Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(1699,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.1699");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.z (of order \(6\), 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: | \(15.5708283941\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.3317760000.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 25x^{4} + 625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1699.1 | ||
Root | \(2.15988 - 0.578737i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.1699 |
Dual form | 1950.2.z.o.1849.1 |
$q$-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 \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | −0.866025 | − | 0.500000i | −0.500000 | − | 0.288675i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.500000 | + | 0.866025i | 0.204124 | + | 0.353553i | ||||
\(7\) | −2.73861 | + | 1.58114i | −1.03510 | + | 0.597614i | −0.918441 | − | 0.395558i | \(-0.870551\pi\) |
−0.116657 | + | 0.993172i | \(0.537218\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.50000 | + | 2.59808i | −0.452267 | + | 0.783349i | −0.998526 | − | 0.0542666i | \(-0.982718\pi\) |
0.546259 | + | 0.837616i | \(0.316051\pi\) | |||||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | −1.87259 | + | 3.08114i | −0.519362 | + | 0.854554i | ||||
\(14\) | 3.16228 | 0.845154 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 6.20271 | − | 3.58114i | 1.50438 | − | 0.868554i | 0.504392 | − | 0.863475i | \(-0.331717\pi\) |
0.999987 | − | 0.00507902i | \(-0.00161671\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | 1.58114 | + | 2.73861i | 0.362738 | + | 0.628281i | 0.988410 | − | 0.151805i | \(-0.0485086\pi\) |
−0.625672 | + | 0.780086i | \(0.715175\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.16228 | 0.690066 | ||||||||
\(22\) | 2.59808 | − | 1.50000i | 0.553912 | − | 0.319801i | ||||
\(23\) | −3.60464 | − | 2.08114i | −0.751619 | − | 0.433947i | 0.0746596 | − | 0.997209i | \(-0.476213\pi\) |
−0.826279 | + | 0.563262i | \(0.809546\pi\) | |||||||
\(24\) | −0.500000 | + | 0.866025i | −0.102062 | + | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.16228 | − | 1.73205i | 0.620174 | − | 0.339683i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −2.73861 | − | 1.58114i | −0.517549 | − | 0.298807i | ||||
\(29\) | −4.16228 | + | 7.20928i | −0.772916 | + | 1.33873i | 0.163043 | + | 0.986619i | \(0.447869\pi\) |
−0.935959 | + | 0.352110i | \(0.885464\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.16228 | 1.64559 | 0.822797 | − | 0.568336i | \(-0.192412\pi\) | ||||
0.822797 | + | 0.568336i | \(0.192412\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 2.59808 | − | 1.50000i | 0.452267 | − | 0.261116i | ||||
\(34\) | −7.16228 | −1.22832 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | −9.08186 | − | 5.24342i | −1.49305 | − | 0.862012i | −0.493081 | − | 0.869983i | \(-0.664129\pi\) |
−0.999968 | + | 0.00797106i | \(0.997463\pi\) | |||||||
\(38\) | − | 3.16228i | − | 0.512989i | ||||||
\(39\) | 3.16228 | − | 1.73205i | 0.506370 | − | 0.277350i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.74342 | − | 8.21584i | 0.740797 | − | 1.28310i | −0.211336 | − | 0.977414i | \(-0.567781\pi\) |
0.952133 | − | 0.305685i | \(-0.0988854\pi\) | |||||||
\(42\) | −2.73861 | − | 1.58114i | −0.422577 | − | 0.243975i | ||||
\(43\) | −4.47066 | + | 2.58114i | −0.681770 | + | 0.393620i | −0.800522 | − | 0.599304i | \(-0.795444\pi\) |
0.118752 | + | 0.992924i | \(0.462111\pi\) | |||||||
\(44\) | −3.00000 | −0.452267 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.08114 | + | 3.60464i | 0.306847 | + | 0.531475i | ||||
\(47\) | 6.00000i | 0.875190i | 0.899172 | + | 0.437595i | \(0.144170\pi\) | ||||
−0.899172 | + | 0.437595i | \(0.855830\pi\) | |||||||
\(48\) | 0.866025 | − | 0.500000i | 0.125000 | − | 0.0721688i | ||||
\(49\) | 1.50000 | − | 2.59808i | 0.214286 | − | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.16228 | −1.00292 | ||||||||
\(52\) | −3.60464 | − | 0.0811388i | −0.499873 | − | 0.0112519i | ||||
\(53\) | − | 7.16228i | − | 0.983814i | −0.870648 | − | 0.491907i | \(-0.836300\pi\) | ||
0.870648 | − | 0.491907i | \(-0.163700\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.58114 | + | 2.73861i | 0.211289 | + | 0.365963i | ||||
\(57\) | − | 3.16228i | − | 0.418854i | ||||||
\(58\) | 7.20928 | − | 4.16228i | 0.946624 | − | 0.546534i | ||||
\(59\) | −3.00000 | − | 5.19615i | −0.390567 | − | 0.676481i | 0.601958 | − | 0.798528i | \(-0.294388\pi\) |
−0.992524 | + | 0.122047i | \(0.961054\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.24342 | − | 12.5460i | −0.927424 | − | 1.60635i | −0.787615 | − | 0.616168i | \(-0.788684\pi\) |
−0.139810 | − | 0.990178i | \(-0.544649\pi\) | |||||||
\(62\) | −7.93477 | − | 4.58114i | −1.00772 | − | 0.581805i | ||||
\(63\) | −2.73861 | − | 1.58114i | −0.345033 | − | 0.199205i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.00000 | −0.369274 | ||||||||
\(67\) | −3.46410 | − | 2.00000i | −0.423207 | − | 0.244339i | 0.273241 | − | 0.961946i | \(-0.411904\pi\) |
−0.696449 | + | 0.717607i | \(0.745238\pi\) | |||||||
\(68\) | 6.20271 | + | 3.58114i | 0.752190 | + | 0.434277i | ||||
\(69\) | 2.08114 | + | 3.60464i | 0.250540 | + | 0.433947i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.91886 | + | 6.78767i | 0.465083 | + | 0.805548i | 0.999205 | − | 0.0398596i | \(-0.0126911\pi\) |
−0.534122 | + | 0.845407i | \(0.679358\pi\) | |||||||
\(72\) | 0.866025 | − | 0.500000i | 0.102062 | − | 0.0589256i | ||||
\(73\) | 1.32456i | 0.155027i | 0.996991 | + | 0.0775137i | \(0.0246982\pi\) | ||||
−0.996991 | + | 0.0775137i | \(0.975302\pi\) | |||||||
\(74\) | 5.24342 | + | 9.08186i | 0.609535 | + | 1.05575i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.58114 | + | 2.73861i | −0.181369 | + | 0.314140i | ||||
\(77\) | − | 9.48683i | − | 1.08112i | ||||||
\(78\) | −3.60464 | − | 0.0811388i | −0.408145 | − | 0.00918716i | ||||
\(79\) | −9.16228 | −1.03084 | −0.515418 | − | 0.856939i | \(-0.672363\pi\) | ||||
−0.515418 | + | 0.856939i | \(0.672363\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −8.21584 | + | 4.74342i | −0.907288 | + | 0.523823i | ||||
\(83\) | 13.6491i | 1.49818i | 0.662466 | + | 0.749092i | \(0.269510\pi\) | ||||
−0.662466 | + | 0.749092i | \(0.730490\pi\) | |||||||
\(84\) | 1.58114 | + | 2.73861i | 0.172516 | + | 0.298807i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.16228 | 0.556663 | ||||||||
\(87\) | 7.20928 | − | 4.16228i | 0.772916 | − | 0.446243i | ||||
\(88\) | 2.59808 | + | 1.50000i | 0.276956 | + | 0.159901i | ||||
\(89\) | −3.58114 | + | 6.20271i | −0.379600 | + | 0.657486i | −0.991004 | − | 0.133832i | \(-0.957272\pi\) |
0.611404 | + | 0.791319i | \(0.290605\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.256584 | − | 11.3989i | 0.0268973 | − | 1.19493i | ||||
\(92\) | − | 4.16228i | − | 0.433947i | ||||||
\(93\) | −7.93477 | − | 4.58114i | −0.822797 | − | 0.475042i | ||||
\(94\) | 3.00000 | − | 5.19615i | 0.309426 | − | 0.535942i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 4.04905 | − | 2.33772i | 0.411119 | − | 0.237360i | −0.280151 | − | 0.959956i | \(-0.590385\pi\) |
0.691270 | + | 0.722596i | \(0.257051\pi\) | |||||||
\(98\) | −2.59808 | + | 1.50000i | −0.262445 | + | 0.151523i | ||||
\(99\) | −3.00000 | −0.301511 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.32456 | − | 14.4186i | 0.828324 | − | 1.43470i | −0.0710278 | − | 0.997474i | \(-0.522628\pi\) |
0.899352 | − | 0.437225i | \(-0.144039\pi\) | |||||||
\(102\) | 6.20271 | + | 3.58114i | 0.614160 | + | 0.354586i | ||||
\(103\) | − | 13.4868i | − | 1.32890i | −0.747334 | − | 0.664449i | \(-0.768666\pi\) | ||
0.747334 | − | 0.664449i | \(-0.231334\pi\) | |||||||
\(104\) | 3.08114 | + | 1.87259i | 0.302131 | + | 0.183622i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.58114 | + | 6.20271i | −0.347831 | + | 0.602461i | ||||
\(107\) | 5.19615 | + | 3.00000i | 0.502331 | + | 0.290021i | 0.729676 | − | 0.683793i | \(-0.239671\pi\) |
−0.227345 | + | 0.973814i | \(0.573004\pi\) | |||||||
\(108\) | 0.866025 | − | 0.500000i | 0.0833333 | − | 0.0481125i | ||||
\(109\) | −8.48683 | −0.812891 | −0.406446 | − | 0.913675i | \(-0.633232\pi\) | ||||
−0.406446 | + | 0.913675i | \(0.633232\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.24342 | + | 9.08186i | 0.497683 | + | 0.862012i | ||||
\(112\) | − | 3.16228i | − | 0.298807i | ||||||
\(113\) | −2.01312 | + | 1.16228i | −0.189379 | + | 0.109338i | −0.591692 | − | 0.806164i | \(-0.701540\pi\) |
0.402313 | + | 0.915502i | \(0.368206\pi\) | |||||||
\(114\) | −1.58114 | + | 2.73861i | −0.148087 | + | 0.256495i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −8.32456 | −0.772916 | ||||||||
\(117\) | −3.60464 | − | 0.0811388i | −0.333249 | − | 0.00750129i | ||||
\(118\) | 6.00000i | 0.552345i | ||||||||
