Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [99,2,Mod(34,99)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(99, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("99.34");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 99 = 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 99.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: | \(0.790518980011\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\zeta_{18})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{3} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 67.3 | ||
Root | \(-0.766044 + 0.642788i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 99.67 |
Dual form | 99.2.e.d.34.3 |
$q$-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 \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(56\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.939693 | + | 1.62760i | 0.664463 | + | 1.15088i | 0.979431 | + | 0.201781i | \(0.0646730\pi\) |
−0.314968 | + | 0.949102i | \(0.601994\pi\) | |||||||
\(3\) | −1.70574 | + | 0.300767i | −0.984808 | + | 0.173648i | ||||
\(4\) | −0.766044 | + | 1.32683i | −0.383022 | + | 0.663414i | ||||
\(5\) | −1.43969 | + | 2.49362i | −0.643850 | + | 1.11518i | 0.340716 | + | 0.940166i | \(0.389331\pi\) |
−0.984566 | + | 0.175015i | \(0.944003\pi\) | |||||||
\(6\) | −2.09240 | − | 2.49362i | −0.854217 | − | 1.01802i | ||||
\(7\) | 0.326352 | + | 0.565258i | 0.123349 | + | 0.213647i | 0.921087 | − | 0.389358i | \(-0.127303\pi\) |
−0.797737 | + | 0.603005i | \(0.793970\pi\) | |||||||
\(8\) | 0.879385 | 0.310910 | ||||||||
\(9\) | 2.81908 | − | 1.02606i | 0.939693 | − | 0.342020i | ||||
\(10\) | −5.41147 | −1.71126 | ||||||||
\(11\) | 0.500000 | + | 0.866025i | 0.150756 | + | 0.261116i | ||||
\(12\) | 0.907604 | − | 2.49362i | 0.262003 | − | 0.719846i | ||||
\(13\) | 3.37939 | − | 5.85327i | 0.937273 | − | 1.62340i | 0.166743 | − | 0.986000i | \(-0.446675\pi\) |
0.770530 | − | 0.637404i | \(-0.219992\pi\) | |||||||
\(14\) | −0.613341 | + | 1.06234i | −0.163922 | + | 0.283922i | ||||
\(15\) | 1.70574 | − | 4.68647i | 0.440419 | − | 1.21004i | ||||
\(16\) | 2.35844 | + | 4.08494i | 0.589610 | + | 1.02123i | ||||
\(17\) | 0.184793 | 0.0448188 | 0.0224094 | − | 0.999749i | \(-0.492866\pi\) | ||||
0.0224094 | + | 0.999749i | \(0.492866\pi\) | |||||||
\(18\) | 4.31908 | + | 3.62414i | 1.01802 | + | 0.854217i | ||||
\(19\) | −5.22668 | −1.19908 | −0.599541 | − | 0.800344i | \(-0.704650\pi\) | ||||
−0.599541 | + | 0.800344i | \(0.704650\pi\) | |||||||
\(20\) | −2.20574 | − | 3.82045i | −0.493218 | − | 0.854278i | ||||
\(21\) | −0.726682 | − | 0.866025i | −0.158575 | − | 0.188982i | ||||
\(22\) | −0.939693 | + | 1.62760i | −0.200343 | + | 0.347004i | ||||
\(23\) | 1.59240 | − | 2.75811i | 0.332038 | − | 0.575106i | −0.650874 | − | 0.759186i | \(-0.725597\pi\) |
0.982911 | + | 0.184080i | \(0.0589306\pi\) | |||||||
\(24\) | −1.50000 | + | 0.264490i | −0.306186 | + | 0.0539889i | ||||
\(25\) | −1.64543 | − | 2.84997i | −0.329086 | − | 0.569994i | ||||
\(26\) | 12.7023 | 2.49113 | ||||||||
\(27\) | −4.50000 | + | 2.59808i | −0.866025 | + | 0.500000i | ||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 2.01114 | + | 3.48340i | 0.373460 | + | 0.646852i | 0.990095 | − | 0.140397i | \(-0.0448379\pi\) |
−0.616635 | + | 0.787249i | \(0.711505\pi\) | |||||||
\(30\) | 9.23055 | − | 1.62760i | 1.68526 | − | 0.297157i | ||||
\(31\) | −0.553033 | + | 0.957882i | −0.0993277 | + | 0.172041i | −0.911407 | − | 0.411507i | \(-0.865003\pi\) |
0.812079 | + | 0.583548i | \(0.198336\pi\) | |||||||
\(32\) | −3.55303 | + | 6.15403i | −0.628094 | + | 1.08789i | ||||
\(33\) | −1.11334 | − | 1.32683i | −0.193808 | − | 0.230971i | ||||
\(34\) | 0.173648 | + | 0.300767i | 0.0297804 | + | 0.0515812i | ||||
\(35\) | −1.87939 | −0.317674 | ||||||||
\(36\) | −0.798133 | + | 4.52644i | −0.133022 | + | 0.754407i | ||||
\(37\) | 0.106067 | 0.0174373 | 0.00871864 | − | 0.999962i | \(-0.497225\pi\) | ||||
0.00871864 | + | 0.999962i | \(0.497225\pi\) | |||||||
\(38\) | −4.91147 | − | 8.50692i | −0.796746 | − | 1.38001i | ||||
\(39\) | −4.00387 | + | 11.0005i | −0.641132 | + | 1.76150i | ||||
\(40\) | −1.26604 | + | 2.19285i | −0.200179 | + | 0.346721i | ||||
\(41\) | 2.80793 | − | 4.86348i | 0.438526 | − | 0.759549i | −0.559050 | − | 0.829134i | \(-0.688834\pi\) |
0.997576 | + | 0.0695851i | \(0.0221675\pi\) | |||||||
\(42\) | 0.726682 | − | 1.99654i | 0.112129 | − | 0.308073i | ||||
\(43\) | −1.92989 | − | 3.34267i | −0.294306 | − | 0.509753i | 0.680517 | − | 0.732732i | \(-0.261755\pi\) |
−0.974823 | + | 0.222979i | \(0.928422\pi\) | |||||||
\(44\) | −1.53209 | −0.230971 | ||||||||
\(45\) | −1.50000 | + | 8.50692i | −0.223607 | + | 1.26814i | ||||
\(46\) | 5.98545 | 0.882507 | ||||||||
\(47\) | −6.00387 | − | 10.3990i | −0.875755 | − | 1.51685i | −0.855957 | − | 0.517047i | \(-0.827031\pi\) |
−0.0197977 | − | 0.999804i | \(-0.506302\pi\) | |||||||
\(48\) | −5.25150 | − | 6.25849i | −0.757988 | − | 0.903335i | ||||
\(49\) | 3.28699 | − | 5.69323i | 0.469570 | − | 0.813319i | ||||
\(50\) | 3.09240 | − | 5.35619i | 0.437331 | − | 0.757479i | ||||
\(51\) | −0.315207 | + | 0.0555796i | −0.0441379 | + | 0.00778270i | ||||
\(52\) | 5.17752 | + | 8.96773i | 0.717993 | + | 1.24360i | ||||
\(53\) | −10.0719 | −1.38348 | −0.691742 | − | 0.722145i | \(-0.743157\pi\) | ||||
−0.691742 | + | 0.722145i | \(0.743157\pi\) | |||||||
\(54\) | −8.45723 | − | 4.88279i | −1.15088 | − | 0.664463i | ||||
\(55\) | −2.87939 | −0.388256 | ||||||||
\(56\) | 0.286989 | + | 0.497079i | 0.0383505 | + | 0.0664250i | ||||
\(57\) | 8.91534 | − | 1.57202i | 1.18087 | − | 0.208219i | ||||
\(58\) | −3.77972 | + | 6.54666i | −0.496301 | + | 0.859618i | ||||
\(59\) | −5.27719 | + | 9.14036i | −0.687031 | + | 1.18997i | 0.285762 | + | 0.958301i | \(0.407753\pi\) |
−0.972794 | + | 0.231673i | \(0.925580\pi\) | |||||||
\(60\) | 4.91147 | + | 5.85327i | 0.634069 | + | 0.755654i | ||||
\(61\) | 3.67365 | + | 6.36295i | 0.470362 | + | 0.814692i | 0.999426 | − | 0.0338908i | \(-0.0107899\pi\) |
−0.529063 | + | 0.848582i | \(0.677457\pi\) | |||||||
\(62\) | −2.07873 | −0.263998 | ||||||||
\(63\) | 1.50000 | + | 1.25865i | 0.188982 | + | 0.158575i | ||||
\(64\) | −3.92127 | −0.490159 | ||||||||
\(65\) | 9.73055 | + | 16.8538i | 1.20693 | + | 2.09046i | ||||
\(66\) | 1.11334 | − | 3.05888i | 0.137043 | − | 0.376522i | ||||
\(67\) | 5.90420 | − | 10.2264i | 0.721313 | − | 1.24935i | −0.239161 | − | 0.970980i | \(-0.576872\pi\) |
0.960474 | − | 0.278371i | \(-0.0897943\pi\) | |||||||
\(68\) | −0.141559 | + | 0.245188i | −0.0171666 | + | 0.0297334i | ||||
\(69\) | −1.88666 | + | 5.18355i | −0.227127 | + | 0.624027i | ||||
\(70\) | −1.76604 | − | 3.05888i | −0.211083 | − | 0.365606i | ||||
\(71\) | −2.47565 | −0.293806 | −0.146903 | − | 0.989151i | \(-0.546930\pi\) | ||||
−0.146903 | + | 0.989151i | \(0.546930\pi\) | |||||||
\(72\) | 2.47906 | − | 0.902302i | 0.292159 | − | 0.106337i | ||||
\(73\) | 10.4611 | 1.22438 | 0.612190 | − | 0.790711i | \(-0.290289\pi\) | ||||
0.612190 | + | 0.790711i | \(0.290289\pi\) | |||||||
\(74\) | 0.0996702 | + | 0.172634i | 0.0115864 | + | 0.0200683i | ||||
\(75\) | 3.66385 | + | 4.36640i | 0.423065 | + | 0.504189i | ||||
\(76\) | 4.00387 | − | 6.93491i | 0.459275 | − | 0.795488i | ||||
\(77\) | −0.326352 | + | 0.565258i | −0.0371912 | + | 0.0644171i | ||||
\(78\) | −21.6668 | + | 3.82045i | −2.45329 | + | 0.432581i | ||||
\(79\) | 0.733956 | + | 1.27125i | 0.0825765 | + | 0.143027i | 0.904356 | − | 0.426779i | \(-0.140352\pi\) |
−0.821779 | + | 0.569806i | \(0.807018\pi\) | |||||||
\(80\) | −13.5817 | −1.51848 | ||||||||
\(81\) | 6.89440 | − | 5.78509i | 0.766044 | − | 0.642788i | ||||
\(82\) | 10.5544 | 1.16554 | ||||||||
\(83\) | 0.520945 | + | 0.902302i | 0.0571811 | + | 0.0990406i | 0.893199 | − | 0.449662i | \(-0.148455\pi\) |
−0.836018 | + | 0.548702i | \(0.815122\pi\) | |||||||
\(84\) | 1.70574 | − | 0.300767i | 0.186111 | − | 0.0328164i | ||||
\(85\) | −0.266044 | + | 0.460802i | −0.0288566 | + | 0.0499810i | ||||
\(86\) | 3.62701 | − | 6.28217i | 0.391111 | − | 0.677424i | ||||
\(87\) | −4.47818 | − | 5.33688i | −0.480111 | − | 0.572174i | ||||
\(88\) | 0.439693 | + | 0.761570i | 0.0468714 | + | 0.0811836i | ||||
\(89\) | −3.01960 | −0.320077 | −0.160038 | − | 0.987111i | \(-0.551162\pi\) | ||||
−0.160038 | + | 0.987111i | \(0.551162\pi\) | |||||||
\(90\) | −15.2554 | + | 5.55250i | −1.60806 | + | 0.585285i | ||||
\(91\) | 4.41147 | 0.462448 | ||||||||
\(92\) | 2.43969 | + | 4.22567i | 0.254356 | + | 0.440557i | ||||
\(93\) | 0.655230 | − | 1.80023i | 0.0679442 | − | 0.186675i | ||||
\(94\) | 11.2836 | − | 19.5437i | 1.16381 | − | 2.01578i | ||||
\(95\) | 7.52481 | − | 13.0334i | 0.772030 | − | 1.33719i | ||||
\(96\) | 4.20961 | − | 11.5658i | 0.429641 | − | 1.18043i | ||||
\(97\) | 2.86959 | + | 4.97027i | 0.291362 | + | 0.504654i | 0.974132 | − | 0.225979i | \(-0.0725582\pi\) |
−0.682770 | + | 0.730633i | \(0.739225\pi\) | |||||||
\(98\) | 12.3550 | 1.24805 | ||||||||
\(99\) | 2.29813 | + | 1.92836i | 0.230971 | + | 0.193808i | ||||
\(100\) | 5.04189 | 0.504189 | ||||||||
\(101\) | 2.20961 | + | 3.82715i | 0.219864 | + | 0.380816i | 0.954766 | − | 0.297357i | \(-0.0961053\pi\) |
−0.734902 | + | 0.678173i | \(0.762772\pi\) | |||||||
\(102\) | −0.386659 | − | 0.460802i | −0.0382850 | − | 0.0456262i | ||||
\(103\) | −5.21941 | + | 9.04028i | −0.514284 | + | 0.890765i | 0.485579 | + | 0.874193i | \(0.338609\pi\) |
−0.999863 | + | 0.0165725i | \(0.994725\pi\) | |||||||
\(104\) | 2.97178 | − | 5.14728i | 0.291407 | − | 0.504732i | ||||
\(105\) | 3.20574 | − | 0.565258i | 0.312848 | − | 0.0551635i | ||||
\(106\) | −9.46451 | − | 16.3930i | −0.919274 | − | 1.59223i | ||||
\(107\) | −8.31315 | −0.803662 | −0.401831 | − | 0.915714i | \(-0.631626\pi\) | ||||
−0.401831 | + | 0.915714i | \(0.631626\pi\) | |||||||
\(108\) | − | 7.96097i | − | 0.766044i | ||||||
\(109\) | −15.9881 | −1.53139 | −0.765693 | − | 0.643206i | \(-0.777604\pi\) | ||||
