Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(148,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.f (of order \(5\), degree \(4\), not 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: | \(6.76332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} + \cdots + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | no (minimal twist has level 77) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 323.4 | ||
Root | \(1.60551 + 1.16647i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.323 |
Dual form | 847.2.f.x.729.4 |
$q$-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 \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.60551 | + | 1.16647i | 1.13526 | + | 0.824818i | 0.986452 | − | 0.164048i | \(-0.0524551\pi\) |
0.148812 | + | 0.988866i | \(0.452455\pi\) | |||||||
\(3\) | 0.861043 | − | 2.65002i | 0.497123 | − | 1.52999i | −0.316498 | − | 0.948593i | \(-0.602507\pi\) |
0.813621 | − | 0.581395i | \(-0.197493\pi\) | |||||||
\(4\) | 0.598967 | + | 1.84343i | 0.299484 | + | 0.921716i | ||||
\(5\) | 0.0217822 | − | 0.0158257i | 0.00974131 | − | 0.00707748i | −0.582904 | − | 0.812541i | \(-0.698084\pi\) |
0.592645 | + | 0.805464i | \(0.298084\pi\) | |||||||
\(6\) | 4.47357 | − | 3.25024i | 1.82633 | − | 1.32691i | ||||
\(7\) | −0.309017 | − | 0.951057i | −0.116797 | − | 0.359466i | ||||
\(8\) | 0.0378378 | − | 0.116453i | 0.0133777 | − | 0.0411723i | ||||
\(9\) | −3.85415 | − | 2.80020i | −1.28472 | − | 0.933401i | ||||
\(10\) | 0.0534317 | 0.0168966 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 5.40087 | 1.55910 | ||||||||
\(13\) | −3.94891 | − | 2.86905i | −1.09523 | − | 0.795731i | −0.114955 | − | 0.993371i | \(-0.536672\pi\) |
−0.980275 | + | 0.197639i | \(0.936672\pi\) | |||||||
\(14\) | 0.613249 | − | 1.88739i | 0.163898 | − | 0.504425i | ||||
\(15\) | −0.0231830 | − | 0.0713500i | −0.00598583 | − | 0.0184225i | ||||
\(16\) | 3.33282 | − | 2.42144i | 0.833205 | − | 0.605359i | ||||
\(17\) | 1.35816 | − | 0.986762i | 0.329402 | − | 0.239325i | −0.410775 | − | 0.911737i | \(-0.634742\pi\) |
0.740177 | + | 0.672412i | \(0.234742\pi\) | |||||||
\(18\) | −2.92151 | − | 8.99149i | −0.688607 | − | 2.11931i | ||||
\(19\) | −0.424571 | + | 1.30670i | −0.0974033 | + | 0.299776i | −0.987873 | − | 0.155267i | \(-0.950376\pi\) |
0.890469 | + | 0.455043i | \(0.150376\pi\) | |||||||
\(20\) | 0.0422205 | + | 0.0306750i | 0.00944079 | + | 0.00685914i | ||||
\(21\) | −2.78639 | −0.608041 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.06246 | 1.68114 | 0.840570 | − | 0.541703i | \(-0.182220\pi\) | ||||
0.840570 | + | 0.541703i | \(0.182220\pi\) | |||||||
\(24\) | −0.276022 | − | 0.200542i | −0.0563428 | − | 0.0409354i | ||||
\(25\) | −1.54486 | + | 4.75459i | −0.308972 | + | 0.950919i | ||||
\(26\) | −2.99334 | − | 9.21255i | −0.587042 | − | 1.80673i | ||||
\(27\) | −3.97645 | + | 2.88906i | −0.765269 | + | 0.556000i | ||||
\(28\) | 1.56812 | − | 1.13930i | 0.296346 | − | 0.215308i | ||||
\(29\) | 1.97560 | + | 6.08026i | 0.366859 | + | 1.12908i | 0.948809 | + | 0.315851i | \(0.102290\pi\) |
−0.581950 | + | 0.813225i | \(0.697710\pi\) | |||||||
\(30\) | 0.0460070 | − | 0.141595i | 0.00839969 | − | 0.0258516i | ||||
\(31\) | −3.24460 | − | 2.35734i | −0.582747 | − | 0.423390i | 0.256967 | − | 0.966420i | \(-0.417277\pi\) |
−0.839713 | + | 0.543030i | \(0.817277\pi\) | |||||||
\(32\) | 7.93050 | 1.40193 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.33156 | 0.571358 | ||||||||
\(35\) | −0.0217822 | − | 0.0158257i | −0.00368187 | − | 0.00267504i | ||||
\(36\) | 2.85347 | − | 8.78209i | 0.475579 | − | 1.46368i | ||||
\(37\) | 0.161010 | + | 0.495536i | 0.0264698 | + | 0.0814657i | 0.963419 | − | 0.268001i | \(-0.0863629\pi\) |
−0.936949 | + | 0.349466i | \(0.886363\pi\) | |||||||
\(38\) | −2.20587 | + | 1.60266i | −0.357839 | + | 0.259986i | ||||
\(39\) | −11.0032 | + | 7.99430i | −1.76192 | + | 1.28011i | ||||
\(40\) | −0.00101876 | − | 0.00313541i | −0.000161080 | − | 0.000495752i | ||||
\(41\) | 3.27519 | − | 10.0800i | 0.511499 | − | 1.57423i | −0.278064 | − | 0.960563i | \(-0.589693\pi\) |
0.789563 | − | 0.613669i | \(-0.210307\pi\) | |||||||
\(42\) | −4.47357 | − | 3.25024i | −0.690287 | − | 0.501523i | ||||
\(43\) | −3.73968 | −0.570296 | −0.285148 | − | 0.958483i | \(-0.592043\pi\) | ||||
−0.285148 | + | 0.958483i | \(0.592043\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.128267 | −0.0191209 | ||||||||
\(46\) | 12.9443 | + | 9.40461i | 1.90854 | + | 1.38663i | ||||
\(47\) | −2.76850 | + | 8.52058i | −0.403828 | + | 1.24285i | 0.518042 | + | 0.855355i | \(0.326661\pi\) |
−0.921870 | + | 0.387499i | \(0.873339\pi\) | |||||||
\(48\) | −3.54715 | − | 10.9170i | −0.511987 | − | 1.57573i | ||||
\(49\) | −0.809017 | + | 0.587785i | −0.115574 | + | 0.0839693i | ||||
\(50\) | −8.02637 | + | 5.83150i | −1.13510 | + | 0.824698i | ||||
\(51\) | −1.44550 | − | 4.44879i | −0.202411 | − | 0.622956i | ||||
\(52\) | 2.92363 | − | 8.99801i | 0.405435 | − | 1.24780i | ||||
\(53\) | 3.20417 | + | 2.32797i | 0.440127 | + | 0.319771i | 0.785685 | − | 0.618626i | \(-0.212311\pi\) |
−0.345558 | + | 0.938397i | \(0.612311\pi\) | |||||||
\(54\) | −9.75422 | −1.32738 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.122446 | −0.0163625 | ||||||||
\(57\) | 3.09719 | + | 2.25024i | 0.410233 | + | 0.298052i | ||||
\(58\) | −3.92060 | + | 12.0664i | −0.514800 | + | 1.58439i | ||||
\(59\) | 3.00680 | + | 9.25399i | 0.391452 | + | 1.20477i | 0.931690 | + | 0.363254i | \(0.118334\pi\) |
−0.540238 | + | 0.841512i | \(0.681666\pi\) | |||||||
\(60\) | 0.117643 | − | 0.0854726i | 0.0151876 | − | 0.0110345i | ||||
\(61\) | 6.85013 | − | 4.97691i | 0.877069 | − | 0.637228i | −0.0554053 | − | 0.998464i | \(-0.517645\pi\) |
0.932474 | + | 0.361236i | \(0.117645\pi\) | |||||||
\(62\) | −2.45946 | − | 7.56944i | −0.312352 | − | 0.961320i | ||||
\(63\) | −1.47215 | + | 4.53082i | −0.185474 | + | 0.570830i | ||||
\(64\) | 6.06683 | + | 4.40781i | 0.758354 | + | 0.550976i | ||||
\(65\) | −0.131421 | −0.0163008 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.81285 | 0.343644 | 0.171822 | − | 0.985128i | \(-0.445035\pi\) | ||||
0.171822 | + | 0.985128i | \(0.445035\pi\) | |||||||
\(68\) | 2.63252 | + | 1.91264i | 0.319240 | + | 0.231942i | ||||
\(69\) | 6.94213 | − | 21.3657i | 0.835734 | − | 2.57212i | ||||
\(70\) | −0.0165113 | − | 0.0508166i | −0.00197348 | − | 0.00607375i | ||||
\(71\) | −1.65485 | + | 1.20232i | −0.196395 | + | 0.142689i | −0.681637 | − | 0.731691i | \(-0.738732\pi\) |
0.485242 | + | 0.874380i | \(0.338732\pi\) | |||||||
\(72\) | −0.471924 | + | 0.342873i | −0.0556168 | + | 0.0404079i | ||||
\(73\) | 3.23520 | + | 9.95693i | 0.378652 | + | 1.16537i | 0.940982 | + | 0.338457i | \(0.109905\pi\) |
−0.562330 | + | 0.826913i | \(0.690095\pi\) | |||||||
\(74\) | −0.319526 | + | 0.983399i | −0.0371441 | + | 0.114318i | ||||
\(75\) | 11.2696 | + | 8.18782i | 1.30130 | + | 0.945448i | ||||
\(76\) | −2.66311 | −0.305479 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −26.9908 | −3.05611 | ||||||||
\(79\) | 4.73697 | + | 3.44161i | 0.532950 | + | 0.387211i | 0.821460 | − | 0.570266i | \(-0.193160\pi\) |
−0.288510 | + | 0.957477i | \(0.593160\pi\) | |||||||
\(80\) | 0.0342753 | − | 0.105489i | 0.00383210 | − | 0.0117940i | ||||
\(81\) | −0.184290 | − | 0.567186i | −0.0204767 | − | 0.0630207i | ||||
\(82\) | 17.0163 | − | 12.3631i | 1.87914 | − | 1.36528i | ||||
\(83\) | 2.10787 | − | 1.53146i | 0.231369 | − | 0.168100i | −0.466060 | − | 0.884753i | \(-0.654327\pi\) |
0.697430 | + | 0.716653i | \(0.254327\pi\) | |||||||
\(84\) | −1.66896 | − | 5.13653i | −0.182098 | − | 0.560441i | ||||
\(85\) | 0.0139676 | − | 0.0429878i | 0.00151500 | − | 0.00466268i | ||||
\(86\) | −6.00409 | − | 4.36222i | −0.647437 | − | 0.470391i | ||||
\(87\) | 17.8139 | 1.90985 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.21791 | 0.129099 | 0.0645493 | − | 0.997915i | \(-0.479439\pi\) | ||||
0.0645493 | + | 0.997915i | \(0.479439\pi\) | |||||||
\(90\) | −0.205934 | − | 0.149620i | −0.0217073 | − | 0.0157713i | ||||
\(91\) | −1.50835 | + | 4.64222i | −0.158118 | + | 0.486637i | ||||
\(92\) | 4.82915 | + | 14.8626i | 0.503474 | + | 1.54953i | ||||
\(93\) | −9.04072 | + | 6.56847i | −0.937479 | + | 0.681119i | ||||
\(94\) | −14.3838 | + | 10.4505i | −1.48358 | + | 1.07788i | ||||
\(95\) | 0.0114313 | + | 0.0351819i | 0.00117283 | + | 0.00360959i | ||||
\(96\) | 6.82851 | − | 21.0160i | 0.696931 | − | 2.14493i | ||||
\(97\) | −2.74799 | − | 1.99653i | −0.279016 | − | 0.202717i | 0.439472 | − | 0.898256i | \(-0.355166\pi\) |
−0.718488 | + | 0.695539i | \(0.755166\pi\) | |||||||
\(98\) | −1.98451 | −0.200466 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −9.69009 | −0.969009 | ||||||||
\(101\) | −3.27519 | − | 2.37956i | −0.325893 | − | 0.236775i | 0.412793 | − | 0.910825i | \(-0.364553\pi\) |
−0.738686 | + | 0.674050i | \(0.764553\pi\) | |||||||
\(102\) | 2.86862 | − | 8.82870i | 0.284036 | − | 0.874171i | ||||
\(103\) | −1.22153 | − | 3.75950i | −0.120361 | − | 0.370434i | 0.872666 | − | 0.488317i | \(-0.162389\pi\) |
−0.993027 | + | 0.117883i | \(0.962389\pi\) | |||||||
\(104\) | −0.483527 | + | 0.351303i | −0.0474137 | + | 0.0344481i | ||||
\(105\) | −0.0606939 | + | 0.0440967i | −0.00592312 | + | 0.00430340i | ||||
\(106\) | 2.42882 | + | 7.47513i | 0.235908 | + | 0.726049i | ||||
\(107\) | −3.21335 | + | 9.88966i | −0.310646 | + | 0.956070i | 0.666864 | + | 0.745179i | \(0.267636\pi\) |
−0.977510 | + | 0.210890i | \(0.932364\pi\) | |||||||
\(108\) | −7.70756 | − | 5.59987i | −0.741660 | − | 0.538848i | ||||
\(109\) | 3.77697 | 0.361768 | 0.180884 | − | 0.983504i | \(-0.442104\pi\) | ||||
0.180884 | + | 0.983504i | \(0.442104\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.45182 | 0.137800 | ||||||||
\(112\) | −3.33282 | − | 2.42144i | −0.314922 | − | 0.228804i | ||||
\(113\) | 1.96185 | − | 6.03796i | 0.184555 | − | 0.568003i | −0.815385 | − | 0.578919i | \(-0.803475\pi\) |
