Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1078,2,Mod(67,1078)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1078, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1078.67");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1078 = 2 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1078.e (of order \(3\), degree \(2\), 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: | \(8.60787333789\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} + 2x^{2} + 4 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 154) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 67.2 | ||
Root | \(0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1078.67 |
Dual form | 1078.2.e.m.177.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(981\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0.207107 | − | 0.358719i | 0.119573 | − | 0.207107i | −0.800025 | − | 0.599966i | \(-0.795181\pi\) |
0.919599 | + | 0.392859i | \(0.128514\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −1.70711 | − | 2.95680i | −0.763441 | − | 1.32232i | −0.941067 | − | 0.338221i | \(-0.890175\pi\) |
0.177625 | − | 0.984098i | \(-0.443158\pi\) | |||||||
\(6\) | −0.414214 | −0.169102 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.41421 | + | 2.44949i | 0.471405 | + | 0.816497i | ||||
\(10\) | −1.70711 | + | 2.95680i | −0.539835 | + | 0.935021i | ||||
\(11\) | −0.500000 | + | 0.866025i | −0.150756 | + | 0.261116i | ||||
\(12\) | 0.207107 | + | 0.358719i | 0.0597866 | + | 0.103553i | ||||
\(13\) | −1.82843 | −0.507114 | −0.253557 | − | 0.967320i | \(-0.581601\pi\) | ||||
−0.253557 | + | 0.967320i | \(0.581601\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.41421 | −0.365148 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −3.82843 | + | 6.63103i | −0.928530 | + | 1.60826i | −0.142747 | + | 0.989759i | \(0.545593\pi\) |
−0.785783 | + | 0.618502i | \(0.787740\pi\) | |||||||
\(18\) | 1.41421 | − | 2.44949i | 0.333333 | − | 0.577350i | ||||
\(19\) | −1.70711 | − | 2.95680i | −0.391637 | − | 0.678335i | 0.601028 | − | 0.799228i | \(-0.294758\pi\) |
−0.992666 | + | 0.120892i | \(0.961424\pi\) | |||||||
\(20\) | 3.41421 | 0.763441 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −1.12132 | − | 1.94218i | −0.233811 | − | 0.404973i | 0.725115 | − | 0.688628i | \(-0.241787\pi\) |
−0.958927 | + | 0.283654i | \(0.908453\pi\) | |||||||
\(24\) | 0.207107 | − | 0.358719i | 0.0422755 | − | 0.0732233i | ||||
\(25\) | −3.32843 | + | 5.76500i | −0.665685 | + | 1.15300i | ||||
\(26\) | 0.914214 | + | 1.58346i | 0.179292 | + | 0.310543i | ||||
\(27\) | 2.41421 | 0.464616 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.65685 | −1.60754 | −0.803769 | − | 0.594942i | \(-0.797175\pi\) | ||||
−0.803769 | + | 0.594942i | \(0.797175\pi\) | |||||||
\(30\) | 0.707107 | + | 1.22474i | 0.129099 | + | 0.223607i | ||||
\(31\) | −2.00000 | + | 3.46410i | −0.359211 | + | 0.622171i | −0.987829 | − | 0.155543i | \(-0.950287\pi\) |
0.628619 | + | 0.777714i | \(0.283621\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0.207107 | + | 0.358719i | 0.0360527 | + | 0.0624450i | ||||
\(34\) | 7.65685 | 1.31314 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.82843 | −0.471405 | ||||||||
\(37\) | 3.29289 | + | 5.70346i | 0.541348 | + | 0.937643i | 0.998827 | + | 0.0484222i | \(0.0154193\pi\) |
−0.457479 | + | 0.889221i | \(0.651247\pi\) | |||||||
\(38\) | −1.70711 | + | 2.95680i | −0.276929 | + | 0.479656i | ||||
\(39\) | −0.378680 | + | 0.655892i | −0.0606373 | + | 0.105027i | ||||
\(40\) | −1.70711 | − | 2.95680i | −0.269917 | − | 0.467510i | ||||
\(41\) | 2.58579 | 0.403832 | 0.201916 | − | 0.979403i | \(-0.435283\pi\) | ||||
0.201916 | + | 0.979403i | \(0.435283\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.65685 | 0.862662 | 0.431331 | − | 0.902194i | \(-0.358044\pi\) | ||||
0.431331 | + | 0.902194i | \(0.358044\pi\) | |||||||
\(44\) | −0.500000 | − | 0.866025i | −0.0753778 | − | 0.130558i | ||||
\(45\) | 4.82843 | − | 8.36308i | 0.719779 | − | 1.24669i | ||||
\(46\) | −1.12132 | + | 1.94218i | −0.165330 | + | 0.286359i | ||||
\(47\) | 3.24264 | + | 5.61642i | 0.472988 | + | 0.819239i | 0.999522 | − | 0.0309151i | \(-0.00984215\pi\) |
−0.526534 | + | 0.850154i | \(0.676509\pi\) | |||||||
\(48\) | −0.414214 | −0.0597866 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 6.65685 | 0.941421 | ||||||||
\(51\) | 1.58579 | + | 2.74666i | 0.222055 | + | 0.384610i | ||||
\(52\) | 0.914214 | − | 1.58346i | 0.126779 | − | 0.219587i | ||||
\(53\) | 5.94975 | − | 10.3053i | 0.817261 | − | 1.41554i | −0.0904325 | − | 0.995903i | \(-0.528825\pi\) |
0.907693 | − | 0.419634i | \(-0.137842\pi\) | |||||||
\(54\) | −1.20711 | − | 2.09077i | −0.164266 | − | 0.284518i | ||||
\(55\) | 3.41421 | 0.460372 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.41421 | −0.187317 | ||||||||
\(58\) | 4.32843 | + | 7.49706i | 0.568350 | + | 0.984412i | ||||
\(59\) | −4.20711 | + | 7.28692i | −0.547719 | + | 0.948677i | 0.450712 | + | 0.892670i | \(0.351170\pi\) |
−0.998430 | + | 0.0560070i | \(0.982163\pi\) | |||||||
\(60\) | 0.707107 | − | 1.22474i | 0.0912871 | − | 0.158114i | ||||
\(61\) | 3.08579 | + | 5.34474i | 0.395094 | + | 0.684324i | 0.993113 | − | 0.117158i | \(-0.0373785\pi\) |
−0.598019 | + | 0.801482i | \(0.704045\pi\) | |||||||
\(62\) | 4.00000 | 0.508001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.12132 | + | 5.40629i | 0.387152 | + | 0.670567i | ||||
\(66\) | 0.207107 | − | 0.358719i | 0.0254931 | − | 0.0441553i | ||||
\(67\) | −5.62132 | + | 9.73641i | −0.686754 | + | 1.18949i | 0.286129 | + | 0.958191i | \(0.407632\pi\) |
−0.972882 | + | 0.231301i | \(0.925702\pi\) | |||||||
\(68\) | −3.82843 | − | 6.63103i | −0.464265 | − | 0.804131i | ||||
\(69\) | −0.928932 | −0.111830 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.07107 | 0.364469 | 0.182234 | − | 0.983255i | \(-0.441667\pi\) | ||||
0.182234 | + | 0.983255i | \(0.441667\pi\) | |||||||
\(72\) | 1.41421 | + | 2.44949i | 0.166667 | + | 0.288675i | ||||
\(73\) | −3.29289 | + | 5.70346i | −0.385404 | + | 0.667539i | −0.991825 | − | 0.127604i | \(-0.959271\pi\) |
0.606421 | + | 0.795144i | \(0.292605\pi\) | |||||||
\(74\) | 3.29289 | − | 5.70346i | 0.382791 | − | 0.663014i | ||||
\(75\) | 1.37868 | + | 2.38794i | 0.159196 | + | 0.275736i | ||||
\(76\) | 3.41421 | 0.391637 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.757359 | 0.0857541 | ||||||||
\(79\) | 2.37868 | + | 4.11999i | 0.267622 | + | 0.463536i | 0.968247 | − | 0.249994i | \(-0.0804287\pi\) |
−0.700625 | + | 0.713530i | \(0.747095\pi\) | |||||||
\(80\) | −1.70711 | + | 2.95680i | −0.190860 | + | 0.330580i | ||||
\(81\) | −3.74264 | + | 6.48244i | −0.415849 | + | 0.720272i | ||||
\(82\) | −1.29289 | − | 2.23936i | −0.142776 | − | 0.247296i | ||||
\(83\) | −16.1421 | −1.77183 | −0.885915 | − | 0.463848i | \(-0.846468\pi\) | ||||
