Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [770,2,Mod(221,770)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(770, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("770.221");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 770.i (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: | \(6.14848095564\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 8x^{6} + 3x^{5} + 50x^{4} - 12x^{3} + 11x^{2} + 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 331.4 | ||
Root | \(1.52336 + 2.63854i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 770.331 |
Dual form | 770.2.i.l.221.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(617\) | \(661\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | 1.52336 | + | 2.63854i | 0.879515 | + | 1.52336i | 0.851874 | + | 0.523747i | \(0.175466\pi\) |
0.0276409 | + | 0.999618i | \(0.491201\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | −3.04673 | −1.24382 | ||||||||
\(7\) | 2.18747 | − | 1.48827i | 0.826788 | − | 0.562514i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −3.14128 | + | 5.44086i | −1.04709 | + | 1.81362i | ||||
\(10\) | 0.500000 | + | 0.866025i | 0.158114 | + | 0.273861i | ||||
\(11\) | 0.500000 | + | 0.866025i | 0.150756 | + | 0.261116i | ||||
\(12\) | 1.52336 | − | 2.63854i | 0.439757 | − | 0.761682i | ||||
\(13\) | 0.517321 | 0.143479 | 0.0717395 | − | 0.997423i | \(-0.477145\pi\) | ||||
0.0717395 | + | 0.997423i | \(0.477145\pi\) | |||||||
\(14\) | 0.195144 | + | 2.63854i | 0.0521544 | + | 0.705181i | ||||
\(15\) | 3.04673 | 0.786662 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 0.664110 | + | 1.15027i | 0.161070 | + | 0.278982i | 0.935253 | − | 0.353980i | \(-0.115172\pi\) |
−0.774182 | + | 0.632963i | \(0.781839\pi\) | |||||||
\(18\) | −3.14128 | − | 5.44086i | −0.740407 | − | 1.28242i | ||||
\(19\) | −1.78969 | + | 3.09984i | −0.410584 | + | 0.711152i | −0.994954 | − | 0.100335i | \(-0.968008\pi\) |
0.584370 | + | 0.811488i | \(0.301342\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 7.25919 | + | 3.50457i | 1.58409 | + | 0.764760i | ||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −2.71851 | + | 4.70859i | −0.566848 | + | 0.981810i | 0.430027 | + | 0.902816i | \(0.358504\pi\) |
−0.996875 | + | 0.0789938i | \(0.974829\pi\) | |||||||
\(24\) | 1.52336 | + | 2.63854i | 0.310955 | + | 0.538591i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | −0.258661 | + | 0.448013i | −0.0507275 | + | 0.0878626i | ||||
\(27\) | −10.0011 | −1.92471 | ||||||||
\(28\) | −2.38262 | − | 1.15027i | −0.450273 | − | 0.217381i | ||||
\(29\) | 0.281492 | 0.0522717 | 0.0261358 | − | 0.999658i | \(-0.491680\pi\) | ||||
0.0261358 | + | 0.999658i | \(0.491680\pi\) | |||||||
\(30\) | −1.52336 | + | 2.63854i | −0.278127 | + | 0.481730i | ||||
\(31\) | 5.16464 | + | 8.94543i | 0.927597 | + | 1.60665i | 0.787330 | + | 0.616532i | \(0.211463\pi\) |
0.140268 | + | 0.990114i | \(0.455204\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −1.52336 | + | 2.63854i | −0.265184 | + | 0.459312i | ||||
\(34\) | −1.32822 | −0.227788 | ||||||||
\(35\) | −0.195144 | − | 2.63854i | −0.0329853 | − | 0.445995i | ||||
\(36\) | 6.28256 | 1.04709 | ||||||||
\(37\) | 2.57172 | − | 4.45435i | 0.422788 | − | 0.732290i | −0.573423 | − | 0.819259i | \(-0.694385\pi\) |
0.996211 | + | 0.0869692i | \(0.0277182\pi\) | |||||||
\(38\) | −1.78969 | − | 3.09984i | −0.290327 | − | 0.502861i | ||||
\(39\) | 0.788069 | + | 1.36497i | 0.126192 | + | 0.218571i | ||||
\(40\) | 0.500000 | − | 0.866025i | 0.0790569 | − | 0.136931i | ||||
\(41\) | 2.65644 | 0.414866 | 0.207433 | − | 0.978249i | \(-0.433489\pi\) | ||||
0.207433 | + | 0.978249i | \(0.433489\pi\) | |||||||
\(42\) | −6.66464 | + | 4.53436i | −1.02838 | + | 0.699667i | ||||
\(43\) | 2.56298 | 0.390851 | 0.195426 | − | 0.980719i | \(-0.437391\pi\) | ||||
0.195426 | + | 0.980719i | \(0.437391\pi\) | |||||||
\(44\) | 0.500000 | − | 0.866025i | 0.0753778 | − | 0.130558i | ||||
\(45\) | 3.14128 | + | 5.44086i | 0.468274 | + | 0.811075i | ||||
\(46\) | −2.71851 | − | 4.70859i | −0.400822 | − | 0.694244i | ||||
\(47\) | −2.37495 | + | 4.11353i | −0.346422 | + | 0.600021i | −0.985611 | − | 0.169029i | \(-0.945937\pi\) |
0.639189 | + | 0.769050i | \(0.279270\pi\) | |||||||
\(48\) | −3.04673 | −0.439757 | ||||||||
\(49\) | 2.57009 | − | 6.51111i | 0.367156 | − | 0.930159i | ||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −2.02336 | + | 3.50457i | −0.283328 | + | 0.490738i | ||||
\(52\) | −0.258661 | − | 0.448013i | −0.0358698 | − | 0.0621283i | ||||
\(53\) | 0.921146 | + | 1.59547i | 0.126529 | + | 0.219155i | 0.922330 | − | 0.386404i | \(-0.126283\pi\) |
−0.795801 | + | 0.605559i | \(0.792950\pi\) | |||||||
\(54\) | 5.00053 | − | 8.66118i | 0.680486 | − | 1.17864i | ||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 2.18747 | − | 1.48827i | 0.292314 | − | 0.198879i | ||||
\(57\) | −10.9054 | −1.44446 | ||||||||
\(58\) | −0.140746 | + | 0.243779i | −0.0184808 | + | 0.0320097i | ||||
\(59\) | −3.11629 | − | 5.39757i | −0.405706 | − | 0.702704i | 0.588697 | − | 0.808354i | \(-0.299641\pi\) |
−0.994403 | + | 0.105650i | \(0.966308\pi\) | |||||||
\(60\) | −1.52336 | − | 2.63854i | −0.196666 | − | 0.340635i | ||||
\(61\) | 5.68801 | − | 9.85192i | 0.728275 | − | 1.26141i | −0.229337 | − | 0.973347i | \(-0.573656\pi\) |
0.957612 | − | 0.288062i | \(-0.0930109\pi\) | |||||||
\(62\) | −10.3293 | −1.31182 | ||||||||
\(63\) | 1.22600 | + | 16.5768i | 0.154462 | + | 2.08848i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.258661 | − | 0.448013i | 0.0320829 | − | 0.0555692i | ||||
\(66\) | −1.52336 | − | 2.63854i | −0.187513 | − | 0.324782i | ||||
\(67\) | −6.54673 | − | 11.3393i | −0.799810 | − | 1.38531i | −0.919739 | − | 0.392530i | \(-0.871600\pi\) |
0.119929 | − | 0.992782i | \(-0.461733\pi\) | |||||||
\(68\) | 0.664110 | − | 1.15027i | 0.0805352 | − | 0.139491i | ||||
\(69\) | −16.5651 | −1.99421 | ||||||||
\(70\) | 2.38262 | + | 1.15027i | 0.284777 | + | 0.137484i | ||||
\(71\) | −11.0792 | −1.31486 | −0.657429 | − | 0.753517i | \(-0.728356\pi\) | ||||
−0.657429 | + | 0.753517i | \(0.728356\pi\) | |||||||
\(72\) | −3.14128 | + | 5.44086i | −0.370203 | + | 0.641211i | ||||
\(73\) | −4.47717 | − | 7.75468i | −0.524013 | − | 0.907617i | −0.999609 | − | 0.0279534i | \(-0.991101\pi\) |
0.475596 | − | 0.879664i | \(-0.342232\pi\) | |||||||
\(74\) | 2.57172 | + | 4.45435i | 0.298956 | + | 0.517807i | ||||
\(75\) | 1.52336 | − | 2.63854i | 0.175903 | − | 0.304673i | ||||
\(76\) | 3.57939 | 0.410584 | ||||||||
\(77\) | 2.38262 | + | 1.15027i | 0.271525 | + | 0.131086i | ||||
\(78\) | −1.57614 | −0.178462 | ||||||||
\(79\) | 5.36746 | − | 9.29671i | 0.603886 | − | 1.04596i | −0.388340 | − | 0.921516i | \(-0.626952\pi\) |
0.992226 | − | 0.124445i | \(-0.0397151\pi\) | |||||||
\(80\) | 0.500000 | + | 0.866025i | 0.0559017 | + | 0.0968246i | ||||
\(81\) | −5.81143 | − | 10.0657i | −0.645715 | − | 1.11841i | ||||
\(82\) | −1.32822 | + | 2.30055i | −0.146677 | + | 0.254053i | ||||
\(83\) | 13.2216 | 1.45125 | 0.725627 | − | 0.688088i | \(-0.241550\pi\) | ||||
0.725627 | + | 0.688088i | \(0.241550\pi\) | |||||||
\(84\) | −0.594550 | − | 8.03893i | −0.0648707 | − | 0.877119i | ||||
\(85\) | 1.32822 | 0.144066 | ||||||||
\(86\) | −1.28149 | + | 2.21961i | −0.138187 | + | 0.239347i | ||||
\(87\) | 0.428814 | + | 0.742728i | 0.0459737 | + | 0.0796288i | ||||
\(88\) | 0.500000 | + | 0.866025i | 0.0533002 | + | 0.0923186i | ||||
\(89\) | 8.06458 | − | 13.9683i | 0.854844 | − | 1.48063i | −0.0219454 | − | 0.999759i | \(-0.506986\pi\) |
0.876790 | − | 0.480874i | \(-0.159681\pi\) | |||||||
\(90\) | −6.28256 | −0.662240 | ||||||||
\(91\) | 1.13163 | − | 0.769914i | 0.118627 | − | 0.0807090i | ||||
\(92\) | 5.43702 | 0.566848 | ||||||||
\(93\) | −15.7353 | + | 27.2543i | −1.63167 | + | 2.82614i | ||||
\(94\) | −2.37495 | − | 4.11353i | −0.244957 | − | 0.424279i | ||||
\(95\) | 1.78969 | + | 3.09984i | 0.183619 | + | 0.318037i | ||||
\(96\) | 1.52336 | − | 2.63854i | 0.155478 | − | 0.269295i | ||||
\(97\) | −15.3607 | −1.55964 | −0.779820 | − | 0.626003i | \(-0.784690\pi\) | ||||
−0.779820 | + | 0.626003i | \(0.784690\pi\) | |||||||
\(98\) | 4.35374 | + | 5.48132i | 0.439795 | + | 0.553697i | ||||
\(99\) | −6.28256 | −0.631421 | ||||||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | −2.89029 | − | 5.00612i | −0.287594 | − | 0.498128i | 0.685641 | − | 0.727940i | \(-0.259522\pi\) |
−0.973235 | + | 0.229812i | \(0.926189\pi\) | |||||||
\(102\) | −2.02336 | − | 3.50457i | −0.200343 | − | 0.347004i | ||||
\(103\) | −1.18910 | + | 2.05958i | −0.117166 | + | 0.202937i | −0.918643 | − | 0.395088i | \(-0.870714\pi\) |
0.801478 | + | 0.598025i | \(0.204047\pi\) | |||||||
\(104\) | 0.517321 | 0.0507275 | ||||||||
\(105\) | 6.66464 | − | 4.53436i | 0.650403 | − | 0.442508i | ||||
\(106\) | −1.84229 | −0.178939 | ||||||||
\(107\) | −1.67178 | + | 2.89561i | −0.161617 | + | 0.279929i | −0.935449 | − | 0.353462i | \(-0.885004\pi\) |
0.773832 | + | 0.633391i | \(0.218338\pi\) | |||||||
\(108\) | 5.00053 | + | 8.66118i | 0.481177 | + | 0.833422i | ||||
\(109\) | 5.04122 | + | 8.73165i | 0.482861 | + | 0.836340i | 0.999806 | − | 0.0196784i | \(-0.00626422\pi\) |
−0.516945 | + | 0.856019i | \(0.672931\pi\) | |||||||
\(110\) | −0.500000 | + | 0.866025i | −0.0476731 | + | 0.0825723i | ||||
\(111\) | 15.6707 | 1.48739 | ||||||||
\(112\) | 0.195144 | + | 2.63854i | 0.0184394 | + | 0.249319i | ||||
\(113\) | −1.29790 | −0.122096 | −0.0610479 | − | 0.998135i | \(-0.519444\pi\) | ||||
−0.0610479 | + | 0.998135i | \(0.519444\pi\) | |||||||
