Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(49,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 5, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.bx (of order \(10\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{14} + 15x^{12} - 59x^{10} + 104x^{8} - 59x^{6} + 15x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 724.3 | ||
Root | \(1.23158 + 1.69513i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.724 |
Dual form | 825.2.bx.f.49.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(e\left(\frac{3}{5}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.04169 | + | 0.338464i | 0.736584 | + | 0.239331i | 0.653198 | − | 0.757187i | \(-0.273427\pi\) |
0.0833853 | + | 0.996517i | \(0.473427\pi\) | |||||||
\(3\) | 0.587785 | + | 0.809017i | 0.339358 | + | 0.467086i | ||||
\(4\) | −0.647481 | − | 0.470423i | −0.323741 | − | 0.235211i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.338464 | + | 1.04169i | 0.138178 | + | 0.425267i | ||||
\(7\) | −0.414410 | + | 0.570387i | −0.156632 | + | 0.215586i | −0.880120 | − | 0.474751i | \(-0.842538\pi\) |
0.723487 | + | 0.690337i | \(0.242538\pi\) | |||||||
\(8\) | −1.80285 | − | 2.48141i | −0.637403 | − | 0.877309i | ||||
\(9\) | −0.309017 | + | 0.951057i | −0.103006 | + | 0.317019i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.31118 | − | 0.189896i | 0.998360 | − | 0.0572559i | ||||
\(12\) | − | 0.800331i | − | 0.231036i | ||||||
\(13\) | 4.48264 | + | 1.45650i | 1.24326 | + | 0.403960i | 0.855501 | − | 0.517801i | \(-0.173249\pi\) |
0.387760 | + | 0.921761i | \(0.373249\pi\) | |||||||
\(14\) | −0.624741 | + | 0.453901i | −0.166969 | + | 0.121310i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.543502 | − | 1.67273i | −0.135875 | − | 0.418181i | ||||
\(17\) | 7.39971 | − | 2.40431i | 1.79469 | − | 0.583131i | 0.794969 | − | 0.606649i | \(-0.207487\pi\) |
0.999723 | + | 0.0235184i | \(0.00748682\pi\) | |||||||
\(18\) | −0.643798 | + | 0.886111i | −0.151745 | + | 0.208858i | ||||
\(19\) | −0.970553 | + | 0.705148i | −0.222660 | + | 0.161772i | −0.693523 | − | 0.720434i | \(-0.743943\pi\) |
0.470863 | + | 0.882206i | \(0.343943\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.705037 | −0.153852 | ||||||||
\(22\) | 3.51349 | + | 0.922906i | 0.749078 | + | 0.196764i | ||||
\(23\) | 6.89318i | 1.43733i | 0.695358 | + | 0.718664i | \(0.255246\pi\) | ||||
−0.695358 | + | 0.718664i | \(0.744754\pi\) | |||||||
\(24\) | 0.947813 | − | 2.91707i | 0.193471 | − | 0.595444i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.17653 | + | 3.03443i | 0.819086 | + | 0.595101i | ||||
\(27\) | −0.951057 | + | 0.309017i | −0.183031 | + | 0.0594703i | ||||
\(28\) | 0.536646 | − | 0.174367i | 0.101417 | − | 0.0329522i | ||||
\(29\) | 1.07389 | + | 0.780229i | 0.199417 | + | 0.144885i | 0.683013 | − | 0.730407i | \(-0.260669\pi\) |
−0.483596 | + | 0.875292i | \(0.660669\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.37364 | + | 7.30532i | −0.426318 | + | 1.31207i | 0.475408 | + | 0.879766i | \(0.342301\pi\) |
−0.901726 | + | 0.432308i | \(0.857699\pi\) | |||||||
\(32\) | 4.20796i | 0.743869i | ||||||||
\(33\) | 2.09989 | + | 2.56719i | 0.365545 | + | 0.446890i | ||||
\(34\) | 8.52195 | 1.46150 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.647481 | − | 0.470423i | 0.107914 | − | 0.0784038i | ||||
\(37\) | 4.95951 | − | 6.82618i | 0.815339 | − | 1.12222i | −0.175139 | − | 0.984544i | \(-0.556037\pi\) |
0.990478 | − | 0.137674i | \(-0.0439625\pi\) | |||||||
\(38\) | −1.24968 | + | 0.406045i | −0.202725 | + | 0.0658692i | ||||
\(39\) | 1.45650 | + | 4.48264i | 0.233226 | + | 0.717797i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.188421 | − | 0.136896i | 0.0294264 | − | 0.0213795i | −0.572975 | − | 0.819573i | \(-0.694211\pi\) |
0.602401 | + | 0.798193i | \(0.294211\pi\) | |||||||
\(42\) | −0.734428 | − | 0.238630i | −0.113325 | − | 0.0368214i | ||||
\(43\) | − | 7.32892i | − | 1.11765i | −0.829286 | − | 0.558825i | \(-0.811252\pi\) | ||
0.829286 | − | 0.558825i | \(-0.188748\pi\) | |||||||
\(44\) | −2.23326 | − | 1.43470i | −0.336677 | − | 0.216289i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.33310 | + | 7.18053i | −0.343996 | + | 1.05871i | ||||
\(47\) | −4.89171 | − | 6.73287i | −0.713530 | − | 0.982090i | −0.999714 | − | 0.0239149i | \(-0.992387\pi\) |
0.286184 | − | 0.958175i | \(-0.407613\pi\) | |||||||
\(48\) | 1.03380 | − | 1.42291i | 0.149216 | − | 0.205379i | ||||
\(49\) | 2.00951 | + | 6.18465i | 0.287073 | + | 0.883521i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.29457 | + | 4.57327i | 0.881416 | + | 0.640386i | ||||
\(52\) | −2.21726 | − | 3.05179i | −0.307478 | − | 0.423207i | ||||
\(53\) | −6.48936 | − | 2.10852i | −0.891382 | − | 0.289628i | −0.172707 | − | 0.984973i | \(-0.555251\pi\) |
−0.718675 | + | 0.695346i | \(0.755251\pi\) | |||||||
\(54\) | −1.09529 | −0.149051 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.16248 | 0.288974 | ||||||||
\(57\) | −1.14095 | − | 0.370718i | −0.151123 | − | 0.0491028i | ||||
\(58\) | 0.854580 | + | 1.17623i | 0.112212 | + | 0.154446i | ||||
\(59\) | −2.86401 | − | 2.08083i | −0.372862 | − | 0.270900i | 0.385534 | − | 0.922693i | \(-0.374017\pi\) |
−0.758397 | + | 0.651793i | \(0.774017\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.35959 | − | 10.3397i | −0.430151 | − | 1.32387i | −0.897975 | − | 0.440047i | \(-0.854962\pi\) |
0.467824 | − | 0.883822i | \(-0.345038\pi\) | |||||||
\(62\) | −4.94518 | + | 6.80645i | −0.628038 | + | 0.864421i | ||||
\(63\) | −0.414410 | − | 0.570387i | −0.0522108 | − | 0.0718620i | ||||
\(64\) | −2.51125 | + | 7.72883i | −0.313906 | + | 0.966103i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.31853 | + | 3.38494i | 0.162300 | + | 0.416658i | ||||
\(67\) | − | 2.04036i | − | 0.249269i | −0.992203 | − | 0.124635i | \(-0.960224\pi\) | ||
0.992203 | − | 0.124635i | \(-0.0397759\pi\) | |||||||
\(68\) | −5.92222 | − | 1.92424i | −0.718174 | − | 0.233349i | ||||
\(69\) | −5.57670 | + | 4.05171i | −0.671356 | + | 0.487768i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.207204 | + | 0.637709i | 0.0245906 | + | 0.0756821i | 0.962599 | − | 0.270931i | \(-0.0873316\pi\) |
−0.938008 | + | 0.346613i | \(0.887332\pi\) | |||||||
\(72\) | 2.91707 | − | 0.947813i | 0.343780 | − | 0.111701i | ||||
\(73\) | 2.94147 | − | 4.04859i | 0.344273 | − | 0.473852i | −0.601410 | − | 0.798941i | \(-0.705394\pi\) |
0.945684 | + | 0.325089i | \(0.105394\pi\) | |||||||
\(74\) | 7.47668 | − | 5.43212i | 0.869146 | − | 0.631472i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.960132 | 0.110135 | ||||||||
\(77\) | −1.26387 | + | 1.96735i | −0.144032 | + | 0.224200i | ||||
\(78\) | 5.16248i | 0.584536i | ||||||||
\(79\) | −0.704642 | + | 2.16867i | −0.0792784 | + | 0.243994i | −0.982839 | − | 0.184467i | \(-0.940944\pi\) |
0.903560 | + | 0.428461i | \(0.140944\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | − | 0.587785i | −0.0898908 | − | 0.0653095i | ||||
\(82\) | 0.242610 | − | 0.0788288i | 0.0267918 | − | 0.00870518i | ||||
\(83\) | −2.00672 | + | 0.652022i | −0.220266 | + | 0.0715687i | −0.417071 | − | 0.908874i | \(-0.636943\pi\) |
0.196805 | + | 0.980443i | \(0.436943\pi\) | |||||||
\(84\) | 0.456498 | + | 0.331666i | 0.0498081 | + | 0.0361877i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.48058 | − | 7.63443i | 0.267488 | − | 0.823242i | ||||
\(87\) | 1.32741i | 0.142313i | ||||||||
\(88\) | −6.44077 | − | 7.87404i | −0.686588 | − | 0.839375i | ||||
\(89\) | 3.34722 | 0.354805 | 0.177402 | − | 0.984138i | \(-0.443231\pi\) | ||||
0.177402 | + | 0.984138i | \(0.443231\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.68842 | + | 1.95325i | −0.281823 | + | 0.204756i | ||||
\(92\) | 3.24271 | − | 4.46321i | 0.338076 | − | 0.465321i | ||||
\(93\) | −7.30532 | + | 2.37364i | −0.757526 | + | 0.246135i | ||||
\(94\) | −2.81680 | − | 8.66921i | −0.290530 | − | 0.894160i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.40431 | + | 2.47338i | −0.347451 | + | 0.252438i | ||||
\(97\) | 3.15968 | + | 1.02664i | 0.320817 | + | 0.104240i | 0.464998 | − | 0.885312i | \(-0.346055\pi\) |
−0.144182 | + | 0.989551i | \(0.546055\pi\) | |||||||
\(98\) | 7.12261i | 0.719492i | ||||||||
\(99\) | −0.842610 | + | 3.20780i | −0.0846855 | + | 0.322396i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.84715 | + | 17.9957i | −0.581813 | + | 1.79064i | 0.0298945 | + | 0.999553i | \(0.490483\pi\) |
−0.611708 | + | 0.791084i | \(0.709517\pi\) | |||||||
\(102\) | 5.00908 | + | 6.89440i | 0.495972 | + | 0.682648i | ||||
\(103\) | 10.6368 | − | 14.6403i | 1.04807 | − | 1.44255i | 0.157608 | − | 0.987502i | \(-0.449622\pi\) |
0.890467 | − | 0.455049i | \(-0.150378\pi\) | |||||||
\(104\) | −4.46735 | − | 13.7491i | −0.438060 | − | 1.34821i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.04622 | − | 4.39283i | −0.587261 | − | 0.426670i | ||||
\(107\) | 3.59692 | + | 4.95074i | 0.347727 | + | 0.478606i | 0.946678 | − | 0.322180i | \(-0.104416\pi\) |
−0.598951 | + | 0.800786i | \(0.704416\pi\) | |||||||
\(108\) | 0.761160 | + | 0.247316i | 0.0732427 | + | 0.0237980i | ||||
\(109\) | −9.03128 | −0.865039 | −0.432520 | − | 0.901625i | \(-0.642375\pi\) | ||||
−0.432520 | + | 0.901625i | \(0.642375\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.43763 | 0.800864 | ||||||||
\(112\) | 1.17933 | + | 0.383189i | 0.111437 | + | 0.0362079i | ||||
