Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(148,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(10))
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("847.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.f (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.76332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} - 1175 x^{7} + 2135 x^{6} - 2300 x^{5} + 1850 x^{4} - 925 x^{3} + 700 x^{2} + \cdots + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | no (minimal twist has level 77) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 148.2 | ||
Root | \(0.901622 - 0.655067i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.148 |
Dual form | 847.2.f.v.372.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.344389 | − | 1.05992i | −0.243520 | − | 0.749477i | −0.995876 | − | 0.0907209i | \(-0.971083\pi\) |
0.752356 | − | 0.658756i | \(-0.228917\pi\) | |||||||
\(3\) | 2.31283 | + | 1.68037i | 1.33531 | + | 0.970163i | 0.999602 | + | 0.0281981i | \(0.00897692\pi\) |
0.335712 | + | 0.941965i | \(0.391023\pi\) | |||||||
\(4\) | 0.613206 | − | 0.445520i | 0.306603 | − | 0.222760i | ||||
\(5\) | 1.06799 | − | 3.28693i | 0.477618 | − | 1.46996i | −0.364776 | − | 0.931095i | \(-0.618854\pi\) |
0.842394 | − | 0.538862i | \(-0.181146\pi\) | |||||||
\(6\) | 0.984546 | − | 3.03012i | 0.401939 | − | 1.23704i | ||||
\(7\) | 0.809017 | − | 0.587785i | 0.305780 | − | 0.222162i | ||||
\(8\) | −2.48664 | − | 1.80665i | −0.879161 | − | 0.638748i | ||||
\(9\) | 1.59850 | + | 4.91966i | 0.532832 | + | 1.63989i | ||||
\(10\) | −3.85168 | −1.21801 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 2.16688 | 0.625525 | ||||||||
\(13\) | 0.636468 | + | 1.95885i | 0.176524 | + | 0.543286i | 0.999700 | − | 0.0245009i | \(-0.00779967\pi\) |
−0.823175 | + | 0.567787i | \(0.807800\pi\) | |||||||
\(14\) | −0.901622 | − | 0.655067i | −0.240969 | − | 0.175074i | ||||
\(15\) | 7.99333 | − | 5.80749i | 2.06387 | − | 1.49949i | ||||
\(16\) | −0.590087 | + | 1.81610i | −0.147522 | + | 0.454025i | ||||
\(17\) | −0.597555 | + | 1.83909i | −0.144928 | + | 0.446044i | −0.997002 | − | 0.0773786i | \(-0.975345\pi\) |
0.852073 | + | 0.523422i | \(0.175345\pi\) | |||||||
\(18\) | 4.66395 | − | 3.38856i | 1.09930 | − | 0.798691i | ||||
\(19\) | 1.31300 | + | 0.953952i | 0.301223 | + | 0.218852i | 0.728121 | − | 0.685448i | \(-0.240394\pi\) |
−0.426898 | + | 0.904300i | \(0.640394\pi\) | |||||||
\(20\) | −0.809496 | − | 2.49137i | −0.181009 | − | 0.557088i | ||||
\(21\) | 2.85882 | 0.623845 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.807136 | −0.168299 | −0.0841497 | − | 0.996453i | \(-0.526817\pi\) | ||||
−0.0841497 | + | 0.996453i | \(0.526817\pi\) | |||||||
\(24\) | −2.71534 | − | 8.35696i | −0.554267 | − | 1.70586i | ||||
\(25\) | −5.61820 | − | 4.08186i | −1.12364 | − | 0.816372i | ||||
\(26\) | 1.85703 | − | 1.34921i | 0.364193 | − | 0.264602i | ||||
\(27\) | −1.91954 | + | 5.90773i | −0.369415 | + | 1.13694i | ||||
\(28\) | 0.234224 | − | 0.720867i | 0.0442641 | − | 0.136231i | ||||
\(29\) | 6.45084 | − | 4.68681i | 1.19789 | − | 0.870319i | 0.203815 | − | 0.979009i | \(-0.434666\pi\) |
0.994076 | + | 0.108690i | \(0.0346657\pi\) | |||||||
\(30\) | −8.90830 | − | 6.47226i | −1.62643 | − | 1.18167i | ||||
\(31\) | 0.243635 | + | 0.749832i | 0.0437582 | + | 0.134674i | 0.970549 | − | 0.240905i | \(-0.0774441\pi\) |
−0.926791 | + | 0.375578i | \(0.877444\pi\) | |||||||
\(32\) | −4.01918 | −0.710497 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.15508 | 0.369592 | ||||||||
\(35\) | −1.06799 | − | 3.28693i | −0.180523 | − | 0.555592i | ||||
\(36\) | 3.17202 | + | 2.30461i | 0.528669 | + | 0.384101i | ||||
\(37\) | −8.14014 | + | 5.91416i | −1.33823 | + | 0.972282i | −0.338724 | + | 0.940886i | \(0.609995\pi\) |
−0.999507 | + | 0.0313960i | \(0.990005\pi\) | |||||||
\(38\) | 0.558930 | − | 1.72021i | 0.0906704 | − | 0.279055i | ||||
\(39\) | −1.81955 | + | 5.59998i | −0.291360 | + | 0.896715i | ||||
\(40\) | −8.59403 | + | 6.24393i | −1.35884 | + | 0.987252i | ||||
\(41\) | −1.72008 | − | 1.24971i | −0.268631 | − | 0.195172i | 0.445312 | − | 0.895375i | \(-0.353093\pi\) |
−0.713943 | + | 0.700203i | \(0.753093\pi\) | |||||||
\(42\) | −0.984546 | − | 3.03012i | −0.151919 | − | 0.467558i | ||||
\(43\) | −3.08043 | −0.469761 | −0.234880 | − | 0.972024i | \(-0.575470\pi\) | ||||
−0.234880 | + | 0.972024i | \(0.575470\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 17.8777 | 2.66506 | ||||||||
\(46\) | 0.277969 | + | 0.855500i | 0.0409842 | + | 0.126137i | ||||
\(47\) | −6.12128 | − | 4.44737i | −0.892881 | − | 0.648716i | 0.0437469 | − | 0.999043i | \(-0.486070\pi\) |
−0.936627 | + | 0.350327i | \(0.886070\pi\) | |||||||
\(48\) | −4.41650 | + | 3.20877i | −0.637466 | + | 0.463146i | ||||
\(49\) | 0.309017 | − | 0.951057i | 0.0441453 | − | 0.135865i | ||||
\(50\) | −2.39160 | + | 7.36059i | −0.338224 | + | 1.04094i | ||||
\(51\) | −4.47239 | + | 3.24938i | −0.626260 | + | 0.455004i | ||||
\(52\) | 1.26299 | + | 0.917617i | 0.175145 | + | 0.127251i | ||||
\(53\) | 3.34432 | + | 10.2928i | 0.459378 | + | 1.41382i | 0.865918 | + | 0.500186i | \(0.166735\pi\) |
−0.406540 | + | 0.913633i | \(0.633265\pi\) | |||||||
\(54\) | 6.92280 | 0.942073 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.07366 | −0.410735 | ||||||||
\(57\) | 1.43376 | + | 4.41266i | 0.189906 | + | 0.584471i | ||||
\(58\) | −7.18925 | − | 5.22329i | −0.943994 | − | 0.685852i | ||||
\(59\) | 2.66704 | − | 1.93771i | 0.347218 | − | 0.252269i | −0.400483 | − | 0.916304i | \(-0.631158\pi\) |
0.747701 | + | 0.664035i | \(0.231158\pi\) | |||||||
\(60\) | 2.31420 | − | 7.12238i | 0.298762 | − | 0.919495i | ||||
\(61\) | 0.332696 | − | 1.02393i | 0.0425974 | − | 0.131101i | −0.927496 | − | 0.373833i | \(-0.878043\pi\) |
0.970094 | + | 0.242731i | \(0.0780434\pi\) | |||||||
\(62\) | 0.710857 | − | 0.516468i | 0.0902789 | − | 0.0655915i | ||||
\(63\) | 4.18492 | + | 3.04052i | 0.527250 | + | 0.383069i | ||||
\(64\) | 2.56433 | + | 7.89221i | 0.320542 | + | 0.986526i | ||||
\(65\) | 7.11832 | 0.882919 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.40314 | 0.293590 | 0.146795 | − | 0.989167i | \(-0.453104\pi\) | ||||
0.146795 | + | 0.989167i | \(0.453104\pi\) | |||||||
\(68\) | 0.452925 | + | 1.39396i | 0.0549253 | + | 0.169043i | ||||
\(69\) | −1.86677 | − | 1.35629i | −0.224733 | − | 0.163278i | ||||
\(70\) | −3.11608 | + | 2.26396i | −0.372442 | + | 0.270595i | ||||
\(71\) | −0.985330 | + | 3.03253i | −0.116937 | + | 0.359896i | −0.992346 | − | 0.123487i | \(-0.960592\pi\) |
0.875409 | + | 0.483383i | \(0.160592\pi\) | |||||||
\(72\) | 4.91323 | − | 15.1214i | 0.579030 | − | 1.78207i | ||||
\(73\) | 0.992078 | − | 0.720787i | 0.116114 | − | 0.0843617i | −0.528213 | − | 0.849112i | \(-0.677138\pi\) |
0.644327 | + | 0.764750i | \(0.277138\pi\) | |||||||
\(74\) | 9.07192 | + | 6.59113i | 1.05459 | + | 0.766204i | ||||
\(75\) | −6.13491 | − | 18.8813i | −0.708399 | − | 2.18023i | ||||
\(76\) | 1.23015 | 0.141107 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 6.56217 | 0.743020 | ||||||||
\(79\) | 2.93004 | + | 9.01775i | 0.329656 | + | 1.01458i | 0.969295 | + | 0.245901i | \(0.0790838\pi\) |
−0.639639 | + | 0.768675i | \(0.720916\pi\) | |||||||
\(80\) | 5.33918 | + | 3.87914i | 0.596939 | + | 0.433701i | ||||
\(81\) | −1.81200 | + | 1.31650i | −0.201334 | + | 0.146278i | ||||
\(82\) | −0.732217 | + | 2.25353i | −0.0808599 | + | 0.248861i | ||||
\(83\) | 4.96572 | − | 15.2829i | 0.545058 | − | 1.67752i | −0.175793 | − | 0.984427i | \(-0.556249\pi\) |
0.720851 | − | 0.693090i | \(-0.243751\pi\) | |||||||
\(84\) | 1.75304 | − | 1.27366i | 0.191273 | − | 0.138968i | ||||
\(85\) | 5.40676 | + | 3.92824i | 0.586445 | + | 0.426077i | ||||
\(86\) | 1.06087 | + | 3.26501i | 0.114396 | + | 0.352075i | ||||
\(87\) | 22.7953 | 2.44391 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.43830 | −0.470459 | −0.235230 | − | 0.971940i | \(-0.575584\pi\) | ||||
−0.235230 | + | 0.971940i | \(0.575584\pi\) | |||||||
\(90\) | −6.15690 | − | 18.9490i | −0.648994 | − | 1.99740i | ||||
\(91\) | 1.66629 | + | 1.21063i | 0.174675 | + | 0.126909i | ||||
\(92\) | −0.494940 | + | 0.359595i | −0.0516011 | + | 0.0374904i | ||||
\(93\) | −0.696508 | + | 2.14363i | −0.0722246 | + | 0.222284i | ||||
\(94\) | −2.60576 | + | 8.01970i | −0.268763 | + | 0.827169i | ||||
\(95\) | 4.53784 | − | 3.29693i | 0.465572 | − | 0.338258i | ||||
\(96\) | −9.29568 | − | 6.75371i | −0.948736 | − | 0.689297i | ||||
\(97\) | 1.99874 | + | 6.15150i | 0.202942 | + | 0.624590i | 0.999792 | + | 0.0204129i | \(0.00649807\pi\) |
−0.796850 | + | 0.604177i | \(0.793502\pi\) | |||||||
\(98\) | −1.11447 | −0.112578 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.26366 | −0.526366 | ||||||||
\(101\) | 4.77274 | + | 14.6890i | 0.474905 | + | 1.46161i | 0.846086 | + | 0.533047i | \(0.178953\pi\) |
−0.371181 | + | 0.928561i | \(0.621047\pi\) | |||||||
\(102\) | 4.98433 | + | 3.62133i | 0.493522 | + | 0.358565i | ||||
\(103\) | −7.20682 | + | 5.23606i | −0.710109 | + | 0.515925i | −0.883209 | − | 0.468980i | \(-0.844622\pi\) |
0.173100 | + | 0.984904i | \(0.444622\pi\) | |||||||
\(104\) | 1.95628 | − | 6.02083i | 0.191829 | − | 0.590390i | ||||
\(105\) | 3.05318 | − | 9.39672i | 0.297960 | − | 0.917026i | ||||
\(106\) | 9.75776 | − | 7.08943i | 0.947757 | − | 0.688586i | ||||
\(107\) | 2.84142 | + | 2.06441i | 0.274691 | + | 0.199574i | 0.716598 | − | 0.697486i | \(-0.245698\pi\) |
−0.441908 | + | 0.897061i | \(0.645698\pi\) | |||||||
\(108\) | 1.45494 | + | 4.47785i | 0.140002 | + | 0.430881i | ||||
\(109\) | −3.87655 | −0.371306 | −0.185653 | − | 0.982615i | \(-0.559440\pi\) | ||||
−0.185653 | + | 0.982615i | \(0.559440\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −28.7648 | −2.73023 | ||||||||
\(112\) | 0.590087 | + | 1.81610i | 0.0557580 | + | 0.171605i | ||||
