Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1800,2,Mod(901,1800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1800.901");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1800.k (of order \(2\), degree \(1\), 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: | \(14.3730723638\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | 12.0.180227832610816.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + x^{10} - 8x^{6} + 16x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | no (minimal twist has level 120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 901.4 | ||
Root | \(-0.806504 - 1.16170i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1800.901 |
Dual form | 1800.2.k.u.901.3 |
$q$-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 \(\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1001\) | \(1351\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.806504 | + | 1.16170i | −0.570284 | + | 0.821447i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.699104 | − | 1.87383i | −0.349552 | − | 0.936917i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.746175 | 0.282028 | 0.141014 | − | 0.990008i | \(-0.454964\pi\) | ||||
0.141014 | + | 0.990008i | \(0.454964\pi\) | |||||||
\(8\) | 2.74067 | + | 0.699104i | 0.968972 | + | 0.247170i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.36068i | 1.61630i | 0.588974 | + | 0.808152i | \(0.299532\pi\) | ||||
−0.588974 | + | 0.808152i | \(0.700468\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.92520i | − | 0.811304i | −0.914028 | − | 0.405652i | \(-0.867045\pi\) | ||
0.914028 | − | 0.405652i | \(-0.132955\pi\) | |||||||
\(14\) | −0.601793 | + | 0.866833i | −0.160836 | + | 0.231671i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.02251 | + | 2.62001i | −0.755627 | + | 0.655002i | ||||
\(17\) | −2.13466 | −0.517731 | −0.258866 | − | 0.965913i | \(-0.583349\pi\) | ||||
−0.258866 | + | 0.965913i | \(0.583349\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.73367i | − | 0.397730i | −0.980027 | − | 0.198865i | \(-0.936274\pi\) | ||
0.980027 | − | 0.198865i | \(-0.0637255\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.22751 | − | 4.32340i | −1.32771 | − | 0.921753i | ||||
\(23\) | −7.49534 | −1.56289 | −0.781443 | − | 0.623977i | \(-0.785516\pi\) | ||||
−0.781443 | + | 0.623977i | \(0.785516\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.39821 | + | 2.35918i | 0.666443 | + | 0.462674i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.521653 | − | 1.39821i | −0.0985832 | − | 0.264236i | ||||
\(29\) | 6.74916i | 1.25329i | 0.779306 | + | 0.626644i | \(0.215572\pi\) | ||||
−0.779306 | + | 0.626644i | \(0.784428\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.64681 | 0.475381 | 0.237690 | − | 0.971341i | \(-0.423610\pi\) | ||||
0.237690 | + | 0.971341i | \(0.423610\pi\) | |||||||
\(32\) | −0.606006 | − | 5.62430i | −0.107128 | − | 0.994245i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.72161 | − | 2.47984i | 0.295254 | − | 0.425289i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.07480i | 0.176697i | 0.996090 | + | 0.0883483i | \(0.0281588\pi\) | ||||
−0.996090 | + | 0.0883483i | \(0.971841\pi\) | |||||||
\(38\) | 2.01400 | + | 1.39821i | 0.326714 | + | 0.226819i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.2936 | 1.76377 | 0.881883 | − | 0.471468i | \(-0.156276\pi\) | ||||
0.881883 | + | 0.471468i | \(0.156276\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.44322i | 1.13508i | 0.823346 | + | 0.567540i | \(0.192105\pi\) | ||||
−0.823346 | + | 0.567540i | \(0.807895\pi\) | |||||||
\(44\) | 10.0450 | − | 3.74767i | 1.51434 | − | 0.564982i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.04502 | − | 8.70735i | 0.891289 | − | 1.28383i | ||||
\(47\) | −1.73367 | −0.252881 | −0.126441 | − | 0.991974i | \(-0.540355\pi\) | ||||
−0.126441 | + | 0.991974i | \(0.540355\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.44322 | −0.920460 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.48133 | + | 2.04502i | −0.760124 | + | 0.283593i | ||||
\(53\) | − | 7.72161i | − | 1.06064i | −0.847796 | − | 0.530322i | \(-0.822071\pi\) | ||
0.847796 | − | 0.530322i | \(-0.177929\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.04502 | + | 0.521653i | 0.273277 | + | 0.0697089i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.84052 | − | 5.44322i | −1.02951 | − | 0.714730i | ||||
\(59\) | 6.85302i | 0.892188i | 0.894986 | + | 0.446094i | \(0.147185\pi\) | ||||
−0.894986 | + | 0.446094i | \(0.852815\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.45203i | 0.826098i | 0.910709 | + | 0.413049i | \(0.135536\pi\) | ||||
−0.910709 | + | 0.413049i | \(0.864464\pi\) | |||||||
\(62\) | −2.13466 | + | 3.07480i | −0.271102 | + | 0.390500i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.02251 | + | 3.83202i | 0.877813 | + | 0.479003i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.44322i | 0.909334i | 0.890661 | + | 0.454667i | \(0.150242\pi\) | ||||
−0.890661 | + | 0.454667i | \(0.849758\pi\) | |||||||
\(68\) | 1.49235 | + | 4.00000i | 0.180974 | + | 0.485071i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.2936 | −1.57766 | −0.788831 | − | 0.614610i | \(-0.789313\pi\) | ||||
−0.788831 | + | 0.614610i | \(0.789313\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.690358 | −0.0808003 | −0.0404002 | − | 0.999184i | \(-0.512863\pi\) | ||||
−0.0404002 | + | 0.999184i | \(0.512863\pi\) | |||||||
\(74\) | −1.24860 | − | 0.866833i | −0.145147 | − | 0.100767i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.24860 | + | 1.21201i | −0.372640 | + | 0.139027i | ||||
\(77\) | 4.00000i | 0.455842i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.64681 | 0.297789 | 0.148895 | − | 0.988853i | \(-0.452428\pi\) | ||||
0.148895 | + | 0.988853i | \(0.452428\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −9.10834 | + | 13.1198i | −1.00585 | + | 1.44884i | ||||
\(83\) | 5.85039i | 0.642164i | 0.947051 | + | 0.321082i | \(0.104047\pi\) | ||||
−0.947051 | + | 0.321082i | \(0.895953\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −8.64681 | − | 6.00299i | −0.932409 | − | 0.647319i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.74767 | + | 14.6918i | −0.399503 | + | 1.56615i | ||||
\(89\) | −7.59283 | −0.804838 | −0.402419 | − | 0.915456i | \(-0.631831\pi\) | ||||
−0.402419 | + | 0.915456i | \(0.631831\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 2.18271i | − | 0.228810i | ||||||
\(92\) | 5.24002 | + | 14.0450i | 0.546310 | + | 1.46429i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.39821 | − | 2.01400i | 0.144214 | − | 0.207729i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.1887 | −1.44064 | −0.720321 | − | 0.693641i | \(-0.756006\pi\) | ||||
−0.720321 | + | 0.693641i | \(0.756006\pi\) | |||||||
\(98\) | 5.19648 | − | 7.48511i | 0.524924 | − | 0.756110i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 7.43952i | − | 0.740260i | −0.928980 | − | 0.370130i | \(-0.879313\pi\) | ||
0.928980 | − | 0.370130i | \(-0.120687\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.19820 | 0.709260 | 0.354630 | − | 0.935007i | \(-0.384607\pi\) | ||||
