Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,2,Mod(689,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.689");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.h (of order \(2\), degree \(1\), 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: | \(5.50967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 689.6 | ||
Character | \(\chi\) | \(=\) | 690.689 |
Dual form | 690.2.h.a.689.8 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.29400 | − | 1.15133i | −0.747093 | − | 0.664720i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.22484 | + | 0.223804i | 0.994979 | + | 0.100088i | ||||
\(6\) | 1.29400 | + | 1.15133i | 0.528274 | + | 0.470028i | ||||
\(7\) | −0.666856 | −0.252048 | −0.126024 | − | 0.992027i | \(-0.540222\pi\) | ||||
−0.126024 | + | 0.992027i | \(0.540222\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.348885 | + | 2.97964i | 0.116295 | + | 0.993215i | ||||
\(10\) | −2.22484 | − | 0.223804i | −0.703556 | − | 0.0707731i | ||||
\(11\) | −4.92726 | −1.48562 | −0.742812 | − | 0.669500i | \(-0.766509\pi\) | ||||
−0.742812 | + | 0.669500i | \(0.766509\pi\) | |||||||
\(12\) | −1.29400 | − | 1.15133i | −0.373546 | − | 0.332360i | ||||
\(13\) | − | 3.71145i | − | 1.02937i | −0.857379 | − | 0.514685i | \(-0.827909\pi\) | ||
0.857379 | − | 0.514685i | \(-0.172091\pi\) | |||||||
\(14\) | 0.666856 | 0.178225 | ||||||||
\(15\) | −2.62128 | − | 2.85112i | −0.676811 | − | 0.736157i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 0.810614i | − | 0.196603i | −0.995157 | − | 0.0983013i | \(-0.968659\pi\) | ||
0.995157 | − | 0.0983013i | \(-0.0313409\pi\) | |||||||
\(18\) | −0.348885 | − | 2.97964i | −0.0822330 | − | 0.702309i | ||||
\(19\) | − | 4.16671i | − | 0.955908i | −0.878385 | − | 0.477954i | \(-0.841379\pi\) | ||
0.878385 | − | 0.477954i | \(-0.158621\pi\) | |||||||
\(20\) | 2.22484 | + | 0.223804i | 0.497489 | + | 0.0500441i | ||||
\(21\) | 0.862914 | + | 0.767771i | 0.188303 | + | 0.167541i | ||||
\(22\) | 4.92726 | 1.05050 | ||||||||
\(23\) | −1.14656 | + | 4.65676i | −0.239074 | + | 0.971001i | ||||
\(24\) | 1.29400 | + | 1.15133i | 0.264137 | + | 0.235014i | ||||
\(25\) | 4.89982 | + | 0.995856i | 0.979965 | + | 0.199171i | ||||
\(26\) | 3.71145i | 0.727874i | ||||||||
\(27\) | 2.97909 | − | 4.25735i | 0.573326 | − | 0.819327i | ||||
\(28\) | −0.666856 | −0.126024 | ||||||||
\(29\) | − | 9.02232i | − | 1.67540i | −0.546129 | − | 0.837701i | \(-0.683899\pi\) | ||
0.546129 | − | 0.837701i | \(-0.316101\pi\) | |||||||
\(30\) | 2.62128 | + | 2.85112i | 0.478577 | + | 0.520542i | ||||
\(31\) | −6.13458 | −1.10180 | −0.550902 | − | 0.834570i | \(-0.685716\pi\) | ||||
−0.550902 | + | 0.834570i | \(0.685716\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 6.37589 | + | 5.67289i | 1.10990 | + | 0.987524i | ||||
\(34\) | 0.810614i | 0.139019i | ||||||||
\(35\) | −1.48365 | − | 0.149245i | −0.250782 | − | 0.0252270i | ||||
\(36\) | 0.348885 | + | 2.97964i | 0.0581475 | + | 0.496607i | ||||
\(37\) | −2.21928 | −0.364848 | −0.182424 | − | 0.983220i | \(-0.558394\pi\) | ||||
−0.182424 | + | 0.983220i | \(0.558394\pi\) | |||||||
\(38\) | 4.16671i | 0.675929i | ||||||||
\(39\) | −4.27309 | + | 4.80262i | −0.684243 | + | 0.769035i | ||||
\(40\) | −2.22484 | − | 0.223804i | −0.351778 | − | 0.0353865i | ||||
\(41\) | − | 2.54295i | − | 0.397143i | −0.980086 | − | 0.198571i | \(-0.936370\pi\) | ||
0.980086 | − | 0.198571i | \(-0.0636302\pi\) | |||||||
\(42\) | −0.862914 | − | 0.767771i | −0.133151 | − | 0.118470i | ||||
\(43\) | 3.56526 | 0.543698 | 0.271849 | − | 0.962340i | \(-0.412365\pi\) | ||||
0.271849 | + | 0.962340i | \(0.412365\pi\) | |||||||
\(44\) | −4.92726 | −0.742812 | ||||||||
\(45\) | 0.109357 | + | 6.70731i | 0.0163019 | + | 0.999867i | ||||
\(46\) | 1.14656 | − | 4.65676i | 0.169051 | − | 0.686602i | ||||
\(47\) | −10.0928 | −1.47218 | −0.736090 | − | 0.676883i | \(-0.763330\pi\) | ||||
−0.736090 | + | 0.676883i | \(0.763330\pi\) | |||||||
\(48\) | −1.29400 | − | 1.15133i | −0.186773 | − | 0.166180i | ||||
\(49\) | −6.55530 | −0.936472 | ||||||||
\(50\) | −4.89982 | − | 0.995856i | −0.692940 | − | 0.140835i | ||||
\(51\) | −0.933283 | + | 1.04894i | −0.130686 | + | 0.146880i | ||||
\(52\) | − | 3.71145i | − | 0.514685i | ||||||
\(53\) | − | 10.6281i | − | 1.45988i | −0.683511 | − | 0.729940i | \(-0.739548\pi\) | ||
0.683511 | − | 0.729940i | \(-0.260452\pi\) | |||||||
\(54\) | −2.97909 | + | 4.25735i | −0.405403 | + | 0.579352i | ||||
\(55\) | −10.9624 | − | 1.10274i | −1.47816 | − | 0.148694i | ||||
\(56\) | 0.666856 | 0.0891124 | ||||||||
\(57\) | −4.79725 | + | 5.39173i | −0.635411 | + | 0.714152i | ||||
\(58\) | 9.02232i | 1.18469i | ||||||||
\(59\) | − | 6.81080i | − | 0.886690i | −0.896351 | − | 0.443345i | \(-0.853792\pi\) | ||
0.896351 | − | 0.443345i | \(-0.146208\pi\) | |||||||
\(60\) | −2.62128 | − | 2.85112i | −0.338405 | − | 0.368079i | ||||
\(61\) | 9.21371i | 1.17969i | 0.807515 | + | 0.589847i | \(0.200812\pi\) | ||||
−0.807515 | + | 0.589847i | \(0.799188\pi\) | |||||||
\(62\) | 6.13458 | 0.779092 | ||||||||
\(63\) | −0.232656 | − | 1.98699i | −0.0293119 | − | 0.250338i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.830637 | − | 8.25737i | 0.103028 | − | 1.02420i | ||||
\(66\) | −6.37589 | − | 5.67289i | −0.784817 | − | 0.698285i | ||||
\(67\) | −7.95053 | −0.971312 | −0.485656 | − | 0.874150i | \(-0.661419\pi\) | ||||
−0.485656 | + | 0.874150i | \(0.661419\pi\) | |||||||
\(68\) | − | 0.810614i | − | 0.0983013i | ||||||
\(69\) | 6.84511 | − | 4.70579i | 0.824054 | − | 0.566511i | ||||
\(70\) | 1.48365 | + | 0.149245i | 0.177330 | + | 0.0178382i | ||||
\(71\) | − | 14.5288i | − | 1.72425i | −0.506695 | − | 0.862126i | \(-0.669133\pi\) | ||
0.506695 | − | 0.862126i | \(-0.330867\pi\) | |||||||
\(72\) | −0.348885 | − | 2.97964i | −0.0411165 | − | 0.351154i | ||||
\(73\) | − | 4.84561i | − | 0.567136i | −0.958952 | − | 0.283568i | \(-0.908482\pi\) | ||
0.958952 | − | 0.283568i | \(-0.0915181\pi\) | |||||||
\(74\) | 2.21928 | 0.257986 | ||||||||
\(75\) | −5.19383 | − | 6.92995i | −0.599731 | − | 0.800201i | ||||
\(76\) | − | 4.16671i | − | 0.477954i | ||||||
\(77\) | 3.28577 | 0.374449 | ||||||||
\(78\) | 4.27309 | − | 4.80262i | 0.483833 | − | 0.543790i | ||||
\(79\) | 11.5161i | 1.29566i | 0.761785 | + | 0.647830i | \(0.224323\pi\) | ||||
−0.761785 | + | 0.647830i | \(0.775677\pi\) | |||||||
\(80\) | 2.22484 | + | 0.223804i | 0.248745 | + | 0.0250221i | ||||
\(81\) | −8.75656 | + | 2.07911i | −0.972951 | + | 0.231012i | ||||
\(82\) | 2.54295i | 0.280822i | ||||||||
\(83\) | 13.5358i | 1.48575i | 0.669433 | + | 0.742873i | \(0.266537\pi\) | ||||
−0.669433 | + | 0.742873i | \(0.733463\pi\) | |||||||
\(84\) | 0.862914 | + | 0.767771i | 0.0941516 | + | 0.0837707i | ||||
\(85\) | 0.181419 | − | 1.80349i | 0.0196776 | − | 0.195615i | ||||
\(86\) | −3.56526 | −0.384452 | ||||||||
\(87\) | −10.3877 | + | 11.6749i | −1.11367 | + | 1.25168i | ||||
\(88\) | 4.92726 | 0.525248 | ||||||||
\(89\) | −12.5342 | −1.32862 | −0.664312 | − | 0.747455i | \(-0.731275\pi\) | ||||
−0.664312 | + | 0.747455i | \(0.731275\pi\) | |||||||
\(90\) | −0.109357 | − | 6.70731i | −0.0115272 | − | 0.707013i | ||||
\(91\) | 2.47500i | 0.259451i | ||||||||
\(92\) | −1.14656 | + | 4.65676i | −0.119537 | + | 0.485501i | ||||
\(93\) | 7.93816 | + | 7.06292i | 0.823149 | + | 0.732390i | ||||
\(94\) | 10.0928 | 1.04099 | ||||||||
\(95\) | 0.932526 | − | 9.27026i | 0.0956752 | − | 0.951108i | ||||
\(96\) | 1.29400 | + | 1.15133i | 0.132069 | + | 0.117507i | ||||
\(97\) | 1.04670 | 0.106277 | 0.0531383 | − | 0.998587i | \(-0.483078\pi\) | ||||
0.0531383 | + | 0.998587i | \(0.483078\pi\) | |||||||
\(98\) | 6.55530 | 0.662186 | ||||||||
\(99\) | −1.71905 | − | 14.6815i | −0.172771 | − | 1.47554i | ||||
\(100\) | 4.89982 | + | 0.995856i | 0.489982 | + | 0.0995856i | ||||
\(101\) | 11.5777i | 1.15203i | 0.817440 | + | 0.576013i | \(0.195392\pi\) | ||||
−0.817440 | + | 0.576013i | \(0.804608\pi\) | |||||||
\(102\) | 0.933283 | − | 1.04894i | 0.0924087 | − | 0.103860i | ||||
\(103\) | 14.2870 | 1.40774 | 0.703871 | − | 0.710327i | \(-0.251453\pi\) | ||||
0.703871 | + | 0.710327i | \(0.251453\pi\) | |||||||
\(104\) | 3.71145i | 0.363937i | ||||||||
\(105\) | 1.74801 | + | 1.90129i | 0.170589 | + | 0.185547i | ||||
\(106\) | 10.6281i | 1.03229i | ||||||||
\(107\) | − | 10.4647i | − | 1.01166i | −0.862633 | − | 0.505830i | \(-0.831186\pi\) | ||
0.862633 | − | 0.505830i | \(-0.168814\pi\) | |||||||
\(108\) | 2.97909 | − | 4.25735i | 0.286663 | − | 0.409664i | ||||
\(109\) | − | 7.00879i | − | 0.671321i | −0.941983 | − | 0.335660i | \(-0.891041\pi\) | ||
0.941983 | − | 0.335660i | \(-0.108959\pi\) | |||||||
\(110\) | 10.9624 | + | 1.10274i | 1.04522 | + | 0.105142i | ||||
\(111\) | 2.87176 | + | 2.55512i | 0.272575 | + | 0.242522i | ||||
\(112\) | −0.666856 | −0.0630120 | ||||||||
\(113\) | 14.6901i | 1.38193i | 0.722888 | + | 0.690965i | \(0.242814\pi\) | ||||
−0.722888 | + | 0.690965i | \(0.757186\pi\) | |||||||
\(114\) | 4.79725 | − | 5.39173i | 0.449304 | − | 0.504982i | ||||
