Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [370,2,Mod(117,370)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(370, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("370.117");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 370 = 2 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 370.h (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: | \(2.95446487479\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} + 8 x^{18} + 4 x^{17} + 103 x^{16} - 394 x^{15} + 760 x^{14} + 278 x^{13} + 2009 x^{12} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 253.9 | ||
Root | \(1.82785 + 1.82785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 370.253 |
Dual form | 370.2.h.e.117.9 |
$q$-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 \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(297\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.82785 | − | 1.82785i | 1.05531 | − | 1.05531i | 0.0569322 | − | 0.998378i | \(-0.481868\pi\) |
0.998378 | − | 0.0569322i | \(-0.0181319\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.23698 | − | 1.86276i | −0.553196 | − | 0.833051i | ||||
\(6\) | −1.82785 | + | 1.82785i | −0.746217 | + | 0.746217i | ||||
\(7\) | 3.41332 | − | 3.41332i | 1.29011 | − | 1.29011i | 0.355399 | − | 0.934715i | \(-0.384345\pi\) |
0.934715 | − | 0.355399i | \(-0.115655\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | − | 3.68208i | − | 1.22736i | ||||||
\(10\) | 1.23698 | + | 1.86276i | 0.391168 | + | 0.589056i | ||||
\(11\) | 3.97950i | 1.19987i | 0.800051 | + | 0.599933i | \(0.204806\pi\) | ||||
−0.800051 | + | 0.599933i | \(0.795194\pi\) | |||||||
\(12\) | 1.82785 | − | 1.82785i | 0.527655 | − | 0.527655i | ||||
\(13\) | −4.28763 | −1.18917 | −0.594587 | − | 0.804031i | \(-0.702684\pi\) | ||||
−0.594587 | + | 0.804031i | \(0.702684\pi\) | |||||||
\(14\) | −3.41332 | + | 3.41332i | −0.912248 | + | 0.912248i | ||||
\(15\) | −5.66587 | − | 1.14383i | −1.46292 | − | 0.295335i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 2.57516i | − | 0.624569i | −0.949989 | − | 0.312284i | \(-0.898906\pi\) | ||
0.949989 | − | 0.312284i | \(-0.101094\pi\) | |||||||
\(18\) | 3.68208i | 0.867874i | ||||||||
\(19\) | 5.24415 | + | 5.24415i | 1.20309 | + | 1.20309i | 0.973222 | + | 0.229868i | \(0.0738296\pi\) |
0.229868 | + | 0.973222i | \(0.426170\pi\) | |||||||
\(20\) | −1.23698 | − | 1.86276i | −0.276598 | − | 0.416526i | ||||
\(21\) | − | 12.4781i | − | 2.72294i | ||||||
\(22\) | − | 3.97950i | − | 0.848433i | ||||||
\(23\) | −2.21783 | −0.462451 | −0.231225 | − | 0.972900i | \(-0.574273\pi\) | ||||
−0.231225 | + | 0.972900i | \(0.574273\pi\) | |||||||
\(24\) | −1.82785 | + | 1.82785i | −0.373109 | + | 0.373109i | ||||
\(25\) | −1.93975 | + | 4.60840i | −0.387949 | + | 0.921681i | ||||
\(26\) | 4.28763 | 0.840873 | ||||||||
\(27\) | −1.24674 | − | 1.24674i | −0.239935 | − | 0.239935i | ||||
\(28\) | 3.41332 | − | 3.41332i | 0.645057 | − | 0.645057i | ||||
\(29\) | −2.03524 | + | 2.03524i | −0.377935 | + | 0.377935i | −0.870357 | − | 0.492422i | \(-0.836112\pi\) |
0.492422 | + | 0.870357i | \(0.336112\pi\) | |||||||
\(30\) | 5.66587 | + | 1.14383i | 1.03444 | + | 0.208833i | ||||
\(31\) | −3.23732 | − | 3.23732i | −0.581439 | − | 0.581439i | 0.353859 | − | 0.935299i | \(-0.384869\pi\) |
−0.935299 | + | 0.353859i | \(0.884869\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 7.27394 | + | 7.27394i | 1.26623 | + | 1.26623i | ||||
\(34\) | 2.57516i | 0.441637i | ||||||||
\(35\) | −10.5804 | − | 2.13598i | −1.78842 | − | 0.361046i | ||||
\(36\) | − | 3.68208i | − | 0.613680i | ||||||
\(37\) | 5.60171 | − | 2.37084i | 0.920915 | − | 0.389764i | ||||
\(38\) | −5.24415 | − | 5.24415i | −0.850713 | − | 0.850713i | ||||
\(39\) | −7.83714 | + | 7.83714i | −1.25495 | + | 1.25495i | ||||
\(40\) | 1.23698 | + | 1.86276i | 0.195584 | + | 0.294528i | ||||
\(41\) | − | 2.50763i | − | 0.391627i | −0.980641 | − | 0.195813i | \(-0.937265\pi\) | ||
0.980641 | − | 0.195813i | \(-0.0627347\pi\) | |||||||
\(42\) | 12.4781i | 1.92541i | ||||||||
\(43\) | 9.00337 | 1.37300 | 0.686501 | − | 0.727129i | \(-0.259146\pi\) | ||||
0.686501 | + | 0.727129i | \(0.259146\pi\) | |||||||
\(44\) | 3.97950i | 0.599933i | ||||||||
\(45\) | −6.85883 | + | 4.55467i | −1.02245 | + | 0.678970i | ||||
\(46\) | 2.21783 | 0.327002 | ||||||||
\(47\) | −0.943466 | + | 0.943466i | −0.137619 | + | 0.137619i | −0.772560 | − | 0.634942i | \(-0.781024\pi\) |
0.634942 | + | 0.772560i | \(0.281024\pi\) | |||||||
\(48\) | 1.82785 | − | 1.82785i | 0.263828 | − | 0.263828i | ||||
\(49\) | − | 16.3015i | − | 2.32879i | ||||||
\(50\) | 1.93975 | − | 4.60840i | 0.274321 | − | 0.651727i | ||||
\(51\) | −4.70702 | − | 4.70702i | −0.659114 | − | 0.659114i | ||||
\(52\) | −4.28763 | −0.594587 | ||||||||
\(53\) | 2.84055 | + | 2.84055i | 0.390180 | + | 0.390180i | 0.874751 | − | 0.484572i | \(-0.161025\pi\) |
−0.484572 | + | 0.874751i | \(0.661025\pi\) | |||||||
\(54\) | 1.24674 | + | 1.24674i | 0.169660 | + | 0.169660i | ||||
\(55\) | 7.41286 | − | 4.92258i | 0.999549 | − | 0.663760i | ||||
\(56\) | −3.41332 | + | 3.41332i | −0.456124 | + | 0.456124i | ||||
\(57\) | 19.1710 | 2.53927 | ||||||||
\(58\) | 2.03524 | − | 2.03524i | 0.267240 | − | 0.267240i | ||||
\(59\) | −2.91109 | − | 2.91109i | −0.378991 | − | 0.378991i | 0.491747 | − | 0.870738i | \(-0.336359\pi\) |
−0.870738 | + | 0.491747i | \(0.836359\pi\) | |||||||
\(60\) | −5.66587 | − | 1.14383i | −0.731460 | − | 0.147667i | ||||
\(61\) | −5.71266 | − | 5.71266i | −0.731431 | − | 0.731431i | 0.239472 | − | 0.970903i | \(-0.423026\pi\) |
−0.970903 | + | 0.239472i | \(0.923026\pi\) | |||||||
\(62\) | 3.23732 | + | 3.23732i | 0.411140 | + | 0.411140i | ||||
\(63\) | −12.5681 | − | 12.5681i | −1.58343 | − | 1.58343i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.30372 | + | 7.98682i | 0.657846 | + | 0.990643i | ||||
\(66\) | −7.27394 | − | 7.27394i | −0.895360 | − | 0.895360i | ||||
\(67\) | −1.28531 | − | 1.28531i | −0.157026 | − | 0.157026i | 0.624222 | − | 0.781247i | \(-0.285416\pi\) |
−0.781247 | + | 0.624222i | \(0.785416\pi\) | |||||||
\(68\) | − | 2.57516i | − | 0.312284i | ||||||
\(69\) | −4.05387 | + | 4.05387i | −0.488029 | + | 0.488029i | ||||
\(70\) | 10.5804 | + | 2.13598i | 1.26460 | + | 0.255298i | ||||
\(71\) | 8.40334 | 0.997293 | 0.498646 | − | 0.866806i | \(-0.333831\pi\) | ||||
0.498646 | + | 0.866806i | \(0.333831\pi\) | |||||||
\(72\) | 3.68208i | 0.433937i | ||||||||
\(73\) | −5.32492 | + | 5.32492i | −0.623235 | + | 0.623235i | −0.946357 | − | 0.323123i | \(-0.895267\pi\) |
0.323123 | + | 0.946357i | \(0.395267\pi\) | |||||||
\(74\) | −5.60171 | + | 2.37084i | −0.651185 | + | 0.275605i | ||||
\(75\) | 4.87791 | + | 11.9690i | 0.563253 | + | 1.38207i | ||||
\(76\) | 5.24415 | + | 5.24415i | 0.601545 | + | 0.601545i | ||||
\(77\) | 13.5833 | + | 13.5833i | 1.54796 | + | 1.54796i | ||||
\(78\) | 7.83714 | − | 7.83714i | 0.887382 | − | 0.887382i | ||||
\(79\) | 9.77118 | + | 9.77118i | 1.09934 | + | 1.09934i | 0.994487 | + | 0.104856i | \(0.0334382\pi\) |
0.104856 | + | 0.994487i | \(0.466562\pi\) | |||||||
\(80\) | −1.23698 | − | 1.86276i | −0.138299 | − | 0.208263i | ||||
\(81\) | 6.48853 | 0.720948 | ||||||||
\(82\) | 2.50763i | 0.276922i | ||||||||
\(83\) | 2.57398 | + | 2.57398i | 0.282531 | + | 0.282531i | 0.834117 | − | 0.551587i | \(-0.185977\pi\) |
−0.551587 | + | 0.834117i | \(0.685977\pi\) | |||||||
\(84\) | − | 12.4781i | − | 1.36147i | ||||||
\(85\) | −4.79691 | + | 3.18543i | −0.520298 | + | 0.345509i | ||||
\(86\) | −9.00337 | −0.970859 | ||||||||
\(87\) | 7.44024i | 0.797678i | ||||||||
\(88\) | − | 3.97950i | − | 0.424216i | ||||||
\(89\) | −9.42876 | + | 9.42876i | −0.999447 | + | 0.999447i | −1.00000 | 0.000552868i | \(-0.999824\pi\) | |
0.000552868 | 1.00000i | \(0.499824\pi\) | ||||||||
\(90\) | 6.85883 | − | 4.55467i | 0.722984 | − | 0.480104i | ||||
\(91\) | −14.6350 | + | 14.6350i | −1.53417 | + | 1.53417i | ||||
\(92\) | −2.21783 | −0.231225 | ||||||||
\(93\) | −11.8347 | −1.22720 | ||||||||
\(94\) | 0.943466 | − | 0.943466i | 0.0973111 | − | 0.0973111i | ||||
\(95\) | 3.28166 | − | 16.2555i | 0.336692 | − | 1.66778i | ||||
\(96\) | −1.82785 | + | 1.82785i | −0.186554 | + | 0.186554i | ||||
\(97\) | − | 5.92246i | − | 0.601335i | −0.953729 | − | 0.300668i | \(-0.902791\pi\) | ||
0.953729 | − | 0.300668i | \(-0.0972095\pi\) | |||||||
\(98\) | 16.3015i | 1.64670i | ||||||||
\(99\) | 14.6528 | 1.47267 | ||||||||
\(100\) | −1.93975 | + | 4.60840i | −0.193975 | + | 0.460840i | ||||
\(101\) | 1.64079i | 0.163265i | 0.996663 | + | 0.0816323i | \(0.0260133\pi\) | ||||
−0.996663 | + | 0.0816323i | \(0.973987\pi\) | |||||||
\(102\) | 4.70702 | + | 4.70702i | 0.466064 | + | 0.466064i | ||||
\(103\) | − | 2.79089i | − | 0.274994i | −0.990502 | − | 0.137497i | \(-0.956094\pi\) | ||
0.990502 | − | 0.137497i | \(-0.0439058\pi\) | |||||||
\(104\) | 4.28763 | 0.420436 | ||||||||
\(105\) | −23.2437 | + | 15.4352i | −2.26835 | + | 1.50632i | ||||
\(106\) | −2.84055 | − | 2.84055i | −0.275899 | − | 0.275899i | ||||
\(107\) | −3.77209 | + | 3.77209i | −0.364662 | + | 0.364662i | −0.865526 | − | 0.500864i | \(-0.833016\pi\) |
0.500864 | + | 0.865526i | \(0.333016\pi\) | |||||||
\(108\) | −1.24674 | − | 1.24674i | −0.119967 | − | 0.119967i | ||||
\(109\) | 11.9302 | + | 11.9302i | 1.14271 | + | 1.14271i | 0.987953 | + | 0.154756i | \(0.0494590\pi\) |