\(113\) | 2.30226 | + | 3.16879i | 0.216579 | + | 0.298095i | 0.903458 | − | 0.428676i | \(-0.141020\pi\) |
−0.686879 | + | 0.726771i | \(0.741020\pi\) | |||||||
\(114\) | −1.06304 | − | 0.772344i | −0.0995629 | − | 0.0723366i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.328288 | − | 1.01037i | −0.0304808 | − | 0.0938103i | ||||
\(117\) | −2.77042 | + | 3.81316i | −0.256126 | + | 0.352527i | ||||
\(118\) | −2.27912 | − | 3.13693i | −0.209810 | − | 0.288778i | ||||
\(119\) | −1.69513 | + | 5.21707i | −0.155392 | + | 0.478248i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.9279 | − | 1.25756i | 0.993444 | − | 0.114324i | ||||
\(122\) | − | 11.9079i | − | 1.07809i | ||||||
\(123\) | 0.221502 | + | 0.0719704i | 0.0199722 | + | 0.00648935i | ||||
\(124\) | 4.97348 | − | 3.61344i | 0.446631 | − | 0.324497i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.238630 | − | 0.734428i | −0.0212588 | − | 0.0654280i | ||||
\(127\) | −10.3356 | + | 3.35825i | −0.917138 | + | 0.297996i | −0.729292 | − | 0.684202i | \(-0.760151\pi\) |
−0.187846 | + | 0.982199i | \(0.560151\pi\) | |||||||
\(128\) | −0.285113 | + | 0.392424i | −0.0252006 | + | 0.0346857i | ||||
\(129\) | 5.92922 | − | 4.30783i | 0.522039 | − | 0.379283i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.7094 | −1.02305 | −0.511526 | − | 0.859268i | \(-0.670920\pi\) | ||||
−0.511526 | + | 0.859268i | \(0.670920\pi\) | |||||||
\(132\) | −0.151980 | − | 2.65004i | −0.0132282 | − | 0.230657i | ||||
\(133\) | − | 0.845811i | − | 0.0733411i | ||||||
\(134\) | 0.690588 | − | 2.12541i | 0.0596577 | − | 0.183608i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −19.3066 | − | 14.0271i | −1.65553 | − | 1.20281i | ||||
\(137\) | −19.4303 | + | 6.31328i | −1.66004 | + | 0.539380i | −0.980881 | − | 0.194611i | \(-0.937656\pi\) |
−0.679160 | + | 0.733990i | \(0.737656\pi\) | |||||||
\(138\) | −7.18053 | + | 2.33310i | −0.611247 | + | 0.198606i | ||||
\(139\) | −6.61048 | − | 4.80280i | −0.560694 | − | 0.407368i | 0.271019 | − | 0.962574i | \(-0.412639\pi\) |
−0.831713 | + | 0.555206i | \(0.812639\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.57173 | − | 7.91496i | 0.216578 | − | 0.666560i | ||||
\(142\) | 0.734424i | 0.0616315i | ||||||||
\(143\) | 15.1194 | + | 3.97150i | 1.26435 | + | 0.332113i | ||||
\(144\) | 1.75881 | 0.146567 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.43440 | − | 3.22178i | 0.366993 | − | 0.266636i | ||||
\(147\) | −3.82232 | + | 5.26097i | −0.315260 | + | 0.433918i | ||||
\(148\) | −6.42238 | + | 2.08676i | −0.527917 | + | 0.171531i | ||||
\(149\) | 2.96723 | + | 9.13221i | 0.243085 | + | 0.748140i | 0.995945 | + | 0.0899592i | \(0.0286737\pi\) |
−0.752860 | + | 0.658181i | \(0.771326\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.58850 | + | 4.06028i | −0.454785 | + | 0.330421i | −0.791482 | − | 0.611192i | \(-0.790690\pi\) |
0.336697 | + | 0.941613i | \(0.390690\pi\) | |||||||
\(152\) | 3.49951 | + | 1.13706i | 0.283848 | + | 0.0922278i | ||||
\(153\) | 7.78051i | 0.629017i | ||||||||
\(154\) | −1.98244 | + | 1.62159i | −0.159750 | + | 0.130671i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.16568 | − | 3.58760i | 0.0933292 | − | 0.287238i | ||||
\(157\) | −6.67248 | − | 9.18388i | −0.532522 | − | 0.732953i | 0.454990 | − | 0.890496i | \(-0.349643\pi\) |
−0.987512 | + | 0.157543i | \(0.949643\pi\) | |||||||
\(158\) | −1.46803 | + | 2.02057i | −0.116790 | + | 0.160748i | ||||
\(159\) | −2.10852 | − | 6.48936i | −0.167217 | − | 0.514640i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.93178 | − | 2.85661i | −0.309868 | − | 0.225132i | ||||
\(162\) | −0.643798 | − | 0.886111i | −0.0505815 | − | 0.0696195i | ||||
\(163\) | 1.70480 | + | 0.553922i | 0.133530 | + | 0.0433865i | 0.375020 | − | 0.927017i | \(-0.377636\pi\) |
−0.241490 | + | 0.970403i | \(0.577636\pi\) | |||||||
\(164\) | −0.186398 | −0.0145552 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.31106 | −0.179373 | ||||||||
\(167\) | 5.72964 | + | 1.86167i | 0.443373 | + | 0.144060i | 0.522191 | − | 0.852829i | \(-0.325115\pi\) |
−0.0788186 | + | 0.996889i | \(0.525115\pi\) | |||||||
\(168\) | 1.27107 | + | 1.74948i | 0.0980655 | + | 0.134976i | ||||
\(169\) | 7.45546 | + | 5.41671i | 0.573497 | + | 0.416670i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.370718 | − | 1.14095i | −0.0283495 | − | 0.0872509i | ||||
\(172\) | −3.44769 | + | 4.74534i | −0.262884 | + | 0.361829i | ||||
\(173\) | 2.46091 | + | 3.38715i | 0.187099 | + | 0.257520i | 0.892254 | − | 0.451533i | \(-0.149123\pi\) |
−0.705155 | + | 0.709053i | \(0.749123\pi\) | |||||||
\(174\) | −0.449279 | + | 1.38274i | −0.0340598 | + | 0.104825i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.11728 | − | 5.43549i | −0.159596 | − | 0.409716i | ||||
\(177\) | − | 3.54011i | − | 0.266091i | ||||||
\(178\) | 3.48676 | + | 1.13292i | 0.261343 | + | 0.0849156i | ||||
\(179\) | 3.92507 | − | 2.85173i | 0.293374 | − | 0.213148i | −0.431356 | − | 0.902182i | \(-0.641965\pi\) |
0.724730 | + | 0.689033i | \(0.241965\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.13450 | − | 21.9577i | −0.530303 | − | 1.63211i | −0.753584 | − | 0.657351i | \(-0.771677\pi\) |
0.223281 | − | 0.974754i | \(-0.428323\pi\) | |||||||
\(182\) | −3.46160 | + | 1.12474i | −0.256591 | + | 0.0833714i | ||||
\(183\) | 6.39031 | − | 8.79551i | 0.472386 | − | 0.650183i | ||||
\(184\) | 17.1048 | − | 12.4273i | 1.26098 | − | 0.916156i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −8.41324 | −0.616889 | ||||||||
\(187\) | 24.0452 | − | 9.36629i | 1.75836 | − | 0.684931i | ||||
\(188\) | 6.66058i | 0.485773i | ||||||||
\(189\) | 0.217868 | − | 0.670530i | 0.0158476 | − | 0.0487739i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.03670 | − | 3.65938i | −0.364443 | − | 0.264783i | 0.390460 | − | 0.920620i | \(-0.372316\pi\) |
−0.754903 | + | 0.655837i | \(0.772316\pi\) | |||||||
\(192\) | −7.72883 | + | 2.51125i | −0.557780 | + | 0.181234i | ||||
\(193\) | 18.1526 | − | 5.89815i | 1.30666 | − | 0.424558i | 0.428764 | − | 0.903417i | \(-0.358949\pi\) |
0.877892 | + | 0.478858i | \(0.158949\pi\) | |||||||
\(194\) | 2.94391 | + | 2.13888i | 0.211361 | + | 0.153562i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.60828 | − | 4.94977i | 0.114877 | − | 0.353555i | ||||
\(197\) | 6.80056i | 0.484520i | 0.970211 | + | 0.242260i | \(0.0778887\pi\) | ||||
−0.970211 | + | 0.242260i | \(0.922111\pi\) | |||||||
\(198\) | −1.96346 | + | 3.05633i | −0.139537 | + | 0.217204i | ||||
\(199\) | −21.2972 | −1.50972 | −0.754860 | − | 0.655886i | \(-0.772295\pi\) | ||||
−0.754860 | + | 0.655886i | \(0.772295\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.65068 | − | 1.19929i | 0.116430 | − | 0.0845915i | ||||
\(202\) | −12.1818 | + | 16.7668i | −0.857108 | + | 1.17971i | ||||
\(203\) | −0.890065 | + | 0.289200i | −0.0624703 | + | 0.0202978i | ||||
\(204\) | −1.92424 | − | 5.92222i | −0.134724 | − | 0.414638i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 16.0354 | − | 11.6504i | 1.11724 | − | 0.811723i | ||||
\(207\) | −6.55580 | − | 2.13011i | −0.455660 | − | 0.148053i | ||||
\(208\) | − | 8.28984i | − | 0.574797i | ||||||
\(209\) | −3.07977 | + | 2.51918i | −0.213032 | + | 0.174255i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.74739 | + | 8.45559i | −0.189138 | + | 0.582107i | −0.999995 | − | 0.00313734i | \(-0.999001\pi\) |
0.810857 | + | 0.585244i | \(0.199001\pi\) | |||||||
\(212\) | 3.20984 | + | 4.41797i | 0.220453 | + | 0.303427i | ||||
\(213\) | −0.394126 | + | 0.542467i | −0.0270050 | + | 0.0371692i | ||||
\(214\) | 2.07121 | + | 6.37454i | 0.141585 | + | 0.435755i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.48141 | + | 1.80285i | 0.168838 | + | 0.122668i | ||||
\(217\) | −3.18320 | − | 4.38129i | −0.216089 | − | 0.297422i | ||||
\(218\) | −9.40776 | − | 3.05677i | −0.637174 | − | 0.207030i | ||||
\(219\) | 5.00433 | 0.338162 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 36.6721 | 2.46683 | ||||||||
\(222\) | 8.78936 | + | 2.85584i | 0.589903 | + | 0.191671i | ||||
\(223\) | 3.18415 | + | 4.38261i | 0.213226 | + | 0.293481i | 0.902211 | − | 0.431295i | \(-0.141943\pi\) |
−0.688985 | + | 0.724776i | \(0.741943\pi\) | |||||||
\(224\) | −2.40017 | − | 1.74382i | −0.160368 | − | 0.116514i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.32571 | + | 4.08012i | 0.0881850 | + | 0.271406i | ||||
\(227\) | −4.95998 | + | 6.82682i | −0.329205 | + | 0.453112i | −0.941250 | − | 0.337711i | \(-0.890347\pi\) |
0.612045 | + | 0.790823i | \(0.290347\pi\) | |||||||
\(228\) | 0.564352 | + | 0.776763i | 0.0373751 | + | 0.0514424i | ||||
\(229\) | 3.46262 | − | 10.6569i | 0.228817 | − | 0.704225i | −0.769065 | − | 0.639170i | \(-0.779278\pi\) |
0.997882 | − | 0.0650545i | \(-0.0207221\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.33451 | + | 0.133884i | −0.153599 | + | 0.00880892i | ||||
\(232\) | − | 4.07140i | − | 0.267300i | ||||||
\(233\) | −5.55397 | − | 1.80459i | −0.363852 | − | 0.118223i | 0.121384 | − | 0.992606i | \(-0.461267\pi\) |
−0.485237 | + | 0.874383i | \(0.661267\pi\) | |||||||
\(234\) | −4.17653 | + | 3.03443i | −0.273029 | + | 0.198367i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.875526 | + | 2.69459i | 0.0569919 | + | 0.175403i | ||||
\(237\) | −2.16867 | + | 0.704642i | −0.140870 | + | 0.0457714i | ||||
\(238\) | −3.53158 | + | 4.86081i | −0.228919 | + | 0.315079i | ||||
