Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(221,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.221");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.s (of order \(6\), 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: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 521.4 | ||
Character | \(\chi\) | \(=\) | 570.521 |
Dual form | 570.2.s.a.221.4 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | −0.929852 | + | 1.46129i | −0.536850 | + | 0.843678i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0.866025 | + | 0.500000i | 0.387298 | + | 0.223607i | ||||
\(6\) | −0.800591 | − | 1.53592i | −0.326840 | − | 0.627037i | ||||
\(7\) | −4.66317 | −1.76251 | −0.881257 | − | 0.472638i | \(-0.843302\pi\) | ||||
−0.881257 | + | 0.472638i | \(0.843302\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.27075 | − | 2.71757i | −0.423584 | − | 0.905857i | ||||
\(10\) | −0.866025 | + | 0.500000i | −0.273861 | + | 0.158114i | ||||
\(11\) | − | 3.04774i | − | 0.918928i | −0.888196 | − | 0.459464i | \(-0.848041\pi\) | ||
0.888196 | − | 0.459464i | \(-0.151959\pi\) | |||||||
\(12\) | 1.73044 | + | 0.0746290i | 0.499536 | + | 0.0215435i | ||||
\(13\) | 3.56832 | − | 2.06017i | 0.989674 | − | 0.571389i | 0.0844972 | − | 0.996424i | \(-0.473072\pi\) |
0.905177 | + | 0.425035i | \(0.139738\pi\) | |||||||
\(14\) | 2.33159 | − | 4.03843i | 0.623143 | − | 1.07931i | ||||
\(15\) | −1.53592 | + | 0.800591i | −0.396573 | + | 0.206712i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 2.22857 | + | 1.28666i | 0.540506 | + | 0.312062i | 0.745284 | − | 0.666747i | \(-0.232314\pi\) |
−0.204778 | + | 0.978808i | \(0.565647\pi\) | |||||||
\(18\) | 2.98886 | + | 0.258282i | 0.704481 | + | 0.0608777i | ||||
\(19\) | −3.71368 | − | 2.28223i | −0.851977 | − | 0.523579i | ||||
\(20\) | − | 1.00000i | − | 0.223607i | ||||||
\(21\) | 4.33606 | − | 6.81426i | 0.946206 | − | 1.48699i | ||||
\(22\) | 2.63942 | + | 1.52387i | 0.562726 | + | 0.324890i | ||||
\(23\) | 0.586222 | − | 0.338456i | 0.122236 | − | 0.0705729i | −0.437635 | − | 0.899153i | \(-0.644184\pi\) |
0.559871 | + | 0.828580i | \(0.310851\pi\) | |||||||
\(24\) | −0.929852 | + | 1.46129i | −0.189805 | + | 0.298285i | ||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | 4.12034i | 0.808066i | ||||||||
\(27\) | 5.15278 | + | 0.669999i | 0.991652 | + | 0.128941i | ||||
\(28\) | 2.33159 | + | 4.03843i | 0.440628 | + | 0.763191i | ||||
\(29\) | −0.992204 | − | 1.71855i | −0.184248 | − | 0.319126i | 0.759075 | − | 0.651003i | \(-0.225652\pi\) |
−0.943323 | + | 0.331877i | \(0.892318\pi\) | |||||||
\(30\) | 0.0746290 | − | 1.73044i | 0.0136253 | − | 0.315934i | ||||
\(31\) | − | 4.29688i | − | 0.771742i | −0.922553 | − | 0.385871i | \(-0.873901\pi\) | ||
0.922553 | − | 0.385871i | \(-0.126099\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 4.45364 | + | 2.83395i | 0.775279 | + | 0.493327i | ||||
\(34\) | −2.22857 | + | 1.28666i | −0.382196 | + | 0.220661i | ||||
\(35\) | −4.03843 | − | 2.33159i | −0.682619 | − | 0.394110i | ||||
\(36\) | −1.71811 | + | 2.45929i | −0.286352 | + | 0.409881i | ||||
\(37\) | − | 4.49734i | − | 0.739358i | −0.929160 | − | 0.369679i | \(-0.879468\pi\) | ||
0.929160 | − | 0.369679i | \(-0.120532\pi\) | |||||||
\(38\) | 3.83331 | − | 2.07503i | 0.621845 | − | 0.336614i | ||||
\(39\) | −0.307497 | + | 7.13001i | −0.0492389 | + | 1.14172i | ||||
\(40\) | 0.866025 | + | 0.500000i | 0.136931 | + | 0.0790569i | ||||
\(41\) | −1.65691 | + | 2.86985i | −0.258766 | + | 0.448195i | −0.965912 | − | 0.258872i | \(-0.916649\pi\) |
0.707146 | + | 0.707068i | \(0.249982\pi\) | |||||||
\(42\) | 3.73329 | + | 7.16227i | 0.576059 | + | 1.10516i | ||||
\(43\) | 2.86613 | − | 4.96428i | 0.437080 | − | 0.757045i | −0.560383 | − | 0.828234i | \(-0.689346\pi\) |
0.997463 | + | 0.0711889i | \(0.0226793\pi\) | |||||||
\(44\) | −2.63942 | + | 1.52387i | −0.397908 | + | 0.229732i | ||||
\(45\) | 0.258282 | − | 2.98886i | 0.0385025 | − | 0.445553i | ||||
\(46\) | 0.676911i | 0.0998051i | ||||||||
\(47\) | −7.58882 | + | 4.38141i | −1.10694 | + | 0.639094i | −0.938036 | − | 0.346538i | \(-0.887357\pi\) |
−0.168907 | + | 0.985632i | \(0.554024\pi\) | |||||||
\(48\) | −0.800591 | − | 1.53592i | −0.115555 | − | 0.221691i | ||||
\(49\) | 14.7452 | 2.10645 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −3.95243 | + | 2.06018i | −0.553450 | + | 0.288483i | ||||
\(52\) | −3.56832 | − | 2.06017i | −0.494837 | − | 0.285694i | ||||
\(53\) | 4.57343 | + | 7.92141i | 0.628209 | + | 1.08809i | 0.987911 | + | 0.155023i | \(0.0495450\pi\) |
−0.359702 | + | 0.933067i | \(0.617122\pi\) | |||||||
\(54\) | −3.15662 | + | 4.12744i | −0.429562 | + | 0.561673i | ||||
\(55\) | 1.52387 | − | 2.63942i | 0.205479 | − | 0.355899i | ||||
\(56\) | −4.66317 | −0.623143 | ||||||||
\(57\) | 6.78818 | − | 3.30464i | 0.899116 | − | 0.437711i | ||||
\(58\) | 1.98441 | 0.260566 | ||||||||
\(59\) | 6.02522 | − | 10.4360i | 0.784417 | − | 1.35865i | −0.144930 | − | 0.989442i | \(-0.546296\pi\) |
0.929347 | − | 0.369208i | \(-0.120371\pi\) | |||||||
\(60\) | 1.46129 | + | 0.929852i | 0.188652 | + | 0.120043i | ||||
\(61\) | −6.95089 | − | 12.0393i | −0.889971 | − | 1.54147i | −0.839908 | − | 0.542729i | \(-0.817391\pi\) |
−0.0500626 | − | 0.998746i | \(-0.515942\pi\) | |||||||
\(62\) | 3.72120 | + | 2.14844i | 0.472593 | + | 0.272852i | ||||
\(63\) | 5.92573 | + | 12.6725i | 0.746572 | + | 1.59659i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.12034 | 0.511066 | ||||||||
\(66\) | −4.68109 | + | 2.43999i | −0.576202 | + | 0.300342i | ||||
\(67\) | −2.56373 | + | 1.48017i | −0.313210 | + | 0.180832i | −0.648362 | − | 0.761332i | \(-0.724546\pi\) |
0.335152 | + | 0.942164i | \(0.391212\pi\) | |||||||
\(68\) | − | 2.57333i | − | 0.312062i | ||||||
\(69\) | −0.0505172 | + | 1.17136i | −0.00608156 | + | 0.141015i | ||||
\(70\) | 4.03843 | − | 2.33159i | 0.482684 | − | 0.278678i | ||||
\(71\) | 6.25422 | − | 10.8326i | 0.742239 | − | 1.28560i | −0.209234 | − | 0.977866i | \(-0.567097\pi\) |
0.951473 | − | 0.307731i | \(-0.0995696\pi\) | |||||||
\(72\) | −1.27075 | − | 2.71757i | −0.149759 | − | 0.320269i | ||||
\(73\) | 2.18577 | − | 3.78586i | 0.255825 | − | 0.443101i | −0.709295 | − | 0.704912i | \(-0.750986\pi\) |
0.965119 | + | 0.261811i | \(0.0843197\pi\) | |||||||
\(74\) | 3.89481 | + | 2.24867i | 0.452763 | + | 0.261403i | ||||
\(75\) | −1.73044 | − | 0.0746290i | −0.199814 | − | 0.00861742i | ||||
\(76\) | −0.119625 | + | 4.35726i | −0.0137219 | + | 0.499812i | ||||
\(77\) | 14.2121i | 1.61962i | ||||||||
\(78\) | −6.02102 | − | 3.83131i | −0.681747 | − | 0.433810i | ||||
\(79\) | 6.74543 | + | 3.89448i | 0.758921 | + | 0.438163i | 0.828908 | − | 0.559385i | \(-0.188963\pi\) |
−0.0699875 | + | 0.997548i | \(0.522296\pi\) | |||||||
\(80\) | −0.866025 | + | 0.500000i | −0.0968246 | + | 0.0559017i | ||||
\(81\) | −5.77038 | + | 6.90671i | −0.641154 | + | 0.767413i | ||||
\(82\) | −1.65691 | − | 2.86985i | −0.182975 | − | 0.316922i | ||||
\(83\) | 2.61607i | 0.287151i | 0.989639 | + | 0.143576i | \(0.0458601\pi\) | ||||
−0.989639 | + | 0.143576i | \(0.954140\pi\) | |||||||
\(84\) | −8.06935 | − | 0.348008i | −0.880438 | − | 0.0379708i | ||||
\(85\) | 1.28666 | + | 2.22857i | 0.139558 | + | 0.241722i | ||||
\(86\) | 2.86613 | + | 4.96428i | 0.309062 | + | 0.535312i | ||||
\(87\) | 3.43390 | + | 0.148094i | 0.368153 | + | 0.0158774i | ||||
\(88\) | − | 3.04774i | − | 0.324890i | ||||||
\(89\) | −4.81262 | − | 8.33571i | −0.510137 | − | 0.883583i | −0.999931 | − | 0.0117449i | \(-0.996261\pi\) |
0.489794 | − | 0.871838i | \(-0.337072\pi\) | |||||||
\(90\) | 2.45929 | + | 1.71811i | 0.259232 | + | 0.181105i | ||||
\(91\) | −16.6397 | + | 9.60693i | −1.74431 | + | 1.00708i | ||||
\(92\) | −0.586222 | − | 0.338456i | −0.0611179 | − | 0.0352864i | ||||
\(93\) | 6.27899 | + | 3.99546i | 0.651101 | + | 0.414310i | ||||
\(94\) | − | 8.76281i | − | 0.903815i | ||||||
\(95\) | −2.07503 | − | 3.83331i | −0.212894 | − | 0.393289i | ||||
\(96\) | 1.73044 | + | 0.0746290i | 0.176613 | + | 0.00761679i | ||||
\(97\) | −8.00346 | − | 4.62080i | −0.812628 | − | 0.469171i | 0.0352396 | − | 0.999379i | \(-0.488781\pi\) |
−0.847868 | + | 0.530208i | \(0.822114\pi\) | |||||||
\(98\) | −7.37259 | + | 12.7697i | −0.744744 | + | 1.28993i | ||||
\(99\) | −8.28245 | + | 3.87292i | −0.832417 | + | 0.389243i | ||||
\(100\) | 0.500000 | − | 0.866025i | 0.0500000 | − | 0.0866025i | ||||
\(101\) | −9.90594 | + | 5.71920i | −0.985678 | + | 0.569081i | −0.903980 | − | 0.427576i | \(-0.859368\pi\) |
−0.0816985 | + | 0.996657i | \(0.526034\pi\) | |||||||
\(102\) | 0.192045 | − | 4.45299i | 0.0190153 | − | 0.440912i | ||||
\(103\) | − | 17.4744i | − | 1.72181i | −0.508767 | − | 0.860904i | \(-0.669899\pi\) | ||
0.508767 | − | 0.860904i | \(-0.330101\pi\) | |||||||
\(104\) | 3.56832 | − | 2.06017i | 0.349903 | − | 0.202016i | ||||
\(105\) | 7.16227 | − | 3.73329i | 0.698966 | − | 0.364332i | ||||
\(106\) | −9.14686 | −0.888422 | ||||||||
\(107\) | −18.8110 | −1.81853 | −0.909265 | − | 0.416217i | \(-0.863356\pi\) | ||||
−0.909265 | + | 0.416217i | \(0.863356\pi\) | |||||||
\(108\) | −1.99615 | − | 4.79743i | −0.192080 | − | 0.461633i | ||||
\(109\) | −6.30002 | − | 3.63732i | −0.603432 | − | 0.348392i | 0.166958 | − | 0.985964i | \(-0.446605\pi\) |
−0.770391 | + | 0.637572i | \(0.779939\pi\) | |||||||
\(110\) | 1.52387 | + | 2.63942i | 0.145295 | + | 0.251659i | ||||
\(111\) | 6.57193 | + | 4.18186i | 0.623780 | + | 0.396925i | ||||
\(112\) | 2.33159 | − | 4.03843i | 0.220314 | − | 0.381595i | ||||
\(113\) | −12.7918 | −1.20335 | −0.601675 | − | 0.798741i | \(-0.705500\pi\) | ||||
−0.601675 | + | 0.798741i | \(0.705500\pi\) | |||||||
\(114\) | −0.532181 | + | 7.53105i | −0.0498433 | + | 0.705348i | ||||
\(115\) | 0.676911 | 0.0631223 | ||||||||
\(116\) | −0.992204 | + | 1.71855i | −0.0921238 | + | 0.159563i | ||||