0.154756 | + | 0.987953i | \(0.450541\pi\) | |||||||
\(110\) | −7.41286 | + | 4.92258i | −0.706788 | + | 0.469349i | ||||
\(111\) | 5.90554 | − | 14.5726i | 0.560529 | − | 1.38317i | ||||
\(112\) | 3.41332 | − | 3.41332i | 0.322528 | − | 0.322528i | ||||
\(113\) | 15.5469i | 1.46253i | 0.682091 | + | 0.731267i | \(0.261071\pi\) | ||||
−0.682091 | + | 0.731267i | \(0.738929\pi\) | |||||||
\(114\) | −19.1710 | −1.79553 | ||||||||
\(115\) | 2.74342 | + | 4.13129i | 0.255826 | + | 0.385245i | ||||
\(116\) | −2.03524 | + | 2.03524i | −0.188968 | + | 0.188968i | ||||
\(117\) | 15.7874i | 1.45954i | ||||||||
\(118\) | 2.91109 | + | 2.91109i | 0.267987 | + | 0.267987i | ||||
\(119\) | −8.78986 | − | 8.78986i | −0.805765 | − | 0.805765i | ||||
\(120\) | 5.66587 | + | 1.14383i | 0.517221 | + | 0.104417i | ||||
\(121\) | −4.83644 | −0.439676 | ||||||||
\(122\) | 5.71266 | + | 5.71266i | 0.517200 | + | 0.517200i | ||||
\(123\) | −4.58358 | − | 4.58358i | −0.413288 | − | 0.413288i | ||||
\(124\) | −3.23732 | − | 3.23732i | −0.290720 | − | 0.290720i | ||||
\(125\) | 10.9838 | − | 2.08724i | 0.982419 | − | 0.186688i | ||||
\(126\) | 12.5681 | + | 12.5681i | 1.11966 | + | 1.11966i | ||||
\(127\) | 0.0553748 | − | 0.0553748i | 0.00491372 | − | 0.00491372i | −0.704646 | − | 0.709559i | \(-0.748894\pi\) |
0.709559 | + | 0.704646i | \(0.248894\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 16.4568 | − | 16.4568i | 1.44894 | − | 1.44894i | ||||
\(130\) | −5.30372 | − | 7.98682i | −0.465167 | − | 0.700490i | ||||
\(131\) | 3.08937 | + | 3.08937i | 0.269920 | + | 0.269920i | 0.829068 | − | 0.559148i | \(-0.188872\pi\) |
−0.559148 | + | 0.829068i | \(0.688872\pi\) | |||||||
\(132\) | 7.27394 | + | 7.27394i | 0.633115 | + | 0.633115i | ||||
\(133\) | 35.7999 | 3.10425 | ||||||||
\(134\) | 1.28531 | + | 1.28531i | 0.111034 | + | 0.111034i | ||||
\(135\) | −0.780179 | + | 3.86457i | −0.0671471 | + | 0.332609i | ||||
\(136\) | 2.57516i | 0.220818i | ||||||||
\(137\) | −1.84871 | + | 1.84871i | −0.157946 | + | 0.157946i | −0.781656 | − | 0.623710i | \(-0.785625\pi\) |
0.623710 | + | 0.781656i | \(0.285625\pi\) | |||||||
\(138\) | 4.05387 | − | 4.05387i | 0.345088 | − | 0.345088i | ||||
\(139\) | −10.9433 | −0.928195 | −0.464097 | − | 0.885784i | \(-0.653621\pi\) | ||||
−0.464097 | + | 0.885784i | \(0.653621\pi\) | |||||||
\(140\) | −10.5804 | − | 2.13598i | −0.894208 | − | 0.180523i | ||||
\(141\) | 3.44903i | 0.290461i | ||||||||
\(142\) | −8.40334 | −0.705192 | ||||||||
\(143\) | − | 17.0626i | − | 1.42685i | ||||||
\(144\) | − | 3.68208i | − | 0.306840i | ||||||
\(145\) | 6.30873 | + | 1.27361i | 0.523911 | + | 0.105767i | ||||
\(146\) | 5.32492 | − | 5.32492i | 0.440693 | − | 0.440693i | ||||
\(147\) | −29.7967 | − | 29.7967i | −2.45759 | − | 2.45759i | ||||
\(148\) | 5.60171 | − | 2.37084i | 0.460457 | − | 0.194882i | ||||
\(149\) | − | 13.0913i | − | 1.07248i | −0.844066 | − | 0.536240i | \(-0.819844\pi\) | ||
0.844066 | − | 0.536240i | \(-0.180156\pi\) | |||||||
\(150\) | −4.87791 | − | 11.9690i | −0.398280 | − | 0.977268i | ||||
\(151\) | − | 9.37187i | − | 0.762672i | −0.924437 | − | 0.381336i | \(-0.875464\pi\) | ||
0.924437 | − | 0.381336i | \(-0.124536\pi\) | |||||||
\(152\) | −5.24415 | − | 5.24415i | −0.425357 | − | 0.425357i | ||||
\(153\) | −9.48196 | −0.766571 | ||||||||
\(154\) | −13.5833 | − | 13.5833i | −1.09457 | − | 1.09457i | ||||
\(155\) | −2.02584 | + | 10.0349i | −0.162719 | + | 0.806019i | ||||
\(156\) | −7.83714 | + | 7.83714i | −0.627474 | + | 0.627474i | ||||
\(157\) | −16.2868 | + | 16.2868i | −1.29983 | + | 1.29983i | −0.371321 | + | 0.928504i | \(0.621095\pi\) |
−0.928504 | + | 0.371321i | \(0.878905\pi\) | |||||||
\(158\) | −9.77118 | − | 9.77118i | −0.777353 | − | 0.777353i | ||||
\(159\) | 10.3842 | 0.823521 | ||||||||
\(160\) | 1.23698 | + | 1.86276i | 0.0977921 | + | 0.147264i | ||||
\(161\) | −7.57018 | + | 7.57018i | −0.596614 | + | 0.596614i | ||||
\(162\) | −6.48853 | −0.509787 | ||||||||
\(163\) | − | 2.14382i | − | 0.167917i | −0.996469 | − | 0.0839586i | \(-0.973244\pi\) | ||
0.996469 | − | 0.0839586i | \(-0.0267564\pi\) | |||||||
\(164\) | − | 2.50763i | − | 0.195813i | ||||||
\(165\) | 4.55186 | − | 22.5473i | 0.354362 | − | 1.75531i | ||||
\(166\) | −2.57398 | − | 2.57398i | −0.199779 | − | 0.199779i | ||||
\(167\) | − | 20.3382i | − | 1.57382i | −0.617071 | − | 0.786908i | \(-0.711681\pi\) | ||
0.617071 | − | 0.786908i | \(-0.288319\pi\) | |||||||
\(168\) | 12.4781i | 0.962705i | ||||||||
\(169\) | 5.38374 | 0.414134 | ||||||||
\(170\) | 4.79691 | − | 3.18543i | 0.367906 | − | 0.244312i | ||||
\(171\) | 19.3094 | − | 19.3094i | 1.47662 | − | 1.47662i | ||||
\(172\) | 9.00337 | 0.686501 | ||||||||
\(173\) | 13.7435 | − | 13.7435i | 1.04490 | − | 1.04490i | 0.0459570 | − | 0.998943i | \(-0.485366\pi\) |
0.998943 | − | 0.0459570i | \(-0.0146337\pi\) | |||||||
\(174\) | − | 7.44024i | − | 0.564043i | ||||||
\(175\) | 9.10899 | + | 22.3509i | 0.688575 | + | 1.68957i | ||||
\(176\) | 3.97950i | 0.299966i | ||||||||
\(177\) | −10.6421 | −0.799907 | ||||||||
\(178\) | 9.42876 | − | 9.42876i | 0.706716 | − | 0.706716i | ||||
\(179\) | 13.4168 | − | 13.4168i | 1.00282 | − | 1.00282i | 0.00281938 | − | 0.999996i | \(-0.499103\pi\) |
0.999996 | − | 0.00281938i | \(-0.000897436\pi\) | |||||||
\(180\) | −6.85883 | + | 4.55467i | −0.511227 | + | 0.339485i | ||||
\(181\) | −15.3711 | −1.14252 | −0.571261 | − | 0.820768i | \(-0.693546\pi\) | ||||
−0.571261 | + | 0.820768i | \(0.693546\pi\) | |||||||
\(182\) | 14.6350 | − | 14.6350i | 1.08482 | − | 1.08482i | ||||
\(183\) | −20.8838 | −1.54377 | ||||||||
\(184\) | 2.21783 | 0.163501 | ||||||||
\(185\) | −11.3455 | − | 7.50194i | −0.834139 | − | 0.551554i | ||||
\(186\) | 11.8347 | 0.867760 | ||||||||
\(187\) | 10.2479 | 0.749398 | ||||||||
\(188\) | −0.943466 | + | 0.943466i | −0.0688093 | + | 0.0688093i | ||||
\(189\) | −8.51103 | −0.619087 | ||||||||
\(190\) | −3.28166 | + | 16.2555i | −0.238077 | + | 1.17930i | ||||
\(191\) | −16.9686 | + | 16.9686i | −1.22781 | + | 1.22781i | −0.263016 | + | 0.964791i | \(0.584717\pi\) |
−0.964791 | + | 0.263016i | \(0.915283\pi\) | |||||||
\(192\) | 1.82785 | − | 1.82785i | 0.131914 | − | 0.131914i | ||||
\(193\) | −5.70785 | −0.410860 | −0.205430 | − | 0.978672i | \(-0.565859\pi\) | ||||
−0.205430 | + | 0.978672i | \(0.565859\pi\) | |||||||
\(194\) | 5.92246i | 0.425208i | ||||||||
\(195\) | 24.2931 | + | 4.90430i | 1.73967 | + | 0.351204i | ||||
\(196\) | − | 16.3015i | − | 1.16439i | ||||||
\(197\) | 9.14763 | − | 9.14763i | 0.651742 | − | 0.651742i | −0.301670 | − | 0.953412i | \(-0.597544\pi\) |
0.953412 | + | 0.301670i | \(0.0975442\pi\) | |||||||
\(198\) | −14.6528 | −1.04133 | ||||||||
\(199\) | −6.66896 | + | 6.66896i | −0.472750 | + | 0.472750i | −0.902803 | − | 0.430053i | \(-0.858495\pi\) |
0.430053 | + | 0.902803i | \(0.358495\pi\) | |||||||
\(200\) | 1.93975 | − | 4.60840i | 0.137161 | − | 0.325863i | ||||
\(201\) | −4.69872 | −0.331422 | ||||||||
\(202\) | − | 1.64079i | − | 0.115445i | ||||||
\(203\) | 13.8939i | 0.975159i | ||||||||
\(204\) | −4.70702 | − | 4.70702i | −0.329557 | − | 0.329557i | ||||
\(205\) | −4.67112 | + | 3.10190i | −0.326245 | + | 0.216646i | ||||
\(206\) | 2.79089i | 0.194450i | ||||||||
\(207\) | 8.16624i | 0.567593i | ||||||||
\(208\) | −4.28763 | −0.297293 | ||||||||
\(209\) | −20.8691 | + | 20.8691i | −1.44355 | + | 1.44355i | ||||
\(210\) | 23.2437 | − | 15.4352i | 1.60397 | − | 1.06513i | ||||
\(211\) | 15.1553 | 1.04334 | 0.521668 | − | 0.853149i | \(-0.325310\pi\) | ||||
0.521668 | + | 0.853149i | \(0.325310\pi\) | |||||||
\(212\) | 2.84055 | + | 2.84055i | 0.195090 | + | 0.195090i | ||||
\(213\) | 15.3600 | − | 15.3600i | 1.05245 | − | 1.05245i | ||||
\(214\) | 3.77209 | − | 3.77209i | 0.257855 | − | 0.257855i | ||||
\(215\) | −11.1370 | − | 16.7711i | −0.759539 | − | 1.14378i | ||||
\(216\) | 1.24674 | + | 1.24674i | 0.0848298 | + | 0.0848298i | ||||
\(217\) | −22.1000 | −1.50025 | ||||||||
\(218\) | −11.9302 | − | 11.9302i | −0.808017 | − | 0.808017i | ||||
\(219\) | 19.4663i | 1.31541i | ||||||||
\(220\) | 7.41286 | − | 4.92258i | 0.499775 | − | 0.331880i | ||||
\(221\) | 11.0413i | 0.742721i | ||||||||
\(222\) | −5.90554 | + | 14.5726i | −0.396354 | + | 0.978051i | ||||
\(223\) | −6.25546 | − | 6.25546i | −0.418896 | − | 0.418896i | 0.465927 | − | 0.884823i | \(-0.345721\pi\) |
−0.884823 | + | 0.465927i | \(0.845721\pi\) | |||||||
\(224\) | −3.41332 | + | 3.41332i | −0.228062 | + | 0.228062i | ||||
\(225\) | 16.9685 | + | 7.14229i | 1.13123 | + | 0.476153i | ||||
\(226\) | − | 15.5469i | − | 1.03417i | ||||||
\(227\) | − | 9.87949i | − | 0.655725i | −0.944725 | − | 0.327862i | \(-0.893672\pi\) | ||
0.944725 | − | 0.327862i | \(-0.106328\pi\) | |||||||
\(228\) | 19.1710 | 1.26963 | ||||||||
\(229\) | 21.9472i | 1.45031i | 0.688586 | + | 0.725155i | \(0.258232\pi\) | ||||
−0.688586 | + | 0.725155i | \(0.741768\pi\) | |||||||
\(230\) | −2.74342 | − | 4.13129i | −0.180896 | − | 0.272409i | ||||
\(231\) | 49.6566 | 3.26716 | ||||||||
\(232\) | 2.03524 | − | 2.03524i | 0.133620 | − | 0.133620i | ||||
\(233\) | −8.96601 | + | 8.96601i | −0.587383 | + | 0.587383i | −0.936922 | − | 0.349539i | \(-0.886338\pi\) |
0.349539 | + | 0.936922i | \(0.386338\pi\) | |||||||
\(234\) | − | 15.7874i | − | 1.03205i | ||||||
