Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [966,2,Mod(277,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 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("966.277");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.71354883526\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.1768034304.4 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - x^{6} - 6x^{5} + 14x^{4} + 18x^{3} - 31x^{2} - 14x + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 277.2 | ||
Root | \(2.09279 + 0.185573i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 966.277 |
Dual form | 966.2.i.l.415.2 |
$q$-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 \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(829\) | \(925\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | ||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −0.914214 | − | 1.58346i | −0.408849 | − | 0.708147i | 0.585912 | − | 0.810374i | \(-0.300736\pi\) |
−0.994761 | + | 0.102228i | \(0.967403\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 2.45965 | − | 0.974732i | 0.929662 | − | 0.368414i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −0.914214 | + | 1.58346i | −0.289100 | + | 0.500735i | ||||
\(11\) | −0.840244 | + | 1.45535i | −0.253343 | + | 0.438803i | −0.964444 | − | 0.264287i | \(-0.914864\pi\) |
0.711101 | + | 0.703090i | \(0.248197\pi\) | |||||||
\(12\) | −0.500000 | − | 0.866025i | −0.144338 | − | 0.250000i | ||||
\(13\) | 3.77137 | 1.04599 | 0.522995 | − | 0.852336i | \(-0.324815\pi\) | ||||
0.522995 | + | 0.852336i | \(0.324815\pi\) | |||||||
\(14\) | −2.07397 | − | 1.64276i | −0.554292 | − | 0.439045i | ||||
\(15\) | 1.82843 | 0.472098 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.29990 | + | 2.25149i | −0.315272 | + | 0.546066i | −0.979495 | − | 0.201467i | \(-0.935429\pi\) |
0.664224 | + | 0.747534i | \(0.268762\pi\) | |||||||
\(18\) | −0.500000 | + | 0.866025i | −0.117851 | + | 0.204124i | ||||
\(19\) | −0.545441 | − | 0.944731i | −0.125133 | − | 0.216736i | 0.796652 | − | 0.604438i | \(-0.206602\pi\) |
−0.921785 | + | 0.387702i | \(0.873269\pi\) | |||||||
\(20\) | 1.82843 | 0.408849 | ||||||||
\(21\) | −0.385685 | + | 2.61749i | −0.0841633 | + | 0.571183i | ||||
\(22\) | 1.68049 | 0.358281 | ||||||||
\(23\) | −0.500000 | − | 0.866025i | −0.104257 | − | 0.180579i | ||||
\(24\) | −0.500000 | + | 0.866025i | −0.102062 | + | 0.176777i | ||||
\(25\) | 0.828427 | − | 1.43488i | 0.165685 | − | 0.286976i | ||||
\(26\) | −1.88568 | − | 3.26610i | −0.369813 | − | 0.640535i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.385685 | + | 2.61749i | −0.0728876 | + | 0.494659i | ||||
\(29\) | −0.771369 | −0.143240 | −0.0716199 | − | 0.997432i | \(-0.522817\pi\) | ||||
−0.0716199 | + | 0.997432i | \(0.522817\pi\) | |||||||
\(30\) | −0.914214 | − | 1.58346i | −0.166912 | − | 0.289100i | ||||
\(31\) | 1.93113 | − | 3.34481i | 0.346840 | − | 0.600745i | −0.638846 | − | 0.769335i | \(-0.720588\pi\) |
0.985686 | + | 0.168590i | \(0.0539212\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −0.840244 | − | 1.45535i | −0.146268 | − | 0.253343i | ||||
\(34\) | 2.59980 | 0.445861 | ||||||||
\(35\) | −3.79210 | − | 3.00366i | −0.640982 | − | 0.507711i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −1.22593 | − | 2.12337i | −0.201541 | − | 0.349080i | 0.747484 | − | 0.664280i | \(-0.231262\pi\) |
−0.949025 | + | 0.315200i | \(0.897928\pi\) | |||||||
\(38\) | −0.545441 | + | 0.944731i | −0.0884821 | + | 0.153256i | ||||
\(39\) | −1.88568 | + | 3.26610i | −0.301951 | + | 0.522995i | ||||
\(40\) | −0.914214 | − | 1.58346i | −0.144550 | − | 0.250368i | ||||
\(41\) | −1.09088 | −0.170367 | −0.0851835 | − | 0.996365i | \(-0.527148\pi\) | ||||
−0.0851835 | + | 0.996365i | \(0.527148\pi\) | |||||||
\(42\) | 2.45965 | − | 0.974732i | 0.379533 | − | 0.150404i | ||||
\(43\) | 10.2959 | 1.57011 | 0.785053 | − | 0.619428i | \(-0.212636\pi\) | ||||
0.785053 | + | 0.619428i | \(0.212636\pi\) | |||||||
\(44\) | −0.840244 | − | 1.45535i | −0.126672 | − | 0.219402i | ||||
\(45\) | −0.914214 | + | 1.58346i | −0.136283 | + | 0.236049i | ||||
\(46\) | −0.500000 | + | 0.866025i | −0.0737210 | + | 0.127688i | ||||
\(47\) | 1.11161 | + | 1.92537i | 0.162146 | + | 0.280844i | 0.935638 | − | 0.352961i | \(-0.114825\pi\) |
−0.773492 | + | 0.633806i | \(0.781492\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 5.09980 | − | 4.79501i | 0.728542 | − | 0.685001i | ||||
\(50\) | −1.65685 | −0.234315 | ||||||||
\(51\) | −1.29990 | − | 2.25149i | −0.182022 | − | 0.315272i | ||||
\(52\) | −1.88568 | + | 3.26610i | −0.261497 | + | 0.452927i | ||||
\(53\) | 3.68558 | − | 6.38362i | 0.506254 | − | 0.876857i | −0.493720 | − | 0.869621i | \(-0.664363\pi\) |
0.999974 | − | 0.00723633i | \(-0.00230342\pi\) | |||||||
\(54\) | −0.500000 | − | 0.866025i | −0.0680414 | − | 0.117851i | ||||
\(55\) | 3.07265 | 0.414316 | ||||||||
\(56\) | 2.45965 | − | 0.974732i | 0.328685 | − | 0.130254i | ||||
\(57\) | 1.09088 | 0.144491 | ||||||||
\(58\) | 0.385685 | + | 0.668025i | 0.0506429 | + | 0.0877160i | ||||
\(59\) | 3.21411 | − | 5.56700i | 0.418442 | − | 0.724762i | −0.577341 | − | 0.816503i | \(-0.695910\pi\) |
0.995783 | + | 0.0917407i | \(0.0292431\pi\) | |||||||
\(60\) | −0.914214 | + | 1.58346i | −0.118024 | + | 0.204424i | ||||
\(61\) | −4.54274 | − | 7.86825i | −0.581638 | − | 1.00743i | −0.995285 | − | 0.0969895i | \(-0.969079\pi\) |
0.413647 | − | 0.910437i | \(-0.364255\pi\) | |||||||
\(62\) | −3.86225 | −0.490506 | ||||||||
\(63\) | −2.07397 | − | 1.64276i | −0.261296 | − | 0.206968i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.44784 | − | 5.97183i | −0.427652 | − | 0.740714i | ||||
\(66\) | −0.840244 | + | 1.45535i | −0.103427 | + | 0.179141i | ||||
\(67\) | 6.44514 | − | 11.1633i | 0.787399 | − | 1.36381i | −0.140157 | − | 0.990129i | \(-0.544761\pi\) |
0.927556 | − | 0.373685i | \(-0.121906\pi\) | |||||||
\(68\) | −1.29990 | − | 2.25149i | −0.157636 | − | 0.273033i | ||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | −0.705196 | + | 4.78589i | −0.0842871 | + | 0.572023i | ||||
\(71\) | 8.22863 | 0.976559 | 0.488279 | − | 0.872687i | \(-0.337625\pi\) | ||||
0.488279 | + | 0.872687i | \(0.337625\pi\) | |||||||
\(72\) | −0.500000 | − | 0.866025i | −0.0589256 | − | 0.102062i | ||||
\(73\) | 1.43113 | − | 2.47878i | 0.167501 | − | 0.290119i | −0.770040 | − | 0.637996i | \(-0.779764\pi\) |
0.937540 | + | 0.347876i | \(0.113097\pi\) | |||||||
\(74\) | −1.22593 | + | 2.12337i | −0.142511 | + | 0.246837i | ||||
\(75\) | 0.828427 | + | 1.43488i | 0.0956585 | + | 0.165685i | ||||
\(76\) | 1.09088 | 0.125133 | ||||||||
\(77\) | −0.648139 | + | 4.39866i | −0.0738623 | + | 0.501274i | ||||
\(78\) | 3.77137 | 0.427023 | ||||||||
\(79\) | −0.385685 | − | 0.668025i | −0.0433929 | − | 0.0751587i | 0.843513 | − | 0.537108i | \(-0.180483\pi\) |
−0.886906 | + | 0.461950i | \(0.847150\pi\) | |||||||
\(80\) | −0.914214 | + | 1.58346i | −0.102212 | + | 0.177037i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0.545441 | + | 0.944731i | 0.0602338 | + | 0.104328i | ||||
\(83\) | 3.33734 | 0.366321 | 0.183160 | − | 0.983083i | \(-0.441367\pi\) | ||||
0.183160 | + | 0.983083i | \(0.441367\pi\) | |||||||
\(84\) | −2.07397 | − | 1.64276i | −0.226289 | − | 0.179239i | ||||
\(85\) | 4.75354 | 0.515594 | ||||||||
\(86\) | −5.14794 | − | 8.91649i | −0.555117 | − | 0.961490i | ||||
\(87\) | 0.385685 | − | 0.668025i | 0.0413497 | − | 0.0716199i | ||||
\(88\) | −0.840244 | + | 1.45535i | −0.0895703 | + | 0.155140i | ||||
\(89\) | −1.60250 | − | 2.77561i | −0.169864 | − | 0.294214i | 0.768508 | − | 0.639841i | \(-0.221000\pi\) |
−0.938372 | + | 0.345627i | \(0.887666\pi\) | |||||||
\(90\) | 1.82843 | 0.192733 | ||||||||
\(91\) | 9.27626 | − | 3.67607i | 0.972417 | − | 0.385357i | ||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | 1.93113 | + | 3.34481i | 0.200248 | + | 0.346840i | ||||
\(94\) | 1.11161 | − | 1.92537i | 0.114654 | − | 0.198587i | ||||
\(95\) | −0.997298 | + | 1.72737i | −0.102321 | + | 0.177225i | ||||
\(96\) | −0.500000 | − | 0.866025i | −0.0510310 | − | 0.0883883i | ||||
\(97\) | −10.4282 | −1.05883 | −0.529413 | − | 0.848364i | \(-0.677588\pi\) | ||||
−0.529413 | + | 0.848364i | \(0.677588\pi\) | |||||||
\(98\) | −6.70249 | − | 2.01905i | −0.677054 | − | 0.203955i | ||||
\(99\) | 1.68049 | 0.168895 | ||||||||
\(100\) | 0.828427 | + | 1.43488i | 0.0828427 | + | 0.143488i | ||||
\(101\) | 3.23882 | − | 5.60980i | 0.322275 | − | 0.558196i | −0.658682 | − | 0.752421i | \(-0.728886\pi\) |
0.980957 | + | 0.194225i | \(0.0622192\pi\) | |||||||
\(102\) | −1.29990 | + | 2.25149i | −0.128709 | + | 0.222931i | ||||
\(103\) | 9.44514 | + | 16.3595i | 0.930657 | + | 1.61194i | 0.782201 | + | 0.623026i | \(0.214097\pi\) |
0.148456 | + | 0.988919i | \(0.452570\pi\) | |||||||
\(104\) | 3.77137 | 0.369813 | ||||||||
\(105\) | 4.49730 | − | 1.78223i | 0.438891 | − | 0.173927i | ||||
\(106\) | −7.37117 | −0.715951 | ||||||||
\(107\) | −6.90749 | − | 11.9641i | −0.667772 | − | 1.15662i | −0.978526 | − | 0.206125i | \(-0.933915\pi\) |
0.310753 | − | 0.950491i | \(-0.399419\pi\) | |||||||
\(108\) | −0.500000 | + | 0.866025i | −0.0481125 | + | 0.0833333i | ||||
\(109\) | −5.03382 | + | 8.71884i | −0.482153 | + | 0.835113i | −0.999790 | − | 0.0204870i | \(-0.993478\pi\) |
0.517637 | + | 0.855600i | \(0.326812\pi\) | |||||||
\(110\) | −1.53633 | − | 2.66099i | −0.146483 | − | 0.253716i | ||||
\(111\) | 2.45186 | 0.232720 | ||||||||
\(112\) | −2.07397 | − | 1.64276i | −0.195972 | − | 0.155226i | ||||
\(113\) | 6.30392 | 0.593023 | 0.296511 | − | 0.955029i | \(-0.404177\pi\) | ||||
0.296511 | + | 0.955029i | \(0.404177\pi\) | |||||||