\(113\) | −8.61920 | − | 6.26221i | −0.810826 | − | 0.589099i | 0.103244 | − | 0.994656i | \(-0.467078\pi\) |
−0.914070 | + | 0.405557i | \(0.867078\pi\) | |||||||
\(114\) | 4.18330 | − | 3.03935i | 0.391802 | − | 0.284661i | ||||
\(115\) | −0.862010 | + | 2.65299i | −0.0803829 | + | 0.247393i | ||||
\(116\) | 1.86763 | − | 5.74796i | 0.173405 | − | 0.533685i | ||||
\(117\) | −8.61947 | + | 6.26241i | −0.796871 | + | 0.578960i | ||||
\(118\) | −2.97232 | − | 2.15952i | −0.273624 | − | 0.198800i | ||||
\(119\) | 0.597555 | + | 1.83909i | 0.0547778 | + | 0.168589i | ||||
\(120\) | −30.3687 | −2.77227 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −1.19987 | −0.108631 | ||||||||
\(123\) | −1.87828 | − | 5.78074i | −0.169358 | − | 0.521232i | ||||
\(124\) | 0.483464 | + | 0.351257i | 0.0434163 | + | 0.0315438i | ||||
\(125\) | −5.43680 | + | 3.95007i | −0.486282 | + | 0.353305i | ||||
\(126\) | 1.78147 | − | 5.48280i | 0.158706 | − | 0.488447i | ||||
\(127\) | −6.01066 | + | 18.4989i | −0.533360 | + | 1.64151i | 0.213807 | + | 0.976876i | \(0.431414\pi\) |
−0.747167 | + | 0.664637i | \(0.768586\pi\) | |||||||
\(128\) | 0.978825 | − | 0.711158i | 0.0865167 | − | 0.0628581i | ||||
\(129\) | −7.12451 | − | 5.17626i | −0.627278 | − | 0.455744i | ||||
\(130\) | −2.45147 | − | 7.54486i | −0.215008 | − | 0.661728i | ||||
\(131\) | −5.11284 | −0.446711 | −0.223355 | − | 0.974737i | \(-0.571701\pi\) | ||||
−0.223355 | + | 0.974737i | \(0.571701\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.62296 | 0.140728 | ||||||||
\(134\) | −0.827615 | − | 2.54714i | −0.0714951 | − | 0.220039i | ||||
\(135\) | 17.3682 | + | 12.6188i | 1.49482 | + | 1.08605i | ||||
\(136\) | 4.80849 | − | 3.49357i | 0.412325 | − | 0.299571i | ||||
\(137\) | 2.81221 | − | 8.65511i | 0.240264 | − | 0.739456i | −0.756116 | − | 0.654438i | \(-0.772905\pi\) |
0.996379 | − | 0.0850177i | \(-0.0270947\pi\) | |||||||
\(138\) | −0.794662 | + | 2.44572i | −0.0676461 | + | 0.208193i | ||||
\(139\) | −10.5306 | + | 7.65095i | −0.893197 | + | 0.648945i | −0.936710 | − | 0.350108i | \(-0.886145\pi\) |
0.0435129 | + | 0.999053i | \(0.486145\pi\) | |||||||
\(140\) | −2.11929 | − | 1.53975i | −0.179112 | − | 0.130133i | ||||
\(141\) | −6.68426 | − | 20.5720i | −0.562916 | − | 1.73248i | ||||
\(142\) | 3.55358 | 0.298210 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −9.87786 | −0.823155 | ||||||||
\(145\) | −8.51578 | − | 26.2089i | −0.707197 | − | 2.17653i | ||||
\(146\) | −1.10564 | − | 0.803293i | −0.0915032 | − | 0.0664810i | ||||
\(147\) | 2.31283 | − | 1.68037i | 0.190759 | − | 0.138595i | ||||
\(148\) | −2.35671 | + | 7.25320i | −0.193720 | + | 0.596209i | ||||
\(149\) | 0.972321 | − | 2.99250i | 0.0796557 | − | 0.245155i | −0.903296 | − | 0.429017i | \(-0.858860\pi\) |
0.982952 | + | 0.183862i | \(0.0588600\pi\) | |||||||
\(150\) | −17.8999 | + | 13.0050i | −1.46152 | + | 1.06186i | ||||
\(151\) | 2.31942 | + | 1.68516i | 0.188752 | + | 0.137136i | 0.678148 | − | 0.734925i | \(-0.262783\pi\) |
−0.489396 | + | 0.872062i | \(0.662783\pi\) | |||||||
\(152\) | −1.54151 | − | 4.74427i | −0.125033 | − | 0.384811i | ||||
\(153\) | −10.0029 | −0.808684 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.72484 | 0.218864 | ||||||||
\(156\) | 1.37915 | + | 4.24459i | 0.110420 | + | 0.339839i | ||||
\(157\) | 17.3854 | + | 12.6312i | 1.38750 | + | 1.00808i | 0.996134 | + | 0.0878468i | \(0.0279986\pi\) |
0.391370 | + | 0.920234i | \(0.372001\pi\) | |||||||
\(158\) | 8.54902 | − | 6.21123i | 0.680124 | − | 0.494139i | ||||
\(159\) | −9.56080 | + | 29.4251i | −0.758221 | + | 2.33356i | ||||
\(160\) | −4.29243 | + | 13.2107i | −0.339346 | + | 1.04440i | ||||
\(161\) | −0.652986 | + | 0.474422i | −0.0514625 | + | 0.0373897i | ||||
\(162\) | 2.01942 | + | 1.46719i | 0.158661 | + | 0.115274i | ||||
\(163\) | −2.54088 | − | 7.82002i | −0.199017 | − | 0.612511i | −0.999906 | − | 0.0136985i | \(-0.995639\pi\) |
0.800889 | − | 0.598812i | \(-0.204361\pi\) | |||||||
\(164\) | −1.61153 | −0.125840 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −17.9088 | −1.38999 | ||||||||
\(167\) | 6.70832 | + | 20.6461i | 0.519105 | + | 1.59764i | 0.775686 | + | 0.631119i | \(0.217404\pi\) |
−0.256581 | + | 0.966523i | \(0.582596\pi\) | |||||||
\(168\) | −7.10886 | − | 5.16489i | −0.548460 | − | 0.398480i | ||||
\(169\) | 7.08523 | − | 5.14772i | 0.545018 | − | 0.395979i | ||||
\(170\) | 2.30159 | − | 7.08357i | 0.176524 | − | 0.543285i | ||||
\(171\) | −2.59429 | + | 7.98442i | −0.198391 | + | 0.610584i | ||||
\(172\) | −1.88894 | + | 1.37239i | −0.144030 | + | 0.104644i | ||||
\(173\) | −6.50905 | − | 4.72910i | −0.494874 | − | 0.359547i | 0.312181 | − | 0.950022i | \(-0.398940\pi\) |
−0.807056 | + | 0.590475i | \(0.798940\pi\) | |||||||
\(174\) | −7.85045 | − | 24.1612i | −0.595141 | − | 1.83166i | ||||
\(175\) | −6.94447 | −0.524953 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.42449 | 0.708388 | ||||||||
\(178\) | 1.52850 | + | 4.70425i | 0.114566 | + | 0.352598i | ||||
\(179\) | 2.92938 | + | 2.12832i | 0.218952 | + | 0.159078i | 0.691855 | − | 0.722037i | \(-0.256794\pi\) |
−0.472903 | + | 0.881115i | \(0.656794\pi\) | |||||||
\(180\) | 10.9627 | − | 7.96490i | 0.817114 | − | 0.593668i | ||||
\(181\) | 4.88800 | − | 15.0437i | 0.363322 | − | 1.11819i | −0.587703 | − | 0.809077i | \(-0.699967\pi\) |
0.951025 | − | 0.309114i | \(-0.100033\pi\) | |||||||
\(182\) | 0.709322 | − | 2.18307i | 0.0525784 | − | 0.161820i | ||||
\(183\) | 2.49006 | − | 1.80913i | 0.184070 | − | 0.133735i | ||||
\(184\) | 2.00706 | + | 1.45821i | 0.147962 | + | 0.107501i | ||||
\(185\) | 10.7458 | + | 33.0723i | 0.790050 | + | 2.43152i | ||||
\(186\) | 2.51195 | 0.184185 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −5.73500 | −0.418268 | ||||||||
\(189\) | 1.91954 | + | 5.90773i | 0.139626 | + | 0.429724i | ||||
\(190\) | −5.05727 | − | 3.67432i | −0.366893 | − | 0.266563i | ||||
\(191\) | −0.347134 | + | 0.252207i | −0.0251177 | + | 0.0182491i | −0.600273 | − | 0.799795i | \(-0.704942\pi\) |
0.575156 | + | 0.818044i | \(0.304942\pi\) | |||||||
\(192\) | −7.33097 | + | 22.5624i | −0.529067 | + | 1.62830i | ||||
\(193\) | 4.68928 | − | 14.4321i | 0.337542 | − | 1.03885i | −0.627915 | − | 0.778282i | \(-0.716091\pi\) |
0.965456 | − | 0.260564i | \(-0.0839086\pi\) | |||||||
\(194\) | 5.83176 | − | 4.23702i | 0.418696 | − | 0.304200i | ||||
\(195\) | 16.4635 | + | 11.9614i | 1.17897 | + | 0.856575i | ||||
\(196\) | −0.234224 | − | 0.720867i | −0.0167303 | − | 0.0514905i | ||||
\(197\) | 20.8082 | 1.48252 | 0.741262 | − | 0.671216i | \(-0.234228\pi\) | ||||
0.741262 | + | 0.671216i | \(0.234228\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.44567 | 0.598698 | 0.299349 | − | 0.954144i | \(-0.403231\pi\) | ||||
0.299349 | + | 0.954144i | \(0.403231\pi\) | |||||||
\(200\) | 6.59595 | + | 20.3003i | 0.466404 | + | 1.43544i | ||||
\(201\) | 5.55806 | + | 4.03817i | 0.392035 | + | 0.284830i | ||||
\(202\) | 13.9255 | − | 10.1174i | 0.979792 | − | 0.711861i | ||||
\(203\) | 2.46400 | − | 7.58342i | 0.172939 | − | 0.532252i | ||||
\(204\) | −1.29483 | + | 3.98508i | −0.0906563 | + | 0.279011i | ||||
\(205\) | −5.94472 | + | 4.31910i | −0.415198 | + | 0.301659i | ||||
\(206\) | 8.03176 | + | 5.83542i | 0.559599 | + | 0.406573i | ||||
\(207\) | −1.29020 | − | 3.97084i | −0.0896753 | − | 0.275992i | ||||
\(208\) | −3.93303 | −0.272707 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −11.0113 | −0.759849 | ||||||||
\(211\) | 3.04668 | + | 9.37672i | 0.209742 | + | 0.645520i | 0.999485 | + | 0.0320823i | \(0.0102139\pi\) |
−0.789743 | + | 0.613438i | \(0.789786\pi\) | |||||||
\(212\) | 6.63639 | + | 4.82162i | 0.455789 | + | 0.331150i | ||||
\(213\) | −7.37469 | + | 5.35802i | −0.505305 | + | 0.367126i | ||||
\(214\) | 1.20956 | − | 3.72264i | 0.0826838 | − | 0.254475i | ||||
\(215\) | −3.28986 | + | 10.1251i | −0.224366 | + | 0.690528i | ||||
\(216\) | 15.4464 | − | 11.2225i | 1.05100 | − | 0.763593i | ||||
\(217\) | 0.637845 | + | 0.463421i | 0.0432997 | + | 0.0314591i | ||||
\(218\) | 1.33504 | + | 4.10883i | 0.0904204 | + | 0.278285i | ||||
\(219\) | 3.50570 | 0.236893 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.98281 | −0.267913 | ||||||||
\(222\) | 9.90627 | + | 30.4884i | 0.664865 | + | 2.04625i | ||||
\(223\) | −14.0736 | − | 10.2250i | −0.942436 | − | 0.684720i | 0.00656992 | − | 0.999978i | \(-0.497909\pi\) |
−0.949006 | + | 0.315259i | \(0.897909\pi\) | |||||||
\(224\) | −3.25158 | + | 2.36241i | −0.217255 | + | 0.157845i | ||||
\(225\) | 11.1007 | − | 34.1645i | 0.740048 | − | 2.27763i | ||||
\(226\) | −3.66909 | + | 11.2923i | −0.244064 | + | 0.751153i | ||||
\(227\) | −10.2191 | + | 7.42460i | −0.678264 | + | 0.492788i | −0.872781 | − | 0.488111i | \(-0.837686\pi\) |
0.194517 | + | 0.980899i | \(0.437686\pi\) | |||||||
\(228\) | 2.84512 | + | 2.06710i | 0.188423 | + | 0.136897i | ||||
\(229\) | 1.41326 | + | 4.34958i | 0.0933910 | + | 0.287428i | 0.986831 | − | 0.161755i | \(-0.0517153\pi\) |
−0.893440 | + | 0.449183i | \(0.851715\pi\) | |||||||
\(230\) | 3.10883 | 0.204990 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −24.5084 | −1.60905 | ||||||||
\(233\) | −7.37218 | − | 22.6893i | −0.482968 | − | 1.48642i | −0.834903 | − | 0.550398i | \(-0.814476\pi\) |
0.351935 | − | 0.936025i | \(-0.385524\pi\) | |||||||
\(234\) | 9.60612 | + | 6.97925i | 0.627971 | + | 0.456248i | ||||
\(235\) | −21.1556 | + | 15.3705i | −1.38004 | + | 1.00266i | ||||
\(236\) | 0.772151 | − | 2.37644i | 0.0502628 | − | 0.154693i | ||||
\(237\) | −8.37646 | + | 25.7801i | −0.544110 | + | 1.67460i | ||||
\(238\) | 1.74349 | − | 1.26672i | 0.113014 | − | 0.0821094i | ||||
\(239\) | 7.15021 | + | 5.19493i | 0.462509 | + | 0.336032i | 0.794515 | − | 0.607245i | \(-0.207725\pi\) |