\(235\) | 2.92450 | + | 0.590399i | 0.190773 | + | 0.0385134i | ||||
\(236\) | −2.91109 | − | 2.91109i | −0.189496 | − | 0.189496i | ||||
\(237\) | 35.7205 | 2.32030 | ||||||||
\(238\) | 8.78986 | + | 8.78986i | 0.569762 | + | 0.569762i | ||||
\(239\) | −13.0815 | − | 13.0815i | −0.846174 | − | 0.846174i | 0.143479 | − | 0.989653i | \(-0.454171\pi\) |
−0.989653 | + | 0.143479i | \(0.954171\pi\) | |||||||
\(240\) | −5.66587 | − | 1.14383i | −0.365730 | − | 0.0738336i | ||||
\(241\) | 5.41196 | − | 5.41196i | 0.348615 | − | 0.348615i | −0.510978 | − | 0.859594i | \(-0.670717\pi\) |
0.859594 | + | 0.510978i | \(0.170717\pi\) | |||||||
\(242\) | 4.83644 | 0.310898 | ||||||||
\(243\) | 15.6003 | − | 15.6003i | 1.00076 | − | 1.00076i | ||||
\(244\) | −5.71266 | − | 5.71266i | −0.365716 | − | 0.365716i | ||||
\(245\) | −30.3658 | + | 20.1647i | −1.94000 | + | 1.28828i | ||||
\(246\) | 4.58358 | + | 4.58358i | 0.292239 | + | 0.292239i | ||||
\(247\) | −22.4849 | − | 22.4849i | −1.43068 | − | 1.43068i | ||||
\(248\) | 3.23732 | + | 3.23732i | 0.205570 | + | 0.205570i | ||||
\(249\) | 9.40969 | 0.596315 | ||||||||
\(250\) | −10.9838 | + | 2.08724i | −0.694675 | + | 0.132009i | ||||
\(251\) | 2.34715 | + | 2.34715i | 0.148151 | + | 0.148151i | 0.777292 | − | 0.629141i | \(-0.216593\pi\) |
−0.629141 | + | 0.777292i | \(0.716593\pi\) | |||||||
\(252\) | −12.5681 | − | 12.5681i | −0.791717 | − | 0.791717i | ||||
\(253\) | − | 8.82588i | − | 0.554878i | ||||||
\(254\) | −0.0553748 | + | 0.0553748i | −0.00347453 | + | 0.00347453i | ||||
\(255\) | −2.94554 | + | 14.5905i | −0.184457 | + | 0.913695i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 5.80813i | 0.362301i | 0.983455 | + | 0.181151i | \(0.0579822\pi\) | ||||
−0.983455 | + | 0.181151i | \(0.942018\pi\) | |||||||
\(258\) | −16.4568 | + | 16.4568i | −1.02456 | + | 1.02456i | ||||
\(259\) | 11.0280 | − | 27.2129i | 0.685245 | − | 1.69092i | ||||
\(260\) | 5.30372 | + | 7.98682i | 0.328923 | + | 0.495321i | ||||
\(261\) | 7.49392 | + | 7.49392i | 0.463862 | + | 0.463862i | ||||
\(262\) | −3.08937 | − | 3.08937i | −0.190862 | − | 0.190862i | ||||
\(263\) | −15.2944 | + | 15.2944i | −0.943090 | + | 0.943090i | −0.998466 | − | 0.0553752i | \(-0.982365\pi\) |
0.0553752 | + | 0.998466i | \(0.482365\pi\) | |||||||
\(264\) | −7.27394 | − | 7.27394i | −0.447680 | − | 0.447680i | ||||
\(265\) | 1.77755 | − | 8.80497i | 0.109194 | − | 0.540885i | ||||
\(266\) | −35.7999 | −2.19503 | ||||||||
\(267\) | 34.4688i | 2.10945i | ||||||||
\(268\) | −1.28531 | − | 1.28531i | −0.0785129 | − | 0.0785129i | ||||
\(269\) | 18.2273i | 1.11134i | 0.831404 | + | 0.555668i | \(0.187537\pi\) | ||||
−0.831404 | + | 0.555668i | \(0.812463\pi\) | |||||||
\(270\) | 0.780179 | − | 3.86457i | 0.0474802 | − | 0.235190i | ||||
\(271\) | −26.6096 | −1.61642 | −0.808208 | − | 0.588898i | \(-0.799562\pi\) | ||||
−0.808208 | + | 0.588898i | \(0.799562\pi\) | |||||||
\(272\) | − | 2.57516i | − | 0.156142i | ||||||
\(273\) | 53.5014i | 3.23805i | ||||||||
\(274\) | 1.84871 | − | 1.84871i | 0.111685 | − | 0.111685i | ||||
\(275\) | −18.3392 | − | 7.71922i | −1.10589 | − | 0.465487i | ||||
\(276\) | −4.05387 | + | 4.05387i | −0.244014 | + | 0.244014i | ||||
\(277\) | 0.845623 | 0.0508086 | 0.0254043 | − | 0.999677i | \(-0.491913\pi\) | ||||
0.0254043 | + | 0.999677i | \(0.491913\pi\) | |||||||
\(278\) | 10.9433 | 0.656333 | ||||||||
\(279\) | −11.9201 | + | 11.9201i | −0.713635 | + | 0.713635i | ||||
\(280\) | 10.5804 | + | 2.13598i | 0.632301 | + | 0.127649i | ||||
\(281\) | 11.3809 | − | 11.3809i | 0.678927 | − | 0.678927i | −0.280830 | − | 0.959757i | \(-0.590610\pi\) |
0.959757 | + | 0.280830i | \(0.0906098\pi\) | |||||||
\(282\) | − | 3.44903i | − | 0.205387i | ||||||
\(283\) | 6.37857i | 0.379167i | 0.981865 | + | 0.189583i | \(0.0607137\pi\) | ||||
−0.981865 | + | 0.189583i | \(0.939286\pi\) | |||||||
\(284\) | 8.40334 | 0.498646 | ||||||||
\(285\) | −23.7143 | − | 35.7110i | −1.40471 | − | 2.11534i | ||||
\(286\) | 17.0626i | 1.00893i | ||||||||
\(287\) | −8.55936 | − | 8.55936i | −0.505243 | − | 0.505243i | ||||
\(288\) | 3.68208i | 0.216969i | ||||||||
\(289\) | 10.3685 | 0.609914 | ||||||||
\(290\) | −6.30873 | − | 1.27361i | −0.370461 | − | 0.0747888i | ||||
\(291\) | −10.8254 | − | 10.8254i | −0.634595 | − | 0.634595i | ||||
\(292\) | −5.32492 | + | 5.32492i | −0.311617 | + | 0.311617i | ||||
\(293\) | −6.47894 | − | 6.47894i | −0.378504 | − | 0.378504i | 0.492058 | − | 0.870562i | \(-0.336245\pi\) |
−0.870562 | + | 0.492058i | \(0.836245\pi\) | |||||||
\(294\) | 29.7967 | + | 29.7967i | 1.73778 | + | 1.73778i | ||||
\(295\) | −1.82169 | + | 9.02362i | −0.106063 | + | 0.525376i | ||||
\(296\) | −5.60171 | + | 2.37084i | −0.325593 | + | 0.137802i | ||||
\(297\) | 4.96140 | − | 4.96140i | 0.287889 | − | 0.287889i | ||||
\(298\) | 13.0913i | 0.758358i | ||||||||
\(299\) | 9.50925 | 0.549934 | ||||||||
\(300\) | 4.87791 | + | 11.9690i | 0.281626 | + | 0.691033i | ||||
\(301\) | 30.7314 | − | 30.7314i | 1.77133 | − | 1.77133i | ||||
\(302\) | 9.37187i | 0.539290i | ||||||||
\(303\) | 2.99912 | + | 2.99912i | 0.172295 | + | 0.172295i | ||||
\(304\) | 5.24415 | + | 5.24415i | 0.300773 | + | 0.300773i | ||||
\(305\) | −3.57485 | + | 17.7078i | −0.204695 | + | 1.01394i | ||||
\(306\) | 9.48196 | 0.542047 | ||||||||
\(307\) | 3.64587 | + | 3.64587i | 0.208081 | + | 0.208081i | 0.803451 | − | 0.595371i | \(-0.202995\pi\) |
−0.595371 | + | 0.803451i | \(0.702995\pi\) | |||||||
\(308\) | 13.5833 | + | 13.5833i | 0.773981 | + | 0.773981i | ||||
\(309\) | −5.10132 | − | 5.10132i | −0.290204 | − | 0.290204i | ||||
\(310\) | 2.02584 | − | 10.0349i | 0.115060 | − | 0.569941i | ||||
\(311\) | −0.480637 | − | 0.480637i | −0.0272545 | − | 0.0272545i | 0.693348 | − | 0.720603i | \(-0.256135\pi\) |
−0.720603 | + | 0.693348i | \(0.756135\pi\) | |||||||
\(312\) | 7.83714 | − | 7.83714i | 0.443691 | − | 0.443691i | ||||
\(313\) | −18.2772 | −1.03309 | −0.516543 | − | 0.856261i | \(-0.672781\pi\) | ||||
−0.516543 | + | 0.856261i | \(0.672781\pi\) | |||||||
\(314\) | 16.2868 | − | 16.2868i | 0.919116 | − | 0.919116i | ||||
\(315\) | −7.86483 | + | 38.9579i | −0.443133 | + | 2.19503i | ||||
\(316\) | 9.77118 | + | 9.77118i | 0.549672 | + | 0.549672i | ||||
\(317\) | −4.85997 | − | 4.85997i | −0.272963 | − | 0.272963i | 0.557329 | − | 0.830292i | \(-0.311826\pi\) |
−0.830292 | + | 0.557329i | \(0.811826\pi\) | |||||||
\(318\) | −10.3842 | −0.582317 | ||||||||
\(319\) | −8.09925 | − | 8.09925i | −0.453471 | − | 0.453471i | ||||
\(320\) | −1.23698 | − | 1.86276i | −0.0691495 | − | 0.104131i | ||||
\(321\) | 13.7896i | 0.769662i | ||||||||
\(322\) | 7.57018 | − | 7.57018i | 0.421870 | − | 0.421870i | ||||
\(323\) | 13.5045 | − | 13.5045i | 0.751413 | − | 0.751413i | ||||
\(324\) | 6.48853 | 0.360474 | ||||||||
\(325\) | 8.31690 | − | 19.7591i | 0.461339 | − | 1.09604i | ||||
\(326\) | 2.14382i | 0.118735i | ||||||||
\(327\) | 43.6134 | 2.41182 | ||||||||
\(328\) | 2.50763i | 0.138461i | ||||||||
\(329\) | 6.44070i | 0.355088i | ||||||||
\(330\) | −4.55186 | + | 22.5473i | −0.250571 | + | 1.24119i | ||||
\(331\) | −20.7472 | + | 20.7472i | −1.14037 | + | 1.14037i | −0.151986 | + | 0.988383i | \(0.548567\pi\) |
−0.988383 | + | 0.151986i | \(0.951433\pi\) | |||||||
\(332\) | 2.57398 | + | 2.57398i | 0.141265 | + | 0.141265i | ||||
\(333\) | −8.72962 | − | 20.6259i | −0.478380 | − | 1.13029i | ||||
\(334\) | 20.3382i | 1.11286i | ||||||||
\(335\) | −0.804317 | + | 3.98413i | −0.0439446 | + | 0.217677i | ||||
\(336\) | − | 12.4781i | − | 0.680735i | ||||||
\(337\) | 6.47001 | + | 6.47001i | 0.352444 | + | 0.352444i | 0.861018 | − | 0.508574i | \(-0.169827\pi\) |
−0.508574 | + | 0.861018i | \(0.669827\pi\) | |||||||
\(338\) | −5.38374 | −0.292837 | ||||||||
\(339\) | 28.4175 | + | 28.4175i | 1.54343 | + | 1.54343i | ||||
\(340\) | −4.79691 | + | 3.18543i | −0.260149 | + | 0.172754i | ||||
\(341\) | 12.8829 | − | 12.8829i | 0.697649 | − | 0.697649i | ||||
\(342\) | −19.3094 | + | 19.3094i | −1.04413 | + | 1.04413i | ||||
\(343\) | −31.7491 | − | 31.7491i | −1.71429 | − | 1.71429i | ||||
\(344\) | −9.00337 | −0.485429 | ||||||||
\(345\) | 12.5660 | + | 2.53682i | 0.676528 | + | 0.136578i | ||||
\(346\) | −13.7435 | + | 13.7435i | −0.738856 | + | 0.738856i | ||||
\(347\) | −6.44807 | −0.346151 | −0.173075 | − | 0.984909i | \(-0.555370\pi\) | ||||
−0.173075 | + | 0.984909i | \(0.555370\pi\) | |||||||
\(348\) | 7.44024i | 0.398839i | ||||||||
\(349\) | − | 4.70014i | − | 0.251593i | −0.992056 | − | 0.125796i | \(-0.959851\pi\) | ||
0.992056 | − | 0.125796i | \(-0.0401486\pi\) | |||||||
\(350\) | −9.10899 | − | 22.3509i | −0.486896 | − | 1.19471i | ||||
\(351\) | 5.34555 | + | 5.34555i | 0.285324 | + | 0.285324i | ||||
\(352\) | − | 3.97950i | − | 0.212108i | ||||||
\(353\) | − | 19.6162i | − | 1.04406i | −0.852926 | − | 0.522031i | \(-0.825174\pi\) | ||
0.852926 | − | 0.522031i | \(-0.174826\pi\) | |||||||
\(354\) | 10.6421 | 0.565620 | ||||||||
\(355\) | −10.3948 | − | 15.6534i | −0.551698 | − | 0.830796i | ||||
\(356\) | −9.42876 | + | 9.42876i | −0.499723 | + | 0.499723i | ||||
\(357\) | −32.1331 | −1.70066 | ||||||||
\(358\) | −13.4168 | + | 13.4168i | −0.709098 | + | 0.709098i | ||||
\(359\) | − | 7.60520i | − | 0.401387i | −0.979654 | − | 0.200694i | \(-0.935680\pi\) | ||
0.979654 | − | 0.200694i | \(-0.0643196\pi\) | |||||||
