Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(296,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.296");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.t (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(104\) |
Relative dimension: | \(52\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 296.2 | ||
Character | \(\chi\) | \(=\) | 429.296 |
Dual form | 429.2.t.a.329.2 |
$q$-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 \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.31547 | + | 1.33684i | −1.63728 | + | 0.945286i | −0.655521 | + | 0.755177i | \(0.727551\pi\) |
−0.981763 | + | 0.190109i | \(0.939116\pi\) | |||||||
\(3\) | 1.48761 | + | 0.887132i | 0.858875 | + | 0.512186i | ||||
\(4\) | 2.57426 | − | 4.45876i | 1.28713 | − | 2.22938i | ||||
\(5\) | −2.76446 | −1.23630 | −0.618152 | − | 0.786059i | \(-0.712118\pi\) | ||||
−0.618152 | + | 0.786059i | \(0.712118\pi\) | |||||||
\(6\) | −4.63048 | − | 0.0654292i | −1.89038 | − | 0.0267114i | ||||
\(7\) | −0.565134 | + | 0.978841i | −0.213601 | + | 0.369967i | −0.952839 | − | 0.303477i | \(-0.901852\pi\) |
0.739238 | + | 0.673444i | \(0.235186\pi\) | |||||||
\(8\) | 8.41814i | 2.97626i | ||||||||
\(9\) | 1.42599 | + | 2.63942i | 0.475331 | + | 0.879807i | ||||
\(10\) | 6.40102 | − | 3.69563i | 2.02418 | − | 1.16866i | ||||
\(11\) | 3.16940 | + | 0.977207i | 0.955609 | + | 0.294639i | ||||
\(12\) | 7.78502 | − | 4.34920i | 2.24734 | − | 1.25551i | ||||
\(13\) | −2.86710 | + | 2.18626i | −0.795190 | + | 0.606361i | ||||
\(14\) | − | 3.02197i | − | 0.807655i | ||||||
\(15\) | −4.11245 | − | 2.45244i | −1.06183 | − | 0.633217i | ||||
\(16\) | −6.10514 | − | 10.5744i | −1.52629 | − | 2.64360i | ||||
\(17\) | 1.85321 | − | 3.20985i | 0.449469 | − | 0.778504i | −0.548882 | − | 0.835900i | \(-0.684946\pi\) |
0.998351 | + | 0.0573959i | \(0.0182797\pi\) | |||||||
\(18\) | −6.83032 | − | 4.20518i | −1.60992 | − | 0.991170i | ||||
\(19\) | −0.848514 | + | 1.46967i | −0.194662 | + | 0.337165i | −0.946790 | − | 0.321853i | \(-0.895694\pi\) |
0.752127 | + | 0.659018i | \(0.229028\pi\) | |||||||
\(20\) | −7.11645 | + | 12.3260i | −1.59129 | + | 2.75619i | ||||
\(21\) | −1.70906 | + | 0.954790i | −0.372948 | + | 0.208352i | ||||
\(22\) | −8.64500 | + | 1.97427i | −1.84312 | + | 0.420916i | ||||
\(23\) | −7.29596 | + | 4.21232i | −1.52131 | + | 0.878330i | −0.521628 | + | 0.853173i | \(0.674675\pi\) |
−0.999684 | + | 0.0251570i | \(0.991991\pi\) | |||||||
\(24\) | −7.46800 | + | 12.5229i | −1.52440 | + | 2.55623i | ||||
\(25\) | 2.64223 | 0.528447 | ||||||||
\(26\) | 3.71600 | − | 8.89507i | 0.728767 | − | 1.74447i | ||||
\(27\) | −0.220186 | + | 5.19149i | −0.0423749 | + | 0.999102i | ||||
\(28\) | 2.90961 | + | 5.03959i | 0.549865 | + | 0.952393i | ||||
\(29\) | −0.295904 | − | 0.512520i | −0.0549479 | − | 0.0951726i | 0.837243 | − | 0.546831i | \(-0.184166\pi\) |
−0.892191 | + | 0.451658i | \(0.850833\pi\) | |||||||
\(30\) | 12.8008 | + | 0.180876i | 2.33709 | + | 0.0330234i | ||||
\(31\) | − | 4.08080i | − | 0.732933i | −0.930431 | − | 0.366467i | \(-0.880567\pi\) | ||
0.930431 | − | 0.366467i | \(-0.119433\pi\) | |||||||
\(32\) | 13.6919 | + | 7.90502i | 2.42041 | + | 1.39742i | ||||
\(33\) | 3.84793 | + | 4.26538i | 0.669838 | + | 0.742507i | ||||
\(34\) | 9.90976i | 1.69951i | ||||||||
\(35\) | 1.56229 | − | 2.70597i | 0.264075 | − | 0.457392i | ||||
\(36\) | 15.4394 | + | 0.436409i | 2.57324 | + | 0.0727349i | ||||
\(37\) | −8.55581 | + | 4.93970i | −1.40657 | + | 0.812082i | −0.995055 | − | 0.0993227i | \(-0.968332\pi\) |
−0.411512 | + | 0.911404i | \(0.634999\pi\) | |||||||
\(38\) | − | 4.53730i | − | 0.736047i | ||||||
\(39\) | −6.20464 | + | 0.708824i | −0.993538 | + | 0.113503i | ||||
\(40\) | − | 23.2716i | − | 3.67956i | ||||||
\(41\) | −8.76317 | + | 5.05942i | −1.36858 | + | 0.790148i | −0.990746 | − | 0.135726i | \(-0.956663\pi\) |
−0.377831 | + | 0.925875i | \(0.623330\pi\) | |||||||
\(42\) | 2.68089 | − | 4.49552i | 0.413670 | − | 0.693674i | ||||
\(43\) | −7.31991 | − | 4.22615i | −1.11628 | − | 0.644482i | −0.175828 | − | 0.984421i | \(-0.556260\pi\) |
−0.940448 | + | 0.339939i | \(0.889594\pi\) | |||||||
\(44\) | 12.5160 | − | 11.6160i | 1.88686 | − | 1.75117i | ||||
\(45\) | −3.94210 | − | 7.29657i | −0.587654 | − | 1.08771i | ||||
\(46\) | 11.2624 | − | 19.5070i | 1.66055 | − | 2.87615i | ||||
\(47\) | −1.04557 | −0.152512 | −0.0762559 | − | 0.997088i | \(-0.524297\pi\) | ||||
−0.0762559 | + | 0.997088i | \(0.524297\pi\) | |||||||
\(48\) | 0.298806 | − | 21.1467i | 0.0431289 | − | 3.05227i | ||||
\(49\) | 2.86125 | + | 4.95582i | 0.408749 | + | 0.707975i | ||||
\(50\) | −6.11801 | + | 3.53224i | −0.865217 | + | 0.499534i | ||||
\(51\) | 5.60443 | − | 3.13098i | 0.784777 | − | 0.438425i | ||||
\(52\) | 2.36735 | + | 18.4117i | 0.328293 | + | 2.55324i | ||||
\(53\) | − | 1.18874i | − | 0.163286i | −0.996662 | − | 0.0816428i | \(-0.973983\pi\) | ||
0.996662 | − | 0.0816428i | \(-0.0260167\pi\) | |||||||
\(54\) | −6.43033 | − | 12.3151i | −0.875057 | − | 1.67587i | ||||
\(55\) | −8.76166 | − | 2.70145i | −1.18142 | − | 0.364263i | ||||
\(56\) | −8.24002 | − | 4.75738i | −1.10112 | − | 0.635731i | ||||
\(57\) | −2.56605 | + | 1.43356i | −0.339882 | + | 0.189879i | ||||
\(58\) | 1.37031 | + | 0.791149i | 0.179931 | + | 0.103883i | ||||
\(59\) | 1.43147 | − | 2.47938i | 0.186362 | − | 0.322788i | −0.757673 | − | 0.652634i | \(-0.773664\pi\) |
0.944034 | + | 0.329847i | \(0.106997\pi\) | |||||||
\(60\) | −21.5214 | + | 12.0232i | −2.77840 | + | 1.55219i | ||||
\(61\) | 8.12322 | + | 4.68995i | 1.04007 | + | 0.600486i | 0.919854 | − | 0.392261i | \(-0.128307\pi\) |
0.120219 | + | 0.992747i | \(0.461640\pi\) | |||||||
\(62\) | 5.45536 | + | 9.44896i | 0.692832 | + | 1.20002i | ||||
\(63\) | −3.38945 | − | 0.0958059i | −0.427031 | − | 0.0120704i | ||||
\(64\) | −17.8503 | −2.23129 | ||||||||
\(65\) | 7.92597 | − | 6.04384i | 0.983096 | − | 0.749646i | ||||
\(66\) | −14.6119 | − | 4.73231i | −1.79860 | − | 0.582507i | ||||
\(67\) | 1.49115 | − | 0.860914i | 0.182173 | − | 0.105177i | −0.406140 | − | 0.913811i | \(-0.633126\pi\) |
0.588313 | + | 0.808633i | \(0.299792\pi\) | |||||||
\(68\) | −9.54130 | − | 16.5260i | −1.15705 | − | 2.00407i | ||||
\(69\) | −14.5905 | − | 0.206165i | −1.75648 | − | 0.0248194i | ||||
\(70\) | 8.35411i | 0.998507i | ||||||||
\(71\) | 4.35002 | − | 7.53446i | 0.516253 | − | 0.894176i | −0.483569 | − | 0.875306i | \(-0.660660\pi\) |
0.999822 | − | 0.0188697i | \(-0.00600676\pi\) | |||||||
\(72\) | −22.2190 | + | 12.0042i | −2.61853 | + | 1.41471i | ||||
\(73\) | 7.15945 | 0.837950 | 0.418975 | − | 0.907998i | \(-0.362389\pi\) | ||||
0.418975 | + | 0.907998i | \(0.362389\pi\) | |||||||
\(74\) | 13.2071 | − | 22.8754i | 1.53530 | − | 2.65922i | ||||
\(75\) | 3.93063 | + | 2.34401i | 0.453870 | + | 0.270663i | ||||
\(76\) | 4.36860 | + | 7.56663i | 0.501112 | + | 0.867952i | ||||
\(77\) | −2.74766 | + | 2.55008i | −0.313125 | + | 0.290609i | ||||
\(78\) | 13.4191 | − | 9.93585i | 1.51941 | − | 1.12501i | ||||
\(79\) | 1.41460i | 0.159155i | 0.996829 | + | 0.0795776i | \(0.0253571\pi\) | ||||
−0.996829 | + | 0.0795776i | \(0.974643\pi\) | |||||||
\(80\) | 16.8774 | + | 29.2325i | 1.88695 | + | 3.26830i | ||||
\(81\) | −4.93309 | + | 7.52759i | −0.548121 | + | 0.836399i | ||||
\(82\) | 13.5272 | − | 23.4299i | 1.49383 | − | 2.58739i | ||||
\(83\) | 6.53336i | 0.717129i | 0.933505 | + | 0.358565i | \(0.116734\pi\) | ||||
−0.933505 | + | 0.358565i | \(0.883266\pi\) | |||||||
\(84\) | −0.142406 | + | 10.0782i | −0.0155378 | + | 1.09962i | ||||
\(85\) | −5.12312 | + | 8.87351i | −0.555681 | + | 0.962467i | ||||
\(86\) | 22.5987 | 2.43688 | ||||||||
\(87\) | 0.0144825 | − | 1.02494i | 0.00155269 | − | 0.109885i | ||||
\(88\) | −8.22626 | + | 26.6804i | −0.876923 | + | 2.84414i | ||||
\(89\) | −3.41519 | − | 5.91528i | −0.362009 | − | 0.627019i | 0.626282 | − | 0.779597i | \(-0.284576\pi\) |
−0.988291 | + | 0.152578i | \(0.951242\pi\) | |||||||
\(90\) | 18.8821 | + | 11.6250i | 1.99035 | + | 1.22539i | ||||
\(91\) | −0.519711 | − | 4.04197i | −0.0544805 | − | 0.423713i | ||||
\(92\) | 43.3745i | 4.52211i | ||||||||
\(93\) | 3.62021 | − | 6.07066i | 0.375398 | − | 0.629498i | ||||
\(94\) | 2.42098 | − | 1.39775i | 0.249705 | − | 0.144167i | ||||
\(95\) | 2.34568 | − | 4.06284i | 0.240662 | − | 0.416839i | ||||
\(96\) | 13.3555 | + | 23.9061i | 1.36309 | + | 2.43991i | ||||
\(97\) | 4.33663 | + | 2.50376i | 0.440318 | + | 0.254218i | 0.703733 | − | 0.710465i | \(-0.251515\pi\) |
−0.263414 | + | 0.964683i | \(0.584849\pi\) | |||||||
\(98\) | −13.2503 | − | 7.65004i | −1.33848 | − | 0.772771i | ||||
\(99\) | 1.94027 | + | 9.75886i | 0.195005 | + | 0.980802i | ||||
\(100\) | 6.80181 | − | 11.7811i | 0.680181 | − | 1.17811i | ||||
\(101\) | 6.27893 | + | 10.8754i | 0.624777 | + | 1.08215i | 0.988584 | + | 0.150671i | \(0.0481436\pi\) |
−0.363807 | + | 0.931474i | \(0.618523\pi\) | |||||||
\(102\) | −8.79126 | + | 14.7419i | −0.870465 | + | 1.45967i | ||||
\(103\) | −4.21360 | −0.415179 | −0.207589 | − | 0.978216i | \(-0.566562\pi\) | ||||
−0.207589 | + | 0.978216i | \(0.566562\pi\) | |||||||
\(104\) | −18.4043 | − | 24.1356i | −1.80469 | − | 2.36669i | ||||
\(105\) | 4.72464 | − | 2.63948i | 0.461077 | − | 0.257587i | ||||
\(106\) | 1.58915 | + | 2.75248i | 0.154352 | + | 0.267345i | ||||
\(107\) | 9.09797 | + | 15.7581i | 0.879534 | + | 1.52340i | 0.851853 | + | 0.523780i | \(0.175479\pi\) |
0.0276802 | + | 0.999617i | \(0.491188\pi\) | |||||||
\(108\) | 22.5807 | + | 14.3460i | 2.17283 | + | 1.38045i | ||||
\(109\) | 3.66800 | 0.351331 | 0.175666 | − | 0.984450i | \(-0.443792\pi\) | ||||
0.175666 | + | 0.984450i | \(0.443792\pi\) | |||||||
\(110\) | 23.8988 | − | 5.45779i | 2.27866 | − | 0.520380i | ||||
\(111\) | −17.1099 | − | 0.241765i | −1.62400 | − | 0.0229474i | ||||
\(112\) | 13.8009 | 1.30406 | ||||||||
\(113\) | 7.69319 | + | 4.44167i | 0.723714 | + | 0.417837i | 0.816118 | − | 0.577885i | \(-0.196122\pi\) |