−0.765693 | + | 0.643206i | \(0.777604\pi\) | |||||||
\(110\) | −2.70574 | − | 4.68647i | −0.257982 | − | 0.446838i | ||||
\(111\) | −0.180922 | + | 0.0319015i | −0.0171724 | + | 0.00302795i | ||||
\(112\) | −1.53936 | + | 2.66625i | −0.145456 | + | 0.251937i | ||||
\(113\) | 2.53209 | − | 4.38571i | 0.238199 | − | 0.412573i | −0.721999 | − | 0.691894i | \(-0.756776\pi\) |
0.960198 | + | 0.279322i | \(0.0901097\pi\) | |||||||
\(114\) | 10.9363 | + | 13.0334i | 1.02428 | + | 1.22069i | ||||
\(115\) | 4.58512 | + | 7.94166i | 0.427565 | + | 0.740564i | ||||
\(116\) | −6.16250 | −0.572174 | ||||||||
\(117\) | 3.52094 | − | 19.9683i | 0.325511 | − | 1.84607i | ||||
\(118\) | −19.8357 | −1.82603 | ||||||||
\(119\) | 0.0603074 | + | 0.104455i | 0.00552837 | + | 0.00957541i | ||||
\(120\) | 1.50000 | − | 4.12122i | 0.136931 | − | 0.376214i | ||||
\(121\) | −0.500000 | + | 0.866025i | −0.0454545 | + | 0.0787296i | ||||
\(122\) | −6.90420 | + | 11.9584i | −0.625077 | + | 1.08266i | ||||
\(123\) | −3.32682 | + | 9.14036i | −0.299969 | + | 0.824158i | ||||
\(124\) | −0.847296 | − | 1.46756i | −0.0760895 | − | 0.131791i | ||||
\(125\) | −4.92127 | −0.440172 | ||||||||
\(126\) | −0.639033 | + | 3.62414i | −0.0569296 | + | 0.322864i | ||||
\(127\) | 7.80066 | 0.692197 | 0.346098 | − | 0.938198i | \(-0.387506\pi\) | ||||
0.346098 | + | 0.938198i | \(0.387506\pi\) | |||||||
\(128\) | 3.42127 | + | 5.92582i | 0.302401 | + | 0.523774i | ||||
\(129\) | 4.29726 | + | 5.12127i | 0.378352 | + | 0.450903i | ||||
\(130\) | −18.2875 | + | 31.6748i | −1.60392 | + | 2.77806i | ||||
\(131\) | 6.24897 | − | 10.8235i | 0.545975 | − | 0.945657i | −0.452570 | − | 0.891729i | \(-0.649493\pi\) |
0.998545 | − | 0.0539276i | \(-0.0171740\pi\) | |||||||
\(132\) | 2.61334 | − | 0.460802i | 0.227462 | − | 0.0401077i | ||||
\(133\) | −1.70574 | − | 2.95442i | −0.147906 | − | 0.256181i | ||||
\(134\) | 22.1925 | 1.91714 | ||||||||
\(135\) | − | 14.9617i | − | 1.28770i | ||||||
\(136\) | 0.162504 | 0.0139346 | ||||||||
\(137\) | −7.61334 | − | 13.1867i | −0.650452 | − | 1.12662i | −0.983013 | − | 0.183534i | \(-0.941246\pi\) |
0.332562 | − | 0.943081i | \(-0.392087\pi\) | |||||||
\(138\) | −10.2096 | + | 1.80023i | −0.869100 | + | 0.153246i | ||||
\(139\) | −7.25150 | + | 12.5600i | −0.615064 | + | 1.06532i | 0.375309 | + | 0.926900i | \(0.377536\pi\) |
−0.990373 | + | 0.138422i | \(0.955797\pi\) | |||||||
\(140\) | 1.43969 | − | 2.49362i | 0.121676 | − | 0.210749i | ||||
\(141\) | 13.3687 | + | 15.9322i | 1.12585 | + | 1.34173i | ||||
\(142\) | −2.32635 | − | 4.02936i | −0.195223 | − | 0.338136i | ||||
\(143\) | 6.75877 | 0.565197 | ||||||||
\(144\) | 10.8400 | + | 9.09586i | 0.903335 | + | 0.757988i | ||||
\(145\) | −11.5817 | −0.961809 | ||||||||
\(146\) | 9.83022 | + | 17.0264i | 0.813555 | + | 1.40912i | ||||
\(147\) | −3.89440 | + | 10.6998i | −0.321205 | + | 0.882503i | ||||
\(148\) | −0.0812519 | + | 0.140732i | −0.00667887 | + | 0.0115681i | ||||
\(149\) | −7.30453 | + | 12.6518i | −0.598410 | + | 1.03648i | 0.394645 | + | 0.918833i | \(0.370867\pi\) |
−0.993056 | + | 0.117644i | \(0.962466\pi\) | |||||||
\(150\) | −3.66385 | + | 10.0663i | −0.299152 | + | 0.821913i | ||||
\(151\) | 10.5535 | + | 18.2792i | 0.858832 | + | 1.48754i | 0.873044 | + | 0.487641i | \(0.162143\pi\) |
−0.0142125 | + | 0.999899i | \(0.504524\pi\) | |||||||
\(152\) | −4.59627 | −0.372806 | ||||||||
\(153\) | 0.520945 | − | 0.189608i | 0.0421159 | − | 0.0153289i | ||||
\(154\) | −1.22668 | −0.0988488 | ||||||||
\(155\) | −1.59240 | − | 2.75811i | −0.127904 | − | 0.221537i | ||||
\(156\) | −11.5287 | − | 13.7394i | −0.923034 | − | 1.10003i | ||||
\(157\) | 2.21554 | − | 3.83742i | 0.176819 | − | 0.306260i | −0.763970 | − | 0.645252i | \(-0.776753\pi\) |
0.940789 | + | 0.338992i | \(0.110086\pi\) | |||||||
\(158\) | −1.37939 | + | 2.38917i | −0.109738 | + | 0.190072i | ||||
\(159\) | 17.1800 | − | 3.02931i | 1.36247 | − | 0.240240i | ||||
\(160\) | −10.2306 | − | 17.7198i | −0.808796 | − | 1.40088i | ||||
\(161\) | 2.07873 | 0.163827 | ||||||||
\(162\) | 15.8944 | + | 5.78509i | 1.24878 | + | 0.454519i | ||||
\(163\) | −2.12567 | −0.166495 | −0.0832476 | − | 0.996529i | \(-0.526529\pi\) | ||||
−0.0832476 | + | 0.996529i | \(0.526529\pi\) | |||||||
\(164\) | 4.30200 | + | 7.45129i | 0.335930 | + | 0.581848i | ||||
\(165\) | 4.91147 | − | 0.866025i | 0.382358 | − | 0.0674200i | ||||
\(166\) | −0.979055 | + | 1.69577i | −0.0759894 | + | 0.131618i | ||||
\(167\) | −6.21554 | + | 10.7656i | −0.480973 | + | 0.833069i | −0.999762 | − | 0.0218332i | \(-0.993050\pi\) |
0.518789 | + | 0.854902i | \(0.326383\pi\) | |||||||
\(168\) | −0.639033 | − | 0.761570i | −0.0493025 | − | 0.0587564i | ||||
\(169\) | −16.3405 | − | 28.3026i | −1.25696 | − | 2.17712i | ||||
\(170\) | −1.00000 | −0.0766965 | ||||||||
\(171\) | −14.7344 | + | 5.36289i | −1.12677 | + | 0.410111i | ||||
\(172\) | 5.91353 | 0.450903 | ||||||||
\(173\) | −1.80200 | − | 3.12116i | −0.137004 | − | 0.237298i | 0.789357 | − | 0.613934i | \(-0.210414\pi\) |
−0.926361 | + | 0.376636i | \(0.877081\pi\) | |||||||
\(174\) | 4.47818 | − | 12.3037i | 0.339490 | − | 0.932741i | ||||
\(175\) | 1.07398 | − | 1.86018i | 0.0811851 | − | 0.140617i | ||||
\(176\) | −2.35844 | + | 4.08494i | −0.177774 | + | 0.307914i | ||||
\(177\) | 6.25237 | − | 17.1783i | 0.469957 | − | 1.29120i | ||||
\(178\) | −2.83750 | − | 4.91469i | −0.212679 | − | 0.368371i | ||||
\(179\) | 12.8726 | 0.962142 | 0.481071 | − | 0.876682i | \(-0.340248\pi\) | ||||
0.481071 | + | 0.876682i | \(0.340248\pi\) | |||||||
\(180\) | −10.1382 | − | 8.50692i | −0.755654 | − | 0.634069i | ||||
\(181\) | −24.3405 | −1.80921 | −0.904607 | − | 0.426246i | \(-0.859836\pi\) | ||||
−0.904607 | + | 0.426246i | \(0.859836\pi\) | |||||||
\(182\) | 4.14543 | + | 7.18009i | 0.307280 | + | 0.532224i | ||||
\(183\) | −8.18004 | − | 9.74860i | −0.604686 | − | 0.720637i | ||||
\(184\) | 1.40033 | − | 2.42544i | 0.103234 | − | 0.178806i | ||||
\(185\) | −0.152704 | + | 0.264490i | −0.0112270 | + | 0.0194457i | ||||
\(186\) | 3.54576 | − | 0.625213i | 0.259988 | − | 0.0458428i | ||||
\(187\) | 0.0923963 | + | 0.160035i | 0.00675668 | + | 0.0117029i | ||||
\(188\) | 18.3969 | 1.34173 | ||||||||
\(189\) | −2.93717 | − | 1.69577i | −0.213647 | − | 0.123349i | ||||
\(190\) | 28.2841 | 2.05194 | ||||||||
\(191\) | −2.97906 | − | 5.15988i | −0.215557 | − | 0.373355i | 0.737888 | − | 0.674923i | \(-0.235823\pi\) |
−0.953445 | + | 0.301568i | \(0.902490\pi\) | |||||||
\(192\) | 6.68866 | − | 1.17939i | 0.482713 | − | 0.0851153i | ||||
\(193\) | −5.41147 | + | 9.37295i | −0.389526 | + | 0.674680i | −0.992386 | − | 0.123168i | \(-0.960695\pi\) |
0.602859 | + | 0.797847i | \(0.294028\pi\) | |||||||
\(194\) | −5.39306 | + | 9.34105i | −0.387199 | + | 0.670648i | ||||
\(195\) | −21.6668 | − | 25.8215i | −1.55159 | − | 1.84912i | ||||
\(196\) | 5.03596 | + | 8.72254i | 0.359711 | + | 0.623038i | ||||
\(197\) | 3.07192 | 0.218865 | 0.109433 | − | 0.993994i | \(-0.465097\pi\) | ||||
0.109433 | + | 0.993994i | \(0.465097\pi\) | |||||||
\(198\) | −0.979055 | + | 5.55250i | −0.0695784 | + | 0.394599i | ||||
\(199\) | 1.54664 | 0.109638 | 0.0548191 | − | 0.998496i | \(-0.482542\pi\) | ||||
0.0548191 | + | 0.998496i | \(0.482542\pi\) | |||||||
\(200\) | −1.44697 | − | 2.50622i | −0.102316 | − | 0.177216i | ||||
\(201\) | −6.99525 | + | 19.2193i | −0.493407 | + | 1.35562i | ||||
\(202\) | −4.15270 | + | 7.19269i | −0.292183 | + | 0.506076i | ||||
\(203\) | −1.31268 | + | 2.27363i | −0.0921322 | + | 0.159578i | ||||
\(204\) | 0.167718 | − | 0.460802i | 0.0117426 | − | 0.0322626i | ||||
\(205\) | 8.08512 | + | 14.0038i | 0.564689 | + | 0.978071i | ||||
\(206\) | −19.6186 | −1.36689 | ||||||||
\(207\) | 1.65910 | − | 9.40923i | 0.115315 | − | 0.653986i | ||||
\(208\) | 31.8803 | 2.21050 | ||||||||
\(209\) | −2.61334 | − | 4.52644i | −0.180769 | − | 0.313100i | ||||
\(210\) | 3.93242 | + | 4.68647i | 0.271363 | + | 0.323397i | ||||
\(211\) | 7.92649 | − | 13.7291i | 0.545682 | − | 0.945149i | −0.452882 | − | 0.891571i | \(-0.649604\pi\) |
0.998564 | − | 0.0535783i | \(-0.0170627\pi\) | |||||||
\(212\) | 7.71554 | − | 13.3637i | 0.529905 | − | 0.917823i | ||||
\(213\) | 4.22281 | − | 0.744596i | 0.289342 | − | 0.0510188i | ||||
\(214\) | −7.81180 | − | 13.5304i | −0.534004 | − | 0.924922i | ||||
\(215\) | 11.1138 | 0.757955 | ||||||||
\(216\) | −3.95723 | + | 2.28471i | −0.269256 | + | 0.155455i | ||||
\(217\) | −0.721934 | −0.0490081 | ||||||||
\(218\) | −15.0239 | − | 26.0222i | −1.01755 | − | 1.76245i | ||||
\(219\) | −17.8439 | + | 3.14636i | −1.20578 | + | 0.212611i | ||||
\(220\) | 2.20574 | − | 3.82045i | 0.148711 | − | 0.257575i | ||||
\(221\) | 0.624485 | − | 1.08164i | 0.0420074 | − | 0.0727590i | ||||
\(222\) | −0.221934 | − | 0.264490i | −0.0148952 | − | 0.0177514i | ||||
\(223\) | −3.12314 | − | 5.40944i | −0.209141 | − | 0.362243i | 0.742303 | − | 0.670064i | \(-0.233733\pi\) |
−0.951444 | + | 0.307821i | \(0.900400\pi\) | |||||||
\(224\) | −4.63816 | −0.309900 | ||||||||
\(225\) | −7.56283 | − | 6.34597i | −0.504189 | − | 0.423065i | ||||
\(226\) | 9.51754 | 0.633097 | ||||||||
\(227\) | −1.63088 | − | 2.82477i | −0.108245 | − | 0.187487i | 0.806814 | − | 0.590805i | \(-0.201190\pi\) |
−0.915060 | + | 0.403319i | \(0.867857\pi\) | |||||||
\(228\) | −4.74376 | + | 13.0334i | −0.314163 | + | 0.863155i | ||||
\(229\) | 5.40760 | − | 9.36624i | 0.357345 | − | 0.618939i | −0.630172 | − | 0.776456i | \(-0.717016\pi\) |
0.987516 | + | 0.157517i | \(0.0503489\pi\) | |||||||
\(230\) | −8.61721 | + | 14.9254i | −0.568202 | + | 0.984155i | ||||
\(231\) | 0.386659 | − | 1.06234i | 0.0254403 | − | 0.0698967i | ||||
\(232\) | 1.76857 | + | 3.06325i | 0.116112 | + | 0.201112i | ||||
\(233\) | −3.71688 | −0.243501 | −0.121750 | − | 0.992561i | \(-0.538851\pi\) | ||||
−0.121750 | + | 0.992561i | \(0.538851\pi\) | |||||||