\(239\) | −13.3699 | + | 9.71382i | −0.864829 | + | 0.628335i | −0.929194 | − | 0.369592i | \(-0.879498\pi\) |
0.0643656 | + | 0.997926i | \(0.479498\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.29180 | −0.212043 | −0.106022 | − | 0.994364i | \(-0.533811\pi\) | ||||
−0.106022 | + | 0.994364i | \(0.533811\pi\) | |||||||
\(242\) | 11.8091 | + | 2.38871i | 0.759115 | + | 0.153552i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | −2.68878 | + | 8.27522i | −0.172132 | + | 0.529767i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.206376 | + | 0.149941i | 0.0131581 | + | 0.00955990i | ||||
\(247\) | −5.37769 | + | 1.74732i | −0.342174 | + | 0.111179i | ||||
\(248\) | 22.4068 | − | 7.28040i | 1.42283 | − | 0.462306i | ||||
\(249\) | −1.70702 | − | 1.24022i | −0.108178 | − | 0.0785957i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.28652 | + | 7.03719i | −0.144324 | + | 0.444183i | −0.996923 | − | 0.0783815i | \(-0.975025\pi\) |
0.852600 | + | 0.522565i | \(0.175025\pi\) | |||||||
\(252\) | 0.564263i | 0.0355452i | ||||||||
\(253\) | 1.30899 | + | 22.8246i | 0.0822955 | + | 1.43497i | ||||
\(254\) | −11.9031 | −0.746869 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 12.7192 | − | 9.24107i | 0.794953 | − | 0.577567i | ||||
\(257\) | −10.9911 | + | 15.1279i | −0.685604 | + | 0.943653i | −0.999984 | − | 0.00564422i | \(-0.998203\pi\) |
0.314380 | + | 0.949297i | \(0.398203\pi\) | |||||||
\(258\) | 7.63443 | − | 2.48058i | 0.475299 | − | 0.154434i | ||||
\(259\) | 1.83829 | + | 5.65768i | 0.114226 | + | 0.351551i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.07389 | + | 0.780229i | −0.0664723 | + | 0.0482950i | ||||
\(262\) | −12.1975 | − | 3.96321i | −0.753564 | − | 0.244848i | ||||
\(263\) | − | 3.99020i | − | 0.246046i | −0.992404 | − | 0.123023i | \(-0.960741\pi\) | ||
0.992404 | − | 0.123023i | \(-0.0392589\pi\) | |||||||
\(264\) | 2.58444 | − | 9.83893i | 0.159061 | − | 0.605544i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.286277 | − | 0.881070i | 0.0175528 | − | 0.0540219i | ||||
\(267\) | 1.96745 | + | 2.70796i | 0.120406 | + | 0.165724i | ||||
\(268\) | −0.959830 | + | 1.32109i | −0.0586309 | + | 0.0806986i | ||||
\(269\) | 3.92915 | + | 12.0927i | 0.239564 | + | 0.737303i | 0.996483 | + | 0.0837941i | \(0.0267038\pi\) |
−0.756919 | + | 0.653509i | \(0.773296\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.2773 | − | 14.0057i | −1.17101 | − | 0.850788i | −0.179880 | − | 0.983689i | \(-0.557571\pi\) |
−0.991129 | + | 0.132900i | \(0.957571\pi\) | |||||||
\(272\) | −8.04351 | − | 11.0709i | −0.487709 | − | 0.671274i | ||||
\(273\) | −3.16043 | − | 1.02689i | −0.191278 | − | 0.0621499i | ||||
\(274\) | −22.3771 | −1.35185 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5.51683 | 0.332074 | ||||||||
\(277\) | 7.04973 | + | 2.29059i | 0.423577 | + | 0.137628i | 0.513046 | − | 0.858361i | \(-0.328517\pi\) |
−0.0894691 | + | 0.995990i | \(0.528517\pi\) | |||||||
\(278\) | −5.26047 | − | 7.24042i | −0.315502 | − | 0.434252i | ||||
\(279\) | −6.21427 | − | 4.51493i | −0.372039 | − | 0.270302i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.98667 | − | 27.6581i | −0.536100 | − | 1.64994i | −0.741261 | − | 0.671217i | \(-0.765772\pi\) |
0.205161 | − | 0.978728i | \(-0.434228\pi\) | |||||||
\(282\) | 5.35786 | − | 7.37447i | 0.319056 | − | 0.439143i | ||||
\(283\) | −12.7390 | − | 17.5337i | −0.757256 | − | 1.04227i | −0.997437 | − | 0.0715451i | \(-0.977207\pi\) |
0.240182 | − | 0.970728i | \(-0.422793\pi\) | |||||||
\(284\) | 0.165832 | − | 0.510378i | 0.00984031 | − | 0.0302854i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 14.4055 | + | 9.25445i | 0.851815 | + | 0.547227i | ||||
\(287\) | 0.164204i | 0.00969265i | ||||||||
\(288\) | −4.00201 | − | 1.30033i | −0.235821 | − | 0.0766227i | ||||
\(289\) | 35.2217 | − | 25.5901i | 2.07186 | − | 1.50530i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.02664 | + | 3.15968i | 0.0601828 | + | 0.185224i | ||||
\(292\) | −3.80910 | + | 1.23765i | −0.222911 | + | 0.0724281i | ||||
\(293\) | 4.94456 | − | 6.80561i | 0.288865 | − | 0.397588i | −0.639780 | − | 0.768558i | \(-0.720975\pi\) |
0.928645 | + | 0.370970i | \(0.120975\pi\) | |||||||
\(294\) | −5.76231 | + | 4.18657i | −0.336065 | + | 0.244166i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −25.8798 | −1.50423 | ||||||||
\(297\) | −3.09044 | + | 1.20381i | −0.179326 | + | 0.0698524i | ||||
\(298\) | 10.5172i | 0.609245i | ||||||||
\(299\) | −10.0399 | + | 30.8997i | −0.580623 | + | 1.78697i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.18032 | + | 3.03718i | 0.240950 | + | 0.175060i | ||||
\(302\) | −7.19572 | + | 2.33803i | −0.414067 | + | 0.134539i | ||||
\(303\) | −17.9957 | + | 5.84715i | −1.03382 | + | 0.335910i | ||||
\(304\) | 1.70702 | + | 1.24022i | 0.0979041 | + | 0.0711315i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.63343 | + | 8.10486i | −0.150543 | + | 0.463324i | ||||
\(307\) | 23.7431i | 1.35509i | 0.735481 | + | 0.677545i | \(0.236956\pi\) | ||||
−0.735481 | + | 0.677545i | \(0.763044\pi\) | |||||||
\(308\) | 1.74382 | − | 0.679268i | 0.0993635 | − | 0.0387049i | ||||
\(309\) | 18.0964 | 1.02947 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.6455 | + | 13.5467i | −1.05729 | + | 0.768164i | −0.973585 | − | 0.228326i | \(-0.926675\pi\) |
−0.0837029 | + | 0.996491i | \(0.526675\pi\) | |||||||
\(312\) | 8.49741 | − | 11.6957i | 0.481071 | − | 0.662137i | ||||
\(313\) | −16.5140 | + | 5.36571i | −0.933424 | + | 0.303288i | −0.735962 | − | 0.677023i | \(-0.763270\pi\) |
−0.197462 | + | 0.980311i | \(0.563270\pi\) | |||||||
\(314\) | −3.84221 | − | 11.8251i | −0.216829 | − | 0.667330i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.47643 | − | 1.07269i | 0.0830558 | − | 0.0603436i | ||||
\(317\) | −5.84990 | − | 1.90075i | −0.328563 | − | 0.106757i | 0.140090 | − | 0.990139i | \(-0.455261\pi\) |
−0.468654 | + | 0.883382i | \(0.655261\pi\) | |||||||
\(318\) | − | 7.47354i | − | 0.419095i | ||||||
\(319\) | 3.70402 | + | 2.37955i | 0.207385 | + | 0.133229i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.89101 | + | 5.81994i | −0.105546 | + | 0.324837i | ||||
\(322\) | −3.12882 | − | 4.30645i | −0.174362 | − | 0.239989i | ||||
\(323\) | −5.48641 | + | 7.55140i | −0.305272 | + | 0.420171i | ||||
\(324\) | 0.247316 | + | 0.761160i | 0.0137398 | + | 0.0422867i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.58838 | + | 1.15403i | 0.0879722 | + | 0.0639156i | ||||
\(327\) | −5.30845 | − | 7.30645i | −0.293558 | − | 0.404048i | ||||
\(328\) | −0.679388 | − | 0.220747i | −0.0375129 | − | 0.0121887i | ||||
\(329\) | 5.86752 | 0.323487 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.4191 | 1.06737 | 0.533685 | − | 0.845683i | \(-0.320807\pi\) | ||||
0.533685 | + | 0.845683i | \(0.320807\pi\) | |||||||
\(332\) | 1.60604 | + | 0.521833i | 0.0881428 | + | 0.0286393i | ||||
\(333\) | 4.95951 | + | 6.82618i | 0.271780 | + | 0.374072i | ||||
\(334\) | 5.33837 | + | 3.87856i | 0.292103 | + | 0.212225i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.383189 | + | 1.17933i | 0.0209047 | + | 0.0643379i | ||||
\(337\) | 18.6250 | − | 25.6352i | 1.01457 | − | 1.39644i | 0.0986291 | − | 0.995124i | \(-0.468554\pi\) |
0.915941 | − | 0.401312i | \(-0.131446\pi\) | |||||||
\(338\) | 5.93289 | + | 8.16593i | 0.322707 | + | 0.444168i | ||||
\(339\) | −1.21037 | + | 3.72514i | −0.0657383 | + | 0.202322i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.47231 | + | 24.6400i | −0.350495 | + | 1.33433i | ||||
\(342\) | − | 1.31399i | − | 0.0710524i | ||||||
\(343\) | −9.05412 | − | 2.94186i | −0.488876 | − | 0.158846i | ||||
\(344\) | −18.1860 | + | 13.2129i | −0.980524 | + | 0.712392i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.41706 | + | 4.36127i | 0.0761818 | + | 0.234463i | ||||
\(347\) | 26.5758 | − | 8.63499i | 1.42666 | − | 0.463551i | 0.508950 | − | 0.860796i | \(-0.330034\pi\) |
0.917712 | + | 0.397246i | \(0.130034\pi\) | |||||||
\(348\) | 0.624442 | − | 0.859470i | 0.0334736 | − | 0.0460724i | ||||
\(349\) | −0.552827 | + | 0.401652i | −0.0295921 | + | 0.0214999i | −0.602483 | − | 0.798132i | \(-0.705822\pi\) |
0.572891 | + | 0.819632i | \(0.305822\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.71333 | −0.251579 | ||||||||
\(352\) | 0.799077 | + | 13.9333i | 0.0425909 | + | 0.742649i | ||||
\(353\) | − | 1.55900i | − | 0.0829769i | −0.999139 | − | 0.0414885i | \(-0.986790\pi\) | ||
0.999139 | − | 0.0414885i | \(-0.0132100\pi\) | |||||||
\(354\) | 1.19820 | − | 3.68769i | 0.0636837 | − | 0.195998i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.16726 | − | 1.57461i | −0.114865 | − | 0.0834542i | ||||
\(357\) | −5.21707 | + | 1.69513i | −0.276117 | + | 0.0897157i | ||||
\(358\) | 5.05390 | − | 1.64211i | 0.267107 | − | 0.0867884i | ||||
\(359\) | 12.8151 | + | 9.31073i | 0.676356 | + | 0.491402i | 0.872147 | − | 0.489244i | \(-0.162727\pi\) |
−0.195791 | + | 0.980646i | \(0.562727\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.42658 | + | 16.7013i | −0.285610 | + | 0.879016i | ||||
\(362\) | − | 25.2878i | − | 1.32910i | ||||||
\(363\) | 7.44064 | + | 8.10166i | 0.390532 | + | 0.425227i | ||||
\(364\) | 2.65956 | 0.139399 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 9.63367 | − | 6.99927i | 0.503560 | − | 0.365858i | ||||
\(367\) | 9.24947 | − | 12.7308i | 0.482818 | − | 0.664542i | −0.496225 | − | 0.868194i | \(-0.665281\pi\) |
