Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(49,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 5, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.bx (of order \(10\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{14} + 15x^{12} - 59x^{10} + 104x^{8} - 59x^{6} + 15x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 499.2 | ||
Root | \(1.23158 - 1.69513i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.499 |
Dual form | 825.2.bx.h.124.2 |
$q$-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 \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(e\left(\frac{1}{5}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.817172 | + | 1.12474i | −0.577828 | + | 0.795312i | −0.993455 | − | 0.114223i | \(-0.963562\pi\) |
0.415627 | + | 0.909535i | \(0.363562\pi\) | |||||||
\(3\) | −0.951057 | − | 0.309017i | −0.549093 | − | 0.178411i | ||||
\(4\) | 0.0207616 | + | 0.0638975i | 0.0103808 | + | 0.0319487i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.12474 | − | 0.817172i | 0.459174 | − | 0.333609i | ||||
\(7\) | −1.21506 | + | 0.394797i | −0.459250 | + | 0.149219i | −0.529500 | − | 0.848310i | \(-0.677620\pi\) |
0.0702498 | + | 0.997529i | \(0.477620\pi\) | |||||||
\(8\) | −2.73326 | − | 0.888090i | −0.966353 | − | 0.313987i | ||||
\(9\) | 0.809017 | + | 0.587785i | 0.269672 | + | 0.195928i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.20381 | + | 3.09044i | −0.362964 | + | 0.931803i | ||||
\(12\) | − | 0.0671858i | − | 0.0193949i | ||||||
\(13\) | 0.833694 | − | 1.14748i | 0.231225 | − | 0.318254i | −0.677601 | − | 0.735430i | \(-0.736980\pi\) |
0.908826 | + | 0.417176i | \(0.136980\pi\) | |||||||
\(14\) | 0.548870 | − | 1.68925i | 0.146692 | − | 0.451470i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.12371 | − | 2.26951i | 0.780927 | − | 0.567377i | ||||
\(17\) | −2.93893 | − | 4.04508i | −0.712794 | − | 0.981077i | −0.999733 | − | 0.0231281i | \(-0.992637\pi\) |
0.286938 | − | 0.957949i | \(-0.407363\pi\) | |||||||
\(18\) | −1.32221 | + | 0.429613i | −0.311649 | + | 0.101261i | ||||
\(19\) | −0.0488697 | + | 0.150406i | −0.0112115 | + | 0.0345054i | −0.956506 | − | 0.291713i | \(-0.905775\pi\) |
0.945294 | + | 0.326219i | \(0.105775\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.27759 | 0.278793 | ||||||||
\(22\) | −2.49222 | − | 3.87940i | −0.531344 | − | 0.827092i | ||||
\(23\) | 5.00829i | 1.04430i | 0.852853 | + | 0.522150i | \(0.174870\pi\) | ||||
−0.852853 | + | 0.522150i | \(0.825130\pi\) | |||||||
\(24\) | 2.32505 | + | 1.68925i | 0.474599 | + | 0.344816i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.609348 | + | 1.87538i | 0.119503 | + | 0.367792i | ||||
\(27\) | −0.587785 | − | 0.809017i | −0.113119 | − | 0.155695i | ||||
\(28\) | −0.0504531 | − | 0.0694428i | −0.00953474 | − | 0.0131234i | ||||
\(29\) | −1.93913 | − | 5.96802i | −0.360087 | − | 1.10823i | −0.953001 | − | 0.302967i | \(-0.902023\pi\) |
0.592914 | − | 0.805266i | \(-0.297977\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.46735 | − | 1.79264i | −0.443149 | − | 0.321967i | 0.343736 | − | 0.939066i | \(-0.388308\pi\) |
−0.786885 | + | 0.617100i | \(0.788308\pi\) | |||||||
\(32\) | − | 0.379898i | − | 0.0671570i | ||||||
\(33\) | 2.09989 | − | 2.56719i | 0.365545 | − | 0.446890i | ||||
\(34\) | 6.95128 | 1.19214 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.0207616 | + | 0.0638975i | −0.00346026 | + | 0.0106496i | ||||
\(37\) | 4.46988 | − | 1.45235i | 0.734844 | − | 0.238765i | 0.0823971 | − | 0.996600i | \(-0.473742\pi\) |
0.652447 | + | 0.757834i | \(0.273742\pi\) | |||||||
\(38\) | −0.129232 | − | 0.177873i | −0.0209643 | − | 0.0288548i | ||||
\(39\) | −1.14748 | + | 0.833694i | −0.183744 | + | 0.133498i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.34419 | − | 7.21469i | 0.366101 | − | 1.12674i | −0.583187 | − | 0.812338i | \(-0.698194\pi\) |
0.949288 | − | 0.314407i | \(-0.101806\pi\) | |||||||
\(42\) | −1.04401 | + | 1.43696i | −0.161095 | + | 0.221728i | ||||
\(43\) | − | 5.41324i | − | 0.825512i | −0.910842 | − | 0.412756i | \(-0.864566\pi\) | ||
0.910842 | − | 0.412756i | \(-0.135434\pi\) | |||||||
\(44\) | −0.222465 | − | 0.0127583i | −0.0335378 | − | 0.00192339i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.63303 | − | 4.09264i | −0.830545 | − | 0.603426i | ||||
\(47\) | −7.82920 | − | 2.54386i | −1.14201 | − | 0.371060i | −0.323880 | − | 0.946098i | \(-0.604987\pi\) |
−0.818127 | + | 0.575038i | \(0.804987\pi\) | |||||||
\(48\) | −3.67214 | + | 1.19315i | −0.530027 | + | 0.172216i | ||||
\(49\) | −4.34261 | + | 3.15509i | −0.620373 | + | 0.450727i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.54508 | + | 4.75528i | 0.216355 | + | 0.665873i | ||||
\(52\) | 0.0906300 | + | 0.0294475i | 0.0125681 | + | 0.00408363i | ||||
\(53\) | −5.50548 | + | 7.57764i | −0.756236 | + | 1.04087i | 0.241282 | + | 0.970455i | \(0.422432\pi\) |
−0.997518 | + | 0.0704143i | \(0.977568\pi\) | |||||||
\(54\) | 1.39026 | 0.189190 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.67169 | 0.490651 | ||||||||
\(57\) | 0.0929558 | − | 0.127943i | 0.0123123 | − | 0.0169464i | ||||
\(58\) | 8.29708 | + | 2.69588i | 1.08946 | + | 0.353987i | ||||
\(59\) | −2.50256 | − | 7.70209i | −0.325806 | − | 1.00273i | −0.971076 | − | 0.238772i | \(-0.923255\pi\) |
0.645270 | − | 0.763955i | \(-0.276745\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.5623 | − | 8.40047i | 1.48039 | − | 1.07557i | 0.502965 | − | 0.864307i | \(-0.332242\pi\) |
0.977429 | − | 0.211263i | \(-0.0677576\pi\) | |||||||
\(62\) | 4.03250 | − | 1.31024i | 0.512128 | − | 0.166401i | ||||
\(63\) | −1.21506 | − | 0.394797i | −0.153083 | − | 0.0497398i | ||||
\(64\) | 6.67470 | + | 4.84945i | 0.834338 | + | 0.606182i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.17144 | + | 4.45967i | 0.144195 | + | 0.548948i | ||||
\(67\) | − | 7.38362i | − | 0.902053i | −0.892511 | − | 0.451026i | \(-0.851058\pi\) | ||
0.892511 | − | 0.451026i | \(-0.148942\pi\) | |||||||
\(68\) | 0.197454 | − | 0.271772i | 0.0239448 | − | 0.0329572i | ||||
\(69\) | 1.54765 | − | 4.76317i | 0.186315 | − | 0.573418i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.48204 | − | 3.98294i | 0.650599 | − | 0.472688i | −0.212876 | − | 0.977079i | \(-0.568283\pi\) |
0.863475 | + | 0.504391i | \(0.168283\pi\) | |||||||
\(72\) | −1.68925 | − | 2.32505i | −0.199080 | − | 0.274010i | ||||
\(73\) | 8.23717 | − | 2.67642i | 0.964087 | − | 0.313251i | 0.215661 | − | 0.976468i | \(-0.430810\pi\) |
0.748427 | + | 0.663217i | \(0.230810\pi\) | |||||||
\(74\) | −2.01914 | + | 6.21429i | −0.234721 | + | 0.722396i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.0106252 | −0.00121879 | ||||||||
\(77\) | 0.242610 | − | 4.23034i | 0.0276480 | − | 0.482092i | ||||
\(78\) | − | 1.97189i | − | 0.223273i | ||||||
\(79\) | −2.05953 | − | 1.49634i | −0.231716 | − | 0.168351i | 0.465869 | − | 0.884854i | \(-0.345742\pi\) |
−0.697585 | + | 0.716502i | \(0.745742\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.309017 | + | 0.951057i | 0.0343352 | + | 0.105673i | ||||
\(82\) | 6.19905 | + | 8.53225i | 0.684570 | + | 0.942230i | ||||
\(83\) | 5.94964 | + | 8.18897i | 0.653057 | + | 0.898856i | 0.999227 | − | 0.0393157i | \(-0.0125178\pi\) |
−0.346170 | + | 0.938172i | \(0.612518\pi\) | |||||||
\(84\) | 0.0265248 | + | 0.0816349i | 0.00289409 | + | 0.00890709i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 6.08850 | + | 4.42355i | 0.656539 | + | 0.477004i | ||||
\(87\) | 6.27515i | 0.672766i | ||||||||
\(88\) | 6.03493 | − | 7.37788i | 0.643325 | − | 0.786485i | ||||
\(89\) | −11.0447 | −1.17073 | −0.585367 | − | 0.810768i | \(-0.699050\pi\) | ||||
−0.585367 | + | 0.810768i | \(0.699050\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.559967 | + | 1.72340i | −0.0587005 | + | 0.180661i | ||||
\(92\) | −0.320017 | + | 0.103980i | −0.0333641 | + | 0.0108407i | ||||
\(93\) | 1.79264 | + | 2.46735i | 0.185888 | + | 0.255852i | ||||
\(94\) | 9.25900 | − | 6.72705i | 0.954993 | − | 0.693843i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.117395 | + | 0.361304i | −0.0119816 | + | 0.0368754i | ||||
\(97\) | 3.76886 | − | 5.18739i | 0.382669 | − | 0.526699i | −0.573620 | − | 0.819122i | \(-0.694461\pi\) |
0.956289 | + | 0.292422i | \(0.0944613\pi\) | |||||||
\(98\) | − | 7.46257i | − | 0.753833i | ||||||
\(99\) | −2.79042 | + | 1.79264i | −0.280448 | + | 0.180167i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.09624 | − | 5.15572i | −0.706102 | − | 0.513013i | 0.175812 | − | 0.984424i | \(-0.443745\pi\) |
−0.881914 | + | 0.471411i | \(0.843745\pi\) | |||||||
\(102\) | −6.61106 | − | 2.14807i | −0.654593 | − | 0.212690i | ||||
\(103\) | 11.0005 | − | 3.57429i | 1.08391 | − | 0.352185i | 0.288022 | − | 0.957624i | \(-0.407002\pi\) |
0.795892 | + | 0.605439i | \(0.207002\pi\) | |||||||
\(104\) | −3.29777 | + | 2.39597i | −0.323373 | + | 0.234944i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.02396 | − | 12.3845i | −0.390842 | − | 1.20289i | ||||
\(107\) | 14.5955 | + | 4.74238i | 1.41100 | + | 0.458463i | 0.912733 | − | 0.408557i | \(-0.133968\pi\) |
0.498272 | + | 0.867021i | \(0.333968\pi\) | |||||||
\(108\) | 0.0394908 | − | 0.0543544i | 0.00380001 | − | 0.00523026i | ||||
\(109\) | −14.4004 | −1.37931 | −0.689656 | − | 0.724137i | \(-0.742238\pi\) | ||||
−0.689656 | + | 0.724137i | \(0.742238\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.69991 | −0.446096 | ||||||||
