Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(41,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.41");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.bl (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.51528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 41.7 | ||
Character | \(\chi\) | \(=\) | 315.41 |
Dual form | 315.2.bl.j.146.7 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.963349 | − | 0.556190i | 0.681191 | − | 0.393286i | −0.119113 | − | 0.992881i | \(-0.538005\pi\) |
0.800304 | + | 0.599595i | \(0.204672\pi\) | |||||||
\(3\) | 1.73166 | + | 0.0368078i | 0.999774 | + | 0.0212510i | ||||
\(4\) | −0.381305 | + | 0.660440i | −0.190653 | + | 0.330220i | ||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | 1.68867 | − | 0.927673i | 0.689395 | − | 0.378721i | ||||
\(7\) | 2.64533 | − | 0.0472671i | 0.999840 | − | 0.0178653i | ||||
\(8\) | 3.07307i | 1.08650i | ||||||||
\(9\) | 2.99729 | + | 0.127477i | 0.999097 | + | 0.0424924i | ||||
\(10\) | 1.11238i | 0.351765i | ||||||||
\(11\) | −2.20054 | + | 1.27048i | −0.663487 | + | 0.383064i | −0.793604 | − | 0.608434i | \(-0.791798\pi\) |
0.130117 | + | 0.991499i | \(0.458465\pi\) | |||||||
\(12\) | −0.684601 | + | 1.12962i | −0.197627 | + | 0.326094i | ||||
\(13\) | −5.31914 | − | 3.07101i | −1.47527 | − | 0.851745i | −0.475654 | − | 0.879632i | \(-0.657789\pi\) |
−0.999611 | + | 0.0278878i | \(0.991122\pi\) | |||||||
\(14\) | 2.52209 | − | 1.51684i | 0.674056 | − | 0.405393i | ||||
\(15\) | −0.897706 | + | 1.48126i | −0.231787 | + | 0.382459i | ||||
\(16\) | 0.946601 | + | 1.63956i | 0.236650 | + | 0.409890i | ||||
\(17\) | 3.62169 | 0.878388 | 0.439194 | − | 0.898392i | \(-0.355264\pi\) | ||||
0.439194 | + | 0.898392i | \(0.355264\pi\) | |||||||
\(18\) | 2.95834 | − | 1.54426i | 0.697287 | − | 0.363985i | ||||
\(19\) | − | 5.85603i | − | 1.34346i | −0.740794 | − | 0.671732i | \(-0.765550\pi\) | ||
0.740794 | − | 0.671732i | \(-0.234450\pi\) | |||||||
\(20\) | −0.381305 | − | 0.660440i | −0.0852625 | − | 0.147679i | ||||
\(21\) | 4.58255 | + | 0.0155182i | 0.999994 | + | 0.00338635i | ||||
\(22\) | −1.41326 | + | 2.44783i | −0.301307 | + | 0.521880i | ||||
\(23\) | −0.351180 | − | 0.202754i | −0.0732261 | − | 0.0422771i | 0.462940 | − | 0.886390i | \(-0.346795\pi\) |
−0.536166 | + | 0.844113i | \(0.680128\pi\) | |||||||
\(24\) | −0.113113 | + | 5.32152i | −0.0230891 | + | 1.08625i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | −6.83226 | −1.33992 | ||||||||
\(27\) | 5.18559 | + | 0.331071i | 0.997968 | + | 0.0637146i | ||||
\(28\) | −0.977461 | + | 1.76511i | −0.184723 | + | 0.333574i | ||||
\(29\) | 7.74651 | − | 4.47245i | 1.43849 | − | 0.830513i | 0.440746 | − | 0.897632i | \(-0.354714\pi\) |
0.997745 | + | 0.0671185i | \(0.0213805\pi\) | |||||||
\(30\) | −0.0409443 | + | 1.92626i | −0.00747536 | + | 0.351686i | ||||
\(31\) | −2.10988 | − | 1.21814i | −0.378946 | − | 0.218785i | 0.298414 | − | 0.954437i | \(-0.403543\pi\) |
−0.677360 | + | 0.735652i | \(0.736876\pi\) | |||||||
\(32\) | −3.49890 | − | 2.02009i | −0.618524 | − | 0.357105i | ||||
\(33\) | −3.85734 | + | 2.11904i | −0.671477 | + | 0.368878i | ||||
\(34\) | 3.48895 | − | 2.01435i | 0.598350 | − | 0.345457i | ||||
\(35\) | −1.28173 | + | 2.31456i | −0.216652 | + | 0.391231i | ||||
\(36\) | −1.22707 | + | 1.93092i | −0.204512 | + | 0.321821i | ||||
\(37\) | −10.9304 | −1.79694 | −0.898472 | − | 0.439030i | \(-0.855322\pi\) | ||||
−0.898472 | + | 0.439030i | \(0.855322\pi\) | |||||||
\(38\) | −3.25706 | − | 5.64140i | −0.528365 | − | 0.915156i | ||||
\(39\) | −9.09791 | − | 5.51373i | −1.45683 | − | 0.882903i | ||||
\(40\) | −2.66136 | − | 1.53654i | −0.420798 | − | 0.242948i | ||||
\(41\) | −2.20219 | + | 3.81430i | −0.343924 | + | 0.595694i | −0.985158 | − | 0.171652i | \(-0.945090\pi\) |
0.641234 | + | 0.767346i | \(0.278423\pi\) | |||||||
\(42\) | 4.42323 | − | 2.53382i | 0.682519 | − | 0.390977i | ||||
\(43\) | −1.15431 | − | 1.99933i | −0.176031 | − | 0.304895i | 0.764487 | − | 0.644640i | \(-0.222993\pi\) |
−0.940518 | + | 0.339745i | \(0.889659\pi\) | |||||||
\(44\) | − | 1.93776i | − | 0.292129i | ||||||
\(45\) | −1.60904 | + | 2.53199i | −0.239862 | + | 0.377447i | ||||
\(46\) | −0.451079 | −0.0665079 | ||||||||
\(47\) | −1.93276 | − | 3.34763i | −0.281922 | − | 0.488303i | 0.689936 | − | 0.723870i | \(-0.257638\pi\) |
−0.971858 | + | 0.235567i | \(0.924305\pi\) | |||||||
\(48\) | 1.57884 | + | 2.87401i | 0.227886 | + | 0.414827i | ||||
\(49\) | 6.99553 | − | 0.250074i | 0.999362 | − | 0.0357249i | ||||
\(50\) | −0.963349 | − | 0.556190i | −0.136238 | − | 0.0786571i | ||||
\(51\) | 6.27153 | + | 0.133306i | 0.878190 | + | 0.0186666i | ||||
\(52\) | 4.05644 | − | 2.34198i | 0.562527 | − | 0.324775i | ||||
\(53\) | 11.3035i | 1.55266i | 0.630327 | + | 0.776330i | \(0.282921\pi\) | ||||
−0.630327 | + | 0.776330i | \(0.717079\pi\) | |||||||
\(54\) | 5.17968 | − | 2.56524i | 0.704865 | − | 0.349085i | ||||
\(55\) | − | 2.54096i | − | 0.342623i | ||||||
\(56\) | 0.145255 | + | 8.12929i | 0.0194105 | + | 1.08632i | ||||
\(57\) | 0.215547 | − | 10.1406i | 0.0285500 | − | 1.34316i | ||||
\(58\) | 4.97506 | − | 8.61706i | 0.653258 | − | 1.13148i | ||||
\(59\) | −5.15614 | + | 8.93070i | −0.671272 | + | 1.16268i | 0.306271 | + | 0.951944i | \(0.400919\pi\) |
−0.977544 | + | 0.210734i | \(0.932415\pi\) | |||||||
\(60\) | −0.635982 | − | 1.15769i | −0.0821049 | − | 0.149458i | ||||
\(61\) | −4.26123 | + | 2.46022i | −0.545595 | + | 0.314999i | −0.747343 | − | 0.664438i | \(-0.768671\pi\) |
0.201749 | + | 0.979437i | \(0.435338\pi\) | |||||||
\(62\) | −2.71007 | −0.344179 | ||||||||
\(63\) | 7.93484 | + | 0.195546i | 0.999696 | + | 0.0246365i | ||||
\(64\) | −8.28063 | −1.03508 | ||||||||
\(65\) | 5.31914 | − | 3.07101i | 0.659759 | − | 0.380912i | ||||
\(66\) | −2.53738 | + | 4.18679i | −0.312330 | + | 0.515359i | ||||
\(67\) | 4.48543 | − | 7.76899i | 0.547982 | − | 0.949133i | −0.450430 | − | 0.892812i | \(-0.648729\pi\) |
0.998413 | − | 0.0563215i | \(-0.0179372\pi\) | |||||||
\(68\) | −1.38097 | + | 2.39191i | −0.167467 | + | 0.290061i | ||||
\(69\) | −0.600661 | − | 0.364027i | −0.0723111 | − | 0.0438237i | ||||
\(70\) | 0.0525790 | + | 2.94261i | 0.00628439 | + | 0.351709i | ||||
\(71\) | − | 3.50126i | − | 0.415523i | −0.978179 | − | 0.207762i | \(-0.933382\pi\) | ||
0.978179 | − | 0.207762i | \(-0.0666178\pi\) | |||||||
\(72\) | −0.391747 | + | 9.21089i | −0.0461678 | + | 1.08551i | ||||
\(73\) | − | 2.90225i | − | 0.339683i | −0.985471 | − | 0.169841i | \(-0.945674\pi\) | ||
0.985471 | − | 0.169841i | \(-0.0543255\pi\) | |||||||
\(74\) | −10.5298 | + | 6.07937i | −1.22406 | + | 0.706713i | ||||
\(75\) | −0.833953 | − | 1.51807i | −0.0962966 | − | 0.175291i | ||||
\(76\) | 3.86756 | + | 2.23294i | 0.443639 | + | 0.256135i | ||||
\(77\) | −5.76109 | + | 3.46485i | −0.656537 | + | 0.394856i | ||||
\(78\) | −11.8311 | − | 0.251480i | −1.33961 | − | 0.0284745i | ||||
\(79\) | 5.76974 | + | 9.99349i | 0.649147 | + | 1.12436i | 0.983327 | + | 0.181846i | \(0.0582073\pi\) |
−0.334180 | + | 0.942509i | \(0.608459\pi\) | |||||||
\(80\) | −1.89320 | −0.211667 | ||||||||
\(81\) | 8.96750 | + | 0.764172i | 0.996389 | + | 0.0849080i | ||||
\(82\) | 4.89934i | 0.541042i | ||||||||
\(83\) | 2.99978 | + | 5.19577i | 0.329269 | + | 0.570310i | 0.982367 | − | 0.186963i | \(-0.0598645\pi\) |
−0.653098 | + | 0.757273i | \(0.726531\pi\) | |||||||
\(84\) | −1.75760 | + | 3.02058i | −0.191770 | + | 0.329573i | ||||
\(85\) | −1.81084 | + | 3.13647i | −0.196414 | + | 0.340198i | ||||
\(86\) | −2.22401 | − | 1.28403i | −0.239822 | − | 0.138461i | ||||
\(87\) | 13.5789 | − | 7.45963i | 1.45582 | − | 0.799756i | ||||
\(88\) | −3.90428 | − | 6.76241i | −0.416198 | − | 0.720875i | ||||
\(89\) | −10.4075 | −1.10320 | −0.551598 | − | 0.834110i | \(-0.685982\pi\) | ||||
−0.551598 | + | 0.834110i | \(0.685982\pi\) | |||||||
\(90\) | −0.141803 | + | 3.33413i | −0.0149474 | + | 0.351448i | ||||
\(91\) | −14.2160 | − | 7.87241i | −1.49025 | − | 0.825253i | ||||
\(92\) | 0.267814 | − | 0.154622i | 0.0279215 | − | 0.0161205i | ||||
\(93\) | −3.60876 | − | 2.18707i | −0.374211 | − | 0.226788i | ||||
\(94\) | −3.72384 | − | 2.14996i | −0.384085 | − | 0.221752i | ||||
\(95\) | 5.07147 | + | 2.92801i | 0.520322 | + | 0.300408i | ||||
\(96\) | −5.98455 | − | 3.62690i | −0.610796 | − | 0.370169i | ||||
\(97\) | 9.04377 | − | 5.22142i | 0.918256 | − | 0.530155i | 0.0351775 | − | 0.999381i | \(-0.488800\pi\) |
0.883078 | + | 0.469226i | \(0.155467\pi\) | |||||||
\(98\) | 6.60005 | − | 4.13175i | 0.666706 | − | 0.417370i | ||||
\(99\) | −6.75760 | + | 3.52748i | −0.679165 | + | 0.354525i | ||||
\(100\) | 0.762611 | 0.0762611 | ||||||||
\(101\) | −1.55268 | − | 2.68932i | −0.154497 | − | 0.267597i | 0.778379 | − | 0.627795i | \(-0.216042\pi\) |
−0.932876 | + | 0.360198i | \(0.882709\pi\) | |||||||
\(102\) | 6.11582 | − | 3.35974i | 0.605556 | − | 0.332664i | ||||
\(103\) | −7.51109 | − | 4.33653i | −0.740090 | − | 0.427291i | 0.0820122 | − | 0.996631i | \(-0.473865\pi\) |
−0.822102 | + | 0.569340i | \(0.807199\pi\) | |||||||
\(104\) | 9.43743 | − | 16.3461i | 0.925417 | − | 1.60287i | ||||
\(105\) | −2.30471 | + | 3.96085i | −0.224917 | + | 0.386539i | ||||
\(106\) | 6.28691 | + | 10.8892i | 0.610639 | + | 1.05766i | ||||
\(107\) | − | 1.63329i | − | 0.157896i | −0.996879 | − | 0.0789480i | \(-0.974844\pi\) | ||
0.996879 | − | 0.0789480i | \(-0.0251561\pi\) | |||||||
\(108\) | −2.19595 | + | 3.29854i | −0.211305 | + | 0.317402i | ||||
\(109\) | 6.29576 | 0.603024 | 0.301512 | − | 0.953462i | \(-0.402509\pi\) | ||||
0.301512 | + | 0.953462i | \(0.402509\pi\) | |||||||
\(110\) | −1.41326 | − | 2.44783i | −0.134749 | − | 0.233392i | ||||
\(111\) | −18.9277 | − | 0.402323i | −1.79654 | − | 0.0381868i | ||||
\(112\) | 2.58157 | + | 4.29244i | 0.243935 | + | 0.405597i | ||||
\(113\) | 9.42835 | + | 5.44346i | 0.886945 | + | 0.512078i | 0.872942 | − | 0.487824i | \(-0.162209\pi\) |
0.0140027 | + | 0.999902i | \(0.495543\pi\) | |||||||