\(117\) | −10.1331 | − | 7.07920i | −0.936806 | − | 0.654472i | ||||
\(118\) | 6.02522 | + | 10.4360i | 0.554667 | + | 0.960711i | ||||
\(119\) | −10.3922 | − | 5.99993i | −0.952650 | − | 0.550013i | ||||
\(120\) | −1.53592 | + | 0.800591i | −0.140210 | + | 0.0730836i | ||||
\(121\) | 1.71128 | 0.155571 | ||||||||
\(122\) | 13.9018 | 1.25861 | ||||||||
\(123\) | −2.65301 | − | 5.08976i | −0.239214 | − | 0.458928i | ||||
\(124\) | −3.72120 | + | 2.14844i | −0.334174 | + | 0.192935i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −13.9376 | − | 1.20442i | −1.24166 | − | 0.107298i | ||||
\(127\) | −17.7898 | + | 10.2710i | −1.57859 | + | 0.911401i | −0.583536 | + | 0.812087i | \(0.698331\pi\) |
−0.995056 | + | 0.0993135i | \(0.968335\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 4.58919 | + | 8.80429i | 0.404055 | + | 0.775174i | ||||
\(130\) | −2.06017 | + | 3.56832i | −0.180689 | + | 0.312962i | ||||
\(131\) | 3.28692 | + | 1.89770i | 0.287180 | + | 0.165803i | 0.636669 | − | 0.771137i | \(-0.280312\pi\) |
−0.349490 | + | 0.936940i | \(0.613645\pi\) | |||||||
\(132\) | 0.227450 | − | 5.27394i | 0.0197970 | − | 0.459037i | ||||
\(133\) | 17.3175 | + | 10.6424i | 1.50162 | + | 0.922815i | ||||
\(134\) | − | 2.96034i | − | 0.255735i | ||||||
\(135\) | 4.12744 | + | 3.15662i | 0.355233 | + | 0.271679i | ||||
\(136\) | 2.22857 | + | 1.28666i | 0.191098 | + | 0.110330i | ||||
\(137\) | 5.64269 | − | 3.25781i | 0.482087 | − | 0.278333i | −0.239199 | − | 0.970971i | \(-0.576885\pi\) |
0.721286 | + | 0.692637i | \(0.243551\pi\) | |||||||
\(138\) | −0.989165 | − | 0.629427i | −0.0842033 | − | 0.0535804i | ||||
\(139\) | 4.11100 | + | 7.12045i | 0.348690 | + | 0.603949i | 0.986017 | − | 0.166645i | \(-0.0532932\pi\) |
−0.637327 | + | 0.770594i | \(0.719960\pi\) | |||||||
\(140\) | 4.66317i | 0.394110i | ||||||||
\(141\) | 0.653960 | − | 15.1635i | 0.0550734 | − | 1.27700i | ||||
\(142\) | 6.25422 | + | 10.8326i | 0.524843 | + | 0.909054i | ||||
\(143\) | −6.27887 | − | 10.8753i | −0.525065 | − | 0.909439i | ||||
\(144\) | 2.98886 | + | 0.258282i | 0.249072 | + | 0.0215235i | ||||
\(145\) | − | 1.98441i | − | 0.164796i | ||||||
\(146\) | 2.18577 | + | 3.78586i | 0.180895 | + | 0.313320i | ||||
\(147\) | −13.7108 | + | 21.5470i | −1.13085 | + | 1.77717i | ||||
\(148\) | −3.89481 | + | 2.24867i | −0.320151 | + | 0.184840i | ||||
\(149\) | 2.16323 | + | 1.24894i | 0.177219 | + | 0.102317i | 0.585985 | − | 0.810322i | \(-0.300708\pi\) |
−0.408767 | + | 0.912639i | \(0.634041\pi\) | |||||||
\(150\) | 0.929852 | − | 1.46129i | 0.0759221 | − | 0.119314i | ||||
\(151\) | − | 9.36390i | − | 0.762023i | −0.924570 | − | 0.381012i | \(-0.875576\pi\) | ||
0.924570 | − | 0.381012i | \(-0.124424\pi\) | |||||||
\(152\) | −3.71368 | − | 2.28223i | −0.301219 | − | 0.185113i | ||||
\(153\) | 0.664645 | − | 7.69131i | 0.0537333 | − | 0.621806i | ||||
\(154\) | −12.3081 | − | 7.10607i | −0.991813 | − | 0.572623i | ||||
\(155\) | 2.14844 | − | 3.72120i | 0.172567 | − | 0.298894i | ||||
\(156\) | 6.32852 | − | 3.29871i | 0.506687 | − | 0.264108i | ||||
\(157\) | 7.71370 | − | 13.3605i | 0.615620 | − | 1.06629i | −0.374655 | − | 0.927164i | \(-0.622239\pi\) |
0.990275 | − | 0.139121i | \(-0.0444277\pi\) | |||||||
\(158\) | −6.74543 | + | 3.89448i | −0.536638 | + | 0.309828i | ||||
\(159\) | −15.8281 | − | 0.682621i | −1.25525 | − | 0.0541354i | ||||
\(160\) | − | 1.00000i | − | 0.0790569i | ||||||
\(161\) | −2.73366 | + | 1.57828i | −0.215442 | + | 0.124386i | ||||
\(162\) | −3.09620 | − | 8.45065i | −0.243260 | − | 0.663946i | ||||
\(163\) | 7.94366 | 0.622196 | 0.311098 | − | 0.950378i | \(-0.399303\pi\) | ||||
0.311098 | + | 0.950378i | \(0.399303\pi\) | |||||||
\(164\) | 3.31382 | 0.258766 | ||||||||
\(165\) | 2.43999 | + | 4.68109i | 0.189953 | + | 0.364422i | ||||
\(166\) | −2.26559 | − | 1.30804i | −0.175844 | − | 0.101523i | ||||
\(167\) | −2.97913 | − | 5.16001i | −0.230532 | − | 0.399293i | 0.727433 | − | 0.686179i | \(-0.240713\pi\) |
−0.957965 | + | 0.286886i | \(0.907380\pi\) | |||||||
\(168\) | 4.33606 | − | 6.81426i | 0.334534 | − | 0.525732i | ||||
\(169\) | 1.98861 | − | 3.44437i | 0.152970 | − | 0.264952i | ||||
\(170\) | −2.57333 | −0.197365 | ||||||||
\(171\) | −1.48294 | + | 12.9923i | −0.113404 | + | 0.993549i | ||||
\(172\) | −5.73225 | −0.437080 | ||||||||
\(173\) | −4.02441 | + | 6.97047i | −0.305970 | + | 0.529955i | −0.977477 | − | 0.211043i | \(-0.932314\pi\) |
0.671507 | + | 0.740998i | \(0.265647\pi\) | |||||||
\(174\) | −1.84521 | + | 2.89980i | −0.139885 | + | 0.219833i | ||||
\(175\) | −2.33159 | − | 4.03843i | −0.176251 | − | 0.305276i | ||||
\(176\) | 2.63942 | + | 1.52387i | 0.198954 | + | 0.114866i | ||||
\(177\) | 9.64747 | + | 18.5085i | 0.725148 | + | 1.39119i | ||||
\(178\) | 9.62524 | 0.721443 | ||||||||
\(179\) | 9.52738 | 0.712109 | 0.356055 | − | 0.934465i | \(-0.384122\pi\) | ||||
0.356055 | + | 0.934465i | \(0.384122\pi\) | |||||||
\(180\) | −2.71757 | + | 1.27075i | −0.202556 | + | 0.0947162i | ||||
\(181\) | −14.9311 | + | 8.62045i | −1.10982 | + | 0.640753i | −0.938782 | − | 0.344512i | \(-0.888045\pi\) |
−0.171035 | + | 0.985265i | \(0.554711\pi\) | |||||||
\(182\) | − | 19.2139i | − | 1.42423i | ||||||
\(183\) | 24.0562 | + | 1.03748i | 1.77829 | + | 0.0766925i | ||||
\(184\) | 0.586222 | − | 0.338456i | 0.0432169 | − | 0.0249513i | ||||
\(185\) | 2.24867 | − | 3.89481i | 0.165325 | − | 0.286352i | ||||
\(186\) | −6.59966 | + | 3.44004i | −0.483911 | + | 0.252236i | ||||
\(187\) | 3.92141 | − | 6.79209i | 0.286762 | − | 0.496687i | ||||
\(188\) | 7.58882 | + | 4.38141i | 0.553472 | + | 0.319547i | ||||
\(189\) | −24.0283 | − | 3.12432i | −1.74780 | − | 0.227261i | ||||
\(190\) | 4.35726 | + | 0.119625i | 0.316109 | + | 0.00867847i | ||||
\(191\) | 14.9575i | 1.08228i | 0.840931 | + | 0.541142i | \(0.182008\pi\) | ||||
−0.840931 | + | 0.541142i | \(0.817992\pi\) | |||||||
\(192\) | −0.929852 | + | 1.46129i | −0.0671063 | + | 0.105460i | ||||
\(193\) | 18.0958 | + | 10.4476i | 1.30257 | + | 0.752037i | 0.980844 | − | 0.194797i | \(-0.0624047\pi\) |
0.321723 | + | 0.946834i | \(0.395738\pi\) | |||||||
\(194\) | 8.00346 | − | 4.62080i | 0.574615 | − | 0.331754i | ||||
\(195\) | −3.83131 | + | 6.02102i | −0.274366 | + | 0.431175i | ||||
\(196\) | −7.37259 | − | 12.7697i | −0.526614 | − | 0.912122i | ||||
\(197\) | − | 22.6541i | − | 1.61404i | −0.590526 | − | 0.807019i | \(-0.701080\pi\) | ||
0.590526 | − | 0.807019i | \(-0.298920\pi\) | |||||||
\(198\) | 0.787178 | − | 9.10927i | 0.0559423 | − | 0.647368i | ||||
\(199\) | 3.33437 | + | 5.77531i | 0.236367 | + | 0.409401i | 0.959669 | − | 0.281132i | \(-0.0907097\pi\) |
−0.723302 | + | 0.690532i | \(0.757376\pi\) | |||||||
\(200\) | 0.500000 | + | 0.866025i | 0.0353553 | + | 0.0612372i | ||||
\(201\) | 0.220927 | − | 5.12270i | 0.0155830 | − | 0.361327i | ||||
\(202\) | − | 11.4384i | − | 0.804803i | ||||||
\(203\) | 4.62682 | + | 8.01389i | 0.324739 | + | 0.562465i | ||||
\(204\) | 3.76038 | + | 2.39281i | 0.263279 | + | 0.167530i | ||||
\(205\) | −2.86985 | + | 1.65691i | −0.200439 | + | 0.115724i | ||||
\(206\) | 15.1333 | + | 8.73722i | 1.05439 | + | 0.608751i | ||||
\(207\) | −1.66472 | − | 1.16301i | −0.115706 | − | 0.0808346i | ||||
\(208\) | 4.12034i | 0.285694i | ||||||||
\(209\) | −6.95563 | + | 11.3183i | −0.481131 | + | 0.782906i | ||||
\(210\) | −0.348008 | + | 8.06935i | −0.0240148 | + | 0.556838i | ||||
\(211\) | 21.3930 | + | 12.3513i | 1.47276 | + | 0.850297i | 0.999530 | − | 0.0306440i | \(-0.00975581\pi\) |
0.473227 | + | 0.880941i | \(0.343089\pi\) | |||||||
\(212\) | 4.57343 | − | 7.92141i | 0.314104 | − | 0.544045i | ||||
\(213\) | 10.0141 | + | 19.2120i | 0.686158 | + | 1.31638i | ||||
\(214\) | 9.40551 | − | 16.2908i | 0.642948 | − | 1.11362i | ||||
\(215\) | 4.96428 | − | 2.86613i | 0.338561 | − | 0.195468i | ||||
\(216\) | 5.15278 | + | 0.669999i | 0.350602 | + | 0.0455876i | ||||
\(217\) | 20.0371i | 1.36021i | ||||||||
\(218\) | 6.30002 | − | 3.63732i | 0.426691 | − | 0.246350i | ||||
\(219\) | 3.49981 | + | 6.71433i | 0.236495 | + | 0.453713i | ||||
\(220\) | −3.04774 | −0.205479 | ||||||||
\(221\) | 10.6030 | 0.713234 | ||||||||
\(222\) | −6.90756 | + | 3.60053i | −0.463605 | + | 0.241652i | ||||
\(223\) | −4.59604 | − | 2.65352i | −0.307774 | − | 0.177693i | 0.338156 | − | 0.941090i | \(-0.390197\pi\) |
−0.645930 | + | 0.763397i | \(0.723530\pi\) | |||||||
\(224\) | 2.33159 | + | 4.03843i | 0.155786 | + | 0.269829i | ||||
\(225\) | 1.71811 | − | 2.45929i | 0.114541 | − | 0.163953i | ||||
\(226\) | 6.39589 | − | 11.0780i | 0.425448 | − | 0.736898i | ||||
\(227\) | −5.17010 | −0.343152 | −0.171576 | − | 0.985171i | \(-0.554886\pi\) | ||||
−0.171576 | + | 0.985171i | \(0.554886\pi\) | |||||||
\(228\) | −6.25599 | − | 4.22641i | −0.414313 | − | 0.279901i | ||||
\(229\) | −12.5671 | −0.830459 | −0.415230 | − | 0.909717i | \(-0.636299\pi\) | ||||
−0.415230 | + | 0.909717i | \(0.636299\pi\) | |||||||
\(230\) | −0.338456 | + | 0.586222i | −0.0223171 | + | 0.0386544i | ||||
\(231\) | −20.7681 | − | 13.2152i | −1.36644 | − | 0.869495i | ||||
\(232\) | −0.992204 | − | 1.71855i | −0.0651414 | − | 0.112828i | ||||
\(233\) | −20.8093 | − | 12.0142i | −1.36326 | − | 0.787079i | −0.373205 | − | 0.927749i | \(-0.621741\pi\) |
−0.990057 | + | 0.140669i | \(0.955075\pi\) | |||||||
\(234\) | 11.1973 | − | 5.23593i | 0.731992 | − | 0.342283i | ||||
\(235\) | −8.76281 | −0.571623 | ||||||||
\(236\) | −12.0504 | −0.784417 | ||||||||
\(237\) | −11.9632 | + | 6.23576i | −0.777095 | + | 0.405056i | ||||
\(238\) | 10.3922 | − | 5.99993i | 0.673625 | − | 0.388918i | ||||
\(239\) | 12.9191i | 0.835668i | 0.908523 | + | 0.417834i | \(0.137211\pi\) | ||||
−0.908523 | + | 0.417834i | \(0.862789\pi\) | |||||||
\(240\) | 0.0746290 | − | 1.73044i | 0.00481728 | − | 0.111700i | ||||
\(241\) | 18.3610 | − | 10.6007i | 1.18273 | − | 0.682851i | 0.226088 | − | 0.974107i | \(-0.427406\pi\) |
