Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [171,2,Mod(106,171)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(171, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("171.106");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 171 = 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 171.g (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.36544187456\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 106.7 | ||
Character | \(\chi\) | \(=\) | 171.106 |
Dual form | 171.2.g.c.121.7 |
$q$-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 \(\left(\mathbb{Z}/171\mathbb{Z}\right)^\times\).
\(n\) | \(20\) | \(154\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.269545 | − | 0.466866i | −0.190597 | − | 0.330124i | 0.754851 | − | 0.655896i | \(-0.227709\pi\) |
−0.945448 | + | 0.325772i | \(0.894376\pi\) | |||||||
\(3\) | −1.40907 | + | 1.00723i | −0.813528 | + | 0.581525i | ||||
\(4\) | 0.854691 | − | 1.48037i | 0.427345 | − | 0.740184i | ||||
\(5\) | −0.947325 | −0.423656 | −0.211828 | − | 0.977307i | \(-0.567942\pi\) | ||||
−0.211828 | + | 0.977307i | \(0.567942\pi\) | |||||||
\(6\) | 0.850050 | + | 0.386354i | 0.347032 | + | 0.157728i | ||||
\(7\) | 1.18430 | − | 2.05126i | 0.447622 | − | 0.775304i | −0.550609 | − | 0.834763i | \(-0.685604\pi\) |
0.998231 | + | 0.0594594i | \(0.0189377\pi\) | |||||||
\(8\) | −1.99969 | −0.706998 | ||||||||
\(9\) | 0.970970 | − | 2.83852i | 0.323657 | − | 0.946175i | ||||
\(10\) | 0.255347 | + | 0.442274i | 0.0807477 | + | 0.139859i | ||||
\(11\) | 1.76580 | − | 3.05845i | 0.532407 | − | 0.922157i | −0.466877 | − | 0.884322i | \(-0.654621\pi\) |
0.999284 | − | 0.0378342i | \(-0.0120459\pi\) | |||||||
\(12\) | 0.286752 | + | 2.94682i | 0.0827780 | + | 0.850673i | ||||
\(13\) | 0.514122 | − | 0.890485i | 0.142592 | − | 0.246976i | −0.785880 | − | 0.618379i | \(-0.787790\pi\) |
0.928472 | + | 0.371403i | \(0.121123\pi\) | |||||||
\(14\) | −1.27689 | −0.341262 | ||||||||
\(15\) | 1.33485 | − | 0.954175i | 0.344657 | − | 0.246367i | ||||
\(16\) | −1.17037 | − | 2.02715i | −0.292594 | − | 0.506787i | ||||
\(17\) | −0.347984 | + | 0.602725i | −0.0843984 | + | 0.146182i | −0.905135 | − | 0.425125i | \(-0.860230\pi\) |
0.820736 | + | 0.571307i | \(0.193564\pi\) | |||||||
\(18\) | −1.58693 | + | 0.311797i | −0.374043 | + | 0.0734913i | ||||
\(19\) | 2.46688 | − | 3.59367i | 0.565942 | − | 0.824445i | ||||
\(20\) | −0.809670 | + | 1.40239i | −0.181048 | + | 0.313584i | ||||
\(21\) | 0.397335 | + | 4.08324i | 0.0867057 | + | 0.891035i | ||||
\(22\) | −1.90385 | −0.405901 | ||||||||
\(23\) | −1.69005 | + | 2.92725i | −0.352399 | + | 0.610374i | −0.986669 | − | 0.162738i | \(-0.947967\pi\) |
0.634270 | + | 0.773112i | \(0.281301\pi\) | |||||||
\(24\) | 2.81771 | − | 2.01415i | 0.575163 | − | 0.411137i | ||||
\(25\) | −4.10258 | −0.820515 | ||||||||
\(26\) | −0.554316 | −0.108710 | ||||||||
\(27\) | 1.49088 | + | 4.97768i | 0.286920 | + | 0.957954i | ||||
\(28\) | −2.02441 | − | 3.50639i | −0.382578 | − | 0.662645i | ||||
\(29\) | 3.53104 | 0.655697 | 0.327849 | − | 0.944730i | \(-0.393676\pi\) | ||||
0.327849 | + | 0.944730i | \(0.393676\pi\) | |||||||
\(30\) | −0.805274 | − | 0.366002i | −0.147022 | − | 0.0668226i | ||||
\(31\) | 4.48279 | + | 7.76442i | 0.805133 | + | 1.39453i | 0.916201 | + | 0.400719i | \(0.131240\pi\) |
−0.111068 | + | 0.993813i | \(0.535427\pi\) | |||||||
\(32\) | −2.63063 | + | 4.55638i | −0.465034 | + | 0.805462i | ||||
\(33\) | 0.592430 | + | 6.08814i | 0.103129 | + | 1.05981i | ||||
\(34\) | 0.375189 | 0.0643444 | ||||||||
\(35\) | −1.12191 | + | 1.94321i | −0.189638 | + | 0.328463i | ||||
\(36\) | −3.37218 | − | 3.86345i | −0.562030 | − | 0.643909i | ||||
\(37\) | 0.345685 | 0.0568303 | 0.0284151 | − | 0.999596i | \(-0.490954\pi\) | ||||
0.0284151 | + | 0.999596i | \(0.490954\pi\) | |||||||
\(38\) | −2.34270 | − | 0.183047i | −0.380036 | − | 0.0296941i | ||||
\(39\) | 0.172489 | + | 1.77260i | 0.0276204 | + | 0.283843i | ||||
\(40\) | 1.89436 | 0.299524 | ||||||||
\(41\) | −11.3850 | −1.77803 | −0.889016 | − | 0.457876i | \(-0.848610\pi\) | ||||
−0.889016 | + | 0.457876i | \(0.848610\pi\) | |||||||
\(42\) | 1.79922 | − | 1.28612i | 0.277626 | − | 0.198452i | ||||
\(43\) | 2.10829 | + | 3.65166i | 0.321511 | + | 0.556873i | 0.980800 | − | 0.195016i | \(-0.0624760\pi\) |
−0.659289 | + | 0.751890i | \(0.729143\pi\) | |||||||
\(44\) | −3.01842 | − | 5.22805i | −0.455044 | − | 0.788159i | ||||
\(45\) | −0.919824 | + | 2.68900i | −0.137119 | + | 0.400853i | ||||
\(46\) | 1.82218 | 0.268665 | ||||||||
\(47\) | 10.2525 | 1.49548 | 0.747742 | − | 0.663990i | \(-0.231138\pi\) | ||||
0.747742 | + | 0.663990i | \(0.231138\pi\) | |||||||
\(48\) | 3.69095 | + | 1.67756i | 0.532743 | + | 0.242135i | ||||
\(49\) | 0.694884 | + | 1.20357i | 0.0992691 | + | 0.171939i | ||||
\(50\) | 1.10583 | + | 1.91535i | 0.156388 | + | 0.270872i | ||||
\(51\) | −0.116750 | − | 1.19978i | −0.0163482 | − | 0.168003i | ||||
\(52\) | −0.878830 | − | 1.52218i | −0.121872 | − | 0.211088i | ||||
\(53\) | −3.33188 | − | 5.77099i | −0.457669 | − | 0.792706i | 0.541168 | − | 0.840914i | \(-0.317982\pi\) |
−0.998837 | + | 0.0482080i | \(0.984649\pi\) | |||||||
\(54\) | 1.92205 | − | 2.03775i | 0.261558 | − | 0.277303i | ||||
\(55\) | −1.67278 | + | 2.89734i | −0.225558 | + | 0.390678i | ||||
\(56\) | −2.36823 | + | 4.10189i | −0.316468 | + | 0.548138i | ||||
\(57\) | 0.143642 | + | 7.54847i | 0.0190259 | + | 0.999819i | ||||
\(58\) | −0.951774 | − | 1.64852i | −0.124974 | − | 0.216461i | ||||
\(59\) | 11.0780 | 1.44223 | 0.721117 | − | 0.692814i | \(-0.243629\pi\) | ||||
0.721117 | + | 0.692814i | \(0.243629\pi\) | |||||||
\(60\) | −0.271647 | − | 2.79159i | −0.0350695 | − | 0.360393i | ||||
\(61\) | 3.47551 | 0.444994 | 0.222497 | − | 0.974933i | \(-0.428579\pi\) | ||||
0.222497 | + | 0.974933i | \(0.428579\pi\) | |||||||
\(62\) | 2.41663 | − | 4.18573i | 0.306912 | − | 0.531588i | ||||
\(63\) | −4.67264 | − | 5.35337i | −0.588697 | − | 0.674461i | ||||
\(64\) | −1.84521 | −0.230651 | ||||||||
\(65\) | −0.487040 | + | 0.843578i | −0.0604099 | + | 0.104633i | ||||
\(66\) | 2.68266 | − | 1.91761i | 0.330212 | − | 0.236042i | ||||
\(67\) | 1.02176 | − | 1.76975i | 0.124828 | − | 0.216209i | −0.796838 | − | 0.604194i | \(-0.793495\pi\) |
0.921666 | + | 0.387985i | \(0.126829\pi\) | |||||||
\(68\) | 0.594837 | + | 1.03029i | 0.0721345 | + | 0.124941i | ||||
\(69\) | −0.567017 | − | 5.82698i | −0.0682608 | − | 0.701485i | ||||
\(70\) | 1.20962 | 0.144578 | ||||||||
\(71\) | 1.75729 | − | 3.04372i | 0.208552 | − | 0.361223i | −0.742707 | − | 0.669617i | \(-0.766458\pi\) |
0.951259 | + | 0.308394i | \(0.0997916\pi\) | |||||||
\(72\) | −1.94164 | + | 5.67617i | −0.228825 | + | 0.668943i | ||||
\(73\) | −4.57554 | + | 7.92508i | −0.535527 | + | 0.927560i | 0.463611 | + | 0.886039i | \(0.346554\pi\) |
−0.999138 | + | 0.0415210i | \(0.986780\pi\) | |||||||
\(74\) | −0.0931777 | − | 0.161389i | −0.0108317 | − | 0.0187610i | ||||
\(75\) | 5.78083 | − | 4.13224i | 0.667512 | − | 0.477150i | ||||
\(76\) | −3.21154 | − | 6.72337i | −0.368388 | − | 0.771224i | ||||
\(77\) | −4.18245 | − | 7.24422i | −0.476635 | − | 0.825555i | ||||
\(78\) | 0.781071 | − | 0.558324i | 0.0884389 | − | 0.0632178i | ||||
\(79\) | −6.87486 | − | 11.9076i | −0.773482 | − | 1.33971i | −0.935644 | − | 0.352946i | \(-0.885180\pi\) |
0.162162 | − | 0.986764i | \(-0.448153\pi\) | |||||||
\(80\) | 1.10872 | + | 1.92037i | 0.123959 | + | 0.214704i | ||||
\(81\) | −7.11443 | − | 5.51225i | −0.790493 | − | 0.612472i | ||||
\(82\) | 3.06876 | + | 5.31525i | 0.338888 | + | 0.586971i | ||||
\(83\) | 2.41817 | − | 4.18839i | 0.265428 | − | 0.459735i | −0.702248 | − | 0.711933i | \(-0.747820\pi\) |
0.967676 | + | 0.252198i | \(0.0811533\pi\) | |||||||
\(84\) | 6.38429 | + | 2.90170i | 0.696583 | + | 0.316602i | ||||
\(85\) | 0.329653 | − | 0.570976i | 0.0357559 | − | 0.0619311i | ||||
\(86\) | 1.13656 | − | 1.96858i | 0.122558 | − | 0.212277i | ||||
\(87\) | −4.97549 | + | 3.55657i | −0.533428 | + | 0.381305i | ||||
\(88\) | −3.53105 | + | 6.11595i | −0.376411 | + | 0.651963i | ||||
\(89\) | −0.902296 | − | 1.56282i | −0.0956432 | − | 0.165659i | 0.814234 | − | 0.580537i | \(-0.197157\pi\) |
−0.909877 | + | 0.414878i | \(0.863824\pi\) | |||||||
\(90\) | 1.50334 | − | 0.295373i | 0.158466 | − | 0.0311351i | ||||
\(91\) | −1.21774 | − | 2.10920i | −0.127654 | − | 0.221104i | ||||
\(92\) | 2.88894 | + | 5.00379i | 0.301193 | + | 0.521681i | ||||
\(93\) | −14.1372 | − | 6.42543i | −1.46595 | − | 0.666286i | ||||
\(94\) | −2.76352 | − | 4.78655i | −0.285035 | − | 0.493695i | ||||
\(95\) | −2.33694 | + | 3.40438i | −0.239765 | + | 0.349282i | ||||
\(96\) | −0.882584 | − | 9.06993i | −0.0900784 | − | 0.925695i | ||||
\(97\) | 7.02204 | + | 12.1625i | 0.712980 | + | 1.23492i | 0.963734 | + | 0.266866i | \(0.0859883\pi\) |
−0.250754 | + | 0.968051i | \(0.580678\pi\) | |||||||
\(98\) | 0.374605 | − | 0.648835i | 0.0378408 | − | 0.0655422i | ||||
\(99\) | −6.96694 | − | 7.98192i | −0.700204 | − | 0.802213i | ||||
\(100\) | −3.50643 | + | 6.07332i | −0.350643 | + | 0.607332i | ||||
\(101\) | 3.69542 | 0.367708 | 0.183854 | − | 0.982954i | \(-0.441143\pi\) | ||||
0.183854 | + | 0.982954i | \(0.441143\pi\) | |||||||
\(102\) | −0.528669 | + | 0.377902i | −0.0523460 | + | 0.0374179i | ||||
\(103\) | 2.16977 | + | 3.75815i | 0.213793 | + | 0.370301i | 0.952899 | − | 0.303289i | \(-0.0980847\pi\) |
−0.739105 | + | 0.673590i | \(0.764751\pi\) | |||||||
\(104\) | −1.02808 | + | 1.78070i | −0.100812 | + | 0.174612i | ||||
\(105\) | −0.376405 | − | 3.86815i | −0.0367334 | − | 0.377493i | ||||
\(106\) | −1.79619 | + | 3.11108i | −0.174461 | + | 0.302175i | ||||
\(107\) | 7.15846 | 0.692035 | 0.346017 | − | 0.938228i | \(-0.387534\pi\) | ||||
0.346017 | + | 0.938228i | \(0.387534\pi\) | |||||||
\(108\) | 8.64304 | + | 2.04732i | 0.831677 | + | 0.197004i | ||||
\(109\) | −0.360189 | + | 0.623866i | −0.0344999 | + | 0.0597555i | −0.882760 | − | 0.469825i | \(-0.844317\pi\) |
