Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,3,Mod(701,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1620.701");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.o (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(44.1418028264\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1241.4 | ||
Character | \(\chi\) | \(=\) | 1620.1241 |
Dual form | 1620.3.o.g.701.4 |
$q$-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 \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.93649 | + | 1.11803i | −0.387298 | + | 0.223607i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.57283 | − | 6.18832i | 0.510404 | − | 0.884046i | −0.489523 | − | 0.871990i | \(-0.662829\pi\) |
0.999927 | − | 0.0120555i | \(-0.00383748\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.20431 | + | 1.27266i | 0.200392 | + | 0.115696i | 0.596838 | − | 0.802361i | \(-0.296423\pi\) |
−0.396446 | + | 0.918058i | \(0.629757\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.57892 | − | 9.66297i | −0.429147 | − | 0.743305i | 0.567650 | − | 0.823270i | \(-0.307853\pi\) |
−0.996798 | + | 0.0799646i | \(0.974519\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.05814i | 0.121067i | 0.998166 | + | 0.0605335i | \(0.0192802\pi\) | ||||
−0.998166 | + | 0.0605335i | \(0.980720\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −19.3781 | −1.01990 | −0.509949 | − | 0.860204i | \(-0.670336\pi\) | ||||
−0.509949 | + | 0.860204i | \(0.670336\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 10.4254 | − | 6.01908i | 0.453276 | − | 0.261699i | −0.255937 | − | 0.966694i | \(-0.582384\pi\) |
0.709213 | + | 0.704994i | \(0.249051\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.50000 | − | 4.33013i | 0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 19.3077 | + | 11.1473i | 0.665782 | + | 0.384390i | 0.794477 | − | 0.607295i | \(-0.207745\pi\) |
−0.128694 | + | 0.991684i | \(0.541079\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.08342 | − | 12.2689i | −0.228498 | − | 0.395769i | 0.728865 | − | 0.684657i | \(-0.240048\pi\) |
−0.957363 | + | 0.288888i | \(0.906715\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 15.9782i | 0.456519i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −46.3319 | −1.25221 | −0.626107 | − | 0.779737i | \(-0.715353\pi\) | ||||
−0.626107 | + | 0.779737i | \(0.715353\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −15.0752 | + | 8.70366i | −0.367687 | + | 0.212284i | −0.672448 | − | 0.740145i | \(-0.734757\pi\) |
0.304760 | + | 0.952429i | \(0.401424\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −13.5098 | + | 23.3997i | −0.314183 | + | 0.544180i | −0.979263 | − | 0.202591i | \(-0.935064\pi\) |
0.665081 | + | 0.746771i | \(0.268397\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −42.2514 | − | 24.3938i | −0.898965 | − | 0.519018i | −0.0221009 | − | 0.999756i | \(-0.507036\pi\) |
−0.876864 | + | 0.480738i | \(0.840369\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.03020 | − | 1.78437i | −0.0210246 | − | 0.0364157i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 9.84048i | − | 0.185670i | −0.995682 | − | 0.0928348i | \(-0.970407\pi\) | ||
0.995682 | − | 0.0928348i | \(-0.0295928\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.69151 | −0.103482 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 76.1103 | − | 43.9423i | 1.29001 | − | 0.744785i | 0.311350 | − | 0.950295i | \(-0.399219\pi\) |
0.978655 | + | 0.205510i | \(0.0658854\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −29.9240 | + | 51.8300i | −0.490558 | + | 0.849672i | −0.999941 | − | 0.0108684i | \(-0.996540\pi\) |
0.509383 | + | 0.860540i | \(0.329874\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 21.6071 | + | 12.4748i | 0.332416 | + | 0.191921i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.85720 | + | 6.68087i | 0.0575701 | + | 0.0997144i | 0.893374 | − | 0.449314i | \(-0.148331\pi\) |
−0.835804 | + | 0.549028i | \(0.814998\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 79.5282i | 1.12012i | 0.828453 | + | 0.560058i | \(0.189221\pi\) | ||||
−0.828453 | + | 0.560058i | \(0.810779\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.01802 | −0.0824387 | −0.0412193 | − | 0.999150i | \(-0.513124\pi\) | ||||
−0.0412193 | + | 0.999150i | \(0.513124\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 15.7513 | − | 9.09400i | 0.204562 | − | 0.118104i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.46386 | − | 14.6598i | 0.107137 | − | 0.185568i | −0.807472 | − | 0.589906i | \(-0.799165\pi\) |
0.914609 | + | 0.404338i | \(0.132498\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −127.148 | − | 73.4091i | −1.53191 | − | 0.884447i | −0.999274 | − | 0.0381001i | \(-0.987869\pi\) |
−0.532633 | − | 0.846347i | \(-0.678797\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.30107 | − | 3.98557i | −0.0270714 | − | 0.0468890i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 100.304i | 1.12701i | 0.826113 | + | 0.563504i | \(0.190547\pi\) | ||||
−0.826113 | + | 0.563504i | \(0.809453\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −79.7301 | −0.876154 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 37.5255 | − | 21.6653i | 0.395005 | − | 0.228056i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −36.3075 | + | 62.8865i | −0.374304 | + | 0.648314i | −0.990223 | − | 0.139496i | \(-0.955452\pi\) |
0.615918 | + | 0.787810i | \(0.288785\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −128.595 | − | 74.2442i | −1.27321 | − | 0.735091i | −0.297623 | − | 0.954683i | \(-0.596194\pi\) |
−0.975592 | + | 0.219593i | \(0.929527\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −70.9917 | − | 122.961i | −0.689240 | − | 1.19380i | −0.972084 | − | 0.234633i | \(-0.924611\pi\) |
0.282844 | − | 0.959166i | \(-0.408722\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 3.62138i | − | 0.0338447i | −0.999857 | − | 0.0169224i | \(-0.994613\pi\) | ||
