Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [700,2,Mod(199,700)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(700, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("700.199");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 700.t (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.58952814149\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 140) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 299.13 | ||
Character | \(\chi\) | \(=\) | 700.299 |
Dual form | 700.2.t.c.199.13 |
$q$-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 \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(351\) | \(477\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.14053 | + | 0.836177i | 0.806476 | + | 0.591267i | ||||
\(3\) | 2.62152 | − | 1.51353i | 1.51353 | − | 0.873839i | 0.513659 | − | 0.857995i | \(-0.328290\pi\) |
0.999874 | − | 0.0158441i | \(-0.00504353\pi\) | |||||||
\(4\) | 0.601615 | + | 1.90737i | 0.300808 | + | 0.953685i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 4.25550 | + | 0.465823i | 1.73730 | + | 0.190171i | ||||
\(7\) | 0.602834 | − | 2.57616i | 0.227850 | − | 0.973696i | ||||
\(8\) | −0.908739 | + | 2.67847i | −0.321288 | + | 0.946982i | ||||
\(9\) | 3.08156 | − | 5.33743i | 1.02719 | − | 1.77914i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.03659 | − | 0.598478i | 0.312545 | − | 0.180448i | −0.335520 | − | 0.942033i | \(-0.608912\pi\) |
0.648065 | + | 0.761585i | \(0.275579\pi\) | |||||||
\(12\) | 4.46401 | + | 4.08964i | 1.28865 | + | 1.18058i | ||||
\(13\) | −4.83692 | −1.34152 | −0.670760 | − | 0.741674i | \(-0.734032\pi\) | ||||
−0.670760 | + | 0.741674i | \(0.734032\pi\) | |||||||
\(14\) | 2.84167 | − | 2.43411i | 0.759469 | − | 0.650543i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.27612 | + | 2.29501i | −0.819030 | + | 0.573751i | ||||
\(17\) | 1.27265 | + | 2.20430i | 0.308664 | + | 0.534621i | 0.978070 | − | 0.208275i | \(-0.0667850\pi\) |
−0.669407 | + | 0.742896i | \(0.733452\pi\) | |||||||
\(18\) | 7.97765 | − | 3.51076i | 1.88035 | − | 0.827494i | ||||
\(19\) | 0.711130 | − | 1.23171i | 0.163144 | − | 0.282575i | −0.772850 | − | 0.634588i | \(-0.781170\pi\) |
0.935995 | + | 0.352014i | \(0.114503\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.31876 | − | 7.66585i | −0.505996 | − | 1.67283i | ||||
\(22\) | 1.68270 | + | 0.184195i | 0.358753 | + | 0.0392704i | ||||
\(23\) | −2.90326 | + | 5.02859i | −0.605371 | + | 1.04853i | 0.386622 | + | 0.922238i | \(0.373642\pi\) |
−0.991993 | + | 0.126295i | \(0.959691\pi\) | |||||||
\(24\) | 1.67168 | + | 8.39706i | 0.341229 | + | 1.71404i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5.51665 | − | 4.04452i | −1.08190 | − | 0.793197i | ||||
\(27\) | − | 9.57500i | − | 1.84271i | ||||||
\(28\) | 5.27636 | − | 0.400029i | 0.997138 | − | 0.0755985i | ||||
\(29\) | −0.774233 | −0.143772 | −0.0718858 | − | 0.997413i | \(-0.522902\pi\) | ||||
−0.0718858 | + | 0.997413i | \(0.522902\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.31933 | + | 5.74924i | 0.596169 | + | 1.03259i | 0.993381 | + | 0.114867i | \(0.0366443\pi\) |
−0.397212 | + | 0.917727i | \(0.630022\pi\) | |||||||
\(32\) | −5.65554 | − | 0.121894i | −0.999768 | − | 0.0215481i | ||||
\(33\) | 1.81163 | − | 3.13784i | 0.315365 | − | 0.546228i | ||||
\(34\) | −0.391687 | + | 3.57823i | −0.0671737 | + | 0.613661i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 12.0344 | + | 2.66661i | 2.00573 | + | 0.444434i | ||||
\(37\) | −4.42479 | − | 2.55465i | −0.727431 | − | 0.419982i | 0.0900509 | − | 0.995937i | \(-0.471297\pi\) |
−0.817481 | + | 0.575955i | \(0.804630\pi\) | |||||||
\(38\) | 1.84100 | − | 0.810175i | 0.298649 | − | 0.131428i | ||||
\(39\) | −12.6801 | + | 7.32084i | −2.03044 | + | 1.17227i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.46685i | 1.16613i | 0.812427 | + | 0.583063i | \(0.198146\pi\) | ||||
−0.812427 | + | 0.583063i | \(0.801854\pi\) | |||||||
\(42\) | 3.76539 | − | 10.6820i | 0.581013 | − | 1.64827i | ||||
\(43\) | 1.38202 | 0.210756 | 0.105378 | − | 0.994432i | \(-0.466395\pi\) | ||||
0.105378 | + | 0.994432i | \(0.466395\pi\) | |||||||
\(44\) | 1.76515 | + | 1.61711i | 0.266106 | + | 0.243789i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.51604 | + | 3.30762i | −1.10818 | + | 0.487681i | ||||
\(47\) | 0.927389 | + | 0.535428i | 0.135274 | + | 0.0781002i | 0.566110 | − | 0.824330i | \(-0.308448\pi\) |
−0.430836 | + | 0.902430i | \(0.641781\pi\) | |||||||
\(48\) | −5.11483 | + | 10.9749i | −0.738262 | + | 1.58409i | ||||
\(49\) | −6.27318 | − | 3.10599i | −0.896169 | − | 0.443713i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.67256 | + | 3.85240i | 0.934345 | + | 0.539444i | ||||
\(52\) | −2.90997 | − | 9.22580i | −0.403540 | − | 1.27939i | ||||
\(53\) | −2.91156 | + | 1.68099i | −0.399934 | + | 0.230902i | −0.686456 | − | 0.727172i | \(-0.740834\pi\) |
0.286521 | + | 0.958074i | \(0.407501\pi\) | |||||||
\(54\) | 8.00640 | − | 10.9206i | 1.08953 | − | 1.48610i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 6.35234 | + | 3.95573i | 0.848867 | + | 0.528606i | ||||
\(57\) | − | 4.30528i | − | 0.570248i | ||||||
\(58\) | −0.883036 | − | 0.647396i | −0.115948 | − | 0.0850073i | ||||
\(59\) | 4.94206 | + | 8.55990i | 0.643402 | + | 1.11440i | 0.984668 | + | 0.174438i | \(0.0558108\pi\) |
−0.341267 | + | 0.939967i | \(0.610856\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.31115 | + | 4.79845i | 1.06413 | + | 0.614378i | 0.926573 | − | 0.376115i | \(-0.122740\pi\) |
0.137561 | + | 0.990493i | \(0.456074\pi\) | |||||||
\(62\) | −1.02160 | + | 9.33272i | −0.129743 | + | 1.18526i | ||||
\(63\) | −11.8924 | − | 11.1562i | −1.49830 | − | 1.40555i | ||||
\(64\) | −6.34839 | − | 4.86806i | −0.793548 | − | 0.608507i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.69001 | − | 2.06395i | 0.577300 | − | 0.254055i | ||||
\(67\) | −5.27776 | − | 9.14135i | −0.644781 | − | 1.11679i | −0.984352 | − | 0.176213i | \(-0.943615\pi\) |
0.339571 | − | 0.940580i | \(-0.389718\pi\) | |||||||
\(68\) | −3.43876 | + | 3.75356i | −0.417011 | + | 0.455186i | ||||
\(69\) | 17.5767i | 2.11599i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 16.3277i | − | 1.93775i | −0.247558 | − | 0.968873i | \(-0.579628\pi\) | ||
0.247558 | − | 0.968873i | \(-0.420372\pi\) | |||||||
\(72\) | 11.4958 | + | 13.1042i | 1.35479 | + | 1.54435i | ||||
\(73\) | −0.0535547 | − | 0.0927594i | −0.00626810 | − | 0.0108567i | 0.862874 | − | 0.505419i | \(-0.168662\pi\) |
−0.869142 | + | 0.494562i | \(0.835329\pi\) | |||||||
\(74\) | −2.91046 | − | 6.61356i | −0.338334 | − | 0.768811i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.77716 | + | 0.615371i | 0.318562 | + | 0.0705879i | ||||
\(77\) | −0.916880 | − | 3.03121i | −0.104488 | − | 0.345439i | ||||
\(78\) | −20.5835 | − | 2.25315i | −2.33062 | − | 0.255119i | ||||
\(79\) | −9.32609 | − | 5.38442i | −1.04927 | − | 0.605795i | −0.126823 | − | 0.991925i | \(-0.540478\pi\) |
−0.922444 | + | 0.386130i | \(0.873811\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.24739 | − | 9.08874i | −0.583043 | − | 1.00986i | ||||
\(82\) | −6.24361 | + | 8.51617i | −0.689492 | + | 0.940453i | ||||
\(83\) | − | 15.8027i | − | 1.73457i | −0.497808 | − | 0.867287i | \(-0.665862\pi\) | ||
0.497808 | − | 0.867287i | \(-0.334138\pi\) | |||||||
\(84\) | 13.2266 | − | 9.03463i | 1.44314 | − | 0.985759i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.57623 | + | 1.15561i | 0.169969 | + | 0.124613i | ||||
\(87\) | −2.02967 | + | 1.17183i | −0.217603 | + | 0.125633i | ||||
\(88\) | 0.661010 | + | 3.32035i | 0.0704639 | + | 0.353950i | ||||
\(89\) | 3.41325 | + | 1.97064i | 0.361803 | + | 0.208887i | 0.669872 | − | 0.742477i | \(-0.266349\pi\) |
−0.308068 | + | 0.951364i | \(0.599682\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.91586 | + | 12.4607i | −0.305665 | + | 1.30623i | ||||
\(92\) | −11.3380 | − | 2.51231i | −1.18207 | − | 0.261926i | ||||
\(93\) | 17.4033 | + | 10.0478i | 1.80464 | + | 1.04191i | ||||
\(94\) | 0.610001 | + | 1.38613i | 0.0629168 | + | 0.142969i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −15.0106 | + | 8.24030i | −1.53201 | + | 0.841022i | ||||
\(97\) | 8.71387 | 0.884760 | 0.442380 | − | 0.896828i | \(-0.354134\pi\) | ||||
0.442380 | + | 0.896828i | \(0.354134\pi\) | |||||||
\(98\) | −4.55759 | − | 8.78797i | −0.460386 | − | 0.887719i | ||||
\(99\) | − | 7.37699i | − | 0.741416i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.60279 | + | 1.50272i | −0.258987 | + | 0.149526i | −0.623872 | − | 0.781526i | \(-0.714442\pi\) |
0.364885 | + | 0.931052i | \(0.381108\pi\) | |||||||
\(102\) | 4.38896 | + | 9.97322i | 0.434571 | + | 0.987496i | ||||
\(103\) | 0.331470 | + | 0.191374i | 0.0326607 | + | 0.0188567i | 0.516241 | − | 0.856443i | \(-0.327331\pi\) |
−0.483581 | + | 0.875300i | \(0.660664\pi\) | |||||||
\(104\) | 4.39550 | − | 12.9555i | 0.431014 | − | 1.27040i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.72633 | − | 0.517362i | −0.459062 | − | 0.0502507i | ||||
\(107\) | 0.421235 | − | 0.729600i | 0.0407223 | − | 0.0705331i | −0.844946 | − | 0.534852i | \(-0.820367\pi\) |
0.885668 | + | 0.464319i | \(0.153701\pi\) | |||||||
\(108\) | 18.2631 | − | 5.76047i | 1.75736 | − | 0.554301i | ||||
\(109\) | 1.97534 | + | 3.42139i | 0.189203 | + | 0.327710i | 0.944985 | − | 0.327114i | \(-0.106076\pi\) |
−0.755781 | + | 0.654824i | \(0.772743\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −15.4662 | −1.46799 | ||||||||
\(112\) | 3.93734 | + | 9.82331i | 0.372044 | + | 0.928215i | ||||