\(360\) | 6.85883 | − | 4.55467i | 0.361492 | − | 0.240052i | ||||
\(361\) | 36.0022i | 1.89485i | ||||||||
\(362\) | 15.3711 | 0.807885 | ||||||||
\(363\) | −8.84029 | + | 8.84029i | −0.463995 | + | 0.463995i | ||||
\(364\) | −14.6350 | + | 14.6350i | −0.767085 | + | 0.767085i | ||||
\(365\) | 16.5059 | + | 3.33221i | 0.863957 | + | 0.174416i | ||||
\(366\) | 20.8838 | 1.09161 | ||||||||
\(367\) | −10.3061 | + | 10.3061i | −0.537975 | + | 0.537975i | −0.922934 | − | 0.384959i | \(-0.874216\pi\) |
0.384959 | + | 0.922934i | \(0.374216\pi\) | |||||||
\(368\) | −2.21783 | −0.115613 | ||||||||
\(369\) | −9.23331 | −0.480667 | ||||||||
\(370\) | 11.3455 | + | 7.50194i | 0.589826 | + | 0.390007i | ||||
\(371\) | 19.3914 | 1.00675 | ||||||||
\(372\) | −11.8347 | −0.613599 | ||||||||
\(373\) | 0.690871 | − | 0.690871i | 0.0357719 | − | 0.0357719i | −0.688995 | − | 0.724767i | \(-0.741948\pi\) |
0.724767 | + | 0.688995i | \(0.241948\pi\) | |||||||
\(374\) | −10.2479 | −0.529905 | ||||||||
\(375\) | 16.2616 | − | 23.8919i | 0.839743 | − | 1.23377i | ||||
\(376\) | 0.943466 | − | 0.943466i | 0.0486555 | − | 0.0486555i | ||||
\(377\) | 8.72636 | − | 8.72636i | 0.449430 | − | 0.449430i | ||||
\(378\) | 8.51103 | 0.437760 | ||||||||
\(379\) | 0.266778i | 0.0137035i | 0.999977 | + | 0.00685174i | \(0.00218099\pi\) | ||||
−0.999977 | + | 0.00685174i | \(0.997819\pi\) | |||||||
\(380\) | 3.28166 | − | 16.2555i | 0.168346 | − | 0.833890i | ||||
\(381\) | − | 0.202434i | − | 0.0103710i | ||||||
\(382\) | 16.9686 | − | 16.9686i | 0.868191 | − | 0.868191i | ||||
\(383\) | 32.6980 | 1.67079 | 0.835395 | − | 0.549650i | \(-0.185239\pi\) | ||||
0.835395 | + | 0.549650i | \(0.185239\pi\) | |||||||
\(384\) | −1.82785 | + | 1.82785i | −0.0932771 | + | 0.0932771i | ||||
\(385\) | 8.50012 | − | 42.1048i | 0.433206 | − | 2.14586i | ||||
\(386\) | 5.70785 | 0.290522 | ||||||||
\(387\) | − | 33.1511i | − | 1.68517i | ||||||
\(388\) | − | 5.92246i | − | 0.300668i | ||||||
\(389\) | 24.7831 | + | 24.7831i | 1.25655 | + | 1.25655i | 0.952728 | + | 0.303825i | \(0.0982639\pi\) |
0.303825 | + | 0.952728i | \(0.401736\pi\) | |||||||
\(390\) | −24.2931 | − | 4.90430i | −1.23013 | − | 0.248339i | ||||
\(391\) | 5.71129i | 0.288832i | ||||||||
\(392\) | 16.3015i | 0.823351i | ||||||||
\(393\) | 11.2938 | 0.569698 | ||||||||
\(394\) | −9.14763 | + | 9.14763i | −0.460851 | + | 0.460851i | ||||
\(395\) | 6.11457 | − | 30.2881i | 0.307658 | − | 1.52396i | ||||
\(396\) | 14.6528 | 0.736333 | ||||||||
\(397\) | −11.3967 | − | 11.3967i | −0.571984 | − | 0.571984i | 0.360698 | − | 0.932683i | \(-0.382538\pi\) |
−0.932683 | + | 0.360698i | \(0.882538\pi\) | |||||||
\(398\) | 6.66896 | − | 6.66896i | 0.334285 | − | 0.334285i | ||||
\(399\) | 65.4369 | − | 65.4369i | 3.27594 | − | 3.27594i | ||||
\(400\) | −1.93975 | + | 4.60840i | −0.0969873 | + | 0.230420i | ||||
\(401\) | −14.6783 | − | 14.6783i | −0.733000 | − | 0.733000i | 0.238213 | − | 0.971213i | \(-0.423438\pi\) |
−0.971213 | + | 0.238213i | \(0.923438\pi\) | |||||||
\(402\) | 4.69872 | 0.234351 | ||||||||
\(403\) | 13.8804 | + | 13.8804i | 0.691432 | + | 0.691432i | ||||
\(404\) | 1.64079i | 0.0816323i | ||||||||
\(405\) | −8.02621 | − | 12.0866i | −0.398825 | − | 0.600587i | ||||
\(406\) | − | 13.8939i | − | 0.689541i | ||||||
\(407\) | 9.43477 | + | 22.2920i | 0.467664 | + | 1.10497i | ||||
\(408\) | 4.70702 | + | 4.70702i | 0.233032 | + | 0.233032i | ||||
\(409\) | −10.7756 | + | 10.7756i | −0.532819 | + | 0.532819i | −0.921410 | − | 0.388591i | \(-0.872962\pi\) |
0.388591 | + | 0.921410i | \(0.372962\pi\) | |||||||
\(410\) | 4.67112 | − | 3.10190i | 0.230690 | − | 0.153192i | ||||
\(411\) | 6.75833i | 0.333364i | ||||||||
\(412\) | − | 2.79089i | − | 0.137497i | ||||||
\(413\) | −19.8730 | −0.977884 | ||||||||
\(414\) | − | 8.16624i | − | 0.401349i | ||||||
\(415\) | 1.61073 | − | 7.97866i | 0.0790678 | − | 0.391657i | ||||
\(416\) | 4.28763 | 0.210218 | ||||||||
\(417\) | −20.0026 | + | 20.0026i | −0.979533 | + | 0.979533i | ||||
\(418\) | 20.8691 | − | 20.8691i | 1.02074 | − | 1.02074i | ||||
\(419\) | 24.0943i | 1.17709i | 0.808466 | + | 0.588543i | \(0.200298\pi\) | ||||
−0.808466 | + | 0.588543i | \(0.799702\pi\) | |||||||
\(420\) | −23.2437 | + | 15.4352i | −1.13417 | + | 0.753160i | ||||
\(421\) | 21.6407 | + | 21.6407i | 1.05470 | + | 1.05470i | 0.998415 | + | 0.0562888i | \(0.0179267\pi\) |
0.0562888 | + | 0.998415i | \(0.482073\pi\) | |||||||
\(422\) | −15.1553 | −0.737750 | ||||||||
\(423\) | 3.47392 | + | 3.47392i | 0.168908 | + | 0.168908i | ||||
\(424\) | −2.84055 | − | 2.84055i | −0.137949 | − | 0.137949i | ||||
\(425\) | 11.8674 | + | 4.99516i | 0.575653 | + | 0.242301i | ||||
\(426\) | −15.3600 | + | 15.3600i | −0.744197 | + | 0.744197i | ||||
\(427\) | −38.9983 | −1.88726 | ||||||||
\(428\) | −3.77209 | + | 3.77209i | −0.182331 | + | 0.182331i | ||||
\(429\) | −31.1879 | − | 31.1879i | −1.50577 | − | 1.50577i | ||||
\(430\) | 11.1370 | + | 16.7711i | 0.537075 | + | 0.808775i | ||||
\(431\) | 1.23281 | + | 1.23281i | 0.0593825 | + | 0.0593825i | 0.736174 | − | 0.676792i | \(-0.236630\pi\) |
−0.676792 | + | 0.736174i | \(0.736630\pi\) | |||||||
\(432\) | −1.24674 | − | 1.24674i | −0.0599837 | − | 0.0599837i | ||||
\(433\) | −12.5825 | − | 12.5825i | −0.604678 | − | 0.604678i | 0.336872 | − | 0.941550i | \(-0.390631\pi\) |
−0.941550 | + | 0.336872i | \(0.890631\pi\) | |||||||
\(434\) | 22.1000 | 1.06083 | ||||||||
\(435\) | 13.8594 | − | 9.20345i | 0.664506 | − | 0.441272i | ||||
\(436\) | 11.9302 | + | 11.9302i | 0.571354 | + | 0.571354i | ||||
\(437\) | −11.6307 | − | 11.6307i | −0.556370 | − | 0.556370i | ||||
\(438\) | − | 19.4663i | − | 0.930137i | ||||||
\(439\) | −13.6362 | + | 13.6362i | −0.650822 | + | 0.650822i | −0.953191 | − | 0.302369i | \(-0.902223\pi\) |
0.302369 | + | 0.953191i | \(0.402223\pi\) | |||||||
\(440\) | −7.41286 | + | 4.92258i | −0.353394 | + | 0.234675i | ||||
\(441\) | −60.0235 | −2.85826 | ||||||||
\(442\) | − | 11.0413i | − | 0.525183i | ||||||
\(443\) | −23.2157 | + | 23.2157i | −1.10301 | + | 1.10301i | −0.108963 | + | 0.994046i | \(0.534753\pi\) |
−0.994046 | + | 0.108963i | \(0.965247\pi\) | |||||||
\(444\) | 5.90554 | − | 14.5726i | 0.280265 | − | 0.691586i | ||||
\(445\) | 29.2267 | + | 5.90030i | 1.38548 | + | 0.279701i | ||||
\(446\) | 6.25546 | + | 6.25546i | 0.296204 | + | 0.296204i | ||||
\(447\) | −23.9289 | − | 23.9289i | −1.13180 | − | 1.13180i | ||||
\(448\) | 3.41332 | − | 3.41332i | 0.161264 | − | 0.161264i | ||||
\(449\) | 16.0955 | + | 16.0955i | 0.759594 | + | 0.759594i | 0.976248 | − | 0.216654i | \(-0.0695144\pi\) |
−0.216654 | + | 0.976248i | \(0.569514\pi\) | |||||||
\(450\) | −16.9685 | − | 7.14229i | −0.799903 | − | 0.336691i | ||||
\(451\) | 9.97914 | 0.469899 | ||||||||
\(452\) | 15.5469i | 0.731267i | ||||||||
\(453\) | −17.1304 | − | 17.1304i | −0.804855 | − | 0.804855i | ||||
\(454\) | 9.87949i | 0.463668i | ||||||||
\(455\) | 45.3649 | + | 9.15826i | 2.12674 | + | 0.429346i | ||||
\(456\) | −19.1710 | −0.897766 | ||||||||
\(457\) | − | 3.34685i | − | 0.156559i | −0.996931 | − | 0.0782794i | \(-0.975057\pi\) | ||
0.996931 | − | 0.0782794i | \(-0.0249426\pi\) | |||||||
\(458\) | − | 21.9472i | − | 1.02552i | ||||||
\(459\) | −3.21055 | + | 3.21055i | −0.149856 | + | 0.149856i | ||||
\(460\) | 2.74342 | + | 4.13129i | 0.127913 | + | 0.192623i | ||||
\(461\) | 22.0325 | − | 22.0325i | 1.02616 | − | 1.02616i | 0.0265068 | − | 0.999649i | \(-0.491562\pi\) |
0.999649 | − | 0.0265068i | \(-0.00843837\pi\) | |||||||
\(462\) | −49.6566 | −2.31023 | ||||||||
\(463\) | −10.8598 | −0.504696 | −0.252348 | − | 0.967637i | \(-0.581203\pi\) | ||||
−0.252348 | + | 0.967637i | \(0.581203\pi\) | |||||||
\(464\) | −2.03524 | + | 2.03524i | −0.0944838 | + | 0.0944838i | ||||
\(465\) | 14.6393 | + | 22.0451i | 0.678881 | + | 1.02232i | ||||
\(466\) | 8.96601 | − | 8.96601i | 0.415342 | − | 0.415342i | ||||
\(467\) | 12.9597i | 0.599702i | 0.953986 | + | 0.299851i | \(0.0969371\pi\) | ||||
−0.953986 | + | 0.299851i | \(0.903063\pi\) | |||||||
\(468\) | 15.7874i | 0.729772i | ||||||||
\(469\) | −8.77436 | −0.405162 | ||||||||
\(470\) | −2.92450 | − | 0.590399i | −0.134897 | − | 0.0272331i | ||||
\(471\) | 59.5396i | 2.74344i | ||||||||
\(472\) | 2.91109 | + | 2.91109i | 0.133994 | + | 0.133994i | ||||
\(473\) | 35.8289i | 1.64742i | ||||||||
\(474\) | −35.7205 | −1.64070 | ||||||||
\(475\) | −34.3395 | + | 13.9948i | −1.57560 | + | 0.642127i | ||||
\(476\) | −8.78986 | − | 8.78986i | −0.402883 | − | 0.402883i | ||||
\(477\) | 10.4591 | − | 10.4591i | 0.478891 | − | 0.478891i | ||||
\(478\) | 13.0815 | + | 13.0815i | 0.598335 | + | 0.598335i | ||||
\(479\) | −2.98032 | − | 2.98032i | −0.136174 | − | 0.136174i | 0.635734 | − | 0.771908i | \(-0.280698\pi\) |
−0.771908 | + | 0.635734i | \(0.780698\pi\) | |||||||
\(480\) | 5.66587 | + | 1.14383i | 0.258610 | + | 0.0522083i | ||||
\(481\) | −24.0180 | + | 10.1653i | −1.09513 | + | 0.463497i | ||||
\(482\) | −5.41196 | + | 5.41196i | −0.246508 | + | 0.246508i | ||||
\(483\) | 27.6743i | 1.25923i | ||||||||
\(484\) | −4.83644 | −0.219838 | ||||||||
\(485\) | −11.0321 | + | 7.32599i | −0.500943 | + | 0.332656i | ||||
\(486\) | −15.6003 | + | 15.6003i | −0.707643 | + | 0.707643i | ||||
\(487\) | − | 4.69219i | − | 0.212624i | −0.994333 | − | 0.106312i | \(-0.966096\pi\) | ||
0.994333 | − | 0.106312i | \(-0.0339042\pi\) | |||||||