\(112\) | −2.89950 | + | 3.99082i | −0.273977 | + | 0.377097i | ||||
\(113\) | −18.4168 | − | 5.98397i | −1.73250 | − | 0.562924i | −0.738695 | − | 0.674039i | \(-0.764558\pi\) |
−0.993808 | + | 0.111115i | \(0.964558\pi\) | |||||||
\(114\) | 0.0679415 | + | 0.209102i | 0.00636330 | + | 0.0195842i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.341082 | − | 0.247811i | 0.0316687 | − | 0.0230086i | ||||
\(117\) | 1.34895 | − | 0.438299i | 0.124710 | − | 0.0405207i | ||||
\(118\) | 10.7079 | + | 3.47920i | 0.985741 | + | 0.320287i | ||||
\(119\) | 5.16796 | + | 3.75475i | 0.473747 | + | 0.344197i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.10166 | − | 7.44064i | −0.736515 | − | 0.676422i | ||||
\(122\) | 19.8692i | 1.79887i | ||||||||
\(123\) | −4.45892 | + | 6.13718i | −0.402047 | + | 0.553371i | ||||
\(124\) | 0.0633189 | − | 0.194875i | 0.00568620 | − | 0.0175003i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.43696 | − | 1.04401i | 0.128015 | − | 0.0930080i | ||||
\(127\) | 3.54091 | + | 4.87364i | 0.314205 | + | 0.432466i | 0.936687 | − | 0.350168i | \(-0.113876\pi\) |
−0.622482 | + | 0.782634i | \(0.713876\pi\) | |||||||
\(128\) | −10.1862 | + | 3.30968i | −0.900337 | + | 0.292537i | ||||
\(129\) | −1.67278 | + | 5.14830i | −0.147280 | + | 0.453282i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.7278 | −1.63626 | −0.818130 | − | 0.575034i | \(-0.804989\pi\) | ||||
−0.818130 | + | 0.575034i | \(0.804989\pi\) | |||||||
\(132\) | 0.207634 | + | 0.0808792i | 0.0180722 | + | 0.00703963i | ||||
\(133\) | − | 0.202046i | − | 0.0175196i | ||||||
\(134\) | 8.30467 | + | 6.03369i | 0.717414 | + | 0.521232i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.44045 | + | 13.6663i | 0.380765 | + | 1.17188i | ||||
\(137\) | −1.78521 | − | 2.45714i | −0.152521 | − | 0.209927i | 0.725918 | − | 0.687781i | \(-0.241415\pi\) |
−0.878440 | + | 0.477853i | \(0.841415\pi\) | |||||||
\(138\) | 4.09264 | + | 5.63303i | 0.348388 | + | 0.479516i | ||||
\(139\) | 0.683520 | + | 2.10366i | 0.0579754 | + | 0.178430i | 0.975851 | − | 0.218439i | \(-0.0700966\pi\) |
−0.917875 | + | 0.396869i | \(0.870097\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.65992 | + | 4.83871i | 0.560866 | + | 0.407493i | ||||
\(142\) | 9.42063i | 0.790562i | ||||||||
\(143\) | 2.54261 | + | 3.95784i | 0.212624 | + | 0.330971i | ||||
\(144\) | 3.86111 | 0.321760 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.72091 | + | 11.4518i | −0.307945 | + | 0.947756i | ||||
\(147\) | 5.10504 | − | 1.65873i | 0.421057 | − | 0.136810i | ||||
\(148\) | 0.185603 | + | 0.255461i | 0.0152565 | + | 0.0209988i | ||||
\(149\) | 1.19833 | − | 0.870637i | 0.0981710 | − | 0.0713254i | −0.537617 | − | 0.843189i | \(-0.680675\pi\) |
0.635788 | + | 0.771864i | \(0.280675\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.79165 | + | 8.59180i | −0.227181 | + | 0.699191i | 0.770882 | + | 0.636978i | \(0.219816\pi\) |
−0.998063 | + | 0.0622129i | \(0.980184\pi\) | |||||||
\(152\) | 0.267147 | − | 0.367697i | 0.0216685 | − | 0.0298242i | ||||
\(153\) | − | 5.00000i | − | 0.404226i | ||||||
\(154\) | 4.55978 | + | 3.72979i | 0.367438 | + | 0.300555i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.0770945 | − | 0.0560124i | −0.00617250 | − | 0.00448458i | ||||
\(157\) | −16.7744 | − | 5.45034i | −1.33874 | − | 0.434985i | −0.449853 | − | 0.893102i | \(-0.648524\pi\) |
−0.888891 | + | 0.458118i | \(0.848524\pi\) | |||||||
\(158\) | 3.36599 | − | 1.09368i | 0.267784 | − | 0.0870082i | ||||
\(159\) | 7.57764 | − | 5.50548i | 0.600946 | − | 0.436613i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.97726 | − | 6.08538i | −0.155830 | − | 0.479595i | ||||
\(162\) | −1.32221 | − | 0.429613i | −0.103883 | − | 0.0337536i | ||||
\(163\) | −13.8153 | + | 19.0152i | −1.08210 | + | 1.48938i | −0.224910 | + | 0.974379i | \(0.572209\pi\) |
−0.857189 | + | 0.515002i | \(0.827791\pi\) | |||||||
\(164\) | 0.509669 | 0.0397985 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.0724 | −1.09223 | ||||||||
\(167\) | 0.354276 | − | 0.487619i | 0.0274147 | − | 0.0377331i | −0.795090 | − | 0.606492i | \(-0.792576\pi\) |
0.822504 | + | 0.568759i | \(0.192576\pi\) | |||||||
\(168\) | −3.49199 | − | 1.13462i | −0.269413 | − | 0.0875375i | ||||
\(169\) | 3.39555 | + | 10.4504i | 0.261196 | + | 0.803880i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.127943 | + | 0.0929558i | −0.00978402 | + | 0.00710851i | ||||
\(172\) | 0.345893 | − | 0.112387i | 0.0263741 | − | 0.00856945i | ||||
\(173\) | −9.19091 | − | 2.98631i | −0.698772 | − | 0.227045i | −0.0619764 | − | 0.998078i | \(-0.519740\pi\) |
−0.636795 | + | 0.771033i | \(0.719740\pi\) | |||||||
\(174\) | −7.05792 | − | 5.12788i | −0.535059 | − | 0.388743i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.25341 | + | 12.3857i | 0.245235 | + | 0.933607i | ||||
\(177\) | 8.09846i | 0.608718i | ||||||||
\(178\) | 9.02542 | − | 12.4224i | 0.676484 | − | 0.931100i | ||||
\(179\) | 0.369495 | − | 1.13719i | 0.0276174 | − | 0.0849975i | −0.936298 | − | 0.351207i | \(-0.885771\pi\) |
0.963915 | + | 0.266210i | \(0.0857713\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.5997 | + | 9.15421i | −0.936527 | + | 0.680427i | −0.947582 | − | 0.319512i | \(-0.896481\pi\) |
0.0110551 | + | 0.999939i | \(0.496481\pi\) | |||||||
\(182\) | −1.48079 | − | 2.03813i | −0.109763 | − | 0.151076i | ||||
\(183\) | −13.5922 | + | 4.41639i | −1.00477 | + | 0.326469i | ||||
\(184\) | 4.44781 | − | 13.6890i | 0.327897 | − | 1.00916i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −4.24002 | −0.310894 | ||||||||
\(187\) | 16.0390 | − | 4.21305i | 1.17289 | − | 0.308089i | ||||
\(188\) | − | 0.553081i | − | 0.0403376i | ||||||
\(189\) | 1.03359 | + | 0.750949i | 0.0751828 | + | 0.0546235i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.68641 | + | 17.5010i | 0.411454 | + | 1.26633i | 0.915384 | + | 0.402581i | \(0.131887\pi\) |
−0.503930 | + | 0.863744i | \(0.668113\pi\) | |||||||
\(192\) | −4.84945 | − | 6.67470i | −0.349979 | − | 0.481705i | ||||
\(193\) | 0.921640 | + | 1.26853i | 0.0663411 | + | 0.0913107i | 0.840898 | − | 0.541193i | \(-0.182027\pi\) |
−0.774557 | + | 0.632504i | \(0.782027\pi\) | |||||||
\(194\) | 2.75466 | + | 8.47798i | 0.197773 | + | 0.608683i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.291762 | − | 0.211977i | −0.0208401 | − | 0.0151412i | ||||
\(197\) | 7.97000i | 0.567839i | 0.958848 | + | 0.283920i | \(0.0916349\pi\) | ||||
−0.958848 | + | 0.283920i | \(0.908365\pi\) | |||||||
\(198\) | 0.264005 | − | 4.60340i | 0.0187620 | − | 0.327149i | ||||
\(199\) | −3.53141 | −0.250335 | −0.125167 | − | 0.992136i | \(-0.539947\pi\) | ||||
−0.125167 | + | 0.992136i | \(0.539947\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.28166 | + | 7.02224i | −0.160936 | + | 0.495311i | ||||
\(202\) | 11.5977 | − | 3.76832i | 0.816011 | − | 0.265138i | ||||
\(203\) | 4.71232 | + | 6.48595i | 0.330740 | + | 0.455224i | ||||
\(204\) | −0.271772 | + | 0.197454i | −0.0190279 | + | 0.0138246i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.96918 | + | 15.2936i | −0.346219 | + | 1.06555i | ||||
\(207\) | −2.94380 | + | 4.05179i | −0.204608 | + | 0.281619i | ||||
\(208\) | − | 5.47647i | − | 0.379725i | ||||||
\(209\) | −0.405990 | − | 0.332090i | −0.0280829 | − | 0.0229711i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.3867 | − | 11.9056i | −1.12810 | − | 0.819616i | −0.142686 | − | 0.989768i | \(-0.545574\pi\) |
−0.985418 | + | 0.170152i | \(0.945574\pi\) | |||||||
\(212\) | −0.598495 | − | 0.194463i | −0.0411048 | − | 0.0133558i | ||||
\(213\) | −6.44453 | + | 2.09395i | −0.441572 | + | 0.143475i | ||||
\(214\) | −17.2610 | + | 12.5409i | −1.17994 | + | 0.857276i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.888090 | + | 2.73326i | 0.0604269 | + | 0.185975i | ||||
\(217\) | 3.70571 | + | 1.20406i | 0.251560 | + | 0.0817368i | ||||
\(218\) | 11.7676 | − | 16.1968i | 0.797005 | − | 1.09698i | ||||
\(219\) | −8.66107 | −0.585261 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.09183 | −0.477048 | ||||||||
\(222\) | 3.84064 | − | 5.28619i | 0.257767 | − | 0.354786i | ||||
\(223\) | −21.4463 | − | 6.96833i | −1.43615 | − | 0.466634i | −0.515456 | − | 0.856916i | \(-0.672377\pi\) |
−0.920695 | + | 0.390282i | \(0.872377\pi\) | |||||||
\(224\) | 0.149983 | + | 0.461599i | 0.0100211 | + | 0.0308419i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 21.7801 | − | 15.8242i | 1.44879 | − | 1.05261i | ||||
\(227\) | −17.8857 | + | 5.81143i | −1.18712 | + | 0.385718i | −0.835007 | − | 0.550240i | \(-0.814536\pi\) |
−0.352112 | + | 0.935958i | \(0.614536\pi\) | |||||||
\(228\) | 0.0101051 | + | 0.00328335i | 0.000669228 | + | 0.000217445i | ||||
\(229\) | −19.2805 | − | 14.0081i | −1.27409 | − | 0.925681i | −0.274732 | − | 0.961521i | \(-0.588589\pi\) |
−0.999358 | + | 0.0358402i | \(0.988589\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.53798 | + | 3.94832i | −0.101192 | + | 0.259780i | ||||
\(232\) | 18.0343i | 1.18401i | ||||||||
\(233\) | 5.93183 | − | 8.16446i | 0.388607 | − | 0.534871i | −0.569232 | − | 0.822177i | \(-0.692759\pi\) |
0.957839 | + | 0.287305i | \(0.0927595\pi\) | |||||||
\(234\) | −0.609348 | + | 1.87538i | −0.0398343 | + | 0.122597i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.440187 | − | 0.319815i | 0.0286538 | − | 0.0208182i | ||||
\(237\) | 1.49634 | + | 2.05953i | 0.0971977 | + | 0.133781i | ||||
\(238\) | −8.44624 | + | 2.74435i | −0.547488 | + | 0.177890i | ||||
