Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(491,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.491");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.q (of order \(6\), 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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.2346760387617129.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + 16 x^{2} - 96 x + 64 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 491.3 | ||
Root | \(-1.18541 + 0.771231i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.491 |
Dual form | 637.2.q.g.589.3 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.433001 | + | 0.249993i | −0.306178 | + | 0.176772i | −0.645215 | − | 0.764001i | \(-0.723232\pi\) |
0.339037 | + | 0.940773i | \(0.389899\pi\) | |||||||
\(3\) | −0.424801 | − | 0.735776i | −0.245259 | − | 0.424801i | 0.716946 | − | 0.697129i | \(-0.245540\pi\) |
−0.962204 | + | 0.272328i | \(0.912206\pi\) | |||||||
\(4\) | −0.875007 | + | 1.51556i | −0.437503 | + | 0.757778i | ||||
\(5\) | 1.04248i | 0.466209i | 0.972452 | + | 0.233105i | \(0.0748884\pi\) | ||||
−0.972452 | + | 0.233105i | \(0.925112\pi\) | |||||||
\(6\) | 0.367878 | + | 0.212395i | 0.150186 | + | 0.0867098i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.87496i | − | 0.662897i | ||||||
\(9\) | 1.13909 | − | 1.97296i | 0.379696 | − | 0.657653i | ||||
\(10\) | −0.260612 | − | 0.451393i | −0.0824127 | − | 0.142743i | ||||
\(11\) | 3.43579 | − | 1.98365i | 1.03593 | − | 0.598094i | 0.117251 | − | 0.993102i | \(-0.462592\pi\) |
0.918677 | + | 0.395009i | \(0.129258\pi\) | |||||||
\(12\) | 1.48681 | 0.429206 | ||||||||
\(13\) | −3.57504 | − | 0.468096i | −0.991537 | − | 0.129827i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.767029 | − | 0.442844i | 0.198046 | − | 0.114342i | ||||
\(16\) | −1.28129 | − | 2.21925i | −0.320322 | − | 0.554813i | ||||
\(17\) | −0.0710177 | + | 0.123006i | −0.0172243 | + | 0.0298334i | −0.874509 | − | 0.485009i | \(-0.838816\pi\) |
0.857285 | + | 0.514843i | \(0.172150\pi\) | |||||||
\(18\) | 1.13906i | 0.268479i | ||||||||
\(19\) | 4.77160 | + | 2.75488i | 1.09468 | + | 0.632014i | 0.934818 | − | 0.355126i | \(-0.115562\pi\) |
0.159861 | + | 0.987140i | \(0.448895\pi\) | |||||||
\(20\) | −1.57993 | − | 0.912173i | −0.353283 | − | 0.203968i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.991800 | + | 1.71785i | −0.211452 | + | 0.366246i | ||||
\(23\) | 2.19549 | + | 3.80270i | 0.457791 | + | 0.792917i | 0.998844 | − | 0.0480711i | \(-0.0153074\pi\) |
−0.541053 | + | 0.840989i | \(0.681974\pi\) | |||||||
\(24\) | −1.37955 | + | 0.796483i | −0.281599 | + | 0.162581i | ||||
\(25\) | 3.91325 | 0.782649 | ||||||||
\(26\) | 1.66502 | − | 0.691049i | 0.326536 | − | 0.135526i | ||||
\(27\) | −4.48435 | −0.863013 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.19880 | + | 7.27253i | 0.779697 | + | 1.35047i | 0.932116 | + | 0.362159i | \(0.117960\pi\) |
−0.152419 | + | 0.988316i | \(0.548706\pi\) | |||||||
\(30\) | −0.221416 | + | 0.383504i | −0.0404249 | + | 0.0700179i | ||||
\(31\) | 2.84652i | 0.511251i | 0.966776 | + | 0.255625i | \(0.0822813\pi\) | ||||
−0.966776 | + | 0.255625i | \(0.917719\pi\) | |||||||
\(32\) | 4.35712 | + | 2.51558i | 0.770237 | + | 0.444696i | ||||
\(33\) | −2.91905 | − | 1.68531i | −0.508141 | − | 0.293376i | ||||
\(34\) | − | 0.0710158i | − | 0.0121791i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.99342 | + | 3.45271i | 0.332237 | + | 0.575451i | ||||
\(37\) | 0.730221 | − | 0.421593i | 0.120048 | − | 0.0693095i | −0.438774 | − | 0.898598i | \(-0.644587\pi\) |
0.558821 | + | 0.829288i | \(0.311254\pi\) | |||||||
\(38\) | −2.75481 | −0.446889 | ||||||||
\(39\) | 1.17426 | + | 2.82928i | 0.188033 | + | 0.453047i | ||||
\(40\) | 1.95460 | 0.309049 | ||||||||
\(41\) | 10.4766 | − | 6.04869i | 1.63618 | − | 0.944647i | 0.654044 | − | 0.756457i | \(-0.273071\pi\) |
0.982133 | − | 0.188190i | \(-0.0602621\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.41161 | − | 4.17704i | 0.367768 | − | 0.636993i | −0.621448 | − | 0.783455i | \(-0.713455\pi\) |
0.989216 | + | 0.146463i | \(0.0467888\pi\) | |||||||
\(44\) | 6.94284i | 1.04667i | ||||||||
\(45\) | 2.05676 | + | 1.18747i | 0.306604 | + | 0.177018i | ||||
\(46\) | −1.90130 | − | 1.09772i | −0.280331 | − | 0.161849i | ||||
\(47\) | 4.55648i | 0.664630i | 0.943168 | + | 0.332315i | \(0.107830\pi\) | ||||
−0.943168 | + | 0.332315i | \(0.892170\pi\) | |||||||
\(48\) | −1.08858 | + | 1.88548i | −0.157123 | + | 0.272146i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.69444 | + | 0.978285i | −0.239630 | + | 0.138350i | ||||
\(51\) | 0.120673 | 0.0168977 | ||||||||
\(52\) | 3.83761 | − | 5.00858i | 0.532180 | − | 0.694565i | ||||
\(53\) | −0.279600 | −0.0384060 | −0.0192030 | − | 0.999816i | \(-0.506113\pi\) | ||||
−0.0192030 | + | 0.999816i | \(0.506113\pi\) | |||||||
\(54\) | 1.94173 | − | 1.12106i | 0.264236 | − | 0.152557i | ||||
\(55\) | 2.06791 | + | 3.58172i | 0.278837 | + | 0.482959i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 4.68111i | − | 0.620028i | ||||||
\(58\) | −3.63617 | − | 2.09934i | −0.477452 | − | 0.275657i | ||||
\(59\) | −9.33705 | − | 5.39075i | −1.21558 | − | 0.701815i | −0.251611 | − | 0.967829i | \(-0.580960\pi\) |
−0.963969 | + | 0.266013i | \(0.914294\pi\) | |||||||
\(60\) | 1.54997i | 0.200100i | ||||||||
\(61\) | 2.93177 | − | 5.07797i | 0.375374 | − | 0.650168i | −0.615009 | − | 0.788520i | \(-0.710847\pi\) |
0.990383 | + | 0.138353i | \(0.0441808\pi\) | |||||||
\(62\) | −0.711612 | − | 1.23255i | −0.0903748 | − | 0.156534i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.60963 | 0.326204 | ||||||||
\(65\) | 0.487979 | − | 3.72689i | 0.0605263 | − | 0.462263i | ||||
\(66\) | 1.68527 | 0.207442 | ||||||||
\(67\) | 4.45524 | − | 2.57223i | 0.544294 | − | 0.314248i | −0.202523 | − | 0.979277i | \(-0.564914\pi\) |
0.746818 | + | 0.665029i | \(0.231581\pi\) | |||||||
\(68\) | −0.124282 | − | 0.215263i | −0.0150714 | − | 0.0261044i | ||||
\(69\) | 1.86529 | − | 3.23078i | 0.224555 | − | 0.388940i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.20326 | − | 1.84940i | −0.380157 | − | 0.219484i | 0.297730 | − | 0.954650i | \(-0.403771\pi\) |
−0.677887 | + | 0.735167i | \(0.737104\pi\) | |||||||
\(72\) | −3.69921 | − | 2.13574i | −0.435956 | − | 0.251700i | ||||
\(73\) | 6.61281i | 0.773970i | 0.922086 | + | 0.386985i | \(0.126484\pi\) | ||||
−0.922086 | + | 0.386985i | \(0.873516\pi\) | |||||||
\(74\) | −0.210791 | + | 0.365101i | −0.0245040 | + | 0.0424421i | ||||
\(75\) | −1.66235 | − | 2.87927i | −0.191952 | − | 0.332470i | ||||
\(76\) | −8.35036 | + | 4.82108i | −0.957852 | + | 0.553016i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.21576 | − | 0.931521i | −0.137657 | − | 0.105474i | ||||
\(79\) | 11.9227 | 1.34141 | 0.670705 | − | 0.741725i | \(-0.265992\pi\) | ||||
0.670705 | + | 0.741725i | \(0.265992\pi\) | |||||||
\(80\) | 2.31352 | − | 1.33571i | 0.258659 | − | 0.149337i | ||||
\(81\) | −1.51231 | − | 2.61940i | −0.168035 | − | 0.291045i | ||||
\(82\) | −3.02426 | + | 5.23818i | −0.333974 | + | 0.578460i | ||||
\(83\) | 2.87321i | 0.315376i | 0.987489 | + | 0.157688i | \(0.0504040\pi\) | ||||
−0.987489 | + | 0.157688i | \(0.949596\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.128231 | − | 0.0740342i | −0.0139086 | − | 0.00803013i | ||||
\(86\) | 2.41155i | 0.260044i | ||||||||
\(87\) | 3.56730 | − | 6.17875i | 0.382455 | − | 0.662432i | ||||
\(88\) | −3.71926 | − | 6.44195i | −0.396475 | − | 0.686714i | ||||
\(89\) | −1.51351 | + | 0.873824i | −0.160432 | + | 0.0926252i | −0.578066 | − | 0.815990i | \(-0.696193\pi\) |
0.417635 | + | 0.908615i | \(0.362859\pi\) | |||||||
\(90\) | −1.18744 | −0.125167 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −7.68427 | −0.801141 | ||||||||
\(93\) | 2.09440 | − | 1.20921i | 0.217180 | − | 0.125389i | ||||
\(94\) | −1.13909 | − | 1.97296i | −0.117488 | − | 0.203495i | ||||
\(95\) | −2.87190 | + | 4.97427i | −0.294650 | + | 0.510350i | ||||
\(96\) | − | 4.27449i | − | 0.436263i | ||||||
\(97\) | 2.34079 | + | 1.35145i | 0.237671 | + | 0.137219i | 0.614106 | − | 0.789224i | \(-0.289517\pi\) |
−0.376435 | + | 0.926443i | \(0.622850\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 9.03822i | − | 0.908376i | ||||||
\(100\) | −3.42412 | + | 5.93074i | −0.342412 | + | 0.593074i | ||||
\(101\) | 5.73612 | + | 9.93524i | 0.570765 | + | 0.988594i | 0.996488 | + | 0.0837401i | \(0.0266866\pi\) |
−0.425723 | + | 0.904854i | \(0.639980\pi\) | |||||||
\(102\) | −0.0522517 | + | 0.0301676i | −0.00517369 | + | 0.00298703i | ||||
\(103\) | −4.16950 | −0.410834 | −0.205417 | − | 0.978675i | \(-0.565855\pi\) | ||||
−0.205417 | + | 0.978675i | \(0.565855\pi\) | |||||||
\(104\) | −0.877660 | + | 6.70304i | −0.0860617 | + | 0.657287i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.121067 | − | 0.0698982i | 0.0117591 | − | 0.00678911i | ||||
\(107\) | −4.24371 | − | 7.35032i | −0.410255 | − | 0.710583i | 0.584662 | − | 0.811277i | \(-0.301227\pi\) |
−0.994917 | + | 0.100694i | \(0.967894\pi\) | |||||||
\(108\) | 3.92383 | − | 6.79628i | 0.377571 | − | 0.653972i | ||||
\(109\) | 6.43036i | 0.615917i | 0.951400 | + | 0.307958i | \(0.0996458\pi\) | ||||
−0.951400 | + | 0.307958i | \(0.900354\pi\) | |||||||
\(110\) | −1.79081 | − | 1.03393i | −0.170747 | − | 0.0985810i | ||||