0.999857 | − | 0.0169224i | \(-0.00538681\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −193.000 | −1.77064 | −0.885320 | − | 0.464983i | \(-0.846060\pi\) | ||||
−0.885320 | + | 0.464983i | \(0.846060\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 75.2851 | − | 43.4659i | 0.666240 | − | 0.384654i | −0.128411 | − | 0.991721i | \(-0.540988\pi\) |
0.794650 | + | 0.607067i | \(0.207654\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −13.4591 | + | 23.3118i | −0.117035 | + | 0.202711i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.7364 | + | 7.35337i | 0.107029 | + | 0.0617931i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −57.2607 | − | 99.1784i | −0.473229 | − | 0.819656i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1803i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −83.5634 | −0.657979 | −0.328990 | − | 0.944334i | \(-0.606708\pi\) | ||||
−0.328990 | + | 0.944334i | \(0.606708\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.2345 | + | 11.1050i | −0.146828 | + | 0.0847712i | −0.571614 | − | 0.820522i | \(-0.693683\pi\) |
0.424786 | + | 0.905294i | \(0.360349\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −69.2345 | + | 119.918i | −0.520560 | + | 0.901637i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.28159 | − | 5.35873i | −0.0677489 | − | 0.0391148i | 0.465743 | − | 0.884920i | \(-0.345787\pi\) |
−0.533492 | + | 0.845805i | \(0.679120\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 21.2704 | + | 36.8414i | 0.153025 | + | 0.265046i | 0.932338 | − | 0.361588i | \(-0.117765\pi\) |
−0.779313 | + | 0.626634i | \(0.784432\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 28.4003i | − | 0.198603i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −49.8522 | −0.343808 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −84.7559 | + | 48.9338i | −0.568831 | + | 0.328415i | −0.756682 | − | 0.653783i | \(-0.773181\pi\) |
0.187851 | + | 0.982198i | \(0.439848\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.06713 | − | 3.58037i | 0.0136896 | − | 0.0237111i | −0.859099 | − | 0.511809i | \(-0.828976\pi\) |
0.872789 | + | 0.488098i | \(0.162309\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 27.4340 | + | 15.8390i | 0.176993 | + | 0.102187i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −115.393 | − | 199.866i | −0.734986 | − | 1.27303i | −0.954730 | − | 0.297475i | \(-0.903855\pi\) |
0.219744 | − | 0.975558i | \(-0.429478\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 86.0205i | − | 0.534289i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −76.8009 | −0.471171 | −0.235586 | − | 0.971854i | \(-0.575701\pi\) | ||||
−0.235586 | + | 0.971854i | \(0.575701\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 83.0831 | − | 47.9680i | 0.497503 | − | 0.287234i | −0.230179 | − | 0.973148i | \(-0.573931\pi\) |
0.727682 | + | 0.685915i | \(0.240598\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 22.2514 | − | 38.5405i | 0.131665 | − | 0.228050i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 88.2873 | + | 50.9727i | 0.510331 | + | 0.294640i | 0.732970 | − | 0.680261i | \(-0.238134\pi\) |
−0.222639 | + | 0.974901i | \(0.571467\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −17.8641 | − | 30.9416i | −0.102081 | − | 0.176809i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 174.549i | 0.975131i | 0.873086 | + | 0.487566i | \(0.162115\pi\) | ||||
−0.873086 | + | 0.487566i | \(0.837885\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −299.220 | −1.65315 | −0.826575 | − | 0.562827i | \(-0.809714\pi\) | ||||
−0.826575 | + | 0.562827i | \(0.809714\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 89.7214 | − | 51.8006i | 0.484980 | − | 0.280003i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.61931 | + | 4.53678i | −0.0140070 | + | 0.0242609i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −123.233 | − | 71.1486i | −0.645199 | − | 0.372506i | 0.141415 | − | 0.989950i | \(-0.454835\pi\) |
−0.786615 | + | 0.617444i | \(0.788168\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −111.425 | − | 192.995i | −0.577334 | − | 0.999972i | −0.995784 | − | 0.0917319i | \(-0.970760\pi\) |
0.418450 | − | 0.908240i | \(-0.362574\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 270.569i | 1.37345i | 0.726919 | + | 0.686723i | \(0.240952\pi\) | ||||
−0.726919 | + | 0.686723i | \(0.759048\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −140.476 | −0.705912 | −0.352956 | − | 0.935640i | \(-0.614823\pi\) | ||||
−0.352956 | + | 0.935640i | \(0.614823\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 137.966 | − | 79.6548i | 0.679636 | − | 0.392388i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 19.4620 | − | 33.7091i | 0.0949365 | − | 0.164435i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −42.7154 | − | 24.6617i | −0.204380 | − | 0.117999i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 103.996 | + | 180.127i | 0.492874 | + | 0.853682i | 0.999966 | − | 0.00820932i | \(-0.00261314\pi\) |
−0.507093 | + | 0.861892i | \(0.669280\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 60.4179i | − | 0.281013i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −101.231 | −0.466504 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 19.8877 | − | 11.4822i | 0.0899897 | − | 0.0519556i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −110.548 | + | 191.476i | −0.495733 | + | 0.858635i | −0.999988 | − | 0.00491996i | \(-0.998434\pi\) |
0.504255 | + | 0.863555i | \(0.331767\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −151.949 | − | 87.7280i | −0.669380 | − | 0.386467i | 0.126461 | − | 0.991972i | \(-0.459638\pi\) |
−0.795842 | + | 0.605505i | \(0.792971\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −107.009 | − | 185.344i | −0.467287 | − | 0.809364i | 0.532015 | − | 0.846735i | \(-0.321435\pi\) |