−0.0924038 | + | 0.995722i | \(0.529455\pi\) | |||||||
\(114\) | 4.02518 | − | 6.74975i | 0.376993 | − | 0.632172i | ||||
\(115\) | 20.1694 | − | 11.6448i | 1.88080 | − | 1.08588i | ||||
\(116\) | −3.04694 | −0.282901 | ||||||||
\(117\) | −9.85893 | − | 4.44988i | −0.911459 | − | 0.411391i | ||||
\(118\) | 7.65457i | 0.704660i | ||||||||
\(119\) | 2.09462 | + | 3.62800i | 0.192014 | + | 0.332578i | ||||
\(120\) | 20.6450 | − | 34.6192i | 1.88462 | − | 3.16028i | ||||
\(121\) | 9.09013 | + | 6.19431i | 0.826376 | + | 0.563119i | ||||
\(122\) | −25.0788 | −2.27052 | ||||||||
\(123\) | −17.5246 | − | 0.247625i | −1.58014 | − | 0.0223276i | ||||
\(124\) | −18.1953 | − | 10.5051i | −1.63399 | − | 0.943382i | ||||
\(125\) | 6.51795 | 0.582983 | ||||||||
\(126\) | 7.97625 | − | 4.30931i | 0.710581 | − | 0.383904i | ||||
\(127\) | −8.61325 | + | 4.97286i | −0.764302 | + | 0.441270i | −0.830838 | − | 0.556514i | \(-0.812139\pi\) |
0.0665360 | + | 0.997784i | \(0.478805\pi\) | |||||||
\(128\) | 13.9481 | − | 8.05291i | 1.23285 | − | 0.711784i | ||||
\(129\) | −7.14005 | − | 12.7806i | −0.628646 | − | 1.12527i | ||||
\(130\) | −10.2727 | + | 24.5901i | −0.900977 | + | 2.15669i | ||||
\(131\) | −0.480341 | −0.0419676 | −0.0209838 | − | 0.999780i | \(-0.506680\pi\) | ||||
−0.0209838 | + | 0.999780i | \(0.506680\pi\) | |||||||
\(132\) | 28.9239 | − | 6.17675i | 2.51750 | − | 0.537617i | ||||
\(133\) | −0.959049 | − | 1.66112i | −0.0831601 | − | 0.144037i | ||||
\(134\) | −2.30180 | + | 3.98684i | −0.198846 | + | 0.344411i | ||||
\(135\) | 0.608696 | − | 14.3516i | 0.0523882 | − | 1.23519i | ||||
\(136\) | 27.0210 | + | 15.6006i | 2.31703 | + | 1.33774i | ||||
\(137\) | 1.34325 | − | 2.32658i | 0.114761 | − | 0.198773i | −0.802923 | − | 0.596083i | \(-0.796723\pi\) |
0.917684 | + | 0.397310i | \(0.130056\pi\) | |||||||
\(138\) | 34.0594 | − | 19.0277i | 2.89932 | − | 1.61974i | ||||
\(139\) | −8.48434 | − | 4.89844i | −0.719633 | − | 0.415480i | 0.0949848 | − | 0.995479i | \(-0.469720\pi\) |
−0.814617 | + | 0.579999i | \(0.803053\pi\) | |||||||
\(140\) | −8.04350 | − | 13.9317i | −0.679800 | − | 1.17745i | ||||
\(141\) | −1.55540 | − | 0.927557i | −0.130988 | − | 0.0781144i | ||||
\(142\) | 23.2611i | 1.95203i | ||||||||
\(143\) | −11.2234 | + | 4.12739i | −0.938548 | + | 0.345149i | ||||
\(144\) | 19.2044 | − | 31.1931i | 1.60037 | − | 2.59942i | ||||
\(145\) | 0.818013 | + | 1.41684i | 0.0679323 | + | 0.117662i | ||||
\(146\) | −16.5775 | + | 9.57101i | −1.37196 | + | 0.792103i | ||||
\(147\) | −0.140039 | + | 9.91066i | −0.0115502 | + | 0.817417i | ||||
\(148\) | 50.8644i | 4.18103i | ||||||||
\(149\) | −14.9158 | − | 8.61166i | −1.22195 | − | 0.705494i | −0.256618 | − | 0.966513i | \(-0.582608\pi\) |
−0.965334 | + | 0.261018i | \(0.915942\pi\) | |||||||
\(150\) | −12.2348 | − | 0.172879i | −0.998967 | − | 0.0141155i | ||||
\(151\) | 5.40037 | 0.439476 | 0.219738 | − | 0.975559i | \(-0.429480\pi\) | ||||
0.219738 | + | 0.975559i | \(0.429480\pi\) | |||||||
\(152\) | −12.3719 | − | 7.14290i | −1.00349 | − | 0.579366i | ||||
\(153\) | 11.1148 | + | 0.314171i | 0.898580 | + | 0.0253992i | ||||
\(154\) | 2.95309 | − | 9.57781i | 0.237967 | − | 0.771802i | ||||
\(155\) | 11.2812i | 0.906128i | ||||||||
\(156\) | −12.8119 | + | 29.4897i | −1.02577 | + | 2.36106i | ||||
\(157\) | 3.51966 | 0.280900 | 0.140450 | − | 0.990088i | \(-0.455145\pi\) | ||||
0.140450 | + | 0.990088i | \(0.455145\pi\) | |||||||
\(158\) | −1.89109 | − | 3.27547i | −0.150447 | − | 0.260582i | ||||
\(159\) | 1.05457 | − | 1.76838i | 0.0836325 | − | 0.140242i | ||||
\(160\) | −37.8507 | − | 21.8531i | −2.99236 | − | 1.72764i | ||||
\(161\) | − | 9.52211i | − | 0.750447i | ||||||
\(162\) | 1.35924 | − | 24.0246i | 0.106792 | − | 1.88755i | ||||
\(163\) | 13.2575 | + | 7.65423i | 1.03841 | + | 0.599525i | 0.919382 | − | 0.393366i | \(-0.128689\pi\) |
0.119026 | + | 0.992891i | \(0.462023\pi\) | |||||||
\(164\) | 52.0971i | 4.06810i | ||||||||
\(165\) | −10.6374 | − | 11.7915i | −0.828123 | − | 0.917965i | ||||
\(166\) | −8.73403 | − | 15.1278i | −0.677893 | − | 1.17414i | ||||
\(167\) | 1.33893 | − | 0.773032i | 0.103610 | − | 0.0598190i | −0.447300 | − | 0.894384i | \(-0.647614\pi\) |
0.550909 | + | 0.834565i | \(0.314281\pi\) | |||||||
\(168\) | −8.03755 | − | 14.3871i | −0.620110 | − | 1.10999i | ||||
\(169\) | 3.44050 | − | 12.5365i | 0.264654 | − | 0.964344i | ||||
\(170\) | − | 27.3951i | − | 2.10111i | ||||||
\(171\) | −5.08905 | − | 0.143847i | −0.389169 | − | 0.0110002i | ||||
\(172\) | −37.6868 | + | 21.7585i | −2.87359 | + | 1.65907i | ||||
\(173\) | 0.247842 | − | 0.429275i | 0.0188431 | − | 0.0326372i | −0.856450 | − | 0.516230i | \(-0.827335\pi\) |
0.875293 | + | 0.483593i | \(0.160668\pi\) | |||||||
\(174\) | 1.33664 | + | 2.39257i | 0.101330 | + | 0.181380i | ||||
\(175\) | −1.49322 | + | 2.58633i | −0.112877 | + | 0.195508i | ||||
\(176\) | −9.01621 | − | 39.4805i | −0.679622 | − | 2.97595i | ||||
\(177\) | 4.32901 | − | 2.41846i | 0.325388 | − | 0.181782i | ||||
\(178\) | 15.8155 | + | 9.13110i | 1.18542 | + | 0.684405i | ||||
\(179\) | −20.6337 | + | 11.9129i | −1.54224 | + | 0.890410i | −0.543538 | + | 0.839385i | \(0.682916\pi\) |
−0.998697 | + | 0.0510255i | \(0.983751\pi\) | |||||||
\(180\) | −42.6816 | − | 1.20644i | −3.18130 | − | 0.0899224i | ||||
\(181\) | 5.91482 | 0.439645 | 0.219823 | − | 0.975540i | \(-0.429452\pi\) | ||||
0.219823 | + | 0.975540i | \(0.429452\pi\) | |||||||
\(182\) | 6.60682 | + | 8.66428i | 0.489730 | + | 0.642239i | ||||
\(183\) | 7.92362 | + | 14.1832i | 0.585731 | + | 1.04845i | ||||
\(184\) | −35.4599 | − | 61.4183i | −2.61414 | − | 4.52782i | ||||
\(185\) | 23.6522 | − | 13.6556i | 1.73894 | − | 1.00398i | ||||
\(186\) | −0.267004 | + | 18.8960i | −0.0195777 | + | 1.38552i | ||||
\(187\) | 9.01025 | − | 8.36232i | 0.658895 | − | 0.611514i | ||||
\(188\) | −2.69157 | + | 4.66193i | −0.196303 | + | 0.340006i | ||||
\(189\) | −4.95721 | − | 3.14941i | −0.360584 | − | 0.229086i | ||||
\(190\) | 12.5432i | 0.909977i | ||||||||
\(191\) | 2.58659 | + | 1.49337i | 0.187159 | + | 0.108056i | 0.590652 | − | 0.806926i | \(-0.298871\pi\) |
−0.403493 | + | 0.914983i | \(0.632204\pi\) | |||||||
\(192\) | −26.5544 | − | 15.8356i | −1.91640 | − | 1.14284i | ||||
\(193\) | −7.45257 | − | 12.9082i | −0.536448 | − | 0.929155i | −0.999092 | − | 0.0426108i | \(-0.986432\pi\) |
0.462644 | − | 0.886544i | \(-0.346901\pi\) | |||||||
\(194\) | −13.3885 | −0.961235 | ||||||||
\(195\) | 17.1525 | − | 1.95952i | 1.22831 | − | 0.140324i | ||||
\(196\) | 29.4624 | 2.10446 | ||||||||
\(197\) | 11.0611 | − | 6.38612i | 0.788069 | − | 0.454992i | −0.0512130 | − | 0.998688i | \(-0.516309\pi\) |
0.839282 | + | 0.543696i | \(0.182975\pi\) | |||||||
\(198\) | −17.5386 | − | 20.0025i | −1.24642 | − | 1.42152i | ||||
\(199\) | −1.65383 | + | 2.86452i | −0.117237 | + | 0.203060i | −0.918672 | − | 0.395022i | \(-0.870737\pi\) |
0.801435 | + | 0.598082i | \(0.204070\pi\) | |||||||
\(200\) | 22.2427i | 1.57280i | ||||||||
\(201\) | 2.98200 | + | 0.0421360i | 0.210334 | + | 0.00297205i | ||||
\(202\) | −29.0774 | − | 16.7878i | −2.04588 | − | 1.18119i | ||||
\(203\) | 0.668901 | 0.0469476 | ||||||||
\(204\) | 0.466983 | − | 33.0487i | 0.0326954 | − | 2.31388i | ||||
\(205\) | 24.2254 | − | 13.9866i | 1.69198 | − | 0.976863i | ||||
\(206\) | 9.75646 | − | 5.63290i | 0.679765 | − | 0.392463i | ||||
\(207\) | −21.5221 | − | 13.2504i | −1.49589 | − | 0.920963i | ||||
\(208\) | 40.6225 | + | 16.9704i | 2.81666 | + | 1.17669i | ||||
\(209\) | −4.12545 | + | 3.82879i | −0.285363 | + | 0.264843i | ||||
\(210\) | −7.41120 | + | 12.4277i | −0.511421 | + | 0.857592i | ||||
\(211\) | 17.9917 | − | 10.3875i | 1.23860 | − | 0.715105i | 0.269790 | − | 0.962919i | \(-0.413046\pi\) |
0.968808 | + | 0.247814i | \(0.0797123\pi\) | |||||||
\(212\) | −5.30029 | − | 3.06012i | −0.364025 | − | 0.210170i | ||||
\(213\) | 13.1552 | − | 7.34933i | 0.901380 | − | 0.503568i | ||||
\(214\) | −42.1321 | − | 24.3250i | −2.88009 | − | 1.66282i | ||||
\(215\) | 20.2356 | + | 11.6830i | 1.38006 | + | 0.796776i | ||||
\(216\) | −43.7026 | − | 1.85356i | −2.97359 | − | 0.126119i | ||||
\(217\) | 3.99445 | + | 2.30620i | 0.271161 | + | 0.156555i | ||||
\(218\) | −8.49315 | + | 4.90352i | −0.575229 | + | 0.332108i | ||||
\(219\) | 10.6505 | + | 6.35138i | 0.719694 | + | 0.429186i | ||||
\(220\) | −34.5999 | + | 32.1119i | −2.33273 | + | 2.16498i | ||||
\(221\) | 1.70426 | + | 13.2546i | 0.114641 | + | 0.891599i | ||||
\(222\) | 39.9407 | − | 22.3134i | 2.68064 | − | 1.49757i | ||||
\(223\) | 10.9221 | − | 6.30590i | 0.731401 | − | 0.422274i | −0.0875337 | − | 0.996162i | \(-0.527899\pi\) |
0.818934 | + | 0.573887i | \(0.194565\pi\) | |||||||
\(224\) | −15.4755 | + | 8.93480i | −1.03400 | + | 0.596981i | ||||
\(225\) | 3.76781 | + | 6.97397i | 0.251187 | + | 0.464931i | ||||
\(226\) | −23.7511 | −1.57990 | ||||||||
\(227\) | 13.7653 | + | 7.94738i | 0.913633 | + | 0.527486i | 0.881598 | − | 0.472001i | \(-0.156468\pi\) |
0.0320344 | + | 0.999487i | \(0.489801\pi\) | |||||||
\(228\) | −0.213814 | + | 15.1318i | −0.0141602 | + | 1.00212i | ||||
\(229\) | 11.8755i | 0.784754i | 0.919804 | + | 0.392377i | \(0.128347\pi\) | ||||
−0.919804 | + | 0.392377i | \(0.871653\pi\) | |||||||
\(230\) | −31.1344 | + | 53.9263i | −2.05294 | + | 3.55580i | ||||
\(231\) | −6.34972 | + | 1.35600i | −0.417781 | + | 0.0892180i | ||||
\(232\) | 4.31446 | − | 2.49096i | 0.283258 | − | 0.163539i | ||||
\(233\) | −14.4815 | −0.948718 | −0.474359 | − | 0.880332i | \(-0.657320\pi\) | ||||
−0.474359 | + | 0.880332i | \(0.657320\pi\) | |||||||
\(234\) | 28.7768 | − | 2.87623i | 1.88120 | − | 0.188025i | ||||
\(235\) | 2.89043 | 0.188551 | ||||||||
\(236\) | −7.36996 | − | 12.7652i | −0.479744 | − | 0.830941i | ||||
\(237\) | −1.25494 | + | 2.10438i | −0.0815171 | + | 0.136694i | ||||
\(238\) | −9.70008 | − | 5.60034i | −0.628763 | − | 0.363016i | ||||
\(239\) | − | 0.372520i | − | 0.0240963i | −0.999927 | − | 0.0120482i | \(-0.996165\pi\) | ||
