Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [456,2,Mod(419,456)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(456, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("456.419");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 456 = 2^{3} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 456.j (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: | \(3.64117833217\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 419.2 | ||
Character | \(\chi\) | \(=\) | 456.419 |
Dual form | 456.2.j.e.419.1 |
$q$-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 \(\left(\mathbb{Z}/456\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(343\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.34037 | + | 0.450999i | −0.947787 | + | 0.318904i | ||||
\(3\) | −1.59320 | − | 0.679496i | −0.919834 | − | 0.392307i | ||||
\(4\) | 1.59320 | − | 1.20901i | 0.796600 | − | 0.604507i | ||||
\(5\) | 2.84644 | 1.27296 | 0.636482 | − | 0.771291i | \(-0.280389\pi\) | ||||
0.636482 | + | 0.771291i | \(0.280389\pi\) | |||||||
\(6\) | 2.44193 | + | 0.192246i | 0.996915 | + | 0.0784842i | ||||
\(7\) | 0.466225i | 0.176216i | 0.996111 | + | 0.0881082i | \(0.0280821\pi\) | ||||
−0.996111 | + | 0.0881082i | \(0.971918\pi\) | |||||||
\(8\) | −1.59022 | + | 2.33906i | −0.562227 | + | 0.826983i | ||||
\(9\) | 2.07657 | + | 2.16515i | 0.692190 | + | 0.721715i | ||||
\(10\) | −3.81529 | + | 1.28374i | −1.20650 | + | 0.405954i | ||||
\(11\) | 4.27688i | 1.28953i | 0.764382 | + | 0.644764i | \(0.223044\pi\) | ||||
−0.764382 | + | 0.644764i | \(0.776956\pi\) | |||||||
\(12\) | −3.35981 | + | 0.843628i | −0.969892 | + | 0.243534i | ||||
\(13\) | − | 4.00344i | − | 1.11036i | −0.831732 | − | 0.555178i | \(-0.812650\pi\) | ||
0.831732 | − | 0.555178i | \(-0.187350\pi\) | |||||||
\(14\) | −0.210267 | − | 0.624915i | −0.0561962 | − | 0.167016i | ||||
\(15\) | −4.53494 | − | 1.93414i | −1.17092 | − | 0.499393i | ||||
\(16\) | 1.07657 | − | 3.85240i | 0.269143 | − | 0.963100i | ||||
\(17\) | 3.48404i | 0.845004i | 0.906362 | + | 0.422502i | \(0.138848\pi\) | ||||
−0.906362 | + | 0.422502i | \(0.861152\pi\) | |||||||
\(18\) | −3.75986 | − | 1.96557i | −0.886207 | − | 0.463289i | ||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 4.53494 | − | 3.44138i | 1.01404 | − | 0.769516i | ||||
\(21\) | 0.316798 | − | 0.742789i | 0.0691309 | − | 0.162090i | ||||
\(22\) | −1.92887 | − | 5.73261i | −0.411236 | − | 1.22220i | ||||
\(23\) | −1.49782 | −0.312317 | −0.156158 | − | 0.987732i | \(-0.549911\pi\) | ||||
−0.156158 | + | 0.987732i | \(0.549911\pi\) | |||||||
\(24\) | 4.12292 | − | 2.64605i | 0.841587 | − | 0.540122i | ||||
\(25\) | 3.10219 | 0.620439 | ||||||||
\(26\) | 1.80555 | + | 5.36611i | 0.354097 | + | 1.05238i | ||||
\(27\) | −1.83719 | − | 4.86053i | −0.353566 | − | 0.935409i | ||||
\(28\) | 0.563672 | + | 0.742789i | 0.106524 | + | 0.140374i | ||||
\(29\) | 8.54193 | 1.58620 | 0.793098 | − | 0.609094i | \(-0.208467\pi\) | ||||
0.793098 | + | 0.609094i | \(0.208467\pi\) | |||||||
\(30\) | 6.95081 | + | 0.547217i | 1.26904 | + | 0.0999076i | ||||
\(31\) | 7.64656i | 1.37336i | 0.726959 | + | 0.686681i | \(0.240933\pi\) | ||||
−0.726959 | + | 0.686681i | \(0.759067\pi\) | |||||||
\(32\) | 0.294423 | + | 5.64919i | 0.0520471 | + | 0.998645i | ||||
\(33\) | 2.90612 | − | 6.81392i | 0.505891 | − | 1.18615i | ||||
\(34\) | −1.57130 | − | 4.66992i | −0.269476 | − | 0.800884i | ||||
\(35\) | 1.32708i | 0.224317i | ||||||||
\(36\) | 5.92608 | + | 0.938906i | 0.987680 | + | 0.156484i | ||||
\(37\) | 0.360333i | 0.0592385i | 0.999561 | + | 0.0296192i | \(0.00942947\pi\) | ||||
−0.999561 | + | 0.0296192i | \(0.990571\pi\) | |||||||
\(38\) | −1.34037 | + | 0.450999i | −0.217437 | + | 0.0731617i | ||||
\(39\) | −2.72032 | + | 6.37829i | −0.435600 | + | 1.02134i | ||||
\(40\) | −4.52645 | + | 6.65799i | −0.715695 | + | 1.05272i | ||||
\(41\) | 3.88529i | 0.606780i | 0.952867 | + | 0.303390i | \(0.0981184\pi\) | ||||
−0.952867 | + | 0.303390i | \(0.901882\pi\) | |||||||
\(42\) | −0.0896300 | + | 1.13849i | −0.0138302 | + | 0.175673i | ||||
\(43\) | 6.31001 | 0.962268 | 0.481134 | − | 0.876647i | \(-0.340225\pi\) | ||||
0.481134 | + | 0.876647i | \(0.340225\pi\) | |||||||
\(44\) | 5.17081 | + | 6.81392i | 0.779528 | + | 1.02724i | ||||
\(45\) | 5.91082 | + | 6.16295i | 0.881134 | + | 0.918718i | ||||
\(46\) | 2.00764 | − | 0.675515i | 0.296010 | − | 0.0995992i | ||||
\(47\) | 3.96323 | 0.578097 | 0.289048 | − | 0.957314i | \(-0.406661\pi\) | ||||
0.289048 | + | 0.957314i | \(0.406661\pi\) | |||||||
\(48\) | −4.33288 | + | 5.40612i | −0.625398 | + | 0.780306i | ||||
\(49\) | 6.78263 | 0.968948 | ||||||||
\(50\) | −4.15810 | + | 1.39909i | −0.588044 | + | 0.197861i | ||||
\(51\) | 2.36739 | − | 5.55077i | 0.331501 | − | 0.777264i | ||||
\(52\) | −4.84022 | − | 6.37829i | −0.671218 | − | 0.884509i | ||||
\(53\) | 1.30160 | 0.178788 | 0.0893940 | − | 0.995996i | \(-0.471507\pi\) | ||||
0.0893940 | + | 0.995996i | \(0.471507\pi\) | |||||||
\(54\) | 4.65461 | + | 5.68635i | 0.633412 | + | 0.773815i | ||||
\(55\) | 12.1739i | 1.64152i | ||||||||
\(56\) | −1.09053 | − | 0.741399i | −0.145728 | − | 0.0990736i | ||||
\(57\) | −1.59320 | − | 0.679496i | −0.211024 | − | 0.0900014i | ||||
\(58\) | −11.4494 | + | 3.85240i | −1.50338 | + | 0.505845i | ||||
\(59\) | − | 3.00712i | − | 0.391494i | −0.980654 | − | 0.195747i | \(-0.937287\pi\) | ||
0.980654 | − | 0.195747i | \(-0.0627132\pi\) | |||||||
\(60\) | −9.56347 | + | 2.40133i | −1.23464 | + | 0.310011i | ||||
\(61\) | − | 2.20911i | − | 0.282848i | −0.989949 | − | 0.141424i | \(-0.954832\pi\) | ||
0.989949 | − | 0.141424i | \(-0.0451681\pi\) | |||||||
\(62\) | −3.44859 | − | 10.2492i | −0.437971 | − | 1.30165i | ||||
\(63\) | −1.00944 | + | 0.968149i | −0.127178 | + | 0.121975i | ||||
\(64\) | −2.94241 | − | 7.43923i | −0.367802 | − | 0.929904i | ||||
\(65\) | − | 11.3955i | − | 1.41344i | ||||||
\(66\) | −0.822214 | + | 10.4439i | −0.101208 | + | 1.28555i | ||||
\(67\) | 11.7881 | 1.44015 | 0.720073 | − | 0.693898i | \(-0.244108\pi\) | ||||
0.720073 | + | 0.693898i | \(0.244108\pi\) | |||||||
\(68\) | 4.21226 | + | 5.55077i | 0.510811 | + | 0.673130i | ||||
\(69\) | 2.38632 | + | 1.01776i | 0.287280 | + | 0.122524i | ||||
\(70\) | −0.598511 | − | 1.77878i | −0.0715358 | − | 0.212605i | ||||
\(71\) | −6.80967 | −0.808159 | −0.404079 | − | 0.914724i | \(-0.632408\pi\) | ||||
−0.404079 | + | 0.914724i | \(0.632408\pi\) | |||||||
\(72\) | −8.36661 | + | 1.41417i | −0.986014 | + | 0.166662i | ||||
\(73\) | −1.40984 | −0.165009 | −0.0825044 | − | 0.996591i | \(-0.526292\pi\) | ||||
−0.0825044 | + | 0.996591i | \(0.526292\pi\) | |||||||
\(74\) | −0.162510 | − | 0.482981i | −0.0188914 | − | 0.0561454i | ||||
\(75\) | −4.94241 | − | 2.10793i | −0.570701 | − | 0.243403i | ||||
\(76\) | 1.59320 | − | 1.20901i | 0.182753 | − | 0.138683i | ||||
\(77\) | −1.99399 | −0.227236 | ||||||||
\(78\) | 0.769648 | − | 9.77615i | 0.0871454 | − | 1.10693i | ||||
\(79\) | − | 14.6441i | − | 1.64759i | −0.566890 | − | 0.823794i | \(-0.691853\pi\) | ||
0.566890 | − | 0.823794i | \(-0.308147\pi\) | |||||||
\(80\) | 3.06439 | − | 10.9656i | 0.342609 | − | 1.22599i | ||||
\(81\) | −0.375707 | + | 8.99215i | −0.0417452 | + | 0.999128i | ||||
\(82\) | −1.75226 | − | 5.20773i | −0.193505 | − | 0.575098i | ||||
\(83\) | − | 14.6883i | − | 1.61225i | −0.591743 | − | 0.806126i | \(-0.701560\pi\) | ||
0.591743 | − | 0.806126i | \(-0.298440\pi\) | |||||||
\(84\) | −0.393320 | − | 1.56642i | −0.0429148 | − | 0.170911i | ||||
\(85\) | 9.91710i | 1.07566i | ||||||||
\(86\) | −8.45777 | + | 2.84581i | −0.912025 | + | 0.306872i | ||||
\(87\) | −13.6090 | − | 5.80420i | −1.45904 | − | 0.622276i | ||||
\(88\) | −10.0039 | − | 6.80117i | −1.06642 | − | 0.725007i | ||||
\(89\) | 15.8556i | 1.68069i | 0.542050 | + | 0.840346i | \(0.317648\pi\) | ||||
−0.542050 | + | 0.840346i | \(0.682352\pi\) | |||||||
\(90\) | −10.7022 | − | 5.59487i | −1.12811 | − | 0.589751i | ||||
\(91\) | 1.86651 | 0.195663 | ||||||||
\(92\) | −2.38632 | + | 1.81088i | −0.248791 | + | 0.188798i | ||||
\(93\) | 5.19580 | − | 12.1825i | 0.538780 | − | 1.26327i | ||||
\(94\) | −5.31221 | + | 1.78741i | −0.547913 | + | 0.184358i | ||||
\(95\) | 2.84644 | 0.292038 | ||||||||
\(96\) | 3.36952 | − | 9.20034i | 0.343901 | − | 0.939006i | ||||
\(97\) | −14.3334 | −1.45534 | −0.727668 | − | 0.685930i | \(-0.759396\pi\) | ||||
−0.727668 | + | 0.685930i | \(0.759396\pi\) | |||||||
\(98\) | −9.09126 | + | 3.05896i | −0.918356 | + | 0.309002i | ||||
\(99\) | −9.26006 | + | 8.88124i | −0.930671 | + | 0.892598i | ||||
\(100\) | 4.94241 | − | 3.75060i | 0.494241 | − | 0.375060i | ||||
\(101\) | −0.908973 | −0.0904462 | −0.0452231 | − | 0.998977i | \(-0.514400\pi\) | ||||
−0.0452231 | + | 0.998977i | \(0.514400\pi\) | |||||||
\(102\) | −0.669794 | + | 8.50780i | −0.0663195 | + | 0.842398i | ||||
\(103\) | 19.6382i | 1.93501i | 0.252849 | + | 0.967506i | \(0.418632\pi\) | ||||
−0.252849 | + | 0.967506i | \(0.581368\pi\) | |||||||
\(104\) | 9.36430 | + | 6.36635i | 0.918245 | + | 0.624272i | ||||
\(105\) | 0.901744 | − | 2.11430i | 0.0880012 | − | 0.206335i | ||||
\(106\) | −1.74463 | + | 0.587019i | −0.169453 | + | 0.0570163i | ||||
\(107\) | − | 5.24428i | − | 0.506983i | −0.967338 | − | 0.253492i | \(-0.918421\pi\) | ||
0.967338 | − | 0.253492i | \(-0.0815791\pi\) | |||||||
\(108\) | −8.80345 | − | 5.52261i | −0.847112 | − | 0.531414i | ||||
\(109\) | − | 0.135163i | − | 0.0129463i | −0.999979 | − | 0.00647315i | \(-0.997940\pi\) | ||
0.999979 | − | 0.00647315i | \(-0.00206048\pi\) | |||||||
\(110\) | −5.49040 | − | 16.3175i | −0.523489 | − | 1.55581i | ||||