\(239\) | −0.0516759 | + | 0.159042i | −0.00334264 | + | 0.0102876i | −0.952714 | − | 0.303869i | \(-0.901722\pi\) |
0.949371 | + | 0.314156i | \(0.101722\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.965256 | 0.0621776 | 0.0310888 | − | 0.999517i | \(-0.490103\pi\) | ||||
0.0310888 | + | 0.999517i | \(0.490103\pi\) | |||||||
\(242\) | 14.9892 | − | 3.03199i | 0.963545 | − | 0.194904i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0.776819 | + | 0.564392i | 0.0497307 | + | 0.0361315i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.25903 | − | 10.0303i | −0.207788 | − | 0.639506i | ||||
\(247\) | 0.131845 | + | 0.181469i | 0.00838911 | + | 0.0115466i | ||||
\(248\) | 5.15189 | + | 7.09097i | 0.327145 | + | 0.450277i | ||||
\(249\) | −3.12791 | − | 9.62671i | −0.198223 | − | 0.610068i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.0201 | + | 13.8189i | 1.20054 | + | 0.872244i | 0.994338 | − | 0.106265i | \(-0.0338893\pi\) |
0.206203 | + | 0.978509i | \(0.433889\pi\) | |||||||
\(252\) | − | 0.0858360i | − | 0.00540716i | ||||||
\(253\) | −15.4778 | − | 6.02905i | −0.973083 | − | 0.379043i | ||||
\(254\) | −8.37512 | −0.525502 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.497709 | + | 1.53179i | −0.0311068 | + | 0.0957369i | ||||
\(257\) | 6.26055 | − | 2.03418i | 0.390522 | − | 0.126888i | −0.107173 | − | 0.994240i | \(-0.534180\pi\) |
0.497695 | + | 0.867352i | \(0.334180\pi\) | |||||||
\(258\) | −4.42355 | − | 6.08850i | −0.275398 | − | 0.379053i | ||||
\(259\) | −4.85780 | + | 3.52940i | −0.301849 | + | 0.219306i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.93913 | − | 5.96802i | 0.120029 | − | 0.369411i | ||||
\(262\) | 15.3039 | − | 21.0640i | 0.945477 | − | 1.30134i | ||||
\(263\) | − | 12.4538i | − | 0.767936i | −0.923346 | − | 0.383968i | \(-0.874557\pi\) | ||
0.923346 | − | 0.383968i | \(-0.125443\pi\) | |||||||
\(264\) | −8.01945 | + | 5.15189i | −0.493563 | + | 0.317077i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.227249 | + | 0.165106i | 0.0139335 | + | 0.0101233i | ||||
\(267\) | 10.5041 | + | 3.41300i | 0.642842 | + | 0.208872i | ||||
\(268\) | 0.471795 | − | 0.153295i | 0.0288195 | − | 0.00936401i | ||||
\(269\) | 16.8057 | − | 12.2100i | 1.02466 | − | 0.744459i | 0.0574266 | − | 0.998350i | \(-0.481710\pi\) |
0.967233 | + | 0.253891i | \(0.0817105\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.44683 | + | 13.6859i | 0.270126 | + | 0.831362i | 0.990468 | + | 0.137743i | \(0.0439848\pi\) |
−0.720342 | + | 0.693619i | \(0.756015\pi\) | |||||||
\(272\) | −18.3607 | − | 5.96575i | −1.11328 | − | 0.361727i | ||||
\(273\) | 1.06512 | − | 1.46601i | 0.0644640 | − | 0.0887271i | ||||
\(274\) | 4.22247 | 0.255089 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.336486 | 0.0202541 | ||||||||
\(277\) | −10.2787 | + | 14.1474i | −0.617589 | + | 0.850038i | −0.997175 | − | 0.0751187i | \(-0.976066\pi\) |
0.379586 | + | 0.925156i | \(0.376066\pi\) | |||||||
\(278\) | −2.92462 | − | 0.950268i | −0.175407 | − | 0.0569933i | ||||
\(279\) | −0.942444 | − | 2.90055i | −0.0564227 | − | 0.173651i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.2791 | − | 11.1009i | 0.911474 | − | 0.662224i | −0.0299134 | − | 0.999552i | \(-0.509523\pi\) |
0.941387 | + | 0.337328i | \(0.109523\pi\) | |||||||
\(282\) | −10.8846 | + | 3.53662i | −0.648169 | + | 0.210603i | ||||
\(283\) | 12.9166 | + | 4.19686i | 0.767813 | + | 0.249478i | 0.666629 | − | 0.745390i | \(-0.267737\pi\) |
0.101185 | + | 0.994868i | \(0.467737\pi\) | |||||||
\(284\) | 0.368316 | + | 0.267597i | 0.0218555 | + | 0.0158790i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.52930 | − | 0.374455i | −0.386085 | − | 0.0221420i | ||||
\(287\) | 9.69177i | 0.572087i | ||||||||
\(288\) | 0.223298 | − | 0.307344i | 0.0131580 | − | 0.0181104i | ||||
\(289\) | −2.47214 | + | 7.60845i | −0.145420 | + | 0.447556i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.18739 | + | 3.76886i | −0.304090 | + | 0.220934i | ||||
\(292\) | 0.342033 | + | 0.470768i | 0.0200159 | + | 0.0275496i | ||||
\(293\) | 18.9282 | − | 6.15016i | 1.10580 | − | 0.359296i | 0.301468 | − | 0.953476i | \(-0.402523\pi\) |
0.804332 | + | 0.594180i | \(0.202523\pi\) | |||||||
\(294\) | −2.30606 | + | 7.09732i | −0.134492 | + | 0.413924i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −13.5072 | −0.785088 | ||||||||
\(297\) | 3.20780 | − | 0.842610i | 0.186136 | − | 0.0488932i | ||||
\(298\) | 2.05927i | 0.119290i | ||||||||
\(299\) | 5.74692 | + | 4.17538i | 0.332353 | + | 0.241469i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.13713 | + | 6.57742i | 0.123182 | + | 0.379116i | ||||
\(302\) | −7.38230 | − | 10.1609i | −0.424804 | − | 0.584692i | ||||
\(303\) | 5.15572 | + | 7.09624i | 0.296188 | + | 0.407668i | ||||
\(304\) | 0.188692 | + | 0.580733i | 0.0108222 | + | 0.0333073i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 5.62371 | + | 4.08586i | 0.321486 | + | 0.233573i | ||||
\(307\) | − | 14.9354i | − | 0.852410i | −0.904627 | − | 0.426205i | \(-0.859850\pi\) | ||
0.904627 | − | 0.426205i | \(-0.140150\pi\) | |||||||
\(308\) | 0.275345 | − | 0.0723262i | 0.0156892 | − | 0.00412117i | ||||
\(309\) | −11.5666 | −0.658003 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.54416 | + | 4.75243i | −0.0875611 | + | 0.269485i | −0.985244 | − | 0.171157i | \(-0.945249\pi\) |
0.897683 | + | 0.440643i | \(0.145249\pi\) | |||||||
\(312\) | 3.87676 | − | 1.25964i | 0.219478 | − | 0.0713128i | ||||
\(313\) | 5.52311 | + | 7.60191i | 0.312185 | + | 0.429685i | 0.936061 | − | 0.351838i | \(-0.114443\pi\) |
−0.623876 | + | 0.781523i | \(0.714443\pi\) | |||||||
\(314\) | 19.8378 | − | 14.4130i | 1.11951 | − | 0.813374i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.0528532 | − | 0.162665i | 0.00297322 | − | 0.00915064i | ||||
\(317\) | 1.26523 | − | 1.74144i | 0.0710623 | − | 0.0978088i | −0.772006 | − | 0.635615i | \(-0.780747\pi\) |
0.843069 | + | 0.537806i | \(0.180747\pi\) | |||||||
\(318\) | 13.0218i | 0.730227i | ||||||||
\(319\) | 20.7782 | + | 1.19163i | 1.16335 | + | 0.0667183i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.4157 | − | 9.02054i | −0.692978 | − | 0.503478i | ||||
\(322\) | 8.46024 | + | 2.74890i | 0.471471 | + | 0.153190i | ||||
\(323\) | 0.752028 | − | 0.244349i | 0.0418440 | − | 0.0135959i | ||||
\(324\) | −0.0543544 | + | 0.0394908i | −0.00301969 | + | 0.00219393i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −10.0976 | − | 31.0773i | −0.559256 | − | 1.72121i | ||||
\(327\) | 13.6956 | + | 4.44998i | 0.757370 | + | 0.246084i | ||||
\(328\) | −12.8146 | + | 17.6378i | −0.707567 | + | 0.973882i | ||||
\(329\) | 10.5173 | 0.579836 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.5116 | −1.07245 | −0.536227 | − | 0.844074i | \(-0.680151\pi\) | ||||
−0.536227 | + | 0.844074i | \(0.680151\pi\) | |||||||
\(332\) | −0.399731 | + | 0.550182i | −0.0219381 | + | 0.0301952i | ||||
\(333\) | 4.46988 | + | 1.45235i | 0.244948 | + | 0.0795885i | ||||
\(334\) | 0.258941 | + | 0.796938i | 0.0141686 | + | 0.0436065i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.99082 | − | 2.89950i | 0.217717 | − | 0.158181i | ||||
\(337\) | −30.0579 | + | 9.76639i | −1.63736 | + | 0.532009i | −0.975945 | − | 0.218015i | \(-0.930042\pi\) |
−0.661410 | + | 0.750024i | \(0.730042\pi\) | |||||||
\(338\) | −14.5288 | − | 4.72069i | −0.790262 | − | 0.256772i | ||||
\(339\) | 15.6662 | + | 11.3822i | 0.850873 | + | 0.618195i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.51027 | − | 5.46721i | 0.460857 | − | 0.296066i | ||||
\(342\) | − | 0.219863i | − | 0.0118888i | ||||||
\(343\) | 9.28756 | − | 12.7832i | 0.501481 | − | 0.690230i | ||||
\(344\) | −4.80744 | + | 14.7958i | −0.259200 | + | 0.797736i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.8694 | − | 7.89707i | 0.584341 | − | 0.424549i | ||||
\(347\) | −5.51527 | − | 7.59111i | −0.296075 | − | 0.407512i | 0.634900 | − | 0.772594i | \(-0.281041\pi\) |
−0.930976 | + | 0.365082i | \(0.881041\pi\) | |||||||
\(348\) | −0.400966 | + | 0.130282i | −0.0214940 | + | 0.00698384i | ||||
\(349\) | 7.66768 | − | 23.5987i | 0.410441 | − | 1.26321i | −0.505824 | − | 0.862637i | \(-0.668812\pi\) |
0.916265 | − | 0.400572i | \(-0.131188\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.41837 | −0.0757067 | ||||||||
\(352\) | 1.17405 | + | 0.457326i | 0.0625771 | + | 0.0243756i | ||||
\(353\) | 19.4788i | 1.03675i | 0.855153 | + | 0.518375i | \(0.173463\pi\) | ||||
−0.855153 | + | 0.518375i | \(0.826537\pi\) | |||||||
\(354\) | −9.10867 | − | 6.61784i | −0.484121 | − | 0.351734i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.229305 | − | 0.705728i | −0.0121531 | − | 0.0374035i | ||||
\(357\) | −3.75475 | − | 5.16796i | −0.198722 | − | 0.273518i | ||||
\(358\) | 0.977103 | + | 1.34487i | 0.0516415 | + | 0.0710784i | ||||
\(359\) | −9.19946 | − | 28.3130i | −0.485529 | − | 1.49430i | −0.831213 | − | 0.555954i | \(-0.812353\pi\) |
0.345684 | − | 0.938351i | \(-0.387647\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.3511 | + | 11.1532i | 0.807952 | + | 0.587012i | ||||
\(362\) | − | 21.6520i | − | 1.13800i | ||||||
\(363\) | 5.40586 | + | 9.58002i | 0.283734 | + | 0.502820i | ||||
\(364\) | −0.121747 | −0.00638126 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 6.13991 | − | 18.8967i | 0.320938 | − | 0.987747i | ||||
\(367\) | 6.12097 | − | 1.98882i | 0.319512 | − | 0.103816i | −0.144870 | − | 0.989451i | \(-0.546276\pi\) |
