Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [731,2,Mod(307,731)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(731, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("731.307");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 731 = 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 731.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.83706438776\) |
Analytic rank: | \(0\) |
Dimension: | \(58\) |
Relative dimension: | \(29\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 307.19 | ||
Character | \(\chi\) | \(=\) | 731.307 |
Dual form | 731.2.e.b.681.19 |
$q$-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 \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).
\(n\) | \(173\) | \(562\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.34037 | 0.947782 | 0.473891 | − | 0.880583i | \(-0.342849\pi\) | ||||
0.473891 | + | 0.880583i | \(0.342849\pi\) | |||||||
\(3\) | −0.719541 | + | 1.24628i | −0.415427 | + | 0.719541i | −0.995473 | − | 0.0950428i | \(-0.969701\pi\) |
0.580046 | + | 0.814584i | \(0.303035\pi\) | |||||||
\(4\) | −0.203418 | −0.101709 | ||||||||
\(5\) | 2.16961 | − | 3.75787i | 0.970278 | − | 1.68057i | 0.275567 | − | 0.961282i | \(-0.411134\pi\) |
0.694711 | − | 0.719289i | \(-0.255532\pi\) | |||||||
\(6\) | −0.964449 | + | 1.67047i | −0.393734 | + | 0.681968i | ||||
\(7\) | −1.07792 | − | 1.86701i | −0.407414 | − | 0.705662i | 0.587185 | − | 0.809453i | \(-0.300236\pi\) |
−0.994599 | + | 0.103791i | \(0.966903\pi\) | |||||||
\(8\) | −2.95339 | −1.04418 | ||||||||
\(9\) | 0.464522 | + | 0.804575i | 0.154841 | + | 0.268192i | ||||
\(10\) | 2.90807 | − | 5.03692i | 0.919612 | − | 1.59282i | ||||
\(11\) | −4.35461 | −1.31296 | −0.656481 | − | 0.754342i | \(-0.727956\pi\) | ||||
−0.656481 | + | 0.754342i | \(0.727956\pi\) | |||||||
\(12\) | 0.146367 | − | 0.253516i | 0.0422526 | − | 0.0731837i | ||||
\(13\) | −2.54109 | − | 4.40129i | −0.704771 | − | 1.22070i | −0.966774 | − | 0.255631i | \(-0.917717\pi\) |
0.262004 | − | 0.965067i | \(-0.415617\pi\) | |||||||
\(14\) | −1.44480 | − | 2.50247i | −0.386140 | − | 0.668813i | ||||
\(15\) | 3.12224 | + | 5.40788i | 0.806160 | + | 1.39631i | ||||
\(16\) | −3.55179 | −0.887946 | ||||||||
\(17\) | −0.500000 | − | 0.866025i | −0.121268 | − | 0.210042i | ||||
\(18\) | 0.622629 | + | 1.07843i | 0.146755 | + | 0.254187i | ||||
\(19\) | −0.476959 | + | 0.826117i | −0.109422 | + | 0.189524i | −0.915536 | − | 0.402236i | \(-0.868233\pi\) |
0.806114 | + | 0.591760i | \(0.201567\pi\) | |||||||
\(20\) | −0.441337 | + | 0.764418i | −0.0986859 | + | 0.170929i | ||||
\(21\) | 3.10242 | 0.677003 | ||||||||
\(22\) | −5.83677 | −1.24440 | ||||||||
\(23\) | 0.518993 | − | 0.898922i | 0.108218 | − | 0.187438i | −0.806831 | − | 0.590783i | \(-0.798819\pi\) |
0.915048 | + | 0.403345i | \(0.132152\pi\) | |||||||
\(24\) | 2.12508 | − | 3.68075i | 0.433781 | − | 0.751330i | ||||
\(25\) | −6.91440 | − | 11.9761i | −1.38288 | − | 2.39522i | ||||
\(26\) | −3.40599 | − | 5.89934i | −0.667969 | − | 1.15696i | ||||
\(27\) | −5.65422 | −1.08815 | ||||||||
\(28\) | 0.219267 | + | 0.379782i | 0.0414376 | + | 0.0717720i | ||||
\(29\) | 3.28660 | + | 5.69256i | 0.610307 | + | 1.05708i | 0.991189 | + | 0.132459i | \(0.0422872\pi\) |
−0.380882 | + | 0.924624i | \(0.624379\pi\) | |||||||
\(30\) | 4.18495 | + | 7.24855i | 0.764064 | + | 1.32340i | ||||
\(31\) | −0.897787 | + | 1.55501i | −0.161247 | + | 0.279288i | −0.935316 | − | 0.353813i | \(-0.884885\pi\) |
0.774069 | + | 0.633101i | \(0.218218\pi\) | |||||||
\(32\) | 1.14608 | 0.202600 | ||||||||
\(33\) | 3.13332 | − | 5.42706i | 0.545440 | − | 0.944731i | ||||
\(34\) | −0.670183 | − | 1.16079i | −0.114935 | − | 0.199074i | ||||
\(35\) | −9.35462 | −1.58122 | ||||||||
\(36\) | −0.0944919 | − | 0.163665i | −0.0157487 | − | 0.0272775i | ||||
\(37\) | 1.28100 | − | 2.21875i | 0.210594 | − | 0.364760i | −0.741306 | − | 0.671167i | \(-0.765793\pi\) |
0.951901 | + | 0.306407i | \(0.0991267\pi\) | |||||||
\(38\) | −0.639300 | + | 1.10730i | −0.103708 | + | 0.179628i | ||||
\(39\) | 7.31366 | 1.17112 | ||||||||
\(40\) | −6.40769 | + | 11.0984i | −1.01315 | + | 1.75482i | ||||
\(41\) | 10.9569 | 1.71119 | 0.855594 | − | 0.517648i | \(-0.173192\pi\) | ||||
0.855594 | + | 0.517648i | \(0.173192\pi\) | |||||||
\(42\) | 4.15838 | 0.641652 | ||||||||
\(43\) | 4.03207 | − | 5.17131i | 0.614884 | − | 0.788617i | ||||
\(44\) | 0.885804 | 0.133540 | ||||||||
\(45\) | 4.03132 | 0.600954 | ||||||||
\(46\) | 0.695641 | − | 1.20489i | 0.102567 | − | 0.177651i | ||||
\(47\) | 2.71691 | 0.396302 | 0.198151 | − | 0.980172i | \(-0.436506\pi\) | ||||
0.198151 | + | 0.980172i | \(0.436506\pi\) | |||||||
\(48\) | 2.55566 | − | 4.42652i | 0.368877 | − | 0.638914i | ||||
\(49\) | 1.17619 | − | 2.03723i | 0.168028 | − | 0.291033i | ||||
\(50\) | −9.26783 | − | 16.0523i | −1.31067 | − | 2.27014i | ||||
\(51\) | 1.43908 | 0.201512 | ||||||||
\(52\) | 0.516902 | + | 0.895300i | 0.0716814 | + | 0.124156i | ||||
\(53\) | 5.32875 | − | 9.22967i | 0.731960 | − | 1.26779i | −0.224084 | − | 0.974570i | \(-0.571939\pi\) |
0.956044 | − | 0.293223i | \(-0.0947277\pi\) | |||||||
\(54\) | −7.57872 | −1.03133 | ||||||||
\(55\) | −9.44779 | + | 16.3640i | −1.27394 | + | 2.20653i | ||||
\(56\) | 3.18350 | + | 5.51399i | 0.425413 | + | 0.736838i | ||||
\(57\) | −0.686383 | − | 1.18885i | −0.0909136 | − | 0.157467i | ||||
\(58\) | 4.40525 | + | 7.63012i | 0.578438 | + | 1.00188i | ||||
\(59\) | −10.9632 | −1.42728 | −0.713642 | − | 0.700511i | \(-0.752956\pi\) | ||||
−0.713642 | + | 0.700511i | \(0.752956\pi\) | |||||||
\(60\) | −0.635120 | − | 1.10006i | −0.0819936 | − | 0.142017i | ||||
\(61\) | 3.94784 | + | 6.83786i | 0.505469 | + | 0.875498i | 0.999980 | + | 0.00632695i | \(0.00201395\pi\) |
−0.494511 | + | 0.869172i | \(0.664653\pi\) | |||||||
\(62\) | −1.20336 | + | 2.08429i | −0.152827 | + | 0.264705i | ||||
\(63\) | 1.00143 | − | 1.73453i | 0.126168 | − | 0.218530i | ||||
\(64\) | 8.63974 | 1.07997 | ||||||||
\(65\) | −22.0526 | −2.73529 | ||||||||
\(66\) | 4.19979 | − | 7.27425i | 0.516959 | − | 0.895399i | ||||
\(67\) | 2.80430 | − | 4.85718i | 0.342599 | − | 0.593400i | −0.642315 | − | 0.766441i | \(-0.722026\pi\) |
0.984915 | + | 0.173041i | \(0.0553593\pi\) | |||||||
\(68\) | 0.101709 | + | 0.176165i | 0.0123340 | + | 0.0213631i | ||||
\(69\) | 0.746873 | + | 1.29362i | 0.0899130 | + | 0.155734i | ||||
\(70\) | −12.5386 | −1.49865 | ||||||||
\(71\) | 0.806022 | + | 1.39607i | 0.0956572 | + | 0.165683i | 0.909883 | − | 0.414866i | \(-0.136171\pi\) |
−0.814225 | + | 0.580549i | \(0.802838\pi\) | |||||||
\(72\) | −1.37191 | − | 2.37622i | −0.161681 | − | 0.280040i | ||||
\(73\) | −0.802311 | − | 1.38964i | −0.0939034 | − | 0.162646i | 0.815247 | − | 0.579113i | \(-0.196601\pi\) |
−0.909150 | + | 0.416468i | \(0.863268\pi\) | |||||||
\(74\) | 1.71700 | − | 2.97394i | 0.199598 | − | 0.345713i | ||||
\(75\) | 19.9008 | 2.29794 | ||||||||
\(76\) | 0.0970219 | − | 0.168047i | 0.0111292 | − | 0.0192763i | ||||
\(77\) | 4.69390 | + | 8.13007i | 0.534919 | + | 0.926507i | ||||
\(78\) | 9.80299 | 1.10997 | ||||||||
\(79\) | −1.85195 | − | 3.20767i | −0.208360 | − | 0.360891i | 0.742838 | − | 0.669471i | \(-0.233479\pi\) |
−0.951198 | + | 0.308581i | \(0.900146\pi\) | |||||||
\(80\) | −7.70598 | + | 13.3472i | −0.861555 | + | 1.49226i | ||||
\(81\) | 2.67487 | − | 4.63302i | 0.297208 | − | 0.514780i | ||||
\(82\) | 14.6863 | 1.62183 | ||||||||
\(83\) | 4.52149 | − | 7.83144i | 0.496298 | − | 0.859613i | −0.503693 | − | 0.863883i | \(-0.668026\pi\) |
0.999991 | + | 0.00426984i | \(0.00135914\pi\) | |||||||
\(84\) | −0.631087 | −0.0688572 | ||||||||
\(85\) | −4.33922 | −0.470654 | ||||||||
\(86\) | 5.40445 | − | 6.93145i | 0.582776 | − | 0.747438i | ||||
\(87\) | −9.45938 | −1.01415 | ||||||||
\(88\) | 12.8608 | 1.37097 | ||||||||
\(89\) | −2.13561 | + | 3.69898i | −0.226374 | + | 0.392091i | −0.956731 | − | 0.290975i | \(-0.906020\pi\) |
0.730357 | + | 0.683066i | \(0.239354\pi\) | |||||||
\(90\) | 5.40345 | 0.569573 | ||||||||
\(91\) | −5.47815 | + | 9.48844i | −0.574267 | + | 0.994659i | ||||
\(92\) | −0.105572 | + | 0.182857i | −0.0110067 | + | 0.0190641i | ||||
\(93\) | −1.29199 | − | 2.23779i | −0.133973 | − | 0.232048i | ||||
\(94\) | 3.64165 | 0.375608 | ||||||||
\(95\) | 2.06963 | + | 3.58470i | 0.212339 | + | 0.367782i | ||||
\(96\) | −0.824651 | + | 1.42834i | −0.0841656 | + | 0.145779i | ||||
\(97\) | −10.4038 | −1.05635 | −0.528174 | − | 0.849136i | \(-0.677123\pi\) | ||||
−0.528174 | + | 0.849136i | \(0.677123\pi\) | |||||||
\(98\) | 1.57653 | − | 2.73063i | 0.159254 | − | 0.275836i | ||||
\(99\) | −2.02281 | − | 3.50361i | −0.203300 | − | 0.352126i | ||||
\(100\) | 1.40651 | + | 2.43615i | 0.140651 | + | 0.243615i | ||||
\(101\) | 1.51800 | + | 2.62926i | 0.151047 | + | 0.261621i | 0.931613 | − | 0.363453i | \(-0.118402\pi\) |
−0.780566 | + | 0.625074i | \(0.785069\pi\) | |||||||
\(102\) | 1.92890 | 0.190989 | ||||||||
\(103\) | 8.32473 | + | 14.4189i | 0.820260 | + | 1.42073i | 0.905488 | + | 0.424371i | \(0.139505\pi\) |
−0.0852282 | + | 0.996361i | \(0.527162\pi\) | |||||||
\(104\) | 7.50481 | + | 12.9987i | 0.735907 | + | 1.27463i | ||||
\(105\) | 6.73103 | − | 11.6585i | 0.656881 | − | 1.13775i | ||||
\(106\) | 7.14248 | − | 12.3711i | 0.693739 | − | 1.20159i | ||||
\(107\) | −14.3054 | −1.38296 | −0.691479 | − | 0.722396i | \(-0.743041\pi\) | ||||
−0.691479 | + | 0.722396i | \(0.743041\pi\) | |||||||
\(108\) | 1.15017 | 0.110675 | ||||||||