\(114\) | −0.545441 | − | 0.944731i | −0.0510852 | − | 0.0884821i | ||||
\(115\) | −0.914214 | + | 1.58346i | −0.0852509 | + | 0.147659i | ||||
\(116\) | 0.385685 | − | 0.668025i | 0.0358099 | − | 0.0620246i | ||||
\(117\) | −1.88568 | − | 3.26610i | −0.174332 | − | 0.301951i | ||||
\(118\) | −6.42822 | −0.591766 | ||||||||
\(119\) | −1.00270 | + | 6.80494i | −0.0919175 | + | 0.623808i | ||||
\(120\) | 1.82843 | 0.166912 | ||||||||
\(121\) | 4.08798 | + | 7.08059i | 0.371634 | + | 0.643690i | ||||
\(122\) | −4.54274 | + | 7.86825i | −0.411280 | + | 0.712358i | ||||
\(123\) | 0.545441 | − | 0.944731i | 0.0491807 | − | 0.0851835i | ||||
\(124\) | 1.93113 | + | 3.34481i | 0.173420 | + | 0.300373i | ||||
\(125\) | −12.1716 | −1.08866 | ||||||||
\(126\) | −0.385685 | + | 2.61749i | −0.0343595 | + | 0.233184i | ||||
\(127\) | 4.02363 | 0.357040 | 0.178520 | − | 0.983936i | \(-0.442869\pi\) | ||||
0.178520 | + | 0.983936i | \(0.442869\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | −5.14794 | + | 8.91649i | −0.453251 | + | 0.785053i | ||||
\(130\) | −3.44784 | + | 5.97183i | −0.302395 | + | 0.523764i | ||||
\(131\) | −5.49730 | − | 9.52160i | −0.480301 | − | 0.831906i | 0.519443 | − | 0.854505i | \(-0.326139\pi\) |
−0.999745 | + | 0.0225988i | \(0.992806\pi\) | |||||||
\(132\) | 1.68049 | 0.146268 | ||||||||
\(133\) | −2.26245 | − | 1.79205i | −0.196180 | − | 0.155391i | ||||
\(134\) | −12.8903 | −1.11355 | ||||||||
\(135\) | −0.914214 | − | 1.58346i | −0.0786830 | − | 0.136283i | ||||
\(136\) | −1.29990 | + | 2.25149i | −0.111465 | + | 0.193064i | ||||
\(137\) | −2.07397 | + | 3.59222i | −0.177191 | + | 0.306904i | −0.940917 | − | 0.338636i | \(-0.890034\pi\) |
0.763726 | + | 0.645540i | \(0.223368\pi\) | |||||||
\(138\) | −0.500000 | − | 0.866025i | −0.0425628 | − | 0.0737210i | ||||
\(139\) | −13.3137 | −1.12925 | −0.564627 | − | 0.825346i | \(-0.690980\pi\) | ||||
−0.564627 | + | 0.825346i | \(0.690980\pi\) | |||||||
\(140\) | 4.49730 | − | 1.78223i | 0.380091 | − | 0.150626i | ||||
\(141\) | −2.22323 | −0.187229 | ||||||||
\(142\) | −4.11432 | − | 7.12620i | −0.345266 | − | 0.598018i | ||||
\(143\) | −3.16887 | + | 5.48865i | −0.264994 | + | 0.458984i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | 0.705196 | + | 1.22144i | 0.0585634 | + | 0.101435i | ||||
\(146\) | −2.86225 | −0.236882 | ||||||||
\(147\) | 1.60270 | + | 6.81406i | 0.132188 | + | 0.562014i | ||||
\(148\) | 2.45186 | 0.201541 | ||||||||
\(149\) | 5.93622 | + | 10.2818i | 0.486314 | + | 0.842321i | 0.999876 | − | 0.0157317i | \(-0.00500776\pi\) |
−0.513562 | + | 0.858052i | \(0.671674\pi\) | |||||||
\(150\) | 0.828427 | − | 1.43488i | 0.0676408 | − | 0.117157i | ||||
\(151\) | −0.536325 | + | 0.928943i | −0.0436455 | + | 0.0755963i | −0.887023 | − | 0.461725i | \(-0.847231\pi\) |
0.843377 | + | 0.537322i | \(0.180564\pi\) | |||||||
\(152\) | −0.545441 | − | 0.944731i | −0.0442411 | − | 0.0766278i | ||||
\(153\) | 2.59980 | 0.210181 | ||||||||
\(154\) | 4.13342 | − | 1.63803i | 0.333080 | − | 0.131996i | ||||
\(155\) | −7.06184 | −0.567221 | ||||||||
\(156\) | −1.88568 | − | 3.26610i | −0.150976 | − | 0.261497i | ||||
\(157\) | −10.6880 | + | 18.5121i | −0.852993 | + | 1.47743i | 0.0255009 | + | 0.999675i | \(0.491882\pi\) |
−0.878494 | + | 0.477753i | \(0.841451\pi\) | |||||||
\(158\) | −0.385685 | + | 0.668025i | −0.0306834 | + | 0.0531453i | ||||
\(159\) | 3.68558 | + | 6.38362i | 0.292286 | + | 0.506254i | ||||
\(160\) | 1.82843 | 0.144550 | ||||||||
\(161\) | −2.07397 | − | 1.64276i | −0.163452 | − | 0.129467i | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −0.940241 | − | 1.62854i | −0.0736453 | − | 0.127557i | 0.826851 | − | 0.562421i | \(-0.190130\pi\) |
−0.900496 | + | 0.434864i | \(0.856797\pi\) | |||||||
\(164\) | 0.545441 | − | 0.944731i | 0.0425917 | − | 0.0737711i | ||||
\(165\) | −1.53633 | + | 2.66099i | −0.119603 | + | 0.207158i | ||||
\(166\) | −1.66867 | − | 2.89022i | −0.129514 | − | 0.224325i | ||||
\(167\) | −19.6511 | −1.52064 | −0.760322 | − | 0.649546i | \(-0.774959\pi\) | ||||
−0.760322 | + | 0.649546i | \(0.774959\pi\) | |||||||
\(168\) | −0.385685 | + | 2.61749i | −0.0297562 | + | 0.201944i | ||||
\(169\) | 1.22323 | 0.0940944 | ||||||||
\(170\) | −2.37677 | − | 4.11669i | −0.182290 | − | 0.315735i | ||||
\(171\) | −0.545441 | + | 0.944731i | −0.0417109 | + | 0.0722454i | ||||
\(172\) | −5.14794 | + | 8.91649i | −0.392527 | + | 0.679876i | ||||
\(173\) | 0.885485 | + | 1.53370i | 0.0673222 | + | 0.116605i | 0.897722 | − | 0.440563i | \(-0.145221\pi\) |
−0.830400 | + | 0.557168i | \(0.811888\pi\) | |||||||
\(174\) | −0.771369 | −0.0584774 | ||||||||
\(175\) | 0.639023 | − | 4.33680i | 0.0483056 | − | 0.327831i | ||||
\(176\) | 1.68049 | 0.126672 | ||||||||
\(177\) | 3.21411 | + | 5.56700i | 0.241587 | + | 0.418442i | ||||
\(178\) | −1.60250 | + | 2.77561i | −0.120112 | + | 0.208041i | ||||
\(179\) | 6.11161 | − | 10.5856i | 0.456803 | − | 0.791207i | −0.541986 | − | 0.840387i | \(-0.682328\pi\) |
0.998790 | + | 0.0491804i | \(0.0156609\pi\) | |||||||
\(180\) | −0.914214 | − | 1.58346i | −0.0681415 | − | 0.118024i | ||||
\(181\) | 0.820785 | 0.0610085 | 0.0305043 | − | 0.999535i | \(-0.490289\pi\) | ||||
0.0305043 | + | 0.999535i | \(0.490289\pi\) | |||||||
\(182\) | −7.82170 | − | 6.19544i | −0.579783 | − | 0.459237i | ||||
\(183\) | 9.08548 | 0.671618 | ||||||||
\(184\) | −0.500000 | − | 0.866025i | −0.0368605 | − | 0.0638442i | ||||
\(185\) | −2.24152 | + | 3.88243i | −0.164800 | + | 0.285442i | ||||
\(186\) | 1.93113 | − | 3.34481i | 0.141597 | − | 0.245253i | ||||
\(187\) | −2.18446 | − | 3.78360i | −0.159744 | − | 0.276684i | ||||
\(188\) | −2.22323 | −0.162146 | ||||||||
\(189\) | 2.45965 | − | 0.974732i | 0.178914 | − | 0.0709013i | ||||
\(190\) | 1.99460 | 0.144703 | ||||||||
\(191\) | 6.22593 | + | 10.7836i | 0.450492 | + | 0.780276i | 0.998417 | − | 0.0562523i | \(-0.0179151\pi\) |
−0.547924 | + | 0.836528i | \(0.684582\pi\) | |||||||
\(192\) | −0.500000 | + | 0.866025i | −0.0360844 | + | 0.0625000i | ||||
\(193\) | −3.35206 | + | 5.80594i | −0.241287 | + | 0.417921i | −0.961081 | − | 0.276267i | \(-0.910903\pi\) |
0.719794 | + | 0.694187i | \(0.244236\pi\) | |||||||
\(194\) | 5.21411 | + | 9.03111i | 0.374351 | + | 0.648396i | ||||
\(195\) | 6.89567 | 0.493809 | ||||||||
\(196\) | 1.60270 | + | 6.81406i | 0.114478 | + | 0.486718i | ||||
\(197\) | 16.5606 | 1.17989 | 0.589946 | − | 0.807443i | \(-0.299149\pi\) | ||||
0.589946 | + | 0.807443i | \(0.299149\pi\) | |||||||
\(198\) | −0.840244 | − | 1.45535i | −0.0597136 | − | 0.103427i | ||||
\(199\) | 2.50892 | − | 4.34557i | 0.177852 | − | 0.308049i | −0.763292 | − | 0.646053i | \(-0.776418\pi\) |
0.941145 | + | 0.338004i | \(0.109752\pi\) | |||||||
\(200\) | 0.828427 | − | 1.43488i | 0.0585786 | − | 0.101461i | ||||
\(201\) | 6.44514 | + | 11.1633i | 0.454605 | + | 0.787399i | ||||
\(202\) | −6.47764 | −0.455765 | ||||||||
\(203\) | −1.89730 | + | 0.751878i | −0.133164 | + | 0.0527715i | ||||
\(204\) | 2.59980 | 0.182022 | ||||||||
\(205\) | 0.997298 | + | 1.72737i | 0.0696543 | + | 0.120645i | ||||
\(206\) | 9.44514 | − | 16.3595i | 0.658074 | − | 1.13982i | ||||
\(207\) | −0.500000 | + | 0.866025i | −0.0347524 | + | 0.0601929i | ||||
\(208\) | −1.88568 | − | 3.26610i | −0.130749 | − | 0.226463i | ||||
\(209\) | 1.83321 | 0.126806 | ||||||||
\(210\) | −3.79210 | − | 3.00366i | −0.261680 | − | 0.207272i | ||||
\(211\) | 17.1523 | 1.18081 | 0.590407 | − | 0.807105i | \(-0.298967\pi\) | ||||
0.590407 | + | 0.807105i | \(0.298967\pi\) | |||||||
\(212\) | 3.68558 | + | 6.38362i | 0.253127 | + | 0.438429i | ||||
\(213\) | −4.11432 | + | 7.12620i | −0.281908 | + | 0.488279i | ||||
\(214\) | −6.90749 | + | 11.9641i | −0.472186 | + | 0.817851i | ||||
\(215\) | −9.41263 | − | 16.3032i | −0.641936 | − | 1.11187i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 1.48961 | − | 10.1094i | 0.101121 | − | 0.686271i | ||||
\(218\) | 10.0676 | 0.681867 | ||||||||
\(219\) | 1.43113 | + | 2.47878i | 0.0967065 | + | 0.167501i | ||||
\(220\) | −1.53633 | + | 2.66099i | −0.103579 | + | 0.179404i | ||||
\(221\) | −4.90240 | + | 8.49120i | −0.329771 | + | 0.571180i | ||||
\(222\) | −1.22593 | − | 2.12337i | −0.0822790 | − | 0.142511i | ||||
\(223\) | 4.42282 | 0.296174 | 0.148087 | − | 0.988974i | \(-0.452688\pi\) | ||||
0.148087 | + | 0.988974i | \(0.452688\pi\) | |||||||
\(224\) | −0.385685 | + | 2.61749i | −0.0257696 | + | 0.174888i | ||||
\(225\) | −1.65685 | −0.110457 | ||||||||
\(226\) | −3.15196 | − | 5.45935i | −0.209665 | − | 0.363151i | ||||
\(227\) | 6.04524 | − | 10.4707i | 0.401237 | − | 0.694962i | −0.592639 | − | 0.805468i | \(-0.701914\pi\) |
0.993875 | + | 0.110506i | \(0.0352471\pi\) | |||||||
\(228\) | −0.545441 | + | 0.944731i | −0.0361227 | + | 0.0625663i | ||||
\(229\) | 4.54544 | + | 7.87293i | 0.300371 | + | 0.520258i | 0.976220 | − | 0.216782i | \(-0.0695561\pi\) |
−0.675849 | + | 0.737040i | \(0.736223\pi\) | |||||||
\(230\) | 1.82843 | 0.120563 | ||||||||
\(231\) | −3.48528 | − | 2.76063i | −0.229315 | − | 0.181636i | ||||
\(232\) | −0.771369 | −0.0506429 | ||||||||
\(233\) | −3.37387 | − | 5.84371i | −0.221029 | − | 0.382834i | 0.734091 | − | 0.679051i | \(-0.237608\pi\) |
−0.955121 | + | 0.296216i | \(0.904275\pi\) | |||||||
\(234\) | −1.88568 | + | 3.26610i | −0.123271 | + | 0.213512i | ||||
\(235\) | 2.03250 | − | 3.52040i | 0.132586 | − | 0.229646i | ||||
\(236\) | 3.21411 | + | 5.56700i | 0.209221 | + | 0.362381i | ||||
\(237\) | 0.771369 | 0.0501058 | ||||||||
\(238\) | 6.39460 | − | 2.53410i | 0.414500 | − | 0.164262i | ||||
\(239\) | 20.5918 | 1.33197 | 0.665985 | − | 0.745965i | \(-0.268011\pi\) | ||||