0.999940 | + | 0.0109158i | \(0.00347467\pi\) | |||||||
\(114\) | 2.34772 | + | 7.22555i | 0.219885 | + | 0.676735i | ||||
\(115\) | 0.175619 | − | 0.127594i | 0.0163765 | − | 0.0118982i | ||||
\(116\) | −10.0252 | + | 7.28375i | −0.930819 | + | 0.676279i | ||||
\(117\) | 7.18576 | + | 22.1155i | 0.664323 | + | 2.04458i | ||||
\(118\) | −5.96704 | + | 18.3647i | −0.549311 | + | 1.69061i | ||||
\(119\) | −1.35816 | − | 0.986762i | −0.124502 | − | 0.0904563i | ||||
\(120\) | −0.00918610 | −0.000838572 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 16.8033 | 1.52130 | ||||||||
\(123\) | −23.8921 | − | 17.3586i | −2.15428 | − | 1.56518i | ||||
\(124\) | 2.40218 | − | 7.39316i | 0.215722 | − | 0.663926i | ||||
\(125\) | 0.0831947 | + | 0.256047i | 0.00744116 | + | 0.0229015i | ||||
\(126\) | −7.64861 | + | 5.55704i | −0.681393 | + | 0.495061i | ||||
\(127\) | −4.07039 | + | 2.95731i | −0.361189 | + | 0.262419i | −0.753548 | − | 0.657393i | \(-0.771659\pi\) |
0.392359 | + | 0.919812i | \(0.371659\pi\) | |||||||
\(128\) | −0.302558 | − | 0.931179i | −0.0267426 | − | 0.0823054i | ||||
\(129\) | −3.22003 | + | 9.91023i | −0.283508 | + | 0.872547i | ||||
\(130\) | −0.210997 | − | 0.153298i | −0.0185057 | − | 0.0134452i | ||||
\(131\) | 3.76357 | 0.328825 | 0.164412 | − | 0.986392i | \(-0.447427\pi\) | ||||
0.164412 | + | 0.986392i | \(0.447427\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.37394 | 0.119136 | ||||||||
\(134\) | 4.51604 | + | 3.28110i | 0.390127 | + | 0.283444i | ||||
\(135\) | −0.0408946 | + | 0.125861i | −0.00351964 | + | 0.0108324i | ||||
\(136\) | −0.0635213 | − | 0.195499i | −0.00544691 | − | 0.0167639i | ||||
\(137\) | −15.4829 | + | 11.2490i | −1.32279 | + | 0.961063i | −0.322897 | + | 0.946434i | \(0.604657\pi\) |
−0.999893 | + | 0.0146288i | \(0.995343\pi\) | |||||||
\(138\) | 36.0680 | − | 26.2049i | 3.07031 | − | 2.23071i | ||||
\(139\) | −1.08498 | − | 3.33924i | −0.0920272 | − | 0.283231i | 0.894440 | − | 0.447187i | \(-0.147574\pi\) |
−0.986468 | + | 0.163957i | \(0.947574\pi\) | |||||||
\(140\) | 0.0161268 | − | 0.0496332i | 0.00136296 | − | 0.00419477i | ||||
\(141\) | 20.1959 | + | 14.6732i | 1.70080 | + | 1.23570i | ||||
\(142\) | −4.05934 | −0.340652 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −19.6257 | −1.63548 | ||||||||
\(145\) | 0.139257 | + | 0.101176i | 0.0115647 | + | 0.00840224i | ||||
\(146\) | −6.42031 | + | 19.7597i | −0.531348 | + | 1.63532i | ||||
\(147\) | 0.861043 | + | 2.65002i | 0.0710176 | + | 0.218570i | ||||
\(148\) | −0.817048 | + | 0.593620i | −0.0671610 | + | 0.0487953i | ||||
\(149\) | −2.52933 | + | 1.83767i | −0.207211 | + | 0.150548i | −0.686551 | − | 0.727082i | \(-0.740876\pi\) |
0.479340 | + | 0.877629i | \(0.340876\pi\) | |||||||
\(150\) | 8.54252 | + | 26.2912i | 0.697494 | + | 2.14667i | ||||
\(151\) | −6.09427 | + | 18.7562i | −0.495945 | + | 1.52636i | 0.319534 | + | 0.947575i | \(0.396474\pi\) |
−0.815479 | + | 0.578787i | \(0.803526\pi\) | |||||||
\(152\) | 0.136103 | + | 0.0988850i | 0.0110395 | + | 0.00802063i | ||||
\(153\) | −7.99769 | −0.646575 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.107981 | −0.00867326 | ||||||||
\(156\) | −21.3275 | − | 15.4953i | −1.70757 | − | 1.24062i | ||||
\(157\) | −7.09335 | + | 21.8311i | −0.566111 | + | 1.74231i | 0.0985151 | + | 0.995136i | \(0.468591\pi\) |
−0.664626 | + | 0.747176i | \(0.731409\pi\) | |||||||
\(158\) | 3.59070 | + | 11.0510i | 0.285661 | + | 0.879174i | ||||
\(159\) | 8.92808 | − | 6.48663i | 0.708043 | − | 0.514423i | ||||
\(160\) | 0.172744 | − | 0.125506i | 0.0136566 | − | 0.00992212i | ||||
\(161\) | −2.49144 | − | 7.66786i | −0.196353 | − | 0.604312i | ||||
\(162\) | 0.365726 | − | 1.12559i | 0.0287342 | − | 0.0884346i | ||||
\(163\) | −15.3625 | − | 11.1615i | −1.20328 | − | 0.874236i | −0.208679 | − | 0.977984i | \(-0.566917\pi\) |
−0.994604 | + | 0.103748i | \(0.966917\pi\) | |||||||
\(164\) | 20.5435 | 1.60418 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.17061 | 0.401317 | ||||||||
\(167\) | −2.44358 | − | 1.77537i | −0.189090 | − | 0.137382i | 0.489213 | − | 0.872165i | \(-0.337284\pi\) |
−0.678303 | + | 0.734783i | \(0.737284\pi\) | |||||||
\(168\) | −0.105431 | + | 0.324483i | −0.00813418 | + | 0.0250344i | ||||
\(169\) | 3.34521 | + | 10.2955i | 0.257324 | + | 0.791961i | ||||
\(170\) | 0.0725689 | − | 0.0527244i | 0.00556578 | − | 0.00404378i | ||||
\(171\) | 5.29537 | − | 3.84731i | 0.404947 | − | 0.294211i | ||||
\(172\) | −2.23995 | − | 6.89385i | −0.170794 | − | 0.525651i | ||||
\(173\) | −2.73056 | + | 8.40381i | −0.207601 | + | 0.638930i | 0.791996 | + | 0.610527i | \(0.209042\pi\) |
−0.999597 | + | 0.0284032i | \(0.990958\pi\) | |||||||
\(174\) | 28.6003 | + | 20.7793i | 2.16818 | + | 1.57528i | ||||
\(175\) | 4.99928 | 0.377910 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 27.1122 | 2.03788 | ||||||||
\(178\) | 1.95537 | + | 1.42066i | 0.146561 | + | 0.106483i | ||||
\(179\) | 2.61562 | − | 8.05006i | 0.195501 | − | 0.601690i | −0.804469 | − | 0.593994i | \(-0.797550\pi\) |
0.999970 | − | 0.00769596i | \(-0.00244972\pi\) | |||||||
\(180\) | −0.0768279 | − | 0.236452i | −0.00572641 | − | 0.0176241i | ||||
\(181\) | 19.5789 | − | 14.2249i | 1.45528 | − | 1.05733i | 0.470724 | − | 0.882280i | \(-0.343993\pi\) |
0.984560 | − | 0.175046i | \(-0.0560073\pi\) | |||||||
\(182\) | −7.83667 | + | 5.69367i | −0.580892 | + | 0.422043i | ||||
\(183\) | −7.29064 | − | 22.4383i | −0.538940 | − | 1.65869i | ||||
\(184\) | 0.305066 | − | 0.938896i | 0.0224898 | − | 0.0692164i | ||||
\(185\) | 0.0113494 | + | 0.00824580i | 0.000834422 | + | 0.000606243i | ||||
\(186\) | −22.1769 | −1.62609 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −17.3653 | −1.26650 | ||||||||
\(189\) | 3.97645 | + | 2.88906i | 0.289245 | + | 0.210148i | ||||
\(190\) | −0.0226856 | + | 0.0698190i | −0.00164578 | + | 0.00506520i | ||||
\(191\) | −2.40637 | − | 7.40605i | −0.174119 | − | 0.535883i | 0.825473 | − | 0.564441i | \(-0.190908\pi\) |
−0.999592 | + | 0.0285585i | \(0.990908\pi\) | |||||||
\(192\) | 16.9046 | − | 12.2819i | 1.21998 | − | 0.886370i | ||||
\(193\) | 13.8048 | − | 10.0298i | 0.993690 | − | 0.721958i | 0.0329643 | − | 0.999457i | \(-0.489505\pi\) |
0.960726 | + | 0.277498i | \(0.0895052\pi\) | |||||||
\(194\) | −2.08302 | − | 6.41089i | −0.149552 | − | 0.460275i | ||||
\(195\) | −0.113159 | + | 0.348268i | −0.00810349 | + | 0.0249400i | ||||
\(196\) | −1.56812 | − | 1.13930i | −0.112008 | − | 0.0813788i | ||||
\(197\) | 6.05536 | 0.431426 | 0.215713 | − | 0.976457i | \(-0.430792\pi\) | ||||
0.215713 | + | 0.976457i | \(0.430792\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.7181 | −0.972451 | −0.486226 | − | 0.873833i | \(-0.661627\pi\) | ||||
−0.486226 | + | 0.873833i | \(0.661627\pi\) | |||||||
\(200\) | 0.495232 | + | 0.359807i | 0.0350182 | + | 0.0254422i | ||||
\(201\) | 2.42198 | − | 7.45410i | 0.170833 | − | 0.525771i | ||||
\(202\) | −2.48265 | − | 7.64081i | −0.174679 | − | 0.537605i | ||||
\(203\) | 5.17218 | − | 3.75781i | 0.363016 | − | 0.263746i | ||||
\(204\) | 7.33524 | − | 5.32937i | 0.513570 | − | 0.373130i | ||||
\(205\) | −0.0881823 | − | 0.271397i | −0.00615892 | − | 0.0189552i | ||||
\(206\) | 2.42415 | − | 7.46078i | 0.168899 | − | 0.519817i | ||||
\(207\) | −31.0739 | − | 22.5765i | −2.15979 | − | 1.56918i | ||||
\(208\) | −20.1082 | −1.39425 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −0.148882 | −0.0102738 | ||||||||
\(211\) | 14.5908 | + | 10.6009i | 1.00447 | + | 0.729793i | 0.963043 | − | 0.269349i | \(-0.0868083\pi\) |
0.0414309 | + | 0.999141i | \(0.486808\pi\) | |||||||
\(212\) | −2.37226 | + | 7.30105i | −0.162927 | + | 0.501438i | ||||
\(213\) | 1.76127 | + | 5.42063i | 0.120680 | + | 0.371416i | ||||
\(214\) | −16.6950 | + | 12.1296i | −1.14125 | + | 0.829165i | ||||
\(215\) | −0.0814587 | + | 0.0591832i | −0.00555544 | + | 0.00403626i | ||||
\(216\) | 0.185979 | + | 0.572385i | 0.0126543 | + | 0.0389459i | ||||
\(217\) | −1.23933 | + | 3.81425i | −0.0841309 | + | 0.258928i | ||||
\(218\) | 6.06395 | + | 4.40572i | 0.410703 | + | 0.298393i | ||||
\(219\) | 29.1717 | 1.97124 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.19432 | −0.551210 | ||||||||
\(222\) | 2.33090 | + | 1.69350i | 0.156440 | + | 0.113660i | ||||
\(223\) | −2.01885 | + | 6.21338i | −0.135192 | + | 0.416079i | −0.995620 | − | 0.0934937i | \(-0.970197\pi\) |
0.860428 | + | 0.509573i | \(0.170197\pi\) | |||||||
\(224\) | −2.45066 | − | 7.54236i | −0.163742 | − | 0.503945i | ||||
\(225\) | 19.2679 | − | 13.9990i | 1.28453 | − | 0.933266i | ||||
\(226\) | 10.1929 | − | 7.40554i | 0.678019 | − | 0.492609i | ||||
\(227\) | −4.20501 | − | 12.9417i | −0.279097 | − | 0.858971i | −0.988106 | − | 0.153772i | \(-0.950858\pi\) |
0.709010 | − | 0.705199i | \(-0.249142\pi\) | |||||||
\(228\) | −2.29305 | + | 7.05728i | −0.151861 | + | 0.467380i | ||||
\(229\) | 15.7120 | + | 11.4154i | 1.03828 | + | 0.754352i | 0.969948 | − | 0.243311i | \(-0.0782334\pi\) |
0.0683285 | + | 0.997663i | \(0.478233\pi\) | |||||||
\(230\) | 0.430791 | 0.0284055 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.782815 | 0.0513943 | ||||||||
\(233\) | 3.52853 | + | 2.56363i | 0.231162 | + | 0.167949i | 0.697337 | − | 0.716744i | \(-0.254368\pi\) |
−0.466175 | + | 0.884693i | \(0.654368\pi\) | |||||||
\(234\) | −14.2602 | + | 43.8885i | −0.932221 | + | 2.86908i | ||||
\(235\) | 0.0745401 | + | 0.229411i | 0.00486246 | + | 0.0149651i | ||||
\(236\) | −15.2581 | + | 11.0857i | −0.993219 | + | 0.721616i | ||||
\(237\) | 13.1991 | − | 9.58967i | 0.857371 | − | 0.622916i | ||||
\(238\) | −1.02951 | − | 3.16850i | −0.0667332 | − | 0.205384i | ||||
\(239\) | −3.27253 | + | 10.0718i | −0.211682 | + | 0.651491i | 0.787690 | + | 0.616071i | \(0.211277\pi\) |
−0.999373 | + | 0.0354193i | \(0.988723\pi\) | |||||||
\(240\) | −0.250034 | − | 0.181661i | −0.0161396 | − | 0.0117261i | ||||