\(119\) | −11.3246 | + | 19.6147i | −1.03812 | + | 1.79808i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | + | 1.73205i | 0.0909091 | + | 0.157459i | ||||
\(122\) | 14.4868i | 1.31158i | ||||||||
\(123\) | −8.21584 | + | 4.74342i | −0.740797 | + | 0.427699i | ||||
\(124\) | 4.58114 | + | 7.93477i | 0.411398 | + | 0.712563i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.58114 | + | 2.73861i | 0.140859 | + | 0.243975i | ||||
\(127\) | −6.64713 | − | 3.83772i | −0.589837 | − | 0.340543i | 0.175196 | − | 0.984534i | \(-0.443944\pi\) |
−0.765033 | + | 0.643991i | \(0.777277\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 5.16228 | 0.454513 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.67544 | 0.321125 | 0.160563 | − | 0.987026i | \(-0.448669\pi\) | ||||
0.160563 | + | 0.987026i | \(0.448669\pi\) | |||||||
\(132\) | 2.59808 | + | 1.50000i | 0.226134 | + | 0.130558i | ||||
\(133\) | −8.66025 | − | 5.00000i | −0.750939 | − | 0.433555i | ||||
\(134\) | 2.00000 | + | 3.46410i | 0.172774 | + | 0.299253i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.58114 | − | 6.20271i | −0.307080 | − | 0.531878i | ||||
\(137\) | 10.3923 | − | 6.00000i | 0.887875 | − | 0.512615i | 0.0146279 | − | 0.999893i | \(-0.495344\pi\) |
0.873247 | + | 0.487278i | \(0.162010\pi\) | |||||||
\(138\) | − | 4.16228i | − | 0.354317i | ||||||
\(139\) | −9.16228 | − | 15.8695i | −0.777134 | − | 1.34604i | −0.933587 | − | 0.358351i | \(-0.883339\pi\) |
0.156453 | − | 0.987685i | \(-0.449994\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.00000 | − | 5.19615i | 0.252646 | − | 0.437595i | ||||
\(142\) | − | 7.83772i | − | 0.657727i | ||||||
\(143\) | −5.19615 | − | 9.48683i | −0.434524 | − | 0.793329i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.662278 | − | 1.14710i | 0.0548105 | − | 0.0949346i | ||||
\(147\) | −2.59808 | + | 1.50000i | −0.214286 | + | 0.123718i | ||||
\(148\) | − | 10.4868i | − | 0.862012i | ||||||
\(149\) | −6.58114 | − | 11.3989i | −0.539148 | − | 0.933832i | −0.998950 | − | 0.0458102i | \(-0.985413\pi\) |
0.459802 | − | 0.888021i | \(-0.347920\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.8114 | −1.77499 | −0.887493 | − | 0.460822i | \(-0.847555\pi\) | ||||
−0.887493 | + | 0.460822i | \(0.847555\pi\) | |||||||
\(152\) | 2.73861 | − | 1.58114i | 0.222131 | − | 0.128247i | ||||
\(153\) | 6.20271 | + | 3.58114i | 0.501460 | + | 0.289518i | ||||
\(154\) | −4.74342 | + | 8.21584i | −0.382235 | + | 0.662051i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.08114 | + | 1.87259i | 0.246689 | + | 0.149927i | ||||
\(157\) | − | 9.83772i | − | 0.785136i | −0.919723 | − | 0.392568i | \(-0.871587\pi\) | ||
0.919723 | − | 0.392568i | \(-0.128413\pi\) | |||||||
\(158\) | 7.93477 | + | 4.58114i | 0.631256 | + | 0.364456i | ||||
\(159\) | −3.58114 | + | 6.20271i | −0.284003 | + | 0.491907i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.1623 | 1.03733 | ||||||||
\(162\) | 0.866025 | − | 0.500000i | 0.0680414 | − | 0.0392837i | ||||
\(163\) | −13.6931 | + | 7.90569i | −1.07252 | + | 0.619222i | −0.928870 | − | 0.370406i | \(-0.879218\pi\) |
−0.143654 | + | 0.989628i | \(0.545885\pi\) | |||||||
\(164\) | 9.48683 | 0.740797 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.82456 | − | 11.8205i | 0.529688 | − | 0.917447i | ||||
\(167\) | 1.59151 | + | 0.918861i | 0.123155 | + | 0.0711036i | 0.560312 | − | 0.828282i | \(-0.310681\pi\) |
−0.437157 | + | 0.899385i | \(0.644015\pi\) | |||||||
\(168\) | − | 3.16228i | − | 0.243975i | ||||||
\(169\) | −5.98683 | − | 11.5394i | −0.460526 | − | 0.887646i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.58114 | + | 2.73861i | −0.120913 | + | 0.209427i | ||||
\(172\) | −4.47066 | − | 2.58114i | −0.340885 | − | 0.196810i | ||||
\(173\) | −12.4054 | + | 7.16228i | −0.943167 | + | 0.544538i | −0.890952 | − | 0.454098i | \(-0.849962\pi\) |
−0.0522155 | + | 0.998636i | \(0.516628\pi\) | |||||||
\(174\) | −8.32456 | −0.631083 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.50000 | − | 2.59808i | −0.113067 | − | 0.195837i | ||||
\(177\) | 6.00000i | 0.450988i | ||||||||
\(178\) | 6.20271 | − | 3.58114i | 0.464913 | − | 0.268418i | ||||
\(179\) | −0.824555 | + | 1.42817i | −0.0616302 | + | 0.106747i | −0.895194 | − | 0.445676i | \(-0.852963\pi\) |
0.833564 | + | 0.552423i | \(0.186297\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.8114 | −1.39824 | −0.699120 | − | 0.715005i | \(-0.746425\pi\) | ||||
−0.699120 | + | 0.715005i | \(0.746425\pi\) | |||||||
\(182\) | −5.92164 | + | 9.74342i | −0.438941 | + | 0.722230i | ||||
\(183\) | 14.4868i | 1.07090i | ||||||||
\(184\) | −2.08114 | + | 3.60464i | −0.153424 | + | 0.265737i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.58114 | + | 7.93477i | 0.335905 | + | 0.581805i | ||||
\(187\) | 21.4868i | 1.57127i | ||||||||
\(188\) | −5.19615 | + | 3.00000i | −0.378968 | + | 0.218797i | ||||
\(189\) | 1.58114 | + | 2.73861i | 0.115011 | + | 0.199205i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.0811 | − | 19.1931i | −0.801803 | − | 1.38876i | −0.918428 | − | 0.395588i | \(-0.870541\pi\) |
0.116625 | − | 0.993176i | \(-0.462792\pi\) | |||||||
\(192\) | 0.866025 | + | 0.500000i | 0.0625000 | + | 0.0360844i | ||||
\(193\) | 4.04905 | + | 2.33772i | 0.291457 | + | 0.168273i | 0.638599 | − | 0.769540i | \(-0.279514\pi\) |
−0.347142 | + | 0.937813i | \(0.612848\pi\) | |||||||
\(194\) | −4.67544 | −0.335677 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.00000 | 0.214286 | ||||||||
\(197\) | −5.19615 | − | 3.00000i | −0.370211 | − | 0.213741i | 0.303340 | − | 0.952882i | \(-0.401898\pi\) |
−0.673550 | + | 0.739141i | \(0.735232\pi\) | |||||||
\(198\) | 2.59808 | + | 1.50000i | 0.184637 | + | 0.106600i | ||||
\(199\) | 7.58114 | + | 13.1309i | 0.537413 | + | 0.930826i | 0.999042 | + | 0.0437533i | \(0.0139316\pi\) |
−0.461630 | + | 0.887073i | \(0.652735\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.00000 | + | 3.46410i | 0.141069 | + | 0.244339i | ||||
\(202\) | −14.4186 | + | 8.32456i | −1.01449 | + | 0.585714i | ||||
\(203\) | − | 26.3246i | − | 1.84762i | ||||||
\(204\) | −3.58114 | − | 6.20271i | −0.250730 | − | 0.434277i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −6.74342 | + | 11.6799i | −0.469836 | + | 0.813780i | ||||
\(207\) | − | 4.16228i | − | 0.289298i | ||||||
\(208\) | −1.73205 | − | 3.16228i | −0.120096 | − | 0.219265i | ||||
\(209\) | −9.48683 | −0.656218 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.41886 | + | 5.92164i | −0.235364 | + | 0.407663i | −0.959378 | − | 0.282122i | \(-0.908962\pi\) |
0.724014 | + | 0.689785i | \(0.242295\pi\) | |||||||
\(212\) | 6.20271 | − | 3.58114i | 0.426004 | − | 0.245954i | ||||
\(213\) | − | 7.83772i | − | 0.537032i | ||||||
\(214\) | −3.00000 | − | 5.19615i | −0.205076 | − | 0.355202i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −25.0919 | + | 14.4868i | −1.70335 | + | 0.983430i | ||||
\(218\) | 7.34981 | + | 4.24342i | 0.497792 | + | 0.287400i | ||||
\(219\) | 0.662278 | − | 1.14710i | 0.0447526 | − | 0.0775137i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.581139 | + | 25.8174i | −0.0390916 | + | 1.73667i | ||||
\(222\) | − | 10.4868i | − | 0.703830i | ||||||
\(223\) | 15.7062 | + | 9.06797i | 1.05176 | + | 0.607236i | 0.923143 | − | 0.384457i | \(-0.125611\pi\) |
0.128621 | + | 0.991694i | \(0.458945\pi\) | |||||||
\(224\) | −1.58114 | + | 2.73861i | −0.105644 | + | 0.182981i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.32456 | 0.154627 | ||||||||
\(227\) | 13.8336 | − | 7.98683i | 0.918168 | − | 0.530105i | 0.0351181 | − | 0.999383i | \(-0.488819\pi\) |
0.883050 | + | 0.469278i | \(0.155486\pi\) | |||||||
\(228\) | 2.73861 | − | 1.58114i | 0.181369 | − | 0.104713i | ||||
\(229\) | −2.48683 | −0.164335 | −0.0821673 | − | 0.996619i | \(-0.526184\pi\) | ||||
−0.0821673 | + | 0.996619i | \(0.526184\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.74342 | + | 8.21584i | −0.312094 | + | 0.540562i | ||||
\(232\) | 7.20928 | + | 4.16228i | 0.473312 | + | 0.273267i | ||||
\(233\) | 26.3246i | 1.72458i | 0.506416 | + | 0.862289i | \(0.330970\pi\) | ||||
−0.506416 | + | 0.862289i | \(0.669030\pi\) | |||||||
\(234\) | 3.08114 | + | 1.87259i | 0.201420 | + | 0.122415i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.00000 | − | 5.19615i | 0.195283 | − | 0.338241i | ||||
\(237\) | 7.93477 | + | 4.58114i | 0.515418 | + | 0.297577i | ||||
\(238\) | 19.6147 | − | 11.3246i | 1.27143 | − | 0.734062i | ||||
\(239\) | 0.486833 | 0.0314906 | 0.0157453 | − | 0.999876i | \(-0.494988\pi\) | ||||
0.0157453 | + | 0.999876i | \(0.494988\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.00000 | − | 6.92820i | −0.257663 | − | 0.446285i | 0.707953 | − | 0.706260i | \(-0.249619\pi\) |
−0.965615 | + | 0.259975i | \(0.916286\pi\) | |||||||