\(113\) | − | 2.68201i | − | 0.252302i | −0.992011 | − | 0.126151i | \(-0.959738\pi\) | ||
0.992011 | − | 0.126151i | \(-0.0402625\pi\) | |||||||
\(114\) | 3.59997 | − | 4.91030i | 0.337169 | − | 0.459891i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.465791 | − | 1.47675i | −0.0432476 | − | 0.137113i | ||||
\(117\) | −14.9053 | + | 25.8167i | −1.37799 | + | 2.38676i | ||||
\(118\) | −1.52103 | + | 13.8953i | −0.140022 | + | 1.27916i | ||||
\(119\) | 6.44582 | − | 1.94973i | 0.590887 | − | 0.178731i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.78365 | + | 8.28552i | −0.434877 | + | 0.753229i | ||||
\(122\) | 5.46676 | + | 12.4224i | 0.494938 | + | 1.12467i | ||||
\(123\) | 11.3013 | + | 19.5745i | 1.01901 | + | 1.76497i | ||||
\(124\) | −8.96897 | + | 9.79001i | −0.805437 | + | 0.879169i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.23507 | − | 22.6681i | −0.377290 | − | 2.01943i | ||||
\(127\) | 2.14034 | 0.189925 | 0.0949624 | − | 0.995481i | \(-0.469727\pi\) | ||||
0.0949624 | + | 0.995481i | \(0.469727\pi\) | |||||||
\(128\) | −3.16996 | − | 10.8605i | −0.280188 | − | 0.959945i | ||||
\(129\) | 3.62298 | − | 2.09173i | 0.318986 | − | 0.184166i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.83287 | − | 8.37078i | 0.422250 | − | 0.731359i | −0.573909 | − | 0.818919i | \(-0.694574\pi\) |
0.996159 | + | 0.0875604i | \(0.0279071\pi\) | |||||||
\(132\) | 7.07493 | + | 1.56768i | 0.615793 | + | 0.136449i | ||||
\(133\) | −2.74440 | − | 2.57450i | −0.237969 | − | 0.223238i | ||||
\(134\) | 1.62435 | − | 14.8391i | 0.140322 | − | 1.28190i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.06065 | + | 1.40563i | −0.605446 | + | 0.120531i | ||||
\(137\) | 3.70285 | − | 2.13784i | 0.316356 | − | 0.182648i | −0.333411 | − | 0.942781i | \(-0.608200\pi\) |
0.649767 | + | 0.760133i | \(0.274866\pi\) | |||||||
\(138\) | −14.6972 | + | 20.0467i | −1.25111 | + | 1.70649i | ||||
\(139\) | −7.53742 | −0.639316 | −0.319658 | − | 0.947533i | \(-0.603568\pi\) | ||||
−0.319658 | + | 0.947533i | \(0.603568\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.24155 | 0.272988 | ||||||||
\(142\) | 13.6529 | − | 18.6223i | 1.14572 | − | 1.56275i | ||||
\(143\) | −5.01393 | + | 2.89479i | −0.419286 | + | 0.242075i | ||||
\(144\) | 2.15385 | + | 24.5582i | 0.179488 | + | 2.04652i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.0164826 | − | 0.150576i | 0.00136411 | − | 0.0124618i | ||||
\(147\) | −21.1463 | + | 1.35227i | −1.74411 | + | 0.111533i | ||||
\(148\) | 2.21065 | − | 9.97662i | 0.181714 | − | 0.820073i | ||||
\(149\) | −1.42882 | + | 2.47480i | −0.117054 | + | 0.202743i | −0.918599 | − | 0.395191i | \(-0.870678\pi\) |
0.801545 | + | 0.597934i | \(0.204012\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.72359 | + | 3.30451i | −0.465779 | + | 0.268918i | −0.714471 | − | 0.699665i | \(-0.753333\pi\) |
0.248692 | + | 0.968583i | \(0.419999\pi\) | |||||||
\(152\) | 2.65287 | + | 3.02405i | 0.215177 | + | 0.245283i | ||||
\(153\) | 15.6870 | 1.26822 | ||||||||
\(154\) | 1.48890 | − | 4.22386i | 0.119979 | − | 0.340369i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −21.5921 | − | 19.7813i | −1.72875 | − | 1.58377i | ||||
\(157\) | −7.79155 | − | 13.4954i | −0.621834 | − | 1.07705i | −0.989144 | − | 0.146949i | \(-0.953055\pi\) |
0.367310 | − | 0.930098i | \(-0.380279\pi\) | |||||||
\(158\) | −6.13435 | − | 13.9394i | −0.488023 | − | 1.10896i | ||||
\(159\) | −5.08847 | + | 8.81350i | −0.403542 | + | 0.698956i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.2043 | + | 10.5107i | 0.883019 | + | 0.828355i | ||||
\(162\) | 1.61500 | − | 14.7537i | 0.126886 | − | 1.15916i | ||||
\(163\) | −4.82015 | + | 8.34874i | −0.377543 | + | 0.653924i | −0.990704 | − | 0.136034i | \(-0.956564\pi\) |
0.613161 | + | 0.789958i | \(0.289898\pi\) | |||||||
\(164\) | −14.2421 | + | 4.49217i | −1.11212 | + | 0.350780i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 13.2139 | − | 18.0235i | 1.02560 | − | 1.39889i | ||||
\(167\) | 4.94876i | 0.382947i | 0.981498 | + | 0.191473i | \(0.0613265\pi\) | ||||
−0.981498 | + | 0.191473i | \(0.938673\pi\) | |||||||
\(168\) | 22.6399 | + | 0.755525i | 1.74671 | + | 0.0582901i | ||||
\(169\) | 10.3958 | 0.799678 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.38279 | − | 7.59121i | −0.335160 | − | 0.580514i | ||||
\(172\) | 0.831443 | + | 2.63602i | 0.0633969 | + | 0.200994i | ||||
\(173\) | −3.46535 | + | 6.00216i | −0.263465 | + | 0.456336i | −0.967160 | − | 0.254167i | \(-0.918199\pi\) |
0.703695 | + | 0.710502i | \(0.251532\pi\) | |||||||
\(174\) | −3.29475 | − | 0.360656i | −0.249774 | − | 0.0273412i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.02250 | + | 4.33967i | −0.152451 | + | 0.327115i | ||||
\(177\) | 25.9114 | + | 14.9599i | 1.94762 | + | 1.12446i | ||||
\(178\) | 2.24510 | + | 5.10165i | 0.168278 | + | 0.382385i | ||||
\(179\) | 18.2838 | − | 10.5561i | 1.36659 | − | 0.789003i | 0.376103 | − | 0.926578i | \(-0.377264\pi\) |
0.990491 | + | 0.137575i | \(0.0439307\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.10438i | 0.453735i | 0.973926 | + | 0.226868i | \(0.0728485\pi\) | ||||
−0.973926 | + | 0.226868i | \(0.927152\pi\) | |||||||
\(182\) | −13.7450 | + | 11.7736i | −1.01884 | + | 0.872717i | ||||
\(183\) | 29.0504 | 2.14747 | ||||||||
\(184\) | −10.8306 | − | 12.3460i | −0.798443 | − | 0.910156i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 11.4473 | + | 26.0121i | 0.839354 | + | 1.90730i | ||||
\(187\) | 2.63845 | + | 1.52331i | 0.192942 | + | 0.111395i | ||||
\(188\) | −0.463328 | + | 2.09099i | −0.0337917 | + | 0.152501i | ||||
\(189\) | −24.6667 | − | 5.77213i | −1.79424 | − | 0.419861i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.21572 | + | 1.85660i | 0.232681 | + | 0.134339i | 0.611808 | − | 0.791006i | \(-0.290442\pi\) |
−0.379127 | + | 0.925345i | \(0.623776\pi\) | |||||||
\(192\) | −24.0104 | − | 3.15320i | −1.73280 | − | 0.227563i | ||||
\(193\) | −13.2769 | + | 7.66545i | −0.955695 | + | 0.551771i | −0.894846 | − | 0.446376i | \(-0.852714\pi\) |
−0.0608498 | + | 0.998147i | \(0.519381\pi\) | |||||||
\(194\) | 9.93843 | + | 7.28634i | 0.713538 | + | 0.523129i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.15023 | − | 13.8339i | 0.153588 | − | 0.988135i | ||||
\(197\) | − | 24.4602i | − | 1.74272i | −0.490644 | − | 0.871360i | \(-0.663239\pi\) | ||
0.490644 | − | 0.871360i | \(-0.336761\pi\) | |||||||
\(198\) | 6.16847 | − | 8.41368i | 0.438374 | − | 0.597934i | ||||
\(199\) | −6.43311 | − | 11.1425i | −0.456031 | − | 0.789868i | 0.542716 | − | 0.839916i | \(-0.317396\pi\) |
−0.998747 | + | 0.0500478i | \(0.984063\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −27.6715 | − | 15.9761i | −1.95179 | − | 1.12687i | ||||
\(202\) | −4.22510 | − | 0.462495i | −0.297277 | − | 0.0325410i | ||||
\(203\) | −0.466734 | + | 1.99455i | −0.0327583 | + | 0.139990i | ||||
\(204\) | −3.33364 | + | 15.0447i | −0.233402 | + | 1.05334i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.218029 | + | 0.495436i | 0.0151908 | + | 0.0345186i | ||||
\(207\) | 17.8931 | + | 30.9918i | 1.24366 | + | 2.15408i | ||||
\(208\) | 15.8463 | − | 11.1008i | 1.09875 | − | 0.769699i | ||||
\(209\) | − | 1.70238i | − | 0.117756i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 16.9384i | − | 1.16609i | −0.812441 | − | 0.583044i | \(-0.801862\pi\) | ||
0.812441 | − | 0.583044i | \(-0.198138\pi\) | |||||||
\(212\) | −4.95791 | − | 4.54212i | −0.340511 | − | 0.311954i | ||||
\(213\) | −24.7126 | − | 42.8034i | −1.69328 | − | 2.93284i | ||||
\(214\) | 1.09051 | − | 0.479903i | 0.0745454 | − | 0.0328055i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 25.6463 | + | 8.70118i | 1.74501 | + | 0.592040i | ||||
\(217\) | 16.8120 | − | 5.08527i | 1.14127 | − | 0.345211i | ||||
\(218\) | −0.607955 | + | 5.55393i | −0.0411759 | + | 0.376160i | ||||
\(219\) | −0.280789 | − | 0.162114i | −0.0189740 | − | 0.0109546i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.15572 | − | 10.6620i | −0.414079 | − | 0.717205i | ||||
\(222\) | −17.6397 | − | 12.9325i | −1.18390 | − | 0.867972i | ||||
\(223\) | − | 18.9687i | − | 1.27024i | −0.772414 | − | 0.635119i | \(-0.780951\pi\) | ||
0.772414 | − | 0.635119i | \(-0.219049\pi\) | |||||||
\(224\) | −3.72337 | + | 14.4961i | −0.248778 | + | 0.968561i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.24264 | − | 3.05891i | 0.149178 | − | 0.203476i | ||||
\(227\) | −0.809262 | + | 0.467228i | −0.0537126 | + | 0.0310110i | −0.526616 | − | 0.850103i | \(-0.676539\pi\) |
0.472903 | + | 0.881114i | \(0.343206\pi\) | |||||||
\(228\) | 8.21175 | − | 2.59012i | 0.543837 | − | 0.171535i | ||||
\(229\) | 11.3283 | + | 6.54038i | 0.748594 | + | 0.432201i | 0.825185 | − | 0.564862i | \(-0.191071\pi\) |
−0.0765920 | + | 0.997063i | \(0.524404\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.99146 | − | 6.55865i | −0.460004 | − | 0.431527i | ||||
\(232\) | 0.703576 | − | 2.07376i | 0.0461920 | − | 0.136149i | ||||
\(233\) | −13.5114 | − | 7.80080i | −0.885160 | − | 0.511047i | −0.0128037 | − | 0.999918i | \(-0.504076\pi\) |
−0.872356 | + | 0.488871i | \(0.837409\pi\) | |||||||
\(234\) | −38.5873 | + | 16.9813i | −2.52253 | + | 1.11010i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −13.3537 | + | 14.5761i | −0.869250 | + | 0.948824i | ||||
\(237\) | −32.5980 | −2.11747 | ||||||||
\(238\) | 8.98197 | + | 3.16612i | 0.582214 | + | 0.205229i | ||||
\(239\) | 14.1327i | 0.914167i | 0.889424 | + | 0.457084i | \(0.151106\pi\) | ||||
−0.889424 | + | 0.457084i | \(0.848894\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.6916 | − | 10.7916i | 1.20403 | − | 0.695146i | 0.242580 | − | 0.970131i | \(-0.422006\pi\) |
