Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [735,2,Mod(178,735)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(735, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 9, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("735.178");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 735 = 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 735.v (of order \(12\), 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: | \(5.86900454856\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 178.3 | ||
Character | \(\chi\) | \(=\) | 735.178 |
Dual form | 735.2.v.a.607.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).
\(n\) | \(346\) | \(442\) | \(491\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.737849 | − | 0.197706i | −0.521738 | − | 0.139799i | −0.0116677 | − | 0.999932i | \(-0.503714\pi\) |
−0.510071 | + | 0.860133i | \(0.670381\pi\) | |||||||
\(3\) | −0.258819 | − | 0.965926i | −0.149429 | − | 0.557678i | ||||
\(4\) | −1.22672 | − | 0.708245i | −0.613358 | − | 0.354123i | ||||
\(5\) | 1.19764 | − | 1.88830i | 0.535600 | − | 0.844472i | ||||
\(6\) | 0.763878i | 0.311852i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.84539 | + | 1.84539i | 0.652445 | + | 0.652445i | ||||
\(9\) | −0.866025 | + | 0.500000i | −0.288675 | + | 0.166667i | ||||
\(10\) | −1.25700 | + | 1.15650i | −0.397500 | + | 0.365717i | ||||
\(11\) | 1.92568 | − | 3.33538i | 0.580615 | − | 1.00565i | −0.414792 | − | 0.909916i | \(-0.636146\pi\) |
0.995407 | − | 0.0957376i | \(-0.0305210\pi\) | |||||||
\(12\) | −0.366615 | + | 1.36822i | −0.105833 | + | 0.394973i | ||||
\(13\) | 3.66816 | − | 3.66816i | 1.01737 | − | 1.01737i | 0.0175187 | − | 0.999847i | \(-0.494423\pi\) |
0.999847 | − | 0.0175187i | \(-0.00557667\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.13393 | − | 0.668102i | −0.550977 | − | 0.172503i | ||||
\(16\) | 0.419714 | + | 0.726965i | 0.104928 | + | 0.181741i | ||||
\(17\) | 2.03548 | − | 0.545404i | 0.493675 | − | 0.132280i | −0.00338789 | − | 0.999994i | \(-0.501078\pi\) |
0.497063 | + | 0.867714i | \(0.334412\pi\) | |||||||
\(18\) | 0.737849 | − | 0.197706i | 0.173913 | − | 0.0465998i | ||||
\(19\) | 0.0348837 | + | 0.0604203i | 0.00800286 | + | 0.0138614i | 0.869999 | − | 0.493053i | \(-0.164119\pi\) |
−0.861996 | + | 0.506915i | \(0.830786\pi\) | |||||||
\(20\) | −2.80654 | + | 1.46818i | −0.627561 | + | 0.328296i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.08029 | + | 2.08029i | −0.443519 | + | 0.443519i | ||||
\(23\) | −0.195522 | + | 0.729698i | −0.0407692 | + | 0.152153i | −0.983310 | − | 0.181939i | \(-0.941763\pi\) |
0.942541 | + | 0.334091i | \(0.108429\pi\) | |||||||
\(24\) | 1.30489 | − | 2.26014i | 0.266360 | − | 0.461349i | ||||
\(25\) | −2.13133 | − | 4.52299i | −0.426265 | − | 0.904598i | ||||
\(26\) | −3.43177 | + | 1.98133i | −0.673025 | + | 0.388571i | ||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 2.77107i | − | 0.514576i | −0.966335 | − | 0.257288i | \(-0.917171\pi\) | ||
0.966335 | − | 0.257288i | \(-0.0828288\pi\) | |||||||
\(30\) | 1.44243 | + | 0.914849i | 0.263350 | + | 0.167028i | ||||