\(115\) | −3.59311 | + | 10.1039i | −0.335059 | + | 0.942197i | ||||
\(116\) | − | 9.02232i | − | 0.837701i | ||||||
\(117\) | 11.0588 | − | 1.29487i | 1.02239 | − | 0.119711i | ||||
\(118\) | 6.81080i | 0.626985i | ||||||||
\(119\) | 0.540563i | 0.0495533i | ||||||||
\(120\) | 2.62128 | + | 2.85112i | 0.239289 | + | 0.260271i | ||||
\(121\) | 13.2779 | 1.20708 | ||||||||
\(122\) | − | 9.21371i | − | 0.834170i | ||||||
\(123\) | −2.92778 | + | 3.29059i | −0.263989 | + | 0.296702i | ||||
\(124\) | −6.13458 | −0.550902 | ||||||||
\(125\) | 10.6784 | + | 3.31222i | 0.955109 | + | 0.296254i | ||||
\(126\) | 0.232656 | + | 1.98699i | 0.0207267 | + | 0.177016i | ||||
\(127\) | − | 1.83972i | − | 0.163249i | −0.996663 | − | 0.0816245i | \(-0.973989\pi\) | ||
0.996663 | − | 0.0816245i | \(-0.0260108\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −4.61346 | − | 4.10479i | −0.406192 | − | 0.361407i | ||||
\(130\) | −0.830637 | + | 8.25737i | −0.0728517 | + | 0.724219i | ||||
\(131\) | − | 6.59703i | − | 0.576385i | −0.957573 | − | 0.288192i | \(-0.906946\pi\) | ||
0.957573 | − | 0.288192i | \(-0.0930543\pi\) | |||||||
\(132\) | 6.37589 | + | 5.67289i | 0.554950 | + | 0.493762i | ||||
\(133\) | 2.77860i | 0.240935i | ||||||||
\(134\) | 7.95053 | 0.686821 | ||||||||
\(135\) | 7.58081 | − | 8.80518i | 0.652452 | − | 0.757830i | ||||
\(136\) | 0.810614i | 0.0695095i | ||||||||
\(137\) | − | 16.5441i | − | 1.41346i | −0.707485 | − | 0.706728i | \(-0.750170\pi\) | ||
0.707485 | − | 0.706728i | \(-0.249830\pi\) | |||||||
\(138\) | −6.84511 | + | 4.70579i | −0.582694 | + | 0.400584i | ||||
\(139\) | 5.46913 | 0.463885 | 0.231943 | − | 0.972729i | \(-0.425492\pi\) | ||||
0.231943 | + | 0.972729i | \(0.425492\pi\) | |||||||
\(140\) | −1.48365 | − | 0.149245i | −0.125391 | − | 0.0126135i | ||||
\(141\) | 13.0601 | + | 11.6201i | 1.09986 | + | 0.978588i | ||||
\(142\) | 14.5288i | 1.21923i | ||||||||
\(143\) | 18.2873i | 1.52926i | ||||||||
\(144\) | 0.348885 | + | 2.97964i | 0.0290737 | + | 0.248304i | ||||
\(145\) | 2.01923 | − | 20.0732i | 0.167688 | − | 1.66699i | ||||
\(146\) | 4.84561i | 0.401026i | ||||||||
\(147\) | 8.48258 | + | 7.54731i | 0.699631 | + | 0.622491i | ||||
\(148\) | −2.21928 | −0.182424 | ||||||||
\(149\) | −2.91067 | −0.238452 | −0.119226 | − | 0.992867i | \(-0.538041\pi\) | ||||
−0.119226 | + | 0.992867i | \(0.538041\pi\) | |||||||
\(150\) | 5.19383 | + | 6.92995i | 0.424074 | + | 0.565828i | ||||
\(151\) | 5.50476 | 0.447971 | 0.223985 | − | 0.974592i | \(-0.428093\pi\) | ||||
0.223985 | + | 0.974592i | \(0.428093\pi\) | |||||||
\(152\) | 4.16671i | 0.337965i | ||||||||
\(153\) | 2.41534 | − | 0.282811i | 0.195269 | − | 0.0228639i | ||||
\(154\) | −3.28577 | −0.264775 | ||||||||
\(155\) | −13.6485 | − | 1.37294i | −1.09627 | − | 0.110278i | ||||
\(156\) | −4.27309 | + | 4.80262i | −0.342121 | + | 0.384517i | ||||
\(157\) | −8.36290 | −0.667432 | −0.333716 | − | 0.942674i | \(-0.608303\pi\) | ||||
−0.333716 | + | 0.942674i | \(0.608303\pi\) | |||||||
\(158\) | − | 11.5161i | − | 0.916170i | ||||||
\(159\) | −12.2364 | + | 13.7528i | −0.970412 | + | 1.09067i | ||||
\(160\) | −2.22484 | − | 0.223804i | −0.175889 | − | 0.0176933i | ||||
\(161\) | 0.764590 | − | 3.10539i | 0.0602581 | − | 0.244739i | ||||
\(162\) | 8.75656 | − | 2.07911i | 0.687980 | − | 0.163350i | ||||
\(163\) | − | 12.1701i | − | 0.953233i | −0.879111 | − | 0.476617i | \(-0.841863\pi\) | ||
0.879111 | − | 0.476617i | \(-0.158137\pi\) | |||||||
\(164\) | − | 2.54295i | − | 0.198571i | ||||||
\(165\) | 12.9157 | + | 14.0482i | 1.00549 | + | 1.09365i | ||||
\(166\) | − | 13.5358i | − | 1.05058i | ||||||
\(167\) | 14.3712 | 1.11208 | 0.556038 | − | 0.831157i | \(-0.312321\pi\) | ||||
0.556038 | + | 0.831157i | \(0.312321\pi\) | |||||||
\(168\) | −0.862914 | − | 0.767771i | −0.0665753 | − | 0.0592348i | ||||
\(169\) | −0.774832 | −0.0596025 | ||||||||
\(170\) | −0.181419 | + | 1.80349i | −0.0139142 | + | 0.138321i | ||||
\(171\) | 12.4153 | − | 1.45370i | 0.949422 | − | 0.111167i | ||||
\(172\) | 3.56526 | 0.271849 | ||||||||
\(173\) | 18.2848 | 1.39017 | 0.695085 | − | 0.718927i | \(-0.255367\pi\) | ||||
0.695085 | + | 0.718927i | \(0.255367\pi\) | |||||||
\(174\) | 10.3877 | − | 11.6749i | 0.787486 | − | 0.885072i | ||||
\(175\) | −3.26748 | − | 0.664093i | −0.246998 | − | 0.0502007i | ||||
\(176\) | −4.92726 | −0.371406 | ||||||||
\(177\) | −7.84146 | + | 8.81319i | −0.589401 | + | 0.662440i | ||||
\(178\) | 12.5342 | 0.939479 | ||||||||
\(179\) | 5.02306i | 0.375441i | 0.982222 | + | 0.187721i | \(0.0601099\pi\) | ||||
−0.982222 | + | 0.187721i | \(0.939890\pi\) | |||||||
\(180\) | 0.109357 | + | 6.70731i | 0.00815096 | + | 0.499934i | ||||
\(181\) | 0.342921i | 0.0254891i | 0.999919 | + | 0.0127445i | \(0.00405682\pi\) | ||||
−0.999919 | + | 0.0127445i | \(0.995943\pi\) | |||||||
\(182\) | − | 2.47500i | − | 0.183459i | ||||||
\(183\) | 10.6080 | − | 11.9226i | 0.784166 | − | 0.881341i | ||||
\(184\) | 1.14656 | − | 4.65676i | 0.0845254 | − | 0.343301i | ||||
\(185\) | −4.93755 | − | 0.496684i | −0.363016 | − | 0.0365170i | ||||
\(186\) | −7.93816 | − | 7.06292i | −0.582054 | − | 0.517878i | ||||
\(187\) | 3.99410i | 0.292078i | ||||||||
\(188\) | −10.0928 | −0.736090 | ||||||||
\(189\) | −1.98663 | + | 2.83904i | −0.144506 | + | 0.206510i | ||||
\(190\) | −0.932526 | + | 9.27026i | −0.0676525 | + | 0.672535i | ||||
\(191\) | 26.5716 | 1.92265 | 0.961325 | − | 0.275416i | \(-0.0888155\pi\) | ||||
0.961325 | + | 0.275416i | \(0.0888155\pi\) | |||||||
\(192\) | −1.29400 | − | 1.15133i | −0.0933866 | − | 0.0830900i | ||||
\(193\) | − | 0.121042i | − | 0.00871281i | −0.999991 | − | 0.00435640i | \(-0.998613\pi\) | ||
0.999991 | − | 0.00435640i | \(-0.00138669\pi\) | |||||||
\(194\) | −1.04670 | −0.0751489 | ||||||||
\(195\) | −10.5818 | + | 9.72873i | −0.757778 | + | 0.696688i | ||||
\(196\) | −6.55530 | −0.468236 | ||||||||
\(197\) | −4.06795 | −0.289829 | −0.144915 | − | 0.989444i | \(-0.546291\pi\) | ||||
−0.144915 | + | 0.989444i | \(0.546291\pi\) | |||||||
\(198\) | 1.71905 | + | 14.6815i | 0.122167 | + | 1.04337i | ||||
\(199\) | − | 3.82379i | − | 0.271061i | −0.990773 | − | 0.135531i | \(-0.956726\pi\) | ||
0.990773 | − | 0.135531i | \(-0.0432739\pi\) | |||||||
\(200\) | −4.89982 | − | 0.995856i | −0.346470 | − | 0.0704177i | ||||
\(201\) | 10.2880 | + | 9.15367i | 0.725660 | + | 0.645650i | ||||
\(202\) | − | 11.5777i | − | 0.814606i | ||||||
\(203\) | 6.01659i | 0.422282i | ||||||||
\(204\) | −0.933283 | + | 1.04894i | −0.0653429 | + | 0.0734402i | ||||
\(205\) | 0.569123 | − | 5.65766i | 0.0397493 | − | 0.395148i | ||||
\(206\) | −14.2870 | −0.995425 | ||||||||
\(207\) | −14.2755 | − | 1.79166i | −0.992216 | − | 0.124529i | ||||
\(208\) | − | 3.71145i | − | 0.257342i | ||||||
\(209\) | 20.5304i | 1.42012i | ||||||||
\(210\) | −1.74801 | − | 1.90129i | −0.120624 | − | 0.131202i | ||||
\(211\) | −10.9491 | −0.753765 | −0.376882 | − | 0.926261i | \(-0.623004\pi\) | ||||
−0.376882 | + | 0.926261i | \(0.623004\pi\) | |||||||
\(212\) | − | 10.6281i | − | 0.729940i | ||||||
\(213\) | −16.7274 | + | 18.8003i | −1.14614 | + | 1.28818i | ||||
\(214\) | 10.4647i | 0.715352i | ||||||||
\(215\) | 7.93214 | + | 0.797920i | 0.540967 | + | 0.0544177i | ||||
\(216\) | −2.97909 | + | 4.25735i | −0.202702 | + | 0.289676i | ||||
\(217\) | 4.09088 | 0.277707 | ||||||||
\(218\) | 7.00879i | 0.474695i | ||||||||
\(219\) | −5.57889 | + | 6.27023i | −0.376986 | + | 0.423703i | ||||
\(220\) | −10.9624 | − | 1.10274i | −0.739082 | − | 0.0743468i | ||||
\(221\) | −3.00855 | −0.202377 | ||||||||
\(222\) | −2.87176 | − | 2.55512i | −0.192740 | − | 0.171489i | ||||
\(223\) | 3.05235i | 0.204401i | 0.994764 | + | 0.102200i | \(0.0325883\pi\) | ||||
−0.994764 | + | 0.102200i | \(0.967412\pi\) | |||||||
\(224\) | 0.666856 | 0.0445562 | ||||||||
\(225\) | −1.25782 | + | 14.9472i | −0.0838549 | + | 0.996478i | ||||
\(226\) | − | 14.6901i | − | 0.977172i | ||||||
\(227\) | − | 16.8065i | − | 1.11549i | −0.830014 | − | 0.557743i | \(-0.811668\pi\) | ||
0.830014 | − | 0.557743i | \(-0.188332\pi\) | |||||||
\(228\) | −4.79725 | + | 5.39173i | −0.317706 | + | 0.357076i | ||||
\(229\) | 10.0750i | 0.665775i | 0.942966 | + | 0.332888i | \(0.108023\pi\) | ||||
−0.942966 | + | 0.332888i | \(0.891977\pi\) | |||||||
\(230\) | 3.59311 | − | 10.1039i | 0.236923 | − | 0.666234i | ||||
\(231\) | −4.25180 | − | 3.78301i | −0.279748 | − | 0.248904i | ||||
\(232\) | 9.02232i | 0.592344i | ||||||||
\(233\) | 13.0601 | 0.855593 | 0.427796 | − | 0.903875i | \(-0.359290\pi\) | ||||
0.427796 | + | 0.903875i | \(0.359290\pi\) | |||||||
\(234\) | −11.0588 | + | 1.29487i | −0.722936 | + | 0.0846481i | ||||
\(235\) | −22.4548 | − | 2.25880i | −1.46479 | − | 0.147348i | ||||
\(236\) | − | 6.81080i | − | 0.443345i | ||||||
\(237\) | 13.2588 | − | 14.9018i | 0.861251 | − | 0.967978i | ||||
\(238\) | − | 0.540563i | − | 0.0350395i | ||||||
\(239\) | − | 14.5163i | − | 0.938984i | −0.882937 | − | 0.469492i | \(-0.844437\pi\) | ||