\(488\) | 5.71266 | + | 5.71266i | 0.258600 | + | 0.258600i | ||||
\(489\) | −3.91859 | − | 3.91859i | −0.177205 | − | 0.177205i | ||||
\(490\) | 30.3658 | − | 20.1647i | 1.37179 | − | 0.910948i | ||||
\(491\) | −4.44735 | −0.200706 | −0.100353 | − | 0.994952i | \(-0.531997\pi\) | ||||
−0.100353 | + | 0.994952i | \(0.531997\pi\) | |||||||
\(492\) | −4.58358 | − | 4.58358i | −0.206644 | − | 0.206644i | ||||
\(493\) | 5.24108 | + | 5.24108i | 0.236047 | + | 0.236047i | ||||
\(494\) | 22.4849 | + | 22.4849i | 1.01165 | + | 1.01165i | ||||
\(495\) | −18.1253 | − | 27.2947i | −0.814672 | − | 1.22681i | ||||
\(496\) | −3.23732 | − | 3.23732i | −0.145360 | − | 0.145360i | ||||
\(497\) | 28.6833 | − | 28.6833i | 1.28662 | − | 1.28662i | ||||
\(498\) | −9.40969 | −0.421658 | ||||||||
\(499\) | −24.3133 | + | 24.3133i | −1.08841 | + | 1.08841i | −0.0927210 | + | 0.995692i | \(0.529556\pi\) |
−0.995692 | + | 0.0927210i | \(0.970444\pi\) | |||||||
\(500\) | 10.9838 | − | 2.08724i | 0.491210 | − | 0.0933442i | ||||
\(501\) | −37.1752 | − | 37.1752i | −1.66086 | − | 1.66086i | ||||
\(502\) | −2.34715 | − | 2.34715i | −0.104759 | − | 0.104759i | ||||
\(503\) | 15.7435 | 0.701968 | 0.350984 | − | 0.936381i | \(-0.385847\pi\) | ||||
0.350984 | + | 0.936381i | \(0.385847\pi\) | |||||||
\(504\) | 12.5681 | + | 12.5681i | 0.559828 | + | 0.559828i | ||||
\(505\) | 3.05639 | − | 2.02963i | 0.136008 | − | 0.0903173i | ||||
\(506\) | 8.82588i | 0.392358i | ||||||||
\(507\) | 9.84067 | − | 9.84067i | 0.437040 | − | 0.437040i | ||||
\(508\) | 0.0553748 | − | 0.0553748i | 0.00245686 | − | 0.00245686i | ||||
\(509\) | −32.8974 | −1.45815 | −0.729077 | − | 0.684432i | \(-0.760050\pi\) | ||||
−0.729077 | + | 0.684432i | \(0.760050\pi\) | |||||||
\(510\) | 2.94554 | − | 14.5905i | 0.130431 | − | 0.646080i | ||||
\(511\) | 36.3513i | 1.60809i | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | − | 13.0762i | − | 0.577327i | ||||||
\(514\) | − | 5.80813i | − | 0.256186i | ||||||
\(515\) | −5.19875 | + | 3.45228i | −0.229084 | + | 0.152126i | ||||
\(516\) | 16.4568 | − | 16.4568i | 0.724471 | − | 0.724471i | ||||
\(517\) | −3.75453 | − | 3.75453i | −0.165124 | − | 0.165124i | ||||
\(518\) | −11.0280 | + | 27.2129i | −0.484542 | + | 1.19566i | ||||
\(519\) | − | 50.2422i | − | 2.20539i | ||||||
\(520\) | −5.30372 | − | 7.98682i | −0.232584 | − | 0.350245i | ||||
\(521\) | − | 21.7965i | − | 0.954920i | −0.878653 | − | 0.477460i | \(-0.841558\pi\) | ||
0.878653 | − | 0.477460i | \(-0.158442\pi\) | |||||||
\(522\) | −7.49392 | − | 7.49392i | −0.328000 | − | 0.328000i | ||||
\(523\) | −20.7364 | −0.906739 | −0.453369 | − | 0.891323i | \(-0.649778\pi\) | ||||
−0.453369 | + | 0.891323i | \(0.649778\pi\) | |||||||
\(524\) | 3.08937 | + | 3.08937i | 0.134960 | + | 0.134960i | ||||
\(525\) | 57.5040 | + | 24.2043i | 2.50968 | + | 1.05636i | ||||
\(526\) | 15.2944 | − | 15.2944i | 0.666866 | − | 0.666866i | ||||
\(527\) | −8.33662 | + | 8.33662i | −0.363149 | + | 0.363149i | ||||
\(528\) | 7.27394 | + | 7.27394i | 0.316557 | + | 0.316557i | ||||
\(529\) | −18.0812 | −0.786140 | ||||||||
\(530\) | −1.77755 | + | 8.80497i | −0.0772118 | + | 0.382464i | ||||
\(531\) | −10.7189 | + | 10.7189i | −0.465159 | + | 0.465159i | ||||
\(532\) | 35.7999 | 1.55212 | ||||||||
\(533\) | 10.7518i | 0.465712i | ||||||||
\(534\) | − | 34.4688i | − | 1.49161i | ||||||
\(535\) | 11.6925 | + | 2.36048i | 0.505511 | + | 0.102053i | ||||
\(536\) | 1.28531 | + | 1.28531i | 0.0555170 | + | 0.0555170i | ||||
\(537\) | − | 49.0477i | − | 2.11656i | ||||||
\(538\) | − | 18.2273i | − | 0.785833i | ||||||
\(539\) | 64.8719 | 2.79423 | ||||||||
\(540\) | −0.780179 | + | 3.86457i | −0.0335736 | + | 0.166304i | ||||
\(541\) | 3.55548 | − | 3.55548i | 0.152862 | − | 0.152862i | −0.626533 | − | 0.779395i | \(-0.715527\pi\) |
0.779395 | + | 0.626533i | \(0.215527\pi\) | |||||||
\(542\) | 26.6096 | 1.14298 | ||||||||
\(543\) | −28.0960 | + | 28.0960i | −1.20572 | + | 1.20572i | ||||
\(544\) | 2.57516i | 0.110409i | ||||||||
\(545\) | 7.46565 | − | 36.9806i | 0.319793 | − | 1.58408i | ||||
\(546\) | − | 53.5014i | − | 2.28965i | ||||||
\(547\) | 10.3831 | 0.443950 | 0.221975 | − | 0.975052i | \(-0.428750\pi\) | ||||
0.221975 | + | 0.975052i | \(0.428750\pi\) | |||||||
\(548\) | −1.84871 | + | 1.84871i | −0.0789729 | + | 0.0789729i | ||||
\(549\) | −21.0345 | + | 21.0345i | −0.897729 | + | 0.897729i | ||||
\(550\) | 18.3392 | + | 7.71922i | 0.781984 | + | 0.329149i | ||||
\(551\) | −21.3462 | −0.909380 | ||||||||
\(552\) | 4.05387 | − | 4.05387i | 0.172544 | − | 0.172544i | ||||
\(553\) | 66.7043 | 2.83656 | ||||||||
\(554\) | −0.845623 | −0.0359271 | ||||||||
\(555\) | −34.4504 | + | 7.02549i | −1.46234 | + | 0.298216i | ||||
\(556\) | −10.9433 | −0.464097 | ||||||||
\(557\) | −4.73501 | −0.200629 | −0.100314 | − | 0.994956i | \(-0.531985\pi\) | ||||
−0.100314 | + | 0.994956i | \(0.531985\pi\) | |||||||
\(558\) | 11.9201 | − | 11.9201i | 0.504616 | − | 0.504616i | ||||
\(559\) | −38.6031 | −1.63274 | ||||||||
\(560\) | −10.5804 | − | 2.13598i | −0.447104 | − | 0.0902614i | ||||
\(561\) | 18.7316 | − | 18.7316i | 0.790848 | − | 0.790848i | ||||
\(562\) | −11.3809 | + | 11.3809i | −0.480074 | + | 0.480074i | ||||
\(563\) | 3.05563 | 0.128779 | 0.0643897 | − | 0.997925i | \(-0.479490\pi\) | ||||
0.0643897 | + | 0.997925i | \(0.479490\pi\) | |||||||
\(564\) | 3.44903i | 0.145230i | ||||||||
\(565\) | 28.9602 | − | 19.2313i | 1.21837 | − | 0.809068i | ||||
\(566\) | − | 6.37857i | − | 0.268111i | ||||||
\(567\) | 22.1474 | − | 22.1474i | 0.930105 | − | 0.930105i | ||||
\(568\) | −8.40334 | −0.352596 | ||||||||
\(569\) | 29.4912 | − | 29.4912i | 1.23633 | − | 1.23633i | 0.274845 | − | 0.961488i | \(-0.411373\pi\) |
0.961488 | − | 0.274845i | \(-0.0886266\pi\) | |||||||
\(570\) | 23.7143 | + | 35.7110i | 0.993281 | + | 1.49577i | ||||
\(571\) | 14.8841 | 0.622881 | 0.311440 | − | 0.950266i | \(-0.399189\pi\) | ||||
0.311440 | + | 0.950266i | \(0.399189\pi\) | |||||||
\(572\) | − | 17.0626i | − | 0.713424i | ||||||
\(573\) | 62.0323i | 2.59144i | ||||||||
\(574\) | 8.55936 | + | 8.55936i | 0.357261 | + | 0.357261i | ||||
\(575\) | 4.30203 | − | 10.2207i | 0.179407 | − | 0.426232i | ||||
\(576\) | − | 3.68208i | − | 0.153420i | ||||||
\(577\) | − | 9.65939i | − | 0.402126i | −0.979578 | − | 0.201063i | \(-0.935560\pi\) | ||
0.979578 | − | 0.201063i | \(-0.0644395\pi\) | |||||||
\(578\) | −10.3685 | −0.431274 | ||||||||
\(579\) | −10.4331 | + | 10.4331i | −0.433584 | + | 0.433584i | ||||
\(580\) | 6.30873 | + | 1.27361i | 0.261956 | + | 0.0528836i | ||||
\(581\) | 17.5716 | 0.728993 | ||||||||
\(582\) | 10.8254 | + | 10.8254i | 0.448726 | + | 0.448726i | ||||
\(583\) | −11.3040 | + | 11.3040i | −0.468163 | + | 0.468163i | ||||
\(584\) | 5.32492 | − | 5.32492i | 0.220347 | − | 0.220347i | ||||
\(585\) | 29.4081 | − | 19.5287i | 1.21587 | − | 0.807413i | ||||
\(586\) | 6.47894 | + | 6.47894i | 0.267643 | + | 0.267643i | ||||
\(587\) | −0.789320 | −0.0325787 | −0.0162894 | − | 0.999867i | \(-0.505185\pi\) | ||||
−0.0162894 | + | 0.999867i | \(0.505185\pi\) | |||||||
\(588\) | −29.7967 | − | 29.7967i | −1.22880 | − | 1.22880i | ||||
\(589\) | − | 33.9539i | − | 1.39905i | ||||||
\(590\) | 1.82169 | − | 9.02362i | 0.0749978 | − | 0.371497i | ||||
\(591\) | − | 33.4410i | − | 1.37558i | ||||||
\(592\) | 5.60171 | − | 2.37084i | 0.230229 | − | 0.0974410i | ||||
\(593\) | 4.13138 | + | 4.13138i | 0.169656 | + | 0.169656i | 0.786828 | − | 0.617172i | \(-0.211722\pi\) |
−0.617172 | + | 0.786828i | \(0.711722\pi\) | |||||||
\(594\) | −4.96140 | + | 4.96140i | −0.203569 | + | 0.203569i | ||||
\(595\) | −5.50049 | + | 27.2463i | −0.225498 | + | 1.11699i | ||||
\(596\) | − | 13.0913i | − | 0.536240i | ||||||
\(597\) | 24.3797i | 0.997796i | ||||||||
\(598\) | −9.50925 | −0.388862 | ||||||||
\(599\) | − | 38.0949i | − | 1.55652i | −0.627944 | − | 0.778258i | \(-0.716104\pi\) | ||
0.627944 | − | 0.778258i | \(-0.283896\pi\) | |||||||
\(600\) | −4.87791 | − | 11.9690i | −0.199140 | − | 0.488634i | ||||
\(601\) | −43.6207 | −1.77933 | −0.889663 | − | 0.456617i | \(-0.849061\pi\) | ||||
−0.889663 | + | 0.456617i | \(0.849061\pi\) | |||||||
\(602\) | −30.7314 | + | 30.7314i | −1.25252 | + | 1.25252i | ||||
\(603\) | −4.73262 | + | 4.73262i | −0.192727 | + | 0.192727i | ||||
\(604\) | − | 9.37187i | − | 0.381336i | ||||||
\(605\) | 5.98259 | + | 9.00912i | 0.243227 | + | 0.366273i | ||||
\(606\) | −2.99912 | − | 2.99912i | −0.121831 | − | 0.121831i | ||||
\(607\) | −4.59751 | −0.186607 | −0.0933036 | − | 0.995638i | \(-0.529743\pi\) | ||||
−0.0933036 | + | 0.995638i | \(0.529743\pi\) | |||||||
\(608\) | −5.24415 | − | 5.24415i | −0.212678 | − | 0.212678i | ||||
\(609\) | 25.3959 | + | 25.3959i | 1.02909 | + | 1.02909i | ||||
\(610\) | 3.57485 | − | 17.7078i | 0.144741 | − | 0.716967i | ||||
\(611\) | 4.04523 | − | 4.04523i | 0.163652 | − | 0.163652i | ||||
\(612\) | −9.48196 | −0.383285 | ||||||||
\(613\) | 9.19983 | − | 9.19983i | 0.371578 | − | 0.371578i | −0.496474 | − | 0.868052i | \(-0.665372\pi\) |
0.868052 | + | 0.496474i | \(0.165372\pi\) | |||||||
\(614\) | −3.64587 | − | 3.64587i | −0.147135 | − | 0.147135i | ||||
\(615\) | −2.86830 | + | 14.2079i | −0.115661 | + | 0.572919i | ||||
\(616\) | −13.5833 | − | 13.5833i | −0.547287 | − | 0.547287i | ||||
