Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [418,2,Mod(45,418)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(418, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("418.45");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 418 = 2 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 418.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.33774680449\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.101617200.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 8x^{4} - 4x^{3} + 64x^{2} - 16x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 45.3 | ||
Root | \(-1.47300 - 2.55131i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 418.45 |
Dual form | 418.2.e.i.353.3 |
$q$-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 \(\left(\mathbb{Z}/418\mathbb{Z}\right)^\times\).
\(n\) | \(287\) | \(343\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | 1.47300 | + | 2.55131i | 0.850436 | + | 1.47300i | 0.880816 | + | 0.473459i | \(0.156995\pi\) |
−0.0303802 | + | 0.999538i | \(0.509672\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −1.00000 | − | 1.73205i | −0.447214 | − | 0.774597i | 0.550990 | − | 0.834512i | \(-0.314250\pi\) |
−0.998203 | + | 0.0599153i | \(0.980917\pi\) | |||||||
\(6\) | −1.47300 | + | 2.55131i | −0.601349 | + | 1.04157i | ||||
\(7\) | 4.94600 | 1.86941 | 0.934705 | − | 0.355424i | \(-0.115663\pi\) | ||||
0.934705 | + | 0.355424i | \(0.115663\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.83944 | + | 4.91806i | −0.946481 | + | 1.63935i | ||||
\(10\) | 1.00000 | − | 1.73205i | 0.316228 | − | 0.547723i | ||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −2.94600 | −0.850436 | ||||||||
\(13\) | −2.83944 | + | 4.91806i | −0.787520 | + | 1.36402i | 0.139962 | + | 0.990157i | \(0.455302\pi\) |
−0.927482 | + | 0.373868i | \(0.878031\pi\) | |||||||
\(14\) | 2.47300 | + | 4.28336i | 0.660936 | + | 1.14478i | ||||
\(15\) | 2.94600 | − | 5.10261i | 0.760653 | − | 1.31749i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.86645 | − | 3.23278i | −0.452680 | − | 0.784064i | 0.545872 | − | 0.837869i | \(-0.316199\pi\) |
−0.998551 | + | 0.0538045i | \(0.982865\pi\) | |||||||
\(18\) | −5.67889 | −1.33853 | ||||||||
\(19\) | −2.70589 | − | 3.41733i | −0.620774 | − | 0.783990i | ||||
\(20\) | 2.00000 | 0.447214 | ||||||||
\(21\) | 7.28544 | + | 12.6188i | 1.58981 | + | 2.75364i | ||||
\(22\) | 0.500000 | + | 0.866025i | 0.106600 | + | 0.184637i | ||||
\(23\) | 0.945995 | − | 1.63851i | 0.197254 | − | 0.341653i | −0.750383 | − | 0.661003i | \(-0.770131\pi\) |
0.947637 | + | 0.319350i | \(0.103464\pi\) | |||||||
\(24\) | −1.47300 | − | 2.55131i | −0.300674 | − | 0.520783i | ||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | −5.67889 | −1.11372 | ||||||||
\(27\) | −7.89199 | −1.51881 | ||||||||
\(28\) | −2.47300 | + | 4.28336i | −0.467353 | + | 0.809478i | ||||
\(29\) | 0.500000 | − | 0.866025i | 0.0928477 | − | 0.160817i | −0.815861 | − | 0.578249i | \(-0.803736\pi\) |
0.908708 | + | 0.417432i | \(0.137070\pi\) | |||||||
\(30\) | 5.89199 | 1.07573 | ||||||||
\(31\) | 3.21310 | 0.577090 | 0.288545 | − | 0.957466i | \(-0.406828\pi\) | ||||
0.288545 | + | 0.957466i | \(0.406828\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 1.47300 | + | 2.55131i | 0.256416 | + | 0.444125i | ||||
\(34\) | 1.86645 | − | 3.23278i | 0.320093 | − | 0.554417i | ||||
\(35\) | −4.94600 | − | 8.56671i | −0.836026 | − | 1.44804i | ||||
\(36\) | −2.83944 | − | 4.91806i | −0.473241 | − | 0.819677i | ||||
\(37\) | −4.15910 | −0.683751 | −0.341876 | − | 0.939745i | \(-0.611062\pi\) | ||||
−0.341876 | + | 0.939745i | \(0.611062\pi\) | |||||||
\(38\) | 1.60655 | − | 4.05204i | 0.260617 | − | 0.657327i | ||||
\(39\) | −16.7300 | −2.67894 | ||||||||
\(40\) | 1.00000 | + | 1.73205i | 0.158114 | + | 0.273861i | ||||
\(41\) | −4.81244 | − | 8.33539i | −0.751577 | − | 1.30177i | −0.947058 | − | 0.321062i | \(-0.895960\pi\) |
0.195481 | − | 0.980707i | \(-0.437373\pi\) | |||||||
\(42\) | −7.28544 | + | 12.6188i | −1.12417 | + | 1.94712i | ||||
\(43\) | 2.31244 | + | 4.00527i | 0.352644 | + | 0.610797i | 0.986712 | − | 0.162480i | \(-0.0519493\pi\) |
−0.634068 | + | 0.773277i | \(0.718616\pi\) | |||||||
\(44\) | −0.500000 | + | 0.866025i | −0.0753778 | + | 0.130558i | ||||
\(45\) | 11.3578 | 1.69312 | ||||||||
\(46\) | 1.89199 | 0.278959 | ||||||||
\(47\) | 3.70589 | − | 6.41879i | 0.540560 | − | 0.936277i | −0.458312 | − | 0.888791i | \(-0.651546\pi\) |
0.998872 | − | 0.0474855i | \(-0.0151208\pi\) | |||||||
\(48\) | 1.47300 | − | 2.55131i | 0.212609 | − | 0.368249i | ||||
\(49\) | 17.4629 | 2.49470 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 5.49854 | − | 9.52375i | 0.769950 | − | 1.33359i | ||||
\(52\) | −2.83944 | − | 4.91806i | −0.393760 | − | 0.682012i | ||||
\(53\) | −5.89199 | + | 10.2052i | −0.809327 | + | 1.40180i | 0.104004 | + | 0.994577i | \(0.466835\pi\) |
−0.913331 | + | 0.407219i | \(0.866499\pi\) | |||||||
\(54\) | −3.94600 | − | 6.83466i | −0.536982 | − | 0.930080i | ||||
\(55\) | −1.00000 | − | 1.73205i | −0.134840 | − | 0.233550i | ||||
\(56\) | −4.94600 | −0.660936 | ||||||||
\(57\) | 4.73289 | − | 11.9373i | 0.626887 | − | 1.58113i | ||||
\(58\) | 1.00000 | 0.131306 | ||||||||
\(59\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(60\) | 2.94600 | + | 5.10261i | 0.380326 | + | 0.658745i | ||||
\(61\) | 2.78544 | − | 4.82452i | 0.356639 | − | 0.617717i | −0.630758 | − | 0.775980i | \(-0.717256\pi\) |
0.987397 | + | 0.158263i | \(0.0505893\pi\) | |||||||
\(62\) | 1.60655 | + | 2.78263i | 0.204032 | + | 0.353394i | ||||
\(63\) | −14.0439 | + | 24.3247i | −1.76936 | + | 3.06462i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 11.3578 | 1.40876 | ||||||||
\(66\) | −1.47300 | + | 2.55131i | −0.181313 | + | 0.314044i | ||||
\(67\) | −4.41899 | + | 7.65392i | −0.539866 | + | 0.935075i | 0.459045 | + | 0.888413i | \(0.348192\pi\) |
−0.998911 | + | 0.0466621i | \(0.985142\pi\) | |||||||
\(68\) | 3.73289 | 0.452680 | ||||||||
\(69\) | 5.57379 | 0.671006 | ||||||||
\(70\) | 4.94600 | − | 8.56671i | 0.591159 | − | 1.02392i | ||||
\(71\) | −2.31244 | − | 4.00527i | −0.274436 | − | 0.475338i | 0.695556 | − | 0.718471i | \(-0.255158\pi\) |
−0.969993 | + | 0.243134i | \(0.921825\pi\) | |||||||
\(72\) | 2.83944 | − | 4.91806i | 0.334632 | − | 0.579599i | ||||
\(73\) | 1.81244 | + | 3.13924i | 0.212130 | + | 0.367420i | 0.952381 | − | 0.304911i | \(-0.0986266\pi\) |
−0.740251 | + | 0.672331i | \(0.765293\pi\) | |||||||
\(74\) | −2.07955 | − | 3.60188i | −0.241743 | − | 0.418711i | ||||
\(75\) | 2.94600 | 0.340174 | ||||||||
\(76\) | 4.31244 | − | 0.634704i | 0.494671 | − | 0.0728055i | ||||
\(77\) | 4.94600 | 0.563648 | ||||||||
\(78\) | −8.36499 | − | 14.4886i | −0.947148 | − | 1.64051i | ||||
\(79\) | 3.41899 | + | 5.92187i | 0.384667 | + | 0.666262i | 0.991723 | − | 0.128397i | \(-0.0409830\pi\) |
−0.607056 | + | 0.794659i | \(0.707650\pi\) | |||||||
\(80\) | −1.00000 | + | 1.73205i | −0.111803 | + | 0.193649i | ||||
\(81\) | −3.10655 | − | 5.38070i | −0.345172 | − | 0.597856i | ||||
\(82\) | 4.81244 | − | 8.33539i | 0.531445 | − | 0.920490i | ||||
\(83\) | 14.5169 | 1.59343 | 0.796717 | − | 0.604353i | \(-0.206568\pi\) | ||||
0.796717 | + | 0.604353i | \(0.206568\pi\) | |||||||
\(84\) | −14.5709 | −1.58981 | ||||||||
\(85\) | −3.73289 | + | 6.46556i | −0.404889 | + | 0.701288i | ||||
\(86\) | −2.31244 | + | 4.00527i | −0.249357 | + | 0.431899i | ||||
\(87\) | 2.94600 | 0.315844 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | 0.232893 | − | 0.403382i | 0.0246866 | − | 0.0427584i | −0.853418 | − | 0.521227i | \(-0.825475\pi\) |
0.878105 | + | 0.478468i | \(0.158808\pi\) | |||||||
\(90\) | 5.67889 | + | 9.83612i | 0.598607 | + | 1.03682i | ||||
\(91\) | −14.0439 | + | 24.3247i | −1.47220 | + | 2.54992i | ||||
\(92\) | 0.945995 | + | 1.63851i | 0.0986268 | + | 0.170827i | ||||
\(93\) | 4.73289 | + | 8.19761i | 0.490778 | + | 0.850053i | ||||
\(94\) | 7.41178 | 0.764467 | ||||||||
\(95\) | −3.21310 | + | 8.10407i | −0.329657 | + | 0.831460i | ||||
\(96\) | 2.94600 | 0.300674 | ||||||||
\(97\) | 0.767107 | + | 1.32867i | 0.0778880 | + | 0.134906i | 0.902339 | − | 0.431028i | \(-0.141849\pi\) |
−0.824451 | + | 0.565934i | \(0.808516\pi\) | |||||||
\(98\) | 8.73143 | + | 15.1233i | 0.882008 | + | 1.52768i | ||||
\(99\) | −2.83944 | + | 4.91806i | −0.285375 | + | 0.494284i | ||||
\(100\) | 0.500000 | + | 0.866025i | 0.0500000 | + | 0.0866025i | ||||
\(101\) | 0.839444 | − | 1.45396i | 0.0835278 | − | 0.144674i | −0.821235 | − | 0.570590i | \(-0.806715\pi\) |
0.904763 | + | 0.425916i | \(0.140048\pi\) | |||||||
\(102\) | 10.9971 | 1.08887 | ||||||||
\(103\) | −7.41178 | −0.730304 | −0.365152 | − | 0.930948i | \(-0.618983\pi\) | ||||
−0.365152 | + | 0.930948i | \(0.618983\pi\) | |||||||
\(104\) | 2.83944 | − | 4.91806i | 0.278430 | − | 0.482256i | ||||
\(105\) | 14.5709 | − | 25.2375i | 1.42197 | − | 2.46293i | ||||
\(106\) | −11.7840 | −1.14456 | ||||||||
\(107\) | 16.3722 | 1.58276 | 0.791380 | − | 0.611324i | \(-0.209363\pi\) | ||||
0.791380 | + | 0.611324i | \(0.209363\pi\) | |||||||
\(108\) | 3.94600 | − | 6.83466i | 0.379704 | − | 0.657666i | ||||
\(109\) | −8.73143 | − | 15.1233i | −0.836320 | − | 1.44855i | −0.892951 | − | 0.450153i | \(-0.851369\pi\) |
0.0566317 | − | 0.998395i | \(-0.481964\pi\) | |||||||
\(110\) | 1.00000 | − | 1.73205i | 0.0953463 | − | 0.165145i | ||||
\(111\) | −6.12634 | − | 10.6111i | −0.581487 | − | 1.00716i | ||||
