Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [720,2,Mod(181,720)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(720, base_ring=CyclotomicField(4))
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("720.181");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 720.t (of order \(4\), 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: | \(5.74922894553\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 4 x^{14} + 7 x^{12} - 8 x^{11} - 28 x^{10} + 28 x^{9} + 17 x^{8} + 56 x^{7} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 80) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 181.6 | ||
Root | \(1.21331 - 0.726558i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 720.181 |
Dual form | 720.2.t.c.541.6 |
$q$-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 \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(271\) | \(577\) | \(641\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.376912 | + | 1.36306i | 0.266517 | + | 0.963830i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.71587 | + | 1.02751i | −0.857937 | + | 0.513754i | ||||
\(5\) | 0.707107 | + | 0.707107i | 0.316228 | + | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.50961i | 1.70447i | 0.523158 | + | 0.852236i | \(0.324754\pi\) | ||||
−0.523158 | + | 0.852236i | \(0.675246\pi\) | |||||||
\(8\) | −2.04729 | − | 1.95156i | −0.723827 | − | 0.689982i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.697313 | + | 1.23035i | −0.220510 | + | 0.389070i | ||||
\(11\) | 1.64080 | + | 1.64080i | 0.494721 | + | 0.494721i | 0.909790 | − | 0.415069i | \(-0.136243\pi\) |
−0.415069 | + | 0.909790i | \(0.636243\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.51857 | − | 1.51857i | 0.421176 | − | 0.421176i | −0.464432 | − | 0.885609i | \(-0.653742\pi\) |
0.885609 | + | 0.464432i | \(0.153742\pi\) | |||||||
\(14\) | −6.14687 | + | 1.69972i | −1.64282 | + | 0.454270i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.88845 | − | 3.52615i | 0.472113 | − | 0.881538i | ||||
\(17\) | −1.45616 | −0.353170 | −0.176585 | − | 0.984285i | \(-0.556505\pi\) | ||||
−0.176585 | + | 0.984285i | \(0.556505\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.67964 | + | 2.67964i | −0.614752 | + | 0.614752i | −0.944181 | − | 0.329428i | \(-0.893144\pi\) |
0.329428 | + | 0.944181i | \(0.393144\pi\) | |||||||
\(20\) | −1.93986 | − | 0.486749i | −0.433767 | − | 0.108840i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.61808 | + | 2.85495i | −0.344975 | + | 0.608678i | ||||
\(23\) | − | 2.37423i | − | 0.495061i | −0.968880 | − | 0.247530i | \(-0.920381\pi\) | ||
0.968880 | − | 0.247530i | \(-0.0796190\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000i | 0.200000i | ||||||||
\(26\) | 2.64228 | + | 1.49754i | 0.518193 | + | 0.293692i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.63366 | − | 7.73792i | −0.875679 | − | 1.46233i | ||||
\(29\) | −0.924966 | + | 0.924966i | −0.171762 | + | 0.171762i | −0.787753 | − | 0.615991i | \(-0.788756\pi\) |
0.615991 | + | 0.787753i | \(0.288756\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.20435 | −1.29394 | −0.646970 | − | 0.762515i | \(-0.723964\pi\) | ||||
−0.646970 | + | 0.762515i | \(0.723964\pi\) | |||||||
\(32\) | 5.51814 | + | 1.24503i | 0.975479 | + | 0.220092i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.548843 | − | 1.98483i | −0.0941259 | − | 0.340396i | ||||
\(35\) | −3.18877 | + | 3.18877i | −0.539001 | + | 0.539001i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.21123 | − | 5.21123i | −0.856720 | − | 0.856720i | 0.134230 | − | 0.990950i | \(-0.457144\pi\) |
−0.990950 | + | 0.134230i | \(0.957144\pi\) | |||||||
\(38\) | −4.66251 | − | 2.64253i | −0.756359 | − | 0.428675i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.0676894 | − | 2.82762i | −0.0107026 | − | 0.447086i | ||||
\(41\) | 6.41166i | 1.00133i | 0.865640 | + | 0.500667i | \(0.166912\pi\) | ||||
−0.865640 | + | 0.500667i | \(0.833088\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.65800 | + | 7.65800i | 1.16783 | + | 1.16783i | 0.982716 | + | 0.185118i | \(0.0592669\pi\) |
0.185118 | + | 0.982716i | \(0.440733\pi\) | |||||||
\(44\) | −4.50135 | − | 1.12947i | −0.678604 | − | 0.170275i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.23622 | − | 0.894875i | 0.477155 | − | 0.131942i | ||||
\(47\) | 2.51027 | 0.366161 | 0.183081 | − | 0.983098i | \(-0.441393\pi\) | ||||
0.183081 | + | 0.983098i | \(0.441393\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −13.3366 | −1.90522 | ||||||||
\(50\) | −1.36306 | + | 0.376912i | −0.192766 | + | 0.0533034i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.04534 | + | 4.16603i | −0.144962 | + | 0.577724i | ||||
\(53\) | −1.50312 | − | 1.50312i | −0.206470 | − | 0.206470i | 0.596295 | − | 0.802765i | \(-0.296639\pi\) |
−0.802765 | + | 0.596295i | \(0.796639\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.32045i | 0.312889i | ||||||||
\(56\) | 8.80078 | − | 9.23248i | 1.17605 | − | 1.23374i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.60942 | − | 0.912155i | −0.211327 | − | 0.119772i | ||||
\(59\) | 5.31807 | + | 5.31807i | 0.692353 | + | 0.692353i | 0.962749 | − | 0.270396i | \(-0.0871546\pi\) |
−0.270396 | + | 0.962749i | \(0.587155\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.02169 | + | 1.02169i | −0.130815 | + | 0.130815i | −0.769483 | − | 0.638668i | \(-0.779486\pi\) |
0.638668 | + | 0.769483i | \(0.279486\pi\) | |||||||
\(62\) | −2.71541 | − | 9.81998i | −0.344857 | − | 1.24714i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.382800 | + | 7.99084i | 0.0478499 | + | 0.998855i | ||||
\(65\) | 2.14759 | 0.266375 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.22745 | − | 5.22745i | 0.638635 | − | 0.638635i | −0.311584 | − | 0.950219i | \(-0.600859\pi\) |
0.950219 | + | 0.311584i | \(0.100859\pi\) | |||||||
\(68\) | 2.49859 | − | 1.49622i | 0.302998 | − | 0.181443i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.54838 | − | 3.14461i | −0.663158 | − | 0.375853i | ||||
\(71\) | 1.92097i | 0.227978i | 0.993482 | + | 0.113989i | \(0.0363628\pi\) | ||||
−0.993482 | + | 0.113989i | \(0.963637\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1.39412i | − | 0.163169i | −0.996666 | − | 0.0815847i | \(-0.974002\pi\) | ||
0.996666 | − | 0.0815847i | \(-0.0259981\pi\) | |||||||
\(74\) | 5.13905 | − | 9.06740i | 0.597403 | − | 1.05406i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.84458 | − | 7.35129i | 0.211587 | − | 0.843250i | ||||
\(77\) | −7.39938 | + | 7.39938i | −0.843237 | + | 0.843237i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.06317 | 0.569651 | 0.284825 | − | 0.958579i | \(-0.408064\pi\) | ||||
0.284825 | + | 0.958579i | \(0.408064\pi\) | |||||||
\(80\) | 3.82870 | − | 1.15803i | 0.428062 | − | 0.129471i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −8.73949 | + | 2.41663i | −0.965115 | + | 0.266872i | ||||
\(83\) | 2.44974 | − | 2.44974i | 0.268894 | − | 0.268894i | −0.559761 | − | 0.828654i | \(-0.689107\pi\) |
0.828654 | + | 0.559761i | \(0.189107\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.02966 | − | 1.02966i | −0.111682 | − | 0.111682i | ||||
\(86\) | −7.55194 | + | 13.3247i | −0.814347 | + | 1.43684i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.157070 | − | 6.56133i | −0.0167437 | − | 0.699440i | ||||
\(89\) | − | 9.36007i | − | 0.992165i | −0.868275 | − | 0.496083i | \(-0.834771\pi\) | ||
0.868275 | − | 0.496083i | \(-0.165229\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.84817 | + | 6.84817i | 0.717883 | + | 0.717883i | ||||
\(92\) | 2.43954 | + | 4.07388i | 0.254340 | + | 0.424731i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.946152 | + | 3.42166i | 0.0975882 | + | 0.352917i | ||||
\(95\) | −3.78959 | −0.388803 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.6313 | 1.89172 | 0.945859 | − | 0.324579i | \(-0.105223\pi\) | ||||
0.945859 | + | 0.324579i | \(0.105223\pi\) | |||||||
\(98\) | −5.02671 | − | 18.1785i | −0.507774 | − | 1.83631i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.02751 | − | 1.71587i | −0.102751 | − | 0.171587i | ||||
\(101\) | 4.84108 | + | 4.84108i | 0.481705 | + | 0.481705i | 0.905676 | − | 0.423971i | \(-0.139364\pi\) |
−0.423971 | + | 0.905676i | \(0.639364\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 9.12540i | − | 0.899153i | −0.893242 | − | 0.449576i | \(-0.851575\pi\) | ||
0.893242 | − | 0.449576i | \(-0.148425\pi\) | |||||||
\(104\) | −6.07255 | + | 0.145369i | −0.595463 | + | 0.0142546i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.48230 | − | 2.61539i | 0.143974 | − | 0.254029i | ||||
\(107\) | 10.1505 | + | 10.1505i | 0.981290 | + | 0.981290i | 0.999828 | − | 0.0185385i | \(-0.00590132\pi\) |
−0.0185385 | + | 0.999828i | \(0.505901\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.35489 | − | 1.35489i | 0.129775 | − | 0.129775i | −0.639236 | − | 0.769011i | \(-0.720749\pi\) |
