Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [462,2,Mod(419,462)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(462, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("462.419");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 462.g (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: | \(3.68908857338\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.342102016.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + x^{6} + 4x^{4} + 4x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 419.8 | ||
Root | \(-1.17915 + 0.780776i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 462.419 |
Dual form | 462.2.g.e.419.4 |
$q$-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 \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 1.51022 | + | 0.848071i | 0.871928 | + | 0.489634i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.69614 | −0.758537 | −0.379269 | − | 0.925287i | \(-0.623824\pi\) | ||||
−0.379269 | + | 0.925287i | \(0.623824\pi\) | |||||||
\(6\) | −0.848071 | + | 1.51022i | −0.346223 | + | 0.616546i | ||||
\(7\) | −2.56155 | + | 0.662153i | −0.968176 | + | 0.250270i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 1.56155 | + | 2.56155i | 0.520518 | + | 0.853851i | ||||
\(10\) | − | 1.69614i | − | 0.536367i | ||||||
\(11\) | 1.00000i | 0.301511i | ||||||||
\(12\) | −1.51022 | − | 0.848071i | −0.435964 | − | 0.244817i | ||||
\(13\) | 4.34475i | 1.20502i | 0.798112 | + | 0.602509i | \(0.205832\pi\) | ||||
−0.798112 | + | 0.602509i | \(0.794168\pi\) | |||||||
\(14\) | −0.662153 | − | 2.56155i | −0.176968 | − | 0.684604i | ||||
\(15\) | −2.56155 | − | 1.43845i | −0.661390 | − | 0.371405i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.71659 | −1.14394 | −0.571970 | − | 0.820274i | \(-0.693821\pi\) | ||||
−0.571970 | + | 0.820274i | \(0.693821\pi\) | |||||||
\(18\) | −2.56155 | + | 1.56155i | −0.603764 | + | 0.368062i | ||||
\(19\) | 6.41273i | 1.47118i | 0.677426 | + | 0.735591i | \(0.263095\pi\) | ||||
−0.677426 | + | 0.735591i | \(0.736905\pi\) | |||||||
\(20\) | 1.69614 | 0.379269 | ||||||||
\(21\) | −4.43007 | − | 1.17238i | −0.966721 | − | 0.255834i | ||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | − | 6.00000i | − | 1.25109i | −0.780189 | − | 0.625543i | \(-0.784877\pi\) | ||
0.780189 | − | 0.625543i | \(-0.215123\pi\) | |||||||
\(24\) | 0.848071 | − | 1.51022i | 0.173112 | − | 0.308273i | ||||
\(25\) | −2.12311 | −0.424621 | ||||||||
\(26\) | −4.34475 | −0.852077 | ||||||||
\(27\) | 0.185917 | + | 5.19283i | 0.0357798 | + | 0.999360i | ||||
\(28\) | 2.56155 | − | 0.662153i | 0.484088 | − | 0.125135i | ||||
\(29\) | − | 2.00000i | − | 0.371391i | −0.982607 | − | 0.185695i | \(-0.940546\pi\) | ||
0.982607 | − | 0.185695i | \(-0.0594537\pi\) | |||||||
\(30\) | 1.43845 | − | 2.56155i | 0.262623 | − | 0.467673i | ||||
\(31\) | 1.32431i | 0.237853i | 0.992903 | + | 0.118926i | \(0.0379452\pi\) | ||||
−0.992903 | + | 0.118926i | \(0.962055\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | −0.848071 | + | 1.51022i | −0.147630 | + | 0.262896i | ||||
\(34\) | − | 4.71659i | − | 0.808888i | ||||||
\(35\) | 4.34475 | − | 1.12311i | 0.734398 | − | 0.189839i | ||||
\(36\) | −1.56155 | − | 2.56155i | −0.260259 | − | 0.426925i | ||||
\(37\) | 8.24621 | 1.35567 | 0.677834 | − | 0.735215i | \(-0.262919\pi\) | ||||
0.677834 | + | 0.735215i | \(0.262919\pi\) | |||||||
\(38\) | −6.41273 | −1.04028 | ||||||||
\(39\) | −3.68466 | + | 6.56155i | −0.590018 | + | 1.05069i | ||||
\(40\) | 1.69614i | 0.268183i | ||||||||
\(41\) | 7.36520 | 1.15025 | 0.575126 | − | 0.818065i | \(-0.304953\pi\) | ||||
0.575126 | + | 0.818065i | \(0.304953\pi\) | |||||||
\(42\) | 1.17238 | − | 4.43007i | 0.180902 | − | 0.683575i | ||||
\(43\) | 11.1231 | 1.69626 | 0.848129 | − | 0.529790i | \(-0.177729\pi\) | ||||
0.848129 | + | 0.529790i | \(0.177729\pi\) | |||||||
\(44\) | − | 1.00000i | − | 0.150756i | ||||||
\(45\) | −2.64861 | − | 4.34475i | −0.394832 | − | 0.647678i | ||||
\(46\) | 6.00000 | 0.884652 | ||||||||
\(47\) | −7.36520 | −1.07433 | −0.537163 | − | 0.843479i | \(-0.680504\pi\) | ||||
−0.537163 | + | 0.843479i | \(0.680504\pi\) | |||||||
\(48\) | 1.51022 | + | 0.848071i | 0.217982 | + | 0.122408i | ||||
\(49\) | 6.12311 | − | 3.39228i | 0.874729 | − | 0.484612i | ||||
\(50\) | − | 2.12311i | − | 0.300252i | ||||||
\(51\) | −7.12311 | − | 4.00000i | −0.997434 | − | 0.560112i | ||||
\(52\) | − | 4.34475i | − | 0.602509i | ||||||
\(53\) | − | 2.00000i | − | 0.274721i | −0.990521 | − | 0.137361i | \(-0.956138\pi\) | ||
0.990521 | − | 0.137361i | \(-0.0438619\pi\) | |||||||
\(54\) | −5.19283 | + | 0.185917i | −0.706654 | + | 0.0253001i | ||||
\(55\) | − | 1.69614i | − | 0.228708i | ||||||
\(56\) | 0.662153 | + | 2.56155i | 0.0884840 | + | 0.342302i | ||||
\(57\) | −5.43845 | + | 9.68466i | −0.720340 | + | 1.28276i | ||||
\(58\) | 2.00000 | 0.262613 | ||||||||
\(59\) | 11.7100 | 1.52451 | 0.762253 | − | 0.647279i | \(-0.224093\pi\) | ||||
0.762253 | + | 0.647279i | \(0.224093\pi\) | |||||||
\(60\) | 2.56155 | + | 1.43845i | 0.330695 | + | 0.185703i | ||||
\(61\) | 1.69614i | 0.217169i | 0.994087 | + | 0.108584i | \(0.0346317\pi\) | ||||
−0.994087 | + | 0.108584i | \(0.965368\pi\) | |||||||
\(62\) | −1.32431 | −0.168187 | ||||||||
\(63\) | −5.69614 | − | 5.52757i | −0.717646 | − | 0.696408i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − | 7.36932i | − | 0.914051i | ||||||
\(66\) | −1.51022 | − | 0.848071i | −0.185896 | − | 0.104390i | ||||
\(67\) | −12.0000 | −1.46603 | −0.733017 | − | 0.680211i | \(-0.761888\pi\) | ||||
−0.733017 | + | 0.680211i | \(0.761888\pi\) | |||||||
\(68\) | 4.71659 | 0.571970 | ||||||||
\(69\) | 5.08842 | − | 9.06134i | 0.612574 | − | 1.09086i | ||||
\(70\) | 1.12311 | + | 4.34475i | 0.134237 | + | 0.519298i | ||||
\(71\) | 9.36932i | 1.11193i | 0.831205 | + | 0.555967i | \(0.187652\pi\) | ||||
−0.831205 | + | 0.555967i | \(0.812348\pi\) | |||||||
\(72\) | 2.56155 | − | 1.56155i | 0.301882 | − | 0.184031i | ||||
\(73\) | 8.68951i | 1.01703i | 0.861053 | + | 0.508515i | \(0.169805\pi\) | ||||
−0.861053 | + | 0.508515i | \(0.830195\pi\) | |||||||
\(74\) | 8.24621i | 0.958603i | ||||||||
\(75\) | −3.20636 | − | 1.80054i | −0.370239 | − | 0.207909i | ||||
\(76\) | − | 6.41273i | − | 0.735591i | ||||||
\(77\) | −0.662153 | − | 2.56155i | −0.0754594 | − | 0.291916i | ||||
\(78\) | −6.56155 | − | 3.68466i | −0.742950 | − | 0.417205i | ||||
\(79\) | −6.87689 | −0.773711 | −0.386856 | − | 0.922140i | \(-0.626439\pi\) | ||||
−0.386856 | + | 0.922140i | \(0.626439\pi\) | |||||||
\(80\) | −1.69614 | −0.189634 | ||||||||
\(81\) | −4.12311 | + | 8.00000i | −0.458123 | + | 0.888889i | ||||
\(82\) | 7.36520i | 0.813351i | ||||||||
\(83\) | 6.41273 | 0.703889 | 0.351944 | − | 0.936021i | \(-0.385521\pi\) | ||||
0.351944 | + | 0.936021i | \(0.385521\pi\) | |||||||
\(84\) | 4.43007 | + | 1.17238i | 0.483360 | + | 0.127917i | ||||
\(85\) | 8.00000 | 0.867722 | ||||||||
\(86\) | 11.1231i | 1.19944i | ||||||||
\(87\) | 1.69614 | − | 3.02045i | 0.181845 | − | 0.323826i | ||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | 6.78456 | 0.719162 | 0.359581 | − | 0.933114i | \(-0.382920\pi\) | ||||
0.359581 | + | 0.933114i | \(0.382920\pi\) | |||||||
\(90\) | 4.34475 | − | 2.64861i | 0.457977 | − | 0.279188i | ||||
\(91\) | −2.87689 | − | 11.1293i | −0.301580 | − | 1.16667i | ||||
\(92\) | 6.00000i | 0.625543i | ||||||||
\(93\) | −1.12311 | + | 2.00000i | −0.116461 | + | 0.207390i | ||||
\(94\) | − | 7.36520i | − | 0.759663i | ||||||
\(95\) | − | 10.8769i | − | 1.11595i | ||||||
\(96\) | −0.848071 | + | 1.51022i | −0.0865558 | + | 0.154137i | ||||
\(97\) | − | 6.04090i | − | 0.613360i | −0.951813 | − | 0.306680i | \(-0.900782\pi\) | ||
0.951813 | − | 0.306680i | \(-0.0992181\pi\) | |||||||
\(98\) | 3.39228 | + | 6.12311i | 0.342672 | + | 0.618527i | ||||
\(99\) | −2.56155 | + | 1.56155i | −0.257446 | + | 0.156942i | ||||
\(100\) | 2.12311 | 0.212311 | ||||||||
\(101\) | −7.73704 | −0.769864 | −0.384932 | − | 0.922945i | \(-0.625775\pi\) | ||||
−0.384932 | + | 0.922945i | \(0.625775\pi\) | |||||||
\(102\) | 4.00000 | − | 7.12311i | 0.396059 | − | 0.705293i | ||||
\(103\) | − | 3.97292i | − | 0.391464i | −0.980657 | − | 0.195732i | \(-0.937292\pi\) | ||
0.980657 | − | 0.195732i | \(-0.0627082\pi\) | |||||||
\(104\) | 4.34475 | 0.426038 | ||||||||
\(105\) | 7.51403 | + | 1.98852i | 0.733294 | + | 0.194059i | ||||
\(106\) | 2.00000 | 0.194257 | ||||||||
\(107\) | 14.2462i | 1.37723i | 0.725126 | + | 0.688617i | \(0.241782\pi\) | ||||
−0.725126 | + | 0.688617i | \(0.758218\pi\) | |||||||
\(108\) | −0.185917 | − | 5.19283i | −0.0178899 | − | 0.499680i | ||||
\(109\) | 5.12311 | 0.490705 | 0.245352 | − | 0.969434i | \(-0.421096\pi\) | ||||
0.245352 | + | 0.969434i | \(0.421096\pi\) | |||||||
\(110\) | 1.69614 | 0.161721 | ||||||||