\(112\) | −2.47300 | − | 4.28336i | −0.233676 | − | 0.404739i | ||||
\(113\) | −3.53421 | −0.332471 | −0.166235 | − | 0.986086i | \(-0.553161\pi\) | ||||
−0.166235 | + | 0.986086i | \(0.553161\pi\) | |||||||
\(114\) | 12.7044 | − | 1.86983i | 1.18988 | − | 0.175126i | ||||
\(115\) | −3.78398 | −0.352858 | ||||||||
\(116\) | 0.500000 | + | 0.866025i | 0.0464238 | + | 0.0804084i | ||||
\(117\) | −16.1249 | − | 27.9291i | −1.49075 | − | 2.58205i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.23143 | − | 15.9893i | −0.846244 | − | 1.46574i | ||||
\(120\) | −2.94600 | + | 5.10261i | −0.268931 | + | 0.465803i | ||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 5.57088 | 0.504364 | ||||||||
\(123\) | 14.1774 | − | 24.5560i | 1.27834 | − | 2.21414i | ||||
\(124\) | −1.60655 | + | 2.78263i | −0.144273 | + | 0.249887i | ||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | −28.0878 | −2.50226 | ||||||||
\(127\) | 2.67889 | − | 4.63997i | 0.237713 | − | 0.411731i | −0.722345 | − | 0.691533i | \(-0.756936\pi\) |
0.960058 | + | 0.279802i | \(0.0902689\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | −6.81244 | + | 11.7995i | −0.599802 | + | 1.03889i | ||||
\(130\) | 5.67889 | + | 9.83612i | 0.498071 | + | 0.862685i | ||||
\(131\) | −5.18610 | − | 8.98259i | −0.453112 | − | 0.784812i | 0.545466 | − | 0.838133i | \(-0.316353\pi\) |
−0.998577 | + | 0.0533206i | \(0.983019\pi\) | |||||||
\(132\) | −2.94600 | −0.256416 | ||||||||
\(133\) | −13.3833 | − | 16.9021i | −1.16048 | − | 1.46560i | ||||
\(134\) | −8.83799 | −0.763486 | ||||||||
\(135\) | 7.89199 | + | 13.6693i | 0.679234 | + | 1.17647i | ||||
\(136\) | 1.86645 | + | 3.23278i | 0.160046 | + | 0.277209i | ||||
\(137\) | −7.05255 | + | 12.2154i | −0.602540 | + | 1.04363i | 0.389895 | + | 0.920859i | \(0.372511\pi\) |
−0.992435 | + | 0.122770i | \(0.960822\pi\) | |||||||
\(138\) | 2.78690 | + | 4.82705i | 0.237236 | + | 0.410906i | ||||
\(139\) | 6.83799 | − | 11.8437i | 0.579990 | − | 1.00457i | −0.415489 | − | 0.909598i | \(-0.636390\pi\) |
0.995480 | − | 0.0949747i | \(-0.0302770\pi\) | |||||||
\(140\) | 9.89199 | 0.836026 | ||||||||
\(141\) | 21.8351 | 1.83884 | ||||||||
\(142\) | 2.31244 | − | 4.00527i | 0.194056 | − | 0.336114i | ||||
\(143\) | −2.83944 | + | 4.91806i | −0.237446 | + | 0.411269i | ||||
\(144\) | 5.67889 | 0.473241 | ||||||||
\(145\) | −2.00000 | −0.166091 | ||||||||
\(146\) | −1.81244 | + | 3.13924i | −0.149999 | + | 0.259805i | ||||
\(147\) | 25.7228 | + | 44.5531i | 2.12158 | + | 3.67468i | ||||
\(148\) | 2.07955 | − | 3.60188i | 0.170938 | − | 0.296073i | ||||
\(149\) | −9.49854 | − | 16.4520i | −0.778151 | − | 1.34780i | −0.933006 | − | 0.359860i | \(-0.882825\pi\) |
0.154856 | − | 0.987937i | \(-0.450509\pi\) | |||||||
\(150\) | 1.47300 | + | 2.55131i | 0.120270 | + | 0.208313i | ||||
\(151\) | −23.6615 | −1.92555 | −0.962775 | − | 0.270305i | \(-0.912875\pi\) | ||||
−0.962775 | + | 0.270305i | \(0.912875\pi\) | |||||||
\(152\) | 2.70589 | + | 3.41733i | 0.219477 | + | 0.277182i | ||||
\(153\) | 21.1987 | 1.71381 | ||||||||
\(154\) | 2.47300 | + | 4.28336i | 0.199280 | + | 0.345163i | ||||
\(155\) | −3.21310 | − | 5.56526i | −0.258083 | − | 0.447012i | ||||
\(156\) | 8.36499 | − | 14.4886i | 0.669735 | − | 1.16002i | ||||
\(157\) | 5.89199 | + | 10.2052i | 0.470232 | + | 0.814466i | 0.999421 | − | 0.0340385i | \(-0.0108369\pi\) |
−0.529188 | + | 0.848504i | \(0.677504\pi\) | |||||||
\(158\) | −3.41899 | + | 5.92187i | −0.272000 | + | 0.471119i | ||||
\(159\) | −34.7156 | −2.75312 | ||||||||
\(160\) | −2.00000 | −0.158114 | ||||||||
\(161\) | 4.67889 | − | 8.10407i | 0.368748 | − | 0.638690i | ||||
\(162\) | 3.10655 | − | 5.38070i | 0.244074 | − | 0.422748i | ||||
\(163\) | −10.8236 | −0.847767 | −0.423883 | − | 0.905717i | \(-0.639333\pi\) | ||||
−0.423883 | + | 0.905717i | \(0.639333\pi\) | |||||||
\(164\) | 9.62488 | 0.751577 | ||||||||
\(165\) | 2.94600 | − | 5.10261i | 0.229345 | − | 0.397238i | ||||
\(166\) | 7.25844 | + | 12.5720i | 0.563364 | + | 0.975775i | ||||
\(167\) | −2.00721 | + | 3.47659i | −0.155323 | + | 0.269027i | −0.933177 | − | 0.359418i | \(-0.882975\pi\) |
0.777854 | + | 0.628445i | \(0.216308\pi\) | |||||||
\(168\) | −7.28544 | − | 12.6188i | −0.562084 | − | 0.973558i | ||||
\(169\) | −9.62488 | − | 16.6708i | −0.740376 | − | 1.28237i | ||||
\(170\) | −7.46579 | −0.572600 | ||||||||
\(171\) | 24.4899 | − | 3.60441i | 1.87279 | − | 0.275636i | ||||
\(172\) | −4.62488 | −0.352644 | ||||||||
\(173\) | 3.60655 | + | 6.24673i | 0.274201 | + | 0.474930i | 0.969933 | − | 0.243371i | \(-0.0782533\pi\) |
−0.695732 | + | 0.718301i | \(0.744920\pi\) | |||||||
\(174\) | 1.47300 | + | 2.55131i | 0.111668 | + | 0.193414i | ||||
\(175\) | 2.47300 | − | 4.28336i | 0.186941 | − | 0.323791i | ||||
\(176\) | −0.500000 | − | 0.866025i | −0.0376889 | − | 0.0652791i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.465785 | 0.0349121 | ||||||||
\(179\) | 4.10801 | 0.307047 | 0.153524 | − | 0.988145i | \(-0.450938\pi\) | ||||
0.153524 | + | 0.988145i | \(0.450938\pi\) | |||||||
\(180\) | −5.67889 | + | 9.83612i | −0.423279 | + | 0.733141i | ||||
\(181\) | −7.70443 | + | 13.3445i | −0.572666 | + | 0.991886i | 0.423625 | + | 0.905838i | \(0.360757\pi\) |
−0.996291 | + | 0.0860488i | \(0.972576\pi\) | |||||||
\(182\) | −28.0878 | −2.08200 | ||||||||
\(183\) | 16.4118 | 1.21319 | ||||||||
\(184\) | −0.945995 | + | 1.63851i | −0.0697397 | + | 0.120793i | ||||
\(185\) | 4.15910 | + | 7.20377i | 0.305783 | + | 0.529632i | ||||
\(186\) | −4.73289 | + | 8.19761i | −0.347033 | + | 0.601078i | ||||
\(187\) | −1.86645 | − | 3.23278i | −0.136488 | − | 0.236404i | ||||
\(188\) | 3.70589 | + | 6.41879i | 0.270280 | + | 0.468138i | ||||
\(189\) | −39.0337 | −2.83929 | ||||||||
\(190\) | −8.62488 | + | 1.26941i | −0.625715 | + | 0.0920925i | ||||
\(191\) | 10.5882 | 0.766137 | 0.383068 | − | 0.923720i | \(-0.374867\pi\) | ||||
0.383068 | + | 0.923720i | \(0.374867\pi\) | |||||||
\(192\) | 1.47300 | + | 2.55131i | 0.106304 | + | 0.184125i | ||||
\(193\) | 2.75844 | + | 4.77775i | 0.198557 | + | 0.343910i | 0.948061 | − | 0.318090i | \(-0.103041\pi\) |
−0.749504 | + | 0.662000i | \(0.769708\pi\) | |||||||
\(194\) | −0.767107 | + | 1.32867i | −0.0550751 | + | 0.0953929i | ||||
\(195\) | 16.7300 | + | 28.9772i | 1.19806 | + | 2.07510i | ||||
\(196\) | −8.73143 | + | 15.1233i | −0.623674 | + | 1.08023i | ||||
\(197\) | −9.53421 | −0.679285 | −0.339642 | − | 0.940555i | \(-0.610306\pi\) | ||||
−0.339642 | + | 0.940555i | \(0.610306\pi\) | |||||||
\(198\) | −5.67889 | −0.403581 | ||||||||
\(199\) | −10.3124 | + | 17.8617i | −0.731030 | + | 1.26618i | 0.225414 | + | 0.974263i | \(0.427627\pi\) |
−0.956444 | + | 0.291917i | \(0.905707\pi\) | |||||||
\(200\) | −0.500000 | + | 0.866025i | −0.0353553 | + | 0.0612372i | ||||
\(201\) | −26.0367 | −1.83648 | ||||||||
\(202\) | 1.67889 | 0.118126 | ||||||||
\(203\) | 2.47300 | − | 4.28336i | 0.173570 | − | 0.300633i | ||||
\(204\) | 5.49854 | + | 9.52375i | 0.384975 | + | 0.666796i | ||||
\(205\) | −9.62488 | + | 16.6708i | −0.672231 | + | 1.16434i | ||||
\(206\) | −3.70589 | − | 6.41879i | −0.258202 | − | 0.447218i | ||||
\(207\) | 5.37220 | + | 9.30492i | 0.373394 | + | 0.646737i | ||||
\(208\) | 5.67889 | 0.393760 | ||||||||
\(209\) | −2.70589 | − | 3.41733i | −0.187170 | − | 0.236382i | ||||
\(210\) | 29.1418 | 2.01097 | ||||||||
\(211\) | 12.8380 | + | 22.2360i | 0.883803 | + | 1.53079i | 0.847079 | + | 0.531467i | \(0.178359\pi\) |
0.0367243 | + | 0.999325i | \(0.488308\pi\) | |||||||
\(212\) | −5.89199 | − | 10.2052i | −0.404664 | − | 0.700898i | ||||
\(213\) | 6.81244 | − | 11.7995i | 0.466781 | − | 0.808488i | ||||
\(214\) | 8.18610 | + | 14.1787i | 0.559590 | + | 0.969239i | ||||
\(215\) | 4.62488 | − | 8.01053i | 0.315414 | − | 0.546314i | ||||
\(216\) | 7.89199 | 0.536982 | ||||||||
\(217\) | 15.8920 | 1.07882 | ||||||||
\(218\) | 8.73143 | − | 15.1233i | 0.591367 | − | 1.02428i | ||||
\(219\) | −5.33944 | + | 9.24819i | −0.360806 | + | 0.624935i | ||||
\(220\) | 2.00000 | 0.134840 | ||||||||
\(221\) | 21.1987 | 1.42598 | ||||||||
\(222\) | 6.12634 | − | 10.6111i | 0.411173 | − | 0.712173i | ||||
\(223\) | 3.68756 | + | 6.38704i | 0.246937 | + | 0.427708i | 0.962674 | − | 0.270662i | \(-0.0872425\pi\) |
−0.715737 | + | 0.698370i | \(0.753909\pi\) | |||||||
\(224\) | 2.47300 | − | 4.28336i | 0.165234 | − | 0.286194i | ||||
\(225\) | 2.83944 | + | 4.91806i | 0.189296 | + | 0.327871i | ||||
\(226\) | −1.76711 | − | 3.06072i | −0.117546 | − | 0.203596i | ||||
\(227\) | −28.3549 | −1.88198 | −0.940989 | − | 0.338437i | \(-0.890102\pi\) | ||||
−0.940989 | + | 0.338437i | \(0.890102\pi\) | |||||||
\(228\) | 7.97154 | + | 10.0674i | 0.527928 | + | 0.666733i | ||||
\(229\) | −4.98266 | −0.329263 | −0.164632 | − | 0.986355i | \(-0.552644\pi\) | ||||
−0.164632 | + | 0.986355i | \(0.552644\pi\) | |||||||
\(230\) | −1.89199 | − | 3.27702i | −0.124754 | − | 0.216081i | ||||
\(231\) | 7.28544 | + | 12.6188i | 0.479347 | + | 0.830253i | ||||
\(232\) | −0.500000 | + | 0.866025i | −0.0328266 | + | 0.0568574i | ||||
\(233\) | −11.2242 | − | 19.4409i | −0.735323 | − | 1.27362i | −0.954581 | − | 0.297950i | \(-0.903697\pi\) |
0.219258 | − | 0.975667i | \(-0.429636\pi\) | |||||||
\(234\) | 16.1249 | − | 27.9291i | 1.05412 | − | 1.82578i | ||||
\(235\) | −14.8236 | −0.966982 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.0723 | + | 17.4458i | −0.654269 | + | 1.13323i | ||||