0.665985 | + | 0.745965i | \(0.268011\pi\) | |||||||
\(240\) | −0.914214 | − | 1.58346i | −0.0590122 | − | 0.102212i | ||||
\(241\) | −8.59068 | + | 14.8795i | −0.553374 | + | 0.958473i | 0.444654 | + | 0.895703i | \(0.353327\pi\) |
−0.998028 | + | 0.0627700i | \(0.980007\pi\) | |||||||
\(242\) | 4.08798 | − | 7.08059i | 0.262785 | − | 0.455157i | ||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 9.08548 | 0.581638 | ||||||||
\(245\) | −12.2550 | − | 3.69169i | −0.782945 | − | 0.235853i | ||||
\(246\) | −1.09088 | −0.0695520 | ||||||||
\(247\) | −2.05706 | − | 3.56293i | −0.130887 | − | 0.226704i | ||||
\(248\) | 1.93113 | − | 3.34481i | 0.122627 | − | 0.212395i | ||||
\(249\) | −1.66867 | + | 2.89022i | −0.105748 | + | 0.183160i | ||||
\(250\) | 6.08579 | + | 10.5409i | 0.384899 | + | 0.666665i | ||||
\(251\) | −15.1760 | −0.957898 | −0.478949 | − | 0.877843i | \(-0.658982\pi\) | ||||
−0.478949 | + | 0.877843i | \(0.658982\pi\) | |||||||
\(252\) | 2.45965 | − | 0.974732i | 0.154944 | − | 0.0614023i | ||||
\(253\) | 1.68049 | 0.105651 | ||||||||
\(254\) | −2.01182 | − | 3.48457i | −0.126233 | − | 0.218641i | ||||
\(255\) | −2.37677 | + | 4.11669i | −0.148839 | + | 0.257797i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 7.99730 | + | 13.8517i | 0.498858 | + | 0.864047i | 0.999999 | − | 0.00131844i | \(-0.000419674\pi\) |
−0.501141 | + | 0.865365i | \(0.667086\pi\) | |||||||
\(258\) | 10.2959 | 0.640993 | ||||||||
\(259\) | −5.08508 | − | 4.02781i | −0.315971 | − | 0.250276i | ||||
\(260\) | 6.89567 | 0.427652 | ||||||||
\(261\) | 0.385685 | + | 0.668025i | 0.0238733 | + | 0.0413497i | ||||
\(262\) | −5.49730 | + | 9.52160i | −0.339624 | + | 0.588246i | ||||
\(263\) | −10.8801 | + | 18.8449i | −0.670895 | + | 1.16202i | 0.306756 | + | 0.951788i | \(0.400756\pi\) |
−0.977651 | + | 0.210235i | \(0.932577\pi\) | |||||||
\(264\) | −0.840244 | − | 1.45535i | −0.0517135 | − | 0.0895703i | ||||
\(265\) | −13.4776 | −0.827925 | ||||||||
\(266\) | −0.420736 | + | 2.85537i | −0.0257970 | + | 0.175074i | ||||
\(267\) | 3.20500 | 0.196143 | ||||||||
\(268\) | 6.44514 | + | 11.1633i | 0.393699 | + | 0.681907i | ||||
\(269\) | −10.2814 | + | 17.8078i | −0.626866 | + | 1.08576i | 0.361311 | + | 0.932445i | \(0.382329\pi\) |
−0.988177 | + | 0.153318i | \(0.951004\pi\) | |||||||
\(270\) | −0.914214 | + | 1.58346i | −0.0556373 | + | 0.0963666i | ||||
\(271\) | −1.93113 | − | 3.34481i | −0.117308 | − | 0.203183i | 0.801392 | − | 0.598139i | \(-0.204093\pi\) |
−0.918700 | + | 0.394957i | \(0.870760\pi\) | |||||||
\(272\) | 2.59980 | 0.157636 | ||||||||
\(273\) | −1.45456 | + | 9.87152i | −0.0880339 | + | 0.597451i | ||||
\(274\) | 4.14794 | 0.250586 | ||||||||
\(275\) | 1.39216 | + | 2.41130i | 0.0839505 | + | 0.145407i | ||||
\(276\) | −0.500000 | + | 0.866025i | −0.0300965 | + | 0.0521286i | ||||
\(277\) | −12.0647 | + | 20.8968i | −0.724900 | + | 1.25556i | 0.234115 | + | 0.972209i | \(0.424781\pi\) |
−0.959015 | + | 0.283355i | \(0.908552\pi\) | |||||||
\(278\) | 6.65685 | + | 11.5300i | 0.399252 | + | 0.691524i | ||||
\(279\) | −3.86225 | −0.231227 | ||||||||
\(280\) | −3.79210 | − | 3.00366i | −0.226621 | − | 0.179503i | ||||
\(281\) | 27.6853 | 1.65156 | 0.825782 | − | 0.563989i | \(-0.190734\pi\) | ||||
0.825782 | + | 0.563989i | \(0.190734\pi\) | |||||||
\(282\) | 1.11161 | + | 1.92537i | 0.0661956 | + | 0.114654i | ||||
\(283\) | −2.98309 | + | 5.16686i | −0.177326 | + | 0.307138i | −0.940964 | − | 0.338507i | \(-0.890078\pi\) |
0.763638 | + | 0.645645i | \(0.223411\pi\) | |||||||
\(284\) | −4.11432 | + | 7.12620i | −0.244140 | + | 0.422862i | ||||
\(285\) | −0.997298 | − | 1.72737i | −0.0590749 | − | 0.102321i | ||||
\(286\) | 6.33774 | 0.374759 | ||||||||
\(287\) | −2.68319 | + | 1.06332i | −0.158384 | + | 0.0627656i | ||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 5.12053 | + | 8.86902i | 0.301208 | + | 0.521707i | ||||
\(290\) | 0.705196 | − | 1.22144i | 0.0414106 | − | 0.0717252i | ||||
\(291\) | 5.21411 | − | 9.03111i | 0.305657 | − | 0.529413i | ||||
\(292\) | 1.43113 | + | 2.47878i | 0.0837503 | + | 0.145060i | ||||
\(293\) | −31.4853 | −1.83939 | −0.919695 | − | 0.392634i | \(-0.871564\pi\) | ||||
−0.919695 | + | 0.392634i | \(0.871564\pi\) | |||||||
\(294\) | 5.09980 | − | 4.79501i | 0.297426 | − | 0.279650i | ||||
\(295\) | −11.7535 | −0.684317 | ||||||||
\(296\) | −1.22593 | − | 2.12337i | −0.0712557 | − | 0.123418i | ||||
\(297\) | −0.840244 | + | 1.45535i | −0.0487559 | + | 0.0844477i | ||||
\(298\) | 5.93622 | − | 10.2818i | 0.343876 | − | 0.595611i | ||||
\(299\) | −1.88568 | − | 3.26610i | −0.109052 | − | 0.188884i | ||||
\(300\) | −1.65685 | −0.0956585 | ||||||||
\(301\) | 25.3243 | − | 10.0357i | 1.45967 | − | 0.578449i | ||||
\(302\) | 1.07265 | 0.0617241 | ||||||||
\(303\) | 3.23882 | + | 5.60980i | 0.186065 | + | 0.322275i | ||||
\(304\) | −0.545441 | + | 0.944731i | −0.0312832 | + | 0.0541840i | ||||
\(305\) | −8.30607 | + | 14.3865i | −0.475604 | + | 0.823770i | ||||
\(306\) | −1.29990 | − | 2.25149i | −0.0743102 | − | 0.128709i | ||||
\(307\) | 5.13815 | 0.293250 | 0.146625 | − | 0.989192i | \(-0.453159\pi\) | ||||
0.146625 | + | 0.989192i | \(0.453159\pi\) | |||||||
\(308\) | −3.48528 | − | 2.76063i | −0.198592 | − | 0.157302i | ||||
\(309\) | −18.8903 | −1.07463 | ||||||||
\(310\) | 3.53092 | + | 6.11574i | 0.200543 | + | 0.347350i | ||||
\(311\) | 7.78136 | − | 13.4777i | 0.441240 | − | 0.764251i | −0.556541 | − | 0.830820i | \(-0.687872\pi\) |
0.997782 | + | 0.0665691i | \(0.0212053\pi\) | |||||||
\(312\) | −1.88568 | + | 3.26610i | −0.106756 | + | 0.184907i | ||||
\(313\) | 11.0764 | + | 19.1848i | 0.626073 | + | 1.08439i | 0.988332 | + | 0.152313i | \(0.0486722\pi\) |
−0.362259 | + | 0.932077i | \(0.617995\pi\) | |||||||
\(314\) | 21.3760 | 1.20631 | ||||||||
\(315\) | −0.705196 | + | 4.78589i | −0.0397333 | + | 0.269654i | ||||
\(316\) | 0.771369 | 0.0433929 | ||||||||
\(317\) | −9.28136 | − | 16.0758i | −0.521293 | − | 0.902906i | −0.999693 | − | 0.0247642i | \(-0.992117\pi\) |
0.478400 | − | 0.878142i | \(-0.341217\pi\) | |||||||
\(318\) | 3.68558 | − | 6.38362i | 0.206677 | − | 0.357975i | ||||
\(319\) | 0.648139 | − | 1.12261i | 0.0362888 | − | 0.0628540i | ||||
\(320\) | −0.914214 | − | 1.58346i | −0.0511061 | − | 0.0885183i | ||||
\(321\) | 13.8150 | 0.771077 | ||||||||
\(322\) | −0.385685 | + | 2.61749i | −0.0214934 | + | 0.145867i | ||||
\(323\) | 2.83607 | 0.157803 | ||||||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 3.12430 | − | 5.41145i | 0.173305 | − | 0.300173i | ||||
\(326\) | −0.940241 | + | 1.62854i | −0.0520751 | + | 0.0901967i | ||||
\(327\) | −5.03382 | − | 8.71884i | −0.278371 | − | 0.482153i | ||||
\(328\) | −1.09088 | −0.0602338 | ||||||||
\(329\) | 4.61091 | + | 3.65222i | 0.254207 | + | 0.201354i | ||||
\(330\) | 3.07265 | 0.169144 | ||||||||
\(331\) | −1.43133 | − | 2.47913i | −0.0786727 | − | 0.136265i | 0.824005 | − | 0.566583i | \(-0.191735\pi\) |
−0.902678 | + | 0.430318i | \(0.858402\pi\) | |||||||
\(332\) | −1.66867 | + | 2.89022i | −0.0915802 | + | 0.158622i | ||||
\(333\) | −1.22593 | + | 2.12337i | −0.0671805 | + | 0.116360i | ||||
\(334\) | 9.82553 | + | 17.0183i | 0.537629 | + | 0.931200i | ||||
\(335\) | −23.5689 | −1.28771 | ||||||||
\(336\) | 2.45965 | − | 0.974732i | 0.134185 | − | 0.0531760i | ||||
\(337\) | −7.70627 | −0.419787 | −0.209894 | − | 0.977724i | \(-0.567312\pi\) | ||||
−0.209894 | + | 0.977724i | \(0.567312\pi\) | |||||||
\(338\) | −0.611614 | − | 1.05935i | −0.0332674 | − | 0.0576208i | ||||
\(339\) | −3.15196 | + | 5.45935i | −0.171191 | + | 0.296511i | ||||
\(340\) | −2.37677 | + | 4.11669i | −0.128898 | + | 0.223259i | ||||
\(341\) | 3.24523 | + | 5.62091i | 0.175739 | + | 0.304389i | ||||
\(342\) | 1.09088 | 0.0589881 | ||||||||
\(343\) | 7.86989 | − | 16.7650i | 0.424934 | − | 0.905224i | ||||
\(344\) | 10.2959 | 0.555117 | ||||||||
\(345\) | −0.914214 | − | 1.58346i | −0.0492196 | − | 0.0852509i | ||||
\(346\) | 0.885485 | − | 1.53370i | 0.0476040 | − | 0.0824525i | ||||
\(347\) | 4.97386 | − | 8.61499i | 0.267011 | − | 0.462477i | −0.701078 | − | 0.713085i | \(-0.747297\pi\) |
0.968089 | + | 0.250608i | \(0.0806307\pi\) | |||||||
\(348\) | 0.385685 | + | 0.668025i | 0.0206749 | + | 0.0358099i | ||||
\(349\) | −8.54489 | −0.457397 | −0.228699 | − | 0.973497i | \(-0.573447\pi\) | ||||
−0.228699 | + | 0.973497i | \(0.573447\pi\) | |||||||
\(350\) | −4.07529 | + | 1.61499i | −0.217833 | + | 0.0863248i | ||||
\(351\) | 3.77137 | 0.201301 | ||||||||
\(352\) | −0.840244 | − | 1.45535i | −0.0447852 | − | 0.0775702i | ||||
\(353\) | 0.997298 | − | 1.72737i | 0.0530808 | − | 0.0919387i | −0.838264 | − | 0.545264i | \(-0.816429\pi\) |
0.891345 | + | 0.453326i | \(0.149763\pi\) | |||||||
\(354\) | 3.21411 | − | 5.56700i | 0.170828 | − | 0.295883i | ||||
\(355\) | −7.52273 | − | 13.0297i | −0.399265 | − | 0.691547i | ||||
\(356\) | 3.20500 | 0.169864 | ||||||||
\(357\) | −5.39190 | − | 4.27083i | −0.285370 | − | 0.226037i | ||||
\(358\) | −12.2232 | −0.646018 | ||||||||
\(359\) | 13.8564 | + | 24.0001i | 0.731315 | + | 1.26668i | 0.956321 | + | 0.292318i | \(0.0944265\pi\) |
−0.225006 | + | 0.974357i | \(0.572240\pi\) | |||||||
\(360\) | −0.914214 | + | 1.58346i | −0.0481833 | + | 0.0834559i | ||||
\(361\) | 8.90499 | − | 15.4239i | 0.468684 | − | 0.811784i | ||||
\(362\) | −0.410393 | − | 0.710821i | −0.0215698 | − | 0.0373599i | ||||
\(363\) | −8.17596 | −0.429127 | ||||||||
\(364\) | −1.45456 | + | 9.87152i | −0.0762396 | + | 0.517408i | ||||
\(365\) | −5.23342 | −0.273930 | ||||||||
\(366\) | −4.54274 | − | 7.86825i | −0.237453 | − | 0.411280i | ||||