\(109\) | 3.64210 | − | 6.30831i | 0.348850 | − | 0.604226i | −0.637195 | − | 0.770702i | \(-0.719906\pi\) |
0.986045 | + | 0.166476i | \(0.0532389\pi\) | |||||||
\(110\) | −12.6635 | + | 21.9338i | −1.20742 | + | 2.09131i | ||||
\(111\) | 1.84346 | + | 3.19296i | 0.174973 | + | 0.303063i | ||||
\(112\) | 3.82853 | + | 6.63120i | 0.361762 | + | 0.626590i | ||||
\(113\) | 0.636898 | 0.0599144 | 0.0299572 | − | 0.999551i | \(-0.490463\pi\) | ||||
0.0299572 | + | 0.999551i | \(0.490463\pi\) | |||||||
\(114\) | −0.920004 | − | 1.59349i | −0.0861663 | − | 0.149244i | ||||
\(115\) | −2.25202 | − | 3.90062i | −0.210002 | − | 0.363734i | ||||
\(116\) | −0.668553 | − | 1.15797i | −0.0620736 | − | 0.107515i | ||||
\(117\) | 2.36078 | − | 4.08899i | 0.218254 | − | 0.378027i | ||||
\(118\) | −14.6947 | −1.35275 | ||||||||
\(119\) | −1.07792 | + | 1.86701i | −0.0988124 | + | 0.171148i | ||||
\(120\) | −9.22119 | − | 15.9716i | −0.841776 | − | 1.45800i | ||||
\(121\) | 7.96259 | 0.723872 | ||||||||
\(122\) | 5.29155 | + | 9.16524i | 0.479075 | + | 0.829782i | ||||
\(123\) | −7.88397 | + | 13.6554i | −0.710874 | + | 1.23127i | ||||
\(124\) | 0.182626 | − | 0.316317i | 0.0164003 | − | 0.0284061i | ||||
\(125\) | −38.3100 | −3.42655 | ||||||||
\(126\) | 1.34228 | − | 2.32490i | 0.119580 | − | 0.207119i | ||||
\(127\) | −6.97708 | −0.619115 | −0.309558 | − | 0.950881i | \(-0.600181\pi\) | ||||
−0.309558 | + | 0.950881i | \(0.600181\pi\) | |||||||
\(128\) | 9.28826 | 0.820974 | ||||||||
\(129\) | 3.54367 | + | 8.74606i | 0.312003 | + | 0.770047i | ||||
\(130\) | −29.5586 | −2.59246 | ||||||||
\(131\) | 9.74079 | 0.851057 | 0.425528 | − | 0.904945i | \(-0.360088\pi\) | ||||
0.425528 | + | 0.904945i | \(0.360088\pi\) | |||||||
\(132\) | −0.637372 | + | 1.10396i | −0.0554761 | + | 0.0960875i | ||||
\(133\) | 2.05649 | 0.178320 | ||||||||
\(134\) | 3.75879 | − | 6.51041i | 0.324710 | − | 0.562414i | ||||
\(135\) | −12.2674 | + | 21.2478i | −1.05581 | + | 1.82872i | ||||
\(136\) | 1.47669 | + | 2.55771i | 0.126625 | + | 0.219322i | ||||
\(137\) | −1.76816 | −0.151064 | −0.0755321 | − | 0.997143i | \(-0.524066\pi\) | ||||
−0.0755321 | + | 0.997143i | \(0.524066\pi\) | |||||||
\(138\) | 1.00108 | + | 1.73393i | 0.0852179 | + | 0.147602i | ||||
\(139\) | −6.70923 | + | 11.6207i | −0.569069 | + | 0.985657i | 0.427589 | + | 0.903973i | \(0.359363\pi\) |
−0.996658 | + | 0.0816836i | \(0.973970\pi\) | |||||||
\(140\) | 1.90290 | 0.160824 | ||||||||
\(141\) | −1.95493 | + | 3.38603i | −0.164634 | + | 0.285155i | ||||
\(142\) | 1.08036 | + | 1.87125i | 0.0906622 | + | 0.157032i | ||||
\(143\) | 11.0654 | + | 19.1659i | 0.925338 | + | 1.60273i | ||||
\(144\) | −1.64988 | − | 2.85768i | −0.137490 | − | 0.238140i | ||||
\(145\) | 28.5226 | 2.36867 | ||||||||
\(146\) | −1.07539 | − | 1.86263i | −0.0890000 | − | 0.154153i | ||||
\(147\) | 1.69264 | + | 2.93174i | 0.139607 | + | 0.241806i | ||||
\(148\) | −0.260577 | + | 0.451333i | −0.0214193 | + | 0.0370993i | ||||
\(149\) | −9.02044 | + | 15.6239i | −0.738983 | + | 1.27996i | 0.213971 | + | 0.976840i | \(0.431360\pi\) |
−0.952954 | + | 0.303116i | \(0.901973\pi\) | |||||||
\(150\) | 26.6743 | 2.17795 | ||||||||
\(151\) | 19.3015 | 1.57073 | 0.785366 | − | 0.619032i | \(-0.212475\pi\) | ||||
0.785366 | + | 0.619032i | \(0.212475\pi\) | |||||||
\(152\) | 1.40864 | − | 2.43984i | 0.114256 | − | 0.197897i | ||||
\(153\) | 0.464522 | − | 0.804575i | 0.0375544 | − | 0.0650460i | ||||
\(154\) | 6.29154 | + | 10.8973i | 0.506987 | + | 0.878127i | ||||
\(155\) | 3.89569 | + | 6.74753i | 0.312909 | + | 0.541975i | ||||
\(156\) | −1.48773 | −0.119114 | ||||||||
\(157\) | −5.91251 | − | 10.2408i | −0.471870 | − | 0.817303i | 0.527612 | − | 0.849485i | \(-0.323087\pi\) |
−0.999482 | + | 0.0321827i | \(0.989754\pi\) | |||||||
\(158\) | −2.48229 | − | 4.29945i | −0.197480 | − | 0.342046i | ||||
\(159\) | 7.66851 | + | 13.2822i | 0.608152 | + | 1.05335i | ||||
\(160\) | 2.48654 | − | 4.30682i | 0.196579 | − | 0.340484i | ||||
\(161\) | −2.23772 | −0.176357 | ||||||||
\(162\) | 3.58531 | − | 6.20994i | 0.281689 | − | 0.487899i | ||||
\(163\) | 3.57678 | + | 6.19517i | 0.280155 | + | 0.485243i | 0.971423 | − | 0.237356i | \(-0.0762807\pi\) |
−0.691268 | + | 0.722599i | \(0.742947\pi\) | |||||||
\(164\) | −2.22884 | −0.174043 | ||||||||
\(165\) | −13.5961 | − | 23.5492i | −1.05846 | − | 1.83330i | ||||
\(166\) | 6.06045 | − | 10.4970i | 0.470382 | − | 0.814726i | ||||
\(167\) | 0.362695 | − | 0.628206i | 0.0280662 | − | 0.0486120i | −0.851651 | − | 0.524109i | \(-0.824398\pi\) |
0.879717 | + | 0.475497i | \(0.157732\pi\) | |||||||
\(168\) | −9.16264 | −0.706913 | ||||||||
\(169\) | −6.41424 | + | 11.1098i | −0.493403 | + | 0.854599i | ||||
\(170\) | −5.81614 | −0.446078 | ||||||||
\(171\) | −0.886231 | −0.0677718 | ||||||||
\(172\) | −0.820194 | + | 1.05194i | −0.0625392 | + | 0.0802094i | ||||
\(173\) | −10.6906 | −0.812790 | −0.406395 | − | 0.913697i | \(-0.633214\pi\) | ||||
−0.406395 | + | 0.913697i | \(0.633214\pi\) | |||||||
\(174\) | −12.6790 | −0.961195 | ||||||||
\(175\) | −14.9063 | + | 25.8184i | −1.12681 | + | 1.95169i | ||||
\(176\) | 15.4666 | 1.16584 | ||||||||
\(177\) | 7.88845 | − | 13.6632i | 0.592932 | − | 1.02699i | ||||
\(178\) | −2.86249 | + | 4.95799i | −0.214553 | + | 0.371617i | ||||
\(179\) | −10.9988 | − | 19.0505i | −0.822090 | − | 1.42390i | −0.904123 | − | 0.427272i | \(-0.859475\pi\) |
0.0820335 | − | 0.996630i | \(-0.473859\pi\) | |||||||
\(180\) | −0.820042 | −0.0611223 | ||||||||
\(181\) | −7.97236 | − | 13.8085i | −0.592580 | − | 1.02638i | −0.993883 | − | 0.110434i | \(-0.964776\pi\) |
0.401303 | − | 0.915945i | \(-0.368557\pi\) | |||||||
\(182\) | −7.34273 | + | 12.7180i | −0.544280 | + | 0.942720i | ||||
\(183\) | −11.3625 | −0.839943 | ||||||||
\(184\) | −1.53279 | + | 2.65487i | −0.112999 | + | 0.195719i | ||||
\(185\) | −5.55852 | − | 9.62763i | −0.408670 | − | 0.707838i | ||||
\(186\) | −1.73174 | − | 2.99946i | −0.126977 | − | 0.219931i | ||||
\(187\) | 2.17730 | + | 3.77120i | 0.159220 | + | 0.275777i | ||||
\(188\) | −0.552667 | −0.0403074 | ||||||||
\(189\) | 6.09477 | + | 10.5564i | 0.443329 | + | 0.767869i | ||||
\(190\) | 2.77406 | + | 4.80481i | 0.201251 | + | 0.348578i | ||||
\(191\) | 8.96734 | − | 15.5319i | 0.648854 | − | 1.12385i | −0.334543 | − | 0.942380i | \(-0.608582\pi\) |
0.983397 | − | 0.181467i | \(-0.0580847\pi\) | |||||||
\(192\) | −6.21665 | + | 10.7675i | −0.448648 | + | 0.777081i | ||||
\(193\) | 12.4557 | 0.896584 | 0.448292 | − | 0.893887i | \(-0.352033\pi\) | ||||
0.448292 | + | 0.893887i | \(0.352033\pi\) | |||||||
\(194\) | −13.9449 | −1.00119 | ||||||||
\(195\) | 15.8678 | − | 27.4838i | 1.13632 | − | 1.96816i | ||||
\(196\) | −0.239259 | + | 0.414409i | −0.0170899 | + | 0.0296006i | ||||
\(197\) | −10.1245 | − | 17.5361i | −0.721338 | − | 1.24939i | −0.960464 | − | 0.278406i | \(-0.910194\pi\) |
0.239125 | − | 0.970989i | \(-0.423139\pi\) | |||||||
\(198\) | −2.71130 | − | 4.69612i | −0.192684 | − | 0.333739i | ||||
\(199\) | 4.75936 | 0.337382 | 0.168691 | − | 0.985669i | \(-0.446046\pi\) | ||||
0.168691 | + | 0.985669i | \(0.446046\pi\) | |||||||
\(200\) | 20.4209 | + | 35.3700i | 1.44397 | + | 2.50104i | ||||
\(201\) | 4.03561 | + | 6.98989i | 0.284650 | + | 0.493029i | ||||
\(202\) | 2.03468 | + | 3.52417i | 0.143160 | + | 0.247960i | ||||
\(203\) | 7.08536 | − | 12.2722i | 0.497295 | − | 0.861340i | ||||
\(204\) | −0.292735 | −0.0204955 | ||||||||
\(205\) | 23.7723 | − | 41.1748i | 1.66033 | − | 2.87577i | ||||
\(206\) | 11.1582 | + | 19.3266i | 0.777428 | + | 1.34654i | ||||
\(207\) | 0.964334 | 0.0670258 | ||||||||
\(208\) | 9.02539 | + | 15.6324i | 0.625798 | + | 1.08391i | ||||
\(209\) | 2.07697 | − | 3.59741i | 0.143667 | − | 0.248838i | ||||
\(210\) | 9.02205 | − | 15.6266i | 0.622580 | − | 1.07834i | ||||
\(211\) | 6.59363 | 0.453924 | 0.226962 | − | 0.973904i | \(-0.427121\pi\) | ||||
0.226962 | + | 0.973904i | \(0.427121\pi\) | |||||||
\(212\) | −1.08396 | + | 1.87748i | −0.0744468 | + | 0.128946i | ||||
\(213\) | −2.31986 | −0.158954 | ||||||||
\(214\) | −19.1745 | −1.31074 | ||||||||
\(215\) | −10.6851 | − | 26.3717i | −0.728719 | − | 1.79853i | ||||
\(216\) | 16.6991 | 1.13623 | ||||||||
\(217\) | 3.87095 | 0.262777 | ||||||||
\(218\) | 4.88175 | − | 8.45544i | 0.330634 | − | 0.572675i | ||||
\(219\) | 2.30918 | 0.156040 | ||||||||
\(220\) | 1.92185 | − | 3.32874i | 0.129571 | − | 0.224423i | ||||
\(221\) | −2.54109 | + | 4.40129i | −0.170932 | + | 0.296063i | ||||
\(222\) | 2.47091 | + | 4.27974i | 0.165837 | + | 0.287237i | ||||
\(223\) | −1.90792 | −0.127764 | −0.0638819 | − | 0.997957i | \(-0.520348\pi\) | ||||
−0.0638819 | + | 0.997957i | \(0.520348\pi\) | |||||||
\(224\) | −1.23538 | − | 2.13974i | −0.0825421 | − | 0.142967i | ||||
\(225\) | 6.42377 | − | 11.1263i | 0.428252 | − | 0.741754i | ||||
\(226\) | 0.853677 | 0.0567858 | ||||||||
\(227\) | 4.79418 | − | 8.30376i | 0.318201 | − | 0.551140i | −0.661912 | − | 0.749582i | \(-0.730255\pi\) |
0.980113 | + | 0.198442i | \(0.0635880\pi\) | |||||||
\(228\) | 0.139622 | + | 0.241833i | 0.00924672 | + | 0.0160158i | ||||
\(229\) | 8.75644 | + | 15.1666i | 0.578642 | + | 1.00224i | 0.995635 | + | 0.0933273i | \(0.0297503\pi\) |
−0.416994 | + | 0.908909i | \(0.636916\pi\) | |||||||
\(230\) | −3.01854 | − | 5.22826i | −0.199036 | − | 0.344741i | ||||
\(231\) | −13.5098 | −0.888880 | ||||||||
\(232\) | −9.70661 | − | 16.8123i | −0.637270 | − | 1.10378i | ||||
\(233\) | 7.32426 | + | 12.6860i | 0.479828 | + | 0.831087i | 0.999732 | − | 0.0231376i | \(-0.00736558\pi\) |