0.769011 | + | 0.639236i | \(0.220749\pi\) | |||||||
\(110\) | −3.16291 | + | 0.874603i | −0.301572 | + | 0.0833902i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 15.9016 | + | 8.51618i | 1.50256 | + | 0.804704i | ||||
\(113\) | 2.56039 | 0.240861 | 0.120431 | − | 0.992722i | \(-0.461572\pi\) | ||||
0.120431 | + | 0.992722i | \(0.461572\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.67883 | − | 1.67883i | 0.156552 | − | 0.156552i | ||||
\(116\) | 0.636716 | − | 2.53754i | 0.0591176 | − | 0.235604i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.24441 | + | 9.25329i | −0.482787 | + | 0.851835i | ||||
\(119\) | − | 6.56670i | − | 0.601969i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 5.61553i | − | 0.510503i | ||||||
\(122\) | −1.77772 | − | 1.00754i | −0.160947 | − | 0.0912188i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 12.3618 | − | 7.40253i | 1.11012 | − | 0.664767i | ||||
\(125\) | −0.707107 | + | 0.707107i | −0.0632456 | + | 0.0632456i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.7354 | 1.21882 | 0.609409 | − | 0.792856i | \(-0.291407\pi\) | ||||
0.609409 | + | 0.792856i | \(0.291407\pi\) | |||||||
\(128\) | −10.7477 | + | 3.53362i | −0.949973 | + | 0.312331i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.809451 | + | 2.92729i | 0.0709935 | + | 0.256741i | ||||
\(131\) | −5.20726 | + | 5.20726i | −0.454960 | + | 0.454960i | −0.896997 | − | 0.442037i | \(-0.854256\pi\) |
0.442037 | + | 0.896997i | \(0.354256\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.0841 | − | 12.0841i | −1.04783 | − | 1.04783i | ||||
\(134\) | 9.09563 | + | 5.15505i | 0.785743 | + | 0.445329i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.98118 | + | 2.84179i | 0.255634 | + | 0.243681i | ||||
\(137\) | − | 22.7563i | − | 1.94420i | −0.234559 | − | 0.972102i | \(-0.575365\pi\) | ||
0.234559 | − | 0.972102i | \(-0.424635\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.28085 | + | 6.28085i | 0.532734 | + | 0.532734i | 0.921385 | − | 0.388651i | \(-0.127059\pi\) |
−0.388651 | + | 0.921385i | \(0.627059\pi\) | |||||||
\(140\) | 2.19505 | − | 8.74803i | 0.185515 | − | 0.739343i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.61841 | + | 0.724038i | −0.219732 | + | 0.0607599i | ||||
\(143\) | 4.98336 | 0.416729 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.30810 | −0.108632 | ||||||||
\(146\) | 1.90027 | − | 0.525460i | 0.157268 | − | 0.0434874i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 14.2964 | + | 3.58723i | 1.17516 | + | 0.294869i | ||||
\(149\) | 12.9574 | + | 12.9574i | 1.06151 | + | 1.06151i | 0.997980 | + | 0.0635329i | \(0.0202368\pi\) |
0.0635329 | + | 0.997980i | \(0.479763\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.3417i | 1.16711i | 0.812073 | + | 0.583555i | \(0.198339\pi\) | ||||
−0.812073 | + | 0.583555i | \(0.801661\pi\) | |||||||
\(152\) | 10.7155 | − | 0.256515i | 0.869142 | − | 0.0208061i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −12.8747 | − | 7.29689i | −1.03747 | − | 0.588001i | ||||
\(155\) | −5.09425 | − | 5.09425i | −0.409180 | − | 0.409180i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.10564 | + | 2.10564i | −0.168049 | + | 0.168049i | −0.786121 | − | 0.618073i | \(-0.787914\pi\) |
0.618073 | + | 0.786121i | \(0.287914\pi\) | |||||||
\(158\) | 1.90837 | + | 6.90141i | 0.151822 | + | 0.549047i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.02155 | + | 4.78229i | 0.238874 | + | 0.378073i | ||||
\(161\) | 10.7068 | 0.843817 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.34004 | + | 5.34004i | −0.418265 | + | 0.418265i | −0.884605 | − | 0.466341i | \(-0.845572\pi\) |
0.466341 | + | 0.884605i | \(0.345572\pi\) | |||||||
\(164\) | −6.58804 | − | 11.0016i | −0.514439 | − | 0.859081i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.26248 | + | 2.41581i | 0.330833 | + | 0.187503i | ||||
\(167\) | 16.0686i | 1.24343i | 0.783245 | + | 0.621714i | \(0.213563\pi\) | ||||
−0.783245 | + | 0.621714i | \(0.786437\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.38787i | 0.645221i | ||||||||
\(170\) | 1.01540 | − | 1.79158i | 0.0778775 | − | 0.137408i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −21.0088 | − | 5.27151i | −1.60191 | − | 0.401949i | ||||
\(173\) | −17.1133 | + | 17.1133i | −1.30110 | + | 1.30110i | −0.373453 | + | 0.927649i | \(0.621826\pi\) |
−0.927649 | + | 0.373453i | \(0.878174\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.50961 | −0.340894 | ||||||||
\(176\) | 8.88430 | − | 2.68714i | 0.669679 | − | 0.202551i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 12.7584 | − | 3.52792i | 0.956279 | − | 0.264429i | ||||
\(179\) | −1.04482 | + | 1.04482i | −0.0780933 | + | 0.0780933i | −0.745075 | − | 0.666981i | \(-0.767586\pi\) |
0.666981 | + | 0.745075i | \(0.267586\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.9886 | + | 11.9886i | 0.891104 | + | 0.891104i | 0.994627 | − | 0.103523i | \(-0.0330115\pi\) |
−0.103523 | + | 0.994627i | \(0.533012\pi\) | |||||||
\(182\) | −6.75332 | + | 11.9156i | −0.500589 | + | 0.883245i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.63346 | + | 4.86074i | −0.341583 | + | 0.358338i | ||||
\(185\) | − | 7.36979i | − | 0.541838i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.38927 | − | 2.38927i | −0.174721 | − | 0.174721i | ||||
\(188\) | −4.30732 | + | 2.57933i | −0.314143 | + | 0.188117i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.42834 | − | 5.16544i | −0.103623 | − | 0.374741i | ||||
\(191\) | −0.0667471 | −0.00482965 | −0.00241483 | − | 0.999997i | \(-0.500769\pi\) | ||||
−0.00241483 | + | 0.999997i | \(0.500769\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.09895 | −0.0791039 | −0.0395520 | − | 0.999218i | \(-0.512593\pi\) | ||||
−0.0395520 | + | 0.999218i | \(0.512593\pi\) | |||||||
\(194\) | 7.02234 | + | 25.3956i | 0.504175 | + | 1.82329i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 22.8839 | − | 13.7034i | 1.63456 | − | 0.978816i | ||||
\(197\) | −11.9289 | − | 11.9289i | −0.849899 | − | 0.849899i | 0.140222 | − | 0.990120i | \(-0.455218\pi\) |
−0.990120 | + | 0.140222i | \(0.955218\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 11.0397i | − | 0.782584i | −0.920267 | − | 0.391292i | \(-0.872028\pi\) | ||
0.920267 | − | 0.391292i | \(-0.127972\pi\) | |||||||
\(200\) | 1.95156 | − | 2.04729i | 0.137996 | − | 0.144765i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.77403 | + | 8.42334i | −0.335899 | + | 0.592664i | ||||
\(203\) | −4.17123 | − | 4.17123i | −0.292763 | − | 0.292763i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.53373 | + | 4.53373i | −0.316649 | + | 0.316649i | ||||
\(206\) | 12.4385 | − | 3.43947i | 0.866631 | − | 0.239639i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.48696 | − | 8.22247i | −0.172440 | − | 0.570126i | ||||
\(209\) | −8.79353 | −0.608261 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.59737 | + | 8.59737i | −0.591868 | + | 0.591868i | −0.938136 | − | 0.346268i | \(-0.887449\pi\) |
0.346268 | + | 0.938136i | \(0.387449\pi\) | |||||||
\(212\) | 4.12364 | + | 1.03470i | 0.283213 | + | 0.0710634i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −10.0100 | + | 17.6617i | −0.684266 | + | 1.20733i | ||||
\(215\) | 10.8301i | 0.738603i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 32.4888i | − | 2.20548i | ||||||
\(218\) | 2.35748 | + | 1.33613i | 0.159669 | + | 0.0904941i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.38428 | − | 3.98159i | −0.160748 | − | 0.268439i | ||||
\(221\) | −2.21128 | + | 2.21128i | −0.148747 | + | 0.148747i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.4238 | −1.43465 | −0.717323 | − | 0.696741i | \(-0.754633\pi\) | ||||
−0.717323 | + | 0.696741i | \(0.754633\pi\) | |||||||
\(224\) | −5.61460 | + | 24.8847i | −0.375141 | + | 1.66268i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.965041 | + | 3.48997i | 0.0641936 | + | 0.232149i | ||||
\(227\) | 8.06331 | − | 8.06331i | 0.535181 | − | 0.535181i | −0.386929 | − | 0.922110i | \(-0.626464\pi\) |
0.922110 | + | 0.386929i | \(0.126464\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.63169 | + | 4.63169i | 0.306071 | + | 0.306071i | 0.843383 | − | 0.537313i | \(-0.180560\pi\) |
−0.537313 | + | 0.843383i | \(0.680560\pi\) | |||||||
\(230\) | 2.92112 | + | 1.65558i | 0.192613 | + | 0.109166i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.69880 | − | 0.0885445i | 0.242838 | − | 0.00581323i | ||||
\(233\) | − | 26.0672i | − | 1.70772i | −0.520502 | − | 0.853860i | \(-0.674255\pi\) | ||
0.520502 | − | 0.853860i | \(-0.325745\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.77503 | + | 1.77503i | 0.115790 | + | 0.115790i | ||||
\(236\) | −14.5895 | − | 3.66078i | −0.949695 | − | 0.238296i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 8.95082 | − | 2.47507i | 0.580196 | − | 0.160435i | ||||