0.848260 | + | 0.529580i | \(0.177650\pi\) | |||||||
\(110\) | 1.80356 | 0.171963 | ||||||||
\(111\) | −0.487095 | + | 0.348185i | −0.0462330 | + | 0.0330482i | ||||
\(112\) | −5.54428 | −0.523885 | ||||||||
\(113\) | 1.28139 | + | 2.21942i | 0.120543 | + | 0.208786i | 0.919982 | − | 0.391961i | \(-0.128203\pi\) |
−0.799439 | + | 0.600747i | \(0.794870\pi\) | |||||||
\(114\) | 3.48540 | − | 2.10171i | 0.326438 | − | 0.196844i | ||||
\(115\) | 1.60102 | − | 2.77306i | 0.149296 | − | 0.258589i | ||||
\(116\) | 3.01795 | − | 5.22724i | 0.280209 | − | 0.485337i | ||||
\(117\) | −2.02847 | − | 2.32398i | −0.187532 | − | 0.214852i | ||||
\(118\) | −2.98602 | − | 5.17194i | −0.274886 | − | 0.476116i | ||||
\(119\) | 0.824231 | + | 1.42761i | 0.0755572 | + | 0.130869i | ||||
\(120\) | −2.66929 | + | 1.90806i | −0.243671 | + | 0.174181i | ||||
\(121\) | −0.736069 | − | 1.27491i | −0.0669153 | − | 0.115901i | ||||
\(122\) | −0.936808 | − | 1.62260i | −0.0848146 | − | 0.146903i | ||||
\(123\) | 16.0422 | − | 11.4673i | 1.44648 | − | 1.03397i | ||||
\(124\) | 15.3256 | 1.37628 | ||||||||
\(125\) | 8.62310 | 0.771273 | ||||||||
\(126\) | −1.23982 | + | 3.62447i | −0.110452 | + | 0.322893i | ||||
\(127\) | −0.409916 | − | 0.709995i | −0.0363741 | − | 0.0630018i | 0.847265 | − | 0.531170i | \(-0.178247\pi\) |
−0.883639 | + | 0.468168i | \(0.844914\pi\) | |||||||
\(128\) | 5.75862 | + | 9.97423i | 0.508995 | + | 0.881606i | ||||
\(129\) | −6.64880 | − | 3.02192i | −0.585394 | − | 0.266065i | ||||
\(130\) | 0.525117 | 0.0460558 | ||||||||
\(131\) | 16.5214 | 1.44348 | 0.721741 | − | 0.692163i | \(-0.243342\pi\) | ||||
0.721741 | + | 0.692163i | \(0.243342\pi\) | |||||||
\(132\) | 9.51903 | + | 4.32646i | 0.828525 | + | 0.376570i | ||||
\(133\) | −4.45004 | − | 9.31620i | −0.385868 | − | 0.807817i | ||||
\(134\) | −1.10164 | −0.0951676 | ||||||||
\(135\) | −1.41235 | − | 4.71548i | −0.121556 | − | 0.405844i | ||||
\(136\) | 0.695860 | − | 1.20526i | 0.0596695 | − | 0.103351i | ||||
\(137\) | −11.1976 | −0.956675 | −0.478337 | − | 0.878176i | \(-0.658760\pi\) | ||||
−0.478337 | + | 0.878176i | \(0.658760\pi\) | |||||||
\(138\) | −2.56758 | + | 1.83535i | −0.218567 | + | 0.156236i | ||||
\(139\) | −5.27461 | + | 9.13590i | −0.447387 | + | 0.774897i | −0.998215 | − | 0.0597219i | \(-0.980979\pi\) |
0.550828 | + | 0.834619i | \(0.314312\pi\) | |||||||
\(140\) | 1.91778 | + | 3.32169i | 0.162082 | + | 0.280734i | ||||
\(141\) | −14.4465 | + | 10.3267i | −1.21662 | + | 0.869661i | ||||
\(142\) | −1.89468 | −0.158998 | ||||||||
\(143\) | −1.81567 | − | 3.14483i | −0.151834 | − | 0.262984i | ||||
\(144\) | −6.89051 | + | 1.35383i | −0.574209 | + | 0.112820i | ||||
\(145\) | −3.34504 | −0.277790 | ||||||||
\(146\) | 4.93326 | 0.408280 | ||||||||
\(147\) | −2.19142 | − | 0.996015i | −0.180745 | − | 0.0821499i | ||||
\(148\) | 0.295454 | − | 0.511741i | 0.0242862 | − | 0.0420649i | ||||
\(149\) | 18.8982 | 1.54820 | 0.774100 | − | 0.633063i | \(-0.218203\pi\) | ||||
0.774100 | + | 0.633063i | \(0.218203\pi\) | |||||||
\(150\) | −3.48740 | − | 1.58504i | −0.284745 | − | 0.129418i | ||||
\(151\) | −10.5000 | + | 18.1865i | −0.854475 | + | 1.47999i | 0.0226553 | + | 0.999743i | \(0.492788\pi\) |
−0.877131 | + | 0.480252i | \(0.840545\pi\) | |||||||
\(152\) | −4.93301 | + | 7.18624i | −0.400120 | + | 0.582881i | ||||
\(153\) | 1.37297 | + | 1.57299i | 0.110998 | + | 0.127169i | ||||
\(154\) | −2.25472 | + | 3.90529i | −0.181690 | + | 0.314697i | ||||
\(155\) | −4.24666 | − | 7.35543i | −0.341100 | − | 0.590802i | ||||
\(156\) | 2.77152 | + | 1.25967i | 0.221899 | + | 0.100855i | ||||
\(157\) | −14.6970 | −1.17294 | −0.586472 | − | 0.809969i | \(-0.699484\pi\) | ||||
−0.586472 | + | 0.809969i | \(0.699484\pi\) | |||||||
\(158\) | −3.70617 | + | 6.41927i | −0.294847 | + | 0.510690i | ||||
\(159\) | 10.5076 | + | 4.77577i | 0.833306 | + | 0.378743i | ||||
\(160\) | 2.49206 | − | 4.31637i | 0.197015 | − | 0.341239i | ||||
\(161\) | 4.00304 | + | 6.93346i | 0.315483 | + | 0.546433i | ||||
\(162\) | −0.655818 | + | 4.80728i | −0.0515260 | + | 0.377696i | ||||
\(163\) | 9.33899 | 0.731486 | 0.365743 | − | 0.930716i | \(-0.380815\pi\) | ||||
0.365743 | + | 0.930716i | \(0.380815\pi\) | |||||||
\(164\) | −9.73062 | + | 16.8539i | −0.759834 | + | 1.31607i | ||||
\(165\) | −0.561224 | − | 5.76744i | −0.0436912 | − | 0.448995i | ||||
\(166\) | −2.60722 | −0.202359 | ||||||||
\(167\) | −10.2970 | + | 17.8349i | −0.796805 | + | 1.38011i | 0.124882 | + | 0.992172i | \(0.460145\pi\) |
−0.921687 | + | 0.387935i | \(0.873189\pi\) | |||||||
\(168\) | −0.794548 | − | 8.16521i | −0.0613007 | − | 0.629960i | ||||
\(169\) | 5.97136 | + | 10.3427i | 0.459335 | + | 0.795592i | ||||
\(170\) | −0.355426 | −0.0272599 | ||||||||
\(171\) | −7.80546 | − | 10.4917i | −0.596898 | − | 0.802317i | ||||
\(172\) | 7.20774 | 0.549585 | ||||||||
\(173\) | −1.66479 | − | 2.88350i | −0.126571 | − | 0.219228i | 0.795775 | − | 0.605593i | \(-0.207064\pi\) |
−0.922346 | + | 0.386365i | \(0.873731\pi\) | |||||||
\(174\) | 3.00156 | + | 1.36423i | 0.227548 | + | 0.103422i | ||||
\(175\) | −4.85867 | + | 8.41546i | −0.367281 | + | 0.636149i | ||||
\(176\) | −8.26657 | −0.623116 | ||||||||
\(177\) | −15.6097 | + | 11.1581i | −1.17330 | + | 0.838695i | ||||
\(178\) | −0.486419 | + | 0.842503i | −0.0364587 | + | 0.0631482i | ||||
\(179\) | −20.0903 | −1.50162 | −0.750809 | − | 0.660519i | \(-0.770336\pi\) | ||||
−0.750809 | + | 0.660519i | \(0.770336\pi\) | |||||||
\(180\) | 3.19455 | + | 3.65995i | 0.238108 | + | 0.272796i | ||||
\(181\) | −0.0120393 | − | 0.0208527i | −0.000894875 | − | 0.00154997i | 0.865578 | − | 0.500775i | \(-0.166952\pi\) |
−0.866472 | + | 0.499225i | \(0.833618\pi\) | |||||||
\(182\) | −0.656474 | + | 1.13705i | −0.0486611 | + | 0.0842835i | ||||
\(183\) | −4.89725 | + | 3.50065i | −0.362015 | + | 0.258775i | ||||
\(184\) | 3.37957 | − | 5.85360i | 0.249146 | − | 0.431533i | ||||
\(185\) | −0.327476 | −0.0240765 | ||||||||
\(186\) | 0.810787 | + | 8.33210i | 0.0594498 | + | 0.610939i | ||||
\(187\) | 1.22894 | + | 2.12858i | 0.0898687 | + | 0.155657i | ||||
\(188\) | 8.76273 | − | 15.1775i | 0.639088 | − | 1.10693i | ||||
\(189\) | 11.9762 | + | 2.83686i | 0.871138 | + | 0.206351i | ||||
\(190\) | 2.21930 | + | 0.173404i | 0.161005 | + | 0.0125801i | ||||
\(191\) | 8.71659 | − | 15.0976i | 0.630710 | − | 1.09242i | −0.356697 | − | 0.934220i | \(-0.616097\pi\) |
0.987407 | − | 0.158202i | \(-0.0505697\pi\) | |||||||
\(192\) | 2.60003 | − | 1.85855i | 0.187641 | − | 0.134129i | ||||
\(193\) | 20.8338 | 1.49965 | 0.749826 | − | 0.661635i | \(-0.230137\pi\) | ||||
0.749826 | + | 0.661635i | \(0.230137\pi\) | |||||||
\(194\) | 3.78551 | − | 6.55670i | 0.271784 | − | 0.470744i | ||||
\(195\) | −0.163404 | − | 1.67923i | −0.0117016 | − | 0.120252i | ||||
\(196\) | 2.37564 | 0.169689 | ||||||||
\(197\) | −19.7858 | −1.40968 | −0.704841 | − | 0.709365i | \(-0.748982\pi\) | ||||
−0.704841 | + | 0.709365i | \(0.748982\pi\) | |||||||
\(198\) | −1.84858 | + | 5.40411i | −0.131373 | + | 0.384054i | ||||
\(199\) | −11.3938 | − | 19.7347i | −0.807686 | − | 1.39895i | −0.914463 | − | 0.404670i | \(-0.867386\pi\) |
0.106777 | − | 0.994283i | \(-0.465947\pi\) | |||||||
\(200\) | 8.20389 | 0.580102 | ||||||||
\(201\) | 0.342805 | + | 3.52285i | 0.0241796 | + | 0.248483i | ||||
\(202\) | −0.996083 | − | 1.72527i | −0.0700842 | − | 0.121389i | ||||
\(203\) | 4.18180 | − | 7.24308i | 0.293505 | − | 0.508365i | ||||
\(204\) | −1.87591 | − | 0.852612i | −0.131340 | − | 0.0596947i | ||||
\(205\) | 10.7853 | 0.753275 | ||||||||
\(206\) | 1.16970 | − | 2.02598i | 0.0814969 | − | 0.141157i | ||||
\(207\) | 6.66808 | + | 7.63951i | 0.463464 | + | 0.530983i | ||||
\(208\) | −2.40686 | −0.166886 | ||||||||
\(209\) | −6.63505 | − | 13.8905i | −0.458956 | − | 0.960828i | ||||
\(210\) | −1.70445 | + | 1.21837i | −0.117618 | + | 0.0840757i | ||||
\(211\) | 12.7643 | 0.878727 | 0.439364 | − | 0.898309i | \(-0.355204\pi\) | ||||
0.439364 | + | 0.898309i | \(0.355204\pi\) | |||||||
\(212\) | −11.3909 | −0.782331 | ||||||||
\(213\) | 0.589576 | + | 6.05881i | 0.0403971 | + | 0.415143i | ||||
\(214\) | −1.92953 | − | 3.34204i | −0.131900 | − | 0.228457i | ||||
\(215\) | −1.99723 | − | 3.45931i | −0.136210 | − | 0.235923i | ||||
\(216\) | −2.98130 | − | 9.95382i | −0.202852 | − | 0.677272i | ||||
\(217\) | 21.2358 | 1.44158 | ||||||||
\(218\) | 0.388349 | 0.0263023 | ||||||||
\(219\) | −1.53511 | − | 15.7756i | −0.103733 | − | 1.06602i | ||||
\(220\) | 2.85942 | + | 4.95267i | 0.192782 | + | 0.333909i | ||||
\(221\) | 0.357812 | + | 0.619748i | 0.0240690 | + | 0.0416888i | ||||
\(222\) | 0.293850 | + | 0.133557i | 0.0197219 | + | 0.00896374i | ||||
\(223\) | −7.47832 | − | 12.9528i | −0.500785 | − | 0.867385i | −1.00000 | 0.000906894i | \(-0.999711\pi\) | |
0.499214 | − | 0.866478i | \(-0.333622\pi\) | |||||||
\(224\) | 6.23089 | + | 10.7922i | 0.416319 | + | 0.721085i | ||||
\(225\) | −3.98348 | + | 11.6453i | −0.265565 | + | 0.776351i | ||||
\(226\) | 0.690782 | − | 1.19647i | 0.0459502 | − | 0.0795880i | ||||
\(227\) | −4.57627 | + | 7.92633i | −0.303737 | + | 0.526089i | −0.976979 | − | 0.213333i | \(-0.931568\pi\) |
0.673242 | + | 0.739422i | \(0.264901\pi\) | |||||||
\(228\) | 11.2973 | + | 6.23896i | 0.748181 | + | 0.413185i | ||||
\(229\) | −9.50543 | − | 16.4639i | −0.628136 | − | 1.08796i | −0.987925 | − | 0.154930i | \(-0.950485\pi\) |
0.359789 | − | 0.933034i | \(-0.382849\pi\) | |||||||
\(230\) | −1.72619 | −0.113822 | ||||||||
\(231\) | 13.1900 | + | 5.99493i | 0.867837 | + | 0.394438i | ||||
\(232\) | −7.06099 | −0.463576 | ||||||||
\(233\) | 4.25468 | − | 7.36932i | 0.278733 | − | 0.482780i | −0.692337 | − | 0.721574i | \(-0.743419\pi\) |
0.971070 | + | 0.238794i | \(0.0767521\pi\) | |||||||
\(234\) | −0.538224 | + | 1.57344i | −0.0351848 | + | 0.102859i | ||||
\(235\) | −9.71246 | −0.633571 | ||||||||
\(236\) | 9.46827 | − | 16.3995i | 0.616332 | − | 1.06752i | ||||