−0.885915 | + | 0.463848i | \(0.846468\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 26.1421 | 2.83551 | ||||||||
\(86\) | −2.82843 | − | 4.89898i | −0.304997 | − | 0.528271i | ||||
\(87\) | −1.79289 | + | 3.10538i | −0.192218 | + | 0.332932i | ||||
\(88\) | −0.500000 | + | 0.866025i | −0.0533002 | + | 0.0923186i | ||||
\(89\) | −2.24264 | − | 3.88437i | −0.237719 | − | 0.411742i | 0.722340 | − | 0.691538i | \(-0.243067\pi\) |
−0.960060 | + | 0.279796i | \(0.909733\pi\) | |||||||
\(90\) | −9.65685 | −1.01792 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.24264 | 0.233811 | ||||||||
\(93\) | 0.828427 | + | 1.43488i | 0.0859039 | + | 0.148790i | ||||
\(94\) | 3.24264 | − | 5.61642i | 0.334453 | − | 0.579289i | ||||
\(95\) | −5.82843 | + | 10.0951i | −0.597984 | + | 1.03574i | ||||
\(96\) | 0.207107 | + | 0.358719i | 0.0211377 | + | 0.0366117i | ||||
\(97\) | −1.82843 | −0.185649 | −0.0928243 | − | 0.995683i | \(-0.529589\pi\) | ||||
−0.0928243 | + | 0.995683i | \(0.529589\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.82843 | −0.284268 | ||||||||
\(100\) | −3.32843 | − | 5.76500i | −0.332843 | − | 0.576500i | ||||
\(101\) | 5.91421 | − | 10.2437i | 0.588486 | − | 1.01929i | −0.405945 | − | 0.913898i | \(-0.633057\pi\) |
0.994431 | − | 0.105390i | \(-0.0336092\pi\) | |||||||
\(102\) | 1.58579 | − | 2.74666i | 0.157016 | − | 0.271960i | ||||
\(103\) | 5.29289 | + | 9.16756i | 0.521524 | + | 0.903307i | 0.999687 | + | 0.0250350i | \(0.00796973\pi\) |
−0.478162 | + | 0.878271i | \(0.658697\pi\) | |||||||
\(104\) | −1.82843 | −0.179292 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11.8995 | −1.15578 | ||||||||
\(107\) | −5.53553 | − | 9.58783i | −0.535140 | − | 0.926890i | −0.999157 | − | 0.0410635i | \(-0.986925\pi\) |
0.464016 | − | 0.885827i | \(-0.346408\pi\) | |||||||
\(108\) | −1.20711 | + | 2.09077i | −0.116154 | + | 0.201184i | ||||
\(109\) | 0.242641 | − | 0.420266i | 0.0232408 | − | 0.0402542i | −0.854171 | − | 0.519992i | \(-0.825935\pi\) |
0.877412 | + | 0.479738i | \(0.159268\pi\) | |||||||
\(110\) | −1.70711 | − | 2.95680i | −0.162766 | − | 0.281919i | ||||
\(111\) | 2.72792 | 0.258923 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.8284 | −1.30087 | −0.650434 | − | 0.759562i | \(-0.725413\pi\) | ||||
−0.650434 | + | 0.759562i | \(0.725413\pi\) | |||||||
\(114\) | 0.707107 | + | 1.22474i | 0.0662266 | + | 0.114708i | ||||
\(115\) | −3.82843 | + | 6.63103i | −0.357003 | + | 0.618347i | ||||
\(116\) | 4.32843 | − | 7.49706i | 0.401884 | − | 0.696084i | ||||
\(117\) | −2.58579 | − | 4.47871i | −0.239056 | − | 0.414057i | ||||
\(118\) | 8.41421 | 0.774591 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.41421 | −0.129099 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | 3.08579 | − | 5.34474i | 0.279374 | − | 0.483890i | ||||
\(123\) | 0.535534 | − | 0.927572i | 0.0482875 | − | 0.0836363i | ||||
\(124\) | −2.00000 | − | 3.46410i | −0.179605 | − | 0.311086i | ||||
\(125\) | 5.65685 | 0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.72792 | −0.863213 | −0.431607 | − | 0.902062i | \(-0.642053\pi\) | ||||
−0.431607 | + | 0.902062i | \(0.642053\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 1.17157 | − | 2.02922i | 0.103151 | − | 0.178663i | ||||
\(130\) | 3.12132 | − | 5.40629i | 0.273758 | − | 0.474163i | ||||
\(131\) | −1.70711 | − | 2.95680i | −0.149151 | − | 0.258336i | 0.781763 | − | 0.623575i | \(-0.214321\pi\) |
−0.930914 | + | 0.365239i | \(0.880987\pi\) | |||||||
\(132\) | −0.414214 | −0.0360527 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 11.2426 | 0.971216 | ||||||||
\(135\) | −4.12132 | − | 7.13834i | −0.354707 | − | 0.614370i | ||||
\(136\) | −3.82843 | + | 6.63103i | −0.328285 | + | 0.568606i | ||||
\(137\) | 2.67157 | − | 4.62730i | 0.228248 | − | 0.395337i | −0.729041 | − | 0.684470i | \(-0.760034\pi\) |
0.957289 | + | 0.289133i | \(0.0933670\pi\) | |||||||
\(138\) | 0.464466 | + | 0.804479i | 0.0395380 | + | 0.0684818i | ||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.68629 | 0.226227 | ||||||||
\(142\) | −1.53553 | − | 2.65962i | −0.128859 | − | 0.223191i | ||||
\(143\) | 0.914214 | − | 1.58346i | 0.0764504 | − | 0.132416i | ||||
\(144\) | 1.41421 | − | 2.44949i | 0.117851 | − | 0.204124i | ||||
\(145\) | 14.7782 | + | 25.5965i | 1.22726 | + | 2.12568i | ||||
\(146\) | 6.58579 | 0.545044 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.58579 | −0.541348 | ||||||||
\(149\) | −3.17157 | − | 5.49333i | −0.259825 | − | 0.450031i | 0.706370 | − | 0.707843i | \(-0.250332\pi\) |
−0.966195 | + | 0.257812i | \(0.916998\pi\) | |||||||
\(150\) | 1.37868 | − | 2.38794i | 0.112569 | − | 0.194975i | ||||
\(151\) | −4.86396 | + | 8.42463i | −0.395824 | + | 0.685586i | −0.993206 | − | 0.116370i | \(-0.962874\pi\) |
0.597382 | + | 0.801957i | \(0.296207\pi\) | |||||||
\(152\) | −1.70711 | − | 2.95680i | −0.138465 | − | 0.239828i | ||||
\(153\) | −21.6569 | −1.75085 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.6569 | 1.09694 | ||||||||
\(156\) | −0.378680 | − | 0.655892i | −0.0303186 | − | 0.0525134i | ||||
\(157\) | 3.17157 | − | 5.49333i | 0.253119 | − | 0.438415i | −0.711264 | − | 0.702925i | \(-0.751877\pi\) |
0.964383 | + | 0.264510i | \(0.0852102\pi\) | |||||||
\(158\) | 2.37868 | − | 4.11999i | 0.189238 | − | 0.327769i | ||||
\(159\) | −2.46447 | − | 4.26858i | −0.195445 | − | 0.338520i | ||||
\(160\) | 3.41421 | 0.269917 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 7.48528 | 0.588099 | ||||||||
\(163\) | 7.86396 | + | 13.6208i | 0.615953 | + | 1.06686i | 0.990217 | + | 0.139539i | \(0.0445622\pi\) |
−0.374264 | + | 0.927322i | \(0.622104\pi\) | |||||||
\(164\) | −1.29289 | + | 2.23936i | −0.100958 | + | 0.174864i | ||||
\(165\) | 0.707107 | − | 1.22474i | 0.0550482 | − | 0.0953463i | ||||
\(166\) | 8.07107 | + | 13.9795i | 0.626436 | + | 1.08502i | ||||
\(167\) | 11.7279 | 0.907534 | 0.453767 | − | 0.891120i | \(-0.350080\pi\) | ||||
0.453767 | + | 0.891120i | \(0.350080\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.65685 | −0.742835 | ||||||||
\(170\) | −13.0711 | − | 22.6398i | −1.00251 | − | 1.73639i | ||||
\(171\) | 4.82843 | − | 8.36308i | 0.369239 | − | 0.639541i | ||||
\(172\) | −2.82843 | + | 4.89898i | −0.215666 | + | 0.373544i | ||||
\(173\) | −2.08579 | − | 3.61269i | −0.158579 | − | 0.274668i | 0.775777 | − | 0.631007i | \(-0.217358\pi\) |
−0.934357 | + | 0.356339i | \(0.884025\pi\) | |||||||
\(174\) | 3.58579 | 0.271838 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 1.74264 | + | 3.01834i | 0.130985 | + | 0.226872i | ||||
\(178\) | −2.24264 | + | 3.88437i | −0.168093 | + | 0.291146i | ||||
\(179\) | 9.44975 | − | 16.3674i | 0.706307 | − | 1.22336i | −0.259910 | − | 0.965633i | \(-0.583693\pi\) |
0.966218 | − | 0.257727i | \(-0.0829736\pi\) | |||||||
\(180\) | 4.82843 | + | 8.36308i | 0.359890 | + | 0.623347i | ||||
\(181\) | −3.65685 | −0.271812 | −0.135906 | − | 0.990722i | \(-0.543394\pi\) | ||||