−0.332006 | + | 0.943277i | \(0.607725\pi\) | |||||||
\(240\) | 5.83024 | + | 17.9436i | 0.376340 | + | 1.15826i | ||||
\(241\) | −18.9464 | −1.22045 | −0.610224 | − | 0.792229i | \(-0.708921\pi\) | ||||
−0.610224 | + | 0.792229i | \(0.708921\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.2322 | 0.784696 | ||||||||
\(244\) | −0.252172 | − | 0.776105i | −0.0161436 | − | 0.0496850i | ||||
\(245\) | −2.79603 | − | 2.03143i | −0.178632 | − | 0.129783i | ||||
\(246\) | −5.48027 | + | 3.98165i | −0.349409 | + | 0.253861i | ||||
\(247\) | −1.03296 | + | 3.17913i | −0.0657258 | + | 0.202283i | ||||
\(248\) | 0.748851 | − | 2.30473i | 0.0475521 | − | 0.146350i | ||||
\(249\) | 37.1658 | − | 27.0026i | 2.35529 | − | 1.71122i | ||||
\(250\) | 6.05913 | + | 4.40222i | 0.383213 | + | 0.278421i | ||||
\(251\) | −0.885925 | − | 2.72660i | −0.0559191 | − | 0.172101i | 0.919196 | − | 0.393800i | \(-0.128840\pi\) |
−0.975115 | + | 0.221699i | \(0.928840\pi\) | |||||||
\(252\) | 3.92083 | 0.246989 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 21.6774 | 1.36016 | ||||||||
\(255\) | 5.90402 | + | 18.1707i | 0.369724 | + | 1.13789i | ||||
\(256\) | 12.3362 | + | 8.96275i | 0.771010 | + | 0.560172i | ||||
\(257\) | −18.1348 | + | 13.1757i | −1.13122 | + | 0.821879i | −0.985872 | − | 0.167502i | \(-0.946430\pi\) |
−0.145347 | + | 0.989381i | \(0.546430\pi\) | |||||||
\(258\) | −3.03282 | + | 9.33406i | −0.188815 | + | 0.581113i | ||||
\(259\) | −3.10926 | + | 9.56931i | −0.193200 | + | 0.594608i | ||||
\(260\) | 4.36500 | − | 3.17136i | 0.270706 | − | 0.196679i | ||||
\(261\) | 33.3692 | + | 24.2441i | 2.06550 | + | 1.50067i | ||||
\(262\) | 1.76080 | + | 5.41920i | 0.108783 | + | 0.334799i | ||||
\(263\) | −0.990706 | −0.0610895 | −0.0305448 | − | 0.999533i | \(-0.509724\pi\) | ||||
−0.0305448 | + | 0.999533i | \(0.509724\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 37.4032 | 2.29766 | ||||||||
\(266\) | −0.558930 | − | 1.72021i | −0.0342702 | − | 0.105473i | ||||
\(267\) | −10.2650 | − | 7.45800i | −0.628211 | − | 0.456422i | ||||
\(268\) | 1.47362 | − | 1.07065i | 0.0900156 | − | 0.0654002i | ||||
\(269\) | −2.22194 | + | 6.83844i | −0.135474 | + | 0.416947i | −0.995664 | − | 0.0930279i | \(-0.970345\pi\) |
0.860189 | + | 0.509975i | \(0.170345\pi\) | |||||||
\(270\) | 7.39345 | − | 22.7547i | 0.449951 | − | 1.38481i | ||||
\(271\) | −21.9764 | + | 15.9668i | −1.33497 | + | 0.969912i | −0.335356 | + | 0.942091i | \(0.608857\pi\) |
−0.999613 | + | 0.0278207i | \(0.991143\pi\) | |||||||
\(272\) | −2.98736 | − | 2.17044i | −0.181135 | − | 0.131602i | ||||
\(273\) | 1.81955 | + | 5.59998i | 0.110124 | + | 0.338927i | ||||
\(274\) | −10.1422 | −0.612714 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.74897 | −0.105275 | ||||||||
\(277\) | −6.48491 | − | 19.9585i | −0.389640 | − | 1.19919i | −0.933058 | − | 0.359727i | \(-0.882870\pi\) |
0.543417 | − | 0.839463i | \(-0.317130\pi\) | |||||||
\(278\) | 11.7360 | + | 8.52673i | 0.703881 | + | 0.511399i | ||||
\(279\) | −3.29947 | + | 2.39721i | −0.197534 | + | 0.143517i | ||||
\(280\) | −3.28263 | + | 10.1029i | −0.196174 | + | 0.603763i | ||||
\(281\) | 8.70130 | − | 26.7798i | 0.519076 | − | 1.59755i | −0.256665 | − | 0.966500i | \(-0.582624\pi\) |
0.775741 | − | 0.631051i | \(-0.217376\pi\) | |||||||
\(282\) | −19.5027 | + | 14.1696i | −1.16137 | + | 0.843786i | ||||
\(283\) | −21.1896 | − | 15.3951i | −1.25959 | − | 0.915145i | −0.260851 | − | 0.965379i | \(-0.584003\pi\) |
−0.998737 | + | 0.0502344i | \(0.984003\pi\) | |||||||
\(284\) | 0.746845 | + | 2.29855i | 0.0443171 | + | 0.136394i | ||||
\(285\) | 16.0353 | 0.949851 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.12613 | −0.125502 | ||||||||
\(288\) | −6.42463 | − | 19.7730i | −0.378575 | − | 1.16513i | ||||
\(289\) | 10.7281 | + | 7.79444i | 0.631066 | + | 0.458496i | ||||
\(290\) | −24.8466 | + | 18.0521i | −1.45904 | + | 1.06006i | ||||
\(291\) | −5.71404 | + | 17.5860i | −0.334963 | + | 1.03091i | ||||
\(292\) | 0.287223 | − | 0.883981i | 0.0168085 | − | 0.0517311i | ||||
\(293\) | −3.61133 | + | 2.62379i | −0.210976 | + | 0.153283i | −0.688255 | − | 0.725469i | \(-0.741623\pi\) |
0.477279 | + | 0.878752i | \(0.341623\pi\) | |||||||
\(294\) | −2.57757 | − | 1.87272i | −0.150327 | − | 0.109219i | ||||
\(295\) | −3.52077 | − | 10.8358i | −0.204987 | − | 0.630885i | ||||
\(296\) | 30.9264 | 1.79756 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.50667 | −0.203136 | ||||||||
\(299\) | −0.513716 | − | 1.58105i | −0.0297089 | − | 0.0914347i | ||||
\(300\) | −12.1740 | − | 8.84491i | −0.702865 | − | 0.510661i | ||||
\(301\) | −2.49212 | + | 1.81063i | −0.143643 | + | 0.104363i | ||||
\(302\) | 0.987351 | − | 3.03875i | 0.0568157 | − | 0.174861i | ||||
\(303\) | −13.6444 | + | 41.9931i | −0.783849 | + | 2.41244i | ||||
\(304\) | −2.50726 | + | 1.82163i | −0.143801 | + | 0.104478i | ||||
\(305\) | −3.01028 | − | 2.18710i | −0.172368 | − | 0.125233i | ||||
\(306\) | 3.44488 | + | 10.6023i | 0.196931 | + | 0.606090i | ||||
\(307\) | −12.8841 | −0.735334 | −0.367667 | − | 0.929957i | \(-0.619843\pi\) | ||||
−0.367667 | + | 0.929957i | \(0.619843\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −25.4667 | −1.44875 | ||||||||
\(310\) | −0.938405 | − | 2.88811i | −0.0532978 | − | 0.164034i | ||||
\(311\) | −21.6977 | − | 15.7643i | −1.23036 | − | 0.893912i | −0.233447 | − | 0.972370i | \(-0.575001\pi\) |
−0.996917 | + | 0.0784574i | \(0.975001\pi\) | |||||||
\(312\) | 14.6418 | − | 10.6379i | 0.828928 | − | 0.602251i | ||||
\(313\) | 1.10896 | − | 3.41304i | 0.0626824 | − | 0.192917i | −0.914811 | − | 0.403882i | \(-0.867661\pi\) |
0.977494 | + | 0.210965i | \(0.0676607\pi\) | |||||||
\(314\) | 7.40075 | − | 22.7772i | 0.417648 | − | 1.28539i | ||||
\(315\) | 14.4634 | − | 10.5083i | 0.814920 | − | 0.592074i | ||||
\(316\) | 5.81431 | + | 4.22434i | 0.327081 | + | 0.237638i | ||||
\(317\) | −5.22797 | − | 16.0900i | −0.293632 | − | 0.903706i | −0.983678 | − | 0.179940i | \(-0.942410\pi\) |
0.690046 | − | 0.723766i | \(-0.257590\pi\) | |||||||
\(318\) | 34.4809 | 1.93359 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 28.6798 | 1.60325 | ||||||||
\(321\) | 3.10275 | + | 9.54929i | 0.173179 | + | 0.532989i | ||||
\(322\) | 0.727732 | + | 0.528728i | 0.0405549 | + | 0.0294649i | ||||
\(323\) | −2.53899 | + | 1.84468i | −0.141273 | + | 0.102641i | ||||
\(324\) | −0.524605 | + | 1.61457i | −0.0291447 | + | 0.0896983i | ||||
\(325\) | 4.41993 | − | 13.6032i | 0.245174 | − | 0.754567i | ||||
\(326\) | −7.41355 | + | 5.38626i | −0.410598 | + | 0.298317i | ||||
\(327\) | −8.96581 | − | 6.51404i | −0.495810 | − | 0.360227i | ||||
\(328\) | 2.01943 | + | 6.21516i | 0.111504 | + | 0.343175i | ||||
\(329\) | −7.56632 | −0.417145 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.23826 | −0.0680610 | −0.0340305 | − | 0.999421i | \(-0.510834\pi\) | ||||
−0.0340305 | + | 0.999421i | \(0.510834\pi\) | |||||||
\(332\) | −3.76384 | − | 11.5839i | −0.206567 | − | 0.635749i | ||||
\(333\) | −42.1077 | − | 30.5930i | −2.30749 | − | 1.67649i | ||||
\(334\) | 19.5729 | − | 14.2206i | 1.07098 | − | 0.778115i | ||||
\(335\) | 2.56652 | − | 7.89894i | 0.140224 | − | 0.431565i | ||||
\(336\) | −1.68695 | + | 5.19190i | −0.0920307 | + | 0.283242i | ||||
\(337\) | −16.5691 | + | 12.0382i | −0.902579 | + | 0.655762i | −0.939127 | − | 0.343570i | \(-0.888364\pi\) |
0.0365484 | + | 0.999332i | \(0.488364\pi\) | |||||||
\(338\) | −7.89626 | − | 5.73697i | −0.429500 | − | 0.312050i | ||||
\(339\) | −9.41192 | − | 28.9669i | −0.511185 | − | 1.57327i | ||||
\(340\) | 5.06556 | 0.274719 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 9.35630 | 0.505931 | ||||||||
\(343\) | −0.309017 | − | 0.951057i | −0.0166853 | − | 0.0513522i | ||||
\(344\) | 7.65992 | + | 5.56526i | 0.412995 | + | 0.300059i | ||||
\(345\) | −6.45170 | + | 4.68743i | −0.347348 | + | 0.252363i | ||||
\(346\) | −2.77083 | + | 8.52773i | −0.148961 | + | 0.458454i | ||||
\(347\) | −8.42685 | + | 25.9352i | −0.452377 | + | 1.39227i | 0.421810 | + | 0.906684i | \(0.361395\pi\) |
−0.874187 | + | 0.485589i | \(0.838605\pi\) | |||||||
\(348\) | 13.9782 | − | 10.1558i | 0.749311 | − | 0.544406i | ||||
\(349\) | 6.45947 | + | 4.69308i | 0.345767 | + | 0.251215i | 0.747091 | − | 0.664721i | \(-0.231450\pi\) |
−0.401324 | + | 0.915936i | \(0.631450\pi\) | |||||||
\(350\) | 2.39160 | + | 7.36059i | 0.127836 | + | 0.393440i | ||||
\(351\) | −12.7941 | −0.682897 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.93472 | 0.315873 | 0.157937 | − | 0.987449i | \(-0.449516\pi\) | ||||
0.157937 | + | 0.987449i | \(0.449516\pi\) | |||||||
\(354\) | −3.24569 | − | 9.98921i | −0.172507 | − | 0.530920i | ||||
\(355\) | 8.91539 | + | 6.47741i | 0.473180 | + | 0.343785i | ||||
\(356\) | −2.72159 | + | 1.97735i | −0.144244 | + | 0.104800i | ||||
\(357\) | −1.70830 | + | 5.25761i | −0.0904129 | + | 0.278262i | ||||
\(358\) | 1.24700 | − | 3.83788i | 0.0659061 | − | 0.202838i | ||||
\(359\) | 22.9925 | − | 16.7050i | 1.21350 | − | 0.881657i | 0.217953 | − | 0.975959i | \(-0.430062\pi\) |
0.995544 | + | 0.0943020i | \(0.0300619\pi\) | |||||||
\(360\) | −44.4555 | − | 32.2988i | −2.34301 | − | 1.70230i | ||||
\(361\) | −5.05737 | − | 15.5650i | −0.266178 | − | 0.819210i | ||||
\(362\) | −17.6285 | −0.926535 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.56114 | 0.0818261 | ||||||||
\(365\) | −1.30965 | − | 4.03068i | −0.0685500 | − | 0.210975i | ||||
\(366\) | −2.77509 | − | 2.01622i | −0.145056 | − | 0.105389i | ||||
\(367\) | 24.5953 | − | 17.8695i | 1.28386 | − | 0.932781i | 0.284200 | − | 0.958765i | \(-0.408272\pi\) |
0.999662 | + | 0.0259840i | \(0.00827188\pi\) | |||||||
\(368\) | 0.476280 | − | 1.46584i | 0.0248278 | − | 0.0764122i | ||||
\(369\) | 3.39862 | − | 10.4599i | 0.176925 | − | 0.544519i | ||||
\(370\) | 31.3532 | − | 22.7795i | 1.62998 | − | 1.18425i | ||||
