Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1800,2,Mod(901,1800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1800.901");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1800.k (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.3730723638\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.212336640000.29 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 2x^{4} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 901.2 | ||
Root | \(-1.26979 + 0.622597i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1800.901 |
Dual form | 1800.2.k.r.901.1 |
$q$-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 \(\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1001\) | \(1351\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.26979 | + | 0.622597i | −0.897879 | + | 0.440243i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.22474 | − | 1.58114i | 0.612372 | − | 0.790569i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.44949 | −1.30378 | −0.651892 | − | 0.758312i | \(-0.726025\pi\) | ||||
−0.651892 | + | 0.758312i | \(0.726025\pi\) | |||||||
\(8\) | −0.570759 | + | 2.77024i | −0.201794 | + | 0.979428i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 5.54048i | − | 1.67052i | −0.549857 | − | 0.835259i | \(-0.685318\pi\) | ||
0.549857 | − | 0.835259i | \(-0.314682\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.87298i | 1.07417i | 0.843527 | + | 0.537086i | \(0.180475\pi\) | ||||
−0.843527 | + | 0.537086i | \(0.819525\pi\) | |||||||
\(14\) | 4.38014 | − | 2.14764i | 1.17064 | − | 0.573982i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | − | 3.87298i | −0.250000 | − | 0.968246i | ||||
\(17\) | 6.22069 | 1.50874 | 0.754369 | − | 0.656451i | \(-0.227943\pi\) | ||||
0.754369 | + | 0.656451i | \(0.227943\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.03526i | 1.61400i | 0.590552 | + | 0.807000i | \(0.298910\pi\) | ||||
−0.590552 | + | 0.807000i | \(0.701090\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.44949 | + | 7.03526i | 0.735434 | + | 1.49992i | ||||
\(23\) | −1.14152 | −0.238023 | −0.119011 | − | 0.992893i | \(-0.537973\pi\) | ||||
−0.119011 | + | 0.992893i | \(0.537973\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.41131 | − | 4.91788i | −0.472897 | − | 0.964476i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.22474 | + | 5.45412i | −0.798402 | + | 1.03073i | ||||
\(29\) | − | 3.05009i | − | 0.566388i | −0.959063 | − | 0.283194i | \(-0.908606\pi\) | ||
0.959063 | − | 0.283194i | \(-0.0913940\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.44949 | −0.260336 | −0.130168 | − | 0.991492i | \(-0.541552\pi\) | ||||
−0.130168 | + | 0.991492i | \(0.541552\pi\) | |||||||
\(32\) | 3.68110 | + | 4.29529i | 0.650733 | + | 0.759307i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.89898 | + | 3.87298i | −1.35466 | + | 0.664211i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 6.32456i | − | 1.03975i | −0.854242 | − | 0.519875i | \(-0.825978\pi\) | ||
0.854242 | − | 0.519875i | \(-0.174022\pi\) | |||||||
\(38\) | −4.38014 | − | 8.93332i | −0.710552 | − | 1.44918i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.93765 | 0.614958 | 0.307479 | − | 0.951555i | \(-0.400515\pi\) | ||||
0.307479 | + | 0.951555i | \(0.400515\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.710706i | 0.108382i | 0.998531 | + | 0.0541908i | \(0.0172579\pi\) | ||||
−0.998531 | + | 0.0541908i | \(0.982742\pi\) | |||||||
\(44\) | −8.76027 | − | 6.78568i | −1.32066 | − | 1.02298i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.44949 | − | 0.710706i | 0.213716 | − | 0.104788i | ||||
\(47\) | −10.1583 | −1.48175 | −0.740873 | − | 0.671645i | \(-0.765588\pi\) | ||||
−0.740873 | + | 0.671645i | \(0.765588\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.89898 | 0.699854 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.12372 | + | 4.74342i | 0.849208 | + | 0.657794i | ||||
\(53\) | − | 8.03087i | − | 1.10313i | −0.834134 | − | 0.551563i | \(-0.814032\pi\) | ||
0.834134 | − | 0.551563i | \(-0.185968\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.96883 | − | 9.55592i | 0.263095 | − | 1.27696i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.89898 | + | 3.87298i | 0.249348 | + | 0.508548i | ||||
\(59\) | − | 4.98078i | − | 0.648442i | −0.945981 | − | 0.324221i | \(-0.894898\pi\) | ||
0.945981 | − | 0.324221i | \(-0.105102\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 10.1975i | − | 1.30566i | −0.757504 | − | 0.652831i | \(-0.773581\pi\) | ||
0.757504 | − | 0.652831i | \(-0.226419\pi\) | |||||||
\(62\) | 1.84055 | − | 0.902449i | 0.233750 | − | 0.114611i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.34847 | − | 3.16228i | −0.918559 | − | 0.395285i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 5.61385i | − | 0.685841i | −0.939364 | − | 0.342920i | \(-0.888584\pi\) | ||
0.939364 | − | 0.342920i | \(-0.111416\pi\) | |||||||
\(68\) | 7.61875 | − | 9.83577i | 0.923910 | − | 1.19276i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.5829 | −1.61199 | −0.805996 | − | 0.591921i | \(-0.798370\pi\) | ||||
−0.805996 | + | 0.591921i | \(0.798370\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.89898 | −0.807464 | −0.403732 | − | 0.914877i | \(-0.632287\pi\) | ||||
−0.403732 | + | 0.914877i | \(0.632287\pi\) | |||||||
\(74\) | 3.93765 | + | 8.03087i | 0.457743 | + | 0.933570i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 11.1237 | + | 8.61640i | 1.27598 | + | 0.988369i | ||||
\(77\) | 19.1118i | 2.17800i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.89898 | 0.326161 | 0.163080 | − | 0.986613i | \(-0.447857\pi\) | ||||
0.163080 | + | 0.986613i | \(0.447857\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.00000 | + | 2.45157i | −0.552158 | + | 0.270731i | ||||
\(83\) | − | 6.10018i | − | 0.669582i | −0.942292 | − | 0.334791i | \(-0.891334\pi\) | ||
0.942292 | − | 0.334791i | \(-0.108666\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.442484 | − | 0.902449i | −0.0477142 | − | 0.0973135i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 15.3485 | + | 3.16228i | 1.63615 | + | 0.337100i | ||||
\(89\) | 7.87530 | 0.834781 | 0.417390 | − | 0.908727i | \(-0.362945\pi\) | ||||
0.417390 | + | 0.908727i | \(0.362945\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 13.3598i | − | 1.40049i | ||||||
\(92\) | −1.39807 | + | 1.80490i | −0.145759 | + | 0.188174i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 12.8990 | − | 6.32456i | 1.33043 | − | 0.652328i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.6969 | −1.59378 | −0.796891 | − | 0.604123i | \(-0.793524\pi\) | ||||
−0.796891 | + | 0.604123i | \(0.793524\pi\) | |||||||
\(98\) | −6.22069 | + | 3.05009i | −0.628384 | + | 0.308106i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 14.1311i | − | 1.40609i | −0.711144 | − | 0.703046i | \(-0.751823\pi\) | ||
0.711144 | − | 0.703046i | \(-0.248177\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.89898 | −0.679777 | −0.339888 | − | 0.940466i | \(-0.610389\pi\) | ||||
−0.339888 | + | 0.940466i | \(0.610389\pi\) | |||||||