0.961449 | + | 0.274985i | \(0.0886728\pi\) | |||||||
\(242\) | −12.3841 | + | 5.44990i | −0.796077 | + | 0.350333i | ||||
\(243\) | −2.63564 | − | 1.52169i | −0.169076 | − | 0.0976163i | ||||
\(244\) | −4.15230 | + | 18.7393i | −0.265824 | + | 1.19966i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.47823 | + | 31.7752i | −0.221764 | + | 2.02591i | ||||
\(247\) | −3.43968 | + | 5.95770i | −0.218862 | + | 0.379080i | ||||
\(248\) | −18.4156 | + | 3.66615i | −1.16939 | + | 0.232801i | ||||
\(249\) | −23.9179 | − | 41.4271i | −1.51574 | − | 2.62534i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.04460 | −0.0659345 | −0.0329673 | − | 0.999456i | \(-0.510496\pi\) | ||||
−0.0329673 | + | 0.999456i | \(0.510496\pi\) | |||||||
\(252\) | 14.1243 | − | 29.3949i | 0.889748 | − | 1.85170i | ||||
\(253\) | 6.95014i | 0.436952i | ||||||||
\(254\) | 2.44113 | + | 1.78971i | 0.153170 | + | 0.112296i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5.46590 | − | 15.0374i | 0.341619 | − | 0.939839i | ||||
\(257\) | −2.45194 | + | 4.24688i | −0.152948 | + | 0.264913i | −0.932310 | − | 0.361661i | \(-0.882210\pi\) |
0.779362 | + | 0.626574i | \(0.215543\pi\) | |||||||
\(258\) | 5.88117 | + | 0.643775i | 0.366146 | + | 0.0400797i | ||||
\(259\) | −9.24860 | + | 9.85892i | −0.574680 | + | 0.612604i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.38585 | + | 4.13241i | −0.147680 | + | 0.255790i | ||||
\(262\) | 12.5115 | − | 5.50599i | 0.772963 | − | 0.340161i | ||||
\(263\) | −3.89819 | − | 6.75186i | −0.240373 | − | 0.416337i | 0.720448 | − | 0.693509i | \(-0.243936\pi\) |
−0.960820 | + | 0.277172i | \(0.910603\pi\) | |||||||
\(264\) | 6.75830 | + | 7.70388i | 0.415945 | + | 0.474141i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.977325 | − | 5.23110i | −0.0599236 | − | 0.320739i | ||||
\(267\) | 11.9305 | 0.730135 | ||||||||
\(268\) | 14.2608 | − | 15.5662i | 0.871114 | − | 0.950858i | ||||
\(269\) | 18.2838 | − | 10.5562i | 1.11479 | − | 0.643622i | 0.174721 | − | 0.984618i | \(-0.444098\pi\) |
0.940065 | + | 0.340996i | \(0.110764\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.7604 | + | 18.6375i | −0.653647 | + | 1.13215i | 0.328584 | + | 0.944475i | \(0.393429\pi\) |
−0.982231 | + | 0.187676i | \(0.939905\pi\) | |||||||
\(272\) | −9.22824 | − | 4.30080i | −0.559544 | − | 0.260774i | ||||
\(273\) | 11.2157 | + | 37.0791i | 0.678804 | + | 2.24413i | ||||
\(274\) | 6.01082 | + | 0.657967i | 0.363127 | + | 0.0397492i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −33.5253 | + | 10.5744i | −2.01798 | + | 0.636505i | ||||
\(277\) | −4.47513 | + | 2.58372i | −0.268884 | + | 0.155241i | −0.628381 | − | 0.777906i | \(-0.716282\pi\) |
0.359496 | + | 0.933147i | \(0.382949\pi\) | |||||||
\(278\) | −8.59665 | − | 6.30262i | −0.515593 | − | 0.378006i | ||||
\(279\) | 40.9149 | 2.44951 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.6322 | 0.932539 | 0.466270 | − | 0.884643i | \(-0.345598\pi\) | ||||
0.466270 | + | 0.884643i | \(0.345598\pi\) | |||||||
\(282\) | 3.69709 | + | 2.71051i | 0.220158 | + | 0.161409i | ||||
\(283\) | −24.7424 | + | 14.2850i | −1.47078 | + | 0.849156i | −0.999462 | − | 0.0328062i | \(-0.989556\pi\) |
−0.471320 | + | 0.881962i | \(0.656222\pi\) | |||||||
\(284\) | 31.1430 | − | 9.82302i | 1.84800 | − | 0.582889i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −8.13909 | − | 0.890936i | −0.481274 | − | 0.0526821i | ||||
\(287\) | 19.2358 | + | 4.50127i | 1.13545 | + | 0.265702i | ||||
\(288\) | −18.0785 | + | 29.8104i | −1.06529 | + | 1.75660i | ||||
\(289\) | 5.26071 | − | 9.11182i | 0.309454 | − | 0.535990i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 22.8436 | − | 13.1887i | 1.33911 | − | 0.773137i | ||||
\(292\) | 0.144707 | − | 0.157954i | 0.00846835 | − | 0.00924356i | ||||
\(293\) | −0.657174 | −0.0383925 | −0.0191963 | − | 0.999816i | \(-0.506111\pi\) | ||||
−0.0191963 | + | 0.999816i | \(0.506111\pi\) | |||||||
\(294\) | −25.2487 | − | 16.1397i | −1.47253 | − | 0.941288i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 10.8635 | − | 9.53014i | 0.631430 | − | 0.553928i | ||||
\(297\) | −5.73043 | − | 9.92539i | −0.332513 | − | 0.575930i | ||||
\(298\) | −3.69898 | + | 1.62783i | −0.214276 | + | 0.0942975i | ||||
\(299\) | 14.0428 | − | 24.3229i | 0.812118 | − | 1.40663i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.833126 | − | 3.56030i | 0.0480206 | − | 0.205212i | ||||
\(302\) | −9.29108 | − | 1.01704i | −0.534642 | − | 0.0585239i | ||||
\(303\) | −4.54883 | + | 7.87881i | −0.261324 | + | 0.452626i | ||||
\(304\) | 0.497043 | + | 5.66729i | 0.0285073 | + | 0.325041i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 17.8915 | + | 13.1171i | 1.02279 | + | 0.749857i | ||||
\(307\) | 4.88042i | 0.278540i | 0.990254 | + | 0.139270i | \(0.0444756\pi\) | ||||
−0.990254 | + | 0.139270i | \(0.955524\pi\) | |||||||
\(308\) | 5.23004 | − | 3.57245i | 0.298009 | − | 0.203559i | ||||
\(309\) | 1.15861 | 0.0659108 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.94840 | + | 10.3029i | 0.337303 | + | 0.584226i | 0.983924 | − | 0.178585i | \(-0.0571520\pi\) |
−0.646621 | + | 0.762811i | \(0.723819\pi\) | |||||||
\(312\) | −8.08577 | − | 40.6159i | −0.457766 | − | 2.29942i | ||||
\(313\) | 13.3037 | − | 23.0427i | 0.751970 | − | 1.30245i | −0.194897 | − | 0.980824i | \(-0.562437\pi\) |
0.946867 | − | 0.321626i | \(-0.104229\pi\) | |||||||
\(314\) | 2.39802 | − | 21.9070i | 0.135328 | − | 1.23628i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.65936 | − | 21.0277i | 0.262110 | − | 1.18290i | ||||
\(317\) | 22.9113 | + | 13.2278i | 1.28683 | + | 0.742950i | 0.978087 | − | 0.208197i | \(-0.0667595\pi\) |
0.308739 | + | 0.951147i | \(0.400093\pi\) | |||||||
\(318\) | −13.1732 | + | 5.79719i | −0.738716 | + | 0.325090i | ||||
\(319\) | −0.802566 | + | 0.463362i | −0.0449351 | + | 0.0259433i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 2.55021i | − | 0.142339i | ||||||
\(322\) | 3.99002 | + | 21.3565i | 0.222355 | + | 1.19015i | ||||
\(323\) | 3.62009 | 0.201427 | ||||||||
\(324\) | 14.1787 | − | 15.4766i | 0.787705 | − | 0.859813i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −12.4786 | + | 5.49149i | −0.691123 | + | 0.304145i | ||||
\(327\) | 10.3568 | + | 5.97949i | 0.572731 | + | 0.330667i | ||||
\(328\) | −19.9997 | − | 6.78542i | −1.10430 | − | 0.374662i | ||||
\(329\) | 1.93841 | − | 2.06633i | 0.106868 | − | 0.113920i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.0294 | + | 12.1414i | 1.15588 | + | 0.667349i | 0.950314 | − | 0.311294i | \(-0.100762\pi\) |
0.205569 | + | 0.978643i | \(0.434096\pi\) | |||||||
\(332\) | 30.1416 | − | 9.50716i | 1.65424 | − | 0.521773i | ||||
\(333\) | −27.2705 | + | 15.7447i | −1.49442 | + | 0.862802i | ||||
\(334\) | −4.13804 | + | 5.64421i | −0.226423 | + | 0.308837i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 25.1897 | + | 19.7927i | 1.37421 | + | 1.07978i | ||||
\(337\) | 19.7077i | 1.07355i | 0.843726 | + | 0.536774i | \(0.180357\pi\) | ||||
−0.843726 | + | 0.536774i | \(0.819643\pi\) | |||||||
\(338\) | 11.8567 | + | 8.69275i | 0.644922 | + | 0.472823i | ||||
\(339\) | −4.05931 | − | 7.03094i | −0.220472 | − | 0.381868i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.88159 | + | 3.97309i | 0.372659 | + | 0.215155i | ||||
\(342\) | 1.34890 | − | 12.3228i | 0.0729401 | − | 0.666340i | ||||
\(343\) | −11.7832 | + | 14.2883i | −0.636233 | + | 0.771497i | ||||
\(344\) | −1.25589 | + | 3.70169i | −0.0677132 | + | 0.199582i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.97120 | + | 3.94799i | −0.482295 | + | 0.212245i | ||||
\(347\) | −4.21851 | − | 7.30667i | −0.226461 | − | 0.392242i | 0.730296 | − | 0.683131i | \(-0.239382\pi\) |
−0.956757 | + | 0.290889i | \(0.906049\pi\) | |||||||
\(348\) | −3.45619 | − | 3.16633i | −0.185271 | − | 0.169733i | ||||
\(349\) | 23.5784i | 1.26212i | 0.775732 | + | 0.631062i | \(0.217381\pi\) | ||||
−0.775732 | + | 0.631062i | \(0.782619\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 46.3135i | 2.47203i | ||||||||
\(352\) | −5.93545 | + | 3.25836i | −0.316361 | + | 0.173671i | ||||
\(353\) | 10.3362 | + | 17.9028i | 0.550141 | + | 0.952872i | 0.998264 | + | 0.0589002i | \(0.0187594\pi\) |
−0.448123 | + | 0.893972i | \(0.647907\pi\) | |||||||
\(354\) | 17.0435 | + | 38.7288i | 0.905854 | + | 2.05841i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.70528 | + | 7.69589i | −0.0903794 | + | 0.407881i | ||||
\(357\) | 13.9468 | − | 14.8672i | 0.738145 | − | 0.786856i | ||||
\(358\) | 29.6800 | + | 3.24889i | 1.56864 | + | 0.171709i | ||||
\(359\) | 23.7741 | + | 13.7260i | 1.25475 | + | 0.724429i | 0.972049 | − | 0.234780i | \(-0.0754369\pi\) |
0.282699 | + | 0.959209i | \(0.408770\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.48859 | + | 14.7027i | 0.446768 | + | 0.773824i | ||||
\(362\) | −5.10435 | + | 6.96223i | −0.268278 | + | 0.365927i | ||||
\(363\) | 28.9608i | 1.52005i | ||||||||
\(364\) | −25.5213 | + | 1.93491i | −1.33768 | + | 0.101417i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 33.1329 | + | 24.2913i | 1.73188 | + | 1.26973i | ||||
\(367\) | −17.3574 | + | 10.0213i | −0.906051 | + | 0.523109i | −0.879159 | − | 0.476529i | \(-0.841895\pi\) |
−0.0268927 | + | 0.999638i | \(0.508561\pi\) | |||||||
\(368\) | −2.02922 | − | 23.1372i | −0.105781 | − | 1.20611i | ||||
\(369\) | 39.8538 | + | 23.0096i | 2.07471 | + | 1.19783i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.57531 | + | 8.51401i | 0.133704 | + | 0.442025i | ||||