0.464382 | + | 0.885635i | \(0.346276\pi\) | |||||||
\(368\) | 11.3663 | + | 15.6444i | 0.592512 | + | 0.815523i | ||||
\(369\) | 6.13718 | − | 4.45892i | 0.319489 | − | 0.232122i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.69786 | − | 11.3809i | 0.191983 | − | 0.590864i | ||||
\(372\) | −0.120440 | + | 0.165771i | −0.00624451 | + | 0.00859482i | ||||
\(373\) | 20.8924i | 1.08177i | 0.841098 | + | 0.540883i | \(0.181910\pi\) | ||||
−0.841098 | + | 0.540883i | \(0.818090\pi\) | |||||||
\(374\) | −8.36806 | + | 21.4825i | −0.432702 | + | 1.11084i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 19.1401 | + | 13.9061i | 0.987074 | + | 0.717151i | ||||
\(377\) | −8.46483 | − | 2.75039i | −0.435961 | − | 0.141652i | ||||
\(378\) | −1.68925 | + | 0.548870i | −0.0868855 | + | 0.0282308i | ||||
\(379\) | −11.4873 | + | 8.34603i | −0.590064 | + | 0.428707i | −0.842338 | − | 0.538949i | \(-0.818822\pi\) |
0.252274 | + | 0.967656i | \(0.418822\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.86157 | − | 5.72931i | −0.0953709 | − | 0.293521i | ||||
\(382\) | −24.3308 | − | 7.90557i | −1.24487 | − | 0.404484i | ||||
\(383\) | 15.5635 | − | 21.4214i | 0.795260 | − | 1.09458i | −0.198173 | − | 0.980167i | \(-0.563501\pi\) |
0.993433 | − | 0.114415i | \(-0.0364992\pi\) | |||||||
\(384\) | 10.7104 | 0.546561 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.17990 | −0.110954 | ||||||||
\(387\) | 3.18182 | − | 4.37940i | 0.161741 | − | 0.222618i | ||||
\(388\) | 0.409708 | + | 0.133122i | 0.0207998 | + | 0.00675826i | ||||
\(389\) | 11.2780 | + | 34.7102i | 0.571819 | + | 1.75988i | 0.646766 | + | 0.762689i | \(0.276121\pi\) |
−0.0749470 | + | 0.997188i | \(0.523879\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.2590 | − | 14.7190i | 1.02454 | − | 0.744372i | ||||
\(392\) | 14.6715 | − | 4.76705i | 0.741022 | − | 0.240773i | ||||
\(393\) | 17.8112 | + | 5.78722i | 0.898458 | + | 0.291927i | ||||
\(394\) | −8.96419 | − | 6.51287i | −0.451610 | − | 0.328114i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.172478 | − | 0.141083i | −0.00866737 | − | 0.00708969i | ||||
\(397\) | − | 8.03969i | − | 0.403500i | −0.979437 | − | 0.201750i | \(-0.935337\pi\) | ||
0.979437 | − | 0.201750i | \(-0.0646629\pi\) | |||||||
\(398\) | 2.88577 | − | 3.97192i | 0.144651 | − | 0.199094i | ||||
\(399\) | −0.0624355 | + | 0.192157i | −0.00312569 | + | 0.00961988i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.7255 | − | 16.5110i | 1.13486 | − | 0.824521i | 0.148461 | − | 0.988918i | \(-0.452568\pi\) |
0.986394 | + | 0.164397i | \(0.0525679\pi\) | |||||||
\(402\) | −6.03369 | − | 8.30467i | −0.300933 | − | 0.414199i | ||||
\(403\) | −4.11403 | + | 1.33673i | −0.204935 | + | 0.0665873i | ||||
\(404\) | 0.182109 | − | 0.560473i | 0.00906024 | − | 0.0278846i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −11.1458 | −0.553156 | ||||||||
\(407\) | −0.892497 | + | 15.5623i | −0.0442394 | + | 0.771393i | ||||
\(408\) | − | 14.3696i | − | 0.711401i | ||||||
\(409\) | −4.83752 | − | 3.51466i | −0.239200 | − | 0.173789i | 0.461727 | − | 0.887022i | \(-0.347230\pi\) |
−0.700927 | + | 0.713233i | \(0.747230\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.938543 | + | 2.88854i | 0.0462949 | + | 0.142481i | ||||
\(412\) | 0.456776 | + | 0.628698i | 0.0225037 | + | 0.0309737i | ||||
\(413\) | 6.08153 | + | 8.37051i | 0.299253 | + | 0.411886i | ||||
\(414\) | −2.15163 | − | 6.62203i | −0.105747 | − | 0.325455i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.435925 | − | 0.316718i | −0.0213730 | − | 0.0155284i | ||||
\(417\) | − | 2.21192i | − | 0.108318i | ||||||
\(418\) | 0.705278 | − | 0.185259i | 0.0344963 | − | 0.00906131i | ||||
\(419\) | 15.4707 | 0.755795 | 0.377897 | − | 0.925847i | \(-0.376647\pi\) | ||||
0.377897 | + | 0.925847i | \(0.376647\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.6841 | − | 32.8824i | 0.520713 | − | 1.60259i | −0.251927 | − | 0.967746i | \(-0.581064\pi\) |
0.772640 | − | 0.634844i | \(-0.218936\pi\) | |||||||
\(422\) | 26.7815 | − | 8.70182i | 1.30370 | − | 0.423598i | ||||
\(423\) | −4.83871 | − | 6.65992i | −0.235266 | − | 0.323816i | ||||
\(424\) | 21.7775 | − | 15.8223i | 1.05761 | − | 0.768399i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.91113 | − | 8.95955i | 0.141045 | − | 0.434092i | ||||
\(427\) | −10.7324 | + | 14.7718i | −0.519375 | + | 0.714859i | ||||
\(428\) | 1.03108i | 0.0498390i | ||||||||
\(429\) | −1.19513 | − | 4.54984i | −0.0577013 | − | 0.219668i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.71871 | − | 1.97526i | −0.130956 | − | 0.0951450i | 0.520379 | − | 0.853935i | \(-0.325791\pi\) |
−0.651335 | + | 0.758790i | \(0.725791\pi\) | |||||||
\(432\) | −3.67214 | − | 1.19315i | −0.176676 | − | 0.0574055i | ||||
\(433\) | 3.49779 | − | 1.13650i | 0.168093 | − | 0.0546167i | −0.223761 | − | 0.974644i | \(-0.571834\pi\) |
0.391855 | + | 0.920027i | \(0.371834\pi\) | |||||||
\(434\) | −4.38246 | + | 3.18404i | −0.210365 | + | 0.152839i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.298975 | − | 0.920152i | −0.0143183 | − | 0.0440673i | ||||
\(437\) | −0.753275 | − | 0.244754i | −0.0360340 | − | 0.0117082i | ||||
\(438\) | 7.07759 | − | 9.74146i | 0.338180 | − | 0.465465i | ||||
\(439\) | 1.55432 | 0.0741835 | 0.0370917 | − | 0.999312i | \(-0.488191\pi\) | ||||
0.0370917 | + | 0.999312i | \(0.488191\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.36776 | −0.255608 | ||||||||
\(442\) | 5.79524 | − | 7.97647i | 0.275652 | − | 0.379402i | ||||
\(443\) | −20.1680 | − | 6.55298i | −0.958211 | − | 0.311342i | −0.212163 | − | 0.977234i | \(-0.568051\pi\) |
−0.746047 | + | 0.665893i | \(0.768051\pi\) | |||||||
\(444\) | −0.0975775 | − | 0.300313i | −0.00463082 | − | 0.0142522i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 25.3629 | − | 18.4272i | 1.20097 | − | 0.872555i | ||||
\(447\) | −1.40872 | + | 0.457721i | −0.0666302 | + | 0.0216495i | ||||
\(448\) | −10.0247 | − | 3.25723i | −0.473624 | − | 0.153890i | ||||
\(449\) | 12.2247 | + | 8.88179i | 0.576921 | + | 0.419157i | 0.837613 | − | 0.546265i | \(-0.183951\pi\) |
−0.260692 | + | 0.965422i | \(0.583951\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.4746 | + | 15.9297i | 0.917023 | + | 0.750102i | ||||
\(452\) | − | 1.30102i | − | 0.0611949i | ||||||
\(453\) | 5.31002 | − | 7.30862i | 0.249487 | − | 0.343389i | ||||
\(454\) | 8.07938 | − | 24.8658i | 0.379184 | − | 1.16701i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.367697 | + | 0.267147i | −0.0172190 | + | 0.0125103i | ||||
\(457\) | −24.2780 | − | 33.4158i | −1.13568 | − | 1.56312i | −0.776810 | − | 0.629735i | \(-0.783163\pi\) |
−0.358866 | − | 0.933389i | \(-0.616837\pi\) | |||||||
\(458\) | 31.5110 | − | 10.2385i | 1.47241 | − | 0.478415i | ||||
\(459\) | −1.54508 | + | 4.75528i | −0.0721184 | + | 0.221958i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.3158 | −0.759901 | −0.379951 | − | 0.925007i | \(-0.624059\pi\) | ||||
−0.379951 | + | 0.925007i | \(0.624059\pi\) | |||||||
\(462\) | −3.18404 | − | 4.95629i | −0.148135 | − | 0.230588i | ||||
\(463\) | − | 8.47904i | − | 0.394054i | −0.980398 | − | 0.197027i | \(-0.936871\pi\) | ||
0.980398 | − | 0.197027i | \(-0.0631287\pi\) | |||||||
\(464\) | −19.6017 | − | 14.2415i | −0.909987 | − | 0.661144i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.33558 | + | 13.3435i | 0.200842 | + | 0.618128i | ||||
\(467\) | 21.4935 | + | 29.5833i | 0.994601 | + | 1.36895i | 0.928580 | + | 0.371133i | \(0.121031\pi\) |
0.0660214 | + | 0.997818i | \(0.478969\pi\) | |||||||
\(468\) | 0.0560124 | + | 0.0770945i | 0.00258917 | + | 0.00356369i | ||||
\(469\) | 2.91503 | + | 8.97155i | 0.134604 | + | 0.414268i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.2692 | + | 10.3672i | 0.657489 | + | 0.477694i | ||||
\(472\) | 23.2743i | 1.07129i | ||||||||
\(473\) | 16.7293 | + | 6.51654i | 0.769214 | + | 0.299631i | ||||
\(474\) | −3.53921 | −0.162561 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.132624 | + | 0.408174i | −0.00607881 | + | 0.0187086i | ||||
\(477\) | −8.90805 | + | 2.89440i | −0.407872 | + | 0.132526i | ||||
\(478\) | −0.136653 | − | 0.188087i | −0.00625037 | − | 0.00860289i | ||||
\(479\) | −31.5123 | + | 22.8950i | −1.43983 | + | 1.04610i | −0.451756 | + | 0.892142i | \(0.649202\pi\) |
−0.988077 | + | 0.153958i | \(0.950798\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.05997 | − | 6.33993i | 0.0939264 | − | 0.289076i | ||||
\(482\) | −0.788781 | + | 1.08566i | −0.0359280 | + | 0.0494506i | ||||
\(483\) | 6.39855i | 0.291144i | ||||||||
\(484\) | 0.307235 | − | 0.672155i | 0.0139652 | − | 0.0305525i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.12474 | + | 0.817172i | 0.0510193 | + | 0.0370677i | ||||
\(487\) | 7.86723 | + | 2.55622i | 0.356498 | + | 0.115833i | 0.481790 | − | 0.876287i | \(-0.339987\pi\) |
−0.125292 | + | 0.992120i | \(0.539987\pi\) | |||||||
\(488\) | −39.0630 | + | 12.6923i | −1.76830 | + | 0.574555i | ||||
\(489\) | 19.0152 | − | 13.8153i | 0.859895 | − | 0.624750i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.74905 | − | 11.5384i | −0.169192 | − | 0.520720i | 0.830128 | − | 0.557572i | \(-0.188267\pi\) |
−0.999321 | + | 0.0368519i | \(0.988267\pi\) | |||||||
\(492\) | −0.484724 | − | 0.157496i | −0.0218531 | − | 0.00710049i | ||||
\(493\) | −18.4422 | + | 25.3835i | −0.830594 | + | 1.14322i | ||||
\(494\) | −0.311846 | −0.0140306 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −11.7757 | −0.528744 | ||||||||