\(234\) | 35.8089 | − | 13.0334i | 2.34090 | − | 0.852018i | ||||
\(235\) | 34.5749 | 2.25542 | ||||||||
\(236\) | −8.08512 | − | 14.0038i | −0.526297 | − | 0.911573i | ||||
\(237\) | −1.63429 | − | 1.94767i | −0.106158 | − | 0.126514i | ||||
\(238\) | −0.113341 | + | 0.196312i | −0.00734679 | + | 0.0127250i | ||||
\(239\) | −4.02869 | + | 6.97789i | −0.260594 | + | 0.451362i | −0.966400 | − | 0.257043i | \(-0.917252\pi\) |
0.705806 | + | 0.708405i | \(0.250585\pi\) | |||||||
\(240\) | 23.1668 | − | 4.08494i | 1.49541 | − | 0.263682i | ||||
\(241\) | 2.15998 | + | 3.74119i | 0.139136 | + | 0.240991i | 0.927170 | − | 0.374641i | \(-0.122234\pi\) |
−0.788034 | + | 0.615632i | \(0.788901\pi\) | |||||||
\(242\) | −1.87939 | −0.120811 | ||||||||
\(243\) | −10.0201 | + | 11.9415i | −0.642788 | + | 0.766044i | ||||
\(244\) | −11.2567 | −0.720637 | ||||||||
\(245\) | 9.46451 | + | 16.3930i | 0.604665 | + | 1.04731i | ||||
\(246\) | −18.0030 | + | 3.17441i | −1.14783 | + | 0.202393i | ||||
\(247\) | −17.6630 | + | 30.5932i | −1.12387 | + | 1.94660i | ||||
\(248\) | −0.486329 | + | 0.842347i | −0.0308819 | + | 0.0534891i | ||||
\(249\) | −1.15998 | − | 1.38241i | −0.0735106 | − | 0.0876065i | ||||
\(250\) | −4.62449 | − | 8.00984i | −0.292478 | − | 0.506587i | ||||
\(251\) | 14.1753 | 0.894737 | 0.447368 | − | 0.894350i | \(-0.352361\pi\) | ||||
0.447368 | + | 0.894350i | \(0.352361\pi\) | |||||||
\(252\) | −2.81908 | + | 1.02606i | −0.177585 | + | 0.0646357i | ||||
\(253\) | 3.18479 | 0.200226 | ||||||||
\(254\) | 7.33022 | + | 12.6963i | 0.459939 | + | 0.796638i | ||||
\(255\) | 0.315207 | − | 0.866025i | 0.0197391 | − | 0.0542326i | ||||
\(256\) | −10.3512 | + | 17.9287i | −0.646948 | + | 1.12055i | ||||
\(257\) | 4.31655 | − | 7.47649i | 0.269259 | − | 0.466370i | −0.699412 | − | 0.714719i | \(-0.746555\pi\) |
0.968671 | + | 0.248349i | \(0.0798879\pi\) | |||||||
\(258\) | −4.29726 | + | 11.8066i | −0.267535 | + | 0.735048i | ||||
\(259\) | 0.0346151 | + | 0.0599551i | 0.00215088 | + | 0.00372543i | ||||
\(260\) | −29.8161 | −1.84912 | ||||||||
\(261\) | 9.24376 | + | 7.75643i | 0.572174 | + | 0.480111i | ||||
\(262\) | 23.4884 | 1.45112 | ||||||||
\(263\) | −0.599670 | − | 1.03866i | −0.0369773 | − | 0.0640465i | 0.846945 | − | 0.531681i | \(-0.178440\pi\) |
−0.883922 | + | 0.467635i | \(0.845106\pi\) | |||||||
\(264\) | −0.979055 | − | 1.16679i | −0.0602567 | − | 0.0718111i | ||||
\(265\) | 14.5005 | − | 25.1155i | 0.890757 | − | 1.54284i | ||||
\(266\) | 3.20574 | − | 5.55250i | 0.196556 | − | 0.340446i | ||||
\(267\) | 5.15064 | − | 0.908198i | 0.315214 | − | 0.0555808i | ||||
\(268\) | 9.04576 | + | 15.6677i | 0.552558 | + | 0.957058i | ||||
\(269\) | 27.9213 | 1.70239 | 0.851195 | − | 0.524849i | \(-0.175878\pi\) | ||||
0.851195 | + | 0.524849i | \(0.175878\pi\) | |||||||
\(270\) | 24.3516 | − | 14.0594i | 1.48199 | − | 0.855629i | ||||
\(271\) | −13.4311 | −0.815880 | −0.407940 | − | 0.913009i | \(-0.633753\pi\) | ||||
−0.407940 | + | 0.913009i | \(0.633753\pi\) | |||||||
\(272\) | 0.435822 | + | 0.754866i | 0.0264256 | + | 0.0457705i | ||||
\(273\) | −7.52481 | + | 1.32683i | −0.455423 | + | 0.0803033i | ||||
\(274\) | 14.3084 | − | 24.7829i | 0.864402 | − | 1.49719i | ||||
\(275\) | 1.64543 | − | 2.84997i | 0.0992231 | − | 0.171860i | ||||
\(276\) | −5.43242 | − | 6.47410i | −0.326993 | − | 0.389695i | ||||
\(277\) | 4.24035 | + | 7.34451i | 0.254778 | + | 0.441289i | 0.964835 | − | 0.262855i | \(-0.0846642\pi\) |
−0.710057 | + | 0.704144i | \(0.751331\pi\) | |||||||
\(278\) | −27.2567 | −1.63475 | ||||||||
\(279\) | −0.576199 | + | 3.26779i | −0.0344962 | + | 0.195637i | ||||
\(280\) | −1.65270 | −0.0987679 | ||||||||
\(281\) | 1.26945 | + | 2.19875i | 0.0757289 | + | 0.131166i | 0.901403 | − | 0.432981i | \(-0.142538\pi\) |
−0.825674 | + | 0.564147i | \(0.809205\pi\) | |||||||
\(282\) | −13.3687 | + | 36.7302i | −0.796095 | + | 2.18725i | ||||
\(283\) | 2.33750 | − | 4.04866i | 0.138950 | − | 0.240668i | −0.788150 | − | 0.615484i | \(-0.788961\pi\) |
0.927099 | + | 0.374816i | \(0.122294\pi\) | |||||||
\(284\) | 1.89646 | − | 3.28476i | 0.112534 | − | 0.194915i | ||||
\(285\) | −8.91534 | + | 24.4947i | −0.528099 | + | 1.45094i | ||||
\(286\) | 6.35117 | + | 11.0005i | 0.375552 | + | 0.650476i | ||||
\(287\) | 3.66550 | 0.216367 | ||||||||
\(288\) | −3.70187 | + | 20.9943i | −0.218135 | + | 1.23710i | ||||
\(289\) | −16.9659 | −0.997991 | ||||||||
\(290\) | −10.8833 | − | 18.8504i | −0.639087 | − | 1.10693i | ||||
\(291\) | −6.38965 | − | 7.61489i | −0.374568 | − | 0.446393i | ||||
\(292\) | −8.01367 | + | 13.8801i | −0.468965 | + | 0.812271i | ||||
\(293\) | −3.92262 | + | 6.79417i | −0.229162 | + | 0.396920i | −0.957560 | − | 0.288234i | \(-0.906932\pi\) |
0.728398 | + | 0.685154i | \(0.240265\pi\) | |||||||
\(294\) | −21.0744 | + | 3.71599i | −1.22909 | + | 0.216721i | ||||
\(295\) | −15.1951 | − | 26.3186i | −0.884691 | − | 1.53233i | ||||
\(296\) | 0.0932736 | 0.00542142 | ||||||||
\(297\) | −4.50000 | − | 2.59808i | −0.261116 | − | 0.150756i | ||||
\(298\) | −27.4561 | −1.59049 | ||||||||
\(299\) | −10.7626 | − | 18.6414i | −0.622420 | − | 1.07806i | ||||
\(300\) | −8.60014 | + | 1.51644i | −0.496529 | + | 0.0875515i | ||||
\(301\) | 1.25965 | − | 2.18177i | 0.0726049 | − | 0.125755i | ||||
\(302\) | −19.8341 | + | 34.3537i | −1.14132 | + | 1.97683i | ||||
\(303\) | −4.92009 | − | 5.86354i | −0.282652 | − | 0.336851i | ||||
\(304\) | −12.3268 | − | 21.3507i | −0.706992 | − | 1.22455i | ||||
\(305\) | −21.1557 | −1.21137 | ||||||||
\(306\) | 0.798133 | + | 0.669713i | 0.0456262 | + | 0.0382850i | ||||
\(307\) | 26.4047 | 1.50699 | 0.753497 | − | 0.657451i | \(-0.228365\pi\) | ||||
0.753497 | + | 0.657451i | \(0.228365\pi\) | |||||||
\(308\) | −0.500000 | − | 0.866025i | −0.0284901 | − | 0.0493464i | ||||
\(309\) | 6.18392 | − | 16.9902i | 0.351791 | − | 0.966537i | ||||
\(310\) | 2.99273 | − | 5.18355i | 0.169975 | − | 0.294406i | ||||
\(311\) | 9.57057 | − | 16.5767i | 0.542697 | − | 0.939980i | −0.456050 | − | 0.889954i | \(-0.650736\pi\) |
0.998748 | − | 0.0500257i | \(-0.0159303\pi\) | |||||||
\(312\) | −3.52094 | + | 9.67372i | −0.199334 | + | 0.547666i | ||||
\(313\) | 4.48545 | + | 7.76903i | 0.253533 | + | 0.439132i | 0.964496 | − | 0.264098i | \(-0.0850741\pi\) |
−0.710963 | + | 0.703229i | \(0.751741\pi\) | |||||||
\(314\) | 8.32770 | 0.469959 | ||||||||
\(315\) | −5.29813 | + | 1.92836i | −0.298516 | + | 0.108651i | ||||
\(316\) | −2.24897 | −0.126514 | ||||||||
\(317\) | −3.13903 | − | 5.43696i | −0.176306 | − | 0.305370i | 0.764307 | − | 0.644853i | \(-0.223081\pi\) |
−0.940612 | + | 0.339483i | \(0.889748\pi\) | |||||||
\(318\) | 21.0744 | + | 25.1155i | 1.18180 | + | 1.40841i | ||||
\(319\) | −2.01114 | + | 3.48340i | −0.112602 | + | 0.195033i | ||||
\(320\) | 5.64543 | − | 9.77817i | 0.315589 | − | 0.546616i | ||||
\(321\) | 14.1800 | − | 2.50032i | 0.791453 | − | 0.139555i | ||||
\(322\) | 1.95336 | + | 3.38332i | 0.108857 | + | 0.188545i | ||||
\(323\) | −0.965852 | −0.0537414 | ||||||||
\(324\) | 2.39440 | + | 13.5793i | 0.133022 | + | 0.754407i | ||||
\(325\) | −22.2422 | −1.23377 | ||||||||
\(326\) | −1.99747 | − | 3.45973i | −0.110630 | − | 0.191617i | ||||
\(327\) | 27.2716 | − | 4.80871i | 1.50812 | − | 0.265922i | ||||
\(328\) | 2.46926 | − | 4.27688i | 0.136342 | − | 0.236151i | ||||
\(329\) | 3.91875 | − | 6.78747i | 0.216048 | − | 0.374205i | ||||
\(330\) | 6.02481 | + | 7.18009i | 0.331655 | + | 0.395251i | ||||
\(331\) | 5.93629 | + | 10.2820i | 0.326288 | + | 0.565147i | 0.981772 | − | 0.190062i | \(-0.0608688\pi\) |
−0.655484 | + | 0.755209i | \(0.727535\pi\) | |||||||
\(332\) | −1.59627 | −0.0876065 | ||||||||
\(333\) | 0.299011 | − | 0.108831i | 0.0163857 | − | 0.00596390i | ||||
\(334\) | −23.3628 | −1.27835 | ||||||||
\(335\) | 17.0005 | + | 29.4457i | 0.928835 | + | 1.60879i | ||||
\(336\) | 1.82383 | − | 5.01092i | 0.0994978 | − | 0.273368i | ||||
\(337\) | −4.52094 | + | 7.83051i | −0.246272 | + | 0.426555i | −0.962488 | − | 0.271323i | \(-0.912539\pi\) |
0.716217 | + | 0.697878i | \(0.245872\pi\) | |||||||
\(338\) | 30.7101 | − | 53.1914i | 1.67041 | − | 2.89323i | ||||
\(339\) | −3.00000 | + | 8.24243i | −0.162938 | + | 0.447667i | ||||
\(340\) | −0.407604 | − | 0.705990i | −0.0221054 | − | 0.0382877i | ||||
\(341\) | −1.10607 | −0.0598969 | ||||||||
\(342\) | −22.5744 | − | 18.9422i | −1.22069 | − | 1.02428i | ||||
\(343\) | 8.85978 | 0.478383 | ||||||||
\(344\) | −1.69712 | − | 2.93950i | −0.0915025 | − | 0.158487i | ||||
\(345\) | −10.2096 | − | 12.1673i | −0.549667 | − | 0.655067i | ||||
\(346\) | 3.38666 | − | 5.86587i | 0.182068 | − | 0.315351i | ||||
\(347\) | 9.48158 | − | 16.4226i | 0.508998 | − | 0.881610i | −0.490948 | − | 0.871189i | \(-0.663349\pi\) |
0.999946 | − | 0.0104213i | \(-0.00331727\pi\) | |||||||
\(348\) | 10.5116 | − | 1.85348i | 0.563482 | − | 0.0993570i | ||||
\(349\) | 11.0642 | + | 19.1637i | 0.592252 | + | 1.02581i | 0.993928 | + | 0.110029i | \(0.0350943\pi\) |
−0.401677 | + | 0.915782i | \(0.631572\pi\) | |||||||
\(350\) | 4.03684 | 0.215778 | ||||||||
\(351\) | 35.1196i | 1.87455i | ||||||||
\(352\) | −7.10607 | −0.378755 | ||||||||
\(353\) | 12.2208 | + | 21.1670i | 0.650445 | + | 1.12660i | 0.983015 | + | 0.183525i | \(0.0587509\pi\) |
−0.332570 | + | 0.943079i | \(0.607916\pi\) | |||||||
\(354\) | 33.8346 | − | 5.96595i | 1.79829 | − | 0.317086i | ||||
\(355\) | 3.56418 | − | 6.17334i | 0.189167 | − | 0.327647i | ||||
\(356\) | 2.31315 | − | 4.00649i | 0.122597 | − | 0.212344i | ||||
\(357\) | −0.134285 | − | 0.160035i | −0.00710713 | − | 0.00846995i | ||||
\(358\) | 12.0963 | + | 20.9513i | 0.639308 | + | 1.10731i | ||||
\(359\) | −4.68685 | −0.247363 | −0.123681 | − | 0.992322i | \(-0.539470\pi\) | ||||
−0.123681 | + | 0.992322i | \(0.539470\pi\) | |||||||
\(360\) | −1.31908 | + | 7.48086i | −0.0695215 | + | 0.394276i | ||||
\(361\) | 8.31820 | 0.437800 | ||||||||
\(362\) | −22.8726 | − | 39.6165i | −1.20216 | − | 2.08220i | ||||