−0.135906 | + | 0.990722i | \(0.543394\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.55635 | 0.188971 | ||||||||
\(184\) | −1.12132 | − | 1.94218i | −0.0826648 | − | 0.143180i | ||||
\(185\) | 11.2426 | − | 19.4728i | 0.826575 | − | 1.43167i | ||||
\(186\) | 0.828427 | − | 1.43488i | 0.0607432 | − | 0.105210i | ||||
\(187\) | −3.82843 | − | 6.63103i | −0.279962 | − | 0.484909i | ||||
\(188\) | −6.48528 | −0.472988 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 11.6569 | 0.845677 | ||||||||
\(191\) | 6.41421 | + | 11.1097i | 0.464116 | + | 0.803873i | 0.999161 | − | 0.0409507i | \(-0.0130387\pi\) |
−0.535045 | + | 0.844824i | \(0.679705\pi\) | |||||||
\(192\) | 0.207107 | − | 0.358719i | 0.0149466 | − | 0.0258883i | ||||
\(193\) | −1.05025 | + | 1.81909i | −0.0755988 | + | 0.130941i | −0.901347 | − | 0.433099i | \(-0.857420\pi\) |
0.825748 | + | 0.564040i | \(0.190754\pi\) | |||||||
\(194\) | 0.914214 | + | 1.58346i | 0.0656367 | + | 0.113686i | ||||
\(195\) | 2.58579 | 0.185172 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.4853 | −1.24577 | −0.622887 | − | 0.782312i | \(-0.714041\pi\) | ||||
−0.622887 | + | 0.782312i | \(0.714041\pi\) | |||||||
\(198\) | 1.41421 | + | 2.44949i | 0.100504 | + | 0.174078i | ||||
\(199\) | 9.94975 | − | 17.2335i | 0.705319 | − | 1.22165i | −0.261257 | − | 0.965269i | \(-0.584137\pi\) |
0.966576 | − | 0.256379i | \(-0.0825295\pi\) | |||||||
\(200\) | −3.32843 | + | 5.76500i | −0.235355 | + | 0.407647i | ||||
\(201\) | 2.32843 | + | 4.03295i | 0.164235 | + | 0.284463i | ||||
\(202\) | −11.8284 | −0.832245 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −3.17157 | −0.222055 | ||||||||
\(205\) | −4.41421 | − | 7.64564i | −0.308302 | − | 0.533995i | ||||
\(206\) | 5.29289 | − | 9.16756i | 0.368773 | − | 0.638734i | ||||
\(207\) | 3.17157 | − | 5.49333i | 0.220440 | − | 0.381813i | ||||
\(208\) | 0.914214 | + | 1.58346i | 0.0633893 | + | 0.109793i | ||||
\(209\) | 3.41421 | 0.236166 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.58579 | 0.315699 | 0.157849 | − | 0.987463i | \(-0.449544\pi\) | ||||
0.157849 | + | 0.987463i | \(0.449544\pi\) | |||||||
\(212\) | 5.94975 | + | 10.3053i | 0.408630 | + | 0.707768i | ||||
\(213\) | 0.636039 | − | 1.10165i | 0.0435807 | − | 0.0754839i | ||||
\(214\) | −5.53553 | + | 9.58783i | −0.378401 | + | 0.655410i | ||||
\(215\) | −9.65685 | − | 16.7262i | −0.658592 | − | 1.14071i | ||||
\(216\) | 2.41421 | 0.164266 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.485281 | −0.0328674 | ||||||||
\(219\) | 1.36396 | + | 2.36245i | 0.0921679 | + | 0.159640i | ||||
\(220\) | −1.70711 | + | 2.95680i | −0.115093 | + | 0.199347i | ||||
\(221\) | 7.00000 | − | 12.1244i | 0.470871 | − | 0.815572i | ||||
\(222\) | −1.36396 | − | 2.36245i | −0.0915431 | − | 0.158557i | ||||
\(223\) | −11.4142 | −0.764352 | −0.382176 | − | 0.924089i | \(-0.624825\pi\) | ||||
−0.382176 | + | 0.924089i | \(0.624825\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −18.8284 | −1.25523 | ||||||||
\(226\) | 6.91421 | + | 11.9758i | 0.459927 | + | 0.796616i | ||||
\(227\) | −11.5858 | + | 20.0672i | −0.768976 | + | 1.33190i | 0.169143 | + | 0.985591i | \(0.445900\pi\) |
−0.938119 | + | 0.346313i | \(0.887433\pi\) | |||||||
\(228\) | 0.707107 | − | 1.22474i | 0.0468293 | − | 0.0811107i | ||||
\(229\) | 0.343146 | + | 0.594346i | 0.0226757 | + | 0.0392755i | 0.877141 | − | 0.480234i | \(-0.159448\pi\) |
−0.854465 | + | 0.519509i | \(0.826115\pi\) | |||||||
\(230\) | 7.65685 | 0.504878 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.65685 | −0.568350 | ||||||||
\(233\) | 0.707107 | + | 1.22474i | 0.0463241 | + | 0.0802357i | 0.888258 | − | 0.459345i | \(-0.151916\pi\) |
−0.841934 | + | 0.539581i | \(0.818583\pi\) | |||||||
\(234\) | −2.58579 | + | 4.47871i | −0.169038 | + | 0.292783i | ||||
\(235\) | 11.0711 | − | 19.1757i | 0.722197 | − | 1.25088i | ||||
\(236\) | −4.20711 | − | 7.28692i | −0.273859 | − | 0.474338i | ||||
\(237\) | 1.97056 | 0.128002 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.2132 | −1.43685 | −0.718426 | − | 0.695603i | \(-0.755137\pi\) | ||||
−0.718426 | + | 0.695603i | \(0.755137\pi\) | |||||||
\(240\) | 0.707107 | + | 1.22474i | 0.0456435 | + | 0.0790569i | ||||
\(241\) | 1.87868 | − | 3.25397i | 0.121016 | − | 0.209607i | −0.799152 | − | 0.601129i | \(-0.794718\pi\) |
0.920169 | + | 0.391522i | \(0.128051\pi\) | |||||||
\(242\) | −0.500000 | + | 0.866025i | −0.0321412 | + | 0.0556702i | ||||
\(243\) | 5.17157 | + | 8.95743i | 0.331757 | + | 0.574619i | ||||
\(244\) | −6.17157 | −0.395094 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.07107 | −0.0682888 | ||||||||
\(247\) | 3.12132 | + | 5.40629i | 0.198605 | + | 0.343994i | ||||
\(248\) | −2.00000 | + | 3.46410i | −0.127000 | + | 0.219971i | ||||
\(249\) | −3.34315 | + | 5.79050i | −0.211863 | + | 0.366958i | ||||
\(250\) | −2.82843 | − | 4.89898i | −0.178885 | − | 0.309839i | ||||
\(251\) | −2.14214 | −0.135210 | −0.0676052 | − | 0.997712i | \(-0.521536\pi\) | ||||
−0.0676052 | + | 0.997712i | \(0.521536\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.24264 | 0.140994 | ||||||||
\(254\) | 4.86396 | + | 8.42463i | 0.305192 | + | 0.528608i | ||||
\(255\) | 5.41421 | − | 9.37769i | 0.339051 | − | 0.587254i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 1.57107 | + | 2.72117i | 0.0980005 | + | 0.169742i | 0.910857 | − | 0.412722i | \(-0.135422\pi\) |
−0.812856 | + | 0.582464i | \(0.802089\pi\) | |||||||
\(258\) | −2.34315 | −0.145878 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −6.24264 | −0.387152 | ||||||||
\(261\) | −12.2426 | − | 21.2049i | −0.757800 | − | 1.31255i | ||||
\(262\) | −1.70711 | + | 2.95680i | −0.105465 | + | 0.182671i | ||||
\(263\) | −15.5208 | + | 26.8828i | −0.957054 | + | 1.65767i | −0.227459 | + | 0.973788i | \(0.573042\pi\) |
−0.729595 | + | 0.683879i | \(0.760291\pi\) | |||||||
\(264\) | 0.207107 | + | 0.358719i | 0.0127465 | + | 0.0220777i | ||||
\(265\) | −40.6274 | −2.49572 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.85786 | −0.113699 | ||||||||
\(268\) | −5.62132 | − | 9.73641i | −0.343377 | − | 0.594746i | ||||
\(269\) | 6.82843 | − | 11.8272i | 0.416337 | − | 0.721116i | −0.579231 | − | 0.815163i | \(-0.696647\pi\) |
0.995568 | + | 0.0940473i | \(0.0299805\pi\) | |||||||
\(270\) | −4.12132 | + | 7.13834i | −0.250816 | + | 0.434425i | ||||
\(271\) | −13.2782 | − | 22.9985i | −0.806592 | − | 1.39706i | −0.915211 | − | 0.402974i | \(-0.867976\pi\) |
0.108620 | − | 0.994083i | \(-0.465357\pi\) | |||||||
\(272\) | 7.65685 | 0.464265 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.34315 | −0.322791 | ||||||||
\(275\) | −3.32843 | − | 5.76500i | −0.200712 | − | 0.347643i | ||||
\(276\) | 0.464466 | − | 0.804479i | 0.0279576 | − | 0.0484239i | ||||
\(277\) | 1.91421 | − | 3.31552i | 0.115014 | − | 0.199210i | −0.802771 | − | 0.596287i | \(-0.796642\pi\) |