−0.519904 | + | 0.854225i | \(0.674032\pi\) | |||||||
\(234\) | 3.16431 | − | 5.48074i | 0.206857 | − | 0.358287i | ||||
\(235\) | 5.89462 | − | 10.2098i | 0.384523 | − | 0.666013i | ||||
\(236\) | 2.23010 | 0.145167 | ||||||||
\(237\) | 5.33021 | 0.346234 | ||||||||
\(238\) | −1.44480 | + | 2.50247i | −0.0936526 | + | 0.162211i | ||||
\(239\) | 2.64507 | − | 4.58139i | 0.171095 | − | 0.296345i | −0.767708 | − | 0.640800i | \(-0.778603\pi\) |
0.938803 | + | 0.344455i | \(0.111936\pi\) | |||||||
\(240\) | −11.0895 | − | 19.2076i | −0.715827 | − | 1.23985i | ||||
\(241\) | −7.63513 | − | 13.2244i | −0.491822 | − | 0.851860i | 0.508134 | − | 0.861278i | \(-0.330336\pi\) |
−0.999956 | + | 0.00941781i | \(0.997002\pi\) | |||||||
\(242\) | 10.6728 | 0.686073 | ||||||||
\(243\) | −4.63196 | − | 8.02279i | −0.297140 | − | 0.514662i | ||||
\(244\) | −0.803061 | − | 1.39094i | −0.0514107 | − | 0.0890460i | ||||
\(245\) | −5.10376 | − | 8.83998i | −0.326067 | − | 0.564765i | ||||
\(246\) | −10.5674 | + | 18.3033i | −0.673754 | + | 1.16698i | ||||
\(247\) | 4.84797 | 0.308469 | ||||||||
\(248\) | 2.65151 | − | 4.59255i | 0.168371 | − | 0.291627i | ||||
\(249\) | 6.50679 | + | 11.2701i | 0.412351 | + | 0.714213i | ||||
\(250\) | −51.3495 | −3.24763 | ||||||||
\(251\) | −2.47162 | − | 4.28098i | −0.156007 | − | 0.270213i | 0.777418 | − | 0.628984i | \(-0.216529\pi\) |
−0.933425 | + | 0.358772i | \(0.883196\pi\) | |||||||
\(252\) | −0.203709 | + | 0.352834i | −0.0128324 | + | 0.0222264i | ||||
\(253\) | −2.26001 | + | 3.91445i | −0.142086 | + | 0.246099i | ||||
\(254\) | −9.35184 | −0.586787 | ||||||||
\(255\) | 3.12224 | − | 5.40788i | 0.195522 | − | 0.338655i | ||||
\(256\) | −4.82981 | −0.301863 | ||||||||
\(257\) | 3.26185 | 0.203469 | 0.101734 | − | 0.994812i | \(-0.467561\pi\) | ||||
0.101734 | + | 0.994812i | \(0.467561\pi\) | |||||||
\(258\) | 4.74982 | + | 11.7229i | 0.295711 | + | 0.729837i | ||||
\(259\) | −5.52322 | −0.343196 | ||||||||
\(260\) | 4.48590 | 0.278204 | ||||||||
\(261\) | −3.05340 | + | 5.28864i | −0.189001 | + | 0.327359i | ||||
\(262\) | 13.0562 | 0.806616 | ||||||||
\(263\) | 15.4307 | − | 26.7268i | 0.951500 | − | 1.64805i | 0.209317 | − | 0.977848i | \(-0.432876\pi\) |
0.742182 | − | 0.670198i | \(-0.233791\pi\) | |||||||
\(264\) | −9.25390 | + | 16.0282i | −0.569538 | + | 0.986469i | ||||
\(265\) | −23.1226 | − | 40.0495i | −1.42041 | − | 2.46022i | ||||
\(266\) | 2.75644 | 0.169008 | ||||||||
\(267\) | −3.07331 | − | 5.32313i | −0.188084 | − | 0.325770i | ||||
\(268\) | −0.570444 | + | 0.988037i | −0.0348454 | + | 0.0603540i | ||||
\(269\) | 9.82089 | 0.598790 | 0.299395 | − | 0.954129i | \(-0.403215\pi\) | ||||
0.299395 | + | 0.954129i | \(0.403215\pi\) | |||||||
\(270\) | −16.4429 | + | 28.4799i | −1.00068 | + | 1.73323i | ||||
\(271\) | −4.93949 | − | 8.55545i | −0.300053 | − | 0.519707i | 0.676095 | − | 0.736815i | \(-0.263671\pi\) |
−0.976148 | + | 0.217108i | \(0.930338\pi\) | |||||||
\(272\) | 1.77589 | + | 3.07594i | 0.107679 | + | 0.186506i | ||||
\(273\) | −7.88351 | − | 13.6546i | −0.477132 | − | 0.826417i | ||||
\(274\) | −2.36998 | −0.143176 | ||||||||
\(275\) | 30.1095 | + | 52.1511i | 1.81567 | + | 3.14483i | ||||
\(276\) | −0.151927 | − | 0.263146i | −0.00914495 | − | 0.0158395i | ||||
\(277\) | −9.40910 | + | 16.2970i | −0.565338 | + | 0.979194i | 0.431680 | + | 0.902027i | \(0.357921\pi\) |
−0.997018 | + | 0.0771673i | \(0.975412\pi\) | |||||||
\(278\) | −8.99282 | + | 15.5760i | −0.539354 | + | 0.934188i | ||||
\(279\) | −1.66817 | −0.0998705 | ||||||||
\(280\) | 27.6278 | 1.65108 | ||||||||
\(281\) | 7.91428 | − | 13.7079i | 0.472126 | − | 0.817747i | −0.527365 | − | 0.849639i | \(-0.676820\pi\) |
0.999491 | + | 0.0318920i | \(0.0101532\pi\) | |||||||
\(282\) | −2.62032 | + | 4.53852i | −0.156038 | + | 0.270265i | ||||
\(283\) | 2.70722 | + | 4.68904i | 0.160928 | + | 0.278735i | 0.935202 | − | 0.354116i | \(-0.115218\pi\) |
−0.774274 | + | 0.632850i | \(0.781885\pi\) | |||||||
\(284\) | −0.163959 | − | 0.283986i | −0.00972919 | − | 0.0168514i | ||||
\(285\) | −5.95673 | −0.352846 | ||||||||
\(286\) | 14.8317 | + | 25.6893i | 0.877018 | + | 1.51904i | ||||
\(287\) | −11.8107 | − | 20.4567i | −0.697162 | − | 1.20752i | ||||
\(288\) | 0.532379 | + | 0.922107i | 0.0313707 | + | 0.0543357i | ||||
\(289\) | −0.500000 | + | 0.866025i | −0.0294118 | + | 0.0509427i | ||||
\(290\) | 38.2307 | 2.24498 | ||||||||
\(291\) | 7.48597 | − | 12.9661i | 0.438836 | − | 0.760085i | ||||
\(292\) | 0.163204 | + | 0.282678i | 0.00955081 | + | 0.0165425i | ||||
\(293\) | 28.1036 | 1.64183 | 0.820914 | − | 0.571052i | \(-0.193465\pi\) | ||||
0.820914 | + | 0.571052i | \(0.193465\pi\) | |||||||
\(294\) | 2.26876 | + | 3.92961i | 0.132317 | + | 0.229179i | ||||
\(295\) | −23.7858 | + | 41.1982i | −1.38486 | + | 2.39865i | ||||
\(296\) | −3.78328 | + | 6.55283i | −0.219899 | + | 0.380875i | ||||
\(297\) | 24.6219 | 1.42871 | ||||||||
\(298\) | −12.0907 | + | 20.9417i | −0.700395 | + | 1.21312i | ||||
\(299\) | −5.27522 | −0.305074 | ||||||||
\(300\) | −4.04817 | −0.233721 | ||||||||
\(301\) | −14.0011 | − | 1.95365i | −0.807009 | − | 0.112607i | ||||
\(302\) | 25.8710 | 1.48871 | ||||||||
\(303\) | −4.36906 | −0.250996 | ||||||||
\(304\) | 1.69406 | − | 2.93419i | 0.0971607 | − | 0.168287i | ||||
\(305\) | 34.2611 | 1.96178 | ||||||||
\(306\) | 0.622629 | − | 1.07843i | 0.0355933 | − | 0.0616495i | ||||
\(307\) | −4.40471 | + | 7.62919i | −0.251390 | + | 0.435421i | −0.963909 | − | 0.266233i | \(-0.914221\pi\) |
0.712519 | + | 0.701653i | \(0.247554\pi\) | |||||||
\(308\) | −0.954822 | − | 1.65380i | −0.0544060 | − | 0.0942340i | ||||
\(309\) | −23.9599 | −1.36303 | ||||||||
\(310\) | 5.22165 | + | 9.04417i | 0.296570 | + | 0.513674i | ||||
\(311\) | −10.1821 | + | 17.6359i | −0.577374 | + | 1.00004i | 0.418405 | + | 0.908260i | \(0.362589\pi\) |
−0.995779 | + | 0.0917805i | \(0.970744\pi\) | |||||||
\(312\) | −21.6001 | −1.22286 | ||||||||
\(313\) | 6.34778 | − | 10.9947i | 0.358798 | − | 0.621456i | −0.628962 | − | 0.777436i | \(-0.716520\pi\) |
0.987760 | + | 0.155980i | \(0.0498534\pi\) | |||||||
\(314\) | −7.92493 | − | 13.7264i | −0.447230 | − | 0.774625i | ||||
\(315\) | −4.34542 | − | 7.52649i | −0.244837 | − | 0.424070i | ||||
\(316\) | 0.376719 | + | 0.652496i | 0.0211921 | + | 0.0367058i | ||||
\(317\) | 33.2343 | 1.86662 | 0.933311 | − | 0.359069i | \(-0.116906\pi\) | ||||
0.933311 | + | 0.359069i | \(0.116906\pi\) | |||||||
\(318\) | 10.2786 | + | 17.8031i | 0.576396 | + | 0.998347i | ||||
\(319\) | −14.3119 | − | 24.7889i | −0.801310 | − | 1.38791i | ||||
\(320\) | 18.7448 | − | 32.4670i | 1.04787 | − | 1.81496i | ||||
\(321\) | 10.2933 | − | 17.8286i | 0.574518 | − | 0.995095i | ||||
\(322\) | −2.99937 | −0.167148 | ||||||||
\(323\) | 0.953918 | 0.0530774 | ||||||||
\(324\) | −0.544117 | + | 0.942438i | −0.0302287 | + | 0.0523577i | ||||
\(325\) | −35.1402 | + | 60.8645i | −1.94923 | + | 3.37616i | ||||
\(326\) | 4.79420 | + | 8.30380i | 0.265526 | + | 0.459905i | ||||
\(327\) | 5.24129 | + | 9.07817i | 0.289844 | + | 0.502024i | ||||
\(328\) | −32.3601 | −1.78679 | ||||||||
\(329\) | −2.92860 | − | 5.07248i | −0.161459 | − | 0.279655i | ||||
\(330\) | −18.2238 | − | 31.5646i | −1.00319 | − | 1.73757i | ||||
\(331\) | 1.63717 | + | 2.83567i | 0.0899872 | + | 0.155862i | 0.907505 | − | 0.420040i | \(-0.137984\pi\) |
−0.817518 | + | 0.575903i | \(0.804651\pi\) | |||||||
\(332\) | −0.919751 | + | 1.59305i | −0.0504779 | + | 0.0874302i | ||||
\(333\) | 2.38020 | 0.130434 | ||||||||
\(334\) | 0.486144 | − | 0.842026i | 0.0266006 | − | 0.0460736i | ||||
\(335\) | −12.1684 | − | 21.0764i | −0.664833 | − | 1.15153i | ||||
\(336\) | −11.0191 | −0.601143 | ||||||||
\(337\) | 1.77204 | + | 3.06927i | 0.0965293 | + | 0.167194i | 0.910246 | − | 0.414068i | \(-0.135893\pi\) |
−0.813717 | + | 0.581262i | \(0.802559\pi\) | |||||||
\(338\) | −8.59743 | + | 14.8912i | −0.467639 | + | 0.809974i | ||||
\(339\) | −0.458274 | + | 0.793755i | −0.0248901 | + | 0.0431108i | ||||
\(340\) | 0.882673 | 0.0478697 | ||||||||
\(341\) | 3.90951 | − | 6.77146i | 0.211712 | − | 0.366695i | ||||
\(342\) | −1.18787 | −0.0642329 | ||||||||
\(343\) | −20.1622 | −1.08866 | ||||||||
\(344\) | −11.9083 | + | 15.2729i | −0.642050 | + | 0.823459i | ||||
\(345\) | 6.48169 | 0.348962 | ||||||||
\(346\) | −14.3293 | −0.770348 | ||||||||
\(347\) | −10.7373 | + | 18.5975i | −0.576408 | + | 0.998369i | 0.419479 | + | 0.907765i | \(0.362213\pi\) |
−0.995887 | + | 0.0906034i | \(0.971120\pi\) | |||||||
\(348\) | 1.92421 | 0.103148 | ||||||||
\(349\) | −8.23099 | + | 14.2565i | −0.440595 | + | 0.763132i | −0.997734 | − | 0.0672869i | \(-0.978566\pi\) |
0.557139 | + | 0.830419i | \(0.311899\pi\) | |||||||
\(350\) | −19.9799 | + | 34.6062i | −1.06797 | + | 1.84978i | ||||
\(351\) | 14.3678 | + | 24.8858i | 0.766899 | + | 1.32831i | ||||
\(352\) | −4.99073 | −0.266007 | ||||||||
\(353\) | −11.9581 | − | 20.7121i | −0.636466 | − | 1.10239i | −0.986202 | − | 0.165544i | \(-0.947062\pi\) |
0.349736 | − | 0.936848i | \(-0.386271\pi\) | |||||||
\(354\) | 10.5734 | − | 18.3137i | 0.561971 | − | 0.973362i | ||||
\(355\) | 6.99501 | 0.371256 | ||||||||
\(356\) | 0.434420 | − | 0.752438i | 0.0230242 | − | 0.0398791i | ||||
\(357\) | −1.55121 | − | 2.68677i | −0.0820987 | − | 0.142199i | ||||
\(358\) | −14.7424 | − | 25.5347i | −0.779162 | − | 1.34955i | ||||
\(359\) | −4.59779 | − | 7.96361i | −0.242662 | − | 0.420303i | 0.718809 | − | 0.695207i | \(-0.244687\pi\) |
