Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(221,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.221");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.s (of order \(6\), 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: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 221.12 | ||
Character | \(\chi\) | \(=\) | 570.221 |
Dual form | 570.2.s.a.521.12 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 | ||||
\(3\) | 1.72438 | − | 0.162784i | 0.995574 | − | 0.0939833i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0.866025 | − | 0.500000i | 0.387298 | − | 0.223607i | ||||
\(6\) | −1.00317 | − | 1.41197i | −0.409541 | − | 0.576434i | ||||
\(7\) | 3.36569 | 1.27211 | 0.636055 | − | 0.771644i | \(-0.280565\pi\) | ||||
0.636055 | + | 0.771644i | \(0.280565\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 2.94700 | − | 0.561404i | 0.982334 | − | 0.187135i | ||||
\(10\) | −0.866025 | − | 0.500000i | −0.273861 | − | 0.158114i | ||||
\(11\) | 0.795353i | 0.239808i | 0.992785 | + | 0.119904i | \(0.0382587\pi\) | ||||
−0.992785 | + | 0.119904i | \(0.961741\pi\) | |||||||
\(12\) | −0.721217 | + | 1.57475i | −0.208197 | + | 0.454592i | ||||
\(13\) | 1.59822 | + | 0.922734i | 0.443267 | + | 0.255920i | 0.704982 | − | 0.709225i | \(-0.250955\pi\) |
−0.261715 | + | 0.965145i | \(0.584288\pi\) | |||||||
\(14\) | −1.68284 | − | 2.91477i | −0.449759 | − | 0.779005i | ||||
\(15\) | 1.41197 | − | 1.00317i | 0.364569 | − | 0.259017i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −6.17887 | + | 3.56737i | −1.49860 | + | 0.865214i | −0.999999 | − | 0.00161968i | \(-0.999484\pi\) |
−0.498597 | + | 0.866834i | \(0.666151\pi\) | |||||||
\(18\) | −1.95969 | − | 2.27148i | −0.461904 | − | 0.535392i | ||||
\(19\) | −0.831025 | + | 4.27895i | −0.190650 | + | 0.981658i | ||||
\(20\) | 1.00000i | 0.223607i | ||||||||
\(21\) | 5.80374 | − | 0.547880i | 1.26648 | − | 0.119557i | ||||
\(22\) | 0.688796 | − | 0.397676i | 0.146852 | − | 0.0847849i | ||||
\(23\) | −1.72727 | − | 0.997241i | −0.360161 | − | 0.207939i | 0.308990 | − | 0.951065i | \(-0.400009\pi\) |
−0.669151 | + | 0.743126i | \(0.733342\pi\) | |||||||
\(24\) | 1.72438 | − | 0.162784i | 0.351988 | − | 0.0332281i | ||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | − | 1.84547i | − | 0.361926i | ||||||
\(27\) | 4.99038 | − | 1.44780i | 0.960399 | − | 0.278629i | ||||
\(28\) | −1.68284 | + | 2.91477i | −0.318028 | + | 0.550840i | ||||
\(29\) | 1.95032 | − | 3.37805i | 0.362165 | − | 0.627288i | −0.626152 | − | 0.779701i | \(-0.715371\pi\) |
0.988317 | + | 0.152413i | \(0.0487043\pi\) | |||||||
\(30\) | −1.57475 | − | 0.721217i | −0.287509 | − | 0.131676i | ||||
\(31\) | − | 8.28909i | − | 1.48876i | −0.667753 | − | 0.744382i | \(-0.732744\pi\) | ||
0.667753 | − | 0.744382i | \(-0.267256\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0.129471 | + | 1.37149i | 0.0225379 | + | 0.238746i | ||||
\(34\) | 6.17887 | + | 3.56737i | 1.05967 | + | 0.611799i | ||||
\(35\) | 2.91477 | − | 1.68284i | 0.492686 | − | 0.284452i | ||||
\(36\) | −0.987311 | + | 2.83288i | −0.164552 | + | 0.472147i | ||||
\(37\) | 3.63511i | 0.597608i | 0.954314 | + | 0.298804i | \(0.0965877\pi\) | ||||
−0.954314 | + | 0.298804i | \(0.903412\pi\) | |||||||
\(38\) | 4.12119 | − | 1.41979i | 0.668545 | − | 0.230320i | ||||
\(39\) | 2.90616 | + | 1.33098i | 0.465357 | + | 0.213128i | ||||
\(40\) | 0.866025 | − | 0.500000i | 0.136931 | − | 0.0790569i | ||||
\(41\) | −2.08497 | − | 3.61128i | −0.325618 | − | 0.563987i | 0.656019 | − | 0.754744i | \(-0.272239\pi\) |
−0.981637 | + | 0.190757i | \(0.938906\pi\) | |||||||
\(42\) | −3.37635 | − | 4.75224i | −0.520982 | − | 0.733287i | ||||
\(43\) | −1.75379 | − | 3.03766i | −0.267451 | − | 0.463238i | 0.700752 | − | 0.713405i | \(-0.252848\pi\) |
−0.968203 | + | 0.250167i | \(0.919515\pi\) | |||||||
\(44\) | −0.688796 | − | 0.397676i | −0.103840 | − | 0.0599520i | ||||
\(45\) | 2.27148 | − | 1.95969i | 0.338612 | − | 0.292134i | ||||
\(46\) | 1.99448i | 0.294070i | ||||||||
\(47\) | −3.13074 | − | 1.80753i | −0.456665 | − | 0.263656i | 0.253976 | − | 0.967211i | \(-0.418262\pi\) |
−0.710641 | + | 0.703555i | \(0.751595\pi\) | |||||||
\(48\) | −1.00317 | − | 1.41197i | −0.144795 | − | 0.203800i | ||||
\(49\) | 4.32785 | 0.618264 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −10.0740 | + | 7.15734i | −1.41065 | + | 1.00223i | ||||
\(52\) | −1.59822 | + | 0.922734i | −0.221634 | + | 0.127960i | ||||
\(53\) | 3.21210 | − | 5.56351i | 0.441215 | − | 0.764207i | −0.556565 | − | 0.830804i | \(-0.687881\pi\) |
0.997780 | + | 0.0665970i | \(0.0212142\pi\) | |||||||
\(54\) | −3.74902 | − | 3.59789i | −0.510177 | − | 0.489611i | ||||
\(55\) | 0.397676 | + | 0.688796i | 0.0536227 | + | 0.0928772i | ||||
\(56\) | 3.36569 | 0.449759 | ||||||||
\(57\) | −0.736463 | + | 7.51383i | −0.0975469 | + | 0.995231i | ||||
\(58\) | −3.90064 | −0.512179 | ||||||||
\(59\) | 4.40416 | + | 7.62824i | 0.573373 | + | 0.993112i | 0.996216 | + | 0.0869089i | \(0.0276989\pi\) |
−0.422843 | + | 0.906203i | \(0.638968\pi\) | |||||||
\(60\) | 0.162784 | + | 1.72438i | 0.0210153 | + | 0.222617i | ||||
\(61\) | −3.34905 | + | 5.80073i | −0.428802 | + | 0.742707i | −0.996767 | − | 0.0803454i | \(-0.974398\pi\) |
0.567965 | + | 0.823053i | \(0.307731\pi\) | |||||||
\(62\) | −7.17856 | + | 4.14455i | −0.911679 | + | 0.526358i | ||||
\(63\) | 9.91869 | − | 1.88951i | 1.24964 | − | 0.238056i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.84547 | 0.228902 | ||||||||
\(66\) | 1.12301 | − | 0.797872i | 0.138233 | − | 0.0982112i | ||||
\(67\) | −3.16763 | − | 1.82883i | −0.386987 | − | 0.223427i | 0.293867 | − | 0.955846i | \(-0.405058\pi\) |
−0.680854 | + | 0.732419i | \(0.738391\pi\) | |||||||
\(68\) | − | 7.13474i | − | 0.865214i | ||||||
\(69\) | −3.14081 | − | 1.43845i | −0.378110 | − | 0.173170i | ||||
\(70\) | −2.91477 | − | 1.68284i | −0.348382 | − | 0.201138i | ||||
\(71\) | 0.800066 | + | 1.38576i | 0.0949504 | + | 0.164459i | 0.909588 | − | 0.415512i | \(-0.136397\pi\) |
−0.814637 | + | 0.579970i | \(0.803064\pi\) | |||||||
\(72\) | 2.94700 | − | 0.561404i | 0.347308 | − | 0.0661621i | ||||
\(73\) | −7.05458 | − | 12.2189i | −0.825676 | − | 1.43011i | −0.901402 | − | 0.432984i | \(-0.857461\pi\) |
0.0757258 | − | 0.997129i | \(-0.475873\pi\) | |||||||
\(74\) | 3.14810 | − | 1.81755i | 0.365959 | − | 0.211286i | ||||
\(75\) | 0.721217 | − | 1.57475i | 0.0832790 | − | 0.181837i | ||||
\(76\) | −3.29017 | − | 2.85916i | −0.377408 | − | 0.327968i | ||||
\(77\) | 2.67691i | 0.305062i | ||||||||
\(78\) | −0.300413 | − | 3.18230i | −0.0340150 | − | 0.360324i | ||||
\(79\) | −10.3514 | + | 5.97636i | −1.16462 | + | 0.672394i | −0.952407 | − | 0.304830i | \(-0.901400\pi\) |
−0.212213 | + | 0.977223i | \(0.568067\pi\) | |||||||
\(80\) | −0.866025 | − | 0.500000i | −0.0968246 | − | 0.0559017i | ||||
\(81\) | 8.36965 | − | 3.30892i | 0.929961 | − | 0.367658i | ||||
\(82\) | −2.08497 | + | 3.61128i | −0.230247 | + | 0.398799i | ||||
\(83\) | − | 13.9932i | − | 1.53595i | −0.640479 | − | 0.767976i | \(-0.721264\pi\) | ||
0.640479 | − | 0.767976i | \(-0.278736\pi\) | |||||||
\(84\) | −2.42739 | + | 5.30012i | −0.264850 | + | 0.578291i | ||||
\(85\) | −3.56737 | + | 6.17887i | −0.386936 | + | 0.670192i | ||||
\(86\) | −1.75379 | + | 3.03766i | −0.189116 | + | 0.327559i | ||||
\(87\) | 2.81321 | − | 6.14254i | 0.301607 | − | 0.658549i | ||||
\(88\) | 0.795353i | 0.0847849i | ||||||||
\(89\) | −1.83681 | + | 3.18145i | −0.194701 | + | 0.337233i | −0.946803 | − | 0.321815i | \(-0.895707\pi\) |
0.752101 | + | 0.659048i | \(0.229040\pi\) | |||||||
\(90\) | −2.83288 | − | 0.987311i | −0.298612 | − | 0.104072i | ||||
\(91\) | 5.37912 | + | 3.10563i | 0.563885 | + | 0.325559i | ||||
\(92\) | 1.72727 | − | 0.997241i | 0.180080 | − | 0.103970i | ||||
\(93\) | −1.34933 | − | 14.2936i | −0.139919 | − | 1.48218i | ||||
\(94\) | 3.61507i | 0.372866i | ||||||||
\(95\) | 1.41979 | + | 4.12119i | 0.145667 | + | 0.422825i | ||||
\(96\) | −0.721217 | + | 1.57475i | −0.0736089 | + | 0.160723i | ||||
\(97\) | −15.9344 | + | 9.19973i | −1.61789 | + | 0.934092i | −0.630430 | + | 0.776246i | \(0.717121\pi\) |
−0.987464 | + | 0.157846i | \(0.949545\pi\) | |||||||
\(98\) | −2.16392 | − | 3.74803i | −0.218589 | − | 0.378608i | ||||
\(99\) | 0.446514 | + | 2.34391i | 0.0448764 | + | 0.235572i | ||||
\(100\) | 0.500000 | + | 0.866025i | 0.0500000 | + | 0.0866025i | ||||
\(101\) | 1.03574 | + | 0.597984i | 0.103060 | + | 0.0595017i | 0.550644 | − | 0.834740i | \(-0.314382\pi\) |
−0.447584 | + | 0.894242i | \(0.647716\pi\) | |||||||
\(102\) | 11.2355 | + | 5.14570i | 1.11248 | + | 0.509500i | ||||
\(103\) | 2.19200i | 0.215984i | 0.994152 | + | 0.107992i | \(0.0344421\pi\) | ||||
−0.994152 | + | 0.107992i | \(0.965558\pi\) | |||||||
\(104\) | 1.59822 | + | 0.922734i | 0.156719 | + | 0.0904815i | ||||
\(105\) | 4.75224 | − | 3.37635i | 0.463772 | − | 0.329498i | ||||
\(106\) | −6.42419 | −0.623973 | ||||||||
\(107\) | −1.07225 | −0.103659 | −0.0518293 | − | 0.998656i | \(-0.516505\pi\) | ||||
−0.0518293 | + | 0.998656i | \(0.516505\pi\) | |||||||
\(108\) | −1.24136 | + | 5.04569i | −0.119450 | + | 0.485522i | ||||
\(109\) | 0.897440 | − | 0.518137i | 0.0859592 | − | 0.0496285i | −0.456404 | − | 0.889773i | \(-0.650863\pi\) |
0.542363 | + | 0.840144i | \(0.317530\pi\) | |||||||
\(110\) | 0.397676 | − | 0.688796i | 0.0379170 | − | 0.0656741i | ||||
\(111\) | 0.591737 | + | 6.26833i | 0.0561652 | + | 0.594963i | ||||
\(112\) | −1.68284 | − | 2.91477i | −0.159014 | − | 0.275420i | ||||
\(113\) | 11.7127 | 1.10183 | 0.550917 | − | 0.834560i | \(-0.314278\pi\) | ||||
0.550917 | + | 0.834560i | \(0.314278\pi\) | |||||||
\(114\) | 6.87540 | − | 3.11912i | 0.643940 | − | 0.292132i | ||||
\(115\) | −1.99448 | −0.185986 | ||||||||
\(116\) | 1.95032 | + | 3.37805i | 0.181083 | + | 0.313644i | ||||