\(111\) | 0.244845 | − | 0.574083i | 0.0232397 | − | 0.0544896i | ||||
\(112\) | 1.79608 | + | 0.501924i | 0.169714 | + | 0.0474274i | ||||
\(113\) | − | 16.7462i | − | 1.57535i | −0.616092 | − | 0.787674i | \(-0.711285\pi\) | ||
0.616092 | − | 0.787674i | \(-0.288715\pi\) | |||||||
\(114\) | 2.44193 | + | 0.192246i | 0.228708 | + | 0.0180055i | ||||
\(115\) | −4.26344 | −0.397568 | ||||||||
\(116\) | 13.6090 | − | 10.3273i | 1.26356 | − | 0.958867i | ||||
\(117\) | 8.66804 | − | 8.31344i | 0.801361 | − | 0.768578i | ||||
\(118\) | 1.35621 | + | 4.03067i | 0.124849 | + | 0.371053i | ||||
\(119\) | −1.62435 | −0.148904 | ||||||||
\(120\) | 11.7356 | − | 7.53180i | 1.07131 | − | 0.687556i | ||||
\(121\) | −7.29169 | −0.662881 | ||||||||
\(122\) | 0.996308 | + | 2.96104i | 0.0902015 | + | 0.268080i | ||||
\(123\) | 2.64004 | − | 6.19004i | 0.238044 | − | 0.558137i | ||||
\(124\) | 9.24479 | + | 12.1825i | 0.830207 | + | 1.09402i | ||||
\(125\) | −5.40198 | −0.483168 | ||||||||
\(126\) | 0.916398 | − | 1.75294i | 0.0816392 | − | 0.156164i | ||||
\(127\) | − | 2.61709i | − | 0.232229i | −0.993236 | − | 0.116115i | \(-0.962956\pi\) | ||
0.993236 | − | 0.116115i | \(-0.0370440\pi\) | |||||||
\(128\) | 7.29902 | + | 8.64432i | 0.645148 | + | 0.764057i | ||||
\(129\) | −10.0531 | − | 4.28763i | −0.885127 | − | 0.377505i | ||||
\(130\) | 5.13938 | + | 15.2743i | 0.450753 | + | 1.33964i | ||||
\(131\) | 8.90568i | 0.778093i | 0.921218 | + | 0.389046i | \(0.127195\pi\) | ||||
−0.921218 | + | 0.389046i | \(0.872805\pi\) | |||||||
\(132\) | −3.60809 | − | 14.3695i | −0.314044 | − | 1.25070i | ||||
\(133\) | 0.466225i | 0.0404268i | ||||||||
\(134\) | −15.8005 | + | 5.31642i | −1.36495 | + | 0.459269i | ||||
\(135\) | −5.22943 | − | 13.8352i | −0.450078 | − | 1.19074i | ||||
\(136\) | −8.14939 | − | 5.54039i | −0.698804 | − | 0.475084i | ||||
\(137\) | 6.78619i | 0.579783i | 0.957059 | + | 0.289892i | \(0.0936193\pi\) | ||||
−0.957059 | + | 0.289892i | \(0.906381\pi\) | |||||||
\(138\) | −3.65757 | − | 0.287950i | −0.311353 | − | 0.0245119i | ||||
\(139\) | 14.1008 | 1.19601 | 0.598005 | − | 0.801492i | \(-0.295960\pi\) | ||||
0.598005 | + | 0.801492i | \(0.295960\pi\) | |||||||
\(140\) | 1.60446 | + | 2.11430i | 0.135601 | + | 0.178691i | ||||
\(141\) | −6.31422 | − | 2.69300i | −0.531753 | − | 0.226791i | ||||
\(142\) | 9.12749 | − | 3.07115i | 0.765962 | − | 0.257725i | ||||
\(143\) | 17.1222 | 1.43183 | ||||||||
\(144\) | 10.5766 | − | 5.66885i | 0.881382 | − | 0.472404i | ||||
\(145\) | 24.3140 | 2.01917 | ||||||||
\(146\) | 1.88971 | − | 0.635834i | 0.156393 | − | 0.0526220i | ||||
\(147\) | −10.8061 | − | 4.60877i | −0.891271 | − | 0.380125i | ||||
\(148\) | 0.435648 | + | 0.574083i | 0.0358101 | + | 0.0471894i | ||||
\(149\) | −11.5732 | −0.948110 | −0.474055 | − | 0.880495i | \(-0.657210\pi\) | ||||
−0.474055 | + | 0.880495i | \(0.657210\pi\) | |||||||
\(150\) | 7.57535 | + | 0.596385i | 0.618525 | + | 0.0486947i | ||||
\(151\) | − | 12.6407i | − | 1.02869i | −0.857585 | − | 0.514343i | \(-0.828036\pi\) | ||
0.857585 | − | 0.514343i | \(-0.171964\pi\) | |||||||
\(152\) | −1.59022 | + | 2.33906i | −0.128984 | + | 0.189723i | ||||
\(153\) | −7.54346 | + | 7.23486i | −0.609852 | + | 0.584904i | ||||
\(154\) | 2.67269 | − | 0.899286i | 0.215371 | − | 0.0724665i | ||||
\(155\) | 21.7654i | 1.74824i | ||||||||
\(156\) | 3.37742 | + | 13.4508i | 0.270410 | + | 1.07693i | ||||
\(157\) | 0.932449i | 0.0744176i | 0.999308 | + | 0.0372088i | \(0.0118467\pi\) | ||||
−0.999308 | + | 0.0372088i | \(0.988153\pi\) | |||||||
\(158\) | 6.60447 | + | 19.6285i | 0.525423 | + | 1.56156i | ||||
\(159\) | −2.07370 | − | 0.884429i | −0.164455 | − | 0.0701398i | ||||
\(160\) | 0.838055 | + | 16.0800i | 0.0662541 | + | 1.27124i | ||||
\(161\) | − | 0.698320i | − | 0.0550353i | ||||||
\(162\) | −3.55187 | − | 12.2223i | −0.279061 | − | 0.960273i | ||||
\(163\) | −23.1233 | −1.81115 | −0.905577 | − | 0.424182i | \(-0.860562\pi\) | ||||
−0.905577 | + | 0.424182i | \(0.860562\pi\) | |||||||
\(164\) | 4.69736 | + | 6.19004i | 0.366803 | + | 0.483361i | ||||
\(165\) | 8.27209 | − | 19.3954i | 0.643981 | − | 1.50993i | ||||
\(166\) | 6.62442 | + | 19.6878i | 0.514155 | + | 1.52807i | ||||
\(167\) | −18.6761 | −1.44520 | −0.722599 | − | 0.691268i | \(-0.757053\pi\) | ||||
−0.722599 | + | 0.691268i | \(0.757053\pi\) | |||||||
\(168\) | 1.23365 | + | 1.92221i | 0.0951783 | + | 0.148301i | ||||
\(169\) | −3.02757 | −0.232890 | ||||||||
\(170\) | −4.47260 | − | 13.2926i | −0.343033 | − | 1.01950i | ||||
\(171\) | 2.07657 | + | 2.16515i | 0.158799 | + | 0.165573i | ||||
\(172\) | 10.0531 | − | 7.62889i | 0.766543 | − | 0.581698i | ||||
\(173\) | −15.6538 | −1.19014 | −0.595069 | − | 0.803675i | \(-0.702875\pi\) | ||||
−0.595069 | + | 0.803675i | \(0.702875\pi\) | |||||||
\(174\) | 20.8588 | + | 1.64215i | 1.58130 | + | 0.124491i | ||||
\(175\) | 1.44632i | 0.109331i | ||||||||
\(176\) | 16.4763 | + | 4.60436i | 1.24194 | + | 0.347067i | ||||
\(177\) | −2.04333 | + | 4.79095i | −0.153586 | + | 0.360110i | ||||
\(178\) | −7.15087 | − | 21.2525i | −0.535981 | − | 1.59294i | ||||
\(179\) | − | 1.31831i | − | 0.0985351i | −0.998786 | − | 0.0492676i | \(-0.984311\pi\) | ||
0.998786 | − | 0.0492676i | \(-0.0156887\pi\) | |||||||
\(180\) | 16.8682 | + | 2.67253i | 1.25728 | + | 0.199199i | ||||
\(181\) | 21.7722i | 1.61832i | 0.587591 | + | 0.809158i | \(0.300076\pi\) | ||||
−0.587591 | + | 0.809158i | \(0.699924\pi\) | |||||||
\(182\) | −2.50181 | + | 0.841792i | −0.185447 | + | 0.0623978i | ||||
\(183\) | −1.50108 | + | 3.51956i | −0.110963 | + | 0.260173i | ||||
\(184\) | 2.38186 | − | 3.50349i | 0.175593 | − | 0.258281i | ||||
\(185\) | 1.02567i | 0.0754085i | ||||||||
\(186\) | −1.47002 | + | 18.6724i | −0.107787 | + | 1.36913i | ||||
\(187\) | −14.9008 | −1.08966 | ||||||||
\(188\) | 6.31422 | − | 4.79160i | 0.460512 | − | 0.349464i | ||||
\(189\) | 2.26610 | − | 0.856541i | 0.164834 | − | 0.0623042i | ||||
\(190\) | −3.81529 | + | 1.28374i | −0.276790 | + | 0.0931323i | ||||
\(191\) | −3.41715 | −0.247256 | −0.123628 | − | 0.992329i | \(-0.539453\pi\) | ||||
−0.123628 | + | 0.992329i | \(0.539453\pi\) | |||||||
\(192\) | −0.367075 | + | 13.8515i | −0.0264913 | + | 0.999649i | ||||
\(193\) | 22.3929 | 1.61187 | 0.805937 | − | 0.592002i | \(-0.201662\pi\) | ||||
0.805937 | + | 0.592002i | \(0.201662\pi\) | |||||||
\(194\) | 19.2121 | − | 6.46435i | 1.37935 | − | 0.464113i | ||||
\(195\) | −7.74323 | + | 18.1554i | −0.554504 | + | 1.30013i | ||||
\(196\) | 10.8061 | − | 8.20030i | 0.771864 | − | 0.585736i | ||||
\(197\) | −18.8339 | −1.34186 | −0.670930 | − | 0.741521i | \(-0.734105\pi\) | ||||
−0.670930 | + | 0.741521i | \(0.734105\pi\) | |||||||
\(198\) | 8.40651 | − | 16.0805i | 0.597424 | − | 1.14279i | ||||
\(199\) | − | 19.2624i | − | 1.36547i | −0.730664 | − | 0.682737i | \(-0.760789\pi\) | ||
0.730664 | − | 0.682737i | \(-0.239211\pi\) | |||||||
\(200\) | −4.93316 | + | 7.25622i | −0.348827 | + | 0.513092i | ||||
\(201\) | −18.7808 | − | 8.00997i | −1.32470 | − | 0.564980i | ||||
\(202\) | 1.21836 | − | 0.409946i | 0.0857237 | − | 0.0288437i | ||||
\(203\) | 3.98246i | 0.279514i | ||||||||
\(204\) | −2.93924 | − | 11.7057i | −0.205788 | − | 0.819563i | ||||
\(205\) | 11.0592i | 0.772409i | ||||||||
\(206\) | −8.85682 | − | 26.3225i | −0.617084 | − | 1.83398i | ||||
\(207\) | −3.11033 | − | 3.24299i | −0.216183 | − | 0.225404i | ||||
\(208\) | −15.4229 | − | 4.30999i | −1.06938 | − | 0.298844i | ||||
\(209\) | 4.27688i | 0.295838i | ||||||||
\(210\) | −0.255126 | + | 3.24064i | −0.0176054 | + | 0.223625i | ||||
\(211\) | −14.6747 | −1.01025 | −0.505124 | − | 0.863047i | \(-0.668553\pi\) | ||||
−0.505124 | + | 0.863047i | \(0.668553\pi\) | |||||||
\(212\) | 2.07370 | − | 1.57365i | 0.142423 | − | 0.108079i | ||||
\(213\) | 10.8492 | + | 4.62714i | 0.743372 | + | 0.317046i | ||||
\(214\) | 2.36516 | + | 7.02929i | 0.161679 | + | 0.480512i | ||||
\(215\) | 17.9610 | 1.22493 | ||||||||
\(216\) | 14.2906 | + | 3.43201i | 0.972352 | + | 0.233519i | ||||
\(217\) | −3.56501 | −0.242009 | ||||||||
\(218\) | 0.0609585 | + | 0.181169i | 0.00412863 | + | 0.0122703i | ||||
\(219\) | 2.24615 | + | 0.957977i | 0.151781 | + | 0.0647341i | ||||
\(220\) | 14.7184 | + | 19.3954i | 0.992312 | + | 1.30764i | ||||
\(221\) | 13.9482 | 0.938255 | ||||||||
\(222\) | −0.0692728 | + | 0.879911i | −0.00464928 | + | 0.0590557i | ||||
\(223\) | 11.7498i | 0.786827i | 0.919362 | + | 0.393414i | \(0.128706\pi\) | ||||
−0.919362 | + | 0.393414i | \(0.871294\pi\) | |||||||
\(224\) | −2.63379 | + | 0.137267i | −0.175978 | + | 0.00917154i | ||||
\(225\) | 6.44192 | + | 6.71670i | 0.429462 | + | 0.447780i | ||||
\(226\) | 7.55251 | + | 22.4461i | 0.502386 | + | 1.49309i | ||||
\(227\) | − | 1.12266i | − | 0.0745135i | −0.999306 | − | 0.0372568i | \(-0.988138\pi\) | ||
0.999306 | − | 0.0372568i | \(-0.0118619\pi\) | |||||||
\(228\) | −3.35981 | + | 0.843628i | −0.222509 | + | 0.0558706i | ||||
\(229\) | − | 25.6416i | − | 1.69445i | −0.531236 | − | 0.847224i | \(-0.678272\pi\) | ||
0.531236 | − | 0.847224i | \(-0.321728\pi\) | |||||||
\(230\) | 5.71460 | − | 1.92281i | 0.376810 | − | 0.126786i | ||||
\(231\) | 3.17682 | + | 1.35491i | 0.209019 | + | 0.0891462i | ||||
\(232\) | −13.5835 | + | 19.9801i | −0.891802 | + | 1.31176i | ||||
\(233\) | − | 9.09416i | − | 0.595778i | −0.954600 | − | 0.297889i | \(-0.903717\pi\) | ||
0.954600 | − | 0.297889i | \(-0.0962826\pi\) | |||||||
\(234\) | −7.86905 | + | 15.0524i | −0.514416 | + | 0.984005i | ||||
\(235\) | 11.2811 | 0.735897 | ||||||||