0.882937 | − | 0.469492i | \(-0.155563\pi\) | |||||||
\(240\) | −2.62128 | − | 2.85112i | −0.169203 | − | 0.184039i | ||||
\(241\) | 7.90101i | 0.508949i | 0.967079 | + | 0.254475i | \(0.0819025\pi\) | ||||
−0.967079 | + | 0.254475i | \(0.918098\pi\) | |||||||
\(242\) | −13.2779 | −0.853535 | ||||||||
\(243\) | 13.7247 | + | 7.39131i | 0.880443 | + | 0.474153i | ||||
\(244\) | 9.21371i | 0.589847i | ||||||||
\(245\) | −14.5845 | − | 1.46710i | −0.931769 | − | 0.0937298i | ||||
\(246\) | 2.92778 | − | 3.29059i | 0.186668 | − | 0.209800i | ||||
\(247\) | −15.4645 | −0.983983 | ||||||||
\(248\) | 6.13458 | 0.389546 | ||||||||
\(249\) | 15.5841 | − | 17.5153i | 0.987604 | − | 1.10999i | ||||
\(250\) | −10.6784 | − | 3.31222i | −0.675364 | − | 0.209483i | ||||
\(251\) | 6.40105 | 0.404031 | 0.202015 | − | 0.979382i | \(-0.435251\pi\) | ||||
0.202015 | + | 0.979382i | \(0.435251\pi\) | |||||||
\(252\) | −0.232656 | − | 1.98699i | −0.0146560 | − | 0.125169i | ||||
\(253\) | 5.64939 | − | 22.9451i | 0.355174 | − | 1.44254i | ||||
\(254\) | 1.83972i | 0.115434i | ||||||||
\(255\) | −2.31116 | + | 2.12484i | −0.144730 | + | 0.133063i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −14.7993 | −0.923153 | −0.461576 | − | 0.887101i | \(-0.652716\pi\) | ||||
−0.461576 | + | 0.887101i | \(0.652716\pi\) | |||||||
\(258\) | 4.61346 | + | 4.10479i | 0.287221 | + | 0.255553i | ||||
\(259\) | 1.47994 | 0.0919592 | ||||||||
\(260\) | 0.830637 | − | 8.25737i | 0.0515139 | − | 0.512101i | ||||
\(261\) | 26.8833 | − | 3.14775i | 1.66403 | − | 0.194841i | ||||
\(262\) | 6.59703i | 0.407566i | ||||||||
\(263\) | 1.33588i | 0.0823737i | 0.999151 | + | 0.0411868i | \(0.0131139\pi\) | ||||
−0.999151 | + | 0.0411868i | \(0.986886\pi\) | |||||||
\(264\) | −6.37589 | − | 5.67289i | −0.392409 | − | 0.349143i | ||||
\(265\) | 2.37861 | − | 23.6458i | 0.146117 | − | 1.45255i | ||||
\(266\) | − | 2.77860i | − | 0.170367i | ||||||
\(267\) | 16.2193 | + | 14.4310i | 0.992605 | + | 0.883163i | ||||
\(268\) | −7.95053 | −0.485656 | ||||||||
\(269\) | 12.2843i | 0.748989i | 0.927229 | + | 0.374495i | \(0.122184\pi\) | ||||
−0.927229 | + | 0.374495i | \(0.877816\pi\) | |||||||
\(270\) | −7.58081 | + | 8.80518i | −0.461354 | + | 0.535866i | ||||
\(271\) | −19.5706 | −1.18883 | −0.594415 | − | 0.804158i | \(-0.702616\pi\) | ||||
−0.594415 | + | 0.804158i | \(0.702616\pi\) | |||||||
\(272\) | − | 0.810614i | − | 0.0491507i | ||||||
\(273\) | 2.84954 | − | 3.20266i | 0.172462 | − | 0.193834i | ||||
\(274\) | 16.5441i | 0.999464i | ||||||||
\(275\) | −24.1427 | − | 4.90684i | −1.45586 | − | 0.295894i | ||||
\(276\) | 6.84511 | − | 4.70579i | 0.412027 | − | 0.283255i | ||||
\(277\) | − | 13.9776i | − | 0.839830i | −0.907563 | − | 0.419915i | \(-0.862060\pi\) | ||
0.907563 | − | 0.419915i | \(-0.137940\pi\) | |||||||
\(278\) | −5.46913 | −0.328016 | ||||||||
\(279\) | −2.14026 | − | 18.2789i | −0.128134 | − | 1.09433i | ||||
\(280\) | 1.48365 | + | 0.149245i | 0.0886650 | + | 0.00891911i | ||||
\(281\) | 9.12634 | 0.544432 | 0.272216 | − | 0.962236i | \(-0.412244\pi\) | ||||
0.272216 | + | 0.962236i | \(0.412244\pi\) | |||||||
\(282\) | −13.0601 | − | 11.6201i | −0.777715 | − | 0.691966i | ||||
\(283\) | 30.4398 | 1.80946 | 0.904730 | − | 0.425984i | \(-0.140072\pi\) | ||||
0.904730 | + | 0.425984i | \(0.140072\pi\) | |||||||
\(284\) | − | 14.5288i | − | 0.862126i | ||||||
\(285\) | −11.8798 | + | 10.9221i | −0.703699 | + | 0.646969i | ||||
\(286\) | − | 18.2873i | − | 1.08135i | ||||||
\(287\) | 1.69579i | 0.100099i | ||||||||
\(288\) | −0.348885 | − | 2.97964i | −0.0205582 | − | 0.175577i | ||||
\(289\) | 16.3429 | 0.961347 | ||||||||
\(290\) | −2.01923 | + | 20.0732i | −0.118573 | + | 1.17874i | ||||
\(291\) | −1.35444 | − | 1.20510i | −0.0793985 | − | 0.0706442i | ||||
\(292\) | − | 4.84561i | − | 0.283568i | ||||||
\(293\) | 27.1711i | 1.58735i | 0.608341 | + | 0.793676i | \(0.291835\pi\) | ||||
−0.608341 | + | 0.793676i | \(0.708165\pi\) | |||||||
\(294\) | −8.48258 | − | 7.54731i | −0.494714 | − | 0.440168i | ||||
\(295\) | 1.52428 | − | 15.1529i | 0.0887472 | − | 0.882238i | ||||
\(296\) | 2.21928 | 0.128993 | ||||||||
\(297\) | −14.6788 | + | 20.9771i | −0.851748 | + | 1.21721i | ||||
\(298\) | 2.91067 | 0.168611 | ||||||||
\(299\) | 17.2833 | + | 4.25539i | 0.999520 | + | 0.246095i | ||||
\(300\) | −5.19383 | − | 6.92995i | −0.299866 | − | 0.400101i | ||||
\(301\) | −2.37752 | −0.137038 | ||||||||
\(302\) | −5.50476 | −0.316763 | ||||||||
\(303\) | 13.3298 | − | 14.9816i | 0.765775 | − | 0.860671i | ||||
\(304\) | − | 4.16671i | − | 0.238977i | ||||||
\(305\) | −2.06207 | + | 20.4990i | −0.118074 | + | 1.17377i | ||||
\(306\) | −2.41534 | + | 0.282811i | −0.138076 | + | 0.0161672i | ||||
\(307\) | − | 8.27262i | − | 0.472144i | −0.971736 | − | 0.236072i | \(-0.924140\pi\) | ||
0.971736 | − | 0.236072i | \(-0.0758601\pi\) | |||||||
\(308\) | 3.28577 | 0.187224 | ||||||||
\(309\) | −18.4875 | − | 16.4491i | −1.05171 | − | 0.935755i | ||||
\(310\) | 13.6485 | + | 1.37294i | 0.775180 | + | 0.0779780i | ||||
\(311\) | − | 0.256130i | − | 0.0145238i | −0.999974 | − | 0.00726189i | \(-0.997688\pi\) | ||
0.999974 | − | 0.00726189i | \(-0.00231155\pi\) | |||||||
\(312\) | 4.27309 | − | 4.80262i | 0.241916 | − | 0.271895i | ||||
\(313\) | −7.18955 | −0.406377 | −0.203189 | − | 0.979140i | \(-0.565130\pi\) | ||||
−0.203189 | + | 0.979140i | \(0.565130\pi\) | |||||||
\(314\) | 8.36290 | 0.471946 | ||||||||
\(315\) | −0.0729252 | − | 4.47281i | −0.00410887 | − | 0.252015i | ||||
\(316\) | 11.5161i | 0.647830i | ||||||||
\(317\) | 16.3815 | 0.920075 | 0.460037 | − | 0.887900i | \(-0.347836\pi\) | ||||
0.460037 | + | 0.887900i | \(0.347836\pi\) | |||||||
\(318\) | 12.2364 | − | 13.7528i | 0.686185 | − | 0.771218i | ||||
\(319\) | 44.4553i | 2.48902i | ||||||||
\(320\) | 2.22484 | + | 0.223804i | 0.124372 | + | 0.0125110i | ||||
\(321\) | −12.0483 | + | 13.5413i | −0.672471 | + | 0.755804i | ||||
\(322\) | −0.764590 | + | 3.10539i | −0.0426089 | + | 0.173057i | ||||
\(323\) | −3.37759 | −0.187934 | ||||||||
\(324\) | −8.75656 | + | 2.07911i | −0.486475 | + | 0.115506i | ||||
\(325\) | 3.69607 | − | 18.1854i | 0.205021 | − | 1.00875i | ||||
\(326\) | 12.1701i | 0.674038i | ||||||||
\(327\) | −8.06943 | + | 9.06940i | −0.446240 | + | 0.501539i | ||||
\(328\) | 2.54295i | 0.140411i | ||||||||
\(329\) | 6.73042 | 0.371060 | ||||||||
\(330\) | −12.9157 | − | 14.0482i | −0.710986 | − | 0.773330i | ||||
\(331\) | 22.0597 | 1.21251 | 0.606255 | − | 0.795271i | \(-0.292671\pi\) | ||||
0.606255 | + | 0.795271i | \(0.292671\pi\) | |||||||
\(332\) | 13.5358i | 0.742873i | ||||||||
\(333\) | −0.774274 | − | 6.61267i | −0.0424300 | − | 0.362372i | ||||
\(334\) | −14.3712 | −0.786357 | ||||||||
\(335\) | −17.6887 | − | 1.77936i | −0.966434 | − | 0.0972169i | ||||
\(336\) | 0.862914 | + | 0.767771i | 0.0470758 | + | 0.0418853i | ||||
\(337\) | −11.1835 | −0.609203 | −0.304601 | − | 0.952480i | \(-0.598523\pi\) | ||||
−0.304601 | + | 0.952480i | \(0.598523\pi\) | |||||||
\(338\) | 0.774832 | 0.0421453 | ||||||||
\(339\) | 16.9131 | − | 19.0090i | 0.918596 | − | 1.03243i | ||||
\(340\) | 0.181419 | − | 1.80349i | 0.00983881 | − | 0.0978077i | ||||
\(341\) | 30.2267 | 1.63687 | ||||||||
\(342\) | −12.4153 | + | 1.45370i | −0.671343 | + | 0.0786072i | ||||
\(343\) | 9.03944 | 0.488084 | ||||||||
\(344\) | −3.56526 | −0.192226 | ||||||||
\(345\) | 16.2824 | − | 8.93767i | 0.876617 | − | 0.481188i | ||||
\(346\) | −18.2848 | −0.982999 | ||||||||
\(347\) | −13.1611 | −0.706525 | −0.353262 | − | 0.935524i | \(-0.614928\pi\) | ||||
−0.353262 | + | 0.935524i | \(0.614928\pi\) | |||||||
\(348\) | −10.3877 | + | 11.6749i | −0.556837 | + | 0.625840i | ||||
\(349\) | 7.16860 | 0.383726 | 0.191863 | − | 0.981422i | \(-0.438547\pi\) | ||||
0.191863 | + | 0.981422i | \(0.438547\pi\) | |||||||
\(350\) | 3.26748 | + | 0.664093i | 0.174654 | + | 0.0354973i | ||||
\(351\) | −15.8009 | − | 11.0567i | −0.843391 | − | 0.590165i | ||||
\(352\) | 4.92726 | 0.262624 | ||||||||
\(353\) | −29.9100 | −1.59195 | −0.795976 | − | 0.605329i | \(-0.793042\pi\) | ||||
−0.795976 | + | 0.605329i | \(0.793042\pi\) | |||||||
\(354\) | 7.84146 | − | 8.81319i | 0.416769 | − | 0.468416i | ||||
\(355\) | 3.25160 | − | 32.3243i | 0.172577 | − | 1.71559i | ||||
\(356\) | −12.5342 | −0.664312 | ||||||||
\(357\) | 0.622366 | − | 0.699490i | 0.0329391 | − | 0.0370209i | ||||
\(358\) | − | 5.02306i | − | 0.265477i | ||||||
\(359\) | −13.4801 | −0.711452 | −0.355726 | − | 0.934590i | \(-0.615766\pi\) | ||||
−0.355726 | + | 0.934590i | \(0.615766\pi\) | |||||||
\(360\) | −0.109357 | − | 6.70731i | −0.00576360 | − | 0.353506i | ||||
\(361\) | 1.63855 | 0.0862395 | ||||||||
\(362\) | − | 0.342921i | − | 0.0180235i | ||||||
\(363\) | −17.1816 | − | 15.2872i | −0.901801 | − | 0.802370i | ||||
\(364\) | 2.47500i | 0.129725i | ||||||||
\(365\) | 1.08447 | − | 10.7807i | 0.0567636 | − | 0.564288i | ||||
\(366\) | −10.6080 | + | 11.9226i | −0.554489 | + | 0.623202i | ||||
\(367\) | 11.3468 | 0.592297 | 0.296148 | − | 0.955142i | \(-0.404298\pi\) | ||||