\(617\) | 8.47786 | + | 8.47786i | 0.341306 | + | 0.341306i | 0.856858 | − | 0.515552i | \(-0.172413\pi\) |
−0.515552 | + | 0.856858i | \(0.672413\pi\) | |||||||
\(618\) | 5.10132 | + | 5.10132i | 0.205205 | + | 0.205205i | ||||
\(619\) | −12.3858 | −0.497827 | −0.248914 | − | 0.968526i | \(-0.580074\pi\) | ||||
−0.248914 | + | 0.968526i | \(0.580074\pi\) | |||||||
\(620\) | −2.02584 | + | 10.0349i | −0.0813596 | + | 0.403009i | ||||
\(621\) | 2.76506 | + | 2.76506i | 0.110958 | + | 0.110958i | ||||
\(622\) | 0.480637 | + | 0.480637i | 0.0192718 | + | 0.0192718i | ||||
\(623\) | 64.3668i | 2.57880i | ||||||||
\(624\) | −7.83714 | + | 7.83714i | −0.313737 | + | 0.313737i | ||||
\(625\) | −17.4748 | − | 17.8783i | −0.698991 | − | 0.715130i | ||||
\(626\) | 18.2772 | 0.730502 | ||||||||
\(627\) | 76.2912i | 3.04678i | ||||||||
\(628\) | −16.2868 | + | 16.2868i | −0.649913 | + | 0.649913i | ||||
\(629\) | −6.10530 | − | 14.4253i | −0.243434 | − | 0.575175i | ||||
\(630\) | 7.86483 | − | 38.9579i | 0.313342 | − | 1.55212i | ||||
\(631\) | −19.2781 | − | 19.2781i | −0.767448 | − | 0.767448i | 0.210208 | − | 0.977657i | \(-0.432586\pi\) |
−0.977657 | + | 0.210208i | \(0.932586\pi\) | |||||||
\(632\) | −9.77118 | − | 9.77118i | −0.388677 | − | 0.388677i | ||||
\(633\) | 27.7017 | − | 27.7017i | 1.10104 | − | 1.10104i | ||||
\(634\) | 4.85997 | + | 4.85997i | 0.193014 | + | 0.193014i | ||||
\(635\) | −0.171648 | − | 0.0346523i | −0.00681163 | − | 0.00137513i | ||||
\(636\) | 10.3842 | 0.411761 | ||||||||
\(637\) | 69.8948i | 2.76933i | ||||||||
\(638\) | 8.09925 | + | 8.09925i | 0.320653 | + | 0.320653i | ||||
\(639\) | − | 30.9417i | − | 1.22404i | ||||||
\(640\) | 1.23698 | + | 1.86276i | 0.0488961 | + | 0.0736320i | ||||
\(641\) | 0.616340 | 0.0243440 | 0.0121720 | − | 0.999926i | \(-0.496125\pi\) | ||||
0.0121720 | + | 0.999926i | \(0.496125\pi\) | |||||||
\(642\) | − | 13.7896i | − | 0.544233i | ||||||
\(643\) | − | 42.0640i | − | 1.65884i | −0.558622 | − | 0.829422i | \(-0.688670\pi\) | ||
0.558622 | − | 0.829422i | \(-0.311330\pi\) | |||||||
\(644\) | −7.57018 | + | 7.57018i | −0.298307 | + | 0.298307i | ||||
\(645\) | −51.0119 | − | 10.2983i | −2.00859 | − | 0.405495i | ||||
\(646\) | −13.5045 | + | 13.5045i | −0.531329 | + | 0.531329i | ||||
\(647\) | −35.3320 | −1.38904 | −0.694521 | − | 0.719472i | \(-0.744384\pi\) | ||||
−0.694521 | + | 0.719472i | \(0.744384\pi\) | |||||||
\(648\) | −6.48853 | −0.254894 | ||||||||
\(649\) | 11.5847 | − | 11.5847i | 0.454738 | − | 0.454738i | ||||
\(650\) | −8.31690 | + | 19.7591i | −0.326216 | + | 0.775016i | ||||
\(651\) | −40.3955 | + | 40.3955i | −1.58323 | + | 1.58323i | ||||
\(652\) | − | 2.14382i | − | 0.0839586i | ||||||
\(653\) | − | 12.3601i | − | 0.483687i | −0.970315 | − | 0.241844i | \(-0.922248\pi\) | ||
0.970315 | − | 0.241844i | \(-0.0777521\pi\) | |||||||
\(654\) | −43.6134 | −1.70542 | ||||||||
\(655\) | 1.93326 | − | 9.57626i | 0.0755385 | − | 0.374175i | ||||
\(656\) | − | 2.50763i | − | 0.0979067i | ||||||
\(657\) | 19.6068 | + | 19.6068i | 0.764933 | + | 0.764933i | ||||
\(658\) | − | 6.44070i | − | 0.251085i | ||||||
\(659\) | −37.7706 | −1.47133 | −0.735667 | − | 0.677344i | \(-0.763131\pi\) | ||||
−0.735667 | + | 0.677344i | \(0.763131\pi\) | |||||||
\(660\) | 4.55186 | − | 22.5473i | 0.177181 | − | 0.877654i | ||||
\(661\) | 25.3521 | + | 25.3521i | 0.986082 | + | 0.986082i | 0.999904 | − | 0.0138228i | \(-0.00440006\pi\) |
−0.0138228 | + | 0.999904i | \(0.504400\pi\) | |||||||
\(662\) | 20.7472 | − | 20.7472i | 0.806362 | − | 0.806362i | ||||
\(663\) | 20.1819 | + | 20.1819i | 0.783801 | + | 0.783801i | ||||
\(664\) | −2.57398 | − | 2.57398i | −0.0998896 | − | 0.0998896i | ||||
\(665\) | −44.2839 | − | 66.6866i | −1.71726 | − | 2.58600i | ||||
\(666\) | 8.72962 | + | 20.6259i | 0.338266 | + | 0.799238i | ||||
\(667\) | 4.51383 | − | 4.51383i | 0.174776 | − | 0.174776i | ||||
\(668\) | − | 20.3382i | − | 0.786908i | ||||||
\(669\) | −22.8681 | −0.884131 | ||||||||
\(670\) | 0.804317 | − | 3.98413i | 0.0310735 | − | 0.153921i | ||||
\(671\) | 22.7335 | − | 22.7335i | 0.877619 | − | 0.877619i | ||||
\(672\) | 12.4781i | 0.481353i | ||||||||
\(673\) | −0.303990 | − | 0.303990i | −0.0117180 | − | 0.0117180i | 0.701224 | − | 0.712941i | \(-0.252637\pi\) |
−0.712941 | + | 0.701224i | \(0.752637\pi\) | |||||||
\(674\) | −6.47001 | − | 6.47001i | −0.249215 | − | 0.249215i | ||||
\(675\) | 8.16383 | − | 3.32712i | 0.314226 | − | 0.128061i | ||||
\(676\) | 5.38374 | 0.207067 | ||||||||
\(677\) | 19.2022 | + | 19.2022i | 0.738000 | + | 0.738000i | 0.972191 | − | 0.234191i | \(-0.0752440\pi\) |
−0.234191 | + | 0.972191i | \(0.575244\pi\) | |||||||
\(678\) | −28.4175 | − | 28.4175i | −1.09137 | − | 1.09137i | ||||
\(679\) | −20.2153 | − | 20.2153i | −0.775791 | − | 0.775791i | ||||
\(680\) | 4.79691 | − | 3.18543i | 0.183953 | − | 0.122156i | ||||
\(681\) | −18.0582 | − | 18.0582i | −0.691993 | − | 0.691993i | ||||
\(682\) | −12.8829 | + | 12.8829i | −0.493312 | + | 0.493312i | ||||
\(683\) | −16.4834 | −0.630719 | −0.315359 | − | 0.948972i | \(-0.602125\pi\) | ||||
−0.315359 | + | 0.948972i | \(0.602125\pi\) | |||||||
\(684\) | 19.3094 | − | 19.3094i | 0.738312 | − | 0.738312i | ||||
\(685\) | 5.73052 | + | 1.15688i | 0.218952 | + | 0.0442020i | ||||
\(686\) | 31.7491 | + | 31.7491i | 1.21218 | + | 1.21218i | ||||
\(687\) | 40.1161 | + | 40.1161i | 1.53053 | + | 1.53053i | ||||
\(688\) | 9.00337 | 0.343250 | ||||||||
\(689\) | −12.1792 | − | 12.1792i | −0.463991 | − | 0.463991i | ||||
\(690\) | −12.5660 | − | 2.53682i | −0.478378 | − | 0.0965750i | ||||
\(691\) | 27.8853i | 1.06081i | 0.847745 | + | 0.530403i | \(0.177959\pi\) | ||||
−0.847745 | + | 0.530403i | \(0.822041\pi\) | |||||||
\(692\) | 13.7435 | − | 13.7435i | 0.522450 | − | 0.522450i | ||||
\(693\) | 50.0148 | − | 50.0148i | 1.89991 | − | 1.89991i | ||||
\(694\) | 6.44807 | 0.244765 | ||||||||
\(695\) | 13.5366 | + | 20.3846i | 0.513473 | + | 0.773234i | ||||
\(696\) | − | 7.44024i | − | 0.282022i | ||||||
\(697\) | −6.45757 | −0.244598 | ||||||||
\(698\) | 4.70014i | 0.177903i | ||||||||
\(699\) | 32.7771i | 1.23974i | ||||||||
\(700\) | 9.10899 | + | 22.3509i | 0.344287 | + | 0.844786i | ||||
\(701\) | 5.25849 | − | 5.25849i | 0.198610 | − | 0.198610i | −0.600794 | − | 0.799404i | \(-0.705149\pi\) |
0.799404 | + | 0.600794i | \(0.205149\pi\) | |||||||
\(702\) | −5.34555 | − | 5.34555i | −0.201755 | − | 0.201755i | ||||
\(703\) | 41.8092 | + | 16.9431i | 1.57686 | + | 0.639023i | ||||
\(704\) | 3.97950i | 0.149983i | ||||||||
\(705\) | 6.42471 | − | 4.26639i | 0.241969 | − | 0.160682i | ||||
\(706\) | 19.6162i | 0.738264i | ||||||||
\(707\) | 5.60054 | + | 5.60054i | 0.210630 | + | 0.210630i | ||||
\(708\) | −10.6421 | −0.399953 | ||||||||
\(709\) | 25.3783 | + | 25.3783i | 0.953101 | + | 0.953101i | 0.998948 | − | 0.0458470i | \(-0.0145987\pi\) |
−0.0458470 | + | 0.998948i | \(0.514599\pi\) | |||||||
\(710\) | 10.3948 | + | 15.6534i | 0.390109 | + | 0.587461i | ||||
\(711\) | 35.9783 | − | 35.9783i | 1.34929 | − | 1.34929i | ||||
\(712\) | 9.42876 | − | 9.42876i | 0.353358 | − | 0.353358i | ||||
\(713\) | 7.17984 | + | 7.17984i | 0.268887 | + | 0.268887i | ||||
\(714\) | 32.1331 | 1.20255 | ||||||||
\(715\) | −31.7836 | + | 21.1062i | −1.18864 | + | 0.789326i | ||||
\(716\) | 13.4168 | − | 13.4168i | 0.501408 | − | 0.501408i | ||||
\(717\) | −47.8222 | −1.78595 | ||||||||
\(718\) | 7.60520i | 0.283824i | ||||||||
\(719\) | − | 0.372987i | − | 0.0139101i | −0.999976 | − | 0.00695503i | \(-0.997786\pi\) | ||
0.999976 | − | 0.00695503i | \(-0.00221387\pi\) | |||||||
\(720\) | −6.85883 | + | 4.55467i | −0.255613 | + | 0.169743i | ||||
\(721\) | −9.52619 | − | 9.52619i | −0.354774 | − | 0.354774i | ||||
\(722\) | − | 36.0022i | − | 1.33986i | ||||||
\(723\) | − | 19.7845i | − | 0.735794i | ||||||
\(724\) | −15.3711 | −0.571261 | ||||||||
\(725\) | −5.43137 | − | 13.3271i | −0.201716 | − | 0.494955i | ||||
\(726\) | 8.84029 | − | 8.84029i | 0.328094 | − | 0.328094i | ||||
\(727\) | −14.7295 | −0.546286 | −0.273143 | − | 0.961973i | \(-0.588063\pi\) | ||||
−0.273143 | + | 0.961973i | \(0.588063\pi\) | |||||||
\(728\) | 14.6350 | − | 14.6350i | 0.542411 | − | 0.542411i | ||||
\(729\) | − | 37.5644i | − | 1.39127i | ||||||
\(730\) | −16.5059 | − | 3.33221i | −0.610910 | − | 0.123331i | ||||
\(731\) | − | 23.1852i | − | 0.857534i | ||||||
\(732\) | −20.8838 | −0.771887 | ||||||||
\(733\) | 10.6225 | − | 10.6225i | 0.392351 | − | 0.392351i | −0.483173 | − | 0.875525i | \(-0.660516\pi\) |
0.875525 | + | 0.483173i | \(0.160516\pi\) | |||||||
\(734\) | 10.3061 | − | 10.3061i | 0.380406 | − | 0.380406i | ||||
\(735\) | −18.6461 | + | 92.3622i | −0.687772 | + | 3.40683i | ||||
\(736\) | 2.21783 | 0.0817505 | ||||||||
\(737\) | 5.11490 | − | 5.11490i | 0.188410 | − | 0.188410i | ||||
\(738\) | 9.23331 | 0.339883 | ||||||||
\(739\) | 27.4110 | 1.00833 | 0.504165 | − | 0.863608i | \(-0.331800\pi\) | ||||
0.504165 | + | 0.863608i | \(0.331800\pi\) | |||||||
\(740\) | −11.3455 | − | 7.50194i | −0.417070 | − | 0.275777i | ||||
\(741\) | −82.1983 | −3.01963 | ||||||||
\(742\) | −19.3914 | −0.711881 | ||||||||
\(743\) | 31.6154 | − | 31.6154i | 1.15986 | − | 1.15986i | 0.175349 | − | 0.984506i | \(-0.443895\pi\) |
0.984506 | − | 0.175349i | \(-0.0561053\pi\) | |||||||
\(744\) | 11.8347 | 0.433880 | ||||||||
\(745\) | −24.3859 | + | 16.1937i | −0.893431 | + | 0.593291i | ||||