\(371\) | 8.75554 | + | 6.36127i | 0.454565 | + | 0.330261i | ||||
\(372\) | 0.527928 | + | 1.62480i | 0.0273718 | + | 0.0842418i | ||||
\(373\) | −14.4226 | −0.746772 | −0.373386 | − | 0.927676i | \(-0.621803\pi\) | ||||
−0.373386 | + | 0.927676i | \(0.621803\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −19.2120 | −0.992103 | ||||||||
\(376\) | 7.18659 | + | 22.1180i | 0.370620 | + | 1.14065i | ||||
\(377\) | 13.2865 | + | 9.65320i | 0.684289 | + | 0.497165i | ||||
\(378\) | 5.60066 | − | 4.06912i | 0.288067 | − | 0.209293i | ||||
\(379\) | −6.92421 | + | 21.3105i | −0.355673 | + | 1.09465i | 0.599946 | + | 0.800041i | \(0.295189\pi\) |
−0.955618 | + | 0.294607i | \(0.904811\pi\) | |||||||
\(380\) | 1.31378 | − | 4.04340i | 0.0673955 | − | 0.207422i | ||||
\(381\) | −44.9867 | + | 32.6847i | −2.30474 | + | 1.67449i | ||||
\(382\) | 0.386869 | + | 0.281077i | 0.0197939 | + | 0.0143811i | ||||
\(383\) | 10.4072 | + | 32.0302i | 0.531785 | + | 1.63667i | 0.750495 | + | 0.660876i | \(0.229815\pi\) |
−0.218710 | + | 0.975790i | \(0.570185\pi\) | |||||||
\(384\) | 3.45887 | 0.176510 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −16.9118 | −0.860790 | ||||||||
\(387\) | −4.92405 | − | 15.1547i | −0.250304 | − | 0.770355i | ||||
\(388\) | 3.96626 | + | 2.88166i | 0.201356 | + | 0.146294i | ||||
\(389\) | −1.96416 | + | 1.42704i | −0.0995866 | + | 0.0723539i | −0.636464 | − | 0.771306i | \(-0.719604\pi\) |
0.536878 | + | 0.843660i | \(0.319604\pi\) | |||||||
\(390\) | 7.00831 | − | 21.5694i | 0.354880 | − | 1.09221i | ||||
\(391\) | 0.482308 | − | 1.48439i | 0.0243914 | − | 0.0750689i | ||||
\(392\) | −2.48664 | + | 1.80665i | −0.125594 | + | 0.0912497i | ||||
\(393\) | −11.8251 | − | 8.59146i | −0.596499 | − | 0.433382i | ||||
\(394\) | −7.16612 | − | 22.0550i | −0.361024 | − | 1.11112i | ||||
\(395\) | 32.7699 | 1.64883 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.89696 | −0.295960 | −0.147980 | − | 0.988990i | \(-0.547277\pi\) | ||||
−0.147980 | + | 0.988990i | \(0.547277\pi\) | |||||||
\(398\) | −2.90860 | − | 8.95175i | −0.145795 | − | 0.448710i | ||||
\(399\) | 3.75363 | + | 2.72717i | 0.187917 | + | 0.136530i | ||||
\(400\) | 10.7283 | − | 7.79456i | 0.536415 | − | 0.389728i | ||||
\(401\) | 3.47322 | − | 10.6895i | 0.173445 | − | 0.533807i | −0.826114 | − | 0.563502i | \(-0.809454\pi\) |
0.999559 | + | 0.0296950i | \(0.00945359\pi\) | |||||||
\(402\) | 2.36600 | − | 7.28180i | 0.118005 | − | 0.363183i | ||||
\(403\) | −1.31374 | + | 0.954487i | −0.0654420 | + | 0.0475464i | ||||
\(404\) | 9.47090 | + | 6.88102i | 0.471195 | + | 0.342343i | ||||
\(405\) | 2.39204 | + | 7.36193i | 0.118861 | + | 0.365817i | ||||
\(406\) | −8.88640 | −0.441025 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 16.9917 | 0.841216 | ||||||||
\(409\) | −9.06482 | − | 27.8987i | −0.448227 | − | 1.37950i | −0.878906 | − | 0.476995i | \(-0.841726\pi\) |
0.430679 | − | 0.902505i | \(-0.358274\pi\) | |||||||
\(410\) | 6.62520 | + | 4.81349i | 0.327195 | + | 0.237721i | ||||
\(411\) | 21.0480 | − | 15.2922i | 1.03822 | − | 0.754311i | ||||
\(412\) | −2.08649 | + | 6.42157i | −0.102794 | + | 0.316368i | ||||
\(413\) | 1.01872 | − | 3.13529i | 0.0501278 | − | 0.154277i | ||||
\(414\) | −3.76444 | + | 2.73503i | −0.185012 | + | 0.134419i | ||||
\(415\) | −44.9305 | − | 32.6439i | −2.20555 | − | 1.60243i | ||||
\(416\) | −2.55808 | − | 7.87295i | −0.125420 | − | 0.386003i | ||||
\(417\) | −37.2120 | −1.82228 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.2858 | −0.991027 | −0.495514 | − | 0.868600i | \(-0.665020\pi\) | ||||
−0.495514 | + | 0.868600i | \(0.665020\pi\) | |||||||
\(420\) | −2.31420 | − | 7.12238i | −0.112921 | − | 0.347537i | ||||
\(421\) | 2.47561 | + | 1.79864i | 0.120654 | + | 0.0876603i | 0.646476 | − | 0.762934i | \(-0.276242\pi\) |
−0.525822 | + | 0.850595i | \(0.676242\pi\) | |||||||
\(422\) | 8.88934 | − | 6.45848i | 0.432726 | − | 0.314394i | ||||
\(423\) | 12.0947 | − | 37.2237i | 0.588066 | − | 1.80988i | ||||
\(424\) | 10.2793 | − | 31.6364i | 0.499207 | − | 1.53640i | ||||
\(425\) | 10.8641 | − | 7.89321i | 0.526985 | − | 0.382877i | ||||
\(426\) | 8.21884 | + | 5.97134i | 0.398204 | + | 0.289312i | ||||
\(427\) | −0.332696 | − | 1.02393i | −0.0161003 | − | 0.0495516i | ||||
\(428\) | 2.66211 | 0.128678 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 11.8648 | 0.572173 | ||||||||
\(431\) | −2.33060 | − | 7.17284i | −0.112261 | − | 0.345503i | 0.879105 | − | 0.476628i | \(-0.158141\pi\) |
−0.991366 | + | 0.131125i | \(0.958141\pi\) | |||||||
\(432\) | −9.59634 | − | 6.97215i | −0.461704 | − | 0.335448i | ||||
\(433\) | 26.0193 | − | 18.9041i | 1.25041 | − | 0.908474i | 0.252161 | − | 0.967685i | \(-0.418859\pi\) |
0.998245 | + | 0.0592114i | \(0.0188586\pi\) | |||||||
\(434\) | 0.271523 | − | 0.835662i | 0.0130335 | − | 0.0401131i | ||||
\(435\) | 24.3451 | − | 74.9264i | 1.16726 | − | 3.59245i | ||||
\(436\) | −2.37712 | + | 1.72708i | −0.113844 | + | 0.0827122i | ||||
\(437\) | −1.05977 | − | 0.769968i | −0.0506957 | − | 0.0368326i | ||||
\(438\) | −1.20732 | − | 3.71576i | −0.0576882 | − | 0.177546i | ||||
\(439\) | 4.66725 | 0.222756 | 0.111378 | − | 0.993778i | \(-0.464474\pi\) | ||||
0.111378 | + | 0.993778i | \(0.464474\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.17284 | 0.246326 | ||||||||
\(442\) | 1.37164 | + | 4.22146i | 0.0652421 | + | 0.200794i | ||||
\(443\) | −13.9775 | − | 10.1553i | −0.664091 | − | 0.482491i | 0.203951 | − | 0.978981i | \(-0.434622\pi\) |
−0.868042 | + | 0.496490i | \(0.834622\pi\) | |||||||
\(444\) | −17.6387 | + | 12.8153i | −0.837097 | + | 0.608187i | ||||
\(445\) | −4.74005 | + | 14.5884i | −0.224700 | + | 0.691555i | ||||
\(446\) | −5.99095 | + | 18.4383i | −0.283680 | + | 0.873077i | ||||
\(447\) | 7.27732 | − | 5.28728i | 0.344206 | − | 0.250080i | ||||
\(448\) | 6.71351 | + | 4.87765i | 0.317184 | + | 0.230447i | ||||
\(449\) | −5.17297 | − | 15.9208i | −0.244128 | − | 0.751347i | −0.995779 | − | 0.0917865i | \(-0.970742\pi\) |
0.751651 | − | 0.659561i | \(-0.229258\pi\) | |||||||
\(450\) | −40.0346 | −1.88725 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −8.07529 | −0.379829 | ||||||||
\(453\) | 2.53274 | + | 7.79498i | 0.118999 | + | 0.366240i | ||||
\(454\) | 11.3888 | + | 8.27447i | 0.534504 | + | 0.388340i | ||||
\(455\) | 5.75884 | − | 4.18404i | 0.269979 | − | 0.196151i | ||||
\(456\) | 4.40689 | − | 13.5630i | 0.206372 | − | 0.635146i | ||||
\(457\) | 6.70487 | − | 20.6355i | 0.313640 | − | 0.965286i | −0.662670 | − | 0.748912i | \(-0.730577\pi\) |
0.976310 | − | 0.216375i | \(-0.0694232\pi\) | |||||||
\(458\) | 4.12349 | − | 2.99589i | 0.192678 | − | 0.139989i | ||||
\(459\) | −9.71779 | − | 7.06039i | −0.453588 | − | 0.329551i | ||||
\(460\) | 0.653373 | + | 2.01087i | 0.0304637 | + | 0.0937575i | ||||
\(461\) | 6.07778 | 0.283070 | 0.141535 | − | 0.989933i | \(-0.454796\pi\) | ||||
0.141535 | + | 0.989933i | \(0.454796\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.14719 | −0.239210 | −0.119605 | − | 0.992822i | \(-0.538163\pi\) | ||||
−0.119605 | + | 0.992822i | \(0.538163\pi\) | |||||||
\(464\) | 4.70516 | + | 14.4810i | 0.218432 | + | 0.672264i | ||||
\(465\) | 6.30210 | + | 4.57874i | 0.292253 | + | 0.212334i | ||||
\(466\) | −21.5099 | + | 15.6279i | −0.996427 | + | 0.723947i | ||||
\(467\) | −1.21112 | + | 3.72745i | −0.0560441 | + | 0.172486i | −0.975160 | − | 0.221501i | \(-0.928904\pi\) |
0.919116 | + | 0.393987i | \(0.128904\pi\) | |||||||
\(468\) | −2.49548 | + | 7.68030i | −0.115354 | + | 0.355022i | ||||
\(469\) | 1.94418 | − | 1.41253i | 0.0897739 | − | 0.0652246i | ||||
\(470\) | 23.5772 | + | 17.1299i | 1.08754 | + | 0.790142i | ||||
\(471\) | 18.9843 | + | 58.4277i | 0.874752 | + | 2.69221i | ||||
\(472\) | −10.1327 | −0.466397 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 30.2096 | 1.38757 | ||||||||
\(475\) | −3.48281 | − | 10.7190i | −0.159802 | − | 0.491821i | ||||
\(476\) | 1.18577 | + | 0.861515i | 0.0543499 | + | 0.0394875i | ||||
\(477\) | −45.2910 | + | 32.9059i | −2.07373 | + | 1.50666i | ||||
\(478\) | 3.04376 | − | 9.36773i | 0.139218 | − | 0.428470i | ||||
\(479\) | 4.67015 | − | 14.3732i | 0.213385 | − | 0.656730i | −0.785880 | − | 0.618379i | \(-0.787790\pi\) |
0.999264 | − | 0.0383508i | \(-0.0122104\pi\) | |||||||
\(480\) | −32.1266 | + | 23.3413i | −1.46637 | + | 1.06538i | ||||
\(481\) | −16.7659 | − | 12.1811i | −0.764458 | − | 0.555411i | ||||
\(482\) | 6.52495 | + | 20.0817i | 0.297203 | + | 0.914698i | ||||
\(483\) | −2.30745 | −0.104993 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 22.3541 | 1.01505 | ||||||||
\(486\) | −4.21264 | − | 12.9652i | −0.191089 | − | 0.588112i | ||||
\(487\) | −20.2876 | − | 14.7398i | −0.919317 | − | 0.667923i | 0.0240370 | − | 0.999711i | \(-0.492348\pi\) |
−0.943354 | + | 0.331788i | \(0.892348\pi\) | |||||||
\(488\) | −2.67719 | + | 1.94509i | −0.121191 | + | 0.0880501i | ||||
\(489\) | 7.26391 | − | 22.3560i | 0.328485 | − | 1.01097i | ||||
\(490\) | −1.19024 | + | 3.66317i | −0.0537694 | + | 0.165485i | ||||
\(491\) | 30.1122 | − | 21.8778i | 1.35895 | − | 0.987332i | 0.360435 | − | 0.932784i | \(-0.382628\pi\) |
0.998511 | − | 0.0545479i | \(-0.0173718\pi\) | |||||||
\(492\) | −3.72721 | − | 2.70797i | −0.168035 | − | 0.122085i | ||||
\(493\) | 4.76471 | + | 14.6643i | 0.214592 | + | 0.660446i | ||||
\(494\) | 3.72536 | 0.167612 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.50554 | −0.0676006 | ||||||||
\(497\) | 0.985330 | + | 3.03253i | 0.0441981 | + | 0.136028i | ||||
\(498\) | −41.4201 | − | 30.0934i | −1.85608 | − | 1.34852i | ||||
\(499\) | 25.7375 | − | 18.6994i | 1.15217 | − | 0.837101i | 0.163403 | − | 0.986559i | \(-0.447753\pi\) |
0.988768 | + | 0.149458i | \(0.0477530\pi\) | |||||||