−0.999301 | + | 0.0373707i | \(0.988102\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 9.77506i | − | 0.0419530i | −0.999780 | − | 0.0209765i | \(-0.993322\pi\) | ||
0.999780 | − | 0.0209765i | \(-0.00667752\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 109.093 | 0.464224 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 248.842 | − | 143.669i | 1.04118 | − | 0.601125i | 0.121012 | − | 0.992651i | \(-0.461386\pi\) |
0.920167 | + | 0.391526i | \(0.128053\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 163.672 | − | 283.488i | 0.679137 | − | 1.17630i | −0.296105 | − | 0.955155i | \(-0.595688\pi\) |
0.975241 | − | 0.221143i | \(-0.0709789\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.98997 | + | 2.30361i | 0.0162856 | + | 0.00940248i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 108.109 | + | 187.250i | 0.437687 | + | 0.758096i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 290.903i | 1.15897i | 0.814981 | + | 0.579487i | \(0.196747\pi\) | ||||
−0.814981 | + | 0.579487i | \(0.803253\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 30.6410 | 0.121111 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −276.077 | + | 159.393i | −1.07423 | + | 0.620207i | −0.929334 | − | 0.369240i | \(-0.879618\pi\) |
−0.144896 | + | 0.989447i | \(0.546285\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −165.536 | + | 286.717i | −0.639135 | + | 1.10701i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 145.630 | + | 84.0798i | 0.553728 | + | 0.319695i | 0.750624 | − | 0.660729i | \(-0.229753\pi\) |
−0.196896 | + | 0.980424i | \(0.563086\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.0020 | + | 19.0560i | 0.0415170 | + | 0.0719095i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 129.572i | − | 0.481679i | −0.970565 | − | 0.240839i | \(-0.922577\pi\) | ||
0.970565 | − | 0.240839i | \(-0.0774227\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.6638 | −0.0578000 | −0.0289000 | − | 0.999582i | \(-0.509200\pi\) | ||||
−0.0289000 | + | 0.999582i | \(0.509200\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.0216 | − | 6.36331i | 0.0400784 | − | 0.0231393i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 46.1348 | − | 79.9078i | 0.166552 | − | 0.288476i | −0.770654 | − | 0.637254i | \(-0.780070\pi\) |
0.937205 | + | 0.348778i | \(0.113403\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −72.8094 | − | 42.0365i | −0.259108 | − | 0.149596i | 0.364819 | − | 0.931078i | \(-0.381131\pi\) |
−0.623928 | + | 0.781482i | \(0.714464\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 131.855 | + | 228.380i | 0.465920 | + | 0.806996i | 0.999243 | − | 0.0389154i | \(-0.0123903\pi\) |
−0.533323 | + | 0.845912i | \(0.679057\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 124.387i | 0.433403i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 284.764 | 0.985343 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 475.043 | − | 274.266i | 1.62131 | − | 0.936061i | 0.634735 | − | 0.772730i | \(-0.281109\pi\) |
0.986571 | − | 0.163331i | \(-0.0522239\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −98.2580 | + | 170.188i | −0.333078 | + | 0.576908i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −116.324 | − | 67.1599i | −0.389045 | − | 0.224615i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 96.5367 | + | 167.207i | 0.320720 | + | 0.555503i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 133.824i | − | 0.438769i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −192.466 | −0.626926 | −0.313463 | − | 0.949600i | \(-0.601489\pi\) | ||||
−0.313463 | + | 0.949600i | \(0.601489\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −392.392 | + | 226.548i | −1.26171 | + | 0.728449i | −0.973405 | − | 0.229090i | \(-0.926425\pi\) |
−0.288305 | + | 0.957539i | \(0.593092\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 32.8644 | − | 56.9228i | 0.104998 | − | 0.181862i | −0.808739 | − | 0.588167i | \(-0.799850\pi\) |
0.913737 | + | 0.406305i | \(0.133183\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.16081 | + | 2.40225i | 0.0131256 | + | 0.00757806i | 0.506548 | − | 0.862212i | \(-0.330921\pi\) |
−0.493423 | + | 0.869790i | \(0.664254\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 28.3735 | + | 49.1443i | 0.0889450 | + | 0.154057i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 39.8827i | − | 0.123476i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −55.7892 | −0.171659 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −301.914 | + | 174.310i | −0.917671 | + | 0.529818i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −72.6006 | + | 125.748i | −0.219337 | + | 0.379903i | −0.954605 | − | 0.297873i | \(-0.903723\pi\) |
0.735268 | + | 0.677776i | \(0.237056\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14.9389 | − | 8.62496i | −0.0445936 | − | 0.0257462i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 72.8538 | + | 126.187i | 0.216183 | + | 0.374441i | 0.953638 | − | 0.300956i | \(-0.0973057\pi\) |
−0.737455 | + | 0.675397i | \(0.763972\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 36.0592i | − | 0.105745i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 335.414 | 0.977884 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −161.823 | + | 93.4285i | −0.466349 | + | 0.269246i | −0.714710 | − | 0.699421i | \(-0.753441\pi\) |
0.248361 | + | 0.968667i | \(0.420108\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 90.7738 | − | 157.225i | 0.260097 | − | 0.450501i | −0.706171 | − | 0.708042i | \(-0.749579\pi\) |
0.966267 | + | 0.257541i | \(0.0829122\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 584.949 | + | 337.721i | 1.65708 | + | 0.956715i | 0.974052 | + | 0.226322i | \(0.0726703\pi\) |
0.683027 | + | 0.730393i | \(0.260663\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −88.9153 | − | 154.006i | −0.250466 | − | 0.433819i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 361.492i | − | 1.00694i | −0.864012 | − | 0.503471i | \(-0.832056\pi\) | ||