0.956645 | + | 0.291256i | \(0.0940731\pi\) | |||||||
\(242\) | −0.855640 | + | 1.48201i | −0.0550026 | + | 0.0952674i | ||||
\(243\) | −4.72713 | − | 14.8544i | −0.303245 | − | 0.952912i | ||||
\(244\) | −6.95089 | + | 12.0393i | −0.444985 | + | 0.770737i | ||||
\(245\) | 12.7697 | + | 7.37259i | 0.815826 | + | 0.471018i | ||||
\(246\) | 5.73437 | + | 0.247307i | 0.365610 | + | 0.0157677i | ||||
\(247\) | −17.9534 | − | 0.492894i | −1.14235 | − | 0.0313621i | ||||
\(248\) | − | 4.29688i | − | 0.272852i | ||||||
\(249\) | −3.82285 | − | 2.43256i | −0.242263 | − | 0.154157i | ||||
\(250\) | −0.866025 | − | 0.500000i | −0.0547723 | − | 0.0316228i | ||||
\(251\) | 16.2979 | − | 9.40959i | 1.02871 | − | 0.593928i | 0.112098 | − | 0.993697i | \(-0.464243\pi\) |
0.916616 | + | 0.399769i | \(0.130910\pi\) | |||||||
\(252\) | 8.01184 | − | 11.4681i | 0.504699 | − | 0.722422i | ||||
\(253\) | −1.03152 | − | 1.78665i | −0.0648514 | − | 0.112326i | ||||
\(254\) | − | 20.5419i | − | 1.28892i | ||||||
\(255\) | −4.45299 | − | 0.192045i | −0.278857 | − | 0.0120263i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 4.00449 | + | 6.93597i | 0.249793 | + | 0.432654i | 0.963468 | − | 0.267823i | \(-0.0863041\pi\) |
−0.713675 | + | 0.700477i | \(0.752971\pi\) | |||||||
\(258\) | −9.91933 | − | 0.427792i | −0.617550 | − | 0.0266332i | ||||
\(259\) | 20.9719i | 1.30313i | ||||||||
\(260\) | −2.06017 | − | 3.56832i | −0.127766 | − | 0.221298i | ||||
\(261\) | −3.40943 | + | 4.88023i | −0.211038 | + | 0.302079i | ||||
\(262\) | −3.28692 | + | 1.89770i | −0.203067 | + | 0.117241i | ||||
\(263\) | 24.6525 | + | 14.2331i | 1.52014 | + | 0.877653i | 0.999718 | + | 0.0237431i | \(0.00755838\pi\) |
0.520421 | + | 0.853910i | \(0.325775\pi\) | |||||||
\(264\) | 4.45364 | + | 2.83395i | 0.274103 | + | 0.174417i | ||||
\(265\) | 9.14686i | 0.561887i | ||||||||
\(266\) | −17.8754 | + | 9.67623i | −1.09601 | + | 0.593288i | ||||
\(267\) | 16.6559 | + | 0.718322i | 1.01933 | + | 0.0439606i | ||||
\(268\) | 2.56373 | + | 1.48017i | 0.156605 | + | 0.0904158i | ||||
\(269\) | 2.93694 | − | 5.08693i | 0.179068 | − | 0.310155i | −0.762493 | − | 0.646996i | \(-0.776025\pi\) |
0.941562 | + | 0.336841i | \(0.109358\pi\) | |||||||
\(270\) | −4.79743 | + | 1.99615i | −0.291963 | + | 0.121482i | ||||
\(271\) | −6.85354 | + | 11.8707i | −0.416323 | + | 0.721092i | −0.995566 | − | 0.0940622i | \(-0.970015\pi\) |
0.579243 | + | 0.815155i | \(0.303348\pi\) | |||||||
\(272\) | −2.22857 | + | 1.28666i | −0.135127 | + | 0.0780154i | ||||
\(273\) | 1.43391 | − | 33.2485i | 0.0867843 | − | 2.01229i | ||||
\(274\) | 6.51561i | 0.393622i | ||||||||
\(275\) | 2.63942 | − | 1.52387i | 0.159163 | − | 0.0918928i | ||||
\(276\) | 1.03968 | − | 0.541929i | 0.0625815 | − | 0.0326203i | ||||
\(277\) | 15.1954 | 0.913004 | 0.456502 | − | 0.889722i | \(-0.349102\pi\) | ||||
0.456502 | + | 0.889722i | \(0.349102\pi\) | |||||||
\(278\) | −8.22199 | −0.493122 | ||||||||
\(279\) | −11.6771 | + | 5.46026i | −0.699087 | + | 0.326897i | ||||
\(280\) | −4.03843 | − | 2.33159i | −0.241342 | − | 0.139339i | ||||
\(281\) | 4.27607 | + | 7.40636i | 0.255089 | + | 0.441827i | 0.964920 | − | 0.262545i | \(-0.0845620\pi\) |
−0.709831 | + | 0.704372i | \(0.751229\pi\) | |||||||
\(282\) | 12.8050 | + | 8.14812i | 0.762529 | + | 0.485213i | ||||
\(283\) | −14.1879 | + | 24.5741i | −0.843382 | + | 1.46078i | 0.0436361 | + | 0.999047i | \(0.486106\pi\) |
−0.887019 | + | 0.461734i | \(0.847228\pi\) | |||||||
\(284\) | −12.5084 | −0.742239 | ||||||||
\(285\) | 7.53105 | + | 0.532181i | 0.446101 | + | 0.0315237i | ||||
\(286\) | 12.5577 | 0.742554 | ||||||||
\(287\) | 7.72645 | − | 13.3826i | 0.456078 | − | 0.789950i | ||||
\(288\) | −1.71811 | + | 2.45929i | −0.101241 | + | 0.144915i | ||||
\(289\) | −5.18900 | − | 8.98761i | −0.305235 | − | 0.528683i | ||||
\(290\) | 1.71855 | + | 0.992204i | 0.100917 | + | 0.0582642i | ||||
\(291\) | 14.1944 | − | 7.39874i | 0.832089 | − | 0.433722i | ||||
\(292\) | −4.37153 | −0.255825 | ||||||||
\(293\) | −7.22309 | −0.421977 | −0.210989 | − | 0.977489i | \(-0.567668\pi\) | ||||
−0.210989 | + | 0.977489i | \(0.567668\pi\) | |||||||
\(294\) | −11.8049 | − | 22.6474i | −0.688473 | − | 1.32083i | ||||
\(295\) | 10.4360 | − | 6.02522i | 0.607607 | − | 0.350802i | ||||
\(296\) | − | 4.49734i | − | 0.261403i | ||||||
\(297\) | 2.04198 | − | 15.7043i | 0.118488 | − | 0.911257i | ||||
\(298\) | −2.16323 | + | 1.24894i | −0.125313 | + | 0.0723493i | ||||
\(299\) | 1.39455 | − | 2.41544i | 0.0806491 | − | 0.139688i | ||||
\(300\) | 0.800591 | + | 1.53592i | 0.0462221 | + | 0.0886765i | ||||
\(301\) | −13.3652 | + | 23.1493i | −0.770360 | + | 1.33430i | ||||
\(302\) | 8.10937 | + | 4.68195i | 0.466642 | + | 0.269416i | ||||
\(303\) | 0.853636 | − | 19.7935i | 0.0490401 | − | 1.13711i | ||||
\(304\) | 3.83331 | − | 2.07503i | 0.219855 | − | 0.119011i | ||||
\(305\) | − | 13.9018i | − | 0.796014i | ||||||
\(306\) | 6.32855 | + | 4.42125i | 0.361779 | + | 0.252746i | ||||
\(307\) | 0.356034 | + | 0.205556i | 0.0203199 | + | 0.0117317i | 0.510126 | − | 0.860100i | \(-0.329599\pi\) |
−0.489806 | + | 0.871832i | \(0.662932\pi\) | |||||||
\(308\) | 12.3081 | − | 7.10607i | 0.701318 | − | 0.404906i | ||||
\(309\) | 25.5353 | + | 16.2486i | 1.45265 | + | 0.924353i | ||||
\(310\) | 2.14844 | + | 3.72120i | 0.122023 | + | 0.211350i | ||||
\(311\) | − | 10.4640i | − | 0.593361i | −0.954977 | − | 0.296680i | \(-0.904120\pi\) | ||
0.954977 | − | 0.296680i | \(-0.0958796\pi\) | |||||||
\(312\) | −0.307497 | + | 7.13001i | −0.0174086 | + | 0.403658i | ||||
\(313\) | −0.872105 | − | 1.51053i | −0.0492943 | − | 0.0853802i | 0.840325 | − | 0.542082i | \(-0.182364\pi\) |
−0.889620 | + | 0.456702i | \(0.849031\pi\) | |||||||
\(314\) | 7.71370 | + | 13.3605i | 0.435309 | + | 0.753978i | ||||
\(315\) | −1.20442 | + | 13.9376i | −0.0678611 | + | 0.785293i | ||||
\(316\) | − | 7.78896i | − | 0.438163i | ||||||
\(317\) | 10.2023 | + | 17.6710i | 0.573021 | + | 0.992501i | 0.996254 | + | 0.0864798i | \(0.0275618\pi\) |
−0.423233 | + | 0.906021i | \(0.639105\pi\) | |||||||
\(318\) | 8.50522 | − | 13.3662i | 0.476949 | − | 0.749541i | ||||
\(319\) | −5.23769 | + | 3.02398i | −0.293254 | + | 0.169310i | ||||
\(320\) | 0.866025 | + | 0.500000i | 0.0484123 | + | 0.0279508i | ||||
\(321\) | 17.4915 | − | 27.4884i | 0.976278 | − | 1.53425i | ||||
\(322\) | − | 3.15655i | − | 0.175908i | ||||||
\(323\) | −5.33973 | − | 9.86435i | −0.297110 | − | 0.548867i | ||||
\(324\) | 8.86658 | + | 1.54394i | 0.492588 | + | 0.0857745i | ||||
\(325\) | 3.56832 | + | 2.06017i | 0.197935 | + | 0.114278i | ||||
\(326\) | −3.97183 | + | 6.87941i | −0.219979 | + | 0.381015i | ||||
\(327\) | 11.1733 | − | 5.82400i | 0.617883 | − | 0.322068i | ||||
\(328\) | −1.65691 | + | 2.86985i | −0.0914875 | + | 0.158461i | ||||
\(329\) | 35.3880 | − | 20.4313i | 1.95100 | − | 1.12641i | ||||
\(330\) | −5.27394 | − | 0.227450i | −0.290321 | − | 0.0125207i | ||||
\(331\) | − | 3.45155i | − | 0.189714i | −0.995491 | − | 0.0948572i | \(-0.969761\pi\) | ||
0.995491 | − | 0.0948572i | \(-0.0302395\pi\) | |||||||
\(332\) | 2.26559 | − | 1.30804i | 0.124340 | − | 0.0717879i | ||||
\(333\) | −12.2218 | + | 5.71500i | −0.669753 | + | 0.313180i | ||||
\(334\) | 5.95826 | 0.326022 | ||||||||
\(335\) | −2.96034 | −0.161741 | ||||||||
\(336\) | 3.73329 | + | 7.16227i | 0.203668 | + | 0.390734i | ||||
\(337\) | −23.1281 | − | 13.3530i | −1.25987 | − | 0.727384i | −0.286818 | − | 0.957985i | \(-0.592598\pi\) |
−0.973049 | + | 0.230601i | \(0.925931\pi\) | |||||||
\(338\) | 1.98861 | + | 3.44437i | 0.108166 | + | 0.187349i | ||||
\(339\) | 11.8945 | − | 18.6925i | 0.646019 | − | 1.01524i | ||||
\(340\) | 1.28666 | − | 2.22857i | 0.0697791 | − | 0.120861i | ||||
\(341\) | −13.0958 | −0.709175 | ||||||||
\(342\) | −10.5102 | − | 7.78044i | −0.568328 | − | 0.420718i | ||||
\(343\) | −36.1171 | −1.95014 | ||||||||
\(344\) | 2.86613 | − | 4.96428i | 0.154531 | − | 0.267656i | ||||
\(345\) | −0.629427 | + | 0.989165i | −0.0338872 | + | 0.0532549i | ||||
\(346\) | −4.02441 | − | 6.97047i | −0.216353 | − | 0.374735i | ||||
\(347\) | 14.4663 | + | 8.35210i | 0.776590 | + | 0.448364i | 0.835220 | − | 0.549915i | \(-0.185340\pi\) |
−0.0586306 | + | 0.998280i | \(0.518673\pi\) | |||||||
\(348\) | −1.58870 | − | 3.04790i | −0.0851632 | − | 0.163384i | ||||
\(349\) | 32.2768 | 1.72773 | 0.863867 | − | 0.503719i | \(-0.168035\pi\) | ||||
0.863867 | + | 0.503719i | \(0.168035\pi\) | |||||||
\(350\) | 4.66317 | 0.249257 | ||||||||
\(351\) | 19.7671 | − | 8.22483i | 1.05509 | − | 0.439009i | ||||
\(352\) | −2.63942 | + | 1.52387i | −0.140682 | + | 0.0812225i | ||||
\(353\) | − | 15.2843i | − | 0.813501i | −0.913539 | − | 0.406751i | \(-0.866662\pi\) | ||
0.913539 | − | 0.406751i | \(-0.133338\pi\) | |||||||
\(354\) | −20.8526 | − | 0.899313i | −1.10830 | − | 0.0477979i | ||||
\(355\) | 10.8326 | − | 6.25422i | 0.574936 | − | 0.331940i | ||||
\(356\) | −4.81262 | + | 8.33571i | −0.255068 | + | 0.441792i | ||||
\(357\) | 18.4308 | − | 9.60697i | 0.975464 | − | 0.508455i | ||||
\(358\) | −4.76369 | + | 8.25095i | −0.251769 | + | 0.436076i | ||||
\(359\) | 0.917556 | + | 0.529751i | 0.0484267 | + | 0.0279592i | 0.524018 | − | 0.851707i | \(-0.324432\pi\) |
−0.475591 | + | 0.879666i | \(0.657766\pi\) | |||||||
\(360\) | 0.258282 | − | 2.98886i | 0.0136127 | − | 0.157527i | ||||
\(361\) | 8.58288 | + | 16.9509i | 0.451731 | + | 0.892154i | ||||
\(362\) | − | 17.2409i | − | 0.906162i | ||||||
\(363\) | −1.59124 | + | 2.50068i | −0.0835183 | + | 0.131252i | ||||
\(364\) | 16.6397 | + | 9.60693i | 0.872157 | + | 0.503540i | ||||
\(365\) | 3.78586 | − | 2.18577i | 0.198161 | − | 0.114408i | ||||
\(366\) | −12.9266 | + | 20.3146i | −0.675684 | + | 1.06186i | ||||
\(367\) | 10.2507 | + | 17.7547i | 0.535080 | + | 0.926786i | 0.999159 | + | 0.0409927i | \(0.0130520\pi\) |
