386i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 238.527i | 0.262118i | ||||||||
\(911\) | − | 981.585i | − | 1.07748i | −0.842472 | − | 0.538740i | \(-0.818900\pi\) | ||
0.842472 | − | 0.538740i | \(-0.181100\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1219.64 | 1.33586 | ||||||||
\(914\) | −1731.31 | −1.89421 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −507.789 | −0.554355 | ||||||||
\(917\) | 16.3650 | 0.0178462 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1148.89 | −1.25015 | −0.625075 | − | 0.780564i | \(-0.714932\pi\) | ||||
−0.625075 | + | 0.780564i | \(0.714932\pi\) | |||||||
\(920\) | −421.562 | −0.458220 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1439.82i | 1.56162i | ||||||||
\(923\) | − | 803.384i | − | 0.870405i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 791.164i | − | 0.855312i | ||||||
\(926\) | −300.940 | −0.324989 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −289.114 | −0.311546 | ||||||||
\(929\) | − | 870.176i | − | 0.936680i | −0.883548 | − | 0.468340i | \(-0.844852\pi\) | ||
0.883548 | − | 0.468340i | \(-0.155148\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1491.36i | 1.60189i | ||||||||
\(932\) | − | 559.086i | − | 0.599878i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1202.37 | −1.28733 | ||||||||
\(935\) | − | 710.752i | − | 0.760162i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1301.72i | − | 1.38925i | −0.719374 | − | 0.694623i | \(-0.755571\pi\) | ||
0.719374 | − | 0.694623i | \(-0.244429\pi\) | |||||||
\(938\) | 19.6659 | 0.0209658 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 483.896i | 0.514783i | ||||||||
\(941\) | 539.895 | 0.573746 | 0.286873 | − | 0.957969i | \(-0.407384\pi\) | ||||
0.286873 | + | 0.957969i | \(0.407384\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −322.879 | −0.342396 | ||||||||
\(944\) | 360.150 | 0.381515 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1382.11 | − | 837.142i | −1.46101 | − | 0.884928i | ||||
\(947\) | −80.2459 | −0.0847369 | −0.0423685 | − | 0.999102i | \(-0.513490\pi\) | ||||
−0.0423685 | + | 0.999102i | \(0.513490\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1204.47i | 1.26920i | ||||||||
\(950\) | 1940.38 | 2.04251 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −20.1686 | −0.0211855 | ||||||||
\(953\) | 127.129i | 0.133399i | 0.997773 | + | 0.0666996i | \(0.0212469\pi\) | ||||
−0.997773 | + | 0.0666996i | \(0.978753\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1471.26 | 1.54058 | ||||||||
\(956\) | −182.253 | −0.190641 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 63.9998i | − | 0.0668057i | ||||||
\(959\) | 63.3159 | 0.0660229 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2373.55 | 2.46988 | ||||||||
\(962\) | 1306.75 | 1.35836 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 1018.10i | − | 1.05612i | ||||||
\(965\) | 1835.07i | 1.90162i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −487.850 | −0.504498 | −0.252249 | − | 0.967662i | \(-0.581170\pi\) | ||||
−0.252249 | + | 0.967662i | \(0.581170\pi\) | |||||||
\(968\) | 310.742i | 0.321015i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2829.56 | −2.91707 | ||||||||
\(971\) | −706.443 | −0.727542 | −0.363771 | − | 0.931488i | \(-0.618511\pi\) | ||||
−0.363771 | + | 0.931488i | \(0.618511\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 40.8559i | − | 0.0419896i | ||||||
\(974\) | 920.013i | 0.944572i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1487.78i | 1.52436i | ||||||||
\(977\) | −1385.87 | −1.41849 | −0.709247 | − | 0.704961i | \(-0.750965\pi\) | ||||
−0.709247 | + | 0.704961i | \(0.750965\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1335.93i | 1.36459i | ||||||||
\(980\) | 906.299i | 0.924795i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1286.70 | 1.31029 | ||||||||
\(983\) | 868.493i | 0.883513i | 0.897135 | + | 0.441756i | \(0.145644\pi\) | ||||
−0.897135 | + | 0.441756i | \(0.854356\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 660.600i | 0.670660i | ||||||||
\(986\) | −141.264 | −0.143270 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1283.68i | 1.29927i | ||||||||
\(989\) | −390.015 | + | 643.911i | −0.394353 | + | 0.651073i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1678.05i | 1.69329i | 0.532162 | + | 0.846643i | \(0.321380\pi\) | ||||
−0.532162 | + | 0.846643i | \(0.678620\pi\) | |||||||
\(992\) | 2123.85i | 2.14098i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 112.840i | 0.113521i | ||||||||
\(995\) | 200.848 | 0.201857 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 83.7411i | 0.0839931i | 0.999118 | + | 0.0419965i | \(0.0133718\pi\) | ||||
−0.999118 | + | 0.0419965i | \(0.986628\pi\) | |||||||
\(998\) | 1.73272 | 0.00173619 | ||||||||
\(999\) | 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 | 387.3.b.c.343.5 | 6 | ||
3.2 | odd | 2 | 43.3.b.b.42.2 | ✓ | 6 | ||
12.11 | even | 2 | 688.3.b.e.257.5 | 6 | |||
43.42 | odd | 2 | inner | 387.3.b.c.343.2 | 6 | ||
129.128 | even | 2 | 43.3.b.b.42.5 | yes | 6 | ||
516.515 | odd | 2 | 688.3.b.e.257.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.3.b.b.42.2 | ✓ | 6 | 3.2 | odd | 2 | ||
43.3.b.b.42.5 | yes | 6 | 129.128 | even | 2 | ||
387.3.b.c.343.2 | 6 | 43.42 | odd | 2 | inner | ||
387.3.b.c.343.5 | 6 | 1.1 | even | 1 | trivial | ||
688.3.b.e.257.2 | 6 | 516.515 | odd | 2 | |||
688.3.b.e.257.5 | 6 | 12.11 | even | 2 |