\(367\) | 10.8879 | − | 18.8584i | 0.568343 | − | 0.984398i | −0.428387 | − | 0.903595i | \(-0.640918\pi\) |
0.996730 | − | 0.0808031i | \(-0.0257485\pi\) | |||||||
\(368\) | −0.500000 | + | 0.866025i | −0.0260643 | + | 0.0451447i | ||||
\(369\) | 0.545441 | + | 0.944731i | 0.0283945 | + | 0.0491807i | ||||
\(370\) | 4.48304 | 0.233062 | ||||||||
\(371\) | 2.84295 | − | 19.2939i | 0.147598 | − | 1.00169i | ||||
\(372\) | −3.86225 | −0.200248 | ||||||||
\(373\) | −6.68049 | − | 11.5709i | −0.345903 | − | 0.599121i | 0.639615 | − | 0.768696i | \(-0.279094\pi\) |
−0.985517 | + | 0.169575i | \(0.945761\pi\) | |||||||
\(374\) | −2.18446 | + | 3.78360i | −0.112956 | + | 0.195645i | ||||
\(375\) | 6.08579 | − | 10.5409i | 0.314269 | − | 0.544329i | ||||
\(376\) | 1.11161 | + | 1.92537i | 0.0573271 | + | 0.0992934i | ||||
\(377\) | −2.90912 | −0.149827 | ||||||||
\(378\) | −2.07397 | − | 1.64276i | −0.106673 | − | 0.0844943i | ||||
\(379\) | −3.50892 | −0.180241 | −0.0901204 | − | 0.995931i | \(-0.528725\pi\) | ||||
−0.0901204 | + | 0.995931i | \(0.528725\pi\) | |||||||
\(380\) | −0.997298 | − | 1.72737i | −0.0511603 | − | 0.0886123i | ||||
\(381\) | −2.01182 | + | 3.48457i | −0.103069 | + | 0.178520i | ||||
\(382\) | 6.22593 | − | 10.7836i | 0.318546 | − | 0.551738i | ||||
\(383\) | −0.241522 | − | 0.418328i | −0.0123412 | − | 0.0213755i | 0.859789 | − | 0.510650i | \(-0.170595\pi\) |
−0.872130 | + | 0.489274i | \(0.837262\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 7.55766 | − | 2.99501i | 0.385174 | − | 0.152640i | ||||
\(386\) | 6.70412 | 0.341231 | ||||||||
\(387\) | −5.14794 | − | 8.91649i | −0.261684 | − | 0.453251i | ||||
\(388\) | 5.21411 | − | 9.03111i | 0.264706 | − | 0.458485i | ||||
\(389\) | −9.31411 | + | 16.1325i | −0.472244 | + | 0.817951i | −0.999496 | − | 0.0317586i | \(-0.989889\pi\) |
0.527252 | + | 0.849709i | \(0.323223\pi\) | |||||||
\(390\) | −3.44784 | − | 5.97183i | −0.174588 | − | 0.302395i | ||||
\(391\) | 2.59980 | 0.131477 | ||||||||
\(392\) | 5.09980 | − | 4.79501i | 0.257579 | − | 0.242184i | ||||
\(393\) | 10.9946 | 0.554604 | ||||||||
\(394\) | −8.28028 | − | 14.3419i | −0.417155 | − | 0.722533i | ||||
\(395\) | −0.705196 | + | 1.22144i | −0.0354823 | + | 0.0614571i | ||||
\(396\) | −0.840244 | + | 1.45535i | −0.0422239 | + | 0.0731339i | ||||
\(397\) | −15.8722 | − | 27.4915i | −0.796605 | − | 1.37976i | −0.921815 | − | 0.387630i | \(-0.873294\pi\) |
0.125210 | − | 0.992130i | \(-0.460039\pi\) | |||||||
\(398\) | −5.01783 | −0.251521 | ||||||||
\(399\) | 2.68319 | − | 1.06332i | 0.134328 | − | 0.0532324i | ||||
\(400\) | −1.65685 | −0.0828427 | ||||||||
\(401\) | 10.3881 | + | 17.9927i | 0.518756 | + | 0.898511i | 0.999762 | + | 0.0217945i | \(0.00693796\pi\) |
−0.481007 | + | 0.876717i | \(0.659729\pi\) | |||||||
\(402\) | 6.44514 | − | 11.1633i | 0.321454 | − | 0.556775i | ||||
\(403\) | 7.28299 | − | 12.6145i | 0.362791 | − | 0.628373i | ||||
\(404\) | 3.23882 | + | 5.60980i | 0.161137 | + | 0.279098i | ||||
\(405\) | 1.82843 | 0.0908553 | ||||||||
\(406\) | 1.59980 | + | 1.26717i | 0.0793966 | + | 0.0628887i | ||||
\(407\) | 4.12032 | 0.204237 | ||||||||
\(408\) | −1.29990 | − | 2.25149i | −0.0643546 | − | 0.111465i | ||||
\(409\) | −9.84753 | + | 17.0564i | −0.486929 | + | 0.843386i | −0.999887 | − | 0.0150278i | \(-0.995216\pi\) |
0.512958 | + | 0.858414i | \(0.328550\pi\) | |||||||
\(410\) | 0.997298 | − | 1.72737i | 0.0492531 | − | 0.0853088i | ||||
\(411\) | −2.07397 | − | 3.59222i | −0.102301 | − | 0.177191i | ||||
\(412\) | −18.8903 | −0.930657 | ||||||||
\(413\) | 2.47927 | − | 16.8258i | 0.121997 | − | 0.827944i | ||||
\(414\) | 1.00000 | 0.0491473 | ||||||||
\(415\) | −3.05104 | − | 5.28456i | −0.149770 | − | 0.259409i | ||||
\(416\) | −1.88568 | + | 3.26610i | −0.0924533 | + | 0.160134i | ||||
\(417\) | 6.65685 | − | 11.5300i | 0.325988 | − | 0.564627i | ||||
\(418\) | −0.916606 | − | 1.58761i | −0.0448327 | − | 0.0776525i | ||||
\(419\) | −1.70412 | −0.0832518 | −0.0416259 | − | 0.999133i | \(-0.513254\pi\) | ||||
−0.0416259 | + | 0.999133i | \(0.513254\pi\) | |||||||
\(420\) | −0.705196 | + | 4.78589i | −0.0344101 | + | 0.233527i | ||||
\(421\) | −12.8564 | −0.626585 | −0.313292 | − | 0.949657i | \(-0.601432\pi\) | ||||
−0.313292 | + | 0.949657i | \(0.601432\pi\) | |||||||
\(422\) | −8.57616 | − | 14.8543i | −0.417481 | − | 0.723098i | ||||
\(423\) | 1.11161 | − | 1.92537i | 0.0540485 | − | 0.0936147i | ||||
\(424\) | 3.68558 | − | 6.38362i | 0.178988 | − | 0.310016i | ||||
\(425\) | 2.15374 | + | 3.73039i | 0.104472 | + | 0.180951i | ||||
\(426\) | 8.22863 | 0.398678 | ||||||||
\(427\) | −18.8430 | − | 14.9252i | −0.911877 | − | 0.722283i | ||||
\(428\) | 13.8150 | 0.667772 | ||||||||
\(429\) | −3.16887 | − | 5.48865i | −0.152995 | − | 0.264994i | ||||
\(430\) | −9.41263 | + | 16.3032i | −0.453917 | + | 0.786208i | ||||
\(431\) | 5.77097 | − | 9.99561i | 0.277978 | − | 0.481472i | −0.692904 | − | 0.721030i | \(-0.743669\pi\) |
0.970882 | + | 0.239558i | \(0.0770025\pi\) | |||||||
\(432\) | −0.500000 | − | 0.866025i | −0.0240563 | − | 0.0416667i | ||||
\(433\) | −24.7627 | −1.19002 | −0.595010 | − | 0.803718i | \(-0.702852\pi\) | ||||
−0.595010 | + | 0.803718i | \(0.702852\pi\) | |||||||
\(434\) | −9.49980 | + | 3.76466i | −0.456005 | + | 0.180709i | ||||
\(435\) | −1.41039 | −0.0676232 | ||||||||
\(436\) | −5.03382 | − | 8.71884i | −0.241076 | − | 0.417557i | ||||
\(437\) | −0.545441 | + | 0.944731i | −0.0260920 | + | 0.0451926i | ||||
\(438\) | 1.43113 | − | 2.47878i | 0.0683818 | − | 0.118441i | ||||
\(439\) | 3.91289 | + | 6.77733i | 0.186752 | + | 0.323464i | 0.944166 | − | 0.329471i | \(-0.106870\pi\) |
−0.757413 | + | 0.652936i | \(0.773537\pi\) | |||||||
\(440\) | 3.07265 | 0.146483 | ||||||||
\(441\) | −6.70249 | − | 2.01905i | −0.319166 | − | 0.0961453i | ||||
\(442\) | 9.80479 | 0.466366 | ||||||||
\(443\) | 0.497298 | + | 0.861346i | 0.0236274 | + | 0.0409238i | 0.877597 | − | 0.479399i | \(-0.159145\pi\) |
−0.853970 | + | 0.520322i | \(0.825812\pi\) | |||||||
\(444\) | −1.22593 | + | 2.12337i | −0.0581800 | + | 0.100771i | ||||
\(445\) | −2.93005 | + | 5.07500i | −0.138898 | + | 0.240578i | ||||
\(446\) | −2.21141 | − | 3.83027i | −0.104713 | − | 0.181369i | ||||
\(447\) | −11.8724 | −0.561547 | ||||||||
\(448\) | 2.45965 | − | 0.974732i | 0.116208 | − | 0.0460517i | ||||
\(449\) | 26.1291 | 1.23311 | 0.616554 | − | 0.787313i | \(-0.288528\pi\) | ||||
0.616554 | + | 0.787313i | \(0.288528\pi\) | |||||||
\(450\) | 0.828427 | + | 1.43488i | 0.0390524 | + | 0.0676408i | ||||
\(451\) | 0.916606 | − | 1.58761i | 0.0431613 | − | 0.0747576i | ||||
\(452\) | −3.15196 | + | 5.45935i | −0.148256 | + | 0.256786i | ||||
\(453\) | −0.536325 | − | 0.928943i | −0.0251988 | − | 0.0436455i | ||||
\(454\) | −12.0905 | −0.567434 | ||||||||
\(455\) | −14.3014 | − | 11.3279i | −0.670461 | − | 0.531061i | ||||
\(456\) | 1.09088 | 0.0510852 | ||||||||
\(457\) | −9.37224 | − | 16.2332i | −0.438415 | − | 0.759357i | 0.559153 | − | 0.829065i | \(-0.311127\pi\) |
−0.997567 | + | 0.0697079i | \(0.977793\pi\) | |||||||
\(458\) | 4.54544 | − | 7.87293i | 0.212394 | − | 0.367878i | ||||
\(459\) | −1.29990 | + | 2.25149i | −0.0606741 | + | 0.105091i | ||||
\(460\) | −0.914214 | − | 1.58346i | −0.0426254 | − | 0.0738294i | ||||
\(461\) | −5.63648 | −0.262517 | −0.131258 | − | 0.991348i | \(-0.541902\pi\) | ||||
−0.131258 | + | 0.991348i | \(0.541902\pi\) | |||||||
\(462\) | −0.648139 | + | 4.39866i | −0.0301541 | + | 0.204644i | ||||
\(463\) | −20.5337 | −0.954281 | −0.477141 | − | 0.878827i | \(-0.658327\pi\) | ||||
−0.477141 | + | 0.878827i | \(0.658327\pi\) | |||||||
\(464\) | 0.385685 | + | 0.668025i | 0.0179050 | + | 0.0310123i | ||||
\(465\) | 3.53092 | − | 6.11574i | 0.163743 | − | 0.283610i | ||||
\(466\) | −3.37387 | + | 5.84371i | −0.156291 | + | 0.270705i | ||||
\(467\) | 0.589607 | + | 1.02123i | 0.0272838 | + | 0.0472569i | 0.879345 | − | 0.476185i | \(-0.157981\pi\) |
−0.852061 | + | 0.523442i | \(0.824648\pi\) | |||||||
\(468\) | 3.77137 | 0.174332 | ||||||||
\(469\) | 4.97158 | − | 33.7401i | 0.229566 | − | 1.55797i | ||||
\(470\) | −4.06501 | −0.187505 | ||||||||
\(471\) | −10.6880 | − | 18.5121i | −0.492476 | − | 0.852993i | ||||
\(472\) | 3.21411 | − | 5.56700i | 0.147941 | − | 0.256242i | ||||
\(473\) | −8.65105 | + | 14.9841i | −0.397776 | + | 0.688968i | ||||
\(474\) | −0.385685 | − | 0.668025i | −0.0177151 | − | 0.0306834i | ||||
\(475\) | −1.80743 | −0.0829306 | ||||||||
\(476\) | −5.39190 | − | 4.27083i | −0.247137 | − | 0.195753i | ||||
\(477\) | −7.37117 | −0.337503 | ||||||||
\(478\) | −10.2959 | − | 17.8330i | −0.470922 | − | 0.815662i | ||||
\(479\) | −0.841318 | + | 1.45721i | −0.0384408 | + | 0.0665814i | −0.884606 | − | 0.466340i | \(-0.845572\pi\) |
0.846165 | + | 0.532921i | \(0.178906\pi\) | |||||||
\(480\) | −0.914214 | + | 1.58346i | −0.0417279 | + | 0.0722749i | ||||
\(481\) | −4.62343 | − | 8.00802i | −0.210810 | − | 0.365134i | ||||
\(482\) | 17.1814 | 0.782590 | ||||||||
\(483\) | 2.45965 | − | 0.974732i | 0.111918 | − | 0.0443518i | ||||
\(484\) | −8.17596 | −0.371634 | ||||||||
\(485\) | 9.53362 | + | 16.5127i | 0.432900 | + | 0.749804i | ||||
\(486\) | −0.500000 | + | 0.866025i | −0.0226805 | + | 0.0392837i | ||||
\(487\) | 8.64504 | − | 14.9736i | 0.391744 | − | 0.678521i | −0.600936 | − | 0.799297i | \(-0.705205\pi\) |
0.992680 | + | 0.120777i | \(0.0385385\pi\) | |||||||
\(488\) | −4.54274 | − | 7.86825i | −0.205640 | − | 0.356179i | ||||
\(489\) | 1.88048 | 0.0850383 | ||||||||
\(490\) | 2.93042 | + | 12.4590i | 0.132383 | + | 0.562840i | ||||
