Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [731,2,Mod(307,731)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(731, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("731.307");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 731 = 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 731.e (of order \(3\), degree \(2\), 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: | \(5.83706438776\) |
Analytic rank: | \(0\) |
Dimension: | \(58\) |
Relative dimension: | \(29\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 307.18 | ||
Character | \(\chi\) | \(=\) | 731.307 |
Dual form | 731.2.e.a.681.18 |
$q$-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 \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).
\(n\) | \(173\) | \(562\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.576537 | 0.407673 | 0.203836 | − | 0.979005i | \(-0.434659\pi\) | ||||
0.203836 | + | 0.979005i | \(0.434659\pi\) | |||||||
\(3\) | 0.0377307 | − | 0.0653514i | 0.0217838 | − | 0.0377307i | −0.854928 | − | 0.518747i | \(-0.826399\pi\) |
0.876712 | + | 0.481016i | \(0.159732\pi\) | |||||||
\(4\) | −1.66761 | −0.833803 | ||||||||
\(5\) | 0.551580 | − | 0.955365i | 0.246674 | − | 0.427252i | −0.715927 | − | 0.698175i | \(-0.753996\pi\) |
0.962601 | + | 0.270923i | \(0.0873289\pi\) | |||||||
\(6\) | 0.0217531 | − | 0.0376775i | 0.00888067 | − | 0.0153818i | ||||
\(7\) | 0.781254 | + | 1.35317i | 0.295286 | + | 0.511450i | 0.975051 | − | 0.221979i | \(-0.0712517\pi\) |
−0.679765 | + | 0.733430i | \(0.737918\pi\) | |||||||
\(8\) | −2.11451 | −0.747592 | ||||||||
\(9\) | 1.49715 | + | 2.59314i | 0.499051 | + | 0.864382i | ||||
\(10\) | 0.318006 | − | 0.550803i | 0.100562 | − | 0.174179i | ||||
\(11\) | −3.20387 | −0.966002 | −0.483001 | − | 0.875620i | \(-0.660453\pi\) | ||||
−0.483001 | + | 0.875620i | \(0.660453\pi\) | |||||||
\(12\) | −0.0629199 | + | 0.108980i | −0.0181634 | + | 0.0314599i | ||||
\(13\) | 1.63462 | + | 2.83124i | 0.453361 | + | 0.785244i | 0.998592 | − | 0.0530413i | \(-0.0168915\pi\) |
−0.545231 | + | 0.838286i | \(0.683558\pi\) | |||||||
\(14\) | 0.450421 | + | 0.780152i | 0.120380 | + | 0.208505i | ||||
\(15\) | −0.0416230 | − | 0.0720931i | −0.0107470 | − | 0.0186144i | ||||
\(16\) | 2.11612 | 0.529030 | ||||||||
\(17\) | 0.500000 | + | 0.866025i | 0.121268 | + | 0.210042i | ||||
\(18\) | 0.863163 | + | 1.49504i | 0.203450 | + | 0.352385i | ||||
\(19\) | 2.42124 | − | 4.19371i | 0.555470 | − | 0.962103i | −0.442397 | − | 0.896820i | \(-0.645872\pi\) |
0.997867 | − | 0.0652831i | \(-0.0207950\pi\) | |||||||
\(20\) | −0.919818 | + | 1.59317i | −0.205678 | + | 0.356244i | ||||
\(21\) | 0.117909 | 0.0257298 | ||||||||
\(22\) | −1.84715 | −0.393813 | ||||||||
\(23\) | −3.80446 | + | 6.58951i | −0.793284 | + | 1.37401i | 0.130639 | + | 0.991430i | \(0.458297\pi\) |
−0.923923 | + | 0.382578i | \(0.875036\pi\) | |||||||
\(24\) | −0.0797818 | + | 0.138186i | −0.0162854 | + | 0.0282071i | ||||
\(25\) | 1.89152 | + | 3.27621i | 0.378304 | + | 0.655241i | ||||
\(26\) | 0.942416 | + | 1.63231i | 0.184823 | + | 0.320123i | ||||
\(27\) | 0.452338 | 0.0870526 | ||||||||
\(28\) | −1.30282 | − | 2.25656i | −0.246210 | − | 0.426449i | ||||
\(29\) | 4.10020 | + | 7.10176i | 0.761388 | + | 1.31876i | 0.942135 | + | 0.335234i | \(0.108815\pi\) |
−0.180747 | + | 0.983530i | \(0.557851\pi\) | |||||||
\(30\) | −0.0239972 | − | 0.0415643i | −0.00438126 | − | 0.00758857i | ||||
\(31\) | −0.597849 | + | 1.03551i | −0.107377 | + | 0.185982i | −0.914707 | − | 0.404118i | \(-0.867578\pi\) |
0.807330 | + | 0.590100i | \(0.200912\pi\) | |||||||
\(32\) | 5.44904 | 0.963263 | ||||||||
\(33\) | −0.120884 | + | 0.209377i | −0.0210432 | + | 0.0364479i | ||||
\(34\) | 0.288268 | + | 0.499295i | 0.0494376 | + | 0.0856284i | ||||
\(35\) | 1.72370 | 0.291358 | ||||||||
\(36\) | −2.49666 | − | 4.32434i | −0.416110 | − | 0.720724i | ||||
\(37\) | −0.803255 | + | 1.39128i | −0.132054 | + | 0.228725i | −0.924468 | − | 0.381259i | \(-0.875491\pi\) |
0.792414 | + | 0.609984i | \(0.208824\pi\) | |||||||
\(38\) | 1.39593 | − | 2.41783i | 0.226450 | − | 0.392223i | ||||
\(39\) | 0.246701 | 0.0395037 | ||||||||
\(40\) | −1.16632 | + | 2.02013i | −0.184412 | + | 0.319410i | ||||
\(41\) | 5.43670 | 0.849070 | 0.424535 | − | 0.905412i | \(-0.360438\pi\) | ||||
0.424535 | + | 0.905412i | \(0.360438\pi\) | |||||||
\(42\) | 0.0679788 | 0.0104894 | ||||||||
\(43\) | 4.43002 | − | 4.83476i | 0.675572 | − | 0.737294i | ||||
\(44\) | 5.34279 | 0.805455 | ||||||||
\(45\) | 3.30320 | 0.492412 | ||||||||
\(46\) | −2.19341 | + | 3.79909i | −0.323400 | + | 0.560146i | ||||
\(47\) | −6.80050 | −0.991955 | −0.495978 | − | 0.868335i | \(-0.665190\pi\) | ||||
−0.495978 | + | 0.868335i | \(0.665190\pi\) | |||||||
\(48\) | 0.0798426 | − | 0.138291i | 0.0115243 | − | 0.0199607i | ||||
\(49\) | 2.27929 | − | 3.94784i | 0.325612 | − | 0.563977i | ||||
\(50\) | 1.09053 | + | 1.88885i | 0.154224 | + | 0.267124i | ||||
\(51\) | 0.0754613 | 0.0105667 | ||||||||
\(52\) | −2.72590 | − | 4.72139i | −0.378014 | − | 0.654739i | ||||
\(53\) | −6.18028 | + | 10.7046i | −0.848927 | + | 1.47038i | 0.0332404 | + | 0.999447i | \(0.489417\pi\) |
−0.882167 | + | 0.470937i | \(0.843916\pi\) | |||||||
\(54\) | 0.260790 | 0.0354890 | ||||||||
\(55\) | −1.76719 | + | 3.06086i | −0.238288 | + | 0.412727i | ||||
\(56\) | −1.65197 | − | 2.86129i | −0.220753 | − | 0.382356i | ||||
\(57\) | −0.182710 | − | 0.316463i | −0.0242005 | − | 0.0419165i | ||||
\(58\) | 2.36392 | + | 4.09442i | 0.310397 | + | 0.537624i | ||||
\(59\) | 2.33740 | 0.304304 | 0.152152 | − | 0.988357i | \(-0.451380\pi\) | ||||
0.152152 | + | 0.988357i | \(0.451380\pi\) | |||||||
\(60\) | 0.0694107 | + | 0.120223i | 0.00896089 | + | 0.0155207i | ||||
\(61\) | 0.222026 | + | 0.384561i | 0.0284276 | + | 0.0492380i | 0.879889 | − | 0.475179i | \(-0.157617\pi\) |
−0.851462 | + | 0.524417i | \(0.824283\pi\) | |||||||
\(62\) | −0.344682 | + | 0.597007i | −0.0437747 | + | 0.0758199i | ||||
\(63\) | −2.33931 | + | 4.05181i | −0.294726 | + | 0.510480i | ||||
\(64\) | −1.09067 | −0.136334 | ||||||||
\(65\) | 3.60649 | 0.447330 | ||||||||
\(66\) | −0.0696941 | + | 0.120714i | −0.00857875 | + | 0.0148588i | ||||
\(67\) | −0.315484 | + | 0.546434i | −0.0385425 | + | 0.0667575i | −0.884653 | − | 0.466250i | \(-0.845605\pi\) |
0.846111 | + | 0.533007i | \(0.178938\pi\) | |||||||
\(68\) | −0.833803 | − | 1.44419i | −0.101113 | − | 0.175134i | ||||
\(69\) | 0.287089 | + | 0.497253i | 0.0345615 | + | 0.0598623i | ||||
\(70\) | 0.993774 | 0.118779 | ||||||||
\(71\) | 4.82381 | + | 8.35508i | 0.572480 | + | 0.991565i | 0.996310 | + | 0.0858233i | \(0.0273521\pi\) |
−0.423830 | + | 0.905742i | \(0.639315\pi\) | |||||||
\(72\) | −3.16574 | − | 5.48323i | −0.373086 | − | 0.646204i | ||||
\(73\) | −4.07923 | − | 7.06544i | −0.477438 | − | 0.826947i | 0.522228 | − | 0.852806i | \(-0.325101\pi\) |
−0.999666 | + | 0.0258592i | \(0.991768\pi\) | |||||||
\(74\) | −0.463106 | + | 0.802123i | −0.0538350 | + | 0.0932449i | ||||
\(75\) | 0.285473 | 0.0329636 | ||||||||
\(76\) | −4.03767 | + | 6.99345i | −0.463153 | + | 0.802204i | ||||
\(77\) | −2.50303 | − | 4.33538i | −0.285247 | − | 0.494062i | ||||
\(78\) | 0.142232 | 0.0161046 | ||||||||
\(79\) | −3.27184 | − | 5.66699i | −0.368110 | − | 0.637586i | 0.621160 | − | 0.783684i | \(-0.286662\pi\) |
−0.989270 | + | 0.146098i | \(0.953328\pi\) | |||||||
\(80\) | 1.16721 | − | 2.02167i | 0.130498 | − | 0.226029i | ||||
\(81\) | −4.47439 | + | 7.74987i | −0.497155 | + | 0.861097i | ||||
\(82\) | 3.13446 | 0.346143 | ||||||||
\(83\) | 4.40743 | − | 7.63388i | 0.483778 | − | 0.837928i | −0.516049 | − | 0.856559i | \(-0.672598\pi\) |
0.999826 | + | 0.0186316i | \(0.00593096\pi\) | |||||||
\(84\) | −0.196626 | −0.0214536 | ||||||||
\(85\) | 1.10316 | 0.119655 | ||||||||
\(86\) | 2.55407 | − | 2.78742i | 0.275412 | − | 0.300575i | ||||
\(87\) | 0.618813 | 0.0663438 | ||||||||
\(88\) | 6.77460 | 0.722175 | ||||||||
\(89\) | −2.55776 | + | 4.43018i | −0.271122 | + | 0.469598i | −0.969150 | − | 0.246474i | \(-0.920728\pi\) |
0.698027 | + | 0.716071i | \(0.254061\pi\) | |||||||
\(90\) | 1.90442 | 0.200743 | ||||||||
\(91\) | −2.55410 | + | 4.42383i | −0.267742 | + | 0.463743i | ||||
\(92\) | 6.34433 | − | 10.9887i | 0.661442 | − | 1.14565i | ||||
\(93\) | 0.0451145 | + | 0.0781406i | 0.00467816 | + | 0.00810281i | ||||
\(94\) | −3.92074 | −0.404393 | ||||||||
\(95\) | −2.67101 | − | 4.62633i | −0.274040 | − | 0.474652i | ||||
\(96\) | 0.205596 | − | 0.356102i | 0.0209835 | − | 0.0363446i | ||||
\(97\) | −16.9192 | −1.71789 | −0.858944 | − | 0.512070i | \(-0.828879\pi\) | ||||
−0.858944 | + | 0.512070i | \(0.828879\pi\) | |||||||
\(98\) | 1.31409 | − | 2.27607i | 0.132743 | − | 0.229918i | ||||
\(99\) | −4.79668 | − | 8.30809i | −0.482084 | − | 0.834994i | ||||
\(100\) | −3.15431 | − | 5.46342i | −0.315431 | − | 0.546342i | ||||
\(101\) | −7.36305 | − | 12.7532i | −0.732651 | − | 1.26899i | −0.955746 | − | 0.294192i | \(-0.904949\pi\) |
0.223095 | − | 0.974797i | \(-0.428384\pi\) | |||||||
\(102\) | 0.0435062 | 0.00430776 | ||||||||
\(103\) | −8.43683 | − | 14.6130i | −0.831306 | − | 1.43986i | −0.897003 | − | 0.442024i | \(-0.854261\pi\) |
0.0656978 | − | 0.997840i | \(-0.479073\pi\) | |||||||
\(104\) | −3.45641 | − | 5.98668i | −0.338929 | − | 0.587042i | ||||
\(105\) | 0.0650362 | − | 0.112646i | 0.00634688 | − | 0.0109931i | ||||
\(106\) | −3.56316 | + | 6.17157i | −0.346084 | + | 0.599436i | ||||
\(107\) | 10.2509 | 0.990990 | 0.495495 | − | 0.868611i | \(-0.334987\pi\) | ||||
0.495495 | + | 0.868611i | \(0.334987\pi\) | |||||||
\(108\) | −0.754322 | −0.0725847 | ||||||||