\(241\) | −18.6887 | −1.20384 | −0.601921 | − | 0.798555i | \(-0.705598\pi\) | ||||
−0.601921 | + | 0.798555i | \(0.705598\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.4072 | −1.05252 | ||||||||
\(244\) | 13.2776 | + | 9.64674i | 0.850011 | + | 0.617569i | ||||
\(245\) | −0.00832008 | + | 0.0256066i | −0.000531550 | + | 0.00163594i | ||||
\(246\) | −18.1106 | − | 55.7388i | −1.15469 | − | 3.55377i | ||||
\(247\) | 5.42557 | − | 3.94190i | 0.345220 | − | 0.250817i | ||||
\(248\) | −0.397287 | + | 0.288646i | −0.0252277 | + | 0.0183290i | ||||
\(249\) | −2.24343 | − | 6.90456i | −0.142171 | − | 0.437559i | ||||
\(250\) | −0.165101 | + | 0.508129i | −0.0104419 | + | 0.0321369i | ||||
\(251\) | −15.3577 | − | 11.1580i | −0.969369 | − | 0.704288i | −0.0140616 | − | 0.999901i | \(-0.504476\pi\) |
−0.955308 | + | 0.295613i | \(0.904476\pi\) | |||||||
\(252\) | −9.23404 | −0.581690 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −9.98465 | −0.626493 | ||||||||
\(255\) | −0.101892 | − | 0.0740286i | −0.00638070 | − | 0.00463585i | ||||
\(256\) | 5.23508 | − | 16.1119i | 0.327192 | − | 1.00699i | ||||
\(257\) | −4.23633 | − | 13.0381i | −0.264255 | − | 0.813293i | −0.991864 | − | 0.127301i | \(-0.959369\pi\) |
0.727609 | − | 0.685992i | \(-0.240631\pi\) | |||||||
\(258\) | −16.7297 | + | 12.1549i | −1.04155 | + | 0.756729i | ||||
\(259\) | 0.421528 | − | 0.306258i | 0.0261925 | − | 0.0190300i | ||||
\(260\) | −0.0787168 | − | 0.242265i | −0.00488181 | − | 0.0150247i | ||||
\(261\) | 9.41171 | − | 28.9663i | 0.582571 | − | 1.79297i | ||||
\(262\) | 6.04244 | + | 4.39009i | 0.373303 | + | 0.271221i | ||||
\(263\) | −16.5767 | −1.02217 | −0.511083 | − | 0.859531i | \(-0.670756\pi\) | ||||
−0.511083 | + | 0.859531i | \(0.670756\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.106636 | 0.00655059 | ||||||||
\(266\) | 2.20587 | + | 1.60266i | 0.135251 | + | 0.0982653i | ||||
\(267\) | 1.04868 | − | 3.22749i | 0.0641779 | − | 0.197519i | ||||
\(268\) | 1.68480 | + | 5.18529i | 0.102916 | + | 0.316742i | ||||
\(269\) | 6.91193 | − | 5.02181i | 0.421428 | − | 0.306185i | −0.356784 | − | 0.934187i | \(-0.616127\pi\) |
0.778212 | + | 0.628002i | \(0.216127\pi\) | |||||||
\(270\) | −0.212469 | + | 0.154368i | −0.0129304 | + | 0.00939452i | ||||
\(271\) | 1.96088 | + | 6.03496i | 0.119115 | + | 0.366597i | 0.992783 | − | 0.119925i | \(-0.0382653\pi\) |
−0.873668 | + | 0.486522i | \(0.838265\pi\) | |||||||
\(272\) | 2.13713 | − | 6.57740i | 0.129582 | − | 0.398814i | ||||
\(273\) | 11.0032 | + | 7.99430i | 0.665945 | + | 0.483837i | ||||
\(274\) | −37.9794 | −2.29442 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 43.5443 | 2.62106 | ||||||||
\(277\) | −19.4200 | − | 14.1094i | −1.16683 | − | 0.847753i | −0.176206 | − | 0.984353i | \(-0.556382\pi\) |
−0.990626 | + | 0.136600i | \(0.956382\pi\) | |||||||
\(278\) | 2.15317 | − | 6.62677i | 0.129138 | − | 0.397447i | ||||
\(279\) | 5.90413 | + | 18.1711i | 0.353471 | + | 1.08787i | ||||
\(280\) | −0.00266714 | + | 0.00193779i | −0.000159392 | + | 0.000115805i | ||||
\(281\) | −2.59811 | + | 1.88764i | −0.154990 | + | 0.112607i | −0.662577 | − | 0.748993i | \(-0.730537\pi\) |
0.507587 | + | 0.861600i | \(0.330537\pi\) | |||||||
\(282\) | 15.3088 | + | 47.1157i | 0.911627 | + | 2.80570i | ||||
\(283\) | 6.42860 | − | 19.7852i | 0.382141 | − | 1.17611i | −0.556393 | − | 0.830919i | \(-0.687815\pi\) |
0.938533 | − | 0.345188i | \(-0.112185\pi\) | |||||||
\(284\) | −3.20760 | − | 2.33046i | −0.190336 | − | 0.138287i | ||||
\(285\) | 0.103075 | 0.00610567 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.5987 | −0.625624 | ||||||||
\(288\) | −30.5653 | − | 22.2070i | −1.80108 | − | 1.30856i | ||||
\(289\) | −4.38239 | + | 13.4876i | −0.257787 | + | 0.793388i | ||||
\(290\) | 0.105559 | + | 0.324879i | 0.00619867 | + | 0.0190775i | ||||
\(291\) | −7.65698 | + | 5.56312i | −0.448860 | + | 0.326116i | ||||
\(292\) | −16.4171 | + | 11.9278i | −0.960741 | + | 0.698019i | ||||
\(293\) | −1.70498 | − | 5.24740i | −0.0996062 | − | 0.306556i | 0.888821 | − | 0.458255i | \(-0.151526\pi\) |
−0.988427 | + | 0.151699i | \(0.951526\pi\) | |||||||
\(294\) | −1.70875 | + | 5.25900i | −0.0996565 | + | 0.306711i | ||||
\(295\) | 0.211946 | + | 0.153988i | 0.0123400 | + | 0.00896551i | ||||
\(296\) | 0.0637988 | 0.00370823 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.20444 | −0.359414 | ||||||||
\(299\) | −31.8379 | − | 23.1316i | −1.84123 | − | 1.33774i | ||||
\(300\) | −8.34359 | + | 25.6789i | −0.481717 | + | 1.48257i | ||||
\(301\) | 1.15563 | + | 3.55665i | 0.0666092 | + | 0.205002i | ||||
\(302\) | −31.6630 | + | 23.0045i | −1.82200 | + | 1.32376i | ||||
\(303\) | −9.12596 | + | 6.63040i | −0.524273 | + | 0.380907i | ||||
\(304\) | 1.74906 | + | 5.38305i | 0.100315 | + | 0.308739i | ||||
\(305\) | 0.0704480 | − | 0.216817i | 0.00403384 | − | 0.0124149i | ||||
\(306\) | −12.8403 | − | 9.32905i | −0.734033 | − | 0.533306i | ||||
\(307\) | −8.60991 | −0.491394 | −0.245697 | − | 0.969347i | \(-0.579017\pi\) | ||||
−0.245697 | + | 0.969347i | \(0.579017\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.0145 | −0.626594 | ||||||||
\(310\) | −0.173364 | − | 0.125957i | −0.00984644 | − | 0.00715386i | ||||
\(311\) | 5.91021 | − | 18.1897i | 0.335137 | − | 1.03145i | −0.631517 | − | 0.775362i | \(-0.717568\pi\) |
0.966654 | − | 0.256084i | \(-0.0824325\pi\) | |||||||
\(312\) | 0.514621 | + | 1.58384i | 0.0291347 | + | 0.0896674i | ||||
\(313\) | 0.490875 | − | 0.356642i | 0.0277459 | − | 0.0201586i | −0.573826 | − | 0.818977i | \(-0.694541\pi\) |
0.601572 | + | 0.798819i | \(0.294541\pi\) | |||||||
\(314\) | −36.8537 | + | 26.7758i | −2.07978 | + | 1.51105i | ||||
\(315\) | 0.0396368 | + | 0.121989i | 0.00223328 | + | 0.00687332i | ||||
\(316\) | −3.50708 | + | 10.7937i | −0.197289 | + | 0.607192i | ||||
\(317\) | 4.21727 | + | 3.06402i | 0.236865 | + | 0.172093i | 0.699886 | − | 0.714255i | \(-0.253234\pi\) |
−0.463020 | + | 0.886348i | \(0.653234\pi\) | |||||||
\(318\) | 21.9005 | 1.22812 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.201906 | 0.0112869 | ||||||||
\(321\) | 23.4409 | + | 17.0308i | 1.30835 | + | 0.950569i | ||||
\(322\) | 4.94430 | − | 15.2170i | 0.275535 | − | 0.848009i | ||||
\(323\) | 0.712761 | + | 2.19365i | 0.0396591 | + | 0.122058i | ||||
\(324\) | 0.935185 | − | 0.679452i | 0.0519547 | − | 0.0377473i | ||||
\(325\) | 19.7417 | − | 14.3432i | 1.09507 | − | 0.795616i | ||||
\(326\) | −11.6450 | − | 35.8397i | −0.644959 | − | 1.98498i | ||||
\(327\) | 3.25213 | − | 10.0090i | 0.179843 | − | 0.553501i | ||||
\(328\) | −1.04992 | − | 0.762810i | −0.0579720 | − | 0.0421192i | ||||
\(329\) | 8.95906 | 0.493929 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.669012 | 0.0367722 | 0.0183861 | − | 0.999831i | \(-0.494147\pi\) | ||||
0.0183861 | + | 0.999831i | \(0.494147\pi\) | |||||||
\(332\) | 4.08569 | + | 2.96843i | 0.224231 | + | 0.162914i | ||||
\(333\) | 0.767048 | − | 2.36073i | 0.0420340 | − | 0.129367i | ||||
\(334\) | −1.85228 | − | 5.70073i | −0.101352 | − | 0.311930i | ||||
\(335\) | 0.0612701 | − | 0.0445154i | 0.00334754 | − | 0.00243213i | ||||
\(336\) | −9.28655 | + | 6.74708i | −0.506623 | + | 0.368083i | ||||
\(337\) | 2.04018 | + | 6.27902i | 0.111136 | + | 0.342040i | 0.991121 | − | 0.132960i | \(-0.0424481\pi\) |
−0.879986 | + | 0.475000i | \(0.842448\pi\) | |||||||
\(338\) | −6.63862 | + | 20.4316i | −0.361093 | + | 1.11133i | ||||
\(339\) | −14.3115 | − | 10.3979i | −0.777292 | − | 0.564736i | ||||
\(340\) | 0.0876111 | 0.00475138 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 12.9895 | 0.702393 | ||||||||
\(343\) | 0.809017 | + | 0.587785i | 0.0436828 | + | 0.0317374i | ||||
\(344\) | −0.141501 | + | 0.435497i | −0.00762925 | + | 0.0234804i | ||||
\(345\) | −0.186912 | − | 0.575256i | −0.0100630 | − | 0.0309708i | ||||
\(346\) | −14.1867 | + | 10.3073i | −0.762683 | + | 0.554122i | ||||
\(347\) | 9.87011 | − | 7.17106i | 0.529855 | − | 0.384963i | −0.290448 | − | 0.956891i | \(-0.593804\pi\) |
0.820304 | + | 0.571928i | \(0.193804\pi\) | |||||||
\(348\) | 10.6699 | + | 32.8386i | 0.571968 | + | 1.76034i | ||||
\(349\) | 0.273727 | − | 0.842446i | 0.0146523 | − | 0.0450951i | −0.943463 | − | 0.331478i | \(-0.892453\pi\) |
0.958115 | + | 0.286383i | \(0.0924528\pi\) | |||||||
\(350\) | 8.02637 | + | 5.83150i | 0.429027 | + | 0.311707i | ||||
\(351\) | 23.9915 | 1.28057 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.36012 | 0.285291 | 0.142645 | − | 0.989774i | \(-0.454439\pi\) | ||||
0.142645 | + | 0.989774i | \(0.454439\pi\) | |||||||
\(354\) | 43.5288 | + | 31.6255i | 2.31353 | + | 1.68088i | ||||
\(355\) | −0.0170188 | + | 0.0523784i | −0.000903263 | + | 0.00277996i | ||||
\(356\) | 0.729491 | + | 2.24514i | 0.0386629 | + | 0.118992i | ||||
\(357\) | −3.78437 | + | 2.74951i | −0.200290 | + | 0.145519i | ||||
\(358\) | 13.5895 | − | 9.87338i | 0.718230 | − | 0.521825i | ||||
\(359\) | −7.98654 | − | 24.5801i | −0.421514 | − | 1.29729i | −0.906293 | − | 0.422649i | \(-0.861100\pi\) |
0.484780 | − | 0.874636i | \(-0.338900\pi\) | |||||||
\(360\) | −0.00485335 | + | 0.0149371i | −0.000255794 | + | 0.000787253i | ||||
\(361\) | 13.8441 | + | 10.0583i | 0.728638 | + | 0.529387i | ||||
\(362\) | 48.0268 | 2.52423 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −9.46107 | −0.495895 | ||||||||
\(365\) | 0.228046 | + | 0.165685i | 0.0119365 | + | 0.00867234i | ||||
\(366\) | 14.4684 | − | 44.5291i | 0.756275 | − | 2.32758i | ||||
\(367\) | −6.31953 | − | 19.4495i | −0.329877 | − | 1.01526i | −0.969191 | − | 0.246311i | \(-0.920782\pi\) |
0.639314 | − | 0.768946i | \(-0.279218\pi\) | |||||||
\(368\) | 26.8708 | − | 19.5227i | 1.40073 | − | 1.01769i | ||||
\(369\) | −40.8491 | + | 29.6786i | −2.12652 | + | 1.54501i | ||||
\(370\) | 0.00860302 | + | 0.0264774i | 0.000447250 | + | 0.00137649i | ||||