0.354630 | + | 0.935007i | \(0.384607\pi\) | |||||||
\(104\) | 2.04502 | − | 8.01699i | 0.200530 | − | 0.786131i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.97021 | + | 6.22751i | 0.871264 | + | 0.604869i | ||||
\(107\) | − | 4.00000i | − | 0.386695i | −0.981130 | − | 0.193347i | \(-0.938066\pi\) | ||
0.981130 | − | 0.193347i | \(-0.0619344\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 19.9504i | 1.91090i | 0.295158 | + | 0.955449i | \(0.404628\pi\) | ||||
−0.295158 | + | 0.955449i | \(0.595372\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.25532 | + | 1.95498i | −0.213108 | + | 0.184729i | ||||
\(113\) | −12.0540 | −1.13395 | −0.566973 | − | 0.823736i | \(-0.691886\pi\) | ||||
−0.566973 | + | 0.823736i | \(0.691886\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 12.6468 | − | 4.71836i | 1.17423 | − | 0.438089i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.96117 | − | 5.52699i | −0.732885 | − | 0.508801i | ||||
\(119\) | −1.59283 | −0.146014 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −17.7368 | −1.61244 | ||||||||
\(122\) | −7.49534 | − | 5.20359i | −0.678596 | − | 0.471110i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.85039 | − | 4.95968i | −0.166170 | − | 0.445392i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.21351 | −0.373888 | −0.186944 | − | 0.982371i | \(-0.559858\pi\) | ||||
−0.186944 | + | 0.982371i | \(0.559858\pi\) | |||||||
\(128\) | −10.1153 | + | 5.06752i | −0.894079 | + | 0.447910i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.3204i | 0.901694i | 0.892601 | + | 0.450847i | \(0.148878\pi\) | ||||
−0.892601 | + | 0.450847i | \(0.851122\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 1.29362i | − | 0.112171i | ||||||
\(134\) | −8.64681 | − | 6.00299i | −0.746970 | − | 0.518579i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.85039 | − | 1.49235i | −0.501667 | − | 0.127968i | ||||
\(137\) | −15.0387 | −1.28484 | −0.642422 | − | 0.766351i | \(-0.722070\pi\) | ||||
−0.642422 | + | 0.766351i | \(0.722070\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.47032i | 0.803262i | 0.915802 | + | 0.401631i | \(0.131557\pi\) | ||||
−0.915802 | + | 0.401631i | \(0.868443\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 10.7214 | − | 15.4432i | 0.899716 | − | 1.29597i | ||||
\(143\) | 15.6810 | 1.31131 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.556777 | − | 0.801991i | 0.0460792 | − | 0.0663732i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.01400 | − | 0.751399i | 0.165550 | − | 0.0617646i | ||||
\(149\) | 1.78948i | 0.146600i | 0.997310 | + | 0.0733000i | \(0.0233531\pi\) | ||||
−0.997310 | + | 0.0733000i | \(0.976647\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.6468 | 0.866425 | 0.433212 | − | 0.901292i | \(-0.357380\pi\) | ||||
0.433212 | + | 0.901292i | \(0.357380\pi\) | |||||||
\(152\) | 1.21201 | − | 4.75140i | 0.0983071 | − | 0.385389i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.64681 | − | 3.22601i | −0.374451 | − | 0.259960i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 6.92520i | − | 0.552691i | −0.961058 | − | 0.276345i | \(-0.910877\pi\) | ||
0.961058 | − | 0.276345i | \(-0.0891234\pi\) | |||||||
\(158\) | −2.13466 | + | 3.07480i | −0.169824 | + | 0.244618i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.59283 | −0.440777 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.70079i | 0.603172i | 0.953439 | + | 0.301586i | \(0.0975161\pi\) | ||||
−0.953439 | + | 0.301586i | \(0.902484\pi\) | |||||||
\(164\) | −7.89541 | − | 21.1624i | −0.616528 | − | 1.65250i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.79641 | − | 4.71836i | −0.527504 | − | 0.366216i | ||||
\(167\) | 3.22601 | 0.249637 | 0.124818 | − | 0.992180i | \(-0.460165\pi\) | ||||
0.124818 | + | 0.992180i | \(0.460165\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.44322 | 0.341786 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 13.9474 | − | 5.20359i | 1.06348 | − | 0.396770i | ||||
\(173\) | 6.42799i | 0.488711i | 0.969686 | + | 0.244356i | \(0.0785764\pi\) | ||||
−0.969686 | + | 0.244356i | \(0.921424\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −14.0450 | − | 16.2027i | −1.05868 | − | 1.22132i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.12364 | − | 8.82061i | 0.458987 | − | 0.661132i | ||||
\(179\) | 8.13765i | 0.608236i | 0.952634 | + | 0.304118i | \(0.0983618\pi\) | ||||
−0.952634 | + | 0.304118i | \(0.901638\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.49235i | 0.110925i | 0.998461 | + | 0.0554627i | \(0.0176634\pi\) | ||||
−0.998461 | + | 0.0554627i | \(0.982337\pi\) | |||||||
\(182\) | 2.53566 | + | 1.76036i | 0.187955 | + | 0.130487i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −20.5422 | − | 5.24002i | −1.51439 | − | 0.386299i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 11.4432i | − | 0.836811i | ||||||
\(188\) | 1.21201 | + | 3.24860i | 0.0883951 | + | 0.236929i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.88645 | −0.498286 | −0.249143 | − | 0.968467i | \(-0.580149\pi\) | ||||
−0.249143 | + | 0.968467i | \(0.580149\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.4830 | −1.18647 | −0.593237 | − | 0.805028i | \(-0.702150\pi\) | ||||
−0.593237 | + | 0.805028i | \(0.702150\pi\) | |||||||
\(194\) | 11.4432 | − | 16.4830i | 0.821576 | − | 1.18341i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.50448 | + | 12.0735i | 0.321749 | + | 0.862395i | ||||
\(197\) | − | 13.5720i | − | 0.966965i | −0.875354 | − | 0.483483i | \(-0.839372\pi\) | ||
0.875354 | − | 0.483483i | \(-0.160628\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.05398 | 0.641820 | 0.320910 | − | 0.947110i | \(-0.396011\pi\) | ||||
0.320910 | + | 0.947110i | \(0.396011\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 8.64251 | + | 6.00000i | 0.608085 | + | 0.422159i | ||||
\(203\) | 5.03605i | 0.353462i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −5.80538 | + | 8.36217i | −0.404480 | + | 0.582620i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 7.66404 | + | 8.84143i | 0.531406 | + | 0.613043i | ||||
\(209\) | 9.29362 | 0.642853 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 2.53566i | − | 0.174562i | −0.996184 | − | 0.0872809i | \(-0.972182\pi\) | ||
0.996184 | − | 0.0872809i | \(-0.0278178\pi\) | |||||||
\(212\) | −14.4690 | + | 5.39821i | −0.993736 | + | 0.370750i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.64681 | + | 3.22601i | 0.317649 | + | 0.220526i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.97498 | 0.134070 | ||||||||
\(218\) | −23.1764 | − | 16.0900i | −1.56970 | − | 1.08975i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.24430i | 0.420037i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.1579 | 0.814152 | 0.407076 | − | 0.913394i | \(-0.366548\pi\) | ||||
0.407076 | + | 0.913394i | \(0.366548\pi\) | |||||||
\(224\) | −0.452186 | − | 4.19671i | −0.0302130 | − | 0.280405i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.72161 | − | 14.0032i | 0.646672 | − | 0.931478i | ||||