\(497\) | −5.08857 | + | 7.00381i | −0.228253 | + | 0.314164i | ||||
\(498\) | 13.3836 | + | 4.34860i | 0.599734 | + | 0.194865i | ||||
\(499\) | 8.76312 | + | 26.9701i | 0.392291 | + | 1.20735i | 0.931051 | + | 0.364889i | \(0.118893\pi\) |
−0.538760 | + | 0.842459i | \(0.681107\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.487619 | + | 0.354276i | −0.0217852 | + | 0.0158279i | ||||
\(502\) | −31.0855 | + | 10.1003i | −1.38741 | + | 0.450798i | ||||
\(503\) | 14.5321 | + | 4.72177i | 0.647955 | + | 0.210533i | 0.614512 | − | 0.788907i | \(-0.289353\pi\) |
0.0334427 | + | 0.999441i | \(0.489353\pi\) | |||||||
\(504\) | 2.97046 | + | 2.15817i | 0.132315 | + | 0.0961324i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 19.4292 | − | 12.4818i | 0.863733 | − | 0.554883i | ||||
\(507\) | − | 10.9882i | − | 0.488005i | ||||||
\(508\) | −0.237899 | + | 0.327439i | −0.0105550 | + | 0.0145278i | ||||
\(509\) | 6.81363 | − | 20.9702i | 0.302009 | − | 0.929488i | −0.678768 | − | 0.734353i | \(-0.737486\pi\) |
0.980776 | − | 0.195134i | \(-0.0625143\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.95202 | + | 6.50402i | −0.396014 | + | 0.287721i | ||||
\(512\) | −13.9069 | − | 19.1413i | −0.614605 | − | 0.845932i | ||||
\(513\) | 0.150406 | − | 0.0488697i | 0.00664057 | − | 0.00215765i | ||||
\(514\) | −2.82803 | + | 8.70377i | −0.124739 | + | 0.383907i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.363693 | −0.0160107 | ||||||||
\(517\) | 17.2866 | − | 21.1334i | 0.760262 | − | 0.929444i | ||||
\(518\) | − | 8.34789i | − | 0.366785i | ||||||
\(519\) | 7.81825 | + | 5.68029i | 0.343183 | + | 0.249337i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.39725 | − | 22.7664i | −0.324079 | − | 0.997413i | −0.971855 | − | 0.235582i | \(-0.924300\pi\) |
0.647775 | − | 0.761831i | \(-0.275700\pi\) | |||||||
\(522\) | 5.12788 | + | 7.05792i | 0.224441 | + | 0.308917i | ||||
\(523\) | −14.8957 | − | 20.5022i | −0.651344 | − | 0.896498i | 0.347812 | − | 0.937564i | \(-0.386925\pi\) |
−0.999156 | + | 0.0410660i | \(0.986925\pi\) | |||||||
\(524\) | −0.388819 | − | 1.19666i | −0.0169856 | − | 0.0522764i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 14.0073 | + | 10.1769i | 0.610749 | + | 0.443735i | ||||
\(527\) | 15.2491i | 0.664260i | ||||||||
\(528\) | 0.733212 | − | 12.7849i | 0.0319089 | − | 0.556390i | ||||
\(529\) | −2.08298 | −0.0905642 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.50256 | − | 7.70209i | 0.108602 | − | 0.334242i | ||||
\(532\) | 0.0129102 | − | 0.00419478i | 0.000559729 | − | 0.000181867i | ||||
\(533\) | −6.32438 | − | 8.70476i | −0.273939 | − | 0.377045i | ||||
\(534\) | −12.4224 | + | 9.02542i | −0.537571 | + | 0.390568i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6.55732 | + | 20.1814i | −0.283233 | + | 0.871702i | ||||
\(537\) | −0.702822 | + | 0.967351i | −0.0303290 | + | 0.0417443i | ||||
\(538\) | 28.8797i | 1.24509i | ||||||||
\(539\) | −4.52293 | − | 17.2187i | −0.194816 | − | 0.741663i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.3669 | + | 20.6097i | 1.21959 | + | 0.886082i | 0.996066 | − | 0.0886168i | \(-0.0282447\pi\) |
0.223522 | + | 0.974699i | \(0.428245\pi\) | |||||||
\(542\) | −19.0270 | − | 6.18224i | −0.817279 | − | 0.265550i | ||||
\(543\) | 14.8118 | − | 4.81265i | 0.635636 | − | 0.206531i | ||||
\(544\) | −1.53672 | + | 1.11649i | −0.0658862 | + | 0.0478692i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.778498 | + | 2.39597i | 0.0333166 | + | 0.102538i | ||||
\(547\) | −1.05364 | − | 0.342349i | −0.0450505 | − | 0.0146378i | 0.286405 | − | 0.958109i | \(-0.407540\pi\) |
−0.331456 | + | 0.943471i | \(0.607540\pi\) | |||||||
\(548\) | 0.119941 | − | 0.165085i | 0.00512363 | − | 0.00705207i | ||||
\(549\) | 14.2917 | 0.609956 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.992388 | 0.0422771 | ||||||||
\(552\) | −8.46024 | + | 11.6445i | −0.360092 | + | 0.495624i | ||||
\(553\) | 3.09321 | + | 1.00505i | 0.131537 | + | 0.0427389i | ||||
\(554\) | −7.51273 | − | 23.1218i | −0.319185 | − | 0.982352i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.120228 | + | 0.0873504i | −0.00509878 | + | 0.00370448i | ||||
\(557\) | 5.15461 | − | 1.67483i | 0.218408 | − | 0.0709650i | −0.197769 | − | 0.980249i | \(-0.563370\pi\) |
0.416177 | + | 0.909284i | \(0.363370\pi\) | |||||||
\(558\) | 4.03250 | + | 1.31024i | 0.170709 | + | 0.0554669i | ||||
\(559\) | −6.21159 | − | 4.51299i | −0.262722 | − | 0.190879i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.5559 | − | 0.949482i | −0.698991 | − | 0.0400872i | ||||
\(562\) | 26.2564i | 1.10756i | ||||||||
\(563\) | −19.2469 | + | 26.4911i | −0.811161 | + | 1.11647i | 0.179982 | + | 0.983670i | \(0.442396\pi\) |
−0.991143 | + | 0.132798i | \(0.957604\pi\) | |||||||
\(564\) | −0.170911 | + | 0.526011i | −0.00719667 | + | 0.0221491i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −15.2755 | + | 11.0983i | −0.642077 | + | 0.466496i | ||||
\(567\) | −0.750949 | − | 1.03359i | −0.0315369 | − | 0.0434068i | ||||
\(568\) | −18.5211 | + | 6.01786i | −0.777126 | + | 0.252504i | ||||
\(569\) | 1.08692 | − | 3.34521i | 0.0455662 | − | 0.140238i | −0.925685 | − | 0.378295i | \(-0.876510\pi\) |
0.971251 | + | 0.238057i | \(0.0765104\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −36.0252 | −1.50761 | −0.753804 | − | 0.657099i | \(-0.771783\pi\) | ||||
−0.753804 | + | 0.657099i | \(0.771783\pi\) | |||||||
\(572\) | −0.200107 | + | 0.244637i | −0.00836691 | + | 0.0102288i | ||||
\(573\) | − | 18.4016i | − | 0.768738i | ||||||
\(574\) | −10.9007 | − | 7.91984i | −0.454988 | − | 0.330568i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.54951 | + | 7.84658i | 0.106230 | + | 0.326941i | ||||
\(577\) | −9.14009 | − | 12.5803i | −0.380507 | − | 0.523723i | 0.575212 | − | 0.818005i | \(-0.304920\pi\) |
−0.955719 | + | 0.294281i | \(0.904920\pi\) | |||||||
\(578\) | −6.53738 | − | 8.99793i | −0.271919 | − | 0.374265i | ||||
\(579\) | −0.484535 | − | 1.49124i | −0.0201366 | − | 0.0619740i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.4622 | − | 7.60120i | −0.434043 | − | 0.315351i | ||||
\(582\) | − | 8.91428i | − | 0.369509i | ||||||
\(583\) | −16.7907 | − | 26.1364i | −0.695399 | − | 1.08246i | ||||
\(584\) | −24.8912 | −1.03001 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.55030 | + | 26.3151i | −0.353210 | + | 1.08707i | ||||
\(587\) | 23.0730 | − | 7.49687i | 0.952324 | − | 0.309429i | 0.208665 | − | 0.977987i | \(-0.433088\pi\) |
0.743660 | + | 0.668558i | \(0.233088\pi\) | |||||||
\(588\) | 0.211977 | + | 0.291762i | 0.00874180 | + | 0.0120320i | ||||
\(589\) | 0.390201 | − | 0.283498i | 0.0160780 | − | 0.0116813i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.46287 | − | 7.57992i | 0.101309 | − | 0.311796i | ||||
\(592\) | 10.6665 | − | 14.6812i | 0.438390 | − | 0.603392i | ||||
\(593\) | − | 27.4019i | − | 1.12526i | −0.826709 | − | 0.562630i | \(-0.809790\pi\) | ||
0.826709 | − | 0.562630i | \(-0.190210\pi\) | |||||||
\(594\) | −1.67361 | + | 4.29651i | −0.0686691 | + | 0.176288i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.0805107 | + | 0.0584945i | 0.00329785 | + | 0.00239603i | ||||
\(597\) | 3.35857 | + | 1.09127i | 0.137457 | + | 0.0446625i | ||||
\(598\) | −9.39245 | + | 3.05179i | −0.384086 | + | 0.124797i | ||||
\(599\) | 8.63810 | − | 6.27594i | 0.352943 | − | 0.256428i | −0.397160 | − | 0.917750i | \(-0.630004\pi\) |
0.750103 | + | 0.661321i | \(0.230004\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.41967 | + | 10.5247i | 0.139491 | + | 0.429310i | 0.996262 | − | 0.0863885i | \(-0.0275326\pi\) |
−0.856770 | + | 0.515698i | \(0.827533\pi\) | |||||||
\(602\) | −9.14430 | − | 2.97116i | −0.372694 | − | 0.121096i | ||||
\(603\) | 4.33998 | − | 5.97348i | 0.176738 | − | 0.243259i | ||||
\(604\) | −0.606953 | −0.0246966 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −12.1945 | −0.495370 | ||||||||
\(607\) | −0.302426 | + | 0.416254i | −0.0122751 | + | 0.0168952i | −0.815110 | − | 0.579306i | \(-0.803324\pi\) |
0.802835 | + | 0.596201i | \(0.203324\pi\) | |||||||
\(608\) | 0.0571387 | + | 0.0185655i | 0.00231728 | + | 0.000752930i | ||||
\(609\) | −2.47741 | − | 7.62469i | −0.100390 | − | 0.308968i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.44619 | + | 6.86306i | −0.382152 | + | 0.277650i | ||||
\(612\) | 0.319487 | − | 0.103808i | 0.0129145 | − | 0.00419618i | ||||
\(613\) | −18.1630 | − | 5.90150i | −0.733595 | − | 0.238360i | −0.0816877 | − | 0.996658i | \(-0.526031\pi\) |
−0.651908 | + | 0.758298i | \(0.726031\pi\) | |||||||
\(614\) | 16.7985 | + | 12.2048i | 0.677932 | + | 0.492546i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.42004 | + | 11.3472i | −0.178088 | + | 0.457190i | ||||
\(617\) | − | 4.70745i | − | 0.189515i | −0.995500 | − | 0.0947573i | \(-0.969792\pi\) | ||
0.995500 | − | 0.0947573i | \(-0.0302075\pi\) | |||||||
\(618\) | 9.45194 | − | 13.0095i | 0.380213 | − | 0.523318i | ||||
\(619\) | −11.5477 | + | 35.5402i | −0.464141 | + | 1.42848i | 0.395919 | + | 0.918286i | \(0.370426\pi\) |
−0.860060 | + | 0.510194i | \(0.829574\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.05179 | − | 2.94380i | 0.162593 | − | 0.118131i | ||||
\(622\) | −4.08341 | − | 5.62033i | −0.163730 | − | 0.225355i | ||||
\(623\) | 13.4200 | − | 4.36041i | 0.537660 | − | 0.174696i | ||||
\(624\) | −1.69232 | + | 5.20843i | −0.0677471 | + | 0.208504i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −13.0635 | −0.522123 | ||||||||
