Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,2,Mod(257,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([10, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.257");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.p (of order \(12\), degree \(4\), 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: | \(3.59326809096\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{12})\) |
Coefficient field: | 16.0.9349208943630483456.9 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 90) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 257.1 | ||
Root | \(0.500000 + 2.74530i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.257 |
Dual form | 450.2.p.h.443.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.965926 | − | 0.258819i | −0.683013 | − | 0.183013i | ||||
\(3\) | −0.933998 | + | 1.45865i | −0.539244 | + | 0.842150i | ||||
\(4\) | 0.866025 | + | 0.500000i | 0.433013 | + | 0.250000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.27970 | − | 1.16721i | 0.522435 | − | 0.476510i | ||||
\(7\) | 0.521929 | − | 1.94786i | 0.197270 | − | 0.736223i | −0.794397 | − | 0.607399i | \(-0.792213\pi\) |
0.991667 | − | 0.128824i | \(-0.0411204\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | −1.25529 | − | 2.72474i | −0.418432 | − | 0.908248i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.70563 | + | 0.984748i | −0.514268 | + | 0.296913i | −0.734586 | − | 0.678515i | \(-0.762624\pi\) |
0.220318 | + | 0.975428i | \(0.429290\pi\) | |||||||
\(12\) | −1.53819 | + | 0.796225i | −0.444037 | + | 0.229850i | ||||
\(13\) | −1.05248 | − | 3.92790i | −0.291905 | − | 1.08940i | −0.943644 | − | 0.330961i | \(-0.892627\pi\) |
0.651739 | − | 0.758443i | \(-0.274040\pi\) | |||||||
\(14\) | −1.00829 | + | 1.74641i | −0.269476 | + | 0.466747i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | + | 0.866025i | 0.125000 | + | 0.216506i | ||||
\(17\) | −2.35877 | + | 2.35877i | −0.572085 | + | 0.572085i | −0.932711 | − | 0.360626i | \(-0.882563\pi\) |
0.360626 | + | 0.932711i | \(0.382563\pi\) | |||||||
\(18\) | 0.507306 | + | 2.95680i | 0.119573 | + | 0.696923i | ||||
\(19\) | − | 3.70753i | − | 0.850565i | −0.905061 | − | 0.425282i | \(-0.860175\pi\) | ||
0.905061 | − | 0.425282i | \(-0.139825\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.35376 | + | 2.58061i | 0.513633 | + | 0.563135i | ||||
\(22\) | 1.90239 | − | 0.509743i | 0.405590 | − | 0.108678i | ||||
\(23\) | 6.05338 | − | 1.62200i | 1.26222 | − | 0.338210i | 0.435173 | − | 0.900347i | \(-0.356687\pi\) |
0.827044 | + | 0.562137i | \(0.190021\pi\) | |||||||
\(24\) | 1.69185 | − | 0.370982i | 0.345348 | − | 0.0757264i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.06647i | 0.797499i | ||||||||
\(27\) | 5.14688 | + | 0.713876i | 0.990518 | + | 0.137386i | ||||
\(28\) | 1.42594 | − | 1.42594i | 0.269476 | − | 0.269476i | ||||
\(29\) | −3.74863 | − | 6.49281i | −0.696103 | − | 1.20569i | −0.969808 | − | 0.243872i | \(-0.921582\pi\) |
0.273705 | − | 0.961814i | \(-0.411751\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.48837 | − | 6.04204i | 0.626530 | − | 1.08518i | −0.361713 | − | 0.932289i | \(-0.617808\pi\) |
0.988243 | − | 0.152892i | \(-0.0488587\pi\) | |||||||
\(32\) | −0.258819 | − | 0.965926i | −0.0457532 | − | 0.170753i | ||||
\(33\) | 0.156660 | − | 3.40767i | 0.0272710 | − | 0.593199i | ||||
\(34\) | 2.88889 | − | 1.66790i | 0.495440 | − | 0.286042i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.275255 | − | 2.98735i | 0.0458759 | − | 0.497891i | ||||
\(37\) | −4.26692 | − | 4.26692i | −0.701478 | − | 0.701478i | 0.263250 | − | 0.964728i | \(-0.415206\pi\) |
−0.964728 | + | 0.263250i | \(0.915206\pi\) | |||||||
\(38\) | −0.959578 | + | 3.58120i | −0.155664 | + | 0.580947i | ||||
\(39\) | 6.71243 | + | 2.13346i | 1.07485 | + | 0.341627i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.13601 | + | 3.54263i | 0.958284 | + | 0.553266i | 0.895644 | − | 0.444771i | \(-0.146715\pi\) |
0.0626396 | + | 0.998036i | \(0.480048\pi\) | |||||||
\(42\) | −1.60565 | − | 3.10188i | −0.247757 | − | 0.478630i | ||||
\(43\) | 9.09714 | + | 2.43757i | 1.38730 | + | 0.371726i | 0.873767 | − | 0.486344i | \(-0.161670\pi\) |
0.513533 | + | 0.858070i | \(0.328336\pi\) | |||||||
\(44\) | −1.96950 | −0.296913 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.26692 | −0.924007 | ||||||||
\(47\) | −7.49533 | − | 2.00837i | −1.09331 | − | 0.292951i | −0.333270 | − | 0.942831i | \(-0.608152\pi\) |
−0.760036 | + | 0.649881i | \(0.774819\pi\) | |||||||
\(48\) | −1.73022 | − | 0.0795432i | −0.249736 | − | 0.0114811i | ||||
\(49\) | 2.54041 | + | 1.46671i | 0.362916 | + | 0.209530i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.23752 | − | 5.64369i | −0.173288 | − | 0.790274i | ||||
\(52\) | 1.05248 | − | 3.92790i | 0.145953 | − | 0.544702i | ||||
\(53\) | −7.03027 | − | 7.03027i | −0.965682 | − | 0.965682i | 0.0337485 | − | 0.999430i | \(-0.489255\pi\) |
−0.999430 | + | 0.0337485i | \(0.989255\pi\) | |||||||
\(54\) | −4.78674 | − | 2.02166i | −0.651393 | − | 0.275113i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.74641 | + | 1.00829i | −0.233373 | + | 0.134738i | ||||
\(57\) | 5.40797 | + | 3.46282i | 0.716303 | + | 0.458662i | ||||
\(58\) | 1.94043 | + | 7.24179i | 0.254791 | + | 0.950894i | ||||
\(59\) | 1.34967 | − | 2.33769i | 0.175712 | − | 0.304341i | −0.764696 | − | 0.644392i | \(-0.777111\pi\) |
0.940407 | + | 0.340050i | \(0.110444\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.37353 | − | 7.57518i | −0.559973 | − | 0.969902i | −0.997498 | − | 0.0706960i | \(-0.977478\pi\) |
0.437524 | − | 0.899207i | \(-0.355855\pi\) | |||||||
\(62\) | −4.93330 | + | 4.93330i | −0.626530 | + | 0.626530i | ||||
\(63\) | −5.96261 | + | 1.02302i | −0.751218 | + | 0.128889i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.03329 | + | 3.25101i | −0.127189 | + | 0.400171i | ||||
\(67\) | 8.18285 | − | 2.19259i | 0.999694 | − | 0.267867i | 0.278377 | − | 0.960472i | \(-0.410204\pi\) |
0.721317 | + | 0.692605i | \(0.243537\pi\) | |||||||
\(68\) | −3.22213 | + | 0.863368i | −0.390741 | + | 0.104699i | ||||
\(69\) | −3.28793 | + | 10.3447i | −0.395820 | + | 1.24535i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.68481i | 0.674663i | 0.941386 | + | 0.337332i | \(0.109524\pi\) | ||||
−0.941386 | + | 0.337332i | \(0.890476\pi\) | |||||||
\(72\) | −1.03906 | + | 2.81431i | −0.122454 | + | 0.331670i | ||||
\(73\) | −1.14928 | + | 1.14928i | −0.134513 | + | 0.134513i | −0.771157 | − | 0.636645i | \(-0.780322\pi\) |
0.636645 | + | 0.771157i | \(0.280322\pi\) | |||||||
\(74\) | 3.01717 | + | 5.22589i | 0.350739 | + | 0.607498i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.85376 | − | 3.21081i | 0.212641 | − | 0.368305i | ||||
\(77\) | 1.02794 | + | 3.83631i | 0.117144 | + | 0.437188i | ||||
\(78\) | −5.93153 | − | 3.79807i | −0.671614 | − | 0.430047i | ||||
\(79\) | −10.0535 | + | 5.80440i | −1.13111 | + | 0.653046i | −0.944214 | − | 0.329334i | \(-0.893176\pi\) |
−0.186895 | + | 0.982380i | \(0.559842\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.84847 | + | 6.84072i | −0.649830 | + | 0.760080i | ||||
\(82\) | −5.01003 | − | 5.01003i | −0.553266 | − | 0.553266i | ||||
\(83\) | 0.440961 | − | 1.64569i | 0.0484017 | − | 0.180638i | −0.937493 | − | 0.348004i | \(-0.886860\pi\) |
0.985895 | + | 0.167366i | \(0.0535262\pi\) | |||||||
\(84\) | 0.748114 | + | 3.41176i | 0.0816259 | + | 0.372253i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −8.15627 | − | 4.70902i | −0.879513 | − | 0.507787i | ||||
\(87\) | 12.9719 | + | 0.596356i | 1.39074 | + | 0.0639361i | ||||
\(88\) | 1.90239 | + | 0.509743i | 0.202795 | + | 0.0543388i | ||||
\(89\) | −2.04989 | −0.217288 | −0.108644 | − | 0.994081i | \(-0.534651\pi\) | ||||
−0.108644 | + | 0.994081i | \(0.534651\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.20034 | −0.859629 | ||||||||
\(92\) | 6.05338 | + | 1.62200i | 0.631109 | + | 0.169105i | ||||
\(93\) | 5.55506 | + | 10.7315i | 0.576033 | + | 1.11281i | ||||
\(94\) | 6.72013 | + | 3.87987i | 0.693128 | + | 0.400178i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.65068 | + | 0.524648i | 0.168472 | + | 0.0535466i | ||||
\(97\) | −2.60421 | + | 9.71905i | −0.264418 | + | 0.986820i | 0.698188 | + | 0.715914i | \(0.253990\pi\) |
−0.962606 | + | 0.270906i | \(0.912677\pi\) | |||||||
\(98\) | −2.07424 | − | 2.07424i | −0.209530 | − | 0.209530i | ||||
\(99\) | 4.82426 | + | 3.41127i | 0.484856 | + | 0.342845i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.09014 | + | 2.36144i | −0.406984 | + | 0.234972i | −0.689493 | − | 0.724292i | \(-0.742167\pi\) |
0.282509 | + | 0.959265i | \(0.408833\pi\) | |||||||
\(102\) | −0.265340 | + | 5.77168i | −0.0262726 | + | 0.571481i | ||||
\(103\) | −1.03662 | − | 3.86872i | −0.102141 | − | 0.381196i | 0.895864 | − | 0.444329i | \(-0.146558\pi\) |
−0.998005 | + | 0.0631321i | \(0.979891\pi\) | |||||||
\(104\) | −2.03323 | + | 3.52166i | −0.199375 | + | 0.345327i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.97115 | + | 8.61029i | 0.482841 | + | 0.836305i | ||||
\(107\) | 5.40296 | − | 5.40296i | 0.522324 | − | 0.522324i | −0.395949 | − | 0.918273i | \(-0.629584\pi\) |
0.918273 | + | 0.395949i | \(0.129584\pi\) | |||||||
\(108\) | 4.10039 | + | 3.19168i | 0.394560 | + | 0.307119i | ||||
\(109\) | − | 4.35357i | − | 0.416996i | −0.978023 | − | 0.208498i | \(-0.933142\pi\) | ||
0.978023 | − | 0.208498i | \(-0.0668575\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.2092 | − | 2.23863i | 0.969017 | − | 0.212481i | ||||
\(112\) | 1.94786 | − | 0.521929i | 0.184056 | − | 0.0493176i | ||||