0.917785 | + | 0.397077i | \(0.129975\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −11.3137 | −0.677334 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.7279 | −0.997904 | −0.498952 | − | 0.866630i | \(-0.666282\pi\) | ||||
−0.498952 | + | 0.866630i | \(0.666282\pi\) | |||||||
\(282\) | −1.34315 | − | 2.32640i | −0.0799832 | − | 0.138535i | ||||
\(283\) | −10.2929 | + | 17.8278i | −0.611849 | + | 1.05975i | 0.379080 | + | 0.925364i | \(0.376241\pi\) |
−0.990929 | + | 0.134389i | \(0.957093\pi\) | |||||||
\(284\) | −1.53553 | + | 2.65962i | −0.0911172 | + | 0.157820i | ||||
\(285\) | 2.41421 | + | 4.18154i | 0.143006 | + | 0.247693i | ||||
\(286\) | −1.82843 | −0.108117 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.82843 | −0.166667 | ||||||||
\(289\) | −20.8137 | − | 36.0504i | −1.22434 | − | 2.12061i | ||||
\(290\) | 14.7782 | − | 25.5965i | 0.867804 | − | 1.50308i | ||||
\(291\) | −0.378680 | + | 0.655892i | −0.0221986 | + | 0.0384491i | ||||
\(292\) | −3.29289 | − | 5.70346i | −0.192702 | − | 0.333770i | ||||
\(293\) | 5.17157 | 0.302127 | 0.151063 | − | 0.988524i | \(-0.451730\pi\) | ||||
0.151063 | + | 0.988524i | \(0.451730\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 28.7279 | 1.67260 | ||||||||
\(296\) | 3.29289 | + | 5.70346i | 0.191396 | + | 0.331507i | ||||
\(297\) | −1.20711 | + | 2.09077i | −0.0700434 | + | 0.121319i | ||||
\(298\) | −3.17157 | + | 5.49333i | −0.183724 | + | 0.318220i | ||||
\(299\) | 2.05025 | + | 3.55114i | 0.118569 | + | 0.205368i | ||||
\(300\) | −2.75736 | −0.159196 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 9.72792 | 0.559779 | ||||||||
\(303\) | −2.44975 | − | 4.24309i | −0.140734 | − | 0.243759i | ||||
\(304\) | −1.70711 | + | 2.95680i | −0.0979093 | + | 0.169584i | ||||
\(305\) | 10.5355 | − | 18.2481i | 0.603263 | − | 1.04488i | ||||
\(306\) | 10.8284 | + | 18.7554i | 0.619020 | + | 1.07217i | ||||
\(307\) | 9.89949 | 0.564994 | 0.282497 | − | 0.959268i | \(-0.408837\pi\) | ||||
0.282497 | + | 0.959268i | \(0.408837\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.38478 | 0.249441 | ||||||||
\(310\) | −6.82843 | − | 11.8272i | −0.387829 | − | 0.671739i | ||||
\(311\) | −4.36396 | + | 7.55860i | −0.247458 | + | 0.428609i | −0.962820 | − | 0.270145i | \(-0.912928\pi\) |
0.715362 | + | 0.698754i | \(0.246262\pi\) | |||||||
\(312\) | −0.378680 | + | 0.655892i | −0.0214385 | + | 0.0371326i | ||||
\(313\) | −4.67157 | − | 8.09140i | −0.264053 | − | 0.457353i | 0.703262 | − | 0.710931i | \(-0.251726\pi\) |
−0.967315 | + | 0.253578i | \(0.918393\pi\) | |||||||
\(314\) | −6.34315 | −0.357964 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.75736 | −0.267622 | ||||||||
\(317\) | −15.6569 | − | 27.1185i | −0.879377 | − | 1.52312i | −0.852026 | − | 0.523499i | \(-0.824626\pi\) |
−0.0273502 | − | 0.999626i | \(-0.508707\pi\) | |||||||
\(318\) | −2.46447 | + | 4.26858i | −0.138200 | + | 0.239370i | ||||
\(319\) | 4.32843 | − | 7.49706i | 0.242345 | − | 0.419755i | ||||
\(320\) | −1.70711 | − | 2.95680i | −0.0954302 | − | 0.165290i | ||||
\(321\) | −4.58579 | −0.255954 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 26.1421 | 1.45459 | ||||||||
\(324\) | −3.74264 | − | 6.48244i | −0.207924 | − | 0.360136i | ||||
\(325\) | 6.08579 | − | 10.5409i | 0.337579 | − | 0.584703i | ||||
\(326\) | 7.86396 | − | 13.6208i | 0.435545 | − | 0.754385i | ||||
\(327\) | −0.100505 | − | 0.174080i | −0.00555794 | − | 0.00962664i | ||||
\(328\) | 2.58579 | 0.142776 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.41421 | −0.0778499 | ||||||||
\(331\) | 4.96447 | + | 8.59871i | 0.272872 | + | 0.472628i | 0.969596 | − | 0.244711i | \(-0.0786932\pi\) |
−0.696724 | + | 0.717339i | \(0.745360\pi\) | |||||||
\(332\) | 8.07107 | − | 13.9795i | 0.442957 | − | 0.767225i | ||||
\(333\) | −9.31371 | + | 16.1318i | −0.510388 | + | 0.884018i | ||||
\(334\) | −5.86396 | − | 10.1567i | −0.320862 | − | 0.555749i | ||||
\(335\) | 38.3848 | 2.09718 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.7574 | −1.07625 | −0.538126 | − | 0.842864i | \(-0.680868\pi\) | ||||
−0.538126 | + | 0.842864i | \(0.680868\pi\) | |||||||
\(338\) | 4.82843 | + | 8.36308i | 0.262632 | + | 0.454892i | ||||
\(339\) | −2.86396 | + | 4.96053i | −0.155549 | + | 0.269419i | ||||
\(340\) | −13.0711 | + | 22.6398i | −0.708878 | + | 1.22781i | ||||
\(341\) | −2.00000 | − | 3.46410i | −0.108306 | − | 0.187592i | ||||
\(342\) | −9.65685 | −0.522183 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 5.65685 | 0.304997 | ||||||||
\(345\) | 1.58579 | + | 2.74666i | 0.0853759 | + | 0.147875i | ||||
\(346\) | −2.08579 | + | 3.61269i | −0.112133 | + | 0.194219i | ||||
\(347\) | −7.29289 | + | 12.6317i | −0.391503 | + | 0.678103i | −0.992648 | − | 0.121037i | \(-0.961378\pi\) |
0.601145 | + | 0.799140i | \(0.294711\pi\) | |||||||
\(348\) | −1.79289 | − | 3.10538i | −0.0961092 | − | 0.166466i | ||||
\(349\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.41421 | −0.235613 | ||||||||
\(352\) | −0.500000 | − | 0.866025i | −0.0266501 | − | 0.0461593i | ||||
\(353\) | −12.6569 | + | 21.9223i | −0.673656 | + | 1.16681i | 0.303203 | + | 0.952926i | \(0.401944\pi\) |
−0.976860 | + | 0.213881i | \(0.931389\pi\) | |||||||
\(354\) | 1.74264 | − | 3.01834i | 0.0926203 | − | 0.160423i | ||||
\(355\) | −5.24264 | − | 9.08052i | −0.278250 | − | 0.481944i | ||||
\(356\) | 4.48528 | 0.237719 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −18.8995 | −0.998869 | ||||||||
\(359\) | −5.37868 | − | 9.31615i | −0.283876 | − | 0.491687i | 0.688460 | − | 0.725274i | \(-0.258287\pi\) |
−0.972336 | + | 0.233587i | \(0.924954\pi\) | |||||||
\(360\) | 4.82843 | − | 8.36308i | 0.254480 | − | 0.440773i | ||||
\(361\) | 3.67157 | − | 6.35935i | 0.193241 | − | 0.334703i | ||||
\(362\) | 1.82843 | + | 3.16693i | 0.0961000 | + | 0.166450i | ||||
\(363\) | −0.414214 | −0.0217406 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 22.4853 | 1.17693 | ||||||||
\(366\) | −1.27817 | − | 2.21386i | −0.0668113 | − | 0.115720i | ||||
\(367\) | 7.36396 | − | 12.7548i | 0.384396 | − | 0.665793i | −0.607290 | − | 0.794481i | \(-0.707743\pi\) |
0.991685 | + | 0.128688i | \(0.0410765\pi\) | |||||||
\(368\) | −1.12132 | + | 1.94218i | −0.0584529 | + | 0.101243i | ||||
\(369\) | 3.65685 | + | 6.33386i | 0.190368 | + | 0.329727i | ||||
\(370\) | −22.4853 | −1.16895 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.65685 | −0.0859039 | ||||||||
\(373\) | −6.98528 | − | 12.0989i | −0.361684 | − | 0.626455i | 0.626554 | − | 0.779378i | \(-0.284465\pi\) |
−0.988238 | + | 0.152923i | \(0.951131\pi\) | |||||||
\(374\) | −3.82843 | + | 6.63103i | −0.197963 | + | 0.342882i | ||||
\(375\) | 1.17157 | − | 2.02922i | 0.0604998 | − | 0.104789i | ||||
\(376\) | 3.24264 | + | 5.61642i | 0.167226 | + | 0.289645i | ||||
\(377\) | 15.8284 | 0.815205 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.8701 | −1.32886 | −0.664428 | − | 0.747352i | \(-0.731325\pi\) | ||||
−0.664428 | + | 0.747352i | \(0.731325\pi\) | |||||||
