Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(19,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([10, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.19");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.x (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 19.6 | ||
Character | \(\chi\) | \(=\) | 637.19 |
Dual form | 637.2.x.b.570.5 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.33353 | + | 0.357317i | 0.942945 | + | 0.252661i | 0.697366 | − | 0.716715i | \(-0.254355\pi\) |
0.245579 | + | 0.969377i | \(0.421022\pi\) | |||||||
\(3\) | 1.07207i | 0.618958i | 0.950906 | + | 0.309479i | \(0.100155\pi\) | ||||
−0.950906 | + | 0.309479i | \(0.899845\pi\) | |||||||
\(4\) | −0.0814361 | − | 0.0470171i | −0.0407180 | − | 0.0235086i | ||||
\(5\) | 2.77200 | − | 0.742756i | 1.23968 | − | 0.332171i | 0.421337 | − | 0.906904i | \(-0.361561\pi\) |
0.818341 | + | 0.574734i | \(0.194894\pi\) | |||||||
\(6\) | −0.383068 | + | 1.42963i | −0.156387 | + | 0.583644i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.04421 | − | 2.04421i | −0.722739 | − | 0.722739i | ||||
\(9\) | 1.85067 | 0.616891 | ||||||||
\(10\) | 3.96194 | 1.25287 | ||||||||
\(11\) | −1.00979 | − | 1.00979i | −0.304465 | − | 0.304465i | 0.538293 | − | 0.842758i | \(-0.319069\pi\) |
−0.842758 | + | 0.538293i | \(0.819069\pi\) | |||||||
\(12\) | 0.0504055 | − | 0.0873049i | 0.0145508 | − | 0.0252028i | ||||
\(13\) | 3.54926 | + | 0.634621i | 0.984388 | + | 0.176012i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.796284 | + | 2.97177i | 0.205600 | + | 0.767309i | ||||
\(16\) | −1.90154 | − | 3.29357i | −0.475386 | − | 0.823393i | ||||
\(17\) | 2.09909 | − | 3.63573i | 0.509105 | − | 0.881795i | −0.490840 | − | 0.871250i | \(-0.663310\pi\) |
0.999944 | − | 0.0105451i | \(-0.00335669\pi\) | |||||||
\(18\) | 2.46792 | + | 0.661277i | 0.581694 | + | 0.155864i | ||||
\(19\) | 4.35974 | + | 4.35974i | 1.00019 | + | 1.00019i | 1.00000 | 0.000191931i | \(6.10936e-5\pi\) | |
0.000191931 | 1.00000i | \(0.499939\pi\) | ||||||||
\(20\) | −0.260663 | − | 0.0698445i | −0.0582861 | − | 0.0156177i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.985770 | − | 1.70740i | −0.210167 | − | 0.364020i | ||||
\(23\) | −6.77658 | + | 3.91246i | −1.41302 | + | 0.815805i | −0.995671 | − | 0.0929436i | \(-0.970372\pi\) |
−0.417344 | + | 0.908748i | \(0.637039\pi\) | |||||||
\(24\) | 2.19153 | − | 2.19153i | 0.447345 | − | 0.447345i | ||||
\(25\) | 2.80219 | − | 1.61784i | 0.560438 | − | 0.323569i | ||||
\(26\) | 4.50627 | + | 2.11449i | 0.883752 | + | 0.414687i | ||||
\(27\) | 5.20025i | 1.00079i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.441485 | − | 0.764674i | 0.0819817 | − | 0.141996i | −0.822119 | − | 0.569315i | \(-0.807208\pi\) |
0.904101 | + | 0.427319i | \(0.140542\pi\) | |||||||
\(30\) | 4.24746i | 0.775477i | ||||||||
\(31\) | −0.237463 | + | 0.886225i | −0.0426497 | + | 0.159171i | −0.983966 | − | 0.178354i | \(-0.942923\pi\) |
0.941317 | + | 0.337524i | \(0.109590\pi\) | |||||||
\(32\) | 0.137560 | + | 0.513380i | 0.0243174 | + | 0.0907536i | ||||
\(33\) | 1.08257 | − | 1.08257i | 0.188451 | − | 0.188451i | ||||
\(34\) | 4.09830 | − | 4.09830i | 0.702853 | − | 0.702853i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.150711 | − | 0.0870133i | −0.0251186 | − | 0.0145022i | ||||
\(37\) | 1.92747 | − | 7.19341i | 0.316874 | − | 1.18259i | −0.605358 | − | 0.795953i | \(-0.706970\pi\) |
0.922232 | − | 0.386637i | \(-0.126363\pi\) | |||||||
\(38\) | 4.25601 | + | 7.37163i | 0.690416 | + | 1.19584i | ||||
\(39\) | −0.680356 | + | 3.80505i | −0.108944 | + | 0.609295i | ||||
\(40\) | −7.18492 | − | 4.14822i | −1.13604 | − | 0.655890i | ||||
\(41\) | −11.4714 | + | 3.07376i | −1.79154 | + | 0.480041i | −0.992606 | − | 0.121379i | \(-0.961268\pi\) |
−0.798933 | + | 0.601421i | \(0.794602\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.809734 | − | 0.467500i | 0.123483 | − | 0.0712931i | −0.436986 | − | 0.899468i | \(-0.643954\pi\) |
0.560469 | + | 0.828175i | \(0.310621\pi\) | |||||||
\(44\) | 0.0347561 | + | 0.129711i | 0.00523967 | + | 0.0195547i | ||||
\(45\) | 5.13007 | − | 1.37460i | 0.764746 | − | 0.204913i | ||||
\(46\) | −10.4347 | + | 2.79598i | −1.53852 | + | 0.412245i | ||||
\(47\) | 0.808679 | + | 3.01803i | 0.117958 | + | 0.440225i | 0.999491 | − | 0.0318968i | \(-0.0101548\pi\) |
−0.881533 | + | 0.472122i | \(0.843488\pi\) | |||||||
\(48\) | 3.53093 | − | 2.03858i | 0.509646 | − | 0.294244i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.31487 | − | 1.15617i | 0.610215 | − | 0.163507i | ||||
\(51\) | 3.89775 | + | 2.25037i | 0.545794 | + | 0.315114i | ||||
\(52\) | −0.259200 | − | 0.218557i | −0.0359446 | − | 0.0303084i | ||||
\(53\) | −1.26243 | − | 2.18659i | −0.173408 | − | 0.300351i | 0.766201 | − | 0.642601i | \(-0.222145\pi\) |
−0.939609 | + | 0.342249i | \(0.888811\pi\) | |||||||
\(54\) | −1.85814 | + | 6.93466i | −0.252860 | + | 0.943688i | ||||
\(55\) | −3.54919 | − | 2.04912i | −0.478572 | − | 0.276304i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.67393 | + | 4.67393i | −0.619077 | + | 0.619077i | ||||
\(58\) | 0.861962 | − | 0.861962i | 0.113181 | − | 0.113181i | ||||
\(59\) | −1.51488 | − | 5.65360i | −0.197220 | − | 0.736035i | −0.991681 | − | 0.128720i | \(-0.958913\pi\) |
0.794461 | − | 0.607315i | \(-0.207754\pi\) | |||||||
\(60\) | 0.0748780 | − | 0.279449i | 0.00966671 | − | 0.0360767i | ||||
\(61\) | − | 0.0854082i | − | 0.0109354i | −0.999985 | − | 0.00546770i | \(-0.998260\pi\) | ||
0.999985 | − | 0.00546770i | \(-0.00174043\pi\) | |||||||
\(62\) | −0.633327 | + | 1.09695i | −0.0804326 | + | 0.139313i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.33994i | 1.04249i | ||||||||
\(65\) | 10.3099 | − | 0.877064i | 1.27879 | − | 0.108786i | ||||
\(66\) | 1.83045 | − | 1.05681i | 0.225313 | − | 0.130085i | ||||
\(67\) | 0.728594 | − | 0.728594i | 0.0890119 | − | 0.0890119i | −0.661199 | − | 0.750211i | \(-0.729952\pi\) |
0.750211 | + | 0.661199i | \(0.229952\pi\) | |||||||
\(68\) | −0.341884 | + | 0.197387i | −0.0414595 | + | 0.0239366i | ||||
\(69\) | −4.19442 | − | 7.26495i | −0.504949 | − | 0.874598i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.79996 | + | 0.750247i | 0.332294 | + | 0.0890380i | 0.421109 | − | 0.907010i | \(-0.361641\pi\) |
−0.0888143 | + | 0.996048i | \(0.528308\pi\) | |||||||
\(72\) | −3.78317 | − | 3.78317i | −0.445851 | − | 0.445851i | ||||
\(73\) | −2.75156 | − | 0.737278i | −0.322046 | − | 0.0862919i | 0.0941746 | − | 0.995556i | \(-0.469979\pi\) |
−0.416220 | + | 0.909264i | \(0.636645\pi\) | |||||||
\(74\) | 5.14066 | − | 8.90388i | 0.597589 | − | 1.03506i | ||||
\(75\) | 1.73444 | + | 3.00414i | 0.200276 | + | 0.346888i | ||||
\(76\) | −0.150057 | − | 0.560022i | −0.0172128 | − | 0.0642389i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.26688 | + | 4.83102i | −0.256674 | + | 0.547006i | ||||
\(79\) | −4.71534 | + | 8.16721i | −0.530517 | + | 0.918883i | 0.468849 | + | 0.883279i | \(0.344669\pi\) |
−0.999366 | + | 0.0356045i | \(0.988664\pi\) | |||||||
\(80\) | −7.71741 | − | 7.71741i | −0.862832 | − | 0.862832i | ||||
\(81\) | −0.0229961 | −0.00255513 | ||||||||
\(82\) | −16.3958 | −1.81061 | ||||||||
\(83\) | 1.54040 | + | 1.54040i | 0.169081 | + | 0.169081i | 0.786575 | − | 0.617494i | \(-0.211852\pi\) |
−0.617494 | + | 0.786575i | \(0.711852\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.11823 | − | 11.6374i | 0.338219 | − | 1.26225i | ||||
\(86\) | 1.24685 | − | 0.334092i | 0.134451 | − | 0.0360260i | ||||
\(87\) | 0.819782 | + | 0.473301i | 0.0878898 | + | 0.0507432i | ||||
\(88\) | 4.12847i | 0.440097i | ||||||||
\(89\) | −4.75720 | − | 1.27469i | −0.504262 | − | 0.135117i | −0.00228491 | − | 0.999997i | \(-0.500727\pi\) |
−0.501977 | + | 0.864881i | \(0.667394\pi\) | |||||||
\(90\) | 7.33225 | 0.772887 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.735811 | 0.0767136 | ||||||||
\(93\) | −0.950093 | − | 0.254577i | −0.0985201 | − | 0.0263984i | ||||
\(94\) | 4.31358i | 0.444912i | ||||||||
\(95\) | 15.3234 | + | 8.84698i | 1.57215 | + | 0.907681i | ||||
\(96\) | −0.550378 | + | 0.147473i | −0.0561727 | + | 0.0150514i | ||||
\(97\) | −2.37752 | + | 8.87303i | −0.241401 | + | 0.900920i | 0.733758 | + | 0.679411i | \(0.237765\pi\) |
−0.975158 | + | 0.221509i | \(0.928902\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.86880 | − | 1.86880i | −0.187821 | − | 0.187821i | ||||
\(100\) | −0.304266 | −0.0304266 | ||||||||
\(101\) | −6.54977 | −0.651726 | −0.325863 | − | 0.945417i | \(-0.605655\pi\) | ||||
−0.325863 | + | 0.945417i | \(0.605655\pi\) | |||||||
\(102\) | 4.39366 | + | 4.39366i | 0.435037 | + | 0.435037i | ||||
\(103\) | 4.92770 | − | 8.53503i | 0.485541 | − | 0.840982i | −0.514321 | − | 0.857598i | \(-0.671956\pi\) |
0.999862 | + | 0.0166161i | \(0.00528932\pi\) | |||||||
\(104\) | −5.95815 | − | 8.55275i | −0.584245 | − | 0.838666i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.902174 | − | 3.36696i | −0.0876269 | − | 0.327028i | ||||
\(107\) | −5.29678 | − | 9.17430i | −0.512059 | − | 0.886913i | −0.999902 | − | 0.0139814i | \(-0.995549\pi\) |
0.487843 | − | 0.872931i | \(-0.337784\pi\) | |||||||
\(108\) | 0.244501 | − | 0.423488i | 0.0235271 | − | 0.0407501i | ||||
\(109\) | −15.9403 | − | 4.27118i | −1.52680 | − | 0.409105i | −0.604827 | − | 0.796357i | \(-0.706758\pi\) |
−0.921974 | + | 0.387252i | \(0.873424\pi\) | |||||||
\(110\) | −4.00074 | − | 4.00074i | −0.381456 | − | 0.381456i | ||||
\(111\) | 7.71182 | + | 2.06638i | 0.731974 | + | 0.196132i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.322118 | − | 0.557925i | −0.0303023 | − | 0.0524851i | 0.850477 | − | 0.526013i | \(-0.176314\pi\) |
−0.880779 | + | 0.473528i | \(0.842980\pi\) | |||||||