\(371\) | 1.22388 | − | 3.76673i | 0.0635409 | − | 0.195559i | ||||
\(372\) | −17.5236 | − | 12.7317i | −0.908558 | − | 0.660106i | ||||
\(373\) | −9.39109 | −0.486252 | −0.243126 | − | 0.969995i | \(-0.578173\pi\) | ||||
−0.243126 | + | 0.969995i | \(0.578173\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.750163 | 0.0387383 | ||||||||
\(376\) | 0.887491 | + | 0.644800i | 0.0457688 | + | 0.0332530i | ||||
\(377\) | 9.64312 | − | 29.6785i | 0.496646 | − | 1.52852i | ||||
\(378\) | 3.01422 | + | 9.27682i | 0.155035 | + | 0.477148i | ||||
\(379\) | 4.55956 | − | 3.31272i | 0.234209 | − | 0.170163i | −0.464490 | − | 0.885578i | \(-0.653762\pi\) |
0.698699 | + | 0.715415i | \(0.253762\pi\) | |||||||
\(380\) | −0.0580085 | + | 0.0421456i | −0.00297577 | + | 0.00216202i | ||||
\(381\) | 4.33215 | + | 13.3330i | 0.221943 | + | 0.683069i | ||||
\(382\) | 4.77548 | − | 14.6974i | 0.244335 | − | 0.751985i | ||||
\(383\) | 1.01891 | + | 0.740281i | 0.0520638 | + | 0.0378266i | 0.613513 | − | 0.789685i | \(-0.289756\pi\) |
−0.561449 | + | 0.827511i | \(0.689756\pi\) | |||||||
\(384\) | −2.72816 | −0.139221 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 33.8631 | 1.72359 | ||||||||
\(387\) | 14.4133 | + | 10.4719i | 0.732669 | + | 0.532315i | ||||
\(388\) | 2.03451 | − | 6.26159i | 0.103287 | − | 0.317884i | ||||
\(389\) | −1.81828 | − | 5.59610i | −0.0921906 | − | 0.283734i | 0.894321 | − | 0.447427i | \(-0.147659\pi\) |
−0.986511 | + | 0.163693i | \(0.947659\pi\) | |||||||
\(390\) | −0.587921 | + | 0.427149i | −0.0297705 | + | 0.0216296i | ||||
\(391\) | 10.9501 | − | 7.95573i | 0.553771 | − | 0.402339i | ||||
\(392\) | 0.0378378 | + | 0.116453i | 0.00191110 | + | 0.00588175i | ||||
\(393\) | 3.24060 | − | 9.97354i | 0.163467 | − | 0.503098i | ||||
\(394\) | 9.72191 | + | 7.06338i | 0.489783 | + | 0.355848i | ||||
\(395\) | 0.157648 | 0.00793212 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.86018 | 0.243925 | 0.121963 | − | 0.992535i | \(-0.461081\pi\) | ||||
0.121963 | + | 0.992535i | \(0.461081\pi\) | |||||||
\(398\) | −22.0245 | − | 16.0017i | −1.10399 | − | 0.802095i | ||||
\(399\) | 1.18302 | − | 3.64097i | 0.0592252 | − | 0.182276i | ||||
\(400\) | 6.36420 | + | 19.5870i | 0.318210 | + | 0.979350i | ||||
\(401\) | 20.6560 | − | 15.0074i | 1.03151 | − | 0.749435i | 0.0628990 | − | 0.998020i | \(-0.479965\pi\) |
0.968610 | + | 0.248585i | \(0.0799654\pi\) | |||||||
\(402\) | 12.5835 | − | 9.14243i | 0.627607 | − | 0.455983i | ||||
\(403\) | 6.04930 | + | 18.6178i | 0.301337 | + | 0.927420i | ||||
\(404\) | 2.42483 | − | 7.46287i | 0.120640 | − | 0.371292i | ||||
\(405\) | −0.0129904 | − | 0.00943806i | −0.000645497 | − | 0.000468981i | ||||
\(406\) | 12.6873 | 0.629661 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −0.572769 | −0.0283563 | ||||||||
\(409\) | 17.0109 | + | 12.3592i | 0.841136 | + | 0.611121i | 0.922688 | − | 0.385548i | \(-0.125988\pi\) |
−0.0815517 | + | 0.996669i | \(0.525988\pi\) | |||||||
\(410\) | 0.174999 | − | 0.538592i | 0.00864259 | − | 0.0265992i | ||||
\(411\) | 16.4785 | + | 50.7157i | 0.812826 | + | 2.50162i | ||||
\(412\) | 6.19872 | − | 4.50363i | 0.305389 | − | 0.221878i | ||||
\(413\) | 7.87191 | − | 5.71928i | 0.387351 | − | 0.281427i | ||||
\(414\) | −23.5546 | − | 72.4935i | −1.15764 | − | 3.56286i | ||||
\(415\) | 0.0216778 | − | 0.0667173i | 0.00106412 | − | 0.00327502i | ||||
\(416\) | −31.3168 | − | 22.7530i | −1.53543 | − | 1.11556i | ||||
\(417\) | −9.78326 | −0.479088 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −31.3141 | −1.52980 | −0.764898 | − | 0.644151i | \(-0.777211\pi\) | ||||
−0.764898 | + | 0.644151i | \(0.777211\pi\) | |||||||
\(420\) | −0.117643 | − | 0.0854726i | −0.00574039 | − | 0.00417064i | ||||
\(421\) | 3.95191 | − | 12.1627i | 0.192604 | − | 0.592775i | −0.807392 | − | 0.590015i | \(-0.799122\pi\) |
0.999996 | − | 0.00275943i | \(-0.000878355\pi\) | |||||||
\(422\) | 11.0601 | + | 34.0395i | 0.538397 | + | 1.65702i | ||||
\(423\) | 34.5296 | − | 25.0872i | 1.67888 | − | 1.21978i | ||||
\(424\) | 0.392337 | − | 0.285050i | 0.0190536 | − | 0.0138432i | ||||
\(425\) | 2.59348 | + | 7.98191i | 0.125802 | + | 0.387180i | ||||
\(426\) | −3.49527 | + | 10.7573i | −0.169346 | + | 0.521194i | ||||
\(427\) | −6.85013 | − | 4.97691i | −0.331501 | − | 0.240850i | ||||
\(428\) | −20.1556 | −0.974258 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.199818 | −0.00963607 | ||||||||
\(431\) | 17.0443 | + | 12.3834i | 0.820994 | + | 0.596487i | 0.916997 | − | 0.398894i | \(-0.130606\pi\) |
−0.0960031 | + | 0.995381i | \(0.530606\pi\) | |||||||
\(432\) | −6.25713 | + | 19.2575i | −0.301046 | + | 0.926525i | ||||
\(433\) | 11.7436 | + | 36.1430i | 0.564361 | + | 1.73692i | 0.669844 | + | 0.742502i | \(0.266361\pi\) |
−0.105483 | + | 0.994421i | \(0.533639\pi\) | |||||||
\(434\) | −6.43895 | + | 4.67817i | −0.309079 | + | 0.224559i | ||||
\(435\) | 0.388026 | − | 0.281917i | 0.0186044 | − | 0.0135169i | ||||
\(436\) | 2.26228 | + | 6.96259i | 0.108344 | + | 0.333448i | ||||
\(437\) | −3.42309 | + | 10.5352i | −0.163749 | + | 0.503966i | ||||
\(438\) | 46.8353 | + | 34.0279i | 2.23788 | + | 1.62591i | ||||
\(439\) | 37.7677 | 1.80256 | 0.901278 | − | 0.433241i | \(-0.142630\pi\) | ||||
0.901278 | + | 0.433241i | \(0.142630\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.76399 | 0.226857 | ||||||||
\(442\) | −13.1560 | − | 9.55842i | −0.625769 | − | 0.454648i | ||||
\(443\) | −0.317646 | + | 0.977613i | −0.0150918 | + | 0.0464478i | −0.958319 | − | 0.285701i | \(-0.907774\pi\) |
0.943227 | + | 0.332149i | \(0.107774\pi\) | |||||||
\(444\) | 0.869591 | + | 2.67633i | 0.0412689 | + | 0.127013i | ||||
\(445\) | 0.0265289 | − | 0.0192744i | 0.00125759 | − | 0.000913693i | ||||
\(446\) | −10.4890 | + | 7.62070i | −0.496668 | + | 0.360851i | ||||
\(447\) | 2.69199 | + | 8.28509i | 0.127327 | + | 0.391871i | ||||
\(448\) | 2.31732 | − | 7.13199i | 0.109483 | − | 0.336955i | ||||
\(449\) | −16.2882 | − | 11.8341i | −0.768687 | − | 0.558483i | 0.132876 | − | 0.991133i | \(-0.457579\pi\) |
−0.901562 | + | 0.432649i | \(0.857579\pi\) | |||||||
\(450\) | 47.2642 | 2.22806 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 12.3057 | 0.578809 | ||||||||
\(453\) | 44.4570 | + | 32.2999i | 2.08877 | + | 1.51758i | ||||
\(454\) | 8.34491 | − | 25.6830i | 0.391646 | − | 1.20536i | ||||
\(455\) | 0.0406113 | + | 0.124989i | 0.00190389 | + | 0.00585956i | ||||
\(456\) | 0.379238 | − | 0.275532i | 0.0177594 | − | 0.0129030i | ||||
\(457\) | −19.5342 | + | 14.1924i | −0.913771 | + | 0.663894i | −0.941966 | − | 0.335709i | \(-0.891024\pi\) |
0.0281947 | + | 0.999602i | \(0.491024\pi\) | |||||||
\(458\) | 11.9100 | + | 36.6551i | 0.556516 | + | 1.71278i | ||||
\(459\) | −2.54985 | + | 7.84763i | −0.119017 | + | 0.366296i | ||||
\(460\) | 0.340401 | + | 0.247316i | 0.0158713 | + | 0.0115312i | ||||
\(461\) | −11.5885 | −0.539731 | −0.269865 | − | 0.962898i | \(-0.586979\pi\) | ||||
−0.269865 | + | 0.962898i | \(0.586979\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.6077 | 1.00419 | 0.502097 | − | 0.864811i | \(-0.332562\pi\) | ||||
0.502097 | + | 0.864811i | \(0.332562\pi\) | |||||||
\(464\) | 21.3073 | + | 15.4806i | 0.989165 | + | 0.718670i | ||||
\(465\) | −0.0929764 | + | 0.286152i | −0.00431168 | + | 0.0132700i | ||||
\(466\) | 2.67469 | + | 8.23184i | 0.123902 | + | 0.381332i | ||||
\(467\) | −12.8755 | + | 9.35457i | −0.595805 | + | 0.432878i | −0.844388 | − | 0.535733i | \(-0.820035\pi\) |
0.248582 | + | 0.968611i | \(0.420035\pi\) | |||||||
\(468\) | −36.4644 | + | 26.4929i | −1.68557 | + | 1.22464i | ||||
\(469\) | −0.869218 | − | 2.67518i | −0.0401367 | − | 0.123528i | ||||
\(470\) | −0.147926 | + | 0.455269i | −0.00682331 | + | 0.0210000i | ||||
\(471\) | 51.7451 | + | 37.5950i | 2.38429 | + | 1.73229i | ||||
\(472\) | 1.19142 | 0.0548397 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 32.3772 | 1.48713 | ||||||||
\(475\) | −5.55690 | − | 4.03733i | −0.254968 | − | 0.185245i | ||||
\(476\) | 1.00553 | − | 3.09472i | 0.0460886 | − | 0.141846i | ||||
\(477\) | −5.83057 | − | 17.9447i | −0.266964 | − | 0.821630i | ||||
\(478\) | −17.0025 | + | 12.3530i | −0.777676 | + | 0.565015i | ||||
\(479\) | 4.27462 | − | 3.10569i | 0.195312 | − | 0.141903i | −0.485831 | − | 0.874053i | \(-0.661483\pi\) |
0.681143 | + | 0.732150i | \(0.261483\pi\) | |||||||
\(480\) | −0.183853 | − | 0.565841i | −0.00839170 | − | 0.0258270i | ||||
\(481\) | 0.785907 | − | 2.41877i | 0.0358343 | − | 0.110287i | ||||
\(482\) | −30.0048 | − | 21.7997i | −1.36668 | − | 0.992951i | ||||
\(483\) | −22.4652 | −1.02220 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.0914540 | −0.00415271 | ||||||||
\(486\) | −26.3419 | − | 19.1385i | −1.19489 | − | 0.868141i | ||||
\(487\) | −8.36372 | + | 25.7409i | −0.378996 | + | 1.16643i | 0.561747 | + | 0.827309i | \(0.310130\pi\) |
−0.940743 | + | 0.339121i | \(0.889870\pi\) | |||||||
\(488\) | −0.320381 | − | 0.986032i | −0.0145030 | − | 0.0446356i | ||||
\(489\) | −42.8059 | + | 31.1003i | −1.93575 | + | 1.40641i | ||||
\(490\) | −0.0432272 | + | 0.0314064i | −0.00195281 | + | 0.00141880i | ||||
\(491\) | −5.80951 | − | 17.8798i | −0.262179 | − | 0.806905i | −0.992330 | − | 0.123619i | \(-0.960550\pi\) |
0.730150 | − | 0.683287i | \(-0.239450\pi\) | |||||||
\(492\) | 17.6889 | − | 54.4407i | 0.797476 | − | 2.45438i | ||||
\(493\) | 8.68294 | + | 6.30853i | 0.391060 | + | 0.284122i | ||||
\(494\) | 13.3089 | 0.598795 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −16.5218 | −0.741851 | ||||||||
\(497\) | 1.65485 | + | 1.20232i | 0.0742302 | + | 0.0539314i | ||||
\(498\) | 4.45211 | − | 13.7022i | 0.199504 | − | 0.614010i | ||||
\(499\) | −12.2886 | − | 37.8203i | −0.550112 | − | 1.69307i | −0.708514 | − | 0.705696i | \(-0.750634\pi\) |
0.158402 | − | 0.987375i | \(-0.449366\pi\) | |||||||
\(500\) | −0.422174 | + | 0.306728i | −0.0188802 | + | 0.0137173i | ||||