0.296148 | + | 0.955142i | \(0.404298\pi\) | |||||||
\(368\) | −1.14656 | + | 4.65676i | −0.0597685 | + | 0.242750i | ||||
\(369\) | 7.57710 | − | 0.887198i | 0.394448 | − | 0.0461857i | ||||
\(370\) | 4.93755 | + | 0.496684i | 0.256691 | + | 0.0258214i | ||||
\(371\) | 7.08741i | 0.367960i | ||||||||
\(372\) | 7.93816 | + | 7.06292i | 0.411574 | + | 0.366195i | ||||
\(373\) | −25.0799 | −1.29859 | −0.649295 | − | 0.760537i | \(-0.724936\pi\) | ||||
−0.649295 | + | 0.760537i | \(0.724936\pi\) | |||||||
\(374\) | − | 3.99410i | − | 0.206530i | ||||||
\(375\) | −10.0045 | − | 16.5804i | −0.516629 | − | 0.856209i | ||||
\(376\) | 10.0928 | 0.520494 | ||||||||
\(377\) | −33.4858 | −1.72461 | ||||||||
\(378\) | 1.98663 | − | 2.83904i | 0.102181 | − | 0.146024i | ||||
\(379\) | 19.4678i | 0.999992i | 0.866028 | + | 0.499996i | \(0.166665\pi\) | ||||
−0.866028 | + | 0.499996i | \(0.833335\pi\) | |||||||
\(380\) | 0.932526 | − | 9.27026i | 0.0478376 | − | 0.475554i | ||||
\(381\) | −2.11812 | + | 2.38060i | −0.108515 | + | 0.121962i | ||||
\(382\) | −26.5716 | −1.35952 | ||||||||
\(383\) | − | 26.1779i | − | 1.33763i | −0.743429 | − | 0.668815i | \(-0.766802\pi\) | ||
0.743429 | − | 0.668815i | \(-0.233198\pi\) | |||||||
\(384\) | 1.29400 | + | 1.15133i | 0.0660343 | + | 0.0587535i | ||||
\(385\) | 7.31032 | + | 0.735370i | 0.372569 | + | 0.0374779i | ||||
\(386\) | 0.121042i | 0.00616089i | ||||||||
\(387\) | 1.24387 | + | 10.6232i | 0.0632293 | + | 0.540008i | ||||
\(388\) | 1.04670 | 0.0531383 | ||||||||
\(389\) | −22.4773 | −1.13965 | −0.569823 | − | 0.821768i | \(-0.692988\pi\) | ||||
−0.569823 | + | 0.821768i | \(0.692988\pi\) | |||||||
\(390\) | 10.5818 | − | 9.72873i | 0.535830 | − | 0.492633i | ||||
\(391\) | 3.77483 | + | 0.929415i | 0.190901 | + | 0.0470026i | ||||
\(392\) | 6.55530 | 0.331093 | ||||||||
\(393\) | −7.59535 | + | 8.53657i | −0.383135 | + | 0.430613i | ||||
\(394\) | 4.06795 | 0.204940 | ||||||||
\(395\) | −2.57734 | + | 25.6214i | −0.129680 | + | 1.28915i | ||||
\(396\) | −1.71905 | − | 14.6815i | −0.0863853 | − | 0.737772i | ||||
\(397\) | − | 11.5042i | − | 0.577380i | −0.957423 | − | 0.288690i | \(-0.906780\pi\) | ||
0.957423 | − | 0.288690i | \(-0.0932197\pi\) | |||||||
\(398\) | 3.82379i | 0.191669i | ||||||||
\(399\) | 3.19908 | − | 3.59551i | 0.160154 | − | 0.180001i | ||||
\(400\) | 4.89982 | + | 0.995856i | 0.244991 | + | 0.0497928i | ||||
\(401\) | 9.84524 | 0.491648 | 0.245824 | − | 0.969315i | \(-0.420942\pi\) | ||||
0.245824 | + | 0.969315i | \(0.420942\pi\) | |||||||
\(402\) | −10.2880 | − | 9.15367i | −0.513119 | − | 0.456544i | ||||
\(403\) | 22.7682i | 1.13416i | ||||||||
\(404\) | 11.5777i | 0.576013i | ||||||||
\(405\) | −19.9473 | + | 2.66592i | −0.991187 | + | 0.132471i | ||||
\(406\) | − | 6.01659i | − | 0.298598i | ||||||
\(407\) | 10.9350 | 0.542027 | ||||||||
\(408\) | 0.933283 | − | 1.04894i | 0.0462044 | − | 0.0519301i | ||||
\(409\) | 18.8120 | 0.930195 | 0.465098 | − | 0.885259i | \(-0.346019\pi\) | ||||
0.465098 | + | 0.885259i | \(0.346019\pi\) | |||||||
\(410\) | −0.569123 | + | 5.65766i | −0.0281070 | + | 0.279412i | ||||
\(411\) | −19.0477 | + | 21.4081i | −0.939552 | + | 1.05598i | ||||
\(412\) | 14.2870 | 0.703871 | ||||||||
\(413\) | 4.54182i | 0.223489i | ||||||||
\(414\) | 14.2755 | + | 1.79166i | 0.701603 | + | 0.0880553i | ||||
\(415\) | −3.02936 | + | 30.1149i | −0.148706 | + | 1.47828i | ||||
\(416\) | 3.71145i | 0.181969i | ||||||||
\(417\) | −7.07706 | − | 6.29676i | −0.346565 | − | 0.308354i | ||||
\(418\) | − | 20.5304i | − | 1.00418i | ||||||
\(419\) | 8.48762 | 0.414647 | 0.207324 | − | 0.978272i | \(-0.433525\pi\) | ||||
0.207324 | + | 0.978272i | \(0.433525\pi\) | |||||||
\(420\) | 1.74801 | + | 1.90129i | 0.0852944 | + | 0.0927735i | ||||
\(421\) | − | 30.8277i | − | 1.50245i | −0.660045 | − | 0.751226i | \(-0.729463\pi\) | ||
0.660045 | − | 0.751226i | \(-0.270537\pi\) | |||||||
\(422\) | 10.9491 | 0.532992 | ||||||||
\(423\) | −3.52121 | − | 30.0728i | −0.171207 | − | 1.46219i | ||||
\(424\) | 10.6281i | 0.516146i | ||||||||
\(425\) | 0.807255 | − | 3.97186i | 0.0391576 | − | 0.192664i | ||||
\(426\) | 16.7274 | − | 18.8003i | 0.810446 | − | 0.910878i | ||||
\(427\) | − | 6.14422i | − | 0.297340i | ||||||
\(428\) | − | 10.4647i | − | 0.505830i | ||||||
\(429\) | 21.0546 | − | 23.6638i | 1.01653 | − | 1.14250i | ||||
\(430\) | −7.93214 | − | 0.797920i | −0.382522 | − | 0.0384791i | ||||
\(431\) | −27.9563 | −1.34661 | −0.673303 | − | 0.739367i | \(-0.735125\pi\) | ||||
−0.673303 | + | 0.739367i | \(0.735125\pi\) | |||||||
\(432\) | 2.97909 | − | 4.25735i | 0.143332 | − | 0.204832i | ||||
\(433\) | −37.3143 | −1.79321 | −0.896606 | − | 0.442829i | \(-0.853975\pi\) | ||||
−0.896606 | + | 0.442829i | \(0.853975\pi\) | |||||||
\(434\) | −4.09088 | −0.196369 | ||||||||
\(435\) | −25.7238 | + | 23.6500i | −1.23336 | + | 1.13393i | ||||
\(436\) | − | 7.00879i | − | 0.335660i | ||||||
\(437\) | 19.4034 | + | 4.77737i | 0.928188 | + | 0.228533i | ||||
\(438\) | 5.57889 | − | 6.27023i | 0.266570 | − | 0.299603i | ||||
\(439\) | −24.1100 | −1.15071 | −0.575354 | − | 0.817904i | \(-0.695136\pi\) | ||||
−0.575354 | + | 0.817904i | \(0.695136\pi\) | |||||||
\(440\) | 10.9624 | + | 1.10274i | 0.522610 | + | 0.0525711i | ||||
\(441\) | −2.28705 | − | 19.5325i | −0.108907 | − | 0.930118i | ||||
\(442\) | 3.00855 | 0.143102 | ||||||||
\(443\) | 14.5534 | 0.691451 | 0.345726 | − | 0.938336i | \(-0.387633\pi\) | ||||
0.345726 | + | 0.938336i | \(0.387633\pi\) | |||||||
\(444\) | 2.87176 | + | 2.55512i | 0.136288 | + | 0.121261i | ||||
\(445\) | −27.8866 | − | 2.80521i | −1.32195 | − | 0.132980i | ||||
\(446\) | − | 3.05235i | − | 0.144533i | ||||||
\(447\) | 3.76642 | + | 3.35114i | 0.178146 | + | 0.158504i | ||||
\(448\) | −0.666856 | −0.0315060 | ||||||||
\(449\) | 25.8545i | 1.22015i | 0.792344 | + | 0.610075i | \(0.208861\pi\) | ||||
−0.792344 | + | 0.610075i | \(0.791139\pi\) | |||||||
\(450\) | 1.25782 | − | 14.9472i | 0.0592943 | − | 0.704616i | ||||
\(451\) | 12.5298i | 0.590005i | ||||||||
\(452\) | 14.6901i | 0.690965i | ||||||||
\(453\) | −7.12317 | − | 6.33778i | −0.334676 | − | 0.297775i | ||||
\(454\) | 16.8065i | 0.788767i | ||||||||
\(455\) | −0.553915 | + | 5.50648i | −0.0259680 | + | 0.258148i | ||||
\(456\) | 4.79725 | − | 5.39173i | 0.224652 | − | 0.252491i | ||||
\(457\) | 23.6100 | 1.10443 | 0.552214 | − | 0.833702i | \(-0.313783\pi\) | ||||
0.552214 | + | 0.833702i | \(0.313783\pi\) | |||||||
\(458\) | − | 10.0750i | − | 0.470774i | ||||||
\(459\) | −3.45106 | − | 2.41489i | −0.161082 | − | 0.112718i | ||||
\(460\) | −3.59311 | + | 10.1039i | −0.167530 | + | 0.471099i | ||||
\(461\) | 38.3275i | 1.78509i | 0.450959 | + | 0.892545i | \(0.351082\pi\) | ||||
−0.450959 | + | 0.892545i | \(0.648918\pi\) | |||||||
\(462\) | 4.25180 | + | 3.78301i | 0.197812 | + | 0.176001i | ||||
\(463\) | − | 1.86463i | − | 0.0866567i | −0.999061 | − | 0.0433284i | \(-0.986204\pi\) | ||
0.999061 | − | 0.0433284i | \(-0.0137962\pi\) | |||||||
\(464\) | − | 9.02232i | − | 0.418851i | ||||||
\(465\) | 16.0804 | + | 17.4905i | 0.745712 | + | 0.811100i | ||||
\(466\) | −13.0601 | −0.604996 | ||||||||
\(467\) | − | 22.7789i | − | 1.05408i | −0.849840 | − | 0.527040i | \(-0.823302\pi\) | ||
0.849840 | − | 0.527040i | \(-0.176698\pi\) | |||||||
\(468\) | 11.0588 | − | 1.29487i | 0.511193 | − | 0.0598553i | ||||
\(469\) | 5.30186 | 0.244817 | ||||||||
\(470\) | 22.4548 | + | 2.25880i | 1.03576 | + | 0.104191i | ||||
\(471\) | 10.8216 | + | 9.62845i | 0.498634 | + | 0.443655i | ||||
\(472\) | 6.81080i | 0.313492i | ||||||||
\(473\) | −17.5670 | −0.807731 | ||||||||
\(474\) | −13.2588 | + | 14.9018i | −0.608996 | + | 0.684464i | ||||
\(475\) | 4.14944 | − | 20.4161i | 0.190389 | − | 0.936756i | ||||
\(476\) | 0.540563i | 0.0247767i | ||||||||
\(477\) | 31.6679 | − | 3.70798i | 1.44998 | − | 0.169777i | ||||
\(478\) | 14.5163i | 0.663962i | ||||||||
\(479\) | 22.7286 | 1.03849 | 0.519247 | − | 0.854624i | \(-0.326212\pi\) | ||||
0.519247 | + | 0.854624i | \(0.326212\pi\) | |||||||
\(480\) | 2.62128 | + | 2.85112i | 0.119644 | + | 0.130135i | ||||
\(481\) | 8.23675i | 0.375563i | ||||||||
\(482\) | − | 7.90101i | − | 0.359881i | ||||||
\(483\) | −4.56470 | + | 3.13809i | −0.207701 | + | 0.142788i | ||||
\(484\) | 13.2779 | 0.603540 | ||||||||
\(485\) | 2.32875 | + | 0.234257i | 0.105743 | + | 0.0106370i | ||||
\(486\) | −13.7247 | − | 7.39131i | −0.622567 | − | 0.335277i | ||||
\(487\) | − | 9.28752i | − | 0.420858i | −0.977609 | − | 0.210429i | \(-0.932514\pi\) | ||
0.977609 | − | 0.210429i | \(-0.0674860\pi\) | |||||||
\(488\) | − | 9.21371i | − | 0.417085i | ||||||
\(489\) | −14.0117 | + | 15.7481i | −0.633633 | + | 0.712154i | ||||
\(490\) | 14.5845 | + | 1.46710i | 0.658860 | + | 0.0662770i | ||||
\(491\) | 16.4543i | 0.742571i | 0.928519 | + | 0.371286i | \(0.121083\pi\) | ||||
−0.928519 | + | 0.371286i | \(0.878917\pi\) | |||||||
\(492\) | −2.92778 | + | 3.29059i | −0.131994 | + | 0.148351i | ||||