\(111\) | 12.4536 | + | 6.99337i | 1.18205 | + | 0.663781i | ||||
\(112\) | −2.56155 | + | 0.662153i | −0.242044 | + | 0.0625676i | ||||
\(113\) | 2.87689i | 0.270635i | 0.990802 | + | 0.135318i | \(0.0432055\pi\) | ||||
−0.990802 | + | 0.135318i | \(0.956794\pi\) | |||||||
\(114\) | −9.68466 | − | 5.43845i | −0.907051 | − | 0.509357i | ||||
\(115\) | 10.1768i | 0.948996i | ||||||||
\(116\) | 2.00000i | 0.185695i | ||||||||
\(117\) | −11.1293 | + | 6.78456i | −1.02891 | + | 0.627233i | ||||
\(118\) | 11.7100i | 1.07799i | ||||||||
\(119\) | 12.0818 | − | 3.12311i | 1.10754 | − | 0.286295i | ||||
\(120\) | −1.43845 | + | 2.56155i | −0.131312 | + | 0.233837i | ||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | −1.69614 | −0.153561 | ||||||||
\(123\) | 11.1231 | + | 6.24621i | 1.00294 | + | 0.563202i | ||||
\(124\) | − | 1.32431i | − | 0.118926i | ||||||
\(125\) | 12.0818 | 1.08063 | ||||||||
\(126\) | 5.52757 | − | 5.69614i | 0.492435 | − | 0.507453i | ||||
\(127\) | 14.2462 | 1.26415 | 0.632073 | − | 0.774909i | \(-0.282204\pi\) | ||||
0.632073 | + | 0.774909i | \(0.282204\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 16.7984 | + | 9.43318i | 1.47901 | + | 0.830545i | ||||
\(130\) | 7.36932 | 0.646332 | ||||||||
\(131\) | −15.8459 | −1.38446 | −0.692232 | − | 0.721675i | \(-0.743372\pi\) | ||||
−0.692232 | + | 0.721675i | \(0.743372\pi\) | |||||||
\(132\) | 0.848071 | − | 1.51022i | 0.0738151 | − | 0.131448i | ||||
\(133\) | −4.24621 | − | 16.4265i | −0.368193 | − | 1.42436i | ||||
\(134\) | − | 12.0000i | − | 1.03664i | ||||||
\(135\) | −0.315342 | − | 8.80776i | −0.0271403 | − | 0.758052i | ||||
\(136\) | 4.71659i | 0.404444i | ||||||||
\(137\) | − | 16.4924i | − | 1.40904i | −0.709683 | − | 0.704521i | \(-0.751162\pi\) | ||
0.709683 | − | 0.704521i | \(-0.248838\pi\) | |||||||
\(138\) | 9.06134 | + | 5.08842i | 0.771353 | + | 0.433155i | ||||
\(139\) | 21.1431i | 1.79334i | 0.442702 | + | 0.896669i | \(0.354020\pi\) | ||||
−0.442702 | + | 0.896669i | \(0.645980\pi\) | |||||||
\(140\) | −4.34475 | + | 1.12311i | −0.367199 | + | 0.0949197i | ||||
\(141\) | −11.1231 | − | 6.24621i | −0.936734 | − | 0.526026i | ||||
\(142\) | −9.36932 | −0.786256 | ||||||||
\(143\) | −4.34475 | −0.363327 | ||||||||
\(144\) | 1.56155 | + | 2.56155i | 0.130129 | + | 0.213463i | ||||
\(145\) | 3.39228i | 0.281714i | ||||||||
\(146\) | −8.68951 | −0.719149 | ||||||||
\(147\) | 12.1242 | + | 0.0697197i | 0.999983 | + | 0.00575038i | ||||
\(148\) | −8.24621 | −0.677834 | ||||||||
\(149\) | − | 4.24621i | − | 0.347863i | −0.984758 | − | 0.173932i | \(-0.944353\pi\) | ||
0.984758 | − | 0.173932i | \(-0.0556472\pi\) | |||||||
\(150\) | 1.80054 | − | 3.20636i | 0.147014 | − | 0.261799i | ||||
\(151\) | −1.75379 | −0.142721 | −0.0713607 | − | 0.997451i | \(-0.522734\pi\) | ||||
−0.0713607 | + | 0.997451i | \(0.522734\pi\) | |||||||
\(152\) | 6.41273 | 0.520141 | ||||||||
\(153\) | −7.36520 | − | 12.0818i | −0.595441 | − | 0.976755i | ||||
\(154\) | 2.56155 | − | 0.662153i | 0.206416 | − | 0.0533578i | ||||
\(155\) | − | 2.24621i | − | 0.180420i | ||||||
\(156\) | 3.68466 | − | 6.56155i | 0.295009 | − | 0.525345i | ||||
\(157\) | − | 24.5354i | − | 1.95814i | −0.203525 | − | 0.979070i | \(-0.565240\pi\) | ||
0.203525 | − | 0.979070i | \(-0.434760\pi\) | |||||||
\(158\) | − | 6.87689i | − | 0.547096i | ||||||
\(159\) | 1.69614 | − | 3.02045i | 0.134513 | − | 0.239537i | ||||
\(160\) | − | 1.69614i | − | 0.134092i | ||||||
\(161\) | 3.97292 | + | 15.3693i | 0.313110 | + | 1.21127i | ||||
\(162\) | −8.00000 | − | 4.12311i | −0.628539 | − | 0.323942i | ||||
\(163\) | 16.0000 | 1.25322 | 0.626608 | − | 0.779334i | \(-0.284443\pi\) | ||||
0.626608 | + | 0.779334i | \(0.284443\pi\) | |||||||
\(164\) | −7.36520 | −0.575126 | ||||||||
\(165\) | 1.43845 | − | 2.56155i | 0.111983 | − | 0.199417i | ||||
\(166\) | 6.41273i | 0.497724i | ||||||||
\(167\) | 6.04090 | 0.467459 | 0.233729 | − | 0.972302i | \(-0.424907\pi\) | ||||
0.233729 | + | 0.972302i | \(0.424907\pi\) | |||||||
\(168\) | −1.17238 | + | 4.43007i | −0.0904509 | + | 0.341787i | ||||
\(169\) | −5.87689 | −0.452069 | ||||||||
\(170\) | 8.00000i | 0.613572i | ||||||||
\(171\) | −16.4265 | + | 10.0138i | −1.25617 | + | 0.765776i | ||||
\(172\) | −11.1231 | −0.848129 | ||||||||
\(173\) | −13.0343 | −0.990977 | −0.495488 | − | 0.868615i | \(-0.665011\pi\) | ||||
−0.495488 | + | 0.868615i | \(0.665011\pi\) | |||||||
\(174\) | 3.02045 | + | 1.69614i | 0.228980 | + | 0.128584i | ||||
\(175\) | 5.43845 | − | 1.40582i | 0.411108 | − | 0.106270i | ||||
\(176\) | 1.00000i | 0.0753778i | ||||||||
\(177\) | 17.6847 | + | 9.93087i | 1.32926 | + | 0.746450i | ||||
\(178\) | 6.78456i | 0.508525i | ||||||||
\(179\) | 14.2462i | 1.06481i | 0.846489 | + | 0.532406i | \(0.178712\pi\) | ||||
−0.846489 | + | 0.532406i | \(0.821288\pi\) | |||||||
\(180\) | 2.64861 | + | 4.34475i | 0.197416 | + | 0.323839i | ||||
\(181\) | − | 3.02045i | − | 0.224508i | −0.993680 | − | 0.112254i | \(-0.964193\pi\) | ||
0.993680 | − | 0.112254i | \(-0.0358070\pi\) | |||||||
\(182\) | 11.1293 | − | 2.87689i | 0.824960 | − | 0.213250i | ||||
\(183\) | −1.43845 | + | 2.56155i | −0.106333 | + | 0.189355i | ||||
\(184\) | −6.00000 | −0.442326 | ||||||||
\(185\) | −13.9867 | −1.02833 | ||||||||
\(186\) | −2.00000 | − | 1.12311i | −0.146647 | − | 0.0823501i | ||||
\(187\) | − | 4.71659i | − | 0.344911i | ||||||
\(188\) | 7.36520 | 0.537163 | ||||||||
\(189\) | −3.91468 | − | 13.1786i | −0.284751 | − | 0.958601i | ||||
\(190\) | 10.8769 | 0.789093 | ||||||||
\(191\) | 9.36932i | 0.677940i | 0.940797 | + | 0.338970i | \(0.110079\pi\) | ||||
−0.940797 | + | 0.338970i | \(0.889921\pi\) | |||||||
\(192\) | −1.51022 | − | 0.848071i | −0.108991 | − | 0.0612042i | ||||
\(193\) | −9.36932 | −0.674418 | −0.337209 | − | 0.941430i | \(-0.609483\pi\) | ||||
−0.337209 | + | 0.941430i | \(0.609483\pi\) | |||||||
\(194\) | 6.04090 | 0.433711 | ||||||||
\(195\) | 6.24970 | − | 11.1293i | 0.447550 | − | 0.796987i | ||||
\(196\) | −6.12311 | + | 3.39228i | −0.437365 | + | 0.242306i | ||||
\(197\) | − | 14.4924i | − | 1.03254i | −0.856425 | − | 0.516271i | \(-0.827320\pi\) | ||
0.856425 | − | 0.516271i | \(-0.172680\pi\) | |||||||
\(198\) | −1.56155 | − | 2.56155i | −0.110975 | − | 0.182042i | ||||
\(199\) | − | 1.32431i | − | 0.0938776i | −0.998898 | − | 0.0469388i | \(-0.985053\pi\) | ||
0.998898 | − | 0.0469388i | \(-0.0149466\pi\) | |||||||
\(200\) | 2.12311i | 0.150126i | ||||||||
\(201\) | −18.1227 | − | 10.1768i | −1.27828 | − | 0.717819i | ||||
\(202\) | − | 7.73704i | − | 0.544376i | ||||||
\(203\) | 1.32431 | + | 5.12311i | 0.0929481 | + | 0.359572i | ||||
\(204\) | 7.12311 | + | 4.00000i | 0.498717 | + | 0.280056i | ||||
\(205\) | −12.4924 | −0.872509 | ||||||||
\(206\) | 3.97292 | 0.276807 | ||||||||
\(207\) | 15.3693 | − | 9.36932i | 1.06824 | − | 0.651213i | ||||
\(208\) | 4.34475i | 0.301255i | ||||||||
\(209\) | −6.41273 | −0.443578 | ||||||||
\(210\) | −1.98852 | + | 7.51403i | −0.137221 | + | 0.518517i | ||||
\(211\) | −1.36932 | −0.0942677 | −0.0471338 | − | 0.998889i | \(-0.515009\pi\) | ||||
−0.0471338 | + | 0.998889i | \(0.515009\pi\) | |||||||
\(212\) | 2.00000i | 0.137361i | ||||||||
\(213\) | −7.94584 | + | 14.1498i | −0.544440 | + | 0.969526i | ||||
\(214\) | −14.2462 | −0.973851 | ||||||||
\(215\) | −18.8664 | −1.28667 | ||||||||
\(216\) | 5.19283 | − | 0.185917i | 0.353327 | − | 0.0126501i | ||||
\(217\) | −0.876894 | − | 3.39228i | −0.0595275 | − | 0.230283i | ||||
\(218\) | 5.12311i | 0.346980i | ||||||||
\(219\) | −7.36932 | + | 13.1231i | −0.497972 | + | 0.886777i | ||||
\(220\) | 1.69614i | 0.114354i | ||||||||
\(221\) | − | 20.4924i | − | 1.37847i | ||||||
\(222\) | −6.99337 | + | 12.4536i | −0.469364 | + | 0.835833i | ||||
\(223\) | − | 2.06798i | − | 0.138482i | −0.997600 | − | 0.0692409i | \(-0.977942\pi\) | ||
0.997600 | − | 0.0692409i | \(-0.0220577\pi\) | |||||||
\(224\) | −0.662153 | − | 2.56155i | −0.0442420 | − | 0.171151i | ||||
\(225\) | −3.31534 | − | 5.43845i | −0.221023 | − | 0.362563i | ||||
\(226\) | −2.87689 | −0.191368 | ||||||||
\(227\) | −3.02045 | −0.200474 | −0.100237 | − | 0.994964i | \(-0.531960\pi\) | ||||
−0.100237 | + | 0.994964i | \(0.531960\pi\) | |||||||
\(228\) | 5.43845 | − | 9.68466i | 0.360170 | − | 0.641382i | ||||
\(229\) | − | 9.06134i | − | 0.598790i | −0.954129 | − | 0.299395i | \(-0.903215\pi\) | ||
0.954129 | − | 0.299395i | \(-0.0967849\pi\) | |||||||
\(230\) | −10.1768 | −0.671041 | ||||||||
\(231\) | 1.17238 | − | 4.43007i | 0.0771368 | − | 0.291477i | ||||
\(232\) | −2.00000 | −0.131306 | ||||||||
\(233\) | − | 8.87689i | − | 0.581545i | −0.956792 | − | 0.290772i | \(-0.906088\pi\) | ||
0.956792 | − | 0.290772i | \(-0.0939122\pi\) | |||||||
\(234\) | −6.78456 | − | 11.1293i | −0.443521 | − | 0.727546i | ||||