\(501\) | −6.80879 | + | 4.94687i | −0.304194 | + | 0.221010i | ||||
\(502\) | −11.6414 | − | 35.8285i | −0.519581 | − | 1.59911i | ||||
\(503\) | −12.5345 | + | 38.5771i | −0.558885 | + | 1.72007i | 0.126573 | + | 0.991957i | \(0.459602\pi\) |
−0.685458 | + | 0.728113i | \(0.740398\pi\) | |||||||
\(504\) | 0.471924 | + | 0.342873i | 0.0210212 | + | 0.0152728i | ||||
\(505\) | −0.108999 | −0.00485040 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 30.1636 | 1.33961 | ||||||||
\(508\) | −7.88964 | − | 5.73216i | −0.350046 | − | 0.254323i | ||||
\(509\) | −4.78386 | + | 14.7232i | −0.212041 | + | 0.652595i | 0.787309 | + | 0.616558i | \(0.211473\pi\) |
−0.999350 | + | 0.0360372i | \(0.988527\pi\) | |||||||
\(510\) | −0.0772356 | − | 0.237707i | −0.00342005 | − | 0.0105258i | ||||
\(511\) | 8.46987 | − | 6.15372i | 0.374685 | − | 0.272225i | ||||
\(512\) | 25.6148 | − | 18.6102i | 1.13202 | − | 0.822464i | ||||
\(513\) | −2.08684 | − | 6.42263i | −0.0921361 | − | 0.283566i | ||||
\(514\) | 8.40705 | − | 25.8743i | 0.370819 | − | 1.14126i | ||||
\(515\) | −0.0861045 | − | 0.0625586i | −0.00379422 | − | 0.00275666i | ||||
\(516\) | −20.1975 | −0.889147 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 1.03401 | 0.0454317 | ||||||||
\(519\) | 19.9191 | + | 14.4721i | 0.874352 | + | 0.635254i | ||||
\(520\) | −0.00497268 | + | 0.0153043i | −0.000218066 | + | 0.000671139i | ||||
\(521\) | 11.5800 | + | 35.6397i | 0.507331 | + | 1.56140i | 0.796817 | + | 0.604221i | \(0.206516\pi\) |
−0.289486 | + | 0.957182i | \(0.593484\pi\) | |||||||
\(522\) | 48.8988 | − | 35.5271i | 2.14024 | − | 1.55498i | ||||
\(523\) | −16.8369 | + | 12.2327i | −0.736225 | + | 0.534899i | −0.891527 | − | 0.452968i | \(-0.850365\pi\) |
0.155302 | + | 0.987867i | \(0.450365\pi\) | |||||||
\(524\) | 2.25426 | + | 6.93789i | 0.0984777 | + | 0.303083i | ||||
\(525\) | 4.30459 | − | 13.2482i | 0.187868 | − | 0.578197i | ||||
\(526\) | −26.6141 | − | 19.3363i | −1.16043 | − | 0.843101i | ||||
\(527\) | −6.73281 | −0.293286 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 42.0033 | 1.82623 | ||||||||
\(530\) | 0.171204 | + | 0.124387i | 0.00743665 | + | 0.00540304i | ||||
\(531\) | 14.3244 | − | 44.0859i | 0.621625 | − | 1.91316i | ||||
\(532\) | 0.822946 | + | 2.53277i | 0.0356792 | + | 0.109809i | ||||
\(533\) | −41.8535 | + | 30.4083i | −1.81287 | + | 1.31713i | ||||
\(534\) | 5.44843 | − | 3.95851i | 0.235776 | − | 0.171302i | ||||
\(535\) | 0.0865172 | + | 0.266272i | 0.00374046 | + | 0.0115120i | ||||
\(536\) | 0.106432 | − | 0.327564i | 0.00459716 | − | 0.0141486i | ||||
\(537\) | −19.0806 | − | 13.8629i | −0.823391 | − | 0.598228i | ||||
\(538\) | 16.9549 | 0.730979 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.256510 | −0.0110384 | ||||||||
\(541\) | −14.0978 | − | 10.2427i | −0.606112 | − | 0.440366i | 0.241931 | − | 0.970293i | \(-0.422219\pi\) |
−0.848043 | + | 0.529927i | \(0.822219\pi\) | |||||||
\(542\) | −3.89139 | + | 11.9765i | −0.167149 | + | 0.514433i | ||||
\(543\) | −20.8379 | − | 64.1325i | −0.894241 | − | 2.75219i | ||||
\(544\) | 10.7709 | − | 7.82552i | 0.461799 | − | 0.335516i | ||||
\(545\) | 0.0822709 | − | 0.0597733i | 0.00352410 | − | 0.00256041i | ||||
\(546\) | 8.34062 | + | 25.6698i | 0.356946 | + | 1.09857i | ||||
\(547\) | 4.88122 | − | 15.0228i | 0.208706 | − | 0.642331i | −0.790835 | − | 0.612029i | \(-0.790353\pi\) |
0.999541 | − | 0.0303011i | \(-0.00964663\pi\) | |||||||
\(548\) | −30.0104 | − | 21.8038i | −1.28198 | − | 0.931414i | ||||
\(549\) | −40.3378 | −1.72157 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.78382 | −0.374203 | ||||||||
\(552\) | −2.22542 | − | 1.61686i | −0.0947201 | − | 0.0688181i | ||||
\(553\) | 1.80936 | − | 5.56864i | 0.0769418 | − | 0.236803i | ||||
\(554\) | −14.7207 | − | 45.3055i | −0.625421 | − | 1.92485i | ||||
\(555\) | 0.0316238 | − | 0.0229760i | 0.00134236 | − | 0.000975279i | ||||
\(556\) | 5.50579 | − | 4.00019i | 0.233498 | − | 0.169646i | ||||
\(557\) | 5.20233 | + | 16.0111i | 0.220430 | + | 0.678413i | 0.998723 | + | 0.0505123i | \(0.0160854\pi\) |
−0.778294 | + | 0.627900i | \(0.783915\pi\) | |||||||
\(558\) | −11.7168 | + | 36.0607i | −0.496013 | + | 1.52657i | ||||
\(559\) | 14.7677 | + | 10.7293i | 0.624606 | + | 0.453803i | ||||
\(560\) | −0.110917 | −0.00468711 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.37315 | −0.268835 | ||||||||
\(563\) | −30.2818 | − | 22.0010i | −1.27623 | − | 0.927233i | −0.276794 | − | 0.960929i | \(-0.589272\pi\) |
−0.999432 | + | 0.0336966i | \(0.989272\pi\) | |||||||
\(564\) | −14.9523 | + | 46.0185i | −0.629606 | + | 1.93773i | ||||
\(565\) | −0.0528215 | − | 0.162568i | −0.00222222 | − | 0.00683929i | ||||
\(566\) | 33.4000 | − | 24.2665i | 1.40391 | − | 1.02000i | ||||
\(567\) | −0.482477 | + | 0.350540i | −0.0202621 | + | 0.0147213i | ||||
\(568\) | 0.0773976 | + | 0.238205i | 0.00324753 | + | 0.00999487i | ||||
\(569\) | 0.855698 | − | 2.63357i | 0.0358727 | − | 0.110405i | −0.931517 | − | 0.363698i | \(-0.881514\pi\) |
0.967389 | + | 0.253294i | \(0.0815139\pi\) | |||||||
\(570\) | 0.165488 | + | 0.120234i | 0.00693154 | + | 0.00503606i | ||||
\(571\) | 8.85289 | 0.370482 | 0.185241 | − | 0.982693i | \(-0.440693\pi\) | ||||
0.185241 | + | 0.982693i | \(0.440693\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −21.6981 | −0.906453 | ||||||||
\(574\) | −17.0163 | − | 12.3631i | −0.710249 | − | 0.516026i | ||||
\(575\) | −12.4554 | + | 38.3337i | −0.519425 | + | 1.59863i | ||||
\(576\) | −11.0397 | − | 33.9767i | −0.459988 | − | 1.41570i | ||||
\(577\) | −30.0697 | + | 21.8469i | −1.25182 | + | 0.909500i | −0.998326 | − | 0.0578373i | \(-0.981580\pi\) |
−0.253493 | + | 0.967337i | \(0.581580\pi\) | |||||||
\(578\) | −22.7688 | + | 16.5425i | −0.947058 | + | 0.688078i | ||||
\(579\) | −14.6925 | − | 45.2190i | −0.610601 | − | 1.87924i | ||||
\(580\) | −0.103101 | + | 0.317313i | −0.00428105 | + | 0.0131757i | ||||
\(581\) | −2.10787 | − | 1.53146i | −0.0874494 | − | 0.0635357i | ||||
\(582\) | −18.7825 | −0.778562 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 1.28193 | 0.0530464 | ||||||||
\(585\) | 0.506515 | + | 0.368005i | 0.0209418 | + | 0.0152151i | ||||
\(586\) | 3.38356 | − | 10.4135i | 0.139774 | − | 0.430179i | ||||
\(587\) | −10.9141 | − | 33.5903i | −0.450475 | − | 1.38642i | −0.876367 | − | 0.481645i | \(-0.840040\pi\) |
0.425892 | − | 0.904774i | \(-0.359960\pi\) | |||||||
\(588\) | −4.36939 | + | 3.17455i | −0.180191 | + | 0.130916i | ||||
\(589\) | 4.45788 | − | 3.23884i | 0.183684 | − | 0.133454i | ||||
\(590\) | 0.160659 | + | 0.494457i | 0.00661421 | + | 0.0203565i | ||||
\(591\) | 5.21392 | − | 16.0468i | 0.214472 | − | 0.660077i | ||||
\(592\) | 1.73653 | + | 1.26166i | 0.0713708 | + | 0.0518539i | ||||
\(593\) | 8.09224 | 0.332308 | 0.166154 | − | 0.986100i | \(-0.446865\pi\) | ||||
0.166154 | + | 0.986100i | \(0.446865\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.0452000 | −0.00185302 | ||||||||
\(596\) | −4.90260 | − | 3.56195i | −0.200818 | − | 0.145903i | ||||
\(597\) | −11.8119 | + | 36.3532i | −0.483428 | + | 1.48784i | ||||
\(598\) | −24.1337 | − | 74.2759i | −0.986900 | − | 3.03737i | ||||
\(599\) | −3.10352 | + | 2.25484i | −0.126806 | + | 0.0921302i | −0.649381 | − | 0.760464i | \(-0.724972\pi\) |
0.522574 | + | 0.852594i | \(0.324972\pi\) | |||||||
\(600\) | 1.37991 | − | 1.00256i | 0.0563346 | − | 0.0409295i | ||||
\(601\) | 4.43027 | + | 13.6350i | 0.180714 | + | 0.556182i | 0.999848 | − | 0.0174208i | \(-0.00554549\pi\) |
−0.819134 | + | 0.573602i | \(0.805545\pi\) | |||||||
\(602\) | −2.29336 | + | 7.05823i | −0.0934702 | + | 0.287672i | ||||
\(603\) | −10.8411 | − | 7.87654i | −0.441485 | − | 0.320758i | ||||
\(604\) | −38.2261 | −1.55540 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −22.3859 | −0.909367 | ||||||||
\(607\) | 11.1471 | + | 8.09883i | 0.452446 | + | 0.328722i | 0.790561 | − | 0.612383i | \(-0.209789\pi\) |
−0.338114 | + | 0.941105i | \(0.609789\pi\) | |||||||
\(608\) | −3.36706 | + | 10.3628i | −0.136552 | + | 0.420265i | ||||
\(609\) | −5.50479 | − | 16.9420i | −0.223065 | − | 0.686524i | ||||
\(610\) | 0.366014 | − | 0.265925i | 0.0148195 | − | 0.0107670i | ||||
\(611\) | 35.3785 | − | 25.7040i | 1.43126 | − | 1.03987i | ||||
\(612\) | −4.79035 | − | 14.7432i | −0.193639 | − | 0.595958i | ||||
\(613\) | 2.94937 | − | 9.07722i | 0.119124 | − | 0.366625i | −0.873661 | − | 0.486535i | \(-0.838261\pi\) |
0.992785 | + | 0.119910i | \(0.0382605\pi\) | |||||||
\(614\) | −13.8233 | − | 10.0432i | −0.557862 | − | 0.405310i | ||||
\(615\) | −0.795137 | −0.0320630 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −31.5153 | −1.26876 | −0.634379 | − | 0.773023i | \(-0.718744\pi\) | ||||
−0.634379 | + | 0.773023i | \(0.718744\pi\) | |||||||
\(618\) | −17.6839 | − | 12.8481i | −0.711350 | − | 0.516826i | ||||
\(619\) | 6.34403 | − | 19.5249i | 0.254988 | − | 0.784773i | −0.738844 | − | 0.673877i | \(-0.764628\pi\) |
0.993832 | − | 0.110896i | \(-0.0353721\pi\) | |||||||
\(620\) | −0.0646772 | − | 0.199056i | −0.00259750 | − | 0.00799428i | ||||
\(621\) | −32.0600 | + | 23.2930i | −1.28652 | + | 0.934715i | ||||
\(622\) | 30.7066 | − | 22.3097i | 1.23122 | − | 0.894537i | ||||
\(623\) | −0.376356 | − | 1.15831i | −0.0150784 | − | 0.0464065i | ||||
\(624\) | −17.3140 | + | 53.2872i | −0.693117 | + | 2.13319i | ||||
\(625\) | −20.2166 | − | 14.6882i | −0.808665 | − | 0.587530i | ||||
\(626\) | 1.20411 | 0.0481261 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −44.4928 | −1.77546 | ||||||||
\(629\) | 0.707653 | + | 0.514140i | 0.0282160 | + | 0.0205001i | ||||
\(630\) | −0.0786597 | + | 0.242090i | −0.00313388 | + | 0.00964509i | ||||
\(631\) | 11.1141 | + | 34.2055i | 0.442444 | + | 1.36170i | 0.885263 | + | 0.465091i | \(0.153978\pi\) |
−0.442819 | + | 0.896611i | \(0.646022\pi\) | |||||||
\(632\) | 0.580021 | − | 0.421410i | 0.0230720 | − | 0.0167628i | ||||