\(237\) | 21.6809 | + | 9.85411i | 1.40833 | + | 0.640093i | ||||
\(238\) | 0.444335 | − | 0.769611i | 0.0288020 | − | 0.0498865i | ||||
\(239\) | −9.82003 | − | 17.0088i | −0.635205 | − | 1.10021i | −0.986472 | − | 0.163932i | \(-0.947582\pi\) |
0.351266 | − | 0.936276i | \(-0.385751\pi\) | |||||||
\(240\) | −3.49653 | − | 1.58920i | −0.225700 | − | 0.102582i | ||||
\(241\) | −9.05577 | −0.583334 | −0.291667 | − | 0.956520i | \(-0.594210\pi\) | ||||
−0.291667 | + | 0.956520i | \(0.594210\pi\) | |||||||
\(242\) | −0.396807 | + | 0.687291i | −0.0255078 | + | 0.0441807i | ||||
\(243\) | 15.5769 | + | 0.601274i | 0.999256 | + | 0.0385718i | ||||
\(244\) | 2.97049 | − | 5.14504i | 0.190166 | − | 0.329377i | ||||
\(245\) | −0.658281 | − | 1.14018i | −0.0420560 | − | 0.0728432i | ||||
\(246\) | −9.67779 | − | 4.39862i | −0.617033 | − | 0.280446i | ||||
\(247\) | −1.93183 | − | 4.04431i | −0.122920 | − | 0.257333i | ||||
\(248\) | −8.96420 | − | 15.5265i | −0.569227 | − | 0.985931i | ||||
\(249\) | 0.811302 | + | 8.33739i | 0.0514142 | + | 0.528361i | ||||
\(250\) | −2.32431 | − | 4.02583i | −0.147002 | − | 0.254616i | ||||
\(251\) | 13.7418 | + | 23.8015i | 0.867376 | + | 1.50234i | 0.864668 | + | 0.502343i | \(0.167529\pi\) |
0.00270775 | + | 0.999996i | \(0.499138\pi\) | |||||||
\(252\) | −11.9186 | + | 2.34175i | −0.750802 | + | 0.147516i | ||||
\(253\) | 5.96856 | + | 10.3378i | 0.375240 | + | 0.649935i | ||||
\(254\) | −0.220982 | + | 0.382751i | −0.0138656 | + | 0.0240159i | ||||
\(255\) | 0.110600 | + | 1.13658i | 0.00692603 | + | 0.0711757i | ||||
\(256\) | 1.25921 | − | 2.18102i | 0.0787008 | − | 0.136314i | ||||
\(257\) | 4.20065 | − | 7.27574i | 0.262029 | − | 0.453848i | −0.704752 | − | 0.709454i | \(-0.748942\pi\) |
0.966781 | + | 0.255606i | \(0.0822750\pi\) | |||||||
\(258\) | 0.381319 | + | 3.91864i | 0.0237399 | + | 0.243964i | ||||
\(259\) | 0.409394 | − | 0.709091i | 0.0254385 | − | 0.0440607i | ||||
\(260\) | 0.832538 | + | 1.44200i | 0.0516318 | + | 0.0894289i | ||||
\(261\) | 3.42853 | − | 10.0229i | 0.212221 | − | 0.620404i | ||||
\(262\) | −4.45326 | − | 7.71328i | −0.275124 | − | 0.476528i | ||||
\(263\) | −4.90800 | − | 8.50091i | −0.302641 | − | 0.524189i | 0.674093 | − | 0.738647i | \(-0.264535\pi\) |
−0.976733 | + | 0.214458i | \(0.931201\pi\) | |||||||
\(264\) | −1.18468 | − | 12.1744i | −0.0729119 | − | 0.749283i | ||||
\(265\) | 3.15637 | + | 5.46700i | 0.193895 | + | 0.335835i | ||||
\(266\) | −3.14993 | + | 4.58871i | −0.193134 | + | 0.281352i | ||||
\(267\) | 2.84553 | + | 1.29331i | 0.174143 | + | 0.0791493i | ||||
\(268\) | −1.74658 | − | 3.02517i | −0.106690 | − | 0.184792i | ||||
\(269\) | −11.0550 | + | 19.1479i | −0.674037 | + | 1.16747i | 0.302712 | + | 0.953082i | \(0.402108\pi\) |
−0.976749 | + | 0.214384i | \(0.931226\pi\) | |||||||
\(270\) | −1.82080 | + | 1.93041i | −0.110811 | + | 0.117481i | ||||
\(271\) | 1.32540 | − | 2.29566i | 0.0805124 | − | 0.139452i | −0.822958 | − | 0.568103i | \(-0.807678\pi\) |
0.903470 | + | 0.428651i | \(0.141011\pi\) | |||||||
\(272\) | 1.62908 | 0.0987778 | ||||||||
\(273\) | 3.84034 | + | 1.74546i | 0.232428 | + | 0.105640i | ||||
\(274\) | 3.01826 | + | 5.22777i | 0.182340 | + | 0.315821i | ||||
\(275\) | −7.24431 | + | 12.5475i | −0.436848 | + | 0.756644i | ||||
\(276\) | −9.11069 | − | 4.14087i | −0.548399 | − | 0.249251i | ||||
\(277\) | 12.5575 | − | 21.7502i | 0.754507 | − | 1.30684i | −0.191113 | − | 0.981568i | \(-0.561210\pi\) |
0.945619 | − | 0.325276i | \(-0.105457\pi\) | |||||||
\(278\) | 5.68699 | 0.341083 | ||||||||
\(279\) | 26.3922 | − | 5.18549i | 1.58006 | − | 0.310447i | ||||
\(280\) | 2.24348 | − | 3.88582i | 0.134074 | − | 0.232222i | ||||
\(281\) | −18.6546 | −1.11284 | −0.556419 | − | 0.830902i | \(-0.687825\pi\) | ||||
−0.556419 | + | 0.830902i | \(0.687825\pi\) | |||||||
\(282\) | 8.71516 | + | 3.96110i | 0.518980 | + | 0.235880i | ||||
\(283\) | −21.8745 | −1.30031 | −0.650153 | − | 0.759803i | \(-0.725295\pi\) | ||||
−0.650153 | + | 0.759803i | \(0.725295\pi\) | |||||||
\(284\) | −3.00388 | − | 5.20287i | −0.178247 | − | 0.308734i | ||||
\(285\) | −0.136076 | − | 7.15085i | −0.00806045 | − | 0.423580i | ||||
\(286\) | −0.978809 | + | 1.69535i | −0.0578782 | + | 0.100248i | ||||
\(287\) | −13.4832 | + | 23.3535i | −0.795886 | + | 1.37852i | ||||
\(288\) | 10.3791 | + | 11.8912i | 0.611597 | + | 0.700697i | ||||
\(289\) | 8.25781 | + | 14.3030i | 0.485754 | + | 0.841350i | ||||
\(290\) | 0.901639 | + | 1.56168i | 0.0529461 | + | 0.0917053i | ||||
\(291\) | −22.1450 | − | 10.0651i | −1.29816 | − | 0.590025i | ||||
\(292\) | 7.82135 | + | 13.5470i | 0.457710 | + | 0.792777i | ||||
\(293\) | −14.7038 | − | 25.4677i | −0.859003 | − | 1.48784i | −0.872881 | − | 0.487932i | \(-0.837751\pi\) |
0.0138789 | − | 0.999904i | \(-0.495582\pi\) | |||||||
\(294\) | 0.125681 | + | 1.29157i | 0.00732988 | + | 0.0753259i | ||||
\(295\) | −10.4945 | −0.611012 | ||||||||
\(296\) | −0.691264 | −0.0401789 | ||||||||
\(297\) | 17.8566 | + | 4.22978i | 1.03614 | + | 0.245437i | ||||
\(298\) | −5.09391 | − | 8.82292i | −0.295083 | − | 0.511098i | ||||
\(299\) | 1.73778 | + | 3.00992i | 0.100498 | + | 0.174068i | ||||
\(300\) | −1.17642 | − | 12.0895i | −0.0679206 | − | 0.697990i | ||||
\(301\) | 9.98735 | 0.575661 | ||||||||
\(302\) | 11.3209 | 0.651442 | ||||||||
\(303\) | −5.20712 | + | 3.72215i | −0.299141 | + | 0.213832i | ||||
\(304\) | −10.1721 | − | 0.794795i | −0.583409 | − | 0.0455846i | ||||
\(305\) | −3.29244 | −0.188525 | ||||||||
\(306\) | 0.364298 | − | 1.06498i | 0.0208255 | − | 0.0608810i | ||||
\(307\) | 10.3513 | − | 17.9289i | 0.590777 | − | 1.02326i | −0.403350 | − | 0.915046i | \(-0.632154\pi\) |
0.994128 | − | 0.108211i | \(-0.0345122\pi\) | |||||||
\(308\) | −14.2988 | −0.814750 | ||||||||
\(309\) | −6.84268 | − | 3.11004i | −0.389266 | − | 0.176924i | ||||
\(310\) | −2.28933 | + | 3.96524i | −0.130025 | + | 0.225211i | ||||
\(311\) | 14.0205 | + | 24.2843i | 0.795031 | + | 1.37703i | 0.922819 | + | 0.385233i | \(0.125879\pi\) |
−0.127788 | + | 0.991802i | \(0.540788\pi\) | |||||||
\(312\) | −0.344926 | − | 3.54465i | −0.0195276 | − | 0.200676i | ||||
\(313\) | 3.50819 | 0.198294 | 0.0991472 | − | 0.995073i | \(-0.468389\pi\) | ||||
0.0991472 | + | 0.995073i | \(0.468389\pi\) | |||||||
\(314\) | 3.96149 | + | 6.86151i | 0.223560 | + | 0.387217i | ||||
\(315\) | 4.42651 | + | 5.07138i | 0.249405 | + | 0.285740i | ||||
\(316\) | −23.5035 | −1.32218 | ||||||||
\(317\) | −8.85899 | −0.497571 | −0.248785 | − | 0.968559i | \(-0.580031\pi\) | ||||
−0.248785 | + | 0.968559i | \(0.580031\pi\) | |||||||
\(318\) | −0.602626 | − | 6.19292i | −0.0337936 | − | 0.347282i | ||||
\(319\) | 6.23509 | − | 10.7995i | 0.349098 | − | 0.604656i | ||||
\(320\) | 1.74801 | 0.0977167 | ||||||||
\(321\) | −10.0868 | + | 7.21023i | −0.562990 | + | 0.402436i | ||||
\(322\) | 2.15800 | − | 3.73776i | 0.120260 | − | 0.208297i | ||||
\(323\) | 1.30756 | + | 2.73739i | 0.0727547 | + | 0.152313i | ||||
\(324\) | −14.2408 | + | 5.82071i | −0.791155 | + | 0.323373i | ||||
\(325\) | −2.10922 | + | 3.65328i | −0.116999 | + | 0.202648i | ||||
\(326\) | −2.51728 | − | 4.36006i | −0.139419 | − | 0.241481i | ||||
\(327\) | −0.120845 | − | 1.24187i | −0.00668272 | − | 0.0686753i | ||||
\(328\) | 22.7664 | 1.25706 | ||||||||
\(329\) | 12.1420 | − | 21.0306i | 0.669411 | − | 1.15945i | ||||
\(330\) | −2.54135 | + | 1.81660i | −0.139897 | + | 0.100001i | ||||
\(331\) | −3.61586 | + | 6.26286i | −0.198746 | + | 0.344238i | −0.948122 | − | 0.317907i | \(-0.897020\pi\) |
0.749376 | + | 0.662144i | \(0.230353\pi\) | |||||||
\(332\) | −4.13357 | − | 7.15955i | −0.226859 | − | 0.392931i | ||||
\(333\) | 0.335650 | − | 0.981235i | 0.0183935 | − | 0.0537714i | ||||
\(334\) | 11.1020 | 0.607475 | ||||||||
\(335\) | −0.967941 | + | 1.67652i | −0.0528843 | + | 0.0915983i | ||||
\(336\) | 7.81230 | − | 5.58437i | 0.426196 | − | 0.304653i | ||||
\(337\) | 4.80486 | 0.261737 | 0.130869 | − | 0.991400i | \(-0.458223\pi\) | ||||
0.130869 | + | 0.991400i | \(0.458223\pi\) | |||||||
\(338\) | 3.21910 | − | 5.57565i | 0.175096 | − | 0.303275i | ||||
\(339\) | −4.04104 | − | 1.83668i | −0.219479 | − | 0.0997547i | ||||
\(340\) | −0.563504 | − | 0.976017i | −0.0305603 | − | 0.0529319i | ||||
\(341\) | 31.6628 | 1.71464 | ||||||||
\(342\) | −2.79427 | + | 6.47208i | −0.151097 | + | 0.349970i | ||||
\(343\) | 19.8719 | 1.07298 | ||||||||
\(344\) | −4.21592 | − | 7.30220i | −0.227307 | − | 0.393708i | ||||
\(345\) | 0.537149 | + | 5.52004i | 0.0289191 | + | 0.297189i | ||||
\(346\) | −0.897470 | + | 1.55446i | −0.0482483 | + | 0.0835685i | ||||
\(347\) | 7.25377 | 0.389403 | 0.194701 | − | 0.980863i | \(-0.437626\pi\) | ||||
0.194701 | + | 0.980863i | \(0.437626\pi\) | |||||||
\(348\) | 1.01253 | + | 10.4053i | 0.0542773 | + | 0.557784i | ||||
\(349\) | 2.96597 | − | 5.13721i | 0.158765 | − | 0.274988i | −0.775659 | − | 0.631152i | \(-0.782582\pi\) |
0.934423 | + | 0.356164i | \(0.115916\pi\) | |||||||
\(350\) | 5.23852 | 0.280011 | ||||||||
\(351\) | 5.19904 | + | 1.23152i | 0.277504 | + | 0.0657339i | ||||
\(352\) | 9.29031 | + | 16.0913i | 0.495175 | + | 0.857668i | ||||
\(353\) | −14.9677 | + | 25.9249i | −0.796652 | + | 1.37984i | 0.125133 | + | 0.992140i | \(0.460064\pi\) |
−0.921785 | + | 0.387702i | \(0.873269\pi\) | |||||||
\(354\) | 9.41686 | + | 4.28003i | 0.500501 | + | 0.227481i | ||||
\(355\) | −1.66472 | + | 2.88339i | −0.0883544 | + | 0.153034i | ||||
\(356\) | −3.08474 | −0.163491 | ||||||||
\(357\) | −2.59934 | − | 1.18142i | −0.137571 | − | 0.0625271i | ||||
\(358\) | 5.41524 | + | 9.37946i | 0.286204 | + | 0.495720i | ||||
\(359\) | −4.75528 | + | 8.23638i | −0.250974 | + | 0.434700i | −0.963794 | − | 0.266647i | \(-0.914084\pi\) |
0.712820 | + | 0.701347i | \(0.247418\pi\) | |||||||
\(360\) | 1.83936 | − | 5.37718i | 0.0969430 | − | 0.283402i | ||||
\(361\) | −6.82897 | − | 17.7303i | −0.359420 | − | 0.933176i | ||||
\(362\) | −0.00649028 | + | 0.0112415i | −0.000341121 | + | 0.000590839i | ||||