\(235\) | 12.4924 | 0.814916 | ||||||||
\(236\) | −11.7100 | −0.762253 | ||||||||
\(237\) | −10.3857 | − | 5.83209i | −0.674621 | − | 0.378835i | ||||
\(238\) | 3.12311 | + | 12.0818i | 0.202441 | + | 0.783146i | ||||
\(239\) | 19.3693i | 1.25290i | 0.779463 | + | 0.626448i | \(0.215492\pi\) | ||||
−0.779463 | + | 0.626448i | \(0.784508\pi\) | |||||||
\(240\) | −2.56155 | − | 1.43845i | −0.165348 | − | 0.0928514i | ||||
\(241\) | 12.0818i | 0.778257i | 0.921184 | + | 0.389128i | \(0.127224\pi\) | ||||
−0.921184 | + | 0.389128i | \(0.872776\pi\) | |||||||
\(242\) | − | 1.00000i | − | 0.0642824i | ||||||
\(243\) | −13.0114 | + | 8.58511i | −0.834680 | + | 0.550735i | ||||
\(244\) | − | 1.69614i | − | 0.108584i | ||||||
\(245\) | −10.3857 | + | 5.75379i | −0.663515 | + | 0.367596i | ||||
\(246\) | −6.24621 | + | 11.1231i | −0.398244 | + | 0.709183i | ||||
\(247\) | −27.8617 | −1.77280 | ||||||||
\(248\) | 1.32431 | 0.0840936 | ||||||||
\(249\) | 9.68466 | + | 5.43845i | 0.613740 | + | 0.344648i | ||||
\(250\) | 12.0818i | 0.764120i | ||||||||
\(251\) | −14.3586 | −0.906305 | −0.453152 | − | 0.891433i | \(-0.649701\pi\) | ||||
−0.453152 | + | 0.891433i | \(0.649701\pi\) | |||||||
\(252\) | 5.69614 | + | 5.52757i | 0.358823 | + | 0.348204i | ||||
\(253\) | 6.00000 | 0.377217 | ||||||||
\(254\) | 14.2462i | 0.893887i | ||||||||
\(255\) | 12.0818 | + | 6.78456i | 0.756591 | + | 0.424866i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.13595 | −0.257993 | −0.128997 | − | 0.991645i | \(-0.541176\pi\) | ||||
−0.128997 | + | 0.991645i | \(0.541176\pi\) | |||||||
\(258\) | −9.43318 | + | 16.7984i | −0.587284 | + | 1.04582i | ||||
\(259\) | −21.1231 | + | 5.46026i | −1.31253 | + | 0.339284i | ||||
\(260\) | 7.36932i | 0.457026i | ||||||||
\(261\) | 5.12311 | − | 3.12311i | 0.317112 | − | 0.193315i | ||||
\(262\) | − | 15.8459i | − | 0.978963i | ||||||
\(263\) | − | 14.2462i | − | 0.878459i | −0.898375 | − | 0.439230i | \(-0.855251\pi\) | ||
0.898375 | − | 0.439230i | \(-0.144749\pi\) | |||||||
\(264\) | 1.51022 | + | 0.848071i | 0.0929479 | + | 0.0521951i | ||||
\(265\) | 3.39228i | 0.208386i | ||||||||
\(266\) | 16.4265 | − | 4.24621i | 1.00718 | − | 0.260352i | ||||
\(267\) | 10.2462 | + | 5.75379i | 0.627058 | + | 0.352126i | ||||
\(268\) | 12.0000 | 0.733017 | ||||||||
\(269\) | −1.69614 | −0.103416 | −0.0517078 | − | 0.998662i | \(-0.516466\pi\) | ||||
−0.0517078 | + | 0.998662i | \(0.516466\pi\) | |||||||
\(270\) | 8.80776 | − | 0.315342i | 0.536023 | − | 0.0191911i | ||||
\(271\) | 13.4061i | 0.814362i | 0.913347 | + | 0.407181i | \(0.133488\pi\) | ||||
−0.913347 | + | 0.407181i | \(0.866512\pi\) | |||||||
\(272\) | −4.71659 | −0.285985 | ||||||||
\(273\) | 5.09369 | − | 19.2476i | 0.308284 | − | 1.16492i | ||||
\(274\) | 16.4924 | 0.996344 | ||||||||
\(275\) | − | 2.12311i | − | 0.128028i | ||||||
\(276\) | −5.08842 | + | 9.06134i | −0.306287 | + | 0.545429i | ||||
\(277\) | −13.6155 | −0.818078 | −0.409039 | − | 0.912517i | \(-0.634136\pi\) | ||||
−0.409039 | + | 0.912517i | \(0.634136\pi\) | |||||||
\(278\) | −21.1431 | −1.26808 | ||||||||
\(279\) | −3.39228 | + | 2.06798i | −0.203091 | + | 0.123806i | ||||
\(280\) | −1.12311 | − | 4.34475i | −0.0671184 | − | 0.259649i | ||||
\(281\) | − | 16.8769i | − | 1.00679i | −0.864056 | − | 0.503396i | \(-0.832084\pi\) | ||
0.864056 | − | 0.503396i | \(-0.167916\pi\) | |||||||
\(282\) | 6.24621 | − | 11.1231i | 0.371956 | − | 0.662371i | ||||
\(283\) | 14.3586i | 0.853528i | 0.904363 | + | 0.426764i | \(0.140347\pi\) | ||||
−0.904363 | + | 0.426764i | \(0.859653\pi\) | |||||||
\(284\) | − | 9.36932i | − | 0.555967i | ||||||
\(285\) | 9.22437 | − | 16.4265i | 0.546405 | − | 0.973025i | ||||
\(286\) | − | 4.34475i | − | 0.256911i | ||||||
\(287\) | −18.8664 | + | 4.87689i | −1.11365 | + | 0.287874i | ||||
\(288\) | −2.56155 | + | 1.56155i | −0.150941 | + | 0.0920154i | ||||
\(289\) | 5.24621 | 0.308601 | ||||||||
\(290\) | −3.39228 | −0.199202 | ||||||||
\(291\) | 5.12311 | − | 9.12311i | 0.300322 | − | 0.534806i | ||||
\(292\) | − | 8.68951i | − | 0.508515i | ||||||
\(293\) | 3.60109 | 0.210378 | 0.105189 | − | 0.994452i | \(-0.466455\pi\) | ||||
0.105189 | + | 0.994452i | \(0.466455\pi\) | |||||||
\(294\) | −0.0697197 | + | 12.1242i | −0.00406614 | + | 0.707095i | ||||
\(295\) | −19.8617 | −1.15640 | ||||||||
\(296\) | − | 8.24621i | − | 0.479301i | ||||||
\(297\) | −5.19283 | + | 0.185917i | −0.301318 | + | 0.0107880i | ||||
\(298\) | 4.24621 | 0.245976 | ||||||||
\(299\) | 26.0685 | 1.50758 | ||||||||
\(300\) | 3.20636 | + | 1.80054i | 0.185120 | + | 0.103954i | ||||
\(301\) | −28.4924 | + | 7.36520i | −1.64228 | + | 0.424523i | ||||
\(302\) | − | 1.75379i | − | 0.100919i | ||||||
\(303\) | −11.6847 | − | 6.56155i | −0.671266 | − | 0.376951i | ||||
\(304\) | 6.41273i | 0.367795i | ||||||||
\(305\) | − | 2.87689i | − | 0.164730i | ||||||
\(306\) | 12.0818 | − | 7.36520i | 0.690670 | − | 0.421041i | ||||
\(307\) | − | 27.1840i | − | 1.55147i | −0.631056 | − | 0.775737i | \(-0.717378\pi\) | ||
0.631056 | − | 0.775737i | \(-0.282622\pi\) | |||||||
\(308\) | 0.662153 | + | 2.56155i | 0.0377297 | + | 0.145958i | ||||
\(309\) | 3.36932 | − | 6.00000i | 0.191674 | − | 0.341328i | ||||
\(310\) | 2.24621 | 0.127576 | ||||||||
\(311\) | 26.9752 | 1.52962 | 0.764812 | − | 0.644253i | \(-0.222832\pi\) | ||||
0.764812 | + | 0.644253i | \(0.222832\pi\) | |||||||
\(312\) | 6.56155 | + | 3.68466i | 0.371475 | + | 0.208603i | ||||
\(313\) | − | 8.68951i | − | 0.491160i | −0.969376 | − | 0.245580i | \(-0.921022\pi\) | ||
0.969376 | − | 0.245580i | \(-0.0789784\pi\) | |||||||
\(314\) | 24.5354 | 1.38461 | ||||||||
\(315\) | 9.66146 | + | 9.37553i | 0.544362 | + | 0.528251i | ||||
\(316\) | 6.87689 | 0.386856 | ||||||||
\(317\) | 24.7386i | 1.38946i | 0.719271 | + | 0.694730i | \(0.244476\pi\) | ||||
−0.719271 | + | 0.694730i | \(0.755524\pi\) | |||||||
\(318\) | 3.02045 | + | 1.69614i | 0.169378 | + | 0.0951149i | ||||
\(319\) | 2.00000 | 0.111979 | ||||||||
\(320\) | 1.69614 | 0.0948172 | ||||||||
\(321\) | −12.0818 | + | 21.5150i | −0.674340 | + | 1.20085i | ||||
\(322\) | −15.3693 | + | 3.97292i | −0.856499 | + | 0.221402i | ||||
\(323\) | − | 30.2462i | − | 1.68294i | ||||||
\(324\) | 4.12311 | − | 8.00000i | 0.229061 | − | 0.444444i | ||||
\(325\) | − | 9.22437i | − | 0.511676i | ||||||
\(326\) | 16.0000i | 0.886158i | ||||||||
\(327\) | 7.73704 | + | 4.34475i | 0.427859 | + | 0.240265i | ||||
\(328\) | − | 7.36520i | − | 0.406675i | ||||||
\(329\) | 18.8664 | − | 4.87689i | 1.04014 | − | 0.268872i | ||||
\(330\) | 2.56155 | + | 1.43845i | 0.141009 | + | 0.0791839i | ||||
\(331\) | 20.0000 | 1.09930 | 0.549650 | − | 0.835395i | \(-0.314761\pi\) | ||||
0.549650 | + | 0.835395i | \(0.314761\pi\) | |||||||
\(332\) | −6.41273 | −0.351944 | ||||||||
\(333\) | 12.8769 | + | 21.1231i | 0.705649 | + | 1.15754i | ||||
\(334\) | 6.04090i | 0.330543i | ||||||||
\(335\) | 20.3537 | 1.11204 | ||||||||
\(336\) | −4.43007 | − | 1.17238i | −0.241680 | − | 0.0639584i | ||||
\(337\) | 21.3693 | 1.16406 | 0.582030 | − | 0.813167i | \(-0.302258\pi\) | ||||
0.582030 | + | 0.813167i | \(0.302258\pi\) | |||||||
\(338\) | − | 5.87689i | − | 0.319661i | ||||||
\(339\) | −2.43981 | + | 4.34475i | −0.132512 | + | 0.235975i | ||||
\(340\) | −8.00000 | −0.433861 | ||||||||
\(341\) | −1.32431 | −0.0717152 | ||||||||
\(342\) | −10.0138 | − | 16.4265i | −0.541485 | − | 0.888246i | ||||
\(343\) | −13.4384 | + | 12.7439i | −0.725608 | + | 0.688108i | ||||
\(344\) | − | 11.1231i | − | 0.599718i | ||||||
\(345\) | −8.63068 | + | 15.3693i | −0.464660 | + | 0.827456i | ||||
\(346\) | − | 13.0343i | − | 0.700726i | ||||||
\(347\) | − | 4.00000i | − | 0.214731i | −0.994220 | − | 0.107366i | \(-0.965758\pi\) | ||
0.994220 | − | 0.107366i | \(-0.0342415\pi\) | |||||||
\(348\) | −1.69614 | + | 3.02045i | −0.0909227 | + | 0.161913i | ||||
\(349\) | − | 31.1570i | − | 1.66779i | −0.551921 | − | 0.833897i | \(-0.686105\pi\) | ||
0.551921 | − | 0.833897i | \(-0.313895\pi\) | |||||||
\(350\) | 1.40582 | + | 5.43845i | 0.0751443 | + | 0.290697i | ||||
\(351\) | −22.5616 | + | 0.807764i | −1.20425 | + | 0.0431153i | ||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | 14.7304 | 0.784020 | 0.392010 | − | 0.919961i | \(-0.371780\pi\) | ||||
0.392010 | + | 0.919961i | \(0.371780\pi\) | |||||||
\(354\) | −9.93087 | + | 17.6847i | −0.527820 | + | 0.939929i | ||||
\(355\) | − | 15.8917i | − | 0.843443i | ||||||
\(356\) | −6.78456 | −0.359581 | ||||||||
\(357\) | 20.8948 | + | 5.52962i | 1.10587 | + | 0.292659i | ||||
\(358\) | −14.2462 | −0.752936 | ||||||||
\(359\) | − | 1.12311i | − | 0.0592752i | −0.999561 | − | 0.0296376i | \(-0.990565\pi\) | ||
0.999561 | − | 0.0296376i | \(-0.00943533\pi\) | |||||||
\(360\) | −4.34475 | + | 2.64861i | −0.228989 | + | 0.139594i | ||||