\(114\) | −7.90288 | + | 4.56273i | −0.740172 | + | 0.427339i | ||||
\(115\) | −15.8787 | + | 15.8787i | −1.48070 | + | 1.48070i | ||||
\(116\) | −0.0719056 | + | 0.0415147i | −0.00667627 | + | 0.00385454i | ||||
\(117\) | 6.56852 | + | 1.17448i | 0.607260 | + | 0.108580i | ||||
\(118\) | − | 8.08051i | − | 0.743871i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 4.44717 | − | 7.70272i | 0.405969 | − | 0.703159i | ||||
\(121\) | − | 8.96063i | − | 0.814603i | ||||||
\(122\) | 0.0305178 | − | 0.113894i | 0.00276295 | − | 0.0103115i | ||||
\(123\) | −3.29528 | − | 12.2982i | −0.297126 | − | 1.10889i | ||||
\(124\) | 0.0610059 | − | 0.0610059i | 0.00547849 | − | 0.00547849i | ||||
\(125\) | −3.58022 | + | 3.58022i | −0.320225 | + | 0.320225i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.1284 | − | 8.15702i | −1.25369 | − | 0.723819i | −0.281850 | − | 0.959458i | \(-0.590948\pi\) |
−0.971841 | + | 0.235640i | \(0.924282\pi\) | |||||||
\(128\) | −2.70488 | + | 10.0948i | −0.239080 | + | 0.892259i | ||||
\(129\) | 0.501191 | + | 0.868089i | 0.0441274 | + | 0.0764310i | ||||
\(130\) | 14.0619 | + | 2.51433i | 1.23331 | + | 0.220521i | ||||
\(131\) | −2.03759 | − | 1.17640i | −0.178025 | − | 0.102783i | 0.408340 | − | 0.912830i | \(-0.366108\pi\) |
−0.586364 | + | 0.810047i | \(0.699441\pi\) | |||||||
\(132\) | −0.139059 | + | 0.0372608i | −0.0121036 | + | 0.00324314i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.23194 | − | 0.711259i | 0.106423 | − | 0.0614435i | ||||
\(135\) | 3.86251 | + | 14.4151i | 0.332432 | + | 1.24065i | ||||
\(136\) | −11.7232 | + | 3.14122i | −1.00526 | + | 0.269358i | ||||
\(137\) | −10.0332 | + | 2.68838i | −0.857190 | + | 0.229683i | −0.660541 | − | 0.750790i | \(-0.729673\pi\) |
−0.196650 | + | 0.980474i | \(0.563006\pi\) | |||||||
\(138\) | −2.99748 | − | 11.1867i | −0.255162 | − | 0.952278i | ||||
\(139\) | 5.33208 | − | 3.07848i | 0.452261 | − | 0.261113i | −0.256524 | − | 0.966538i | \(-0.582577\pi\) |
0.708784 | + | 0.705425i | \(0.249244\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.23553 | + | 0.866959i | −0.272481 | + | 0.0730111i | ||||
\(142\) | 3.46574 | + | 2.00095i | 0.290839 | + | 0.167916i | ||||
\(143\) | −2.94319 | − | 4.22486i | −0.246122 | − | 0.353301i | ||||
\(144\) | −3.51914 | − | 6.09532i | −0.293261 | − | 0.507943i | ||||
\(145\) | 0.655831 | − | 2.44759i | 0.0544638 | − | 0.203262i | ||||
\(146\) | −3.40583 | − | 1.96636i | −0.281869 | − | 0.162737i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.495179 | + | 0.495179i | −0.0407035 | + | 0.0407035i | ||||
\(149\) | 6.15629 | − | 6.15629i | 0.504343 | − | 0.504343i | −0.408442 | − | 0.912784i | \(-0.633928\pi\) |
0.912784 | + | 0.408442i | \(0.133928\pi\) | |||||||
\(150\) | 1.23949 | + | 4.62584i | 0.101204 | + | 0.377698i | ||||
\(151\) | 3.49627 | − | 13.0482i | 0.284522 | − | 1.06185i | −0.664665 | − | 0.747141i | \(-0.731426\pi\) |
0.949188 | − | 0.314710i | \(-0.101907\pi\) | |||||||
\(152\) | − | 17.8245i | − | 1.44575i | ||||||
\(153\) | 3.88473 | − | 6.72855i | 0.314062 | − | 0.543971i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.63300i | 0.211487i | ||||||||
\(156\) | 0.234308 | − | 0.277880i | 0.0187597 | − | 0.0222482i | ||||
\(157\) | −5.87142 | + | 3.38986i | −0.468590 | + | 0.270541i | −0.715649 | − | 0.698460i | \(-0.753869\pi\) |
0.247059 | + | 0.969000i | \(0.420536\pi\) | |||||||
\(158\) | −9.20631 | + | 9.20631i | −0.732415 | + | 0.732415i | ||||
\(159\) | 2.34417 | − | 1.35341i | 0.185905 | − | 0.107332i | ||||
\(160\) | 0.762632 | + | 1.32092i | 0.0602914 | + | 0.104428i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.0306659 | − | 0.00821691i | −0.00240934 | − | 0.000645582i | ||||
\(163\) | −7.72493 | − | 7.72493i | −0.605063 | − | 0.605063i | 0.336588 | − | 0.941652i | \(-0.390727\pi\) |
−0.941652 | + | 0.336588i | \(0.890727\pi\) | |||||||
\(164\) | 1.07871 | + | 0.289039i | 0.0842330 | + | 0.0225702i | ||||
\(165\) | 2.19680 | − | 3.80497i | 0.171020 | − | 0.296216i | ||||
\(166\) | 1.50375 | + | 2.60458i | 0.116714 | + | 0.202155i | ||||
\(167\) | 4.71387 | + | 17.5924i | 0.364770 | + | 1.36134i | 0.867732 | + | 0.497032i | \(0.165577\pi\) |
−0.502962 | + | 0.864308i | \(0.667756\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.1945 | + | 4.50487i | 0.938039 | + | 0.346529i | ||||
\(170\) | 8.31647 | − | 14.4045i | 0.637844 | − | 1.10478i | ||||
\(171\) | 8.06844 | + | 8.06844i | 0.617009 | + | 0.617009i | ||||
\(172\) | −0.0879221 | −0.00670400 | ||||||||
\(173\) | 20.1522 | 1.53214 | 0.766070 | − | 0.642757i | \(-0.222209\pi\) | ||||
0.766070 | + | 0.642757i | \(0.222209\pi\) | |||||||
\(174\) | 0.924081 | + | 0.924081i | 0.0700544 | + | 0.0700544i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.40566 | + | 5.24600i | −0.105956 | + | 0.395432i | ||||
\(177\) | 6.06103 | − | 1.62405i | 0.455575 | − | 0.122071i | ||||
\(178\) | −5.88838 | − | 3.39966i | −0.441353 | − | 0.254815i | ||||
\(179\) | 16.5322i | 1.23567i | 0.786306 | + | 0.617837i | \(0.211991\pi\) | ||||
−0.786306 | + | 0.617837i | \(0.788009\pi\) | |||||||
\(180\) | −0.482402 | − | 0.129259i | −0.0359562 | − | 0.00963442i | ||||
\(181\) | 13.6897 | 1.01755 | 0.508774 | − | 0.860900i | \(-0.330099\pi\) | ||||
0.508774 | + | 0.860900i | \(0.330099\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.0915633 | 0.00676855 | ||||||||
\(184\) | 21.8507 | + | 5.85488i | 1.61085 | + | 0.431627i | ||||
\(185\) | − | 21.3718i | − | 1.57129i | ||||||
\(186\) | −1.17601 | − | 0.678969i | −0.0862292 | − | 0.0497844i | ||||
\(187\) | −5.79100 | + | 1.55169i | −0.423480 | + | 0.113471i | ||||
\(188\) | 0.0760436 | − | 0.283799i | 0.00554605 | − | 0.0206981i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 17.2730 | + | 17.2730i | 1.25311 | + | 1.25311i | ||||
\(191\) | −8.14890 | −0.589633 | −0.294817 | − | 0.955554i | \(-0.595259\pi\) | ||||
−0.294817 | + | 0.955554i | \(0.595259\pi\) | |||||||
\(192\) | −8.94097 | −0.645259 | ||||||||
\(193\) | 18.9414 | + | 18.9414i | 1.36343 | + | 1.36343i | 0.869499 | + | 0.493935i | \(0.164442\pi\) |
0.493935 | + | 0.869499i | \(0.335558\pi\) | |||||||
\(194\) | −6.34097 | + | 10.9829i | −0.455255 | + | 0.788525i | ||||
\(195\) | 0.940271 | + | 11.0529i | 0.0673342 | + | 0.791517i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.77033 | + | 17.8031i | 0.339872 | + | 1.26842i | 0.898490 | + | 0.438995i | \(0.144665\pi\) |
−0.558617 | + | 0.829426i | \(0.688668\pi\) | |||||||
\(198\) | −1.82434 | − | 3.15985i | −0.129650 | − | 0.224560i | ||||
\(199\) | −6.35578 | + | 11.0085i | −0.450550 | + | 0.780375i | −0.998420 | − | 0.0561884i | \(-0.982105\pi\) |
0.547871 | + | 0.836563i | \(0.315439\pi\) | |||||||
\(200\) | −9.03550 | − | 2.42105i | −0.638906 | − | 0.171194i | ||||
\(201\) | 0.781101 | + | 0.781101i | 0.0550947 | + | 0.0550947i | ||||
\(202\) | −8.73428 | − | 2.34034i | −0.614542 | − | 0.164666i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.211612 | − | 0.366522i | −0.0148158 | − | 0.0256617i | ||||
\(205\) | −29.5158 | + | 17.0410i | −2.06147 | + | 1.19019i | ||||
\(206\) | 9.62093 | − | 9.62093i | 0.670322 | − | 0.670322i | ||||
\(207\) | −12.5412 | + | 7.24069i | −0.871676 | + | 0.503262i | ||||
\(208\) | −4.65891 | − | 12.8965i | −0.323037 | − | 0.894212i | ||||
\(209\) | − | 8.80488i | − | 0.609046i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.26459 | + | 3.92239i | −0.155901 | + | 0.270028i | −0.933387 | − | 0.358872i | \(-0.883161\pi\) |
0.777486 | + | 0.628900i | \(0.216495\pi\) | |||||||
\(212\) | 0.237423i | 0.0163063i | ||||||||
\(213\) | −0.804316 | + | 3.00175i | −0.0551108 | + | 0.205676i | ||||
\(214\) | −3.78526 | − | 14.1268i | −0.258755 | − | 0.965688i | ||||
\(215\) | 1.89735 | − | 1.89735i | 0.129398 | − | 0.129398i | ||||
\(216\) | 10.6304 | − | 10.6304i | 0.723308 | − | 0.723308i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −19.7306 | − | 11.3915i | −1.33632 | − | 0.771527i | ||||
\(219\) | 0.790412 | − | 2.94986i | 0.0534111 | − | 0.199333i | ||||
\(220\) | 0.192688 | + | 0.333745i | 0.0129910 | + | 0.0225011i | ||||
\(221\) | 9.75754 | − | 11.5720i | 0.656363 | − | 0.778420i | ||||
\(222\) | 9.54556 | + | 5.51113i | 0.640656 | + | 0.369883i | ||||
\(223\) | 22.4788 | − | 6.02318i | 1.50529 | − | 0.403342i | 0.590423 | − | 0.807094i | \(-0.298961\pi\) |
0.914868 | + | 0.403752i | \(0.132294\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.18593 | − | 2.99410i | 0.345729 | − | 0.199607i | ||||
\(226\) | −0.230197 | − | 0.859105i | −0.0153124 | − | 0.0571468i | ||||
\(227\) | −10.0685 | + | 2.69786i | −0.668273 | + | 0.179063i | −0.576977 | − | 0.816761i | \(-0.695768\pi\) |
−0.0912961 | + | 0.995824i | \(0.529101\pi\) | |||||||
\(228\) | 0.600381 | − | 0.160872i | 0.0397612 | − | 0.0106540i | ||||
\(229\) | 0.499191 | + | 1.86301i | 0.0329875 | + | 0.123111i | 0.980456 | − | 0.196738i | \(-0.0630347\pi\) |
−0.947469 | + | 0.319848i | \(0.896368\pi\) | |||||||
\(230\) | −26.8484 | + | 15.5009i | −1.77033 | + | 1.02210i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.46565 | + | 0.660668i | −0.161878 | + | 0.0433750i | ||||
\(233\) | 7.44377 | + | 4.29766i | 0.487657 | + | 0.281549i | 0.723602 | − | 0.690217i | \(-0.242485\pi\) |
−0.235945 | + | 0.971766i | \(0.575818\pi\) | |||||||
\(234\) | 8.33963 | + | 3.91324i | 0.545179 | + | 0.255816i | ||||
\(235\) | 4.48332 | + | 7.76535i | 0.292460 | + | 0.506555i | ||||
\(236\) | −0.142450 | + | 0.531632i | −0.00927273 | + | 0.0346063i | ||||
\(237\) | −8.75580 | − | 5.05516i | −0.568750 | − | 0.328368i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.45158 | + | 6.45158i | −0.417318 | + | 0.417318i | −0.884278 | − | 0.466960i | \(-0.845349\pi\) |
0.466960 | + | 0.884278i | \(0.345349\pi\) | |||||||