\(113\) | −2.86451 | + | 0.767544i | −0.269471 | + | 0.0722045i | −0.391024 | − | 0.920380i | \(-0.627879\pi\) |
0.121553 | + | 0.992585i | \(0.461212\pi\) | |||||||
\(114\) | −4.32745 | − | 4.74451i | −0.405303 | − | 0.444364i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 7.49726i | − | 0.696103i | ||||||
\(117\) | −9.38136 | + | 7.79841i | −0.867307 | + | 0.720964i | ||||
\(118\) | −1.90872 | + | 1.90872i | −0.175712 | + | 0.175712i | ||||
\(119\) | 3.36345 | + | 5.82566i | 0.308327 | + | 0.534037i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.56054 | + | 6.16704i | −0.323686 | + | 0.560640i | ||||
\(122\) | 2.26391 | + | 8.44902i | 0.204965 | + | 0.764938i | ||||
\(123\) | −10.8985 | + | 5.64146i | −0.982681 | + | 0.508673i | ||||
\(124\) | 6.04204 | − | 3.48837i | 0.542591 | − | 0.313265i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 6.02421 | + | 0.555073i | 0.536680 | + | 0.0494498i | ||||
\(127\) | 3.41734 | + | 3.41734i | 0.303240 | + | 0.303240i | 0.842280 | − | 0.539040i | \(-0.181213\pi\) |
−0.539040 | + | 0.842280i | \(0.681213\pi\) | |||||||
\(128\) | 0.258819 | − | 0.965926i | 0.0228766 | − | 0.0853766i | ||||
\(129\) | −12.0523 | + | 10.9928i | −1.06114 | + | 0.967863i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.411267 | − | 0.237445i | −0.0359326 | − | 0.0207457i | 0.481926 | − | 0.876212i | \(-0.339937\pi\) |
−0.517859 | + | 0.855466i | \(0.673271\pi\) | |||||||
\(132\) | 1.83951 | − | 2.87280i | 0.160108 | − | 0.250045i | ||||
\(133\) | −7.22176 | − | 1.93506i | −0.626206 | − | 0.167791i | ||||
\(134\) | −8.47151 | −0.731827 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.33580 | 0.286042 | ||||||||
\(137\) | −9.51618 | − | 2.54985i | −0.813022 | − | 0.217849i | −0.171728 | − | 0.985144i | \(-0.554935\pi\) |
−0.641293 | + | 0.767296i | \(0.721602\pi\) | |||||||
\(138\) | 5.85329 | − | 9.14122i | 0.498265 | − | 0.778152i | ||||
\(139\) | 0.608318 | + | 0.351212i | 0.0515968 | + | 0.0297894i | 0.525577 | − | 0.850746i | \(-0.323850\pi\) |
−0.473980 | + | 0.880536i | \(0.657183\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.93012 | − | 9.05722i | 0.836267 | − | 0.762755i | ||||
\(142\) | 1.47134 | − | 5.49111i | 0.123472 | − | 0.460803i | ||||
\(143\) | 5.66314 | + | 5.66314i | 0.473575 | + | 0.473575i | ||||
\(144\) | 1.73205 | − | 2.44949i | 0.144338 | − | 0.204124i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.40757 | − | 0.812661i | 0.116491 | − | 0.0672563i | ||||
\(147\) | −4.51215 | + | 2.33566i | −0.372156 | + | 0.192642i | ||||
\(148\) | −1.56180 | − | 5.82872i | −0.128379 | − | 0.479118i | ||||
\(149\) | 4.05609 | − | 7.02536i | 0.332288 | − | 0.575540i | −0.650672 | − | 0.759359i | \(-0.725513\pi\) |
0.982960 | + | 0.183819i | \(0.0588460\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.61739 | + | 7.99755i | 0.375758 | + | 0.650832i | 0.990440 | − | 0.137943i | \(-0.0440491\pi\) |
−0.614682 | + | 0.788775i | \(0.710716\pi\) | |||||||
\(152\) | −2.62162 | + | 2.62162i | −0.212641 | + | 0.212641i | ||||
\(153\) | 9.38798 | + | 3.46609i | 0.758973 | + | 0.280217i | ||||
\(154\) | − | 3.97164i | − | 0.320044i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 4.74641 | + | 5.20385i | 0.380017 | + | 0.416641i | ||||
\(157\) | −10.4848 | + | 2.80938i | −0.836775 | + | 0.224213i | −0.651667 | − | 0.758505i | \(-0.725930\pi\) |
−0.185108 | + | 0.982718i | \(0.559264\pi\) | |||||||
\(158\) | 11.2132 | − | 3.00458i | 0.892077 | − | 0.239031i | ||||
\(159\) | 16.8209 | − | 3.68841i | 1.33399 | − | 0.292510i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 12.6377i | − | 0.995993i | ||||||
\(162\) | 7.41970 | − | 5.09393i | 0.582946 | − | 0.400217i | ||||
\(163\) | −9.68197 | + | 9.68197i | −0.758351 | + | 0.758351i | −0.976022 | − | 0.217671i | \(-0.930154\pi\) |
0.217671 | + | 0.976022i | \(0.430154\pi\) | |||||||
\(164\) | 3.54263 | + | 6.13601i | 0.276633 | + | 0.479142i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.851871 | + | 1.47548i | −0.0661180 | + | 0.114520i | ||||
\(167\) | −1.32254 | − | 4.93579i | −0.102341 | − | 0.381943i | 0.895689 | − | 0.444682i | \(-0.146683\pi\) |
−0.998030 | + | 0.0627387i | \(0.980017\pi\) | |||||||
\(168\) | 0.160405 | − | 3.48913i | 0.0123755 | − | 0.269192i | ||||
\(169\) | −3.06239 | + | 1.76807i | −0.235568 | + | 0.136005i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −10.1021 | + | 4.65404i | −0.772524 | + | 0.355903i | ||||
\(172\) | 6.65957 | + | 6.65957i | 0.507787 | + | 0.507787i | ||||
\(173\) | 1.91916 | − | 7.16239i | 0.145911 | − | 0.544546i | −0.853802 | − | 0.520597i | \(-0.825709\pi\) |
0.999713 | − | 0.0239492i | \(-0.00762400\pi\) | |||||||
\(174\) | −12.3756 | − | 3.93342i | −0.938190 | − | 0.298192i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.70563 | − | 0.984748i | −0.128567 | − | 0.0742282i | ||||
\(177\) | 2.14928 | + | 4.15208i | 0.161550 | + | 0.312090i | ||||
\(178\) | 1.98004 | + | 0.530550i | 0.148410 | + | 0.0397664i | ||||
\(179\) | 2.73426 | 0.204369 | 0.102184 | − | 0.994765i | \(-0.467417\pi\) | ||||
0.102184 | + | 0.994765i | \(0.467417\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.7081 | −1.68788 | −0.843941 | − | 0.536437i | \(-0.819770\pi\) | ||||
−0.843941 | + | 0.536437i | \(0.819770\pi\) | |||||||
\(182\) | 7.92092 | + | 2.12240i | 0.587138 | + | 0.157323i | ||||
\(183\) | 15.1344 | + | 0.695770i | 1.11877 | + | 0.0514328i | ||||
\(184\) | −5.42731 | − | 3.13346i | −0.400107 | − | 0.231002i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.58824 | − | 11.8036i | −0.189779 | − | 0.865484i | ||||
\(187\) | 1.70040 | − | 6.34598i | 0.124346 | − | 0.464064i | ||||
\(188\) | −5.48696 | − | 5.48696i | −0.400178 | − | 0.400178i | ||||
\(189\) | 4.07684 | − | 9.65283i | 0.296546 | − | 0.702140i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.11154 | + | 0.641749i | −0.0804283 | + | 0.0464353i | −0.539675 | − | 0.841874i | \(-0.681453\pi\) |
0.459246 | + | 0.888309i | \(0.348119\pi\) | |||||||
\(192\) | −1.45865 | − | 0.933998i | −0.105269 | − | 0.0674055i | ||||
\(193\) | −1.41494 | − | 5.28063i | −0.101850 | − | 0.380108i | 0.896119 | − | 0.443814i | \(-0.146375\pi\) |
−0.997969 | + | 0.0637057i | \(0.979708\pi\) | |||||||
\(194\) | 5.03095 | − | 8.71386i | 0.361201 | − | 0.625619i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.46671 | + | 2.54041i | 0.104765 | + | 0.181458i | ||||
\(197\) | 12.0386 | − | 12.0386i | 0.857716 | − | 0.857716i | −0.133353 | − | 0.991069i | \(-0.542574\pi\) |
0.991069 | + | 0.133353i | \(0.0425744\pi\) | |||||||
\(198\) | −3.77698 | − | 4.54364i | −0.268418 | − | 0.322903i | ||||
\(199\) | − | 4.43831i | − | 0.314623i | −0.987549 | − | 0.157312i | \(-0.949717\pi\) | ||
0.987549 | − | 0.157312i | \(-0.0502827\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.44456 | + | 13.9838i | −0.313495 | + | 0.986338i | ||||
\(202\) | 4.56196 | − | 1.22237i | 0.320978 | − | 0.0860058i | ||||
\(203\) | −14.6036 | + | 3.91303i | −1.02497 | + | 0.274641i | ||||
\(204\) | 1.75012 | − | 5.50634i | 0.122533 | − | 0.385521i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.00520i | 0.279055i | ||||||||
\(207\) | −12.0183 | − | 14.4578i | −0.835331 | − | 1.00489i | ||||
\(208\) | 2.87542 | − | 2.87542i | 0.199375 | − | 0.199375i | ||||
\(209\) | 3.65098 | + | 6.32368i | 0.252543 | + | 0.437418i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.0425 | − | 20.8582i | 0.829038 | − | 1.43594i | −0.0697556 | − | 0.997564i | \(-0.522222\pi\) |
0.898794 | − | 0.438372i | \(-0.144445\pi\) | |||||||
\(212\) | −2.57326 | − | 9.60353i | −0.176732 | − | 0.659573i | ||||
\(213\) | −8.29213 | − | 5.30960i | −0.568167 | − | 0.363808i | ||||
\(214\) | −6.61725 | + | 3.82047i | −0.452346 | + | 0.261162i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.13461 | − | 4.14418i | −0.213283 | − | 0.281976i | ||||
\(217\) | −9.94838 | − | 9.94838i | −0.675340 | − | 0.675340i | ||||
\(218\) | −1.12679 | + | 4.20523i | −0.0763156 | + | 0.284814i | ||||
\(219\) | −0.602965 | − | 2.74981i | −0.0407446 | − | 0.185815i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.7476 | + | 6.78245i | 0.790226 | + | 0.456237i | ||||
\(222\) | −10.4408 | − | 0.479991i | −0.700738 | − | 0.0322149i | ||||
\(223\) | 16.2073 | + | 4.34272i | 1.08532 | + | 0.290810i | 0.756773 | − | 0.653678i | \(-0.226775\pi\) |
0.328546 | + | 0.944488i | \(0.393441\pi\) | |||||||
\(224\) | −2.01658 | −0.134738 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.96556 | 0.197266 | ||||||||
\(227\) | −7.18543 | − | 1.92533i | −0.476914 | − | 0.127789i | 0.0123515 | − | 0.999924i | \(-0.496068\pi\) |
−0.489265 | + | 0.872135i | \(0.662735\pi\) | |||||||
\(228\) | 2.95203 | + | 5.70288i | 0.195503 | + | 0.377682i | ||||
\(229\) | −7.74183 | − | 4.46975i | −0.511595 | − | 0.295369i | 0.221894 | − | 0.975071i | \(-0.428776\pi\) |
−0.733489 | + | 0.679701i | \(0.762109\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.55591 | − | 2.08371i | −0.431347 | − | 0.137098i | ||||
\(232\) | −1.94043 | + | 7.24179i | −0.127396 | + | 0.475447i | ||||
\(233\) | 15.0591 | + | 15.0591i | 0.986558 | + | 0.986558i | 0.999911 | − | 0.0133533i | \(-0.00425061\pi\) |
−0.0133533 | + | 0.999911i | \(0.504251\pi\) | |||||||
\(234\) | 11.0801 | − | 5.10461i | 0.724327 | − | 0.333699i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.33769 | − | 1.34967i | 0.152171 | − | 0.0878558i | ||||
\(237\) | 0.923401 | − | 20.0858i | 0.0599814 | − | 1.30471i | ||||
\(238\) | −1.74105 | − | 6.49768i | −0.112855 | − | 0.421182i | ||||
\(239\) | 5.42731 | − | 9.40038i | 0.351064 | − | 0.608060i | −0.635372 | − | 0.772206i | \(-0.719153\pi\) |