\(117\) | 5.22799 | + | 1.82205i | 0.483328 | + | 0.168449i | ||||
\(118\) | 4.40416 | − | 7.62824i | 0.405436 | − | 0.702236i | ||||
\(119\) | −20.7961 | + | 12.0067i | −1.90638 | + | 1.10065i | ||||
\(120\) | 1.41197 | − | 1.00317i | 0.128895 | − | 0.0915762i | ||||
\(121\) | 10.3674 | 0.942492 | ||||||||
\(122\) | 6.69811 | 0.606418 | ||||||||
\(123\) | −4.18315 | − | 5.88783i | −0.377182 | − | 0.530888i | ||||
\(124\) | 7.17856 | + | 4.14455i | 0.644654 | + | 0.372191i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | −6.59571 | − | 7.64508i | −0.587592 | − | 0.681078i | ||||
\(127\) | 3.29108 | + | 1.90011i | 0.292036 | + | 0.168607i | 0.638860 | − | 0.769323i | \(-0.279406\pi\) |
−0.346823 | + | 0.937930i | \(0.612740\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | −3.51869 | − | 4.95260i | −0.309803 | − | 0.436052i | ||||
\(130\) | −0.922734 | − | 1.59822i | −0.0809291 | − | 0.140173i | ||||
\(131\) | −4.80319 | + | 2.77312i | −0.419656 | + | 0.242289i | −0.694930 | − | 0.719077i | \(-0.744565\pi\) |
0.275274 | + | 0.961366i | \(0.411231\pi\) | |||||||
\(132\) | −1.25248 | − | 0.573622i | −0.109015 | − | 0.0499274i | ||||
\(133\) | −2.79697 | + | 14.4016i | −0.242528 | + | 1.24878i | ||||
\(134\) | 3.65766i | 0.315974i | ||||||||
\(135\) | 3.59789 | − | 3.74902i | 0.309657 | − | 0.322664i | ||||
\(136\) | −6.17887 | + | 3.56737i | −0.529833 | + | 0.305899i | ||||
\(137\) | 17.2616 | + | 9.96597i | 1.47475 | + | 0.851450i | 0.999595 | − | 0.0284500i | \(-0.00905713\pi\) |
0.475159 | + | 0.879900i | \(0.342390\pi\) | |||||||
\(138\) | 0.324669 | + | 3.43925i | 0.0276377 | + | 0.292769i | ||||
\(139\) | −5.17049 | + | 8.95556i | −0.438556 | + | 0.759600i | −0.997578 | − | 0.0695518i | \(-0.977843\pi\) |
0.559023 | + | 0.829152i | \(0.311176\pi\) | |||||||
\(140\) | 3.36569i | 0.284452i | ||||||||
\(141\) | −5.69284 | − | 2.60725i | −0.479423 | − | 0.219570i | ||||
\(142\) | 0.800066 | − | 1.38576i | 0.0671401 | − | 0.116290i | ||||
\(143\) | −0.733899 | + | 1.27115i | −0.0613717 | + | 0.106299i | ||||
\(144\) | −1.95969 | − | 2.27148i | −0.163308 | − | 0.189290i | ||||
\(145\) | − | 3.90064i | − | 0.323930i | ||||||
\(146\) | −7.05458 | + | 12.2189i | −0.583841 | + | 1.01124i | ||||
\(147\) | 7.46288 | − | 0.704504i | 0.615528 | − | 0.0581065i | ||||
\(148\) | −3.14810 | − | 1.81755i | −0.258772 | − | 0.149402i | ||||
\(149\) | −7.24356 | + | 4.18207i | −0.593415 | + | 0.342608i | −0.766447 | − | 0.642308i | \(-0.777977\pi\) |
0.173031 | + | 0.984916i | \(0.444644\pi\) | |||||||
\(150\) | −1.72438 | + | 0.162784i | −0.140795 | + | 0.0132912i | ||||
\(151\) | 22.3534i | 1.81909i | 0.415601 | + | 0.909547i | \(0.363571\pi\) | ||||
−0.415601 | + | 0.909547i | \(0.636429\pi\) | |||||||
\(152\) | −0.831025 | + | 4.27895i | −0.0674050 | + | 0.347069i | ||||
\(153\) | −16.2064 | + | 13.9819i | −1.31021 | + | 1.13037i | ||||
\(154\) | 2.31827 | − | 1.33845i | 0.186812 | − | 0.107856i | ||||
\(155\) | −4.14455 | − | 7.17856i | −0.332898 | − | 0.576596i | ||||
\(156\) | −2.60574 | + | 1.85131i | −0.208626 | + | 0.148224i | ||||
\(157\) | −9.07185 | − | 15.7129i | −0.724013 | − | 1.25403i | −0.959379 | − | 0.282120i | \(-0.908962\pi\) |
0.235367 | − | 0.971907i | \(-0.424371\pi\) | |||||||
\(158\) | 10.3514 | + | 5.97636i | 0.823511 | + | 0.475454i | ||||
\(159\) | 4.63324 | − | 10.1165i | 0.367440 | − | 0.802292i | ||||
\(160\) | 1.00000i | 0.0790569i | ||||||||
\(161\) | −5.81345 | − | 3.35640i | −0.458164 | − | 0.264521i | ||||
\(162\) | −7.05043 | − | 5.59387i | −0.553934 | − | 0.439496i | ||||
\(163\) | −18.5170 | −1.45037 | −0.725184 | − | 0.688556i | \(-0.758245\pi\) | ||||
−0.725184 | + | 0.688556i | \(0.758245\pi\) | |||||||
\(164\) | 4.16994 | 0.325618 | ||||||||
\(165\) | 0.797872 | + | 1.12301i | 0.0621142 | + | 0.0874265i | ||||
\(166\) | −12.1185 | + | 6.99659i | −0.940575 | + | 0.543041i | ||||
\(167\) | −9.91145 | + | 17.1671i | −0.766971 | + | 1.32843i | 0.172227 | + | 0.985057i | \(0.444904\pi\) |
−0.939198 | + | 0.343376i | \(0.888430\pi\) | |||||||
\(168\) | 5.80374 | − | 0.547880i | 0.447768 | − | 0.0422698i | ||||
\(169\) | −4.79712 | − | 8.30886i | −0.369009 | − | 0.639143i | ||||
\(170\) | 7.13474 | 0.547210 | ||||||||
\(171\) | −0.0468143 | + | 13.0766i | −0.00357998 | + | 0.999994i | ||||
\(172\) | 3.50758 | 0.267451 | ||||||||
\(173\) | −3.72918 | − | 6.45913i | −0.283524 | − | 0.491079i | 0.688726 | − | 0.725022i | \(-0.258170\pi\) |
−0.972250 | + | 0.233943i | \(0.924837\pi\) | |||||||
\(174\) | −6.72620 | + | 0.634961i | −0.509912 | + | 0.0481363i | ||||
\(175\) | 1.68284 | − | 2.91477i | 0.127211 | − | 0.220336i | ||||
\(176\) | 0.688796 | − | 0.397676i | 0.0519199 | − | 0.0299760i | ||||
\(177\) | 8.83623 | + | 12.4371i | 0.664172 | + | 0.934829i | ||||
\(178\) | 3.67362 | 0.275349 | ||||||||
\(179\) | −0.307151 | −0.0229575 | −0.0114788 | − | 0.999934i | \(-0.503654\pi\) | ||||
−0.0114788 | + | 0.999934i | \(0.503654\pi\) | |||||||
\(180\) | 0.561404 | + | 2.94700i | 0.0418446 | + | 0.219657i | ||||
\(181\) | 11.6567 | + | 6.72999i | 0.866435 | + | 0.500236i | 0.866162 | − | 0.499763i | \(-0.166580\pi\) |
0.000273100 | 1.00000i | \(0.499913\pi\) | ||||||||
\(182\) | − | 6.21127i | − | 0.460410i | ||||||
\(183\) | −4.83079 | + | 10.5479i | −0.357102 | + | 0.779720i | ||||
\(184\) | −1.72727 | − | 0.997241i | −0.127336 | − | 0.0735176i | ||||
\(185\) | 1.81755 | + | 3.14810i | 0.133629 | + | 0.231453i | ||||
\(186\) | −11.7039 | + | 8.31535i | −0.858174 | + | 0.609711i | ||||
\(187\) | −2.83732 | − | 4.91438i | −0.207485 | − | 0.359375i | ||||
\(188\) | 3.13074 | − | 1.80753i | 0.228333 | − | 0.131828i | ||||
\(189\) | 16.7961 | − | 4.87284i | 1.22173 | − | 0.354447i | ||||
\(190\) | 2.85916 | − | 3.29017i | 0.207425 | − | 0.238694i | ||||
\(191\) | 20.3011i | 1.46893i | 0.678644 | + | 0.734467i | \(0.262568\pi\) | ||||
−0.678644 | + | 0.734467i | \(0.737432\pi\) | |||||||
\(192\) | 1.72438 | − | 0.162784i | 0.124447 | − | 0.0117479i | ||||
\(193\) | −4.00713 | + | 2.31352i | −0.288439 | + | 0.166531i | −0.637238 | − | 0.770667i | \(-0.719923\pi\) |
0.348798 | + | 0.937198i | \(0.386590\pi\) | |||||||
\(194\) | 15.9344 | + | 9.19973i | 1.14402 | + | 0.660502i | ||||
\(195\) | 3.18230 | − | 0.300413i | 0.227889 | − | 0.0215130i | ||||
\(196\) | −2.16392 | + | 3.74803i | −0.154566 | + | 0.267716i | ||||
\(197\) | − | 17.5153i | − | 1.24791i | −0.781460 | − | 0.623956i | \(-0.785524\pi\) | ||
0.781460 | − | 0.623956i | \(-0.214476\pi\) | |||||||
\(198\) | 1.80663 | − | 1.55865i | 0.128391 | − | 0.110768i | ||||
\(199\) | −0.637900 | + | 1.10487i | −0.0452195 | + | 0.0783225i | −0.887749 | − | 0.460327i | \(-0.847732\pi\) |
0.842530 | + | 0.538650i | \(0.181065\pi\) | |||||||
\(200\) | 0.500000 | − | 0.866025i | 0.0353553 | − | 0.0612372i | ||||
\(201\) | −5.75991 | − | 2.63797i | −0.406273 | − | 0.186068i | ||||
\(202\) | − | 1.19597i | − | 0.0841481i | ||||||
\(203\) | 6.56416 | − | 11.3695i | 0.460714 | − | 0.797980i | ||||
\(204\) | −1.16142 | − | 12.3030i | −0.0813157 | − | 0.861385i | ||||
\(205\) | −3.61128 | − | 2.08497i | −0.252223 | − | 0.145621i | ||||
\(206\) | 1.89833 | − | 1.09600i | 0.132263 | − | 0.0763620i | ||||
\(207\) | −5.65013 | − | 1.96917i | −0.392711 | − | 0.136867i | ||||
\(208\) | − | 1.84547i | − | 0.127960i | ||||||
\(209\) | −3.40327 | − | 0.660958i | −0.235409 | − | 0.0457194i | ||||
\(210\) | −5.30012 | − | 2.42739i | −0.365743 | − | 0.167506i | ||||
\(211\) | 23.3524 | − | 13.4825i | 1.60765 | − | 0.928177i | 0.617754 | − | 0.786371i | \(-0.288043\pi\) |
0.989895 | − | 0.141805i | \(-0.0452907\pi\) | |||||||
\(212\) | 3.21210 | + | 5.56351i | 0.220608 | + | 0.382104i | ||||
\(213\) | 1.60520 | + | 2.25934i | 0.109987 | + | 0.154807i | ||||
\(214\) | 0.536127 | + | 0.928599i | 0.0366489 | + | 0.0634777i | ||||
\(215\) | −3.03766 | − | 1.75379i | −0.207166 | − | 0.119608i | ||||
\(216\) | 4.99038 | − | 1.44780i | 0.339552 | − | 0.0985104i | ||||
\(217\) | − | 27.8985i | − | 1.89387i | ||||||
\(218\) | −0.897440 | − | 0.518137i | −0.0607823 | − | 0.0350927i | ||||
\(219\) | −14.1538 | − | 19.9217i | −0.956428 | − | 1.34618i | ||||
\(220\) | −0.795353 | −0.0536227 | ||||||||
\(221\) | −13.1669 | −0.885704 | ||||||||
\(222\) | 5.13266 | − | 3.64662i | 0.344482 | − | 0.244745i | ||||
\(223\) | 19.3951 | − | 11.1978i | 1.29879 | − | 0.749857i | 0.318595 | − | 0.947891i | \(-0.396789\pi\) |
0.980195 | + | 0.198034i | \(0.0634557\pi\) | |||||||
\(224\) | −1.68284 | + | 2.91477i | −0.112440 | + | 0.194751i | ||||
\(225\) | 0.987311 | − | 2.83288i | 0.0658208 | − | 0.188859i | ||||
\(226\) | −5.85633 | − | 10.1435i | −0.389557 | − | 0.674733i | ||||
\(227\) | −17.4096 | −1.15552 | −0.577758 | − | 0.816208i | \(-0.696072\pi\) | ||||
−0.577758 | + | 0.816208i | \(0.696072\pi\) | |||||||
\(228\) | −6.13894 | − | 4.39471i | −0.406561 | − | 0.291047i | ||||
\(229\) | 1.93992 | 0.128193 | 0.0640966 | − | 0.997944i | \(-0.479583\pi\) | ||||
0.0640966 | + | 0.997944i | \(0.479583\pi\) | |||||||
\(230\) | 0.997241 | + | 1.72727i | 0.0657561 | + | 0.113893i | ||||
\(231\) | 0.435758 | + | 4.61602i | 0.0286707 | + | 0.303712i | ||||
\(232\) | 1.95032 | − | 3.37805i | 0.128045 | − | 0.221780i | ||||
\(233\) | 2.14005 | − | 1.23556i | 0.140199 | − | 0.0809440i | −0.428260 | − | 0.903656i | \(-0.640873\pi\) |
0.568459 | + | 0.822712i | \(0.307540\pi\) | |||||||
\(234\) | −1.03605 | − | 5.43860i | −0.0677289 | − | 0.355532i | ||||
\(235\) | −3.61507 | −0.235821 | ||||||||
\(236\) | −8.80833 | −0.573373 | ||||||||
\(237\) | −16.8769 | + | 11.9906i | −1.09627 | + | 0.778872i | ||||
\(238\) | 20.7961 | + | 12.0067i | 1.34801 | + | 0.778276i | ||||
\(239\) | 13.1953i | 0.853534i | 0.904362 | + | 0.426767i | \(0.140348\pi\) | ||||
−0.904362 | + | 0.426767i | \(0.859652\pi\) | |||||||
\(240\) | −1.57475 | − | 0.721217i | −0.101650 | − | 0.0465544i | ||||
