Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,2,Mod(22,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(6))
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("507.22");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.e (of order \(3\), degree \(2\), 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: | \(4.04841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.64827.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 484.2 | ||
Root | \(0.222521 + 0.385418i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.484 |
Dual form | 507.2.e.l.22.2 |
$q$-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 \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.17845 | + | 2.04113i | 0.833289 | + | 1.44330i | 0.895416 | + | 0.445230i | \(0.146878\pi\) |
−0.0621278 | + | 0.998068i | \(0.519789\pi\) | |||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | −1.77748 | + | 3.07868i | −0.888740 | + | 1.53934i | ||||
\(5\) | −3.69202 | −1.65112 | −0.825561 | − | 0.564313i | \(-0.809141\pi\) | ||||
−0.825561 | + | 0.564313i | \(0.809141\pi\) | |||||||
\(6\) | −1.17845 | + | 2.04113i | −0.481099 | + | 0.833289i | ||||
\(7\) | −0.400969 | + | 0.694498i | −0.151552 | + | 0.262496i | −0.931798 | − | 0.362977i | \(-0.881760\pi\) |
0.780246 | + | 0.625473i | \(0.215094\pi\) | |||||||
\(8\) | −3.66487 | −1.29573 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −4.35086 | − | 7.53590i | −1.37586 | − | 2.38306i | ||||
\(11\) | −1.42543 | − | 2.46891i | −0.429783 | − | 0.744405i | 0.567071 | − | 0.823669i | \(-0.308076\pi\) |
−0.996854 | + | 0.0792636i | \(0.974743\pi\) | |||||||
\(12\) | −3.55496 | −1.02623 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.89008 | −0.505146 | ||||||||
\(15\) | −1.84601 | − | 3.19738i | −0.476638 | − | 0.825561i | ||||
\(16\) | −0.763906 | − | 1.32312i | −0.190976 | − | 0.330781i | ||||
\(17\) | −1.46950 | + | 2.54525i | −0.356406 | + | 0.617314i | −0.987358 | − | 0.158509i | \(-0.949331\pi\) |
0.630951 | + | 0.775822i | \(0.282665\pi\) | |||||||
\(18\) | −2.35690 | −0.555526 | ||||||||
\(19\) | −1.22252 | + | 2.11747i | −0.280466 | + | 0.485781i | −0.971499 | − | 0.237042i | \(-0.923822\pi\) |
0.691034 | + | 0.722822i | \(0.257156\pi\) | |||||||
\(20\) | 6.56249 | − | 11.3666i | 1.46742 | − | 2.54164i | ||||
\(21\) | −0.801938 | −0.174997 | ||||||||
\(22\) | 3.35958 | − | 5.81897i | 0.716266 | − | 1.24061i | ||||
\(23\) | 3.89493 | + | 6.74621i | 0.812149 | + | 1.40668i | 0.911357 | + | 0.411616i | \(0.135036\pi\) |
−0.0992087 | + | 0.995067i | \(0.531631\pi\) | |||||||
\(24\) | −1.83244 | − | 3.17387i | −0.374045 | − | 0.647864i | ||||
\(25\) | 8.63102 | 1.72620 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.42543 | − | 2.46891i | −0.269380 | − | 0.466581i | ||||
\(29\) | −1.92543 | − | 3.33494i | −0.357543 | − | 0.619282i | 0.630007 | − | 0.776590i | \(-0.283052\pi\) |
−0.987550 | + | 0.157307i | \(0.949719\pi\) | |||||||
\(30\) | 4.35086 | − | 7.53590i | 0.794354 | − | 1.37586i | ||||
\(31\) | −2.34481 | −0.421141 | −0.210571 | − | 0.977579i | \(-0.567532\pi\) | ||||
−0.210571 | + | 0.977579i | \(0.567532\pi\) | |||||||
\(32\) | −1.86443 | + | 3.22929i | −0.329588 | + | 0.570862i | ||||
\(33\) | 1.42543 | − | 2.46891i | 0.248135 | − | 0.429783i | ||||
\(34\) | −6.92692 | −1.18796 | ||||||||
\(35\) | 1.48039 | − | 2.56410i | 0.250231 | − | 0.433413i | ||||
\(36\) | −1.77748 | − | 3.07868i | −0.296247 | − | 0.513114i | ||||
\(37\) | 3.72252 | + | 6.44760i | 0.611979 | + | 1.05998i | 0.990907 | + | 0.134552i | \(0.0429595\pi\) |
−0.378928 | + | 0.925426i | \(0.623707\pi\) | |||||||
\(38\) | −5.76271 | −0.934835 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 13.5308 | 2.13941 | ||||||||
\(41\) | −0.425428 | − | 0.736862i | −0.0664406 | − | 0.115079i | 0.830892 | − | 0.556434i | \(-0.187831\pi\) |
−0.897332 | + | 0.441356i | \(0.854498\pi\) | |||||||
\(42\) | −0.945042 | − | 1.63686i | −0.145823 | − | 0.252573i | ||||
\(43\) | 0.807979 | − | 1.39946i | 0.123216 | − | 0.213416i | −0.797818 | − | 0.602898i | \(-0.794013\pi\) |
0.921034 | + | 0.389482i | \(0.127346\pi\) | |||||||
\(44\) | 10.1347 | 1.52786 | ||||||||
\(45\) | 1.84601 | − | 3.19738i | 0.275187 | − | 0.476638i | ||||
\(46\) | −9.17994 | + | 15.9001i | −1.35351 | + | 2.34435i | ||||
\(47\) | −2.44504 | −0.356646 | −0.178323 | − | 0.983972i | \(-0.557067\pi\) | ||||
−0.178323 | + | 0.983972i | \(0.557067\pi\) | |||||||
\(48\) | 0.763906 | − | 1.32312i | 0.110260 | − | 0.190976i | ||||
\(49\) | 3.17845 | + | 5.50523i | 0.454064 | + | 0.786462i | ||||
\(50\) | 10.1712 | + | 17.6171i | 1.43843 | + | 2.49143i | ||||
\(51\) | −2.93900 | −0.411542 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.96077 | −1.36822 | −0.684109 | − | 0.729380i | \(-0.739809\pi\) | ||||
−0.684109 | + | 0.729380i | \(0.739809\pi\) | |||||||
\(54\) | −1.17845 | − | 2.04113i | −0.160366 | − | 0.277763i | ||||
\(55\) | 5.26271 | + | 9.11528i | 0.709624 | + | 1.22910i | ||||
\(56\) | 1.46950 | − | 2.54525i | 0.196370 | − | 0.340123i | ||||
\(57\) | −2.44504 | −0.323854 | ||||||||
\(58\) | 4.53803 | − | 7.86010i | 0.595873 | − | 1.03208i | ||||
\(59\) | −2.69202 | + | 4.66272i | −0.350471 | + | 0.607034i | −0.986332 | − | 0.164770i | \(-0.947312\pi\) |
0.635861 | + | 0.771804i | \(0.280645\pi\) | |||||||
\(60\) | 13.1250 | 1.69443 | ||||||||
\(61\) | 6.62833 | − | 11.4806i | 0.848671 | − | 1.46994i | −0.0337232 | − | 0.999431i | \(-0.510736\pi\) |
0.882394 | − | 0.470510i | \(-0.155930\pi\) | |||||||
\(62\) | −2.76324 | − | 4.78607i | −0.350932 | − | 0.607832i | ||||
\(63\) | −0.400969 | − | 0.694498i | −0.0505173 | − | 0.0874986i | ||||
\(64\) | −11.8442 | −1.48052 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 6.71917 | 0.827072 | ||||||||
\(67\) | 7.19687 | + | 12.4653i | 0.879237 | + | 1.52288i | 0.852180 | + | 0.523249i | \(0.175280\pi\) |
0.0270575 | + | 0.999634i | \(0.491386\pi\) | |||||||
\(68\) | −5.22401 | − | 9.04826i | −0.633505 | − | 1.09726i | ||||
\(69\) | −3.89493 | + | 6.74621i | −0.468894 | + | 0.812149i | ||||
\(70\) | 6.97823 | 0.834058 | ||||||||
\(71\) | 4.06249 | − | 7.03644i | 0.482129 | − | 0.835072i | −0.517661 | − | 0.855586i | \(-0.673197\pi\) |
0.999790 | + | 0.0205142i | \(0.00653033\pi\) | |||||||
\(72\) | 1.83244 | − | 3.17387i | 0.215955 | − | 0.374045i | ||||
\(73\) | 11.8877 | 1.39135 | 0.695674 | − | 0.718357i | \(-0.255106\pi\) | ||||
0.695674 | + | 0.718357i | \(0.255106\pi\) | |||||||
\(74\) | −8.77359 | + | 15.1963i | −1.01991 | + | 1.76654i | ||||
\(75\) | 4.31551 | + | 7.47468i | 0.498312 | + | 0.863102i | ||||
\(76\) | −4.34601 | − | 7.52751i | −0.498522 | − | 0.863465i | ||||
\(77\) | 2.28621 | 0.260538 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.40581 | 0.608202 | 0.304101 | − | 0.952640i | \(-0.401644\pi\) | ||||
0.304101 | + | 0.952640i | \(0.401644\pi\) | |||||||
\(80\) | 2.82036 | + | 4.88500i | 0.315325 | + | 0.546160i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 1.00269 | − | 1.73671i | 0.110728 | − | 0.191787i | ||||
\(83\) | −7.04892 | −0.773719 | −0.386860 | − | 0.922139i | \(-0.626440\pi\) | ||||
−0.386860 | + | 0.922139i | \(0.626440\pi\) | |||||||
\(84\) | 1.42543 | − | 2.46891i | 0.155527 | − | 0.269380i | ||||
\(85\) | 5.42543 | − | 9.39712i | 0.588470 | − | 1.01926i | ||||
\(86\) | 3.80864 | 0.410696 | ||||||||
\(87\) | 1.92543 | − | 3.33494i | 0.206427 | − | 0.357543i | ||||
\(88\) | 5.22401 | + | 9.04826i | 0.556882 | + | 0.964547i | ||||
\(89\) | 0.565843 | + | 0.980069i | 0.0599793 | + | 0.103887i | 0.894456 | − | 0.447156i | \(-0.147563\pi\) |
−0.834477 | + | 0.551043i | \(0.814230\pi\) | |||||||
\(90\) | 8.70171 | 0.917241 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −27.6926 | −2.88715 | ||||||||
\(93\) | −1.17241 | − | 2.03067i | −0.121573 | − | 0.210571i | ||||
\(94\) | −2.88135 | − | 4.99065i | −0.297189 | − | 0.514746i | ||||
\(95\) | 4.51357 | − | 7.81774i | 0.463083 | − | 0.802083i | ||||
\(96\) | −3.72886 | −0.380575 | ||||||||
\(97\) | −2.97219 | + | 5.14798i | −0.301780 | + | 0.522698i | −0.976539 | − | 0.215340i | \(-0.930914\pi\) |
0.674759 | + | 0.738038i | \(0.264247\pi\) | |||||||
\(98\) | −7.49127 | + | 12.9753i | −0.756733 | + | 1.31070i | ||||
\(99\) | 2.85086 | 0.286522 | ||||||||
\(100\) | −15.3415 | + | 26.5722i | −1.53415 | + | 2.65722i | ||||
\(101\) | −2.31282 | − | 4.00593i | −0.230134 | − | 0.398605i | 0.727713 | − | 0.685882i | \(-0.240583\pi\) |
−0.957848 | + | 0.287277i | \(0.907250\pi\) | |||||||
\(102\) | −3.46346 | − | 5.99889i | −0.342934 | − | 0.593978i | ||||
\(103\) | 1.20775 | 0.119003 | 0.0595016 | − | 0.998228i | \(-0.481049\pi\) | ||||
0.0595016 | + | 0.998228i | \(0.481049\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.96077 | 0.288942 | ||||||||
\(106\) | −11.7383 | − | 20.3312i | −1.14012 | − | 1.97475i | ||||
\(107\) | 4.76055 | + | 8.24552i | 0.460220 | + | 0.797124i | 0.998972 | − | 0.0453402i | \(-0.0144372\pi\) |
−0.538752 | + | 0.842465i | \(0.681104\pi\) | |||||||
\(108\) | 1.77748 | − | 3.07868i | 0.171038 | − | 0.296247i | ||||
\(109\) | 1.78448 | 0.170922 | 0.0854611 | − | 0.996342i | \(-0.472764\pi\) | ||||
0.0854611 | + | 0.996342i | \(0.472764\pi\) | |||||||
\(110\) | −12.4037 | + | 21.4838i | −1.18264 | + | 2.04840i | ||||
\(111\) | −3.72252 | + | 6.44760i | −0.353326 | + | 0.611979i | ||||