\(114\) | 5.45271 | − | 9.44438i | 0.510693 | − | 0.884547i | ||||
\(115\) | 2.71851 | + | 4.70859i | 0.253502 | + | 0.439079i | ||||
\(116\) | −0.140746 | − | 0.243779i | −0.0130679 | − | 0.0226343i | ||||
\(117\) | −1.62505 | + | 2.81467i | −0.150236 | + | 0.260216i | ||||
\(118\) | 6.23258 | 0.573755 | ||||||||
\(119\) | 3.16464 | + | 1.52782i | 0.290102 | + | 0.140055i | ||||
\(120\) | 3.04673 | 0.278127 | ||||||||
\(121\) | −0.500000 | + | 0.866025i | −0.0454545 | + | 0.0787296i | ||||
\(122\) | 5.68801 | + | 9.85192i | 0.514968 | + | 0.891951i | ||||
\(123\) | 4.04673 | + | 7.00914i | 0.364881 | + | 0.631993i | ||||
\(124\) | 5.16464 | − | 8.94543i | 0.463799 | − | 0.803323i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −14.9689 | − | 7.22666i | −1.33354 | − | 0.643802i | ||||
\(127\) | 15.8740 | 1.40859 | 0.704296 | − | 0.709906i | \(-0.251263\pi\) | ||||
0.704296 | + | 0.709906i | \(0.251263\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 3.90436 | + | 6.76255i | 0.343760 | + | 0.595409i | ||||
\(130\) | 0.258661 | + | 0.448013i | 0.0226860 | + | 0.0392934i | ||||
\(131\) | 2.33589 | − | 4.04588i | 0.204088 | − | 0.353490i | −0.745754 | − | 0.666221i | \(-0.767911\pi\) |
0.949842 | + | 0.312731i | \(0.101244\pi\) | |||||||
\(132\) | 3.04673 | 0.265184 | ||||||||
\(133\) | 0.698495 | + | 9.44438i | 0.0605672 | + | 0.818931i | ||||
\(134\) | 13.0935 | 1.13110 | ||||||||
\(135\) | −5.00053 | + | 8.66118i | −0.430377 | + | 0.745436i | ||||
\(136\) | 0.664110 | + | 1.15027i | 0.0569470 | + | 0.0986351i | ||||
\(137\) | −3.17836 | − | 5.50507i | −0.271545 | − | 0.470330i | 0.697712 | − | 0.716378i | \(-0.254201\pi\) |
−0.969258 | + | 0.246048i | \(0.920868\pi\) | |||||||
\(138\) | 8.28256 | − | 14.3458i | 0.705058 | − | 1.22120i | ||||
\(139\) | 15.9218 | 1.35047 | 0.675236 | − | 0.737602i | \(-0.264042\pi\) | ||||
0.675236 | + | 0.737602i | \(0.264042\pi\) | |||||||
\(140\) | −2.18747 | + | 1.48827i | −0.184875 | + | 0.125782i | ||||
\(141\) | −14.4717 | −1.21873 | ||||||||
\(142\) | 5.53959 | − | 9.59486i | 0.464872 | − | 0.805183i | ||||
\(143\) | 0.258661 | + | 0.448013i | 0.0216303 | + | 0.0374647i | ||||
\(144\) | −3.14128 | − | 5.44086i | −0.261773 | − | 0.453405i | ||||
\(145\) | 0.140746 | − | 0.243779i | 0.0116883 | − | 0.0202447i | ||||
\(146\) | 8.95434 | 0.741066 | ||||||||
\(147\) | 21.0951 | − | 3.13749i | 1.73989 | − | 0.258776i | ||||
\(148\) | −5.14344 | −0.422788 | ||||||||
\(149\) | −9.64397 | + | 16.7038i | −0.790065 | + | 1.36843i | 0.135861 | + | 0.990728i | \(0.456620\pi\) |
−0.925926 | + | 0.377705i | \(0.876713\pi\) | |||||||
\(150\) | 1.52336 | + | 2.63854i | 0.124382 | + | 0.215436i | ||||
\(151\) | −3.54015 | − | 6.13172i | −0.288094 | − | 0.498993i | 0.685261 | − | 0.728297i | \(-0.259688\pi\) |
−0.973355 | + | 0.229305i | \(0.926355\pi\) | |||||||
\(152\) | −1.78969 | + | 3.09984i | −0.145163 | + | 0.251430i | ||||
\(153\) | −8.34463 | −0.674623 | ||||||||
\(154\) | −2.18747 | + | 1.48827i | −0.176272 | + | 0.119928i | ||||
\(155\) | 10.3293 | 0.829668 | ||||||||
\(156\) | 0.788069 | − | 1.36497i | 0.0630960 | − | 0.109285i | ||||
\(157\) | −9.63199 | − | 16.6831i | −0.768716 | − | 1.33146i | −0.938259 | − | 0.345933i | \(-0.887563\pi\) |
0.169543 | − | 0.985523i | \(-0.445771\pi\) | |||||||
\(158\) | 5.36746 | + | 9.29671i | 0.427012 | + | 0.739606i | ||||
\(159\) | −2.80648 | + | 4.86097i | −0.222568 | + | 0.385500i | ||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 1.06100 | + | 14.3458i | 0.0836185 | + | 1.13061i | ||||
\(162\) | 11.6229 | 0.913179 | ||||||||
\(163\) | 2.17981 | − | 3.77554i | 0.170736 | − | 0.295723i | −0.767942 | − | 0.640520i | \(-0.778719\pi\) |
0.938677 | + | 0.344797i | \(0.112052\pi\) | |||||||
\(164\) | −1.32822 | − | 2.30055i | −0.103717 | − | 0.179642i | ||||
\(165\) | 1.52336 | + | 2.63854i | 0.118594 | + | 0.205410i | ||||
\(166\) | −6.61078 | + | 11.4502i | −0.513096 | + | 0.888708i | ||||
\(167\) | 1.42493 | 0.110264 | 0.0551322 | − | 0.998479i | \(-0.482442\pi\) | ||||
0.0551322 | + | 0.998479i | \(0.482442\pi\) | |||||||
\(168\) | 7.25919 | + | 3.50457i | 0.560059 | + | 0.270383i | ||||
\(169\) | −12.7324 | −0.979414 | ||||||||
\(170\) | −0.664110 | + | 1.15027i | −0.0509349 | + | 0.0882219i | ||||
\(171\) | −11.2439 | − | 19.4749i | −0.859839 | − | 1.48929i | ||||
\(172\) | −1.28149 | − | 2.21961i | −0.0977128 | − | 0.169244i | ||||
\(173\) | −12.5076 | + | 21.6639i | −0.950939 | + | 1.64707i | −0.207538 | + | 0.978227i | \(0.566545\pi\) |
−0.743400 | + | 0.668847i | \(0.766788\pi\) | |||||||
\(174\) | −0.857629 | −0.0650167 | ||||||||
\(175\) | −2.38262 | − | 1.15027i | −0.180109 | − | 0.0869525i | ||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 9.49449 | − | 16.4449i | 0.713650 | − | 1.23608i | ||||
\(178\) | 8.06458 | + | 13.9683i | 0.604466 | + | 1.04697i | ||||
\(179\) | 1.94253 | + | 3.36455i | 0.145191 | + | 0.251479i | 0.929444 | − | 0.368962i | \(-0.120287\pi\) |
−0.784253 | + | 0.620441i | \(0.786954\pi\) | |||||||
\(180\) | 3.14128 | − | 5.44086i | 0.234137 | − | 0.405537i | ||||
\(181\) | 25.9108 | 1.92594 | 0.962968 | − | 0.269617i | \(-0.0868971\pi\) | ||||
0.962968 | + | 0.269617i | \(0.0868971\pi\) | |||||||
\(182\) | 0.100952 | + | 1.36497i | 0.00748306 | + | 0.101179i | ||||
\(183\) | 34.6596 | 2.56211 | ||||||||
\(184\) | −2.71851 | + | 4.70859i | −0.200411 | + | 0.347122i | ||||
\(185\) | −2.57172 | − | 4.45435i | −0.189077 | − | 0.327490i | ||||
\(186\) | −15.7353 | − | 27.2543i | −1.15377 | − | 1.99838i | ||||
\(187\) | −0.664110 | + | 1.15027i | −0.0485646 | + | 0.0841163i | ||||
\(188\) | 4.74990 | 0.346422 | ||||||||
\(189\) | −21.8771 | + | 14.8843i | −1.59132 | + | 1.08267i | ||||
\(190\) | −3.57939 | −0.259676 | ||||||||
\(191\) | −5.75541 | + | 9.96866i | −0.416447 | + | 0.721307i | −0.995579 | − | 0.0939265i | \(-0.970058\pi\) |
0.579132 | + | 0.815234i | \(0.303391\pi\) | |||||||
\(192\) | 1.52336 | + | 2.63854i | 0.109939 | + | 0.190421i | ||||
\(193\) | 0.797363 | + | 1.38107i | 0.0573954 | + | 0.0994118i | 0.893295 | − | 0.449470i | \(-0.148387\pi\) |
−0.835900 | + | 0.548882i | \(0.815054\pi\) | |||||||
\(194\) | 7.68034 | − | 13.3027i | 0.551416 | − | 0.955081i | ||||
\(195\) | 1.57614 | 0.112870 | ||||||||
\(196\) | −6.92384 | + | 1.02979i | −0.494560 | + | 0.0735565i | ||||
\(197\) | −3.39135 | −0.241624 | −0.120812 | − | 0.992675i | \(-0.538550\pi\) | ||||
−0.120812 | + | 0.992675i | \(0.538550\pi\) | |||||||
\(198\) | 3.14128 | − | 5.44086i | 0.223241 | − | 0.386665i | ||||
\(199\) | −11.4049 | − | 19.7539i | −0.808471 | − | 1.40031i | −0.913922 | − | 0.405889i | \(-0.866962\pi\) |
0.105451 | − | 0.994424i | \(-0.466371\pi\) | |||||||
\(200\) | −0.500000 | − | 0.866025i | −0.0353553 | − | 0.0612372i | ||||
\(201\) | 19.9461 | − | 34.5477i | 1.40689 | − | 2.43681i | ||||
\(202\) | 5.78057 | 0.406720 | ||||||||
\(203\) | 0.615756 | − | 0.418936i | 0.0432176 | − | 0.0294036i | ||||
\(204\) | 4.04673 | 0.283328 | ||||||||
\(205\) | 1.32822 | − | 2.30055i | 0.0927670 | − | 0.160677i | ||||
\(206\) | −1.18910 | − | 2.05958i | −0.0828485 | − | 0.143498i | ||||
\(207\) | −17.0792 | − | 29.5820i | −1.18709 | − | 2.05609i | ||||
\(208\) | −0.258661 | + | 0.448013i | −0.0179349 | + | 0.0310641i | ||||
\(209\) | −3.57939 | −0.247591 | ||||||||
\(210\) | 0.594550 | + | 8.03893i | 0.0410279 | + | 0.554739i | ||||
\(211\) | 7.76630 | 0.534654 | 0.267327 | − | 0.963606i | \(-0.413860\pi\) | ||||
0.267327 | + | 0.963606i | \(0.413860\pi\) | |||||||
\(212\) | 0.921146 | − | 1.59547i | 0.0632645 | − | 0.109577i | ||||
\(213\) | −16.8776 | − | 29.2329i | −1.15644 | − | 2.00301i | ||||
\(214\) | −1.67178 | − | 2.89561i | −0.114280 | − | 0.197940i | ||||
\(215\) | 1.28149 | − | 2.21961i | 0.0873970 | − | 0.151376i | ||||
\(216\) | −10.0011 | −0.680486 | ||||||||
\(217\) | 24.6108 | + | 11.8815i | 1.67069 | + | 0.806569i | ||||
\(218\) | −10.0824 | −0.682869 | ||||||||
\(219\) | 13.6407 | − | 23.6264i | 0.921754 | − | 1.59653i | ||||
\(220\) | −0.500000 | − | 0.866025i | −0.0337100 | − | 0.0583874i | ||||
\(221\) | 0.343558 | + | 0.595060i | 0.0231102 | + | 0.0400281i | ||||
\(222\) | −7.83533 | + | 13.5712i | −0.525873 | + | 0.910839i | ||||
\(223\) | 3.22156 | 0.215732 | 0.107866 | − | 0.994165i | \(-0.465598\pi\) | ||||
0.107866 | + | 0.994165i | \(0.465598\pi\) | |||||||
\(224\) | −2.38262 | − | 1.15027i | −0.159195 | − | 0.0768558i | ||||
\(225\) | 6.28256 | 0.418837 | ||||||||
\(226\) | 0.648948 | − | 1.12401i | 0.0431674 | − | 0.0747681i | ||||
\(227\) | −7.48268 | − | 12.9604i | −0.496643 | − | 0.860211i | 0.503350 | − | 0.864083i | \(-0.332101\pi\) |
−0.999993 | + | 0.00387218i | \(0.998767\pi\) | |||||||
\(228\) | 5.45271 | + | 9.44438i | 0.361115 | + | 0.625469i | ||||
\(229\) | 2.82730 | − | 4.89703i | 0.186834 | − | 0.323605i | −0.757359 | − | 0.652998i | \(-0.773511\pi\) |
0.944193 | + | 0.329393i | \(0.106844\pi\) | |||||||
\(230\) | −5.43702 | −0.358506 | ||||||||
\(231\) | 0.594550 | + | 8.03893i | 0.0391185 | + | 0.528923i | ||||
\(232\) | 0.281492 | 0.0184808 | ||||||||
\(233\) | 12.0189 | − | 20.8174i | 0.787386 | − | 1.36379i | −0.140178 | − | 0.990126i | \(-0.544767\pi\) |
0.927563 | − | 0.373666i | \(-0.121899\pi\) | |||||||
\(234\) | −1.62505 | − | 2.81467i | −0.106233 | − | 0.184001i | ||||
\(235\) | 2.37495 | + | 4.11353i | 0.154925 | + | 0.268337i | ||||
\(236\) | −3.11629 | + | 5.39757i | −0.202853 | + | 0.351352i | ||||
\(237\) | 32.7064 | 2.12451 | ||||||||
\(238\) | −2.90545 | + | 1.97675i | −0.188332 | + | 0.128134i | ||||
\(239\) | 27.0824 | 1.75182 | 0.875909 | − | 0.482477i | \(-0.160263\pi\) | ||||