\(236\) | −3.63566 | − | 4.79095i | −0.236661 | − | 0.311864i | ||||
\(237\) | −9.95059 | + | 23.3309i | −0.646360 | + | 1.51551i | ||||
\(238\) | 2.17723 | − | 0.732579i | 0.141129 | − | 0.0474860i | ||||
\(239\) | 4.14167 | 0.267903 | 0.133951 | − | 0.990988i | \(-0.457233\pi\) | ||||
0.133951 | + | 0.990988i | \(0.457233\pi\) | |||||||
\(240\) | −12.3333 | + | 15.3882i | −0.796109 | + | 0.993302i | ||||
\(241\) | −8.61961 | −0.555238 | −0.277619 | − | 0.960691i | \(-0.589545\pi\) | ||||
−0.277619 | + | 0.960691i | \(0.589545\pi\) | |||||||
\(242\) | 9.77359 | − | 3.28855i | 0.628270 | − | 0.211396i | ||||
\(243\) | 6.70871 | − | 14.0710i | 0.430364 | − | 0.902656i | ||||
\(244\) | −2.67085 | − | 3.51956i | −0.170984 | − | 0.225317i | ||||
\(245\) | 19.3063 | 1.23344 | ||||||||
\(246\) | −0.746932 | + | 9.48761i | −0.0476226 | + | 0.604908i | ||||
\(247\) | − | 4.00344i | − | 0.254733i | ||||||
\(248\) | −17.8858 | − | 12.1597i | −1.13575 | − | 0.772141i | ||||
\(249\) | −9.98065 | + | 23.4014i | −0.632498 | + | 1.48301i | ||||
\(250\) | 7.24067 | − | 2.43629i | 0.457940 | − | 0.154084i | ||||
\(251\) | 3.05061i | 0.192553i | 0.995355 | + | 0.0962763i | \(0.0306932\pi\) | ||||
−0.995355 | + | 0.0962763i | \(0.969307\pi\) | |||||||
\(252\) | −0.437741 | + | 2.76289i | −0.0275751 | + | 0.174045i | ||||
\(253\) | − | 6.40599i | − | 0.402741i | ||||||
\(254\) | 1.18031 | + | 3.50788i | 0.0740590 | + | 0.220104i | ||||
\(255\) | 6.73863 | − | 15.7999i | 0.421989 | − | 0.989429i | ||||
\(256\) | −13.6820 | − | 8.29477i | −0.855124 | − | 0.518423i | ||||
\(257\) | 4.18627i | 0.261133i | 0.991440 | + | 0.130566i | \(0.0416795\pi\) | ||||
−0.991440 | + | 0.130566i | \(0.958320\pi\) | |||||||
\(258\) | 15.4086 | + | 1.21308i | 0.959300 | + | 0.0755229i | ||||
\(259\) | −0.167996 | −0.0104388 | ||||||||
\(260\) | −13.7774 | − | 18.1554i | −0.854436 | − | 1.12595i | ||||
\(261\) | 17.7379 | + | 18.4945i | 1.09795 | + | 1.14478i | ||||
\(262\) | −4.01645 | − | 11.9369i | −0.248137 | − | 0.737466i | ||||
\(263\) | 21.1464 | 1.30394 | 0.651971 | − | 0.758244i | \(-0.273943\pi\) | ||||
0.651971 | + | 0.758244i | \(0.273943\pi\) | |||||||
\(264\) | 11.3168 | + | 17.6332i | 0.696502 | + | 1.08525i | ||||
\(265\) | 3.70491 | 0.227591 | ||||||||
\(266\) | −0.210267 | − | 0.624915i | −0.0128923 | − | 0.0383160i | ||||
\(267\) | 10.7738 | − | 25.2612i | 0.659348 | − | 1.54596i | ||||
\(268\) | 18.7808 | − | 14.2520i | 1.14722 | − | 0.870578i | ||||
\(269\) | 7.73388 | 0.471543 | 0.235771 | − | 0.971809i | \(-0.424238\pi\) | ||||
0.235771 | + | 0.971809i | \(0.424238\pi\) | |||||||
\(270\) | 13.2490 | + | 16.1858i | 0.806311 | + | 0.985039i | ||||
\(271\) | − | 3.05116i | − | 0.185345i | −0.995697 | − | 0.0926723i | \(-0.970459\pi\) | ||
0.995697 | − | 0.0926723i | \(-0.0295409\pi\) | |||||||
\(272\) | 13.4219 | + | 3.75082i | 0.813824 | + | 0.227427i | ||||
\(273\) | −2.97372 | − | 1.26828i | −0.179977 | − | 0.0767599i | ||||
\(274\) | −3.06056 | − | 9.09603i | −0.184895 | − | 0.549511i | ||||
\(275\) | 13.2677i | 0.800073i | ||||||||
\(276\) | 5.03238 | − | 1.26360i | 0.302914 | − | 0.0760599i | ||||
\(277\) | − | 18.8564i | − | 1.13297i | −0.824071 | − | 0.566487i | \(-0.808302\pi\) | ||
0.824071 | − | 0.566487i | \(-0.191698\pi\) | |||||||
\(278\) | −18.9003 | + | 6.35943i | −1.13356 | + | 0.381413i | ||||
\(279\) | −16.5559 | + | 15.8786i | −0.991176 | + | 0.950628i | ||||
\(280\) | −3.10412 | − | 2.11034i | −0.185507 | − | 0.126117i | ||||
\(281\) | − | 15.4367i | − | 0.920876i | −0.887692 | − | 0.460438i | \(-0.847692\pi\) | ||
0.887692 | − | 0.460438i | \(-0.152308\pi\) | |||||||
\(282\) | 9.67795 | + | 0.761917i | 0.576314 | + | 0.0453715i | ||||
\(283\) | 16.4832 | 0.979823 | 0.489911 | − | 0.871772i | \(-0.337029\pi\) | ||||
0.489911 | + | 0.871772i | \(0.337029\pi\) | |||||||
\(284\) | −10.8492 | + | 8.23298i | −0.643779 | + | 0.488538i | ||||
\(285\) | −4.53494 | − | 1.93414i | −0.268627 | − | 0.114569i | ||||
\(286\) | −22.9502 | + | 7.72212i | −1.35707 | + | 0.456618i | ||||
\(287\) | −1.81142 | −0.106925 | ||||||||
\(288\) | −11.6199 | + | 12.3684i | −0.684710 | + | 0.728815i | ||||
\(289\) | 4.86145 | 0.285968 | ||||||||
\(290\) | −32.5899 | + | 10.9656i | −1.91374 | + | 0.643923i | ||||
\(291\) | 22.8360 | + | 9.73948i | 1.33867 | + | 0.570938i | ||||
\(292\) | −2.24615 | + | 1.70451i | −0.131446 | + | 0.0997489i | ||||
\(293\) | −29.2733 | −1.71016 | −0.855082 | − | 0.518493i | \(-0.826493\pi\) | ||||
−0.855082 | + | 0.518493i | \(0.826493\pi\) | |||||||
\(294\) | 16.5627 | + | 1.30394i | 0.965959 | + | 0.0760471i | ||||
\(295\) | − | 8.55958i | − | 0.498358i | ||||||
\(296\) | −0.842842 | − | 0.573009i | −0.0489892 | − | 0.0333055i | ||||
\(297\) | 20.7879 | − | 7.85742i | 1.20624 | − | 0.455934i | ||||
\(298\) | 15.5124 | − | 5.21949i | 0.898607 | − | 0.302357i | ||||
\(299\) | 5.99643i | 0.346783i | ||||||||
\(300\) | −10.4228 | + | 2.61710i | −0.601759 | + | 0.151098i | ||||
\(301\) | 2.94188i | 0.169567i | ||||||||
\(302\) | 5.70094 | + | 16.9432i | 0.328052 | + | 0.974974i | ||||
\(303\) | 1.44818 | + | 0.617643i | 0.0831955 | + | 0.0354827i | ||||
\(304\) | 1.07657 | − | 3.85240i | 0.0617456 | − | 0.220950i | ||||
\(305\) | − | 6.28810i | − | 0.360055i | ||||||
\(306\) | 6.84813 | − | 13.0995i | 0.391482 | − | 0.748849i | ||||
\(307\) | −21.4068 | −1.22175 | −0.610875 | − | 0.791727i | \(-0.709182\pi\) | ||||
−0.610875 | + | 0.791727i | \(0.709182\pi\) | |||||||
\(308\) | −3.17682 | + | 2.41076i | −0.181016 | + | 0.137366i | ||||
\(309\) | 13.3441 | − | 31.2876i | 0.759119 | − | 1.77989i | ||||
\(310\) | −9.81619 | − | 29.1738i | −0.557522 | − | 1.65696i | ||||
\(311\) | 8.16716 | 0.463117 | 0.231559 | − | 0.972821i | \(-0.425617\pi\) | ||||
0.231559 | + | 0.972821i | \(0.425617\pi\) | |||||||
\(312\) | −10.5933 | − | 16.5059i | −0.599727 | − | 0.934461i | ||||
\(313\) | −17.6187 | −0.995866 | −0.497933 | − | 0.867215i | \(-0.665907\pi\) | ||||
−0.497933 | + | 0.867215i | \(0.665907\pi\) | |||||||
\(314\) | −0.420534 | − | 1.24983i | −0.0237321 | − | 0.0705320i | ||||
\(315\) | −2.87332 | + | 2.75577i | −0.161893 | + | 0.155270i | ||||
\(316\) | −17.7049 | − | 23.3309i | −0.995978 | − | 1.31247i | ||||
\(317\) | 2.52671 | 0.141914 | 0.0709571 | − | 0.997479i | \(-0.477395\pi\) | ||||
0.0709571 | + | 0.997479i | \(0.477395\pi\) | |||||||
\(318\) | 3.17841 | + | 0.250227i | 0.178237 | + | 0.0140320i | ||||
\(319\) | 36.5328i | 2.04544i | ||||||||
\(320\) | −8.37539 | − | 21.1753i | −0.468199 | − | 1.18374i | ||||
\(321\) | −3.56346 | + | 8.35518i | −0.198893 | + | 0.466341i | ||||
\(322\) | 0.314942 | + | 0.936009i | 0.0175510 | + | 0.0521617i | ||||
\(323\) | 3.48404i | 0.193857i | ||||||||
\(324\) | 10.2731 | + | 14.7805i | 0.570726 | + | 0.821141i | ||||
\(325\) | − | 12.4195i | − | 0.688908i | ||||||
\(326\) | 30.9938 | − | 10.4286i | 1.71659 | − | 0.577585i | ||||
\(327\) | −0.0918429 | + | 0.215342i | −0.00507892 | + | 0.0119084i | ||||
\(328\) | −9.08792 | − | 6.17845i | −0.501796 | − | 0.341148i | ||||
\(329\) | 1.84776i | 0.101870i | ||||||||
\(330\) | −2.34038 | + | 29.7278i | −0.128834 | + | 1.63646i | ||||
\(331\) | 19.9850 | 1.09848 | 0.549238 | − | 0.835666i | \(-0.314918\pi\) | ||||
0.549238 | + | 0.835666i | \(0.314918\pi\) | |||||||
\(332\) | −17.7584 | − | 23.4014i | −0.974618 | − | 1.28432i | ||||
\(333\) | −0.780174 | + | 0.748258i | −0.0427533 | + | 0.0410043i | ||||
\(334\) | 25.0329 | − | 8.42289i | 1.36974 | − | 0.460880i | ||||
\(335\) | 33.5541 | 1.83325 | ||||||||
\(336\) | −2.52047 | − | 2.02010i | −0.137503 | − | 0.110205i | ||||
\(337\) | 11.8512 | 0.645578 | 0.322789 | − | 0.946471i | \(-0.395380\pi\) | ||||
0.322789 | + | 0.946471i | \(0.395380\pi\) | |||||||
\(338\) | 4.05807 | − | 1.36543i | 0.220730 | − | 0.0742697i | ||||
\(339\) | −11.3790 | + | 26.6800i | −0.618021 | + | 1.44906i | ||||
\(340\) | 11.9899 | + | 15.7999i | 0.650244 | + | 0.856871i | ||||
\(341\) | −32.7034 | −1.77099 | ||||||||
\(342\) | −3.75986 | − | 1.96557i | −0.203310 | − | 0.106286i | ||||
\(343\) | 6.42581i | 0.346961i | ||||||||
\(344\) | −10.0343 | + | 14.7595i | −0.541013 | + | 0.795779i | ||||
\(345\) | 6.79252 | + | 2.89699i | 0.365697 | + | 0.155969i | ||||
\(346\) | 20.9819 | − | 7.05985i | 1.12800 | − | 0.379540i | ||||
\(347\) | − | 22.9770i | − | 1.23347i | −0.787170 | − | 0.616736i | \(-0.788455\pi\) | ||
0.787170 | − | 0.616736i | \(-0.211545\pi\) | |||||||
\(348\) | −28.6992 | + | 7.20621i | −1.53844 | + | 0.386293i | ||||
\(349\) | − | 21.1528i | − | 1.13228i | −0.824308 | − | 0.566141i | \(-0.808436\pi\) | ||
0.824308 | − | 0.566141i | \(-0.191564\pi\) | |||||||
\(350\) | −0.652289 | − | 1.93861i | −0.0348663 | − | 0.103623i | ||||
\(351\) | −19.4589 | + | 7.35507i | −1.03864 | + | 0.392585i | ||||
\(352\) | −24.1609 | + | 1.25921i | −1.28778 | + | 0.0671161i | ||||
\(353\) | 18.5723i | 0.988504i | 0.869319 | + | 0.494252i | \(0.164558\pi\) | ||||
−0.869319 | + | 0.494252i | \(0.835442\pi\) | |||||||
\(354\) | 0.578109 | − | 7.34320i | 0.0307261 | − | 0.390287i | ||||
\(355\) | −19.3833 | −1.02876 | ||||||||
\(356\) | 19.1697 | + | 25.2612i | 1.01599 | + | 1.33884i | ||||
\(357\) | 2.58791 | + | 1.10374i | 0.136967 | + | 0.0584159i | ||||
\(358\) | 0.594557 | + | 1.76703i | 0.0314233 | + | 0.0933903i | ||||
\(359\) | −7.11376 | −0.375450 | −0.187725 | − | 0.982222i | \(-0.560111\pi\) | ||||
−0.187725 | + | 0.982222i | \(0.560111\pi\) | |||||||
\(360\) | −23.8150 | + | 4.02535i | −1.25516 | + | 0.212155i | ||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −9.81925 | − | 29.1829i | −0.516088 | − | 1.53382i | ||||
\(363\) | 11.6171 | + | 4.95467i | 0.609741 | + | 0.260053i | ||||