\(112\) | 1.22521 | 0.115771 | ||||||||
\(113\) | −2.47554 | + | 4.28776i | −0.232879 | + | 0.403359i | −0.958654 | − | 0.284573i | \(-0.908148\pi\) |
0.725775 | + | 0.687932i | \(0.241481\pi\) | |||||||
\(114\) | −2.88135 | − | 4.99065i | −0.269864 | − | 0.467417i | ||||
\(115\) | −14.3802 | − | 24.9072i | −1.34096 | − | 2.32261i | ||||
\(116\) | 13.6896 | 1.27105 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −12.6896 | −1.16817 | ||||||||
\(119\) | −1.17845 | − | 2.04113i | −0.108028 | − | 0.187110i | ||||
\(120\) | 6.76540 | + | 11.7180i | 0.617593 | + | 1.06970i | ||||
\(121\) | 1.43631 | − | 2.48777i | 0.130574 | − | 0.226161i | ||||
\(122\) | 31.2446 | 2.82875 | ||||||||
\(123\) | 0.425428 | − | 0.736862i | 0.0383595 | − | 0.0664406i | ||||
\(124\) | 4.16786 | − | 7.21894i | 0.374285 | − | 0.648280i | ||||
\(125\) | −13.4058 | −1.19905 | ||||||||
\(126\) | 0.945042 | − | 1.63686i | 0.0841910 | − | 0.145823i | ||||
\(127\) | −2.83513 | − | 4.91058i | −0.251577 | − | 0.435744i | 0.712383 | − | 0.701791i | \(-0.247616\pi\) |
−0.963960 | + | 0.266047i | \(0.914282\pi\) | |||||||
\(128\) | −10.2289 | − | 17.7169i | −0.904112 | − | 1.56597i | ||||
\(129\) | 1.61596 | 0.142277 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.2228 | 1.59213 | 0.796067 | − | 0.605208i | \(-0.206910\pi\) | ||||
0.796067 | + | 0.605208i | \(0.206910\pi\) | |||||||
\(132\) | 5.06734 | + | 8.77688i | 0.441055 | + | 0.763930i | ||||
\(133\) | −0.980386 | − | 1.69808i | −0.0850102 | − | 0.147242i | ||||
\(134\) | −16.9623 | + | 29.3795i | −1.46532 | + | 2.53800i | ||||
\(135\) | 3.69202 | 0.317759 | ||||||||
\(136\) | 5.38553 | − | 9.32802i | 0.461806 | − | 0.799871i | ||||
\(137\) | 4.72521 | − | 8.18430i | 0.403702 | − | 0.699232i | −0.590468 | − | 0.807061i | \(-0.701057\pi\) |
0.994169 | + | 0.107829i | \(0.0343900\pi\) | |||||||
\(138\) | −18.3599 | −1.56290 | ||||||||
\(139\) | −2.00753 | + | 3.47715i | −0.170277 | + | 0.294928i | −0.938517 | − | 0.345234i | \(-0.887799\pi\) |
0.768240 | + | 0.640162i | \(0.221133\pi\) | |||||||
\(140\) | 5.26271 | + | 9.11528i | 0.444780 | + | 0.770382i | ||||
\(141\) | −1.22252 | − | 2.11747i | −0.102955 | − | 0.178323i | ||||
\(142\) | 19.1497 | 1.60701 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.52781 | 0.127318 | ||||||||
\(145\) | 7.10872 | + | 12.3127i | 0.590347 | + | 1.02251i | ||||
\(146\) | 14.0090 | + | 24.2643i | 1.15940 | + | 2.00813i | ||||
\(147\) | −3.17845 | + | 5.50523i | −0.262154 | + | 0.454064i | ||||
\(148\) | −26.4668 | −2.17556 | ||||||||
\(149\) | 9.70291 | − | 16.8059i | 0.794893 | − | 1.37680i | −0.128014 | − | 0.991772i | \(-0.540860\pi\) |
0.922907 | − | 0.385023i | \(-0.125806\pi\) | |||||||
\(150\) | −10.1712 | + | 17.6171i | −0.830476 | + | 1.43843i | ||||
\(151\) | 12.3623 | 1.00603 | 0.503014 | − | 0.864278i | \(-0.332225\pi\) | ||||
0.503014 | + | 0.864278i | \(0.332225\pi\) | |||||||
\(152\) | 4.48039 | − | 7.76026i | 0.363407 | − | 0.629440i | ||||
\(153\) | −1.46950 | − | 2.54525i | −0.118802 | − | 0.205771i | ||||
\(154\) | 2.69418 | + | 4.66645i | 0.217103 | + | 0.376033i | ||||
\(155\) | 8.65710 | 0.695355 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.6775 | −1.49063 | −0.745315 | − | 0.666712i | \(-0.767701\pi\) | ||||
−0.745315 | + | 0.666712i | \(0.767701\pi\) | |||||||
\(158\) | 6.37047 | + | 11.0340i | 0.506807 | + | 0.877816i | ||||
\(159\) | −4.98039 | − | 8.62628i | −0.394970 | − | 0.684109i | ||||
\(160\) | 6.88351 | − | 11.9226i | 0.544189 | − | 0.942563i | ||||
\(161\) | −6.24698 | −0.492331 | ||||||||
\(162\) | 1.17845 | − | 2.04113i | 0.0925876 | − | 0.160366i | ||||
\(163\) | 6.16972 | − | 10.6863i | 0.483250 | − | 0.837013i | −0.516565 | − | 0.856248i | \(-0.672790\pi\) |
0.999815 | + | 0.0192348i | \(0.00612301\pi\) | |||||||
\(164\) | 3.02475 | 0.236194 | ||||||||
\(165\) | −5.26271 | + | 9.11528i | −0.409701 | + | 0.709624i | ||||
\(166\) | −8.30678 | − | 14.3878i | −0.644731 | − | 1.11671i | ||||
\(167\) | 5.74698 | + | 9.95406i | 0.444715 | + | 0.770268i | 0.998032 | − | 0.0627020i | \(-0.0199718\pi\) |
−0.553318 | + | 0.832970i | \(0.686638\pi\) | |||||||
\(168\) | 2.93900 | 0.226749 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 25.5743 | 1.96146 | ||||||||
\(171\) | −1.22252 | − | 2.11747i | −0.0934885 | − | 0.161927i | ||||
\(172\) | 2.87233 | + | 4.97502i | 0.219013 | + | 0.379342i | ||||
\(173\) | −6.05711 | + | 10.4912i | −0.460514 | + | 0.797633i | −0.998987 | − | 0.0450096i | \(-0.985668\pi\) |
0.538473 | + | 0.842643i | \(0.319002\pi\) | |||||||
\(174\) | 9.07606 | 0.688055 | ||||||||
\(175\) | −3.46077 | + | 5.99423i | −0.261610 | + | 0.453121i | ||||
\(176\) | −2.17778 | + | 3.77203i | −0.164157 | + | 0.284328i | ||||
\(177\) | −5.38404 | −0.404689 | ||||||||
\(178\) | −1.33363 | + | 2.30992i | −0.0999601 | + | 0.173136i | ||||
\(179\) | 0.269282 | + | 0.466411i | 0.0201271 | + | 0.0348612i | 0.875914 | − | 0.482468i | \(-0.160260\pi\) |
−0.855786 | + | 0.517329i | \(0.826926\pi\) | |||||||
\(180\) | 6.56249 | + | 11.3666i | 0.489139 | + | 0.847214i | ||||
\(181\) | −23.2838 | −1.73067 | −0.865336 | − | 0.501192i | \(-0.832895\pi\) | ||||
−0.865336 | + | 0.501192i | \(0.832895\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.2567 | 0.979961 | ||||||||
\(184\) | −14.2744 | − | 24.7240i | −1.05232 | − | 1.82268i | ||||
\(185\) | −13.7436 | − | 23.8047i | −1.01045 | − | 1.75015i | ||||
\(186\) | 2.76324 | − | 4.78607i | 0.202611 | − | 0.350932i | ||||
\(187\) | 8.37867 | 0.612709 | ||||||||
\(188\) | 4.34601 | − | 7.52751i | 0.316965 | − | 0.549000i | ||||
\(189\) | 0.400969 | − | 0.694498i | 0.0291662 | − | 0.0505173i | ||||
\(190\) | 21.2760 | 1.54353 | ||||||||
\(191\) | −8.38285 | + | 14.5195i | −0.606561 | + | 1.05060i | 0.385241 | + | 0.922816i | \(0.374118\pi\) |
−0.991803 | + | 0.127779i | \(0.959215\pi\) | |||||||
\(192\) | −5.92208 | − | 10.2573i | −0.427389 | − | 0.740259i | ||||
\(193\) | 12.8720 | + | 22.2949i | 0.926544 | + | 1.60482i | 0.789059 | + | 0.614318i | \(0.210569\pi\) |
0.137485 | + | 0.990504i | \(0.456098\pi\) | |||||||
\(194\) | −14.0103 | −1.00588 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −22.5985 | −1.61418 | ||||||||
\(197\) | 10.7104 | + | 18.5510i | 0.763087 | + | 1.32171i | 0.941252 | + | 0.337705i | \(0.109651\pi\) |
−0.178165 | + | 0.984001i | \(0.557016\pi\) | |||||||
\(198\) | 3.35958 | + | 5.81897i | 0.238755 | + | 0.413536i | ||||
\(199\) | −1.76391 | + | 3.05517i | −0.125040 | + | 0.216576i | −0.921749 | − | 0.387788i | \(-0.873239\pi\) |
0.796709 | + | 0.604364i | \(0.206573\pi\) | |||||||
\(200\) | −31.6316 | −2.23669 | ||||||||
\(201\) | −7.19687 | + | 12.4653i | −0.507628 | + | 0.879237i | ||||
\(202\) | 5.45108 | − | 9.44155i | 0.383537 | − | 0.664305i | ||||
\(203\) | 3.08815 | 0.216745 | ||||||||
\(204\) | 5.22401 | − | 9.04826i | 0.365754 | − | 0.633505i | ||||
\(205\) | 1.57069 | + | 2.72051i | 0.109702 | + | 0.190009i | ||||
\(206\) | 1.42327 | + | 2.46518i | 0.0991640 | + | 0.171757i | ||||
\(207\) | −7.78986 | −0.541432 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.97046 | 0.482157 | ||||||||
\(210\) | 3.48911 | + | 6.04332i | 0.240772 | + | 0.417029i | ||||
\(211\) | −0.607760 | − | 1.05267i | −0.0418399 | − | 0.0724689i | 0.844347 | − | 0.535797i | \(-0.179989\pi\) |
−0.886187 | + | 0.463328i | \(0.846655\pi\) | |||||||
\(212\) | 17.7051 | − | 30.6661i | 1.21599 | − | 2.10615i | ||||
\(213\) | 8.12498 | 0.556715 | ||||||||
\(214\) | −11.2201 | + | 19.4338i | −0.766992 | + | 1.32847i | ||||
\(215\) | −2.98307 | + | 5.16684i | −0.203444 | + | 0.352375i | ||||
\(216\) | 3.66487 | 0.249363 | ||||||||
\(217\) | 0.940198 | − | 1.62847i | 0.0638248 | − | 0.110548i | ||||
\(218\) | 2.10292 | + | 3.64236i | 0.142427 | + | 0.246692i | ||||
\(219\) | 5.94385 | + | 10.2950i | 0.401648 | + | 0.695674i | ||||
\(220\) | −37.4174 | −2.52268 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −17.5472 | −1.17769 | ||||||||
\(223\) | −8.69418 | − | 15.0588i | −0.582205 | − | 1.00841i | −0.995218 | − | 0.0976835i | \(-0.968857\pi\) |
0.413012 | − | 0.910725i | \(-0.364477\pi\) | |||||||
\(224\) | −1.49516 | − | 2.58969i | −0.0998993 | − | 0.173031i | ||||
\(225\) | −4.31551 | + | 7.47468i | −0.287701 | + | 0.498312i | ||||
\(226\) | −11.6692 | −0.776223 | ||||||||
\(227\) | 8.70775 | − | 15.0823i | 0.577954 | − | 1.00105i | −0.417760 | − | 0.908557i | \(-0.637185\pi\) |
0.995714 | − | 0.0924878i | \(-0.0294819\pi\) | |||||||
\(228\) | 4.34601 | − | 7.52751i | 0.287822 | − | 0.498522i | ||||
\(229\) | −18.7603 | −1.23972 | −0.619858 | − | 0.784714i | \(-0.712810\pi\) | ||||
−0.619858 | + | 0.784714i | \(0.712810\pi\) | |||||||
\(230\) | 33.8925 | − | 58.7036i | 2.23481 | − | 3.87080i | ||||
\(231\) | 1.14310 | + | 1.97991i | 0.0752107 | + | 0.130269i | ||||
\(232\) | 7.05645 | + | 12.2221i | 0.463279 | + | 0.802422i | ||||
\(233\) | 3.95108 | 0.258844 | 0.129422 | − | 0.991590i | \(-0.458688\pi\) | ||||
0.129422 | + | 0.991590i | \(0.458688\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.02715 | 0.588866 | ||||||||
\(236\) | −9.57002 | − | 16.5758i | −0.622955 | − | 1.07899i | ||||
\(237\) | 2.70291 | + | 4.68157i | 0.175573 | + | 0.304101i | ||||
\(238\) | 2.77748 | − | 4.81073i | 0.180037 | − | 0.311834i | ||||
\(239\) | −0.818331 | −0.0529334 | −0.0264667 | − | 0.999650i | \(-0.508426\pi\) | ||||