\(227\) | 20.7368i | 1.37635i | 0.725544 | + | 0.688176i | \(0.241588\pi\) | ||||
−0.725544 | + | 0.688176i | \(0.758412\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 19.9504i | − | 1.31836i | −0.751987 | − | 0.659178i | \(-0.770904\pi\) | ||
0.751987 | − | 0.659178i | \(-0.229096\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.71836 | + | 18.4972i | −0.309776 | + | 1.21440i | ||||
\(233\) | 13.3386 | 0.873844 | 0.436922 | − | 0.899499i | \(-0.356069\pi\) | ||||
0.436922 | + | 0.899499i | \(0.356069\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 12.8414 | − | 4.79097i | 0.835906 | − | 0.311866i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.28462 | − | 1.85039i | 0.0832697 | − | 0.119943i | ||||
\(239\) | −22.8864 | −1.48040 | −0.740201 | − | 0.672386i | \(-0.765269\pi\) | ||||
−0.740201 | + | 0.672386i | \(0.765269\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.59283 | 0.231435 | 0.115717 | − | 0.993282i | \(-0.463083\pi\) | ||||
0.115717 | + | 0.993282i | \(0.463083\pi\) | |||||||
\(242\) | 14.3048 | − | 20.6049i | 0.919549 | − | 1.32453i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 12.0900 | − | 4.51064i | 0.773985 | − | 0.288764i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.07131 | −0.322680 | ||||||||
\(248\) | 7.25402 | + | 1.85039i | 0.460631 | + | 0.117500i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 8.82801i | − | 0.557219i | −0.960404 | − | 0.278609i | \(-0.910127\pi\) | ||
0.960404 | − | 0.278609i | \(-0.0898735\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 40.1801i | − | 2.52610i | ||||||
\(254\) | 3.39821 | − | 4.89484i | 0.213222 | − | 0.307129i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.27111 | − | 15.8380i | 0.141944 | − | 0.989875i | ||||
\(257\) | 22.2927 | 1.39058 | 0.695291 | − | 0.718728i | \(-0.255275\pi\) | ||||
0.695291 | + | 0.718728i | \(0.255275\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.801991i | 0.0498333i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −11.9892 | − | 8.32340i | −0.740694 | − | 0.514222i | ||||
\(263\) | 21.2014 | 1.30733 | 0.653667 | − | 0.756783i | \(-0.273230\pi\) | ||||
0.653667 | + | 0.756783i | \(0.273230\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.50280 | + | 1.04331i | 0.0921424 | + | 0.0639693i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 13.9474 | − | 5.20359i | 0.851971 | − | 0.317860i | ||||
\(269\) | 14.6935i | 0.895881i | 0.894063 | + | 0.447940i | \(0.147842\pi\) | ||||
−0.894063 | + | 0.447940i | \(0.852158\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.2396 | −1.22947 | −0.614735 | − | 0.788734i | \(-0.710737\pi\) | ||||
−0.614735 | + | 0.788734i | \(0.710737\pi\) | |||||||
\(272\) | 6.45203 | − | 5.59283i | 0.391212 | − | 0.339115i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.1288 | − | 17.4705i | 0.732727 | − | 1.05543i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 0.518027i | − | 0.0311252i | −0.999879 | − | 0.0155626i | \(-0.995046\pi\) | ||
0.999879 | − | 0.0155626i | \(-0.00495393\pi\) | |||||||
\(278\) | −11.0017 | − | 7.63785i | −0.659837 | − | 0.458088i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.7008 | −0.817320 | −0.408660 | − | 0.912687i | \(-0.634004\pi\) | ||||
−0.408660 | + | 0.912687i | \(0.634004\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.0305i | 1.07180i | 0.844282 | + | 0.535900i | \(0.180027\pi\) | ||||
−0.844282 | + | 0.535900i | \(0.819973\pi\) | |||||||
\(284\) | 9.29362 | + | 24.9100i | 0.551475 | + | 1.47814i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −12.6468 | + | 18.2167i | −0.747821 | + | 1.07718i | ||||
\(287\) | 8.42701 | 0.497431 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.4432 | −0.731954 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.482632 | + | 1.29362i | 0.0282439 | + | 0.0757032i | ||||
\(293\) | − | 15.9792i | − | 0.933513i | −0.884386 | − | 0.466757i | \(-0.845422\pi\) | ||
0.884386 | − | 0.466757i | \(-0.154578\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.751399 | + | 2.94568i | −0.0436742 | + | 0.171214i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.07884 | − | 1.44322i | −0.120424 | − | 0.0836037i | ||||
\(299\) | 21.9253i | 1.26797i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.55394i | 0.320124i | ||||||||
\(302\) | −8.58669 | + | 12.3684i | −0.494108 | + | 0.711723i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.54222 | + | 5.24002i | 0.260514 | + | 0.300536i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.5872i | 1.28912i | 0.764553 | + | 0.644561i | \(0.222960\pi\) | ||||
−0.764553 | + | 0.644561i | \(0.777040\pi\) | |||||||
\(308\) | 7.49534 | − | 2.79641i | 0.427086 | − | 0.159341i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.5872 | 1.05399 | 0.526993 | − | 0.849870i | \(-0.323320\pi\) | ||||
0.526993 | + | 0.849870i | \(0.323320\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −29.3871 | −1.66106 | −0.830528 | − | 0.556977i | \(-0.811961\pi\) | ||||
−0.830528 | + | 0.556977i | \(0.811961\pi\) | |||||||
\(314\) | 8.04502 | + | 5.58520i | 0.454007 | + | 0.315191i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.85039 | − | 4.95968i | −0.104093 | − | 0.279004i | ||||
\(317\) | − | 5.57201i | − | 0.312955i | −0.987682 | − | 0.156478i | \(-0.949986\pi\) | ||
0.987682 | − | 0.156478i | \(-0.0500139\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −36.1801 | −2.02569 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.51064 | − | 6.49720i | 0.251368 | − | 0.362075i | ||||
\(323\) | 3.70079i | 0.205917i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8.94602 | − | 6.21071i | −0.495474 | − | 0.343980i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 30.9520 | + | 7.89541i | 1.70904 | + | 0.435951i | ||||
\(329\) | −1.29362 | −0.0713194 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 13.7396i | − | 0.755199i | −0.925969 | − | 0.377599i | \(-0.876750\pi\) | ||
0.925969 | − | 0.377599i | \(-0.123250\pi\) | |||||||
\(332\) | 10.9627 | − | 4.09003i | 0.601655 | − | 0.224470i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.60179 | + | 3.74767i | −0.142364 | + | 0.205063i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.7523 | 1.13045 | 0.565226 | − | 0.824936i | \(-0.308789\pi\) | ||||
0.565226 | + | 0.824936i | \(0.308789\pi\) | |||||||
\(338\) | −3.58348 | + | 5.16170i | −0.194915 | + | 0.280760i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.1887i | 0.768360i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0310 | −0.541623 | ||||||||
\(344\) | −5.20359 | + | 20.3994i | −0.280559 | + | 1.09986i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.46742 | − | 5.18420i | −0.401451 | − | 0.278704i | ||||
\(347\) | − | 4.73684i | − | 0.254287i | −0.991884 | − | 0.127143i | \(-0.959419\pi\) | ||
0.991884 | − | 0.127143i | \(-0.0405809\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 0.482632i | − | 0.0258347i | −0.999917 | − | 0.0129174i | \(-0.995888\pi\) | ||
0.999917 | − | 0.0129174i | \(-0.00411184\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 30.1500 | − | 3.24860i | 1.60700 | − | 0.173151i | ||||