\(31\) | 2.07564 | + | 1.19837i | 0.372795 | + | 0.215233i | 0.674679 | − | 0.738111i | \(-0.264282\pi\) |
−0.301884 | + | 0.953345i | \(0.597615\pi\) | |||||||
\(32\) | −1.51688 | − | 5.66108i | −0.268149 | − | 1.00075i | ||||
\(33\) | −3.72013 | − | 0.996806i | −0.647591 | − | 0.173522i | ||||
\(34\) | −1.60970 | −0.276062 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.41649 | 0.236082 | ||||||||
\(37\) | −8.45237 | − | 2.26481i | −1.38956 | − | 0.372332i | −0.514976 | − | 0.857204i | \(-0.672199\pi\) |
−0.874585 | + | 0.484872i | \(0.838866\pi\) | |||||||
\(38\) | −0.0137934 | − | 0.0514778i | −0.00223759 | − | 0.00835080i | ||||
\(39\) | −4.49256 | − | 2.59378i | −0.719386 | − | 0.415338i | ||||
\(40\) | 5.69477 | − | 1.27454i | 0.900421 | − | 0.201522i | ||||
\(41\) | 8.68077i | 1.35571i | 0.735196 | + | 0.677854i | \(0.237090\pi\) | ||||
−0.735196 | + | 0.677854i | \(0.762910\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.77107 | − | 2.77107i | −0.422585 | − | 0.422585i | 0.463508 | − | 0.886093i | \(-0.346591\pi\) |
−0.886093 | + | 0.463508i | \(0.846591\pi\) | |||||||
\(44\) | −4.72453 | + | 2.72771i | −0.712250 | + | 0.411218i | ||||
\(45\) | −0.0930365 | + | 2.23413i | −0.0138691 | + | 0.333045i | ||||
\(46\) | 0.288532 | − | 0.499752i | 0.0425417 | − | 0.0736843i | ||||
\(47\) | −2.00963 | + | 7.50006i | −0.293135 | + | 1.09400i | 0.649552 | + | 0.760317i | \(0.274957\pi\) |
−0.942687 | + | 0.333678i | \(0.891710\pi\) | |||||||
\(48\) | 0.593565 | − | 0.593565i | 0.0856737 | − | 0.0856737i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.678376 | + | 3.75866i | 0.0959368 | + | 0.531555i | ||||
\(51\) | −1.05364 | − | 1.82496i | −0.147539 | − | 0.255545i | ||||
\(52\) | −7.09776 | + | 1.90184i | −0.984282 | + | 0.263737i | ||||
\(53\) | −8.38498 | + | 2.24675i | −1.15177 | + | 0.308615i | −0.783673 | − | 0.621174i | \(-0.786656\pi\) |
−0.368093 | + | 0.929789i | \(0.619989\pi\) | |||||||
\(54\) | −0.381939 | − | 0.661538i | −0.0519753 | − | 0.0900239i | ||||
\(55\) | −3.99191 | − | 7.63083i | −0.538269 | − | 1.02894i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.0493330 | − | 0.0493330i | 0.00653431 | − | 0.00653431i | ||||
\(58\) | −0.547858 | + | 2.04464i | −0.0719373 | + | 0.268474i | ||||
\(59\) | −3.48720 | + | 6.04001i | −0.453995 | + | 0.786342i | −0.998630 | − | 0.0523310i | \(-0.983335\pi\) |
0.544635 | + | 0.838673i | \(0.316668\pi\) | |||||||
\(60\) | 2.14454 | + | 2.33092i | 0.276859 | + | 0.300920i | ||||
\(61\) | 12.3935 | − | 7.15536i | 1.58682 | − | 0.916150i | 0.592992 | − | 0.805208i | \(-0.297946\pi\) |
0.993827 | − | 0.110942i | \(-0.0353869\pi\) | |||||||
\(62\) | −1.29458 | − | 1.29458i | −0.164412 | − | 0.164412i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.79807i | 0.349758i | ||||||||
\(65\) | −2.53345 | − | 11.3197i | −0.314236 | − | 1.40404i | ||||
\(66\) | 2.54782 | + | 1.47098i | 0.313615 | + | 0.181066i | ||||
\(67\) | 0.152446 | + | 0.568937i | 0.0186243 | + | 0.0695067i | 0.974613 | − | 0.223898i | \(-0.0718783\pi\) |
−0.955988 | + | 0.293405i | \(0.905212\pi\) | |||||||