−0.0264667 | + | 0.999650i | \(0.508426\pi\) | |||||||
\(240\) | −2.82036 | + | 4.88500i | −0.182053 | + | 0.315325i | ||||
\(241\) | 3.01626 | − | 5.22432i | 0.194295 | − | 0.336528i | −0.752375 | − | 0.658736i | \(-0.771092\pi\) |
0.946669 | + | 0.322208i | \(0.104425\pi\) | |||||||
\(242\) | 6.77048 | 0.435223 | ||||||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 23.5635 | + | 40.8131i | 1.50850 | + | 2.61279i | ||||
\(245\) | −11.7349 | − | 20.3254i | −0.749715 | − | 1.29854i | ||||
\(246\) | 2.00538 | 0.127858 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 8.59345 | 0.545685 | ||||||||
\(249\) | −3.52446 | − | 6.10454i | −0.223353 | − | 0.386860i | ||||
\(250\) | −15.7981 | − | 27.3630i | −0.999157 | − | 1.73059i | ||||
\(251\) | 13.4400 | − | 23.2787i | 0.848323 | − | 1.46934i | −0.0343812 | − | 0.999409i | \(-0.510946\pi\) |
0.882704 | − | 0.469929i | \(-0.155721\pi\) | |||||||
\(252\) | 2.85086 | 0.179587 | ||||||||
\(253\) | 11.1039 | − | 19.2325i | 0.698095 | − | 1.20914i | ||||
\(254\) | 6.68210 | − | 11.5737i | 0.419272 | − | 0.726200i | ||||
\(255\) | 10.8509 | 0.679507 | ||||||||
\(256\) | 12.2642 | − | 21.2422i | 0.766513 | − | 1.32764i | ||||
\(257\) | 4.52661 | + | 7.84033i | 0.282362 | + | 0.489066i | 0.971966 | − | 0.235121i | \(-0.0755486\pi\) |
−0.689604 | + | 0.724187i | \(0.742215\pi\) | |||||||
\(258\) | 1.90432 | + | 3.29838i | 0.118558 | + | 0.205348i | ||||
\(259\) | −5.97046 | −0.370986 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.85086 | 0.238362 | ||||||||
\(262\) | 21.4746 | + | 37.1952i | 1.32671 | + | 2.29793i | ||||
\(263\) | −11.5755 | − | 20.0494i | −0.713778 | − | 1.23630i | −0.963429 | − | 0.267964i | \(-0.913649\pi\) |
0.249651 | − | 0.968336i | \(-0.419684\pi\) | |||||||
\(264\) | −5.22401 | + | 9.04826i | −0.321516 | + | 0.556882i | ||||
\(265\) | 36.7754 | 2.25909 | ||||||||
\(266\) | 2.31067 | − | 4.00219i | 0.141676 | − | 0.245390i | ||||
\(267\) | −0.565843 | + | 0.980069i | −0.0346290 | + | 0.0599793i | ||||
\(268\) | −51.1691 | −3.12565 | ||||||||
\(269\) | 1.21044 | − | 2.09654i | 0.0738018 | − | 0.127828i | −0.826763 | − | 0.562551i | \(-0.809820\pi\) |
0.900565 | + | 0.434722i | \(0.143153\pi\) | |||||||
\(270\) | 4.35086 | + | 7.53590i | 0.264785 | + | 0.458620i | ||||
\(271\) | −10.7225 | − | 18.5720i | −0.651347 | − | 1.12817i | −0.982796 | − | 0.184693i | \(-0.940871\pi\) |
0.331450 | − | 0.943473i | \(-0.392462\pi\) | |||||||
\(272\) | 4.49024 | 0.272261 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 22.2737 | 1.34560 | ||||||||
\(275\) | −12.3029 | − | 21.3092i | −0.741893 | − | 1.28500i | ||||
\(276\) | −13.8463 | − | 23.9825i | −0.833450 | − | 1.44358i | ||||
\(277\) | 7.40366 | − | 12.8235i | 0.444843 | − | 0.770490i | −0.553199 | − | 0.833049i | \(-0.686593\pi\) |
0.998041 | + | 0.0625593i | \(0.0199263\pi\) | |||||||
\(278\) | −9.46309 | −0.567558 | ||||||||
\(279\) | 1.17241 | − | 2.03067i | 0.0701902 | − | 0.121573i | ||||
\(280\) | −5.42543 | + | 9.39712i | −0.324231 | + | 0.561585i | ||||
\(281\) | −14.5036 | −0.865215 | −0.432608 | − | 0.901582i | \(-0.642406\pi\) | ||||
−0.432608 | + | 0.901582i | \(0.642406\pi\) | |||||||
\(282\) | 2.88135 | − | 4.99065i | 0.171582 | − | 0.297189i | ||||
\(283\) | −12.8361 | − | 22.2328i | −0.763026 | − | 1.32160i | −0.941284 | − | 0.337616i | \(-0.890379\pi\) |
0.178258 | − | 0.983984i | \(-0.442954\pi\) | |||||||
\(284\) | 14.4420 | + | 25.0143i | 0.856974 | + | 1.48432i | ||||
\(285\) | 9.02715 | 0.534722 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.682333 | 0.0402768 | ||||||||
\(288\) | −1.86443 | − | 3.22929i | −0.109863 | − | 0.190287i | ||||
\(289\) | 4.18114 | + | 7.24194i | 0.245949 | + | 0.425997i | ||||
\(290\) | −16.7545 | + | 29.0197i | −0.983859 | + | 1.70409i | ||||
\(291\) | −5.94438 | −0.348466 | ||||||||
\(292\) | −21.1301 | + | 36.5984i | −1.23655 | + | 2.14176i | ||||
\(293\) | −13.2615 | + | 22.9696i | −0.774746 | + | 1.34190i | 0.160191 | + | 0.987086i | \(0.448789\pi\) |
−0.934937 | + | 0.354813i | \(0.884544\pi\) | |||||||
\(294\) | −14.9825 | −0.873800 | ||||||||
\(295\) | 9.93900 | − | 17.2149i | 0.578671 | − | 1.00229i | ||||
\(296\) | −13.6426 | − | 23.6296i | −0.792958 | − | 1.37344i | ||||
\(297\) | 1.42543 | + | 2.46891i | 0.0827117 | + | 0.143261i | ||||
\(298\) | 45.7375 | 2.64950 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −30.6829 | −1.77148 | ||||||||
\(301\) | 0.647948 | + | 1.12228i | 0.0373471 | + | 0.0646871i | ||||
\(302\) | 14.5683 | + | 25.2330i | 0.838311 | + | 1.45200i | ||||
\(303\) | 2.31282 | − | 4.00593i | 0.132868 | − | 0.230134i | ||||
\(304\) | 3.73556 | 0.214249 | ||||||||
\(305\) | −24.4720 | + | 42.3867i | −1.40126 | + | 2.42705i | ||||
\(306\) | 3.46346 | − | 5.99889i | 0.197993 | − | 0.342934i | ||||
\(307\) | 8.24698 | 0.470680 | 0.235340 | − | 0.971913i | \(-0.424380\pi\) | ||||
0.235340 | + | 0.971913i | \(0.424380\pi\) | |||||||
\(308\) | −4.06369 | + | 7.03851i | −0.231550 | + | 0.401056i | ||||
\(309\) | 0.603875 | + | 1.04594i | 0.0343533 | + | 0.0595016i | ||||
\(310\) | 10.2019 | + | 17.6703i | 0.579432 | + | 1.00361i | ||||
\(311\) | −14.4179 | −0.817564 | −0.408782 | − | 0.912632i | \(-0.634046\pi\) | ||||
−0.408782 | + | 0.912632i | \(0.634046\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.2338 | 0.804544 | 0.402272 | − | 0.915520i | \(-0.368221\pi\) | ||||
0.402272 | + | 0.915520i | \(0.368221\pi\) | |||||||
\(314\) | −22.0105 | − | 38.1233i | −1.24213 | − | 2.15142i | ||||
\(315\) | 1.48039 | + | 2.56410i | 0.0834103 | + | 0.144471i | ||||
\(316\) | −9.60872 | + | 16.6428i | −0.540533 | + | 0.936230i | ||||
\(317\) | 6.84415 | 0.384406 | 0.192203 | − | 0.981355i | \(-0.438437\pi\) | ||||
0.192203 | + | 0.981355i | \(0.438437\pi\) | |||||||
\(318\) | 11.7383 | − | 20.3312i | 0.658248 | − | 1.14012i | ||||
\(319\) | −5.48911 | + | 9.50743i | −0.307331 | + | 0.532314i | ||||
\(320\) | 43.7289 | 2.44452 | ||||||||
\(321\) | −4.76055 | + | 8.24552i | −0.265708 | + | 0.460220i | ||||
\(322\) | −7.36174 | − | 12.7509i | −0.410254 | − | 0.710580i | ||||
\(323\) | −3.59299 | − | 6.22324i | −0.199919 | − | 0.346270i | ||||
\(324\) | 3.55496 | 0.197498 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 29.0828 | 1.61075 | ||||||||
\(327\) | 0.892240 | + | 1.54540i | 0.0493410 | + | 0.0854611i | ||||
\(328\) | 1.55914 | + | 2.70051i | 0.0860890 | + | 0.149111i | ||||
\(329\) | 0.980386 | − | 1.69808i | 0.0540504 | − | 0.0936181i | ||||
\(330\) | −24.8073 | −1.36560 | ||||||||
\(331\) | 4.72132 | − | 8.17757i | 0.259507 | − | 0.449480i | −0.706603 | − | 0.707611i | \(-0.749773\pi\) |
0.966110 | + | 0.258130i | \(0.0831065\pi\) | |||||||
\(332\) | 12.5293 | − | 21.7014i | 0.687635 | − | 1.19102i | ||||
\(333\) | −7.44504 | −0.407986 | ||||||||
\(334\) | −13.5450 | + | 23.4607i | −0.741151 | + | 1.28371i | ||||
\(335\) | −26.5710 | − | 46.0223i | −1.45173 | − | 2.51447i | ||||
\(336\) | 0.612605 | + | 1.06106i | 0.0334203 | + | 0.0578857i | ||||
\(337\) | 2.64310 | 0.143979 | 0.0719895 | − | 0.997405i | \(-0.477065\pi\) | ||||
0.0719895 | + | 0.997405i | \(0.477065\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.95108 | −0.268906 | ||||||||
\(340\) | 19.2872 | + | 33.4064i | 1.04599 | + | 1.81171i | ||||
\(341\) | 3.34236 | + | 5.78914i | 0.180999 | + | 0.313500i | ||||
\(342\) | 2.88135 | − | 4.99065i | 0.155806 | − | 0.269864i | ||||
\(343\) | −10.7114 | −0.578361 | ||||||||
\(344\) | −2.96114 | + | 5.12884i | −0.159654 | + | 0.276529i | ||||
\(345\) | 14.3802 | − | 24.9072i | 0.774202 | − | 1.34096i | ||||
\(346\) | −28.5520 | −1.53496 | ||||||||
\(347\) | 5.07942 | − | 8.79781i | 0.272677 | − | 0.472291i | −0.696869 | − | 0.717198i | \(-0.745424\pi\) |
0.969547 | + | 0.244907i | \(0.0787575\pi\) | |||||||
\(348\) | 6.84481 | + | 11.8556i | 0.366921 | + | 0.635525i | ||||
\(349\) | 5.21983 | + | 9.04102i | 0.279411 | + | 0.483954i | 0.971239 | − | 0.238109i | \(-0.0765274\pi\) |
−0.691827 | + | 0.722063i | \(0.743194\pi\) | |||||||
\(350\) | −16.3134 | −0.871986 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 10.6304 | 0.566604 | ||||||||
\(353\) | 9.14556 | + | 15.8406i | 0.486769 | + | 0.843108i | 0.999884 | − | 0.0152113i | \(-0.00484208\pi\) |
−0.513115 | + | 0.858320i | \(0.671509\pi\) | |||||||
\(354\) | −6.34481 | − | 10.9895i | −0.337223 | − | 0.584087i | ||||
\(355\) | −14.9988 | + | 25.9787i | −0.796054 | + | 1.37881i | ||||
\(356\) | −4.02310 | −0.213224 | ||||||||
\(357\) | 1.17845 | − | 2.04113i | 0.0623701 | − | 0.108028i | ||||
\(358\) | −0.634670 | + | 1.09928i | −0.0335434 | + | 0.0580988i | ||||
\(359\) | 15.2731 | 0.806081 | 0.403041 | − | 0.915182i | \(-0.367953\pi\) | ||||
0.403041 | + | 0.915182i | \(0.367953\pi\) | |||||||
\(360\) | −6.76540 | + | 11.7180i | −0.356568 | + | 0.617593i | ||||
\(361\) | 6.51089 | + | 11.2772i | 0.342678 | + | 0.593536i | ||||
\(362\) | −27.4388 | − | 47.5253i | −1.44215 | − | 2.49788i | ||||
\(363\) | 2.87263 | 0.150774 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −43.8896 | −2.29729 | ||||||||
\(366\) | 15.6223 | + | 27.0586i | 0.816590 | + | 1.41438i | ||||
\(367\) | 11.1359 | + | 19.2879i | 0.581288 | + | 1.00682i | 0.995327 | + | 0.0965606i | \(0.0307842\pi\) |
−0.414040 | + | 0.910259i | \(0.635882\pi\) | |||||||