\(633\) | 40.6558 | − | 29.5382i | 1.61592 | − | 1.17404i | ||||
\(634\) | 3.19676 | + | 9.83862i | 0.126960 | + | 0.390741i | ||||
\(635\) | −0.0418606 | + | 0.128834i | −0.00166119 | + | 0.00511261i | ||||
\(636\) | 17.3053 | + | 12.5730i | 0.686200 | + | 0.498553i | ||||
\(637\) | 4.88112 | 0.193397 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.74478 | 0.385498 | ||||||||
\(640\) | −0.0213270 | − | 0.0154950i | −0.000843023 | − | 0.000612492i | ||||
\(641\) | 4.20895 | − | 12.9538i | 0.166244 | − | 0.511645i | −0.832882 | − | 0.553450i | \(-0.813311\pi\) |
0.999126 | + | 0.0418050i | \(0.0133108\pi\) | |||||||
\(642\) | 17.7686 | + | 54.6863i | 0.701272 | + | 2.15829i | ||||
\(643\) | −17.7896 | + | 12.9249i | −0.701552 | + | 0.509707i | −0.880437 | − | 0.474163i | \(-0.842751\pi\) |
0.178885 | + | 0.983870i | \(0.442751\pi\) | |||||||
\(644\) | 12.6429 | − | 9.18560i | 0.498200 | − | 0.361963i | ||||
\(645\) | 0.0866971 | + | 0.266826i | 0.00341370 | + | 0.0105063i | ||||
\(646\) | −1.41448 | + | 4.35334i | −0.0556522 | + | 0.171280i | ||||
\(647\) | 11.9898 | + | 8.71112i | 0.471369 | + | 0.342470i | 0.797975 | − | 0.602691i | \(-0.205905\pi\) |
−0.326606 | + | 0.945161i | \(0.605905\pi\) | |||||||
\(648\) | −0.0730235 | −0.00286863 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 48.4262 | 1.89943 | ||||||||
\(651\) | 9.04072 | + | 6.56847i | 0.354334 | + | 0.257439i | ||||
\(652\) | 11.3738 | − | 35.0051i | 0.445434 | − | 1.37090i | ||||
\(653\) | 13.4044 | + | 41.2545i | 0.524555 | + | 1.61441i | 0.765194 | + | 0.643800i | \(0.222643\pi\) |
−0.240639 | + | 0.970615i | \(0.577357\pi\) | |||||||
\(654\) | 16.8966 | − | 12.2761i | 0.660707 | − | 0.480032i | ||||
\(655\) | 0.0819791 | − | 0.0595613i | 0.00320319 | − | 0.00232725i | ||||
\(656\) | −13.4925 | − | 41.5255i | −0.526792 | − | 1.62130i | ||||
\(657\) | 15.4125 | − | 47.4347i | 0.601298 | − | 1.85060i | ||||
\(658\) | 14.3838 | + | 10.4505i | 0.560740 | + | 0.407402i | ||||
\(659\) | −42.2093 | −1.64424 | −0.822121 | − | 0.569313i | \(-0.807209\pi\) | ||||
−0.822121 | + | 0.569313i | \(0.807209\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.2794 | 0.633197 | 0.316599 | − | 0.948560i | \(-0.397459\pi\) | ||||
0.316599 | + | 0.948560i | \(0.397459\pi\) | |||||||
\(662\) | 1.07410 | + | 0.780382i | 0.0417462 | + | 0.0303304i | ||||
\(663\) | −7.05566 | + | 21.7151i | −0.274019 | + | 0.843344i | ||||
\(664\) | −0.0985855 | − | 0.303415i | −0.00382586 | − | 0.0117748i | ||||
\(665\) | 0.0299275 | − | 0.0217436i | 0.00116054 | − | 0.000843181i | ||||
\(666\) | 3.98522 | − | 2.89543i | 0.154424 | − | 0.112196i | ||||
\(667\) | 15.9282 | + | 49.0219i | 0.616741 | + | 1.89813i | ||||
\(668\) | 1.80914 | − | 5.56797i | 0.0699978 | − | 0.215431i | ||||
\(669\) | 14.7273 | + | 10.7000i | 0.569389 | + | 0.413685i | ||||
\(670\) | 0.150295 | 0.00580642 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −22.0975 | −0.852430 | ||||||||
\(673\) | −4.29626 | − | 3.12142i | −0.165609 | − | 0.120322i | 0.501894 | − | 0.864929i | \(-0.332637\pi\) |
−0.667503 | + | 0.744607i | \(0.732637\pi\) | |||||||
\(674\) | −4.04876 | + | 12.4608i | −0.155952 | + | 0.479972i | ||||
\(675\) | −7.59325 | − | 23.3696i | −0.292264 | − | 0.899497i | ||||
\(676\) | −16.9754 | + | 12.3333i | −0.652899 | + | 0.474359i | ||||
\(677\) | −27.3405 | + | 19.8640i | −1.05078 | + | 0.763437i | −0.972361 | − | 0.233483i | \(-0.924988\pi\) |
−0.0784205 | + | 0.996920i | \(0.524988\pi\) | |||||||
\(678\) | −10.8483 | − | 33.3877i | −0.416628 | − | 1.28225i | ||||
\(679\) | −1.04964 | + | 3.23046i | −0.0402815 | + | 0.123974i | ||||
\(680\) | −0.00447754 | − | 0.00325313i | −0.000171706 | − | 0.000124752i | ||||
\(681\) | −37.9164 | −1.45296 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.8834 | −0.607761 | −0.303880 | − | 0.952710i | \(-0.598282\pi\) | ||||
−0.303880 | + | 0.952710i | \(0.598282\pi\) | |||||||
\(684\) | 10.2640 | + | 7.45724i | 0.392454 | + | 0.285135i | ||||
\(685\) | −0.159228 | + | 0.490055i | −0.00608381 | + | 0.0187240i | ||||
\(686\) | 0.613249 | + | 1.88739i | 0.0234139 | + | 0.0720607i | ||||
\(687\) | 43.7798 | − | 31.8079i | 1.67030 | − | 1.21355i | ||||
\(688\) | −12.4637 | + | 9.05541i | −0.475174 | + | 0.345234i | ||||
\(689\) | −5.97393 | − | 18.3859i | −0.227589 | − | 0.700445i | ||||
\(690\) | 0.370930 | − | 1.14160i | 0.0141211 | − | 0.0434602i | ||||
\(691\) | −20.6602 | − | 15.0105i | −0.785952 | − | 0.571028i | 0.120807 | − | 0.992676i | \(-0.461452\pi\) |
−0.906759 | + | 0.421648i | \(0.861452\pi\) | |||||||
\(692\) | −17.1274 | −0.651085 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 24.2113 | 0.919050 | ||||||||
\(695\) | −0.0764793 | − | 0.0555655i | −0.00290103 | − | 0.00210772i | ||||
\(696\) | 0.674037 | − | 2.07447i | 0.0255493 | − | 0.0786327i | ||||
\(697\) | −5.49832 | − | 16.9221i | −0.208264 | − | 0.640970i | ||||
\(698\) | 1.42216 | − | 1.03326i | 0.0538295 | − | 0.0391094i | ||||
\(699\) | 9.83187 | − | 7.14327i | 0.371876 | − | 0.270183i | ||||
\(700\) | 2.99440 | + | 9.21583i | 0.113178 | + | 0.348325i | ||||
\(701\) | 1.01832 | − | 3.13407i | 0.0384614 | − | 0.118372i | −0.929982 | − | 0.367604i | \(-0.880178\pi\) |
0.968444 | + | 0.249232i | \(0.0801782\pi\) | |||||||
\(702\) | 38.5185 | + | 27.9854i | 1.45379 | + | 1.05624i | ||||
\(703\) | −0.715875 | −0.0269997 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.672125 | 0.0253137 | ||||||||
\(706\) | 8.60571 | + | 6.25242i | 0.323880 | + | 0.235313i | ||||
\(707\) | −1.25101 | + | 3.85021i | −0.0470491 | + | 0.144802i | ||||
\(708\) | 16.2393 | + | 49.9795i | 0.610312 | + | 1.87835i | ||||
\(709\) | 36.3269 | − | 26.3931i | 1.36429 | − | 0.991213i | 0.366128 | − | 0.930565i | \(-0.380683\pi\) |
0.998159 | − | 0.0606480i | \(-0.0193167\pi\) | |||||||
\(710\) | −0.0884216 | + | 0.0642420i | −0.00331840 | + | 0.00241096i | ||||
\(711\) | −8.61977 | − | 26.5289i | −0.323267 | − | 0.994913i | ||||
\(712\) | 0.0460832 | − | 0.141829i | 0.00172704 | − | 0.00531528i | ||||
\(713\) | −26.1594 | − | 19.0059i | −0.979679 | − | 0.711778i | ||||
\(714\) | −9.28304 | −0.347409 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 16.4064 | 0.613137 | ||||||||
\(717\) | 23.8727 | + | 17.3445i | 0.891541 | + | 0.647742i | ||||
\(718\) | 15.8494 | − | 48.7795i | 0.591495 | − | 1.82043i | ||||
\(719\) | 0.986580 | + | 3.03638i | 0.0367932 | + | 0.113238i | 0.967766 | − | 0.251850i | \(-0.0810389\pi\) |
−0.930973 | + | 0.365088i | \(0.881039\pi\) | |||||||
\(720\) | −0.427492 | + | 0.310591i | −0.0159317 | + | 0.0115750i | ||||
\(721\) | −3.19802 | + | 2.32350i | −0.119100 | + | 0.0865315i | ||||
\(722\) | 10.4941 | + | 32.2975i | 0.390550 | + | 1.20199i | ||||
\(723\) | −16.0917 | + | 49.5253i | −0.598458 | + | 1.84187i | ||||
\(724\) | 37.9497 | + | 27.5721i | 1.41039 | + | 1.02471i | ||||
\(725\) | −31.9612 | −1.18701 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.1654 | 0.747891 | 0.373946 | − | 0.927451i | \(-0.378005\pi\) | ||||
0.373946 | + | 0.927451i | \(0.378005\pi\) | |||||||
\(728\) | 0.483527 | + | 0.351303i | 0.0179207 | + | 0.0130201i | ||||
\(729\) | −13.5745 | + | 41.7779i | −0.502758 | + | 1.54733i | ||||
\(730\) | 0.172862 | + | 0.532016i | 0.00639793 | + | 0.0196908i | ||||
\(731\) | −5.07909 | + | 3.69018i | −0.187857 | + | 0.136486i | ||||
\(732\) | 36.9966 | − | 26.8796i | 1.36743 | − | 0.993499i | ||||
\(733\) | 6.09055 | + | 18.7448i | 0.224960 | + | 0.692355i | 0.998296 | + | 0.0583583i | \(0.0185866\pi\) |
−0.773336 | + | 0.633996i | \(0.781413\pi\) | |||||||
\(734\) | 12.5412 | − | 38.5979i | 0.462904 | − | 1.42467i | ||||
\(735\) | 0.0606939 | + | 0.0440967i | 0.00223873 | + | 0.00162653i | ||||
\(736\) | 63.9394 | 2.35684 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −100.203 | −3.68851 | ||||||||
\(739\) | −27.9576 | − | 20.3124i | −1.02844 | − | 0.747204i | −0.0604429 | − | 0.998172i | \(-0.519251\pi\) |
−0.967996 | + | 0.250967i | \(0.919251\pi\) | |||||||
\(740\) | −0.00840267 | + | 0.0258608i | −0.000308888 | + | 0.000950661i | ||||
\(741\) | −5.77447 | − | 17.7720i | −0.212130 | − | 0.652871i | ||||
\(742\) | 6.35873 | − | 4.61989i | 0.233436 | − | 0.169601i | ||||
\(743\) | −20.9035 | + | 15.1873i | −0.766875 | + | 0.557167i | −0.901011 | − | 0.433796i | \(-0.857174\pi\) |
0.134136 | + | 0.990963i | \(0.457174\pi\) | |||||||
\(744\) | 0.422836 | + | 1.30135i | 0.0155019 | + | 0.0477100i | ||||
\(745\) | −0.0260121 | + | 0.0800570i | −0.000953010 | + | 0.00293306i | ||||
\(746\) | −15.0775 | − | 10.9544i | −0.552025 | − | 0.401069i | ||||
\(747\) | −12.4125 | −0.454148 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.3986 | 0.379957 | ||||||||
\(750\) | 1.20439 | + | 0.875042i | 0.0439782 | + | 0.0319520i | ||||
\(751\) | −11.0381 | + | 33.9717i | −0.402785 | + | 1.23964i | 0.519946 | + | 0.854199i | \(0.325952\pi\) |
−0.922731 | + | 0.385445i | \(0.874048\pi\) | |||||||
\(752\) | 11.4051 | + | 35.1013i | 0.415902 | + | 1.28001i | ||||
\(753\) | −42.7926 | + | 31.0906i | −1.55945 | + | 1.13301i | ||||
\(754\) | 50.1011 | − | 36.4006i | 1.82457 | − | 1.32563i | ||||
\(755\) | 0.164084 | + | 0.504999i | 0.00597164 | + | 0.0183788i | ||||
\(756\) | −2.94403 | + | 9.06078i | −0.107073 | + | 0.329537i | ||||
\(757\) | 11.9893 | + | 8.71077i | 0.435760 | + | 0.316598i | 0.783948 | − | 0.620826i | \(-0.213203\pi\) |
−0.348188 | + | 0.937425i | \(0.613203\pi\) | |||||||
\(758\) | 11.1846 | 0.406242 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.00452957 | 0.000164305 | ||||||||
\(761\) | −17.6171 | − | 12.7996i | −0.638619 | − | 0.463984i | 0.220756 | − | 0.975329i | \(-0.429148\pi\) |
−0.859376 | + | 0.511345i | \(0.829148\pi\) | |||||||
\(762\) | −8.59721 | + | 26.4595i | −0.311444 | + | 0.958527i | ||||
\(763\) | −1.16715 | − | 3.59211i | −0.0422536 | − | 0.130043i | ||||
\(764\) | 12.2112 | − | 8.87196i | 0.441786 | − | 0.320976i | ||||