0.979043 | + | 0.203652i | \(0.0652810\pi\) | |||||||
\(368\) | 11.5304 | − | 3.74645i | 0.601064 | − | 0.195297i | ||||
\(369\) | 0.0719704 | + | 0.221502i | 0.00374663 | + | 0.0115309i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.89193 | − | 2.82765i | 0.202059 | − | 0.146804i | ||||
\(372\) | 5.84667 | + | 1.89970i | 0.303136 | + | 0.0984948i | ||||
\(373\) | 5.27703i | 0.273234i | 0.990624 | + | 0.136617i | \(0.0436230\pi\) | ||||
−0.990624 | + | 0.136617i | \(0.956377\pi\) | |||||||
\(374\) | 28.2177 | − | 1.61829i | 1.45910 | − | 0.0836797i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.88796 | + | 24.2767i | −0.406791 | + | 1.25197i | ||||
\(377\) | 3.67748 | + | 5.06161i | 0.189400 | + | 0.260686i | ||||
\(378\) | 0.453901 | − | 0.624741i | 0.0233462 | − | 0.0321332i | ||||
\(379\) | −10.3549 | − | 31.8692i | −0.531897 | − | 1.63701i | −0.750260 | − | 0.661143i | \(-0.770072\pi\) |
0.218363 | − | 0.975868i | \(-0.429928\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.79201 | − | 6.38777i | −0.450428 | − | 0.327255i | ||||
\(382\) | −4.00810 | − | 5.51667i | −0.205072 | − | 0.282257i | ||||
\(383\) | 19.2420 | + | 6.25212i | 0.983222 | + | 0.319468i | 0.756142 | − | 0.654408i | \(-0.227082\pi\) |
0.227080 | + | 0.973876i | \(0.427082\pi\) | |||||||
\(384\) | −0.485063 | −0.0247532 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 20.9057 | 1.06407 | ||||||||
\(387\) | 6.97021 | + | 2.26476i | 0.354316 | + | 0.115124i | ||||
\(388\) | −1.56288 | − | 2.15112i | −0.0793430 | − | 0.109206i | ||||
\(389\) | −22.3069 | − | 16.2069i | −1.13101 | − | 0.821724i | −0.145165 | − | 0.989408i | \(-0.546371\pi\) |
−0.985841 | + | 0.167684i | \(0.946371\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.5733 | + | 51.0075i | 0.838150 | + | 2.57956i | ||||
\(392\) | 11.7238 | − | 16.1364i | 0.592140 | − | 0.815011i | ||||
\(393\) | −6.88260 | − | 9.47308i | −0.347181 | − | 0.477854i | ||||
\(394\) | −2.30175 | + | 7.08406i | −0.115960 | + | 0.356890i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.05460 | − | 1.68061i | 0.103247 | − | 0.0844539i | ||||
\(397\) | 11.7601i | 0.590222i | 0.955463 | + | 0.295111i | \(0.0953566\pi\) | ||||
−0.955463 | + | 0.295111i | \(0.904643\pi\) | |||||||
\(398\) | −22.1850 | − | 7.20835i | −1.11204 | − | 0.361322i | ||||
\(399\) | 0.684276 | − | 0.497155i | 0.0342566 | − | 0.0248889i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.38687 | − | 7.34602i | −0.119194 | − | 0.366843i | 0.873604 | − | 0.486637i | \(-0.161777\pi\) |
−0.992799 | + | 0.119794i | \(0.961777\pi\) | |||||||
\(402\) | 2.12541 | − | 0.690588i | 0.106006 | − | 0.0344434i | ||||
\(403\) | −21.2804 | + | 29.2899i | −1.06005 | + | 1.45903i | ||||
\(404\) | 12.2515 | − | 8.90124i | 0.609535 | − | 0.442853i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.02505 | −0.0508725 | ||||||||
\(407\) | 15.1256 | − | 23.5445i | 0.749748 | − | 1.16706i | ||||
\(408\) | − | 23.8643i | − | 1.18146i | ||||||
\(409\) | −5.17322 | + | 15.9215i | −0.255799 | + | 0.787269i | 0.737872 | + | 0.674941i | \(0.235831\pi\) |
−0.993671 | + | 0.112328i | \(0.964169\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.5284 | − | 12.0086i | −0.815285 | − | 0.592339i | ||||
\(412\) | −13.7743 | + | 4.47553i | −0.678609 | + | 0.220493i | ||||
\(413\) | 2.37375 | − | 0.771279i | 0.116805 | − | 0.0379521i | ||||
\(414\) | −6.10813 | − | 4.43781i | −0.300198 | − | 0.218107i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −6.12889 | + | 18.8628i | −0.300493 | + | 0.924824i | ||||
\(417\) | − | 8.17100i | − | 0.400136i | ||||||
\(418\) | −4.06081 | + | 1.58180i | −0.198621 | + | 0.0773684i | ||||
\(419\) | 38.0968 | 1.86115 | 0.930576 | − | 0.366100i | \(-0.119307\pi\) | ||||
0.930576 | + | 0.366100i | \(0.119307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.3350 | − | 13.3212i | 0.893594 | − | 0.649234i | −0.0432184 | − | 0.999066i | \(-0.513761\pi\) |
0.936813 | + | 0.349831i | \(0.113761\pi\) | |||||||
\(422\) | −5.72383 | + | 7.87818i | −0.278632 | + | 0.383504i | ||||
\(423\) | 7.91496 | − | 2.57173i | 0.384839 | − | 0.125042i | ||||
\(424\) | 6.46722 | + | 19.9041i | 0.314076 | + | 0.966627i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.594161 | + | 0.431683i | −0.0287872 | + | 0.0209151i | ||||
\(427\) | 7.28990 | + | 2.36863i | 0.352783 | + | 0.114626i | ||||
\(428\) | − | 4.89758i | − | 0.236734i | ||||||
\(429\) | 5.67397 | + | 14.5663i | 0.273942 | + | 0.703266i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.4994 | + | 32.3137i | −0.505736 | + | 1.55650i | 0.293793 | + | 0.955869i | \(0.405082\pi\) |
−0.799529 | + | 0.600627i | \(0.794918\pi\) | |||||||
\(432\) | 1.03380 | + | 1.42291i | 0.0497388 | + | 0.0684596i | ||||
\(433\) | 21.5572 | − | 29.6709i | 1.03597 | − | 1.42589i | 0.135605 | − | 0.990763i | \(-0.456702\pi\) |
0.900367 | − | 0.435131i | \(-0.143298\pi\) | |||||||
\(434\) | −1.83298 | − | 5.64133i | −0.0879858 | − | 0.270793i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.84758 | + | 4.24852i | 0.280048 | + | 0.203467i | ||||
\(437\) | −4.86071 | − | 6.69019i | −0.232519 | − | 0.320035i | ||||
\(438\) | 5.21295 | + | 1.69379i | 0.249084 | + | 0.0809324i | ||||
\(439\) | −1.05012 | −0.0501193 | −0.0250596 | − | 0.999686i | \(-0.507978\pi\) | ||||
−0.0250596 | + | 0.999686i | \(0.507978\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.50292 | −0.309663 | ||||||||
\(442\) | 38.2008 | + | 12.4122i | 1.81703 | + | 0.590388i | ||||
\(443\) | −17.9396 | − | 24.6917i | −0.852334 | − | 1.17314i | −0.983344 | − | 0.181756i | \(-0.941822\pi\) |
0.131009 | − | 0.991381i | \(-0.458178\pi\) | |||||||
\(444\) | −5.46321 | − | 3.96925i | −0.259272 | − | 0.188372i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.83353 | + | 5.64302i | 0.0868201 | + | 0.267205i | ||||
\(447\) | −5.64402 | + | 7.76832i | −0.266953 | + | 0.367429i | ||||
\(448\) | −3.36773 | − | 4.63529i | −0.159111 | − | 0.218997i | ||||
\(449\) | 11.3006 | − | 34.7796i | 0.533308 | − | 1.64135i | −0.213969 | − | 0.976840i | \(-0.568639\pi\) |
0.747277 | − | 0.664513i | \(-0.231361\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.597901 | − | 0.489068i | 0.0281540 | − | 0.0230293i | ||||
\(452\) | − | 3.13477i | − | 0.147447i | ||||||
\(453\) | −6.56967 | − | 2.13462i | −0.308670 | − | 0.100293i | ||||
\(454\) | −7.47738 | + | 5.43263i | −0.350931 | + | 0.254966i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.13706 | + | 3.49951i | 0.0532478 | + | 0.163880i | ||||
\(457\) | 2.26740 | − | 0.736724i | 0.106065 | − | 0.0344625i | −0.255504 | − | 0.966808i | \(-0.582241\pi\) |
0.361568 | + | 0.932346i | \(0.382241\pi\) | |||||||
\(458\) | 7.21393 | − | 9.92913i | 0.337085 | − | 0.463958i | ||||
\(459\) | −6.29457 | + | 4.57327i | −0.293805 | + | 0.213462i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.5962 | 1.33186 | 0.665929 | − | 0.746015i | \(-0.268035\pi\) | ||||
0.665929 | + | 0.746015i | \(0.268035\pi\) | |||||||
\(462\) | −2.47714 | − | 0.650683i | −0.115247 | − | 0.0302725i | ||||
\(463\) | 30.5806i | 1.42120i | 0.703596 | + | 0.710600i | \(0.251577\pi\) | ||||
−0.703596 | + | 0.710600i | \(0.748423\pi\) | |||||||
\(464\) | 0.721447 | − | 2.22038i | 0.0334923 | − | 0.103079i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.17470 | − | 3.75964i | −0.239713 | − | 0.174162i | ||||
\(467\) | 3.55903 | − | 1.15640i | 0.164692 | − | 0.0535118i | −0.225510 | − | 0.974241i | \(-0.572405\pi\) |
0.390203 | + | 0.920729i | \(0.372405\pi\) | |||||||
\(468\) | 3.58760 | − | 1.16568i | 0.165837 | − | 0.0538836i | ||||
\(469\) | 1.16379 | + | 0.845545i | 0.0537389 | + | 0.0390436i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.50793 | − | 10.7963i | 0.161637 | − | 0.497467i | ||||
\(472\) | 10.8582i | 0.499788i | ||||||||
\(473\) | −1.39174 | − | 24.2674i | −0.0639920 | − | 1.11582i | ||||
\(474\) | −2.49757 | −0.114717 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.55179 | − | 2.58053i | 0.162796 | − | 0.118278i | ||||
\(477\) | 4.01064 | − | 5.52018i | 0.183635 | − | 0.252752i | ||||
\(478\) | −17.2151 | + | 5.59351i | −0.787398 | + | 0.255841i | ||||
\(479\) | 0.292006 | + | 0.898702i | 0.0133421 | + | 0.0410627i | 0.957506 | − | 0.288414i | \(-0.0931278\pi\) |
−0.944164 | + | 0.329476i | \(0.893128\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 32.1740 | − | 23.3758i | 1.46701 | − | 1.06584i | ||||
\(482\) | −3.42902 | − | 1.11416i | −0.156188 | − | 0.0507484i | ||||
\(483\) | − | 4.85995i | − | 0.221135i | ||||||
\(484\) | −7.66719 | − | 4.32647i | −0.348508 | − | 0.196658i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.338464 | − | 1.04169i | 0.0153531 | − | 0.0472519i | ||||
\(487\) | 7.86887 | + | 10.8306i | 0.356573 | + | 0.490780i | 0.949190 | − | 0.314704i | \(-0.101905\pi\) |
−0.592617 | + | 0.805484i | \(0.701905\pi\) | |||||||
\(488\) | −19.6003 | + | 26.9775i | −0.887263 | + | 1.22121i | ||||
\(489\) | 0.553922 | + | 1.70480i | 0.0250492 | + | 0.0770935i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.25625 | + | 1.63926i | 0.101823 | + | 0.0739787i | 0.637532 | − | 0.770424i | \(-0.279955\pi\) |
−0.535709 | + | 0.844403i | \(0.679955\pi\) | |||||||
\(492\) | −0.109562 | − | 0.150799i | −0.00493944 | − | 0.00679855i | ||||
\(493\) | 9.82241 | + | 3.19149i | 0.442379 | + | 0.143738i | ||||
\(494\) | −6.19327 | −0.278648 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 13.5099 | 0.606611 | ||||||||