\(238\) | 9.23143 | − | 15.9893i | 0.598385 | − | 1.03643i | ||||
\(239\) | −23.7840 | −1.53846 | −0.769229 | − | 0.638973i | \(-0.779359\pi\) | ||||
−0.769229 | + | 0.638973i | \(0.779359\pi\) | |||||||
\(240\) | −5.89199 | −0.380326 | ||||||||
\(241\) | 10.5709 | − | 18.3093i | 0.680930 | − | 1.17941i | −0.293767 | − | 0.955877i | \(-0.594909\pi\) |
0.974697 | − | 0.223529i | \(-0.0717576\pi\) | |||||||
\(242\) | 0.500000 | + | 0.866025i | 0.0321412 | + | 0.0556702i | ||||
\(243\) | −2.68610 | + | 4.65246i | −0.172313 | + | 0.298456i | ||||
\(244\) | 2.78544 | + | 4.82452i | 0.178319 | + | 0.308858i | ||||
\(245\) | −17.4629 | − | 30.2466i | −1.11566 | − | 1.93238i | ||||
\(246\) | 28.3549 | 1.80784 | ||||||||
\(247\) | 24.4899 | − | 3.60441i | 1.55825 | − | 0.229343i | ||||
\(248\) | −3.21310 | −0.204032 | ||||||||
\(249\) | 21.3833 | + | 37.0370i | 1.35511 | + | 2.34712i | ||||
\(250\) | −6.00000 | − | 10.3923i | −0.379473 | − | 0.657267i | ||||
\(251\) | −0.259895 | + | 0.450151i | −0.0164044 | + | 0.0284133i | −0.874111 | − | 0.485726i | \(-0.838555\pi\) |
0.857707 | + | 0.514139i | \(0.171889\pi\) | |||||||
\(252\) | −14.0439 | − | 24.3247i | −0.884681 | − | 1.53231i | ||||
\(253\) | 0.945995 | − | 1.63851i | 0.0594742 | − | 0.103012i | ||||
\(254\) | 5.35778 | 0.336177 | ||||||||
\(255\) | −21.9942 | −1.37733 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 5.41178 | − | 9.37348i | 0.337578 | − | 0.584702i | −0.646399 | − | 0.763000i | \(-0.723726\pi\) |
0.983977 | + | 0.178298i | \(0.0570591\pi\) | |||||||
\(258\) | −13.6249 | −0.848248 | ||||||||
\(259\) | −20.5709 | −1.27821 | ||||||||
\(260\) | −5.67889 | + | 9.83612i | −0.352190 | + | 0.610010i | ||||
\(261\) | 2.83944 | + | 4.91806i | 0.175757 | + | 0.304420i | ||||
\(262\) | 5.18610 | − | 8.98259i | 0.320398 | − | 0.554946i | ||||
\(263\) | 6.51687 | + | 11.2876i | 0.401848 | + | 0.696021i | 0.993949 | − | 0.109843i | \(-0.0350348\pi\) |
−0.592101 | + | 0.805864i | \(0.701701\pi\) | |||||||
\(264\) | −1.47300 | − | 2.55131i | −0.0906567 | − | 0.157022i | ||||
\(265\) | 23.5680 | 1.44777 | ||||||||
\(266\) | 7.94600 | − | 20.0413i | 0.487200 | − | 1.22881i | ||||
\(267\) | 1.37220 | 0.0839773 | ||||||||
\(268\) | −4.41899 | − | 7.65392i | −0.269933 | − | 0.467538i | ||||
\(269\) | 2.86645 | + | 4.96483i | 0.174770 | + | 0.302711i | 0.940082 | − | 0.340949i | \(-0.110748\pi\) |
−0.765311 | + | 0.643660i | \(0.777415\pi\) | |||||||
\(270\) | −7.89199 | + | 13.6693i | −0.480291 | + | 0.831889i | ||||
\(271\) | 6.00000 | + | 10.3923i | 0.364474 | + | 0.631288i | 0.988692 | − | 0.149963i | \(-0.0479155\pi\) |
−0.624218 | + | 0.781251i | \(0.714582\pi\) | |||||||
\(272\) | −1.86645 | + | 3.23278i | −0.113170 | + | 0.196016i | ||||
\(273\) | −82.7464 | −5.00804 | ||||||||
\(274\) | −14.1051 | −0.852120 | ||||||||
\(275\) | 0.500000 | − | 0.866025i | 0.0301511 | − | 0.0522233i | ||||
\(276\) | −2.78690 | + | 4.82705i | −0.167752 | + | 0.290554i | ||||
\(277\) | 13.5709 | 0.815395 | 0.407698 | − | 0.913117i | \(-0.366332\pi\) | ||||
0.407698 | + | 0.913117i | \(0.366332\pi\) | |||||||
\(278\) | 13.6760 | 0.820230 | ||||||||
\(279\) | −9.12342 | + | 15.8022i | −0.546205 | + | 0.946055i | ||||
\(280\) | 4.94600 | + | 8.56671i | 0.295580 | + | 0.511959i | ||||
\(281\) | −0.599339 | + | 1.03809i | −0.0357536 | + | 0.0619270i | −0.883348 | − | 0.468717i | \(-0.844716\pi\) |
0.847595 | + | 0.530644i | \(0.178050\pi\) | |||||||
\(282\) | 10.9175 | + | 18.9097i | 0.650130 | + | 1.12606i | ||||
\(283\) | 2.41178 | + | 4.17733i | 0.143365 | + | 0.248316i | 0.928762 | − | 0.370677i | \(-0.120874\pi\) |
−0.785396 | + | 0.618993i | \(0.787541\pi\) | |||||||
\(284\) | 4.62488 | 0.274436 | ||||||||
\(285\) | −25.4089 | + | 3.73967i | −1.50509 | + | 0.221519i | ||||
\(286\) | −5.67889 | −0.335800 | ||||||||
\(287\) | −23.8023 | − | 41.2268i | −1.40501 | − | 2.43354i | ||||
\(288\) | 2.83944 | + | 4.91806i | 0.167316 | + | 0.289800i | ||||
\(289\) | 1.53276 | − | 2.65481i | 0.0901622 | − | 0.156165i | ||||
\(290\) | −1.00000 | − | 1.73205i | −0.0587220 | − | 0.101710i | ||||
\(291\) | −2.25989 | + | 3.91425i | −0.132477 | + | 0.229458i | ||||
\(292\) | −3.62488 | −0.212130 | ||||||||
\(293\) | 1.21602 | 0.0710406 | 0.0355203 | − | 0.999369i | \(-0.488691\pi\) | ||||
0.0355203 | + | 0.999369i | \(0.488691\pi\) | |||||||
\(294\) | −25.7228 | + | 44.5531i | −1.50018 | + | 2.59839i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.15910 | 0.241743 | ||||||||
\(297\) | −7.89199 | −0.457940 | ||||||||
\(298\) | 9.49854 | − | 16.4520i | 0.550236 | − | 0.953036i | ||||
\(299\) | 5.37220 | + | 9.30492i | 0.310682 | + | 0.538118i | ||||
\(300\) | −1.47300 | + | 2.55131i | −0.0850436 | + | 0.147300i | ||||
\(301\) | 11.4373 | + | 19.8100i | 0.659236 | + | 1.14183i | ||||
\(302\) | −11.8308 | − | 20.4915i | −0.680784 | − | 1.17915i | ||||
\(303\) | 4.94600 | 0.284140 | ||||||||
\(304\) | −1.60655 | + | 4.05204i | −0.0921420 | + | 0.232400i | ||||
\(305\) | −11.1418 | −0.637975 | ||||||||
\(306\) | 10.5993 | + | 18.3586i | 0.605924 | + | 1.04949i | ||||
\(307\) | −16.0241 | − | 27.7545i | −0.914543 | − | 1.58403i | −0.807569 | − | 0.589773i | \(-0.799217\pi\) |
−0.106974 | − | 0.994262i | \(-0.534116\pi\) | |||||||
\(308\) | −2.47300 | + | 4.28336i | −0.140912 | + | 0.244067i | ||||
\(309\) | −10.9175 | − | 18.9097i | −0.621077 | − | 1.07574i | ||||
\(310\) | 3.21310 | − | 5.56526i | 0.182492 | − | 0.316085i | ||||
\(311\) | −18.3722 | −1.04179 | −0.520896 | − | 0.853620i | \(-0.674402\pi\) | ||||
−0.520896 | + | 0.853620i | \(0.674402\pi\) | |||||||
\(312\) | 16.7300 | 0.947148 | ||||||||
\(313\) | −0.572336 | + | 0.991316i | −0.0323504 | + | 0.0560325i | −0.881747 | − | 0.471722i | \(-0.843633\pi\) |
0.849397 | + | 0.527755i | \(0.176966\pi\) | |||||||
\(314\) | −5.89199 | + | 10.2052i | −0.332504 | + | 0.575914i | ||||
\(315\) | 56.1755 | 3.16513 | ||||||||
\(316\) | −6.83799 | −0.384667 | ||||||||
\(317\) | −12.2242 | + | 21.1730i | −0.686581 | + | 1.18919i | 0.286357 | + | 0.958123i | \(0.407556\pi\) |
−0.972937 | + | 0.231070i | \(0.925778\pi\) | |||||||
\(318\) | −17.3578 | − | 30.0645i | −0.973376 | − | 1.68594i | ||||
\(319\) | 0.500000 | − | 0.866025i | 0.0279946 | − | 0.0484881i | ||||
\(320\) | −1.00000 | − | 1.73205i | −0.0559017 | − | 0.0968246i | ||||
\(321\) | 24.1162 | + | 41.7705i | 1.34604 | + | 2.33140i | ||||
\(322\) | 9.35778 | 0.521488 | ||||||||
\(323\) | −5.99708 | + | 15.1258i | −0.333687 | + | 0.841623i | ||||
\(324\) | 6.21310 | 0.345172 | ||||||||
\(325\) | 2.83944 | + | 4.91806i | 0.157504 | + | 0.272805i | ||||
\(326\) | −5.41178 | − | 9.37348i | −0.299731 | − | 0.519149i | ||||
\(327\) | 25.7228 | − | 44.5531i | 1.42247 | − | 2.46379i | ||||
\(328\) | 4.81244 | + | 8.33539i | 0.265723 | + | 0.460245i | ||||
\(329\) | 18.3293 | − | 31.7473i | 1.01053 | − | 1.75029i | ||||
\(330\) | 5.89199 | 0.324343 | ||||||||
\(331\) | −6.30377 | −0.346487 | −0.173243 | − | 0.984879i | \(-0.555425\pi\) | ||||
−0.173243 | + | 0.984879i | \(0.555425\pi\) | |||||||
\(332\) | −7.25844 | + | 12.5720i | −0.398358 | + | 0.689977i | ||||
\(333\) | 11.8095 | − | 20.4547i | 0.647158 | − | 1.12091i | ||||
\(334\) | −4.01443 | −0.219660 | ||||||||
\(335\) | 17.6760 | 0.965741 | ||||||||
\(336\) | 7.28544 | − | 12.6188i | 0.397453 | − | 0.688409i | ||||
\(337\) | 5.14467 | + | 8.91083i | 0.280248 | + | 0.485404i | 0.971446 | − | 0.237262i | \(-0.0762499\pi\) |
−0.691198 | + | 0.722666i | \(0.742917\pi\) | |||||||
\(338\) | 9.62488 | − | 16.6708i | 0.523525 | − | 0.906771i | ||||
\(339\) | −5.20589 | − | 9.01687i | −0.282745 | − | 0.489729i | ||||
\(340\) | −3.73289 | − | 6.46556i | −0.202445 | − | 0.350644i | ||||
\(341\) | 3.21310 | 0.173999 | ||||||||
\(342\) | 15.3664 | + | 19.4066i | 0.830922 | + | 1.04939i | ||||
\(343\) | 51.7493 | 2.79420 | ||||||||
\(344\) | −2.31244 | − | 4.00527i | −0.124678 | − | 0.215949i | ||||
\(345\) | −5.57379 | − | 9.65410i | −0.300083 | − | 0.519759i | ||||
\(346\) | −3.60655 | + | 6.24673i | −0.193889 | + | 0.335826i | ||||
\(347\) | 9.59788 | + | 16.6240i | 0.515241 | + | 0.892424i | 0.999844 | + | 0.0176894i | \(0.00563100\pi\) |
−0.484602 | + | 0.874735i | \(0.661036\pi\) | |||||||
\(348\) | −1.47300 | + | 2.55131i | −0.0789610 | + | 0.136764i | ||||
\(349\) | 32.9653 | 1.76459 | 0.882296 | − | 0.470694i | \(-0.155996\pi\) | ||||
0.882296 | + | 0.470694i | \(0.155996\pi\) | |||||||
\(350\) | 4.94600 | 0.264375 | ||||||||
\(351\) | 22.4089 | − | 38.8133i | 1.19610 | − | 2.07170i | ||||
\(352\) | 0.500000 | − | 0.866025i | 0.0266501 | − | 0.0461593i | ||||
\(353\) | 33.2835 | 1.77150 | 0.885751 | − | 0.464160i | \(-0.153644\pi\) | ||||
0.885751 | + | 0.464160i | \(0.153644\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.62488 | + | 8.01053i | −0.245463 | + | 0.425155i | ||||
\(356\) | 0.232893 | + | 0.403382i | 0.0123433 | + | 0.0213792i | ||||
\(357\) | 27.1958 | − | 47.1044i | 1.43935 | − | 2.49303i | ||||
\(358\) | 2.05400 | + | 3.55764i | 0.108558 | + | 0.188027i | ||||
\(359\) | −2.84090 | − | 4.92059i | −0.149937 | − | 0.259699i | 0.781267 | − | 0.624197i | \(-0.214574\pi\) |
−0.931204 | + | 0.364498i | \(0.881240\pi\) | |||||||
\(360\) | −11.3578 | −0.598607 | ||||||||
\(361\) | −4.35632 | + | 18.4939i | −0.229280 | + | 0.973361i | ||||
\(362\) | −15.4089 | −0.809872 | ||||||||
\(363\) | 1.47300 | + | 2.55131i | 0.0773123 | + | 0.133909i | ||||