\(109\) | −3.67488 | + | 6.36507i | −0.351989 | + | 0.609663i | −0.986598 | − | 0.163170i | \(-0.947828\pi\) |
0.634609 | + | 0.772834i | \(0.281161\pi\) | |||||||
\(110\) | −1.01885 | + | 1.76470i | −0.0971435 | + | 0.168257i | ||||
\(111\) | 0.0606147 | + | 0.104988i | 0.00575329 | + | 0.00996500i | ||||
\(112\) | 1.65323 | + | 2.86347i | 0.156215 | + | 0.270573i | ||||
\(113\) | 14.2462 | 1.34017 | 0.670085 | − | 0.742284i | \(-0.266258\pi\) | ||||
0.670085 | + | 0.742284i | \(0.266258\pi\) | |||||||
\(114\) | −0.105339 | − | 0.182452i | −0.00986590 | − | 0.0170882i | ||||
\(115\) | 4.19693 | + | 7.26929i | 0.391365 | + | 0.677865i | ||||
\(116\) | −6.83752 | − | 11.8429i | −0.634848 | − | 1.09959i | ||||
\(117\) | −4.89454 | + | 8.47759i | −0.452501 | + | 0.783754i | ||||
\(118\) | 1.34760 | 0.124057 | ||||||||
\(119\) | −0.781254 | + | 1.35317i | −0.0716174 | + | 0.124045i | ||||
\(120\) | 0.0880122 | + | 0.152442i | 0.00803437 | + | 0.0139159i | ||||
\(121\) | −0.735238 | −0.0668398 | ||||||||
\(122\) | 0.128006 | + | 0.221714i | 0.0115892 | + | 0.0200730i | ||||
\(123\) | 0.205130 | − | 0.355296i | 0.0184960 | − | 0.0320360i | ||||
\(124\) | 0.996977 | − | 1.72681i | 0.0895312 | − | 0.155073i | ||||
\(125\) | 9.68910 | 0.866619 | ||||||||
\(126\) | −1.34870 | + | 2.33601i | −0.120152 | + | 0.208109i | ||||
\(127\) | 3.30243 | 0.293043 | 0.146522 | − | 0.989207i | \(-0.453192\pi\) | ||||
0.146522 | + | 0.989207i | \(0.453192\pi\) | |||||||
\(128\) | −11.5269 | −1.01884 | ||||||||
\(129\) | −0.148811 | − | 0.471927i | −0.0131021 | − | 0.0415509i | ||||
\(130\) | 2.07927 | 0.182364 | ||||||||
\(131\) | −7.56871 | −0.661281 | −0.330640 | − | 0.943757i | \(-0.607265\pi\) | ||||
−0.330640 | + | 0.943757i | \(0.607265\pi\) | |||||||
\(132\) | 0.201587 | − | 0.349159i | 0.0175459 | − | 0.0303904i | ||||
\(133\) | 7.56640 | 0.656090 | ||||||||
\(134\) | −0.181888 | + | 0.315039i | −0.0157127 | + | 0.0272152i | ||||
\(135\) | 0.249501 | − | 0.432148i | 0.0214736 | − | 0.0371934i | ||||
\(136\) | −1.05725 | − | 1.83122i | −0.0906588 | − | 0.157026i | ||||
\(137\) | 0.103039 | 0.00880318 | 0.00440159 | − | 0.999990i | \(-0.498599\pi\) | ||||
0.00440159 | + | 0.999990i | \(0.498599\pi\) | |||||||
\(138\) | 0.165518 | + | 0.286685i | 0.0140898 | + | 0.0244042i | ||||
\(139\) | 7.71565 | − | 13.3639i | 0.654433 | − | 1.13351i | −0.327602 | − | 0.944816i | \(-0.606241\pi\) |
0.982036 | − | 0.188696i | \(-0.0604261\pi\) | |||||||
\(140\) | −2.87445 | −0.242935 | ||||||||
\(141\) | −0.256587 | + | 0.444423i | −0.0216086 | + | 0.0374271i | ||||
\(142\) | 2.78110 | + | 4.81701i | 0.233385 | + | 0.404234i | ||||
\(143\) | −5.23709 | − | 9.07091i | −0.437948 | − | 0.758548i | ||||
\(144\) | 3.16815 | + | 5.48740i | 0.264013 | + | 0.457284i | ||||
\(145\) | 9.04636 | 0.751259 | ||||||||
\(146\) | −2.35183 | − | 4.07348i | −0.194639 | − | 0.337124i | ||||
\(147\) | −0.171998 | − | 0.297909i | −0.0141862 | − | 0.0245711i | ||||
\(148\) | 1.33951 | − | 2.32010i | 0.110107 | − | 0.190711i | ||||
\(149\) | 7.22399 | − | 12.5123i | 0.591812 | − | 1.02505i | −0.402176 | − | 0.915562i | \(-0.631746\pi\) |
0.993988 | − | 0.109487i | \(-0.0349207\pi\) | |||||||
\(150\) | 0.164586 | 0.0134384 | ||||||||
\(151\) | 12.6411 | 1.02872 | 0.514360 | − | 0.857574i | \(-0.328030\pi\) | ||||
0.514360 | + | 0.857574i | \(0.328030\pi\) | |||||||
\(152\) | −5.11973 | + | 8.86763i | −0.415265 | + | 0.719260i | ||||
\(153\) | −1.49715 | + | 2.59314i | −0.121038 | + | 0.209643i | ||||
\(154\) | −1.44309 | − | 2.49950i | −0.116287 | − | 0.201416i | ||||
\(155\) | 0.659524 | + | 1.14233i | 0.0529742 | + | 0.0917540i | ||||
\(156\) | −0.411400 | −0.0329383 | ||||||||
\(157\) | −1.88503 | − | 3.26497i | −0.150442 | − | 0.260573i | 0.780948 | − | 0.624596i | \(-0.214736\pi\) |
−0.931390 | + | 0.364023i | \(0.881403\pi\) | |||||||
\(158\) | −1.88633 | − | 3.26722i | −0.150069 | − | 0.259926i | ||||
\(159\) | 0.466372 | + | 0.807780i | 0.0369857 | + | 0.0640611i | ||||
\(160\) | 3.00558 | − | 5.20582i | 0.237612 | − | 0.411556i | ||||
\(161\) | −11.8890 | −0.936983 | ||||||||
\(162\) | −2.57965 | + | 4.46809i | −0.202676 | + | 0.351046i | ||||
\(163\) | −2.05350 | − | 3.55677i | −0.160842 | − | 0.278587i | 0.774329 | − | 0.632784i | \(-0.218088\pi\) |
−0.935171 | + | 0.354196i | \(0.884754\pi\) | |||||||
\(164\) | −9.06627 | −0.707957 | ||||||||
\(165\) | 0.133354 | + | 0.230977i | 0.0103816 | + | 0.0179815i | ||||
\(166\) | 2.54104 | − | 4.40121i | 0.197223 | − | 0.341600i | ||||
\(167\) | 4.11199 | − | 7.12217i | 0.318195 | − | 0.551130i | −0.661916 | − | 0.749578i | \(-0.730257\pi\) |
0.980112 | + | 0.198448i | \(0.0635900\pi\) | |||||||
\(168\) | −0.249319 | −0.0192354 | ||||||||
\(169\) | 1.15606 | − | 2.00235i | 0.0889275 | − | 0.154027i | ||||
\(170\) | 0.636012 | 0.0487799 | ||||||||
\(171\) | 14.4999 | 1.10883 | ||||||||
\(172\) | −7.38753 | + | 8.06247i | −0.563294 | + | 0.614758i | ||||
\(173\) | 4.17383 | 0.317330 | 0.158665 | − | 0.987332i | \(-0.449281\pi\) | ||||
0.158665 | + | 0.987332i | \(0.449281\pi\) | |||||||
\(174\) | 0.356769 | 0.0270466 | ||||||||
\(175\) | −2.95551 | + | 5.11910i | −0.223416 | + | 0.386967i | ||||
\(176\) | −6.77977 | −0.511044 | ||||||||
\(177\) | 0.0881918 | − | 0.152753i | 0.00662890 | − | 0.0114816i | ||||
\(178\) | −1.47464 | + | 2.55416i | −0.110529 | + | 0.191442i | ||||
\(179\) | 3.01879 | + | 5.22870i | 0.225635 | + | 0.390812i | 0.956510 | − | 0.291700i | \(-0.0942209\pi\) |
−0.730875 | + | 0.682512i | \(0.760888\pi\) | |||||||
\(180\) | −5.50843 | −0.410574 | ||||||||
\(181\) | 8.91907 | + | 15.4483i | 0.662949 | + | 1.14826i | 0.979837 | + | 0.199799i | \(0.0640289\pi\) |
−0.316887 | + | 0.948463i | \(0.602638\pi\) | |||||||
\(182\) | −1.47253 | + | 2.55050i | −0.109151 | + | 0.189056i | ||||
\(183\) | 0.0335088 | 0.00247704 | ||||||||
\(184\) | 8.04456 | − | 13.9336i | 0.593053 | − | 1.02720i | ||||
\(185\) | 0.886119 | + | 1.53480i | 0.0651488 | + | 0.112841i | ||||
\(186\) | 0.0260102 | + | 0.0450509i | 0.00190716 | + | 0.00330329i | ||||
\(187\) | −1.60193 | − | 2.77463i | −0.117145 | − | 0.202901i | ||||
\(188\) | 11.3406 | 0.827095 | ||||||||
\(189\) | 0.353391 | + | 0.612091i | 0.0257054 | + | 0.0445231i | ||||
\(190\) | −1.53994 | − | 2.66725i | −0.111719 | − | 0.193503i | ||||
\(191\) | −8.08708 | + | 14.0072i | −0.585160 | + | 1.01353i | 0.409695 | + | 0.912223i | \(0.365635\pi\) |
−0.994855 | + | 0.101305i | \(0.967698\pi\) | |||||||
\(192\) | −0.0411517 | + | 0.0712769i | −0.00296987 | + | 0.00514396i | ||||
\(193\) | −8.29926 | −0.597394 | −0.298697 | − | 0.954348i | \(-0.596552\pi\) | ||||
−0.298697 | + | 0.954348i | \(0.596552\pi\) | |||||||
\(194\) | −9.75455 | −0.700336 | ||||||||
\(195\) | 0.136075 | − | 0.235689i | 0.00974455 | − | 0.0168781i | ||||
\(196\) | −3.80095 | + | 6.58344i | −0.271496 | + | 0.470246i | ||||
\(197\) | 3.36468 | + | 5.82780i | 0.239724 | + | 0.415214i | 0.960635 | − | 0.277814i | \(-0.0896098\pi\) |
−0.720911 | + | 0.693028i | \(0.756276\pi\) | |||||||
\(198\) | −2.76546 | − | 4.78992i | −0.196533 | − | 0.340405i | ||||
\(199\) | −7.23463 | −0.512849 | −0.256425 | − | 0.966564i | \(-0.582545\pi\) | ||||
−0.256425 | + | 0.966564i | \(0.582545\pi\) | |||||||
\(200\) | −3.99963 | − | 6.92757i | −0.282817 | − | 0.489853i | ||||
\(201\) | 0.0238068 | + | 0.0412346i | 0.00167920 | + | 0.00290847i | ||||
\(202\) | −4.24507 | − | 7.35267i | −0.298682 | − | 0.517332i | ||||
\(203\) | −6.40659 | + | 11.0965i | −0.449655 | + | 0.778825i | ||||
\(204\) | −0.125840 | −0.00881055 | ||||||||
\(205\) | 2.99878 | − | 5.19403i | 0.209444 | − | 0.362767i | ||||
\(206\) | −4.86414 | − | 8.42494i | −0.338901 | − | 0.586993i | ||||
\(207\) | −22.7834 | −1.58356 | ||||||||
\(208\) | 3.45904 | + | 5.99124i | 0.239842 | + | 0.415418i | ||||
\(209\) | −7.75733 | + | 13.4361i | −0.536585 | + | 0.929393i | ||||
\(210\) | 0.0374957 | − | 0.0649445i | 0.00258745 | − | 0.00448160i | ||||
\(211\) | 15.6814 | 1.07955 | 0.539775 | − | 0.841809i | \(-0.318509\pi\) | ||||
0.539775 | + | 0.841809i | \(0.318509\pi\) | |||||||
\(212\) | 10.3063 | − | 17.8510i | 0.707837 | − | 1.22601i | ||||
\(213\) | 0.728022 | 0.0498832 | ||||||||
\(214\) | 5.91001 | 0.404000 | ||||||||
\(215\) | −2.17545 | − | 6.89905i | −0.148364 | − | 0.470511i | ||||
\(216\) | −0.956473 | −0.0650798 | ||||||||
\(217\) | −1.86829 | −0.126828 | ||||||||
\(218\) | −2.11870 | + | 3.66970i | −0.143496 | + | 0.248543i | ||||
\(219\) | −0.615649 | −0.0416017 | ||||||||
\(220\) | 2.94698 | − | 5.10431i | 0.198685 | − | 0.344133i | ||||
\(221\) | −1.63462 | + | 2.83124i | −0.109956 | + | 0.190450i | ||||
\(222\) | 0.0349466 | + | 0.0605293i | 0.00234546 | + | 0.00406246i | ||||
\(223\) | 20.7561 | 1.38993 | 0.694965 | − | 0.719043i | \(-0.255420\pi\) | ||||
0.694965 | + | 0.719043i | \(0.255420\pi\) | |||||||
\(224\) | 4.25708 | + | 7.37348i | 0.284438 | + | 0.492661i | ||||
\(225\) | −5.66378 | + | 9.80996i | −0.377586 | + | 0.653997i | ||||
\(226\) | 8.21346 | 0.546351 | ||||||||
\(227\) | −8.57834 | + | 14.8581i | −0.569364 | + | 0.986168i | 0.427265 | + | 0.904127i | \(0.359477\pi\) |
−0.996629 | + | 0.0820412i | \(0.973856\pi\) | |||||||
\(228\) | 0.304688 | + | 0.527735i | 0.0201785 | + | 0.0349501i | ||||
\(229\) | −6.56925 | − | 11.3783i | −0.434108 | − | 0.751898i | 0.563114 | − | 0.826379i | \(-0.309603\pi\) |
−0.997222 | + | 0.0744813i | \(0.976270\pi\) | |||||||
\(230\) | 2.41968 | + | 4.19101i | 0.159549 | + | 0.276347i | ||||
\(231\) | −0.377764 | −0.0248551 | ||||||||
\(232\) | −8.66991 | − | 15.0167i | −0.569208 | − | 0.985896i | ||||