\(372\) | −8.69480 | + | 39.2395i | −0.450804 | + | 2.03447i | ||||
\(373\) | 17.8325 | + | 10.2956i | 0.923331 | + | 0.533085i | 0.884696 | − | 0.466168i | \(-0.154366\pi\) |
0.0386345 | + | 0.999253i | \(0.487699\pi\) | |||||||
\(374\) | 1.73547 | + | 3.94359i | 0.0897391 | + | 0.203918i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.27688 | + | 1.99742i | −0.117421 | + | 0.103009i | ||||
\(377\) | 3.74491 | 0.192873 | ||||||||
\(378\) | −23.3066 | − | 27.2090i | −1.19876 | − | 1.39948i | ||||
\(379\) | 3.26339i | 0.167629i | 0.996481 | + | 0.0838145i | \(0.0267103\pi\) | ||||
−0.996481 | + | 0.0838145i | \(0.973290\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.61095 | − | 3.23948i | 0.287458 | − | 0.165964i | ||||
\(382\) | 2.11518 | + | 4.80641i | 0.108222 | + | 0.245917i | ||||
\(383\) | 29.2293 | + | 16.8755i | 1.49355 | + | 0.862300i | 0.999973 | − | 0.00740376i | \(-0.00235671\pi\) |
0.493574 | + | 0.869704i | \(0.335690\pi\) | |||||||
\(384\) | −24.7479 | − | 23.6732i | −1.26291 | − | 1.20807i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −21.5524 | − | 2.35921i | −1.09699 | − | 0.120081i | ||||
\(387\) | 4.25878 | − | 7.37642i | 0.216486 | − | 0.374964i | ||||
\(388\) | 5.24240 | + | 16.6206i | 0.266142 | + | 0.843782i | ||||
\(389\) | −1.80604 | − | 3.12816i | −0.0915701 | − | 0.158604i | 0.816602 | − | 0.577201i | \(-0.195855\pi\) |
−0.908172 | + | 0.418597i | \(0.862522\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.7793 | −0.747424 | ||||||||
\(392\) | 14.0200 | − | 13.9800i | 0.708116 | − | 0.706096i | ||||
\(393\) | − | 29.2589i | − | 1.47591i | ||||||
\(394\) | 20.4531 | − | 27.8976i | 1.03041 | − | 1.40546i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 14.0707 | − | 4.43811i | 0.707077 | − | 0.223024i | ||||
\(397\) | 3.73862 | − | 6.47548i | 0.187636 | − | 0.324995i | −0.756826 | − | 0.653617i | \(-0.773251\pi\) |
0.944462 | + | 0.328622i | \(0.106584\pi\) | |||||||
\(398\) | 1.97993 | − | 18.0875i | 0.0992449 | − | 0.906646i | ||||
\(399\) | −11.0911 | − | 2.59537i | −0.555248 | − | 0.129931i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.77337 | − | 8.26772i | 0.238371 | − | 0.412870i | −0.721876 | − | 0.692022i | \(-0.756720\pi\) |
0.960247 | + | 0.279152i | \(0.0900533\pi\) | |||||||
\(402\) | −18.2013 | − | 41.3595i | −0.907796 | − | 2.06282i | ||||
\(403\) | −16.0553 | − | 27.8086i | −0.799773 | − | 1.38525i | ||||
\(404\) | −4.43212 | − | 4.06042i | −0.220506 | − | 0.202013i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.20012 | + | 1.88457i | −0.109190 | + | 0.0935296i | ||||
\(407\) | −6.11561 | −0.303140 | ||||||||
\(408\) | −16.3822 | + | 14.3714i | −0.811037 | + | 0.711490i | ||||
\(409\) | −18.7682 | + | 10.8358i | −0.928026 | + | 0.535796i | −0.886187 | − | 0.463328i | \(-0.846655\pi\) |
−0.0418392 | + | 0.999124i | \(0.513322\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.47138 | − | 11.2088i | 0.319210 | − | 0.552887i | ||||
\(412\) | −0.165604 | + | 0.747370i | −0.00815873 | + | 0.0368203i | ||||
\(413\) | 25.0309 | − | 7.57134i | 1.23169 | − | 0.372561i | ||||
\(414\) | −5.50701 | + | 50.3090i | −0.270655 | + | 2.47255i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 27.3554 | + | 0.589594i | 1.34121 | + | 0.0289072i | ||||
\(417\) | −19.7595 | + | 11.4081i | −0.967625 | + | 0.558659i | ||||
\(418\) | 1.42349 | − | 1.94162i | 0.0696254 | − | 0.0949677i | ||||
\(419\) | −13.0327 | −0.636690 | −0.318345 | − | 0.947975i | \(-0.603127\pi\) | ||||
−0.318345 | + | 0.947975i | \(0.603127\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.2800 | −1.67070 | −0.835352 | − | 0.549715i | \(-0.814736\pi\) | ||||
−0.835352 | + | 0.549715i | \(0.814736\pi\) | |||||||
\(422\) | 14.1635 | − | 19.3187i | 0.689469 | − | 0.940422i | ||||
\(423\) | 5.71562 | − | 3.29991i | 0.277903 | − | 0.160447i | ||||
\(424\) | −1.85663 | − | 9.32612i | −0.0901660 | − | 0.452916i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7.60584 | − | 69.4827i | 0.368504 | − | 3.36645i | ||||
\(427\) | 17.3718 | − | 18.5182i | 0.840681 | − | 0.896158i | ||||
\(428\) | 1.64504 | + | 0.364512i | 0.0795159 | + | 0.0176194i | ||||
\(429\) | −8.76273 | + | 15.1775i | −0.423068 | + | 0.732776i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.47034 | − | 1.42625i | 0.118992 | − | 0.0687001i | −0.439323 | − | 0.898329i | \(-0.644781\pi\) |
0.558315 | + | 0.829629i | \(0.311448\pi\) | |||||||
\(432\) | 21.9747 | + | 31.3688i | 1.05726 | + | 1.50923i | ||||
\(433\) | 34.6179 | 1.66363 | 0.831815 | − | 0.555053i | \(-0.187302\pi\) | ||||
0.831815 | + | 0.555053i | \(0.187302\pi\) | |||||||
\(434\) | 23.4267 | + | 8.25787i | 1.12452 | + | 0.396390i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.33746 | + | 5.82607i | −0.255618 | + | 0.279018i | ||||
\(437\) | 4.12919 | + | 7.15196i | 0.197526 | + | 0.342125i | ||||
\(438\) | −0.184692 | − | 0.419685i | −0.00882495 | − | 0.0200533i | ||||
\(439\) | 5.46905 | − | 9.47267i | 0.261023 | − | 0.452106i | −0.705491 | − | 0.708719i | \(-0.749273\pi\) |
0.966514 | + | 0.256613i | \(0.0826067\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −35.9092 | + | 23.9113i | −1.70996 | + | 1.13864i | ||||
\(442\) | 1.89456 | − | 17.3076i | 0.0901149 | − | 0.823240i | ||||
\(443\) | 17.6971 | − | 30.6522i | 0.840813 | − | 1.45633i | −0.0483948 | − | 0.998828i | \(-0.515411\pi\) |
0.889208 | − | 0.457503i | \(-0.151256\pi\) | |||||||
\(444\) | −9.30470 | − | 29.4998i | −0.441582 | − | 1.40000i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 15.8612 | − | 21.6344i | 0.751050 | − | 1.02442i | ||||
\(447\) | 8.65029i | 0.409145i | ||||||||
\(448\) | −16.3679 | + | 13.4198i | −0.773311 | + | 0.634027i | ||||
\(449\) | −28.0029 | −1.32154 | −0.660768 | − | 0.750590i | \(-0.729769\pi\) | ||||
−0.660768 | + | 0.750590i | \(0.729769\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.46875 | + | 7.74010i | 0.210425 | + | 0.364467i | ||||
\(452\) | 5.11559 | − | 1.61354i | 0.240617 | − | 0.0758945i | ||||
\(453\) | −10.0030 | + | 17.3257i | −0.469981 | + | 0.814031i | ||||
\(454\) | −1.31367 | − | 0.143800i | −0.0616537 | − | 0.00674885i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 11.5315 | + | 3.91237i | 0.540014 | + | 0.183214i | ||||
\(457\) | −17.4849 | − | 10.0949i | −0.817908 | − | 0.472220i | 0.0317863 | − | 0.999495i | \(-0.489880\pi\) |
−0.849695 | + | 0.527275i | \(0.823214\pi\) | |||||||
\(458\) | 7.45131 | + | 16.9319i | 0.348177 | + | 0.791178i | ||||
\(459\) | 21.1062 | − | 12.1856i | 0.985151 | − | 0.568777i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.127845i | 0.00595433i | 0.999996 | + | 0.00297717i | \(0.000947663\pi\) | ||||
−0.999996 | + | 0.00297717i | \(0.999052\pi\) | |||||||
\(462\) | −2.48977 | − | 13.3264i | −0.115835 | − | 0.620002i | ||||
\(463\) | −17.8655 | −0.830282 | −0.415141 | − | 0.909757i | \(-0.636268\pi\) | ||||
−0.415141 | + | 0.909757i | \(0.636268\pi\) | |||||||
\(464\) | 2.53648 | − | 1.77687i | 0.117753 | − | 0.0824891i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.88728 | − | 20.1950i | −0.411695 | − | 0.935513i | ||||
\(467\) | 12.7042 | + | 7.33477i | 0.587880 | + | 0.339413i | 0.764259 | − | 0.644910i | \(-0.223105\pi\) |
−0.176379 | + | 0.984322i | \(0.556438\pi\) | |||||||
\(468\) | −58.2093 | − | 12.8982i | −2.69072 | − | 0.596218i | ||||
\(469\) | −26.7312 | + | 8.08563i | −1.23433 | + | 0.373360i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −40.8514 | − | 23.5855i | −1.88233 | − | 1.08676i | ||||
\(472\) | −27.4185 | + | 5.45844i | −1.26204 | + | 0.251245i | ||||
\(473\) | 1.43259 | − | 0.827107i | 0.0658706 | − | 0.0380304i | ||||
\(474\) | −37.1790 | − | 27.2577i | −1.70769 | − | 1.25199i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 7.59676 | + | 11.1216i | 0.348197 | + | 0.509756i | ||||
\(477\) | 20.7203i | 0.948719i | ||||||||
\(478\) | −11.8174 | + | 16.1187i | −0.540517 | + | 0.737254i | ||||
\(479\) | −13.0757 | − | 22.6478i | −0.597444 | − | 1.03480i | −0.993197 | − | 0.116446i | \(-0.962850\pi\) |
0.395753 | − | 0.918357i | \(-0.370483\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.4024 | + | 12.3567i | 0.975863 | + | 0.563415i | ||||
\(482\) | 30.3419 | + | 3.32134i | 1.38204 | + | 0.151283i | ||||
\(483\) | 45.2804 | + | 10.5958i | 2.06033 | + | 0.482127i | ||||
\(484\) | −18.6815 | − | 4.13949i | −0.849158 | − | 0.188159i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.73362 | − | 3.93939i | −0.0786388 | − | 0.178694i | ||||
\(487\) | −8.31227 | − | 14.3973i | −0.376665 | − | 0.652403i | 0.613910 | − | 0.789376i | \(-0.289596\pi\) |
−0.990575 | + | 0.136974i | \(0.956262\pi\) | |||||||
\(488\) | −20.4052 | + | 17.9006i | −0.923698 | + | 0.810323i | ||||
\(489\) | 29.1818i | 1.31965i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 21.9094i | − | 0.988758i | −0.869246 | − | 0.494379i | \(-0.835395\pi\) | ||
0.869246 | − | 0.494379i | \(-0.164605\pi\) | |||||||
\(492\) | −30.5367 | + | 33.3321i | −1.37670 | + | 1.50273i | ||||
\(493\) | −0.985330 | − | 1.70664i | −0.0443770 | − | 0.0768633i | ||||
\(494\) | −8.90476 | + | 3.91875i | −0.400644 | + | 0.176313i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −24.0690 | − | 11.2173i | −1.08073 | − | 0.503673i | ||||
\(497\) | −42.0628 | − | 9.84291i | −1.88678 | − | 0.441515i | ||||
\(498\) | 7.36127 | − | 67.2485i | 0.329867 | − | 3.01348i | ||||
\(499\) | 35.2377 | + | 20.3445i | 1.57746 | + | 0.910745i | 0.995213 | + | 0.0977301i | \(0.0311582\pi\) |
0.582243 | + | 0.813015i | \(0.302175\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.49011 | + | 12.9733i | 0.334633 | + | 0.579602i | ||||