\(493\) | −7.31361 | −0.329389 | ||||||||
\(494\) | 15.4645 | 0.695781 | ||||||||
\(495\) | −0.538828 | − | 33.0487i | −0.0242185 | − | 1.48543i | ||||
\(496\) | −6.13458 | −0.275451 | ||||||||
\(497\) | 9.68862i | 0.434594i | ||||||||
\(498\) | −15.5841 | + | 17.5153i | −0.698342 | + | 0.784881i | ||||
\(499\) | 14.8139 | 0.663163 | 0.331582 | − | 0.943427i | \(-0.392418\pi\) | ||||
0.331582 | + | 0.943427i | \(0.392418\pi\) | |||||||
\(500\) | 10.6784 | + | 3.31222i | 0.477555 | + | 0.148127i | ||||
\(501\) | −18.5964 | − | 16.5460i | −0.830824 | − | 0.739219i | ||||
\(502\) | −6.40105 | −0.285693 | ||||||||
\(503\) | 6.33019i | 0.282249i | 0.989992 | + | 0.141125i | \(0.0450718\pi\) | ||||
−0.989992 | + | 0.141125i | \(0.954928\pi\) | |||||||
\(504\) | 0.232656 | + | 1.98699i | 0.0103633 | + | 0.0885078i | ||||
\(505\) | −2.59114 | + | 25.7586i | −0.115304 | + | 1.14624i | ||||
\(506\) | −5.64939 | + | 22.9451i | −0.251146 | + | 1.02003i | ||||
\(507\) | 1.00263 | + | 0.892086i | 0.0445286 | + | 0.0396190i | ||||
\(508\) | − | 1.83972i | − | 0.0816245i | ||||||
\(509\) | 3.11552i | 0.138093i | 0.997613 | + | 0.0690465i | \(0.0219957\pi\) | ||||
−0.997613 | + | 0.0690465i | \(0.978004\pi\) | |||||||
\(510\) | 2.31116 | − | 2.12484i | 0.102340 | − | 0.0940896i | ||||
\(511\) | 3.23133i | 0.142945i | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −17.7391 | − | 12.4130i | −0.783201 | − | 0.548047i | ||||
\(514\) | 14.7993 | 0.652767 | ||||||||
\(515\) | 31.7864 | + | 3.19750i | 1.40067 | + | 0.140898i | ||||
\(516\) | −4.61346 | − | 4.10479i | −0.203096 | − | 0.180703i | ||||
\(517\) | 49.7297 | 2.18711 | ||||||||
\(518\) | −1.47994 | −0.0650250 | ||||||||
\(519\) | −23.6606 | − | 21.0519i | −1.03859 | − | 0.924074i | ||||
\(520\) | −0.830637 | + | 8.25737i | −0.0364258 | + | 0.362110i | ||||
\(521\) | 4.59001 | 0.201092 | 0.100546 | − | 0.994932i | \(-0.467941\pi\) | ||||
0.100546 | + | 0.994932i | \(0.467941\pi\) | |||||||
\(522\) | −26.8833 | + | 3.14775i | −1.17665 | + | 0.137773i | ||||
\(523\) | −25.4462 | −1.11269 | −0.556343 | − | 0.830953i | \(-0.687796\pi\) | ||||
−0.556343 | + | 0.830953i | \(0.687796\pi\) | |||||||
\(524\) | − | 6.59703i | − | 0.288192i | ||||||
\(525\) | 3.46354 | + | 4.62128i | 0.151161 | + | 0.201689i | ||||
\(526\) | − | 1.33588i | − | 0.0582470i | ||||||
\(527\) | 4.97277i | 0.216617i | ||||||||
\(528\) | 6.37589 | + | 5.67289i | 0.277475 | + | 0.246881i | ||||
\(529\) | −20.3708 | − | 10.6785i | −0.885687 | − | 0.464282i | ||||
\(530\) | −2.37861 | + | 23.6458i | −0.103320 | + | 1.02711i | ||||
\(531\) | 20.2937 | − | 2.37618i | 0.880674 | − | 0.103118i | ||||
\(532\) | 2.77860i | 0.120467i | ||||||||
\(533\) | −9.43804 | −0.408807 | ||||||||
\(534\) | −16.2193 | − | 14.4310i | −0.701878 | − | 0.624490i | ||||
\(535\) | 2.34204 | − | 23.2823i | 0.101255 | − | 1.00658i | ||||
\(536\) | 7.95053 | 0.343411 | ||||||||
\(537\) | 5.78319 | − | 6.49985i | 0.249563 | − | 0.280489i | ||||
\(538\) | − | 12.2843i | − | 0.529615i | ||||||
\(539\) | 32.2997 | 1.39125 | ||||||||
\(540\) | 7.58081 | − | 8.80518i | 0.326226 | − | 0.378915i | ||||
\(541\) | 21.7426 | 0.934787 | 0.467394 | − | 0.884049i | \(-0.345193\pi\) | ||||
0.467394 | + | 0.884049i | \(0.345193\pi\) | |||||||
\(542\) | 19.5706 | 0.840630 | ||||||||
\(543\) | 0.394814 | − | 0.443740i | 0.0169431 | − | 0.0190427i | ||||
\(544\) | 0.810614i | 0.0347548i | ||||||||
\(545\) | 1.56860 | − | 15.5934i | 0.0671913 | − | 0.667950i | ||||
\(546\) | −2.84954 | + | 3.20266i | −0.121949 | + | 0.137061i | ||||
\(547\) | 23.9240i | 1.02292i | 0.859308 | + | 0.511459i | \(0.170895\pi\) | ||||
−0.859308 | + | 0.511459i | \(0.829105\pi\) | |||||||
\(548\) | − | 16.5441i | − | 0.706728i | ||||||
\(549\) | −27.4536 | + | 3.21452i | −1.17169 | + | 0.137193i | ||||
\(550\) | 24.1427 | + | 4.90684i | 1.02945 | + | 0.209228i | ||||
\(551\) | −37.5934 | −1.60153 | ||||||||
\(552\) | −6.84511 | + | 4.70579i | −0.291347 | + | 0.200292i | ||||
\(553\) | − | 7.67957i | − | 0.326569i | ||||||
\(554\) | 13.9776i | 0.593850i | ||||||||
\(555\) | 5.81735 | + | 6.32745i | 0.246933 | + | 0.268585i | ||||
\(556\) | 5.46913 | 0.231943 | ||||||||
\(557\) | 25.3753i | 1.07519i | 0.843204 | + | 0.537593i | \(0.180666\pi\) | ||||
−0.843204 | + | 0.537593i | \(0.819334\pi\) | |||||||
\(558\) | 2.14026 | + | 18.2789i | 0.0906045 | + | 0.773806i | ||||
\(559\) | − | 13.2323i | − | 0.559666i | ||||||
\(560\) | −1.48365 | − | 0.149245i | −0.0626956 | − | 0.00630676i | ||||
\(561\) | 4.59853 | − | 5.16838i | 0.194150 | − | 0.218209i | ||||
\(562\) | −9.12634 | −0.384971 | ||||||||
\(563\) | − | 10.1241i | − | 0.426681i | −0.976978 | − | 0.213340i | \(-0.931566\pi\) | ||
0.976978 | − | 0.213340i | \(-0.0684343\pi\) | |||||||
\(564\) | 13.0601 | + | 11.6201i | 0.549928 | + | 0.489294i | ||||
\(565\) | −3.28771 | + | 32.6831i | −0.138315 | + | 1.37499i | ||||
\(566\) | −30.4398 | −1.27948 | ||||||||
\(567\) | 5.83937 | − | 1.38647i | 0.245230 | − | 0.0582261i | ||||
\(568\) | 14.5288i | 0.609615i | ||||||||
\(569\) | 5.98029 | 0.250707 | 0.125353 | − | 0.992112i | \(-0.459994\pi\) | ||||
0.125353 | + | 0.992112i | \(0.459994\pi\) | |||||||
\(570\) | 11.8798 | − | 10.9221i | 0.497590 | − | 0.457476i | ||||
\(571\) | − | 15.5442i | − | 0.650504i | −0.945627 | − | 0.325252i | \(-0.894551\pi\) | ||
0.945627 | − | 0.325252i | \(-0.105449\pi\) | |||||||
\(572\) | 18.2873i | 0.764629i | ||||||||
\(573\) | −34.3837 | − | 30.5926i | −1.43640 | − | 1.27802i | ||||
\(574\) | − | 1.69579i | − | 0.0707807i | ||||||
\(575\) | −10.2554 | + | 21.6755i | −0.427679 | + | 0.903930i | ||||
\(576\) | 0.348885 | + | 2.97964i | 0.0145369 | + | 0.124152i | ||||
\(577\) | 2.43133i | 0.101218i | 0.998719 | + | 0.0506088i | \(0.0161162\pi\) | ||||
−0.998719 | + | 0.0506088i | \(0.983884\pi\) | |||||||
\(578\) | −16.3429 | −0.679775 | ||||||||
\(579\) | −0.139359 | + | 0.156629i | −0.00579158 | + | 0.00650928i | ||||
\(580\) | 2.01923 | − | 20.0732i | 0.0838440 | − | 0.833495i | ||||
\(581\) | − | 9.02642i | − | 0.374479i | ||||||
\(582\) | 1.35444 | + | 1.20510i | 0.0561432 | + | 0.0499530i | ||||
\(583\) | 52.3674i | 2.16884i | ||||||||
\(584\) | 4.84561i | 0.200513i | ||||||||
\(585\) | 24.8938 | − | 0.405871i | 1.02923 | − | 0.0167807i | ||||
\(586\) | − | 27.1711i | − | 1.12243i | ||||||
\(587\) | −25.0136 | −1.03242 | −0.516211 | − | 0.856461i | \(-0.672658\pi\) | ||||
−0.516211 | + | 0.856461i | \(0.672658\pi\) | |||||||
\(588\) | 8.48258 | + | 7.54731i | 0.349816 | + | 0.311246i | ||||
\(589\) | 25.5610i | 1.05322i | ||||||||
\(590\) | −1.52428 | + | 15.1529i | −0.0627538 | + | 0.623836i | ||||
\(591\) | 5.26393 | + | 4.68354i | 0.216529 | + | 0.192655i | ||||
\(592\) | −2.21928 | −0.0912120 | ||||||||
\(593\) | 12.0918 | 0.496551 | 0.248276 | − | 0.968689i | \(-0.420136\pi\) | ||||
0.248276 | + | 0.968689i | \(0.420136\pi\) | |||||||
\(594\) | 14.6788 | − | 20.9771i | 0.602277 | − | 0.860699i | ||||
\(595\) | −0.120980 | + | 1.20267i | −0.00495970 | + | 0.0493045i | ||||
\(596\) | −2.91067 | −0.119226 | ||||||||
\(597\) | −4.40244 | + | 4.94799i | −0.180180 | + | 0.202508i | ||||
\(598\) | −17.2833 | − | 4.25539i | −0.706767 | − | 0.174016i | ||||
\(599\) | − | 44.0064i | − | 1.79805i | −0.437892 | − | 0.899027i | \(-0.644275\pi\) | ||
0.437892 | − | 0.899027i | \(-0.355725\pi\) | |||||||
\(600\) | 5.19383 | + | 6.92995i | 0.212037 | + | 0.282914i | ||||
\(601\) | −17.6495 | −0.719937 | −0.359968 | − | 0.932964i | \(-0.617213\pi\) | ||||
−0.359968 | + | 0.932964i | \(0.617213\pi\) | |||||||
\(602\) | 2.37752 | 0.0969004 | ||||||||
\(603\) | −2.77382 | − | 23.6897i | −0.112959 | − | 0.964721i | ||||
\(604\) | 5.50476 | 0.223985 | ||||||||
\(605\) | 29.5412 | + | 2.97165i | 1.20102 | + | 0.120815i | ||||
\(606\) | −13.3298 | + | 14.9816i | −0.541485 | + | 0.608586i | ||||
\(607\) | 16.4500i | 0.667686i | 0.942629 | + | 0.333843i | \(0.108346\pi\) | ||||
−0.942629 | + | 0.333843i | \(0.891654\pi\) | |||||||
\(608\) | 4.16671i | 0.168982i | ||||||||
\(609\) | 6.92707 | − | 7.78548i | 0.280699 | − | 0.315484i | ||||
\(610\) | 2.06207 | − | 20.4990i | 0.0834906 | − | 0.829981i | ||||
\(611\) | 37.4587i | 1.51542i | ||||||||
\(612\) | 2.41534 | − | 0.282811i | 0.0976343 | − | 0.0114320i | ||||
\(613\) | 21.9260 | 0.885583 | 0.442792 | − | 0.896625i | \(-0.353988\pi\) | ||||
0.442792 | + | 0.896625i | \(0.353988\pi\) | |||||||
\(614\) | 8.27262i | 0.333856i | ||||||||
\(615\) | −7.25028 | + | 6.66578i | −0.292359 | + | 0.268790i | ||||
\(616\) | −3.28577 | −0.132388 | ||||||||
\(617\) | − | 3.85770i | − | 0.155305i | −0.996980 | − | 0.0776526i | \(-0.975257\pi\) | ||
0.996980 | − | 0.0776526i | \(-0.0247425\pi\) | |||||||
\(618\) | 18.4875 | + | 16.4491i | 0.743674 | + | 0.661678i | ||||
\(619\) | 35.4506i | 1.42488i | 0.701732 | + | 0.712441i | \(0.252410\pi\) | ||||
−0.701732 | + | 0.712441i | \(0.747590\pi\) | |||||||
\(620\) | −13.6485 | − | 1.37294i | −0.548135 | − | 0.0551388i | ||||
\(621\) | 16.4097 | + | 18.7542i | 0.658500 | + | 0.752580i | ||||