\(239\) | −5.12209 | −0.331320 | −0.165660 | − | 0.986183i | \(-0.552975\pi\) | ||||
−0.165660 | + | 0.986183i | \(0.552975\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.4987 | 0.740695 | 0.370347 | − | 0.928893i | \(-0.379239\pi\) | ||||
0.370347 | + | 0.928893i | \(0.379239\pi\) | |||||||
\(242\) | 7.65432 | − | 2.11656i | 0.492038 | − | 0.136058i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.703301 | − | 2.80290i | 0.0450242 | − | 0.179437i | ||||
\(245\) | −9.43037 | − | 9.43037i | −0.602484 | − | 0.602484i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.13847i | 0.517838i | ||||||||
\(248\) | 14.7494 | + | 14.0598i | 0.936588 | + | 0.892795i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.23035 | − | 0.697313i | −0.0778140 | − | 0.0441020i | ||||
\(251\) | 19.8270 | + | 19.8270i | 1.25147 | + | 1.25147i | 0.955061 | + | 0.296408i | \(0.0957889\pi\) |
0.296408 | + | 0.955061i | \(0.404211\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.89564 | − | 3.89564i | 0.244917 | − | 0.244917i | ||||
\(254\) | 5.17703 | + | 18.7222i | 0.324836 | + | 1.17473i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.86749 | − | 13.3179i | −0.554218 | − | 0.832372i | ||||
\(257\) | 24.2494 | 1.51264 | 0.756319 | − | 0.654203i | \(-0.226996\pi\) | ||||
0.756319 | + | 0.654203i | \(0.226996\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 23.5006 | − | 23.5006i | 1.46026 | − | 1.46026i | ||||
\(260\) | −3.68499 | + | 2.20666i | −0.228533 | + | 0.136851i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9.06049 | − | 5.13514i | −0.559759 | − | 0.317250i | ||||
\(263\) | − | 22.5680i | − | 1.39160i | −0.718234 | − | 0.695802i | \(-0.755049\pi\) | ||
0.718234 | − | 0.695802i | \(-0.244951\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 2.12574i | − | 0.130583i | ||||||
\(266\) | 11.9168 | − | 21.0261i | 0.730664 | − | 1.28919i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.59840 | + | 14.3409i | −0.219807 | + | 0.876010i | ||||
\(269\) | 5.10558 | − | 5.10558i | 0.311293 | − | 0.311293i | −0.534117 | − | 0.845410i | \(-0.679356\pi\) |
0.845410 | + | 0.534117i | \(0.179356\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.67920 | 0.405733 | 0.202866 | − | 0.979206i | \(-0.434974\pi\) | ||||
0.202866 | + | 0.979206i | \(0.434974\pi\) | |||||||
\(272\) | −2.74989 | + | 5.13464i | −0.166736 | + | 0.311333i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 31.0183 | − | 8.57713i | 1.87388 | − | 0.518163i | ||||
\(275\) | −1.64080 | + | 1.64080i | −0.0989441 | + | 0.0989441i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.8524 | − | 11.8524i | −0.712141 | − | 0.712141i | 0.254842 | − | 0.966983i | \(-0.417977\pi\) |
−0.966983 | + | 0.254842i | \(0.917977\pi\) | |||||||
\(278\) | −6.19386 | + | 10.9285i | −0.371483 | + | 0.655448i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 12.7514 | − | 0.305253i | 0.762044 | − | 0.0182423i | ||||
\(281\) | − | 0.477460i | − | 0.0284829i | −0.999899 | − | 0.0142414i | \(-0.995467\pi\) | ||
0.999899 | − | 0.0142414i | \(-0.00453334\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.482914 | − | 0.482914i | −0.0287063 | − | 0.0287063i | 0.692608 | − | 0.721314i | \(-0.256462\pi\) |
−0.721314 | + | 0.692608i | \(0.756462\pi\) | |||||||
\(284\) | −1.97382 | − | 3.29615i | −0.117124 | − | 0.195591i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.87829 | + | 6.79263i | 0.111065 | + | 0.401656i | ||||
\(287\) | −28.9141 | −1.70674 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.8796 | −0.875271 | ||||||||
\(290\) | −0.493038 | − | 1.78302i | −0.0289522 | − | 0.104703i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.43247 | + | 2.39214i | 0.0838290 | + | 0.139989i | ||||
\(293\) | −7.46638 | − | 7.46638i | −0.436190 | − | 0.436190i | 0.454537 | − | 0.890728i | \(-0.349805\pi\) |
−0.890728 | + | 0.454537i | \(0.849805\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.52088i | 0.437883i | ||||||||
\(296\) | 0.498857 | + | 20.8389i | 0.0289955 | + | 1.21124i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −12.7780 | + | 22.5456i | −0.740207 | + | 1.30603i | ||||
\(299\) | −3.60544 | − | 3.60544i | −0.208508 | − | 0.208508i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −34.5346 | + | 34.5346i | −1.99054 | + | 1.99054i | ||||
\(302\) | −19.5486 | + | 5.40556i | −1.12490 | + | 0.311055i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.38845 | + | 14.5092i | 0.251695 | + | 0.832160i | ||||
\(305\) | −1.44489 | −0.0827344 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.39349 | − | 2.39349i | 0.136604 | − | 0.136604i | −0.635498 | − | 0.772102i | \(-0.719205\pi\) |
0.772102 | + | 0.635498i | \(0.219205\pi\) | |||||||
\(308\) | 5.09348 | − | 20.2993i | 0.290228 | − | 1.15666i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 5.02369 | − | 8.86386i | 0.285327 | − | 0.503433i | ||||
\(311\) | − | 20.4404i | − | 1.15907i | −0.814948 | − | 0.579534i | \(-0.803235\pi\) | ||
0.814948 | − | 0.579534i | \(-0.196765\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 2.46975i | − | 0.139598i | −0.997561 | − | 0.0697992i | \(-0.977764\pi\) | ||
0.997561 | − | 0.0697992i | \(-0.0222359\pi\) | |||||||
\(314\) | −3.66376 | − | 2.07648i | −0.206758 | − | 0.117182i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.68776 | + | 5.20245i | −0.488725 | + | 0.292660i | ||||
\(317\) | 16.2241 | − | 16.2241i | 0.911234 | − | 0.911234i | −0.0851350 | − | 0.996369i | \(-0.527132\pi\) |
0.996369 | + | 0.0851350i | \(0.0271322\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.03537 | −0.169948 | ||||||||
\(320\) | −5.37969 | + | 5.92105i | −0.300734 | + | 0.330997i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.03553 | + | 14.5941i | 0.224891 | + | 0.813296i | ||||
\(323\) | 3.90198 | − | 3.90198i | 0.217112 | − | 0.217112i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.51857 | + | 1.51857i | 0.0842353 | + | 0.0842353i | ||||
\(326\) | −9.29154 | − | 5.26608i | −0.514611 | − | 0.291661i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 12.5128 | − | 13.1265i | 0.690902 | − | 0.724792i | ||||
\(329\) | 11.3204i | 0.624111i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.42340 | + | 3.42340i | 0.188167 | + | 0.188167i | 0.794903 | − | 0.606736i | \(-0.207521\pi\) |
−0.606736 | + | 0.794903i | \(0.707521\pi\) | |||||||
\(332\) | −1.68632 | + | 6.72057i | −0.0925487 | + | 0.368839i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −21.9025 | + | 6.05645i | −1.19845 | + | 0.331394i | ||||
\(335\) | 7.39273 | 0.403908 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.40017 | −0.294166 | −0.147083 | − | 0.989124i | \(-0.546988\pi\) | ||||
−0.147083 | + | 0.989124i | \(0.546988\pi\) | |||||||
\(338\) | −11.4332 | + | 3.16149i | −0.621883 | + | 0.171962i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.82475 | + | 0.708783i | 0.153194 | + | 0.0384392i | ||||
\(341\) | −11.8209 | − | 11.8209i | −0.640139 | − | 0.640139i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 28.5754i | − | 1.54292i | ||||||
\(344\) | −0.733080 | − | 30.6232i | −0.0395250 | − | 1.65109i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −29.7767 | − | 16.8763i | −1.60081 | − | 0.907276i | ||||
\(347\) | 4.07531 | + | 4.07531i | 0.218774 | + | 0.218774i | 0.807982 | − | 0.589208i | \(-0.200560\pi\) |
−0.589208 | + | 0.807982i | \(0.700560\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.55681 | − | 1.55681i | 0.0833339 | − | 0.0833339i | −0.664211 | − | 0.747545i | \(-0.731232\pi\) |
0.747545 | + | 0.664211i | \(0.231232\pi\) | |||||||
\(350\) | −1.69972 | − | 6.14687i | −0.0908541 | − | 0.328564i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7.01133 | + | 11.0970i | 0.373705 | + | 0.591474i | ||||
\(353\) | −1.34919 | −0.0718103 | −0.0359052 | − | 0.999355i | \(-0.511431\pi\) | ||||
−0.0359052 | + | 0.999355i | \(0.511431\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.35833 | + | 1.35833i | −0.0720929 | + | 0.0720929i | ||||
\(356\) | 9.61755 | + | 16.0607i | 0.509729 | + | 0.851216i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.81795 | − | 1.03035i | −0.0960819 | − | 0.0544555i | ||||
\(359\) | − | 23.2192i | − | 1.22546i | −0.790291 | − | 0.612732i | \(-0.790071\pi\) | ||
0.790291 | − | 0.612732i | \(-0.209929\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.63903i | 0.244159i | ||||||||
\(362\) | −11.8225 | + | 20.8598i | −0.621379 | + | 1.09637i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −18.7871 | − | 4.71405i | −0.984714 | − | 0.247083i | ||||
\(365\) | 0.985792 | − | 0.985792i | 0.0515987 | − | 0.0515987i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.16452 | −0.269586 | −0.134793 | − | 0.990874i | \(-0.543037\pi\) | ||||
−0.134793 | + | 0.990874i | \(0.543037\pi\) | |||||||