\(104\) | −10.7291 | − | 2.21054i | −1.05207 | − | 0.216761i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.00000 | + | 10.1975i | 0.485643 | + | 0.990473i | ||||
\(107\) | 0.559702i | 0.0541085i | 0.999634 | + | 0.0270542i | \(0.00861268\pi\) | ||||
−0.999634 | + | 0.0270542i | \(0.991387\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.5221i | 1.58253i | 0.611474 | + | 0.791265i | \(0.290577\pi\) | ||||
−0.611474 | + | 0.791265i | \(0.709423\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.44949 | + | 13.3598i | 0.325946 | + | 1.26238i | ||||
\(113\) | −12.4414 | −1.17039 | −0.585193 | − | 0.810894i | \(-0.698981\pi\) | ||||
−0.585193 | + | 0.810894i | \(0.698981\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.82262 | − | 3.73558i | −0.447769 | − | 0.346840i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.10102 | + | 6.32456i | 0.285472 | + | 0.582223i | ||||
\(119\) | −21.4582 | −1.96707 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −19.6969 | −1.79063 | ||||||||
\(122\) | 6.34896 | + | 12.9488i | 0.574808 | + | 1.17233i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.77526 | + | 2.29184i | −0.159423 | + | 0.205814i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.79796 | −0.337014 | −0.168507 | − | 0.985700i | \(-0.553895\pi\) | ||||
−0.168507 | + | 0.985700i | \(0.553895\pi\) | |||||||
\(128\) | 11.2999 | − | 0.559702i | 0.998776 | − | 0.0494712i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 10.5213i | − | 0.919247i | −0.888114 | − | 0.459623i | \(-0.847984\pi\) | ||
0.888114 | − | 0.459623i | \(-0.152016\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 24.2681i | − | 2.10431i | ||||||
\(134\) | 3.49517 | + | 7.12842i | 0.301937 | + | 0.615802i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.55051 | + | 17.2328i | −0.304454 | + | 1.47770i | ||||
\(137\) | 10.1583 | 0.867885 | 0.433943 | − | 0.900940i | \(-0.357122\pi\) | ||||
0.433943 | + | 0.900940i | \(0.357122\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 9.16738i | − | 0.777567i | −0.921329 | − | 0.388783i | \(-0.872895\pi\) | ||
0.921329 | − | 0.388783i | \(-0.127105\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 17.2474 | − | 8.45667i | 1.44737 | − | 0.709668i | ||||
\(143\) | 21.4582 | 1.79442 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 8.76027 | − | 4.29529i | 0.725005 | − | 0.355480i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10.0000 | − | 7.74597i | −0.821995 | − | 0.636715i | ||||
\(149\) | 21.0425i | 1.72387i | 0.507018 | + | 0.861935i | \(0.330748\pi\) | ||||
−0.507018 | + | 0.861935i | \(0.669252\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.3485 | −1.00490 | −0.502452 | − | 0.864605i | \(-0.667569\pi\) | ||||
−0.502452 | + | 0.864605i | \(0.667569\pi\) | |||||||
\(152\) | −19.4894 | − | 4.01544i | −1.58080 | − | 0.325695i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −11.8990 | − | 24.2681i | −0.958847 | − | 1.95558i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 8.77613i | − | 0.700411i | −0.936673 | − | 0.350206i | \(-0.886112\pi\) | ||
0.936673 | − | 0.350206i | \(-0.113888\pi\) | |||||||
\(158\) | −3.68110 | + | 1.80490i | −0.292853 | + | 0.143590i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.93765 | 0.310330 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 14.7812i | − | 1.15776i | −0.815414 | − | 0.578878i | \(-0.803491\pi\) | ||
0.815414 | − | 0.578878i | \(-0.196509\pi\) | |||||||
\(164\) | 4.82262 | − | 6.22597i | 0.376583 | − | 0.486167i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.79796 | + | 7.74597i | 0.294779 | + | 0.601204i | ||||
\(167\) | 3.42455 | 0.265000 | 0.132500 | − | 0.991183i | \(-0.457700\pi\) | ||||
0.132500 | + | 0.991183i | \(0.457700\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.00000 | −0.153846 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.12372 | + | 0.870433i | 0.0856832 | + | 0.0663699i | ||||
\(173\) | − | 1.93069i | − | 0.146787i | −0.997303 | − | 0.0733937i | \(-0.976617\pi\) | ||
0.997303 | − | 0.0733937i | \(-0.0233830\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −21.4582 | + | 5.54048i | −1.61747 | + | 0.417630i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −10.0000 | + | 4.90314i | −0.749532 | + | 0.367506i | ||||
\(179\) | − | 21.0425i | − | 1.57279i | −0.617723 | − | 0.786396i | \(-0.711945\pi\) | ||
0.617723 | − | 0.786396i | \(-0.288055\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.29439i | 0.393529i | 0.980451 | + | 0.196765i | \(0.0630435\pi\) | ||||
−0.980451 | + | 0.196765i | \(0.936957\pi\) | |||||||
\(182\) | 8.31779 | + | 16.9642i | 0.616555 | + | 1.25747i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.651531 | − | 3.16228i | 0.0480315 | − | 0.233126i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 34.4656i | − | 2.52037i | ||||||
\(188\) | −12.4414 | + | 16.0617i | −0.907380 | + | 1.17142i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.5829 | 0.982823 | 0.491412 | − | 0.870927i | \(-0.336481\pi\) | ||||
0.491412 | + | 0.870927i | \(0.336481\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.8990 | 0.856507 | 0.428254 | − | 0.903659i | \(-0.359129\pi\) | ||||
0.428254 | + | 0.903659i | \(0.359129\pi\) | |||||||
\(194\) | 19.9319 | − | 9.77287i | 1.43102 | − | 0.701651i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.00000 | − | 7.74597i | 0.428571 | − | 0.553283i | ||||
\(197\) | − | 23.2813i | − | 1.65873i | −0.558710 | − | 0.829363i | \(-0.688704\pi\) | ||
0.558710 | − | 0.829363i | \(-0.311296\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.2474 | 1.50619 | 0.753096 | − | 0.657911i | \(-0.228560\pi\) | ||||
0.753096 | + | 0.657911i | \(0.228560\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 8.79796 | + | 17.9435i | 0.619022 | + | 1.26250i | ||||
\(203\) | 10.5213i | 0.738448i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 8.76027 | − | 4.29529i | 0.610357 | − | 0.299267i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 15.0000 | − | 3.87298i | 1.04006 | − | 0.268543i | ||||
\(209\) | 38.9787 | 2.69622 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.13212i | 0.146781i | 0.997303 | + | 0.0733905i | \(0.0233819\pi\) | ||||
−0.997303 | + | 0.0733905i | \(0.976618\pi\) | |||||||
\(212\) | −12.6979 | − | 9.83577i | −0.872097 | − | 0.675523i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.348469 | − | 0.710706i | −0.0238209 | − | 0.0485828i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.00000 | 0.339422 | ||||||||
\(218\) | −10.2866 | − | 20.9796i | −0.696697 | − | 1.42092i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 24.0926i | 1.62064i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.348469 | −0.0233352 | −0.0116676 | − | 0.999932i | \(-0.503714\pi\) | ||||
−0.0116676 | + | 0.999932i | \(0.503714\pi\) | |||||||
\(224\) | −12.6979 | − | 14.8165i | −0.848416 | − | 0.989972i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 15.7980 | − | 7.74597i | 1.05086 | − | 0.515254i | ||||
\(227\) | − | 4.42108i | − | 0.293437i | −0.989178 | − | 0.146719i | \(-0.953129\pi\) | ||