\(497\) | −0.449608 | − | 0.146087i | −0.0201677 | − | 0.00655288i | ||||
\(498\) | −1.35840 | − | 1.86968i | −0.0608716 | − | 0.0837825i | ||||
\(499\) | 14.3835 | + | 10.4503i | 0.643896 | + | 0.467818i | 0.861187 | − | 0.508289i | \(-0.169722\pi\) |
−0.217290 | + | 0.976107i | \(0.569722\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.86167 | + | 5.72964i | 0.0831733 | + | 0.255981i | ||||
\(502\) | −4.76368 | + | 6.55664i | −0.212613 | + | 0.292637i | ||||
\(503\) | 15.1554 | + | 20.8596i | 0.675744 | + | 0.930081i | 0.999873 | − | 0.0159313i | \(-0.00507131\pi\) |
−0.324129 | + | 0.946013i | \(0.605071\pi\) | |||||||
\(504\) | −0.668243 | + | 2.05664i | −0.0297659 | + | 0.0916100i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −6.36175 | + | 24.2191i | −0.282814 | + | 1.07667i | ||||
\(507\) | 9.21546i | 0.409273i | ||||||||
\(508\) | 8.27192 | + | 2.68771i | 0.367007 | + | 0.119248i | ||||
\(509\) | −22.8386 | + | 16.5932i | −1.01231 | + | 0.735483i | −0.964691 | − | 0.263383i | \(-0.915162\pi\) |
−0.0476138 | + | 0.998866i | \(0.515162\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.09029 | + | 3.35556i | 0.0482314 | + | 0.148441i | ||||
\(512\) | 17.2999 | − | 5.62107i | 0.764554 | − | 0.248419i | ||||
\(513\) | 0.705148 | − | 0.970553i | 0.0311330 | − | 0.0428509i | ||||
\(514\) | −16.5695 | + | 12.0385i | −0.730850 | + | 0.530993i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.86556 | −0.258217 | ||||||||
\(517\) | −17.4759 | − | 21.3648i | −0.768590 | − | 0.939625i | ||||
\(518\) | 6.51573i | 0.286285i | ||||||||
\(519\) | −1.29377 | + | 3.98183i | −0.0567904 | + | 0.174783i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.46183 | − | 6.87442i | −0.414530 | − | 0.301174i | 0.360903 | − | 0.932603i | \(-0.382469\pi\) |
−0.775433 | + | 0.631429i | \(0.782469\pi\) | |||||||
\(522\) | −1.38274 | + | 0.449279i | −0.0605209 | + | 0.0196644i | ||||
\(523\) | −18.7236 | + | 6.08365i | −0.818724 | + | 0.266019i | −0.688288 | − | 0.725437i | \(-0.741638\pi\) |
−0.130436 | + | 0.991457i | \(0.541638\pi\) | |||||||
\(524\) | 7.58160 | + | 5.50836i | 0.331204 | + | 0.240634i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.35054 | − | 4.15654i | 0.0588863 | − | 0.181234i | ||||
\(527\) | 59.7642i | 2.60337i | ||||||||
\(528\) | 3.15290 | − | 4.90782i | 0.137212 | − | 0.213585i | ||||
\(529\) | −24.5159 | −1.06591 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.86401 | − | 2.08083i | 0.124287 | − | 0.0903001i | ||||
\(532\) | −0.397889 | + | 0.547647i | −0.0172507 | + | 0.0237435i | ||||
\(533\) | 1.04401 | − | 0.339220i | 0.0452212 | − | 0.0146933i | ||||
\(534\) | 1.13292 | + | 3.48676i | 0.0490261 | + | 0.150887i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −5.06295 | + | 3.67845i | −0.218686 | + | 0.158885i | ||||
\(537\) | 4.61420 | + | 1.49924i | 0.199117 | + | 0.0646972i | ||||
\(538\) | 13.9266i | 0.600420i | ||||||||
\(539\) | 7.82831 | + | 20.0969i | 0.337189 | + | 0.865635i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.68443 | + | 5.18413i | −0.0724191 | + | 0.222883i | −0.980714 | − | 0.195447i | \(-0.937384\pi\) |
0.908295 | + | 0.418330i | \(0.137384\pi\) | |||||||
\(542\) | −15.3404 | − | 21.1143i | −0.658927 | − | 0.906935i | ||||
\(543\) | 13.5706 | − | 18.6784i | 0.582371 | − | 0.801565i | ||||
\(544\) | 10.1172 | + | 31.1377i | 0.433773 | + | 1.33502i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.94461 | − | 2.13939i | −0.126018 | − | 0.0915572i | ||||
\(547\) | −7.51731 | − | 10.3467i | −0.321417 | − | 0.442393i | 0.617482 | − | 0.786585i | \(-0.288153\pi\) |
−0.938899 | + | 0.344192i | \(0.888153\pi\) | |||||||
\(548\) | 15.5507 | + | 5.05271i | 0.664291 | + | 0.215841i | ||||
\(549\) | 10.8719 | 0.463999 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.59245 | −0.0678405 | ||||||||
\(552\) | 20.1079 | + | 6.53344i | 0.855848 | + | 0.278082i | ||||
\(553\) | −0.944967 | − | 1.30064i | −0.0401841 | − | 0.0553087i | ||||
\(554\) | 6.56832 | + | 4.77216i | 0.279061 | + | 0.202750i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.02082 | + | 6.21944i | 0.0857018 | + | 0.263763i | ||||
\(557\) | −0.208351 | + | 0.286771i | −0.00882812 | + | 0.0121509i | −0.813408 | − | 0.581693i | \(-0.802390\pi\) |
0.804580 | + | 0.593844i | \(0.202390\pi\) | |||||||
\(558\) | −4.94518 | − | 6.80645i | −0.209346 | − | 0.288140i | ||||
\(559\) | 10.6746 | − | 32.8529i | 0.451486 | − | 1.38953i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 21.7109 | + | 13.9476i | 0.916636 | + | 0.588869i | ||||
\(562\) | − | 31.8528i | − | 1.34363i | ||||||
\(563\) | −33.3648 | − | 10.8409i | −1.40616 | − | 0.456888i | −0.494981 | − | 0.868904i | \(-0.664825\pi\) |
−0.911177 | + | 0.412015i | \(0.864825\pi\) | |||||||
\(564\) | −5.38852 | + | 3.91499i | −0.226898 | + | 0.164851i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −7.33551 | − | 22.5764i | −0.308334 | − | 0.948956i | ||||
\(567\) | 0.670530 | − | 0.217868i | 0.0281596 | − | 0.00914961i | ||||
\(568\) | 1.20886 | − | 1.66385i | 0.0507225 | − | 0.0698135i | ||||
\(569\) | −13.2015 | + | 9.59145i | −0.553436 | + | 0.402094i | −0.829051 | − | 0.559174i | \(-0.811119\pi\) |
0.275615 | + | 0.961268i | \(0.411119\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.4160 | −0.603291 | −0.301645 | − | 0.953420i | \(-0.597536\pi\) | ||||
−0.301645 | + | 0.953420i | \(0.597536\pi\) | |||||||
\(572\) | −7.92127 | − | 9.68400i | −0.331205 | − | 0.404908i | ||||
\(573\) | − | 6.22571i | − | 0.260083i | ||||||
\(574\) | −0.0555772 | + | 0.171049i | −0.00231975 | + | 0.00713945i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −6.57453 | − | 4.77668i | −0.273939 | − | 0.199028i | ||||
\(577\) | −8.47261 | + | 2.75292i | −0.352719 | + | 0.114605i | −0.480017 | − | 0.877259i | \(-0.659370\pi\) |
0.127298 | + | 0.991865i | \(0.459370\pi\) | |||||||
\(578\) | 45.3513 | − | 14.7355i | 1.88636 | − | 0.612917i | ||||
\(579\) | 15.4416 | + | 11.2190i | 0.641730 | + | 0.466244i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.459700 | − | 1.41481i | 0.0190716 | − | 0.0586962i | ||||
\(582\) | 3.63887i | 0.150836i | ||||||||
\(583\) | −21.8879 | − | 5.74939i | −0.906503 | − | 0.238116i | ||||
\(584\) | −15.3492 | −0.635155 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.45414 | − | 5.41575i | 0.307928 | − | 0.223723i | ||||
\(587\) | −8.11225 | + | 11.1655i | −0.334828 | + | 0.460851i | −0.942922 | − | 0.333014i | \(-0.891934\pi\) |
0.608094 | + | 0.793865i | \(0.291934\pi\) | |||||||
\(588\) | 4.94977 | − | 1.60828i | 0.204125 | − | 0.0663242i | ||||
\(589\) | −2.84758 | − | 8.76396i | −0.117333 | − | 0.361113i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.50177 | + | 3.99727i | −0.226313 | + | 0.164426i | ||||
\(592\) | −14.1138 | − | 4.58586i | −0.580075 | − | 0.188478i | ||||
\(593\) | 16.4676i | 0.676242i | 0.941103 | + | 0.338121i | \(0.109791\pi\) | ||||
−0.941103 | + | 0.338121i | \(0.890209\pi\) | |||||||
\(594\) | −3.62672 | + | 0.207992i | −0.148806 | + | 0.00853403i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.37477 | − | 7.30879i | 0.0972744 | − | 0.299380i | ||||
\(597\) | −12.5182 | − | 17.2298i | −0.512336 | − | 0.705170i | ||||
\(598\) | −20.9169 | + | 28.7896i | −0.855354 | + | 1.17729i | ||||
\(599\) | −11.6994 | − | 36.0069i | −0.478023 | − | 1.47120i | −0.841837 | − | 0.539732i | \(-0.818525\pi\) |
0.363814 | − | 0.931472i | \(-0.381475\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.26563 | − | 0.919535i | −0.0516262 | − | 0.0375086i | 0.561673 | − | 0.827359i | \(-0.310158\pi\) |
−0.613299 | + | 0.789851i | \(0.710158\pi\) | |||||||
\(602\) | 3.32660 | + | 4.57868i | 0.135582 | + | 0.186613i | ||||
\(603\) | 1.94049 | + | 0.630505i | 0.0790230 | + | 0.0256761i | ||||
\(604\) | 5.52850 | 0.224951 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −20.7249 | −0.841892 | ||||||||
\(607\) | 17.9296 | + | 5.82568i | 0.727740 | + | 0.236457i | 0.649376 | − | 0.760468i | \(-0.275030\pi\) |
0.0783641 | + | 0.996925i | \(0.475030\pi\) | |||||||
\(608\) | −2.96723 | − | 4.08405i | −0.120337 | − | 0.165630i | ||||
\(609\) | −0.757135 | − | 0.550090i | −0.0306806 | − | 0.0222908i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.1214 | − | 37.3058i | −0.490379 | − | 1.50923i | ||||
\(612\) | 3.66013 | − | 5.03774i | 0.147952 | − | 0.203639i | ||||
\(613\) | 19.2030 | + | 26.4306i | 0.775601 | + | 1.06752i | 0.995754 | + | 0.0920574i | \(0.0293443\pi\) |
−0.220153 | + | 0.975465i | \(0.570656\pi\) | |||||||
\(614\) | −8.03619 | + | 24.7329i | −0.324314 | + | 0.998137i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.16037 | − | 0.410647i | 0.288499 | − | 0.0165454i | ||||
\(617\) | − | 33.6559i | − | 1.35493i | −0.735553 | − | 0.677467i | \(-0.763078\pi\) | ||
0.735553 | − | 0.677467i | \(-0.236922\pi\) | |||||||
\(618\) | 18.8508 | + | 6.12499i | 0.758289 | + | 0.246383i | ||||
\(619\) | −7.23262 | + | 5.25480i | −0.290703 | + | 0.211208i | −0.723572 | − | 0.690248i | \(-0.757501\pi\) |
0.432869 | + | 0.901457i | \(0.357501\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.13011 | − | 6.55580i | −0.0854784 | − | 0.263075i | ||||
\(622\) | −24.0078 | + | 7.80061i | −0.962626 | + | 0.312776i | ||||
\(623\) | −1.38712 | + | 1.90921i | −0.0555739 | + | 0.0764910i | ||||
\(624\) | 6.70662 | − | 4.87265i | 0.268480 | − | 0.195062i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −19.0185 | −0.760131 | ||||||||