\(364\) | 2.97372 | − | 2.25663i | 0.155865 | − | 0.118280i | ||||
\(365\) | −4.01301 | −0.210050 | ||||||||
\(366\) | 0.424694 | − | 5.39451i | 0.0221991 | − | 0.281975i | ||||
\(367\) | − | 0.517055i | − | 0.0269900i | −0.999909 | − | 0.0134950i | \(-0.995704\pi\) | ||
0.999909 | − | 0.0134950i | \(-0.00429573\pi\) | |||||||
\(368\) | −1.61251 | + | 5.77020i | −0.0840578 | + | 0.300792i | ||||
\(369\) | −8.41221 | + | 8.06807i | −0.437922 | + | 0.420007i | ||||
\(370\) | −0.462574 | − | 1.37477i | −0.0240481 | − | 0.0714711i | ||||
\(371\) | 0.606837i | 0.0315054i | ||||||||
\(372\) | −6.45085 | − | 25.6909i | −0.334461 | − | 1.33201i | ||||
\(373\) | 27.1084i | 1.40362i | 0.712364 | + | 0.701810i | \(0.247624\pi\) | ||||
−0.712364 | + | 0.701810i | \(0.752376\pi\) | |||||||
\(374\) | 19.9727 | − | 6.72026i | 1.03276 | − | 0.347496i | ||||
\(375\) | 8.60644 | + | 3.67062i | 0.444435 | + | 0.189550i | ||||
\(376\) | −6.30240 | + | 9.27024i | −0.325022 | + | 0.478076i | ||||
\(377\) | − | 34.1971i | − | 1.76124i | ||||||
\(378\) | −2.65112 | + | 2.17009i | −0.136359 | + | 0.111618i | ||||
\(379\) | −4.55933 | −0.234197 | −0.117098 | − | 0.993120i | \(-0.537359\pi\) | ||||
−0.117098 | + | 0.993120i | \(0.537359\pi\) | |||||||
\(380\) | 4.53494 | − | 3.44138i | 0.232638 | − | 0.176539i | ||||
\(381\) | −1.77830 | + | 4.16955i | −0.0911052 | + | 0.213612i | ||||
\(382\) | 4.58025 | − | 1.54113i | 0.234346 | − | 0.0788511i | ||||
\(383\) | −8.31238 | −0.424743 | −0.212371 | − | 0.977189i | \(-0.568119\pi\) | ||||
−0.212371 | + | 0.977189i | \(0.568119\pi\) | |||||||
\(384\) | −5.75502 | − | 18.7318i | −0.293684 | − | 0.955902i | ||||
\(385\) | −5.67575 | −0.289263 | ||||||||
\(386\) | −30.0148 | + | 10.0992i | −1.52771 | + | 0.514034i | ||||
\(387\) | 13.1032 | + | 13.6621i | 0.666073 | + | 0.694483i | ||||
\(388\) | −22.8360 | + | 17.3293i | −1.15932 | + | 0.879760i | ||||
\(389\) | −18.9309 | −0.959835 | −0.479918 | − | 0.877314i | \(-0.659333\pi\) | ||||
−0.479918 | + | 0.877314i | \(0.659333\pi\) | |||||||
\(390\) | 2.19075 | − | 27.8272i | 0.110933 | − | 1.40908i | ||||
\(391\) | − | 5.21846i | − | 0.263909i | ||||||
\(392\) | −10.7859 | + | 15.8650i | −0.544769 | + | 0.801303i | ||||
\(393\) | 6.05137 | − | 14.1885i | 0.305251 | − | 0.715717i | ||||
\(394\) | 25.2444 | − | 8.49407i | 1.27180 | − | 0.427925i | ||||
\(395\) | − | 41.6834i | − | 2.09732i | ||||||
\(396\) | −4.01559 | + | 25.3451i | −0.201791 | + | 1.27364i | ||||
\(397\) | − | 19.7700i | − | 0.992227i | −0.868258 | − | 0.496113i | \(-0.834760\pi\) | ||
0.868258 | − | 0.496113i | \(-0.165240\pi\) | |||||||
\(398\) | 8.68732 | + | 25.8188i | 0.435456 | + | 1.29418i | ||||
\(399\) | 0.316798 | − | 0.742789i | 0.0158597 | − | 0.0371860i | ||||
\(400\) | 3.33973 | − | 11.9509i | 0.166987 | − | 0.597545i | ||||
\(401\) | − | 8.03205i | − | 0.401102i | −0.979683 | − | 0.200551i | \(-0.935727\pi\) | ||
0.979683 | − | 0.200551i | \(-0.0642732\pi\) | |||||||
\(402\) | 28.7858 | + | 2.26622i | 1.43570 | + | 0.113029i | ||||
\(403\) | 30.6126 | 1.52492 | ||||||||
\(404\) | −1.44818 | + | 1.09896i | −0.0720494 | + | 0.0546753i | ||||
\(405\) | −1.06942 | + | 25.5956i | −0.0531401 | + | 1.27185i | ||||
\(406\) | −1.79608 | − | 5.33798i | −0.0891382 | − | 0.264919i | ||||
\(407\) | −1.54110 | −0.0763896 | ||||||||
\(408\) | 9.21893 | + | 14.3644i | 0.456405 | + | 0.711145i | ||||
\(409\) | −29.4278 | −1.45511 | −0.727556 | − | 0.686048i | \(-0.759344\pi\) | ||||
−0.727556 | + | 0.686048i | \(0.759344\pi\) | |||||||
\(410\) | −4.98769 | − | 14.8235i | −0.246325 | − | 0.732079i | ||||
\(411\) | 4.61119 | − | 10.8118i | 0.227453 | − | 0.533305i | ||||
\(412\) | 23.7429 | + | 31.2876i | 1.16973 | + | 1.54143i | ||||
\(413\) | 1.40200 | 0.0689877 | ||||||||
\(414\) | 5.63158 | + | 2.94407i | 0.276777 | + | 0.144693i | ||||
\(415\) | − | 41.8094i | − | 2.05234i | ||||||
\(416\) | 22.6162 | − | 1.17870i | 1.10885 | − | 0.0577908i | ||||
\(417\) | −22.4653 | − | 9.58140i | −1.10013 | − | 0.469203i | ||||
\(418\) | −1.92887 | − | 5.73261i | −0.0943440 | − | 0.280391i | ||||
\(419\) | − | 12.7128i | − | 0.621062i | −0.950563 | − | 0.310531i | \(-0.899493\pi\) | ||
0.950563 | − | 0.310531i | \(-0.100507\pi\) | |||||||
\(420\) | −1.11956 | − | 4.45873i | −0.0546290 | − | 0.217564i | ||||
\(421\) | 26.4745i | 1.29029i | 0.764061 | + | 0.645143i | \(0.223202\pi\) | ||||
−0.764061 | + | 0.645143i | \(0.776798\pi\) | |||||||
\(422\) | 19.6696 | − | 6.61828i | 0.957500 | − | 0.322173i | ||||
\(423\) | 8.22993 | + | 8.58097i | 0.400153 | + | 0.417221i | ||||
\(424\) | −2.06982 | + | 3.04451i | −0.100519 | + | 0.147855i | ||||
\(425\) | 10.8082i | 0.524273i | ||||||||
\(426\) | −16.6288 | − | 1.30913i | −0.805666 | − | 0.0634277i | ||||
\(427\) | 1.02994 | 0.0498424 | ||||||||
\(428\) | −6.34040 | − | 8.35518i | −0.306475 | − | 0.403863i | ||||
\(429\) | −27.2792 | − | 11.6345i | −1.31705 | − | 0.561719i | ||||
\(430\) | −24.0745 | + | 8.10041i | −1.16098 | + | 0.390637i | ||||
\(431\) | −4.48203 | −0.215892 | −0.107946 | − | 0.994157i | \(-0.534427\pi\) | ||||
−0.107946 | + | 0.994157i | \(0.534427\pi\) | |||||||
\(432\) | −20.7026 | + | 1.84487i | −0.996053 | + | 0.0887613i | ||||
\(433\) | 31.5853 | 1.51789 | 0.758947 | − | 0.651152i | \(-0.225714\pi\) | ||||
0.758947 | + | 0.651152i | \(0.225714\pi\) | |||||||
\(434\) | 4.77845 | − | 1.60782i | 0.229373 | − | 0.0771777i | ||||
\(435\) | −38.7371 | − | 16.5213i | −1.85730 | − | 0.792135i | ||||
\(436\) | −0.163414 | − | 0.215342i | −0.00782613 | − | 0.0103130i | ||||
\(437\) | −1.49782 | −0.0716504 | ||||||||
\(438\) | −3.44273 | − | 0.271036i | −0.164500 | − | 0.0129506i | ||||
\(439\) | − | 30.8696i | − | 1.47333i | −0.676259 | − | 0.736664i | \(-0.736400\pi\) | ||
0.676259 | − | 0.736664i | \(-0.263600\pi\) | |||||||
\(440\) | −28.4754 | − | 19.3591i | −1.35751 | − | 0.922908i | ||||
\(441\) | 14.0846 | + | 14.6854i | 0.670696 | + | 0.699304i | ||||
\(442\) | −18.6958 | + | 6.29061i | −0.889266 | + | 0.299214i | ||||
\(443\) | − | 13.5157i | − | 0.642152i | −0.947053 | − | 0.321076i | \(-0.895955\pi\) | ||
0.947053 | − | 0.321076i | \(-0.104045\pi\) | |||||||
\(444\) | −0.303987 | − | 1.21065i | −0.0144266 | − | 0.0574549i | ||||
\(445\) | 45.1320i | 2.13946i | ||||||||
\(446\) | −5.29917 | − | 15.7492i | −0.250923 | − | 0.745745i | ||||
\(447\) | 18.4384 | + | 7.86392i | 0.872105 | + | 0.371950i | ||||
\(448\) | 3.46835 | − | 1.37183i | 0.163864 | − | 0.0648127i | ||||
\(449\) | − | 39.6229i | − | 1.86992i | −0.354753 | − | 0.934960i | \(-0.615435\pi\) | ||
0.354753 | − | 0.934960i | \(-0.384565\pi\) | |||||||
\(450\) | −11.6638 | − | 6.09758i | −0.549837 | − | 0.287443i | ||||
\(451\) | −16.6169 | −0.782459 | ||||||||
\(452\) | −20.2464 | − | 26.6800i | −0.952309 | − | 1.25492i | ||||
\(453\) | −8.58930 | + | 20.1392i | −0.403561 | + | 0.946220i | ||||
\(454\) | 0.506318 | + | 1.50478i | 0.0237627 | + | 0.0706229i | ||||
\(455\) | 5.31289 | 0.249072 | ||||||||
\(456\) | 4.12292 | − | 2.64605i | 0.193073 | − | 0.123912i | ||||
\(457\) | −35.9360 | −1.68102 | −0.840508 | − | 0.541799i | \(-0.817743\pi\) | ||||
−0.840508 | + | 0.541799i | \(0.817743\pi\) | |||||||
\(458\) | 11.5644 | + | 34.3694i | 0.540367 | + | 1.60598i | ||||
\(459\) | 16.9343 | − | 6.40083i | 0.790425 | − | 0.298765i | ||||
\(460\) | −6.79252 | + | 5.15456i | −0.316703 | + | 0.240333i | ||||
\(461\) | −40.7343 | −1.89719 | −0.948593 | − | 0.316499i | \(-0.897493\pi\) | ||||
−0.948593 | + | 0.316499i | \(0.897493\pi\) | |||||||
\(462\) | −4.86918 | − | 0.383337i | −0.226535 | − | 0.0178344i | ||||
\(463\) | 11.2414i | 0.522433i | 0.965280 | + | 0.261216i | \(0.0841236\pi\) | ||||
−0.965280 | + | 0.261216i | \(0.915876\pi\) | |||||||
\(464\) | 9.19599 | − | 32.9069i | 0.426913 | − | 1.52767i | ||||
\(465\) | 14.7895 | − | 34.6767i | 0.685847 | − | 1.60809i | ||||
\(466\) | 4.10146 | + | 12.1896i | 0.189996 | + | 0.564671i | ||||
\(467\) | 22.1470i | 1.02484i | 0.858734 | + | 0.512421i | \(0.171251\pi\) | ||||
−0.858734 | + | 0.512421i | \(0.828749\pi\) | |||||||
\(468\) | 3.75886 | − | 23.7247i | 0.173753 | − | 1.09668i | ||||
\(469\) | 5.49591i | 0.253777i | ||||||||
\(470\) | −15.1209 | + | 5.08776i | −0.697473 | + | 0.234681i | ||||
\(471\) | 0.633596 | − | 1.48558i | 0.0291945 | − | 0.0684518i | ||||
\(472\) | 7.03385 | + | 4.78198i | 0.323759 | + | 0.220109i | ||||
\(473\) | 26.9872i | 1.24087i | ||||||||
\(474\) | 2.81527 | − | 35.7599i | 0.129310 | − | 1.64251i | ||||
\(475\) | 3.10219 | 0.142338 | ||||||||
\(476\) | −2.58791 | + | 1.96386i | −0.118617 | + | 0.0900133i | ||||
\(477\) | 2.70286 | + | 2.81815i | 0.123755 | + | 0.129034i | ||||
\(478\) | −5.55139 | + | 1.86789i | −0.253915 | + | 0.0854353i | ||||
\(479\) | 14.4920 | 0.662158 | 0.331079 | − | 0.943603i | \(-0.392587\pi\) | ||||
0.331079 | + | 0.943603i | \(0.392587\pi\) | |||||||
\(480\) | 9.59113 | − | 26.1882i | 0.437773 | − | 1.19532i | ||||
\(481\) | 1.44258 | 0.0657758 | ||||||||
\(482\) | 11.5535 | − | 3.88744i | 0.526247 | − | 0.177068i | ||||
\(483\) | −0.474505 | + | 1.11256i | −0.0215907 | + | 0.0506234i | ||||
\(484\) | −11.6171 | + | 8.81576i | −0.528051 | + | 0.400716i | ||||
\(485\) | −40.7991 | −1.85259 | ||||||||
\(486\) | −2.64616 | + | 21.8860i | −0.120032 | + | 0.992770i | ||||
\(487\) | 21.3493i | 0.967431i | 0.875225 | + | 0.483716i | \(0.160713\pi\) | ||||
−0.875225 | + | 0.483716i | \(0.839287\pi\) | |||||||
\(488\) | 5.16725 | + | 3.51297i | 0.233910 | + | 0.159025i | ||||
\(489\) | 36.8400 | + | 15.7122i | 1.66596 | + | 0.710529i | ||||
\(490\) | −25.8777 | + | 8.70714i | −1.16903 | + | 0.393348i | ||||