0.989178 | − | 0.146719i | \(-0.0468712\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 5.29439i | − | 0.349863i | −0.984581 | − | 0.174932i | \(-0.944030\pi\) | ||
0.984581 | − | 0.174932i | \(-0.0559705\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.44949 | + | 1.74087i | 0.554736 | + | 0.114293i | ||||
\(233\) | −24.2543 | −1.58895 | −0.794477 | − | 0.607294i | \(-0.792255\pi\) | ||||
−0.794477 | + | 0.607294i | \(0.792255\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −7.87530 | − | 6.10018i | −0.512639 | − | 0.397088i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 27.2474 | − | 13.3598i | 1.76619 | − | 0.865988i | ||||
\(239\) | −29.3335 | −1.89743 | −0.948713 | − | 0.316138i | \(-0.897614\pi\) | ||||
−0.948713 | + | 0.316138i | \(0.897614\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.6969 | 1.52645 | 0.763227 | − | 0.646130i | \(-0.223614\pi\) | ||||
0.763227 | + | 0.646130i | \(0.223614\pi\) | |||||||
\(242\) | 25.0110 | − | 12.2633i | 1.60777 | − | 0.788312i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −16.1237 | − | 12.4894i | −1.03222 | − | 0.799551i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −27.2474 | −1.73371 | ||||||||
\(248\) | 0.827309 | − | 4.01544i | 0.0525342 | − | 0.254980i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.10018i | 0.385040i | 0.981293 | + | 0.192520i | \(0.0616661\pi\) | ||||
−0.981293 | + | 0.192520i | \(0.938334\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.32456i | 0.397621i | ||||||||
\(254\) | 4.82262 | − | 2.36460i | 0.302598 | − | 0.148368i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −14.0000 | + | 7.74597i | −0.875000 | + | 0.484123i | ||||
\(257\) | −2.28303 | −0.142412 | −0.0712059 | − | 0.997462i | \(-0.522685\pi\) | ||||
−0.0712059 | + | 0.997462i | \(0.522685\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 21.8165i | 1.35561i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.55051 | + | 13.3598i | 0.404692 | + | 0.825372i | ||||
\(263\) | 9.01682 | 0.556001 | 0.278001 | − | 0.960581i | \(-0.410328\pi\) | ||||
0.278001 | + | 0.960581i | \(0.410328\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 15.1092 | + | 30.8154i | 0.926406 | + | 1.88941i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −8.87628 | − | 6.87553i | −0.542205 | − | 0.419990i | ||||
\(269\) | − | 4.16950i | − | 0.254219i | −0.991889 | − | 0.127109i | \(-0.959430\pi\) | ||
0.991889 | − | 0.127109i | \(-0.0405699\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.10102 | 0.309865 | 0.154932 | − | 0.987925i | \(-0.450484\pi\) | ||||
0.154932 | + | 0.987925i | \(0.450484\pi\) | |||||||
\(272\) | −6.22069 | − | 24.0926i | −0.377185 | − | 1.46083i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.8990 | + | 6.32456i | −0.779256 | + | 0.382080i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 24.2681i | − | 1.45813i | −0.684446 | − | 0.729063i | \(-0.739956\pi\) | ||
0.684446 | − | 0.729063i | \(-0.260044\pi\) | |||||||
\(278\) | 5.70759 | + | 11.6407i | 0.342318 | + | 0.698161i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.93765 | −0.234901 | −0.117450 | − | 0.993079i | \(-0.537472\pi\) | ||||
−0.117450 | + | 0.993079i | \(0.537472\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.710706i | 0.0422471i | 0.999777 | + | 0.0211235i | \(0.00672433\pi\) | ||||
−0.999777 | + | 0.0211235i | \(0.993276\pi\) | |||||||
\(284\) | −16.6356 | + | 21.4764i | −0.987140 | + | 1.27439i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −27.2474 | + | 13.3598i | −1.61118 | + | 0.789983i | ||||
\(287\) | −13.5829 | −0.801773 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 21.6969 | 1.27629 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.44949 | + | 10.9082i | −0.494469 | + | 0.638357i | ||||
\(293\) | − | 16.0617i | − | 0.938337i | −0.883109 | − | 0.469169i | \(-0.844554\pi\) | ||
0.883109 | − | 0.469169i | \(-0.155446\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 17.5205 | + | 3.60979i | 1.01836 | + | 0.209815i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −13.1010 | − | 26.7196i | −0.758922 | − | 1.54783i | ||||
\(299\) | − | 4.42108i | − | 0.255677i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 2.45157i | − | 0.141306i | ||||||
\(302\) | 15.6800 | − | 7.68813i | 0.902282 | − | 0.442402i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 27.2474 | − | 7.03526i | 1.56275 | − | 0.403500i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.7812i | 0.843609i | 0.906687 | + | 0.421805i | \(0.138603\pi\) | ||||
−0.906687 | + | 0.421805i | \(0.861397\pi\) | |||||||
\(308\) | 30.2185 | + | 23.4071i | 1.72186 | + | 1.33374i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.7506 | −0.893135 | −0.446568 | − | 0.894750i | \(-0.647354\pi\) | ||||
−0.446568 | + | 0.894750i | \(0.647354\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.5959 | −1.27720 | −0.638598 | − | 0.769540i | \(-0.720485\pi\) | ||||
−0.638598 | + | 0.769540i | \(0.720485\pi\) | |||||||
\(314\) | 5.46399 | + | 11.1439i | 0.308351 | + | 0.628884i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.55051 | − | 4.58369i | 0.199732 | − | 0.257853i | ||||
\(317\) | 21.0425i | 1.18187i | 0.806721 | + | 0.590933i | \(0.201240\pi\) | ||||
−0.806721 | + | 0.590933i | \(0.798760\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.8990 | −0.946161 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.00000 | + | 2.45157i | −0.278639 | + | 0.136621i | ||||
\(323\) | 43.7642i | 2.43510i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 9.20275 | + | 18.7691i | 0.509693 | + | 1.03952i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.24745 | + | 10.9082i | −0.124095 | + | 0.602307i | ||||
\(329\) | 35.0411 | 1.93188 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.6491i | 0.695258i | 0.937632 | + | 0.347629i | \(0.113013\pi\) | ||||
−0.937632 | + | 0.347629i | \(0.886987\pi\) | |||||||
\(332\) | −9.64524 | − | 7.47117i | −0.529351 | − | 0.410034i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.34847 | + | 2.13212i | −0.237938 | + | 0.116664i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.7980 | −1.02399 | −0.511995 | − | 0.858988i | \(-0.671093\pi\) | ||||
−0.511995 | + | 0.858988i | \(0.671093\pi\) | |||||||
\(338\) | 2.53958 | − | 1.24519i | 0.138135 | − | 0.0677297i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.03087i | 0.434896i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.24745 | 0.391325 | ||||||||
\(344\) | −1.96883 | − | 0.405641i | −0.106152 | − | 0.0218707i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.20204 | + | 2.45157i | 0.0646221 | + | 0.131797i | ||||
\(347\) | − | 16.0617i | − | 0.862240i | −0.902295 | − | 0.431120i | \(-0.858119\pi\) | ||
0.902295 | − | 0.431120i | \(-0.141881\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 12.6491i | − | 0.677091i | −0.940950 | − | 0.338546i | \(-0.890065\pi\) | ||
0.940950 | − | 0.338546i | \(-0.109935\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 23.7980 | − | 20.3951i | 1.26844 | − | 1.08706i | ||||