\(627\) | 0.283498 | + | 0.441294i | 0.0113218 | + | 0.0176236i | ||||
\(628\) | − | 1.18500i | − | 0.0472867i | ||||||
\(629\) | −19.0115 | − | 13.8127i | −0.758040 | − | 0.550748i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.9908 | + | 33.8262i | 0.437536 | + | 1.34660i | 0.890465 | + | 0.455052i | \(0.150379\pi\) |
−0.452928 | + | 0.891547i | \(0.649621\pi\) | |||||||
\(632\) | 4.30036 | + | 5.91893i | 0.171059 | + | 0.235443i | ||||
\(633\) | 11.9056 | + | 16.3867i | 0.473205 | + | 0.651311i | ||||
\(634\) | 0.924756 | + | 2.84611i | 0.0367268 | + | 0.113033i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.509110 | + | 0.369890i | 0.0201875 | + | 0.0146671i | ||||
\(637\) | 7.61344i | 0.301656i | ||||||||
\(638\) | −18.3196 | + | 22.3963i | −0.725281 | + | 0.886678i | ||||
\(639\) | 6.77618 | 0.268062 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.77305 | − | 11.6123i | 0.149027 | − | 0.458657i | −0.848480 | − | 0.529227i | \(-0.822482\pi\) |
0.997507 | + | 0.0705705i | \(0.0224820\pi\) | |||||||
\(642\) | 20.2916 | − | 6.59313i | 0.800844 | − | 0.260210i | ||||
\(643\) | −12.3197 | − | 16.9567i | −0.485843 | − | 0.668705i | 0.493772 | − | 0.869591i | \(-0.335618\pi\) |
−0.979615 | + | 0.200886i | \(0.935618\pi\) | |||||||
\(644\) | 0.347790 | − | 0.252684i | 0.0137048 | − | 0.00995714i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.339707 | + | 1.04551i | −0.0133656 | + | 0.0411351i | ||||
\(647\) | 8.74424 | − | 12.0354i | 0.343772 | − | 0.473161i | −0.601767 | − | 0.798672i | \(-0.705536\pi\) |
0.945538 | + | 0.325511i | \(0.105536\pi\) | |||||||
\(648\) | − | 2.87392i | − | 0.112898i | ||||||
\(649\) | 26.8155 | + | 1.53787i | 1.05260 | + | 0.0603666i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.15227 | − | 2.29026i | −0.123547 | − | 0.0897622i | ||||
\(652\) | −1.50185 | − | 0.487980i | −0.0588169 | − | 0.0191108i | ||||
\(653\) | −11.5370 | + | 3.74861i | −0.451479 | + | 0.146694i | −0.525926 | − | 0.850531i | \(-0.676281\pi\) |
0.0744465 | + | 0.997225i | \(0.476281\pi\) | |||||||
\(654\) | −16.1968 | + | 11.7676i | −0.633344 | + | 0.460151i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −9.05120 | − | 27.8567i | −0.353390 | − | 1.08762i | ||||
\(657\) | 8.23717 | + | 2.67642i | 0.321362 | + | 0.104417i | ||||
\(658\) | −8.59443 | + | 11.8292i | −0.335046 | + | 0.461151i | ||||
\(659\) | −7.49994 | −0.292156 | −0.146078 | − | 0.989273i | \(-0.546665\pi\) | ||||
−0.146078 | + | 0.989273i | \(0.546665\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.65248 | 0.375438 | 0.187719 | − | 0.982223i | \(-0.439891\pi\) | ||||
0.187719 | + | 0.982223i | \(0.439891\pi\) | |||||||
\(662\) | 15.9443 | − | 21.9455i | 0.619694 | − | 0.852936i | ||||
\(663\) | 6.74473 | + | 2.19149i | 0.261943 | + | 0.0851106i | ||||
\(664\) | −8.98936 | − | 27.6664i | −0.348855 | − | 1.07366i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.28619 | + | 3.84064i | −0.204836 | + | 0.148822i | ||||
\(667\) | 29.8896 | − | 9.71171i | 1.15733 | − | 0.376039i | ||||
\(668\) | 0.0385130 | + | 0.0125136i | 0.00149011 | + | 0.000484167i | ||||
\(669\) | 18.2433 | + | 13.2546i | 0.705328 | + | 0.512451i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.0424 | + | 45.8451i | 0.464890 | + | 1.76983i | ||||
\(672\) | − | 0.485354i | − | 0.0187229i | ||||||
\(673\) | −14.3711 | + | 19.7801i | −0.553966 | + | 0.762469i | −0.990544 | − | 0.137198i | \(-0.956190\pi\) |
0.436578 | + | 0.899667i | \(0.356190\pi\) | |||||||
\(674\) | 13.5778 | − | 41.7881i | 0.522997 | − | 1.60962i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.597260 | + | 0.433935i | −0.0229715 | + | 0.0166898i | ||||
\(677\) | −27.4728 | − | 37.8130i | −1.05586 | − | 1.45327i | −0.883613 | − | 0.468219i | \(-0.844896\pi\) |
−0.172251 | − | 0.985053i | \(-0.555104\pi\) | |||||||
\(678\) | −25.6040 | + | 8.31925i | −0.983317 | + | 0.319499i | ||||
\(679\) | −2.53143 | + | 7.79093i | −0.0971472 | + | 0.298988i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18.8062 | 0.720654 | ||||||||
\(682\) | −0.805166 | + | 14.0395i | −0.0308314 | + | 0.537600i | ||||
\(683\) | 28.1941i | 1.07882i | 0.842045 | + | 0.539408i | \(0.181352\pi\) | ||||
−0.842045 | + | 0.539408i | \(0.818648\pi\) | |||||||
\(684\) | −0.00859593 | − | 0.00624531i | −0.000328674 | − | 0.000238795i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 6.78829 | + | 20.8922i | 0.259178 | + | 0.797668i | ||||
\(687\) | 14.0081 | + | 19.2805i | 0.534442 | + | 0.735596i | ||||
\(688\) | −12.2854 | − | 16.9094i | −0.468376 | − | 0.644664i | ||||
\(689\) | 4.10532 | + | 12.6349i | 0.156400 | + | 0.481350i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.38225 | − | 6.81661i | −0.356918 | − | 0.259316i | 0.394848 | − | 0.918747i | \(-0.370797\pi\) |
−0.751765 | + | 0.659431i | \(0.770797\pi\) | |||||||
\(692\) | − | 0.649276i | − | 0.0246818i | ||||||
\(693\) | 2.68281 | − | 3.27981i | 0.101911 | − | 0.124590i | ||||
\(694\) | 13.0450 | 0.495180 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5.57289 | − | 17.1516i | 0.211240 | − | 0.650130i | ||||
\(697\) | −36.0734 | + | 11.7210i | −1.36638 | + | 0.443963i | ||||
\(698\) | 20.2766 | + | 27.9083i | 0.767481 | + | 1.05635i | ||||
\(699\) | −8.16446 | + | 5.93183i | −0.308808 | + | 0.224362i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.3415 | + | 34.9056i | −0.428363 | + | 1.31837i | 0.471373 | + | 0.881934i | \(0.343759\pi\) |
−0.899737 | + | 0.436433i | \(0.856241\pi\) | |||||||
\(702\) | 1.15905 | − | 1.59529i | 0.0437455 | − | 0.0602105i | ||||
\(703\) | 0.743272i | 0.0280330i | ||||||||
\(704\) | −23.0221 | + | 14.7899i | −0.867676 | + | 0.557417i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −21.9086 | − | 15.9175i | −0.824540 | − | 0.599064i | ||||
\(707\) | 10.6578 | + | 3.46294i | 0.400829 | + | 0.130237i | ||||
\(708\) | −0.517471 | + | 0.168137i | −0.0194478 | + | 0.00631896i | ||||
\(709\) | 29.5214 | − | 21.4486i | 1.10870 | − | 0.805518i | 0.126242 | − | 0.991999i | \(-0.459708\pi\) |
0.982458 | + | 0.186482i | \(0.0597085\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.786672 | − | 2.42113i | −0.0295025 | − | 0.0907994i | ||||
\(712\) | 30.1880 | + | 9.80868i | 1.13134 | + | 0.367596i | ||||
\(713\) | 8.97804 | − | 12.3572i | 0.336230 | − | 0.462781i | ||||
\(714\) | 8.88090 | 0.332359 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.0803349 | 0.00300225 | ||||||||
\(717\) | 0.0982934 | − | 0.135289i | 0.00367084 | − | 0.00505247i | ||||
\(718\) | 39.3624 | + | 12.7896i | 1.46899 | + | 0.477304i | ||||
\(719\) | 2.88278 | + | 8.87229i | 0.107510 | + | 0.330881i | 0.990311 | − | 0.138865i | \(-0.0443455\pi\) |
−0.882802 | + | 0.469746i | \(0.844346\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.9552 | + | 8.68596i | −0.445235 | + | 0.323482i | ||||
\(722\) | −25.0890 | + | 8.15190i | −0.933715 | + | 0.303382i | ||||
\(723\) | −0.918013 | − | 0.298281i | −0.0341413 | − | 0.0110932i | ||||
\(724\) | −0.846520 | − | 0.615033i | −0.0314607 | − | 0.0228575i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −15.1926 | − | 1.74834i | −0.563849 | − | 0.0648869i | ||||
\(727\) | − | 8.46883i | − | 0.314091i | −0.987591 | − | 0.157046i | \(-0.949803\pi\) | ||
0.987591 | − | 0.157046i | \(-0.0501970\pi\) | |||||||
\(728\) | 3.06107 | − | 4.21320i | 0.113451 | − | 0.156152i | ||||
\(729\) | −0.309017 | + | 0.951057i | −0.0114451 | + | 0.0352243i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −21.8970 | + | 15.9091i | −0.809891 | + | 0.588420i | ||||
\(732\) | −0.564392 | − | 0.776819i | −0.0208605 | − | 0.0287121i | ||||
\(733\) | 27.6253 | − | 8.97601i | 1.02036 | − | 0.331537i | 0.249391 | − | 0.968403i | \(-0.419770\pi\) |
0.770974 | + | 0.636866i | \(0.219770\pi\) | |||||||
\(734\) | −2.76498 | + | 8.50972i | −0.102057 | + | 0.314100i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.90264 | 0.0701322 | ||||||||
\(737\) | 22.8187 | + | 8.88851i | 0.840536 | + | 0.327412i | ||||
\(738\) | 10.5464i | 0.388220i | ||||||||
\(739\) | −11.1281 | − | 8.08505i | −0.409354 | − | 0.297413i | 0.363986 | − | 0.931404i | \(-0.381416\pi\) |
−0.773340 | + | 0.633991i | \(0.781416\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.0693151 | − | 0.213330i | −0.00254636 | − | 0.00783688i | ||||
\(742\) | 9.77872 | + | 13.4593i | 0.358988 | + | 0.494105i | ||||
\(743\) | −20.5217 | − | 28.2456i | −0.752867 | − | 1.03623i | −0.997774 | − | 0.0666857i | \(-0.978758\pi\) |
0.244907 | − | 0.969547i | \(-0.421242\pi\) | |||||||
\(744\) | −2.70851 | − | 8.33593i | −0.0992988 | − | 0.305610i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −23.4985 | − | 17.0727i | −0.860343 | − | 0.625075i | ||||
\(747\) | 10.1221i | 0.370349i | ||||||||
\(748\) | 0.602198 | + | 0.937384i | 0.0220185 | + | 0.0342741i | ||||
\(749\) | −19.6068 | −0.716416 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.82903 | − | 21.0176i | 0.249195 | − | 0.766943i | −0.745723 | − | 0.666256i | \(-0.767896\pi\) |
0.994918 | − | 0.100687i | \(-0.0321042\pi\) | |||||||
\(752\) | −30.2294 | + | 9.82214i | −1.10235 | + | 0.358177i | ||||
\(753\) | −13.8189 | − | 19.0201i | −0.503590 | − | 0.693133i | ||||
\(754\) | 10.0107 | − | 7.27320i | 0.364568 | − | 0.264874i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.0265248 | + | 0.0816349i | −0.000964697 | + | 0.00296903i | ||||
\(757\) | −26.4680 | + | 36.4300i | −0.961994 | + | 1.32407i | −0.0160057 | + | 0.999872i | \(0.505095\pi\) |