0.999927 | − | 0.0120482i | \(-0.00383515\pi\) | |||||||
\(240\) | −0.826037 | + | 58.4593i | −0.0533205 | + | 3.77353i | ||||
\(241\) | −8.44225 | + | 14.6224i | −0.543813 | + | 0.941912i | 0.454868 | + | 0.890559i | \(0.349687\pi\) |
−0.998681 | + | 0.0513526i | \(0.983647\pi\) | |||||||
\(242\) | −29.3287 | − | 2.19072i | −1.88532 | − | 0.140825i | ||||
\(243\) | −14.0165 | + | 6.82186i | −0.899159 | + | 0.437622i | ||||
\(244\) | 41.8227 | − | 24.1463i | 2.67742 | − | 1.54581i | ||||
\(245\) | −7.90980 | − | 13.7002i | −0.505339 | − | 0.875272i | ||||
\(246\) | 40.9087 | − | 22.8541i | 2.60824 | − | 1.45713i | ||||
\(247\) | −0.780313 | − | 6.06876i | −0.0496501 | − | 0.386146i | ||||
\(248\) | 34.3527 | 2.18140 | ||||||||
\(249\) | −5.79595 | + | 9.71912i | −0.367304 | + | 0.615924i | ||||
\(250\) | −15.0921 | + | 8.71343i | −0.954508 | + | 0.551086i | ||||
\(251\) | 16.0934 | + | 9.29153i | 1.01581 | + | 0.586476i | 0.912886 | − | 0.408214i | \(-0.133848\pi\) |
0.102920 | + | 0.994690i | \(0.467181\pi\) | |||||||
\(252\) | −9.15252 | + | 14.8661i | −0.576555 | + | 0.936477i | ||||
\(253\) | −27.2401 | + | 6.22085i | −1.71257 | + | 0.391101i | ||||
\(254\) | 13.2958 | − | 23.0290i | 0.834253 | − | 1.44497i | ||||
\(255\) | −15.4932 | + | 8.65547i | −0.970222 | + | 0.542027i | ||||
\(256\) | −3.68054 | + | 6.37489i | −0.230034 | + | 0.398430i | ||||
\(257\) | 10.2321 | − | 5.90750i | 0.638260 | − | 0.368500i | −0.145684 | − | 0.989331i | \(-0.546538\pi\) |
0.783944 | + | 0.620831i | \(0.213205\pi\) | |||||||
\(258\) | 33.6182 | + | 20.0480i | 2.09298 | + | 1.24814i | ||||
\(259\) | − | 11.1664i | − | 0.693845i | ||||||
\(260\) | −6.54445 | − | 50.8984i | −0.405870 | − | 3.15659i | ||||
\(261\) | 0.930799 | − | 1.51186i | 0.0576150 | − | 0.0935820i | ||||
\(262\) | 1.11222 | − | 0.642138i | 0.0687129 | − | 0.0396714i | ||||
\(263\) | −5.58258 | − | 9.66932i | −0.344237 | − | 0.596236i | 0.640978 | − | 0.767559i | \(-0.278529\pi\) |
−0.985215 | + | 0.171324i | \(0.945196\pi\) | |||||||
\(264\) | −35.9065 | + | 32.3924i | −2.20990 | + | 1.99361i | ||||
\(265\) | 3.28621i | 0.201870i | ||||||||
\(266\) | 4.44129 | + | 2.56418i | 0.272313 | + | 0.157220i | ||||
\(267\) | 0.167151 | − | 11.8294i | 0.0102295 | − | 0.723946i | ||||
\(268\) | − | 8.86489i | − | 0.541509i | ||||||
\(269\) | −11.1760 | − | 6.45248i | −0.681414 | − | 0.393414i | 0.118974 | − | 0.992897i | \(-0.462040\pi\) |
−0.800388 | + | 0.599483i | \(0.795373\pi\) | |||||||
\(270\) | 17.7764 | + | 34.0445i | 1.08184 | + | 2.07188i | ||||
\(271\) | 13.5276 | + | 23.4306i | 0.821746 | + | 1.42331i | 0.904381 | + | 0.426725i | \(0.140333\pi\) |
−0.0826357 | + | 0.996580i | \(0.526334\pi\) | |||||||
\(272\) | −45.2564 | −2.74408 | ||||||||
\(273\) | 2.81263 | − | 6.47394i | 0.170228 | − | 0.391821i | ||||
\(274\) | 7.18282i | 0.433930i | ||||||||
\(275\) | 8.37428 | + | 2.58201i | 0.504988 | + | 0.155701i | ||||
\(276\) | −38.4789 | + | 64.5246i | −2.31616 | + | 3.88392i | ||||
\(277\) | −0.416135 | − | 0.240255i | −0.0250031 | − | 0.0144356i | 0.487446 | − | 0.873153i | \(-0.337928\pi\) |
−0.512449 | + | 0.858717i | \(0.671262\pi\) | |||||||
\(278\) | 26.1936 | 1.57099 | ||||||||
\(279\) | 10.7709 | − | 5.81919i | 0.644840 | − | 0.348386i | ||||
\(280\) | 22.7792 | + | 13.1516i | 1.36132 | + | 0.785957i | ||||
\(281\) | − | 13.2614i | − | 0.791111i | −0.918442 | − | 0.395555i | \(-0.870552\pi\) | ||
0.918442 | − | 0.395555i | \(-0.129448\pi\) | |||||||
\(282\) | 4.84148 | + | 0.0684107i | 0.288306 | + | 0.00407380i | ||||
\(283\) | −0.259912 | + | 0.150060i | −0.0154502 | + | 0.00892017i | −0.507705 | − | 0.861531i | \(-0.669506\pi\) |
0.492255 | + | 0.870451i | \(0.336173\pi\) | |||||||
\(284\) | −22.3962 | − | 38.7914i | −1.32897 | − | 2.30184i | ||||
\(285\) | 7.09375 | − | 3.96301i | 0.420197 | − | 0.234748i | ||||
\(286\) | 20.4698 | − | 24.5607i | 1.21040 | − | 1.45230i | ||||
\(287\) | − | 11.4370i | − | 0.675105i | ||||||
\(288\) | −1.34012 | + | 47.4112i | −0.0789674 | + | 2.79373i | ||||
\(289\) | 1.63123 | + | 2.82537i | 0.0959545 | + | 0.166198i | ||||
\(290\) | −3.78817 | − | 2.18710i | −0.222449 | − | 0.128431i | ||||
\(291\) | 4.23008 | + | 7.57179i | 0.247971 | + | 0.443866i | ||||
\(292\) | 18.4303 | − | 31.9222i | 1.07855 | − | 1.86811i | ||||
\(293\) | 11.6147 | + | 6.70573i | 0.678536 | + | 0.391753i | 0.799303 | − | 0.600928i | \(-0.205202\pi\) |
−0.120767 | + | 0.992681i | \(0.538535\pi\) | |||||||
\(294\) | −12.9247 | − | 23.1350i | −0.753782 | − | 1.34926i | ||||
\(295\) | −3.95724 | + | 6.85414i | −0.230399 | + | 0.399064i | ||||
\(296\) | −41.5831 | − | 72.0240i | −2.41697 | − | 4.18631i | ||||
\(297\) | −5.77102 | + | 16.2387i | −0.334868 | + | 0.942265i | ||||
\(298\) | 46.0495 | 2.66758 | ||||||||
\(299\) | 11.7090 | − | 28.0280i | 0.677147 | − | 1.62090i | ||||
\(300\) | 20.5698 | − | 11.4916i | 1.18760 | − | 0.663468i | ||||
\(301\) | 8.27347 | − | 4.77669i | 0.476875 | − | 0.275324i | ||||
\(302\) | −12.5044 | + | 7.21941i | −0.719546 | + | 0.415430i | ||||
\(303\) | −0.307312 | + | 21.7487i | −0.0176546 | + | 1.24943i | ||||
\(304\) | 20.7212 | 1.18844 | ||||||||
\(305\) | −22.4563 | − | 12.9652i | −1.28585 | − | 0.742383i | ||||
\(306\) | −26.1560 | + | 14.1312i | −1.49524 | + | 0.807830i | ||||
\(307\) | 20.5352 | 1.17201 | 0.586003 | − | 0.810309i | \(-0.300701\pi\) | ||||
0.586003 | + | 0.810309i | \(0.300701\pi\) | |||||||
\(308\) | 4.29698 | + | 18.8158i | 0.244843 | + | 1.07213i | ||||
\(309\) | −6.26822 | − | 3.73802i | −0.356586 | − | 0.212649i | ||||
\(310\) | −15.0811 | − | 26.1213i | −0.856550 | − | 1.48359i | ||||
\(311\) | 14.0325i | 0.795710i | 0.917448 | + | 0.397855i | \(0.130245\pi\) | ||||
−0.917448 | + | 0.397855i | \(0.869755\pi\) | |||||||
\(312\) | −5.96698 | − | 52.2315i | −0.337814 | − | 2.95703i | ||||
\(313\) | −21.6594 | −1.22426 | −0.612130 | − | 0.790757i | \(-0.709687\pi\) | ||||
−0.612130 | + | 0.790757i | \(0.709687\pi\) | |||||||
\(314\) | −8.14967 | + | 4.70522i | −0.459913 | + | 0.265531i | ||||
\(315\) | 9.37000 | + | 0.264852i | 0.527940 | + | 0.0149227i | ||||
\(316\) | 6.30737 | + | 3.64156i | 0.354817 | + | 0.204854i | ||||
\(317\) | 24.4539 | 1.37347 | 0.686735 | − | 0.726908i | \(-0.259043\pi\) | ||||
0.686735 | + | 0.726908i | \(0.259043\pi\) | |||||||
\(318\) | −0.0777781 | + | 5.50441i | −0.00436158 | + | 0.308672i | ||||
\(319\) | −0.436997 | − | 1.91354i | −0.0244671 | − | 0.107138i | ||||
\(320\) | 49.3465 | 2.75855 | ||||||||
\(321\) | −0.445285 | + | 31.5131i | −0.0248534 | + | 1.75889i | ||||
\(322\) | 12.7295 | + | 22.0481i | 0.709388 | + | 1.22870i | ||||
\(323\) | 3.14495 | + | 5.44721i | 0.174990 | + | 0.303091i | ||||
\(324\) | 20.8646 | + | 41.3734i | 1.15915 | + | 2.29852i | ||||
\(325\) | −7.57554 | + | 5.77662i | −0.420216 | + | 0.320429i | ||||
\(326\) | −40.9298 | −2.26689 | ||||||||
\(327\) | 5.45658 | + | 3.25400i | 0.301749 | + | 0.179947i | ||||
\(328\) | −42.5909 | − | 73.7695i | −2.35169 | − | 4.07324i | ||||
\(329\) | 0.590886 | − | 1.02344i | 0.0325766 | − | 0.0564243i | ||||
\(330\) | 40.3939 | + | 13.0823i | 2.22361 | + | 0.720155i | ||||
\(331\) | −20.2155 | − | 11.6714i | −1.11114 | − | 0.641519i | −0.172018 | − | 0.985094i | \(-0.555029\pi\) |
−0.939125 | + | 0.343575i | \(0.888362\pi\) | |||||||
\(332\) | 29.1307 | + | 16.8186i | 1.59875 | + | 0.923040i | ||||
\(333\) | −25.2385 | − | 15.5384i | −1.38306 | − | 0.851500i | ||||
\(334\) | −2.06683 | + | 3.57986i | −0.113092 | + | 0.195881i | ||||
\(335\) | −4.12222 | + | 2.37996i | −0.225221 | + | 0.130031i | ||||
\(336\) | 20.5304 | + | 12.2432i | 1.12003 | + | 0.667923i | ||||
\(337\) | − | 35.9796i | − | 1.95993i | −0.199165 | − | 0.979966i | \(-0.563823\pi\) | ||
0.199165 | − | 0.979966i | \(-0.436177\pi\) | |||||||
\(338\) | 8.79285 | + | 33.6272i | 0.478268 | + | 1.82908i | ||||
\(339\) | 7.50416 | + | 13.4324i | 0.407570 | + | 0.729546i | ||||
\(340\) | 26.3765 | + | 45.6855i | 1.43047 | + | 2.47764i | ||||
\(341\) | 3.98779 | − | 12.9337i | 0.215951 | − | 0.700397i | ||||
\(342\) | 11.9758 | − | 6.47016i | 0.647579 | − | 0.349866i | ||||
\(343\) | −14.3798 | −0.776438 | ||||||||
\(344\) | 35.5763 | − | 61.6200i | 1.91815 | − | 3.32233i | ||||
\(345\) | 40.3347 | + | 0.569935i | 2.17155 | + | 0.0306843i | ||||
\(346\) | 1.32530i | 0.0712484i | ||||||||
\(347\) | 15.4394 | − | 26.7417i | 0.828828 | − | 1.43557i | −0.0701302 | − | 0.997538i | \(-0.522341\pi\) |
0.898958 | − | 0.438034i | \(-0.144325\pi\) | |||||||
\(348\) | −4.53267 | − | 2.70303i | −0.242976 | − | 0.144898i | ||||
\(349\) | −12.1184 | − | 20.9898i | −0.648685 | − | 1.12356i | −0.983437 | − | 0.181250i | \(-0.941986\pi\) |
0.334752 | − | 0.942306i | \(-0.391347\pi\) | |||||||
\(350\) | − | 7.98475i | − | 0.426803i | ||||||
\(351\) | −10.7187 | − | 15.3659i | −0.572120 | − | 0.820170i | ||||
\(352\) | 35.6702 | + | 38.4340i | 1.90123 | + | 2.04854i | ||||
\(353\) | −5.88781 | − | 10.1980i | −0.313376 | − | 0.542784i | 0.665715 | − | 0.746206i | \(-0.268127\pi\) |
−0.979091 | + | 0.203423i | \(0.934793\pi\) | |||||||
\(354\) | −6.79061 | + | 11.3870i | −0.360917 | + | 0.605214i | ||||
\(355\) | −12.0255 | + | 20.8287i | −0.638245 | + | 1.10547i | ||||
\(356\) | −35.1664 | −1.86382 | ||||||||
\(357\) | −0.102518 | + | 7.25527i | −0.00542582 | + | 0.383990i | ||||
\(358\) | 31.8511 | − | 55.1678i | 1.68338 | − | 2.91571i | ||||
\(359\) | 29.2458i | 1.54354i | 0.635904 | + | 0.771768i | \(0.280628\pi\) | ||||
−0.635904 | + | 0.771768i | \(0.719372\pi\) | |||||||
\(360\) | 61.4235 | − | 33.1851i | 3.23730 | − | 1.74901i | ||||
\(361\) | 8.06005 | + | 13.9604i | 0.424213 | + | 0.734759i | ||||
\(362\) | −13.6956 | + | 7.90715i | −0.719824 | + | 0.415591i | ||||
\(363\) | 8.02744 | + | 17.2789i | 0.421331 | + | 0.906907i | ||||
\(364\) | −19.3600 | − | 8.08783i | −1.01474 | − | 0.423917i | ||||
\(365\) | −19.7920 | −1.03596 | ||||||||
\(366\) | −37.3075 | − | 22.2482i | −1.95010 | − | 1.16293i | ||||
\(367\) | 8.59155 | + | 14.8810i | 0.448475 | + | 0.776782i | 0.998287 | − | 0.0585069i | \(-0.0186340\pi\) |