\(353\) | 0.628417 | 0.0334473 | 0.0167236 | − | 0.999860i | \(-0.494676\pi\) | ||||
0.0167236 | + | 0.999860i | \(0.494676\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 9.64524 | − | 12.4519i | 0.511197 | − | 0.659952i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 13.1010 | + | 26.7196i | 0.692410 | + | 1.41218i | ||||
\(359\) | −21.4582 | −1.13252 | −0.566260 | − | 0.824227i | \(-0.691610\pi\) | ||||
−0.566260 | + | 0.824227i | \(0.691610\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −30.4949 | −1.60499 | ||||||||
\(362\) | −3.29628 | − | 6.72278i | −0.173248 | − | 0.353342i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −21.1237 | − | 16.3624i | −1.10718 | − | 0.857621i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.4495 | 1.22405 | 0.612027 | − | 0.790837i | \(-0.290354\pi\) | ||||
0.612027 | + | 0.790837i | \(0.290354\pi\) | |||||||
\(368\) | 1.14152 | + | 4.42108i | 0.0595057 | + | 0.230465i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 27.7024i | 1.43824i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.6895i | 1.33015i | 0.746776 | + | 0.665075i | \(0.231601\pi\) | ||||
−0.746776 | + | 0.665075i | \(0.768399\pi\) | |||||||
\(374\) | 21.4582 | + | 43.7642i | 1.10958 | + | 2.26299i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.79796 | − | 28.1410i | 0.299007 | − | 1.45126i | ||||
\(377\) | 11.8130 | 0.608398 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.3598i | 0.686248i | 0.939290 | + | 0.343124i | \(0.111485\pi\) | ||||
−0.939290 | + | 0.343124i | \(0.888515\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −17.2474 | + | 8.45667i | −0.882456 | + | 0.432681i | ||||
\(383\) | 12.4414 | 0.635724 | 0.317862 | − | 0.948137i | \(-0.397035\pi\) | ||||
0.317862 | + | 0.948137i | \(0.397035\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −15.1092 | + | 7.40827i | −0.769040 | + | 0.377071i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −19.2247 | + | 24.8190i | −0.975989 | + | 1.26000i | ||||
\(389\) | 35.1736i | 1.78337i | 0.452655 | + | 0.891686i | \(0.350477\pi\) | ||||
−0.452655 | + | 0.891686i | \(0.649523\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.10102 | −0.359114 | ||||||||
\(392\) | −2.79613 | + | 13.5714i | −0.141226 | + | 0.685457i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 14.4949 | + | 29.5625i | 0.730242 | + | 1.48933i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.45157i | 0.123041i | 0.998106 | + | 0.0615204i | \(0.0195949\pi\) | ||||
−0.998106 | + | 0.0615204i | \(0.980405\pi\) | |||||||
\(398\) | −26.9798 | + | 13.2286i | −1.35238 | + | 0.663090i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 31.1034 | 1.55323 | 0.776616 | − | 0.629975i | \(-0.216935\pi\) | ||||
0.776616 | + | 0.629975i | \(0.216935\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 5.61385i | − | 0.279646i | ||||||
\(404\) | −22.3432 | − | 17.3069i | −1.11161 | − | 0.861052i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.55051 | − | 13.3598i | −0.325096 | − | 0.663037i | ||||
\(407\) | −35.0411 | −1.73692 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.89898 | −0.390579 | −0.195290 | − | 0.980746i | \(-0.562565\pi\) | ||||
−0.195290 | + | 0.980746i | \(0.562565\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8.44949 | + | 10.9082i | −0.416276 | + | 0.537411i | ||||
\(413\) | 17.1811i | 0.845429i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −16.6356 | + | 14.2568i | −0.815626 | + | 0.698999i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −49.4949 | + | 24.2681i | −2.42087 | + | 1.18699i | ||||
\(419\) | 23.8410i | 1.16471i | 0.812934 | + | 0.582355i | \(0.197869\pi\) | ||||
−0.812934 | + | 0.582355i | \(0.802131\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 24.6593i | − | 1.20182i | −0.799316 | − | 0.600911i | \(-0.794805\pi\) | ||
0.799316 | − | 0.600911i | \(-0.205195\pi\) | |||||||
\(422\) | −1.32745 | − | 2.70735i | −0.0646193 | − | 0.131792i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 22.2474 | + | 4.58369i | 1.08043 | + | 0.222604i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 35.1763i | 1.70230i | ||||||||
\(428\) | 0.884967 | + | 0.685493i | 0.0427765 | + | 0.0331345i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.4582 | −1.03360 | −0.516802 | − | 0.856105i | \(-0.672878\pi\) | ||||
−0.516802 | + | 0.856105i | \(0.672878\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.5959 | 0.605321 | 0.302661 | − | 0.953098i | \(-0.402125\pi\) | ||||
0.302661 | + | 0.953098i | \(0.402125\pi\) | |||||||
\(434\) | −6.34896 | + | 3.11299i | −0.304760 | + | 0.149428i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 26.1237 | + | 20.2353i | 1.25110 | + | 0.969098i | ||||
\(437\) | − | 8.03087i | − | 0.384169i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.0454 | −0.813533 | −0.406766 | − | 0.913532i | \(-0.633344\pi\) | ||||
−0.406766 | + | 0.913532i | \(0.633344\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −15.0000 | − | 30.5926i | −0.713477 | − | 1.45514i | ||||
\(443\) | − | 7.21959i | − | 0.343013i | −0.985183 | − | 0.171507i | \(-0.945137\pi\) | ||
0.985183 | − | 0.171507i | \(-0.0548635\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.442484 | − | 0.216956i | 0.0209522 | − | 0.0102732i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 25.3485 | + | 10.9082i | 1.19760 | + | 0.515366i | ||||
\(449\) | −19.2905 | −0.910374 | −0.455187 | − | 0.890396i | \(-0.650428\pi\) | ||||
−0.455187 | + | 0.890396i | \(0.650428\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 21.8165i | − | 1.02730i | ||||||
\(452\) | −15.2375 | + | 19.6715i | −0.716712 | + | 0.925271i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.75255 | + | 5.61385i | 0.129184 | + | 0.263471i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.6969 | 0.968162 | 0.484081 | − | 0.875023i | \(-0.339154\pi\) | ||||
0.484081 | + | 0.875023i | \(0.339154\pi\) | |||||||
\(458\) | 3.29628 | + | 6.72278i | 0.154025 | + | 0.314135i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 25.2120i | 1.17424i | 0.809500 | + | 0.587120i | \(0.199738\pi\) | ||||
−0.809500 | + | 0.587120i | \(0.800262\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.89898 | 0.320623 | 0.160311 | − | 0.987066i | \(-0.448750\pi\) | ||||
0.160311 | + | 0.987066i | \(0.448750\pi\) | |||||||
\(464\) | −11.8130 | + | 3.05009i | −0.548403 | + | 0.141597i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 30.7980 | − | 15.1007i | 1.42669 | − | 0.699526i | ||||
\(467\) | − | 32.6832i | − | 1.51240i | −0.654342 | − | 0.756199i | \(-0.727054\pi\) | ||
0.654342 | − | 0.756199i | \(-0.272946\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 19.3649i | 0.894189i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 13.7980 | + | 2.84282i | 0.635103 | + | 0.130852i | ||||
\(473\) | 3.93765 | 0.181053 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −26.2808 | + | 33.9284i | −1.20458 | + | 1.55510i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 37.2474 | − | 18.2630i | 1.70366 | − | 0.835328i | ||||