\(622\) | 0.256130i | 0.0102699i | ||||||||
\(623\) | 8.35852 | 0.334877 | ||||||||
\(624\) | −4.27309 | + | 4.80262i | −0.171061 | + | 0.192259i | ||||
\(625\) | 23.0165 | + | 9.75904i | 0.920662 | + | 0.390362i | ||||
\(626\) | 7.18955 | 0.287352 | ||||||||
\(627\) | 23.6373 | − | 26.5665i | 0.943983 | − | 1.06096i | ||||
\(628\) | −8.36290 | −0.333716 | ||||||||
\(629\) | 1.79898i | 0.0717301i | ||||||||
\(630\) | 0.0729252 | + | 4.47281i | 0.00290541 | + | 0.178201i | ||||
\(631\) | − | 28.1979i | − | 1.12254i | −0.827632 | − | 0.561271i | \(-0.810312\pi\) | ||
0.827632 | − | 0.561271i | \(-0.189688\pi\) | |||||||
\(632\) | − | 11.5161i | − | 0.458085i | ||||||
\(633\) | 14.1681 | + | 12.6060i | 0.563132 | + | 0.501043i | ||||
\(634\) | −16.3815 | −0.650591 | ||||||||
\(635\) | 0.411737 | − | 4.09309i | 0.0163393 | − | 0.162429i | ||||
\(636\) | −12.2364 | + | 13.7528i | −0.485206 | + | 0.545333i | ||||
\(637\) | 24.3297i | 0.963976i | ||||||||
\(638\) | − | 44.4553i | − | 1.76000i | ||||||
\(639\) | 43.2907 | − | 5.06888i | 1.71255 | − | 0.200522i | ||||
\(640\) | −2.22484 | − | 0.223804i | −0.0879445 | − | 0.00884663i | ||||
\(641\) | 10.3529 | 0.408915 | 0.204457 | − | 0.978875i | \(-0.434457\pi\) | ||||
0.204457 | + | 0.978875i | \(0.434457\pi\) | |||||||
\(642\) | 12.0483 | − | 13.5413i | 0.475509 | − | 0.534434i | ||||
\(643\) | −0.851752 | −0.0335898 | −0.0167949 | − | 0.999859i | \(-0.505346\pi\) | ||||
−0.0167949 | + | 0.999859i | \(0.505346\pi\) | |||||||
\(644\) | 0.764590 | − | 3.10539i | 0.0301290 | − | 0.122370i | ||||
\(645\) | −9.34554 | − | 10.1650i | −0.367980 | − | 0.400247i | ||||
\(646\) | 3.37759 | 0.132889 | ||||||||
\(647\) | 44.6917 | 1.75701 | 0.878505 | − | 0.477732i | \(-0.158541\pi\) | ||||
0.878505 | + | 0.477732i | \(0.158541\pi\) | |||||||
\(648\) | 8.75656 | − | 2.07911i | 0.343990 | − | 0.0816750i | ||||
\(649\) | 33.5586i | 1.31729i | ||||||||
\(650\) | −3.69607 | + | 18.1854i | −0.144972 | + | 0.713291i | ||||
\(651\) | −5.29361 | − | 4.70995i | −0.207473 | − | 0.184598i | ||||
\(652\) | − | 12.1701i | − | 0.476617i | ||||||
\(653\) | 27.2860 | 1.06779 | 0.533893 | − | 0.845552i | \(-0.320729\pi\) | ||||
0.533893 | + | 0.845552i | \(0.320729\pi\) | |||||||
\(654\) | 8.06943 | − | 9.06940i | 0.315539 | − | 0.354642i | ||||
\(655\) | 1.47644 | − | 14.6773i | 0.0576893 | − | 0.573491i | ||||
\(656\) | − | 2.54295i | − | 0.0992857i | ||||||
\(657\) | 14.4382 | − | 1.69056i | 0.563288 | − | 0.0659551i | ||||
\(658\) | −6.73042 | −0.262379 | ||||||||
\(659\) | −8.99528 | −0.350406 | −0.175203 | − | 0.984532i | \(-0.556058\pi\) | ||||
−0.175203 | + | 0.984532i | \(0.556058\pi\) | |||||||
\(660\) | 12.9157 | + | 14.0482i | 0.502743 | + | 0.546827i | ||||
\(661\) | − | 19.4246i | − | 0.755530i | −0.925902 | − | 0.377765i | \(-0.876693\pi\) | ||
0.925902 | − | 0.377765i | \(-0.123307\pi\) | |||||||
\(662\) | −22.0597 | −0.857374 | ||||||||
\(663\) | 3.89307 | + | 3.46383i | 0.151194 | + | 0.134524i | ||||
\(664\) | − | 13.5358i | − | 0.525290i | ||||||
\(665\) | −0.621861 | + | 6.18193i | −0.0241147 | + | 0.239725i | ||||
\(666\) | 0.774274 | + | 6.61267i | 0.0300025 | + | 0.256236i | ||||
\(667\) | 42.0148 | + | 10.3446i | 1.62682 | + | 0.400545i | ||||
\(668\) | 14.3712 | 0.556038 | ||||||||
\(669\) | 3.51426 | − | 3.94975i | 0.135869 | − | 0.152706i | ||||
\(670\) | 17.6887 | + | 1.77936i | 0.683372 | + | 0.0687427i | ||||
\(671\) | − | 45.3983i | − | 1.75258i | ||||||
\(672\) | −0.862914 | − | 0.767771i | −0.0332876 | − | 0.0296174i | ||||
\(673\) | 43.1690i | 1.66404i | 0.554744 | + | 0.832021i | \(0.312816\pi\) | ||||
−0.554744 | + | 0.832021i | \(0.687184\pi\) | |||||||
\(674\) | 11.1835 | 0.430771 | ||||||||
\(675\) | 18.8367 | − | 17.8935i | 0.725026 | − | 0.688721i | ||||
\(676\) | −0.774832 | −0.0298012 | ||||||||
\(677\) | − | 27.0862i | − | 1.04101i | −0.853859 | − | 0.520504i | \(-0.825744\pi\) | ||
0.853859 | − | 0.520504i | \(-0.174256\pi\) | |||||||
\(678\) | −16.9131 | + | 19.0090i | −0.649546 | + | 0.730038i | ||||
\(679\) | −0.698001 | −0.0267868 | ||||||||
\(680\) | −0.181419 | + | 1.80349i | −0.00695709 | + | 0.0691605i | ||||
\(681\) | −19.3498 | + | 21.7476i | −0.741485 | + | 0.833371i | ||||
\(682\) | −30.2267 | −1.15744 | ||||||||
\(683\) | 25.8177 | 0.987886 | 0.493943 | − | 0.869494i | \(-0.335555\pi\) | ||||
0.493943 | + | 0.869494i | \(0.335555\pi\) | |||||||
\(684\) | 12.4153 | − | 1.45370i | 0.474711 | − | 0.0555837i | ||||
\(685\) | 3.70263 | − | 36.8079i | 0.141470 | − | 1.40636i | ||||
\(686\) | −9.03944 | −0.345127 | ||||||||
\(687\) | 11.5996 | − | 13.0371i | 0.442554 | − | 0.497396i | ||||
\(688\) | 3.56526 | 0.135924 | ||||||||
\(689\) | −39.4456 | −1.50276 | ||||||||
\(690\) | −16.2824 | + | 8.93767i | −0.619862 | + | 0.340251i | ||||
\(691\) | −7.66316 | −0.291520 | −0.145760 | − | 0.989320i | \(-0.546563\pi\) | ||||
−0.145760 | + | 0.989320i | \(0.546563\pi\) | |||||||
\(692\) | 18.2848 | 0.695085 | ||||||||
\(693\) | 1.14636 | + | 9.79044i | 0.0435465 | + | 0.371908i | ||||
\(694\) | 13.1611 | 0.499588 | ||||||||
\(695\) | 12.1679 | + | 1.22401i | 0.461556 | + | 0.0464294i | ||||
\(696\) | 10.3877 | − | 11.6749i | 0.393743 | − | 0.442536i | ||||
\(697\) | −2.06135 | −0.0780793 | ||||||||
\(698\) | −7.16860 | −0.271335 | ||||||||
\(699\) | −16.8998 | − | 15.0364i | −0.639207 | − | 0.568730i | ||||
\(700\) | −3.26748 | − | 0.664093i | −0.123499 | − | 0.0251004i | ||||
\(701\) | −19.8123 | −0.748301 | −0.374150 | − | 0.927368i | \(-0.622066\pi\) | ||||
−0.374150 | + | 0.927368i | \(0.622066\pi\) | |||||||
\(702\) | 15.8009 | + | 11.0567i | 0.596367 | + | 0.417310i | ||||
\(703\) | 9.24710i | 0.348761i | ||||||||
\(704\) | −4.92726 | −0.185703 | ||||||||
\(705\) | 26.4559 | + | 28.7757i | 0.996388 | + | 1.08376i | ||||
\(706\) | 29.9100 | 1.12568 | ||||||||
\(707\) | − | 7.72068i | − | 0.290366i | ||||||
\(708\) | −7.84146 | + | 8.81319i | −0.294700 | + | 0.331220i | ||||
\(709\) | − | 32.3675i | − | 1.21559i | −0.794096 | − | 0.607793i | \(-0.792055\pi\) | ||
0.794096 | − | 0.607793i | \(-0.207945\pi\) | |||||||
\(710\) | −3.25160 | + | 32.3243i | −0.122031 | + | 1.21311i | ||||
\(711\) | −34.3138 | + | 4.01779i | −1.28687 | + | 0.150679i | ||||
\(712\) | 12.5342 | 0.469739 | ||||||||
\(713\) | 7.03365 | − | 28.5673i | 0.263412 | − | 1.06985i | ||||
\(714\) | −0.622366 | + | 0.699490i | −0.0232914 | + | 0.0261777i | ||||
\(715\) | −4.09276 | + | 40.6862i | −0.153061 | + | 1.52158i | ||||
\(716\) | 5.02306i | 0.187721i | ||||||||
\(717\) | −16.7131 | + | 18.7842i | −0.624162 | + | 0.701508i | ||||
\(718\) | 13.4801 | 0.503073 | ||||||||
\(719\) | 3.18213i | 0.118673i | 0.998238 | + | 0.0593367i | \(0.0188986\pi\) | ||||
−0.998238 | + | 0.0593367i | \(0.981101\pi\) | |||||||
\(720\) | 0.109357 | + | 6.70731i | 0.00407548 | + | 0.249967i | ||||
\(721\) | −9.52740 | −0.354819 | ||||||||
\(722\) | −1.63855 | −0.0609805 | ||||||||
\(723\) | 9.09666 | − | 10.2239i | 0.338309 | − | 0.380232i | ||||
\(724\) | 0.342921i | 0.0127445i | ||||||||
\(725\) | 8.98493 | − | 44.2078i | 0.333692 | − | 1.64184i | ||||
\(726\) | 17.1816 | + | 15.2872i | 0.637670 | + | 0.567362i | ||||
\(727\) | −11.1704 | −0.414288 | −0.207144 | − | 0.978310i | \(-0.566417\pi\) | ||||
−0.207144 | + | 0.978310i | \(0.566417\pi\) | |||||||
\(728\) | − | 2.47500i | − | 0.0917297i | ||||||
\(729\) | −9.25003 | − | 25.3661i | −0.342594 | − | 0.939484i | ||||
\(730\) | −1.08447 | + | 10.7807i | −0.0401379 | + | 0.399012i | ||||
\(731\) | − | 2.89005i | − | 0.106892i | ||||||
\(732\) | 10.6080 | − | 11.9226i | 0.392083 | − | 0.440671i | ||||
\(733\) | −50.0167 | −1.84741 | −0.923704 | − | 0.383107i | \(-0.874854\pi\) | ||||
−0.923704 | + | 0.383107i | \(0.874854\pi\) | |||||||
\(734\) | −11.3468 | −0.418817 | ||||||||
\(735\) | 17.1833 | + | 18.6900i | 0.633814 | + | 0.689390i | ||||
\(736\) | 1.14656 | − | 4.65676i | 0.0422627 | − | 0.171650i | ||||
\(737\) | 39.1743 | 1.44300 | ||||||||
\(738\) | −7.57710 | + | 0.887198i | −0.278917 | + | 0.0326582i | ||||
\(739\) | −15.4765 | −0.569314 | −0.284657 | − | 0.958629i | \(-0.591880\pi\) | ||||
−0.284657 | + | 0.958629i | \(0.591880\pi\) | |||||||
\(740\) | −4.93755 | − | 0.496684i | −0.181508 | − | 0.0182585i | ||||
\(741\) | 20.0111 | + | 17.8047i | 0.735127 | + | 0.654073i | ||||
\(742\) | − | 7.08741i | − | 0.260187i | ||||||
\(743\) | − | 13.3519i | − | 0.489833i | −0.969544 | − | 0.244917i | \(-0.921239\pi\) | ||
0.969544 | − | 0.244917i | \(-0.0787606\pi\) | |||||||
\(744\) | −7.93816 | − | 7.06292i | −0.291027 | − | 0.258939i | ||||
\(745\) | −6.47578 | − | 0.651421i | −0.237254 | − | 0.0238662i | ||||
\(746\) | 25.0799 | 0.918242 | ||||||||
\(747\) | −40.3318 | + | 4.72243i | −1.47566 | + | 0.172785i | ||||
\(748\) | 3.99410i | 0.146039i | ||||||||
\(749\) | 6.97845i | 0.254987i | ||||||||
\(750\) | 10.0045 | + | 16.5804i | 0.365312 | + | 0.605431i | ||||
\(751\) | − | 46.8490i | − | 1.70955i | −0.519002 | − | 0.854773i | \(-0.673696\pi\) | ||
0.519002 | − | 0.854773i | \(-0.326304\pi\) | |||||||
