Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [552,2,Mod(277,552)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(552, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("552.277");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 552 = 2^{3} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 552.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.40774219157\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{19} + 2 x^{18} - 2 x^{17} + x^{16} - 4 x^{15} + 16 x^{14} - 24 x^{13} + 32 x^{12} + \cdots + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 277.13 | ||
Root | \(-0.238838 + 1.39390i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 552.277 |
Dual form | 552.2.f.d.277.14 |
$q$-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 \(\left(\mathbb{Z}/552\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(185\) | \(277\) | \(415\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.238838 | − | 1.39390i | 0.168884 | − | 0.985636i | ||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −1.88591 | − | 0.665833i | −0.942956 | − | 0.332916i | ||||
\(5\) | − | 4.08024i | − | 1.82474i | −0.409368 | − | 0.912369i | \(-0.634251\pi\) | ||
0.409368 | − | 0.912369i | \(-0.365749\pi\) | |||||||
\(6\) | 1.39390 | + | 0.238838i | 0.569057 | + | 0.0975052i | ||||
\(7\) | −1.92513 | −0.727630 | −0.363815 | − | 0.931471i | \(-0.618526\pi\) | ||||
−0.363815 | + | 0.931471i | \(0.618526\pi\) | |||||||
\(8\) | −1.37853 | + | 2.46975i | −0.487384 | + | 0.873187i | ||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −5.68744 | − | 0.974516i | −1.79853 | − | 0.308169i | ||||
\(11\) | − | 3.31713i | − | 1.00015i | −0.865982 | − | 0.500076i | \(-0.833306\pi\) | ||
0.865982 | − | 0.500076i | \(-0.166694\pi\) | |||||||
\(12\) | 0.665833 | − | 1.88591i | 0.192209 | − | 0.544416i | ||||
\(13\) | 3.23474i | 0.897155i | 0.893744 | + | 0.448578i | \(0.148069\pi\) | ||||
−0.893744 | + | 0.448578i | \(0.851931\pi\) | |||||||
\(14\) | −0.459794 | + | 2.68344i | −0.122885 | + | 0.717179i | ||||
\(15\) | 4.08024 | 1.05351 | ||||||||
\(16\) | 3.11333 | + | 2.51140i | 0.778334 | + | 0.627851i | ||||
\(17\) | −5.13964 | −1.24655 | −0.623273 | − | 0.782005i | \(-0.714197\pi\) | ||||
−0.623273 | + | 0.782005i | \(0.714197\pi\) | |||||||
\(18\) | −0.238838 | + | 1.39390i | −0.0562947 | + | 0.328545i | ||||
\(19\) | 5.11222i | 1.17282i | 0.810013 | + | 0.586412i | \(0.199460\pi\) | ||||
−0.810013 | + | 0.586412i | \(0.800540\pi\) | |||||||
\(20\) | −2.71676 | + | 7.69498i | −0.607485 | + | 1.72065i | ||||
\(21\) | − | 1.92513i | − | 0.420098i | ||||||
\(22\) | −4.62374 | − | 0.792256i | −0.985785 | − | 0.168910i | ||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −2.46975 | − | 1.37853i | −0.504135 | − | 0.281392i | ||||
\(25\) | −11.6484 | −2.32967 | ||||||||
\(26\) | 4.50890 | + | 0.772579i | 0.884268 | + | 0.151515i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 3.63062 | + | 1.28181i | 0.686124 | + | 0.242240i | ||||
\(29\) | − | 7.41361i | − | 1.37667i | −0.725391 | − | 0.688337i | \(-0.758341\pi\) | ||
0.725391 | − | 0.688337i | \(-0.241659\pi\) | |||||||
\(30\) | 0.974516 | − | 5.68744i | 0.177922 | − | 1.03838i | ||||
\(31\) | −1.83802 | −0.330117 | −0.165059 | − | 0.986284i | \(-0.552781\pi\) | ||||
−0.165059 | + | 0.986284i | \(0.552781\pi\) | |||||||
\(32\) | 4.24423 | − | 3.73986i | 0.750281 | − | 0.661120i | ||||
\(33\) | 3.31713 | 0.577438 | ||||||||
\(34\) | −1.22754 | + | 7.16414i | −0.210521 | + | 1.22864i | ||||
\(35\) | 7.85499i | 1.32773i | ||||||||
\(36\) | 1.88591 | + | 0.665833i | 0.314319 | + | 0.110972i | ||||
\(37\) | − | 7.80968i | − | 1.28390i | −0.766745 | − | 0.641952i | \(-0.778125\pi\) | ||
0.766745 | − | 0.641952i | \(-0.221875\pi\) | |||||||
\(38\) | 7.12592 | + | 1.22099i | 1.15598 | + | 0.198071i | ||||
\(39\) | −3.23474 | −0.517973 | ||||||||
\(40\) | 10.0772 | + | 5.62474i | 1.59334 | + | 0.889349i | ||||
\(41\) | −11.9521 | −1.86661 | −0.933304 | − | 0.359087i | \(-0.883088\pi\) | ||||
−0.933304 | + | 0.359087i | \(0.883088\pi\) | |||||||
\(42\) | −2.68344 | − | 0.459794i | −0.414063 | − | 0.0709477i | ||||
\(43\) | − | 2.04224i | − | 0.311439i | −0.987801 | − | 0.155719i | \(-0.950230\pi\) | ||
0.987801 | − | 0.155719i | \(-0.0497695\pi\) | |||||||
\(44\) | −2.20865 | + | 6.25581i | −0.332967 | + | 0.943099i | ||||
\(45\) | 4.08024i | 0.608246i | ||||||||
\(46\) | 0.238838 | − | 1.39390i | 0.0352147 | − | 0.205519i | ||||
\(47\) | 10.9404 | 1.59582 | 0.797909 | − | 0.602778i | \(-0.205940\pi\) | ||||
0.797909 | + | 0.602778i | \(0.205940\pi\) | |||||||
\(48\) | −2.51140 | + | 3.11333i | −0.362490 | + | 0.449371i | ||||
\(49\) | −3.29388 | −0.470554 | ||||||||
\(50\) | −2.78207 | + | 16.2366i | −0.393444 | + | 2.29621i | ||||
\(51\) | − | 5.13964i | − | 0.719693i | ||||||
\(52\) | 2.15379 | − | 6.10044i | 0.298678 | − | 0.845978i | ||||
\(53\) | − | 3.69447i | − | 0.507474i | −0.967273 | − | 0.253737i | \(-0.918340\pi\) | ||
0.967273 | − | 0.253737i | \(-0.0816597\pi\) | |||||||
\(54\) | −1.39390 | − | 0.238838i | −0.189686 | − | 0.0325017i | ||||
\(55\) | −13.5347 | −1.82501 | ||||||||
\(56\) | 2.65385 | − | 4.75458i | 0.354636 | − | 0.635358i | ||||
\(57\) | −5.11222 | −0.677130 | ||||||||
\(58\) | −10.3338 | − | 1.77065i | −1.35690 | − | 0.232498i | ||||
\(59\) | 10.0230i | 1.30489i | 0.757838 | + | 0.652443i | \(0.226256\pi\) | ||||
−0.757838 | + | 0.652443i | \(0.773744\pi\) | |||||||
\(60\) | −7.69498 | − | 2.71676i | −0.993417 | − | 0.350732i | ||||
\(61\) | − | 3.89795i | − | 0.499081i | −0.968364 | − | 0.249541i | \(-0.919720\pi\) | ||
0.968364 | − | 0.249541i | \(-0.0802797\pi\) | |||||||
\(62\) | −0.438988 | + | 2.56201i | −0.0557515 | + | 0.325375i | ||||
\(63\) | 1.92513 | 0.242543 | ||||||||
\(64\) | −4.19930 | − | 6.80925i | −0.524913 | − | 0.851156i | ||||
\(65\) | 13.1985 | 1.63707 | ||||||||
\(66\) | 0.792256 | − | 4.62374i | 0.0975200 | − | 0.569143i | ||||
\(67\) | − | 11.4934i | − | 1.40415i | −0.712105 | − | 0.702073i | \(-0.752258\pi\) | ||
0.712105 | − | 0.702073i | \(-0.247742\pi\) | |||||||
\(68\) | 9.69291 | + | 3.42214i | 1.17544 | + | 0.414995i | ||||
\(69\) | 1.00000i | 0.120386i | ||||||||
\(70\) | 10.9491 | + | 1.87607i | 1.30866 | + | 0.224233i | ||||
\(71\) | 1.12076 | 0.133009 | 0.0665046 | − | 0.997786i | \(-0.478815\pi\) | ||||
0.0665046 | + | 0.997786i | \(0.478815\pi\) | |||||||
\(72\) | 1.37853 | − | 2.46975i | 0.162461 | − | 0.291062i | ||||
\(73\) | 12.8000 | 1.49813 | 0.749066 | − | 0.662495i | \(-0.230503\pi\) | ||||
0.749066 | + | 0.662495i | \(0.230503\pi\) | |||||||
\(74\) | −10.8859 | − | 1.86525i | −1.26546 | − | 0.216831i | ||||
\(75\) | − | 11.6484i | − | 1.34504i | ||||||
\(76\) | 3.40388 | − | 9.64120i | 0.390452 | − | 1.10592i | ||||
\(77\) | 6.38590i | 0.727740i | ||||||||
\(78\) | −0.772579 | + | 4.50890i | −0.0874773 | + | 0.510533i | ||||
\(79\) | 3.52506 | 0.396600 | 0.198300 | − | 0.980141i | \(-0.436458\pi\) | ||||
0.198300 | + | 0.980141i | \(0.436458\pi\) | |||||||
\(80\) | 10.2471 | − | 12.7031i | 1.14566 | − | 1.42026i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.85462 | + | 16.6601i | −0.315240 | + | 1.83980i | ||||
\(83\) | − | 10.1903i | − | 1.11853i | −0.828988 | − | 0.559266i | \(-0.811083\pi\) | ||
0.828988 | − | 0.559266i | \(-0.188917\pi\) | |||||||
\(84\) | −1.28181 | + | 3.63062i | −0.139857 | + | 0.396134i | ||||
\(85\) | 20.9709i | 2.27462i | ||||||||
\(86\) | −2.84668 | − | 0.487765i | −0.306965 | − | 0.0525970i | ||||
\(87\) | 7.41361 | 0.794823 | ||||||||
\(88\) | 8.19246 | + | 4.57276i | 0.873320 | + | 0.487458i | ||||
\(89\) | −5.70580 | −0.604813 | −0.302407 | − | 0.953179i | \(-0.597790\pi\) | ||||
−0.302407 | + | 0.953179i | \(0.597790\pi\) | |||||||
\(90\) | 5.68744 | + | 0.974516i | 0.599509 | + | 0.102723i | ||||
\(91\) | − | 6.22729i | − | 0.652797i | ||||||
\(92\) | −1.88591 | − | 0.665833i | −0.196620 | − | 0.0694178i | ||||
\(93\) | − | 1.83802i | − | 0.190593i | ||||||
\(94\) | 2.61298 | − | 15.2498i | 0.269508 | − | 1.57290i | ||||
\(95\) | 20.8591 | 2.14010 | ||||||||
\(96\) | 3.73986 | + | 4.24423i | 0.381698 | + | 0.433175i | ||||
\(97\) | 0.894897 | 0.0908630 | 0.0454315 | − | 0.998967i | \(-0.485534\pi\) | ||||
0.0454315 | + | 0.998967i | \(0.485534\pi\) | |||||||
\(98\) | −0.786704 | + | 4.59134i | −0.0794691 | + | 0.463795i | ||||
\(99\) | 3.31713i | 0.333384i | ||||||||
\(100\) | 21.9678 | + | 7.75585i | 2.19678 | + | 0.775585i | ||||
\(101\) | 0.154427i | 0.0153661i | 0.999970 | + | 0.00768303i | \(0.00244561\pi\) | ||||
−0.999970 | + | 0.00768303i | \(0.997554\pi\) | |||||||
\(102\) | −7.16414 | − | 1.22754i | −0.709355 | − | 0.121545i | ||||
\(103\) | 3.94598 | 0.388809 | 0.194405 | − | 0.980921i | \(-0.437722\pi\) | ||||
0.194405 | + | 0.980921i | \(0.437722\pi\) | |||||||
\(104\) | −7.98899 | − | 4.45919i | −0.783385 | − | 0.437259i | ||||
\(105\) | −7.85499 | −0.766568 | ||||||||
\(106\) | −5.14971 | − | 0.882379i | −0.500184 | − | 0.0857042i | ||||
\(107\) | − | 0.972312i | − | 0.0939969i | −0.998895 | − | 0.0469985i | \(-0.985034\pi\) | ||