\(502\) | −1.19140 | − | 0.873470i | −0.0531746 | − | 0.0389849i | ||||
\(503\) | − | 7.19624i | − | 0.320864i | −0.987047 | − | 0.160432i | \(-0.948711\pi\) | ||
0.987047 | − | 0.160432i | \(-0.0512888\pi\) | |||||||
\(504\) | 40.6885 | − | 21.7153i | 1.81241 | − | 0.967277i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5.81155 | + | 7.92684i | −0.258355 | + | 0.352391i | ||||
\(507\) | 27.2528 | − | 15.7344i | 1.21034 | − | 0.698790i | ||||
\(508\) | 1.28766 | + | 4.08243i | 0.0571308 | + | 0.181128i | ||||
\(509\) | −4.45357 | − | 2.57127i | −0.197401 | − | 0.113970i | 0.398042 | − | 0.917367i | \(-0.369690\pi\) |
−0.595443 | + | 0.803398i | \(0.703023\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.271248 | + | 0.0820469i | −0.0119993 | + | 0.00362954i | ||||
\(512\) | 18.8080 | − | 12.5802i | 0.831203 | − | 0.555970i | ||||
\(513\) | −11.7937 | − | 6.80907i | −0.520703 | − | 0.300628i | ||||
\(514\) | −6.34765 | + | 2.79344i | −0.279983 | + | 0.123213i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 6.16934 | + | 5.65195i | 0.271590 | + | 0.248813i | ||||
\(517\) | 1.28177 | 0.0563721 | ||||||||
\(518\) | −18.7921 | + | 3.51092i | −0.825678 | + | 0.154261i | ||||
\(519\) | 20.9797i | 0.920905i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.85043 | − | 4.53245i | 0.343934 | − | 0.198570i | −0.318077 | − | 0.948065i | \(-0.603037\pi\) |
0.662010 | + | 0.749495i | \(0.269704\pi\) | |||||||
\(522\) | −6.17656 | + | 2.71815i | −0.270341 | + | 0.118970i | ||||
\(523\) | −15.2485 | − | 8.80370i | −0.666768 | − | 0.384959i | 0.128083 | − | 0.991764i | \(-0.459118\pi\) |
−0.794851 | + | 0.606805i | \(0.792451\pi\) | |||||||
\(524\) | 18.8737 | + | 4.18209i | 0.824502 | + | 0.182695i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.19975 | − | 10.9603i | 0.0523117 | − | 0.477890i | ||||
\(527\) | −8.44869 | + | 14.6336i | −0.368031 | + | 0.637448i | ||||
\(528\) | 1.26624 | + | 14.4376i | 0.0551058 | + | 0.628318i | ||||
\(529\) | −5.35780 | − | 9.27999i | −0.232948 | − | 0.403478i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 60.9171 | 2.64358 | ||||||||
\(532\) | 3.25946 | − | 6.78344i | 0.141315 | − | 0.294099i | ||||
\(533\) | − | 36.1166i | − | 1.56438i | ||||||
\(534\) | 13.6071 | + | 9.97602i | 0.588837 | + | 0.431705i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 29.2809 | − | 5.82921i | 1.26474 | − | 0.251784i | ||||
\(537\) | 31.9542 | − | 55.3462i | 1.37892 | − | 2.38837i | ||||
\(538\) | 29.6801 | + | 3.24890i | 1.27960 | + | 0.140070i | ||||
\(539\) | −8.36161 | + | 0.534711i | −0.360160 | + | 0.0230316i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.9811 | − | 24.2160i | 0.601094 | − | 1.04113i | −0.391561 | − | 0.920152i | \(-0.628065\pi\) |
0.992656 | − | 0.120974i | \(-0.0386018\pi\) | |||||||
\(542\) | −27.8568 | + | 12.2591i | −1.19655 | + | 0.526573i | ||||
\(543\) | 9.23918 | + | 16.0027i | 0.396491 | + | 0.686743i | ||||
\(544\) | −6.92884 | − | 12.6216i | −0.297072 | − | 0.541148i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −18.2129 | + | 51.6681i | −0.779440 | + | 2.21119i | ||||
\(547\) | −29.6385 | −1.26725 | −0.633626 | − | 0.773640i | \(-0.718434\pi\) | ||||
−0.633626 | + | 0.773640i | \(0.718434\pi\) | |||||||
\(548\) | 6.30534 | + | 5.77654i | 0.269351 | + | 0.246762i | ||||
\(549\) | 51.2227 | − | 29.5735i | 2.18613 | − | 1.26216i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.550581 | + | 0.953634i | −0.0234555 | + | 0.0406262i | ||||
\(552\) | −47.0786 | − | 15.9726i | −2.00380 | − | 0.679841i | ||||
\(553\) | −19.4932 | + | 20.7796i | −0.828935 | + | 0.883638i | ||||
\(554\) | −7.26446 | − | 0.795196i | −0.308637 | − | 0.0337846i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.53463 | − | 14.3766i | −0.192311 | − | 0.609706i | ||||
\(557\) | 30.9460 | − | 17.8667i | 1.31123 | − | 0.757037i | 0.328927 | − | 0.944355i | \(-0.393313\pi\) |
0.982299 | + | 0.187319i | \(0.0599798\pi\) | |||||||
\(558\) | 46.6646 | + | 34.2121i | 1.97547 | + | 1.44831i | ||||
\(559\) | −6.68471 | −0.282733 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.22231 | 0.389366 | ||||||||
\(562\) | 17.8290 | + | 13.0713i | 0.752071 | + | 0.551379i | ||||
\(563\) | 19.9226 | − | 11.5023i | 0.839639 | − | 0.484766i | −0.0175025 | − | 0.999847i | \(-0.505571\pi\) |
0.857142 | + | 0.515081i | \(0.172238\pi\) | |||||||
\(564\) | 1.95017 | + | 6.18284i | 0.0821169 | + | 0.260345i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −40.1642 | − | 4.39653i | −1.68823 | − | 0.184800i | ||||
\(567\) | −26.5773 | + | 8.03910i | −1.11614 | + | 0.337611i | ||||
\(568\) | 43.7333 | + | 14.8377i | 1.83501 | + | 0.622574i | ||||
\(569\) | −9.43937 | + | 16.3495i | −0.395719 | + | 0.685405i | −0.993193 | − | 0.116483i | \(-0.962838\pi\) |
0.597474 | + | 0.801888i | \(0.296171\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.7520 | + | 11.9812i | −0.868446 | + | 0.501397i | −0.866831 | − | 0.498601i | \(-0.833847\pi\) |
−0.00161422 | + | 0.999999i | \(0.500514\pi\) | |||||||
\(572\) | −8.53789 | − | 7.82186i | −0.356987 | − | 0.327048i | ||||
\(573\) | 11.2401 | 0.469561 | ||||||||
\(574\) | 18.1751 | + | 21.2184i | 0.758616 | + | 0.885638i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −45.5459 | + | 18.8828i | −1.89774 | + | 0.786784i | ||||
\(577\) | 5.31557 | + | 9.20684i | 0.221290 | + | 0.383286i | 0.955200 | − | 0.295961i | \(-0.0956399\pi\) |
−0.733910 | + | 0.679247i | \(0.762307\pi\) | |||||||
\(578\) | 13.6191 | − | 5.99341i | 0.566480 | − | 0.249293i | ||||
\(579\) | −23.2038 | + | 40.1902i | −0.964318 | + | 1.67025i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −40.7103 | − | 9.52641i | −1.68895 | − | 0.395222i | ||||
\(582\) | 37.0819 | + | 4.05912i | 1.53709 | + | 0.168256i | ||||
\(583\) | −2.01207 | + | 3.48501i | −0.0833316 | + | 0.144335i | ||||
\(584\) | 0.297120 | − | 0.0591504i | 0.0122949 | − | 0.00244766i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.749527 | − | 0.549514i | −0.0309627 | − | 0.0227002i | ||||
\(587\) | 0.240690i | 0.00993436i | 0.999988 | + | 0.00496718i | \(0.00158111\pi\) | ||||
−0.999988 | + | 0.00496718i | \(0.998419\pi\) | |||||||
\(588\) | −15.3012 | − | 39.5202i | −0.631011 | − | 1.62979i | ||||
\(589\) | 9.44189 | 0.389046 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −37.0214 | − | 64.1229i | −1.52286 | − | 2.63766i | ||||
\(592\) | 20.3591 | − | 1.78557i | 0.836753 | − | 0.0733864i | ||||
\(593\) | −15.4627 | + | 26.7822i | −0.634977 | + | 1.09981i | 0.351543 | + | 0.936172i | \(0.385657\pi\) |
−0.986520 | + | 0.163640i | \(0.947676\pi\) | |||||||
\(594\) | 1.76366 | − | 16.1119i | 0.0723640 | − | 0.661077i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.57995 | − | 1.23642i | −0.228564 | − | 0.0506458i | ||||
\(597\) | −33.7290 | − | 19.4734i | −1.38044 | − | 0.796995i | ||||
\(598\) | 36.3545 | − | 15.9987i | 1.48665 | − | 0.654235i | ||||
\(599\) | −25.9364 | + | 14.9744i | −1.05973 | + | 0.611838i | −0.925359 | − | 0.379092i | \(-0.876236\pi\) |
−0.134376 | + | 0.990930i | \(0.542903\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 23.0748i | − | 0.941241i | −0.882336 | − | 0.470621i | \(-0.844030\pi\) | ||
0.882336 | − | 0.470621i | \(-0.155970\pi\) | |||||||
\(602\) | 3.92724 | − | 3.36398i | 0.160062 | − | 0.137106i | ||||
\(603\) | −65.0550 | −2.64925 | ||||||||
\(604\) | −9.74633 | − | 8.92895i | −0.396572 | − | 0.363314i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −11.7762 | + | 5.18238i | −0.478374 | + | 0.210520i | ||||
\(607\) | −15.4846 | − | 8.94004i | −0.628501 | − | 0.362865i | 0.151670 | − | 0.988431i | \(-0.451535\pi\) |
−0.780171 | + | 0.625566i | \(0.784868\pi\) | |||||||
\(608\) | −4.17197 | + | 6.87932i | −0.169196 | + | 0.278993i | ||||
\(609\) | 1.79526 | + | 5.93516i | 0.0727477 | + | 0.240505i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.48571 | − | 2.58982i | −0.181472 | − | 0.104773i | ||||
\(612\) | 9.43756 | + | 29.9210i | 0.381491 | + | 1.20948i | ||||
\(613\) | 7.24872 | − | 4.18505i | 0.292773 | − | 0.169033i | −0.346419 | − | 0.938080i | \(-0.612602\pi\) |
0.639192 | + | 0.769047i | \(0.279269\pi\) | |||||||
\(614\) | −4.08090 | + | 5.56626i | −0.164692 | + | 0.224636i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.95221 | + | 0.298748i | 0.360695 | + | 0.0120369i | ||||
\(617\) | 33.7886i | 1.36028i | 0.733084 | + | 0.680139i | \(0.238080\pi\) | ||||
−0.733084 | + | 0.680139i | \(0.761920\pi\) | |||||||
\(618\) | 1.32142 | + | 0.968800i | 0.0531555 | + | 0.0389708i | ||||
\(619\) | 16.6442 | + | 28.8285i | 0.668986 | + | 1.15872i | 0.978188 | + | 0.207721i | \(0.0666046\pi\) |
−0.309203 | + | 0.950996i | \(0.600062\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 48.1487 | + | 27.7987i | 1.93214 | + | 1.11552i | ||||
\(622\) | −1.83075 | + | 16.7247i | −0.0734065 | + | 0.670600i | ||||
\(623\) | 7.13430 | − | 7.60510i | 0.285830 | − | 0.304692i | ||||
\(624\) | 24.7400 | − | 53.0848i | 0.990394 | − | 2.12509i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 34.4410 | − | 15.1566i | 1.37654 | − | 0.605780i | ||||
\(627\) | −2.57661 | − | 4.46283i | −0.102900 | − | 0.178228i | ||||
\(628\) | 21.0531 | − | 22.9804i | 0.840112 | − | 0.917017i | ||||
\(629\) | − | 13.0047i | − | 0.518533i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 43.1690i | 1.71853i | 0.511528 | + | 0.859266i | \(0.329079\pi\) | ||||
−0.511528 | + | 0.859266i | \(0.670921\pi\) | |||||||
\(632\) | 22.8970 | − | 20.0866i | 0.910793 | − | 0.799002i | ||||