\(111\) | −0.620397 | − | 0.358186i | −0.0588855 | − | 0.0339975i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.48164 | + | 9.49448i | −0.515670 | + | 0.893166i | 0.484165 | + | 0.874977i | \(0.339123\pi\) |
−0.999835 | + | 0.0181892i | \(0.994210\pi\) | |||||||
\(114\) | 1.17025 | + | 2.02692i | 0.109603 | + | 0.189839i | ||||
\(115\) | −3.96422 | + | 2.28874i | −0.369665 | + | 0.213426i | ||||
\(116\) | −14.6959 | −1.36448 | ||||||||
\(117\) | −4.99582 | + | 6.52020i | −0.461864 | + | 0.602793i | ||||
\(118\) | 5.39060 | 0.496245 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.830314 | − | 1.43815i | −0.0757969 | − | 0.131284i | ||||
\(121\) | 2.36975 | − | 4.10453i | 0.215432 | − | 0.373139i | ||||
\(122\) | 2.93169i | 0.265423i | ||||||||
\(123\) | −8.90097 | − | 5.13898i | −0.802573 | − | 0.463366i | ||||
\(124\) | −4.31406 | − | 2.49073i | −0.387414 | − | 0.223674i | ||||
\(125\) | 9.29184i | 0.831087i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00394 | − | 1.73887i | −0.0890849 | − | 0.154300i | 0.818040 | − | 0.575162i | \(-0.195061\pi\) |
−0.907125 | + | 0.420862i | \(0.861728\pi\) | |||||||
\(128\) | −9.84421 | + | 5.68356i | −0.870113 | + | 0.502360i | ||||
\(129\) | −4.09782 | −0.360793 | ||||||||
\(130\) | 0.720401 | + | 1.73574i | 0.0631834 | + | 0.152234i | ||||
\(131\) | −12.4502 | −1.08778 | −0.543890 | − | 0.839156i | \(-0.683049\pi\) | ||||
−0.543890 | + | 0.839156i | \(0.683049\pi\) | |||||||
\(132\) | 5.10838 | − | 2.94932i | 0.444627 | − | 0.256706i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.28608 | + | 2.22756i | −0.111101 | + | 0.192432i | ||||
\(135\) | − | 4.67482i | − | 0.402344i | ||||||
\(136\) | 0.230631 | + | 0.133155i | 0.0197765 | + | 0.0114180i | ||||
\(137\) | −4.54246 | − | 2.62259i | −0.388088 | − | 0.224063i | 0.293243 | − | 0.956038i | \(-0.405265\pi\) |
−0.681332 | + | 0.731975i | \(0.738599\pi\) | |||||||
\(138\) | 1.86524i | 0.158780i | ||||||||
\(139\) | 10.3693 | − | 17.9601i | 0.879510 | − | 1.52336i | 0.0276301 | − | 0.999618i | \(-0.491204\pi\) |
0.851880 | − | 0.523737i | \(-0.175463\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.35255 | − | 1.93559i | 0.282335 | − | 0.163006i | ||||
\(142\) | 1.84935 | 0.155194 | ||||||||
\(143\) | −13.2116 | + | 5.48335i | −1.10481 | + | 0.458541i | ||||
\(144\) | −5.83800 | −0.486500 | ||||||||
\(145\) | −7.58143 | + | 4.37714i | −0.629604 | + | 0.363502i | ||||
\(146\) | −1.65316 | − | 2.86335i | −0.136816 | − | 0.236973i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.47559i | 0.121293i | ||||||||
\(149\) | −0.00985188 | − | 0.00568799i | −0.000807098 | − | 0.000465978i | 0.499596 | − | 0.866258i | \(-0.333482\pi\) |
−0.500403 | + | 0.865792i | \(0.666815\pi\) | |||||||
\(150\) | 1.43960 | + | 0.831153i | 0.117543 | + | 0.0678633i | ||||
\(151\) | − | 18.9054i | − | 1.53850i | −0.638947 | − | 0.769251i | \(-0.720630\pi\) | ||
0.638947 | − | 0.769251i | \(-0.279370\pi\) | |||||||
\(152\) | 5.16529 | − | 8.94654i | 0.418960 | − | 0.725660i | ||||
\(153\) | 0.161791 | + | 0.280230i | 0.0130800 | + | 0.0226553i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.96743 | −0.238350 | ||||||||
\(156\) | −5.31541 | − | 0.695972i | −0.425574 | − | 0.0557224i | ||||
\(157\) | 19.7937 | 1.57971 | 0.789856 | − | 0.613292i | \(-0.210155\pi\) | ||||
0.789856 | + | 0.613292i | \(0.210155\pi\) | |||||||
\(158\) | −5.16255 | + | 2.98060i | −0.410710 | + | 0.237124i | ||||
\(159\) | 0.118774 | + | 0.205723i | 0.00941942 | + | 0.0163149i | ||||
\(160\) | −2.62243 | + | 4.54219i | −0.207321 | + | 0.359091i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.30967 | + | 0.756136i | 0.102897 | + | 0.0594076i | ||||
\(163\) | −7.73581 | − | 4.46627i | −0.605915 | − | 0.349825i | 0.165450 | − | 0.986218i | \(-0.447092\pi\) |
−0.771365 | + | 0.636393i | \(0.780426\pi\) | |||||||
\(164\) | 21.1706i | 1.65314i | ||||||||
\(165\) | 1.75690 | − | 3.04304i | 0.136774 | − | 0.236900i | ||||
\(166\) | −0.718284 | − | 1.24410i | −0.0557496 | − | 0.0965612i | ||||
\(167\) | 5.31279 | − | 3.06734i | 0.411116 | − | 0.237358i | −0.280153 | − | 0.959955i | \(-0.590385\pi\) |
0.691269 | + | 0.722597i | \(0.257052\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.5618 | + | 3.34692i | 0.966290 | + | 0.257456i | ||||
\(170\) | 0.0740322 | 0.00567801 | ||||||||
\(171\) | 10.8705 | − | 6.27611i | 0.831291 | − | 0.479946i | ||||
\(172\) | 4.22036 | + | 7.30987i | 0.321799 | + | 0.557373i | ||||
\(173\) | 12.1314 | − | 21.0122i | 0.922332 | − | 1.59753i | 0.126535 | − | 0.991962i | \(-0.459614\pi\) |
0.795797 | − | 0.605563i | \(-0.207052\pi\) | |||||||
\(174\) | 3.56721i | 0.270429i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −8.80446 | − | 5.08325i | −0.663661 | − | 0.383165i | ||||
\(177\) | 9.15997i | 0.688506i | ||||||||
\(178\) | 0.436901 | − | 0.756734i | 0.0327471 | − | 0.0567196i | ||||
\(179\) | −2.06838 | − | 3.58253i | −0.154598 | − | 0.267771i | 0.778315 | − | 0.627874i | \(-0.216075\pi\) |
−0.932912 | + | 0.360103i | \(0.882741\pi\) | |||||||
\(180\) | −3.59936 | + | 2.07809i | −0.268280 | + | 0.154892i | ||||
\(181\) | −7.86568 | −0.584651 | −0.292326 | − | 0.956319i | \(-0.594429\pi\) | ||||
−0.292326 | + | 0.956319i | \(0.594429\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.98167 | −0.368256 | ||||||||
\(184\) | 7.12989 | − | 4.11645i | 0.525623 | − | 0.303468i | ||||
\(185\) | 0.439501 | + | 0.761237i | 0.0323127 | + | 0.0559673i | ||||
\(186\) | −0.604586 | + | 1.04717i | −0.0443304 | + | 0.0767825i | ||||
\(187\) | 0.563498i | 0.0412070i | ||||||||
\(188\) | −6.90560 | − | 3.98695i | −0.503642 | − | 0.290778i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 2.87182i | − | 0.208344i | ||||||
\(191\) | 3.23933 | − | 5.61069i | 0.234390 | − | 0.405975i | −0.724705 | − | 0.689059i | \(-0.758024\pi\) |
0.959095 | + | 0.283084i | \(0.0913574\pi\) | |||||||
\(192\) | −1.10857 | − | 1.92011i | −0.0800044 | − | 0.138572i | ||||
\(193\) | −4.18228 | + | 2.41464i | −0.301047 | + | 0.173810i | −0.642913 | − | 0.765939i | \(-0.722274\pi\) |
0.341866 | + | 0.939749i | \(0.388941\pi\) | |||||||
\(194\) | −1.35142 | −0.0970261 | ||||||||
\(195\) | −2.94945 | + | 1.22414i | −0.211214 | + | 0.0876626i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.3748 | + | 12.9181i | −1.59414 | + | 0.920377i | −0.601554 | + | 0.798832i | \(0.705452\pi\) |
−0.992586 | + | 0.121545i | \(0.961215\pi\) | |||||||
\(198\) | 2.25950 | + | 3.91356i | 0.160575 | + | 0.278125i | ||||
\(199\) | 8.55731 | − | 14.8217i | 0.606612 | − | 1.05068i | −0.385183 | − | 0.922840i | \(-0.625862\pi\) |
0.991795 | − | 0.127842i | \(-0.0408050\pi\) | |||||||
\(200\) | − | 7.33717i | − | 0.518816i | ||||||
\(201\) | −3.78518 | − | 2.18537i | −0.266986 | − | 0.154144i | ||||
\(202\) | −4.96749 | − | 2.86798i | −0.349511 | − | 0.201790i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.105590 | + | 0.182887i | −0.00739278 | + | 0.0128047i | ||||
\(205\) | 6.30561 | + | 10.9216i | 0.440403 | + | 0.762800i | ||||
\(206\) | 1.80540 | − | 1.04235i | 0.125788 | − | 0.0726238i | ||||
\(207\) | 10.0034 | 0.695286 | ||||||||
\(208\) | 3.54182 | + | 8.53368i | 0.245581 | + | 0.591704i | ||||
\(209\) | 21.8589 | 1.51201 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.14557 | − | 15.8406i | −0.629607 | − | 1.09051i | −0.987631 | − | 0.156799i | \(-0.949883\pi\) |
0.358024 | − | 0.933713i | \(-0.383451\pi\) | |||||||
\(212\) | 0.244652 | − | 0.423750i | 0.0168028 | − | 0.0291032i | ||||
\(213\) | 3.14251i | 0.215321i | ||||||||
\(214\) | 3.67506 | + | 2.12180i | 0.251222 | + | 0.145043i | ||||
\(215\) | 4.35446 | + | 2.51405i | 0.296972 | + | 0.171457i | ||||
\(216\) | 8.40796i | 0.572089i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.60755 | − | 2.78435i | −0.108877 | − | 0.188580i | ||||
\(219\) | 4.86555 | − | 2.80912i | 0.328783 | − | 0.189823i | ||||
\(220\) | −7.23773 | −0.487968 | ||||||||
\(221\) | 0.311470 | − | 0.406509i | 0.0209517 | − | 0.0273447i | ||||
\(222\) | 0.358177 | 0.0240392 | ||||||||
\(223\) | −9.96682 | + | 5.75435i | −0.667428 | + | 0.385340i | −0.795101 | − | 0.606477i | \(-0.792582\pi\) |
0.127674 | + | 0.991816i | \(0.459249\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.45753 | − | 7.72067i | 0.297169 | − | 0.514712i | ||||
\(226\) | − | 5.48150i | − | 0.364624i | ||||||
\(227\) | −15.5057 | − | 8.95223i | −1.02915 | − | 0.594181i | −0.112410 | − | 0.993662i | \(-0.535857\pi\) |
−0.916741 | + | 0.399481i | \(0.869190\pi\) | |||||||
\(228\) | 7.09448 | + | 4.09600i | 0.469843 | + | 0.271264i | ||||
\(229\) | 3.86350i | 0.255307i | 0.991819 | + | 0.127654i | \(0.0407446\pi\) | ||||
−0.991819 | + | 0.127654i | \(0.959255\pi\) | |||||||
\(230\) | 1.14434 | − | 1.98206i | 0.0754556 | − | 0.130693i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 13.6357 | − | 7.87256i | 0.895226 | − | 0.516859i | ||||
\(233\) | −25.0642 | −1.64201 | −0.821004 | − | 0.570922i | \(-0.806586\pi\) | ||||
−0.821004 | + | 0.570922i | \(0.806586\pi\) | |||||||
\(234\) | 0.533189 | − | 4.07217i | 0.0348556 | − | 0.266206i | ||||
\(235\) | −4.75001 | −0.309857 | ||||||||
\(236\) | 16.3400 | − | 9.43388i | 1.06364 | − | 0.614093i | ||||
\(237\) | −5.06477 | − | 8.77245i | −0.328992 | − | 0.569832i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.80462i | 0.504839i | 0.967618 | + | 0.252419i | \(0.0812263\pi\) | ||||
−0.967618 | + | 0.252419i | \(0.918774\pi\) | |||||||
\(240\) | −1.96557 | − | 1.13482i | −0.126877 | − | 0.0732524i | ||||