0.864012 | − | 0.503471i | \(-0.167944\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.5096 | 0.0401929 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.6539 | − | 6.72836i | 0.0319284 | − | 0.0184339i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 47.6816 | − | 82.5869i | 0.129923 | − | 0.225033i | −0.793724 | − | 0.608278i | \(-0.791860\pi\) |
0.923646 | + | 0.383246i | \(0.125194\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −60.8961 | − | 35.1584i | −0.164140 | − | 0.0947665i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −296.189 | − | 513.014i | −0.794071 | − | 1.37537i | −0.923427 | − | 0.383774i | \(-0.874624\pi\) |
0.129356 | − | 0.991598i | \(-0.458709\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 248.759i | − | 0.659839i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 289.491 | 0.763830 | 0.381915 | − | 0.924198i | \(-0.375265\pi\) | ||||
0.381915 | + | 0.924198i | \(0.375265\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 543.273 | − | 313.659i | 1.41847 | − | 0.818953i | 0.422304 | − | 0.906454i | \(-0.361221\pi\) |
0.996164 | + | 0.0875011i | \(0.0278881\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −20.3348 | + | 35.2209i | −0.0528177 | + | 0.0914829i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −345.046 | − | 199.212i | −0.887008 | − | 0.512114i | −0.0140453 | − | 0.999901i | \(-0.504471\pi\) |
−0.872963 | + | 0.487787i | \(0.837804\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.3881 | + | 21.4568i | 0.0316831 | + | 0.0548767i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 37.8515i | 0.0958267i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 101.894 | 0.256660 | 0.128330 | − | 0.991731i | \(-0.459038\pi\) | ||||
0.128330 | + | 0.991731i | \(0.459038\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −445.055 | + | 256.953i | −1.10986 | + | 0.640779i | −0.938794 | − | 0.344480i | \(-0.888055\pi\) |
−0.171069 | + | 0.985259i | \(0.554722\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −79.0357 | + | 136.894i | −0.196118 | + | 0.339687i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −102.130 | − | 58.9648i | −0.250934 | − | 0.144877i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −87.3358 | − | 151.270i | −0.213535 | − | 0.369854i | 0.739283 | − | 0.673394i | \(-0.235164\pi\) |
−0.952818 | + | 0.303541i | \(0.901831\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 627.993i | − | 1.52056i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 328.295 | 0.791073 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −404.169 | + | 233.347i | −0.964604 | + | 0.556914i | −0.897587 | − | 0.440837i | \(-0.854682\pi\) |
−0.0670171 | + | 0.997752i | \(0.521348\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 335.886 | − | 581.771i | 0.797828 | − | 1.38188i | −0.123200 | − | 0.992382i | \(-0.539316\pi\) |
0.921028 | − | 0.389497i | \(-0.127351\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.91200 | + | 5.14534i | 0.0209694 | + | 0.0121067i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 213.827 | + | 370.359i | 0.500766 | + | 0.867352i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 690.758i | 1.60269i | 0.598204 | + | 0.801344i | \(0.295881\pi\) | ||||
−0.598204 | + | 0.801344i | \(0.704119\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 418.521 | 0.966562 | 0.483281 | − | 0.875465i | \(-0.339445\pi\) | ||||
0.483281 | + | 0.875465i | \(0.339445\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −202.023 | + | 116.638i | −0.462296 | + | 0.266906i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 180.726 | − | 313.027i | 0.411677 | − | 0.713045i | −0.583397 | − | 0.812187i | \(-0.698277\pi\) |
0.995073 | + | 0.0991427i | \(0.0316100\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 579.959 | + | 334.839i | 1.30916 | + | 0.755845i | 0.981956 | − | 0.189108i | \(-0.0605595\pi\) |
0.327206 | + | 0.944953i | \(0.393893\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −112.143 | − | 194.237i | −0.252007 | − | 0.436489i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 236.187i | − | 0.526028i | −0.964792 | − | 0.263014i | \(-0.915283\pi\) | ||
0.964792 | − | 0.263014i | \(-0.0847166\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −44.3072 | −0.0982422 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 154.397 | − | 89.1409i | 0.339333 | − | 0.195914i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 346.900 | − | 600.848i | 0.759080 | − | 1.31477i | −0.184240 | − | 0.982881i | \(-0.558982\pi\) |
0.943320 | − | 0.331884i | \(-0.107684\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 290.417 | + | 167.672i | 0.629971 | + | 0.363714i | 0.780741 | − | 0.624855i | \(-0.214842\pi\) |
−0.150770 | + | 0.988569i | \(0.548175\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 180.088 | + | 311.922i | 0.388960 | + | 0.673698i | 0.992310 | − | 0.123778i | \(-0.0395012\pi\) |
−0.603350 | + | 0.797476i | \(0.706168\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 679.050i | − | 1.45407i | −0.686602 | − | 0.727034i | \(-0.740898\pi\) | ||
0.686602 | − | 0.727034i | \(-0.259102\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 55.1245 | 0.117536 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −59.5599 | + | 34.3869i | −0.125919 | + | 0.0726996i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −48.4452 | + | 83.9095i | −0.101990 | + | 0.176652i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −188.160 | − | 108.634i | −0.392818 | − | 0.226794i | 0.290562 | − | 0.956856i | \(-0.406158\pi\) |
−0.683381 | + | 0.730062i | \(0.739491\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 258.482 | + | 447.704i | 0.537384 | + | 0.930777i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 162.372i | − | 0.334788i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 737.594 | 1.51457 | 0.757283 | − | 0.653086i | \(-0.226526\pi\) | ||||