\(633\) | −25.6368 | − | 44.4043i | −1.01897 | − | 1.76491i | ||||
\(634\) | 15.0702 | + | 34.2446i | 0.598514 | + | 1.36003i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −19.8719 | − | 4.40327i | −0.787972 | − | 0.174601i | ||||
\(637\) | 30.3429 | + | 15.0234i | 1.20223 | + | 0.595250i | ||||
\(638\) | −1.30280 | − | 0.142610i | −0.0515784 | − | 0.00564597i | ||||
\(639\) | −87.1481 | − | 50.3150i | −3.44753 | − | 1.99043i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.0131 | − | 27.7355i | −0.632479 | − | 1.09548i | −0.987043 | − | 0.160454i | \(-0.948704\pi\) |
0.354565 | − | 0.935031i | \(-0.384629\pi\) | |||||||
\(642\) | 2.13243 | − | 2.90859i | 0.0841602 | − | 0.114793i | ||||
\(643\) | 37.9515i | 1.49666i | 0.663326 | + | 0.748331i | \(0.269144\pi\) | ||||
−0.663326 | + | 0.748331i | \(0.730856\pi\) | |||||||
\(644\) | −13.3070 | + | 27.6940i | −0.524371 | + | 1.09130i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.12882 | + | 3.02703i | 0.162446 | + | 0.119097i | ||||
\(647\) | 7.78359 | − | 4.49386i | 0.306004 | − | 0.176672i | −0.339133 | − | 0.940739i | \(-0.610134\pi\) |
0.645137 | + | 0.764067i | \(0.276800\pi\) | |||||||
\(648\) | 29.1124 | − | 5.79567i | 1.14364 | − | 0.227675i | ||||
\(649\) | 10.2458 | + | 5.91543i | 0.402184 | + | 0.232201i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 36.3761 | − | 38.7766i | 1.42569 | − | 1.51977i | ||||
\(652\) | −18.8240 | − | 4.17108i | −0.737205 | − | 0.163352i | ||||
\(653\) | 15.8302 | + | 9.13956i | 0.619483 | + | 0.357658i | 0.776668 | − | 0.629911i | \(-0.216909\pi\) |
−0.157185 | + | 0.987569i | \(0.550242\pi\) | |||||||
\(654\) | 6.81230 | + | 15.4799i | 0.266382 | + | 0.605312i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −17.1365 | − | 24.4623i | −0.669067 | − | 0.955092i | ||||
\(657\) | −0.660129 | −0.0257541 | ||||||||
\(658\) | 3.93863 | − | 0.735853i | 0.153544 | − | 0.0286865i | ||||
\(659\) | − | 36.9643i | − | 1.43992i | −0.694014 | − | 0.719962i | \(-0.744159\pi\) | ||
0.694014 | − | 0.719962i | \(-0.255841\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.9261 | + | 11.5043i | −0.775035 | + | 0.447466i | −0.834668 | − | 0.550754i | \(-0.814340\pi\) |
0.0596330 | + | 0.998220i | \(0.481007\pi\) | |||||||
\(662\) | 13.8324 | + | 31.4319i | 0.537610 | + | 1.22164i | ||||
\(663\) | −32.2746 | − | 18.6338i | −1.25344 | − | 0.723676i | ||||
\(664\) | 42.3271 | + | 14.3606i | 1.64261 | + | 0.557298i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −44.2682 | − | 4.84576i | −1.71536 | − | 0.187769i | ||||
\(667\) | 2.24780 | − | 3.89330i | 0.0870351 | − | 0.150749i | ||||
\(668\) | −9.43911 | + | 2.97725i | −0.365210 | + | 0.115193i | ||||
\(669\) | −28.7098 | − | 49.7268i | −1.10998 | − | 1.92255i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.4871 | 0.443453 | ||||||||
\(672\) | 12.1794 | + | 43.6372i | 0.469832 | + | 1.68334i | ||||
\(673\) | 42.0925i | 1.62255i | 0.584668 | + | 0.811273i | \(0.301225\pi\) | ||||
−0.584668 | + | 0.811273i | \(0.698775\pi\) | |||||||
\(674\) | −16.4791 | + | 22.4772i | −0.634753 | + | 0.865791i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.25428 | + | 19.8287i | 0.240549 | + | 0.762641i | ||||
\(677\) | −12.1626 | + | 21.0662i | −0.467447 | + | 0.809642i | −0.999308 | − | 0.0371897i | \(-0.988159\pi\) |
0.531861 | + | 0.846831i | \(0.321493\pi\) | |||||||
\(678\) | 1.24934 | − | 11.4133i | 0.0479807 | − | 0.438325i | ||||
\(679\) | 5.25302 | − | 22.4483i | 0.201592 | − | 0.861487i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.41433 | + | 2.44969i | −0.0541972 | + | 0.0938723i | ||||
\(682\) | 4.52645 | + | 10.2856i | 0.173327 | + | 0.393858i | ||||
\(683\) | −9.59853 | − | 16.6251i | −0.367278 | − | 0.636144i | 0.621861 | − | 0.783127i | \(-0.286377\pi\) |
−0.989139 | + | 0.146984i | \(0.953043\pi\) | |||||||
\(684\) | 11.8425 | − | 12.9266i | 0.452809 | − | 0.494260i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −25.3867 | + | 6.44340i | −0.969267 | + | 0.246010i | ||||
\(687\) | 39.5963 | 1.51069 | ||||||||
\(688\) | −4.52765 | + | 3.17174i | −0.172615 | + | 0.120921i | ||||
\(689\) | 14.0830 | − | 8.13083i | 0.536520 | − | 0.309760i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.00274 | − | 12.1291i | 0.266397 | − | 0.461413i | −0.701532 | − | 0.712638i | \(-0.747500\pi\) |
0.967929 | + | 0.251225i | \(0.0808335\pi\) | |||||||
\(692\) | −13.5331 | − | 2.99871i | −0.514453 | − | 0.113994i | ||||
\(693\) | −19.0043 | − | 4.44710i | −0.721914 | − | 0.168931i | ||||
\(694\) | 1.29834 | − | 11.8609i | 0.0492842 | − | 0.450233i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.29427 | − | 6.50128i | −0.0490591 | − | 0.246430i | ||||
\(697\) | −16.4592 | + | 9.50271i | −0.623436 | + | 0.359941i | ||||
\(698\) | −19.7157 | + | 26.8919i | −0.746252 | + | 1.01787i | ||||
\(699\) | −47.2271 | −1.78629 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.9124 | 0.449923 | 0.224962 | − | 0.974368i | \(-0.427774\pi\) | ||||
0.224962 | + | 0.974368i | \(0.427774\pi\) | |||||||
\(702\) | −38.7263 | + | 52.8220i | −1.46163 | + | 1.99364i | ||||
\(703\) | −6.29320 | + | 3.63338i | −0.237353 | + | 0.137036i | ||||
\(704\) | −9.49413 | − | 1.24683i | −0.357823 | − | 0.0469918i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.18120 | + | 29.0616i | −0.119726 | + | 1.09375i | ||||
\(707\) | 2.30220 | + | 7.61108i | 0.0865830 | + | 0.286244i | ||||
\(708\) | −12.9455 | + | 58.4227i | −0.486520 | + | 2.19566i | ||||
\(709\) | 23.6490 | − | 40.9613i | 0.888158 | − | 1.53833i | 0.0461071 | − | 0.998937i | \(-0.485318\pi\) |
0.842051 | − | 0.539398i | \(-0.181348\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −57.4779 | + | 33.1849i | −2.15559 | + | 1.24453i | ||||
\(712\) | −8.38004 | + | 7.35148i | −0.314055 | + | 0.275508i | ||||
\(713\) | −38.5474 | −1.44361 | ||||||||
\(714\) | 28.3384 | − | 5.29446i | 1.06054 | − | 0.198140i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 31.1343 | + | 28.5232i | 1.16354 | + | 1.06596i | ||||
\(717\) | 21.3903 | + | 37.0491i | 0.798835 | + | 1.38362i | ||||
\(718\) | 15.6377 | + | 35.5342i | 0.583593 | + | 1.32613i | ||||
\(719\) | −0.888951 | + | 1.53971i | −0.0331523 | + | 0.0574214i | −0.882125 | − | 0.471014i | \(-0.843888\pi\) |
0.848973 | + | 0.528436i | \(0.177221\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.692832 | − | 0.738552i | 0.0258024 | − | 0.0275051i | ||||
\(722\) | −2.61255 | + | 23.8668i | −0.0972290 | + | 0.888230i | ||||
\(723\) | 32.6668 | − | 56.5806i | 1.21489 | − | 2.10425i | ||||
\(724\) | −11.6433 | + | 3.67249i | −0.432720 | + | 0.136487i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −24.2164 | + | 33.0307i | −0.898755 | + | 1.22588i | ||||
\(727\) | 27.1619i | 1.00738i | 0.863885 | + | 0.503689i | \(0.168024\pi\) | ||||
−0.863885 | + | 0.503689i | \(0.831976\pi\) | |||||||
\(728\) | −30.7258 | − | 19.1335i | −1.13877 | − | 0.709136i | ||||
\(729\) | 22.2718 | 0.824883 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.75883 | + | 3.04638i | 0.0650526 | + | 0.112674i | ||||
\(732\) | 17.4772 | + | 55.4099i | 0.645975 | + | 2.04801i | ||||
\(733\) | 11.3880 | − | 19.7246i | 0.420625 | − | 0.728543i | −0.575376 | − | 0.817889i | \(-0.695144\pi\) |
0.996001 | + | 0.0893459i | \(0.0284777\pi\) | |||||||
\(734\) | −28.1763 | − | 3.08428i | −1.04001 | − | 0.113843i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 17.0324 | − | 28.0855i | 0.627824 | − | 1.03525i | ||||
\(737\) | −10.9418 | − | 6.31725i | −0.403046 | − | 0.232699i | ||||
\(738\) | 26.2143 | + | 59.5680i | 0.964963 | + | 2.19273i | ||||
\(739\) | −28.1611 | + | 16.2588i | −1.03592 | + | 0.598091i | −0.918676 | − | 0.395012i | \(-0.870740\pi\) |
−0.117247 | + | 0.993103i | \(0.537407\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 20.8243i | 0.764999i | ||||||||
\(742\) | −4.18200 | + | 11.8639i | −0.153526 | + | 0.435537i | ||||
\(743\) | 9.19402 | 0.337296 | 0.168648 | − | 0.985676i | \(-0.446060\pi\) | ||||
0.168648 | + | 0.985676i | \(0.446060\pi\) | |||||||
\(744\) | −42.7279 | + | 37.4834i | −1.56648 | + | 1.37421i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 11.7295 | + | 26.6535i | 0.429449 | + | 0.975855i | ||||
\(747\) | −84.3459 | − | 48.6971i | −3.08605 | − | 1.78173i | ||||
\(748\) | −1.31818 | + | 5.94894i | −0.0481975 | + | 0.217515i | ||||
\(749\) | −1.62563 | − | 1.52499i | −0.0593993 | − | 0.0557221i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.5852 | − | 10.1528i | −0.641692 | − | 0.370481i | 0.143574 | − | 0.989640i | \(-0.454140\pi\) |
−0.785266 | + | 0.619159i | \(0.787474\pi\) | |||||||
\(752\) | −4.26705 | + | 0.374236i | −0.155603 | + | 0.0136470i | ||||
\(753\) | −2.73843 | + | 1.58104i | −0.0997941 | + | 0.0576161i | ||||
\(754\) | 4.27118 | + | 3.13141i | 0.155547 | + | 0.114039i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.83028 | − | 50.5212i | −0.139306 | − | 1.83744i | ||||
\(757\) | 10.9555i | 0.398184i | 0.979981 | + | 0.199092i | \(0.0637992\pi\) | ||||
−0.979981 | + | 0.199092i | \(0.936201\pi\) | |||||||
\(758\) | −2.72877 | + | 3.72199i | −0.0991134 | + | 0.135189i | ||||
\(759\) | 10.5193 | + | 18.2199i | 0.381825 | + | 0.661341i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.2104 | − | 15.7099i | −0.986375 | − | 0.569484i | −0.0821860 | − | 0.996617i | \(-0.526190\pi\) |
−0.904189 | + | 0.427133i | \(0.859523\pi\) | |||||||
\(762\) | 9.10823 | + | 0.997022i | 0.329957 | + | 0.0361183i | ||||
\(763\) | 10.0048 | − | 3.02626i | 0.362200 | − | 0.109558i | ||||
\(764\) | −1.60659 | + | 7.25052i | −0.0581243 | + | 0.262314i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 19.2259 | + | 43.6879i | 0.694661 | + | 1.57851i | ||||