\(242\) | − | 2.00000i | − | 0.128565i | ||||||
\(243\) | 0.866025 | − | 0.500000i | 0.0555556 | − | 0.0320750i | ||||
\(244\) | 7.24342 | − | 12.5460i | 0.463712 | − | 0.803173i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.48683 | 0.604858 | ||||||||
\(247\) | −11.3989 | − | 0.256584i | −0.725293 | − | 0.0163260i | ||||
\(248\) | − | 9.16228i | − | 0.581805i | ||||||
\(249\) | 6.82456 | − | 11.8205i | 0.432489 | − | 0.749092i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.50000 | − | 12.9904i | −0.473396 | − | 0.819946i | 0.526140 | − | 0.850398i | \(-0.323639\pi\) |
−0.999536 | + | 0.0304521i | \(0.990305\pi\) | |||||||
\(252\) | − | 3.16228i | − | 0.199205i | ||||||
\(253\) | 10.8139 | − | 6.24342i | 0.679865 | − | 0.392520i | ||||
\(254\) | 3.83772 | + | 6.64713i | 0.240800 | + | 0.417078i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 5.03281 | + | 2.90569i | 0.313938 | + | 0.181252i | 0.648687 | − | 0.761055i | \(-0.275318\pi\) |
−0.334749 | + | 0.942307i | \(0.608652\pi\) | |||||||
\(258\) | −4.47066 | − | 2.58114i | −0.278331 | − | 0.160695i | ||||
\(259\) | 33.1623 | 2.06060 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.32456 | −0.515277 | ||||||||
\(262\) | −3.18303 | − | 1.83772i | −0.196648 | − | 0.113535i | ||||
\(263\) | −16.0101 | − | 9.24342i | −0.987223 | − | 0.569973i | −0.0827800 | − | 0.996568i | \(-0.526380\pi\) |
−0.904443 | + | 0.426594i | \(0.859713\pi\) | |||||||
\(264\) | −1.50000 | − | 2.59808i | −0.0923186 | − | 0.159901i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 5.00000 | + | 8.66025i | 0.306570 | + | 0.530994i | ||||
\(267\) | 6.20271 | − | 3.58114i | 0.379600 | − | 0.219162i | ||||
\(268\) | − | 4.00000i | − | 0.244339i | ||||||
\(269\) | −9.58114 | − | 16.5950i | −0.584172 | − | 1.01182i | −0.994978 | − | 0.100093i | \(-0.968086\pi\) |
0.410806 | − | 0.911723i | \(-0.365247\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.16228 | − | 10.6734i | 0.374332 | − | 0.648362i | −0.615895 | − | 0.787828i | \(-0.711205\pi\) |
0.990227 | + | 0.139467i | \(0.0445388\pi\) | |||||||
\(272\) | 7.16228i | 0.434277i | ||||||||
\(273\) | −5.92164 | + | 9.74342i | −0.358394 | + | 0.589698i | ||||
\(274\) | −12.0000 | −0.724947 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.08114 | + | 3.60464i | −0.125270 | + | 0.216974i | ||||
\(277\) | −19.7552 | + | 11.4057i | −1.18698 | + | 0.685302i | −0.957618 | − | 0.288040i | \(-0.906996\pi\) |
−0.229359 | + | 0.973342i | \(0.573663\pi\) | |||||||
\(278\) | 18.3246i | 1.09903i | ||||||||
\(279\) | 4.58114 | + | 7.93477i | 0.274266 | + | 0.475042i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.51317 | −0.149923 | −0.0749615 | − | 0.997186i | \(-0.523883\pi\) | ||||
−0.0749615 | + | 0.997186i | \(0.523883\pi\) | |||||||
\(282\) | −5.19615 | + | 3.00000i | −0.309426 | + | 0.178647i | ||||
\(283\) | 0.444416 | + | 0.256584i | 0.0264178 | + | 0.0152523i | 0.513151 | − | 0.858299i | \(-0.328478\pi\) |
−0.486733 | + | 0.873551i | \(0.661812\pi\) | |||||||
\(284\) | −3.91886 | + | 6.78767i | −0.232542 | + | 0.402774i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.243416 | + | 10.8139i | −0.0143935 | + | 0.639440i | ||||
\(287\) | 30.0000i | 1.77084i | ||||||||
\(288\) | 0.866025 | + | 0.500000i | 0.0510310 | + | 0.0294628i | ||||
\(289\) | 17.1491 | − | 29.7031i | 1.00877 | − | 1.74724i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.67544 | −0.274079 | ||||||||
\(292\) | −1.14710 | + | 0.662278i | −0.0671289 | + | 0.0387569i | ||||
\(293\) | 2.17647 | − | 1.25658i | 0.127151 | − | 0.0734104i | −0.435076 | − | 0.900394i | \(-0.643278\pi\) |
0.562226 | + | 0.826984i | \(0.309945\pi\) | |||||||
\(294\) | 3.00000 | 0.174964 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −5.24342 | + | 9.08186i | −0.304767 | + | 0.527873i | ||||
\(297\) | 2.59808 | + | 1.50000i | 0.150756 | + | 0.0870388i | ||||
\(298\) | 13.1623i | 0.762470i | ||||||||
\(299\) | 13.1623 | − | 7.20928i | 0.761194 | − | 0.416923i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.16228 | − | 14.1375i | 0.470466 | − | 0.814871i | ||||
\(302\) | 18.8892 | + | 10.9057i | 1.08695 | + | 0.627552i | ||||
\(303\) | −14.4186 | + | 8.32456i | −0.828324 | + | 0.478233i | ||||
\(304\) | −3.16228 | −0.181369 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.58114 | − | 6.20271i | −0.204720 | − | 0.354586i | ||||
\(307\) | 8.64911i | 0.493631i | 0.969063 | + | 0.246815i | \(0.0793841\pi\) | ||||
−0.969063 | + | 0.246815i | \(0.920616\pi\) | |||||||
\(308\) | 8.21584 | − | 4.74342i | 0.468141 | − | 0.270281i | ||||
\(309\) | −6.74342 | + | 11.6799i | −0.383620 | + | 0.664449i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.4868 | 0.708063 | 0.354032 | − | 0.935233i | \(-0.384811\pi\) | ||||
0.354032 | + | 0.935233i | \(0.384811\pi\) | |||||||
\(312\) | −1.73205 | − | 3.16228i | −0.0980581 | − | 0.179029i | ||||
\(313\) | − | 17.6491i | − | 0.997587i | −0.866721 | − | 0.498793i | \(-0.833777\pi\) | ||
0.866721 | − | 0.498793i | \(-0.166223\pi\) | |||||||
\(314\) | −4.91886 | + | 8.51972i | −0.277587 | + | 0.480795i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.58114 | − | 7.93477i | −0.257709 | − | 0.446365i | ||||
\(317\) | 0.188612i | 0.0105935i | 0.999986 | + | 0.00529674i | \(0.00168601\pi\) | ||||
−0.999986 | + | 0.00529674i | \(0.998314\pi\) | |||||||
\(318\) | 6.20271 | − | 3.58114i | 0.347831 | − | 0.200820i | ||||
\(319\) | −12.4868 | − | 21.6278i | −0.699128 | − | 1.21093i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.00000 | − | 5.19615i | −0.167444 | − | 0.290021i | ||||
\(322\) | −11.3989 | − | 6.58114i | −0.635234 | − | 0.366753i | ||||
\(323\) | 19.6147 | + | 11.3246i | 1.09139 | + | 0.630115i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 15.8114 | 0.875712 | ||||||||
\(327\) | 7.34981 | + | 4.24342i | 0.406446 | + | 0.234661i | ||||
\(328\) | −8.21584 | − | 4.74342i | −0.453644 | − | 0.261911i | ||||
\(329\) | −9.48683 | − | 16.4317i | −0.523026 | − | 0.905908i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.41886 | + | 7.65369i | 0.242883 | + | 0.420685i | 0.961534 | − | 0.274685i | \(-0.0885737\pi\) |
−0.718652 | + | 0.695370i | \(0.755240\pi\) | |||||||
\(332\) | −11.8205 | + | 6.82456i | −0.648733 | + | 0.374546i | ||||
\(333\) | − | 10.4868i | − | 0.574675i | ||||||
\(334\) | −0.918861 | − | 1.59151i | −0.0502778 | − | 0.0870838i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.58114 | + | 2.73861i | −0.0862582 | + | 0.149404i | ||||
\(337\) | 4.00000i | 0.217894i | 0.994048 | + | 0.108947i | \(0.0347479\pi\) | ||||
−0.994048 | + | 0.108947i | \(0.965252\pi\) | |||||||
\(338\) | −0.584952 | + | 12.9868i | −0.0318172 | + | 0.706391i | ||||
\(339\) | 2.32456 | 0.126253 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −13.7434 | + | 23.8043i | −0.744248 | + | 1.28907i | ||||
\(342\) | 2.73861 | − | 1.58114i | 0.148087 | − | 0.0854982i | ||||
\(343\) | − | 12.6491i | − | 0.682988i | ||||||
\(344\) | 2.58114 | + | 4.47066i | 0.139166 | + | 0.241042i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.3246 | 0.770093 | ||||||||
\(347\) | 9.80735 | − | 5.66228i | 0.526486 | − | 0.303967i | −0.213098 | − | 0.977031i | \(-0.568355\pi\) |
0.739584 | + | 0.673064i | \(0.235022\pi\) | |||||||
\(348\) | 7.20928 | + | 4.16228i | 0.386458 | + | 0.223122i | ||||
\(349\) | 10.7302 | − | 18.5853i | 0.574377 | − | 0.994850i | −0.421732 | − | 0.906721i | \(-0.638578\pi\) |
0.996109 | − | 0.0881297i | \(-0.0280890\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.08114 | + | 1.87259i | 0.164459 | + | 0.0999513i | ||||
\(352\) | 3.00000i | 0.159901i | ||||||||
\(353\) | −10.2290 | − | 5.90569i | −0.544433 | − | 0.314328i | 0.202441 | − | 0.979295i | \(-0.435113\pi\) |
−0.746874 | + | 0.664966i | \(0.768446\pi\) | |||||||
\(354\) | 3.00000 | − | 5.19615i | 0.159448 | − | 0.276172i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7.16228 | −0.379600 | ||||||||
\(357\) | 19.6147 | − | 11.3246i | 1.03812 | − | 0.599359i | ||||
\(358\) | 1.42817 | − | 0.824555i | 0.0754812 | − | 0.0435791i | ||||
\(359\) | 12.0000 | 0.633336 | 0.316668 | − | 0.948536i | \(-0.397436\pi\) | ||||
0.316668 | + | 0.948536i | \(0.397436\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.50000 | − | 7.79423i | 0.236842 | − | 0.410223i | ||||
\(362\) | 16.2911 | + | 9.40569i | 0.856243 | + | 0.494352i | ||||
\(363\) | − | 2.00000i | − | 0.104973i | ||||||
\(364\) | 10.0000 | − | 5.47723i | 0.524142 | − | 0.287085i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 7.24342 | − | 12.5460i | 0.378619 | − | 0.655788i | ||||
\(367\) | 5.75830 | + | 3.32456i | 0.300581 | + | 0.173540i | 0.642704 | − | 0.766115i | \(-0.277813\pi\) |
−0.342123 | + | 0.939655i | \(0.611146\pi\) | |||||||
\(368\) | 3.60464 | − | 2.08114i | 0.187905 | − | 0.108487i | ||||