\(233\) | 8.43527 | + | 14.6103i | 0.552613 | + | 0.957154i | 0.998085 | + | 0.0618577i | \(0.0197025\pi\) |
−0.445472 | + | 0.895296i | \(0.646964\pi\) | |||||||
\(234\) | −2.82188 | + | 4.88764i | −0.184472 | + | 0.319515i | ||||
\(235\) | −3.75102 | + | 6.49696i | −0.244690 | + | 0.423815i | ||||
\(236\) | −3.89787 | −0.253730 | ||||||||
\(237\) | −0.493794 | −0.0320754 | ||||||||
\(238\) | −0.450421 | + | 0.780152i | −0.0291965 | + | 0.0505698i | ||||
\(239\) | 8.87667 | − | 15.3748i | 0.574184 | − | 0.994516i | −0.421945 | − | 0.906621i | \(-0.638653\pi\) |
0.996130 | − | 0.0878951i | \(-0.0280140\pi\) | |||||||
\(240\) | −0.0880792 | − | 0.152558i | −0.00568549 | − | 0.00984756i | ||||
\(241\) | −10.3456 | − | 17.9191i | −0.666417 | − | 1.15427i | −0.978899 | − | 0.204344i | \(-0.934494\pi\) |
0.312482 | − | 0.949924i | \(-0.398840\pi\) | |||||||
\(242\) | −0.423892 | −0.0272488 | ||||||||
\(243\) | 1.01615 | + | 1.76003i | 0.0651861 | + | 0.112906i | ||||
\(244\) | −0.370253 | − | 0.641296i | −0.0237030 | − | 0.0410548i | ||||
\(245\) | −2.51442 | − | 4.35510i | −0.160640 | − | 0.278237i | ||||
\(246\) | 0.118265 | − | 0.204841i | 0.00754031 | − | 0.0130602i | ||||
\(247\) | 15.8312 | 1.00731 | ||||||||
\(248\) | 1.26416 | − | 2.18959i | 0.0802741 | − | 0.139039i | ||||
\(249\) | −0.332590 | − | 0.576063i | −0.0210770 | − | 0.0365065i | ||||
\(250\) | 5.58612 | 0.353297 | ||||||||
\(251\) | 10.6492 | + | 18.4450i | 0.672173 | + | 1.16424i | 0.977287 | + | 0.211922i | \(0.0679722\pi\) |
−0.305114 | + | 0.952316i | \(0.598694\pi\) | |||||||
\(252\) | 3.90105 | − | 6.75682i | 0.245743 | − | 0.425639i | ||||
\(253\) | 12.1890 | − | 21.1119i | 0.766314 | − | 1.32729i | ||||
\(254\) | 1.90397 | 0.119466 | ||||||||
\(255\) | 0.0416230 | − | 0.0720931i | 0.00260653 | − | 0.00451465i | ||||
\(256\) | −4.46433 | −0.279021 | ||||||||
\(257\) | −15.4160 | −0.961624 | −0.480812 | − | 0.876824i | \(-0.659658\pi\) | ||||
−0.480812 | + | 0.876824i | \(0.659658\pi\) | |||||||
\(258\) | −0.0857949 | − | 0.272083i | −0.00534136 | − | 0.0169392i | ||||
\(259\) | −2.51018 | −0.155975 | ||||||||
\(260\) | −6.01420 | −0.372985 | ||||||||
\(261\) | −12.2773 | + | 21.2648i | −0.759943 | + | 1.31626i | ||||
\(262\) | −4.36364 | −0.269586 | ||||||||
\(263\) | 11.2503 | − | 19.4861i | 0.693722 | − | 1.20156i | −0.276888 | − | 0.960902i | \(-0.589303\pi\) |
0.970610 | − | 0.240659i | \(-0.0773636\pi\) | |||||||
\(264\) | 0.255610 | − | 0.442730i | 0.0157317 | − | 0.0272482i | ||||
\(265\) | 6.81784 | + | 11.8088i | 0.418817 | + | 0.725412i | ||||
\(266\) | 4.36231 | 0.267470 | ||||||||
\(267\) | 0.193012 | + | 0.334307i | 0.0118122 | + | 0.0204593i | ||||
\(268\) | 0.526102 | − | 0.911236i | 0.0321368 | − | 0.0556626i | ||||
\(269\) | 17.4368 | 1.06314 | 0.531570 | − | 0.847014i | \(-0.321602\pi\) | ||||
0.531570 | + | 0.847014i | \(0.321602\pi\) | |||||||
\(270\) | 0.143846 | − | 0.249149i | 0.00875421 | − | 0.0151627i | ||||
\(271\) | −13.2168 | − | 22.8922i | −0.802866 | − | 1.39060i | −0.917722 | − | 0.397223i | \(-0.869974\pi\) |
0.114856 | − | 0.993382i | \(-0.463359\pi\) | |||||||
\(272\) | 1.05806 | + | 1.83261i | 0.0641543 | + | 0.111119i | ||||
\(273\) | 0.192736 | + | 0.333828i | 0.0116649 | + | 0.0202042i | ||||
\(274\) | 0.0594055 | 0.00358882 | ||||||||
\(275\) | −6.06017 | − | 10.4965i | −0.365442 | − | 0.632964i | ||||
\(276\) | −0.478752 | − | 0.829223i | −0.0288175 | − | 0.0499133i | ||||
\(277\) | −13.8870 | + | 24.0530i | −0.834390 | + | 1.44521i | 0.0601364 | + | 0.998190i | \(0.480846\pi\) |
−0.894526 | + | 0.447015i | \(0.852487\pi\) | |||||||
\(278\) | 4.44836 | − | 7.70478i | 0.266795 | − | 0.462102i | ||||
\(279\) | −3.58029 | −0.214346 | ||||||||
\(280\) | −3.64477 | −0.217817 | ||||||||
\(281\) | −7.75408 | + | 13.4305i | −0.462570 | + | 0.801194i | −0.999088 | − | 0.0426945i | \(-0.986406\pi\) |
0.536519 | + | 0.843889i | \(0.319739\pi\) | |||||||
\(282\) | −0.147932 | + | 0.256226i | −0.00880923 | + | 0.0152580i | ||||
\(283\) | −1.92623 | − | 3.33632i | −0.114502 | − | 0.198324i | 0.803078 | − | 0.595873i | \(-0.203194\pi\) |
−0.917581 | + | 0.397550i | \(0.869861\pi\) | |||||||
\(284\) | −8.04421 | − | 13.9330i | −0.477336 | − | 0.826770i | ||||
\(285\) | −0.403117 | −0.0238786 | ||||||||
\(286\) | −3.01938 | − | 5.22971i | −0.178539 | − | 0.309239i | ||||
\(287\) | 4.24744 | + | 7.35678i | 0.250718 | + | 0.434257i | ||||
\(288\) | 8.15804 | + | 14.1301i | 0.480717 | + | 0.832627i | ||||
\(289\) | −0.500000 | + | 0.866025i | −0.0294118 | + | 0.0509427i | ||||
\(290\) | 5.21556 | 0.306268 | ||||||||
\(291\) | −0.638374 | + | 1.10570i | −0.0374221 | + | 0.0648170i | ||||
\(292\) | 6.80255 | + | 11.7824i | 0.398089 | + | 0.689511i | ||||
\(293\) | 11.7268 | 0.685087 | 0.342544 | − | 0.939502i | \(-0.388712\pi\) | ||||
0.342544 | + | 0.939502i | \(0.388712\pi\) | |||||||
\(294\) | −0.0991631 | − | 0.171756i | −0.00578331 | − | 0.0100170i | ||||
\(295\) | 1.28927 | − | 2.23307i | 0.0750640 | − | 0.130015i | ||||
\(296\) | 1.69849 | − | 2.94187i | 0.0987227 | − | 0.170993i | ||||
\(297\) | −1.44923 | −0.0840930 | ||||||||
\(298\) | 4.16489 | − | 7.21381i | 0.241266 | − | 0.417885i | ||||
\(299\) | −24.8753 | −1.43858 | ||||||||
\(300\) | −0.476056 | −0.0274851 | ||||||||
\(301\) | 10.0032 | + | 2.21740i | 0.576576 | + | 0.127809i | ||||
\(302\) | 7.28807 | 0.419381 | ||||||||
\(303\) | −1.11125 | −0.0638397 | ||||||||
\(304\) | 5.12363 | − | 8.87439i | 0.293860 | − | 0.508981i | ||||
\(305\) | 0.489862 | 0.0280494 | ||||||||
\(306\) | −0.863163 | + | 1.49504i | −0.0493438 | + | 0.0854659i | ||||
\(307\) | 8.48641 | − | 14.6989i | 0.484345 | − | 0.838910i | −0.515493 | − | 0.856894i | \(-0.672391\pi\) |
0.999838 | + | 0.0179834i | \(0.00572459\pi\) | |||||||
\(308\) | 4.17407 | + | 7.22970i | 0.237840 | + | 0.411951i | ||||
\(309\) | −1.27331 | −0.0724360 | ||||||||
\(310\) | 0.380240 | + | 0.658594i | 0.0215962 | + | 0.0374056i | ||||
\(311\) | −14.5094 | + | 25.1311i | −0.822755 | + | 1.42505i | 0.0808686 | + | 0.996725i | \(0.474231\pi\) |
−0.903623 | + | 0.428328i | \(0.859103\pi\) | |||||||
\(312\) | −0.521651 | −0.0295327 | ||||||||
\(313\) | 5.82162 | − | 10.0833i | 0.329058 | − | 0.569945i | −0.653267 | − | 0.757127i | \(-0.726602\pi\) |
0.982325 | + | 0.187183i | \(0.0599356\pi\) | |||||||
\(314\) | −1.08679 | − | 1.88238i | −0.0613311 | − | 0.106229i | ||||
\(315\) | 2.58064 | + | 4.46979i | 0.145402 | + | 0.251844i | ||||
\(316\) | 5.45613 | + | 9.45030i | 0.306931 | + | 0.531621i | ||||
\(317\) | 25.1023 | 1.40989 | 0.704944 | − | 0.709263i | \(-0.250972\pi\) | ||||
0.704944 | + | 0.709263i | \(0.250972\pi\) | |||||||
\(318\) | 0.268881 | + | 0.465715i | 0.0150781 | + | 0.0261160i | ||||
\(319\) | −13.1365 | − | 22.7531i | −0.735503 | − | 1.27393i | ||||
\(320\) | −0.601592 | + | 1.04199i | −0.0336300 | + | 0.0582489i | ||||
\(321\) | 0.386773 | − | 0.669910i | 0.0215875 | − | 0.0373907i | ||||
\(322\) | −6.85443 | −0.381983 | ||||||||
\(323\) | 4.84248 | 0.269443 | ||||||||
\(324\) | 7.46152 | − | 12.9237i | 0.414529 | − | 0.717985i | ||||
\(325\) | −6.18382 | + | 10.7107i | −0.343016 | + | 0.594122i | ||||
\(326\) | −1.18392 | − | 2.05061i | −0.0655711 | − | 0.113573i | ||||
\(327\) | 0.277311 | + | 0.480317i | 0.0153353 | + | 0.0265616i | ||||
\(328\) | −11.4959 | −0.634758 | ||||||||
\(329\) | −5.31292 | − | 9.20224i | −0.292911 | − | 0.507336i | ||||
\(330\) | 0.0768837 | + | 0.133167i | 0.00423231 | + | 0.00733058i | ||||
\(331\) | 6.42684 | + | 11.1316i | 0.353251 | + | 0.611849i | 0.986817 | − | 0.161840i | \(-0.0517427\pi\) |
−0.633566 | + | 0.773689i | \(0.718409\pi\) | |||||||
\(332\) | −7.34985 | + | 12.7303i | −0.403375 | + | 0.698666i | ||||
\(333\) | −4.81038 | −0.263607 | ||||||||
\(334\) | 2.37071 | − | 4.10619i | 0.129720 | − | 0.224681i | ||||
\(335\) | 0.348029 | + | 0.602804i | 0.0190149 | + | 0.0329347i | ||||
\(336\) | 0.249509 | 0.0136118 | ||||||||
\(337\) | 1.30157 | + | 2.25439i | 0.0709011 | + | 0.122804i | 0.899296 | − | 0.437339i | \(-0.144079\pi\) |
−0.828395 | + | 0.560144i | \(0.810746\pi\) | |||||||
\(338\) | 0.666509 | − | 1.15443i | 0.0362533 | − | 0.0627926i | ||||
\(339\) | 0.537519 | − | 0.931010i | 0.0291940 | − | 0.0505655i | ||||
\(340\) | −1.83964 | −0.0997683 | ||||||||
\(341\) | 1.91543 | − | 3.31762i | 0.103726 | − | 0.179659i | ||||
\(342\) | 8.35970 | 0.452041 | ||||||||
\(343\) | 18.0603 | 0.975167 | ||||||||
\(344\) | −9.36732 | + | 10.2231i | −0.505052 | + | 0.551195i | ||||
\(345\) | 0.633411 | 0.0341017 | ||||||||
\(346\) | 2.40637 | 0.129367 | ||||||||
\(347\) | −7.65209 | + | 13.2538i | −0.410786 | + | 0.711502i | −0.994976 | − | 0.100115i | \(-0.968079\pi\) |
0.584190 | + | 0.811617i | \(0.301412\pi\) | |||||||
\(348\) | −1.03194 | −0.0553176 | ||||||||
\(349\) | 11.4288 | − | 19.7952i | 0.611767 | − | 1.05961i | −0.379175 | − | 0.925325i | \(-0.623792\pi\) |
0.990942 | − | 0.134287i | \(-0.0428744\pi\) | |||||||
\(350\) | −1.70396 | + | 2.95135i | −0.0910805 | + | 0.157756i | ||||
\(351\) | 0.739400 | + | 1.28068i | 0.0394662 | + | 0.0683575i | ||||
\(352\) | −17.4580 | −0.930514 | ||||||||
\(353\) | −7.78945 | − | 13.4917i | −0.414591 | − | 0.718092i | 0.580795 | − | 0.814050i | \(-0.302742\pi\) |
−0.995385 | + | 0.0959581i | \(0.969409\pi\) | |||||||
\(354\) | 0.0508458 | − | 0.0880675i | 0.00270242 | − | 0.00468074i | ||||
\(355\) | 10.6429 | 0.564865 | ||||||||
\(356\) | 4.26534 | − | 7.38779i | 0.226063 | − | 0.391552i | ||||
\(357\) | 0.0589544 | + | 0.102112i | 0.00312020 | + | 0.00540434i | ||||
\(358\) | 1.74044 | + | 3.01454i | 0.0919854 | + | 0.159323i | ||||
\(359\) | 11.8151 | + | 20.4644i | 0.623577 | + | 1.08007i | 0.988814 | + | 0.149153i | \(0.0476547\pi\) |