0.757283 | + | 0.653086i | \(0.226526\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −657.536 | + | 379.629i | −1.33918 | + | 0.773175i | −0.986685 | − | 0.162640i | \(-0.947999\pi\) |
−0.352492 | + | 0.935815i | \(0.614666\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −22.9427 | + | 39.7379i | −0.0465369 | + | 0.0806042i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 492.146 | + | 284.141i | 0.990234 | + | 0.571712i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 333.289 | + | 577.274i | 0.667915 | + | 1.15686i | 0.978486 | + | 0.206312i | \(0.0661462\pi\) |
−0.310572 | + | 0.950550i | \(0.600520\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 180.800i | 0.359444i | 0.983717 | + | 0.179722i | \(0.0575199\pi\) | ||||
−0.983717 | + | 0.179722i | \(0.942480\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 332.030 | 0.657485 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −318.561 | + | 183.921i | −0.625856 | + | 0.361338i | −0.779146 | − | 0.626843i | \(-0.784347\pi\) |
0.153289 | + | 0.988181i | \(0.451013\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −21.5014 | + | 37.2415i | −0.0420770 | + | 0.0728796i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 274.950 | + | 158.742i | 0.533883 | + | 0.308238i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −62.0902 | − | 107.543i | −0.120097 | − | 0.208014i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 428.171i | − | 0.821825i | −0.911675 | − | 0.410913i | \(-0.865210\pi\) | ||
0.911675 | − | 0.410913i | \(-0.134790\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 742.878 | 1.42042 | 0.710208 | − | 0.703992i | \(-0.248601\pi\) | ||||
0.710208 | + | 0.703992i | \(0.248601\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 25.2510 | − | 14.5787i | 0.0479146 | − | 0.0276635i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −192.041 | + | 332.625i | −0.363027 | + | 0.628782i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 168.206 | + | 97.1140i | 0.315584 | + | 0.182203i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.04883 | + | 7.01278i | 0.00756791 | + | 0.0131080i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 5.24441i | − | 0.00972989i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −431.532 | −0.797656 | −0.398828 | − | 0.917026i | \(-0.630583\pi\) | ||||
−0.398828 | + | 0.917026i | \(0.630583\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 373.742 | − | 215.780i | 0.685766 | − | 0.395927i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −72.9216 | + | 126.304i | −0.133312 | + | 0.230903i | −0.924951 | − | 0.380086i | \(-0.875895\pi\) |
0.791639 | + | 0.610989i | \(0.209228\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −374.146 | − | 216.013i | −0.679030 | − | 0.392038i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −60.4799 | − | 104.754i | −0.109367 | − | 0.189429i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 680.396i | 1.22154i | 0.791809 | + | 0.610769i | \(0.209140\pi\) | ||||
−0.791809 | + | 0.610769i | \(0.790860\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 301.481 | 0.539323 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 797.888 | − | 460.661i | 1.41721 | − | 0.818226i | 0.421155 | − | 0.906988i | \(-0.361625\pi\) |
0.996053 | + | 0.0887629i | \(0.0282914\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −97.1926 | + | 168.343i | −0.172022 | + | 0.297951i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 685.403 | + | 395.717i | 1.20457 | + | 0.695461i | 0.961569 | − | 0.274564i | \(-0.0885335\pi\) |
0.243005 | + | 0.970025i | \(0.421867\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 529.700 | + | 917.468i | 0.927672 | + | 1.60677i | 0.787207 | + | 0.616688i | \(0.211526\pi\) |
0.140464 | + | 0.990086i | \(0.455141\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 60.1908i | − | 0.104680i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −526.293 | −0.912119 | −0.456060 | − | 0.889949i | \(-0.650740\pi\) | ||||
−0.456060 | + | 0.889949i | \(0.650740\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −908.558 | + | 524.556i | −1.56378 | + | 0.902850i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.5236 | − | 21.6915i | 0.0214813 | − | 0.0372067i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −808.682 | − | 466.893i | −1.37765 | − | 0.795388i | −0.385776 | − | 0.922592i | \(-0.626066\pi\) |
−0.991877 | + | 0.127204i | \(0.959400\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 137.263 | + | 237.747i | 0.233044 | + | 0.403645i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 686.623i | − | 1.15788i | −0.815370 | − | 0.578940i | \(-0.803467\pi\) | ||
0.815370 | − | 0.578940i | \(-0.196533\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −32.8853 | −0.0552694 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 217.781 | − | 125.736i | 0.363574 | − | 0.209910i | −0.307073 | − | 0.951686i | \(-0.599350\pi\) |
0.670647 | + | 0.741776i | \(0.266016\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 304.733 | − | 527.812i | 0.507043 | − | 0.878223i | −0.492924 | − | 0.870072i | \(-0.664072\pi\) |
0.999967 | − | 0.00815116i | \(-0.00259462\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 221.770 | + | 128.039i | 0.366561 | + | 0.211634i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 414.080 | + | 717.208i | 0.682175 | + | 1.18156i | 0.974316 | + | 0.225187i | \(0.0722993\pi\) |
−0.292140 | + | 0.956375i | \(0.594367\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 544.365i | 0.890941i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 534.809 | 0.872445 | 0.436223 | − | 0.899839i | \(-0.356316\pi\) | ||||
0.436223 | + | 0.899839i | \(0.356316\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −384.859 | + | 222.199i | −0.623759 | + | 0.360127i | −0.778331 | − | 0.627854i | \(-0.783933\pi\) |