\(479\) | −7.87530 | −0.359832 | −0.179916 | − | 0.983682i | \(-0.557583\pi\) | ||||
−0.179916 | + | 0.983682i | \(0.557583\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.4949 | 1.11687 | ||||||||
\(482\) | −30.0902 | + | 14.7537i | −1.37057 | + | 0.672010i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −24.1237 | + | 31.1436i | −1.09653 | + | 1.41562i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.04541 | 0.0473719 | 0.0236860 | − | 0.999719i | \(-0.492460\pi\) | ||||
0.0236860 | + | 0.999719i | \(0.492460\pi\) | |||||||
\(488\) | 28.2496 | + | 5.82033i | 1.27880 | + | 0.263474i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.11940i | 0.0505180i | 0.999681 | + | 0.0252590i | \(0.00804105\pi\) | ||||
−0.999681 | + | 0.0252590i | \(0.991959\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 18.9737i | − | 0.854531i | ||||||
\(494\) | 34.5986 | − | 16.9642i | 1.55666 | − | 0.763255i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.44949 | + | 5.61385i | 0.0650840 | + | 0.252069i | ||||
\(497\) | 46.8540 | 2.10169 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 19.6844i | − | 0.881193i | −0.897705 | − | 0.440597i | \(-0.854767\pi\) | ||
0.897705 | − | 0.440597i | \(-0.145233\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.79796 | − | 7.74597i | −0.169511 | − | 0.345719i | ||||
\(503\) | 28.3073 | 1.26216 | 0.631080 | − | 0.775718i | \(-0.282612\pi\) | ||||
0.631080 | + | 0.775718i | \(0.282612\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3.93765 | − | 8.03087i | −0.175050 | − | 0.357016i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.65153 | + | 6.00510i | −0.206378 | + | 0.266433i | ||||
\(509\) | 21.0425i | 0.932693i | 0.884602 | + | 0.466347i | \(0.154430\pi\) | ||||
−0.884602 | + | 0.466347i | \(0.845570\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23.7980 | 1.05276 | ||||||||
\(512\) | 12.9545 | − | 18.5521i | 0.572512 | − | 0.819896i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.89898 | − | 1.42141i | 0.127869 | − | 0.0626958i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 56.2821i | 2.47528i | ||||||||
\(518\) | −13.5829 | − | 27.7024i | −0.596798 | − | 1.21717i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 31.1034 | 1.36267 | 0.681333 | − | 0.731974i | \(-0.261401\pi\) | ||||
0.681333 | + | 0.731974i | \(0.261401\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.7549i | 1.47600i | 0.674802 | + | 0.737999i | \(0.264229\pi\) | ||||
−0.674802 | + | 0.737999i | \(0.735771\pi\) | |||||||
\(524\) | −16.6356 | − | 12.8859i | −0.726728 | − | 0.562921i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.4495 | + | 5.61385i | −0.499221 | + | 0.244775i | ||||
\(527\) | −9.01682 | −0.392779 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.6969 | −0.943345 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −38.3712 | − | 29.7222i | −1.66360 | − | 1.28862i | ||||
\(533\) | 15.2505i | 0.660571i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 15.5517 | + | 3.20415i | 0.671732 | + | 0.138398i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.59592 | + | 5.29439i | 0.111918 | + | 0.228258i | ||||
\(539\) | − | 27.1427i | − | 1.16912i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.77613i | 0.377315i | 0.982043 | + | 0.188658i | \(0.0604136\pi\) | ||||
−0.982043 | + | 0.188658i | \(0.939586\pi\) | |||||||
\(542\) | −6.47724 | + | 3.17588i | −0.278221 | + | 0.136416i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 22.8990 | + | 26.7196i | 0.981786 | + | 1.14559i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 9.16738i | − | 0.391969i | −0.980607 | − | 0.195984i | \(-0.937210\pi\) | ||
0.980607 | − | 0.195984i | \(-0.0627902\pi\) | |||||||
\(548\) | 12.4414 | − | 16.0617i | 0.531469 | − | 0.686124i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.4582 | 0.914150 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.0000 | −0.425243 | ||||||||
\(554\) | 15.1092 | + | 30.8154i | 0.641930 | + | 1.30922i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −14.4949 | − | 11.2277i | −0.614721 | − | 0.476161i | ||||
\(557\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.75255 | −0.116421 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.00000 | − | 2.45157i | 0.210912 | − | 0.103413i | ||||
\(563\) | − | 43.7642i | − | 1.84444i | −0.386667 | − | 0.922220i | \(-0.626374\pi\) | ||
0.386667 | − | 0.922220i | \(-0.373626\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −0.442484 | − | 0.902449i | −0.0185990 | − | 0.0379327i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.75255 | − | 37.6279i | 0.325290 | − | 1.57883i | ||||
\(569\) | −3.93765 | −0.165075 | −0.0825375 | − | 0.996588i | \(-0.526302\pi\) | ||||
−0.0825375 | + | 0.996588i | \(0.526302\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 8.45667i | − | 0.353901i | −0.984220 | − | 0.176950i | \(-0.943377\pi\) | ||
0.984220 | − | 0.176950i | \(-0.0566232\pi\) | |||||||
\(572\) | 26.2808 | − | 33.9284i | 1.09886 | − | 1.41862i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 17.2474 | − | 8.45667i | 0.719895 | − | 0.352975i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.6969 | 0.653472 | 0.326736 | − | 0.945116i | \(-0.394051\pi\) | ||||
0.326736 | + | 0.945116i | \(0.394051\pi\) | |||||||
\(578\) | −27.5506 | + | 13.5085i | −1.14595 | + | 0.561878i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 21.0425i | 0.872991i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −44.4949 | −1.84279 | ||||||||
\(584\) | 3.93765 | − | 19.1118i | 0.162941 | − | 0.790853i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.0000 | + | 20.3951i | 0.413096 | + | 0.842513i | ||||
\(587\) | − | 16.6214i | − | 0.686040i | −0.939328 | − | 0.343020i | \(-0.888550\pi\) | ||
0.939328 | − | 0.343020i | \(-0.111450\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 10.1975i | − | 0.420182i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −24.4949 | + | 6.32456i | −1.00673 | + | 0.259938i | ||||
\(593\) | −26.5374 | −1.08976 | −0.544879 | − | 0.838514i | \(-0.683425\pi\) | ||||
−0.544879 | + | 0.838514i | \(0.683425\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 33.2711 | + | 25.7717i | 1.36284 | + | 1.05565i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.75255 | + | 5.61385i | 0.112560 | + | 0.229567i | ||||
\(599\) | 19.2905 | 0.788187 | 0.394094 | − | 0.919070i | \(-0.371059\pi\) | ||||
0.394094 | + | 0.919070i | \(0.371059\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.101021 | −0.00412071 | −0.00206036 | − | 0.999998i | \(-0.500656\pi\) | ||||
−0.00206036 | + | 0.999998i | \(0.500656\pi\) | |||||||
\(602\) | 1.52634 | + | 3.11299i | 0.0622091 | + | 0.126876i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −15.1237 | + | 19.5246i | −0.615376 | + | 0.794447i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 40.6969 | 1.65184 | 0.825919 | − | 0.563789i | \(-0.190657\pi\) | ||||
0.825919 | + | 0.563789i | \(0.190657\pi\) | |||||||