\(369\) | 9.48683 | 0.493865 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.3246 | + | 19.6147i | 0.587942 | + | 1.01834i | ||||
\(372\) | − | 9.16228i | − | 0.475042i | ||||||
\(373\) | 7.34981 | − | 4.24342i | 0.380559 | − | 0.219716i | −0.297503 | − | 0.954721i | \(-0.596154\pi\) |
0.678061 | + | 0.735005i | \(0.262820\pi\) | |||||||
\(374\) | 10.7434 | − | 18.6081i | 0.555529 | − | 0.962204i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.00000 | 0.309426 | ||||||||
\(377\) | −14.4186 | − | 26.3246i | −0.742593 | − | 1.35578i | ||||
\(378\) | − | 3.16228i | − | 0.162650i | ||||||
\(379\) | 1.00000 | − | 1.73205i | 0.0513665 | − | 0.0889695i | −0.839199 | − | 0.543825i | \(-0.816976\pi\) |
0.890565 | + | 0.454855i | \(0.150309\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.83772 | + | 6.64713i | 0.196612 | + | 0.340543i | ||||
\(382\) | 22.1623i | 1.13392i | ||||||||
\(383\) | 3.60464 | − | 2.08114i | 0.184188 | − | 0.106341i | −0.405071 | − | 0.914285i | \(-0.632753\pi\) |
0.589259 | + | 0.807944i | \(0.299420\pi\) | |||||||
\(384\) | −0.500000 | − | 0.866025i | −0.0255155 | − | 0.0441942i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.33772 | − | 4.04905i | −0.118987 | − | 0.206091i | ||||
\(387\) | −4.47066 | − | 2.58114i | −0.227257 | − | 0.131207i | ||||
\(388\) | 4.04905 | + | 2.33772i | 0.205560 | + | 0.118680i | ||||
\(389\) | 15.6754 | 0.794777 | 0.397388 | − | 0.917651i | \(-0.369917\pi\) | ||||
0.397388 | + | 0.917651i | \(0.369917\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −29.8114 | −1.50763 | ||||||||
\(392\) | −2.59808 | − | 1.50000i | −0.131223 | − | 0.0757614i | ||||
\(393\) | −3.18303 | − | 1.83772i | −0.160563 | − | 0.0927008i | ||||
\(394\) | 3.00000 | + | 5.19615i | 0.151138 | + | 0.261778i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.50000 | − | 2.59808i | −0.0753778 | − | 0.130558i | ||||
\(397\) | 21.0657 | − | 12.1623i | 1.05726 | − | 0.610407i | 0.132584 | − | 0.991172i | \(-0.457672\pi\) |
0.924672 | + | 0.380765i | \(0.124339\pi\) | |||||||
\(398\) | − | 15.1623i | − | 0.760016i | ||||||
\(399\) | 5.00000 | + | 8.66025i | 0.250313 | + | 0.433555i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.83772 | + | 3.18303i | −0.0917715 | + | 0.158953i | −0.908257 | − | 0.418414i | \(-0.862586\pi\) |
0.816485 | + | 0.577366i | \(0.195920\pi\) | |||||||
\(402\) | − | 4.00000i | − | 0.199502i | ||||||
\(403\) | −17.1572 | + | 28.2302i | −0.854659 | + | 1.40625i | ||||
\(404\) | 16.6491 | 0.828324 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −13.1623 | + | 22.7977i | −0.653233 | + | 1.13143i | ||||
\(407\) | 27.2456 | − | 15.7302i | 1.35051 | − | 0.779720i | ||||
\(408\) | 7.16228i | 0.354586i | ||||||||
\(409\) | 8.83772 | + | 15.3074i | 0.436997 | + | 0.756901i | 0.997456 | − | 0.0712807i | \(-0.0227086\pi\) |
−0.560459 | + | 0.828182i | \(0.689375\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.0000 | −0.591916 | ||||||||
\(412\) | 11.6799 | − | 6.74342i | 0.575429 | − | 0.332224i | ||||
\(413\) | 16.4317 | + | 9.48683i | 0.808550 | + | 0.466817i | ||||
\(414\) | −2.08114 | + | 3.60464i | −0.102282 | + | 0.177158i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.0811388 | + | 3.60464i | −0.00397816 | + | 0.176732i | ||||
\(417\) | 18.3246i | 0.897357i | ||||||||
\(418\) | 8.21584 | + | 4.74342i | 0.401850 | + | 0.232008i | ||||
\(419\) | 4.50000 | − | 7.79423i | 0.219839 | − | 0.380773i | −0.734919 | − | 0.678155i | \(-0.762780\pi\) |
0.954759 | + | 0.297382i | \(0.0961133\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.8377 | 1.06431 | 0.532153 | − | 0.846648i | \(-0.321383\pi\) | ||||
0.532153 | + | 0.846648i | \(0.321383\pi\) | |||||||
\(422\) | 5.92164 | − | 3.41886i | 0.288261 | − | 0.166428i | ||||
\(423\) | −5.19615 | + | 3.00000i | −0.252646 | + | 0.145865i | ||||
\(424\) | −7.16228 | −0.347831 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −3.91886 | + | 6.78767i | −0.189869 | + | 0.328864i | ||||
\(427\) | 39.6738 | + | 22.9057i | 1.91995 | + | 1.10848i | ||||
\(428\) | 6.00000i | 0.290021i | ||||||||
\(429\) | −0.243416 | + | 10.8139i | −0.0117523 | + | 0.522101i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.75658 | − | 4.77454i | 0.132780 | − | 0.229982i | −0.791967 | − | 0.610564i | \(-0.790943\pi\) |
0.924747 | + | 0.380582i | \(0.124276\pi\) | |||||||
\(432\) | 0.866025 | + | 0.500000i | 0.0416667 | + | 0.0240563i | ||||
\(433\) | 24.7881 | − | 14.3114i | 1.19124 | − | 0.687761i | 0.232650 | − | 0.972560i | \(-0.425260\pi\) |
0.958587 | + | 0.284799i | \(0.0919269\pi\) | |||||||
\(434\) | 28.9737 | 1.39078 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.24342 | − | 7.34981i | −0.203223 | − | 0.351992i | ||||
\(437\) | − | 13.1623i | − | 0.629637i | ||||||
\(438\) | −1.14710 | + | 0.662278i | −0.0548105 | + | 0.0316449i | ||||
\(439\) | −5.67544 | + | 9.83016i | −0.270874 | + | 0.469168i | −0.969086 | − | 0.246723i | \(-0.920646\pi\) |
0.698212 | + | 0.715891i | \(0.253979\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.00000 | 0.142857 | ||||||||
\(442\) | 13.4120 | − | 22.0680i | 0.637943 | − | 1.04967i | ||||
\(443\) | − | 9.00000i | − | 0.427603i | −0.976877 | − | 0.213801i | \(-0.931415\pi\) | ||
0.976877 | − | 0.213801i | \(-0.0685846\pi\) | |||||||
\(444\) | −5.24342 | + | 9.08186i | −0.248842 | + | 0.431006i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −9.06797 | − | 15.7062i | −0.429381 | − | 0.743710i | ||||
\(447\) | 13.1623i | 0.622554i | ||||||||
\(448\) | 2.73861 | − | 1.58114i | 0.129387 | − | 0.0747018i | ||||
\(449\) | 10.7434 | + | 18.6081i | 0.507013 | + | 0.878173i | 0.999967 | + | 0.00811713i | \(0.00258379\pi\) |
−0.492954 | + | 0.870055i | \(0.664083\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.2302 | + | 24.6475i | 0.670076 | + | 1.16061i | ||||
\(452\) | −2.01312 | − | 1.16228i | −0.0946894 | − | 0.0546689i | ||||
\(453\) | 18.8892 | + | 10.9057i | 0.887493 | + | 0.512394i | ||||
\(454\) | −15.9737 | −0.749681 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.16228 | −0.148087 | ||||||||
\(457\) | −30.8730 | − | 17.8246i | −1.44418 | − | 0.833798i | −0.446055 | − | 0.895006i | \(-0.647171\pi\) |
−0.998125 | + | 0.0612082i | \(0.980505\pi\) | |||||||
\(458\) | 2.15366 | + | 1.24342i | 0.100634 | + | 0.0581010i | ||||
\(459\) | −3.58114 | − | 6.20271i | −0.167153 | − | 0.289518i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.41886 | + | 9.38574i | 0.252382 | + | 0.437138i | 0.964181 | − | 0.265245i | \(-0.0854529\pi\) |
−0.711799 | + | 0.702383i | \(0.752120\pi\) | |||||||
\(462\) | 8.21584 | − | 4.74342i | 0.382235 | − | 0.220684i | ||||
\(463\) | 23.4868i | 1.09153i | 0.837940 | + | 0.545763i | \(0.183760\pi\) | ||||
−0.837940 | + | 0.545763i | \(0.816240\pi\) | |||||||
\(464\) | −4.16228 | − | 7.20928i | −0.193229 | − | 0.334682i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 13.1623 | − | 22.7977i | 0.609731 | − | 1.05608i | ||||
\(467\) | 3.00000i | 0.138823i | 0.997588 | + | 0.0694117i | \(0.0221122\pi\) | ||||
−0.997588 | + | 0.0694117i | \(0.977888\pi\) | |||||||
\(468\) | −1.73205 | − | 3.16228i | −0.0800641 | − | 0.146176i | ||||
\(469\) | 12.6491 | 0.584082 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.91886 | + | 8.51972i | −0.226649 | + | 0.392568i | ||||
\(472\) | −5.19615 | + | 3.00000i | −0.239172 | + | 0.138086i | ||||
\(473\) | − | 15.4868i | − | 0.712085i | ||||||
\(474\) | −4.58114 | − | 7.93477i | −0.210419 | − | 0.364456i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −22.6491 | −1.03812 | ||||||||
\(477\) | 6.20271 | − | 3.58114i | 0.284003 | − | 0.163969i | ||||
\(478\) | −0.421610 | − | 0.243416i | −0.0192840 | − | 0.0111336i | ||||
\(479\) | −13.1623 | + | 22.7977i | −0.601400 | + | 1.04166i | 0.391210 | + | 0.920302i | \(0.372057\pi\) |
−0.992609 | + | 0.121353i | \(0.961277\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 33.1623 | − | 18.1637i | 1.51207 | − | 0.828195i | ||||
\(482\) | 8.00000i | 0.364390i | ||||||||
\(483\) | −11.3989 | − | 6.58114i | −0.518666 | − | 0.299452i | ||||
\(484\) | −1.00000 | + | 1.73205i | −0.0454545 | + | 0.0787296i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −2.73861 | + | 1.58114i | −0.124098 | + | 0.0716482i | −0.560764 | − | 0.827976i | \(-0.689493\pi\) |
0.436666 | + | 0.899624i | \(0.356159\pi\) | |||||||
\(488\) | −12.5460 | + | 7.24342i | −0.567929 | + | 0.327894i | ||||
\(489\) | 15.8114 | 0.715016 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.98683 | + | 13.8336i | −0.360441 | + | 0.624302i | −0.988033 | − | 0.154240i | \(-0.950707\pi\) |
0.627593 | + | 0.778542i | \(0.284040\pi\) | |||||||
\(492\) | −8.21584 | − | 4.74342i | −0.370399 | − | 0.213850i | ||||
\(493\) | 59.6228i | 2.68527i | ||||||||
\(494\) | 9.74342 | + | 5.92164i | 0.438377 | + | 0.266427i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.58114 | + | 7.93477i | −0.205699 | + | 0.356281i | ||||