\(353\) | 2.13466 | 0.113617 | 0.0568083 | − | 0.998385i | \(-0.481908\pi\) | ||||
0.0568083 | + | 0.998385i | \(0.481908\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.30818 | + | 14.2277i | 0.281333 | + | 0.754067i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.45352 | − | 6.56304i | −0.499634 | − | 0.346868i | ||||
\(359\) | 9.59283 | 0.506290 | 0.253145 | − | 0.967428i | \(-0.418535\pi\) | ||||
0.253145 | + | 0.967428i | \(0.418535\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.9944 | 0.841811 | ||||||||
\(362\) | −1.73367 | − | 1.20359i | −0.0911194 | − | 0.0632590i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.09003 | + | 1.52594i | −0.214376 | + | 0.0799809i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 34.0832 | 1.77913 | 0.889565 | − | 0.456809i | \(-0.151008\pi\) | ||||
0.889565 | + | 0.456809i | \(0.151008\pi\) | |||||||
\(368\) | 22.6547 | − | 19.6378i | 1.18096 | − | 1.02369i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 5.76167i | − | 0.299131i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.33796i | 0.224611i | 0.993674 | + | 0.112306i | \(0.0358236\pi\) | ||||
−0.993674 | + | 0.112306i | \(0.964176\pi\) | |||||||
\(374\) | 13.2936 | + | 9.22900i | 0.687397 | + | 0.477220i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.75140 | − | 1.21201i | −0.245035 | − | 0.0625047i | ||||
\(377\) | 19.7426 | 1.01680 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.90107i | 0.354484i | 0.984167 | + | 0.177242i | \(0.0567176\pi\) | ||||
−0.984167 | + | 0.177242i | \(0.943282\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.55394 | − | 8.00000i | 0.284165 | − | 0.409316i | ||||
\(383\) | −22.3744 | −1.14328 | −0.571639 | − | 0.820506i | \(-0.693692\pi\) | ||||
−0.571639 | + | 0.820506i | \(0.693692\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 13.2936 | − | 19.1484i | 0.676627 | − | 0.974626i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 9.91936 | + | 26.5872i | 0.503579 | + | 1.34976i | ||||
\(389\) | − | 11.0185i | − | 0.558659i | −0.960195 | − | 0.279330i | \(-0.909888\pi\) | ||
0.960195 | − | 0.279330i | \(-0.0901122\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.0000 | 0.809155 | ||||||||
\(392\) | −17.6587 | − | 4.50448i | −0.891900 | − | 0.227511i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 15.7666 | + | 10.9459i | 0.794311 | + | 0.551445i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 25.2549i | − | 1.26751i | −0.773536 | − | 0.633753i | \(-0.781514\pi\) | ||
0.773536 | − | 0.633753i | \(-0.218486\pi\) | |||||||
\(398\) | −7.30207 | + | 10.5180i | −0.366020 | + | 0.527221i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.29362 | −0.364226 | −0.182113 | − | 0.983278i | \(-0.558294\pi\) | ||||
−0.182113 | + | 0.983278i | \(0.558294\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 7.74244i | − | 0.385678i | ||||||
\(404\) | −13.9404 | + | 5.20100i | −0.693562 | + | 0.258759i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.85039 | − | 4.06160i | −0.290350 | − | 0.201574i | ||||
\(407\) | −5.76167 | −0.285595 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.8504 | 0.783752 | 0.391876 | − | 0.920018i | \(-0.371826\pi\) | ||||
0.391876 | + | 0.920018i | \(0.371826\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.03229 | − | 13.4882i | −0.247923 | − | 0.664518i | ||||
\(413\) | 5.11355i | 0.251622i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −16.4522 | + | 1.77269i | −0.806635 | + | 0.0869131i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −7.49534 | + | 10.7964i | −0.366609 | + | 0.528070i | ||||
\(419\) | − | 8.02602i | − | 0.392097i | −0.980594 | − | 0.196048i | \(-0.937189\pi\) | ||
0.980594 | − | 0.196048i | \(-0.0628109\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 22.9351i | − | 1.11779i | −0.829240 | − | 0.558893i | \(-0.811226\pi\) | ||
0.829240 | − | 0.558893i | \(-0.188774\pi\) | |||||||
\(422\) | 2.94568 | + | 2.04502i | 0.143393 | + | 0.0995498i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.39821 | − | 21.1624i | 0.262160 | − | 1.02774i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.81434i | 0.232982i | ||||||||
\(428\) | −7.49534 | + | 2.79641i | −0.362301 | + | 0.135170i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 35.0665 | 1.68909 | 0.844547 | − | 0.535481i | \(-0.179870\pi\) | ||||
0.844547 | + | 0.535481i | \(0.179870\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.0773 | 0.820682 | 0.410341 | − | 0.911932i | \(-0.365410\pi\) | ||||
0.410341 | + | 0.911932i | \(0.365410\pi\) | |||||||
\(434\) | −1.59283 | + | 2.29434i | −0.0764583 | + | 0.110132i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 37.3836 | − | 13.9474i | 1.79035 | − | 0.667958i | ||||
\(437\) | 12.9944i | 0.621607i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.53885 | 0.407537 | 0.203769 | − | 0.979019i | \(-0.434681\pi\) | ||||
0.203769 | + | 0.979019i | \(0.434681\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −7.25402 | − | 5.03605i | −0.345039 | − | 0.239541i | ||||
\(443\) | 20.7368i | 0.985237i | 0.870245 | + | 0.492619i | \(0.163960\pi\) | ||||
−0.870245 | + | 0.492619i | \(0.836040\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −9.80538 | + | 14.1238i | −0.464298 | + | 0.668783i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 5.24002 | + | 2.85936i | 0.247568 | + | 0.135092i | ||||
\(449\) | 2.00000 | 0.0943858 | 0.0471929 | − | 0.998886i | \(-0.484972\pi\) | ||||
0.0471929 | + | 0.998886i | \(0.484972\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 60.5414i | 2.85078i | ||||||||
\(452\) | 8.42701 | + | 22.5872i | 0.396373 | + | 1.06241i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −24.0900 | − | 16.7243i | −1.13060 | − | 0.784912i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.28462 | 0.0600921 | 0.0300461 | − | 0.999549i | \(-0.490435\pi\) | ||||
0.0300461 | + | 0.999549i | \(0.490435\pi\) | |||||||
\(458\) | 23.1764 | + | 16.0900i | 1.08296 | + | 0.751838i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.7033i | 0.731374i | 0.930738 | + | 0.365687i | \(0.119166\pi\) | ||||
−0.930738 | + | 0.365687i | \(0.880834\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.7215 | 0.870064 | 0.435032 | − | 0.900415i | \(-0.356737\pi\) | ||||
0.435032 | + | 0.900415i | \(0.356737\pi\) | |||||||
\(464\) | −17.6829 | − | 20.3994i | −0.820906 | − | 0.947018i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.7577 | + | 15.4955i | −0.498339 | + | 0.717817i | ||||
\(467\) | − | 2.14961i | − | 0.0994719i | −0.998762 | − | 0.0497360i | \(-0.984162\pi\) | ||
0.998762 | − | 0.0497360i | \(-0.0158380\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.55394i | 0.256457i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.79097 | + | 18.7819i | −0.220522 | + | 0.864505i | ||||
\(473\) | −39.9007 | −1.83464 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.11355 | + | 2.98470i | 0.0510396 | + | 0.136803i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 18.4580 | − | 26.5872i | 0.844249 | − | 1.21607i | ||||