\(627\) | −3.84830 | − | 1.01085i | −0.153686 | − | 0.0403696i | ||||
\(628\) | 9.08528i | 0.362542i | ||||||||
\(629\) | 20.2867 | − | 62.4360i | 0.808883 | − | 2.48949i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.5798 | + | 11.3194i | 0.620224 | + | 0.450619i | 0.853000 | − | 0.521912i | \(-0.174781\pi\) |
−0.232776 | + | 0.972530i | \(0.574781\pi\) | |||||||
\(632\) | 6.65170 | − | 2.16127i | 0.264590 | − | 0.0859706i | ||||
\(633\) | −8.45559 | + | 2.74739i | −0.336080 | + | 0.109199i | ||||
\(634\) | −5.45043 | − | 3.95997i | −0.216464 | − | 0.157270i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.68751 | + | 5.19364i | −0.0669143 | + | 0.205941i | ||||
\(637\) | 30.6504i | 1.21441i | ||||||||
\(638\) | 3.05303 | + | 3.73243i | 0.120871 | + | 0.147768i | ||||
\(639\) | −0.670527 | −0.0265256 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.0485 | − | 8.75375i | 0.475887 | − | 0.345752i | −0.323844 | − | 0.946110i | \(-0.604975\pi\) |
0.799731 | + | 0.600358i | \(0.204975\pi\) | |||||||
\(642\) | −3.93968 | + | 5.42251i | −0.155487 | + | 0.214009i | ||||
\(643\) | 33.5907 | − | 10.9143i | 1.32469 | − | 0.430417i | 0.440584 | − | 0.897711i | \(-0.354771\pi\) |
0.884102 | + | 0.467295i | \(0.154771\pi\) | |||||||
\(644\) | 1.20194 | + | 3.69920i | 0.0473632 | + | 0.145769i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.27100 | + | 6.00923i | −0.325418 | + | 0.236430i | ||||
\(647\) | 29.6186 | + | 9.62366i | 1.16443 | + | 0.378345i | 0.826560 | − | 0.562849i | \(-0.190295\pi\) |
0.337867 | + | 0.941194i | \(0.390295\pi\) | |||||||
\(648\) | 3.06719i | 0.120490i | ||||||||
\(649\) | −9.87841 | − | 6.34613i | −0.387761 | − | 0.249107i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.67350 | − | 5.15052i | 0.0655898 | − | 0.201865i | ||||
\(652\) | −0.843246 | − | 1.16063i | −0.0330241 | − | 0.0454537i | ||||
\(653\) | −2.97122 | + | 4.08953i | −0.116273 | + | 0.160036i | −0.863186 | − | 0.504885i | \(-0.831535\pi\) |
0.746914 | + | 0.664921i | \(0.231535\pi\) | |||||||
\(654\) | −3.05677 | − | 9.40776i | −0.119529 | − | 0.367872i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.331396 | − | 0.240774i | −0.0129389 | − | 0.00940063i | ||||
\(657\) | 2.94147 | + | 4.04859i | 0.114758 | + | 0.157951i | ||||
\(658\) | 6.11211 | + | 1.98595i | 0.238275 | + | 0.0774202i | ||||
\(659\) | 14.4486 | 0.562837 | 0.281419 | − | 0.959585i | \(-0.409195\pi\) | ||||
0.281419 | + | 0.959585i | \(0.409195\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.8696 | 0.578361 | 0.289181 | − | 0.957275i | \(-0.406617\pi\) | ||||
0.289181 | + | 0.957275i | \(0.406617\pi\) | |||||||
\(662\) | 20.2286 | + | 6.57267i | 0.786207 | + | 0.255454i | ||||
\(663\) | 21.5553 | + | 29.6684i | 0.837140 | + | 1.15222i | ||||
\(664\) | 5.23573 | + | 3.80398i | 0.203186 | + | 0.147623i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.85584 | + | 8.78936i | 0.110661 | + | 0.340581i | ||||
\(667\) | −5.37826 | + | 7.40254i | −0.208247 | + | 0.286627i | ||||
\(668\) | −2.83406 | − | 3.90075i | −0.109653 | − | 0.150925i | ||||
\(669\) | −1.67401 | + | 5.15206i | −0.0647208 | + | 0.199190i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.0877 | − | 33.5988i | −0.505245 | − | 1.29707i | ||||
\(672\) | − | 2.96677i | − | 0.114446i | ||||||
\(673\) | 39.5785 | + | 12.8598i | 1.52564 | + | 0.495710i | 0.947371 | − | 0.320138i | \(-0.103729\pi\) |
0.578267 | + | 0.815848i | \(0.303729\pi\) | |||||||
\(674\) | 28.0780 | − | 20.3999i | 1.08153 | − | 0.785774i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.27913 | − | 7.01444i | −0.0876588 | − | 0.269786i | ||||
\(677\) | −42.0715 | + | 13.6699i | −1.61694 | + | 0.525376i | −0.971217 | − | 0.238195i | \(-0.923444\pi\) |
−0.645724 | + | 0.763571i | \(0.723444\pi\) | |||||||
\(678\) | −2.52165 | + | 3.47076i | −0.0968435 | + | 0.133294i | ||||
\(679\) | −1.89499 | + | 1.37679i | −0.0727229 | + | 0.0528363i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.43842 | −0.323361 | ||||||||
\(682\) | −15.0819 | + | 23.4765i | −0.577515 | + | 0.898962i | ||||
\(683\) | − | 24.5318i | − | 0.938683i | −0.883017 | − | 0.469342i | \(-0.844491\pi\) | ||
0.883017 | − | 0.469342i | \(-0.155509\pi\) | |||||||
\(684\) | −0.296697 | + | 0.913140i | −0.0113445 | + | 0.0349148i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −8.43584 | − | 6.12899i | −0.322082 | − | 0.234006i | ||||
\(687\) | 10.6569 | − | 3.46262i | 0.406584 | − | 0.132107i | ||||
\(688\) | −12.2593 | + | 3.98328i | −0.467380 | + | 0.151861i | ||||
\(689\) | −26.0184 | − | 18.9035i | −0.991222 | − | 0.720165i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.34440 | − | 22.6037i | 0.279394 | − | 0.859887i | −0.708629 | − | 0.705581i | \(-0.750686\pi\) |
0.988023 | − | 0.154306i | \(-0.0493141\pi\) | |||||||
\(692\) | − | 3.35078i | − | 0.127378i | ||||||
\(693\) | −1.48050 | − | 1.80996i | −0.0562397 | − | 0.0687547i | ||||
\(694\) | 30.6063 | 1.16180 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.29383 | − | 2.39311i | 0.124852 | − | 0.0907105i | ||||
\(697\) | 1.06512 | − | 1.46601i | 0.0403443 | − | 0.0555292i | ||||
\(698\) | −0.711817 | + | 0.231283i | −0.0269427 | + | 0.00875420i | ||||
\(699\) | −1.80459 | − | 5.55397i | −0.0682560 | − | 0.210070i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.4499 | − | 19.2170i | 0.998999 | − | 0.725816i | 0.0371259 | − | 0.999311i | \(-0.488180\pi\) |
0.961873 | + | 0.273495i | \(0.0881797\pi\) | |||||||
\(702\) | −4.90981 | − | 1.59529i | −0.185309 | − | 0.0602105i | ||||
\(703\) | 10.1224i | 0.381772i | ||||||||
\(704\) | −6.84753 | + | 26.0684i | −0.258076 | + | 0.982491i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.527664 | − | 1.62398i | 0.0198589 | − | 0.0611194i | ||||
\(707\) | −7.84138 | − | 10.7927i | −0.294905 | − | 0.405903i | ||||
\(708\) | −1.66535 | + | 2.29216i | −0.0625877 | + | 0.0861445i | ||||
\(709\) | −7.36278 | − | 22.6603i | −0.276515 | − | 0.851025i | −0.988815 | − | 0.149150i | \(-0.952346\pi\) |
0.712300 | − | 0.701875i | \(-0.247654\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.84478 | − | 1.34031i | −0.0691845 | − | 0.0502655i | ||||
\(712\) | −6.03453 | − | 8.30582i | −0.226154 | − | 0.311274i | ||||
\(713\) | −50.3568 | − | 16.3619i | −1.88588 | − | 0.612759i | ||||
\(714\) | −6.00829 | −0.224855 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.88293 | −0.145112 | ||||||||
\(717\) | −15.7173 | − | 5.10686i | −0.586973 | − | 0.190719i | ||||
\(718\) | 10.1980 | + | 14.0363i | 0.380586 | + | 0.523831i | ||||
\(719\) | −2.30311 | − | 1.67331i | −0.0858914 | − | 0.0624038i | 0.544011 | − | 0.839078i | \(-0.316905\pi\) |
−0.629902 | + | 0.776674i | \(0.716905\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.94263 | + | 12.1342i | 0.146831 | + | 0.451900i | ||||
\(722\) | −11.3056 | + | 15.5608i | −0.420751 | + | 0.579114i | ||||
\(723\) | −1.93487 | − | 2.66312i | −0.0719586 | − | 0.0990425i | ||||
\(724\) | −5.70996 | + | 17.5735i | −0.212209 | + | 0.653112i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 5.00869 | + | 10.9578i | 0.185890 | + | 0.406681i | ||||
\(727\) | − | 13.5192i | − | 0.501399i | −0.968065 | − | 0.250700i | \(-0.919339\pi\) | ||
0.968065 | − | 0.250700i | \(-0.0806606\pi\) | |||||||
\(728\) | 9.69362 | + | 3.14965i | 0.359270 | + | 0.116734i | ||||
\(729\) | 0.809017 | − | 0.587785i | 0.0299636 | − | 0.0217698i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.6210 | − | 54.2318i | −0.651736 | − | 2.00584i | ||||
\(732\) | −8.27522 | + | 2.68878i | −0.305861 | + | 0.0993802i | ||||
\(733\) | −19.3001 | + | 26.5643i | −0.712864 | + | 0.981174i | 0.286866 | + | 0.957971i | \(0.407386\pi\) |
−0.999731 | + | 0.0232030i | \(0.992614\pi\) | |||||||
\(734\) | 13.9440 | − | 10.1309i | 0.514681 | − | 0.373938i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −29.0062 | −1.06918 | ||||||||
\(737\) | −0.387456 | − | 6.75599i | −0.0142721 | − | 0.248860i | ||||
\(738\) | 0.255095i | 0.00939018i | ||||||||
\(739\) | −15.7267 | + | 48.4018i | −0.578516 | + | 1.78049i | 0.0453660 | + | 0.998970i | \(0.485555\pi\) |
−0.623882 | + | 0.781519i | \(0.714445\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.57453 | − | 3.32359i | −0.168050 | − | 0.122095i | ||||
\(742\) | 5.01123 | − | 1.62825i | 0.183968 | − | 0.0597749i | ||||
\(743\) | −14.7276 | + | 4.78528i | −0.540302 | + | 0.175555i | −0.566439 | − | 0.824104i | \(-0.691679\pi\) |
0.0261370 | + | 0.999658i | \(0.491679\pi\) | |||||||
\(744\) | 19.0603 | + | 13.8481i | 0.698786 | + | 0.507697i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.78609 | + | 5.49702i | −0.0653933 | + | 0.201260i | ||||
\(747\) | − | 2.10999i | − | 0.0772004i | ||||||
\(748\) | −19.9750 | − | 5.24692i | −0.730357 | − | 0.191846i | ||||
\(749\) | −4.31444 | −0.157646 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.94571 | + | 6.49944i | −0.326434 | + | 0.237168i | −0.738916 | − | 0.673798i | \(-0.764662\pi\) |
0.412482 | + | 0.910966i | \(0.364662\pi\) | |||||||
\(752\) | −8.60359 | + | 11.8418i | −0.313740 | + | 0.431827i | ||||
\(753\) | −7.03719 | + | 2.28652i | −0.256449 | + | 0.0833255i | ||||
\(754\) | 2.11760 | + | 6.51731i | 0.0771185 | + | 0.237346i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.456498 | + | 0.331666i | −0.0166027 | + | 0.0120626i | ||||
\(757\) | 8.56219 | + | 2.78203i | 0.311198 | + | 0.101114i | 0.460452 | − | 0.887684i | \(-0.347687\pi\) |