\(368\) | −8.37189 | − | 4.48362i | −0.436415 | − | 0.233725i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 10.0455 | − | 2.77776i | 0.522239 | − | 0.144409i | ||||
\(371\) | 6.77849 | − | 6.77849i | 0.351922 | − | 0.351922i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.5056 | + | 18.5056i | 0.958185 | + | 0.958185i | 0.999160 | − | 0.0409750i | \(-0.0130464\pi\) |
−0.0409750 | + | 0.999160i | \(0.513046\pi\) | |||||||
\(374\) | 2.35618 | − | 4.15727i | 0.121835 | − | 0.214967i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.13926 | − | 4.89896i | −0.265037 | − | 0.252645i | ||||
\(377\) | 2.80926i | 0.144684i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.5254 | − | 13.5254i | −0.694754 | − | 0.694754i | 0.268520 | − | 0.963274i | \(-0.413465\pi\) |
−0.963274 | + | 0.268520i | \(0.913465\pi\) | |||||||
\(380\) | 6.50246 | − | 3.89383i | 0.333569 | − | 0.199749i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.0251578 | − | 0.0909805i | −0.00128718 | − | 0.00465497i | ||||
\(383\) | −21.9051 | −1.11930 | −0.559650 | − | 0.828729i | \(-0.689064\pi\) | ||||
−0.559650 | + | 0.828729i | \(0.689064\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.4643 | −0.533310 | ||||||||
\(386\) | −0.414206 | − | 1.49793i | −0.0210825 | − | 0.0762427i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −31.9689 | + | 19.1438i | −1.62298 | + | 0.971878i | ||||
\(389\) | −4.48844 | − | 4.48844i | −0.227573 | − | 0.227573i | 0.584105 | − | 0.811678i | \(-0.301446\pi\) |
−0.811678 | + | 0.584105i | \(0.801446\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.45725i | 0.174841i | ||||||||
\(392\) | 27.3038 | + | 26.0271i | 1.37905 | + | 1.31457i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 11.7637 | − | 20.7560i | 0.592646 | − | 1.04567i | ||||
\(395\) | 3.58020 | + | 3.58020i | 0.180139 | + | 0.180139i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.7892 | − | 11.7892i | 0.591682 | − | 0.591682i | −0.346404 | − | 0.938086i | \(-0.612597\pi\) |
0.938086 | + | 0.346404i | \(0.112597\pi\) | |||||||
\(398\) | 15.0478 | − | 4.16100i | 0.754278 | − | 0.208572i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.52615 | + | 1.88845i | 0.176308 | + | 0.0944227i | ||||
\(401\) | −24.9259 | −1.24474 | −0.622371 | − | 0.782722i | \(-0.713830\pi\) | ||||
−0.622371 | + | 0.782722i | \(0.713830\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.9403 | + | 10.9403i | −0.544977 | + | 0.544977i | ||||
\(404\) | −13.2809 | − | 3.33244i | −0.660751 | − | 0.165795i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.11346 | − | 7.25784i | 0.204148 | − | 0.360200i | ||||
\(407\) | − | 17.1012i | − | 0.847675i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 21.5355i | − | 1.06486i | −0.846474 | − | 0.532430i | \(-0.821279\pi\) | ||
0.846474 | − | 0.532430i | \(-0.178721\pi\) | |||||||
\(410\) | −7.88857 | − | 4.47094i | −0.389589 | − | 0.220804i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9.37643 | + | 15.6581i | 0.461943 | + | 0.771417i | ||||
\(413\) | −23.9824 | + | 23.9824i | −1.18010 | + | 1.18010i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.46445 | 0.170063 | ||||||||
\(416\) | 10.2704 | − | 6.48903i | 0.503546 | − | 0.318151i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.31439 | − | 11.9861i | −0.162112 | − | 0.586261i | ||||
\(419\) | 17.2979 | − | 17.2979i | 0.845060 | − | 0.845060i | −0.144452 | − | 0.989512i | \(-0.546142\pi\) |
0.989512 | + | 0.144452i | \(0.0461419\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.4330 | − | 19.4330i | −0.947105 | − | 0.947105i | 0.0515648 | − | 0.998670i | \(-0.483579\pi\) |
−0.998670 | + | 0.0515648i | \(0.983579\pi\) | |||||||
\(422\) | −14.9592 | − | 8.47830i | −0.728203 | − | 0.412717i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.143890 | + | 6.01077i | 0.00698791 | + | 0.291909i | ||||
\(425\) | − | 1.45616i | − | 0.0706341i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.60744 | − | 4.60744i | −0.222970 | − | 0.222970i | ||||
\(428\) | −27.8468 | − | 6.98729i | −1.34603 | − | 0.337744i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −14.7620 | + | 4.08198i | −0.711888 | + | 0.196850i | ||||
\(431\) | −28.3769 | −1.36687 | −0.683433 | − | 0.730013i | \(-0.739514\pi\) | ||||
−0.683433 | + | 0.730013i | \(0.739514\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.04007 | 0.434438 | 0.217219 | − | 0.976123i | \(-0.430301\pi\) | ||||
0.217219 | + | 0.976123i | \(0.430301\pi\) | |||||||
\(434\) | 44.2842 | − | 12.2454i | 2.12571 | − | 0.587799i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.932664 | + | 3.71699i | −0.0446665 | + | 0.178012i | ||||
\(437\) | 6.36208 | + | 6.36208i | 0.304340 | + | 0.304340i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 28.2949i | − | 1.35044i | −0.737615 | − | 0.675221i | \(-0.764048\pi\) | ||
0.737615 | − | 0.675221i | \(-0.235952\pi\) | |||||||
\(440\) | 4.52850 | − | 4.75063i | 0.215888 | − | 0.226477i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.84757 | − | 2.18066i | −0.183010 | − | 0.103723i | ||||
\(443\) | 13.1232 | + | 13.1232i | 0.623504 | + | 0.623504i | 0.946426 | − | 0.322922i | \(-0.104665\pi\) |
−0.322922 | + | 0.946426i | \(0.604665\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.61857 | − | 6.61857i | 0.313750 | − | 0.313750i | ||||
\(446\) | −8.07489 | − | 29.2020i | −0.382357 | − | 1.38275i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −36.0355 | + | 1.72628i | −1.70252 | + | 0.0815588i | ||||
\(449\) | 14.3902 | 0.679116 | 0.339558 | − | 0.940585i | \(-0.389723\pi\) | ||||
0.339558 | + | 0.940585i | \(0.389723\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.5203 | + | 10.5203i | −0.495380 | + | 0.495380i | ||||
\(452\) | −4.39331 | + | 2.63082i | −0.206644 | + | 0.123743i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 14.0299 | + | 7.95163i | 0.658458 | + | 0.373189i | ||||
\(455\) | 9.68477i | 0.454029i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.54538i | 0.212624i | 0.994333 | + | 0.106312i | \(0.0339042\pi\) | ||||
−0.994333 | + | 0.106312i | \(0.966096\pi\) | |||||||
\(458\) | −4.56754 | + | 8.05902i | −0.213427 | + | 0.376573i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.15565 | + | 4.60568i | −0.0538826 | + | 0.214741i | ||||
\(461\) | −19.8046 | + | 19.8046i | −0.922393 | + | 0.922393i | −0.997198 | − | 0.0748050i | \(-0.976167\pi\) |
0.0748050 | + | 0.997198i | \(0.476167\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.5997 | −0.678506 | −0.339253 | − | 0.940695i | \(-0.610174\pi\) | ||||
−0.339253 | + | 0.940695i | \(0.610174\pi\) | |||||||
\(464\) | 1.51481 | + | 5.00833i | 0.0703235 | + | 0.232506i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 35.5312 | − | 9.82505i | 1.64595 | − | 0.455137i | ||||
\(467\) | −19.8105 | + | 19.8105i | −0.916722 | + | 0.916722i | −0.996789 | − | 0.0800671i | \(-0.974487\pi\) |
0.0800671 | + | 0.996789i | \(0.474487\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23.5738 | + | 23.5738i | 1.08853 | + | 1.08853i | ||||
\(470\) | −1.75045 | + | 3.08851i | −0.0807421 | + | 0.142462i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.509084 | − | 21.2662i | −0.0234325 | − | 0.978855i | ||||
\(473\) | 25.1306i | 1.15550i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.67964 | − | 2.67964i | −0.122950 | − | 0.122950i | ||||
\(476\) | 6.74734 | + | 11.2676i | 0.309264 | + | 0.516451i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.93058 | − | 6.98172i | −0.0883025 | − | 0.319337i | ||||
\(479\) | −21.0378 | −0.961243 | −0.480621 | − | 0.876928i | \(-0.659589\pi\) | ||||
−0.480621 | + | 0.876928i | \(0.659589\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.8273 | −0.721661 | ||||||||
\(482\) | 4.33399 | + | 15.6734i | 0.197408 | + | 0.713904i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.77000 | + | 9.63555i | 0.262273 | + | 0.437980i | ||||
\(485\) | 13.1743 | + | 13.1743i | 0.598214 | + | 0.598214i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 10.2724i | − | 0.465485i | −0.972538 | − | 0.232743i | \(-0.925230\pi\) | ||
0.972538 | − | 0.232743i | \(-0.0747699\pi\) | |||||||
\(488\) | 4.08561 | − | 0.0978041i | 0.184947 | − | 0.00442738i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 9.29976 | − | 16.4086i | 0.420120 | − | 0.741265i | ||||
\(491\) | 5.95681 | + | 5.95681i | 0.268827 | + | 0.268827i | 0.828627 | − | 0.559801i | \(-0.189122\pi\) |
−0.559801 | + | 0.828627i | \(0.689122\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.34690 | − | 1.34690i | 0.0606612 | − | 0.0606612i | ||||
\(494\) | −11.0932 | + | 3.06748i | −0.499108 | + | 0.138013i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −13.6051 | + | 25.4036i | −0.610886 | + | 1.14066i | ||||
\(497\) | −8.66284 | −0.388581 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.81466 | + | 2.81466i | −0.126002 | + | 0.126002i | −0.767295 | − | 0.641294i | \(-0.778398\pi\) |
0.641294 | + | 0.767295i | \(0.278398\pi\) | |||||||