\(608\) | −30.2185 | + | 25.8975i | −1.22552 | + | 1.05028i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 39.3431i | − | 1.59165i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 31.6228i | 1.27723i | 0.769526 | + | 0.638616i | \(0.220493\pi\) | ||||
−0.769526 | + | 0.638616i | \(0.779507\pi\) | |||||||
\(614\) | −9.20275 | − | 18.7691i | −0.371393 | − | 0.757459i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −52.9444 | − | 10.9082i | −2.13319 | − | 0.439506i | ||||
\(617\) | 13.0698 | 0.526170 | 0.263085 | − | 0.964773i | \(-0.415260\pi\) | ||||
0.263085 | + | 0.964773i | \(0.415260\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 37.2366i | − | 1.49667i | −0.663323 | − | 0.748333i | \(-0.730854\pi\) | ||
0.663323 | − | 0.748333i | \(-0.269146\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 20.0000 | − | 9.80629i | 0.801927 | − | 0.393196i | ||||
\(623\) | −27.1658 | −1.08837 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 28.6921 | − | 14.0682i | 1.14677 | − | 0.562277i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −13.8763 | − | 10.7485i | −0.553724 | − | 0.428913i | ||||
\(629\) | − | 39.3431i | − | 1.56871i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.5505 | −0.738484 | −0.369242 | − | 0.929333i | \(-0.620383\pi\) | ||||
−0.369242 | + | 0.929333i | \(0.620383\pi\) | |||||||
\(632\) | −1.65462 | + | 8.03087i | −0.0658171 | + | 0.319451i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −13.1010 | − | 26.7196i | −0.520308 | − | 1.06117i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18.9737i | 0.751764i | ||||||||
\(638\) | 21.4582 | − | 10.5213i | 0.849538 | − | 0.416541i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −35.0411 | −1.38404 | −0.692020 | − | 0.721879i | \(-0.743279\pi\) | ||||
−0.692020 | + | 0.721879i | \(0.743279\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 34.4656i | 1.35919i | 0.733587 | + | 0.679595i | \(0.237845\pi\) | ||||
−0.733587 | + | 0.679595i | \(0.762155\pi\) | |||||||
\(644\) | 4.82262 | − | 6.22597i | 0.190038 | − | 0.245338i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −27.2474 | − | 55.5714i | −1.07204 | − | 2.18643i | ||||
\(647\) | −24.8827 | −0.978242 | −0.489121 | − | 0.872216i | \(-0.662682\pi\) | ||||
−0.489121 | + | 0.872216i | \(0.662682\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −27.5959 | −1.08323 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −23.3712 | − | 18.1032i | −0.915286 | − | 0.708977i | ||||
\(653\) | − | 6.10018i | − | 0.238719i | −0.992851 | − | 0.119359i | \(-0.961916\pi\) | ||
0.992851 | − | 0.119359i | \(-0.0380840\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.93765 | − | 15.2505i | −0.153739 | − | 0.595430i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −44.4949 | + | 21.8165i | −1.73459 | + | 0.850495i | ||||
\(659\) | − | 22.7216i | − | 0.885109i | −0.896742 | − | 0.442555i | \(-0.854072\pi\) | ||
0.896742 | − | 0.442555i | \(-0.145928\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37.3084i | 1.45113i | 0.688154 | + | 0.725565i | \(0.258421\pi\) | ||||
−0.688154 | + | 0.725565i | \(0.741579\pi\) | |||||||
\(662\) | −7.87530 | − | 16.0617i | −0.306082 | − | 0.624257i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 16.8990 | + | 3.48173i | 0.655808 | + | 0.135117i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.48173i | 0.134813i | ||||||||
\(668\) | 4.19420 | − | 5.41469i | 0.162279 | − | 0.209501i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −56.4993 | −2.18113 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.8990 | 1.03688 | 0.518440 | − | 0.855114i | \(-0.326513\pi\) | ||||
0.518440 | + | 0.855114i | \(0.326513\pi\) | |||||||
\(674\) | 23.8695 | − | 11.7036i | 0.919419 | − | 0.450804i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.44949 | + | 3.16228i | −0.0942111 | + | 0.121626i | ||||
\(677\) | 35.1736i | 1.35183i | 0.736979 | + | 0.675915i | \(0.236251\pi\) | ||||
−0.736979 | + | 0.675915i | \(0.763749\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 54.1464 | 2.07795 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5.00000 | − | 10.1975i | −0.191460 | − | 0.390484i | ||||
\(683\) | 33.2429i | 1.27200i | 0.771687 | + | 0.636002i | \(0.219413\pi\) | ||||
−0.771687 | + | 0.636002i | \(0.780587\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −9.20275 | + | 4.51224i | −0.351363 | + | 0.172278i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.75255 | − | 0.710706i | 0.104940 | − | 0.0270954i | ||||
\(689\) | 31.1034 | 1.18495 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 37.9473i | 1.44358i | 0.692110 | + | 0.721792i | \(0.256681\pi\) | ||||
−0.692110 | + | 0.721792i | \(0.743319\pi\) | |||||||
\(692\) | −3.05268 | − | 2.36460i | −0.116046 | − | 0.0898886i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10.0000 | + | 20.3951i | 0.379595 | + | 0.774187i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.4949 | 0.927810 | ||||||||
\(698\) | 7.87530 | + | 16.0617i | 0.298085 | + | 0.607946i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 41.2738i | − | 1.55889i | −0.626472 | − | 0.779444i | \(-0.715502\pi\) | ||
0.626472 | − | 0.779444i | \(-0.284498\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 44.4949 | 1.67816 | ||||||||
\(704\) | −17.5205 | + | 40.7141i | −0.660330 | + | 1.53447i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.797959 | + | 0.391251i | −0.0300316 | + | 0.0147249i | ||||
\(707\) | 48.7449i | 1.83324i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 1.03016i | − | 0.0386885i | −0.999813 | − | 0.0193442i | \(-0.993842\pi\) | ||
0.999813 | − | 0.0193442i | \(-0.00615785\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.49490 | + | 21.8165i | −0.168453 | + | 0.817607i | ||||
\(713\) | 1.65462 | 0.0619659 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −33.2711 | − | 25.7717i | −1.24340 | − | 0.963134i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 27.2474 | − | 13.3598i | 1.01687 | − | 0.498584i | ||||
\(719\) | 2.16772 | 0.0808422 | 0.0404211 | − | 0.999183i | \(-0.487130\pi\) | ||||
0.0404211 | + | 0.999183i | \(0.487130\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23.7980 | 0.886282 | ||||||||
\(722\) | 38.7222 | − | 18.9860i | 1.44109 | − | 0.706587i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8.37117 | + | 6.48428i | 0.311112 | + | 0.240986i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −43.4495 | −1.61145 | −0.805726 | − | 0.592288i | \(-0.798225\pi\) | ||||
−0.805726 | + | 0.592288i | \(0.798225\pi\) | |||||||
\(728\) | 37.0099 | + | 7.62523i | 1.37168 | + | 0.282610i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.42108i | 0.163519i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 30.9839i | − | 1.14442i | −0.820109 | − | 0.572208i | \(-0.806087\pi\) | ||
0.820109 | − | 0.572208i | \(-0.193913\pi\) | |||||||
\(734\) | −29.7760 | + | 14.5996i | −1.09905 | + | 0.538881i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.20204 | − | 4.90314i | −0.154889 | − | 0.180732i | ||||
\(737\) | −31.1034 | −1.14571 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 30.9839i | − | 1.13976i | −0.821728 | − | 0.569880i | \(-0.806990\pi\) | ||