0.998895 | − | 0.0469985i | \(-0.0149656\pi\) | |||||||
\(108\) | −0.665833 | + | 1.88591i | −0.0640698 | + | 0.181472i | ||||
\(109\) | 0.105755i | 0.0101295i | 0.999987 | + | 0.00506477i | \(0.00161217\pi\) | ||||
−0.999987 | + | 0.00506477i | \(0.998388\pi\) | |||||||
\(110\) | −3.23259 | + | 18.8660i | −0.308216 | + | 1.79880i | ||||
\(111\) | 7.80968 | 0.741262 | ||||||||
\(112\) | −5.99357 | − | 4.83478i | −0.566339 | − | 0.456843i | ||||
\(113\) | 5.59603 | 0.526430 | 0.263215 | − | 0.964737i | \(-0.415217\pi\) | ||||
0.263215 | + | 0.964737i | \(0.415217\pi\) | |||||||
\(114\) | −1.22099 | + | 7.12592i | −0.114356 | + | 0.667403i | ||||
\(115\) | − | 4.08024i | − | 0.380484i | ||||||
\(116\) | −4.93623 | + | 13.9814i | −0.458317 | + | 1.29814i | ||||
\(117\) | − | 3.23474i | − | 0.299052i | ||||||
\(118\) | 13.9711 | + | 2.39388i | 1.28614 | + | 0.220374i | ||||
\(119\) | 9.89446 | 0.907024 | ||||||||
\(120\) | −5.62474 | + | 10.0772i | −0.513466 | + | 0.919915i | ||||
\(121\) | −0.00332879 | −0.000302617 | ||||||||
\(122\) | −5.43335 | − | 0.930979i | −0.491913 | − | 0.0842869i | ||||
\(123\) | − | 11.9521i | − | 1.07769i | ||||||
\(124\) | 3.46634 | + | 1.22381i | 0.311286 | + | 0.109901i | ||||
\(125\) | 27.1269i | 2.42630i | ||||||||
\(126\) | 0.459794 | − | 2.68344i | 0.0409617 | − | 0.239060i | ||||
\(127\) | −12.5841 | −1.11666 | −0.558330 | − | 0.829619i | \(-0.688558\pi\) | ||||
−0.558330 | + | 0.829619i | \(0.688558\pi\) | |||||||
\(128\) | −10.4944 | + | 4.22710i | −0.927579 | + | 0.373626i | ||||
\(129\) | 2.04224 | 0.179809 | ||||||||
\(130\) | 3.15231 | − | 18.3974i | 0.276476 | − | 1.61356i | ||||
\(131\) | − | 8.63751i | − | 0.754663i | −0.926078 | − | 0.377332i | \(-0.876842\pi\) | ||
0.926078 | − | 0.377332i | \(-0.123158\pi\) | |||||||
\(132\) | −6.25581 | − | 2.20865i | −0.544498 | − | 0.192238i | ||||
\(133\) | − | 9.84168i | − | 0.853382i | ||||||
\(134\) | −16.0207 | − | 2.74507i | −1.38398 | − | 0.237138i | ||||
\(135\) | −4.08024 | −0.351171 | ||||||||
\(136\) | 7.08515 | − | 12.6936i | 0.607547 | − | 1.08847i | ||||
\(137\) | 13.0277 | 1.11303 | 0.556514 | − | 0.830838i | \(-0.312139\pi\) | ||||
0.556514 | + | 0.830838i | \(0.312139\pi\) | |||||||
\(138\) | 1.39390 | + | 0.238838i | 0.118657 | + | 0.0203312i | ||||
\(139\) | − | 5.78691i | − | 0.490839i | −0.969417 | − | 0.245420i | \(-0.921074\pi\) | ||
0.969417 | − | 0.245420i | \(-0.0789257\pi\) | |||||||
\(140\) | 5.23010 | − | 14.8138i | 0.442025 | − | 1.25200i | ||||
\(141\) | 10.9404i | 0.921346i | ||||||||
\(142\) | 0.267679 | − | 1.56222i | 0.0224631 | − | 0.131099i | ||||
\(143\) | 10.7300 | 0.897291 | ||||||||
\(144\) | −3.11333 | − | 2.51140i | −0.259445 | − | 0.209284i | ||||
\(145\) | −30.2493 | −2.51207 | ||||||||
\(146\) | 3.05714 | − | 17.8420i | 0.253011 | − | 1.47661i | ||||
\(147\) | − | 3.29388i | − | 0.271675i | ||||||
\(148\) | −5.19994 | + | 14.7284i | −0.427432 | + | 1.21067i | ||||
\(149\) | − | 5.29865i | − | 0.434083i | −0.976162 | − | 0.217041i | \(-0.930359\pi\) | ||
0.976162 | − | 0.217041i | \(-0.0696406\pi\) | |||||||
\(150\) | −16.2366 | − | 2.78207i | −1.32572 | − | 0.227155i | ||||
\(151\) | −9.39903 | −0.764882 | −0.382441 | − | 0.923980i | \(-0.624917\pi\) | ||||
−0.382441 | + | 0.923980i | \(0.624917\pi\) | |||||||
\(152\) | −12.6259 | − | 7.04735i | −1.02409 | − | 0.571616i | ||||
\(153\) | 5.13964 | 0.415515 | ||||||||
\(154\) | 8.90130 | + | 1.52519i | 0.717287 | + | 0.122904i | ||||
\(155\) | 7.49954i | 0.602378i | ||||||||
\(156\) | 6.10044 | + | 2.15379i | 0.488426 | + | 0.172442i | ||||
\(157\) | − | 16.1651i | − | 1.29011i | −0.764135 | − | 0.645057i | \(-0.776834\pi\) | ||
0.764135 | − | 0.645057i | \(-0.223166\pi\) | |||||||
\(158\) | 0.841918 | − | 4.91358i | 0.0669794 | − | 0.390903i | ||||
\(159\) | 3.69447 | 0.292990 | ||||||||
\(160\) | −15.2595 | − | 17.3175i | −1.20637 | − | 1.36907i | ||||
\(161\) | −1.92513 | −0.151721 | ||||||||
\(162\) | 0.238838 | − | 1.39390i | 0.0187649 | − | 0.109515i | ||||
\(163\) | − | 5.09700i | − | 0.399227i | −0.979875 | − | 0.199614i | \(-0.936031\pi\) | ||
0.979875 | − | 0.199614i | \(-0.0639687\pi\) | |||||||
\(164\) | 22.5407 | + | 7.95811i | 1.76013 | + | 0.621424i | ||||
\(165\) | − | 13.5347i | − | 1.05367i | ||||||
\(166\) | −14.2043 | − | 2.43383i | −1.10247 | − | 0.188902i | ||||
\(167\) | −18.3213 | −1.41774 | −0.708871 | − | 0.705338i | \(-0.750795\pi\) | ||||
−0.708871 | + | 0.705338i | \(0.750795\pi\) | |||||||
\(168\) | 4.75458 | + | 2.65385i | 0.366824 | + | 0.204749i | ||||
\(169\) | 2.53646 | 0.195113 | ||||||||
\(170\) | 29.2314 | + | 5.00866i | 2.24195 | + | 0.384147i | ||||
\(171\) | − | 5.11222i | − | 0.390941i | ||||||
\(172\) | −1.35979 | + | 3.85149i | −0.103683 | + | 0.293673i | ||||
\(173\) | − | 25.3158i | − | 1.92472i | −0.271776 | − | 0.962361i | \(-0.587611\pi\) | ||
0.271776 | − | 0.962361i | \(-0.412389\pi\) | |||||||
\(174\) | 1.77065 | − | 10.3338i | 0.134233 | − | 0.783406i | ||||
\(175\) | 22.4246 | 1.69514 | ||||||||
\(176\) | 8.33065 | − | 10.3273i | 0.627946 | − | 0.778451i | ||||
\(177\) | −10.0230 | −0.753376 | ||||||||
\(178\) | −1.36276 | + | 7.95331i | −0.102143 | + | 0.596126i | ||||
\(179\) | 19.5389i | 1.46041i | 0.683229 | + | 0.730205i | \(0.260575\pi\) | ||||
−0.683229 | + | 0.730205i | \(0.739425\pi\) | |||||||
\(180\) | 2.71676 | − | 7.69498i | 0.202495 | − | 0.573550i | ||||
\(181\) | − | 0.895809i | − | 0.0665850i | −0.999446 | − | 0.0332925i | \(-0.989401\pi\) | ||
0.999446 | − | 0.0332925i | \(-0.0105993\pi\) | |||||||
\(182\) | −8.68022 | − | 1.48731i | −0.643420 | − | 0.110247i | ||||
\(183\) | 3.89795 | 0.288145 | ||||||||
\(184\) | −1.37853 | + | 2.46975i | −0.101627 | + | 0.182072i | ||||
\(185\) | −31.8654 | −2.34279 | ||||||||
\(186\) | −2.56201 | − | 0.438988i | −0.187856 | − | 0.0321882i | ||||
\(187\) | 17.0488i | 1.24673i | ||||||||
\(188\) | −20.6326 | − | 7.28446i | −1.50479 | − | 0.531274i | ||||
\(189\) | 1.92513i | 0.140033i | ||||||||
\(190\) | 4.98194 | − | 29.0755i | 0.361428 | − | 2.10936i | ||||
\(191\) | 6.97535 | 0.504718 | 0.252359 | − | 0.967634i | \(-0.418794\pi\) | ||||
0.252359 | + | 0.967634i | \(0.418794\pi\) | |||||||
\(192\) | 6.80925 | − | 4.19930i | 0.491415 | − | 0.303059i | ||||
\(193\) | −12.7853 | −0.920307 | −0.460153 | − | 0.887839i | \(-0.652206\pi\) | ||||
−0.460153 | + | 0.887839i | \(0.652206\pi\) | |||||||
\(194\) | 0.213735 | − | 1.24740i | 0.0153453 | − | 0.0895579i | ||||
\(195\) | 13.1985i | 0.945165i | ||||||||
\(196\) | 6.21197 | + | 2.19317i | 0.443712 | + | 0.156655i | ||||
\(197\) | 0.521510i | 0.0371560i | 0.999827 | + | 0.0185780i | \(0.00591391\pi\) | ||||
−0.999827 | + | 0.0185780i | \(0.994086\pi\) | |||||||
\(198\) | 4.62374 | + | 0.792256i | 0.328595 | + | 0.0563032i | ||||
\(199\) | 1.33738 | 0.0948042 | 0.0474021 | − | 0.998876i | \(-0.484906\pi\) | ||||
0.0474021 | + | 0.998876i | \(0.484906\pi\) | |||||||
\(200\) | 16.0576 | − | 28.7685i | 1.13545 | − | 2.03424i | ||||
\(201\) | 11.4934 | 0.810684 | ||||||||
\(202\) | 0.215256 | + | 0.0368830i | 0.0151453 | + | 0.00259508i | ||||
\(203\) | 14.2722i | 1.00171i | ||||||||
\(204\) | −3.42214 | + | 9.69291i | −0.239598 | + | 0.678639i | ||||
\(205\) | 48.7675i | 3.40607i | ||||||||
\(206\) | 0.942451 | − | 5.50031i | 0.0656637 | − | 0.383225i | ||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | −8.12374 | + | 10.0708i | −0.563280 | + | 0.698286i | ||||
\(209\) | 16.9579 | 1.17300 | ||||||||
\(210\) | −1.87607 | + | 10.9491i | −0.129461 | + | 0.755557i | ||||
\(211\) | 23.2302i | 1.59923i | 0.600510 | + | 0.799617i | \(0.294964\pi\) | ||||
−0.600510 | + | 0.799617i | \(0.705036\pi\) | |||||||
\(212\) | −2.45990 | + | 6.96744i | −0.168946 | + | 0.478526i | ||||
\(213\) | 1.12076i | 0.0767929i | ||||||||
\(214\) | −1.35531 | − | 0.232225i | −0.0926468 | − | 0.0158746i | ||||
\(215\) | −8.33283 | −0.568294 | ||||||||
\(216\) | 2.46975 | + | 1.37853i | 0.168045 | + | 0.0937972i | ||||
\(217\) | 3.53842 | 0.240203 | ||||||||
\(218\) | 0.147413 | + | 0.0252584i | 0.00998404 | + | 0.00171072i | ||||
\(219\) | 12.8000i | 0.864947i | ||||||||
\(220\) | 25.5252 | + | 9.01182i | 1.72091 | + | 0.607577i | ||||
\(221\) | − | 16.6254i | − | 1.11834i | ||||||
\(222\) | 1.86525 | − | 10.8859i | 0.125187 | − | 0.730615i | ||||
\(223\) | 17.7737 | 1.19022 | 0.595108 | − | 0.803645i | \(-0.297109\pi\) | ||||
0.595108 | + | 0.803645i | \(0.297109\pi\) | |||||||
\(224\) | −8.17069 | + | 7.19971i | −0.545927 | + | 0.481051i | ||||
\(225\) | 11.6484 | 0.776557 | ||||||||
\(226\) | 1.33654 | − | 7.80030i | 0.0889056 | − | 0.518869i | ||||
\(227\) | 24.1023i | 1.59972i | 0.600184 | + | 0.799862i | \(0.295094\pi\) | ||||
−0.600184 | + | 0.799862i | \(0.704906\pi\) | |||||||
\(228\) | 9.64120 | + | 3.40388i | 0.638504 | + | 0.225428i | ||||
\(229\) | 15.5589i | 1.02816i | 0.857743 | + | 0.514079i | \(0.171866\pi\) | ||||
−0.857743 | + | 0.514079i | \(0.828134\pi\) | |||||||
\(230\) | −5.68744 | − | 0.974516i | −0.375019 | − | 0.0642577i | ||||
\(231\) | −6.38590 | −0.420161 | ||||||||