\(380\) | −5.82843 | − | 10.0951i | −0.298992 | − | 0.517869i | ||||
\(381\) | −2.01472 | + | 3.48960i | −0.103217 | + | 0.178777i | ||||
\(382\) | 6.41421 | − | 11.1097i | 0.328180 | − | 0.568424i | ||||
\(383\) | 15.1924 | + | 26.3140i | 0.776295 | + | 1.34458i | 0.934064 | + | 0.357106i | \(0.116236\pi\) |
−0.157769 | + | 0.987476i | \(0.550430\pi\) | |||||||
\(384\) | −0.414214 | −0.0211377 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.10051 | 0.106913 | ||||||||
\(387\) | 8.00000 | + | 13.8564i | 0.406663 | + | 0.704361i | ||||
\(388\) | 0.914214 | − | 1.58346i | 0.0464122 | − | 0.0803882i | ||||
\(389\) | −1.36396 | + | 2.36245i | −0.0691556 | + | 0.119781i | −0.898530 | − | 0.438912i | \(-0.855364\pi\) |
0.829374 | + | 0.558693i | \(0.188697\pi\) | |||||||
\(390\) | −1.29289 | − | 2.23936i | −0.0654682 | − | 0.113394i | ||||
\(391\) | 17.1716 | 0.868404 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.41421 | −0.0713376 | ||||||||
\(394\) | 8.74264 | + | 15.1427i | 0.440448 | + | 0.762878i | ||||
\(395\) | 8.12132 | − | 14.0665i | 0.408628 | − | 0.707764i | ||||
\(396\) | 1.41421 | − | 2.44949i | 0.0710669 | − | 0.123091i | ||||
\(397\) | 11.0000 | + | 19.0526i | 0.552074 | + | 0.956221i | 0.998125 | + | 0.0612128i | \(0.0194968\pi\) |
−0.446051 | + | 0.895008i | \(0.647170\pi\) | |||||||
\(398\) | −19.8995 | −0.997472 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.65685 | 0.332843 | ||||||||
\(401\) | 2.15685 | + | 3.73578i | 0.107708 | + | 0.186556i | 0.914841 | − | 0.403813i | \(-0.132315\pi\) |
−0.807133 | + | 0.590369i | \(0.798982\pi\) | |||||||
\(402\) | 2.32843 | − | 4.03295i | 0.116131 | − | 0.201145i | ||||
\(403\) | 3.65685 | − | 6.33386i | 0.182161 | − | 0.315512i | ||||
\(404\) | 5.91421 | + | 10.2437i | 0.294243 | + | 0.509644i | ||||
\(405\) | 25.5563 | 1.26991 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.58579 | −0.326445 | ||||||||
\(408\) | 1.58579 | + | 2.74666i | 0.0785081 | + | 0.135980i | ||||
\(409\) | −11.3640 | + | 19.6830i | −0.561912 | + | 0.973260i | 0.435418 | + | 0.900228i | \(0.356601\pi\) |
−0.997330 | + | 0.0730312i | \(0.976733\pi\) | |||||||
\(410\) | −4.41421 | + | 7.64564i | −0.218002 | + | 0.377591i | ||||
\(411\) | −1.10660 | − | 1.91669i | −0.0545846 | − | 0.0945434i | ||||
\(412\) | −10.5858 | −0.521524 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −6.34315 | −0.311749 | ||||||||
\(415\) | 27.5563 | + | 47.7290i | 1.35269 | + | 2.34292i | ||||
\(416\) | 0.914214 | − | 1.58346i | 0.0448230 | − | 0.0776357i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.70711 | − | 2.95680i | −0.0834973 | − | 0.144622i | ||||
\(419\) | −2.14214 | −0.104650 | −0.0523251 | − | 0.998630i | \(-0.516663\pi\) | ||||
−0.0523251 | + | 0.998630i | \(0.516663\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.3137 | 1.13624 | 0.568120 | − | 0.822946i | \(-0.307671\pi\) | ||||
0.568120 | + | 0.822946i | \(0.307671\pi\) | |||||||
\(422\) | −2.29289 | − | 3.97141i | −0.111616 | − | 0.193325i | ||||
\(423\) | −9.17157 | + | 15.8856i | −0.445937 | + | 0.772386i | ||||
\(424\) | 5.94975 | − | 10.3053i | 0.288945 | − | 0.500468i | ||||
\(425\) | −25.4853 | − | 44.1418i | −1.23622 | − | 2.14119i | ||||
\(426\) | −1.27208 | −0.0616324 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 11.0711 | 0.535140 | ||||||||
\(429\) | −0.378680 | − | 0.655892i | −0.0182828 | − | 0.0316668i | ||||
\(430\) | −9.65685 | + | 16.7262i | −0.465695 | + | 0.806607i | ||||
\(431\) | 10.2071 | − | 17.6792i | 0.491659 | − | 0.851578i | −0.508295 | − | 0.861183i | \(-0.669724\pi\) |
0.999954 | + | 0.00960469i | \(0.00305731\pi\) | |||||||
\(432\) | −1.20711 | − | 2.09077i | −0.0580770 | − | 0.100592i | ||||
\(433\) | 2.14214 | 0.102944 | 0.0514722 | − | 0.998674i | \(-0.483609\pi\) | ||||
0.0514722 | + | 0.998674i | \(0.483609\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 12.2426 | 0.586990 | ||||||||
\(436\) | 0.242641 | + | 0.420266i | 0.0116204 | + | 0.0201271i | ||||
\(437\) | −3.82843 | + | 6.63103i | −0.183139 | + | 0.317205i | ||||
\(438\) | 1.36396 | − | 2.36245i | 0.0651726 | − | 0.112882i | ||||
\(439\) | 4.69239 | + | 8.12745i | 0.223955 | + | 0.387902i | 0.956006 | − | 0.293349i | \(-0.0947696\pi\) |
−0.732050 | + | 0.681251i | \(0.761436\pi\) | |||||||
\(440\) | 3.41421 | 0.162766 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −14.0000 | −0.665912 | ||||||||
\(443\) | 16.3137 | + | 28.2562i | 0.775088 | + | 1.34249i | 0.934745 | + | 0.355319i | \(0.115628\pi\) |
−0.159658 | + | 0.987172i | \(0.551039\pi\) | |||||||
\(444\) | −1.36396 | + | 2.36245i | −0.0647307 | + | 0.112117i | ||||
\(445\) | −7.65685 | + | 13.2621i | −0.362970 | + | 0.628682i | ||||
\(446\) | 5.70711 | + | 9.88500i | 0.270239 | + | 0.468068i | ||||
\(447\) | −2.62742 | −0.124273 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.6569 | 1.58837 | 0.794183 | − | 0.607679i | \(-0.207899\pi\) | ||||
0.794183 | + | 0.607679i | \(0.207899\pi\) | |||||||
\(450\) | 9.41421 | + | 16.3059i | 0.443790 | + | 0.768667i | ||||
\(451\) | −1.29289 | + | 2.23936i | −0.0608800 | + | 0.105447i | ||||
\(452\) | 6.91421 | − | 11.9758i | 0.325217 | − | 0.563293i | ||||
\(453\) | 2.01472 | + | 3.48960i | 0.0946597 | + | 0.163955i | ||||
\(454\) | 23.1716 | 1.08750 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.41421 | −0.0662266 | ||||||||
\(457\) | 0.171573 | + | 0.297173i | 0.00802584 | + | 0.0139012i | 0.870010 | − | 0.493033i | \(-0.164112\pi\) |
−0.861985 | + | 0.506934i | \(0.830779\pi\) | |||||||
\(458\) | 0.343146 | − | 0.594346i | 0.0160341 | − | 0.0277720i | ||||
\(459\) | −9.24264 | + | 16.0087i | −0.431410 | + | 0.747223i | ||||
\(460\) | −3.82843 | − | 6.63103i | −0.178501 | − | 0.309173i | ||||
\(461\) | −14.3137 | −0.666656 | −0.333328 | − | 0.942811i | \(-0.608172\pi\) | ||||
−0.333328 | + | 0.942811i | \(0.608172\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.17157 | 0.333291 | 0.166646 | − | 0.986017i | \(-0.446706\pi\) | ||||
0.166646 | + | 0.986017i | \(0.446706\pi\) | |||||||
\(464\) | 4.32843 | + | 7.49706i | 0.200942 | + | 0.348042i | ||||
\(465\) | 2.82843 | − | 4.89898i | 0.131165 | − | 0.227185i | ||||
\(466\) | 0.707107 | − | 1.22474i | 0.0327561 | − | 0.0567352i | ||||
\(467\) | −17.0000 | − | 29.4449i | −0.786666 | − | 1.36255i | −0.927999 | − | 0.372584i | \(-0.878472\pi\) |
0.141332 | − | 0.989962i | \(-0.454861\pi\) | |||||||
\(468\) | 5.17157 | 0.239056 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −22.1421 | −1.02134 | ||||||||
\(471\) | −1.31371 | − | 2.27541i | −0.0605325 | − | 0.104845i | ||||
\(472\) | −4.20711 | + | 7.28692i | −0.193648 | + | 0.335408i | ||||
\(473\) | −2.82843 | + | 4.89898i | −0.130051 | + | 0.225255i | ||||
\(474\) | −0.985281 | − | 1.70656i | −0.0452555 | − | 0.0783848i | ||||
\(475\) | 22.7279 | 1.04283 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 33.6569 | 1.54104 | ||||||||