\(368\) | 5.95071 | − | 10.3069i | 0.310202 | − | 0.537286i | ||||
\(369\) | 0.850855 | 0.0442937 | ||||||||
\(370\) | 32.3923 | − | 56.1051i | 1.68400 | − | 2.91677i | ||||
\(371\) | 3.99396 | − | 6.91774i | 0.207356 | − | 0.359151i | ||||
\(372\) | 8.33572 | 0.432187 | ||||||||
\(373\) | −2.06315 | + | 3.57349i | −0.106826 | + | 0.185028i | −0.914483 | − | 0.404625i | \(-0.867402\pi\) |
0.807657 | + | 0.589653i | \(0.200735\pi\) | |||||||
\(374\) | 9.87382 | + | 17.1020i | 0.510563 | + | 0.884321i | ||||
\(375\) | −6.70291 | − | 11.6098i | −0.346137 | − | 0.599526i | ||||
\(376\) | 8.96077 | 0.462116 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.89008 | 0.0972154 | ||||||||
\(379\) | −5.35354 | − | 9.27261i | −0.274993 | − | 0.476302i | 0.695140 | − | 0.718874i | \(-0.255342\pi\) |
−0.970133 | + | 0.242572i | \(0.922009\pi\) | |||||||
\(380\) | 16.0456 | + | 27.7917i | 0.823120 | + | 1.42569i | ||||
\(381\) | 2.83513 | − | 4.91058i | 0.145248 | − | 0.251577i | ||||
\(382\) | −39.5150 | −2.02176 | ||||||||
\(383\) | 3.26324 | − | 5.65210i | 0.166744 | − | 0.288809i | −0.770529 | − | 0.637405i | \(-0.780008\pi\) |
0.937273 | + | 0.348596i | \(0.113341\pi\) | |||||||
\(384\) | 10.2289 | − | 17.7169i | 0.521989 | − | 0.904112i | ||||
\(385\) | −8.44073 | −0.430179 | ||||||||
\(386\) | −30.3379 | + | 52.5467i | −1.54416 | + | 2.67456i | ||||
\(387\) | 0.807979 | + | 1.39946i | 0.0410719 | + | 0.0711385i | ||||
\(388\) | −10.5660 | − | 18.3009i | −0.536408 | − | 0.929085i | ||||
\(389\) | −11.7922 | −0.597891 | −0.298945 | − | 0.954270i | \(-0.596635\pi\) | ||||
−0.298945 | + | 0.954270i | \(0.596635\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −22.8944 | −1.15782 | ||||||||
\(392\) | −11.6486 | − | 20.1760i | −0.588344 | − | 1.01904i | ||||
\(393\) | 9.11141 | + | 15.7814i | 0.459610 | + | 0.796067i | ||||
\(394\) | −25.2434 | + | 43.7228i | −1.27174 | + | 2.20272i | ||||
\(395\) | −19.9584 | −1.00422 | ||||||||
\(396\) | −5.06734 | + | 8.77688i | −0.254643 | + | 0.441055i | ||||
\(397\) | −6.27144 | + | 10.8624i | −0.314754 | + | 0.545171i | −0.979385 | − | 0.202001i | \(-0.935256\pi\) |
0.664631 | + | 0.747172i | \(0.268589\pi\) | |||||||
\(398\) | −8.31468 | −0.416777 | ||||||||
\(399\) | 0.980386 | − | 1.69808i | 0.0490807 | − | 0.0850102i | ||||
\(400\) | −6.59329 | − | 11.4199i | −0.329664 | − | 0.570995i | ||||
\(401\) | 8.93512 | + | 15.4761i | 0.446198 | + | 0.772838i | 0.998135 | − | 0.0610479i | \(-0.0194442\pi\) |
−0.551936 | + | 0.833886i | \(0.686111\pi\) | |||||||
\(402\) | −33.9245 | −1.69200 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 16.4440 | 0.818118 | ||||||||
\(405\) | 1.84601 | + | 3.19738i | 0.0917290 | + | 0.158879i | ||||
\(406\) | 3.63922 | + | 6.30331i | 0.180611 | + | 0.312828i | ||||
\(407\) | 10.6124 | − | 18.3812i | 0.526036 | − | 0.911120i | ||||
\(408\) | 10.7711 | 0.533247 | ||||||||
\(409\) | −13.9559 | + | 24.1724i | −0.690076 | + | 1.19525i | 0.281736 | + | 0.959492i | \(0.409090\pi\) |
−0.971812 | + | 0.235755i | \(0.924244\pi\) | |||||||
\(410\) | −3.70195 | + | 6.41196i | −0.182826 | + | 0.316664i | ||||
\(411\) | 9.45042 | 0.466155 | ||||||||
\(412\) | −2.14675 | + | 3.71828i | −0.105763 | + | 0.183187i | ||||
\(413\) | −2.15883 | − | 3.73921i | −0.106229 | − | 0.183994i | ||||
\(414\) | −9.17994 | − | 15.9001i | −0.451169 | − | 0.781448i | ||||
\(415\) | 26.0248 | 1.27750 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.01507 | −0.196619 | ||||||||
\(418\) | 8.21432 | + | 14.2276i | 0.401776 | + | 0.695896i | ||||
\(419\) | 8.20171 | + | 14.2058i | 0.400680 | + | 0.693998i | 0.993808 | − | 0.111110i | \(-0.0354407\pi\) |
−0.593128 | + | 0.805108i | \(0.702107\pi\) | |||||||
\(420\) | −5.26271 | + | 9.11528i | −0.256794 | + | 0.444780i | ||||
\(421\) | 3.03684 | 0.148006 | 0.0740032 | − | 0.997258i | \(-0.476423\pi\) | ||||
0.0740032 | + | 0.997258i | \(0.476423\pi\) | |||||||
\(422\) | 1.43243 | − | 2.48104i | 0.0697295 | − | 0.120775i | ||||
\(423\) | 1.22252 | − | 2.11747i | 0.0594410 | − | 0.102955i | ||||
\(424\) | 36.5050 | 1.77284 | ||||||||
\(425\) | −12.6833 | + | 21.9681i | −0.615230 | + | 1.06561i | ||||
\(426\) | 9.57487 | + | 16.5842i | 0.463904 | + | 0.803505i | ||||
\(427\) | 5.31551 | + | 9.20674i | 0.257236 | + | 0.445545i | ||||
\(428\) | −33.8471 | −1.63606 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −14.0616 | −0.678110 | ||||||||
\(431\) | −1.66905 | − | 2.89089i | −0.0803955 | − | 0.139249i | 0.823024 | − | 0.568006i | \(-0.192285\pi\) |
−0.903420 | + | 0.428757i | \(0.858952\pi\) | |||||||
\(432\) | 0.763906 | + | 1.32312i | 0.0367534 | + | 0.0636588i | ||||
\(433\) | −5.95138 | + | 10.3081i | −0.286005 | + | 0.495375i | −0.972852 | − | 0.231426i | \(-0.925661\pi\) |
0.686847 | + | 0.726802i | \(0.258994\pi\) | |||||||
\(434\) | 4.43190 | 0.212738 | ||||||||
\(435\) | −7.10872 | + | 12.3127i | −0.340837 | + | 0.590347i | ||||
\(436\) | −3.17187 | + | 5.49385i | −0.151905 | + | 0.263108i | ||||
\(437\) | −19.0465 | −0.911119 | ||||||||
\(438\) | −14.0090 | + | 24.2643i | −0.669377 | + | 1.15940i | ||||
\(439\) | −1.85905 | − | 3.21997i | −0.0887277 | − | 0.153681i | 0.818246 | − | 0.574868i | \(-0.194947\pi\) |
−0.906974 | + | 0.421188i | \(0.861613\pi\) | |||||||
\(440\) | −19.2872 | − | 33.4064i | −0.919480 | − | 1.59259i | ||||
\(441\) | −6.35690 | −0.302709 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.45712 | 0.0692300 | 0.0346150 | − | 0.999401i | \(-0.488979\pi\) | ||||
0.0346150 | + | 0.999401i | \(0.488979\pi\) | |||||||
\(444\) | −13.2334 | − | 22.9209i | −0.628030 | − | 1.08778i | ||||
\(445\) | −2.08911 | − | 3.61844i | −0.0990331 | − | 0.171530i | ||||
\(446\) | 20.4913 | − | 35.4919i | 0.970290 | − | 1.68059i | ||||
\(447\) | 19.4058 | 0.917863 | ||||||||
\(448\) | 4.74914 | − | 8.22574i | 0.224376 | − | 0.388630i | ||||
\(449\) | −6.06369 | + | 10.5026i | −0.286163 | + | 0.495649i | −0.972891 | − | 0.231266i | \(-0.925713\pi\) |
0.686727 | + | 0.726915i | \(0.259047\pi\) | |||||||
\(450\) | −20.3424 | −0.958951 | ||||||||
\(451\) | −1.21283 | + | 2.10069i | −0.0571100 | + | 0.0989175i | ||||
\(452\) | −8.80045 | − | 15.2428i | −0.413938 | − | 0.716962i | ||||
\(453\) | 6.18114 | + | 10.7060i | 0.290415 | + | 0.503014i | ||||
\(454\) | 41.0465 | 1.92641 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.96077 | 0.419627 | ||||||||
\(457\) | −1.72401 | − | 2.98608i | −0.0806459 | − | 0.139683i | 0.822882 | − | 0.568213i | \(-0.192365\pi\) |
−0.903528 | + | 0.428530i | \(0.859032\pi\) | |||||||
\(458\) | −22.1081 | − | 38.2923i | −1.03304 | − | 1.78928i | ||||
\(459\) | 1.46950 | − | 2.54525i | 0.0685904 | − | 0.118802i | ||||
\(460\) | 102.242 | 4.76704 | ||||||||
\(461\) | −3.37800 | + | 5.85087i | −0.157329 | + | 0.272502i | −0.933905 | − | 0.357522i | \(-0.883622\pi\) |
0.776575 | + | 0.630024i | \(0.216955\pi\) | |||||||
\(462\) | −2.69418 | + | 4.66645i | −0.125344 | + | 0.217103i | ||||
\(463\) | 7.45175 | 0.346312 | 0.173156 | − | 0.984894i | \(-0.444604\pi\) | ||||
0.173156 | + | 0.984894i | \(0.444604\pi\) | |||||||
\(464\) | −2.94169 | + | 5.09516i | −0.136565 | + | 0.236537i | ||||
\(465\) | 4.32855 | + | 7.49727i | 0.200732 | + | 0.347678i | ||||
\(466\) | 4.65615 | + | 8.06468i | 0.215692 | + | 0.373589i | ||||
\(467\) | 32.6098 | 1.50900 | 0.754502 | − | 0.656298i | \(-0.227879\pi\) | ||||
0.754502 | + | 0.656298i | \(0.227879\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.5429 | −0.533001 | ||||||||
\(470\) | 10.6380 | + | 18.4256i | 0.490695 | + | 0.849909i | ||||
\(471\) | −9.33877 | − | 16.1752i | −0.430308 | − | 0.745315i | ||||
\(472\) | 9.86592 | − | 17.0883i | 0.454116 | − | 0.786552i | ||||
\(473\) | −4.60686 | −0.211824 | ||||||||
\(474\) | −6.37047 | + | 11.0340i | −0.292605 | + | 0.506807i | ||||
\(475\) | −10.5516 | + | 18.2759i | −0.484141 | + | 0.838557i | ||||
\(476\) | 8.37867 | 0.384036 | ||||||||
\(477\) | 4.98039 | − | 8.62628i | 0.228036 | − | 0.394970i | ||||
\(478\) | −0.964361 | − | 1.67032i | −0.0441088 | − | 0.0763987i | ||||
\(479\) | 1.41454 | + | 2.45006i | 0.0646321 | + | 0.111946i | 0.896531 | − | 0.442982i | \(-0.146079\pi\) |
−0.831899 | + | 0.554928i | \(0.812746\pi\) | |||||||
\(480\) | 13.7670 | 0.628376 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 14.2180 | 0.647614 | ||||||||
\(483\) | −3.12349 | − | 5.41004i | −0.142124 | − | 0.246165i | ||||
\(484\) | 5.10603 | + | 8.84391i | 0.232092 | + | 0.401996i | ||||
\(485\) | 10.9734 | − | 19.0065i | 0.498276 | − | 0.863039i | ||||
\(486\) | 2.35690 | 0.106911 | ||||||||
\(487\) | −20.6468 | + | 35.7612i | −0.935594 | + | 1.62050i | −0.162022 | + | 0.986787i | \(0.551801\pi\) |
−0.773572 | + | 0.633709i | \(0.781532\pi\) | |||||||
\(488\) | −24.2920 | + | 42.0750i | −1.09965 | + | 1.90465i | ||||
\(489\) | 12.3394 | 0.558009 | ||||||||
\(490\) | 27.6579 | − | 47.9049i | 1.24946 | − | 2.16412i | ||||
\(491\) | 17.3349 | + | 30.0249i | 0.782313 | + | 1.35501i | 0.930591 | + | 0.366060i | \(0.119293\pi\) |
−0.148279 | + | 0.988946i | \(0.547373\pi\) | |||||||
\(492\) | 1.51238 | + | 2.61951i | 0.0681832 | + | 0.118097i | ||||
\(493\) | 11.3177 | 0.509722 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −10.5254 | −0.473082 | ||||||||
\(496\) | 1.79122 | + | 3.10248i | 0.0804280 | + | 0.139305i | ||||