\(500\) | −1.57404 | + | 4.84441i | −0.0703934 | + | 0.216649i | ||||
\(501\) | −19.1779 | + | 59.0234i | −0.856804 | + | 2.63697i | ||||
\(502\) | −2.58487 | + | 1.87802i | −0.115369 | + | 0.0838201i | ||||
\(503\) | −15.5379 | − | 11.2889i | −0.692799 | − | 0.503348i | 0.184780 | − | 0.982780i | \(-0.440843\pi\) |
−0.877579 | + | 0.479432i | \(0.840843\pi\) | |||||||
\(504\) | −4.91323 | − | 15.1214i | −0.218853 | − | 0.673559i | ||||
\(505\) | 53.3788 | 2.37532 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 25.0370 | 1.11193 | ||||||||
\(508\) | 4.55587 | + | 14.0215i | 0.202134 | + | 0.622104i | ||||
\(509\) | −2.03507 | − | 1.47857i | −0.0902029 | − | 0.0655363i | 0.541770 | − | 0.840527i | \(-0.317754\pi\) |
−0.631973 | + | 0.774991i | \(0.717754\pi\) | |||||||
\(510\) | 17.2262 | − | 12.5156i | 0.762790 | − | 0.554200i | ||||
\(511\) | 0.378940 | − | 1.16626i | 0.0167633 | − | 0.0515922i | ||||
\(512\) | 5.99912 | − | 18.4634i | 0.265126 | − | 0.815974i | ||||
\(513\) | −8.15605 | + | 5.92572i | −0.360098 | + | 0.261627i | ||||
\(514\) | 20.2107 | + | 14.6839i | 0.891454 | + | 0.647679i | ||||
\(515\) | 9.51376 | + | 29.2803i | 0.419226 | + | 1.29025i | ||||
\(516\) | −6.67492 | −0.293847 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 11.2135 | 0.492693 | ||||||||
\(519\) | −7.10770 | − | 21.8753i | −0.311993 | − | 0.960217i | ||||
\(520\) | −17.7007 | − | 12.8603i | −0.776228 | − | 0.563962i | ||||
\(521\) | −12.0517 | + | 8.75610i | −0.527996 | + | 0.383612i | −0.819608 | − | 0.572925i | \(-0.805809\pi\) |
0.291612 | + | 0.956537i | \(0.405809\pi\) | |||||||
\(522\) | 14.2049 | − | 43.7181i | 0.621730 | − | 1.91349i | ||||
\(523\) | 3.06082 | − | 9.42024i | 0.133840 | − | 0.411918i | −0.861567 | − | 0.507643i | \(-0.830517\pi\) |
0.995408 | + | 0.0957248i | \(0.0305169\pi\) | |||||||
\(524\) | −3.13522 | + | 2.27787i | −0.136963 | + | 0.0995093i | ||||
\(525\) | −16.0614 | − | 11.6693i | −0.700977 | − | 0.509290i | ||||
\(526\) | 0.341188 | + | 1.05007i | 0.0148765 | + | 0.0457852i | ||||
\(527\) | −1.52459 | −0.0664122 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3485 | −0.971675 | ||||||||
\(530\) | −12.8813 | − | 39.6444i | −0.559526 | − | 1.72204i | ||||
\(531\) | 13.7962 | + | 10.0235i | 0.598702 | + | 0.434982i | ||||
\(532\) | 0.995209 | − | 0.723061i | 0.0431478 | − | 0.0313487i | ||||
\(533\) | 1.35322 | − | 4.16477i | 0.0586143 | − | 0.180396i | ||||
\(534\) | −4.36971 | + | 13.4486i | −0.189096 | + | 0.581977i | ||||
\(535\) | 9.82017 | − | 7.13477i | 0.424563 | − | 0.308463i | ||||
\(536\) | −5.97575 | − | 4.34164i | −0.258113 | − | 0.187530i | ||||
\(537\) | 3.19880 | + | 9.84488i | 0.138038 | + | 0.424838i | ||||
\(538\) | 8.01342 | 0.345483 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 16.2722 | 0.700245 | ||||||||
\(541\) | 6.80096 | + | 20.9312i | 0.292396 | + | 0.899903i | 0.984084 | + | 0.177706i | \(0.0568676\pi\) |
−0.691687 | + | 0.722197i | \(0.743132\pi\) | |||||||
\(542\) | 24.4919 | + | 17.7944i | 1.05202 | + | 0.764336i | ||||
\(543\) | 36.5842 | − | 26.5800i | 1.56998 | − | 1.14066i | ||||
\(544\) | 2.40168 | − | 7.39161i | 0.102971 | − | 0.316912i | ||||
\(545\) | −4.14010 | + | 12.7419i | −0.177342 | + | 0.545804i | ||||
\(546\) | 5.30891 | − | 3.85715i | 0.227200 | − | 0.165071i | ||||
\(547\) | −8.78938 | − | 6.38586i | −0.375807 | − | 0.273040i | 0.383808 | − | 0.923413i | \(-0.374612\pi\) |
−0.759615 | + | 0.650373i | \(0.774612\pi\) | |||||||
\(548\) | −2.13156 | − | 6.56026i | −0.0910557 | − | 0.280240i | ||||
\(549\) | 5.56922 | 0.237689 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.9410 | 0.551303 | ||||||||
\(552\) | 2.19165 | + | 6.74520i | 0.0932828 | + | 0.287095i | ||||
\(553\) | 7.67096 | + | 5.57328i | 0.326202 | + | 0.237000i | ||||
\(554\) | −18.9211 | + | 13.7470i | −0.803880 | + | 0.584053i | ||||
\(555\) | −30.7204 | + | 94.5476i | −1.30401 | + | 4.01332i | ||||
\(556\) | −3.04879 | + | 9.38322i | −0.129298 | + | 0.397937i | ||||
\(557\) | 27.1932 | − | 19.7570i | 1.15221 | − | 0.837130i | 0.163438 | − | 0.986554i | \(-0.447742\pi\) |
0.988773 | + | 0.149423i | \(0.0477418\pi\) | |||||||
\(558\) | 3.67715 | + | 2.67161i | 0.155666 | + | 0.113098i | ||||
\(559\) | −1.96059 | − | 6.03408i | −0.0829242 | − | 0.255214i | ||||
\(560\) | 6.59959 | 0.278884 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −31.3811 | −1.32373 | ||||||||
\(563\) | 0.634561 | + | 1.95298i | 0.0267436 | + | 0.0823082i | 0.963537 | − | 0.267573i | \(-0.0862218\pi\) |
−0.936794 | + | 0.349882i | \(0.886222\pi\) | |||||||
\(564\) | −13.2641 | − | 9.63693i | −0.558519 | − | 0.405788i | ||||
\(565\) | −29.7886 | + | 21.6427i | −1.25322 | + | 0.910515i | ||||
\(566\) | −9.02015 | + | 27.7612i | −0.379145 | + | 1.16689i | ||||
\(567\) | −0.692124 | + | 2.13014i | −0.0290665 | + | 0.0894575i | ||||
\(568\) | 7.92890 | − | 5.76068i | 0.332689 | − | 0.241713i | ||||
\(569\) | 2.64885 | + | 1.92450i | 0.111046 | + | 0.0806793i | 0.641922 | − | 0.766770i | \(-0.278137\pi\) |
−0.530877 | + | 0.847449i | \(0.678137\pi\) | |||||||
\(570\) | −5.52239 | − | 16.9962i | −0.231308 | − | 0.711891i | ||||
\(571\) | 43.8897 | 1.83673 | 0.918363 | − | 0.395738i | \(-0.129511\pi\) | ||||
0.918363 | + | 0.395738i | \(0.129511\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.22666 | −0.0512446 | ||||||||
\(574\) | 0.732217 | + | 2.25353i | 0.0305622 | + | 0.0940607i | ||||
\(575\) | 4.53465 | + | 3.29461i | 0.189108 | + | 0.137395i | ||||
\(576\) | −34.7279 | + | 25.2313i | −1.44700 | + | 1.05131i | ||||
\(577\) | −13.5629 | + | 41.7422i | −0.564630 | + | 1.73775i | 0.104418 | + | 0.994533i | \(0.466702\pi\) |
−0.669048 | + | 0.743219i | \(0.733298\pi\) | |||||||
\(578\) | 4.56684 | − | 14.0553i | 0.189955 | − | 0.584623i | ||||
\(579\) | 35.0968 | − | 25.4993i | 1.45857 | − | 1.05972i | ||||
\(580\) | −16.8985 | − | 12.2775i | −0.701673 | − | 0.509795i | ||||
\(581\) | −4.96572 | − | 15.2829i | −0.206013 | − | 0.634042i | ||||
\(582\) | 20.6076 | 0.854214 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −3.76915 | −0.155969 | ||||||||
\(585\) | 11.3786 | + | 35.0197i | 0.470447 | + | 1.44789i | ||||
\(586\) | 4.02471 | + | 2.92412i | 0.166259 | + | 0.120794i | ||||
\(587\) | −2.25850 | + | 1.64090i | −0.0932183 | + | 0.0677271i | −0.633418 | − | 0.773810i | \(-0.718349\pi\) |
0.540200 | + | 0.841537i | \(0.318349\pi\) | |||||||
\(588\) | 0.669603 | − | 2.06083i | 0.0276140 | − | 0.0849871i | ||||
\(589\) | −0.395410 | + | 1.21695i | −0.0162926 | + | 0.0501434i | ||||
\(590\) | −10.2726 | + | 7.46346i | −0.422915 | + | 0.307266i | ||||
\(591\) | 48.1259 | + | 34.9655i | 1.97963 | + | 1.43829i | ||||
\(592\) | −5.93732 | − | 18.2732i | −0.244022 | − | 0.751023i | ||||
\(593\) | −23.2526 | −0.954871 | −0.477435 | − | 0.878667i | \(-0.658434\pi\) | ||||
−0.477435 | + | 0.878667i | \(0.658434\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.68312 | 0.273981 | ||||||||
\(596\) | −0.736985 | − | 2.26821i | −0.0301881 | − | 0.0929093i | ||||
\(597\) | 19.5334 | + | 14.1919i | 0.799450 | + | 0.580835i | ||||
\(598\) | −1.49887 | + | 1.08900i | −0.0612935 | + | 0.0445324i | ||||
\(599\) | 3.23215 | − | 9.94753i | 0.132062 | − | 0.406445i | −0.863059 | − | 0.505102i | \(-0.831455\pi\) |
0.995121 | + | 0.0986573i | \(0.0314547\pi\) | |||||||
\(600\) | −18.8566 | + | 58.0347i | −0.769818 | + | 2.36926i | ||||
\(601\) | 18.0489 | − | 13.1133i | 0.736229 | − | 0.534902i | −0.155299 | − | 0.987868i | \(-0.549634\pi\) |
0.891528 | + | 0.452966i | \(0.149634\pi\) | |||||||
\(602\) | 2.77738 | + | 2.01789i | 0.113198 | + | 0.0822429i | ||||
\(603\) | 3.84141 | + | 11.8226i | 0.156434 | + | 0.481455i | ||||
\(604\) | 2.17306 | 0.0884204 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 49.2083 | 1.99895 | ||||||||
\(607\) | −5.86774 | − | 18.0591i | −0.238164 | − | 0.732994i | −0.996686 | − | 0.0813464i | \(-0.974078\pi\) |
0.758522 | − | 0.651648i | \(-0.225922\pi\) | |||||||
\(608\) | −5.27719 | − | 3.83410i | −0.214018 | − | 0.155493i | ||||
\(609\) | 18.4418 | − | 13.3987i | 0.747299 | − | 0.542944i | ||||
\(610\) | −1.28144 | + | 3.94387i | −0.0518840 | + | 0.159683i | ||||
\(611\) | 4.81572 | − | 14.8213i | 0.194823 | − | 0.599604i | ||||
\(612\) | −6.13382 | + | 4.45648i | −0.247945 | + | 0.180143i | ||||
\(613\) | 16.3111 | + | 11.8507i | 0.658801 | + | 0.478647i | 0.866258 | − | 0.499597i | \(-0.166519\pi\) |
−0.207457 | + | 0.978244i | \(0.566519\pi\) | |||||||
\(614\) | 4.43714 | + | 13.6561i | 0.179068 | + | 0.551116i | ||||
\(615\) | −21.0068 | −0.847077 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.03919 | 0.283387 | 0.141694 | − | 0.989911i | \(-0.454745\pi\) | ||||
0.141694 | + | 0.989911i | \(0.454745\pi\) | |||||||
\(618\) | 8.77046 | + | 26.9927i | 0.352799 | + | 1.08581i | ||||
\(619\) | 25.1467 | + | 18.2702i | 1.01073 | + | 0.734340i | 0.964363 | − | 0.264584i | \(-0.0852346\pi\) |
0.0463701 | + | 0.998924i | \(0.485235\pi\) | |||||||
\(620\) | 1.67089 | − | 1.21397i | 0.0671045 | − | 0.0487543i | ||||
\(621\) | 1.54933 | − | 4.76834i | 0.0621724 | − | 0.191347i | ||||
\(622\) | −9.23646 | + | 28.4269i | −0.370348 | + | 1.13982i | ||||
\(623\) | −3.59066 | + | 2.60877i | −0.143857 | + | 0.104518i | ||||
\(624\) | −9.09645 | − | 6.60896i | −0.364149 | − | 0.264570i | ||||
\(625\) | −3.55266 | − | 10.9340i | −0.142106 | − | 0.437358i | ||||
\(626\) | −3.99947 | −0.159851 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 16.2883 | 0.649973 | ||||||||
\(629\) | −6.01246 | − | 18.5045i | −0.239733 | − | 0.737821i | ||||
\(630\) | −16.1190 | − | 11.7111i | −0.642195 | − | 0.466582i | ||||
\(631\) | −17.7757 | + | 12.9148i | −0.707639 | + | 0.514130i | −0.882411 | − | 0.470479i | \(-0.844081\pi\) |
0.174772 | + | 0.984609i | \(0.444081\pi\) | |||||||
\(632\) | 9.00596 | − | 27.7175i | 0.358238 | − | 1.10254i | ||||