\(752\) | −10.0928 | −0.368045 | ||||||||
\(753\) | −8.28298 | − | 7.36972i | −0.301849 | − | 0.268567i | ||||
\(754\) | 33.4858 | 1.21948 | ||||||||
\(755\) | 12.2472 | + | 1.23199i | 0.445721 | + | 0.0448366i | ||||
\(756\) | −1.98663 | + | 2.83904i | −0.0722529 | + | 0.103255i | ||||
\(757\) | −23.6532 | −0.859692 | −0.429846 | − | 0.902902i | \(-0.641432\pi\) | ||||
−0.429846 | + | 0.902902i | \(0.641432\pi\) | |||||||
\(758\) | − | 19.4678i | − | 0.707101i | ||||||
\(759\) | −33.7276 | + | 23.1867i | −1.22424 | + | 0.841623i | ||||
\(760\) | −0.932526 | + | 9.27026i | −0.0338263 | + | 0.336268i | ||||
\(761\) | − | 42.4465i | − | 1.53869i | −0.638836 | − | 0.769343i | \(-0.720584\pi\) | ||
0.638836 | − | 0.769343i | \(-0.279416\pi\) | |||||||
\(762\) | 2.11812 | − | 2.38060i | 0.0767316 | − | 0.0862402i | ||||
\(763\) | 4.67386i | 0.169205i | ||||||||
\(764\) | 26.5716 | 0.961325 | ||||||||
\(765\) | 5.43704 | − | 0.0886460i | 0.196577 | − | 0.00320500i | ||||
\(766\) | 26.1779i | 0.945848i | ||||||||
\(767\) | −25.2779 | −0.912732 | ||||||||
\(768\) | −1.29400 | − | 1.15133i | −0.0466933 | − | 0.0415450i | ||||
\(769\) | − | 30.3882i | − | 1.09582i | −0.836536 | − | 0.547912i | \(-0.815423\pi\) | ||
0.836536 | − | 0.547912i | \(-0.184577\pi\) | |||||||
\(770\) | −7.31032 | − | 0.735370i | −0.263446 | − | 0.0265009i | ||||
\(771\) | 19.1503 | + | 17.0388i | 0.689680 | + | 0.613638i | ||||
\(772\) | − | 0.121042i | − | 0.00435640i | ||||||
\(773\) | − | 35.3747i | − | 1.27234i | −0.771550 | − | 0.636169i | \(-0.780518\pi\) | ||
0.771550 | − | 0.636169i | \(-0.219482\pi\) | |||||||
\(774\) | −1.24387 | − | 10.6232i | −0.0447099 | − | 0.381844i | ||||
\(775\) | −30.0584 | − | 6.10916i | −1.07973 | − | 0.219448i | ||||
\(776\) | −1.04670 | −0.0375745 | ||||||||
\(777\) | −1.91505 | − | 1.70390i | −0.0687020 | − | 0.0611271i | ||||
\(778\) | 22.4773 | 0.805851 | ||||||||
\(779\) | −10.5957 | −0.379632 | ||||||||
\(780\) | −10.5818 | + | 9.72873i | −0.378889 | + | 0.348344i | ||||
\(781\) | 71.5872i | 2.56159i | ||||||||
\(782\) | −3.77483 | − | 0.929415i | −0.134988 | − | 0.0332358i | ||||
\(783\) | −38.4111 | − | 26.8783i | −1.37270 | − | 0.960552i | ||||
\(784\) | −6.55530 | −0.234118 | ||||||||
\(785\) | −18.6061 | − | 1.87165i | −0.664081 | − | 0.0668021i | ||||
\(786\) | 7.59535 | − | 8.53657i | 0.270917 | − | 0.304489i | ||||
\(787\) | 2.58816 | 0.0922578 | 0.0461289 | − | 0.998935i | \(-0.485312\pi\) | ||||
0.0461289 | + | 0.998935i | \(0.485312\pi\) | |||||||
\(788\) | −4.06795 | −0.144915 | ||||||||
\(789\) | 1.53803 | − | 1.72863i | 0.0547554 | − | 0.0615408i | ||||
\(790\) | 2.57734 | − | 25.6214i | 0.0916978 | − | 0.911569i | ||||
\(791\) | − | 9.79620i | − | 0.348313i | ||||||
\(792\) | 1.71905 | + | 14.6815i | 0.0610837 | + | 0.521684i | ||||
\(793\) | 34.1962 | 1.21434 | ||||||||
\(794\) | 11.5042i | 0.408269i | ||||||||
\(795\) | −30.3020 | + | 27.8592i | −1.07470 | + | 0.988063i | ||||
\(796\) | − | 3.82379i | − | 0.135531i | ||||||
\(797\) | 41.0402i | 1.45372i | 0.686786 | + | 0.726859i | \(0.259021\pi\) | ||||
−0.686786 | + | 0.726859i | \(0.740979\pi\) | |||||||
\(798\) | −3.19908 | + | 3.59551i | −0.113246 | + | 0.127280i | ||||
\(799\) | 8.18133i | 0.289435i | ||||||||
\(800\) | −4.89982 | − | 0.995856i | −0.173235 | − | 0.0352088i | ||||
\(801\) | −4.37300 | − | 37.3475i | −0.154512 | − | 1.31961i | ||||
\(802\) | −9.84524 | −0.347647 | ||||||||
\(803\) | 23.8756i | 0.842551i | ||||||||
\(804\) | 10.2880 | + | 9.15367i | 0.362830 | + | 0.322825i | ||||
\(805\) | 2.39609 | − | 6.73788i | 0.0844510 | − | 0.237479i | ||||
\(806\) | − | 22.7682i | − | 0.801974i | ||||||
\(807\) | 14.1433 | − | 15.8960i | 0.497868 | − | 0.559564i | ||||
\(808\) | − | 11.5777i | − | 0.407303i | ||||||
\(809\) | − | 6.18091i | − | 0.217309i | −0.994080 | − | 0.108655i | \(-0.965346\pi\) | ||
0.994080 | − | 0.108655i | \(-0.0346542\pi\) | |||||||
\(810\) | 19.9473 | − | 2.66592i | 0.700875 | − | 0.0936710i | ||||
\(811\) | −2.55486 | −0.0897134 | −0.0448567 | − | 0.998993i | \(-0.514283\pi\) | ||||
−0.0448567 | + | 0.998993i | \(0.514283\pi\) | |||||||
\(812\) | 6.01659i | 0.211141i | ||||||||
\(813\) | 25.3244 | + | 22.5322i | 0.888166 | + | 0.790239i | ||||
\(814\) | −10.9350 | −0.383271 | ||||||||
\(815\) | 2.72371 | − | 27.0765i | 0.0954074 | − | 0.948447i | ||||
\(816\) | −0.933283 | + | 1.04894i | −0.0326714 | + | 0.0367201i | ||||
\(817\) | − | 14.8554i | − | 0.519725i | ||||||
\(818\) | −18.8120 | −0.657747 | ||||||||
\(819\) | −7.37462 | + | 0.863491i | −0.257690 | + | 0.0301728i | ||||
\(820\) | 0.569123 | − | 5.65766i | 0.0198747 | − | 0.197574i | ||||
\(821\) | − | 8.36428i | − | 0.291915i | −0.989291 | − | 0.145958i | \(-0.953374\pi\) | ||
0.989291 | − | 0.145958i | \(-0.0466263\pi\) | |||||||
\(822\) | 19.0477 | − | 21.4081i | 0.664364 | − | 0.746692i | ||||
\(823\) | 22.8495i | 0.796484i | 0.917280 | + | 0.398242i | \(0.130380\pi\) | ||||
−0.917280 | + | 0.398242i | \(0.869620\pi\) | |||||||
\(824\) | −14.2870 | −0.497712 | ||||||||
\(825\) | 25.5913 | + | 34.1457i | 0.890976 | + | 1.18880i | ||||
\(826\) | − | 4.54182i | − | 0.158030i | ||||||
\(827\) | 49.9487i | 1.73689i | 0.495789 | + | 0.868443i | \(0.334879\pi\) | ||||
−0.495789 | + | 0.868443i | \(0.665121\pi\) | |||||||
\(828\) | −14.2755 | − | 1.79166i | −0.496108 | − | 0.0622645i | ||||
\(829\) | −5.29100 | −0.183764 | −0.0918820 | − | 0.995770i | \(-0.529288\pi\) | ||||
−0.0918820 | + | 0.995770i | \(0.529288\pi\) | |||||||
\(830\) | 3.02936 | − | 30.1149i | 0.105151 | − | 1.04530i | ||||
\(831\) | −16.0928 | + | 18.0870i | −0.558252 | + | 0.627431i | ||||
\(832\) | − | 3.71145i | − | 0.128671i | ||||||
\(833\) | 5.31382i | 0.184113i | ||||||||
\(834\) | 7.07706 | + | 6.29676i | 0.245059 | + | 0.218039i | ||||
\(835\) | 31.9736 | + | 3.21633i | 1.10649 | + | 0.111306i | ||||
\(836\) | 20.5304i | 0.710060i | ||||||||
\(837\) | −18.2755 | + | 26.1170i | −0.631693 | + | 0.902737i | ||||
\(838\) | −8.48762 | −0.293200 | ||||||||
\(839\) | −32.3193 | −1.11579 | −0.557893 | − | 0.829913i | \(-0.688390\pi\) | ||||
−0.557893 | + | 0.829913i | \(0.688390\pi\) | |||||||
\(840\) | −1.74801 | − | 1.90129i | −0.0603122 | − | 0.0656008i | ||||
\(841\) | −52.4022 | −1.80697 | ||||||||
\(842\) | 30.8277i | 1.06239i | ||||||||
\(843\) | −11.8095 | − | 10.5074i | −0.406741 | − | 0.361894i | ||||
\(844\) | −10.9491 | −0.376882 | ||||||||
\(845\) | −1.72388 | − | 0.173411i | −0.0593032 | − | 0.00596551i | ||||
\(846\) | 3.52121 | + | 30.0728i | 0.121062 | + | 1.03393i | ||||
\(847\) | −8.85444 | −0.304242 | ||||||||
\(848\) | − | 10.6281i | − | 0.364970i | ||||||
\(849\) | −39.3892 | − | 35.0463i | −1.35184 | − | 1.20278i | ||||
\(850\) | −0.807255 | + | 3.97186i | −0.0276886 | + | 0.136234i | ||||
\(851\) | 2.54454 | − | 10.3347i | 0.0872256 | − | 0.354268i | ||||
\(852\) | −16.7274 | + | 18.8003i | −0.573072 | + | 0.644088i | ||||
\(853\) | − | 26.1818i | − | 0.896448i | −0.893921 | − | 0.448224i | \(-0.852057\pi\) | ||
0.893921 | − | 0.448224i | \(-0.147943\pi\) | |||||||
\(854\) | 6.14422i | 0.210251i | ||||||||
\(855\) | 27.9474 | − | 0.455657i | 0.955781 | − | 0.0155831i | ||||
\(856\) | 10.4647i | 0.357676i | ||||||||
\(857\) | −4.33206 | −0.147980 | −0.0739902 | − | 0.997259i | \(-0.523573\pi\) | ||||
−0.0739902 | + | 0.997259i | \(0.523573\pi\) | |||||||
\(858\) | −21.0546 | + | 23.6638i | −0.718794 | + | 0.807867i | ||||
\(859\) | 16.2823 | 0.555545 | 0.277772 | − | 0.960647i | \(-0.410404\pi\) | ||||
0.277772 | + | 0.960647i | \(0.410404\pi\) | |||||||
\(860\) | 7.93214 | + | 0.797920i | 0.270484 | + | 0.0272089i | ||||
\(861\) | 1.95241 | − | 2.19435i | 0.0665378 | − | 0.0747833i | ||||
\(862\) | 27.9563 | 0.952194 | ||||||||
\(863\) | −47.3991 | −1.61348 | −0.806742 | − | 0.590903i | \(-0.798771\pi\) | ||||
−0.806742 | + | 0.590903i | \(0.798771\pi\) | |||||||
\(864\) | −2.97909 | + | 4.25735i | −0.101351 | + | 0.144838i | ||||
\(865\) | 40.6808 | + | 4.09222i | 1.38319 | + | 0.139140i | ||||
\(866\) | 37.3143 | 1.26799 | ||||||||
\(867\) | −21.1478 | − | 18.8161i | −0.718216 | − | 0.639027i | ||||
\(868\) | 4.09088 | 0.138854 | ||||||||
\(869\) | − | 56.7427i | − | 1.92486i | ||||||
\(870\) | 25.7238 | − | 23.6500i | 0.872117 | − | 0.801810i | ||||
\(871\) | 29.5080i | 0.999839i | ||||||||
\(872\) | 7.00879i | 0.237348i | ||||||||
\(873\) | 0.365179 | + | 3.11880i | 0.0123594 | + | 0.105556i | ||||
\(874\) | −19.4034 | − | 4.77737i | −0.656328 | − | 0.161597i | ||||
\(875\) | −7.12099 | − | 2.20878i | −0.240733 | − | 0.0746703i | ||||
\(876\) | −5.57889 | + | 6.27023i | −0.188493 | + | 0.211852i | ||||
\(877\) | 6.13247i | 0.207079i | 0.994625 | + | 0.103539i | \(0.0330168\pi\) | ||||
−0.994625 | + | 0.103539i | \(0.966983\pi\) | |||||||
\(878\) | 24.1100 | 0.813674 | ||||||||
\(879\) | 31.2829 | − | 35.1595i | 1.05514 | − | 1.18590i | ||||
\(880\) | −10.9624 | − | 1.10274i | −0.369541 | − | 0.0371734i | ||||
\(881\) | 16.6943 | 0.562445 | 0.281222 | − | 0.959643i | \(-0.409260\pi\) | ||||
0.281222 | + | 0.959643i | \(0.409260\pi\) | |||||||