−0.961472 | + | 0.274904i | \(0.911354\pi\) | |||||||
\(360\) | −11.9060 | −0.627504 | ||||||||
\(361\) | 9.04502 | + | 15.6664i | 0.476054 | + | 0.824549i | ||||
\(362\) | −10.6859 | − | 18.5085i | −0.561637 | − | 0.972784i | ||||
\(363\) | −5.72941 | + | 9.92363i | −0.300716 | + | 0.520855i | ||||
\(364\) | 1.11435 | − | 1.93012i | 0.0584080 | − | 0.101166i | ||||
\(365\) | −6.96280 | −0.364450 | ||||||||
\(366\) | −15.2300 | −0.796083 | ||||||||
\(367\) | −16.8169 | + | 29.1278i | −0.877838 | + | 1.52046i | −0.0241286 | + | 0.999709i | \(0.507681\pi\) |
−0.853709 | + | 0.520750i | \(0.825652\pi\) | |||||||
\(368\) | −1.84335 | + | 3.19278i | −0.0960914 | + | 0.166435i | ||||
\(369\) | 5.08974 | + | 8.81569i | 0.264961 | + | 0.458926i | ||||
\(370\) | −7.45045 | − | 12.9046i | −0.387330 | − | 0.670876i | ||||
\(371\) | −22.9758 | −1.19284 | ||||||||
\(372\) | 0.262813 | + | 0.455206i | 0.0136262 | + | 0.0236013i | ||||
\(373\) | −7.25065 | − | 12.5585i | −0.375425 | − | 0.650254i | 0.614966 | − | 0.788554i | \(-0.289170\pi\) |
−0.990390 | + | 0.138299i | \(0.955836\pi\) | |||||||
\(374\) | 2.91838 | + | 5.05479i | 0.150906 | + | 0.261377i | ||||
\(375\) | 27.5656 | − | 47.7451i | 1.42348 | − | 2.46555i | ||||
\(376\) | −8.02408 | −0.413810 | ||||||||
\(377\) | 16.7031 | − | 28.9306i | 0.860253 | − | 1.49000i | ||||
\(378\) | 8.16922 | + | 14.1495i | 0.420179 | + | 0.727772i | ||||
\(379\) | 21.9952 | 1.12982 | 0.564910 | − | 0.825153i | \(-0.308911\pi\) | ||||
0.564910 | + | 0.825153i | \(0.308911\pi\) | |||||||
\(380\) | −0.420999 | − | 0.729191i | −0.0215968 | − | 0.0374067i | ||||
\(381\) | 5.02029 | − | 8.69540i | 0.257197 | − | 0.445479i | ||||
\(382\) | 12.0195 | − | 20.8184i | 0.614972 | − | 1.06516i | ||||
\(383\) | 30.7013 | 1.56877 | 0.784383 | − | 0.620277i | \(-0.212980\pi\) | ||||
0.784383 | + | 0.620277i | \(0.212980\pi\) | |||||||
\(384\) | −6.68328 | + | 11.5758i | −0.341055 | + | 0.590724i | ||||
\(385\) | 40.7357 | 2.07608 | ||||||||
\(386\) | 16.6953 | 0.849766 | ||||||||
\(387\) | 6.03369 | + | 0.841914i | 0.306710 | + | 0.0427969i | ||||
\(388\) | 2.11632 | 0.107440 | ||||||||
\(389\) | −36.7768 | −1.86466 | −0.932328 | − | 0.361614i | \(-0.882226\pi\) | ||||
−0.932328 | + | 0.361614i | \(0.882226\pi\) | |||||||
\(390\) | 21.2686 | − | 36.8384i | 1.07698 | − | 1.86538i | ||||
\(391\) | −1.03799 | −0.0524932 | ||||||||
\(392\) | −3.47376 | + | 6.01673i | −0.175451 | + | 0.303891i | ||||
\(393\) | −7.00890 | + | 12.1398i | −0.353552 | + | 0.612370i | ||||
\(394\) | −13.5705 | − | 23.5048i | −0.683672 | − | 1.18415i | ||||
\(395\) | −16.0720 | −0.808670 | ||||||||
\(396\) | 0.411475 | + | 0.712696i | 0.0206774 | + | 0.0358143i | ||||
\(397\) | −3.96148 | + | 6.86148i | −0.198821 | + | 0.344368i | −0.948146 | − | 0.317834i | \(-0.897045\pi\) |
0.749325 | + | 0.662202i | \(0.230378\pi\) | |||||||
\(398\) | 6.37929 | 0.319765 | ||||||||
\(399\) | −1.47973 | + | 2.56296i | −0.0740789 | + | 0.128308i | ||||
\(400\) | 24.5585 | + | 42.5365i | 1.22792 | + | 2.12682i | ||||
\(401\) | 7.18159 | + | 12.4389i | 0.358631 | + | 0.621168i | 0.987732 | − | 0.156156i | \(-0.0499101\pi\) |
−0.629101 | + | 0.777324i | \(0.716577\pi\) | |||||||
\(402\) | 5.40920 | + | 9.36901i | 0.269786 | + | 0.467284i | ||||
\(403\) | 9.12541 | 0.454569 | ||||||||
\(404\) | −0.308789 | − | 0.534838i | −0.0153628 | − | 0.0266092i | ||||
\(405\) | −11.6069 | − | 20.1037i | −0.576749 | − | 0.998959i | ||||
\(406\) | 9.49698 | − | 16.4493i | 0.471327 | − | 0.816363i | ||||
\(407\) | −5.57823 | + | 9.66178i | −0.276503 | + | 0.478917i | ||||
\(408\) | −4.25017 | −0.210415 | ||||||||
\(409\) | 2.01227 | 0.0995005 | 0.0497503 | − | 0.998762i | \(-0.484157\pi\) | ||||
0.0497503 | + | 0.998762i | \(0.484157\pi\) | |||||||
\(410\) | 31.8636 | − | 55.1893i | 1.57363 | − | 2.72561i | ||||
\(411\) | 1.27226 | − | 2.20363i | 0.0627562 | − | 0.108697i | ||||
\(412\) | −1.69340 | − | 2.93305i | −0.0834277 | − | 0.144501i | ||||
\(413\) | 11.8174 | + | 20.4683i | 0.581495 | + | 1.00718i | ||||
\(414\) | 1.29256 | 0.0635259 | ||||||||
\(415\) | −19.6197 | − | 33.9823i | −0.963094 | − | 1.66813i | ||||
\(416\) | −2.91229 | − | 5.04423i | −0.142787 | − | 0.247314i | ||||
\(417\) | −9.65513 | − | 16.7232i | −0.472814 | − | 0.818937i | ||||
\(418\) | 2.78390 | − | 4.82185i | 0.136165 | − | 0.235844i | ||||
\(419\) | 14.8728 | 0.726585 | 0.363292 | − | 0.931675i | \(-0.381653\pi\) | ||||
0.363292 | + | 0.931675i | \(0.381653\pi\) | |||||||
\(420\) | −1.36921 | + | 2.37154i | −0.0668107 | + | 0.115719i | ||||
\(421\) | −15.2612 | − | 26.4332i | −0.743786 | − | 1.28827i | −0.950760 | − | 0.309928i | \(-0.899695\pi\) |
0.206974 | − | 0.978346i | \(-0.433638\pi\) | |||||||
\(422\) | 8.83788 | 0.430221 | ||||||||
\(423\) | 1.26206 | + | 2.18596i | 0.0613636 | + | 0.106285i | ||||
\(424\) | −15.7379 | + | 27.2588i | −0.764298 | + | 1.32380i | ||||
\(425\) | −6.91440 | + | 11.9761i | −0.335397 | + | 0.580925i | ||||
\(426\) | −3.10947 | −0.150654 | ||||||||
\(427\) | 8.51088 | − | 14.7413i | 0.411870 | − | 0.713381i | ||||
\(428\) | 2.90998 | 0.140659 | ||||||||
\(429\) | −31.8481 | −1.53764 | ||||||||
\(430\) | −14.3220 | − | 35.3477i | −0.690667 | − | 1.70462i | ||||
\(431\) | 4.91194 | 0.236600 | 0.118300 | − | 0.992978i | \(-0.462256\pi\) | ||||
0.118300 | + | 0.992978i | \(0.462256\pi\) | |||||||
\(432\) | 20.0826 | 0.966223 | ||||||||
\(433\) | −18.9320 | + | 32.7911i | −0.909813 | + | 1.57584i | −0.0954890 | + | 0.995430i | \(0.530441\pi\) |
−0.814324 | + | 0.580411i | \(0.802892\pi\) | |||||||
\(434\) | 5.18850 | 0.249056 | ||||||||
\(435\) | −20.5232 | + | 35.5471i | −0.984010 | + | 1.70435i | ||||
\(436\) | −0.740868 | + | 1.28322i | −0.0354812 | + | 0.0614552i | ||||
\(437\) | 0.495077 | + | 0.857498i | 0.0236827 | + | 0.0410197i | ||||
\(438\) | 3.09515 | 0.147892 | ||||||||
\(439\) | −14.8055 | − | 25.6439i | −0.706630 | − | 1.22392i | −0.966100 | − | 0.258167i | \(-0.916881\pi\) |
0.259470 | − | 0.965751i | \(-0.416452\pi\) | |||||||
\(440\) | 27.9030 | − | 48.3294i | 1.33022 | − | 2.30401i | ||||
\(441\) | 2.18547 | 0.104070 | ||||||||
\(442\) | −3.40599 | + | 5.89934i | −0.162006 | + | 0.280603i | ||||
\(443\) | 15.7188 | + | 27.2258i | 0.746824 | + | 1.29354i | 0.949338 | + | 0.314258i | \(0.101756\pi\) |
−0.202513 | + | 0.979280i | \(0.564911\pi\) | |||||||
\(444\) | −0.374992 | − | 0.649505i | −0.0177963 | − | 0.0308242i | ||||
\(445\) | 9.26686 | + | 16.0507i | 0.439291 | + | 0.760874i | ||||
\(446\) | −2.55731 | −0.121092 | ||||||||
\(447\) | −12.9811 | − | 22.4840i | −0.613987 | − | 1.06346i | ||||
\(448\) | −9.31291 | − | 16.1304i | −0.439994 | − | 0.762091i | ||||
\(449\) | −8.20779 | + | 14.2163i | −0.387349 | + | 0.670909i | −0.992092 | − | 0.125512i | \(-0.959943\pi\) |
0.604743 | + | 0.796421i | \(0.293276\pi\) | |||||||
\(450\) | 8.61021 | − | 14.9133i | 0.405889 | − | 0.703021i | ||||
\(451\) | −47.7132 | −2.24673 | ||||||||
\(452\) | −0.129556 | −0.00609382 | ||||||||
\(453\) | −13.8882 | + | 24.0551i | −0.652524 | + | 1.13021i | ||||
\(454\) | 6.42596 | − | 11.1301i | 0.301585 | − | 0.522361i | ||||
\(455\) | 23.7709 | + | 41.1724i | 1.11440 | + | 1.93019i | ||||
\(456\) | 2.02715 | + | 3.51113i | 0.0949302 | + | 0.164424i | ||||
\(457\) | 33.3958 | 1.56219 | 0.781096 | − | 0.624412i | \(-0.214661\pi\) | ||||
0.781096 | + | 0.624412i | \(0.214661\pi\) | |||||||
\(458\) | 11.7368 | + | 20.3288i | 0.548426 | + | 0.949902i | ||||
\(459\) | 2.82711 | + | 4.89669i | 0.131958 | + | 0.228558i | ||||
\(460\) | 0.458101 | + | 0.793455i | 0.0213591 | + | 0.0369950i | ||||
\(461\) | 14.5174 | − | 25.1448i | 0.676141 | − | 1.17111i | −0.299993 | − | 0.953941i | \(-0.596984\pi\) |
0.976134 | − | 0.217169i | \(-0.0696824\pi\) | |||||||
\(462\) | −18.1081 | −0.842465 | ||||||||
\(463\) | 2.74539 | − | 4.75516i | 0.127589 | − | 0.220991i | −0.795153 | − | 0.606409i | \(-0.792609\pi\) |
0.922742 | + | 0.385418i | \(0.125943\pi\) | |||||||
\(464\) | −11.6733 | − | 20.2188i | −0.541920 | − | 0.938633i | ||||
\(465\) | −11.2124 | −0.519964 | ||||||||
\(466\) | 9.81720 | + | 17.0039i | 0.454773 | + | 0.787690i | ||||
\(467\) | 18.7768 | − | 32.5224i | 0.868887 | − | 1.50496i | 0.00575141 | − | 0.999983i | \(-0.498169\pi\) |
0.863135 | − | 0.504973i | \(-0.168497\pi\) | |||||||
\(468\) | −0.480224 | + | 0.831773i | −0.0221984 | + | 0.0384487i | ||||
\(469\) | −12.0912 | −0.558319 | ||||||||
\(470\) | 7.90096 | − | 13.6849i | 0.364444 | − | 0.631235i | ||||
\(471\) | 17.0172 | 0.784110 | ||||||||
\(472\) | 32.3785 | 1.49034 | ||||||||
\(473\) | −17.5581 | + | 22.5190i | −0.807320 | + | 1.03543i | ||||
\(474\) | 7.14443 | 0.328155 | ||||||||
\(475\) | 13.1915 | 0.605269 | ||||||||
\(476\) | 0.219267 | − | 0.379782i | 0.0100501 | − | 0.0174073i | ||||
\(477\) | 9.90128 | 0.453349 | ||||||||
\(478\) | 3.54536 | − | 6.14074i | 0.162161 | − | 0.280871i | ||||
\(479\) | −1.37345 | + | 2.37888i | −0.0627545 | + | 0.108694i | −0.895696 | − | 0.444667i | \(-0.853322\pi\) |
0.832941 | + | 0.553362i | \(0.186655\pi\) | |||||||
\(480\) | 3.57834 | + | 6.19787i | 0.163328 | + | 0.282893i | ||||
\(481\) | −13.0205 | −0.593683 | ||||||||
\(482\) | −10.2339 | − | 17.7256i | −0.466140 | − | 0.807378i | ||||
\(483\) | 1.61013 | − | 2.78883i | 0.0732636 | − | 0.126896i | ||||
\(484\) | −1.61973 | −0.0736242 | ||||||||
\(485\) | −22.5722 | + | 39.0962i | −1.02495 | + | 1.77527i | ||||
\(486\) | −6.20852 | − | 10.7535i | −0.281624 | − | 0.487788i | ||||