\(241\) | 23.5846 | + | 13.6166i | 1.51922 | + | 0.877122i | 0.999744 | + | 0.0226375i | \(0.00720636\pi\) |
0.519477 | + | 0.854485i | \(0.326127\pi\) | |||||||
\(242\) | −5.18371 | − | 8.97844i | −0.333221 | − | 0.577156i | ||||
\(243\) | 13.8939 | − | 7.06829i | 0.891291 | − | 0.453431i | ||||
\(244\) | −3.34905 | − | 5.80073i | −0.214401 | − | 0.371354i | ||||
\(245\) | 3.74803 | − | 2.16392i | 0.239453 | − | 0.138248i | ||||
\(246\) | −3.00744 | + | 6.56663i | −0.191747 | + | 0.418673i | ||||
\(247\) | −5.27649 | + | 6.07190i | −0.335735 | + | 0.386345i | ||||
\(248\) | − | 8.28909i | − | 0.526358i | ||||||
\(249\) | −2.27787 | − | 24.1296i | −0.144354 | − | 1.52915i | ||||
\(250\) | −0.866025 | + | 0.500000i | −0.0547723 | + | 0.0316228i | ||||
\(251\) | −18.6598 | − | 10.7733i | −1.17780 | − | 0.680002i | −0.222294 | − | 0.974980i | \(-0.571354\pi\) |
−0.955504 | + | 0.294978i | \(0.904688\pi\) | |||||||
\(252\) | −3.32298 | + | 9.53459i | −0.209328 | + | 0.600623i | ||||
\(253\) | 0.793158 | − | 1.37379i | 0.0498654 | − | 0.0863694i | ||||
\(254\) | − | 3.80022i | − | 0.238447i | ||||||
\(255\) | −5.14570 | + | 11.2355i | −0.322236 | + | 0.703591i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 14.4617 | − | 25.0484i | 0.902096 | − | 1.56248i | 0.0773283 | − | 0.997006i | \(-0.475361\pi\) |
0.824768 | − | 0.565471i | \(-0.191306\pi\) | |||||||
\(258\) | −2.52973 | + | 5.52357i | −0.157494 | + | 0.343883i | ||||
\(259\) | 12.2346i | 0.760224i | ||||||||
\(260\) | −0.922734 | + | 1.59822i | −0.0572255 | + | 0.0991175i | ||||
\(261\) | 3.85114 | − | 11.0500i | 0.238380 | − | 0.683980i | ||||
\(262\) | 4.80319 | + | 2.77312i | 0.296742 | + | 0.171324i | ||||
\(263\) | −13.9401 | + | 8.04833i | −0.859585 | + | 0.496281i | −0.863873 | − | 0.503709i | \(-0.831968\pi\) |
0.00428849 | + | 0.999991i | \(0.498635\pi\) | |||||||
\(264\) | 0.129471 | + | 1.37149i | 0.00796837 | + | 0.0844096i | ||||
\(265\) | − | 6.42419i | − | 0.394635i | ||||||
\(266\) | 13.8706 | − | 4.77855i | 0.850463 | − | 0.292992i | ||||
\(267\) | −2.64948 | + | 5.78504i | −0.162145 | + | 0.354039i | ||||
\(268\) | 3.16763 | − | 1.82883i | 0.193494 | − | 0.111714i | ||||
\(269\) | 7.78283 | + | 13.4803i | 0.474528 | + | 0.821906i | 0.999575 | − | 0.0291674i | \(-0.00928560\pi\) |
−0.525047 | + | 0.851073i | \(0.675952\pi\) | |||||||
\(270\) | −5.04569 | − | 1.24136i | −0.307071 | − | 0.0755466i | ||||
\(271\) | 1.20476 | + | 2.08670i | 0.0731839 | + | 0.126758i | 0.900295 | − | 0.435280i | \(-0.143351\pi\) |
−0.827111 | + | 0.562038i | \(0.810017\pi\) | |||||||
\(272\) | 6.17887 | + | 3.56737i | 0.374649 | + | 0.216304i | ||||
\(273\) | 9.78121 | + | 4.47967i | 0.591986 | + | 0.271122i | ||||
\(274\) | − | 19.9319i | − | 1.20413i | ||||||
\(275\) | 0.688796 | + | 0.397676i | 0.0415359 | + | 0.0239808i | ||||
\(276\) | 2.81615 | − | 2.00080i | 0.169512 | − | 0.120434i | ||||
\(277\) | 30.7890 | 1.84993 | 0.924965 | − | 0.380052i | \(-0.124094\pi\) | ||||
0.924965 | + | 0.380052i | \(0.124094\pi\) | |||||||
\(278\) | 10.3410 | 0.620211 | ||||||||
\(279\) | −4.65353 | − | 24.4280i | −0.278600 | − | 1.46246i | ||||
\(280\) | 2.91477 | − | 1.68284i | 0.174191 | − | 0.100569i | ||||
\(281\) | 12.6678 | − | 21.9413i | 0.755698 | − | 1.30891i | −0.189329 | − | 0.981914i | \(-0.560631\pi\) |
0.945027 | − | 0.326993i | \(-0.106035\pi\) | |||||||
\(282\) | 0.588475 | + | 6.23377i | 0.0350432 | + | 0.371215i | ||||
\(283\) | 4.10956 | + | 7.11797i | 0.244288 | + | 0.423119i | 0.961931 | − | 0.273292i | \(-0.0881124\pi\) |
−0.717643 | + | 0.696411i | \(0.754779\pi\) | |||||||
\(284\) | −1.60013 | −0.0949504 | ||||||||
\(285\) | 3.11912 | + | 6.87540i | 0.184761 | + | 0.407263i | ||||
\(286\) | 1.46780 | 0.0867927 | ||||||||
\(287\) | −7.01736 | − | 12.1544i | −0.414222 | − | 0.717453i | ||||
\(288\) | −0.987311 | + | 2.83288i | −0.0581779 | + | 0.166929i | ||||
\(289\) | 16.9523 | − | 29.3622i | 0.997192 | − | 1.72719i | ||||
\(290\) | −3.37805 | + | 1.95032i | −0.198366 | + | 0.114527i | ||||
\(291\) | −25.9795 | + | 18.4577i | −1.52294 | + | 1.08201i | ||||
\(292\) | 14.1092 | 0.825676 | ||||||||
\(293\) | 24.4468 | 1.42820 | 0.714099 | − | 0.700045i | \(-0.246837\pi\) | ||||
0.714099 | + | 0.700045i | \(0.246837\pi\) | |||||||
\(294\) | −4.34156 | − | 6.11079i | −0.253205 | − | 0.356388i | ||||
\(295\) | 7.62824 | + | 4.40416i | 0.444133 | + | 0.256420i | ||||
\(296\) | 3.63511i | 0.211286i | ||||||||
\(297\) | 1.15151 | + | 3.96911i | 0.0668175 | + | 0.230311i | ||||
\(298\) | 7.24356 | + | 4.18207i | 0.419608 | + | 0.242261i | ||||
\(299\) | −1.84038 | − | 3.18762i | −0.106432 | − | 0.184345i | ||||
\(300\) | 1.00317 | + | 1.41197i | 0.0579179 | + | 0.0815201i | ||||
\(301\) | −5.90271 | − | 10.2238i | −0.340227 | − | 0.589290i | ||||
\(302\) | 19.3586 | − | 11.1767i | 1.11396 | − | 0.643147i | ||||
\(303\) | 1.88335 | + | 0.862553i | 0.108196 | + | 0.0495524i | ||||
\(304\) | 4.12119 | − | 1.41979i | 0.236366 | − | 0.0814303i | ||||
\(305\) | 6.69811i | 0.383532i | ||||||||
\(306\) | 20.2119 | + | 7.04421i | 1.15544 | + | 0.402691i | ||||
\(307\) | −9.65029 | + | 5.57160i | −0.550771 | + | 0.317988i | −0.749433 | − | 0.662080i | \(-0.769674\pi\) |
0.198662 | + | 0.980068i | \(0.436340\pi\) | |||||||
\(308\) | −2.31827 | − | 1.33845i | −0.132096 | − | 0.0762655i | ||||
\(309\) | 0.356823 | + | 3.77985i | 0.0202989 | + | 0.215028i | ||||
\(310\) | −4.14455 | + | 7.17856i | −0.235394 | + | 0.407715i | ||||
\(311\) | − | 24.4400i | − | 1.38587i | −0.721002 | − | 0.692933i | \(-0.756318\pi\) | ||
0.721002 | − | 0.692933i | \(-0.243682\pi\) | |||||||
\(312\) | 2.90616 | + | 1.33098i | 0.164529 | + | 0.0753521i | ||||
\(313\) | −1.06464 | + | 1.84401i | −0.0601771 | + | 0.104230i | −0.894544 | − | 0.446979i | \(-0.852500\pi\) |
0.834367 | + | 0.551209i | \(0.185833\pi\) | |||||||
\(314\) | −9.07185 | + | 15.7129i | −0.511954 | + | 0.886731i | ||||
\(315\) | 7.64508 | − | 6.59571i | 0.430752 | − | 0.371626i | ||||
\(316\) | − | 11.9527i | − | 0.672394i | ||||||
\(317\) | −3.03351 | + | 5.25419i | −0.170379 | + | 0.295105i | −0.938552 | − | 0.345137i | \(-0.887832\pi\) |
0.768173 | + | 0.640242i | \(0.221166\pi\) | |||||||
\(318\) | −11.0778 | + | 1.04575i | −0.621211 | + | 0.0586430i | ||||
\(319\) | 2.68674 | + | 1.55119i | 0.150429 | + | 0.0868500i | ||||
\(320\) | 0.866025 | − | 0.500000i | 0.0484123 | − | 0.0279508i | ||||
\(321\) | −1.84898 | + | 0.174546i | −0.103200 | + | 0.00974219i | ||||
\(322\) | 6.71280i | 0.374090i | ||||||||
\(323\) | −10.1298 | − | 29.4036i | −0.563637 | − | 1.63606i | ||||
\(324\) | −1.31922 | + | 8.90279i | −0.0732899 | + | 0.494599i | ||||
\(325\) | 1.59822 | − | 0.922734i | 0.0886534 | − | 0.0511841i | ||||
\(326\) | 9.25852 | + | 16.0362i | 0.512782 | + | 0.888165i | ||||
\(327\) | 1.46319 | − | 1.03956i | 0.0809144 | − | 0.0574876i | ||||
\(328\) | −2.08497 | − | 3.61128i | −0.115123 | − | 0.199399i | ||||
\(329\) | −10.5371 | − | 6.08359i | −0.580929 | − | 0.335399i | ||||
\(330\) | 0.573622 | − | 1.25248i | 0.0315769 | − | 0.0689470i | ||||
\(331\) | − | 7.63334i | − | 0.419566i | −0.977748 | − | 0.209783i | \(-0.932724\pi\) | ||
0.977748 | − | 0.209783i | \(-0.0672758\pi\) | |||||||
\(332\) | 12.1185 | + | 6.99659i | 0.665087 | + | 0.383988i | ||||
\(333\) | 2.04077 | + | 10.7127i | 0.111833 | + | 0.587051i | ||||
\(334\) | 19.8229 | 1.08466 | ||||||||
\(335\) | −3.65766 | −0.199839 | ||||||||
\(336\) | −3.37635 | − | 4.75224i | −0.184195 | − | 0.259256i | ||||
\(337\) | −4.98568 | + | 2.87848i | −0.271587 | + | 0.156801i | −0.629609 | − | 0.776912i | \(-0.716785\pi\) |
0.358022 | + | 0.933713i | \(0.383451\pi\) | |||||||
\(338\) | −4.79712 | + | 8.30886i | −0.260929 | + | 0.451942i | ||||
\(339\) | 20.1971 | − | 1.90663i | 1.09696 | − | 0.103554i | ||||
\(340\) | −3.56737 | − | 6.17887i | −0.193468 | − | 0.335096i | ||||
\(341\) | 6.59275 | 0.357018 | ||||||||
\(342\) | 11.3481 | − | 6.49776i | 0.613634 | − | 0.351359i | ||||
\(343\) | −8.99362 | −0.485610 | ||||||||
\(344\) | −1.75379 | − | 3.03766i | −0.0945581 | − | 0.163779i | ||||
\(345\) | −3.43925 | + | 0.324669i | −0.185163 | + | 0.0174796i | ||||
\(346\) | −3.72918 | + | 6.45913i | −0.200482 | + | 0.347245i | ||||
\(347\) | −16.8904 | + | 9.75166i | −0.906723 | + | 0.523497i | −0.879375 | − | 0.476129i | \(-0.842039\pi\) |
−0.0273475 | + | 0.999626i | \(0.508706\pi\) | |||||||
\(348\) | 3.91299 | + | 5.50758i | 0.209758 | + | 0.295237i | ||||
\(349\) | −0.423234 | −0.0226552 | −0.0113276 | − | 0.999936i | \(-0.503606\pi\) | ||||
−0.0113276 | + | 0.999936i | \(0.503606\pi\) | |||||||
\(350\) | −3.36569 | −0.179904 | ||||||||
\(351\) | 9.31167 | + | 2.29088i | 0.497020 | + | 0.122278i | ||||
\(352\) | −0.688796 | − | 0.397676i | −0.0367129 | − | 0.0211962i | ||||
\(353\) | − | 24.0186i | − | 1.27838i | −0.769049 | − | 0.639190i | \(-0.779270\pi\) | ||
0.769049 | − | 0.639190i | \(-0.220730\pi\) | |||||||
\(354\) | 6.35272 | − | 13.8709i | 0.337643 | − | 0.737232i | ||||
\(355\) | 1.38576 | + | 0.800066i | 0.0735483 | + | 0.0424631i | ||||
\(356\) | −1.83681 | − | 3.18145i | −0.0973507 | − | 0.168616i | ||||
\(357\) | −33.9060 | + | 24.0894i | −1.79450 | + | 1.27494i | ||||
\(358\) | 0.153575 | + | 0.266000i | 0.00811671 | + | 0.0140586i | ||||
\(359\) | −9.83401 | + | 5.67767i | −0.519019 | + | 0.299656i | −0.736533 | − | 0.676401i | \(-0.763539\pi\) |
0.217514 | + | 0.976057i | \(0.430205\pi\) | |||||||
\(360\) | 2.27148 | − | 1.95969i | 0.119717 | − | 0.103285i | ||||
\(361\) | −17.6188 | − | 7.11183i | −0.927305 | − | 0.374307i | ||||
\(362\) | − | 13.4600i | − | 0.707441i | ||||||
\(363\) | 17.8774 | − | 1.68765i | 0.938320 | − | 0.0885785i | ||||
\(364\) | −5.37912 | + | 3.10563i | −0.281942 | + | 0.162779i | ||||
\(365\) | −12.2189 | − | 7.05458i | −0.639566 | − | 0.369253i | ||||
\(366\) | 11.5501 | − | 1.09034i | 0.603734 | − | 0.0569932i | ||||