\(497\) | 3.25786 | + | 5.64279i | 0.146135 | + | 0.253114i | ||||
\(498\) | 8.30678 | − | 14.3878i | 0.372236 | − | 0.644731i | ||||
\(499\) | −17.9409 | −0.803146 | −0.401573 | − | 0.915827i | \(-0.631536\pi\) | ||||
−0.401573 | + | 0.915827i | \(0.631536\pi\) | |||||||
\(500\) | 23.8286 | − | 41.2723i | 1.06565 | − | 1.84575i | ||||
\(501\) | −5.74698 | + | 9.95406i | −0.256756 | + | 0.444715i | ||||
\(502\) | 63.3532 | 2.82759 | ||||||||
\(503\) | 13.0906 | − | 22.6736i | 0.583681 | − | 1.01096i | −0.411358 | − | 0.911474i | \(-0.634945\pi\) |
0.995038 | − | 0.0994909i | \(-0.0317214\pi\) | |||||||
\(504\) | 1.46950 | + | 2.54525i | 0.0654568 | + | 0.113374i | ||||
\(505\) | 8.53899 | + | 14.7900i | 0.379980 | + | 0.658145i | ||||
\(506\) | 52.3414 | 2.32686 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 20.1575 | 0.894345 | ||||||||
\(509\) | −2.75302 | − | 4.76837i | −0.122025 | − | 0.211354i | 0.798541 | − | 0.601941i | \(-0.205606\pi\) |
−0.920566 | + | 0.390586i | \(0.872272\pi\) | |||||||
\(510\) | 12.7872 | + | 22.1480i | 0.566225 | + | 0.980731i | ||||
\(511\) | −4.76659 | + | 8.25598i | −0.210862 | + | 0.365223i | ||||
\(512\) | 16.8955 | 0.746681 | ||||||||
\(513\) | 1.22252 | − | 2.11747i | 0.0539756 | − | 0.0934885i | ||||
\(514\) | −10.6688 | + | 18.4788i | −0.470579 | + | 0.815066i | ||||
\(515\) | −4.45904 | −0.196489 | ||||||||
\(516\) | −2.87233 | + | 4.97502i | −0.126447 | + | 0.219013i | ||||
\(517\) | 3.48523 | + | 6.03660i | 0.153280 | + | 0.265489i | ||||
\(518\) | −7.03588 | − | 12.1865i | −0.309139 | − | 0.535444i | ||||
\(519\) | −12.1142 | −0.531756 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.7211 | −1.17067 | −0.585336 | − | 0.810791i | \(-0.699037\pi\) | ||||
−0.585336 | + | 0.810791i | \(0.699037\pi\) | |||||||
\(522\) | 4.53803 | + | 7.86010i | 0.198624 | + | 0.344027i | ||||
\(523\) | −18.2615 | − | 31.6299i | −0.798520 | − | 1.38308i | −0.920580 | − | 0.390555i | \(-0.872283\pi\) |
0.122060 | − | 0.992523i | \(-0.461050\pi\) | |||||||
\(524\) | −32.3907 | + | 56.1023i | −1.41499 | + | 2.45084i | ||||
\(525\) | −6.92154 | −0.302081 | ||||||||
\(526\) | 27.2823 | − | 47.2544i | 1.18957 | − | 2.06039i | ||||
\(527\) | 3.44571 | − | 5.96814i | 0.150097 | − | 0.259976i | ||||
\(528\) | −4.35557 | −0.189552 | ||||||||
\(529\) | −18.8409 | + | 32.6334i | −0.819171 | + | 1.41885i | ||||
\(530\) | 43.3379 | + | 75.0634i | 1.88248 | + | 3.26055i | ||||
\(531\) | −2.69202 | − | 4.66272i | −0.116824 | − | 0.202345i | ||||
\(532\) | 6.97046 | 0.302208 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −2.66727 | −0.115424 | ||||||||
\(535\) | −17.5761 | − | 30.4426i | −0.759880 | − | 1.31615i | ||||
\(536\) | −26.3756 | − | 45.6839i | −1.13925 | − | 1.97324i | ||||
\(537\) | −0.269282 | + | 0.466411i | −0.0116204 | + | 0.0201271i | ||||
\(538\) | 5.70576 | 0.245993 | ||||||||
\(539\) | 9.06129 | − | 15.6946i | 0.390298 | − | 0.676015i | ||||
\(540\) | −6.56249 | + | 11.3666i | −0.282405 | + | 0.489139i | ||||
\(541\) | −18.4655 | −0.793893 | −0.396947 | − | 0.917842i | \(-0.629930\pi\) | ||||
−0.396947 | + | 0.917842i | \(0.629930\pi\) | |||||||
\(542\) | 25.2719 | − | 43.7722i | 1.08552 | − | 1.88018i | ||||
\(543\) | −11.6419 | − | 20.1644i | −0.499602 | − | 0.865336i | ||||
\(544\) | −5.47956 | − | 9.49087i | −0.234934 | − | 0.406918i | ||||
\(545\) | −6.58834 | −0.282213 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.8471 | 1.70374 | 0.851870 | − | 0.523753i | \(-0.175468\pi\) | ||||
0.851870 | + | 0.523753i | \(0.175468\pi\) | |||||||
\(548\) | 16.7979 | + | 29.0949i | 0.717572 | + | 1.24287i | ||||
\(549\) | 6.62833 | + | 11.4806i | 0.282890 | + | 0.489981i | ||||
\(550\) | 28.9966 | − | 50.2237i | 1.23642 | − | 2.14154i | ||||
\(551\) | 9.41550 | 0.401114 | ||||||||
\(552\) | 14.2744 | − | 24.7240i | 0.607560 | − | 1.05232i | ||||
\(553\) | −2.16756 | + | 3.75433i | −0.0921741 | + | 0.159650i | ||||
\(554\) | 34.8993 | 1.48273 | ||||||||
\(555\) | 13.7436 | − | 23.8047i | 0.583384 | − | 1.01045i | ||||
\(556\) | −7.13669 | − | 12.3611i | −0.302663 | − | 0.524228i | ||||
\(557\) | 4.60238 | + | 7.97156i | 0.195009 | + | 0.337766i | 0.946904 | − | 0.321518i | \(-0.104193\pi\) |
−0.751894 | + | 0.659284i | \(0.770860\pi\) | |||||||
\(558\) | 5.52648 | 0.233955 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −4.52350 | −0.191153 | ||||||||
\(561\) | 4.18933 | + | 7.25614i | 0.176874 | + | 0.306354i | ||||
\(562\) | −17.0918 | − | 29.6039i | −0.720974 | − | 1.24876i | ||||
\(563\) | 0.487623 | − | 0.844588i | 0.0205509 | − | 0.0355951i | −0.855567 | − | 0.517692i | \(-0.826791\pi\) |
0.876118 | + | 0.482097i | \(0.160125\pi\) | |||||||
\(564\) | 8.69202 | 0.366000 | ||||||||
\(565\) | 9.13975 | − | 15.8305i | 0.384512 | − | 0.665995i | ||||
\(566\) | 30.2533 | − | 52.4003i | 1.27164 | − | 2.20255i | ||||
\(567\) | 0.801938 | 0.0336782 | ||||||||
\(568\) | −14.8885 | + | 25.7877i | −0.624708 | + | 1.08203i | ||||
\(569\) | 8.44720 | + | 14.6310i | 0.354125 | + | 0.613362i | 0.986968 | − | 0.160918i | \(-0.0514454\pi\) |
−0.632843 | + | 0.774280i | \(0.718112\pi\) | |||||||
\(570\) | 10.6380 | + | 18.4256i | 0.445578 | + | 0.771763i | ||||
\(571\) | −44.3226 | −1.85484 | −0.927421 | − | 0.374019i | \(-0.877979\pi\) | ||||
−0.927421 | + | 0.374019i | \(0.877979\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.7657 | −0.700397 | ||||||||
\(574\) | 0.804094 | + | 1.39273i | 0.0335622 | + | 0.0581315i | ||||
\(575\) | 33.6172 | + | 58.2267i | 1.40193 | + | 2.42822i | ||||
\(576\) | 5.92208 | − | 10.2573i | 0.246753 | − | 0.427389i | ||||
\(577\) | −3.56704 | −0.148498 | −0.0742489 | − | 0.997240i | \(-0.523656\pi\) | ||||
−0.0742489 | + | 0.997240i | \(0.523656\pi\) | |||||||
\(578\) | −9.85450 | + | 17.0685i | −0.409893 | + | 0.709956i | ||||
\(579\) | −12.8720 | + | 22.2949i | −0.534940 | + | 0.926544i | ||||
\(580\) | −50.5424 | −2.09866 | ||||||||
\(581\) | 2.82640 | − | 4.89546i | 0.117259 | − | 0.203098i | ||||
\(582\) | −7.00514 | − | 12.1333i | −0.290372 | − | 0.502940i | ||||
\(583\) | 14.1984 | + | 24.5923i | 0.588036 | + | 1.01851i | ||||
\(584\) | −43.5669 | −1.80281 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −62.5120 | −2.58235 | ||||||||
\(587\) | −8.05861 | − | 13.9579i | −0.332614 | − | 0.576105i | 0.650409 | − | 0.759584i | \(-0.274597\pi\) |
−0.983024 | + | 0.183479i | \(0.941264\pi\) | |||||||
\(588\) | −11.2992 | − | 19.5709i | −0.465973 | − | 0.807089i | ||||
\(589\) | 2.86658 | − | 4.96507i | 0.118116 | − | 0.204582i | ||||
\(590\) | 46.8504 | 1.92880 | ||||||||
\(591\) | −10.7104 | + | 18.5510i | −0.440569 | + | 0.763087i | ||||
\(592\) | 5.68731 | − | 9.85071i | 0.233747 | − | 0.404862i | ||||
\(593\) | 42.8611 | 1.76010 | 0.880048 | − | 0.474885i | \(-0.157510\pi\) | ||||
0.880048 | + | 0.474885i | \(0.157510\pi\) | |||||||
\(594\) | −3.35958 | + | 5.81897i | −0.137845 | + | 0.238755i | ||||
\(595\) | 4.35086 | + | 7.53590i | 0.178368 | + | 0.308942i | ||||
\(596\) | 34.4934 | + | 59.7444i | 1.41291 | + | 2.44722i | ||||
\(597\) | −3.52781 | −0.144384 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 40.9420 | 1.67284 | 0.836422 | − | 0.548086i | \(-0.184643\pi\) | ||||
0.836422 | + | 0.548086i | \(0.184643\pi\) | |||||||
\(600\) | −15.8158 | − | 27.3938i | −0.645678 | − | 1.11835i | ||||
\(601\) | −0.593523 | − | 1.02801i | −0.0242103 | − | 0.0419335i | 0.853666 | − | 0.520820i | \(-0.174374\pi\) |
−0.877877 | + | 0.478887i | \(0.841040\pi\) | |||||||
\(602\) | −1.52715 | + | 2.64510i | −0.0622419 | + | 0.107806i | ||||
\(603\) | −14.3937 | −0.586158 | ||||||||
\(604\) | −21.9737 | + | 38.0595i | −0.894096 | + | 1.54862i | ||||
\(605\) | −5.30290 | + | 9.18489i | −0.215593 | + | 0.373419i | ||||
\(606\) | 10.9022 | 0.442870 | ||||||||
\(607\) | −9.99612 | + | 17.3138i | −0.405730 | + | 0.702745i | −0.994406 | − | 0.105624i | \(-0.966316\pi\) |
0.588676 | + | 0.808369i | \(0.299649\pi\) | |||||||
\(608\) | −4.55861 | − | 7.89574i | −0.184876 | − | 0.320214i | ||||
\(609\) | 1.54407 | + | 2.67441i | 0.0625690 | + | 0.108373i | ||||
\(610\) | −115.356 | −4.67062 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 10.4480 | 0.422336 | ||||||||
\(613\) | −16.6809 | − | 28.8922i | −0.673735 | − | 1.16694i | −0.976837 | − | 0.213985i | \(-0.931356\pi\) |
0.303102 | − | 0.952958i | \(-0.401978\pi\) | |||||||
\(614\) | 9.71864 | + | 16.8332i | 0.392212 | + | 0.679332i | ||||
\(615\) | −1.57069 | + | 2.72051i | −0.0633362 | + | 0.109702i | ||||
\(616\) | −8.37867 | −0.337586 | ||||||||
\(617\) | 5.81163 | − | 10.0660i | 0.233967 | − | 0.405243i | −0.725005 | − | 0.688744i | \(-0.758162\pi\) |
0.958972 | + | 0.283501i | \(0.0914958\pi\) | |||||||
\(618\) | −1.42327 | + | 2.46518i | −0.0572524 | + | 0.0991640i | ||||
\(619\) | 16.5381 | 0.664722 | 0.332361 | − | 0.943152i | \(-0.392155\pi\) | ||||
0.332361 | + | 0.943152i | \(0.392155\pi\) | |||||||
\(620\) | −15.3878 | + | 26.6525i | −0.617990 | + | 1.07039i | ||||
\(621\) | −3.89493 | − | 6.74621i | −0.156298 | − | 0.270716i | ||||
\(622\) | −16.9907 | − | 29.4288i | −0.681267 | − | 1.17999i | ||||
\(623\) | −0.907542 | −0.0363599 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.33944 | 0.253577 | ||||||||
\(626\) | 16.7738 | + | 29.0531i | 0.670417 | + | 1.16120i | ||||
\(627\) | 3.48523 | + | 6.03660i | 0.139187 | + | 0.241078i | ||||