\(487\) | 20.8994 | + | 36.1988i | 0.947043 | + | 1.64033i | 0.751608 | + | 0.659610i | \(0.229278\pi\) |
0.195435 | + | 0.980717i | \(0.437388\pi\) | |||||||
\(488\) | −11.6595 | − | 20.1949i | −0.527801 | − | 0.914178i | ||||
\(489\) | −10.2946 | −0.465536 | ||||||||
\(490\) | −6.84091 | − | 11.8488i | −0.309041 | − | 0.535275i | ||||
\(491\) | −7.29797 | − | 12.6405i | −0.329353 | − | 0.570456i | 0.653031 | − | 0.757331i | \(-0.273497\pi\) |
−0.982384 | + | 0.186876i | \(0.940164\pi\) | |||||||
\(492\) | 1.60374 | − | 2.77776i | 0.0723022 | − | 0.125231i | ||||
\(493\) | 3.28660 | − | 5.69256i | 0.148021 | − | 0.256380i | ||||
\(494\) | 6.49806 | 0.292362 | ||||||||
\(495\) | −17.5548 | −0.789030 | ||||||||
\(496\) | 3.18875 | − | 5.52307i | 0.143179 | − | 0.247993i | ||||
\(497\) | 1.73765 | − | 3.00969i | 0.0779442 | − | 0.135003i | ||||
\(498\) | 8.72148 | + | 15.1061i | 0.390819 | + | 0.676918i | ||||
\(499\) | 10.1686 | + | 17.6124i | 0.455207 | + | 0.788441i | 0.998700 | − | 0.0509721i | \(-0.0162320\pi\) |
−0.543493 | + | 0.839414i | \(0.682899\pi\) | |||||||
\(500\) | 7.79294 | 0.348511 | ||||||||
\(501\) | 0.521948 | + | 0.904040i | 0.0233189 | + | 0.0403895i | ||||
\(502\) | −3.31288 | − | 5.73808i | −0.147861 | − | 0.256103i | ||||
\(503\) | −6.67890 | − | 11.5682i | −0.297797 | − | 0.515800i | 0.677834 | − | 0.735215i | \(-0.262919\pi\) |
−0.975632 | + | 0.219414i | \(0.929585\pi\) | |||||||
\(504\) | −2.95761 | + | 5.12273i | −0.131743 | + | 0.228185i | ||||
\(505\) | 13.1739 | 0.586230 | ||||||||
\(506\) | −3.02924 | + | 5.24680i | −0.134666 | + | 0.233249i | ||||
\(507\) | −9.23061 | − | 15.9879i | −0.409946 | − | 0.710047i | ||||
\(508\) | 1.41926 | 0.0629695 | ||||||||
\(509\) | 2.48732 | + | 4.30816i | 0.110248 | + | 0.190956i | 0.915870 | − | 0.401474i | \(-0.131502\pi\) |
−0.805622 | + | 0.592430i | \(0.798169\pi\) | |||||||
\(510\) | 4.18495 | − | 7.24855i | 0.185313 | − | 0.320971i | ||||
\(511\) | −1.72965 | + | 2.99584i | −0.0765151 | + | 0.132528i | ||||
\(512\) | −25.0502 | −1.10707 | ||||||||
\(513\) | 2.69683 | − | 4.67104i | 0.119068 | − | 0.206232i | ||||
\(514\) | 4.37208 | 0.192844 | ||||||||
\(515\) | 72.2456 | 3.18352 | ||||||||
\(516\) | −0.720846 | − | 1.77910i | −0.0317335 | − | 0.0783207i | ||||
\(517\) | −11.8311 | −0.520329 | ||||||||
\(518\) | −7.40314 | −0.325275 | ||||||||
\(519\) | 7.69232 | − | 13.3235i | 0.337655 | − | 0.584836i | ||||
\(520\) | 65.1300 | 2.85614 | ||||||||
\(521\) | −11.6827 | + | 20.2350i | −0.511829 | + | 0.886513i | 0.488077 | + | 0.872800i | \(0.337698\pi\) |
−0.999906 | + | 0.0137129i | \(0.995635\pi\) | |||||||
\(522\) | −4.09267 | + | 7.08871i | −0.179131 | + | 0.310265i | ||||
\(523\) | −13.1400 | − | 22.7591i | −0.574570 | − | 0.995184i | −0.996088 | − | 0.0883645i | \(-0.971836\pi\) |
0.421518 | − | 0.906820i | \(-0.361497\pi\) | |||||||
\(524\) | −1.98145 | −0.0865600 | ||||||||
\(525\) | −21.4514 | − | 37.1548i | −0.936214 | − | 1.62157i | ||||
\(526\) | 20.6828 | − | 35.8237i | 0.901814 | − | 1.56199i | ||||
\(527\) | 1.79557 | 0.0782164 | ||||||||
\(528\) | −11.1289 | + | 19.2758i | −0.484322 | + | 0.838870i | ||||
\(529\) | 10.9613 | + | 18.9855i | 0.476578 | + | 0.825457i | ||||
\(530\) | −30.9928 | − | 53.6810i | −1.34624 | − | 2.33176i | ||||
\(531\) | −5.09263 | − | 8.82070i | −0.221001 | − | 0.382786i | ||||
\(532\) | −0.418326 | −0.0181367 | ||||||||
\(533\) | −27.8425 | − | 48.2247i | −1.20599 | − | 2.08884i | ||||
\(534\) | −4.11936 | − | 7.13495i | −0.178262 | − | 0.308759i | ||||
\(535\) | −31.0372 | + | 53.7580i | −1.34185 | + | 2.32416i | ||||
\(536\) | −8.28217 | + | 14.3451i | −0.357735 | + | 0.619616i | ||||
\(537\) | 31.6564 | 1.36607 | ||||||||
\(538\) | 13.1636 | 0.567523 | ||||||||
\(539\) | −5.12186 | + | 8.87133i | −0.220614 | + | 0.382115i | ||||
\(540\) | 2.49541 | − | 4.32218i | 0.107385 | − | 0.185997i | ||||
\(541\) | −2.33746 | − | 4.04859i | −0.100495 | − | 0.174063i | 0.811394 | − | 0.584500i | \(-0.198709\pi\) |
−0.911889 | + | 0.410437i | \(0.865376\pi\) | |||||||
\(542\) | −6.62073 | − | 11.4674i | −0.284385 | − | 0.492569i | ||||
\(543\) | 22.9457 | 0.984696 | ||||||||
\(544\) | −0.573040 | − | 0.992534i | −0.0245689 | − | 0.0425546i | ||||
\(545\) | −15.8039 | − | 27.3731i | −0.676964 | − | 1.17254i | ||||
\(546\) | −10.5668 | − | 18.3022i | −0.452217 | − | 0.783263i | ||||
\(547\) | −5.12112 | + | 8.87004i | −0.218963 | + | 0.379256i | −0.954491 | − | 0.298239i | \(-0.903601\pi\) |
0.735528 | + | 0.677494i | \(0.236934\pi\) | |||||||
\(548\) | 0.359675 | 0.0153646 | ||||||||
\(549\) | −3.66772 | + | 6.35267i | −0.156534 | + | 0.271125i | ||||
\(550\) | 40.3577 | + | 69.9016i | 1.72086 | + | 2.98062i | ||||
\(551\) | −6.27030 | −0.267124 | ||||||||
\(552\) | −2.20581 | − | 3.82057i | −0.0938853 | − | 0.162614i | ||||
\(553\) | −3.99249 | + | 6.91519i | −0.169778 | + | 0.294064i | ||||
\(554\) | −12.6116 | + | 21.8440i | −0.535817 | + | 0.928063i | ||||
\(555\) | 15.9983 | 0.679091 | ||||||||
\(556\) | 1.36478 | − | 2.36386i | 0.0578794 | − | 0.100250i | ||||
\(557\) | −2.99255 | −0.126799 | −0.0633993 | − | 0.997988i | \(-0.520194\pi\) | ||||
−0.0633993 | + | 0.997988i | \(0.520194\pi\) | |||||||
\(558\) | −2.23595 | −0.0946554 | ||||||||
\(559\) | −33.0063 | − | 4.60555i | −1.39602 | − | 0.194794i | ||||
\(560\) | 33.2256 | 1.40404 | ||||||||
\(561\) | −6.26663 | −0.264577 | ||||||||
\(562\) | 10.6080 | − | 18.3737i | 0.447473 | − | 0.775046i | ||||
\(563\) | −12.4117 | −0.523090 | −0.261545 | − | 0.965191i | \(-0.584232\pi\) | ||||
−0.261545 | + | 0.965191i | \(0.584232\pi\) | |||||||
\(564\) | 0.397667 | − | 0.688779i | 0.0167448 | − | 0.0290028i | ||||
\(565\) | 1.38182 | − | 2.39338i | 0.0581336 | − | 0.100690i | ||||
\(566\) | 3.62867 | + | 6.28503i | 0.152524 | + | 0.264180i | ||||
\(567\) | −11.5332 | −0.484347 | ||||||||
\(568\) | −2.38050 | − | 4.12314i | −0.0998834 | − | 0.173003i | ||||
\(569\) | 21.7587 | − | 37.6872i | 0.912172 | − | 1.57993i | 0.101181 | − | 0.994868i | \(-0.467738\pi\) |
0.810990 | − | 0.585060i | \(-0.198929\pi\) | |||||||
\(570\) | −7.98420 | −0.334421 | ||||||||
\(571\) | 21.3381 | − | 36.9586i | 0.892970 | − | 1.54667i | 0.0566729 | − | 0.998393i | \(-0.481951\pi\) |
0.836297 | − | 0.548277i | \(-0.184716\pi\) | |||||||
\(572\) | −2.25090 | − | 3.89868i | −0.0941150 | − | 0.163012i | ||||
\(573\) | 12.9047 | + | 22.3517i | 0.539103 | + | 0.933754i | ||||
\(574\) | −15.8306 | − | 27.4194i | −0.660757 | − | 1.14447i | ||||
\(575\) | −14.3541 | −0.598607 | ||||||||
\(576\) | 4.01335 | + | 6.95132i | 0.167223 | + | 0.289638i | ||||
\(577\) | 5.00651 | + | 8.67152i | 0.208424 | + | 0.361000i | 0.951218 | − | 0.308519i | \(-0.0998334\pi\) |
−0.742795 | + | 0.669519i | \(0.766500\pi\) | |||||||
\(578\) | −0.670183 | + | 1.16079i | −0.0278759 | + | 0.0482826i | ||||
\(579\) | −8.96241 | + | 15.5234i | −0.372465 | + | 0.645129i | ||||
\(580\) | −5.80199 | −0.240915 | ||||||||
\(581\) | −19.4951 | −0.808794 | ||||||||
\(582\) | 10.0339 | − | 17.3793i | 0.415920 | − | 0.720395i | ||||
\(583\) | −23.2046 | + | 40.1916i | −0.961037 | + | 1.66456i | ||||
\(584\) | 2.36954 | + | 4.10416i | 0.0980521 | + | 0.169831i | ||||
\(585\) | −10.2439 | − | 17.7430i | −0.423534 | − | 0.733583i | ||||
\(586\) | 37.6691 | 1.55610 | ||||||||
\(587\) | −2.41137 | − | 4.17661i | −0.0995278 | − | 0.172387i | 0.811962 | − | 0.583711i | \(-0.198400\pi\) |
−0.911489 | + | 0.411324i | \(0.865067\pi\) | |||||||
\(588\) | −0.344313 | − | 0.596368i | −0.0141992 | − | 0.0245938i | ||||
\(589\) | −0.856415 | − | 1.48335i | −0.0352879 | − | 0.0611205i | ||||
\(590\) | −31.8817 | + | 55.2207i | −1.31255 | + | 2.27340i | ||||
\(591\) | 29.1399 | 1.19865 | ||||||||
\(592\) | −4.54982 | + | 7.88052i | −0.186997 | + | 0.323888i | ||||
\(593\) | 12.1810 | + | 21.0982i | 0.500215 | + | 0.866398i | 1.00000 | 0.000248476i | \(7.90923e-5\pi\) | |
−0.499785 | + | 0.866150i | \(0.666588\pi\) | |||||||
\(594\) | 33.0023 | 1.35410 | ||||||||
\(595\) | 4.67731 | + | 8.10134i | 0.191751 | + | 0.332122i | ||||
\(596\) | 1.83492 | − | 3.17817i | 0.0751611 | − | 0.130183i | ||||
\(597\) | −3.42456 | + | 5.93151i | −0.140158 | + | 0.242760i | ||||
\(598\) | −7.07073 | −0.289144 | ||||||||
\(599\) | 1.63080 | − | 2.82463i | 0.0666328 | − | 0.115411i | −0.830784 | − | 0.556594i | \(-0.812108\pi\) |
0.897417 | + | 0.441183i | \(0.145441\pi\) | |||||||
\(600\) | −58.7747 | −2.39947 | ||||||||
\(601\) | 0.984057 | 0.0401405 | 0.0200703 | − | 0.999799i | \(-0.493611\pi\) | ||||
0.0200703 | + | 0.999799i | \(0.493611\pi\) | |||||||
\(602\) | −18.7666 | − | 2.61861i | −0.764869 | − | 0.106726i | ||||
\(603\) | 5.21063 | 0.212193 | ||||||||
\(604\) | −3.92626 | −0.159757 | ||||||||
\(605\) | 17.2757 | − | 29.9224i | 0.702357 | − | 1.21652i | ||||
\(606\) | −5.85614 | −0.237890 | ||||||||
\(607\) | −13.9823 | + | 24.2180i | −0.567523 | + | 0.982979i | 0.429287 | + | 0.903168i | \(0.358765\pi\) |
−0.996810 | + | 0.0798106i | \(0.974568\pi\) | |||||||
\(608\) | −0.546633 | + | 0.946796i | −0.0221689 | + | 0.0383976i | ||||
\(609\) | 10.1964 | + | 17.6607i | 0.413180 | + | 0.715648i | ||||
\(610\) | 45.9224 | 1.85934 | ||||||||
\(611\) | −6.90390 | − | 11.9579i | −0.279302 | − | 0.483765i | ||||
\(612\) | −0.0944919 | + | 0.163665i | −0.00381961 | + | 0.00661576i | ||||
\(613\) | −35.8340 | −1.44732 | −0.723662 | − | 0.690155i | \(-0.757542\pi\) | ||||
−0.723662 | + | 0.690155i | \(0.757542\pi\) | |||||||
\(614\) | −5.90393 | + | 10.2259i | −0.238263 | + | 0.412684i | ||||