\(363\) | 2.32130 | + | 1.05505i | 0.121837 | + | 0.0553756i | ||||
\(364\) | −4.16318 | −0.218210 | ||||||||
\(365\) | 4.33453 | − | 7.50762i | 0.226880 | − | 0.392967i | ||||
\(366\) | 2.95436 | + | 1.34278i | 0.154427 | + | 0.0701881i | ||||
\(367\) | 13.9990 | 0.730740 | 0.365370 | − | 0.930862i | \(-0.380942\pi\) | ||||
0.365370 | + | 0.930862i | \(0.380942\pi\) | |||||||
\(368\) | 7.91196 | 0.412439 | ||||||||
\(369\) | −11.0545 | + | 32.3165i | −0.575472 | + | 1.68233i | ||||
\(370\) | 0.0882696 | + | 0.152887i | 0.00458892 | + | 0.00794824i | ||||
\(371\) | −15.7837 | −0.819451 | ||||||||
\(372\) | −21.5949 | + | 15.4364i | −1.11964 | + | 0.800342i | ||||
\(373\) | −5.05690 | − | 8.75881i | −0.261836 | − | 0.453514i | 0.704893 | − | 0.709313i | \(-0.250995\pi\) |
−0.966730 | + | 0.255799i | \(0.917661\pi\) | |||||||
\(374\) | 0.662507 | − | 1.14750i | 0.0342574 | − | 0.0593356i | ||||
\(375\) | −12.1506 | + | 8.68545i | −0.627453 | + | 0.448515i | ||||
\(376\) | −20.5019 | −1.05730 | ||||||||
\(377\) | 1.81538 | − | 3.14434i | 0.0934970 | − | 0.161942i | ||||
\(378\) | −1.90369 | − | 6.35592i | −0.0979150 | − | 0.326913i | ||||
\(379\) | −34.5838 | −1.77645 | −0.888226 | − | 0.459407i | \(-0.848062\pi\) | ||||
−0.888226 | + | 0.459407i | \(0.848062\pi\) | |||||||
\(380\) | 3.04237 | + | 6.36922i | 0.156070 | + | 0.326734i | ||||
\(381\) | 1.29273 | + | 0.587554i | 0.0662285 | + | 0.0301013i | ||||
\(382\) | −9.39806 | −0.480846 | ||||||||
\(383\) | −20.6916 | −1.05729 | −0.528646 | − | 0.848842i | \(-0.677300\pi\) | ||||
−0.528646 | + | 0.848842i | \(0.677300\pi\) | |||||||
\(384\) | −18.1607 | − | 8.25415i | −0.926758 | − | 0.421218i | ||||
\(385\) | 3.96214 | + | 6.86263i | 0.201929 | + | 0.349752i | ||||
\(386\) | −5.61566 | − | 9.72661i | −0.285829 | − | 0.495071i | ||||
\(387\) | 12.4124 | − | 2.43877i | 0.630958 | − | 0.123970i | ||||
\(388\) | 24.0067 | 1.21875 | ||||||||
\(389\) | −20.8651 | −1.05790 | −0.528951 | − | 0.848652i | \(-0.677415\pi\) | ||||
−0.528951 | + | 0.848652i | \(0.677415\pi\) | |||||||
\(390\) | −0.739928 | + | 0.528914i | −0.0374677 | + | 0.0267826i | ||||
\(391\) | −1.17622 | − | 2.03727i | −0.0594839 | − | 0.103029i | ||||
\(392\) | −1.38955 | − | 2.40678i | −0.0701831 | − | 0.121561i | ||||
\(393\) | −23.2799 | + | 16.6409i | −1.17431 | + | 0.839421i | ||||
\(394\) | 5.33317 | + | 9.23733i | 0.268681 | + | 0.465370i | ||||
\(395\) | 6.51272 | + | 11.2804i | 0.327691 | + | 0.567577i | ||||
\(396\) | −17.7708 | + | 3.49157i | −0.893014 | + | 0.175458i | ||||
\(397\) | −18.2808 | + | 31.6633i | −0.917488 | + | 1.58914i | −0.114271 | + | 0.993450i | \(0.536453\pi\) |
−0.803217 | + | 0.595686i | \(0.796880\pi\) | |||||||
\(398\) | −6.14229 | + | 10.6388i | −0.307885 | + | 0.533273i | ||||
\(399\) | 15.6540 | + | 8.64498i | 0.783680 | + | 0.432790i | ||||
\(400\) | 4.80155 | + | 8.31653i | 0.240078 | + | 0.415826i | ||||
\(401\) | 30.1489 | 1.50556 | 0.752782 | − | 0.658270i | \(-0.228712\pi\) | ||||
0.752782 | + | 0.658270i | \(0.228712\pi\) | |||||||
\(402\) | 1.55230 | − | 1.10961i | 0.0774216 | − | 0.0553424i | ||||
\(403\) | 9.21880 | 0.459221 | ||||||||
\(404\) | 3.15844 | − | 5.47059i | 0.157139 | − | 0.272172i | ||||
\(405\) | 6.73968 | + | 5.22189i | 0.334897 | + | 0.259478i | ||||
\(406\) | −4.50873 | −0.223765 | ||||||||
\(407\) | 0.610409 | − | 1.05726i | 0.0302569 | − | 0.0524064i | ||||
\(408\) | 0.233463 | + | 2.39920i | 0.0115581 | + | 0.118778i | ||||
\(409\) | −1.41342 | + | 2.44812i | −0.0698891 | + | 0.121051i | −0.898852 | − | 0.438252i | \(-0.855598\pi\) |
0.828963 | + | 0.559303i | \(0.188931\pi\) | |||||||
\(410\) | −2.90711 | − | 5.03527i | −0.143572 | − | 0.248674i | ||||
\(411\) | 15.7782 | − | 11.2786i | 0.778282 | − | 0.556330i | ||||
\(412\) | 7.41792 | 0.365455 | ||||||||
\(413\) | 13.1196 | − | 22.7239i | 0.645575 | − | 1.11817i | ||||
\(414\) | 1.76928 | − | 5.17229i | 0.0869554 | − | 0.254204i | ||||
\(415\) | −2.29079 | + | 3.96776i | −0.112450 | + | 0.194770i | ||||
\(416\) | 2.70493 | + | 4.68507i | 0.132620 | + | 0.229704i | ||||
\(417\) | −1.76965 | − | 18.1859i | −0.0866601 | − | 0.890567i | ||||
\(418\) | −4.69657 | + | 6.84180i | −0.229717 | + | 0.334643i | ||||
\(419\) | 10.4274 | + | 18.0609i | 0.509414 | + | 0.882331i | 0.999941 | + | 0.0109044i | \(0.00347106\pi\) |
−0.490527 | + | 0.871426i | \(0.663196\pi\) | |||||||
\(420\) | −6.04800 | − | 2.74885i | −0.295112 | − | 0.134130i | ||||
\(421\) | 4.98528 | + | 8.63476i | 0.242968 | + | 0.420832i | 0.961558 | − | 0.274601i | \(-0.0885457\pi\) |
−0.718591 | + | 0.695433i | \(0.755212\pi\) | |||||||
\(422\) | −3.44054 | − | 5.95919i | −0.167483 | − | 0.290089i | ||||
\(423\) | 9.95489 | − | 29.1020i | 0.484023 | − | 1.41499i | ||||
\(424\) | 6.66274 | + | 11.5402i | 0.323571 | + | 0.560442i | ||||
\(425\) | 1.42763 | − | 2.47273i | 0.0692502 | − | 0.119945i | ||||
\(426\) | 2.66974 | − | 1.90838i | 0.129349 | − | 0.0924612i | ||||
\(427\) | 4.11604 | − | 7.12919i | 0.199189 | − | 0.345006i | ||||
\(428\) | 6.11827 | − | 10.5972i | 0.295738 | − | 0.512233i | ||||
\(429\) | 5.72598 | + | 2.60249i | 0.276453 | + | 0.125650i | ||||
\(430\) | −1.07669 | + | 1.86488i | −0.0519225 | + | 0.0899325i | ||||
\(431\) | 14.8144 | + | 25.6593i | 0.713586 | + | 1.23597i | 0.963502 | + | 0.267700i | \(0.0862635\pi\) |
−0.249917 | + | 0.968267i | \(0.580403\pi\) | |||||||
\(432\) | 8.34560 | − | 8.84799i | 0.401528 | − | 0.425699i | ||||
\(433\) | −7.08725 | − | 12.2755i | −0.340592 | − | 0.589922i | 0.643951 | − | 0.765067i | \(-0.277294\pi\) |
−0.984543 | + | 0.175145i | \(0.943961\pi\) | |||||||
\(434\) | −5.72401 | − | 9.91428i | −0.274761 | − | 0.475901i | ||||
\(435\) | 4.71340 | − | 3.36923i | 0.225990 | − | 0.161542i | ||||
\(436\) | 0.615701 | + | 1.06642i | 0.0294867 | + | 0.0510725i | ||||
\(437\) | 6.35043 | + | 13.2947i | 0.303782 | + | 0.635970i | ||||
\(438\) | −6.95133 | + | 4.96894i | −0.332147 | + | 0.237425i | ||||
\(439\) | −11.4942 | − | 19.9085i | −0.548587 | − | 0.950181i | −0.998372 | − | 0.0570438i | \(-0.981833\pi\) |
0.449785 | − | 0.893137i | \(-0.351501\pi\) | |||||||
\(440\) | 3.34505 | − | 5.79379i | 0.159469 | − | 0.276208i | ||||
\(441\) | 4.09109 | − | 0.803809i | 0.194814 | − | 0.0382766i | ||||
\(442\) | 0.192893 | − | 0.334100i | 0.00917498 | − | 0.0158915i | ||||
\(443\) | 38.0848 | 1.80946 | 0.904732 | − | 0.425981i | \(-0.140071\pi\) | ||||
0.904732 | + | 0.425981i | \(0.140071\pi\) | |||||||
\(444\) | 0.0991257 | + | 1.01867i | 0.00470430 | + | 0.0483440i | ||||
\(445\) | 0.854768 | + | 1.48050i | 0.0405199 | + | 0.0701825i | ||||
\(446\) | −4.03149 | + | 6.98274i | −0.190896 | + | 0.330642i | ||||
\(447\) | −26.6289 | + | 19.0348i | −1.25950 | + | 0.900317i | ||||
\(448\) | −2.18527 | + | 3.78500i | −0.103244 | + | 0.178824i | ||||
\(449\) | 0.792571 | 0.0374037 | 0.0187019 | − | 0.999825i | \(-0.494047\pi\) | ||||
0.0187019 | + | 0.999825i | \(0.494047\pi\) | |||||||
\(450\) | 6.51050 | − | 1.27917i | 0.306908 | − | 0.0603007i | ||||
\(451\) | −20.1035 | + | 34.8203i | −0.946637 | + | 1.63962i | ||||
\(452\) | 4.38075 | 0.206053 | ||||||||
\(453\) | −3.52277 | − | 36.2020i | −0.165514 | − | 1.70092i | ||||
\(454\) | 4.93404 | 0.231566 | ||||||||
\(455\) | 1.15360 | + | 1.99809i | 0.0540816 | + | 0.0936721i | ||||
\(456\) | −0.287240 | − | 15.0946i | −0.0134513 | − | 0.706870i | ||||
\(457\) | 7.21629 | − | 12.4990i | 0.337564 | − | 0.584677i | −0.646410 | − | 0.762990i | \(-0.723731\pi\) |
0.983974 | + | 0.178313i | \(0.0570639\pi\) | |||||||
\(458\) | −5.12428 | + | 8.87552i | −0.239442 | + | 0.414726i | ||||
\(459\) | −3.51897 | − | 0.833558i | −0.164252 | − | 0.0389071i | ||||
\(460\) | −2.73676 | − | 4.74021i | −0.127602 | − | 0.221013i | ||||
\(461\) | 9.66701 | + | 16.7437i | 0.450237 | + | 0.779834i | 0.998400 | − | 0.0565374i | \(-0.0180060\pi\) |
−0.548163 | + | 0.836371i | \(0.684673\pi\) | |||||||
\(462\) | −0.756465 | − | 7.77386i | −0.0351939 | − | 0.361672i | ||||
\(463\) | −4.19274 | − | 7.26204i | −0.194853 | − | 0.337496i | 0.751999 | − | 0.659164i | \(-0.229090\pi\) |
−0.946852 | + | 0.321668i | \(0.895756\pi\) | |||||||
\(464\) | −4.13264 | − | 7.15794i | −0.191853 | − | 0.332299i | ||||
\(465\) | 13.3925 | + | 6.08697i | 0.621061 | + | 0.282276i | ||||
\(466\) | −4.58731 | −0.212503 | ||||||||
\(467\) | −28.8610 | −1.33553 | −0.667764 | − | 0.744373i | \(-0.732748\pi\) | ||||
−0.667764 | + | 0.744373i | \(0.732748\pi\) | |||||||
\(468\) | −5.17406 | + | 1.01659i | −0.239171 | + | 0.0469919i | ||||
\(469\) | −2.42014 | − | 4.19181i | −0.111752 | − | 0.193560i | ||||
\(470\) | 2.61795 | + | 4.53442i | 0.120757 | + | 0.209157i | ||||
\(471\) | 20.7091 | − | 14.8032i | 0.954224 | − | 0.682097i | ||||
\(472\) | −22.1526 | −1.01966 | ||||||||
\(473\) | 14.8912 | 0.684699 | ||||||||
\(474\) | −1.24343 | − | 12.7782i | −0.0571127 | − | 0.586922i | ||||
\(475\) | −10.1206 | + | 14.7433i | −0.464364 | + | 0.676470i | ||||
\(476\) | 2.81785 | 0.129156 | ||||||||
\(477\) | −19.6163 | + | 3.85417i | −0.898166 | + | 0.176470i | ||||
\(478\) | −5.29388 | + | 9.16928i | −0.242137 | + | 0.419393i | ||||
\(479\) | 13.2299 | 0.604491 | 0.302245 | − | 0.953230i | \(-0.402264\pi\) | ||||
0.302245 | + | 0.953230i | \(0.402264\pi\) | |||||||
\(480\) | 0.836094 | + | 8.59216i | 0.0381623 | + | 0.392177i | ||||
\(481\) | 0.177724 | − | 0.307827i | 0.00810353 | − | 0.0140357i | ||||
\(482\) | 2.44094 | + | 4.22783i | 0.111182 | + | 0.192572i | ||||
\(483\) | −12.6242 | − | 5.73777i | −0.574419 | − | 0.261077i | ||||
\(484\) | −2.51645 | −0.114384 | ||||||||
\(485\) | −6.65215 | − | 11.5219i | −0.302059 | − | 0.523181i | ||||
\(486\) | −3.91795 | − | 7.43437i | −0.177722 | − | 0.337230i | ||||
\(487\) | 20.4407 | 0.926254 | 0.463127 | − | 0.886292i | \(-0.346727\pi\) | ||||
0.463127 | + | 0.886292i | \(0.346727\pi\) | |||||||
\(488\) | −6.94996 | −0.314610 | ||||||||
\(489\) | −13.1593 | + | 9.40652i | −0.595085 | + | 0.425378i | ||||
\(490\) | −0.354873 | + | 0.614658i | −0.0160315 | + | 0.0277674i | ||||