\(241\) | −18.8493 | − | 10.8826i | −1.21419 | − | 0.701012i | −0.250519 | − | 0.968112i | \(-0.580601\pi\) |
−0.963669 | + | 0.267100i | \(0.913935\pi\) | |||||||
\(242\) | 2.36969i | 0.152329i | ||||||||
\(243\) | −8.01138 | + | 13.8761i | −0.513930 | + | 0.890154i | ||||
\(244\) | 5.13063 | + | 8.88652i | 0.328455 | + | 0.568901i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.13884 | 0.327640 | ||||||||
\(247\) | −15.7691 | − | 12.0824i | −1.00336 | − | 0.768783i | ||||
\(248\) | 5.33711 | 0.338907 | ||||||||
\(249\) | 2.11404 | − | 1.22054i | 0.133972 | − | 0.0773488i | ||||
\(250\) | −2.32290 | − | 4.02338i | −0.146913 | − | 0.254461i | ||||
\(251\) | 3.83990 | − | 6.65090i | 0.242372 | − | 0.419801i | −0.719017 | − | 0.694992i | \(-0.755408\pi\) |
0.961390 | + | 0.275191i | \(0.0887411\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.0865 | + | 8.71017i | 0.948478 | + | 0.547604i | ||||
\(254\) | 0.869411 | + | 0.501955i | 0.0545517 | + | 0.0314954i | ||||
\(255\) | 0.125799i | 0.00787784i | ||||||||
\(256\) | 0.232070 | − | 0.401958i | 0.0145044 | − | 0.0251224i | ||||
\(257\) | 6.81187 | + | 11.7985i | 0.424913 | + | 0.735971i | 0.996412 | − | 0.0846316i | \(-0.0269713\pi\) |
−0.571499 | + | 0.820603i | \(0.693638\pi\) | |||||||
\(258\) | 1.77436 | − | 1.02443i | 0.110467 | − | 0.0637781i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 5.22132 | + | 4.00061i | 0.323813 | + | 0.248107i | ||||
\(261\) | 19.1312 | 1.18419 | ||||||||
\(262\) | 5.39096 | − | 3.11247i | 0.333055 | − | 0.192289i | ||||
\(263\) | 5.86158 | + | 10.1525i | 0.361440 | + | 0.626033i | 0.988198 | − | 0.153181i | \(-0.0489518\pi\) |
−0.626758 | + | 0.779214i | \(0.715618\pi\) | |||||||
\(264\) | −3.15989 | + | 5.47309i | −0.194478 | + | 0.336845i | ||||
\(265\) | − | 0.291476i | − | 0.0179052i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.28588 | + | 0.742403i | 0.0786945 | + | 0.0454343i | ||||
\(268\) | 9.00289i | 0.549939i | ||||||||
\(269\) | −4.59938 | + | 7.96636i | −0.280429 | + | 0.485717i | −0.971490 | − | 0.237079i | \(-0.923810\pi\) |
0.691061 | + | 0.722796i | \(0.257143\pi\) | |||||||
\(270\) | 1.16867 | + | 2.02420i | 0.0711232 | + | 0.123189i | ||||
\(271\) | −2.22022 | + | 1.28184i | −0.134869 | + | 0.0778665i | −0.565916 | − | 0.824463i | \(-0.691477\pi\) |
0.431048 | + | 0.902329i | \(0.358144\pi\) | |||||||
\(272\) | 0.363976 | 0.0220693 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.62252 | 0.158432 | ||||||||
\(275\) | 13.4451 | − | 7.76252i | 0.810769 | − | 0.468097i | ||||
\(276\) | 3.26428 | + | 5.65391i | 0.196487 | + | 0.340325i | ||||
\(277\) | −0.466941 | + | 0.808765i | −0.0280558 | + | 0.0485940i | −0.879712 | − | 0.475506i | \(-0.842265\pi\) |
0.851657 | + | 0.524100i | \(0.175598\pi\) | |||||||
\(278\) | 10.3690i | 0.621891i | ||||||||
\(279\) | 5.61607 | + | 3.24244i | 0.336226 | + | 0.194120i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.45288i | 0.384947i | 0.981302 | + | 0.192473i | \(0.0616509\pi\) | ||||
−0.981302 | + | 0.192473i | \(0.938349\pi\) | |||||||
\(282\) | −0.967771 | + | 1.67623i | −0.0576299 | + | 0.0998180i | ||||
\(283\) | 11.0873 | + | 19.2037i | 0.659071 | + | 1.14154i | 0.980857 | + | 0.194731i | \(0.0623835\pi\) |
−0.321786 | + | 0.946812i | \(0.604283\pi\) | |||||||
\(284\) | 5.60575 | − | 3.23648i | 0.332640 | − | 0.192050i | ||||
\(285\) | 4.87994 | 0.289062 | ||||||||
\(286\) | 4.34984 | − | 5.67711i | 0.257211 | − | 0.335695i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 9.92629 | − | 5.73094i | 0.584912 | − | 0.337699i | ||||
\(289\) | 8.48991 | + | 14.7050i | 0.499407 | + | 0.864998i | ||||
\(290\) | 2.18851 | − | 3.79061i | 0.128514 | − | 0.222593i | ||||
\(291\) | − | 2.29639i | − | 0.134617i | ||||||
\(292\) | −10.0221 | − | 5.78625i | −0.586498 | − | 0.338615i | ||||
\(293\) | −20.9600 | − | 12.1013i | −1.22450 | − | 0.706964i | −0.258624 | − | 0.965978i | \(-0.583269\pi\) |
−0.965874 | + | 0.259014i | \(0.916602\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.61972 | − | 9.73364i | 0.327193 | − | 0.566714i | ||||
\(296\) | −0.790469 | − | 1.36913i | −0.0459451 | − | 0.0795792i | ||||
\(297\) | −15.4073 | + | 8.89539i | −0.894020 | + | 0.516163i | ||||
\(298\) | 0.00568784 | 0.000329487 | ||||||||
\(299\) | −6.06892 | − | 14.6225i | −0.350975 | − | 0.845640i | ||||
\(300\) | 5.81827 | 0.335918 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 4.72623 | + | 8.18607i | 0.271964 | + | 0.471055i | ||||
\(303\) | 4.87341 | − | 8.44100i | 0.279970 | − | 0.484923i | ||||
\(304\) | − | 14.1192i | − | 0.809791i | ||||||
\(305\) | 5.29366 | + | 3.05630i | 0.303114 | + | 0.175003i | ||||
\(306\) | −0.140111 | − | 0.0808933i | −0.00800963 | − | 0.00462436i | ||||
\(307\) | 24.2924i | 1.38644i | 0.720726 | + | 0.693220i | \(0.243809\pi\) | ||||
−0.720726 | + | 0.693220i | \(0.756191\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.77121 | + | 3.06782i | 0.100761 | + | 0.174522i | ||||
\(310\) | 1.28490 | − | 0.741837i | 0.0729774 | − | 0.0421335i | ||||
\(311\) | −3.98711 | −0.226088 | −0.113044 | − | 0.993590i | \(-0.536060\pi\) | ||||
−0.113044 | + | 0.993590i | \(0.536060\pi\) | |||||||
\(312\) | 5.30477 | − | 2.20169i | 0.300323 | − | 0.124646i | ||||
\(313\) | 28.4754 | 1.60953 | 0.804763 | − | 0.593597i | \(-0.202293\pi\) | ||||
0.804763 | + | 0.593597i | \(0.202293\pi\) | |||||||
\(314\) | −8.57071 | + | 4.94830i | −0.483673 | + | 0.279249i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.4324 | + | 18.0695i | −0.586871 | + | 1.01649i | ||||
\(317\) | 16.8161i | 0.944487i | 0.881468 | + | 0.472244i | \(0.156556\pi\) | ||||
−0.881468 | + | 0.472244i | \(0.843444\pi\) | |||||||
\(318\) | −0.102859 | − | 0.0593856i | −0.00576804 | − | 0.00333018i | ||||
\(319\) | 28.8523 | + | 16.6579i | 1.61542 | + | 0.932664i | ||||
\(320\) | 2.72048i | 0.152079i | ||||||||
\(321\) | −3.60546 | + | 6.24485i | −0.201237 | + | 0.348553i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.677736 | + | 0.391291i | −0.0377102 | + | 0.0217720i | ||||
\(324\) | 5.29313 | 0.294063 | ||||||||
\(325\) | −13.9900 | − | 1.83178i | −0.776025 | − | 0.101609i | ||||
\(326\) | 4.46615 | 0.247357 | ||||||||
\(327\) | 4.73131 | − | 2.73162i | 0.261642 | − | 0.151059i | ||||
\(328\) | −11.3410 | − | 19.6432i | −0.626204 | − | 1.08462i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1.75685i | 0.0967115i | ||||||||
\(331\) | −5.37730 | − | 3.10459i | −0.295563 | − | 0.170644i | 0.344885 | − | 0.938645i | \(-0.387918\pi\) |
−0.640448 | + | 0.768002i | \(0.721251\pi\) | |||||||
\(332\) | −4.35451 | − | 2.51408i | −0.238985 | − | 0.137978i | ||||
\(333\) | − | 1.92093i | − | 0.105266i | ||||||
\(334\) | −1.53363 | + | 2.65633i | −0.0839165 | + | 0.145348i | ||||
\(335\) | 2.68149 | + | 4.64448i | 0.146505 | + | 0.253755i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.69650 | 0.419255 | 0.209628 | − | 0.977781i | \(-0.432775\pi\) | ||||
0.209628 | + | 0.977781i | \(0.432775\pi\) | |||||||
\(338\) | −6.27597 | + | 1.69114i | −0.341368 | + | 0.0919858i | ||||
\(339\) | 9.31442 | 0.505890 | ||||||||
\(340\) | 0.224406 | − | 0.129561i | 0.0121701 | − | 0.00702642i | ||||
\(341\) | 5.64651 | + | 9.78005i | 0.305776 | + | 0.529619i | ||||
\(342\) | −3.13797 | + | 5.43513i | −0.169682 | + | 0.293898i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −7.83177 | − | 4.52167i | −0.422261 | − | 0.243792i | ||||
\(345\) | 3.36801 | + | 1.94452i | 0.181327 | + | 0.104689i | ||||
\(346\) | 12.1311i | 0.652170i | ||||||||
\(347\) | −15.2047 | + | 26.3353i | −0.816231 | + | 1.41375i | 0.0922088 | + | 0.995740i | \(0.470607\pi\) |
−0.908440 | + | 0.418015i | \(0.862726\pi\) | |||||||
\(348\) | 6.24283 | + | 10.8129i | 0.334651 | + | 0.579632i | ||||
\(349\) | −13.9933 | + | 8.07906i | −0.749046 | + | 0.432462i | −0.825349 | − | 0.564623i | \(-0.809022\pi\) |
0.0763028 | + | 0.997085i | \(0.475688\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 16.0317 | + | 2.09911i | 0.855709 | + | 0.112042i | ||||
\(352\) | 19.9602 | 1.06388 | ||||||||
\(353\) | 10.2558 | − | 5.92119i | 0.545861 | − | 0.315153i | −0.201590 | − | 0.979470i | \(-0.564611\pi\) |
0.747451 | + | 0.664317i | \(0.231277\pi\) | |||||||
\(354\) | −2.28993 | − | 3.96628i | −0.121709 | − | 0.210805i | ||||
\(355\) | 1.92796 | − | 3.33932i | 0.102325 | − | 0.177233i | ||||
\(356\) | − | 3.05841i | − | 0.162095i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.79122 | + | 1.03416i | 0.0946688 | + | 0.0546571i | ||||
\(359\) | 31.3653i | 1.65540i | 0.561174 | + | 0.827698i | \(0.310350\pi\) | ||||
−0.561174 | + | 0.827698i | \(0.689650\pi\) | |||||||
\(360\) | 2.22646 | − | 3.85634i | 0.117345 | − | 0.203247i | ||||
\(361\) | 5.67876 | + | 9.83591i | 0.298882 | + | 0.517679i | ||||
\(362\) | 3.40585 | − | 1.96637i | 0.179007 | − | 0.103350i | ||||
\(363\) | −4.02669 | −0.211346 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.89369 | −0.360832 | ||||||||
\(366\) | 2.15707 | − | 1.24538i | 0.112752 | − | 0.0650973i | ||||
\(367\) | −12.0387 | − | 20.8517i | −0.628415 | − | 1.08845i | −0.987870 | − | 0.155285i | \(-0.950370\pi\) |
0.359454 | − | 0.933163i | \(-0.382963\pi\) | |||||||
\(368\) | 5.62610 | − | 9.74470i | 0.293281 | − | 0.507977i | ||||
\(369\) | − | 27.5600i | − | 1.43472i | ||||||
\(370\) | −0.380608 | − | 0.219744i | −0.0197869 | − | 0.0114240i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 4.23225i | 0.219432i | ||||||||