\(478\) | 11.1066 | + | 19.2372i | 0.508004 | + | 0.879889i | ||||
\(479\) | −13.0355 | + | 22.5782i | −0.595609 | + | 1.03162i | 0.397852 | + | 0.917450i | \(0.369756\pi\) |
−0.993461 | + | 0.114175i | \(0.963578\pi\) | |||||||
\(480\) | 0.707107 | − | 1.22474i | 0.0322749 | − | 0.0559017i | ||||
\(481\) | −6.02082 | − | 10.4284i | −0.274526 | − | 0.475492i | ||||
\(482\) | −3.75736 | −0.171143 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 3.12132 | + | 5.40629i | 0.141732 | + | 0.245487i | ||||
\(486\) | 5.17157 | − | 8.95743i | 0.234587 | − | 0.406317i | ||||
\(487\) | −0.828427 | + | 1.43488i | −0.0375396 | + | 0.0650205i | −0.884185 | − | 0.467137i | \(-0.845285\pi\) |
0.846645 | + | 0.532158i | \(0.178619\pi\) | |||||||
\(488\) | 3.08579 | + | 5.34474i | 0.139687 | + | 0.241945i | ||||
\(489\) | 6.51472 | 0.294606 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.8284 | 1.12049 | 0.560246 | − | 0.828327i | \(-0.310707\pi\) | ||||
0.560246 | + | 0.828327i | \(0.310707\pi\) | |||||||
\(492\) | 0.535534 | + | 0.927572i | 0.0241437 | + | 0.0418182i | ||||
\(493\) | 33.1421 | − | 57.4039i | 1.49265 | − | 2.58534i | ||||
\(494\) | 3.12132 | − | 5.40629i | 0.140435 | − | 0.243240i | ||||
\(495\) | 4.82843 | + | 8.36308i | 0.217022 | + | 0.375893i | ||||
\(496\) | 4.00000 | 0.179605 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 6.68629 | 0.299620 | ||||||||
\(499\) | 3.07107 | + | 5.31925i | 0.137480 | + | 0.238122i | 0.926542 | − | 0.376191i | \(-0.122766\pi\) |
−0.789062 | + | 0.614313i | \(0.789433\pi\) | |||||||
\(500\) | −2.82843 | + | 4.89898i | −0.126491 | + | 0.219089i | ||||
\(501\) | 2.42893 | − | 4.20703i | 0.108517 | − | 0.187956i | ||||
\(502\) | 1.07107 | + | 1.85514i | 0.0478041 | + | 0.0827991i | ||||
\(503\) | 38.2132 | 1.70384 | 0.851921 | − | 0.523670i | \(-0.175437\pi\) | ||||
0.851921 | + | 0.523670i | \(0.175437\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −40.3848 | −1.79710 | ||||||||
\(506\) | −1.12132 | − | 1.94218i | −0.0498488 | − | 0.0863406i | ||||
\(507\) | −2.00000 | + | 3.46410i | −0.0888231 | + | 0.153846i | ||||
\(508\) | 4.86396 | − | 8.42463i | 0.215803 | − | 0.373782i | ||||
\(509\) | −6.65685 | − | 11.5300i | −0.295060 | − | 0.511059i | 0.679939 | − | 0.733269i | \(-0.262006\pi\) |
−0.974999 | + | 0.222210i | \(0.928673\pi\) | |||||||
\(510\) | −10.8284 | −0.479491 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −4.12132 | − | 7.13834i | −0.181961 | − | 0.315165i | ||||
\(514\) | 1.57107 | − | 2.72117i | 0.0692968 | − | 0.120026i | ||||
\(515\) | 18.0711 | − | 31.3000i | 0.796306 | − | 1.37924i | ||||
\(516\) | 1.17157 | + | 2.02922i | 0.0515756 | + | 0.0893316i | ||||
\(517\) | −6.48528 | −0.285222 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.72792 | −0.0758474 | ||||||||
\(520\) | 3.12132 | + | 5.40629i | 0.136879 | + | 0.237081i | ||||
\(521\) | 14.1421 | − | 24.4949i | 0.619578 | − | 1.07314i | −0.369984 | − | 0.929038i | \(-0.620637\pi\) |
0.989563 | − | 0.144103i | \(-0.0460297\pi\) | |||||||
\(522\) | −12.2426 | + | 21.2049i | −0.535846 | + | 0.928112i | ||||
\(523\) | 6.36396 | + | 11.0227i | 0.278277 | + | 0.481989i | 0.970957 | − | 0.239256i | \(-0.0769035\pi\) |
−0.692680 | + | 0.721245i | \(0.743570\pi\) | |||||||
\(524\) | 3.41421 | 0.149151 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 31.0416 | 1.35348 | ||||||||
\(527\) | −15.3137 | − | 26.5241i | −0.667076 | − | 1.15541i | ||||
\(528\) | 0.207107 | − | 0.358719i | 0.00901317 | − | 0.0156113i | ||||
\(529\) | 8.98528 | − | 15.5630i | 0.390664 | − | 0.676651i | ||||
\(530\) | 20.3137 | + | 35.1844i | 0.882371 | + | 1.52831i | ||||
\(531\) | −23.7990 | −1.03279 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.72792 | −0.204789 | ||||||||
\(534\) | 0.928932 | + | 1.60896i | 0.0401988 | + | 0.0696264i | ||||
\(535\) | −18.8995 | + | 32.7349i | −0.817096 | + | 1.41525i | ||||
\(536\) | −5.62132 | + | 9.73641i | −0.242804 | + | 0.420549i | ||||
\(537\) | −3.91421 | − | 6.77962i | −0.168911 | − | 0.292562i | ||||
\(538\) | −13.6569 | −0.588789 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 8.24264 | 0.354707 | ||||||||
\(541\) | 20.5711 | + | 35.6301i | 0.884419 | + | 1.53186i | 0.846378 | + | 0.532583i | \(0.178779\pi\) |
0.0380415 | + | 0.999276i | \(0.487888\pi\) | |||||||
\(542\) | −13.2782 | + | 22.9985i | −0.570346 | + | 0.987869i | ||||
\(543\) | −0.757359 | + | 1.31178i | −0.0325014 | + | 0.0562941i | ||||
\(544\) | −3.82843 | − | 6.63103i | −0.164142 | − | 0.284303i | ||||
\(545\) | −1.65685 | −0.0709718 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.8701 | −0.806825 | −0.403413 | − | 0.915018i | \(-0.632176\pi\) | ||||
−0.403413 | + | 0.915018i | \(0.632176\pi\) | |||||||
\(548\) | 2.67157 | + | 4.62730i | 0.114124 | + | 0.197668i | ||||
\(549\) | −8.72792 | + | 15.1172i | −0.372499 | + | 0.645187i | ||||
\(550\) | −3.32843 | + | 5.76500i | −0.141925 | + | 0.245821i | ||||
\(551\) | 14.7782 | + | 25.5965i | 0.629571 | + | 1.09045i | ||||
\(552\) | −0.928932 | −0.0395380 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3.82843 | −0.162654 | ||||||||
\(555\) | −4.65685 | − | 8.06591i | −0.197672 | − | 0.342379i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.2426 | + | 21.2049i | −0.518737 | + | 0.898479i | 0.481026 | + | 0.876707i | \(0.340264\pi\) |
−0.999763 | + | 0.0217729i | \(0.993069\pi\) | |||||||
\(558\) | 5.65685 | + | 9.79796i | 0.239474 | + | 0.414781i | ||||
\(559\) | −10.3431 | −0.437468 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.17157 | −0.133904 | ||||||||
\(562\) | 8.36396 | + | 14.4868i | 0.352812 | + | 0.611089i | ||||
\(563\) | −2.53553 | + | 4.39167i | −0.106860 | + | 0.185087i | −0.914497 | − | 0.404594i | \(-0.867413\pi\) |
0.807637 | + | 0.589681i | \(0.200746\pi\) | |||||||
\(564\) | −1.34315 | + | 2.32640i | −0.0565566 | + | 0.0979590i | ||||
\(565\) | 23.6066 | + | 40.8878i | 0.993137 | + | 1.72016i | ||||
\(566\) | 20.5858 | 0.865285 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.07107 | 0.128859 | ||||||||
\(569\) | 2.00000 | + | 3.46410i | 0.0838444 | + | 0.145223i | 0.904898 | − | 0.425628i | \(-0.139947\pi\) |
−0.821054 | + | 0.570851i | \(0.806613\pi\) | |||||||
\(570\) | 2.41421 | − | 4.18154i | 0.101120 | − | 0.175145i | ||||
\(571\) | 5.19239 | − | 8.99348i | 0.217295 | − | 0.376365i | −0.736685 | − | 0.676236i | \(-0.763610\pi\) |
0.953980 | + | 0.299870i | \(0.0969434\pi\) | |||||||
\(572\) | 0.914214 | + | 1.58346i | 0.0382252 | + | 0.0662080i | ||||
\(573\) | 5.31371 | 0.221983 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 14.9289 | 0.622580 | ||||||||
\(576\) | 1.41421 | + | 2.44949i | 0.0589256 | + | 0.102062i | ||||
\(577\) | −16.1569 | + | 27.9845i | −0.672619 | + | 1.16501i | 0.304540 | + | 0.952499i | \(0.401497\pi\) |
−0.977159 | + | 0.212510i | \(0.931836\pi\) | |||||||
\(578\) | −20.8137 | + | 36.0504i | −0.865736 | + | 1.49950i | ||||