\(765\) | −0.174208 | + | 0.126569i | −0.00629849 | + | 0.00457612i | ||||
\(766\) | 0.772350 | + | 2.37705i | 0.0279062 | + | 0.0858863i | ||||
\(767\) | 14.6766 | − | 45.1698i | 0.529940 | − | 1.63099i | ||||
\(768\) | −38.1892 | − | 27.7461i | −1.37804 | − | 1.00120i | ||||
\(769\) | 35.6991 | 1.28734 | 0.643672 | − | 0.765302i | \(-0.277410\pi\) | ||||
0.643672 | + | 0.765302i | \(0.277410\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −38.1988 | −1.37570 | ||||||||
\(772\) | 26.7578 | + | 19.4407i | 0.963035 | + | 0.699686i | ||||
\(773\) | 13.1712 | − | 40.5368i | 0.473735 | − | 1.45801i | −0.373920 | − | 0.927461i | \(-0.621987\pi\) |
0.847656 | − | 0.530547i | \(-0.178013\pi\) | |||||||
\(774\) | 10.9255 | + | 33.6253i | 0.392710 | + | 1.20864i | ||||
\(775\) | 16.2206 | − | 11.7850i | 0.582662 | − | 0.423329i | ||||
\(776\) | −0.336480 | + | 0.244467i | −0.0120789 | + | 0.00877585i | ||||
\(777\) | −0.448636 | − | 1.38076i | −0.0160947 | − | 0.0495345i | ||||
\(778\) | 3.60841 | − | 11.1055i | 0.129368 | − | 0.398153i | ||||
\(779\) | 11.7809 | + | 8.55935i | 0.422096 | + | 0.306671i | ||||
\(780\) | −0.709786 | −0.0254144 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 26.8606 | 0.960533 | ||||||||
\(783\) | −25.4221 | − | 18.4702i | −0.908512 | − | 0.660073i | ||||
\(784\) | −1.27302 | + | 3.91797i | −0.0454652 | + | 0.139927i | ||||
\(785\) | 0.190984 | + | 0.587788i | 0.00681650 | + | 0.0209790i | ||||
\(786\) | 16.8366 | − | 12.2325i | 0.600542 | − | 0.436320i | ||||
\(787\) | −38.0939 | + | 27.6769i | −1.35790 | + | 0.986574i | −0.359327 | + | 0.933212i | \(0.616994\pi\) |
−0.998575 | + | 0.0533617i | \(0.983006\pi\) | |||||||
\(788\) | 3.62696 | + | 11.1626i | 0.129205 | + | 0.397653i | ||||
\(789\) | −14.2733 | + | 43.9287i | −0.508143 | + | 1.56390i | ||||
\(790\) | 0.253104 | + | 0.183891i | 0.00900505 | + | 0.00654255i | ||||
\(791\) | −6.34869 | −0.225733 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −41.3295 | −1.46765 | ||||||||
\(794\) | 7.80304 | + | 5.66924i | 0.276920 | + | 0.201194i | ||||
\(795\) | 0.0918180 | − | 0.282587i | 0.00325645 | − | 0.0100223i | ||||
\(796\) | −8.21670 | − | 25.2884i | −0.291233 | − | 0.896324i | ||||
\(797\) | 6.05358 | − | 4.39818i | 0.214429 | − | 0.155792i | −0.475386 | − | 0.879777i | \(-0.657692\pi\) |
0.689815 | + | 0.723985i | \(0.257692\pi\) | |||||||
\(798\) | 6.14642 | − | 4.46564i | 0.217581 | − | 0.158082i | ||||
\(799\) | 4.64771 | + | 14.3042i | 0.164424 | + | 0.506045i | ||||
\(800\) | −12.2515 | + | 37.7063i | −0.433157 | + | 1.33312i | ||||
\(801\) | −4.69402 | − | 3.41041i | −0.165855 | − | 0.120501i | ||||
\(802\) | 50.6690 | 1.78918 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 15.1918 | 0.535774 | ||||||||
\(805\) | −0.175619 | − | 0.127594i | −0.00618974 | − | 0.00449711i | ||||
\(806\) | −12.0049 | + | 36.9473i | −0.422855 | + | 1.30141i | ||||
\(807\) | −7.35642 | − | 22.6407i | −0.258958 | − | 0.796991i | ||||
\(808\) | −0.401033 | + | 0.291367i | −0.0141083 | + | 0.0102503i | ||||
\(809\) | 28.1125 | − | 20.4249i | 0.988384 | − | 0.718103i | 0.0288171 | − | 0.999585i | \(-0.490826\pi\) |
0.959567 | + | 0.281482i | \(0.0908259\pi\) | |||||||
\(810\) | −0.00984693 | − | 0.0303057i | −0.000345986 | − | 0.00106483i | ||||
\(811\) | −3.95952 | + | 12.1862i | −0.139038 | + | 0.427914i | −0.996196 | − | 0.0871388i | \(-0.972228\pi\) |
0.857159 | + | 0.515053i | \(0.172228\pi\) | |||||||
\(812\) | 10.0252 | + | 7.28375i | 0.351816 | + | 0.255610i | ||||
\(813\) | 17.6811 | 0.620105 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.511268 | −0.0179089 | ||||||||
\(816\) | −15.5901 | − | 11.3268i | −0.545762 | − | 0.396519i | ||||
\(817\) | 1.58776 | − | 4.88663i | 0.0555487 | − | 0.170961i | ||||
\(818\) | 12.8946 | + | 39.6854i | 0.450848 | + | 1.38757i | ||||
\(819\) | 18.8126 | − | 13.6681i | 0.657364 | − | 0.477603i | ||||
\(820\) | 0.447484 | − | 0.325116i | 0.0156268 | − | 0.0113536i | ||||
\(821\) | 16.7866 | + | 51.6638i | 0.585856 | + | 1.80308i | 0.595807 | + | 0.803128i | \(0.296832\pi\) |
−0.00995123 | + | 0.999950i | \(0.503168\pi\) | |||||||
\(822\) | −32.7019 | + | 100.646i | −1.14061 | + | 3.51043i | ||||
\(823\) | 15.9940 | + | 11.6203i | 0.557517 | + | 0.405060i | 0.830549 | − | 0.556945i | \(-0.188027\pi\) |
−0.273032 | + | 0.962005i | \(0.588027\pi\) | |||||||
\(824\) | −0.484024 | −0.0168618 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 19.3098 | 0.671873 | ||||||||
\(827\) | 9.95887 | + | 7.23554i | 0.346304 | + | 0.251605i | 0.747317 | − | 0.664468i | \(-0.231342\pi\) |
−0.401013 | + | 0.916072i | \(0.631342\pi\) | |||||||
\(828\) | 23.0060 | − | 70.8053i | 0.799515 | − | 2.46065i | ||||
\(829\) | −7.94973 | − | 24.4668i | −0.276106 | − | 0.849765i | −0.988925 | − | 0.148418i | \(-0.952582\pi\) |
0.712819 | − | 0.701348i | \(-0.247418\pi\) | |||||||
\(830\) | 0.112627 | − | 0.0818286i | 0.00390935 | − | 0.00284031i | ||||
\(831\) | −54.1116 | + | 39.3144i | −1.87711 | + | 1.36380i | ||||
\(832\) | −11.3111 | − | 34.8121i | −0.392143 | − | 1.20689i | ||||
\(833\) | −0.518771 | + | 1.59661i | −0.0179744 | + | 0.0553194i | ||||
\(834\) | −15.7071 | − | 11.4119i | −0.543892 | − | 0.395161i | ||||
\(835\) | −0.0813232 | −0.00281431 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 19.7125 | 0.681363 | ||||||||
\(838\) | −50.2751 | − | 36.5270i | −1.73672 | − | 1.26180i | ||||
\(839\) | −14.4044 | + | 44.3322i | −0.497295 | + | 1.53052i | 0.316054 | + | 0.948741i | \(0.397642\pi\) |
−0.813349 | + | 0.581776i | \(0.802358\pi\) | |||||||
\(840\) | 0.00283866 | + | 0.00873650i | 9.79431e−5 | + | 0.000301438i | ||||
\(841\) | −9.60506 | + | 6.97848i | −0.331209 | + | 0.240637i | ||||
\(842\) | 20.5322 | − | 14.9176i | 0.707588 | − | 0.514093i | ||||
\(843\) | 2.76519 | + | 8.51037i | 0.0952380 | + | 0.293113i | ||||
\(844\) | −10.8025 | + | 33.2468i | −0.371838 | + | 1.14440i | ||||
\(845\) | 0.235800 | + | 0.171319i | 0.00811176 | + | 0.00589354i | ||||
\(846\) | 84.7009 | 2.91208 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 16.3160 | 0.560292 | ||||||||
\(849\) | −46.8958 | − | 34.0718i | −1.60946 | − | 1.16934i | ||||
\(850\) | −5.14680 | + | 15.8402i | −0.176534 | + | 0.543315i | ||||
\(851\) | 1.29813 | + | 3.99524i | 0.0444994 | + | 0.136955i | ||||
\(852\) | −8.93763 | + | 6.49357i | −0.306198 | + | 0.222466i | ||||
\(853\) | −7.93549 | + | 5.76547i | −0.271706 | + | 0.197406i | −0.715292 | − | 0.698826i | \(-0.753706\pi\) |
0.443586 | + | 0.896232i | \(0.353706\pi\) | |||||||
\(854\) | −5.19252 | − | 15.9809i | −0.177684 | − | 0.546856i | ||||
\(855\) | 0.0544585 | − | 0.167606i | 0.00186244 | − | 0.00573201i | ||||
\(856\) | 1.03009 | + | 0.748406i | 0.0352078 | + | 0.0255800i | ||||
\(857\) | 32.9168 | 1.12442 | 0.562208 | − | 0.826996i | \(-0.309952\pi\) | ||||
0.562208 | + | 0.826996i | \(0.309952\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.4747 | −0.971543 | −0.485772 | − | 0.874086i | \(-0.661461\pi\) | ||||
−0.485772 | + | 0.874086i | \(0.661461\pi\) | |||||||
\(860\) | −0.157891 | − | 0.114715i | −0.00538405 | − | 0.00391174i | ||||
\(861\) | −9.12597 | + | 28.0869i | −0.311012 | + | 0.957197i | ||||
\(862\) | 12.9199 | + | 39.7632i | 0.440052 | + | 1.35434i | ||||
\(863\) | −23.6856 | + | 17.2086i | −0.806267 | + | 0.585787i | −0.912746 | − | 0.408528i | \(-0.866042\pi\) |
0.106479 | + | 0.994315i | \(0.466042\pi\) | |||||||
\(864\) | −31.5353 | + | 22.9117i | −1.07285 | + | 0.779473i | ||||
\(865\) | 0.0735186 | + | 0.226267i | 0.00249971 | + | 0.00769331i | ||||
\(866\) | −23.3053 | + | 71.7264i | −0.791947 | + | 2.43736i | ||||
\(867\) | 31.9690 | + | 23.2268i | 1.08572 | + | 0.788824i | ||||
\(868\) | −7.77363 | −0.263854 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0.951826 | 0.0322699 | ||||||||
\(871\) | −11.1077 | − | 8.07020i | −0.376369 | − | 0.273448i | ||||
\(872\) | 0.142912 | − | 0.439839i | 0.00483962 | − | 0.0148948i | ||||
\(873\) | 5.00047 | + | 15.3899i | 0.169240 | + | 0.520868i | ||||
\(874\) | −17.7848 | + | 12.9214i | −0.601578 | + | 0.437072i | ||||
\(875\) | 0.217807 | − | 0.158246i | 0.00736321 | − | 0.00534968i | ||||
\(876\) | 17.4729 | + | 53.7760i | 0.590354 | + | 1.81692i | ||||
\(877\) | 6.98456 | − | 21.4963i | 0.235852 | − | 0.725877i | −0.761155 | − | 0.648570i | \(-0.775368\pi\) |
0.997007 | − | 0.0773079i | \(-0.0246324\pi\) | |||||||
\(878\) | 60.6363 | + | 44.0549i | 2.04638 | + | 1.48678i | ||||
\(879\) | −15.3738 | −0.518544 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −35.1102 | −1.18289 | −0.591447 | − | 0.806344i | \(-0.701443\pi\) | ||||
−0.591447 | + | 0.806344i | \(0.701443\pi\) | |||||||
\(882\) | 7.64861 | + | 5.55704i | 0.257542 | + | 0.187115i | ||||
\(883\) | 4.69804 | − | 14.4591i | 0.158102 | − | 0.486587i | −0.840360 | − | 0.542028i | \(-0.817657\pi\) |
0.998462 | + | 0.0554413i | \(0.0176566\pi\) | |||||||
\(884\) | −4.90813 | − | 15.1057i | −0.165078 | − | 0.508059i | ||||
\(885\) | 0.590565 | − | 0.429070i | 0.0198516 | − | 0.0144230i | ||||
\(886\) | −1.65034 | + | 1.19904i | −0.0554441 | + | 0.0402825i | ||||
\(887\) | 11.9069 | + | 36.6458i | 0.399796 | + | 1.23044i | 0.925163 | + | 0.379569i | \(0.123928\pi\) |
−0.525368 | + | 0.850875i | \(0.676072\pi\) | |||||||
\(888\) | 0.0549335 | − | 0.169068i | 0.00184345 | − | 0.00567355i | ||||
\(889\) | 4.07039 | + | 2.95731i | 0.136517 | + | 0.0991851i | ||||
\(890\) | 0.0650753 | 0.00218133 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −12.6632 | −0.423995 | ||||||||
\(893\) | −9.95837 | − | 7.23518i | −0.333244 | − | 0.242116i | ||||
\(894\) | −5.34229 | + | 16.4419i | −0.178673 | + | 0.549899i | ||||
\(895\) | −0.0704239 | − | 0.216743i | −0.00235401 | − | 0.00724491i | ||||
\(896\) | −0.792108 | + | 0.575500i | −0.0264625 | + | 0.0192261i | ||||
\(897\) | −88.7130 | + | 64.4538i | −2.96204 | + | 2.15205i | ||||
\(898\) | −12.3467 | − | 37.9993i | −0.412015 | − | 1.26805i | ||||