\(500\) | 0.486749 | − | 1.93986i | 0.0217681 | − | 0.0867534i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −19.5524 | + | 34.4985i | −0.872666 | + | 1.53974i | ||||
\(503\) | − | 5.49759i | − | 0.245125i | −0.992461 | − | 0.122563i | \(-0.960889\pi\) | ||
0.992461 | − | 0.122563i | \(-0.0391113\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.84632i | 0.304657i | ||||||||
\(506\) | 6.77831 | + | 3.84169i | 0.301333 | + | 0.170784i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −23.5682 | + | 14.1132i | −1.04567 | + | 0.626173i | ||||
\(509\) | 4.37578 | − | 4.37578i | 0.193953 | − | 0.193953i | −0.603449 | − | 0.797402i | \(-0.706207\pi\) |
0.797402 | + | 0.603449i | \(0.206207\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.28693 | 0.278118 | ||||||||
\(512\) | 14.8109 | − | 17.1066i | 0.654556 | − | 0.756013i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 9.13990 | + | 33.0535i | 0.403144 | + | 1.45793i | ||||
\(515\) | 6.45263 | − | 6.45263i | 0.284337 | − | 0.284337i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.11887 | + | 4.11887i | 0.181148 | + | 0.181148i | ||||
\(518\) | 40.8904 | + | 23.1751i | 1.79662 | + | 1.01826i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.39673 | − | 4.19115i | −0.192810 | − | 0.183794i | ||||
\(521\) | 33.8729i | 1.48400i | 0.670401 | + | 0.741999i | \(0.266122\pi\) | ||||
−0.670401 | + | 0.741999i | \(0.733878\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 27.8060 | + | 27.8060i | 1.21587 | + | 1.21587i | 0.969065 | + | 0.246804i | \(0.0793803\pi\) |
0.246804 | + | 0.969065i | \(0.420620\pi\) | |||||||
\(524\) | 3.58450 | − | 14.2855i | 0.156590 | − | 0.624065i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 30.7616 | − | 8.50615i | 1.34127 | − | 0.370886i | ||||
\(527\) | 10.4907 | 0.456981 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.3630 | 0.754915 | ||||||||
\(530\) | 2.89751 | − | 0.801215i | 0.125860 | − | 0.0348025i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 33.1514 | + | 8.31832i | 1.43730 | + | 0.360645i | ||||
\(533\) | 9.73658 | + | 9.73658i | 0.421738 | + | 0.421738i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.3550i | 0.620622i | ||||||||
\(536\) | −20.9038 | + | 0.500410i | −0.902907 | + | 0.0216144i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8.88358 | + | 5.03487i | 0.382998 | + | 0.217069i | ||||
\(539\) | −21.8827 | − | 21.8827i | −0.942553 | − | 0.942553i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.03066 | − | 3.03066i | 0.130298 | − | 0.130298i | −0.638950 | − | 0.769248i | \(-0.720631\pi\) |
0.769248 | + | 0.638950i | \(0.220631\pi\) | |||||||
\(542\) | 2.51747 | + | 9.10416i | 0.108135 | + | 0.391057i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −8.03529 | − | 1.81296i | −0.344510 | − | 0.0777301i | ||||
\(545\) | 1.91611 | 0.0820771 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.4783 | + | 18.4783i | −0.790074 | + | 0.790074i | −0.981506 | − | 0.191432i | \(-0.938687\pi\) |
0.191432 | + | 0.981506i | \(0.438687\pi\) | |||||||
\(548\) | 23.3823 | + | 39.0470i | 0.998843 | + | 1.66801i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.85495 | − | 1.61808i | −0.121736 | − | 0.0689951i | ||||
\(551\) | − | 4.95716i | − | 0.211182i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 22.8329i | 0.970953i | ||||||||
\(554\) | 11.6882 | − | 20.6228i | 0.496585 | − | 0.876181i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −17.2308 | − | 4.32353i | −0.730747 | − | 0.183358i | ||||
\(557\) | 30.2060 | − | 30.2060i | 1.27987 | − | 1.27987i | 0.339127 | − | 0.940741i | \(-0.389868\pi\) |
0.940741 | − | 0.339127i | \(-0.110132\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23.2585 | 0.983729 | ||||||||
\(560\) | 5.22225 | + | 17.2659i | 0.220680 | + | 0.729620i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.650807 | − | 0.179960i | 0.0274526 | − | 0.00759117i | ||||
\(563\) | −2.86747 | + | 2.86747i | −0.120850 | + | 0.120850i | −0.764945 | − | 0.644095i | \(-0.777234\pi\) |
0.644095 | + | 0.764945i | \(0.277234\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.81047 | + | 1.81047i | 0.0761670 | + | 0.0761670i | ||||
\(566\) | 0.476226 | − | 0.840258i | 0.0200173 | − | 0.0353187i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.74890 | − | 3.93279i | 0.157300 | − | 0.165016i | ||||
\(569\) | 35.8628i | 1.50345i | 0.659479 | + | 0.751723i | \(0.270777\pi\) | ||||
−0.659479 | + | 0.751723i | \(0.729223\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.6509 | − | 17.6509i | −0.738667 | − | 0.738667i | 0.233653 | − | 0.972320i | \(-0.424932\pi\) |
−0.972320 | + | 0.233653i | \(0.924932\pi\) | |||||||
\(572\) | −8.55082 | + | 5.12044i | −0.357528 | + | 0.214096i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −10.8981 | − | 39.4117i | −0.454876 | − | 1.64501i | ||||
\(575\) | 2.37423 | 0.0990122 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.1387 | 1.50448 | 0.752238 | − | 0.658892i | \(-0.228975\pi\) | ||||
0.752238 | + | 0.658892i | \(0.228975\pi\) | |||||||
\(578\) | −5.60830 | − | 20.2818i | −0.233274 | − | 0.843612i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.24454 | − | 1.34408i | 0.0931993 | − | 0.0558100i | ||||
\(581\) | 11.0474 | + | 11.0474i | 0.458322 | + | 0.458322i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 4.93265i | − | 0.204290i | ||||||
\(584\) | −2.72071 | + | 2.85417i | −0.112584 | + | 0.118106i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.36297 | − | 12.9913i | 0.304161 | − | 0.536666i | ||||
\(587\) | 11.4005 | + | 11.4005i | 0.470550 | + | 0.470550i | 0.902093 | − | 0.431542i | \(-0.142030\pi\) |
−0.431542 | + | 0.902093i | \(0.642030\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19.3051 | − | 19.3051i | 0.795453 | − | 0.795453i | ||||
\(590\) | −10.2514 | + | 2.83471i | −0.422045 | + | 0.116703i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −28.2167 | + | 8.53441i | −1.15970 | + | 0.350762i | ||||
\(593\) | 35.0454 | 1.43914 | 0.719572 | − | 0.694418i | \(-0.244338\pi\) | ||||
0.719572 | + | 0.694418i | \(0.244338\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.64336 | − | 4.64336i | 0.190359 | − | 0.190359i | ||||
\(596\) | −35.5472 | − | 8.91945i | −1.45607 | − | 0.365355i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.55550 | − | 6.27337i | 0.145395 | − | 0.256537i | ||||
\(599\) | 18.2753i | 0.746707i | 0.927689 | + | 0.373354i | \(0.121792\pi\) | ||||
−0.927689 | + | 0.373354i | \(0.878208\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.480142i | 0.0195854i | 0.999952 | + | 0.00979269i | \(0.00311716\pi\) | ||||
−0.999952 | + | 0.00979269i | \(0.996883\pi\) | |||||||
\(602\) | −60.0893 | − | 34.0563i | −2.44906 | − | 1.38803i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −14.7362 | − | 24.6086i | −0.599608 | − | 1.00131i | ||||
\(605\) | 3.97078 | − | 3.97078i | 0.161435 | − | 0.161435i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −38.6107 | −1.56716 | −0.783581 | − | 0.621290i | \(-0.786609\pi\) | ||||
−0.783581 | + | 0.621290i | \(0.786609\pi\) | |||||||
\(608\) | −18.1229 | + | 11.4504i | −0.734980 | + | 0.464376i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.544598 | − | 1.96948i | −0.0220501 | − | 0.0797419i | ||||
\(611\) | 3.81204 | − | 3.81204i | 0.154218 | − | 0.154218i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.53592 | − | 5.53592i | −0.223594 | − | 0.223594i | 0.586416 | − | 0.810010i | \(-0.300538\pi\) |
−0.810010 | + | 0.586416i | \(0.800538\pi\) | |||||||
\(614\) | 4.16461 | + | 2.36034i | 0.168070 | + | 0.0952557i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 29.5890 | − | 0.708322i | 1.19218 | − | 0.0285391i | ||||
\(617\) | − | 31.8836i | − | 1.28358i | −0.766879 | − | 0.641792i | \(-0.778191\pi\) | ||
0.766879 | − | 0.641792i | \(-0.221809\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.4054 | − | 29.4054i | −1.18190 | − | 1.18190i | −0.979251 | − | 0.202650i | \(-0.935045\pi\) |
−0.202650 | − | 0.979251i | \(-0.564955\pi\) | |||||||
\(620\) | 13.9755 | + | 3.50671i | 0.561269 | + | 0.140833i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 27.8615 | − | 7.70422i | 1.11714 | − | 0.308911i | ||||
\(623\) | 42.2102 | 1.69112 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 3.36642 | − | 0.930878i | 0.134549 | − | 0.0372054i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.44945 | − | 5.77658i | 0.0578395 | − | 0.230511i | ||||
\(629\) | 7.58837 | + | 7.58837i | 0.302568 | + | 0.302568i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 30.7381i | − | 1.22367i | −0.790987 | − | 0.611833i | \(-0.790432\pi\) | ||
0.790987 | − | 0.611833i | \(-0.209568\pi\) | |||||||
\(632\) | −10.3658 | − | 9.88109i | −0.412328 | − | 0.393049i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 28.2294 | + | 15.9994i | 1.12113 | + | 0.635416i | ||||