\(373\) | 9.19612 | − | 15.9281i | 0.476157 | − | 0.824728i | −0.523470 | − | 0.852044i | \(-0.675363\pi\) |
0.999627 | + | 0.0273160i | \(0.00869604\pi\) | |||||||
\(374\) | −0.140871 | − | 0.243995i | −0.00728425 | − | 0.0126167i | ||||
\(375\) | 6.83672 | − | 3.94718i | 0.353046 | − | 0.203831i | ||||
\(376\) | 8.54320 | 0.440582 | ||||||||
\(377\) | −11.6066 | − | 27.9650i | −0.597771 | − | 1.44027i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.04719 | + | 4.06870i | −0.361990 | + | 0.208995i | −0.669953 | − | 0.742403i | \(-0.733686\pi\) |
0.307963 | + | 0.951398i | \(0.400353\pi\) | |||||||
\(380\) | −5.02586 | − | 8.70504i | −0.257821 | − | 0.446559i | ||||
\(381\) | −0.852946 | + | 1.47735i | −0.0436977 | + | 0.0756867i | ||||
\(382\) | 3.23925i | 0.165734i | ||||||||
\(383\) | 19.3739 | + | 11.1856i | 0.989962 | + | 0.571555i | 0.905263 | − | 0.424852i | \(-0.139674\pi\) |
0.0846992 | + | 0.996407i | \(0.473007\pi\) | |||||||
\(384\) | 8.36365 | + | 4.82876i | 0.426806 | + | 0.246417i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.20729 | − | 2.09108i | 0.0614493 | − | 0.106433i | ||||
\(387\) | −5.49409 | − | 9.51604i | −0.279280 | − | 0.483727i | ||||
\(388\) | −4.09641 | + | 2.36506i | −0.207963 | + | 0.120068i | ||||
\(389\) | 21.3946 | 1.08475 | 0.542374 | − | 0.840137i | \(-0.317525\pi\) | ||||
0.542374 | + | 0.840137i | \(0.317525\pi\) | |||||||
\(390\) | 0.971088 | − | 1.26740i | 0.0491729 | − | 0.0641771i | ||||
\(391\) | −0.623674 | −0.0315406 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.28886 | + | 9.16058i | 0.266788 | + | 0.462090i | ||||
\(394\) | 6.45888 | − | 11.1871i | 0.325394 | − | 0.563599i | ||||
\(395\) | 12.4291i | 0.625377i | ||||||||
\(396\) | 13.6979 | + | 7.90851i | 0.688347 | + | 0.397417i | ||||
\(397\) | −1.03640 | − | 0.598365i | −0.0520154 | − | 0.0300311i | 0.473767 | − | 0.880650i | \(-0.342894\pi\) |
−0.525782 | + | 0.850619i | \(0.676227\pi\) | |||||||
\(398\) | 8.55708i | 0.428928i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.01399 | − | 8.68449i | −0.250699 | − | 0.434224i | ||||
\(401\) | −31.4150 | + | 18.1375i | −1.56879 | + | 0.905741i | −0.572479 | + | 0.819919i | \(0.694018\pi\) |
−0.996310 | + | 0.0858220i | \(0.972648\pi\) | |||||||
\(402\) | 2.18532 | 0.108994 | ||||||||
\(403\) | 1.33245 | − | 10.1764i | 0.0663739 | − | 0.506924i | ||||
\(404\) | −20.0766 | −0.998846 | ||||||||
\(405\) | 2.73066 | − | 1.57655i | 0.135688 | − | 0.0783393i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.67259 | − | 2.89701i | 0.0829072 | − | 0.143599i | ||||
\(408\) | − | 0.226257i | − | 0.0112014i | ||||||
\(409\) | 12.7066 | + | 7.33616i | 0.628301 | + | 0.362750i | 0.780094 | − | 0.625662i | \(-0.215171\pi\) |
−0.151793 | + | 0.988412i | \(0.548505\pi\) | |||||||
\(410\) | −5.46067 | − | 3.15272i | −0.269683 | − | 0.155702i | ||||
\(411\) | 4.45631i | 0.219814i | ||||||||
\(412\) | 3.64834 | − | 6.31912i | 0.179741 | − | 0.311321i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −4.33150 | + | 2.50079i | −0.212881 | + | 0.122907i | ||||
\(415\) | −2.99525 | −0.147031 | ||||||||
\(416\) | −14.3993 | − | 11.0329i | −0.705985 | − | 0.540930i | ||||
\(417\) | −17.6195 | −0.862830 | ||||||||
\(418\) | −9.46494 | + | 5.46458i | −0.462945 | + | 0.267282i | ||||
\(419\) | 2.96674 | + | 5.13855i | 0.144935 | + | 0.251034i | 0.929349 | − | 0.369203i | \(-0.120369\pi\) |
−0.784414 | + | 0.620238i | \(0.787036\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 2.63174i | − | 0.128263i | −0.997941 | − | 0.0641317i | \(-0.979572\pi\) | ||
0.997941 | − | 0.0641317i | \(-0.0204278\pi\) | |||||||
\(422\) | 7.92008 | + | 4.57266i | 0.385544 | + | 0.222594i | ||||
\(423\) | 8.98974 | + | 5.19023i | 0.437096 | + | 0.252358i | ||||
\(424\) | 0.524238i | 0.0254593i | ||||||||
\(425\) | −0.277910 | + | 0.481354i | −0.0134806 | + | 0.0233491i | ||||
\(426\) | −0.785606 | − | 1.36071i | −0.0380628 | − | 0.0659266i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 14.8531 | 0.717952 | ||||||||
\(429\) | 9.64682 | + | 7.39146i | 0.465753 | + | 0.356863i | ||||
\(430\) | −2.51398 | −0.121235 | ||||||||
\(431\) | −16.3139 | + | 9.41883i | −0.785812 | + | 0.453689i | −0.838486 | − | 0.544923i | \(-0.816559\pi\) |
0.0526738 | + | 0.998612i | \(0.483226\pi\) | |||||||
\(432\) | 5.74573 | + | 9.95190i | 0.276442 | + | 0.478811i | ||||
\(433\) | 9.56773 | − | 16.5718i | 0.459796 | − | 0.796389i | −0.539154 | − | 0.842207i | \(-0.681256\pi\) |
0.998950 | + | 0.0458176i | \(0.0145893\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.44119 | + | 3.71883i | 0.308832 | + | 0.178304i | ||||
\(436\) | −9.74557 | − | 5.62661i | −0.466728 | − | 0.269466i | ||||
\(437\) | 24.1933i | 1.15732i | ||||||||
\(438\) | −1.40452 | + | 2.43271i | −0.0671108 | + | 0.116239i | ||||
\(439\) | −0.632554 | − | 1.09561i | −0.0301901 | − | 0.0522908i | 0.850536 | − | 0.525918i | \(-0.176278\pi\) |
−0.880726 | + | 0.473627i | \(0.842945\pi\) | |||||||
\(440\) | 6.71557 | − | 3.87724i | 0.320152 | − | 0.184840i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.0332422 | + | 0.253884i | −0.00158117 | + | 0.0120760i | ||||
\(443\) | −20.9392 | −0.994853 | −0.497426 | − | 0.867506i | \(-0.665722\pi\) | ||||
−0.497426 | + | 0.867506i | \(0.665722\pi\) | |||||||
\(444\) | 1.08570 | − | 0.626831i | 0.0515252 | − | 0.0297481i | ||||
\(445\) | −0.910940 | − | 1.57779i | −0.0431827 | − | 0.0747946i | ||||
\(446\) | 2.87710 | − | 4.98328i | 0.136234 | − | 0.235965i | ||||
\(447\) | 0.00966505i | 0.000457141i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.4700 | + | 8.93162i | 0.730075 | + | 0.421509i | 0.818450 | − | 0.574578i | \(-0.194834\pi\) |
−0.0883746 | + | 0.996087i | \(0.528167\pi\) | |||||||
\(450\) | 4.45741i | 0.210125i | ||||||||
\(451\) | 23.9970 | − | 41.5640i | 1.12997 | − | 1.95717i | ||||
\(452\) | −9.59295 | − | 16.6155i | −0.451214 | − | 0.781526i | ||||
\(453\) | −13.9102 | + | 8.03104i | −0.653557 | + | 0.377331i | ||||
\(454\) | 8.95199 | 0.420138 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8.77687 | −0.411015 | ||||||||
\(457\) | 5.68629 | − | 3.28298i | 0.265994 | − | 0.153571i | −0.361072 | − | 0.932538i | \(-0.617589\pi\) |
0.627066 | + | 0.778966i | \(0.284256\pi\) | |||||||
\(458\) | −0.965850 | − | 1.67290i | −0.0451312 | − | 0.0781695i | ||||
\(459\) | 0.318468 | − | 0.551603i | 0.0148648 | − | 0.0257466i | ||||
\(460\) | − | 8.01066i | − | 0.373499i | ||||||
\(461\) | −4.42854 | − | 2.55682i | −0.206258 | − | 0.119083i | 0.393313 | − | 0.919404i | \(-0.371329\pi\) |
−0.599571 | + | 0.800322i | \(0.704662\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 33.3239i | − | 1.54869i | −0.632761 | − | 0.774347i | \(-0.718079\pi\) | ||
0.632761 | − | 0.774347i | \(-0.281921\pi\) | |||||||
\(464\) | 10.7597 | − | 18.6364i | 0.499508 | − | 0.865173i | ||||
\(465\) | 1.26057 | + | 2.18336i | 0.0584574 | + | 0.101251i | ||||
\(466\) | 10.8528 | − | 6.26587i | 0.502747 | − | 0.290261i | ||||
\(467\) | 12.9494 | 0.599229 | 0.299614 | − | 0.954060i | \(-0.403142\pi\) | ||||
0.299614 | + | 0.954060i | \(0.403142\pi\) | |||||||
\(468\) | −5.51035 | − | 13.2767i | −0.254716 | − | 0.613714i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2.05676 | − | 1.18747i | 0.0948713 | − | 0.0547740i | ||||
\(471\) | −8.40840 | − | 14.5638i | −0.387439 | − | 0.671063i | ||||
\(472\) | −10.1074 | + | 17.5066i | −0.465231 | + | 0.805805i | ||||
\(473\) | − | 19.1352i | − | 0.879838i | ||||||
\(474\) | 4.38611 | + | 2.53232i | 0.201461 | + | 0.116313i | ||||
\(475\) | 18.6724 | + | 10.7805i | 0.856750 | + | 0.494645i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.318489 | + | 0.551640i | −0.0145826 | + | 0.0252578i | ||||
\(478\) | −1.95110 | − | 3.37941i | −0.0892414 | − | 0.154571i | ||||
\(479\) | −23.3930 | + | 13.5060i | −1.06885 | + | 0.617104i | −0.927868 | − | 0.372908i | \(-0.878361\pi\) |
−0.140987 | + | 0.990012i | \(0.545027\pi\) | |||||||
\(480\) | 4.45605 | 0.203390 | ||||||||
\(481\) | −2.80791 | + | 1.16540i | −0.128030 | + | 0.0531376i | ||||
\(482\) | 10.8823 | 0.495677 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.14710 | + | 7.18299i | 0.188505 | + | 0.326499i | ||||
\(485\) | −1.40886 | + | 2.44021i | −0.0639729 | + | 0.110804i | ||||
\(486\) | − | 8.01117i | − | 0.363394i | ||||||
\(487\) | −27.7854 | − | 16.0419i | −1.25908 | − | 0.726928i | −0.286182 | − | 0.958175i | \(-0.592386\pi\) |
−0.972895 | + | 0.231247i | \(0.925720\pi\) | |||||||
\(488\) | −9.52097 | − | 5.49694i | −0.430994 | − | 0.248835i | ||||
\(489\) | 7.58910i | 0.343191i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.3020 | − | 24.7718i | −0.645440 | − | 1.11793i | −0.984200 | − | 0.177061i | \(-0.943341\pi\) |
0.338760 | − | 0.940873i | \(-0.389992\pi\) | |||||||
\(492\) | 15.5768 | − | 8.99328i | 0.702257 | − | 0.405448i | ||||
\(493\) | −1.19276 | −0.0537190 | ||||||||
\(494\) | 9.84854 | + | 1.28952i | 0.443107 | + | 0.0580181i | ||||
\(495\) | 9.42212 | 0.423493 | ||||||||
\(496\) | 6.31716 | − | 3.64721i | 0.283649 | − | 0.163765i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.610255 | + | 1.05699i | −0.0273462 | + | 0.0473650i | ||||
\(499\) | − | 1.79816i | − | 0.0804969i | −0.999190 | − | 0.0402484i | \(-0.987185\pi\) | ||
0.999190 | − | 0.0402484i | \(-0.0128149\pi\) | |||||||
\(500\) | −14.0823 | − | 8.13042i | −0.629780 | − | 0.363603i | ||||