\(68\) | −2.88323 | − | 0.772560i | −0.349643 | − | 0.0936866i | ||||
\(69\) | 0.755439 | 0.0909442 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.12783 | −0.964595 | −0.482298 | − | 0.876007i | \(-0.660198\pi\) | ||||
−0.482298 | + | 0.876007i | \(0.660198\pi\) | |||||||
\(72\) | −2.52086 | − | 0.675461i | −0.297086 | − | 0.0796039i | ||||
\(73\) | −3.49631 | − | 13.0484i | −0.409212 | − | 1.52720i | −0.796152 | − | 0.605096i | \(-0.793135\pi\) |
0.386940 | − | 0.922105i | \(-0.373532\pi\) | |||||||
\(74\) | 5.78881 | + | 3.34217i | 0.672936 | + | 0.388520i | ||||
\(75\) | −3.81725 | + | 3.22934i | −0.440778 | + | 0.372892i | ||||
\(76\) | − | 0.0988248i | − | 0.0113360i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.80203 | + | 2.80203i | 0.317267 | + | 0.317267i | ||||
\(79\) | 8.54186 | − | 4.93165i | 0.961035 | − | 0.554854i | 0.0645434 | − | 0.997915i | \(-0.479441\pi\) |
0.896491 | + | 0.443061i | \(0.146108\pi\) | |||||||
\(80\) | 1.87539 | + | 0.0780974i | 0.209675 | + | 0.00873155i | ||||
\(81\) | 0.500000 | − | 0.866025i | 0.0555556 | − | 0.0962250i | ||||
\(82\) | 1.71624 | − | 6.40510i | 0.189527 | − | 0.707325i | ||||
\(83\) | −1.63570 | + | 1.63570i | −0.179541 | + | 0.179541i | −0.791156 | − | 0.611615i | \(-0.790520\pi\) |
0.611615 | + | 0.791156i | \(0.290520\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.40788 | − | 4.49678i | 0.152706 | − | 0.487744i | ||||
\(86\) | 1.49678 | + | 2.59249i | 0.161402 | + | 0.279556i | ||||
\(87\) | −2.67665 | + | 0.717207i | −0.286967 | + | 0.0768926i | ||||
\(88\) | 9.70872 | − | 2.60144i | 1.03495 | − | 0.277315i | ||||
\(89\) | −2.52657 | − | 4.37614i | −0.267815 | − | 0.463870i | 0.700482 | − | 0.713670i | \(-0.252968\pi\) |
−0.968297 | + | 0.249800i | \(0.919635\pi\) | |||||||
\(90\) | 0.510348 | − | 1.63006i | 0.0537954 | − | 0.171823i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.756656 | − | 0.756656i | 0.0788868 | − | 0.0788868i | ||||
\(93\) | 0.620321 | − | 2.31507i | 0.0643243 | − | 0.240062i | ||||
\(94\) | 2.96561 | − | 5.13659i | 0.305880 | − | 0.529799i | ||||
\(95\) | 0.155869 | + | 0.00649091i | 0.0159919 | + | 0.000665953i | ||||
\(96\) | −5.07559 | + | 2.93039i | −0.518025 | + | 0.299082i | ||||
\(97\) | −6.85851 | − | 6.85851i | −0.696376 | − | 0.696376i | 0.267251 | − | 0.963627i | \(-0.413885\pi\) |
−0.963627 | + | 0.267251i | \(0.913885\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.85136i | 0.387076i | ||||||||
\(100\) | −0.588852 | + | 7.05793i | −0.0588852 | + | 0.705793i | ||||
\(101\) | 16.6236 | + | 9.59763i | 1.65411 | + | 0.955000i | 0.975357 | + | 0.220632i | \(0.0708121\pi\) |
0.678752 | + | 0.734368i | \(0.262521\pi\) | |||||||
\(102\) | 0.416622 | + | 1.55485i | 0.0412517 | + | 0.153954i | ||||
\(103\) | 3.19410 | + | 0.855857i | 0.314724 | + | 0.0843301i | 0.412723 | − | 0.910856i | \(-0.364578\pi\) |
−0.0979992 | + | 0.995186i | \(0.531244\pi\) | |||||||
\(104\) | 13.5384 | 1.32755 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.63105 | 0.644064 | ||||||||
\(107\) | 8.73911 | + | 2.34164i | 0.844841 | + | 0.226375i | 0.655178 | − | 0.755475i | \(-0.272594\pi\) |