\(364\) | −14.0439 | − | 24.3247i | −0.736099 | − | 1.27496i | ||||
\(365\) | 3.62488 | − | 6.27848i | 0.189735 | − | 0.328631i | ||||
\(366\) | 8.20589 | + | 14.2130i | 0.428929 | + | 0.742926i | ||||
\(367\) | −8.84666 | + | 15.3229i | −0.461792 | + | 0.799847i | −0.999050 | − | 0.0435709i | \(-0.986127\pi\) |
0.537259 | + | 0.843418i | \(0.319460\pi\) | |||||||
\(368\) | −1.89199 | −0.0986268 | ||||||||
\(369\) | 54.6586 | 2.84541 | ||||||||
\(370\) | −4.15910 | + | 7.20377i | −0.216221 | + | 0.374506i | ||||
\(371\) | −29.1418 | + | 50.4750i | −1.51296 | + | 2.62053i | ||||
\(372\) | −9.46579 | −0.490778 | ||||||||
\(373\) | −37.1051 | −1.92123 | −0.960614 | − | 0.277885i | \(-0.910367\pi\) | ||||
−0.960614 | + | 0.277885i | \(0.910367\pi\) | |||||||
\(374\) | 1.86645 | − | 3.23278i | 0.0965116 | − | 0.167163i | ||||
\(375\) | −17.6760 | − | 30.6157i | −0.912783 | − | 1.58099i | ||||
\(376\) | −3.70589 | + | 6.41879i | −0.191117 | + | 0.331024i | ||||
\(377\) | 2.83944 | + | 4.91806i | 0.146239 | + | 0.253293i | ||||
\(378\) | −19.5169 | − | 33.8042i | −1.00384 | − | 1.73870i | ||||
\(379\) | 13.5535 | 0.696198 | 0.348099 | − | 0.937458i | \(-0.386827\pi\) | ||||
0.348099 | + | 0.937458i | \(0.386827\pi\) | |||||||
\(380\) | −5.41178 | − | 6.83466i | −0.277618 | − | 0.350611i | ||||
\(381\) | 15.7840 | 0.808638 | ||||||||
\(382\) | 5.29411 | + | 9.16967i | 0.270870 | + | 0.469161i | ||||
\(383\) | −4.83799 | − | 8.37964i | −0.247210 | − | 0.428179i | 0.715541 | − | 0.698571i | \(-0.246180\pi\) |
−0.962751 | + | 0.270391i | \(0.912847\pi\) | |||||||
\(384\) | −1.47300 | + | 2.55131i | −0.0751686 | + | 0.130196i | ||||
\(385\) | −4.94600 | − | 8.56671i | −0.252071 | − | 0.436600i | ||||
\(386\) | −2.75844 | + | 4.77775i | −0.140401 | + | 0.243181i | ||||
\(387\) | −26.2642 | −1.33508 | ||||||||
\(388\) | −1.53421 | −0.0778880 | ||||||||
\(389\) | −6.40066 | + | 11.0863i | −0.324526 | + | 0.562096i | −0.981416 | − | 0.191890i | \(-0.938538\pi\) |
0.656890 | + | 0.753986i | \(0.271872\pi\) | |||||||
\(390\) | −16.7300 | + | 28.9772i | −0.847155 | + | 1.46732i | ||||
\(391\) | −7.06260 | −0.357171 | ||||||||
\(392\) | −17.4629 | −0.882008 | ||||||||
\(393\) | 15.2782 | − | 26.4627i | 0.770685 | − | 1.33486i | ||||
\(394\) | −4.76711 | − | 8.25687i | −0.240163 | − | 0.415975i | ||||
\(395\) | 6.83799 | − | 11.8437i | 0.344056 | − | 0.595923i | ||||
\(396\) | −2.83944 | − | 4.91806i | −0.142687 | − | 0.247142i | ||||
\(397\) | 9.07955 | + | 15.7262i | 0.455689 | + | 0.789277i | 0.998728 | − | 0.0504307i | \(-0.0160594\pi\) |
−0.543038 | + | 0.839708i | \(0.682726\pi\) | |||||||
\(398\) | −20.6249 | −1.03383 | ||||||||
\(399\) | 23.4089 | − | 59.0417i | 1.17191 | − | 2.95578i | ||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 3.91032 | + | 6.77288i | 0.195272 | + | 0.338221i | 0.946990 | − | 0.321264i | \(-0.104108\pi\) |
−0.751718 | + | 0.659485i | \(0.770774\pi\) | |||||||
\(402\) | −13.0183 | − | 22.5484i | −0.649295 | − | 1.12461i | ||||
\(403\) | −9.12342 | + | 15.8022i | −0.454470 | + | 0.787165i | ||||
\(404\) | 0.839444 | + | 1.45396i | 0.0417639 | + | 0.0723372i | ||||
\(405\) | −6.21310 | + | 10.7614i | −0.308732 | + | 0.534739i | ||||
\(406\) | 4.94600 | 0.245466 | ||||||||
\(407\) | −4.15910 | −0.206159 | ||||||||
\(408\) | −5.49854 | + | 9.52375i | −0.272218 | + | 0.471496i | ||||
\(409\) | 10.5058 | − | 18.1965i | 0.519476 | − | 0.899759i | −0.480268 | − | 0.877122i | \(-0.659460\pi\) |
0.999744 | − | 0.0226370i | \(-0.00720621\pi\) | |||||||
\(410\) | −19.2498 | −0.950678 | ||||||||
\(411\) | −41.5535 | −2.04968 | ||||||||
\(412\) | 3.70589 | − | 6.41879i | 0.182576 | − | 0.316231i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −5.37220 | + | 9.30492i | −0.264029 | + | 0.457312i | ||||
\(415\) | −14.5169 | − | 25.1440i | −0.712605 | − | 1.23427i | ||||
\(416\) | 2.83944 | + | 4.91806i | 0.139215 | + | 0.241128i | ||||
\(417\) | 40.2893 | 1.97298 | ||||||||
\(418\) | 1.60655 | − | 4.05204i | 0.0785790 | − | 0.198192i | ||||
\(419\) | −11.0540 | −0.540023 | −0.270012 | − | 0.962857i | \(-0.587028\pi\) | ||||
−0.270012 | + | 0.962857i | \(0.587028\pi\) | |||||||
\(420\) | 14.5709 | + | 25.2375i | 0.710986 | + | 1.23146i | ||||
\(421\) | −2.24156 | − | 3.88250i | −0.109247 | − | 0.189222i | 0.806218 | − | 0.591618i | \(-0.201511\pi\) |
−0.915465 | + | 0.402397i | \(0.868177\pi\) | |||||||
\(422\) | −12.8380 | + | 22.2360i | −0.624943 | + | 1.08243i | ||||
\(423\) | 21.0453 | + | 36.4516i | 1.02326 | + | 1.77234i | ||||
\(424\) | 5.89199 | − | 10.2052i | 0.286140 | − | 0.495610i | ||||
\(425\) | −3.73289 | −0.181072 | ||||||||
\(426\) | 13.6249 | 0.660128 | ||||||||
\(427\) | 13.7768 | − | 23.8621i | 0.666705 | − | 1.15477i | ||||
\(428\) | −8.18610 | + | 14.1787i | −0.395690 | + | 0.685355i | ||||
\(429\) | −16.7300 | −0.807731 | ||||||||
\(430\) | 9.24977 | 0.446063 | ||||||||
\(431\) | −1.09788 | + | 1.90158i | −0.0528830 | + | 0.0915961i | −0.891255 | − | 0.453502i | \(-0.850174\pi\) |
0.838372 | + | 0.545098i | \(0.183508\pi\) | |||||||
\(432\) | 3.94600 | + | 6.83466i | 0.189852 | + | 0.328833i | ||||
\(433\) | 15.9301 | − | 27.5918i | 0.765552 | − | 1.32598i | −0.174402 | − | 0.984675i | \(-0.555799\pi\) |
0.939954 | − | 0.341301i | \(-0.110868\pi\) | |||||||
\(434\) | 7.94600 | + | 13.7629i | 0.381420 | + | 0.660639i | ||||
\(435\) | −2.94600 | − | 5.10261i | −0.141250 | − | 0.244652i | ||||
\(436\) | 17.4629 | 0.836320 | ||||||||
\(437\) | −8.15910 | + | 1.20085i | −0.390303 | + | 0.0574446i | ||||
\(438\) | −10.6789 | −0.510257 | ||||||||
\(439\) | 5.32111 | + | 9.21644i | 0.253963 | + | 0.439877i | 0.964613 | − | 0.263669i | \(-0.0849326\pi\) |
−0.710650 | + | 0.703545i | \(0.751599\pi\) | |||||||
\(440\) | 1.00000 | + | 1.73205i | 0.0476731 | + | 0.0825723i | ||||
\(441\) | −49.5848 | + | 85.8835i | −2.36118 | + | 4.08969i | ||||
\(442\) | 10.5993 | + | 18.3586i | 0.504159 | + | 0.873229i | ||||
\(443\) | −15.7228 | + | 27.2326i | −0.747011 | + | 1.29386i | 0.202238 | + | 0.979336i | \(0.435178\pi\) |
−0.949249 | + | 0.314525i | \(0.898155\pi\) | |||||||
\(444\) | 12.2527 | 0.581487 | ||||||||
\(445\) | −0.931570 | −0.0441607 | ||||||||
\(446\) | −3.68756 | + | 6.38704i | −0.174611 | + | 0.302435i | ||||
\(447\) | 27.9827 | − | 48.4674i | 1.32353 | − | 2.29243i | ||||
\(448\) | 4.94600 | 0.233676 | ||||||||
\(449\) | 13.8553 | 0.653873 | 0.326937 | − | 0.945046i | \(-0.393984\pi\) | ||||
0.326937 | + | 0.945046i | \(0.393984\pi\) | |||||||
\(450\) | −2.83944 | + | 4.91806i | −0.133853 | + | 0.231840i | ||||
\(451\) | −4.81244 | − | 8.33539i | −0.226609 | − | 0.392498i | ||||
\(452\) | 1.76711 | − | 3.06072i | 0.0831177 | − | 0.143964i | ||||
\(453\) | −34.8534 | − | 60.3679i | −1.63756 | − | 2.83633i | ||||
\(454\) | −14.1774 | − | 24.5560i | −0.665380 | − | 1.15247i | ||||
\(455\) | 56.1755 | 2.63355 | ||||||||
\(456\) | −4.73289 | + | 11.9373i | −0.221638 | + | 0.559014i | ||||
\(457\) | −15.7329 | −0.735954 | −0.367977 | − | 0.929835i | \(-0.619949\pi\) | ||||
−0.367977 | + | 0.929835i | \(0.619949\pi\) | |||||||
\(458\) | −2.49133 | − | 4.31511i | −0.116412 | − | 0.201632i | ||||
\(459\) | 14.7300 | + | 25.5131i | 0.687536 | + | 1.19085i | ||||
\(460\) | 1.89199 | − | 3.27702i | 0.0882145 | − | 0.152792i | ||||
\(461\) | 10.3563 | + | 17.9377i | 0.482342 | + | 0.835440i | 0.999795 | − | 0.0202713i | \(-0.00645300\pi\) |
−0.517453 | + | 0.855712i | \(0.673120\pi\) | |||||||
\(462\) | −7.28544 | + | 12.6188i | −0.338949 | + | 0.587077i | ||||
\(463\) | −14.3722 | −0.667933 | −0.333966 | − | 0.942585i | \(-0.608387\pi\) | ||||
−0.333966 | + | 0.942585i | \(0.608387\pi\) | |||||||
\(464\) | −1.00000 | −0.0464238 | ||||||||
\(465\) | 9.46579 | − | 16.3952i | 0.438965 | − | 0.760310i | ||||
\(466\) | 11.2242 | − | 19.4409i | 0.519952 | − | 0.900583i | ||||
\(467\) | −10.3038 | −0.476802 | −0.238401 | − | 0.971167i | \(-0.576623\pi\) | ||||
−0.238401 | + | 0.971167i | \(0.576623\pi\) | |||||||
\(468\) | 32.2498 | 1.49075 | ||||||||
\(469\) | −21.8563 | + | 37.8563i | −1.00923 | + | 1.74804i | ||||
\(470\) | −7.41178 | − | 12.8376i | −0.341880 | − | 0.592153i | ||||
\(471\) | −17.3578 | + | 30.0645i | −0.799804 | + | 1.38530i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.31244 | + | 4.00527i | 0.106326 | + | 0.184162i | ||||
\(474\) | −20.1447 | −0.925275 | ||||||||
\(475\) | −4.31244 | + | 0.634704i | −0.197868 | + | 0.0291222i | ||||
\(476\) | 18.4629 | 0.846244 | ||||||||
\(477\) | −33.4600 | − | 57.9543i | −1.53203 | − | 2.65355i | ||||
\(478\) | −11.8920 | − | 20.5975i | −0.543927 | − | 0.942109i | ||||
\(479\) | −3.79411 | + | 6.57159i | −0.173357 | + | 0.300264i | −0.939592 | − | 0.342298i | \(-0.888795\pi\) |
0.766234 | + | 0.642561i | \(0.222128\pi\) | |||||||
\(480\) | −2.94600 | − | 5.10261i | −0.134466 | − | 0.232901i | ||||
\(481\) | 11.8095 | − | 20.4547i | 0.538468 | − | 0.932654i | ||||
\(482\) | 21.1418 | 0.962981 | ||||||||
\(483\) | 27.5680 | 1.25439 | ||||||||
\(484\) | −0.500000 | + | 0.866025i | −0.0227273 | + | 0.0393648i | ||||
\(485\) | 1.53421 | − | 2.65734i | 0.0696651 | − | 0.120664i | ||||
\(486\) | −5.37220 | −0.243688 | ||||||||
\(487\) | −0.414697 | −0.0187917 | −0.00939585 | − | 0.999956i | \(-0.502991\pi\) | ||||
−0.00939585 | + | 0.999956i | \(0.502991\pi\) | |||||||
\(488\) | −2.78544 | + | 4.82452i | −0.126091 | + | 0.218396i | ||||
\(489\) | −15.9431 | − | 27.6142i | −0.720971 | − | 1.24876i | ||||