\(232\) | 18.3098 | + | 10.2199i | 1.20209 | + | 0.670969i | ||||
\(233\) | −17.7810 | −1.16487 | −0.582437 | − | 0.812876i | \(-0.697901\pi\) | ||||
−0.582437 | + | 0.812876i | \(0.697901\pi\) | |||||||
\(234\) | −4.50890 | − | 0.772579i | −0.294756 | − | 0.0505050i | ||||
\(235\) | − | 44.6393i | − | 2.91195i | ||||||
\(236\) | 6.67365 | − | 18.9025i | 0.434418 | − | 1.23045i | ||||
\(237\) | 3.52506i | 0.228977i | ||||||||
\(238\) | 2.36317 | − | 13.7919i | 0.153182 | − | 0.893995i | ||||
\(239\) | −17.9002 | −1.15787 | −0.578933 | − | 0.815375i | \(-0.696531\pi\) | ||||
−0.578933 | + | 0.815375i | \(0.696531\pi\) | |||||||
\(240\) | 12.7031 | + | 10.2471i | 0.819985 | + | 0.661449i | ||||
\(241\) | −8.00122 | −0.515404 | −0.257702 | − | 0.966224i | \(-0.582965\pi\) | ||||
−0.257702 | + | 0.966224i | \(0.582965\pi\) | |||||||
\(242\) | −0.000795041 | 0.00464000i | −5.11072e−5 | 0.000298270i | ||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −2.59538 | + | 7.35120i | −0.166152 | + | 0.470612i | ||||
\(245\) | 13.4398i | 0.858638i | ||||||||
\(246\) | −16.6601 | − | 2.85462i | −1.06221 | − | 0.182004i | ||||
\(247\) | −16.5367 | −1.05220 | ||||||||
\(248\) | 2.53376 | − | 4.53943i | 0.160894 | − | 0.288254i | ||||
\(249\) | 10.1903 | 0.645785 | ||||||||
\(250\) | 37.8121 | + | 6.47893i | 2.39145 | + | 0.409763i | ||||
\(251\) | − | 12.4116i | − | 0.783414i | −0.920090 | − | 0.391707i | \(-0.871885\pi\) | ||
0.920090 | − | 0.391707i | \(-0.128115\pi\) | |||||||
\(252\) | −3.63062 | − | 1.28181i | −0.228708 | − | 0.0807466i | ||||
\(253\) | − | 3.31713i | − | 0.208546i | ||||||
\(254\) | −3.00557 | + | 17.5410i | −0.188586 | + | 1.10062i | ||||
\(255\) | −20.9709 | −1.31325 | ||||||||
\(256\) | 3.38570 | + | 15.6377i | 0.211606 | + | 0.977355i | ||||
\(257\) | 24.5211 | 1.52959 | 0.764793 | − | 0.644276i | \(-0.222841\pi\) | ||||
0.764793 | + | 0.644276i | \(0.222841\pi\) | |||||||
\(258\) | 0.487765 | − | 2.84668i | 0.0303669 | − | 0.177226i | ||||
\(259\) | 15.0346i | 0.934207i | ||||||||
\(260\) | −24.8912 | − | 8.78800i | −1.54369 | − | 0.545008i | ||||
\(261\) | 7.41361i | 0.458891i | ||||||||
\(262\) | −12.0398 | − | 2.06297i | −0.743823 | − | 0.127451i | ||||
\(263\) | −18.7706 | −1.15745 | −0.578724 | − | 0.815524i | \(-0.696449\pi\) | ||||
−0.578724 | + | 0.815524i | \(0.696449\pi\) | |||||||
\(264\) | −4.57276 | + | 8.19246i | −0.281434 | + | 0.504211i | ||||
\(265\) | −15.0743 | −0.926007 | ||||||||
\(266\) | −13.7183 | − | 2.35057i | −0.841124 | − | 0.144123i | ||||
\(267\) | − | 5.70580i | − | 0.349189i | ||||||
\(268\) | −7.65270 | + | 21.6756i | −0.467463 | + | 1.32405i | ||||
\(269\) | − | 20.6183i | − | 1.25712i | −0.777761 | − | 0.628560i | \(-0.783645\pi\) | ||
0.777761 | − | 0.628560i | \(-0.216355\pi\) | |||||||
\(270\) | −0.974516 | + | 5.68744i | −0.0593072 | + | 0.346127i | ||||
\(271\) | −3.31648 | −0.201462 | −0.100731 | − | 0.994914i | \(-0.532118\pi\) | ||||
−0.100731 | + | 0.994914i | \(0.532118\pi\) | |||||||
\(272\) | −16.0014 | − | 12.9077i | −0.970228 | − | 0.782645i | ||||
\(273\) | 6.22729 | 0.376893 | ||||||||
\(274\) | 3.11150 | − | 18.1592i | 0.187973 | − | 1.09704i | ||||
\(275\) | 38.6391i | 2.33002i | ||||||||
\(276\) | 0.665833 | − | 1.88591i | 0.0400784 | − | 0.113519i | ||||
\(277\) | 12.3940i | 0.744683i | 0.928096 | + | 0.372342i | \(0.121445\pi\) | ||||
−0.928096 | + | 0.372342i | \(0.878555\pi\) | |||||||
\(278\) | −8.06637 | − | 1.38213i | −0.483789 | − | 0.0828949i | ||||
\(279\) | 1.83802 | 0.110039 | ||||||||
\(280\) | −19.3998 | − | 10.8283i | −1.15936 | − | 0.647117i | ||||
\(281\) | 19.4045 | 1.15757 | 0.578786 | − | 0.815479i | \(-0.303527\pi\) | ||||
0.578786 | + | 0.815479i | \(0.303527\pi\) | |||||||
\(282\) | 15.2498 | + | 2.61298i | 0.908112 | + | 0.155601i | ||||
\(283\) | 16.9344i | 1.00664i | 0.864099 | + | 0.503322i | \(0.167889\pi\) | ||||
−0.864099 | + | 0.503322i | \(0.832111\pi\) | |||||||
\(284\) | −2.11365 | − | 0.746236i | −0.125422 | − | 0.0442810i | ||||
\(285\) | 20.8591i | 1.23558i | ||||||||
\(286\) | 2.56274 | − | 14.9566i | 0.151538 | − | 0.884402i | ||||
\(287\) | 23.0094 | 1.35820 | ||||||||
\(288\) | −4.24423 | + | 3.73986i | −0.250094 | + | 0.220373i | ||||
\(289\) | 9.41587 | 0.553874 | ||||||||
\(290\) | −7.22469 | + | 42.1645i | −0.424248 | + | 2.47599i | ||||
\(291\) | 0.894897i | 0.0524598i | ||||||||
\(292\) | −24.1398 | − | 8.52269i | −1.41267 | − | 0.498753i | ||||
\(293\) | 19.2392i | 1.12397i | 0.827148 | + | 0.561984i | \(0.189962\pi\) | ||||
−0.827148 | + | 0.561984i | \(0.810038\pi\) | |||||||
\(294\) | −4.59134 | − | 0.786704i | −0.267772 | − | 0.0458815i | ||||
\(295\) | 40.8963 | 2.38108 | ||||||||
\(296\) | 19.2879 | + | 10.7659i | 1.12109 | + | 0.625755i | ||||
\(297\) | −3.31713 | −0.192479 | ||||||||
\(298\) | −7.38579 | − | 1.26552i | −0.427848 | − | 0.0733096i | ||||
\(299\) | 3.23474i | 0.187070i | ||||||||
\(300\) | −7.75585 | + | 21.9678i | −0.447784 | + | 1.26831i | ||||
\(301\) | 3.93157i | 0.226612i | ||||||||
\(302\) | −2.24485 | + | 13.1013i | −0.129176 | + | 0.753895i | ||||
\(303\) | −0.154427 | −0.00887159 | ||||||||
\(304\) | −12.8388 | + | 15.9160i | −0.736358 | + | 0.912848i | ||||
\(305\) | −15.9046 | −0.910693 | ||||||||
\(306\) | 1.22754 | − | 7.16414i | 0.0701738 | − | 0.409547i | ||||
\(307\) | 13.1991i | 0.753314i | 0.926353 | + | 0.376657i | \(0.122926\pi\) | ||||
−0.926353 | + | 0.376657i | \(0.877074\pi\) | |||||||
\(308\) | 4.25194 | − | 12.0432i | 0.242277 | − | 0.686227i | ||||
\(309\) | 3.94598i | 0.224479i | ||||||||
\(310\) | 10.4536 | + | 1.79118i | 0.593725 | + | 0.101732i | ||||
\(311\) | 31.9088 | 1.80938 | 0.904691 | − | 0.426069i | \(-0.140102\pi\) | ||||
0.904691 | + | 0.426069i | \(0.140102\pi\) | |||||||
\(312\) | 4.45919 | − | 7.98899i | 0.252452 | − | 0.452287i | ||||
\(313\) | 17.2307 | 0.973934 | 0.486967 | − | 0.873420i | \(-0.338103\pi\) | ||||
0.486967 | + | 0.873420i | \(0.338103\pi\) | |||||||
\(314\) | −22.5325 | − | 3.86083i | −1.27158 | − | 0.217879i | ||||
\(315\) | − | 7.85499i | − | 0.442578i | ||||||
\(316\) | −6.64795 | − | 2.34710i | −0.373977 | − | 0.132035i | ||||
\(317\) | − | 29.5721i | − | 1.66094i | −0.557066 | − | 0.830468i | \(-0.688073\pi\) | ||
0.557066 | − | 0.830468i | \(-0.311927\pi\) | |||||||
\(318\) | 0.882379 | − | 5.14971i | 0.0494813 | − | 0.288782i | ||||
\(319\) | −24.5919 | −1.37688 | ||||||||
\(320\) | −27.7834 | + | 17.1342i | −1.55314 | + | 0.957829i | ||||
\(321\) | 0.972312 | 0.0542692 | ||||||||
\(322\) | −0.459794 | + | 2.68344i | −0.0256233 | + | 0.149542i | ||||
\(323\) | − | 26.2749i | − | 1.46198i | ||||||
\(324\) | −1.88591 | − | 0.665833i | −0.104773 | − | 0.0369907i | ||||
\(325\) | − | 37.6794i | − | 2.09008i | ||||||
\(326\) | −7.10470 | − | 1.21736i | −0.393493 | − | 0.0674231i | ||||
\(327\) | −0.105755 | −0.00584829 | ||||||||
\(328\) | 16.4764 | − | 29.5187i | 0.909756 | − | 1.62990i | ||||
\(329\) | −21.0616 | −1.16117 | ||||||||
\(330\) | −18.8660 | − | 3.23259i | −1.03854 | − | 0.177948i | ||||
\(331\) | 14.3757i | 0.790161i | 0.918647 | + | 0.395080i | \(0.129283\pi\) | ||||
−0.918647 | + | 0.395080i | \(0.870717\pi\) | |||||||
\(332\) | −6.78504 | + | 19.2180i | −0.372377 | + | 1.05473i | ||||
\(333\) | 7.80968i | 0.427968i | ||||||||
\(334\) | −4.37581 | + | 25.5380i | −0.239434 | + | 1.39738i | ||||
\(335\) | −46.8959 | −2.56220 | ||||||||
\(336\) | 4.83478 | − | 5.99357i | 0.263759 | − | 0.326976i | ||||
\(337\) | 14.0736 | 0.766637 | 0.383319 | − | 0.923616i | \(-0.374781\pi\) | ||||
0.383319 | + | 0.923616i | \(0.374781\pi\) | |||||||
\(338\) | 0.605804 | − | 3.53558i | 0.0329514 | − | 0.192310i | ||||
\(339\) | 5.59603i | 0.303935i | ||||||||
\(340\) | 13.9631 | − | 39.5494i | 0.757258 | − | 2.14487i | ||||
\(341\) | 6.09693i | 0.330167i | ||||||||
\(342\) | −7.12592 | − | 1.22099i | −0.385326 | − | 0.0660237i | ||||
\(343\) | 19.8170 | 1.07002 | ||||||||
\(344\) | 5.04382 | + | 2.81529i | 0.271944 | + | 0.151790i | ||||
\(345\) | 4.08024 | 0.219673 | ||||||||
\(346\) | −35.2876 | − | 6.04636i | −1.89707 | − | 0.325055i | ||||
\(347\) | − | 28.2414i | − | 1.51608i | −0.652209 | − | 0.758039i | \(-0.726158\pi\) | ||
0.652209 | − | 0.758039i | \(-0.273842\pi\) | |||||||
\(348\) | −13.9814 | − | 4.93623i | −0.749483 | − | 0.264609i | ||||
\(349\) | 22.9236i | 1.22707i | 0.789666 | + | 0.613537i | \(0.210254\pi\) | ||||
−0.789666 | + | 0.613537i | \(0.789746\pi\) | |||||||
\(350\) | 5.35584 | − | 31.2576i | 0.286282 | − | 1.67079i | ||||
\(351\) | 3.23474 | 0.172658 | ||||||||
\(352\) | −12.4056 | − | 14.0786i | −0.661220 | − | 0.750394i | ||||
\(353\) | 0.954617 | 0.0508091 | 0.0254046 | − | 0.999677i | \(-0.491913\pi\) | ||||
0.0254046 | + | 0.999677i | \(0.491913\pi\) | |||||||
\(354\) | −2.39388 | + | 13.9711i | −0.127233 | + | 0.742555i | ||||
\(355\) | − | 4.57295i | − | 0.242707i | ||||||
\(356\) | 10.7606 | + | 3.79910i | 0.570312 | + | 0.201352i | ||||
\(357\) | 9.89446i | 0.523670i | ||||||||
\(358\) | 27.2353 | + | 4.66664i | 1.43943 | + | 0.246640i | ||||
\(359\) | −8.13384 | −0.429288 | −0.214644 | − | 0.976692i | \(-0.568859\pi\) | ||||