−0.365237 | + | 0.930915i | \(0.619012\pi\) | |||||||
\(360\) | −6.98464 | −0.368123 | ||||||||
\(361\) | −2.22479 | − | 3.85345i | −0.117094 | − | 0.202813i | ||||
\(362\) | 5.14217 | + | 8.90650i | 0.270267 | + | 0.468115i | ||||
\(363\) | −0.0277410 | + | 0.0480489i | −0.00145603 | + | 0.00252191i | ||||
\(364\) | 4.25923 | − | 7.37721i | 0.223244 | − | 0.386671i | ||||
\(365\) | −9.00010 | −0.471087 | ||||||||
\(366\) | 0.0193191 | 0.00100982 | ||||||||
\(367\) | −0.870077 | + | 1.50702i | −0.0454176 | + | 0.0786656i | −0.887841 | − | 0.460151i | \(-0.847795\pi\) |
0.842423 | + | 0.538817i | \(0.181129\pi\) | |||||||
\(368\) | −8.05069 | + | 13.9442i | −0.419671 | + | 0.726891i | ||||
\(369\) | 8.13957 | + | 14.0981i | 0.423729 | + | 0.733920i | ||||
\(370\) | 0.510880 | + | 0.884870i | 0.0265594 | + | 0.0460022i | ||||
\(371\) | −19.3135 | −1.00270 | ||||||||
\(372\) | −0.0752332 | − | 0.130308i | −0.00390066 | − | 0.00675614i | ||||
\(373\) | 11.2019 | + | 19.4023i | 0.580015 | + | 1.00461i | 0.995477 | + | 0.0950043i | \(0.0302865\pi\) |
−0.415462 | + | 0.909610i | \(0.636380\pi\) | |||||||
\(374\) | −0.923573 | − | 1.59968i | −0.0477568 | − | 0.0827173i | ||||
\(375\) | 0.365576 | − | 0.633197i | 0.0188783 | − | 0.0326981i | ||||
\(376\) | 14.3797 | 0.741577 | ||||||||
\(377\) | −13.4045 | + | 23.2173i | −0.690368 | + | 1.19575i | ||||
\(378\) | 0.203743 | + | 0.352893i | 0.0104794 | + | 0.0181508i | ||||
\(379\) | 8.33592 | 0.428188 | 0.214094 | − | 0.976813i | \(-0.431320\pi\) | ||||
0.214094 | + | 0.976813i | \(0.431320\pi\) | |||||||
\(380\) | 4.45420 | + | 7.71490i | 0.228496 | + | 0.395766i | ||||
\(381\) | 0.124603 | − | 0.215819i | 0.00638360 | − | 0.0110567i | ||||
\(382\) | −4.66250 | + | 8.07568i | −0.238554 | + | 0.413188i | ||||
\(383\) | −34.7108 | −1.77364 | −0.886819 | − | 0.462117i | \(-0.847090\pi\) | ||||
−0.886819 | + | 0.462117i | \(0.847090\pi\) | |||||||
\(384\) | −0.434917 | + | 0.753299i | −0.0221943 | + | 0.0384416i | ||||
\(385\) | −5.52249 | −0.281452 | ||||||||
\(386\) | −4.78483 | −0.243541 | ||||||||
\(387\) | 19.1697 | + | 4.24931i | 0.974448 | + | 0.216005i | ||||
\(388\) | 28.2146 | 1.43238 | ||||||||
\(389\) | 14.6740 | 0.743999 | 0.371999 | − | 0.928233i | \(-0.378672\pi\) | ||||
0.371999 | + | 0.928233i | \(0.378672\pi\) | |||||||
\(390\) | 0.0784524 | − | 0.135883i | 0.00397259 | − | 0.00688073i | ||||
\(391\) | −7.60891 | −0.384799 | ||||||||
\(392\) | −4.81957 | + | 8.34774i | −0.243425 | + | 0.421625i | ||||
\(393\) | −0.285572 | + | 0.494626i | −0.0144052 | + | 0.0249506i | ||||
\(394\) | 1.93986 | + | 3.35994i | 0.0977289 | + | 0.169271i | ||||
\(395\) | −7.21872 | −0.363213 | ||||||||
\(396\) | 7.99897 | + | 13.8546i | 0.401963 | + | 0.696221i | ||||
\(397\) | −0.0734515 | + | 0.127222i | −0.00368642 | + | 0.00638508i | −0.867863 | − | 0.496804i | \(-0.834507\pi\) |
0.864176 | + | 0.503189i | \(0.167840\pi\) | |||||||
\(398\) | −4.17103 | −0.209075 | ||||||||
\(399\) | 0.285486 | − | 0.494475i | 0.0142922 | − | 0.0247547i | ||||
\(400\) | 4.00268 | + | 6.93284i | 0.200134 | + | 0.346642i | ||||
\(401\) | 11.2343 | + | 19.4584i | 0.561014 | + | 0.971705i | 0.997408 | + | 0.0719495i | \(0.0229220\pi\) |
−0.436394 | + | 0.899756i | \(0.643745\pi\) | |||||||
\(402\) | 0.0137255 | + | 0.0237733i | 0.000684566 | + | 0.00118570i | ||||
\(403\) | −3.90902 | −0.194722 | ||||||||
\(404\) | 12.2787 | + | 21.2673i | 0.610886 | + | 1.05809i | ||||
\(405\) | 4.93597 | + | 8.54935i | 0.245270 | + | 0.424821i | ||||
\(406\) | −3.69364 | + | 6.39756i | −0.183312 | + | 0.317506i | ||||
\(407\) | 2.57352 | − | 4.45747i | 0.127565 | − | 0.220949i | ||||
\(408\) | −0.159564 | −0.00789958 | ||||||||
\(409\) | 35.8298 | 1.77167 | 0.885834 | − | 0.464002i | \(-0.153587\pi\) | ||||
0.885834 | + | 0.464002i | \(0.153587\pi\) | |||||||
\(410\) | 1.72890 | − | 2.99455i | 0.0853845 | − | 0.147890i | ||||
\(411\) | 0.00388771 | − | 0.00673372i | 0.000191767 | − | 0.000332150i | ||||
\(412\) | 14.0693 | + | 24.3688i | 0.693145 | + | 1.20056i | ||||
\(413\) | 1.82610 | + | 3.16291i | 0.0898567 | + | 0.155636i | ||||
\(414\) | −13.1355 | −0.645573 | ||||||||
\(415\) | −4.86210 | − | 8.42140i | −0.238671 | − | 0.413390i | ||||
\(416\) | 8.90709 | + | 15.4275i | 0.436706 | + | 0.756397i | ||||
\(417\) | −0.582234 | − | 1.00846i | −0.0285121 | − | 0.0493844i | ||||
\(418\) | −4.47238 | + | 7.74639i | −0.218751 | + | 0.378888i | ||||
\(419\) | −4.32288 | −0.211186 | −0.105593 | − | 0.994409i | \(-0.533674\pi\) | ||||
−0.105593 | + | 0.994409i | \(0.533674\pi\) | |||||||
\(420\) | −0.108455 | + | 0.187849i | −0.00529205 | + | 0.00916610i | ||||
\(421\) | −11.5406 | − | 19.9890i | −0.562457 | − | 0.974204i | −0.997281 | − | 0.0736885i | \(-0.976523\pi\) |
0.434824 | − | 0.900515i | \(-0.356810\pi\) | |||||||
\(422\) | 9.04089 | 0.440104 | ||||||||
\(423\) | −10.1814 | − | 17.6347i | −0.495036 | − | 0.857428i | ||||
\(424\) | 13.0683 | − | 22.6349i | 0.634651 | − | 1.09925i | ||||
\(425\) | −1.89152 | + | 3.27621i | −0.0917521 | + | 0.158919i | ||||
\(426\) | 0.419731 | 0.0203360 | ||||||||
\(427\) | −0.346918 | + | 0.600879i | −0.0167885 | + | 0.0290786i | ||||
\(428\) | −17.0944 | −0.826290 | ||||||||
\(429\) | −0.790396 | −0.0381607 | ||||||||
\(430\) | −1.25423 | − | 3.97755i | −0.0604841 | − | 0.191815i | ||||
\(431\) | −15.8020 | −0.761153 | −0.380577 | − | 0.924749i | \(-0.624275\pi\) | ||||
−0.380577 | + | 0.924749i | \(0.624275\pi\) | |||||||
\(432\) | 0.957202 | 0.0460534 | ||||||||
\(433\) | 11.4695 | − | 19.8658i | 0.551191 | − | 0.954691i | −0.446998 | − | 0.894535i | \(-0.647507\pi\) |
0.998189 | − | 0.0601563i | \(-0.0191599\pi\) | |||||||
\(434\) | −1.07714 | −0.0517042 | ||||||||
\(435\) | 0.341325 | − | 0.591193i | 0.0163653 | − | 0.0283455i | ||||
\(436\) | 6.12824 | − | 10.6144i | 0.293490 | − | 0.508339i | ||||
\(437\) | 18.4230 | + | 31.9096i | 0.881291 | + | 1.52644i | ||||
\(438\) | −0.354944 | −0.0169599 | ||||||||
\(439\) | 12.1766 | + | 21.0905i | 0.581156 | + | 1.00659i | 0.995343 | + | 0.0964002i | \(0.0307329\pi\) |
−0.414186 | + | 0.910192i | \(0.635934\pi\) | |||||||
\(440\) | 3.73674 | − | 6.47222i | 0.178142 | − | 0.308551i | ||||
\(441\) | 13.6498 | 0.649988 | ||||||||
\(442\) | −0.942416 | + | 1.63231i | −0.0448262 | + | 0.0776412i | ||||
\(443\) | −13.9170 | − | 24.1050i | −0.661219 | − | 1.14526i | −0.980296 | − | 0.197536i | \(-0.936706\pi\) |
0.319077 | − | 0.947729i | \(-0.396627\pi\) | |||||||
\(444\) | −0.101081 | − | 0.175078i | −0.00479711 | − | 0.00830884i | ||||
\(445\) | 2.82162 | + | 4.88720i | 0.133758 | + | 0.231675i | ||||
\(446\) | 11.9666 | 0.566637 | ||||||||
\(447\) | −0.545132 | − | 0.944196i | −0.0257839 | − | 0.0446590i | ||||
\(448\) | −0.852090 | − | 1.47586i | −0.0402575 | − | 0.0697280i | ||||
\(449\) | 20.4595 | − | 35.4370i | 0.965545 | − | 1.67237i | 0.257403 | − | 0.966304i | \(-0.417133\pi\) |
0.708143 | − | 0.706069i | \(-0.249533\pi\) | |||||||
\(450\) | −3.26538 | + | 5.65580i | −0.153931 | + | 0.266617i | ||||
\(451\) | −17.4185 | −0.820203 | ||||||||
\(452\) | −23.7571 | −1.11744 | ||||||||
\(453\) | 0.476958 | − | 0.826115i | 0.0224094 | − | 0.0388143i | ||||
\(454\) | −4.94572 | + | 8.56625i | −0.232114 | + | 0.402034i | ||||
\(455\) | 2.81758 | + | 4.88020i | 0.132090 | + | 0.228787i | ||||
\(456\) | 0.386342 | + | 0.669163i | 0.0180921 | + | 0.0313364i | ||||
\(457\) | −5.43823 | −0.254390 | −0.127195 | − | 0.991878i | \(-0.540597\pi\) | ||||
−0.127195 | + | 0.991878i | \(0.540597\pi\) | |||||||
\(458\) | −3.78741 | − | 6.55999i | −0.176974 | − | 0.306528i | ||||
\(459\) | 0.226169 | + | 0.391736i | 0.0105567 | + | 0.0182847i | ||||
\(460\) | −6.99882 | − | 12.1223i | −0.326322 | − | 0.565205i | ||||
\(461\) | −6.56899 | + | 11.3778i | −0.305948 | + | 0.529918i | −0.977472 | − | 0.211065i | \(-0.932307\pi\) |
0.671524 | + | 0.740983i | \(0.265640\pi\) | |||||||
\(462\) | −0.217795 | −0.0101327 | ||||||||
\(463\) | −2.68453 | + | 4.64974i | −0.124761 | + | 0.216092i | −0.921639 | − | 0.388048i | \(-0.873150\pi\) |
0.796879 | + | 0.604139i | \(0.206483\pi\) | |||||||
\(464\) | 8.67652 | + | 15.0282i | 0.402797 | + | 0.697665i | ||||
\(465\) | 0.0995371 | 0.00461592 | ||||||||
\(466\) | 4.86324 | + | 8.42338i | 0.225285 | + | 0.390206i | ||||
\(467\) | 5.24976 | − | 9.09286i | 0.242930 | − | 0.420767i | −0.718618 | − | 0.695406i | \(-0.755225\pi\) |
0.961548 | + | 0.274638i | \(0.0885581\pi\) | |||||||
\(468\) | 8.16217 | − | 14.1373i | 0.377296 | − | 0.653496i | ||||
\(469\) | −0.985891 | −0.0455242 | ||||||||
\(470\) | −2.16260 | + | 3.74574i | −0.0997534 | + | 0.172778i | ||||
\(471\) | −0.284494 | −0.0131088 | ||||||||
\(472\) | −4.94246 | −0.227495 | ||||||||
\(473\) | −14.1932 | + | 15.4899i | −0.652604 | + | 0.712228i | ||||
\(474\) | −0.284690 | −0.0130763 | ||||||||
\(475\) | 18.3193 | 0.840546 | ||||||||
\(476\) | 1.30282 | − | 2.25656i | 0.0597148 | − | 0.103429i | ||||
\(477\) | −37.0113 | −1.69463 | ||||||||
\(478\) | 5.11773 | − | 8.86416i | 0.234079 | − | 0.405437i | ||||
\(479\) | −0.00930282 | + | 0.0161130i | −0.000425057 | + | 0.000736220i | −0.866238 | − | 0.499632i | \(-0.833469\pi\) |
0.865813 | + | 0.500368i | \(0.166802\pi\) | |||||||
\(480\) | −0.226805 | − | 0.392838i | −0.0103522 | − | 0.0179305i | ||||
\(481\) | −5.25206 | −0.239473 | ||||||||
\(482\) | −5.96460 | − | 10.3310i | −0.271680 | − | 0.470564i | ||||
\(483\) | −0.448579 | + | 0.776962i | −0.0204111 | + | 0.0353530i | ||||
\(484\) | 1.22609 | 0.0557312 | ||||||||
\(485\) | −9.33231 | + | 16.1640i | −0.423758 | + | 0.733971i | ||||
\(486\) | 0.585848 | + | 1.01472i | 0.0265746 | + | 0.0460286i | ||||