\(633\) | −8.70991 | + | 26.8063i | −0.346188 | + | 1.06546i | ||||
\(634\) | −15.2537 | + | 11.0825i | −0.605802 | + | 0.440141i | ||||
\(635\) | 54.3852 | + | 39.5132i | 2.15821 | + | 1.56803i | ||||
\(636\) | 7.24675 | + | 22.3032i | 0.287352 | + | 0.884379i | ||||
\(637\) | 2.05965 | 0.0816064 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −16.4941 | −0.652496 | ||||||||
\(640\) | −1.29215 | − | 3.97683i | −0.0510768 | − | 0.157198i | ||||
\(641\) | 10.7526 | + | 7.81222i | 0.424702 | + | 0.308564i | 0.779527 | − | 0.626369i | \(-0.215460\pi\) |
−0.354825 | + | 0.934933i | \(0.615460\pi\) | |||||||
\(642\) | 9.05293 | − | 6.57734i | 0.357291 | − | 0.259587i | ||||
\(643\) | 4.53958 | − | 13.9714i | 0.179024 | − | 0.550978i | −0.820771 | − | 0.571258i | \(-0.806456\pi\) |
0.999794 | + | 0.0202797i | \(0.00645568\pi\) | |||||||
\(644\) | −0.189050 | + | 0.581837i | −0.00744963 | + | 0.0229276i | ||||
\(645\) | −24.6229 | + | 17.8896i | −0.969524 | + | 0.704401i | ||||
\(646\) | 2.82962 | + | 2.05584i | 0.111330 | + | 0.0808859i | ||||
\(647\) | −1.89898 | − | 5.84446i | −0.0746566 | − | 0.229770i | 0.906764 | − | 0.421639i | \(-0.138545\pi\) |
−0.981420 | + | 0.191869i | \(0.938545\pi\) | |||||||
\(648\) | 6.88426 | 0.270439 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −15.9404 | −0.625236 | ||||||||
\(651\) | 0.696508 | + | 2.14363i | 0.0272983 | + | 0.0840156i | ||||
\(652\) | −5.04206 | − | 3.66327i | −0.197462 | − | 0.143465i | ||||
\(653\) | 32.9020 | − | 23.9047i | 1.28755 | − | 0.935463i | 0.287802 | − | 0.957690i | \(-0.407076\pi\) |
0.999753 | + | 0.0222266i | \(0.00707554\pi\) | |||||||
\(654\) | −3.81664 | + | 11.7464i | −0.149242 | + | 0.459321i | ||||
\(655\) | −5.46044 | + | 16.8055i | −0.213357 | + | 0.656646i | ||||
\(656\) | 3.28460 | − | 2.38640i | 0.128242 | − | 0.0931732i | ||||
\(657\) | 5.13186 | + | 3.72852i | 0.200213 | + | 0.145463i | ||||
\(658\) | 2.60576 | + | 8.01970i | 0.101583 | + | 0.312640i | ||||
\(659\) | −18.0090 | −0.701531 | −0.350765 | − | 0.936463i | \(-0.614079\pi\) | ||||
−0.350765 | + | 0.936463i | \(0.614079\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.1420 | −0.666745 | −0.333373 | − | 0.942795i | \(-0.608187\pi\) | ||||
−0.333373 | + | 0.942795i | \(0.608187\pi\) | |||||||
\(662\) | 0.426444 | + | 1.31246i | 0.0165742 | + | 0.0510102i | ||||
\(663\) | −9.21157 | − | 6.69260i | −0.357748 | − | 0.259919i | ||||
\(664\) | −39.9588 | + | 29.0318i | −1.55070 | + | 1.12665i | ||||
\(665\) | 1.73330 | − | 5.33455i | 0.0672145 | − | 0.206865i | ||||
\(666\) | −17.9247 | + | 55.1667i | −0.694570 | + | 2.13767i | ||||
\(667\) | −5.20670 | + | 3.78289i | −0.201604 | + | 0.146474i | ||||
\(668\) | 13.3118 | + | 9.67161i | 0.515050 | + | 0.374206i | ||||
\(669\) | −15.3679 | − | 47.2976i | −0.594159 | − | 1.82863i | ||||
\(670\) | −9.25613 | −0.357596 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −11.4901 | −0.443240 | ||||||||
\(673\) | 7.16690 | + | 22.0574i | 0.276264 | + | 0.850252i | 0.988882 | + | 0.148700i | \(0.0475090\pi\) |
−0.712619 | + | 0.701552i | \(0.752491\pi\) | |||||||
\(674\) | 18.4658 | + | 13.4162i | 0.711274 | + | 0.516771i | ||||
\(675\) | 34.8989 | − | 25.3555i | 1.34326 | − | 0.975934i | ||||
\(676\) | 2.05129 | − | 6.31323i | 0.0788959 | − | 0.242817i | ||||
\(677\) | 8.51976 | − | 26.2211i | 0.327441 | − | 1.00776i | −0.642886 | − | 0.765962i | \(-0.722263\pi\) |
0.970327 | − | 0.241798i | \(-0.0777371\pi\) | |||||||
\(678\) | −27.4613 | + | 19.9518i | −1.05464 | + | 0.766243i | ||||
\(679\) | 5.23278 | + | 3.80184i | 0.200816 | + | 0.145901i | ||||
\(680\) | −6.34771 | − | 19.5362i | −0.243424 | − | 0.749181i | ||||
\(681\) | −36.1111 | −1.38378 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.9351 | 0.839322 | 0.419661 | − | 0.907681i | \(-0.362149\pi\) | ||||
0.419661 | + | 0.907681i | \(0.362149\pi\) | |||||||
\(684\) | 1.96638 | + | 6.05190i | 0.0751865 | + | 0.231400i | ||||
\(685\) | −25.4453 | − | 18.4871i | −0.972214 | − | 0.706355i | ||||
\(686\) | −0.901622 | + | 0.655067i | −0.0344241 | + | 0.0250106i | ||||
\(687\) | −4.04026 | + | 12.4346i | −0.154146 | + | 0.474411i | ||||
\(688\) | 1.81772 | − | 5.59437i | 0.0692999 | − | 0.213283i | ||||
\(689\) | −18.0334 | + | 13.1020i | −0.687017 | + | 0.499147i | ||||
\(690\) | 7.19020 | + | 5.22399i | 0.273726 | + | 0.198874i | ||||
\(691\) | −7.93142 | − | 24.4104i | −0.301726 | − | 0.928616i | −0.980879 | − | 0.194619i | \(-0.937653\pi\) |
0.679153 | − | 0.733996i | \(-0.262347\pi\) | |||||||
\(692\) | −6.09830 | −0.231823 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 30.3913 | 1.15364 | ||||||||
\(695\) | 13.9015 | + | 42.7845i | 0.527315 | + | 1.62291i | ||||
\(696\) | −56.6837 | − | 41.1832i | −2.14859 | − | 1.56104i | ||||
\(697\) | 3.32616 | − | 2.41660i | 0.125987 | − | 0.0915353i | ||||
\(698\) | 2.74972 | − | 8.46277i | 0.104078 | − | 0.320321i | ||||
\(699\) | 21.0757 | − | 64.8644i | 0.797157 | − | 2.45340i | ||||
\(700\) | −4.25839 | + | 3.09390i | −0.160952 | + | 0.116939i | ||||
\(701\) | −14.8968 | − | 10.8232i | −0.562644 | − | 0.408785i | 0.269781 | − | 0.962922i | \(-0.413049\pi\) |
−0.832426 | + | 0.554137i | \(0.813049\pi\) | |||||||
\(702\) | 4.40614 | + | 13.5607i | 0.166299 | + | 0.511815i | ||||
\(703\) | −16.3298 | −0.615892 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −74.7575 | −2.81553 | ||||||||
\(706\) | −2.04385 | − | 6.29033i | −0.0769214 | − | 0.236740i | ||||
\(707\) | 12.4952 | + | 9.07828i | 0.469930 | + | 0.341424i | ||||
\(708\) | 5.77915 | − | 4.19880i | 0.217194 | − | 0.157801i | ||||
\(709\) | 7.31198 | − | 22.5039i | 0.274607 | − | 0.845153i | −0.714716 | − | 0.699415i | \(-0.753444\pi\) |
0.989323 | − | 0.145739i | \(-0.0465559\pi\) | |||||||
\(710\) | 3.79518 | − | 11.6804i | 0.142431 | − | 0.438356i | ||||
\(711\) | −39.6806 | + | 28.8297i | −1.48814 | + | 1.08120i | ||||
\(712\) | 11.0365 | + | 8.01847i | 0.413609 | + | 0.300505i | ||||
\(713\) | −0.196647 | − | 0.605216i | −0.00736447 | − | 0.0226655i | ||||
\(714\) | 6.16097 | 0.230569 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.74452 | 0.102568 | ||||||||
\(717\) | 7.80782 | + | 24.0300i | 0.291589 | + | 0.897417i | ||||
\(718\) | −25.6244 | − | 18.6172i | −0.956293 | − | 0.694787i | ||||
\(719\) | −8.99808 | + | 6.53749i | −0.335572 | + | 0.243807i | −0.742791 | − | 0.669523i | \(-0.766498\pi\) |
0.407219 | + | 0.913330i | \(0.366498\pi\) | |||||||
\(720\) | −10.5494 | + | 32.4678i | −0.393154 | + | 1.21000i | ||||
\(721\) | −2.75276 | + | 8.47213i | −0.102518 | + | 0.315519i | ||||
\(722\) | −14.7560 | + | 10.7208i | −0.549160 | + | 0.398988i | ||||
\(723\) | −43.8200 | − | 31.8371i | −1.62968 | − | 1.18403i | ||||
\(724\) | −3.70493 | − | 11.4026i | −0.137693 | − | 0.423775i | ||||
\(725\) | −55.3730 | −2.05650 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 42.4803 | 1.57551 | 0.787753 | − | 0.615991i | \(-0.211244\pi\) | ||||
0.787753 | + | 0.615991i | \(0.211244\pi\) | |||||||
\(728\) | −1.95628 | − | 6.02083i | −0.0725047 | − | 0.223147i | ||||
\(729\) | 33.7270 | + | 24.5041i | 1.24915 | + | 0.907561i | ||||
\(730\) | −3.82117 | + | 2.77624i | −0.141428 | + | 0.102753i | ||||
\(731\) | 1.84072 | − | 5.66517i | 0.0680817 | − | 0.209534i | ||||
\(732\) | 0.720913 | − | 2.21874i | 0.0266457 | − | 0.0820071i | ||||
\(733\) | 17.9508 | − | 13.0420i | 0.663029 | − | 0.481719i | −0.204656 | − | 0.978834i | \(-0.565607\pi\) |
0.867684 | + | 0.497116i | \(0.165607\pi\) | |||||||
\(734\) | −27.4106 | − | 19.9150i | −1.01174 | − | 0.735075i | ||||
\(735\) | −3.05318 | − | 9.39672i | −0.112618 | − | 0.346603i | ||||
\(736\) | 3.24402 | 0.119576 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −12.2571 | −0.451189 | ||||||||
\(739\) | −9.09997 | − | 28.0068i | −0.334748 | − | 1.03025i | −0.966846 | − | 0.255359i | \(-0.917806\pi\) |
0.632098 | − | 0.774888i | \(-0.282194\pi\) | |||||||
\(740\) | 21.3238 | + | 15.4926i | 0.783878 | + | 0.569521i | ||||
\(741\) | −7.73118 | + | 5.61703i | −0.284012 | + | 0.206347i | ||||
\(742\) | 3.72713 | − | 11.4709i | 0.136827 | − | 0.421111i | ||||
\(743\) | −5.22421 | + | 16.0785i | −0.191658 | + | 0.589862i | 0.808342 | + | 0.588714i | \(0.200365\pi\) |
−0.999999 | + | 0.00114815i | \(0.999635\pi\) | |||||||
\(744\) | 5.60476 | − | 4.07210i | 0.205481 | − | 0.149290i | ||||
\(745\) | −8.79769 | − | 6.39190i | −0.322322 | − | 0.234181i | ||||
\(746\) | 4.96697 | + | 15.2868i | 0.181854 | + | 0.559688i | ||||
\(747\) | 83.1244 | 3.04136 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.51219 | 0.128333 | ||||||||
\(750\) | 6.61640 | + | 20.3632i | 0.241597 | + | 0.743558i | ||||
\(751\) | 1.25516 | + | 0.911929i | 0.0458015 | + | 0.0332767i | 0.610450 | − | 0.792054i | \(-0.290988\pi\) |
−0.564649 | + | 0.825331i | \(0.690988\pi\) | |||||||
\(752\) | 11.6890 | − | 8.49253i | 0.426253 | − | 0.309691i | ||||
\(753\) | 2.53270 | − | 7.79484i | 0.0922966 | − | 0.284060i | ||||
\(754\) | 5.65591 | − | 17.4071i | 0.205976 | − | 0.633929i | ||||
\(755\) | 8.01610 | − | 5.82404i | 0.291736 | − | 0.211958i | ||||
\(756\) | 3.80909 | + | 2.76746i | 0.138535 | + | 0.100652i | ||||
\(757\) | 3.87713 | + | 11.9326i | 0.140917 | + | 0.433697i | 0.996463 | − | 0.0840286i | \(-0.0267787\pi\) |
−0.855547 | + | 0.517726i | \(0.826779\pi\) | |||||||
\(758\) | 24.9721 | 0.907027 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −17.2404 | −0.625375 | ||||||||
\(761\) | 2.79177 | + | 8.59218i | 0.101202 | + | 0.311466i | 0.988820 | − | 0.149113i | \(-0.0476417\pi\) |
−0.887619 | + | 0.460579i | \(0.847642\pi\) | |||||||
\(762\) | 50.1362 | + | 36.4260i | 1.81624 | + | 1.31958i | ||||
\(763\) | −3.13619 | + | 2.27858i | −0.113538 | + | 0.0824901i | ||||
\(764\) | −0.100501 | + | 0.309310i | −0.00363600 | + | 0.0111904i | ||||
\(765\) | −10.6829 | + | 32.8787i | −0.386242 | + | 1.18873i | ||||