\(615\) | 34.2103 | + | 59.2539i | 1.37949 | + | 2.38935i | ||||
\(616\) | −13.8629 | − | 24.0112i | −0.558552 | − | 0.967441i | ||||
\(617\) | −11.4184 | − | 19.7772i | −0.459686 | − | 0.796200i | 0.539258 | − | 0.842141i | \(-0.318705\pi\) |
−0.998944 | + | 0.0459405i | \(0.985372\pi\) | |||||||
\(618\) | −32.1151 | −1.29186 | ||||||||
\(619\) | 0.770758 | + | 1.33499i | 0.0309794 | + | 0.0536578i | 0.881099 | − | 0.472931i | \(-0.156804\pi\) |
−0.850120 | + | 0.526589i | \(0.823471\pi\) | |||||||
\(620\) | −0.792452 | − | 1.37257i | −0.0318257 | − | 0.0551237i | ||||
\(621\) | −2.93450 | + | 5.08270i | −0.117757 | + | 0.203962i | ||||
\(622\) | −13.6477 | + | 23.6386i | −0.547225 | + | 0.947821i | ||||
\(623\) | 9.20801 | 0.368911 | ||||||||
\(624\) | −25.9766 | −1.03989 | ||||||||
\(625\) | −48.5458 | + | 84.0837i | −1.94183 | + | 3.36335i | ||||
\(626\) | 8.50835 | − | 14.7369i | 0.340062 | − | 0.589005i | ||||
\(627\) | 2.98893 | + | 5.17697i | 0.119366 | + | 0.206748i | ||||
\(628\) | 1.20271 | + | 2.08315i | 0.0479934 | + | 0.0831269i | ||||
\(629\) | −2.56199 | −0.102153 | ||||||||
\(630\) | −5.82446 | − | 10.0883i | −0.232052 | − | 0.401926i | ||||
\(631\) | 10.2304 | + | 17.7195i | 0.407265 | + | 0.705404i | 0.994582 | − | 0.103953i | \(-0.0331492\pi\) |
−0.587317 | + | 0.809357i | \(0.699816\pi\) | |||||||
\(632\) | 5.46952 | + | 9.47348i | 0.217566 | + | 0.376835i | ||||
\(633\) | −4.74438 | + | 8.21751i | −0.188572 | + | 0.326617i | ||||
\(634\) | 44.5461 | 1.76915 | ||||||||
\(635\) | −15.1375 | + | 26.2190i | −0.600714 | + | 1.04047i | ||||
\(636\) | −1.55991 | − | 2.70184i | −0.0618545 | − | 0.107135i | ||||
\(637\) | −11.9553 | −0.473684 | ||||||||
\(638\) | −19.1831 | − | 33.2262i | −0.759468 | − | 1.31544i | ||||
\(639\) | −0.748829 | + | 1.29701i | −0.0296232 | + | 0.0513089i | ||||
\(640\) | 20.1519 | − | 34.9041i | 0.796573 | − | 1.37970i | ||||
\(641\) | 0.150539 | 0.00594595 | 0.00297298 | − | 0.999996i | \(-0.499054\pi\) | ||||
0.00297298 | + | 0.999996i | \(0.499054\pi\) | |||||||
\(642\) | 13.7969 | − | 23.8969i | 0.544518 | − | 0.943133i | ||||
\(643\) | 16.2152 | 0.639464 | 0.319732 | − | 0.947508i | \(-0.396407\pi\) | ||||
0.319732 | + | 0.947508i | \(0.396407\pi\) | |||||||
\(644\) | 0.455192 | 0.0179371 | ||||||||
\(645\) | 40.5549 | + | 5.65886i | 1.59685 | + | 0.222817i | ||||
\(646\) | 1.27860 | 0.0503058 | ||||||||
\(647\) | 37.4429 | 1.47203 | 0.736017 | − | 0.676964i | \(-0.236705\pi\) | ||||
0.736017 | + | 0.676964i | \(0.236705\pi\) | |||||||
\(648\) | −7.89994 | + | 13.6831i | −0.310339 | + | 0.537523i | ||||
\(649\) | 47.7403 | 1.87397 | ||||||||
\(650\) | −47.1007 | + | 81.5808i | −1.84744 | + | 3.19986i | ||||
\(651\) | −2.78531 | + | 4.82430i | −0.109165 | + | 0.189079i | ||||
\(652\) | −0.727581 | − | 1.26021i | −0.0284943 | − | 0.0493535i | ||||
\(653\) | 32.9918 | 1.29107 | 0.645534 | − | 0.763731i | \(-0.276635\pi\) | ||||
0.645534 | + | 0.763731i | \(0.276635\pi\) | |||||||
\(654\) | 7.02524 | + | 12.1681i | 0.274709 | + | 0.475809i | ||||
\(655\) | 21.1337 | − | 36.6046i | 0.825762 | − | 1.43026i | ||||
\(656\) | −38.9167 | −1.51944 | ||||||||
\(657\) | 0.745382 | − | 1.29104i | 0.0290801 | − | 0.0503682i | ||||
\(658\) | −3.92539 | − | 6.79898i | −0.153028 | − | 0.265052i | ||||
\(659\) | −5.46477 | − | 9.46526i | −0.212877 | − | 0.368714i | 0.739737 | − | 0.672897i | \(-0.234950\pi\) |
−0.952614 | + | 0.304182i | \(0.901617\pi\) | |||||||
\(660\) | 2.76570 | + | 4.79032i | 0.107655 | + | 0.186463i | ||||
\(661\) | −22.2747 | −0.866384 | −0.433192 | − | 0.901302i | \(-0.642613\pi\) | ||||
−0.433192 | + | 0.901302i | \(0.642613\pi\) | |||||||
\(662\) | 2.19441 | + | 3.80084i | 0.0852883 | + | 0.147724i | ||||
\(663\) | −3.65683 | − | 6.33382i | −0.142020 | − | 0.245985i | ||||
\(664\) | −13.3537 | + | 23.1293i | −0.518224 | + | 0.897591i | ||||
\(665\) | 4.46177 | − | 7.72801i | 0.173020 | − | 0.299679i | ||||
\(666\) | 3.19034 | 0.123623 | ||||||||
\(667\) | 6.82290 | 0.264184 | ||||||||
\(668\) | −0.0737786 | + | 0.127788i | −0.00285458 | + | 0.00494427i | ||||
\(669\) | 1.37283 | − | 2.37780i | 0.0530765 | − | 0.0919312i | ||||
\(670\) | −16.3102 | − | 28.2501i | −0.630117 | − | 1.09140i | ||||
\(671\) | −17.1913 | − | 29.7762i | −0.663662 | − | 1.14950i | ||||
\(672\) | 3.55562 | 0.137161 | ||||||||
\(673\) | −22.9705 | − | 39.7861i | −0.885448 | − | 1.53364i | −0.845200 | − | 0.534451i | \(-0.820518\pi\) |
−0.0402482 | − | 0.999190i | \(-0.512815\pi\) | |||||||
\(674\) | 2.37519 | + | 4.11394i | 0.0914888 | + | 0.158463i | ||||
\(675\) | 39.0955 | + | 67.7154i | 1.50479 | + | 2.60637i | ||||
\(676\) | 1.30477 | − | 2.25993i | 0.0501835 | − | 0.0869203i | ||||
\(677\) | −50.1762 | −1.92843 | −0.964214 | − | 0.265124i | \(-0.914587\pi\) | ||||
−0.964214 | + | 0.265124i | \(0.914587\pi\) | |||||||
\(678\) | −0.614256 | + | 1.06392i | −0.0235903 | + | 0.0408597i | ||||
\(679\) | 11.2144 | + | 19.4240i | 0.430371 | + | 0.745424i | ||||
\(680\) | 12.8154 | 0.491448 | ||||||||
\(681\) | 6.89922 | + | 11.9498i | 0.264379 | + | 0.457917i | ||||
\(682\) | 5.24017 | − | 9.07624i | 0.200657 | − | 0.347547i | ||||
\(683\) | −17.0189 | + | 29.4777i | −0.651212 | + | 1.12793i | 0.331618 | + | 0.943414i | \(0.392406\pi\) |
−0.982829 | + | 0.184518i | \(0.940928\pi\) | |||||||
\(684\) | 0.180275 | 0.00689299 | ||||||||
\(685\) | −3.83622 | + | 6.64452i | −0.146574 | + | 0.253874i | ||||
\(686\) | −27.0247 | −1.03181 | ||||||||
\(687\) | −25.2025 | −0.961534 | ||||||||
\(688\) | −14.3210 | + | 18.3674i | −0.545984 | + | 0.700250i | ||||
\(689\) | −54.1633 | −2.06346 | ||||||||
\(690\) | 8.68784 | 0.330740 | ||||||||
\(691\) | 9.56776 | − | 16.5719i | 0.363975 | − | 0.630423i | −0.624636 | − | 0.780916i | \(-0.714753\pi\) |
0.988611 | + | 0.150493i | \(0.0480860\pi\) | |||||||
\(692\) | 2.17466 | 0.0826680 | ||||||||
\(693\) | −4.36083 | + | 7.55319i | −0.165654 | + | 0.286922i | ||||
\(694\) | −14.3919 | + | 24.9275i | −0.546310 | + | 0.946236i | ||||
\(695\) | 29.1128 | + | 50.4248i | 1.10431 | + | 1.91272i | ||||
\(696\) | 27.9372 | 1.05896 | ||||||||
\(697\) | −5.47847 | − | 9.48900i | −0.207512 | − | 0.359421i | ||||
\(698\) | −11.0325 | + | 19.1089i | −0.417588 | + | 0.723283i | ||||
\(699\) | −21.0804 | −0.797335 | ||||||||
\(700\) | 3.03220 | − | 5.25193i | 0.114606 | − | 0.198504i | ||||
\(701\) | 0.660487 | + | 1.14400i | 0.0249463 | + | 0.0432082i | 0.878229 | − | 0.478240i | \(-0.158725\pi\) |
−0.853283 | + | 0.521448i | \(0.825392\pi\) | |||||||
\(702\) | 19.2582 | + | 33.3561i | 0.726853 | + | 1.25895i | ||||
\(703\) | 1.22196 | + | 2.11650i | 0.0460873 | + | 0.0798255i | ||||
\(704\) | −37.6227 | −1.41796 | ||||||||
\(705\) | 8.48285 | + | 14.6927i | 0.319482 | + | 0.553360i | ||||
\(706\) | −16.0283 | − | 27.7618i | −0.603232 | − | 1.04483i | ||||
\(707\) | 3.27256 | − | 5.66824i | 0.123077 | − | 0.213176i | ||||
\(708\) | −1.60465 | + | 2.77934i | −0.0603065 | + | 0.104454i | ||||
\(709\) | 1.62908 | 0.0611814 | 0.0305907 | − | 0.999532i | \(-0.490261\pi\) | ||||
0.0305907 | + | 0.999532i | \(0.490261\pi\) | |||||||
\(710\) | 9.37587 | 0.351870 | ||||||||
\(711\) | 1.72054 | − | 2.98006i | 0.0645253 | − | 0.111761i | ||||
\(712\) | 6.30727 | − | 10.9245i | 0.236375 | − | 0.409414i | ||||
\(713\) | 0.931890 | + | 1.61408i | 0.0348996 | + | 0.0604478i | ||||
\(714\) | −2.07919 | − | 3.60126i | −0.0778117 | − | 0.134774i | ||||
\(715\) | 96.0306 | 3.59134 | ||||||||
\(716\) | 2.23735 | + | 3.87521i | 0.0836138 | + | 0.144823i | ||||
\(717\) | 3.80647 | + | 6.59299i | 0.142155 | + | 0.246220i | ||||
\(718\) | −6.16273 | − | 10.6742i | −0.229991 | − | 0.398356i | ||||
\(719\) | −3.49095 | + | 6.04651i | −0.130191 | + | 0.225497i | −0.923750 | − | 0.382996i | \(-0.874892\pi\) |
0.793559 | + | 0.608493i | \(0.208226\pi\) | |||||||
\(720\) | −14.3184 | −0.533615 | ||||||||
\(721\) | 17.9467 | − | 31.0846i | 0.668371 | − | 1.15765i | ||||
\(722\) | 12.1236 | + | 20.9988i | 0.451195 | + | 0.781493i | ||||
\(723\) | 21.9751 | 0.817264 | ||||||||
\(724\) | 1.62172 | + | 2.80890i | 0.0602707 | + | 0.104392i | ||||
\(725\) | 45.4498 | − | 78.7213i | 1.68796 | − | 2.92364i | ||||
\(726\) | −7.67951 | + | 13.3013i | −0.285013 | + | 0.493657i | ||||
\(727\) | −14.2138 | −0.527161 | −0.263581 | − | 0.964637i | \(-0.584903\pi\) | ||||
−0.263581 | + | 0.964637i | \(0.584903\pi\) | |||||||
\(728\) | 16.1791 | − | 28.0230i | 0.599638 | − | 1.03860i | ||||
\(729\) | 29.3808 | 1.08818 | ||||||||
\(730\) | −9.33271 | −0.345419 | ||||||||
\(731\) | −6.49452 | − | 0.906216i | −0.240208 | − | 0.0335176i | ||||
\(732\) | 2.31134 | 0.0854296 | ||||||||
\(733\) | −3.40208 | −0.125659 | −0.0628294 | − | 0.998024i | \(-0.520012\pi\) | ||||
−0.0628294 | + | 0.998024i | \(0.520012\pi\) | |||||||
\(734\) | −22.5409 | + | 39.0419i | −0.831999 | + | 1.44106i | ||||
\(735\) | 14.6895 | 0.541829 | ||||||||
\(736\) | 0.594807 | − | 1.03024i | 0.0219249 | − | 0.0379750i | ||||
\(737\) | −12.2116 | + | 21.1511i | −0.449820 | + | 0.779112i | ||||
\(738\) | 6.82212 | + | 11.8163i | 0.251126 | + | 0.434962i | ||||
\(739\) | −6.88779 | −0.253371 | −0.126686 | − | 0.991943i | \(-0.540434\pi\) | ||||
−0.126686 | + | 0.991943i | \(0.540434\pi\) | |||||||
\(740\) | 1.13070 | + | 1.95843i | 0.0415654 | + | 0.0719934i | ||||
\(741\) | −3.48832 | + | 6.04194i | −0.128146 | + | 0.221956i | ||||
\(742\) | −30.7960 | −1.13056 | ||||||||
\(743\) | 14.3559 | − | 24.8651i | 0.526666 | − | 0.912213i | −0.472851 | − | 0.881142i | \(-0.656775\pi\) |