\(899\) | 7.92321 | − | 24.3851i | 0.264254 | − | 0.813289i | ||||
\(900\) | 37.3471 | + | 27.1342i | 1.24490 | + | 0.904474i | ||||
\(901\) | 6.64893 | 0.221508 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.4202 | 0.346764 | ||||||||
\(904\) | −0.628905 | − | 0.456926i | −0.0209171 | − | 0.0151971i | ||||
\(905\) | 0.201352 | − | 0.619699i | 0.00669318 | − | 0.0205995i | ||||
\(906\) | 33.6991 | + | 103.715i | 1.11958 | + | 3.44571i | ||||
\(907\) | 45.6459 | − | 33.1637i | 1.51565 | − | 1.10118i | 0.552054 | − | 0.833808i | \(-0.313844\pi\) |
0.963593 | − | 0.267374i | \(-0.0861559\pi\) | |||||||
\(908\) | 21.3385 | − | 15.5033i | 0.708143 | − | 0.514496i | ||||
\(909\) | 5.95980 | + | 18.3424i | 0.197674 | + | 0.608378i | ||||
\(910\) | −0.0805937 | + | 0.248042i | −0.00267165 | + | 0.00822251i | ||||
\(911\) | 24.7481 | + | 17.9806i | 0.819942 | + | 0.595723i | 0.916696 | − | 0.399585i | \(-0.130846\pi\) |
−0.0967538 | + | 0.995308i | \(0.530846\pi\) | |||||||
\(912\) | 15.7712 | 0.522237 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −47.9173 | −1.58496 | ||||||||
\(915\) | −0.513909 | − | 0.373377i | −0.0169893 | − | 0.0123435i | ||||
\(916\) | −11.6326 | + | 35.8014i | −0.384352 | + | 1.18291i | ||||
\(917\) | −1.16301 | − | 3.57937i | −0.0384059 | − | 0.118201i | ||||
\(918\) | −13.2478 | + | 9.62509i | −0.437243 | + | 0.317675i | ||||
\(919\) | 26.6089 | − | 19.3325i | 0.877745 | − | 0.637719i | −0.0549086 | − | 0.998491i | \(-0.517487\pi\) |
0.932654 | + | 0.360772i | \(0.117487\pi\) | |||||||
\(920\) | −0.00821370 | − | 0.0252792i | −0.000270798 | − | 0.000833429i | ||||
\(921\) | −7.41350 | + | 22.8164i | −0.244283 | + | 0.751827i | ||||
\(922\) | −18.6054 | − | 13.5176i | −0.612737 | − | 0.445180i | ||||
\(923\) | 9.98437 | 0.328640 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.60481 | −0.0856457 | ||||||||
\(926\) | 34.6913 | + | 25.2047i | 1.14003 | + | 0.828277i | ||||
\(927\) | −5.81938 | + | 17.9102i | −0.191133 | + | 0.588248i | ||||
\(928\) | 15.6675 | + | 48.2195i | 0.514310 | + | 1.58288i | ||||
\(929\) | −17.6630 | + | 12.8329i | −0.579503 | + | 0.421033i | −0.838545 | − | 0.544833i | \(-0.816593\pi\) |
0.259042 | + | 0.965866i | \(0.416593\pi\) | |||||||
\(930\) | −0.483062 | + | 0.350965i | −0.0158402 | + | 0.0115086i | ||||
\(931\) | −0.424571 | − | 1.30670i | −0.0139148 | − | 0.0428252i | ||||
\(932\) | −2.61240 | + | 8.04013i | −0.0855719 | + | 0.263363i | ||||
\(933\) | −43.1142 | − | 31.3243i | −1.41150 | − | 1.02551i | ||||
\(934\) | −31.5835 | −1.03344 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.84730 | 0.0930670 | ||||||||
\(937\) | −28.2770 | − | 20.5444i | −0.923769 | − | 0.671157i | 0.0206903 | − | 0.999786i | \(-0.493414\pi\) |
−0.944459 | + | 0.328628i | \(0.893414\pi\) | |||||||
\(938\) | 1.72498 | − | 5.30893i | 0.0563224 | − | 0.173343i | ||||
\(939\) | −0.522442 | − | 1.60791i | −0.0170493 | − | 0.0524722i | ||||
\(940\) | −0.378256 | + | 0.274819i | −0.0123374 | + | 0.00896362i | ||||
\(941\) | −16.5205 | + | 12.0029i | −0.538554 | + | 0.391282i | −0.823548 | − | 0.567247i | \(-0.808008\pi\) |
0.284994 | + | 0.958529i | \(0.408008\pi\) | |||||||
\(942\) | 39.2237 | + | 120.718i | 1.27798 | + | 3.93321i | ||||
\(943\) | 26.4061 | − | 81.2697i | 0.859901 | − | 2.64650i | ||||
\(944\) | 32.4291 | + | 23.5611i | 1.05548 | + | 0.766849i | ||||
\(945\) | 0.132338 | 0.00430494 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −11.3122 | −0.367597 | −0.183799 | − | 0.982964i | \(-0.558839\pi\) | ||||
−0.183799 | + | 0.982964i | \(0.558839\pi\) | |||||||
\(948\) | 25.5837 | + | 18.5877i | 0.830921 | + | 0.603699i | ||||
\(949\) | 15.7914 | − | 48.6010i | 0.512611 | − | 1.57765i | ||||
\(950\) | −4.21223 | − | 12.9639i | −0.136663 | − | 0.420605i | ||||
\(951\) | 11.7510 | − | 8.53757i | 0.381051 | − | 0.276850i | ||||
\(952\) | −0.166301 | + | 0.120825i | −0.00538985 | + | 0.00391595i | ||||
\(953\) | 1.40887 | + | 4.33605i | 0.0456377 | + | 0.140458i | 0.971279 | − | 0.237944i | \(-0.0764735\pi\) |
−0.925641 | + | 0.378403i | \(0.876474\pi\) | |||||||
\(954\) | 11.5709 | − | 35.6114i | 0.374620 | − | 1.15296i | ||||
\(955\) | −0.169622 | − | 0.123238i | −0.00548885 | − | 0.00398788i | ||||
\(956\) | −20.5268 | −0.663885 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 10.4856 | 0.338775 | ||||||||
\(959\) | 15.4829 | + | 11.2490i | 0.499968 | + | 0.363248i | ||||
\(960\) | 0.173850 | − | 0.535055i | 0.00561098 | − | 0.0172688i | ||||
\(961\) | −4.60916 | − | 14.1855i | −0.148683 | − | 0.457598i | ||||
\(962\) | 4.08320 | − | 2.96662i | 0.131648 | − | 0.0956476i | ||||
\(963\) | 40.0778 | − | 29.1182i | 1.29149 | − | 0.938321i | ||||
\(964\) | −11.1939 | − | 34.4513i | −0.360531 | − | 1.10960i | ||||
\(965\) | 0.141971 | − | 0.436942i | 0.00457021 | − | 0.0140656i | ||||
\(966\) | −36.0680 | − | 26.2049i | −1.16047 | − | 0.843130i | ||||
\(967\) | 38.9153 | 1.25143 | 0.625715 | − | 0.780052i | \(-0.284807\pi\) | ||||
0.625715 | + | 0.780052i | \(0.284807\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.42694 | 0.206463 | ||||||||
\(970\) | −0.146830 | − | 0.106678i | −0.00471442 | − | 0.00342523i | ||||
\(971\) | 13.0841 | − | 40.2686i | 0.419888 | − | 1.29228i | −0.487918 | − | 0.872890i | \(-0.662243\pi\) |
0.907805 | − | 0.419392i | \(-0.137757\pi\) | |||||||
\(972\) | −9.82740 | − | 30.2456i | −0.315214 | − | 0.970129i | ||||
\(973\) | −2.84053 | + | 2.06376i | −0.0910631 | + | 0.0661612i | ||||
\(974\) | −43.4539 | + | 31.5711i | −1.39235 | + | 1.01160i | ||||
\(975\) | −21.0112 | − | 64.6659i | −0.672898 | − | 2.07097i | ||||
\(976\) | 10.7790 | − | 33.1743i | 0.345027 | − | 1.06188i | ||||
\(977\) | −28.8475 | − | 20.9590i | −0.922914 | − | 0.670536i | 0.0213336 | − | 0.999772i | \(-0.493209\pi\) |
−0.944248 | + | 0.329236i | \(0.893209\pi\) | |||||||
\(978\) | −105.003 | −3.35762 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −0.0521874 | −0.00166707 | ||||||||
\(981\) | −14.5570 | − | 10.5763i | −0.464769 | − | 0.337675i | ||||
\(982\) | 11.5291 | − | 35.4828i | 0.367907 | − | 1.13230i | ||||
\(983\) | −9.12258 | − | 28.0764i | −0.290965 | − | 0.895498i | −0.984547 | − | 0.175121i | \(-0.943968\pi\) |
0.693582 | − | 0.720378i | \(-0.256032\pi\) | |||||||
\(984\) | −2.92549 | + | 2.12549i | −0.0932611 | + | 0.0677581i | ||||
\(985\) | 0.131899 | − | 0.0958304i | 0.00420266 | − | 0.00305341i | ||||
\(986\) | 6.58182 | + | 20.2568i | 0.209608 | + | 0.645107i | ||||
\(987\) | 7.71414 | − | 23.7417i | 0.245544 | − | 0.755706i | ||||
\(988\) | 10.5164 | + | 7.64059i | 0.334570 | + | 0.243080i | ||||
\(989\) | −30.1511 | −0.958748 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30.7292 | −0.976145 | −0.488072 | − | 0.872803i | \(-0.662300\pi\) | ||||
−0.488072 | + | 0.872803i | \(0.662300\pi\) | |||||||
\(992\) | −25.7313 | − | 18.6949i | −0.816969 | − | 0.593563i | ||||
\(993\) | 0.576048 | − | 1.77289i | 0.0182803 | − | 0.0562611i | ||||
\(994\) | 1.25441 | + | 3.86066i | 0.0397873 | + | 0.122453i | ||||
\(995\) | −0.298811 | + | 0.217099i | −0.00947295 | + | 0.00688250i | ||||
\(996\) | 11.3843 | − | 8.27121i | 0.360727 | − | 0.262083i | ||||
\(997\) | −15.4495 | − | 47.5488i | −0.489292 | − | 1.50589i | −0.825667 | − | 0.564158i | \(-0.809201\pi\) |
0.336375 | − | 0.941728i | \(-0.390799\pi\) | |||||||
\(998\) | 24.3869 | − | 75.0550i | 0.771952 | − | 2.37583i | ||||
\(999\) | −2.07188 | − | 1.50531i | −0.0655515 | − | 0.0476259i |
(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 | 847.2.f.x.323.4 | 16 | ||
11.2 | odd | 10 | 847.2.f.w.148.4 | 16 | |||
11.3 | even | 5 | inner | 847.2.f.x.729.4 | 16 | ||
11.4 | even | 5 | 847.2.f.v.372.1 | 16 | |||
11.5 | even | 5 | 847.2.a.o.1.2 | 8 | |||
11.6 | odd | 10 | 847.2.a.p.1.7 | 8 | |||
11.7 | odd | 10 | 847.2.f.w.372.4 | 16 | |||
11.8 | odd | 10 | 77.2.f.b.36.1 | yes | 16 | ||
11.9 | even | 5 | 847.2.f.v.148.1 | 16 | |||
11.10 | odd | 2 | 77.2.f.b.15.1 | ✓ | 16 | ||
33.5 | odd | 10 | 7623.2.a.cw.1.7 | 8 | |||
33.8 | even | 10 | 693.2.m.i.190.4 | 16 | |||
33.17 | even | 10 | 7623.2.a.ct.1.2 | 8 | |||
33.32 | even | 2 | 693.2.m.i.631.4 | 16 | |||
77.6 | even | 10 | 5929.2.a.bt.1.7 | 8 | |||
77.10 | even | 6 | 539.2.q.f.422.4 | 32 | |||
77.19 | even | 30 | 539.2.q.f.410.4 | 32 | |||
77.27 | odd | 10 | 5929.2.a.bs.1.2 | 8 | |||
77.30 | odd | 30 | 539.2.q.g.410.4 | 32 | |||
77.32 | odd | 6 | 539.2.q.g.422.4 | 32 | |||
77.41 | even | 10 | 539.2.f.e.344.1 | 16 | |||
77.52 | even | 30 | 539.2.q.f.520.1 | 32 | |||
77.54 | even | 6 | 539.2.q.f.312.1 | 32 | |||
77.65 | odd | 6 | 539.2.q.g.312.1 | 32 | |||
77.74 | odd | 30 | 539.2.q.g.520.1 | 32 | |||
77.76 | even | 2 | 539.2.f.e.246.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.f.b.15.1 | ✓ | 16 | 11.10 | odd | 2 | ||
77.2.f.b.36.1 | yes | 16 | 11.8 | odd | 10 | ||
539.2.f.e.246.1 | 16 | 77.76 | even | 2 | |||
539.2.f.e.344.1 | 16 | 77.41 | even | 10 | |||
539.2.q.f.312.1 | 32 | 77.54 | even | 6 | |||
539.2.q.f.410.4 | 32 | 77.19 | even | 30 | |||
539.2.q.f.422.4 | 32 | 77.10 | even | 6 | |||
539.2.q.f.520.1 | 32 | 77.52 | even | 30 | |||
539.2.q.g.312.1 | 32 | 77.65 | odd | 6 | |||
539.2.q.g.410.4 | 32 | 77.30 | odd | 30 | |||
539.2.q.g.422.4 | 32 | 77.32 | odd | 6 | |||
539.2.q.g.520.1 | 32 | 77.74 | odd | 30 | |||
693.2.m.i.190.4 | 16 | 33.8 | even | 10 | |||
693.2.m.i.631.4 | 16 | 33.32 | even | 2 | |||
847.2.a.o.1.2 | 8 | 11.5 | even | 5 | |||
847.2.a.p.1.7 | 8 | 11.6 | odd | 10 | |||
847.2.f.v.148.1 | 16 | 11.9 | even | 5 | |||
847.2.f.v.372.1 | 16 | 11.4 | even | 5 | |||
847.2.f.w.148.4 | 16 | 11.2 | odd | 10 | |||
847.2.f.w.372.4 | 16 | 11.7 | odd | 10 | |||
847.2.f.x.323.4 | 16 | 1.1 | even | 1 | trivial | ||
847.2.f.x.729.4 | 16 | 11.3 | even | 5 | inner | ||
5929.2.a.bs.1.2 | 8 | 77.27 | odd | 10 | |||
5929.2.a.bt.1.7 | 8 | 77.6 | even | 10 | |||
7623.2.a.ct.1.2 | 8 | 33.17 | even | 10 | |||
7623.2.a.cw.1.7 | 8 | 33.5 | odd | 10 |