\(767\) | −23.9044 | − | 41.4036i | −0.863137 | − | 1.49500i | ||||
\(768\) | −8.43068 | − | 47.6937i | −0.304216 | − | 1.72100i | ||||
\(769\) | − | 23.9511i | − | 0.863700i | −0.901945 | − | 0.431850i | \(-0.857861\pi\) | ||
0.901945 | − | 0.431850i | \(-0.142139\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.8444i | 0.534606i | ||||||||
\(772\) | −22.6085 | − | 20.7124i | −0.813696 | − | 0.745455i | ||||
\(773\) | 7.59249 | + | 13.1506i | 0.273083 | + | 0.472993i | 0.969650 | − | 0.244499i | \(-0.0786234\pi\) |
−0.696567 | + | 0.717492i | \(0.745290\pi\) | |||||||
\(774\) | 11.0252 | − | 4.85193i | 0.396294 | − | 0.174399i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −7.91864 | + | 23.3398i | −0.284263 | + | 0.837851i | ||||
\(777\) | −9.32355 | + | 39.8434i | −0.334480 | + | 1.42937i | ||||
\(778\) | 0.555850 | − | 5.07793i | 0.0199282 | − | 0.182053i | ||||
\(779\) | 9.19703 | + | 5.30991i | 0.329518 | + | 0.190247i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.77179 | − | 16.9252i | −0.349662 | − | 0.605633i | ||||
\(782\) | −16.8563 | − | 12.3582i | −0.602779 | − | 0.441927i | ||||
\(783\) | 7.41329i | 0.264929i | ||||||||
\(784\) | 27.6800 | − | 4.22140i | 0.988570 | − | 0.150764i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 24.4656 | − | 33.3706i | 0.872659 | − | 1.19029i | ||||
\(787\) | −15.8480 | + | 9.14982i | −0.564919 | + | 0.326156i | −0.755117 | − | 0.655590i | \(-0.772420\pi\) |
0.190199 | + | 0.981746i | \(0.439087\pi\) | |||||||
\(788\) | 46.6547 | − | 14.7157i | 1.66201 | − | 0.524223i | ||||
\(789\) | −20.4383 | − | 11.8001i | −0.727624 | − | 0.420094i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.90929 | − | 1.61681i | −0.245666 | − | 0.0574870i | ||||
\(792\) | 19.7590 | + | 6.70376i | 0.702107 | + | 0.238208i | ||||
\(793\) | −40.2004 | − | 23.2097i | −1.42756 | − | 0.824201i | ||||
\(794\) | 9.67866 | − | 4.25933i | 0.343483 | − | 0.151158i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17.3825 | − | 18.9738i | 0.616108 | − | 0.672508i | ||||
\(797\) | 15.0960 | 0.534728 | 0.267364 | − | 0.963596i | \(-0.413847\pi\) | ||||
0.267364 | + | 0.963596i | \(0.413847\pi\) | |||||||
\(798\) | −10.4795 | − | 12.2342i | −0.370971 | − | 0.433086i | ||||
\(799\) | 2.72566i | 0.0964268i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 21.0363 | − | 12.1453i | 0.743280 | − | 0.429133i | ||||
\(802\) | 12.3574 | − | 5.43820i | 0.436357 | − | 0.192029i | ||||
\(803\) | −0.111029 | − | 0.0641026i | −0.00391813 | − | 0.00226213i | ||||
\(804\) | 13.8248 | − | 62.3912i | 0.487563 | − | 2.20037i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.94138 | − | 45.1417i | 0.174053 | − | 1.59005i | ||||
\(807\) | 31.9543 | − | 55.3464i | 1.12484 | − | 1.94829i | ||||
\(808\) | −1.65973 | − | 8.33706i | −0.0583892 | − | 0.293297i | ||||
\(809\) | 22.2240 | + | 38.4931i | 0.781355 | + | 1.35335i | 0.931153 | + | 0.364630i | \(0.118804\pi\) |
−0.149797 | + | 0.988717i | \(0.547862\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34.6449 | −1.21655 | −0.608274 | − | 0.793727i | \(-0.708138\pi\) | ||||
−0.608274 | + | 0.793727i | \(0.708138\pi\) | |||||||
\(812\) | −4.08513 | + | 0.309716i | −0.143360 | + | 0.0108689i | ||||
\(813\) | 65.1449i | 2.28473i | ||||||||
\(814\) | −6.97504 | − | 5.11374i | −0.244475 | − | 0.179236i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −30.7014 | + | 2.69263i | −1.07476 | + | 0.0942608i | ||||
\(817\) | 0.982794 | − | 1.70225i | 0.0343836 | − | 0.0595542i | ||||
\(818\) | −30.4663 | − | 3.33496i | −1.06523 | − | 0.116604i | ||||
\(819\) | 57.5225 | + | 53.9616i | 2.01000 | + | 1.88557i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.8550 | + | 20.5335i | −0.413742 | + | 0.716622i | −0.995296 | − | 0.0968858i | \(-0.969112\pi\) |
0.581553 | + | 0.813508i | \(0.302445\pi\) | |||||||
\(822\) | 16.7533 | − | 7.37270i | 0.584339 | − | 0.257152i | ||||
\(823\) | 3.24588 | + | 5.62203i | 0.113144 | + | 0.195972i | 0.917036 | − | 0.398803i | \(-0.130574\pi\) |
−0.803892 | + | 0.594775i | \(0.797241\pi\) | |||||||
\(824\) | −0.813810 | + | 0.713923i | −0.0283504 | + | 0.0248707i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 34.8795 | + | 12.2949i | 1.21361 | + | 0.427796i | ||||
\(827\) | −39.4872 | −1.37310 | −0.686552 | − | 0.727081i | \(-0.740877\pi\) | ||||
−0.686552 | + | 0.727081i | \(0.740877\pi\) | |||||||
\(828\) | −48.3481 | + | 52.7740i | −1.68021 | + | 1.83402i | ||||
\(829\) | 2.82562 | − | 1.63137i | 0.0981377 | − | 0.0566598i | −0.450128 | − | 0.892964i | \(-0.648622\pi\) |
0.548266 | + | 0.836304i | \(0.315288\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.82108 | + | 13.5465i | −0.271310 | + | 0.469923i | ||||
\(832\) | 30.7067 | + | 23.5464i | 1.06456 | + | 0.816325i | ||||
\(833\) | −1.13705 | − | 17.7808i | −0.0393966 | − | 0.616069i | ||||
\(834\) | −32.0755 | − | 3.51110i | −1.11068 | − | 0.121580i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.24707 | − | 1.02418i | 0.112302 | − | 0.0354220i | ||||
\(837\) | 55.0490 | − | 31.7826i | 1.90277 | − | 1.09857i | ||||
\(838\) | −14.8642 | − | 10.8977i | −0.513475 | − | 0.376454i | ||||
\(839\) | −5.39522 | −0.186264 | −0.0931318 | − | 0.995654i | \(-0.529688\pi\) | ||||
−0.0931318 | + | 0.995654i | \(0.529688\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.4006 | −0.979330 | ||||||||
\(842\) | −39.0973 | − | 28.6642i | −1.34738 | − | 0.987832i | ||||
\(843\) | 40.9801 | − | 23.6599i | 1.41143 | − | 0.814889i | ||||
\(844\) | 32.3078 | − | 10.1904i | 1.11208 | − | 0.350768i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 9.27814 | + | 1.01562i | 0.318989 | + | 0.0349178i | ||||
\(847\) | 18.4611 | + | 17.3182i | 0.634330 | + | 0.595061i | ||||
\(848\) | 5.68074 | − | 12.1892i | 0.195077 | − | 0.418578i | ||||
\(849\) | −43.2417 | + | 74.8968i | −1.48405 | + | 2.57045i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 25.6926 | − | 14.8336i | 0.880731 | − | 0.508490i | ||||
\(852\) | 66.7745 | − | 72.8872i | 2.28766 | − | 2.49707i | ||||
\(853\) | 10.7675 | 0.368672 | 0.184336 | − | 0.982863i | \(-0.440987\pi\) | ||||
0.184336 | + | 0.982863i | \(0.440987\pi\) | |||||||
\(854\) | 35.2975 | − | 6.59463i | 1.20786 | − | 0.225664i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.57142 | + | 1.79128i | 0.0537100 | + | 0.0612247i | ||||
\(857\) | −17.5949 | − | 30.4752i | −0.601029 | − | 1.04101i | −0.992666 | − | 0.120892i | \(-0.961424\pi\) |
0.391637 | − | 0.920120i | \(-0.371909\pi\) | |||||||
\(858\) | −22.6852 | + | 9.98318i | −0.774460 | + | 0.340820i | ||||
\(859\) | 20.6193 | − | 35.7136i | 0.703520 | − | 1.21853i | −0.263703 | − | 0.964604i | \(-0.584944\pi\) |
0.967223 | − | 0.253929i | \(-0.0817228\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 57.2398 | − | 17.3139i | 1.95073 | − | 0.590055i | ||||
\(862\) | 4.01010 | + | 0.438960i | 0.136584 | + | 0.0149510i | ||||
\(863\) | −11.5147 | + | 19.9441i | −0.391966 | + | 0.678906i | −0.992709 | − | 0.120537i | \(-0.961538\pi\) |
0.600742 | + | 0.799443i | \(0.294872\pi\) | |||||||
\(864\) | −1.16714 | + | 54.1518i | −0.0397069 | + | 1.84228i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 39.4827 | + | 28.9467i | 1.34168 | + | 0.983649i | ||||
\(867\) | − | 31.8491i | − | 1.08165i | ||||||
\(868\) | 19.8138 | + | 29.0072i | 0.672525 | + | 0.984570i | ||||
\(869\) | −12.8898 | −0.437258 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 25.5281 | + | 44.2160i | 0.864987 | + | 1.49820i | ||||
\(872\) | −10.9592 | + | 2.18174i | −0.371124 | + | 0.0738829i | ||||
\(873\) | 26.8524 | − | 46.5097i | 0.908815 | − | 1.57411i | ||||
\(874\) | −1.27085 | + | 11.6098i | −0.0429871 | + | 0.392706i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.140284 | − | 0.633098i | 0.00473974 | − | 0.0213904i | ||||
\(877\) | −3.51842 | − | 2.03136i | −0.118809 | − | 0.0685941i | 0.439418 | − | 0.898283i | \(-0.355185\pi\) |
−0.558227 | + | 0.829689i | \(0.688518\pi\) | |||||||
\(878\) | 14.1584 | − | 6.23077i | 0.477824 | − | 0.210278i | ||||
\(879\) | −1.72279 | + | 0.994655i | −0.0581084 | + | 0.0335489i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 42.0606i | 1.41706i | 0.705682 | + | 0.708529i | \(0.250641\pi\) | ||||
−0.705682 | + | 0.708529i | \(0.749359\pi\) | |||||||
\(882\) | −60.9496 | − | 2.75487i | −2.05228 | − | 0.0927612i | ||||
\(883\) | −54.8918 | −1.84725 | −0.923627 | − | 0.383291i | \(-0.874790\pi\) | ||||
−0.923627 | + | 0.383291i | \(0.874790\pi\) | |||||||
\(884\) | 16.6330 | − | 18.1557i | 0.559430 | − | 0.610641i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 45.8147 | − | 20.1619i | 1.53918 | − | 0.677352i | ||||
\(887\) | 33.0168 | + | 19.0622i | 1.10859 | + | 0.640047i | 0.938465 | − | 0.345375i | \(-0.112248\pi\) |
0.170129 | + | 0.985422i | \(0.445581\pi\) | |||||||
\(888\) | 14.0547 | − | 41.4257i | 0.471646 | − | 1.39016i | ||||
\(889\) | 1.29027 | − | 5.51387i | 0.0432743 | − | 0.184929i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10.8788 | − | 6.28089i | −0.364454 | − | 0.210418i | ||||
\(892\) | 36.1803 | − | 11.4119i | 1.21141 | − | 0.382097i | ||||
\(893\) | 1.31899 | − | 0.761518i | 0.0441383 | − | 0.0254832i | ||||
\(894\) | −7.23317 | + | 9.86591i | −0.241913 | + | 0.329965i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −29.8894 | + | 1.61922i | −0.998536 | + | 0.0540945i | ||||
\(897\) | − | 85.0171i | − | 2.83864i | ||||||
\(898\) | −31.9381 | − | 23.4154i | −1.06579 | − | 0.781380i | ||||