\(361\) | −22.1231 | −1.16437 | ||||||||
\(362\) | 3.02045 | 0.158751 | ||||||||
\(363\) | −1.51022 | − | 0.848071i | −0.0792662 | − | 0.0445122i | ||||
\(364\) | 2.87689 | + | 11.1293i | 0.150790 | + | 0.583335i | ||||
\(365\) | − | 14.7386i | − | 0.771455i | ||||||
\(366\) | −2.56155 | − | 1.43845i | −0.133895 | − | 0.0751888i | ||||
\(367\) | 30.3675i | 1.58517i | 0.609761 | + | 0.792586i | \(0.291266\pi\) | ||||
−0.609761 | + | 0.792586i | \(0.708734\pi\) | |||||||
\(368\) | − | 6.00000i | − | 0.312772i | ||||||
\(369\) | 11.5012 | + | 18.8664i | 0.598726 | + | 0.982143i | ||||
\(370\) | − | 13.9867i | − | 0.727136i | ||||||
\(371\) | 1.32431 | + | 5.12311i | 0.0687546 | + | 0.265978i | ||||
\(372\) | 1.12311 | − | 2.00000i | 0.0582303 | − | 0.103695i | ||||
\(373\) | 17.6155 | 0.912097 | 0.456049 | − | 0.889955i | \(-0.349264\pi\) | ||||
0.456049 | + | 0.889955i | \(0.349264\pi\) | |||||||
\(374\) | 4.71659 | 0.243889 | ||||||||
\(375\) | 18.2462 | + | 10.2462i | 0.942230 | + | 0.529112i | ||||
\(376\) | 7.36520i | 0.379831i | ||||||||
\(377\) | 8.68951 | 0.447533 | ||||||||
\(378\) | 13.1786 | − | 3.91468i | 0.677834 | − | 0.201350i | ||||
\(379\) | 30.7386 | 1.57894 | 0.789469 | − | 0.613791i | \(-0.210356\pi\) | ||||
0.789469 | + | 0.613791i | \(0.210356\pi\) | |||||||
\(380\) | 10.8769i | 0.557973i | ||||||||
\(381\) | 21.5150 | + | 12.0818i | 1.10225 | + | 0.618969i | ||||
\(382\) | −9.36932 | −0.479376 | ||||||||
\(383\) | −33.0161 | −1.68705 | −0.843523 | − | 0.537094i | \(-0.819522\pi\) | ||||
−0.843523 | + | 0.537094i | \(0.819522\pi\) | |||||||
\(384\) | 0.848071 | − | 1.51022i | 0.0432779 | − | 0.0770683i | ||||
\(385\) | 1.12311 | + | 4.34475i | 0.0572388 | + | 0.221429i | ||||
\(386\) | − | 9.36932i | − | 0.476886i | ||||||
\(387\) | 17.3693 | + | 28.4924i | 0.882932 | + | 1.44835i | ||||
\(388\) | 6.04090i | 0.306680i | ||||||||
\(389\) | 4.24621i | 0.215291i | 0.994189 | + | 0.107646i | \(0.0343312\pi\) | ||||
−0.994189 | + | 0.107646i | \(0.965669\pi\) | |||||||
\(390\) | 11.1293 | + | 6.24970i | 0.563555 | + | 0.316466i | ||||
\(391\) | 28.2995i | 1.43117i | ||||||||
\(392\) | −3.39228 | − | 6.12311i | −0.171336 | − | 0.309264i | ||||
\(393\) | −23.9309 | − | 13.4384i | −1.20715 | − | 0.677880i | ||||
\(394\) | 14.4924 | 0.730118 | ||||||||
\(395\) | 11.6642 | 0.586889 | ||||||||
\(396\) | 2.56155 | − | 1.56155i | 0.128723 | − | 0.0784710i | ||||
\(397\) | 9.06134i | 0.454776i | 0.973804 | + | 0.227388i | \(0.0730185\pi\) | ||||
−0.973804 | + | 0.227388i | \(0.926981\pi\) | |||||||
\(398\) | 1.32431 | 0.0663815 | ||||||||
\(399\) | 7.51814 | − | 28.4089i | 0.376378 | − | 1.42222i | ||||
\(400\) | −2.12311 | −0.106155 | ||||||||
\(401\) | − | 19.3693i | − | 0.967258i | −0.875273 | − | 0.483629i | \(-0.839318\pi\) | ||
0.875273 | − | 0.483629i | \(-0.160682\pi\) | |||||||
\(402\) | 10.1768 | − | 18.1227i | 0.507575 | − | 0.903877i | ||||
\(403\) | −5.75379 | −0.286617 | ||||||||
\(404\) | 7.73704 | 0.384932 | ||||||||
\(405\) | 6.99337 | − | 13.5691i | 0.347503 | − | 0.674255i | ||||
\(406\) | −5.12311 | + | 1.32431i | −0.254255 | + | 0.0657242i | ||||
\(407\) | 8.24621i | 0.408750i | ||||||||
\(408\) | −4.00000 | + | 7.12311i | −0.198030 | + | 0.352646i | ||||
\(409\) | 24.1636i | 1.19481i | 0.801939 | + | 0.597406i | \(0.203802\pi\) | ||||
−0.801939 | + | 0.597406i | \(0.796198\pi\) | |||||||
\(410\) | − | 12.4924i | − | 0.616957i | ||||||
\(411\) | 13.9867 | − | 24.9073i | 0.689915 | − | 1.22858i | ||||
\(412\) | 3.97292i | 0.195732i | ||||||||
\(413\) | −29.9957 | + | 7.75379i | −1.47599 | + | 0.381539i | ||||
\(414\) | 9.36932 | + | 15.3693i | 0.460477 | + | 0.755361i | ||||
\(415\) | −10.8769 | −0.533926 | ||||||||
\(416\) | −4.34475 | −0.213019 | ||||||||
\(417\) | −17.9309 | + | 31.9309i | −0.878078 | + | 1.56366i | ||||
\(418\) | − | 6.41273i | − | 0.313657i | ||||||
\(419\) | −22.6305 | −1.10557 | −0.552785 | − | 0.833324i | \(-0.686435\pi\) | ||||
−0.552785 | + | 0.833324i | \(0.686435\pi\) | |||||||
\(420\) | −7.51403 | − | 1.98852i | −0.366647 | − | 0.0970297i | ||||
\(421\) | −8.24621 | −0.401896 | −0.200948 | − | 0.979602i | \(-0.564402\pi\) | ||||
−0.200948 | + | 0.979602i | \(0.564402\pi\) | |||||||
\(422\) | − | 1.36932i | − | 0.0666573i | ||||||
\(423\) | −11.5012 | − | 18.8664i | −0.559205 | − | 0.917314i | ||||
\(424\) | −2.00000 | −0.0971286 | ||||||||
\(425\) | 10.0138 | 0.485741 | ||||||||
\(426\) | −14.1498 | − | 7.94584i | −0.685558 | − | 0.384977i | ||||
\(427\) | −1.12311 | − | 4.34475i | −0.0543509 | − | 0.210257i | ||||
\(428\) | − | 14.2462i | − | 0.688617i | ||||||
\(429\) | −6.56155 | − | 3.68466i | −0.316795 | − | 0.177897i | ||||
\(430\) | − | 18.8664i | − | 0.909816i | ||||||
\(431\) | 29.6155i | 1.42653i | 0.700895 | + | 0.713265i | \(0.252784\pi\) | ||||
−0.700895 | + | 0.713265i | \(0.747216\pi\) | |||||||
\(432\) | 0.185917 | + | 5.19283i | 0.00894494 | + | 0.249840i | ||||
\(433\) | − | 10.1768i | − | 0.489068i | −0.969641 | − | 0.244534i | \(-0.921365\pi\) | ||
0.969641 | − | 0.244534i | \(-0.0786350\pi\) | |||||||
\(434\) | 3.39228 | − | 0.876894i | 0.162835 | − | 0.0420923i | ||||
\(435\) | −2.87689 | + | 5.12311i | −0.137937 | + | 0.245634i | ||||
\(436\) | −5.12311 | −0.245352 | ||||||||
\(437\) | 38.4764 | 1.84057 | ||||||||
\(438\) | −13.1231 | − | 7.36932i | −0.627046 | − | 0.352120i | ||||
\(439\) | − | 36.4084i | − | 1.73768i | −0.495094 | − | 0.868839i | \(-0.664867\pi\) | ||
0.495094 | − | 0.868839i | \(-0.335133\pi\) | |||||||
\(440\) | −1.69614 | −0.0808604 | ||||||||
\(441\) | 18.2511 | + | 10.3874i | 0.869098 | + | 0.494640i | ||||
\(442\) | 20.4924 | 0.974725 | ||||||||
\(443\) | − | 22.7386i | − | 1.08035i | −0.841554 | − | 0.540173i | \(-0.818359\pi\) | ||
0.841554 | − | 0.540173i | \(-0.181641\pi\) | |||||||
\(444\) | −12.4536 | − | 6.99337i | −0.591023 | − | 0.331891i | ||||
\(445\) | −11.5076 | −0.545511 | ||||||||
\(446\) | 2.06798 | 0.0979215 | ||||||||
\(447\) | 3.60109 | − | 6.41273i | 0.170326 | − | 0.303312i | ||||
\(448\) | 2.56155 | − | 0.662153i | 0.121022 | − | 0.0312838i | ||||
\(449\) | 34.2462i | 1.61618i | 0.589060 | + | 0.808089i | \(0.299498\pi\) | ||||
−0.589060 | + | 0.808089i | \(0.700502\pi\) | |||||||
\(450\) | 5.43845 | − | 3.31534i | 0.256371 | − | 0.156287i | ||||
\(451\) | 7.36520i | 0.346814i | ||||||||
\(452\) | − | 2.87689i | − | 0.135318i | ||||||
\(453\) | −2.64861 | − | 1.48734i | −0.124443 | − | 0.0698812i | ||||
\(454\) | − | 3.02045i | − | 0.141757i | ||||||
\(455\) | 4.87962 | + | 18.8769i | 0.228760 | + | 0.884962i | ||||
\(456\) | 9.68466 | + | 5.43845i | 0.453526 | + | 0.254679i | ||||
\(457\) | −15.6155 | −0.730464 | −0.365232 | − | 0.930917i | \(-0.619010\pi\) | ||||
−0.365232 | + | 0.930917i | \(0.619010\pi\) | |||||||
\(458\) | 9.06134 | 0.423409 | ||||||||
\(459\) | −0.876894 | − | 24.4924i | −0.0409299 | − | 1.14321i | ||||
\(460\) | − | 10.1768i | − | 0.474498i | ||||||
\(461\) | −24.6984 | −1.15032 | −0.575161 | − | 0.818040i | \(-0.695060\pi\) | ||||
−0.575161 | + | 0.818040i | \(0.695060\pi\) | |||||||
\(462\) | 4.43007 | + | 1.17238i | 0.206106 | + | 0.0545439i | ||||
\(463\) | −7.36932 | −0.342481 | −0.171241 | − | 0.985229i | \(-0.554778\pi\) | ||||
−0.171241 | + | 0.985229i | \(0.554778\pi\) | |||||||
\(464\) | − | 2.00000i | − | 0.0928477i | ||||||
\(465\) | 1.90495 | − | 3.39228i | 0.0883397 | − | 0.157313i | ||||
\(466\) | 8.87689 | 0.411214 | ||||||||
\(467\) | 24.5354 | 1.13536 | 0.567682 | − | 0.823248i | \(-0.307840\pi\) | ||||
0.567682 | + | 0.823248i | \(0.307840\pi\) | |||||||
\(468\) | 11.1293 | − | 6.78456i | 0.514453 | − | 0.313617i | ||||
\(469\) | 30.7386 | − | 7.94584i | 1.41938 | − | 0.366905i | ||||
\(470\) | 12.4924i | 0.576232i | ||||||||
\(471\) | 20.8078 | − | 37.0540i | 0.958771 | − | 1.70736i | ||||
\(472\) | − | 11.7100i | − | 0.538994i | ||||||
\(473\) | 11.1231i | 0.511441i | ||||||||
\(474\) | 5.83209 | − | 10.3857i | 0.267877 | − | 0.477029i | ||||
\(475\) | − | 13.6149i | − | 0.624695i | ||||||
\(476\) | −12.0818 | + | 3.12311i | −0.553768 | + | 0.143147i | ||||
\(477\) | 5.12311 | − | 3.12311i | 0.234571 | − | 0.142997i | ||||
\(478\) | −19.3693 | −0.885932 | ||||||||
\(479\) | 26.0685 | 1.19110 | 0.595551 | − | 0.803318i | \(-0.296934\pi\) | ||||
0.595551 | + | 0.803318i | \(0.296934\pi\) | |||||||
\(480\) | 1.43845 | − | 2.56155i | 0.0656558 | − | 0.116918i | ||||
\(481\) | 35.8278i | 1.63361i | ||||||||
\(482\) | −12.0818 | −0.550311 | ||||||||
\(483\) | −7.03426 | + | 26.5804i | −0.320070 | + | 1.20945i | ||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 10.2462i | 0.465256i | ||||||||
\(486\) | −8.58511 | − | 13.0114i | −0.389428 | − | 0.590208i | ||||
\(487\) | 3.50758 | 0.158944 | 0.0794718 | − | 0.996837i | \(-0.474677\pi\) | ||||