\(363\) | 0.592396 | − | 1.62760i | 0.0310927 | − | 0.0854266i | ||||
\(364\) | −3.37939 | + | 5.85327i | −0.177128 | + | 0.306795i | ||||
\(365\) | −15.0608 | + | 26.0860i | −0.788317 | + | 1.36541i | ||||
\(366\) | 8.18004 | − | 22.4745i | 0.427578 | − | 1.17476i | ||||
\(367\) | 4.50134 | + | 7.79656i | 0.234968 | + | 0.406977i | 0.959263 | − | 0.282513i | \(-0.0911680\pi\) |
−0.724295 | + | 0.689490i | \(0.757835\pi\) | |||||||
\(368\) | 15.0223 | 0.783091 | ||||||||
\(369\) | 2.92556 | − | 16.5916i | 0.152298 | − | 0.863727i | ||||
\(370\) | −0.573978 | −0.0298397 | ||||||||
\(371\) | −3.28699 | − | 5.69323i | −0.170652 | − | 0.295578i | ||||
\(372\) | 1.88666 | + | 2.24843i | 0.0978187 | + | 0.116576i | ||||
\(373\) | −5.13950 | + | 8.90187i | −0.266113 | + | 0.460922i | −0.967855 | − | 0.251510i | \(-0.919073\pi\) |
0.701741 | + | 0.712432i | \(0.252406\pi\) | |||||||
\(374\) | −0.173648 | + | 0.300767i | −0.00897913 | + | 0.0155523i | ||||
\(375\) | 8.39440 | − | 1.48016i | 0.433485 | − | 0.0764351i | ||||
\(376\) | −5.27972 | − | 9.14473i | −0.272281 | − | 0.471604i | ||||
\(377\) | 27.1857 | 1.40014 | ||||||||
\(378\) | − | 6.37402i | − | 0.327844i | ||||||
\(379\) | 14.2540 | 0.732180 | 0.366090 | − | 0.930579i | \(-0.380696\pi\) | ||||
0.366090 | + | 0.930579i | \(0.380696\pi\) | |||||||
\(380\) | 11.5287 | + | 19.9683i | 0.591409 | + | 1.02435i | ||||
\(381\) | −13.3059 | + | 2.34618i | −0.681681 | + | 0.120199i | ||||
\(382\) | 5.59879 | − | 9.69739i | 0.286459 | − | 0.496162i | ||||
\(383\) | −7.41740 | + | 12.8473i | −0.379012 | + | 0.656467i | −0.990919 | − | 0.134462i | \(-0.957069\pi\) |
0.611907 | + | 0.790930i | \(0.290403\pi\) | |||||||
\(384\) | −7.61809 | − | 9.07888i | −0.388759 | − | 0.463305i | ||||
\(385\) | −0.939693 | − | 1.62760i | −0.0478912 | − | 0.0829499i | ||||
\(386\) | −20.3405 | −1.03530 | ||||||||
\(387\) | −8.87030 | − | 7.44307i | −0.450903 | − | 0.378352i | ||||
\(388\) | −8.79292 | −0.446393 | ||||||||
\(389\) | −5.46064 | − | 9.45810i | −0.276865 | − | 0.479545i | 0.693739 | − | 0.720227i | \(-0.255962\pi\) |
−0.970604 | + | 0.240682i | \(0.922629\pi\) | |||||||
\(390\) | 21.6668 | − | 59.5292i | 1.09714 | − | 3.01438i | ||||
\(391\) | 0.294263 | − | 0.509678i | 0.0148815 | − | 0.0257755i | ||||
\(392\) | 2.89053 | − | 5.00654i | 0.145994 | − | 0.252869i | ||||
\(393\) | −7.40373 | + | 20.3416i | −0.373469 | + | 1.02610i | ||||
\(394\) | 2.88666 | + | 4.99984i | 0.145428 | + | 0.251888i | ||||
\(395\) | −4.22668 | −0.212667 | ||||||||
\(396\) | −4.31908 | + | 1.57202i | −0.217042 | + | 0.0789968i | ||||
\(397\) | −34.5945 | −1.73625 | −0.868124 | − | 0.496347i | \(-0.834674\pi\) | ||||
−0.868124 | + | 0.496347i | \(0.834674\pi\) | |||||||
\(398\) | 1.45336 | + | 2.51730i | 0.0728505 | + | 0.126181i | ||||
\(399\) | 3.79813 | + | 4.52644i | 0.190144 | + | 0.226605i | ||||
\(400\) | 7.76130 | − | 13.4430i | 0.388065 | − | 0.672148i | ||||
\(401\) | −8.62061 | + | 14.9313i | −0.430493 | + | 0.745636i | −0.996916 | − | 0.0784791i | \(-0.974994\pi\) |
0.566423 | + | 0.824115i | \(0.308327\pi\) | |||||||
\(402\) | −37.8546 | + | 6.67479i | −1.88802 | + | 0.332908i | ||||
\(403\) | 3.73783 | + | 6.47410i | 0.186194 | + | 0.322498i | ||||
\(404\) | −6.77063 | −0.336851 | ||||||||
\(405\) | 4.50000 | + | 25.5208i | 0.223607 | + | 1.26814i | ||||
\(406\) | −4.93407 | −0.244874 | ||||||||
\(407\) | 0.0530334 | + | 0.0918566i | 0.00262877 | + | 0.00455316i | ||||
\(408\) | −0.277189 | + | 0.0488759i | −0.0137229 | + | 0.00241972i | ||||
\(409\) | 2.21167 | − | 3.83072i | 0.109360 | − | 0.189417i | −0.806151 | − | 0.591710i | \(-0.798453\pi\) |
0.915511 | + | 0.402293i | \(0.131787\pi\) | |||||||
\(410\) | −15.1951 | + | 26.3186i | −0.750431 | + | 1.29978i | ||||
\(411\) | 16.9525 | + | 20.2032i | 0.836204 | + | 0.996550i | ||||
\(412\) | −7.99660 | − | 13.8505i | −0.393964 | − | 0.682366i | ||||
\(413\) | −6.88888 | −0.338980 | ||||||||
\(414\) | 16.8735 | − | 6.14144i | 0.829285 | − | 0.301835i | ||||
\(415\) | −3.00000 | −0.147264 | ||||||||
\(416\) | 24.0141 | + | 41.5937i | 1.17739 | + | 2.03930i | ||||
\(417\) | 8.59152 | − | 23.6050i | 0.420728 | − | 1.15594i | ||||
\(418\) | 4.91147 | − | 8.50692i | 0.240228 | − | 0.416087i | ||||
\(419\) | 8.75877 | − | 15.1706i | 0.427894 | − | 0.741134i | −0.568792 | − | 0.822481i | \(-0.692589\pi\) |
0.996686 | + | 0.0813475i | \(0.0259223\pi\) | |||||||
\(420\) | −1.70574 | + | 4.68647i | −0.0832314 | + | 0.228677i | ||||
\(421\) | −4.95858 | − | 8.58851i | −0.241666 | − | 0.418578i | 0.719523 | − | 0.694469i | \(-0.244361\pi\) |
−0.961189 | + | 0.275891i | \(0.911027\pi\) | |||||||
\(422\) | 29.7939 | 1.45034 | ||||||||
\(423\) | −27.5954 | − | 23.1553i | −1.34173 | − | 1.12585i | ||||
\(424\) | −8.85710 | −0.430139 | ||||||||
\(425\) | −0.304063 | − | 0.526653i | −0.0147492 | − | 0.0255464i | ||||
\(426\) | 5.18004 | + | 6.17334i | 0.250974 | + | 0.299099i | ||||
\(427\) | −2.39780 | + | 4.15312i | −0.116038 | + | 0.200983i | ||||
\(428\) | 6.36824 | − | 11.0301i | 0.307821 | − | 0.533161i | ||||
\(429\) | −11.5287 | + | 2.03282i | −0.556610 | + | 0.0981454i | ||||
\(430\) | 10.4436 | + | 18.0888i | 0.503633 | + | 0.872319i | ||||
\(431\) | −2.38238 | −0.114755 | −0.0573776 | − | 0.998353i | \(-0.518274\pi\) | ||||
−0.0573776 | + | 0.998353i | \(0.518274\pi\) | |||||||
\(432\) | −21.2260 | − | 12.2548i | −1.02123 | − | 0.589610i | ||||
\(433\) | 31.1661 | 1.49775 | 0.748874 | − | 0.662712i | \(-0.230595\pi\) | ||||
0.748874 | + | 0.662712i | \(0.230595\pi\) | |||||||
\(434\) | −0.678396 | − | 1.17502i | −0.0325640 | − | 0.0564026i | ||||
\(435\) | 19.7554 | − | 3.48340i | 0.947197 | − | 0.167016i | ||||
\(436\) | 12.2476 | − | 21.2135i | 0.586555 | − | 1.01594i | ||||
\(437\) | −8.32295 | + | 14.4158i | −0.398141 | + | 0.689600i | ||||
\(438\) | −21.8888 | − | 26.0860i | −1.04589 | − | 1.24644i | ||||
\(439\) | −4.02734 | − | 6.97556i | −0.192215 | − | 0.332925i | 0.753769 | − | 0.657139i | \(-0.228234\pi\) |
−0.945984 | + | 0.324214i | \(0.894900\pi\) | |||||||
\(440\) | −2.53209 | −0.120713 | ||||||||
\(441\) | 3.42468 | − | 19.4223i | 0.163080 | − | 0.924872i | ||||
\(442\) | 2.34730 | 0.111650 | ||||||||
\(443\) | 5.81773 | + | 10.0766i | 0.276409 | + | 0.478754i | 0.970490 | − | 0.241143i | \(-0.0775223\pi\) |
−0.694081 | + | 0.719897i | \(0.744189\pi\) | |||||||
\(444\) | 0.0962667 | − | 0.264490i | 0.00456861 | − | 0.0125522i | ||||
\(445\) | 4.34730 | − | 7.52974i | 0.206082 | − | 0.356944i | ||||
\(446\) | 5.86959 | − | 10.1664i | 0.277933 | − | 0.481394i | ||||
\(447\) | 8.65435 | − | 23.7776i | 0.409337 | − | 1.12464i | ||||
\(448\) | −1.27972 | − | 2.21653i | −0.0604609 | − | 0.104721i | ||||
\(449\) | −25.7442 | −1.21494 | −0.607472 | − | 0.794341i | \(-0.707817\pi\) | ||||
−0.607472 | + | 0.794341i | \(0.707817\pi\) | |||||||
\(450\) | 3.22193 | − | 18.2725i | 0.151883 | − | 0.861374i | ||||
\(451\) | 5.61587 | 0.264441 | ||||||||
\(452\) | 3.87939 | + | 6.71929i | 0.182471 | + | 0.316049i | ||||
\(453\) | −23.4993 | − | 28.0054i | −1.10409 | − | 1.31581i | ||||
\(454\) | 3.06506 | − | 5.30883i | 0.143850 | − | 0.249156i | ||||
\(455\) | −6.35117 | + | 11.0005i | −0.297747 | + | 0.515713i | ||||
\(456\) | 7.84002 | − | 1.38241i | 0.367143 | − | 0.0647372i | ||||
\(457\) | −19.2160 | − | 33.2831i | −0.898887 | − | 1.55692i | −0.828919 | − | 0.559368i | \(-0.811044\pi\) |
−0.0699675 | − | 0.997549i | \(-0.522290\pi\) | |||||||
\(458\) | 20.3259 | 0.949769 | ||||||||
\(459\) | −0.831566 | + | 0.480105i | −0.0388142 | + | 0.0224094i | ||||
\(460\) | −14.0496 | −0.655067 | ||||||||
\(461\) | −2.79948 | − | 4.84884i | −0.130385 | − | 0.225833i | 0.793440 | − | 0.608648i | \(-0.208288\pi\) |
−0.923825 | + | 0.382815i | \(0.874955\pi\) | |||||||
\(462\) | 2.09240 | − | 0.368946i | 0.0973471 | − | 0.0171649i | ||||
\(463\) | −4.64677 | + | 8.04845i | −0.215954 | + | 0.374043i | −0.953567 | − | 0.301180i | \(-0.902619\pi\) |
0.737613 | + | 0.675223i | \(0.235953\pi\) | |||||||
\(464\) | −9.48633 | + | 16.4308i | −0.440392 | + | 0.762781i | ||||
\(465\) | 3.54576 | + | 4.22567i | 0.164431 | + | 0.195961i | ||||
\(466\) | −3.49273 | − | 6.04958i | −0.161797 | − | 0.280241i | ||||
\(467\) | 17.0642 | 0.789636 | 0.394818 | − | 0.918759i | \(-0.370808\pi\) | ||||
0.394818 | + | 0.918759i | \(0.370808\pi\) | |||||||
\(468\) | 23.7973 | + | 19.9683i | 1.10003 | + | 0.923034i | ||||
\(469\) | 7.70739 | 0.355894 | ||||||||
\(470\) | 32.4898 | + | 56.2740i | 1.49864 | + | 2.59572i | ||||
\(471\) | −2.62495 | + | 7.21200i | −0.120951 | + | 0.332311i | ||||
\(472\) | −4.64068 | + | 8.03790i | −0.213605 | + | 0.369974i | ||||
\(473\) | 1.92989 | − | 3.34267i | 0.0887365 | − | 0.153696i | ||||
\(474\) | 1.63429 | − | 4.49016i | 0.0750652 | − | 0.206240i | ||||
\(475\) | 8.60014 | + | 14.8959i | 0.394601 | + | 0.683470i | ||||
\(476\) | −0.184793 | −0.00846995 | ||||||||
\(477\) | −28.3935 | + | 10.3344i | −1.30005 | + | 0.473180i | ||||
\(478\) | −15.1429 | −0.692620 | ||||||||
\(479\) | 19.7101 | + | 34.1389i | 0.900576 | + | 1.55984i | 0.826748 | + | 0.562573i | \(0.190188\pi\) |
0.0738286 | + | 0.997271i | \(0.476478\pi\) | |||||||
\(480\) | 22.7802 | + | 27.1484i | 1.03977 | + | 1.23915i | ||||
\(481\) | 0.358441 | − | 0.620838i | 0.0163435 | − | 0.0283078i | ||||
\(482\) | −4.05943 | + | 7.03114i | −0.184902 | + | 0.320260i | ||||
\(483\) | −3.54576 | + | 0.625213i | −0.161338 | + | 0.0284482i | ||||
\(484\) | −0.766044 | − | 1.32683i | −0.0348202 | − | 0.0603104i | ||||
\(485\) | −16.5253 | −0.750374 | ||||||||
\(486\) | −28.8516 | − | 5.08732i | −1.30874 | − | 0.230766i | ||||
\(487\) | −34.9522 | −1.58384 | −0.791919 | − | 0.610627i | \(-0.790918\pi\) | ||||
−0.791919 | + | 0.610627i | \(0.790918\pi\) | |||||||
\(488\) | 3.23055 | + | 5.59548i | 0.146240 | + | 0.253295i | ||||
\(489\) | 3.62583 | − | 0.639332i | 0.163966 | − | 0.0289116i | ||||