\(490\) | 17.4629 | − | 30.2466i | 0.788892 | − | 1.36640i | ||||
\(491\) | 0.411780 | + | 0.713224i | 0.0185834 | + | 0.0321874i | 0.875168 | − | 0.483820i | \(-0.160751\pi\) |
−0.856584 | + | 0.516007i | \(0.827418\pi\) | |||||||
\(492\) | 14.1774 | + | 24.5560i | 0.639168 | + | 1.10707i | ||||
\(493\) | −3.73289 | −0.168121 | ||||||||
\(494\) | 15.3664 | + | 19.4066i | 0.691369 | + | 0.873146i | ||||
\(495\) | 11.3578 | 0.510494 | ||||||||
\(496\) | −1.60655 | − | 2.78263i | −0.0721363 | − | 0.124944i | ||||
\(497\) | −11.4373 | − | 19.8100i | −0.513034 | − | 0.888601i | ||||
\(498\) | −21.3833 | + | 37.0370i | −0.958209 | + | 1.65967i | ||||
\(499\) | −2.67889 | − | 4.63997i | −0.119923 | − | 0.207714i | 0.799814 | − | 0.600248i | \(-0.204932\pi\) |
−0.919737 | + | 0.392535i | \(0.871598\pi\) | |||||||
\(500\) | 6.00000 | − | 10.3923i | 0.268328 | − | 0.464758i | ||||
\(501\) | −11.8265 | −0.528368 | ||||||||
\(502\) | −0.519790 | −0.0231994 | ||||||||
\(503\) | −2.78690 | + | 4.82705i | −0.124262 | + | 0.215227i | −0.921444 | − | 0.388511i | \(-0.872990\pi\) |
0.797182 | + | 0.603738i | \(0.206323\pi\) | |||||||
\(504\) | 14.0439 | − | 24.3247i | 0.625564 | − | 1.08351i | ||||
\(505\) | −3.35778 | −0.149419 | ||||||||
\(506\) | 1.89199 | 0.0841092 | ||||||||
\(507\) | 28.3549 | − | 49.1121i | 1.25928 | − | 2.18114i | ||||
\(508\) | 2.67889 | + | 4.63997i | 0.118856 | + | 0.205865i | ||||
\(509\) | 9.21310 | − | 15.9576i | 0.408364 | − | 0.707306i | −0.586343 | − | 0.810063i | \(-0.699433\pi\) |
0.994707 | + | 0.102756i | \(0.0327662\pi\) | |||||||
\(510\) | −10.9971 | − | 19.0475i | −0.486959 | − | 0.843438i | ||||
\(511\) | 8.96433 | + | 15.5267i | 0.396558 | + | 0.686859i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 21.3549 | + | 26.9696i | 0.942840 | + | 1.19073i | ||||
\(514\) | 10.8236 | 0.477407 | ||||||||
\(515\) | 7.41178 | + | 12.8376i | 0.326602 | + | 0.565691i | ||||
\(516\) | −6.81244 | − | 11.7995i | −0.299901 | − | 0.519444i | ||||
\(517\) | 3.70589 | − | 6.41879i | 0.162985 | − | 0.282298i | ||||
\(518\) | −10.2854 | − | 17.8149i | −0.451916 | − | 0.782742i | ||||
\(519\) | −10.6249 | + | 18.4028i | −0.466381 | + | 0.807795i | ||||
\(520\) | −11.3578 | −0.498071 | ||||||||
\(521\) | −9.24685 | −0.405112 | −0.202556 | − | 0.979271i | \(-0.564925\pi\) | ||||
−0.202556 | + | 0.979271i | \(0.564925\pi\) | |||||||
\(522\) | −2.83944 | + | 4.91806i | −0.124279 | + | 0.215258i | ||||
\(523\) | 9.70589 | − | 16.8111i | 0.424409 | − | 0.735098i | −0.571956 | − | 0.820284i | \(-0.693815\pi\) |
0.996365 | + | 0.0851864i | \(0.0271486\pi\) | |||||||
\(524\) | 10.3722 | 0.453112 | ||||||||
\(525\) | 14.5709 | 0.635925 | ||||||||
\(526\) | −6.51687 | + | 11.2876i | −0.284149 | + | 0.492161i | ||||
\(527\) | −5.99708 | − | 10.3873i | −0.261237 | − | 0.452476i | ||||
\(528\) | 1.47300 | − | 2.55131i | 0.0641040 | − | 0.111031i | ||||
\(529\) | 9.71019 | + | 16.8185i | 0.422182 | + | 0.731241i | ||||
\(530\) | 11.7840 | + | 20.4105i | 0.511863 | + | 0.886573i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 21.3293 | − | 3.13924i | 0.924743 | − | 0.136103i | ||||
\(533\) | 54.6586 | 2.36753 | ||||||||
\(534\) | 0.686100 | + | 1.18836i | 0.0296905 | + | 0.0514254i | ||||
\(535\) | −16.3722 | − | 28.3575i | −0.707832 | − | 1.22600i | ||||
\(536\) | 4.41899 | − | 7.65392i | 0.190871 | − | 0.330599i | ||||
\(537\) | 6.05109 | + | 10.4808i | 0.261124 | + | 0.452280i | ||||
\(538\) | −2.86645 | + | 4.96483i | −0.123581 | + | 0.214049i | ||||
\(539\) | 17.4629 | 0.752179 | ||||||||
\(540\) | −15.7840 | −0.679234 | ||||||||
\(541\) | −9.80231 | + | 16.9781i | −0.421434 | + | 0.729946i | −0.996080 | − | 0.0884566i | \(-0.971807\pi\) |
0.574646 | + | 0.818402i | \(0.305140\pi\) | |||||||
\(542\) | −6.00000 | + | 10.3923i | −0.257722 | + | 0.446388i | ||||
\(543\) | −45.3944 | −1.94806 | ||||||||
\(544\) | −3.73289 | −0.160046 | ||||||||
\(545\) | −17.4629 | + | 30.2466i | −0.748027 | + | 1.29562i | ||||
\(546\) | −41.3732 | − | 71.6605i | −1.77061 | − | 3.06678i | ||||
\(547\) | 2.31244 | − | 4.00527i | 0.0988729 | − | 0.171253i | −0.812346 | − | 0.583176i | \(-0.801810\pi\) |
0.911218 | + | 0.411924i | \(0.135143\pi\) | |||||||
\(548\) | −7.05255 | − | 12.2154i | −0.301270 | − | 0.521815i | ||||
\(549\) | 15.8182 | + | 27.3979i | 0.675104 | + | 1.16931i | ||||
\(550\) | 1.00000 | 0.0426401 | ||||||||
\(551\) | −4.31244 | + | 0.634704i | −0.183716 | + | 0.0270393i | ||||
\(552\) | −5.57379 | −0.237236 | ||||||||
\(553\) | 16.9103 | + | 29.2895i | 0.719100 | + | 1.24552i | ||||
\(554\) | 6.78544 | + | 11.7527i | 0.288286 | + | 0.499325i | ||||
\(555\) | −12.2527 | + | 21.2223i | −0.520097 | + | 0.900835i | ||||
\(556\) | 6.83799 | + | 11.8437i | 0.289995 | + | 0.502286i | ||||
\(557\) | −11.1606 | + | 19.3307i | −0.472888 | + | 0.819066i | −0.999519 | − | 0.0310283i | \(-0.990122\pi\) |
0.526631 | + | 0.850094i | \(0.323455\pi\) | |||||||
\(558\) | −18.2468 | −0.772451 | ||||||||
\(559\) | −26.2642 | −1.11086 | ||||||||
\(560\) | −4.94600 | + | 8.56671i | −0.209006 | + | 0.362010i | ||||
\(561\) | 5.49854 | − | 9.52375i | 0.232149 | − | 0.402093i | ||||
\(562\) | −1.19868 | −0.0505632 | ||||||||
\(563\) | 29.6760 | 1.25069 | 0.625347 | − | 0.780347i | \(-0.284958\pi\) | ||||
0.625347 | + | 0.780347i | \(0.284958\pi\) | |||||||
\(564\) | −10.9175 | + | 18.9097i | −0.459711 | + | 0.796243i | ||||
\(565\) | 3.53421 | + | 6.12144i | 0.148686 | + | 0.257531i | ||||
\(566\) | −2.41178 | + | 4.17733i | −0.101375 | + | 0.175586i | ||||
\(567\) | −15.3650 | − | 26.6129i | −0.645269 | − | 1.11764i | ||||
\(568\) | 2.31244 | + | 4.00527i | 0.0970279 | + | 0.168057i | ||||
\(569\) | −34.0733 | −1.42843 | −0.714214 | − | 0.699927i | \(-0.753216\pi\) | ||||
−0.714214 | + | 0.699927i | \(0.753216\pi\) | |||||||
\(570\) | −15.9431 | − | 20.1349i | −0.667782 | − | 0.843358i | ||||
\(571\) | 16.3722 | 0.685155 | 0.342578 | − | 0.939490i | \(-0.388700\pi\) | ||||
0.342578 | + | 0.939490i | \(0.388700\pi\) | |||||||
\(572\) | −2.83944 | − | 4.91806i | −0.118723 | − | 0.205634i | ||||
\(573\) | 15.5964 | + | 27.0138i | 0.651550 | + | 1.12852i | ||||
\(574\) | 23.8023 | − | 41.2268i | 0.993489 | − | 1.72077i | ||||
\(575\) | −0.945995 | − | 1.63851i | −0.0394507 | − | 0.0683307i | ||||
\(576\) | −2.83944 | + | 4.91806i | −0.118310 | + | 0.204919i | ||||
\(577\) | 23.2864 | 0.969427 | 0.484713 | − | 0.874673i | \(-0.338924\pi\) | ||||
0.484713 | + | 0.874673i | \(0.338924\pi\) | |||||||
\(578\) | 3.06551 | 0.127509 | ||||||||
\(579\) | −8.12634 | + | 14.0752i | −0.337719 | + | 0.584947i | ||||
\(580\) | 1.00000 | − | 1.73205i | 0.0415227 | − | 0.0719195i | ||||
\(581\) | 71.8004 | 2.97878 | ||||||||
\(582\) | −4.51979 | −0.187351 | ||||||||
\(583\) | −5.89199 | + | 10.2052i | −0.244021 | + | 0.422657i | ||||
\(584\) | −1.81244 | − | 3.13924i | −0.0749994 | − | 0.129903i | ||||
\(585\) | −32.2498 | + | 55.8582i | −1.33336 | + | 2.30945i | ||||
\(586\) | 0.608010 | + | 1.05310i | 0.0251166 | + | 0.0435033i | ||||
\(587\) | −9.52700 | − | 16.5013i | −0.393221 | − | 0.681080i | 0.599651 | − | 0.800262i | \(-0.295306\pi\) |
−0.992872 | + | 0.119182i | \(0.961973\pi\) | |||||||
\(588\) | −51.4455 | −2.12158 | ||||||||
\(589\) | −8.69430 | − | 10.9802i | −0.358243 | − | 0.452433i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.0439 | − | 24.3247i | −0.577688 | − | 1.00058i | ||||
\(592\) | 2.07955 | + | 3.60188i | 0.0854689 | + | 0.148037i | ||||
\(593\) | −0.786897 | + | 1.36295i | −0.0323140 | + | 0.0559695i | −0.881730 | − | 0.471754i | \(-0.843621\pi\) |
0.849416 | + | 0.527724i | \(0.176954\pi\) | |||||||
\(594\) | −3.94600 | − | 6.83466i | −0.161906 | − | 0.280430i | ||||
\(595\) | −18.4629 | + | 31.9786i | −0.756904 | + | 1.31100i | ||||
\(596\) | 18.9971 | 0.778151 | ||||||||
\(597\) | −60.7608 | −2.48677 | ||||||||
\(598\) | −5.37220 | + | 9.30492i | −0.219686 | + | 0.380507i | ||||
\(599\) | 11.3664 | − | 19.6873i | 0.464420 | − | 0.804400i | −0.534755 | − | 0.845007i | \(-0.679596\pi\) |
0.999175 | + | 0.0406076i | \(0.0129293\pi\) | |||||||
\(600\) | −2.94600 | −0.120270 | ||||||||
\(601\) | 10.8524 | 0.442679 | 0.221340 | − | 0.975197i | \(-0.428957\pi\) | ||||
0.221340 | + | 0.975197i | \(0.428957\pi\) | |||||||
\(602\) | −11.4373 | + | 19.8100i | −0.466151 | + | 0.807396i | ||||
\(603\) | −25.0950 | − | 43.4658i | −1.02195 | − | 1.77006i | ||||
\(604\) | 11.8308 | − | 20.4915i | 0.481387 | − | 0.833787i | ||||
\(605\) | −1.00000 | − | 1.73205i | −0.0406558 | − | 0.0704179i | ||||
\(606\) | 2.47300 | + | 4.28336i | 0.100459 | + | 0.174000i | ||||
\(607\) | −12.3038 | −0.499395 | −0.249697 | − | 0.968324i | \(-0.580331\pi\) | ||||
−0.249697 | + | 0.968324i | \(0.580331\pi\) | |||||||
\(608\) | −4.31244 | + | 0.634704i | −0.174893 | + | 0.0257406i | ||||
\(609\) | 14.5709 | 0.590442 | ||||||||
\(610\) | −5.57088 | − | 9.64904i | −0.225558 | − | 0.390678i | ||||
\(611\) | 21.0453 | + | 36.4516i | 0.851403 | + | 1.47467i | ||||
\(612\) | −10.5993 | + | 18.3586i | −0.428453 | + | 0.742102i | ||||
\(613\) | −22.5154 | − | 38.9978i | −0.909389 | − | 1.57511i | −0.814915 | − | 0.579581i | \(-0.803216\pi\) |
−0.0944742 | − | 0.995527i | \(-0.530117\pi\) | |||||||
\(614\) | 16.0241 | − | 27.7545i | 0.646679 | − | 1.12008i | ||||
\(615\) | −56.7097 | −2.28676 | ||||||||
\(616\) | −4.94600 | −0.199280 | ||||||||
\(617\) | −10.7314 | + | 18.5874i | −0.432031 | + | 0.748300i | −0.997048 | − | 0.0767793i | \(-0.975536\pi\) |