\(487\) | −8.09791 | − | 14.0260i | −0.366951 | − | 0.635578i | 0.622136 | − | 0.782909i | \(-0.286265\pi\) |
−0.989087 | + | 0.147331i | \(0.952932\pi\) | |||||||
\(488\) | −0.469477 | − | 0.813158i | −0.0212522 | − | 0.0368099i | ||||
\(489\) | −0.309920 | −0.0140151 | ||||||||
\(490\) | −1.44965 | − | 2.51087i | −0.0654887 | − | 0.113430i | ||||
\(491\) | −1.25459 | − | 2.17301i | −0.0566186 | − | 0.0980664i | 0.836327 | − | 0.548231i | \(-0.184699\pi\) |
−0.892946 | + | 0.450165i | \(0.851365\pi\) | |||||||
\(492\) | −0.342076 | + | 0.592494i | −0.0154220 | + | 0.0267117i | ||||
\(493\) | −4.10020 | + | 7.10176i | −0.184664 | + | 0.319847i | ||||
\(494\) | 9.12726 | 0.410655 | ||||||||
\(495\) | −10.5830 | −0.475671 | ||||||||
\(496\) | −1.26512 | + | 2.19125i | −0.0568056 | + | 0.0983902i | ||||
\(497\) | −7.53723 | + | 13.0549i | −0.338091 | + | 0.585591i | ||||
\(498\) | −0.191750 | − | 0.332121i | −0.00859254 | − | 0.0148827i | ||||
\(499\) | 11.2034 | + | 19.4048i | 0.501531 | + | 0.868677i | 0.999998 | + | 0.00176877i | \(0.000563017\pi\) |
−0.498467 | + | 0.866908i | \(0.666104\pi\) | |||||||
\(500\) | −16.1576 | −0.722590 | ||||||||
\(501\) | −0.310296 | − | 0.537449i | −0.0138630 | − | 0.0240114i | ||||
\(502\) | 6.13967 | + | 10.6342i | 0.274027 | + | 0.474628i | ||||
\(503\) | −13.8446 | − | 23.9796i | −0.617302 | − | 1.06920i | −0.989976 | − | 0.141236i | \(-0.954892\pi\) |
0.372674 | − | 0.927962i | \(-0.378441\pi\) | |||||||
\(504\) | 4.94649 | − | 8.56758i | 0.220334 | − | 0.381630i | ||||
\(505\) | −16.2453 | −0.722904 | ||||||||
\(506\) | 7.02739 | − | 12.1718i | 0.312405 | − | 0.541102i | ||||
\(507\) | −0.0872376 | − | 0.151100i | −0.00387436 | − | 0.00671058i | ||||
\(508\) | −5.50715 | −0.244340 | ||||||||
\(509\) | 10.4527 | + | 18.1045i | 0.463306 | + | 0.802470i | 0.999123 | − | 0.0418642i | \(-0.0133297\pi\) |
−0.535817 | + | 0.844334i | \(0.679996\pi\) | |||||||
\(510\) | 0.0239972 | − | 0.0415643i | 0.00106261 | − | 0.00184050i | ||||
\(511\) | 6.37383 | − | 11.0398i | 0.281962 | − | 0.488372i | ||||
\(512\) | 20.4799 | 0.905093 | ||||||||
\(513\) | 1.09522 | − | 1.89697i | 0.0483551 | − | 0.0837535i | ||||
\(514\) | −8.88789 | −0.392028 | ||||||||
\(515\) | −18.6144 | −0.820246 | ||||||||
\(516\) | 0.248158 | + | 0.786988i | 0.0109245 | + | 0.0346452i | ||||
\(517\) | 21.7879 | 0.958231 | ||||||||
\(518\) | −1.44721 | −0.0635869 | ||||||||
\(519\) | 0.157481 | − | 0.272766i | 0.00691267 | − | 0.0119731i | ||||
\(520\) | −7.62595 | −0.334420 | ||||||||
\(521\) | 16.5945 | − | 28.7424i | 0.727016 | − | 1.25923i | −0.231123 | − | 0.972925i | \(-0.574240\pi\) |
0.958139 | − | 0.286304i | \(-0.0924268\pi\) | |||||||
\(522\) | −7.07829 | + | 12.2600i | −0.309808 | + | 0.536604i | ||||
\(523\) | −12.8697 | − | 22.2910i | −0.562754 | − | 0.974719i | −0.997255 | − | 0.0740473i | \(-0.976408\pi\) |
0.434501 | − | 0.900672i | \(-0.356925\pi\) | |||||||
\(524\) | 12.6216 | 0.551378 | ||||||||
\(525\) | 0.223027 | + | 0.386294i | 0.00973369 | + | 0.0168592i | ||||
\(526\) | 6.48620 | − | 11.2344i | 0.282812 | − | 0.489844i | ||||
\(527\) | −1.19570 | −0.0520855 | ||||||||
\(528\) | −0.255805 | + | 0.443067i | −0.0111325 | + | 0.0192820i | ||||
\(529\) | −17.4478 | − | 30.2204i | −0.758599 | − | 1.31393i | ||||
\(530\) | 3.93073 | + | 6.80823i | 0.170740 | + | 0.295731i | ||||
\(531\) | 3.49945 | + | 6.06123i | 0.151863 | + | 0.263035i | ||||
\(532\) | −12.6178 | −0.547050 | ||||||||
\(533\) | 8.88692 | + | 15.3926i | 0.384935 | + | 0.666727i | ||||
\(534\) | 0.111279 | + | 0.192740i | 0.00481550 | + | 0.00834069i | ||||
\(535\) | 5.65418 | − | 9.79333i | 0.244452 | − | 0.423403i | ||||
\(536\) | 0.667093 | − | 1.15544i | 0.0288140 | − | 0.0499074i | ||||
\(537\) | 0.455604 | 0.0196608 | ||||||||
\(538\) | 10.0529 | 0.433413 | ||||||||
\(539\) | −7.30253 | + | 12.6483i | −0.314542 | + | 0.544803i | ||||
\(540\) | −0.416069 | + | 0.720653i | −0.0179048 | + | 0.0310120i | ||||
\(541\) | −0.769661 | − | 1.33309i | −0.0330903 | − | 0.0573141i | 0.849006 | − | 0.528383i | \(-0.177202\pi\) |
−0.882096 | + | 0.471069i | \(0.843868\pi\) | |||||||
\(542\) | −7.61999 | − | 13.1982i | −0.327307 | − | 0.566912i | ||||
\(543\) | 1.34609 | 0.0577663 | ||||||||
\(544\) | 2.72452 | + | 4.71901i | 0.116813 | + | 0.202326i | ||||
\(545\) | 4.05398 | + | 7.02169i | 0.173653 | + | 0.300776i | ||||
\(546\) | 0.111119 | + | 0.192464i | 0.00475546 | + | 0.00823671i | ||||
\(547\) | −17.4221 | + | 30.1760i | −0.744915 | + | 1.29023i | 0.205319 | + | 0.978695i | \(0.434177\pi\) |
−0.950234 | + | 0.311536i | \(0.899157\pi\) | |||||||
\(548\) | −0.171828 | −0.00734012 | ||||||||
\(549\) | −0.664815 | + | 1.15149i | −0.0283736 | + | 0.0491445i | ||||
\(550\) | −3.49391 | − | 6.05163i | −0.148981 | − | 0.258042i | ||||
\(551\) | 39.7103 | 1.69171 | ||||||||
\(552\) | −0.607053 | − | 1.05145i | −0.0258379 | − | 0.0447525i | ||||
\(553\) | 5.11227 | − | 8.85470i | 0.217396 | − | 0.376540i | ||||
\(554\) | −8.00637 | + | 13.8674i | −0.340158 | + | 0.589171i | ||||
\(555\) | 0.133735 | 0.00567676 | ||||||||
\(556\) | −12.8667 | + | 22.2857i | −0.545668 | + | 0.945125i | ||||
\(557\) | 25.3487 | 1.07406 | 0.537029 | − | 0.843564i | \(-0.319547\pi\) | ||||
0.537029 | + | 0.843564i | \(0.319547\pi\) | |||||||
\(558\) | −2.06417 | −0.0873831 | ||||||||
\(559\) | 20.9297 | + | 4.63947i | 0.885234 | + | 0.196229i | ||||
\(560\) | 3.64755 | 0.154137 | ||||||||
\(561\) | −0.241768 | −0.0102075 | ||||||||
\(562\) | −4.47051 | + | 7.74315i | −0.188577 | + | 0.326625i | ||||
\(563\) | −5.50735 | −0.232107 | −0.116054 | − | 0.993243i | \(-0.537024\pi\) | ||||
−0.116054 | + | 0.993243i | \(0.537024\pi\) | |||||||
\(564\) | 0.427887 | − | 0.741122i | 0.0180173 | − | 0.0312068i | ||||
\(565\) | 7.85793 | − | 13.6103i | 0.330585 | − | 0.572591i | ||||
\(566\) | −1.11054 | − | 1.92351i | −0.0466795 | − | 0.0808512i | ||||
\(567\) | −13.9825 | −0.587211 | ||||||||
\(568\) | −10.2000 | − | 17.6669i | −0.427982 | − | 0.741286i | ||||
\(569\) | 12.4688 | − | 21.5966i | 0.522720 | − | 0.905377i | −0.476931 | − | 0.878941i | \(-0.658251\pi\) |
0.999650 | − | 0.0264363i | \(-0.00841592\pi\) | |||||||
\(570\) | −0.232412 | −0.00973465 | ||||||||
\(571\) | 22.1813 | − | 38.4191i | 0.928257 | − | 1.60779i | 0.142021 | − | 0.989864i | \(-0.454640\pi\) |
0.786237 | − | 0.617925i | \(-0.212027\pi\) | |||||||
\(572\) | 8.73341 | + | 15.1267i | 0.365162 | + | 0.632479i | ||||
\(573\) | 0.610262 | + | 1.05700i | 0.0254941 | + | 0.0441570i | ||||
\(574\) | 2.44880 | + | 4.24145i | 0.102211 | + | 0.177035i | ||||
\(575\) | −28.7848 | −1.20041 | ||||||||
\(576\) | −1.63290 | − | 2.82827i | −0.0680375 | − | 0.117844i | ||||
\(577\) | 7.80634 | + | 13.5210i | 0.324982 | + | 0.562885i | 0.981509 | − | 0.191417i | \(-0.0613084\pi\) |
−0.656527 | + | 0.754303i | \(0.727975\pi\) | |||||||
\(578\) | −0.288268 | + | 0.499295i | −0.0119904 | + | 0.0207679i | ||||
\(579\) | −0.313137 | + | 0.542369i | −0.0130135 | + | 0.0225401i | ||||
\(580\) | −15.0858 | −0.626402 | ||||||||
\(581\) | 13.7733 | 0.571411 | ||||||||
\(582\) | −0.368046 | + | 0.637474i | −0.0152560 | + | 0.0264242i | ||||
\(583\) | 19.8008 | − | 34.2960i | 0.820065 | − | 1.42039i | ||||
\(584\) | 8.62557 | + | 14.9399i | 0.356929 | + | 0.618219i | ||||
\(585\) | 5.39946 | + | 9.35215i | 0.223240 | + | 0.386664i | ||||
\(586\) | 6.76093 | 0.279291 | ||||||||
\(587\) | −8.32286 | − | 14.4156i | −0.343521 | − | 0.594996i | 0.641563 | − | 0.767070i | \(-0.278286\pi\) |
−0.985084 | + | 0.172075i | \(0.944953\pi\) | |||||||
\(588\) | 0.286825 | + | 0.496795i | 0.0118285 | + | 0.0204875i | ||||
\(589\) | 2.89507 | + | 5.01441i | 0.119289 | + | 0.206615i | ||||
\(590\) | 0.743309 | − | 1.28745i | 0.0306015 | − | 0.0530034i | ||||
\(591\) | 0.507807 | 0.0208884 | ||||||||
\(592\) | −1.69978 | + | 2.94411i | −0.0698607 | + | 0.121002i | ||||
\(593\) | −4.41409 | − | 7.64544i | −0.181265 | − | 0.313960i | 0.761046 | − | 0.648697i | \(-0.224686\pi\) |
−0.942312 | + | 0.334737i | \(0.891353\pi\) | |||||||
\(594\) | −0.835535 | −0.0342824 | ||||||||
\(595\) | 0.861848 | + | 1.49276i | 0.0353323 | + | 0.0611974i | ||||
\(596\) | −12.0468 | + | 20.8656i | −0.493455 | + | 0.854689i | ||||
\(597\) | −0.272968 | + | 0.472794i | −0.0111718 | + | 0.0193502i | ||||
\(598\) | −14.3415 | −0.586469 | ||||||||
\(599\) | 11.3047 | − | 19.5803i | 0.461897 | − | 0.800030i | −0.537158 | − | 0.843482i | \(-0.680502\pi\) |
0.999056 | + | 0.0434517i | \(0.0138355\pi\) | |||||||
\(600\) | −0.603635 | −0.0246433 | ||||||||
\(601\) | 5.98956 | 0.244319 | 0.122160 | − | 0.992510i | \(-0.461018\pi\) | ||||
0.122160 | + | 0.992510i | \(0.461018\pi\) | |||||||
\(602\) | 5.76723 | + | 1.27841i | 0.235055 | + | 0.0521043i | ||||
\(603\) | −1.88931 | −0.0769386 | ||||||||
\(604\) | −21.0804 | −0.857749 | ||||||||
\(605\) | −0.405543 | + | 0.702421i | −0.0164877 | + | 0.0285575i | ||||
\(606\) | −0.640677 | −0.0260257 | ||||||||
\(607\) | −1.89509 | + | 3.28239i | −0.0769192 | + | 0.133228i | −0.901919 | − | 0.431905i | \(-0.857842\pi\) |
0.825000 | + | 0.565133i | \(0.191175\pi\) | |||||||
\(608\) | 13.1934 | − | 22.8517i | 0.535064 | − | 0.926758i | ||||
\(609\) | 0.483450 | + | 0.837360i | 0.0195904 | + | 0.0339315i | ||||
\(610\) | 0.282423 | 0.0114350 | ||||||||
\(611\) | −11.1162 | − | 19.2538i | −0.449714 | − | 0.778927i | ||||
\(612\) | 2.49666 | − | 4.32434i | 0.100922 | − | 0.174801i | ||||
\(613\) | 37.8274 | 1.52783 | 0.763917 | − | 0.645315i | \(-0.223274\pi\) | ||||
0.763917 | + | 0.645315i | \(0.223274\pi\) | |||||||
\(614\) | 4.89273 | − | 8.47445i | 0.197454 | − | 0.342001i | ||||