\(114\) | −5.43248 | − | 9.88887i | −0.508798 | − | 0.926177i | ||||
\(115\) | 0.351180 | − | 0.202754i | 0.0327477 | − | 0.0189069i | ||||
\(116\) | 6.82148i | 0.633358i | ||||||||
\(117\) | −15.5515 | − | 9.88277i | −1.43774 | − | 0.913663i | ||||
\(118\) | 11.4712i | 1.05601i | ||||||||
\(119\) | 9.58055 | − | 0.171187i | 0.878248 | − | 0.0156926i | ||||
\(120\) | −4.55201 | − | 2.75872i | −0.415540 | − | 0.251835i | ||||
\(121\) | −2.27176 | + | 3.93480i | −0.206524 | + | 0.357709i | ||||
\(122\) | −2.73670 | + | 4.74011i | −0.247769 | + | 0.429149i | ||||
\(123\) | −3.95384 | + | 6.52402i | −0.356506 | + | 0.588251i | ||||
\(124\) | 1.60902 | − | 0.928967i | 0.144494 | − | 0.0834237i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 7.75279 | − | 4.22490i | 0.690673 | − | 0.376384i | ||||
\(127\) | 15.9326 | 1.41379 | 0.706893 | − | 0.707320i | \(-0.250096\pi\) | ||||
0.706893 | + | 0.707320i | \(0.250096\pi\) | |||||||
\(128\) | −0.979330 | + | 0.565416i | −0.0865613 | + | 0.0499762i | ||||
\(129\) | −1.92529 | − | 3.50465i | −0.169512 | − | 0.308567i | ||||
\(130\) | 3.41613 | − | 5.91691i | 0.299614 | − | 0.518947i | ||||
\(131\) | −6.31539 | + | 10.9386i | −0.551778 | + | 0.955708i | 0.446368 | + | 0.894849i | \(0.352717\pi\) |
−0.998146 | + | 0.0608584i | \(0.980616\pi\) | |||||||
\(132\) | 0.0713248 | − | 3.35555i | 0.00620803 | − | 0.292063i | ||||
\(133\) | −0.276797 | − | 15.4911i | −0.0240014 | − | 1.34325i | ||||
\(134\) | − | 9.97900i | − | 0.862054i | ||||||
\(135\) | −2.87951 | + | 4.32532i | −0.247829 | + | 0.372264i | ||||
\(136\) | 11.1297i | 0.954365i | ||||||||
\(137\) | 4.88855 | − | 2.82240i | 0.417657 | − | 0.241134i | −0.276418 | − | 0.961038i | \(-0.589147\pi\) |
0.694074 | + | 0.719903i | \(0.255814\pi\) | |||||||
\(138\) | −0.781115 | − | 0.0166032i | −0.0664929 | − | 0.00141336i | ||||
\(139\) | 7.83919 | + | 4.52596i | 0.664911 | + | 0.383887i | 0.794146 | − | 0.607727i | \(-0.207919\pi\) |
−0.129235 | + | 0.991614i | \(0.541252\pi\) | |||||||
\(140\) | −1.03990 | − | 1.72906i | −0.0878872 | − | 0.146132i | ||||
\(141\) | −3.22366 | − | 5.86810i | −0.271481 | − | 0.494184i | ||||
\(142\) | −1.94737 | − | 3.37294i | −0.163419 | − | 0.283051i | ||||
\(143\) | 15.6066 | 1.30509 | ||||||||
\(144\) | 2.62823 | + | 5.03491i | 0.219019 | + | 0.419576i | ||||
\(145\) | 8.94490i | 0.742834i | ||||||||
\(146\) | −1.61420 | − | 2.79588i | −0.133592 | − | 0.231389i | ||||
\(147\) | 12.1231 | − | 0.175553i | 0.999895 | − | 0.0144794i | ||||
\(148\) | 4.16782 | − | 7.21887i | 0.342592 | − | 0.593387i | ||||
\(149\) | −11.3745 | − | 6.56709i | −0.931838 | − | 0.537997i | −0.0444457 | − | 0.999012i | \(-0.514152\pi\) |
−0.887392 | + | 0.461015i | \(0.847486\pi\) | |||||||
\(150\) | −1.64772 | − | 0.998590i | −0.134536 | − | 0.0815346i | ||||
\(151\) | 3.73419 | + | 6.46781i | 0.303884 | + | 0.526343i | 0.977012 | − | 0.213183i | \(-0.0683831\pi\) |
−0.673128 | + | 0.739526i | \(0.735050\pi\) | |||||||
\(152\) | 17.9960 | 1.45967 | ||||||||
\(153\) | 10.8552 | + | 0.461682i | 0.877595 | + | 0.0373248i | ||||
\(154\) | −3.62283 | + | 6.54212i | −0.291936 | + | 0.527179i | ||||
\(155\) | 2.10988 | − | 1.21814i | 0.169470 | − | 0.0978434i | ||||
\(156\) | 7.11057 | − | 3.90621i | 0.569301 | − | 0.312747i | ||||
\(157\) | −10.0153 | − | 5.78234i | −0.799309 | − | 0.461481i | 0.0439207 | − | 0.999035i | \(-0.486015\pi\) |
−0.843229 | + | 0.537554i | \(0.819348\pi\) | |||||||
\(158\) | 11.1166 | + | 6.41815i | 0.884386 | + | 0.510600i | ||||
\(159\) | −0.416058 | + | 19.5739i | −0.0329955 | + | 1.55231i | ||||
\(160\) | 3.49890 | − | 2.02009i | 0.276613 | − | 0.159702i | ||||
\(161\) | −0.938571 | − | 0.519752i | −0.0739697 | − | 0.0409622i | ||||
\(162\) | 9.06386 | − | 4.25147i | 0.712124 | − | 0.334027i | ||||
\(163\) | −5.87805 | −0.460404 | −0.230202 | − | 0.973143i | \(-0.573939\pi\) | ||||
−0.230202 | + | 0.973143i | \(0.573939\pi\) | |||||||
\(164\) | −1.67941 | − | 2.90883i | −0.131140 | − | 0.227141i | ||||
\(165\) | 0.0935272 | − | 4.40008i | 0.00728108 | − | 0.342546i | ||||
\(166\) | 5.77967 | + | 3.33689i | 0.448589 | + | 0.258993i | ||||
\(167\) | 0.357648 | − | 0.619464i | 0.0276756 | − | 0.0479356i | −0.851856 | − | 0.523776i | \(-0.824523\pi\) |
0.879531 | + | 0.475841i | \(0.157856\pi\) | |||||||
\(168\) | −0.0476886 | + | 14.0825i | −0.00367926 | + | 1.08649i | ||||
\(169\) | 12.3622 | + | 21.4119i | 0.950938 | + | 1.64707i | ||||
\(170\) | 4.02869i | 0.308987i | ||||||||
\(171\) | 0.746510 | − | 17.5522i | 0.0570870 | − | 1.34225i | ||||
\(172\) | 1.76058 | 0.134243 | ||||||||
\(173\) | −0.933569 | − | 1.61699i | −0.0709779 | − | 0.122937i | 0.828352 | − | 0.560208i | \(-0.189279\pi\) |
−0.899330 | + | 0.437270i | \(0.855945\pi\) | |||||||
\(174\) | 8.93229 | − | 14.7387i | 0.677155 | − | 1.11734i | ||||
\(175\) | −1.36360 | − | 2.26729i | −0.103078 | − | 0.171391i | ||||
\(176\) | −4.16606 | − | 2.40528i | −0.314029 | − | 0.181305i | ||||
\(177\) | −9.25740 | + | 15.2751i | −0.695829 | + | 1.14815i | ||||
\(178\) | −10.0261 | + | 5.78856i | −0.751487 | + | 0.433871i | ||||
\(179\) | 11.2227i | 0.838827i | 0.907795 | + | 0.419414i | \(0.137764\pi\) | ||||
−0.907795 | + | 0.419414i | \(0.862236\pi\) | |||||||
\(180\) | −1.05869 | − | 2.02814i | −0.0789103 | − | 0.151169i | ||||
\(181\) | 8.14976i | 0.605767i | 0.953028 | + | 0.302883i | \(0.0979493\pi\) | ||||
−0.953028 | + | 0.302883i | \(0.902051\pi\) | |||||||
\(182\) | −18.0736 | + | 0.322941i | −1.33970 | + | 0.0239380i | ||||
\(183\) | −7.46956 | + | 4.10342i | −0.552166 | + | 0.303334i | ||||
\(184\) | 0.623078 | − | 1.07920i | 0.0459339 | − | 0.0795598i | ||||
\(185\) | 5.46519 | − | 9.46599i | 0.401809 | − | 0.695954i | ||||
\(186\) | −4.69292 | − | 0.0997517i | −0.344102 | − | 0.00731415i | ||||
\(187\) | −7.96965 | + | 4.60128i | −0.582799 | + | 0.336479i | ||||
\(188\) | 2.94788 | 0.214997 | ||||||||
\(189\) | 13.7333 | + | 0.630683i | 0.998947 | + | 0.0458754i | ||||
\(190\) | 6.51413 | 0.472584 | ||||||||
\(191\) | 7.17435 | − | 4.14211i | 0.519118 | − | 0.299713i | −0.217456 | − | 0.976070i | \(-0.569776\pi\) |
0.736574 | + | 0.676357i | \(0.236442\pi\) | |||||||
\(192\) | −14.3392 | − | 0.304792i | −1.03484 | − | 0.0219964i | ||||
\(193\) | 11.0068 | − | 19.0643i | 0.792285 | − | 1.37228i | −0.132263 | − | 0.991215i | \(-0.542224\pi\) |
0.924549 | − | 0.381064i | \(-0.124442\pi\) | |||||||
\(194\) | 5.80821 | − | 10.0601i | 0.417005 | − | 0.722274i | ||||
\(195\) | 9.32398 | − | 5.12216i | 0.667704 | − | 0.366805i | ||||
\(196\) | −2.50228 | + | 4.71549i | −0.178734 | + | 0.336820i | ||||
\(197\) | − | 18.2349i | − | 1.29919i | −0.760282 | − | 0.649593i | \(-0.774939\pi\) | ||
0.760282 | − | 0.649593i | \(-0.225061\pi\) | |||||||
\(198\) | −4.54798 | + | 7.15671i | −0.323211 | + | 0.508605i | ||||
\(199\) | − | 0.0632401i | − | 0.00448297i | −0.999997 | − | 0.00224149i | \(-0.999287\pi\) | ||
0.999997 | − | 0.00224149i | \(-0.000713488\pi\) | |||||||
\(200\) | 2.66136 | − | 1.53654i | 0.188187 | − | 0.108650i | ||||
\(201\) | 8.05319 | − | 13.2881i | 0.568028 | − | 0.937274i | ||||
\(202\) | −2.99155 | − | 1.72717i | −0.210484 | − | 0.121523i | ||||
\(203\) | 20.2807 | − | 12.1973i | 1.42342 | − | 0.856080i | ||||
\(204\) | −2.47941 | + | 4.09114i | −0.173593 | + | 0.286437i | ||||
\(205\) | −2.20219 | − | 3.81430i | −0.153808 | − | 0.266403i | ||||
\(206\) | −9.64774 | −0.672190 | ||||||||
\(207\) | −1.02674 | − | 0.652480i | −0.0713635 | − | 0.0453505i | ||||
\(208\) | − | 11.6281i | − | 0.806263i | ||||||
\(209\) | 7.43997 | + | 12.8864i | 0.514633 | + | 0.891371i | ||||
\(210\) | −0.0172622 | + | 5.09754i | −0.00119120 | + | 0.351763i | ||||
\(211\) | −10.0442 | + | 17.3971i | −0.691471 | + | 1.19766i | 0.279885 | + | 0.960034i | \(0.409704\pi\) |
−0.971356 | + | 0.237629i | \(0.923630\pi\) | |||||||
\(212\) | −7.46531 | − | 4.31010i | −0.512720 | − | 0.296019i | ||||
\(213\) | 0.128874 | − | 6.06299i | 0.00883028 | − | 0.415429i | ||||
\(214\) | −0.908419 | − | 1.57343i | −0.0620982 | − | 0.107557i | ||||
\(215\) | 2.30863 | 0.157447 | ||||||||
\(216\) | −1.01740 | + | 15.9357i | −0.0692256 | + | 1.08429i | ||||
\(217\) | −5.63891 | − | 3.12266i | −0.382794 | − | 0.211980i | ||||
\(218\) | 6.06501 | − | 3.50164i | 0.410775 | − | 0.237161i | ||||
\(219\) | 0.106825 | − | 5.02571i | 0.00721860 | − | 0.339606i | ||||
\(220\) | 1.67815 | + | 0.968882i | 0.113141 | + | 0.0653220i | ||||
\(221\) | −19.2643 | − | 11.1222i | −1.29586 | − | 0.748162i | ||||
\(222\) | −18.4578 | + | 10.1398i | −1.23880 | + | 0.680540i | ||||
\(223\) | −13.3549 | + | 7.71045i | −0.894309 | + | 0.516330i | −0.875350 | − | 0.483491i | \(-0.839369\pi\) |
−0.0189597 | + | 0.999820i | \(0.506035\pi\) | |||||||
\(224\) | −9.35123 | − | 5.17843i | −0.624806 | − | 0.345998i | ||||
\(225\) | −1.38825 | − | 2.65947i | −0.0925498 | − | 0.177298i | ||||
\(226\) | 12.1104 | 0.805571 | ||||||||
\(227\) | 2.08023 | + | 3.60307i | 0.138070 | + | 0.239144i | 0.926766 | − | 0.375639i | \(-0.122577\pi\) |
−0.788696 | + | 0.614783i | \(0.789243\pi\) | |||||||
\(228\) | 6.61510 | + | 4.00904i | 0.438096 | + | 0.265505i | ||||
\(229\) | −0.917307 | − | 0.529608i | −0.0606174 | − | 0.0349975i | 0.469385 | − | 0.882994i | \(-0.344476\pi\) |
−0.530002 | + | 0.847996i | \(0.677809\pi\) | |||||||
\(230\) | 0.225539 | − | 0.390646i | 0.0148716 | − | 0.0257584i | ||||
\(231\) | −10.1038 | + | 5.78789i | −0.664780 | + | 0.380815i | ||||
\(232\) | 13.7442 | + | 23.8056i | 0.902349 | + | 1.56291i | ||||
\(233\) | − | 3.64514i | − | 0.238801i | −0.992846 | − | 0.119401i | \(-0.961903\pi\) | ||
0.992846 | − | 0.119401i | \(-0.0380973\pi\) | |||||||
\(234\) | −20.4783 | − | 0.870957i | −1.33871 | − | 0.0569362i | ||||
\(235\) | 3.86552 | 0.252158 | ||||||||
\(236\) | −3.93213 | − | 6.81065i | −0.255960 | − | 0.443335i | ||||
\(237\) | 9.62340 | + | 17.5177i | 0.625107 | + | 1.13790i | ||||
\(238\) | 9.13421 | − | 5.49352i | 0.592083 | − | 0.356092i | ||||
\(239\) | 1.21540 | + | 0.701710i | 0.0786175 | + | 0.0453898i | 0.538793 | − | 0.842438i | \(-0.318880\pi\) |