\(367\) | −4.59216 | + | 7.95386i | −0.239709 | + | 0.415188i | −0.960631 | − | 0.277828i | \(-0.910385\pi\) |
0.720922 | + | 0.693016i | \(0.243719\pi\) | |||||||
\(368\) | 1.99448i | 0.103970i | ||||||||
\(369\) | −8.17180 | − | 9.47193i | −0.425407 | − | 0.493089i | ||||
\(370\) | 1.81755 | − | 3.14810i | 0.0944902 | − | 0.163662i | ||||
\(371\) | 10.8109 | − | 18.7250i | 0.561274 | − | 0.972156i | ||||
\(372\) | 13.0533 | + | 5.97824i | 0.676781 | + | 0.309957i | ||||
\(373\) | 26.2996i | 1.36174i | 0.732404 | + | 0.680870i | \(0.238398\pi\) | ||||
−0.732404 | + | 0.680870i | \(0.761602\pi\) | |||||||
\(374\) | −2.83732 | + | 4.91438i | −0.146714 | + | 0.254116i | ||||
\(375\) | −0.162784 | − | 1.72438i | −0.00840612 | − | 0.0890468i | ||||
\(376\) | −3.13074 | − | 1.80753i | −0.161456 | − | 0.0932164i | ||||
\(377\) | 6.23409 | − | 3.59925i | 0.321072 | − | 0.185371i | ||||
\(378\) | −12.6180 | − | 12.1094i | −0.649002 | − | 0.622840i | ||||
\(379\) | − | 9.26609i | − | 0.475967i | −0.971269 | − | 0.237984i | \(-0.923514\pi\) | ||
0.971269 | − | 0.237984i | \(-0.0764864\pi\) | |||||||
\(380\) | −4.27895 | − | 0.831025i | −0.219505 | − | 0.0426307i | ||||
\(381\) | 5.98440 | + | 2.74078i | 0.306590 | + | 0.140414i | ||||
\(382\) | 17.5813 | − | 10.1505i | 0.899535 | − | 0.519347i | ||||
\(383\) | 11.1774 | + | 19.3598i | 0.571137 | + | 0.989238i | 0.996450 | + | 0.0841912i | \(0.0268307\pi\) |
−0.425313 | + | 0.905046i | \(0.639836\pi\) | |||||||
\(384\) | −1.00317 | − | 1.41197i | −0.0511927 | − | 0.0720542i | ||||
\(385\) | 1.33845 | + | 2.31827i | 0.0682139 | + | 0.118150i | ||||
\(386\) | 4.00713 | + | 2.31352i | 0.203957 | + | 0.117755i | ||||
\(387\) | −6.87378 | − | 7.96739i | −0.349414 | − | 0.405005i | ||||
\(388\) | − | 18.3995i | − | 0.934092i | ||||||
\(389\) | −2.10271 | − | 1.21400i | −0.106612 | − | 0.0615522i | 0.445746 | − | 0.895159i | \(-0.352938\pi\) |
−0.552358 | + | 0.833607i | \(0.686272\pi\) | |||||||
\(390\) | −1.85131 | − | 2.60574i | −0.0937449 | − | 0.131947i | ||||
\(391\) | 14.2301 | 0.719647 | ||||||||
\(392\) | 4.32785 | 0.218589 | ||||||||
\(393\) | −7.83112 | + | 5.56381i | −0.395028 | + | 0.280657i | ||||
\(394\) | −15.1687 | + | 8.75764i | −0.764187 | + | 0.441203i | ||||
\(395\) | −5.97636 | + | 10.3514i | −0.300704 | + | 0.520834i | ||||
\(396\) | −2.25314 | − | 0.785261i | −0.113225 | − | 0.0394608i | ||||
\(397\) | −13.4569 | − | 23.3080i | −0.675383 | − | 1.16980i | −0.976357 | − | 0.216165i | \(-0.930645\pi\) |
0.300974 | − | 0.953632i | \(-0.402688\pi\) | |||||||
\(398\) | 1.27580 | 0.0639500 | ||||||||
\(399\) | −2.47870 | + | 25.2892i | −0.124090 | + | 1.26604i | ||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 5.27439 | + | 9.13551i | 0.263390 | + | 0.456206i | 0.967141 | − | 0.254242i | \(-0.0818259\pi\) |
−0.703750 | + | 0.710447i | \(0.748493\pi\) | |||||||
\(402\) | 0.595408 | + | 6.30722i | 0.0296963 | + | 0.314575i | ||||
\(403\) | 7.64863 | − | 13.2478i | 0.381005 | − | 0.659921i | ||||
\(404\) | −1.03574 | + | 0.597984i | −0.0515300 | + | 0.0297508i | ||||
\(405\) | 5.59387 | − | 7.05043i | 0.277962 | − | 0.350339i | ||||
\(406\) | −13.1283 | −0.651548 | ||||||||
\(407\) | −2.89119 | −0.143311 | ||||||||
\(408\) | −10.0740 | + | 7.15734i | −0.498739 | + | 0.354341i | ||||
\(409\) | 15.0416 | + | 8.68429i | 0.743761 | + | 0.429410i | 0.823435 | − | 0.567410i | \(-0.192055\pi\) |
−0.0796743 | + | 0.996821i | \(0.525388\pi\) | |||||||
\(410\) | 4.16994i | 0.205939i | ||||||||
\(411\) | 31.3879 | + | 14.3753i | 1.54825 | + | 0.709079i | ||||
\(412\) | −1.89833 | − | 1.09600i | −0.0935240 | − | 0.0539961i | ||||
\(413\) | 14.8230 | + | 25.6743i | 0.729394 | + | 1.26335i | ||||
\(414\) | 1.11971 | + | 5.87774i | 0.0550307 | + | 0.288875i | ||||
\(415\) | −6.99659 | − | 12.1185i | −0.343449 | − | 0.594872i | ||||
\(416\) | −1.59822 | + | 0.922734i | −0.0783593 | + | 0.0452408i | ||||
\(417\) | −7.45810 | + | 16.2845i | −0.365225 | + | 0.797455i | ||||
\(418\) | 1.12923 | + | 3.27780i | 0.0552325 | + | 0.160322i | ||||
\(419\) | 29.5663i | 1.44441i | 0.691680 | + | 0.722204i | \(0.256871\pi\) | ||||
−0.691680 | + | 0.722204i | \(0.743129\pi\) | |||||||
\(420\) | 0.547880 | + | 5.80374i | 0.0267338 | + | 0.283193i | ||||
\(421\) | 2.75755 | − | 1.59207i | 0.134395 | − | 0.0775930i | −0.431295 | − | 0.902211i | \(-0.641943\pi\) |
0.565690 | + | 0.824618i | \(0.308610\pi\) | |||||||
\(422\) | −23.3524 | − | 13.4825i | −1.13678 | − | 0.656320i | ||||
\(423\) | −10.2411 | − | 3.56920i | −0.497937 | − | 0.173540i | ||||
\(424\) | 3.21210 | − | 5.56351i | 0.155993 | − | 0.270188i | ||||
\(425\) | 7.13474i | 0.346086i | ||||||||
\(426\) | 1.15404 | − | 2.51981i | 0.0559136 | − | 0.122085i | ||||
\(427\) | −11.2719 | + | 19.5234i | −0.545484 | + | 0.944806i | ||||
\(428\) | 0.536127 | − | 0.928599i | 0.0259147 | − | 0.0448855i | ||||
\(429\) | −1.05860 | + | 2.31142i | −0.0511098 | + | 0.111596i | ||||
\(430\) | 3.50758i | 0.169151i | ||||||||
\(431\) | −12.6847 | + | 21.9705i | −0.611000 | + | 1.05828i | 0.380073 | + | 0.924957i | \(0.375899\pi\) |
−0.991072 | + | 0.133326i | \(0.957434\pi\) | |||||||
\(432\) | −3.74902 | − | 3.59789i | −0.180375 | − | 0.173104i | ||||
\(433\) | −34.0276 | − | 19.6459i | −1.63526 | − | 0.944120i | −0.982433 | − | 0.186617i | \(-0.940248\pi\) |
−0.652832 | − | 0.757503i | \(-0.726419\pi\) | |||||||
\(434\) | −24.1608 | + | 13.9492i | −1.15976 | + | 0.669585i | ||||
\(435\) | −0.634961 | − | 6.72620i | −0.0304440 | − | 0.322496i | ||||
\(436\) | 1.03627i | 0.0496285i | ||||||||
\(437\) | 5.70255 | − | 6.56217i | 0.272790 | − | 0.313911i | ||||
\(438\) | −10.1758 | + | 22.2184i | −0.486217 | + | 1.06164i | ||||
\(439\) | 9.49324 | − | 5.48093i | 0.453088 | − | 0.261590i | −0.256046 | − | 0.966665i | \(-0.582420\pi\) |
0.709133 | + | 0.705074i | \(0.249086\pi\) | |||||||
\(440\) | 0.397676 | + | 0.688796i | 0.0189585 | + | 0.0328370i | ||||
\(441\) | 12.7542 | − | 2.42967i | 0.607342 | − | 0.115699i | ||||
\(442\) | 6.58347 | + | 11.4029i | 0.313144 | + | 0.542381i | ||||
\(443\) | −28.0730 | − | 16.2079i | −1.33379 | − | 0.770062i | −0.347909 | − | 0.937528i | \(-0.613108\pi\) |
−0.985878 | + | 0.167466i | \(0.946442\pi\) | |||||||
\(444\) | −5.72440 | − | 2.62170i | −0.271668 | − | 0.124421i | ||||
\(445\) | 3.67362i | 0.174146i | ||||||||
\(446\) | −19.3951 | − | 11.1978i | −0.918383 | − | 0.530229i | ||||
\(447\) | −11.8099 | + | 8.39063i | −0.558589 | + | 0.396863i | ||||
\(448\) | 3.36569 | 0.159014 | ||||||||
\(449\) | 1.66858 | 0.0787453 | 0.0393727 | − | 0.999225i | \(-0.487464\pi\) | ||||
0.0393727 | + | 0.999225i | \(0.487464\pi\) | |||||||
\(450\) | −2.94700 | + | 0.561404i | −0.138923 | + | 0.0264648i | ||||
\(451\) | 2.87224 | − | 1.65829i | 0.135248 | − | 0.0780857i | ||||
\(452\) | −5.85633 | + | 10.1435i | −0.275458 | + | 0.477108i | ||||
\(453\) | 3.63877 | + | 38.5459i | 0.170964 | + | 1.81104i | ||||
\(454\) | 8.70480 | + | 15.0772i | 0.408536 | + | 0.707606i | ||||
\(455\) | 6.21127 | 0.291189 | ||||||||
\(456\) | −0.736463 | + | 7.51383i | −0.0344880 | + | 0.351867i | ||||
\(457\) | −14.4764 | −0.677179 | −0.338589 | − | 0.940934i | \(-0.609950\pi\) | ||||
−0.338589 | + | 0.940934i | \(0.609950\pi\) | |||||||
\(458\) | −0.969958 | − | 1.68002i | −0.0453232 | − | 0.0785020i | ||||
\(459\) | −25.6700 | + | 26.7483i | −1.19817 | + | 1.24850i | ||||
\(460\) | 0.997241 | − | 1.72727i | 0.0464966 | − | 0.0805344i | ||||
\(461\) | 25.3943 | − | 14.6614i | 1.18273 | − | 0.682851i | 0.226087 | − | 0.974107i | \(-0.427407\pi\) |
0.956645 | + | 0.291256i | \(0.0940732\pi\) | |||||||
\(462\) | 3.77971 | − | 2.68539i | 0.175848 | − | 0.124936i | ||||
\(463\) | 41.3040 | 1.91956 | 0.959781 | − | 0.280751i | \(-0.0905836\pi\) | ||||
0.959781 | + | 0.280751i | \(0.0905836\pi\) | |||||||
\(464\) | −3.90064 | −0.181083 | ||||||||
\(465\) | −8.31535 | − | 11.7039i | −0.385615 | − | 0.542757i | ||||
\(466\) | −2.14005 | − | 1.23556i | −0.0991358 | − | 0.0572361i | ||||
\(467\) | 13.2112i | 0.611341i | 0.952137 | + | 0.305671i | \(0.0988806\pi\) | ||||
−0.952137 | + | 0.305671i | \(0.901119\pi\) | |||||||
\(468\) | −4.19194 | + | 3.61655i | −0.193772 | + | 0.167175i | ||||
\(469\) | −10.6612 | − | 6.15527i | −0.492291 | − | 0.284224i | ||||
\(470\) | 1.80753 | + | 3.13074i | 0.0833753 | + | 0.144410i | ||||
\(471\) | −18.2012 | − | 25.6183i | −0.838666 | − | 1.18043i | ||||
\(472\) | 4.40416 | + | 7.62824i | 0.202718 | + | 0.351118i | ||||
\(473\) | 2.41601 | − | 1.39488i | 0.111088 | − | 0.0641368i | ||||
\(474\) | 18.8226 | + | 8.62051i | 0.864550 | + | 0.395953i | ||||
\(475\) | 3.29017 | + | 2.85916i | 0.150963 | + | 0.131187i | ||||
\(476\) | − | 24.0133i | − | 1.10065i | ||||||
\(477\) | 6.34268 | − | 18.1990i | 0.290411 | − | 0.833274i | ||||
\(478\) | 11.4275 | − | 6.59766i | 0.522681 | − | 0.301770i | ||||
\(479\) | 29.9827 | + | 17.3105i | 1.36995 | + | 0.790939i | 0.990921 | − | 0.134448i | \(-0.0429261\pi\) |
0.379025 | + | 0.925386i | \(0.376259\pi\) | |||||||
\(480\) | 0.162784 | + | 1.72438i | 0.00743003 | + | 0.0787070i | ||||
\(481\) | −3.35424 | + | 5.80971i | −0.152940 | + | 0.264900i | ||||
\(482\) | − | 27.2332i | − | 1.24044i | ||||||
\(483\) | −10.5710 | − | 4.84139i | −0.480997 | − | 0.220291i | ||||
\(484\) | −5.18371 | + | 8.97844i | −0.235623 | + | 0.408111i | ||||
\(485\) | −9.19973 | + | 15.9344i | −0.417738 | + | 0.723544i | ||||
\(486\) | −13.0682 | − | 8.49829i | −0.592788 | − | 0.385490i | ||||
\(487\) | − | 20.7783i | − | 0.941554i | −0.882252 | − | 0.470777i | \(-0.843974\pi\) | ||
0.882252 | − | 0.470777i | \(-0.156026\pi\) | |||||||
\(488\) | −3.34905 | + | 5.80073i | −0.151605 | + | 0.262587i | ||||
\(489\) | −31.9305 | + | 3.01428i | −1.44395 | + | 0.136310i | ||||
\(490\) | −3.74803 | − | 2.16392i | −0.169319 | − | 0.0977562i | ||||
\(491\) | 3.62316 | − | 2.09183i | 0.163511 | − | 0.0944030i | −0.416012 | − | 0.909359i | \(-0.636572\pi\) |