0.999517 | − | 0.0310703i | \(-0.00989158\pi\) | |||||||
\(744\) | 3.81574 | + | 6.60906i | 0.139892 | + | 0.242300i | ||||
\(745\) | 39.1416 | + | 67.7953i | 1.43404 | + | 2.48383i | ||||
\(746\) | −9.71853 | − | 16.8330i | −0.355821 | − | 0.616300i | ||||
\(747\) | 8.40131 | 0.307388 | ||||||||
\(748\) | −0.442902 | − | 0.767129i | −0.0161941 | − | 0.0280490i | ||||
\(749\) | 15.4201 | + | 26.7083i | 0.563436 | + | 0.975901i | ||||
\(750\) | 36.9481 | − | 63.9959i | 1.34915 | − | 2.33680i | ||||
\(751\) | 7.09430 | − | 12.2877i | 0.258875 | − | 0.448384i | −0.707066 | − | 0.707148i | \(-0.749982\pi\) |
0.965941 | + | 0.258763i | \(0.0833149\pi\) | |||||||
\(752\) | −9.64987 | −0.351895 | ||||||||
\(753\) | 7.11373 | 0.259239 | ||||||||
\(754\) | 22.3883 | − | 38.7776i | 0.815332 | − | 1.41220i | ||||
\(755\) | 41.8766 | − | 72.5324i | 1.52405 | − | 2.63973i | ||||
\(756\) | −1.23978 | − | 2.14737i | −0.0450905 | − | 0.0780990i | ||||
\(757\) | 24.8520 | + | 43.0449i | 0.903260 | + | 1.56449i | 0.823236 | + | 0.567700i | \(0.192167\pi\) |
0.0800247 | + | 0.996793i | \(0.474500\pi\) | |||||||
\(758\) | 29.4817 | 1.07082 | ||||||||
\(759\) | −3.25234 | − | 5.63322i | −0.118052 | − | 0.204473i | ||||
\(760\) | −6.11241 | − | 10.5870i | −0.221720 | − | 0.384031i | ||||
\(761\) | 5.88447 | + | 10.1922i | 0.213312 | + | 0.369467i | 0.952749 | − | 0.303759i | \(-0.0982417\pi\) |
−0.739437 | + | 0.673225i | \(0.764908\pi\) | |||||||
\(762\) | 6.72903 | − | 11.6550i | 0.243767 | − | 0.422217i | ||||
\(763\) | −15.7035 | −0.568506 | ||||||||
\(764\) | −1.82412 | + | 3.15946i | −0.0659942 | + | 0.114305i | ||||
\(765\) | −2.01566 | − | 3.49123i | −0.0728763 | − | 0.126226i | ||||
\(766\) | 41.1510 | 1.48685 | ||||||||
\(767\) | 27.8584 | + | 48.2521i | 1.00591 | + | 1.74228i | ||||
\(768\) | 3.47525 | − | 6.01930i | 0.125402 | − | 0.217203i | ||||
\(769\) | −21.9294 | + | 37.9828i | −0.790793 | + | 1.36969i | 0.134683 | + | 0.990889i | \(0.456998\pi\) |
−0.925476 | + | 0.378805i | \(0.876335\pi\) | |||||||
\(770\) | 54.6007 | 1.96767 | ||||||||
\(771\) | −2.34704 | + | 4.06518i | −0.0845264 | + | 0.146404i | ||||
\(772\) | −2.53372 | −0.0911905 | ||||||||
\(773\) | 50.2312 | 1.80669 | 0.903345 | − | 0.428914i | \(-0.141104\pi\) | ||||
0.903345 | + | 0.428914i | \(0.141104\pi\) | |||||||
\(774\) | 8.08735 | + | 1.12847i | 0.290694 | + | 0.0405622i | ||||
\(775\) | 24.8306 | 0.891942 | ||||||||
\(776\) | 30.7265 | 1.10302 | ||||||||
\(777\) | 3.97419 | − | 6.88349i | 0.142573 | − | 0.246944i | ||||
\(778\) | −49.2943 | −1.76729 | ||||||||
\(779\) | −5.22601 | + | 9.05172i | −0.187241 | + | 0.324312i | ||||
\(780\) | −3.22779 | + | 5.59069i | −0.115573 | + | 0.200179i | ||||
\(781\) | −3.50991 | − | 6.07934i | −0.125594 | − | 0.217536i | ||||
\(782\) | −1.39128 | −0.0497521 | ||||||||
\(783\) | −18.5832 | − | 32.1870i | −0.664108 | − | 1.15027i | ||||
\(784\) | −4.17759 | + | 7.23580i | −0.149200 | + | 0.258421i | ||||
\(785\) | −51.3113 | −1.83138 | ||||||||
\(786\) | −9.39449 | + | 16.2717i | −0.335090 | + | 0.580393i | ||||
\(787\) | −4.37166 | − | 7.57194i | −0.155833 | − | 0.269911i | 0.777529 | − | 0.628847i | \(-0.216473\pi\) |
−0.933362 | + | 0.358936i | \(0.883139\pi\) | |||||||
\(788\) | 2.05950 | + | 3.56715i | 0.0733665 | + | 0.127074i | ||||
\(789\) | 22.2061 | + | 38.4621i | 0.790558 | + | 1.36929i | ||||
\(790\) | −21.5424 | −0.766443 | ||||||||
\(791\) | −0.686523 | − | 1.18909i | −0.0244099 | − | 0.0422793i | ||||
\(792\) | 5.97414 | + | 10.3475i | 0.212282 | + | 0.367683i | ||||
\(793\) | 20.0636 | − | 34.7512i | 0.712480 | − | 1.23405i | ||||
\(794\) | −5.30983 | + | 9.19690i | −0.188439 | + | 0.326386i | ||||
\(795\) | 66.5506 | 2.36031 | ||||||||
\(796\) | −0.968139 | −0.0343148 | ||||||||
\(797\) | −6.83607 | + | 11.8404i | −0.242146 | + | 0.419409i | −0.961325 | − | 0.275415i | \(-0.911185\pi\) |
0.719179 | + | 0.694825i | \(0.244518\pi\) | |||||||
\(798\) | −1.98337 | + | 3.43531i | −0.0702107 | + | 0.121609i | ||||
\(799\) | −1.35845 | − | 2.35291i | −0.0480586 | − | 0.0832400i | ||||
\(800\) | −7.92445 | − | 13.7256i | −0.280172 | − | 0.485272i | ||||
\(801\) | −3.96814 | −0.140207 | ||||||||
\(802\) | 9.62596 | + | 16.6727i | 0.339905 | + | 0.588732i | ||||
\(803\) | 3.49375 | + | 6.05135i | 0.123292 | + | 0.213548i | ||||
\(804\) | −0.820915 | − | 1.42187i | −0.0289514 | − | 0.0501454i | ||||
\(805\) | −4.85498 | + | 8.40907i | −0.171116 | + | 0.296381i | ||||
\(806\) | 12.2314 | 0.430833 | ||||||||
\(807\) | −7.06653 | + | 12.2396i | −0.248754 | + | 0.430854i | ||||
\(808\) | −4.48325 | − | 7.76522i | −0.157720 | − | 0.273179i | ||||
\(809\) | −49.3139 | −1.73378 | −0.866892 | − | 0.498496i | \(-0.833886\pi\) | ||||
−0.866892 | + | 0.498496i | \(0.833886\pi\) | |||||||
\(810\) | −15.5574 | − | 26.9463i | −0.546633 | − | 0.946796i | ||||
\(811\) | 4.12218 | − | 7.13982i | 0.144749 | − | 0.250713i | −0.784530 | − | 0.620091i | \(-0.787096\pi\) |
0.929279 | + | 0.369378i | \(0.120429\pi\) | |||||||
\(812\) | −1.44129 | + | 2.49638i | −0.0505793 | + | 0.0876059i | ||||
\(813\) | 14.2167 | 0.498600 | ||||||||
\(814\) | −7.47687 | + | 12.9503i | −0.262064 | + | 0.453909i | ||||
\(815\) | 31.0409 | 1.08731 | ||||||||
\(816\) | −5.11131 | −0.178932 | ||||||||
\(817\) | 2.34898 | + | 5.79746i | 0.0821803 | + | 0.202827i | ||||
\(818\) | 2.69718 | 0.0943048 | ||||||||
\(819\) | −10.1789 | −0.355679 | ||||||||
\(820\) | −4.83570 | + | 8.37568i | −0.168870 | + | 0.292492i | ||||
\(821\) | −42.7785 | −1.49298 | −0.746490 | − | 0.665396i | \(-0.768263\pi\) | ||||
−0.746490 | + | 0.665396i | \(0.768263\pi\) | |||||||
\(822\) | 1.70530 | − | 2.95367i | 0.0594792 | − | 0.103021i | ||||
\(823\) | −10.6286 | + | 18.4093i | −0.370490 | + | 0.641708i | −0.989641 | − | 0.143564i | \(-0.954144\pi\) |
0.619151 | + | 0.785272i | \(0.287477\pi\) | |||||||
\(824\) | −24.5862 | − | 42.5845i | −0.856499 | − | 1.48350i | ||||
\(825\) | −86.6600 | −3.01711 | ||||||||
\(826\) | 15.8396 | + | 27.4350i | 0.551131 | + | 0.954587i | ||||
\(827\) | 0.450476 | − | 0.780247i | 0.0156646 | − | 0.0271319i | −0.858087 | − | 0.513505i | \(-0.828347\pi\) |
0.873751 | + | 0.486373i | \(0.161680\pi\) | |||||||
\(828\) | −0.196163 | −0.00681712 | ||||||||
\(829\) | −3.79302 | + | 6.56970i | −0.131737 | + | 0.228175i | −0.924346 | − | 0.381555i | \(-0.875389\pi\) |
0.792609 | + | 0.609730i | \(0.208722\pi\) | |||||||
\(830\) | −26.2976 | − | 45.5488i | −0.912803 | − | 1.58102i | ||||
\(831\) | −13.5405 | − | 23.4528i | −0.469713 | − | 0.813568i | ||||
\(832\) | −21.9543 | − | 38.0260i | −0.761129 | − | 1.31831i | ||||
\(833\) | −2.35239 | −0.0815055 | ||||||||
\(834\) | −12.9414 | − | 22.4152i | −0.448124 | − | 0.776174i | ||||
\(835\) | −1.57381 | − | 2.72592i | −0.0544640 | − | 0.0943344i | ||||
\(836\) | −0.422492 | + | 0.731778i | −0.0146122 | + | 0.0253091i | ||||
\(837\) | 5.07628 | − | 8.79237i | 0.175462 | − | 0.303909i | ||||
\(838\) | 19.9350 | 0.688644 | ||||||||
\(839\) | 46.1269 | 1.59248 | 0.796239 | − | 0.604983i | \(-0.206820\pi\) | ||||
0.796239 | + | 0.604983i | \(0.206820\pi\) | |||||||
\(840\) | −19.8793 | + | 34.4320i | −0.685902 | + | 1.18802i | ||||
\(841\) | −7.10352 | + | 12.3037i | −0.244949 | + | 0.424264i | ||||
\(842\) | −20.4556 | − | 35.4302i | −0.704947 | − | 1.22100i | ||||
\(843\) | 11.3893 | + | 19.7268i | 0.392268 | + | 0.679429i | ||||
\(844\) | −1.34126 | −0.0461681 | ||||||||
\(845\) | 27.8328 | + | 48.2078i | 0.957476 | + | 1.65840i | ||||
\(846\) | 1.69163 | + | 2.92998i | 0.0581593 | + | 0.100735i | ||||
\(847\) | −8.58300 | − | 14.8662i | −0.294915 | − | 0.510808i | ||||
\(848\) | −18.9266 | + | 32.7818i | −0.649942 | + | 1.12573i | ||||
\(849\) | −7.79182 | −0.267415 | ||||||||
\(850\) | −9.26783 | + | 16.0523i | −0.317884 | + | 0.550591i | ||||
\(851\) | −1.32966 | − | 2.30303i | −0.0455800 | − | 0.0789469i | ||||
\(852\) | 0.471901 | 0.0161671 | ||||||||
\(853\) | −2.15658 | − | 3.73530i | −0.0738399 | − | 0.127894i | 0.826741 | − | 0.562582i | \(-0.190192\pi\) |
−0.900581 | + | 0.434688i | \(0.856859\pi\) | |||||||
\(854\) | 11.4077 | − | 19.7587i | 0.390363 | − | 0.676129i | ||||
\(855\) | −1.92277 | + | 3.33034i | −0.0657575 | + | 0.113895i | ||||
\(856\) | 42.2495 | 1.44406 | ||||||||
\(857\) | 2.37205 | − | 4.10852i | 0.0810278 | − | 0.140344i | −0.822664 | − | 0.568528i | \(-0.807513\pi\) |
0.903692 | + | 0.428184i | \(0.140846\pi\) | |||||||
\(858\) | −42.6881 | −1.45735 | ||||||||
\(859\) | −31.5897 | −1.07783 | −0.538913 | − | 0.842361i | \(-0.681165\pi\) | ||||
−0.538913 | + | 0.842361i | \(0.681165\pi\) | |||||||
\(860\) | 2.17354 | + | 5.36447i | 0.0741172 | + | 0.182927i | ||||
\(861\) | 33.9930 | 1.15848 | ||||||||
\(862\) | 6.58380 | 0.224245 | ||||||||
\(863\) | −5.58640 | + | 9.67593i | −0.190163 | + | 0.329372i | −0.945304 | − | 0.326190i | \(-0.894235\pi\) |
0.755141 | + | 0.655562i | \(0.227568\pi\) | |||||||
\(864\) | −6.48018 | −0.220460 | ||||||||
\(865\) | −23.1944 | + | 40.1739i | −0.788633 | + | 1.36595i | ||||
\(866\) | −25.3758 | + | 43.9521i | −0.862304 | + | 1.49355i | ||||
\(867\) | −0.719541 | − | 1.24628i | −0.0244369 | − | 0.0423259i | ||||
\(868\) | −0.787421 | −0.0267268 | ||||||||
\(869\) | 8.06450 | + | 13.9681i | 0.273569 | + | 0.473836i | ||||
\(870\) | −27.5085 | + | 47.6462i | −0.932627 | + | 1.61536i | ||||
\(871\) | −28.5038 | −0.965816 | ||||||||
\(872\) | −10.7565 | + | 18.6309i | −0.364262 | + | 0.630921i | ||||
\(873\) | −4.83280 | − | 8.37065i | −0.163565 | − | 0.283304i | ||||