−0.460176 | + | 0.887828i | \(0.652214\pi\) | |||||||
\(240\) | −3.27838 | − | 0.0696846i | −0.211619 | − | 0.00449812i | ||||
\(241\) | 13.7967 | − | 7.96556i | 0.888727 | − | 0.513107i | 0.0152009 | − | 0.999884i | \(-0.495161\pi\) |
0.873526 | + | 0.486778i | \(0.161828\pi\) | |||||||
\(242\) | 5.05412i | 0.324891i | ||||||||
\(243\) | 15.5005 | + | 1.65336i | 0.994359 | + | 0.106063i | ||||
\(244\) | − | 3.75239i | − | 0.240222i | ||||||
\(245\) | −3.28120 | + | 6.18335i | −0.209628 | + | 0.395039i | ||||
\(246\) | −0.180334 | + | 8.48399i | −0.0114977 | + | 0.540920i | ||||
\(247\) | −17.9839 | + | 31.1491i | −1.14429 | + | 1.98197i | ||||
\(248\) | 3.74344 | − | 6.48382i | 0.237708 | − | 0.411723i | ||||
\(249\) | 5.00335 | + | 9.10772i | 0.317075 | + | 0.577178i | ||||
\(250\) | 0.963349 | − | 0.556190i | 0.0609276 | − | 0.0351765i | ||||
\(251\) | 25.9869 | 1.64028 | 0.820140 | − | 0.572163i | \(-0.193896\pi\) | ||||
0.820140 | + | 0.572163i | \(0.193896\pi\) | |||||||
\(252\) | −3.15475 | + | 5.16593i | −0.198730 | + | 0.325423i | ||||
\(253\) | 1.03038 | 0.0647794 | ||||||||
\(254\) | 15.3486 | − | 8.86153i | 0.963059 | − | 0.556022i | ||||
\(255\) | −3.25121 | + | 5.36465i | −0.203599 | + | 0.335947i | ||||
\(256\) | 7.65167 | − | 13.2531i | 0.478229 | − | 0.828317i | ||||
\(257\) | 2.25204 | − | 3.90065i | 0.140479 | − | 0.243316i | −0.787198 | − | 0.616700i | \(-0.788469\pi\) |
0.927677 | + | 0.373384i | \(0.121803\pi\) | |||||||
\(258\) | −3.80397 | − | 2.30537i | −0.236825 | − | 0.143526i | ||||
\(259\) | −28.9145 | + | 0.516648i | −1.79666 | + | 0.0321029i | ||||
\(260\) | 4.68397i | 0.290487i | ||||||||
\(261\) | 23.7887 | − | 12.4177i | 1.47248 | − | 0.768638i | ||||
\(262\) | 14.0502i | 0.868026i | ||||||||
\(263\) | −23.7175 | + | 13.6933i | −1.46248 | + | 0.844365i | −0.999126 | − | 0.0418070i | \(-0.986689\pi\) |
−0.463357 | + | 0.886172i | \(0.653355\pi\) | |||||||
\(264\) | −6.51197 | − | 11.8539i | −0.400784 | − | 0.729557i | ||||
\(265\) | −9.78915 | − | 5.65177i | −0.601342 | − | 0.347185i | ||||
\(266\) | −8.88266 | − | 14.7694i | −0.544631 | − | 0.905570i | ||||
\(267\) | −18.0223 | − | 0.383078i | −1.10295 | − | 0.0234440i | ||||
\(268\) | 3.42064 | + | 5.92472i | 0.208949 | + | 0.361910i | ||||
\(269\) | 0.995833 | 0.0607170 | 0.0303585 | − | 0.999539i | \(-0.490335\pi\) | ||||
0.0303585 | + | 0.999539i | \(0.490335\pi\) | |||||||
\(270\) | −0.368276 | + | 5.76835i | −0.0224126 | + | 0.351051i | ||||
\(271\) | 4.16640i | 0.253091i | 0.991961 | + | 0.126545i | \(0.0403889\pi\) | ||||
−0.991961 | + | 0.126545i | \(0.959611\pi\) | |||||||
\(272\) | 3.42829 | + | 5.93798i | 0.207871 | + | 0.360043i | ||||
\(273\) | −24.3276 | − | 14.1556i | −1.47237 | − | 0.856736i | ||||
\(274\) | 3.13959 | − | 5.43792i | 0.189669 | − | 0.328517i | ||||
\(275\) | 2.20054 | + | 1.27048i | 0.132697 | + | 0.0766128i | ||||
\(276\) | 0.469454 | − | 0.257896i | 0.0282578 | − | 0.0155235i | ||||
\(277\) | −9.42722 | − | 16.3284i | −0.566427 | − | 0.981080i | −0.996915 | − | 0.0784837i | \(-0.974992\pi\) |
0.430489 | − | 0.902596i | \(-0.358341\pi\) | |||||||
\(278\) | 10.0692 | 0.603908 | ||||||||
\(279\) | −6.16864 | − | 3.92008i | −0.369307 | − | 0.234689i | ||||
\(280\) | −7.11280 | − | 3.93885i | −0.425071 | − | 0.235391i | ||||
\(281\) | −7.91463 | + | 4.56951i | −0.472147 | + | 0.272594i | −0.717138 | − | 0.696931i | \(-0.754548\pi\) |
0.244991 | + | 0.969525i | \(0.421215\pi\) | |||||||
\(282\) | −6.36929 | − | 3.86007i | −0.379286 | − | 0.229864i | ||||
\(283\) | 5.69196 | + | 3.28625i | 0.338352 | + | 0.195348i | 0.659543 | − | 0.751667i | \(-0.270750\pi\) |
−0.321191 | + | 0.947014i | \(0.604083\pi\) | |||||||
\(284\) | 2.31237 | + | 1.33505i | 0.137214 | + | 0.0792207i | ||||
\(285\) | 8.67428 | + | 5.25699i | 0.513820 | + | 0.311397i | ||||
\(286\) | 15.0346 | − | 8.68025i | 0.889016 | − | 0.513274i | ||||
\(287\) | −5.64522 | + | 10.1942i | −0.333227 | + | 0.601743i | ||||
\(288\) | −10.2297 | − | 6.50083i | −0.602792 | − | 0.383065i | ||||
\(289\) | −3.88338 | −0.228434 | ||||||||
\(290\) | 4.97506 | + | 8.61706i | 0.292146 | + | 0.506011i | ||||
\(291\) | 15.8529 | − | 8.70885i | 0.929315 | − | 0.510522i | ||||
\(292\) | 1.91676 | + | 1.10664i | 0.112170 | + | 0.0647615i | ||||
\(293\) | −7.27736 | + | 12.6048i | −0.425148 | + | 0.736378i | −0.996434 | − | 0.0843728i | \(-0.973111\pi\) |
0.571286 | + | 0.820751i | \(0.306445\pi\) | |||||||
\(294\) | 11.5811 | − | 6.91186i | 0.675425 | − | 0.403108i | ||||
\(295\) | −5.15614 | − | 8.93070i | −0.300202 | − | 0.519965i | ||||
\(296\) | − | 33.5899i | − | 1.95237i | ||||||
\(297\) | −11.8317 | + | 5.85966i | −0.686545 | + | 0.340012i | ||||
\(298\) | −14.6102 | −0.846346 | ||||||||
\(299\) | 1.24532 | + | 2.15695i | 0.0720186 | + | 0.124740i | ||||
\(300\) | 1.32058 | + | 0.0280700i | 0.0762439 | + | 0.00162062i | ||||
\(301\) | −3.14804 | − | 5.23432i | −0.181450 | − | 0.301701i | ||||
\(302\) | 7.19466 | + | 4.15384i | 0.414006 | + | 0.239027i | ||||
\(303\) | −2.58972 | − | 4.71414i | −0.148776 | − | 0.270820i | ||||
\(304\) | 9.60132 | − | 5.54332i | 0.550673 | − | 0.317931i | ||||
\(305\) | − | 4.92045i | − | 0.281744i | ||||||
\(306\) | 10.7142 | − | 5.59282i | 0.612489 | − | 0.319720i | ||||
\(307\) | 28.7032i | 1.63818i | 0.573666 | + | 0.819089i | \(0.305521\pi\) | ||||
−0.573666 | + | 0.819089i | \(0.694479\pi\) | |||||||
\(308\) | −0.0915925 | − | 5.12602i | −0.00521897 | − | 0.292082i | ||||
\(309\) | −12.8470 | − | 7.78586i | −0.730842 | − | 0.442922i | ||||
\(310\) | 1.35504 | − | 2.34699i | 0.0769608 | − | 0.133300i | ||||
\(311\) | −0.409925 | + | 0.710011i | −0.0232447 | + | 0.0402610i | −0.877414 | − | 0.479734i | \(-0.840733\pi\) |
0.854169 | + | 0.519995i | \(0.174066\pi\) | |||||||
\(312\) | 16.9441 | − | 27.9585i | 0.959270 | − | 1.58284i | ||||
\(313\) | −15.8748 | + | 9.16531i | −0.897295 | + | 0.518054i | −0.876322 | − | 0.481726i | \(-0.840010\pi\) |
−0.0209737 | + | 0.999780i | \(0.506677\pi\) | |||||||
\(314\) | −12.8643 | −0.725976 | ||||||||
\(315\) | −4.13677 | + | 6.77400i | −0.233081 | + | 0.381672i | ||||
\(316\) | −8.80014 | −0.495047 | ||||||||
\(317\) | −13.9537 | + | 8.05619i | −0.783719 | + | 0.452481i | −0.837747 | − | 0.546059i | \(-0.816127\pi\) |
0.0540274 | + | 0.998539i | \(0.482794\pi\) | |||||||
\(318\) | 10.4860 | + | 19.0879i | 0.588025 | + | 1.07040i | ||||
\(319\) | −11.3643 | + | 19.6836i | −0.636280 | + | 1.10207i | ||||
\(320\) | 4.14031 | − | 7.17123i | 0.231451 | − | 0.400884i | ||||
\(321\) | 0.0601177 | − | 2.82830i | 0.00335544 | − | 0.157860i | ||||
\(322\) | −1.19325 | + | 0.0213212i | −0.0664973 | + | 0.00118818i | ||||
\(323\) | − | 21.2087i | − | 1.18008i | ||||||
\(324\) | −3.92405 | + | 5.63112i | −0.218003 | + | 0.312840i | ||||
\(325\) | 6.14202i | 0.340698i | ||||||||
\(326\) | −5.66261 | + | 3.26931i | −0.313623 | + | 0.181070i | ||||
\(327\) | 10.9021 | + | 0.231733i | 0.602888 | + | 0.0128149i | ||||
\(328\) | −11.7216 | − | 6.76749i | −0.647219 | − | 0.373672i | ||||
\(329\) | −5.27101 | − | 8.76424i | −0.290600 | − | 0.483188i | ||||
\(330\) | −2.35718 | − | 4.29083i | −0.129759 | − | 0.236203i | ||||
\(331\) | 1.52862 | + | 2.64765i | 0.0840208 | + | 0.145528i | 0.904974 | − | 0.425468i | \(-0.139890\pi\) |
−0.820953 | + | 0.570996i | \(0.806557\pi\) | |||||||
\(332\) | −4.57533 | −0.251104 | ||||||||
\(333\) | −32.7615 | − | 1.39337i | −1.79532 | − | 0.0763564i | ||||
\(334\) | − | 0.795680i | − | 0.0435377i | ||||||
\(335\) | 4.48543 | + | 7.76899i | 0.245065 | + | 0.424465i | ||||
\(336\) | 4.31240 | + | 7.52806i | 0.235261 | + | 0.410689i | ||||
\(337\) | 5.93691 | − | 10.2830i | 0.323404 | − | 0.560152i | −0.657784 | − | 0.753206i | \(-0.728506\pi\) |
0.981188 | + | 0.193055i | \(0.0618394\pi\) | |||||||
\(338\) | 23.8182 | + | 13.7515i | 1.29554 | + | 0.747981i | ||||
\(339\) | 16.1263 | + | 9.77326i | 0.875862 | + | 0.530810i | ||||
\(340\) | −1.38097 | − | 2.39191i | −0.0748936 | − | 0.129719i | ||||
\(341\) | 6.19050 | 0.335234 | ||||||||
\(342\) | −9.04322 | − | 17.3241i | −0.489001 | − | 0.936781i | ||||
\(343\) | 18.4937 | − | 0.992186i | 0.998564 | − | 0.0535730i | ||||
\(344\) | 6.14408 | − | 3.54729i | 0.331267 | − | 0.191257i | ||||
\(345\) | 0.615587 | − | 0.338175i | 0.0331421 | − | 0.0182067i | ||||
\(346\) | −1.79871 | − | 1.03848i | −0.0966990 | − | 0.0558292i | ||||
\(347\) | 2.78217 | + | 1.60629i | 0.149355 | + | 0.0862299i | 0.572815 | − | 0.819685i | \(-0.305851\pi\) |
−0.423460 | + | 0.905915i | \(0.639185\pi\) | |||||||
\(348\) | −0.251084 | + | 11.8125i | −0.0134595 | + | 0.633215i | ||||
\(349\) | −7.02188 | + | 4.05409i | −0.375873 | + | 0.217010i | −0.676021 | − | 0.736882i | \(-0.736297\pi\) |
0.300148 | + | 0.953893i | \(0.402964\pi\) | |||||||
\(350\) | −2.57467 | − | 1.42577i | −0.137622 | − | 0.0762107i | ||||
\(351\) | −26.5662 | − | 17.6860i | −1.41800 | − | 0.944010i | ||||
\(352\) | 10.2660 | 0.547177 | ||||||||
\(353\) | −18.5056 | − | 32.0526i | −0.984952 | − | 1.70599i | −0.642148 | − | 0.766580i | \(-0.721957\pi\) |
−0.342804 | − | 0.939407i | \(-0.611377\pi\) | |||||||
\(354\) | −0.422229 | + | 19.8642i | −0.0224412 | + | 1.05577i | ||||
\(355\) | 3.03218 | + | 1.75063i | 0.160931 | + | 0.0929138i | ||||
\(356\) | 3.96845 | − | 6.87355i | 0.210327 | − | 0.364298i | ||||
\(357\) | 16.5966 | + | 0.0562021i | 0.878383 | + | 0.00297453i | ||||
\(358\) | 6.24198 | + | 10.8114i | 0.329899 | + | 0.571401i | ||||
\(359\) | − | 3.91704i | − | 0.206733i | −0.994643 | − | 0.103367i | \(-0.967038\pi\) | ||
0.994643 | − | 0.103367i | \(-0.0329615\pi\) | |||||||
\(360\) | −7.78099 | − | 4.94471i | −0.410094 | − | 0.260609i | ||||
\(361\) | −15.2931 | −0.804898 | ||||||||
\(362\) | 4.53281 | + | 7.85106i | 0.238239 | + | 0.412643i | ||||
\(363\) | −4.07875 | + | 6.73012i | −0.214079 | + | 0.353240i | ||||
\(364\) | 10.6199 | − | 6.38706i | 0.556635 | − | 0.334773i | ||||
\(365\) | 2.51342 | + | 1.45113i | 0.131559 | + | 0.0759554i | ||||
\(366\) | −4.91351 | + | 8.10752i | −0.256833 | + | 0.423787i | ||||