0.875909 | + | 0.482477i | \(0.160263\pi\) | |||||||
\(240\) | −1.52336 | + | 2.63854i | −0.0983328 | + | 0.170317i | ||||
\(241\) | −7.61078 | − | 13.1823i | −0.490253 | − | 0.849144i | 0.509684 | − | 0.860362i | \(-0.329762\pi\) |
−0.999937 | + | 0.0112181i | \(0.996429\pi\) | |||||||
\(242\) | −0.500000 | − | 0.866025i | −0.0321412 | − | 0.0556702i | ||||
\(243\) | 2.70426 | − | 4.68392i | 0.173479 | − | 0.300474i | ||||
\(244\) | −11.3760 | −0.728275 | ||||||||
\(245\) | −4.35374 | − | 5.48132i | −0.278151 | − | 0.350189i | ||||
\(246\) | −8.09346 | −0.516020 | ||||||||
\(247\) | −0.925846 | + | 1.60361i | −0.0589102 | + | 0.102035i | ||||
\(248\) | 5.16464 | + | 8.94543i | 0.327955 | + | 0.568035i | ||||
\(249\) | 20.1413 | + | 34.8857i | 1.27640 | + | 2.21079i | ||||
\(250\) | 0.500000 | − | 0.866025i | 0.0316228 | − | 0.0547723i | ||||
\(251\) | −16.9433 | −1.06945 | −0.534726 | − | 0.845025i | \(-0.679585\pi\) | ||||
−0.534726 | + | 0.845025i | \(0.679585\pi\) | |||||||
\(252\) | 13.7429 | − | 9.35016i | 0.865724 | − | 0.589004i | ||||
\(253\) | −5.43702 | −0.341822 | ||||||||
\(254\) | −7.93702 | + | 13.7473i | −0.498013 | + | 0.862583i | ||||
\(255\) | 2.02336 | + | 3.50457i | 0.126708 | + | 0.219465i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −3.05422 | + | 5.29007i | −0.190517 | + | 0.329985i | −0.945422 | − | 0.325849i | \(-0.894350\pi\) |
0.754905 | + | 0.655835i | \(0.227683\pi\) | |||||||
\(258\) | −7.80872 | −0.486149 | ||||||||
\(259\) | −1.00371 | − | 13.5712i | −0.0623675 | − | 0.843273i | ||||
\(260\) | −0.517321 | −0.0320829 | ||||||||
\(261\) | −0.884244 | + | 1.53156i | −0.0547333 | + | 0.0948009i | ||||
\(262\) | 2.33589 | + | 4.04588i | 0.144312 | + | 0.249955i | ||||
\(263\) | 7.50803 | + | 13.0043i | 0.462965 | + | 0.801879i | 0.999107 | − | 0.0422491i | \(-0.0134523\pi\) |
−0.536142 | + | 0.844128i | \(0.680119\pi\) | |||||||
\(264\) | −1.52336 | + | 2.63854i | −0.0937566 | + | 0.162391i | ||||
\(265\) | 1.84229 | 0.113171 | ||||||||
\(266\) | −8.52832 | − | 4.11727i | −0.522905 | − | 0.252446i | ||||
\(267\) | 49.1412 | 3.00739 | ||||||||
\(268\) | −6.54673 | + | 11.3393i | −0.399905 | + | 0.692656i | ||||
\(269\) | 12.0824 | + | 20.9274i | 0.736679 | + | 1.27597i | 0.953983 | + | 0.299862i | \(0.0969406\pi\) |
−0.217303 | + | 0.976104i | \(0.569726\pi\) | |||||||
\(270\) | −5.00053 | − | 8.66118i | −0.304323 | − | 0.527103i | ||||
\(271\) | −9.16627 | + | 15.8764i | −0.556811 | + | 0.964425i | 0.440949 | + | 0.897532i | \(0.354642\pi\) |
−0.997760 | + | 0.0668931i | \(0.978691\pi\) | |||||||
\(272\) | −1.32822 | −0.0805352 | ||||||||
\(273\) | 3.75533 | + | 1.81299i | 0.227283 | + | 0.109727i | ||||
\(274\) | 6.35671 | 0.384023 | ||||||||
\(275\) | 0.500000 | − | 0.866025i | 0.0301511 | − | 0.0522233i | ||||
\(276\) | 8.28256 | + | 14.3458i | 0.498551 | + | 0.863516i | ||||
\(277\) | −12.8826 | − | 22.3133i | −0.774040 | − | 1.34068i | −0.935332 | − | 0.353770i | \(-0.884900\pi\) |
0.161292 | − | 0.986907i | \(-0.448434\pi\) | |||||||
\(278\) | −7.96091 | + | 13.7887i | −0.477464 | + | 0.826992i | ||||
\(279\) | −64.8944 | −3.88512 | ||||||||
\(280\) | −0.195144 | − | 2.63854i | −0.0116621 | − | 0.157683i | ||||
\(281\) | −1.25010 | −0.0745747 | −0.0372874 | − | 0.999305i | \(-0.511872\pi\) | ||||
−0.0372874 | + | 0.999305i | \(0.511872\pi\) | |||||||
\(282\) | 7.23583 | − | 12.5328i | 0.430887 | − | 0.746319i | ||||
\(283\) | −4.64110 | − | 8.03863i | −0.275885 | − | 0.477847i | 0.694473 | − | 0.719519i | \(-0.255638\pi\) |
−0.970358 | + | 0.241672i | \(0.922304\pi\) | |||||||
\(284\) | 5.53959 | + | 9.59486i | 0.328714 | + | 0.569350i | ||||
\(285\) | −5.45271 | + | 9.44438i | −0.322991 | + | 0.559436i | ||||
\(286\) | −0.517321 | −0.0305898 | ||||||||
\(287\) | 5.81090 | − | 3.95351i | 0.343007 | − | 0.233368i | ||||
\(288\) | 6.28256 | 0.370203 | ||||||||
\(289\) | 7.61791 | − | 13.1946i | 0.448113 | − | 0.776154i | ||||
\(290\) | 0.140746 | + | 0.243779i | 0.00826488 | + | 0.0143152i | ||||
\(291\) | −23.3999 | − | 40.5298i | −1.37173 | − | 2.37590i | ||||
\(292\) | −4.47717 | + | 7.75468i | −0.262006 | + | 0.453809i | ||||
\(293\) | −19.7845 | −1.15583 | −0.577913 | − | 0.816099i | \(-0.696133\pi\) | ||||
−0.577913 | + | 0.816099i | \(0.696133\pi\) | |||||||
\(294\) | −7.83038 | + | 19.8376i | −0.456677 | + | 1.15695i | ||||
\(295\) | −6.23258 | −0.362875 | ||||||||
\(296\) | 2.57172 | − | 4.45435i | 0.149478 | − | 0.258904i | ||||
\(297\) | −5.00053 | − | 8.66118i | −0.290160 | − | 0.502573i | ||||
\(298\) | −9.64397 | − | 16.7038i | −0.558660 | − | 0.967628i | ||||
\(299\) | −1.40634 | + | 2.43586i | −0.0813308 | + | 0.140869i | ||||
\(300\) | −3.04673 | −0.175903 | ||||||||
\(301\) | 5.60646 | − | 3.81442i | 0.323151 | − | 0.219859i | ||||
\(302\) | 7.08030 | 0.407426 | ||||||||
\(303\) | 8.80592 | − | 15.2523i | 0.505887 | − | 0.876222i | ||||
\(304\) | −1.78969 | − | 3.09984i | −0.102646 | − | 0.177788i | ||||
\(305\) | −5.68801 | − | 9.85192i | −0.325694 | − | 0.564119i | ||||
\(306\) | 4.17231 | − | 7.22666i | 0.238515 | − | 0.413121i | ||||
\(307\) | −25.3150 | −1.44480 | −0.722402 | − | 0.691473i | \(-0.756962\pi\) | ||||
−0.722402 | + | 0.691473i | \(0.756962\pi\) | |||||||
\(308\) | −0.195144 | − | 2.63854i | −0.0111193 | − | 0.150345i | ||||
\(309\) | −7.24573 | −0.412195 | ||||||||
\(310\) | −5.16464 | + | 8.94543i | −0.293332 | + | 0.508066i | ||||
\(311\) | −5.08472 | − | 8.80700i | −0.288328 | − | 0.499399i | 0.685083 | − | 0.728465i | \(-0.259766\pi\) |
−0.973411 | + | 0.229066i | \(0.926433\pi\) | |||||||
\(312\) | 0.788069 | + | 1.36497i | 0.0446156 | + | 0.0772765i | ||||
\(313\) | −0.196594 | + | 0.340511i | −0.0111121 | + | 0.0192468i | −0.871528 | − | 0.490346i | \(-0.836871\pi\) |
0.860416 | + | 0.509593i | \(0.170204\pi\) | |||||||
\(314\) | 19.2640 | 1.08713 | ||||||||
\(315\) | 14.9689 | + | 7.22666i | 0.843404 | + | 0.407176i | ||||
\(316\) | −10.7349 | −0.603886 | ||||||||
\(317\) | −12.5243 | + | 21.6926i | −0.703432 | + | 1.21838i | 0.263822 | + | 0.964571i | \(0.415017\pi\) |
−0.967254 | + | 0.253809i | \(0.918316\pi\) | |||||||
\(318\) | −2.80648 | − | 4.86097i | −0.157380 | − | 0.272590i | ||||
\(319\) | 0.140746 | + | 0.243779i | 0.00788025 | + | 0.0136490i | ||||
\(320\) | 0.500000 | − | 0.866025i | 0.0279508 | − | 0.0484123i | ||||
\(321\) | −10.1869 | −0.568578 | ||||||||
\(322\) | −12.9543 | − | 6.25405i | −0.721917 | − | 0.348525i | ||||
\(323\) | −4.75422 | −0.264532 | ||||||||
\(324\) | −5.81143 | + | 10.0657i | −0.322857 | + | 0.559205i | ||||
\(325\) | −0.258661 | − | 0.448013i | −0.0143479 | − | 0.0248513i | ||||
\(326\) | 2.17981 | + | 3.77554i | 0.120728 | + | 0.209108i | ||||
\(327\) | −15.3592 | + | 26.6030i | −0.849367 | + | 1.47115i | ||||
\(328\) | 2.65644 | 0.146677 | ||||||||
\(329\) | 0.926913 | + | 12.5328i | 0.0511024 | + | 0.690957i | ||||
\(330\) | −3.04673 | −0.167717 | ||||||||
\(331\) | −12.8391 | + | 22.2380i | −0.705702 | + | 1.22231i | 0.260736 | + | 0.965410i | \(0.416035\pi\) |
−0.966438 | + | 0.256901i | \(0.917299\pi\) | |||||||
\(332\) | −6.61078 | − | 11.4502i | −0.362814 | − | 0.628412i | ||||
\(333\) | 16.1570 | + | 27.9847i | 0.885397 | + | 1.53355i | ||||
\(334\) | −0.712465 | + | 1.23403i | −0.0389843 | + | 0.0675229i | ||||
\(335\) | −13.0935 | −0.715372 | ||||||||
\(336\) | −6.66464 | + | 4.53436i | −0.363586 | + | 0.247370i | ||||
\(337\) | 0.293579 | 0.0159922 | 0.00799612 | − | 0.999968i | \(-0.497455\pi\) | ||||
0.00799612 | + | 0.999968i | \(0.497455\pi\) | |||||||
\(338\) | 6.36619 | − | 11.0266i | 0.346275 | − | 0.599766i | ||||
\(339\) | −1.97717 | − | 3.42456i | −0.107385 | − | 0.185996i | ||||
\(340\) | −0.664110 | − | 1.15027i | −0.0360164 | − | 0.0623823i | ||||
\(341\) | −5.16464 | + | 8.94543i | −0.279681 | + | 0.484422i | ||||
\(342\) | 22.4877 | 1.21600 | ||||||||
\(343\) | −4.06829 | − | 18.0679i | −0.219667 | − | 0.975575i | ||||
\(344\) | 2.56298 | 0.138187 | ||||||||
\(345\) | −8.28256 | + | 14.3458i | −0.445918 | + | 0.772353i | ||||
\(346\) | −12.5076 | − | 21.6639i | −0.672415 | − | 1.16466i | ||||
\(347\) | 16.6575 | + | 28.8517i | 0.894222 | + | 1.54884i | 0.834765 | + | 0.550607i | \(0.185604\pi\) |
0.0594573 | + | 0.998231i | \(0.481063\pi\) | |||||||
\(348\) | 0.428814 | − | 0.742728i | 0.0229869 | − | 0.0398144i | ||||
\(349\) | 20.9172 | 1.11967 | 0.559835 | − | 0.828604i | \(-0.310865\pi\) | ||||
0.559835 | + | 0.828604i | \(0.310865\pi\) | |||||||
\(350\) | 2.18747 | − | 1.48827i | 0.116925 | − | 0.0795515i | ||||
\(351\) | −5.17376 | −0.276155 | ||||||||
\(352\) | 0.500000 | − | 0.866025i | 0.0266501 | − | 0.0461593i | ||||
\(353\) | −2.81090 | − | 4.86862i | −0.149609 | − | 0.259131i | 0.781474 | − | 0.623938i | \(-0.214468\pi\) |
−0.931083 | + | 0.364807i | \(0.881135\pi\) | |||||||
\(354\) | 9.49449 | + | 16.4449i | 0.504626 | + | 0.874039i | ||||
\(355\) | −5.53959 | + | 9.59486i | −0.294011 | + | 0.509242i | ||||
\(356\) | −16.1292 | −0.854844 | ||||||||
\(357\) | 0.789694 | + | 10.6775i | 0.0417950 | + | 0.565112i | ||||
\(358\) | −3.88505 | −0.205331 | ||||||||
\(359\) | 10.6336 | − | 18.4180i | 0.561220 | − | 0.972062i | −0.436170 | − | 0.899864i | \(-0.643665\pi\) |
0.997390 | − | 0.0721980i | \(-0.0230014\pi\) | |||||||
\(360\) | 3.14128 | + | 5.44086i | 0.165560 | + | 0.286758i | ||||
\(361\) | 3.09399 | + | 5.35895i | 0.162842 | + | 0.282050i | ||||
\(362\) | −12.9554 | + | 22.4394i | −0.680921 | + | 1.17939i | ||||
\(363\) | −3.04673 | −0.159912 | ||||||||
\(364\) | −1.23258 | − | 0.595060i | −0.0646047 | − | 0.0311896i | ||||
\(365\) | −8.95434 | −0.468691 | ||||||||