\(497\) | −21.4645 | − | 12.3925i | −0.962814 | − | 0.555881i | ||||
\(498\) | −11.8205 | + | 6.82456i | −0.529688 | + | 0.305816i | ||||
\(499\) | −8.18861 | −0.366573 | −0.183286 | − | 0.983060i | \(-0.558674\pi\) | ||||
−0.183286 | + | 0.983060i | \(0.558674\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.918861 | − | 1.59151i | −0.0410517 | − | 0.0711036i | ||||
\(502\) | 15.0000i | 0.669483i | ||||||||
\(503\) | 12.8270 | − | 7.40569i | 0.571929 | − | 0.330204i | −0.185990 | − | 0.982552i | \(-0.559549\pi\) |
0.757920 | + | 0.652348i | \(0.226216\pi\) | |||||||
\(504\) | −1.58114 | + | 2.73861i | −0.0704295 | + | 0.121988i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −12.4868 | −0.555107 | ||||||||
\(507\) | −0.584952 | + | 12.9868i | −0.0259786 | + | 0.576766i | ||||
\(508\) | − | 7.67544i | − | 0.340543i | ||||||
\(509\) | 21.3925 | − | 37.0529i | 0.948207 | − | 1.64234i | 0.199008 | − | 0.979998i | \(-0.436228\pi\) |
0.749199 | − | 0.662345i | \(-0.230439\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.09431 | − | 3.62744i | −0.0926466 | − | 0.160469i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 2.73861 | − | 1.58114i | 0.120913 | − | 0.0698090i | ||||
\(514\) | −2.90569 | − | 5.03281i | −0.128165 | − | 0.221988i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.58114 | + | 4.47066i | 0.113628 | + | 0.196810i | ||||
\(517\) | −15.5885 | − | 9.00000i | −0.685580 | − | 0.395820i | ||||
\(518\) | −28.7194 | − | 16.5811i | −1.26186 | − | 0.728533i | ||||
\(519\) | 14.3246 | 0.628778 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.64911 | 0.203681 | 0.101841 | − | 0.994801i | \(-0.467527\pi\) | ||||
0.101841 | + | 0.994801i | \(0.467527\pi\) | |||||||
\(522\) | 7.20928 | + | 4.16228i | 0.315541 | + | 0.182178i | ||||
\(523\) | 4.30732 | + | 2.48683i | 0.188346 | + | 0.108742i | 0.591208 | − | 0.806519i | \(-0.298651\pi\) |
−0.402862 | + | 0.915261i | \(0.631985\pi\) | |||||||
\(524\) | 1.83772 | + | 3.18303i | 0.0802813 | + | 0.139051i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.24342 | + | 16.0101i | 0.403032 | + | 0.698072i | ||||
\(527\) | 56.8310 | − | 32.8114i | 2.47560 | − | 1.42929i | ||||
\(528\) | 3.00000i | 0.130558i | ||||||||
\(529\) | −2.83772 | − | 4.91508i | −0.123379 | − | 0.213699i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.00000 | − | 5.19615i | 0.130189 | − | 0.225494i | ||||
\(532\) | − | 10.0000i | − | 0.433555i | ||||||
\(533\) | 16.4317 | + | 30.0000i | 0.711735 | + | 1.29944i | ||||
\(534\) | −7.16228 | −0.309942 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.00000 | + | 3.46410i | −0.0863868 | + | 0.149626i | ||||
\(537\) | 1.42817 | − | 0.824555i | 0.0616302 | − | 0.0355822i | ||||
\(538\) | 19.1623i | 0.826144i | ||||||||
\(539\) | 4.50000 | + | 7.79423i | 0.193829 | + | 0.335721i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.811388 | −0.0348843 | −0.0174422 | − | 0.999848i | \(-0.505552\pi\) | ||||
−0.0174422 | + | 0.999848i | \(0.505552\pi\) | |||||||
\(542\) | −10.6734 | + | 6.16228i | −0.458461 | + | 0.264692i | ||||
\(543\) | 16.2911 | + | 9.40569i | 0.699120 | + | 0.403637i | ||||
\(544\) | 3.58114 | − | 6.20271i | 0.153540 | − | 0.265939i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 10.0000 | − | 5.47723i | 0.427960 | − | 0.234404i | ||||
\(547\) | 30.1359i | 1.28852i | 0.764807 | + | 0.644260i | \(0.222835\pi\) | ||||
−0.764807 | + | 0.644260i | \(0.777165\pi\) | |||||||
\(548\) | 10.3923 | + | 6.00000i | 0.443937 | + | 0.256307i | ||||
\(549\) | 7.24342 | − | 12.5460i | 0.309141 | − | 0.535449i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −26.3246 | −1.12146 | ||||||||
\(552\) | 3.60464 | − | 2.08114i | 0.153424 | − | 0.0885792i | ||||
\(553\) | 25.0919 | − | 14.4868i | 1.06702 | − | 0.616043i | ||||
\(554\) | 22.8114 | 0.969163 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.16228 | − | 15.8695i | 0.388567 | − | 0.673018i | ||||
\(557\) | −16.4317 | − | 9.48683i | −0.696232 | − | 0.401970i | 0.109710 | − | 0.993964i | \(-0.465008\pi\) |
−0.805943 | + | 0.591994i | \(0.798341\pi\) | |||||||
\(558\) | − | 9.16228i | − | 0.387870i | ||||||
\(559\) | 0.418861 | − | 18.6081i | 0.0177159 | − | 0.787041i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.7434 | − | 18.6081i | 0.453587 | − | 0.785636i | ||||
\(562\) | 2.17647 | + | 1.25658i | 0.0918087 | + | 0.0530058i | ||||
\(563\) | −3.44130 | + | 1.98683i | −0.145033 | + | 0.0837350i | −0.570761 | − | 0.821116i | \(-0.693352\pi\) |
0.425727 | + | 0.904851i | \(0.360018\pi\) | |||||||
\(564\) | 6.00000 | 0.252646 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −0.256584 | − | 0.444416i | −0.0107850 | − | 0.0186802i | ||||
\(567\) | − | 3.16228i | − | 0.132803i | ||||||
\(568\) | 6.78767 | − | 3.91886i | 0.284804 | − | 0.164432i | ||||
\(569\) | 15.4868 | − | 26.8240i | 0.649242 | − | 1.12452i | −0.334062 | − | 0.942551i | \(-0.608420\pi\) |
0.983304 | − | 0.181969i | \(-0.0582470\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.6754 | −0.823392 | −0.411696 | − | 0.911321i | \(-0.635063\pi\) | ||||
−0.411696 | + | 0.911321i | \(0.635063\pi\) | |||||||
\(572\) | 5.61776 | − | 9.24342i | 0.234890 | − | 0.386487i | ||||
\(573\) | 22.1623i | 0.925842i | ||||||||
\(574\) | 15.0000 | − | 25.9808i | 0.626088 | − | 1.08442i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 43.0000i | 1.79011i | 0.445952 | + | 0.895057i | \(0.352865\pi\) | ||||
−0.445952 | + | 0.895057i | \(0.647135\pi\) | |||||||
\(578\) | −29.7031 | + | 17.1491i | −1.23549 | + | 0.713309i | ||||
\(579\) | −2.33772 | − | 4.04905i | −0.0971524 | − | 0.168273i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −21.5811 | − | 37.3796i | −0.895337 | − | 1.55077i | ||||
\(582\) | 4.04905 | + | 2.33772i | 0.167839 | + | 0.0969017i | ||||
\(583\) | 18.6081 | + | 10.7434i | 0.770671 | + | 0.444947i | ||||
\(584\) | 1.32456 | 0.0548105 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.51317 | −0.103818 | ||||||||
\(587\) | −18.1865 | − | 10.5000i | −0.750639 | − | 0.433381i | 0.0752860 | − | 0.997162i | \(-0.476013\pi\) |
−0.825925 | + | 0.563781i | \(0.809346\pi\) | |||||||
\(588\) | −2.59808 | − | 1.50000i | −0.107143 | − | 0.0618590i | ||||
\(589\) | 14.4868 | + | 25.0919i | 0.596920 | + | 1.03389i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.00000 | + | 5.19615i | 0.123404 | + | 0.213741i | ||||
\(592\) | 9.08186 | − | 5.24342i | 0.373262 | − | 0.215503i | ||||
\(593\) | 1.16228i | 0.0477290i | 0.999715 | + | 0.0238645i | \(0.00759703\pi\) | ||||
−0.999715 | + | 0.0238645i | \(0.992403\pi\) | |||||||
\(594\) | −1.50000 | − | 2.59808i | −0.0615457 | − | 0.106600i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.58114 | − | 11.3989i | 0.269574 | − | 0.466916i | ||||
\(597\) | − | 15.1623i | − | 0.620551i | ||||||
\(598\) | −15.0035 | − | 0.337722i | −0.613539 | − | 0.0138105i | ||||
\(599\) | −32.8114 | −1.34064 | −0.670318 | − | 0.742074i | \(-0.733843\pi\) | ||||
−0.670318 | + | 0.742074i | \(0.733843\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.64911 | − | 6.32045i | 0.148850 | − | 0.257816i | −0.781952 | − | 0.623338i | \(-0.785776\pi\) |
0.930803 | + | 0.365522i | \(0.119109\pi\) | |||||||
\(602\) | −14.1375 | + | 8.16228i | −0.576201 | + | 0.332670i | ||||
\(603\) | − | 4.00000i | − | 0.162893i | ||||||
\(604\) | −10.9057 | − | 18.8892i | −0.443746 | − | 0.768591i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 16.6491 | 0.676324 | ||||||||
\(607\) | −20.5035 | + | 11.8377i | −0.832213 | + | 0.480478i | −0.854610 | − | 0.519271i | \(-0.826204\pi\) |
0.0223969 | + | 0.999749i | \(0.492870\pi\) | |||||||
\(608\) | 2.73861 | + | 1.58114i | 0.111065 | + | 0.0641236i | ||||
\(609\) | −13.1623 | + | 22.7977i | −0.533362 | + | 0.923811i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18.4868 | − | 11.2355i | −0.747897 | − | 0.454541i | ||||
\(612\) | 7.16228i | 0.289518i | ||||||||
\(613\) | −25.6997 | − | 14.8377i | −1.03800 | − | 0.599290i | −0.118734 | − | 0.992926i | \(-0.537884\pi\) |
−0.919266 | + | 0.393636i | \(0.871217\pi\) | |||||||
\(614\) | 4.32456 | − | 7.49035i | 0.174525 | − | 0.302286i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9.48683 | −0.382235 | ||||||||
\(617\) | −2.85634 | + | 1.64911i | −0.114992 | + | 0.0663907i | −0.556393 | − | 0.830919i | \(-0.687815\pi\) |
0.441401 | + | 0.897310i | \(0.354482\pi\) | |||||||
\(618\) | 11.6799 | − | 6.74342i | 0.469836 | − | 0.271260i | ||||
\(619\) | −8.00000 | −0.321547 | −0.160774 | − | 0.986991i | \(-0.551399\pi\) | ||||
−0.160774 | + | 0.986991i | \(0.551399\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.08114 | + | 3.60464i | −0.0835132 | + | 0.144649i | ||||
\(622\) | −10.8139 | − | 6.24342i | −0.433598 | − | 0.250338i | ||||
\(623\) | − | 22.6491i | − | 0.907417i | ||||||