\(746\) | −0.690871 | + | 0.690871i | −0.0252946 | + | 0.0252946i | ||||
\(747\) | 9.47758 | − | 9.47758i | 0.346767 | − | 0.346767i | ||||
\(748\) | 10.2479 | 0.374699 | ||||||||
\(749\) | 25.7507i | 0.940910i | ||||||||
\(750\) | −16.2616 | + | 23.8919i | −0.593788 | + | 0.872408i | ||||
\(751\) | 25.5768i | 0.933311i | 0.884439 | + | 0.466655i | \(0.154541\pi\) | ||||
−0.884439 | + | 0.466655i | \(0.845459\pi\) | |||||||
\(752\) | −0.943466 | + | 0.943466i | −0.0344047 | + | 0.0344047i | ||||
\(753\) | 8.58049 | 0.312690 | ||||||||
\(754\) | −8.72636 | + | 8.72636i | −0.317795 | + | 0.317795i | ||||
\(755\) | −17.4575 | + | 11.5928i | −0.635345 | + | 0.421907i | ||||
\(756\) | −8.51103 | −0.309543 | ||||||||
\(757\) | − | 14.8725i | − | 0.540552i | −0.962783 | − | 0.270276i | \(-0.912885\pi\) | ||
0.962783 | − | 0.270276i | \(-0.0871149\pi\) | |||||||
\(758\) | − | 0.266778i | − | 0.00968982i | ||||||
\(759\) | −16.1324 | − | 16.1324i | −0.585569 | − | 0.585569i | ||||
\(760\) | −3.28166 | + | 16.2555i | −0.119038 | + | 0.589649i | ||||
\(761\) | − | 41.3732i | − | 1.49978i | −0.661564 | − | 0.749888i | \(-0.730107\pi\) | ||
0.661564 | − | 0.749888i | \(-0.269893\pi\) | |||||||
\(762\) | 0.202434i | 0.00733341i | ||||||||
\(763\) | 81.4434 | 2.94845 | ||||||||
\(764\) | −16.9686 | + | 16.9686i | −0.613904 | + | 0.613904i | ||||
\(765\) | 11.7290 | + | 17.6626i | 0.424064 | + | 0.638593i | ||||
\(766\) | −32.6980 | −1.18143 | ||||||||
\(767\) | 12.4817 | + | 12.4817i | 0.450686 | + | 0.450686i | ||||
\(768\) | 1.82785 | − | 1.82785i | 0.0659569 | − | 0.0659569i | ||||
\(769\) | 0.831140 | − | 0.831140i | 0.0299717 | − | 0.0299717i | −0.691962 | − | 0.721934i | \(-0.743253\pi\) |
0.721934 | + | 0.691962i | \(0.243253\pi\) | |||||||
\(770\) | −8.50012 | + | 42.1048i | −0.306323 | + | 1.51735i | ||||
\(771\) | 10.6164 | + | 10.6164i | 0.382340 | + | 0.382340i | ||||
\(772\) | −5.70785 | −0.205430 | ||||||||
\(773\) | −24.1870 | − | 24.1870i | −0.869946 | − | 0.869946i | 0.122520 | − | 0.992466i | \(-0.460903\pi\) |
−0.992466 | + | 0.122520i | \(0.960903\pi\) | |||||||
\(774\) | 33.1511i | 1.19159i | ||||||||
\(775\) | 21.1984 | − | 8.63930i | 0.761470 | − | 0.310333i | ||||
\(776\) | 5.92246i | 0.212604i | ||||||||
\(777\) | −29.5835 | − | 69.8986i | −1.06130 | − | 2.50760i | ||||
\(778\) | −24.7831 | − | 24.7831i | −0.888517 | − | 0.888517i | ||||
\(779\) | 13.1504 | − | 13.1504i | 0.471162 | − | 0.471162i | ||||
\(780\) | 24.2931 | + | 4.90430i | 0.869833 | + | 0.175602i | ||||
\(781\) | 33.4411i | 1.19662i | ||||||||
\(782\) | − | 5.71129i | − | 0.204235i | ||||||
\(783\) | 5.07483 | 0.181360 | ||||||||
\(784\) | − | 16.3015i | − | 0.582197i | ||||||
\(785\) | 50.4848 | + | 10.1919i | 1.80188 | + | 0.363764i | ||||
\(786\) | −11.2938 | −0.402837 | ||||||||
\(787\) | 17.1870 | − | 17.1870i | 0.612650 | − | 0.612650i | −0.330986 | − | 0.943636i | \(-0.607381\pi\) |
0.943636 | + | 0.330986i | \(0.107381\pi\) | |||||||
\(788\) | 9.14763 | − | 9.14763i | 0.325871 | − | 0.325871i | ||||
\(789\) | 55.9116i | 1.99051i | ||||||||
\(790\) | −6.11457 | + | 30.2881i | −0.217547 | + | 1.07760i | ||||
\(791\) | 53.0667 | + | 53.0667i | 1.88684 | + | 1.88684i | ||||
\(792\) | −14.6528 | −0.520666 | ||||||||
\(793\) | 24.4938 | + | 24.4938i | 0.869799 | + | 0.869799i | ||||
\(794\) | 11.3967 | + | 11.3967i | 0.404454 | + | 0.404454i | ||||
\(795\) | −12.8451 | − | 19.3433i | −0.455568 | − | 0.686035i | ||||
\(796\) | −6.66896 | + | 6.66896i | −0.236375 | + | 0.236375i | ||||
\(797\) | 10.6790 | 0.378270 | 0.189135 | − | 0.981951i | \(-0.439432\pi\) | ||||
0.189135 | + | 0.981951i | \(0.439432\pi\) | |||||||
\(798\) | −65.4369 | + | 65.4369i | −2.31644 | + | 2.31644i | ||||
\(799\) | 2.42958 | + | 2.42958i | 0.0859523 | + | 0.0859523i | ||||
\(800\) | 1.93975 | − | 4.60840i | 0.0685804 | − | 0.162932i | ||||
\(801\) | 34.7175 | + | 34.7175i | 1.22668 | + | 1.22668i | ||||
\(802\) | 14.6783 | + | 14.6783i | 0.518309 | + | 0.518309i | ||||
\(803\) | −21.1905 | − | 21.1905i | −0.747797 | − | 0.747797i | ||||
\(804\) | −4.69872 | −0.165711 | ||||||||
\(805\) | 23.4656 | + | 4.73724i | 0.827054 | + | 0.166966i | ||||
\(806\) | −13.8804 | − | 13.8804i | −0.488917 | − | 0.488917i | ||||
\(807\) | 33.3167 | + | 33.3167i | 1.17280 | + | 1.17280i | ||||
\(808\) | − | 1.64079i | − | 0.0577227i | ||||||
\(809\) | −9.53144 | + | 9.53144i | −0.335108 | + | 0.335108i | −0.854522 | − | 0.519415i | \(-0.826150\pi\) |
0.519415 | + | 0.854522i | \(0.326150\pi\) | |||||||
\(810\) | 8.02621 | + | 12.0866i | 0.282012 | + | 0.424679i | ||||
\(811\) | 29.6048 | 1.03956 | 0.519782 | − | 0.854299i | \(-0.326013\pi\) | ||||
0.519782 | + | 0.854299i | \(0.326013\pi\) | |||||||
\(812\) | 13.8939i | 0.487579i | ||||||||
\(813\) | −48.6383 | + | 48.6383i | −1.70582 | + | 1.70582i | ||||
\(814\) | −9.43477 | − | 22.2920i | −0.330688 | − | 0.781334i | ||||
\(815\) | −3.99343 | + | 2.65187i | −0.139884 | + | 0.0928911i | ||||
\(816\) | −4.70702 | − | 4.70702i | −0.164779 | − | 0.164779i | ||||
\(817\) | 47.2150 | + | 47.2150i | 1.65184 | + | 1.65184i | ||||
\(818\) | 10.7756 | − | 10.7756i | 0.376760 | − | 0.376760i | ||||
\(819\) | 53.8874 | + | 53.8874i | 1.88298 | + | 1.88298i | ||||
\(820\) | −4.67112 | + | 3.10190i | −0.163123 | + | 0.108323i | ||||
\(821\) | −24.3165 | −0.848651 | −0.424325 | − | 0.905510i | \(-0.639489\pi\) | ||||
−0.424325 | + | 0.905510i | \(0.639489\pi\) | |||||||
\(822\) | − | 6.75833i | − | 0.235724i | ||||||
\(823\) | −35.9075 | − | 35.9075i | −1.25166 | − | 1.25166i | −0.954976 | − | 0.296682i | \(-0.904120\pi\) |
−0.296682 | − | 0.954976i | \(-0.595880\pi\) | |||||||
\(824\) | 2.79089i | 0.0972251i | ||||||||
\(825\) | −47.6308 | + | 19.4117i | −1.65829 | + | 0.675827i | ||||
\(826\) | 19.8730 | 0.691468 | ||||||||
\(827\) | 7.03825i | 0.244744i | 0.992484 | + | 0.122372i | \(0.0390501\pi\) | ||||
−0.992484 | + | 0.122372i | \(0.960950\pi\) | |||||||
\(828\) | 8.16624i | 0.283797i | ||||||||
\(829\) | 12.4360 | − | 12.4360i | 0.431920 | − | 0.431920i | −0.457361 | − | 0.889281i | \(-0.651205\pi\) |
0.889281 | + | 0.457361i | \(0.151205\pi\) | |||||||
\(830\) | −1.61073 | + | 7.97866i | −0.0559094 | + | 0.276943i | ||||
\(831\) | 1.54567 | − | 1.54567i | 0.0536188 | − | 0.0536188i | ||||
\(832\) | −4.28763 | −0.148647 | ||||||||
\(833\) | −41.9791 | −1.45449 | ||||||||
\(834\) | 20.0026 | − | 20.0026i | 0.692635 | − | 0.692635i | ||||
\(835\) | −37.8851 | + | 25.1580i | −1.31107 | + | 0.870628i | ||||
\(836\) | −20.8691 | + | 20.8691i | −0.721773 | + | 0.721773i | ||||
\(837\) | 8.07217i | 0.279015i | ||||||||
\(838\) | − | 24.0943i | − | 0.832325i | ||||||
\(839\) | 21.4518 | 0.740598 | 0.370299 | − | 0.928913i | \(-0.379255\pi\) | ||||
0.370299 | + | 0.928913i | \(0.379255\pi\) | |||||||
\(840\) | 23.2437 | − | 15.4352i | 0.801983 | − | 0.532564i | ||||
\(841\) | 20.7156i | 0.714330i | ||||||||
\(842\) | −21.6407 | − | 21.6407i | −0.745788 | − | 0.745788i | ||||
\(843\) | − | 41.6051i | − | 1.43296i | ||||||
\(844\) | 15.1553 | 0.521668 | ||||||||
\(845\) | −6.65959 | − | 10.0286i | −0.229097 | − | 0.344995i | ||||
\(846\) | −3.47392 | − | 3.47392i | −0.119436 | − | 0.119436i | ||||
\(847\) | −16.5083 | + | 16.5083i | −0.567232 | + | 0.567232i | ||||
\(848\) | 2.84055 | + | 2.84055i | 0.0975449 | + | 0.0975449i | ||||
\(849\) | 11.6591 | + | 11.6591i | 0.400139 | + | 0.400139i | ||||
\(850\) | −11.8674 | − | 4.99516i | −0.407048 | − | 0.171333i | ||||
\(851\) | −12.4237 | + | 5.25813i | −0.425878 | + | 0.180246i | ||||
\(852\) | 15.3600 | − | 15.3600i | 0.526227 | − | 0.526227i | ||||
\(853\) | − | 9.13898i | − | 0.312913i | −0.987685 | − | 0.156456i | \(-0.949993\pi\) | ||
0.987685 | − | 0.156456i | \(-0.0500071\pi\) | |||||||
\(854\) | 38.9983 | 1.33449 | ||||||||
\(855\) | −59.8541 | − | 12.0833i | −2.04697 | − | 0.413242i | ||||
\(856\) | 3.77209 | − | 3.77209i | 0.128927 | − | 0.128927i | ||||
\(857\) | 13.4472i | 0.459346i | 0.973268 | + | 0.229673i | \(0.0737657\pi\) | ||||
−0.973268 | + | 0.229673i | \(0.926234\pi\) | |||||||
\(858\) | 31.1879 | + | 31.1879i | 1.06474 | + | 1.06474i | ||||
\(859\) | −29.5713 | − | 29.5713i | −1.00896 | − | 1.00896i | −0.999959 | − | 0.00900160i | \(-0.997135\pi\) |
−0.00900160 | − | 0.999959i | \(-0.502865\pi\) | |||||||
\(860\) | −11.1370 | − | 16.7711i | −0.379769 | − | 0.571890i | ||||
\(861\) | −31.2905 | −1.06638 | ||||||||
\(862\) | −1.23281 | − | 1.23281i | −0.0419898 | − | 0.0419898i | ||||
\(863\) | 9.53473 | + | 9.53473i | 0.324566 | + | 0.324566i | 0.850516 | − | 0.525950i | \(-0.176290\pi\) |
−0.525950 | + | 0.850516i | \(0.676290\pi\) | |||||||
\(864\) | 1.24674 | + | 1.24674i | 0.0424149 | + | 0.0424149i | ||||
\(865\) | −42.6014 | − | 8.60037i | −1.44849 | − | 0.292421i | ||||
\(866\) | 12.5825 | + | 12.5825i | 0.427572 | + | 0.427572i | ||||
\(867\) | 18.9521 | − | 18.9521i | 0.643648 | − | 0.643648i | ||||
\(868\) | −22.1000 | −0.750123 | ||||||||
\(869\) | −38.8844 | + | 38.8844i | −1.31906 | + | 1.31906i | ||||
\(870\) | −13.8594 | + | 9.20345i | −0.469877 | + | 0.312026i | ||||
\(871\) | 5.51094 | + | 5.51094i | 0.186731 | + | 0.186731i | ||||
\(872\) | −11.9302 | − | 11.9302i | −0.404008 | − | 0.404008i | ||||
\(873\) | −21.8070 | −0.738054 | ||||||||
\(874\) | 11.6307 | + | 11.6307i | 0.393413 | + | 0.393413i | ||||