\(367\) | 7.45062 | − | 4.30162i | 0.388919 | − | 0.224543i | −0.292772 | − | 0.956182i | \(-0.594578\pi\) |
0.681692 | + | 0.731639i | \(0.261244\pi\) | |||||||
\(368\) | − | 0.767709i | − | 0.0400196i | ||||||
\(369\) | −7.08684 | + | 11.1518i | −0.368926 | + | 0.580542i | ||||
\(370\) | − | 12.1587i | − | 0.632103i | ||||||
\(371\) | 0.534285 | + | 29.9016i | 0.0277387 | + | 1.55241i | ||||
\(372\) | 2.82047 | − | 1.54943i | 0.146234 | − | 0.0803343i | ||||
\(373\) | 0.578049 | − | 1.00121i | 0.0299302 | − | 0.0518407i | −0.850672 | − | 0.525696i | \(-0.823805\pi\) |
0.880603 | + | 0.473856i | \(0.157138\pi\) | |||||||
\(374\) | −5.11837 | + | 8.86528i | −0.264665 | + | 0.458413i | ||||
\(375\) | 1.73166 | + | 0.0368078i | 0.0894225 | + | 0.00190075i | ||||
\(376\) | 10.2875 | − | 5.93951i | 0.530539 | − | 0.306307i | ||||
\(377\) | −54.9397 | −2.82954 | ||||||||
\(378\) | 13.5807 | − | 7.03073i | 0.698516 | − | 0.361622i | ||||
\(379\) | 13.9300 | 0.715533 | 0.357767 | − | 0.933811i | \(-0.383538\pi\) | ||||
0.357767 | + | 0.933811i | \(0.383538\pi\) | |||||||
\(380\) | −3.86756 | + | 2.23294i | −0.198401 | + | 0.114547i | ||||
\(381\) | 27.5898 | + | 0.586443i | 1.41347 | + | 0.0300444i | ||||
\(382\) | 4.60760 | − | 7.98060i | 0.235746 | − | 0.408323i | ||||
\(383\) | −10.7212 | + | 18.5696i | −0.547826 | + | 0.948863i | 0.450597 | + | 0.892727i | \(0.351211\pi\) |
−0.998423 | + | 0.0561353i | \(0.982122\pi\) | |||||||
\(384\) | −1.71668 | + | 0.943062i | −0.0876038 | + | 0.0481254i | ||||
\(385\) | −0.120104 | − | 6.72168i | −0.00612106 | − | 0.342568i | ||||
\(386\) | − | 24.4874i | − | 1.24638i | ||||||
\(387\) | −3.20494 | − | 6.13972i | −0.162916 | − | 0.312099i | ||||
\(388\) | 7.96383i | 0.404302i | ||||||||
\(389\) | −12.0956 | + | 6.98342i | −0.613273 | + | 0.354073i | −0.774245 | − | 0.632886i | \(-0.781870\pi\) |
0.160972 | + | 0.986959i | \(0.448537\pi\) | |||||||
\(390\) | 6.13336 | − | 10.1203i | 0.310575 | − | 0.512463i | ||||
\(391\) | −1.27186 | − | 0.734311i | −0.0643209 | − | 0.0371357i | ||||
\(392\) | 0.768496 | + | 21.4978i | 0.0388149 | + | 1.08580i | ||||
\(393\) | −11.3387 | + | 18.7094i | −0.571963 | + | 0.943766i | ||||
\(394\) | −10.1421 | − | 17.5666i | −0.510951 | − | 0.884993i | ||||
\(395\) | −11.5395 | −0.580615 | ||||||||
\(396\) | 0.247021 | − | 5.80804i | 0.0124133 | − | 0.291865i | ||||
\(397\) | − | 19.7087i | − | 0.989150i | −0.869135 | − | 0.494575i | \(-0.835324\pi\) | ||
0.869135 | − | 0.494575i | \(-0.164676\pi\) | |||||||
\(398\) | −0.0351735 | − | 0.0609223i | −0.00176309 | − | 0.00305376i | ||||
\(399\) | 0.0908751 | − | 26.8355i | 0.00454944 | − | 1.34346i | ||||
\(400\) | 0.946601 | − | 1.63956i | 0.0473301 | − | 0.0819781i | ||||
\(401\) | 13.9721 | + | 8.06682i | 0.697736 | + | 0.402838i | 0.806504 | − | 0.591229i | \(-0.201357\pi\) |
−0.108768 | + | 0.994067i | \(0.534691\pi\) | |||||||
\(402\) | 0.367305 | − | 17.2802i | 0.0183195 | − | 0.861860i | ||||
\(403\) | 7.48184 | + | 12.9589i | 0.372697 | + | 0.645530i | ||||
\(404\) | 2.36818 | 0.117821 | ||||||||
\(405\) | −5.14554 | + | 7.38400i | −0.255684 | + | 0.366914i | ||||
\(406\) | 12.7534 | − | 23.0301i | 0.632940 | − | 1.14297i | ||||
\(407\) | 24.0527 | − | 13.8868i | 1.19225 | − | 0.688345i | ||||
\(408\) | −0.409660 | + | 19.2729i | −0.0202812 | + | 0.954149i | ||||
\(409\) | −1.29227 | − | 0.746092i | −0.0638986 | − | 0.0368919i | 0.467710 | − | 0.883882i | \(-0.345079\pi\) |
−0.531609 | + | 0.846990i | \(0.678412\pi\) | |||||||
\(410\) | −4.24295 | − | 2.44967i | −0.209545 | − | 0.120981i | ||||
\(411\) | 8.56919 | − | 4.70751i | 0.422687 | − | 0.232204i | ||||
\(412\) | 5.72804 | − | 3.30709i | 0.282200 | − | 0.162928i | ||||
\(413\) | −13.2176 | + | 23.8684i | −0.650394 | + | 1.17448i | ||||
\(414\) | −1.35201 | − | 0.0575022i | −0.0664479 | − | 0.00282608i | ||||
\(415\) | −5.99956 | −0.294507 | ||||||||
\(416\) | 12.4074 | + | 21.4903i | 0.608325 | + | 1.05365i | ||||
\(417\) | 13.4082 | + | 8.12596i | 0.656603 | + | 0.397930i | ||||
\(418\) | 14.3346 | + | 8.27607i | 0.701127 | + | 0.404796i | ||||
\(419\) | −1.54293 | + | 2.67244i | −0.0753773 | + | 0.130557i | −0.901250 | − | 0.433299i | \(-0.857349\pi\) |
0.825873 | + | 0.563856i | \(0.190683\pi\) | |||||||
\(420\) | −1.73710 | − | 3.03242i | −0.0847619 | − | 0.147967i | ||||
\(421\) | −6.21491 | − | 10.7645i | −0.302896 | − | 0.524631i | 0.673895 | − | 0.738827i | \(-0.264620\pi\) |
−0.976791 | + | 0.214196i | \(0.931287\pi\) | |||||||
\(422\) | 22.3459i | 1.08778i | ||||||||
\(423\) | −5.36629 | − | 10.2802i | −0.260918 | − | 0.499841i | ||||
\(424\) | −34.7366 | −1.68696 | ||||||||
\(425\) | −1.81084 | − | 3.13647i | −0.0878388 | − | 0.152141i | ||||
\(426\) | −3.24803 | − | 5.91246i | −0.157367 | − | 0.286460i | ||||
\(427\) | −11.1561 | + | 6.70952i | −0.539880 | + | 0.324696i | ||||
\(428\) | 1.07869 | + | 0.622782i | 0.0521404 | + | 0.0301033i | ||||
\(429\) | 27.0254 | + | 0.574445i | 1.30480 | + | 0.0277345i | ||||
\(430\) | 2.22401 | − | 1.28403i | 0.107251 | − | 0.0619217i | ||||
\(431\) | 7.30330i | 0.351788i | 0.984409 | + | 0.175894i | \(0.0562815\pi\) | ||||
−0.984409 | + | 0.175894i | \(0.943718\pi\) | |||||||
\(432\) | 4.36588 | + | 8.81549i | 0.210054 | + | 0.424136i | ||||
\(433\) | − | 33.7509i | − | 1.62197i | −0.585069 | − | 0.810983i | \(-0.698933\pi\) | ||
0.585069 | − | 0.810983i | \(-0.301067\pi\) | |||||||
\(434\) | −7.16903 | + | 0.128097i | −0.344124 | + | 0.00614886i | ||||
\(435\) | −0.329242 | + | 15.4895i | −0.0157860 | + | 0.742666i | ||||
\(436\) | −2.40061 | + | 4.15797i | −0.114968 | + | 0.199131i | ||||
\(437\) | −1.18733 | + | 2.05652i | −0.0567978 | + | 0.0983767i | ||||
\(438\) | −2.69234 | − | 4.90093i | −0.128645 | − | 0.234176i | ||||
\(439\) | 1.83444 | − | 1.05912i | 0.0875532 | − | 0.0505489i | −0.455584 | − | 0.890193i | \(-0.650570\pi\) |
0.543137 | + | 0.839644i | \(0.317236\pi\) | |||||||
\(440\) | 7.80856 | 0.372258 | ||||||||
\(441\) | 20.9995 | + | 0.142226i | 0.999977 | + | 0.00677267i | ||||
\(442\) | −24.7443 | −1.17697 | ||||||||
\(443\) | 18.9054 | − | 10.9150i | 0.898221 | − | 0.518588i | 0.0215986 | − | 0.999767i | \(-0.493124\pi\) |
0.876623 | + | 0.481178i | \(0.159791\pi\) | |||||||
\(444\) | 7.48295 | − | 12.3472i | 0.355125 | − | 0.585973i | ||||
\(445\) | 5.20377 | − | 9.01319i | 0.246682 | − | 0.427266i | ||||
\(446\) | −8.57695 | + | 14.8557i | −0.406130 | + | 0.703438i | ||||
\(447\) | −19.4551 | − | 11.7906i | −0.920195 | − | 0.557678i | ||||
\(448\) | −21.9050 | + | 0.391401i | −1.03491 | + | 0.0184920i | ||||
\(449\) | 33.1318i | 1.56358i | 0.623539 | + | 0.781792i | \(0.285694\pi\) | ||||
−0.623539 | + | 0.781792i | \(0.714306\pi\) | |||||||
\(450\) | −2.81654 | − | 1.78987i | −0.132773 | − | 0.0843752i | ||||
\(451\) | − | 11.1914i | − | 0.526980i | ||||||
\(452\) | −7.19016 | + | 4.15124i | −0.338197 | + | 0.195258i | ||||
\(453\) | 6.22828 | + | 11.3375i | 0.292630 | + | 0.532682i | ||||
\(454\) | 4.00798 | + | 2.31401i | 0.188104 | + | 0.108602i | ||||
\(455\) | 13.9257 | − | 8.37525i | 0.652848 | − | 0.392638i | ||||
\(456\) | 31.1629 | + | 0.662393i | 1.45934 | + | 0.0310194i | ||||
\(457\) | 9.43213 | + | 16.3369i | 0.441217 | + | 0.764210i | 0.997780 | − | 0.0665955i | \(-0.0212137\pi\) |
−0.556563 | + | 0.830805i | \(0.687880\pi\) | |||||||
\(458\) | −1.17825 | −0.0550560 | ||||||||
\(459\) | 18.7806 | + | 1.19903i | 0.876603 | + | 0.0559661i | ||||
\(460\) | 0.309245i | 0.0144186i | ||||||||
\(461\) | −17.0738 | − | 29.5726i | −0.795204 | − | 1.37733i | −0.922709 | − | 0.385496i | \(-0.874030\pi\) |
0.127505 | − | 0.991838i | \(-0.459303\pi\) | |||||||
\(462\) | −6.51431 | + | 11.1954i | −0.303073 | + | 0.520856i | ||||
\(463\) | −11.1023 | + | 19.2297i | −0.515966 | + | 0.893679i | 0.483862 | + | 0.875144i | \(0.339234\pi\) |
−0.999828 | + | 0.0185349i | \(0.994100\pi\) | |||||||
\(464\) | 14.6657 | + | 8.46726i | 0.680839 | + | 0.393083i | ||||
\(465\) | 3.69843 | − | 2.03175i | 0.171511 | − | 0.0942199i | ||||
\(466\) | −2.02739 | − | 3.51154i | −0.0939171 | − | 0.162669i | ||||
\(467\) | 31.1952 | 1.44354 | 0.721772 | − | 0.692131i | \(-0.243328\pi\) | ||||
0.721772 | + | 0.692131i | \(0.243328\pi\) | |||||||
\(468\) | 12.4569 | − | 6.50251i | 0.575819 | − | 0.300578i | ||||
\(469\) | 11.4982 | − | 20.7635i | 0.530938 | − | 0.958771i | ||||
\(470\) | 3.72384 | − | 2.14996i | 0.171768 | − | 0.0991703i | ||||
\(471\) | −17.1303 | − | 10.3817i | −0.789321 | − | 0.478363i | ||||
\(472\) | −27.4447 | − | 15.8452i | −1.26324 | − | 0.729334i | ||||
\(473\) | 5.08022 | + | 2.93306i | 0.233589 | + | 0.134862i | ||||
\(474\) | 19.0139 | + | 11.5232i | 0.873335 | + | 0.529279i | ||||
\(475\) | −5.07147 | + | 2.92801i | −0.232695 | + | 0.134346i | ||||
\(476\) | −3.54006 | + | 6.39266i | −0.162258 | + | 0.293007i | ||||
\(477\) | −1.44094 | + | 33.8800i | −0.0659762 | + | 1.55126i | ||||
\(478\) | 1.56114 | 0.0714047 | ||||||||
\(479\) | 20.0150 | + | 34.6670i | 0.914508 | + | 1.58397i | 0.807620 | + | 0.589704i | \(0.200755\pi\) |
0.106888 | + | 0.994271i | \(0.465911\pi\) | |||||||
\(480\) | 6.13326 | − | 3.36933i | 0.279944 | − | 0.153788i | ||||
\(481\) | 58.1403 | + | 33.5673i | 2.65097 | + | 1.53054i | ||||
\(482\) | 8.86072 | − | 15.3472i | 0.403595 | − | 0.699047i | ||||
\(483\) | −1.60615 | − | 0.934580i | −0.0730825 | − | 0.0425248i | ||||
\(484\) | −1.73247 | − | 3.00072i | −0.0787486 | − | 0.136397i | ||||
\(485\) | 10.4428i | 0.474185i | ||||||||
\(486\) | 15.8520 | − | 7.02848i | 0.719062 | − | 0.318818i | ||||
\(487\) | 34.1091 | 1.54563 | 0.772815 | − | 0.634631i | \(-0.218848\pi\) | ||||
0.772815 | + | 0.634631i | \(0.218848\pi\) | |||||||
\(488\) | −7.56045 | − | 13.0951i | −0.342245 | − | 0.592786i | ||||
\(489\) | −10.1788 | − | 0.216358i | −0.460300 | − | 0.00978404i | ||||
\(490\) | 0.278177 | + | 7.78169i | 0.0125668 | + | 0.351541i | ||||
\(491\) | 6.69917 | + | 3.86777i | 0.302329 | + | 0.174550i | 0.643489 | − | 0.765456i | \(-0.277486\pi\) |
−0.341160 | + | 0.940005i | \(0.610820\pi\) | |||||||