−0.464079 | + | 0.885794i | \(0.653615\pi\) | |||||||
\(368\) | 0.676911i | 0.0352864i | ||||||||
\(369\) | 9.90454 | + | 0.855901i | 0.515610 | + | 0.0445564i | ||||
\(370\) | 2.24867 | + | 3.89481i | 0.116903 | + | 0.202482i | ||||
\(371\) | −21.3267 | − | 36.9389i | −1.10723 | − | 1.91777i | ||||
\(372\) | 0.320672 | − | 7.43549i | 0.0166260 | − | 0.385512i | ||||
\(373\) | − | 14.8122i | − | 0.766944i | −0.923552 | − | 0.383472i | \(-0.874728\pi\) | ||
0.923552 | − | 0.383472i | \(-0.125272\pi\) | |||||||
\(374\) | 3.92141 | + | 6.79209i | 0.202771 | + | 0.351210i | ||||
\(375\) | −1.46129 | − | 0.929852i | −0.0754608 | − | 0.0480173i | ||||
\(376\) | −7.58882 | + | 4.38141i | −0.391364 | + | 0.225954i | ||||
\(377\) | −7.08101 | − | 4.08822i | −0.364690 | − | 0.210554i | ||||
\(378\) | 14.7199 | − | 19.2469i | 0.757109 | − | 0.989956i | ||||
\(379\) | 4.23226i | 0.217397i | 0.994075 | + | 0.108698i | \(0.0346682\pi\) | ||||
−0.994075 | + | 0.108698i | \(0.965332\pi\) | |||||||
\(380\) | −2.28223 | + | 3.71368i | −0.117076 | + | 0.190508i | ||||
\(381\) | 1.53302 | − | 35.5466i | 0.0785392 | − | 1.82111i | ||||
\(382\) | −12.9535 | − | 7.47873i | −0.662761 | − | 0.382645i | ||||
\(383\) | −11.7377 | + | 20.3303i | −0.599768 | + | 1.03883i | 0.393087 | + | 0.919501i | \(0.371407\pi\) |
−0.992855 | + | 0.119328i | \(0.961926\pi\) | |||||||
\(384\) | −0.800591 | − | 1.53592i | −0.0408550 | − | 0.0783797i | ||||
\(385\) | −7.10607 | + | 12.3081i | −0.362159 | + | 0.627278i | ||||
\(386\) | −18.0958 | + | 10.4476i | −0.921054 | + | 0.531771i | ||||
\(387\) | −17.1329 | − | 1.48054i | −0.870914 | − | 0.0752601i | ||||
\(388\) | 9.24160i | 0.469171i | ||||||||
\(389\) | −14.8140 | + | 8.55289i | −0.751102 | + | 0.433649i | −0.826092 | − | 0.563536i | \(-0.809441\pi\) |
0.0749902 | + | 0.997184i | \(0.476107\pi\) | |||||||
\(390\) | −3.29871 | − | 6.32852i | −0.167037 | − | 0.320457i | ||||
\(391\) | 1.74191 | 0.0880923 | ||||||||
\(392\) | 14.7452 | 0.744744 | ||||||||
\(393\) | −5.82945 | + | 3.03857i | −0.294057 | + | 0.153275i | ||||
\(394\) | 19.6190 | + | 11.3270i | 0.988392 | + | 0.570648i | ||||
\(395\) | 3.89448 | + | 6.74543i | 0.195952 | + | 0.339400i | ||||
\(396\) | 7.49527 | + | 5.23635i | 0.376652 | + | 0.263137i | ||||
\(397\) | 3.27587 | − | 5.67397i | 0.164411 | − | 0.284768i | −0.772035 | − | 0.635580i | \(-0.780761\pi\) |
0.936446 | + | 0.350812i | \(0.114094\pi\) | |||||||
\(398\) | −6.66875 | −0.334274 | ||||||||
\(399\) | −31.6544 | + | 15.4101i | −1.58470 | + | 0.771472i | ||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 12.4043 | − | 21.4849i | 0.619442 | − | 1.07290i | −0.370146 | − | 0.928974i | \(-0.620692\pi\) |
0.989588 | − | 0.143931i | \(-0.0459744\pi\) | |||||||
\(402\) | 4.32592 | + | 2.75268i | 0.215758 | + | 0.137291i | ||||
\(403\) | −8.85230 | − | 15.3326i | −0.440964 | − | 0.763773i | ||||
\(404\) | 9.90594 | + | 5.71920i | 0.492839 | + | 0.284541i | ||||
\(405\) | −8.45065 | + | 3.09620i | −0.419916 | + | 0.153851i | ||||
\(406\) | −9.25364 | −0.459250 | ||||||||
\(407\) | −13.7067 | −0.679417 | ||||||||
\(408\) | −3.95243 | + | 2.06018i | −0.195674 | + | 0.101994i | ||||
\(409\) | 2.94189 | − | 1.69850i | 0.145467 | − | 0.0839854i | −0.425500 | − | 0.904958i | \(-0.639902\pi\) |
0.570967 | + | 0.820973i | \(0.306568\pi\) | |||||||
\(410\) | − | 3.31382i | − | 0.163658i | ||||||
\(411\) | −0.486254 | + | 11.2749i | −0.0239851 | + | 0.556149i | ||||
\(412\) | −15.1333 | + | 8.73722i | −0.745565 | + | 0.430452i | ||||
\(413\) | −28.0966 | + | 48.6648i | −1.38255 | + | 2.39464i | ||||
\(414\) | 1.83955 | − | 0.860186i | 0.0904092 | − | 0.0422758i | ||||
\(415\) | −1.30804 | + | 2.26559i | −0.0642090 | + | 0.111213i | ||||
\(416\) | −3.56832 | − | 2.06017i | −0.174951 | − | 0.101008i | ||||
\(417\) | −14.2277 | − | 0.613599i | −0.696733 | − | 0.0300481i | ||||
\(418\) | −6.32415 | − | 11.6829i | −0.309324 | − | 0.571431i | ||||
\(419\) | 25.4266i | 1.24217i | 0.783742 | + | 0.621086i | \(0.213308\pi\) | ||||
−0.783742 | + | 0.621086i | \(0.786692\pi\) | |||||||
\(420\) | −6.81426 | − | 4.33606i | −0.332502 | − | 0.211578i | ||||
\(421\) | 9.79175 | + | 5.65327i | 0.477221 | + | 0.275523i | 0.719257 | − | 0.694744i | \(-0.244482\pi\) |
−0.242037 | + | 0.970267i | \(0.577815\pi\) | |||||||
\(422\) | −21.3930 | + | 12.3513i | −1.04140 | + | 0.601251i | ||||
\(423\) | 21.5503 | + | 15.0555i | 1.04781 | + | 0.732022i | ||||
\(424\) | 4.57343 | + | 7.92141i | 0.222105 | + | 0.384698i | ||||
\(425\) | 2.57333i | 0.124825i | ||||||||
\(426\) | −21.6451 | − | 0.933493i | −1.04871 | − | 0.0452279i | ||||
\(427\) | 32.4132 | + | 56.1413i | 1.56859 | + | 2.71687i | ||||
\(428\) | 9.40551 | + | 16.2908i | 0.454633 | + | 0.787447i | ||||
\(429\) | 21.7304 | + | 0.937171i | 1.04915 | + | 0.0452470i | ||||
\(430\) | 5.73225i | 0.276434i | ||||||||
\(431\) | 0.210664 | + | 0.364881i | 0.0101473 | + | 0.0175757i | 0.871054 | − | 0.491186i | \(-0.163437\pi\) |
−0.860907 | + | 0.508762i | \(0.830103\pi\) | |||||||
\(432\) | −3.15662 | + | 4.12744i | −0.151873 | + | 0.198581i | ||||
\(433\) | 4.84430 | − | 2.79686i | 0.232802 | − | 0.134409i | −0.379062 | − | 0.925371i | \(-0.623753\pi\) |
0.611864 | + | 0.790963i | \(0.290420\pi\) | |||||||
\(434\) | −17.3526 | − | 10.0185i | −0.832952 | − | 0.480905i | ||||
\(435\) | 2.89980 | + | 1.84521i | 0.139035 | + | 0.0884708i | ||||
\(436\) | 7.27464i | 0.348392i | ||||||||
\(437\) | −2.94948 | − | 0.0809752i | −0.141093 | − | 0.00387357i | ||||
\(438\) | −7.56469 | − | 0.326243i | −0.361455 | − | 0.0155885i | ||||
\(439\) | −33.0674 | − | 19.0915i | −1.57822 | − | 0.911186i | −0.995108 | − | 0.0987947i | \(-0.968501\pi\) |
−0.583113 | − | 0.812391i | \(-0.698165\pi\) | |||||||
\(440\) | 1.52387 | − | 2.63942i | 0.0726477 | − | 0.125829i | ||||
\(441\) | −18.7375 | − | 40.0711i | −0.892260 | − | 1.90815i | ||||
\(442\) | −5.30149 | + | 9.18245i | −0.252166 | + | 0.436765i | ||||
\(443\) | 22.2103 | − | 12.8231i | 1.05524 | − | 0.609246i | 0.131132 | − | 0.991365i | \(-0.458139\pi\) |
0.924113 | + | 0.382119i | \(0.124806\pi\) | |||||||
\(444\) | 0.335632 | − | 7.78239i | 0.0159284 | − | 0.369336i | ||||
\(445\) | − | 9.62524i | − | 0.456280i | ||||||
\(446\) | 4.59604 | − | 2.65352i | 0.217629 | − | 0.125648i | ||||
\(447\) | −3.83655 | + | 1.99978i | −0.181463 | + | 0.0945864i | ||||
\(448\) | −4.66317 | −0.220314 | ||||||||
\(449\) | 23.6894 | 1.11797 | 0.558986 | − | 0.829177i | \(-0.311191\pi\) | ||||
0.558986 | + | 0.829177i | \(0.311191\pi\) | |||||||
\(450\) | 1.27075 | + | 2.71757i | 0.0599038 | + | 0.128108i | ||||
\(451\) | 8.74656 | + | 5.04983i | 0.411859 | + | 0.237787i | ||||
\(452\) | 6.39589 | + | 11.0780i | 0.300837 | + | 0.521066i | ||||
\(453\) | 13.6834 | + | 8.70704i | 0.642902 | + | 0.409092i | ||||
\(454\) | 2.58505 | − | 4.47744i | 0.121322 | − | 0.210137i | ||||
\(455\) | −19.2139 | −0.900760 | ||||||||
\(456\) | 6.78818 | − | 3.30464i | 0.317885 | − | 0.154754i | ||||
\(457\) | −17.2801 | −0.808330 | −0.404165 | − | 0.914686i | \(-0.632438\pi\) | ||||
−0.404165 | + | 0.914686i | \(0.632438\pi\) | |||||||
\(458\) | 6.28356 | − | 10.8835i | 0.293612 | − | 0.508550i | ||||
\(459\) | 10.6212 | + | 8.12302i | 0.495757 | + | 0.379150i | ||||
\(460\) | −0.338456 | − | 0.586222i | −0.0157806 | − | 0.0273328i | ||||
\(461\) | −27.4943 | − | 15.8738i | −1.28053 | − | 0.739317i | −0.303589 | − | 0.952803i | \(-0.598185\pi\) |
−0.976946 | + | 0.213486i | \(0.931518\pi\) | |||||||
\(462\) | 21.8287 | − | 11.3781i | 1.01556 | − | 0.529357i | ||||
\(463\) | −24.4190 | −1.13485 | −0.567423 | − | 0.823426i | \(-0.692060\pi\) | ||||
−0.567423 | + | 0.823426i | \(0.692060\pi\) | |||||||
\(464\) | 1.98441 | 0.0921238 | ||||||||
\(465\) | 3.44004 | + | 6.59966i | 0.159528 | + | 0.306052i | ||||
\(466\) | 20.8093 | − | 12.0142i | 0.963972 | − | 0.556549i | ||||
\(467\) | 13.4425i | 0.622047i | 0.950402 | + | 0.311023i | \(0.100672\pi\) | ||||
−0.950402 | + | 0.311023i | \(0.899328\pi\) | |||||||
\(468\) | −1.06421 | + | 12.3151i | −0.0491932 | + | 0.569267i | ||||
\(469\) | 11.9551 | − | 6.90229i | 0.552036 | − | 0.318718i | ||||
\(470\) | 4.38141 | − | 7.58882i | 0.202099 | − | 0.350046i | ||||
\(471\) | 12.3510 | + | 23.6953i | 0.569105 | + | 1.09182i | ||||
\(472\) | 6.02522 | − | 10.4360i | 0.277333 | − | 0.480355i | ||||
\(473\) | −15.1298 | − | 8.73521i | −0.695670 | − | 0.401645i | ||||
\(474\) | 0.581282 | − | 13.4783i | 0.0266992 | − | 0.619081i | ||||
\(475\) | 0.119625 | − | 4.35726i | 0.00548875 | − | 0.199925i | ||||
\(476\) | 11.9999i | 0.550013i | ||||||||
\(477\) | 15.7153 | − | 22.4948i | 0.719555 | − | 1.02996i | ||||
\(478\) | −11.1883 | − | 6.45956i | −0.511740 | − | 0.295453i | ||||
\(479\) | −8.44584 | + | 4.87621i | −0.385900 | + | 0.222800i | −0.680382 | − | 0.732857i | \(-0.738186\pi\) |
0.294482 | + | 0.955657i | \(0.404853\pi\) | |||||||
\(480\) | 1.46129 | + | 0.929852i | 0.0666986 | + | 0.0424417i | ||||
\(481\) | −9.26529 | − | 16.0480i | −0.422461 | − | 0.731724i | ||||
\(482\) | 21.2014i | 0.965697i | ||||||||
\(483\) | 0.235571 | − | 5.46224i | 0.0107188 | − | 0.248540i | ||||
\(484\) | −0.855640 | − | 1.48201i | −0.0388927 | − | 0.0673642i | ||||
\(485\) | −4.62080 | − | 8.00346i | −0.209820 | − | 0.363418i | ||||
\(486\) | 15.2279 | + | 3.33340i | 0.690751 | + | 0.151206i | ||||
\(487\) | − | 16.0127i | − | 0.725606i | −0.931866 | − | 0.362803i | \(-0.881820\pi\) | ||
0.931866 | − | 0.362803i | \(-0.118180\pi\) | |||||||
\(488\) | −6.95089 | − | 12.0393i | −0.314652 | − | 0.544994i | ||||
\(489\) | −7.38643 | + | 11.6080i | −0.334026 | + | 0.524932i | ||||
\(490\) | −12.7697 | + | 7.37259i | −0.576876 | + | 0.333060i | ||||
\(491\) | 18.5831 | + | 10.7290i | 0.838645 | + | 0.484192i | 0.856803 | − | 0.515643i | \(-0.172447\pi\) |
−0.0181585 | + | 0.999835i | \(0.505780\pi\) | |||||||