\(479\) | 12.1801 | 0.556521 | 0.278261 | − | 0.960506i | \(-0.410242\pi\) | ||||
0.278261 | + | 0.960506i | \(0.410242\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.14401 | 0.143355 | ||||||||
\(482\) | −2.89763 | + | 4.17380i | −0.131983 | + | 0.190111i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 12.3999 | + | 33.2359i | 0.563631 | + | 1.51072i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.7678 | 1.16765 | 0.583826 | − | 0.811879i | \(-0.301555\pi\) | ||||
0.583826 | + | 0.811879i | \(0.301555\pi\) | |||||||
\(488\) | −4.51064 | + | 17.6829i | −0.204187 | + | 0.800466i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 16.7724i | − | 0.756927i | −0.925616 | − | 0.378464i | \(-0.876453\pi\) | ||
0.925616 | − | 0.378464i | \(-0.123547\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 14.4072i | − | 0.648866i | ||||||
\(494\) | 4.09003 | − | 5.89135i | 0.184019 | − | 0.265065i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.00000 | + | 6.93466i | −0.359211 | + | 0.311375i | ||||
\(497\) | −9.91936 | −0.444944 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 17.6224i | − | 0.788888i | −0.918920 | − | 0.394444i | \(-0.870937\pi\) | ||
0.918920 | − | 0.394444i | \(-0.129063\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 10.2555 | + | 7.11982i | 0.457726 | + | 0.317773i | ||||
\(503\) | 27.1263 | 1.20950 | 0.604752 | − | 0.796414i | \(-0.293272\pi\) | ||||
0.604752 | + | 0.796414i | \(0.293272\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 46.6773 | + | 32.4054i | 2.07506 | + | 1.44059i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.94568 | + | 7.89541i | 0.130693 | + | 0.350302i | ||||
\(509\) | − | 15.9782i | − | 0.708220i | −0.935204 | − | 0.354110i | \(-0.884784\pi\) | ||
0.935204 | − | 0.354110i | \(-0.115216\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.515128 | −0.0227879 | ||||||||
\(512\) | 16.5674 | + | 15.4118i | 0.732181 | + | 0.681110i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −17.9792 | + | 25.8975i | −0.793027 | + | 1.14229i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 9.29362i | − | 0.408733i | ||||||
\(518\) | −0.931674 | − | 0.646809i | −0.0409354 | − | 0.0284191i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.886447 | −0.0388359 | −0.0194180 | − | 0.999811i | \(-0.506181\pi\) | ||||
−0.0194180 | + | 0.999811i | \(0.506181\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 41.7729i | 1.82660i | 0.407286 | + | 0.913301i | \(0.366475\pi\) | ||||
−0.407286 | + | 0.913301i | \(0.633525\pi\) | |||||||
\(524\) | 19.3386 | − | 7.21500i | 0.844812 | − | 0.315189i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −17.0990 | + | 24.6297i | −0.745552 | + | 1.07391i | ||||
\(527\) | −5.65004 | −0.246120 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 33.1801 | 1.44261 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.42402 | + | 0.904373i | −0.105095 | + | 0.0392095i | ||||
\(533\) | − | 33.0361i | − | 1.43095i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −5.20359 | + | 20.3994i | −0.224761 | + | 0.881120i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −17.0695 | − | 11.8504i | −0.735919 | − | 0.510907i | ||||
\(539\) | − | 34.5400i | − | 1.48774i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.47705i | 0.192483i | 0.995358 | + | 0.0962417i | \(0.0306822\pi\) | ||||
−0.995358 | + | 0.0962417i | \(0.969318\pi\) | |||||||
\(542\) | 16.3233 | − | 23.5124i | 0.701148 | − | 1.00995i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.29362 | + | 12.0060i | 0.0554634 | + | 0.514752i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.3297i | 0.612692i | 0.951920 | + | 0.306346i | \(0.0991065\pi\) | ||||
−0.951920 | + | 0.306346i | \(0.900893\pi\) | |||||||
\(548\) | 10.5136 | + | 28.1801i | 0.449120 | + | 1.20379i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.7008 | 0.498470 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.97498 | 0.0839848 | ||||||||
\(554\) | 0.601793 | + | 0.417790i | 0.0255677 | + | 0.0177502i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 17.7458 | − | 6.62073i | 0.752590 | − | 0.280782i | ||||
\(557\) | 2.68556i | 0.113791i | 0.998380 | + | 0.0568954i | \(0.0181201\pi\) | ||||
−0.998380 | + | 0.0568954i | \(0.981880\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.7729 | 0.920895 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 11.0497 | − | 15.9162i | 0.466105 | − | 0.671386i | ||||
\(563\) | − | 20.7368i | − | 0.873954i | −0.899473 | − | 0.436977i | \(-0.856049\pi\) | ||
0.899473 | − | 0.436977i | \(-0.143951\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −20.9460 | − | 14.5416i | −0.880427 | − | 0.611230i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −36.4334 | − | 9.29362i | −1.52871 | − | 0.389952i | ||||
\(569\) | −4.40717 | −0.184758 | −0.0923791 | − | 0.995724i | \(-0.529447\pi\) | ||||
−0.0923791 | + | 0.995724i | \(0.529447\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 23.6590i | − | 0.990098i | −0.868865 | − | 0.495049i | \(-0.835150\pi\) | ||
0.868865 | − | 0.495049i | \(-0.164850\pi\) | |||||||
\(572\) | −10.9627 | − | 29.3836i | −0.458372 | − | 1.22859i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6.79641 | + | 9.78968i | −0.283677 | + | 0.408613i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.56366 | −0.273249 | −0.136624 | − | 0.990623i | \(-0.543625\pi\) | ||||
−0.136624 | + | 0.990623i | \(0.543625\pi\) | |||||||
\(578\) | 10.0355 | − | 14.4553i | 0.417422 | − | 0.601262i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.36542i | 0.181108i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 41.3931 | 1.71433 | ||||||||
\(584\) | −1.89204 | − | 0.482632i | −0.0782933 | − | 0.0199715i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18.5630 | + | 12.8873i | 0.766832 | + | 0.532368i | ||||
\(587\) | − | 16.2992i | − | 0.672741i | −0.941730 | − | 0.336370i | \(-0.890801\pi\) | ||
0.941730 | − | 0.336370i | \(-0.109199\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 4.58868i | − | 0.189073i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.81599 | − | 3.24860i | −0.115737 | − | 0.133517i | ||||
\(593\) | 16.3233 | 0.670319 | 0.335160 | − | 0.942161i | \(-0.391210\pi\) | ||||
0.335160 | + | 0.942161i | \(0.391210\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.35319 | − | 1.25103i | 0.137352 | − | 0.0512443i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −25.4707 | − | 17.6829i | −1.04157 | − | 0.723106i | ||||
\(599\) | 25.5928 | 1.04569 | 0.522847 | − | 0.852426i | \(-0.324870\pi\) | ||||
0.522847 | + | 0.852426i | \(0.324870\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.9225 | 1.22056 | 0.610282 | − | 0.792184i | \(-0.291056\pi\) | ||||
0.610282 | + | 0.792184i | \(0.291056\pi\) | |||||||
\(602\) | −6.45203 | − | 4.47928i | −0.262965 | − | 0.182562i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7.44322 | − | 19.9504i | −0.302860 | − | 0.811768i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.6965 | −0.840046 | −0.420023 | − | 0.907513i | \(-0.637978\pi\) | ||||
−0.420023 | + | 0.907513i | \(0.637978\pi\) | |||||||