0.565017 | + | 0.825079i | \(0.308870\pi\) | |||||||
\(618\) | 10.9175 | − | 18.9097i | 0.439168 | − | 0.760661i | ||||
\(619\) | 6.96625 | 0.279997 | 0.139999 | − | 0.990152i | \(-0.455290\pi\) | ||||
0.139999 | + | 0.990152i | \(0.455290\pi\) | |||||||
\(620\) | 6.42621 | 0.258083 | ||||||||
\(621\) | −7.46579 | + | 12.9311i | −0.299592 | + | 0.518908i | ||||
\(622\) | −9.18610 | − | 15.9108i | −0.368329 | − | 0.637965i | ||||
\(623\) | 1.15189 | − | 1.99512i | 0.0461493 | − | 0.0799330i | ||||
\(624\) | 8.36499 | + | 14.4886i | 0.334868 | + | 0.580008i | ||||
\(625\) | 9.50000 | + | 16.4545i | 0.380000 | + | 0.658179i | ||||
\(626\) | −1.14467 | −0.0457503 | ||||||||
\(627\) | 4.73289 | − | 11.9373i | 0.189014 | − | 0.476729i | ||||
\(628\) | −11.7840 | −0.470232 | ||||||||
\(629\) | 7.76273 | + | 13.4454i | 0.309520 | + | 0.536105i | ||||
\(630\) | 28.0878 | + | 48.6494i | 1.11904 | + | 1.93824i | ||||
\(631\) | 20.2044 | − | 34.9951i | 0.804326 | − | 1.39313i | −0.112420 | − | 0.993661i | \(-0.535860\pi\) |
0.916745 | − | 0.399472i | \(-0.130807\pi\) | |||||||
\(632\) | −3.41899 | − | 5.92187i | −0.136000 | − | 0.235559i | ||||
\(633\) | −37.8206 | + | 65.5073i | −1.50324 | + | 2.60368i | ||||
\(634\) | −24.4484 | −0.970972 | ||||||||
\(635\) | −10.7156 | −0.425234 | ||||||||
\(636\) | 17.3578 | − | 30.0645i | 0.688281 | − | 1.19214i | ||||
\(637\) | −49.5848 | + | 85.8835i | −1.96462 | + | 3.40283i | ||||
\(638\) | 1.00000 | 0.0395904 | ||||||||
\(639\) | 26.2642 | 1.03900 | ||||||||
\(640\) | 1.00000 | − | 1.73205i | 0.0395285 | − | 0.0684653i | ||||
\(641\) | 13.3920 | + | 23.1956i | 0.528952 | + | 0.916171i | 0.999430 | + | 0.0337598i | \(0.0107481\pi\) |
−0.470478 | + | 0.882412i | \(0.655919\pi\) | |||||||
\(642\) | −24.1162 | + | 41.7705i | −0.951791 | + | 1.64855i | ||||
\(643\) | 1.63210 | + | 2.82687i | 0.0643636 | + | 0.111481i | 0.896411 | − | 0.443223i | \(-0.146165\pi\) |
−0.832048 | + | 0.554704i | \(0.812832\pi\) | |||||||
\(644\) | 4.67889 | + | 8.10407i | 0.184374 | + | 0.319345i | ||||
\(645\) | 27.2498 | 1.07296 | ||||||||
\(646\) | −16.0979 | + | 2.36928i | −0.633363 | + | 0.0932181i | ||||
\(647\) | −10.3355 | −0.406332 | −0.203166 | − | 0.979144i | \(-0.565123\pi\) | ||||
−0.203166 | + | 0.979144i | \(0.565123\pi\) | |||||||
\(648\) | 3.10655 | + | 5.38070i | 0.122037 | + | 0.211374i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −2.83944 | + | 4.91806i | −0.111372 | + | 0.192902i | ||||
\(651\) | 23.4089 | + | 40.5453i | 0.917466 | + | 1.58910i | ||||
\(652\) | 5.41178 | − | 9.37348i | 0.211942 | − | 0.367094i | ||||
\(653\) | 16.5853 | 0.649033 | 0.324517 | − | 0.945880i | \(-0.394798\pi\) | ||||
0.324517 | + | 0.945880i | \(0.394798\pi\) | |||||||
\(654\) | 51.4455 | 2.01168 | ||||||||
\(655\) | −10.3722 | + | 17.9652i | −0.405275 | + | 0.701958i | ||||
\(656\) | −4.81244 | + | 8.33539i | −0.187894 | + | 0.325442i | ||||
\(657\) | −20.5853 | −0.803109 | ||||||||
\(658\) | 36.6586 | 1.42910 | ||||||||
\(659\) | 16.7059 | − | 28.9355i | 0.650769 | − | 1.12717i | −0.332168 | − | 0.943220i | \(-0.607780\pi\) |
0.982937 | − | 0.183945i | \(-0.0588867\pi\) | |||||||
\(660\) | 2.94600 | + | 5.10261i | 0.114673 | + | 0.198619i | ||||
\(661\) | 5.13355 | − | 8.89158i | 0.199672 | − | 0.345842i | −0.748750 | − | 0.662852i | \(-0.769346\pi\) |
0.948422 | + | 0.317010i | \(0.102679\pi\) | |||||||
\(662\) | −3.15189 | − | 5.45923i | −0.122502 | − | 0.212179i | ||||
\(663\) | 31.2256 | + | 54.0843i | 1.21270 | + | 2.10046i | ||||
\(664\) | −14.5169 | −0.563364 | ||||||||
\(665\) | −15.8920 | + | 40.0827i | −0.616265 | + | 1.55434i | ||||
\(666\) | 23.6190 | 0.915220 | ||||||||
\(667\) | −0.945995 | − | 1.63851i | −0.0366291 | − | 0.0634434i | ||||
\(668\) | −2.00721 | − | 3.47659i | −0.0776614 | − | 0.134513i | ||||
\(669\) | −10.8635 | + | 18.8162i | −0.420008 | + | 0.727476i | ||||
\(670\) | 8.83799 | + | 15.3078i | 0.341441 | + | 0.591393i | ||||
\(671\) | 2.78544 | − | 4.82452i | 0.107531 | − | 0.186249i | ||||
\(672\) | 14.5709 | 0.562084 | ||||||||
\(673\) | 47.6190 | 1.83558 | 0.917790 | − | 0.397067i | \(-0.129972\pi\) | ||||
0.917790 | + | 0.397067i | \(0.129972\pi\) | |||||||
\(674\) | −5.14467 | + | 8.91083i | −0.198165 | + | 0.343233i | ||||
\(675\) | −3.94600 | + | 6.83466i | −0.151881 | + | 0.263066i | ||||
\(676\) | 19.2498 | 0.740376 | ||||||||
\(677\) | 6.64514 | 0.255394 | 0.127697 | − | 0.991813i | \(-0.459242\pi\) | ||||
0.127697 | + | 0.991813i | \(0.459242\pi\) | |||||||
\(678\) | 5.20589 | − | 9.01687i | 0.199931 | − | 0.346291i | ||||
\(679\) | 3.79411 | + | 6.57159i | 0.145605 | + | 0.252195i | ||||
\(680\) | 3.73289 | − | 6.46556i | 0.143150 | − | 0.247943i | ||||
\(681\) | −41.7666 | − | 72.3419i | −1.60050 | − | 2.77215i | ||||
\(682\) | 1.60655 | + | 2.78263i | 0.0615180 | + | 0.106552i | ||||
\(683\) | 21.7984 | 0.834093 | 0.417046 | − | 0.908885i | \(-0.363065\pi\) | ||||
0.417046 | + | 0.908885i | \(0.363065\pi\) | |||||||
\(684\) | −9.12342 | + | 23.0111i | −0.348843 | + | 0.879850i | ||||
\(685\) | 28.2102 | 1.07786 | ||||||||
\(686\) | 25.8746 | + | 44.8162i | 0.987899 | + | 1.71109i | ||||
\(687\) | −7.33944 | − | 12.7123i | −0.280017 | − | 0.485004i | ||||
\(688\) | 2.31244 | − | 4.00527i | 0.0881610 | − | 0.152699i | ||||
\(689\) | −33.4600 | − | 57.9543i | −1.27472 | − | 2.20788i | ||||
\(690\) | 5.57379 | − | 9.65410i | 0.212191 | − | 0.367525i | ||||
\(691\) | −13.2700 | −0.504816 | −0.252408 | − | 0.967621i | \(-0.581222\pi\) | ||||
−0.252408 | + | 0.967621i | \(0.581222\pi\) | |||||||
\(692\) | −7.21310 | −0.274201 | ||||||||
\(693\) | −14.0439 | + | 24.3247i | −0.533483 | + | 0.924019i | ||||
\(694\) | −9.59788 | + | 16.6240i | −0.364331 | + | 0.631039i | ||||
\(695\) | −27.3519 | −1.03752 | ||||||||
\(696\) | −2.94600 | −0.111668 | ||||||||
\(697\) | −17.9643 | + | 31.1151i | −0.680447 | + | 1.17857i | ||||
\(698\) | 16.4827 | + | 28.5488i | 0.623878 | + | 1.08059i | ||||
\(699\) | 33.0665 | − | 57.2729i | 1.25069 | − | 2.16626i | ||||
\(700\) | 2.47300 | + | 4.28336i | 0.0934705 | + | 0.161896i | ||||
\(701\) | −6.34090 | − | 10.9828i | −0.239493 | − | 0.414813i | 0.721076 | − | 0.692856i | \(-0.243648\pi\) |
−0.960569 | + | 0.278042i | \(0.910314\pi\) | |||||||
\(702\) | 44.8177 | 1.69154 | ||||||||
\(703\) | 11.2541 | + | 14.2130i | 0.424455 | + | 0.536054i | ||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | −21.8351 | − | 37.8194i | −0.822356 | − | 1.42436i | ||||
\(706\) | 16.6418 | + | 28.8244i | 0.626321 | + | 1.08482i | ||||
\(707\) | 4.15189 | − | 7.19128i | 0.156148 | − | 0.270456i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.7840 | + | 32.5348i | −0.705447 | + | 1.22187i | 0.261083 | + | 0.965316i | \(0.415920\pi\) |
−0.966530 | + | 0.256554i | \(0.917413\pi\) | |||||||
\(710\) | −9.24977 | −0.347138 | ||||||||
\(711\) | −38.8322 | −1.45632 | ||||||||
\(712\) | −0.232893 | + | 0.403382i | −0.00872802 | + | 0.0151174i | ||||
\(713\) | 3.03958 | − | 5.26471i | 0.113833 | − | 0.197165i | ||||
\(714\) | 54.3915 | 2.03555 | ||||||||
\(715\) | 11.3578 | 0.424757 | ||||||||
\(716\) | −2.05400 | + | 3.55764i | −0.0767618 | + | 0.132955i | ||||
\(717\) | −35.0337 | − | 60.6802i | −1.30836 | − | 2.26614i | ||||
\(718\) | 2.84090 | − | 4.92059i | 0.106022 | − | 0.183635i | ||||
\(719\) | 1.47154 | + | 2.54878i | 0.0548792 | + | 0.0950535i | 0.892160 | − | 0.451720i | \(-0.149189\pi\) |
−0.837281 | + | 0.546773i | \(0.815856\pi\) | |||||||
\(720\) | −5.67889 | − | 9.83612i | −0.211640 | − | 0.366571i | ||||
\(721\) | −36.6586 | −1.36524 | ||||||||
\(722\) | −18.1943 | + | 5.47424i | −0.677122 | + | 0.203730i | ||||
\(723\) | 62.2835 | 2.31635 | ||||||||
\(724\) | −7.70443 | − | 13.3445i | −0.286333 | − | 0.495943i | ||||
\(725\) | −0.500000 | − | 0.866025i | −0.0185695 | − | 0.0321634i | ||||
\(726\) | −1.47300 | + | 2.55131i | −0.0546681 | + | 0.0946879i | ||||
\(727\) | −13.7753 | − | 23.8595i | −0.510898 | − | 0.884901i | −0.999920 | − | 0.0126299i | \(-0.995980\pi\) |
0.489022 | − | 0.872271i | \(-0.337354\pi\) | |||||||
\(728\) | 14.0439 | − | 24.3247i | 0.520501 | − | 0.901534i | ||||
\(729\) | −34.4658 | −1.27651 | ||||||||
\(730\) | 7.24977 | 0.268326 | ||||||||
\(731\) | 8.63210 | − | 14.9512i | 0.319270 | − | 0.552991i | ||||
\(732\) | −8.20589 | + | 14.2130i | −0.303298 | + | 0.525328i | ||||
\(733\) | 37.6393 | 1.39024 | 0.695120 | − | 0.718894i | \(-0.255351\pi\) | ||||
0.695120 | + | 0.718894i | \(0.255351\pi\) | |||||||
\(734\) | −17.6933 | −0.653072 | ||||||||
\(735\) | 51.4455 | − | 89.1063i | 1.89760 | − | 3.28673i | ||||
\(736\) | −0.945995 | − | 1.63851i | −0.0348698 | − | 0.0603963i | ||||
\(737\) | −4.41899 | + | 7.65392i | −0.162776 | + | 0.281936i | ||||
\(738\) | 27.3293 | + | 47.3358i | 1.00601 | + | 1.74245i | ||||
\(739\) | −2.59788 | − | 4.49966i | −0.0955646 | − | 0.165523i | 0.814280 | − | 0.580473i | \(-0.197132\pi\) |
−0.909844 | + | 0.414950i | \(0.863799\pi\) | |||||||
\(740\) | −8.31820 | −0.305783 | ||||||||
\(741\) | 45.2695 | + | 57.1719i | 1.66302 | + | 2.10026i | ||||
\(742\) | −58.2835 | −2.13966 | ||||||||
\(743\) | 0.989871 | + | 1.71451i | 0.0363148 | + | 0.0628992i | 0.883612 | − | 0.468221i | \(-0.155105\pi\) |
−0.847297 | + | 0.531120i | \(0.821771\pi\) | |||||||
\(744\) | −4.73289 | − | 8.19761i | −0.173516 | − | 0.300539i | ||||
\(745\) | −18.9971 | + | 32.9039i | −0.695999 | + | 1.20551i | ||||