\(766\) | 30.3653 | − | 22.0617i | 1.09714 | − | 0.797122i | ||||
\(767\) | 5.49317 | + | 3.99102i | 0.198347 | + | 0.144107i | ||||
\(768\) | 13.4707 | + | 41.4587i | 0.486083 | + | 1.49601i | ||||
\(769\) | 16.1383 | 0.581963 | 0.290981 | − | 0.956729i | \(-0.406018\pi\) | ||||
0.290981 | + | 0.956729i | \(0.406018\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −64.0829 | −2.30789 | ||||||||
\(772\) | −3.55431 | − | 10.9390i | −0.127922 | − | 0.393704i | ||||
\(773\) | 14.8968 | + | 10.8231i | 0.535800 | + | 0.389282i | 0.822523 | − | 0.568732i | \(-0.192566\pi\) |
−0.286723 | + | 0.958014i | \(0.592566\pi\) | |||||||
\(774\) | −14.3670 | + | 10.4382i | −0.516410 | + | 0.375193i | ||||
\(775\) | 1.69192 | − | 5.20719i | 0.0607755 | − | 0.187048i | ||||
\(776\) | 6.14345 | − | 18.9076i | 0.220537 | − | 0.678744i | ||||
\(777\) | −23.2712 | + | 16.9075i | −0.834849 | + | 0.606553i | ||||
\(778\) | 2.18899 | + | 1.59039i | 0.0784789 | + | 0.0570183i | ||||
\(779\) | −1.06630 | − | 3.28174i | −0.0382043 | − | 0.117581i | ||||
\(780\) | 15.4246 | 0.552288 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −1.73944 | −0.0622022 | ||||||||
\(783\) | 15.3058 | + | 47.1064i | 0.546984 | + | 1.68344i | ||||
\(784\) | 1.54487 | + | 1.12241i | 0.0551739 | + | 0.0400861i | ||||
\(785\) | 60.0852 | − | 43.6544i | 2.14453 | − | 1.55809i | ||||
\(786\) | −5.03382 | + | 15.4925i | −0.179550 | + | 0.552599i | ||||
\(787\) | −14.5198 | + | 44.6873i | −0.517575 | + | 1.59293i | 0.260973 | + | 0.965346i | \(0.415957\pi\) |
−0.778548 | + | 0.627585i | \(0.784043\pi\) | |||||||
\(788\) | 12.7597 | − | 9.27048i | 0.454546 | − | 0.330247i | ||||
\(789\) | −2.29134 | − | 1.66475i | −0.0815737 | − | 0.0592668i | ||||
\(790\) | −11.2856 | − | 34.7335i | −0.401524 | − | 1.23576i | ||||
\(791\) | −10.6539 | −0.378810 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.21748 | 0.0787450 | ||||||||
\(794\) | 2.03085 | + | 6.25031i | 0.0720722 | + | 0.221815i | ||||
\(795\) | 86.5074 | + | 62.8513i | 3.06810 | + | 2.22911i | ||||
\(796\) | 5.17894 | − | 3.76272i | 0.183563 | − | 0.133366i | ||||
\(797\) | −0.965537 | + | 2.97162i | −0.0342011 | + | 0.105260i | −0.966700 | − | 0.255913i | \(-0.917624\pi\) |
0.932499 | + | 0.361173i | \(0.117624\pi\) | |||||||
\(798\) | 1.59788 | − | 4.91776i | 0.0565643 | − | 0.174087i | ||||
\(799\) | 11.8369 | − | 8.60001i | 0.418759 | − | 0.304246i | ||||
\(800\) | 22.5805 | + | 16.4057i | 0.798342 | + | 0.580029i | ||||
\(801\) | −7.09461 | − | 21.8350i | −0.250676 | − | 0.771500i | ||||
\(802\) | −12.5261 | −0.442314 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 5.20732 | 0.183648 | ||||||||
\(805\) | 0.862010 | + | 2.65299i | 0.0303819 | + | 0.0935058i | ||||
\(806\) | 1.46412 | + | 1.06374i | 0.0515714 | + | 0.0374688i | ||||
\(807\) | −16.6301 | + | 12.0825i | −0.585408 | + | 0.425323i | ||||
\(808\) | 14.6698 | − | 45.1489i | 0.516081 | − | 1.58833i | ||||
\(809\) | 10.1128 | − | 31.1240i | 0.355547 | − | 1.09426i | −0.600145 | − | 0.799891i | \(-0.704891\pi\) |
0.955692 | − | 0.294369i | \(-0.0951094\pi\) | |||||||
\(810\) | 6.97927 | − | 5.07074i | 0.245227 | − | 0.178167i | ||||
\(811\) | 26.4236 | + | 19.1978i | 0.927856 | + | 0.674127i | 0.945467 | − | 0.325718i | \(-0.105606\pi\) |
−0.0176106 | + | 0.999845i | \(0.505606\pi\) | |||||||
\(812\) | −1.86763 | − | 5.74796i | −0.0655408 | − | 0.201714i | ||||
\(813\) | −77.6578 | −2.72358 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −28.4174 | −0.995419 | ||||||||
\(816\) | −3.26211 | − | 10.0397i | −0.114197 | − | 0.351461i | ||||
\(817\) | −4.04461 | − | 2.93858i | −0.141503 | − | 0.102808i | ||||
\(818\) | −26.4485 | + | 19.2160i | −0.924751 | + | 0.671871i | ||||
\(819\) | −3.29235 | + | 10.1328i | −0.115044 | + | 0.354069i | ||||
\(820\) | −1.72110 | + | 5.29699i | −0.0601033 | + | 0.184979i | ||||
\(821\) | −6.01215 | + | 4.36808i | −0.209825 | + | 0.152447i | −0.687735 | − | 0.725962i | \(-0.741395\pi\) |
0.477909 | + | 0.878409i | \(0.341395\pi\) | |||||||
\(822\) | −23.4573 | − | 17.0427i | −0.818166 | − | 0.594432i | ||||
\(823\) | 2.02674 | + | 6.23766i | 0.0706477 | + | 0.217431i | 0.980146 | − | 0.198276i | \(-0.0635342\pi\) |
−0.909499 | + | 0.415707i | \(0.863534\pi\) | |||||||
\(824\) | 27.3805 | 0.953846 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.67399 | −0.127835 | ||||||||
\(827\) | −7.37124 | − | 22.6863i | −0.256323 | − | 0.788881i | −0.993566 | − | 0.113254i | \(-0.963873\pi\) |
0.737243 | − | 0.675628i | \(-0.236127\pi\) | |||||||
\(828\) | −2.56025 | − | 1.86013i | −0.0889748 | − | 0.0646439i | ||||
\(829\) | 21.1502 | − | 15.3666i | 0.734578 | − | 0.533702i | −0.156430 | − | 0.987689i | \(-0.549999\pi\) |
0.891008 | + | 0.453987i | \(0.149999\pi\) | |||||||
\(830\) | −19.1264 | + | 58.8649i | −0.663886 | + | 2.04323i | ||||
\(831\) | 18.5392 | − | 57.0577i | 0.643117 | − | 1.97931i | ||||
\(832\) | −13.8275 | + | 10.0463i | −0.479383 | + | 0.348292i | ||||
\(833\) | 1.56442 | + | 1.13662i | 0.0542039 | + | 0.0393815i | ||||
\(834\) | 12.8154 | + | 39.4418i | 0.443762 | + | 1.36576i | ||||
\(835\) | 75.0265 | 2.59640 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.89747 | −0.169281 | ||||||||
\(838\) | 6.98622 | + | 21.5014i | 0.241335 | + | 0.742752i | ||||
\(839\) | −27.7404 | − | 20.1545i | −0.957703 | − | 0.695812i | −0.00508714 | − | 0.999987i | \(-0.501619\pi\) |
−0.952616 | + | 0.304175i | \(0.901619\pi\) | |||||||
\(840\) | −24.5688 | + | 17.8503i | −0.847703 | + | 0.615892i | ||||
\(841\) | 10.6857 | − | 32.8871i | 0.368471 | − | 1.13404i | ||||
\(842\) | 1.05384 | − | 3.24339i | 0.0363177 | − | 0.111774i | ||||
\(843\) | 65.1247 | − | 47.3159i | 2.24301 | − | 1.62965i | ||||
\(844\) | 6.04576 | + | 4.39250i | 0.208104 | + | 0.151196i | ||||
\(845\) | −9.35325 | − | 28.7863i | −0.321761 | − | 0.990280i | ||||
\(846\) | −43.6195 | −1.49967 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −20.6661 | −0.709678 | ||||||||
\(849\) | −23.1384 | − | 71.2126i | −0.794108 | − | 2.44401i | ||||
\(850\) | −12.1076 | − | 8.79672i | −0.415289 | − | 0.301725i | ||||
\(851\) | 6.57020 | − | 4.77353i | 0.225223 | − | 0.163634i | ||||
\(852\) | −2.13509 | + | 6.57114i | −0.0731471 | + | 0.225124i | ||||
\(853\) | −6.60808 | + | 20.3376i | −0.226256 | + | 0.696345i | 0.771905 | + | 0.635737i | \(0.219304\pi\) |
−0.998162 | + | 0.0606079i | \(0.980696\pi\) | |||||||
\(854\) | −0.970711 | + | 0.705263i | −0.0332171 | + | 0.0241336i | ||||
\(855\) | 23.4735 | + | 17.0545i | 0.802777 | + | 0.583252i | ||||
\(856\) | −3.33592 | − | 10.2669i | −0.114020 | − | 0.350916i | ||||
\(857\) | −42.8697 | −1.46440 | −0.732200 | − | 0.681090i | \(-0.761506\pi\) | ||||
−0.732200 | + | 0.681090i | \(0.761506\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30.3915 | −1.03695 | −0.518473 | − | 0.855094i | \(-0.673499\pi\) | ||||
−0.518473 | + | 0.855094i | \(0.673499\pi\) | |||||||
\(860\) | 2.49359 | + | 7.67449i | 0.0850308 | + | 0.261698i | ||||
\(861\) | −4.91739 | − | 3.57269i | −0.167584 | − | 0.121757i | ||||
\(862\) | −6.80001 | + | 4.94049i | −0.231609 | + | 0.168274i | ||||
\(863\) | 3.65209 | − | 11.2400i | 0.124319 | − | 0.382614i | −0.869458 | − | 0.494008i | \(-0.835532\pi\) |
0.993776 | + | 0.111394i | \(0.0355315\pi\) | |||||||
\(864\) | 7.71496 | − | 23.7442i | 0.262468 | − | 0.807794i | ||||
\(865\) | −22.4958 | + | 16.3442i | −0.764880 | + | 0.555718i | ||||
\(866\) | −28.9976 | − | 21.0680i | −0.985379 | − | 0.715920i | ||||
\(867\) | 11.7148 | + | 36.0545i | 0.397856 | + | 1.22447i | ||||
\(868\) | 0.597594 | 0.0202837 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −87.8003 | −2.97671 | ||||||||
\(871\) | 1.52952 | + | 4.70738i | 0.0518258 | + | 0.159503i | ||||
\(872\) | 9.63959 | + | 7.00357i | 0.326438 | + | 0.237171i | ||||
\(873\) | −27.0683 | + | 19.6663i | −0.916124 | + | 0.665603i | ||||
\(874\) | −0.451132 | + | 1.38844i | −0.0152598 | + | 0.0469647i | ||||
\(875\) | −2.07667 | + | 6.39134i | −0.0702044 | + | 0.216067i | ||||
\(876\) | 2.14972 | − | 1.56186i | 0.0726322 | − | 0.0527703i | ||||
\(877\) | −7.44690 | − | 5.41049i | −0.251464 | − | 0.182699i | 0.454911 | − | 0.890537i | \(-0.349671\pi\) |
−0.706375 | + | 0.707837i | \(0.749671\pi\) | |||||||
\(878\) | −1.60735 | − | 4.94692i | −0.0542454 | − | 0.166950i | ||||
\(879\) | −12.7613 | −0.430429 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −41.9030 | −1.41175 | −0.705874 | − | 0.708338i | \(-0.749445\pi\) | ||||
−0.705874 | + | 0.708338i | \(0.749445\pi\) | |||||||
\(882\) | −1.78147 | − | 5.48280i | −0.0599852 | − | 0.184616i | ||||
\(883\) | 12.9830 | + | 9.43269i | 0.436912 | + | 0.317435i | 0.784407 | − | 0.620247i | \(-0.212968\pi\) |
−0.347495 | + | 0.937682i | \(0.612968\pi\) | |||||||
\(884\) | −2.44228 | + | 1.77442i | −0.0821429 | + | 0.0596803i | ||||
\(885\) | 10.0652 | − | 30.9776i | 0.338339 | − | 1.04130i | ||||
\(886\) | −5.95006 | + | 18.3124i | −0.199896 | + | 0.615217i | ||||
\(887\) | −27.3839 | + | 19.8956i | −0.919461 | + | 0.668027i | −0.943390 | − | 0.331686i | \(-0.892382\pi\) |
0.0239289 | + | 0.999714i | \(0.492382\pi\) | |||||||
\(888\) | 71.5277 | + | 51.9679i | 2.40031 | + | 1.74393i | ||||
\(889\) | 6.01066 | + | 18.4989i | 0.201591 | + | 0.620433i | ||||
\(890\) | 17.0949 | 0.573024 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −13.1855 | −0.441482 | ||||||||
\(893\) | −3.79468 | − | 11.6788i | −0.126984 | − | 0.390817i | ||||
\(894\) | −8.11033 | − | 5.89250i | −0.271250 | − | 0.197075i | ||||
\(895\) | 10.1242 | − | 7.35563i | 0.338413 | − | 0.245872i | ||||
\(896\) | 0.373878 | − | 1.15068i | 0.0124904 | − | 0.0384414i | ||||
\(897\) | 1.46862 | − | 4.51995i | 0.0490358 | − | 0.150917i | ||||
\(898\) | −15.0932 | + | 10.9659i | −0.503668 | + | 0.365936i | ||||