\(492\) | −2.80110 | − | 5.09892i | −0.126284 | − | 0.229877i | ||||
\(493\) | 28.0554 | − | 16.1978i | 1.26355 | − | 0.729513i | ||||
\(494\) | 40.0099i | 1.80013i | ||||||||
\(495\) | 0.323914 | − | 7.61600i | 0.0145589 | − | 0.342314i | ||||
\(496\) | − | 4.61237i | − | 0.207102i | ||||||
\(497\) | −0.165494 | − | 9.26199i | −0.00742344 | − | 0.415457i | ||||
\(498\) | 9.88560 | + | 5.99110i | 0.442984 | + | 0.268468i | ||||
\(499\) | 12.8837 | − | 22.3153i | 0.576754 | − | 0.998968i | −0.419094 | − | 0.907943i | \(-0.637652\pi\) |
0.995849 | − | 0.0910253i | \(-0.0290144\pi\) | |||||||
\(500\) | −0.381305 | + | 0.660440i | −0.0170525 | + | 0.0295358i | ||||
\(501\) | 0.642125 | − | 1.05954i | 0.0286880 | − | 0.0473366i | ||||
\(502\) | 25.0345 | − | 14.4537i | 1.11734 | − | 0.645099i | ||||
\(503\) | −8.17014 | −0.364289 | −0.182144 | − | 0.983272i | \(-0.558304\pi\) | ||||
−0.182144 | + | 0.983272i | \(0.558304\pi\) | |||||||
\(504\) | −0.600926 | + | 24.3844i | −0.0267674 | + | 1.08617i | ||||
\(505\) | 3.10536 | 0.138187 | ||||||||
\(506\) | 0.992615 | − | 0.573087i | 0.0441271 | − | 0.0254768i | ||||
\(507\) | 20.6190 | + | 37.5332i | 0.915721 | + | 1.66691i | ||||
\(508\) | −6.07517 | + | 10.5225i | −0.269542 | + | 0.466861i | ||||
\(509\) | −3.11003 | + | 5.38673i | −0.137850 | + | 0.238763i | −0.926682 | − | 0.375845i | \(-0.877352\pi\) |
0.788833 | + | 0.614608i | \(0.210686\pi\) | |||||||
\(510\) | −0.148287 | + | 6.97632i | −0.00656627 | + | 0.308917i | ||||
\(511\) | −0.137181 | − | 7.67741i | −0.00606853 | − | 0.339629i | ||||
\(512\) | − | 19.2848i | − | 0.852275i | ||||||
\(513\) | 1.93876 | − | 30.3670i | 0.0855983 | − | 1.34074i | ||||
\(514\) | − | 5.01025i | − | 0.220993i | ||||||
\(515\) | 7.51109 | − | 4.33653i | 0.330978 | − | 0.191090i | ||||
\(516\) | 3.04873 | + | 0.0648032i | 0.134213 | + | 0.00285280i | ||||
\(517\) | 8.50621 | + | 4.91106i | 0.374103 | + | 0.215988i | ||||
\(518\) | −27.5674 | + | 16.5796i | −1.21124 | + | 0.728468i | ||||
\(519\) | −1.55711 | − | 2.83444i | −0.0683494 | − | 0.124418i | ||||
\(520\) | 9.43743 | + | 16.3461i | 0.413859 | + | 0.716825i | ||||
\(521\) | −9.25984 | −0.405681 | −0.202840 | − | 0.979212i | \(-0.565017\pi\) | ||||
−0.202840 | + | 0.979212i | \(0.565017\pi\) | |||||||
\(522\) | 16.0102 | − | 25.1936i | 0.700747 | − | 1.10270i | ||||
\(523\) | − | 30.4725i | − | 1.33247i | −0.745743 | − | 0.666234i | \(-0.767905\pi\) | ||
0.745743 | − | 0.666234i | \(-0.232095\pi\) | |||||||
\(524\) | −4.81618 | − | 8.34188i | −0.210396 | − | 0.364417i | ||||
\(525\) | −2.27784 | − | 3.97636i | −0.0994129 | − | 0.173543i | ||||
\(526\) | −15.2321 | + | 26.3829i | −0.664153 | + | 1.15035i | ||||
\(527\) | −7.64133 | − | 4.41172i | −0.332862 | − | 0.192178i | ||||
\(528\) | −7.12567 | − | 4.31846i | −0.310105 | − | 0.187937i | ||||
\(529\) | −11.4178 | − | 19.7762i | −0.496425 | − | 0.859834i | ||||
\(530\) | −12.5738 | −0.546172 | ||||||||
\(531\) | −16.5929 | + | 26.1106i | −0.720071 | + | 1.13310i | ||||
\(532\) | 10.3365 | + | 5.72404i | 0.448144 | + | 0.248169i | ||||
\(533\) | 23.4275 | − | 13.5259i | 1.01476 | − | 0.585871i | ||||
\(534\) | −17.5748 | + | 9.65478i | −0.760537 | + | 0.417803i | ||||
\(535\) | 1.41447 | + | 0.816644i | 0.0611528 | + | 0.0353066i | ||||
\(536\) | 23.8747 | + | 13.7840i | 1.03123 | + | 0.595380i | ||||
\(537\) | −0.413084 | + | 19.4340i | −0.0178259 | + | 0.838638i | ||||
\(538\) | 0.959335 | − | 0.553872i | 0.0413599 | − | 0.0238791i | ||||
\(539\) | −15.0762 | + | 9.43798i | −0.649378 | + | 0.406523i | ||||
\(540\) | −1.75864 | − | 3.55102i | −0.0756799 | − | 0.152811i | ||||
\(541\) | 20.0897 | 0.863723 | 0.431862 | − | 0.901940i | \(-0.357857\pi\) | ||||
0.431862 | + | 0.901940i | \(0.357857\pi\) | |||||||
\(542\) | 2.31731 | + | 4.01370i | 0.0995370 | + | 0.172403i | ||||
\(543\) | −0.299975 | + | 14.1126i | −0.0128731 | + | 0.605630i | ||||
\(544\) | −12.6719 | − | 7.31614i | −0.543305 | − | 0.313677i | ||||
\(545\) | −3.14788 | + | 5.45229i | −0.134840 | + | 0.233550i | ||||
\(546\) | −31.3092 | − | 0.106024i | −1.33991 | − | 0.00453743i | ||||
\(547\) | −9.14422 | − | 15.8383i | −0.390979 | − | 0.677195i | 0.601600 | − | 0.798797i | \(-0.294530\pi\) |
−0.992579 | + | 0.121602i | \(0.961197\pi\) | |||||||
\(548\) | 4.30479i | 0.183892i | ||||||||
\(549\) | −13.0858 | + | 6.83079i | −0.558487 | + | 0.291531i | ||||
\(550\) | 2.82651 | 0.120523 | ||||||||
\(551\) | −26.1908 | − | 45.3638i | −1.11577 | − | 1.93256i | ||||
\(552\) | 1.11868 | − | 1.84588i | 0.0476142 | − | 0.0785657i | ||||
\(553\) | 15.7352 | + | 26.1634i | 0.669130 | + | 1.11258i | ||||
\(554\) | −18.1634 | − | 10.4866i | −0.771689 | − | 0.445535i | ||||
\(555\) | 9.81228 | − | 16.1907i | 0.416508 | − | 0.687258i | ||||
\(556\) | −5.97825 | + | 3.45154i | −0.253534 | + | 0.146378i | ||||
\(557\) | − | 41.4921i | − | 1.75808i | −0.476749 | − | 0.879039i | \(-0.658185\pi\) | ||
0.476749 | − | 0.879039i | \(-0.341815\pi\) | |||||||
\(558\) | −8.12287 | − | 0.345472i | −0.343868 | − | 0.0146250i | ||||
\(559\) | 14.1796i | 0.599734i | ||||||||
\(560\) | −5.00814 | + | 0.0894862i | −0.211633 | + | 0.00378148i | ||||
\(561\) | −13.9701 | + | 7.67451i | −0.589818 | + | 0.324018i | ||||
\(562\) | −5.08303 | + | 8.80407i | −0.214415 | + | 0.371377i | ||||
\(563\) | 1.18747 | − | 2.05676i | 0.0500460 | − | 0.0866822i | −0.839917 | − | 0.542715i | \(-0.817397\pi\) |
0.889963 | + | 0.456032i | \(0.150730\pi\) | |||||||
\(564\) | 5.10473 | + | 0.108505i | 0.214948 | + | 0.00456889i | ||||
\(565\) | −9.42835 | + | 5.44346i | −0.396654 | + | 0.229008i | ||||
\(566\) | 7.31113 | 0.307310 | ||||||||
\(567\) | 23.7581 | + | 1.59762i | 0.997747 | + | 0.0670937i | ||||
\(568\) | 10.7596 | 0.451464 | ||||||||
\(569\) | −5.01551 | + | 2.89570i | −0.210261 | + | 0.121394i | −0.601433 | − | 0.798923i | \(-0.705403\pi\) |
0.391172 | + | 0.920318i | \(0.372070\pi\) | |||||||
\(570\) | 11.2803 | + | 0.239771i | 0.472478 | + | 0.0100429i | ||||
\(571\) | −8.66539 | + | 15.0089i | −0.362635 | + | 0.628102i | −0.988394 | − | 0.151914i | \(-0.951456\pi\) |
0.625759 | + | 0.780017i | \(0.284790\pi\) | |||||||
\(572\) | −5.95089 | + | 10.3072i | −0.248819 | + | 0.430968i | ||||
\(573\) | 12.5760 | − | 6.90866i | 0.525370 | − | 0.288613i | ||||
\(574\) | 0.231578 | + | 12.9604i | 0.00966586 | + | 0.540955i | ||||
\(575\) | 0.405508i | 0.0169108i | ||||||||
\(576\) | −24.8194 | − | 1.05559i | −1.03414 | − | 0.0439829i | ||||
\(577\) | − | 0.500645i | − | 0.0208421i | −0.999946 | − | 0.0104211i | \(-0.996683\pi\) | ||
0.999946 | − | 0.0104211i | \(-0.00331718\pi\) | |||||||
\(578\) | −3.74106 | + | 2.15990i | −0.155607 | + | 0.0898400i | ||||
\(579\) | 19.7617 | − | 32.6077i | 0.821269 | − | 1.35513i | ||||
\(580\) | −5.90757 | − | 3.41074i | −0.245299 | − | 0.141623i | ||||
\(581\) | 8.18099 | + | 13.6027i | 0.339405 | + | 0.564336i | ||||
\(582\) | 10.4281 | − | 17.2069i | 0.432260 | − | 0.713249i | ||||
\(583\) | −14.3609 | − | 24.8738i | −0.594768 | − | 1.03017i | ||||
\(584\) | 8.91883 | 0.369064 | ||||||||
\(585\) | 16.3345 | − | 8.52664i | 0.675349 | − | 0.352533i | ||||
\(586\) | 16.1904i | 0.668819i | ||||||||
\(587\) | −3.88771 | − | 6.73371i | −0.160463 | − | 0.277930i | 0.774572 | − | 0.632486i | \(-0.217965\pi\) |
−0.935035 | + | 0.354556i | \(0.884632\pi\) | |||||||
\(588\) | −4.50666 | + | 8.07351i | −0.185851 | + | 0.332946i | ||||
\(589\) | −7.13347 | + | 12.3555i | −0.293929 | + | 0.509101i | ||||
\(590\) | −9.93433 | − | 5.73559i | −0.408990 | − | 0.236130i | ||||
\(591\) | 0.671188 | − | 31.5767i | 0.0276090 | − | 1.29889i | ||||
\(592\) | −10.3467 | − | 17.9210i | −0.425248 | − | 0.736550i | ||||
\(593\) | 38.4594 | 1.57934 | 0.789668 | − | 0.613534i | \(-0.210253\pi\) | ||||
0.789668 | + | 0.613534i | \(0.210253\pi\) | |||||||
\(594\) | −8.13898 | + | 12.2256i | −0.333947 | + | 0.501622i | ||||
\(595\) | −4.64202 | + | 8.38260i | −0.190304 | + | 0.343653i | ||||
\(596\) | 8.67434 | − | 5.00814i | 0.355315 | − | 0.205141i | ||||
\(597\) | 0.00232773 | − | 0.109510i | 9.52676e−5 | − | 0.00448196i | ||||
\(598\) | 2.39935 | + | 1.38527i | 0.0981168 | + | 0.0566478i | ||||
\(599\) | −41.6146 | − | 24.0262i | −1.70033 | − | 0.981685i | −0.945421 | − | 0.325852i | \(-0.894349\pi\) |
−0.754907 | − | 0.655832i | \(-0.772318\pi\) | |||||||
\(600\) | 4.66512 | − | 2.56280i | 0.190453 | − | 0.104626i | ||||
\(601\) | 0.576973 | − | 0.333116i | 0.0235352 | − | 0.0135881i | −0.488186 | − | 0.872739i | \(-0.662341\pi\) |
0.511721 | + | 0.859151i | \(0.329008\pi\) | |||||||
\(602\) | −5.94394 | − | 3.29157i | −0.242257 | − | 0.134154i | ||||
\(603\) | 14.4345 | − | 22.7141i | 0.587818 | − | 0.924991i | ||||
\(604\) | −5.69547 | −0.231745 | ||||||||
\(605\) | −2.27176 | − | 3.93480i | −0.0923601 | − | 0.159972i | ||||
\(606\) | −5.11676 | − | 3.10098i | −0.207854 | − | 0.125969i | ||||
\(607\) | −16.6252 | − | 9.59855i | −0.674795 | − | 0.389593i | 0.123096 | − | 0.992395i | \(-0.460718\pi\) |
−0.797891 | + | 0.602802i | \(0.794051\pi\) | |||||||
\(608\) | −11.8297 | + | 20.4897i | −0.479758 | + | 0.830966i | ||||
\(609\) | 35.5682 | − | 20.3750i | 1.44130 | − | 0.825637i | ||||
\(610\) | −2.73670 | − | 4.74011i | −0.110806 | − | 0.191921i | ||||
\(611\) | 23.7421i | 0.960501i | ||||||||
\(612\) | −4.44408 | + | 6.99320i | −0.179641 | + | 0.282683i | ||||
\(613\) | −0.0966368 | −0.00390312 | −0.00195156 | − | 0.999998i | \(-0.500621\pi\) | ||||
−0.00195156 | + | 0.999998i | \(0.500621\pi\) | |||||||
\(614\) | 15.9644 | + | 27.6512i | 0.644272 | + | 1.11591i | ||||
\(615\) | −3.67305 | − | 6.68613i | −0.148112 | − | 0.269611i | ||||
\(616\) | −10.6477 | − | 17.7043i | −0.429010 | − | 0.713325i | ||||
\(617\) | 15.4782 | + | 8.93632i | 0.623127 | + | 0.359763i | 0.778086 | − | 0.628158i | \(-0.216191\pi\) |
−0.154958 | + | 0.987921i | \(0.549524\pi\) | |||||||
\(618\) | −16.7066 | − | 0.355112i | −0.672038 | − | 0.0142847i | ||||
\(619\) | 2.72063 | − | 1.57075i | 0.109351 | − | 0.0631339i | −0.444327 | − | 0.895865i | \(-0.646557\pi\) |