0.986436 | + | 0.164146i | \(0.0524867\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.6659 | + | 20.2059i | 0.751467 | + | 1.30158i | 0.947112 | + | 0.320904i | \(0.103987\pi\) |
−0.195645 | + | 0.980675i | \(0.562680\pi\) | |||||||
\(242\) | 5.03537 | − | 5.03537i | 0.323686 | − | 0.323686i | ||||
\(243\) | −4.51572 | − | 14.9201i | −0.289684 | − | 0.957122i | ||||
\(244\) | − | 8.74707i | − | 0.559973i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 11.9872 | − | 2.62850i | 0.764277 | − | 0.167587i | ||||
\(247\) | −14.5628 | + | 3.90209i | −0.926609 | + | 0.248284i | ||||
\(248\) | −6.73901 | + | 1.80571i | −0.427928 | + | 0.114663i | ||||
\(249\) | 1.98862 | + | 2.18027i | 0.126024 | + | 0.138169i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 13.3860i | − | 0.844914i | −0.906383 | − | 0.422457i | \(-0.861168\pi\) | ||
0.906383 | − | 0.422457i | \(-0.138832\pi\) | |||||||
\(252\) | −5.67528 | − | 2.09534i | −0.357509 | − | 0.131994i | ||||
\(253\) | −8.72759 | + | 8.72759i | −0.548699 | + | 0.548699i | ||||
\(254\) | −2.41643 | − | 4.18538i | −0.151620 | − | 0.262614i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 1.95494 | + | 7.29595i | 0.121946 | + | 0.455109i | 0.999712 | − | 0.0239802i | \(-0.00763386\pi\) |
−0.877766 | + | 0.479089i | \(0.840967\pi\) | |||||||
\(258\) | 14.4867 | − | 7.49889i | 0.901905 | − | 0.466860i | ||||
\(259\) | −10.5384 | + | 6.08436i | −0.654825 | + | 0.378063i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12.9856 | + | 18.3645i | −0.803790 | + | 1.13673i | ||||
\(262\) | 0.335798 | + | 0.335798i | 0.0207457 | + | 0.0207457i | ||||
\(263\) | −2.88569 | + | 10.7695i | −0.177939 | + | 0.664078i | 0.818093 | + | 0.575086i | \(0.195031\pi\) |
−0.996032 | + | 0.0889923i | \(0.971635\pi\) | |||||||
\(264\) | −2.52036 | + | 2.29881i | −0.155117 | + | 0.141482i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 6.47485 | + | 3.73826i | 0.396998 | + | 0.229207i | ||||
\(267\) | 1.91459 | − | 2.99006i | 0.117171 | − | 0.182989i | ||||
\(268\) | 8.18285 | + | 2.19259i | 0.499847 | + | 0.133934i | ||||
\(269\) | 13.4707 | 0.821326 | 0.410663 | − | 0.911787i | \(-0.365297\pi\) | ||||
0.410663 | + | 0.911787i | \(0.365297\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.4402 | 1.24165 | 0.620827 | − | 0.783947i | \(-0.286797\pi\) | ||||
0.620827 | + | 0.783947i | \(0.286797\pi\) | |||||||
\(272\) | −3.22213 | − | 0.863368i | −0.195371 | − | 0.0523494i | ||||
\(273\) | 7.65910 | − | 11.9614i | 0.463550 | − | 0.723936i | ||||
\(274\) | 8.53197 | + | 4.92594i | 0.515435 | + | 0.297587i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −8.01977 | + | 7.31480i | −0.482733 | + | 0.440299i | ||||
\(277\) | −6.27326 | + | 23.4121i | −0.376924 | + | 1.40670i | 0.473590 | + | 0.880745i | \(0.342958\pi\) |
−0.850514 | + | 0.525953i | \(0.823709\pi\) | |||||||
\(278\) | −0.496689 | − | 0.496689i | −0.0297894 | − | 0.0297894i | ||||
\(279\) | −20.8419 | − | 1.92038i | −1.24777 | − | 0.114970i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.5424 | − | 11.2828i | 1.16580 | − | 0.673076i | 0.213114 | − | 0.977027i | \(-0.431640\pi\) |
0.952687 | + | 0.303952i | \(0.0983062\pi\) | |||||||
\(282\) | −11.9359 | + | 6.17850i | −0.710775 | + | 0.367924i | ||||
\(283\) | −0.549660 | − | 2.05136i | −0.0326739 | − | 0.121941i | 0.947663 | − | 0.319273i | \(-0.103439\pi\) |
−0.980337 | + | 0.197333i | \(0.936772\pi\) | |||||||
\(284\) | −2.84241 | + | 4.92319i | −0.168666 | + | 0.292138i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.00444 | − | 6.93590i | −0.236788 | − | 0.410128i | ||||
\(287\) | 10.1031 | − | 10.1031i | 0.596368 | − | 0.596368i | ||||
\(288\) | −2.30701 | + | 1.91774i | −0.135942 | + | 0.113004i | ||||
\(289\) | 5.87245i | 0.345438i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.7443 | − | 12.8762i | −0.688464 | − | 0.754816i | ||||
\(292\) | −1.56994 | + | 0.420664i | −0.0918738 | + | 0.0246175i | ||||
\(293\) | 3.53204 | − | 0.946406i | 0.206344 | − | 0.0552896i | −0.154167 | − | 0.988045i | \(-0.549269\pi\) |
0.360510 | + | 0.932755i | \(0.382603\pi\) | |||||||
\(294\) | 4.96292 | − | 1.08824i | 0.289443 | − | 0.0634677i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6.03434i | 0.350739i | ||||||||
\(297\) | −9.48168 | + | 3.85077i | −0.550183 | + | 0.223444i | ||||
\(298\) | −5.73618 | + | 5.73618i | −0.332288 | + | 0.332288i | ||||
\(299\) | −12.7421 | − | 22.0700i | −0.736895 | − | 1.27634i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.49611 | − | 16.4477i | 0.547347 | − | 0.948032i | ||||
\(302\) | −2.39014 | − | 8.92011i | −0.137537 | − | 0.513295i | ||||
\(303\) | 0.375673 | − | 8.17164i | 0.0215819 | − | 0.469449i | ||||
\(304\) | 3.21081 | − | 1.85376i | 0.184153 | − | 0.106321i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −8.17100 | − | 5.77777i | −0.467105 | − | 0.330293i | ||||
\(307\) | 10.5436 | + | 10.5436i | 0.601754 | + | 0.601754i | 0.940778 | − | 0.339024i | \(-0.110097\pi\) |
−0.339024 | + | 0.940778i | \(0.610097\pi\) | |||||||
\(308\) | −1.02794 | + | 3.83631i | −0.0585721 | + | 0.218594i | ||||
\(309\) | 6.61130 | + | 2.10132i | 0.376104 | + | 0.119540i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.08436 | − | 5.24485i | −0.515127 | − | 0.297408i | 0.219812 | − | 0.975542i | \(-0.429456\pi\) |
−0.734938 | + | 0.678134i | \(0.762789\pi\) | |||||||
\(312\) | −3.23782 | − | 6.25499i | −0.183306 | − | 0.354119i | ||||
\(313\) | −17.0518 | − | 4.56901i | −0.963824 | − | 0.258256i | −0.257606 | − | 0.966250i | \(-0.582934\pi\) |
−0.706218 | + | 0.707994i | \(0.749600\pi\) | |||||||
\(314\) | 10.8546 | 0.612562 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.6088 | −0.653046 | ||||||||
\(317\) | 22.3972 | + | 6.00131i | 1.25795 | + | 0.337067i | 0.825403 | − | 0.564543i | \(-0.190948\pi\) |
0.432549 | + | 0.901611i | \(0.357614\pi\) | |||||||
\(318\) | −17.2024 | − | 0.790843i | −0.964663 | − | 0.0443483i | ||||
\(319\) | 12.7876 | + | 7.38291i | 0.715966 | + | 0.413363i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.83465 | + | 12.9274i | 0.158215 | + | 0.721535i | ||||
\(322\) | −3.27089 | + | 12.2071i | −0.182279 | + | 0.680276i | ||||
\(323\) | 8.74518 | + | 8.74518i | 0.486595 | + | 0.486595i | ||||
\(324\) | −8.48528 | + | 3.00000i | −0.471405 | + | 0.166667i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 11.8579 | − | 6.84619i | 0.656751 | − | 0.379175i | ||||
\(327\) | 6.35032 | + | 4.06623i | 0.351173 | + | 0.224863i | ||||
\(328\) | −1.83380 | − | 6.84383i | −0.101255 | − | 0.377887i | ||||
\(329\) | −7.82405 | + | 13.5517i | −0.431354 | + | 0.747127i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.9130 | + | 22.3659i | 0.709761 | + | 1.22934i | 0.964946 | + | 0.262450i | \(0.0845303\pi\) |
−0.255185 | + | 0.966892i | \(0.582136\pi\) | |||||||
\(332\) | 1.20473 | − | 1.20473i | 0.0661180 | − | 0.0661180i | ||||
\(333\) | −6.27003 | + | 16.9825i | −0.343595 | + | 0.930636i | ||||
\(334\) | 5.10991i | 0.279602i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.05799 | + | 3.32872i | −0.0577182 | + | 0.181597i | ||||
\(337\) | 30.9889 | − | 8.30344i | 1.68807 | − | 0.452317i | 0.718180 | − | 0.695858i | \(-0.244976\pi\) |
0.969891 | + | 0.243541i | \(0.0783089\pi\) | |||||||
\(338\) | 3.41565 | − | 0.915220i | 0.185787 | − | 0.0497814i | ||||
\(339\) | 1.55588 | − | 4.89519i | 0.0845035 | − | 0.265870i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.7407i | 0.744099i | ||||||||
\(342\) | 10.9624 | − | 1.88085i | 0.592779 | − | 0.101705i | ||||
\(343\) | 14.1644 | − | 14.1644i | 0.764806 | − | 0.764806i | ||||
\(344\) | −4.70902 | − | 8.15627i | −0.253894 | − | 0.439757i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.70753 | + | 6.42162i | −0.199318 | + | 0.345229i | ||||
\(347\) | 3.83170 | + | 14.3001i | 0.205696 | + | 0.767670i | 0.989236 | + | 0.146328i | \(0.0467454\pi\) |
−0.783540 | + | 0.621342i | \(0.786588\pi\) | |||||||
\(348\) | 10.9358 | + | 7.00242i | 0.586223 | + | 0.375369i | ||||
\(349\) | 13.3741 | − | 7.72151i | 0.715897 | − | 0.413323i | −0.0973439 | − | 0.995251i | \(-0.531035\pi\) |
0.813241 | + | 0.581928i | \(0.197701\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.61295 | − | 20.9678i | −0.139469 | − | 1.11918i | ||||
\(352\) | 1.39264 | + | 1.39264i | 0.0742282 | + | 0.0742282i | ||||
\(353\) | 5.39774 | − | 20.1446i | 0.287293 | − | 1.07219i | −0.659855 | − | 0.751393i | \(-0.729382\pi\) |
0.947148 | − | 0.320798i | \(-0.103951\pi\) | |||||||
\(354\) | −1.00140 | − | 4.56688i | −0.0532240 | − | 0.242727i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.77526 | − | 1.02494i | −0.0940883 | − | 0.0543219i | ||||
\(357\) | −11.6390 | − | 0.535079i | −0.616003 | − | 0.0283194i | ||||
\(358\) | −2.64110 | − | 0.707680i | −0.139586 | − | 0.0374020i | ||||
\(359\) | −3.39466 | −0.179163 | −0.0895815 | − | 0.995979i | \(-0.528553\pi\) | ||||
−0.0895815 | + | 0.995979i | \(0.528553\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.25425 | 0.276540 | ||||||||
\(362\) | 21.9344 | + | 5.87729i | 1.15284 | + | 0.308904i | ||||
\(363\) | −5.66999 | − | 10.9536i | −0.297597 | − | 0.574914i | ||||
\(364\) | −7.10170 | − | 4.10017i | −0.372230 | − | 0.214907i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −14.4386 | − | 4.58913i | −0.754718 | − | 0.239878i | ||||
\(367\) | −5.68801 | + | 21.2279i | −0.296912 | + | 1.10809i | 0.642776 | + | 0.766054i | \(0.277783\pi\) |
−0.939687 | + | 0.342035i | \(0.888884\pi\) | |||||||
\(368\) | 4.43138 | + | 4.43138i | 0.231002 | + | 0.231002i | ||||
\(369\) | 1.95025 | − | 21.1661i | 0.101526 | − | 1.10186i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −17.3633 | + | 10.0247i | −0.901458 | + | 0.520457i | ||||