\(615\) | −0.226292 | − | 0.391949i | −0.00912496 | − | 0.0158049i | ||||
\(616\) | 5.29268 | + | 9.16720i | 0.213248 | + | 0.369357i | ||||
\(617\) | −8.38633 | − | 14.5256i | −0.337621 | − | 0.584777i | 0.646364 | − | 0.763030i | \(-0.276289\pi\) |
−0.983985 | + | 0.178253i | \(0.942956\pi\) | |||||||
\(618\) | −0.734109 | −0.0295302 | ||||||||
\(619\) | −10.3903 | − | 17.9965i | −0.417620 | − | 0.723339i | 0.578080 | − | 0.815980i | \(-0.303802\pi\) |
−0.995700 | + | 0.0926413i | \(0.970469\pi\) | |||||||
\(620\) | −1.09983 | − | 1.90495i | −0.0441701 | − | 0.0765048i | ||||
\(621\) | −1.72090 | + | 2.98069i | −0.0690574 | + | 0.119611i | ||||
\(622\) | −8.36522 | + | 14.4890i | −0.335415 | + | 0.580955i | ||||
\(623\) | −7.99305 | −0.320235 | ||||||||
\(624\) | 0.522048 | 0.0208987 | ||||||||
\(625\) | −4.11328 | + | 7.12440i | −0.164531 | + | 0.284976i | ||||
\(626\) | 3.35638 | − | 5.81342i | 0.134148 | − | 0.232351i | ||||
\(627\) | 0.585378 | + | 1.01390i | 0.0233778 | + | 0.0404915i | ||||
\(628\) | 3.14349 | + | 5.44468i | 0.125439 | + | 0.217267i | ||||
\(629\) | −1.60651 | −0.0640558 | ||||||||
\(630\) | 1.48783 | + | 2.57700i | 0.0592766 | + | 0.102670i | ||||
\(631\) | −10.8198 | − | 18.7404i | −0.430728 | − | 0.746043i | 0.566208 | − | 0.824262i | \(-0.308410\pi\) |
−0.996936 | + | 0.0782193i | \(0.975077\pi\) | |||||||
\(632\) | 6.91832 | + | 11.9829i | 0.275196 | + | 0.476654i | ||||
\(633\) | 0.591669 | − | 1.02480i | 0.0235167 | − | 0.0407322i | ||||
\(634\) | 14.4724 | 0.574773 | ||||||||
\(635\) | 1.82156 | − | 3.15503i | 0.0722863 | − | 0.125203i | ||||
\(636\) | −0.777725 | − | 1.34706i | −0.0308388 | − | 0.0534144i | ||||
\(637\) | 14.9030 | 0.590480 | ||||||||
\(638\) | −7.57367 | − | 13.1180i | −0.299845 | − | 0.519346i | ||||
\(639\) | −14.4439 | + | 25.0177i | −0.571394 | + | 0.989683i | ||||
\(640\) | −6.35800 | + | 11.0124i | −0.251322 | + | 0.435303i | ||||
\(641\) | −20.9472 | −0.827364 | −0.413682 | − | 0.910421i | \(-0.635758\pi\) | ||||
−0.413682 | + | 0.910421i | \(0.635758\pi\) | |||||||
\(642\) | 0.222988 | − | 0.386227i | 0.00880065 | − | 0.0152432i | ||||
\(643\) | −40.0814 | −1.58066 | −0.790328 | − | 0.612684i | \(-0.790090\pi\) | ||||
−0.790328 | + | 0.612684i | \(0.790090\pi\) | |||||||
\(644\) | 19.8261 | 0.781259 | ||||||||
\(645\) | −0.532944 | − | 0.118137i | −0.0209846 | − | 0.00465164i | ||||
\(646\) | 2.79186 | 0.109844 | ||||||||
\(647\) | 26.6008 | 1.04579 | 0.522893 | − | 0.852398i | \(-0.324853\pi\) | ||||
0.522893 | + | 0.852398i | \(0.324853\pi\) | |||||||
\(648\) | 9.46114 | − | 16.3872i | 0.371669 | − | 0.643749i | ||||
\(649\) | −7.48873 | −0.293958 | ||||||||
\(650\) | −3.56520 | + | 6.17510i | −0.139838 | + | 0.242207i | ||||
\(651\) | −0.0704917 | + | 0.122095i | −0.00276279 | + | 0.00478529i | ||||
\(652\) | 3.42443 | + | 5.93128i | 0.134111 | + | 0.232287i | ||||
\(653\) | −23.3963 | −0.915569 | −0.457785 | − | 0.889063i | \(-0.651357\pi\) | ||||
−0.457785 | + | 0.889063i | \(0.651357\pi\) | |||||||
\(654\) | 0.159880 | + | 0.276920i | 0.00625180 | + | 0.0108284i | ||||
\(655\) | −4.17475 | + | 7.23088i | −0.163121 | + | 0.282534i | ||||
\(656\) | 11.5047 | 0.449183 | ||||||||
\(657\) | 12.2145 | − | 21.1561i | 0.476532 | − | 0.825377i | ||||
\(658\) | −3.06309 | − | 5.30543i | −0.119412 | − | 0.206827i | ||||
\(659\) | −15.7508 | − | 27.2812i | −0.613565 | − | 1.06273i | −0.990635 | − | 0.136540i | \(-0.956402\pi\) |
0.377070 | − | 0.926185i | \(-0.376932\pi\) | |||||||
\(660\) | −0.222383 | − | 0.385178i | −0.00865623 | − | 0.0149930i | ||||
\(661\) | −19.5370 | −0.759900 | −0.379950 | − | 0.925007i | \(-0.624059\pi\) | ||||
−0.379950 | + | 0.925007i | \(0.624059\pi\) | |||||||
\(662\) | 3.70531 | + | 6.41779i | 0.144011 | + | 0.249434i | ||||
\(663\) | 0.123350 | + | 0.213649i | 0.00479053 | + | 0.00829744i | ||||
\(664\) | −9.31954 | + | 16.1419i | −0.361668 | + | 0.626428i | ||||
\(665\) | 4.17348 | − | 7.22868i | 0.161841 | − | 0.280316i | ||||
\(666\) | −2.77336 | −0.107466 | ||||||||
\(667\) | −62.3962 | −2.41599 | ||||||||
\(668\) | −6.85717 | + | 11.8770i | −0.265312 | + | 0.459534i | ||||
\(669\) | 0.783141 | − | 1.35644i | 0.0302780 | − | 0.0524430i | ||||
\(670\) | 0.200652 | + | 0.347539i | 0.00775185 | + | 0.0134266i | ||||
\(671\) | −0.711343 | − | 1.23208i | −0.0274611 | − | 0.0475640i | ||||
\(672\) | 0.642490 | 0.0247846 | ||||||||
\(673\) | 24.3356 | + | 42.1506i | 0.938070 | + | 1.62479i | 0.769065 | + | 0.639170i | \(0.220722\pi\) |
0.169005 | + | 0.985615i | \(0.445945\pi\) | |||||||
\(674\) | 0.750404 | + | 1.29974i | 0.0289045 | + | 0.0500640i | ||||
\(675\) | 0.855606 | + | 1.48195i | 0.0329323 | + | 0.0570404i | ||||
\(676\) | −1.92785 | + | 3.33913i | −0.0741480 | + | 0.128428i | ||||
\(677\) | −17.1876 | −0.660572 | −0.330286 | − | 0.943881i | \(-0.607145\pi\) | ||||
−0.330286 | + | 0.943881i | \(0.607145\pi\) | |||||||
\(678\) | 0.309899 | − | 0.536761i | 0.0119016 | − | 0.0206142i | ||||
\(679\) | −13.2182 | − | 22.8946i | −0.507268 | − | 0.878614i | ||||
\(680\) | −2.33264 | −0.0894528 | ||||||||
\(681\) | 0.647333 | + | 1.12121i | 0.0248058 | + | 0.0429650i | ||||
\(682\) | 1.10432 | − | 1.91273i | 0.0422864 | − | 0.0732422i | ||||
\(683\) | −2.96851 | + | 5.14162i | −0.113587 | + | 0.196738i | −0.917214 | − | 0.398395i | \(-0.869567\pi\) |
0.803627 | + | 0.595133i | \(0.202901\pi\) | |||||||
\(684\) | −24.1800 | −0.924547 | ||||||||
\(685\) | 0.0568340 | − | 0.0984395i | 0.00217152 | − | 0.00376118i | ||||
\(686\) | 10.4125 | 0.397549 | ||||||||
\(687\) | −0.991449 | −0.0378262 | ||||||||
\(688\) | 9.37446 | − | 10.2309i | 0.357398 | − | 0.390051i | ||||
\(689\) | −40.4095 | −1.53948 | ||||||||
\(690\) | 0.365185 | 0.0139023 | ||||||||
\(691\) | 21.3689 | − | 37.0120i | 0.812911 | − | 1.40800i | −0.0979079 | − | 0.995195i | \(-0.531215\pi\) |
0.910819 | − | 0.412807i | \(-0.135452\pi\) | |||||||
\(692\) | −6.96030 | −0.264591 | ||||||||
\(693\) | 7.49484 | − | 12.9814i | 0.284706 | − | 0.493124i | ||||
\(694\) | −4.41171 | + | 7.64130i | −0.167466 | + | 0.290060i | ||||
\(695\) | −8.51161 | − | 14.7425i | −0.322864 | − | 0.559216i | ||||
\(696\) | −1.30849 | −0.0495980 | ||||||||
\(697\) | 2.71835 | + | 4.70832i | 0.102965 | + | 0.178340i | ||||
\(698\) | 6.58909 | − | 11.4126i | 0.249401 | − | 0.431975i | ||||
\(699\) | 1.27307 | 0.0481521 | ||||||||
\(700\) | 4.92863 | − | 8.53663i | 0.186285 | − | 0.322654i | ||||
\(701\) | −13.1199 | − | 22.7243i | −0.495530 | − | 0.858283i | 0.504457 | − | 0.863437i | \(-0.331693\pi\) |
−0.999987 | + | 0.00515370i | \(0.998360\pi\) | |||||||
\(702\) | 0.426291 | + | 0.738358i | 0.0160893 | + | 0.0278675i | ||||
\(703\) | 3.88974 | + | 6.73723i | 0.146704 | + | 0.254100i | ||||
\(704\) | 3.49436 | 0.131699 | ||||||||
\(705\) | 0.283057 | + | 0.490269i | 0.0106605 | + | 0.0184646i | ||||
\(706\) | −4.49090 | − | 7.77847i | −0.169017 | − | 0.292747i | ||||
\(707\) | 11.5048 | − | 19.9269i | 0.432683 | − | 0.749429i | ||||
\(708\) | −0.147069 | + | 0.254731i | −0.00552720 | + | 0.00957339i | ||||
\(709\) | −7.84763 | −0.294724 | −0.147362 | − | 0.989083i | \(-0.547078\pi\) | ||||
−0.147362 | + | 0.989083i | \(0.547078\pi\) | |||||||
\(710\) | 6.13600 | 0.230280 | ||||||||
\(711\) | 9.79688 | − | 16.9687i | 0.367412 | − | 0.636375i | ||||
\(712\) | 5.40841 | − | 9.36765i | 0.202689 | − | 0.351067i | ||||
\(713\) | −4.54898 | − | 7.87907i | −0.170361 | − | 0.295074i | ||||
\(714\) | 0.0339894 | + | 0.0588713i | 0.00127202 | + | 0.00220320i | ||||
\(715\) | −11.5547 | −0.432122 | ||||||||
\(716\) | −5.03416 | − | 8.71942i | −0.188135 | − | 0.325860i | ||||
\(717\) | −0.669846 | − | 1.16021i | −0.0250158 | − | 0.0433287i | ||||
\(718\) | 6.81184 | + | 11.7985i | 0.254216 | + | 0.440314i | ||||
\(719\) | 10.8532 | − | 18.7984i | 0.404758 | − | 0.701061i | −0.589536 | − | 0.807742i | \(-0.700689\pi\) |
0.994293 | + | 0.106682i | \(0.0340226\pi\) | |||||||
\(720\) | 6.98997 | 0.260501 | ||||||||
\(721\) | 13.1826 | − | 22.8329i | 0.490946 | − | 0.850343i | ||||
\(722\) | −1.28267 | − | 2.22166i | −0.0477362 | − | 0.0826815i | ||||
\(723\) | −1.56138 | −0.0580684 | ||||||||
\(724\) | −14.8735 | − | 25.7616i | −0.552769 | − | 0.957424i | ||||
\(725\) | −15.5112 | + | 26.8662i | −0.576072 | + | 0.997786i | ||||
\(726\) | −0.0159937 | + | 0.0277019i | −0.000593582 | + | 0.00102812i | ||||
\(727\) | −2.10971 | −0.0782449 | −0.0391224 | − | 0.999234i | \(-0.512456\pi\) | ||||
−0.0391224 | + | 0.999234i | \(0.512456\pi\) | |||||||
\(728\) | 5.40067 | − | 9.35423i | 0.200162 | − | 0.346691i | ||||
\(729\) | −26.6930 | −0.988629 | ||||||||
\(730\) | −5.18888 | −0.192049 | ||||||||
\(731\) | 6.40204 | + | 1.41913i | 0.236788 | + | 0.0524885i | ||||
\(732\) | −0.0558795 | −0.00206537 | ||||||||
\(733\) | 31.6318 | 1.16835 | 0.584174 | − | 0.811628i | \(-0.301418\pi\) | ||||
0.584174 | + | 0.811628i | \(0.301418\pi\) | |||||||
\(734\) | −0.501631 | + | 0.868850i | −0.0185155 | + | 0.0320699i | ||||
\(735\) | −0.379483 | −0.0139974 | ||||||||
\(736\) | −20.7306 | + | 35.9065i | −0.764141 | + | 1.32353i | ||||
\(737\) | 1.01077 | − | 1.75070i | 0.0372321 | − | 0.0644879i | ||||
\(738\) | 4.69276 | + | 8.12810i | 0.172743 | + | 0.299199i | ||||
\(739\) | −14.1562 | −0.520743 | −0.260372 | − | 0.965508i | \(-0.583845\pi\) | ||||
−0.260372 | + | 0.965508i | \(0.583845\pi\) | |||||||
\(740\) | −1.47770 | − | 2.55945i | −0.0543212 | − | 0.0940871i | ||||
\(741\) | 0.597321 | − | 1.03459i | 0.0219431 | − | 0.0380066i | ||||
\(742\) | −11.1349 | −0.408776 | ||||||||
\(743\) | −9.94804 | + | 17.2305i | −0.364958 | + | 0.632126i | −0.988769 | − | 0.149449i | \(-0.952250\pi\) |