\(624\) | −0.0811388 | + | 3.60464i | −0.00324815 | + | 0.144301i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −8.82456 | + | 15.2846i | −0.352700 | + | 0.610895i | ||||
\(627\) | 8.21584 | + | 4.74342i | 0.328109 | + | 0.189434i | ||||
\(628\) | 8.51972 | − | 4.91886i | 0.339974 | − | 0.196284i | ||||
\(629\) | −75.1096 | −2.99482 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.6491 | − | 30.5692i | −0.702600 | − | 1.21694i | −0.967551 | − | 0.252677i | \(-0.918689\pi\) |
0.264951 | − | 0.964262i | \(-0.414644\pi\) | |||||||
\(632\) | 9.16228i | 0.364456i | ||||||||
\(633\) | 5.92164 | − | 3.41886i | 0.235364 | − | 0.135888i | ||||
\(634\) | 0.0943058 | − | 0.163343i | 0.00374536 | − | 0.00648716i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −7.16228 | −0.284003 | ||||||||
\(637\) | 5.19615 | + | 9.48683i | 0.205879 | + | 0.375882i | ||||
\(638\) | 24.9737i | 0.988717i | ||||||||
\(639\) | −3.91886 | + | 6.78767i | −0.155028 | + | 0.268516i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24.9737 | + | 43.2557i | 0.986400 | + | 1.70850i | 0.635540 | + | 0.772068i | \(0.280778\pi\) |
0.350861 | + | 0.936428i | \(0.385889\pi\) | |||||||
\(642\) | 6.00000i | 0.236801i | ||||||||
\(643\) | −21.0657 | + | 12.1623i | −0.830749 | + | 0.479633i | −0.854109 | − | 0.520094i | \(-0.825897\pi\) |
0.0233598 | + | 0.999727i | \(0.492564\pi\) | |||||||
\(644\) | 6.58114 | + | 11.3989i | 0.259333 | + | 0.449178i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −11.3246 | − | 19.6147i | −0.445559 | − | 0.771730i | ||||
\(647\) | −36.7947 | − | 21.2434i | −1.44655 | − | 0.835165i | −0.448274 | − | 0.893896i | \(-0.647961\pi\) |
−0.998274 | + | 0.0587312i | \(0.981295\pi\) | |||||||
\(648\) | 0.866025 | + | 0.500000i | 0.0340207 | + | 0.0196419i | ||||
\(649\) | 18.0000 | 0.706562 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 28.9737 | 1.13557 | ||||||||
\(652\) | −13.6931 | − | 7.90569i | −0.536262 | − | 0.309611i | ||||
\(653\) | −8.21584 | − | 4.74342i | −0.321511 | − | 0.185624i | 0.330555 | − | 0.943787i | \(-0.392764\pi\) |
−0.652066 | + | 0.758162i | \(0.726097\pi\) | |||||||
\(654\) | −4.24342 | − | 7.34981i | −0.165931 | − | 0.287400i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.74342 | + | 8.21584i | 0.185199 | + | 0.320775i | ||||
\(657\) | −1.14710 | + | 0.662278i | −0.0447526 | + | 0.0258379i | ||||
\(658\) | 18.9737i | 0.739671i | ||||||||
\(659\) | −7.50000 | − | 12.9904i | −0.292159 | − | 0.506033i | 0.682161 | − | 0.731202i | \(-0.261040\pi\) |
−0.974320 | + | 0.225168i | \(0.927707\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.0000 | + | 22.5167i | −0.505641 | + | 0.875797i | 0.494337 | + | 0.869270i | \(0.335411\pi\) |
−0.999979 | + | 0.00652642i | \(0.997923\pi\) | |||||||
\(662\) | − | 8.83772i | − | 0.343488i | ||||||
\(663\) | 13.4120 | − | 22.0680i | 0.520879 | − | 0.857049i | ||||
\(664\) | 13.6491 | 0.529688 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.24342 | + | 9.08186i | −0.203178 | + | 0.351915i | ||||
\(667\) | 30.0070 | − | 17.3246i | 1.16188 | − | 0.670809i | ||||
\(668\) | 1.83772i | 0.0711036i | ||||||||
\(669\) | −9.06797 | − | 15.7062i | −0.350588 | − | 0.607236i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 43.4605 | 1.67777 | ||||||||
\(672\) | 2.73861 | − | 1.58114i | 0.105644 | − | 0.0609938i | ||||
\(673\) | −18.7487 | − | 10.8246i | −0.722708 | − | 0.417256i | 0.0930403 | − | 0.995662i | \(-0.470341\pi\) |
−0.815749 | + | 0.578406i | \(0.803675\pi\) | |||||||
\(674\) | 2.00000 | − | 3.46410i | 0.0770371 | − | 0.133432i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.00000 | − | 10.9545i | 0.269231 | − | 0.421325i | ||||
\(677\) | 7.35089i | 0.282518i | 0.989973 | + | 0.141259i | \(0.0451150\pi\) | ||||
−0.989973 | + | 0.141259i | \(0.954885\pi\) | |||||||
\(678\) | −2.01312 | − | 1.16228i | −0.0773136 | − | 0.0446370i | ||||
\(679\) | −7.39253 | + | 12.8042i | −0.283699 | + | 0.491381i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.9737 | −0.612112 | ||||||||
\(682\) | 23.8043 | − | 13.7434i | 0.911514 | − | 0.526263i | ||||
\(683\) | 40.6576 | − | 23.4737i | 1.55572 | − | 0.898195i | 0.558061 | − | 0.829800i | \(-0.311546\pi\) |
0.997658 | − | 0.0683948i | \(-0.0217878\pi\) | |||||||
\(684\) | −3.16228 | −0.120913 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −6.32456 | + | 10.9545i | −0.241473 | + | 0.418243i | ||||
\(687\) | 2.15366 | + | 1.24342i | 0.0821673 | + | 0.0474393i | ||||
\(688\) | − | 5.16228i | − | 0.196810i | ||||||
\(689\) | 22.0680 | + | 13.4120i | 0.840723 | + | 0.510956i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.9737 | + | 44.9877i | −0.988085 | + | 1.71141i | −0.360752 | + | 0.932662i | \(0.617480\pi\) |
−0.627333 | + | 0.778751i | \(0.715853\pi\) | |||||||
\(692\) | −12.4054 | − | 7.16228i | −0.471584 | − | 0.272269i | ||||
\(693\) | 8.21584 | − | 4.74342i | 0.312094 | − | 0.180187i | ||||
\(694\) | −11.3246 | −0.429874 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −4.16228 | − | 7.20928i | −0.157771 | − | 0.273267i | ||||
\(697\) | − | 67.9473i | − | 2.57369i | ||||||
\(698\) | −18.5853 | + | 10.7302i | −0.703465 | + | 0.406146i | ||||
\(699\) | 13.1623 | − | 22.7977i | 0.497843 | − | 0.862289i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.4605 | 1.30156 | 0.650778 | − | 0.759268i | \(-0.274443\pi\) | ||||
0.650778 | + | 0.759268i | \(0.274443\pi\) | |||||||
\(702\) | −1.73205 | − | 3.16228i | −0.0653720 | − | 0.119352i | ||||
\(703\) | − | 33.1623i | − | 1.25074i | ||||||
\(704\) | 1.50000 | − | 2.59808i | 0.0565334 | − | 0.0979187i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.90569 | + | 10.2290i | 0.222264 | + | 0.384972i | ||||
\(707\) | 52.6491i | 1.98007i | ||||||||
\(708\) | −5.19615 | + | 3.00000i | −0.195283 | + | 0.112747i | ||||
\(709\) | 10.2434 | + | 17.7421i | 0.384700 | + | 0.666319i | 0.991727 | − | 0.128361i | \(-0.0409717\pi\) |
−0.607028 | + | 0.794681i | \(0.707638\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.58114 | − | 7.93477i | −0.171806 | − | 0.297577i | ||||
\(712\) | 6.20271 | + | 3.58114i | 0.232457 | + | 0.134209i | ||||
\(713\) | −33.0267 | − | 19.0680i | −1.23686 | − | 0.714101i | ||||
\(714\) | −22.6491 | −0.847622 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.64911 | −0.0616302 | ||||||||
\(717\) | −0.421610 | − | 0.243416i | −0.0157453 | − | 0.00909056i | ||||
\(718\) | −10.3923 | − | 6.00000i | −0.387837 | − | 0.223918i | ||||
\(719\) | −7.59431 | − | 13.1537i | −0.283220 | − | 0.490551i | 0.688956 | − | 0.724803i | \(-0.258069\pi\) |
−0.972176 | + | 0.234252i | \(0.924736\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 21.3246 | + | 36.9352i | 0.794168 | + | 1.37554i | ||||
\(722\) | −7.79423 | + | 4.50000i | −0.290071 | + | 0.167473i | ||||
\(723\) | 8.00000i | 0.297523i | ||||||||
\(724\) | −9.40569 | − | 16.2911i | −0.349560 | − | 0.605455i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.00000 | + | 1.73205i | −0.0371135 | + | 0.0642824i | ||||
\(727\) | 0.324555i | 0.0120371i | 0.999982 | + | 0.00601855i | \(0.00191577\pi\) | ||||
−0.999982 | + | 0.00601855i | \(0.998084\pi\) | |||||||
\(728\) | −11.3989 | − | 0.256584i | −0.422470 | − | 0.00950962i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18.4868 | + | 32.0201i | −0.683760 | + | 1.18431i | ||||
\(732\) | −12.5460 | + | 7.24342i | −0.463712 | + | 0.267724i | ||||
\(733\) | 38.4868i | 1.42154i | 0.703423 | + | 0.710772i | \(0.251654\pi\) | ||||
−0.703423 | + | 0.710772i | \(0.748346\pi\) | |||||||
\(734\) | −3.32456 | − | 5.75830i | −0.122712 | − | 0.212543i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.16228 | −0.153424 | ||||||||
\(737\) | 10.3923 | − | 6.00000i | 0.382805 | − | 0.221013i | ||||
\(738\) | −8.21584 | − | 4.74342i | −0.302429 | − | 0.174608i | ||||
\(739\) | −15.6491 | + | 27.1051i | −0.575662 | + | 0.997076i | 0.420308 | + | 0.907382i | \(0.361922\pi\) |
−0.995969 | + | 0.0896938i | \(0.971411\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.74342 | + | 5.92164i | 0.357933 | + | 0.217537i | ||||
\(742\) | − | 22.6491i | − | 0.831475i | ||||||
\(743\) | 16.7584 | + | 9.67544i | 0.614805 | + | 0.354958i | 0.774844 | − | 0.632153i | \(-0.217829\pi\) |
−0.160039 | + | 0.987111i | \(0.551162\pi\) | |||||||
\(744\) | −4.58114 | + | 7.93477i | −0.167953 | + | 0.290903i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −8.48683 | −0.310725 | ||||||||
\(747\) | −11.8205 | + | 6.82456i | −0.432489 | + | 0.249697i | ||||
\(748\) | −18.6081 | + | 10.7434i | −0.680381 | + | 0.392818i | ||||
\(749\) | −18.9737 | −0.693283 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.1623 | − | 26.2618i | 0.553279 | − | 0.958308i | −0.444756 | − | 0.895652i | \(-0.646710\pi\) |
0.998035 | − | 0.0626561i | \(-0.0199571\pi\) | |||||||
\(752\) | −5.19615 | − | 3.00000i | −0.189484 | − | 0.109399i | ||||