\(579\) | 0.435029 | + | 0.753492i | 0.0180792 | + | 0.0313141i | ||||
\(580\) | −29.5563 | −1.22726 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0.757359 | 0.0313936 | ||||||||
\(583\) | 5.94975 | + | 10.3053i | 0.246413 | + | 0.426800i | ||||
\(584\) | −3.29289 | + | 5.70346i | −0.136261 | + | 0.236011i | ||||
\(585\) | −8.82843 | + | 15.2913i | −0.365011 | + | 0.632217i | ||||
\(586\) | −2.58579 | − | 4.47871i | −0.106818 | − | 0.185014i | ||||
\(587\) | 44.8995 | 1.85320 | 0.926600 | − | 0.376048i | \(-0.122717\pi\) | ||||
0.926600 | + | 0.376048i | \(0.122717\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.6569 | 0.562721 | ||||||||
\(590\) | −14.3640 | − | 24.8791i | −0.591355 | − | 1.02426i | ||||
\(591\) | −3.62132 | + | 6.27231i | −0.148961 | + | 0.258008i | ||||
\(592\) | 3.29289 | − | 5.70346i | 0.135337 | − | 0.234411i | ||||
\(593\) | −17.8492 | − | 30.9158i | −0.732981 | − | 1.26956i | −0.955604 | − | 0.294655i | \(-0.904795\pi\) |
0.222623 | − | 0.974905i | \(-0.428538\pi\) | |||||||
\(594\) | 2.41421 | 0.0990564 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.34315 | 0.259825 | ||||||||
\(597\) | −4.12132 | − | 7.13834i | −0.168674 | − | 0.292153i | ||||
\(598\) | 2.05025 | − | 3.55114i | 0.0838411 | − | 0.145217i | ||||
\(599\) | 1.31371 | − | 2.27541i | 0.0536767 | − | 0.0929707i | −0.837939 | − | 0.545765i | \(-0.816239\pi\) |
0.891615 | + | 0.452794i | \(0.149573\pi\) | |||||||
\(600\) | 1.37868 | + | 2.38794i | 0.0562844 | + | 0.0974874i | ||||
\(601\) | 35.9411 | 1.46607 | 0.733035 | − | 0.680191i | \(-0.238103\pi\) | ||||
0.733035 | + | 0.680191i | \(0.238103\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −31.7990 | −1.29495 | ||||||||
\(604\) | −4.86396 | − | 8.42463i | −0.197912 | − | 0.342793i | ||||
\(605\) | −1.70711 | + | 2.95680i | −0.0694038 | + | 0.120211i | ||||
\(606\) | −2.44975 | + | 4.24309i | −0.0995142 | + | 0.172364i | ||||
\(607\) | −4.51472 | − | 7.81972i | −0.183247 | − | 0.317393i | 0.759738 | − | 0.650230i | \(-0.225327\pi\) |
−0.942984 | + | 0.332837i | \(0.891994\pi\) | |||||||
\(608\) | 3.41421 | 0.138465 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −21.0711 | −0.853143 | ||||||||
\(611\) | −5.92893 | − | 10.2692i | −0.239859 | − | 0.415448i | ||||
\(612\) | 10.8284 | − | 18.7554i | 0.437713 | − | 0.758142i | ||||
\(613\) | 8.31371 | − | 14.3998i | 0.335788 | − | 0.581601i | −0.647848 | − | 0.761769i | \(-0.724331\pi\) |
0.983636 | + | 0.180168i | \(0.0576643\pi\) | |||||||
\(614\) | −4.94975 | − | 8.57321i | −0.199756 | − | 0.345987i | ||||
\(615\) | −3.65685 | −0.147459 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.02944 | −0.323253 | −0.161626 | − | 0.986852i | \(-0.551674\pi\) | ||||
−0.161626 | + | 0.986852i | \(0.551674\pi\) | |||||||
\(618\) | −2.19239 | − | 3.79733i | −0.0881908 | − | 0.152751i | ||||
\(619\) | 22.9706 | − | 39.7862i | 0.923265 | − | 1.59914i | 0.128937 | − | 0.991653i | \(-0.458844\pi\) |
0.794328 | − | 0.607489i | \(-0.207823\pi\) | |||||||
\(620\) | −6.82843 | + | 11.8272i | −0.274236 | + | 0.474991i | ||||
\(621\) | −2.70711 | − | 4.68885i | −0.108632 | − | 0.188157i | ||||
\(622\) | 8.72792 | 0.349958 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0.757359 | 0.0303186 | ||||||||
\(625\) | 6.98528 | + | 12.0989i | 0.279411 | + | 0.483954i | ||||
\(626\) | −4.67157 | + | 8.09140i | −0.186714 | + | 0.323397i | ||||
\(627\) | 0.707107 | − | 1.22474i | 0.0282391 | − | 0.0489116i | ||||
\(628\) | 3.17157 | + | 5.49333i | 0.126560 | + | 0.219208i | ||||
\(629\) | −50.4264 | −2.01063 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 48.7279 | 1.93983 | 0.969914 | − | 0.243448i | \(-0.0782785\pi\) | ||||
0.969914 | + | 0.243448i | \(0.0782785\pi\) | |||||||
\(632\) | 2.37868 | + | 4.11999i | 0.0946188 | + | 0.163885i | ||||
\(633\) | 0.949747 | − | 1.64501i | 0.0377491 | − | 0.0653833i | ||||
\(634\) | −15.6569 | + | 27.1185i | −0.621813 | + | 1.07701i | ||||
\(635\) | 16.6066 | + | 28.7635i | 0.659013 | + | 1.14144i | ||||
\(636\) | 4.92893 | 0.195445 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −8.65685 | −0.342728 | ||||||||
\(639\) | 4.34315 | + | 7.52255i | 0.171812 | + | 0.297587i | ||||
\(640\) | −1.70711 | + | 2.95680i | −0.0674793 | + | 0.116878i | ||||
\(641\) | 20.6421 | − | 35.7532i | 0.815315 | − | 1.41217i | −0.0937859 | − | 0.995592i | \(-0.529897\pi\) |
0.909101 | − | 0.416575i | \(-0.136770\pi\) | |||||||
\(642\) | 2.29289 | + | 3.97141i | 0.0904933 | + | 0.156739i | ||||
\(643\) | −4.41421 | −0.174080 | −0.0870398 | − | 0.996205i | \(-0.527741\pi\) | ||||
−0.0870398 | + | 0.996205i | \(0.527741\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.00000 | −0.315000 | ||||||||
\(646\) | −13.0711 | − | 22.6398i | −0.514274 | − | 0.890749i | ||||
\(647\) | −23.0919 | + | 39.9963i | −0.907836 | + | 1.57242i | −0.0907706 | + | 0.995872i | \(0.528933\pi\) |
−0.817065 | + | 0.576546i | \(0.804400\pi\) | |||||||
\(648\) | −3.74264 | + | 6.48244i | −0.147025 | + | 0.254654i | ||||
\(649\) | −4.20711 | − | 7.28692i | −0.165143 | − | 0.286037i | ||||
\(650\) | −12.1716 | −0.477408 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −15.7279 | −0.615953 | ||||||||
\(653\) | −9.19239 | − | 15.9217i | −0.359726 | − | 0.623064i | 0.628189 | − | 0.778061i | \(-0.283796\pi\) |
−0.987915 | + | 0.154997i | \(0.950463\pi\) | |||||||
\(654\) | −0.100505 | + | 0.174080i | −0.00393006 | + | 0.00680706i | ||||
\(655\) | −5.82843 | + | 10.0951i | −0.227735 | + | 0.394449i | ||||
\(656\) | −1.29289 | − | 2.23936i | −0.0504790 | − | 0.0874322i | ||||
\(657\) | −18.6274 | −0.726725 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.0000 | −0.467454 | −0.233727 | − | 0.972302i | \(-0.575092\pi\) | ||||
−0.233727 | + | 0.972302i | \(0.575092\pi\) | |||||||
\(660\) | 0.707107 | + | 1.22474i | 0.0275241 | + | 0.0476731i | ||||
\(661\) | −7.48528 | + | 12.9649i | −0.291144 | + | 0.504276i | −0.974080 | − | 0.226202i | \(-0.927369\pi\) |
0.682937 | + | 0.730478i | \(0.260702\pi\) | |||||||
\(662\) | 4.96447 | − | 8.59871i | 0.192949 | − | 0.334198i | ||||
\(663\) | −2.89949 | − | 5.02207i | −0.112607 | − | 0.195041i | ||||
\(664\) | −16.1421 | −0.626436 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 18.6274 | 0.721798 | ||||||||
\(667\) | 9.70711 | + | 16.8132i | 0.375861 | + | 0.651010i | ||||
\(668\) | −5.86396 | + | 10.1567i | −0.226883 | + | 0.392974i | ||||
\(669\) | −2.36396 | + | 4.09450i | −0.0913960 | + | 0.158303i | ||||
\(670\) | −19.1924 | − | 33.2422i | −0.741467 | − | 1.28426i | ||||
\(671\) | −6.17157 | −0.238251 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.5563 | −0.985125 | −0.492562 | − | 0.870277i | \(-0.663940\pi\) | ||||
−0.492562 | + | 0.870277i | \(0.663940\pi\) | |||||||
\(674\) | 9.87868 | + | 17.1104i | 0.380513 | + | 0.659067i | ||||
\(675\) | −8.03553 | + | 13.9180i | −0.309288 | + | 0.535702i | ||||
\(676\) | 4.82843 | − | 8.36308i | 0.185709 | − | 0.321657i | ||||