0.623811 | + | 0.781575i | \(0.285583\pi\) | |||||||
\(744\) | −0.0953950 | − | 0.165229i | −0.00349735 | − | 0.00605759i | ||||
\(745\) | −7.96922 | − | 13.8031i | −0.291970 | − | 0.505706i | ||||
\(746\) | 6.45833 | + | 11.1862i | 0.236456 | + | 0.409554i | ||||
\(747\) | 26.3944 | 0.965719 | ||||||||
\(748\) | 2.67139 | + | 4.62699i | 0.0976758 | + | 0.169179i | ||||
\(749\) | 8.00853 | + | 13.8712i | 0.292625 | + | 0.506842i | ||||
\(750\) | 0.210768 | − | 0.365061i | 0.00769616 | − | 0.0133301i | ||||
\(751\) | −24.5751 | + | 42.5652i | −0.896756 | + | 1.55323i | −0.0651408 | + | 0.997876i | \(0.520750\pi\) |
−0.831616 | + | 0.555352i | \(0.812584\pi\) | |||||||
\(752\) | −14.3907 | −0.524774 | ||||||||
\(753\) | 1.60721 | 0.0585700 | ||||||||
\(754\) | −7.72819 | + | 13.3856i | −0.281444 | + | 0.487476i | ||||
\(755\) | 6.97259 | − | 12.0769i | 0.253759 | − | 0.439523i | ||||
\(756\) | −0.589317 | − | 1.02073i | −0.0214332 | − | 0.0371235i | ||||
\(757\) | 3.35258 | + | 5.80685i | 0.121852 | + | 0.211053i | 0.920498 | − | 0.390747i | \(-0.127783\pi\) |
−0.798646 | + | 0.601801i | \(0.794450\pi\) | |||||||
\(758\) | 4.80596 | 0.174560 | ||||||||
\(759\) | −0.919796 | − | 1.59313i | −0.0333865 | − | 0.0578271i | ||||
\(760\) | 5.64788 | + | 9.78242i | 0.204870 | + | 0.354846i | ||||
\(761\) | 16.0707 | + | 27.8353i | 0.582562 | + | 1.00903i | 0.995175 | + | 0.0981207i | \(0.0312831\pi\) |
−0.412612 | + | 0.910907i | \(0.635384\pi\) | |||||||
\(762\) | 0.0718382 | − | 0.124427i | 0.00260242 | − | 0.00450753i | ||||
\(763\) | −11.4840 | −0.415750 | ||||||||
\(764\) | 13.4861 | − | 23.3585i | 0.487908 | − | 0.845082i | ||||
\(765\) | 1.65160 | + | 2.86065i | 0.0597137 | + | 0.103427i | ||||
\(766\) | −20.0120 | −0.723064 | ||||||||
\(767\) | 3.82076 | + | 6.61775i | 0.137960 | + | 0.238953i | ||||
\(768\) | −0.168442 | + | 0.291750i | −0.00607813 | + | 0.0105276i | ||||
\(769\) | 1.54913 | − | 2.68316i | 0.0558629 | − | 0.0967573i | −0.836742 | − | 0.547598i | \(-0.815542\pi\) |
0.892605 | + | 0.450841i | \(0.148876\pi\) | |||||||
\(770\) | −3.18392 | −0.114740 | ||||||||
\(771\) | −0.581656 | + | 1.00746i | −0.0209478 | + | 0.0362827i | ||||
\(772\) | 13.8399 | 0.498109 | ||||||||
\(773\) | −9.71394 | −0.349386 | −0.174693 | − | 0.984623i | \(-0.555893\pi\) | ||||
−0.174693 | + | 0.984623i | \(0.555893\pi\) | |||||||
\(774\) | 11.0520 | + | 2.44988i | 0.397256 | + | 0.0880593i | ||||
\(775\) | −4.52337 | −0.162484 | ||||||||
\(776\) | 35.7759 | 1.28428 | ||||||||
\(777\) | −0.0947109 | + | 0.164044i | −0.00339773 | + | 0.00588505i | ||||
\(778\) | 8.46007 | 0.303308 | ||||||||
\(779\) | 13.1635 | − | 22.7999i | 0.471633 | − | 0.816892i | ||||
\(780\) | −0.226920 | + | 0.393037i | −0.00812503 | + | 0.0140730i | ||||
\(781\) | −15.4548 | − | 26.7686i | −0.553017 | − | 0.957854i | ||||
\(782\) | −4.38682 | −0.156872 | ||||||||
\(783\) | 1.85468 | + | 3.21240i | 0.0662808 | + | 0.114802i | ||||
\(784\) | 4.82324 | − | 8.35410i | 0.172259 | − | 0.298361i | ||||
\(785\) | −4.15899 | −0.148441 | ||||||||
\(786\) | −0.164643 | + | 0.285170i | −0.00587262 | + | 0.0101717i | ||||
\(787\) | −11.3864 | − | 19.7218i | −0.405882 | − | 0.703008i | 0.588542 | − | 0.808467i | \(-0.299702\pi\) |
−0.994424 | + | 0.105459i | \(0.966369\pi\) | |||||||
\(788\) | −5.61097 | − | 9.71848i | −0.199882 | − | 0.346207i | ||||
\(789\) | −0.848961 | − | 1.47044i | −0.0302238 | − | 0.0523492i | ||||
\(790\) | −4.16186 | −0.148072 | ||||||||
\(791\) | 11.1299 | + | 19.2776i | 0.395734 | + | 0.685431i | ||||
\(792\) | 10.1426 | + | 17.5675i | 0.360402 | + | 0.624235i | ||||
\(793\) | −0.725856 | + | 1.25722i | −0.0257759 | + | 0.0446452i | ||||
\(794\) | −0.0423475 | + | 0.0733480i | −0.00150286 | + | 0.00260302i | ||||
\(795\) | 1.02897 | 0.0364937 | ||||||||
\(796\) | 12.0645 | 0.427615 | ||||||||
\(797\) | 1.44949 | − | 2.51058i | 0.0513434 | − | 0.0889294i | −0.839211 | − | 0.543805i | \(-0.816983\pi\) |
0.890555 | + | 0.454876i | \(0.150316\pi\) | |||||||
\(798\) | 0.164593 | − | 0.285083i | 0.00582652 | − | 0.0100918i | ||||
\(799\) | −3.40025 | − | 5.88941i | −0.120292 | − | 0.208352i | ||||
\(800\) | 10.3070 | + | 17.8522i | 0.364406 | + | 0.631170i | ||||
\(801\) | −15.3175 | −0.541216 | ||||||||
\(802\) | 6.47698 | + | 11.2185i | 0.228710 | + | 0.396138i | ||||
\(803\) | 13.0693 | + | 22.6367i | 0.461206 | + | 0.798833i | ||||
\(804\) | −0.0397004 | − | 0.0687631i | −0.00140013 | − | 0.00242509i | ||||
\(805\) | −6.55773 | + | 11.3583i | −0.231129 | + | 0.400328i | ||||
\(806\) | −2.25369 | −0.0793829 | ||||||||
\(807\) | 0.657902 | − | 1.13952i | 0.0231592 | − | 0.0401130i | ||||
\(808\) | 15.5692 | + | 26.9667i | 0.547724 | + | 0.948685i | ||||
\(809\) | 11.9566 | 0.420371 | 0.210186 | − | 0.977661i | \(-0.432593\pi\) | ||||
0.210186 | + | 0.977661i | \(0.432593\pi\) | |||||||
\(810\) | 2.84577 | + | 4.92901i | 0.0999901 | + | 0.173188i | ||||
\(811\) | 11.0931 | − | 19.2139i | 0.389532 | − | 0.674690i | −0.602854 | − | 0.797851i | \(-0.705970\pi\) |
0.992387 | + | 0.123162i | \(0.0393034\pi\) | |||||||
\(812\) | 10.6837 | − | 18.5047i | 0.374923 | − | 0.649386i | ||||
\(813\) | −1.99472 | −0.0699579 | ||||||||
\(814\) | 1.48373 | − | 2.56990i | 0.0520047 | − | 0.0900748i | ||||
\(815\) | −4.53068 | −0.158703 | ||||||||
\(816\) | 0.159685 | 0.00559010 | ||||||||
\(817\) | −9.54943 | − | 30.2843i | −0.334092 | − | 1.05951i | ||||
\(818\) | 20.6572 | 0.722261 | ||||||||
\(819\) | −15.2955 | −0.534468 | ||||||||
\(820\) | −5.00078 | + | 8.66160i | −0.174635 | + | 0.302476i | ||||
\(821\) | −34.8395 | −1.21591 | −0.607954 | − | 0.793972i | \(-0.708010\pi\) | ||||
−0.607954 | + | 0.793972i | \(0.708010\pi\) | |||||||
\(822\) | 0.00224141 | − | 0.00388224i | 7.81781e−5 | − | 0.000135409i | ||||
\(823\) | 14.2837 | − | 24.7402i | 0.497900 | − | 0.862387i | −0.502097 | − | 0.864811i | \(-0.667438\pi\) |
0.999997 | + | 0.00242361i | \(0.000771458\pi\) | |||||||
\(824\) | 17.8397 | + | 30.8994i | 0.621477 | + | 1.07643i | ||||
\(825\) | −0.914618 | −0.0318429 | ||||||||
\(826\) | 1.05282 | + | 1.82353i | 0.0366322 | + | 0.0634488i | ||||
\(827\) | 16.4024 | − | 28.4098i | 0.570367 | − | 0.987905i | −0.426161 | − | 0.904647i | \(-0.640134\pi\) |
0.996528 | − | 0.0832577i | \(-0.0265325\pi\) | |||||||
\(828\) | 37.9937 | 1.32037 | ||||||||
\(829\) | 14.3569 | − | 24.8669i | 0.498637 | − | 0.863665i | −0.501362 | − | 0.865238i | \(-0.667167\pi\) |
0.999999 | + | 0.00157299i | \(0.000500699\pi\) | |||||||
\(830\) | −2.80318 | − | 4.85524i | −0.0972997 | − | 0.168528i | ||||
\(831\) | 1.04793 | + | 1.81507i | 0.0363524 | + | 0.0629642i | ||||
\(832\) | −1.78283 | − | 3.08795i | −0.0618084 | − | 0.107055i | ||||
\(833\) | 4.55857 | 0.157945 | ||||||||
\(834\) | −0.335679 | − | 0.581413i | −0.0116236 | − | 0.0201327i | ||||
\(835\) | −4.53618 | − | 7.85690i | −0.156981 | − | 0.271899i | ||||
\(836\) | 12.9362 | − | 22.4061i | 0.447406 | − | 0.774931i | ||||
\(837\) | −0.270430 | + | 0.468399i | −0.00934743 | + | 0.0161902i | ||||
\(838\) | −2.49230 | −0.0860949 | ||||||||
\(839\) | −6.08644 | −0.210127 | −0.105064 | − | 0.994466i | \(-0.533505\pi\) | ||||
−0.105064 | + | 0.994466i | \(0.533505\pi\) | |||||||
\(840\) | −0.137520 | + | 0.238191i | −0.00474488 | + | 0.00821837i | ||||
\(841\) | −19.1233 | + | 33.1225i | −0.659424 | + | 1.14216i | ||||
\(842\) | −6.65361 | − | 11.5244i | −0.229298 | − | 0.397156i | ||||
\(843\) | 0.585133 | + | 1.01348i | 0.0201531 | + | 0.0349061i | ||||
\(844\) | −26.1504 | −0.900132 | ||||||||
\(845\) | −1.27532 | − | 2.20891i | −0.0438722 | − | 0.0759889i | ||||
\(846\) | −5.86994 | − | 10.1670i | −0.201813 | − | 0.349550i | ||||
\(847\) | −0.574407 | − | 0.994903i | −0.0197369 | − | 0.0341853i | ||||
\(848\) | −13.0782 | + | 22.6521i | −0.449108 | + | 0.777877i | ||||
\(849\) | −0.290711 | −0.00997718 | ||||||||
\(850\) | −1.09053 | + | 1.88885i | −0.0374049 | + | 0.0647871i | ||||
\(851\) | −6.11190 | − | 10.5861i | −0.209513 | − | 0.362887i | ||||
\(852\) | −1.21405 | −0.0415928 | ||||||||
\(853\) | 2.88336 | + | 4.99413i | 0.0987244 | + | 0.170996i | 0.911157 | − | 0.412060i | \(-0.135190\pi\) |
−0.812433 | + | 0.583055i | \(0.801857\pi\) | |||||||
\(854\) | −0.200011 | + | 0.346429i | −0.00684423 | + | 0.0118546i | ||||
\(855\) | 7.99783 | − | 13.8527i | 0.273520 | − | 0.473751i | ||||
\(856\) | −21.6756 | −0.740856 | ||||||||
\(857\) | −28.5831 | + | 49.5074i | −0.976380 | + | 1.69114i | −0.301075 | + | 0.953601i | \(0.597345\pi\) |
−0.675305 | + | 0.737539i | \(0.735988\pi\) | |||||||
\(858\) | −0.455692 | −0.0155571 | ||||||||
\(859\) | 58.3532 | 1.99099 | 0.995493 | − | 0.0948346i | \(-0.0302322\pi\) | ||||
0.995493 | + | 0.0948346i | \(0.0302322\pi\) | |||||||
\(860\) | 3.62779 | + | 11.5049i | 0.123707 | + | 0.392313i | ||||
\(861\) | 0.641035 | 0.0218464 | ||||||||
\(862\) | −9.11041 | −0.310302 | ||||||||
\(863\) | 16.3413 | − | 28.3039i | 0.556263 | − | 0.963476i | −0.441541 | − | 0.897241i | \(-0.645568\pi\) |
0.997804 | − | 0.0662349i | \(-0.0210987\pi\) | |||||||
\(864\) | 2.46481 | 0.0838545 | ||||||||
\(865\) | 2.30220 | − | 3.98753i | 0.0782772 | − | 0.135580i | ||||
\(866\) | 6.61261 | − | 11.4534i | 0.224706 | − | 0.389202i | ||||
\(867\) | 0.0377307 | + | 0.0653514i | 0.00128140 | + | 0.00221945i | ||||
\(868\) | 3.11557 | 0.105749 | ||||||||
\(869\) | 10.4825 | + | 18.1563i | 0.355595 | + | 0.615909i | ||||
\(870\) | 0.196786 | − | 0.340844i | 0.00667169 | − | 0.0115557i | ||||
\(871\) | −2.06278 | −0.0698946 | ||||||||
\(872\) | 7.77056 | − | 13.4590i | 0.263144 | − | 0.455779i | ||||
\(873\) | −25.3307 | − | 43.8740i | −0.857313 | − | 1.48491i | ||||