0.821728 | − | 0.569880i | \(-0.193010\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −17.2474 | − | 35.1763i | −0.633174 | − | 1.29136i | ||||
\(743\) | −6.84910 | −0.251269 | −0.125635 | − | 0.992077i | \(-0.540097\pi\) | ||||
−0.125635 | + | 0.992077i | \(0.540097\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −15.9942 | − | 32.6203i | −0.585589 | − | 1.19431i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −54.4949 | − | 42.2116i | −1.99253 | − | 1.54341i | ||||
\(749\) | − | 1.93069i | − | 0.0705458i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35.7980 | 1.30629 | 0.653143 | − | 0.757235i | \(-0.273450\pi\) | ||||
0.653143 | + | 0.757235i | \(0.273450\pi\) | |||||||
\(752\) | 10.1583 | + | 39.3431i | 0.370436 | + | 1.43469i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −15.0000 | + | 7.35472i | −0.546268 | + | 0.267843i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.2579i | 0.445519i | 0.974873 | + | 0.222760i | \(0.0715065\pi\) | ||||
−0.974873 | + | 0.222760i | \(0.928493\pi\) | |||||||
\(758\) | −8.31779 | − | 16.9642i | −0.302116 | − | 0.616167i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.7506 | 0.570959 | 0.285480 | − | 0.958385i | \(-0.407847\pi\) | ||||
0.285480 | + | 0.958385i | \(0.407847\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 56.9928i | − | 2.06328i | ||||||
\(764\) | 16.6356 | − | 21.4764i | 0.601854 | − | 0.776990i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −15.7980 | + | 7.74597i | −0.570803 | + | 0.279873i | ||||
\(767\) | 19.2905 | 0.696539 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.20204 | 0.187590 | 0.0937952 | − | 0.995592i | \(-0.470100\pi\) | ||||
0.0937952 | + | 0.995592i | \(0.470100\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 14.5732 | − | 18.8139i | 0.524501 | − | 0.677128i | ||||
\(773\) | − | 9.15028i | − | 0.329113i | −0.986368 | − | 0.164556i | \(-0.947381\pi\) | ||
0.986368 | − | 0.164556i | \(-0.0526192\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 8.95916 | − | 43.4843i | 0.321615 | − | 1.56100i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −21.8990 | − | 44.6631i | −0.785116 | − | 1.60125i | ||||
\(779\) | 27.7024i | 0.992542i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 75.2558i | 2.69286i | ||||||||
\(782\) | 9.01682 | − | 4.42108i | 0.322441 | − | 0.158097i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.89898 | − | 18.9737i | −0.174964 | − | 0.677631i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.5170i | 0.374890i | 0.982275 | + | 0.187445i | \(0.0600207\pi\) | ||||
−0.982275 | + | 0.187445i | \(0.939979\pi\) | |||||||
\(788\) | −36.8110 | − | 28.5137i | −1.31134 | − | 1.01576i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 42.9164 | 1.52593 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 39.4949 | 1.40250 | ||||||||
\(794\) | −1.52634 | − | 3.11299i | −0.0541679 | − | 0.110476i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 26.0227 | − | 33.5952i | 0.922350 | − | 1.19075i | ||||
\(797\) | − | 27.1427i | − | 0.961444i | −0.876873 | − | 0.480722i | \(-0.840375\pi\) | ||
0.876873 | − | 0.480722i | \(-0.159625\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −63.1918 | −2.23557 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −39.4949 | + | 19.3649i | −1.39461 | + | 0.683799i | ||||
\(803\) | 38.2237i | 1.34888i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.49517 | + | 7.12842i | 0.123112 | + | 0.251088i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 39.1464 | + | 8.06542i | 1.37717 | + | 0.283741i | ||||
\(809\) | 3.93765 | 0.138440 | 0.0692202 | − | 0.997601i | \(-0.477949\pi\) | ||||
0.0692202 | + | 0.997601i | \(0.477949\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 39.4405i | 1.38494i | 0.721444 | + | 0.692472i | \(0.243479\pi\) | ||||
−0.721444 | + | 0.692472i | \(0.756521\pi\) | |||||||
\(812\) | 16.6356 | + | 12.8859i | 0.583794 | + | 0.452205i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 44.4949 | − | 21.8165i | 1.55955 | − | 0.764668i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.00000 | −0.174928 | ||||||||
\(818\) | 10.0301 | − | 4.91788i | 0.350693 | − | 0.171950i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 26.0233i | − | 0.908220i | −0.890946 | − | 0.454110i | \(-0.849957\pi\) | ||
0.890946 | − | 0.454110i | \(-0.150043\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.8434 | 1.21456 | 0.607282 | − | 0.794487i | \(-0.292260\pi\) | ||||
0.607282 | + | 0.794487i | \(0.292260\pi\) | |||||||
\(824\) | 3.93765 | − | 19.1118i | 0.137175 | − | 0.665792i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10.6969 | − | 21.8165i | −0.372194 | − | 0.759093i | ||||
\(827\) | 11.6407i | 0.404786i | 0.979304 | + | 0.202393i | \(0.0648718\pi\) | ||||
−0.979304 | + | 0.202393i | \(0.935128\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 37.3084i | − | 1.29578i | −0.761736 | − | 0.647888i | \(-0.775653\pi\) | ||
0.761736 | − | 0.647888i | \(-0.224347\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 12.2474 | − | 28.4605i | 0.424604 | − | 0.986690i | ||||
\(833\) | 30.4750 | 1.05590 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 47.7390 | − | 61.6308i | 1.65109 | − | 2.13155i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −14.8434 | − | 30.2732i | −0.512756 | − | 1.04577i | ||||
\(839\) | −5.70759 | −0.197048 | −0.0985239 | − | 0.995135i | \(-0.531412\pi\) | ||||
−0.0985239 | + | 0.995135i | \(0.531412\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.6969 | 0.679205 | ||||||||
\(842\) | 15.3528 | + | 31.3122i | 0.529093 | + | 1.07909i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.37117 | + | 2.61130i | 0.116041 | + | 0.0898846i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 67.9444 | 2.33460 | ||||||||
\(848\) | −31.1034 | + | 8.03087i | −1.06810 | + | 0.275781i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.21959i | 0.247484i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.29439i | 0.181277i | 0.995884 | + | 0.0906383i | \(0.0288907\pi\) | ||||
−0.995884 | + | 0.0906383i | \(0.971109\pi\) | |||||||
\(854\) | −21.9007 | − | 44.6666i | −0.749426 | − | 1.52846i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.55051 | − | 0.319455i | −0.0529953 | − | 0.0109187i | ||||
\(857\) | −18.0336 | −0.616017 | −0.308009 | − | 0.951384i | \(-0.599663\pi\) | ||||
−0.308009 | + | 0.951384i | \(0.599663\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43.6330i | 1.48874i | 0.667769 | + | 0.744369i | \(0.267250\pi\) | ||||
−0.667769 | + | 0.744369i | \(0.732750\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 27.2474 | − | 13.3598i | 0.928052 | − | 0.455037i | ||||
\(863\) | −12.4414 | −0.423509 | −0.211755 | − | 0.977323i | \(-0.567918\pi\) | ||||
−0.211755 | + | 0.977323i | \(0.567918\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −15.9942 | + | 7.84219i | −0.543505 | + | 0.266488i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6.12372 | − | 7.90569i | 0.207853 | − | 0.268337i | ||||