\(372\) | −0.554953 | + | 12.0713i | −0.0287730 | + | 0.625869i | ||||
\(373\) | 0.381044 | + | 1.42207i | 0.0197297 | + | 0.0736322i | 0.975089 | − | 0.221815i | \(-0.0711981\pi\) |
−0.955359 | + | 0.295447i | \(0.904531\pi\) | |||||||
\(374\) | −3.28492 | + | 5.68965i | −0.169859 | + | 0.294205i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.87987 | + | 6.72013i | 0.200089 | + | 0.346564i | ||||
\(377\) | −21.5578 | + | 21.5578i | −1.11028 | + | 1.11028i | ||||
\(378\) | −6.43626 | + | 8.26875i | −0.331045 | + | 0.425299i | ||||
\(379\) | 30.1323i | 1.54779i | 0.633314 | + | 0.773895i | \(0.281694\pi\) | ||||
−0.633314 | + | 0.773895i | \(0.718306\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.17649 | + | 1.79290i | −0.418894 | + | 0.0918531i | ||||
\(382\) | 1.23976 | − | 0.332194i | 0.0634318 | − | 0.0169965i | ||||
\(383\) | 16.5638 | − | 4.43826i | 0.846372 | − | 0.226785i | 0.190528 | − | 0.981682i | \(-0.438980\pi\) |
0.655843 | + | 0.754897i | \(0.272313\pi\) | |||||||
\(384\) | 1.16721 | + | 1.27970i | 0.0595638 | + | 0.0653043i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.46691i | 0.278258i | ||||||||
\(387\) | −4.77783 | − | 27.8472i | −0.242871 | − | 1.41556i | ||||
\(388\) | −7.11484 | + | 7.11484i | −0.361201 | + | 0.361201i | ||||
\(389\) | 15.1070 | + | 26.1660i | 0.765953 | + | 1.32667i | 0.939741 | + | 0.341886i | \(0.111066\pi\) |
−0.173789 | + | 0.984783i | \(0.555601\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.4526 | + | 18.1044i | −0.528610 | + | 0.915580i | ||||
\(392\) | −0.759224 | − | 2.83346i | −0.0383466 | − | 0.143112i | ||||
\(393\) | 0.730471 | − | 0.378120i | 0.0368474 | − | 0.0190736i | ||||
\(394\) | −14.7442 | + | 8.51258i | −0.742803 | + | 0.428858i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.47230 | + | 5.36637i | 0.124238 | + | 0.269670i | ||||
\(397\) | 2.16969 | + | 2.16969i | 0.108893 | + | 0.108893i | 0.759454 | − | 0.650561i | \(-0.225466\pi\) |
−0.650561 | + | 0.759454i | \(0.725466\pi\) | |||||||
\(398\) | −1.14872 | + | 4.28708i | −0.0575801 | + | 0.214892i | ||||
\(399\) | 9.56768 | − | 8.72664i | 0.478983 | − | 0.436878i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.3209 | − | 7.11346i | −0.615275 | − | 0.355229i | 0.159752 | − | 0.987157i | \(-0.448931\pi\) |
−0.775027 | + | 0.631928i | \(0.782264\pi\) | |||||||
\(402\) | 7.91238 | − | 12.3569i | 0.394633 | − | 0.616308i | ||||
\(403\) | −27.4040 | − | 7.34287i | −1.36509 | − | 0.365774i | ||||
\(404\) | −4.72288 | −0.234972 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 15.1188 | 0.750333 | ||||||||
\(407\) | 11.4796 | + | 3.07596i | 0.569025 | + | 0.152470i | ||||
\(408\) | −3.11563 | + | 4.86575i | −0.154247 | + | 0.240890i | ||||
\(409\) | −10.2963 | − | 5.94456i | −0.509118 | − | 0.293939i | 0.223353 | − | 0.974738i | \(-0.428300\pi\) |
−0.732471 | + | 0.680798i | \(0.761633\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.6074 | − | 11.4992i | 0.621878 | − | 0.567212i | ||||
\(412\) | 1.03662 | − | 3.86872i | 0.0510706 | − | 0.190598i | ||||
\(413\) | −3.84907 | − | 3.84907i | −0.189401 | − | 0.189401i | ||||
\(414\) | 7.86684 | + | 17.0758i | 0.386634 | + | 0.839228i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.52166 | + | 2.03323i | −0.172664 | + | 0.0996874i | ||||
\(417\) | −1.08046 | + | 0.559288i | −0.0529104 | + | 0.0273885i | ||||
\(418\) | −1.88989 | − | 7.05315i | −0.0924373 | − | 0.344981i | ||||
\(419\) | −19.6354 | + | 34.0095i | −0.959251 | + | 1.66147i | −0.234926 | + | 0.972013i | \(0.575485\pi\) |
−0.724325 | + | 0.689458i | \(0.757849\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.2493 | − | 21.2163i | −0.596992 | − | 1.03402i | −0.993262 | − | 0.115887i | \(-0.963029\pi\) |
0.396270 | − | 0.918134i | \(-0.370304\pi\) | |||||||
\(422\) | −17.0306 | + | 17.0306i | −0.829038 | + | 0.829038i | ||||
\(423\) | 3.93656 | + | 22.9440i | 0.191402 | + | 1.11557i | ||||
\(424\) | 9.94230i | 0.482841i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6.63535 | + | 7.27484i | 0.321484 | + | 0.352467i | ||||
\(427\) | −17.0381 | + | 4.56534i | −0.824531 | + | 0.220932i | ||||
\(428\) | 7.38058 | − | 1.97762i | 0.356754 | − | 0.0955920i | ||||
\(429\) | −13.5499 | + | 2.97115i | −0.654194 | + | 0.143449i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 6.10703i | − | 0.294165i | −0.989124 | − | 0.147083i | \(-0.953012\pi\) | ||
0.989124 | − | 0.147083i | \(-0.0469883\pi\) | |||||||
\(432\) | 1.95521 | + | 4.81427i | 0.0940699 | + | 0.231627i | ||||
\(433\) | −10.2605 | + | 10.2605i | −0.493088 | + | 0.493088i | −0.909278 | − | 0.416190i | \(-0.863365\pi\) |
0.416190 | + | 0.909278i | \(0.363365\pi\) | |||||||
\(434\) | 7.03457 | + | 12.1842i | 0.337670 | + | 0.584862i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.17679 | − | 3.77030i | 0.104249 | − | 0.180565i | ||||
\(437\) | −6.01360 | − | 22.4431i | −0.287670 | − | 1.07360i | ||||
\(438\) | −0.129283 | + | 2.81217i | −0.00617740 | + | 0.134371i | ||||
\(439\) | 1.96604 | − | 1.13510i | 0.0938342 | − | 0.0541752i | −0.452349 | − | 0.891841i | \(-0.649414\pi\) |
0.546183 | + | 0.837666i | \(0.316080\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.807438 | − | 8.76313i | 0.0384494 | − | 0.417292i | ||||
\(442\) | −9.59184 | − | 9.59184i | −0.456237 | − | 0.456237i | ||||
\(443\) | −7.20031 | + | 26.8719i | −0.342097 | + | 1.27672i | 0.553870 | + | 0.832603i | \(0.313150\pi\) |
−0.895967 | + | 0.444120i | \(0.853516\pi\) | |||||||
\(444\) | 9.96076 | + | 3.16590i | 0.472717 | + | 0.150247i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −14.5310 | − | 8.38950i | −0.688065 | − | 0.397254i | ||||
\(447\) | 6.45913 | + | 12.4781i | 0.305506 | + | 0.590193i | ||||
\(448\) | 1.94786 | + | 0.521929i | 0.0920279 | + | 0.0246588i | ||||
\(449\) | 11.7712 | 0.555516 | 0.277758 | − | 0.960651i | \(-0.410409\pi\) | ||||
0.277758 | + | 0.960651i | \(0.410409\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.9544 | −0.657086 | ||||||||
\(452\) | −2.86451 | − | 0.767544i | −0.134735 | − | 0.0361022i | ||||
\(453\) | −15.9782 | − | 0.734564i | −0.750723 | − | 0.0345128i | ||||
\(454\) | 6.44228 | + | 3.71945i | 0.302351 | + | 0.174562i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.37542 | − | 6.27260i | −0.0644102 | − | 0.293741i | ||||
\(457\) | 10.0741 | − | 37.5970i | 0.471246 | − | 1.75871i | −0.164058 | − | 0.986451i | \(-0.552458\pi\) |
0.635303 | − | 0.772263i | \(-0.280875\pi\) | |||||||
\(458\) | 6.32118 | + | 6.32118i | 0.295369 | + | 0.295369i | ||||
\(459\) | −13.8242 | + | 10.4564i | −0.645256 | + | 0.488064i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.62200 | + | 1.51381i | −0.122119 | + | 0.0705053i | −0.559815 | − | 0.828618i | \(-0.689128\pi\) |
0.437696 | + | 0.899123i | \(0.355795\pi\) | |||||||
\(462\) | 5.79322 | + | 3.70950i | 0.269525 | + | 0.172582i | ||||
\(463\) | −1.76940 | − | 6.60350i | −0.0822311 | − | 0.306891i | 0.912544 | − | 0.408978i | \(-0.134115\pi\) |
−0.994775 | + | 0.102087i | \(0.967448\pi\) | |||||||
\(464\) | 3.74863 | − | 6.49281i | 0.174026 | − | 0.301421i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.6484 | − | 18.4436i | −0.493279 | − | 0.854384i | ||||
\(467\) | 8.05359 | − | 8.05359i | 0.372676 | − | 0.372676i | −0.495775 | − | 0.868451i | \(-0.665116\pi\) |
0.868451 | + | 0.495775i | \(0.165116\pi\) | |||||||
\(468\) | −12.0237 | + | 2.06294i | −0.555796 | + | 0.0953595i | ||||
\(469\) | − | 17.0835i | − | 0.788841i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.69485 | − | 17.9175i | 0.262405 | − | 0.825596i | ||||
\(472\) | −2.60736 | + | 0.698639i | −0.120013 | + | 0.0321575i | ||||
\(473\) | −17.9168 | + | 4.80079i | −0.823814 | + | 0.220740i | ||||
\(474\) | −6.09053 | + | 19.1624i | −0.279747 | + | 0.880159i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6.72689i | 0.308327i | ||||||||
\(477\) | −10.3306 | + | 27.9808i | −0.473007 | + | 1.28115i | ||||
\(478\) | −7.67538 | + | 7.67538i | −0.351064 | + | 0.351064i | ||||
\(479\) | −16.5711 | − | 28.7020i | −0.757154 | − | 1.31143i | −0.944296 | − | 0.329097i | \(-0.893256\pi\) |
0.187142 | − | 0.982333i | \(-0.440078\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.2692 | + | 21.2509i | −0.559428 | + | 0.968958i | ||||
\(482\) | −6.03872 | − | 22.5368i | −0.275056 | − | 1.02652i | ||||
\(483\) | 18.4340 | + | 11.8036i | 0.838775 | + | 0.537083i | ||||
\(484\) | −6.16704 | + | 3.56054i | −0.280320 | + | 0.161843i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.500258 | + | 15.5804i | 0.0226921 | + | 0.706743i | ||||
\(487\) | 14.8248 | + | 14.8248i | 0.671777 | + | 0.671777i | 0.958126 | − | 0.286349i | \(-0.0924415\pi\) |
−0.286349 | + | 0.958126i | \(0.592442\pi\) | |||||||
\(488\) | −2.26391 | + | 8.44902i | −0.102482 | + | 0.382469i | ||||
\(489\) | −5.07962 | − | 23.1655i | −0.229709 | − | 1.04758i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.1505 | + | 9.32449i | 0.728861 | + | 0.420808i | 0.818005 | − | 0.575210i | \(-0.195080\pi\) |
−0.0891441 | + | 0.996019i | \(0.528413\pi\) | |||||||
\(492\) | −12.2591 | − | 0.563584i | −0.552682 | − | 0.0254083i | ||||
\(493\) | 24.1572 | + | 6.47289i | 1.08798 | + | 0.291524i | ||||
\(494\) | 15.0765 | 0.678325 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.97674 | 0.313265 | ||||||||
\(497\) | 11.0732 | + | 2.96707i | 0.496703 | + | 0.133091i | ||||
\(498\) | −1.35656 | − | 2.62068i | −0.0607890 | − | 0.117435i | ||||
\(499\) | 19.6189 | + | 11.3270i | 0.878263 | + | 0.507065i | 0.870085 | − | 0.492901i | \(-0.164064\pi\) |
0.00817742 | + | 0.999967i | \(0.497397\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.43482 | + | 2.68090i | 0.376840 | + | 0.119774i | ||||