\(366\) | −17.3298 | + | 30.0161i | −0.905844 | + | 1.56897i | ||||
\(367\) | −10.8273 | − | 18.7534i | −0.565181 | − | 0.978922i | −0.997033 | − | 0.0769772i | \(-0.975473\pi\) |
0.431852 | − | 0.901944i | \(-0.357860\pi\) | |||||||
\(368\) | −2.71851 | − | 4.70859i | −0.141712 | − | 0.245452i | ||||
\(369\) | −8.34463 | + | 14.4533i | −0.434404 | + | 0.752410i | ||||
\(370\) | 5.14344 | 0.267395 | ||||||||
\(371\) | 4.38948 | + | 2.11914i | 0.227890 | + | 0.110020i | ||||
\(372\) | 31.4705 | 1.63167 | ||||||||
\(373\) | −7.05422 | + | 12.2183i | −0.365254 | + | 0.632638i | −0.988817 | − | 0.149135i | \(-0.952351\pi\) |
0.623563 | + | 0.781773i | \(0.285684\pi\) | |||||||
\(374\) | −0.664110 | − | 1.15027i | −0.0343403 | − | 0.0594792i | ||||
\(375\) | −1.52336 | − | 2.63854i | −0.0786662 | − | 0.136254i | ||||
\(376\) | −2.37495 | + | 4.11353i | −0.122479 | + | 0.212139i | ||||
\(377\) | 0.145622 | 0.00749989 | ||||||||
\(378\) | −1.95165 | − | 26.3883i | −0.100382 | − | 1.35727i | ||||
\(379\) | 13.7674 | 0.707185 | 0.353592 | − | 0.935400i | \(-0.384960\pi\) | ||||
0.353592 | + | 0.935400i | \(0.384960\pi\) | |||||||
\(380\) | 1.78969 | − | 3.09984i | 0.0918094 | − | 0.159018i | ||||
\(381\) | 24.1819 | + | 41.8843i | 1.23888 | + | 2.14580i | ||||
\(382\) | −5.75541 | − | 9.96866i | −0.294472 | − | 0.510041i | ||||
\(383\) | 11.2205 | − | 19.4345i | 0.573340 | − | 0.993055i | −0.422879 | − | 0.906186i | \(-0.638981\pi\) |
0.996220 | − | 0.0868687i | \(-0.0276860\pi\) | |||||||
\(384\) | −3.04673 | −0.155478 | ||||||||
\(385\) | 2.18747 | − | 1.48827i | 0.111484 | − | 0.0758494i | ||||
\(386\) | −1.59473 | −0.0811694 | ||||||||
\(387\) | −8.05105 | + | 13.9448i | −0.409258 | + | 0.708855i | ||||
\(388\) | 7.68034 | + | 13.3027i | 0.389910 | + | 0.675344i | ||||
\(389\) | 8.82695 | + | 15.2887i | 0.447544 | + | 0.775170i | 0.998226 | − | 0.0595461i | \(-0.0189653\pi\) |
−0.550681 | + | 0.834716i | \(0.685632\pi\) | |||||||
\(390\) | −0.788069 | + | 1.36497i | −0.0399054 | + | 0.0691182i | ||||
\(391\) | −7.22156 | −0.365210 | ||||||||
\(392\) | 2.57009 | − | 6.51111i | 0.129809 | − | 0.328861i | ||||
\(393\) | 14.2336 | 0.717992 | ||||||||
\(394\) | 1.69568 | − | 2.93700i | 0.0854270 | − | 0.147964i | ||||
\(395\) | −5.36746 | − | 9.29671i | −0.270066 | − | 0.467768i | ||||
\(396\) | 3.14128 | + | 5.44086i | 0.157855 | + | 0.273413i | ||||
\(397\) | −19.2392 | + | 33.3232i | −0.965586 | + | 1.67244i | −0.257552 | + | 0.966264i | \(0.582916\pi\) |
−0.708034 | + | 0.706179i | \(0.750417\pi\) | |||||||
\(398\) | 22.8098 | 1.14335 | ||||||||
\(399\) | −23.8553 | + | 16.2302i | −1.19426 | + | 0.812528i | ||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −1.78952 | + | 3.09954i | −0.0893643 | + | 0.154784i | −0.907243 | − | 0.420608i | \(-0.861817\pi\) |
0.817878 | + | 0.575391i | \(0.195150\pi\) | |||||||
\(402\) | 19.9461 | + | 34.5477i | 0.994822 | + | 1.72308i | ||||
\(403\) | 2.67178 | + | 4.62766i | 0.133091 | + | 0.230520i | ||||
\(404\) | −2.89029 | + | 5.00612i | −0.143797 | + | 0.249064i | ||||
\(405\) | −11.6229 | −0.577545 | ||||||||
\(406\) | 0.0549313 | + | 0.742728i | 0.00272620 | + | 0.0368610i | ||||
\(407\) | 5.14344 | 0.254951 | ||||||||
\(408\) | −2.02336 | + | 3.50457i | −0.100171 | + | 0.173502i | ||||
\(409\) | −19.7827 | − | 34.2647i | −0.978192 | − | 1.69428i | −0.668972 | − | 0.743288i | \(-0.733265\pi\) |
−0.309220 | − | 0.950990i | \(-0.600068\pi\) | |||||||
\(410\) | 1.32822 | + | 2.30055i | 0.0655962 | + | 0.113616i | ||||
\(411\) | 9.68359 | − | 16.7725i | 0.477656 | − | 0.827325i | ||||
\(412\) | 2.37820 | 0.117166 | ||||||||
\(413\) | −14.8499 | − | 7.16917i | −0.730714 | − | 0.352772i | ||||
\(414\) | 34.1584 | 1.67879 | ||||||||
\(415\) | 6.61078 | − | 11.4502i | 0.324510 | − | 0.562068i | ||||
\(416\) | −0.258661 | − | 0.448013i | −0.0126819 | − | 0.0219657i | ||||
\(417\) | 24.2548 | + | 42.0105i | 1.18776 | + | 2.05726i | ||||
\(418\) | 1.78969 | − | 3.09984i | 0.0875368 | − | 0.151618i | ||||
\(419\) | 32.2846 | 1.57721 | 0.788604 | − | 0.614901i | \(-0.210804\pi\) | ||||
0.788604 | + | 0.614901i | \(0.210804\pi\) | |||||||
\(420\) | −7.25919 | − | 3.50457i | −0.354212 | − | 0.171006i | ||||
\(421\) | 35.8437 | 1.74691 | 0.873457 | − | 0.486902i | \(-0.161873\pi\) | ||||
0.873457 | + | 0.486902i | \(0.161873\pi\) | |||||||
\(422\) | −3.88315 | + | 6.72582i | −0.189029 | + | 0.327408i | ||||
\(423\) | −14.9208 | − | 25.8435i | −0.725472 | − | 1.25655i | ||||
\(424\) | 0.921146 | + | 1.59547i | 0.0447348 | + | 0.0774829i | ||||
\(425\) | 0.664110 | − | 1.15027i | 0.0322141 | − | 0.0557964i | ||||
\(426\) | 33.7553 | 1.63545 | ||||||||
\(427\) | −2.21996 | − | 30.0161i | −0.107431 | − | 1.45258i | ||||
\(428\) | 3.34356 | 0.161617 | ||||||||
\(429\) | −0.788069 | + | 1.36497i | −0.0380483 | + | 0.0659016i | ||||
\(430\) | 1.28149 | + | 2.21961i | 0.0617990 | + | 0.107039i | ||||
\(431\) | 1.02283 | + | 1.77160i | 0.0492680 | + | 0.0853348i | 0.889608 | − | 0.456725i | \(-0.150978\pi\) |
−0.840340 | + | 0.542060i | \(0.817644\pi\) | |||||||
\(432\) | 5.00053 | − | 8.66118i | 0.240588 | − | 0.416711i | ||||
\(433\) | −9.62180 | −0.462394 | −0.231197 | − | 0.972907i | \(-0.574264\pi\) | ||||
−0.231197 | + | 0.972907i | \(0.574264\pi\) | |||||||
\(434\) | −22.5951 | + | 15.3728i | −1.08460 | + | 0.737917i | ||||
\(435\) | 0.857629 | 0.0411202 | ||||||||
\(436\) | 5.04122 | − | 8.73165i | 0.241431 | − | 0.418170i | ||||
\(437\) | −9.73060 | − | 16.8539i | −0.465477 | − | 0.806231i | ||||
\(438\) | 13.6407 | + | 23.6264i | 0.651779 | + | 1.12891i | ||||
\(439\) | 1.93151 | − | 3.34547i | 0.0921858 | − | 0.159670i | −0.816245 | − | 0.577706i | \(-0.803948\pi\) |
0.908431 | + | 0.418036i | \(0.137281\pi\) | |||||||
\(440\) | 1.00000 | 0.0476731 | ||||||||
\(441\) | 27.3527 | + | 34.4367i | 1.30251 | + | 1.63984i | ||||
\(442\) | −0.687117 | −0.0326828 | ||||||||
\(443\) | −16.0021 | + | 27.7165i | −0.760284 | + | 1.31685i | 0.182420 | + | 0.983221i | \(0.441607\pi\) |
−0.942704 | + | 0.333630i | \(0.891726\pi\) | |||||||
\(444\) | −7.83533 | − | 13.5712i | −0.371848 | − | 0.644060i | ||||
\(445\) | −8.06458 | − | 13.9683i | −0.382298 | − | 0.662159i | ||||
\(446\) | −1.61078 | + | 2.78995i | −0.0762726 | + | 0.132108i | ||||
\(447\) | −58.7651 | −2.77950 | ||||||||
\(448\) | 2.18747 | − | 1.48827i | 0.103348 | − | 0.0703142i | ||||
\(449\) | −14.7937 | −0.698159 | −0.349080 | − | 0.937093i | \(-0.613506\pi\) | ||||
−0.349080 | + | 0.937093i | \(0.613506\pi\) | |||||||
\(450\) | −3.14128 | + | 5.44086i | −0.148081 | + | 0.256484i | ||||
\(451\) | 1.32822 | + | 2.30055i | 0.0625435 | + | 0.108328i | ||||
\(452\) | 0.648948 | + | 1.12401i | 0.0305239 | + | 0.0528690i | ||||
\(453\) | 10.7859 | − | 18.6817i | 0.506765 | − | 0.877743i | ||||
\(454\) | 14.9654 | 0.702359 | ||||||||
\(455\) | −0.100952 | − | 1.36497i | −0.00473270 | − | 0.0639910i | ||||
\(456\) | −10.9054 | −0.510693 | ||||||||
\(457\) | −10.3537 | + | 17.9332i | −0.484328 | + | 0.838880i | −0.999838 | − | 0.0180032i | \(-0.994269\pi\) |
0.515510 | + | 0.856883i | \(0.327602\pi\) | |||||||
\(458\) | 2.82730 | + | 4.89703i | 0.132111 | + | 0.228823i | ||||
\(459\) | −6.64181 | − | 11.5040i | −0.310013 | − | 0.536959i | ||||
\(460\) | 2.71851 | − | 4.70859i | 0.126751 | − | 0.219539i | ||||
\(461\) | −27.2847 | −1.27077 | −0.635387 | − | 0.772194i | \(-0.719160\pi\) | ||||
−0.635387 | + | 0.772194i | \(0.719160\pi\) | |||||||
\(462\) | −7.25919 | − | 3.50457i | −0.337728 | − | 0.163047i | ||||
\(463\) | 15.5305 | 0.721762 | 0.360881 | − | 0.932612i | \(-0.382476\pi\) | ||||
0.360881 | + | 0.932612i | \(0.382476\pi\) | |||||||
\(464\) | −0.140746 | + | 0.243779i | −0.00653396 | + | 0.0113172i | ||||
\(465\) | 15.7353 | + | 27.2543i | 0.729706 | + | 1.26389i | ||||
\(466\) | 12.0189 | + | 20.8174i | 0.556766 | + | 0.964347i | ||||
\(467\) | −10.6141 | + | 18.3842i | −0.491163 | + | 0.850720i | −0.999948 | − | 0.0101738i | \(-0.996762\pi\) |
0.508785 | + | 0.860894i | \(0.330095\pi\) | |||||||
\(468\) | 3.25010 | 0.150236 | ||||||||
\(469\) | −31.1967 | − | 15.0611i | −1.44053 | − | 0.695455i | ||||
\(470\) | −4.74990 | −0.219097 | ||||||||
\(471\) | 29.3461 | − | 50.8289i | 1.35219 | − | 2.34207i | ||||
\(472\) | −3.11629 | − | 5.39757i | −0.143439 | − | 0.248443i | ||||
\(473\) | 1.28149 | + | 2.21961i | 0.0589231 | + | 0.102058i | ||||
\(474\) | −16.3532 | + | 28.3245i | −0.751127 | + | 1.30099i | ||||
\(475\) | 3.57939 | 0.164234 | ||||||||
\(476\) | −0.259194 | − | 3.50457i | −0.0118801 | − | 0.160632i | ||||
\(477\) | −11.5743 | −0.529951 | ||||||||
\(478\) | −13.5412 | + | 23.4541i | −0.619361 | + | 1.07276i | ||||
\(479\) | −13.8705 | − | 24.0244i | −0.633760 | − | 1.09770i | −0.986776 | − | 0.162087i | \(-0.948178\pi\) |
0.353017 | − | 0.935617i | \(-0.385156\pi\) | |||||||
\(480\) | −1.52336 | − | 2.63854i | −0.0695318 | − | 0.120433i | ||||
\(481\) | 1.33040 | − | 2.30433i | 0.0606612 | − | 0.105068i | ||||
\(482\) | 15.2216 | 0.693323 | ||||||||
\(483\) | −36.2358 | + | 24.6534i | −1.64879 | + | 1.12177i | ||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −7.68034 | + | 13.3027i | −0.348746 | + | 0.604046i | ||||
\(486\) | 2.70426 | + | 4.68392i | 0.122668 | + | 0.212467i | ||||
\(487\) | 3.01209 | + | 5.21709i | 0.136491 | + | 0.236409i | 0.926166 | − | 0.377116i | \(-0.123084\pi\) |
−0.789675 | + | 0.613525i | \(0.789751\pi\) | |||||||
\(488\) | 5.68801 | − | 9.85192i | 0.257484 | − | 0.445975i | ||||
\(489\) | 13.2826 | 0.600658 | ||||||||
\(490\) | 6.92384 | − | 1.02979i | 0.312787 | − | 0.0465212i | ||||