\(628\) | 33.1989 | − | 57.5023i | 1.32478 | − | 2.29459i | ||||
\(629\) | −21.8810 | −0.872452 | ||||||||
\(630\) | −3.48911 | + | 6.04332i | −0.139010 | + | 0.240772i | ||||
\(631\) | −18.2208 | + | 31.5593i | −0.725358 | + | 1.25636i | 0.233468 | + | 0.972364i | \(0.424993\pi\) |
−0.958826 | + | 0.283993i | \(0.908341\pi\) | |||||||
\(632\) | −19.8116 | −0.788064 | ||||||||
\(633\) | 0.607760 | − | 1.05267i | 0.0241563 | − | 0.0418399i | ||||
\(634\) | 8.06547 | + | 13.9698i | 0.320321 | + | 0.554812i | ||||
\(635\) | 10.4673 | + | 18.1300i | 0.415384 | + | 0.719466i | ||||
\(636\) | 35.4101 | 1.40410 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −25.8745 | −1.02438 | ||||||||
\(639\) | 4.06249 | + | 7.03644i | 0.160710 | + | 0.278357i | ||||
\(640\) | 37.7652 | + | 65.4112i | 1.49280 | + | 2.58560i | ||||
\(641\) | −13.6033 | + | 23.5617i | −0.537300 | + | 0.930630i | 0.461748 | + | 0.887011i | \(0.347222\pi\) |
−0.999048 | + | 0.0436195i | \(0.986111\pi\) | |||||||
\(642\) | −22.4403 | −0.885646 | ||||||||
\(643\) | −2.53481 | + | 4.39042i | −0.0999632 | + | 0.173141i | −0.911669 | − | 0.410925i | \(-0.865206\pi\) |
0.811706 | + | 0.584066i | \(0.198539\pi\) | |||||||
\(644\) | 11.1039 | − | 19.2325i | 0.437554 | − | 0.757866i | ||||
\(645\) | −5.96615 | −0.234917 | ||||||||
\(646\) | 8.46830 | − | 14.6675i | 0.333181 | − | 0.577086i | ||||
\(647\) | −9.66033 | − | 16.7322i | −0.379787 | − | 0.657810i | 0.611244 | − | 0.791442i | \(-0.290669\pi\) |
−0.991031 | + | 0.133632i | \(0.957336\pi\) | |||||||
\(648\) | 1.83244 | + | 3.17387i | 0.0719849 | + | 0.124682i | ||||
\(649\) | 15.3491 | 0.602506 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.88040 | 0.0736985 | ||||||||
\(652\) | 21.9331 | + | 37.9892i | 0.858966 | + | 1.48777i | ||||
\(653\) | −17.6177 | − | 30.5148i | −0.689436 | − | 1.19414i | −0.972021 | − | 0.234895i | \(-0.924525\pi\) |
0.282585 | − | 0.959242i | \(-0.408808\pi\) | |||||||
\(654\) | −2.10292 | + | 3.64236i | −0.0822305 | + | 0.142427i | ||||
\(655\) | −67.2790 | −2.62881 | ||||||||
\(656\) | −0.649973 | + | 1.12579i | −0.0253772 | + | 0.0439546i | ||||
\(657\) | −5.94385 | + | 10.2950i | −0.231891 | + | 0.401648i | ||||
\(658\) | 4.62133 | 0.180158 | ||||||||
\(659\) | 2.18084 | − | 3.77733i | 0.0849535 | − | 0.147144i | −0.820418 | − | 0.571764i | \(-0.806259\pi\) |
0.905371 | + | 0.424621i | \(0.139592\pi\) | |||||||
\(660\) | −18.7087 | − | 32.4044i | −0.728236 | − | 1.26134i | ||||
\(661\) | −7.73543 | − | 13.3982i | −0.300873 | − | 0.521128i | 0.675461 | − | 0.737396i | \(-0.263945\pi\) |
−0.976334 | + | 0.216268i | \(0.930611\pi\) | |||||||
\(662\) | 22.2553 | 0.864978 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 25.8334 | 1.00253 | ||||||||
\(665\) | 3.61960 | + | 6.26934i | 0.140362 | + | 0.243115i | ||||
\(666\) | −8.77359 | − | 15.1963i | −0.339970 | − | 0.588845i | ||||
\(667\) | 14.9988 | − | 25.9787i | 0.580756 | − | 1.00590i | ||||
\(668\) | −40.8605 | −1.58094 | ||||||||
\(669\) | 8.69418 | − | 15.0588i | 0.336136 | − | 0.582205i | ||||
\(670\) | 62.6250 | − | 108.470i | 2.41942 | − | 4.19055i | ||||
\(671\) | −37.7928 | −1.45898 | ||||||||
\(672\) | 1.49516 | − | 2.58969i | 0.0576769 | − | 0.0998993i | ||||
\(673\) | 5.87047 | + | 10.1680i | 0.226290 | + | 0.391946i | 0.956706 | − | 0.291057i | \(-0.0940070\pi\) |
−0.730416 | + | 0.683003i | \(0.760674\pi\) | |||||||
\(674\) | 3.11476 | + | 5.39492i | 0.119976 | + | 0.207805i | ||||
\(675\) | −8.63102 | −0.332208 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.44504 | 0.132404 | 0.0662019 | − | 0.997806i | \(-0.478912\pi\) | ||||
0.0662019 | + | 0.997806i | \(0.478912\pi\) | |||||||
\(678\) | −5.83459 | − | 10.1058i | −0.224076 | − | 0.388111i | ||||
\(679\) | −2.38351 | − | 4.12836i | −0.0914707 | − | 0.158432i | ||||
\(680\) | −19.8835 | + | 34.4393i | −0.762498 | + | 1.32068i | ||||
\(681\) | 17.4155 | 0.667363 | ||||||||
\(682\) | −7.87760 | + | 13.6444i | −0.301649 | + | 0.522471i | ||||
\(683\) | 10.2029 | − | 17.6720i | 0.390403 | − | 0.676198i | −0.602099 | − | 0.798421i | \(-0.705669\pi\) |
0.992503 | + | 0.122223i | \(0.0390022\pi\) | |||||||
\(684\) | 8.69202 | 0.332348 | ||||||||
\(685\) | −17.4456 | + | 30.2166i | −0.666561 | + | 1.15452i | ||||
\(686\) | −12.6228 | − | 21.8634i | −0.481942 | − | 0.834748i | ||||
\(687\) | −9.38016 | − | 16.2469i | −0.357875 | − | 0.619858i | ||||
\(688\) | −2.46888 | −0.0941251 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 67.7851 | 2.58053 | ||||||||
\(691\) | 13.9019 | + | 24.0788i | 0.528854 | + | 0.916002i | 0.999434 | + | 0.0336449i | \(0.0107115\pi\) |
−0.470580 | + | 0.882358i | \(0.655955\pi\) | |||||||
\(692\) | −21.5328 | − | 37.2959i | −0.818554 | − | 1.41778i | ||||
\(693\) | −1.14310 | + | 1.97991i | −0.0434229 | + | 0.0752107i | ||||
\(694\) | 23.9433 | 0.908876 | ||||||||
\(695\) | 7.41185 | − | 12.8377i | 0.281148 | − | 0.486962i | ||||
\(696\) | −7.05645 | + | 12.2221i | −0.267474 | + | 0.463279i | ||||
\(697\) | 2.50066 | 0.0947194 | ||||||||
\(698\) | −12.3026 | + | 21.3087i | −0.465660 | + | 0.806547i | ||||
\(699\) | 1.97554 | + | 3.42174i | 0.0747218 | + | 0.129422i | ||||
\(700\) | −12.3029 | − | 21.3092i | −0.465006 | − | 0.805414i | ||||
\(701\) | 11.9715 | 0.452158 | 0.226079 | − | 0.974109i | \(-0.427409\pi\) | ||||
0.226079 | + | 0.974109i | \(0.427409\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.2034 | −0.686556 | ||||||||
\(704\) | 16.8830 | + | 29.2422i | 0.636301 | + | 1.10211i | ||||
\(705\) | 4.51357 | + | 7.81774i | 0.169991 | + | 0.294433i | ||||
\(706\) | −21.5551 | + | 37.3346i | −0.811238 | + | 1.40510i | ||||
\(707\) | 3.70948 | 0.139509 | ||||||||
\(708\) | 9.57002 | − | 16.5758i | 0.359664 | − | 0.622955i | ||||
\(709\) | 16.1332 | − | 27.9435i | 0.605894 | − | 1.04944i | −0.386015 | − | 0.922492i | \(-0.626149\pi\) |
0.991909 | − | 0.126947i | \(-0.0405179\pi\) | |||||||
\(710\) | −70.7012 | −2.65337 | ||||||||
\(711\) | −2.70291 | + | 4.68157i | −0.101367 | + | 0.175573i | ||||
\(712\) | −2.07374 | − | 3.59183i | −0.0777169 | − | 0.134610i | ||||
\(713\) | −9.13288 | − | 15.8186i | −0.342029 | − | 0.592412i | ||||
\(714\) | 5.55496 | 0.207889 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.91457 | −0.0715510 | ||||||||
\(717\) | −0.409166 | − | 0.708696i | −0.0152806 | − | 0.0264667i | ||||
\(718\) | 17.9985 | + | 31.1743i | 0.671698 | + | 1.16342i | ||||
\(719\) | −6.05429 | + | 10.4863i | −0.225787 | + | 0.391075i | −0.956555 | − | 0.291551i | \(-0.905829\pi\) |
0.730768 | + | 0.682626i | \(0.239162\pi\) | |||||||
\(720\) | −5.64071 | −0.210217 | ||||||||
\(721\) | −0.484271 | + | 0.838781i | −0.0180352 | + | 0.0312378i | ||||
\(722\) | −15.3455 | + | 26.5791i | −0.571100 | + | 0.989173i | ||||
\(723\) | 6.03252 | 0.224352 | ||||||||
\(724\) | 41.3865 | − | 71.6835i | 1.53812 | − | 2.66410i | ||||
\(725\) | −16.6184 | − | 28.7839i | −0.617192 | − | 1.06901i | ||||
\(726\) | 3.38524 | + | 5.86341i | 0.125638 | + | 0.217611i | ||||
\(727\) | −16.6200 | −0.616402 | −0.308201 | − | 0.951321i | \(-0.599727\pi\) | ||||
−0.308201 | + | 0.951321i | \(0.599727\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −51.7216 | − | 89.5845i | −1.91430 | − | 3.31567i | ||||
\(731\) | 2.37465 | + | 4.11301i | 0.0878296 | + | 0.152125i | ||||
\(732\) | −23.5635 | + | 40.8131i | −0.870930 | + | 1.50850i | ||||
\(733\) | −17.7912 | −0.657132 | −0.328566 | − | 0.944481i | \(-0.606565\pi\) | ||||
−0.328566 | + | 0.944481i | \(0.606565\pi\) | |||||||
\(734\) | −26.2461 | + | 45.4595i | −0.968760 | + | 1.67794i | ||||
\(735\) | 11.7349 | − | 20.3254i | 0.432848 | − | 0.749715i | ||||
\(736\) | −29.0473 | −1.07070 | ||||||||
\(737\) | 20.5172 | − | 35.5369i | 0.755762 | − | 1.30902i | ||||
\(738\) | 1.00269 | + | 1.73671i | 0.0369095 | + | 0.0639291i | ||||
\(739\) | −13.6809 | − | 23.6960i | −0.503260 | − | 0.871672i | −0.999993 | − | 0.00376844i | \(-0.998800\pi\) |
0.496733 | − | 0.867903i | \(-0.334533\pi\) | |||||||
\(740\) | 97.7160 | 3.59211 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 18.8267 | 0.691150 | ||||||||
\(743\) | 4.19298 | + | 7.26246i | 0.153826 | + | 0.266434i | 0.932631 | − | 0.360832i | \(-0.117507\pi\) |
−0.778805 | + | 0.627266i | \(0.784174\pi\) | |||||||
\(744\) | 4.29672 | + | 7.44215i | 0.157526 | + | 0.272842i | ||||
\(745\) | −35.8233 | + | 62.0478i | −1.31247 | + | 2.27326i | ||||
\(746\) | −9.72528 | −0.356068 | ||||||||
\(747\) | 3.52446 | − | 6.10454i | 0.128953 | − | 0.223353i | ||||
\(748\) | −14.8929 | + | 25.7953i | −0.544538 | + | 0.943168i | ||||
\(749\) | −7.63533 | −0.278989 | ||||||||
\(750\) | 15.7981 | − | 27.3630i | 0.576863 | − | 0.999157i | ||||
\(751\) | 19.3889 | + | 33.5825i | 0.707511 | + | 1.22544i | 0.965778 | + | 0.259371i | \(0.0835151\pi\) |
−0.258267 | + | 0.966073i | \(0.583152\pi\) | |||||||
\(752\) | 1.86778 | + | 3.23509i | 0.0681110 | + | 0.117972i | ||||
\(753\) | 26.8799 | 0.979559 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −45.6418 | −1.66107 | ||||||||
\(756\) | 1.42543 | + | 2.46891i | 0.0518423 | + | 0.0897935i | ||||
\(757\) | −6.48643 | − | 11.2348i | −0.235753 | − | 0.408336i | 0.723738 | − | 0.690075i | \(-0.242422\pi\) |
−0.959491 | + | 0.281738i | \(0.909089\pi\) | |||||||
\(758\) | 12.6177 | − | 21.8546i | 0.458297 | − | 0.793794i | ||||