0.553678 | + | 0.832731i | \(0.313224\pi\) | |||||||
\(620\) | 1.85793i | 0.0746165i | ||||||||
\(621\) | −1.75395 | − | 1.16767i | −0.0703837 | − | 0.0468568i | ||||
\(622\) | 0.911985i | 0.0365673i | ||||||||
\(623\) | −27.5313 | + | 0.491934i | −1.10302 | + | 0.0197089i | ||||
\(624\) | 0.428004 | − | 20.1359i | 0.0171339 | − | 0.806081i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −10.1953 | + | 17.6588i | −0.407486 | + | 0.705787i | ||||
\(627\) | 12.4092 | + | 22.5887i | 0.495575 | + | 0.902106i | ||||
\(628\) | 7.63778 | − | 4.40968i | 0.304781 | − | 0.175965i | ||||
\(629\) | −39.5864 | −1.57841 | ||||||||
\(630\) | −0.217521 | + | 8.82656i | −0.00866625 | + | 0.351659i | ||||
\(631\) | 39.6381 | 1.57797 | 0.788985 | − | 0.614413i | \(-0.210607\pi\) | ||||
0.788985 | + | 0.614413i | \(0.210607\pi\) | |||||||
\(632\) | −30.7107 | + | 17.7308i | −1.22161 | + | 0.705295i | ||||
\(633\) | −18.0335 | + | 29.7561i | −0.716766 | + | 1.18270i | ||||
\(634\) | −8.96154 | + | 15.5218i | −0.355908 | + | 0.616451i | ||||
\(635\) | −7.96628 | + | 13.7980i | −0.316132 | + | 0.547557i | ||||
\(636\) | −12.7687 | − | 7.73840i | −0.506313 | − | 0.306848i | ||||
\(637\) | −37.9782 | − | 20.1532i | −1.50475 | − | 0.798497i | ||||
\(638\) | 25.2829i | 1.00096i | ||||||||
\(639\) | 0.446331 | − | 10.4943i | 0.0176566 | − | 0.415148i | ||||
\(640\) | − | 1.13083i | − | 0.0447001i | ||||||
\(641\) | 12.9030 | − | 7.44956i | 0.509638 | − | 0.294240i | −0.223047 | − | 0.974808i | \(-0.571600\pi\) |
0.732685 | + | 0.680568i | \(0.238267\pi\) | |||||||
\(642\) | −1.51516 | − | 2.75808i | −0.0597985 | − | 0.108853i | ||||
\(643\) | −30.1617 | − | 17.4139i | −1.18946 | − | 0.686737i | −0.231278 | − | 0.972888i | \(-0.574291\pi\) |
−0.958185 | + | 0.286151i | \(0.907624\pi\) | |||||||
\(644\) | 0.701147 | − | 0.421686i | 0.0276291 | − | 0.0166167i | ||||
\(645\) | 3.99776 | + | 0.0849755i | 0.157411 | + | 0.00334591i | ||||
\(646\) | −11.7961 | − | 20.4314i | −0.464110 | − | 0.803862i | ||||
\(647\) | 6.52021 | 0.256336 | 0.128168 | − | 0.991752i | \(-0.459090\pi\) | ||||
0.128168 | + | 0.991752i | \(0.459090\pi\) | |||||||
\(648\) | −2.34836 | + | 27.5578i | −0.0922521 | + | 1.08257i | ||||
\(649\) | − | 26.2031i | − | 1.02856i | ||||||
\(650\) | 3.41613 | + | 5.91691i | 0.133992 | + | 0.232080i | ||||
\(651\) | −9.64973 | − | 5.61493i | −0.378203 | − | 0.220067i | ||||
\(652\) | 2.24133 | − | 3.88210i | 0.0877773 | − | 0.152035i | ||||
\(653\) | −25.9570 | − | 14.9863i | −1.01577 | − | 0.586458i | −0.102897 | − | 0.994692i | \(-0.532811\pi\) |
−0.912877 | + | 0.408234i | \(0.866145\pi\) | |||||||
\(654\) | 10.6314 | − | 5.84041i | 0.415722 | − | 0.228378i | ||||
\(655\) | −6.31539 | − | 10.9386i | −0.246763 | − | 0.427405i | ||||
\(656\) | −8.33838 | −0.325559 | ||||||||
\(657\) | 0.369971 | − | 8.69889i | 0.0144339 | − | 0.339376i | ||||
\(658\) | −9.95241 | − | 5.51134i | −0.387985 | − | 0.214854i | ||||
\(659\) | −11.1768 | + | 6.45295i | −0.435388 | + | 0.251371i | −0.701639 | − | 0.712532i | \(-0.747548\pi\) |
0.266251 | + | 0.963904i | \(0.414215\pi\) | |||||||
\(660\) | 2.87033 | + | 1.73954i | 0.111727 | + | 0.0677116i | ||||
\(661\) | −27.6131 | − | 15.9424i | −1.07402 | − | 0.620088i | −0.144746 | − | 0.989469i | \(-0.546236\pi\) |
−0.929278 | + | 0.369381i | \(0.879570\pi\) | |||||||
\(662\) | 2.94520 | + | 1.70041i | 0.114468 | + | 0.0660883i | ||||
\(663\) | −32.9498 | − | 19.9690i | −1.27966 | − | 0.775532i | ||||
\(664\) | −15.9670 | + | 9.21854i | −0.619639 | + | 0.357749i | ||||
\(665\) | 13.5541 | + | 7.50585i | 0.525606 | + | 0.291064i | ||||
\(666\) | −32.3358 | + | 16.8793i | −1.25299 | + | 0.654061i | ||||
\(667\) | −3.62723 | −0.140447 | ||||||||
\(668\) | 0.272746 | + | 0.472410i | 0.0105529 | + | 0.0182781i | ||||
\(669\) | −23.4099 | + | 12.8603i | −0.905080 | + | 0.497208i | ||||
\(670\) | 8.64207 | + | 4.98950i | 0.333872 | + | 0.192761i | ||||
\(671\) | 6.25133 | − | 10.8276i | 0.241330 | − | 0.417996i | ||||
\(672\) | −16.0025 | − | 9.31147i | −0.617312 | − | 0.359198i | ||||
\(673\) | 10.0600 | + | 17.4244i | 0.387784 | + | 0.671662i | 0.992151 | − | 0.125044i | \(-0.0399072\pi\) |
−0.604367 | + | 0.796706i | \(0.706574\pi\) | |||||||
\(674\) | − | 13.2082i | − | 0.508760i | ||||||
\(675\) | −2.30608 | − | 4.65639i | −0.0887611 | − | 0.179225i | ||||
\(676\) | −18.8551 | −0.725196 | ||||||||
\(677\) | 4.43197 | + | 7.67639i | 0.170334 | + | 0.295028i | 0.938537 | − | 0.345179i | \(-0.112182\pi\) |
−0.768202 | + | 0.640207i | \(0.778849\pi\) | |||||||
\(678\) | 20.9711 | + | 0.445757i | 0.805389 | + | 0.0171192i | ||||
\(679\) | 23.6769 | − | 14.2399i | 0.908638 | − | 0.546475i | ||||
\(680\) | −9.63861 | − | 5.56485i | −0.369624 | − | 0.213402i | ||||
\(681\) | 3.46963 | + | 6.31585i | 0.132957 | + | 0.242024i | ||||
\(682\) | 5.96361 | − | 3.44309i | 0.228358 | − | 0.131843i | ||||
\(683\) | − | 44.7970i | − | 1.71411i | −0.515226 | − | 0.857054i | \(-0.672292\pi\) | ||
0.515226 | − | 0.857054i | \(-0.327708\pi\) | |||||||
\(684\) | 11.3075 | + | 7.18578i | 0.432355 | + | 0.274755i | ||||
\(685\) | 5.64481i | 0.215677i | ||||||||
\(686\) | 17.2640 | − | 11.2418i | 0.659143 | − | 0.429214i | ||||
\(687\) | −1.56897 | − | 0.950864i | −0.0598600 | − | 0.0362777i | ||||
\(688\) | 2.18535 | − | 3.78514i | 0.0833157 | − | 0.144307i | ||||
\(689\) | 34.7132 | − | 60.1251i | 1.32247 | − | 2.29058i | ||||
\(690\) | 0.404936 | − | 0.668164i | 0.0154157 | − | 0.0254366i | ||||
\(691\) | −34.1809 | + | 19.7344i | −1.30030 | + | 0.750730i | −0.980456 | − | 0.196739i | \(-0.936965\pi\) |
−0.319847 | + | 0.947469i | \(0.603632\pi\) | |||||||
\(692\) | 1.42390 | 0.0541285 | ||||||||
\(693\) | −17.7094 | + | 9.65076i | −0.672723 | + | 0.366602i | ||||
\(694\) | 3.57360 | 0.135652 | ||||||||
\(695\) | −7.83919 | + | 4.52596i | −0.297357 | + | 0.171679i | ||||
\(696\) | 22.9240 | + | 41.7291i | 0.868932 | + | 1.58174i | ||||
\(697\) | −7.97564 | + | 13.8142i | −0.302099 | + | 0.523251i | ||||
\(698\) | −4.50968 | + | 7.81100i | −0.170694 | + | 0.295651i | ||||
\(699\) | 0.134170 | − | 6.31214i | 0.00507476 | − | 0.238747i | ||||
\(700\) | 2.01736 | − | 0.0360464i | 0.0762489 | − | 0.00136243i | ||||
\(701\) | − | 12.5209i | − | 0.472906i | −0.971643 | − | 0.236453i | \(-0.924015\pi\) | ||
0.971643 | − | 0.236453i | \(-0.0759850\pi\) | |||||||
\(702\) | −35.4293 | − | 2.26196i | −1.33719 | − | 0.0853722i | ||||
\(703\) | 64.0086i | 2.41413i | ||||||||
\(704\) | 18.2218 | − | 10.5204i | 0.686761 | − | 0.396501i | ||||
\(705\) | 6.69376 | + | 0.142281i | 0.252101 | + | 0.00535862i | ||||
\(706\) | −35.6547 | − | 20.5852i | −1.34188 | − | 0.774735i | ||||
\(707\) | −4.23446 | − | 7.04074i | −0.159253 | − | 0.264794i | ||||
\(708\) | −6.55842 | − | 11.9385i | −0.246481 | − | 0.448675i | ||||
\(709\) | 4.28894 | + | 7.42866i | 0.161074 | + | 0.278989i | 0.935254 | − | 0.353977i | \(-0.115171\pi\) |
−0.774180 | + | 0.632966i | \(0.781837\pi\) | |||||||
\(710\) | 3.89473 | 0.146167 | ||||||||
\(711\) | 16.0197 | + | 30.6889i | 0.600784 | + | 1.15092i | ||||
\(712\) | − | 31.9831i | − | 1.19862i | ||||||
\(713\) | 0.493966 | + | 0.855574i | 0.0184992 | + | 0.0320415i | ||||
\(714\) | 16.0195 | − | 9.17670i | 0.599516 | − | 0.343429i | ||||
\(715\) | −7.80331 | + | 13.5157i | −0.291827 | + | 0.505460i | ||||
\(716\) | −7.41195 | − | 4.27929i | −0.276998 | − | 0.159925i | ||||
\(717\) | 2.07883 | + | 1.25986i | 0.0776352 | + | 0.0470503i | ||||
\(718\) | −2.17862 | − | 3.77348i | −0.0813053 | − | 0.140825i | ||||
\(719\) | 35.0591 | 1.30748 | 0.653741 | − | 0.756718i | \(-0.273199\pi\) | ||||
0.653741 | + | 0.756718i | \(0.273199\pi\) | |||||||
\(720\) | −5.67448 | − | 0.241340i | −0.211475 | − | 0.00899421i | ||||
\(721\) | −20.0743 | − | 11.1165i | −0.747605 | − | 0.414001i | ||||
\(722\) | −14.7326 | + | 8.50584i | −0.548289 | + | 0.316555i | ||||
\(723\) | 24.1845 | − | 13.2858i | 0.899430 | − | 0.494104i | ||||
\(724\) | −5.38243 | − | 3.10755i | −0.200036 | − | 0.115491i | ||||
\(725\) | −7.74651 | − | 4.47245i | −0.287698 | − | 0.166103i | ||||
\(726\) | −0.186031 | + | 8.75201i | −0.00690426 | + | 0.324818i | ||||
\(727\) | −13.1610 | + | 7.59851i | −0.488115 | + | 0.281813i | −0.723792 | − | 0.690018i | \(-0.757603\pi\) |
0.235677 | + | 0.971831i | \(0.424269\pi\) | |||||||
\(728\) | 24.1925 | − | 43.6869i | 0.896633 | − | 1.61915i | ||||
\(729\) | 26.7808 | + | 3.43360i | 0.991881 | + | 0.127170i | ||||
\(730\) | 3.22841 | 0.119489 | ||||||||
\(731\) | −4.18056 | − | 7.24094i | −0.154624 | − | 0.267816i | ||||
\(732\) | 0.138117 | − | 6.49786i | 0.00510495 | − | 0.240168i | ||||
\(733\) | 26.8615 | + | 15.5085i | 0.992151 | + | 0.572818i | 0.905916 | − | 0.423456i | \(-0.139183\pi\) |
0.0862342 | + | 0.996275i | \(0.472517\pi\) | |||||||
\(734\) | 4.78504 | − | 8.28792i | 0.176619 | − | 0.305913i | ||||
\(735\) | −5.90951 | + | 10.5867i | −0.217976 | + | 0.390495i | ||||
\(736\) | 0.819163 | + | 1.41883i | 0.0301948 | + | 0.0522989i | ||||
\(737\) | 22.7946i | 0.839650i | ||||||||
\(738\) | −0.624554 | + | 14.6848i | −0.0229902 | + | 0.540553i | ||||
\(739\) | 37.9318 | 1.39534 | 0.697671 | − | 0.716418i | \(-0.254220\pi\) | ||||
0.697671 | + | 0.716418i | \(0.254220\pi\) | |||||||
\(740\) | 4.16782 | + | 7.21887i | 0.153212 | + | 0.265371i | ||||
\(741\) | −32.2885 | + | 53.2776i | −1.18615 | + | 1.95720i | ||||
\(742\) | 17.1457 | + | 28.5085i | 0.629437 | + | 1.04658i | ||||
\(743\) | −31.5513 | − | 18.2161i | −1.15750 | − | 0.668285i | −0.206799 | − | 0.978383i | \(-0.566305\pi\) |
−0.950704 | + | 0.310099i | \(0.899638\pi\) | |||||||
\(744\) | 6.72101 | − | 11.0900i | 0.246404 | − | 0.406578i | ||||
\(745\) | 11.3745 | − | 6.56709i | 0.416731 | − | 0.240600i | ||||
\(746\) | − | 1.28602i | − | 0.0470845i | ||||||
\(747\) | 8.32887 | + | 15.9556i | 0.304737 | + | 0.583786i | ||||
\(748\) | − | 7.01798i | − | 0.256603i | ||||||
\(749\) | −0.0772008 | − | 4.32059i | −0.00282086 | − | 0.157871i | ||||
\(750\) | 1.68867 | − | 0.927673i | 0.0616613 | − | 0.0338738i | ||||