0.0794718 | + | 0.996837i | \(0.474677\pi\) | |||||||
\(488\) | 1.69614 | 0.0767807 | ||||||||
\(489\) | 24.1636 | + | 13.5691i | 1.09272 | + | 0.613617i | ||||
\(490\) | −5.75379 | − | 10.3857i | −0.259930 | − | 0.469176i | ||||
\(491\) | 34.7386i | 1.56773i | 0.620930 | + | 0.783866i | \(0.286755\pi\) | ||||
−0.620930 | + | 0.783866i | \(0.713245\pi\) | |||||||
\(492\) | −11.1231 | − | 6.24621i | −0.501468 | − | 0.281601i | ||||
\(493\) | 9.43318i | 0.424849i | ||||||||
\(494\) | − | 27.8617i | − | 1.25356i | ||||||
\(495\) | 4.34475 | − | 2.64861i | 0.195282 | − | 0.119046i | ||||
\(496\) | 1.32431i | 0.0594631i | ||||||||
\(497\) | −6.20393 | − | 24.0000i | −0.278284 | − | 1.07655i | ||||
\(498\) | −5.43845 | + | 9.68466i | −0.243703 | + | 0.433980i | ||||
\(499\) | 24.0000 | 1.07439 | 0.537194 | − | 0.843459i | \(-0.319484\pi\) | ||||
0.537194 | + | 0.843459i | \(0.319484\pi\) | |||||||
\(500\) | −12.0818 | −0.540314 | ||||||||
\(501\) | 9.12311 | + | 5.12311i | 0.407590 | + | 0.228883i | ||||
\(502\) | − | 14.3586i | − | 0.640854i | ||||||
\(503\) | −1.16128 | −0.0517788 | −0.0258894 | − | 0.999665i | \(-0.508242\pi\) | ||||
−0.0258894 | + | 0.999665i | \(0.508242\pi\) | |||||||
\(504\) | −5.52757 | + | 5.69614i | −0.246217 | + | 0.253726i | ||||
\(505\) | 13.1231 | 0.583971 | ||||||||
\(506\) | 6.00000i | 0.266733i | ||||||||
\(507\) | −8.87543 | − | 4.98402i | −0.394172 | − | 0.221348i | ||||
\(508\) | −14.2462 | −0.632073 | ||||||||
\(509\) | 17.1702 | 0.761056 | 0.380528 | − | 0.924769i | \(-0.375742\pi\) | ||||
0.380528 | + | 0.924769i | \(0.375742\pi\) | |||||||
\(510\) | −6.78456 | + | 12.0818i | −0.300426 | + | 0.534991i | ||||
\(511\) | −5.75379 | − | 22.2586i | −0.254533 | − | 0.984664i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −33.3002 | + | 1.19224i | −1.47024 | + | 0.0526385i | ||||
\(514\) | − | 4.13595i | − | 0.182429i | ||||||
\(515\) | 6.73863i | 0.296940i | ||||||||
\(516\) | −16.7984 | − | 9.43318i | −0.739507 | − | 0.415273i | ||||
\(517\) | − | 7.36520i | − | 0.323921i | ||||||
\(518\) | −5.46026 | − | 21.1231i | −0.239910 | − | 0.928096i | ||||
\(519\) | −19.6847 | − | 11.0540i | −0.864061 | − | 0.485216i | ||||
\(520\) | −7.36932 | −0.323166 | ||||||||
\(521\) | 12.8255 | 0.561894 | 0.280947 | − | 0.959723i | \(-0.409352\pi\) | ||||
0.280947 | + | 0.959723i | \(0.409352\pi\) | |||||||
\(522\) | 3.12311 | + | 5.12311i | 0.136695 | + | 0.224232i | ||||
\(523\) | − | 17.3332i | − | 0.757930i | −0.925411 | − | 0.378965i | \(-0.876280\pi\) | ||
0.925411 | − | 0.378965i | \(-0.123720\pi\) | |||||||
\(524\) | 15.8459 | 0.692232 | ||||||||
\(525\) | 9.40551 | + | 2.48908i | 0.410490 | + | 0.108632i | ||||
\(526\) | 14.2462 | 0.621164 | ||||||||
\(527\) | − | 6.24621i | − | 0.272089i | ||||||
\(528\) | −0.848071 | + | 1.51022i | −0.0369075 | + | 0.0657241i | ||||
\(529\) | −13.0000 | −0.565217 | ||||||||
\(530\) | −3.39228 | −0.147351 | ||||||||
\(531\) | 18.2857 | + | 29.9957i | 0.793533 | + | 1.30170i | ||||
\(532\) | 4.24621 | + | 16.4265i | 0.184097 | + | 0.712181i | ||||
\(533\) | 32.0000i | 1.38607i | ||||||||
\(534\) | −5.75379 | + | 10.2462i | −0.248991 | + | 0.443397i | ||||
\(535\) | − | 24.1636i | − | 1.04468i | ||||||
\(536\) | 12.0000i | 0.518321i | ||||||||
\(537\) | −12.0818 | + | 21.5150i | −0.521368 | + | 0.928439i | ||||
\(538\) | − | 1.69614i | − | 0.0731258i | ||||||
\(539\) | 3.39228 | + | 6.12311i | 0.146116 | + | 0.263741i | ||||
\(540\) | 0.315342 | + | 8.80776i | 0.0135701 | + | 0.379026i | ||||
\(541\) | 21.6155 | 0.929324 | 0.464662 | − | 0.885488i | \(-0.346176\pi\) | ||||
0.464662 | + | 0.885488i | \(0.346176\pi\) | |||||||
\(542\) | −13.4061 | −0.575841 | ||||||||
\(543\) | 2.56155 | − | 4.56155i | 0.109927 | − | 0.195755i | ||||
\(544\) | − | 4.71659i | − | 0.202222i | ||||||
\(545\) | −8.68951 | −0.372218 | ||||||||
\(546\) | 19.2476 | + | 5.09369i | 0.823720 | + | 0.217990i | ||||
\(547\) | −19.1231 | −0.817645 | −0.408822 | − | 0.912614i | \(-0.634060\pi\) | ||||
−0.408822 | + | 0.912614i | \(0.634060\pi\) | |||||||
\(548\) | 16.4924i | 0.704521i | ||||||||
\(549\) | −4.34475 | + | 2.64861i | −0.185430 | + | 0.113040i | ||||
\(550\) | 2.12311 | 0.0905295 | ||||||||
\(551\) | 12.8255 | 0.546383 | ||||||||
\(552\) | −9.06134 | − | 5.08842i | −0.385676 | − | 0.216578i | ||||
\(553\) | 17.6155 | − | 4.55356i | 0.749088 | − | 0.193637i | ||||
\(554\) | − | 13.6155i | − | 0.578468i | ||||||
\(555\) | −21.1231 | − | 11.8617i | −0.896626 | − | 0.503503i | ||||
\(556\) | − | 21.1431i | − | 0.896669i | ||||||
\(557\) | − | 22.4924i | − | 0.953035i | −0.879165 | − | 0.476517i | \(-0.841899\pi\) | ||
0.879165 | − | 0.476517i | \(-0.158101\pi\) | |||||||
\(558\) | −2.06798 | − | 3.39228i | −0.0875444 | − | 0.143607i | ||||
\(559\) | 48.3272i | 2.04402i | ||||||||
\(560\) | 4.34475 | − | 1.12311i | 0.183599 | − | 0.0474599i | ||||
\(561\) | 4.00000 | − | 7.12311i | 0.168880 | − | 0.300738i | ||||
\(562\) | 16.8769 | 0.711909 | ||||||||
\(563\) | −26.4404 | −1.11433 | −0.557164 | − | 0.830402i | \(-0.688111\pi\) | ||||
−0.557164 | + | 0.830402i | \(0.688111\pi\) | |||||||
\(564\) | 11.1231 | + | 6.24621i | 0.468367 | + | 0.263013i | ||||
\(565\) | − | 4.87962i | − | 0.205287i | ||||||
\(566\) | −14.3586 | −0.603536 | ||||||||
\(567\) | 5.26433 | − | 23.2226i | 0.221081 | − | 0.975255i | ||||
\(568\) | 9.36932 | 0.393128 | ||||||||
\(569\) | − | 15.7538i | − | 0.660433i | −0.943905 | − | 0.330217i | \(-0.892878\pi\) | ||
0.943905 | − | 0.330217i | \(-0.107122\pi\) | |||||||
\(570\) | 16.4265 | + | 9.22437i | 0.688032 | + | 0.386366i | ||||
\(571\) | −27.1231 | −1.13507 | −0.567533 | − | 0.823350i | \(-0.692102\pi\) | ||||
−0.567533 | + | 0.823350i | \(0.692102\pi\) | |||||||
\(572\) | 4.34475 | 0.181663 | ||||||||
\(573\) | −7.94584 | + | 14.1498i | −0.331942 | + | 0.591115i | ||||
\(574\) | −4.87689 | − | 18.8664i | −0.203558 | − | 0.787466i | ||||
\(575\) | 12.7386i | 0.531238i | ||||||||
\(576\) | −1.56155 | − | 2.56155i | −0.0650647 | − | 0.106731i | ||||
\(577\) | 10.9205i | 0.454627i | 0.973822 | + | 0.227313i | \(0.0729942\pi\) | ||||
−0.973822 | + | 0.227313i | \(0.927006\pi\) | |||||||
\(578\) | 5.24621i | 0.218214i | ||||||||
\(579\) | −14.1498 | − | 7.94584i | −0.588044 | − | 0.330218i | ||||
\(580\) | − | 3.39228i | − | 0.140857i | ||||||
\(581\) | −16.4265 | + | 4.24621i | −0.681488 | + | 0.176163i | ||||
\(582\) | 9.12311 | + | 5.12311i | 0.378165 | + | 0.212360i | ||||
\(583\) | 2.00000 | 0.0828315 | ||||||||
\(584\) | 8.68951 | 0.359574 | ||||||||
\(585\) | 18.8769 | − | 11.5076i | 0.780464 | − | 0.475780i | ||||
\(586\) | 3.60109i | 0.148760i | ||||||||
\(587\) | −1.11550 | −0.0460417 | −0.0230209 | − | 0.999735i | \(-0.507328\pi\) | ||||
−0.0230209 | + | 0.999735i | \(0.507328\pi\) | |||||||
\(588\) | −12.1242 | − | 0.0697197i | −0.499992 | − | 0.00287519i | ||||
\(589\) | −8.49242 | −0.349924 | ||||||||
\(590\) | − | 19.8617i | − | 0.817695i | ||||||
\(591\) | 12.2906 | − | 21.8868i | 0.505568 | − | 0.900303i | ||||
\(592\) | 8.24621 | 0.338917 | ||||||||
\(593\) | 33.4337 | 1.37296 | 0.686479 | − | 0.727149i | \(-0.259155\pi\) | ||||
0.686479 | + | 0.727149i | \(0.259155\pi\) | |||||||
\(594\) | −0.185917 | − | 5.19283i | −0.00762827 | − | 0.213064i | ||||
\(595\) | −20.4924 | + | 5.29723i | −0.840107 | + | 0.217165i | ||||
\(596\) | 4.24621i | 0.173932i | ||||||||
\(597\) | 1.12311 | − | 2.00000i | 0.0459657 | − | 0.0818546i | ||||
\(598\) | 26.0685i | 1.06602i | ||||||||
\(599\) | 36.1080i | 1.47533i | 0.675166 | + | 0.737665i | \(0.264072\pi\) | ||||
−0.675166 | + | 0.737665i | \(0.735928\pi\) | |||||||
\(600\) | −1.80054 | + | 3.20636i | −0.0735069 | + | 0.130899i | ||||
\(601\) | 15.4741i | 0.631201i | 0.948892 | + | 0.315600i | \(0.102206\pi\) | ||||
−0.948892 | + | 0.315600i | \(0.897794\pi\) | |||||||
\(602\) | −7.36520 | − | 28.4924i | −0.300183 | − | 1.16126i | ||||
\(603\) | −18.7386 | − | 30.7386i | −0.763096 | − | 1.25177i | ||||
\(604\) | 1.75379 | 0.0713607 | ||||||||
\(605\) | 1.69614 | 0.0689579 | ||||||||
\(606\) | 6.56155 | − | 11.6847i | 0.266545 | − | 0.474657i | ||||
\(607\) | − | 21.6780i | − | 0.879883i | −0.898026 | − | 0.439941i | \(-0.854999\pi\) | ||
0.898026 | − | 0.439941i | \(-0.145001\pi\) | |||||||
\(608\) | −6.41273 | −0.260071 | ||||||||
\(609\) | −2.34475 | + | 8.86014i | −0.0950143 | + | 0.359031i | ||||
\(610\) | 2.87689 | 0.116482 | ||||||||
\(611\) | − | 32.0000i | − | 1.29458i | ||||||
\(612\) | 7.36520 | + | 12.0818i | 0.297721 | + | 0.488377i | ||||
\(613\) | 35.3693 | 1.42855 | 0.714277 | − | 0.699863i | \(-0.246756\pi\) | ||||
0.714277 | + | 0.699863i | \(0.246756\pi\) | |||||||
\(614\) | 27.1840 | 1.09706 | ||||||||
\(615\) | −18.8664 | − | 10.5945i | −0.760765 | − | 0.427210i | ||||
\(616\) | −2.56155 | + | 0.662153i | −0.103208 | + | 0.0266789i | ||||