−0.214644 | + | 0.976692i | \(0.568859\pi\) | |||||||
\(360\) | −10.0772 | − | 5.62474i | −0.531113 | − | 0.296450i | ||||
\(361\) | −7.13477 | −0.375514 | ||||||||
\(362\) | −1.24867 | − | 0.213953i | −0.0656285 | − | 0.0112451i | ||||
\(363\) | − | 0.00332879i | − | 0.000174716i | ||||||
\(364\) | −4.14633 | + | 11.7441i | −0.217327 | + | 0.615559i | ||||
\(365\) | − | 52.2273i | − | 2.73370i | ||||||
\(366\) | 0.930979 | − | 5.43335i | 0.0486630 | − | 0.284006i | ||||
\(367\) | 11.5663 | 0.603754 | 0.301877 | − | 0.953347i | \(-0.402387\pi\) | ||||
0.301877 | + | 0.953347i | \(0.402387\pi\) | |||||||
\(368\) | 3.11333 | + | 2.51140i | 0.162294 | + | 0.130916i | ||||
\(369\) | 11.9521 | 0.622203 | ||||||||
\(370\) | −7.61066 | + | 44.4171i | −0.395659 | + | 2.30914i | ||||
\(371\) | 7.11232i | 0.369253i | ||||||||
\(372\) | −1.22381 | + | 3.46634i | −0.0634516 | + | 0.179721i | ||||
\(373\) | 6.53297i | 0.338264i | 0.985593 | + | 0.169132i | \(0.0540965\pi\) | ||||
−0.985593 | + | 0.169132i | \(0.945904\pi\) | |||||||
\(374\) | 23.7644 | + | 4.07191i | 1.22883 | + | 0.210553i | ||||
\(375\) | −27.1269 | −1.40083 | ||||||||
\(376\) | −15.0817 | + | 27.0200i | −0.777777 | + | 1.39345i | ||||
\(377\) | 23.9811 | 1.23509 | ||||||||
\(378\) | 2.68344 | + | 0.459794i | 0.138021 | + | 0.0236492i | ||||
\(379\) | − | 26.3450i | − | 1.35325i | −0.736326 | − | 0.676627i | \(-0.763441\pi\) | ||
0.736326 | − | 0.676627i | \(-0.236559\pi\) | |||||||
\(380\) | −39.3384 | − | 13.8886i | −2.01802 | − | 0.712473i | ||||
\(381\) | − | 12.5841i | − | 0.644704i | ||||||
\(382\) | 1.66598 | − | 9.72293i | 0.0852388 | − | 0.497468i | ||||
\(383\) | 4.71284 | 0.240815 | 0.120407 | − | 0.992725i | \(-0.461580\pi\) | ||||
0.120407 | + | 0.992725i | \(0.461580\pi\) | |||||||
\(384\) | −4.22710 | − | 10.4944i | −0.215713 | − | 0.535538i | ||||
\(385\) | 26.0560 | 1.32794 | ||||||||
\(386\) | −3.05362 | + | 17.8214i | −0.155425 | + | 0.907088i | ||||
\(387\) | 2.04224i | 0.103813i | ||||||||
\(388\) | −1.68770 | − | 0.595852i | −0.0856799 | − | 0.0302498i | ||||
\(389\) | − | 0.597157i | − | 0.0302771i | −0.999885 | − | 0.0151385i | \(-0.995181\pi\) | ||
0.999885 | − | 0.0151385i | \(-0.00481893\pi\) | |||||||
\(390\) | 18.3974 | + | 3.15231i | 0.931588 | + | 0.159623i | ||||
\(391\) | −5.13964 | −0.259923 | ||||||||
\(392\) | 4.54072 | − | 8.13505i | 0.229341 | − | 0.410882i | ||||
\(393\) | 8.63751 | 0.435705 | ||||||||
\(394\) | 0.726933 | + | 0.124556i | 0.0366223 | + | 0.00627506i | ||||
\(395\) | − | 14.3831i | − | 0.723691i | ||||||
\(396\) | 2.20865 | − | 6.25581i | 0.110989 | − | 0.314366i | ||||
\(397\) | − | 28.7445i | − | 1.44264i | −0.692600 | − | 0.721321i | \(-0.743535\pi\) | ||
0.692600 | − | 0.721321i | \(-0.256465\pi\) | |||||||
\(398\) | 0.319417 | − | 1.86417i | 0.0160109 | − | 0.0934424i | ||||
\(399\) | 9.84168 | 0.492700 | ||||||||
\(400\) | −36.2652 | − | 29.2537i | −1.81326 | − | 1.46269i | ||||
\(401\) | −14.0440 | −0.701322 | −0.350661 | − | 0.936502i | \(-0.614043\pi\) | ||||
−0.350661 | + | 0.936502i | \(0.614043\pi\) | |||||||
\(402\) | 2.74507 | − | 16.0207i | 0.136912 | − | 0.799039i | ||||
\(403\) | − | 5.94550i | − | 0.296166i | ||||||
\(404\) | 0.102822 | − | 0.291236i | 0.00511561 | − | 0.0144895i | ||||
\(405\) | − | 4.08024i | − | 0.202749i | ||||||
\(406\) | 19.8940 | + | 3.40873i | 0.987321 | + | 0.169173i | ||||
\(407\) | −25.9057 | −1.28410 | ||||||||
\(408\) | 12.6936 | + | 7.08515i | 0.628427 | + | 0.350767i | ||||
\(409\) | −7.87046 | −0.389169 | −0.194585 | − | 0.980886i | \(-0.562336\pi\) | ||||
−0.194585 | + | 0.980886i | \(0.562336\pi\) | |||||||
\(410\) | 67.9770 | + | 11.6475i | 3.35715 | + | 0.575231i | ||||
\(411\) | 13.0277i | 0.642607i | ||||||||
\(412\) | −7.44178 | − | 2.62736i | −0.366630 | − | 0.129441i | ||||
\(413\) | − | 19.2956i | − | 0.949475i | ||||||
\(414\) | −0.238838 | + | 1.39390i | −0.0117382 | + | 0.0685064i | ||||
\(415\) | −41.5789 | −2.04103 | ||||||||
\(416\) | 12.0975 | + | 13.7290i | 0.593127 | + | 0.673118i | ||||
\(417\) | 5.78691 | 0.283386 | ||||||||
\(418\) | 4.05019 | − | 23.6376i | 0.198101 | − | 1.15615i | ||||
\(419\) | − | 17.2220i | − | 0.841349i | −0.907212 | − | 0.420674i | \(-0.861794\pi\) | ||
0.907212 | − | 0.420674i | \(-0.138206\pi\) | |||||||
\(420\) | 14.8138 | + | 5.23010i | 0.722840 | + | 0.255203i | ||||
\(421\) | 16.8128i | 0.819404i | 0.912220 | + | 0.409702i | \(0.134367\pi\) | ||||
−0.912220 | + | 0.409702i | \(0.865633\pi\) | |||||||
\(422\) | 32.3806 | + | 5.54826i | 1.57626 | + | 0.270085i | ||||
\(423\) | −10.9404 | −0.531939 | ||||||||
\(424\) | 9.12440 | + | 5.09294i | 0.443120 | + | 0.247335i | ||||
\(425\) | 59.8683 | 2.90404 | ||||||||
\(426\) | 1.56222 | + | 0.267679i | 0.0756899 | + | 0.0129691i | ||||
\(427\) | 7.50406i | 0.363147i | ||||||||
\(428\) | −0.647397 | + | 1.83370i | −0.0312931 | + | 0.0886350i | ||||
\(429\) | 10.7300i | 0.518051i | ||||||||
\(430\) | −1.99020 | + | 11.6151i | −0.0959758 | + | 0.560131i | ||||
\(431\) | 15.9583 | 0.768683 | 0.384341 | − | 0.923191i | \(-0.374429\pi\) | ||||
0.384341 | + | 0.923191i | \(0.374429\pi\) | |||||||
\(432\) | 2.51140 | − | 3.11333i | 0.120830 | − | 0.149790i | ||||
\(433\) | −30.1498 | −1.44891 | −0.724453 | − | 0.689324i | \(-0.757908\pi\) | ||||
−0.724453 | + | 0.689324i | \(0.757908\pi\) | |||||||
\(434\) | 0.845108 | − | 4.93220i | 0.0405665 | − | 0.236753i | ||||
\(435\) | − | 30.2493i | − | 1.45034i | ||||||
\(436\) | 0.0704154 | − | 0.199446i | 0.00337229 | − | 0.00955171i | ||||
\(437\) | 5.11222i | 0.244551i | ||||||||
\(438\) | 17.8420 | + | 3.05714i | 0.852523 | + | 0.146076i | ||||
\(439\) | −6.77425 | −0.323317 | −0.161659 | − | 0.986847i | \(-0.551684\pi\) | ||||
−0.161659 | + | 0.986847i | \(0.551684\pi\) | |||||||
\(440\) | 18.6580 | − | 33.4272i | 0.889484 | − | 1.59358i | ||||
\(441\) | 3.29388 | 0.156851 | ||||||||
\(442\) | −23.1741 | − | 3.97077i | −1.10228 | − | 0.188870i | ||||
\(443\) | 7.38479i | 0.350862i | 0.984492 | + | 0.175431i | \(0.0561319\pi\) | ||||
−0.984492 | + | 0.175431i | \(0.943868\pi\) | |||||||
\(444\) | −14.7284 | − | 5.19994i | −0.698978 | − | 0.246778i | ||||
\(445\) | 23.2810i | 1.10363i | ||||||||
\(446\) | 4.24504 | − | 24.7748i | 0.201009 | − | 1.17312i | ||||
\(447\) | 5.29865 | 0.250618 | ||||||||
\(448\) | 8.08420 | + | 13.1087i | 0.381942 | + | 0.619327i | ||||
\(449\) | −7.22755 | −0.341089 | −0.170545 | − | 0.985350i | \(-0.554553\pi\) | ||||
−0.170545 | + | 0.985350i | \(0.554553\pi\) | |||||||
\(450\) | 2.78207 | − | 16.2366i | 0.131148 | − | 0.765402i | ||||
\(451\) | 39.6467i | 1.86689i | ||||||||
\(452\) | −10.5536 | − | 3.72602i | −0.496401 | − | 0.175257i | ||||
\(453\) | − | 9.39903i | − | 0.441605i | ||||||
\(454\) | 33.5961 | + | 5.75654i | 1.57674 | + | 0.270168i | ||||
\(455\) | −25.4088 | −1.19118 | ||||||||
\(456\) | 7.04735 | − | 12.6259i | 0.330023 | − | 0.591261i | ||||
\(457\) | −18.5420 | −0.867360 | −0.433680 | − | 0.901067i | \(-0.642785\pi\) | ||||
−0.433680 | + | 0.901067i | \(0.642785\pi\) | |||||||
\(458\) | 21.6875 | + | 3.71605i | 1.01339 | + | 0.173640i | ||||
\(459\) | 5.13964i | 0.239898i | ||||||||
\(460\) | −2.71676 | + | 7.69498i | −0.126669 | + | 0.358780i | ||||
\(461\) | 19.9468i | 0.929014i | 0.885569 | + | 0.464507i | \(0.153768\pi\) | ||||
−0.885569 | + | 0.464507i | \(0.846232\pi\) | |||||||
\(462\) | −1.52519 | + | 8.90130i | −0.0709585 | + | 0.414126i | ||||
\(463\) | −12.5401 | −0.582786 | −0.291393 | − | 0.956603i | \(-0.594119\pi\) | ||||
−0.291393 | + | 0.956603i | \(0.594119\pi\) | |||||||
\(464\) | 18.6186 | − | 23.0811i | 0.864346 | − | 1.07151i | ||||
\(465\) | −7.49954 | −0.347783 | ||||||||
\(466\) | −4.24678 | + | 24.7850i | −0.196728 | + | 1.14814i | ||||
\(467\) | 31.8637i | 1.47448i | 0.675632 | + | 0.737239i | \(0.263871\pi\) | ||||
−0.675632 | + | 0.737239i | \(0.736129\pi\) | |||||||
\(468\) | −2.15379 | + | 6.10044i | −0.0995592 | + | 0.281993i | ||||
\(469\) | 22.1263i | 1.02170i | ||||||||
\(470\) | −62.2228 | − | 10.6616i | −2.87012 | − | 0.491782i | ||||
\(471\) | 16.1651 | 0.744847 | ||||||||
\(472\) | −24.7543 | − | 13.8171i | −1.13941 | − | 0.635981i | ||||
\(473\) | −6.77437 | −0.311486 | ||||||||
\(474\) | 4.91358 | + | 0.841918i | 0.225688 | + | 0.0386706i | ||||
\(475\) | − | 59.5489i | − | 2.73229i | ||||||
\(476\) | −18.6601 | − | 6.58805i | −0.855284 | − | 0.301963i | ||||
\(477\) | 3.69447i | 0.169158i | ||||||||
\(478\) | −4.27524 | + | 24.9510i | −0.195545 | + | 1.14123i | ||||
\(479\) | −35.6996 | −1.63116 | −0.815578 | − | 0.578647i | \(-0.803581\pi\) | ||||
−0.815578 | + | 0.578647i | \(0.803581\pi\) | |||||||
\(480\) | 17.3175 | − | 15.2595i | 0.790431 | − | 0.696498i | ||||
\(481\) | 25.2623 | 1.15186 | ||||||||
\(482\) | −1.91100 | + | 11.1529i | −0.0870435 | + | 0.508001i | ||||
\(483\) | − | 1.92513i | − | 0.0875964i | ||||||
\(484\) | 0.00627780 | + | 0.00221641i | 0.000285355 | + | 0.000100746i | ||||
\(485\) | − | 3.65139i | − | 0.165801i | ||||||
\(486\) | 1.39390 | + | 0.238838i | 0.0632286 | + | 0.0108339i | ||||