\(492\) | −3.08136 | + | 4.84246i | −0.138918 | + | 0.218315i | ||||
\(493\) | − | 5.10653i | − | 0.229986i | ||||||
\(494\) | 9.40355 | − | 15.3016i | 0.423086 | − | 0.688454i | ||||
\(495\) | −9.10927 | − | 0.787178i | −0.409431 | − | 0.0353810i | ||||
\(496\) | 3.72120 | + | 2.14844i | 0.167087 | + | 0.0964677i | ||||
\(497\) | −29.1645 | + | 50.5144i | −1.30821 | + | 2.26588i | ||||
\(498\) | 4.01809 | − | 2.09440i | 0.180055 | − | 0.0938525i | ||||
\(499\) | 9.93532 | − | 17.2085i | 0.444766 | − | 0.770358i | −0.553270 | − | 0.833002i | \(-0.686620\pi\) |
0.998036 | + | 0.0626445i | \(0.0199534\pi\) | |||||||
\(500\) | 0.866025 | − | 0.500000i | 0.0387298 | − | 0.0223607i | ||||
\(501\) | 10.3104 | + | 0.444659i | 0.460636 | + | 0.0198659i | ||||
\(502\) | 18.8192i | 0.839941i | ||||||||
\(503\) | −25.5440 | + | 14.7478i | −1.13895 | + | 0.657574i | −0.946171 | − | 0.323668i | \(-0.895084\pi\) |
−0.192780 | + | 0.981242i | \(0.561750\pi\) | |||||||
\(504\) | 5.92573 | + | 12.6725i | 0.263953 | + | 0.564478i | ||||
\(505\) | −11.4384 | −0.509002 | ||||||||
\(506\) | 2.06305 | 0.0917137 | ||||||||
\(507\) | 3.18412 | + | 6.10869i | 0.141412 | + | 0.271297i | ||||
\(508\) | 17.7898 | + | 10.2710i | 0.789296 | + | 0.455700i | ||||
\(509\) | 7.10434 | + | 12.3051i | 0.314894 | + | 0.545413i | 0.979415 | − | 0.201857i | \(-0.0646976\pi\) |
−0.664521 | + | 0.747270i | \(0.731364\pi\) | |||||||
\(510\) | 2.39281 | − | 3.76038i | 0.105955 | − | 0.166512i | ||||
\(511\) | −10.1926 | + | 17.6541i | −0.450894 | + | 0.780972i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −17.6067 | − | 14.2480i | −0.777354 | − | 0.629063i | ||||
\(514\) | −8.00897 | −0.353261 | ||||||||
\(515\) | 8.73722 | − | 15.1333i | 0.385008 | − | 0.666854i | ||||
\(516\) | 5.33014 | − | 8.37650i | 0.234646 | − | 0.368755i | ||||
\(517\) | 13.3534 | + | 23.1288i | 0.587281 | + | 1.01720i | ||||
\(518\) | −18.1622 | − | 10.4859i | −0.798000 | − | 0.460726i | ||||
\(519\) | −6.44380 | − | 12.3623i | −0.282852 | − | 0.542647i | ||||
\(520\) | 4.12034 | 0.180689 | ||||||||
\(521\) | 6.13334 | 0.268707 | 0.134353 | − | 0.990934i | \(-0.457104\pi\) | ||||
0.134353 | + | 0.990934i | \(0.457104\pi\) | |||||||
\(522\) | −2.52169 | − | 5.39277i | −0.110371 | − | 0.236035i | ||||
\(523\) | 3.86418 | − | 2.23098i | 0.168969 | − | 0.0975541i | −0.413131 | − | 0.910672i | \(-0.635565\pi\) |
0.582099 | + | 0.813118i | \(0.302231\pi\) | |||||||
\(524\) | − | 3.79541i | − | 0.165803i | ||||||
\(525\) | 8.06935 | + | 0.348008i | 0.352175 | + | 0.0151883i | ||||
\(526\) | −24.6525 | + | 14.2331i | −1.07490 | + | 0.620594i | ||||
\(527\) | 5.52863 | − | 9.57587i | 0.240831 | − | 0.417131i | ||||
\(528\) | −4.68109 | + | 2.43999i | −0.203718 | + | 0.106187i | ||||
\(529\) | −11.2709 | + | 19.5218i | −0.490039 | + | 0.848772i | ||||
\(530\) | −7.92141 | − | 4.57343i | −0.344084 | − | 0.198657i | ||||
\(531\) | −36.0171 | − | 3.11242i | −1.56301 | − | 0.135067i | ||||
\(532\) | 0.557830 | − | 20.3186i | 0.0241850 | − | 0.880925i | ||||
\(533\) | 13.6541i | 0.591423i | ||||||||
\(534\) | −8.95005 | + | 14.0653i | −0.387307 | + | 0.608665i | ||||
\(535\) | −16.2908 | − | 9.40551i | −0.704314 | − | 0.406636i | ||||
\(536\) | −2.56373 | + | 1.48017i | −0.110736 | + | 0.0639336i | ||||
\(537\) | −8.85905 | + | 13.9223i | −0.382296 | + | 0.600791i | ||||
\(538\) | 2.93694 | + | 5.08693i | 0.126620 | + | 0.219313i | ||||
\(539\) | − | 44.9395i | − | 1.93568i | ||||||
\(540\) | 0.669999 | − | 5.15278i | 0.0288321 | − | 0.221740i | ||||
\(541\) | 0.177929 | + | 0.308182i | 0.00764975 | + | 0.0132498i | 0.869825 | − | 0.493360i | \(-0.164232\pi\) |
−0.862175 | + | 0.506610i | \(0.830898\pi\) | |||||||
\(542\) | −6.85354 | − | 11.8707i | −0.294385 | − | 0.509889i | ||||
\(543\) | 1.28667 | − | 29.8344i | 0.0552164 | − | 1.28032i | ||||
\(544\) | − | 2.57333i | − | 0.110330i | ||||||
\(545\) | −3.63732 | − | 6.30002i | −0.155806 | − | 0.269863i | ||||
\(546\) | 28.0771 | + | 17.8660i | 1.20159 | + | 0.764596i | ||||
\(547\) | 29.5616 | − | 17.0674i | 1.26396 | − | 0.729750i | 0.290124 | − | 0.956989i | \(-0.406303\pi\) |
0.973839 | + | 0.227239i | \(0.0729700\pi\) | |||||||
\(548\) | −5.64269 | − | 3.25781i | −0.241044 | − | 0.139167i | ||||
\(549\) | −23.8848 | + | 34.1885i | −1.01938 | + | 1.45913i | ||||
\(550\) | 3.04774i | 0.129956i | ||||||||
\(551\) | −0.237384 | + | 8.64658i | −0.0101129 | + | 0.368357i | ||||
\(552\) | −0.0505172 | + | 1.17136i | −0.00215016 | + | 0.0498562i | ||||
\(553\) | −31.4551 | − | 18.1606i | −1.33761 | − | 0.772268i | ||||
\(554\) | −7.59771 | + | 13.1596i | −0.322796 | + | 0.559098i | ||||
\(555\) | 3.60053 | + | 6.90756i | 0.152834 | + | 0.293210i | ||||
\(556\) | 4.11100 | − | 7.12045i | 0.174345 | − | 0.301974i | ||||
\(557\) | −22.5889 | + | 13.0417i | −0.957124 | + | 0.552596i | −0.895287 | − | 0.445490i | \(-0.853029\pi\) |
−0.0618376 | + | 0.998086i | \(0.519696\pi\) | |||||||
\(558\) | 1.10981 | − | 12.8428i | 0.0469819 | − | 0.543677i | ||||
\(559\) | − | 23.6188i | − | 0.998970i | ||||||
\(560\) | 4.03843 | − | 2.33159i | 0.170655 | − | 0.0985275i | ||||
\(561\) | 6.27889 | + | 12.0460i | 0.265095 | + | 0.508581i | ||||
\(562\) | −8.55213 | −0.360750 | ||||||||
\(563\) | −17.0740 | −0.719585 | −0.359792 | − | 0.933032i | \(-0.617153\pi\) | ||||
−0.359792 | + | 0.933032i | \(0.617153\pi\) | |||||||
\(564\) | −13.4590 | + | 7.01543i | −0.566726 | + | 0.295403i | ||||
\(565\) | −11.0780 | − | 6.39589i | −0.466055 | − | 0.269077i | ||||
\(566\) | −14.1879 | − | 24.5741i | −0.596361 | − | 1.03293i | ||||
\(567\) | 26.9083 | − | 32.2072i | 1.13004 | − | 1.35258i | ||||
\(568\) | 6.25422 | − | 10.8326i | 0.262421 | − | 0.454527i | ||||
\(569\) | −15.0406 | −0.630534 | −0.315267 | − | 0.949003i | \(-0.602094\pi\) | ||||
−0.315267 | + | 0.949003i | \(0.602094\pi\) | |||||||
\(570\) | −4.22641 | + | 6.25599i | −0.177025 | + | 0.262035i | ||||
\(571\) | 39.0424 | 1.63388 | 0.816938 | − | 0.576726i | \(-0.195670\pi\) | ||||
0.816938 | + | 0.576726i | \(0.195670\pi\) | |||||||
\(572\) | −6.27887 | + | 10.8753i | −0.262533 | + | 0.454720i | ||||
\(573\) | −21.8572 | − | 13.9082i | −0.913099 | − | 0.581024i | ||||
\(574\) | 7.72645 | + | 13.3826i | 0.322496 | + | 0.558579i | ||||
\(575\) | 0.586222 | + | 0.338456i | 0.0244472 | + | 0.0141146i | ||||
\(576\) | −1.27075 | − | 2.71757i | −0.0529480 | − | 0.113232i | ||||
\(577\) | 23.9982 | 0.999059 | 0.499529 | − | 0.866297i | \(-0.333506\pi\) | ||||
0.499529 | + | 0.866297i | \(0.333506\pi\) | |||||||
\(578\) | 10.3780 | 0.431668 | ||||||||
\(579\) | −32.0935 | + | 16.7286i | −1.33376 | + | 0.695215i | ||||
\(580\) | −1.71855 | + | 0.992204i | −0.0713588 | + | 0.0411990i | ||||
\(581\) | − | 12.1992i | − | 0.506108i | ||||||
\(582\) | −0.689691 | + | 15.9921i | −0.0285886 | + | 0.662892i | ||||
\(583\) | 24.1424 | − | 13.9386i | 0.999876 | − | 0.577279i | ||||
\(584\) | 2.18577 | − | 3.78586i | 0.0904477 | − | 0.156660i | ||||
\(585\) | −5.23593 | − | 11.1973i | −0.216479 | − | 0.462952i | ||||
\(586\) | 3.61154 | − | 6.25538i | 0.149191 | − | 0.258407i | ||||
\(587\) | 28.1004 | + | 16.2238i | 1.15983 | + | 0.669626i | 0.951262 | − | 0.308382i | \(-0.0997876\pi\) |
0.208564 | + | 0.978009i | \(0.433121\pi\) | |||||||
\(588\) | 25.5157 | + | 1.10042i | 1.05225 | + | 0.0453805i | ||||
\(589\) | −9.80644 | + | 15.9572i | −0.404067 | + | 0.657506i | ||||
\(590\) | 12.0504i | 0.496109i | ||||||||
\(591\) | 33.1043 | + | 21.0650i | 1.36173 | + | 0.866496i | ||||
\(592\) | 3.89481 | + | 2.24867i | 0.160076 | + | 0.0924198i | ||||
\(593\) | 15.6411 | − | 9.03038i | 0.642302 | − | 0.370833i | −0.143199 | − | 0.989694i | \(-0.545739\pi\) |
0.785501 | + | 0.618861i | \(0.212406\pi\) | |||||||
\(594\) | 12.5794 | + | 9.62057i | 0.516137 | + | 0.394737i | ||||
\(595\) | −5.99993 | − | 10.3922i | −0.245973 | − | 0.426038i | ||||
\(596\) | − | 2.49788i | − | 0.102317i | ||||||
\(597\) | −11.5399 | − | 0.497682i | −0.472296 | − | 0.0203688i | ||||
\(598\) | 1.39455 | + | 2.41544i | 0.0570275 | + | 0.0987745i | ||||
\(599\) | −20.2381 | − | 35.0535i | −0.826907 | − | 1.43225i | −0.900453 | − | 0.434953i | \(-0.856765\pi\) |
0.0735458 | − | 0.997292i | \(-0.476568\pi\) | |||||||
\(600\) | −1.73044 | − | 0.0746290i | −0.0706450 | − | 0.00304672i | ||||
\(601\) | − | 20.2964i | − | 0.827907i | −0.910298 | − | 0.413953i | \(-0.864148\pi\) | ||
0.910298 | − | 0.413953i | \(-0.135852\pi\) | |||||||
\(602\) | −13.3652 | − | 23.1493i | −0.544727 | − | 0.943494i | ||||
\(603\) | 7.28033 | + | 5.08619i | 0.296478 | + | 0.207126i | ||||
\(604\) | −8.10937 | + | 4.68195i | −0.329966 | + | 0.190506i | ||||
\(605\) | 1.48201 | + | 0.855640i | 0.0602524 | + | 0.0347867i | ||||
\(606\) | 16.7148 | + | 10.6360i | 0.678994 | + | 0.432058i | ||||
\(607\) | − | 9.59148i | − | 0.389306i | −0.980872 | − | 0.194653i | \(-0.937642\pi\) | ||
0.980872 | − | 0.194653i | \(-0.0623581\pi\) | |||||||
\(608\) | −0.119625 | + | 4.35726i | −0.00485141 | + | 0.176710i | ||||
\(609\) | −16.0129 | − | 0.690590i | −0.648875 | − | 0.0279841i | ||||
\(610\) | 12.0393 | + | 6.95089i | 0.487457 | + | 0.281433i | ||||
\(611\) | −18.0529 | + | 31.2685i | −0.730342 | + | 1.26499i | ||||
\(612\) | −6.99319 | + | 3.27006i | −0.282683 | + | 0.132184i | ||||
\(613\) | −9.78722 | + | 16.9520i | −0.395302 | + | 0.684683i | −0.993140 | − | 0.116934i | \(-0.962693\pi\) |
0.597838 | + | 0.801617i | \(0.296027\pi\) | |||||||
\(614\) | −0.356034 | + | 0.205556i | −0.0143684 | + | 0.00829558i | ||||
\(615\) | 0.247307 | − | 5.73437i | 0.00997238 | − | 0.231232i | ||||
\(616\) | 14.2121i | 0.572623i | ||||||||
\(617\) | 15.9625 | − | 9.21594i | 0.642625 | − | 0.371020i | −0.143000 | − | 0.989723i | \(-0.545675\pi\) |
0.785625 | + | 0.618703i | \(0.212341\pi\) | |||||||
\(618\) | −26.8394 | + | 13.9899i | −1.07964 | + | 0.562755i | ||||