−0.549812 | + | 0.835288i | \(0.685301\pi\) | |||||||
\(368\) | 89.0857 | + | 51.4337i | 4.64391 | + | 2.68116i | ||||
\(369\) | −25.8502 | − | 15.9150i | −1.34571 | − | 0.828502i | ||||
\(370\) | −36.5106 | + | 63.2382i | −1.89810 | + | 3.28760i | ||||
\(371\) | 1.16358 | + | 0.671796i | 0.0604103 | + | 0.0348779i | ||||
\(372\) | −17.7482 | − | 31.7691i | −0.920201 | − | 1.64715i | ||||
\(373\) | −24.0932 | − | 13.9102i | −1.24750 | − | 0.720243i | −0.276888 | − | 0.960902i | \(-0.589303\pi\) |
−0.970610 | + | 0.240659i | \(0.922637\pi\) | |||||||
\(374\) | −9.68389 | + | 31.4079i | −0.500742 | + | 1.62407i | ||||
\(375\) | 9.69619 | + | 5.78228i | 0.500709 | + | 0.298596i | ||||
\(376\) | − | 8.80173i | − | 0.453915i | ||||||
\(377\) | 1.96889 | + | 0.822521i | 0.101403 | + | 0.0423620i | ||||
\(378\) | 15.6885 | + | 0.665396i | 0.806930 | + | 0.0342243i | ||||
\(379\) | −30.7429 | + | 17.7494i | −1.57916 | + | 0.911726i | −0.584178 | + | 0.811625i | \(0.698583\pi\) |
−0.994977 | + | 0.100101i | \(0.968083\pi\) | |||||||
\(380\) | −12.0768 | − | 20.9176i | −0.619527 | − | 1.07305i | ||||
\(381\) | −17.2248 | − | 0.243388i | −0.882452 | − | 0.0124692i | ||||
\(382\) | −7.98556 | −0.408577 | ||||||||
\(383\) | −0.861035 | + | 1.49136i | −0.0439968 | + | 0.0762047i | −0.887185 | − | 0.461413i | \(-0.847342\pi\) |
0.843188 | + | 0.537618i | \(0.180676\pi\) | |||||||
\(384\) | 27.8933 | + | 0.394136i | 1.42343 | + | 0.0201132i | ||||
\(385\) | 7.59581 | − | 7.04960i | 0.387118 | − | 0.359281i | ||||
\(386\) | 34.5124 | + | 19.9257i | 1.75663 | + | 1.01419i | ||||
\(387\) | 0.716450 | − | 25.3468i | 0.0364192 | − | 1.28845i | ||||
\(388\) | 22.3273 | − | 12.8907i | 1.13350 | − | 0.654424i | ||||
\(389\) | 19.5377i | 0.990600i | 0.868722 | + | 0.495300i | \(0.164942\pi\) | ||||
−0.868722 | + | 0.495300i | \(0.835058\pi\) | |||||||
\(390\) | −37.0965 | + | 27.4673i | −1.87845 | + | 1.39086i | ||||
\(391\) | 31.2253i | 1.57913i | ||||||||
\(392\) | −41.7188 | + | 24.0864i | −2.10712 | + | 1.21654i | ||||
\(393\) | −0.714563 | − | 0.426126i | −0.0360449 | − | 0.0214952i | ||||
\(394\) | −17.0744 | + | 29.5737i | −0.860196 | + | 1.48990i | ||||
\(395\) | − | 3.91061i | − | 0.196764i | ||||||
\(396\) | 48.5072 | + | 16.4707i | 2.43758 | + | 0.827682i | ||||
\(397\) | 26.8655 | + | 15.5108i | 1.34834 | + | 0.778464i | 0.988014 | − | 0.154364i | \(-0.0493327\pi\) |
0.360324 | + | 0.932827i | \(0.382666\pi\) | |||||||
\(398\) | − | 8.84360i | − | 0.443290i | ||||||
\(399\) | 0.0469390 | − | 3.32191i | 0.00234989 | − | 0.166304i | ||||
\(400\) | −16.1312 | − | 27.9401i | −0.806561 | − | 1.39700i | ||||
\(401\) | −5.00517 | − | 8.66921i | −0.249946 | − | 0.432920i | 0.713564 | − | 0.700590i | \(-0.247080\pi\) |
−0.963511 | + | 0.267670i | \(0.913746\pi\) | |||||||
\(402\) | −6.96105 | + | 3.88888i | −0.347186 | + | 0.193960i | ||||
\(403\) | 8.92171 | + | 11.7000i | 0.444422 | + | 0.582821i | ||||
\(404\) | 64.6545 | 3.21668 | ||||||||
\(405\) | 13.6373 | − | 20.8097i | 0.677644 | − | 1.03404i | ||||
\(406\) | −1.54882 | + | 0.894211i | −0.0768666 | + | 0.0443790i | ||||
\(407\) | −31.9439 | + | 7.29506i | −1.58340 | + | 0.361603i | ||||
\(408\) | 26.3570 | + | 47.1788i | 1.30487 | + | 2.33570i | ||||
\(409\) | −17.7089 | + | 30.6727i | −0.875648 | + | 1.51667i | −0.0195767 | + | 0.999808i | \(0.506232\pi\) |
−0.856071 | + | 0.516858i | \(0.827101\pi\) | |||||||
\(410\) | −37.3955 | + | 64.7709i | −1.84683 | + | 3.19881i | ||||
\(411\) | 4.06222 | − | 2.26941i | 0.200374 | − | 0.111942i | ||||
\(412\) | −10.8469 | + | 18.7874i | −0.534390 | + | 0.925590i | ||||
\(413\) | 1.61795 | + | 2.80236i | 0.0796139 | + | 0.137895i | ||||
\(414\) | 67.5473 | + | 1.90928i | 3.31977 | + | 0.0938362i | ||||
\(415\) | − | 18.0612i | − | 0.886590i | ||||||
\(416\) | −56.5385 | + | 7.26964i | −2.77203 | + | 0.356424i | ||||
\(417\) | −8.27587 | − | 14.8137i | −0.405271 | − | 0.725431i | ||||
\(418\) | 4.43388 | − | 14.3805i | 0.216868 | − | 0.703373i | ||||
\(419\) | −2.45192 | + | 1.41562i | −0.119784 | + | 0.0691573i | −0.558695 | − | 0.829373i | \(-0.688698\pi\) |
0.438911 | + | 0.898531i | \(0.355364\pi\) | |||||||
\(420\) | 0.393676 | − | 27.8607i | 0.0192094 | − | 1.35946i | ||||
\(421\) | − | 24.8977i | − | 1.21344i | −0.794915 | − | 0.606721i | \(-0.792485\pi\) | ||
0.794915 | − | 0.606721i | \(-0.207515\pi\) | |||||||
\(422\) | −27.7728 | + | 48.1038i | −1.35196 | + | 2.34166i | ||||
\(423\) | −1.49097 | − | 2.75969i | −0.0724936 | − | 0.134181i | ||||
\(424\) | 10.0069 | 0.485980 | ||||||||
\(425\) | 4.89662 | − | 8.48119i | 0.237521 | − | 0.411398i | ||||
\(426\) | −20.6356 | + | 34.6035i | −0.999800 | + | 1.67655i | ||||
\(427\) | −9.18143 | + | 5.30090i | −0.444320 | + | 0.256528i | ||||
\(428\) | 93.6823 | 4.52830 | ||||||||
\(429\) | −20.3576 | − | 3.81668i | −0.982875 | − | 0.184271i | ||||
\(430\) | −62.4732 | −3.01272 | ||||||||
\(431\) | 2.36616 | − | 1.36610i | 0.113974 | − | 0.0658027i | −0.441929 | − | 0.897050i | \(-0.645706\pi\) |
0.555903 | + | 0.831247i | \(0.312373\pi\) | |||||||
\(432\) | 56.2412 | − | 29.3664i | 2.70591 | − | 1.41289i | ||||
\(433\) | 5.34129 | − | 9.25139i | 0.256686 | − | 0.444594i | −0.708666 | − | 0.705544i | \(-0.750703\pi\) |
0.965352 | + | 0.260951i | \(0.0840360\pi\) | |||||||
\(434\) | −12.3320 | −0.591957 | ||||||||
\(435\) | −0.0400363 | + | 2.83340i | −0.00191959 | + | 0.135851i | ||||
\(436\) | 9.44241 | − | 16.3547i | 0.452210 | − | 0.783250i | ||||
\(437\) | − | 14.2969i | − | 0.683911i | ||||||
\(438\) | −33.1517 | − | 0.468437i | −1.58405 | − | 0.0223828i | ||||
\(439\) | 10.6889 | − | 6.17124i | 0.510154 | − | 0.294537i | −0.222743 | − | 0.974877i | \(-0.571501\pi\) |
0.732897 | + | 0.680340i | \(0.238168\pi\) | |||||||
\(440\) | 22.7412 | − | 73.7569i | 1.08414 | − | 3.51622i | ||||
\(441\) | −9.00039 | + | 14.6190i | −0.428590 | + | 0.696143i | ||||
\(442\) | −21.6653 | − | 28.4122i | −1.03052 | − | 1.35143i | ||||
\(443\) | 5.22827i | 0.248403i | 0.992257 | + | 0.124201i | \(0.0396369\pi\) | ||||
−0.992257 | + | 0.124201i | \(0.960363\pi\) | |||||||
\(444\) | −45.1234 | + | 75.6666i | −2.14146 | + | 3.59098i | ||||
\(445\) | 9.44115 | + | 16.3526i | 0.447553 | + | 0.775185i | ||||
\(446\) | −16.8599 | + | 29.2022i | −0.798340 | + | 1.38277i | ||||
\(447\) | −14.5493 | − | 26.0431i | −0.688159 | − | 1.23180i | ||||
\(448\) | 10.0878 | − | 17.4726i | 0.476605 | − | 0.825504i | ||||
\(449\) | 12.0394 | − | 20.8529i | 0.568175 | − | 0.984108i | −0.428571 | − | 0.903508i | \(-0.640983\pi\) |
0.996747 | − | 0.0806003i | \(-0.0256837\pi\) | |||||||
\(450\) | −18.0473 | − | 11.1111i | −0.850758 | − | 0.523781i | ||||
\(451\) | −32.7180 | + | 7.47186i | −1.54063 | + | 0.351836i | ||||
\(452\) | 39.6086 | − | 22.8680i | 1.86303 | − | 1.07562i | ||||
\(453\) | 8.03366 | + | 4.79084i | 0.377454 | + | 0.225093i | ||||
\(454\) | −42.4974 | −1.99450 | ||||||||
\(455\) | 1.43672 | + | 11.1739i | 0.0673544 | + | 0.523838i | ||||
\(456\) | −12.0679 | − | 21.6014i | −0.565130 | − | 1.01158i | ||||
\(457\) | −0.324040 | − | 0.561253i | −0.0151579 | − | 0.0262543i | 0.858347 | − | 0.513070i | \(-0.171492\pi\) |
−0.873505 | + | 0.486815i | \(0.838158\pi\) | |||||||
\(458\) | −15.8756 | − | 27.4973i | −0.741817 | − | 1.28487i | ||||
\(459\) | 16.2559 | + | 10.3277i | 0.758758 | + | 0.482055i | ||||
\(460\) | − | 119.907i | − | 5.59070i | ||||||
\(461\) | 5.33706 | + | 3.08135i | 0.248572 | + | 0.143513i | 0.619110 | − | 0.785304i | \(-0.287493\pi\) |
−0.370538 | + | 0.928817i | \(0.620827\pi\) | |||||||
\(462\) | 12.8898 | − | 11.6283i | 0.599690 | − | 0.540998i | ||||
\(463\) | 30.4408i | 1.41471i | 0.706861 | + | 0.707353i | \(0.250111\pi\) | ||||
−0.706861 | + | 0.707353i | \(0.749889\pi\) | |||||||
\(464\) | −3.61307 | + | 6.25802i | −0.167732 | + | 0.290521i | ||||
\(465\) | −10.0079 | + | 16.7821i | −0.464106 | + | 0.778250i | ||||
\(466\) | 33.5316 | − | 19.3595i | 1.55332 | − | 0.896810i | ||||
\(467\) | 5.89082i | 0.272595i | 0.990668 | + | 0.136297i | \(0.0435202\pi\) | ||||
−0.990668 | + | 0.136297i | \(0.956480\pi\) | |||||||
\(468\) | −45.2204 | + | 32.5034i | −2.09031 | + | 1.50247i | ||||
\(469\) | 1.94613i | 0.0898639i | ||||||||
\(470\) | −6.69270 | + | 3.86403i | −0.308711 | + | 0.178235i | ||||
\(471\) | 5.23590 | + | 3.12241i | 0.241258 | + | 0.143873i | ||||
\(472\) | 20.8717 | + | 12.0503i | 0.960700 | + | 0.554660i | ||||
\(473\) | −19.0699 | − | 20.5474i | −0.876833 | − | 0.944771i | ||||
\(474\) | 0.0925564 | − | 6.55028i | 0.00425125 | − | 0.300864i | ||||
\(475\) | −2.24197 | + | 3.88321i | −0.102869 | + | 0.178174i | ||||
\(476\) | 21.5685 | 0.988589 | ||||||||
\(477\) | 3.13758 | − | 1.69513i | 0.143660 | − | 0.0776147i | ||||
\(478\) | 0.497999 | + | 0.862560i | 0.0227779 | + | 0.0394526i | ||||
\(479\) | −0.349105 | + | 0.201556i | −0.0159510 | + | 0.00920932i | −0.507954 | − | 0.861384i | \(-0.669598\pi\) |
0.492003 | + | 0.870593i | \(0.336265\pi\) | |||||||
\(480\) | −36.9207 | − | 66.0876i | −1.68519 | − | 3.01647i | ||||
\(481\) | 13.7309 | − | 32.8679i | 0.626073 | − | 1.49865i | ||||
\(482\) | − | 45.1436i | − | 2.05624i | ||||||
\(483\) | 8.44737 | − | 14.1652i | 0.384369 | − | 0.644540i | ||||
\(484\) | 51.0193 | − | 24.5849i | 2.31906 | − | 1.11749i | ||||
\(485\) | −11.9884 | − | 6.92153i | −0.544367 | − | 0.314291i | ||||
\(486\) | 23.3351 | − | 34.5336i | 1.05850 | − | 1.56647i | ||||
\(487\) | −16.6034 | − | 9.58597i | −0.752371 | − | 0.434382i | 0.0741789 | − | 0.997245i | \(-0.476366\pi\) |
−0.826550 | + | 0.562863i | \(0.809700\pi\) | |||||||
\(488\) | −39.4806 | + | 68.3824i | −1.78720 | + | 3.09553i | ||||
\(489\) | 12.9318 | + | 23.1477i | 0.584794 | + | 1.04678i | ||||
\(490\) | 36.6298 | + | 21.1482i | 1.65477 | + | 0.955379i | ||||
\(491\) | 3.27077 | + | 5.66514i | 0.147608 | + | 0.255664i | 0.930343 | − | 0.366691i | \(-0.119509\pi\) |
−0.782735 | + | 0.622355i | \(0.786176\pi\) | |||||||
\(492\) | −46.2170 | + | 77.5004i | −2.08362 | + | 3.49399i | ||||