−0.945989 | + | 0.324200i | \(0.894905\pi\) | |||||||
\(758\) | − | 19.7404i | − | 0.717004i | ||||||
\(759\) | 12.8572 | + | 10.5169i | 0.466687 | + | 0.381739i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.1831 | − | 19.7496i | −0.985385 | − | 0.715924i | −0.0264794 | − | 0.999649i | \(-0.508430\pi\) |
−0.958906 | + | 0.283725i | \(0.908430\pi\) | |||||||
\(762\) | 7.96521 | + | 2.58805i | 0.288549 | + | 0.0937553i | ||||
\(763\) | 17.4974 | − | 5.68525i | 0.633449 | − | 0.205820i | ||||
\(764\) | −1.00021 | + | 0.726694i | −0.0361863 | + | 0.0262909i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 11.3754 | + | 35.0099i | 0.411011 | + | 1.26496i | ||||
\(767\) | −10.9244 | − | 3.54955i | −0.394457 | − | 0.128167i | ||||
\(768\) | 0.946698 | − | 1.30302i | 0.0341610 | − | 0.0470186i | ||||
\(769\) | −24.6086 | −0.887408 | −0.443704 | − | 0.896173i | \(-0.646336\pi\) | ||||
−0.443704 | + | 0.896173i | \(0.646336\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.58273 | −0.237071 | ||||||||
\(772\) | −0.0619211 | + | 0.0852271i | −0.00222859 | + | 0.00306739i | ||||
\(773\) | 22.5225 | + | 7.31802i | 0.810080 | + | 0.263211i | 0.684632 | − | 0.728889i | \(-0.259963\pi\) |
0.125448 | + | 0.992100i | \(0.459963\pi\) | |||||||
\(774\) | 2.32560 | + | 7.15746i | 0.0835919 | + | 0.257269i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −14.9081 | + | 10.8314i | −0.535171 | + | 0.388824i | ||||
\(777\) | 5.71068 | − | 1.85551i | 0.204870 | − | 0.0665662i | ||||
\(778\) | −48.2561 | − | 15.6794i | −1.73006 | − | 0.562132i | ||||
\(779\) | 0.970569 | + | 0.705160i | 0.0347742 | + | 0.0252650i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.70968 | + | 21.7367i | 0.204308 | + | 0.777799i | ||||
\(782\) | 34.8141i | 1.24495i | ||||||||
\(783\) | −3.68844 | + | 5.07670i | −0.131814 | + | 0.181426i | ||||
\(784\) | −6.40454 | + | 19.7112i | −0.228734 | + | 0.703970i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −21.0640 | + | 15.3039i | −0.751327 | + | 0.545871i | ||||
\(787\) | 10.8276 | + | 14.9029i | 0.385963 | + | 0.531232i | 0.957152 | − | 0.289586i | \(-0.0935177\pi\) |
−0.571189 | + | 0.820819i | \(0.693518\pi\) | |||||||
\(788\) | −0.509263 | + | 0.165470i | −0.0181418 | + | 0.00589461i | ||||
\(789\) | −3.84845 | + | 11.8443i | −0.137008 | + | 0.421668i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24.7399 | 0.879651 | ||||||||
\(792\) | 9.21897 | − | 2.42159i | 0.327582 | − | 0.0860476i | ||||
\(793\) | − | 20.2709i | − | 0.719840i | ||||||
\(794\) | 9.04257 | + | 6.56981i | 0.320909 | + | 0.233154i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.0733175 | − | 0.225648i | −0.00259867 | − | 0.00799788i | ||||
\(797\) | 3.82451 | + | 5.26399i | 0.135471 | + | 0.186460i | 0.871363 | − | 0.490639i | \(-0.163237\pi\) |
−0.735892 | + | 0.677099i | \(0.763237\pi\) | |||||||
\(798\) | −0.165106 | − | 0.227249i | −0.00584470 | − | 0.00804453i | ||||
\(799\) | 12.7193 | + | 39.1460i | 0.449977 | + | 1.38489i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.93534 | − | 6.49191i | −0.315715 | − | 0.229380i | ||||
\(802\) | 39.0526i | 1.37900i | ||||||||
\(803\) | −1.64471 | + | 28.6784i | −0.0580404 | + | 1.01204i | ||||
\(804\) | −0.496074 | −0.0174952 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.85840 | − | 5.71956i | 0.0654593 | − | 0.201463i | ||||
\(807\) | −19.7562 | + | 6.41919i | −0.695453 | + | 0.225966i | ||||
\(808\) | 14.8171 | + | 20.3940i | 0.521264 | + | 0.717459i | ||||
\(809\) | 9.58727 | − | 6.96556i | 0.337071 | − | 0.244896i | −0.406354 | − | 0.913716i | \(-0.633200\pi\) |
0.743425 | + | 0.668819i | \(0.233200\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.32193 | − | 7.14616i | 0.0815339 | − | 0.250936i | −0.901977 | − | 0.431784i | \(-0.857884\pi\) |
0.983511 | + | 0.180848i | \(0.0578843\pi\) | |||||||
\(812\) | −0.316601 | + | 0.435763i | −0.0111105 | + | 0.0152923i | ||||
\(813\) | − | 14.3903i | − | 0.504688i | ||||||
\(814\) | −16.7742 | − | 13.7209i | −0.587936 | − | 0.480917i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 15.6185 | + | 11.3475i | 0.546758 | + | 0.397243i | ||||
\(817\) | 0.814182 | + | 0.264544i | 0.0284846 | + | 0.00925521i | ||||
\(818\) | 7.90618 | − | 2.56887i | 0.276433 | − | 0.0898185i | ||||
\(819\) | −1.46601 | + | 1.06512i | −0.0512266 | + | 0.0372183i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.5376 | − | 35.5092i | −0.402666 | − | 1.23928i | −0.922829 | − | 0.385211i | \(-0.874129\pi\) |
0.520163 | − | 0.854067i | \(-0.325871\pi\) | |||||||
\(822\) | −4.01581 | − | 1.30482i | −0.140067 | − | 0.0455107i | ||||
\(823\) | 25.3040 | − | 34.8280i | 0.882043 | − | 1.21403i | −0.0938075 | − | 0.995590i | \(-0.529904\pi\) |
0.975851 | − | 0.218438i | \(-0.0700962\pi\) | |||||||
\(824\) | −33.2416 | −1.15803 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −14.3843 | −0.500495 | ||||||||
\(827\) | −11.7736 | + | 16.2049i | −0.409407 | + | 0.563500i | −0.963074 | − | 0.269238i | \(-0.913228\pi\) |
0.553667 | + | 0.832738i | \(0.313228\pi\) | |||||||
\(828\) | −0.320017 | − | 0.103980i | −0.0111214 | − | 0.00361355i | ||||
\(829\) | 14.8083 | + | 45.5753i | 0.514314 | + | 1.58289i | 0.784527 | + | 0.620094i | \(0.212906\pi\) |
−0.270213 | + | 0.962800i | \(0.587094\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.1474 | − | 10.2787i | 0.490770 | − | 0.356565i | ||||
\(832\) | 11.1293 | − | 3.61613i | 0.385840 | − | 0.125367i | ||||
\(833\) | 25.5252 | + | 8.29365i | 0.884396 | + | 0.287358i | ||||
\(834\) | 2.48783 | + | 1.80752i | 0.0861467 | + | 0.0625892i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.0127907 | − | 0.0328364i | 0.000442376 | − | 0.00113567i | ||||
\(837\) | 3.04981i | 0.105417i | ||||||||
\(838\) | −12.6423 | + | 17.4006i | −0.436720 | + | 0.601093i | ||||
\(839\) | −0.686305 | + | 2.11223i | −0.0236939 | + | 0.0729222i | −0.962204 | − | 0.272329i | \(-0.912206\pi\) |
0.938510 | + | 0.345251i | \(0.112206\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.39554 | + | 6.09971i | −0.289501 | + | 0.210335i | ||||
\(842\) | 28.2534 | + | 38.8875i | 0.973677 | + | 1.34015i | ||||
\(843\) | −17.9616 | + | 5.83609i | −0.618632 | + | 0.201006i | ||||
\(844\) | 0.420526 | − | 1.29425i | 0.0144751 | − | 0.0445498i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 11.4447 | 0.393479 | ||||||||
\(847\) | 12.7816 | + | 5.84231i | 0.439180 | + | 0.200744i | ||||
\(848\) | 36.1651i | 1.24191i | ||||||||
\(849\) | −10.9875 | − | 7.98291i | −0.377091 | − | 0.273973i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.27381 | + | 22.3865i | 0.249343 | + | 0.767398i | ||||
\(852\) | −0.267597 | − | 0.368316i | −0.00916772 | − | 0.0126183i | ||||
\(853\) | −3.74514 | − | 5.15474i | −0.128231 | − | 0.176495i | 0.740074 | − | 0.672525i | \(-0.234790\pi\) |
−0.868305 | + | 0.496030i | \(0.834790\pi\) | |||||||
\(854\) | −7.84430 | − | 24.1423i | −0.268426 | − | 0.826131i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −35.6818 | − | 25.9243i | −1.21958 | − | 0.886075i | ||||
\(857\) | 35.9060i | 1.22653i | 0.789878 | + | 0.613263i | \(0.210144\pi\) | ||||
−0.789878 | + | 0.613263i | \(0.789856\pi\) | |||||||
\(858\) | 6.09402 | + | 2.37379i | 0.208046 | + | 0.0810399i | ||||
\(859\) | −56.4697 | −1.92672 | −0.963360 | − | 0.268212i | \(-0.913567\pi\) | ||||
−0.963360 | + | 0.268212i | \(0.913567\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.99492 | − | 9.21742i | 0.102067 | − | 0.314129i | ||||
\(862\) | 4.44332 | − | 1.44372i | 0.151340 | − | 0.0491733i | ||||
\(863\) | −18.2649 | − | 25.1395i | −0.621745 | − | 0.855759i | 0.375733 | − | 0.926728i | \(-0.377391\pi\) |
−0.997479 | + | 0.0709688i | \(0.977391\pi\) | |||||||
\(864\) | −0.307344 | + | 0.223298i | −0.0104560 | + | 0.00759676i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.58003 | + | 4.86283i | −0.0536915 | + | 0.165246i | ||||
\(867\) | 4.70228 | − | 6.47214i | 0.159698 | − | 0.219805i | ||||
\(868\) | 0.261784i | 0.00888552i | ||||||||
\(869\) | 7.10365 | − | 4.56356i | 0.240975 | − | 0.154808i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.47257 | − | 6.15568i | −0.287082 | − | 0.208577i | ||||
\(872\) | 39.3601 | + | 12.7889i | 1.33290 | + | 0.433086i | ||||
\(873\) | 6.09814 | − | 1.98141i | 0.206391 | − | 0.0670604i | ||||
\(874\) | 0.890840 | − | 0.647233i | 0.0301331 | − | 0.0218930i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.179817 | − | 0.553421i | −0.00607546 | − | 0.0186983i | ||||
\(877\) | 15.9991 | + | 5.19841i | 0.540250 | + | 0.175538i | 0.566416 | − | 0.824120i | \(-0.308330\pi\) |
−0.0261655 | + | 0.999658i | \(0.508330\pi\) | |||||||
\(878\) | −1.27014 | + | 1.74820i | −0.0428653 | + | 0.0589990i | ||||
\(879\) | −19.9023 | −0.671289 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.5633 | 0.894940 | 0.447470 | − | 0.894299i | \(-0.352325\pi\) | ||||
0.447470 | + | 0.894299i | \(0.352325\pi\) | |||||||
\(882\) | 4.38639 | − | 6.03734i | 0.147697 | − | 0.203288i | ||||
\(883\) | 51.7129 | + | 16.8026i | 1.74028 | + | 0.565451i | 0.994870 | − | 0.101157i | \(-0.0322544\pi\) |
0.745409 | + | 0.666608i | \(0.232254\pi\) | |||||||
\(884\) | −0.147237 | − | 0.453150i | −0.00495213 | − | 0.0152411i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 23.8511 | − | 17.3289i | 0.801295 | − | 0.582175i | ||||
\(887\) | 39.2084 | − | 12.7396i | 1.31649 | − | 0.427753i | 0.435202 | − | 0.900333i | \(-0.356677\pi\) |
0.881288 | + | 0.472580i | \(0.156677\pi\) | |||||||