\(608\) | −9.75065 | + | 1.05061i | −0.395441 | + | 0.0426079i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.07131i | 0.205163i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.6676i | 0.915537i | 0.889071 | + | 0.457769i | \(0.151351\pi\) | ||||
−0.889071 | + | 0.457769i | \(0.848649\pi\) | |||||||
\(614\) | −26.2396 | − | 18.2167i | −1.05895 | − | 0.735166i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.79641 | + | 10.9627i | −0.112671 | + | 0.441698i | ||||
\(617\) | −22.1966 | −0.893603 | −0.446802 | − | 0.894633i | \(-0.647437\pi\) | ||||
−0.446802 | + | 0.894633i | \(0.647437\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.8204i | 0.676070i | 0.941133 | + | 0.338035i | \(0.109762\pi\) | ||||
−0.941133 | + | 0.338035i | \(0.890238\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −14.9907 | + | 21.5928i | −0.601071 | + | 0.865794i | ||||
\(623\) | −5.66558 | −0.226987 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 23.7008 | − | 34.1390i | 0.947274 | − | 1.36447i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −12.9767 | + | 4.84143i | −0.517825 | + | 0.193194i | ||||
\(629\) | − | 2.29434i | − | 0.0914813i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −44.1205 | −1.75641 | −0.878204 | − | 0.478285i | \(-0.841258\pi\) | ||||
−0.878204 | + | 0.478285i | \(0.841258\pi\) | |||||||
\(632\) | 7.25402 | + | 1.85039i | 0.288549 | + | 0.0736047i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6.47301 | + | 4.49384i | 0.257076 | + | 0.178473i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18.8477i | 0.746773i | ||||||||
\(638\) | 29.1794 | − | 42.0305i | 1.15522 | − | 1.66400i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.18566 | 0.0468307 | 0.0234154 | − | 0.999726i | \(-0.492546\pi\) | ||||
0.0234154 | + | 0.999726i | \(0.492546\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 22.5872i | − | 0.890754i | −0.895343 | − | 0.445377i | \(-0.853070\pi\) | ||
0.895343 | − | 0.445377i | \(-0.146930\pi\) | |||||||
\(644\) | 3.90997 | + | 10.4800i | 0.154074 | + | 0.412971i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.29921 | − | 2.98470i | −0.169150 | − | 0.117431i | ||||
\(647\) | 19.7090 | 0.774842 | 0.387421 | − | 0.921903i | \(-0.373366\pi\) | ||||
0.387421 | + | 0.921903i | \(0.373366\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −36.7368 | −1.44205 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 14.4300 | − | 5.38365i | 0.565122 | − | 0.210840i | ||||
\(653\) | 44.4585i | 1.73979i | 0.493234 | + | 0.869897i | \(0.335815\pi\) | ||||
−0.493234 | + | 0.869897i | \(0.664185\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −34.1350 | + | 29.5894i | −1.33275 | + | 1.15527i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.04331 | − | 1.50280i | 0.0406723 | − | 0.0585852i | ||||
\(659\) | − | 41.5863i | − | 1.61997i | −0.586448 | − | 0.809987i | \(-0.699474\pi\) | ||
0.586448 | − | 0.809987i | \(-0.300526\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.0060i | 0.466978i | 0.972359 | + | 0.233489i | \(0.0750143\pi\) | ||||
−0.972359 | + | 0.233489i | \(0.924986\pi\) | |||||||
\(662\) | 15.9614 | + | 11.0811i | 0.620356 | + | 0.430678i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.09003 | + | 16.0340i | −0.158724 | + | 0.622239i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 50.5872i | − | 1.95875i | ||||||
\(668\) | −2.25532 | − | 6.04502i | −0.0872609 | − | 0.233889i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −34.5872 | −1.33523 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.5080 | 0.559244 | 0.279622 | − | 0.960110i | \(-0.409791\pi\) | ||||
0.279622 | + | 0.960110i | \(0.409791\pi\) | |||||||
\(674\) | −16.7368 | + | 24.1080i | −0.644679 | + | 0.928607i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.10627 | − | 8.32586i | −0.119472 | − | 0.320226i | ||||
\(677\) | − | 43.8600i | − | 1.68568i | −0.538166 | − | 0.842839i | \(-0.680883\pi\) | ||
0.538166 | − | 0.842839i | \(-0.319117\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.5872 | −0.406301 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −16.4830 | − | 11.4432i | −0.631168 | − | 0.438184i | ||||
\(683\) | − | 5.33527i | − | 0.204148i | −0.994777 | − | 0.102074i | \(-0.967452\pi\) | ||
0.994777 | − | 0.102074i | \(-0.0325479\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 8.09003 | − | 11.6530i | 0.308879 | − | 0.444915i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −19.5013 | − | 22.4972i | −0.743480 | − | 0.857698i | ||||
\(689\) | −22.5872 | −0.860505 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 39.7710i | − | 1.51296i | −0.654016 | − | 0.756480i | \(-0.726917\pi\) | ||
0.654016 | − | 0.756480i | \(-0.273083\pi\) | |||||||
\(692\) | 12.0450 | − | 4.49383i | 0.457882 | − | 0.170830i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.50280 | + | 3.82028i | 0.208883 | + | 0.145016i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24.1080 | −0.913157 | ||||||||
\(698\) | 0.560675 | + | 0.389245i | 0.0212219 | + | 0.0147331i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 27.5015i | − | 1.03872i | −0.854556 | − | 0.519359i | \(-0.826171\pi\) | ||
0.854556 | − | 0.519359i | \(-0.173829\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.86335 | 0.0702775 | ||||||||
\(704\) | −20.5422 | + | 37.6454i | −0.774214 | + | 1.41881i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.72161 | + | 2.47984i | −0.0647937 | + | 0.0933300i | ||||
\(707\) | − | 5.55118i | − | 0.208774i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 0.111632i | − | 0.00419244i | −0.999998 | − | 0.00209622i | \(-0.999333\pi\) | ||
0.999998 | − | 0.00209622i | \(-0.000667249\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −20.8094 | − | 5.30818i | −0.779866 | − | 0.198932i | ||||
\(713\) | −19.8387 | −0.742966 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 15.2486 | − | 5.68906i | 0.569867 | − | 0.212610i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7.73665 | + | 11.1440i | −0.288729 | + | 0.415891i | ||||
\(719\) | −10.7064 | −0.399281 | −0.199640 | − | 0.979869i | \(-0.563977\pi\) | ||||
−0.199640 | + | 0.979869i | \(0.563977\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.37112 | 0.200031 | ||||||||
\(722\) | −12.8995 | + | 18.5807i | −0.480071 | + | 0.691503i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.79641 | − | 1.04331i | 0.103928 | − | 0.0387742i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.6562 | −0.951536 | −0.475768 | − | 0.879571i | \(-0.657830\pi\) | ||||
−0.475768 | + | 0.879571i | \(0.657830\pi\) | |||||||
\(728\) | 1.52594 | − | 5.98207i | 0.0565551 | − | 0.221710i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 15.8888i | − | 0.587667i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 30.3684i | − | 1.12168i | −0.827923 | − | 0.560842i | \(-0.810478\pi\) | ||
0.827923 | − | 0.560842i | \(-0.189522\pi\) | |||||||
\(734\) | −27.4882 | + | 39.5945i | −1.01461 | + | 1.46146i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.54222 | + | 42.1560i | 0.167428 | + | 1.55389i | ||||