\(491\) | 25.7361 | 1.16146 | 0.580728 | − | 0.814098i | \(-0.302768\pi\) | ||||
0.580728 | + | 0.814098i | \(0.302768\pi\) | |||||||
\(492\) | 0.545441 | + | 0.944731i | 0.0245904 | + | 0.0425917i | ||||
\(493\) | 1.00270 | − | 1.73673i | 0.0451594 | − | 0.0782184i | ||||
\(494\) | −2.05706 | + | 3.56293i | −0.0925514 | + | 0.160304i | ||||
\(495\) | −1.53633 | − | 2.66099i | −0.0690527 | − | 0.119603i | ||||
\(496\) | −3.86225 | −0.173420 | ||||||||
\(497\) | 20.2396 | − | 8.02071i | 0.907869 | − | 0.359778i | ||||
\(498\) | 3.33734 | 0.149550 | ||||||||
\(499\) | 11.5998 | + | 20.0914i | 0.519278 | + | 0.899416i | 0.999749 | + | 0.0224055i | \(0.00713249\pi\) |
−0.480471 | + | 0.877011i | \(0.659534\pi\) | |||||||
\(500\) | 6.08579 | − | 10.5409i | 0.272165 | − | 0.471403i | ||||
\(501\) | 9.82553 | − | 17.0183i | 0.438972 | − | 0.760322i | ||||
\(502\) | 7.58798 | + | 13.1428i | 0.338668 | + | 0.586590i | ||||
\(503\) | −42.3054 | −1.88631 | −0.943153 | − | 0.332358i | \(-0.892156\pi\) | ||||
−0.943153 | + | 0.332358i | \(0.892156\pi\) | |||||||
\(504\) | −2.07397 | − | 1.64276i | −0.0923819 | − | 0.0731742i | ||||
\(505\) | −11.8439 | −0.527046 | ||||||||
\(506\) | −0.840244 | − | 1.45535i | −0.0373534 | − | 0.0646980i | ||||
\(507\) | −0.611614 | + | 1.05935i | −0.0271627 | + | 0.0470472i | ||||
\(508\) | −2.01182 | + | 3.48457i | −0.0892599 | + | 0.154603i | ||||
\(509\) | 13.9517 | + | 24.1650i | 0.618396 | + | 1.07109i | 0.989778 | + | 0.142614i | \(0.0455507\pi\) |
−0.371382 | + | 0.928480i | \(0.621116\pi\) | |||||||
\(510\) | 4.75354 | 0.210490 | ||||||||
\(511\) | 1.10393 | − | 7.49191i | 0.0488348 | − | 0.331423i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −0.545441 | − | 0.944731i | −0.0240818 | − | 0.0417109i | ||||
\(514\) | 7.99730 | − | 13.8517i | 0.352746 | − | 0.610973i | ||||
\(515\) | 17.2697 | − | 29.9121i | 0.760996 | − | 1.31808i | ||||
\(516\) | −5.14794 | − | 8.91649i | −0.226625 | − | 0.392527i | ||||
\(517\) | −3.73611 | −0.164314 | ||||||||
\(518\) | −0.945644 | + | 6.41771i | −0.0415492 | + | 0.281978i | ||||
\(519\) | −1.77097 | −0.0777369 | ||||||||
\(520\) | −3.44784 | − | 5.97183i | −0.151198 | − | 0.261882i | ||||
\(521\) | −8.97768 | + | 15.5498i | −0.393320 | + | 0.681249i | −0.992885 | − | 0.119076i | \(-0.962007\pi\) |
0.599566 | + | 0.800326i | \(0.295340\pi\) | |||||||
\(522\) | 0.385685 | − | 0.668025i | 0.0168810 | − | 0.0292387i | ||||
\(523\) | 6.46877 | + | 11.2042i | 0.282860 | + | 0.489927i | 0.972088 | − | 0.234617i | \(-0.0753836\pi\) |
−0.689228 | + | 0.724544i | \(0.742050\pi\) | |||||||
\(524\) | 10.9946 | 0.480301 | ||||||||
\(525\) | 3.43627 | + | 2.72181i | 0.149971 | + | 0.118789i | ||||
\(526\) | 21.7602 | 0.948788 | ||||||||
\(527\) | 5.02053 | + | 8.69582i | 0.218698 | + | 0.378796i | ||||
\(528\) | −0.840244 | + | 1.45535i | −0.0365669 | + | 0.0633358i | ||||
\(529\) | −0.500000 | + | 0.866025i | −0.0217391 | + | 0.0376533i | ||||
\(530\) | 6.73882 | + | 11.6720i | 0.292716 | + | 0.506998i | ||||
\(531\) | −6.42822 | −0.278961 | ||||||||
\(532\) | 2.68319 | − | 1.06332i | 0.116331 | − | 0.0461006i | ||||
\(533\) | −4.11412 | −0.178202 | ||||||||
\(534\) | −1.60250 | − | 2.77561i | −0.0693469 | − | 0.120112i | ||||
\(535\) | −12.6298 | + | 21.8755i | −0.546036 | + | 0.945762i | ||||
\(536\) | 6.44514 | − | 11.1633i | 0.278387 | − | 0.482181i | ||||
\(537\) | 6.11161 | + | 10.5856i | 0.263736 | + | 0.456803i | ||||
\(538\) | 20.5627 | 0.886522 | ||||||||
\(539\) | 2.69332 | + | 11.4509i | 0.116009 | + | 0.493227i | ||||
\(540\) | 1.82843 | 0.0786830 | ||||||||
\(541\) | −20.4899 | − | 35.4895i | −0.880928 | − | 1.52581i | −0.850311 | − | 0.526281i | \(-0.823586\pi\) |
−0.0306176 | − | 0.999531i | \(-0.509747\pi\) | |||||||
\(542\) | −1.93113 | + | 3.34481i | −0.0829489 | + | 0.143672i | ||||
\(543\) | −0.410393 | + | 0.710821i | −0.0176116 | + | 0.0305043i | ||||
\(544\) | −1.29990 | − | 2.25149i | −0.0557327 | − | 0.0965318i | ||||
\(545\) | 18.4080 | 0.788510 | ||||||||
\(546\) | 9.27626 | − | 3.67607i | 0.396987 | − | 0.157321i | ||||
\(547\) | −41.6515 | −1.78089 | −0.890444 | − | 0.455093i | \(-0.849606\pi\) | ||||
−0.890444 | + | 0.455093i | \(0.849606\pi\) | |||||||
\(548\) | −2.07397 | − | 3.59222i | −0.0885956 | − | 0.153452i | ||||
\(549\) | −4.54274 | + | 7.86825i | −0.193879 | + | 0.335809i | ||||
\(550\) | 1.39216 | − | 2.41130i | 0.0593620 | − | 0.102818i | ||||
\(551\) | 0.420736 | + | 0.728736i | 0.0179240 | + | 0.0310452i | ||||
\(552\) | 1.00000 | 0.0425628 | ||||||||
\(553\) | −1.59980 | − | 1.26717i | −0.0680303 | − | 0.0538857i | ||||
\(554\) | 24.1295 | 1.02516 | ||||||||
\(555\) | −2.24152 | − | 3.88243i | −0.0951473 | − | 0.164800i | ||||
\(556\) | 6.65685 | − | 11.5300i | 0.282314 | − | 0.488981i | ||||
\(557\) | 8.90789 | − | 15.4289i | 0.377439 | − | 0.653744i | −0.613249 | − | 0.789889i | \(-0.710138\pi\) |
0.990689 | + | 0.136145i | \(0.0434713\pi\) | |||||||
\(558\) | 1.93113 | + | 3.34481i | 0.0817510 | + | 0.141597i | ||||
\(559\) | 38.8296 | 1.64232 | ||||||||
\(560\) | −0.705196 | + | 4.78589i | −0.0298000 | + | 0.202241i | ||||
\(561\) | 4.36893 | 0.184456 | ||||||||
\(562\) | −13.8426 | − | 23.9762i | −0.583916 | − | 1.01137i | ||||
\(563\) | 0.445844 | − | 0.772224i | 0.0187901 | − | 0.0325454i | −0.856477 | − | 0.516184i | \(-0.827352\pi\) |
0.875268 | + | 0.483639i | \(0.160685\pi\) | |||||||
\(564\) | 1.11161 | − | 1.92537i | 0.0468074 | − | 0.0810728i | ||||
\(565\) | −5.76313 | − | 9.98203i | −0.242457 | − | 0.419947i | ||||
\(566\) | 5.96618 | 0.250777 | ||||||||
\(567\) | −0.385685 | + | 2.61749i | −0.0161972 | + | 0.109924i | ||||
\(568\) | 8.22863 | 0.345266 | ||||||||
\(569\) | 3.64575 | + | 6.31462i | 0.152838 | + | 0.264723i | 0.932270 | − | 0.361764i | \(-0.117826\pi\) |
−0.779432 | + | 0.626487i | \(0.784492\pi\) | |||||||
\(570\) | −0.997298 | + | 1.72737i | −0.0417722 | + | 0.0723516i | ||||
\(571\) | −16.1902 | + | 28.0422i | −0.677537 | + | 1.17353i | 0.298183 | + | 0.954509i | \(0.403620\pi\) |
−0.975720 | + | 0.219021i | \(0.929714\pi\) | |||||||
\(572\) | −3.16887 | − | 5.48865i | −0.132497 | − | 0.229492i | ||||
\(573\) | −12.4519 | −0.520184 | ||||||||
\(574\) | 2.26245 | + | 1.79205i | 0.0944330 | + | 0.0747988i | ||||
\(575\) | −1.65685 | −0.0690956 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 2.22700 | − | 3.85728i | 0.0927113 | − | 0.160581i | −0.815940 | − | 0.578137i | \(-0.803780\pi\) |
0.908651 | + | 0.417556i | \(0.137113\pi\) | |||||||
\(578\) | 5.12053 | − | 8.86902i | 0.212986 | − | 0.368902i | ||||
\(579\) | −3.35206 | − | 5.80594i | −0.139307 | − | 0.241287i | ||||
\(580\) | −1.41039 | −0.0585634 | ||||||||
\(581\) | 8.20871 | − | 3.25301i | 0.340555 | − | 0.134958i | ||||
\(582\) | −10.4282 | −0.432264 | ||||||||
\(583\) | 6.19358 | + | 10.7276i | 0.256512 | + | 0.444292i | ||||
\(584\) | 1.43113 | − | 2.47878i | 0.0592204 | − | 0.102573i | ||||
\(585\) | −3.44784 | + | 5.97183i | −0.142551 | + | 0.246905i | ||||
\(586\) | 15.7426 | + | 27.2671i | 0.650322 | + | 1.12639i | ||||
\(587\) | −13.6693 | −0.564192 | −0.282096 | − | 0.959386i | \(-0.591030\pi\) | ||||
−0.282096 | + | 0.959386i | \(0.591030\pi\) | |||||||
\(588\) | −6.70249 | − | 2.01905i | −0.276406 | − | 0.0832642i | ||||
\(589\) | −4.21326 | −0.173604 | ||||||||
\(590\) | 5.87677 | + | 10.1789i | 0.241943 | + | 0.419057i | ||||
\(591\) | −8.28028 | + | 14.3419i | −0.340605 | + | 0.589946i | ||||
\(592\) | −1.22593 | + | 2.12337i | −0.0503854 | + | 0.0872700i | ||||
\(593\) | 6.60520 | + | 11.4405i | 0.271243 | + | 0.469807i | 0.969180 | − | 0.246352i | \(-0.0792319\pi\) |
−0.697937 | + | 0.716159i | \(0.745899\pi\) | |||||||
\(594\) | 1.68049 | 0.0689513 | ||||||||
\(595\) | 11.6921 | − | 4.63342i | 0.479328 | − | 0.189952i | ||||
\(596\) | −11.8724 | −0.486314 | ||||||||
\(597\) | 2.50892 | + | 4.34557i | 0.102683 | + | 0.177852i | ||||
\(598\) | −1.88568 | + | 3.26610i | −0.0771114 | + | 0.133561i | ||||
\(599\) | −13.6567 | + | 23.6540i | −0.557996 | + | 0.966477i | 0.439668 | + | 0.898160i | \(0.355096\pi\) |
−0.997664 | + | 0.0683166i | \(0.978237\pi\) | |||||||
\(600\) | 0.828427 | + | 1.43488i | 0.0338204 | + | 0.0585786i | ||||
\(601\) | 39.7677 | 1.62216 | 0.811079 | − | 0.584936i | \(-0.198880\pi\) | ||||
0.811079 | + | 0.584936i | \(0.198880\pi\) | |||||||
\(602\) | −21.3533 | − | 16.9136i | −0.870297 | − | 0.689348i | ||||
\(603\) | −12.8903 | −0.524932 | ||||||||
\(604\) | −0.536325 | − | 0.928943i | −0.0218228 | − | 0.0377981i | ||||
\(605\) | 7.47457 | − | 12.9463i | 0.303885 | − | 0.526344i | ||||
\(606\) | 3.23882 | − | 5.60980i | 0.131568 | − | 0.227883i | ||||
\(607\) | 4.75955 | + | 8.24379i | 0.193184 | + | 0.334605i | 0.946304 | − | 0.323279i | \(-0.104785\pi\) |
−0.753120 | + | 0.657884i | \(0.771452\pi\) | |||||||
\(608\) | 1.09088 | 0.0442411 | ||||||||
\(609\) | 0.297505 | − | 2.01905i | 0.0120555 | − | 0.0818161i | ||||
\(610\) | 16.6121 | 0.672606 | ||||||||
\(611\) | 4.19231 | + | 7.26129i | 0.169603 | + | 0.293760i | ||||
\(612\) | −1.29990 | + | 2.25149i | −0.0525453 | + | 0.0910111i | ||||
\(613\) | 22.8903 | − | 39.6471i | 0.924529 | − | 1.60133i | 0.132213 | − | 0.991221i | \(-0.457792\pi\) |
0.792316 | − | 0.610110i | \(-0.208875\pi\) | |||||||
\(614\) | −2.56907 | − | 4.44977i | −0.103679 | − | 0.179578i | ||||
\(615\) | −1.99460 | −0.0804299 | ||||||||
\(616\) | −0.648139 | + | 4.39866i | −0.0261142 | + | 0.177227i | ||||
\(617\) | −23.5293 | −0.947254 | −0.473627 | − | 0.880726i | \(-0.657055\pi\) | ||||
−0.473627 | + | 0.880726i | \(0.657055\pi\) | |||||||
\(618\) | 9.44514 | + | 16.3595i | 0.379939 | + | 0.658074i | ||||