\(753\) | 15.0000i | 0.546630i | ||||||||
\(754\) | −0.675445 | + | 30.0070i | −0.0245982 | + | 1.09279i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.58114 | + | 2.73861i | −0.0575055 | + | 0.0996024i | ||||
\(757\) | 23.3599 | + | 13.4868i | 0.849029 | + | 0.490187i | 0.860323 | − | 0.509749i | \(-0.170262\pi\) |
−0.0112939 | + | 0.999936i | \(0.503595\pi\) | |||||||
\(758\) | −1.73205 | + | 1.00000i | −0.0629109 | + | 0.0363216i | ||||
\(759\) | −12.4868 | −0.453243 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.23025 | − | 9.05906i | −0.189596 | − | 0.328391i | 0.755519 | − | 0.655126i | \(-0.227385\pi\) |
−0.945116 | + | 0.326736i | \(0.894051\pi\) | |||||||
\(762\) | − | 7.67544i | − | 0.278052i | ||||||
\(763\) | 23.2421 | − | 13.4189i | 0.841422 | − | 0.485795i | ||||
\(764\) | 11.0811 | − | 19.1931i | 0.400902 | − | 0.694382i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.16228 | −0.150389 | ||||||||
\(767\) | 21.6278 | + | 0.486833i | 0.780936 | + | 0.0175785i | ||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | −11.4868 | + | 19.8958i | −0.414226 | + | 0.717460i | −0.995347 | − | 0.0963570i | \(-0.969281\pi\) |
0.581121 | + | 0.813817i | \(0.302614\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.90569 | − | 5.03281i | −0.104646 | − | 0.181252i | ||||
\(772\) | 4.67544i | 0.168273i | ||||||||
\(773\) | −30.0070 | + | 17.3246i | −1.07928 | + | 0.623121i | −0.930701 | − | 0.365780i | \(-0.880802\pi\) |
−0.148576 | + | 0.988901i | \(0.547469\pi\) | |||||||
\(774\) | 2.58114 | + | 4.47066i | 0.0927771 | + | 0.160695i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2.33772 | − | 4.04905i | −0.0839193 | − | 0.145353i | ||||
\(777\) | −28.7194 | − | 16.5811i | −1.03030 | − | 0.594845i | ||||
\(778\) | −13.5753 | − | 7.83772i | −0.486699 | − | 0.280996i | ||||
\(779\) | 30.0000 | 1.07486 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23.5132 | −0.841367 | ||||||||
\(782\) | 25.8174 | + | 14.9057i | 0.923229 | + | 0.533027i | ||||
\(783\) | 7.20928 | + | 4.16228i | 0.257639 | + | 0.148748i | ||||
\(784\) | 1.50000 | + | 2.59808i | 0.0535714 | + | 0.0927884i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.83772 | + | 3.18303i | 0.0655494 | + | 0.113535i | ||||
\(787\) | 11.6799 | − | 6.74342i | 0.416345 | − | 0.240377i | −0.277167 | − | 0.960822i | \(-0.589396\pi\) |
0.693512 | + | 0.720445i | \(0.256062\pi\) | |||||||
\(788\) | − | 6.00000i | − | 0.213741i | ||||||
\(789\) | 9.24342 | + | 16.0101i | 0.329074 | + | 0.569973i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.67544 | − | 6.36606i | 0.130684 | − | 0.226351i | ||||
\(792\) | 3.00000i | 0.106600i | ||||||||
\(793\) | 52.2198 | + | 1.17544i | 1.85438 | + | 0.0417413i | ||||
\(794\) | −24.3246 | −0.863246 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.58114 | + | 13.1309i | −0.268706 | + | 0.465413i | ||||
\(797\) | −47.2819 | + | 27.2982i | −1.67481 | + | 0.966953i | −0.709927 | + | 0.704275i | \(0.751272\pi\) |
−0.964884 | + | 0.262678i | \(0.915394\pi\) | |||||||
\(798\) | − | 10.0000i | − | 0.353996i | ||||||
\(799\) | 21.4868 | + | 37.2163i | 0.760150 | + | 1.31662i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.16228 | −0.253067 | ||||||||
\(802\) | 3.18303 | − | 1.83772i | 0.112397 | − | 0.0648922i | ||||
\(803\) | −3.44130 | − | 1.98683i | −0.121441 | − | 0.0701138i | ||||
\(804\) | −2.00000 | + | 3.46410i | −0.0705346 | + | 0.122169i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 28.9737 | − | 15.8695i | 1.02055 | − | 0.558980i | ||||
\(807\) | 19.1623i | 0.674544i | ||||||||
\(808\) | −14.4186 | − | 8.32456i | −0.507243 | − | 0.292857i | ||||
\(809\) | −9.58114 | + | 16.5950i | −0.336855 | + | 0.583450i | −0.983839 | − | 0.179053i | \(-0.942697\pi\) |
0.646984 | + | 0.762503i | \(0.276030\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.6491 | 0.654859 | 0.327429 | − | 0.944876i | \(-0.393818\pi\) | ||||
0.327429 | + | 0.944876i | \(0.393818\pi\) | |||||||
\(812\) | 22.7977 | − | 13.1623i | 0.800044 | − | 0.461905i | ||||
\(813\) | −10.6734 | + | 6.16228i | −0.374332 | + | 0.216121i | ||||
\(814\) | −31.4605 | −1.10269 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.58114 | − | 6.20271i | 0.125365 | − | 0.217138i | ||||
\(817\) | −14.1375 | − | 8.16228i | −0.494608 | − | 0.285562i | ||||
\(818\) | − | 17.6754i | − | 0.618007i | ||||||
\(819\) | 10.0000 | − | 5.47723i | 0.349428 | − | 0.191390i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.16228 | − | 7.20928i | 0.145264 | − | 0.251605i | −0.784207 | − | 0.620499i | \(-0.786930\pi\) |
0.929472 | + | 0.368894i | \(0.120263\pi\) | |||||||
\(822\) | 10.3923 | + | 6.00000i | 0.362473 | + | 0.209274i | ||||
\(823\) | 13.1309 | − | 7.58114i | 0.457715 | − | 0.264262i | −0.253368 | − | 0.967370i | \(-0.581538\pi\) |
0.711083 | + | 0.703108i | \(0.248205\pi\) | |||||||
\(824\) | −13.4868 | −0.469836 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.48683 | − | 16.4317i | −0.330089 | − | 0.571731i | ||||
\(827\) | 9.97367i | 0.346818i | 0.984850 | + | 0.173409i | \(0.0554783\pi\) | ||||
−0.984850 | + | 0.173409i | \(0.944522\pi\) | |||||||
\(828\) | 3.60464 | − | 2.08114i | 0.125270 | − | 0.0723246i | ||||
\(829\) | 16.4868 | − | 28.5560i | 0.572611 | − | 0.991792i | −0.423685 | − | 0.905809i | \(-0.639264\pi\) |
0.996297 | − | 0.0859825i | \(-0.0274029\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.8114 | 0.791318 | ||||||||
\(832\) | 1.87259 | − | 3.08114i | 0.0649203 | − | 0.106819i | ||||
\(833\) | − | 21.4868i | − | 0.744475i | ||||||
\(834\) | 9.16228 | − | 15.8695i | 0.317264 | − | 0.549517i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4.74342 | − | 8.21584i | −0.164054 | − | 0.284151i | ||||
\(837\) | − | 9.16228i | − | 0.316695i | ||||||
\(838\) | −7.79423 | + | 4.50000i | −0.269247 | + | 0.155450i | ||||
\(839\) | 16.8925 | + | 29.2587i | 0.583195 | + | 1.01012i | 0.995098 | + | 0.0988953i | \(0.0315309\pi\) |
−0.411903 | + | 0.911228i | \(0.635136\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.1491 | − | 34.8993i | −0.694797 | − | 1.20342i | ||||
\(842\) | −18.9120 | − | 10.9189i | −0.651751 | − | 0.376289i | ||||
\(843\) | 2.17647 | + | 1.25658i | 0.0749615 | + | 0.0432790i | ||||
\(844\) | −6.83772 | −0.235364 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.00000 | 0.206284 | ||||||||
\(847\) | −5.47723 | − | 3.16228i | −0.188200 | − | 0.108657i | ||||
\(848\) | 6.20271 | + | 3.58114i | 0.213002 | + | 0.122977i | ||||
\(849\) | −0.256584 | − | 0.444416i | −0.00880592 | − | 0.0152523i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 21.8246 | + | 37.8012i | 0.748136 | + | 1.29581i | ||||
\(852\) | 6.78767 | − | 3.91886i | 0.232542 | − | 0.134258i | ||||
\(853\) | 6.64911i | 0.227661i | 0.993500 | + | 0.113831i | \(0.0363121\pi\) | ||||
−0.993500 | + | 0.113831i | \(0.963688\pi\) | |||||||
\(854\) | −22.9057 | − | 39.6738i | −0.783817 | − | 1.35761i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.00000 | − | 5.19615i | 0.102538 | − | 0.177601i | ||||
\(857\) | 46.2719i | 1.58062i | 0.612709 | + | 0.790309i | \(0.290080\pi\) | ||||
−0.612709 | + | 0.790309i | \(0.709920\pi\) | |||||||
\(858\) | 5.61776 | − | 9.24342i | 0.191787 | − | 0.315565i | ||||
\(859\) | −43.8114 | −1.49483 | −0.747413 | − | 0.664360i | \(-0.768704\pi\) | ||||
−0.747413 | + | 0.664360i | \(0.768704\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 15.0000 | − | 25.9808i | 0.511199 | − | 0.885422i | ||||
\(862\) | −4.77454 | + | 2.75658i | −0.162622 | + | 0.0938896i | ||||
\(863\) | − | 37.4605i | − | 1.27517i | −0.770380 | − | 0.637585i | \(-0.779933\pi\) | ||
0.770380 | − | 0.637585i | \(-0.220067\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −28.6228 | −0.972642 | ||||||||
\(867\) | −29.7031 | + | 17.1491i | −1.00877 | + | 0.582414i | ||||
\(868\) | −25.0919 | − | 14.4868i | −0.851676 | − | 0.491715i | ||||
\(869\) | 13.7434 | − | 23.8043i | 0.466213 | − | 0.807505i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.6491 | − | 6.92820i | 0.428599 | − | 0.234753i | ||||
\(872\) | 8.48683i | 0.287400i | ||||||||
\(873\) | 4.04905 | + | 2.33772i | 0.137040 | + | 0.0791199i | ||||
\(874\) | −6.58114 | + | 11.3989i | −0.222610 | + | 0.385572i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.32456 | 0.0447526 | ||||||||
\(877\) | 21.8140 | − | 12.5943i | 0.736606 | − | 0.425279i | −0.0842282 | − | 0.996446i | \(-0.526842\pi\) |
0.820834 | + | 0.571167i | \(0.193509\pi\) | |||||||
\(878\) | 9.83016 | − | 5.67544i | 0.331752 | − | 0.191537i | ||||
\(879\) | −2.51317 | −0.0847670 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −17.2302 | + | 29.8437i | −0.580502 | + | 1.00546i | 0.414918 | + | 0.909859i | \(0.363810\pi\) |
−0.995420 | + | 0.0955999i | \(0.969523\pi\) | |||||||
\(882\) | −2.59808 | − | 1.50000i | −0.0874818 | − | 0.0505076i | ||||