\(751\) | −9.01745 | + | 15.6187i | −0.329051 | + | 0.569934i | −0.982324 | − | 0.187189i | \(-0.940062\pi\) |
0.653272 | + | 0.757123i | \(0.273396\pi\) | |||||||
\(752\) | 3.65910 | − | 6.33775i | 0.133434 | − | 0.231114i | ||||
\(753\) | 45.0005 | + | 0.956521i | 1.63991 | + | 0.0348576i | ||||
\(754\) | −52.9262 | + | 30.5569i | −1.92746 | + | 1.11282i | ||||
\(755\) | −7.46838 | −0.271802 | ||||||||
\(756\) | −5.65309 | + | 8.82951i | −0.205601 | + | 0.321126i | ||||
\(757\) | −24.9919 | −0.908346 | −0.454173 | − | 0.890914i | \(-0.650065\pi\) | ||||
−0.454173 | + | 0.890914i | \(0.650065\pi\) | |||||||
\(758\) | 13.4194 | − | 7.74770i | 0.487415 | − | 0.281409i | ||||
\(759\) | 1.78427 | + | 0.0379260i | 0.0647648 | + | 0.00137663i | ||||
\(760\) | −8.99800 | + | 15.5850i | −0.326392 | + | 0.565327i | ||||
\(761\) | −1.65773 | + | 2.87127i | −0.0600925 | + | 0.104083i | −0.894507 | − | 0.447055i | \(-0.852473\pi\) |
0.834414 | + | 0.551138i | \(0.185806\pi\) | |||||||
\(762\) | 26.9048 | − | 14.7802i | 0.974657 | − | 0.535431i | ||||
\(763\) | 16.6544 | − | 0.297582i | 0.602928 | − | 0.0107732i | ||||
\(764\) | 6.31764i | 0.228564i | ||||||||
\(765\) | −5.82745 | + | 9.17008i | −0.210692 | + | 0.331545i | ||||
\(766\) | 23.8520i | 0.861809i | ||||||||
\(767\) | 54.8525 | − | 31.6691i | 1.98061 | − | 1.14351i | ||||
\(768\) | 13.7379 | − | 22.6682i | 0.495724 | − | 0.817968i | ||||
\(769\) | 3.97840 | + | 2.29693i | 0.143465 | + | 0.0828294i | 0.570014 | − | 0.821635i | \(-0.306938\pi\) |
−0.426550 | + | 0.904464i | \(0.640271\pi\) | |||||||
\(770\) | −3.85423 | − | 6.40852i | −0.138897 | − | 0.230947i | ||||
\(771\) | 4.04335 | − | 6.67171i | 0.145618 | − | 0.240276i | ||||
\(772\) | 8.39389 | + | 14.5386i | 0.302103 | + | 0.523257i | ||||
\(773\) | 15.6304 | 0.562187 | 0.281094 | − | 0.959680i | \(-0.409303\pi\) | ||||
0.281094 | + | 0.959680i | \(0.409303\pi\) | |||||||
\(774\) | −6.50233 | − | 4.13214i | −0.233721 | − | 0.148527i | ||||
\(775\) | 2.43628i | 0.0875138i | ||||||||
\(776\) | 16.0458 | + | 27.7922i | 0.576011 | + | 0.997681i | ||||
\(777\) | −50.0890 | − | 0.169620i | −1.79693 | − | 0.00608509i | ||||
\(778\) | −7.76821 | + | 13.4549i | −0.278504 | + | 0.482383i | ||||
\(779\) | 22.3367 | + | 12.8961i | 0.800294 | + | 0.462050i | ||||
\(780\) | −0.172407 | + | 8.11104i | −0.00617315 | + | 0.290422i | ||||
\(781\) | 4.44828 | + | 7.70465i | 0.159172 | + | 0.275694i | ||||
\(782\) | −1.63367 | −0.0584198 | ||||||||
\(783\) | 41.6510 | − | 20.6277i | 1.48848 | − | 0.737173i | ||||
\(784\) | 7.03199 | + | 11.2329i | 0.251143 | + | 0.401174i | ||||
\(785\) | 10.0153 | − | 5.78234i | 0.357462 | − | 0.206381i | ||||
\(786\) | −0.517158 | + | 24.3302i | −0.0184464 | + | 0.867830i | ||||
\(787\) | 29.5534 | + | 17.0627i | 1.05347 | + | 0.608219i | 0.923618 | − | 0.383315i | \(-0.125218\pi\) |
0.129848 | + | 0.991534i | \(0.458551\pi\) | |||||||
\(788\) | 12.0431 | + | 6.95308i | 0.429017 | + | 0.247693i | ||||
\(789\) | −41.5746 | + | 22.8391i | −1.48010 | + | 0.813095i | ||||
\(790\) | −11.1166 | + | 6.41815i | −0.395509 | + | 0.228347i | ||||
\(791\) | 25.1984 | + | 13.9541i | 0.895951 | + | 0.496150i | ||||
\(792\) | −10.8402 | − | 20.7666i | −0.385190 | − | 0.737909i | ||||
\(793\) | 30.2215 | 1.07320 | ||||||||
\(794\) | −10.9618 | − | 18.9863i | −0.389018 | − | 0.673800i | ||||
\(795\) | −16.7434 | − | 10.1473i | −0.593829 | − | 0.359886i | ||||
\(796\) | 0.0417663 | + | 0.0241138i | 0.00148037 | + | 0.000854691i | ||||
\(797\) | 19.2032 | − | 33.2609i | 0.680211 | − | 1.17816i | −0.294705 | − | 0.955588i | \(-0.595221\pi\) |
0.974916 | − | 0.222572i | \(-0.0714452\pi\) | |||||||
\(798\) | −14.8381 | − | 25.9025i | −0.525263 | − | 0.916940i | ||||
\(799\) | −6.99984 | − | 12.1241i | −0.247637 | − | 0.428919i | ||||
\(800\) | 4.04019i | 0.142842i | ||||||||
\(801\) | −31.1944 | − | 1.32672i | −1.10220 | − | 0.0468774i | ||||
\(802\) | 17.9467 | 0.633721 | ||||||||
\(803\) | 3.68725 | + | 6.38651i | 0.130120 | + | 0.225375i | ||||
\(804\) | 5.70530 | + | 10.3855i | 0.201210 | + | 0.366268i | ||||
\(805\) | 0.919403 | − | 0.552950i | 0.0324047 | − | 0.0194889i | ||||
\(806\) | 14.4153 | + | 8.32265i | 0.507756 | + | 0.293153i | ||||
\(807\) | 1.72444 | + | 0.0366544i | 0.0607033 | + | 0.00129030i | ||||
\(808\) | 8.26448 | − | 4.77150i | 0.290743 | − | 0.167861i | ||||
\(809\) | − | 11.7111i | − | 0.411740i | −0.978579 | − | 0.205870i | \(-0.933998\pi\) | ||
0.978579 | − | 0.205870i | \(-0.0660023\pi\) | |||||||
\(810\) | −0.850050 | + | 9.97527i | −0.0298677 | + | 0.350495i | ||||
\(811\) | − | 34.9447i | − | 1.22707i | −0.789666 | − | 0.613537i | \(-0.789746\pi\) | ||
0.789666 | − | 0.613537i | \(-0.210254\pi\) | |||||||
\(812\) | 0.322431 | + | 18.0451i | 0.0113151 | + | 0.633257i | ||||
\(813\) | −0.153356 | + | 7.21479i | −0.00537843 | + | 0.253034i | ||||
\(814\) | 15.4474 | − | 26.7558i | 0.541433 | − | 0.937789i | ||||
\(815\) | 2.93902 | − | 5.09054i | 0.102949 | − | 0.178314i | ||||
\(816\) | 5.71807 | + | 10.4087i | 0.200173 | + | 0.364379i | ||||
\(817\) | −11.7081 | + | 6.75969i | −0.409616 | + | 0.236492i | ||||
\(818\) | −1.65987 | −0.0580362 | ||||||||
\(819\) | −41.6061 | − | 25.4081i | −1.45383 | − | 0.887831i | ||||
\(820\) | 3.35883 | 0.117295 | ||||||||
\(821\) | −25.8075 | + | 14.9000i | −0.900688 | + | 0.520013i | −0.877423 | − | 0.479717i | \(-0.840739\pi\) |
−0.0232649 | + | 0.999729i | \(0.507406\pi\) | |||||||
\(822\) | 5.63685 | − | 9.30107i | 0.196608 | − | 0.324412i | ||||
\(823\) | −17.6583 | + | 30.5851i | −0.615531 | + | 1.06613i | 0.374761 | + | 0.927122i | \(0.377725\pi\) |
−0.990291 | + | 0.139009i | \(0.955608\pi\) | |||||||
\(824\) | 13.3265 | − | 23.0821i | 0.464250 | − | 0.804104i | ||||
\(825\) | 3.76382 | + | 2.28104i | 0.131039 | + | 0.0794155i | ||||
\(826\) | 0.542209 | + | 30.3450i | 0.0188659 | + | 1.05584i | ||||
\(827\) | 5.77394i | 0.200780i | 0.994948 | + | 0.100390i | \(0.0320090\pi\) | ||||
−0.994948 | + | 0.100390i | \(0.967991\pi\) | |||||||
\(828\) | 0.822426 | − | 0.429308i | 0.0285813 | − | 0.0149195i | ||||
\(829\) | − | 6.24813i | − | 0.217006i | −0.994096 | − | 0.108503i | \(-0.965394\pi\) | ||
0.994096 | − | 0.108503i | \(-0.0346058\pi\) | |||||||
\(830\) | −5.77967 | + | 3.33689i | −0.200615 | + | 0.115825i | ||||
\(831\) | −15.7237 | − | 28.6223i | −0.545450 | − | 0.992895i | ||||
\(832\) | 44.0458 | + | 25.4299i | 1.52701 | + | 0.881622i | ||||
\(833\) | 25.3356 | − | 0.905690i | 0.877827 | − | 0.0313803i | ||||
\(834\) | 17.4364 | + | 0.370624i | 0.603772 | + | 0.0128337i | ||||
\(835\) | 0.357648 | + | 0.619464i | 0.0123769 | + | 0.0214374i | ||||
\(836\) | −11.3476 | −0.392465 | ||||||||
\(837\) | −10.5377 | − | 7.01530i | −0.364236 | − | 0.242484i | ||||
\(838\) | 3.43266i | 0.118579i | ||||||||
\(839\) | 20.5584 | + | 35.6082i | 0.709755 | + | 1.22933i | 0.964948 | + | 0.262442i | \(0.0845277\pi\) |
−0.255193 | + | 0.966890i | \(0.582139\pi\) | |||||||
\(840\) | −12.1720 | − | 7.08255i | −0.419973 | − | 0.244371i | ||||
\(841\) | 25.5056 | − | 44.1771i | 0.879505 | − | 1.52335i | ||||
\(842\) | −11.9742 | − | 6.91334i | −0.412660 | − | 0.238249i | ||||
\(843\) | −13.8736 | + | 7.62152i | −0.477833 | + | 0.262499i | ||||
\(844\) | −7.65981 | − | 13.2672i | −0.263662 | − | 0.456675i | ||||
\(845\) | −24.7244 | −0.850545 | ||||||||
\(846\) | −10.8874 | − | 6.91876i | −0.374315 | − | 0.237872i | ||||
\(847\) | −5.82356 | + | 10.5162i | −0.200100 | + | 0.361342i | ||||
\(848\) | −18.5328 | + | 10.6999i | −0.636420 | + | 0.367437i | ||||
\(849\) | 9.73558 | + | 5.90018i | 0.334124 | + | 0.202494i | ||||
\(850\) | −3.48895 | − | 2.01435i | −0.119670 | − | 0.0690915i | ||||
\(851\) | 3.83853 | + | 2.21618i | 0.131583 | + | 0.0759696i | ||||
\(852\) | 3.95511 | + | 2.39697i | 0.135500 | + | 0.0821187i | ||||
\(853\) | 20.6976 | − | 11.9498i | 0.708672 | − | 0.409152i | −0.101897 | − | 0.994795i | \(-0.532491\pi\) |
0.810569 | + | 0.585643i | \(0.199158\pi\) | |||||||
\(854\) | −7.01543 | + | 12.6685i | −0.240063 | + | 0.433507i | ||||
\(855\) | 14.8274 | + | 9.42260i | 0.507087 | + | 0.322246i | ||||
\(856\) | 5.01921 | 0.171553 | ||||||||
\(857\) | −12.0393 | − | 20.8527i | −0.411255 | − | 0.712315i | 0.583772 | − | 0.811917i | \(-0.301576\pi\) |
−0.995027 | + | 0.0996029i | \(0.968243\pi\) | |||||||
\(858\) | 26.3544 | − | 14.4778i | 0.899723 | − | 0.494266i | ||||
\(859\) | 39.1195 | + | 22.5857i | 1.33474 | + | 0.770613i | 0.986022 | − | 0.166615i | \(-0.0532837\pi\) |
0.348718 | + | 0.937228i | \(0.386617\pi\) | |||||||
\(860\) | −0.880292 | + | 1.52471i | −0.0300177 | + | 0.0519922i | ||||
\(861\) | −10.1508 | + | 17.4451i | −0.345939 | + | 0.594526i | ||||
\(862\) | 4.06202 | + | 7.03563i | 0.138353 | + | 0.239634i | ||||
\(863\) | − | 37.3218i | − | 1.27045i | −0.772327 | − | 0.635225i | \(-0.780907\pi\) | ||
0.772327 | − | 0.635225i | \(-0.219093\pi\) | |||||||
\(864\) | −17.4751 | − | 11.6338i | −0.594515 | − | 0.395789i | ||||
\(865\) | 1.86714 | 0.0634846 | ||||||||
\(866\) | −18.7719 | − | 32.5139i | −0.637896 | − | 1.10487i | ||||
\(867\) | −6.72470 | − | 0.142939i | −0.228383 | − | 0.00485446i | ||||
\(868\) | 4.21247 | − | 2.53348i | 0.142981 | − | 0.0859918i | ||||
\(869\) | −25.3931 | − | 14.6607i | −0.861401 | − | 0.497330i | ||||
\(870\) | 8.29794 | + | 15.1049i | 0.281327 | + | 0.512106i | ||||
\(871\) | −47.7173 | + | 27.5496i | −1.61684 | + | 0.933482i | ||||
\(872\) | 19.3473i | 0.655183i | ||||||||
\(873\) | 27.7724 | − | 14.4972i | 0.939954 | − | 0.490657i | ||||
\(874\) | 2.64153i | 0.0893511i | ||||||||
\(875\) | 2.64533 | − | 0.0472671i | 0.0894284 | − | 0.00159792i | ||||
\(876\) | 3.27845 | + | 1.98688i | 0.110769 | + | 0.0671306i | ||||
\(877\) | 19.5948 | − | 33.9392i | 0.661669 | − | 1.14604i | −0.318508 | − | 0.947920i | \(-0.603182\pi\) |
0.980177 | − | 0.198124i | \(-0.0634848\pi\) | |||||||
\(878\) | 1.17814 | − | 2.04060i | 0.0397603 | − | 0.0688669i | ||||
\(879\) | −13.0659 | + | 21.5593i | −0.440701 | + | 0.727177i | ||||
\(880\) | 4.16606 | − | 2.40528i | 0.140438 | − | 0.0810819i | ||||