0.579522 | + | 0.814956i | \(0.303239\pi\) | |||||||
\(492\) | 7.19059 | − | 0.678800i | 0.324177 | − | 0.0306027i | ||||
\(493\) | 27.8300i | 1.25340i | ||||||||
\(494\) | 7.89666 | + | 1.53363i | 0.355288 | + | 0.0690013i | ||||
\(495\) | 1.55865 | + | 1.80663i | 0.0700559 | + | 0.0812018i | ||||
\(496\) | −7.17856 | + | 4.14455i | −0.322327 | + | 0.186096i | ||||
\(497\) | 2.69277 | + | 4.66402i | 0.120787 | + | 0.209210i | ||||
\(498\) | −19.7579 | + | 14.0375i | −0.885375 | + | 0.629036i | ||||
\(499\) | 2.93329 | + | 5.08061i | 0.131312 | + | 0.227439i | 0.924183 | − | 0.381951i | \(-0.124748\pi\) |
−0.792871 | + | 0.609390i | \(0.791414\pi\) | |||||||
\(500\) | 0.866025 | + | 0.500000i | 0.0387298 | + | 0.0223607i | ||||
\(501\) | −14.2966 | + | 31.2162i | −0.638726 | + | 1.39464i | ||||
\(502\) | 21.5465i | 0.961668i | ||||||||
\(503\) | −9.79822 | − | 5.65701i | −0.436881 | − | 0.252233i | 0.265393 | − | 0.964140i | \(-0.414498\pi\) |
−0.702274 | + | 0.711907i | \(0.747832\pi\) | |||||||
\(504\) | 9.91869 | − | 1.88951i | 0.441814 | − | 0.0841655i | ||||
\(505\) | 1.19597 | 0.0532199 | ||||||||
\(506\) | −1.58632 | −0.0705204 | ||||||||
\(507\) | −9.62463 | − | 13.5468i | −0.427445 | − | 0.601633i | ||||
\(508\) | −3.29108 | + | 1.90011i | −0.146018 | + | 0.0843036i | ||||
\(509\) | 10.8249 | − | 18.7493i | 0.479806 | − | 0.831048i | −0.519926 | − | 0.854211i | \(-0.674040\pi\) |
0.999732 | + | 0.0231634i | \(0.00737381\pi\) | |||||||
\(510\) | 12.3030 | − | 1.16142i | 0.544788 | − | 0.0514286i | ||||
\(511\) | −23.7435 | − | 41.1249i | −1.05035 | − | 1.81926i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 2.04794 | + | 22.5567i | 0.0904186 | + | 0.995904i | ||||
\(514\) | −28.9234 | −1.27576 | ||||||||
\(515\) | 1.09600 | + | 1.89833i | 0.0482956 | + | 0.0836504i | ||||
\(516\) | 6.04842 | − | 0.570978i | 0.266267 | − | 0.0251359i | ||||
\(517\) | 1.43763 | − | 2.49004i | 0.0632268 | − | 0.109512i | ||||
\(518\) | 10.5955 | − | 6.11732i | 0.465540 | − | 0.268780i | ||||
\(519\) | −7.48198 | − | 10.5310i | −0.328423 | − | 0.462259i | ||||
\(520\) | 1.84547 | 0.0809291 | ||||||||
\(521\) | 31.4041 | 1.37584 | 0.687920 | − | 0.725787i | \(-0.258524\pi\) | ||||
0.687920 | + | 0.725787i | \(0.258524\pi\) | |||||||
\(522\) | −11.4952 | + | 2.18983i | −0.503131 | + | 0.0958464i | ||||
\(523\) | 9.94201 | + | 5.74002i | 0.434734 | + | 0.250994i | 0.701361 | − | 0.712806i | \(-0.252576\pi\) |
−0.266627 | + | 0.963800i | \(0.585909\pi\) | |||||||
\(524\) | − | 5.54624i | − | 0.242289i | ||||||
\(525\) | 2.42739 | − | 5.30012i | 0.105940 | − | 0.231316i | ||||
\(526\) | 13.9401 | + | 8.04833i | 0.607818 | + | 0.350924i | ||||
\(527\) | 29.5703 | + | 51.2172i | 1.28810 | + | 2.23106i | ||||
\(528\) | 1.12301 | − | 0.797872i | 0.0488729 | − | 0.0347229i | ||||
\(529\) | −9.51102 | − | 16.4736i | −0.413523 | − | 0.716242i | ||||
\(530\) | −5.56351 | + | 3.21210i | −0.241664 | + | 0.139525i | ||||
\(531\) | 17.2616 | + | 20.0079i | 0.749090 | + | 0.868270i | ||||
\(532\) | −11.0737 | − | 9.62305i | −0.480104 | − | 0.417212i | ||||
\(533\) | − | 7.69550i | − | 0.333329i | ||||||
\(534\) | 6.33473 | − | 0.598006i | 0.274131 | − | 0.0258782i | ||||
\(535\) | −0.928599 | + | 0.536127i | −0.0401468 | + | 0.0231788i | ||||
\(536\) | −3.16763 | − | 1.82883i | −0.136821 | − | 0.0789935i | ||||
\(537\) | −0.529646 | + | 0.0499992i | −0.0228559 | + | 0.00215762i | ||||
\(538\) | 7.78283 | − | 13.4803i | 0.335542 | − | 0.581175i | ||||
\(539\) | 3.44217i | 0.148265i | ||||||||
\(540\) | 1.44780 | + | 4.99038i | 0.0623034 | + | 0.214752i | ||||
\(541\) | 15.6183 | − | 27.0516i | 0.671482 | − | 1.16304i | −0.306002 | − | 0.952031i | \(-0.598991\pi\) |
0.977484 | − | 0.211010i | \(-0.0676752\pi\) | |||||||
\(542\) | 1.20476 | − | 2.08670i | 0.0517488 | − | 0.0896316i | ||||
\(543\) | 21.1962 | + | 9.70757i | 0.909614 | + | 0.416592i | ||||
\(544\) | − | 7.13474i | − | 0.305899i | ||||||
\(545\) | 0.518137 | − | 0.897440i | 0.0221946 | − | 0.0384421i | ||||
\(546\) | −1.01109 | − | 10.7106i | −0.0432708 | − | 0.458372i | ||||
\(547\) | −6.49439 | − | 3.74954i | −0.277680 | − | 0.160319i | 0.354693 | − | 0.934983i | \(-0.384586\pi\) |
−0.632373 | + | 0.774664i | \(0.717919\pi\) | |||||||
\(548\) | −17.2616 | + | 9.96597i | −0.737377 | + | 0.425725i | ||||
\(549\) | −6.61312 | + | 18.9749i | −0.282241 | + | 0.809831i | ||||
\(550\) | − | 0.795353i | − | 0.0339140i | ||||||
\(551\) | 12.8337 | + | 11.1526i | 0.546736 | + | 0.475115i | ||||
\(552\) | −3.14081 | − | 1.43845i | −0.133682 | − | 0.0612247i | ||||
\(553\) | −34.8395 | + | 20.1146i | −1.48152 | + | 0.855359i | ||||
\(554\) | −15.3945 | − | 26.6640i | −0.654049 | − | 1.13285i | ||||
\(555\) | 3.64662 | + | 5.13266i | 0.154791 | + | 0.217869i | ||||
\(556\) | −5.17049 | − | 8.95556i | −0.219278 | − | 0.379800i | ||||
\(557\) | −9.64943 | − | 5.57110i | −0.408860 | − | 0.236055i | 0.281440 | − | 0.959579i | \(-0.409188\pi\) |
−0.690300 | + | 0.723524i | \(0.742521\pi\) | |||||||
\(558\) | −18.8285 | + | 16.2441i | −0.797073 | + | 0.687666i | ||||
\(559\) | − | 6.47313i | − | 0.273784i | ||||||
\(560\) | −2.91477 | − | 1.68284i | −0.123172 | − | 0.0711131i | ||||
\(561\) | −5.69261 | − | 8.01241i | −0.240342 | − | 0.338284i | ||||
\(562\) | −25.3356 | −1.06872 | ||||||||
\(563\) | −25.6386 | −1.08054 | −0.540269 | − | 0.841492i | \(-0.681677\pi\) | ||||
−0.540269 | + | 0.841492i | \(0.681677\pi\) | |||||||
\(564\) | 5.10436 | − | 3.62652i | 0.214932 | − | 0.152704i | ||||
\(565\) | 10.1435 | − | 5.85633i | 0.426738 | − | 0.246378i | ||||
\(566\) | 4.10956 | − | 7.11797i | 0.172738 | − | 0.299191i | ||||
\(567\) | 28.1696 | − | 11.1368i | 1.18301 | − | 0.467701i | ||||
\(568\) | 0.800066 | + | 1.38576i | 0.0335700 | + | 0.0581450i | ||||
\(569\) | 36.2410 | 1.51930 | 0.759651 | − | 0.650331i | \(-0.225370\pi\) | ||||
0.759651 | + | 0.650331i | \(0.225370\pi\) | |||||||
\(570\) | 4.39471 | − | 6.13894i | 0.184074 | − | 0.257132i | ||||
\(571\) | 6.61731 | 0.276926 | 0.138463 | − | 0.990368i | \(-0.455784\pi\) | ||||
0.138463 | + | 0.990368i | \(0.455784\pi\) | |||||||
\(572\) | −0.733899 | − | 1.27115i | −0.0306859 | − | 0.0531495i | ||||
\(573\) | 3.30469 | + | 35.0069i | 0.138055 | + | 1.46243i | ||||
\(574\) | −7.01736 | + | 12.1544i | −0.292899 | + | 0.507316i | ||||
\(575\) | −1.72727 | + | 0.997241i | −0.0720322 | + | 0.0415878i | ||||
\(576\) | 2.94700 | − | 0.561404i | 0.122792 | − | 0.0233918i | ||||
\(577\) | 36.0337 | 1.50010 | 0.750051 | − | 0.661380i | \(-0.230029\pi\) | ||||
0.750051 | + | 0.661380i | \(0.230029\pi\) | |||||||
\(578\) | −33.9045 | −1.41024 | ||||||||
\(579\) | −6.53323 | + | 4.64169i | −0.271512 | + | 0.192902i | ||||
\(580\) | 3.37805 | + | 1.95032i | 0.140266 | + | 0.0809826i | ||||
\(581\) | − | 47.0967i | − | 1.95390i | ||||||
\(582\) | 28.9746 | + | 13.2700i | 1.20104 | + | 0.550060i | ||||
\(583\) | 4.42496 | + | 2.55475i | 0.183263 | + | 0.105807i | ||||
\(584\) | −7.05458 | − | 12.2189i | −0.291920 | − | 0.505621i | ||||
\(585\) | 5.43860 | − | 1.03605i | 0.224858 | − | 0.0428355i | ||||
\(586\) | −12.2234 | − | 21.1716i | −0.504944 | − | 0.874589i | ||||
\(587\) | 24.1606 | − | 13.9491i | 0.997214 | − | 0.575742i | 0.0897909 | − | 0.995961i | \(-0.471380\pi\) |
0.907423 | + | 0.420219i | \(0.138047\pi\) | |||||||
\(588\) | −3.12132 | + | 6.81529i | −0.128721 | + | 0.281058i | ||||
\(589\) | 35.4686 | + | 6.88844i | 1.46146 | + | 0.283833i | ||||
\(590\) | − | 8.80833i | − | 0.362633i | ||||||
\(591\) | −2.85120 | − | 30.2031i | −0.117283 | − | 1.24239i | ||||
\(592\) | 3.14810 | − | 1.81755i | 0.129386 | − | 0.0747010i | ||||
\(593\) | −12.3343 | − | 7.12119i | −0.506508 | − | 0.292432i | 0.224889 | − | 0.974384i | \(-0.427798\pi\) |
−0.731397 | + | 0.681952i | \(0.761131\pi\) | |||||||
\(594\) | 2.86159 | − | 2.98179i | 0.117413 | − | 0.122345i | ||||
\(595\) | −12.0067 | + | 20.7961i | −0.492225 | + | 0.852558i | ||||
\(596\) | − | 8.36414i | − | 0.342608i | ||||||
\(597\) | −0.920128 | + | 2.00907i | −0.0376583 | + | 0.0822257i | ||||
\(598\) | −1.84038 | + | 3.18762i | −0.0752586 | + | 0.130352i | ||||
\(599\) | −9.64054 | + | 16.6979i | −0.393902 | + | 0.682258i | −0.992960 | − | 0.118447i | \(-0.962208\pi\) |
0.599059 | + | 0.800705i | \(0.295542\pi\) | |||||||
\(600\) | 0.721217 | − | 1.57475i | 0.0294436 | − | 0.0642890i | ||||
\(601\) | 41.5244i | 1.69382i | 0.531740 | + | 0.846908i | \(0.321538\pi\) | ||||
−0.531740 | + | 0.846908i | \(0.678462\pi\) | |||||||
\(602\) | −5.90271 | + | 10.2238i | −0.240577 | + | 0.416691i | ||||
\(603\) | −10.3617 | − | 3.61125i | −0.421962 | − | 0.147062i | ||||
\(604\) | −19.3586 | − | 11.1767i | −0.787691 | − | 0.454773i | ||||
\(605\) | 8.97844 | − | 5.18371i | 0.365026 | − | 0.210748i | ||||
\(606\) | −0.194684 | − | 2.06231i | −0.00790852 | − | 0.0837756i | ||||
\(607\) | 24.8694i | 1.00942i | 0.863290 | + | 0.504709i | \(0.168400\pi\) | ||||
−0.863290 | + | 0.504709i | \(0.831600\pi\) | |||||||
\(608\) | −3.29017 | − | 2.85916i | −0.133434 | − | 0.115954i | ||||
\(609\) | 9.46837 | − | 20.6739i | 0.383678 | − | 0.837747i | ||||
\(610\) | 5.80073 | − | 3.34905i | 0.234865 | − | 0.135599i | ||||
\(611\) | −3.33575 | − | 5.77768i | −0.134950 | − | 0.233740i | ||||
\(612\) | −4.00547 | − | 21.0261i | −0.161912 | − | 0.849930i | ||||
\(613\) | 3.40073 | + | 5.89023i | 0.137354 | + | 0.237904i | 0.926494 | − | 0.376309i | \(-0.122807\pi\) |
−0.789140 | + | 0.614213i | \(0.789474\pi\) | |||||||
\(614\) | 9.65029 | + | 5.57160i | 0.389454 | + | 0.224851i | ||||
\(615\) | −6.56663 | − | 3.00744i | −0.264792 | − | 0.121271i | ||||
\(616\) | 2.67691i | 0.107856i | ||||||||
\(617\) | 4.62048 | + | 2.66763i | 0.186013 | + | 0.107395i | 0.590115 | − | 0.807319i | \(-0.299082\pi\) |
−0.404101 | + | 0.914714i | \(0.632416\pi\) | |||||||
\(618\) | 3.09504 | − | 2.19894i | 0.124501 | − | 0.0884545i | ||||