\(619\) | −24.8517 | −0.998874 | −0.499437 | − | 0.866350i | \(-0.666460\pi\) | ||||
−0.499437 | + | 0.866350i | \(0.666460\pi\) | |||||||
\(620\) | −4.29688 | −0.172567 | ||||||||
\(621\) | 3.24744 | − | 1.35122i | 0.130315 | − | 0.0542225i | ||||
\(622\) | 9.06212 | + | 5.23202i | 0.363358 | + | 0.209785i | ||||
\(623\) | 22.4421 | + | 38.8708i | 0.899123 | + | 1.55733i | ||||
\(624\) | −6.02102 | − | 3.83131i | −0.241034 | − | 0.153375i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 1.74421 | 0.0697126 | ||||||||
\(627\) | −10.0717 | − | 20.6886i | −0.402225 | − | 0.826223i | ||||
\(628\) | −15.4274 | −0.615620 | ||||||||
\(629\) | 5.78656 | − | 10.0226i | 0.230725 | − | 0.399628i | ||||
\(630\) | −11.4681 | − | 8.01184i | −0.456900 | − | 0.319199i | ||||
\(631\) | −1.80191 | − | 3.12099i | −0.0717327 | − | 0.124245i | 0.827928 | − | 0.560834i | \(-0.189520\pi\) |
−0.899661 | + | 0.436590i | \(0.856186\pi\) | |||||||
\(632\) | 6.74543 | + | 3.89448i | 0.268319 | + | 0.154914i | ||||
\(633\) | −37.9412 | + | 19.7766i | −1.50803 | + | 0.786050i | ||||
\(634\) | −20.4047 | −0.810373 | ||||||||
\(635\) | −20.5419 | −0.815182 | ||||||||
\(636\) | 7.32289 | + | 14.0489i | 0.290371 | + | 0.557073i | ||||
\(637\) | 52.6155 | − | 30.3776i | 2.08470 | − | 1.20360i | ||||
\(638\) | − | 6.04796i | − | 0.239441i | ||||||
\(639\) | −37.3860 | − | 3.23071i | −1.47897 | − | 0.127805i | ||||
\(640\) | −0.866025 | + | 0.500000i | −0.0342327 | + | 0.0197642i | ||||
\(641\) | 3.94155 | − | 6.82697i | 0.155682 | − | 0.269649i | −0.777625 | − | 0.628728i | \(-0.783576\pi\) |
0.933307 | + | 0.359079i | \(0.116909\pi\) | |||||||
\(642\) | 15.0599 | + | 28.8923i | 0.594368 | + | 1.14029i | ||||
\(643\) | −2.98629 | + | 5.17241i | −0.117768 | + | 0.203980i | −0.918883 | − | 0.394531i | \(-0.870907\pi\) |
0.801115 | + | 0.598510i | \(0.204241\pi\) | |||||||
\(644\) | 2.73366 | + | 1.57828i | 0.107721 | + | 0.0621928i | ||||
\(645\) | −0.427792 | + | 9.91933i | −0.0168443 | + | 0.390573i | ||||
\(646\) | 11.2126 | + | 0.307833i | 0.441155 | + | 0.0121115i | ||||
\(647\) | 27.9832i | 1.10013i | 0.835120 | + | 0.550067i | \(0.185398\pi\) | ||||
−0.835120 | + | 0.550067i | \(0.814602\pi\) | |||||||
\(648\) | −5.77038 | + | 6.90671i | −0.226682 | + | 0.271321i | ||||
\(649\) | −31.8062 | − | 18.3633i | −1.24850 | − | 0.720823i | ||||
\(650\) | −3.56832 | + | 2.06017i | −0.139961 | + | 0.0808066i | ||||
\(651\) | −29.2800 | − | 18.6315i | −1.14757 | − | 0.730226i | ||||
\(652\) | −3.97183 | − | 6.87941i | −0.155549 | − | 0.269419i | ||||
\(653\) | 20.3397i | 0.795953i | 0.917396 | + | 0.397976i | \(0.130287\pi\) | ||||
−0.917396 | + | 0.397976i | \(0.869713\pi\) | |||||||
\(654\) | −0.542899 | + | 12.5883i | −0.0212290 | + | 0.492243i | ||||
\(655\) | 1.89770 | + | 3.28692i | 0.0741494 | + | 0.128431i | ||||
\(656\) | −1.65691 | − | 2.86985i | −0.0646914 | − | 0.112049i | ||||
\(657\) | −13.0659 | − | 1.12909i | −0.509750 | − | 0.0440500i | ||||
\(658\) | 40.8625i | 1.59299i | ||||||||
\(659\) | −12.9141 | − | 22.3678i | −0.503061 | − | 0.871327i | −0.999994 | − | 0.00353811i | \(-0.998874\pi\) |
0.496933 | − | 0.867789i | \(-0.334460\pi\) | |||||||
\(660\) | 2.83395 | − | 4.45364i | 0.110311 | − | 0.173358i | ||||
\(661\) | 24.4404 | − | 14.1107i | 0.950623 | − | 0.548842i | 0.0573484 | − | 0.998354i | \(-0.481735\pi\) |
0.893274 | + | 0.449512i | \(0.148402\pi\) | |||||||
\(662\) | 2.98913 | + | 1.72578i | 0.116176 | + | 0.0670742i | ||||
\(663\) | −9.85920 | + | 15.4941i | −0.382900 | + | 0.601739i | ||||
\(664\) | 2.61607i | 0.101523i | ||||||||
\(665\) | 9.67623 | + | 17.8754i | 0.375228 | + | 0.693177i | ||||
\(666\) | 1.16158 | − | 13.4419i | 0.0450105 | − | 0.520864i | ||||
\(667\) | −1.16330 | − | 0.671634i | −0.0450433 | − | 0.0260058i | ||||
\(668\) | −2.97913 | + | 5.16001i | −0.115266 | + | 0.199647i | ||||
\(669\) | 8.15121 | − | 4.24877i | 0.315144 | − | 0.164267i | ||||
\(670\) | 1.48017 | − | 2.56373i | 0.0571840 | − | 0.0990456i | ||||
\(671\) | −36.6927 | + | 21.1845i | −1.41650 | + | 0.817819i | ||||
\(672\) | −8.06935 | − | 0.348008i | −0.311282 | − | 0.0134247i | ||||
\(673\) | 3.94270i | 0.151980i | 0.997109 | + | 0.0759900i | \(0.0242117\pi\) | ||||
−0.997109 | + | 0.0759900i | \(0.975788\pi\) | |||||||
\(674\) | 23.1281 | − | 13.3530i | 0.890860 | − | 0.514338i | ||||
\(675\) | 1.99615 | + | 4.79743i | 0.0768319 | + | 0.184653i | ||||
\(676\) | −3.97722 | −0.152970 | ||||||||
\(677\) | −45.0353 | −1.73085 | −0.865424 | − | 0.501040i | \(-0.832951\pi\) | ||||
−0.865424 | + | 0.501040i | \(0.832951\pi\) | |||||||
\(678\) | 10.2410 | + | 19.6472i | 0.393303 | + | 0.754545i | ||||
\(679\) | 37.3215 | + | 21.5476i | 1.43227 | + | 0.826920i | ||||
\(680\) | 1.28666 | + | 2.22857i | 0.0493413 | + | 0.0854616i | ||||
\(681\) | 4.80743 | − | 7.55503i | 0.184221 | − | 0.289509i | ||||
\(682\) | 6.54788 | − | 11.3413i | 0.250731 | − | 0.434279i | ||||
\(683\) | 36.9898 | 1.41538 | 0.707688 | − | 0.706525i | \(-0.249738\pi\) | ||||
0.707688 | + | 0.706525i | \(0.249738\pi\) | |||||||
\(684\) | 11.9932 | − | 5.21190i | 0.458570 | − | 0.199282i | ||||
\(685\) | 6.51561 | 0.248949 | ||||||||
\(686\) | 18.0586 | − | 31.2784i | 0.689479 | − | 1.19421i | ||||
\(687\) | 11.6856 | − | 18.3642i | 0.445832 | − | 0.700640i | ||||
\(688\) | 2.86613 | + | 4.96428i | 0.109270 | + | 0.189261i | ||||
\(689\) | 32.6389 | + | 18.8441i | 1.24344 | + | 0.717903i | ||||
\(690\) | −0.541929 | − | 1.03968i | −0.0206309 | − | 0.0395800i | ||||
\(691\) | 40.1246 | 1.52641 | 0.763206 | − | 0.646155i | \(-0.223624\pi\) | ||||
0.763206 | + | 0.646155i | \(0.223624\pi\) | |||||||
\(692\) | 8.04881 | 0.305970 | ||||||||
\(693\) | 38.6225 | − | 18.0601i | 1.46715 | − | 0.686046i | ||||
\(694\) | −14.4663 | + | 8.35210i | −0.549132 | + | 0.317041i | ||||
\(695\) | 8.22199i | 0.311878i | ||||||||
\(696\) | 3.43390 | + | 0.148094i | 0.130162 | + | 0.00561351i | ||||
\(697\) | −7.38506 | + | 4.26376i | −0.279729 | + | 0.161502i | ||||
\(698\) | −16.1384 | + | 27.9525i | −0.610847 | + | 1.05802i | ||||
\(699\) | 36.9059 | − | 19.2370i | 1.39591 | − | 0.727610i | ||||
\(700\) | −2.33159 | + | 4.03843i | −0.0881257 | + | 0.152638i | ||||
\(701\) | 35.9481 | + | 20.7546i | 1.35774 | + | 0.783892i | 0.989319 | − | 0.145766i | \(-0.0465648\pi\) |
0.368422 | + | 0.929659i | \(0.379898\pi\) | |||||||
\(702\) | −2.76062 | + | 21.2312i | −0.104193 | + | 0.801320i | ||||
\(703\) | −10.2639 | + | 16.7017i | −0.387112 | + | 0.629916i | ||||
\(704\) | − | 3.04774i | − | 0.114866i | ||||||
\(705\) | 8.14812 | − | 12.8050i | 0.306876 | − | 0.482266i | ||||
\(706\) | 13.2366 | + | 7.64215i | 0.498166 | + | 0.287616i | ||||
\(707\) | 46.1931 | − | 26.6696i | 1.73727 | − | 1.00301i | ||||
\(708\) | 11.2051 | − | 17.6092i | 0.421114 | − | 0.661795i | ||||
\(709\) | −6.05340 | − | 10.4848i | −0.227340 | − | 0.393765i | 0.729679 | − | 0.683790i | \(-0.239670\pi\) |
−0.957019 | + | 0.290025i | \(0.906336\pi\) | |||||||
\(710\) | 12.5084i | 0.469433i | ||||||||
\(711\) | 2.01175 | − | 23.2801i | 0.0754465 | − | 0.873072i | ||||
\(712\) | −4.81262 | − | 8.33571i | −0.180361 | − | 0.312394i | ||||
\(713\) | −1.45430 | − | 2.51892i | −0.0544640 | − | 0.0943345i | ||||
\(714\) | −0.895538 | + | 20.7651i | −0.0335147 | + | 0.777113i | ||||
\(715\) | − | 12.5577i | − | 0.469633i | ||||||
\(716\) | −4.76369 | − | 8.25095i | −0.178027 | − | 0.308352i | ||||
\(717\) | −18.8786 | − | 12.0129i | −0.705035 | − | 0.448629i | ||||
\(718\) | −0.917556 | + | 0.529751i | −0.0342429 | + | 0.0197701i | ||||
\(719\) | −43.2306 | − | 24.9592i | −1.61223 | − | 0.930821i | −0.988852 | − | 0.148899i | \(-0.952427\pi\) |
−0.623376 | − | 0.781922i | \(-0.714240\pi\) | |||||||
\(720\) | 2.45929 | + | 1.71811i | 0.0916523 | + | 0.0640302i | ||||
\(721\) | 81.4864i | 3.03471i | ||||||||
\(722\) | −18.9714 | − | 1.04247i | −0.706042 | − | 0.0387967i | ||||
\(723\) | −1.58224 | + | 36.6878i | −0.0588441 | + | 1.36443i | ||||
\(724\) | 14.9311 | + | 8.62045i | 0.554909 | + | 0.320377i | ||||
\(725\) | 0.992204 | − | 1.71855i | 0.0368495 | − | 0.0638253i | ||||
\(726\) | −1.37003 | − | 2.62839i | −0.0508468 | − | 0.0975488i | ||||
\(727\) | 3.21384 | − | 5.56653i | 0.119195 | − | 0.206451i | −0.800254 | − | 0.599661i | \(-0.795302\pi\) |
0.919449 | + | 0.393210i | \(0.128635\pi\) | |||||||
\(728\) | −16.6397 | + | 9.60693i | −0.616708 | + | 0.356057i | ||||
\(729\) | 26.1022 | + | 6.90471i | 0.966748 | + | 0.255730i | ||||
\(730\) | 4.37153i | 0.161798i | ||||||||
\(731\) | 12.7747 | − | 7.37547i | 0.472489 | − | 0.272792i | ||||
\(732\) | −11.1296 | − | 21.3521i | −0.411363 | − | 0.789195i | ||||
\(733\) | −16.0152 | −0.591537 | −0.295768 | − | 0.955260i | \(-0.595576\pi\) | ||||
−0.295768 | + | 0.955260i | \(0.595576\pi\) | |||||||
\(734\) | −20.5013 | −0.756718 | ||||||||
\(735\) | −22.6474 | + | 11.8049i | −0.835364 | + | 0.435429i | ||||
\(736\) | −0.586222 | − | 0.338456i | −0.0216084 | − | 0.0124756i | ||||
\(737\) | 4.51118 | + | 7.81359i | 0.166171 | + | 0.287817i | ||||
\(738\) | −5.69350 | + | 8.14963i | −0.209581 | + | 0.299992i | ||||
\(739\) | −9.73673 | + | 16.8645i | −0.358172 | + | 0.620371i | −0.987655 | − | 0.156642i | \(-0.949933\pi\) |
0.629484 | + | 0.777014i | \(0.283266\pi\) | |||||||
\(740\) | −4.49734 | −0.165325 | ||||||||
\(741\) | 17.4143 | − | 25.7768i | 0.639729 | − | 0.946936i | ||||
\(742\) | 42.6534 | 1.56586 | ||||||||
\(743\) | 25.7244 | − | 44.5560i | 0.943738 | − | 1.63460i | 0.185480 | − | 0.982648i | \(-0.440616\pi\) |
0.758258 | − | 0.651955i | \(-0.226051\pi\) | |||||||
\(744\) | 6.27899 | + | 3.99546i | 0.230199 | + | 0.146481i | ||||
\(745\) | 1.24894 | + | 2.16323i | 0.0457577 | + | 0.0792546i | ||||
\(746\) | 12.8277 | + | 7.40608i | 0.469656 | + | 0.271156i | ||||
\(747\) | 7.10937 | − | 3.32438i | 0.260118 | − | 0.121633i | ||||
\(748\) | −7.84283 | −0.286762 | ||||||||