\(635\) | 9.71239 | + | 9.71239i | 0.385424 | + | 0.385424i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −20.2525 | + | 20.2525i | −0.802435 | + | 0.802435i | ||||
\(638\) | −1.14407 | − | 4.13740i | −0.0452941 | − | 0.163801i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −10.0984 | − | 5.10114i | −0.399176 | − | 0.201640i | ||||
\(641\) | −13.6348 | −0.538540 | −0.269270 | − | 0.963065i | \(-0.586782\pi\) | ||||
−0.269270 | + | 0.963065i | \(0.586782\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.9224 | − | 14.9224i | 0.588480 | − | 0.588480i | −0.348740 | − | 0.937220i | \(-0.613390\pi\) |
0.937220 | + | 0.348740i | \(0.113390\pi\) | |||||||
\(644\) | −18.3716 | + | 11.0014i | −0.723942 | + | 0.433514i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.78935 | + | 3.84794i | 0.267123 | + | 0.151395i | ||||
\(647\) | 4.87972i | 0.191841i | 0.995389 | + | 0.0959207i | \(0.0305795\pi\) | ||||
−0.995389 | + | 0.0959207i | \(0.969420\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.4518i | 0.685043i | ||||||||
\(650\) | −1.49754 | + | 2.64228i | −0.0587384 | + | 0.103639i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.67591 | − | 14.6498i | 0.143960 | − | 0.573730i | ||||
\(653\) | 10.2913 | − | 10.2913i | 0.402731 | − | 0.402731i | −0.476463 | − | 0.879194i | \(-0.658081\pi\) |
0.879194 | + | 0.476463i | \(0.158081\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.36417 | −0.287742 | ||||||||
\(656\) | 22.6085 | + | 12.1081i | 0.882713 | + | 0.472743i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −15.4303 | + | 4.26677i | −0.601537 | + | 0.166336i | ||||
\(659\) | 21.9025 | − | 21.9025i | 0.853201 | − | 0.853201i | −0.137325 | − | 0.990526i | \(-0.543851\pi\) |
0.990526 | + | 0.137325i | \(0.0438505\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.40595 | + | 5.40595i | 0.210267 | + | 0.210267i | 0.804381 | − | 0.594114i | \(-0.202497\pi\) |
−0.594114 | + | 0.804381i | \(0.702497\pi\) | |||||||
\(662\) | −3.37599 | + | 5.95663i | −0.131212 | + | 0.231511i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9.79615 | + | 0.234507i | −0.380164 | + | 0.00910063i | ||||
\(665\) | − | 17.0895i | − | 0.662704i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.19608 | + | 2.19608i | 0.0850326 | + | 0.0850326i | ||||
\(668\) | −16.5106 | − | 27.5717i | −0.638816 | − | 1.06678i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.78641 | + | 10.0768i | 0.107648 | + | 0.389299i | ||||
\(671\) | −3.35280 | −0.129433 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.3820 | 1.36388 | 0.681938 | − | 0.731410i | \(-0.261138\pi\) | ||||
0.681938 | + | 0.731410i | \(0.261138\pi\) | |||||||
\(674\) | −2.03539 | − | 7.36076i | −0.0784002 | − | 0.283526i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.61861 | − | 14.3925i | −0.331485 | − | 0.553559i | ||||
\(677\) | −5.17061 | − | 5.17061i | −0.198723 | − | 0.198723i | 0.600730 | − | 0.799452i | \(-0.294877\pi\) |
−0.799452 | + | 0.600730i | \(0.794877\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 84.0196i | 3.22438i | ||||||||
\(680\) | 0.0985665 | + | 4.11746i | 0.00377985 | + | 0.157897i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 11.6572 | − | 20.5681i | 0.446377 | − | 0.787593i | ||||
\(683\) | −26.5989 | − | 26.5989i | −1.01778 | − | 1.01778i | −0.999839 | − | 0.0179409i | \(-0.994289\pi\) |
−0.0179409 | − | 0.999839i | \(-0.505711\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.0912 | − | 16.0912i | 0.614811 | − | 0.614811i | ||||
\(686\) | 38.9500 | − | 10.7704i | 1.48712 | − | 0.411216i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 41.4651 | − | 12.5415i | 1.58084 | − | 0.478140i | ||||
\(689\) | −4.56520 | −0.173920 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.7989 | + | 21.7989i | −0.829270 | + | 0.829270i | −0.987416 | − | 0.158146i | \(-0.949448\pi\) |
0.158146 | + | 0.987416i | \(0.449448\pi\) | |||||||
\(692\) | 11.7802 | − | 46.9484i | 0.447818 | − | 1.78471i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.01887 | + | 7.09093i | −0.152554 | + | 0.269168i | ||||
\(695\) | 8.88246i | 0.336931i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 9.33640i | − | 0.353641i | ||||||
\(698\) | 2.70880 | + | 1.53524i | 0.102530 | + | 0.0581099i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 7.73792 | − | 4.63366i | 0.292466 | − | 0.175136i | ||||
\(701\) | 15.2175 | − | 15.2175i | 0.574756 | − | 0.574756i | −0.358698 | − | 0.933454i | \(-0.616779\pi\) |
0.933454 | + | 0.358698i | \(0.116779\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 27.9285 | 1.05334 | ||||||||
\(704\) | −12.4833 | + | 13.7395i | −0.470482 | + | 0.517826i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.508527 | − | 1.83903i | −0.0191387 | − | 0.0692130i | ||||
\(707\) | −21.8313 | + | 21.8313i | −0.821052 | + | 0.821052i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.87350 | + | 4.87350i | 0.183028 | + | 0.183028i | 0.792674 | − | 0.609646i | \(-0.208688\pi\) |
−0.609646 | + | 0.792674i | \(0.708688\pi\) | |||||||
\(710\) | −2.36346 | − | 1.33952i | −0.0886992 | − | 0.0502713i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −18.2668 | + | 19.1628i | −0.684576 | + | 0.718156i | ||||
\(713\) | 17.1048i | 0.640579i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.52377 | + | 3.52377i | 0.131781 | + | 0.131781i | ||||
\(716\) | 0.719218 | − | 2.86633i | 0.0268784 | − | 0.107120i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 31.6492 | − | 8.75160i | 1.18114 | − | 0.326607i | ||||
\(719\) | −9.27351 | −0.345843 | −0.172922 | − | 0.984936i | \(-0.555321\pi\) | ||||
−0.172922 | + | 0.984936i | \(0.555321\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 41.1520 | 1.53258 | ||||||||
\(722\) | −6.32328 | + | 1.74850i | −0.235328 | + | 0.0650726i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −32.8893 | − | 8.25254i | −1.22232 | − | 0.306703i | ||||
\(725\) | −0.924966 | − | 0.924966i | −0.0343524 | − | 0.0343524i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 10.6056i | − | 0.393341i | −0.980470 | − | 0.196670i | \(-0.936987\pi\) | ||
0.980470 | − | 0.196670i | \(-0.0630129\pi\) | |||||||
\(728\) | −0.655557 | − | 27.3848i | −0.0242965 | − | 1.01495i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.71525 | + | 0.972138i | 0.0634843 | + | 0.0359805i | ||||
\(731\) | −11.1513 | − | 11.1513i | −0.412445 | − | 0.412445i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.6530 | + | 29.6530i | −1.09526 | + | 1.09526i | −0.100301 | + | 0.994957i | \(0.531981\pi\) |
−0.994957 | + | 0.100301i | \(0.968019\pi\) | |||||||
\(734\) | −1.94657 | − | 7.03956i | −0.0718492 | − | 0.259835i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.95599 | − | 13.1013i | 0.108959 | − | 0.482921i | ||||
\(737\) | 17.1544 | 0.631892 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30.8751 | − | 30.8751i | 1.13576 | − | 1.13576i | 0.146559 | − | 0.989202i | \(-0.453180\pi\) |
0.989202 | − | 0.146559i | \(-0.0468197\pi\) | |||||||
\(740\) | 7.57252 | + | 12.6456i | 0.278371 | + | 0.464863i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 11.7944 | + | 6.68461i | 0.432986 | + | 0.245400i | ||||
\(743\) | 22.3956i | 0.821617i | 0.911722 | + | 0.410808i | \(0.134753\pi\) | ||||
−0.911722 | + | 0.410808i | \(0.865247\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.3245i | 0.671360i | ||||||||
\(746\) | −18.2493 | + | 32.1993i | −0.668155 | + | 1.17890i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 6.55468 | + | 1.64469i | 0.239663 | + | 0.0601359i | ||||
\(749\) | −45.7749 | + | 45.7749i | −1.67258 | + | 1.67258i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.6448 | 0.753341 | 0.376670 | − | 0.926347i | \(-0.377069\pi\) | ||||
0.376670 | + | 0.926347i | \(0.377069\pi\) | |||||||
\(752\) | 4.74054 | − | 8.85161i | 0.172870 | − | 0.322785i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.82919 | + | 1.05884i | −0.139451 | + | 0.0385608i | ||||
\(755\) | −10.1411 | + | 10.1411i | −0.369073 | + | 0.369073i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.1323 | + | 24.1323i | 0.877104 | + | 0.877104i | 0.993234 | − | 0.116130i | \(-0.0370490\pi\) |
−0.116130 | + | 0.993234i | \(0.537049\pi\) | |||||||
\(758\) | 13.3381 | − | 23.5339i | 0.484461 | − | 0.854788i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7.75839 | + | 7.39562i | 0.281426 | + | 0.268267i | ||||
\(761\) | − | 50.1874i | − | 1.81929i | −0.415383 | − | 0.909647i | \(-0.636352\pi\) | ||
0.415383 | − | 0.909647i | \(-0.363648\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.11004 | + | 6.11004i | 0.221198 | + | 0.221198i | ||||
\(764\) | 0.114530 | − | 0.0685832i | 0.00414354 | − | 0.00248125i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.25631 | − | 29.8581i | −0.298312 | − | 1.07882i | ||||
\(767\) | 16.1517 | 0.583206 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.6887 | −1.03454 | −0.517270 | − | 0.855822i | \(-0.673052\pi\) | ||||