\(240\) | 8.27358 | − | 8.27358i | 0.534057 | − | 0.534057i | ||||
\(241\) | 1.12940 | + | 4.21497i | 0.0727509 | + | 0.271510i | 0.992714 | − | 0.120495i | \(-0.0384482\pi\) |
−0.919963 | + | 0.392005i | \(0.871782\pi\) | |||||||
\(242\) | 3.20179 | − | 11.9492i | 0.205819 | − | 0.768125i | ||||
\(243\) | 15.5761i | 0.999206i | ||||||||
\(244\) | −0.00401565 | + | 0.00695531i | −0.000257076 | + | 0.000445268i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | − | 17.5774i | − | 1.12069i | ||||||
\(247\) | 12.7071 | + | 18.2406i | 0.808531 | + | 1.16062i | ||||
\(248\) | 2.29706 | − | 1.32621i | 0.145863 | − | 0.0842143i | ||||
\(249\) | −1.65142 | + | 1.65142i | −0.104654 | + | 0.104654i | ||||
\(250\) | −6.05359 | + | 3.49504i | −0.382863 | + | 0.221046i | ||||
\(251\) | 2.27953 | + | 3.94826i | 0.143883 | + | 0.249212i | 0.928956 | − | 0.370191i | \(-0.120708\pi\) |
−0.785073 | + | 0.619403i | \(0.787375\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.7937 | + | 2.89218i | 0.678597 | + | 0.181830i | ||||
\(254\) | −15.9259 | − | 15.9259i | −0.999280 | − | 0.999280i | ||||
\(255\) | 12.4761 | + | 3.34295i | 0.781281 | + | 0.209344i | ||||
\(256\) | 1.12588 | − | 1.95008i | 0.0703674 | − | 0.121880i | ||||
\(257\) | −4.31666 | − | 7.47667i | −0.269266 | − | 0.466382i | 0.699407 | − | 0.714724i | \(-0.253448\pi\) |
−0.968672 | + | 0.248342i | \(0.920114\pi\) | |||||||
\(258\) | 0.358169 | + | 1.33670i | 0.0222986 | + | 0.0832195i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.880838 | − | 0.413319i | −0.0546272 | − | 0.0256330i | ||||
\(261\) | 0.817044 | − | 1.41516i | 0.0505737 | − | 0.0875963i | ||||
\(262\) | −2.29683 | − | 2.29683i | −0.141898 | − | 0.141898i | ||||
\(263\) | −13.0629 | −0.805491 | −0.402745 | − | 0.915312i | \(-0.631944\pi\) | ||||
−0.402745 | + | 0.915312i | \(0.631944\pi\) | |||||||
\(264\) | −4.42600 | −0.272402 | ||||||||
\(265\) | −5.12356 | − | 5.12356i | −0.314738 | − | 0.314738i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.36655 | − | 5.10004i | 0.0836316 | − | 0.312117i | ||||
\(268\) | −0.0935902 | + | 0.0250774i | −0.00571693 | + | 0.00153185i | ||||
\(269\) | 10.8756 | + | 6.27901i | 0.663095 | + | 0.382838i | 0.793455 | − | 0.608629i | \(-0.208280\pi\) |
−0.130360 | + | 0.991467i | \(0.541613\pi\) | |||||||
\(270\) | 20.6030i | 1.25386i | ||||||||
\(271\) | −4.45677 | − | 1.19419i | −0.270730 | − | 0.0725418i | 0.120900 | − | 0.992665i | \(-0.461422\pi\) |
−0.391630 | + | 0.920123i | \(0.628089\pi\) | |||||||
\(272\) | −15.9661 | −0.968085 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14.3401 | −0.866315 | ||||||||
\(275\) | −4.46333 | − | 1.19595i | −0.269149 | − | 0.0721182i | ||||
\(276\) | 0.788839i | 0.0474825i | ||||||||
\(277\) | 1.44840 | + | 0.836232i | 0.0870257 | + | 0.0502443i | 0.542881 | − | 0.839809i | \(-0.317333\pi\) |
−0.455856 | + | 0.890054i | \(0.650667\pi\) | |||||||
\(278\) | 8.21045 | − | 2.19998i | 0.492430 | − | 0.131946i | ||||
\(279\) | −0.439467 | + | 1.64011i | −0.0263102 | + | 0.0981910i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.9259 | − | 13.9259i | −0.830749 | − | 0.830749i | 0.156870 | − | 0.987619i | \(-0.449860\pi\) |
−0.987619 | + | 0.156870i | \(0.949860\pi\) | |||||||
\(282\) | −4.62445 | −0.275382 | ||||||||
\(283\) | 32.9939 | 1.96128 | 0.980642 | − | 0.195810i | \(-0.0627336\pi\) | ||||
0.980642 | + | 0.195810i | \(0.0627336\pi\) | |||||||
\(284\) | −0.192743 | − | 0.192743i | −0.0114372 | − | 0.0114372i | ||||
\(285\) | −9.48456 | + | 16.4277i | −0.561817 | + | 0.973095i | ||||
\(286\) | −2.41520 | − | 6.68561i | −0.142814 | − | 0.395329i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.254578 | + | 0.950098i | 0.0150012 | + | 0.0559851i | ||||
\(289\) | −0.312374 | − | 0.541047i | −0.0183749 | − | 0.0318263i | ||||
\(290\) | 1.74913 | − | 3.02959i | 0.102713 | − | 0.177904i | ||||
\(291\) | −9.51249 | − | 2.54886i | −0.557632 | − | 0.149417i | ||||
\(292\) | 0.189412 | + | 0.189412i | 0.0110845 | + | 0.0110845i | ||||
\(293\) | −21.2120 | − | 5.68375i | −1.23922 | − | 0.332048i | −0.421057 | − | 0.907034i | \(-0.638341\pi\) |
−0.818163 | + | 0.574986i | \(0.805007\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.39849 | − | 14.5466i | −0.488979 | − | 0.846936i | ||||
\(296\) | −18.6450 | + | 10.7647i | −1.08372 | + | 0.625686i | ||||
\(297\) | 5.25118 | − | 5.25118i | 0.304704 | − | 0.304704i | ||||
\(298\) | 10.4093 | − | 6.00982i | 0.602996 | − | 0.348140i | ||||
\(299\) | −26.5348 | + | 9.58579i | −1.53455 | + | 0.554361i | ||||
\(300\) | − | 0.326193i | − | 0.0188328i | ||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 9.32472 | − | 16.1509i | 0.536578 | − | 0.929380i | ||||
\(303\) | − | 7.02179i | − | 0.403391i | ||||||
\(304\) | 6.06887 | − | 22.6493i | 0.348074 | − | 1.29903i | ||||
\(305\) | −0.0634374 | − | 0.236752i | −0.00363242 | − | 0.0135564i | ||||
\(306\) | 7.58461 | − | 7.58461i | 0.433584 | − | 0.433584i | ||||
\(307\) | −13.7833 | + | 13.7833i | −0.786656 | + | 0.786656i | −0.980944 | − | 0.194289i | \(-0.937760\pi\) |
0.194289 | + | 0.980944i | \(0.437760\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.15013 | + | 5.28283i | 0.520533 | + | 0.300530i | ||||
\(310\) | −0.940815 | + | 3.51117i | −0.0534347 | + | 0.199421i | ||||
\(311\) | −12.9133 | − | 22.3666i | −0.732248 | − | 1.26829i | −0.955920 | − | 0.293627i | \(-0.905138\pi\) |
0.223672 | − | 0.974664i | \(-0.428196\pi\) | |||||||
\(312\) | 9.16912 | − | 6.38753i | 0.519099 | − | 0.361623i | ||||
\(313\) | 24.8257 | + | 14.3331i | 1.40323 | + | 0.810155i | 0.994723 | − | 0.102600i | \(-0.0327162\pi\) |
0.408507 | + | 0.912755i | \(0.366050\pi\) | |||||||
\(314\) | −9.04094 | + | 2.42251i | −0.510210 | + | 0.136710i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.767998 | − | 0.443404i | 0.0432033 | − | 0.0249434i | ||||
\(317\) | 3.22651 | + | 12.0415i | 0.181219 | + | 0.676317i | 0.995408 | + | 0.0957183i | \(0.0305148\pi\) |
−0.814190 | + | 0.580599i | \(0.802819\pi\) | |||||||
\(318\) | 3.60961 | − | 0.967191i | 0.202417 | − | 0.0542374i | ||||
\(319\) | −1.21797 | + | 0.326355i | −0.0681934 | + | 0.0182724i | ||||
\(320\) | 6.19454 | + | 23.1183i | 0.346285 | + | 1.29235i | ||||
\(321\) | 9.83546 | − | 5.67851i | 0.548962 | − | 0.316943i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 25.0023 | − | 6.69935i | 1.39117 | − | 0.372762i | ||||
\(324\) | 0.00187272 | + | 0.00108121i | 0.000104040 | + | 6.00674e-5i | ||||
\(325\) | 10.9724 | − | 3.96383i | 0.608640 | − | 0.219873i | ||||
\(326\) | −7.54114 | − | 13.0616i | −0.417665 | − | 0.723418i | ||||
\(327\) | 4.57899 | − | 17.0890i | 0.253219 | − | 0.945026i | ||||
\(328\) | 29.7335 | + | 17.1667i | 1.64176 | + | 0.947870i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 4.28907 | − | 4.28907i | 0.236105 | − | 0.236105i | ||||
\(331\) | 21.1797 | − | 21.1797i | 1.16414 | − | 1.16414i | 0.180578 | − | 0.983561i | \(-0.442203\pi\) |
0.983561 | − | 0.180578i | \(-0.0577970\pi\) | |||||||
\(332\) | −0.0530190 | − | 0.197870i | −0.00290980 | − | 0.0108595i | ||||
\(333\) | 3.56711 | − | 13.3126i | 0.195477 | − | 0.729529i | ||||
\(334\) | 25.1443i | 1.37583i | ||||||||
\(335\) | 1.47850 | − | 2.56083i | 0.0807789 | − | 0.139913i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.4402i | 0.732137i | 0.930588 | + | 0.366068i | \(0.119296\pi\) | ||||
−0.930588 | + | 0.366068i | \(0.880704\pi\) | |||||||
\(338\) | 14.6520 | + | 10.3647i | 0.796965 | + | 0.563764i | ||||
\(339\) | 0.598133 | − | 0.345332i | 0.0324861 | − | 0.0187559i | ||||
\(340\) | −0.801093 | + | 0.801093i | −0.0434453 | + | 0.0434453i | ||||
\(341\) | 1.13470 | − | 0.655117i | 0.0614472 | − | 0.0354766i | ||||
\(342\) | 7.87648 | + | 13.6425i | 0.425911 | + | 0.737700i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2.61094 | − | 0.699599i | −0.140772 | − | 0.0377199i | ||||
\(345\) | −17.0230 | − | 17.0230i | −0.916490 | − | 0.916490i | ||||
\(346\) | 26.8734 | + | 7.20071i | 1.44472 | + | 0.387113i | ||||
\(347\) | 7.24936 | − | 12.5563i | 0.389166 | − | 0.674055i | −0.603172 | − | 0.797611i | \(-0.706097\pi\) |
0.992338 | + | 0.123556i | \(0.0394299\pi\) | |||||||
\(348\) | −0.0445066 | − | 0.0770876i | −0.00238580 | − | 0.00413233i | ||||
\(349\) | −5.68220 | − | 21.2063i | −0.304161 | − | 1.13515i | −0.933665 | − | 0.358148i | \(-0.883408\pi\) |
0.629504 | − | 0.776998i | \(-0.283258\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.30019 | + | 18.4570i | −0.176151 | + | 0.985163i | ||||
\(352\) | 0.379501 | − | 0.657316i | 0.0202275 | − | 0.0350351i | ||||
\(353\) | 8.16512 | + | 8.16512i | 0.434585 | + | 0.434585i | 0.890185 | − | 0.455600i | \(-0.150575\pi\) |
−0.455600 | + | 0.890185i | \(0.650575\pi\) | |||||||
\(354\) | 8.66284 | 0.460425 | ||||||||
\(355\) | 8.31875 | 0.441514 | ||||||||
\(356\) | 0.327476 | + | 0.327476i | 0.0173562 | + | 0.0173562i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.90723 | + | 22.0461i | −0.312207 | + | 1.16517i | ||||
\(359\) | 0.861987 | − | 0.230969i | 0.0454939 | − | 0.0121901i | −0.236000 | − | 0.971753i | \(-0.575837\pi\) |
0.281494 | + | 0.959563i | \(0.409170\pi\) | |||||||
\(360\) | −13.2969 | − | 7.67699i | −0.700810 | − | 0.404613i | ||||
\(361\) | 19.0146i | 1.00077i | ||||||||
\(362\) | 18.2556 | + | 4.89156i | 0.959491 | + | 0.257095i | ||||
\(363\) | 9.60639 | 0.504205 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.17495 | −0.427897 | ||||||||
\(366\) | 0.122102 | + | 0.0327171i | 0.00638237 | + | 0.00171015i | ||||
\(367\) | 14.4731i | 0.755489i | 0.925910 | + | 0.377744i | \(0.123300\pi\) | ||||
−0.925910 | + | 0.377744i | \(0.876700\pi\) | |||||||
\(368\) | 25.7720 | + | 14.8794i | 1.34346 | + | 0.775645i | ||||