\(749\) | 87.7191 | 3.20518 | ||||||||
\(750\) | 1.53592 | − | 0.800591i | 0.0560839 | − | 0.0292334i | ||||
\(751\) | 29.8285 | − | 17.2215i | 1.08846 | − | 0.628421i | 0.155292 | − | 0.987869i | \(-0.450368\pi\) |
0.933165 | + | 0.359448i | \(0.117035\pi\) | |||||||
\(752\) | − | 8.76281i | − | 0.319547i | ||||||
\(753\) | −1.40446 | + | 32.5655i | −0.0511812 | + | 1.18675i | ||||
\(754\) | 7.08101 | − | 4.08822i | 0.257875 | − | 0.148884i | ||||
\(755\) | 4.68195 | − | 8.10937i | 0.170394 | − | 0.295130i | ||||
\(756\) | 9.30840 | + | 22.3713i | 0.338543 | + | 0.813635i | ||||
\(757\) | −5.05555 | + | 8.75646i | −0.183747 | + | 0.318259i | −0.943154 | − | 0.332357i | \(-0.892156\pi\) |
0.759407 | + | 0.650616i | \(0.225489\pi\) | |||||||
\(758\) | −3.66524 | − | 2.11613i | −0.133128 | − | 0.0768613i | ||||
\(759\) | 3.56999 | + | 0.153963i | 0.129582 | + | 0.00558852i | ||||
\(760\) | −2.07503 | − | 3.83331i | −0.0752693 | − | 0.139049i | ||||
\(761\) | 27.1963i | 0.985865i | 0.870067 | + | 0.492933i | \(0.164075\pi\) | ||||
−0.870067 | + | 0.492933i | \(0.835925\pi\) | |||||||
\(762\) | 30.0178 | + | 19.1009i | 1.08743 | + | 0.691954i | ||||
\(763\) | 29.3781 | + | 16.9614i | 1.06356 | + | 0.614045i | ||||
\(764\) | 12.9535 | − | 7.47873i | 0.468643 | − | 0.270571i | ||||
\(765\) | 4.42125 | − | 6.32855i | 0.159851 | − | 0.228809i | ||||
\(766\) | −11.7377 | − | 20.3303i | −0.424100 | − | 0.734563i | ||||
\(767\) | − | 49.6519i | − | 1.79283i | ||||||
\(768\) | 1.73044 | + | 0.0746290i | 0.0624420 | + | 0.00269294i | ||||
\(769\) | −8.24048 | − | 14.2729i | −0.297159 | − | 0.514695i | 0.678326 | − | 0.734761i | \(-0.262706\pi\) |
−0.975485 | + | 0.220067i | \(0.929373\pi\) | |||||||
\(770\) | −7.10607 | − | 12.3081i | −0.256085 | − | 0.443552i | ||||
\(771\) | −13.8591 | − | 0.597702i | −0.499122 | − | 0.0215257i | ||||
\(772\) | − | 20.8953i | − | 0.752037i | ||||||
\(773\) | 1.86208 | + | 3.22522i | 0.0669743 | + | 0.116003i | 0.897568 | − | 0.440876i | \(-0.145332\pi\) |
−0.830594 | + | 0.556879i | \(0.811999\pi\) | |||||||
\(774\) | 9.84864 | − | 14.0973i | 0.354002 | − | 0.506715i | ||||
\(775\) | 3.72120 | − | 2.14844i | 0.133670 | − | 0.0771742i | ||||
\(776\) | −8.00346 | − | 4.62080i | −0.287307 | − | 0.165877i | ||||
\(777\) | −30.6460 | − | 19.5007i | −1.09942 | − | 0.699585i | ||||
\(778\) | − | 17.1058i | − | 0.613272i | ||||||
\(779\) | 12.7029 | − | 6.87627i | 0.455128 | − | 0.246368i | ||||
\(780\) | 7.13001 | + | 0.307497i | 0.255295 | + | 0.0110102i | ||||
\(781\) | −33.0150 | − | 19.0612i | −1.18137 | − | 0.682065i | ||||
\(782\) | −0.870956 | + | 1.50854i | −0.0311453 | + | 0.0539453i | ||||
\(783\) | −3.96118 | − | 9.52007i | −0.141561 | − | 0.340219i | ||||
\(784\) | −7.37259 | + | 12.7697i | −0.263307 | + | 0.456061i | ||||
\(785\) | 13.3605 | − | 7.71370i | 0.476857 | − | 0.275314i | ||||
\(786\) | 0.283248 | − | 6.56773i | 0.0101031 | − | 0.234263i | ||||
\(787\) | 1.38060i | 0.0492131i | 0.999697 | + | 0.0246066i | \(0.00783330\pi\) | ||||
−0.999697 | + | 0.0246066i | \(0.992167\pi\) | |||||||
\(788\) | −19.6190 | + | 11.3270i | −0.698899 | + | 0.403509i | ||||
\(789\) | −43.7220 | + | 22.7898i | −1.55654 | + | 0.811339i | ||||
\(790\) | −7.78896 | −0.277119 | ||||||||
\(791\) | 59.6503 | 2.12092 | ||||||||
\(792\) | −8.28245 | + | 3.87292i | −0.294304 | + | 0.137618i | ||||
\(793\) | −49.6060 | − | 28.6401i | −1.76156 | − | 1.01704i | ||||
\(794\) | 3.27587 | + | 5.67397i | 0.116256 | + | 0.201362i | ||||
\(795\) | −13.3662 | − | 8.50522i | −0.474052 | − | 0.301649i | ||||
\(796\) | 3.33437 | − | 5.77531i | 0.118184 | − | 0.204700i | ||||
\(797\) | 16.3638 | 0.579634 | 0.289817 | − | 0.957082i | \(-0.406406\pi\) | ||||
0.289817 | + | 0.957082i | \(0.406406\pi\) | |||||||
\(798\) | 2.48165 | − | 35.1186i | 0.0878496 | − | 1.24319i | ||||
\(799\) | −22.5496 | −0.797747 | ||||||||
\(800\) | 0.500000 | − | 0.866025i | 0.0176777 | − | 0.0306186i | ||||
\(801\) | −16.5372 | + | 23.6712i | −0.584314 | + | 0.836382i | ||||
\(802\) | 12.4043 | + | 21.4849i | 0.438012 | + | 0.758658i | ||||
\(803\) | −11.5383 | − | 6.66165i | −0.407178 | − | 0.235085i | ||||
\(804\) | −4.54685 | + | 2.37002i | −0.160355 | + | 0.0835842i | ||||
\(805\) | −3.15655 | −0.111254 | ||||||||
\(806\) | 17.7046 | 0.623618 | ||||||||
\(807\) | 4.70257 | + | 9.02182i | 0.165538 | + | 0.317583i | ||||
\(808\) | −9.90594 | + | 5.71920i | −0.348490 | + | 0.201201i | ||||
\(809\) | − | 3.23485i | − | 0.113731i | −0.998382 | − | 0.0568657i | \(-0.981889\pi\) | ||
0.998382 | − | 0.0568657i | \(-0.0181107\pi\) | |||||||
\(810\) | 1.54394 | − | 8.86658i | 0.0542485 | − | 0.311540i | ||||
\(811\) | 34.3026 | − | 19.8046i | 1.20453 | − | 0.695434i | 0.242968 | − | 0.970034i | \(-0.421879\pi\) |
0.961558 | + | 0.274601i | \(0.0885457\pi\) | |||||||
\(812\) | 4.62682 | − | 8.01389i | 0.162370 | − | 0.281232i | ||||
\(813\) | −10.9738 | − | 21.0530i | −0.384866 | − | 0.738361i | ||||
\(814\) | 6.85336 | − | 11.8704i | 0.240210 | − | 0.416056i | ||||
\(815\) | 6.87941 | + | 3.97183i | 0.240975 | + | 0.139127i | ||||
\(816\) | 0.192045 | − | 4.45299i | 0.00672291 | − | 0.155886i | ||||
\(817\) | −21.9735 | + | 11.8946i | −0.768755 | + | 0.416139i | ||||
\(818\) | 3.39700i | 0.118773i | ||||||||
\(819\) | 47.2524 | + | 33.0115i | 1.65113 | + | 1.15352i | ||||
\(820\) | 2.86985 | + | 1.65691i | 0.100219 | + | 0.0578618i | ||||
\(821\) | −47.1571 | + | 27.2262i | −1.64580 | + | 0.950200i | −0.667078 | + | 0.744988i | \(0.732455\pi\) |
−0.978717 | + | 0.205213i | \(0.934211\pi\) | |||||||
\(822\) | −9.52121 | − | 6.05855i | −0.332090 | − | 0.211316i | ||||
\(823\) | −26.5810 | − | 46.0397i | −0.926556 | − | 1.60484i | −0.789039 | − | 0.614343i | \(-0.789421\pi\) |
−0.137517 | − | 0.990499i | \(-0.543912\pi\) | |||||||
\(824\) | − | 17.4744i | − | 0.608751i | ||||||
\(825\) | −0.227450 | + | 5.27394i | −0.00791879 | + | 0.183615i | ||||
\(826\) | −28.0966 | − | 48.6648i | −0.977607 | − | 1.69327i | ||||
\(827\) | 12.2301 | + | 21.1832i | 0.425282 | + | 0.736610i | 0.996447 | − | 0.0842252i | \(-0.0268415\pi\) |
−0.571165 | + | 0.820836i | \(0.693508\pi\) | |||||||
\(828\) | −0.174834 | + | 2.02319i | −0.00607591 | + | 0.0703108i | ||||
\(829\) | 16.6270i | 0.577480i | 0.957408 | + | 0.288740i | \(0.0932364\pi\) | ||||
−0.957408 | + | 0.288740i | \(0.906764\pi\) | |||||||
\(830\) | −1.30804 | − | 2.26559i | −0.0454026 | − | 0.0786397i | ||||
\(831\) | −14.1295 | + | 22.2049i | −0.490146 | + | 0.770281i | ||||
\(832\) | 3.56832 | − | 2.06017i | 0.123709 | − | 0.0714236i | ||||
\(833\) | 32.8606 | + | 18.9721i | 1.13855 | + | 0.657343i | ||||
\(834\) | 7.64523 | − | 12.0147i | 0.264733 | − | 0.416036i | ||||
\(835\) | − | 5.95826i | − | 0.206194i | ||||||
\(836\) | 13.2798 | + | 0.364584i | 0.459291 | + | 0.0126094i | ||||
\(837\) | 2.87890 | − | 22.1408i | 0.0995093 | − | 0.765299i | ||||
\(838\) | −22.0201 | − | 12.7133i | −0.760672 | − | 0.439174i | ||||
\(839\) | 6.13190 | − | 10.6208i | 0.211697 | − | 0.366669i | −0.740549 | − | 0.672002i | \(-0.765434\pi\) |
0.952246 | + | 0.305333i | \(0.0987678\pi\) | |||||||
\(840\) | 7.16227 | − | 3.73329i | 0.247122 | − | 0.128811i | ||||
\(841\) | 12.5311 | − | 21.7044i | 0.432106 | − | 0.748429i | ||||
\(842\) | −9.79175 | + | 5.65327i | −0.337446 | + | 0.194825i | ||||
\(843\) | −14.7990 | − | 0.638237i | −0.509704 | − | 0.0219821i | ||||
\(844\) | − | 24.7025i | − | 0.850297i | ||||||
\(845\) | 3.44437 | − | 1.98861i | 0.118490 | − | 0.0684102i | ||||
\(846\) | −23.8136 | + | 11.1354i | −0.818727 | + | 0.382842i | ||||
\(847\) | −7.98000 | −0.274196 | ||||||||
\(848\) | −9.14686 | −0.314104 | ||||||||
\(849\) | −22.7174 | − | 43.5830i | −0.779658 | − | 1.49576i | ||||
\(850\) | −2.22857 | − | 1.28666i | −0.0764391 | − | 0.0441322i | ||||
\(851\) | −1.52215 | − | 2.63644i | −0.0521786 | − | 0.0903760i | ||||
\(852\) | 11.6310 | − | 18.2785i | 0.398471 | − | 0.626211i | ||||
\(853\) | −17.0728 | + | 29.5710i | −0.584562 | + | 1.01249i | 0.410368 | + | 0.911920i | \(0.365400\pi\) |
−0.994930 | + | 0.100571i | \(0.967933\pi\) | |||||||
\(854\) | −64.8264 | −2.21832 | ||||||||
\(855\) | −7.78044 | + | 10.5102i | −0.266085 | + | 0.359442i | ||||
\(856\) | −18.8110 | −0.642948 | ||||||||
\(857\) | −1.80576 | + | 3.12767i | −0.0616837 | + | 0.106839i | −0.895218 | − | 0.445628i | \(-0.852980\pi\) |
0.833534 | + | 0.552468i | \(0.186314\pi\) | |||||||
\(858\) | −11.6768 | + | 18.3505i | −0.398640 | + | 0.626476i | ||||
\(859\) | −0.655628 | − | 1.13558i | −0.0223697 | − | 0.0387455i | 0.854624 | − | 0.519248i | \(-0.173788\pi\) |
−0.876994 | + | 0.480502i | \(0.840454\pi\) | |||||||
\(860\) | −4.96428 | − | 2.86613i | −0.169280 | − | 0.0977341i | ||||
\(861\) | 12.3714 | + | 23.7344i | 0.421618 | + | 0.808868i | ||||
\(862\) | −0.421328 | −0.0143505 | ||||||||
\(863\) | −5.56476 | −0.189427 | −0.0947134 | − | 0.995505i | \(-0.530193\pi\) | ||||
−0.0947134 | + | 0.995505i | \(0.530193\pi\) | |||||||
\(864\) | −1.99615 | − | 4.79743i | −0.0679105 | − | 0.163212i | ||||
\(865\) | −6.97047 | + | 4.02441i | −0.237003 | + | 0.136834i | ||||
\(866\) | 5.59372i | 0.190082i | ||||||||
\(867\) | 17.9585 | + | 0.774500i | 0.609903 | + | 0.0263034i | ||||
\(868\) | 17.3526 | − | 10.0185i | 0.588986 | − | 0.340051i | ||||
\(869\) | 11.8694 | − | 20.5583i | 0.402640 | − | 0.697394i | ||||
\(870\) | −3.04790 | + | 1.58870i | −0.103333 | + | 0.0538619i | ||||
\(871\) | −6.09881 | + | 10.5634i | −0.206650 | + | 0.357929i | ||||
\(872\) | −6.30002 | − | 3.63732i | −0.213346 | − | 0.123175i | ||||
\(873\) | −2.38694 | + | 27.6218i | −0.0807857 | + | 0.934858i | ||||
\(874\) | 1.54486 | − | 2.51383i | 0.0522558 | − | 0.0850317i | ||||
\(875\) | − | 4.66317i | − | 0.157644i | ||||||
\(876\) | 4.06488 | − | 6.38809i | 0.137340 | − | 0.215834i | ||||
\(877\) | −23.6061 | − | 13.6290i | −0.797120 | − | 0.460218i | 0.0453429 | − | 0.998971i | \(-0.485562\pi\) |