\(491\) | 2.87043 | 0.129541 | 0.0647704 | − | 0.997900i | \(-0.479368\pi\) | ||||
0.0647704 | + | 0.997900i | \(0.479368\pi\) | |||||||
\(492\) | 4.04673 | − | 7.00914i | 0.182441 | − | 0.315996i | ||||
\(493\) | 0.186942 | + | 0.323792i | 0.00841942 | + | 0.0145829i | ||||
\(494\) | −0.925846 | − | 1.60361i | −0.0416558 | − | 0.0721500i | ||||
\(495\) | −3.14128 | + | 5.44086i | −0.141190 | + | 0.244548i | ||||
\(496\) | −10.3293 | −0.463799 | ||||||||
\(497\) | −24.2354 | + | 16.4888i | −1.08711 | + | 0.739626i | ||||
\(498\) | −40.2825 | −1.80510 | ||||||||
\(499\) | 3.33254 | − | 5.77213i | 0.149185 | − | 0.258396i | −0.781742 | − | 0.623603i | \(-0.785668\pi\) |
0.930926 | + | 0.365207i | \(0.119002\pi\) | |||||||
\(500\) | 0.500000 | + | 0.866025i | 0.0223607 | + | 0.0387298i | ||||
\(501\) | 2.17069 | + | 3.75974i | 0.0969792 | + | 0.167973i | ||||
\(502\) | 8.47166 | − | 14.6733i | 0.378109 | − | 0.654903i | ||||
\(503\) | 22.2479 | 0.991983 | 0.495992 | − | 0.868327i | \(-0.334805\pi\) | ||||
0.495992 | + | 0.868327i | \(0.334805\pi\) | |||||||
\(504\) | 1.22600 | + | 16.5768i | 0.0546105 | + | 0.738390i | ||||
\(505\) | −5.78057 | −0.257232 | ||||||||
\(506\) | 2.71851 | − | 4.70859i | 0.120852 | − | 0.209323i | ||||
\(507\) | −19.3961 | − | 33.5950i | −0.861409 | − | 1.49200i | ||||
\(508\) | −7.93702 | − | 13.7473i | −0.352148 | − | 0.609939i | ||||
\(509\) | 16.5954 | − | 28.7441i | 0.735580 | − | 1.27406i | −0.218888 | − | 0.975750i | \(-0.570243\pi\) |
0.954468 | − | 0.298312i | \(-0.0964236\pi\) | |||||||
\(510\) | −4.04673 | −0.179192 | ||||||||
\(511\) | −21.3348 | − | 10.2999i | −0.943795 | − | 0.455642i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 17.8988 | − | 31.0017i | 0.790253 | − | 1.36876i | ||||
\(514\) | −3.05422 | − | 5.29007i | −0.134716 | − | 0.233335i | ||||
\(515\) | 1.18910 | + | 2.05958i | 0.0523980 | + | 0.0907560i | ||||
\(516\) | 3.90436 | − | 6.76255i | 0.171880 | − | 0.297705i | ||||
\(517\) | −4.74990 | −0.208900 | ||||||||
\(518\) | 12.2549 | + | 5.91636i | 0.538447 | + | 0.259950i | ||||
\(519\) | −76.2148 | −3.34546 | ||||||||
\(520\) | 0.258661 | − | 0.448013i | 0.0113430 | − | 0.0196467i | ||||
\(521\) | −6.70975 | − | 11.6216i | −0.293959 | − | 0.509153i | 0.680783 | − | 0.732485i | \(-0.261640\pi\) |
−0.974742 | + | 0.223333i | \(0.928306\pi\) | |||||||
\(522\) | −0.884244 | − | 1.53156i | −0.0387023 | − | 0.0670344i | ||||
\(523\) | 4.29683 | − | 7.44233i | 0.187887 | − | 0.325430i | −0.756658 | − | 0.653810i | \(-0.773169\pi\) |
0.944546 | + | 0.328380i | \(0.106503\pi\) | |||||||
\(524\) | −4.67178 | −0.204088 | ||||||||
\(525\) | −0.594550 | − | 8.03893i | −0.0259483 | − | 0.350848i | ||||
\(526\) | −15.0161 | −0.654731 | ||||||||
\(527\) | −6.85979 | + | 11.8815i | −0.298817 | + | 0.517566i | ||||
\(528\) | −1.52336 | − | 2.63854i | −0.0662959 | − | 0.114828i | ||||
\(529\) | −3.28057 | − | 5.68212i | −0.142634 | − | 0.247049i | ||||
\(530\) | −0.921146 | + | 1.59547i | −0.0400120 | + | 0.0693028i | ||||
\(531\) | 39.1565 | 1.69925 | ||||||||
\(532\) | 7.82982 | − | 5.32710i | 0.339466 | − | 0.230959i | ||||
\(533\) | 1.37423 | 0.0595247 | ||||||||
\(534\) | −24.5706 | + | 42.5575i | −1.06327 | + | 1.84164i | ||||
\(535\) | 1.67178 | + | 2.89561i | 0.0722773 | + | 0.125188i | ||||
\(536\) | −6.54673 | − | 11.3393i | −0.282776 | − | 0.489782i | ||||
\(537\) | −5.91835 | + | 10.2509i | −0.255396 | + | 0.442358i | ||||
\(538\) | −24.1649 | −1.04182 | ||||||||
\(539\) | 6.92384 | − | 1.02979i | 0.298231 | − | 0.0443562i | ||||
\(540\) | 10.0011 | 0.430377 | ||||||||
\(541\) | −13.2897 | + | 23.0184i | −0.571367 | + | 0.989638i | 0.425058 | + | 0.905166i | \(0.360254\pi\) |
−0.996426 | + | 0.0844716i | \(0.973080\pi\) | |||||||
\(542\) | −9.16627 | − | 15.8764i | −0.393725 | − | 0.681952i | ||||
\(543\) | 39.4716 | + | 68.3668i | 1.69389 | + | 2.93390i | ||||
\(544\) | 0.664110 | − | 1.15027i | 0.0284735 | − | 0.0493175i | ||||
\(545\) | 10.0824 | 0.431884 | ||||||||
\(546\) | −3.44776 | + | 2.34572i | −0.147551 | + | 0.100388i | ||||
\(547\) | 7.17431 | 0.306752 | 0.153376 | − | 0.988168i | \(-0.450986\pi\) | ||||
0.153376 | + | 0.988168i | \(0.450986\pi\) | |||||||
\(548\) | −3.17836 | + | 5.50507i | −0.135773 | + | 0.235165i | ||||
\(549\) | 35.7352 | + | 61.8953i | 1.52514 | + | 2.64163i | ||||
\(550\) | 0.500000 | + | 0.866025i | 0.0213201 | + | 0.0369274i | ||||
\(551\) | −0.503784 | + | 0.872579i | −0.0214619 | + | 0.0371731i | ||||
\(552\) | −16.5651 | −0.705058 | ||||||||
\(553\) | −2.09485 | − | 28.3245i | −0.0890821 | − | 1.20448i | ||||
\(554\) | 25.7652 | 1.09466 | ||||||||
\(555\) | 7.83533 | − | 13.5712i | 0.332591 | − | 0.576065i | ||||
\(556\) | −7.96091 | − | 13.7887i | −0.337618 | − | 0.584772i | ||||
\(557\) | −11.9900 | − | 20.7674i | −0.508035 | − | 0.879942i | −0.999957 | − | 0.00930252i | \(-0.997039\pi\) |
0.491922 | − | 0.870639i | \(-0.336294\pi\) | |||||||
\(558\) | 32.4472 | − | 56.2002i | 1.37360 | − | 2.37914i | ||||
\(559\) | 1.32589 | 0.0560790 | ||||||||
\(560\) | 2.38262 | + | 1.15027i | 0.100684 | + | 0.0486079i | ||||
\(561\) | −4.04673 | −0.170853 | ||||||||
\(562\) | 0.625050 | − | 1.08262i | 0.0263661 | − | 0.0456675i | ||||
\(563\) | 2.40669 | + | 4.16851i | 0.101430 | + | 0.175682i | 0.912274 | − | 0.409580i | \(-0.134325\pi\) |
−0.810844 | + | 0.585262i | \(0.800992\pi\) | |||||||
\(564\) | 7.23583 | + | 12.5328i | 0.304683 | + | 0.527727i | ||||
\(565\) | −0.648948 | + | 1.12401i | −0.0273014 | + | 0.0472875i | ||||
\(566\) | 9.28221 | 0.390160 | ||||||||
\(567\) | −27.6929 | − | 13.3695i | −1.16299 | − | 0.561465i | ||||
\(568\) | −11.0792 | −0.464872 | ||||||||
\(569\) | 20.6118 | − | 35.7008i | 0.864094 | − | 1.49665i | −0.00385087 | − | 0.999993i | \(-0.501226\pi\) |
0.867944 | − | 0.496661i | \(-0.165441\pi\) | |||||||
\(570\) | −5.45271 | − | 9.44438i | −0.228389 | − | 0.395581i | ||||
\(571\) | −8.38155 | − | 14.5173i | −0.350757 | − | 0.607529i | 0.635625 | − | 0.771998i | \(-0.280742\pi\) |
−0.986382 | + | 0.164469i | \(0.947409\pi\) | |||||||
\(572\) | 0.258661 | − | 0.448013i | 0.0108151 | − | 0.0187324i | ||||
\(573\) | −35.0704 | −1.46508 | ||||||||
\(574\) | 0.518388 | + | 7.00914i | 0.0216371 | + | 0.292556i | ||||
\(575\) | 5.43702 | 0.226739 | ||||||||
\(576\) | −3.14128 | + | 5.44086i | −0.130887 | + | 0.226702i | ||||
\(577\) | −1.71391 | − | 2.96859i | −0.0713512 | − | 0.123584i | 0.828143 | − | 0.560518i | \(-0.189398\pi\) |
−0.899494 | + | 0.436934i | \(0.856064\pi\) | |||||||
\(578\) | 7.61791 | + | 13.1946i | 0.316863 | + | 0.548824i | ||||
\(579\) | −2.42935 | + | 4.20775i | −0.100960 | + | 0.174868i | ||||
\(580\) | −0.281492 | −0.0116883 | ||||||||
\(581\) | 28.9218 | − | 19.6773i | 1.19988 | − | 0.816351i | ||||
\(582\) | 46.7998 | 1.93992 | ||||||||
\(583\) | −0.921146 | + | 1.59547i | −0.0381500 | + | 0.0660777i | ||||
\(584\) | −4.47717 | − | 7.75468i | −0.185267 | − | 0.320891i | ||||
\(585\) | 1.62505 | + | 2.81467i | 0.0671875 | + | 0.116372i | ||||
\(586\) | 9.89227 | − | 17.1339i | 0.408646 | − | 0.707796i | ||||
\(587\) | −34.6304 | −1.42935 | −0.714674 | − | 0.699457i | \(-0.753425\pi\) | ||||
−0.714674 | + | 0.699457i | \(0.753425\pi\) | |||||||
\(588\) | −13.2647 | − | 16.7001i | −0.547026 | − | 0.688701i | ||||
\(589\) | −36.9725 | −1.52343 | ||||||||
\(590\) | 3.11629 | − | 5.39757i | 0.128296 | − | 0.222215i | ||||
\(591\) | −5.16627 | − | 8.94824i | −0.212512 | − | 0.368081i | ||||
\(592\) | 2.57172 | + | 4.45435i | 0.105697 | + | 0.183073i | ||||
\(593\) | 5.09346 | − | 8.82213i | 0.209163 | − | 0.362281i | −0.742288 | − | 0.670081i | \(-0.766259\pi\) |
0.951451 | + | 0.307800i | \(0.0995927\pi\) | |||||||
\(594\) | 10.0011 | 0.410349 | ||||||||
\(595\) | 2.90545 | − | 1.97675i | 0.119112 | − | 0.0810390i | ||||
\(596\) | 19.2879 | 0.790065 | ||||||||
\(597\) | 34.7476 | − | 60.1846i | 1.42213 | − | 2.46319i | ||||
\(598\) | −1.40634 | − | 2.43586i | −0.0575096 | − | 0.0996095i | ||||
\(599\) | −0.945602 | − | 1.63783i | −0.0386363 | − | 0.0669200i | 0.846061 | − | 0.533087i | \(-0.178968\pi\) |
−0.884697 | + | 0.466167i | \(0.845635\pi\) | |||||||
\(600\) | 1.52336 | − | 2.63854i | 0.0621911 | − | 0.107718i | ||||
\(601\) | −10.5286 | −0.429472 | −0.214736 | − | 0.976672i | \(-0.568889\pi\) | ||||
−0.214736 | + | 0.976672i | \(0.568889\pi\) | |||||||
\(602\) | 0.500150 | + | 6.76255i | 0.0203846 | + | 0.275621i | ||||
\(603\) | 82.2604 | 3.34990 | ||||||||
\(604\) | −3.54015 | + | 6.13172i | −0.144047 | + | 0.249496i | ||||
\(605\) | 0.500000 | + | 0.866025i | 0.0203279 | + | 0.0352089i | ||||
\(606\) | 8.80592 | + | 15.2523i | 0.357716 | + | 0.619583i | ||||
\(607\) | 15.5983 | − | 27.0171i | 0.633116 | − | 1.09659i | −0.353795 | − | 0.935323i | \(-0.615109\pi\) |
0.986911 | − | 0.161266i | \(-0.0515577\pi\) | |||||||
\(608\) | 3.57939 | 0.145163 | ||||||||
\(609\) | 2.04340 | + | 0.986507i | 0.0828029 | + | 0.0399753i | ||||
\(610\) | 11.3760 | 0.460601 | ||||||||
\(611\) | −1.22861 | + | 2.12802i | −0.0497043 | + | 0.0860904i | ||||
\(612\) | 4.17231 | + | 7.22666i | 0.168656 | + | 0.292120i | ||||
\(613\) | 1.78057 | + | 3.08405i | 0.0719167 | + | 0.124563i | 0.899741 | − | 0.436424i | \(-0.143755\pi\) |
−0.827825 | + | 0.560987i | \(0.810422\pi\) | |||||||
\(614\) | 12.6575 | − | 21.9234i | 0.510815 | − | 0.884758i | ||||
\(615\) | 8.09346 | 0.326360 | ||||||||
\(616\) | 2.38262 | + | 1.15027i | 0.0959984 | + | 0.0463458i | ||||
\(617\) | −36.9604 | −1.48797 | −0.743986 | − | 0.668196i | \(-0.767067\pi\) | ||||
−0.743986 | + | 0.668196i | \(0.767067\pi\) | |||||||
\(618\) | 3.62287 | − | 6.27499i | 0.145733 | − | 0.252417i | ||||