\(369\) | −21.2299 | + | 5.68853i | −1.10518 | + | 0.296133i | ||||
\(370\) | 7.63651 | − | 28.4998i | 0.397003 | − | 1.48164i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.0654024 | + | 0.0654024i | 0.00339096 | + | 0.00339096i | ||||
\(373\) | 20.9269 | 1.08356 | 0.541778 | − | 0.840522i | \(-0.317751\pi\) | ||||
0.541778 | + | 0.840522i | \(0.317751\pi\) | |||||||
\(374\) | −8.27689 | −0.427988 | ||||||||
\(375\) | −3.83824 | − | 3.83824i | −0.198206 | − | 0.198206i | ||||
\(376\) | 4.51639 | − | 7.82262i | 0.232915 | − | 0.403421i | ||||
\(377\) | 2.05222 | − | 2.43385i | 0.105695 | − | 0.125350i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.53128 | − | 20.6430i | −0.284123 | − | 1.06036i | −0.949478 | − | 0.313834i | \(-0.898387\pi\) |
0.665355 | − | 0.746527i | \(-0.268280\pi\) | |||||||
\(380\) | −0.831920 | − | 1.44093i | −0.0426766 | − | 0.0739180i | ||||
\(381\) | 8.74488 | − | 15.1466i | 0.448014 | − | 0.775982i | ||||
\(382\) | −10.8668 | − | 2.91174i | −0.555992 | − | 0.148978i | ||||
\(383\) | −12.6750 | − | 12.6750i | −0.647662 | − | 0.647662i | 0.304765 | − | 0.952427i | \(-0.401422\pi\) |
−0.952427 | + | 0.304765i | \(0.901422\pi\) | |||||||
\(384\) | −10.8223 | − | 2.89981i | −0.552271 | − | 0.147981i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 18.4908 | + | 32.0270i | 0.941156 | + | 1.63013i | ||||
\(387\) | 1.49855 | − | 0.865189i | 0.0761757 | − | 0.0439800i | ||||
\(388\) | 0.610801 | − | 0.610801i | 0.0310087 | − | 0.0310087i | ||||
\(389\) | 4.21022 | − | 2.43077i | 0.213467 | − | 0.123245i | −0.389455 | − | 0.921046i | \(-0.627337\pi\) |
0.602921 | + | 0.797801i | \(0.294003\pi\) | |||||||
\(390\) | −2.69553 | + | 15.0754i | −0.136493 | + | 0.763370i | ||||
\(391\) | 32.8505i | 1.66132i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.26118 | − | 2.18443i | 0.0636182 | − | 0.110190i | ||||
\(394\) | 25.4454i | 1.28192i | ||||||||
\(395\) | −7.00470 | + | 26.1419i | −0.352445 | + | 1.31534i | ||||
\(396\) | 0.0643221 | + | 0.240053i | 0.00323231 | + | 0.0120631i | ||||
\(397\) | −13.8333 | + | 13.8333i | −0.694275 | + | 0.694275i | −0.963170 | − | 0.268895i | \(-0.913342\pi\) |
0.268895 | + | 0.963170i | \(0.413342\pi\) | |||||||
\(398\) | −12.4091 | + | 12.4091i | −0.622014 | + | 0.622014i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −10.6570 | − | 6.15281i | −0.532849 | − | 0.307640i | ||||
\(401\) | −1.11204 | + | 4.15019i | −0.0555327 | + | 0.207251i | −0.988118 | − | 0.153700i | \(-0.950881\pi\) |
0.932585 | + | 0.360951i | \(0.117548\pi\) | |||||||
\(402\) | 0.762518 | + | 1.32072i | 0.0380309 | + | 0.0658715i | ||||
\(403\) | −1.40524 | + | 2.99475i | −0.0699998 | + | 0.149179i | ||||
\(404\) | 0.533387 | + | 0.307951i | 0.0265370 | + | 0.0153212i | ||||
\(405\) | −0.0637454 | + | 0.0170805i | −0.00316753 | + | 0.000848738i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.21022 | + | 5.31752i | −0.456534 | + | 0.263580i | ||||
\(408\) | −3.36760 | − | 12.5681i | −0.166721 | − | 0.622212i | ||||
\(409\) | 29.2989 | − | 7.85062i | 1.44874 | − | 0.388188i | 0.553154 | − | 0.833079i | \(-0.313424\pi\) |
0.895585 | + | 0.444891i | \(0.146758\pi\) | |||||||
\(410\) | −45.4491 | + | 12.1781i | −2.24457 | + | 0.601432i | ||||
\(411\) | −2.88212 | − | 10.7562i | −0.142164 | − | 0.530565i | ||||
\(412\) | −0.802586 | + | 0.463373i | −0.0395406 | + | 0.0228288i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −19.3113 | + | 5.17444i | −0.949098 | + | 0.254310i | ||||
\(415\) | 5.41415 | + | 3.12586i | 0.265770 | + | 0.153442i | ||||
\(416\) | 0.162434 | + | 1.90942i | 0.00796397 | + | 0.0936170i | ||||
\(417\) | 3.30033 | + | 5.71634i | 0.161618 | + | 0.279930i | ||||
\(418\) | 3.14613 | − | 11.7415i | 0.153882 | − | 0.574297i | ||||
\(419\) | −6.87240 | − | 3.96778i | −0.335739 | − | 0.193839i | 0.322647 | − | 0.946519i | \(-0.395427\pi\) |
−0.658386 | + | 0.752680i | \(0.728761\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.98090 | + | 5.98090i | −0.291491 | + | 0.291491i | −0.837669 | − | 0.546178i | \(-0.816082\pi\) |
0.546178 | + | 0.837669i | \(0.316082\pi\) | |||||||
\(422\) | −4.42143 | + | 4.42143i | −0.215232 | + | 0.215232i | ||||
\(423\) | 1.49660 | + | 5.58539i | 0.0727672 | + | 0.271571i | ||||
\(424\) | −1.88918 | + | 7.05053i | −0.0917469 | + | 0.342404i | ||||
\(425\) | − | 13.5840i | − | 0.658922i | ||||||
\(426\) | −2.14515 | + | 3.71551i | −0.103933 | + | 0.180017i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.996159i | 0.0481511i | ||||||||
\(429\) | 4.52934 | − | 3.15530i | 0.218678 | − | 0.152339i | ||||
\(430\) | 3.20811 | − | 1.85221i | 0.154709 | − | 0.0893213i | ||||
\(431\) | 0.409100 | − | 0.409100i | 0.0197057 | − | 0.0197057i | −0.697185 | − | 0.716891i | \(-0.745565\pi\) |
0.716891 | + | 0.697185i | \(0.245565\pi\) | |||||||
\(432\) | 17.1274 | − | 9.88850i | 0.824042 | − | 0.475761i | ||||
\(433\) | 4.11334 | + | 7.12452i | 0.197675 | + | 0.342382i | 0.947774 | − | 0.318943i | \(-0.103328\pi\) |
−0.750099 | + | 0.661325i | \(0.769994\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.62399 | + | 0.703095i | 0.125810 | + | 0.0337108i | ||||
\(436\) | 1.09729 | + | 1.09729i | 0.0525509 | + | 0.0525509i | ||||
\(437\) | −46.6014 | − | 12.4868i | −2.22925 | − | 0.597325i | ||||
\(438\) | 2.10807 | − | 3.65128i | 0.100727 | − | 0.174465i | ||||
\(439\) | 6.36168 | + | 11.0188i | 0.303626 | + | 0.525896i | 0.976955 | − | 0.213447i | \(-0.0684692\pi\) |
−0.673328 | + | 0.739344i | \(0.735136\pi\) | |||||||
\(440\) | 3.06645 | + | 11.4441i | 0.146187 | + | 0.545578i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 17.1468 | − | 11.9451i | 0.815591 | − | 0.568169i | ||||
\(443\) | 1.11534 | − | 1.93182i | 0.0529912 | − | 0.0917834i | −0.838313 | − | 0.545189i | \(-0.816458\pi\) |
0.891304 | + | 0.453406i | \(0.149791\pi\) | |||||||
\(444\) | −0.530865 | − | 0.530865i | −0.0251938 | − | 0.0251938i | ||||
\(445\) | −14.1338 | −0.670005 | ||||||||
\(446\) | 32.1282 | 1.52132 | ||||||||
\(447\) | 6.59996 | + | 6.59996i | 0.312167 | + | 0.312167i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.0883 | − | 37.6500i | 0.476096 | − | 1.77682i | −0.141088 | − | 0.989997i | \(-0.545060\pi\) |
0.617184 | − | 0.786819i | \(-0.288273\pi\) | |||||||
\(450\) | 7.98542 | − | 2.13969i | 0.376436 | − | 0.100866i | ||||
\(451\) | 14.6877 | + | 8.47994i | 0.691616 | + | 0.399305i | ||||
\(452\) | 0.0605803i | 0.00284946i | ||||||||
\(453\) | 13.9886 | + | 3.74823i | 0.657242 | + | 0.176107i | ||||
\(454\) | −14.3906 | −0.675387 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 19.1090 | 0.894862 | ||||||||
\(457\) | −22.2431 | − | 5.96003i | −1.04049 | − | 0.278798i | −0.302174 | − | 0.953253i | \(-0.597712\pi\) |
−0.738316 | + | 0.674455i | \(0.764379\pi\) | |||||||
\(458\) | 2.66273i | 0.124421i | ||||||||
\(459\) | 18.9067 | + | 10.9158i | 0.882490 | + | 0.509506i | ||||
\(460\) | 2.03967 | − | 0.546528i | 0.0951002 | − | 0.0254820i | ||||
\(461\) | 7.81461 | − | 29.1645i | 0.363962 | − | 1.35833i | −0.504859 | − | 0.863202i | \(-0.668456\pi\) |
0.868822 | − | 0.495125i | \(-0.164878\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.19856 | + | 2.19856i | 0.102176 | + | 0.102176i | 0.756347 | − | 0.654171i | \(-0.226982\pi\) |
−0.654171 | + | 0.756347i | \(0.726982\pi\) | |||||||
\(464\) | −3.35801 | −0.155892 | ||||||||
\(465\) | −2.82275 | −0.130902 | ||||||||
\(466\) | 8.39083 | + | 8.39083i | 0.388698 | + | 0.388698i | ||||
\(467\) | 10.5856 | − | 18.3348i | 0.489844 | − | 0.848434i | −0.510088 | − | 0.860122i | \(-0.670387\pi\) |
0.999932 | + | 0.0116879i | \(0.00372046\pi\) | |||||||
\(468\) | −0.479694 | − | 0.404478i | −0.0221739 | − | 0.0186970i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3.20394 | + | 11.9573i | 0.147787 | + | 0.551547i | ||||
\(471\) | −3.63416 | − | 6.29455i | −0.167453 | − | 0.290038i | ||||
\(472\) | −8.46043 | + | 14.6539i | −0.389423 | + | 0.674500i | ||||
\(473\) | −1.28974 | − | 0.345586i | −0.0593025 | − | 0.0158901i | ||||
\(474\) | −9.86978 | − | 9.86978i | −0.453334 | − | 0.453334i | ||||
\(475\) | 19.2702 | + | 5.16343i | 0.884176 | + | 0.236914i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.33634 | − | 4.04666i | −0.106974 | − | 0.185284i | ||||
\(478\) | −10.9086 | + | 6.29809i | −0.498948 | + | 0.288068i | ||||
\(479\) | 16.9808 | − | 16.9808i | 0.775871 | − | 0.775871i | −0.203255 | − | 0.979126i | \(-0.565152\pi\) |
0.979126 | + | 0.203255i | \(0.0651521\pi\) | |||||||
\(480\) | −1.41611 | + | 0.817593i | −0.0646364 | + | 0.0373179i | ||||
\(481\) | 11.4062 | − | 24.3081i | 0.520077 | − | 1.10835i | ||||
\(482\) | 6.02432i | 0.274400i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.421303 | + | 0.729719i | −0.0191501 | + | 0.0331690i | ||||
\(485\) | 26.3620i | 1.19704i | ||||||||
\(486\) | −5.56560 | + | 20.7711i | −0.252461 | + | 0.942196i | ||||
\(487\) | −8.81975 | − | 32.9158i | −0.399661 | − | 1.49156i | −0.813694 | − | 0.581294i | \(-0.802547\pi\) |
0.414032 | − | 0.910262i | \(-0.364120\pi\) | |||||||
\(488\) | −0.174593 | + | 0.174593i | −0.00790344 | + | 0.00790344i | ||||
\(489\) | 8.28165 | − | 8.28165i | 0.374509 | − | 0.374509i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.2688 | + | 7.08337i | 0.553681 | + | 0.319668i | 0.750605 | − | 0.660751i | \(-0.229762\pi\) |
−0.196924 | + | 0.980419i | \(0.563095\pi\) | |||||||
\(492\) | −0.309869 | + | 1.15645i | −0.0139700 | + | 0.0521367i | ||||
\(493\) | −1.85343 | − | 3.21024i | −0.0834745 | − | 0.144582i | ||||
\(494\) | 10.4275 | + | 28.8648i | 0.469156 | + | 1.29869i | ||||
\(495\) | −6.56838 | − | 3.79226i | −0.295227 | − | 0.170449i | ||||
\(496\) | 3.37039 | − | 0.903094i | 0.151335 | − | 0.0405501i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −2.79228 | + | 1.61213i | −0.125125 | + | 0.0722411i | ||||