−0.149254 | + | 0.988799i | \(0.547687\pi\) | |||||||
\(758\) | − | 36.7025i | − | 1.33309i | ||||||
\(759\) | −17.6961 | + | 14.4750i | −0.642327 | + | 0.525407i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.56374 | − | 7.89038i | 0.0929355 | − | 0.286026i | −0.893775 | − | 0.448516i | \(-0.851953\pi\) |
0.986710 | + | 0.162490i | \(0.0519526\pi\) | |||||||
\(762\) | −6.99648 | − | 9.62983i | −0.253456 | − | 0.348852i | ||||
\(763\) | 3.74265 | − | 5.15132i | 0.135493 | − | 0.186490i | ||||
\(764\) | 1.53972 | + | 4.73876i | 0.0557050 | + | 0.171442i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 17.9281 | + | 13.0255i | 0.647767 | + | 0.470630i | ||||
\(767\) | −9.80761 | − | 13.4990i | −0.354132 | − | 0.487421i | ||||
\(768\) | 14.9524 | + | 4.85832i | 0.539547 | + | 0.175310i | ||||
\(769\) | −2.89088 | −0.104248 | −0.0521239 | − | 0.998641i | \(-0.516599\pi\) | ||||
−0.0521239 | + | 0.998641i | \(0.516599\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.6991 | −0.673432 | ||||||||
\(772\) | −14.5281 | − | 4.72047i | −0.522879 | − | 0.169894i | ||||
\(773\) | −16.3685 | − | 22.5293i | −0.588734 | − | 0.810322i | 0.405885 | − | 0.913924i | \(-0.366963\pi\) |
−0.994619 | + | 0.103602i | \(0.966963\pi\) | |||||||
\(774\) | 6.49424 | + | 4.71834i | 0.233431 | + | 0.169597i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −3.14890 | − | 9.69132i | −0.113039 | − | 0.347898i | ||||
\(777\) | −3.49664 | + | 4.81271i | −0.125441 | + | 0.172655i | ||||
\(778\) | −17.7513 | − | 24.4326i | −0.636417 | − | 0.875952i | ||||
\(779\) | −0.0863407 | + | 0.265729i | −0.00309348 | + | 0.00952074i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.807189 | + | 2.07222i | 0.0288835 | + | 0.0741500i | ||||
\(782\) | 58.7433i | 2.10066i | ||||||||
\(783\) | −1.26244 | − | 0.410191i | −0.0451158 | − | 0.0146590i | ||||
\(784\) | 9.25304 | − | 6.72273i | 0.330466 | − | 0.240098i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.96321 | − | 12.1975i | −0.141363 | − | 0.435070i | ||||
\(787\) | 23.6200 | − | 7.67461i | 0.841963 | − | 0.273570i | 0.143887 | − | 0.989594i | \(-0.454040\pi\) |
0.698076 | + | 0.716024i | \(0.254040\pi\) | |||||||
\(788\) | 3.19914 | − | 4.40324i | 0.113965 | − | 0.156859i | ||||
\(789\) | 3.22814 | − | 2.34538i | 0.114925 | − | 0.0834977i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.76152 | −0.0981883 | ||||||||
\(792\) | 9.47896 | − | 3.69232i | 0.336820 | − | 0.131201i | ||||
\(793\) | − | 51.2426i | − | 1.81968i | ||||||
\(794\) | −3.98037 | + | 12.2503i | −0.141258 | + | 0.434748i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 13.7896 | + | 10.0187i | 0.488758 | + | 0.355103i | ||||
\(797\) | 2.67348 | − | 0.868668i | 0.0946997 | − | 0.0307698i | −0.261284 | − | 0.965262i | \(-0.584146\pi\) |
0.355984 | + | 0.934492i | \(0.384146\pi\) | |||||||
\(798\) | 0.881070 | − | 0.286277i | 0.0311895 | − | 0.0101341i | ||||
\(799\) | −52.3852 | − | 38.0600i | −1.85325 | − | 1.34647i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.03435 | + | 3.18340i | −0.0365469 | + | 0.112480i | ||||
\(802\) | − | 8.46012i | − | 0.298737i | ||||||
\(803\) | 8.97095 | − | 13.9642i | 0.316578 | − | 0.492786i | ||||
\(804\) | −1.63296 | −0.0575901 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −32.0811 | + | 23.3083i | −1.13001 | + | 0.820998i | ||||
\(807\) | −7.47368 | + | 10.2866i | −0.263086 | + | 0.362107i | ||||
\(808\) | 55.1961 | − | 17.9343i | 1.94179 | − | 0.630926i | ||||
\(809\) | −3.60825 | − | 11.1051i | −0.126859 | − | 0.390433i | 0.867376 | − | 0.497654i | \(-0.165805\pi\) |
−0.994235 | + | 0.107220i | \(0.965805\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.4722 | + | 14.1474i | −0.683761 | + | 0.496782i | −0.874603 | − | 0.484839i | \(-0.838878\pi\) |
0.190842 | + | 0.981621i | \(0.438878\pi\) | |||||||
\(812\) | 0.712347 | + | 0.231455i | 0.0249985 | + | 0.00812250i | ||||
\(813\) | − | 23.8280i | − | 0.835684i | ||||||
\(814\) | 23.7251 | − | 19.4066i | 0.831565 | − | 0.680199i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4.22872 | − | 13.0147i | 0.148035 | − | 0.455604i | ||||
\(817\) | 5.16797 | + | 7.11310i | 0.180804 | + | 0.248856i | ||||
\(818\) | −10.7777 | + | 14.8343i | −0.376835 | + | 0.518669i | ||||
\(819\) | −1.02689 | − | 3.16043i | −0.0358823 | − | 0.110434i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.92827 | − | 2.85406i | −0.137098 | − | 0.0996073i | 0.517123 | − | 0.855911i | \(-0.327003\pi\) |
−0.654220 | + | 0.756304i | \(0.727003\pi\) | |||||||
\(822\) | −13.1529 | − | 18.1034i | −0.458761 | − | 0.631430i | ||||
\(823\) | −24.7846 | − | 8.05300i | −0.863937 | − | 0.280710i | −0.156665 | − | 0.987652i | \(-0.550074\pi\) |
−0.707272 | + | 0.706942i | \(0.750074\pi\) | |||||||
\(824\) | −55.5050 | −1.93361 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.73376 | 0.0951195 | ||||||||
\(827\) | −15.4873 | − | 5.03212i | −0.538546 | − | 0.174984i | 0.0270996 | − | 0.999633i | \(-0.491373\pi\) |
−0.565645 | + | 0.824649i | \(0.691373\pi\) | |||||||
\(828\) | 3.24271 | + | 4.46321i | 0.112692 | + | 0.155107i | ||||
\(829\) | −8.10161 | − | 5.88616i | −0.281380 | − | 0.204435i | 0.438139 | − | 0.898907i | \(-0.355638\pi\) |
−0.719519 | + | 0.694472i | \(0.755638\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.29059 | + | 7.04973i | 0.0794598 | + | 0.244552i | ||||
\(832\) | −22.5140 | + | 30.9879i | −0.780534 | + | 1.07431i | ||||
\(833\) | 29.7396 | + | 40.9331i | 1.03042 | + | 1.41825i | ||||
\(834\) | 2.76559 | − | 8.51162i | 0.0957647 | − | 0.294733i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.17917 | − | 0.182326i | 0.109954 | − | 0.00630587i | ||||
\(837\) | − | 7.68126i | − | 0.265503i | ||||||
\(838\) | 39.6849 | + | 12.8944i | 1.37089 | + | 0.445430i | ||||
\(839\) | 9.50855 | − | 6.90837i | 0.328272 | − | 0.238503i | −0.411425 | − | 0.911444i | \(-0.634969\pi\) |
0.739697 | + | 0.672940i | \(0.234969\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.41700 | − | 25.9049i | −0.290242 | − | 0.893271i | ||||
\(842\) | 23.6081 | − | 7.67073i | 0.813588 | − | 0.264351i | ||||
\(843\) | 17.0937 | − | 23.5274i | 0.588737 | − | 0.810327i | ||||
\(844\) | 5.75659 | − | 4.18240i | 0.198150 | − | 0.143964i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 9.11534 | 0.313392 | ||||||||
\(847\) | −3.81133 | + | 6.75427i | −0.130959 | + | 0.232079i | ||||
\(848\) | 12.0009i | 0.412113i | ||||||||
\(849\) | 6.69730 | − | 20.6122i | 0.229851 | − | 0.707407i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 47.0541 | + | 34.1868i | 1.61299 | + | 1.17191i | ||||
\(852\) | 0.510378 | − | 0.165832i | 0.0174853 | − | 0.00568131i | ||||
\(853\) | −43.4018 | + | 14.1021i | −1.48605 | + | 0.482847i | −0.935914 | − | 0.352229i | \(-0.885424\pi\) |
−0.550135 | + | 0.835076i | \(0.685424\pi\) | |||||||
\(854\) | 6.79210 | + | 4.93475i | 0.232421 | + | 0.168864i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.80009 | − | 17.8508i | 0.198243 | − | 0.610129i | ||||
\(857\) | − | 8.41558i | − | 0.287471i | −0.989616 | − | 0.143735i | \(-0.954089\pi\) | ||
0.989616 | − | 0.143735i | \(-0.0459114\pi\) | |||||||
\(858\) | 0.980336 | + | 17.0939i | 0.0334681 | + | 0.583577i | ||||
\(859\) | 45.3009 | 1.54565 | 0.772823 | − | 0.634622i | \(-0.218844\pi\) | ||||
0.772823 | + | 0.634622i | \(0.218844\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.132844 | + | 0.0965167i | −0.00452730 | + | 0.00328928i | ||||
\(862\) | −21.8741 | + | 30.1071i | −0.745034 | + | 1.02545i | ||||
\(863\) | −11.4688 | + | 3.72644i | −0.390402 | + | 0.126849i | −0.497639 | − | 0.867384i | \(-0.665800\pi\) |
0.107237 | + | 0.994233i | \(0.465800\pi\) | |||||||
\(864\) | −1.30033 | − | 4.00201i | −0.0442382 | − | 0.136151i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 32.4984 | − | 23.6115i | 1.10434 | − | 0.802350i | ||||
\(867\) | 41.4056 | + | 13.4535i | 1.40621 | + | 0.456904i | ||||
\(868\) | 4.33425i | 0.147114i | ||||||||
\(869\) | −1.92138 | + | 7.31466i | −0.0651783 | + | 0.248133i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.97178 | − | 9.14618i | 0.100695 | − | 0.309907i | ||||
\(872\) | 16.2820 | + | 22.4103i | 0.551378 | + | 0.758907i | ||||
\(873\) | −1.95279 | + | 2.68778i | −0.0660919 | + | 0.0909676i | ||||
\(874\) | −2.79894 | − | 8.61426i | −0.0946757 | − | 0.291382i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.24021 | − | 2.35415i | −0.109477 | − | 0.0795395i | ||||
\(877\) | 12.4281 | + | 17.1058i | 0.419666 | + | 0.577621i | 0.965543 | − | 0.260245i | \(-0.0838032\pi\) |
−0.545876 | + | 0.837866i | \(0.683803\pi\) | |||||||
\(878\) | −1.09389 | − | 0.355427i | −0.0369170 | − | 0.0119951i | ||||
\(879\) | 8.41220 | 0.283736 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.1669 | −0.443605 | −0.221803 | − | 0.975092i | \(-0.571194\pi\) | ||||
−0.221803 | + | 0.975092i | \(0.571194\pi\) | |||||||
\(882\) | −6.77401 | − | 2.20101i | −0.228093 | − | 0.0741118i | ||||
\(883\) | −20.4371 | − | 28.1293i | −0.687765 | − | 0.946627i | 0.312230 | − | 0.950007i | \(-0.398924\pi\) |
−0.999994 | + | 0.00337992i | \(0.998924\pi\) | |||||||
\(884\) | −23.7445 | − | 17.2514i | −0.798614 | − | 0.580227i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10.3301 | − | 31.7929i | −0.347048 | − | 1.06810i | ||||
\(887\) | −12.3179 | + | 16.9542i | −0.413596 | + | 0.569266i | −0.964091 | − | 0.265573i | \(-0.914439\pi\) |