−0.517270 | + | 0.855822i | \(0.673052\pi\) | |||||||
\(770\) | −3.94412 | − | 14.2635i | −0.142136 | − | 0.514020i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.88565 | − | 1.12918i | 0.0678662 | − | 0.0406400i | ||||
\(773\) | 37.5957 | + | 37.5957i | 1.35222 | + | 1.35222i | 0.883171 | + | 0.469052i | \(0.155404\pi\) |
0.469052 | + | 0.883171i | \(0.344596\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 7.20435i | − | 0.258788i | ||||||
\(776\) | −38.1436 | − | 36.3601i | −1.36928 | − | 1.30525i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.42628 | − | 7.80977i | 0.158690 | − | 0.279994i | ||||
\(779\) | −17.1810 | − | 17.1810i | −0.615572 | − | 0.615572i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.15194 | + | 3.15194i | −0.112785 | + | 0.112785i | ||||
\(782\) | −4.71245 | + | 1.30308i | −0.168517 | + | 0.0465980i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −25.1855 | + | 47.0267i | −0.899481 | + | 1.67953i | ||||
\(785\) | −2.97783 | −0.106283 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.13285 | + | 3.13285i | −0.111674 | + | 0.111674i | −0.760736 | − | 0.649062i | \(-0.775162\pi\) |
0.649062 | + | 0.760736i | \(0.275162\pi\) | |||||||
\(788\) | 32.7255 | + | 8.21145i | 1.16580 | + | 0.292521i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −3.53061 | + | 6.22945i | −0.125614 | + | 0.221634i | ||||
\(791\) | 11.5463i | 0.410541i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.10304i | 0.110192i | ||||||||
\(794\) | 20.5129 | + | 11.6259i | 0.727974 | + | 0.412588i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.3434 | + | 18.9428i | 0.402056 | + | 0.671408i | ||||
\(797\) | −0.0562195 | + | 0.0562195i | −0.00199140 | + | 0.00199140i | −0.708102 | − | 0.706110i | \(-0.750448\pi\) |
0.706110 | + | 0.708102i | \(0.250448\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.65536 | −0.129317 | ||||||||
\(800\) | −1.24503 | + | 5.51814i | −0.0440185 | + | 0.195096i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9.39488 | − | 33.9756i | −0.331745 | − | 1.19972i | ||||
\(803\) | 2.28748 | − | 2.28748i | 0.0807233 | − | 0.0807233i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.57088 | + | 7.57088i | 0.266838 | + | 0.266838i | ||||
\(806\) | −19.0359 | − | 10.7888i | −0.670511 | − | 0.380020i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.463423 | − | 19.3588i | −0.0163032 | − | 0.681039i | ||||
\(809\) | 3.59856i | 0.126518i | 0.997997 | + | 0.0632592i | \(0.0201495\pi\) | ||||
−0.997997 | + | 0.0632592i | \(0.979851\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.36274 | − | 7.36274i | −0.258541 | − | 0.258541i | 0.565920 | − | 0.824460i | \(-0.308521\pi\) |
−0.824460 | + | 0.565920i | \(0.808521\pi\) | |||||||
\(812\) | 11.4433 | + | 2.87134i | 0.401581 | + | 0.100764i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 23.3100 | − | 6.44564i | 0.817014 | − | 0.225920i | ||||
\(815\) | −7.55196 | −0.264534 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −41.0414 | −1.43586 | ||||||||
\(818\) | 29.3542 | − | 8.11697i | 1.02634 | − | 0.283803i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.12087 | − | 12.4378i | 0.108985 | − | 0.434345i | ||||
\(821\) | −14.7799 | − | 14.7799i | −0.515824 | − | 0.515824i | 0.400481 | − | 0.916305i | \(-0.368843\pi\) |
−0.916305 | + | 0.400481i | \(0.868843\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 52.7544i | − | 1.83890i | −0.393203 | − | 0.919452i | \(-0.628633\pi\) | ||
0.393203 | − | 0.919452i | \(-0.371367\pi\) | |||||||
\(824\) | −17.8088 | + | 18.6824i | −0.620399 | + | 0.650831i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −41.7287 | − | 23.6502i | −1.45193 | − | 0.822897i | ||||
\(827\) | −16.8883 | − | 16.8883i | −0.587265 | − | 0.587265i | 0.349625 | − | 0.936890i | \(-0.386309\pi\) |
−0.936890 | + | 0.349625i | \(0.886309\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.55974 | + | 8.55974i | −0.297292 | + | 0.297292i | −0.839952 | − | 0.542660i | \(-0.817417\pi\) |
0.542660 | + | 0.839952i | \(0.317417\pi\) | |||||||
\(830\) | 1.30579 | + | 4.72226i | 0.0453247 | + | 0.163912i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 12.7160 | + | 11.5534i | 0.440847 | + | 0.400541i | ||||
\(833\) | 19.4201 | 0.672868 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.3622 | + | 11.3622i | −0.393206 | + | 0.393206i | ||||
\(836\) | 15.0886 | − | 9.03543i | 0.521850 | − | 0.312497i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 30.0980 | + | 17.0584i | 1.03972 | + | 0.589271i | ||||
\(839\) | 17.5407i | 0.605572i | 0.953059 | + | 0.302786i | \(0.0979168\pi\) | ||||
−0.953059 | + | 0.302786i | \(0.902083\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.2889i | 0.940996i | ||||||||
\(842\) | 19.1638 | − | 33.8129i | 0.660429 | − | 1.16527i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5.91814 | − | 23.5859i | 0.203711 | − | 0.811860i | ||||
\(845\) | −5.93112 | + | 5.93112i | −0.204037 | + | 0.204037i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 25.3238 | 0.870137 | ||||||||
\(848\) | −8.13881 | + | 2.46166i | −0.279488 | + | 0.0845337i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.98483 | − | 0.548843i | 0.0680793 | − | 0.0188252i | ||||
\(851\) | −12.3726 | + | 12.3726i | −0.424129 | + | 0.424129i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.3577 | − | 15.3577i | −0.525839 | − | 0.525839i | 0.393490 | − | 0.919329i | \(-0.371268\pi\) |
−0.919329 | + | 0.393490i | \(0.871268\pi\) | |||||||
\(854\) | 4.54363 | − | 8.01683i | 0.155480 | − | 0.274330i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.971684 | − | 40.5905i | −0.0332115 | − | 1.38736i | ||||
\(857\) | 17.9553i | 0.613341i | 0.951816 | + | 0.306671i | \(0.0992150\pi\) | ||||
−0.951816 | + | 0.306671i | \(0.900785\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.3048 | − | 33.3048i | −1.13634 | − | 1.13634i | −0.989100 | − | 0.147245i | \(-0.952960\pi\) |
−0.147245 | − | 0.989100i | \(-0.547040\pi\) | |||||||
\(860\) | −11.1280 | − | 18.5830i | −0.379461 | − | 0.633676i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −10.6956 | − | 38.6795i | −0.364293 | − | 1.31743i | ||||
\(863\) | 32.3557 | 1.10140 | 0.550701 | − | 0.834703i | \(-0.314361\pi\) | ||||
0.550701 | + | 0.834703i | \(0.314361\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −24.2019 | −0.822889 | ||||||||
\(866\) | 3.40731 | + | 12.3222i | 0.115785 | + | 0.418724i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 33.3825 | + | 55.7467i | 1.13308 | + | 1.89217i | ||||
\(869\) | 8.30766 | + | 8.30766i | 0.281818 | + | 0.281818i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 15.8765i | − | 0.537956i | ||||||
\(872\) | −5.41803 | + | 0.129700i | −0.183477 | + | 0.00439221i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6.27397 | + | 11.0699i | −0.212220 | + | 0.374444i | ||||
\(875\) | −3.18877 | − | 3.18877i | −0.107800 | − | 0.107800i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.2297 | − | 26.2297i | 0.885714 | − | 0.885714i | −0.108394 | − | 0.994108i | \(-0.534571\pi\) |
0.994108 | + | 0.108394i | \(0.0345707\pi\) | |||||||
\(878\) | 38.5677 | − | 10.6647i | 1.30160 | − | 0.359916i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 8.18224 | + | 4.38205i | 0.275823 | + | 0.147719i | ||||
\(881\) | 47.3359 | 1.59479 | 0.797394 | − | 0.603459i | \(-0.206211\pi\) | ||||
0.797394 | + | 0.603459i | \(0.206211\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.08371 | − | 8.08371i | 0.272039 | − | 0.272039i | −0.557882 | − | 0.829920i | \(-0.688386\pi\) |
0.829920 | + | 0.557882i | \(0.188386\pi\) | |||||||
\(884\) | 1.52217 | − | 6.06640i | 0.0511962 | − | 0.204035i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.9415 | + | 22.8341i | −0.434778 | + | 0.767127i | ||||
\(887\) | 12.9255i | 0.433994i | 0.976172 | + | 0.216997i | \(0.0696263\pi\) | ||||
−0.976172 | + | 0.216997i | \(0.930374\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 61.9412i | 2.07744i | ||||||||
\(890\) | 11.5161 | + | 6.52690i | 0.386022 | + | 0.218782i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 36.7606 | − | 22.0132i | 1.23084 | − | 0.737055i | ||||
\(893\) | −6.72664 | + | 6.72664i | −0.225098 | + | 0.225098i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.47760 | −0.0493906 | ||||||||
\(896\) | −15.9352 | − | 48.4680i | −0.532359 | − | 1.61920i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 5.42384 | + | 19.6147i | 0.180996 | + | 0.654553i | ||||
\(899\) | 6.66378 | − | 6.66378i | 0.222250 | − | 0.222250i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.18878 | + | 2.18878i | 0.0729190 | + | 0.0729190i | ||||
\(902\) | −18.3050 | − | 10.3746i | −0.609490 | − | 0.345435i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.24186 | − | 4.99676i | −0.174342 | − | 0.166190i | ||||