\(619\) | 9.41765 | 0.378528 | 0.189264 | − | 0.981926i | \(-0.439390\pi\) | ||||
0.189264 | + | 0.981926i | \(0.439390\pi\) | |||||||
\(620\) | 8.28909 | 0.332898 | ||||||||
\(621\) | −10.0635 | − | 2.47586i | −0.403836 | − | 0.0993529i | ||||
\(622\) | −21.1657 | + | 12.2200i | −0.848666 | + | 0.489977i | ||||
\(623\) | −6.18212 | + | 10.7078i | −0.247682 | + | 0.428997i | ||||
\(624\) | −0.300413 | − | 3.18230i | −0.0120261 | − | 0.127394i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 2.12928 | 0.0851033 | ||||||||
\(627\) | −5.97614 | − | 0.585748i | −0.238664 | − | 0.0233925i | ||||
\(628\) | 18.1437 | 0.724013 | ||||||||
\(629\) | −12.9678 | − | 22.4609i | −0.517059 | − | 0.895573i | ||||
\(630\) | −9.53459 | − | 3.32298i | −0.379867 | − | 0.132391i | ||||
\(631\) | 14.1067 | − | 24.4335i | 0.561578 | − | 0.972682i | −0.435781 | − | 0.900053i | \(-0.643528\pi\) |
0.997359 | − | 0.0726292i | \(-0.0231390\pi\) | |||||||
\(632\) | −10.3514 | + | 5.97636i | −0.411755 | + | 0.237727i | ||||
\(633\) | 38.0739 | − | 27.0505i | 1.51330 | − | 1.07516i | ||||
\(634\) | 6.06702 | 0.240952 | ||||||||
\(635\) | 3.80022 | 0.150807 | ||||||||
\(636\) | 6.44454 | + | 9.07076i | 0.255543 | + | 0.359679i | ||||
\(637\) | 6.91687 | + | 3.99345i | 0.274056 | + | 0.158226i | ||||
\(638\) | − | 3.10238i | − | 0.122825i | ||||||
\(639\) | 3.13577 | + | 3.63467i | 0.124049 | + | 0.143785i | ||||
\(640\) | −0.866025 | − | 0.500000i | −0.0342327 | − | 0.0197642i | ||||
\(641\) | 4.02668 | + | 6.97441i | 0.159044 | + | 0.275473i | 0.934524 | − | 0.355899i | \(-0.115825\pi\) |
−0.775480 | + | 0.631372i | \(0.782492\pi\) | |||||||
\(642\) | 1.07565 | + | 1.51399i | 0.0424525 | + | 0.0597524i | ||||
\(643\) | −11.4346 | − | 19.8053i | −0.450936 | − | 0.781044i | 0.547509 | − | 0.836800i | \(-0.315576\pi\) |
−0.998444 | + | 0.0557564i | \(0.982243\pi\) | |||||||
\(644\) | 5.81345 | − | 3.35640i | 0.229082 | − | 0.132261i | ||||
\(645\) | −5.52357 | − | 2.52973i | −0.217491 | − | 0.0996080i | ||||
\(646\) | −20.3994 | + | 23.4745i | −0.802603 | + | 0.923591i | ||||
\(647\) | − | 12.1854i | − | 0.479056i | −0.970889 | − | 0.239528i | \(-0.923007\pi\) | ||
0.970889 | − | 0.239528i | \(-0.0769926\pi\) | |||||||
\(648\) | 8.36965 | − | 3.30892i | 0.328791 | − | 0.129987i | ||||
\(649\) | −6.06714 | + | 3.50286i | −0.238156 | + | 0.137499i | ||||
\(650\) | −1.59822 | − | 0.922734i | −0.0626874 | − | 0.0361926i | ||||
\(651\) | −4.54142 | − | 48.1077i | −0.177992 | − | 1.88549i | ||||
\(652\) | 9.25852 | − | 16.0362i | 0.362592 | − | 0.628027i | ||||
\(653\) | 46.1577i | 1.80629i | 0.429335 | + | 0.903145i | \(0.358748\pi\) | ||||
−0.429335 | + | 0.903145i | \(0.641252\pi\) | |||||||
\(654\) | −1.63188 | − | 0.747379i | −0.0638114 | − | 0.0292248i | ||||
\(655\) | −2.77312 | + | 4.80319i | −0.108355 | + | 0.187676i | ||||
\(656\) | −2.08497 | + | 3.61128i | −0.0814045 | + | 0.140997i | ||||
\(657\) | −27.6496 | − | 32.0486i | −1.07871 | − | 1.25034i | ||||
\(658\) | 12.1672i | 0.474326i | ||||||||
\(659\) | 7.15219 | − | 12.3880i | 0.278610 | − | 0.482567i | −0.692430 | − | 0.721485i | \(-0.743460\pi\) |
0.971040 | + | 0.238919i | \(0.0767930\pi\) | |||||||
\(660\) | −1.37149 | + | 0.129471i | −0.0533853 | + | 0.00503964i | ||||
\(661\) | −10.1413 | − | 5.85511i | −0.394452 | − | 0.227737i | 0.289635 | − | 0.957137i | \(-0.406466\pi\) |
−0.684088 | + | 0.729400i | \(0.739799\pi\) | |||||||
\(662\) | −6.61066 | + | 3.81667i | −0.256931 | + | 0.148339i | ||||
\(663\) | −22.7049 | + | 2.14337i | −0.881784 | + | 0.0832414i | ||||
\(664\) | − | 13.9932i | − | 0.543041i | ||||||
\(665\) | 4.77855 | + | 13.8706i | 0.185304 | + | 0.537880i | ||||
\(666\) | 8.25707 | − | 7.12369i | 0.319955 | − | 0.276038i | ||||
\(667\) | −6.73746 | + | 3.88987i | −0.260875 | + | 0.150617i | ||||
\(668\) | −9.91145 | − | 17.1671i | −0.383486 | − | 0.664217i | ||||
\(669\) | 31.6217 | − | 22.4664i | 1.22257 | − | 0.868602i | ||||
\(670\) | 1.82883 | + | 3.16763i | 0.0706539 | + | 0.122376i | ||||
\(671\) | −4.61363 | − | 2.66368i | −0.178107 | − | 0.102830i | ||||
\(672\) | −2.42739 | + | 5.30012i | −0.0936387 | + | 0.204457i | ||||
\(673\) | − | 0.722505i | − | 0.0278505i | −0.999903 | − | 0.0139253i | \(-0.995567\pi\) | ||
0.999903 | − | 0.0139253i | \(-0.00443269\pi\) | |||||||
\(674\) | 4.98568 | + | 2.87848i | 0.192041 | + | 0.110875i | ||||
\(675\) | 1.24136 | − | 5.04569i | 0.0477798 | − | 0.194209i | ||||
\(676\) | 9.59425 | 0.369009 | ||||||||
\(677\) | −13.7283 | −0.527620 | −0.263810 | − | 0.964575i | \(-0.584979\pi\) | ||||
−0.263810 | + | 0.964575i | \(0.584979\pi\) | |||||||
\(678\) | −11.7497 | − | 16.5379i | −0.451246 | − | 0.635134i | ||||
\(679\) | −53.6302 | + | 30.9634i | −2.05814 | + | 1.18827i | ||||
\(680\) | −3.56737 | + | 6.17887i | −0.136802 | + | 0.236949i | ||||
\(681\) | −30.0208 | + | 2.83400i | −1.15040 | + | 0.108599i | ||||
\(682\) | −3.29638 | − | 5.70949i | −0.126225 | − | 0.218628i | ||||
\(683\) | 27.2992 | 1.04457 | 0.522287 | − | 0.852770i | \(-0.325079\pi\) | ||||
0.522287 | + | 0.852770i | \(0.325079\pi\) | |||||||
\(684\) | −11.3013 | − | 6.57885i | −0.432115 | − | 0.251549i | ||||
\(685\) | 19.9319 | 0.761560 | ||||||||
\(686\) | 4.49681 | + | 7.78871i | 0.171689 | + | 0.297374i | ||||
\(687\) | 3.34516 | − | 0.315787i | 0.127626 | − | 0.0120480i | ||||
\(688\) | −1.75379 | + | 3.03766i | −0.0668627 | + | 0.115810i | ||||
\(689\) | 10.2673 | − | 5.92782i | 0.391152 | − | 0.225832i | ||||
\(690\) | 2.00080 | + | 2.81615i | 0.0761691 | + | 0.107209i | ||||
\(691\) | −7.97929 | −0.303546 | −0.151773 | − | 0.988415i | \(-0.548498\pi\) | ||||
−0.151773 | + | 0.988415i | \(0.548498\pi\) | |||||||
\(692\) | 7.45836 | 0.283524 | ||||||||
\(693\) | 1.50283 | + | 7.88886i | 0.0570877 | + | 0.299673i | ||||
\(694\) | 16.8904 | + | 9.75166i | 0.641150 | + | 0.370168i | ||||
\(695\) | 10.3410i | 0.392256i | ||||||||
\(696\) | 2.81321 | − | 6.14254i | 0.106634 | − | 0.232832i | ||||
\(697\) | 25.7655 | + | 14.8757i | 0.975939 | + | 0.563459i | ||||
\(698\) | 0.211617 | + | 0.366531i | 0.00800982 | + | 0.0138734i | ||||
\(699\) | 3.48914 | − | 2.47894i | 0.131971 | − | 0.0937621i | ||||
\(700\) | 1.68284 | + | 2.91477i | 0.0636055 | + | 0.110168i | ||||
\(701\) | −34.6741 | + | 20.0191i | −1.30962 | + | 0.756111i | −0.982033 | − | 0.188710i | \(-0.939569\pi\) |
−0.327589 | + | 0.944820i | \(0.606236\pi\) | |||||||
\(702\) | −2.67187 | − | 9.20958i | −0.100843 | − | 0.347593i | ||||
\(703\) | −15.5544 | − | 3.02087i | −0.586647 | − | 0.113934i | ||||
\(704\) | 0.795353i | 0.0299760i | ||||||||
\(705\) | −6.23377 | + | 0.588475i | −0.234777 | + | 0.0221632i | ||||
\(706\) | −20.8007 | + | 12.0093i | −0.782845 | + | 0.451976i | ||||
\(707\) | 3.48597 | + | 2.01263i | 0.131104 | + | 0.0756927i | ||||
\(708\) | −15.1889 | + | 1.43385i | −0.570836 | + | 0.0538875i | ||||
\(709\) | −7.94313 | + | 13.7579i | −0.298310 | + | 0.516689i | −0.975750 | − | 0.218890i | \(-0.929756\pi\) |
0.677439 | + | 0.735579i | \(0.263090\pi\) | |||||||
\(710\) | − | 1.60013i | − | 0.0600519i | ||||||
\(711\) | −27.1504 | + | 23.4237i | −1.01822 | + | 0.878456i | ||||
\(712\) | −1.83681 | + | 3.18145i | −0.0688373 | + | 0.119230i | ||||
\(713\) | −8.26622 | + | 14.3175i | −0.309572 | + | 0.536195i | ||||
\(714\) | 37.8150 | + | 17.3188i | 1.41519 | + | 0.648140i | ||||
\(715\) | 1.46780i | 0.0548925i | ||||||||
\(716\) | 0.153575 | − | 0.266000i | 0.00573938 | − | 0.00994090i | ||||
\(717\) | 2.14799 | + | 22.7538i | 0.0802180 | + | 0.849756i | ||||
\(718\) | 9.83401 | + | 5.67767i | 0.367002 | + | 0.211889i | ||||
\(719\) | −10.7413 | + | 6.20149i | −0.400583 | + | 0.231276i | −0.686735 | − | 0.726908i | \(-0.740957\pi\) |
0.286153 | + | 0.958184i | \(0.407624\pi\) | |||||||
\(720\) | −2.83288 | − | 0.987311i | −0.105575 | − | 0.0367949i | ||||
\(721\) | 7.37759i | 0.274756i | ||||||||
\(722\) | 2.65038 | + | 18.8142i | 0.0986368 | + | 0.700193i | ||||
\(723\) | 42.8855 | + | 19.6411i | 1.59493 | + | 0.730459i | ||||
\(724\) | −11.6567 | + | 6.72999i | −0.433218 | + | 0.250118i | ||||
\(725\) | −1.95032 | − | 3.37805i | −0.0724330 | − | 0.125458i | ||||
\(726\) | −10.4002 | − | 14.6385i | −0.385989 | − | 0.543284i | ||||
\(727\) | 10.0726 | + | 17.4462i | 0.373571 | + | 0.647044i | 0.990112 | − | 0.140279i | \(-0.0447999\pi\) |
−0.616541 | + | 0.787323i | \(0.711467\pi\) | |||||||
\(728\) | 5.37912 | + | 3.10563i | 0.199363 | + | 0.115102i | ||||
\(729\) | 22.8077 | − | 14.4501i | 0.844731 | − | 0.535191i | ||||
\(730\) | 14.1092i | 0.522203i | ||||||||
\(731\) | 21.6729 | + | 12.5128i | 0.801601 | + | 0.462804i | ||||
\(732\) | −6.71932 | − | 9.45752i | −0.248353 | − | 0.349560i | ||||
\(733\) | −50.0396 | −1.84826 | −0.924128 | − | 0.382084i | \(-0.875207\pi\) | ||||
−0.924128 | + | 0.382084i | \(0.875207\pi\) | |||||||
\(734\) | 9.18432 | 0.339000 | ||||||||
\(735\) | 6.11079 | − | 4.34156i | 0.225400 | − | 0.160141i | ||||
\(736\) | 1.72727 | − | 0.997241i | 0.0636681 | − | 0.0367588i | ||||
\(737\) | 1.45457 | − | 2.51938i | 0.0535796 | − | 0.0928026i | ||||
\(738\) | −4.11703 | + | 11.8130i | −0.151550 | + | 0.434841i | ||||
\(739\) | −6.80780 | − | 11.7914i | −0.250429 | − | 0.433755i | 0.713215 | − | 0.700945i | \(-0.247238\pi\) |
−0.963644 | + | 0.267190i | \(0.913905\pi\) | |||||||
\(740\) | −3.63511 | −0.133629 | ||||||||
\(741\) | −8.11030 | + | 11.3292i | −0.297939 | + | 0.416189i | ||||
\(742\) | −21.6218 | −0.793762 | ||||||||
\(743\) | 9.67139 | + | 16.7513i | 0.354809 | + | 0.614547i | 0.987085 | − | 0.160196i | \(-0.0512126\pi\) |
−0.632276 | + | 0.774743i | \(0.717879\pi\) | |||||||
\(744\) | −1.34933 | − | 14.2936i | −0.0494689 | − | 0.524028i | ||||
\(745\) | −4.18207 | + | 7.24356i | −0.153219 | + | 0.265383i | ||||
\(746\) | 22.7761 | − | 13.1498i | 0.833892 | − | 0.481448i | ||||
\(747\) | −7.85583 | − | 41.2380i | −0.287430 | − | 1.50882i | ||||