\(493\) | −2.19349 | −0.0987896 | ||||||||
\(494\) | 9.91973 | + | 13.0089i | 0.446310 | + | 0.585297i | ||||
\(495\) | −5.36381 | − | 26.9780i | −0.241085 | − | 1.21257i | ||||
\(496\) | −43.1521 | + | 24.9139i | −1.93759 | + | 1.11867i | ||||
\(497\) | 4.91669 | + | 8.51596i | 0.220544 | + | 0.381993i | ||||
\(498\) | 0.427473 | − | 30.2526i | 0.0191555 | − | 1.35565i | ||||
\(499\) | 27.9317i | 1.25039i | 0.780467 | + | 0.625196i | \(0.214981\pi\) | ||||
−0.780467 | + | 0.625196i | \(0.785019\pi\) | |||||||
\(500\) | 16.7789 | − | 29.0619i | 0.750376 | − | 1.29969i | ||||
\(501\) | 2.67759 | + | 0.0378348i | 0.119626 | + | 0.00169033i | ||||
\(502\) | −49.6850 | −2.21755 | ||||||||
\(503\) | −7.46410 | + | 12.9282i | −0.332808 | + | 0.576440i | −0.983061 | − | 0.183277i | \(-0.941329\pi\) |
0.650254 | + | 0.759717i | \(0.274663\pi\) | |||||||
\(504\) | 0.806507 | − | 28.5329i | 0.0359247 | − | 1.27095i | ||||
\(505\) | −17.3579 | − | 30.0647i | −0.772414 | − | 1.33786i | ||||
\(506\) | 54.7573 | − | 50.8197i | 2.43426 | − | 2.25921i | ||||
\(507\) | 16.2396 | − | 15.5973i | 0.721227 | − | 0.692698i | ||||
\(508\) | 51.2058i | 2.27189i | ||||||||
\(509\) | 17.9447 | + | 31.0812i | 0.795387 | + | 1.37765i | 0.922593 | + | 0.385774i | \(0.126065\pi\) |
−0.127207 | + | 0.991876i | \(0.540601\pi\) | |||||||
\(510\) | 24.3031 | − | 40.7534i | 1.07616 | − | 1.80459i | ||||
\(511\) | −4.04605 | + | 7.00796i | −0.178987 | + | 0.310014i | ||||
\(512\) | 12.5305i | 0.553776i | ||||||||
\(513\) | −7.44293 | − | 4.72865i | −0.328614 | − | 0.208775i | ||||
\(514\) | −15.7947 | + | 27.3573i | −0.696675 | + | 1.20668i | ||||
\(515\) | 11.6483 | 0.513287 | ||||||||
\(516\) | −75.3660 | − | 1.06493i | −3.31780 | − | 0.0468810i | ||||
\(517\) | −3.31382 | − | 1.02174i | −0.145742 | − | 0.0449359i | ||||
\(518\) | 14.9276 | + | 25.8554i | 0.655882 | + | 1.13602i | ||||
\(519\) | 0.749517 | − | 0.418727i | 0.0329001 | − | 0.0183801i | ||||
\(520\) | 50.8779 | + | 66.7219i | 2.23114 | + | 2.92595i | ||||
\(521\) | − | 32.3244i | − | 1.41616i | −0.706133 | − | 0.708079i | \(-0.749562\pi\) | ||
0.706133 | − | 0.708079i | \(-0.250438\pi\) | |||||||
\(522\) | −0.134122 | + | 4.74500i | −0.00587035 | + | 0.207683i | ||||
\(523\) | 1.46718 | − | 0.847075i | 0.0641551 | − | 0.0370400i | −0.467579 | − | 0.883951i | \(-0.654874\pi\) |
0.531734 | + | 0.846911i | \(0.321540\pi\) | |||||||
\(524\) | −1.23653 | + | 2.14172i | −0.0540179 | + | 0.0935617i | ||||
\(525\) | −4.51575 | + | 2.52278i | −0.197083 | + | 0.110103i | ||||
\(526\) | 25.8526 | + | 14.9260i | 1.12723 | + | 0.650805i | ||||
\(527\) | −13.0988 | − | 7.56258i | −0.570591 | − | 0.329431i | ||||
\(528\) | 21.6118 | − | 66.7303i | 0.940532 | − | 2.90407i | ||||
\(529\) | 23.9873 | − | 41.5472i | 1.04293 | − | 1.80640i | ||||
\(530\) | −4.39313 | − | 7.60912i | −0.190825 | − | 0.330519i | ||||
\(531\) | 8.58539 | + | 0.242674i | 0.372574 | + | 0.0105311i | ||||
\(532\) | −9.87538 | −0.428152 | ||||||||
\(533\) | 14.0636 | − | 33.6645i | 0.609164 | − | 1.45817i | ||||
\(534\) | 15.4269 | + | 27.6140i | 0.667588 | + | 1.19498i | ||||
\(535\) | −25.1510 | − | 43.5627i | −1.08737 | − | 1.88338i | ||||
\(536\) | 7.24729 | + | 12.5527i | 0.313035 | + | 0.542193i | ||||
\(537\) | −41.2633 | − | 0.583056i | −1.78064 | − | 0.0251607i | ||||
\(538\) | 34.5036 | 1.48756 | ||||||||
\(539\) | 4.22555 | + | 18.5030i | 0.182007 | + | 0.796980i | ||||
\(540\) | −62.4236 | − | 39.6590i | −2.68628 | − | 1.70665i | ||||
\(541\) | −0.557105 | −0.0239518 | −0.0119759 | − | 0.999928i | \(-0.503812\pi\) | ||||
−0.0119759 | + | 0.999928i | \(0.503812\pi\) | |||||||
\(542\) | −62.6457 | − | 36.1685i | −2.69086 | − | 1.55357i | ||||
\(543\) | 8.79898 | + | 5.24723i | 0.377600 | + | 0.225180i | ||||
\(544\) | 50.7479 | − | 29.2993i | 2.17580 | − | 1.25620i | ||||
\(545\) | −10.1400 | −0.434352 | ||||||||
\(546\) | 2.14205 | + | 18.7502i | 0.0916711 | + | 0.802436i | ||||
\(547\) | 39.2321i | 1.67744i | 0.544562 | + | 0.838721i | \(0.316696\pi\) | ||||
−0.544562 | + | 0.838721i | \(0.683304\pi\) | |||||||
\(548\) | −6.91575 | − | 11.9784i | −0.295426 | − | 0.511693i | ||||
\(549\) | −0.795076 | + | 28.1284i | −0.0339330 | + | 1.20049i | ||||
\(550\) | −22.8421 | + | 5.21648i | −0.973991 | + | 0.222432i | ||||
\(551\) | 1.00431 | 0.0427852 | ||||||||
\(552\) | 1.73553 | − | 122.824i | 0.0738689 | − | 5.22775i | ||||
\(553\) | −1.38467 | − | 0.799440i | −0.0588822 | − | 0.0339957i | ||||
\(554\) | 1.28473 | 0.0545829 | ||||||||
\(555\) | 47.2997 | + | 0.668351i | 2.00776 | + | 0.0283699i | ||||
\(556\) | −43.6819 | + | 25.2197i | −1.85252 | + | 1.06956i | ||||
\(557\) | 18.4169 | − | 10.6330i | 0.780350 | − | 0.450535i | −0.0562042 | − | 0.998419i | \(-0.517900\pi\) |
0.836554 | + | 0.547884i | \(0.184566\pi\) | |||||||
\(558\) | −17.1605 | + | 27.8732i | −0.726461 | + | 1.17996i | ||||
\(559\) | 30.2264 | − | 3.88647i | 1.27844 | − | 0.164380i | ||||
\(560\) | −38.1520 | −1.61222 | ||||||||
\(561\) | 20.8223 | − | 4.44663i | 0.879117 | − | 0.187737i | ||||
\(562\) | 17.7284 | + | 30.7064i | 0.747826 | + | 1.29527i | ||||
\(563\) | 3.66666 | − | 6.35084i | 0.154531 | − | 0.267656i | −0.778357 | − | 0.627822i | \(-0.783947\pi\) |
0.932888 | + | 0.360166i | \(0.117280\pi\) | |||||||
\(564\) | −8.13976 | + | 4.54738i | −0.342746 | + | 0.191479i | ||||
\(565\) | −21.2675 | − | 12.2788i | −0.894731 | − | 0.516573i | ||||
\(566\) | 0.401213 | − | 0.694921i | 0.0168642 | − | 0.0292097i | ||||
\(567\) | −4.58046 | − | 9.08281i | −0.192361 | − | 0.381442i | ||||
\(568\) | 63.4261 | + | 36.6191i | 2.66130 | + | 1.53650i | ||||
\(569\) | −13.5513 | − | 23.4716i | −0.568102 | − | 0.983982i | −0.996754 | − | 0.0805117i | \(-0.974345\pi\) |
0.428652 | − | 0.903470i | \(-0.358989\pi\) | |||||||
\(570\) | −11.1275 | + | 18.6594i | −0.466078 | + | 0.781556i | ||||
\(571\) | 13.8007i | 0.577543i | 0.957398 | + | 0.288771i | \(0.0932467\pi\) | ||||
−0.957398 | + | 0.288771i | \(0.906753\pi\) | |||||||
\(572\) | −10.4890 | + | 60.6674i | −0.438566 | + | 2.53663i | ||||
\(573\) | 2.52303 | + | 4.51620i | 0.105401 | + | 0.188667i | ||||
\(574\) | 15.2894 | + | 26.4820i | 0.638167 | + | 1.10534i | ||||
\(575\) | −19.2776 | + | 11.1299i | −0.803932 | + | 0.464151i | ||||
\(576\) | −25.4544 | − | 47.1145i | −1.06060 | − | 1.96310i | ||||
\(577\) | 25.4836i | 1.06090i | 0.847717 | + | 0.530449i | \(0.177977\pi\) | ||||
−0.847717 | + | 0.530449i | \(0.822023\pi\) | |||||||
\(578\) | −7.55411 | − | 4.36136i | −0.314209 | − | 0.181409i | ||||
\(579\) | 0.364754 | − | 25.8139i | 0.0151586 | − | 1.07279i | ||||
\(580\) | 8.42313 | 0.349751 | ||||||||
\(581\) | −6.39512 | − | 3.69223i | −0.265314 | − | 0.153179i | ||||
\(582\) | −19.9169 | − | 11.8773i | −0.825580 | − | 0.492331i | ||||
\(583\) | 1.16164 | − | 3.76758i | 0.0481103 | − | 0.156037i | ||||
\(584\) | 60.2692i | 2.49396i | ||||||||
\(585\) | 27.2546 | + | 12.3015i | 1.12684 | + | 0.508605i | ||||
\(586\) | −35.8579 | −1.48128 | ||||||||
\(587\) | 9.66167 | + | 16.7345i | 0.398780 | + | 0.690707i | 0.993576 | − | 0.113170i | \(-0.0361004\pi\) |
−0.594796 | + | 0.803877i | \(0.702767\pi\) | |||||||
\(588\) | 43.8287 | + | 26.1371i | 1.80747 | + | 1.07787i | ||||
\(589\) | 5.99742 | + | 3.46261i | 0.247120 | + | 0.142675i | ||||
\(590\) | − | 21.1607i | − | 0.871174i | ||||||
\(591\) | 22.1200 | + | 0.312558i | 0.909893 | + | 0.0128569i | ||||
\(592\) | 104.469 | + | 60.3152i | 4.29365 | + | 2.47894i | ||||
\(593\) | 22.6629i | 0.930652i | 0.885139 | + | 0.465326i | \(0.154063\pi\) | ||||
−0.885139 | + | 0.465326i | \(0.845937\pi\) | |||||||
\(594\) | −8.34588 | − | 45.3151i | −0.342436 | − | 1.85930i | ||||
\(595\) | −5.79051 | − | 10.0294i | −0.237388 | − | 0.411167i | ||||
\(596\) | −76.7946 | + | 44.3374i | −3.14563 | + | 1.81613i | ||||
\(597\) | −5.00147 | + | 2.79413i | −0.204696 | + | 0.114356i | ||||
\(598\) | 10.3571 | + | 80.5510i | 0.423535 | + | 3.29398i | ||||
\(599\) | − | 9.06218i | − | 0.370271i | −0.982713 | − | 0.185135i | \(-0.940728\pi\) | ||
0.982713 | − | 0.185135i | \(-0.0592724\pi\) | |||||||
\(600\) | −19.7322 | + | 33.0885i | −0.805564 | + | 1.35083i | ||||
\(601\) | 14.5938 | − | 8.42572i | 0.595292 | − | 0.343692i | −0.171895 | − | 0.985115i | \(-0.554989\pi\) |
0.767187 | + | 0.641423i | \(0.221656\pi\) | |||||||
\(602\) | −12.7713 | + | 22.1205i | −0.520519 | + | 0.901566i | ||||
\(603\) | 4.39868 | + | 2.70811i | 0.179128 | + | 0.110283i | ||||
\(604\) | 13.9020 | − | 24.0789i | 0.565663 | − | 0.979757i | ||||
\(605\) | −25.1293 | − | 17.1239i | −1.02165 | − | 0.696187i | ||||
\(606\) | −28.3629 | − | 50.7692i | −1.15216 | − | 2.06236i | ||||
\(607\) | −37.1851 | − | 21.4689i | −1.50930 | − | 0.871394i | −0.999941 | − | 0.0108386i | \(-0.996550\pi\) |
−0.509357 | − | 0.860555i | \(-0.670117\pi\) | |||||||
\(608\) | −23.2355 | + | 13.4150i | −0.942325 | + | 0.544052i | ||||
\(609\) | 0.995067 | + | 0.593403i | 0.0403221 | + | 0.0240459i | ||||
\(610\) | 69.3292 | 2.80706 | ||||||||
\(611\) | 2.99774 | − | 2.28589i | 0.121276 | − | 0.0924771i | ||||
\(612\) | 30.0133 | − | 48.7495i | 1.21322 | − | 1.97058i | ||||
\(613\) | 10.0723 | + | 17.4458i | 0.406817 | + | 0.704628i | 0.994531 | − | 0.104441i | \(-0.0333053\pi\) |
−0.587714 | + | 0.809069i | \(0.699972\pi\) | |||||||
\(614\) | −47.5486 | + | 27.4522i | −1.91891 | + | 1.10788i | ||||
\(615\) | 48.4460 | + | 0.684549i | 1.95353 | + | 0.0276037i | ||||
\(616\) | −21.4669 | − | 23.1302i | −0.864927 | − | 0.931943i | ||||
\(617\) | 10.3940 | − | 18.0030i | 0.418448 | − | 0.724773i | −0.577336 | − | 0.816507i | \(-0.695908\pi\) |
0.995784 | + | 0.0917338i | \(0.0292409\pi\) | |||||||
\(618\) | 19.5110 | + | 0.275693i | 0.784847 | + | 0.0110900i | ||||
\(619\) | − | 2.37921i | − | 0.0956287i | −0.998856 | − | 0.0478143i | \(-0.984774\pi\) | ||
0.998856 | − | 0.0478143i | \(-0.0152256\pi\) | |||||||
\(620\) | 50.3001 | + | 29.0408i | 2.02010 | + | 1.16631i | ||||
\(621\) | −20.2617 | − | 38.8043i | −0.813075 | − | 1.55716i | ||||