\(619\) | 14.7206 | + | 25.4969i | 0.591673 | + | 1.02481i | 0.994007 | + | 0.109314i | \(0.0348655\pi\) |
−0.402335 | + | 0.915493i | \(0.631801\pi\) | |||||||
\(620\) | −5.16464 | − | 8.94543i | −0.207417 | − | 0.359257i | ||||
\(621\) | 27.1880 | − | 47.0910i | 1.09102 | − | 1.88970i | ||||
\(622\) | 10.1694 | 0.407758 | ||||||||
\(623\) | −3.14751 | − | 42.5575i | −0.126102 | − | 1.70503i | ||||
\(624\) | −1.57614 | −0.0630960 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −0.196594 | − | 0.340511i | −0.00785747 | − | 0.0136095i | ||||
\(627\) | −5.45271 | − | 9.44438i | −0.217760 | − | 0.377172i | ||||
\(628\) | −9.63199 | + | 16.6831i | −0.384358 | + | 0.665728i | ||||
\(629\) | 6.83162 | 0.272395 | ||||||||
\(630\) | −13.7429 | + | 9.35016i | −0.547532 | + | 0.372519i | ||||
\(631\) | 22.5126 | 0.896213 | 0.448106 | − | 0.893980i | \(-0.352099\pi\) | ||||
0.448106 | + | 0.893980i | \(0.352099\pi\) | |||||||
\(632\) | 5.36746 | − | 9.29671i | 0.213506 | − | 0.369803i | ||||
\(633\) | 11.8309 | + | 20.4917i | 0.470237 | + | 0.814474i | ||||
\(634\) | −12.5243 | − | 21.6926i | −0.497402 | − | 0.861525i | ||||
\(635\) | 7.93702 | − | 13.7473i | 0.314971 | − | 0.545546i | ||||
\(636\) | 5.61296 | 0.222568 | ||||||||
\(637\) | 1.32956 | − | 3.36834i | 0.0526792 | − | 0.133458i | ||||
\(638\) | −0.281492 | −0.0111444 | ||||||||
\(639\) | 34.8028 | − | 60.2803i | 1.37678 | − | 2.38465i | ||||
\(640\) | 0.500000 | + | 0.866025i | 0.0197642 | + | 0.0342327i | ||||
\(641\) | 16.2583 | + | 28.1602i | 0.642163 | + | 1.11226i | 0.984949 | + | 0.172846i | \(0.0552962\pi\) |
−0.342786 | + | 0.939414i | \(0.611370\pi\) | |||||||
\(642\) | 5.09346 | − | 8.82213i | 0.201023 | − | 0.348182i | ||||
\(643\) | −3.97258 | −0.156663 | −0.0783315 | − | 0.996927i | \(-0.524959\pi\) | ||||
−0.0783315 | + | 0.996927i | \(0.524959\pi\) | |||||||
\(644\) | 11.8933 | − | 8.09176i | 0.468663 | − | 0.318860i | ||||
\(645\) | 7.80872 | 0.307468 | ||||||||
\(646\) | 2.37711 | − | 4.11727i | 0.0935261 | − | 0.161992i | ||||
\(647\) | 0.610779 | + | 1.05790i | 0.0240122 | + | 0.0415904i | 0.877782 | − | 0.479061i | \(-0.159023\pi\) |
−0.853770 | + | 0.520651i | \(0.825689\pi\) | |||||||
\(648\) | −5.81143 | − | 10.0657i | −0.228295 | − | 0.395418i | ||||
\(649\) | 3.11629 | − | 5.39757i | 0.122325 | − | 0.211873i | ||||
\(650\) | 0.517321 | 0.0202910 | ||||||||
\(651\) | 6.14128 | + | 83.0364i | 0.240696 | + | 3.25445i | ||||
\(652\) | −4.35961 | −0.170736 | ||||||||
\(653\) | −11.6998 | + | 20.2647i | −0.457849 | + | 0.793018i | −0.998847 | − | 0.0480058i | \(-0.984713\pi\) |
0.540998 | + | 0.841024i | \(0.318047\pi\) | |||||||
\(654\) | −15.3592 | − | 26.6030i | −0.600593 | − | 1.04026i | ||||
\(655\) | −2.33589 | − | 4.04588i | −0.0912708 | − | 0.158086i | ||||
\(656\) | −1.32822 | + | 2.30055i | −0.0518583 | + | 0.0898212i | ||||
\(657\) | 56.2562 | 2.19476 | ||||||||
\(658\) | −11.3172 | − | 5.46368i | −0.441190 | − | 0.212996i | ||||
\(659\) | −0.271538 | −0.0105776 | −0.00528882 | − | 0.999986i | \(-0.501683\pi\) | ||||
−0.00528882 | + | 0.999986i | \(0.501683\pi\) | |||||||
\(660\) | 1.52336 | − | 2.63854i | 0.0592969 | − | 0.102705i | ||||
\(661\) | 16.8152 | + | 29.1248i | 0.654036 | + | 1.13282i | 0.982135 | + | 0.188180i | \(0.0602589\pi\) |
−0.328098 | + | 0.944644i | \(0.606408\pi\) | |||||||
\(662\) | −12.8391 | − | 22.2380i | −0.499006 | − | 0.864304i | ||||
\(663\) | −1.04673 | + | 1.81299i | −0.0406516 | + | 0.0704106i | ||||
\(664\) | 13.2216 | 0.513096 | ||||||||
\(665\) | 8.52832 | + | 4.11727i | 0.330714 | + | 0.159661i | ||||
\(666\) | −32.3140 | −1.25214 | ||||||||
\(667\) | −0.765237 | + | 1.32543i | −0.0296301 | + | 0.0513209i | ||||
\(668\) | −0.712465 | − | 1.23403i | −0.0275661 | − | 0.0477459i | ||||
\(669\) | 4.90761 | + | 8.50023i | 0.189739 | + | 0.328638i | ||||
\(670\) | 6.54673 | − | 11.3393i | 0.252922 | − | 0.438074i | ||||
\(671\) | 11.3760 | 0.439166 | ||||||||
\(672\) | −0.594550 | − | 8.03893i | −0.0229353 | − | 0.310109i | ||||
\(673\) | −44.1409 | −1.70151 | −0.850753 | − | 0.525565i | \(-0.823854\pi\) | ||||
−0.850753 | + | 0.525565i | \(0.823854\pi\) | |||||||
\(674\) | −0.146789 | + | 0.254247i | −0.00565411 | + | 0.00979321i | ||||
\(675\) | 5.00053 | + | 8.66118i | 0.192471 | + | 0.333369i | ||||
\(676\) | 6.36619 | + | 11.0266i | 0.244853 | + | 0.424099i | ||||
\(677\) | −13.4249 | + | 23.2527i | −0.515962 | + | 0.893672i | 0.483866 | + | 0.875142i | \(0.339232\pi\) |
−0.999828 | + | 0.0185304i | \(0.994101\pi\) | |||||||
\(678\) | 3.95434 | 0.151865 | ||||||||
\(679\) | −33.6011 | + | 22.8609i | −1.28949 | + | 0.877320i | ||||
\(680\) | 1.32822 | 0.0509349 | ||||||||
\(681\) | 22.7977 | − | 39.4868i | 0.873610 | − | 1.51314i | ||||
\(682\) | −5.16464 | − | 8.94543i | −0.197764 | − | 0.342538i | ||||
\(683\) | 6.33271 | + | 10.9686i | 0.242315 | + | 0.419701i | 0.961373 | − | 0.275248i | \(-0.0887601\pi\) |
−0.719059 | + | 0.694949i | \(0.755427\pi\) | |||||||
\(684\) | −11.2439 | + | 19.4749i | −0.429920 | + | 0.744643i | ||||
\(685\) | −6.35671 | −0.242877 | ||||||||
\(686\) | 17.6814 | + | 5.51070i | 0.675079 | + | 0.210400i | ||||
\(687\) | 17.2281 | 0.657291 | ||||||||
\(688\) | −1.28149 | + | 2.21961i | −0.0488564 | + | 0.0846218i | ||||
\(689\) | 0.476528 | + | 0.825371i | 0.0181543 | + | 0.0314441i | ||||
\(690\) | −8.28256 | − | 14.3458i | −0.315312 | − | 0.546136i | ||||
\(691\) | −6.58505 | + | 11.4056i | −0.250507 | + | 0.433891i | −0.963666 | − | 0.267112i | \(-0.913931\pi\) |
0.713158 | + | 0.701003i | \(0.247264\pi\) | |||||||
\(692\) | 25.0153 | 0.950939 | ||||||||
\(693\) | −13.7429 | + | 9.35016i | −0.522051 | + | 0.355183i | ||||
\(694\) | −33.3150 | −1.26462 | ||||||||
\(695\) | 7.96091 | − | 13.7887i | 0.301975 | − | 0.523036i | ||||
\(696\) | 0.428814 | + | 0.742728i | 0.0162542 | + | 0.0281530i | ||||
\(697\) | 1.76417 | + | 3.05563i | 0.0668227 | + | 0.115740i | ||||
\(698\) | −10.4586 | + | 18.1148i | −0.395863 | + | 0.685655i | ||||
\(699\) | 73.2368 | 2.77007 | ||||||||
\(700\) | 0.195144 | + | 2.63854i | 0.00737574 | + | 0.0997276i | ||||
\(701\) | −24.5503 | −0.927253 | −0.463627 | − | 0.886031i | \(-0.653452\pi\) | ||||
−0.463627 | + | 0.886031i | \(0.653452\pi\) | |||||||
\(702\) | 2.58688 | − | 4.48061i | 0.0976355 | − | 0.169110i | ||||
\(703\) | 9.20518 | + | 15.9438i | 0.347180 | + | 0.601333i | ||||
\(704\) | 0.500000 | + | 0.866025i | 0.0188445 | + | 0.0326396i | ||||
\(705\) | −7.23583 | + | 12.5328i | −0.272517 | + | 0.472013i | ||||
\(706\) | 5.62180 | 0.211579 | ||||||||
\(707\) | −13.7729 | − | 6.64924i | −0.517983 | − | 0.250070i | ||||
\(708\) | −18.9890 | −0.713650 | ||||||||
\(709\) | 1.43992 | − | 2.49401i | 0.0540772 | − | 0.0936645i | −0.837720 | − | 0.546101i | \(-0.816112\pi\) |
0.891797 | + | 0.452436i | \(0.149445\pi\) | |||||||
\(710\) | −5.53959 | − | 9.59486i | −0.207897 | − | 0.360089i | ||||
\(711\) | 33.7214 | + | 58.4071i | 1.26465 | + | 2.19044i | ||||
\(712\) | 8.06458 | − | 13.9683i | 0.302233 | − | 0.523483i | ||||
\(713\) | −56.1605 | −2.10323 | ||||||||
\(714\) | −9.64181 | − | 4.65484i | −0.360836 | − | 0.174203i | ||||
\(715\) | 0.517321 | 0.0193467 | ||||||||
\(716\) | 1.94253 | − | 3.36455i | 0.0725956 | − | 0.125739i | ||||
\(717\) | 41.2564 | + | 71.4582i | 1.54075 | + | 2.66866i | ||||
\(718\) | 10.6336 | + | 18.4180i | 0.396843 | + | 0.687352i | ||||
\(719\) | −6.29599 | + | 10.9050i | −0.234801 | + | 0.406687i | −0.959215 | − | 0.282678i | \(-0.908777\pi\) |
0.724414 | + | 0.689365i | \(0.242111\pi\) | |||||||
\(720\) | −6.28256 | −0.234137 | ||||||||
\(721\) | 0.464091 | + | 6.27499i | 0.0172836 | + | 0.233693i | ||||
\(722\) | −6.18798 | −0.230293 | ||||||||
\(723\) | 23.1880 | − | 40.1628i | 0.862370 | − | 1.49367i | ||||
\(724\) | −12.9554 | − | 22.4394i | −0.481484 | − | 0.833954i | ||||
\(725\) | −0.140746 | − | 0.243779i | −0.00522717 | − | 0.00905372i | ||||
\(726\) | 1.52336 | − | 2.63854i | 0.0565374 | − | 0.0979256i | ||||
\(727\) | 4.93682 | 0.183096 | 0.0915482 | − | 0.995801i | \(-0.470818\pi\) | ||||
0.0915482 | + | 0.995801i | \(0.470818\pi\) | |||||||
\(728\) | 1.13163 | − | 0.769914i | 0.0419409 | − | 0.0285349i | ||||
\(729\) | −18.3903 | −0.681122 | ||||||||
\(730\) | 4.47717 | − | 7.75468i | 0.165707 | − | 0.287014i | ||||
\(731\) | 1.70210 | + | 2.94813i | 0.0629546 | + | 0.109041i | ||||
\(732\) | −17.3298 | − | 30.0161i | −0.640529 | − | 1.10943i | ||||
\(733\) | 17.2119 | − | 29.8119i | 0.635735 | − | 1.10113i | −0.350623 | − | 0.936517i | \(-0.614030\pi\) |
0.986359 | − | 0.164609i | \(-0.0526364\pi\) | |||||||
\(734\) | 21.6546 | 0.799286 | ||||||||
\(735\) | 7.83038 | − | 19.8376i | 0.288828 | − | 0.731721i | ||||
\(736\) | 5.43702 | 0.200411 | ||||||||
\(737\) | 6.54673 | − | 11.3393i | 0.241152 | − | 0.417687i | ||||
\(738\) | −8.34463 | − | 14.4533i | −0.307170 | − | 0.532034i | ||||
\(739\) | −0.663019 | − | 1.14838i | −0.0243895 | − | 0.0422439i | 0.853573 | − | 0.520973i | \(-0.174431\pi\) |
−0.877963 | + | 0.478729i | \(0.841098\pi\) | |||||||
\(740\) | −2.57172 | + | 4.45435i | −0.0945383 | + | 0.163745i | ||||
\(741\) | −5.64161 | −0.207250 | ||||||||
\(742\) | −4.02997 | + | 2.74183i | −0.147945 | + | 0.100656i | ||||
\(743\) | 20.1227 | 0.738229 | 0.369115 | − | 0.929384i | \(-0.379661\pi\) | ||||
0.369115 | + | 0.929384i | \(0.379661\pi\) | |||||||
\(744\) | −15.7353 | + | 27.2543i | −0.576883 | + | 0.999191i | ||||
\(745\) | 9.64397 | + | 16.7038i | 0.353328 | + | 0.611982i | ||||
\(746\) | −7.05422 | − | 12.2183i | −0.258273 | − | 0.447343i | ||||