\(499\) | −7.71779 | − | 28.8032i | −0.345496 | − | 1.28941i | −0.892032 | − | 0.451972i | \(-0.850721\pi\) |
0.546536 | − | 0.837436i | \(-0.315946\pi\) | |||||||
\(500\) | 0.459891 | − | 0.123227i | 0.0205670 | − | 0.00551090i | ||||
\(501\) | −18.8602 | + | 5.05358i | −0.842613 | + | 0.225777i | ||||
\(502\) | 1.62903 | + | 6.07962i | 0.0727072 | + | 0.271347i | ||||
\(503\) | 11.8147 | − | 6.82122i | 0.526791 | − | 0.304143i | −0.212918 | − | 0.977070i | \(-0.568297\pi\) |
0.739709 | + | 0.672927i | \(0.234963\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.1560 | + | 4.86488i | −0.807930 | + | 0.216484i | ||||
\(506\) | 13.3603 | + | 7.71358i | 0.593938 | + | 0.342910i | ||||
\(507\) | −4.82952 | + | 13.0733i | −0.214487 | + | 0.580607i | ||||
\(508\) | 0.767040 | + | 1.32855i | 0.0340319 | + | 0.0589450i | ||||
\(509\) | −0.690957 | + | 2.57869i | −0.0306261 | + | 0.114298i | −0.979547 | − | 0.201216i | \(-0.935511\pi\) |
0.948921 | + | 0.315515i | \(0.102177\pi\) | |||||||
\(510\) | 15.4426 | + | 8.91581i | 0.683812 | + | 0.394799i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 16.9779 | − | 16.9779i | 0.750326 | − | 0.750326i | ||||
\(513\) | −22.6717 | + | 22.6717i | −1.00098 | + | 1.00098i | ||||
\(514\) | −3.08483 | − | 11.5127i | −0.136066 | − | 0.507806i | ||||
\(515\) | 7.32016 | − | 27.3192i | 0.322565 | − | 1.20383i | ||||
\(516\) | − | 0.0942584i | − | 0.00414949i | ||||||
\(517\) | 2.23099 | − | 3.86419i | 0.0981190 | − | 0.169947i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 21.6045i | 0.948331i | ||||||||
\(520\) | −22.8686 | − | 19.2828i | −1.00286 | − | 0.845607i | ||||
\(521\) | −13.4638 | + | 7.77333i | −0.589860 | + | 0.340556i | −0.765042 | − | 0.643980i | \(-0.777282\pi\) |
0.175182 | + | 0.984536i | \(0.443948\pi\) | |||||||
\(522\) | 1.59521 | − | 1.59521i | 0.0698204 | − | 0.0698204i | ||||
\(523\) | 0.102601 | − | 0.0592367i | 0.00448643 | − | 0.00259024i | −0.497755 | − | 0.867318i | \(-0.665842\pi\) |
0.502242 | + | 0.864727i | \(0.332509\pi\) | |||||||
\(524\) | 0.110622 | + | 0.191603i | 0.00483255 | + | 0.00837022i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −17.4197 | − | 4.66758i | −0.759533 | − | 0.203516i | ||||
\(527\) | 2.72362 | + | 2.72362i | 0.118643 | + | 0.118643i | ||||
\(528\) | −5.62407 | − | 1.50696i | −0.244756 | − | 0.0655822i | ||||
\(529\) | 19.1147 | − | 33.1077i | 0.831075 | − | 1.43946i | ||||
\(530\) | −5.00166 | − | 8.66313i | −0.217258 | − | 0.376302i | ||||
\(531\) | −2.80354 | − | 10.4630i | −0.121663 | − | 0.454053i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −42.6658 | + | 3.62957i | −1.84806 | + | 0.157214i | ||||
\(534\) | 3.64466 | − | 6.31274i | 0.157720 | − | 0.273179i | ||||
\(535\) | −21.4970 | − | 21.4970i | −0.929395 | − | 0.929395i | ||||
\(536\) | −2.97880 | −0.128665 | ||||||||
\(537\) | −17.7236 | −0.764830 | ||||||||
\(538\) | 12.2592 | + | 12.2592i | 0.528534 | + | 0.528534i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.363209 | − | 1.35551i | 0.0156300 | − | 0.0583320i | ||||
\(541\) | 4.47060 | − | 1.19789i | 0.192206 | − | 0.0515014i | −0.161432 | − | 0.986884i | \(-0.551611\pi\) |
0.353638 | + | 0.935382i | \(0.384945\pi\) | |||||||
\(542\) | −5.51652 | − | 3.18496i | −0.236955 | − | 0.136806i | ||||
\(543\) | 14.6763i | 0.629819i | ||||||||
\(544\) | 2.15526 | + | 0.577501i | 0.0924062 | + | 0.0247602i | ||||
\(545\) | −47.3589 | −2.02863 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.4860 | 1.26073 | 0.630365 | − | 0.776299i | \(-0.282905\pi\) | ||||
0.630365 | + | 0.776299i | \(0.282905\pi\) | |||||||
\(548\) | 0.943461 | + | 0.252800i | 0.0403026 | + | 0.0107991i | ||||
\(549\) | − | 0.158063i | − | 0.00674594i | ||||||
\(550\) | −5.52463 | − | 3.18965i | −0.235571 | − | 0.136007i | ||||
\(551\) | 5.25853 | − | 1.40902i | 0.224021 | − | 0.0600263i | ||||
\(552\) | −6.27682 | + | 23.4254i | −0.267159 | + | 0.997052i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.63267 | + | 1.63267i | 0.0693657 | + | 0.0693657i | ||||
\(555\) | 22.9120 | 0.972561 | ||||||||
\(556\) | −0.578964 | −0.0245536 | ||||||||
\(557\) | 0.959258 | + | 0.959258i | 0.0406451 | + | 0.0406451i | 0.727137 | − | 0.686492i | \(-0.240850\pi\) |
−0.686492 | + | 0.727137i | \(0.740850\pi\) | |||||||
\(558\) | −1.17208 | + | 2.03010i | −0.0496181 | + | 0.0859411i | ||||
\(559\) | 3.17064 | − | 1.14541i | 0.134104 | − | 0.0484455i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.66352 | − | 6.20834i | −0.0702338 | − | 0.262116i | ||||
\(562\) | −13.5946 | − | 23.5465i | −0.573453 | − | 0.993249i | ||||
\(563\) | −16.4050 | + | 28.4143i | −0.691388 | + | 1.19752i | 0.279995 | + | 0.960001i | \(0.409667\pi\) |
−0.971383 | + | 0.237517i | \(0.923666\pi\) | |||||||
\(564\) | 0.304251 | + | 0.0815238i | 0.0128113 | + | 0.00343277i | ||||
\(565\) | −1.30731 | − | 1.30731i | −0.0549991 | − | 0.0549991i | ||||
\(566\) | 43.9982 | + | 11.7893i | 1.84938 | + | 0.495541i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.19005 | − | 7.25739i | −0.175811 | − | 0.304513i | ||||
\(569\) | 25.8745 | − | 14.9387i | 1.08472 | − | 0.626261i | 0.152552 | − | 0.988296i | \(-0.451251\pi\) |
0.932165 | + | 0.362034i | \(0.117918\pi\) | |||||||
\(570\) | −18.5178 | + | 18.5178i | −0.775626 | + | 0.775626i | ||||
\(571\) | −0.640877 | + | 0.370010i | −0.0268198 | + | 0.0154844i | −0.513350 | − | 0.858179i | \(-0.671596\pi\) |
0.486530 | + | 0.873664i | \(0.338262\pi\) | |||||||
\(572\) | 0.0410408 | + | 0.482437i | 0.00171600 | + | 0.0201717i | ||||
\(573\) | − | 8.73616i | − | 0.364958i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.6595 | + | 21.9269i | −0.527938 | + | 0.914416i | ||||
\(576\) | 15.4345i | 0.643104i | ||||||||
\(577\) | 8.82812 | − | 32.9470i | 0.367519 | − | 1.37160i | −0.496454 | − | 0.868063i | \(-0.665365\pi\) |
0.863973 | − | 0.503538i | \(-0.167969\pi\) | |||||||
\(578\) | −0.223233 | − | 0.833116i | −0.00928526 | − | 0.0346531i | ||||
\(579\) | −20.3065 | + | 20.3065i | −0.843909 | + | 0.843909i | ||||
\(580\) | −0.168487 | + | 0.168487i | −0.00699605 | + | 0.00699605i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −11.7744 | − | 6.79795i | −0.488064 | − | 0.281784i | ||||
\(583\) | −0.933213 | + | 3.48280i | −0.0386498 | + | 0.144243i | ||||
\(584\) | 4.11762 | + | 7.13193i | 0.170388 | + | 0.295121i | ||||
\(585\) | 19.0803 | − | 1.62316i | 0.788874 | − | 0.0671093i | ||||
\(586\) | −26.2559 | − | 15.1588i | −1.08462 | − | 0.626206i | ||||
\(587\) | 11.9740 | − | 3.20842i | 0.494219 | − | 0.132426i | −0.00309648 | − | 0.999995i | \(-0.500986\pi\) |
0.497316 | + | 0.867569i | \(0.334319\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.89899 | + | 2.82843i | −0.201859 | + | 0.116543i | ||||
\(590\) | −6.00184 | − | 22.3992i | −0.247092 | − | 0.922160i | ||||
\(591\) | −19.0861 | + | 5.11412i | −0.785099 | + | 0.210367i | ||||
\(592\) | −27.3572 | + | 7.33034i | −1.12437 | + | 0.301275i | ||||
\(593\) | −5.91611 | − | 22.0792i | −0.242945 | − | 0.906685i | −0.974405 | − | 0.224800i | \(-0.927827\pi\) |
0.731460 | − | 0.681885i | \(-0.238839\pi\) | |||||||
\(594\) | 8.87892 | − | 5.12625i | 0.364307 | − | 0.210333i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.790795 | + | 0.211893i | −0.0323922 | + | 0.00867948i | ||||
\(597\) | −11.8019 | − | 6.81383i | −0.483019 | − | 0.278871i | ||||
\(598\) | −38.8100 | + | 3.30156i | −1.58706 | + | 0.135011i | ||||
\(599\) | −1.24701 | − | 2.15989i | −0.0509516 | − | 0.0882508i | 0.839425 | − | 0.543476i | \(-0.182892\pi\) |
−0.890376 | + | 0.455225i | \(0.849559\pi\) | |||||||
\(600\) | 2.59553 | − | 9.68666i | 0.105962 | − | 0.395456i | ||||
\(601\) | −18.5873 | − | 10.7314i | −0.758193 | − | 0.437743i | 0.0704537 | − | 0.997515i | \(-0.477555\pi\) |
−0.828647 | + | 0.559772i | \(0.810889\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.34839 | − | 1.34839i | 0.0549106 | − | 0.0549106i | ||||
\(604\) | −0.898214 | + | 0.898214i | −0.0365478 | + | 0.0365478i | ||||
\(605\) | −6.65556 | − | 24.8389i | −0.270587 | − | 1.00984i | ||||
\(606\) | 2.50901 | − | 9.36374i | 0.101921 | − | 0.380376i | ||||
\(607\) | 16.0396i | 0.651028i | 0.945537 | + | 0.325514i | \(0.105537\pi\) | ||||
−0.945537 | + | 0.325514i | \(0.894463\pi\) | |||||||
\(608\) | −1.63848 | + | 2.83793i | −0.0664490 | + | 0.115093i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 0.338382i | − | 0.0137007i | ||||||
\(611\) | 0.954908 | + | 11.2250i | 0.0386314 | + | 0.454115i | ||||
\(612\) | −0.632715 | + | 0.365298i | −0.0255760 | + | 0.0147663i | ||||
\(613\) | −4.88837 | + | 4.88837i | −0.197440 | + | 0.197440i | −0.798901 | − | 0.601462i | \(-0.794585\pi\) |
0.601462 | + | 0.798901i | \(0.294585\pi\) | |||||||
\(614\) | −23.3054 | + | 13.4554i | −0.940530 | + | 0.543015i | ||||
\(615\) | −18.2691 | − | 31.6429i | −0.736680 | − | 1.27597i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.9254 | + | 7.21463i | 1.08397 | + | 0.290450i | 0.756223 | − | 0.654314i | \(-0.227043\pi\) |
0.327751 | + | 0.944764i | \(0.393709\pi\) | |||||||
\(618\) | 10.3143 | + | 10.3143i | 0.414901 | + | 0.414901i | ||||
\(619\) | −13.3912 | − | 3.58815i | −0.538237 | − | 0.144220i | −0.0205475 | − | 0.999789i | \(-0.506541\pi\) |
−0.517689 | + | 0.855569i | \(0.673208\pi\) | |||||||
\(620\) | 0.123796 | − | 0.214421i | 0.00497177 | − | 0.00861136i | ||||
\(621\) | −20.3458 | − | 35.2399i | −0.816448 | − | 1.41413i | ||||
\(622\) | −9.22831 | − | 34.4405i | −0.370022 | − | 1.38094i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 13.8259 | − | 4.99466i | 0.553480 | − | 0.199947i | ||||
\(625\) | −15.3544 | + | 26.5946i | −0.614175 | + | 1.06378i | ||||