\(490\) | −17.7875 | + | 30.8088i | −0.803555 | + | 1.39180i | ||||
\(491\) | 12.0235 | − | 20.8253i | 0.542612 | − | 0.939831i | −0.456141 | − | 0.889907i | \(-0.650769\pi\) |
0.998753 | − | 0.0499236i | \(-0.0158978\pi\) | |||||||
\(492\) | −9.57919 | − | 11.4160i | −0.431863 | − | 0.514675i | ||||
\(493\) | 0.371644 | + | 0.643707i | 0.0167380 | + | 0.0289911i | ||||
\(494\) | −66.3911 | −2.98707 | ||||||||
\(495\) | −8.11721 | + | 2.95442i | −0.364842 | + | 0.132791i | ||||
\(496\) | −5.21719 | −0.234259 | ||||||||
\(497\) | −0.807934 | − | 1.39938i | −0.0362408 | − | 0.0627709i | ||||
\(498\) | 1.15998 | − | 3.18701i | 0.0519798 | − | 0.142813i | ||||
\(499\) | −13.5608 | + | 23.4879i | −0.607064 | + | 1.05147i | 0.384658 | + | 0.923059i | \(0.374319\pi\) |
−0.991722 | + | 0.128406i | \(0.959014\pi\) | |||||||
\(500\) | 3.76991 | − | 6.52968i | 0.168596 | − | 0.292016i | ||||
\(501\) | 7.36412 | − | 20.2328i | 0.329005 | − | 0.903933i | ||||
\(502\) | 13.3204 | + | 23.0716i | 0.594520 | + | 1.02974i | ||||
\(503\) | 16.2867 | 0.726190 | 0.363095 | − | 0.931752i | \(-0.381720\pi\) | ||||
0.363095 | + | 0.931752i | \(0.381720\pi\) | |||||||
\(504\) | 1.31908 | + | 1.10684i | 0.0587564 | + | 0.0493025i | ||||
\(505\) | −12.7246 | −0.566238 | ||||||||
\(506\) | 2.99273 | + | 5.18355i | 0.133043 | + | 0.230437i | ||||
\(507\) | 36.3851 | + | 43.3620i | 1.61592 | + | 1.92578i | ||||
\(508\) | −5.97565 | + | 10.3501i | −0.265127 | + | 0.459213i | ||||
\(509\) | −10.6655 | + | 18.4732i | −0.472740 | + | 0.818809i | −0.999513 | − | 0.0311963i | \(-0.990068\pi\) |
0.526773 | + | 0.850006i | \(0.323402\pi\) | |||||||
\(510\) | 1.70574 | − | 0.300767i | 0.0755313 | − | 0.0133182i | ||||
\(511\) | 3.41400 | + | 5.91322i | 0.151026 | + | 0.261586i | ||||
\(512\) | −25.2226 | −1.11469 | ||||||||
\(513\) | 23.5201 | − | 13.5793i | 1.03844 | − | 0.599541i | ||||
\(514\) | 16.2249 | 0.715651 | ||||||||
\(515\) | −15.0287 | − | 26.0304i | −0.662243 | − | 1.14704i | ||||
\(516\) | −10.0869 | + | 1.77860i | −0.444052 | + | 0.0782984i | ||||
\(517\) | 6.00387 | − | 10.3990i | 0.264050 | − | 0.457348i | ||||
\(518\) | −0.0650551 | + | 0.112679i | −0.00285836 | + | 0.00495082i | ||||
\(519\) | 4.01249 | + | 4.78190i | 0.176129 | + | 0.209902i | ||||
\(520\) | 8.55690 | + | 14.8210i | 0.375245 | + | 0.649944i | ||||
\(521\) | −39.4671 | −1.72908 | −0.864542 | − | 0.502560i | \(-0.832392\pi\) | ||||
−0.864542 | + | 0.502560i | \(0.832392\pi\) | |||||||
\(522\) | −3.93804 | + | 22.3338i | −0.172363 | + | 0.977522i | ||||
\(523\) | 4.68779 | 0.204983 | 0.102491 | − | 0.994734i | \(-0.467319\pi\) | ||||
0.102491 | + | 0.994734i | \(0.467319\pi\) | |||||||
\(524\) | 9.57398 | + | 16.5826i | 0.418241 | + | 0.724415i | ||||
\(525\) | −1.27244 | + | 3.49600i | −0.0555339 | + | 0.152578i | ||||
\(526\) | 1.12701 | − | 1.95204i | 0.0491400 | − | 0.0851130i | ||||
\(527\) | −0.102196 | + | 0.177009i | −0.00445175 | + | 0.00771065i | ||||
\(528\) | 2.79426 | − | 7.67717i | 0.121605 | − | 0.334106i | ||||
\(529\) | 6.42855 | + | 11.1346i | 0.279502 | + | 0.484112i | ||||
\(530\) | 54.5039 | 2.36750 | ||||||||
\(531\) | −5.49825 | + | 31.1821i | −0.238604 | + | 1.35319i | ||||
\(532\) | 5.22668 | 0.226605 | ||||||||
\(533\) | −18.9782 | − | 32.8712i | −0.822036 | − | 1.42381i | ||||
\(534\) | 6.31820 | + | 7.52974i | 0.273415 | + | 0.325844i | ||||
\(535\) | 11.9684 | − | 20.7298i | 0.517438 | − | 0.896229i | ||||
\(536\) | 5.19207 | − | 8.99292i | 0.224263 | − | 0.388435i | ||||
\(537\) | −21.9572 | + | 3.87165i | −0.947525 | + | 0.167074i | ||||
\(538\) | 26.2374 | + | 45.4445i | 1.13118 | + | 1.95925i | ||||
\(539\) | 6.57398 | 0.283161 | ||||||||
\(540\) | 19.8516 | + | 11.4613i | 0.854278 | + | 0.493218i | ||||
\(541\) | 0.200274 | 0.00861046 | 0.00430523 | − | 0.999991i | \(-0.498630\pi\) | ||||
0.00430523 | + | 0.999991i | \(0.498630\pi\) | |||||||
\(542\) | −12.6211 | − | 21.8604i | −0.542122 | − | 0.938983i | ||||
\(543\) | 41.5185 | − | 7.32083i | 1.78173 | − | 0.314167i | ||||
\(544\) | −0.656574 | + | 1.13722i | −0.0281504 | + | 0.0487579i | ||||
\(545\) | 23.0180 | − | 39.8684i | 0.985983 | − | 1.70777i | ||||
\(546\) | −9.23055 | − | 11.0005i | −0.395031 | − | 0.470780i | ||||
\(547\) | −17.9697 | − | 31.1245i | −0.768330 | − | 1.33079i | −0.938468 | − | 0.345366i | \(-0.887755\pi\) |
0.170138 | − | 0.985420i | \(-0.445579\pi\) | |||||||
\(548\) | 23.3286 | 0.996550 | ||||||||
\(549\) | 16.8851 | + | 14.1683i | 0.720637 | + | 0.604686i | ||||
\(550\) | 6.18479 | 0.263720 | ||||||||
\(551\) | −10.5116 | − | 18.2066i | −0.447810 | − | 0.775629i | ||||
\(552\) | −1.65910 | + | 4.55834i | −0.0706160 | + | 0.194016i | ||||
\(553\) | −0.479055 | + | 0.829748i | −0.0203715 | + | 0.0352845i | ||||
\(554\) | −7.96926 | + | 13.8032i | −0.338581 | + | 0.586440i | ||||
\(555\) | 0.180922 | − | 0.497079i | 0.00767972 | − | 0.0210998i | ||||
\(556\) | −11.1099 | − | 19.2430i | −0.471166 | − | 0.816084i | ||||
\(557\) | 16.6186 | 0.704151 | 0.352075 | − | 0.935972i | \(-0.385476\pi\) | ||||
0.352075 | + | 0.935972i | \(0.385476\pi\) | |||||||
\(558\) | −5.86009 | + | 2.13290i | −0.248077 | + | 0.0902928i | ||||
\(559\) | −26.0874 | −1.10338 | ||||||||
\(560\) | −4.43242 | − | 7.67717i | −0.187304 | − | 0.324420i | ||||
\(561\) | −0.205737 | − | 0.245188i | −0.00868623 | − | 0.0103518i | ||||
\(562\) | −2.38578 | + | 4.13230i | −0.100638 | + | 0.174310i | ||||
\(563\) | 6.46316 | − | 11.1945i | 0.272390 | − | 0.471793i | −0.697083 | − | 0.716990i | \(-0.745519\pi\) |
0.969473 | + | 0.245197i | \(0.0788526\pi\) | |||||||
\(564\) | −31.3803 | + | 5.53320i | −1.32135 | + | 0.232990i | ||||
\(565\) | 7.29086 | + | 12.6281i | 0.306729 | + | 0.531270i | ||||
\(566\) | 8.78611 | 0.369308 | ||||||||
\(567\) | 5.52007 | + | 2.00914i | 0.231821 | + | 0.0843760i | ||||
\(568\) | −2.17705 | −0.0913471 | ||||||||
\(569\) | −6.73648 | − | 11.6679i | −0.282408 | − | 0.489145i | 0.689569 | − | 0.724220i | \(-0.257800\pi\) |
−0.971977 | + | 0.235075i | \(0.924467\pi\) | |||||||
\(570\) | −48.2452 | + | 8.50692i | −2.02077 | + | 0.356316i | ||||
\(571\) | −0.427204 | + | 0.739939i | −0.0178779 | + | 0.0309655i | −0.874826 | − | 0.484437i | \(-0.839024\pi\) |
0.856948 | + | 0.515403i | \(0.172358\pi\) | |||||||
\(572\) | −5.17752 | + | 8.96773i | −0.216483 | + | 0.374959i | ||||
\(573\) | 6.63341 | + | 7.90539i | 0.277115 | + | 0.330252i | ||||
\(574\) | 3.44444 | + | 5.96595i | 0.143768 | + | 0.249014i | ||||
\(575\) | −10.4807 | −0.437076 | ||||||||
\(576\) | −11.0544 | + | 4.02346i | −0.460599 | + | 0.167644i | ||||
\(577\) | −2.22668 | −0.0926980 | −0.0463490 | − | 0.998925i | \(-0.514759\pi\) | ||||
−0.0463490 | + | 0.998925i | \(0.514759\pi\) | |||||||
\(578\) | −15.9427 | − | 27.6135i | −0.663128 | − | 1.14857i | ||||
\(579\) | 6.41147 | − | 17.6154i | 0.266452 | − | 0.732070i | ||||
\(580\) | 8.87211 | − | 15.3669i | 0.368394 | − | 0.638078i | ||||
\(581\) | −0.340022 | + | 0.588936i | −0.0141065 | + | 0.0244332i | ||||
\(582\) | 6.38965 | − | 17.5554i | 0.264860 | − | 0.727696i | ||||
\(583\) | −5.03596 | − | 8.72254i | −0.208568 | − | 0.361251i | ||||
\(584\) | 9.19934 | 0.380671 | ||||||||
\(585\) | 44.7242 | + | 37.5281i | 1.84912 | + | 1.55159i | ||||
\(586\) | −14.7442 | −0.609078 | ||||||||
\(587\) | −2.41993 | − | 4.19144i | −0.0998812 | − | 0.172999i | 0.811754 | − | 0.583999i | \(-0.198513\pi\) |
−0.911635 | + | 0.411000i | \(0.865180\pi\) | |||||||
\(588\) | −11.2135 | − | 13.3637i | −0.462436 | − | 0.551110i | ||||
\(589\) | 2.89053 | − | 5.00654i | 0.119102 | − | 0.206291i | ||||
\(590\) | 28.5574 | − | 49.4628i | 1.17569 | − | 2.03635i | ||||
\(591\) | −5.23989 | + | 0.923933i | −0.215540 | + | 0.0380055i | ||||
\(592\) | 0.250152 | + | 0.433277i | 0.0102812 | + | 0.0178076i | ||||
\(593\) | 42.2523 | 1.73509 | 0.867546 | − | 0.497356i | \(-0.165696\pi\) | ||||
0.867546 | + | 0.497356i | \(0.165696\pi\) | |||||||
\(594\) | − | 9.76557i | − | 0.400686i | ||||||
\(595\) | −0.347296 | −0.0142378 | ||||||||
\(596\) | −11.1912 | − | 19.3837i | −0.458409 | − | 0.793988i | ||||
\(597\) | −2.63816 | + | 0.465178i | −0.107973 | + | 0.0190385i | ||||
\(598\) | 20.2271 | − | 35.0344i | 0.827150 | − | 1.43267i | ||||
\(599\) | 1.18227 | − | 2.04775i | 0.0483061 | − | 0.0836686i | −0.840861 | − | 0.541251i | \(-0.817951\pi\) |
0.889167 | + | 0.457582i | \(0.151284\pi\) | |||||||
\(600\) | 3.22193 | + | 3.83975i | 0.131535 | + | 0.156757i | ||||
\(601\) | 6.14455 | + | 10.6427i | 0.250642 | + | 0.434124i | 0.963703 | − | 0.266978i | \(-0.0860251\pi\) |
−0.713061 | + | 0.701102i | \(0.752692\pi\) | |||||||
\(602\) | 4.73473 | 0.192973 | ||||||||
\(603\) | 6.15152 | − | 34.8870i | 0.250509 | − | 1.42071i | ||||
\(604\) | −32.3378 | −1.31581 | ||||||||
\(605\) | −1.43969 | − | 2.49362i | −0.0585318 | − | 0.101380i | ||||
\(606\) | 4.92009 | − | 13.5178i | 0.199865 | − | 0.549125i | ||||
\(607\) | −7.08765 | + | 12.2762i | −0.287679 | + | 0.498274i | −0.973255 | − | 0.229726i | \(-0.926217\pi\) |
0.685576 | + | 0.728001i | \(0.259550\pi\) | |||||||
\(608\) | 18.5706 | − | 32.1652i | 0.753136 | − | 1.30447i | ||||
\(609\) | 1.55525 | − | 4.27303i | 0.0630221 | − | 0.173152i | ||||
\(610\) | −19.8799 | − | 34.4329i | −0.804912 | − | 1.39415i | ||||
\(611\) | −81.1576 | −3.28328 | ||||||||
\(612\) | −0.147489 | + | 0.836452i | −0.00596189 | + | 0.0338116i | ||||
\(613\) | 28.5749 | 1.15413 | 0.577065 | − | 0.816698i | \(-0.304198\pi\) | ||||
0.577065 | + | 0.816698i | \(0.304198\pi\) | |||||||
\(614\) | 24.8123 | + | 42.9761i | 1.00134 | + | 1.73437i | ||||
\(615\) | −18.0030 | − | 21.4551i | −0.725951 | − | 0.865154i | ||||
\(616\) | −0.286989 | + | 0.497079i | −0.0115631 | + | 0.0200279i | ||||
\(617\) | −9.03983 | + | 15.6574i | −0.363930 | + | 0.630345i | −0.988604 | − | 0.150541i | \(-0.951899\pi\) |
0.624674 | + | 0.780886i | \(0.285232\pi\) | |||||||
\(618\) | 33.4641 | − | 5.90062i | 1.34612 | − | 0.237358i | ||||