−0.842463 | + | 0.538754i | \(0.818895\pi\) | |||||||
\(878\) | 33.0674 | − | 19.0915i | 1.11597 | − | 0.644306i | ||||
\(879\) | 6.71640 | − | 10.5550i | 0.226539 | − | 0.356013i | ||||
\(880\) | 1.52387 | + | 2.63942i | 0.0513696 | + | 0.0889748i | ||||
\(881\) | 32.5415i | 1.09635i | 0.836363 | + | 0.548176i | \(0.184678\pi\) | ||||
−0.836363 | + | 0.548176i | \(0.815322\pi\) | |||||||
\(882\) | 44.0713 | + | 3.80842i | 1.48396 | + | 0.128236i | ||||
\(883\) | −19.8287 | − | 34.3444i | −0.667291 | − | 1.15578i | −0.978659 | − | 0.205492i | \(-0.934121\pi\) |
0.311368 | − | 0.950289i | \(-0.399213\pi\) | |||||||
\(884\) | −5.30149 | − | 9.18245i | −0.178308 | − | 0.308839i | ||||
\(885\) | −0.899313 | + | 20.8526i | −0.0302301 | + | 0.700952i | ||||
\(886\) | 25.6463i | 0.861604i | ||||||||
\(887\) | −14.5283 | − | 25.1638i | −0.487814 | − | 0.844918i | 0.512088 | − | 0.858933i | \(-0.328872\pi\) |
−0.999902 | + | 0.0140147i | \(0.995539\pi\) | |||||||
\(888\) | 6.57193 | + | 4.18186i | 0.220539 | + | 0.140334i | ||||
\(889\) | 82.9571 | − | 47.8953i | 2.78229 | − | 1.60636i | ||||
\(890\) | 8.33571 | + | 4.81262i | 0.279413 | + | 0.161319i | ||||
\(891\) | 21.0499 | + | 17.5866i | 0.705197 | + | 0.589174i | ||||
\(892\) | 5.30705i | 0.177693i | ||||||||
\(893\) | 38.1818 | + | 1.04825i | 1.27771 | + | 0.0350783i | ||||
\(894\) | 0.186415 | − | 4.32244i | 0.00623464 | − | 0.144564i | ||||
\(895\) | 8.25095 | + | 4.76369i | 0.275799 | + | 0.159233i | ||||
\(896\) | 2.33159 | − | 4.03843i | 0.0778928 | − | 0.134914i | ||||
\(897\) | 2.23293 | + | 4.28385i | 0.0745554 | + | 0.143034i | ||||
\(898\) | −11.8447 | + | 20.5156i | −0.395263 | + | 0.684615i | ||||
\(899\) | −7.38439 | + | 4.26338i | −0.246283 | + | 0.142192i | ||||
\(900\) | −2.98886 | − | 0.258282i | −0.0996287 | − | 0.00860941i | ||||
\(901\) | 23.5378i | 0.784159i | ||||||||
\(902\) | −8.74656 | + | 5.04983i | −0.291228 | + | 0.168141i | ||||
\(903\) | −21.4002 | − | 41.0559i | −0.712153 | − | 1.36626i | ||||
\(904\) | −12.7918 | −0.425448 | ||||||||
\(905\) | −17.2409 | −0.573107 | ||||||||
\(906\) | −14.3822 | + | 7.49665i | −0.477817 | + | 0.249059i | ||||
\(907\) | −22.5403 | − | 13.0136i | −0.748438 | − | 0.432111i | 0.0766912 | − | 0.997055i | \(-0.475564\pi\) |
−0.825129 | + | 0.564944i | \(0.808898\pi\) | |||||||
\(908\) | 2.58505 | + | 4.47744i | 0.0857879 | + | 0.148589i | ||||
\(909\) | 28.1303 | + | 19.6524i | 0.933024 | + | 0.651830i | ||||
\(910\) | 9.60693 | − | 16.6397i | 0.318467 | − | 0.551601i | ||||
\(911\) | 47.2123 | 1.56421 | 0.782107 | − | 0.623144i | \(-0.214145\pi\) | ||||
0.782107 | + | 0.623144i | \(0.214145\pi\) | |||||||
\(912\) | −0.532181 | + | 7.53105i | −0.0176223 | + | 0.249378i | ||||
\(913\) | 7.97312 | 0.263872 | ||||||||
\(914\) | 8.64006 | − | 14.9650i | 0.285788 | − | 0.494999i | ||||
\(915\) | 20.3146 | + | 12.9266i | 0.671579 | + | 0.427340i | ||||
\(916\) | 6.28356 | + | 10.8835i | 0.207615 | + | 0.359599i | ||||
\(917\) | −15.3275 | − | 8.84932i | −0.506158 | − | 0.292230i | ||||
\(918\) | −12.3454 | + | 5.13675i | −0.407458 | + | 0.169538i | ||||
\(919\) | 40.9787 | 1.35176 | 0.675881 | − | 0.737010i | \(-0.263763\pi\) | ||||
0.675881 | + | 0.737010i | \(0.263763\pi\) | |||||||
\(920\) | 0.676911 | 0.0223171 | ||||||||
\(921\) | −0.631437 | + | 0.329133i | −0.0208065 | + | 0.0108453i | ||||
\(922\) | 27.4943 | − | 15.8738i | 0.905475 | − | 0.522776i | ||||
\(923\) | − | 51.5391i | − | 1.69643i | ||||||
\(924\) | −1.06064 | + | 24.5933i | −0.0348924 | + | 0.809060i | ||||
\(925\) | 3.89481 | − | 2.24867i | 0.128061 | − | 0.0739358i | ||||
\(926\) | 12.2095 | − | 21.1475i | 0.401229 | − | 0.694949i | ||||
\(927\) | −47.4881 | + | 22.2057i | −1.55971 | + | 0.729330i | ||||
\(928\) | −0.992204 | + | 1.71855i | −0.0325707 | + | 0.0564141i | ||||
\(929\) | 21.9076 | + | 12.6484i | 0.718767 | + | 0.414980i | 0.814299 | − | 0.580446i | \(-0.197122\pi\) |
−0.0955319 | + | 0.995426i | \(0.530455\pi\) | |||||||
\(930\) | −7.43549 | − | 0.320672i | −0.243819 | − | 0.0105152i | ||||
\(931\) | −54.7589 | − | 33.6518i | −1.79465 | − | 1.10289i | ||||
\(932\) | 24.0285i | 0.787079i | ||||||||
\(933\) | 15.2910 | + | 9.73000i | 0.500605 | + | 0.318546i | ||||
\(934\) | −11.6416 | − | 6.72127i | −0.380924 | − | 0.219927i | ||||
\(935\) | 6.79209 | − | 3.92141i | 0.222125 | − | 0.128244i | ||||
\(936\) | −10.1331 | − | 7.07920i | −0.331211 | − | 0.231391i | ||||
\(937\) | −2.97906 | − | 5.15989i | −0.0973218 | − | 0.168566i | 0.813253 | − | 0.581910i | \(-0.197694\pi\) |
−0.910575 | + | 0.413343i | \(0.864361\pi\) | |||||||
\(938\) | 13.8046i | 0.450736i | ||||||||
\(939\) | 3.01825 | + | 0.130169i | 0.0984970 | + | 0.00424789i | ||||
\(940\) | 4.38141 | + | 7.58882i | 0.142906 | + | 0.247520i | ||||
\(941\) | −18.2842 | − | 31.6692i | −0.596048 | − | 1.03239i | −0.993398 | − | 0.114719i | \(-0.963403\pi\) |
0.397350 | − | 0.917667i | \(-0.369930\pi\) | |||||||
\(942\) | −26.6962 | − | 1.15133i | −0.869810 | − | 0.0375124i | ||||
\(943\) | 2.24316i | 0.0730473i | ||||||||
\(944\) | 6.02522 | + | 10.4360i | 0.196104 | + | 0.339663i | ||||
\(945\) | −19.2469 | − | 14.7199i | −0.626103 | − | 0.478838i | ||||
\(946\) | 15.1298 | − | 8.73521i | 0.491913 | − | 0.284006i | ||||
\(947\) | −8.39698 | − | 4.84800i | −0.272865 | − | 0.157539i | 0.357324 | − | 0.933981i | \(-0.383689\pi\) |
−0.630189 | + | 0.776442i | \(0.717023\pi\) | |||||||
\(948\) | 11.3819 | + | 7.24257i | 0.369668 | + | 0.235228i | ||||
\(949\) | − | 18.0122i | − | 0.584701i | ||||||
\(950\) | 3.71368 | + | 2.28223i | 0.120488 | + | 0.0740452i | ||||
\(951\) | −35.3091 | − | 1.52278i | −1.14498 | − | 0.0493796i | ||||
\(952\) | −10.3922 | − | 5.99993i | −0.336813 | − | 0.194459i | ||||
\(953\) | 5.66534 | − | 9.81266i | 0.183518 | − | 0.317863i | −0.759558 | − | 0.650440i | \(-0.774585\pi\) |
0.943076 | + | 0.332577i | \(0.107918\pi\) | |||||||
\(954\) | 11.6234 | + | 24.8572i | 0.376321 | + | 0.804783i | ||||
\(955\) | −7.47873 | + | 12.9535i | −0.242006 | + | 0.419167i | ||||
\(956\) | 11.1883 | − | 6.45956i | 0.361855 | − | 0.208917i | ||||
\(957\) | 0.451353 | − | 10.4656i | 0.0145902 | − | 0.338306i | ||||
\(958\) | − | 9.75241i | − | 0.315086i | ||||||
\(959\) | −26.3128 | + | 15.1917i | −0.849685 | + | 0.490566i | ||||
\(960\) | −1.53592 | + | 0.800591i | −0.0495717 | + | 0.0258389i | ||||
\(961\) | 12.5369 | 0.404415 | ||||||||
\(962\) | 18.5306 | 0.597450 | ||||||||
\(963\) | 23.9041 | + | 51.1203i | 0.770300 | + | 1.64733i | ||||
\(964\) | −18.3610 | − | 10.6007i | −0.591366 | − | 0.341426i | ||||
\(965\) | 10.4476 | + | 18.0958i | 0.336321 | + | 0.582526i | ||||
\(966\) | 4.61265 | + | 2.93513i | 0.148410 | + | 0.0944362i | ||||
\(967\) | 7.32741 | − | 12.6915i | 0.235634 | − | 0.408130i | −0.723823 | − | 0.689986i | \(-0.757617\pi\) |
0.959457 | + | 0.281856i | \(0.0909501\pi\) | |||||||
\(968\) | 1.71128 | 0.0550026 | ||||||||
\(969\) | 19.3799 | + | 1.36948i | 0.622571 | + | 0.0439939i | ||||
\(970\) | 9.24160 | 0.296730 | ||||||||
\(971\) | −13.8936 | + | 24.0645i | −0.445868 | + | 0.772266i | −0.998112 | − | 0.0614163i | \(-0.980438\pi\) |
0.552244 | + | 0.833682i | \(0.313772\pi\) | |||||||
\(972\) | −10.5008 | + | 11.5210i | −0.336812 | + | 0.369537i | ||||
\(973\) | −19.1703 | − | 33.2039i | −0.614571 | − | 1.06447i | ||||
\(974\) | 13.8674 | + | 8.00637i | 0.444341 | + | 0.256541i | ||||
\(975\) | −6.32852 | + | 3.29871i | −0.202675 | + | 0.105643i | ||||
\(976\) | 13.9018 | 0.444985 | ||||||||
\(977\) | 57.1541 | 1.82852 | 0.914261 | − | 0.405125i | \(-0.132772\pi\) | ||||
0.914261 | + | 0.405125i | \(0.132772\pi\) | |||||||
\(978\) | −6.35962 | − | 12.2008i | −0.203358 | − | 0.390140i | ||||
\(979\) | −25.4051 | + | 14.6676i | −0.811949 | + | 0.468779i | ||||
\(980\) | − | 14.7452i | − | 0.471018i | ||||||
\(981\) | −1.87891 | + | 21.7429i | −0.0599890 | + | 0.694197i | ||||
\(982\) | −18.5831 | + | 10.7290i | −0.593012 | + | 0.342375i | ||||
\(983\) | 15.6251 | − | 27.0635i | 0.498363 | − | 0.863190i | −0.501635 | − | 0.865079i | \(-0.667268\pi\) |
0.999998 | + | 0.00188891i | \(0.000601259\pi\) | |||||||
\(984\) | −2.65301 | − | 5.08976i | −0.0845749 | − | 0.162256i | ||||
\(985\) | 11.3270 | − | 19.6190i | 0.360910 | − | 0.625114i | ||||
\(986\) | 4.42238 | + | 2.55326i | 0.140837 | + | 0.0813125i | ||||
\(987\) | −3.04953 | + | 70.7102i | −0.0970676 | + | 2.25073i | ||||
\(988\) | 8.54984 | + | 15.7945i | 0.272007 | + | 0.502491i | ||||
\(989\) | − | 3.88023i | − | 0.123384i | ||||||
\(990\) | 5.23635 | − | 7.49527i | 0.166422 | − | 0.238215i | ||||
\(991\) | −37.0778 | − | 21.4069i | −1.17782 | − | 0.680012i | −0.222307 | − | 0.974977i | \(-0.571359\pi\) |
−0.955508 | + | 0.294965i | \(0.904692\pi\) | |||||||
\(992\) | −3.72120 | + | 2.14844i | −0.118148 | + | 0.0682130i | ||||
\(993\) | 5.04373 | + | 3.20943i | 0.160058 | + | 0.101848i | ||||
\(994\) | −29.1645 | − | 50.5144i | −0.925042 | − | 1.60222i | ||||
\(995\) | 6.66875i | 0.211414i | ||||||||
\(996\) | −0.195235 | + | 4.52697i | −0.00618626 | + | 0.143442i | ||||
\(997\) | 0.595831 | + | 1.03201i | 0.0188702 | + | 0.0326841i | 0.875306 | − | 0.483569i | \(-0.160660\pi\) |
−0.856436 | + | 0.516253i | \(0.827326\pi\) | |||||||
\(998\) | 9.93532 | + | 17.2085i | 0.314497 | + | 0.544725i | ||||
\(999\) | 3.01321 | − | 23.1738i | 0.0953338 | − | 0.733186i |
(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 | 570.2.s.a.521.4 | yes | 24 | |
3.2 | odd | 2 | 570.2.s.b.521.8 | yes | 24 | ||
19.12 | odd | 6 | 570.2.s.b.221.8 | yes | 24 | ||
57.50 | even | 6 | inner | 570.2.s.a.221.4 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.s.a.221.4 | ✓ | 24 | 57.50 | even | 6 | inner | |
570.2.s.a.521.4 | yes | 24 | 1.1 | even | 1 | trivial | |
570.2.s.b.221.8 | yes | 24 | 19.12 | odd | 6 | ||
570.2.s.b.521.8 | yes | 24 | 3.2 | odd | 2 |