\(491\) | 22.7484 | 1.02662 | 0.513311 | − | 0.858203i | \(-0.328419\pi\) | ||||
0.513311 | + | 0.858203i | \(0.328419\pi\) | |||||||
\(492\) | −3.26465 | − | 33.5494i | −0.147182 | − | 1.51252i | ||||
\(493\) | −1.22874 | + | 2.12825i | −0.0553398 | + | 0.0958514i | ||||
\(494\) | −1.36743 | + | 1.99203i | −0.0615237 | + | 0.0896257i | ||||
\(495\) | 6.59996 | + | 7.56147i | 0.296646 | + | 0.339863i | ||||
\(496\) | 10.4931 | − | 18.1746i | 0.471154 | − | 0.816062i | ||||
\(497\) | −4.16230 | − | 7.20932i | −0.186705 | − | 0.323382i | ||||
\(498\) | 3.67376 | − | 2.62607i | 0.164625 | − | 0.117677i | ||||
\(499\) | −21.2703 | −0.952191 | −0.476096 | − | 0.879394i | \(-0.657948\pi\) | ||||
−0.476096 | + | 0.879394i | \(0.657948\pi\) | |||||||
\(500\) | 7.37008 | − | 12.7654i | 0.329600 | − | 0.570884i | ||||
\(501\) | −3.45467 | − | 35.5021i | −0.154343 | − | 1.58612i | ||||
\(502\) | 7.40808 | − | 12.8312i | 0.330639 | − | 0.572683i | ||||
\(503\) | −3.61842 | − | 6.26728i | −0.161337 | − | 0.279444i | 0.774011 | − | 0.633172i | \(-0.218247\pi\) |
−0.935349 | + | 0.353728i | \(0.884914\pi\) | |||||||
\(504\) | 9.34383 | + | 10.7051i | 0.416207 | + | 0.476842i | ||||
\(505\) | −3.50077 | −0.155782 | ||||||||
\(506\) | 3.21759 | − | 5.57303i | 0.143039 | − | 0.247752i | ||||
\(507\) | −18.8316 | − | 8.55907i | −0.836339 | − | 0.380122i | ||||
\(508\) | −1.40140 | −0.0621773 | ||||||||
\(509\) | −1.54773 | + | 2.68074i | −0.0686017 | + | 0.118822i | −0.898286 | − | 0.439411i | \(-0.855187\pi\) |
0.829684 | + | 0.558233i | \(0.188520\pi\) | |||||||
\(510\) | 0.500821 | − | 0.357996i | 0.0221767 | − | 0.0158523i | ||||
\(511\) | 10.8376 | + | 18.7713i | 0.479427 | + | 0.830392i | ||||
\(512\) | 21.6768 | 0.957990 | ||||||||
\(513\) | 21.5660 | + | 6.92161i | 0.952161 | + | 0.305596i | ||||
\(514\) | −4.52906 | −0.199768 | ||||||||
\(515\) | −2.05547 | − | 3.56018i | −0.0905750 | − | 0.156880i | ||||
\(516\) | −10.1562 | + | 7.25986i | −0.447103 | + | 0.319597i | ||||
\(517\) | 18.1039 | − | 31.3568i | 0.796206 | − | 1.37907i | ||||
\(518\) | −0.441400 | −0.0193940 | ||||||||
\(519\) | 5.25015 | + | 2.38623i | 0.230456 | + | 0.104744i | ||||
\(520\) | 0.973930 | − | 1.68690i | 0.0427097 | − | 0.0739753i | ||||
\(521\) | −6.71566 | −0.294218 | −0.147109 | − | 0.989120i | \(-0.546997\pi\) | ||||
−0.147109 | + | 0.989120i | \(0.546997\pi\) | |||||||
\(522\) | −5.60351 | + | 1.10097i | −0.245259 | + | 0.0481881i | ||||
\(523\) | 3.39597 | + | 5.88200i | 0.148495 | + | 0.257202i | 0.930672 | − | 0.365856i | \(-0.119224\pi\) |
−0.782176 | + | 0.623057i | \(0.785890\pi\) | |||||||
\(524\) | 14.1207 | − | 24.4578i | 0.616865 | − | 1.06844i | ||||
\(525\) | −1.63010 | − | 16.7518i | −0.0711433 | − | 0.731108i | ||||
\(526\) | −2.64586 | + | 4.58276i | −0.115365 | + | 0.199818i | ||||
\(527\) | −6.23975 | −0.271808 | ||||||||
\(528\) | 11.6482 | − | 8.32635i | 0.506923 | − | 0.362358i | ||||
\(529\) | 5.78748 | + | 10.0242i | 0.251629 | + | 0.435835i | ||||
\(530\) | 1.70157 | − | 2.94721i | 0.0739115 | − | 0.128018i | ||||
\(531\) | 10.7564 | − | 31.4452i | 0.466789 | − | 1.36460i | ||||
\(532\) | −17.5948 | − | 1.37477i | −0.762832 | − | 0.0596038i | ||||
\(533\) | −5.85325 | + | 10.1381i | −0.253533 | + | 0.439131i | ||||
\(534\) | −0.163195 | − | 1.67708i | −0.00706215 | − | 0.0725745i | ||||
\(535\) | −6.78139 | −0.293185 | ||||||||
\(536\) | −2.04321 | + | 3.53895i | −0.0882533 | + | 0.152859i | ||||
\(537\) | 28.3087 | − | 20.2356i | 1.22161 | − | 0.873229i | ||||
\(538\) | 11.9193 | 0.513878 | ||||||||
\(539\) | 4.90809 | 0.211407 | ||||||||
\(540\) | −8.18776 | − | 1.93948i | −0.352345 | − | 0.0834619i | ||||
\(541\) | −10.3094 | − | 17.8564i | −0.443236 | − | 0.767707i | 0.554692 | − | 0.832056i | \(-0.312836\pi\) |
−0.997927 | + | 0.0643490i | \(0.979503\pi\) | |||||||
\(542\) | −1.42902 | −0.0613818 | ||||||||
\(543\) | 0.0379678 | + | 0.0172566i | 0.00162935 | + | 0.000740551i | ||||
\(544\) | −1.83083 | − | 3.17109i | −0.0784962 | − | 0.135959i | ||||
\(545\) | 0.341216 | − | 0.591003i | 0.0146161 | − | 0.0253158i | ||||
\(546\) | −0.220249 | − | 2.26340i | −0.00942580 | − | 0.0968647i | ||||
\(547\) | −22.6456 | −0.968257 | −0.484128 | − | 0.874997i | \(-0.660863\pi\) | ||||
−0.484128 | + | 0.874997i | \(0.660863\pi\) | |||||||
\(548\) | −9.57048 | + | 16.5766i | −0.408831 | + | 0.708115i | ||||
\(549\) | 3.37462 | − | 9.86533i | 0.144025 | − | 0.421042i | ||||
\(550\) | 7.81067 | 0.333048 | ||||||||
\(551\) | 8.71066 | − | 12.6894i | 0.371087 | − | 0.540586i | ||||
\(552\) | 1.13386 | + | 11.6522i | 0.0482602 | + | 0.495949i | ||||
\(553\) | −32.5675 | −1.38491 | ||||||||
\(554\) | −13.5392 | −0.575227 | ||||||||
\(555\) | 0.461437 | − | 0.329844i | 0.0195869 | − | 0.0140011i | ||||
\(556\) | 9.01633 | + | 15.6167i | 0.382377 | + | 0.662297i | ||||
\(557\) | −16.0313 | − | 27.7670i | −0.679266 | − | 1.17652i | −0.975202 | − | 0.221316i | \(-0.928965\pi\) |
0.295936 | − | 0.955208i | \(-0.404368\pi\) | |||||||
\(558\) | −9.53480 | − | 10.9239i | −0.403640 | − | 0.462445i | ||||
\(559\) | 4.33567 | 0.183379 | ||||||||
\(560\) | 5.25224 | 0.221947 | ||||||||
\(561\) | −3.87563 | − | 1.76150i | −0.163629 | − | 0.0743706i | ||||
\(562\) | 5.02825 | + | 8.70918i | 0.212104 | + | 0.367374i | ||||
\(563\) | −2.59076 | − | 4.48732i | −0.109187 | − | 0.189118i | 0.806254 | − | 0.591570i | \(-0.201492\pi\) |
−0.915441 | + | 0.402451i | \(0.868158\pi\) | |||||||
\(564\) | 2.93993 | + | 30.2123i | 0.123793 | + | 1.27217i | ||||
\(565\) | −1.21389 | − | 2.10252i | −0.0510687 | − | 0.0884535i | ||||
\(566\) | 5.89617 | + | 10.2125i | 0.247835 | + | 0.429262i | ||||
\(567\) | −19.7327 | + | 8.06543i | −0.828694 | + | 0.338716i | ||||
\(568\) | −3.51404 | + | 6.08649i | −0.147446 | + | 0.255384i | ||||
\(569\) | −10.8816 | + | 18.8474i | −0.456179 | + | 0.790125i | −0.998755 | − | 0.0498815i | \(-0.984116\pi\) |
0.542576 | + | 0.840007i | \(0.317449\pi\) | |||||||
\(570\) | −3.30181 | + | 1.99101i | −0.138298 | + | 0.0833941i | ||||
\(571\) | 19.5931 | + | 33.9363i | 0.819946 | + | 1.42019i | 0.905721 | + | 0.423874i | \(0.139330\pi\) |
−0.0857751 | + | 0.996315i | \(0.527337\pi\) | |||||||
\(572\) | −6.20734 | −0.259542 | ||||||||
\(573\) | 2.92444 | + | 30.0532i | 0.122170 | + | 1.25549i | ||||
\(574\) | 14.5373 | 0.606775 | ||||||||
\(575\) | 6.93355 | − | 12.0093i | 0.289149 | − | 0.500821i | ||||
\(576\) | −1.79164 | + | 5.23766i | −0.0746517 | + | 0.218236i | ||||
\(577\) | −15.9226 | −0.662866 | −0.331433 | − | 0.943479i | \(-0.607532\pi\) | ||||
−0.331433 | + | 0.943479i | \(0.607532\pi\) | |||||||
\(578\) | 4.45171 | − | 7.71058i | 0.185167 | − | 0.320718i | ||||
\(579\) | −29.3564 | + | 20.9845i | −1.22001 | + | 0.872086i | ||||
\(580\) | −2.85897 | + | 4.95189i | −0.118712 | + | 0.205616i | ||||
\(581\) | −5.72765 | − | 9.92058i | −0.237623 | − | 0.411575i | ||||
\(582\) | 1.27005 | + | 13.0517i | 0.0526453 | + | 0.541012i | ||||
\(583\) | −23.5337 | −0.974666 | ||||||||
\(584\) | 9.14968 | − | 15.8477i | 0.378616 | − | 0.655783i | ||||
\(585\) | 1.92162 | + | 2.20156i | 0.0794490 | + | 0.0910235i | ||||
\(586\) | −7.92665 | + | 13.7294i | −0.327447 | + | 0.567155i | ||||
\(587\) | 4.99469 | + | 8.65106i | 0.206153 | + | 0.357067i | 0.950499 | − | 0.310726i | \(-0.100572\pi\) |
−0.744347 | + | 0.667794i | \(0.767239\pi\) | |||||||
\(588\) | −3.34745 | + | 2.39282i | −0.138047 | + | 0.0986783i | ||||
\(589\) | 38.9613 | + | 3.04424i | 1.60537 | + | 0.125436i | ||||
\(590\) | 2.82873 | + | 4.89951i | 0.116457 | + | 0.201710i | ||||
\(591\) | 27.8797 | − | 19.9289i | 1.14682 | − | 0.819766i | ||||
\(592\) | −0.404581 | − | 0.700755i | −0.0166282 | − | 0.0288009i | ||||
\(593\) | −5.45091 | − | 9.44125i | −0.223842 | − | 0.387705i | 0.732129 | − | 0.681165i | \(-0.238527\pi\) |
−0.955971 | + | 0.293460i | \(0.905193\pi\) | |||||||
\(594\) | −2.83841 | − | 9.47673i | −0.116461 | − | 0.388835i | ||||
\(595\) | −0.780815 | − | 1.35241i | −0.0320103 | − | 0.0554434i | ||||
\(596\) | 16.1521 | − | 27.9763i | 0.661616 | − | 1.14595i | ||||
\(597\) | 35.9321 | + | 16.3314i | 1.47060 | + | 0.668398i | ||||
\(598\) | 0.936821 | − | 1.62262i | 0.0383094 | − | 0.0663539i | ||||
\(599\) | 0.160528 | − | 0.278042i | 0.00655898 | − | 0.0113605i | −0.862727 | − | 0.505669i | \(-0.831246\pi\) |
0.869286 | + | 0.494309i | \(0.164579\pi\) | |||||||
\(600\) | −11.5599 | + | 8.26321i | −0.471930 | + | 0.337344i | ||||
\(601\) | −2.05961 | + | 3.56734i | −0.0840131 | + | 0.145515i | −0.904970 | − | 0.425475i | \(-0.860107\pi\) |
0.820957 | + | 0.570990i | \(0.193440\pi\) | |||||||
\(602\) | −2.69204 | − | 4.66275i | −0.109719 | − | 0.190040i | ||||
\(603\) | −4.03136 | − | 4.61867i | −0.164170 | − | 0.188087i | ||||
\(604\) | 17.9485 | + | 31.0876i | 0.730312 | + | 1.26494i | ||||
\(605\) | 0.697296 | + | 1.20775i | 0.0283491 | + | 0.0491021i | ||||
\(606\) | 3.14130 | + | 1.42774i | 0.127606 | + | 0.0579980i | ||||
\(607\) | −16.5062 | − | 28.5895i | −0.669964 | − | 1.16041i | −0.977914 | − | 0.209009i | \(-0.932976\pi\) |
0.307950 | − | 0.951403i | \(-0.400357\pi\) | |||||||
\(608\) | 9.88470 | + | 20.6937i | 0.400877 | + | 0.839240i | ||||
\(609\) | 1.40301 | + | 14.4181i | 0.0568527 | + | 0.584249i | ||||
\(610\) | 0.887461 | + | 1.53713i | 0.0359323 | + | 0.0622365i | ||||
\(611\) | 5.27104 | − | 9.12971i | 0.213244 | − | 0.369349i | ||||
\(612\) | 3.50206 | − | 0.688079i | 0.141563 | − | 0.0278140i | ||||
\(613\) | −4.42444 | + | 7.66335i | −0.178701 | + | 0.309520i | −0.941436 | − | 0.337192i | \(-0.890523\pi\) |
0.762735 | + | 0.646712i | \(0.223856\pi\) | |||||||
\(614\) | −11.1605 | −0.450402 | ||||||||
\(615\) | −15.1972 | + | 10.8632i | −0.612810 | + | 0.438048i | ||||
\(616\) | 8.36361 | + | 14.4862i | 0.336980 | + | 0.583666i | ||||
\(617\) | −18.6601 | + | 32.3203i | −0.751229 | + | 1.30117i | 0.195999 | + | 0.980604i | \(0.437205\pi\) |
−0.947227 | + | 0.320562i | \(0.896128\pi\) | |||||||