\(622\) | −18.7592 | − | 32.4918i | −0.752174 | − | 1.30280i | ||||
\(623\) | 7.72016 | 0.309302 | ||||||||
\(624\) | 45.3756 | + | 61.2830i | 1.81648 | + | 2.45328i | ||||
\(625\) | −31.2298 | −1.24919 | ||||||||
\(626\) | 50.1516 | − | 28.9550i | 2.00446 | − | 1.15728i | ||||
\(627\) | −9.53372 | + | 2.03594i | −0.380740 | + | 0.0813078i | ||||
\(628\) | 9.06054 | − | 15.6933i | 0.361555 | − | 0.626232i | ||||
\(629\) | 36.6172i | 1.46002i | ||||||||
\(630\) | −22.0500 | + | 11.9129i | −0.878493 | + | 0.474621i | ||||
\(631\) | −29.0167 | − | 16.7528i | −1.15514 | − | 0.666919i | −0.205004 | − | 0.978761i | \(-0.565721\pi\) |
−0.950134 | + | 0.311842i | \(0.899054\pi\) | |||||||
\(632\) | −11.9083 | −0.473687 | ||||||||
\(633\) | 35.9797 | + | 0.508399i | 1.43007 | + | 0.0202070i | ||||
\(634\) | −56.6224 | + | 32.6909i | −2.24876 | + | 1.29832i | ||||
\(635\) | 23.8110 | − | 13.7473i | 0.944910 | − | 0.545544i | ||||
\(636\) | −5.17005 | − | 9.25433i | −0.205006 | − | 0.366958i | ||||
\(637\) | −19.0382 | − | 7.95339i | −0.754322 | − | 0.315125i | ||||
\(638\) | 3.56994 | + | 3.84654i | 0.141335 | + | 0.152286i | ||||
\(639\) | 26.0897 | + | 0.737449i | 1.03209 | + | 0.0291730i | ||||
\(640\) | −38.5588 | + | 22.2620i | −1.52417 | + | 0.879981i | ||||
\(641\) | −9.30156 | − | 5.37026i | −0.367390 | − | 0.212112i | 0.304928 | − | 0.952375i | \(-0.401368\pi\) |
−0.672317 | + | 0.740263i | \(0.734701\pi\) | |||||||
\(642\) | −41.0969 | − | 73.5630i | −1.62196 | − | 2.90330i | ||||
\(643\) | −19.7709 | − | 11.4147i | −0.779688 | − | 0.450153i | 0.0566314 | − | 0.998395i | \(-0.481964\pi\) |
−0.836320 | + | 0.548242i | \(0.815297\pi\) | |||||||
\(644\) | −42.4568 | − | 24.5124i | −1.67303 | − | 0.965925i | ||||
\(645\) | 19.7384 | + | 35.3315i | 0.777198 | + | 1.39118i | ||||
\(646\) | −14.5641 | − | 8.40856i | −0.573015 | − | 0.330831i | ||||
\(647\) | 20.5076 | − | 11.8400i | 0.806235 | − | 0.465480i | −0.0394116 | − | 0.999223i | \(-0.512548\pi\) |
0.845647 | + | 0.533743i | \(0.179215\pi\) | |||||||
\(648\) | −63.3683 | − | 41.5274i | −2.48934 | − | 1.63135i | ||||
\(649\) | 6.95976 | − | 6.45929i | 0.273195 | − | 0.253549i | ||||
\(650\) | 9.81853 | − | 23.5029i | 0.385115 | − | 0.921858i | ||||
\(651\) | 3.89630 | + | 6.97434i | 0.152708 | + | 0.273346i | ||||
\(652\) | 68.2567 | − | 39.4080i | 2.67314 | − | 1.54334i | ||||
\(653\) | 14.9752 | − | 8.64595i | 0.586026 | − | 0.338342i | −0.177499 | − | 0.984121i | \(-0.556801\pi\) |
0.763524 | + | 0.645779i | \(0.223467\pi\) | |||||||
\(654\) | −16.9846 | − | 0.239995i | −0.664151 | − | 0.00938454i | ||||
\(655\) | 1.32788 | 0.0518847 | ||||||||
\(656\) | 107.001 | + | 61.7769i | 4.17768 | + | 2.41198i | ||||
\(657\) | 10.2093 | + | 18.8968i | 0.398304 | + | 0.737234i | ||||
\(658\) | 3.15967i | 0.123177i | ||||||||
\(659\) | −3.48802 | + | 6.04142i | −0.135874 | + | 0.235340i | −0.925931 | − | 0.377693i | \(-0.876718\pi\) |
0.790057 | + | 0.613033i | \(0.210051\pi\) | |||||||
\(660\) | −79.9588 | + | 17.0754i | −3.11239 | + | 0.664658i | ||||
\(661\) | 10.6436 | − | 6.14511i | 0.413990 | − | 0.239017i | −0.278513 | − | 0.960432i | \(-0.589842\pi\) |
0.692502 | + | 0.721416i | \(0.256508\pi\) | |||||||
\(662\) | 62.4111 | 2.42568 | ||||||||
\(663\) | −9.22328 | + | 21.2296i | −0.358202 | + | 0.824489i | ||||
\(664\) | −54.9987 | −2.13436 | ||||||||
\(665\) | 2.65125 | + | 4.59210i | 0.102811 | + | 0.178074i | ||||
\(666\) | 79.2112 | + | 2.23898i | 3.06937 | + | 0.0867586i | ||||
\(667\) | 4.31780 | + | 2.49288i | 0.167186 | + | 0.0965248i | ||||
\(668\) | − | 7.95995i | − | 0.307980i | ||||||
\(669\) | 21.8421 | + | 0.308632i | 0.844464 | + | 0.0119324i | ||||
\(670\) | 6.36324 | − | 11.0215i | 0.245834 | − | 0.425796i | ||||
\(671\) | 21.1627 | + | 22.8024i | 0.816975 | + | 0.880276i | ||||
\(672\) | −30.9480 | − | 0.437299i | −1.19384 | − | 0.0168692i | ||||
\(673\) | −4.49827 | + | 2.59708i | −0.173396 | + | 0.100110i | −0.584186 | − | 0.811620i | \(-0.698586\pi\) |
0.410790 | + | 0.911730i | \(0.365253\pi\) | |||||||
\(674\) | 48.0988 | + | 83.3096i | 1.85270 | + | 3.20896i | ||||
\(675\) | −0.581784 | + | 13.7171i | −0.0223929 | + | 0.527972i | ||||
\(676\) | −47.0403 | − | 47.6125i | −1.80924 | − | 1.83125i | ||||
\(677\) | −40.2631 | −1.54744 | −0.773718 | − | 0.633530i | \(-0.781605\pi\) | ||||
−0.773718 | + | 0.633530i | \(0.781605\pi\) | |||||||
\(678\) | −35.3325 | − | 21.0704i | −1.35694 | − | 0.809203i | ||||
\(679\) | −4.90156 | + | 2.82992i | −0.188105 | + | 0.108602i | ||||
\(680\) | −74.6984 | − | 43.1271i | −2.86455 | − | 1.65385i | ||||
\(681\) | 13.4270 | + | 24.0342i | 0.514525 | + | 0.920994i | ||||
\(682\) | 8.05660 | + | 35.2785i | 0.308503 | + | 1.35088i | ||||
\(683\) | −8.28121 | + | 14.3435i | −0.316872 | + | 0.548838i | −0.979834 | − | 0.199815i | \(-0.935966\pi\) |
0.662962 | + | 0.748653i | \(0.269299\pi\) | |||||||
\(684\) | −13.7419 | + | 22.3205i | −0.525436 | + | 0.853447i | ||||
\(685\) | −3.71336 | + | 6.43172i | −0.141880 | + | 0.245743i | ||||
\(686\) | 33.2961 | − | 19.2235i | 1.27125 | − | 0.733956i | ||||
\(687\) | −10.5351 | + | 17.6661i | −0.401940 | + | 0.674006i | ||||
\(688\) | 103.205i | 3.93466i | ||||||||
\(689\) | 2.59889 | + | 3.40822i | 0.0990099 | + | 0.129843i | ||||
\(690\) | −94.1557 | + | 52.6013i | −3.58445 | + | 2.00250i | ||||
\(691\) | −1.43677 | + | 0.829518i | −0.0546572 | + | 0.0315563i | −0.527080 | − | 0.849816i | \(-0.676713\pi\) |
0.472422 | + | 0.881372i | \(0.343380\pi\) | |||||||
\(692\) | −1.27602 | − | 2.21013i | −0.0485071 | − | 0.0840167i | ||||
\(693\) | −10.6489 | − | 3.61584i | −0.404518 | − | 0.137355i | ||||
\(694\) | 82.5596i | 3.13392i | ||||||||
\(695\) | 23.4546 | + | 13.5415i | 0.889685 | + | 0.513660i | ||||
\(696\) | 8.62806 | + | 0.121916i | 0.327046 | + | 0.00462120i | ||||
\(697\) | 37.5047i | 1.42059i | ||||||||
\(698\) | 56.1197 | + | 32.4007i | 2.12416 | + | 1.22639i | ||||
\(699\) | −21.5430 | − | 12.8470i | −0.814829 | − | 0.485920i | ||||
\(700\) | 7.68787 | + | 13.3158i | 0.290574 | + | 0.503289i | ||||
\(701\) | −1.95017 | −0.0736571 | −0.0368285 | − | 0.999322i | \(-0.511726\pi\) | ||||
−0.0368285 | + | 0.999322i | \(0.511726\pi\) | |||||||
\(702\) | 45.3604 | + | 21.2501i | 1.71202 | + | 0.802034i | ||||
\(703\) | − | 16.7656i | − | 0.632327i | ||||||
\(704\) | −56.5747 | − | 17.4435i | −2.13224 | − | 0.657425i | ||||
\(705\) | 4.29984 | + | 2.56419i | 0.161942 | + | 0.0965731i | ||||
\(706\) | 27.2661 | + | 15.7421i | 1.02617 | + | 0.592461i | ||||
\(707\) | −14.1938 | −0.533811 | ||||||||
\(708\) | 0.360711 | − | 25.5278i | 0.0135563 | − | 0.959392i | ||||
\(709\) | −16.9022 | − | 9.75846i | −0.634774 | − | 0.366487i | 0.147825 | − | 0.989014i | \(-0.452773\pi\) |
−0.782598 | + | 0.622527i | \(0.786106\pi\) | |||||||
\(710\) | − | 64.3043i | − | 2.41330i | ||||||
\(711\) | −3.73373 | + | 2.01721i | −0.140026 | + | 0.0756514i | ||||
\(712\) | 49.7956 | − | 28.7495i | 1.86617 | − | 1.07743i | ||||
\(713\) | 17.1896 | + | 29.7733i | 0.643757 | + | 1.11502i | ||||
\(714\) | −9.46173 | − | 16.9364i | −0.354096 | − | 0.633829i | ||||
\(715\) | 31.0266 | − | 11.4100i | 1.16033 | − | 0.426709i | ||||
\(716\) | 122.668i | 4.58430i | ||||||||
\(717\) | 0.330475 | − | 0.554167i | 0.0123418 | − | 0.0206957i | ||||
\(718\) | −39.0969 | − | 67.7179i | −1.45908 | − | 2.52721i | ||||
\(719\) | −11.1197 | − | 6.41995i | −0.414694 | − | 0.239424i | 0.278110 | − | 0.960549i | \(-0.410292\pi\) |
−0.692805 | + | 0.721125i | \(0.743625\pi\) | |||||||
\(720\) | −53.0899 | + | 86.2320i | −1.97854 | + | 3.21368i | ||||
\(721\) | 2.38125 | − | 4.12445i | 0.0886824 | − | 0.153602i | ||||
\(722\) | −37.3256 | − | 21.5499i | −1.38911 | − | 0.802006i | ||||
\(723\) | −25.5308 | + | 14.2631i | −0.949501 | + | 0.530451i | ||||
\(724\) | 15.2263 | − | 26.3728i | 0.565882 | − | 0.980136i | ||||
\(725\) | −0.781847 | − | 1.35420i | −0.0290371 | − | 0.0502936i | ||||
\(726\) | −41.6863 | − | 29.2774i | −1.54713 | − | 1.08659i | ||||
\(727\) | 28.6628 | 1.06304 | 0.531522 | − | 0.847045i | \(-0.321620\pi\) | ||||
0.531522 | + | 0.847045i | \(0.321620\pi\) | |||||||
\(728\) | 34.0258 | − | 4.37500i | 1.26108 | − | 0.162148i | ||||
\(729\) | −26.9030 | − | 2.28619i | −0.996409 | − | 0.0846737i | ||||
\(730\) | 45.8278 | − | 26.4587i | 1.69616 | − | 0.979280i | ||||
\(731\) | −27.1307 | + | 15.6639i | −1.00346 | + | 0.579350i | ||||
\(732\) | 83.6370 | + | 1.18180i | 3.09131 | + | 0.0436806i | ||||
\(733\) | 24.3781 | 0.900424 | 0.450212 | − | 0.892922i | \(-0.351348\pi\) | ||||
0.450212 | + | 0.892922i | \(0.351348\pi\) | |||||||
\(734\) | −39.7869 | − | 22.9710i | −1.46856 | − | 0.847875i | ||||
\(735\) | 0.387132 | − | 27.3976i | 0.0142796 | − | 1.01058i | ||||
\(736\) | −133.194 | −4.90960 | ||||||||
\(737\) | 5.56733 | − | 1.27142i | 0.205075 | − | 0.0468333i | ||||
\(738\) | 81.1310 | + | 2.29324i | 2.98647 | + | 0.0844154i | ||||
\(739\) | 8.78677 | + | 15.2191i | 0.323226 | + | 0.559845i | 0.981152 | − | 0.193239i | \(-0.0618991\pi\) |
−0.657925 | + | 0.753083i | \(0.728566\pi\) | |||||||
\(740\) | − | 140.612i | − | 5.16902i | ||||||
\(741\) | 4.22299 | − | 9.72022i | 0.155135 | − | 0.357081i | ||||
\(742\) | −3.59232 | −0.131878 | ||||||||
\(743\) | −3.28116 | + | 1.89438i | −0.120374 | + | 0.0694981i | −0.558978 | − | 0.829182i | \(-0.688806\pi\) |
0.438604 | + | 0.898680i | \(0.355473\pi\) | |||||||
\(744\) | 51.1036 | + | 30.4754i | 1.87355 | + | 1.11728i | ||||
\(745\) | 41.2342 | + | 23.8066i | 1.51070 | + | 0.872205i | ||||
\(746\) | 74.3827 | 2.72334 | ||||||||
\(747\) | −17.2443 | + | 9.31653i | −0.630935 | + | 0.340874i | ||||
\(748\) | −14.0908 | − | 61.7013i | −0.515211 | − | 2.25602i | ||||
\(749\) | −20.5663 | −0.751476 | ||||||||
\(750\) | −30.1812 | − | 0.426464i | −1.10206 | − | 0.0155723i | ||||
\(751\) | −20.4312 | − | 35.3878i | −0.745544 | − | 1.29132i | −0.949940 | − | 0.312431i | \(-0.898857\pi\) |
0.204397 | − | 0.978888i | \(-0.434477\pi\) | |||||||