\(619\) | 2.43224 | − | 4.21277i | 0.0977602 | − | 0.169326i | −0.812997 | − | 0.582268i | \(-0.802166\pi\) |
0.910757 | + | 0.412942i | \(0.135499\pi\) | |||||||
\(620\) | 3.53092 | − | 6.11574i | 0.141805 | − | 0.245614i | ||||
\(621\) | −0.500000 | − | 0.866025i | −0.0200643 | − | 0.0347524i | ||||
\(622\) | −15.5627 | −0.624008 | ||||||||
\(623\) | −6.64706 | − | 5.26503i | −0.266309 | − | 0.210939i | ||||
\(624\) | 3.77137 | 0.150976 | ||||||||
\(625\) | 6.98528 | + | 12.0989i | 0.279411 | + | 0.483954i | ||||
\(626\) | 11.0764 | − | 19.1848i | 0.442700 | − | 0.766780i | ||||
\(627\) | −0.916606 | + | 1.58761i | −0.0366057 | + | 0.0634030i | ||||
\(628\) | −10.6880 | − | 18.5121i | −0.426497 | − | 0.738714i | ||||
\(629\) | 6.37433 | 0.254161 | ||||||||
\(630\) | 4.49730 | − | 1.78223i | 0.179177 | − | 0.0710056i | ||||
\(631\) | −25.5940 | −1.01888 | −0.509440 | − | 0.860506i | \(-0.670148\pi\) | ||||
−0.509440 | + | 0.860506i | \(0.670148\pi\) | |||||||
\(632\) | −0.385685 | − | 0.668025i | −0.0153417 | − | 0.0265726i | ||||
\(633\) | −8.57616 | + | 14.8543i | −0.340872 | + | 0.590407i | ||||
\(634\) | −9.28136 | + | 16.0758i | −0.368610 | + | 0.638451i | ||||
\(635\) | −3.67846 | − | 6.37128i | −0.145975 | − | 0.252837i | ||||
\(636\) | −7.37117 | −0.292286 | ||||||||
\(637\) | 19.2332 | − | 18.0837i | 0.762048 | − | 0.716504i | ||||
\(638\) | −1.29628 | −0.0513201 | ||||||||
\(639\) | −4.11432 | − | 7.12620i | −0.162760 | − | 0.281908i | ||||
\(640\) | −0.914214 | + | 1.58346i | −0.0361375 | + | 0.0625919i | ||||
\(641\) | 7.31773 | − | 12.6747i | 0.289033 | − | 0.500620i | −0.684546 | − | 0.728969i | \(-0.740000\pi\) |
0.973579 | + | 0.228350i | \(0.0733330\pi\) | |||||||
\(642\) | −6.90749 | − | 11.9641i | −0.272617 | − | 0.472186i | ||||
\(643\) | 41.6246 | 1.64151 | 0.820756 | − | 0.571279i | \(-0.193552\pi\) | ||||
0.820756 | + | 0.571279i | \(0.193552\pi\) | |||||||
\(644\) | 2.45965 | − | 0.974732i | 0.0969239 | − | 0.0384098i | ||||
\(645\) | 18.8253 | 0.741244 | ||||||||
\(646\) | −1.41803 | − | 2.45611i | −0.0557918 | − | 0.0966343i | ||||
\(647\) | 15.8096 | − | 27.3830i | 0.621539 | − | 1.07654i | −0.367661 | − | 0.929960i | \(-0.619841\pi\) |
0.989199 | − | 0.146577i | \(-0.0468255\pi\) | |||||||
\(648\) | −0.500000 | + | 0.866025i | −0.0196419 | + | 0.0340207i | ||||
\(649\) | 5.40128 | + | 9.35529i | 0.212019 | + | 0.367227i | ||||
\(650\) | −6.24861 | −0.245091 | ||||||||
\(651\) | 8.01019 | + | 6.34474i | 0.313944 | + | 0.248670i | ||||
\(652\) | 1.88048 | 0.0736453 | ||||||||
\(653\) | 1.64814 | + | 2.85466i | 0.0644966 | + | 0.111711i | 0.896471 | − | 0.443103i | \(-0.146122\pi\) |
−0.831974 | + | 0.554815i | \(0.812789\pi\) | |||||||
\(654\) | −5.03382 | + | 8.71884i | −0.196838 | + | 0.340934i | ||||
\(655\) | −10.0514 | + | 17.4096i | −0.392741 | + | 0.680247i | ||||
\(656\) | 0.545441 | + | 0.944731i | 0.0212959 | + | 0.0368855i | ||||
\(657\) | −2.86225 | −0.111667 | ||||||||
\(658\) | 0.857465 | − | 5.81927i | 0.0334275 | − | 0.226859i | ||||
\(659\) | 0.0203785 | 0.000793834 | 0.000396917 | − | 1.00000i | \(-0.499874\pi\) | ||||
0.000396917 | 1.00000i | \(0.499874\pi\) | ||||||||
\(660\) | −1.53633 | − | 2.66099i | −0.0598014 | − | 0.103579i | ||||
\(661\) | −21.1007 | + | 36.5474i | −0.820721 | + | 1.42153i | 0.0844251 | + | 0.996430i | \(0.473095\pi\) |
−0.905146 | + | 0.425101i | \(0.860239\pi\) | |||||||
\(662\) | −1.43133 | + | 2.47913i | −0.0556300 | + | 0.0963540i | ||||
\(663\) | −4.90240 | − | 8.49120i | −0.190393 | − | 0.329771i | ||||
\(664\) | 3.33734 | 0.129514 | ||||||||
\(665\) | −0.769285 | + | 5.22083i | −0.0298316 | + | 0.202455i | ||||
\(666\) | 2.45186 | 0.0950076 | ||||||||
\(667\) | 0.385685 | + | 0.668025i | 0.0149338 | + | 0.0258661i | ||||
\(668\) | 9.82553 | − | 17.0183i | 0.380161 | − | 0.658458i | ||||
\(669\) | −2.21141 | + | 3.83027i | −0.0854981 | + | 0.148087i | ||||
\(670\) | 11.7845 | + | 20.4113i | 0.455273 | + | 0.788557i | ||||
\(671\) | 15.2680 | 0.589416 | ||||||||
\(672\) | −2.07397 | − | 1.64276i | −0.0800051 | − | 0.0633707i | ||||
\(673\) | −16.4540 | −0.634255 | −0.317128 | − | 0.948383i | \(-0.602718\pi\) | ||||
−0.317128 | + | 0.948383i | \(0.602718\pi\) | |||||||
\(674\) | 3.85314 | + | 6.67383i | 0.148417 | + | 0.257066i | ||||
\(675\) | 0.828427 | − | 1.43488i | 0.0318862 | − | 0.0552285i | ||||
\(676\) | −0.611614 | + | 1.05935i | −0.0235236 | + | 0.0407441i | ||||
\(677\) | 11.9422 | + | 20.6846i | 0.458977 | + | 0.794972i | 0.998907 | − | 0.0467380i | \(-0.0148826\pi\) |
−0.539930 | + | 0.841710i | \(0.681549\pi\) | |||||||
\(678\) | 6.30392 | 0.242101 | ||||||||
\(679\) | −25.6498 | + | 10.1647i | −0.984350 | + | 0.390086i | ||||
\(680\) | 4.75354 | 0.182290 | ||||||||
\(681\) | 6.04524 | + | 10.4707i | 0.231654 | + | 0.401237i | ||||
\(682\) | 3.24523 | − | 5.62091i | 0.124266 | − | 0.215236i | ||||
\(683\) | −5.54671 | + | 9.60719i | −0.212239 | + | 0.367609i | −0.952415 | − | 0.304804i | \(-0.901409\pi\) |
0.740176 | + | 0.672413i | \(0.234742\pi\) | |||||||
\(684\) | −0.545441 | − | 0.944731i | −0.0208554 | − | 0.0361227i | ||||
\(685\) | 7.58420 | 0.289778 | ||||||||
\(686\) | −18.4539 | + | 1.56697i | −0.704571 | + | 0.0598271i | ||||
\(687\) | −9.09088 | −0.346839 | ||||||||
\(688\) | −5.14794 | − | 8.91649i | −0.196263 | − | 0.339938i | ||||
\(689\) | 13.8997 | − | 24.0750i | 0.529536 | − | 0.917184i | ||||
\(690\) | −0.914214 | + | 1.58346i | −0.0348035 | + | 0.0602815i | ||||
\(691\) | 3.31641 | + | 5.74419i | 0.126162 | + | 0.218519i | 0.922187 | − | 0.386745i | \(-0.126401\pi\) |
−0.796024 | + | 0.605264i | \(0.793067\pi\) | |||||||
\(692\) | −1.77097 | −0.0673222 | ||||||||
\(693\) | 4.13342 | − | 1.63803i | 0.157016 | − | 0.0622234i | ||||
\(694\) | −9.94773 | −0.377611 | ||||||||
\(695\) | 12.1716 | + | 21.0818i | 0.461694 | + | 0.799678i | ||||
\(696\) | 0.385685 | − | 0.668025i | 0.0146193 | − | 0.0253214i | ||||
\(697\) | 1.41803 | − | 2.45611i | 0.0537119 | − | 0.0930317i | ||||
\(698\) | 4.27244 | + | 7.40009i | 0.161714 | + | 0.280097i | ||||
\(699\) | 6.74774 | 0.255223 | ||||||||
\(700\) | 3.43627 | + | 2.72181i | 0.129879 | + | 0.102875i | ||||
\(701\) | −8.07784 | −0.305096 | −0.152548 | − | 0.988296i | \(-0.548748\pi\) | ||||
−0.152548 | + | 0.988296i | \(0.548748\pi\) | |||||||
\(702\) | −1.88568 | − | 3.26610i | −0.0711706 | − | 0.123271i | ||||
\(703\) | −1.33734 | + | 2.31635i | −0.0504388 | + | 0.0873626i | ||||
\(704\) | −0.840244 | + | 1.45535i | −0.0316679 | + | 0.0548504i | ||||
\(705\) | 2.03250 | + | 3.52040i | 0.0765485 | + | 0.132586i | ||||
\(706\) | −1.99460 | −0.0750676 | ||||||||
\(707\) | 2.49833 | − | 16.9551i | 0.0939592 | − | 0.637664i | ||||
\(708\) | −6.42822 | −0.241587 | ||||||||
\(709\) | −18.7446 | − | 32.4667i | −0.703970 | − | 1.21931i | −0.967062 | − | 0.254540i | \(-0.918076\pi\) |
0.263093 | − | 0.964771i | \(-0.415258\pi\) | |||||||
\(710\) | −7.52273 | + | 13.0297i | −0.282323 | + | 0.488998i | ||||
\(711\) | −0.385685 | + | 0.668025i | −0.0144643 | + | 0.0250529i | ||||
\(712\) | −1.60250 | − | 2.77561i | −0.0600562 | − | 0.104020i | ||||
\(713\) | −3.86225 | −0.144642 | ||||||||
\(714\) | −1.00270 | + | 6.80494i | −0.0375252 | + | 0.254668i | ||||
\(715\) | 11.5881 | 0.433370 | ||||||||
\(716\) | 6.11161 | + | 10.5856i | 0.228402 | + | 0.395603i | ||||
\(717\) | −10.2959 | + | 17.8330i | −0.384507 | + | 0.665985i | ||||
\(718\) | 13.8564 | − | 24.0001i | 0.517118 | − | 0.895675i | ||||
\(719\) | −2.70122 | − | 4.67865i | −0.100739 | − | 0.174484i | 0.811251 | − | 0.584699i | \(-0.198787\pi\) |
−0.911989 | + | 0.410214i | \(0.865454\pi\) | |||||||
\(720\) | 1.82843 | 0.0681415 | ||||||||
\(721\) | 39.1778 | + | 31.0321i | 1.45906 | + | 1.15570i | ||||
\(722\) | −17.8100 | −0.662819 | ||||||||
\(723\) | −8.59068 | − | 14.8795i | −0.319491 | − | 0.553374i | ||||
\(724\) | −0.410393 | + | 0.710821i | −0.0152521 | + | 0.0264175i | ||||
\(725\) | −0.639023 | + | 1.10682i | −0.0237327 | + | 0.0411063i | ||||
\(726\) | 4.08798 | + | 7.08059i | 0.151719 | + | 0.262785i | ||||
\(727\) | 15.4461 | 0.572862 | 0.286431 | − | 0.958101i | \(-0.407531\pi\) | ||||
0.286431 | + | 0.958101i | \(0.407531\pi\) | |||||||
\(728\) | 9.27626 | − | 3.67607i | 0.343801 | − | 0.136244i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.61671 | + | 4.53227i | 0.0968487 | + | 0.167747i | ||||
\(731\) | −13.3836 | + | 23.1811i | −0.495010 | + | 0.857383i | ||||
\(732\) | −4.54274 | + | 7.86825i | −0.167904 | + | 0.290819i | ||||
\(733\) | −2.75084 | − | 4.76459i | −0.101604 | − | 0.175984i | 0.810741 | − | 0.585404i | \(-0.199064\pi\) |
−0.912346 | + | 0.409420i | \(0.865731\pi\) | |||||||
\(734\) | −21.7758 | −0.803758 | ||||||||
\(735\) | 9.32461 | − | 8.76732i | 0.343943 | − | 0.323387i | ||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 10.8310 | + | 18.7598i | 0.398964 | + | 0.691026i | ||||
\(738\) | 0.545441 | − | 0.944731i | 0.0200779 | − | 0.0347760i | ||||
\(739\) | 19.9710 | − | 34.5907i | 0.734644 | − | 1.27244i | −0.220236 | − | 0.975447i | \(-0.570683\pi\) |
0.954879 | − | 0.296994i | \(-0.0959840\pi\) | |||||||
\(740\) | −2.24152 | − | 3.88243i | −0.0824000 | − | 0.142721i | ||||
\(741\) | 4.11412 | 0.151136 | ||||||||
\(742\) | −18.1305 | + | 7.18491i | −0.665592 | + | 0.263766i | ||||
\(743\) | 21.5889 | 0.792020 | 0.396010 | − | 0.918246i | \(-0.370395\pi\) | ||||
0.396010 | + | 0.918246i | \(0.370395\pi\) | |||||||
\(744\) | 1.93113 | + | 3.34481i | 0.0707985 | + | 0.122627i | ||||
\(745\) | 10.8539 | − | 18.7996i | 0.397658 | − | 0.688763i | ||||
\(746\) | −6.68049 | + | 11.5709i | −0.244590 | + | 0.423642i | ||||
\(747\) | −1.66867 | − | 2.89022i | −0.0610535 | − | 0.105748i | ||||