\(491\) | − | 18.0569i | − | 0.814896i | −0.913228 | − | 0.407448i | \(-0.866419\pi\) | ||
0.913228 | − | 0.407448i | \(-0.133581\pi\) | |||||||
\(492\) | −3.27774 | − | 13.0538i | −0.147772 | − | 0.588511i | ||||
\(493\) | 29.7604i | 1.34034i | ||||||||
\(494\) | 1.80555 | + | 5.36611i | 0.0812355 | + | 0.241433i | ||||
\(495\) | −26.3582 | + | 25.2799i | −1.18471 | + | 1.13625i | ||||
\(496\) | 29.4576 | + | 8.23206i | 1.32269 | + | 0.369630i | ||||
\(497\) | − | 3.17484i | − | 0.142411i | ||||||
\(498\) | 2.82378 | − | 35.8679i | 0.126536 | − | 1.60728i | ||||
\(499\) | 2.30123 | 0.103017 | 0.0515086 | − | 0.998673i | \(-0.483597\pi\) | ||||
0.0515086 | + | 0.998673i | \(0.483597\pi\) | |||||||
\(500\) | −8.60644 | + | 6.53107i | −0.384892 | + | 0.292078i | ||||
\(501\) | 29.7547 | + | 12.6903i | 1.32934 | + | 0.566961i | ||||
\(502\) | −1.37582 | − | 4.08895i | −0.0614059 | − | 0.182499i | ||||
\(503\) | 42.1587 | 1.87976 | 0.939881 | − | 0.341502i | \(-0.110936\pi\) | ||||
0.939881 | + | 0.341502i | \(0.110936\pi\) | |||||||
\(504\) | −0.659323 | − | 3.90072i | −0.0293686 | − | 0.173752i | ||||
\(505\) | −2.58733 | −0.115135 | ||||||||
\(506\) | 2.88909 | + | 8.58641i | 0.128436 | + | 0.381713i | ||||
\(507\) | 4.82353 | + | 2.05722i | 0.214220 | + | 0.0913644i | ||||
\(508\) | −3.16410 | − | 4.16955i | −0.140384 | − | 0.184994i | ||||
\(509\) | 39.0804 | 1.73221 | 0.866104 | − | 0.499863i | \(-0.166616\pi\) | ||||
0.866104 | + | 0.499863i | \(0.166616\pi\) | |||||||
\(510\) | −1.90653 | + | 24.2169i | −0.0844224 | + | 1.07234i | ||||
\(511\) | − | 0.657300i | − | 0.0290772i | ||||||
\(512\) | 22.0799 | + | 4.94752i | 0.975803 | + | 0.218651i | ||||
\(513\) | −1.83719 | − | 4.86053i | −0.0811137 | − | 0.214598i | ||||
\(514\) | −1.88801 | − | 5.61117i | −0.0832764 | − | 0.247498i | ||||
\(515\) | 55.8989i | 2.46320i | ||||||||
\(516\) | −21.2004 | + | 5.32330i | −0.933296 | + | 0.234345i | ||||
\(517\) | 16.9503i | 0.745472i | ||||||||
\(518\) | 0.225178 | − | 0.0757662i | 0.00989375 | − | 0.00332898i | ||||
\(519\) | 24.9397 | + | 10.6367i | 1.09473 | + | 0.466899i | ||||
\(520\) | 26.6549 | + | 18.1214i | 1.16889 | + | 0.794676i | ||||
\(521\) | − | 26.5526i | − | 1.16329i | −0.813443 | − | 0.581645i | \(-0.802409\pi\) | ||
0.813443 | − | 0.581645i | \(-0.197591\pi\) | |||||||
\(522\) | −32.1164 | − | 16.7898i | −1.40570 | − | 0.734868i | ||||
\(523\) | 30.8111 | 1.34728 | 0.673639 | − | 0.739061i | \(-0.264730\pi\) | ||||
0.673639 | + | 0.739061i | \(0.264730\pi\) | |||||||
\(524\) | 10.7671 | + | 14.1885i | 0.470363 | + | 0.619829i | ||||
\(525\) | 0.982768 | − | 2.30428i | 0.0428915 | − | 0.100567i | ||||
\(526\) | −28.3440 | + | 9.53699i | −1.23586 | + | 0.415833i | ||||
\(527\) | −26.6409 | −1.16050 | ||||||||
\(528\) | −23.1213 | − | 18.5312i | −1.00623 | − | 0.806468i | ||||
\(529\) | −20.7565 | −0.902458 | ||||||||
\(530\) | −4.96596 | + | 1.67091i | −0.215708 | + | 0.0725797i | ||||
\(531\) | 6.51086 | − | 6.24451i | 0.282547 | − | 0.270989i | ||||
\(532\) | 0.563672 | + | 0.742789i | 0.0244383 | + | 0.0322040i | ||||
\(533\) | 15.5545 | 0.673741 | ||||||||
\(534\) | −3.04819 | + | 38.7184i | −0.131908 | + | 1.67551i | ||||
\(535\) | − | 14.9275i | − | 0.645372i | ||||||
\(536\) | −18.7457 | + | 27.5731i | −0.809689 | + | 1.19098i | ||||
\(537\) | −0.895786 | + | 2.10033i | −0.0386560 | + | 0.0906360i | ||||
\(538\) | −10.3663 | + | 3.48797i | −0.446922 | + | 0.150377i | ||||
\(539\) | 29.0085i | 1.24948i | ||||||||
\(540\) | −25.0585 | − | 15.7198i | −1.07834 | − | 0.676471i | ||||
\(541\) | − | 23.5736i | − | 1.01351i | −0.862091 | − | 0.506753i | \(-0.830845\pi\) | ||
0.862091 | − | 0.506753i | \(-0.169155\pi\) | |||||||
\(542\) | 1.37607 | + | 4.08969i | 0.0591072 | + | 0.175667i | ||||
\(543\) | 14.7941 | − | 34.6875i | 0.634877 | − | 1.48858i | ||||
\(544\) | −19.6820 | + | 1.02578i | −0.843859 | + | 0.0439800i | ||||
\(545\) | − | 0.384734i | − | 0.0164802i | ||||||
\(546\) | 4.55788 | + | 0.358829i | 0.195059 | + | 0.0153565i | ||||
\(547\) | −6.72108 | −0.287373 | −0.143686 | − | 0.989623i | \(-0.545896\pi\) | ||||
−0.143686 | + | 0.989623i | \(0.545896\pi\) | |||||||
\(548\) | 8.20460 | + | 10.8118i | 0.350483 | + | 0.461855i | ||||
\(549\) | 4.78305 | − | 4.58738i | 0.204136 | − | 0.195785i | ||||
\(550\) | −5.98372 | − | 17.7837i | −0.255147 | − | 0.758298i | ||||
\(551\) | 8.54193 | 0.363898 | ||||||||
\(552\) | −6.17538 | + | 3.96329i | −0.262842 | + | 0.168689i | ||||
\(553\) | 6.82743 | 0.290332 | ||||||||
\(554\) | 8.50424 | + | 25.2747i | 0.361310 | + | 1.07382i | ||||
\(555\) | 0.696936 | − | 1.63409i | 0.0295833 | − | 0.0693633i | ||||
\(556\) | 22.4653 | − | 17.0480i | 0.952742 | − | 0.722997i | ||||
\(557\) | 16.6408 | 0.705093 | 0.352547 | − | 0.935794i | \(-0.385316\pi\) | ||||
0.352547 | + | 0.935794i | \(0.385316\pi\) | |||||||
\(558\) | 15.0298 | − | 28.7500i | 0.636264 | − | 1.21708i | ||||
\(559\) | − | 25.2618i | − | 1.06846i | ||||||
\(560\) | 5.11244 | + | 1.42869i | 0.216040 | + | 0.0603733i | ||||
\(561\) | 23.7400 | + | 10.1250i | 1.00230 | + | 0.427480i | ||||
\(562\) | 6.96193 | + | 20.6909i | 0.293671 | + | 0.872794i | ||||
\(563\) | 36.2254i | 1.52672i | 0.645973 | + | 0.763360i | \(0.276452\pi\) | ||||
−0.645973 | + | 0.763360i | \(0.723548\pi\) | |||||||
\(564\) | −13.3157 | + | 3.34349i | −0.560692 | + | 0.140786i | ||||
\(565\) | − | 47.6669i | − | 2.00536i | ||||||
\(566\) | −22.0936 | + | 7.43389i | −0.928663 | + | 0.312470i | ||||
\(567\) | −4.19236 | − | 0.175164i | −0.176063 | − | 0.00735618i | ||||
\(568\) | 10.8289 | − | 15.9282i | 0.454369 | − | 0.668334i | ||||
\(569\) | 17.6565i | 0.740200i | 0.928992 | + | 0.370100i | \(0.120677\pi\) | ||||
−0.928992 | + | 0.370100i | \(0.879323\pi\) | |||||||
\(570\) | 6.95081 | + | 0.547217i | 0.291137 | + | 0.0229204i | ||||
\(571\) | 24.7456 | 1.03557 | 0.517786 | − | 0.855510i | \(-0.326757\pi\) | ||||
0.517786 | + | 0.855510i | \(0.326757\pi\) | |||||||
\(572\) | 27.2792 | − | 20.7010i | 1.14060 | − | 0.865554i | ||||
\(573\) | 5.44420 | + | 2.32194i | 0.227435 | + | 0.0970003i | ||||
\(574\) | 2.42797 | − | 0.816947i | 0.101342 | − | 0.0340987i | ||||
\(575\) | −4.64652 | −0.193773 | ||||||||
\(576\) | 9.99689 | − | 21.8188i | 0.416537 | − | 0.909119i | ||||
\(577\) | 17.4071 | 0.724669 | 0.362335 | − | 0.932048i | \(-0.381980\pi\) | ||||
0.362335 | + | 0.932048i | \(0.381980\pi\) | |||||||
\(578\) | −6.51616 | + | 2.19251i | −0.271036 | + | 0.0911964i | ||||
\(579\) | −35.6763 | − | 15.2159i | −1.48266 | − | 0.632349i | ||||
\(580\) | 38.7371 | − | 29.3960i | 1.60847 | − | 1.22060i | ||||
\(581\) | 6.84806 | 0.284105 | ||||||||
\(582\) | −35.0012 | − | 2.75554i | −1.45085 | − | 0.114221i | ||||
\(583\) | 5.56677i | 0.230552i | ||||||||
\(584\) | 2.24195 | − | 3.29769i | 0.0927724 | − | 0.136459i | ||||
\(585\) | 24.6730 | − | 23.6637i | 1.02010 | − | 0.978372i | ||||
\(586\) | 39.2371 | − | 13.2022i | 1.62087 | − | 0.545379i | ||||
\(587\) | 15.1652i | 0.625936i | 0.949764 | + | 0.312968i | \(0.101323\pi\) | ||||
−0.949764 | + | 0.312968i | \(0.898677\pi\) | |||||||
\(588\) | −22.7883 | + | 5.72202i | −0.939775 | + | 0.235972i | ||||
\(589\) | 7.64656i | 0.315071i | ||||||||
\(590\) | 3.86036 | + | 11.4730i | 0.158929 | + | 0.472337i | ||||
\(591\) | 30.0062 | + | 12.7976i | 1.23429 | + | 0.526421i | ||||
\(592\) | 1.38815 | + | 0.387925i | 0.0570526 | + | 0.0159436i | ||||
\(593\) | 2.75839i | 0.113274i | 0.998395 | + | 0.0566368i | \(0.0180377\pi\) | ||||
−0.998395 | + | 0.0566368i | \(0.981962\pi\) | |||||||
\(594\) | −24.3198 | + | 19.9072i | −0.997855 | + | 0.816802i | ||||
\(595\) | −4.62360 | −0.189549 | ||||||||
\(596\) | −18.4384 | + | 13.9921i | −0.755265 | + | 0.573139i | ||||
\(597\) | −13.0887 | + | 30.6888i | −0.535685 | + | 1.25601i | ||||
\(598\) | −2.70439 | − | 8.03746i | −0.110591 | − | 0.328676i | ||||
\(599\) | 10.8449 | 0.443110 | 0.221555 | − | 0.975148i | \(-0.428887\pi\) | ||||
0.221555 | + | 0.975148i | \(0.428887\pi\) | |||||||
\(600\) | 12.7901 | − | 8.20854i | 0.522153 | − | 0.335112i | ||||
\(601\) | 18.9772 | 0.774096 | 0.387048 | − | 0.922060i | \(-0.373495\pi\) | ||||
0.387048 | + | 0.922060i | \(0.373495\pi\) | |||||||
\(602\) | −1.32679 | − | 3.94322i | −0.0540758 | − | 0.160714i | ||||
\(603\) | 24.4788 | + | 25.5230i | 0.996855 | + | 1.03938i | ||||
\(604\) | −15.2828 | − | 20.1392i | −0.621847 | − | 0.819451i | ||||
\(605\) | −20.7553 | −0.843824 | ||||||||
\(606\) | −2.21965 | − | 0.174747i | −0.0901672 | − | 0.00709860i | ||||
\(607\) | − | 11.5022i | − | 0.466860i | −0.972374 | − | 0.233430i | \(-0.925005\pi\) | ||
0.972374 | − | 0.233430i | \(-0.0749950\pi\) | |||||||
\(608\) | 0.294423 | + | 5.64919i | 0.0119404 | + | 0.229105i | ||||
\(609\) | 2.70606 | − | 6.34485i | 0.109655 | − | 0.257106i | ||||
\(610\) | 2.83593 | + | 8.42840i | 0.114823 | + | 0.341256i | ||||
\(611\) | − | 15.8666i | − | 0.641893i | ||||||
\(612\) | −3.27119 | + | 20.6467i | −0.132230 | + | 0.834594i | ||||
\(613\) | 27.9553i | 1.12911i | 0.825397 | + | 0.564553i | \(0.190951\pi\) | ||||
−0.825397 | + | 0.564553i | \(0.809049\pi\) | |||||||
\(614\) | 28.6931 | − | 9.65443i | 1.15796 | − | 0.389621i | ||||
\(615\) | 7.51469 | − | 17.6195i | 0.303022 | − | 0.710488i | ||||
\(616\) | 3.17087 | − | 4.66406i | 0.127758 | − | 0.187920i | ||||
\(617\) | − | 8.63436i | − | 0.347606i | −0.984780 | − | 0.173803i | \(-0.944394\pi\) | ||
0.984780 | − | 0.173803i | \(-0.0556056\pi\) | |||||||
\(618\) | −3.77538 | + | 47.9552i | −0.151868 | + | 1.92904i | ||||
\(619\) | −23.5198 | −0.945342 | −0.472671 | − | 0.881239i | \(-0.656710\pi\) | ||||