0.154572 | + | 0.987982i | \(0.450600\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 149.322 | − | 258.633i | 0.241231 | − | 0.417824i | −0.719834 | − | 0.694146i | \(-0.755782\pi\) |
0.961065 | + | 0.276322i | \(0.0891156\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 620.712 | + | 358.368i | 0.996327 | + | 0.575230i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.5000 | − | 21.6506i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 95.3574i | − | 0.151602i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1154.93 | 1.83031 | 0.915155 | − | 0.403103i | \(-0.132068\pi\) | ||||
0.915155 | + | 0.403103i | \(0.132068\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 161.820 | − | 93.4267i | 0.254834 | − | 0.147129i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11.4949 | + | 19.9097i | −0.0180453 | + | 0.0312554i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −588.759 | − | 339.920i | −0.918502 | − | 0.530297i | −0.0353448 | − | 0.999375i | \(-0.511253\pi\) |
−0.883157 | + | 0.469078i | \(0.844586\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −217.288 | − | 376.354i | −0.337929 | − | 0.585310i | 0.646114 | − | 0.763241i | \(-0.276393\pi\) |
−0.984043 | + | 0.177931i | \(0.943060\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 222.972i | 0.344625i | 0.985042 | + | 0.172312i | \(0.0551239\pi\) | ||||
−0.985042 | + | 0.172312i | \(0.944876\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 223.695 | 0.344676 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 453.763 | − | 261.980i | 0.694889 | − | 0.401194i | −0.110552 | − | 0.993870i | \(-0.535262\pi\) |
0.805441 | + | 0.592676i | \(0.201929\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 24.8316 | − | 43.0096i | 0.0379109 | − | 0.0656635i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 249.789 | + | 144.216i | 0.379043 | + | 0.218841i | 0.677402 | − | 0.735613i | \(-0.263106\pi\) |
−0.298359 | + | 0.954454i | \(0.596439\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.7991 | − | 42.9533i | −0.0375176 | − | 0.0649823i | 0.846657 | − | 0.532139i | \(-0.178612\pi\) |
−0.884174 | + | 0.467157i | \(0.845278\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 309.626i | − | 0.465603i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 268.386 | 0.402378 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −131.924 | + | 76.1664i | −0.196608 | + | 0.113512i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −306.034 | + | 530.066i | −0.454731 | + | 0.787617i | −0.998673 | − | 0.0515058i | \(-0.983598\pi\) |
0.543942 | + | 0.839123i | \(0.316931\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 931.146 | + | 537.597i | 1.37540 | + | 0.794087i | 0.991602 | − | 0.129330i | \(-0.0412825\pi\) |
0.383798 | + | 0.923417i | \(0.374616\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 259.441 | + | 449.365i | 0.382093 | + | 0.661804i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 718.621i | − | 1.05215i | −0.850437 | − | 0.526077i | \(-0.823663\pi\) | ||
0.850437 | − | 0.526077i | \(-0.176337\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 23.9650 | 0.0349854 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −95.0883 | + | 54.8992i | −0.138009 | + | 0.0796796i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 420.368 | − | 728.099i | 0.608347 | − | 1.05369i | −0.383165 | − | 0.923680i | \(-0.625166\pi\) |
0.991513 | − | 0.130009i | \(-0.0415006\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −82.3800 | − | 47.5621i | −0.118532 | − | 0.0684347i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.9133 | − | 31.0268i | −0.0257006 | − | 0.0445148i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 614.419i | − | 0.876490i | −0.898856 | − | 0.438245i | \(-0.855600\pi\) | ||
0.898856 | − | 0.438245i | \(-0.144400\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 897.823 | 1.27713 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −918.893 | + | 530.523i | −1.29971 | + | 0.750387i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 434.681 | − | 752.890i | 0.613091 | − | 1.06190i | −0.377625 | − | 0.925958i | \(-0.623259\pi\) |
0.990716 | − | 0.135946i | \(-0.0434074\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −147.694 | − | 85.2714i | −0.207145 | − | 0.119595i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 31.7525 | + | 54.9969i | 0.0444091 | + | 0.0769188i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1307.10i | 1.81794i | 0.416859 | + | 0.908971i | \(0.363131\pi\) | ||||
−0.416859 | + | 0.908971i | \(0.636869\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1014.57 | −1.40716 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 96.5384 | − | 55.7365i | 0.133156 | − | 0.0768779i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 112.223 | − | 194.376i | 0.154365 | − | 0.267367i | −0.778463 | − | 0.627691i | \(-0.784000\pi\) |
0.932827 | + | 0.360323i | \(0.117334\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −48.1599 | − | 27.8051i | −0.0658822 | − | 0.0380371i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −571.310 | − | 989.538i | −0.779413 | − | 1.34998i | −0.932280 | − | 0.361737i | \(-0.882184\pi\) |
0.152867 | − | 0.988247i | \(-0.451149\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19.6356i | 0.0266427i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −450.991 | −0.610272 | −0.305136 | − | 0.952309i | \(-0.598702\pi\) | ||||
−0.305136 | + | 0.952309i | \(0.598702\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1074.55 | − | 620.394i | 1.44624 | − | 0.834985i | 0.447983 | − | 0.894042i | \(-0.352143\pi\) |
0.998255 | + | 0.0590568i | \(0.0188093\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 109.419 | − | 189.520i | 0.146872 | − | 0.254389i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −22.4103 | − | 12.9386i | −0.0299203 | − | 0.0172745i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 226.995 | + | 393.168i | 0.302257 | + | 0.523525i | 0.976647 | − | 0.214850i | \(-0.0689264\pi\) |