\(502\) | −3.46454 | + | 12.9298i | −0.154630 | + | 0.577087i | ||||
\(503\) | −9.64801 | − | 9.64801i | −0.430183 | − | 0.430183i | 0.458507 | − | 0.888691i | \(-0.348384\pi\) |
−0.888691 | + | 0.458507i | \(0.848384\pi\) | |||||||
\(504\) | 4.93958 | + | 3.49281i | 0.220027 | + | 0.155582i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 10.6891 | − | 6.17134i | 0.475187 | − | 0.274349i | ||||
\(507\) | 0.281276 | − | 6.11831i | 0.0124919 | − | 0.271724i | ||||
\(508\) | 1.25084 | + | 4.66818i | 0.0554968 | + | 0.207117i | ||||
\(509\) | −13.5882 | + | 23.5355i | −0.602286 | + | 1.04319i | 0.390188 | + | 0.920735i | \(0.372410\pi\) |
−0.992474 | + | 0.122455i | \(0.960923\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.63879 | + | 2.83847i | 0.0724959 | + | 0.125567i | ||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 2.64671 | − | 19.0822i | 0.116855 | − | 0.842499i | ||||
\(514\) | − | 7.55332i | − | 0.333163i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −15.9340 | + | 3.49393i | −0.701454 | + | 0.153812i | ||||
\(517\) | 14.7620 | − | 3.95547i | 0.649233 | − | 0.173961i | ||||
\(518\) | 11.7541 | − | 3.14949i | 0.516444 | − | 0.138381i | ||||
\(519\) | 8.65490 | + | 9.48903i | 0.379908 | + | 0.416522i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 18.3542i | − | 0.804114i | −0.915615 | − | 0.402057i | \(-0.868295\pi\) | ||
0.915615 | − | 0.402057i | \(-0.131705\pi\) | |||||||
\(522\) | 17.2962 | − | 14.3778i | 0.757035 | − | 0.629298i | ||||
\(523\) | 25.8576 | − | 25.8576i | 1.13067 | − | 1.13067i | 0.140607 | − | 0.990066i | \(-0.455095\pi\) |
0.990066 | − | 0.140607i | \(-0.0449053\pi\) | |||||||
\(524\) | −0.237445 | − | 0.411267i | −0.0103728 | − | 0.0179663i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.57472 | − | 9.65570i | 0.243069 | − | 0.421009i | ||||
\(527\) | 6.02350 | + | 22.4800i | 0.262388 | + | 0.979244i | ||||
\(528\) | 3.02946 | − | 1.56816i | 0.131840 | − | 0.0682455i | ||||
\(529\) | 14.0940 | − | 8.13716i | 0.612781 | − | 0.353789i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.06384 | − | 0.743005i | −0.349941 | − | 0.0322437i | ||||
\(532\) | −5.28669 | − | 5.28669i | −0.229207 | − | 0.229207i | ||||
\(533\) | 7.45708 | − | 27.8302i | 0.323002 | − | 1.20546i | ||||
\(534\) | −2.62324 | + | 2.39264i | −0.113519 | + | 0.103540i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −7.33654 | − | 4.23576i | −0.316890 | − | 0.182957i | ||||
\(537\) | −2.55380 | + | 3.98832i | −0.110205 | + | 0.172109i | ||||
\(538\) | −13.0117 | − | 3.48649i | −0.560976 | − | 0.150313i | ||||
\(539\) | −5.77735 | −0.248848 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.54804 | −0.195536 | −0.0977678 | − | 0.995209i | \(-0.531170\pi\) | ||||
−0.0977678 | + | 0.995209i | \(0.531170\pi\) | |||||||
\(542\) | −19.7437 | − | 5.29032i | −0.848066 | − | 0.227239i | ||||
\(543\) | 21.2093 | − | 33.1231i | 0.910180 | − | 1.42145i | ||||
\(544\) | 2.88889 | + | 1.66790i | 0.123860 | + | 0.0715106i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −10.4940 | + | 9.57149i | −0.449100 | + | 0.409622i | ||||
\(547\) | 5.79252 | − | 21.6180i | 0.247670 | − | 0.924319i | −0.724352 | − | 0.689430i | \(-0.757861\pi\) |
0.972022 | − | 0.234888i | \(-0.0754724\pi\) | |||||||
\(548\) | −6.96632 | − | 6.96632i | −0.297587 | − | 0.297587i | ||||
\(549\) | −15.1504 | + | 21.4258i | −0.646602 | + | 0.914433i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −24.0723 | + | 13.8981i | −1.02551 | + | 0.592080i | ||||
\(552\) | 9.63971 | − | 4.98988i | 0.410293 | − | 0.212383i | ||||
\(553\) | 6.05896 | + | 22.6124i | 0.257653 | + | 0.961575i | ||||
\(554\) | 12.1190 | − | 20.9907i | 0.514887 | − | 0.891811i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.351212 | + | 0.608318i | 0.0148947 | + | 0.0257984i | ||||
\(557\) | 20.5740 | − | 20.5740i | 0.871749 | − | 0.871749i | −0.120914 | − | 0.992663i | \(-0.538583\pi\) |
0.992663 | + | 0.120914i | \(0.0385825\pi\) | |||||||
\(558\) | 19.6347 | + | 7.24924i | 0.831205 | + | 0.306885i | ||||
\(559\) | − | 38.2982i | − | 1.61984i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.66836 | + | 8.40741i | 0.323759 | + | 0.354961i | ||||
\(562\) | −21.7967 | + | 5.84041i | −0.919438 | + | 0.246363i | ||||
\(563\) | −34.2529 | + | 9.17805i | −1.44359 | + | 0.386809i | −0.893789 | − | 0.448487i | \(-0.851963\pi\) |
−0.549800 | + | 0.835296i | \(0.685296\pi\) | |||||||
\(564\) | 13.1283 | − | 2.87872i | 0.552803 | − | 0.121216i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.12372i | 0.0892668i | ||||||||
\(567\) | 10.2723 | + | 14.9624i | 0.431396 | + | 0.628361i | ||||
\(568\) | 4.01977 | − | 4.01977i | 0.168666 | − | 0.168666i | ||||
\(569\) | −12.0592 | − | 20.8872i | −0.505549 | − | 0.875637i | −0.999979 | − | 0.00641982i | \(-0.997956\pi\) |
0.494430 | − | 0.869217i | \(-0.335377\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.24726 | − | 3.89236i | 0.0940448 | − | 0.162890i | −0.815165 | − | 0.579229i | \(-0.803354\pi\) |
0.909210 | + | 0.416339i | \(0.136687\pi\) | |||||||
\(572\) | 2.07285 | + | 7.73599i | 0.0866703 | + | 0.323458i | ||||
\(573\) | 0.102094 | − | 2.22074i | 0.00426502 | − | 0.0927726i | ||||
\(574\) | −12.3737 | + | 7.14398i | −0.516470 | + | 0.298184i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.72474 | − | 1.25529i | 0.113531 | − | 0.0523040i | ||||
\(577\) | −0.186522 | − | 0.186522i | −0.00776502 | − | 0.00776502i | 0.703214 | − | 0.710979i | \(-0.251748\pi\) |
−0.710979 | + | 0.703214i | \(0.751748\pi\) | |||||||
\(578\) | 1.51990 | − | 5.67235i | 0.0632196 | − | 0.235939i | ||||
\(579\) | 9.02412 | + | 2.86820i | 0.375030 | + | 0.119198i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.97543 | − | 1.71786i | −0.123441 | − | 0.0712689i | ||||
\(582\) | 8.01154 | + | 15.4771i | 0.332089 | + | 0.641547i | ||||
\(583\) | 18.9141 | + | 5.06802i | 0.783342 | + | 0.209896i | ||||
\(584\) | 1.62532 | 0.0672563 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.65663 | −0.151054 | ||||||||
\(587\) | −43.6620 | − | 11.6992i | −1.80212 | − | 0.482878i | −0.807818 | − | 0.589433i | \(-0.799351\pi\) |
−0.994307 | + | 0.106555i | \(0.966018\pi\) | |||||||
\(588\) | −5.07547 | − | 0.233334i | −0.209309 | − | 0.00962251i | ||||
\(589\) | −22.4010 | − | 12.9332i | −0.923017 | − | 0.532904i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.31603 | + | 28.8041i | 0.259807 | + | 1.18484i | ||||
\(592\) | 1.56180 | − | 5.82872i | 0.0641897 | − | 0.239559i | ||||
\(593\) | −3.60323 | − | 3.60323i | −0.147967 | − | 0.147967i | 0.629242 | − | 0.777209i | \(-0.283365\pi\) |
−0.777209 | + | 0.629242i | \(0.783365\pi\) | |||||||
\(594\) | 10.1553 | − | 1.26552i | 0.416675 | − | 0.0519248i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.02536 | − | 4.05609i | 0.287770 | − | 0.166144i | ||||
\(597\) | 6.47392 | + | 4.14537i | 0.264960 | + | 0.169659i | ||||
\(598\) | 6.59580 | + | 24.6159i | 0.269722 | + | 1.00662i | ||||
\(599\) | 23.4581 | − | 40.6307i | 0.958473 | − | 1.66012i | 0.232260 | − | 0.972654i | \(-0.425388\pi\) |
0.726213 | − | 0.687470i | \(-0.241279\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.5688 | − | 35.6263i | −0.839020 | − | 1.45323i | −0.890715 | − | 0.454563i | \(-0.849795\pi\) |
0.0516943 | − | 0.998663i | \(-0.483538\pi\) | |||||||
\(602\) | −13.4295 | + | 13.4295i | −0.547347 | + | 0.547347i | ||||
\(603\) | −16.2461 | − | 19.5438i | −0.661594 | − | 0.795887i | ||||
\(604\) | 9.23478i | 0.375758i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.47785 | + | 7.79597i | −0.100656 | + | 0.316690i | ||||
\(607\) | 15.9755 | − | 4.28061i | 0.648424 | − | 0.173745i | 0.0804079 | − | 0.996762i | \(-0.474378\pi\) |
0.568016 | + | 0.823017i | \(0.307711\pi\) | |||||||
\(608\) | −3.58120 | + | 0.959578i | −0.145237 | + | 0.0389160i | ||||
\(609\) | 7.93204 | − | 24.9563i | 0.321422 | − | 1.01128i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 31.5547i | 1.27657i | ||||||||
\(612\) | 6.39719 | + | 7.69571i | 0.258591 | + | 0.311081i | ||||
\(613\) | 21.1512 | − | 21.1512i | 0.854290 | − | 0.854290i | −0.136368 | − | 0.990658i | \(-0.543543\pi\) |
0.990658 | + | 0.136368i | \(0.0435429\pi\) | |||||||
\(614\) | −7.45544 | − | 12.9132i | −0.300877 | − | 0.521134i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.98582 | − | 3.43954i | 0.0800110 | − | 0.138583i | ||||
\(617\) | 2.72427 | + | 10.1671i | 0.109675 | + | 0.409312i | 0.998834 | − | 0.0482869i | \(-0.0153762\pi\) |
−0.889159 | + | 0.457599i | \(0.848710\pi\) | |||||||
\(618\) | −5.84216 | − | 3.74085i | −0.235006 | − | 0.150479i | ||||
\(619\) | −2.77044 | + | 1.59951i | −0.111353 | + | 0.0642898i | −0.554642 | − | 0.832089i | \(-0.687145\pi\) |
0.443289 | + | 0.896379i | \(0.353812\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 32.3139 | − | 4.02687i | 1.29671 | − | 0.161593i | ||||
\(622\) | 7.41734 | + | 7.41734i | 0.297408 | + | 0.297408i | ||||
\(623\) | −1.06990 | + | 3.99290i | −0.0428644 | + | 0.159972i | ||||
\(624\) | 1.50858 | + | 6.87987i | 0.0603917 | + | 0.275415i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 15.2882 | + | 8.82666i | 0.611040 | + | 0.352784i | ||||
\(627\) | −12.6340 | − | 0.580821i | −0.504554 | − | 0.0231958i | ||||
\(628\) | −10.4848 | − | 2.80938i | −0.418388 | − | 0.112107i | ||||
\(629\) | 20.1293 | 0.802609 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.2335 | 0.845291 | 0.422645 | − | 0.906295i | \(-0.361102\pi\) | ||||
0.422645 | + | 0.906295i | \(0.361102\pi\) | |||||||
\(632\) | 11.2132 | + | 3.00458i | 0.446039 | + | 0.119516i | ||||
\(633\) | 19.1770 | + | 37.0472i | 0.762219 | + | 1.47249i | ||||