\(747\) | −41.5326 | + | 71.9366i | −1.51960 | + | 2.63202i | ||||
\(748\) | 1.32822 | 0.0485646 | ||||||||
\(749\) | 0.652474 | + | 8.82213i | 0.0238409 | + | 0.322354i | ||||
\(750\) | 3.04673 | 0.111251 | ||||||||
\(751\) | −0.0109192 | + | 0.0189127i | −0.000398449 | + | 0.000690133i | −0.866225 | − | 0.499655i | \(-0.833460\pi\) |
0.865826 | + | 0.500345i | \(0.166793\pi\) | |||||||
\(752\) | −2.37495 | − | 4.11353i | −0.0866055 | − | 0.150005i | ||||
\(753\) | −25.8108 | − | 44.7057i | −0.940600 | − | 1.62917i | ||||
\(754\) | −0.0728108 | + | 0.126112i | −0.00265161 | + | 0.00459273i | ||||
\(755\) | −7.08030 | −0.257679 | ||||||||
\(756\) | 23.8287 | + | 11.5040i | 0.866643 | + | 0.418395i | ||||
\(757\) | 19.4216 | 0.705891 | 0.352946 | − | 0.935644i | \(-0.385180\pi\) | ||||
0.352946 | + | 0.935644i | \(0.385180\pi\) | |||||||
\(758\) | −6.88371 | + | 11.9229i | −0.250028 | + | 0.433061i | ||||
\(759\) | −8.28256 | − | 14.3458i | −0.300638 | − | 0.520720i | ||||
\(760\) | 1.78969 | + | 3.09984i | 0.0649190 | + | 0.112443i | ||||
\(761\) | 11.9654 | − | 20.7246i | 0.433744 | − | 0.751266i | −0.563448 | − | 0.826151i | \(-0.690526\pi\) |
0.997192 | + | 0.0748849i | \(0.0238589\pi\) | |||||||
\(762\) | −48.3639 | −1.75204 | ||||||||
\(763\) | 24.0226 | + | 11.5976i | 0.869677 | + | 0.419860i | ||||
\(764\) | 11.5108 | 0.416447 | ||||||||
\(765\) | −4.17231 | + | 7.22666i | −0.150850 | + | 0.261280i | ||||
\(766\) | 11.2205 | + | 19.4345i | 0.405413 | + | 0.702196i | ||||
\(767\) | −1.61212 | − | 2.79228i | −0.0582104 | − | 0.100823i | ||||
\(768\) | 1.52336 | − | 2.63854i | 0.0549697 | − | 0.0952103i | ||||
\(769\) | 21.7153 | 0.783072 | 0.391536 | − | 0.920163i | \(-0.371944\pi\) | ||||
0.391536 | + | 0.920163i | \(0.371944\pi\) | |||||||
\(770\) | 0.195144 | + | 2.63854i | 0.00703249 | + | 0.0950866i | ||||
\(771\) | −18.6108 | −0.670251 | ||||||||
\(772\) | 0.797363 | − | 1.38107i | 0.0286977 | − | 0.0497059i | ||||
\(773\) | −24.9674 | − | 43.2448i | −0.898015 | − | 1.55541i | −0.830029 | − | 0.557721i | \(-0.811676\pi\) |
−0.0679859 | − | 0.997686i | \(-0.521657\pi\) | |||||||
\(774\) | −8.05105 | − | 13.9448i | −0.289389 | − | 0.501236i | ||||
\(775\) | 5.16464 | − | 8.94543i | 0.185519 | − | 0.321329i | ||||
\(776\) | −15.3607 | −0.551416 | ||||||||
\(777\) | 34.2792 | − | 23.3222i | 1.22976 | − | 0.836679i | ||||
\(778\) | −17.6539 | −0.632923 | ||||||||
\(779\) | −4.75422 | + | 8.23455i | −0.170338 | + | 0.295033i | ||||
\(780\) | −0.788069 | − | 1.36497i | −0.0282174 | − | 0.0488739i | ||||
\(781\) | −5.53959 | − | 9.59486i | −0.198222 | − | 0.343331i | ||||
\(782\) | 3.61078 | − | 6.25405i | 0.129121 | − | 0.223644i | ||||
\(783\) | −2.81522 | −0.100608 | ||||||||
\(784\) | 4.35374 | + | 5.48132i | 0.155491 | + | 0.195762i | ||||
\(785\) | −19.2640 | −0.687561 | ||||||||
\(786\) | −7.11682 | + | 12.3267i | −0.253849 | + | 0.439679i | ||||
\(787\) | 19.3347 | + | 33.4886i | 0.689207 | + | 1.19374i | 0.972095 | + | 0.234588i | \(0.0753741\pi\) |
−0.282888 | + | 0.959153i | \(0.591293\pi\) | |||||||
\(788\) | 1.69568 | + | 2.93700i | 0.0604060 | + | 0.104626i | ||||
\(789\) | −22.8749 | + | 39.6205i | −0.814369 | + | 1.41053i | ||||
\(790\) | 10.7349 | 0.381931 | ||||||||
\(791\) | −2.83912 | + | 1.93162i | −0.100947 | + | 0.0686806i | ||||
\(792\) | −6.28256 | −0.223241 | ||||||||
\(793\) | 2.94253 | − | 5.09661i | 0.104492 | − | 0.180986i | ||||
\(794\) | −19.2392 | − | 33.3232i | −0.682772 | − | 1.18260i | ||||
\(795\) | 2.80648 | + | 4.86097i | 0.0995356 | + | 0.172401i | ||||
\(796\) | −11.4049 | + | 19.7539i | −0.404236 | + | 0.700157i | ||||
\(797\) | −31.3996 | −1.11223 | −0.556115 | − | 0.831105i | \(-0.687709\pi\) | ||||
−0.556115 | + | 0.831105i | \(0.687709\pi\) | |||||||
\(798\) | −2.12813 | − | 28.7745i | −0.0753348 | − | 1.01860i | ||||
\(799\) | −6.30892 | −0.223193 | ||||||||
\(800\) | −0.500000 | + | 0.866025i | −0.0176777 | + | 0.0306186i | ||||
\(801\) | 50.6662 | + | 87.7565i | 1.79020 | + | 3.10072i | ||||
\(802\) | −1.78952 | − | 3.09954i | −0.0631901 | − | 0.109448i | ||||
\(803\) | 4.47717 | − | 7.75468i | 0.157996 | − | 0.273657i | ||||
\(804\) | −39.8922 | −1.40689 | ||||||||
\(805\) | 12.9543 | + | 6.25405i | 0.456580 | + | 0.220426i | ||||
\(806\) | −5.34356 | −0.188219 | ||||||||
\(807\) | −36.8119 | + | 63.7601i | −1.29584 | + | 2.24446i | ||||
\(808\) | −2.89029 | − | 5.00612i | −0.101680 | − | 0.176115i | ||||
\(809\) | 14.8587 | + | 25.7360i | 0.522404 | + | 0.904830i | 0.999660 | + | 0.0260660i | \(0.00829800\pi\) |
−0.477256 | + | 0.878764i | \(0.658369\pi\) | |||||||
\(810\) | 5.81143 | − | 10.0657i | 0.204193 | − | 0.353673i | ||||
\(811\) | 49.6021 | 1.74177 | 0.870883 | − | 0.491491i | \(-0.163548\pi\) | ||||
0.870883 | + | 0.491491i | \(0.163548\pi\) | |||||||
\(812\) | −0.670687 | − | 0.323792i | −0.0235365 | − | 0.0113629i | ||||
\(813\) | −55.8543 | −1.95890 | ||||||||
\(814\) | −2.57172 | + | 4.45435i | −0.0901387 | + | 0.156125i | ||||
\(815\) | −2.17981 | − | 3.77554i | −0.0763553 | − | 0.132251i | ||||
\(816\) | −2.02336 | − | 3.50457i | −0.0708319 | − | 0.122684i | ||||
\(817\) | −4.58696 | + | 7.94484i | −0.160477 | + | 0.277955i | ||||
\(818\) | 39.5654 | 1.38337 | ||||||||
\(819\) | 0.634237 | + | 8.57553i | 0.0221620 | + | 0.299653i | ||||
\(820\) | −2.65644 | −0.0927670 | ||||||||
\(821\) | −3.53571 | + | 6.12403i | −0.123397 | + | 0.213730i | −0.921105 | − | 0.389314i | \(-0.872712\pi\) |
0.797708 | + | 0.603044i | \(0.206046\pi\) | |||||||
\(822\) | 9.68359 | + | 16.7725i | 0.337754 | + | 0.585007i | ||||
\(823\) | −21.4891 | − | 37.2203i | −0.749064 | − | 1.29742i | −0.948272 | − | 0.317460i | \(-0.897170\pi\) |
0.199208 | − | 0.979957i | \(-0.436163\pi\) | |||||||
\(824\) | −1.18910 | + | 2.05958i | −0.0414243 | + | 0.0717489i | ||||
\(825\) | 3.04673 | 0.106073 | ||||||||
\(826\) | 13.6336 | − | 9.27577i | 0.474374 | − | 0.322745i | ||||
\(827\) | 43.3864 | 1.50869 | 0.754347 | − | 0.656476i | \(-0.227954\pi\) | ||||
0.754347 | + | 0.656476i | \(0.227954\pi\) | |||||||
\(828\) | −17.0792 | + | 29.5820i | −0.593543 | + | 1.02805i | ||||
\(829\) | 27.6432 | + | 47.8795i | 0.960089 | + | 1.66292i | 0.722266 | + | 0.691615i | \(0.243100\pi\) |
0.237823 | + | 0.971309i | \(0.423566\pi\) | |||||||
\(830\) | 6.61078 | + | 11.4502i | 0.229464 | + | 0.397442i | ||||
\(831\) | 39.2498 | − | 67.9826i | 1.36156 | − | 2.35829i | ||||
\(832\) | 0.517321 | 0.0179349 | ||||||||
\(833\) | 9.19639 | − | 1.36779i | 0.318636 | − | 0.0473911i | ||||
\(834\) | −48.5095 | −1.67975 | ||||||||
\(835\) | 0.712465 | − | 1.23403i | 0.0246559 | − | 0.0427052i | ||||
\(836\) | 1.78969 | + | 3.09984i | 0.0618979 | + | 0.107210i | ||||
\(837\) | −51.6519 | − | 89.4638i | −1.78535 | − | 3.09232i | ||||
\(838\) | −16.1423 | + | 27.9593i | −0.557627 | + | 0.965839i | ||||
\(839\) | −23.1413 | −0.798925 | −0.399462 | − | 0.916750i | \(-0.630803\pi\) | ||||
−0.399462 | + | 0.916750i | \(0.630803\pi\) | |||||||
\(840\) | 6.66464 | − | 4.53436i | 0.229952 | − | 0.156450i | ||||
\(841\) | −28.9208 | −0.997268 | ||||||||
\(842\) | −17.9218 | + | 31.0415i | −0.617627 | + | 1.06976i | ||||
\(843\) | −1.90436 | − | 3.29844i | −0.0655896 | − | 0.113604i | ||||
\(844\) | −3.88315 | − | 6.72582i | −0.133664 | − | 0.231512i | ||||
\(845\) | −6.36619 | + | 11.0266i | −0.219004 | + | 0.379325i | ||||
\(846\) | 29.8415 | 1.02597 | ||||||||
\(847\) | 0.195144 | + | 2.63854i | 0.00670522 | + | 0.0906615i | ||||
\(848\) | −1.84229 | −0.0632645 | ||||||||
\(849\) | 14.1402 | − | 24.4915i | 0.485290 | − | 0.840547i | ||||
\(850\) | 0.664110 | + | 1.15027i | 0.0227788 | + | 0.0394540i | ||||
\(851\) | 13.9825 | + | 24.2184i | 0.479313 | + | 0.830195i | ||||
\(852\) | −16.8776 | + | 29.2329i | −0.578218 | + | 1.00150i | ||||
\(853\) | −24.6972 | −0.845616 | −0.422808 | − | 0.906219i | \(-0.638955\pi\) | ||||
−0.422808 | + | 0.906219i | \(0.638955\pi\) | |||||||
\(854\) | 27.1047 | + | 13.0855i | 0.927504 | + | 0.447777i | ||||
\(855\) | −22.4877 | −0.769064 | ||||||||
\(856\) | −1.67178 | + | 2.89561i | −0.0571402 | + | 0.0989698i | ||||
\(857\) | −6.75937 | − | 11.7076i | −0.230896 | − | 0.399923i | 0.727176 | − | 0.686451i | \(-0.240832\pi\) |
−0.958072 | + | 0.286528i | \(0.907499\pi\) | |||||||
\(858\) | −0.788069 | − | 1.36497i | −0.0269042 | − | 0.0465995i | ||||
\(859\) | −18.0696 | + | 31.2974i | −0.616525 | + | 1.06785i | 0.373589 | + | 0.927594i | \(0.378127\pi\) |
−0.990115 | + | 0.140259i | \(0.955206\pi\) | |||||||
\(860\) | −2.56298 | −0.0873970 | ||||||||
\(861\) | 19.2836 | + | 9.30969i | 0.657184 | + | 0.317273i | ||||
\(862\) | −2.04566 | −0.0696755 | ||||||||
\(863\) | −13.6532 | + | 23.6480i | −0.464760 | + | 0.804988i | −0.999191 | − | 0.0402243i | \(-0.987193\pi\) |
0.534431 | + | 0.845212i | \(0.320526\pi\) | |||||||
\(864\) | 5.00053 | + | 8.66118i | 0.170122 | + | 0.294659i | ||||
\(865\) | 12.5076 | + | 21.6639i | 0.425273 | + | 0.736594i | ||||
\(866\) | 4.81090 | − | 8.33272i | 0.163481 | − | 0.283157i | ||||
\(867\) | 46.4194 | 1.57649 | ||||||||
\(868\) | −2.01570 | − | 27.2543i | −0.0684172 | − | 0.925071i | ||||
\(869\) | 10.7349 | 0.364157 | ||||||||
\(870\) | −0.428814 | + | 0.742728i | −0.0145382 | + | 0.0251809i | ||||
\(871\) | −3.38676 | − | 5.86604i | −0.114756 | − | 0.198763i | ||||
\(872\) | 5.04122 | + | 8.73165i | 0.170717 | + | 0.295691i | ||||
\(873\) | 48.2522 | − | 83.5752i | 1.63309 | − | 2.82859i | ||||
\(874\) | 19.4612 | 0.658285 | ||||||||
\(875\) | −2.18747 | + | 1.48827i | −0.0739502 | + | 0.0503128i | ||||
\(876\) | −27.2814 | −0.921754 | ||||||||