\(881\) | 57.2138 | 1.92758 | 0.963790 | − | 0.266661i | \(-0.0859203\pi\) | ||||
0.963790 | + | 0.266661i | \(0.0859203\pi\) | |||||||
\(882\) | 20.3090 | − | 11.5427i | 0.683839 | − | 0.388663i | ||||
\(883\) | 13.6304 | 0.458700 | 0.229350 | − | 0.973344i | \(-0.426340\pi\) | ||||
0.229350 | + | 0.973344i | \(0.426340\pi\) | |||||||
\(884\) | 14.6911 | − | 8.48194i | 0.494117 | − | 0.285278i | ||||
\(885\) | −8.59996 | − | 15.6547i | −0.289085 | − | 0.526228i | ||||
\(886\) | 12.1416 | − | 21.0300i | 0.407907 | − | 0.706515i | ||||
\(887\) | 8.76193 | − | 15.1761i | 0.294197 | − | 0.509564i | −0.680601 | − | 0.732654i | \(-0.738281\pi\) |
0.974798 | + | 0.223090i | \(0.0716145\pi\) | |||||||
\(888\) | 1.23637 | − | 58.1662i | 0.0414898 | − | 1.95193i | ||||
\(889\) | 42.1469 | − | 0.753086i | 1.41356 | − | 0.0252577i | ||||
\(890\) | − | 11.5771i | − | 0.388066i | ||||||
\(891\) | −20.7042 | + | 9.71144i | −0.693616 | + | 0.325346i | ||||
\(892\) | − | 11.7601i | − | 0.393759i | ||||||
\(893\) | −19.6038 | + | 11.3183i | −0.656017 | + | 0.378752i | ||||
\(894\) | −25.2999 | − | 0.537769i | −0.846155 | − | 0.0179857i | ||||
\(895\) | −9.71918 | − | 5.61137i | −0.324876 | − | 0.187567i | ||||
\(896\) | −2.56392 | + | 1.54200i | −0.0856547 | + | 0.0515147i | ||||
\(897\) | 2.07707 | + | 3.78095i | 0.0693515 | + | 0.126242i | ||||
\(898\) | 18.4276 | + | 31.9175i | 0.614936 | + | 1.06510i | ||||
\(899\) | −21.7923 | −0.726814 | ||||||||
\(900\) | 2.28577 | + | 0.0972155i | 0.0761922 | + | 0.00324052i | ||||
\(901\) | 40.9379i | 1.36384i | ||||||||
\(902\) | −6.22452 | − | 10.7812i | −0.207254 | − | 0.358974i | ||||
\(903\) | −5.25867 | − | 9.17994i | −0.174998 | − | 0.305489i | ||||
\(904\) | −16.7281 | + | 28.9740i | −0.556370 | + | 0.963661i | ||||
\(905\) | −7.05790 | − | 4.07488i | −0.234612 | − | 0.135454i | ||||
\(906\) | 12.3058 | + | 7.45786i | 0.408833 | + | 0.247771i | ||||
\(907\) | −10.4314 | − | 18.0677i | −0.346369 | − | 0.599929i | 0.639233 | − | 0.769014i | \(-0.279252\pi\) |
−0.985602 | + | 0.169085i | \(0.945919\pi\) | |||||||
\(908\) | −3.17281 | −0.105294 | ||||||||
\(909\) | −4.31100 | − | 8.25860i | −0.142987 | − | 0.273921i | ||||
\(910\) | 8.75711 | − | 15.8136i | 0.290295 | − | 0.524217i | ||||
\(911\) | −27.3604 | + | 15.7966i | −0.906492 | + | 0.523363i | −0.879301 | − | 0.476267i | \(-0.841990\pi\) |
−0.0271911 | + | 0.999630i | \(0.508656\pi\) | |||||||
\(912\) | 16.8303 | − | 9.24575i | 0.557305 | − | 0.306157i | ||||
\(913\) | −13.2023 | − | 7.62232i | −0.436931 | − | 0.252262i | ||||
\(914\) | 18.1729 | + | 10.4921i | 0.601105 | + | 0.347048i | ||||
\(915\) | 0.181111 | − | 8.52054i | 0.00598734 | − | 0.281680i | ||||
\(916\) | 0.699549 | − | 0.403885i | 0.0231137 | − | 0.0133447i | ||||
\(917\) | −16.1892 | + | 29.2346i | −0.534616 | + | 0.965413i | ||||
\(918\) | 18.7592 | − | 9.29049i | 0.619145 | − | 0.306632i | ||||
\(919\) | 2.62965 | 0.0867442 | 0.0433721 | − | 0.999059i | \(-0.486190\pi\) | ||||
0.0433721 | + | 0.999059i | \(0.486190\pi\) | |||||||
\(920\) | 0.623078 | + | 1.07920i | 0.0205423 | + | 0.0355802i | ||||
\(921\) | −1.05650 | + | 49.7042i | −0.0348129 | + | 1.63781i | ||||
\(922\) | −32.8960 | − | 18.9925i | −1.08337 | − | 0.625485i | ||||
\(923\) | −10.7524 | + | 18.6237i | −0.353920 | + | 0.613007i | ||||
\(924\) | 0.0300706 | − | 8.87990i | 0.000989252 | − | 0.292127i | ||||
\(925\) | 5.46519 | + | 9.46599i | 0.179694 | + | 0.311240i | ||||
\(926\) | 24.6999i | 0.811688i | ||||||||
\(927\) | −21.9601 | − | 13.9553i | −0.721265 | − | 0.458353i | ||||
\(928\) | −36.1391 | −1.18632 | ||||||||
\(929\) | −5.69968 | − | 9.87213i | −0.187000 | − | 0.323894i | 0.757248 | − | 0.653127i | \(-0.226543\pi\) |
−0.944249 | + | 0.329233i | \(0.893210\pi\) | |||||||
\(930\) | 2.43285 | − | 4.01431i | 0.0797762 | − | 0.131634i | ||||
\(931\) | −1.46444 | − | 40.9660i | −0.0479951 | − | 1.34261i | ||||
\(932\) | 2.40740 | + | 1.38991i | 0.0788570 | + | 0.0455281i | ||||
\(933\) | −0.735985 | + | 1.21441i | −0.0240951 | + | 0.0397580i | ||||
\(934\) | 30.0519 | − | 17.3505i | 0.983329 | − | 0.567725i | ||||
\(935\) | − | 9.20256i | − | 0.300956i | ||||||
\(936\) | 30.3705 | − | 47.7910i | 0.992690 | − | 1.56210i | ||||
\(937\) | 51.1038i | 1.66949i | 0.550639 | + | 0.834743i | \(0.314384\pi\) | ||||
−0.550639 | + | 0.834743i | \(0.685616\pi\) | |||||||
\(938\) | −0.471678 | − | 26.3977i | −0.0154008 | − | 0.861917i | ||||
\(939\) | −27.8271 | + | 15.2869i | −0.908102 | + | 0.498868i | ||||
\(940\) | −1.47394 | + | 2.55294i | −0.0480747 | + | 0.0832678i | ||||
\(941\) | −23.9987 | + | 41.5670i | −0.782336 | + | 1.35505i | 0.148241 | + | 0.988951i | \(0.452639\pi\) |
−0.930577 | + | 0.366095i | \(0.880694\pi\) | |||||||
\(942\) | −22.2766 | − | 0.473507i | −0.725812 | − | 0.0154277i | ||||
\(943\) | 1.54673 | − | 0.893005i | 0.0503685 | − | 0.0290802i | ||||
\(944\) | −19.5232 | −0.635427 | ||||||||
\(945\) | −7.41281 | + | 11.5780i | −0.241139 | + | 0.376633i | ||||
\(946\) | 6.52536 | 0.212158 | ||||||||
\(947\) | 32.6270 | − | 18.8372i | 1.06024 | − | 0.612127i | 0.134738 | − | 0.990881i | \(-0.456981\pi\) |
0.925497 | + | 0.378754i | \(0.123647\pi\) | |||||||
\(948\) | −15.2388 | − | 0.323914i | −0.494935 | − | 0.0105202i | ||||
\(949\) | −8.91284 | + | 15.4375i | −0.289323 | + | 0.501122i | ||||
\(950\) | −3.25706 | + | 5.64140i | −0.105673 | + | 0.183031i | ||||
\(951\) | −24.4596 | + | 13.4370i | −0.793158 | + | 0.435724i | ||||
\(952\) | 0.526069 | + | 29.4417i | 0.0170500 | + | 0.954212i | ||||
\(953\) | 31.5698i | 1.02265i | 0.859388 | + | 0.511323i | \(0.170845\pi\) | ||||
−0.859388 | + | 0.511323i | \(0.829155\pi\) | |||||||
\(954\) | 17.4556 | + | 33.4397i | 0.565145 | + | 1.08265i | ||||
\(955\) | 8.28423i | 0.268071i | ||||||||
\(956\) | −0.926875 | + | 0.535132i | −0.0299773 | + | 0.0173074i | ||||
\(957\) | −20.4036 | + | 33.6670i | −0.659556 | + | 1.08830i | ||||
\(958\) | 38.5628 | + | 22.2643i | 1.24591 | + | 0.719326i | ||||
\(959\) | 12.7984 | − | 7.69725i | 0.413282 | − | 0.248557i | ||||
\(960\) | 7.43357 | − | 12.2657i | 0.239917 | − | 0.395875i | ||||
\(961\) | −12.5323 | − | 21.7065i | −0.404267 | − | 0.700210i | ||||
\(962\) | 74.6792 | 2.40775 | ||||||||
\(963\) | 0.208207 | − | 4.89544i | 0.00670937 | − | 0.157753i | ||||
\(964\) | 12.1492i | 0.391301i | ||||||||
\(965\) | 11.0068 | + | 19.0643i | 0.354321 | + | 0.613702i | ||||
\(966\) | −2.06709 | − | 0.00699994i | −0.0665076 | − | 0.000225219i | ||||
\(967\) | 17.6818 | − | 30.6258i | 0.568609 | − | 0.984860i | −0.428095 | − | 0.903734i | \(-0.640815\pi\) |
0.996704 | − | 0.0811259i | \(-0.0258516\pi\) | |||||||
\(968\) | −12.0919 | − | 6.98128i | −0.388649 | − | 0.224387i | ||||
\(969\) | 0.780645 | − | 36.7262i | 0.0250779 | − | 1.17982i | ||||
\(970\) | 5.80821 | + | 10.0601i | 0.186490 | + | 0.323011i | ||||
\(971\) | −41.4921 | −1.33155 | −0.665773 | − | 0.746154i | \(-0.731898\pi\) | ||||
−0.665773 | + | 0.746154i | \(0.731898\pi\) | |||||||
\(972\) | −7.00238 | + | 9.60674i | −0.224602 | + | 0.308136i | ||||
\(973\) | 20.9512 | + | 11.6021i | 0.671663 | + | 0.371946i | ||||
\(974\) | 32.8590 | − | 18.9711i | 1.05287 | − | 0.607875i | ||||
\(975\) | −0.226074 | + | 10.6359i | −0.00724017 | + | 0.340621i | ||||
\(976\) | −8.06738 | − | 4.65770i | −0.258230 | − | 0.149089i | ||||
\(977\) | −27.2801 | − | 15.7502i | −0.872767 | − | 0.503892i | −0.00449997 | − | 0.999990i | \(-0.501432\pi\) |
−0.868267 | + | 0.496098i | \(0.834766\pi\) | |||||||
\(978\) | −9.92605 | + | 5.45290i | −0.317400 | + | 0.174365i | ||||
\(979\) | 22.9022 | − | 13.2226i | 0.731956 | − | 0.422595i | ||||
\(980\) | −2.83259 | − | 4.52478i | −0.0904839 | − | 0.144539i | ||||
\(981\) | 18.8702 | + | 0.802565i | 0.602480 | + | 0.0256239i | ||||
\(982\) | 8.60485 | 0.274592 | ||||||||
\(983\) | 9.20858 | + | 15.9497i | 0.293708 | + | 0.508717i | 0.974684 | − | 0.223589i | \(-0.0717773\pi\) |
−0.680975 | + | 0.732306i | \(0.738444\pi\) | |||||||
\(984\) | −20.0488 | − | 12.1504i | −0.639132 | − | 0.387342i | ||||
\(985\) | 15.7919 | + | 9.11747i | 0.503173 | + | 0.290507i | ||||
\(986\) | 18.0181 | − | 31.2083i | 0.573814 | − | 0.993875i | ||||
\(987\) | −8.80501 | − | 15.3707i | −0.280266 | − | 0.489255i | ||||
\(988\) | −13.7147 | − | 23.7546i | −0.436324 | − | 0.755735i | ||||
\(989\) | 0.936166i | 0.0297684i | ||||||||
\(990\) | −3.92390 | − | 7.51702i | −0.124710 | − | 0.238907i | ||||
\(991\) | 21.5172 | 0.683517 | 0.341758 | − | 0.939788i | \(-0.388978\pi\) | ||||
0.341758 | + | 0.939788i | \(0.388978\pi\) | |||||||
\(992\) | 4.92151 | + | 8.52431i | 0.156258 | + | 0.270647i | ||||
\(993\) | 2.54960 | + | 4.64110i | 0.0809092 | + | 0.147281i | ||||
\(994\) | −5.31085 | − | 8.83048i | −0.168450 | − | 0.280086i | ||||
\(995\) | 0.0547675 | + | 0.0316200i | 0.00173625 | + | 0.00100242i | ||||
\(996\) | −7.92291 | − | 0.168408i | −0.251047 | − | 0.00533620i | ||||
\(997\) | 10.0534 | − | 5.80435i | 0.318396 | − | 0.183826i | −0.332282 | − | 0.943180i | \(-0.607818\pi\) |
0.650677 | + | 0.759354i | \(0.274485\pi\) | |||||||
\(998\) | − | 28.6632i | − | 0.907317i | ||||||
\(999\) | −56.6806 | − | 3.61873i | −1.79329 | − | 0.114492i |
(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 | 315.2.bl.j.41.7 | yes | 24 | |
3.2 | odd | 2 | 945.2.bl.j.881.6 | 24 | |||
7.6 | odd | 2 | 315.2.bl.i.41.7 | ✓ | 24 | ||
9.2 | odd | 6 | 315.2.bl.i.146.7 | yes | 24 | ||
9.7 | even | 3 | 945.2.bl.i.251.6 | 24 | |||
21.20 | even | 2 | 945.2.bl.i.881.6 | 24 | |||
63.20 | even | 6 | inner | 315.2.bl.j.146.7 | yes | 24 | |
63.34 | odd | 6 | 945.2.bl.j.251.6 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.bl.i.41.7 | ✓ | 24 | 7.6 | odd | 2 | ||
315.2.bl.i.146.7 | yes | 24 | 9.2 | odd | 6 | ||
315.2.bl.j.41.7 | yes | 24 | 1.1 | even | 1 | trivial | |
315.2.bl.j.146.7 | yes | 24 | 63.20 | even | 6 | inner | |
945.2.bl.i.251.6 | 24 | 9.7 | even | 3 | |||
945.2.bl.i.881.6 | 24 | 21.20 | even | 2 | |||
945.2.bl.j.251.6 | 24 | 63.34 | odd | 6 | |||
945.2.bl.j.881.6 | 24 | 3.2 | odd | 2 |