\(618\) | 0.392438 | + | 4.03291i | 0.0157862 | + | 0.162227i | ||||
\(619\) | 19.2996 | − | 33.4279i | 0.775716 | − | 1.34358i | −0.158674 | − | 0.987331i | \(-0.550722\pi\) |
0.934391 | − | 0.356249i | \(-0.115945\pi\) | |||||||
\(620\) | −14.5183 | −0.583070 | ||||||||
\(621\) | −17.0906 | − | 4.04833i | −0.685821 | − | 0.162454i | ||||
\(622\) | 7.55833 | − | 13.0914i | 0.303061 | − | 0.524918i | ||||
\(623\) | −4.27435 | −0.171248 | ||||||||
\(624\) | 3.39144 | − | 2.42426i | 0.135766 | − | 0.0970483i | ||||
\(625\) | 12.3440 | 0.493760 | ||||||||
\(626\) | −0.945615 | − | 1.63785i | −0.0377944 | − | 0.0654617i | ||||
\(627\) | 23.3402 | + | 12.8897i | 0.932119 | + | 0.514766i | ||||
\(628\) | −12.5614 | + | 21.7569i | −0.501252 | + | 0.868195i | ||||
\(629\) | −0.120293 | + | 0.208353i | −0.00479639 | + | 0.00830758i | ||||
\(630\) | 1.17451 | − | 3.43355i | 0.0467936 | − | 0.136796i | ||||
\(631\) | 3.06627 | + | 5.31093i | 0.122066 | + | 0.211425i | 0.920582 | − | 0.390549i | \(-0.127715\pi\) |
−0.798516 | + | 0.601973i | \(0.794381\pi\) | |||||||
\(632\) | 13.7476 | + | 23.8115i | 0.546850 | + | 0.947172i | ||||
\(633\) | −17.9858 | + | 12.8566i | −0.714870 | + | 0.511002i | ||||
\(634\) | 2.38790 | + | 4.13596i | 0.0948356 | + | 0.164260i | ||||
\(635\) | 0.388323 | + | 0.672596i | 0.0154101 | + | 0.0266911i | ||||
\(636\) | 16.0506 | − | 11.4733i | 0.636449 | − | 0.454945i | ||||
\(637\) | 1.42902 | 0.0566198 | ||||||||
\(638\) | −6.72255 | −0.266148 | ||||||||
\(639\) | −6.93338 | − | 7.94347i | −0.274280 | − | 0.314239i | ||||
\(640\) | −5.45529 | − | 9.44883i | −0.215639 | − | 0.373498i | ||||
\(641\) | 8.01360 | + | 13.8800i | 0.316518 | + | 0.548225i | 0.979759 | − | 0.200181i | \(-0.0641529\pi\) |
−0.663241 | + | 0.748406i | \(0.730820\pi\) | |||||||
\(642\) | 6.08505 | + | 2.76570i | 0.240158 | + | 0.109153i | ||||
\(643\) | −49.8726 | −1.96678 | −0.983391 | − | 0.181500i | \(-0.941905\pi\) | ||||
−0.983391 | + | 0.181500i | \(0.941905\pi\) | |||||||
\(644\) | 13.6854 | 0.539282 | ||||||||
\(645\) | 6.29857 | + | 2.86274i | 0.248006 | + | 0.112720i | ||||
\(646\) | 0.925548 | − | 1.34831i | 0.0364152 | − | 0.0530484i | ||||
\(647\) | −38.7875 | −1.52490 | −0.762448 | − | 0.647050i | \(-0.776003\pi\) | ||||
−0.762448 | + | 0.647050i | \(0.776003\pi\) | |||||||
\(648\) | 14.2267 | + | 11.0228i | 0.558876 | + | 0.433016i | ||||
\(649\) | 19.5615 | − | 33.8815i | 0.767856 | − | 1.32997i | ||||
\(650\) | 2.27412 | 0.0891985 | ||||||||
\(651\) | −29.9228 | + | 21.3894i | −1.17277 | + | 0.838316i | ||||
\(652\) | 7.98195 | − | 13.8251i | 0.312597 | − | 0.541434i | ||||
\(653\) | 1.10578 | + | 1.91527i | 0.0432727 | + | 0.0749505i | 0.886851 | − | 0.462056i | \(-0.152888\pi\) |
−0.843578 | + | 0.537007i | \(0.819555\pi\) | |||||||
\(654\) | −0.547212 | + | 0.391157i | −0.0213977 | + | 0.0152955i | ||||
\(655\) | −15.6511 | −0.611541 | ||||||||
\(656\) | 13.3247 | + | 23.0790i | 0.520241 | + | 0.901084i | ||||
\(657\) | 18.0528 | + | 20.6828i | 0.704307 | + | 0.806913i | ||||
\(658\) | −13.0913 | −0.510352 | ||||||||
\(659\) | −38.2285 | −1.48917 | −0.744585 | − | 0.667528i | \(-0.767352\pi\) | ||||
−0.744585 | + | 0.667528i | \(0.767352\pi\) | |||||||
\(660\) | −9.01761 | − | 4.09856i | −0.351010 | − | 0.159536i | ||||
\(661\) | −1.04926 | + | 1.81737i | −0.0408115 | + | 0.0706876i | −0.885710 | − | 0.464240i | \(-0.846328\pi\) |
0.844898 | + | 0.534927i | \(0.179661\pi\) | |||||||
\(662\) | 3.89855 | 0.151522 | ||||||||
\(663\) | −1.12841 | − | 0.512871i | −0.0438239 | − | 0.0199183i | ||||
\(664\) | −4.83559 | + | 8.37548i | −0.187657 | + | 0.325032i | ||||
\(665\) | 4.21564 | + | 8.82546i | 0.163475 | + | 0.342237i | ||||
\(666\) | −0.548578 | + | 0.107784i | −0.0212570 | + | 0.00417653i | ||||
\(667\) | −5.96762 | + | 10.3362i | −0.231067 | + | 0.400220i | ||||
\(668\) | 17.6015 | + | 30.4867i | 0.681022 | + | 1.17956i | ||||
\(669\) | 23.5840 | + | 10.7191i | 0.911809 | + | 0.414423i | ||||
\(670\) | 1.04362 | 0.0403184 | ||||||||
\(671\) | 6.13705 | − | 10.6297i | 0.236918 | − | 0.410354i | ||||
\(672\) | −19.6500 | − | 8.93107i | −0.758016 | − | 0.344523i | ||||
\(673\) | 7.22940 | − | 12.5217i | 0.278673 | − | 0.482675i | −0.692382 | − | 0.721531i | \(-0.743439\pi\) |
0.971055 | + | 0.238855i | \(0.0767722\pi\) | |||||||
\(674\) | −1.29513 | − | 2.24323i | −0.0498864 | − | 0.0864058i | ||||
\(675\) | −6.11646 | − | 20.4213i | −0.235423 | − | 0.786016i | ||||
\(676\) | 20.4147 | 0.785179 | ||||||||
\(677\) | 20.3340 | − | 35.2196i | 0.781500 | − | 1.35360i | −0.149568 | − | 0.988752i | \(-0.547788\pi\) |
0.931068 | − | 0.364847i | \(-0.118879\pi\) | |||||||
\(678\) | 0.231760 | + | 2.38169i | 0.00890068 | + | 0.0914683i | ||||
\(679\) | 33.2647 | 1.27658 | ||||||||
\(680\) | −0.659205 | + | 1.14178i | −0.0252794 | + | 0.0437851i | ||||
\(681\) | −1.53535 | − | 15.7781i | −0.0588348 | − | 0.604619i | ||||
\(682\) | −8.53455 | − | 14.7823i | −0.326805 | − | 0.566042i | ||||
\(683\) | −2.83223 | −0.108372 | −0.0541861 | − | 0.998531i | \(-0.517256\pi\) | ||||
−0.0541861 | + | 0.998531i | \(0.517256\pi\) | |||||||
\(684\) | −22.2028 | + | 2.58782i | −0.848944 | + | 0.0989479i | ||||
\(685\) | 10.6078 | 0.405301 | ||||||||
\(686\) | −5.35639 | − | 9.27753i | −0.204508 | − | 0.354218i | ||||
\(687\) | 29.9768 | + | 13.6246i | 1.14369 | + | 0.519812i | ||||
\(688\) | 4.93497 | − | 8.54762i | 0.188144 | − | 0.325875i | ||||
\(689\) | −6.85197 | −0.261039 | ||||||||
\(690\) | 2.43233 | − | 1.73868i | 0.0925973 | − | 0.0661903i | ||||
\(691\) | −12.1329 | + | 21.0148i | −0.461558 | + | 0.799441i | −0.999039 | − | 0.0438345i | \(-0.986043\pi\) |
0.537481 | + | 0.843276i | \(0.319376\pi\) | |||||||
\(692\) | −5.69151 | −0.216359 | ||||||||
\(693\) | −24.6239 | + | 4.83806i | −0.935385 | + | 0.183783i | ||||
\(694\) | −1.95522 | − | 3.38654i | −0.0742190 | − | 0.128551i | ||||
\(695\) | 4.99677 | − | 8.65466i | 0.189538 | − | 0.328290i | ||||
\(696\) | 9.94944 | − | 7.11205i | 0.377133 | − | 0.269581i | ||||
\(697\) | 3.96178 | − | 6.86200i | 0.150063 | − | 0.259917i | ||||
\(698\) | −3.19785 | −0.121040 | ||||||||
\(699\) | 1.42746 | + | 14.6694i | 0.0539915 | + | 0.554846i | ||||
\(700\) | 8.30531 | + | 14.3852i | 0.313911 | + | 0.543710i | ||||
\(701\) | −1.69604 | + | 2.93763i | −0.0640585 | + | 0.110953i | −0.896276 | − | 0.443497i | \(-0.853738\pi\) |
0.832217 | + | 0.554449i | \(0.187071\pi\) | |||||||
\(702\) | −0.826420 | − | 2.75921i | −0.0311912 | − | 0.104140i | ||||
\(703\) | 0.852765 | − | 1.24228i | 0.0321626 | − | 0.0468534i | ||||
\(704\) | −3.25826 | + | 5.64347i | −0.122800 | + | 0.212696i | ||||
\(705\) | 13.6856 | − | 9.78270i | 0.515428 | − | 0.368438i | ||||
\(706\) | 16.1379 | 0.607359 | ||||||||
\(707\) | 4.37648 | − | 7.58028i | 0.164594 | − | 0.285086i | ||||
\(708\) | 3.17663 | + | 32.6449i | 0.119385 | + | 1.22687i | ||||
\(709\) | 16.7072 | 0.627452 | 0.313726 | − | 0.949514i | \(-0.398423\pi\) | ||||
0.313726 | + | 0.949514i | \(0.398423\pi\) | |||||||
\(710\) | 1.79487 | 0.0673604 | ||||||||
\(711\) | −40.4753 | + | 7.95252i | −1.51794 | + | 0.298243i | ||||
\(712\) | 1.80431 | + | 3.12516i | 0.0676195 | + | 0.117120i | ||||
\(713\) | −30.3045 | −1.13491 | ||||||||
\(714\) | 0.149076 | + | 1.53199i | 0.00557902 | + | 0.0573331i | ||||
\(715\) | 1.72003 | + | 2.97917i | 0.0643254 | + | 0.111415i | ||||
\(716\) | −17.1710 | + | 29.7410i | −0.641710 | + | 1.11147i | ||||
\(717\) | 30.9689 | + | 14.0756i | 1.15656 | + | 0.525662i | ||||
\(718\) | 5.12705 | 0.191340 | ||||||||
\(719\) | −3.10479 | + | 5.37765i | −0.115789 | + | 0.200553i | −0.918095 | − | 0.396361i | \(-0.870273\pi\) |
0.802306 | + | 0.596913i | \(0.203606\pi\) | |||||||
\(720\) | 6.52755 | − | 1.28252i | 0.243267 | − | 0.0477967i | ||||
\(721\) | 10.2786 | 0.382795 | ||||||||
\(722\) | −6.43698 | + | 7.96734i | −0.239559 | + | 0.296514i | ||||
\(723\) | 12.7602 | − | 9.12126i | 0.474558 | − | 0.339223i | ||||
\(724\) | −0.0411596 | −0.00152968 | ||||||||
\(725\) | −14.4864 | −0.538010 | ||||||||
\(726\) | −0.133130 | − | 1.36812i | −0.00494092 | − | 0.0507757i | ||||
\(727\) | −6.07332 | − | 10.5193i | −0.225247 | − | 0.390139i | 0.731147 | − | 0.682220i | \(-0.238986\pi\) |
−0.956393 | + | 0.292081i | \(0.905652\pi\) | |||||||
\(728\) | 2.43511 | + | 4.21774i | 0.0902513 | + | 0.156320i | ||||
\(729\) | −22.5545 | + | 14.8423i | −0.835353 | + | 0.549713i | ||||
\(730\) | −4.67340 | −0.172970 | ||||||||
\(731\) | −2.93460 | −0.108540 | ||||||||
\(732\) | 0.996609 | + | 10.2417i | 0.0368357 | + | 0.378544i | ||||
\(733\) | 7.98422 | + | 13.8291i | 0.294904 | + | 0.510788i | 0.974963 | − | 0.222369i | \(-0.0713791\pi\) |
−0.680059 | + | 0.733158i | \(0.738046\pi\) | |||||||
\(734\) | −3.77335 | − | 6.53564i | −0.139277 | − | 0.241235i | ||||
\(735\) | 2.07599 | + | 0.943549i | 0.0765739 | + | 0.0348033i | ||||
\(736\) | −8.89178 | − | 15.4010i | −0.327755 | − | 0.567689i | ||||
\(737\) | −3.60845 | − | 6.25002i | −0.132919 | − | 0.230222i | ||||
\(738\) | 18.0671 | − | 3.54980i | 0.665060 | − | 0.130670i | ||||
\(739\) | 10.1128 | − | 17.5160i | 0.372007 | − | 0.644335i | −0.617867 | − | 0.786283i | \(-0.712003\pi\) |
0.989874 | + | 0.141947i | \(0.0453363\pi\) | |||||||
\(740\) | −0.279891 | + | 0.484785i | −0.0102890 | + | 0.0178211i | ||||
\(741\) | 6.79565 | + | 3.75292i | 0.249644 | + | 0.137867i | ||||
\(742\) | 4.25443 | + | 7.36889i | 0.156185 | + | 0.270521i | ||||
\(743\) | −45.8605 | −1.68246 | −0.841230 | − | 0.540677i | \(-0.818168\pi\) | ||||
−0.841230 | + | 0.540677i | \(0.818168\pi\) | |||||||
\(744\) | 28.2699 | + | 12.8489i | 1.03643 | + | 0.471063i | ||||
\(745\) | −17.9027 | −0.655905 | ||||||||
\(746\) | −2.72613 | + | 4.72179i | −0.0998106 | + | 0.172877i | ||||
\(747\) | −9.54087 | − | 10.9308i | −0.349082 | − | 0.399938i | ||||
\(748\) | 4.20144 | 0.153620 | ||||||||
\(749\) | 8.47774 | − | 14.6839i | 0.309770 | − | 0.536537i | ||||
\(750\) | 7.33007 | + | 3.33156i | 0.267656 | + | 0.121651i | ||||