\(888\) | 12.8461 | + | 4.17395i | 0.431086 | + | 0.140068i | ||||
\(889\) | −6.22652 | − | 4.52383i | −0.208831 | − | 0.151724i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.31118 | − | 0.189896i | −0.110929 | − | 0.00636177i | ||||
\(892\) | − | 1.51504i | − | 0.0507273i | ||||||
\(893\) | 0.765222 | − | 1.05324i | 0.0256072 | − | 0.0352453i | ||||
\(894\) | 0.636350 | − | 1.95848i | 0.0212827 | − | 0.0655015i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 11.0702 | − | 8.04293i | 0.369828 | − | 0.268696i | ||||
\(897\) | −4.17538 | − | 5.74692i | −0.139412 | − | 0.191884i | ||||
\(898\) | −19.9794 | + | 6.49171i | −0.666722 | + | 0.216631i | ||||
\(899\) | −5.91398 | + | 18.2013i | −0.197242 | + | 0.607049i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 46.8324 | 1.56021 | ||||||||
\(902\) | −33.8309 | + | 8.88654i | −1.12645 | + | 0.295889i | ||||
\(903\) | − | 6.91591i | − | 0.230147i | ||||||
\(904\) | 45.0235 | + | 32.7115i | 1.49746 | + | 1.08797i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3.88110 | + | 11.9448i | 0.128941 | + | 0.396840i | ||||
\(907\) | −24.9248 | − | 34.3060i | −0.827614 | − | 1.13911i | −0.988362 | − | 0.152117i | \(-0.951391\pi\) |
0.160748 | − | 0.986995i | \(-0.448609\pi\) | |||||||
\(908\) | −0.742671 | − | 1.02220i | −0.0246464 | − | 0.0339229i | ||||
\(909\) | −2.71052 | − | 8.34213i | −0.0899023 | − | 0.276691i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.48184 | + | 4.70933i | 0.214753 | + | 0.156027i | 0.689962 | − | 0.723846i | \(-0.257627\pi\) |
−0.475209 | + | 0.879873i | \(0.657627\pi\) | |||||||
\(912\) | − | 0.610619i | − | 0.0202196i | ||||||
\(913\) | −32.4698 | + | 8.52900i | −1.07459 | + | 0.282269i | ||||
\(914\) | 57.4234 | 1.89940 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.494789 | − | 1.52280i | 0.0163483 | − | 0.0503149i | ||||
\(917\) | 22.7555 | − | 7.39370i | 0.751452 | − | 0.244162i | ||||
\(918\) | −4.08586 | − | 5.62371i | −0.134854 | − | 0.185610i | ||||
\(919\) | 33.3587 | − | 24.2365i | 1.10040 | − | 0.799489i | 0.119277 | − | 0.992861i | \(-0.461942\pi\) |
0.981125 | + | 0.193372i | \(0.0619424\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.61530 | + | 14.2044i | −0.152079 | + | 0.468052i | ||||
\(922\) | 13.3328 | − | 18.3510i | 0.439092 | − | 0.604359i | ||||
\(923\) | − | 9.61110i | − | 0.316353i | ||||||
\(924\) | −0.284219 | − | 0.0162999i | −0.00935011 | − | 0.000536229i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 9.53672 | + | 6.92884i | 0.313396 | + | 0.227696i | ||||
\(927\) | 11.0005 | + | 3.57429i | 0.361305 | + | 0.117395i | ||||
\(928\) | −2.26724 | + | 0.736670i | −0.0744257 | + | 0.0241824i | ||||
\(929\) | −12.2921 | + | 8.93073i | −0.403291 | + | 0.293008i | −0.770880 | − | 0.636980i | \(-0.780183\pi\) |
0.367589 | + | 0.929988i | \(0.380183\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.262321 | − | 0.807341i | −0.00859723 | − | 0.0264595i | ||||
\(932\) | 0.644842 | + | 0.209522i | 0.0211225 | + | 0.00686312i | ||||
\(933\) | 2.93716 | − | 4.04266i | 0.0961583 | − | 0.132351i | ||||
\(934\) | −50.8375 | −1.66345 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.07627 | −0.133237 | ||||||||
\(937\) | 15.0011 | − | 20.6472i | 0.490064 | − | 0.674515i | −0.490336 | − | 0.871533i | \(-0.663126\pi\) |
0.980400 | + | 0.197019i | \(0.0631260\pi\) | |||||||
\(938\) | −12.4728 | − | 4.05265i | −0.407250 | − | 0.132324i | ||||
\(939\) | −2.90367 | − | 8.93658i | −0.0947577 | − | 0.291634i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.1857 | + | 19.0250i | −0.853629 | + | 0.620198i | −0.926144 | − | 0.377170i | \(-0.876897\pi\) |
0.0725154 | + | 0.997367i | \(0.476897\pi\) | |||||||
\(942\) | −23.3208 | + | 7.57737i | −0.759831 | + | 0.246884i | ||||
\(943\) | 36.1332 | + | 11.7404i | 1.17666 | + | 0.382320i | ||||
\(944\) | −25.2972 | − | 18.3795i | −0.823354 | − | 0.598202i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −21.0001 | + | 13.4910i | −0.682774 | + | 0.438631i | ||||
\(947\) | − | 40.1516i | − | 1.30475i | −0.757896 | − | 0.652375i | \(-0.773773\pi\) | ||
0.757896 | − | 0.652375i | \(-0.226227\pi\) | |||||||
\(948\) | −0.100533 | + | 0.138371i | −0.00326515 | + | 0.00449410i | ||||
\(949\) | 3.79614 | − | 11.6833i | 0.123228 | − | 0.379256i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.74144 | + | 1.26523i | −0.0564699 | + | 0.0410278i | ||||
\(952\) | −10.7908 | − | 14.8523i | −0.349733 | − | 0.481366i | ||||
\(953\) | 33.9064 | − | 11.0168i | 1.09833 | − | 0.356871i | 0.296873 | − | 0.954917i | \(-0.404056\pi\) |
0.801461 | + | 0.598046i | \(0.204056\pi\) | |||||||
\(954\) | 4.02396 | − | 12.3845i | 0.130281 | − | 0.400962i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.0112353 | −0.000363374 | ||||||||
\(957\) | −19.3930 | − | 7.55411i | −0.626886 | − | 0.244190i | ||||
\(958\) | − | 54.1524i | − | 1.74958i | ||||||
\(959\) | 3.13922 | + | 2.28077i | 0.101371 | + | 0.0736501i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.70525 | − | 20.6366i | −0.216298 | − | 0.665698i | ||||
\(962\) | 5.44743 | + | 7.49774i | 0.175632 | + | 0.241737i | ||||
\(963\) | 9.02054 | + | 12.4157i | 0.290683 | + | 0.400091i | ||||
\(964\) | 0.0200402 | + | 0.0616775i | 0.000645452 | + | 0.00198650i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −7.19671 | − | 5.22872i | −0.231550 | − | 0.168231i | ||||
\(967\) | − | 20.0622i | − | 0.645156i | −0.946543 | − | 0.322578i | \(-0.895451\pi\) | ||
0.946543 | − | 0.322578i | \(-0.104549\pi\) | |||||||
\(968\) | 15.5360 | + | 27.5322i | 0.499346 | + | 0.884918i | ||||
\(969\) | −0.790729 | −0.0254019 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.8646 | + | 39.5931i | −0.412844 | + | 1.27060i | 0.501321 | + | 0.865261i | \(0.332848\pi\) |
−0.914165 | + | 0.405342i | \(0.867152\pi\) | |||||||
\(972\) | 0.0638975 | − | 0.0207616i | 0.00204951 | − | 0.000665927i | ||||
\(973\) | −1.66104 | − | 2.28622i | −0.0532504 | − | 0.0732929i | ||||
\(974\) | −9.30396 | + | 6.75972i | −0.298118 | + | 0.216596i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 17.0522 | − | 52.4812i | 0.545827 | − | 1.67988i | ||||
\(977\) | 11.2104 | − | 15.4297i | 0.358651 | − | 0.493641i | −0.591121 | − | 0.806583i | \(-0.701315\pi\) |
0.949772 | + | 0.312942i | \(0.101315\pi\) | |||||||
\(978\) | 32.6766i | 1.04488i | ||||||||
\(979\) | 13.2958 | − | 34.1330i | 0.424934 | − | 1.09089i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.6502 | − | 8.46436i | −0.371962 | − | 0.270246i | ||||
\(982\) | 16.0413 | + | 5.21214i | 0.511899 | + | 0.166326i | ||||
\(983\) | 25.2566 | − | 8.20635i | 0.805559 | − | 0.261742i | 0.122843 | − | 0.992426i | \(-0.460799\pi\) |
0.682716 | + | 0.730684i | \(0.260799\pi\) | |||||||
\(984\) | 17.6378 | − | 12.8146i | 0.562271 | − | 0.408514i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −13.4794 | − | 41.4854i | −0.429272 | − | 1.32116i | ||||
\(987\) | −10.0025 | − | 3.25002i | −0.318384 | − | 0.103449i | ||||
\(988\) | −0.00885813 | + | 0.0121922i | −0.000281815 | + | 0.000387884i | ||||
\(989\) | 27.1111 | 0.862082 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.2494 | −0.770307 | −0.385153 | − | 0.922853i | \(-0.625851\pi\) | ||||
−0.385153 | + | 0.922853i | \(0.625851\pi\) | |||||||
\(992\) | −0.681018 | + | 0.937341i | −0.0216223 | + | 0.0297606i | ||||
\(993\) | 18.5566 | + | 6.02941i | 0.588877 | + | 0.191338i | ||||
\(994\) | −3.71924 | − | 11.4466i | −0.117967 | − | 0.363065i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.550182 | − | 0.399731i | 0.0174332 | − | 0.0126660i | ||||
\(997\) | −15.2755 | + | 4.96330i | −0.483779 | + | 0.157189i | −0.540745 | − | 0.841187i | \(-0.681857\pi\) |
0.0569657 | + | 0.998376i | \(0.481857\pi\) | |||||||
\(998\) | −37.4954 | − | 12.1830i | −1.18690 | − | 0.385646i | ||||
\(999\) | −3.80231 | − | 2.76254i | −0.120300 | − | 0.0874029i |
(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 | 825.2.bx.h.499.2 | 16 | ||
5.2 | odd | 4 | 825.2.n.k.301.1 | 8 | |||
5.3 | odd | 4 | 165.2.m.a.136.2 | yes | 8 | ||
5.4 | even | 2 | inner | 825.2.bx.h.499.3 | 16 | ||
11.3 | even | 5 | inner | 825.2.bx.h.124.3 | 16 | ||
15.8 | even | 4 | 495.2.n.d.136.1 | 8 | |||
55.3 | odd | 20 | 165.2.m.a.91.2 | ✓ | 8 | ||
55.14 | even | 10 | inner | 825.2.bx.h.124.2 | 16 | ||
55.17 | even | 20 | 9075.2.a.dj.1.1 | 4 | |||
55.27 | odd | 20 | 9075.2.a.cl.1.4 | 4 | |||
55.28 | even | 20 | 1815.2.a.o.1.4 | 4 | |||
55.38 | odd | 20 | 1815.2.a.x.1.1 | 4 | |||
55.47 | odd | 20 | 825.2.n.k.751.1 | 8 | |||
165.38 | even | 20 | 5445.2.a.be.1.4 | 4 | |||
165.83 | odd | 20 | 5445.2.a.bv.1.1 | 4 | |||
165.113 | even | 20 | 495.2.n.d.91.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.m.a.91.2 | ✓ | 8 | 55.3 | odd | 20 | ||
165.2.m.a.136.2 | yes | 8 | 5.3 | odd | 4 | ||
495.2.n.d.91.1 | 8 | 165.113 | even | 20 | |||
495.2.n.d.136.1 | 8 | 15.8 | even | 4 | |||
825.2.n.k.301.1 | 8 | 5.2 | odd | 4 | |||
825.2.n.k.751.1 | 8 | 55.47 | odd | 20 | |||
825.2.bx.h.124.2 | 16 | 55.14 | even | 10 | inner | ||
825.2.bx.h.124.3 | 16 | 11.3 | even | 5 | inner | ||
825.2.bx.h.499.2 | 16 | 1.1 | even | 1 | trivial | ||
825.2.bx.h.499.3 | 16 | 5.4 | even | 2 | inner | ||
1815.2.a.o.1.4 | 4 | 55.28 | even | 20 | |||
1815.2.a.x.1.1 | 4 | 55.38 | odd | 20 | |||
5445.2.a.be.1.4 | 4 | 165.38 | even | 20 | |||
5445.2.a.bv.1.1 | 4 | 165.83 | odd | 20 | |||
9075.2.a.cl.1.4 | 4 | 55.27 | odd | 20 | |||
9075.2.a.dj.1.1 | 4 | 55.17 | even | 20 |