\(746\) | −18.5525 | − | 32.1340i | −0.679257 | − | 1.17651i | ||||
\(747\) | −41.2198 | + | 71.3949i | −1.50816 | + | 2.61220i | ||||
\(748\) | 3.73289 | 0.136488 | ||||||||
\(749\) | 80.9768 | 2.95883 | ||||||||
\(750\) | 17.6760 | − | 30.6157i | 0.645435 | − | 1.11793i | ||||
\(751\) | 1.67022 | − | 2.89290i | 0.0609471 | − | 0.105563i | −0.833942 | − | 0.551852i | \(-0.813921\pi\) |
0.894889 | + | 0.446289i | \(0.147255\pi\) | |||||||
\(752\) | −7.41178 | −0.270280 | ||||||||
\(753\) | −1.53130 | −0.0558036 | ||||||||
\(754\) | −2.83944 | + | 4.91806i | −0.103406 | + | 0.179105i | ||||
\(755\) | 23.6615 | + | 40.9830i | 0.861132 | + | 1.49152i | ||||
\(756\) | 19.5169 | − | 33.8042i | 0.709822 | − | 1.22945i | ||||
\(757\) | 21.3549 | + | 36.9877i | 0.776156 | + | 1.34434i | 0.934143 | + | 0.356900i | \(0.116166\pi\) |
−0.157987 | + | 0.987441i | \(0.550500\pi\) | |||||||
\(758\) | 6.77677 | + | 11.7377i | 0.246143 | + | 0.426333i | ||||
\(759\) | 5.57379 | 0.202316 | ||||||||
\(760\) | 3.21310 | − | 8.10407i | 0.116551 | − | 0.293966i | ||||
\(761\) | −10.5054 | −0.380819 | −0.190410 | − | 0.981705i | \(-0.560982\pi\) | ||||
−0.190410 | + | 0.981705i | \(0.560982\pi\) | |||||||
\(762\) | 7.89199 | + | 13.6693i | 0.285897 | + | 0.495188i | ||||
\(763\) | −43.1856 | − | 74.7997i | −1.56342 | − | 2.70793i | ||||
\(764\) | −5.29411 | + | 9.16967i | −0.191534 | + | 0.331747i | ||||
\(765\) | −21.1987 | − | 36.7172i | −0.766440 | − | 1.32751i | ||||
\(766\) | 4.83799 | − | 8.37964i | 0.174804 | − | 0.302769i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −2.94600 | −0.106304 | ||||||||
\(769\) | 1.53713 | − | 2.66239i | 0.0554304 | − | 0.0960082i | −0.836979 | − | 0.547235i | \(-0.815680\pi\) |
0.892409 | + | 0.451227i | \(0.149014\pi\) | |||||||
\(770\) | 4.94600 | − | 8.56671i | 0.178241 | − | 0.308723i | ||||
\(771\) | 31.8862 | 1.14835 | ||||||||
\(772\) | −5.51687 | −0.198557 | ||||||||
\(773\) | −2.72177 | + | 4.71425i | −0.0978954 | + | 0.169560i | −0.910813 | − | 0.412818i | \(-0.864544\pi\) |
0.812918 | + | 0.582378i | \(0.197878\pi\) | |||||||
\(774\) | −13.1321 | − | 22.7455i | −0.472023 | − | 0.817569i | ||||
\(775\) | 1.60655 | − | 2.78263i | 0.0577090 | − | 0.0999550i | ||||
\(776\) | −0.767107 | − | 1.32867i | −0.0275376 | − | 0.0476964i | ||||
\(777\) | −30.3009 | − | 52.4826i | −1.08704 | − | 1.88280i | ||||
\(778\) | −12.8013 | −0.458950 | ||||||||
\(779\) | −15.4629 | + | 39.0004i | −0.554015 | + | 1.39733i | ||||
\(780\) | −33.4600 | −1.19806 | ||||||||
\(781\) | −2.31244 | − | 4.00527i | −0.0827457 | − | 0.143320i | ||||
\(782\) | −3.53130 | − | 6.11639i | −0.126279 | − | 0.218722i | ||||
\(783\) | −3.94600 | + | 6.83466i | −0.141018 | + | 0.244251i | ||||
\(784\) | −8.73143 | − | 15.1233i | −0.311837 | − | 0.540117i | ||||
\(785\) | 11.7840 | − | 20.4105i | 0.420588 | − | 0.728480i | ||||
\(786\) | 30.5565 | 1.08991 | ||||||||
\(787\) | −4.22753 | −0.150695 | −0.0753475 | − | 0.997157i | \(-0.524007\pi\) | ||||
−0.0753475 | + | 0.997157i | \(0.524007\pi\) | |||||||
\(788\) | 4.76711 | − | 8.25687i | 0.169821 | − | 0.294139i | ||||
\(789\) | −19.1987 | + | 33.2531i | −0.683491 | + | 1.18384i | ||||
\(790\) | 13.6760 | 0.486569 | ||||||||
\(791\) | −17.4802 | −0.621525 | ||||||||
\(792\) | 2.83944 | − | 4.91806i | 0.100895 | − | 0.174756i | ||||
\(793\) | 15.8182 | + | 27.3979i | 0.561721 | + | 0.972929i | ||||
\(794\) | −9.07955 | + | 15.7262i | −0.322221 | + | 0.558103i | ||||
\(795\) | 34.7156 | + | 60.1291i | 1.23123 | + | 2.13256i | ||||
\(796\) | −10.3124 | − | 17.8617i | −0.365515 | − | 0.633090i | ||||
\(797\) | −1.44355 | −0.0511331 | −0.0255665 | − | 0.999673i | \(-0.508139\pi\) | ||||
−0.0255665 | + | 0.999673i | \(0.508139\pi\) | |||||||
\(798\) | 62.8361 | − | 9.24819i | 2.22437 | − | 0.327382i | ||||
\(799\) | −27.6674 | −0.978802 | ||||||||
\(800\) | −0.500000 | − | 0.866025i | −0.0176777 | − | 0.0306186i | ||||
\(801\) | 1.32257 | + | 2.29076i | 0.0467307 | + | 0.0809400i | ||||
\(802\) | −3.91032 | + | 6.77288i | −0.138078 | + | 0.239159i | ||||
\(803\) | 1.81244 | + | 3.13924i | 0.0639597 | + | 0.110781i | ||||
\(804\) | 13.0183 | − | 22.5484i | 0.459121 | − | 0.795221i | ||||
\(805\) | −18.7156 | −0.659636 | ||||||||
\(806\) | −18.2468 | −0.642718 | ||||||||
\(807\) | −8.44454 | + | 14.6264i | −0.297262 | + | 0.514873i | ||||
\(808\) | −0.839444 | + | 1.45396i | −0.0295315 | + | 0.0511501i | ||||
\(809\) | −28.7378 | −1.01037 | −0.505183 | − | 0.863012i | \(-0.668575\pi\) | ||||
−0.505183 | + | 0.863012i | \(0.668575\pi\) | |||||||
\(810\) | −12.4262 | −0.436612 | ||||||||
\(811\) | 12.7242 | − | 22.0390i | 0.446808 | − | 0.773894i | −0.551368 | − | 0.834262i | \(-0.685894\pi\) |
0.998176 | + | 0.0603680i | \(0.0192274\pi\) | |||||||
\(812\) | 2.47300 | + | 4.28336i | 0.0867852 | + | 0.150316i | ||||
\(813\) | −17.6760 | + | 30.6157i | −0.619923 | + | 1.07374i | ||||
\(814\) | −2.07955 | − | 3.60188i | −0.0728882 | − | 0.126246i | ||||
\(815\) | 10.8236 | + | 18.7470i | 0.379133 | + | 0.656677i | ||||
\(816\) | −10.9971 | −0.384975 | ||||||||
\(817\) | 7.43011 | − | 18.7402i | 0.259947 | − | 0.655636i | ||||
\(818\) | 21.0115 | 0.734650 | ||||||||
\(819\) | −79.7536 | − | 138.137i | −2.78682 | − | 4.82691i | ||||
\(820\) | −9.62488 | − | 16.6708i | −0.336115 | − | 0.582169i | ||||
\(821\) | 13.7512 | − | 23.8178i | 0.479921 | − | 0.831248i | −0.519814 | − | 0.854280i | \(-0.673999\pi\) |
0.999735 | + | 0.0230320i | \(0.00733197\pi\) | |||||||
\(822\) | −20.7768 | − | 35.9864i | −0.724673 | − | 1.25517i | ||||
\(823\) | −8.77432 | + | 15.1976i | −0.305854 | + | 0.529754i | −0.977451 | − | 0.211162i | \(-0.932275\pi\) |
0.671597 | + | 0.740916i | \(0.265608\pi\) | |||||||
\(824\) | 7.41178 | 0.258202 | ||||||||
\(825\) | 2.94600 | 0.102566 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.6162 | − | 28.7801i | 0.577802 | − | 1.00078i | −0.417929 | − | 0.908480i | \(-0.637244\pi\) |
0.995731 | − | 0.0923031i | \(-0.0294229\pi\) | |||||||
\(828\) | −10.7444 | −0.373394 | ||||||||
\(829\) | 31.8062 | 1.10468 | 0.552338 | − | 0.833620i | \(-0.313736\pi\) | ||||
0.552338 | + | 0.833620i | \(0.313736\pi\) | |||||||
\(830\) | 14.5169 | − | 25.1440i | 0.503888 | − | 0.872760i | ||||
\(831\) | 19.9899 | + | 34.6235i | 0.693441 | + | 1.20107i | ||||
\(832\) | −2.83944 | + | 4.91806i | −0.0984400 | + | 0.170503i | ||||
\(833\) | −32.5935 | − | 56.4536i | −1.12930 | − | 1.95600i | ||||
\(834\) | 20.1447 | + | 34.8916i | 0.697553 | + | 1.20820i | ||||
\(835\) | 8.02885 | 0.277850 | ||||||||
\(836\) | 4.31244 | − | 0.634704i | 0.149149 | − | 0.0219517i | ||||
\(837\) | −25.3578 | −0.876493 | ||||||||
\(838\) | −5.52700 | − | 9.57305i | −0.190927 | − | 0.330695i | ||||
\(839\) | 1.16777 | + | 2.02263i | 0.0403159 | + | 0.0698291i | 0.885479 | − | 0.464679i | \(-0.153830\pi\) |
−0.845163 | + | 0.534508i | \(0.820497\pi\) | |||||||
\(840\) | −14.5709 | + | 25.2375i | −0.502743 | + | 0.870777i | ||||
\(841\) | 14.0000 | + | 24.2487i | 0.482759 | + | 0.836162i | ||||
\(842\) | 2.24156 | − | 3.88250i | 0.0772494 | − | 0.133800i | ||||
\(843\) | −3.53130 | −0.121624 | ||||||||
\(844\) | −25.6760 | −0.883803 | ||||||||
\(845\) | −19.2498 | + | 33.3416i | −0.662212 | + | 1.14698i | ||||
\(846\) | −21.0453 | + | 36.4516i | −0.723553 | + | 1.25323i | ||||
\(847\) | 4.94600 | 0.169946 | ||||||||
\(848\) | 11.7840 | 0.404664 | ||||||||
\(849\) | −7.10509 | + | 12.3064i | −0.243846 | + | 0.422354i | ||||
\(850\) | −1.86645 | − | 3.23278i | −0.0640186 | − | 0.110883i | ||||
\(851\) | −3.93449 | + | 6.81473i | −0.134872 | + | 0.233606i | ||||
\(852\) | 6.81244 | + | 11.7995i | 0.233390 | + | 0.404244i | ||||
\(853\) | 2.51588 | + | 4.35764i | 0.0861422 | + | 0.149203i | 0.905877 | − | 0.423540i | \(-0.139213\pi\) |
−0.819735 | + | 0.572743i | \(0.805879\pi\) | |||||||
\(854\) | 27.5535 | 0.942863 | ||||||||
\(855\) | −30.7329 | − | 38.8133i | −1.05104 | − | 1.32739i | ||||
\(856\) | −16.3722 | −0.559590 | ||||||||
\(857\) | −4.65043 | − | 8.05478i | −0.158856 | − | 0.275146i | 0.775601 | − | 0.631224i | \(-0.217447\pi\) |
−0.934456 | + | 0.356078i | \(0.884114\pi\) | |||||||
\(858\) | −8.36499 | − | 14.4886i | −0.285576 | − | 0.494632i | ||||
\(859\) | 16.7696 | − | 29.0457i | 0.572170 | − | 0.991027i | −0.424173 | − | 0.905581i | \(-0.639435\pi\) |
0.996343 | − | 0.0854461i | \(-0.0272315\pi\) | |||||||
\(860\) | 4.62488 | + | 8.01053i | 0.157707 | + | 0.273157i | ||||
\(861\) | 70.1215 | − | 121.454i | 2.38973 | − | 4.13914i | ||||
\(862\) | −2.19576 | −0.0747879 | ||||||||
\(863\) | 52.6557 | 1.79242 | 0.896211 | − | 0.443629i | \(-0.146309\pi\) | ||||
0.896211 | + | 0.443629i | \(0.146309\pi\) | |||||||
\(864\) | −3.94600 | + | 6.83466i | −0.134245 | + | 0.232520i | ||||
\(865\) | 7.21310 | − | 12.4935i | 0.245253 | − | 0.424790i | ||||
\(866\) | 31.8602 | 1.08265 | ||||||||
\(867\) | 9.03099 | 0.306708 | ||||||||
\(868\) | −7.94600 | + | 13.7629i | −0.269705 | + | 0.467142i | ||||
\(869\) | 3.41899 | + | 5.92187i | 0.115981 | + | 0.200886i | ||||
\(870\) | 2.94600 | − | 5.10261i | 0.0998786 | − | 0.172995i | ||||
\(871\) | −25.0950 | − | 43.4658i | −0.850310 | − | 1.47278i | ||||
\(872\) | 8.73143 | + | 15.1233i | 0.295684 | + | 0.512139i | ||||
\(873\) | −8.71263 | −0.294878 | ||||||||
\(874\) | −5.11952 | − | 6.46556i | −0.173170 | − | 0.218701i | ||||
\(875\) | −59.3519 | −2.00646 | ||||||||
\(876\) | −5.33944 | − | 9.24819i | −0.180403 | − | 0.312467i | ||||