\(748\) | 4.36893 | 0.159744 | ||||||||
\(749\) | −28.6519 | − | 22.6947i | −1.04692 | − | 0.829245i | ||||
\(750\) | −12.1716 | −0.444443 | ||||||||
\(751\) | 8.11559 | + | 14.0566i | 0.296142 | + | 0.512933i | 0.975250 | − | 0.221105i | \(-0.0709665\pi\) |
−0.679108 | + | 0.734038i | \(0.737633\pi\) | |||||||
\(752\) | 1.11161 | − | 1.92537i | 0.0405364 | − | 0.0702111i | ||||
\(753\) | 7.58798 | − | 13.1428i | 0.276521 | − | 0.478949i | ||||
\(754\) | 1.45456 | + | 2.51937i | 0.0529719 | + | 0.0917501i | ||||
\(755\) | 1.96126 | 0.0713777 | ||||||||
\(756\) | −0.385685 | + | 2.61749i | −0.0140272 | + | 0.0951971i | ||||
\(757\) | −25.4632 | −0.925475 | −0.462737 | − | 0.886495i | \(-0.653133\pi\) | ||||
−0.462737 | + | 0.886495i | \(0.653133\pi\) | |||||||
\(758\) | 1.75446 | + | 3.03881i | 0.0637248 | + | 0.110375i | ||||
\(759\) | −0.840244 | + | 1.45535i | −0.0304989 | + | 0.0528257i | ||||
\(760\) | −0.997298 | + | 1.72737i | −0.0361758 | + | 0.0626583i | ||||
\(761\) | 26.5992 | + | 46.0712i | 0.964222 | + | 1.67008i | 0.711691 | + | 0.702492i | \(0.247929\pi\) |
0.252530 | + | 0.967589i | \(0.418737\pi\) | |||||||
\(762\) | 4.02363 | 0.145761 | ||||||||
\(763\) | −3.88294 | + | 26.3520i | −0.140572 | + | 0.954005i | ||||
\(764\) | −12.4519 | −0.450492 | ||||||||
\(765\) | −2.37677 | − | 4.11669i | −0.0859323 | − | 0.148839i | ||||
\(766\) | −0.241522 | + | 0.418328i | −0.00872653 | + | 0.0151148i | ||||
\(767\) | 12.1216 | − | 20.9952i | 0.437686 | − | 0.758094i | ||||
\(768\) | −0.500000 | − | 0.866025i | −0.0180422 | − | 0.0312500i | ||||
\(769\) | 1.70627 | 0.0615297 | 0.0307648 | − | 0.999527i | \(-0.490206\pi\) | ||||
0.0307648 | + | 0.999527i | \(0.490206\pi\) | |||||||
\(770\) | −6.37258 | − | 5.04762i | −0.229652 | − | 0.181904i | ||||
\(771\) | −15.9946 | −0.576031 | ||||||||
\(772\) | −3.35206 | − | 5.80594i | −0.120643 | − | 0.208960i | ||||
\(773\) | −13.5258 | + | 23.4274i | −0.486490 | + | 0.842626i | −0.999879 | − | 0.0155302i | \(-0.995056\pi\) |
0.513389 | + | 0.858156i | \(0.328390\pi\) | |||||||
\(774\) | −5.14794 | + | 8.91649i | −0.185039 | + | 0.320497i | ||||
\(775\) | −3.19959 | − | 5.54186i | −0.114933 | − | 0.199069i | ||||
\(776\) | −10.4282 | −0.374351 | ||||||||
\(777\) | 6.03072 | − | 2.38990i | 0.216351 | − | 0.0857373i | ||||
\(778\) | 18.6282 | 0.667854 | ||||||||
\(779\) | 0.595011 | + | 1.03059i | 0.0213185 | + | 0.0369247i | ||||
\(780\) | −3.44784 | + | 5.97183i | −0.123452 | + | 0.213826i | ||||
\(781\) | −6.91406 | + | 11.9755i | −0.247404 | + | 0.428517i | ||||
\(782\) | −1.29990 | − | 2.25149i | −0.0464843 | − | 0.0805131i | ||||
\(783\) | −0.771369 | −0.0275665 | ||||||||
\(784\) | −6.70249 | − | 2.01905i | −0.239375 | − | 0.0721090i | ||||
\(785\) | 39.0844 | 1.39498 | ||||||||
\(786\) | −5.49730 | − | 9.52160i | −0.196082 | − | 0.339624i | ||||
\(787\) | −17.1929 | + | 29.7789i | −0.612860 | + | 1.06150i | 0.377896 | + | 0.925848i | \(0.376648\pi\) |
−0.990756 | + | 0.135656i | \(0.956686\pi\) | |||||||
\(788\) | −8.28028 | + | 14.3419i | −0.294973 | + | 0.510908i | ||||
\(789\) | −10.8801 | − | 18.8449i | −0.387341 | − | 0.670895i | ||||
\(790\) | 1.41039 | 0.0501795 | ||||||||
\(791\) | 15.5055 | − | 6.14463i | 0.551311 | − | 0.218478i | ||||
\(792\) | 1.68049 | 0.0597136 | ||||||||
\(793\) | −17.1323 | − | 29.6741i | −0.608387 | − | 1.05376i | ||||
\(794\) | −15.8722 | + | 27.4915i | −0.563285 | + | 0.975638i | ||||
\(795\) | 6.73882 | − | 11.6720i | 0.239001 | − | 0.413962i | ||||
\(796\) | 2.50892 | + | 4.34557i | 0.0889262 | + | 0.154025i | ||||
\(797\) | −7.25705 | −0.257058 | −0.128529 | − | 0.991706i | \(-0.541026\pi\) | ||||
−0.128529 | + | 0.991706i | \(0.541026\pi\) | |||||||
\(798\) | −2.26245 | − | 1.79205i | −0.0800900 | − | 0.0634380i | ||||
\(799\) | −5.77994 | −0.204480 | ||||||||
\(800\) | 0.828427 | + | 1.43488i | 0.0292893 | + | 0.0507306i | ||||
\(801\) | −1.60250 | + | 2.77561i | −0.0566215 | + | 0.0980713i | ||||
\(802\) | 10.3881 | − | 17.9927i | 0.366816 | − | 0.635344i | ||||
\(803\) | 2.40499 | + | 4.16556i | 0.0848702 | + | 0.147000i | ||||
\(804\) | −12.8903 | −0.454605 | ||||||||
\(805\) | −0.705196 | + | 4.78589i | −0.0248549 | + | 0.168680i | ||||
\(806\) | −14.5660 | −0.513065 | ||||||||
\(807\) | −10.2814 | − | 17.8078i | −0.361921 | − | 0.626866i | ||||
\(808\) | 3.23882 | − | 5.60980i | 0.113941 | − | 0.197352i | ||||
\(809\) | 3.22053 | − | 5.57811i | 0.113228 | − | 0.196116i | −0.803842 | − | 0.594843i | \(-0.797214\pi\) |
0.917070 | + | 0.398727i | \(0.130548\pi\) | |||||||
\(810\) | −0.914214 | − | 1.58346i | −0.0321222 | − | 0.0556373i | ||||
\(811\) | 21.6925 | 0.761727 | 0.380864 | − | 0.924631i | \(-0.375627\pi\) | ||||
0.380864 | + | 0.924631i | \(0.375627\pi\) | |||||||
\(812\) | 0.297505 | − | 2.01905i | 0.0104404 | − | 0.0708548i | ||||
\(813\) | 3.86225 | 0.135455 | ||||||||
\(814\) | −2.06016 | − | 3.56830i | −0.0722085 | − | 0.125069i | ||||
\(815\) | −1.71916 | + | 2.97767i | −0.0602196 | + | 0.104303i | ||||
\(816\) | −1.29990 | + | 2.25149i | −0.0455055 | + | 0.0788179i | ||||
\(817\) | −5.61579 | − | 9.72683i | −0.196472 | − | 0.340299i | ||||
\(818\) | 19.6951 | 0.688622 | ||||||||
\(819\) | −7.82170 | − | 6.19544i | −0.273312 | − | 0.216486i | ||||
\(820\) | −1.99460 | −0.0696543 | ||||||||
\(821\) | 2.53903 | + | 4.39772i | 0.0886127 | + | 0.153482i | 0.906925 | − | 0.421292i | \(-0.138423\pi\) |
−0.818312 | + | 0.574774i | \(0.805090\pi\) | |||||||
\(822\) | −2.07397 | + | 3.59222i | −0.0723380 | + | 0.125293i | ||||
\(823\) | −27.1861 | + | 47.0878i | −0.947650 | + | 1.64138i | −0.197292 | + | 0.980345i | \(0.563215\pi\) |
−0.750357 | + | 0.661032i | \(0.770119\pi\) | |||||||
\(824\) | 9.44514 | + | 16.3595i | 0.329037 | + | 0.569909i | ||||
\(825\) | −2.78432 | −0.0969377 | ||||||||
\(826\) | −15.8112 | + | 6.26579i | −0.550142 | + | 0.218015i | ||||
\(827\) | −23.8979 | −0.831012 | −0.415506 | − | 0.909590i | \(-0.636395\pi\) | ||||
−0.415506 | + | 0.909590i | \(0.636395\pi\) | |||||||
\(828\) | −0.500000 | − | 0.866025i | −0.0173762 | − | 0.0300965i | ||||
\(829\) | 4.66995 | − | 8.08858i | 0.162194 | − | 0.280928i | −0.773461 | − | 0.633843i | \(-0.781476\pi\) |
0.935655 | + | 0.352915i | \(0.114810\pi\) | |||||||
\(830\) | −3.05104 | + | 5.28456i | −0.105903 | + | 0.183430i | ||||
\(831\) | −12.0647 | − | 20.8968i | −0.418521 | − | 0.724900i | ||||
\(832\) | 3.77137 | 0.130749 | ||||||||
\(833\) | 4.16669 | + | 17.7152i | 0.144367 | + | 0.613794i | ||||
\(834\) | −13.3137 | −0.461016 | ||||||||
\(835\) | 17.9653 | + | 31.1167i | 0.621713 | + | 1.07684i | ||||
\(836\) | −0.916606 | + | 1.58761i | −0.0317015 | + | 0.0549086i | ||||
\(837\) | 1.93113 | − | 3.34481i | 0.0667495 | − | 0.115613i | ||||
\(838\) | 0.852061 | + | 1.47581i | 0.0294340 | + | 0.0509811i | ||||
\(839\) | 56.1851 | 1.93973 | 0.969863 | − | 0.243651i | \(-0.0783450\pi\) | ||||
0.969863 | + | 0.243651i | \(0.0783450\pi\) | |||||||
\(840\) | 4.49730 | − | 1.78223i | 0.155172 | − | 0.0614926i | ||||
\(841\) | −28.4050 | −0.979482 | ||||||||
\(842\) | 6.42822 | + | 11.1340i | 0.221531 | + | 0.383703i | ||||
\(843\) | −13.8426 | + | 23.9762i | −0.476766 | + | 0.825782i | ||||
\(844\) | −8.57616 | + | 14.8543i | −0.295204 | + | 0.511308i | ||||
\(845\) | −1.11829 | − | 1.93694i | −0.0384704 | − | 0.0666326i | ||||
\(846\) | −2.22323 | −0.0764361 | ||||||||
\(847\) | 16.9567 | + | 13.4311i | 0.582639 | + | 0.461499i | ||||
\(848\) | −7.37117 | −0.253127 | ||||||||
\(849\) | −2.98309 | − | 5.16686i | −0.102379 | − | 0.177326i | ||||
\(850\) | 2.15374 | − | 3.73039i | 0.0738727 | − | 0.127951i | ||||
\(851\) | −1.22593 | + | 2.12337i | −0.0420243 | + | 0.0727882i | ||||
\(852\) | −4.11432 | − | 7.12620i | −0.140954 | − | 0.244140i | ||||
\(853\) | 32.1818 | 1.10188 | 0.550941 | − | 0.834544i | \(-0.314269\pi\) | ||||
0.550941 | + | 0.834544i | \(0.314269\pi\) | |||||||
\(854\) | −3.50413 | + | 23.7811i | −0.119909 | + | 0.813774i | ||||
\(855\) | 1.99460 | 0.0682138 | ||||||||
\(856\) | −6.90749 | − | 11.9641i | −0.236093 | − | 0.408925i | ||||
\(857\) | −7.19465 | + | 12.4615i | −0.245765 | + | 0.425677i | −0.962346 | − | 0.271826i | \(-0.912372\pi\) |
0.716582 | + | 0.697503i | \(0.245706\pi\) | |||||||
\(858\) | −3.16887 | + | 5.48865i | −0.108183 | + | 0.187379i | ||||
\(859\) | 14.4121 | + | 24.9624i | 0.491734 | + | 0.851708i | 0.999955 | − | 0.00951892i | \(-0.00303001\pi\) |
−0.508221 | + | 0.861227i | \(0.669697\pi\) | |||||||
\(860\) | 18.8253 | 0.641936 | ||||||||
\(861\) | 0.420736 | − | 2.85537i | 0.0143386 | − | 0.0973107i | ||||
\(862\) | −11.5419 | −0.393120 | ||||||||
\(863\) | 19.6797 | + | 34.0862i | 0.669904 | + | 1.16031i | 0.977931 | + | 0.208930i | \(0.0669980\pi\) |
−0.308027 | + | 0.951378i | \(0.599669\pi\) | |||||||
\(864\) | −0.500000 | + | 0.866025i | −0.0170103 | + | 0.0294628i | ||||
\(865\) | 1.61904 | − | 2.80427i | 0.0550492 | − | 0.0953480i | ||||
\(866\) | 12.3814 | + | 21.4451i | 0.420736 | + | 0.728735i | ||||
\(867\) | −10.2411 | −0.347805 | ||||||||
\(868\) | 8.01019 | + | 6.34474i | 0.271884 | + | 0.215354i | ||||
\(869\) | 1.29628 | 0.0439732 | ||||||||
\(870\) | 0.705196 | + | 1.22144i | 0.0239084 | + | 0.0414106i | ||||
\(871\) | 24.3070 | − | 42.1009i | 0.823611 | − | 1.42654i | ||||
\(872\) | −5.03382 | + | 8.71884i | −0.170467 | + | 0.295257i | ||||
\(873\) | 5.21411 | + | 9.03111i | 0.176471 | + | 0.305657i | ||||
\(874\) | 1.09088 | 0.0368996 | ||||||||
\(875\) | −29.9379 | + | 11.8640i | −1.01208 | + | 0.401077i | ||||
\(876\) | −2.86225 | −0.0967065 | ||||||||
\(877\) | −15.9191 | − | 27.5727i | −0.537550 | − | 0.931064i | −0.999035 | − | 0.0439161i | \(-0.986017\pi\) |