\(619\) | −7.73190 | − | 13.3920i | −0.310771 | − | 0.538271i | 0.667758 | − | 0.744378i | \(-0.267254\pi\) |
−0.978530 | + | 0.206107i | \(0.933921\pi\) | |||||||
\(620\) | 4.87939 | 0.195961 | ||||||||
\(621\) | 16.5487i | 0.664075i | ||||||||
\(622\) | 35.9736 | 1.44241 | ||||||||
\(623\) | −0.985452 | − | 1.70685i | −0.0394813 | − | 0.0683836i | ||||
\(624\) | −54.3794 | + | 9.58856i | −2.17692 | + | 0.383850i | ||||
\(625\) | 15.3123 | − | 26.5216i | 0.612491 | − | 1.06087i | ||||
\(626\) | −8.42989 | + | 14.6010i | −0.336926 | + | 0.583573i | ||||
\(627\) | 5.81908 | + | 6.93491i | 0.232392 | + | 0.276954i | ||||
\(628\) | 3.39440 | + | 5.87927i | 0.135451 | + | 0.234609i | ||||
\(629\) | 0.0196004 | 0.000781518 | ||||||||
\(630\) | −8.11721 | − | 6.81115i | −0.323397 | − | 0.271363i | ||||
\(631\) | 9.35235 | 0.372311 | 0.186156 | − | 0.982520i | \(-0.440397\pi\) | ||||
0.186156 | + | 0.982520i | \(0.440397\pi\) | |||||||
\(632\) | 0.645430 | + | 1.11792i | 0.0256738 | + | 0.0444684i | ||||
\(633\) | −9.39124 | + | 25.8022i | −0.373268 | + | 1.02555i | ||||
\(634\) | 5.89945 | − | 10.2182i | 0.234297 | − | 0.405815i | ||||
\(635\) | −11.2306 | + | 19.4519i | −0.445671 | + | 0.771925i | ||||
\(636\) | −9.14131 | + | 25.1155i | −0.362477 | + | 0.995896i | ||||
\(637\) | −22.2160 | − | 38.4792i | −0.880230 | − | 1.52460i | ||||
\(638\) | −7.55943 | −0.299281 | ||||||||
\(639\) | −6.97906 | + | 2.54017i | −0.276087 | + | 0.100488i | ||||
\(640\) | −19.7023 | −0.778803 | ||||||||
\(641\) | −0.607411 | − | 1.05207i | −0.0239913 | − | 0.0415541i | 0.853780 | − | 0.520633i | \(-0.174304\pi\) |
−0.877772 | + | 0.479079i | \(0.840971\pi\) | |||||||
\(642\) | 17.3944 | + | 20.7298i | 0.686502 | + | 0.818141i | ||||
\(643\) | 15.9013 | − | 27.5418i | 0.627085 | − | 1.08614i | −0.361049 | − | 0.932547i | \(-0.617581\pi\) |
0.988134 | − | 0.153596i | \(-0.0490853\pi\) | |||||||
\(644\) | −1.59240 | + | 2.75811i | −0.0627492 | + | 0.108685i | ||||
\(645\) | −18.9572 | + | 3.34267i | −0.746440 | + | 0.131618i | ||||
\(646\) | −0.907604 | − | 1.57202i | −0.0357092 | − | 0.0618501i | ||||
\(647\) | 30.6854 | 1.20637 | 0.603184 | − | 0.797602i | \(-0.293898\pi\) | ||||
0.603184 | + | 0.797602i | \(0.293898\pi\) | |||||||
\(648\) | 6.06283 | − | 5.08732i | 0.238171 | − | 0.199849i | ||||
\(649\) | −10.5544 | −0.414296 | ||||||||
\(650\) | −20.9008 | − | 36.2012i | −0.819797 | − | 1.41993i | ||||
\(651\) | 1.23143 | − | 0.217134i | 0.0482635 | − | 0.00851016i | ||||
\(652\) | 1.62836 | − | 2.82039i | 0.0637713 | − | 0.110455i | ||||
\(653\) | −3.63176 | + | 6.29039i | −0.142122 | + | 0.246162i | −0.928295 | − | 0.371844i | \(-0.878726\pi\) |
0.786174 | + | 0.618006i | \(0.212059\pi\) | |||||||
\(654\) | 33.4535 | + | 39.8684i | 1.30814 | + | 1.55898i | ||||
\(655\) | 17.9932 | + | 31.1651i | 0.703052 | + | 1.21772i | ||||
\(656\) | 26.4894 | 1.03424 | ||||||||
\(657\) | 29.4907 | − | 10.7337i | 1.15054 | − | 0.418762i | ||||
\(658\) | 14.7297 | 0.574223 | ||||||||
\(659\) | −12.7939 | − | 22.1596i | −0.498378 | − | 0.863216i | 0.501621 | − | 0.865088i | \(-0.332737\pi\) |
−0.999998 | + | 0.00187222i | \(0.999404\pi\) | |||||||
\(660\) | −2.61334 | + | 7.18009i | −0.101724 | + | 0.279485i | ||||
\(661\) | −3.87804 | + | 6.71696i | −0.150838 | + | 0.261260i | −0.931536 | − | 0.363649i | \(-0.881531\pi\) |
0.780698 | + | 0.624909i | \(0.214864\pi\) | |||||||
\(662\) | −11.1566 | + | 19.3238i | −0.433613 | + | 0.751039i | ||||
\(663\) | −0.739885 | + | 2.03282i | −0.0287348 | + | 0.0789481i | ||||
\(664\) | 0.458111 | + | 0.793471i | 0.0177782 | + | 0.0307927i | ||||
\(665\) | 9.82295 | 0.380918 | ||||||||
\(666\) | 0.458111 | + | 0.384401i | 0.0177514 | + | 0.0148952i | ||||
\(667\) | 12.8102 | 0.496011 | ||||||||
\(668\) | −9.52276 | − | 16.4939i | −0.368446 | − | 0.638168i | ||||
\(669\) | 6.95424 | + | 8.28774i | 0.268866 | + | 0.320423i | ||||
\(670\) | −31.9504 | + | 55.3398i | −1.23435 | + | 2.13796i | ||||
\(671\) | −3.67365 | + | 6.36295i | −0.141820 | + | 0.245639i | ||||
\(672\) | 7.91147 | − | 1.39501i | 0.305192 | − | 0.0538135i | ||||
\(673\) | 21.3025 | + | 36.8970i | 0.821150 | + | 1.42227i | 0.904827 | + | 0.425780i | \(0.140000\pi\) |
−0.0836766 | + | 0.996493i | \(0.526666\pi\) | |||||||
\(674\) | −16.9932 | −0.654553 | ||||||||
\(675\) | 14.8089 | + | 8.54990i | 0.569994 | + | 0.329086i | ||||
\(676\) | 50.0702 | 1.92578 | ||||||||
\(677\) | −11.4256 | − | 19.7897i | −0.439122 | − | 0.760581i | 0.558500 | − | 0.829504i | \(-0.311377\pi\) |
−0.997622 | + | 0.0689230i | \(0.978044\pi\) | |||||||
\(678\) | −16.2344 | + | 2.86257i | −0.623479 | + | 0.109936i | ||||
\(679\) | −1.87299 | + | 3.24411i | −0.0718787 | + | 0.124498i | ||||
\(680\) | −0.233956 | + | 0.405223i | −0.00897179 | + | 0.0155396i | ||||
\(681\) | 3.63145 | + | 4.32780i | 0.139158 | + | 0.165842i | ||||
\(682\) | −1.03936 | − | 1.80023i | −0.0397993 | − | 0.0689343i | ||||
\(683\) | −12.3946 | −0.474265 | −0.237132 | − | 0.971477i | \(-0.576208\pi\) | ||||
−0.237132 | + | 0.971477i | \(0.576208\pi\) | |||||||
\(684\) | 4.17159 | − | 23.6583i | 0.159505 | − | 0.904596i | ||||
\(685\) | 43.8435 | 1.67517 | ||||||||
\(686\) | 8.32547 | + | 14.4201i | 0.317868 | + | 0.550564i | ||||
\(687\) | −6.40689 | + | 17.6028i | −0.244438 | + | 0.671588i | ||||
\(688\) | 9.10307 | − | 15.7670i | 0.347051 | − | 0.601111i | ||||
\(689\) | −34.0369 | + | 58.9536i | −1.29670 | + | 2.24595i | ||||
\(690\) | 10.2096 | − | 28.0507i | 0.388673 | − | 1.06787i | ||||
\(691\) | −8.21823 | − | 14.2344i | −0.312636 | − | 0.541501i | 0.666296 | − | 0.745687i | \(-0.267879\pi\) |
−0.978932 | + | 0.204186i | \(0.934545\pi\) | |||||||
\(692\) | 5.52166 | 0.209902 | ||||||||
\(693\) | −0.340022 | + | 1.92836i | −0.0129164 | + | 0.0732524i | ||||
\(694\) | 35.6391 | 1.35284 | ||||||||
\(695\) | −20.8799 | − | 36.1650i | −0.792018 | − | 1.37182i | ||||
\(696\) | −3.93804 | − | 4.69318i | −0.149271 | − | 0.177894i | ||||
\(697\) | 0.518885 | − | 0.898735i | 0.0196542 | − | 0.0340420i | ||||
\(698\) | −20.7939 | + | 36.0160i | −0.787059 | + | 1.36323i | ||||
\(699\) | 6.34002 | − | 1.11792i | 0.239802 | − | 0.0422835i | ||||
\(700\) | 1.64543 | + | 2.84997i | 0.0621914 | + | 0.107719i | ||||
\(701\) | 23.8084 | 0.899231 | 0.449615 | − | 0.893222i | \(-0.351561\pi\) | ||||
0.449615 | + | 0.893222i | \(0.351561\pi\) | |||||||
\(702\) | −57.1605 | + | 33.0016i | −2.15738 | + | 1.24557i | ||||
\(703\) | −0.554378 | −0.0209087 | ||||||||
\(704\) | −1.96064 | − | 3.39592i | −0.0738943 | − | 0.127989i | ||||
\(705\) | −58.9757 | + | 10.3990i | −2.22115 | + | 0.391649i | ||||
\(706\) | −22.9675 | + | 39.7809i | −0.864393 | + | 1.49717i | ||||
\(707\) | −1.44222 | + | 2.49800i | −0.0542402 | + | 0.0939468i | ||||
\(708\) | 18.0030 | + | 21.4551i | 0.676594 | + | 0.806333i | ||||
\(709\) | 21.2811 | + | 36.8599i | 0.799227 | + | 1.38430i | 0.920120 | + | 0.391636i | \(0.128091\pi\) |
−0.120893 | + | 0.992666i | \(0.538576\pi\) | |||||||
\(710\) | 13.3969 | 0.502778 | ||||||||
\(711\) | 3.37346 | + | 2.83067i | 0.126514 | + | 0.106158i | ||||
\(712\) | −2.65539 | −0.0995150 | ||||||||
\(713\) | 1.76130 | + | 3.05066i | 0.0659611 | + | 0.114248i | ||||
\(714\) | 0.134285 | − | 0.368946i | 0.00502550 | − | 0.0138075i | ||||
\(715\) | −9.73055 | + | 16.8538i | −0.363902 | + | 0.630297i | ||||
\(716\) | −9.86097 | + | 17.0797i | −0.368522 | + | 0.638298i | ||||
\(717\) | 4.77316 | − | 13.1141i | 0.178257 | − | 0.489756i | ||||
\(718\) | −4.40420 | − | 7.62830i | −0.164363 | − | 0.284686i | ||||
\(719\) | 14.9391 | 0.557135 | 0.278568 | − | 0.960417i | \(-0.410140\pi\) | ||||
0.278568 | + | 0.960417i | \(0.410140\pi\) | |||||||
\(720\) | −38.2879 | + | 13.9357i | −1.42691 | + | 0.519352i | ||||
\(721\) | −6.81345 | −0.253746 | ||||||||
\(722\) | 7.81655 | + | 13.5387i | 0.290902 | + | 0.503857i | ||||
\(723\) | −4.80958 | − | 5.73184i | −0.178870 | − | 0.213169i | ||||
\(724\) | 18.6459 | − | 32.2956i | 0.692969 | − | 1.20026i | ||||
\(725\) | 6.61839 | − | 11.4634i | 0.245801 | − | 0.425740i | ||||
\(726\) | 3.20574 | − | 0.565258i | 0.118976 | − | 0.0209787i | ||||
\(727\) | −22.1013 | − | 38.2806i | −0.819693 | − | 1.41975i | −0.905909 | − | 0.423473i | \(-0.860811\pi\) |
0.0862163 | − | 0.996276i | \(-0.472522\pi\) | |||||||
\(728\) | 3.87939 | 0.143780 | ||||||||
\(729\) | 13.5000 | − | 23.3827i | 0.500000 | − | 0.866025i | ||||
\(730\) | −56.6100 | −2.09523 | ||||||||
\(731\) | −0.356630 | − | 0.617701i | −0.0131904 | − | 0.0228465i | ||||
\(732\) | 19.2010 | − | 3.38565i | 0.709689 | − | 0.125137i | ||||
\(733\) | −13.4932 | + | 23.3709i | −0.498382 | + | 0.863224i | −0.999998 | − | 0.00186678i | \(-0.999406\pi\) |
0.501616 | + | 0.865091i | \(0.332739\pi\) | |||||||
\(734\) | −8.45976 | + | 14.6527i | −0.312255 | + | 0.540842i | ||||
\(735\) | −21.0744 | − | 25.1155i | −0.777343 | − | 0.926401i | ||||
\(736\) | 11.3157 | + | 19.5993i | 0.417101 | + | 0.722441i | ||||
\(737\) | 11.8084 | 0.434968 | ||||||||
\(738\) | 29.7536 | − | 10.8294i | 1.09525 | − | 0.398637i | ||||
\(739\) | 10.5689 | 0.388784 | 0.194392 | − | 0.980924i | \(-0.437727\pi\) | ||||
0.194392 | + | 0.980924i | \(0.437727\pi\) | |||||||
\(740\) | −0.233956 | − | 0.405223i | −0.00860038 | − | 0.0148963i | ||||
\(741\) | 20.9270 | − | 57.4963i | 0.768771 | − | 2.11218i | ||||
\(742\) | 6.17752 | − | 10.6998i | 0.226784 | − | 0.392801i | ||||
\(743\) | −21.8803 | + | 37.8978i | −0.802711 | + | 1.39034i | 0.115114 | + | 0.993352i | \(0.463277\pi\) |
−0.917825 | + | 0.396984i | \(0.870057\pi\) | |||||||
\(744\) | 0.576199 | − | 1.58310i | 0.0211245 | − | 0.0580391i | ||||
\(745\) | −21.0326 | − | 36.4295i | −0.770573 | − | 1.33467i | ||||
\(746\) | −19.3182 | −0.707290 | ||||||||
\(747\) | 2.39440 | + | 2.00914i | 0.0876065 | + | 0.0735106i | ||||
\(748\) | −0.283119 | −0.0103518 | ||||||||
\(749\) | −2.71301 | − | 4.69907i | −0.0991313 | − | 0.171700i | ||||
\(750\) | 10.2973 | + | 12.2718i | 0.376003 | + | 0.448102i | ||||