\(905\) | 16.9544i | 0.563584i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.4991 | + | 16.4991i | 0.547844 | + | 0.547844i | 0.925817 | − | 0.377973i | \(-0.123379\pi\) |
−0.377973 | + | 0.925817i | \(0.623379\pi\) | |||||||
\(908\) | −5.55051 | + | 22.1207i | −0.184200 | + | 0.734103i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −13.2009 | + | 3.65031i | −0.437607 | + | 0.121006i | ||||
\(911\) | 26.6745 | 0.883765 | 0.441883 | − | 0.897073i | \(-0.354311\pi\) | ||||
0.441883 | + | 0.897073i | \(0.354311\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.03908 | 0.266055 | ||||||||
\(914\) | −6.19563 | + | 1.71321i | −0.204933 | + | 0.0566678i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −12.7065 | − | 3.18830i | −0.419834 | − | 0.105344i | ||||
\(917\) | −23.4827 | − | 23.4827i | −0.775467 | − | 0.775467i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 57.7425i | 1.90475i | 0.304932 | + | 0.952374i | \(0.401366\pi\) | ||||
−0.304932 | + | 0.952374i | \(0.598634\pi\) | |||||||
\(920\) | −6.71341 | + | 0.160710i | −0.221334 | + | 0.00529846i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −34.4595 | − | 19.5303i | −1.13486 | − | 0.643197i | ||||
\(923\) | 2.91714 | + | 2.91714i | 0.0960188 | + | 0.0960188i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.21123 | − | 5.21123i | 0.171344 | − | 0.171344i | ||||
\(926\) | −5.50280 | − | 19.9003i | −0.180833 | − | 0.653965i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.25571 | + | 3.95248i | −0.205354 | + | 0.129747i | ||||
\(929\) | −42.5386 | −1.39565 | −0.697823 | − | 0.716270i | \(-0.745848\pi\) | ||||
−0.697823 | + | 0.716270i | \(0.745848\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 35.7372 | − | 35.7372i | 1.17124 | − | 1.17124i | ||||
\(932\) | 26.7843 | + | 44.7281i | 0.877349 | + | 1.46512i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −34.4698 | − | 19.5362i | −1.12789 | − | 0.639243i | ||||
\(935\) | − | 3.37894i | − | 0.110503i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 16.6795i | − | 0.544894i | −0.962171 | − | 0.272447i | \(-0.912167\pi\) | ||
0.962171 | − | 0.272447i | \(-0.0878330\pi\) | |||||||
\(938\) | −23.2473 | + | 41.0177i | −0.759050 | + | 1.33928i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.86959 | − | 1.22187i | −0.158829 | − | 0.0398531i | ||||
\(941\) | −9.63152 | + | 9.63152i | −0.313979 | + | 0.313979i | −0.846449 | − | 0.532470i | \(-0.821264\pi\) |
0.532470 | + | 0.846449i | \(0.321264\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.2227 | 0.495721 | ||||||||
\(944\) | 28.7952 | − | 8.70938i | 0.937205 | − | 0.283466i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −34.2545 | + | 9.47200i | −1.11371 | + | 0.307961i | ||||
\(947\) | 3.44034 | − | 3.44034i | 0.111796 | − | 0.111796i | −0.648996 | − | 0.760792i | \(-0.724811\pi\) |
0.760792 | + | 0.648996i | \(0.224811\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.11707 | − | 2.11707i | −0.0687231 | − | 0.0687231i | ||||
\(950\) | 2.64253 | − | 4.66251i | 0.0857350 | − | 0.151272i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −12.8153 | + | 13.4440i | −0.415347 | + | 0.435721i | ||||
\(953\) | − | 17.6965i | − | 0.573247i | −0.958043 | − | 0.286623i | \(-0.907467\pi\) | ||
0.958043 | − | 0.286623i | \(-0.0925328\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.0471973 | − | 0.0471973i | −0.00152727 | − | 0.00152727i | ||||
\(956\) | 8.78886 | − | 5.26299i | 0.284252 | − | 0.170217i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −7.92940 | − | 28.6759i | −0.256187 | − | 0.926475i | ||||
\(959\) | 102.622 | 3.31384 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20.9027 | 0.674281 | ||||||||
\(962\) | −5.96548 | − | 21.5735i | −0.192335 | − | 0.695559i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −19.7303 | + | 11.8150i | −0.635470 | + | 0.380535i | ||||
\(965\) | −0.777073 | − | 0.777073i | −0.0250149 | − | 0.0250149i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 15.0023i | − | 0.482442i | −0.970470 | − | 0.241221i | \(-0.922452\pi\) | ||
0.970470 | − | 0.241221i | \(-0.0775479\pi\) | |||||||
\(968\) | −10.9591 | + | 11.4966i | −0.352238 | + | 0.369516i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −12.9918 | + | 22.9229i | −0.417142 | + | 0.736010i | ||||
\(971\) | 14.3135 | + | 14.3135i | 0.459340 | + | 0.459340i | 0.898439 | − | 0.439098i | \(-0.144702\pi\) |
−0.439098 | + | 0.898439i | \(0.644702\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −28.3241 | + | 28.3241i | −0.908030 | + | 0.908030i | ||||
\(974\) | 14.0019 | − | 3.87177i | 0.448649 | − | 0.124060i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.67323 | + | 5.53207i | 0.0535587 | + | 0.177077i | ||||
\(977\) | −48.1433 | −1.54024 | −0.770120 | − | 0.637900i | \(-0.779804\pi\) | ||||
−0.770120 | + | 0.637900i | \(0.779804\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.3580 | − | 15.3580i | 0.490845 | − | 0.490845i | ||||
\(980\) | 25.8711 | + | 6.49155i | 0.826422 | + | 0.207365i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −5.87430 | + | 10.3647i | −0.187457 | + | 0.330750i | ||||
\(983\) | − | 0.791292i | − | 0.0252383i | −0.999920 | − | 0.0126191i | \(-0.995983\pi\) | ||
0.999920 | − | 0.0126191i | \(-0.00401690\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 16.8700i | − | 0.537523i | ||||||
\(986\) | 2.34357 | + | 1.32824i | 0.0746343 | + | 0.0422999i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.36234 | − | 13.9646i | −0.266042 | − | 0.444273i | ||||
\(989\) | 18.1818 | − | 18.1818i | 0.578149 | − | 0.578149i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −60.2424 | −1.91366 | −0.956832 | − | 0.290643i | \(-0.906131\pi\) | ||||
−0.956832 | + | 0.290643i | \(0.906131\pi\) | |||||||
\(992\) | −39.7547 | − | 8.96964i | −1.26221 | − | 0.284786i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.26513 | − | 11.8080i | −0.103563 | − | 0.374526i | ||||
\(995\) | 7.80625 | − | 7.80625i | 0.247475 | − | 0.247475i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.15773 | + | 1.15773i | 0.0366655 | + | 0.0366655i | 0.725202 | − | 0.688536i | \(-0.241746\pi\) |
−0.688536 | + | 0.725202i | \(0.741746\pi\) | |||||||
\(998\) | −4.89744 | − | 2.77568i | −0.155026 | − | 0.0878626i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 720.2.t.c.181.6 | 16 | ||
3.2 | odd | 2 | 80.2.l.a.21.3 | ✓ | 16 | ||
4.3 | odd | 2 | 2880.2.t.c.2161.5 | 16 | |||
12.11 | even | 2 | 320.2.l.a.241.1 | 16 | |||
15.2 | even | 4 | 400.2.q.g.149.8 | 16 | |||
15.8 | even | 4 | 400.2.q.h.149.1 | 16 | |||
15.14 | odd | 2 | 400.2.l.h.101.6 | 16 | |||
16.3 | odd | 4 | 2880.2.t.c.721.8 | 16 | |||
16.13 | even | 4 | inner | 720.2.t.c.541.6 | 16 | ||
24.5 | odd | 2 | 640.2.l.b.481.1 | 16 | |||
24.11 | even | 2 | 640.2.l.a.481.8 | 16 | |||
48.5 | odd | 4 | 640.2.l.b.161.1 | 16 | |||
48.11 | even | 4 | 640.2.l.a.161.8 | 16 | |||
48.29 | odd | 4 | 80.2.l.a.61.3 | yes | 16 | ||
48.35 | even | 4 | 320.2.l.a.81.1 | 16 | |||
60.23 | odd | 4 | 1600.2.q.g.49.1 | 16 | |||
60.47 | odd | 4 | 1600.2.q.h.49.8 | 16 | |||
60.59 | even | 2 | 1600.2.l.i.1201.8 | 16 | |||
96.29 | odd | 8 | 5120.2.a.v.1.7 | 8 | |||
96.35 | even | 8 | 5120.2.a.t.1.2 | 8 | |||
96.77 | odd | 8 | 5120.2.a.s.1.2 | 8 | |||
96.83 | even | 8 | 5120.2.a.u.1.7 | 8 | |||
240.29 | odd | 4 | 400.2.l.h.301.6 | 16 | |||
240.77 | even | 4 | 400.2.q.h.349.1 | 16 | |||
240.83 | odd | 4 | 1600.2.q.h.849.8 | 16 | |||
240.173 | even | 4 | 400.2.q.g.349.8 | 16 | |||
240.179 | even | 4 | 1600.2.l.i.401.8 | 16 | |||
240.227 | odd | 4 | 1600.2.q.g.849.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.2.l.a.21.3 | ✓ | 16 | 3.2 | odd | 2 | ||
80.2.l.a.61.3 | yes | 16 | 48.29 | odd | 4 | ||
320.2.l.a.81.1 | 16 | 48.35 | even | 4 | |||
320.2.l.a.241.1 | 16 | 12.11 | even | 2 | |||
400.2.l.h.101.6 | 16 | 15.14 | odd | 2 | |||
400.2.l.h.301.6 | 16 | 240.29 | odd | 4 | |||
400.2.q.g.149.8 | 16 | 15.2 | even | 4 | |||
400.2.q.g.349.8 | 16 | 240.173 | even | 4 | |||
400.2.q.h.149.1 | 16 | 15.8 | even | 4 | |||
400.2.q.h.349.1 | 16 | 240.77 | even | 4 | |||
640.2.l.a.161.8 | 16 | 48.11 | even | 4 | |||
640.2.l.a.481.8 | 16 | 24.11 | even | 2 | |||
640.2.l.b.161.1 | 16 | 48.5 | odd | 4 | |||
640.2.l.b.481.1 | 16 | 24.5 | odd | 2 | |||
720.2.t.c.181.6 | 16 | 1.1 | even | 1 | trivial | ||
720.2.t.c.541.6 | 16 | 16.13 | even | 4 | inner | ||
1600.2.l.i.401.8 | 16 | 240.179 | even | 4 | |||
1600.2.l.i.1201.8 | 16 | 60.59 | even | 2 | |||
1600.2.q.g.49.1 | 16 | 60.23 | odd | 4 | |||
1600.2.q.g.849.1 | 16 | 240.227 | odd | 4 | |||
1600.2.q.h.49.8 | 16 | 60.47 | odd | 4 | |||
1600.2.q.h.849.8 | 16 | 240.83 | odd | 4 | |||
2880.2.t.c.721.8 | 16 | 16.3 | odd | 4 | |||
2880.2.t.c.2161.5 | 16 | 4.3 | odd | 2 | |||
5120.2.a.s.1.2 | 8 | 96.77 | odd | 8 | |||
5120.2.a.t.1.2 | 8 | 96.35 | even | 8 | |||
5120.2.a.u.1.7 | 8 | 96.83 | even | 8 | |||
5120.2.a.v.1.7 | 8 | 96.29 | odd | 8 |