\(752\) | 6.38334 | + | 11.0563i | 0.232777 | + | 0.403181i | ||||
\(753\) | 15.6980 | + | 28.0992i | 0.572066 | + | 1.02399i | ||||
\(754\) | −5.65848 | + | 0.727560i | −0.206070 | + | 0.0264962i | ||||
\(755\) | −14.9291 | −0.543325 | ||||||||
\(756\) | −26.8036 | + | 13.9955i | −0.974838 | + | 0.509013i | ||||
\(757\) | 5.13256 | + | 8.88986i | 0.186546 | + | 0.323108i | 0.944096 | − | 0.329669i | \(-0.106937\pi\) |
−0.757550 | + | 0.652777i | \(0.773604\pi\) | |||||||
\(758\) | 47.4561 | − | 82.1964i | 1.72368 | − | 2.98551i | ||||
\(759\) | −46.0414 | − | 14.9113i | −1.67120 | − | 0.541247i | ||||
\(760\) | 34.2015 | + | 19.7463i | 1.24062 | + | 0.716272i | ||||
\(761\) | −9.79680 | − | 5.65618i | −0.355134 | − | 0.205037i | 0.311810 | − | 0.950144i | \(-0.399065\pi\) |
−0.666944 | + | 0.745108i | \(0.732398\pi\) | |||||||
\(762\) | 40.2088 | − | 22.4632i | 1.45661 | − | 0.813754i | ||||
\(763\) | −2.07292 | + | 3.59039i | −0.0750446 | + | 0.129981i | ||||
\(764\) | 13.3171 | − | 7.68865i | 0.481797 | − | 0.278165i | ||||
\(765\) | −30.7265 | − | 0.868512i | −1.11092 | − | 0.0314011i | ||||
\(766\) | − | 4.60425i | − | 0.166358i | ||||||
\(767\) | 1.31641 | + | 10.2382i | 0.0475329 | + | 0.369680i | ||||
\(768\) | −11.1306 | + | 6.21825i | −0.401641 | + | 0.224382i | ||||
\(769\) | −12.6744 | − | 21.9527i | −0.457050 | − | 0.791634i | 0.541753 | − | 0.840537i | \(-0.317761\pi\) |
−0.998804 | + | 0.0489035i | \(0.984427\pi\) | |||||||
\(770\) | −8.16370 | + | 26.4775i | −0.294199 | + | 0.954182i | ||||
\(771\) | 20.4621 | + | 0.289133i | 0.736926 | + | 0.0104129i | ||||
\(772\) | −76.7396 | −2.76192 | ||||||||
\(773\) | −12.4782 | + | 21.6129i | −0.448809 | + | 0.777361i | −0.998309 | − | 0.0581334i | \(-0.981485\pi\) |
0.549499 | + | 0.835494i | \(0.314818\pi\) | |||||||
\(774\) | 32.2256 | + | 59.6475i | 1.15833 | + | 2.14398i | ||||
\(775\) | − | 10.7824i | − | 0.387316i | ||||||
\(776\) | −21.0770 | + | 36.5064i | −0.756619 | + | 1.31050i | ||||
\(777\) | 9.90605 | − | 16.6113i | 0.355378 | − | 0.595926i | ||||
\(778\) | −26.1187 | − | 45.2389i | −0.936401 | − | 1.62189i | ||||
\(779\) | − | 17.1719i | − | 0.615249i | ||||||
\(780\) | 35.4180 | − | 81.5230i | 1.26817 | − | 2.91899i | ||||
\(781\) | 21.1497 | − | 19.6288i | 0.756795 | − | 0.702374i | ||||
\(782\) | −41.7431 | − | 72.3011i | −1.49273 | − | 2.58548i | ||||
\(783\) | 2.72589 | − | 1.42333i | 0.0974155 | − | 0.0508656i | ||||
\(784\) | 34.9366 | − | 60.5120i | 1.24774 | − | 2.16114i | ||||
\(785\) | −9.72997 | −0.347277 | ||||||||
\(786\) | 2.22421 | + | 0.0314284i | 0.0793349 | + | 0.00112101i | ||||
\(787\) | −23.1672 | + | 40.1267i | −0.825820 | + | 1.43036i | 0.0754708 | + | 0.997148i | \(0.475954\pi\) |
−0.901291 | + | 0.433214i | \(0.857379\pi\) | |||||||
\(788\) | − | 65.7582i | − | 2.34254i | ||||||
\(789\) | 0.273230 | − | 19.3367i | 0.00972725 | − | 0.688405i | ||||
\(790\) | 5.22785 | + | 9.05490i | 0.185998 | + | 0.322159i | ||||
\(791\) | −8.69537 | + | 5.02027i | −0.309172 | + | 0.178500i | ||||
\(792\) | −82.1514 | + | 16.3335i | −2.91912 | + | 0.580386i | ||||
\(793\) | −33.5435 | + | 4.31298i | −1.19117 | + | 0.153159i | ||||
\(794\) | −82.9415 | −2.94348 | ||||||||
\(795\) | −2.91531 | + | 4.88862i | −0.103395 | + | 0.173381i | ||||
\(796\) | 8.51479 | + | 14.7480i | 0.301799 | + | 0.522731i | ||||
\(797\) | −3.95180 | − | 2.28157i | −0.139980 | − | 0.0808175i | 0.428374 | − | 0.903601i | \(-0.359086\pi\) |
−0.568354 | + | 0.822784i | \(0.692420\pi\) | |||||||
\(798\) | 4.33216 | + | 7.75453i | 0.153357 | + | 0.274507i | ||||
\(799\) | −1.93766 | + | 3.35612i | −0.0685494 | + | 0.118731i | ||||
\(800\) | 36.1772 | + | 20.8869i | 1.27906 | + | 0.738464i | ||||
\(801\) | 10.7429 | − | 17.4493i | 0.379581 | − | 0.616540i | ||||
\(802\) | 23.1786 | + | 13.3822i | 0.818466 | + | 0.472541i | ||||
\(803\) | 22.6911 | + | 6.99627i | 0.800752 | + | 0.246893i | ||||
\(804\) | 7.86432 | − | 13.1875i | 0.277353 | − | 0.465088i | ||||
\(805\) | 26.3235i | 0.927781i | ||||||||
\(806\) | −36.2990 | − | 15.1642i | −1.27858 | − | 0.534137i | ||||
\(807\) | −10.9014 | − | 19.5134i | −0.383748 | − | 0.686904i | ||||
\(808\) | −91.5509 | + | 52.8569i | −3.22075 | + | 1.85950i | ||||
\(809\) | 11.5826 | + | 20.0617i | 0.407223 | + | 0.705331i | 0.994577 | − | 0.103999i | \(-0.0331638\pi\) |
−0.587354 | + | 0.809330i | \(0.699830\pi\) | |||||||
\(810\) | −3.75757 | + | 66.4151i | −0.132028 | + | 2.33359i | ||||
\(811\) | 37.6598 | 1.32242 | 0.661208 | − | 0.750203i | \(-0.270044\pi\) | ||||
0.661208 | + | 0.750203i | \(0.270044\pi\) | |||||||
\(812\) | 1.72193 | − | 2.98247i | 0.0604278 | − | 0.104664i | ||||
\(813\) | −0.662088 | + | 46.8564i | −0.0232204 | + | 1.64333i | ||||
\(814\) | 64.2127 | − | 59.5952i | 2.25065 | − | 2.08881i | ||||
\(815\) | −36.6498 | − | 21.1598i | −1.28379 | − | 0.741195i | ||||
\(816\) | −67.3241 | − | 40.1484i | −2.35682 | − | 1.40548i | ||||
\(817\) | 12.4221 | − | 7.17190i | 0.434594 | − | 0.250913i | ||||
\(818\) | − | 94.6955i | − | 3.31095i | ||||||
\(819\) | 9.92735 | − | 7.13555i | 0.346890 | − | 0.249336i | ||||
\(820\) | − | 144.020i | − | 5.02941i | ||||||
\(821\) | 7.75918 | − | 4.47977i | 0.270797 | − | 0.156345i | −0.358453 | − | 0.933548i | \(-0.616696\pi\) |
0.629250 | + | 0.777203i | \(0.283362\pi\) | |||||||
\(822\) | −6.37211 | + | 10.6853i | −0.222253 | + | 0.372691i | ||||
\(823\) | 2.34668 | − | 4.06456i | 0.0818000 | − | 0.141682i | −0.822223 | − | 0.569165i | \(-0.807266\pi\) |
0.904023 | + | 0.427484i | \(0.140600\pi\) | |||||||
\(824\) | − | 35.4707i | − | 1.23568i | ||||||
\(825\) | 10.1671 | + | 11.2701i | 0.353974 | + | 0.392376i | ||||
\(826\) | −7.49260 | − | 4.32586i | −0.260701 | − | 0.150516i | ||||
\(827\) | − | 27.2442i | − | 0.947375i | −0.880693 | − | 0.473688i | \(-0.842923\pi\) | ||
0.880693 | − | 0.473688i | \(-0.157077\pi\) | |||||||
\(828\) | −114.484 | + | 61.8518i | −3.97858 | + | 2.14950i | ||||
\(829\) | 9.71045 | + | 16.8190i | 0.337258 | + | 0.584148i | 0.983916 | − | 0.178632i | \(-0.0571673\pi\) |
−0.646658 | + | 0.762780i | \(0.723834\pi\) | |||||||
\(830\) | 24.1449 | + | 41.8202i | 0.838081 | + | 1.45160i | ||||
\(831\) | −0.405910 | − | 0.726574i | −0.0140808 | − | 0.0252046i | ||||
\(832\) | 51.1786 | − | 39.0255i | 1.77430 | − | 1.35297i | ||||
\(833\) | 21.2100 | 0.734882 | ||||||||
\(834\) | 38.9660 | + | 23.2372i | 1.34928 | + | 0.804639i | ||||
\(835\) | −3.70142 | + | 2.13702i | −0.128093 | + | 0.0739545i | ||||
\(836\) | 6.45164 | + | 28.2507i | 0.223135 | + | 0.977070i | ||||
\(837\) | 21.1854 | + | 0.898536i | 0.732275 | + | 0.0310580i | ||||
\(838\) | 3.78489 | − | 6.55563i | 0.130747 | − | 0.226460i | ||||
\(839\) | 6.82812 | − | 11.8267i | 0.235733 | − | 0.408301i | −0.723752 | − | 0.690060i | \(-0.757584\pi\) |
0.959485 | + | 0.281758i | \(0.0909176\pi\) | |||||||
\(840\) | 22.2195 | + | 39.7726i | 0.766645 | + | 1.37229i | ||||
\(841\) | 14.3249 | − | 24.8114i | 0.493961 | − | 0.855566i | ||||
\(842\) | 33.2842 | + | 57.6499i | 1.14705 | + | 1.98675i | ||||
\(843\) | 11.7646 | − | 19.7279i | 0.405196 | − | 0.679465i | ||||
\(844\) | − | 106.961i | − | 3.68174i | ||||||
\(845\) | −9.51111 | + | 34.6565i | −0.327192 | + | 1.19222i | ||||
\(846\) | 7.14156 | + | 4.39680i | 0.245532 | + | 0.151165i | ||||
\(847\) | −11.2004 | + | 5.39718i | −0.384850 | + | 0.185449i | ||||
\(848\) | −12.5702 | + | 7.25741i | −0.431662 | + | 0.249220i | ||||
\(849\) | −0.519773 | − | 0.00734446i | −0.0178386 | − | 0.000252061i | ||||
\(850\) | 26.1839i | 0.898100i | ||||||||
\(851\) | 41.6152 | − | 72.0797i | 1.42655 | − | 2.47086i | ||||
\(852\) | 1.09615 | − | 77.5750i | 0.0375533 | − | 2.65768i | ||||
\(853\) | −1.58442 | −0.0542496 | −0.0271248 | − | 0.999632i | \(-0.508635\pi\) | ||||
−0.0271248 | + | 0.999632i | \(0.508635\pi\) | |||||||
\(854\) | 14.1729 | − | 24.5481i | 0.484986 | − | 0.840020i | ||||
\(855\) | 14.0685 | + | 0.397658i | 0.481132 | + | 0.0135996i | ||||
\(856\) | −132.654 | + | 76.5879i | −4.53403 | + | 2.61772i | ||||
\(857\) | −45.1473 | −1.54220 | −0.771101 | − | 0.636713i | \(-0.780293\pi\) | ||||
−0.771101 | + | 0.636713i | \(0.780293\pi\) | |||||||
\(858\) | 52.2397 | − | 18.3774i | 1.78343 | − | 0.627395i | ||||
\(859\) | −12.4759 | −0.425673 | −0.212836 | − | 0.977088i | \(-0.568270\pi\) | ||||
−0.212836 | + | 0.977088i | \(0.568270\pi\) | |||||||
\(860\) | 104.184 | − | 60.1504i | 3.55263 | − | 2.05111i | ||||
\(861\) | 10.1461 | − | 17.0139i | 0.345779 | − | 0.579830i | ||||
\(862\) | −3.65251 | + | 6.32633i | −0.124405 | + | 0.215476i | ||||
\(863\) | −44.5425 | −1.51624 | −0.758121 | − | 0.652113i | \(-0.773883\pi\) | ||||
−0.758121 | + | 0.652113i | \(0.773883\pi\) | |||||||
\(864\) | −44.0536 | + | 69.3407i | −1.49873 | + | 2.35902i | ||||
\(865\) | −0.685149 | + | 1.18671i | −0.0232958 | + | 0.0403495i | ||||
\(866\) | 28.5618i | 0.970568i | ||||||||
\(867\) | −0.0798376 | + | 5.65017i | −0.00271143 | + | 0.191890i | ||||
\(868\) | 20.5656 | − | 11.8735i | 0.698041 | − | 0.403014i | ||||
\(869\) | −1.38236 | + | 4.48343i | −0.0468934 | + | 0.152090i | ||||
\(870\) | −3.69509 | − | 6.61417i | −0.125275 | − | 0.224241i | ||||
\(871\) | −2.39308 | + | 5.72837i | −0.0810864 | + | 0.194098i | ||||
\(872\) | 30.8778i | 1.04565i | ||||||||
\(873\) | −0.424456 | + | 15.0165i | −0.0143657 | + | 0.508233i | ||||
\(874\) | 19.1126 | + | 33.1039i | 0.646492 | + | 1.11976i | ||||
\(875\) | −3.68352 | + | 6.38004i | −0.124526 | + | 0.215685i | ||||
\(876\) | 55.7364 | − | 31.1379i | 1.88316 | − | 1.05205i | ||||
\(877\) | 1.51193 | − | 2.61874i | 0.0510542 | − | 0.0884285i | −0.839369 | − | 0.543562i | \(-0.817075\pi\) |
0.890423 | + | 0.455134i | \(0.150409\pi\) | |||||||
\(878\) | −16.4999 | + | 28.5786i | −0.556844 | + | 0.964482i | ||||
\(879\) | 11.3293 | + | 20.2793i | 0.382127 | + | 0.684004i | ||||
\(880\) | 24.9249 | + | 109.142i | 0.840220 | + | 3.67918i | ||||
\(881\) | −19.6662 | + | 11.3543i | −0.662572 | + | 0.382536i | −0.793256 | − | 0.608888i | \(-0.791616\pi\) |