−0.472671 | + | 0.881239i | \(0.656710\pi\) | |||||||
\(620\) | 26.3147 | + | 34.6767i | 1.05682 | + | 1.39265i | ||||
\(621\) | 2.75177 | + | 7.28019i | 0.110425 | + | 0.292144i | ||||
\(622\) | −10.9470 | + | 3.68338i | −0.438937 | + | 0.147690i | ||||
\(623\) | −7.39228 | −0.296166 | ||||||||
\(624\) | 21.6431 | + | 17.3465i | 0.866417 | + | 0.694414i | ||||
\(625\) | −30.8874 | −1.23549 | ||||||||
\(626\) | 23.6156 | − | 7.94600i | 0.943869 | − | 0.317586i | ||||
\(627\) | 2.90612 | − | 6.81392i | 0.116059 | − | 0.272122i | ||||
\(628\) | 1.12734 | + | 1.48558i | 0.0449859 | + | 0.0592810i | ||||
\(629\) | −1.25542 | −0.0500568 | ||||||||
\(630\) | 2.60847 | − | 4.98963i | 0.103924 | − | 0.198791i | ||||
\(631\) | 17.9945i | 0.716351i | 0.933654 | + | 0.358176i | \(0.116601\pi\) | ||||
−0.933654 | + | 0.358176i | \(0.883399\pi\) | |||||||
\(632\) | 34.2534 | + | 23.2873i | 1.36253 | + | 0.926318i | ||||
\(633\) | 23.3797 | + | 9.97140i | 0.929261 | + | 0.396328i | ||||
\(634\) | −3.38674 | + | 1.13954i | −0.134504 | + | 0.0452571i | ||||
\(635\) | − | 7.44938i | − | 0.295620i | ||||||
\(636\) | −4.37311 | + | 1.09806i | −0.173405 | + | 0.0435410i | ||||
\(637\) | − | 27.1539i | − | 1.07588i | ||||||
\(638\) | −16.4763 | − | 48.9676i | −0.652301 | − | 1.93864i | ||||
\(639\) | −14.1408 | − | 14.7439i | −0.559400 | − | 0.583260i | ||||
\(640\) | 20.7762 | + | 24.6055i | 0.821251 | + | 0.972618i | ||||
\(641\) | 19.8114i | 0.782505i | 0.920283 | + | 0.391253i | \(0.127958\pi\) | ||||
−0.920283 | + | 0.391253i | \(0.872042\pi\) | |||||||
\(642\) | 1.00819 | − | 12.8062i | 0.0397902 | − | 0.505420i | ||||
\(643\) | −14.6875 | −0.579219 | −0.289610 | − | 0.957145i | \(-0.593526\pi\) | ||||
−0.289610 | + | 0.957145i | \(0.593526\pi\) | |||||||
\(644\) | −0.844278 | − | 1.11256i | −0.0332692 | − | 0.0438411i | ||||
\(645\) | −28.6155 | − | 12.2045i | −1.12674 | − | 0.480550i | ||||
\(646\) | −1.57130 | − | 4.66992i | −0.0618220 | − | 0.183735i | ||||
\(647\) | −12.3332 | −0.484868 | −0.242434 | − | 0.970168i | \(-0.577946\pi\) | ||||
−0.242434 | + | 0.970168i | \(0.577946\pi\) | |||||||
\(648\) | −20.4357 | − | 15.1783i | −0.802792 | − | 0.596259i | ||||
\(649\) | 12.8611 | 0.504843 | ||||||||
\(650\) | 5.60116 | + | 16.6467i | 0.219696 | + | 0.652938i | ||||
\(651\) | 5.67978 | + | 2.42241i | 0.222608 | + | 0.0949418i | ||||
\(652\) | −36.8400 | + | 27.9564i | −1.44277 | + | 1.09486i | ||||
\(653\) | 9.77352 | 0.382467 | 0.191234 | − | 0.981545i | \(-0.438751\pi\) | ||||
0.191234 | + | 0.981545i | \(0.438751\pi\) | |||||||
\(654\) | 0.0259846 | − | 0.330060i | 0.00101608 | − | 0.0129064i | ||||
\(655\) | 25.3494i | 0.990485i | ||||||||
\(656\) | 14.9677 | + | 4.18279i | 0.584390 | + | 0.163310i | ||||
\(657\) | −2.92762 | − | 3.05250i | −0.114217 | − | 0.119089i | ||||
\(658\) | −0.833337 | − | 2.47668i | −0.0324868 | − | 0.0965512i | ||||
\(659\) | − | 26.5173i | − | 1.03297i | −0.856297 | − | 0.516484i | \(-0.827241\pi\) | ||
0.856297 | − | 0.516484i | \(-0.172759\pi\) | |||||||
\(660\) | −10.2702 | − | 40.9018i | −0.399767 | − | 1.59210i | ||||
\(661\) | − | 43.9961i | − | 1.71125i | −0.517597 | − | 0.855625i | \(-0.673173\pi\) | ||
0.517597 | − | 0.855625i | \(-0.326827\pi\) | |||||||
\(662\) | −26.7874 | + | 9.01323i | −1.04112 | + | 0.350309i | ||||
\(663\) | −22.2222 | − | 9.47772i | −0.863040 | − | 0.368084i | ||||
\(664\) | 34.3569 | + | 23.3576i | 1.33331 | + | 0.906452i | ||||
\(665\) | 1.32708i | 0.0514619i | ||||||||
\(666\) | 0.708261 | − | 1.35480i | 0.0274446 | − | 0.0524975i | ||||
\(667\) | −12.7943 | −0.495396 | ||||||||
\(668\) | −29.7547 | + | 22.5796i | −1.15124 | + | 0.873632i | ||||
\(669\) | 7.98397 | − | 18.7198i | 0.308678 | − | 0.723751i | ||||
\(670\) | −44.9750 | + | 15.1329i | −1.73753 | + | 0.584633i | ||||
\(671\) | 9.44811 | 0.364740 | ||||||||
\(672\) | 4.28943 | + | 1.57096i | 0.165468 | + | 0.0606009i | ||||
\(673\) | 7.50506 | 0.289299 | 0.144649 | − | 0.989483i | \(-0.453795\pi\) | ||||
0.144649 | + | 0.989483i | \(0.453795\pi\) | |||||||
\(674\) | −15.8851 | + | 5.34490i | −0.611870 | + | 0.205878i | ||||
\(675\) | −5.69930 | − | 15.0783i | −0.219366 | − | 0.580364i | ||||
\(676\) | −4.82353 | + | 3.66038i | −0.185520 | + | 0.140784i | ||||
\(677\) | −3.17793 | −0.122138 | −0.0610690 | − | 0.998134i | \(-0.519451\pi\) | ||||
−0.0610690 | + | 0.998134i | \(0.519451\pi\) | |||||||
\(678\) | 3.21939 | − | 40.8931i | 0.123640 | − | 1.57049i | ||||
\(679\) | − | 6.68258i | − | 0.256454i | ||||||
\(680\) | −23.1967 | − | 15.7704i | −0.889553 | − | 0.604765i | ||||
\(681\) | −0.762842 | + | 1.78862i | −0.0292322 | + | 0.0685401i | ||||
\(682\) | 43.8347 | − | 14.7492i | 1.67852 | − | 0.564776i | ||||
\(683\) | − | 16.3890i | − | 0.627107i | −0.949571 | − | 0.313554i | \(-0.898480\pi\) | ||
0.949571 | − | 0.313554i | \(-0.101520\pi\) | |||||||
\(684\) | 5.92608 | + | 0.938906i | 0.226589 | + | 0.0359000i | ||||
\(685\) | 19.3164i | 0.738044i | ||||||||
\(686\) | −2.89803 | − | 8.61298i | −0.110647 | − | 0.328845i | ||||
\(687\) | −17.4234 | + | 40.8523i | −0.664744 | + | 1.55861i | ||||
\(688\) | 6.79318 | − | 24.3087i | 0.258987 | − | 0.926761i | ||||
\(689\) | − | 5.21087i | − | 0.198518i | ||||||
\(690\) | −10.4110 | − | 0.819631i | −0.396342 | − | 0.0312028i | ||||
\(691\) | −13.2798 | −0.505186 | −0.252593 | − | 0.967573i | \(-0.581283\pi\) | ||||
−0.252593 | + | 0.967573i | \(0.581283\pi\) | |||||||
\(692\) | −24.9397 | + | 18.9257i | −0.948063 | + | 0.719446i | ||||
\(693\) | −4.14065 | − | 4.31727i | −0.157290 | − | 0.164000i | ||||
\(694\) | 10.3626 | + | 30.7978i | 0.393360 | + | 1.16907i | ||||
\(695\) | 40.1369 | 1.52248 | ||||||||
\(696\) | 35.2177 | − | 22.6023i | 1.33492 | − | 0.856739i | ||||
\(697\) | −13.5365 | −0.512731 | ||||||||
\(698\) | 9.53988 | + | 28.3526i | 0.361090 | + | 1.07316i | ||||
\(699\) | −6.17944 | + | 14.4888i | −0.233728 | + | 0.548017i | ||||
\(700\) | 1.74862 | + | 2.30428i | 0.0660916 | + | 0.0870934i | ||||
\(701\) | 26.1554 | 0.987875 | 0.493938 | − | 0.869497i | \(-0.335557\pi\) | ||||
0.493938 | + | 0.869497i | \(0.335557\pi\) | |||||||
\(702\) | 22.7650 | − | 18.6345i | 0.859210 | − | 0.703313i | ||||
\(703\) | 0.360333i | 0.0135902i | ||||||||
\(704\) | 31.8167 | − | 12.5843i | 1.19914 | − | 0.474290i | ||||
\(705\) | −17.9730 | − | 7.66545i | −0.676903 | − | 0.288698i | ||||
\(706\) | −8.37609 | − | 24.8938i | −0.315238 | − | 0.936891i | ||||
\(707\) | − | 0.423786i | − | 0.0159381i | ||||||
\(708\) | 2.53689 | + | 10.1034i | 0.0953423 | + | 0.379707i | ||||
\(709\) | 3.81405i | 0.143240i | 0.997432 | + | 0.0716198i | \(0.0228168\pi\) | ||||
−0.997432 | + | 0.0716198i | \(0.977183\pi\) | |||||||
\(710\) | 25.9808 | − | 8.74184i | 0.975043 | − | 0.328075i | ||||
\(711\) | 31.7066 | − | 30.4095i | 1.18909 | − | 1.14044i | ||||
\(712\) | −37.0873 | − | 25.2139i | −1.38990 | − | 0.944931i | ||||
\(713\) | − | 11.4532i | − | 0.428924i | ||||||
\(714\) | −3.96655 | − | 0.312275i | −0.148444 | − | 0.0116866i | ||||
\(715\) | 48.7374 | 1.82267 | ||||||||
\(716\) | −1.59386 | − | 2.10033i | −0.0595652 | − | 0.0784931i | ||||
\(717\) | −6.59851 | − | 2.81425i | −0.246426 | − | 0.105100i | ||||
\(718\) | 9.53509 | − | 3.20830i | 0.355847 | − | 0.119733i | ||||
\(719\) | −35.8564 | −1.33722 | −0.668609 | − | 0.743614i | \(-0.733110\pi\) | ||||
−0.668609 | + | 0.743614i | \(0.733110\pi\) | |||||||
\(720\) | 30.1056 | − | 16.1360i | 1.12197 | − | 0.601354i | ||||
\(721\) | −9.15582 | −0.340981 | ||||||||
\(722\) | −1.34037 | + | 0.450999i | −0.0498835 | + | 0.0167844i | ||||
\(723\) | 13.7328 | + | 5.85699i | 0.510727 | + | 0.217824i | ||||
\(724\) | 26.3229 | + | 34.6875i | 0.978283 | + | 1.28915i | ||||
\(725\) | 26.4987 | 0.984138 | ||||||||
\(726\) | −17.8058 | − | 1.40180i | −0.660836 | − | 0.0520257i | ||||
\(727\) | 31.0603i | 1.15196i | 0.817463 | + | 0.575982i | \(0.195380\pi\) | ||||
−0.817463 | + | 0.575982i | \(0.804620\pi\) | |||||||
\(728\) | −2.96815 | + | 4.36587i | −0.110007 | + | 0.161810i | ||||
\(729\) | −20.2495 | + | 17.8594i | −0.749982 | + | 0.661459i | ||||
\(730\) | 5.37892 | − | 1.80986i | 0.199083 | − | 0.0669860i | ||||
\(731\) | 21.9844i | 0.813121i | ||||||||
\(732\) | 1.86367 | + | 7.42219i | 0.0688832 | + | 0.274332i | ||||
\(733\) | 11.3722i | 0.420043i | 0.977697 | + | 0.210022i | \(0.0673534\pi\) | ||||
−0.977697 | + | 0.210022i | \(0.932647\pi\) | |||||||
\(734\) | 0.233191 | + | 0.693046i | 0.00860724 | + | 0.0255808i | ||||
\(735\) | −30.7588 | − | 13.1186i | −1.13456 | − | 0.483886i | ||||
\(736\) | −0.440992 | − | 8.46145i | −0.0162552 | − | 0.311893i | ||||
\(737\) | 50.4163i | 1.85711i | ||||||||
\(738\) | 7.63680 | − | 14.6081i | 0.281115 | − | 0.537732i | ||||
\(739\) | −14.8112 | −0.544840 | −0.272420 | − | 0.962178i | \(-0.587824\pi\) | ||||
−0.272420 | + | 0.962178i | \(0.587824\pi\) | |||||||
\(740\) | 1.24004 | + | 1.63409i | 0.0455849 | + | 0.0600704i | ||||
\(741\) | −2.72032 | + | 6.37829i | −0.0999336 | + | 0.234312i | ||||
\(742\) | −0.273683 | − | 0.813387i | −0.0100472 | − | 0.0298604i | ||||
\(743\) | 14.6124 | 0.536075 | 0.268038 | − | 0.963408i | \(-0.413625\pi\) | ||||
0.268038 | + | 0.963408i | \(0.413625\pi\) | |||||||
\(744\) | 20.2331 | + | 31.5261i | 0.741783 | + | 1.15580i | ||||
\(745\) | −32.9423 | −1.20691 | ||||||||
\(746\) | −12.2259 | − | 36.3354i | −0.447621 | − | 1.33033i | ||||
\(747\) | 31.8024 | − | 30.5013i | 1.16359 | − | 1.11599i | ||||
\(748\) | −23.7400 | + | 18.0153i | −0.868020 | + | 0.658705i | ||||
\(749\) | 2.44501 | 0.0893388 | ||||||||
\(750\) | −13.1913 | − | 1.03851i | −0.481678 | − | 0.0379211i | ||||