\(487\) | 9.00670 | 0.408133 | 0.204066 | − | 0.978957i | \(-0.434584\pi\) | ||||
0.204066 | + | 0.978957i | \(0.434584\pi\) | |||||||
\(488\) | 9.62695 | + | 5.37345i | 0.435792 | + | 0.243245i | ||||
\(489\) | 5.09700 | 0.230494 | ||||||||
\(490\) | 18.7338 | + | 3.20994i | 0.846305 | + | 0.145010i | ||||
\(491\) | − | 16.5070i | − | 0.744951i | −0.928042 | − | 0.372476i | \(-0.878509\pi\) | ||
0.928042 | − | 0.372476i | \(-0.121491\pi\) | |||||||
\(492\) | −7.95811 | + | 22.5407i | −0.358779 | + | 1.01621i | ||||
\(493\) | 38.1033i | 1.71609i | ||||||||
\(494\) | −3.94959 | + | 23.0505i | −0.177700 | + | 1.03709i | ||||
\(495\) | 13.5347 | 0.608338 | ||||||||
\(496\) | −5.72236 | − | 4.61600i | −0.256941 | − | 0.207264i | ||||
\(497\) | −2.15760 | −0.0967816 | ||||||||
\(498\) | 2.43383 | − | 14.2043i | 0.109063 | − | 0.636508i | ||||
\(499\) | 9.39150i | 0.420421i | 0.977656 | + | 0.210211i | \(0.0674150\pi\) | ||||
−0.977656 | + | 0.210211i | \(0.932585\pi\) | |||||||
\(500\) | 18.0620 | − | 51.1589i | 0.807755 | − | 2.28790i | ||||
\(501\) | − | 18.3213i | − | 0.818533i | ||||||
\(502\) | −17.3005 | − | 2.96436i | −0.772161 | − | 0.132306i | ||||
\(503\) | 7.80178 | 0.347864 | 0.173932 | − | 0.984758i | \(-0.444353\pi\) | ||||
0.173932 | + | 0.984758i | \(0.444353\pi\) | |||||||
\(504\) | −2.65385 | + | 4.75458i | −0.118212 | + | 0.211786i | ||||
\(505\) | 0.630099 | 0.0280390 | ||||||||
\(506\) | −4.62374 | − | 0.792256i | −0.205550 | − | 0.0352201i | ||||
\(507\) | 2.53646i | 0.112648i | ||||||||
\(508\) | 23.7326 | + | 8.37892i | 1.05296 | + | 0.371754i | ||||
\(509\) | − | 27.4596i | − | 1.21712i | −0.793506 | − | 0.608562i | \(-0.791747\pi\) | ||
0.793506 | − | 0.608562i | \(-0.208253\pi\) | |||||||
\(510\) | −5.00866 | + | 29.2314i | −0.221787 | + | 1.29439i | ||||
\(511\) | −24.6417 | −1.09009 | ||||||||
\(512\) | 22.6060 | − | 0.984451i | 0.999053 | − | 0.0435070i | ||||
\(513\) | 5.11222 | 0.225710 | ||||||||
\(514\) | 5.85658 | − | 34.1800i | 0.258322 | − | 1.50761i | ||||
\(515\) | − | 16.1006i | − | 0.709476i | ||||||
\(516\) | −3.85149 | − | 1.35979i | −0.169552 | − | 0.0598614i | ||||
\(517\) | − | 36.2906i | − | 1.59606i | ||||||
\(518\) | 20.9568 | + | 3.59084i | 0.920788 | + | 0.157773i | ||||
\(519\) | 25.3158 | 1.11124 | ||||||||
\(520\) | −18.1946 | + | 32.5970i | −0.797884 | + | 1.42947i | ||||
\(521\) | −23.8179 | −1.04348 | −0.521740 | − | 0.853105i | \(-0.674717\pi\) | ||||
−0.521740 | + | 0.853105i | \(0.674717\pi\) | |||||||
\(522\) | 10.3338 | + | 1.77065i | 0.452300 | + | 0.0774994i | ||||
\(523\) | 11.9451i | 0.522324i | 0.965295 | + | 0.261162i | \(0.0841057\pi\) | ||||
−0.965295 | + | 0.261162i | \(0.915894\pi\) | |||||||
\(524\) | −5.75114 | + | 16.2896i | −0.251240 | + | 0.711614i | ||||
\(525\) | 22.4246i | 0.978689i | ||||||||
\(526\) | −4.48314 | + | 26.1644i | −0.195474 | + | 1.14082i | ||||
\(527\) | 9.44673 | 0.411506 | ||||||||
\(528\) | 10.3273 | + | 8.33065i | 0.449439 | + | 0.362545i | ||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −3.60032 | + | 21.0121i | −0.156388 | + | 0.912706i | ||||
\(531\) | − | 10.0230i | − | 0.434962i | ||||||
\(532\) | −6.55291 | + | 18.5605i | −0.284105 | + | 0.804702i | ||||
\(533\) | − | 38.6620i | − | 1.67464i | ||||||
\(534\) | −7.95331 | − | 1.36276i | −0.344173 | − | 0.0589724i | ||||
\(535\) | −3.96727 | −0.171520 | ||||||||
\(536\) | 28.3859 | + | 15.8440i | 1.22608 | + | 0.684359i | ||||
\(537\) | −19.5389 | −0.843168 | ||||||||
\(538\) | −28.7398 | − | 4.92443i | −1.23906 | − | 0.212307i | ||||
\(539\) | 10.9262i | 0.470625i | ||||||||
\(540\) | 7.69498 | + | 2.71676i | 0.331139 | + | 0.116911i | ||||
\(541\) | 5.79103i | 0.248976i | 0.992221 | + | 0.124488i | \(0.0397288\pi\) | ||||
−0.992221 | + | 0.124488i | \(0.960271\pi\) | |||||||
\(542\) | −0.792102 | + | 4.62284i | −0.0340237 | + | 0.198568i | ||||
\(543\) | 0.895809 | 0.0384428 | ||||||||
\(544\) | −21.8138 | + | 19.2215i | −0.935259 | + | 0.824115i | ||||
\(545\) | 0.431508 | 0.0184838 | ||||||||
\(546\) | 1.48731 | − | 8.68022i | 0.0636511 | − | 0.371479i | ||||
\(547\) | − | 27.5144i | − | 1.17643i | −0.808704 | − | 0.588216i | \(-0.799831\pi\) | ||
0.808704 | − | 0.588216i | \(-0.200169\pi\) | |||||||
\(548\) | −24.5690 | − | 8.67424i | −1.04954 | − | 0.370545i | ||||
\(549\) | 3.89795i | 0.166360i | ||||||||
\(550\) | 53.8590 | + | 9.22848i | 2.29655 | + | 0.393504i | ||||
\(551\) | 37.9000 | 1.61459 | ||||||||
\(552\) | −2.46975 | − | 1.37853i | −0.105119 | − | 0.0586742i | ||||
\(553\) | −6.78619 | −0.288578 | ||||||||
\(554\) | 17.2760 | + | 2.96016i | 0.733987 | + | 0.125765i | ||||
\(555\) | − | 31.8654i | − | 1.35261i | ||||||
\(556\) | −3.85311 | + | 10.9136i | −0.163408 | + | 0.462840i | ||||
\(557\) | − | 28.3196i | − | 1.19994i | −0.800023 | − | 0.599969i | \(-0.795179\pi\) | ||
0.800023 | − | 0.599969i | \(-0.204821\pi\) | |||||||
\(558\) | 0.438988 | − | 2.56201i | 0.0185838 | − | 0.108458i | ||||
\(559\) | 6.60611 | 0.279409 | ||||||||
\(560\) | −19.7270 | + | 24.4552i | −0.833620 | + | 1.03342i | ||||
\(561\) | −17.0488 | −0.719802 | ||||||||
\(562\) | 4.63452 | − | 27.0479i | 0.195495 | − | 1.14095i | ||||
\(563\) | − | 1.04911i | − | 0.0442146i | −0.999756 | − | 0.0221073i | \(-0.992962\pi\) | ||
0.999756 | − | 0.0221073i | \(-0.00703755\pi\) | |||||||
\(564\) | 7.28446 | − | 20.6326i | 0.306731 | − | 0.868789i | ||||
\(565\) | − | 22.8331i | − | 0.960597i | ||||||
\(566\) | 23.6048 | + | 4.04457i | 0.992185 | + | 0.170006i | ||||
\(567\) | −1.92513 | −0.0808478 | ||||||||
\(568\) | −1.54500 | + | 2.76798i | −0.0648267 | + | 0.116142i | ||||
\(569\) | 19.5828 | 0.820954 | 0.410477 | − | 0.911871i | \(-0.365362\pi\) | ||||
0.410477 | + | 0.911871i | \(0.365362\pi\) | |||||||
\(570\) | 29.0755 | + | 4.98194i | 1.21784 | + | 0.208671i | ||||
\(571\) | − | 19.2897i | − | 0.807248i | −0.914925 | − | 0.403624i | \(-0.867750\pi\) | ||
0.914925 | − | 0.403624i | \(-0.132250\pi\) | |||||||
\(572\) | −20.2359 | − | 7.14441i | −0.846106 | − | 0.298723i | ||||
\(573\) | 6.97535i | 0.291399i | ||||||||
\(574\) | 5.49551 | − | 32.0728i | 0.229378 | − | 1.33869i | ||||
\(575\) | −11.6484 | −0.485770 | ||||||||
\(576\) | 4.19930 | + | 6.80925i | 0.174971 | + | 0.283719i | ||||
\(577\) | 23.7854 | 0.990200 | 0.495100 | − | 0.868836i | \(-0.335131\pi\) | ||||
0.495100 | + | 0.868836i | \(0.335131\pi\) | |||||||
\(578\) | 2.24887 | − | 13.1248i | 0.0935405 | − | 0.545919i | ||||
\(579\) | − | 12.7853i | − | 0.531339i | ||||||
\(580\) | 57.0476 | + | 20.1410i | 2.36877 | + | 0.836309i | ||||
\(581\) | 19.6177i | 0.813877i | ||||||||
\(582\) | 1.24740 | + | 0.213735i | 0.0517063 | + | 0.00885962i | ||||
\(583\) | −12.2550 | −0.507551 | ||||||||
\(584\) | −17.6453 | + | 31.6129i | −0.730166 | + | 1.30815i | ||||
\(585\) | −13.1985 | −0.545691 | ||||||||
\(586\) | 26.8175 | + | 4.59506i | 1.10782 | + | 0.189820i | ||||
\(587\) | 36.3860i | 1.50181i | 0.660411 | + | 0.750905i | \(0.270382\pi\) | ||||
−0.660411 | + | 0.750905i | \(0.729618\pi\) | |||||||
\(588\) | −2.19317 | + | 6.21197i | −0.0904449 | + | 0.256177i | ||||
\(589\) | − | 9.39633i | − | 0.387169i | ||||||
\(590\) | 9.76760 | − | 57.0054i | 0.402126 | − | 2.34687i | ||||
\(591\) | −0.521510 | −0.0214521 | ||||||||
\(592\) | 19.6133 | − | 24.3141i | 0.806100 | − | 0.999305i | ||||
\(593\) | −14.3327 | −0.588572 | −0.294286 | − | 0.955717i | \(-0.595082\pi\) | ||||
−0.294286 | + | 0.955717i | \(0.595082\pi\) | |||||||
\(594\) | −0.792256 | + | 4.62374i | −0.0325067 | + | 0.189714i | ||||
\(595\) | − | 40.3718i | − | 1.65508i | ||||||
\(596\) | −3.52802 | + | 9.99280i | −0.144513 | + | 0.409321i | ||||
\(597\) | 1.33738i | 0.0547352i | ||||||||
\(598\) | 4.50890 | + | 0.772579i | 0.184383 | + | 0.0315931i | ||||
\(599\) | 11.0889 | 0.453082 | 0.226541 | − | 0.974002i | \(-0.427258\pi\) | ||||
0.226541 | + | 0.974002i | \(0.427258\pi\) | |||||||
\(600\) | 28.7685 | + | 16.0576i | 1.17447 | + | 0.655550i | ||||
\(601\) | 48.2043 | 1.96630 | 0.983148 | − | 0.182811i | \(-0.0585195\pi\) | ||||
0.983148 | + | 0.182811i | \(0.0585195\pi\) | |||||||
\(602\) | 5.48022 | + | 0.939010i | 0.223357 | + | 0.0382712i | ||||
\(603\) | 11.4934i | 0.468049i | ||||||||
\(604\) | 17.7258 | + | 6.25818i | 0.721251 | + | 0.254642i | ||||
\(605\) | 0.0135822i | 0.000552197i | ||||||||
\(606\) | −0.0368830 | + | 0.215256i | −0.00149827 | + | 0.00874416i | ||||
\(607\) | 11.4142 | 0.463288 | 0.231644 | − | 0.972801i | \(-0.425589\pi\) | ||||
0.231644 | + | 0.972801i | \(0.425589\pi\) | |||||||
\(608\) | 19.1190 | + | 21.6974i | 0.775376 | + | 0.879947i | ||||
\(609\) | −14.2722 | −0.578337 | ||||||||
\(610\) | −3.79862 | + | 22.1694i | −0.153802 | + | 0.897612i | ||||
\(611\) | 35.3893i | 1.43170i | ||||||||
\(612\) | −9.69291 | − | 3.42214i | −0.391813 | − | 0.138332i | ||||
\(613\) | − | 43.4698i | − | 1.75573i | −0.478909 | − | 0.877864i | \(-0.658968\pi\) | ||
0.478909 | − | 0.877864i | \(-0.341032\pi\) | |||||||
\(614\) | 18.3983 | + | 3.15245i | 0.742493 | + | 0.127223i | ||||
\(615\) | −48.7675 | −1.96650 | ||||||||