\(877\) | −14.3795 | + | 24.9061i | −0.485563 | + | 0.841019i | −0.999862 | − | 0.0165913i | \(-0.994719\pi\) |
0.514300 | + | 0.857611i | \(0.328052\pi\) | |||||||
\(878\) | 1.93151 | + | 3.34547i | 0.0651852 | + | 0.112904i | ||||
\(879\) | −30.1391 | − | 52.2024i | −1.01657 | − | 1.76074i | ||||
\(880\) | −0.500000 | + | 0.866025i | −0.0168550 | + | 0.0291937i | ||||
\(881\) | 25.7980 | 0.869157 | 0.434578 | − | 0.900634i | \(-0.356897\pi\) | ||||
0.434578 | + | 0.900634i | \(0.356897\pi\) | |||||||
\(882\) | −43.4994 | + | 6.46972i | −1.46470 | + | 0.217847i | ||||
\(883\) | −31.9404 | −1.07488 | −0.537439 | − | 0.843302i | \(-0.680608\pi\) | ||||
−0.537439 | + | 0.843302i | \(0.680608\pi\) | |||||||
\(884\) | 0.343558 | − | 0.595060i | 0.0115551 | − | 0.0200140i | ||||
\(885\) | −9.49449 | − | 16.4449i | −0.319154 | − | 0.552791i | ||||
\(886\) | −16.0021 | − | 27.7165i | −0.537602 | − | 0.931154i | ||||
\(887\) | −5.95751 | + | 10.3187i | −0.200034 | + | 0.346469i | −0.948539 | − | 0.316660i | \(-0.897439\pi\) |
0.748505 | + | 0.663129i | \(0.230772\pi\) | |||||||
\(888\) | 15.6707 | 0.525873 | ||||||||
\(889\) | 34.7241 | − | 23.6249i | 1.16461 | − | 0.792353i | ||||
\(890\) | 16.1292 | 0.540651 | ||||||||
\(891\) | 5.81143 | − | 10.0657i | 0.194690 | − | 0.337214i | ||||
\(892\) | −1.61078 | − | 2.78995i | −0.0539329 | − | 0.0934145i | ||||
\(893\) | −8.50087 | − | 14.7239i | −0.284471 | − | 0.492718i | ||||
\(894\) | 29.3826 | − | 50.8921i | 0.982700 | − | 1.70209i | ||||
\(895\) | 3.88505 | 0.129863 | ||||||||
\(896\) | 0.195144 | + | 2.63854i | 0.00651929 | + | 0.0881476i | ||||
\(897\) | −8.56948 | −0.286127 | ||||||||
\(898\) | 7.39686 | − | 12.8117i | 0.246837 | − | 0.427533i | ||||
\(899\) | 1.45380 | + | 2.51806i | 0.0484871 | + | 0.0839821i | ||||
\(900\) | −3.14128 | − | 5.44086i | −0.104709 | − | 0.181362i | ||||
\(901\) | −1.22348 | + | 2.11914i | −0.0407602 | + | 0.0705987i | ||||
\(902\) | −2.65644 | −0.0884498 | ||||||||
\(903\) | 18.6052 | + | 8.98216i | 0.619142 | + | 0.298907i | ||||
\(904\) | −1.29790 | −0.0431674 | ||||||||
\(905\) | 12.9554 | − | 22.4394i | 0.430652 | − | 0.745912i | ||||
\(906\) | 10.7859 | + | 18.6817i | 0.358337 | + | 0.620658i | ||||
\(907\) | 15.2288 | + | 26.3771i | 0.505665 | + | 0.875838i | 0.999979 | + | 0.00655433i | \(0.00208632\pi\) |
−0.494313 | + | 0.869284i | \(0.664580\pi\) | |||||||
\(908\) | −7.48268 | + | 12.9604i | −0.248321 | + | 0.430105i | ||||
\(909\) | 36.3168 | 1.20455 | ||||||||
\(910\) | 1.23258 | + | 0.595060i | 0.0408596 | + | 0.0197261i | ||||
\(911\) | 13.2127 | 0.437757 | 0.218879 | − | 0.975752i | \(-0.429760\pi\) | ||||
0.218879 | + | 0.975752i | \(0.429760\pi\) | |||||||
\(912\) | 5.45271 | − | 9.44438i | 0.180557 | − | 0.312735i | ||||
\(913\) | 6.61078 | + | 11.4502i | 0.218785 | + | 0.378947i | ||||
\(914\) | −10.3537 | − | 17.9332i | −0.342471 | − | 0.593178i | ||||
\(915\) | 17.3298 | − | 30.0161i | 0.572906 | − | 0.992303i | ||||
\(916\) | −5.65461 | −0.186834 | ||||||||
\(917\) | −0.911668 | − | 12.3267i | −0.0301059 | − | 0.407063i | ||||
\(918\) | 13.2836 | 0.438425 | ||||||||
\(919\) | −8.30080 | + | 14.3774i | −0.273818 | + | 0.474267i | −0.969836 | − | 0.243757i | \(-0.921620\pi\) |
0.696018 | + | 0.718024i | \(0.254953\pi\) | |||||||
\(920\) | 2.71851 | + | 4.70859i | 0.0896266 | + | 0.155238i | ||||
\(921\) | −38.5640 | − | 66.7948i | −1.27073 | − | 2.20096i | ||||
\(922\) | 13.6423 | − | 23.6292i | 0.449287 | − | 0.778187i | ||||
\(923\) | −5.73150 | −0.188655 | ||||||||
\(924\) | 6.66464 | − | 4.53436i | 0.219251 | − | 0.149170i | ||||
\(925\) | −5.14344 | −0.169115 | ||||||||
\(926\) | −7.76524 | + | 13.4498i | −0.255182 | + | 0.441987i | ||||
\(927\) | −7.47059 | − | 12.9394i | −0.245366 | − | 0.424987i | ||||
\(928\) | −0.140746 | − | 0.243779i | −0.00462021 | − | 0.00800244i | ||||
\(929\) | 21.1122 | − | 36.5674i | 0.692669 | − | 1.19974i | −0.278291 | − | 0.960497i | \(-0.589768\pi\) |
0.970960 | − | 0.239241i | \(-0.0768986\pi\) | |||||||
\(930\) | −31.4705 | −1.03196 | ||||||||
\(931\) | 15.5837 | + | 19.6198i | 0.510736 | + | 0.643012i | ||||
\(932\) | −24.0378 | −0.787386 | ||||||||
\(933\) | 15.4918 | − | 26.8325i | 0.507178 | − | 0.878458i | ||||
\(934\) | −10.6141 | − | 18.3842i | −0.347305 | − | 0.601550i | ||||
\(935\) | 0.664110 | + | 1.15027i | 0.0217187 | + | 0.0376179i | ||||
\(936\) | −1.62505 | + | 2.81467i | −0.0531164 | + | 0.0920003i | ||||
\(937\) | 57.6174 | 1.88228 | 0.941140 | − | 0.338018i | \(-0.109756\pi\) | ||||
0.941140 | + | 0.338018i | \(0.109756\pi\) | |||||||
\(938\) | 28.6416 | − | 19.4866i | 0.935182 | − | 0.636261i | ||||
\(939\) | −1.19794 | −0.0390932 | ||||||||
\(940\) | 2.37495 | − | 4.11353i | 0.0774623 | − | 0.134169i | ||||
\(941\) | 6.02535 | + | 10.4362i | 0.196421 | + | 0.340211i | 0.947365 | − | 0.320155i | \(-0.103735\pi\) |
−0.750945 | + | 0.660365i | \(0.770401\pi\) | |||||||
\(942\) | 29.3461 | + | 50.8289i | 0.956146 | + | 1.65609i | ||||
\(943\) | −7.22156 | + | 12.5081i | −0.235166 | + | 0.407320i | ||||
\(944\) | 6.23258 | 0.202853 | ||||||||
\(945\) | 1.95165 | + | 26.3883i | 0.0634870 | + | 0.858410i | ||||
\(946\) | −2.56298 | −0.0833298 | ||||||||
\(947\) | 17.6407 | − | 30.5546i | 0.573246 | − | 0.992892i | −0.422983 | − | 0.906137i | \(-0.639017\pi\) |
0.996230 | − | 0.0867544i | \(-0.0276496\pi\) | |||||||
\(948\) | −16.3532 | − | 28.3245i | −0.531127 | − | 0.919939i | ||||
\(949\) | −2.31613 | − | 4.01166i | −0.0751849 | − | 0.130224i | ||||
\(950\) | −1.78969 | + | 3.09984i | −0.0580653 | + | 0.100572i | ||||
\(951\) | −76.3160 | −2.47472 | ||||||||
\(952\) | 3.16464 | + | 1.52782i | 0.102567 | + | 0.0495168i | ||||
\(953\) | 16.0167 | 0.518832 | 0.259416 | − | 0.965766i | \(-0.416470\pi\) | ||||
0.259416 | + | 0.965766i | \(0.416470\pi\) | |||||||
\(954\) | 5.78715 | − | 10.0236i | 0.187366 | − | 0.324527i | ||||
\(955\) | 5.75541 | + | 9.96866i | 0.186241 | + | 0.322578i | ||||
\(956\) | −13.5412 | − | 23.4541i | −0.437954 | − | 0.758559i | ||||
\(957\) | −0.428814 | + | 0.742728i | −0.0138616 | + | 0.0240090i | ||||
\(958\) | 27.7410 | 0.896271 | ||||||||
\(959\) | −15.1456 | − | 7.31195i | −0.489078 | − | 0.236115i | ||||
\(960\) | 3.04673 | 0.0983328 | ||||||||
\(961\) | −37.8471 | + | 65.5531i | −1.22087 | + | 2.11462i | ||||
\(962\) | 1.33040 | + | 2.30433i | 0.0428940 | + | 0.0742945i | ||||
\(963\) | −10.5031 | − | 18.1918i | −0.338456 | − | 0.586223i | ||||
\(964\) | −7.61078 | + | 13.1823i | −0.245127 | + | 0.424572i | ||||
\(965\) | 1.59473 | 0.0513360 | ||||||||
\(966\) | −3.23258 | − | 43.7078i | −0.104007 | − | 1.40628i | ||||
\(967\) | 7.74000 | 0.248902 | 0.124451 | − | 0.992226i | \(-0.460283\pi\) | ||||
0.124451 | + | 0.992226i | \(0.460283\pi\) | |||||||
\(968\) | −0.500000 | + | 0.866025i | −0.0160706 | + | 0.0278351i | ||||
\(969\) | −7.24241 | − | 12.5442i | −0.232660 | − | 0.402978i | ||||
\(970\) | −7.68034 | − | 13.3027i | −0.246601 | − | 0.427125i | ||||
\(971\) | 7.78375 | − | 13.4819i | 0.249792 | − | 0.432653i | −0.713676 | − | 0.700476i | \(-0.752971\pi\) |
0.963468 | + | 0.267823i | \(0.0863043\pi\) | |||||||
\(972\) | −5.40853 | −0.173479 | ||||||||
\(973\) | 34.8286 | − | 23.6960i | 1.11655 | − | 0.759659i | ||||
\(974\) | −6.02417 | −0.193027 | ||||||||
\(975\) | 0.788069 | − | 1.36497i | 0.0252384 | − | 0.0437142i | ||||
\(976\) | 5.68801 | + | 9.85192i | 0.182069 | + | 0.315352i | ||||
\(977\) | −4.57939 | − | 7.93173i | −0.146508 | − | 0.253759i | 0.783427 | − | 0.621484i | \(-0.213470\pi\) |
−0.929934 | + | 0.367725i | \(0.880137\pi\) | |||||||
\(978\) | −6.64128 | + | 11.5030i | −0.212365 | + | 0.367826i | ||||
\(979\) | 16.1292 | 0.515490 | ||||||||
\(980\) | −2.57009 | + | 6.51111i | −0.0820986 | + | 0.207990i | ||||
\(981\) | −63.3435 | −2.02240 | ||||||||
\(982\) | −1.43522 | + | 2.48587i | −0.0457996 | + | 0.0793272i | ||||
\(983\) | −7.09564 | − | 12.2900i | −0.226316 | − | 0.391991i | 0.730398 | − | 0.683022i | \(-0.239335\pi\) |
−0.956713 | + | 0.291032i | \(0.906001\pi\) | |||||||
\(984\) | 4.04673 | + | 7.00914i | 0.129005 | + | 0.223443i | ||||
\(985\) | −1.69568 | + | 2.93700i | −0.0540288 | + | 0.0935806i | ||||
\(986\) | −0.373883 | −0.0119069 | ||||||||
\(987\) | −31.6564 | + | 21.5378i | −1.00763 | + | 0.685555i | ||||
\(988\) | 1.85169 | 0.0589102 | ||||||||
\(989\) | −6.96749 | + | 12.0680i | −0.221553 | + | 0.383742i | ||||
\(990\) | −3.14128 | − | 5.44086i | −0.0998364 | − | 0.172922i | ||||
\(991\) | 21.7465 | + | 37.6661i | 0.690801 | + | 1.19650i | 0.971576 | + | 0.236729i | \(0.0760753\pi\) |
−0.280775 | + | 0.959774i | \(0.590591\pi\) | |||||||
\(992\) | 5.16464 | − | 8.94543i | 0.163978 | − | 0.284018i | ||||
\(993\) | −78.2346 | −2.48270 | ||||||||
\(994\) | −2.16203 | − | 29.2329i | −0.0685756 | − | 0.927212i | ||||
\(995\) | −22.8098 | −0.723119 | ||||||||
\(996\) | 20.1413 | − | 34.8857i | 0.638200 | − | 1.10539i | ||||
\(997\) | 5.26722 | + | 9.12309i | 0.166815 | + | 0.288931i | 0.937298 | − | 0.348528i | \(-0.113319\pi\) |
−0.770484 | + | 0.637460i | \(0.779985\pi\) | |||||||
\(998\) | 3.33254 | + | 5.77213i | 0.105490 | + | 0.182713i | ||||
\(999\) | −25.7199 | + | 44.5482i | −0.813743 | + | 1.40944i |
(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 | 770.2.i.l.331.4 | yes | 8 | |
7.2 | even | 3 | 5390.2.a.ce.1.1 | 4 | |||
7.4 | even | 3 | inner | 770.2.i.l.221.4 | ✓ | 8 | |
7.5 | odd | 6 | 5390.2.a.cf.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.i.l.221.4 | ✓ | 8 | 7.4 | even | 3 | inner | |
770.2.i.l.331.4 | yes | 8 | 1.1 | even | 1 | trivial | |
5390.2.a.ce.1.1 | 4 | 7.2 | even | 3 | |||
5390.2.a.cf.1.4 | 4 | 7.5 | odd | 6 |