\(751\) | − | 16.2098i | − | 0.591503i | −0.955265 | − | 0.295751i | \(-0.904430\pi\) | ||
0.955265 | − | 0.295751i | \(-0.0955700\pi\) | |||||||
\(752\) | 4.26670 | − | 15.2680i | 0.155591 | − | 0.556765i | ||||
\(753\) | 2.07287 | − | 4.86022i | 0.0755397 | − | 0.177116i | ||||
\(754\) | 15.4229 | + | 45.8369i | 0.561668 | + | 1.66928i | ||||
\(755\) | − | 35.9809i | − | 1.30948i | ||||||
\(756\) | 2.57478 | − | 4.10439i | 0.0936438 | − | 0.149275i | ||||
\(757\) | − | 25.0524i | − | 0.910547i | −0.890352 | − | 0.455273i | \(-0.849542\pi\) | ||
0.890352 | − | 0.455273i | \(-0.150458\pi\) | |||||||
\(758\) | 6.11120 | − | 2.05625i | 0.221969 | − | 0.0746864i | ||||
\(759\) | −4.35284 | + | 10.2060i | −0.157998 | + | 0.370455i | ||||
\(760\) | −4.52645 | + | 6.65799i | −0.164192 | + | 0.241511i | ||||
\(761\) | 5.42352i | 0.196602i | 0.995157 | + | 0.0983012i | \(0.0313408\pi\) | ||||
−0.995157 | + | 0.0983012i | \(0.968659\pi\) | |||||||
\(762\) | 0.503126 | − | 6.39076i | 0.0182263 | − | 0.231513i | ||||
\(763\) | 0.0630165 | 0.00228135 | ||||||||
\(764\) | −5.44420 | + | 4.13138i | −0.196964 | + | 0.149468i | ||||
\(765\) | −21.4720 | + | 20.5936i | −0.776320 | + | 0.744562i | ||||
\(766\) | 11.1417 | − | 3.74887i | 0.402566 | − | 0.135452i | ||||
\(767\) | −12.0389 | −0.434698 | ||||||||
\(768\) | 16.1619 | + | 22.5121i | 0.583192 | + | 0.812335i | ||||
\(769\) | −29.2196 | −1.05369 | −0.526843 | − | 0.849963i | \(-0.676624\pi\) | ||||
−0.526843 | + | 0.849963i | \(0.676624\pi\) | |||||||
\(770\) | 7.60763 | − | 2.55976i | 0.274160 | − | 0.0922473i | ||||
\(771\) | 2.84456 | − | 6.66957i | 0.102444 | − | 0.240199i | ||||
\(772\) | 35.6763 | − | 27.0733i | 1.28402 | − | 0.974389i | ||||
\(773\) | 14.1117 | 0.507564 | 0.253782 | − | 0.967262i | \(-0.418325\pi\) | ||||
0.253782 | + | 0.967262i | \(0.418325\pi\) | |||||||
\(774\) | −23.7248 | − | 12.4028i | −0.852769 | − | 0.445809i | ||||
\(775\) | 23.7211i | 0.852087i | ||||||||
\(776\) | 22.7932 | − | 33.5267i | 0.818229 | − | 1.20354i | ||||
\(777\) | 0.267652 | + | 0.114153i | 0.00960195 | + | 0.00409521i | ||||
\(778\) | 25.3745 | − | 8.53782i | 0.909719 | − | 0.306096i | ||||
\(779\) | 3.88529i | 0.139205i | ||||||||
\(780\) | 9.61360 | + | 38.2868i | 0.344222 | + | 1.37089i | ||||
\(781\) | − | 29.1241i | − | 1.04214i | ||||||
\(782\) | 2.35352 | + | 6.99468i | 0.0841617 | + | 0.250129i | ||||
\(783\) | −15.6931 | − | 41.5183i | −0.560826 | − | 1.48374i | ||||
\(784\) | 7.30199 | − | 26.1294i | 0.260785 | − | 0.933194i | ||||
\(785\) | 2.65416i | 0.0947309i | ||||||||
\(786\) | −1.71208 | + | 21.7471i | −0.0610680 | + | 0.775693i | ||||
\(787\) | 1.16977 | 0.0416978 | 0.0208489 | − | 0.999783i | \(-0.493363\pi\) | ||||
0.0208489 | + | 0.999783i | \(0.493363\pi\) | |||||||
\(788\) | −30.0062 | + | 22.7704i | −1.06893 | + | 0.811163i | ||||
\(789\) | −33.6904 | − | 14.3689i | −1.19941 | − | 0.511545i | ||||
\(790\) | 18.7992 | + | 55.8713i | 0.668845 | + | 1.98781i | ||||
\(791\) | 7.80749 | 0.277602 | ||||||||
\(792\) | −6.04825 | − | 35.7830i | −0.214915 | − | 1.27149i | ||||
\(793\) | −8.84406 | −0.314062 | ||||||||
\(794\) | 8.91624 | + | 26.4992i | 0.316426 | + | 0.940420i | ||||
\(795\) | −5.90266 | − | 2.51747i | −0.209346 | − | 0.0892855i | ||||
\(796\) | −23.2885 | − | 30.6888i | −0.825438 | − | 1.08774i | ||||
\(797\) | 27.3497 | 0.968776 | 0.484388 | − | 0.874853i | \(-0.339042\pi\) | ||||
0.484388 | + | 0.874853i | \(0.339042\pi\) | |||||||
\(798\) | −0.0896300 | + | 1.13849i | −0.00317287 | + | 0.0403021i | ||||
\(799\) | 13.8081i | 0.488494i | ||||||||
\(800\) | 0.913356 | + | 17.5249i | 0.0322920 | + | 0.619598i | ||||
\(801\) | −34.3297 | + | 32.9253i | −1.21298 | + | 1.16336i | ||||
\(802\) | 3.62245 | + | 10.7659i | 0.127913 | + | 0.380159i | ||||
\(803\) | − | 6.02970i | − | 0.212783i | ||||||
\(804\) | −39.6057 | + | 9.94478i | −1.39679 | + | 0.350725i | ||||
\(805\) | − | 1.98772i | − | 0.0700580i | ||||||
\(806\) | −41.0323 | + | 13.8062i | −1.44530 | + | 0.486304i | ||||
\(807\) | −12.3216 | − | 5.25514i | −0.433741 | − | 0.184990i | ||||
\(808\) | 1.44547 | − | 2.12614i | 0.0508513 | − | 0.0747975i | ||||
\(809\) | 20.4291i | 0.718249i | 0.933290 | + | 0.359124i | \(0.116925\pi\) | ||||
−0.933290 | + | 0.359124i | \(0.883075\pi\) | |||||||
\(810\) | −10.1102 | − | 34.7899i | −0.355235 | − | 1.22239i | ||||
\(811\) | −15.2642 | −0.535998 | −0.267999 | − | 0.963419i | \(-0.586362\pi\) | ||||
−0.267999 | + | 0.963419i | \(0.586362\pi\) | |||||||
\(812\) | 4.81485 | + | 6.34485i | 0.168968 | + | 0.222661i | ||||
\(813\) | −2.07325 | + | 4.86110i | −0.0727120 | + | 0.170486i | ||||
\(814\) | 2.06565 | − | 0.695036i | 0.0724011 | − | 0.0243610i | ||||
\(815\) | −65.8189 | −2.30554 | ||||||||
\(816\) | −18.8351 | − | 15.0959i | −0.659362 | − | 0.528464i | ||||
\(817\) | 6.31001 | 0.220759 | ||||||||
\(818\) | 39.4442 | − | 13.2719i | 1.37914 | − | 0.464042i | ||||
\(819\) | 3.87593 | + | 4.04125i | 0.135436 | + | 0.141213i | ||||
\(820\) | 13.3707 | + | 17.6195i | 0.466927 | + | 0.615301i | ||||
\(821\) | 22.7493 | 0.793956 | 0.396978 | − | 0.917828i | \(-0.370059\pi\) | ||||
0.396978 | + | 0.917828i | \(0.370059\pi\) | |||||||
\(822\) | −1.30462 | + | 16.5714i | −0.0455038 | + | 0.577995i | ||||
\(823\) | − | 10.0940i | − | 0.351854i | −0.984403 | − | 0.175927i | \(-0.943708\pi\) | ||
0.984403 | − | 0.175927i | \(-0.0562923\pi\) | |||||||
\(824\) | −45.9350 | − | 31.2290i | −1.60022 | − | 1.08792i | ||||
\(825\) | 9.01535 | − | 21.1381i | 0.313874 | − | 0.735934i | ||||
\(826\) | −1.87920 | + | 0.632299i | −0.0653856 | + | 0.0220005i | ||||
\(827\) | − | 8.22962i | − | 0.286172i | −0.989710 | − | 0.143086i | \(-0.954297\pi\) | ||
0.989710 | − | 0.143086i | \(-0.0457026\pi\) | |||||||
\(828\) | −8.87619 | − | 1.40631i | −0.308469 | − | 0.0488726i | ||||
\(829\) | 26.0198i | 0.903706i | 0.892092 | + | 0.451853i | \(0.149237\pi\) | ||||
−0.892092 | + | 0.451853i | \(0.850763\pi\) | |||||||
\(830\) | 18.8560 | + | 56.0401i | 0.654501 | + | 1.94518i | ||||
\(831\) | −12.8129 | + | 30.0421i | −0.444474 | + | 1.04215i | ||||
\(832\) | −29.7826 | + | 11.7798i | −1.03252 | + | 0.408391i | ||||
\(833\) | 23.6310i | 0.818765i | ||||||||
\(834\) | 34.4331 | + | 2.71082i | 1.19232 | + | 0.0938680i | ||||
\(835\) | −53.1602 | −1.83969 | ||||||||
\(836\) | 5.17081 | + | 6.81392i | 0.178836 | + | 0.235664i | ||||
\(837\) | 37.1663 | − | 14.0481i | 1.28466 | − | 0.485575i | ||||
\(838\) | 5.73347 | + | 17.0399i | 0.198060 | + | 0.588635i | ||||
\(839\) | −37.2701 | −1.28671 | −0.643353 | − | 0.765569i | \(-0.722457\pi\) | ||||
−0.643353 | + | 0.765569i | \(0.722457\pi\) | |||||||
\(840\) | 3.51151 | + | 5.47143i | 0.121159 | + | 0.188782i | ||||
\(841\) | 43.9645 | 1.51602 | ||||||||
\(842\) | −11.9400 | − | 35.4857i | −0.411478 | − | 1.22292i | ||||
\(843\) | −10.4892 | + | 24.5937i | −0.361266 | + | 0.847053i | ||||
\(844\) | −23.3797 | + | 17.7419i | −0.804764 | + | 0.610702i | ||||
\(845\) | −8.61779 | −0.296461 | ||||||||
\(846\) | −14.9012 | − | 7.79001i | −0.512313 | − | 0.267826i | ||||
\(847\) | − | 3.39957i | − | 0.116810i | ||||||
\(848\) | 1.40126 | − | 5.01427i | 0.0481195 | − | 0.172191i | ||||
\(849\) | −26.2610 | − | 11.2002i | −0.901275 | − | 0.384391i | ||||
\(850\) | −4.87448 | − | 14.4870i | −0.167193 | − | 0.496899i | ||||
\(851\) | − | 0.539714i | − | 0.0185012i | ||||||
\(852\) | 22.8792 | − | 5.74483i | 0.783827 | − | 0.196815i | ||||
\(853\) | − | 49.0827i | − | 1.68056i | −0.542153 | − | 0.840280i | \(-0.682391\pi\) | ||
0.542153 | − | 0.840280i | \(-0.317609\pi\) | |||||||
\(854\) | −1.38051 | + | 0.464503i | −0.0472400 | + | 0.0158950i | ||||
\(855\) | 5.91082 | + | 6.16295i | 0.202146 | + | 0.210768i | ||||
\(856\) | 12.2667 | + | 8.33954i | 0.419267 | + | 0.285040i | ||||
\(857\) | 23.7686i | 0.811919i | 0.913891 | + | 0.405959i | \(0.133063\pi\) | ||||
−0.913891 | + | 0.405959i | \(0.866937\pi\) | |||||||
\(858\) | 41.8114 | + | 3.29169i | 1.42742 | + | 0.112376i | ||||
\(859\) | −3.42519 | −0.116866 | −0.0584330 | − | 0.998291i | \(-0.518610\pi\) | ||||
−0.0584330 | + | 0.998291i | \(0.518610\pi\) | |||||||
\(860\) | 28.6155 | − | 21.7152i | 0.975782 | − | 0.740481i | ||||
\(861\) | 2.88595 | + | 1.23085i | 0.0983528 | + | 0.0419472i | ||||
\(862\) | 6.00760 | − | 2.02139i | 0.204620 | − | 0.0688489i | ||||
\(863\) | 46.0387 | 1.56717 | 0.783587 | − | 0.621282i | \(-0.213388\pi\) | ||||
0.783587 | + | 0.621282i | \(0.213388\pi\) | |||||||
\(864\) | 26.9171 | − | 11.8097i | 0.915739 | − | 0.401773i | ||||
\(865\) | −44.5576 | −1.51500 | ||||||||
\(866\) | −42.3361 | + | 14.2450i | −1.43864 | + | 0.484063i | ||||
\(867\) | −7.74526 | − | 3.30334i | −0.263043 | − | 0.112187i | ||||
\(868\) | −5.67978 | + | 4.31015i | −0.192784 | + | 0.146296i | ||||
\(869\) | 62.6310 | 2.12461 | ||||||||
\(870\) | 59.3733 | + | 4.67429i | 2.01294 | + | 0.158473i | ||||
\(871\) | − | 47.1930i | − | 1.59907i | ||||||
\(872\) | 0.316155 | + | 0.214939i | 0.0107064 | + | 0.00727876i | ||||
\(873\) | −29.7643 | − | 31.0339i | −1.00737 | − | 1.05034i | ||||
\(874\) | 2.00764 | − | 0.675515i | 0.0679093 | − | 0.0228496i | ||||
\(875\) | − | 2.51854i | − | 0.0851421i | ||||||
\(876\) | 4.73677 | − | 1.18938i | 0.160041 | − | 0.0401853i | ||||
\(877\) | − | 41.7008i | − | 1.40814i | −0.710132 | − | 0.704068i | \(-0.751365\pi\) | ||
0.710132 | − | 0.704068i | \(-0.248635\pi\) | |||||||
\(878\) | 13.9222 | + | 41.3768i | 0.469851 | + | 1.39640i | ||||
\(879\) | 46.6382 | + | 19.8911i | 1.57307 | + | 0.670909i | ||||
\(880\) | 46.8986 | + | 13.1060i | 1.58095 | + | 0.441804i | ||||