\(501\) | −4.51376 | − | 2.60602i | −0.201660 | − | 0.116428i | ||||
\(502\) | 3.83980i | 0.171379i | ||||||||
\(503\) | −14.5386 | + | 25.1816i | −0.648245 | + | 1.12279i | 0.335297 | + | 0.942112i | \(0.391163\pi\) |
−0.983542 | + | 0.180681i | \(0.942170\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.3572 | + | 5.97976i | −0.460891 | + | 0.266096i | ||||
\(506\) | −8.70994 | −0.387204 | ||||||||
\(507\) | −2.87366 | − | 10.6644i | −0.127624 | − | 0.473624i | ||||
\(508\) | 3.51380 | 0.155900 | ||||||||
\(509\) | −20.0843 | + | 11.5957i | −0.890220 | + | 0.513969i | −0.874014 | − | 0.485900i | \(-0.838492\pi\) |
−0.0162054 | + | 0.999869i | \(0.505159\pi\) | |||||||
\(510\) | −0.0314489 | − | 0.0544711i | −0.00139258 | − | 0.00241202i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 22.5022i | − | 0.994464i | ||||||
\(513\) | −21.3975 | − | 12.3539i | −0.944723 | − | 0.545436i | ||||
\(514\) | −5.89910 | − | 3.40585i | −0.260198 | − | 0.150225i | ||||
\(515\) | − | 4.34660i | − | 0.191534i | ||||||
\(516\) | 3.58562 | − | 6.21048i | 0.157848 | − | 0.273401i | ||||
\(517\) | 9.03847 | + | 15.6551i | 0.397511 | + | 0.688510i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20.6137 | −0.904840 | ||||||||
\(520\) | −6.98775 | − | 0.914939i | −0.306433 | − | 0.0401227i | ||||
\(521\) | 33.2510 | 1.45675 | 0.728376 | − | 0.685178i | \(-0.240275\pi\) | ||||
0.728376 | + | 0.685178i | \(0.240275\pi\) | |||||||
\(522\) | −8.28383 | + | 4.78267i | −0.362574 | + | 0.209332i | ||||
\(523\) | −19.3560 | − | 33.5256i | −0.846380 | − | 1.46597i | −0.884417 | − | 0.466697i | \(-0.845444\pi\) |
0.0380367 | − | 0.999276i | \(-0.487890\pi\) | |||||||
\(524\) | 10.8940 | − | 18.8690i | 0.475908 | − | 0.824296i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.07614 | − | 2.93071i | −0.221330 | − | 0.127785i | ||||
\(527\) | −0.350140 | − | 0.202153i | −0.0152523 | − | 0.00880594i | ||||
\(528\) | 8.63748i | 0.375898i | ||||||||
\(529\) | 1.85966 | − | 3.22102i | 0.0808546 | − | 0.140044i | ||||
\(530\) | 0.0728671 | + | 0.126210i | 0.00316514 | + | 0.00548219i | ||||
\(531\) | −21.2714 | + | 12.2811i | −0.923102 | + | 0.532953i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −40.2857 | + | 16.7202i | −1.74497 | + | 0.724233i | ||||
\(534\) | −0.742383 | −0.0321260 | ||||||||
\(535\) | 7.66253 | − | 4.42396i | 0.331280 | − | 0.191265i | ||||
\(536\) | −4.82283 | − | 8.35338i | −0.208314 | − | 0.360811i | ||||
\(537\) | −1.75730 | + | 3.04372i | −0.0758329 | + | 0.131346i | ||||
\(538\) | − | 4.59926i | − | 0.198288i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 7.08495 | + | 4.09050i | 0.304888 | + | 0.176027i | ||||
\(541\) | 22.6675i | 0.974551i | 0.873248 | + | 0.487275i | \(0.162009\pi\) | ||||
−0.873248 | + | 0.487275i | \(0.837991\pi\) | |||||||
\(542\) | 0.640905 | − | 1.11008i | 0.0275292 | − | 0.0476820i | ||||
\(543\) | 3.34135 | + | 5.78738i | 0.143391 | + | 0.248360i | ||||
\(544\) | −0.618865 | + | 0.357302i | −0.0265336 | + | 0.0153192i | ||||
\(545\) | −6.70349 | −0.287146 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.21134 | −0.393848 | −0.196924 | − | 0.980419i | \(-0.563095\pi\) | ||||
−0.196924 | + | 0.980419i | \(0.563095\pi\) | |||||||
\(548\) | 7.94936 | − | 4.58957i | 0.339580 | − | 0.196057i | ||||
\(549\) | −6.67909 | − | 11.5685i | −0.285056 | − | 0.493732i | ||||
\(550\) | −3.88116 | + | 6.72236i | −0.165493 | + | 0.286642i | ||||
\(551\) | 46.2688i | 1.97112i | ||||||||
\(552\) | −6.05757 | − | 3.49734i | −0.257827 | − | 0.148857i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 0.466928i | − | 0.0198379i | ||||||
\(555\) | 0.373400 | − | 0.646748i | 0.0158500 | − | 0.0274529i | ||||
\(556\) | 18.1464 | + | 31.4304i | 0.769577 | + | 1.33295i | ||||
\(557\) | −9.81039 | + | 5.66403i | −0.415680 | + | 0.239993i | −0.693227 | − | 0.720719i | \(-0.743812\pi\) |
0.277547 | + | 0.960712i | \(0.410478\pi\) | |||||||
\(558\) | −3.24236 | −0.137260 | ||||||||
\(559\) | −10.5769 | + | 13.8042i | −0.447354 | + | 0.583855i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.414608 | − | 0.239374i | 0.0175048 | − | 0.0101064i | ||||
\(562\) | −1.61318 | − | 2.79411i | −0.0680478 | − | 0.117862i | ||||
\(563\) | 16.3193 | − | 28.2659i | 0.687777 | − | 1.19127i | −0.284778 | − | 0.958594i | \(-0.591920\pi\) |
0.972555 | − | 0.232672i | \(-0.0747469\pi\) | |||||||
\(564\) | 6.77463i | 0.285264i | ||||||||
\(565\) | −9.89776 | − | 5.71448i | −0.416402 | − | 0.240410i | ||||
\(566\) | −9.60161 | − | 5.54349i | −0.403586 | − | 0.233010i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.46755 | + | 6.00597i | −0.145495 | + | 0.252005i | ||||
\(569\) | 17.5045 | + | 30.3188i | 0.733829 | + | 1.27103i | 0.955235 | + | 0.295847i | \(0.0956019\pi\) |
−0.221407 | + | 0.975182i | \(0.571065\pi\) | |||||||
\(570\) | −2.11302 | + | 1.21995i | −0.0885046 | + | 0.0510981i | ||||
\(571\) | −26.2546 | −1.09872 | −0.549360 | − | 0.835586i | \(-0.685128\pi\) | ||||
−0.549360 | + | 0.835586i | \(0.685128\pi\) | |||||||
\(572\) | 3.24992 | − | 24.8209i | 0.135886 | − | 1.03781i | ||||
\(573\) | −5.50428 | −0.229945 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.59149 | + | 14.8809i | 0.358290 | + | 0.620576i | ||||
\(576\) | 2.97260 | − | 5.14870i | 0.123858 | − | 0.214529i | ||||
\(577\) | 24.5727i | 1.02297i | 0.859291 | + | 0.511487i | \(0.170905\pi\) | ||||
−0.859291 | + | 0.511487i | \(0.829095\pi\) | |||||||
\(578\) | −7.35228 | − | 4.24484i | −0.305815 | − | 0.176562i | ||||
\(579\) | 3.55327 | + | 2.05148i | 0.147669 | + | 0.0852567i | ||||
\(580\) | − | 15.3201i | − | 0.636133i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0.574083 | + | 0.994341i | 0.0237965 | + | 0.0412167i | ||||
\(583\) | −0.960646 | + | 0.554629i | −0.0397859 | + | 0.0229704i | ||||
\(584\) | 12.3987 | 0.513063 | ||||||||
\(585\) | −6.79714 | − | 5.20802i | −0.281027 | − | 0.215325i | ||||
\(586\) | 12.1010 | 0.499886 | ||||||||
\(587\) | 17.7777 | − | 10.2640i | 0.733765 | − | 0.423639i | −0.0860331 | − | 0.996292i | \(-0.527419\pi\) |
0.819798 | + | 0.572653i | \(0.194086\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.84184 | + | 13.5825i | −0.323117 | + | 0.559656i | ||||
\(590\) | 5.61957i | 0.231354i | ||||||||
\(591\) | 19.0097 | + | 10.9752i | 0.781954 | + | 0.451461i | ||||
\(592\) | −1.87124 | − | 1.08036i | −0.0769077 | − | 0.0444027i | ||||
\(593\) | − | 38.2835i | − | 1.57211i | −0.618154 | − | 0.786057i | \(-0.712119\pi\) | ||
0.618154 | − | 0.786057i | \(-0.287881\pi\) | |||||||
\(594\) | 4.44757 | − | 7.70342i | 0.182486 | − | 0.316075i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.0172409 | − | 0.00995405i | 0.000706216 | − | 0.000407734i | ||||
\(597\) | −14.5406 | −0.595107 | ||||||||
\(598\) | 6.28338 | + | 4.81436i | 0.256946 | + | 0.196874i | ||||
\(599\) | 14.0713 | 0.574939 | 0.287470 | − | 0.957790i | \(-0.407186\pi\) | ||||
0.287470 | + | 0.957790i | \(0.407186\pi\) | |||||||
\(600\) | −5.39851 | + | 3.11683i | −0.220393 | + | 0.127244i | ||||
\(601\) | 10.1171 | + | 17.5233i | 0.412685 | + | 0.714791i | 0.995182 | − | 0.0980417i | \(-0.0312579\pi\) |
−0.582498 | + | 0.812832i | \(0.697925\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 11.7200i | − | 0.477276i | ||||||
\(604\) | 28.6522 | + | 16.5424i | 1.16584 | + | 0.673099i | ||||
\(605\) | 4.27887 | + | 2.47041i | 0.173961 | + | 0.100436i | ||||
\(606\) | 4.87328i | 0.197964i | ||||||||
\(607\) | −3.27563 | + | 5.67356i | −0.132954 | + | 0.230283i | −0.924814 | − | 0.380420i | \(-0.875780\pi\) |
0.791860 | + | 0.610703i | \(0.209113\pi\) | |||||||
\(608\) | 13.8603 | + | 24.0067i | 0.562108 | + | 0.973600i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.05621 | −0.123742 | ||||||||
\(611\) | 2.13287 | − | 16.2896i | 0.0862867 | − | 0.659005i | ||||
\(612\) | −0.566272 | −0.0228902 | ||||||||
\(613\) | −28.8598 | + | 16.6622i | −1.16564 | + | 0.672980i | −0.952648 | − | 0.304075i | \(-0.901653\pi\) |
−0.212988 | + | 0.977055i | \(0.568319\pi\) | |||||||
\(614\) | −6.07294 | − | 10.5186i | −0.245084 | − | 0.424498i | ||||
\(615\) | 5.35726 | − | 9.27904i | 0.216025 | − | 0.374167i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.85466 | + | 3.38019i | 0.235700 | + | 0.136081i | 0.613199 | − | 0.789929i | \(-0.289883\pi\) |
−0.377499 | + | 0.926010i | \(0.623216\pi\) | |||||||
\(618\) | −1.53387 | − | 0.885581i | −0.0617013 | − | 0.0356233i | ||||
\(619\) | 17.6186i | 0.708152i | 0.935217 | + | 0.354076i | \(0.115205\pi\) | ||||
−0.935217 | + | 0.354076i | \(0.884795\pi\) | |||||||
\(620\) | 2.59652 | − | 4.49731i | 0.104279 | − | 0.180616i | ||||
\(621\) | −9.84534 | − | 17.0526i | −0.395080 | − | 0.684298i | ||||
\(622\) | 1.72642 | − | 0.996751i | 0.0692233 | − | 0.0399661i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 4.77431 | − | 6.23110i | 0.191125 | − | 0.249444i | ||||
\(625\) | 9.87972 | 0.395189 | ||||||||
\(626\) | −12.3299 | + | 7.11866i | −0.492801 | + | 0.284519i | ||||
\(627\) | −9.28569 | − | 16.0833i | −0.370835 | − | 0.642304i | ||||
\(628\) | −17.3197 | + | 29.9985i | −0.691130 | + | 1.19707i | ||||
\(629\) | 0.119762i | 0.00477524i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.6416 | + | 7.87596i | 0.543062 | + | 0.313537i | 0.746319 | − | 0.665588i | \(-0.231819\pi\) |
−0.203257 | + | 0.979125i | \(0.565153\pi\) | |||||||
\(632\) | − | 22.3546i | − | 0.889216i | ||||||