\(616\) | −15.7715 | − | 8.80316i | −0.635454 | − | 0.354689i | ||||
\(617\) | −1.84391 | −0.0742332 | −0.0371166 | − | 0.999311i | \(-0.511817\pi\) | ||||
−0.0371166 | + | 0.999311i | \(0.511817\pi\) | |||||||
\(618\) | 5.50031 | + | 0.942451i | 0.221255 | + | 0.0379109i | ||||
\(619\) | 19.4509i | 0.781799i | 0.920433 | + | 0.390900i | \(0.127836\pi\) | ||||
−0.920433 | + | 0.390900i | \(0.872164\pi\) | |||||||
\(620\) | 4.99344 | − | 14.1435i | 0.200541 | − | 0.568016i | ||||
\(621\) | − | 1.00000i | − | 0.0401286i | ||||||
\(622\) | 7.62103 | − | 44.4776i | 0.305576 | − | 1.78339i | ||||
\(623\) | 10.9844 | 0.440080 | ||||||||
\(624\) | −10.0708 | − | 8.12374i | −0.403156 | − | 0.325210i | ||||
\(625\) | 52.4424 | 2.09769 | ||||||||
\(626\) | 4.11534 | − | 24.0178i | 0.164482 | − | 0.959945i | ||||
\(627\) | 16.9579i | 0.677232i | ||||||||
\(628\) | −10.7632 | + | 30.4859i | −0.429500 | + | 1.21652i | ||||
\(629\) | 40.1389i | 1.60044i | ||||||||
\(630\) | −10.9491 | − | 1.87607i | −0.436221 | − | 0.0747444i | ||||
\(631\) | −13.5872 | −0.540897 | −0.270449 | − | 0.962734i | \(-0.587172\pi\) | ||||
−0.270449 | + | 0.962734i | \(0.587172\pi\) | |||||||
\(632\) | −4.85940 | + | 8.70600i | −0.193297 | + | 0.346306i | ||||
\(633\) | −23.2302 | −0.923318 | ||||||||
\(634\) | −41.2206 | − | 7.06295i | −1.63708 | − | 0.280506i | ||||
\(635\) | 51.3462i | 2.03761i | ||||||||
\(636\) | −6.96744 | − | 2.45990i | −0.276277 | − | 0.0975412i | ||||
\(637\) | − | 10.6548i | − | 0.422160i | ||||||
\(638\) | −5.87348 | + | 34.2786i | −0.232533 | + | 1.35710i | ||||
\(639\) | −1.12076 | −0.0443364 | ||||||||
\(640\) | 17.2476 | + | 42.8195i | 0.681770 | + | 1.69259i | ||||
\(641\) | 32.1785 | 1.27097 | 0.635487 | − | 0.772111i | \(-0.280799\pi\) | ||||
0.635487 | + | 0.772111i | \(0.280799\pi\) | |||||||
\(642\) | 0.232225 | − | 1.35531i | 0.00916519 | − | 0.0534896i | ||||
\(643\) | 11.0232i | 0.434711i | 0.976093 | + | 0.217355i | \(0.0697431\pi\) | ||||
−0.976093 | + | 0.217355i | \(0.930257\pi\) | |||||||
\(644\) | 3.63062 | + | 1.28181i | 0.143067 | + | 0.0505105i | ||||
\(645\) | − | 8.33283i | − | 0.328105i | ||||||
\(646\) | −36.6246 | − | 6.27546i | −1.44098 | − | 0.246905i | ||||
\(647\) | −15.4900 | −0.608974 | −0.304487 | − | 0.952516i | \(-0.598485\pi\) | ||||
−0.304487 | + | 0.952516i | \(0.598485\pi\) | |||||||
\(648\) | −1.37853 | + | 2.46975i | −0.0541538 | + | 0.0970208i | ||||
\(649\) | 33.2476 | 1.30508 | ||||||||
\(650\) | −52.5213 | − | 8.99927i | −2.06005 | − | 0.352980i | ||||
\(651\) | 3.53842i | 0.138681i | ||||||||
\(652\) | −3.39375 | + | 9.61249i | −0.132909 | + | 0.376454i | ||||
\(653\) | − | 4.68969i | − | 0.183522i | −0.995781 | − | 0.0917609i | \(-0.970750\pi\) | ||
0.995781 | − | 0.0917609i | \(-0.0292495\pi\) | |||||||
\(654\) | −0.0252584 | + | 0.147413i | −0.000987683 | + | 0.00576429i | ||||
\(655\) | −35.2431 | −1.37706 | ||||||||
\(656\) | −37.2110 | − | 30.0166i | −1.45284 | − | 1.17195i | ||||
\(657\) | −12.8000 | −0.499377 | ||||||||
\(658\) | −5.03032 | + | 29.3578i | −0.196102 | + | 1.14449i | ||||
\(659\) | − | 0.419811i | − | 0.0163535i | −0.999967 | − | 0.00817675i | \(-0.997397\pi\) | ||
0.999967 | − | 0.00817675i | \(-0.00260277\pi\) | |||||||
\(660\) | −9.01182 | + | 25.5252i | −0.350785 | + | 0.993567i | ||||
\(661\) | − | 12.2432i | − | 0.476206i | −0.971240 | − | 0.238103i | \(-0.923474\pi\) | ||
0.971240 | − | 0.238103i | \(-0.0765256\pi\) | |||||||
\(662\) | 20.0383 | + | 3.43347i | 0.778811 | + | 0.133445i | ||||
\(663\) | 16.6254 | 0.645676 | ||||||||
\(664\) | 25.1675 | + | 14.0477i | 0.976688 | + | 0.545155i | ||||
\(665\) | −40.1564 | −1.55720 | ||||||||
\(666\) | 10.8859 | + | 1.86525i | 0.421821 | + | 0.0722769i | ||||
\(667\) | − | 7.41361i | − | 0.287056i | ||||||
\(668\) | 34.5523 | + | 12.1989i | 1.33687 | + | 0.471989i | ||||
\(669\) | 17.7737i | 0.687172i | ||||||||
\(670\) | −11.2005 | + | 65.3682i | −0.432714 | + | 2.52539i | ||||
\(671\) | −12.9300 | −0.499157 | ||||||||
\(672\) | −7.19971 | − | 8.17069i | −0.277735 | − | 0.315191i | ||||
\(673\) | 40.6490 | 1.56691 | 0.783453 | − | 0.621452i | \(-0.213457\pi\) | ||||
0.783453 | + | 0.621452i | \(0.213457\pi\) | |||||||
\(674\) | 3.36131 | − | 19.6172i | 0.129473 | − | 0.755625i | ||||
\(675\) | 11.6484i | 0.448345i | ||||||||
\(676\) | −4.78355 | − | 1.68886i | −0.183983 | − | 0.0649562i | ||||
\(677\) | − | 19.3500i | − | 0.743681i | −0.928297 | − | 0.371840i | \(-0.878727\pi\) | ||
0.928297 | − | 0.371840i | \(-0.121273\pi\) | |||||||
\(678\) | 7.80030 | + | 1.33654i | 0.299569 | + | 0.0513297i | ||||
\(679\) | −1.72279 | −0.0661147 | ||||||||
\(680\) | −51.7929 | − | 28.9091i | −1.98617 | − | 1.10861i | ||||
\(681\) | −24.1023 | −0.923601 | ||||||||
\(682\) | 8.49851 | + | 1.45618i | 0.325425 | + | 0.0557600i | ||||
\(683\) | − | 33.9615i | − | 1.29950i | −0.760147 | − | 0.649751i | \(-0.774873\pi\) | ||
0.760147 | − | 0.649751i | \(-0.225127\pi\) | |||||||
\(684\) | −3.40388 | + | 9.64120i | −0.130151 | + | 0.368640i | ||||
\(685\) | − | 53.1559i | − | 2.03098i | ||||||
\(686\) | 4.73306 | − | 27.6230i | 0.180709 | − | 1.05465i | ||||
\(687\) | −15.5589 | −0.593608 | ||||||||
\(688\) | 5.12889 | − | 6.35818i | 0.195537 | − | 0.242403i | ||||
\(689\) | 11.9506 | 0.455283 | ||||||||
\(690\) | 0.974516 | − | 5.68744i | 0.0370992 | − | 0.216517i | ||||
\(691\) | − | 13.8308i | − | 0.526150i | −0.964775 | − | 0.263075i | \(-0.915263\pi\) | ||
0.964775 | − | 0.263075i | \(-0.0847367\pi\) | |||||||
\(692\) | −16.8561 | + | 47.7433i | −0.640771 | + | 1.81493i | ||||
\(693\) | − | 6.38590i | − | 0.242580i | ||||||
\(694\) | −39.3657 | − | 6.74512i | −1.49430 | − | 0.256041i | ||||
\(695\) | −23.6120 | −0.895653 | ||||||||
\(696\) | −10.2199 | + | 18.3098i | −0.387384 | + | 0.694029i | ||||
\(697\) | 61.4296 | 2.32681 | ||||||||
\(698\) | 31.9532 | + | 5.47503i | 1.20945 | + | 0.207233i | ||||
\(699\) | − | 17.7810i | − | 0.672540i | ||||||
\(700\) | −42.2908 | − | 14.9310i | −1.59844 | − | 0.564339i | ||||
\(701\) | 21.2319i | 0.801918i | 0.916096 | + | 0.400959i | \(0.131323\pi\) | ||||
−0.916096 | + | 0.400959i | \(0.868677\pi\) | |||||||
\(702\) | 0.772579 | − | 4.50890i | 0.0291591 | − | 0.170178i | ||||
\(703\) | 39.9248 | 1.50579 | ||||||||
\(704\) | −22.5871 | + | 13.9296i | −0.851285 | + | 0.524992i | ||||
\(705\) | 44.6393 | 1.68122 | ||||||||
\(706\) | 0.227999 | − | 1.33064i | 0.00858085 | − | 0.0500793i | ||||
\(707\) | − | 0.297292i | − | 0.0111808i | ||||||
\(708\) | 18.9025 | + | 6.67365i | 0.710401 | + | 0.250811i | ||||
\(709\) | 9.49852i | 0.356725i | 0.983965 | + | 0.178362i | \(0.0570799\pi\) | ||||
−0.983965 | + | 0.178362i | \(0.942920\pi\) | |||||||
\(710\) | −6.37424 | − | 1.09220i | −0.239221 | − | 0.0409894i | ||||
\(711\) | −3.52506 | −0.132200 | ||||||||
\(712\) | 7.86562 | − | 14.0919i | 0.294777 | − | 0.528115i | ||||
\(713\) | −1.83802 | −0.0688342 | ||||||||
\(714\) | 13.7919 | + | 2.36317i | 0.516148 | + | 0.0884396i | ||||
\(715\) | − | 43.7811i | − | 1.63732i | ||||||
\(716\) | 13.0097 | − | 36.8487i | 0.486194 | − | 1.37710i | ||||
\(717\) | − | 17.9002i | − | 0.668494i | ||||||
\(718\) | −1.94267 | + | 11.3378i | −0.0724998 | + | 0.423121i | ||||
\(719\) | 34.2920 | 1.27888 | 0.639438 | − | 0.768843i | \(-0.279167\pi\) | ||||
0.639438 | + | 0.768843i | \(0.279167\pi\) | |||||||
\(720\) | −10.2471 | + | 12.7031i | −0.381888 | + | 0.473418i | ||||
\(721\) | −7.59653 | −0.282909 | ||||||||
\(722\) | −1.70406 | + | 9.94516i | −0.0634184 | + | 0.370120i | ||||
\(723\) | − | 8.00122i | − | 0.297569i | ||||||
\(724\) | −0.596459 | + | 1.68942i | −0.0221672 | + | 0.0627867i | ||||
\(725\) | 86.3564i | 3.20720i | ||||||||
\(726\) | −0.00464000 | 0.000795041i | −0.000172206 | 2.95067e-5i | ||||||
\(727\) | 5.75020 | 0.213263 | 0.106631 | − | 0.994299i | \(-0.465993\pi\) | ||||
0.106631 | + | 0.994299i | \(0.465993\pi\) | |||||||
\(728\) | 15.3798 | + | 8.58451i | 0.570014 | + | 0.318163i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −72.7996 | − | 12.4739i | −2.69443 | − | 0.461678i | ||||
\(731\) | 10.4964i | 0.388222i | ||||||||
\(732\) | −7.35120 | − | 2.59538i | −0.271708 | − | 0.0959281i | ||||
\(733\) | − | 42.8684i | − | 1.58338i | −0.610923 | − | 0.791690i | \(-0.709201\pi\) | ||
0.610923 | − | 0.791690i | \(-0.290799\pi\) | |||||||
\(734\) | 2.76247 | − | 16.1222i | 0.101964 | − | 0.595082i | ||||
\(735\) | −13.4398 | −0.495735 | ||||||||
\(736\) | 4.24423 | − | 3.73986i | 0.156444 | − | 0.137853i | ||||
\(737\) | −38.1252 | −1.40436 | ||||||||
\(738\) | 2.85462 | − | 16.6601i | 0.105080 | − | 0.613265i | ||||
\(739\) | 9.76913i | 0.359363i | 0.983725 | + | 0.179682i | \(0.0575067\pi\) | ||||
−0.983725 | + | 0.179682i | \(0.942493\pi\) | |||||||
\(740\) | 60.0953 | + | 21.2170i | 2.20915 | + | 0.779952i | ||||
\(741\) | − | 16.5367i | − | 0.607491i | ||||||
\(742\) | 9.91386 | + | 1.69869i | 0.363949 | + | 0.0623610i | ||||
\(743\) | 47.7415 | 1.75146 | 0.875732 | − | 0.482797i | \(-0.160379\pi\) | ||||
0.875732 | + | 0.482797i | \(0.160379\pi\) | |||||||