\(875\) | 30.3667 | − | 44.6156i | 1.02658 | − | 1.50828i | ||||
\(876\) | 19.4663i | 0.657706i | ||||||||
\(877\) | −7.17655 | + | 7.17655i | −0.242335 | + | 0.242335i | −0.817815 | − | 0.575481i | \(-0.804815\pi\) |
0.575481 | + | 0.817815i | \(0.304815\pi\) | |||||||
\(878\) | 13.6362 | − | 13.6362i | 0.460201 | − | 0.460201i | ||||
\(879\) | −23.6851 | −0.798878 | ||||||||
\(880\) | 7.41286 | − | 4.92258i | 0.249887 | − | 0.165940i | ||||
\(881\) | 10.0748i | 0.339428i | 0.985493 | + | 0.169714i | \(0.0542844\pi\) | ||||
−0.985493 | + | 0.169714i | \(0.945716\pi\) | |||||||
\(882\) | 60.0235 | 2.02110 | ||||||||
\(883\) | − | 33.1203i | − | 1.11459i | −0.830316 | − | 0.557293i | \(-0.811840\pi\) | ||
0.830316 | − | 0.557293i | \(-0.188160\pi\) | |||||||
\(884\) | 11.0413i | 0.371360i | ||||||||
\(885\) | 13.1641 | + | 19.8236i | 0.442505 | + | 0.666364i | ||||
\(886\) | 23.2157 | − | 23.2157i | 0.779945 | − | 0.779945i | ||||
\(887\) | 27.8387 | + | 27.8387i | 0.934731 | + | 0.934731i | 0.997997 | − | 0.0632658i | \(-0.0201516\pi\) |
−0.0632658 | + | 0.997997i | \(0.520152\pi\) | |||||||
\(888\) | −5.90554 | + | 14.5726i | −0.198177 | + | 0.489025i | ||||
\(889\) | − | 0.378024i | − | 0.0126785i | ||||||
\(890\) | −29.2267 | − | 5.90030i | −0.979683 | − | 0.197778i | ||||
\(891\) | 25.8211i | 0.865040i | ||||||||
\(892\) | −6.25546 | − | 6.25546i | −0.209448 | − | 0.209448i | ||||
\(893\) | −9.89535 | −0.331135 | ||||||||
\(894\) | 23.9289 | + | 23.9289i | 0.800303 | + | 0.800303i | ||||
\(895\) | −41.5885 | − | 8.39589i | −1.39015 | − | 0.280644i | ||||
\(896\) | −3.41332 | + | 3.41332i | −0.114031 | + | 0.114031i | ||||
\(897\) | 17.3815 | − | 17.3815i | 0.580351 | − | 0.580351i | ||||
\(898\) | −16.0955 | − | 16.0955i | −0.537114 | − | 0.537114i | ||||
\(899\) | 13.1775 | 0.439493 | ||||||||
\(900\) | 16.9685 | + | 7.14229i | 0.565617 | + | 0.238076i | ||||
\(901\) | 7.31488 | − | 7.31488i | 0.243694 | − | 0.243694i | ||||
\(902\) | −9.97914 | −0.332269 | ||||||||
\(903\) | − | 112.345i | − | 3.73860i | ||||||
\(904\) | − | 15.5469i | − | 0.517084i | ||||||
\(905\) | 19.0138 | + | 28.6326i | 0.632039 | + | 0.951780i | ||||
\(906\) | 17.1304 | + | 17.1304i | 0.569119 | + | 0.569119i | ||||
\(907\) | − | 11.8792i | − | 0.394444i | −0.980359 | − | 0.197222i | \(-0.936808\pi\) | ||
0.980359 | − | 0.197222i | \(-0.0631920\pi\) | |||||||
\(908\) | − | 9.87949i | − | 0.327862i | ||||||
\(909\) | 6.04151 | 0.200384 | ||||||||
\(910\) | −45.3649 | − | 9.15826i | −1.50383 | − | 0.303593i | ||||
\(911\) | 27.0290 | − | 27.0290i | 0.895512 | − | 0.895512i | −0.0995236 | − | 0.995035i | \(-0.531732\pi\) |
0.995035 | + | 0.0995236i | \(0.0317319\pi\) | |||||||
\(912\) | 19.1710 | 0.634817 | ||||||||
\(913\) | −10.2431 | + | 10.2431i | −0.338999 | + | 0.338999i | ||||
\(914\) | 3.34685i | 0.110704i | ||||||||
\(915\) | 25.8329 | + | 38.9015i | 0.854009 | + | 1.28604i | ||||
\(916\) | 21.9472i | 0.725155i | ||||||||
\(917\) | 21.0900 | 0.696454 | ||||||||
\(918\) | 3.21055 | − | 3.21055i | 0.105964 | − | 0.105964i | ||||
\(919\) | −39.7559 | + | 39.7559i | −1.31143 | + | 1.31143i | −0.391062 | + | 0.920364i | \(0.627892\pi\) |
−0.920364 | + | 0.391062i | \(0.872108\pi\) | |||||||
\(920\) | −2.74342 | − | 4.13129i | −0.0904480 | − | 0.136205i | ||||
\(921\) | 13.3282 | 0.439179 | ||||||||
\(922\) | −22.0325 | + | 22.0325i | −0.725601 | + | 0.725601i | ||||
\(923\) | −36.0304 | −1.18595 | ||||||||
\(924\) | 49.6566 | 1.63358 | ||||||||
\(925\) | 0.0599082 | + | 30.4138i | 0.00196977 | + | 0.999998i | ||||
\(926\) | 10.8598 | 0.356874 | ||||||||
\(927\) | −10.2763 | −0.337517 | ||||||||
\(928\) | 2.03524 | − | 2.03524i | 0.0668101 | − | 0.0668101i | ||||
\(929\) | 28.8922 | 0.947923 | 0.473961 | − | 0.880546i | \(-0.342824\pi\) | ||||
0.473961 | + | 0.880546i | \(0.342824\pi\) | |||||||
\(930\) | −14.6393 | − | 22.0451i | −0.480041 | − | 0.722889i | ||||
\(931\) | 85.4876 | − | 85.4876i | 2.80174 | − | 2.80174i | ||||
\(932\) | −8.96601 | + | 8.96601i | −0.293691 | + | 0.293691i | ||||
\(933\) | −1.75707 | −0.0575238 | ||||||||
\(934\) | − | 12.9597i | − | 0.424054i | ||||||
\(935\) | −12.6764 | − | 19.0893i | −0.414564 | − | 0.624287i | ||||
\(936\) | − | 15.7874i | − | 0.516027i | ||||||
\(937\) | 29.8795 | − | 29.8795i | 0.976119 | − | 0.976119i | −0.0236021 | − | 0.999721i | \(-0.507513\pi\) |
0.999721 | + | 0.0236021i | \(0.00751348\pi\) | |||||||
\(938\) | 8.77436 | 0.286493 | ||||||||
\(939\) | −33.4079 | + | 33.4079i | −1.09023 | + | 1.09023i | ||||
\(940\) | 2.92450 | + | 0.590399i | 0.0953867 | + | 0.0192567i | ||||
\(941\) | −29.7963 | −0.971333 | −0.485666 | − | 0.874144i | \(-0.661423\pi\) | ||||
−0.485666 | + | 0.874144i | \(0.661423\pi\) | |||||||
\(942\) | − | 59.5396i | − | 1.93990i | ||||||
\(943\) | 5.56152i | 0.181108i | ||||||||
\(944\) | −2.91109 | − | 2.91109i | −0.0947478 | − | 0.0947478i | ||||
\(945\) | 10.5280 | + | 15.8540i | 0.342476 | + | 0.515731i | ||||
\(946\) | − | 35.8289i | − | 1.16490i | ||||||
\(947\) | 41.7971i | 1.35822i | 0.734035 | + | 0.679112i | \(0.237635\pi\) | ||||
−0.734035 | + | 0.679112i | \(0.762365\pi\) | |||||||
\(948\) | 35.7205 | 1.16015 | ||||||||
\(949\) | 22.8313 | − | 22.8313i | 0.741134 | − | 0.741134i | ||||
\(950\) | 34.3395 | − | 13.9948i | 1.11412 | − | 0.454053i | ||||
\(951\) | −17.7666 | −0.576121 | ||||||||
\(952\) | 8.78986 | + | 8.78986i | 0.284881 | + | 0.284881i | ||||
\(953\) | 6.33457 | − | 6.33457i | 0.205197 | − | 0.205197i | −0.597025 | − | 0.802222i | \(-0.703651\pi\) |
0.802222 | + | 0.597025i | \(0.203651\pi\) | |||||||
\(954\) | −10.4591 | + | 10.4591i | −0.338627 | + | 0.338627i | ||||
\(955\) | 52.5984 | + | 10.6186i | 1.70204 | + | 0.343609i | ||||
\(956\) | −13.0815 | − | 13.0815i | −0.423087 | − | 0.423087i | ||||
\(957\) | −29.6085 | −0.957105 | ||||||||
\(958\) | 2.98032 | + | 2.98032i | 0.0962898 | + | 0.0962898i | ||||
\(959\) | 12.6205i | 0.407536i | ||||||||
\(960\) | −5.66587 | − | 1.14383i | −0.182865 | − | 0.0369168i | ||||
\(961\) | − | 10.0396i | − | 0.323856i | ||||||
\(962\) | 24.0180 | − | 10.1653i | 0.774372 | − | 0.327742i | ||||
\(963\) | 13.8891 | + | 13.8891i | 0.447571 | + | 0.447571i | ||||
\(964\) | 5.41196 | − | 5.41196i | 0.174308 | − | 0.174308i | ||||
\(965\) | 7.06051 | + | 10.6323i | 0.227286 | + | 0.342267i | ||||
\(966\) | − | 27.6743i | − | 0.890407i | ||||||
\(967\) | − | 39.3087i | − | 1.26408i | −0.774935 | − | 0.632041i | \(-0.782217\pi\) | ||
0.774935 | − | 0.632041i | \(-0.217783\pi\) | |||||||
\(968\) | 4.83644 | 0.155449 | ||||||||
\(969\) | − | 49.3686i | − | 1.58595i | ||||||
\(970\) | 11.0321 | − | 7.32599i | 0.354220 | − | 0.235223i | ||||
\(971\) | 23.7788 | 0.763098 | 0.381549 | − | 0.924349i | \(-0.375391\pi\) | ||||
0.381549 | + | 0.924349i | \(0.375391\pi\) | |||||||
\(972\) | 15.6003 | − | 15.6003i | 0.500379 | − | 0.500379i | ||||
\(973\) | −37.3528 | + | 37.3528i | −1.19748 | + | 1.19748i | ||||
\(974\) | 4.69219i | 0.150348i | ||||||||
\(975\) | −20.9147 | − | 51.3188i | −0.669805 | − | 1.64352i | ||||
\(976\) | −5.71266 | − | 5.71266i | −0.182858 | − | 0.182858i | ||||
\(977\) | −0.684369 | −0.0218949 | −0.0109474 | − | 0.999940i | \(-0.503485\pi\) | ||||
−0.0109474 | + | 0.999940i | \(0.503485\pi\) | |||||||
\(978\) | 3.91859 | + | 3.91859i | 0.125303 | + | 0.125303i | ||||
\(979\) | −37.5218 | − | 37.5218i | −1.19920 | − | 1.19920i | ||||
\(980\) | −30.3658 | + | 20.1647i | −0.970000 | + | 0.644138i | ||||
\(981\) | 43.9280 | − | 43.9280i | 1.40251 | − | 1.40251i | ||||
\(982\) | 4.44735 | 0.141921 | ||||||||
\(983\) | −31.2059 | + | 31.2059i | −0.995314 | + | 0.995314i | −0.999989 | − | 0.00467471i | \(-0.998512\pi\) |
0.00467471 | + | 0.999989i | \(0.498512\pi\) | |||||||
\(984\) | 4.58358 | + | 4.58358i | 0.146119 | + | 0.146119i | ||||
\(985\) | −28.3553 | − | 5.72437i | −0.903475 | − | 0.182394i | ||||
\(986\) | −5.24108 | − | 5.24108i | −0.166910 | − | 0.166910i | ||||
\(987\) | 11.7726 | + | 11.7726i | 0.374728 | + | 0.374728i | ||||
\(988\) | −22.4849 | − | 22.4849i | −0.715342 | − | 0.715342i | ||||
\(989\) | −19.9680 | −0.634945 | ||||||||
\(990\) | 18.1253 | + | 27.2947i | 0.576060 | + | 0.867483i | ||||
\(991\) | −13.0082 | − | 13.0082i | −0.413219 | − | 0.413219i | 0.469639 | − | 0.882858i | \(-0.344384\pi\) |
−0.882858 | + | 0.469639i | \(0.844384\pi\) | |||||||
\(992\) | 3.23732 | + | 3.23732i | 0.102785 | + | 0.102785i | ||||
\(993\) | 75.8455i | 2.40688i | ||||||||
\(994\) | −28.6833 | + | 28.6833i | −0.909779 | + | 0.909779i | ||||
\(995\) | 20.6721 | + | 4.17328i | 0.655348 | + | 0.132302i | ||||
\(996\) | 9.40969 | 0.298157 | ||||||||
\(997\) | 26.5817i | 0.841852i | 0.907095 | + | 0.420926i | \(0.138295\pi\) | ||||
−0.907095 | + | 0.420926i | \(0.861705\pi\) | |||||||
\(998\) | 24.3133 | − | 24.3133i | 0.769624 | − | 0.769624i | ||||
\(999\) | −9.93968 | − | 4.02804i | −0.314478 | − | 0.127442i |
(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 | 370.2.h.e.253.9 | yes | 20 | |
5.2 | odd | 4 | 370.2.g.e.327.2 | yes | 20 | ||
37.6 | odd | 4 | 370.2.g.e.43.2 | ✓ | 20 | ||
185.117 | even | 4 | inner | 370.2.h.e.117.9 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.g.e.43.2 | ✓ | 20 | 37.6 | odd | 4 | ||
370.2.g.e.327.2 | yes | 20 | 5.2 | odd | 4 | ||
370.2.h.e.117.9 | yes | 20 | 185.117 | even | 4 | inner | |
370.2.h.e.253.9 | yes | 20 | 1.1 | even | 1 | trivial |