\(626\) | 27.9842 | + | 27.9842i | 1.11847 | + | 1.11847i | ||||
\(627\) | 9.43942 | 0.376974 | ||||||||
\(628\) | 0.637527 | 0.0254401 | ||||||||
\(629\) | −22.1074 | − | 22.1074i | −0.881480 | − | 0.881480i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.69536 | − | 24.9874i | 0.266538 | − | 0.994733i | −0.694764 | − | 0.719237i | \(-0.744491\pi\) |
0.961302 | − | 0.275496i | \(-0.0888419\pi\) | |||||||
\(632\) | 26.3347 | − | 7.05636i | 1.04754 | − | 0.280687i | ||||
\(633\) | −4.20506 | − | 2.42779i | −0.167136 | − | 0.0964961i | ||||
\(634\) | 17.2105i | 0.683517i | ||||||||
\(635\) | −45.2226 | − | 12.1174i | −1.79460 | − | 0.480863i | ||||
\(636\) | −0.254533 | −0.0100929 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.74081 | −0.0689193 | ||||||||
\(639\) | 5.18181 | + | 1.38846i | 0.204989 | + | 0.0549267i | ||||
\(640\) | 29.9918i | 1.18553i | ||||||||
\(641\) | 10.8902 | + | 6.28745i | 0.430136 | + | 0.248339i | 0.699405 | − | 0.714726i | \(-0.253449\pi\) |
−0.269269 | + | 0.963065i | \(0.586782\pi\) | |||||||
\(642\) | 15.1449 | − | 4.05806i | 0.597720 | − | 0.160159i | ||||
\(643\) | −6.40174 | + | 23.8916i | −0.252460 | + | 0.942193i | 0.717026 | + | 0.697046i | \(0.245503\pi\) |
−0.969486 | + | 0.245147i | \(0.921164\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.03408 | + | 2.03408i | 0.0800919 | + | 0.0800919i | ||||
\(646\) | 35.7350 | 1.40598 | ||||||||
\(647\) | −34.6235 | −1.36119 | −0.680595 | − | 0.732660i | \(-0.738279\pi\) | ||||
−0.680595 | + | 0.732660i | \(0.738279\pi\) | |||||||
\(648\) | 0.0470090 | + | 0.0470090i | 0.00184669 | + | 0.00184669i | ||||
\(649\) | −4.17926 | + | 7.23869i | −0.164050 | + | 0.284143i | ||||
\(650\) | 16.0483 | − | 1.36523i | 0.629468 | − | 0.0535487i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.265884 | + | 0.992293i | 0.0104128 | + | 0.0388612i | ||||
\(653\) | 13.7001 | + | 23.7293i | 0.536127 | + | 0.928600i | 0.999108 | + | 0.0422314i | \(0.0134467\pi\) |
−0.462980 | + | 0.886368i | \(0.653220\pi\) | |||||||
\(654\) | 12.2124 | − | 21.1525i | 0.477543 | − | 0.827129i | ||||
\(655\) | −6.52198 | − | 1.74756i | −0.254835 | − | 0.0682828i | ||||
\(656\) | 31.9371 | + | 31.9371i | 1.24694 | + | 1.24694i | ||||
\(657\) | −5.09224 | − | 1.36446i | −0.198667 | − | 0.0532327i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.14617 | + | 3.71728i | 0.0836031 | + | 0.144805i | 0.904795 | − | 0.425847i | \(-0.140024\pi\) |
−0.821192 | + | 0.570652i | \(0.806691\pi\) | |||||||
\(660\) | −0.357797 | + | 0.206574i | −0.0139272 | + | 0.00804090i | ||||
\(661\) | −10.7570 | + | 10.7570i | −0.418399 | + | 0.418399i | −0.884652 | − | 0.466252i | \(-0.845604\pi\) |
0.466252 | + | 0.884652i | \(0.345604\pi\) | |||||||
\(662\) | 35.8115 | − | 20.6758i | 1.39185 | − | 0.803586i | ||||
\(663\) | 12.4060 | + | 10.4607i | 0.481809 | + | 0.406261i | ||||
\(664\) | − | 6.29783i | − | 0.244403i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9.51367 | − | 16.4782i | 0.368647 | − | 0.638516i | ||||
\(667\) | 6.90917i | 0.267524i | ||||||||
\(668\) | 0.443265 | − | 1.65429i | 0.0171504 | − | 0.0640063i | ||||
\(669\) | 6.45725 | + | 24.0988i | 0.249652 | + | 0.931713i | ||||
\(670\) | 2.88664 | − | 2.88664i | 0.111521 | − | 0.111521i | ||||
\(671\) | −0.0862447 | + | 0.0862447i | −0.00332944 | + | 0.00332944i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.3013 | + | 15.1851i | 1.01384 | + | 0.585341i | 0.912314 | − | 0.409492i | \(-0.134294\pi\) |
0.101526 | + | 0.994833i | \(0.467627\pi\) | |||||||
\(674\) | −4.80243 | + | 17.9229i | −0.184983 | + | 0.690365i | ||||
\(675\) | 8.41319 | + | 14.5721i | 0.323824 | + | 0.560879i | ||||
\(676\) | −0.781267 | − | 0.940210i | −0.0300487 | − | 0.0361619i | ||||
\(677\) | −31.7593 | − | 18.3363i | −1.22061 | − | 0.704720i | −0.255562 | − | 0.966793i | \(-0.582261\pi\) |
−0.965048 | + | 0.262073i | \(0.915594\pi\) | |||||||
\(678\) | 0.921018 | − | 0.246786i | 0.0353715 | − | 0.00947776i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −30.1636 | + | 17.4150i | −1.15672 | + | 0.667834i | ||||
\(681\) | −2.89228 | − | 10.7942i | −0.110833 | − | 0.413633i | ||||
\(682\) | 1.74723 | − | 0.468169i | 0.0669049 | − | 0.0179271i | ||||
\(683\) | −15.4630 | + | 4.14330i | −0.591676 | + | 0.158539i | −0.542219 | − | 0.840237i | \(-0.682416\pi\) |
−0.0494567 | + | 0.998776i | \(0.515749\pi\) | |||||||
\(684\) | −0.277707 | − | 1.03642i | −0.0106184 | − | 0.0396284i | ||||
\(685\) | −25.8151 | + | 14.9044i | −0.986346 | + | 0.569467i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.99727 | + | 0.535166i | −0.0762005 | + | 0.0204179i | ||||
\(688\) | −3.07949 | − | 1.77794i | −0.117404 | − | 0.0677835i | ||||
\(689\) | −3.09303 | − | 8.56194i | −0.117835 | − | 0.326184i | ||||
\(690\) | −16.6180 | − | 28.7833i | −0.632638 | − | 1.09576i | ||||
\(691\) | −4.67596 | + | 17.4509i | −0.177882 | + | 0.663864i | 0.818161 | + | 0.574989i | \(0.194994\pi\) |
−0.996043 | + | 0.0888748i | \(0.971673\pi\) | |||||||
\(692\) | −1.64111 | − | 0.947497i | −0.0623858 | − | 0.0360184i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.1538 | − | 14.1538i | 0.537270 | − | 0.537270i | ||||
\(695\) | 12.4940 | − | 12.4940i | 0.473923 | − | 0.473923i | ||||
\(696\) | −0.708280 | − | 2.64334i | −0.0268473 | − | 0.100195i | ||||
\(697\) | −12.9042 | + | 48.1592i | −0.488783 | + | 1.82416i | ||||
\(698\) | − | 30.3094i | − | 1.14723i | ||||||
\(699\) | −4.60738 | + | 7.98022i | −0.174267 | + | 0.301840i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 37.6363i | − | 1.42150i | −0.703444 | − | 0.710751i | \(-0.748355\pi\) | ||
0.703444 | − | 0.710751i | \(-0.251645\pi\) | |||||||
\(702\) | −10.9959 | + | 23.4337i | −0.415013 | + | 0.884448i | ||||
\(703\) | 39.7646 | − | 22.9581i | 1.49975 | − | 0.865882i | ||||
\(704\) | 8.42163 | − | 8.42163i | 0.317402 | − | 0.317402i | ||||
\(705\) | −8.32497 | + | 4.80642i | −0.313537 | + | 0.181020i | ||||
\(706\) | 7.97086 | + | 13.8059i | 0.299987 | + | 0.519593i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.569945 | − | 0.152716i | −0.0214198 | − | 0.00573943i | ||||
\(709\) | −8.15239 | − | 8.15239i | −0.306169 | − | 0.306169i | 0.537252 | − | 0.843422i | \(-0.319462\pi\) |
−0.843422 | + | 0.537252i | \(0.819462\pi\) | |||||||
\(710\) | 11.0933 | + | 2.97243i | 0.416323 | + | 0.111553i | ||||
\(711\) | −8.72655 | + | 15.1148i | −0.327271 | + | 0.566850i | ||||
\(712\) | 7.11900 | + | 12.3305i | 0.266796 | + | 0.462104i | ||||
\(713\) | −1.85813 | − | 6.93465i | −0.0695876 | − | 0.259705i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.2966 | − | 9.52526i | −0.422468 | − | 0.356225i | ||||
\(716\) | 0.777296 | − | 1.34632i | 0.0290489 | − | 0.0503142i | ||||
\(717\) | −6.91652 | − | 6.91652i | −0.258302 | − | 0.258302i | ||||
\(718\) | 1.23201 | 0.0459782 | ||||||||
\(719\) | −46.1930 | −1.72271 | −0.861355 | − | 0.508004i | \(-0.830384\pi\) | ||||
−0.861355 | + | 0.508004i | \(0.830384\pi\) | |||||||
\(720\) | −14.2824 | − | 14.2824i | −0.532273 | − | 0.532273i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −6.79424 | + | 25.3564i | −0.252855 | + | 0.943669i | ||||
\(723\) | −4.51873 | + | 1.21079i | −0.168053 | + | 0.0450298i | ||||
\(724\) | −1.11484 | − | 0.643651i | −0.0414325 | − | 0.0239211i | ||||
\(725\) | − | 2.85702i | − | 0.106107i | ||||||
\(726\) | 12.8104 | + | 3.43253i | 0.475438 | + | 0.127393i | ||||
\(727\) | 3.27502 | 0.121464 | 0.0607318 | − | 0.998154i | \(-0.480657\pi\) | ||||
0.0607318 | + | 0.998154i | \(0.480657\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −16.7676 | −0.621022 | ||||||||
\(730\) | −10.9015 | − | 2.92105i | −0.403483 | − | 0.108113i | ||||
\(731\) | − | 3.92530i | − | 0.145183i | ||||||
\(732\) | −0.00745656 | − | 0.00430505i | −0.000275602 | − | 0.000159119i | ||||
\(733\) | 32.5986 | − | 8.73478i | 1.20406 | − | 0.322626i | 0.399630 | − | 0.916676i | \(-0.369139\pi\) |
0.804428 | + | 0.594050i | \(0.202472\pi\) | |||||||
\(734\) | −5.17148 | + | 19.3002i | −0.190883 | + | 0.712384i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.94077 | − | 2.94077i | −0.108398 | − | 0.108398i | ||||
\(737\) | −1.47146 | −0.0542020 | ||||||||
\(738\) | −30.3432 | −1.11695 | ||||||||
\(739\) | −1.49619 | − | 1.49619i | −0.0550382 | − | 0.0550382i | 0.679052 | − | 0.734090i | \(-0.262391\pi\) |
−0.734090 | + | 0.679052i | \(0.762391\pi\) | |||||||
\(740\) | −1.00484 | + | 1.74044i | −0.0369387 | + | 0.0639797i | ||||
\(741\) | −19.5552 | + | 13.6228i | −0.718377 | + | 0.500447i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.14174 | − | 26.6533i | −0.262005 | − | 0.977816i | −0.964058 | − | 0.265692i | \(-0.914400\pi\) |
0.702053 | − | 0.712125i | \(-0.252267\pi\) | |||||||
\(744\) | 1.42178 | + | 2.46260i | 0.0521251 | + | 0.0902834i | ||||
\(745\) | 12.4926 | − | 21.6379i | 0.457695 | − | 0.792751i | ||||
\(746\) | 27.9066 | + | 7.47755i | 1.02173 | + | 0.273773i | ||||
\(747\) | 2.85078 | + | 2.85078i | 0.104305 | + | 0.104305i | ||||
\(748\) | 0.544552 | + | 0.145912i | 0.0199108 | + | 0.00533508i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −3.74692 | − | 6.48986i | −0.136818 | − | 0.236976i | ||||
\(751\) | 6.52544 | − | 3.76747i | 0.238117 | − | 0.137477i | −0.376194 | − | 0.926541i | \(-0.622767\pi\) |
0.614311 | + | 0.789064i | \(0.289434\pi\) | |||||||
\(752\) | 8.40237 | − | 8.40237i | 0.306403 | − | 0.306403i | ||||
\(753\) | −4.23280 | + | 2.44381i | −0.154252 | + | 0.0890574i | ||||
\(754\) | 3.60635 | − | 2.51231i | 0.131335 | − | 0.0914929i | ||||
\(755\) | − | 38.7667i | − | 1.41086i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.0971 | + | 36.5412i | −0.766786 | + | 1.32811i | 0.172512 | + | 0.985007i | \(0.444812\pi\) |
−0.939297 | + | 0.343104i | \(0.888522\pi\) | |||||||