\(744\) | 4.53943 | + | 2.53376i | 0.166424 | + | 0.0928922i | ||||
\(745\) | −21.6198 | −0.792087 | ||||||||
\(746\) | 9.10631 | + | 1.56032i | 0.333406 | + | 0.0571275i | ||||
\(747\) | 10.1903i | 0.372844i | ||||||||
\(748\) | 11.3517 | − | 32.1526i | 0.415058 | − | 1.17562i | ||||
\(749\) | 1.87183i | 0.0683950i | ||||||||
\(750\) | −6.47893 | + | 37.8121i | −0.236577 | + | 1.38070i | ||||
\(751\) | 11.8095 | 0.430934 | 0.215467 | − | 0.976511i | \(-0.430873\pi\) | ||||
0.215467 | + | 0.976511i | \(0.430873\pi\) | |||||||
\(752\) | 34.0610 | + | 27.4757i | 1.24208 | + | 1.00194i | ||||
\(753\) | 12.4116 | 0.452304 | ||||||||
\(754\) | 5.72760 | − | 33.4273i | 0.208587 | − | 1.21735i | ||||
\(755\) | 38.3503i | 1.39571i | ||||||||
\(756\) | 1.28181 | − | 3.63062i | 0.0466191 | − | 0.132045i | ||||
\(757\) | 24.5255i | 0.891396i | 0.895183 | + | 0.445698i | \(0.147044\pi\) | ||||
−0.895183 | + | 0.445698i | \(0.852956\pi\) | |||||||
\(758\) | −36.7223 | − | 6.29220i | −1.33382 | − | 0.228543i | ||||
\(759\) | 3.31713 | 0.120404 | ||||||||
\(760\) | −28.7549 | + | 51.5166i | −1.04305 | + | 1.86870i | ||||
\(761\) | 8.83638 | 0.320318 | 0.160159 | − | 0.987091i | \(-0.448799\pi\) | ||||
0.160159 | + | 0.987091i | \(0.448799\pi\) | |||||||
\(762\) | −17.5410 | − | 3.00557i | −0.635444 | − | 0.108880i | ||||
\(763\) | − | 0.203593i | − | 0.00737056i | ||||||
\(764\) | −13.1549 | − | 4.64441i | −0.475927 | − | 0.168029i | ||||
\(765\) | − | 20.9709i | − | 0.758206i | ||||||
\(766\) | 1.12561 | − | 6.56923i | 0.0406698 | − | 0.237356i | ||||
\(767\) | −32.4219 | −1.17069 | ||||||||
\(768\) | −15.6377 | + | 3.38570i | −0.564276 | + | 0.122171i | ||||
\(769\) | −10.8352 | −0.390728 | −0.195364 | − | 0.980731i | \(-0.562589\pi\) | ||||
−0.195364 | + | 0.980731i | \(0.562589\pi\) | |||||||
\(770\) | 6.22316 | − | 36.3194i | 0.224267 | − | 1.30886i | ||||
\(771\) | 24.5211i | 0.883107i | ||||||||
\(772\) | 24.1120 | + | 8.51288i | 0.867809 | + | 0.306385i | ||||
\(773\) | − | 43.8425i | − | 1.57691i | −0.615095 | − | 0.788453i | \(-0.710882\pi\) | ||
0.615095 | − | 0.788453i | \(-0.289118\pi\) | |||||||
\(774\) | 2.84668 | + | 0.487765i | 0.102322 | + | 0.0175323i | ||||
\(775\) | 21.4098 | 0.769064 | ||||||||
\(776\) | −1.23364 | + | 2.21017i | −0.0442852 | + | 0.0793405i | ||||
\(777\) | −15.0346 | −0.539365 | ||||||||
\(778\) | −0.832377 | − | 0.142624i | −0.0298422 | − | 0.00511331i | ||||
\(779\) | − | 61.1019i | − | 2.18920i | ||||||
\(780\) | 8.78800 | − | 24.8912i | 0.314661 | − | 0.891249i | ||||
\(781\) | − | 3.71769i | − | 0.133029i | ||||||
\(782\) | −1.22754 | + | 7.16414i | −0.0438968 | + | 0.256189i | ||||
\(783\) | −7.41361 | −0.264941 | ||||||||
\(784\) | −10.2549 | − | 8.27226i | −0.366248 | − | 0.295438i | ||||
\(785\) | −65.9574 | −2.35412 | ||||||||
\(786\) | 2.06297 | − | 12.0398i | 0.0735836 | − | 0.429446i | ||||
\(787\) | 17.2645i | 0.615413i | 0.951481 | + | 0.307707i | \(0.0995615\pi\) | ||||
−0.951481 | + | 0.307707i | \(0.900438\pi\) | |||||||
\(788\) | 0.347238 | − | 0.983522i | 0.0123699 | − | 0.0350365i | ||||
\(789\) | − | 18.7706i | − | 0.668253i | ||||||
\(790\) | −20.0486 | − | 3.43523i | −0.713296 | − | 0.122220i | ||||
\(791\) | −10.7731 | −0.383047 | ||||||||
\(792\) | −8.19246 | − | 4.57276i | −0.291107 | − | 0.162486i | ||||
\(793\) | 12.6089 | 0.447754 | ||||||||
\(794\) | −40.0669 | − | 6.86527i | −1.42192 | − | 0.243639i | ||||
\(795\) | − | 15.0743i | − | 0.534630i | ||||||
\(796\) | −2.52218 | − | 0.890470i | −0.0893962 | − | 0.0315619i | ||||
\(797\) | 53.2281i | 1.88544i | 0.333590 | + | 0.942718i | \(0.391740\pi\) | ||||
−0.333590 | + | 0.942718i | \(0.608260\pi\) | |||||||
\(798\) | 2.35057 | − | 13.7183i | 0.0832092 | − | 0.485623i | ||||
\(799\) | −56.2296 | −1.98926 | ||||||||
\(800\) | −49.4383 | + | 43.5632i | −1.74791 | + | 1.54019i | ||||
\(801\) | 5.70580 | 0.201604 | ||||||||
\(802\) | −3.35423 | + | 19.5759i | −0.118442 | + | 0.691248i | ||||
\(803\) | − | 42.4594i | − | 1.49836i | ||||||
\(804\) | −21.6756 | − | 7.65270i | −0.764439 | − | 0.269890i | ||||
\(805\) | 7.85499i | 0.276852i | ||||||||
\(806\) | −8.28743 | − | 1.42001i | −0.291912 | − | 0.0500178i | ||||
\(807\) | 20.6183 | 0.725798 | ||||||||
\(808\) | −0.381395 | − | 0.212882i | −0.0134174 | − | 0.00748917i | ||||
\(809\) | −45.8144 | −1.61075 | −0.805375 | − | 0.592766i | \(-0.798036\pi\) | ||||
−0.805375 | + | 0.592766i | \(0.798036\pi\) | |||||||
\(810\) | −5.68744 | − | 0.974516i | −0.199836 | − | 0.0342410i | ||||
\(811\) | 28.9020i | 1.01489i | 0.861685 | + | 0.507443i | \(0.169409\pi\) | ||||
−0.861685 | + | 0.507443i | \(0.830591\pi\) | |||||||
\(812\) | 9.50287 | − | 26.9161i | 0.333485 | − | 0.944568i | ||||
\(813\) | − | 3.31648i | − | 0.116314i | ||||||
\(814\) | −6.18727 | + | 36.1099i | −0.216864 | + | 1.26565i | ||||
\(815\) | −20.7970 | −0.728486 | ||||||||
\(816\) | 12.9077 | − | 16.0014i | 0.451860 | − | 0.560161i | ||||
\(817\) | 10.4404 | 0.365263 | ||||||||
\(818\) | −1.87977 | + | 10.9706i | −0.0657244 | + | 0.383579i | ||||
\(819\) | 6.22729i | 0.217599i | ||||||||
\(820\) | 32.4710 | − | 91.9713i | 1.13394 | − | 3.21178i | ||||
\(821\) | 21.4773i | 0.749561i | 0.927113 | + | 0.374781i | \(0.122282\pi\) | ||||
−0.927113 | + | 0.374781i | \(0.877718\pi\) | |||||||
\(822\) | 18.1592 | + | 3.11150i | 0.633376 | + | 0.108526i | ||||
\(823\) | 1.06437 | 0.0371017 | 0.0185509 | − | 0.999828i | \(-0.494095\pi\) | ||||
0.0185509 | + | 0.999828i | \(0.494095\pi\) | |||||||
\(824\) | −5.43966 | + | 9.74558i | −0.189500 | + | 0.339504i | ||||
\(825\) | −38.6391 | −1.34524 | ||||||||
\(826\) | −26.8961 | − | 4.60852i | −0.935836 | − | 0.160351i | ||||
\(827\) | − | 6.65816i | − | 0.231527i | −0.993277 | − | 0.115764i | \(-0.963069\pi\) | ||
0.993277 | − | 0.115764i | \(-0.0369315\pi\) | |||||||
\(828\) | 1.88591 | + | 0.665833i | 0.0655400 | + | 0.0231393i | ||||
\(829\) | − | 11.1460i | − | 0.387117i | −0.981089 | − | 0.193559i | \(-0.937997\pi\) | ||
0.981089 | − | 0.193559i | \(-0.0620029\pi\) | |||||||
\(830\) | −9.93062 | + | 57.9568i | −0.344697 | + | 2.01171i | ||||
\(831\) | −12.3940 | −0.429943 | ||||||||
\(832\) | 22.0261 | − | 13.5836i | 0.763619 | − | 0.470928i | ||||
\(833\) | 16.9293 | 0.586567 | ||||||||
\(834\) | 1.38213 | − | 8.06637i | 0.0478594 | − | 0.279316i | ||||
\(835\) | 74.7551i | 2.58701i | ||||||||
\(836\) | −31.9811 | − | 11.2911i | −1.10609 | − | 0.390511i | ||||
\(837\) | 1.83802i | 0.0635311i | ||||||||
\(838\) | −24.0057 | − | 4.11326i | −0.829263 | − | 0.142090i | ||||
\(839\) | 45.5904 | 1.57396 | 0.786979 | − | 0.616980i | \(-0.211644\pi\) | ||||
0.786979 | + | 0.616980i | \(0.211644\pi\) | |||||||
\(840\) | 10.8283 | − | 19.3998i | 0.373613 | − | 0.669358i | ||||
\(841\) | −25.9617 | −0.895230 | ||||||||
\(842\) | 23.4353 | + | 4.01553i | 0.807634 | + | 0.138384i | ||||
\(843\) | 19.4045i | 0.668325i | ||||||||
\(844\) | 15.4674 | − | 43.8102i | 0.532411 | − | 1.50801i | ||||
\(845\) | − | 10.3494i | − | 0.356029i | ||||||
\(846\) | −2.61298 | + | 15.2498i | −0.0898360 | + | 0.524298i | ||||
\(847\) | 0.00640834 | 0.000220193 | ||||||||
\(848\) | 9.27830 | − | 11.5021i | 0.318618 | − | 0.394984i | ||||
\(849\) | −16.9344 | −0.581186 | ||||||||
\(850\) | 14.2988 | − | 83.4504i | 0.490446 | − | 2.86233i | ||||
\(851\) | − | 7.80968i | − | 0.267712i | ||||||
\(852\) | 0.746236 | − | 2.11365i | 0.0255656 | − | 0.0724124i | ||||
\(853\) | − | 39.3936i | − | 1.34881i | −0.738362 | − | 0.674405i | \(-0.764400\pi\) | ||
0.738362 | − | 0.674405i | \(-0.235600\pi\) | |||||||
\(854\) | 10.4599 | + | 1.79225i | 0.357931 | + | 0.0613297i | ||||
\(855\) | −20.8591 | −0.713365 | ||||||||
\(856\) | 2.40136 | + | 1.34036i | 0.0820770 | + | 0.0458127i | ||||
\(857\) | 8.67083 | 0.296190 | 0.148095 | − | 0.988973i | \(-0.452686\pi\) | ||||
0.148095 | + | 0.988973i | \(0.452686\pi\) | |||||||
\(858\) | 14.9566 | + | 2.56274i | 0.510610 | + | 0.0874905i | ||||
\(859\) | − | 27.1809i | − | 0.927402i | −0.885992 | − | 0.463701i | \(-0.846521\pi\) | ||
0.885992 | − | 0.463701i | \(-0.153479\pi\) | |||||||
\(860\) | 15.7150 | + | 5.54827i | 0.535877 | + | 0.189194i | ||||
\(861\) | 23.0094i | 0.784157i | ||||||||
\(862\) | 3.81144 | − | 22.2442i | 0.129818 | − | 0.757641i | ||||
\(863\) | −48.5298 | −1.65198 | −0.825988 | − | 0.563688i | \(-0.809382\pi\) | ||||
−0.825988 | + | 0.563688i | \(0.809382\pi\) | |||||||
\(864\) | −3.73986 | − | 4.24423i | −0.127233 | − | 0.144392i | ||||
\(865\) | −103.294 | −3.51211 | ||||||||
\(866\) | −7.20091 | + | 42.0258i | −0.244697 | + | 1.42809i | ||||
\(867\) | 9.41587i | 0.319780i | ||||||||
\(868\) | −6.67314 | − | 2.35599i | −0.226501 | − | 0.0799676i | ||||
\(869\) | − | 11.6931i | − | 0.396660i | ||||||
\(870\) | −42.1645 | − | 7.22469i | −1.42951 | − | 0.244940i | ||||
\(871\) | 37.1782 | 1.25974 | ||||||||
\(872\) | −0.261189 | − | 0.145787i | −0.00884499 | − | 0.00493698i | ||||
\(873\) | −0.894897 | −0.0302877 | ||||||||
\(874\) | 7.12592 | + | 1.22099i | 0.241038 | + | 0.0413007i | ||||
\(875\) | − | 52.2227i | − | 1.76545i | ||||||