\(633\) | −7.77009 | + | 13.4582i | −0.308833 | + | 0.534915i | ||||
\(634\) | −4.20392 | − | 7.28140i | −0.166959 | − | 0.289181i | ||||
\(635\) | 1.81273 | − | 1.04658i | 0.0719359 | − | 0.0415322i | ||||
\(636\) | −0.415713 | −0.0164841 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −16.6575 | −0.659475 | ||||||||
\(639\) | −7.29759 | + | 4.21327i | −0.288688 | + | 0.166674i | ||||
\(640\) | −5.92497 | − | 10.2623i | −0.234205 | − | 0.405655i | ||||
\(641\) | −10.4702 | + | 18.1350i | −0.413550 | + | 0.716289i | −0.995275 | − | 0.0970962i | \(-0.969045\pi\) |
0.581725 | + | 0.813385i | \(0.302378\pi\) | |||||||
\(642\) | − | 3.60537i | − | 0.142293i | ||||||
\(643\) | −16.3952 | − | 9.46576i | −0.646563 | − | 0.373293i | 0.140575 | − | 0.990070i | \(-0.455105\pi\) |
−0.787138 | + | 0.616777i | \(0.788438\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 4.27188i | − | 0.168205i | ||||||
\(646\) | 0.195640 | − | 0.338859i | 0.00769736 | − | 0.0133322i | ||||
\(647\) | −18.8384 | − | 32.6291i | −0.740614 | − | 1.28278i | −0.952216 | − | 0.305426i | \(-0.901201\pi\) |
0.211601 | − | 0.977356i | \(-0.432132\pi\) | |||||||
\(648\) | −4.91126 | + | 2.83552i | −0.192933 | + | 0.111390i | ||||
\(649\) | −42.7735 | −1.67901 | ||||||||
\(650\) | 6.51562 | − | 2.70424i | 0.255563 | − | 0.106069i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.5378 | − | 7.81604i | 0.530180 | − | 0.306100i | ||||
\(653\) | −14.5163 | − | 25.1430i | −0.568066 | − | 0.983920i | −0.996757 | − | 0.0804686i | \(-0.974358\pi\) |
0.428691 | − | 0.903451i | \(-0.358975\pi\) | |||||||
\(654\) | −1.36577 | + | 2.36559i | −0.0534060 | + | 0.0925019i | ||||
\(655\) | − | 12.9790i | − | 0.507133i | ||||||
\(656\) | −26.8472 | − | 15.5002i | −1.04821 | − | 0.605182i | ||||
\(657\) | 13.0468 | + | 7.53257i | 0.509004 | + | 0.293874i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.709152 | − | 1.22829i | 0.0276247 | − | 0.0478473i | −0.851883 | − | 0.523733i | \(-0.824539\pi\) |
0.879507 | + | 0.475886i | \(0.157872\pi\) | |||||||
\(660\) | 3.07459 | + | 5.32535i | 0.119678 | + | 0.207289i | ||||
\(661\) | 3.97764 | − | 2.29649i | 0.154712 | − | 0.0893231i | −0.420645 | − | 0.907225i | \(-0.638196\pi\) |
0.575357 | + | 0.817902i | \(0.304863\pi\) | |||||||
\(662\) | 3.10450 | 0.120660 | ||||||||
\(663\) | −0.431412 | − | 0.0564868i | −0.0167547 | − | 0.00219377i | ||||
\(664\) | 5.38715 | 0.209062 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.480219 | + | 0.831764i | 0.0186081 | + | 0.0322302i | ||||
\(667\) | −18.4368 | + | 31.9335i | −0.713877 | + | 1.23647i | ||||
\(668\) | 10.7358i | 0.415380i | ||||||||
\(669\) | 8.46782 | + | 4.88890i | 0.327385 | + | 0.189016i | ||||
\(670\) | −2.32218 | − | 1.34071i | −0.0897135 | − | 0.0517961i | ||||
\(671\) | − | 23.2624i | − | 0.898036i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.10111 | − | 3.63924i | −0.0809920 | − | 0.140282i | 0.822684 | − | 0.568499i | \(-0.192475\pi\) |
−0.903676 | + | 0.428216i | \(0.859142\pi\) | |||||||
\(674\) | −3.33259 | + | 1.92407i | −0.128367 | + | 0.0741126i | ||||
\(675\) | −17.5484 | −0.675436 | ||||||||
\(676\) | −16.0641 | + | 16.1095i | −0.617849 | + | 0.619596i | ||||
\(677\) | 8.08708 | 0.310812 | 0.155406 | − | 0.987851i | \(-0.450331\pi\) | ||||
0.155406 | + | 0.987851i | \(0.450331\pi\) | |||||||
\(678\) | −4.03316 | + | 2.32854i | −0.154892 | + | 0.0894272i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −0.138811 | + | 0.240427i | −0.00532315 | + | 0.00921997i | ||||
\(681\) | 15.2117i | 0.582912i | ||||||||
\(682\) | −4.88989 | − | 2.82318i | −0.187244 | − | 0.108105i | ||||
\(683\) | −21.3792 | − | 12.3433i | −0.818051 | − | 0.472302i | 0.0316929 | − | 0.999498i | \(-0.489910\pi\) |
−0.849744 | + | 0.527196i | \(0.823243\pi\) | |||||||
\(684\) | 21.9666i | 0.839912i | ||||||||
\(685\) | 2.73398 | − | 4.73540i | 0.104460 | − | 0.180930i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.84267 | − | 1.64122i | 0.108455 | − | 0.0626164i | ||||
\(688\) | −12.3599 | −0.471216 | ||||||||
\(689\) | 0.999581 | + | 0.130880i | 0.0380810 | + | 0.00498612i | ||||
\(690\) | −1.94447 | −0.0740246 | ||||||||
\(691\) | 9.74859 | − | 5.62835i | 0.370854 | − | 0.214113i | −0.302978 | − | 0.952998i | \(-0.597981\pi\) |
0.673831 | + | 0.738885i | \(0.264647\pi\) | |||||||
\(692\) | 21.2301 | + | 36.7716i | 0.807047 | + | 1.39785i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 15.2043i | − | 0.577147i | ||||||
\(695\) | 18.7230 | + | 10.8097i | 0.710202 | + | 0.410035i | ||||
\(696\) | −11.5849 | − | 6.68854i | −0.439124 | − | 0.253528i | ||||
\(697\) | 1.71826i | 0.0650836i | ||||||||
\(698\) | 4.03942 | − | 6.99648i | 0.152894 | − | 0.264821i | ||||
\(699\) | 10.6473 | + | 18.4416i | 0.402717 | + | 0.697526i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.2305 | 0.839635 | 0.419818 | − | 0.907608i | \(-0.362094\pi\) | ||||
0.419818 | + | 0.907608i | \(0.362094\pi\) | |||||||
\(702\) | −7.46651 | + | 3.09890i | −0.281805 | + | 0.116961i | ||||
\(703\) | 4.64576 | 0.175218 | ||||||||
\(704\) | 8.96614 | − | 5.17660i | 0.337924 | − | 0.195101i | ||||
\(705\) | 2.01781 | + | 3.49495i | 0.0759951 | + | 0.131627i | ||||
\(706\) | −2.96052 | + | 5.12776i | −0.111420 | + | 0.192986i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −13.8825 | − | 8.01504i | −0.521734 | − | 0.301224i | ||||
\(709\) | −20.5889 | − | 11.8870i | −0.773234 | − | 0.446427i | 0.0607929 | − | 0.998150i | \(-0.480637\pi\) |
−0.834027 | + | 0.551723i | \(0.813970\pi\) | |||||||
\(710\) | 1.92790i | 0.0723530i | ||||||||
\(711\) | 13.5810 | − | 23.5230i | 0.509328 | − | 0.882182i | ||||
\(712\) | 1.63838 | + | 2.83776i | 0.0614010 | + | 0.106350i | ||||
\(713\) | −10.8245 | + | 6.24951i | −0.405380 | + | 0.234046i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.71626 | − | 13.7728i | −0.213776 | − | 0.515072i | ||||
\(716\) | 7.23937 | 0.270548 | ||||||||
\(717\) | 5.74246 | − | 3.31541i | 0.214456 | − | 0.123816i | ||||
\(718\) | −7.84111 | − | 13.5812i | −0.292628 | − | 0.506846i | ||||
\(719\) | 10.3904 | − | 17.9967i | 0.387496 | − | 0.671163i | −0.604616 | − | 0.796517i | \(-0.706673\pi\) |
0.992112 | + | 0.125354i | \(0.0400068\pi\) | |||||||
\(720\) | − | 6.08597i | − | 0.226811i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −4.91782 | − | 2.83931i | −0.183022 | − | 0.105668i | ||||
\(723\) | 18.4918i | 0.687717i | ||||||||
\(724\) | 6.88252 | − | 11.9209i | 0.255787 | − | 0.443036i | ||||
\(725\) | 16.4309 | + | 28.4592i | 0.610229 | + | 1.05695i | ||||
\(726\) | 1.74356 | − | 1.00665i | 0.0647097 | − | 0.0373601i | ||||
\(727\) | −26.7719 | −0.992915 | −0.496457 | − | 0.868061i | \(-0.665366\pi\) | ||||
−0.496457 | + | 0.868061i | \(0.665366\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.53910 | 0.168115 | ||||||||
\(730\) | 2.98497 | − | 1.72338i | 0.110479 | − | 0.0637850i | ||||
\(731\) | 0.342535 | + | 0.593287i | 0.0126691 | + | 0.0219435i | ||||
\(732\) | 4.35899 | − | 7.55000i | 0.161113 | − | 0.279056i | ||||
\(733\) | − | 5.25647i | − | 0.194152i | −0.995277 | − | 0.0970761i | \(-0.969051\pi\) | ||
0.995277 | − | 0.0970761i | \(-0.0309490\pi\) | |||||||
\(734\) | 10.4255 | + | 6.01919i | 0.384814 | + | 0.222172i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 22.0917i | 0.814312i | ||||||||
\(737\) | 10.2048 | − | 17.6753i | 0.375900 | − | 0.651078i | ||||
\(738\) | 6.88981 | + | 11.9335i | 0.253617 | + | 0.439278i | ||||
\(739\) | −6.19209 | + | 3.57501i | −0.227780 | + | 0.131509i | −0.609547 | − | 0.792750i | \(-0.708649\pi\) |
0.381768 | + | 0.924258i | \(0.375315\pi\) | |||||||
\(740\) | −1.53826 | −0.0565477 | ||||||||
\(741\) | −2.19121 | + | 16.7351i | −0.0804960 | + | 0.614780i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.618032 | + | 0.356821i | −0.0226734 | + | 0.0130905i | −0.511294 | − | 0.859406i | \(-0.670834\pi\) |
0.488620 | + | 0.872496i | \(0.337500\pi\) | |||||||
\(744\) | −2.26721 | − | 3.92692i | −0.0831198 | − | 0.143968i | ||||
\(745\) | 0.00592959 | − | 0.0102703i | 0.000217243 | − | 0.000376276i | ||||
\(746\) | 9.19587i | 0.336685i | ||||||||
\(747\) | 5.66873 | + | 3.27284i | 0.207408 | + | 0.119747i | ||||
\(748\) | −0.854012 | − | 0.493064i | −0.0312258 | − | 0.0180282i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.97354 | + | 3.41827i | −0.0720634 | + | 0.124817i | ||||
\(751\) | −12.8507 | − | 22.2580i | −0.468927 | − | 0.812205i | 0.530442 | − | 0.847721i | \(-0.322026\pi\) |
−0.999369 | + | 0.0355158i | \(0.988693\pi\) | |||||||
\(752\) | 10.1120 | − | 5.83815i | 0.368746 | − | 0.212896i | ||||
\(753\) | −6.52477 | −0.237776 | ||||||||
\(754\) | 12.0167 | + | 9.20730i | 0.437624 | + | 0.335310i | ||||
\(755\) | 19.7084 | 0.717263 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.19425 | − | 14.1928i | −0.297825 | − | 0.515848i | 0.677813 | − | 0.735234i | \(-0.262928\pi\) |
−0.975638 | + | 0.219386i | \(0.929594\pi\) | |||||||
\(758\) | 2.03430 | − | 3.52350i | 0.0738889 | − | 0.127979i | ||||
\(759\) | − | 14.8004i | − | 0.537219i | ||||||
\(760\) | 9.32654 | + | 5.38468i | 0.338309 | + | 0.195323i | ||||
\(761\) | −7.20531 | − | 4.15999i | −0.261192 | − | 0.150800i | 0.363686 | − | 0.931522i | \(-0.381518\pi\) |
−0.624878 | + | 0.780722i | \(0.714851\pi\) | |||||||
\(762\) | − | 0.852923i | − | 0.0308981i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 5.66888 | + | 9.81878i | 0.205093 | + | 0.355231i | ||||