\(751\) | −3.03091 | + | 5.24968i | −0.110599 | + | 0.191564i | −0.916012 | − | 0.401151i | \(-0.868610\pi\) |
0.805413 | + | 0.592714i | \(0.201944\pi\) | |||||||
\(752\) | 28.3195 | − | 49.0509i | 1.03271 | − | 1.78870i | ||||
\(753\) | −24.1793 | + | 4.26347i | −0.881144 | + | 0.155369i | ||||
\(754\) | 25.5462 | + | 44.2474i | 0.930339 | + | 1.61139i | ||||
\(755\) | −60.7752 | −2.21184 | ||||||||
\(756\) | 4.50000 | − | 2.59808i | 0.163663 | − | 0.0944911i | ||||
\(757\) | 20.7192 | 0.753054 | 0.376527 | − | 0.926406i | \(-0.377118\pi\) | ||||
0.376527 | + | 0.926406i | \(0.377118\pi\) | |||||||
\(758\) | 13.3944 | + | 23.1998i | 0.486507 | + | 0.842654i | ||||
\(759\) | −5.43242 | + | 0.957882i | −0.197184 | + | 0.0347689i | ||||
\(760\) | 6.61721 | − | 11.4613i | 0.240031 | − | 0.415747i | ||||
\(761\) | 23.7788 | − | 41.1862i | 0.861982 | − | 1.49300i | −0.00803057 | − | 0.999968i | \(-0.502556\pi\) |
0.870013 | − | 0.493029i | \(-0.164110\pi\) | |||||||
\(762\) | −16.3221 | − | 19.4519i | −0.591286 | − | 0.704668i | ||||
\(763\) | −5.21776 | − | 9.03742i | −0.188896 | − | 0.327177i | ||||
\(764\) | 9.12836 | 0.330252 | ||||||||
\(765\) | −0.277189 | + | 1.57202i | −0.0100218 | + | 0.0568364i | ||||
\(766\) | −27.8803 | −1.00736 | ||||||||
\(767\) | 35.6673 | + | 61.7776i | 1.28787 | + | 2.23066i | ||||
\(768\) | 12.2640 | − | 33.6950i | 0.442538 | − | 1.21586i | ||||
\(769\) | −20.8384 | + | 36.0932i | −0.751453 | + | 1.30155i | 0.195665 | + | 0.980671i | \(0.437313\pi\) |
−0.947118 | + | 0.320884i | \(0.896020\pi\) | |||||||
\(770\) | 1.76604 | − | 3.05888i | 0.0636438 | − | 0.110234i | ||||
\(771\) | −5.11422 | + | 14.0512i | −0.184184 | + | 0.506042i | ||||
\(772\) | −8.29086 | − | 14.3602i | −0.298395 | − | 0.516835i | ||||
\(773\) | −40.1652 | −1.44464 | −0.722321 | − | 0.691558i | \(-0.756925\pi\) | ||||
−0.722321 | + | 0.691558i | \(0.756925\pi\) | |||||||
\(774\) | 3.77894 | − | 21.4315i | 0.135831 | − | 0.770338i | ||||
\(775\) | 3.63991 | 0.130749 | ||||||||
\(776\) | 2.52347 | + | 4.37078i | 0.0905873 | + | 0.156902i | ||||
\(777\) | −0.0770768 | − | 0.0918566i | −0.00276512 | − | 0.00329534i | ||||
\(778\) | 10.2626 | − | 17.7754i | 0.367934 | − | 0.637280i | ||||
\(779\) | −14.6762 | + | 25.4199i | −0.525829 | + | 0.910762i | ||||
\(780\) | 50.8585 | − | 8.96773i | 1.82103 | − | 0.321096i | ||||
\(781\) | −1.23783 | − | 2.14398i | −0.0442929 | − | 0.0767175i | ||||
\(782\) | 1.10607 | 0.0395529 | ||||||||
\(783\) | −18.1003 | − | 10.4502i | −0.646852 | − | 0.373460i | ||||
\(784\) | 31.0087 | 1.10745 | ||||||||
\(785\) | 6.37939 | + | 11.0494i | 0.227690 | + | 0.394371i | ||||
\(786\) | −40.0651 | + | 7.06456i | −1.42908 | + | 0.251985i | ||||
\(787\) | 11.2408 | − | 19.4697i | 0.400692 | − | 0.694019i | −0.593118 | − | 0.805116i | \(-0.702103\pi\) |
0.993810 | + | 0.111097i | \(0.0354364\pi\) | |||||||
\(788\) | −2.35323 | + | 4.07591i | −0.0838302 | + | 0.145198i | ||||
\(789\) | 1.33527 | + | 1.59132i | 0.0475370 | + | 0.0566524i | ||||
\(790\) | −3.97178 | − | 6.87933i | −0.141310 | − | 0.244755i | ||||
\(791\) | 3.30541 | 0.117527 | ||||||||
\(792\) | 2.02094 | + | 1.69577i | 0.0718111 | + | 0.0602567i | ||||
\(793\) | 49.6587 | 1.76343 | ||||||||
\(794\) | −32.5082 | − | 56.3059i | −1.15367 | − | 1.99822i | ||||
\(795\) | −17.1800 | + | 47.2018i | −0.609313 | + | 1.67407i | ||||
\(796\) | −1.18479 | + | 2.05212i | −0.0419939 | + | 0.0727355i | ||||
\(797\) | 19.9688 | − | 34.5871i | 0.707333 | − | 1.22514i | −0.258510 | − | 0.966009i | \(-0.583232\pi\) |
0.965843 | − | 0.259128i | \(-0.0834351\pi\) | |||||||
\(798\) | −3.79813 | + | 10.4353i | −0.134452 | + | 0.369405i | ||||
\(799\) | −1.10947 | − | 1.92166i | −0.0392502 | − | 0.0679834i | ||||
\(800\) | 23.3851 | 0.826787 | ||||||||
\(801\) | −8.51249 | + | 3.09829i | −0.300774 | + | 0.109473i | ||||
\(802\) | −32.4029 | −1.14419 | ||||||||
\(803\) | 5.23055 | + | 9.05958i | 0.184582 | + | 0.319706i | ||||
\(804\) | −20.1420 | − | 24.0043i | −0.710354 | − | 0.846568i | ||||
\(805\) | −2.99273 | + | 5.18355i | −0.105480 | + | 0.182696i | ||||
\(806\) | −7.02481 | + | 12.1673i | −0.247439 | + | 0.428576i | ||||
\(807\) | −47.6264 | + | 8.39781i | −1.67653 | + | 0.295617i | ||||
\(808\) | 1.94310 | + | 3.36554i | 0.0683579 | + | 0.118399i | ||||
\(809\) | 17.9240 | 0.630173 | 0.315086 | − | 0.949063i | \(-0.397966\pi\) | ||||
0.315086 | + | 0.949063i | \(0.397966\pi\) | |||||||
\(810\) | −37.3089 | + | 31.3059i | −1.31090 | + | 1.09998i | ||||
\(811\) | 26.8972 | 0.944490 | 0.472245 | − | 0.881467i | \(-0.343444\pi\) | ||||
0.472245 | + | 0.881467i | \(0.343444\pi\) | |||||||
\(812\) | −2.01114 | − | 3.48340i | −0.0705773 | − | 0.122244i | ||||
\(813\) | 22.9099 | − | 4.03963i | 0.803485 | − | 0.141676i | ||||
\(814\) | −0.0996702 | + | 0.172634i | −0.00349344 | + | 0.00605081i | ||||
\(815\) | 3.06031 | − | 5.30061i | 0.107198 | − | 0.185672i | ||||
\(816\) | −0.970437 | − | 1.15652i | −0.0339721 | − | 0.0404864i | ||||
\(817\) | 10.0869 | + | 17.4711i | 0.352897 | + | 0.611236i | ||||
\(818\) | 8.31315 | 0.290662 | ||||||||
\(819\) | 12.4363 | − | 4.52644i | 0.434559 | − | 0.158167i | ||||
\(820\) | −24.7743 | −0.865154 | ||||||||
\(821\) | 6.00387 | + | 10.3990i | 0.209537 | + | 0.362928i | 0.951569 | − | 0.307436i | \(-0.0994712\pi\) |
−0.742032 | + | 0.670364i | \(0.766138\pi\) | |||||||
\(822\) | −16.9525 | + | 46.5766i | −0.591286 | + | 1.62454i | ||||
\(823\) | 6.47952 | − | 11.2229i | 0.225862 | − | 0.391204i | −0.730716 | − | 0.682682i | \(-0.760814\pi\) |
0.956578 | + | 0.291477i | \(0.0941468\pi\) | |||||||
\(824\) | −4.58987 | + | 7.94989i | −0.159896 | + | 0.276947i | ||||
\(825\) | −1.94949 | + | 5.35619i | −0.0678726 | + | 0.186479i | ||||
\(826\) | −6.47343 | − | 11.2123i | −0.225239 | − | 0.390126i | ||||
\(827\) | −23.3678 | −0.812579 | −0.406290 | − | 0.913744i | \(-0.633178\pi\) | ||||
−0.406290 | + | 0.913744i | \(0.633178\pi\) | |||||||
\(828\) | 11.2135 | + | 9.40923i | 0.389695 | + | 0.326993i | ||||
\(829\) | −54.3164 | −1.88649 | −0.943244 | − | 0.332100i | \(-0.892243\pi\) | ||||
−0.943244 | + | 0.332100i | \(0.892243\pi\) | |||||||
\(830\) | −2.81908 | − | 4.88279i | −0.0978516 | − | 0.169484i | ||||
\(831\) | −9.44191 | − | 11.2524i | −0.327536 | − | 0.390343i | ||||
\(832\) | −13.2515 | + | 22.9523i | −0.459413 | + | 0.795727i | ||||
\(833\) | 0.607411 | − | 1.05207i | 0.0210455 | − | 0.0364520i | ||||
\(834\) | 46.4928 | − | 8.19793i | 1.60991 | − | 0.283871i | ||||
\(835\) | −17.8969 | − | 30.9984i | −0.619349 | − | 1.07274i | ||||
\(836\) | 8.00774 | 0.276954 | ||||||||
\(837\) | − | 5.74729i | − | 0.198655i | ||||||
\(838\) | 32.9222 | 1.13728 | ||||||||
\(839\) | 22.3790 | + | 38.7615i | 0.772608 | + | 1.33820i | 0.936129 | + | 0.351656i | \(0.114381\pi\) |
−0.163521 | + | 0.986540i | \(0.552285\pi\) | |||||||
\(840\) | 2.81908 | − | 0.497079i | 0.0972674 | − | 0.0171509i | ||||
\(841\) | 6.41060 | − | 11.1035i | 0.221055 | − | 0.382879i | ||||
\(842\) | 9.31908 | − | 16.1411i | 0.321157 | − | 0.556260i | ||||
\(843\) | −2.82666 | − | 3.36868i | −0.0973552 | − | 0.116023i | ||||
\(844\) | 12.1441 | + | 21.0342i | 0.418017 | + | 0.724026i | ||||
\(845\) | 94.1011 | 3.23718 | ||||||||
\(846\) | 11.7562 | − | 66.6730i | 0.404188 | − | 2.29226i | ||||
\(847\) | −0.652704 | −0.0224272 | ||||||||
\(848\) | −23.7540 | − | 41.1432i | −0.815716 | − | 1.41286i | ||||
\(849\) | −2.76945 | + | 7.60900i | −0.0950472 | + | 0.261140i | ||||
\(850\) | 0.571452 | − | 0.989783i | 0.0196006 | − | 0.0339493i | ||||
\(851\) | 0.168900 | − | 0.292544i | 0.00578983 | − | 0.0100283i | ||||
\(852\) | −2.24691 | + | 6.17334i | −0.0769779 | + | 0.211495i | ||||
\(853\) | −7.06402 | − | 12.2352i | −0.241867 | − | 0.418926i | 0.719379 | − | 0.694618i | \(-0.244427\pi\) |
−0.961246 | + | 0.275691i | \(0.911093\pi\) | |||||||
\(854\) | −9.01279 | −0.308411 | ||||||||
\(855\) | 7.84002 | − | 44.4630i | 0.268123 | − | 1.52060i | ||||
\(856\) | −7.31046 | −0.249866 | ||||||||
\(857\) | 9.47906 | + | 16.4182i | 0.323798 | + | 0.560835i | 0.981268 | − | 0.192645i | \(-0.0617067\pi\) |
−0.657470 | + | 0.753481i | \(0.728373\pi\) | |||||||
\(858\) | −14.1420 | − | 16.8538i | −0.482801 | − | 0.575380i | ||||
\(859\) | −19.0587 | + | 33.0107i | −0.650275 | + | 1.12631i | 0.332781 | + | 0.943004i | \(0.392013\pi\) |
−0.983056 | + | 0.183305i | \(0.941320\pi\) | |||||||
\(860\) | −8.51367 | + | 14.7461i | −0.290314 | + | 0.502838i | ||||
\(861\) | −6.25237 | + | 1.10246i | −0.213080 | + | 0.0375718i | ||||
\(862\) | −2.23870 | − | 3.87755i | −0.0762505 | − | 0.132070i | ||||
\(863\) | −37.9665 | −1.29239 | −0.646197 | − | 0.763171i | \(-0.723641\pi\) | ||||
−0.646197 | + | 0.763171i | \(0.723641\pi\) | |||||||
\(864\) | − | 36.9242i | − | 1.25619i | ||||||
\(865\) | 10.3773 | 0.352840 | ||||||||
\(866\) | 29.2866 | + | 50.7258i | 0.995198 | + | 1.72373i | ||||
\(867\) | 28.9393 | − | 5.10278i | 0.982830 | − | 0.173299i | ||||
\(868\) | 0.553033 | − | 0.957882i | 0.0187712 | − | 0.0325126i | ||||
\(869\) | −0.733956 | + | 1.27125i | −0.0248977 | + | 0.0431241i | ||||
\(870\) | 24.2335 | + | 28.8804i | 0.821594 | + | 0.979138i | ||||
\(871\) | −39.9051 | − | 69.1177i | −1.35213 | − | 2.34196i | ||||
\(872\) | −14.0597 | −0.476123 | ||||||||
\(873\) | 13.1894 | + | 11.0672i | 0.446393 | + | 0.374568i | ||||
\(874\) | −31.2841 | −1.05820 | ||||||||
\(875\) | −1.60607 | − | 2.78179i | −0.0542950 | − | 0.0940416i | ||||
\(876\) | 9.49454 | − | 26.0860i | 0.320791 | − | 0.881365i | ||||
\(877\) | −12.5488 | + | 21.7351i | −0.423741 | + | 0.733941i | −0.996302 | − | 0.0859209i | \(-0.972617\pi\) |
0.572561 | + | 0.819862i | \(0.305950\pi\) | |||||||
\(878\) | 7.56893 | − | 13.1098i | 0.255439 | − | 0.442433i | ||||
\(879\) | 4.64749 | − | 12.7689i | 0.156756 | − | 0.430683i | ||||
\(880\) | −6.79086 | − | 11.7621i | −0.228920 | − | 0.396501i | ||||
\(881\) | −7.51485 | −0.253182 | −0.126591 | − | 0.991955i | \(-0.540404\pi\) | ||||