\(899\) | −2.56993 | − | 4.45125i | −0.0857121 | − | 0.148458i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.41082 | − | 4.27864i | −0.246890 | − | 0.142542i | ||||
\(902\) | −1.37536 | + | 12.5645i | −0.0457943 | + | 0.418351i | ||||
\(903\) | −3.20457 | − | 10.5943i | −0.106641 | − | 0.352557i | ||||
\(904\) | 7.18369 | + | 2.43725i | 0.238926 | + | 0.0810617i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −25.8960 | + | 11.3962i | −0.860338 | + | 0.378613i | ||||
\(907\) | 0.177354 | + | 0.307186i | 0.00588894 | + | 0.0101999i | 0.868955 | − | 0.494891i | \(-0.164792\pi\) |
−0.863066 | + | 0.505091i | \(0.831459\pi\) | |||||||
\(908\) | −1.37804 | − | 1.26247i | −0.0457319 | − | 0.0418966i | ||||
\(909\) | 18.5229i | 0.614366i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 12.2958i | − | 0.407379i | −0.979036 | − | 0.203690i | \(-0.934707\pi\) | ||
0.979036 | − | 0.203690i | \(-0.0652934\pi\) | |||||||
\(912\) | 9.88063 | + | 14.1046i | 0.327180 | + | 0.467050i | ||||
\(913\) | −9.45758 | − | 16.3810i | −0.313000 | − | 0.542132i | ||||
\(914\) | −11.5009 | − | 26.1340i | −0.380416 | − | 0.864436i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.65967 | + | 25.5420i | −0.187001 | + | 0.843932i | ||||
\(917\) | −18.6510 | − | 17.4964i | −0.615912 | − | 0.577783i | ||||
\(918\) | 34.2616 | + | 3.75040i | 1.13080 | + | 0.123782i | ||||
\(919\) | −0.243118 | − | 0.140364i | −0.00801973 | − | 0.00463019i | 0.495985 | − | 0.868331i | \(-0.334807\pi\) |
−0.504005 | + | 0.863701i | \(0.668141\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.38668 | + | 12.7941i | 0.243399 | + | 0.421580i | ||||
\(922\) | −0.106901 | + | 0.145811i | −0.00352060 | + | 0.00480203i | ||||
\(923\) | 78.9760i | 2.59953i | ||||||||
\(924\) | 8.30360 | − | 17.2811i | 0.273168 | − | 0.568506i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −20.3762 | − | 14.9388i | −0.669603 | − | 0.490918i | ||||
\(927\) | 2.04289 | − | 1.17946i | 0.0670974 | − | 0.0387387i | ||||
\(928\) | 4.37871 | + | 0.0943747i | 0.143738 | + | 0.00309800i | ||||
\(929\) | −28.1316 | − | 16.2418i | −0.922967 | − | 0.532875i | −0.0383868 | − | 0.999263i | \(-0.512222\pi\) |
−0.884580 | + | 0.466388i | \(0.845555\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.28674 | + | 5.51800i | −0.271587 | + | 0.180845i | ||||
\(932\) | 6.75036 | − | 30.4643i | 0.221115 | − | 0.997891i | ||||
\(933\) | 31.1877 | + | 18.0062i | 1.02104 | + | 0.589497i | ||||
\(934\) | 8.35634 | + | 18.9885i | 0.273428 | + | 0.621322i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −55.6042 | − | 63.3840i | −1.81748 | − | 2.07177i | ||||
\(937\) | −59.7020 | −1.95038 | −0.975190 | − | 0.221368i | \(-0.928948\pi\) | ||||
−0.975190 | + | 0.221368i | \(0.928948\pi\) | |||||||
\(938\) | −37.2487 | − | 13.1301i | −1.21621 | − | 0.428713i | ||||
\(939\) | − | 80.5424i | − | 2.62840i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.3373 | − | 7.12292i | 0.402183 | − | 0.232201i | −0.285242 | − | 0.958455i | \(-0.592074\pi\) |
0.687426 | + | 0.726255i | \(0.258741\pi\) | |||||||
\(942\) | −26.8705 | − | 61.0590i | −0.875488 | − | 1.98941i | ||||
\(943\) | −37.5477 | − | 21.6782i | −1.22272 | − | 0.705939i | ||||
\(944\) | −35.8358 | − | 16.7012i | −1.16636 | − | 0.543578i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.32552 | + | 0.254560i | 0.0756092 | + | 0.00827647i | ||||
\(947\) | 15.0513 | − | 26.0696i | 0.489101 | − | 0.847148i | −0.510820 | − | 0.859688i | \(-0.670658\pi\) |
0.999921 | + | 0.0125394i | \(0.00399152\pi\) | |||||||
\(948\) | −19.6115 | − | 62.1764i | −0.636950 | − | 2.01940i | ||||
\(949\) | 0.259040 | + | 0.448670i | 0.00840879 | + | 0.0145645i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 80.0831 | 2.59687 | ||||||||
\(952\) | −0.635283 | + | 19.0367i | −0.0205896 | + | 0.616984i | ||||
\(953\) | − | 3.58515i | − | 0.116134i | −0.998313 | − | 0.0580672i | \(-0.981506\pi\) | ||
0.998313 | − | 0.0580672i | \(-0.0184938\pi\) | |||||||
\(954\) | −17.3259 | + | 23.6322i | −0.560946 | + | 0.765120i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −26.9563 | + | 8.50244i | −0.871827 | + | 0.274988i | ||||
\(957\) | −1.40263 | + | 2.42942i | −0.0453405 | + | 0.0785320i | ||||
\(958\) | 4.02433 | − | 36.7640i | 0.130020 | − | 1.18779i | ||||
\(959\) | −3.27521 | − | 10.8279i | −0.105762 | − | 0.349650i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.53585 | + | 11.3204i | −0.210834 | + | 0.365175i | ||||
\(962\) | 14.0777 | + | 31.9893i | 0.453882 | + | 1.03138i | ||||
\(963\) | −2.59612 | − | 4.49662i | −0.0836589 | − | 0.144902i | ||||
\(964\) | 31.8286 | + | 29.1593i | 1.02513 | + | 0.939159i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 42.7836 | + | 49.9473i | 1.37654 | + | 1.60703i | ||||
\(967\) | −46.1614 | −1.48445 | −0.742226 | − | 0.670150i | \(-0.766230\pi\) | ||||
−0.742226 | + | 0.670150i | \(0.766230\pi\) | |||||||
\(968\) | −17.8454 | − | 20.3422i | −0.573574 | − | 0.653824i | ||||
\(969\) | 9.49011 | − | 5.47912i | 0.304866 | − | 0.176015i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.83113 | − | 10.0998i | 0.187130 | − | 0.324118i | −0.757162 | − | 0.653227i | \(-0.773415\pi\) |
0.944292 | + | 0.329108i | \(0.106748\pi\) | |||||||
\(972\) | 1.31678 | − | 5.94261i | 0.0422357 | − | 0.190609i | ||||
\(973\) | −4.54381 | + | 19.4176i | −0.145668 | + | 0.622499i | ||||
\(974\) | 2.55828 | − | 23.3710i | 0.0819727 | − | 0.748856i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −38.2408 | + | 3.35386i | −1.22406 | + | 0.107355i | ||||
\(977\) | −36.7913 | + | 21.2415i | −1.17706 | + | 0.679575i | −0.955332 | − | 0.295534i | \(-0.904503\pi\) |
−0.221726 | + | 0.975109i | \(0.571169\pi\) | |||||||
\(978\) | −24.4012 | + | 33.2827i | −0.780263 | + | 1.06426i | ||||
\(979\) | 4.71754 | 0.150773 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 24.3486 | 0.777390 | ||||||||
\(982\) | 18.3202 | − | 24.9883i | 0.584620 | − | 0.797410i | ||||
\(983\) | 27.4903 | − | 15.8715i | 0.876804 | − | 0.506223i | 0.00720094 | − | 0.999974i | \(-0.497708\pi\) |
0.869603 | + | 0.493751i | \(0.164375\pi\) | |||||||
\(984\) | −62.6996 | + | 12.4822i | −1.99879 | + | 0.397917i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.303257 | − | 2.77039i | 0.00965767 | − | 0.0882270i | ||||
\(987\) | 1.95412 | − | 8.35075i | 0.0622002 | − | 0.265807i | ||||
\(988\) | −13.4329 | − | 2.97650i | −0.427358 | − | 0.0946951i | ||||
\(989\) | −4.01235 | + | 6.94960i | −0.127585 | + | 0.220984i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.4182 | − | 14.6752i | 0.807436 | − | 0.466173i | −0.0386286 | − | 0.999254i | \(-0.512299\pi\) |
0.846065 | + | 0.533080i | \(0.178966\pi\) | |||||||
\(992\) | −18.0718 | − | 32.9197i | −0.573780 | − | 1.04520i | ||||
\(993\) | 73.5053 | 2.33262 | ||||||||
\(994\) | −39.7435 | − | 46.3981i | −1.26059 | − | 1.47166i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 64.6274 | − | 70.5435i | 2.04780 | − | 2.23526i | ||||
\(997\) | 5.40341 | + | 9.35899i | 0.171128 | + | 0.296402i | 0.938814 | − | 0.344423i | \(-0.111926\pi\) |
−0.767687 | + | 0.640825i | \(0.778592\pi\) | |||||||
\(998\) | 23.1780 | + | 52.6685i | 0.733688 | + | 1.66719i | ||||
\(999\) | −24.4608 | + | 42.3673i | −0.773905 | + | 1.34044i |
(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 | 700.2.t.c.299.13 | 32 | ||
4.3 | odd | 2 | inner | 700.2.t.c.299.14 | 32 | ||
5.2 | odd | 4 | 700.2.p.c.551.6 | 32 | |||
5.3 | odd | 4 | 140.2.o.a.131.11 | yes | 32 | ||
5.4 | even | 2 | 700.2.t.d.299.4 | 32 | |||
7.3 | odd | 6 | 700.2.t.d.199.3 | 32 | |||
20.3 | even | 4 | 140.2.o.a.131.10 | yes | 32 | ||
20.7 | even | 4 | 700.2.p.c.551.7 | 32 | |||
20.19 | odd | 2 | 700.2.t.d.299.3 | 32 | |||
28.3 | even | 6 | 700.2.t.d.199.4 | 32 | |||
35.3 | even | 12 | 140.2.o.a.31.10 | ✓ | 32 | ||
35.13 | even | 4 | 980.2.o.f.411.11 | 32 | |||
35.17 | even | 12 | 700.2.p.c.451.7 | 32 | |||
35.18 | odd | 12 | 980.2.o.f.31.10 | 32 | |||
35.23 | odd | 12 | 980.2.g.a.391.1 | 32 | |||
35.24 | odd | 6 | inner | 700.2.t.c.199.14 | 32 | ||
35.33 | even | 12 | 980.2.g.a.391.2 | 32 | |||
140.3 | odd | 12 | 140.2.o.a.31.11 | yes | 32 | ||
140.23 | even | 12 | 980.2.g.a.391.4 | 32 | |||
140.59 | even | 6 | inner | 700.2.t.c.199.13 | 32 | ||
140.83 | odd | 4 | 980.2.o.f.411.10 | 32 | |||
140.87 | odd | 12 | 700.2.p.c.451.6 | 32 | |||
140.103 | odd | 12 | 980.2.g.a.391.3 | 32 | |||
140.123 | even | 12 | 980.2.o.f.31.11 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
140.2.o.a.31.10 | ✓ | 32 | 35.3 | even | 12 | ||
140.2.o.a.31.11 | yes | 32 | 140.3 | odd | 12 | ||
140.2.o.a.131.10 | yes | 32 | 20.3 | even | 4 | ||
140.2.o.a.131.11 | yes | 32 | 5.3 | odd | 4 | ||
700.2.p.c.451.6 | 32 | 140.87 | odd | 12 | |||
700.2.p.c.451.7 | 32 | 35.17 | even | 12 | |||
700.2.p.c.551.6 | 32 | 5.2 | odd | 4 | |||
700.2.p.c.551.7 | 32 | 20.7 | even | 4 | |||
700.2.t.c.199.13 | 32 | 140.59 | even | 6 | inner | ||
700.2.t.c.199.14 | 32 | 35.24 | odd | 6 | inner | ||
700.2.t.c.299.13 | 32 | 1.1 | even | 1 | trivial | ||
700.2.t.c.299.14 | 32 | 4.3 | odd | 2 | inner | ||
700.2.t.d.199.3 | 32 | 7.3 | odd | 6 | |||
700.2.t.d.199.4 | 32 | 28.3 | even | 6 | |||
700.2.t.d.299.3 | 32 | 20.19 | odd | 2 | |||
700.2.t.d.299.4 | 32 | 5.4 | even | 2 | |||
980.2.g.a.391.1 | 32 | 35.23 | odd | 12 | |||
980.2.g.a.391.2 | 32 | 35.33 | even | 12 | |||
980.2.g.a.391.3 | 32 | 140.103 | odd | 12 | |||
980.2.g.a.391.4 | 32 | 140.23 | even | 12 | |||
980.2.o.f.31.10 | 32 | 35.18 | odd | 12 | |||
980.2.o.f.31.11 | 32 | 140.123 | even | 12 | |||
980.2.o.f.411.10 | 32 | 140.83 | odd | 4 | |||
980.2.o.f.411.11 | 32 | 35.13 | even | 4 |