\(881\) | − | 30.3385i | − | 1.02213i | −0.859542 | − | 0.511065i | \(-0.829251\pi\) | ||
0.859542 | − | 0.511065i | \(-0.170749\pi\) | |||||||
\(882\) | −25.5017 | − | 13.3317i | −0.858688 | − | 0.448903i | ||||
\(883\) | 30.8512 | 1.03823 | 0.519113 | − | 0.854706i | \(-0.326262\pi\) | ||||
0.519113 | + | 0.854706i | \(0.326262\pi\) | |||||||
\(884\) | 22.2222 | − | 16.8635i | 0.747414 | − | 0.567182i | ||||
\(885\) | −5.81620 | + | 13.6371i | −0.195509 | + | 0.458407i | ||||
\(886\) | 6.09559 | + | 18.1161i | 0.204785 | + | 0.608623i | ||||
\(887\) | −49.1511 | −1.65033 | −0.825166 | − | 0.564890i | \(-0.808919\pi\) | ||||
−0.825166 | + | 0.564890i | \(0.808919\pi\) | |||||||
\(888\) | 0.953459 | + | 1.48563i | 0.0319960 | + | 0.0498543i | ||||
\(889\) | 1.22015 | 0.0409226 | ||||||||
\(890\) | −20.3545 | − | 60.4937i | −0.682284 | − | 2.02775i | ||||
\(891\) | −38.4584 | − | 1.60685i | −1.28840 | − | 0.0538316i | ||||
\(892\) | 14.2057 | + | 18.7198i | 0.475643 | + | 0.626787i | ||||
\(893\) | 3.96323 | 0.132625 | ||||||||
\(894\) | −28.2609 | − | 2.22490i | −0.945186 | − | 0.0744117i | ||||
\(895\) | − | 3.75248i | − | 0.125432i | ||||||
\(896\) | −4.03020 | + | 3.40298i | −0.134639 | + | 0.113686i | ||||
\(897\) | 4.07455 | − | 9.55351i | 0.136045 | − | 0.318983i | ||||
\(898\) | 17.8699 | + | 53.1095i | 0.596326 | + | 1.77229i | ||||
\(899\) | 65.3163i | 2.17842i | ||||||||
\(900\) | 18.3839 | + | 2.91267i | 0.612795 | + | 0.0970889i | ||||
\(901\) | 4.53482i | 0.151077i | ||||||||
\(902\) | 22.2728 | − | 7.49420i | 0.741604 | − | 0.249530i | ||||
\(903\) | 1.99900 | − | 4.68701i | 0.0665225 | − | 0.155974i | ||||
\(904\) | 39.1704 | + | 26.6301i | 1.30279 | + | 0.885704i | ||||
\(905\) | 61.9732i | 2.06006i | ||||||||
\(906\) | 2.43013 | − | 30.8677i | 0.0807356 | − | 1.02551i | ||||
\(907\) | −0.778059 | −0.0258350 | −0.0129175 | − | 0.999917i | \(-0.504112\pi\) | ||||
−0.0129175 | + | 0.999917i | \(0.504112\pi\) | |||||||
\(908\) | −1.35731 | − | 1.78862i | −0.0450439 | − | 0.0593575i | ||||
\(909\) | −1.88755 | − | 1.96806i | −0.0626060 | − | 0.0652764i | ||||
\(910\) | −7.12125 | + | 2.39611i | −0.236067 | + | 0.0794302i | ||||
\(911\) | −30.2563 | −1.00243 | −0.501217 | − | 0.865321i | \(-0.667114\pi\) | ||||
−0.501217 | + | 0.865321i | \(0.667114\pi\) | |||||||
\(912\) | −4.33288 | + | 5.40612i | −0.143476 | + | 0.179014i | ||||
\(913\) | 62.8202 | 2.07904 | ||||||||
\(914\) | 48.1677 | − | 16.2071i | 1.59325 | − | 0.536084i | ||||
\(915\) | −4.27274 | + | 10.0182i | −0.141252 | + | 0.331191i | ||||
\(916\) | −31.0011 | − | 40.8523i | −1.02431 | − | 1.34980i | ||||
\(917\) | −4.15205 | −0.137113 | ||||||||
\(918\) | −19.8115 | + | 16.2168i | −0.653877 | + | 0.535236i | ||||
\(919\) | 3.71572i | 0.122570i | 0.998120 | + | 0.0612851i | \(0.0195199\pi\) | ||||
−0.998120 | + | 0.0612851i | \(0.980480\pi\) | |||||||
\(920\) | 6.77980 | − | 9.97245i | 0.223523 | − | 0.328782i | ||||
\(921\) | 34.1053 | + | 14.5458i | 1.12381 | + | 0.479301i | ||||
\(922\) | 54.5992 | − | 18.3711i | 1.79813 | − | 0.605021i | ||||
\(923\) | 27.2621i | 0.897344i | ||||||||
\(924\) | 6.69941 | − | 1.68218i | 0.220394 | − | 0.0553398i | ||||
\(925\) | 1.11782i | 0.0367538i | ||||||||
\(926\) | −5.06986 | − | 15.0677i | −0.166606 | − | 0.495155i | ||||
\(927\) | −42.5196 | + | 40.7802i | −1.39653 | + | 1.33940i | ||||
\(928\) | 2.51494 | + | 48.2549i | 0.0825568 | + | 1.58405i | ||||
\(929\) | 47.2890i | 1.55150i | 0.631039 | + | 0.775751i | \(0.282629\pi\) | ||||
−0.631039 | + | 0.775751i | \(0.717371\pi\) | |||||||
\(930\) | −4.18432 | + | 53.1497i | −0.137209 | + | 1.74285i | ||||
\(931\) | 6.78263 | 0.222292 | ||||||||
\(932\) | −10.9950 | − | 14.4888i | −0.360152 | − | 0.474597i | ||||
\(933\) | −13.0119 | − | 5.54955i | −0.425991 | − | 0.181684i | ||||
\(934\) | −9.98829 | − | 29.6853i | −0.326827 | − | 0.971332i | ||||
\(935\) | −42.4142 | −1.38709 | ||||||||
\(936\) | 5.66157 | + | 33.4953i | 0.185054 | + | 1.09483i | ||||
\(937\) | 14.3287 | 0.468099 | 0.234049 | − | 0.972225i | \(-0.424802\pi\) | ||||
0.234049 | + | 0.972225i | \(0.424802\pi\) | |||||||
\(938\) | −2.47865 | − | 7.36656i | −0.0809307 | − | 0.240527i | ||||
\(939\) | 28.0701 | + | 11.9718i | 0.916032 | + | 0.390685i | ||||
\(940\) | 17.9730 | − | 13.6390i | 0.586215 | − | 0.444855i | ||||
\(941\) | 12.3295 | 0.401931 | 0.200965 | − | 0.979598i | \(-0.435592\pi\) | ||||
0.200965 | + | 0.979598i | \(0.435592\pi\) | |||||||
\(942\) | −0.179260 | + | 2.27698i | −0.00584061 | + | 0.0741880i | ||||
\(943\) | − | 5.81945i | − | 0.189507i | ||||||
\(944\) | −11.5846 | − | 3.23738i | −0.377048 | − | 0.105368i | ||||
\(945\) | 6.45030 | − | 2.43809i | 0.209828 | − | 0.0793110i | ||||
\(946\) | −12.1712 | − | 36.1729i | −0.395719 | − | 1.17608i | ||||
\(947\) | 22.0884i | 0.717776i | 0.933381 | + | 0.358888i | \(0.116844\pi\) | ||||
−0.933381 | + | 0.358888i | \(0.883156\pi\) | |||||||
\(948\) | 12.3542 | + | 49.2013i | 0.401244 | + | 1.59798i | ||||
\(949\) | 5.64420i | 0.183218i | ||||||||
\(950\) | −4.15810 | + | 1.39909i | −0.134906 | + | 0.0453924i | ||||
\(951\) | −4.02556 | − | 1.71689i | −0.130538 | − | 0.0556740i | ||||
\(952\) | 2.58307 | − | 3.79945i | 0.0837176 | − | 0.123141i | ||||
\(953\) | − | 51.7883i | − | 1.67759i | −0.544449 | − | 0.838794i | \(-0.683261\pi\) | ||
0.544449 | − | 0.838794i | \(-0.316739\pi\) | |||||||
\(954\) | −4.89382 | − | 2.55838i | −0.158443 | − | 0.0828306i | ||||
\(955\) | −9.72669 | −0.314748 | ||||||||
\(956\) | 6.59851 | − | 5.00734i | 0.213411 | − | 0.161949i | ||||
\(957\) | 24.8239 | − | 58.2040i | 0.802442 | − | 1.88147i | ||||
\(958\) | −19.4247 | + | 6.53590i | −0.627585 | + | 0.211165i | ||||
\(959\) | −3.16389 | −0.102167 | ||||||||
\(960\) | −1.04485 | + | 39.4275i | −0.0337225 | + | 1.27252i | ||||
\(961\) | −27.4698 | −0.886123 | ||||||||
\(962\) | −1.93359 | + | 0.650600i | −0.0623414 | + | 0.0209762i | ||||
\(963\) | 11.3546 | − | 10.8901i | 0.365898 | − | 0.350929i | ||||
\(964\) | −13.7328 | + | 10.4212i | −0.442303 | + | 0.335645i | ||||
\(965\) | 63.7398 | 2.05186 | ||||||||
\(966\) | 0.134249 | − | 1.70525i | 0.00431940 | − | 0.0548656i | ||||
\(967\) | − | 7.70555i | − | 0.247794i | −0.992295 | − | 0.123897i | \(-0.960461\pi\) | ||
0.992295 | − | 0.123897i | \(-0.0395392\pi\) | |||||||
\(968\) | 11.5954 | − | 17.0557i | 0.372690 | − | 0.548191i | ||||
\(969\) | 2.36739 | − | 5.55077i | 0.0760516 | − | 0.178317i | ||||
\(970\) | 54.6860 | − | 18.4003i | 1.75586 | − | 0.590799i | ||||
\(971\) | − | 56.4878i | − | 1.81278i | −0.422443 | − | 0.906389i | \(-0.638827\pi\) | ||
0.422443 | − | 0.906389i | \(-0.361173\pi\) | |||||||
\(972\) | −6.32373 | − | 30.5288i | −0.202834 | − | 0.979213i | ||||
\(973\) | 6.57412i | 0.210757i | ||||||||
\(974\) | −9.62853 | − | 28.6161i | −0.308518 | − | 0.916919i | ||||
\(975\) | −8.43897 | + | 19.7867i | −0.270263 | + | 0.633681i | ||||
\(976\) | −8.51039 | − | 2.37827i | −0.272411 | − | 0.0761265i | ||||
\(977\) | 15.5457i | 0.497352i | 0.968587 | + | 0.248676i | \(0.0799954\pi\) | ||||
−0.968587 | + | 0.248676i | \(0.920005\pi\) | |||||||
\(978\) | −56.4655 | − | 4.44536i | −1.80557 | − | 0.142147i | ||||
\(979\) | −67.8126 | −2.16730 | ||||||||
\(980\) | 30.7588 | − | 23.3416i | 0.982555 | − | 0.745621i | ||||
\(981\) | 0.292648 | − | 0.280676i | 0.00934354 | − | 0.00896130i | ||||
\(982\) | 8.14364 | + | 24.2030i | 0.259874 | + | 0.772348i | ||||
\(983\) | −18.2981 | −0.583618 | −0.291809 | − | 0.956477i | \(-0.594257\pi\) | ||||
−0.291809 | + | 0.956477i | \(0.594257\pi\) | |||||||
\(984\) | 10.2806 | + | 16.0187i | 0.327735 | + | 0.510658i | ||||
\(985\) | −53.6095 | −1.70814 | ||||||||
\(986\) | −13.4219 | − | 39.8901i | −0.427441 | − | 1.27036i | ||||
\(987\) | 1.25554 | − | 2.94385i | 0.0399644 | − | 0.0937036i | ||||
\(988\) | −4.84022 | − | 6.37829i | −0.153988 | − | 0.202920i | ||||
\(989\) | −9.45125 | −0.300532 | ||||||||
\(990\) | 23.9286 | − | 45.7720i | 0.760500 | − | 1.45473i | ||||
\(991\) | 57.6946i | 1.83273i | 0.400346 | + | 0.916364i | \(0.368890\pi\) | ||||
−0.400346 | + | 0.916364i | \(0.631110\pi\) | |||||||
\(992\) | −43.1968 | + | 2.25132i | −1.37150 | + | 0.0714795i | ||||
\(993\) | −31.8401 | − | 13.5797i | −1.01042 | − | 0.430940i | ||||
\(994\) | 1.43185 | + | 4.25546i | 0.0454155 | + | 0.134975i | ||||
\(995\) | − | 54.8291i | − | 1.73820i | ||||||
\(996\) | 12.3915 | + | 49.3499i | 0.392639 | + | 1.56371i | ||||
\(997\) | − | 36.9642i | − | 1.17067i | −0.810793 | − | 0.585333i | \(-0.800964\pi\) | ||
0.810793 | − | 0.585333i | \(-0.199036\pi\) | |||||||
\(998\) | −3.08451 | + | 1.03785i | −0.0976383 | + | 0.0328526i | ||||
\(999\) | 1.75141 | − | 0.661999i | 0.0554122 | − | 0.0209447i |
(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 | 456.2.j.e.419.2 | yes | 24 | |
3.2 | odd | 2 | inner | 456.2.j.e.419.23 | yes | 24 | |
4.3 | odd | 2 | 1824.2.j.d.1103.24 | 24 | |||
8.3 | odd | 2 | inner | 456.2.j.e.419.24 | yes | 24 | |
8.5 | even | 2 | 1824.2.j.d.1103.23 | 24 | |||
12.11 | even | 2 | 1824.2.j.d.1103.21 | 24 | |||
24.5 | odd | 2 | 1824.2.j.d.1103.22 | 24 | |||
24.11 | even | 2 | inner | 456.2.j.e.419.1 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
456.2.j.e.419.1 | ✓ | 24 | 24.11 | even | 2 | inner | |
456.2.j.e.419.2 | yes | 24 | 1.1 | even | 1 | trivial | |
456.2.j.e.419.23 | yes | 24 | 3.2 | odd | 2 | inner | |
456.2.j.e.419.24 | yes | 24 | 8.3 | odd | 2 | inner | |
1824.2.j.d.1103.21 | 24 | 12.11 | even | 2 | |||
1824.2.j.d.1103.22 | 24 | 24.5 | odd | 2 | |||
1824.2.j.d.1103.23 | 24 | 8.5 | even | 2 | |||
1824.2.j.d.1103.24 | 24 | 4.3 | odd | 2 |