\(758\) | − | 29.5044i | − | 1.07165i | ||||||
\(759\) | −3.10061 | + | 11.5716i | −0.112545 | + | 0.420023i | ||||
\(760\) | −13.2392 | − | 49.4095i | −0.480237 | − | 1.79227i | ||||
\(761\) | −1.20610 | + | 1.20610i | −0.0437212 | + | 0.0437212i | −0.728629 | − | 0.684908i | \(-0.759842\pi\) |
0.684908 | + | 0.728629i | \(0.259842\pi\) | |||||||
\(762\) | 17.0736 | − | 17.0736i | 0.618513 | − | 0.618513i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0.663614 | + | 0.383138i | 0.0240087 | + | 0.0138614i | ||||
\(765\) | 5.77082 | − | 21.5370i | 0.208644 | − | 0.778671i | ||||
\(766\) | −12.3734 | − | 21.4314i | −0.447070 | − | 0.774349i | ||||
\(767\) | −1.78880 | − | 21.0275i | −0.0645899 | − | 0.759258i | ||||
\(768\) | 2.09061 | + | 1.20702i | 0.0754385 | + | 0.0435545i | ||||
\(769\) | 3.49612 | − | 0.936782i | 0.126073 | − | 0.0337812i | −0.195231 | − | 0.980757i | \(-0.562546\pi\) |
0.321304 | + | 0.946976i | \(0.395879\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.01550 | − | 4.62775i | 0.288671 | − | 0.166664i | ||||
\(772\) | −0.651944 | − | 2.43309i | −0.0234640 | − | 0.0875688i | ||||
\(773\) | 25.8153 | − | 6.91718i | 0.928510 | − | 0.248794i | 0.237291 | − | 0.971439i | \(-0.423741\pi\) |
0.691219 | + | 0.722645i | \(0.257074\pi\) | |||||||
\(774\) | 2.30750 | − | 0.618294i | 0.0829415 | − | 0.0222241i | ||||
\(775\) | 0.768358 | + | 2.86755i | 0.0276002 | + | 0.103005i | ||||
\(776\) | 22.9985 | − | 13.2782i | 0.825600 | − | 0.476660i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.48299 | − | 1.73711i | 0.232426 | − | 0.0622785i | ||||
\(779\) | −63.4133 | − | 36.6117i | −2.27202 | − | 1.31175i | ||||
\(780\) | 0.443106 | − | 0.944317i | 0.0158657 | − | 0.0338120i | ||||
\(781\) | −2.06979 | − | 3.58498i | −0.0740629 | − | 0.128281i | ||||
\(782\) | −11.7380 | + | 43.8069i | −0.419751 | + | 1.56653i | ||||
\(783\) | 3.97649 | + | 2.29583i | 0.142108 | + | 0.0820463i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −13.7577 | + | 13.7577i | −0.491035 | + | 0.491035i | ||||
\(786\) | 2.46235 | − | 2.46235i | 0.0878292 | − | 0.0878292i | ||||
\(787\) | 11.3925 | + | 42.5173i | 0.406098 | + | 1.51558i | 0.802021 | + | 0.597296i | \(0.203758\pi\) |
−0.395923 | + | 0.918284i | \(0.629575\pi\) | |||||||
\(788\) | 0.448575 | − | 1.67410i | 0.0159798 | − | 0.0596375i | ||||
\(789\) | − | 14.0043i | − | 0.498565i | ||||||
\(790\) | −18.6819 | + | 32.3580i | −0.664672 | + | 1.15124i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 7.64045i | 0.271492i | ||||||||
\(793\) | 0.0542018 | − | 0.303136i | 0.00192476 | − | 0.0107647i | ||||
\(794\) | −23.3900 | + | 13.5042i | −0.830079 | + | 0.479246i | ||||
\(795\) | 5.49280 | − | 5.49280i | 0.194809 | − | 0.194809i | ||||
\(796\) | 1.03518 | − | 0.597662i | 0.0366910 | − | 0.0211836i | ||||
\(797\) | 6.94770 | + | 12.0338i | 0.246100 | + | 0.426258i | 0.962440 | − | 0.271493i | \(-0.0875175\pi\) |
−0.716340 | + | 0.697751i | \(0.754184\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.6703 | + | 3.39499i | 0.448241 | + | 0.120106i | ||||
\(800\) | 1.21604 | + | 1.21604i | 0.0429934 | + | 0.0429934i | ||||
\(801\) | −8.80402 | − | 2.35903i | −0.311075 | − | 0.0833522i | ||||
\(802\) | −2.96587 | + | 5.13704i | −0.104728 | + | 0.181395i | ||||
\(803\) | 2.03401 | + | 3.52301i | 0.0717787 | + | 0.124324i | ||||
\(804\) | −0.0268847 | − | 0.100335i | −0.000948150 | − | 0.00353854i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.94399 | + | 3.49146i | −0.103698 | + | 0.122981i | ||||
\(807\) | −6.73152 | + | 11.6593i | −0.236961 | + | 0.410428i | ||||
\(808\) | 13.3891 | + | 13.3891i | 0.471028 | + | 0.471028i | ||||
\(809\) | −44.4045 | −1.56118 | −0.780589 | − | 0.625045i | \(-0.785081\pi\) | ||||
−0.780589 | + | 0.625045i | \(0.785081\pi\) | |||||||
\(810\) | −0.0911092 | −0.00320125 | ||||||||
\(811\) | −9.49597 | − | 9.49597i | −0.333449 | − | 0.333449i | 0.520446 | − | 0.853895i | \(-0.325766\pi\) |
−0.853895 | + | 0.520446i | \(0.825766\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.28025 | − | 4.77796i | 0.0449004 | − | 0.167570i | ||||
\(814\) | −14.1821 | + | 3.80008i | −0.497083 | + | 0.133193i | ||||
\(815\) | −27.1513 | − | 15.6758i | −0.951068 | − | 0.549099i | ||||
\(816\) | − | 17.1167i | − | 0.599204i | ||||||
\(817\) | 5.56840 | + | 1.49205i | 0.194814 | + | 0.0522002i | ||||
\(818\) | 41.8760 | 1.46416 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.20487 | 0.111919 | ||||||||
\(821\) | −49.6560 | − | 13.3053i | −1.73301 | − | 0.464358i | −0.752135 | − | 0.659009i | \(-0.770976\pi\) |
−0.980873 | + | 0.194651i | \(0.937643\pi\) | |||||||
\(822\) | − | 15.3735i | − | 0.536213i | ||||||
\(823\) | −22.4979 | − | 12.9892i | −0.784227 | − | 0.452774i | 0.0536991 | − | 0.998557i | \(-0.482899\pi\) |
−0.837926 | + | 0.545783i | \(0.816232\pi\) | |||||||
\(824\) | −27.5207 | + | 7.37415i | −0.958729 | + | 0.256891i | ||||
\(825\) | 1.28213 | − | 4.78499i | 0.0446382 | − | 0.166592i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.05853 | − | 1.05853i | −0.0368089 | − | 0.0368089i | 0.688463 | − | 0.725272i | \(-0.258286\pi\) |
−0.725272 | + | 0.688463i | \(0.758286\pi\) | |||||||
\(828\) | 1.36175 | 0.0473239 | ||||||||
\(829\) | 14.6896 | 0.510192 | 0.255096 | − | 0.966916i | \(-0.417893\pi\) | ||||
0.255096 | + | 0.966916i | \(0.417893\pi\) | |||||||
\(830\) | 6.10298 | + | 6.10298i | 0.211837 | + | 0.211837i | ||||
\(831\) | −0.896497 | + | 1.55278i | −0.0310991 | + | 0.0538653i | ||||
\(832\) | −5.29270 | + | 29.6006i | −0.183491 | + | 1.02622i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 2.35853 | + | 8.80215i | 0.0816692 | + | 0.304794i | ||||
\(835\) | 26.1337 | + | 45.2649i | 0.904395 | + | 1.56646i | ||||
\(836\) | −0.413980 | + | 0.717035i | −0.0143178 | + | 0.0247992i | ||||
\(837\) | −4.60859 | − | 1.23487i | −0.159296 | − | 0.0426833i | ||||
\(838\) | −7.74676 | − | 7.74676i | −0.267607 | − | 0.267607i | ||||
\(839\) | 18.7042 | + | 5.01177i | 0.645740 | + | 0.173025i | 0.566802 | − | 0.823854i | \(-0.308180\pi\) |
0.0789379 | + | 0.996880i | \(0.474847\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.1102 | + | 24.4396i | 0.486558 | + | 0.842743i | ||||
\(842\) | −10.1128 | + | 5.83860i | −0.348509 | + | 0.201211i | ||||
\(843\) | 14.9295 | − | 14.9295i | 0.514199 | − | 0.514199i | ||||
\(844\) | 0.368839 | − | 0.212949i | 0.0126960 | − | 0.00733001i | ||||
\(845\) | 37.1493 | + | 3.42997i | 1.27797 | + | 0.117995i | ||||
\(846\) | 7.98302i | 0.274462i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −4.80113 | + | 8.31579i | −0.164871 | + | 0.285566i | ||||
\(849\) | 35.3717i | 1.21395i | ||||||||
\(850\) | 4.85380 | − | 18.1146i | 0.166484 | − | 0.621327i | ||||
\(851\) | 15.0823 | + | 56.2879i | 0.517015 | + | 1.92953i | ||||
\(852\) | 0.206634 | − | 0.206634i | 0.00707916 | − | 0.00707916i | ||||
\(853\) | 16.7852 | − | 16.7852i | 0.574713 | − | 0.574713i | −0.358728 | − | 0.933442i | \(-0.616790\pi\) |
0.933442 | + | 0.358728i | \(0.116790\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 28.3586 | + | 16.3729i | 0.969845 | + | 0.559940i | ||||
\(856\) | −7.92647 | + | 29.5820i | −0.270921 | + | 1.01109i | ||||
\(857\) | 25.5716 | + | 44.2913i | 0.873508 | + | 1.51296i | 0.858343 | + | 0.513076i | \(0.171494\pi\) |
0.0151651 | + | 0.999885i | \(0.495173\pi\) | |||||||
\(858\) | 7.16743 | − | 2.58926i | 0.244692 | − | 0.0883958i | ||||
\(859\) | 13.0666 | + | 7.54398i | 0.445825 | + | 0.257397i | 0.706065 | − | 0.708147i | \(-0.250468\pi\) |
−0.260240 | + | 0.965544i | \(0.583802\pi\) | |||||||
\(860\) | −0.243720 | + | 0.0653047i | −0.00831079 | + | 0.00222687i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.691725 | − | 0.399367i | 0.0235602 | − | 0.0136025i | ||||
\(863\) | −3.41659 | − | 12.7509i | −0.116302 | − | 0.434045i | 0.883079 | − | 0.469225i | \(-0.155467\pi\) |
−0.999381 | + | 0.0351791i | \(0.988800\pi\) | |||||||
\(864\) | −2.66970 | + | 0.715345i | −0.0908251 | + | 0.0243365i | ||||
\(865\) | 55.8619 | − | 14.9681i | 1.89936 | − | 0.508932i | ||||
\(866\) | 2.93953 | + | 10.9705i | 0.0998895 | + | 0.372793i | ||||
\(867\) | 0.580039 | − | 0.334885i | 0.0196991 | − | 0.0113733i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.0087 | − | 3.48568i | 0.441291 | − | 0.118244i | ||||
\(870\) | 3.24792 | + | 1.87519i | 0.110115 | + | 0.0635749i | ||||
\(871\) | 3.04835 | − | 2.12359i | 0.103289 | − | 0.0719551i | ||||
\(872\) | 23.8541 | + | 41.3165i | 0.807802 | + | 1.39915i | ||||
\(873\) | −4.40001 | + | 16.4211i | −0.148918 | + | 0.555769i | ||||
\(874\) | −57.6824 | − | 33.3030i | −1.95114 | − | 1.12649i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.203062 | + | 0.203062i | −0.00686083 | + | 0.00686083i | ||||
\(877\) | 27.5566 | − | 27.5566i | 0.930519 | − | 0.930519i | −0.0672193 | − | 0.997738i | \(-0.521413\pi\) |
0.997738 | + | 0.0672193i | \(0.0214127\pi\) | |||||||
\(878\) | 4.54627 | + | 16.9669i | 0.153429 | + | 0.572606i | ||||
\(879\) | 6.09336 | − | 22.7407i | 0.205524 | − | 0.767025i | ||||
\(880\) | 15.5860i | 0.525404i | ||||||||
\(881\) | −14.6029 | + | 25.2929i | −0.491983 | + | 0.852140i | −0.999957 | − | 0.00923231i | \(-0.997061\pi\) |
0.507974 | + | 0.861372i | \(0.330395\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.58799i | 0.0870929i | 0.999051 | + | 0.0435464i | \(0.0138656\pi\) | ||||
−0.999051 | + | 0.0435464i | \(0.986134\pi\) | |||||||
\(884\) | −1.33870 | + | 0.483610i | −0.0450254 | + | 0.0162656i | ||||
\(885\) | 15.5949 | − | 9.00374i | 0.524218 | − | 0.302657i | ||||
\(886\) | 2.17760 | − | 2.17760i | 0.0731579 | − | 0.0731579i | ||||
\(887\) | 32.6723 | − | 18.8634i | 1.09703 | − | 0.633370i | 0.161590 | − | 0.986858i | \(-0.448338\pi\) |