\(874\) | 10.6215 | + | 18.3970i | 0.359279 | + | 0.622289i | ||||
\(875\) | 7.56964 | + | 13.1110i | 0.255901 | + | 0.443233i | ||||
\(876\) | 1.02666 | 0.0346876 | ||||||||
\(877\) | −16.2401 | − | 28.1287i | −0.548390 | − | 0.949839i | −0.998385 | − | 0.0568078i | \(-0.981908\pi\) |
0.449996 | − | 0.893031i | \(-0.351426\pi\) | |||||||
\(878\) | 7.02024 | + | 12.1594i | 0.236922 | + | 0.410360i | ||||
\(879\) | 0.442460 | − | 0.766363i | 0.0149238 | − | 0.0258488i | ||||
\(880\) | −3.73958 | + | 6.47715i | −0.126061 | + | 0.218345i | ||||
\(881\) | −7.63960 | −0.257385 | −0.128692 | − | 0.991685i | \(-0.541078\pi\) | ||||
−0.128692 | + | 0.991685i | \(0.541078\pi\) | |||||||
\(882\) | 7.86958 | 0.264983 | ||||||||
\(883\) | −24.3699 | + | 42.2098i | −0.820111 | + | 1.42047i | 0.0854878 | + | 0.996339i | \(0.472755\pi\) |
−0.905599 | + | 0.424135i | \(0.860578\pi\) | |||||||
\(884\) | 2.72590 | − | 4.72139i | 0.0916818 | − | 0.158798i | ||||
\(885\) | −0.0972897 | − | 0.168511i | −0.00327036 | − | 0.00566443i | ||||
\(886\) | −8.02369 | − | 13.8974i | −0.269561 | − | 0.466893i | ||||
\(887\) | −53.2382 | −1.78757 | −0.893783 | − | 0.448501i | \(-0.851958\pi\) | ||||
−0.893783 | + | 0.448501i | \(0.851958\pi\) | |||||||
\(888\) | −0.128170 | − | 0.221998i | −0.00430111 | − | 0.00744975i | ||||
\(889\) | 2.58004 | + | 4.46876i | 0.0865317 | + | 0.149877i | ||||
\(890\) | 1.62677 | + | 2.81765i | 0.0545294 | + | 0.0944477i | ||||
\(891\) | 14.3354 | − | 24.8296i | 0.480252 | − | 0.831822i | ||||
\(892\) | −34.6130 | −1.15893 | ||||||||
\(893\) | −16.4656 | + | 28.5193i | −0.551002 | + | 0.954363i | ||||
\(894\) | −0.314289 | − | 0.544364i | −0.0105114 | − | 0.0182062i | ||||
\(895\) | 6.66043 | 0.222634 | ||||||||
\(896\) | −9.00542 | − | 15.5978i | −0.300850 | − | 0.521087i | ||||
\(897\) | −0.938562 | + | 1.62564i | −0.0313377 | + | 0.0542785i | ||||
\(898\) | 11.7957 | − | 20.4307i | 0.393627 | − | 0.681781i | ||||
\(899\) | −9.80521 | −0.327022 | ||||||||
\(900\) | 9.44496 | − | 16.3591i | 0.314832 | − | 0.545305i | ||||
\(901\) | −12.3606 | −0.411790 | ||||||||
\(902\) | −10.0424 | −0.334375 | ||||||||
\(903\) | 0.522339 | − | 0.570061i | 0.0173824 | − | 0.0189704i | ||||
\(904\) | −30.1237 | −1.00190 | ||||||||
\(905\) | 19.6783 | 0.654130 | ||||||||
\(906\) | 0.274984 | − | 0.476286i | 0.00913572 | − | 0.0158235i | ||||
\(907\) | −20.4498 | −0.679023 | −0.339512 | − | 0.940602i | \(-0.610262\pi\) | ||||
−0.339512 | + | 0.940602i | \(0.610262\pi\) | |||||||
\(908\) | 14.3053 | − | 24.7775i | 0.474737 | − | 0.822269i | ||||
\(909\) | 22.0472 | − | 38.1869i | 0.731260 | − | 1.26658i | ||||
\(910\) | 1.62444 | + | 2.81361i | 0.0538496 | + | 0.0932703i | ||||
\(911\) | −25.2629 | −0.836999 | −0.418499 | − | 0.908217i | \(-0.637444\pi\) | ||||
−0.418499 | + | 0.908217i | \(0.637444\pi\) | |||||||
\(912\) | −0.386636 | − | 0.669673i | −0.0128028 | − | 0.0221751i | ||||
\(913\) | −14.1208 | + | 24.4579i | −0.467330 | + | 0.809440i | ||||
\(914\) | −3.13534 | −0.103708 | ||||||||
\(915\) | 0.0184828 | − | 0.0320132i | 0.000611023 | − | 0.00105832i | ||||
\(916\) | 10.9549 | + | 18.9745i | 0.361961 | + | 0.626935i | ||||
\(917\) | −5.91308 | − | 10.2418i | −0.195267 | − | 0.338212i | ||||
\(918\) | 0.130395 | + | 0.225850i | 0.00430367 | + | 0.00745417i | ||||
\(919\) | 47.0039 | 1.55051 | 0.775257 | − | 0.631646i | \(-0.217620\pi\) | ||||
0.775257 | + | 0.631646i | \(0.217620\pi\) | |||||||
\(920\) | −8.87444 | − | 15.3710i | −0.292581 | − | 0.506766i | ||||
\(921\) | −0.640396 | − | 1.10920i | −0.0211018 | − | 0.0365493i | ||||
\(922\) | −3.78726 | + | 6.55973i | −0.124727 | + | 0.216033i | ||||
\(923\) | −15.7701 | + | 27.3147i | −0.519081 | + | 0.899074i | ||||
\(924\) | 0.629962 | 0.0207242 | ||||||||
\(925\) | −6.07749 | −0.199827 | ||||||||
\(926\) | −1.54773 | + | 2.68075i | −0.0508615 | + | 0.0880948i | ||||
\(927\) | 25.2624 | − | 43.7558i | 0.829728 | − | 1.43713i | ||||
\(928\) | 22.3422 | + | 38.6977i | 0.733417 | + | 1.27032i | ||||
\(929\) | −27.0489 | − | 46.8501i | −0.887447 | − | 1.53710i | −0.842884 | − | 0.538096i | \(-0.819144\pi\) |
−0.0445629 | − | 0.999007i | \(-0.514190\pi\) | |||||||
\(930\) | 0.0573868 | 0.00188179 | ||||||||
\(931\) | −11.0374 | − | 19.1173i | −0.361736 | − | 0.626545i | ||||
\(932\) | −14.0667 | − | 24.3642i | −0.460770 | − | 0.798077i | ||||
\(933\) | 1.09490 | + | 1.89643i | 0.0358455 | + | 0.0620862i | ||||
\(934\) | 3.02668 | − | 5.24236i | 0.0990360 | − | 0.171535i | ||||
\(935\) | −3.53438 | −0.115587 | ||||||||
\(936\) | 10.3496 | − | 17.9259i | 0.338286 | − | 0.585928i | ||||
\(937\) | 6.96391 | + | 12.0618i | 0.227501 | + | 0.394043i | 0.957067 | − | 0.289867i | \(-0.0936112\pi\) |
−0.729566 | + | 0.683911i | \(0.760278\pi\) | |||||||
\(938\) | −0.568402 | −0.0185590 | ||||||||
\(939\) | −0.439308 | − | 0.760903i | −0.0143363 | − | 0.0248311i | ||||
\(940\) | 6.25523 | − | 10.8344i | 0.204023 | − | 0.353378i | ||||
\(941\) | 24.3647 | − | 42.2009i | 0.794266 | − | 1.37571i | −0.129038 | − | 0.991640i | \(-0.541189\pi\) |
0.923304 | − | 0.384069i | \(-0.125478\pi\) | |||||||
\(942\) | −0.164021 | −0.00534410 | ||||||||
\(943\) | −20.6837 | + | 35.8252i | −0.673554 | + | 1.16663i | ||||
\(944\) | 4.94623 | 0.160986 | ||||||||
\(945\) | 0.779694 | 0.0253634 | ||||||||
\(946\) | −8.18290 | + | 8.93051i | −0.266049 | + | 0.290356i | ||||
\(947\) | 13.1775 | 0.428212 | 0.214106 | − | 0.976810i | \(-0.431316\pi\) | ||||
0.214106 | + | 0.976810i | \(0.431316\pi\) | |||||||
\(948\) | 0.823454 | 0.0267445 | ||||||||
\(949\) | 13.3360 | − | 23.0986i | 0.432904 | − | 0.749811i | ||||
\(950\) | 10.5617 | 0.342668 | ||||||||
\(951\) | 0.947128 | − | 1.64047i | 0.0307127 | − | 0.0531960i | ||||
\(952\) | 1.65197 | − | 2.86129i | 0.0535406 | − | 0.0927350i | ||||
\(953\) | −23.3609 | − | 40.4623i | −0.756734 | − | 1.31070i | −0.944507 | − | 0.328490i | \(-0.893460\pi\) |
0.187773 | − | 0.982212i | \(-0.439873\pi\) | |||||||
\(954\) | −21.3384 | −0.690855 | ||||||||
\(955\) | 8.92134 | + | 15.4522i | 0.288688 | + | 0.500022i | ||||
\(956\) | −14.8028 | + | 25.6392i | −0.478756 | + | 0.829230i | ||||
\(957\) | −1.98260 | −0.0640882 | ||||||||
\(958\) | −0.00536341 | + | 0.00928971i | −0.000173284 | + | 0.000300137i | ||||
\(959\) | 0.0804993 | + | 0.139429i | 0.00259946 | + | 0.00450239i | ||||
\(960\) | 0.0453969 | + | 0.0786298i | 0.00146518 | + | 0.00253777i | ||||
\(961\) | 14.7852 | + | 25.6086i | 0.476940 | + | 0.826085i | ||||
\(962\) | −3.02800 | −0.0976267 | ||||||||
\(963\) | 15.3471 | + | 26.5820i | 0.494554 | + | 0.856593i | ||||
\(964\) | 17.2523 | + | 29.8819i | 0.555660 | + | 0.962432i | ||||
\(965\) | −4.57771 | + | 7.92882i | −0.147362 | + | 0.255238i | ||||
\(966\) | −0.258622 | + | 0.447947i | −0.00832104 | + | 0.0144125i | ||||
\(967\) | 42.0722 | 1.35295 | 0.676476 | − | 0.736465i | \(-0.263506\pi\) | ||||
0.676476 | + | 0.736465i | \(0.263506\pi\) | |||||||
\(968\) | 1.55467 | 0.0499689 | ||||||||
\(969\) | 0.182710 | − | 0.316463i | 0.00586949 | − | 0.0101663i | ||||
\(970\) | −5.38042 | + | 9.31916i | −0.172755 | + | 0.299220i | ||||
\(971\) | 11.6916 | + | 20.2505i | 0.375202 | + | 0.649870i | 0.990357 | − | 0.138537i | \(-0.0442399\pi\) |
−0.615155 | + | 0.788406i | \(0.710907\pi\) | |||||||
\(972\) | −1.69454 | − | 2.93503i | −0.0543524 | − | 0.0941411i | ||||
\(973\) | 24.1115 | 0.772980 | ||||||||
\(974\) | −4.66874 | − | 8.08649i | −0.149596 | − | 0.259108i | ||||
\(975\) | 0.466639 | + | 0.808242i | 0.0149444 | + | 0.0258845i | ||||
\(976\) | 0.469835 | + | 0.813777i | 0.0150390 | + | 0.0260484i | ||||
\(977\) | 6.09288 | − | 10.5532i | 0.194928 | − | 0.337626i | −0.751949 | − | 0.659222i | \(-0.770886\pi\) |
0.946877 | + | 0.321596i | \(0.104219\pi\) | |||||||
\(978\) | −0.178680 | −0.00571356 | ||||||||
\(979\) | 8.19473 | − | 14.1937i | 0.261905 | − | 0.453632i | ||||
\(980\) | 4.19306 | + | 7.26259i | 0.133942 | + | 0.231995i | ||||
\(981\) | −22.0074 | −0.702642 | ||||||||
\(982\) | −0.723314 | − | 1.25282i | −0.0230819 | − | 0.0399790i | ||||
\(983\) | −5.82614 | + | 10.0912i | −0.185825 | + | 0.321858i | −0.943854 | − | 0.330362i | \(-0.892829\pi\) |
0.758029 | + | 0.652221i | \(0.226162\pi\) | |||||||
\(984\) | −0.433750 | + | 0.751277i | −0.0138274 | + | 0.0239498i | ||||
\(985\) | 7.42357 | 0.236535 | ||||||||
\(986\) | −2.36392 | + | 4.09442i | −0.0752824 | + | 0.130393i | ||||
\(987\) | −0.801840 | −0.0255228 | ||||||||
\(988\) | −26.4002 | −0.839902 | ||||||||
\(989\) | 15.0049 | + | 47.5853i | 0.477127 | + | 1.51313i | ||||
\(990\) | −6.10149 | −0.193918 | ||||||||
\(991\) | −24.2157 | −0.769237 | −0.384619 | − | 0.923076i | \(-0.625667\pi\) | ||||
−0.384619 | + | 0.923076i | \(0.625667\pi\) | |||||||
\(992\) | −3.25770 | + | 5.64251i | −0.103432 | + | 0.179150i | ||||
\(993\) | 0.969956 | 0.0307806 | ||||||||
\(994\) | −4.34549 | + | 7.52661i | −0.137831 | + | 0.238729i | ||||
\(995\) | −3.99048 | + | 6.91171i | −0.126507 | + | 0.219116i | ||||
\(996\) | 0.554629 | + | 0.960646i | 0.0175741 | + | 0.0304392i | ||||
\(997\) | 21.8373 | 0.691596 | 0.345798 | − | 0.938309i | \(-0.387608\pi\) | ||||
0.345798 | + | 0.938309i | \(0.387608\pi\) | |||||||
\(998\) | 6.45914 | + | 11.1876i | 0.204461 | + | 0.354136i | ||||
\(999\) | −0.363343 | + | 0.629329i | −0.0114957 | + | 0.0199111i |
(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 | 731.2.e.a.307.18 | ✓ | 58 | |
43.36 | even | 3 | inner | 731.2.e.a.681.18 | yes | 58 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
731.2.e.a.307.18 | ✓ | 58 | 1.1 | even | 1 | trivial | |
731.2.e.a.681.18 | yes | 58 | 43.36 | even | 3 | inner |