−0.674389 | + | 0.738376i | \(0.735593\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.24448i | 0.0122443i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.7572 | −0.0247784 | −0.0123892 | − | 0.999923i | \(-0.503944\pi\) | ||||
−0.0123892 | + | 0.999923i | \(0.503944\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −655.215 | + | 378.289i | −0.860992 | + | 0.497094i | −0.864344 | − | 0.502900i | \(-0.832266\pi\) |
0.00335213 | + | 0.999994i | \(0.498933\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −689.555 | + | 1194.34i | −0.903742 | + | 1.56533i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −849.226 | − | 490.301i | −1.10721 | − | 0.639245i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −583.868 | − | 1011.29i | −0.759257 | − | 1.31507i | −0.943230 | − | 0.332140i | \(-0.892229\pi\) |
0.183974 | − | 0.982931i | \(-0.441104\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 763.809i | − | 0.988110i | −0.869431 | − | 0.494055i | \(-0.835514\pi\) | ||
0.869431 | − | 0.494055i | \(-0.164486\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −70.8342 | −0.0913990 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 292.128 | − | 168.660i | 0.375004 | − | 0.216509i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −101.213 | + | 175.305i | −0.129594 | + | 0.224463i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 446.914 | + | 258.026i | 0.569318 | + | 0.328696i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −248.732 | − | 430.817i | −0.316051 | − | 0.547416i | 0.663609 | − | 0.748079i | \(-0.269024\pi\) |
−0.979660 | + | 0.200663i | \(0.935690\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 621.184i | − | 0.785315i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 667.775 | 0.842087 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1163.28 | + | 671.621i | −1.45958 | + | 0.842686i | −0.998990 | − | 0.0449296i | \(-0.985694\pi\) |
−0.460585 | + | 0.887616i | \(0.652360\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 50.2059 | − | 86.9591i | 0.0628359 | − | 0.108835i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.2656 | − | 7.65891i | −0.0165201 | − | 0.00953787i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 96.1739 | + | 166.578i | 0.119471 | + | 0.206929i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 244.633i | − | 0.302389i | −0.988504 | − | 0.151195i | \(-0.951688\pi\) | ||
0.988504 | − | 0.151195i | \(-0.0483120\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1182.65 | −1.45827 | −0.729133 | − | 0.684372i | \(-0.760076\pi\) | ||||
−0.729133 | + | 0.684372i | \(0.760076\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 148.724 | − | 85.8660i | 0.182484 | − | 0.105357i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 261.795 | − | 453.442i | 0.320434 | − | 0.555008i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −795.256 | − | 459.141i | −0.968643 | − | 0.559246i | −0.0698205 | − | 0.997560i | \(-0.522243\pi\) |
−0.898822 | + | 0.438313i | \(0.855576\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −406.279 | − | 703.695i | −0.493656 | − | 0.855037i | 0.506318 | − | 0.862347i | \(-0.331006\pi\) |
−0.999973 | + | 0.00731049i | \(0.997673\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 476.892i | 0.576653i | 0.957532 | + | 0.288327i | \(0.0930989\pi\) | ||||
−0.957532 | + | 0.288327i | \(0.906901\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −369.534 | −0.445758 | −0.222879 | − | 0.974846i | \(-0.571546\pi\) | ||||
−0.222879 | + | 0.974846i | \(0.571546\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.67247 | − | 2.12030i | 0.00440873 | − | 0.00254538i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −107.260 | + | 185.779i | −0.128455 | + | 0.222490i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 728.282 | + | 420.474i | 0.868036 | + | 0.501161i | 0.866695 | − | 0.498838i | \(-0.166240\pi\) |
0.00134090 | + | 0.999999i | \(0.499573\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −171.976 | − | 297.870i | −0.204489 | − | 0.354186i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 99.5111i | 0.117765i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −818.330 | −0.966151 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −483.026 | + | 278.875i | −0.567599 | + | 0.327703i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −362.604 | + | 628.048i | −0.425092 | + | 0.736282i | −0.996429 | − | 0.0844341i | \(-0.973092\pi\) |
0.571337 | + | 0.820716i | \(0.306425\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −732.868 | − | 423.121i | −0.855155 | − | 0.493724i | 0.00723204 | − | 0.999974i | \(-0.497698\pi\) |
−0.862387 | + | 0.506250i | \(0.831031\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 352.776 | + | 611.025i | 0.410682 | + | 0.711321i | 0.994964 | − | 0.100229i | \(-0.0319574\pi\) |
−0.584283 | + | 0.811550i | \(0.698624\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 626.198i | − | 0.725606i | −0.931866 | − | 0.362803i | \(-0.881820\pi\) | ||
0.931866 | − | 0.362803i | \(-0.118180\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −227.957 | −0.263534 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 37.3140 | − | 21.5433i | 0.0429390 | − | 0.0247909i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 43.0380 | − | 74.5440i | 0.0494122 | − | 0.0855844i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 69.1875 | + | 39.9454i | 0.0790715 | + | 0.0456519i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 288.812 | + | 500.237i | 0.329318 | + | 0.570395i | 0.982377 | − | 0.186912i | \(-0.0598479\pi\) |
−0.653059 | + | 0.757307i | \(0.726515\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1719.11i | 1.95131i | 0.219306 | + | 0.975656i | \(0.429621\pi\) | ||||