\(737\) | −39.9007 | −1.46976 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 20.1917i | − | 0.742763i | −0.928480 | − | 0.371381i | \(-0.878884\pi\) | ||
0.928480 | − | 0.371381i | \(-0.121116\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.69335 | + | 4.64681i | 0.245720 | + | 0.170590i | ||||
\(743\) | −46.3863 | −1.70175 | −0.850875 | − | 0.525369i | \(-0.823927\pi\) | ||||
−0.850875 | + | 0.525369i | \(0.823927\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −5.03942 | − | 3.49858i | −0.184506 | − | 0.128092i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −21.4427 | + | 8.00000i | −0.784023 | + | 0.292509i | ||||
\(749\) | − | 2.98470i | − | 0.109059i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.1261 | −0.989845 | −0.494922 | − | 0.868937i | \(-0.664804\pi\) | ||||
−0.494922 | + | 0.868937i | \(0.664804\pi\) | |||||||
\(752\) | 5.24002 | − | 4.54222i | 0.191084 | − | 0.165638i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −15.9225 | + | 22.9351i | −0.579863 | + | 0.835245i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 45.2549i | 1.64482i | 0.568898 | + | 0.822408i | \(0.307370\pi\) | ||||
−0.568898 | + | 0.822408i | \(0.692630\pi\) | |||||||
\(758\) | −8.01699 | − | 5.56574i | −0.291190 | − | 0.202157i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.8864 | −0.612133 | −0.306067 | − | 0.952010i | \(-0.599013\pi\) | ||||
−0.306067 | + | 0.952010i | \(0.599013\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.8864i | 0.538926i | ||||||||
\(764\) | 4.81434 | + | 12.9041i | 0.174177 | + | 0.466852i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 18.0450 | − | 25.9924i | 0.651993 | − | 0.939142i | ||||
\(767\) | 20.0464 | 0.723835 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.3297 | 0.588863 | 0.294431 | − | 0.955673i | \(-0.404870\pi\) | ||||
0.294431 | + | 0.955673i | \(0.404870\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 11.5233 | + | 30.8864i | 0.414734 | + | 1.11163i | ||||
\(773\) | − | 41.3144i | − | 1.48598i | −0.669304 | − | 0.742989i | \(-0.733408\pi\) | ||
0.669304 | − | 0.742989i | \(-0.266592\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −38.8864 | − | 9.91936i | −1.39594 | − | 0.356084i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 12.8002 | + | 8.88645i | 0.458909 | + | 0.318595i | ||||
\(779\) | − | 19.5794i | − | 0.701503i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 71.2628i | − | 2.54998i | ||||||
\(782\) | −12.9041 | + | 18.5872i | −0.461448 | + | 0.664678i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 19.4747 | − | 16.8813i | 0.695525 | − | 0.602904i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.4849i | 0.409391i | 0.978826 | + | 0.204696i | \(0.0656205\pi\) | ||||
−0.978826 | + | 0.204696i | \(0.934380\pi\) | |||||||
\(788\) | −25.4317 | + | 9.48824i | −0.905966 | + | 0.338005i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.99440 | −0.319804 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.8735 | 0.670216 | ||||||||
\(794\) | 29.3386 | + | 20.3681i | 1.04119 | + | 0.722838i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.32967 | − | 16.9657i | −0.224349 | − | 0.601332i | ||||
\(797\) | 45.4945i | 1.61150i | 0.592257 | + | 0.805749i | \(0.298237\pi\) | ||||
−0.592257 | + | 0.805749i | \(0.701763\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.70079 | 0.130924 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5.88233 | − | 8.47301i | 0.207712 | − | 0.299192i | ||||
\(803\) | − | 3.70079i | − | 0.130598i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 8.99440 | + | 6.24430i | 0.316814 | + | 0.219946i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5.20100 | − | 20.3892i | 0.182970 | − | 0.717291i | ||||
\(809\) | 36.0721 | 1.26823 | 0.634114 | − | 0.773240i | \(-0.281365\pi\) | ||||
0.634114 | + | 0.773240i | \(0.281365\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 44.5230i | 1.56341i | 0.623646 | + | 0.781707i | \(0.285651\pi\) | ||||
−0.623646 | + | 0.781707i | \(0.714349\pi\) | |||||||
\(812\) | 9.43673 | − | 3.52072i | 0.331164 | − | 0.123553i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.64681 | − | 6.69335i | 0.162871 | − | 0.234602i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.9041 | 0.451456 | ||||||||
\(818\) | −12.7834 | + | 18.4134i | −0.446961 | + | 0.643811i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 34.1613i | − | 1.19224i | −0.802897 | − | 0.596118i | \(-0.796709\pi\) | ||
0.802897 | − | 0.596118i | \(-0.203291\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.12689 | −0.0741388 | −0.0370694 | − | 0.999313i | \(-0.511802\pi\) | ||||
−0.0370694 | + | 0.999313i | \(0.511802\pi\) | |||||||
\(824\) | 19.7279 | + | 5.03229i | 0.687253 | + | 0.175308i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.94043 | − | 4.12410i | −0.206694 | − | 0.143496i | ||||
\(827\) | 38.5872i | 1.34181i | 0.741543 | + | 0.670905i | \(0.234094\pi\) | ||||
−0.741543 | + | 0.670905i | \(0.765906\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 34.2351i | − | 1.18904i | −0.804083 | − | 0.594518i | \(-0.797343\pi\) | ||
0.804083 | − | 0.594518i | \(-0.202657\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 11.2094 | − | 20.5422i | 0.388617 | − | 0.712173i | ||||
\(833\) | 13.7541 | 0.476551 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −6.49720 | − | 17.4147i | −0.224710 | − | 0.602300i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 9.32384 | + | 6.47301i | 0.322087 | + | 0.223606i | ||||
\(839\) | 41.5928 | 1.43594 | 0.717972 | − | 0.696072i | \(-0.245071\pi\) | ||||
0.717972 | + | 0.696072i | \(0.245071\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.5512 | −0.570730 | ||||||||
\(842\) | 26.6437 | + | 18.4972i | 0.918202 | + | 0.637456i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.75140 | + | 1.77269i | −0.163550 | + | 0.0610184i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13.2348 | −0.454752 | ||||||||
\(848\) | 20.2307 | + | 23.3386i | 0.694725 | + | 0.801452i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 8.05601i | − | 0.276156i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.1828i | 0.793763i | 0.917870 | + | 0.396881i | \(0.129908\pi\) | ||||
−0.917870 | + | 0.396881i | \(0.870092\pi\) | |||||||
\(854\) | −5.59283 | − | 3.88278i | −0.191383 | − | 0.132866i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.79641 | − | 10.9627i | 0.0955795 | − | 0.374696i | ||||
\(857\) | −9.38868 | −0.320711 | −0.160356 | − | 0.987059i | \(-0.551264\pi\) | ||||
−0.160356 | + | 0.987059i | \(0.551264\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 8.98769i | − | 0.306656i | −0.988175 | − | 0.153328i | \(-0.951001\pi\) | ||
0.988175 | − | 0.153328i | \(-0.0489991\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −28.2813 | + | 40.7368i | −0.963264 | + | 1.38750i | ||||
\(863\) | 12.2473 | 0.416903 | 0.208451 | − | 0.978033i | \(-0.433158\pi\) | ||||
0.208451 | + | 0.978033i | \(0.433158\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −13.7729 | + | 19.8387i | −0.468022 | + | 0.674147i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.38072 | − | 3.70079i | −0.0468646 | − | 0.125613i | ||||