\(874\) | 0.663584 | + | 1.14936i | 0.0224461 | + | 0.0388777i | ||||
\(875\) | 41.2950 | + | 71.5250i | 1.39603 | + | 2.41799i | ||||
\(876\) | −0.469729 | −0.0158707 | ||||||||
\(877\) | 0.507116 | + | 0.878350i | 0.0171241 | + | 0.0296598i | 0.874460 | − | 0.485097i | \(-0.161216\pi\) |
−0.857336 | + | 0.514757i | \(0.827882\pi\) | |||||||
\(878\) | −19.8448 | − | 34.3723i | −0.669731 | − | 1.16001i | ||||
\(879\) | −20.2217 | + | 35.0250i | −0.682060 | + | 1.18136i | ||||
\(880\) | 33.5565 | − | 58.1216i | 1.13119 | − | 1.95928i | ||||
\(881\) | 27.4802 | 0.925830 | 0.462915 | − | 0.886403i | \(-0.346803\pi\) | ||||
0.462915 | + | 0.886403i | \(0.346803\pi\) | |||||||
\(882\) | 2.92933 | 0.0986358 | ||||||||
\(883\) | 24.9022 | − | 43.1319i | 0.838026 | − | 1.45150i | −0.0535166 | − | 0.998567i | \(-0.517043\pi\) |
0.891543 | − | 0.452937i | \(-0.149624\pi\) | |||||||
\(884\) | 0.516902 | − | 0.895300i | 0.0173853 | − | 0.0301122i | ||||
\(885\) | −34.2297 | − | 59.2876i | −1.15062 | − | 1.99293i | ||||
\(886\) | 21.0690 | + | 36.4926i | 0.707827 | + | 1.22599i | ||||
\(887\) | −28.0717 | −0.942555 | −0.471278 | − | 0.881985i | \(-0.656207\pi\) | ||||
−0.471278 | + | 0.881985i | \(0.656207\pi\) | |||||||
\(888\) | −5.44445 | − | 9.43006i | −0.182704 | − | 0.316452i | ||||
\(889\) | 7.52070 | + | 13.0262i | 0.252236 | + | 0.436886i | ||||
\(890\) | 12.4210 | + | 21.5138i | 0.416352 | + | 0.721143i | ||||
\(891\) | −11.6480 | + | 20.1750i | −0.390223 | + | 0.675887i | ||||
\(892\) | 0.388105 | 0.0129947 | ||||||||
\(893\) | −1.29585 | + | 2.24448i | −0.0433641 | + | 0.0751088i | ||||
\(894\) | −17.3995 | − | 30.1368i | −0.581926 | − | 1.00793i | ||||
\(895\) | −95.4524 | −3.19062 | ||||||||
\(896\) | −10.0120 | − | 17.3412i | −0.334476 | − | 0.579330i | ||||
\(897\) | 3.79574 | − | 6.57441i | 0.126736 | − | 0.219513i | ||||
\(898\) | −11.0014 | + | 19.0551i | −0.367123 | + | 0.635875i | ||||
\(899\) | −11.8027 | −0.393641 | ||||||||
\(900\) | −1.30671 | + | 2.26329i | −0.0435570 | + | 0.0754429i | ||||
\(901\) | −10.6575 | −0.355053 | ||||||||
\(902\) | −63.9532 | −2.12941 | ||||||||
\(903\) | 12.5092 | − | 16.0436i | 0.416279 | − | 0.533896i | ||||
\(904\) | −1.88101 | −0.0625614 | ||||||||
\(905\) | −69.1875 | −2.29987 | ||||||||
\(906\) | −18.6153 | + | 32.2426i | −0.618451 | + | 1.07119i | ||||
\(907\) | 55.2863 | 1.83575 | 0.917875 | − | 0.396869i | \(-0.129903\pi\) | ||||
0.917875 | + | 0.396869i | \(0.129903\pi\) | |||||||
\(908\) | −0.975221 | + | 1.68913i | −0.0323638 | + | 0.0560558i | ||||
\(909\) | −1.41029 | + | 2.44269i | −0.0467764 | + | 0.0810191i | ||||
\(910\) | 31.8617 | + | 55.1861i | 1.05621 | + | 1.82940i | ||||
\(911\) | 25.2169 | 0.835473 | 0.417737 | − | 0.908568i | \(-0.362823\pi\) | ||||
0.417737 | + | 0.908568i | \(0.362823\pi\) | |||||||
\(912\) | 2.43788 | + | 4.22254i | 0.0807264 | + | 0.139822i | ||||
\(913\) | −19.6893 | + | 34.1029i | −0.651620 | + | 1.12864i | ||||
\(914\) | 44.7627 | 1.48062 | ||||||||
\(915\) | −24.6522 | + | 42.6989i | −0.814978 | + | 1.41158i | ||||
\(916\) | −1.78121 | − | 3.08515i | −0.0588530 | − | 0.101936i | ||||
\(917\) | −10.4997 | − | 18.1861i | −0.346732 | − | 0.600558i | ||||
\(918\) | 3.78936 | + | 6.56336i | 0.125068 | + | 0.216623i | ||||
\(919\) | 44.5266 | 1.46880 | 0.734398 | − | 0.678719i | \(-0.237465\pi\) | ||||
0.734398 | + | 0.678719i | \(0.237465\pi\) | |||||||
\(920\) | 6.65109 | + | 11.5200i | 0.219280 | + | 0.379804i | ||||
\(921\) | −6.33874 | − | 10.9790i | −0.208869 | − | 0.361771i | ||||
\(922\) | 19.4586 | − | 33.7033i | 0.640835 | − | 1.10996i | ||||
\(923\) | 4.09634 | − | 7.09507i | 0.134833 | − | 0.233537i | ||||
\(924\) | 2.74813 | 0.0904070 | ||||||||
\(925\) | −35.4293 | −1.16491 | ||||||||
\(926\) | 3.67983 | − | 6.37365i | 0.120927 | − | 0.209451i | ||||
\(927\) | −7.73404 | + | 13.3957i | −0.254019 | + | 0.439974i | ||||
\(928\) | 3.76671 | + | 6.52413i | 0.123648 | + | 0.214165i | ||||
\(929\) | 9.56255 | + | 16.5628i | 0.313737 | + | 0.543409i | 0.979168 | − | 0.203051i | \(-0.0650856\pi\) |
−0.665431 | + | 0.746459i | \(0.731752\pi\) | |||||||
\(930\) | −15.0288 | −0.492813 | ||||||||
\(931\) | 1.12199 | + | 1.94335i | 0.0367718 | + | 0.0636907i | ||||
\(932\) | −1.48988 | − | 2.58056i | −0.0488028 | − | 0.0845289i | ||||
\(933\) | −14.6529 | − | 25.3795i | −0.479714 | − | 0.830888i | ||||
\(934\) | 25.1678 | − | 43.5919i | 0.823515 | − | 1.42637i | ||||
\(935\) | 18.8956 | 0.617951 | ||||||||
\(936\) | −6.97230 | + | 12.0764i | −0.227897 | + | 0.394728i | ||||
\(937\) | −7.32103 | − | 12.6804i | −0.239168 | − | 0.414250i | 0.721308 | − | 0.692614i | \(-0.243541\pi\) |
−0.960476 | + | 0.278364i | \(0.910208\pi\) | |||||||
\(938\) | −16.2066 | −0.529165 | ||||||||
\(939\) | 9.13498 | + | 15.8222i | 0.298109 | + | 0.516339i | ||||
\(940\) | −1.19907 | + | 2.07685i | −0.0391094 | + | 0.0677394i | ||||
\(941\) | 2.61589 | − | 4.53085i | 0.0852754 | − | 0.147701i | −0.820233 | − | 0.572029i | \(-0.806156\pi\) |
0.905509 | + | 0.424328i | \(0.139490\pi\) | |||||||
\(942\) | 22.8093 | 0.743166 | ||||||||
\(943\) | 5.68658 | − | 9.84944i | 0.185180 | − | 0.320742i | ||||
\(944\) | 38.9389 | 1.26735 | ||||||||
\(945\) | 52.8930 | 1.72061 | ||||||||
\(946\) | −23.5342 | + | 30.1837i | −0.765164 | + | 0.981358i | ||||
\(947\) | 24.3089 | 0.789932 | 0.394966 | − | 0.918696i | \(-0.370756\pi\) | ||||
0.394966 | + | 0.918696i | \(0.370756\pi\) | |||||||
\(948\) | −1.08426 | −0.0352151 | ||||||||
\(949\) | −4.07748 | + | 7.06241i | −0.132361 | + | 0.229256i | ||||
\(950\) | 17.6815 | 0.573663 | ||||||||
\(951\) | −23.9134 | + | 41.4193i | −0.775446 | + | 1.34311i | ||||
\(952\) | 3.18350 | − | 5.51399i | 0.103178 | − | 0.178709i | ||||
\(953\) | −7.43248 | − | 12.8734i | −0.240762 | − | 0.417011i | 0.720170 | − | 0.693798i | \(-0.244064\pi\) |
−0.960931 | + | 0.276787i | \(0.910731\pi\) | |||||||
\(954\) | 13.2713 | 0.429676 | ||||||||
\(955\) | −38.9112 | − | 67.3962i | −1.25914 | − | 2.18089i | ||||
\(956\) | −0.538053 | + | 0.931936i | −0.0174019 | + | 0.0301410i | ||||
\(957\) | 41.1919 | 1.33154 | ||||||||
\(958\) | −1.84093 | + | 3.18858i | −0.0594776 | + | 0.103018i | ||||
\(959\) | 1.90593 | + | 3.30116i | 0.0615456 | + | 0.106600i | ||||
\(960\) | 26.9754 | + | 46.7227i | 0.870626 | + | 1.50797i | ||||
\(961\) | 13.8880 | + | 24.0546i | 0.447999 | + | 0.775956i | ||||
\(962\) | −17.4522 | −0.562682 | ||||||||
\(963\) | −6.64518 | − | 11.5098i | −0.214138 | − | 0.370898i | ||||
\(964\) | 1.55312 | + | 2.69008i | 0.0500226 | + | 0.0866417i | ||||
\(965\) | 27.0241 | − | 46.8071i | 0.869935 | − | 1.50677i | ||||
\(966\) | 2.15817 | − | 3.73806i | 0.0694379 | − | 0.120270i | ||||
\(967\) | 30.2322 | 0.972203 | 0.486102 | − | 0.873902i | \(-0.338419\pi\) | ||||
0.486102 | + | 0.873902i | \(0.338419\pi\) | |||||||
\(968\) | −23.5166 | −0.755852 | ||||||||
\(969\) | −0.686383 | + | 1.18885i | −0.0220498 | + | 0.0381914i | ||||
\(970\) | −30.2550 | + | 52.4032i | −0.971430 | + | 1.68257i | ||||
\(971\) | −15.5599 | − | 26.9505i | −0.499341 | − | 0.864884i | 0.500659 | − | 0.865645i | \(-0.333091\pi\) |
−1.00000 | 0.000760789i | \(0.999758\pi\) | ||||||||
\(972\) | 0.942223 | + | 1.63198i | 0.0302218 | + | 0.0523457i | ||||
\(973\) | 28.9279 | 0.927387 | ||||||||
\(974\) | 28.0129 | + | 48.5197i | 0.897590 | + | 1.55467i | ||||
\(975\) | −50.5696 | − | 87.5890i | −1.61952 | − | 2.80509i | ||||
\(976\) | −14.0219 | − | 24.2866i | −0.448830 | − | 0.777396i | ||||
\(977\) | 17.0953 | − | 29.6100i | 0.546928 | − | 0.947308i | −0.451554 | − | 0.892244i | \(-0.649130\pi\) |
0.998483 | − | 0.0550642i | \(-0.0175363\pi\) | |||||||
\(978\) | −13.7985 | −0.441227 | ||||||||
\(979\) | 9.29972 | − | 16.1076i | 0.297220 | − | 0.514801i | ||||
\(980\) | 1.03820 | + | 1.79821i | 0.0331640 | + | 0.0574416i | ||||
\(981\) | 6.76734 | 0.216065 | ||||||||
\(982\) | −9.78195 | − | 16.9428i | −0.312155 | − | 0.540668i | ||||
\(983\) | 6.09940 | − | 10.5645i | 0.194541 | − | 0.336954i | −0.752209 | − | 0.658924i | \(-0.771012\pi\) |
0.946750 | + | 0.321970i | \(0.104345\pi\) | |||||||
\(984\) | 23.2844 | − | 40.3298i | 0.742280 | − | 1.28567i | ||||
\(985\) | −87.8645 | −2.79959 | ||||||||
\(986\) | 4.40525 | − | 7.63012i | 0.140292 | − | 0.242993i | ||||
\(987\) | 8.42898 | 0.268297 | ||||||||
\(988\) | −0.986164 | −0.0313740 | ||||||||
\(989\) | −2.55599 | − | 6.30839i | −0.0812758 | − | 0.200595i | ||||
\(990\) | −23.5299 | −0.747828 | ||||||||
\(991\) | −15.2905 | −0.485718 | −0.242859 | − | 0.970062i | \(-0.578085\pi\) | ||||
−0.242859 | + | 0.970062i | \(0.578085\pi\) | |||||||
\(992\) | −1.02894 | + | 1.78217i | −0.0326687 | + | 0.0565839i | ||||
\(993\) | −4.71206 | −0.149533 | ||||||||
\(994\) | 2.32908 | − | 4.03409i | 0.0738741 | − | 0.127954i | ||||
\(995\) | 10.3260 | − | 17.8851i | 0.327355 | − | 0.566995i | ||||
\(996\) | −1.32360 | − | 2.29254i | −0.0419398 | − | 0.0726418i | ||||
\(997\) | 52.0231 | 1.64759 | 0.823794 | − | 0.566889i | \(-0.191853\pi\) | ||||
0.823794 | + | 0.566889i | \(0.191853\pi\) | |||||||
\(998\) | 13.6296 | + | 23.6071i | 0.431437 | + | 0.747271i | ||||
\(999\) | −7.24303 | + | 12.5453i | −0.229159 | + | 0.396915i |
(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 | 731.2.e.b.307.19 | ✓ | 58 | |
43.36 | even | 3 | inner | 731.2.e.b.681.19 | yes | 58 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
731.2.e.b.307.19 | ✓ | 58 | 1.1 | even | 1 | trivial | |
731.2.e.b.681.19 | yes | 58 | 43.36 | even | 3 | inner |