\(883\) | − | 8.64911i | − | 0.291066i | −0.989353 | − | 0.145533i | \(-0.953510\pi\) | ||
0.989353 | − | 0.145533i | \(-0.0464897\pi\) | |||||||
\(884\) | −22.6491 | + | 12.4054i | −0.761772 | + | 0.417240i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.50000 | + | 7.79423i | −0.151180 | + | 0.261852i | ||||
\(887\) | 14.4186 | + | 8.32456i | 0.484128 | + | 0.279511i | 0.722135 | − | 0.691752i | \(-0.243161\pi\) |
−0.238007 | + | 0.971263i | \(0.576494\pi\) | |||||||
\(888\) | 9.08186 | − | 5.24342i | 0.304767 | − | 0.175958i | ||||
\(889\) | 24.2719 | 0.814053 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.50000 | − | 2.59808i | −0.0502519 | − | 0.0870388i | ||||
\(892\) | 18.1359i | 0.607236i | ||||||||
\(893\) | −16.4317 | + | 9.48683i | −0.549865 | + | 0.317465i | ||||
\(894\) | 6.58114 | − | 11.3989i | 0.220106 | − | 0.381235i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.16228 | −0.105644 | ||||||||
\(897\) | −15.0035 | − | 0.337722i | −0.500952 | − | 0.0112762i | ||||
\(898\) | − | 21.4868i | − | 0.717025i | ||||||
\(899\) | −38.1359 | + | 66.0534i | −1.27190 | + | 2.20300i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −25.6491 | − | 44.4256i | −0.854496 | − | 1.48003i | ||||
\(902\) | − | 28.4605i | − | 0.947631i | ||||||
\(903\) | −14.1375 | + | 8.16228i | −0.470466 | + | 0.271624i | ||||
\(904\) | 1.16228 | + | 2.01312i | 0.0386568 | + | 0.0669555i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −10.9057 | − | 18.8892i | −0.362317 | − | 0.627552i | ||||
\(907\) | −44.0268 | − | 25.4189i | −1.46188 | − | 0.844019i | −0.462786 | − | 0.886470i | \(-0.653150\pi\) |
−0.999099 | + | 0.0424506i | \(0.986483\pi\) | |||||||
\(908\) | 13.8336 | + | 7.98683i | 0.459084 | + | 0.265052i | ||||
\(909\) | 16.6491 | 0.552216 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.1359 | −0.368950 | −0.184475 | − | 0.982837i | \(-0.559059\pi\) | ||||
−0.184475 | + | 0.982837i | \(0.559059\pi\) | |||||||
\(912\) | 2.73861 | + | 1.58114i | 0.0906845 | + | 0.0523567i | ||||
\(913\) | −35.4614 | − | 20.4737i | −1.17360 | − | 0.677579i | ||||
\(914\) | 17.8246 | + | 30.8730i | 0.589584 | + | 1.02119i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.24342 | − | 2.15366i | −0.0410836 | − | 0.0711589i | ||||
\(917\) | −10.0656 | + | 5.81139i | −0.332396 | + | 0.191909i | ||||
\(918\) | 7.16228i | 0.236390i | ||||||||
\(919\) | 14.0680 | + | 24.3664i | 0.464060 | + | 0.803775i | 0.999159 | − | 0.0410146i | \(-0.0130590\pi\) |
−0.535099 | + | 0.844789i | \(0.679726\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.32456 | − | 7.49035i | 0.142499 | − | 0.246815i | ||||
\(922\) | − | 10.8377i | − | 0.356921i | ||||||
\(923\) | −28.2522 | − | 0.635944i | −0.929931 | − | 0.0209323i | ||||
\(924\) | −9.48683 | −0.312094 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 11.7434 | − | 20.3402i | 0.385913 | − | 0.668420i | ||||
\(927\) | 11.6799 | − | 6.74342i | 0.383620 | − | 0.221483i | ||||
\(928\) | 8.32456i | 0.273267i | ||||||||
\(929\) | 20.3246 | + | 35.2032i | 0.666827 | + | 1.15498i | 0.978786 | + | 0.204883i | \(0.0656814\pi\) |
−0.311959 | + | 0.950095i | \(0.600985\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.48683 | 0.310918 | ||||||||
\(932\) | −22.7977 | + | 13.1623i | −0.746765 | + | 0.431145i | ||||
\(933\) | −10.8139 | − | 6.24342i | −0.354032 | − | 0.204400i | ||||
\(934\) | 1.50000 | − | 2.59808i | 0.0490815 | − | 0.0850117i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.0811388 | + | 3.60464i | −0.00265211 | + | 0.117821i | ||||
\(937\) | 29.6491i | 0.968594i | 0.874904 | + | 0.484297i | \(0.160925\pi\) | ||||
−0.874904 | + | 0.484297i | \(0.839075\pi\) | |||||||
\(938\) | −10.9545 | − | 6.32456i | −0.357676 | − | 0.206504i | ||||
\(939\) | −8.82456 | + | 15.2846i | −0.287978 | + | 0.498793i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.0000 | −0.391189 | −0.195594 | − | 0.980685i | \(-0.562664\pi\) | ||||
−0.195594 | + | 0.980685i | \(0.562664\pi\) | |||||||
\(942\) | 8.51972 | − | 4.91886i | 0.277587 | − | 0.160265i | ||||
\(943\) | −34.1966 | + | 19.7434i | −1.11359 | + | 0.642934i | ||||
\(944\) | 6.00000 | 0.195283 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.74342 | + | 13.4120i | −0.251760 | + | 0.436061i | ||||
\(947\) | 19.3564 | + | 11.1754i | 0.629000 | + | 0.363153i | 0.780365 | − | 0.625325i | \(-0.215034\pi\) |
−0.151365 | + | 0.988478i | \(0.548367\pi\) | |||||||
\(948\) | 9.16228i | 0.297577i | ||||||||
\(949\) | −4.08114 | − | 2.48035i | −0.132479 | − | 0.0805154i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.0943058 | − | 0.163343i | 0.00305808 | − | 0.00529674i | ||||
\(952\) | 19.6147 | + | 11.3246i | 0.635716 | + | 0.367031i | ||||
\(953\) | 19.4514 | − | 11.2302i | 0.630091 | − | 0.363783i | −0.150696 | − | 0.988580i | \(-0.548151\pi\) |
0.780787 | + | 0.624797i | \(0.214818\pi\) | |||||||
\(954\) | −7.16228 | −0.231887 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0.243416 | + | 0.421610i | 0.00787265 | + | 0.0136358i | ||||
\(957\) | 24.9737i | 0.807284i | ||||||||
\(958\) | 22.7977 | − | 13.1623i | 0.736561 | − | 0.425254i | ||||
\(959\) | −18.9737 | + | 32.8634i | −0.612692 | + | 1.06121i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 52.9473 | 1.70798 | ||||||||
\(962\) | −37.8012 | − | 0.850889i | −1.21876 | − | 0.0274338i | ||||
\(963\) | 6.00000i | 0.193347i | ||||||||
\(964\) | 4.00000 | − | 6.92820i | 0.128831 | − | 0.223142i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 6.58114 | + | 11.3989i | 0.211745 | + | 0.366753i | ||||
\(967\) | 15.0263i | 0.483214i | 0.970374 | + | 0.241607i | \(0.0776745\pi\) | ||||
−0.970374 | + | 0.241607i | \(0.922325\pi\) | |||||||
\(968\) | 1.73205 | − | 1.00000i | 0.0556702 | − | 0.0321412i | ||||
\(969\) | −11.3246 | − | 19.6147i | −0.363797 | − | 0.630115i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.0000 | − | 36.3731i | −0.673922 | − | 1.16727i | −0.976783 | − | 0.214232i | \(-0.931275\pi\) |
0.302861 | − | 0.953035i | \(-0.402058\pi\) | |||||||
\(972\) | 0.866025 | + | 0.500000i | 0.0277778 | + | 0.0160375i | ||||
\(973\) | 50.1839 | + | 28.9737i | 1.60882 | + | 0.928853i | ||||
\(974\) | 3.16228 | 0.101326 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 14.4868 | 0.463712 | ||||||||
\(977\) | −33.1900 | − | 19.1623i | −1.06184 | − | 0.613056i | −0.135902 | − | 0.990722i | \(-0.543393\pi\) |
−0.925942 | + | 0.377667i | \(0.876727\pi\) | |||||||
\(978\) | −13.6931 | − | 7.90569i | −0.437856 | − | 0.252796i | ||||
\(979\) | −10.7434 | − | 18.6081i | −0.343361 | − | 0.594719i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.24342 | − | 7.34981i | −0.135482 | − | 0.234661i | ||||
\(982\) | 13.8336 | − | 7.98683i | 0.441448 | − | 0.254870i | ||||
\(983\) | − | 21.2982i | − | 0.679308i | −0.940550 | − | 0.339654i | \(-0.889690\pi\) | ||
0.940550 | − | 0.339654i | \(-0.110310\pi\) | |||||||
\(984\) | 4.74342 | + | 8.21584i | 0.151215 | + | 0.261911i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 29.8114 | − | 51.6348i | 0.949388 | − | 1.64439i | ||||
\(987\) | 18.9737i | 0.603938i | ||||||||
\(988\) | −5.47723 | − | 10.0000i | −0.174254 | − | 0.318142i | ||||
\(989\) | 21.4868 | 0.683242 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.0680 | + | 50.3472i | −0.923375 | + | 1.59933i | −0.129220 | + | 0.991616i | \(0.541247\pi\) |
−0.794155 | + | 0.607716i | \(0.792086\pi\) | |||||||
\(992\) | 7.93477 | − | 4.58114i | 0.251929 | − | 0.145451i | ||||
\(993\) | − | 8.83772i | − | 0.280457i | ||||||
\(994\) | 12.3925 | + | 21.4645i | 0.393067 | + | 0.680812i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 13.6491 | 0.432489 | ||||||||
\(997\) | −6.08498 | + | 3.51317i | −0.192713 | + | 0.111263i | −0.593252 | − | 0.805017i | \(-0.702156\pi\) |
0.400539 | + | 0.916280i | \(0.368823\pi\) | |||||||
\(998\) | 7.09155 | + | 4.09431i | 0.224479 | + | 0.129603i | ||||
\(999\) | −5.24342 | + | 9.08186i | −0.165894 | + | 0.287337i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1950.2.z.o.1699.1 | 8 | ||
5.2 | odd | 4 | 1950.2.i.bf.451.1 | yes | 4 | ||
5.3 | odd | 4 | 1950.2.i.ba.451.2 | ✓ | 4 | ||
5.4 | even | 2 | inner | 1950.2.z.o.1699.4 | 8 | ||
13.3 | even | 3 | inner | 1950.2.z.o.1849.4 | 8 | ||
65.3 | odd | 12 | 1950.2.i.ba.601.2 | yes | 4 | ||
65.29 | even | 6 | inner | 1950.2.z.o.1849.1 | 8 | ||
65.42 | odd | 12 | 1950.2.i.bf.601.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1950.2.i.ba.451.2 | ✓ | 4 | 5.3 | odd | 4 | ||
1950.2.i.ba.601.2 | yes | 4 | 65.3 | odd | 12 | ||
1950.2.i.bf.451.1 | yes | 4 | 5.2 | odd | 4 | ||
1950.2.i.bf.601.1 | yes | 4 | 65.42 | odd | 12 | ||
1950.2.z.o.1699.1 | 8 | 1.1 | even | 1 | trivial | ||
1950.2.z.o.1699.4 | 8 | 5.4 | even | 2 | inner | ||
1950.2.z.o.1849.1 | 8 | 65.29 | even | 6 | inner | ||
1950.2.z.o.1849.4 | 8 | 13.3 | even | 3 | inner |