0.461485 | − | 0.887148i | \(-0.347317\pi\) | |||||||
\(878\) | 3.91289 | − | 6.77733i | 0.132054 | − | 0.228724i | ||||
\(879\) | 15.7426 | − | 27.2671i | 0.530986 | − | 0.919695i | ||||
\(880\) | −1.53633 | − | 2.66099i | −0.0517895 | − | 0.0897021i | ||||
\(881\) | −3.69068 | −0.124342 | −0.0621710 | − | 0.998066i | \(-0.519802\pi\) | ||||
−0.0621710 | + | 0.998066i | \(0.519802\pi\) | |||||||
\(882\) | 1.60270 | + | 6.81406i | 0.0539657 | + | 0.229441i | ||||
\(883\) | 50.0034 | 1.68275 | 0.841374 | − | 0.540454i | \(-0.181747\pi\) | ||||
0.841374 | + | 0.540454i | \(0.181747\pi\) | |||||||
\(884\) | −4.90240 | − | 8.49120i | −0.164885 | − | 0.285590i | ||||
\(885\) | 5.87677 | − | 10.1789i | 0.197545 | − | 0.342159i | ||||
\(886\) | 0.497298 | − | 0.861346i | 0.0167071 | − | 0.0289375i | ||||
\(887\) | −20.0668 | − | 34.7568i | −0.673779 | − | 1.16702i | −0.976824 | − | 0.214043i | \(-0.931337\pi\) |
0.303045 | − | 0.952976i | \(-0.401997\pi\) | |||||||
\(888\) | 2.45186 | 0.0822790 | ||||||||
\(889\) | 9.89675 | − | 3.92196i | 0.331926 | − | 0.131538i | ||||
\(890\) | 5.86010 | 0.196431 | ||||||||
\(891\) | −0.840244 | − | 1.45535i | −0.0281492 | − | 0.0487559i | ||||
\(892\) | −2.21141 | + | 3.83027i | −0.0740435 | + | 0.128247i | ||||
\(893\) | 1.21264 | − | 2.10035i | 0.0405794 | − | 0.0702856i | ||||
\(894\) | 5.93622 | + | 10.2818i | 0.198537 | + | 0.343876i | ||||
\(895\) | −22.3493 | −0.747054 | ||||||||
\(896\) | −2.07397 | − | 1.64276i | −0.0692865 | − | 0.0548807i | ||||
\(897\) | 3.77137 | 0.125922 | ||||||||
\(898\) | −13.0645 | − | 22.6285i | −0.435970 | − | 0.755121i | ||||
\(899\) | −1.48961 | + | 2.58008i | −0.0496813 | + | 0.0860505i | ||||
\(900\) | 0.828427 | − | 1.43488i | 0.0276142 | − | 0.0478293i | ||||
\(901\) | 9.58177 | + | 16.5961i | 0.319215 | + | 0.552896i | ||||
\(902\) | −1.83321 | −0.0610393 | ||||||||
\(903\) | −3.97096 | + | 26.9493i | −0.132145 | + | 0.896818i | ||||
\(904\) | 6.30392 | 0.209665 | ||||||||
\(905\) | −0.750373 | − | 1.29968i | −0.0249432 | − | 0.0432030i | ||||
\(906\) | −0.536325 | + | 0.928943i | −0.0178182 | + | 0.0308620i | ||||
\(907\) | −8.32792 | + | 14.4244i | −0.276524 | + | 0.478954i | −0.970518 | − | 0.241027i | \(-0.922516\pi\) |
0.693994 | + | 0.719980i | \(0.255849\pi\) | |||||||
\(908\) | 6.04524 | + | 10.4707i | 0.200618 | + | 0.347481i | ||||
\(909\) | −6.47764 | −0.214850 | ||||||||
\(910\) | −2.65956 | + | 18.0493i | −0.0881634 | + | 0.598330i | ||||
\(911\) | −59.6860 | −1.97749 | −0.988743 | − | 0.149625i | \(-0.952193\pi\) | ||||
−0.988743 | + | 0.149625i | \(0.952193\pi\) | |||||||
\(912\) | −0.545441 | − | 0.944731i | −0.0180613 | − | 0.0312832i | ||||
\(913\) | −2.80418 | + | 4.85699i | −0.0928049 | + | 0.160743i | ||||
\(914\) | −9.37224 | + | 16.2332i | −0.310006 | + | 0.536946i | ||||
\(915\) | −8.30607 | − | 14.3865i | −0.274590 | − | 0.475604i | ||||
\(916\) | −9.09088 | −0.300371 | ||||||||
\(917\) | −22.8025 | − | 18.0615i | −0.753003 | − | 0.596442i | ||||
\(918\) | 2.59980 | 0.0858061 | ||||||||
\(919\) | 18.8061 | + | 32.5731i | 0.620356 | + | 1.07449i | 0.989419 | + | 0.145084i | \(0.0463454\pi\) |
−0.369063 | + | 0.929404i | \(0.620321\pi\) | |||||||
\(920\) | −0.914214 | + | 1.58346i | −0.0301407 | + | 0.0522053i | ||||
\(921\) | −2.56907 | + | 4.44977i | −0.0846539 | + | 0.146625i | ||||
\(922\) | 2.81824 | + | 4.88133i | 0.0928137 | + | 0.160758i | ||||
\(923\) | 31.0332 | 1.02147 | ||||||||
\(924\) | 4.13342 | − | 1.63803i | 0.135980 | − | 0.0538871i | ||||
\(925\) | −4.06237 | −0.133570 | ||||||||
\(926\) | 10.2668 | + | 17.7827i | 0.337389 | + | 0.584375i | ||||
\(927\) | 9.44514 | − | 16.3595i | 0.310219 | − | 0.537315i | ||||
\(928\) | 0.385685 | − | 0.668025i | 0.0126607 | − | 0.0219290i | ||||
\(929\) | 7.85476 | + | 13.6048i | 0.257706 | + | 0.446361i | 0.965627 | − | 0.259931i | \(-0.0836999\pi\) |
−0.707921 | + | 0.706292i | \(0.750367\pi\) | |||||||
\(930\) | −7.06184 | −0.231567 | ||||||||
\(931\) | −7.31162 | − | 2.20254i | −0.239629 | − | 0.0721855i | ||||
\(932\) | 6.74774 | 0.221029 | ||||||||
\(933\) | 7.78136 | + | 13.4777i | 0.254750 | + | 0.441240i | ||||
\(934\) | 0.589607 | − | 1.02123i | 0.0192925 | − | 0.0334157i | ||||
\(935\) | −3.99413 | + | 6.91804i | −0.130622 | + | 0.226244i | ||||
\(936\) | −1.88568 | − | 3.26610i | −0.0616355 | − | 0.106756i | ||||
\(937\) | −42.2196 | −1.37925 | −0.689627 | − | 0.724165i | \(-0.742225\pi\) | ||||
−0.689627 | + | 0.724165i | \(0.742225\pi\) | |||||||
\(938\) | −31.7056 | + | 12.5646i | −1.03522 | + | 0.410247i | ||||
\(939\) | −22.1527 | −0.722927 | ||||||||
\(940\) | 2.03250 | + | 3.52040i | 0.0662930 | + | 0.114823i | ||||
\(941\) | −13.3361 | + | 23.0988i | −0.434745 | + | 0.753000i | −0.997275 | − | 0.0737767i | \(-0.976495\pi\) |
0.562530 | + | 0.826777i | \(0.309828\pi\) | |||||||
\(942\) | −10.6880 | + | 18.5121i | −0.348233 | + | 0.603157i | ||||
\(943\) | 0.545441 | + | 0.944731i | 0.0177620 | + | 0.0307647i | ||||
\(944\) | −6.42822 | −0.209221 | ||||||||
\(945\) | −3.79210 | − | 3.00366i | −0.123357 | − | 0.0977091i | ||||
\(946\) | 17.3021 | 0.562540 | ||||||||
\(947\) | 20.5394 | + | 35.5753i | 0.667442 | + | 1.15604i | 0.978617 | + | 0.205691i | \(0.0659441\pi\) |
−0.311175 | + | 0.950353i | \(0.600723\pi\) | |||||||
\(948\) | −0.385685 | + | 0.668025i | −0.0125265 | + | 0.0216965i | ||||
\(949\) | 5.39730 | − | 9.34840i | 0.175204 | − | 0.303462i | ||||
\(950\) | 0.903715 | + | 1.56528i | 0.0293204 | + | 0.0507844i | ||||
\(951\) | 18.5627 | 0.601937 | ||||||||
\(952\) | −1.00270 | + | 6.80494i | −0.0324977 | + | 0.220549i | ||||
\(953\) | −35.0374 | −1.13497 | −0.567487 | − | 0.823383i | \(-0.692084\pi\) | ||||
−0.567487 | + | 0.823383i | \(0.692084\pi\) | |||||||
\(954\) | 3.68558 | + | 6.38362i | 0.119325 | + | 0.206677i | ||||
\(955\) | 11.3837 | − | 19.7171i | 0.368366 | − | 0.638029i | ||||
\(956\) | −10.2959 | + | 17.8330i | −0.332992 | + | 0.576760i | ||||
\(957\) | 0.648139 | + | 1.12261i | 0.0209513 | + | 0.0362888i | ||||
\(958\) | 1.68264 | 0.0543635 | ||||||||
\(959\) | −1.59980 | + | 10.8572i | −0.0516601 | + | 0.350597i | ||||
\(960\) | 1.82843 | 0.0590122 | ||||||||
\(961\) | 8.04151 | + | 13.9283i | 0.259404 | + | 0.449300i | ||||
\(962\) | −4.62343 | + | 8.00802i | −0.149065 | + | 0.258189i | ||||
\(963\) | −6.90749 | + | 11.9641i | −0.222591 | + | 0.385539i | ||||
\(964\) | −8.59068 | − | 14.8795i | −0.276687 | − | 0.479236i | ||||
\(965\) | 12.2580 | 0.394599 | ||||||||
\(966\) | −2.07397 | − | 1.64276i | −0.0667289 | − | 0.0528548i | ||||
\(967\) | 6.28833 | 0.202219 | 0.101109 | − | 0.994875i | \(-0.467761\pi\) | ||||
0.101109 | + | 0.994875i | \(0.467761\pi\) | |||||||
\(968\) | 4.08798 | + | 7.08059i | 0.131393 | + | 0.227579i | ||||
\(969\) | −1.41803 | + | 2.45611i | −0.0455538 | + | 0.0789015i | ||||
\(970\) | 9.53362 | − | 16.5127i | 0.306106 | − | 0.530191i | ||||
\(971\) | −17.4971 | − | 30.3059i | −0.561509 | − | 0.972561i | −0.997365 | − | 0.0725453i | \(-0.976888\pi\) |
0.435857 | − | 0.900016i | \(-0.356446\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −32.7471 | + | 12.9773i | −1.04982 | + | 0.416033i | ||||
\(974\) | −17.2901 | −0.554010 | ||||||||
\(975\) | 3.12430 | + | 5.41145i | 0.100058 | + | 0.173305i | ||||
\(976\) | −4.54274 | + | 7.86825i | −0.145410 | + | 0.251857i | ||||
\(977\) | −6.08161 | + | 10.5337i | −0.194568 | + | 0.337002i | −0.946759 | − | 0.321944i | \(-0.895664\pi\) |
0.752191 | + | 0.658945i | \(0.228997\pi\) | |||||||
\(978\) | −0.940241 | − | 1.62854i | −0.0300656 | − | 0.0520751i | ||||
\(979\) | 5.38596 | 0.172136 | ||||||||
\(980\) | 9.32461 | − | 8.76732i | 0.297864 | − | 0.280062i | ||||
\(981\) | 10.0676 | 0.321435 | ||||||||
\(982\) | −12.8681 | − | 22.2881i | −0.410636 | − | 0.711243i | ||||
\(983\) | 15.6542 | − | 27.1138i | 0.499290 | − | 0.864796i | −0.500710 | − | 0.865615i | \(-0.666928\pi\) |
1.00000 | 0.000819731i | \(0.000260929\pi\) | ||||||||
\(984\) | 0.545441 | − | 0.944731i | 0.0173880 | − | 0.0301169i | ||||
\(985\) | −15.1399 | − | 26.2231i | −0.482397 | − | 0.835537i | ||||
\(986\) | −2.00540 | −0.0638651 | ||||||||
\(987\) | −5.46837 | + | 2.16705i | −0.174060 | + | 0.0689780i | ||||
\(988\) | 4.11412 | 0.130887 | ||||||||
\(989\) | −5.14794 | − | 8.91649i | −0.163695 | − | 0.283528i | ||||
\(990\) | −1.53633 | + | 2.66099i | −0.0488276 | + | 0.0845719i | ||||
\(991\) | 22.1980 | − | 38.4480i | 0.705142 | − | 1.22134i | −0.261499 | − | 0.965204i | \(-0.584217\pi\) |
0.966640 | − | 0.256137i | \(-0.0824499\pi\) | |||||||
\(992\) | 1.93113 | + | 3.34481i | 0.0613133 | + | 0.106198i | ||||
\(993\) | 2.86265 | 0.0908435 | ||||||||
\(994\) | −17.0659 | − | 13.5176i | −0.541298 | − | 0.428754i | ||||
\(995\) | −9.17474 | −0.290859 | ||||||||
\(996\) | −1.66867 | − | 2.89022i | −0.0528739 | − | 0.0915802i | ||||
\(997\) | −22.6407 | + | 39.2149i | −0.717038 | + | 1.24195i | 0.245130 | + | 0.969490i | \(0.421169\pi\) |
−0.962168 | + | 0.272457i | \(0.912164\pi\) | |||||||
\(998\) | 11.5998 | − | 20.0914i | 0.367185 | − | 0.635983i | ||||
\(999\) | −1.22593 | − | 2.12337i | −0.0387867 | − | 0.0671805i |
(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 | 966.2.i.l.277.2 | ✓ | 8 | |
7.2 | even | 3 | inner | 966.2.i.l.415.2 | yes | 8 | |
7.3 | odd | 6 | 6762.2.a.cm.1.1 | 4 | |||
7.4 | even | 3 | 6762.2.a.cp.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.2.i.l.277.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
966.2.i.l.415.2 | yes | 8 | 7.2 | even | 3 | inner | |
6762.2.a.cm.1.1 | 4 | 7.3 | odd | 6 | |||
6762.2.a.cp.1.3 | 4 | 7.4 | even | 3 |