\(634\) | −20.0808 | − | 11.5936i | −0.797510 | − | 0.460442i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 16.4116 | + | 5.21621i | 0.650761 | + | 0.206836i | ||||
\(637\) | 3.08736 | − | 11.5222i | 0.122326 | − | 0.456525i | ||||
\(638\) | −10.4410 | − | 10.4410i | −0.413363 | − | 0.413363i | ||||
\(639\) | 15.4897 | − | 7.13612i | 0.612762 | − | 0.282300i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 42.6583 | − | 24.6288i | 1.68490 | − | 0.972778i | 0.726582 | − | 0.687080i | \(-0.241108\pi\) |
0.958320 | − | 0.285698i | \(-0.0922254\pi\) | |||||||
\(642\) | 0.607785 | − | 13.2205i | 0.0239874 | − | 0.521773i | ||||
\(643\) | 5.25595 | + | 19.6155i | 0.207274 | + | 0.773559i | 0.988744 | + | 0.149616i | \(0.0478036\pi\) |
−0.781470 | + | 0.623943i | \(0.785530\pi\) | |||||||
\(644\) | 6.31887 | − | 10.9446i | 0.248998 | − | 0.431278i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.18378 | − | 10.7106i | −0.243298 | − | 0.421404i | ||||
\(647\) | −29.0632 | + | 29.0632i | −1.14259 | + | 1.14259i | −0.154619 | + | 0.987974i | \(0.549415\pi\) |
−0.987974 | + | 0.154619i | \(0.950585\pi\) | |||||||
\(648\) | 8.97261 | − | 0.701625i | 0.352477 | − | 0.0275624i | ||||
\(649\) | 5.31632i | 0.208684i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 23.8029 | − | 5.21939i | 0.932911 | − | 0.204564i | ||||
\(652\) | −13.2258 | + | 3.54385i | −0.517963 | + | 0.138788i | ||||
\(653\) | −2.75027 | + | 0.736931i | −0.107626 | + | 0.0288384i | −0.312230 | − | 0.950006i | \(-0.601076\pi\) |
0.204604 | + | 0.978845i | \(0.434409\pi\) | |||||||
\(654\) | −5.08152 | − | 5.57126i | −0.198703 | − | 0.217853i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 7.08526i | 0.276633i | ||||||||
\(657\) | 4.57416 | + | 1.68880i | 0.178455 | + | 0.0658865i | ||||
\(658\) | 11.0649 | − | 11.0649i | 0.431354 | − | 0.431354i | ||||
\(659\) | 18.8486 | + | 32.6467i | 0.734236 | + | 1.27173i | 0.955058 | + | 0.296420i | \(0.0957928\pi\) |
−0.220822 | + | 0.975314i | \(0.570874\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.68907 | − | 6.38966i | 0.143488 | − | 0.248529i | −0.785320 | − | 0.619091i | \(-0.787501\pi\) |
0.928808 | + | 0.370561i | \(0.120835\pi\) | |||||||
\(662\) | −6.68424 | − | 24.9459i | −0.259791 | − | 0.969551i | ||||
\(663\) | −20.8654 | + | 10.8007i | −0.810345 | + | 0.419465i | ||||
\(664\) | −1.47548 | + | 0.851871i | −0.0572598 | + | 0.0330590i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10.4518 | − | 14.7811i | 0.404998 | − | 0.572754i | ||||
\(667\) | −33.2232 | − | 33.2232i | −1.28641 | − | 1.28641i | ||||
\(668\) | 1.32254 | − | 4.93579i | 0.0511707 | − | 0.190971i | ||||
\(669\) | −21.4721 | + | 19.5846i | −0.830157 | + | 0.757183i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.9193 | + | 8.61365i | 0.575953 | + | 0.332526i | ||||
\(672\) | 1.88348 | − | 2.94147i | 0.0726568 | − | 0.113470i | ||||
\(673\) | 6.88414 | + | 1.84460i | 0.265364 | + | 0.0711041i | 0.389048 | − | 0.921218i | \(-0.372804\pi\) |
−0.123684 | + | 0.992322i | \(0.539471\pi\) | |||||||
\(674\) | −32.0820 | −1.23575 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.53614 | −0.136005 | ||||||||
\(677\) | −8.09727 | − | 2.16966i | −0.311203 | − | 0.0833867i | 0.0998372 | − | 0.995004i | \(-0.468168\pi\) |
−0.411040 | + | 0.911617i | \(0.634834\pi\) | |||||||
\(678\) | −2.76983 | + | 4.32570i | −0.106375 | + | 0.166128i | ||||
\(679\) | 17.5722 | + | 10.1453i | 0.674358 | + | 0.389341i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.51955 | − | 8.68274i | 0.364790 | − | 0.332723i | ||||
\(682\) | 3.55635 | − | 13.2725i | 0.136180 | − | 0.508229i | ||||
\(683\) | −15.8873 | − | 15.8873i | −0.607911 | − | 0.607911i | 0.334488 | − | 0.942400i | \(-0.391436\pi\) |
−0.942400 | + | 0.334488i | \(0.891436\pi\) | |||||||
\(684\) | −11.0757 | − | 1.02052i | −0.423489 | − | 0.0390204i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −17.3478 | + | 10.0158i | −0.662342 | + | 0.382403i | ||||
\(687\) | 13.7506 | − | 7.11785i | 0.524619 | − | 0.271563i | ||||
\(688\) | 2.43757 | + | 9.09714i | 0.0929315 | + | 0.346825i | ||||
\(689\) | −20.2150 | + | 35.0134i | −0.770131 | + | 1.33391i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.16297 | + | 15.8707i | 0.348576 | + | 0.603751i | 0.985997 | − | 0.166765i | \(-0.0533321\pi\) |
−0.637421 | + | 0.770516i | \(0.719999\pi\) | |||||||
\(692\) | 5.24323 | − | 5.24323i | 0.199318 | − | 0.199318i | ||||
\(693\) | 9.16260 | − | 7.61656i | 0.348058 | − | 0.289329i | ||||
\(694\) | − | 14.8046i | − | 0.561973i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −8.75085 | − | 9.59422i | −0.331700 | − | 0.363668i | ||||
\(697\) | −22.8296 | + | 6.11718i | −0.864734 | + | 0.231705i | ||||
\(698\) | −14.9168 | + | 3.99695i | −0.564610 | + | 0.151287i | ||||
\(699\) | −36.0312 | + | 7.90075i | −1.36282 | + | 0.298834i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 21.1738i | − | 0.799724i | −0.916575 | − | 0.399862i | \(-0.869058\pi\) | ||
0.916575 | − | 0.399862i | \(-0.130942\pi\) | |||||||
\(702\) | −2.90295 | + | 20.9296i | −0.109565 | + | 0.789937i | ||||
\(703\) | −15.8197 | + | 15.8197i | −0.596652 | + | 0.596652i | ||||
\(704\) | −0.984748 | − | 1.70563i | −0.0371141 | − | 0.0642835i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10.4276 | + | 18.0612i | −0.392449 | + | 0.679742i | ||||
\(707\) | 2.46501 | + | 9.19953i | 0.0927062 | + | 0.345984i | ||||
\(708\) | −0.214714 | + | 4.67045i | −0.00806943 | + | 0.175526i | ||||
\(709\) | 20.4846 | − | 11.8268i | 0.769316 | − | 0.444165i | −0.0633143 | − | 0.997994i | \(-0.520167\pi\) |
0.832631 | + | 0.553829i | \(0.186834\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 28.4356 | + | 20.1070i | 1.06642 | + | 0.754072i | ||||
\(712\) | 1.44949 | + | 1.44949i | 0.0543219 | + | 0.0543219i | ||||
\(713\) | 11.3163 | − | 42.2329i | 0.423798 | − | 1.58163i | ||||
\(714\) | 11.1039 | + | 3.52925i | 0.415555 | + | 0.132079i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.36794 | + | 1.36713i | 0.0884942 | + | 0.0510921i | ||||
\(717\) | 8.64273 | + | 16.6965i | 0.322769 | + | 0.623541i | ||||
\(718\) | 3.27899 | + | 0.878601i | 0.122371 | + | 0.0327891i | ||||
\(719\) | −21.3695 | −0.796947 | −0.398473 | − | 0.917180i | \(-0.630460\pi\) | ||||
−0.398473 | + | 0.917180i | \(0.630460\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.07679 | −0.300795 | ||||||||
\(722\) | −5.07522 | − | 1.35990i | −0.188880 | − | 0.0506102i | ||||
\(723\) | −40.3692 | − | 1.85589i | −1.50135 | − | 0.0690212i | ||||
\(724\) | −19.6658 | − | 11.3541i | −0.730874 | − | 0.421970i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.64179 | + | 12.0478i | 0.0980462 | + | 0.447137i | ||||
\(727\) | 0.796213 | − | 2.97151i | 0.0295299 | − | 0.110207i | −0.949588 | − | 0.313501i | \(-0.898498\pi\) |
0.979118 | + | 0.203294i | \(0.0651647\pi\) | |||||||
\(728\) | 5.79852 | + | 5.79852i | 0.214907 | + | 0.214907i | ||||
\(729\) | 25.9808 | + | 7.34847i | 0.962250 | + | 0.272166i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −27.2077 | + | 15.7084i | −1.00631 | + | 0.580994i | ||||
\(732\) | 12.7589 | + | 8.16974i | 0.471581 | + | 0.301962i | ||||
\(733\) | 6.30661 | + | 23.5366i | 0.232940 | + | 0.869343i | 0.979067 | + | 0.203540i | \(0.0652446\pi\) |
−0.746127 | + | 0.665804i | \(0.768089\pi\) | |||||||
\(734\) | 10.9884 | − | 19.0324i | 0.405589 | − | 0.702500i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.13346 | − | 5.42731i | −0.115501 | − | 0.200053i | ||||
\(737\) | −11.7978 | + | 11.7978i | −0.434578 | + | 0.434578i | ||||
\(738\) | −7.36199 | + | 19.9401i | −0.270999 | + | 0.734006i | ||||
\(739\) | 5.68805i | 0.209238i | 0.994512 | + | 0.104619i | \(0.0333624\pi\) | ||||
−0.994512 | + | 0.104619i | \(0.966638\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.90986 | − | 24.8865i | 0.290576 | − | 0.914229i | ||||
\(742\) | 19.3663 | − | 5.18917i | 0.710958 | − | 0.190500i | ||||
\(743\) | 15.1100 | − | 4.04871i | 0.554332 | − | 0.148533i | 0.0292311 | − | 0.999573i | \(-0.490694\pi\) |
0.525101 | + | 0.851040i | \(0.324027\pi\) | |||||||
\(744\) | 3.66033 | − | 11.5164i | 0.134194 | − | 0.422211i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 1.47224i | − | 0.0539025i | ||||||
\(747\) | −5.03761 | + | 0.864318i | −0.184317 | + | 0.0316237i | ||||
\(748\) | 4.64558 | − | 4.64558i | 0.169859 | − | 0.169859i | ||||
\(749\) | −7.70428 | − | 13.3442i | −0.281508 | − | 0.487586i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.6240 | + | 37.4538i | −0.789070 | + | 1.36671i | 0.137467 | + | 0.990506i | \(0.456104\pi\) |
−0.926537 | + | 0.376203i | \(0.877229\pi\) | |||||||
\(752\) | −2.00837 | − | 7.49533i | −0.0732376 | − | 0.273327i | ||||
\(753\) | 19.5254 | + | 12.5025i | 0.711544 | + | 0.455615i | ||||
\(754\) | 26.4028 | − | 15.2437i | 0.961533 | − | 0.555141i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 8.35706 | − | 6.32118i | 0.303943 | − | 0.229899i | ||||
\(757\) | −22.7266 | − | 22.7266i | −0.826013 | − | 0.826013i | 0.160950 | − | 0.986963i | \(-0.448544\pi\) |
−0.986963 | + | 0.160950i | \(0.948544\pi\) | |||||||
\(758\) | 7.79880 | − | 29.1055i | 0.283265 | − | 1.05716i | ||||
\(759\) | −4.57891 | − | 20.8820i | −0.166204 | − | 0.757969i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.8744 | − | 14.3612i | −0.901696 | − | 0.520595i | −0.0239461 | − | 0.999713i | \(-0.507623\pi\) |
−0.877750 | + | 0.479119i | \(0.840956\pi\) | |||||||
\(762\) | 8.36192 | + | 0.384421i | 0.302920 | + | 0.0139261i | ||||
\(763\) | −8.48016 | − | 2.27225i | −0.307002 | − | 0.0822611i | ||||