\(751\) | −0.779462 | + | 1.35007i | −0.0284430 | + | 0.0492647i | −0.879897 | − | 0.475165i | \(-0.842388\pi\) |
0.851454 | + | 0.524430i | \(0.175722\pi\) | |||||||
\(752\) | −11.9993 | − | 20.7834i | −0.437569 | − | 0.757892i | ||||
\(753\) | −43.3369 | − | 19.6969i | −1.57928 | − | 0.717795i | ||||
\(754\) | −1.95731 | −0.0712811 | ||||||||
\(755\) | 9.94688 | − | 17.2285i | 0.362004 | − | 0.627009i | ||||
\(756\) | 14.4355 | − | 15.3045i | 0.525014 | − | 0.556619i | ||||
\(757\) | 25.2859 | − | 43.7964i | 0.919031 | − | 1.59181i | 0.118141 | − | 0.992997i | \(-0.462307\pi\) |
0.800890 | − | 0.598812i | \(-0.204360\pi\) | |||||||
\(758\) | 9.32190 | + | 16.1460i | 0.338587 | + | 0.586449i | ||||
\(759\) | −18.8227 | − | 8.55506i | −0.683222 | − | 0.310529i | ||||
\(760\) | 4.67316 | − | 6.80770i | 0.169513 | − | 0.246941i | ||||
\(761\) | 9.57656 | + | 16.5871i | 0.347150 | + | 0.601282i | 0.985742 | − | 0.168264i | \(-0.0538161\pi\) |
−0.638592 | + | 0.769546i | \(0.720483\pi\) | |||||||
\(762\) | −0.0741400 | − | 0.761904i | −0.00268581 | − | 0.0276009i | ||||
\(763\) | 0.853141 | + | 1.47768i | 0.0308858 | + | 0.0534958i | ||||
\(764\) | −14.9000 | − | 25.8075i | −0.539062 | − | 0.933683i | ||||
\(765\) | −1.30065 | − | 1.49013i | −0.0470250 | − | 0.0538758i | ||||
\(766\) | 5.57733 | + | 9.66021i | 0.201517 | + | 0.349038i | ||||
\(767\) | 5.69544 | − | 9.86480i | 0.205651 | − | 0.356197i | ||||
\(768\) | 0.422470 | + | 4.34153i | 0.0152446 | + | 0.156662i | ||||
\(769\) | −13.4848 | + | 23.3564i | −0.486274 | + | 0.842252i | −0.999876 | − | 0.0157771i | \(-0.994978\pi\) |
0.513601 | + | 0.858029i | \(0.328311\pi\) | |||||||
\(770\) | 2.13595 | − | 3.69957i | 0.0769743 | − | 0.133323i | ||||
\(771\) | 1.40933 | + | 14.4831i | 0.0507558 | + | 0.521595i | ||||
\(772\) | 17.8065 | − | 30.8417i | 0.640870 | − | 1.11002i | ||||
\(773\) | 16.8163 | + | 29.1266i | 0.604839 | + | 1.04761i | 0.992077 | + | 0.125632i | \(0.0400957\pi\) |
−0.387238 | + | 0.921980i | \(0.626571\pi\) | |||||||
\(774\) | −4.48428 | − | 5.13757i | −0.161184 | − | 0.184666i | ||||
\(775\) | −18.3910 | − | 31.8541i | −0.660624 | − | 1.14423i | ||||
\(776\) | −14.0419 | − | 24.3213i | −0.504075 | − | 0.873084i | ||||
\(777\) | 0.137353 | + | 1.41151i | 0.00492751 | + | 0.0506378i | ||||
\(778\) | 5.62409 | + | 9.74120i | 0.201633 | + | 0.349239i | ||||
\(779\) | −28.0854 | + | 40.9138i | −1.00626 | + | 1.46589i | ||||
\(780\) | −2.62553 | − | 1.19332i | −0.0940091 | − | 0.0427277i | ||||
\(781\) | −6.20603 | − | 10.7492i | −0.222069 | − | 0.384635i | ||||
\(782\) | −0.634088 | + | 1.09827i | −0.0226749 | + | 0.0392741i | ||||
\(783\) | 5.26436 | + | 17.5764i | 0.188133 | + | 0.628128i | ||||
\(784\) | 1.62655 | − | 2.81727i | 0.0580910 | − | 0.100617i | ||||
\(785\) | 13.9228 | 0.496926 | ||||||||
\(786\) | 14.0440 | + | 6.38310i | 0.500934 | + | 0.227678i | ||||
\(787\) | −9.33719 | − | 16.1725i | −0.332835 | − | 0.576487i | 0.650232 | − | 0.759736i | \(-0.274672\pi\) |
−0.983067 | + | 0.183249i | \(0.941338\pi\) | |||||||
\(788\) | −16.9108 | + | 29.2903i | −0.602421 | + | 1.04342i | ||||
\(789\) | 15.4781 | + | 7.03491i | 0.551036 | + | 0.250449i | ||||
\(790\) | 3.51095 | − | 6.08114i | 0.124914 | − | 0.216357i | ||||
\(791\) | 6.07016 | 0.215830 | ||||||||
\(792\) | 13.9317 | + | 15.9614i | 0.495043 | + | 0.567163i | ||||
\(793\) | 1.78684 | − | 3.09489i | 0.0634524 | − | 0.109903i | ||||
\(794\) | 19.7100 | 0.699482 | ||||||||
\(795\) | −9.95410 | − | 4.52420i | −0.353035 | − | 0.160457i | ||||
\(796\) | −38.9528 | −1.38064 | ||||||||
\(797\) | −10.8236 | − | 18.7470i | −0.383391 | − | 0.664053i | 0.608153 | − | 0.793820i | \(-0.291911\pi\) |
−0.991545 | + | 0.129766i | \(0.958577\pi\) | |||||||
\(798\) | −0.183415 | − | 9.63853i | −0.00649282 | − | 0.341200i | ||||
\(799\) | −3.56771 | + | 6.17945i | −0.126216 | + | 0.218613i | ||||
\(800\) | 10.7924 | − | 18.6929i | 0.381567 | − | 0.660894i | ||||
\(801\) | −5.31221 | + | 1.04373i | −0.187698 | + | 0.0368785i | ||||
\(802\) | −8.12649 | − | 14.0755i | −0.286956 | − | 0.497023i | ||||
\(803\) | 16.1590 | + | 27.9881i | 0.570237 | + | 0.987680i | ||||
\(804\) | 5.50811 | + | 2.50347i | 0.194256 | + | 0.0882906i | ||||
\(805\) | −3.79217 | − | 6.56824i | −0.133657 | − | 0.231500i | ||||
\(806\) | −2.48488 | − | 4.30394i | −0.0875263 | − | 0.151600i | ||||
\(807\) | −3.70900 | − | 38.1157i | −0.130563 | − | 1.34174i | ||||
\(808\) | −7.38971 | −0.259969 | ||||||||
\(809\) | 31.4292 | 1.10499 | 0.552497 | − | 0.833515i | \(-0.313675\pi\) | ||||
0.552497 | + | 0.833515i | \(0.313675\pi\) | |||||||
\(810\) | 0.621273 | − | 4.55406i | 0.0218293 | − | 0.160013i | ||||
\(811\) | 11.9511 | + | 20.6999i | 0.419660 | + | 0.726873i | 0.995905 | − | 0.0904042i | \(-0.0288159\pi\) |
−0.576245 | + | 0.817277i | \(0.695483\pi\) | |||||||
\(812\) | −7.14829 | − | 12.3812i | −0.250856 | − | 0.434495i | ||||
\(813\) | 0.444677 | + | 4.56974i | 0.0155955 | + | 0.160268i | ||||
\(814\) | −0.658131 | −0.0230675 | ||||||||
\(815\) | −8.84706 | −0.309899 | ||||||||
\(816\) | −2.29550 | + | 1.64086i | −0.0803585 | + | 0.0574418i | ||||
\(817\) | 18.3238 | + | 1.43173i | 0.641068 | + | 0.0500897i | ||||
\(818\) | 1.52392 | 0.0532827 | ||||||||
\(819\) | −7.16940 | + | 1.40863i | −0.250519 | + | 0.0492215i | ||||
\(820\) | 9.21806 | − | 15.9661i | 0.321909 | − | 0.557562i | ||||
\(821\) | 25.7288 | 0.897941 | 0.448971 | − | 0.893547i | \(-0.351791\pi\) | ||||
0.448971 | + | 0.893547i | \(0.351791\pi\) | |||||||
\(822\) | −9.51852 | − | 4.32623i | −0.331996 | − | 0.150895i | ||||
\(823\) | −4.09677 | + | 7.09581i | −0.142804 | + | 0.247344i | −0.928552 | − | 0.371203i | \(-0.878945\pi\) |
0.785747 | + | 0.618548i | \(0.212279\pi\) | |||||||
\(824\) | −4.33886 | − | 7.51513i | −0.151151 | − | 0.261802i | ||||
\(825\) | −2.43049 | − | 24.9771i | −0.0846188 | − | 0.869589i | ||||
\(826\) | −14.1453 | −0.492179 | ||||||||
\(827\) | −5.21701 | − | 9.03613i | −0.181413 | − | 0.314217i | 0.760949 | − | 0.648812i | \(-0.224734\pi\) |
−0.942362 | + | 0.334595i | \(0.891401\pi\) | |||||||
\(828\) | 17.0084 | − | 3.34179i | 0.591084 | − | 0.116135i | ||||
\(829\) | 12.6151 | 0.438142 | 0.219071 | − | 0.975709i | \(-0.429697\pi\) | ||||
0.219071 | + | 0.975709i | \(0.429697\pi\) | |||||||
\(830\) | 2.46988 | 0.0857309 | ||||||||
\(831\) | 4.21308 | + | 43.2959i | 0.146150 | + | 1.50192i | ||||
\(832\) | −0.948660 | + | 1.64313i | −0.0328889 | + | 0.0569652i | ||||
\(833\) | −0.967233 | −0.0335126 | ||||||||
\(834\) | −8.01337 | + | 5.72811i | −0.277480 | + | 0.198348i | ||||
\(835\) | 9.75459 | − | 16.8954i | 0.337571 | − | 0.584691i | ||||
\(836\) | −26.2340 | − | 2.04979i | −0.907322 | − | 0.0708935i | ||||
\(837\) | −31.9655 | + | 33.8897i | −1.10489 | + | 1.17140i | ||||
\(838\) | 5.62133 | − | 9.73643i | 0.194186 | − | 0.336339i | ||||
\(839\) | 2.96470 | + | 5.13502i | 0.102353 | + | 0.177281i | 0.912654 | − | 0.408734i | \(-0.134030\pi\) |
−0.810301 | + | 0.586014i | \(0.800696\pi\) | |||||||
\(840\) | 0.752695 | + | 7.73511i | 0.0259704 | + | 0.266887i | ||||
\(841\) | −16.5318 | −0.570061 | ||||||||
\(842\) | 2.68752 | − | 4.65492i | 0.0926179 | − | 0.160419i | ||||
\(843\) | 26.2856 | − | 18.7895i | 0.905325 | − | 0.647143i | ||||
\(844\) | 10.9095 | − | 18.8958i | 0.375520 | − | 0.650420i | ||||
\(845\) | −5.65681 | − | 9.79789i | −0.194600 | − | 0.337058i | ||||
\(846\) | −16.2700 | + | 3.19671i | −0.559375 | + | 0.109905i | ||||
\(847\) | −3.48689 | −0.119811 | ||||||||
\(848\) | −7.79910 | + | 13.5084i | −0.267822 | + | 0.463882i | ||||
\(849\) | 30.8228 | − | 22.0327i | 1.05784 | − | 0.756161i | ||||
\(850\) | −1.53924 | −0.0527956 | ||||||||
\(851\) | −0.584224 | + | 1.01191i | −0.0200270 | + | 0.0346877i | ||||
\(852\) | 9.47318 | + | 4.30562i | 0.324546 | + | 0.147508i | ||||
\(853\) | 15.1615 | + | 26.2605i | 0.519119 | + | 0.899141i | 0.999753 | + | 0.0222195i | \(0.00707327\pi\) |
−0.480634 | + | 0.876921i | \(0.659593\pi\) | |||||||
\(854\) | −4.43783 | −0.151859 | ||||||||
\(855\) | 7.39430 | + | 9.93901i | 0.252880 | + | 0.339907i | ||||
\(856\) | −14.3147 | −0.489267 | ||||||||
\(857\) | 11.3907 | + | 19.7292i | 0.389098 | + | 0.673937i | 0.992328 | − | 0.123630i | \(-0.0394535\pi\) |
−0.603231 | + | 0.797567i | \(0.706120\pi\) | |||||||
\(858\) | −0.328393 | − | 3.37475i | −0.0112112 | − | 0.115212i | ||||
\(859\) | −5.66587 | + | 9.81358i | −0.193317 | + | 0.334835i | −0.946348 | − | 0.323151i | \(-0.895258\pi\) |
0.753030 | + | 0.657986i | \(0.228591\pi\) | |||||||
\(860\) | −6.82807 | −0.232835 | ||||||||
\(861\) | −4.52365 | − | 46.4875i | −0.154165 | − | 1.58429i | ||||
\(862\) | 7.98631 | − | 13.8327i | 0.272015 | − | 0.471144i | ||||
\(863\) | −30.4557 | −1.03672 | −0.518362 | − | 0.855162i | \(-0.673458\pi\) | ||||
−0.518362 | + | 0.855162i | \(0.673458\pi\) | |||||||
\(864\) | −26.6022 | − | 6.30139i | −0.905024 | − | 0.214378i | ||||
\(865\) | 1.57709 | + | 2.73161i | 0.0536228 | + | 0.0928774i | ||||
\(866\) | −3.82067 | + | 6.61759i | −0.129832 | + | 0.224875i | ||||
\(867\) | −26.0422 | − | 11.8364i | −0.884441 | − | 0.401984i | ||||
\(868\) | 18.1501 | − | 31.4368i | 0.616053 | − | 1.06704i | ||||
\(869\) | −48.5584 | −1.64723 | ||||||||
\(870\) | −2.84345 | − | 1.29237i | −0.0964021 | − | 0.0438154i | ||||
\(871\) | −1.05062 | − | 1.81973i | −0.0355989 | − | 0.0616592i | ||||
\(872\) | 0.720267 | − | 1.24754i | 0.0243913 | − | 0.0422470i | ||||
\(873\) | 41.3418 | − | 8.12277i | 1.39921 | − | 0.274914i | ||||
\(874\) | 4.49510 | − | 6.54831i | 0.152049 | − | 0.221500i | ||||
\(875\) | 10.2123 | − | 17.6882i | 0.345239 | − | 0.597971i | ||||
\(876\) | −24.6658 | − | 11.2108i | −0.833380 | − | 0.378777i | ||||
\(877\) | 5.47013 | 0.184713 | 0.0923566 | − | 0.995726i | \(-0.470560\pi\) | ||||
0.0923566 | + | 0.995726i | \(0.470560\pi\) | |||||||
\(878\) | −6.19640 | + | 10.7325i | −0.209118 | + | 0.362204i | ||||
\(879\) | 46.3705 | + | 21.0757i | 1.56404 | + | 0.710865i | ||||
\(880\) | 7.83113 | 0.263987 | ||||||||