\(869\) | − | 16.0617i | − | 0.544857i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.7423 | 0.736711 | ||||||||
\(872\) | −45.7702 | − | 9.43013i | −1.54997 | − | 0.319344i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 5.00000 | + | 10.1975i | 0.169128 | + | 0.344937i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 20.7863i | − | 0.701904i | −0.936393 | − | 0.350952i | \(-0.885858\pi\) | ||
0.936393 | − | 0.350952i | \(-0.114142\pi\) | |||||||
\(878\) | 21.6441 | − | 10.6124i | 0.730454 | − | 0.358152i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19.2905 | −0.649913 | −0.324956 | − | 0.945729i | \(-0.605350\pi\) | ||||
−0.324956 | + | 0.945729i | \(0.605350\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.9121i | 1.04027i | 0.854083 | + | 0.520137i | \(0.174119\pi\) | ||||
−0.854083 | + | 0.520137i | \(0.825881\pi\) | |||||||
\(884\) | 38.0938 | + | 29.5073i | 1.28123 | + | 0.992438i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.49490 | + | 9.16738i | 0.151009 | + | 0.307984i | ||||
\(887\) | 53.0747 | 1.78207 | 0.891037 | − | 0.453930i | \(-0.149978\pi\) | ||||
0.891037 | + | 0.453930i | \(0.149978\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.1010 | 0.439394 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.426786 | + | 0.550978i | −0.0142898 | + | 0.0184481i | ||||
\(893\) | − | 71.4666i | − | 2.39154i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −38.9787 | + | 1.93069i | −1.30219 | + | 0.0644997i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 24.4949 | − | 12.0102i | 0.817405 | − | 0.400786i | ||||
\(899\) | 4.42108i | 0.147451i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 49.9575i | − | 1.66433i | ||||||
\(902\) | 13.5829 | + | 27.7024i | 0.452261 | + | 0.922389i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.10102 | − | 34.4656i | 0.236176 | − | 1.14631i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 56.2821i | 1.86882i | 0.356204 | + | 0.934408i | \(0.384071\pi\) | ||||
−0.356204 | + | 0.934408i | \(0.615929\pi\) | |||||||
\(908\) | −6.99034 | − | 5.41469i | −0.231982 | − | 0.179693i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.6259 | 0.782761 | 0.391381 | − | 0.920229i | \(-0.371998\pi\) | ||||
0.391381 | + | 0.920229i | \(0.371998\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −33.7980 | −1.11855 | ||||||||
\(914\) | −26.2808 | + | 12.8859i | −0.869292 | + | 0.426226i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.37117 | − | 6.48428i | −0.276591 | − | 0.214247i | ||||
\(917\) | 36.2930i | 1.19850i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −34.6413 | −1.14271 | −0.571356 | − | 0.820702i | \(-0.693582\pi\) | ||||
−0.571356 | + | 0.820702i | \(0.693582\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −15.6969 | − | 32.0140i | −0.516951 | − | 1.05433i | ||||
\(923\) | − | 52.6063i | − | 1.73156i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −8.76027 | + | 4.29529i | −0.287880 | + | 0.141152i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 13.1010 | − | 11.2277i | 0.430062 | − | 0.368567i | ||||
\(929\) | −38.9787 | −1.27885 | −0.639425 | − | 0.768853i | \(-0.720828\pi\) | ||||
−0.639425 | + | 0.768853i | \(0.720828\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 34.4656i | 1.12956i | ||||||||
\(932\) | −29.7054 | + | 38.3495i | −0.973032 | + | 1.25618i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 20.3485 | + | 41.5009i | 0.665822 | + | 1.35795i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.20204 | −0.0392690 | −0.0196345 | − | 0.999807i | \(-0.506250\pi\) | ||||
−0.0196345 | + | 0.999807i | \(0.506250\pi\) | |||||||
\(938\) | −12.0565 | − | 24.5894i | −0.393660 | − | 0.802873i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 40.4625i | − | 1.31904i | −0.751687 | − | 0.659520i | \(-0.770760\pi\) | ||
0.751687 | − | 0.659520i | \(-0.229240\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.49490 | −0.146374 | ||||||||
\(944\) | −19.2905 | + | 4.98078i | −0.627852 | + | 0.162111i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.00000 | + | 2.45157i | −0.162564 | + | 0.0797075i | ||||
\(947\) | − | 4.42108i | − | 0.143666i | −0.997417 | − | 0.0718329i | \(-0.977115\pi\) | ||
0.997417 | − | 0.0718329i | \(-0.0228848\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 26.7196i | − | 0.867356i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 12.2474 | − | 59.4444i | 0.396942 | − | 1.92660i | ||||
\(953\) | 4.56607 | 0.147909 | 0.0739547 | − | 0.997262i | \(-0.476438\pi\) | ||||
0.0739547 | + | 0.997262i | \(0.476438\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −35.9261 | + | 46.3803i | −1.16193 | + | 1.50005i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 10.0000 | − | 4.90314i | 0.323085 | − | 0.158413i | ||||
\(959\) | −35.0411 | −1.13154 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.8990 | −0.932225 | ||||||||
\(962\) | −31.1034 | + | 15.2505i | −1.00281 | + | 0.491695i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 29.0227 | − | 37.4681i | 0.934758 | − | 1.20677i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.29286 | 0.266680 | 0.133340 | − | 0.991070i | \(-0.457430\pi\) | ||||
0.133340 | + | 0.991070i | \(0.457430\pi\) | |||||||
\(968\) | 11.2422 | − | 54.5653i | 0.361338 | − | 1.75379i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 45.4433i | − | 1.45834i | −0.684331 | − | 0.729172i | \(-0.739906\pi\) | ||
0.684331 | − | 0.729172i | \(-0.260094\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 31.6228i | 1.01378i | ||||||||
\(974\) | −1.32745 | + | 0.650868i | −0.0425343 | + | 0.0208552i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −39.4949 | + | 10.1975i | −1.26420 | + | 0.326415i | ||||
\(977\) | −33.7842 | −1.08085 | −0.540427 | − | 0.841391i | \(-0.681737\pi\) | ||||
−0.540427 | + | 0.841391i | \(0.681737\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 43.6330i | − | 1.39452i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.696938 | − | 1.42141i | −0.0222402 | − | 0.0453591i | ||||
\(983\) | 22.5997 | 0.720819 | 0.360409 | − | 0.932794i | \(-0.382637\pi\) | ||||
0.360409 | + | 0.932794i | \(0.382637\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 11.8130 | + | 24.0926i | 0.376201 | + | 0.767265i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −33.3712 | + | 43.0820i | −1.06168 | + | 1.37062i | ||||
\(989\) | − | 0.811283i | − | 0.0257973i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.75255 | 0.150970 | 0.0754849 | − | 0.997147i | \(-0.475950\pi\) | ||||
0.0754849 | + | 0.997147i | \(0.475950\pi\) | |||||||
\(992\) | −5.33572 | − | 6.22597i | −0.169409 | − | 0.197675i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −59.4949 | + | 29.1712i | −1.88706 | + | 0.925254i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 12.6491i | − | 0.400601i | −0.979734 | − | 0.200301i | \(-0.935808\pi\) | ||
0.979734 | − | 0.200301i | \(-0.0641919\pi\) | |||||||
\(998\) | 12.2554 | + | 24.9951i | 0.387939 | + | 0.791205i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))