\(882\) | 2.28705 | + | 19.5325i | 0.0770089 | + | 0.657692i | ||||
\(883\) | − | 43.1929i | − | 1.45356i | −0.686873 | − | 0.726778i | \(-0.741017\pi\) | ||
0.686873 | − | 0.726778i | \(-0.258983\pi\) | |||||||
\(884\) | −3.00855 | −0.101188 | ||||||||
\(885\) | −19.4184 | + | 17.8530i | −0.652743 | + | 0.600121i | ||||
\(886\) | −14.5534 | −0.488930 | ||||||||
\(887\) | −18.4339 | −0.618951 | −0.309475 | − | 0.950907i | \(-0.600153\pi\) | ||||
−0.309475 | + | 0.950907i | \(0.600153\pi\) | |||||||
\(888\) | −2.87176 | − | 2.55512i | −0.0963699 | − | 0.0857443i | ||||
\(889\) | 1.22683i | 0.0411466i | ||||||||
\(890\) | 27.8866 | + | 2.80521i | 0.934761 | + | 0.0940308i | ||||
\(891\) | 43.1458 | − | 10.2443i | 1.44544 | − | 0.343197i | ||||
\(892\) | 3.05235i | 0.102200i | ||||||||
\(893\) | 42.0536i | 1.40727i | ||||||||
\(894\) | −3.76642 | − | 3.35114i | −0.125968 | − | 0.112079i | ||||
\(895\) | −1.12418 | + | 11.1755i | −0.0375772 | + | 0.373556i | ||||
\(896\) | 0.666856 | 0.0222781 | ||||||||
\(897\) | −17.4653 | − | 25.4053i | −0.583149 | − | 0.848257i | ||||
\(898\) | − | 25.8545i | − | 0.862776i | ||||||
\(899\) | 55.3481i | 1.84596i | ||||||||
\(900\) | −1.25782 | + | 14.9472i | −0.0419274 | + | 0.498239i | ||||
\(901\) | −8.61528 | −0.287017 | ||||||||
\(902\) | − | 12.5298i | − | 0.417197i | ||||||
\(903\) | 3.07652 | + | 2.73731i | 0.102380 | + | 0.0910918i | ||||
\(904\) | − | 14.6901i | − | 0.488586i | ||||||
\(905\) | −0.0767470 | + | 0.762943i | −0.00255116 | + | 0.0253611i | ||||
\(906\) | 7.12317 | + | 6.33778i | 0.236651 | + | 0.210559i | ||||
\(907\) | −33.2776 | −1.10496 | −0.552482 | − | 0.833525i | \(-0.686319\pi\) | ||||
−0.552482 | + | 0.833525i | \(0.686319\pi\) | |||||||
\(908\) | − | 16.8065i | − | 0.557743i | ||||||
\(909\) | −34.4975 | + | 4.03929i | −1.14421 | + | 0.133975i | ||||
\(910\) | 0.553915 | − | 5.50648i | 0.0183621 | − | 0.182538i | ||||
\(911\) | −38.3776 | −1.27151 | −0.635753 | − | 0.771892i | \(-0.719310\pi\) | ||||
−0.635753 | + | 0.771892i | \(0.719310\pi\) | |||||||
\(912\) | −4.79725 | + | 5.39173i | −0.158853 | + | 0.178538i | ||||
\(913\) | − | 66.6943i | − | 2.20726i | ||||||
\(914\) | −23.6100 | −0.780949 | ||||||||
\(915\) | 26.2694 | − | 24.1517i | 0.868441 | − | 0.798430i | ||||
\(916\) | 10.0750i | 0.332888i | ||||||||
\(917\) | 4.39927i | 0.145277i | ||||||||
\(918\) | 3.45106 | + | 2.41489i | 0.113902 | + | 0.0797033i | ||||
\(919\) | 42.5549i | 1.40376i | 0.712297 | + | 0.701878i | \(0.247655\pi\) | ||||
−0.712297 | + | 0.701878i | \(0.752345\pi\) | |||||||
\(920\) | 3.59311 | − | 10.1039i | 0.118461 | − | 0.333117i | ||||
\(921\) | −9.52451 | + | 10.7048i | −0.313843 | + | 0.352735i | ||||
\(922\) | − | 38.3275i | − | 1.26225i | ||||||
\(923\) | −53.9229 | −1.77489 | ||||||||
\(924\) | −4.25180 | − | 3.78301i | −0.139874 | − | 0.124452i | ||||
\(925\) | −10.8741 | − | 2.21009i | −0.357538 | − | 0.0726672i | ||||
\(926\) | 1.86463i | 0.0612756i | ||||||||
\(927\) | 4.98453 | + | 42.5703i | 0.163713 | + | 1.39819i | ||||
\(928\) | 9.02232i | 0.296172i | ||||||||
\(929\) | − | 14.6150i | − | 0.479501i | −0.970834 | − | 0.239751i | \(-0.922934\pi\) | ||
0.970834 | − | 0.239751i | \(-0.0770657\pi\) | |||||||
\(930\) | −16.0804 | − | 17.4905i | −0.527298 | − | 0.573534i | ||||
\(931\) | 27.3140i | 0.895181i | ||||||||
\(932\) | 13.0601 | 0.427796 | ||||||||
\(933\) | −0.294889 | + | 0.331432i | −0.00965424 | + | 0.0108506i | ||||
\(934\) | 22.7789i | 0.745348i | ||||||||
\(935\) | −0.893897 | + | 8.88624i | −0.0292335 | + | 0.290611i | ||||
\(936\) | −11.0588 | + | 1.29487i | −0.361468 | + | 0.0423241i | ||||
\(937\) | −43.2537 | −1.41304 | −0.706519 | − | 0.707694i | \(-0.749735\pi\) | ||||
−0.706519 | + | 0.707694i | \(0.749735\pi\) | |||||||
\(938\) | −5.30186 | −0.173112 | ||||||||
\(939\) | 9.30329 | + | 8.27753i | 0.303601 | + | 0.270127i | ||||
\(940\) | −22.4548 | − | 2.25880i | −0.732394 | − | 0.0736740i | ||||
\(941\) | −9.65494 | −0.314742 | −0.157371 | − | 0.987540i | \(-0.550302\pi\) | ||||
−0.157371 | + | 0.987540i | \(0.550302\pi\) | |||||||
\(942\) | −10.8216 | − | 9.62845i | −0.352587 | − | 0.313712i | ||||
\(943\) | 11.8419 | + | 2.91564i | 0.385626 | + | 0.0949464i | ||||
\(944\) | − | 6.81080i | − | 0.221673i | ||||||
\(945\) | −5.05531 | + | 5.87179i | −0.164449 | + | 0.191009i | ||||
\(946\) | 17.5670 | 0.571152 | ||||||||
\(947\) | 1.54817 | 0.0503088 | 0.0251544 | − | 0.999684i | \(-0.491992\pi\) | ||||
0.0251544 | + | 0.999684i | \(0.491992\pi\) | |||||||
\(948\) | 13.2588 | − | 14.9018i | 0.430625 | − | 0.483989i | ||||
\(949\) | −17.9842 | −0.583793 | ||||||||
\(950\) | −4.14944 | + | 20.4161i | −0.134626 | + | 0.662387i | ||||
\(951\) | −21.1977 | − | 18.8605i | −0.687381 | − | 0.611592i | ||||
\(952\) | − | 0.540563i | − | 0.0175197i | ||||||
\(953\) | − | 50.4280i | − | 1.63352i | −0.576976 | − | 0.816761i | \(-0.695767\pi\) | ||
0.576976 | − | 0.816761i | \(-0.304233\pi\) | |||||||
\(954\) | −31.6679 | + | 3.70798i | −1.02529 | + | 0.120050i | ||||
\(955\) | 59.1175 | + | 5.94682i | 1.91300 | + | 0.192435i | ||||
\(956\) | − | 14.5163i | − | 0.469492i | ||||||
\(957\) | 51.1827 | − | 57.5253i | 1.65450 | − | 1.85953i | ||||
\(958\) | −22.7286 | −0.734326 | ||||||||
\(959\) | 11.0325i | 0.356259i | ||||||||
\(960\) | −2.62128 | − | 2.85112i | −0.0846013 | − | 0.0920197i | ||||
\(961\) | 6.63307 | 0.213970 | ||||||||
\(962\) | − | 8.23675i | − | 0.265563i | ||||||
\(963\) | 31.1811 | − | 3.65098i | 1.00480 | − | 0.117651i | ||||
\(964\) | 7.90101i | 0.254475i | ||||||||
\(965\) | 0.0270897 | − | 0.269299i | 0.000872049 | − | 0.00866906i | ||||
\(966\) | 4.56470 | − | 3.13809i | 0.146867 | − | 0.100966i | ||||
\(967\) | 39.1313i | 1.25838i | 0.777252 | + | 0.629189i | \(0.216613\pi\) | ||||
−0.777252 | + | 0.629189i | \(0.783387\pi\) | |||||||
\(968\) | −13.2779 | −0.426767 | ||||||||
\(969\) | 4.37061 | + | 3.88872i | 0.140404 | + | 0.124924i | ||||
\(970\) | −2.32875 | − | 0.234257i | −0.0747716 | − | 0.00752152i | ||||
\(971\) | 31.3611 | 1.00643 | 0.503214 | − | 0.864162i | \(-0.332151\pi\) | ||||
0.503214 | + | 0.864162i | \(0.332151\pi\) | |||||||
\(972\) | 13.7247 | + | 7.39131i | 0.440221 | + | 0.237076i | ||||
\(973\) | −3.64712 | −0.116921 | ||||||||
\(974\) | 9.28752i | 0.297591i | ||||||||
\(975\) | −25.7201 | + | 19.2766i | −0.823703 | + | 0.617345i | ||||
\(976\) | 9.21371i | 0.294924i | ||||||||
\(977\) | − | 10.1353i | − | 0.324256i | −0.986770 | − | 0.162128i | \(-0.948164\pi\) | ||
0.986770 | − | 0.162128i | \(-0.0518357\pi\) | |||||||
\(978\) | 14.0117 | − | 15.7481i | 0.448046 | − | 0.503569i | ||||
\(979\) | 61.7593 | 1.97384 | ||||||||
\(980\) | −14.5845 | − | 1.46710i | −0.465885 | − | 0.0468649i | ||||
\(981\) | 20.8837 | − | 2.44526i | 0.666766 | − | 0.0780712i | ||||
\(982\) | − | 16.4543i | − | 0.525077i | ||||||
\(983\) | 8.84663i | 0.282164i | 0.989998 | + | 0.141082i | \(0.0450581\pi\) | ||||
−0.989998 | + | 0.141082i | \(0.954942\pi\) | |||||||
\(984\) | 2.92778 | − | 3.29059i | 0.0933341 | − | 0.104900i | ||||
\(985\) | −9.05053 | − | 0.910423i | −0.288374 | − | 0.0290085i | ||||
\(986\) | 7.31361 | 0.232913 | ||||||||
\(987\) | −8.70919 | − | 7.74893i | −0.277216 | − | 0.246651i | ||||
\(988\) | −15.4645 | −0.491992 | ||||||||
\(989\) | −4.08778 | + | 16.6026i | −0.129984 | + | 0.527931i | ||||
\(990\) | 0.538828 | + | 33.0487i | 0.0171251 | + | 1.05036i | ||||
\(991\) | 12.7133 | 0.403850 | 0.201925 | − | 0.979401i | \(-0.435280\pi\) | ||||
0.201925 | + | 0.979401i | \(0.435280\pi\) | |||||||
\(992\) | 6.13458 | 0.194773 | ||||||||
\(993\) | −28.5453 | − | 25.3979i | −0.905857 | − | 0.805979i | ||||
\(994\) | − | 9.68862i | − | 0.307304i | ||||||
\(995\) | 0.855779 | − | 8.50731i | 0.0271300 | − | 0.269700i | ||||
\(996\) | 15.5841 | − | 17.5153i | 0.493802 | − | 0.554995i | ||||
\(997\) | − | 36.9919i | − | 1.17154i | −0.810476 | − | 0.585772i | \(-0.800791\pi\) | ||
0.810476 | − | 0.585772i | \(-0.199209\pi\) | |||||||
\(998\) | −14.8139 | −0.468927 | ||||||||
\(999\) | −6.61145 | + | 9.44826i | −0.209177 | + | 0.298930i |
(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 | 690.2.h.a.689.6 | yes | 24 | |
3.2 | odd | 2 | 690.2.h.b.689.17 | yes | 24 | ||
5.4 | even | 2 | 690.2.h.b.689.20 | yes | 24 | ||
15.14 | odd | 2 | inner | 690.2.h.a.689.7 | yes | 24 | |
23.22 | odd | 2 | inner | 690.2.h.a.689.5 | ✓ | 24 | |
69.68 | even | 2 | 690.2.h.b.689.18 | yes | 24 | ||
115.114 | odd | 2 | 690.2.h.b.689.19 | yes | 24 | ||
345.344 | even | 2 | inner | 690.2.h.a.689.8 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.h.a.689.5 | ✓ | 24 | 23.22 | odd | 2 | inner | |
690.2.h.a.689.6 | yes | 24 | 1.1 | even | 1 | trivial | |
690.2.h.a.689.7 | yes | 24 | 15.14 | odd | 2 | inner | |
690.2.h.a.689.8 | yes | 24 | 345.344 | even | 2 | inner | |
690.2.h.b.689.17 | yes | 24 | 3.2 | odd | 2 | ||
690.2.h.b.689.18 | yes | 24 | 69.68 | even | 2 | ||
690.2.h.b.689.19 | yes | 24 | 115.114 | odd | 2 | ||
690.2.h.b.689.20 | yes | 24 | 5.4 | even | 2 |