\(765\) | −0.292133 | + | 0.168663i | −0.0105621 | + | 0.00609802i | ||||
\(766\) | −11.1853 | −0.404140 | ||||||||
\(767\) | 30.8569 | + | 23.6428i | 1.11418 | + | 0.853690i | ||||
\(768\) | −0.394335 | −0.0142293 | ||||||||
\(769\) | 22.1346 | − | 12.7794i | 0.798194 | − | 0.460838i | −0.0446452 | − | 0.999003i | \(-0.514216\pi\) |
0.842839 | + | 0.538165i | \(0.180882\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.78738 | − | 10.0240i | 0.208427 | − | 0.361007i | ||||
\(772\) | − | 8.45131i | − | 0.304169i | ||||||
\(773\) | −7.27528 | − | 4.20038i | −0.261674 | − | 0.151077i | 0.363424 | − | 0.931624i | \(-0.381608\pi\) |
−0.625098 | + | 0.780546i | \(0.714941\pi\) | |||||||
\(774\) | 4.75789 | + | 2.74697i | 0.171019 | + | 0.0987378i | ||||
\(775\) | 11.1391i | 0.400130i | ||||||||
\(776\) | 2.53392 | − | 4.38887i | 0.0909623 | − | 0.157551i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.26388 | + | 5.34850i | −0.332126 | + | 0.191753i | ||||
\(779\) | 66.6537 | 2.38812 | ||||||||
\(780\) | 0.725534 | − | 5.54119i | 0.0259783 | − | 0.198406i | ||||
\(781\) | −14.6743 | −0.525087 | ||||||||
\(782\) | 0.270052 | − | 0.155914i | 0.00965703 | − | 0.00557549i | ||||
\(783\) | −18.8289 | − | 32.6125i | −0.672889 | − | 1.16548i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.6345i | 0.736476i | ||||||||
\(786\) | −4.58017 | − | 2.64436i | −0.163369 | − | 0.0943212i | ||||
\(787\) | 30.3667 | + | 17.5322i | 1.08246 | + | 0.624956i | 0.931558 | − | 0.363593i | \(-0.118450\pi\) |
0.150898 | + | 0.988549i | \(0.451784\pi\) | |||||||
\(788\) | − | 45.2137i | − | 1.61067i | ||||||
\(789\) | 4.98000 | − | 8.62562i | 0.177293 | − | 0.307080i | ||||
\(790\) | −3.10720 | − | 5.38182i | −0.110549 | − | 0.191477i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −16.9463 | −0.602160 | ||||||||
\(793\) | −12.8582 | + | 16.7816i | −0.456607 | + | 0.595931i | ||||
\(794\) | 0.598349 | 0.0212346 | ||||||||
\(795\) | −0.214461 | + | 0.123819i | −0.00760616 | + | 0.00439142i | ||||
\(796\) | 14.9754 | + | 25.9382i | 0.530789 | + | 0.919354i | ||||
\(797\) | −12.2876 | + | 21.2828i | −0.435250 | + | 0.753875i | −0.997316 | − | 0.0732173i | \(-0.976673\pi\) |
0.562066 | + | 0.827092i | \(0.310007\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.560475 | − | 0.323590i | −0.0198282 | − | 0.0114478i | ||||
\(800\) | 17.0505 | + | 9.84409i | 0.602825 | + | 0.348041i | ||||
\(801\) | 3.98145i | 0.140678i | ||||||||
\(802\) | 9.06848 | − | 15.7071i | 0.320219 | − | 0.554636i | ||||
\(803\) | 13.1175 | + | 22.7202i | 0.462907 | + | 0.801778i | ||||
\(804\) | 6.62411 | − | 3.82443i | 0.233615 | − | 0.134877i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.96709 | + | 4.73951i | 0.0692877 | + | 0.166942i | ||||
\(807\) | 7.81528 | 0.275111 | ||||||||
\(808\) | 18.6282 | − | 10.7550i | 0.655336 | − | 0.378358i | ||||
\(809\) | 15.9006 | + | 27.5406i | 0.559035 | + | 0.968277i | 0.997577 | + | 0.0695667i | \(0.0221617\pi\) |
−0.438542 | + | 0.898711i | \(0.644505\pi\) | |||||||
\(810\) | −0.788253 | + | 1.36529i | −0.0276964 | + | 0.0479715i | ||||
\(811\) | 10.3633i | 0.363905i | 0.983307 | + | 0.181953i | \(0.0582418\pi\) | ||||
−0.983307 | + | 0.181953i | \(0.941758\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.88630 | + | 1.08906i | 0.0661555 | + | 0.0381949i | ||||
\(814\) | 1.67254i | 0.0586226i | ||||||||
\(815\) | 4.65598 | − | 8.06439i | 0.163092 | − | 0.282483i | ||||
\(816\) | −0.154617 | − | 0.267805i | −0.00541269 | − | 0.00937505i | ||||
\(817\) | 23.0145 | − | 13.2874i | 0.805176 | − | 0.464868i | ||||
\(818\) | −7.33597 | −0.256496 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −22.0698 | −0.770711 | ||||||||
\(821\) | −3.51253 | + | 2.02796i | −0.122588 | + | 0.0707762i | −0.560040 | − | 0.828465i | \(-0.689214\pi\) |
0.437452 | + | 0.899242i | \(0.355881\pi\) | |||||||
\(822\) | −1.11405 | − | 1.92959i | −0.0388569 | − | 0.0673021i | ||||
\(823\) | 4.35848 | − | 7.54912i | 0.151927 | − | 0.263146i | −0.780009 | − | 0.625769i | \(-0.784785\pi\) |
0.931936 | + | 0.362623i | \(0.118119\pi\) | |||||||
\(824\) | 7.81764i | 0.272340i | ||||||||
\(825\) | −11.4230 | − | 6.59505i | −0.397696 | − | 0.229610i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 23.5788i | − | 0.819915i | −0.912105 | − | 0.409957i | \(-0.865544\pi\) | ||
0.912105 | − | 0.409957i | \(-0.134456\pi\) | |||||||
\(828\) | −8.75307 | + | 15.1608i | −0.304190 | + | 0.526873i | ||||
\(829\) | −14.5203 | − | 25.1499i | −0.504311 | − | 0.873492i | −0.999988 | − | 0.00498467i | \(-0.998413\pi\) |
0.495677 | − | 0.868507i | \(-0.334920\pi\) | |||||||
\(830\) | 1.29695 | − | 0.748793i | 0.0450177 | − | 0.0259910i | ||||
\(831\) | 0.793427 | 0.0275237 | ||||||||
\(832\) | −9.32953 | − | 1.22156i | −0.323443 | − | 0.0423499i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 7.62926 | − | 4.40475i | 0.264180 | − | 0.152524i | ||||
\(835\) | 3.19763 | + | 5.53846i | 0.110659 | + | 0.191666i | ||||
\(836\) | −19.1267 | + | 33.1284i | −0.661511 | + | 1.14577i | ||||
\(837\) | − | 12.7648i | − | 0.441216i | ||||||
\(838\) | −2.56921 | − | 1.48333i | −0.0887517 | − | 0.0512408i | ||||
\(839\) | −10.0090 | − | 5.77871i | −0.345550 | − | 0.199503i | 0.317174 | − | 0.948367i | \(-0.397266\pi\) |
−0.662723 | + | 0.748864i | \(0.730600\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.7598 | + | 35.9570i | −0.715855 | + | 1.23990i | ||||
\(842\) | 0.657918 | + | 1.13955i | 0.0226734 | + | 0.0392714i | ||||
\(843\) | 4.74788 | − | 2.74119i | 0.163526 | − | 0.0944116i | ||||
\(844\) | 32.0097 | 1.10182 | ||||||||
\(845\) | −3.48908 | + | 13.0953i | −0.120028 | + | 0.450493i | ||||
\(846\) | −5.19009 | −0.178439 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.358248 | + | 0.620504i | 0.0123023 | + | 0.0213082i | ||||
\(849\) | 9.41977 | − | 16.3155i | 0.323286 | − | 0.559947i | ||||
\(850\) | − | 0.277902i | − | 0.00953197i | ||||||
\(851\) | 3.20638 | + | 1.85121i | 0.109913 | + | 0.0634586i | ||||
\(852\) | −4.76265 | − | 2.74972i | −0.163166 | − | 0.0942038i | ||||
\(853\) | − | 1.51845i | − | 0.0519906i | −0.999662 | − | 0.0259953i | \(-0.991725\pi\) | ||
0.999662 | − | 0.0259953i | \(-0.00827550\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.54269 | + | 11.3323i | 0.223755 | + | 0.387556i | ||||
\(856\) | −13.7815 | + | 7.95678i | −0.471043 | + | 0.271957i | ||||
\(857\) | 6.00119 | 0.204997 | 0.102498 | − | 0.994733i | \(-0.467316\pi\) | ||||
0.102498 | + | 0.994733i | \(0.467316\pi\) | |||||||
\(858\) | −6.02490 | − | 0.788868i | −0.205687 | − | 0.0269315i | ||||
\(859\) | 1.67604 | 0.0571858 | 0.0285929 | − | 0.999591i | \(-0.490897\pi\) | ||||
0.0285929 | + | 0.999591i | \(0.490897\pi\) | |||||||
\(860\) | −7.62036 | + | 4.39962i | −0.259852 | + | 0.150026i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.70929 | − | 8.15673i | 0.160399 | − | 0.277819i | ||||
\(863\) | − | 42.0504i | − | 1.43141i | −0.698401 | − | 0.715706i | \(-0.746105\pi\) | ||
0.698401 | − | 0.715706i | \(-0.253895\pi\) | |||||||
\(864\) | −19.5388 | − | 11.2807i | −0.664724 | − | 0.383779i | ||||
\(865\) | 21.9047 | + | 12.6467i | 0.744781 | + | 0.429999i | ||||
\(866\) | 9.56747i | 0.325116i | ||||||||
\(867\) | 7.21304 | − | 12.4934i | 0.244968 | − | 0.424297i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 40.9639 | − | 23.6505i | 1.38960 | − | 0.802288i | ||||
\(870\) | −3.71873 | −0.126077 | ||||||||
\(871\) | −17.1317 | + | 7.11035i | −0.580486 | + | 0.240925i | ||||
\(872\) | 12.0566 | 0.408290 | ||||||||
\(873\) | 5.33272 | − | 3.07885i | 0.180485 | − | 0.104203i | ||||
\(874\) | −6.04815 | − | 10.4757i | −0.204582 | − | 0.354346i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 9.83201i | 0.332193i | ||||||||
\(877\) | −26.7281 | − | 15.4315i | −0.902545 | − | 0.521084i | −0.0245198 | − | 0.999699i | \(-0.507806\pi\) |
−0.878025 | + | 0.478615i | \(0.841139\pi\) | |||||||
\(878\) | 0.547793 | + | 0.316268i | 0.0184871 | + | 0.0106735i | ||||
\(879\) | 20.5625i | 0.693557i | ||||||||
\(880\) | 5.29917 | − | 9.17843i | 0.178635 | − | 0.309405i | ||||
\(881\) | −27.8669 | − | 48.2669i | −0.938860 | − | 1.62615i | −0.767601 | − | 0.640928i | \(-0.778550\pi\) |
−0.171260 | − | 0.985226i | \(-0.554784\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.92007 | −0.0982681 | −0.0491341 | − | 0.998792i | \(-0.515646\pi\) | ||||
−0.0491341 | + | 0.998792i | \(0.515646\pi\) | |||||||
\(884\) | 0.343549 | + | 0.827747i | 0.0115548 | + | 0.0278402i | ||||
\(885\) | −9.54904 | −0.320988 | ||||||||
\(886\) | 9.06671 | − | 5.23467i | 0.304602 | − | 0.175862i | ||||
\(887\) | −0.939545 | − | 1.62734i | −0.0315468 | − | 0.0546407i | 0.849821 | − | 0.527071i | \(-0.176710\pi\) |
−0.881368 | + | 0.472431i | \(0.843377\pi\) | |||||||
\(888\) | −0.671584 | + | 1.16322i | −0.0225369 | + | 0.0390350i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.788876 | + | 0.455458i | 0.0264432 | + | 0.0152670i | ||||
\(891\) | −10.3920 | − | 5.99980i | −0.348144 | − | 0.201001i | ||||
\(892\) | − | 20.1404i | − | 0.674349i | ||||||
\(893\) | −12.5526 | + | 21.7417i | −0.420055 | + | 0.727557i | ||||
\(894\) | −0.00241620 | − | 0.00418498i | −8.08097e−5 | − | 0.000139967i | ||||
\(895\) | 3.73470 | − | 2.15623i | 0.124837 | − | 0.0720748i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.18080 | + | 10.6770i | −0.273149 | + | 0.356495i | ||||