\(677\) | −6.34315 | − | 10.9867i | −0.243787 | − | 0.422251i | 0.718003 | − | 0.696040i | \(-0.245056\pi\) |
−0.961790 | + | 0.273789i | \(0.911723\pi\) | |||||||
\(678\) | 5.72792 | 0.219980 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 26.1421 | 1.00251 | ||||||||
\(681\) | 4.79899 | + | 8.31209i | 0.183898 | + | 0.318520i | ||||
\(682\) | −2.00000 | + | 3.46410i | −0.0765840 | + | 0.132647i | ||||
\(683\) | −8.20711 | + | 14.2151i | −0.314036 | + | 0.543927i | −0.979232 | − | 0.202742i | \(-0.935015\pi\) |
0.665196 | + | 0.746669i | \(0.268348\pi\) | |||||||
\(684\) | 4.82843 | + | 8.36308i | 0.184620 | + | 0.319770i | ||||
\(685\) | −18.2426 | −0.697015 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.284271 | 0.0108456 | ||||||||
\(688\) | −2.82843 | − | 4.89898i | −0.107833 | − | 0.186772i | ||||
\(689\) | −10.8787 | + | 18.8424i | −0.414445 | + | 0.717839i | ||||
\(690\) | 1.58579 | − | 2.74666i | 0.0603699 | − | 0.104564i | ||||
\(691\) | 6.96447 | + | 12.0628i | 0.264941 | + | 0.458891i | 0.967548 | − | 0.252687i | \(-0.0813143\pi\) |
−0.702607 | + | 0.711578i | \(0.747981\pi\) | |||||||
\(692\) | 4.17157 | 0.158579 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.5858 | 0.553669 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.79289 | + | 3.10538i | −0.0679594 | + | 0.117709i | ||||
\(697\) | −9.89949 | + | 17.1464i | −0.374970 | + | 0.649467i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.585786 | 0.0221565 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.1127 | 1.36396 | 0.681979 | − | 0.731372i | \(-0.261120\pi\) | ||||
0.681979 | + | 0.731372i | \(0.261120\pi\) | |||||||
\(702\) | 2.20711 | + | 3.82282i | 0.0833019 | + | 0.144283i | ||||
\(703\) | 11.2426 | − | 19.4728i | 0.424024 | − | 0.734432i | ||||
\(704\) | −0.500000 | + | 0.866025i | −0.0188445 | + | 0.0326396i | ||||
\(705\) | −4.58579 | − | 7.94282i | −0.172711 | − | 0.299144i | ||||
\(706\) | 25.3137 | 0.952694 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −3.48528 | −0.130985 | ||||||||
\(709\) | −18.0208 | − | 31.2130i | −0.676786 | − | 1.17223i | −0.975943 | − | 0.218024i | \(-0.930039\pi\) |
0.299158 | − | 0.954204i | \(-0.403294\pi\) | |||||||
\(710\) | −5.24264 | + | 9.08052i | −0.196753 | + | 0.340786i | ||||
\(711\) | −6.72792 | + | 11.6531i | −0.252317 | + | 0.437026i | ||||
\(712\) | −2.24264 | − | 3.88437i | −0.0840465 | − | 0.145573i | ||||
\(713\) | 8.97056 | 0.335950 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.24264 | −0.233462 | ||||||||
\(716\) | 9.44975 | + | 16.3674i | 0.353154 | + | 0.611680i | ||||
\(717\) | −4.60051 | + | 7.96831i | −0.171809 | + | 0.297582i | ||||
\(718\) | −5.37868 | + | 9.31615i | −0.200731 | + | 0.347675i | ||||
\(719\) | −9.24264 | − | 16.0087i | −0.344692 | − | 0.597025i | 0.640605 | − | 0.767870i | \(-0.278683\pi\) |
−0.985298 | + | 0.170846i | \(0.945350\pi\) | |||||||
\(720\) | −9.65685 | −0.359890 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −7.34315 | −0.273284 | ||||||||
\(723\) | −0.778175 | − | 1.34784i | −0.0289406 | − | 0.0501266i | ||||
\(724\) | 1.82843 | − | 3.16693i | 0.0679530 | − | 0.117698i | ||||
\(725\) | 28.8137 | − | 49.9068i | 1.07011 | − | 1.85349i | ||||
\(726\) | 0.207107 | + | 0.358719i | 0.00768645 | + | 0.0133133i | ||||
\(727\) | 48.4264 | 1.79604 | 0.898018 | − | 0.439959i | \(-0.145007\pi\) | ||||
0.898018 | + | 0.439959i | \(0.145007\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.1716 | −0.673021 | ||||||||
\(730\) | −11.2426 | − | 19.4728i | −0.416109 | − | 0.720722i | ||||
\(731\) | −21.6569 | + | 37.5108i | −0.801008 | + | 1.38739i | ||||
\(732\) | −1.27817 | + | 2.21386i | −0.0472427 | + | 0.0818267i | ||||
\(733\) | −6.50000 | − | 11.2583i | −0.240083 | − | 0.415836i | 0.720655 | − | 0.693294i | \(-0.243841\pi\) |
−0.960738 | + | 0.277458i | \(0.910508\pi\) | |||||||
\(734\) | −14.7279 | −0.543618 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.24264 | 0.0826648 | ||||||||
\(737\) | −5.62132 | − | 9.73641i | −0.207064 | − | 0.358645i | ||||
\(738\) | 3.65685 | − | 6.33386i | 0.134611 | − | 0.233153i | ||||
\(739\) | −16.2132 | + | 28.0821i | −0.596412 | + | 1.03302i | 0.396934 | + | 0.917847i | \(0.370074\pi\) |
−0.993346 | + | 0.115169i | \(0.963259\pi\) | |||||||
\(740\) | 11.2426 | + | 19.4728i | 0.413288 | + | 0.715835i | ||||
\(741\) | 2.58579 | 0.0949912 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.31371 | 0.341687 | 0.170843 | − | 0.985298i | \(-0.445351\pi\) | ||||
0.170843 | + | 0.985298i | \(0.445351\pi\) | |||||||
\(744\) | 0.828427 | + | 1.43488i | 0.0303716 | + | 0.0526052i | ||||
\(745\) | −10.8284 | + | 18.7554i | −0.396723 | + | 0.687144i | ||||
\(746\) | −6.98528 | + | 12.0989i | −0.255749 | + | 0.442971i | ||||
\(747\) | −22.8284 | − | 39.5400i | −0.835248 | − | 1.44669i | ||||
\(748\) | 7.65685 | 0.279962 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −2.34315 | −0.0855596 | ||||||||
\(751\) | −17.1716 | − | 29.7420i | −0.626600 | − | 1.08530i | −0.988229 | − | 0.152980i | \(-0.951113\pi\) |
0.361630 | − | 0.932322i | \(-0.382220\pi\) | |||||||
\(752\) | 3.24264 | − | 5.61642i | 0.118247 | − | 0.204810i | ||||
\(753\) | −0.443651 | + | 0.768426i | −0.0161675 | + | 0.0280030i | ||||
\(754\) | −7.91421 | − | 13.7078i | −0.288219 | − | 0.499209i | ||||
\(755\) | 33.2132 | 1.20875 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.6569 | 0.714441 | 0.357220 | − | 0.934020i | \(-0.383725\pi\) | ||||
0.357220 | + | 0.934020i | \(0.383725\pi\) | |||||||
\(758\) | 12.9350 | + | 22.4041i | 0.469821 | + | 0.813755i | ||||
\(759\) | 0.464466 | − | 0.804479i | 0.0168591 | − | 0.0292007i | ||||
\(760\) | −5.82843 | + | 10.0951i | −0.211419 | + | 0.366189i | ||||
\(761\) | −1.48528 | − | 2.57258i | −0.0538414 | − | 0.0932561i | 0.837849 | − | 0.545903i | \(-0.183813\pi\) |
−0.891690 | + | 0.452647i | \(0.850480\pi\) | |||||||
\(762\) | 4.02944 | 0.145971 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −12.8284 | −0.464116 | ||||||||
\(765\) | 36.9706 | + | 64.0349i | 1.33667 | + | 2.31519i | ||||
\(766\) | 15.1924 | − | 26.3140i | 0.548923 | − | 0.950763i | ||||
\(767\) | 7.69239 | − | 13.3236i | 0.277756 | − | 0.481088i | ||||
\(768\) | 0.207107 | + | 0.358719i | 0.00747332 | + | 0.0129442i | ||||
\(769\) | 10.9706 | 0.395609 | 0.197804 | − | 0.980242i | \(-0.436619\pi\) | ||||
0.197804 | + | 0.980242i | \(0.436619\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.30152 | 0.0468729 | ||||||||
\(772\) | −1.05025 | − | 1.81909i | −0.0377994 | − | 0.0654705i | ||||
\(773\) | 22.9706 | − | 39.7862i | 0.826194 | − | 1.43101i | −0.0748099 | − | 0.997198i | \(-0.523835\pi\) |
0.901004 | − | 0.433812i | \(-0.142832\pi\) | |||||||
\(774\) | 8.00000 | − | 13.8564i | 0.287554 | − | 0.498058i | ||||
\(775\) | −13.3137 | − | 23.0600i | −0.478243 | − | 0.828340i | ||||
\(776\) | −1.82843 | −0.0656367 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.72792 |