\(759\) | 22.2078 | 0.806090 | ||||||||
\(760\) | −16.5417 | + | 28.6510i | −0.600030 | + | 1.03928i | ||||
\(761\) | −2.57792 | + | 4.46510i | −0.0934497 | + | 0.161860i | −0.908961 | − | 0.416882i | \(-0.863123\pi\) |
0.815511 | + | 0.578742i | \(0.196456\pi\) | |||||||
\(762\) | 13.3642 | 0.484134 | ||||||||
\(763\) | −0.715521 | + | 1.23932i | −0.0259036 | + | 0.0448663i | ||||
\(764\) | −29.8007 | − | 51.6163i | −1.07815 | − | 1.86741i | ||||
\(765\) | 5.42543 | + | 9.39712i | 0.196157 | + | 0.339753i | ||||
\(766\) | 15.3822 | 0.555783 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 24.5284 | 0.885092 | ||||||||
\(769\) | −17.7506 | − | 30.7450i | −0.640104 | − | 1.10869i | −0.985409 | − | 0.170202i | \(-0.945558\pi\) |
0.345305 | − | 0.938490i | \(-0.387775\pi\) | |||||||
\(770\) | −9.94696 | − | 17.2286i | −0.358464 | − | 0.620877i | ||||
\(771\) | −4.52661 | + | 7.84033i | −0.163022 | + | 0.282362i | ||||
\(772\) | −91.5186 | −3.29383 | ||||||||
\(773\) | −3.07792 | + | 5.33112i | −0.110705 | + | 0.191747i | −0.916055 | − | 0.401053i | \(-0.868644\pi\) |
0.805350 | + | 0.592800i | \(0.201978\pi\) | |||||||
\(774\) | −1.90432 | + | 3.29838i | −0.0684494 | + | 0.118558i | ||||
\(775\) | −20.2381 | −0.726976 | ||||||||
\(776\) | 10.8927 | − | 18.8667i | 0.391025 | − | 0.677275i | ||||
\(777\) | −2.98523 | − | 5.17057i | −0.107095 | − | 0.185493i | ||||
\(778\) | −13.8966 | − | 24.0695i | −0.498216 | − | 0.862935i | ||||
\(779\) | 2.08038 | 0.0745372 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23.1631 | −0.828843 | ||||||||
\(782\) | −26.9799 | − | 46.7305i | −0.964798 | − | 1.67108i | ||||
\(783\) | 1.92543 | + | 3.33494i | 0.0688092 | + | 0.119181i | ||||
\(784\) | 4.85607 | − | 8.41096i | 0.173431 | − | 0.300391i | ||||
\(785\) | 68.9579 | 2.46121 | ||||||||
\(786\) | −21.4746 | + | 37.1952i | −0.765975 | + | 1.32671i | ||||
\(787\) | 7.10537 | − | 12.3069i | 0.253279 | − | 0.438692i | −0.711148 | − | 0.703043i | \(-0.751824\pi\) |
0.964427 | + | 0.264351i | \(0.0851576\pi\) | |||||||
\(788\) | −76.1503 | −2.71274 | ||||||||
\(789\) | 11.5755 | − | 20.0494i | 0.412100 | − | 0.713778i | ||||
\(790\) | −23.5199 | − | 40.7377i | −0.836801 | − | 1.44938i | ||||
\(791\) | −1.98523 | − | 3.43852i | −0.0705867 | − | 0.122260i | ||||
\(792\) | −10.4480 | −0.371254 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −29.5623 | −1.04913 | ||||||||
\(795\) | 18.3877 | + | 31.8484i | 0.652144 | + | 1.12955i | ||||
\(796\) | −6.27061 | − | 10.8610i | −0.222256 | − | 0.384958i | ||||
\(797\) | −5.95108 | + | 10.3076i | −0.210798 | + | 0.365113i | −0.951965 | − | 0.306208i | \(-0.900940\pi\) |
0.741166 | + | 0.671321i | \(0.234273\pi\) | |||||||
\(798\) | 4.62133 | 0.163593 | ||||||||
\(799\) | 3.59299 | − | 6.22324i | 0.127111 | − | 0.220162i | ||||
\(800\) | −16.0919 | + | 27.8720i | −0.568935 | + | 0.985425i | ||||
\(801\) | −1.13169 | −0.0399862 | ||||||||
\(802\) | −21.0591 | + | 36.4755i | −0.743624 | + | 1.28799i | ||||
\(803\) | −16.9450 | − | 29.3497i | −0.597978 | − | 1.03573i | ||||
\(804\) | −25.5846 | − | 44.3138i | −0.902298 | − | 1.56283i | ||||
\(805\) | 23.0640 | 0.812899 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.42088 | 0.0852190 | ||||||||
\(808\) | 8.47621 | + | 14.6812i | 0.298192 | + | 0.516483i | ||||
\(809\) | −0.807979 | − | 1.39946i | −0.0284070 | − | 0.0492024i | 0.851472 | − | 0.524399i | \(-0.175710\pi\) |
−0.879879 | + | 0.475197i | \(0.842377\pi\) | |||||||
\(810\) | −4.35086 | + | 7.53590i | −0.152873 | + | 0.264785i | ||||
\(811\) | 51.9657 | 1.82476 | 0.912381 | − | 0.409342i | \(-0.134242\pi\) | ||||
0.912381 | + | 0.409342i | \(0.134242\pi\) | |||||||
\(812\) | −5.48911 | + | 9.50743i | −0.192630 | + | 0.333645i | ||||
\(813\) | 10.7225 | − | 18.5720i | 0.376055 | − | 0.651347i | ||||
\(814\) | 50.0245 | 1.75336 | ||||||||
\(815\) | −22.7787 | + | 39.4539i | −0.797904 | + | 1.38201i | ||||
\(816\) | 2.24512 | + | 3.88866i | 0.0785949 | + | 0.136130i | ||||
\(817\) | 1.97554 | + | 3.42174i | 0.0691154 | + | 0.119711i | ||||
\(818\) | −65.7853 | −2.30013 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11.1675 | −0.389985 | ||||||||
\(821\) | 27.4163 | + | 47.4865i | 0.956837 | + | 1.65729i | 0.730108 | + | 0.683331i | \(0.239470\pi\) |
0.226728 | + | 0.973958i | \(0.427197\pi\) | |||||||
\(822\) | 11.1368 | + | 19.2895i | 0.388441 | + | 0.672800i | ||||
\(823\) | 23.4257 | − | 40.5745i | 0.816569 | − | 1.41434i | −0.0916262 | − | 0.995793i | \(-0.529206\pi\) |
0.908196 | − | 0.418546i | \(-0.137460\pi\) | |||||||
\(824\) | −4.42626 | −0.154196 | ||||||||
\(825\) | 12.3029 | − | 21.3092i | 0.428332 | − | 0.741893i | ||||
\(826\) | 5.08815 | − | 8.81293i | 0.177039 | − | 0.306641i | ||||
\(827\) | −21.2021 | −0.737270 | −0.368635 | − | 0.929574i | \(-0.620175\pi\) | ||||
−0.368635 | + | 0.929574i | \(0.620175\pi\) | |||||||
\(828\) | 13.8463 | − | 23.9825i | 0.481192 | − | 0.833450i | ||||
\(829\) | −9.14861 | − | 15.8459i | −0.317744 | − | 0.550350i | 0.662273 | − | 0.749263i | \(-0.269592\pi\) |
−0.980017 | + | 0.198913i | \(0.936259\pi\) | |||||||
\(830\) | 30.6688 | + | 53.1200i | 1.06453 | + | 1.84382i | ||||
\(831\) | 14.8073 | 0.513660 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.6829 | −0.647325 | ||||||||
\(834\) | −4.73155 | − | 8.19528i | −0.163840 | − | 0.283779i | ||||
\(835\) | −21.2180 | − | 36.7506i | −0.734278 | − | 1.27181i | ||||
\(836\) | −12.3898 | + | 21.4598i | −0.428512 | + | 0.742204i | ||||
\(837\) | 2.34481 | 0.0810486 | ||||||||
\(838\) | −19.3306 | + | 33.4815i | −0.667764 | + | 1.15660i | ||||
\(839\) | 10.5707 | − | 18.3090i | 0.364941 | − | 0.632096i | −0.623826 | − | 0.781563i | \(-0.714423\pi\) |
0.988767 | + | 0.149468i | \(0.0477559\pi\) | |||||||
\(840\) | −10.8509 | −0.374390 | ||||||||
\(841\) | 7.08546 | − | 12.2724i | 0.244326 | − | 0.423185i | ||||
\(842\) | 3.57875 | + | 6.19858i | 0.123332 | + | 0.213617i | ||||
\(843\) | −7.25182 | − | 12.5605i | −0.249766 | − | 0.432608i | ||||
\(844\) | 4.32113 | 0.148739 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5.76271 | 0.198126 | ||||||||
\(847\) | 1.15183 | + | 1.99503i | 0.0395775 | + | 0.0685502i | ||||
\(848\) | 7.60909 | + | 13.1793i | 0.261297 | + | 0.452580i | ||||
\(849\) | 12.8361 | − | 22.2328i | 0.440533 | − | 0.763026i | ||||
\(850\) | −59.7864 | −2.05066 | ||||||||
\(851\) | −28.9979 | + | 50.2258i | −0.994035 | + | 1.72172i | ||||
\(852\) | −14.4420 | + | 25.0143i | −0.494774 | + | 0.856974i | ||||
\(853\) | 7.13036 | 0.244139 | 0.122069 | − | 0.992522i | \(-0.461047\pi\) | ||||
0.122069 | + | 0.992522i | \(0.461047\pi\) | |||||||
\(854\) | −12.5281 | + | 21.6993i | −0.428703 | + | 0.742535i | ||||
\(855\) | 4.51357 | + | 7.81774i | 0.154361 | + | 0.267361i | ||||
\(856\) | −17.4468 | − | 30.2188i | −0.596320 | − | 1.03286i | ||||
\(857\) | −44.7741 | −1.52945 | −0.764726 | − | 0.644355i | \(-0.777126\pi\) | ||||
−0.764726 | + | 0.644355i | \(0.777126\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 57.3782 | 1.95772 | 0.978859 | − | 0.204535i | \(-0.0655681\pi\) | ||||
0.978859 | + | 0.204535i | \(0.0655681\pi\) | |||||||
\(860\) | −10.6047 | − | 18.3679i | −0.361617 | − | 0.626340i | ||||
\(861\) | 0.341166 | + | 0.590918i | 0.0116269 | + | 0.0201384i | ||||
\(862\) | 3.93379 | − | 6.81352i | 0.133985 | − | 0.232069i | ||||
\(863\) | 6.67563 | 0.227241 | 0.113621 | − | 0.993524i | \(-0.463755\pi\) | ||||
0.113621 | + | 0.993524i | \(0.463755\pi\) | |||||||
\(864\) | 1.86443 | − | 3.22929i | 0.0634291 | − | 0.109863i | ||||
\(865\) | 22.3630 | − | 38.7338i | 0.760365 | − | 1.31699i | ||||
\(866\) | −28.0536 | −0.953299 | ||||||||
\(867\) | −4.18114 | + | 7.24194i | −0.141999 | + | 0.245949i | ||||
\(868\) | 3.34236 | + | 5.78914i | 0.113447 | + | 0.196496i | ||||
\(869\) | −7.70560 | − | 13.3465i | −0.261394 | − | 0.452748i | ||||
\(870\) | −33.5090 | −1.13606 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −6.53989 | −0.221469 | ||||||||
\(873\) | −2.97219 | − | 5.14798i | −0.100593 | − | 0.174233i | ||||
\(874\) | −22.4453 | − | 38.8765i | −0.759225 | − | 1.31502i | ||||
\(875\) | 5.37531 | − | 9.31032i | 0.181719 | − | 0.314746i | ||||
\(876\) | −42.2602 | −1.42784 | ||||||||
\(877\) | 12.6491 | − | 21.9090i | 0.427131 | − | 0.739813i | −0.569486 | − | 0.822001i | \(-0.692858\pi\) |
0.996617 | + | 0.0821883i | \(0.0261909\pi\) | |||||||
\(878\) | 4.38159 | − | 7.58914i | 0.147872 | − | 0.256121i | ||||
\(879\) | −26.5230 | −0.894599 | ||||||||
\(880\) | 8.04043 | − | 13.9264i | 0.271043 | − | 0.469460i | ||||
\(881\) | 17.6893 | + | 30.6388i | 0.595969 | + | 1.03225i | 0.993409 | + | 0.114620i | \(0.0365651\pi\) |
−0.397441 | + | 0.917628i | \(0.630102\pi\) | |||||||
\(882\) | −7.49127 | − | 12.9753i | −0.252244 | − | 0.436900i | ||||
\(883\) | −11.5851 | −0.389869 | −0.194935 | − | 0.980816i | \(-0.562449\pi\) | ||||
−0.194935 | + | 0.980816i | \(0.562449\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 19.8780 | 0.668192 | ||||||||
\(886\) | 1.71714 | + | 2.97418i | 0.0576886 | + | 0.0999196i | ||||
\(887\) | 13.6446 | + | 23.6331i | 0.458141 | + | 0.793523i | 0.998863 | − | 0.0476784i | \(-0.0151822\pi\) |
−0.540722 | + | 0.841201i | \(0.681849\pi\) | |||||||
\(888\) | 13.6426 | − | 23.6296i | 0.457815 | − | 0.792958i | ||||
\(889\) | 4.54719 | 0.152508 | ||||||||