\(877\) | −5.64222 | − | 9.77262i | −0.190524 | − | 0.329998i | 0.754900 | − | 0.655840i | \(-0.227685\pi\) |
−0.945424 | + | 0.325842i | \(0.894352\pi\) | |||||||
\(878\) | −5.32111 | + | 9.21644i | −0.179579 | + | 0.311040i | ||||
\(879\) | 1.79119 | + | 3.10244i | 0.0604155 | + | 0.104643i | ||||
\(880\) | −1.00000 | + | 1.73205i | −0.0337100 | + | 0.0583874i | ||||
\(881\) | −21.6105 | −0.728075 | −0.364037 | − | 0.931384i | \(-0.618602\pi\) | ||||
−0.364037 | + | 0.931384i | \(0.618602\pi\) | |||||||
\(882\) | −99.1697 | −3.33922 | ||||||||
\(883\) | −8.47008 | + | 14.6706i | −0.285041 | + | 0.493705i | −0.972619 | − | 0.232405i | \(-0.925341\pi\) |
0.687578 | + | 0.726110i | \(0.258674\pi\) | |||||||
\(884\) | −10.5993 | + | 18.3586i | −0.356494 | + | 0.617466i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −31.4455 | −1.05643 | ||||||||
\(887\) | 22.2936 | − | 38.6137i | 0.748547 | − | 1.29652i | −0.199972 | − | 0.979802i | \(-0.564085\pi\) |
0.948519 | − | 0.316720i | \(-0.102582\pi\) | |||||||
\(888\) | 6.12634 | + | 10.6111i | 0.205587 | + | 0.356086i | ||||
\(889\) | 13.2498 | − | 22.9493i | 0.444383 | − | 0.769694i | ||||
\(890\) | −0.465785 | − | 0.806763i | −0.0156132 | − | 0.0270428i | ||||
\(891\) | −3.10655 | − | 5.38070i | −0.104073 | − | 0.180260i | ||||
\(892\) | −7.37512 | −0.246937 | ||||||||
\(893\) | −31.9629 | + | 4.70428i | −1.06960 | + | 0.157423i | ||||
\(894\) | 55.9653 | 1.87176 | ||||||||
\(895\) | −4.10801 | − | 7.11528i | −0.137316 | − | 0.237838i | ||||
\(896\) | 2.47300 | + | 4.28336i | 0.0826171 | + | 0.143097i | ||||
\(897\) | −15.8265 | + | 27.4123i | −0.528431 | + | 0.915269i | ||||
\(898\) | 6.92766 | + | 11.9991i | 0.231179 | + | 0.400414i | ||||
\(899\) | 1.60655 | − | 2.78263i | 0.0535815 | − | 0.0928059i | ||||
\(900\) | −5.67889 | −0.189296 | ||||||||
\(901\) | 43.9883 | 1.46546 | ||||||||
\(902\) | 4.81244 | − | 8.33539i | 0.160237 | − | 0.277538i | ||||
\(903\) | −33.6943 | + | 58.3602i | −1.12128 | + | 1.94211i | ||||
\(904\) | 3.53421 | 0.117546 | ||||||||
\(905\) | 30.8177 | 1.02442 | ||||||||
\(906\) | 34.8534 | − | 60.3679i | 1.15793 | − | 2.00559i | ||||
\(907\) | −17.4484 | − | 30.2216i | −0.579366 | − | 1.00349i | −0.995552 | − | 0.0942120i | \(-0.969967\pi\) |
0.416186 | − | 0.909279i | \(-0.363366\pi\) | |||||||
\(908\) | 14.1774 | − | 24.5560i | 0.470495 | − | 0.814920i | ||||
\(909\) | 4.76711 | + | 8.25687i | 0.158115 | + | 0.273863i | ||||
\(910\) | 28.0878 | + | 48.6494i | 0.931100 | + | 1.61271i | ||||
\(911\) | 21.8631 | 0.724358 | 0.362179 | − | 0.932109i | \(-0.382033\pi\) | ||||
0.362179 | + | 0.932109i | \(0.382033\pi\) | |||||||
\(912\) | −12.7044 | + | 1.86983i | −0.420686 | + | 0.0619164i | ||||
\(913\) | 14.5169 | 0.480438 | ||||||||
\(914\) | −7.86645 | − | 13.6251i | −0.260199 | − | 0.450678i | ||||
\(915\) | −16.4118 | − | 28.4260i | −0.542557 | − | 0.939736i | ||||
\(916\) | 2.49133 | − | 4.31511i | 0.0823158 | − | 0.142575i | ||||
\(917\) | −25.6504 | − | 44.4278i | −0.847052 | − | 1.46714i | ||||
\(918\) | −14.7300 | + | 25.5131i | −0.486162 | + | 0.842057i | ||||
\(919\) | 31.9509 | 1.05396 | 0.526981 | − | 0.849877i | \(-0.323324\pi\) | ||||
0.526981 | + | 0.849877i | \(0.323324\pi\) | |||||||
\(920\) | 3.78398 | 0.124754 | ||||||||
\(921\) | 47.2069 | − | 81.7647i | 1.55552 | − | 2.69424i | ||||
\(922\) | −10.3563 | + | 17.9377i | −0.341067 | + | 0.590746i | ||||
\(923\) | 26.2642 | 0.864496 | ||||||||
\(924\) | −14.5709 | −0.479347 | ||||||||
\(925\) | −2.07955 | + | 3.60188i | −0.0683751 | + | 0.118429i | ||||
\(926\) | −7.18610 | − | 12.4467i | −0.236150 | − | 0.409024i | ||||
\(927\) | 21.0453 | − | 36.4516i | 0.691219 | − | 1.19723i | ||||
\(928\) | −0.500000 | − | 0.866025i | −0.0164133 | − | 0.0284287i | ||||
\(929\) | −10.0342 | − | 17.3798i | −0.329212 | − | 0.570212i | 0.653144 | − | 0.757234i | \(-0.273450\pi\) |
−0.982356 | + | 0.187022i | \(0.940116\pi\) | |||||||
\(930\) | 18.9316 | 0.620791 | ||||||||
\(931\) | −47.2526 | − | 59.6764i | −1.54864 | − | 1.95582i | ||||
\(932\) | 22.4484 | 0.735323 | ||||||||
\(933\) | −27.0622 | − | 46.8731i | −0.885977 | − | 1.53456i | ||||
\(934\) | −5.15189 | − | 8.92333i | −0.168575 | − | 0.291980i | ||||
\(935\) | −3.73289 | + | 6.46556i | −0.122079 | + | 0.211446i | ||||
\(936\) | 16.1249 | + | 27.9291i | 0.527058 | + | 0.912892i | ||||
\(937\) | 22.5680 | − | 39.0889i | 0.737263 | − | 1.27698i | −0.216460 | − | 0.976291i | \(-0.569451\pi\) |
0.953723 | − | 0.300686i | \(-0.0972155\pi\) | |||||||
\(938\) | −43.7126 | −1.42727 | ||||||||
\(939\) | −3.37220 | −0.110048 | ||||||||
\(940\) | 7.41178 | − | 12.8376i | 0.241746 | − | 0.418716i | ||||
\(941\) | −17.0010 | + | 29.4466i | −0.554216 | + | 0.959931i | 0.443748 | + | 0.896152i | \(0.353649\pi\) |
−0.997964 | + | 0.0637792i | \(0.979685\pi\) | |||||||
\(942\) | −34.7156 | −1.13109 | ||||||||
\(943\) | −18.2102 | −0.593005 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 39.0337 | + | 67.6084i | 1.26977 | + | 2.19930i | ||||
\(946\) | −2.31244 | + | 4.00527i | −0.0751840 | + | 0.130222i | ||||
\(947\) | 26.4089 | + | 45.7415i | 0.858173 | + | 1.48640i | 0.873670 | + | 0.486519i | \(0.161734\pi\) |
−0.0154973 | + | 0.999880i | \(0.504933\pi\) | |||||||
\(948\) | −10.0723 | − | 17.4458i | −0.327134 | − | 0.566613i | ||||
\(949\) | −20.5853 | −0.668227 | ||||||||
\(950\) | −2.70589 | − | 3.41733i | −0.0877907 | − | 0.110873i | ||||
\(951\) | −72.0250 | −2.33557 | ||||||||
\(952\) | 9.23143 | + | 15.9893i | 0.299193 | + | 0.518217i | ||||
\(953\) | 6.35778 | + | 11.0120i | 0.205949 | + | 0.356713i | 0.950435 | − | 0.310925i | \(-0.100639\pi\) |
−0.744486 | + | 0.667638i | \(0.767305\pi\) | |||||||
\(954\) | 33.4600 | − | 57.9543i | 1.08331 | − | 1.87634i | ||||
\(955\) | −10.5882 | − | 18.3393i | −0.342627 | − | 0.593447i | ||||
\(956\) | 11.8920 | − | 20.5975i | 0.384614 | − | 0.666172i | ||||
\(957\) | 2.94600 | 0.0952305 | ||||||||
\(958\) | −7.58822 | −0.245164 | ||||||||
\(959\) | −34.8819 | + | 60.4172i | −1.12639 | + | 1.95097i | ||||
\(960\) | 2.94600 | − | 5.10261i | 0.0950816 | − | 0.164686i | ||||
\(961\) | −20.6760 | −0.666967 | ||||||||
\(962\) | 23.6190 | 0.761509 | ||||||||
\(963\) | −46.4879 | + | 80.5195i | −1.49805 | + | 2.59470i | ||||
\(964\) | 10.5709 | + | 18.3093i | 0.340465 | + | 0.589703i | ||||
\(965\) | 5.51687 | − | 9.55550i | 0.177594 | − | 0.307603i | ||||
\(966\) | 13.7840 | + | 23.8746i | 0.443492 | + | 0.768151i | ||||
\(967\) | 4.73289 | + | 8.19761i | 0.152200 | + | 0.263617i | 0.932036 | − | 0.362366i | \(-0.118031\pi\) |
−0.779836 | + | 0.625984i | \(0.784698\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | −47.4243 | + | 6.97989i | −1.52349 | + | 0.224226i | ||||
\(970\) | 3.06843 | 0.0985213 | ||||||||
\(971\) | 14.5607 | + | 25.2200i | 0.467277 | + | 0.809347i | 0.999301 | − | 0.0373821i | \(-0.0119019\pi\) |
−0.532024 | + | 0.846729i | \(0.678569\pi\) | |||||||
\(972\) | −2.68610 | − | 4.65246i | −0.0861567 | − | 0.149228i | ||||
\(973\) | 33.8206 | − | 58.5791i | 1.08424 | − | 1.87796i | ||||
\(974\) | −0.207348 | − | 0.359138i | −0.00664387 | − | 0.0115075i | ||||
\(975\) | −8.36499 | + | 14.4886i | −0.267894 | + | 0.464006i | ||||
\(976\) | −5.57088 | −0.178319 | ||||||||
\(977\) | −1.75023 | −0.0559950 | −0.0279975 | − | 0.999608i | \(-0.508913\pi\) | ||||
−0.0279975 | + | 0.999608i | \(0.508913\pi\) | |||||||
\(978\) | 15.9431 | − | 27.6142i | 0.509803 | − | 0.883005i | ||||
\(979\) | 0.232893 | − | 0.403382i | 0.00744328 | − | 0.0128921i | ||||
\(980\) | 34.9257 | 1.11566 | ||||||||
\(981\) | 99.1697 | 3.16624 | ||||||||
\(982\) | −0.411780 | + | 0.713224i | −0.0131404 | + | 0.0227599i | ||||
\(983\) | 12.0058 | + | 20.7946i | 0.382924 | + | 0.663244i | 0.991479 | − | 0.130268i | \(-0.0415837\pi\) |
−0.608555 | + | 0.793512i | \(0.708250\pi\) | |||||||
\(984\) | −14.1774 | + | 24.5560i | −0.451960 | + | 0.782818i | ||||
\(985\) | 9.53421 | + | 16.5137i | 0.303785 | + | 0.526172i | ||||
\(986\) | −1.86645 | − | 3.23278i | −0.0594398 | − | 0.102953i | ||||
\(987\) | 107.996 | 3.43756 | ||||||||
\(988\) | −9.12342 | + | 23.0111i | −0.290255 | + | 0.732079i | ||||
\(989\) | 8.75023 | 0.278241 | ||||||||
\(990\) | 5.67889 | + | 9.83612i | 0.180487 | + | 0.312612i | ||||
\(991\) | −22.9017 | − | 39.6668i | −0.727495 | − | 1.26006i | −0.957939 | − | 0.286973i | \(-0.907351\pi\) |
0.230444 | − | 0.973086i | \(-0.425982\pi\) | |||||||
\(992\) | 1.60655 | − | 2.78263i | 0.0510081 | − | 0.0883485i | ||||
\(993\) | −9.28544 | − | 16.0829i | −0.294665 | − | 0.510374i | ||||
\(994\) | 11.4373 | − | 19.8100i | 0.362770 | − | 0.628336i | ||||
\(995\) | 41.2498 | 1.30771 | ||||||||
\(996\) | −42.7666 | −1.35511 | ||||||||
\(997\) | −2.57379 | + | 4.45794i | −0.0815129 | + | 0.141184i | −0.903900 | − | 0.427744i | \(-0.859309\pi\) |
0.822387 | + | 0.568928i | \(0.192642\pi\) | |||||||
\(998\) | 2.67889 | − | 4.63997i | 0.0847987 | − | 0.146876i | ||||
\(999\) | 32.8236 | 1.03849 |
(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 | 418.2.e.i.45.3 | ✓ | 6 | |
19.7 | even | 3 | 7942.2.a.bd.1.1 | 3 | |||
19.11 | even | 3 | inner | 418.2.e.i.353.3 | yes | 6 | |
19.12 | odd | 6 | 7942.2.a.bj.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
418.2.e.i.45.3 | ✓ | 6 | 1.1 | even | 1 | trivial | |
418.2.e.i.353.3 | yes | 6 | 19.11 | even | 3 | inner | |
7942.2.a.bd.1.1 | 3 | 19.7 | even | 3 | |||
7942.2.a.bj.1.3 | 3 | 19.12 | odd | 6 |