\(899\) | 5.08597 | + | 3.69517i | 0.169627 | + | 0.123241i | ||||
\(900\) | −8.41394 | − | 25.8955i | −0.280465 | − | 0.863182i | ||||
\(901\) | −20.9277 | −0.697202 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.80638 | −0.293058 | ||||||||
\(904\) | 10.1192 | + | 31.1438i | 0.336560 | + | 1.03583i | ||||
\(905\) | −44.2273 | − | 32.1330i | −1.47016 | − | 1.06814i | ||||
\(906\) | 7.38981 | − | 5.36901i | 0.245510 | − | 0.178373i | ||||
\(907\) | −13.6281 | + | 41.9429i | −0.452512 | + | 1.39269i | 0.421518 | + | 0.906820i | \(0.361497\pi\) |
−0.874031 | + | 0.485870i | \(0.838503\pi\) | |||||||
\(908\) | −2.95859 | + | 9.10562i | −0.0981844 | + | 0.302181i | ||||
\(909\) | −64.6356 | + | 46.9605i | −2.14383 | + | 1.55758i | ||||
\(910\) | −6.41804 | − | 4.66298i | −0.212756 | − | 0.154576i | ||||
\(911\) | 15.3197 | + | 47.1492i | 0.507565 | + | 1.56212i | 0.796416 | + | 0.604750i | \(0.206727\pi\) |
−0.288851 | + | 0.957374i | \(0.593273\pi\) | |||||||
\(912\) | −8.85988 | −0.293380 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −24.1810 | −0.799837 | ||||||||
\(915\) | −3.28714 | − | 10.1168i | −0.108669 | − | 0.334450i | ||||
\(916\) | 2.80445 | + | 2.03755i | 0.0926615 | + | 0.0673225i | ||||
\(917\) | −4.13637 | + | 3.00525i | −0.136595 | + | 0.0992421i | ||||
\(918\) | −4.13675 | + | 12.7316i | −0.136533 | + | 0.420206i | ||||
\(919\) | 12.6056 | − | 38.7961i | 0.415821 | − | 1.27977i | −0.495693 | − | 0.868498i | \(-0.665086\pi\) |
0.911514 | − | 0.411268i | \(-0.134914\pi\) | |||||||
\(920\) | 6.93655 | − | 5.03970i | 0.228691 | − | 0.166154i | ||||
\(921\) | −29.7988 | − | 21.6501i | −0.981902 | − | 0.713394i | ||||
\(922\) | −2.09312 | − | 6.44197i | −0.0689333 | − | 0.212155i | ||||
\(923\) | −6.56740 | −0.216169 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 69.8737 | 2.29743 | ||||||||
\(926\) | 1.77264 | + | 5.45561i | 0.0582525 | + | 0.179283i | ||||
\(927\) | −37.2798 | − | 27.0853i | −1.22443 | − | 0.889599i | ||||
\(928\) | −25.9271 | + | 18.8371i | −0.851097 | + | 0.618359i | ||||
\(929\) | 12.7911 | − | 39.3670i | 0.419663 | − | 1.29159i | −0.488350 | − | 0.872648i | \(-0.662401\pi\) |
0.908013 | − | 0.418942i | \(-0.137599\pi\) | |||||||
\(930\) | 2.68273 | − | 8.25659i | 0.0879702 | − | 0.270744i | ||||
\(931\) | 1.31300 | − | 0.953952i | 0.0430319 | − | 0.0312645i | ||||
\(932\) | −14.6292 | − | 10.6287i | −0.479195 | − | 0.348156i | ||||
\(933\) | −23.6933 | − | 72.9204i | −0.775683 | − | 2.38731i | ||||
\(934\) | 4.36790 | 0.142922 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 32.7476 | 1.07039 | ||||||||
\(937\) | −0.493327 | − | 1.51831i | −0.0161163 | − | 0.0496009i | 0.942675 | − | 0.333712i | \(-0.108301\pi\) |
−0.958791 | + | 0.284111i | \(0.908301\pi\) | |||||||
\(938\) | −2.16672 | − | 1.57422i | −0.0707461 | − | 0.0514000i | ||||
\(939\) | 8.30003 | − | 6.03032i | 0.270861 | − | 0.196792i | ||||
\(940\) | −6.12490 | + | 18.8505i | −0.199772 | + | 0.614836i | ||||
\(941\) | −2.19645 | + | 6.75998i | −0.0716023 | + | 0.220369i | −0.980453 | − | 0.196752i | \(-0.936961\pi\) |
0.908851 | + | 0.417121i | \(0.136961\pi\) | |||||||
\(942\) | 55.3908 | − | 40.2438i | 1.80473 | − | 1.31121i | ||||
\(943\) | 1.38834 | + | 1.00869i | 0.0452105 | + | 0.0328473i | ||||
\(944\) | 1.94530 | + | 5.98703i | 0.0633142 | + | 0.194861i | ||||
\(945\) | 21.4683 | 0.698364 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.45986 | −0.0799347 | −0.0399674 | − | 0.999201i | \(-0.512725\pi\) | ||||
−0.0399674 | + | 0.999201i | \(0.512725\pi\) | |||||||
\(948\) | 6.34906 | + | 19.5404i | 0.206208 | + | 0.634643i | ||||
\(949\) | 2.04334 | + | 1.48457i | 0.0663295 | + | 0.0481912i | ||||
\(950\) | −10.1618 | + | 7.38300i | −0.329693 | + | 0.239536i | ||||
\(951\) | 14.9458 | − | 45.9985i | 0.484651 | − | 1.49160i | ||||
\(952\) | 1.83668 | − | 5.65272i | 0.0595272 | − | 0.183206i | ||||
\(953\) | −23.1379 | + | 16.8107i | −0.749511 | + | 0.544551i | −0.895675 | − | 0.444709i | \(-0.853307\pi\) |
0.146164 | + | 0.989260i | \(0.453307\pi\) | |||||||
\(954\) | 50.4753 | + | 36.6725i | 1.63420 | + | 1.18732i | ||||
\(955\) | 0.458253 | + | 1.41036i | 0.0148287 | + | 0.0456381i | ||||
\(956\) | 6.69900 | 0.216661 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −16.8428 | −0.544168 | ||||||||
\(959\) | −2.81221 | − | 8.65511i | −0.0908111 | − | 0.279488i | ||||
\(960\) | 66.3315 | + | 48.1927i | 2.14084 | + | 1.55541i | ||||
\(961\) | 24.5766 | − | 17.8560i | 0.792795 | − | 0.575999i | ||||
\(962\) | −7.13703 | + | 21.9655i | −0.230107 | + | 0.708197i | ||||
\(963\) | −5.61422 | + | 17.2788i | −0.180916 | + | 0.556801i | ||||
\(964\) | −11.6181 | + | 8.44103i | −0.374193 | + | 0.271867i | ||||
\(965\) | −42.4292 | − | 30.8266i | −1.36584 | − | 0.992344i | ||||
\(966\) | 0.794662 | + | 2.44572i | 0.0255678 | + | 0.0786897i | ||||
\(967\) | 0.213338 | 0.00686047 | 0.00343024 | − | 0.999994i | \(-0.498908\pi\) | ||||
0.00343024 | + | 0.999994i | \(0.498908\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.97201 | −0.288223 | ||||||||
\(970\) | −7.69852 | − | 23.6936i | −0.247185 | − | 0.760756i | ||||
\(971\) | 0.670027 | + | 0.486803i | 0.0215022 | + | 0.0156222i | 0.598484 | − | 0.801134i | \(-0.295770\pi\) |
−0.576982 | + | 0.816757i | \(0.695770\pi\) | |||||||
\(972\) | 7.50086 | − | 5.44969i | 0.240590 | − | 0.174799i | ||||
\(973\) | −4.02234 | + | 12.3795i | −0.128950 | + | 0.396869i | ||||
\(974\) | −8.63618 | + | 26.5794i | −0.276721 | + | 0.851659i | ||||
\(975\) | 33.0809 | − | 24.0347i | 1.05944 | − | 0.769726i | ||||
\(976\) | 1.66325 | + | 1.20842i | 0.0532392 | + | 0.0386806i | ||||
\(977\) | 3.01512 | + | 9.27959i | 0.0964623 | + | 0.296880i | 0.987632 | − | 0.156790i | \(-0.0501145\pi\) |
−0.891170 | + | 0.453670i | \(0.850114\pi\) | |||||||
\(978\) | −26.1972 | −0.837694 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −2.61958 | −0.0836795 | ||||||||
\(981\) | −6.19665 | − | 19.0713i | −0.197844 | − | 0.608900i | ||||
\(982\) | −33.5591 | − | 24.3821i | −1.07091 | − | 0.778064i | ||||
\(983\) | −36.5027 | + | 26.5207i | −1.16425 | + | 0.845880i | −0.990310 | − | 0.138876i | \(-0.955651\pi\) |
−0.173944 | + | 0.984756i | \(0.555651\pi\) | |||||||
\(984\) | −5.77318 | + | 17.7680i | −0.184042 | + | 0.566424i | ||||
\(985\) | 22.2229 | − | 68.3950i | 0.708080 | − | 2.17925i | ||||
\(986\) | 13.9021 | − | 10.1004i | 0.442732 | − | 0.321663i | ||||
\(987\) | −17.4996 | − | 12.7142i | −0.557019 | − | 0.404698i | ||||
\(988\) | 0.782948 | + | 2.40967i | 0.0249089 | + | 0.0766617i | ||||
\(989\) | 2.48632 | 0.0790604 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 53.5405 | 1.70077 | 0.850384 | − | 0.526162i | \(-0.176369\pi\) | ||||
0.850384 | + | 0.526162i | \(0.176369\pi\) | |||||||
\(992\) | −0.979212 | − | 3.01370i | −0.0310900 | − | 0.0956852i | ||||
\(993\) | −2.86389 | − | 2.08074i | −0.0908829 | − | 0.0660303i | ||||
\(994\) | 2.87491 | − | 2.08874i | 0.0911866 | − | 0.0662509i | ||||
\(995\) | 9.01987 | − | 27.7603i | 0.285949 | − | 0.880061i | ||||
\(996\) | 10.7601 | − | 33.1163i | 0.340948 | − | 1.04933i | ||||
\(997\) | −25.2095 | + | 18.3158i | −0.798394 | + | 0.580067i | −0.910443 | − | 0.413636i | \(-0.864259\pi\) |
0.112049 | + | 0.993703i | \(0.464259\pi\) | |||||||
\(998\) | −28.6836 | − | 20.8399i | −0.907965 | − | 0.659675i | ||||
\(999\) | −19.3140 | − | 59.4422i | −0.611066 | − | 1.88067i |
(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 | 847.2.f.v.148.2 | 16 | ||
11.2 | odd | 10 | 847.2.f.w.372.3 | 16 | |||
11.3 | even | 5 | 847.2.a.o.1.3 | 8 | |||
11.4 | even | 5 | 847.2.f.x.729.3 | 16 | |||
11.5 | even | 5 | 847.2.f.x.323.3 | 16 | |||
11.6 | odd | 10 | 77.2.f.b.15.2 | ✓ | 16 | ||
11.7 | odd | 10 | 77.2.f.b.36.2 | yes | 16 | ||
11.8 | odd | 10 | 847.2.a.p.1.6 | 8 | |||
11.9 | even | 5 | inner | 847.2.f.v.372.2 | 16 | ||
11.10 | odd | 2 | 847.2.f.w.148.3 | 16 | |||
33.8 | even | 10 | 7623.2.a.ct.1.3 | 8 | |||
33.14 | odd | 10 | 7623.2.a.cw.1.6 | 8 | |||
33.17 | even | 10 | 693.2.m.i.631.3 | 16 | |||
33.29 | even | 10 | 693.2.m.i.190.3 | 16 | |||
77.6 | even | 10 | 539.2.f.e.246.2 | 16 | |||
77.17 | even | 30 | 539.2.q.f.422.3 | 32 | |||
77.18 | odd | 30 | 539.2.q.g.520.2 | 32 | |||
77.39 | odd | 30 | 539.2.q.g.422.3 | 32 | |||
77.40 | even | 30 | 539.2.q.f.410.3 | 32 | |||
77.41 | even | 10 | 5929.2.a.bt.1.6 | 8 | |||
77.51 | odd | 30 | 539.2.q.g.410.3 | 32 | |||
77.61 | even | 30 | 539.2.q.f.312.2 | 32 | |||
77.62 | even | 10 | 539.2.f.e.344.2 | 16 | |||
77.69 | odd | 10 | 5929.2.a.bs.1.3 | 8 | |||
77.72 | odd | 30 | 539.2.q.g.312.2 | 32 | |||
77.73 | even | 30 | 539.2.q.f.520.2 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.f.b.15.2 | ✓ | 16 | 11.6 | odd | 10 | ||
77.2.f.b.36.2 | yes | 16 | 11.7 | odd | 10 | ||
539.2.f.e.246.2 | 16 | 77.6 | even | 10 | |||
539.2.f.e.344.2 | 16 | 77.62 | even | 10 | |||
539.2.q.f.312.2 | 32 | 77.61 | even | 30 | |||
539.2.q.f.410.3 | 32 | 77.40 | even | 30 | |||
539.2.q.f.422.3 | 32 | 77.17 | even | 30 | |||
539.2.q.f.520.2 | 32 | 77.73 | even | 30 | |||
539.2.q.g.312.2 | 32 | 77.72 | odd | 30 | |||
539.2.q.g.410.3 | 32 | 77.51 | odd | 30 | |||
539.2.q.g.422.3 | 32 | 77.39 | odd | 30 | |||
539.2.q.g.520.2 | 32 | 77.18 | odd | 30 | |||
693.2.m.i.190.3 | 16 | 33.29 | even | 10 | |||
693.2.m.i.631.3 | 16 | 33.17 | even | 10 | |||
847.2.a.o.1.3 | 8 | 11.3 | even | 5 | |||
847.2.a.p.1.6 | 8 | 11.8 | odd | 10 | |||
847.2.f.v.148.2 | 16 | 1.1 | even | 1 | trivial | ||
847.2.f.v.372.2 | 16 | 11.9 | even | 5 | inner | ||
847.2.f.w.148.3 | 16 | 11.10 | odd | 2 | |||
847.2.f.w.372.3 | 16 | 11.2 | odd | 10 | |||
847.2.f.x.323.3 | 16 | 11.5 | even | 5 | |||
847.2.f.x.729.3 | 16 | 11.4 | even | 5 | |||
5929.2.a.bs.1.3 | 8 | 77.69 | odd | 10 | |||
5929.2.a.bt.1.6 | 8 | 77.41 | even | 10 | |||
7623.2.a.ct.1.3 | 8 | 33.8 | even | 10 | |||
7623.2.a.cw.1.6 | 8 | 33.14 | odd | 10 |