\(764\) | −1.28350 | −0.0464353 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −17.1481 | −0.619587 | ||||||||
\(767\) | −10.6027 | − | 2.84099i | −0.382842 | − | 0.102582i | ||||
\(768\) | −0.796225 | − | 1.53819i | −0.0287313 | − | 0.0555046i | ||||
\(769\) | 29.3558 | + | 16.9486i | 1.05860 | + | 0.611180i | 0.925043 | − | 0.379861i | \(-0.124028\pi\) |
0.133552 | + | 0.991042i | \(0.457362\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.4681 | − | 3.96283i | −0.449028 | − | 0.142718i | ||||
\(772\) | 1.41494 | − | 5.28063i | 0.0509248 | − | 0.190054i | ||||
\(773\) | 30.1093 | + | 30.1093i | 1.08296 | + | 1.08296i | 0.996232 | + | 0.0867231i | \(0.0276395\pi\) |
0.0867231 | + | 0.996232i | \(0.472360\pi\) | |||||||
\(774\) | −2.59237 | + | 28.1350i | −0.0931807 | + | 1.01129i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 8.71386 | − | 5.03095i | 0.312809 | − | 0.180601i | ||||
\(777\) | 0.967939 | − | 21.0546i | 0.0347246 | − | 0.755329i | ||||
\(778\) | −7.81993 | − | 29.1844i | −0.280358 | − | 1.04631i | ||||
\(779\) | 13.1344 | − | 22.7494i | 0.470588 | − | 0.815083i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.59811 | − | 9.69621i | −0.200316 | − | 0.346958i | ||||
\(782\) | 14.7822 | − | 14.7822i | 0.528610 | − | 0.528610i | ||||
\(783\) | −14.6587 | − | 36.0938i | −0.523858 | − | 1.28989i | ||||
\(784\) | 2.93342i | 0.104765i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.803445 | + | 0.176176i | −0.0286579 | + | 0.00628398i | ||||
\(787\) | 10.2212 | − | 2.73876i | 0.364346 | − | 0.0976263i | −0.0720011 | − | 0.997405i | \(-0.522939\pi\) |
0.436347 | + | 0.899778i | \(0.356272\pi\) | |||||||
\(788\) | 16.4450 | − | 4.40644i | 0.585831 | − | 0.156973i | ||||
\(789\) | −13.0137 | − | 14.2679i | −0.463300 | − | 0.507952i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.98028i | 0.212634i | ||||||||
\(792\) | −0.999137 | − | 5.82340i | −0.0355028 | − | 0.206925i | ||||
\(793\) | −25.1515 | + | 25.1515i | −0.893157 | + | 0.893157i | ||||
\(794\) | −1.53420 | − | 2.65731i | −0.0544467 | − | 0.0943045i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.21916 | − | 3.84369i | 0.0786559 | − | 0.136236i | ||||
\(797\) | 3.52110 | + | 13.1409i | 0.124724 | + | 0.465476i | 0.999830 | − | 0.0184558i | \(-0.00587500\pi\) |
−0.875106 | + | 0.483932i | \(0.839208\pi\) | |||||||
\(798\) | −11.5003 | + | 5.95299i | −0.407106 | + | 0.210733i | ||||
\(799\) | 22.4170 | − | 12.9425i | 0.793056 | − | 0.457871i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.57321 | + | 5.58542i | 0.0909200 | + | 0.197351i | ||||
\(802\) | 10.0599 | + | 10.0599i | 0.355229 | + | 0.355229i | ||||
\(803\) | 0.828496 | − | 3.09199i | 0.0292370 | − | 0.109114i | ||||
\(804\) | −10.8410 | + | 9.88801i | −0.382332 | + | 0.348723i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 24.5697 | + | 14.1853i | 0.865432 | + | 0.499657i | ||||
\(807\) | −12.5816 | + | 19.6490i | −0.442895 | + | 0.691679i | ||||
\(808\) | 4.56196 | + | 1.22237i | 0.160489 | + | 0.0430029i | ||||
\(809\) | −33.4429 | −1.17579 | −0.587895 | − | 0.808937i | \(-0.700043\pi\) | ||||
−0.587895 | + | 0.808937i | \(0.700043\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.1960 | 0.744294 | 0.372147 | − | 0.928174i | \(-0.378622\pi\) | ||||
0.372147 | + | 0.928174i | \(0.378622\pi\) | |||||||
\(812\) | −14.6036 | − | 3.91303i | −0.512487 | − | 0.137320i | ||||
\(813\) | −19.0911 | + | 29.8150i | −0.669555 | + | 1.04566i | ||||
\(814\) | −10.2924 | − | 5.94230i | −0.360747 | − | 0.208278i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4.26881 | − | 3.89357i | 0.149438 | − | 0.136302i | ||||
\(817\) | 9.03736 | − | 33.7279i | 0.316177 | − | 1.17999i | ||||
\(818\) | 8.40687 | + | 8.40687i | 0.293939 | + | 0.293939i | ||||
\(819\) | 10.2938 | + | 22.3438i | 0.359696 | + | 0.780757i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −38.4941 | + | 22.2246i | −1.34345 | + | 0.775643i | −0.987313 | − | 0.158789i | \(-0.949241\pi\) |
−0.356141 | + | 0.934432i | \(0.615908\pi\) | |||||||
\(822\) | −15.1540 | + | 7.84431i | −0.528558 | + | 0.273602i | ||||
\(823\) | −6.59989 | − | 24.6311i | −0.230058 | − | 0.858588i | −0.980315 | − | 0.197441i | \(-0.936737\pi\) |
0.750257 | − | 0.661146i | \(-0.229930\pi\) | |||||||
\(824\) | −2.00260 | + | 3.46860i | −0.0697638 | + | 0.120834i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.72171 | + | 4.71413i | 0.0947003 | + | 0.164026i | ||||
\(827\) | 10.7808 | − | 10.7808i | 0.374885 | − | 0.374885i | −0.494368 | − | 0.869253i | \(-0.664600\pi\) |
0.869253 | + | 0.494368i | \(0.164600\pi\) | |||||||
\(828\) | −3.17925 | − | 18.5300i | −0.110486 | − | 0.643962i | ||||
\(829\) | − | 4.02079i | − | 0.139648i | −0.997559 | − | 0.0698239i | \(-0.977756\pi\) | ||
0.997559 | − | 0.0698239i | \(-0.0222437\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −28.2908 | − | 31.0173i | −0.981396 | − | 1.07598i | ||||
\(832\) | 3.92790 | − | 1.05248i | 0.136176 | − | 0.0364881i | ||||
\(833\) | −9.45186 | + | 2.53262i | −0.327488 | + | 0.0877500i | ||||
\(834\) | 1.18840 | − | 0.260587i | 0.0411509 | − | 0.00902338i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 7.30196i | 0.252543i | ||||||||
\(837\) | 22.2675 | − | 28.6074i | 0.769677 | − | 0.988815i | ||||
\(838\) | 27.7686 | − | 27.7686i | 0.959251 | − | 0.959251i | ||||
\(839\) | 16.7880 | + | 29.0777i | 0.579588 | + | 1.00388i | 0.995527 | + | 0.0944825i | \(0.0301196\pi\) |
−0.415939 | + | 0.909393i | \(0.636547\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.6044 | + | 23.5635i | −0.469118 | + | 0.812536i | ||||
\(842\) | 6.34068 | + | 23.6637i | 0.218514 | + | 0.815506i | ||||
\(843\) | −1.79494 | + | 39.0435i | −0.0618211 | + | 1.34473i | ||||
\(844\) | 20.8582 | − | 12.0425i | 0.717968 | − | 0.414519i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.13591 | − | 23.1810i | 0.0734340 | − | 0.796980i | ||||
\(847\) | 10.1542 | + | 10.1542i | 0.348903 | + | 0.348903i | ||||
\(848\) | 2.57326 | − | 9.60353i | 0.0883660 | − | 0.329786i | ||||
\(849\) | 3.50559 | + | 1.11421i | 0.120312 | + | 0.0382395i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −32.7503 | − | 18.9084i | −1.12266 | − | 0.648171i | ||||
\(852\) | −4.52639 | − | 8.74432i | −0.155072 | − | 0.299575i | ||||
\(853\) | −22.9734 | − | 6.15572i | −0.786596 | − | 0.210768i | −0.156905 | − | 0.987614i | \(-0.550152\pi\) |
−0.629691 | + | 0.776846i | \(0.716818\pi\) | |||||||
\(854\) | 17.6391 | 0.603599 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.64094 | −0.261162 | ||||||||
\(857\) | −11.4475 | − | 3.06736i | −0.391040 | − | 0.104779i | 0.0579412 | − | 0.998320i | \(-0.481546\pi\) |
−0.448981 | + | 0.893541i | \(0.648213\pi\) | |||||||
\(858\) | 13.8572 | + | 0.637053i | 0.473076 | + | 0.0217486i | ||||
\(859\) | −34.6670 | − | 20.0150i | −1.18282 | − | 0.682904i | −0.226158 | − | 0.974091i | \(-0.572617\pi\) |
−0.956666 | + | 0.291187i | \(0.905950\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.30058 | + | 24.1732i | 0.180643 | + | 0.823819i | ||||
\(862\) | −1.58062 | + | 5.89894i | −0.0538360 | + | 0.200919i | ||||
\(863\) | −1.78680 | − | 1.78680i | −0.0608233 | − | 0.0608233i | 0.676041 | − | 0.736864i | \(-0.263694\pi\) |
−0.736864 | + | 0.676041i | \(0.763694\pi\) | |||||||
\(864\) | −0.642559 | − | 5.15627i | −0.0218603 | − | 0.175420i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 12.5665 | − | 7.25527i | 0.427027 | − | 0.246544i | ||||
\(867\) | −8.56583 | − | 5.48486i | −0.290911 | − | 0.186276i | ||||
\(868\) | −3.64136 | − | 13.5897i | −0.123596 | − | 0.461266i | ||||
\(869\) | 11.4317 | − | 19.8004i | 0.387795 | − | 0.671681i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.2246 | − | 29.8338i | −0.583632 | − | 1.01088i | ||||
\(872\) | −3.07844 | + | 3.07844i | −0.104249 | + | 0.104249i | ||||
\(873\) | 29.7510 | − | 5.10446i | 1.00692 | − | 0.172760i | ||||
\(874\) | 23.2348i | 0.785928i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.852721 | − | 2.68289i | 0.0288108 | − | 0.0906463i | ||||
\(877\) | −6.66309 | + | 1.78537i | −0.224996 | + | 0.0602876i | −0.369556 | − | 0.929208i | \(-0.620490\pi\) |
0.144559 | + | 0.989496i | \(0.453824\pi\) | |||||||
\(878\) | −2.19284 | + | 0.587569i | −0.0740047 | + | 0.0198295i | ||||
\(879\) | −1.91844 | + | 6.03593i | −0.0647075 | + | 0.203587i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 3.01999i | − | 0.101746i | −0.998705 | − | 0.0508731i | \(-0.983800\pi\) | ||
0.998705 | − | 0.0508731i | \(-0.0162004\pi\) | |||||||
\(882\) | −3.04799 | + | 8.25555i | −0.102631 | + | 0.277979i | ||||
\(883\) | 8.50404 | − | 8.50404i | 0.286184 | − | 0.286184i | −0.549385 | − | 0.835569i | \(-0.685138\pi\) |
0.835569 | + | 0.549385i | \(0.185138\pi\) | |||||||
\(884\) | 6.78245 | + | 11.7476i | 0.228119 | + | 0.395113i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13.9099 | − | 24.0927i | 0.467313 | − | 0.809410i | ||||
\(887\) | 4.61020 | + | 17.2055i | 0.154796 | + | 0.577705i | 0.999123 | + | 0.0418769i | \(0.0133337\pi\) |
−0.844327 | + | 0.535828i | \(0.820000\pi\) | |||||||
\(888\) | −8.80196 | − | 5.63606i | −0.295375 | − | 0.189134i | ||||
\(889\) | 8.44013 | − | 4.87291i | 0.283073 | − | 0.163432i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.23896 | − | 17.4270i | 0.108509 | − | 0.583827i | ||||
\(892\) | 11.8645 | + | 11.8645i | 0.397254 | + | 0.397254i | ||||
\(893\) | −7.44607 | + | 27.7891i | −0.249173 | + | 0.929928i | ||||
\(894\) | −3.00947 | − | 13.7246i | −0.100652 | − | 0.459021i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.74641 | − | 1.00829i | −0.0583434 | − | 0.0336846i | ||||
\(897\) | 44.0934 | + | 2.02710i | 1.47224 | + | 0.0676828i | ||||