\(617\) | − | 21.6155i | − | 0.870208i | −0.900380 | − | 0.435104i | \(-0.856712\pi\) | ||
0.900380 | − | 0.435104i | \(-0.143288\pi\) | |||||||
\(618\) | 6.00000 | + | 3.36932i | 0.241355 | + | 0.135534i | ||||
\(619\) | − | 34.5492i | − | 1.38865i | −0.719661 | − | 0.694325i | \(-0.755703\pi\) | ||
0.719661 | − | 0.694325i | \(-0.244297\pi\) | |||||||
\(620\) | 2.24621i | 0.0902100i | ||||||||
\(621\) | 31.1570 | − | 1.11550i | 1.25029 | − | 0.0447636i | ||||
\(622\) | 26.9752i | 1.08161i | ||||||||
\(623\) | −17.3790 | + | 4.49242i | −0.696276 | + | 0.179985i | ||||
\(624\) | −3.68466 | + | 6.56155i | −0.147504 | + | 0.262672i | ||||
\(625\) | −9.87689 | −0.395076 | ||||||||
\(626\) | 8.68951 | 0.347303 | ||||||||
\(627\) | −9.68466 | − | 5.43845i | −0.386768 | − | 0.217191i | ||||
\(628\) | 24.5354i | 0.979070i | ||||||||
\(629\) | −38.8940 | −1.55080 | ||||||||
\(630\) | −9.37553 | + | 9.66146i | −0.373530 | + | 0.384922i | ||||
\(631\) | 18.8769 | 0.751477 | 0.375739 | − | 0.926726i | \(-0.377389\pi\) | ||||
0.375739 | + | 0.926726i | \(0.377389\pi\) | |||||||
\(632\) | 6.87689i | 0.273548i | ||||||||
\(633\) | −2.06798 | − | 1.16128i | −0.0821946 | − | 0.0461566i | ||||
\(634\) | −24.7386 | −0.982497 | ||||||||
\(635\) | −24.1636 | −0.958903 | ||||||||
\(636\) | −1.69614 | + | 3.02045i | −0.0672564 | + | 0.119769i | ||||
\(637\) | 14.7386 | + | 26.6034i | 0.583966 | + | 1.05406i | ||||
\(638\) | 2.00000i | 0.0791808i | ||||||||
\(639\) | −24.0000 | + | 14.6307i | −0.949425 | + | 0.578781i | ||||
\(640\) | 1.69614i | 0.0670459i | ||||||||
\(641\) | − | 12.6307i | − | 0.498882i | −0.968390 | − | 0.249441i | \(-0.919753\pi\) | ||
0.968390 | − | 0.249441i | \(-0.0802469\pi\) | |||||||
\(642\) | −21.5150 | − | 12.0818i | −0.849128 | − | 0.476830i | ||||
\(643\) | 25.1161i | 0.990481i | 0.868756 | + | 0.495240i | \(0.164920\pi\) | ||||
−0.868756 | + | 0.495240i | \(0.835080\pi\) | |||||||
\(644\) | −3.97292 | − | 15.3693i | −0.156555 | − | 0.605636i | ||||
\(645\) | −28.4924 | − | 16.0000i | −1.12189 | − | 0.629999i | ||||
\(646\) | 30.2462 | 1.19002 | ||||||||
\(647\) | −28.8802 | −1.13540 | −0.567698 | − | 0.823237i | \(-0.692166\pi\) | ||||
−0.567698 | + | 0.823237i | \(0.692166\pi\) | |||||||
\(648\) | 8.00000 | + | 4.12311i | 0.314270 | + | 0.161971i | ||||
\(649\) | 11.7100i | 0.459656i | ||||||||
\(650\) | 9.22437 | 0.361810 | ||||||||
\(651\) | 1.55259 | − | 5.86677i | 0.0608507 | − | 0.229937i | ||||
\(652\) | −16.0000 | −0.626608 | ||||||||
\(653\) | 6.49242i | 0.254068i | 0.991898 | + | 0.127034i | \(0.0405458\pi\) | ||||
−0.991898 | + | 0.127034i | \(0.959454\pi\) | |||||||
\(654\) | −4.34475 | + | 7.73704i | −0.169893 | + | 0.302542i | ||||
\(655\) | 26.8769 | 1.05017 | ||||||||
\(656\) | 7.36520 | 0.287563 | ||||||||
\(657\) | −22.2586 | + | 13.5691i | −0.868392 | + | 0.529382i | ||||
\(658\) | 4.87689 | + | 18.8664i | 0.190121 | + | 0.735487i | ||||
\(659\) | 7.50758i | 0.292454i | 0.989251 | + | 0.146227i | \(0.0467129\pi\) | ||||
−0.989251 | + | 0.146227i | \(0.953287\pi\) | |||||||
\(660\) | −1.43845 | + | 2.56155i | −0.0559915 | + | 0.0997083i | ||||
\(661\) | − | 15.1022i | − | 0.587409i | −0.955896 | − | 0.293705i | \(-0.905112\pi\) | ||
0.955896 | − | 0.293705i | \(-0.0948882\pi\) | |||||||
\(662\) | 20.0000i | 0.777322i | ||||||||
\(663\) | 17.3790 | − | 30.9481i | 0.674945 | − | 1.20193i | ||||
\(664\) | − | 6.41273i | − | 0.248862i | ||||||
\(665\) | 7.20217 | + | 27.8617i | 0.279288 | + | 1.08043i | ||||
\(666\) | −21.1231 | + | 12.8769i | −0.818504 | + | 0.498970i | ||||
\(667\) | −12.0000 | −0.464642 | ||||||||
\(668\) | −6.04090 | −0.233729 | ||||||||
\(669\) | 1.75379 | − | 3.12311i | 0.0678054 | − | 0.120746i | ||||
\(670\) | 20.3537i | 0.786332i | ||||||||
\(671\) | −1.69614 | −0.0654788 | ||||||||
\(672\) | 1.17238 | − | 4.43007i | 0.0452254 | − | 0.170894i | ||||
\(673\) | −2.49242 | −0.0960758 | −0.0480379 | − | 0.998846i | \(-0.515297\pi\) | ||||
−0.0480379 | + | 0.998846i | \(0.515297\pi\) | |||||||
\(674\) | 21.3693i | 0.823115i | ||||||||
\(675\) | −0.394722 | − | 11.0249i | −0.0151928 | − | 0.424349i | ||||
\(676\) | 5.87689 | 0.226034 | ||||||||
\(677\) | −13.7779 | −0.529529 | −0.264764 | − | 0.964313i | \(-0.585294\pi\) | ||||
−0.264764 | + | 0.964313i | \(0.585294\pi\) | |||||||
\(678\) | −4.34475 | − | 2.43981i | −0.166859 | − | 0.0937003i | ||||
\(679\) | 4.00000 | + | 15.4741i | 0.153506 | + | 0.593840i | ||||
\(680\) | − | 8.00000i | − | 0.306786i | ||||||
\(681\) | −4.56155 | − | 2.56155i | −0.174799 | − | 0.0981589i | ||||
\(682\) | − | 1.32431i | − | 0.0507103i | ||||||
\(683\) | 30.2462i | 1.15734i | 0.815562 | + | 0.578670i | \(0.196428\pi\) | ||||
−0.815562 | + | 0.578670i | \(0.803572\pi\) | |||||||
\(684\) | 16.4265 | − | 10.0138i | 0.628085 | − | 0.382888i | ||||
\(685\) | 27.9735i | 1.06881i | ||||||||
\(686\) | −12.7439 | − | 13.4384i | −0.486566 | − | 0.513082i | ||||
\(687\) | 7.68466 | − | 13.6847i | 0.293188 | − | 0.522102i | ||||
\(688\) | 11.1231 | 0.424064 | ||||||||
\(689\) | 8.68951 | 0.331044 | ||||||||
\(690\) | −15.3693 | − | 8.63068i | −0.585100 | − | 0.328564i | ||||
\(691\) | − | 12.6167i | − | 0.479960i | −0.970778 | − | 0.239980i | \(-0.922859\pi\) | ||
0.970778 | − | 0.239980i | \(-0.0771409\pi\) | |||||||
\(692\) | 13.0343 | 0.495488 | ||||||||
\(693\) | 5.52757 | − | 5.69614i | 0.209975 | − | 0.216379i | ||||
\(694\) | 4.00000 | 0.151838 | ||||||||
\(695\) | − | 35.8617i | − | 1.36031i | ||||||
\(696\) | −3.02045 | − | 1.69614i | −0.114490 | − | 0.0642921i | ||||
\(697\) | −34.7386 | −1.31582 | ||||||||
\(698\) | 31.1570 | 1.17931 | ||||||||
\(699\) | 7.52823 | − | 13.4061i | 0.284744 | − | 0.507065i | ||||
\(700\) | −5.43845 | + | 1.40582i | −0.205554 | + | 0.0531351i | ||||
\(701\) | 12.2462i | 0.462533i | 0.972890 | + | 0.231267i | \(0.0742869\pi\) | ||||
−0.972890 | + | 0.231267i | \(0.925713\pi\) | |||||||
\(702\) | −0.807764 | − | 22.5616i | −0.0304871 | − | 0.851531i | ||||
\(703\) | 52.8807i | 1.99443i | ||||||||
\(704\) | − | 1.00000i | − | 0.0376889i | ||||||
\(705\) | 18.8664 | + | 10.5945i | 0.710548 | + | 0.399010i | ||||
\(706\) | 14.7304i | 0.554386i | ||||||||
\(707\) | 19.8188 | − | 5.12311i | 0.745364 | − | 0.192674i | ||||
\(708\) | −17.6847 | − | 9.93087i | −0.664630 | − | 0.373225i | ||||
\(709\) | 36.7386 | 1.37975 | 0.689874 | − | 0.723929i | \(-0.257666\pi\) | ||||
0.689874 | + | 0.723929i | \(0.257666\pi\) | |||||||
\(710\) | 15.8917 | 0.596404 | ||||||||
\(711\) | −10.7386 | − | 17.6155i | −0.402730 | − | 0.660634i | ||||
\(712\) | − | 6.78456i | − | 0.254262i | ||||||
\(713\) | 7.94584 | 0.297574 | ||||||||
\(714\) | −5.52962 | + | 20.8948i | −0.206941 | + | 0.781969i | ||||
\(715\) | 7.36932 | 0.275597 | ||||||||
\(716\) | − | 14.2462i | − | 0.532406i | ||||||
\(717\) | −16.4265 | + | 29.2520i | −0.613461 | + | 1.09244i | ||||
\(718\) | 1.12311 | 0.0419139 | ||||||||
\(719\) | −0.580639 | −0.0216542 | −0.0108271 | − | 0.999941i | \(-0.503446\pi\) | ||||
−0.0108271 | + | 0.999941i | \(0.503446\pi\) | |||||||
\(720\) | −2.64861 | − | 4.34475i | −0.0987080 | − | 0.161919i | ||||
\(721\) | 2.63068 | + | 10.1768i | 0.0979718 | + | 0.379006i | ||||
\(722\) | − | 22.1231i | − | 0.823337i | ||||||
\(723\) | −10.2462 | + | 18.2462i | −0.381061 | + | 0.678584i | ||||
\(724\) | 3.02045i | 0.112254i | ||||||||
\(725\) | 4.24621i | 0.157700i | ||||||||
\(726\) | 0.848071 | − | 1.51022i | 0.0314748 | − | 0.0560497i | ||||
\(727\) | 39.0570i | 1.44854i | 0.689514 | + | 0.724272i | \(0.257824\pi\) | ||||
−0.689514 | + | 0.724272i | \(0.742176\pi\) | |||||||
\(728\) | −11.1293 | + | 2.87689i | −0.412480 | + | 0.106625i | ||||
\(729\) | −26.9309 | + | 1.93087i | −0.997440 | + | 0.0715137i | ||||
\(730\) | 14.7386 | 0.545501 | ||||||||
\(731\) | −52.4631 | −1.94042 | ||||||||
\(732\) | 1.43845 | − | 2.56155i | 0.0531665 | − | 0.0946777i | ||||
\(733\) | − | 22.0498i | − | 0.814429i | −0.913333 | − | 0.407215i | \(-0.866500\pi\) | ||
0.913333 | − | 0.407215i | \(-0.133500\pi\) | |||||||
\(734\) | −30.3675 | −1.12089 | ||||||||
\(735\) | −20.5643 | − | 0.118254i | −0.758525 | − | 0.00436188i | ||||
\(736\) | 6.00000 | 0.221163 | ||||||||
\(737\) | − | 12.0000i | − | 0.442026i | ||||||
\(738\) | −18.8664 | + | 11.5012i | −0.694480 | + | 0.423363i | ||||
\(739\) | 38.3542 | 1.41088 | 0.705440 | − | 0.708769i | \(-0.250749\pi\) | ||||
0.705440 | + | 0.708769i | \(0.250749\pi\) | |||||||
\(740\) | 13.9867 | 0.514163 | ||||||||
\(741\) | −42.0775 | − | 23.6287i | −1.54575 | − | 0.868023i | ||||
\(742\) | −5.12311 | + | 1.32431i | −0.188075 | + | 0.0486168i | ||||
\(743\) | 2.87689i | 0.105543i | 0.998607 | + | 0.0527715i | \(0.0168055\pi\) | ||||
−0.998607 | + | 0.0527715i | \(0.983195\pi\) | |||||||
\(744\) | 2.00000 | + | 1.12311i | 0.0733236 | + | 0.0411750i | ||||