\(869\) | 14.1887i | 0.481318i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.7729 | 0.737746 | ||||||||
\(872\) | −13.9474 | + | 54.6773i | −0.472317 | + | 1.85161i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −15.0956 | − | 10.4800i | −0.510617 | − | 0.354492i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 26.1109i | − | 0.881701i | −0.897581 | − | 0.440850i | \(-0.854677\pi\) | ||
0.897581 | − | 0.440850i | \(-0.145323\pi\) | |||||||
\(878\) | −6.88661 | + | 9.91960i | −0.232412 | + | 0.334770i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.4793 | 1.29640 | 0.648200 | − | 0.761470i | \(-0.275522\pi\) | ||||
0.648200 | + | 0.761470i | \(0.275522\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 6.58723i | − | 0.221678i | −0.993838 | − | 0.110839i | \(-0.964646\pi\) | ||
0.993838 | − | 0.110839i | \(-0.0353538\pi\) | |||||||
\(884\) | 11.7008 | − | 4.36542i | 0.393540 | − | 0.146825i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −24.0900 | − | 16.7243i | −0.809320 | − | 0.561865i | ||||
\(887\) | −50.9595 | −1.71105 | −0.855526 | − | 0.517760i | \(-0.826766\pi\) | ||||
−0.855526 | + | 0.517760i | \(0.826766\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.14401 | −0.105447 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8.49962 | − | 22.7819i | −0.284588 | − | 0.762793i | ||||
\(893\) | 3.00560i | 0.100578i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −7.54781 | + | 3.78126i | −0.252155 | + | 0.126323i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.61301 | + | 2.32340i | −0.0538268 | + | 0.0775330i | ||||
\(899\) | 17.8637i | 0.595789i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.4830i | 0.549129i | ||||||||
\(902\) | −70.3311 | − | 48.8269i | −2.34177 | − | 1.62576i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −33.0361 | − | 8.42701i | −1.09876 | − | 0.280278i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.5568i | 0.815394i | 0.913117 | + | 0.407697i | \(0.133668\pi\) | ||||
−0.913117 | + | 0.407697i | \(0.866332\pi\) | |||||||
\(908\) | 38.8574 | − | 14.4972i | 1.28953 | − | 0.481107i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.0000 | −0.530104 | −0.265052 | − | 0.964234i | \(-0.585389\pi\) | ||||
−0.265052 | + | 0.964234i | \(0.585389\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −31.3621 | −1.03793 | ||||||||
\(914\) | −1.03605 | + | 1.49235i | −0.0342696 | + | 0.0493625i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −37.3836 | + | 13.9474i | −1.23519 | + | 0.460834i | ||||
\(917\) | 7.70079i | 0.254302i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.7548 | 0.948532 | 0.474266 | − | 0.880382i | \(-0.342713\pi\) | ||||
0.474266 | + | 0.880382i | \(0.342713\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −18.2425 | − | 12.6647i | −0.600785 | − | 0.417091i | ||||
\(923\) | 38.8864i | 1.27996i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −15.0990 | + | 21.7489i | −0.496184 | + | 0.714712i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 37.9593 | − | 4.09003i | 1.24608 | − | 0.134262i | ||||
\(929\) | −28.2880 | −0.928100 | −0.464050 | − | 0.885809i | \(-0.653604\pi\) | ||||
−0.464050 | + | 0.885809i | \(0.653604\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.1704i | 0.366095i | ||||||||
\(932\) | −9.32510 | − | 24.9944i | −0.305454 | − | 0.818719i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.49720 | + | 1.73367i | 0.0817110 | + | 0.0567273i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.9313 | −1.10849 | −0.554244 | − | 0.832354i | \(-0.686992\pi\) | ||||
−0.554244 | + | 0.832354i | \(0.686992\pi\) | |||||||
\(938\) | −6.45203 | − | 4.47928i | −0.210666 | − | 0.146254i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 38.8016i | − | 1.26490i | −0.774603 | − | 0.632448i | \(-0.782050\pi\) | ||
0.774603 | − | 0.632448i | \(-0.217950\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −84.6495 | −2.75657 | ||||||||
\(944\) | −17.9550 | − | 20.7133i | −0.584385 | − | 0.674161i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 32.1801 | − | 46.3527i | 1.04626 | − | 1.50706i | ||||
\(947\) | 17.7729i | 0.577541i | 0.957398 | + | 0.288771i | \(0.0932465\pi\) | ||||
−0.957398 | + | 0.288771i | \(0.906753\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.01943i | 0.0655536i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.36542 | − | 1.11355i | −0.141484 | − | 0.0360905i | ||||
\(953\) | 46.3047 | 1.49996 | 0.749978 | − | 0.661463i | \(-0.230064\pi\) | ||||
0.749978 | + | 0.661463i | \(0.230064\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 16.0000 | + | 42.8854i | 0.517477 | + | 1.38701i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −9.82327 | + | 14.1496i | −0.317375 | + | 0.457153i | ||||
\(959\) | −11.2215 | −0.362361 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.9944 | −0.774013 | ||||||||
\(962\) | −2.53566 | + | 3.65240i | −0.0817528 | + | 0.117758i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.51176 | − | 6.73237i | −0.0808984 | − | 0.216835i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.28482 | 0.298580 | 0.149290 | − | 0.988793i | \(-0.452301\pi\) | ||||
0.149290 | + | 0.988793i | \(0.452301\pi\) | |||||||
\(968\) | −48.6108 | − | 12.3999i | −1.56241 | − | 0.398548i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.9301i | 0.671678i | 0.941919 | + | 0.335839i | \(0.109020\pi\) | ||||
−0.941919 | + | 0.335839i | \(0.890980\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.06651i | 0.226542i | ||||||||
\(974\) | −20.7819 | + | 29.9346i | −0.665894 | + | 0.959165i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −16.9044 | − | 19.5013i | −0.541096 | − | 0.624222i | ||||
\(977\) | 30.8314 | 0.986383 | 0.493192 | − | 0.869921i | \(-0.335830\pi\) | ||||
0.493192 | + | 0.869921i | \(0.335830\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 40.7027i | − | 1.30086i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 19.4845 | + | 13.5270i | 0.621776 | + | 0.431664i | ||||
\(983\) | −31.3285 | −0.999223 | −0.499612 | − | 0.866250i | \(-0.666524\pi\) | ||||
−0.499612 | + | 0.866250i | \(0.666524\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 16.7368 | + | 11.6194i | 0.533010 | + | 0.370038i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.54537 | + | 9.50280i | 0.112793 | + | 0.302324i | ||||
\(989\) | − | 55.7895i | − | 1.77400i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31.3420 | 0.995611 | 0.497806 | − | 0.867289i | \(-0.334139\pi\) | ||||
0.497806 | + | 0.867289i | \(0.334139\pi\) | |||||||
\(992\) | −1.60398 | − | 14.8864i | −0.0509265 | − | 0.472645i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8.00000 | − | 11.5233i | 0.253745 | − | 0.365498i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 20.9557i | − | 0.663672i | −0.943337 | − | 0.331836i | \(-0.892332\pi\) | ||
0.943337 | − | 0.331836i | \(-0.107668\pi\) | |||||||
\(998\) | 20.4720 | + | 14.2125i | 0.648030 | + | 0.449890i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))