\(748\) | 5.67464 | 0.207485 | ||||||||
\(749\) | −3.60887 | −0.131865 | ||||||||
\(750\) | −1.41197 | + | 1.00317i | −0.0515578 | + | 0.0366305i | ||||
\(751\) | 11.2415 | + | 6.49028i | 0.410208 | + | 0.236834i | 0.690879 | − | 0.722970i | \(-0.257224\pi\) |
−0.280671 | + | 0.959804i | \(0.590557\pi\) | |||||||
\(752\) | 3.61507i | 0.131828i | ||||||||
\(753\) | −33.9304 | − | 15.5397i | −1.23649 | − | 0.566299i | ||||
\(754\) | −6.23409 | − | 3.59925i | −0.227032 | − | 0.131077i | ||||
\(755\) | 11.1767 | + | 19.3586i | 0.406762 | + | 0.704532i | ||||
\(756\) | −4.17802 | + | 16.9822i | −0.151953 | + | 0.617638i | ||||
\(757\) | −18.4177 | − | 31.9004i | −0.669403 | − | 1.15944i | −0.978071 | − | 0.208270i | \(-0.933217\pi\) |
0.308668 | − | 0.951170i | \(-0.400117\pi\) | |||||||
\(758\) | −8.02467 | + | 4.63305i | −0.291469 | + | 0.168280i | ||||
\(759\) | 1.14408 | − | 2.49806i | 0.0415274 | − | 0.0906737i | ||||
\(760\) | 1.41979 | + | 4.12119i | 0.0515010 | + | 0.149491i | ||||
\(761\) | − | 24.0894i | − | 0.873241i | −0.899646 | − | 0.436621i | \(-0.856175\pi\) | ||
0.899646 | − | 0.436621i | \(-0.143825\pi\) | |||||||
\(762\) | −0.618614 | − | 6.55303i | −0.0224100 | − | 0.237391i | ||||
\(763\) | 3.02050 | − | 1.74389i | 0.109350 | − | 0.0631330i | ||||
\(764\) | −17.5813 | − | 10.1505i | −0.636067 | − | 0.367234i | ||||
\(765\) | −7.04421 | + | 20.2119i | −0.254684 | + | 0.730762i | ||||
\(766\) | 11.1774 | − | 19.3598i | 0.403855 | − | 0.699497i | ||||
\(767\) | 16.2555i | 0.586952i | ||||||||
\(768\) | −0.721217 | + | 1.57475i | −0.0260247 | + | 0.0568240i | ||||
\(769\) | 1.39798 | − | 2.42138i | 0.0504126 | − | 0.0873172i | −0.839718 | − | 0.543023i | \(-0.817280\pi\) |
0.890131 | + | 0.455706i | \(0.150613\pi\) | |||||||
\(770\) | 1.33845 | − | 2.31827i | 0.0482345 | − | 0.0835447i | ||||
\(771\) | 20.8601 | − | 45.5472i | 0.751257 | − | 1.64034i | ||||
\(772\) | − | 4.62703i | − | 0.166531i | ||||||
\(773\) | 4.17275 | − | 7.22742i | 0.150084 | − | 0.259952i | −0.781174 | − | 0.624313i | \(-0.785379\pi\) |
0.931258 | + | 0.364361i | \(0.118712\pi\) | |||||||
\(774\) | −3.46308 | + | 9.93656i | −0.124478 | + | 0.357162i | ||||
\(775\) | −7.17856 | − | 4.14455i | −0.257862 | − | 0.148876i | ||||
\(776\) | −15.9344 | + | 9.19973i | −0.572012 | + | 0.330251i | ||||
\(777\) | 1.99160 | + | 21.0972i | 0.0714483 | + | 0.756859i | ||||
\(778\) | 2.42800i | 0.0870480i | ||||||||
\(779\) | 17.1851 | − | 5.92042i | 0.615721 | − | 0.212121i | ||||
\(780\) | −1.33098 | + | 2.90616i | −0.0476569 | + | 0.104057i | ||||
\(781\) | −1.10216 | + | 0.636335i | −0.0394386 | + | 0.0227699i | ||||
\(782\) | −7.11505 | − | 12.3236i | −0.254434 | − | 0.440692i | ||||
\(783\) | 4.84208 | − | 19.6814i | 0.173042 | − | 0.703357i | ||||
\(784\) | −2.16392 | − | 3.74803i | −0.0772830 | − | 0.133858i | ||||
\(785\) | −15.7129 | − | 9.07185i | −0.560818 | − | 0.323788i | ||||
\(786\) | 8.73396 | + | 4.00005i | 0.311530 | + | 0.142677i | ||||
\(787\) | − | 34.0004i | − | 1.21198i | −0.795471 | − | 0.605992i | \(-0.792776\pi\) | ||
0.795471 | − | 0.605992i | \(-0.207224\pi\) | |||||||
\(788\) | 15.1687 | + | 8.75764i | 0.540362 | + | 0.311978i | ||||
\(789\) | −22.7280 | + | 16.1476i | −0.809138 | + | 0.574871i | ||||
\(790\) | 11.9527 | 0.425259 | ||||||||
\(791\) | 39.4211 | 1.40165 | ||||||||
\(792\) | 0.446514 | + | 2.34391i | 0.0158662 | + | 0.0832871i | ||||
\(793\) | −10.7051 | + | 6.18057i | −0.380148 | + | 0.219479i | ||||
\(794\) | −13.4569 | + | 23.3080i | −0.477568 | + | 0.827172i | ||||
\(795\) | −1.04575 | − | 11.0778i | −0.0370891 | − | 0.392888i | ||||
\(796\) | −0.637900 | − | 1.10487i | −0.0226097 | − | 0.0391612i | ||||
\(797\) | 0.634867 | 0.0224881 | 0.0112441 | − | 0.999937i | \(-0.496421\pi\) | ||||
0.0112441 | + | 0.999937i | \(0.496421\pi\) | |||||||
\(798\) | 23.1404 | − | 10.4980i | 0.819163 | − | 0.371624i | ||||
\(799\) | 25.7926 | 0.912475 | ||||||||
\(800\) | 0.500000 | + | 0.866025i | 0.0176777 | + | 0.0306186i | ||||
\(801\) | −3.62700 | + | 10.4069i | −0.128154 | + | 0.367711i | ||||
\(802\) | 5.27439 | − | 9.13551i | 0.186245 | − | 0.322586i | ||||
\(803\) | 9.71833 | − | 5.61088i | 0.342952 | − | 0.198004i | ||||
\(804\) | 5.16450 | − | 3.66925i | 0.182138 | − | 0.129404i | ||||
\(805\) | −6.71280 | −0.236595 | ||||||||
\(806\) | −15.2973 | −0.538823 | ||||||||
\(807\) | 15.6150 | + | 21.9782i | 0.549673 | + | 0.773670i | ||||
\(808\) | 1.03574 | + | 0.597984i | 0.0364372 | + | 0.0210370i | ||||
\(809\) | 47.4357i | 1.66775i | 0.551953 | + | 0.833875i | \(0.313883\pi\) | ||||
−0.551953 | + | 0.833875i | \(0.686117\pi\) | |||||||
\(810\) | −8.90279 | − | 1.31922i | −0.312812 | − | 0.0463526i | ||||
\(811\) | −30.2251 | − | 17.4505i | −1.06135 | − | 0.612770i | −0.135544 | − | 0.990771i | \(-0.543278\pi\) |
−0.925805 | + | 0.378002i | \(0.876611\pi\) | |||||||
\(812\) | 6.56416 | + | 11.3695i | 0.230357 | + | 0.398990i | ||||
\(813\) | 2.41715 | + | 3.40216i | 0.0847731 | + | 0.119319i | ||||
\(814\) | 1.44560 | + | 2.50385i | 0.0506682 | + | 0.0877598i | ||||
\(815\) | −16.0362 | + | 9.25852i | −0.561725 | + | 0.324312i | ||||
\(816\) | 11.2355 | + | 5.14570i | 0.393319 | + | 0.180135i | ||||
\(817\) | 14.4554 | − | 4.98001i | 0.505731 | − | 0.174229i | ||||
\(818\) | − | 17.3686i | − | 0.607278i | ||||||
\(819\) | 17.5958 | + | 6.13246i | 0.614847 | + | 0.214285i | ||||
\(820\) | 3.61128 | − | 2.08497i | 0.126111 | − | 0.0728104i | ||||
\(821\) | 15.1395 | + | 8.74082i | 0.528373 | + | 0.305057i | 0.740354 | − | 0.672217i | \(-0.234658\pi\) |
−0.211980 | + | 0.977274i | \(0.567991\pi\) | |||||||
\(822\) | −3.24460 | − | 34.3703i | −0.113168 | − | 1.19880i | ||||
\(823\) | −4.16579 | + | 7.21536i | −0.145210 | + | 0.251512i | −0.929451 | − | 0.368945i | \(-0.879719\pi\) |
0.784241 | + | 0.620456i | \(0.213053\pi\) | |||||||
\(824\) | 2.19200i | 0.0763620i | ||||||||
\(825\) | 1.25248 | + | 0.573622i | 0.0436059 | + | 0.0199710i | ||||
\(826\) | 14.8230 | − | 25.6743i | 0.515760 | − | 0.893322i | ||||
\(827\) | 26.3348 | − | 45.6132i | 0.915751 | − | 1.58613i | 0.109954 | − | 0.993937i | \(-0.464930\pi\) |
0.805797 | − | 0.592191i | \(-0.201737\pi\) | |||||||
\(828\) | 4.53042 | − | 3.90857i | 0.157443 | − | 0.135832i | ||||
\(829\) | 26.7190i | 0.927990i | 0.885838 | + | 0.463995i | \(0.153584\pi\) | ||||
−0.885838 | + | 0.463995i | \(0.846416\pi\) | |||||||
\(830\) | −6.99659 | + | 12.1185i | −0.242855 | + | 0.420638i | ||||
\(831\) | 53.0920 | − | 5.01195i | 1.84174 | − | 0.173863i | ||||
\(832\) | 1.59822 | + | 0.922734i | 0.0554084 | + | 0.0319901i | ||||
\(833\) | −26.7412 | + | 15.4390i | −0.926528 | + | 0.534931i | ||||
\(834\) | 17.8318 | − | 1.68335i | 0.617466 | − | 0.0582895i | ||||
\(835\) | 19.8229i | 0.686000i | ||||||||
\(836\) | 2.27404 | − | 2.61684i | 0.0786494 | − | 0.0905054i | ||||
\(837\) | −12.0010 | − | 41.3657i | −0.414814 | − | 1.42981i | ||||
\(838\) | 25.6052 | − | 14.7832i | 0.884516 | − | 0.510676i | ||||
\(839\) | −19.4936 | − | 33.7640i | −0.672996 | − | 1.16566i | −0.977050 | − | 0.213008i | \(-0.931674\pi\) |
0.304055 | − | 0.952655i | \(-0.401659\pi\) | |||||||
\(840\) | 4.75224 | − | 3.37635i | 0.163968 | − | 0.116495i | ||||
\(841\) | 6.89251 | + | 11.9382i | 0.237673 | + | 0.411662i | ||||
\(842\) | −2.75755 | − | 1.59207i | −0.0950316 | − | 0.0548665i | ||||
\(843\) | 18.2725 | − | 39.8973i | 0.629337 | − | 1.37414i | ||||
\(844\) | 26.9651i | 0.928177i | ||||||||
\(845\) | −8.30886 | − | 4.79712i | −0.285834 | − | 0.165026i | ||||
\(846\) | 2.02951 | + | 10.6536i | 0.0697761 | + | 0.366279i | ||||
\(847\) | 34.8935 | 1.19895 | ||||||||
\(848\) | −6.42419 | −0.220608 | ||||||||
\(849\) | 8.24515 | + | 11.6051i | 0.282973 | + | 0.398288i | ||||
\(850\) | 6.17887 | − | 3.56737i | 0.211933 | − | 0.122360i | ||||
\(851\) | 3.62508 | − | 6.27882i | 0.124266 | − | 0.215235i | ||||
\(852\) | −2.75924 | + | 0.260476i | −0.0945301 | + | 0.00892376i | ||||
\(853\) | 3.28239 | + | 5.68527i | 0.112387 | + | 0.194660i | 0.916732 | − | 0.399502i | \(-0.130817\pi\) |
−0.804345 | + | 0.594162i | \(0.797484\pi\) | |||||||
\(854\) | 22.5437 | 0.771431 | ||||||||
\(855\) | 6.49776 | + | 11.3481i | 0.222219 | + | 0.388096i | ||||
\(856\) | −1.07225 | −0.0366489 | ||||||||
\(857\) | 0.771649 | + | 1.33654i | 0.0263590 | + | 0.0456552i | 0.878904 | − | 0.476999i | \(-0.158275\pi\) |
−0.852545 | + | 0.522654i | \(0.824942\pi\) | |||||||
\(858\) | 2.53105 | − | 0.238934i | 0.0864086 | − | 0.00815707i | ||||
\(859\) | 2.26168 | − | 3.91734i | 0.0771674 | − | 0.133658i | −0.824859 | − | 0.565338i | \(-0.808746\pi\) |
0.902027 | + | 0.431680i | \(0.142079\pi\) | |||||||
\(860\) | 3.03766 | − | 1.75379i | 0.103583 | − | 0.0598038i | ||||
\(861\) | −14.0792 | − | 19.8166i | −0.479817 | − | 0.675348i | ||||
\(862\) | 25.3694 | 0.864084 | ||||||||
\(863\) | 11.5515 | 0.393217 | 0.196608 | − | 0.980482i | \(-0.437007\pi\) | ||||
0.196608 | + | 0.980482i | \(0.437007\pi\) | |||||||
\(864\) | −1.24136 | + | 5.04569i | −0.0422318 | + | 0.171658i | ||||
\(865\) | −6.45913 | − | 3.72918i | −0.219617 | − | 0.126796i | ||||
\(866\) | 39.2917i | 1.33519i | ||||||||
\(867\) | 24.4525 | − | 53.3912i | 0.830451 | − | 1.81326i | ||||
\(868\) | 24.1608 | + | 13.9492i | 0.820071 | + | 0.473468i | ||||
\(869\) | −4.75332 | − | 8.23299i | −0.161245 | − | 0.279285i | ||||
\(870\) | −5.50758 | + | 3.91299i | −0.186724 | + | 0.132663i | ||||
\(871\) | −3.37505 | − | 5.84576i | −0.114359 | − | 0.198076i | ||||
\(872\) | 0.897440 | − | 0.518137i | 0.0303912 | − | 0.0175463i | ||||
\(873\) | −41.7940 | + | 36.0573i | −1.41451 | + | 1.22035i | ||||
\(874\) | −8.53428 | − | 1.65746i | −0.288676 | − | 0.0560645i | ||||
\(875\) | − | 3.36569i | − | 0.113781i | ||||||
\(876\) | 24.3296 | − | 2.29674i | 0.822021 | − | 0.0775998i | ||||
\(877\) | 44.7475 | − | 25.8350i | 1.51102 | − | 0.872386i | 0.511099 | − | 0.859522i | \(-0.329239\pi\) |