\(745\) | 7.20217i | 0.263867i | ||||||||
\(746\) | 17.6155i | 0.644950i | ||||||||
\(747\) | 10.0138 | + | 16.4265i | 0.366386 | + | 0.601016i | ||||
\(748\) | 4.71659i | 0.172456i | ||||||||
\(749\) | −9.43318 | − | 36.4924i | −0.344681 | − | 1.33340i | ||||
\(750\) | −10.2462 | + | 18.2462i | −0.374139 | + | 0.666257i | ||||
\(751\) | −11.5076 | −0.419917 | −0.209959 | − | 0.977710i | \(-0.567333\pi\) | ||||
−0.209959 | + | 0.977710i | \(0.567333\pi\) | |||||||
\(752\) | −7.36520 | −0.268581 | ||||||||
\(753\) | −21.6847 | − | 12.1771i | −0.790233 | − | 0.443757i | ||||
\(754\) | 8.68951i | 0.316453i | ||||||||
\(755\) | 2.97467 | 0.108259 | ||||||||
\(756\) | 3.91468 | + | 13.1786i | 0.142376 | + | 0.479301i | ||||
\(757\) | −0.246211 | −0.00894870 | −0.00447435 | − | 0.999990i | \(-0.501424\pi\) | ||||
−0.00447435 | + | 0.999990i | \(0.501424\pi\) | |||||||
\(758\) | 30.7386i | 1.11648i | ||||||||
\(759\) | 9.06134 | + | 5.08842i | 0.328906 | + | 0.184698i | ||||
\(760\) | −10.8769 | −0.394546 | ||||||||
\(761\) | 18.2857 | 0.662857 | 0.331428 | − | 0.943480i | \(-0.392469\pi\) | ||||
0.331428 | + | 0.943480i | \(0.392469\pi\) | |||||||
\(762\) | −12.0818 | + | 21.5150i | −0.437677 | + | 0.779405i | ||||
\(763\) | −13.1231 | + | 3.39228i | −0.475088 | + | 0.122809i | ||||
\(764\) | − | 9.36932i | − | 0.338970i | ||||||
\(765\) | 12.4924 | + | 20.4924i | 0.451664 | + | 0.740905i | ||||
\(766\) | − | 33.0161i | − | 1.19292i | ||||||
\(767\) | 50.8769i | 1.83706i | ||||||||
\(768\) | 1.51022 | + | 0.848071i | 0.0544955 | + | 0.0306021i | ||||
\(769\) | − | 48.3272i | − | 1.74272i | −0.490642 | − | 0.871361i | \(-0.663238\pi\) | ||
0.490642 | − | 0.871361i | \(-0.336762\pi\) | |||||||
\(770\) | −4.34475 | + | 1.12311i | −0.156574 | + | 0.0404739i | ||||
\(771\) | −6.24621 | − | 3.50758i | −0.224952 | − | 0.126322i | ||||
\(772\) | 9.36932 | 0.337209 | ||||||||
\(773\) | −39.4289 | −1.41816 | −0.709079 | − | 0.705129i | \(-0.750889\pi\) | ||||
−0.709079 | + | 0.705129i | \(0.750889\pi\) | |||||||
\(774\) | −28.4924 | + | 17.3693i | −1.02414 | + | 0.624327i | ||||
\(775\) | − | 2.81164i | − | 0.100997i | ||||||
\(776\) | −6.04090 | −0.216856 | ||||||||
\(777\) | −36.5313 | − | 9.66767i | −1.31055 | − | 0.346826i | ||||
\(778\) | −4.24621 | −0.152234 | ||||||||
\(779\) | 47.2311i | 1.69223i | ||||||||
\(780\) | −6.24970 | + | 11.1293i | −0.223775 | + | 0.398494i | ||||
\(781\) | −9.36932 | −0.335261 | ||||||||
\(782\) | −28.2995 | −1.01199 | ||||||||
\(783\) | 10.3857 | − | 0.371834i | 0.371153 | − | 0.0132883i | ||||
\(784\) | 6.12311 | − | 3.39228i | 0.218682 | − | 0.121153i | ||||
\(785\) | 41.6155i | 1.48532i | ||||||||
\(786\) | 13.4384 | − | 23.9309i | 0.479334 | − | 0.853586i | ||||
\(787\) | − | 13.1973i | − | 0.470433i | −0.971943 | − | 0.235216i | \(-0.924420\pi\) | ||
0.971943 | − | 0.235216i | \(-0.0755799\pi\) | |||||||
\(788\) | 14.4924i | 0.516271i | ||||||||
\(789\) | 12.0818 | − | 21.5150i | 0.430123 | − | 0.765953i | ||||
\(790\) | 11.6642i | 0.414993i | ||||||||
\(791\) | −1.90495 | − | 7.36932i | −0.0677321 | − | 0.262023i | ||||
\(792\) | 1.56155 | + | 2.56155i | 0.0554874 | + | 0.0910208i | ||||
\(793\) | −7.36932 | −0.261692 | ||||||||
\(794\) | −9.06134 | −0.321575 | ||||||||
\(795\) | −2.87689 | + | 5.12311i | −0.102033 | + | 0.181698i | ||||
\(796\) | 1.32431i | 0.0469388i | ||||||||
\(797\) | −2.11375 | −0.0748729 | −0.0374364 | − | 0.999299i | \(-0.511919\pi\) | ||||
−0.0374364 | + | 0.999299i | \(0.511919\pi\) | |||||||
\(798\) | 28.4089 | + | 7.51814i | 1.00566 | + | 0.266139i | ||||
\(799\) | 34.7386 | 1.22896 | ||||||||
\(800\) | − | 2.12311i | − | 0.0750631i | ||||||
\(801\) | 10.5945 | + | 17.3790i | 0.374337 | + | 0.614057i | ||||
\(802\) | 19.3693 | 0.683954 | ||||||||
\(803\) | −8.68951 | −0.306646 | ||||||||
\(804\) | 18.1227 | + | 10.1768i | 0.639138 | + | 0.358910i | ||||
\(805\) | −6.73863 | − | 26.0685i | −0.237506 | − | 0.918795i | ||||
\(806\) | − | 5.75379i | − | 0.202669i | ||||||
\(807\) | −2.56155 | − | 1.43845i | −0.0901709 | − | 0.0506357i | ||||
\(808\) | 7.73704i | 0.272188i | ||||||||
\(809\) | − | 16.7386i | − | 0.588499i | −0.955729 | − | 0.294250i | \(-0.904930\pi\) | ||
0.955729 | − | 0.294250i | \(-0.0950697\pi\) | |||||||
\(810\) | 13.5691 | + | 6.99337i | 0.476771 | + | 0.245722i | ||||
\(811\) | − | 38.1045i | − | 1.33803i | −0.743248 | − | 0.669016i | \(-0.766716\pi\) | ||
0.743248 | − | 0.669016i | \(-0.233284\pi\) | |||||||
\(812\) | −1.32431 | − | 5.12311i | −0.0464741 | − | 0.179786i | ||||
\(813\) | −11.3693 | + | 20.2462i | −0.398739 | + | 0.710066i | ||||
\(814\) | −8.24621 | −0.289030 | ||||||||
\(815\) | −27.1383 | −0.950612 | ||||||||
\(816\) | −7.12311 | − | 4.00000i | −0.249359 | − | 0.140028i | ||||
\(817\) | 71.3295i | 2.49550i | ||||||||
\(818\) | −24.1636 | −0.844860 | ||||||||
\(819\) | 24.0159 | − | 24.7483i | 0.839184 | − | 0.864777i | ||||
\(820\) | 12.4924 | 0.436254 | ||||||||
\(821\) | 13.5076i | 0.471418i | 0.971824 | + | 0.235709i | \(0.0757412\pi\) | ||||
−0.971824 | + | 0.235709i | \(0.924259\pi\) | |||||||
\(822\) | 24.9073 | + | 13.9867i | 0.868740 | + | 0.487843i | ||||
\(823\) | 13.1231 | 0.457443 | 0.228721 | − | 0.973492i | \(-0.426546\pi\) | ||||
0.228721 | + | 0.973492i | \(0.426546\pi\) | |||||||
\(824\) | −3.97292 | −0.138403 | ||||||||
\(825\) | 1.80054 | − | 3.20636i | 0.0626869 | − | 0.111631i | ||||
\(826\) | −7.75379 | − | 29.9957i | −0.269789 | − | 1.04368i | ||||
\(827\) | − | 24.4924i | − | 0.851685i | −0.904797 | − | 0.425842i | \(-0.859978\pi\) | ||
0.904797 | − | 0.425842i | \(-0.140022\pi\) | |||||||
\(828\) | −15.3693 | + | 9.36932i | −0.534121 | + | 0.325606i | ||||
\(829\) | − | 27.9277i | − | 0.969969i | −0.874523 | − | 0.484985i | \(-0.838825\pi\) | ||
0.874523 | − | 0.484985i | \(-0.161175\pi\) | |||||||
\(830\) | − | 10.8769i | − | 0.377543i | ||||||
\(831\) | −20.5625 | − | 11.5469i | −0.713305 | − | 0.400558i | ||||
\(832\) | − | 4.34475i | − | 0.150627i | ||||||
\(833\) | −28.8802 | + | 16.0000i | −1.00064 | + | 0.554367i | ||||
\(834\) | −31.9309 | − | 17.9309i | −1.10568 | − | 0.620895i | ||||
\(835\) | −10.2462 | −0.354585 | ||||||||
\(836\) | 6.41273 | 0.221789 | ||||||||
\(837\) | −6.87689 | + | 0.246211i | −0.237700 | + | 0.00851031i | ||||
\(838\) | − | 22.6305i | − | 0.781757i | ||||||
\(839\) | 22.4217 | 0.774082 | 0.387041 | − | 0.922063i | \(-0.373497\pi\) | ||||
0.387041 | + | 0.922063i | \(0.373497\pi\) | |||||||
\(840\) | 1.98852 | − | 7.51403i | 0.0686104 | − | 0.259259i | ||||
\(841\) | 25.0000 | 0.862069 | ||||||||
\(842\) | − | 8.24621i | − | 0.284183i | ||||||
\(843\) | 14.3128 | − | 25.4879i | 0.492959 | − | 0.877850i | ||||
\(844\) | 1.36932 | 0.0471338 | ||||||||
\(845\) | 9.96804 | 0.342911 | ||||||||
\(846\) | 18.8664 | − | 11.5012i | 0.648639 | − | 0.395418i | ||||
\(847\) | 2.56155 | − | 0.662153i | 0.0880160 | − | 0.0227519i | ||||
\(848\) | − | 2.00000i | − | 0.0686803i | ||||||
\(849\) | −12.1771 | + | 21.6847i | −0.417916 | + | 0.744216i | ||||
\(850\) | 10.0138i | 0.343471i | ||||||||
\(851\) | − | 49.4773i | − | 1.69606i | ||||||
\(852\) | 7.94584 | − | 14.1498i | 0.272220 | − | 0.484763i | ||||
\(853\) | 42.0775i | 1.44071i | 0.693608 | + | 0.720353i | \(0.256020\pi\) | ||||
−0.693608 | + | 0.720353i | \(0.743980\pi\) | |||||||
\(854\) | 4.34475 | − | 1.12311i | 0.148674 | − | 0.0384319i | ||||
\(855\) | 27.8617 | − | 16.9848i | 0.952851 | − | 0.580869i | ||||
\(856\) | 14.2462 | 0.486925 | ||||||||
\(857\) | 55.6924 | 1.90242 | 0.951208 | − | 0.308552i | \(-0.0998443\pi\) | ||||
0.951208 | + | 0.308552i | \(0.0998443\pi\) | |||||||
\(858\) | 3.68466 | − | 6.56155i | 0.125792 | − | 0.224008i | ||||
\(859\) | − | 40.1725i | − | 1.37067i | −0.728229 | − | 0.685334i | \(-0.759656\pi\) | ||
0.728229 | − | 0.685334i | \(-0.240344\pi\) | |||||||
\(860\) | 18.8664 | 0.643337 | ||||||||
\(861\) | −32.6284 | − | 8.63480i | −1.11197 | − | 0.294273i | ||||
\(862\) | −29.6155 | −1.00871 | ||||||||
\(863\) | 17.3693i | 0.591258i | 0.955303 | + | 0.295629i | \(0.0955293\pi\) | ||||
−0.955303 | + | 0.295629i | \(0.904471\pi\) | |||||||
\(864\) | −5.19283 | + | 0.185917i | −0.176664 | + | 0.00632503i | ||||
\(865\) | 22.1080 | 0.751693 | ||||||||
\(866\) | 10.1768 | 0.345823 | ||||||||
\(867\) | 7.92295 | + | 4.44916i | 0.269078 | + | 0.151101i | ||||
\(868\) | 0.876894 | + | 3.39228i | 0.0297637 | + | 0.115142i | ||||
\(869\) | − | 6.87689i | − | 0.233283i | ||||||
\(870\) | −5.12311 | − | 2.87689i | −0.173690 | − | 0.0975359i | ||||
\(871\) | − | 52.1371i | − | 1.76660i | ||||||
\(872\) | − | 5.12311i | − | 0.173490i | ||||||
\(873\) | 15.4741 | − | 9.43318i | 0.523718 | − | 0.319265i | ||||
\(874\) | 38.4764i | 1.30148i | ||||||||
\(875\) | −30.9481 | + | 8.00000i | −1.04624 | + | 0.270449i | ||||