0.130684 | + | 0.991424i | \(0.458283\pi\) | |||||||
\(882\) | 1.29689 | − | 45.8819i | 0.0436687 | − | 1.54492i | ||||
\(883\) | −35.6943 | −1.20121 | −0.600605 | − | 0.799546i | \(-0.705073\pi\) | ||||
−0.600605 | + | 0.799546i | \(0.705073\pi\) | |||||||
\(884\) | 63.4861 | + | 26.5219i | 2.13527 | + | 0.892028i | ||||
\(885\) | −11.9674 | + | 6.68572i | −0.402279 | + | 0.224738i | ||||
\(886\) | −6.98934 | − | 12.1059i | −0.234812 | − | 0.406706i | ||||
\(887\) | 14.7296 | + | 25.5125i | 0.494573 | + | 0.856626i | 0.999980 | − | 0.00625508i | \(-0.00199107\pi\) |
−0.505407 | + | 0.862881i | \(0.668658\pi\) | |||||||
\(888\) | 2.03521 | − | 144.034i | 0.0682973 | − | 4.83345i | ||||
\(889\) | − | 11.2413i | − | 0.377022i | ||||||
\(890\) | −43.7214 | − | 25.2426i | −1.46554 | − | 0.846132i | ||||
\(891\) | −22.9909 | + | 19.0373i | −0.770225 | + | 0.637773i | ||||
\(892\) | − | 64.9322i | − | 2.17409i | ||||||
\(893\) | 0.887179 | − | 1.53664i | 0.0296883 | − | 0.0514217i | ||||
\(894\) | 68.5039 | + | 40.8520i | 2.29111 | + | 1.36630i | ||||
\(895\) | 57.0410 | − | 32.9327i | 1.90667 | − | 1.10082i | ||||
\(896\) | 18.2039i | 0.608150i | ||||||||
\(897\) | 42.2830 | − | 31.3075i | 1.41179 | − | 1.04533i | ||||
\(898\) | 64.3789i | 2.14835i | ||||||||
\(899\) | −2.09149 | + | 1.20752i | −0.0697551 | + | 0.0402731i | ||||
\(900\) | 40.7946 | + | 1.15310i | 1.35982 | + | 0.0384365i | ||||
\(901\) | −3.81567 | − | 2.20298i | −0.127118 | − | 0.0733918i | ||||
\(902\) | 65.7690 | − | 61.0395i | 2.18987 | − | 2.03239i | ||||
\(903\) | 16.5453 | + | 0.233787i | 0.550592 | + | 0.00777995i | ||||
\(904\) | −37.3905 | + | 64.7623i | −1.24359 | + | 2.15396i | ||||
\(905\) | −16.3513 | −0.543535 | ||||||||
\(906\) | −25.0063 | − | 0.353342i | −0.830777 | − | 0.0117390i | ||||
\(907\) | 2.60584 | + | 4.51345i | 0.0865256 | + | 0.149867i | 0.906040 | − | 0.423191i | \(-0.139090\pi\) |
−0.819515 | + | 0.573058i | \(0.805757\pi\) | |||||||
\(908\) | 70.8708 | − | 40.9173i | 2.35193 | − | 1.35789i | ||||
\(909\) | −19.7511 | + | 32.0810i | −0.655103 | + | 1.06406i | ||||
\(910\) | −18.2643 | − | 23.9520i | −0.605455 | − | 0.794003i | ||||
\(911\) | 49.4367i | 1.63791i | 0.573858 | + | 0.818955i | \(0.305446\pi\) | ||||
−0.573858 | + | 0.818955i | \(0.694554\pi\) | |||||||
\(912\) | 30.8251 | + | 18.3824i | 1.02072 | + | 0.608703i | ||||
\(913\) | −6.38445 | + | 20.7068i | −0.211294 | + | 0.685295i | ||||
\(914\) | 1.50061 | + | 0.866376i | 0.0496357 | + | 0.0286572i | ||||
\(915\) | −21.9045 | − | 39.2089i | −0.724142 | − | 1.29621i | ||||
\(916\) | 52.9499 | + | 30.5706i | 1.74951 | + | 1.01008i | ||||
\(917\) | 0.271457 | − | 0.470178i | 0.00896431 | − | 0.0155266i | ||||
\(918\) | −51.4463 | − | 2.18199i | −1.69798 | − | 0.0720165i | ||||
\(919\) | 30.6269 | + | 17.6824i | 1.01029 | + | 0.583289i | 0.911276 | − | 0.411797i | \(-0.135099\pi\) |
0.0990113 | + | 0.995086i | \(0.468432\pi\) | |||||||
\(920\) | 98.0274 | + | 169.788i | 3.23187 | + | 5.59776i | ||||
\(921\) | 30.5485 | + | 18.2174i | 1.00661 | + | 0.600285i | ||||
\(922\) | −16.4771 | −0.542643 | ||||||||
\(923\) | 4.00038 | + | 31.1123i | 0.131674 | + | 1.02407i | ||||
\(924\) | −10.2998 | + | 31.8026i | −0.338839 | + | 1.04623i | ||||
\(925\) | −22.6065 | + | 13.0518i | −0.743296 | + | 0.429142i | ||||
\(926\) | −40.6944 | − | 70.4848i | −1.33730 | − | 2.31627i | ||||
\(927\) | −6.00857 | − | 11.1215i | −0.197347 | − | 0.365277i | ||||
\(928\) | − | 9.35650i | − | 0.307142i | ||||||
\(929\) | −11.4659 | + | 19.8596i | −0.376185 | + | 0.651572i | −0.990504 | − | 0.137486i | \(-0.956098\pi\) |
0.614318 | + | 0.789058i | \(0.289431\pi\) | |||||||
\(930\) | 0.738120 | − | 52.2373i | 0.0242039 | − | 1.71293i | ||||
\(931\) | −9.71123 | −0.318273 | ||||||||
\(932\) | −37.2793 | + | 64.5697i | −1.22112 | + | 2.11505i | ||||
\(933\) | −12.4487 | + | 20.8749i | −0.407551 | + | 0.683415i | ||||
\(934\) | −7.87506 | − | 13.6400i | −0.257680 | − | 0.446315i | ||||
\(935\) | −24.9085 | + | 23.1173i | −0.814594 | + | 0.756017i | ||||
\(936\) | 37.4597 | − | 82.9938i | 1.22441 | − | 2.71274i | ||||
\(937\) | 19.1102i | 0.624302i | 0.950033 | + | 0.312151i | \(0.101049\pi\) | ||||
−0.950033 | + | 0.312151i | \(0.898951\pi\) | |||||||
\(938\) | −2.60166 | − | 4.50620i | −0.0849471 | − | 0.147133i | ||||
\(939\) | −32.2208 | − | 19.2147i | −1.05149 | − | 0.627049i | ||||
\(940\) | 7.44073 | − | 12.8877i | 0.242690 | − | 0.420351i | ||||
\(941\) | 0.00874113i | 0.000284953i | 1.00000 | 0.000142476i | \(4.53516e-5\pi\) | |||||
−1.00000 | 0.000142476i | \(0.999955\pi\) | ||||||||
\(942\) | −16.2977 | − | 0.230289i | −0.531008 | − | 0.00750322i | ||||
\(943\) | 42.6238 | − | 73.8266i | 1.38802 | − | 2.40412i | ||||
\(944\) | −34.9573 | −1.13776 | ||||||||
\(945\) | 13.7040 | + | 8.70643i | 0.445791 | + | 0.283220i | ||||
\(946\) | 71.6242 | + | 22.0836i | 2.32870 | + | 0.718000i | ||||
\(947\) | −8.81811 | − | 15.2734i | −0.286550 | − | 0.496319i | 0.686434 | − | 0.727192i | \(-0.259175\pi\) |
−0.972984 | + | 0.230873i | \(0.925842\pi\) | |||||||
\(948\) | 6.15239 | + | 11.0127i | 0.199820 | + | 0.357676i | ||||
\(949\) | −20.5268 | + | 15.6524i | −0.666329 | + | 0.508100i | ||||
\(950\) | − | 11.9886i | − | 0.388962i | ||||||
\(951\) | 36.3780 | + | 21.6939i | 1.17964 | + | 0.703472i | ||||
\(952\) | −30.5410 | + | 17.6328i | −0.989838 | + | 0.571484i | ||||
\(953\) | −13.8708 | + | 24.0249i | −0.449319 | + | 0.778243i | −0.998342 | − | 0.0575643i | \(-0.981667\pi\) |
0.549023 | + | 0.835807i | \(0.315000\pi\) | |||||||
\(954\) | −4.99885 | + | 8.11945i | −0.161844 | + | 0.262877i | ||||
\(955\) | −7.15052 | − | 4.12835i | −0.231385 | − | 0.133590i | ||||
\(956\) | −1.66098 | − | 0.958966i | −0.0537199 | − | 0.0310152i | ||||
\(957\) | 1.04748 | − | 3.23428i | 0.0338601 | − | 0.104549i | ||||
\(958\) | 0.538894 | − | 0.933392i | 0.0174109 | − | 0.0301565i | ||||
\(959\) | 1.51823 | + | 2.62965i | 0.0490263 | + | 0.0849160i | ||||
\(960\) | 73.4085 | + | 43.7768i | 2.36925 | + | 1.41289i | ||||
\(961\) | 14.3471 | 0.462809 | ||||||||
\(962\) | 12.1456 | + | 94.4604i | 0.391590 | + | 3.04553i | ||||
\(963\) | −28.6187 | + | 46.4844i | −0.922226 | + | 1.49794i | ||||
\(964\) | 43.4651 | + | 75.2838i | 1.39992 | + | 2.42473i | ||||
\(965\) | 20.6023 | + | 35.6843i | 0.663213 | + | 1.14872i | ||||
\(966\) | −0.623024 | + | 44.0919i | −0.0200455 | + | 1.41863i | ||||
\(967\) | −14.4503 | −0.464689 | −0.232344 | − | 0.972634i | \(-0.574640\pi\) | ||||
−0.232344 | + | 0.972634i | \(0.574640\pi\) | |||||||
\(968\) | −52.1446 | + | 76.5220i | −1.67599 | + | 2.45951i | ||||
\(969\) | −0.153924 | + | 10.8933i | −0.00494476 | + | 0.349944i | ||||
\(970\) | 37.0118 | 1.18838 | ||||||||
\(971\) | 28.4712 | + | 16.4379i | 0.913686 | + | 0.527517i | 0.881615 | − | 0.471969i | \(-0.156457\pi\) |
0.0320706 | + | 0.999486i | \(0.489790\pi\) | |||||||
\(972\) | −5.66516 | + | 80.0574i | −0.181710 | + | 2.56784i | ||||
\(973\) | 9.58959 | − | 5.53655i | 0.307428 | − | 0.177494i | ||||
\(974\) | 51.2595 | 1.64246 | ||||||||
\(975\) | −16.3941 | + | 1.87288i | −0.525032 | + | 0.0599802i | ||||
\(976\) | − | 114.531i | − | 3.66605i | ||||||
\(977\) | 15.8490 | + | 27.4512i | 0.507054 | + | 0.878243i | 0.999967 | + | 0.00816400i | \(0.00259871\pi\) |
−0.492913 | + | 0.870079i | \(0.664068\pi\) | |||||||
\(978\) | −60.8878 | − | 36.3101i | −1.94698 | − | 1.16107i | ||||
\(979\) | −5.04363 | − | 22.0852i | −0.161195 | − | 0.705846i | ||||
\(980\) | −81.4476 | −2.60175 | ||||||||
\(981\) | 5.23055 | + | 9.68141i | 0.166999 | + | 0.309104i | ||||
\(982\) | −15.1467 | − | 8.74497i | −0.483352 | − | 0.279063i | ||||
\(983\) | −33.1591 | −1.05761 | −0.528806 | − | 0.848743i | \(-0.677360\pi\) | ||||
−0.528806 | + | 0.848743i | \(0.677360\pi\) | |||||||
\(984\) | 2.08454 | − | 147.524i | 0.0664527 | − | 4.70291i | ||||
\(985\) | −30.5779 | + | 17.6542i | −0.974293 | + | 0.562508i | ||||
\(986\) | 5.07895 | − | 2.93233i | 0.161747 | − | 0.0933845i | ||||
\(987\) | 1.78694 | − | 0.998297i | 0.0568790 | − | 0.0317762i | ||||
\(988\) | −29.0679 | − | 12.1434i | −0.924772 | − | 0.386332i | ||||
\(989\) | 71.2077 | 2.26427 | ||||||||
\(990\) | 48.4849 | + | 55.2961i | 1.54095 | + | 1.75743i | ||||
\(991\) | −8.51250 | − | 14.7441i | −0.270408 | − | 0.468361i | 0.698558 | − | 0.715553i | \(-0.253825\pi\) |
−0.968966 | + | 0.247192i | \(0.920492\pi\) | |||||||
\(992\) | 32.2588 | − | 55.8739i | 1.02422 | − | 1.77400i | ||||
\(993\) | −19.7188 | − | 35.2964i | −0.625756 | − | 1.12010i | ||||
\(994\) | −22.7689 | − | 13.1456i | −0.722186 | − | 0.416954i | ||||
\(995\) | 4.57195 | − | 7.91884i | 0.144940 | − | 0.251044i | ||||
\(996\) | 28.4149 | + | 50.8623i | 0.900360 | + | 1.61163i | ||||
\(997\) | 26.5317 | + | 15.3181i | 0.840269 | + | 0.485129i | 0.857356 | − | 0.514725i | \(-0.172106\pi\) |
−0.0170869 | + | 0.999854i | \(0.505439\pi\) | |||||||
\(998\) | −37.3401 | − | 64.6749i | −1.18198 | − | 2.04725i | ||||
\(999\) | −23.7605 | − | 45.5050i | −0.751749 | − | 1.43972i |
(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 | 429.2.t.a.296.2 | yes | 104 | |
3.2 | odd | 2 | inner | 429.2.t.a.296.51 | yes | 104 | |
11.10 | odd | 2 | inner | 429.2.t.a.296.52 | yes | 104 | |
13.4 | even | 6 | inner | 429.2.t.a.329.1 | yes | 104 | |
33.32 | even | 2 | inner | 429.2.t.a.296.1 | ✓ | 104 | |
39.17 | odd | 6 | inner | 429.2.t.a.329.52 | yes | 104 | |
143.43 | odd | 6 | inner | 429.2.t.a.329.51 | yes | 104 | |
429.329 | even | 6 | inner | 429.2.t.a.329.2 | yes | 104 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.t.a.296.1 | ✓ | 104 | 33.32 | even | 2 | inner | |
429.2.t.a.296.2 | yes | 104 | 1.1 | even | 1 | trivial | |
429.2.t.a.296.51 | yes | 104 | 3.2 | odd | 2 | inner | |
429.2.t.a.296.52 | yes | 104 | 11.10 | odd | 2 | inner | |
429.2.t.a.329.1 | yes | 104 | 13.4 | even | 6 | inner | |
429.2.t.a.329.2 | yes | 104 | 429.329 | even | 6 | inner | |
429.2.t.a.329.51 | yes | 104 | 143.43 | odd | 6 | inner | |
429.2.t.a.329.52 | yes | 104 | 39.17 | odd | 6 | inner |