\(876\) | 8.52269 | − | 24.1398i | 0.287955 | − | 0.815607i | ||||
\(877\) | 16.5665i | 0.559410i | 0.960086 | + | 0.279705i | \(0.0902367\pi\) | ||||
−0.960086 | + | 0.279705i | \(0.909763\pi\) | |||||||
\(878\) | −1.61795 | + | 9.44262i | −0.0546031 | + | 0.318673i | ||||
\(879\) | −19.2392 | −0.648923 | ||||||||
\(880\) | −42.1380 | − | 33.9910i | −1.42047 | − | 1.14584i | ||||
\(881\) | −6.96876 | −0.234783 | −0.117392 | − | 0.993086i | \(-0.537453\pi\) | ||||
−0.117392 | + | 0.993086i | \(0.537453\pi\) | |||||||
\(882\) | 0.786704 | − | 4.59134i | 0.0264897 | − | 0.154598i | ||||
\(883\) | 16.7729i | 0.564452i | 0.959348 | + | 0.282226i | \(0.0910728\pi\) | ||||
−0.959348 | + | 0.282226i | \(0.908927\pi\) | |||||||
\(884\) | −11.0697 | + | 31.3540i | −0.372315 | + | 1.05455i | ||||
\(885\) | 40.8963i | 1.37472i | ||||||||
\(886\) | 10.2937 | + | 1.76377i | 0.345822 | + | 0.0592550i | ||||
\(887\) | −28.5330 | −0.958046 | −0.479023 | − | 0.877802i | \(-0.659009\pi\) | ||||
−0.479023 | + | 0.877802i | \(0.659009\pi\) | |||||||
\(888\) | −10.7659 | + | 19.2879i | −0.361280 | + | 0.647261i | ||||
\(889\) | 24.2261 | 0.812516 | ||||||||
\(890\) | 32.4514 | + | 5.56039i | 1.08777 | + | 0.186385i | ||||
\(891\) | − | 3.31713i | − | 0.111128i | ||||||
\(892\) | −33.5197 | − | 11.8343i | −1.12232 | − | 0.396243i | ||||
\(893\) | 55.9296i | 1.87161i | ||||||||
\(894\) | 1.26552 | − | 7.38579i | 0.0423253 | − | 0.247018i | ||||
\(895\) | 79.7236 | 2.66486 | ||||||||
\(896\) | 20.2030 | − | 8.13771i | 0.674935 | − | 0.271862i | ||||
\(897\) | −3.23474 | −0.108005 | ||||||||
\(898\) | −1.72621 | + | 10.0745i | −0.0576045 | + | 0.336190i | ||||
\(899\) | 13.6263i | 0.454464i | ||||||||
\(900\) | −21.9678 | − | 7.75585i | −0.732259 | − | 0.258528i | ||||
\(901\) | 18.9882i | 0.632589i | ||||||||
\(902\) | 55.2635 | + | 9.46914i | 1.84007 | + | 0.315288i | ||||
\(903\) | −3.93157 | −0.130835 | ||||||||
\(904\) | −7.71430 | + | 13.8208i | −0.256574 | + | 0.459672i | ||||
\(905\) | −3.65512 | −0.121500 | ||||||||
\(906\) | −13.1013 | − | 2.24485i | −0.435262 | − | 0.0745800i | ||||
\(907\) | − | 9.28967i | − | 0.308458i | −0.988035 | − | 0.154229i | \(-0.950711\pi\) | ||
0.988035 | − | 0.154229i | \(-0.0492894\pi\) | |||||||
\(908\) | 16.0481 | − | 45.4548i | 0.532574 | − | 1.50847i | ||||
\(909\) | − | 0.154427i | − | 0.00512202i | ||||||
\(910\) | −6.06859 | + | 35.4174i | −0.201172 | + | 1.17407i | ||||
\(911\) | −24.2874 | −0.804679 | −0.402339 | − | 0.915491i | \(-0.631803\pi\) | ||||
−0.402339 | + | 0.915491i | \(0.631803\pi\) | |||||||
\(912\) | −15.9160 | − | 12.8388i | −0.527033 | − | 0.425137i | ||||
\(913\) | −33.8025 | −1.11870 | ||||||||
\(914\) | −4.42854 | + | 25.8457i | −0.146483 | + | 0.854901i | ||||
\(915\) | − | 15.9046i | − | 0.525789i | ||||||
\(916\) | 10.3596 | − | 29.3427i | 0.342291 | − | 0.969509i | ||||
\(917\) | 16.6283i | 0.549116i | ||||||||
\(918\) | 7.16414 | + | 1.22754i | 0.236452 | + | 0.0405149i | ||||
\(919\) | −49.6916 | −1.63917 | −0.819587 | − | 0.572955i | \(-0.805797\pi\) | ||||
−0.819587 | + | 0.572955i | \(0.805797\pi\) | |||||||
\(920\) | 10.0772 | + | 5.62474i | 0.332234 | + | 0.185442i | ||||
\(921\) | −13.1991 | −0.434926 | ||||||||
\(922\) | 27.8038 | + | 4.76405i | 0.915669 | + | 0.156896i | ||||
\(923\) | 3.62535i | 0.119330i | ||||||||
\(924\) | 12.0432 | + | 4.25194i | 0.396194 | + | 0.139878i | ||||
\(925\) | 90.9699i | 2.99107i | ||||||||
\(926\) | −2.99504 | + | 17.4796i | −0.0984232 | + | 0.574415i | ||||
\(927\) | −3.94598 | −0.129603 | ||||||||
\(928\) | −27.7259 | − | 31.4651i | −0.910146 | − | 1.03289i | ||||
\(929\) | 24.4855 | 0.803342 | 0.401671 | − | 0.915784i | \(-0.368430\pi\) | ||||
0.401671 | + | 0.915784i | \(0.368430\pi\) | |||||||
\(930\) | −1.79118 | + | 10.4536i | −0.0587350 | + | 0.342787i | ||||
\(931\) | − | 16.8390i | − | 0.551877i | ||||||
\(932\) | 33.5334 | + | 11.8392i | 1.09842 | + | 0.387805i | ||||
\(933\) | 31.9088i | 1.04465i | ||||||||
\(934\) | 44.4149 | + | 7.61027i | 1.45330 | + | 0.249016i | ||||
\(935\) | 69.5633 | 2.27496 | ||||||||
\(936\) | 7.98899 | + | 4.45919i | 0.261128 | + | 0.145753i | ||||
\(937\) | 33.7468 | 1.10246 | 0.551230 | − | 0.834353i | \(-0.314159\pi\) | ||||
0.551230 | + | 0.834353i | \(0.314159\pi\) | |||||||
\(938\) | 30.8419 | + | 5.28461i | 1.00702 | + | 0.172549i | ||||
\(939\) | 17.2307i | 0.562301i | ||||||||
\(940\) | −29.7223 | + | 84.1859i | −0.969436 | + | 2.74584i | ||||
\(941\) | 3.28150i | 0.106974i | 0.998569 | + | 0.0534869i | \(0.0170335\pi\) | ||||
−0.998569 | + | 0.0534869i | \(0.982966\pi\) | |||||||
\(942\) | 3.86083 | − | 22.5325i | 0.125793 | − | 0.734148i | ||||
\(943\) | −11.9521 | −0.389215 | ||||||||
\(944\) | −25.1719 | + | 31.2050i | −0.819274 | + | 1.01564i | ||||
\(945\) | 7.85499 | 0.255523 | ||||||||
\(946\) | −1.61798 | + | 9.44279i | −0.0526050 | + | 0.307012i | ||||
\(947\) | 46.6662i | 1.51645i | 0.651993 | + | 0.758225i | \(0.273933\pi\) | ||||
−0.651993 | + | 0.758225i | \(0.726067\pi\) | |||||||
\(948\) | 2.34710 | − | 6.64795i | 0.0762302 | − | 0.215915i | ||||
\(949\) | 41.4048i | 1.34406i | ||||||||
\(950\) | −83.0052 | − | 14.2225i | −2.69305 | − | 0.461440i | ||||
\(951\) | 29.5721 | 0.958942 | ||||||||
\(952\) | −13.6398 | + | 24.4368i | −0.442069 | + | 0.792002i | ||||
\(953\) | 45.2546 | 1.46594 | 0.732970 | − | 0.680261i | \(-0.238133\pi\) | ||||
0.732970 | + | 0.680261i | \(0.238133\pi\) | |||||||
\(954\) | 5.14971 | + | 0.882379i | 0.166728 | + | 0.0285681i | ||||
\(955\) | − | 28.4611i | − | 0.920979i | ||||||
\(956\) | 33.7581 | + | 11.9185i | 1.09182 | + | 0.385472i | ||||
\(957\) | − | 24.5919i | − | 0.794943i | ||||||
\(958\) | −8.52642 | + | 49.7616i | −0.275476 | + | 1.60773i | ||||
\(959\) | −25.0799 | −0.809873 | ||||||||
\(960\) | −17.1342 | − | 27.7834i | −0.553003 | − | 0.896704i | ||||
\(961\) | −27.6217 | −0.891023 | ||||||||
\(962\) | 6.03359 | − | 35.2131i | 0.194531 | − | 1.13532i | ||||
\(963\) | 0.972312i | 0.0313323i | ||||||||
\(964\) | 15.0896 | + | 5.32747i | 0.486004 | + | 0.171586i | ||||
\(965\) | 52.1671i | 1.67932i | ||||||||
\(966\) | −2.68344 | − | 0.459794i | −0.0863381 | − | 0.0147936i | ||||
\(967\) | 41.0528 | 1.32017 | 0.660084 | − | 0.751192i | \(-0.270521\pi\) | ||||
0.660084 | + | 0.751192i | \(0.270521\pi\) | |||||||
\(968\) | 0.00458884 | − | 0.00822126i | 0.000147491 | − | 0.000264241i | ||||
\(969\) | 26.2749 | 0.844073 | ||||||||
\(970\) | −5.08968 | − | 0.872092i | −0.163420 | − | 0.0280012i | ||||
\(971\) | 21.9250i | 0.703605i | 0.936074 | + | 0.351803i | \(0.114431\pi\) | ||||
−0.936074 | + | 0.351803i | \(0.885569\pi\) | |||||||
\(972\) | 0.665833 | − | 1.88591i | 0.0213566 | − | 0.0604907i | ||||
\(973\) | 11.1405i | 0.357149i | ||||||||
\(974\) | 2.15114 | − | 12.5544i | 0.0689271 | − | 0.402270i | ||||
\(975\) | 37.6794 | 1.20671 | ||||||||
\(976\) | 9.78933 | − | 12.1356i | 0.313349 | − | 0.388452i | ||||
\(977\) | −3.69255 | −0.118135 | −0.0590676 | − | 0.998254i | \(-0.518813\pi\) | ||||
−0.0590676 | + | 0.998254i | \(0.518813\pi\) | |||||||
\(978\) | 1.21736 | − | 7.10470i | 0.0389268 | − | 0.227183i | ||||
\(979\) | 18.9268i | 0.604905i | ||||||||
\(980\) | 8.94867 | − | 25.3463i | 0.285855 | − | 0.809659i | ||||
\(981\) | − | 0.105755i | − | 0.00337651i | ||||||
\(982\) | −23.0091 | − | 3.94250i | −0.734251 | − | 0.125810i | ||||
\(983\) | −2.61252 | −0.0833264 | −0.0416632 | − | 0.999132i | \(-0.513266\pi\) | ||||
−0.0416632 | + | 0.999132i | \(0.513266\pi\) | |||||||
\(984\) | 29.5187 | + | 16.4764i | 0.941022 | + | 0.525248i | ||||
\(985\) | 2.12789 | 0.0678001 | ||||||||
\(986\) | 53.1122 | + | 9.10051i | 1.69144 | + | 0.289819i | ||||
\(987\) | − | 21.0616i | − | 0.670399i | ||||||
\(988\) | 31.1868 | + | 11.0107i | 0.992183 | + | 0.350296i | ||||
\(989\) | − | 2.04224i | − | 0.0649395i | ||||||
\(990\) | 3.23259 | − | 18.8660i | 0.102739 | − | 0.599600i | ||||
\(991\) | −4.00303 | −0.127161 | −0.0635803 | − | 0.997977i | \(-0.520252\pi\) | ||||
−0.0635803 | + | 0.997977i | \(0.520252\pi\) | |||||||
\(992\) | −7.80096 | + | 6.87391i | −0.247681 | + | 0.218247i | ||||
\(993\) | −14.3757 | −0.456199 | ||||||||
\(994\) | −0.515317 | + | 3.00748i | −0.0163449 | + | 0.0953914i | ||||
\(995\) | − | 5.45682i | − | 0.172993i | ||||||
\(996\) | −19.2180 | − | 6.78504i | −0.608947 | − | 0.214992i | ||||
\(997\) | − | 31.8616i | − | 1.00907i | −0.863392 | − | 0.504534i | \(-0.831664\pi\) | ||
0.863392 | − | 0.504534i | \(-0.168336\pi\) | |||||||
\(998\) | 13.0908 | + | 2.24305i | 0.414382 | + | 0.0710024i | ||||
\(999\) | −7.80968 | −0.247087 |
(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 | 552.2.f.d.277.13 | ✓ | 20 | |
4.3 | odd | 2 | 2208.2.f.d.1105.1 | 20 | |||
8.3 | odd | 2 | 2208.2.f.d.1105.20 | 20 | |||
8.5 | even | 2 | inner | 552.2.f.d.277.14 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
552.2.f.d.277.13 | ✓ | 20 | 1.1 | even | 1 | trivial | |
552.2.f.d.277.14 | yes | 20 | 8.5 | even | 2 | inner | |
2208.2.f.d.1105.1 | 20 | 4.3 | odd | 2 | |||
2208.2.f.d.1105.20 | 20 | 8.3 | odd | 2 |