−0.126591 | + | 0.991955i | \(0.540404\pi\) | |||||||
\(882\) | 34.8298 | − | 12.6770i | 1.17278 | − | 0.426857i | ||||
\(883\) | −28.9231 | −0.973341 | −0.486671 | − | 0.873586i | \(-0.661789\pi\) | ||||
−0.486671 | + | 0.873586i | \(0.661789\pi\) | |||||||
\(884\) | 0.956767 | + | 1.65717i | 0.0321795 | + | 0.0557366i | ||||
\(885\) | 33.8346 | + | 40.3225i | 1.13734 | + | 1.35542i | ||||
\(886\) | −10.9338 | + | 18.9378i | −0.367327 | + | 0.636229i | ||||
\(887\) | −0.825008 | + | 1.42896i | −0.0277010 | + | 0.0479796i | −0.879544 | − | 0.475818i | \(-0.842152\pi\) |
0.851843 | + | 0.523798i | \(0.175485\pi\) | |||||||
\(888\) | −0.159100 | + | 0.0280537i | −0.00533906 | + | 0.000941419i | ||||
\(889\) | 2.54576 | + | 4.40938i | 0.0853820 | + | 0.147886i | ||||
\(890\) | 16.3405 | 0.547734 | ||||||||
\(891\) | 8.45723 | + | 3.07818i | 0.283328 | + | 0.103123i | ||||
\(892\) | 9.56986 | 0.320423 | ||||||||
\(893\) | 31.3803 | + | 54.3523i | 1.05010 | + | 1.81883i | ||||
\(894\) | 46.8328 | − | 8.25789i | 1.56632 | − | 0.276185i | ||||
\(895\) | −18.5326 | + | 32.0993i | −0.619475 | + | 1.07296i | ||||
\(896\) | −2.23308 | + | 3.86780i | −0.0746019 | + | 0.129214i | ||||
\(897\) | 23.9650 | + | 28.5603i | 0.800167 | + | 0.953602i | ||||
\(898\) | −24.1917 | − | 41.9012i | −0.807286 | − | 1.39826i | ||||
\(899\) | −4.44892 | −0.148380 | ||||||||
\(900\) | 14.2135 | − | 5.17328i | 0.473783 | − | 0.172443i | ||||
\(901\) | −1.86122 | −0.0620061 | ||||||||
\(902\) | 5.27719 | + | 9.14036i | 0.175711 | + | 0.304341i | ||||
\(903\) | −1.49242 | + | 4.10039i | −0.0496647 | + | 0.136453i | ||||
\(904\) | 2.22668 | − | 3.85673i | 0.0740583 | − | 0.128273i | ||||
\(905\) | 35.0428 | − | 60.6959i | 1.16486 | − | 2.01760i | ||||
\(906\) | 23.4993 | − | 64.5638i | 0.780711 | − | 2.14499i | ||||
\(907\) | −13.9213 | − | 24.1124i | −0.462248 | − | 0.800638i | 0.536824 | − | 0.843694i | \(-0.319624\pi\) |
−0.999073 | + | 0.0430565i | \(0.986290\pi\) | |||||||
\(908\) | 4.99731 | 0.165842 | ||||||||
\(909\) | 10.1559 | + | 8.52185i | 0.336851 | + | 0.282652i | ||||
\(910\) | −23.8726 | −0.791368 | ||||||||
\(911\) | 8.52188 | + | 14.7603i | 0.282342 | + | 0.489031i | 0.971961 | − | 0.235141i | \(-0.0755552\pi\) |
−0.689619 | + | 0.724173i | \(0.742222\pi\) | |||||||
\(912\) | 27.4479 | + | 32.7111i | 0.908891 | + | 1.08317i | ||||
\(913\) | −0.520945 | + | 0.902302i | −0.0172407 | + | 0.0298619i | ||||
\(914\) | 36.1143 | − | 62.5518i | 1.19455 | − | 2.06903i | ||||
\(915\) | 36.0861 | − | 6.36295i | 1.19297 | − | 0.210352i | ||||
\(916\) | 8.28493 | + | 14.3499i | 0.273742 | + | 0.474135i | ||||
\(917\) | 8.15745 | 0.269383 | ||||||||
\(918\) | −1.56283 | − | 0.902302i | −0.0515812 | − | 0.0297804i | ||||
\(919\) | 47.4638 | 1.56569 | 0.782843 | − | 0.622219i | \(-0.213769\pi\) | ||||
0.782843 | + | 0.622219i | \(0.213769\pi\) | |||||||
\(920\) | 4.03209 | + | 6.98378i | 0.132934 | + | 0.230249i | ||||
\(921\) | −45.0394 | + | 7.94166i | −1.48410 | + | 0.261687i | ||||
\(922\) | 5.26130 | − | 9.11283i | 0.173272 | − | 0.300115i | ||||
\(923\) | −8.36618 | + | 14.4907i | −0.275376 | + | 0.476966i | ||||
\(924\) | 1.11334 | + | 1.32683i | 0.0366262 | + | 0.0436494i | ||||
\(925\) | −0.174526 | − | 0.302287i | −0.00573836 | − | 0.00993914i | ||||
\(926\) | −17.4662 | −0.573974 | ||||||||
\(927\) | −5.43804 | + | 30.8407i | −0.178609 | + | 1.01294i | ||||
\(928\) | −28.5827 | −0.938272 | ||||||||
\(929\) | −14.4561 | − | 25.0386i | −0.474288 | − | 0.821490i | 0.525279 | − | 0.850930i | \(-0.323961\pi\) |
−0.999567 | + | 0.0294398i | \(0.990628\pi\) | |||||||
\(930\) | −3.54576 | + | 9.74189i | −0.116270 | + | 0.319449i | ||||
\(931\) | −17.1800 | + | 29.7567i | −0.563053 | + | 0.975237i | ||||
\(932\) | 2.84730 | − | 4.93166i | 0.0932663 | − | 0.161542i | ||||
\(933\) | −11.3391 | + | 31.1540i | −0.371227 | + | 1.01994i | ||||
\(934\) | 16.0351 | + | 27.7736i | 0.524684 | + | 0.908779i | ||||
\(935\) | −0.532089 | −0.0174012 | ||||||||
\(936\) | 3.09627 | − | 17.5598i | 0.101205 | − | 0.573960i | ||||
\(937\) | −4.87258 | −0.159180 | −0.0795901 | − | 0.996828i | \(-0.525361\pi\) | ||||
−0.0795901 | + | 0.996828i | \(0.525361\pi\) | |||||||
\(938\) | 7.24257 | + | 12.5445i | 0.236478 | + | 0.409593i | ||||
\(939\) | −9.98767 | − | 11.9028i | −0.325935 | − | 0.388435i | ||||
\(940\) | −26.4859 | + | 45.8750i | −0.863875 | + | 1.49628i | ||||
\(941\) | 27.1391 | − | 47.0063i | 0.884709 | − | 1.53236i | 0.0386622 | − | 0.999252i | \(-0.487690\pi\) |
0.846047 | − | 0.533109i | \(-0.178976\pi\) | |||||||
\(942\) | −14.2049 | + | 2.50470i | −0.462819 | + | 0.0816075i | ||||
\(943\) | −8.94269 | − | 15.4892i | −0.291214 | − | 0.504397i | ||||
\(944\) | −49.7837 | −1.62032 | ||||||||
\(945\) | 8.45723 | − | 4.88279i | 0.275114 | − | 0.158837i | ||||
\(946\) | 7.25402 | 0.235849 | ||||||||
\(947\) | 10.7253 | + | 18.5768i | 0.348527 | + | 0.603666i | 0.985988 | − | 0.166817i | \(-0.0533488\pi\) |
−0.637461 | + | 0.770482i | \(0.720015\pi\) | |||||||
\(948\) | 3.83615 | − | 0.676417i | 0.124592 | − | 0.0219690i | ||||
\(949\) | 35.3521 | − | 61.2316i | 1.14758 | − | 1.98766i | ||||
\(950\) | −16.1630 | + | 27.9951i | −0.524396 | + | 0.908281i | ||||
\(951\) | 6.98963 | + | 8.32991i | 0.226654 | + | 0.270116i | ||||
\(952\) | 0.0530334 | + | 0.0918566i | 0.00171882 | + | 0.00297709i | ||||
\(953\) | −13.0601 | −0.423057 | −0.211528 | − | 0.977372i | \(-0.567844\pi\) | ||||
−0.211528 | + | 0.977372i | \(0.567844\pi\) | |||||||
\(954\) | −43.5014 | − | 36.5020i | −1.40841 | − | 1.18180i | ||||
\(955\) | 17.1557 | 0.555145 | ||||||||
\(956\) | −6.17230 | − | 10.6907i | −0.199627 | − | 0.345763i | ||||
\(957\) | 2.38279 | − | 6.54666i | 0.0770246 | − | 0.211623i | ||||
\(958\) | −37.0428 | + | 64.1601i | −1.19680 | + | 2.07292i | ||||
\(959\) | 4.96926 | − | 8.60700i | 0.160466 | − | 0.277935i | ||||
\(960\) | −6.68866 | + | 18.3770i | −0.215876 | + | 0.593114i | ||||
\(961\) | 14.8883 | + | 25.7873i | 0.480268 | + | 0.831849i | ||||
\(962\) | 1.34730 | 0.0434386 | ||||||||
\(963\) | −23.4354 | + | 8.52979i | −0.755196 | + | 0.274869i | ||||
\(964\) | −6.61856 | −0.213169 | ||||||||
\(965\) | −15.5817 | − | 26.9883i | −0.501593 | − | 0.868785i | ||||
\(966\) | −4.34952 | − | 5.18355i | −0.139943 | − | 0.166778i | ||||
\(967\) | −5.59240 | + | 9.68631i | −0.179839 | + | 0.311491i | −0.941825 | − | 0.336103i | \(-0.890891\pi\) |
0.761986 | + | 0.647593i | \(0.224224\pi\) | |||||||
\(968\) | −0.439693 | + | 0.761570i | −0.0141323 | + | 0.0244778i | ||||
\(969\) | 1.64749 | − | 0.290497i | 0.0529250 | − | 0.00933210i | ||||
\(970\) | −15.5287 | − | 26.8965i | −0.498596 | − | 0.863594i | ||||
\(971\) | 28.4935 | 0.914400 | 0.457200 | − | 0.889364i | \(-0.348852\pi\) | ||||
0.457200 | + | 0.889364i | \(0.348852\pi\) | |||||||
\(972\) | −8.16843 | − | 22.4426i | −0.262003 | − | 0.719846i | ||||
\(973\) | −9.46616 | −0.303471 | ||||||||
\(974\) | −32.8444 | − | 56.8881i | −1.05240 | − | 1.82281i | ||||
\(975\) | 37.9393 | − | 6.68972i | 1.21503 | − | 0.214242i | ||||
\(976\) | −17.3282 | + | 30.0133i | −0.554661 | + | 0.960701i | ||||
\(977\) | 9.96363 | − | 17.2575i | 0.318765 | − | 0.552117i | −0.661466 | − | 0.749975i | \(-0.730065\pi\) |
0.980231 | + | 0.197859i | \(0.0633987\pi\) | |||||||
\(978\) | 4.44774 | + | 5.30061i | 0.142223 | + | 0.169495i | ||||
\(979\) | −1.50980 | − | 2.61505i | −0.0482534 | − | 0.0835774i | ||||
\(980\) | −29.0009 | −0.926401 | ||||||||
\(981\) | −45.0718 | + | 16.4048i | −1.43903 | + | 0.523765i | ||||
\(982\) | 45.1935 | 1.44218 | ||||||||
\(983\) | 21.5141 | + | 37.2636i | 0.686194 | + | 1.18852i | 0.973060 | + | 0.230553i | \(0.0740534\pi\) |
−0.286865 | + | 0.957971i | \(0.592613\pi\) | |||||||
\(984\) | −2.92556 | + | 8.03790i | −0.0932633 | + | 0.256239i | ||||
\(985\) | −4.42262 | + | 7.66020i | −0.140916 | + | 0.244074i | ||||
\(986\) | −0.698463 | + | 1.20977i | −0.0222436 | + | 0.0385270i | ||||
\(987\) | −4.64290 | + | 12.7563i | −0.147785 | + | 0.406037i | ||||
\(988\) | −27.0612 | − | 46.8714i | −0.860933 | − | 1.49118i | ||||
\(989\) | −12.2926 | −0.390882 | ||||||||
\(990\) | −12.4363 | − | 10.4353i | −0.395251 | − | 0.331655i | ||||
\(991\) | −21.1516 | −0.671902 | −0.335951 | − | 0.941879i | \(-0.609058\pi\) | ||||
−0.335951 | + | 0.941879i | \(0.609058\pi\) | |||||||
\(992\) | −3.92989 | − | 6.80677i | −0.124774 | − | 0.216115i | ||||
\(993\) | −13.2182 | − | 15.7529i | −0.419468 | − | 0.499902i | ||||
\(994\) | 1.51842 | − | 2.62998i | 0.0481613 | − | 0.0834178i | ||||
\(995\) | −2.22668 | + | 3.85673i | −0.0705906 | + | 0.122266i | ||||
\(996\) | 2.72281 | − | 0.480105i | 0.0862756 | − | 0.0152127i | ||||
\(997\) | 13.4204 | + | 23.2448i | 0.425028 | + | 0.736170i | 0.996423 | − | 0.0845048i | \(-0.0269308\pi\) |
−0.571395 | + | 0.820675i | \(0.693597\pi\) | |||||||
\(998\) | −50.9718 | −1.61349 | ||||||||
\(999\) | −0.477301 | + | 0.275570i | −0.0151011 | + | 0.00871864i |
(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 | 99.2.e.d.67.3 | yes | 6 | |
3.2 | odd | 2 | 297.2.e.d.199.1 | 6 | |||
9.2 | odd | 6 | 297.2.e.d.100.1 | 6 | |||
9.4 | even | 3 | 891.2.a.l.1.1 | 3 | |||
9.5 | odd | 6 | 891.2.a.k.1.3 | 3 | |||
9.7 | even | 3 | inner | 99.2.e.d.34.3 | ✓ | 6 | |
11.10 | odd | 2 | 1089.2.e.h.364.1 | 6 | |||
99.32 | even | 6 | 9801.2.a.bd.1.1 | 3 | |||
99.43 | odd | 6 | 1089.2.e.h.727.1 | 6 | |||
99.76 | odd | 6 | 9801.2.a.be.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.2.e.d.34.3 | ✓ | 6 | 9.7 | even | 3 | inner | |
99.2.e.d.67.3 | yes | 6 | 1.1 | even | 1 | trivial | |
297.2.e.d.100.1 | 6 | 9.2 | odd | 6 | |||
297.2.e.d.199.1 | 6 | 3.2 | odd | 2 | |||
891.2.a.k.1.3 | 3 | 9.5 | odd | 6 | |||
891.2.a.l.1.1 | 3 | 9.4 | even | 3 | |||
1089.2.e.h.364.1 | 6 | 11.10 | odd | 2 | |||
1089.2.e.h.727.1 | 6 | 99.43 | odd | 6 | |||
9801.2.a.bd.1.1 | 3 | 99.32 | even | 6 | |||
9801.2.a.be.1.3 | 3 | 99.76 | odd | 6 |