0.550495 | + | 0.834838i | \(0.314439\pi\) | |||||||
\(888\) | −15.2117 | − | 20.9372i | −0.510473 | − | 0.702605i | ||||
\(889\) | 2.36769 | − | 7.28700i | 0.0794097 | − | 0.244398i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.79042 | − | 1.79264i | −0.0934827 | − | 0.0600556i | ||||
\(892\) | − | 4.33555i | − | 0.145165i | ||||||
\(893\) | 9.49533 | + | 3.08522i | 0.317749 | + | 0.103243i | ||||
\(894\) | −8.50860 | + | 6.18186i | −0.284570 | + | 0.206752i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.105680 | − | 0.325249i | −0.00353052 | − | 0.0108658i | ||||
\(897\) | −30.8997 | + | 10.0399i | −1.03171 | + | 0.335223i | ||||
\(898\) | 23.5433 | − | 32.4046i | 0.785652 | − | 1.08136i | ||||
\(899\) | −8.24886 | + | 5.99314i | −0.275115 | + | 0.199883i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −53.0889 | −1.76865 | ||||||||
\(902\) | 0.788357 | − | 0.307087i | 0.0262494 | − | 0.0102249i | ||||
\(903\) | 5.16716i | 0.171952i | ||||||||
\(904\) | 3.71243 | − | 11.4257i | 0.123474 | − | 0.380013i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −6.12105 | − | 4.44720i | −0.203358 | − | 0.147748i | ||||
\(907\) | −24.9565 | + | 8.10886i | −0.828667 | + | 0.269250i | −0.692484 | − | 0.721433i | \(-0.743484\pi\) |
−0.136183 | + | 0.990684i | \(0.543484\pi\) | |||||||
\(908\) | 6.42299 | − | 2.08695i | 0.213154 | − | 0.0692580i | ||||
\(909\) | −15.3080 | − | 11.1219i | −0.507736 | − | 0.368891i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.2556 | + | 37.7188i | −0.406045 | + | 1.24968i | 0.513974 | + | 0.857806i | \(0.328173\pi\) |
−0.920019 | + | 0.391873i | \(0.871827\pi\) | |||||||
\(912\) | 2.10999i | 0.0698687i | ||||||||
\(913\) | −6.52079 | + | 2.54003i | −0.215807 | + | 0.0840628i | ||||
\(914\) | 2.61128 | 0.0863734 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.25521 | + | 5.27122i | −0.239719 | + | 0.174166i | ||||
\(917\) | 4.85249 | − | 6.67887i | 0.160243 | − | 0.220556i | ||||
\(918\) | −8.10486 | + | 2.63343i | −0.267500 | + | 0.0869161i | ||||
\(919\) | −4.62777 | − | 14.2428i | −0.152656 | − | 0.469827i | 0.845260 | − | 0.534356i | \(-0.179446\pi\) |
−0.997916 | + | 0.0645285i | \(0.979446\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −19.2086 | + | 13.9558i | −0.632944 | + | 0.459861i | ||||
\(922\) | 29.7883 | + | 9.67881i | 0.981025 | + | 0.318754i | ||||
\(923\) | 3.16041i | 0.104026i | ||||||||
\(924\) | 1.57453 | + | 1.01152i | 0.0517983 | + | 0.0332765i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −10.3504 | + | 31.8554i | −0.340137 | + | 1.04683i | ||||
\(927\) | 10.6368 | + | 14.6403i | 0.349358 | + | 0.480850i | ||||
\(928\) | −3.28317 | + | 4.51890i | −0.107775 | + | 0.148340i | ||||
\(929\) | 15.3415 | + | 47.2162i | 0.503338 | + | 1.54911i | 0.803547 | + | 0.595241i | \(0.202943\pi\) |
−0.300210 | + | 0.953873i | \(0.597057\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.31143 | − | 4.58552i | −0.206849 | − | 0.150284i | ||||
\(932\) | 2.74717 | + | 3.78115i | 0.0899865 | + | 0.123856i | ||||
\(933\) | −21.9191 | − | 7.12194i | −0.717598 | − | 0.233162i | ||||
\(934\) | 4.09880 | 0.134117 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 14.4567 | 0.472530 | ||||||||
\(937\) | −51.6342 | − | 16.7770i | −1.68682 | − | 0.548079i | −0.700601 | − | 0.713553i | \(-0.747085\pi\) |
−0.986214 | + | 0.165474i | \(0.947085\pi\) | |||||||
\(938\) | 0.926120 | + | 1.27469i | 0.0302389 | + | 0.0416203i | ||||
\(939\) | −14.0476 | − | 10.2062i | −0.458427 | − | 0.333066i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.05826 | + | 6.33466i | 0.0670972 | + | 0.206504i | 0.978984 | − | 0.203938i | \(-0.0653743\pi\) |
−0.911886 | + | 0.410442i | \(0.865374\pi\) | |||||||
\(942\) | 7.30833 | − | 10.0590i | 0.238118 | − | 0.327742i | ||||
\(943\) | 0.943648 | + | 1.29882i | 0.0307294 | + | 0.0422954i | ||||
\(944\) | −1.92406 | + | 5.92164i | −0.0626227 | + | 0.192733i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.76390 | − | 25.7501i | 0.219913 | − | 0.837207i | ||||
\(947\) | − | 42.6250i | − | 1.38513i | −0.721358 | − | 0.692563i | \(-0.756482\pi\) | ||
0.721358 | − | 0.692563i | \(-0.243518\pi\) | |||||||
\(948\) | 1.73565 | + | 0.563947i | 0.0563713 | + | 0.0183161i | ||||
\(949\) | 19.0823 | − | 13.8641i | 0.619439 | − | 0.450049i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.90075 | − | 5.84990i | −0.0616360 | − | 0.189696i | ||||
\(952\) | 16.0017 | − | 5.19927i | 0.518619 | − | 0.168509i | ||||
\(953\) | 9.84772 | − | 13.5542i | 0.318999 | − | 0.439064i | −0.619162 | − | 0.785263i | \(-0.712528\pi\) |
0.938161 | + | 0.346199i | \(0.112528\pi\) | |||||||
\(954\) | 6.04622 | − | 4.39283i | 0.195754 | − | 0.142223i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 13.2264 | 0.427772 | ||||||||
\(957\) | 0.252069 | + | 4.39528i | 0.00814825 | + | 0.142079i | ||||
\(958\) | 1.03500i | 0.0334393i | ||||||||
\(959\) | 4.45110 | − | 13.6991i | 0.143733 | − | 0.442366i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.6539 | − | 16.4590i | −0.730772 | − | 0.530937i | ||||
\(962\) | 41.4271 | − | 13.4605i | 1.33566 | − | 0.433984i | ||||
\(963\) | −5.81994 | + | 1.89101i | −0.187545 | + | 0.0609370i | ||||
\(964\) | 2.13138 | + | 1.54854i | 0.0686470 | + | 0.0498750i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.64492 | − | 5.06254i | 0.0529244 | − | 0.162885i | ||||
\(967\) | − | 50.1233i | − | 1.61186i | −0.592014 | − | 0.805928i | \(-0.701667\pi\) | ||
0.592014 | − | 0.805928i | \(-0.298333\pi\) | |||||||
\(968\) | −22.8218 | − | 24.8493i | −0.733521 | − | 0.798687i | ||||
\(969\) | −9.33404 | −0.299853 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −32.4602 | + | 23.5837i | −1.04170 | + | 0.756837i | −0.970616 | − | 0.240633i | \(-0.922645\pi\) |
−0.0710811 | + | 0.997471i | \(0.522645\pi\) | |||||||
\(972\) | −0.470423 | + | 0.647481i | −0.0150888 | + | 0.0207680i | ||||
\(973\) | 5.47890 | − | 1.78020i | 0.175646 | − | 0.0570707i | ||||
\(974\) | 4.53113 | + | 13.9454i | 0.145187 | + | 0.446839i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −15.4696 | + | 11.2393i | −0.495170 | + | 0.359762i | ||||
\(977\) | −22.9853 | − | 7.46838i | −0.735365 | − | 0.238935i | −0.0826930 | − | 0.996575i | \(-0.526352\pi\) |
−0.652672 | + | 0.757640i | \(0.726352\pi\) | |||||||
\(978\) | 1.96335i | 0.0627809i | ||||||||
\(979\) | 11.0833 | − | 0.635626i | 0.354223 | − | 0.0203147i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.79082 | − | 8.58925i | 0.0891039 | − | 0.274234i | ||||
\(982\) | 1.79547 | + | 2.47125i | 0.0572958 | + | 0.0788608i | ||||
\(983\) | −13.6966 | + | 18.8518i | −0.436854 | + | 0.601278i | −0.969509 | − | 0.245055i | \(-0.921194\pi\) |
0.532656 | + | 0.846332i | \(0.321194\pi\) | |||||||
\(984\) | −0.220747 | − | 0.679388i | −0.00703715 | − | 0.0216581i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 9.15166 | + | 6.64907i | 0.291448 | + | 0.211750i | ||||
\(987\) | 3.44884 | + | 4.74692i | 0.109778 | + | 0.151096i | ||||
\(988\) | 4.30393 | + | 1.39843i | 0.136926 | + | 0.0444900i | ||||
\(989\) | 50.5195 | 1.60643 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −54.0689 | −1.71756 | −0.858778 | − | 0.512348i | \(-0.828776\pi\) | ||||
−0.858778 | + | 0.512348i | \(0.828776\pi\) | |||||||
\(992\) | −30.7405 | − | 9.98818i | −0.976011 | − | 0.317125i | ||||
\(993\) | 11.4143 | + | 15.7104i | 0.362220 | + | 0.498554i | ||||
\(994\) | −0.418906 | − | 0.304353i | −0.0132869 | − | 0.00965348i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.521833 | + | 1.60604i | 0.0165349 | + | 0.0508893i | ||||
\(997\) | 29.8071 | − | 41.0260i | 0.944001 | − | 1.29931i | −0.0101405 | − | 0.999949i | \(-0.503228\pi\) |
0.954141 | − | 0.299357i | \(-0.0967721\pi\) | |||||||
\(998\) | 11.4461 | + | 15.7542i | 0.362320 | + | 0.498691i | ||||
\(999\) | −2.60737 | + | 8.02466i | −0.0824935 | + | 0.253889i |
(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 | 825.2.bx.f.724.3 | 16 | ||
5.2 | odd | 4 | 825.2.n.g.526.1 | 8 | |||
5.3 | odd | 4 | 165.2.m.d.31.2 | yes | 8 | ||
5.4 | even | 2 | inner | 825.2.bx.f.724.2 | 16 | ||
11.5 | even | 5 | inner | 825.2.bx.f.49.2 | 16 | ||
15.8 | even | 4 | 495.2.n.a.361.1 | 8 | |||
55.7 | even | 20 | 9075.2.a.cm.1.4 | 4 | |||
55.18 | even | 20 | 1815.2.a.w.1.1 | 4 | |||
55.27 | odd | 20 | 825.2.n.g.676.1 | 8 | |||
55.37 | odd | 20 | 9075.2.a.di.1.1 | 4 | |||
55.38 | odd | 20 | 165.2.m.d.16.2 | ✓ | 8 | ||
55.48 | odd | 20 | 1815.2.a.p.1.4 | 4 | |||
55.49 | even | 10 | inner | 825.2.bx.f.49.3 | 16 | ||
165.38 | even | 20 | 495.2.n.a.181.1 | 8 | |||
165.128 | odd | 20 | 5445.2.a.bf.1.4 | 4 | |||
165.158 | even | 20 | 5445.2.a.bt.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.m.d.16.2 | ✓ | 8 | 55.38 | odd | 20 | ||
165.2.m.d.31.2 | yes | 8 | 5.3 | odd | 4 | ||
495.2.n.a.181.1 | 8 | 165.38 | even | 20 | |||
495.2.n.a.361.1 | 8 | 15.8 | even | 4 | |||
825.2.n.g.526.1 | 8 | 5.2 | odd | 4 | |||
825.2.n.g.676.1 | 8 | 55.27 | odd | 20 | |||
825.2.bx.f.49.2 | 16 | 11.5 | even | 5 | inner | ||
825.2.bx.f.49.3 | 16 | 55.49 | even | 10 | inner | ||
825.2.bx.f.724.2 | 16 | 5.4 | even | 2 | inner | ||
825.2.bx.f.724.3 | 16 | 1.1 | even | 1 | trivial | ||
1815.2.a.p.1.4 | 4 | 55.48 | odd | 20 | |||
1815.2.a.w.1.1 | 4 | 55.18 | even | 20 | |||
5445.2.a.bf.1.4 | 4 | 165.128 | odd | 20 | |||
5445.2.a.bt.1.1 | 4 | 165.158 | even | 20 | |||
9075.2.a.cm.1.4 | 4 | 55.7 | even | 20 | |||
9075.2.a.di.1.1 | 4 | 55.37 | odd | 20 |