\(898\) | −11.3701 | − | 3.04660i | −0.379424 | − | 0.101666i | ||||
\(899\) | −52.3064 | −1.74452 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 33.1655 | 1.10490 | ||||||||
\(902\) | 13.4789 | + | 3.61166i | 0.448798 | + | 0.120255i | ||||
\(903\) | 15.1221 | + | 29.2136i | 0.503231 | + | 0.972169i | ||||
\(904\) | 2.56825 | + | 1.48278i | 0.0854188 | + | 0.0493166i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 15.2437 | + | 4.84500i | 0.506437 | + | 0.160964i | ||||
\(907\) | −0.324723 | + | 1.21188i | −0.0107822 | + | 0.0402399i | −0.971107 | − | 0.238643i | \(-0.923297\pi\) |
0.960325 | + | 0.278883i | \(0.0899641\pi\) | |||||||
\(908\) | −5.26010 | − | 5.26010i | −0.174562 | − | 0.174562i | ||||
\(909\) | 11.5687 | + | 8.18027i | 0.383708 | + | 0.271323i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.3987 | + | 13.5092i | −0.775232 | + | 0.447581i | −0.834738 | − | 0.550647i | \(-0.814381\pi\) |
0.0595057 | + | 0.998228i | \(0.481048\pi\) | |||||||
\(912\) | −0.294909 | + | 6.41485i | −0.00976540 | + | 0.212417i | ||||
\(913\) | 0.868470 | + | 3.24117i | 0.0287422 | + | 0.107267i | ||||
\(914\) | −19.4616 | + | 33.7085i | −0.643734 | + | 1.11498i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.46975 | − | 7.74183i | −0.147685 | − | 0.255797i | ||||
\(917\) | −0.677163 | + | 0.677163i | −0.0223619 | + | 0.0223619i | ||||
\(918\) | 16.0594 | − | 6.52217i | 0.530040 | − | 0.215264i | ||||
\(919\) | 54.3202i | 1.79186i | 0.444196 | + | 0.895930i | \(0.353489\pi\) | ||||
−0.444196 | + | 0.895930i | \(0.646511\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −25.2270 | + | 5.53167i | −0.831259 | + | 0.182275i | ||||
\(922\) | 2.92446 | − | 0.783607i | 0.0963121 | − | 0.0258067i | ||||
\(923\) | 22.3294 | − | 5.98314i | 0.734981 | − | 0.196938i | ||||
\(924\) | −4.63573 | − | 5.08250i | −0.152504 | − | 0.167202i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 6.83645i | 0.224660i | ||||||||
\(927\) | −9.24002 | + | 7.68091i | −0.303482 | + | 0.252274i | ||||
\(928\) | −5.30136 | + | 5.30136i | −0.174026 | + | 0.174026i | ||||
\(929\) | 13.9274 | + | 24.1230i | 0.456944 | + | 0.791450i | 0.998798 | − | 0.0490228i | \(-0.0156107\pi\) |
−0.541854 | + | 0.840473i | \(0.682277\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.43786 | − | 9.41865i | 0.178219 | − | 0.308684i | ||||
\(932\) | 5.51203 | + | 20.5712i | 0.180553 | + | 0.673831i | ||||
\(933\) | 16.1352 | − | 8.35217i | 0.528241 | − | 0.273438i | ||||
\(934\) | −9.86360 | + | 5.69475i | −0.322747 | + | 0.186338i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 12.1479 | + | 1.11932i | 0.397068 | + | 0.0365860i | ||||
\(937\) | 16.8770 | + | 16.8770i | 0.551349 | + | 0.551349i | 0.926830 | − | 0.375481i | \(-0.122523\pi\) |
−0.375481 | + | 0.926830i | \(0.622523\pi\) | |||||||
\(938\) | −4.42152 | + | 16.5014i | −0.144368 | + | 0.538788i | ||||
\(939\) | 22.5909 | − | 20.6051i | 0.737227 | − | 0.672421i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.5039 | + | 16.4567i | 0.929201 | + | 0.536474i | 0.886559 | − | 0.462616i | \(-0.153089\pi\) |
0.0426420 | + | 0.999090i | \(0.486423\pi\) | |||||||
\(942\) | −10.1382 | + | 15.8331i | −0.330320 | + | 0.515869i | ||||
\(943\) | 42.8898 | + | 11.4923i | 1.39668 | + | 0.374240i | ||||
\(944\) | 2.69933 | 0.0878558 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 18.5488 | 0.603074 | ||||||||
\(947\) | −11.5072 | − | 3.08335i | −0.373934 | − | 0.100195i | 0.0669572 | − | 0.997756i | \(-0.478671\pi\) |
−0.440891 | + | 0.897560i | \(0.645338\pi\) | |||||||
\(948\) | 10.8426 | − | 16.9331i | 0.352151 | − | 0.549962i | ||||
\(949\) | 5.72383 | + | 3.30466i | 0.185804 | + | 0.107274i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −29.6727 | + | 27.0644i | −0.962204 | + | 0.877622i | ||||
\(952\) | 1.74105 | − | 6.49768i | 0.0564277 | − | 0.210591i | ||||
\(953\) | −13.4723 | − | 13.4723i | −0.436411 | − | 0.436411i | 0.454391 | − | 0.890802i | \(-0.349857\pi\) |
−0.890802 | + | 0.454391i | \(0.849857\pi\) | |||||||
\(954\) | 17.2206 | − | 24.3536i | 0.557537 | − | 0.788476i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 9.40038 | − | 5.42731i | 0.304030 | − | 0.175532i | ||||
\(957\) | −22.7126 | + | 11.7569i | −0.734195 | + | 0.380047i | ||||
\(958\) | 8.57785 | + | 32.0130i | 0.277138 | + | 1.03429i | ||||
\(959\) | −9.93353 | + | 17.2054i | −0.320770 | + | 0.555591i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.83746 | − | 15.3069i | −0.285079 | − | 0.493772i | ||||
\(962\) | 17.3513 | − | 17.3513i | 0.559428 | − | 0.559428i | ||||
\(963\) | −21.5040 | − | 7.93938i | −0.692957 | − | 0.255843i | ||||
\(964\) | 23.3318i | 0.751467i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −14.7508 | − | 16.1725i | −0.474601 | − | 0.520341i | ||||
\(967\) | −8.95826 | + | 2.40036i | −0.288078 | + | 0.0771904i | −0.399964 | − | 0.916531i | \(-0.630978\pi\) |
0.111886 | + | 0.993721i | \(0.464311\pi\) | |||||||
\(968\) | 6.87844 | − | 1.84307i | 0.221081 | − | 0.0592386i | ||||
\(969\) | −20.9241 | + | 4.58814i | −0.672179 | + | 0.147392i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 24.7290i | − | 0.793590i | −0.917907 | − | 0.396795i | \(-0.870122\pi\) | ||
0.917907 | − | 0.396795i | \(-0.129878\pi\) | |||||||
\(972\) | 3.54930 | − | 15.1790i | 0.113844 | − | 0.486867i | ||||
\(973\) | 1.00161 | − | 1.00161i | 0.0321102 | − | 0.0321102i | ||||
\(974\) | −10.4827 | − | 18.1566i | −0.335889 | − | 0.581776i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.37353 | − | 7.57518i | 0.139993 | − | 0.242476i | ||||
\(977\) | −6.35548 | − | 23.7190i | −0.203330 | − | 0.758837i | −0.989952 | − | 0.141403i | \(-0.954839\pi\) |
0.786622 | − | 0.617434i | \(-0.211828\pi\) | |||||||
\(978\) | −1.08914 | + | 23.6909i | −0.0348267 | + | 0.757551i | ||||
\(979\) | 3.49636 | − | 2.01862i | 0.111744 | − | 0.0645155i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.8624 | + | 5.46502i | −0.378736 | + | 0.174485i | ||||
\(982\) | −13.1868 | − | 13.1868i | −0.420808 | − | 0.420808i | ||||
\(983\) | −10.7435 | + | 40.0954i | −0.342666 | + | 1.27885i | 0.552650 | + | 0.833414i | \(0.313617\pi\) |
−0.895316 | + | 0.445433i | \(0.853050\pi\) | |||||||
\(984\) | 11.6955 | + | 3.71726i | 0.372839 | + | 0.118502i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −21.6587 | − | 12.5047i | −0.689754 | − | 0.398230i | ||||
\(987\) | −12.4594 | − | 24.0697i | −0.396588 | − | 0.766148i | ||||
\(988\) | −14.5628 | − | 3.90209i | −0.463305 | − | 0.124142i | ||||
\(989\) | 59.0222 | 1.87680 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.6089 | 1.16292 | 0.581460 | − | 0.813575i | \(-0.302481\pi\) | ||||
0.581460 | + | 0.813575i | \(0.302481\pi\) | |||||||
\(992\) | −6.73901 | − | 1.80571i | −0.213964 | − | 0.0573315i | ||||
\(993\) | −44.6846 | − | 2.05428i | −1.41802 | − | 0.0651906i | ||||
\(994\) | −9.92800 | − | 5.73193i | −0.314897 | − | 0.181806i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.632057 | + | 2.88248i | 0.0200275 | + | 0.0913349i | ||||
\(997\) | −3.09617 | + | 11.5550i | −0.0980565 | + | 0.365952i | −0.997465 | − | 0.0711569i | \(-0.977331\pi\) |
0.899409 | + | 0.437109i | \(0.143998\pi\) | |||||||
\(998\) | −16.0188 | − | 16.0188i | −0.507065 | − | 0.507065i | ||||
\(999\) | −18.9153 | − | 25.0074i | −0.598453 | − | 0.791199i |
(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 | 450.2.p.h.257.1 | 16 | ||
3.2 | odd | 2 | 1350.2.q.h.557.4 | 16 | |||
5.2 | odd | 4 | 90.2.l.b.23.4 | ✓ | 16 | ||
5.3 | odd | 4 | inner | 450.2.p.h.293.1 | 16 | ||
5.4 | even | 2 | 90.2.l.b.77.4 | yes | 16 | ||
9.2 | odd | 6 | inner | 450.2.p.h.407.1 | 16 | ||
9.7 | even | 3 | 1350.2.q.h.1007.3 | 16 | |||
15.2 | even | 4 | 270.2.m.b.233.2 | 16 | |||
15.8 | even | 4 | 1350.2.q.h.1043.3 | 16 | |||
15.14 | odd | 2 | 270.2.m.b.17.2 | 16 | |||
20.7 | even | 4 | 720.2.cu.b.113.1 | 16 | |||
20.19 | odd | 2 | 720.2.cu.b.257.2 | 16 | |||
45.2 | even | 12 | 90.2.l.b.83.4 | yes | 16 | ||
45.4 | even | 6 | 810.2.f.c.647.2 | 16 | |||
45.7 | odd | 12 | 270.2.m.b.143.2 | 16 | |||
45.14 | odd | 6 | 810.2.f.c.647.7 | 16 | |||
45.22 | odd | 12 | 810.2.f.c.323.7 | 16 | |||
45.29 | odd | 6 | 90.2.l.b.47.4 | yes | 16 | ||
45.32 | even | 12 | 810.2.f.c.323.2 | 16 | |||
45.34 | even | 6 | 270.2.m.b.197.2 | 16 | |||
45.38 | even | 12 | inner | 450.2.p.h.443.1 | 16 | ||
45.43 | odd | 12 | 1350.2.q.h.143.4 | 16 | |||
180.47 | odd | 12 | 720.2.cu.b.353.2 | 16 | |||
180.119 | even | 6 | 720.2.cu.b.497.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
90.2.l.b.23.4 | ✓ | 16 | 5.2 | odd | 4 | ||
90.2.l.b.47.4 | yes | 16 | 45.29 | odd | 6 | ||
90.2.l.b.77.4 | yes | 16 | 5.4 | even | 2 | ||
90.2.l.b.83.4 | yes | 16 | 45.2 | even | 12 | ||
270.2.m.b.17.2 | 16 | 15.14 | odd | 2 | |||
270.2.m.b.143.2 | 16 | 45.7 | odd | 12 | |||
270.2.m.b.197.2 | 16 | 45.34 | even | 6 | |||
270.2.m.b.233.2 | 16 | 15.2 | even | 4 | |||
450.2.p.h.257.1 | 16 | 1.1 | even | 1 | trivial | ||
450.2.p.h.293.1 | 16 | 5.3 | odd | 4 | inner | ||
450.2.p.h.407.1 | 16 | 9.2 | odd | 6 | inner | ||
450.2.p.h.443.1 | 16 | 45.38 | even | 12 | inner | ||
720.2.cu.b.113.1 | 16 | 20.7 | even | 4 | |||
720.2.cu.b.257.2 | 16 | 20.19 | odd | 2 | |||
720.2.cu.b.353.2 | 16 | 180.47 | odd | 12 | |||
720.2.cu.b.497.1 | 16 | 180.119 | even | 6 | |||
810.2.f.c.323.2 | 16 | 45.32 | even | 12 | |||
810.2.f.c.323.7 | 16 | 45.22 | odd | 12 | |||
810.2.f.c.647.2 | 16 | 45.4 | even | 6 | |||
810.2.f.c.647.7 | 16 | 45.14 | odd | 6 | |||
1350.2.q.h.143.4 | 16 | 45.43 | odd | 12 | |||
1350.2.q.h.557.4 | 16 | 3.2 | odd | 2 | |||
1350.2.q.h.1007.3 | 16 | 9.7 | even | 3 | |||
1350.2.q.h.1043.3 | 16 | 15.8 | even | 4 |