\(881\) | −24.0977 | −0.811874 | −0.405937 | − | 0.913901i | \(-0.633055\pi\) | ||||
−0.405937 | + | 0.913901i | \(0.633055\pi\) | |||||||
\(882\) | −1.47800 | − | 1.69333i | −0.0497670 | − | 0.0570172i | ||||
\(883\) | −0.222594 | − | 0.385545i | −0.00749089 | − | 0.0129746i | 0.862256 | − | 0.506473i | \(-0.169051\pi\) |
−0.869747 | + | 0.493499i | \(0.835718\pi\) | |||||||
\(884\) | 1.22327 | 0.0411432 | ||||||||
\(885\) | 14.7875 | − | 10.5704i | 0.497075 | − | 0.355319i | ||||
\(886\) | −10.2656 | − | 17.7805i | −0.344879 | − | 0.597348i | ||||
\(887\) | 23.4422 | − | 40.6031i | 0.787112 | − | 1.36332i | −0.140618 | − | 0.990064i | \(-0.544909\pi\) |
0.927729 | − | 0.373253i | \(-0.121758\pi\) | |||||||
\(888\) | 0.974040 | − | 0.696262i | 0.0326867 | − | 0.0233650i | ||||
\(889\) | −1.94185 | −0.0651274 | ||||||||
\(890\) | 0.460797 | − | 0.798124i | 0.0154459 | − | 0.0267532i | ||||
\(891\) | −29.4215 | + | 12.0256i | −0.985659 | + | 0.402874i | ||||
\(892\) | −25.5666 | −0.856033 | ||||||||
\(893\) | 25.2918 | − | 36.8442i | 0.846357 | − | 1.23294i | ||||
\(894\) | 16.0644 | + | 7.30138i | 0.537274 | + | 0.244195i | ||||
\(895\) | 19.0320 | 0.636170 | ||||||||
\(896\) | 27.2797 | 0.911350 | ||||||||
\(897\) | −5.48035 | − | 2.49085i | −0.182984 | − | 0.0831672i | ||||
\(898\) | −0.213634 | − | 0.370024i | −0.00712905 | − | 0.0123479i | ||||
\(899\) | 15.8289 | + | 27.4165i | 0.527924 | + | 0.914391i | ||||
\(900\) | 13.8346 | + | 15.8501i | 0.461154 | + | 0.528337i | ||||
\(901\) | 4.63776 | 0.154506 | ||||||||
\(902\) | 21.6752 | 0.721706 | ||||||||
\(903\) | −14.0729 | + | 10.0596i | −0.468317 | + | 0.334762i | ||||
\(904\) | −2.56238 | − | 4.43817i | −0.0852234 | − | 0.147611i | ||||
\(905\) | 0.0114051 | + | 0.0197543i | 0.000379120 | + | 0.000656654i | ||||
\(906\) | −15.9519 | + | 11.4027i | −0.529967 | + | 0.378830i | ||||
\(907\) | 23.8500 | + | 41.3094i | 0.791925 | + | 1.37165i | 0.924773 | + | 0.380518i | \(0.124254\pi\) |
−0.132848 | + | 0.991136i | \(0.542412\pi\) | |||||||
\(908\) | 7.82259 | + | 13.5491i | 0.259602 | + | 0.449643i | ||||
\(909\) | 3.58815 | − | 10.4895i | 0.119011 | − | 0.347916i | ||||
\(910\) | 0.621894 | − | 1.07715i | 0.0206156 | − | 0.0357073i | ||||
\(911\) | 7.61403 | − | 13.1879i | 0.252264 | − | 0.436934i | −0.711885 | − | 0.702296i | \(-0.752158\pi\) |
0.964149 | + | 0.265362i | \(0.0854915\pi\) | |||||||
\(912\) | 15.1337 | − | 9.12572i | 0.501129 | − | 0.302183i | ||||
\(913\) | −8.53997 | − | 14.7917i | −0.282632 | − | 0.489533i | ||||
\(914\) | −7.78046 | −0.257355 | ||||||||
\(915\) | 4.63929 | − | 3.31625i | 0.153370 | − | 0.109632i | ||||
\(916\) | −32.4968 | −1.07372 | ||||||||
\(917\) | 19.5662 | − | 33.8897i | 0.646134 | − | 1.11914i | ||||
\(918\) | 0.559363 | + | 1.86757i | 0.0184617 | + | 0.0616390i | ||||
\(919\) | 14.1764 | 0.467636 | 0.233818 | − | 0.972280i | \(-0.424878\pi\) | ||||
0.233818 | + | 0.972280i | \(0.424878\pi\) | |||||||
\(920\) | −3.20155 | + | 5.54526i | −0.105552 | + | 0.182822i | ||||
\(921\) | 3.47288 | + | 35.6892i | 0.114435 | + | 1.17600i | ||||
\(922\) | 5.21139 | − | 9.02639i | 0.171628 | − | 0.297268i | ||||
\(923\) | −1.80692 | − | 3.12968i | −0.0594756 | − | 0.103015i | ||||
\(924\) | 20.1481 | − | 14.4022i | 0.662823 | − | 0.473798i | ||||
\(925\) | −1.41820 | −0.0466301 | ||||||||
\(926\) | −2.26027 | + | 3.91490i | −0.0742770 | + | 0.128651i | ||||
\(927\) | 12.7744 | − | 2.50988i | 0.419565 | − | 0.0824354i | ||||
\(928\) | −9.28885 | + | 16.0888i | −0.304921 | + | 0.528140i | ||||
\(929\) | 6.82710 | + | 11.8249i | 0.223990 | + | 0.387962i | 0.956016 | − | 0.293315i | \(-0.0947585\pi\) |
−0.732026 | + | 0.681277i | \(0.761425\pi\) | |||||||
\(930\) | −0.768079 | − | 7.89320i | −0.0251863 | − | 0.258828i | ||||
\(931\) | 6.03945 | + | 0.471892i | 0.197935 | + | 0.0154656i | ||||
\(932\) | −7.27287 | − | 12.5970i | −0.238231 | − | 0.412628i | ||||
\(933\) | −44.2158 | − | 20.0964i | −1.44756 | − | 0.657926i | ||||
\(934\) | 7.77934 | + | 13.4742i | 0.254548 | + | 0.440890i | ||||
\(935\) | −1.16420 | − | 2.01646i | −0.0380735 | − | 0.0659452i | ||||
\(936\) | 4.05630 | + | 4.64725i | 0.132584 | + | 0.151900i | ||||
\(937\) | 14.1040 | + | 24.4289i | 0.460759 | + | 0.798058i | 0.998999 | − | 0.0447337i | \(-0.0142439\pi\) |
−0.538240 | + | 0.842792i | \(0.680911\pi\) | |||||||
\(938\) | −1.30467 | + | 2.25976i | −0.0425991 | + | 0.0737838i | ||||
\(939\) | −4.94329 | + | 3.53356i | −0.161318 | + | 0.115313i | ||||
\(940\) | −8.30115 | + | 14.3780i | −0.270754 | + | 0.468959i | ||||
\(941\) | 5.50629 | − | 9.53717i | 0.179500 | − | 0.310903i | −0.762210 | − | 0.647330i | \(-0.775885\pi\) |
0.941709 | + | 0.336428i | \(0.109219\pi\) | |||||||
\(942\) | −12.4932 | − | 5.67822i | −0.407049 | − | 0.185006i | ||||
\(943\) | 19.2411 | − | 33.3266i | 0.626577 | − | 1.08526i | ||||
\(944\) | −12.9654 | − | 22.4568i | −0.421988 | − | 0.730905i | ||||
\(945\) | −11.3453 | − | 2.68742i | −0.369063 | − | 0.0874219i | ||||
\(946\) | −4.01386 | − | 6.95220i | −0.130502 | − | 0.226036i | ||||
\(947\) | 10.4493 | + | 18.0987i | 0.339557 | + | 0.588130i | 0.984349 | − | 0.176228i | \(-0.0563896\pi\) |
−0.644793 | + | 0.764358i | \(0.723056\pi\) | |||||||
\(948\) | 33.1182 | − | 23.6735i | 1.07563 | − | 0.768879i | ||||
\(949\) | 4.70477 | + | 8.14891i | 0.152723 | + | 0.264525i | ||||
\(950\) | 9.61110 | + | 0.750962i | 0.311825 | + | 0.0243644i | ||||
\(951\) | 12.4830 | − | 8.92306i | 0.404788 | − | 0.289350i | ||||
\(952\) | −1.64821 | − | 2.85478i | −0.0534187 | − | 0.0925240i | ||||
\(953\) | 17.8341 | − | 30.8897i | 0.577705 | − | 1.00061i | −0.418037 | − | 0.908430i | \(-0.637282\pi\) |
0.995742 | − | 0.0921841i | \(-0.0293848\pi\) | |||||||
\(954\) | 7.08684 | + | 8.11929i | 0.229445 | + | 0.262872i | ||||
\(955\) | −8.25744 | + | 14.3023i | −0.267204 | + | 0.462812i | ||||
\(956\) | −33.5724 | −1.08581 | ||||||||
\(957\) | 2.09189 | + | 21.4975i | 0.0676213 | + | 0.694914i | ||||
\(958\) | −3.56606 | − | 6.17660i | −0.115214 | − | 0.199557i | ||||
\(959\) | −13.2613 | + | 22.9692i | −0.428229 | + | 0.741714i | ||||
\(960\) | −2.46307 | + | 1.76065i | −0.0794953 | + | 0.0568247i | ||||
\(961\) | −24.6909 | + | 42.7658i | −0.796479 | + | 1.37954i | ||||
\(962\) | −0.191619 | −0.00617804 | ||||||||
\(963\) | 6.95065 | − | 20.3195i | 0.223982 | − | 0.654786i | ||||
\(964\) | −7.73989 | + | 13.4059i | −0.249285 | + | 0.431774i | ||||
\(965\) | −19.7364 | −0.635337 | ||||||||
\(966\) | 0.724015 | + | 7.44038i | 0.0232948 | + | 0.239390i | ||||
\(967\) | 35.1316 | 1.12976 | 0.564878 | − | 0.825174i | \(-0.308923\pi\) | ||||
0.564878 | + | 0.825174i | \(0.308923\pi\) | |||||||
\(968\) | 1.47191 | + | 2.54942i | 0.0473090 | + | 0.0819416i | ||||
\(969\) | −4.59964 | − | 2.54017i | −0.147762 | − | 0.0816019i | ||||
\(970\) | −3.58611 | + | 6.21132i | −0.115143 | + | 0.199434i | ||||
\(971\) | 4.29981 | − | 7.44749i | 0.137987 | − | 0.239001i | −0.788747 | − | 0.614718i | \(-0.789270\pi\) |
0.926735 | + | 0.375716i | \(0.122603\pi\) | |||||||
\(972\) | 14.2035 | − | 22.5456i | 0.455578 | − | 0.723150i | ||||
\(973\) | 12.4934 | + | 21.6392i | 0.400520 | + | 0.693722i | ||||
\(974\) | −5.50968 | − | 9.54304i | −0.176541 | − | 0.305779i | ||||
\(975\) | −0.707651 | − | 7.27221i | −0.0226630 | − | 0.232897i | ||||
\(976\) | −4.06765 | − | 7.04538i | −0.130202 | − | 0.225517i | ||||
\(977\) | 6.03352 | + | 10.4504i | 0.193030 | + | 0.334337i | 0.946253 | − | 0.323428i | \(-0.104835\pi\) |
−0.753223 | + | 0.657765i | \(0.771502\pi\) | |||||||
\(978\) | 7.93861 | + | 3.60815i | 0.253849 | + | 0.115376i | ||||
\(979\) | −6.37308 | −0.203685 | ||||||||
\(980\) | −2.25051 | −0.0718898 | ||||||||
\(981\) | 1.42112 | + | 1.62816i | 0.0453730 | + | 0.0519832i | ||||
\(982\) | −6.13173 | − | 10.6205i | −0.195671 | − | 0.338913i | ||||
\(983\) | 17.8321 | + | 30.8861i | 0.568756 | + | 0.985114i | 0.996689 | + | 0.0813039i | \(0.0259084\pi\) |
−0.427933 | + | 0.903810i | \(0.640758\pi\) | |||||||
\(984\) | −32.0795 | + | 22.9310i | −1.02266 | + | 0.731015i | ||||
\(985\) | 18.7436 | 0.597221 | ||||||||
\(986\) | 1.32481 | 0.0421904 | ||||||||
\(987\) | 4.07369 | + | 41.8635i | 0.129667 | + | 1.33253i | ||||
\(988\) | −7.63818 | − | 0.596808i | −0.243003 | − | 0.0189870i | ||||
\(989\) | −14.2524 | −0.453201 | ||||||||
\(990\) | 1.75120 | − | 5.11945i | 0.0556569 | − | 0.162707i | ||||
\(991\) | 5.41450 | − | 9.37820i | 0.171997 | − | 0.297908i | −0.767121 | − | 0.641503i | \(-0.778311\pi\) |
0.939118 | + | 0.343595i | \(0.111645\pi\) | |||||||
\(992\) | −47.1703 | −1.49766 | ||||||||
\(993\) | −1.21313 | − | 12.4668i | −0.0384976 | − | 0.395623i | ||||
\(994\) | −2.24386 | + | 3.88648i | −0.0711709 | + | 0.123272i | ||||
\(995\) | 10.7936 | + | 18.6951i | 0.342181 | + | 0.592676i | ||||
\(996\) | 13.0358 | + | 5.92487i | 0.413056 | + | 0.187737i | ||||
\(997\) | −5.91267 | −0.187256 | −0.0936280 | − | 0.995607i | \(-0.529846\pi\) | ||||
−0.0936280 | + | 0.995607i | \(0.529846\pi\) | |||||||
\(998\) | 5.73332 | + | 9.93040i | 0.181485 | + | 0.314341i | ||||
\(999\) | 0.515376 | + | 1.72071i | 0.0163058 | + | 0.0544408i |
(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 | 171.2.g.c.106.7 | ✓ | 32 | |
3.2 | odd | 2 | 513.2.g.c.505.10 | 32 | |||
9.4 | even | 3 | 171.2.h.c.49.10 | yes | 32 | ||
9.5 | odd | 6 | 513.2.h.c.334.7 | 32 | |||
19.7 | even | 3 | 171.2.h.c.7.10 | yes | 32 | ||
57.26 | odd | 6 | 513.2.h.c.235.7 | 32 | |||
171.121 | even | 3 | inner | 171.2.g.c.121.7 | yes | 32 | |
171.140 | odd | 6 | 513.2.g.c.64.10 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
171.2.g.c.106.7 | ✓ | 32 | 1.1 | even | 1 | trivial | |
171.2.g.c.121.7 | yes | 32 | 171.121 | even | 3 | inner | |
171.2.h.c.7.10 | yes | 32 | 19.7 | even | 3 | ||
171.2.h.c.49.10 | yes | 32 | 9.4 | even | 3 | ||
513.2.g.c.64.10 | 32 | 171.140 | odd | 6 | |||
513.2.g.c.505.10 | 32 | 3.2 | odd | 2 | |||
513.2.h.c.235.7 | 32 | 57.26 | odd | 6 | |||
513.2.h.c.334.7 | 32 | 9.5 | odd | 6 |