0.935439 | + | 0.353488i | \(0.115004\pi\) | |||||||
\(888\) | −11.5405 | − | 19.9887i | −0.387274 | − | 0.670778i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −18.8477 | − | 5.05023i | −0.631777 | − | 0.169284i | ||||
\(891\) | 0.0232214 | + | 0.0232214i | 0.000777946 | + | 0.000777946i | ||||
\(892\) | −2.11378 | − | 0.566385i | −0.0707745 | − | 0.0189640i | ||||
\(893\) | −9.63220 | + | 16.6835i | −0.322329 | + | 0.558291i | ||||
\(894\) | 6.44293 | + | 11.1595i | 0.215484 | + | 0.373229i | ||||
\(895\) | 12.2794 | + | 45.8273i | 0.410454 | + | 1.53184i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −10.2766 | − | 28.4471i | −0.343126 | − | 0.949821i | ||||
\(898\) | 26.9060 | − | 46.6026i | 0.897865 | − | 1.55515i | ||||
\(899\) | 0.572837 | + | 0.572837i | 0.0191052 | + | 0.0191052i | ||||
\(900\) | −0.563096 | −0.0187699 | ||||||||
\(901\) | −10.5998 | −0.353131 | ||||||||
\(902\) | 16.5564 | + | 16.5564i | 0.551267 | + | 0.551267i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.482039 | + | 1.79900i | −0.0160324 | + | 0.0598337i | ||||
\(905\) | 37.9479 | − | 10.1681i | 1.26143 | − | 0.337999i | ||||
\(906\) | 17.3148 | + | 9.99673i | 0.575247 | + | 0.332119i | ||||
\(907\) | 51.9116i | 1.72369i | 0.507168 | + | 0.861847i | \(0.330692\pi\) | ||||
−0.507168 | + | 0.861847i | \(0.669308\pi\) | |||||||
\(908\) | 0.946788 | + | 0.253691i | 0.0314203 | + | 0.00841904i | ||||
\(909\) | −12.1215 | −0.402044 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.0311 | 0.498003 | 0.249002 | − | 0.968503i | \(-0.419898\pi\) | ||||
0.249002 | + | 0.968503i | \(0.419898\pi\) | |||||||
\(912\) | 24.2816 | + | 6.50624i | 0.804044 | + | 0.215443i | ||||
\(913\) | − | 3.11098i | − | 0.102958i | ||||||
\(914\) | −27.5322 | − | 15.8957i | −0.910683 | − | 0.525783i | ||||
\(915\) | 0.253814 | − | 0.0680092i | 0.00839082 | − | 0.00224831i | ||||
\(916\) | 0.0469410 | − | 0.175186i | 0.00155098 | − | 0.00578832i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 21.3122 | + | 21.3122i | 0.703407 | + | 0.703407i | ||||
\(919\) | 3.25134 | 0.107252 | 0.0536259 | − | 0.998561i | \(-0.482922\pi\) | ||||
0.0536259 | + | 0.998561i | \(0.482922\pi\) | |||||||
\(920\) | 64.9190 | 2.14031 | ||||||||
\(921\) | −14.7766 | − | 14.7766i | −0.486907 | − | 0.486907i | ||||
\(922\) | 20.8420 | − | 36.0993i | 0.686393 | − | 1.18887i | ||||
\(923\) | 9.46167 | + | 4.43974i | 0.311435 | + | 0.146136i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.23669 | − | 23.2757i | −0.205061 | − | 0.765299i | ||||
\(926\) | 2.14626 | + | 3.71742i | 0.0705303 | + | 0.122162i | ||||
\(927\) | 9.11956 | − | 15.7955i | 0.299526 | − | 0.518794i | ||||
\(928\) | 0.453299 | + | 0.121461i | 0.0148803 | + | 0.00398716i | ||||
\(929\) | 30.2470 | + | 30.2470i | 0.992373 | + | 0.992373i | 0.999971 | − | 0.00759811i | \(-0.00241858\pi\) |
−0.00759811 | + | 0.999971i | \(0.502419\pi\) | |||||||
\(930\) | −3.76421 | − | 1.00862i | −0.123433 | − | 0.0330738i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −0.404128 | − | 0.699969i | −0.0132376 | − | 0.0229283i | ||||
\(933\) | 23.9785 | − | 13.8440i | 0.785019 | − | 0.453231i | ||||
\(934\) | 20.6675 | − | 20.6675i | 0.676262 | − | 0.676262i | ||||
\(935\) | −14.9001 | + | 8.60260i | −0.487287 | + | 0.281335i | ||||
\(936\) | −11.0266 | − | 15.8283i | −0.360415 | − | 0.517365i | ||||
\(937\) | − | 14.9401i | − | 0.488071i | −0.969766 | − | 0.244035i | \(-0.921529\pi\) | ||
0.969766 | − | 0.244035i | \(-0.0784713\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15.3661 | + | 26.6148i | −0.501452 | + | 0.868541i | ||||
\(940\) | − | 0.843173i | − | 0.0275013i | ||||||
\(941\) | 2.94635 | − | 10.9959i | 0.0960482 | − | 0.358457i | −0.901128 | − | 0.433553i | \(-0.857260\pi\) |
0.997176 | + | 0.0750961i | \(0.0239264\pi\) | |||||||
\(942\) | −2.59710 | − | 9.69249i | −0.0846180 | − | 0.315799i | ||||
\(943\) | 65.7112 | − | 65.7112i | 2.13985 | − | 2.13985i | ||||
\(944\) | −15.7399 | + | 15.7399i | −0.512291 | + | 0.512291i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.59642 | − | 0.921695i | −0.0519042 | − | 0.0299669i | ||||
\(947\) | −8.32128 | + | 31.0554i | −0.270405 | + | 1.00917i | 0.688453 | + | 0.725281i | \(0.258290\pi\) |
−0.958858 | + | 0.283885i | \(0.908377\pi\) | |||||||
\(948\) | 0.475359 | + | 0.823345i | 0.0154389 | + | 0.0267410i | ||||
\(949\) | −9.29811 | − | 4.36299i | −0.301830 | − | 0.141629i | ||||
\(950\) | 23.8523 | + | 13.7711i | 0.773871 | + | 0.446794i | ||||
\(951\) | −12.9093 | + | 3.45903i | −0.418612 | + | 0.112167i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.4604 | − | 18.7410i | 1.05150 | − | 0.607081i | 0.128428 | − | 0.991719i | \(-0.459007\pi\) |
0.923068 | + | 0.384638i | \(0.125674\pi\) | |||||||
\(954\) | −1.66963 | − | 6.23114i | −0.0540562 | − | 0.201741i | ||||
\(955\) | −22.5888 | + | 6.05264i | −0.730955 | + | 0.195859i | ||||
\(956\) | 0.828726 | − | 0.222056i | 0.0268029 | − | 0.00718182i | ||||
\(957\) | −0.349874 | − | 1.30575i | −0.0113098 | − | 0.0422089i | ||||
\(958\) | 28.7118 | − | 16.5768i | 0.927636 | − | 0.535571i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −24.7844 | + | 6.64096i | −0.799913 | + | 0.214336i | ||||
\(961\) | 26.1178 | + | 15.0791i | 0.842509 | + | 0.486423i | ||||
\(962\) | 23.8961 | − | 28.3398i | 0.770442 | − | 0.913713i | ||||
\(963\) | −9.80261 | − | 16.9786i | −0.315885 | − | 0.547128i | ||||
\(964\) | 0.106202 | − | 0.396352i | 0.00342054 | − | 0.0127656i | ||||
\(965\) | 66.5746 | + | 38.4368i | 2.14311 | + | 1.23733i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.9130 | − | 10.9130i | 0.350939 | − | 0.350939i | −0.509520 | − | 0.860459i | \(-0.670177\pi\) |
0.860459 | + | 0.509520i | \(0.170177\pi\) | |||||||
\(968\) | −18.3174 | + | 18.3174i | −0.588745 | + | 0.588745i | ||||
\(969\) | 7.18216 | + | 26.8042i | 0.230724 | + | 0.861074i | ||||
\(970\) | −9.41959 | + | 35.1544i | −0.302445 | + | 1.12874i | ||||
\(971\) | 1.78526i | 0.0572916i | 0.999590 | + | 0.0286458i | \(0.00911949\pi\) | ||||
−0.999590 | + | 0.0286458i | \(0.990881\pi\) | |||||||
\(972\) | 0.732343 | − | 1.26846i | 0.0234899 | − | 0.0406857i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 47.0455i | − | 1.50743i | ||||||
\(975\) | 4.24949 | + | 11.7632i | 0.136093 | + | 0.376723i | ||||
\(976\) | −0.281298 | + | 0.162407i | −0.00900413 | + | 0.00519854i | ||||
\(977\) | −1.60581 | + | 1.60581i | −0.0513743 | + | 0.0513743i | −0.732327 | − | 0.680953i | \(-0.761566\pi\) |
0.680953 | + | 0.732327i | \(0.261566\pi\) | |||||||
\(978\) | 14.0030 | − | 8.08461i | 0.447765 | − | 0.258517i | ||||
\(979\) | 3.51662 | + | 6.09097i | 0.112392 | + | 0.194668i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −29.5002 | − | 7.90456i | −0.941869 | − | 0.252373i | ||||
\(982\) | 13.8297 | + | 13.8297i | 0.441323 | + | 0.441323i | ||||
\(983\) | 41.3763 | + | 11.0868i | 1.31970 | + | 0.353613i | 0.848865 | − | 0.528609i | \(-0.177286\pi\) |
0.470835 | + | 0.882221i | \(0.343953\pi\) | |||||||
\(984\) | −18.4038 | + | 31.8763i | −0.586692 | + | 1.01618i | ||||
\(985\) | 26.4468 | + | 45.8071i | 0.842664 | + | 1.45954i | ||||
\(986\) | −1.32453 | − | 4.94320i | −0.0421815 | − | 0.157424i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.177191 | − | 2.08289i | −0.00563721 | − | 0.0662657i | ||||
\(989\) | −3.65815 | + | 6.33611i | −0.116323 | + | 0.201477i | ||||
\(990\) | −7.40406 | − | 7.40406i | −0.235317 | − | 0.235317i | ||||
\(991\) | 53.3601 | 1.69504 | 0.847519 | − | 0.530765i | \(-0.178095\pi\) | ||||
0.847519 | + | 0.530765i | \(0.178095\pi\) | |||||||
\(992\) | −0.487636 | −0.0154825 | ||||||||
\(993\) | 22.7060 | + | 22.7060i | 0.720553 | + | 0.720553i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.44159 | + | 35.2365i | −0.299319 | + | 1.11707i | ||||
\(996\) | 0.212130 | − | 0.0568400i | 0.00672158 | − | 0.00180104i | ||||
\(997\) | 40.7247 | + | 23.5124i | 1.28976 | + | 0.744645i | 0.978612 | − | 0.205715i | \(-0.0659519\pi\) |
0.311152 | + | 0.950360i | \(0.399285\pi\) | |||||||
\(998\) | − | 41.1675i | − | 1.30313i | ||||||
\(999\) | 37.4075 | + | 10.0233i | 1.18352 | + | 0.317124i |
(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 | 637.2.x.b.19.6 | 32 | ||
7.2 | even | 3 | 91.2.bc.a.6.3 | ✓ | 32 | ||
7.3 | odd | 6 | 637.2.bb.b.227.3 | 32 | |||
7.4 | even | 3 | 637.2.bb.b.227.4 | 32 | |||
7.5 | odd | 6 | 91.2.bc.a.6.4 | yes | 32 | ||
7.6 | odd | 2 | inner | 637.2.x.b.19.5 | 32 | ||
13.11 | odd | 12 | 637.2.bb.b.362.3 | 32 | |||
21.2 | odd | 6 | 819.2.fm.g.370.6 | 32 | |||
21.5 | even | 6 | 819.2.fm.g.370.5 | 32 | |||
91.11 | odd | 12 | inner | 637.2.x.b.570.6 | 32 | ||
91.24 | even | 12 | inner | 637.2.x.b.570.5 | 32 | ||
91.37 | odd | 12 | 91.2.bc.a.76.4 | yes | 32 | ||
91.76 | even | 12 | 637.2.bb.b.362.4 | 32 | |||
91.89 | even | 12 | 91.2.bc.a.76.3 | yes | 32 | ||
273.89 | odd | 12 | 819.2.fm.g.622.6 | 32 | |||
273.128 | even | 12 | 819.2.fm.g.622.5 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.bc.a.6.3 | ✓ | 32 | 7.2 | even | 3 | ||
91.2.bc.a.6.4 | yes | 32 | 7.5 | odd | 6 | ||
91.2.bc.a.76.3 | yes | 32 | 91.89 | even | 12 | ||
91.2.bc.a.76.4 | yes | 32 | 91.37 | odd | 12 | ||
637.2.x.b.19.5 | 32 | 7.6 | odd | 2 | inner | ||
637.2.x.b.19.6 | 32 | 1.1 | even | 1 | trivial | ||
637.2.x.b.570.5 | 32 | 91.24 | even | 12 | inner | ||
637.2.x.b.570.6 | 32 | 91.11 | odd | 12 | inner | ||
637.2.bb.b.227.3 | 32 | 7.3 | odd | 6 | |||
637.2.bb.b.227.4 | 32 | 7.4 | even | 3 | |||
637.2.bb.b.362.3 | 32 | 13.11 | odd | 12 | |||
637.2.bb.b.362.4 | 32 | 91.76 | even | 12 | |||
819.2.fm.g.370.5 | 32 | 21.5 | even | 6 | |||
819.2.fm.g.370.6 | 32 | 21.2 | odd | 6 | |||
819.2.fm.g.622.5 | 32 | 273.128 | even | 12 | |||
819.2.fm.g.622.6 | 32 | 273.89 | odd | 12 |