−0.219306 | + | 0.975656i | \(0.570379\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −356.656 | −0.403914 | −0.201957 | − | 0.979394i | \(-0.564730\pi\) | ||||
−0.201957 | + | 0.979394i | \(0.564730\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 428.591 | − | 247.447i | 0.483192 | − | 0.278971i | −0.238554 | − | 0.971129i | \(-0.576673\pi\) |
0.721746 | + | 0.692158i | \(0.243340\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −298.558 | + | 517.117i | −0.335835 | + | 0.581684i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 818.750 | + | 472.705i | 0.916853 | + | 0.529345i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −195.151 | − | 338.012i | −0.218046 | − | 0.377667i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 315.844i | − | 0.351328i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.2531 | 0.0224784 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 579.437 | − | 334.538i | 0.640262 | − | 0.369655i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −311.723 | + | 539.919i | −0.343685 | + | 0.595280i | −0.985114 | − | 0.171902i | \(-0.945009\pi\) |
0.641429 | + | 0.767183i | \(0.278342\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1527.46 | − | 881.879i | −1.67668 | − | 0.968034i | −0.963752 | − | 0.266800i | \(-0.914034\pi\) |
−0.712931 | − | 0.701234i | \(-0.752633\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −186.850 | − | 323.633i | −0.204655 | − | 0.354472i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 158.705i | 0.173070i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −540.616 | −0.588266 | −0.294133 | − | 0.955765i | \(-0.595031\pi\) | ||||
−0.294133 | + | 0.955765i | \(0.595031\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 768.479 | − | 443.682i | 0.832588 | − | 0.480695i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −115.830 | + | 200.623i | −0.125221 | + | 0.216890i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 206.950 | + | 119.482i | 0.222766 | + | 0.128614i | 0.607230 | − | 0.794526i | \(-0.292281\pi\) |
−0.384464 | + | 0.923140i | \(0.625614\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19.9634 | + | 34.5776i | 0.0214429 | + | 0.0371403i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 11.7139i | − | 0.0125283i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −75.1773 | −0.0802320 | −0.0401160 | − | 0.999195i | \(-0.512773\pi\) | ||||
−0.0401160 | + | 0.999195i | \(0.512773\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 57.3372 | − | 33.1037i | 0.0609322 | − | 0.0351792i | −0.469224 | − | 0.883079i | \(-0.655466\pi\) |
0.530157 | + | 0.847900i | \(0.322133\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −104.776 | + | 181.477i | −0.111109 | + | 0.192447i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −225.603 | − | 130.252i | −0.238230 | − | 0.137542i | 0.376133 | − | 0.926566i | \(-0.377254\pi\) |
−0.614363 | + | 0.789024i | \(0.710587\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 33.5741 | + | 58.1520i | 0.0353784 | + | 0.0612771i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 502.854i | 0.527654i | 0.964570 | + | 0.263827i | \(0.0849847\pi\) | ||||
−0.964570 | + | 0.263827i | \(0.915015\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 318.186 | 0.333179 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −66.3231 | + | 38.2917i | −0.0691586 | + | 0.0399287i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 380.150 | − | 658.439i | 0.395578 | − | 0.685161i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 431.549 | + | 249.155i | 0.447201 | + | 0.258192i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −308.935 | − | 535.091i | −0.319478 | − | 0.553352i | 0.660901 | − | 0.750473i | \(-0.270174\pi\) |
−0.980379 | + | 0.197121i | \(0.936841\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 240.669i | 0.247856i | 0.992291 | + | 0.123928i | \(0.0395492\pi\) | ||||
−0.992291 | + | 0.123928i | \(0.960451\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 303.982 | 0.312417 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1293.59 | − | 746.857i | 1.32405 | − | 0.764439i | 0.339675 | − | 0.940543i | \(-0.389683\pi\) |
0.984372 | + | 0.176104i | \(0.0563494\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −127.653 | + | 221.101i | −0.130391 | + | 0.225844i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −674.535 | − | 389.443i | −0.686200 | − | 0.396178i | 0.115987 | − | 0.993251i | \(-0.462997\pi\) |
−0.802187 | + | 0.597073i | \(0.796330\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −302.505 | − | 523.955i | −0.307112 | − | 0.531934i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 325.267i | 0.328885i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −703.289 | −0.709676 | −0.354838 | − | 0.934928i | \(-0.615464\pi\) | ||||
−0.354838 | + | 0.934928i | \(0.615464\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 272.032 | − | 157.057i | 0.273399 | − | 0.157847i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 293.948 | − | 509.133i | 0.294833 | − | 0.510665i | −0.680113 | − | 0.733107i | \(-0.738069\pi\) |
0.974946 | + | 0.222442i | \(0.0714027\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1620.3.o.g.1241.4 | 32 | ||
3.2 | odd | 2 | inner | 1620.3.o.g.1241.12 | 32 | ||
9.2 | odd | 6 | 1620.3.g.c.161.10 | yes | 16 | ||
9.4 | even | 3 | inner | 1620.3.o.g.701.12 | 32 | ||
9.5 | odd | 6 | inner | 1620.3.o.g.701.4 | 32 | ||
9.7 | even | 3 | 1620.3.g.c.161.2 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1620.3.g.c.161.2 | ✓ | 16 | 9.7 | even | 3 | ||
1620.3.g.c.161.10 | yes | 16 | 9.2 | odd | 6 | ||
1620.3.o.g.701.4 | 32 | 9.5 | odd | 6 | inner | ||
1620.3.o.g.701.12 | 32 | 9.4 | even | 3 | inner | ||
1620.3.o.g.1241.4 | 32 | 1.1 | even | 1 | trivial | ||
1620.3.o.g.1241.12 | 32 | 3.2 | odd | 2 | inner |