\(890\) | 4.92380 | − | 8.52828i | 0.165046 | − | 0.285869i | ||||
\(891\) | −1.42543 | + | 2.46891i | −0.0477536 | + | 0.0827117i | ||||
\(892\) | 61.8149 | 2.06972 | ||||||||
\(893\) | 2.98911 | − | 5.17730i | 0.100027 | − | 0.173252i | ||||
\(894\) | 22.8687 | + | 39.6098i | 0.764845 | + | 1.32475i | ||||
\(895\) | −0.994196 | − | 1.72200i | −0.0332323 | − | 0.0575601i | ||||
\(896\) | 16.4058 | 0.548080 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −28.5830 | −0.953826 | ||||||||
\(899\) | 4.51477 | + | 7.81981i | 0.150576 | + | 0.260805i | ||||
\(900\) | −15.3415 | − | 26.5722i | −0.511382 | − | 0.885740i | ||||
\(901\) | 14.6374 | − | 25.3526i | 0.487641 | − | 0.844619i | ||||
\(902\) | −5.71704 | −0.190357 | ||||||||
\(903\) | −0.647948 | + | 1.12228i | −0.0215624 | + | 0.0373471i | ||||
\(904\) | 9.07255 | − | 15.7141i | 0.301748 | − | 0.522644i | ||||
\(905\) | 85.9643 | 2.85755 | ||||||||
\(906\) | −14.5683 | + | 25.2330i | −0.483999 | + | 0.838311i | ||||
\(907\) | 15.2110 | + | 26.3462i | 0.505072 | + | 0.874810i | 0.999983 | + | 0.00586661i | \(0.00186741\pi\) |
−0.494911 | + | 0.868944i | \(0.664799\pi\) | |||||||
\(908\) | 30.9557 | + | 53.6168i | 1.02730 | + | 1.77934i | ||||
\(909\) | 4.62565 | 0.153423 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 53.5719 | 1.77492 | 0.887459 | − | 0.460887i | \(-0.152469\pi\) | ||||
0.887459 | + | 0.460887i | \(0.152469\pi\) | |||||||
\(912\) | 1.86778 | + | 3.23509i | 0.0618484 | + | 0.107125i | ||||
\(913\) | 10.0477 | + | 17.4032i | 0.332531 | + | 0.575961i | ||||
\(914\) | 4.06332 | − | 7.03787i | 0.134403 | − | 0.232792i | ||||
\(915\) | −48.9439 | −1.61804 | ||||||||
\(916\) | 33.3461 | − | 57.7571i | 1.10179 | − | 1.90835i | ||||
\(917\) | −7.30678 | + | 12.6557i | −0.241291 | + | 0.417929i | ||||
\(918\) | 6.92692 | 0.228622 | ||||||||
\(919\) | 18.0836 | − | 31.3217i | 0.596523 | − | 1.03321i | −0.396807 | − | 0.917902i | \(-0.629882\pi\) |
0.993330 | − | 0.115306i | \(-0.0367848\pi\) | |||||||
\(920\) | 52.7015 | + | 91.2816i | 1.73752 | + | 3.00947i | ||||
\(921\) | 4.12349 | + | 7.14209i | 0.135874 | + | 0.235340i | ||||
\(922\) | −15.9232 | −0.524403 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −8.12737 | −0.267371 | ||||||||
\(925\) | 32.1292 | + | 55.6493i | 1.05640 | + | 1.82974i | ||||
\(926\) | 8.78150 | + | 15.2100i | 0.288578 | + | 0.499831i | ||||
\(927\) | −0.603875 | + | 1.04594i | −0.0198339 | + | 0.0343533i | ||||
\(928\) | 14.3593 | 0.471367 | ||||||||
\(929\) | −6.67390 | + | 11.5595i | −0.218964 | + | 0.379256i | −0.954491 | − | 0.298239i | \(-0.903601\pi\) |
0.735528 | + | 0.677494i | \(0.236934\pi\) | |||||||
\(930\) | −10.2019 | + | 17.6703i | −0.334535 | + | 0.579432i | ||||
\(931\) | −15.5429 | −0.509397 | ||||||||
\(932\) | −7.02297 | + | 12.1641i | −0.230045 | + | 0.398449i | ||||
\(933\) | −7.20895 | − | 12.4863i | −0.236010 | − | 0.408782i | ||||
\(934\) | 38.4290 | + | 66.5610i | 1.25744 | + | 2.17794i | ||||
\(935\) | −30.9342 | −1.01166 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38.6872 | 1.26386 | 0.631928 | − | 0.775027i | \(-0.282264\pi\) | ||||
0.631928 | + | 0.775027i | \(0.282264\pi\) | |||||||
\(938\) | −13.6027 | − | 23.5605i | −0.444143 | − | 0.769279i | ||||
\(939\) | 7.11692 | + | 12.3269i | 0.232252 | + | 0.402272i | ||||
\(940\) | −16.0456 | + | 27.7917i | −0.523349 | + | 0.906466i | ||||
\(941\) | −35.7275 | −1.16468 | −0.582342 | − | 0.812944i | \(-0.697864\pi\) | ||||
−0.582342 | + | 0.812944i | \(0.697864\pi\) | |||||||
\(942\) | 22.0105 | − | 38.1233i | 0.717141 | − | 1.24213i | ||||
\(943\) | 3.31402 | − | 5.74005i | 0.107919 | − | 0.186922i | ||||
\(944\) | 8.22580 | 0.267727 | ||||||||
\(945\) | −1.48039 | + | 2.56410i | −0.0481569 | + | 0.0834103i | ||||
\(946\) | −5.42894 | − | 9.40321i | −0.176510 | − | 0.305725i | ||||
\(947\) | −8.92178 | − | 15.4530i | −0.289919 | − | 0.502154i | 0.683871 | − | 0.729603i | \(-0.260295\pi\) |
−0.973790 | + | 0.227448i | \(0.926962\pi\) | |||||||
\(948\) | −19.2174 | −0.624153 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −49.7381 | −1.61372 | ||||||||
\(951\) | 3.42208 | + | 5.92721i | 0.110968 | + | 0.192203i | ||||
\(952\) | 4.31886 | + | 7.48049i | 0.139975 | + | 0.242444i | ||||
\(953\) | −10.0846 | + | 17.4670i | −0.326671 | + | 0.565810i | −0.981849 | − | 0.189664i | \(-0.939260\pi\) |
0.655178 | + | 0.755474i | \(0.272594\pi\) | |||||||
\(954\) | 23.4765 | 0.760080 | ||||||||
\(955\) | 30.9496 | − | 53.6064i | 1.00151 | − | 1.73466i | ||||
\(956\) | 1.45457 | − | 2.51938i | 0.0470440 | − | 0.0814827i | ||||
\(957\) | −10.9782 | −0.354876 | ||||||||
\(958\) | −3.33393 | + | 5.77453i | −0.107714 | + | 0.186567i | ||||
\(959\) | 3.78932 | + | 6.56330i | 0.122364 | + | 0.211940i | ||||
\(960\) | 21.8644 | + | 37.8703i | 0.705671 | + | 1.22226i | ||||
\(961\) | −25.5018 | −0.822640 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.52111 | −0.306813 | ||||||||
\(964\) | 10.7227 | + | 18.5722i | 0.345354 | + | 0.598171i | ||||
\(965\) | −47.5236 | − | 82.3132i | −1.52984 | − | 2.64976i | ||||
\(966\) | 7.36174 | − | 12.7509i | 0.236860 | − | 0.410254i | ||||
\(967\) | 32.7894 | 1.05444 | 0.527218 | − | 0.849730i | \(-0.323235\pi\) | ||||
0.527218 | + | 0.849730i | \(0.323235\pi\) | |||||||
\(968\) | −5.26391 | + | 9.11735i | −0.169188 | + | 0.293043i | ||||
\(969\) | 3.59299 | − | 6.22324i | 0.115423 | − | 0.199919i | ||||
\(970\) | 51.7263 | 1.66083 | ||||||||
\(971\) | 13.4922 | − | 23.3692i | 0.432986 | − | 0.749954i | −0.564143 | − | 0.825677i | \(-0.690793\pi\) |
0.997129 | + | 0.0757231i | \(0.0241265\pi\) | |||||||
\(972\) | 1.77748 | + | 3.07868i | 0.0570127 | + | 0.0987488i | ||||
\(973\) | −1.60992 | − | 2.78846i | −0.0516115 | − | 0.0893938i | ||||
\(974\) | −97.3245 | −3.11848 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −20.2537 | −0.648305 | ||||||||
\(977\) | −8.47853 | − | 14.6852i | −0.271252 | − | 0.469822i | 0.697931 | − | 0.716165i | \(-0.254104\pi\) |
−0.969183 | + | 0.246343i | \(0.920771\pi\) | |||||||
\(978\) | 14.5414 | + | 25.1864i | 0.464982 | + | 0.805373i | ||||
\(979\) | 1.61314 | − | 2.79404i | 0.0515561 | − | 0.0892978i | ||||
\(980\) | 83.4341 | 2.66521 | ||||||||
\(981\) | −0.892240 | + | 1.54540i | −0.0284870 | + | 0.0493410i | ||||
\(982\) | −40.8565 | + | 70.7656i | −1.30378 | + | 2.25822i | ||||
\(983\) | 32.6631 | 1.04179 | 0.520895 | − | 0.853621i | \(-0.325598\pi\) | ||||
0.520895 | + | 0.853621i | \(0.325598\pi\) | |||||||
\(984\) | −1.55914 | + | 2.70051i | −0.0497035 | + | 0.0860890i | ||||
\(985\) | −39.5432 | − | 68.4908i | −1.25995 | − | 2.18230i | ||||
\(986\) | 13.3373 | + | 23.1008i | 0.424746 | + | 0.735681i | ||||
\(987\) | 1.96077 | 0.0624120 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.5881 | 0.400277 | ||||||||
\(990\) | −12.4037 | − | 21.4838i | −0.394214 | − | 0.682799i | ||||
\(991\) | −3.82155 | − | 6.61912i | −0.121396 | − | 0.210263i | 0.798923 | − | 0.601434i | \(-0.205404\pi\) |
−0.920318 | + | 0.391170i | \(0.872070\pi\) | |||||||
\(992\) | 4.37174 | − | 7.57207i | 0.138803 | − | 0.240414i | ||||
\(993\) | 9.44265 | 0.299653 | ||||||||
\(994\) | −7.67845 | + | 13.2995i | −0.243546 | + | 0.421833i | ||||
\(995\) | 6.51238 | − | 11.2798i | 0.206456 | − | 0.357593i | ||||
\(996\) | 25.0586 | 0.794012 | ||||||||
\(997\) | −18.0628 | + | 31.2857i | −0.572054 | + | 0.990827i | 0.424301 | + | 0.905521i | \(0.360520\pi\) |
−0.996355 | + | 0.0853055i | \(0.972813\pi\) | |||||||
\(998\) | −21.1424 | − | 36.6198i | −0.669252 | − | 1.15918i | ||||
\(999\) | −3.72252 | − | 6.44760i | −0.117775 | − | 0.203993i |
(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 | 507.2.e.l.484.2 | 6 | ||
13.2 | odd | 12 | 507.2.b.f.337.5 | 6 | |||
13.3 | even | 3 | 507.2.a.i.1.2 | ✓ | 3 | ||
13.4 | even | 6 | 507.2.e.i.22.2 | 6 | |||
13.5 | odd | 4 | 507.2.j.i.361.5 | 12 | |||
13.6 | odd | 12 | 507.2.j.i.316.2 | 12 | |||
13.7 | odd | 12 | 507.2.j.i.316.5 | 12 | |||
13.8 | odd | 4 | 507.2.j.i.361.2 | 12 | |||
13.9 | even | 3 | inner | 507.2.e.l.22.2 | 6 | ||
13.10 | even | 6 | 507.2.a.l.1.2 | yes | 3 | ||
13.11 | odd | 12 | 507.2.b.f.337.2 | 6 | |||
13.12 | even | 2 | 507.2.e.i.484.2 | 6 | |||
39.2 | even | 12 | 1521.2.b.k.1351.2 | 6 | |||
39.11 | even | 12 | 1521.2.b.k.1351.5 | 6 | |||
39.23 | odd | 6 | 1521.2.a.n.1.2 | 3 | |||
39.29 | odd | 6 | 1521.2.a.s.1.2 | 3 | |||
52.3 | odd | 6 | 8112.2.a.cg.1.1 | 3 | |||
52.23 | odd | 6 | 8112.2.a.cp.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.2.a.i.1.2 | ✓ | 3 | 13.3 | even | 3 | ||
507.2.a.l.1.2 | yes | 3 | 13.10 | even | 6 | ||
507.2.b.f.337.2 | 6 | 13.11 | odd | 12 | |||
507.2.b.f.337.5 | 6 | 13.2 | odd | 12 | |||
507.2.e.i.22.2 | 6 | 13.4 | even | 6 | |||
507.2.e.i.484.2 | 6 | 13.12 | even | 2 | |||
507.2.e.l.22.2 | 6 | 13.9 | even | 3 | inner | ||
507.2.e.l.484.2 | 6 | 1.1 | even | 1 | trivial | ||
507.2.j.i.316.2 | 12 | 13.6 | odd | 12 | |||
507.2.j.i.316.5 | 12 | 13.7 | odd | 12 | |||
507.2.j.i.361.2 | 12 | 13.8 | odd | 4 | |||
507.2.j.i.361.5 | 12 | 13.5 | odd | 4 | |||
1521.2.a.n.1.2 | 3 | 39.23 | odd | 6 | |||
1521.2.a.s.1.2 | 3 | 39.29 | odd | 6 | |||
1521.2.b.k.1351.2 | 6 | 39.2 | even | 12 | |||
1521.2.b.k.1351.5 | 6 | 39.11 | even | 12 | |||
8112.2.a.cg.1.1 | 3 | 52.3 | odd | 6 | |||
8112.2.a.cp.1.3 | 3 | 52.23 | odd | 6 |