\(876\) | 7.36932 | − | 13.1231i | 0.248986 | − | 0.443389i | ||||
\(877\) | 14.8769 | 0.502357 | 0.251179 | − | 0.967941i | \(-0.419182\pi\) | ||||
0.251179 | + | 0.967941i | \(0.419182\pi\) | |||||||
\(878\) | 36.4084 | 1.22872 | ||||||||
\(879\) | 5.43845 | + | 3.05398i | 0.183434 | + | 0.103008i | ||||
\(880\) | − | 1.69614i | − | 0.0571769i | ||||||
\(881\) | 32.4355 | 1.09278 | 0.546390 | − | 0.837531i | \(-0.316002\pi\) | ||||
0.546390 | + | 0.837531i | \(0.316002\pi\) | |||||||
\(882\) | −10.3874 | + | 18.2511i | −0.349763 | + | 0.614545i | ||||
\(883\) | 28.4924 | 0.958846 | 0.479423 | − | 0.877584i | \(-0.340846\pi\) | ||||
0.479423 | + | 0.877584i | \(0.340846\pi\) | |||||||
\(884\) | 20.4924i | 0.689235i | ||||||||
\(885\) | −29.9957 | − | 16.8442i | −1.00829 | − | 0.566210i | ||||
\(886\) | 22.7386 | 0.763919 | ||||||||
\(887\) | −20.7713 | −0.697432 | −0.348716 | − | 0.937228i | \(-0.613382\pi\) | ||||
−0.348716 | + | 0.937228i | \(0.613382\pi\) | |||||||
\(888\) | 6.99337 | − | 12.4536i | 0.234682 | − | 0.417916i | ||||
\(889\) | −36.4924 | + | 9.43318i | −1.22392 | + | 0.316379i | ||||
\(890\) | − | 11.5076i | − | 0.385735i | ||||||
\(891\) | −8.00000 | − | 4.12311i | −0.268010 | − | 0.138129i | ||||
\(892\) | 2.06798i | 0.0692409i | ||||||||
\(893\) | − | 47.2311i | − | 1.58053i | ||||||
\(894\) | 6.41273 | + | 3.60109i | 0.214474 | + | 0.120438i | ||||
\(895\) | − | 24.1636i | − | 0.807700i | ||||||
\(896\) | 0.662153 | + | 2.56155i | 0.0221210 | + | 0.0855755i | ||||
\(897\) | 39.3693 | + | 22.1080i | 1.31450 | + | 0.738163i | ||||
\(898\) | −34.2462 | −1.14281 | ||||||||
\(899\) | 2.64861 | 0.0883362 | ||||||||
\(900\) | 3.31534 | + | 5.43845i | 0.110511 | + | 0.181282i | ||||
\(901\) | 9.43318i | 0.314265i | ||||||||
\(902\) | −7.36520 | −0.245234 | ||||||||
\(903\) | −49.2762 | − | 13.0405i | −1.63981 | − | 0.433960i | ||||
\(904\) | 2.87689 | 0.0956841 | ||||||||
\(905\) | 5.12311i | 0.170298i | ||||||||
\(906\) | 1.48734 | − | 2.64861i | 0.0494134 | − | 0.0879943i | ||||
\(907\) | −4.49242 | −0.149168 | −0.0745842 | − | 0.997215i | \(-0.523763\pi\) | ||||
−0.0745842 | + | 0.997215i | \(0.523763\pi\) | |||||||
\(908\) | 3.02045 | 0.100237 | ||||||||
\(909\) | −12.0818 | − | 19.8188i | −0.400728 | − | 0.657349i | ||||
\(910\) | −18.8769 | + | 4.87962i | −0.625763 | + | 0.161758i | ||||
\(911\) | − | 18.4924i | − | 0.612681i | −0.951922 | − | 0.306341i | \(-0.900895\pi\) | ||
0.951922 | − | 0.306341i | \(-0.0991047\pi\) | |||||||
\(912\) | −5.43845 | + | 9.68466i | −0.180085 | + | 0.320691i | ||||
\(913\) | 6.41273i | 0.212230i | ||||||||
\(914\) | − | 15.6155i | − | 0.516516i | ||||||
\(915\) | 2.43981 | − | 4.34475i | 0.0806576 | − | 0.143633i | ||||
\(916\) | 9.06134i | 0.299395i | ||||||||
\(917\) | 40.5901 | − | 10.4924i | 1.34040 | − | 0.346490i | ||||
\(918\) | 24.4924 | − | 0.876894i | 0.808370 | − | 0.0289418i | ||||
\(919\) | 55.8617 | 1.84271 | 0.921354 | − | 0.388724i | \(-0.127084\pi\) | ||||
0.921354 | + | 0.388724i | \(0.127084\pi\) | |||||||
\(920\) | 10.1768 | 0.335521 | ||||||||
\(921\) | 23.0540 | − | 41.0540i | 0.759654 | − | 1.35277i | ||||
\(922\) | − | 24.6984i | − | 0.813400i | ||||||
\(923\) | −40.7074 | −1.33990 | ||||||||
\(924\) | −1.17238 | + | 4.43007i | −0.0385684 | + | 0.145739i | ||||
\(925\) | −17.5076 | −0.575646 | ||||||||
\(926\) | − | 7.36932i | − | 0.242171i | ||||||
\(927\) | 10.1768 | − | 6.20393i | 0.334251 | − | 0.203764i | ||||
\(928\) | 2.00000 | 0.0656532 | ||||||||
\(929\) | 42.6123 | 1.39807 | 0.699033 | − | 0.715090i | \(-0.253614\pi\) | ||||
0.699033 | + | 0.715090i | \(0.253614\pi\) | |||||||
\(930\) | 3.39228 | + | 1.90495i | 0.111237 | + | 0.0624656i | ||||
\(931\) | 21.7538 | + | 39.2658i | 0.712952 | + | 1.28689i | ||||
\(932\) | 8.87689i | 0.290772i | ||||||||
\(933\) | 40.7386 | + | 22.8769i | 1.33372 | + | 0.748956i | ||||
\(934\) | 24.5354i | 0.802823i | ||||||||
\(935\) | 8.00000i | 0.261628i | ||||||||
\(936\) | 6.78456 | + | 11.1293i | 0.221760 | + | 0.363773i | ||||
\(937\) | 10.1768i | 0.332463i | 0.986087 | + | 0.166232i | \(0.0531599\pi\) | ||||
−0.986087 | + | 0.166232i | \(0.946840\pi\) | |||||||
\(938\) | 7.94584 | + | 30.7386i | 0.259441 | + | 1.00365i | ||||
\(939\) | 7.36932 | − | 13.1231i | 0.240489 | − | 0.428256i | ||||
\(940\) | −12.4924 | −0.407458 | ||||||||
\(941\) | 15.6829 | 0.511247 | 0.255624 | − | 0.966776i | \(-0.417719\pi\) | ||||
0.255624 | + | 0.966776i | \(0.417719\pi\) | |||||||
\(942\) | 37.0540 | + | 20.8078i | 1.20728 | + | 0.677954i | ||||
\(943\) | − | 44.1912i | − | 1.43906i | ||||||
\(944\) | 11.7100 | 0.381127 | ||||||||
\(945\) | 6.63986 | + | 22.3527i | 0.215995 | + | 0.727135i | ||||
\(946\) | −11.1231 | −0.361643 | ||||||||
\(947\) | − | 40.0000i | − | 1.29983i | −0.760009 | − | 0.649913i | \(-0.774805\pi\) | ||
0.760009 | − | 0.649913i | \(-0.225195\pi\) | |||||||
\(948\) | 10.3857 | + | 5.83209i | 0.337310 | + | 0.189418i | ||||
\(949\) | −37.7538 | −1.22554 | ||||||||
\(950\) | 13.6149 | 0.441726 | ||||||||
\(951\) | −20.9801 | + | 37.3609i | −0.680327 | + | 1.21151i | ||||
\(952\) | −3.12311 | − | 12.0818i | −0.101220 | − | 0.391573i | ||||
\(953\) | − | 17.3693i | − | 0.562647i | −0.959613 | − | 0.281324i | \(-0.909227\pi\) | ||
0.959613 | − | 0.281324i | \(-0.0907735\pi\) | |||||||
\(954\) | 3.12311 | + | 5.12311i | 0.101114 | + | 0.165867i | ||||
\(955\) | − | 15.8917i | − | 0.514243i | ||||||
\(956\) | − | 19.3693i | − | 0.626448i | ||||||
\(957\) | 3.02045 | + | 1.69614i | 0.0976372 | + | 0.0548285i | ||||
\(958\) | 26.0685i | 0.842236i | ||||||||
\(959\) | 10.9205 | + | 42.2462i | 0.352642 | + | 1.36420i | ||||
\(960\) | 2.56155 | + | 1.43845i | 0.0826738 | + | 0.0464257i | ||||
\(961\) | 29.2462 | 0.943426 | ||||||||
\(962\) | −35.8278 | −1.15513 | ||||||||
\(963\) | −36.4924 | + | 22.2462i | −1.17595 | + | 0.716874i | ||||
\(964\) | − | 12.0818i | − | 0.389128i | ||||||
\(965\) | 15.8917 | 0.511571 | ||||||||
\(966\) | −26.5804 | − | 7.03426i | −0.855211 | − | 0.226324i | ||||
\(967\) | 6.24621 | 0.200865 | 0.100432 | − | 0.994944i | \(-0.467977\pi\) | ||||
0.100432 | + | 0.994944i | \(0.467977\pi\) | |||||||
\(968\) | 1.00000i | 0.0321412i | ||||||||
\(969\) | 25.6509 | − | 45.6786i | 0.824026 | − | 1.46741i | ||||
\(970\) | −10.2462 | −0.328986 | ||||||||
\(971\) | 26.4404 | 0.848512 | 0.424256 | − | 0.905542i | \(-0.360536\pi\) | ||||
0.424256 | + | 0.905542i | \(0.360536\pi\) | |||||||
\(972\) | 13.0114 | − | 8.58511i | 0.417340 | − | 0.275367i | ||||
\(973\) | −14.0000 | − | 54.1593i | −0.448819 | − | 1.73627i | ||||
\(974\) | 3.50758i | 0.112390i | ||||||||
\(975\) | 7.82292 | − | 13.9309i | 0.250534 | − | 0.446145i | ||||
\(976\) | 1.69614i | 0.0542922i | ||||||||
\(977\) | 6.73863i | 0.215588i | 0.994173 | + | 0.107794i | \(0.0343787\pi\) | ||||
−0.994173 | + | 0.107794i | \(0.965621\pi\) | |||||||
\(978\) | −13.5691 | + | 24.1636i | −0.433893 | + | 0.772666i | ||||
\(979\) | 6.78456i | 0.216836i | ||||||||
\(980\) | 10.3857 | − | 5.75379i | 0.331757 | − | 0.183798i | ||||
\(981\) | 8.00000 | + | 13.1231i | 0.255420 | + | 0.418989i | ||||
\(982\) | −34.7386 | −1.10855 | ||||||||
\(983\) | −39.4746 | −1.25905 | −0.629523 | − | 0.776982i | \(-0.716749\pi\) | ||||
−0.629523 | + | 0.776982i | \(0.716749\pi\) | |||||||
\(984\) | 6.24621 | − | 11.1231i | 0.199122 | − | 0.354592i | ||||
\(985\) | 24.5812i | 0.783222i | ||||||||
\(986\) | −9.43318 | −0.300414 | ||||||||
\(987\) | 32.6284 | + | 8.63480i | 1.03857 | + | 0.274849i | ||||
\(988\) | 27.8617 | 0.886400 | ||||||||
\(989\) | − | 66.7386i | − | 2.12217i | ||||||
\(990\) | 2.64861 | + | 4.34475i | 0.0841785 | + | 0.138085i | ||||
\(991\) | −9.61553 | −0.305447 | −0.152724 | − | 0.988269i | \(-0.548804\pi\) | ||||
−0.152724 | + | 0.988269i | \(0.548804\pi\) | |||||||
\(992\) | −1.32431 | −0.0420468 | ||||||||
\(993\) | 30.2045 | + | 16.9614i | 0.958510 | + | 0.538254i | ||||
\(994\) | 24.0000 | − | 6.20393i | 0.761234 | − | 0.196777i | ||||
\(995\) | 2.24621i | 0.0712097i | ||||||||
\(996\) | −9.68466 | − | 5.43845i | −0.306870 | − | 0.172324i | ||||
\(997\) | − | 12.6167i | − | 0.399573i | −0.979839 | − | 0.199787i | \(-0.935975\pi\) | ||
0.979839 | − | 0.199787i | \(-0.0640249\pi\) | |||||||
\(998\) | 24.0000i | 0.759707i | ||||||||
\(999\) | 1.53311 | + | 42.8211i | 0.0485055 | + | 1.35480i |
(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 | 462.2.g.e.419.8 | yes | 8 | |
3.2 | odd | 2 | inner | 462.2.g.e.419.1 | ✓ | 8 | |
7.6 | odd | 2 | inner | 462.2.g.e.419.5 | yes | 8 | |
21.20 | even | 2 | inner | 462.2.g.e.419.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.g.e.419.1 | ✓ | 8 | 3.2 | odd | 2 | inner | |
462.2.g.e.419.4 | yes | 8 | 21.20 | even | 2 | inner | |
462.2.g.e.419.5 | yes | 8 | 7.6 | odd | 2 | inner | |
462.2.g.e.419.8 | yes | 8 | 1.1 | even | 1 | trivial |