0.999917 | − | 0.0128639i | \(-0.00409481\pi\) | |||||||
\(878\) | −9.49324 | − | 5.48093i | −0.320381 | − | 0.184972i | ||||
\(879\) | 42.1557 | − | 3.97955i | 1.42188 | − | 0.134227i | ||||
\(880\) | 0.397676 | − | 0.688796i | 0.0134057 | − | 0.0232193i | ||||
\(881\) | − | 8.64964i | − | 0.291414i | −0.989328 | − | 0.145707i | \(-0.953454\pi\) | ||
0.989328 | − | 0.145707i | \(-0.0465457\pi\) | |||||||
\(882\) | −8.48125 | − | 9.83061i | −0.285579 | − | 0.331014i | ||||
\(883\) | 27.8076 | − | 48.1641i | 0.935799 | − | 1.62085i | 0.162597 | − | 0.986692i | \(-0.448013\pi\) |
0.773202 | − | 0.634160i | \(-0.218654\pi\) | |||||||
\(884\) | 6.58347 | − | 11.4029i | 0.221426 | − | 0.383521i | ||||
\(885\) | 13.8709 | + | 6.35272i | 0.466267 | + | 0.213544i | ||||
\(886\) | 32.4159i | 1.08903i | ||||||||
\(887\) | 15.4908 | − | 26.8308i | 0.520129 | − | 0.900890i | −0.479597 | − | 0.877489i | \(-0.659217\pi\) |
0.999726 | − | 0.0234014i | \(-0.00744958\pi\) | |||||||
\(888\) | 0.591737 | + | 6.26833i | 0.0198574 | + | 0.210351i | ||||
\(889\) | 11.0768 | + | 6.39517i | 0.371502 | + | 0.214487i | ||||
\(890\) | 3.18145 | − | 1.83681i | 0.106642 | − | 0.0615700i | ||||
\(891\) | 2.63176 | + | 6.65683i | 0.0881672 | + | 0.223012i | ||||
\(892\) | 22.3955i | 0.749857i | ||||||||
\(893\) | 10.3361 | − | 11.8942i | 0.345883 | − | 0.398023i | ||||
\(894\) | 13.1714 | + | 6.03236i | 0.440519 | + | 0.201752i | ||||
\(895\) | −0.266000 | + | 0.153575i | −0.00889141 | + | 0.00513346i | ||||
\(896\) | −1.68284 | − | 2.91477i | −0.0562199 | − | 0.0973756i | ||||
\(897\) | −3.69241 | − | 5.19711i | −0.123286 | − | 0.173526i | ||||
\(898\) | −0.834292 | − | 1.44504i | −0.0278407 | − | 0.0482215i | ||||
\(899\) | −28.0010 | − | 16.1664i | −0.933885 | − | 0.539179i | ||||
\(900\) | 1.95969 | + | 2.27148i | 0.0653231 | + | 0.0757159i | ||||
\(901\) | 45.8349i | 1.52698i | ||||||||
\(902\) | −2.87224 | − | 1.65829i | −0.0956351 | − | 0.0552150i | ||||
\(903\) | −11.8428 | − | 16.6689i | −0.394104 | − | 0.554706i | ||||
\(904\) | 11.7127 | 0.389557 | ||||||||
\(905\) | 13.4600 | 0.447425 | ||||||||
\(906\) | 31.5623 | − | 22.4242i | 1.04859 | − | 0.744994i | ||||
\(907\) | −19.5392 | + | 11.2809i | −0.648788 | + | 0.374578i | −0.787992 | − | 0.615686i | \(-0.788879\pi\) |
0.139204 | + | 0.990264i | \(0.455546\pi\) | |||||||
\(908\) | 8.70480 | − | 15.0772i | 0.288879 | − | 0.500353i | ||||
\(909\) | 3.38804 | + | 1.18079i | 0.112374 | + | 0.0391644i | ||||
\(910\) | −3.10563 | − | 5.37912i | −0.102951 | − | 0.178316i | ||||
\(911\) | −33.0252 | −1.09417 | −0.547086 | − | 0.837076i | \(-0.684263\pi\) | ||||
−0.547086 | + | 0.837076i | \(0.684263\pi\) | |||||||
\(912\) | 6.87540 | − | 3.11912i | 0.227667 | − | 0.103284i | ||||
\(913\) | 11.1295 | 0.368333 | ||||||||
\(914\) | 7.23822 | + | 12.5370i | 0.239419 | + | 0.414686i | ||||
\(915\) | 1.09034 | + | 11.5501i | 0.0360457 | + | 0.381835i | ||||
\(916\) | −0.969958 | + | 1.68002i | −0.0320483 | + | 0.0555093i | ||||
\(917\) | −16.1660 | + | 9.33346i | −0.533849 | + | 0.308218i | ||||
\(918\) | 35.9997 | + | 8.85676i | 1.18817 | + | 0.292317i | ||||
\(919\) | 2.71554 | 0.0895776 | 0.0447888 | − | 0.998996i | \(-0.485739\pi\) | ||||
0.0447888 | + | 0.998996i | \(0.485739\pi\) | |||||||
\(920\) | −1.99448 | −0.0657561 | ||||||||
\(921\) | −15.7338 | + | 11.1785i | −0.518448 | + | 0.368344i | ||||
\(922\) | −25.3943 | − | 14.6614i | −0.836318 | − | 0.482848i | ||||
\(923\) | 2.95299i | 0.0971990i | ||||||||
\(924\) | −4.21547 | − | 1.93063i | −0.138679 | − | 0.0635131i | ||||
\(925\) | 3.14810 | + | 1.81755i | 0.103509 | + | 0.0597608i | ||||
\(926\) | −20.6520 | − | 35.7703i | −0.678667 | − | 1.17549i | ||||
\(927\) | 1.23060 | + | 6.45983i | 0.0404182 | + | 0.212169i | ||||
\(928\) | 1.95032 | + | 3.37805i | 0.0640223 | + | 0.110890i | ||||
\(929\) | −45.5906 | + | 26.3217i | −1.49578 | + | 0.863588i | −0.999988 | − | 0.00485418i | \(-0.998455\pi\) |
−0.495790 | + | 0.868442i | \(0.665122\pi\) | |||||||
\(930\) | −5.97824 | + | 13.0533i | −0.196034 | + | 0.428034i | ||||
\(931\) | −3.59655 | + | 18.5186i | −0.117872 | + | 0.606924i | ||||
\(932\) | 2.47111i | 0.0809440i | ||||||||
\(933\) | −3.97844 | − | 42.1440i | −0.130248 | − | 1.37973i | ||||
\(934\) | 11.4412 | − | 6.60560i | 0.374369 | − | 0.216142i | ||||
\(935\) | −4.91438 | − | 2.83732i | −0.160717 | − | 0.0927902i | ||||
\(936\) | 5.22799 | + | 1.82205i | 0.170882 | + | 0.0595556i | ||||
\(937\) | 1.99845 | − | 3.46141i | 0.0652865 | − | 0.113079i | −0.831535 | − | 0.555473i | \(-0.812537\pi\) |
0.896821 | + | 0.442394i | \(0.145871\pi\) | |||||||
\(938\) | 12.3105i | 0.401954i | ||||||||
\(939\) | −1.53568 | + | 3.35310i | −0.0501149 | + | 0.109424i | ||||
\(940\) | 1.80753 | − | 3.13074i | 0.0589552 | − | 0.102113i | ||||
\(941\) | −10.2092 | + | 17.6829i | −0.332811 | + | 0.576446i | −0.983062 | − | 0.183274i | \(-0.941331\pi\) |
0.650251 | + | 0.759720i | \(0.274664\pi\) | |||||||
\(942\) | −13.0856 | + | 28.5718i | −0.426350 | + | 0.930921i | ||||
\(943\) | 8.31687i | 0.270835i | ||||||||
\(944\) | 4.40416 | − | 7.62824i | 0.143343 | − | 0.248278i | ||||
\(945\) | 12.1094 | − | 12.6180i | 0.393918 | − | 0.410465i | ||||
\(946\) | −2.41601 | − | 1.39488i | −0.0785512 | − | 0.0453515i | ||||
\(947\) | 28.8707 | − | 16.6685i | 0.938171 | − | 0.541654i | 0.0487848 | − | 0.998809i | \(-0.484465\pi\) |
0.889387 | + | 0.457156i | \(0.151132\pi\) | |||||||
\(948\) | −1.94571 | − | 20.6111i | −0.0631938 | − | 0.669417i | ||||
\(949\) | − | 26.0380i | − | 0.845229i | ||||||
\(950\) | 0.831025 | − | 4.27895i | 0.0269620 | − | 0.138827i | ||||
\(951\) | −4.37564 | + | 9.55406i | −0.141890 | + | 0.309811i | ||||
\(952\) | −20.7961 | + | 12.0067i | −0.674007 | + | 0.389138i | ||||
\(953\) | −5.27108 | − | 9.12979i | −0.170747 | − | 0.295743i | 0.767934 | − | 0.640529i | \(-0.221285\pi\) |
−0.938681 | + | 0.344786i | \(0.887951\pi\) | |||||||
\(954\) | −18.9321 | + | 3.60657i | −0.612950 | + | 0.116767i | ||||
\(955\) | 10.1505 | + | 17.5813i | 0.328464 | + | 0.568916i | ||||
\(956\) | −11.4275 | − | 6.59766i | −0.369591 | − | 0.213384i | ||||
\(957\) | 4.88549 | + | 2.23749i | 0.157925 | + | 0.0723278i | ||||
\(958\) | − | 34.6211i | − | 1.11856i | ||||||
\(959\) | 58.0970 | + | 33.5423i | 1.87605 | + | 1.08314i | ||||
\(960\) | 1.41197 | − | 1.00317i | 0.0455711 | − | 0.0323771i | ||||
\(961\) | −37.7091 | −1.21642 | ||||||||
\(962\) | 6.70848 | 0.216290 | ||||||||
\(963\) | −3.15993 | + | 0.601968i | −0.101827 | + | 0.0193981i | ||||
\(964\) | −23.5846 | + | 13.6166i | −0.759610 | + | 0.438561i | ||||
\(965\) | −2.31352 | + | 4.00713i | −0.0744747 | + | 0.128994i | ||||
\(966\) | 1.09274 | + | 11.5754i | 0.0351582 | + | 0.372434i | ||||
\(967\) | 28.1558 | + | 48.7673i | 0.905431 | + | 1.56825i | 0.820338 | + | 0.571879i | \(0.193785\pi\) |
0.0850923 | + | 0.996373i | \(0.472881\pi\) | |||||||
\(968\) | 10.3674 | 0.333221 | ||||||||
\(969\) | −22.2541 | − | 49.0542i | −0.714905 | − | 1.57585i | ||||
\(970\) | 18.3995 | 0.590771 | ||||||||
\(971\) | −20.9023 | − | 36.2039i | −0.670787 | − | 1.16184i | −0.977681 | − | 0.210094i | \(-0.932623\pi\) |
0.306894 | − | 0.951744i | \(-0.400710\pi\) | |||||||
\(972\) | −0.825609 | + | 15.5666i | −0.0264814 | + | 0.499298i | ||||
\(973\) | −17.4023 | + | 30.1416i | −0.557891 | + | 0.966295i | ||||
\(974\) | −17.9945 | + | 10.3891i | −0.576582 | + | 0.332890i | ||||
\(975\) | 2.60574 | − | 1.85131i | 0.0834506 | − | 0.0592895i | ||||
\(976\) | 6.69811 | 0.214401 | ||||||||
\(977\) | −15.3174 | −0.490046 | −0.245023 | − | 0.969517i | \(-0.578795\pi\) | ||||
−0.245023 | + | 0.969517i | \(0.578795\pi\) | |||||||
\(978\) | 18.5757 | + | 26.1455i | 0.593985 | + | 0.836041i | ||||
\(979\) | −2.53037 | − | 1.46091i | −0.0808711 | − | 0.0466909i | ||||
\(980\) | 4.32785i | 0.138248i | ||||||||
\(981\) | 2.35387 | − | 2.03078i | 0.0751534 | − | 0.0648378i | ||||
\(982\) | −3.62316 | − | 2.09183i | −0.115620 | − | 0.0667530i | ||||
\(983\) | 1.68463 | + | 2.91786i | 0.0537313 | + | 0.0930654i | 0.891640 | − | 0.452745i | \(-0.149555\pi\) |
−0.837909 | + | 0.545810i | \(0.816222\pi\) | |||||||
\(984\) | −4.18315 | − | 5.88783i | −0.133354 | − | 0.187697i | ||||
\(985\) | −8.75764 | − | 15.1687i | −0.279042 | − | 0.483314i | ||||
\(986\) | 24.1015 | − | 13.9150i | 0.767549 | − | 0.443144i | ||||
\(987\) | −19.1603 | − | 8.77518i | −0.609879 | − | 0.279317i | ||||
\(988\) | −2.62017 | − | 7.60553i | −0.0833587 | − | 0.241964i | ||||
\(989\) | 6.99581i | 0.222454i | ||||||||
\(990\) | 0.785261 | − | 2.25314i | 0.0249572 | − | 0.0716095i | ||||
\(991\) | 38.7708 | − | 22.3843i | 1.23159 | − | 0.711061i | 0.264232 | − | 0.964459i | \(-0.414882\pi\) |
0.967362 | + | 0.253398i | \(0.0815483\pi\) | |||||||
\(992\) | 7.17856 | + | 4.14455i | 0.227920 | + | 0.131589i | ||||
\(993\) | −1.24258 | − | 13.1628i | −0.0394322 | − | 0.417709i | ||||
\(994\) | 2.69277 | − | 4.66402i | 0.0854096 | − | 0.147934i | ||||
\(995\) | 1.27580i | 0.0404455i | ||||||||
\(996\) | 22.0358 | + | 10.0921i | 0.698231 | + | 0.319781i | ||||
\(997\) | −1.88035 | + | 3.25686i | −0.0595512 | + | 0.103146i | −0.894264 | − | 0.447540i | \(-0.852300\pi\) |
0.834713 | + | 0.550685i | \(0.185634\pi\) | |||||||
\(998\) | 2.93329 | − | 5.08061i | 0.0928516 | − | 0.160824i | ||||
\(999\) | 5.26291 | + | 18.1406i | 0.166511 | + | 0.573942i |
(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 | 570.2.s.a.221.12 | ✓ | 24 | |
3.2 | odd | 2 | 570.2.s.b.221.9 | yes | 24 | ||
19.8 | odd | 6 | 570.2.s.b.521.9 | yes | 24 | ||
57.8 | even | 6 | inner | 570.2.s.a.521.12 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.s.a.221.12 | ✓ | 24 | 1.1 | even | 1 | trivial | |
570.2.s.a.521.12 | yes | 24 | 57.8 | even | 6 | inner | |
570.2.s.b.221.9 | yes | 24 | 3.2 | odd | 2 | ||
570.2.s.b.521.9 | yes | 24 | 19.8 | odd | 6 |