\(898\) | −8.93138 | −0.298044 | ||||||||
\(899\) | −20.7014 | + | 11.9520i | −0.690431 | + | 0.398621i | ||||
\(900\) | 7.80074 | + | 13.5113i | 0.260025 | + | 0.450376i | ||||
\(901\) | 0.0198566 | − | 0.0343926i | 0.000661518 | − | 0.00114578i | ||||
\(902\) | 23.9964i | 0.798991i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 17.8017 | + | 10.2778i | 0.592077 | + | 0.341836i | ||||
\(905\) | − | 8.19978i | − | 0.272570i | ||||||
\(906\) | 4.01541 | − | 6.95490i | 0.133403 | − | 0.231061i | ||||
\(907\) | −17.8082 | − | 30.8447i | −0.591311 | − | 1.02418i | −0.994056 | − | 0.108868i | \(-0.965277\pi\) |
0.402745 | − | 0.915312i | \(-0.368056\pi\) | |||||||
\(908\) | 27.1352 | − | 15.6665i | 0.900514 | − | 0.519912i | ||||
\(909\) | 26.1358 | 0.866869 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 44.2844 | 1.46721 | 0.733604 | − | 0.679577i | \(-0.237837\pi\) | ||||
0.733604 | + | 0.679577i | \(0.237837\pi\) | |||||||
\(912\) | −10.3886 | + | 5.99784i | −0.344000 | + | 0.198608i | ||||
\(913\) | 5.69946 | + | 9.87175i | 0.188624 | + | 0.326707i | ||||
\(914\) | −1.64145 | + | 2.84307i | −0.0542943 | + | 0.0940404i | ||||
\(915\) | − | 5.19327i | − | 0.171684i | ||||||
\(916\) | −5.85535 | − | 3.38059i | −0.193466 | − | 0.111698i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.318459i | 0.0105107i | ||||||||
\(919\) | −13.0564 | + | 22.6144i | −0.430691 | + | 0.745979i | −0.996933 | − | 0.0782603i | \(-0.975063\pi\) |
0.566242 | + | 0.824239i | \(0.308397\pi\) | |||||||
\(920\) | 4.29129 | + | 7.43274i | 0.141480 | + | 0.245050i | ||||
\(921\) | 17.8738 | − | 10.3194i | 0.588961 | − | 0.340037i | ||||
\(922\) | 2.55675 | 0.0842021 | ||||||||
\(923\) | 10.5861 | + | 8.11111i | 0.348445 | + | 0.266981i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.85753 | − | 1.64980i | 0.0939551 | − | 0.0542450i | ||||
\(926\) | 8.33076 | + | 14.4293i | 0.273766 | + | 0.474176i | ||||
\(927\) | −4.74944 | + | 8.22626i | −0.155992 | + | 0.270186i | ||||
\(928\) | 42.2497i | 1.38691i | ||||||||
\(929\) | 8.68030 | + | 5.01157i | 0.284791 | + | 0.164424i | 0.635591 | − | 0.772026i | \(-0.280757\pi\) |
−0.350799 | + | 0.936451i | \(0.614090\pi\) | |||||||
\(930\) | −1.09165 | − | 0.630266i | −0.0357967 | − | 0.0206672i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 21.9313 | − | 37.9861i | 0.718384 | − | 1.24428i | ||||
\(933\) | 1.69373 | + | 2.93362i | 0.0554501 | + | 0.0960425i | ||||
\(934\) | −5.60712 | + | 3.23727i | −0.183471 | + | 0.105927i | ||||
\(935\) | −0.587432 | −0.0192111 | ||||||||
\(936\) | 12.2251 | + | 9.36694i | 0.399590 | + | 0.306168i | ||||
\(937\) | −0.916838 | −0.0299518 | −0.0149759 | − | 0.999888i | \(-0.504767\pi\) | ||||
−0.0149759 | + | 0.999888i | \(0.504767\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.0964 | − | 20.9515i | −0.394750 | − | 0.683728i | ||||
\(940\) | 4.15629 | − | 7.19891i | 0.135563 | − | 0.234803i | ||||
\(941\) | − | 17.0896i | − | 0.557107i | −0.960421 | − | 0.278553i | \(-0.910145\pi\) | ||
0.960421 | − | 0.278553i | \(-0.0898549\pi\) | |||||||
\(942\) | 7.28169 | + | 4.20409i | 0.237250 | + | 0.136977i | ||||
\(943\) | 46.0027 | + | 26.5597i | 1.49805 | + | 0.864902i | ||||
\(944\) | 27.6284i | 0.899227i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.78368 | + | 8.28557i | 0.155531 | + | 0.269387i | ||||
\(947\) | −18.8408 | + | 10.8777i | −0.612243 | + | 0.353479i | −0.773843 | − | 0.633378i | \(-0.781668\pi\) |
0.161600 | + | 0.986856i | \(0.448335\pi\) | |||||||
\(948\) | 17.7268 | 0.575741 | ||||||||
\(949\) | 3.09543 | − | 23.6410i | 0.100482 | − | 0.767420i | ||||
\(950\) | −10.7802 | −0.349757 | ||||||||
\(951\) | 12.3729 | − | 7.14350i | 0.401219 | − | 0.231644i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.90406 | + | 15.4223i | −0.288431 | + | 0.499577i | −0.973435 | − | 0.228962i | \(-0.926467\pi\) |
0.685005 | + | 0.728539i | \(0.259800\pi\) | |||||||
\(954\) | − | 0.318481i | − | 0.0103112i | ||||||
\(955\) | 5.84900 | + | 3.37692i | 0.189269 | + | 0.109275i | ||||
\(956\) | −11.8283 | − | 6.82909i | −0.382556 | − | 0.220869i | ||||
\(957\) | − | 28.3052i | − | 0.914976i | ||||||
\(958\) | 6.75281 | − | 11.6962i | 0.218173 | − | 0.377887i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.00166 | − | 1.15566i | 0.0646034 | − | 0.0372988i | ||||
\(961\) | 22.8973 | 0.738623 | ||||||||
\(962\) | 0.924488 | − | 1.20658i | 0.0298067 | − | 0.0389016i | ||||
\(963\) | −19.3359 | −0.623089 | ||||||||
\(964\) | 32.9865 | − | 19.0447i | 1.06242 | − | 0.613390i | ||||
\(965\) | −2.51720 | − | 4.35992i | −0.0810316 | − | 0.140351i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35.3813i | 1.13779i | 0.822412 | + | 0.568893i | \(0.192628\pi\) | ||||
−0.822412 | + | 0.568893i | \(0.807372\pi\) | |||||||
\(968\) | −7.69582 | − | 4.44318i | −0.247353 | − | 0.142809i | ||||
\(969\) | 0.575805 | + | 0.332441i | 0.0184975 | + | 0.0106796i | ||||
\(970\) | − | 1.40882i | − | 0.0452344i | ||||||
\(971\) | −24.8533 | + | 43.0472i | −0.797582 | + | 1.38145i | 0.123605 | + | 0.992331i | \(0.460554\pi\) |
−0.921187 | + | 0.389120i | \(0.872779\pi\) | |||||||
\(972\) | −14.0200 | − | 24.2834i | −0.449693 | − | 0.778890i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 16.0415 | 0.514002 | ||||||||
\(975\) | 4.59518 | + | 11.0716i | 0.147164 | + | 0.354577i | ||||
\(976\) | −15.0257 | −0.480962 | ||||||||
\(977\) | 53.0701 | − | 30.6401i | 1.69786 | − | 0.980262i | 0.750081 | − | 0.661346i | \(-0.230014\pi\) |
0.947783 | − | 0.318917i | \(-0.103319\pi\) | |||||||
\(978\) | −1.89723 | − | 3.28609i | −0.0606666 | − | 0.105078i | ||||
\(979\) | −3.46673 | + | 6.00455i | −0.110797 | + | 0.191906i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.6868 | + | 7.32475i | 0.405060 | + | 0.233861i | ||||
\(982\) | 12.3856 | + | 7.15080i | 0.395239 | + | 0.228191i | ||||
\(983\) | − | 6.98962i | − | 0.222934i | −0.993768 | − | 0.111467i | \(-0.964445\pi\) | ||
0.993768 | − | 0.111467i | \(-0.0355550\pi\) | |||||||
\(984\) | −9.63536 | + | 16.6889i | −0.307164 | + | 0.532024i | ||||
\(985\) | −13.4668 | − | 23.3252i | −0.429088 | − | 0.743203i | ||||
\(986\) | 0.516464 | − | 0.298181i | 0.0164476 | − | 0.00949601i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 32.1096 | − | 13.3268i | 1.02154 | − | 0.423981i | ||||
\(989\) | 21.1787 | 0.673443 | ||||||||
\(990\) | −4.07979 | + | 2.35547i | −0.129664 | + | 0.0748617i | ||||
\(991\) | 16.3671 | + | 28.3486i | 0.519917 | + | 0.900522i | 0.999732 | + | 0.0231525i | \(0.00737033\pi\) |
−0.479815 | + | 0.877370i | \(0.659296\pi\) | |||||||
\(992\) | −7.16066 | + | 12.4026i | −0.227351 | + | 0.393784i | ||||
\(993\) | 5.27532i | 0.167407i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.4512 | + | 8.92078i | 0.489838 | + | 0.282808i | ||||
\(996\) | 4.27193i | 0.135361i | ||||||||
\(997\) | −28.8948 | + | 50.0473i | −0.915109 | + | 1.58502i | −0.108367 | + | 0.994111i | \(0.534562\pi\) |
−0.806742 | + | 0.590904i | \(0.798771\pi\) | |||||||
\(998\) | 0.449529 | + | 0.778607i | 0.0142296 | + | 0.0246464i | ||||
\(999\) | −3.27456 | + | 1.89057i | −0.103603 | + | 0.0598150i |
(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 | 637.2.q.g.491.3 | 12 | ||
7.2 | even | 3 | 91.2.u.b.88.4 | yes | 12 | ||
7.3 | odd | 6 | 637.2.k.i.569.3 | 12 | |||
7.4 | even | 3 | 91.2.k.b.23.3 | yes | 12 | ||
7.5 | odd | 6 | 637.2.u.g.361.4 | 12 | |||
7.6 | odd | 2 | 637.2.q.i.491.3 | 12 | |||
13.2 | odd | 12 | 8281.2.a.cp.1.5 | 12 | |||
13.4 | even | 6 | inner | 637.2.q.g.589.3 | 12 | ||
13.11 | odd | 12 | 8281.2.a.cp.1.8 | 12 | |||
21.2 | odd | 6 | 819.2.do.e.361.3 | 12 | |||
21.11 | odd | 6 | 819.2.bm.f.478.4 | 12 | |||
91.2 | odd | 12 | 1183.2.e.j.508.8 | 24 | |||
91.4 | even | 6 | 91.2.u.b.30.4 | yes | 12 | ||
91.11 | odd | 12 | 1183.2.e.j.170.5 | 24 | |||
91.17 | odd | 6 | 637.2.u.g.30.4 | 12 | |||
91.30 | even | 6 | 91.2.k.b.4.4 | ✓ | 12 | ||
91.37 | odd | 12 | 1183.2.e.j.508.5 | 24 | |||
91.41 | even | 12 | 8281.2.a.co.1.5 | 12 | |||
91.67 | odd | 12 | 1183.2.e.j.170.8 | 24 | |||
91.69 | odd | 6 | 637.2.q.i.589.3 | 12 | |||
91.76 | even | 12 | 8281.2.a.co.1.8 | 12 | |||
91.82 | odd | 6 | 637.2.k.i.459.4 | 12 | |||
273.95 | odd | 6 | 819.2.do.e.667.3 | 12 | |||
273.212 | odd | 6 | 819.2.bm.f.550.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.k.b.4.4 | ✓ | 12 | 91.30 | even | 6 | ||
91.2.k.b.23.3 | yes | 12 | 7.4 | even | 3 | ||
91.2.u.b.30.4 | yes | 12 | 91.4 | even | 6 | ||
91.2.u.b.88.4 | yes | 12 | 7.2 | even | 3 | ||
637.2.k.i.459.4 | 12 | 91.82 | odd | 6 | |||
637.2.k.i.569.3 | 12 | 7.3 | odd | 6 | |||
637.2.q.g.491.3 | 12 | 1.1 | even | 1 | trivial | ||
637.2.q.g.589.3 | 12 | 13.4 | even | 6 | inner | ||
637.2.q.i.491.3 | 12 | 7.6 | odd | 2 | |||
637.2.q.i.589.3 | 12 | 91.69 | odd | 6 | |||
637.2.u.g.30.4 | 12 | 91.17 | odd | 6 | |||
637.2.u.g.361.4 | 12 | 7.5 | odd | 6 | |||
819.2.bm.f.478.4 | 12 | 21.11 | odd | 6 | |||
819.2.bm.f.550.3 | 12 | 273.212 | odd | 6 | |||
819.2.do.e.361.3 | 12 | 21.2 | odd | 6 | |||
819.2.do.e.667.3 | 12 | 273.95 | odd | 6 | |||
1183.2.e.j.170.5 | 24 | 91.11 | odd | 12 | |||
1183.2.e.j.170.8 | 24 | 91.67 | odd | 12 | |||
1183.2.e.j.508.5 | 24 | 91.37 | odd | 12 | |||
1183.2.e.j.508.8 | 24 | 91.2 | odd | 12 | |||
8281.2.a.co.1.5 | 12 | 91.41 | even | 12 | |||
8281.2.a.co.1.8 | 12 | 91.76 | even | 12 | |||
8281.2.a.cp.1.5 | 12 | 13.2 | odd | 12 | |||
8281.2.a.cp.1.8 | 12 | 13.11 | odd | 12 |