0.189663 | + | 0.981849i | \(0.439260\pi\) | |||||||
\(108\) | −0.366615 | − | 1.36822i | −0.0352775 | − | 0.131658i | ||||
\(109\) | −1.87111 | − | 1.08029i | −0.179220 | − | 0.103473i | 0.407706 | − | 0.913113i | \(-0.366329\pi\) |
−0.586926 | + | 0.809641i | \(0.699662\pi\) | |||||||
\(110\) | 1.43677 | + | 6.41963i | 0.136990 | + | 0.612087i | ||||
\(111\) | 8.75054i | 0.830564i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.13823 | − | 4.13823i | −0.389292 | − | 0.389292i | 0.485143 | − | 0.874435i | \(-0.338768\pi\) |
−0.874435 | + | 0.485143i | \(0.838768\pi\) | |||||||
\(114\) | −0.0461537 | + | 0.0266469i | −0.00432269 | + | 0.00249571i | ||||
\(115\) | 1.14372 | + | 1.24312i | 0.106653 | + | 0.115921i | ||||
\(116\) | −1.96260 | + | 3.39932i | −0.182223 | + | 0.315619i | ||||
\(117\) | −1.34264 | + | 5.01080i | −0.124127 | + | 0.463249i | ||||
\(118\) | 3.76718 | − | 3.76718i | 0.346797 | − | 0.346797i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.70502 | − | 5.17085i | −0.246934 | − | 0.472032i | ||||
\(121\) | −1.91649 | − | 3.31946i | −0.174226 | − | 0.301769i | ||||
\(122\) | −10.5592 | + | 2.82932i | −0.955981 | + | 0.256154i | ||||
\(123\) | 8.38498 | − | 2.24675i | 0.756048 | − | 0.202583i | ||||
\(124\) | −1.69748 | − | 2.94012i | −0.152438 | − | 0.264030i | ||||
\(125\) | −11.0933 | − | 1.39233i | −0.992215 | − | 0.124533i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.83298 | + | 4.83298i | −0.428858 | + | 0.428858i | −0.888239 | − | 0.459381i | \(-0.848071\pi\) |
0.459381 | + | 0.888239i | \(0.348071\pi\) | |||||||
\(128\) | −2.48057 | + | 9.25761i | −0.219253 | + | 0.818265i | ||||
\(129\) | −1.95945 | + | 3.39386i | −0.172520 | + | 0.298813i | ||||
\(130\) | −0.368673 | + | 8.85312i | −0.0323347 | + | 0.776470i | ||||
\(131\) | 0.560750 | − | 0.323749i | 0.0489930 | − | 0.0282861i | −0.475303 | − | 0.879822i | \(-0.657662\pi\) |
0.524296 | + | 0.851536i | \(0.324328\pi\) | |||||||
\(132\) | 3.85756 | + | 3.85756i | 0.335758 | + | 0.335758i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 0.449929i | − | 0.0388680i | ||||||
\(135\) | 2.18209 | − | 0.488369i | 0.187804 | − | 0.0420322i | ||||
\(136\) | 4.76274 | + | 2.74977i | 0.408402 | + | 0.235791i | ||||
\(137\) | 3.74696 | + | 13.9839i | 0.320125 | + | 1.19472i | 0.919123 | + | 0.393971i | \(0.128899\pi\) |
−0.598998 | + | 0.800751i | \(0.704434\pi\) | |||||||
\(138\) | −0.557400 | − | 0.149355i | −0.0474491 | − | 0.0127139i | ||||
\(139\) | 22.1663 | 1.88012 | 0.940060 | − | 0.341009i | \(-0.110769\pi\) | ||||
0.940060 | + | 0.341009i | \(0.110769\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.76463 | 0.653900 | ||||||||
\(142\) | 5.99711 | + | 1.60692i | 0.503266 | + | 0.134850i | ||||
\(143\) | −5.17099 | − | 19.2984i | −0.432420 | − | 1.61381i | ||||
\(144\) | −0.726965 | − | 0.419714i | −0.0605804 | − | 0.0349761i | ||||
\(145\) | −5.23261 | − | 3.31874i | −0.434545 | − | 0.275607i | ||||
\(146\) | 10.3190i | 0.854007i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.76463 | + | 8.76463i | 0.720448 | + | 0.720448i | ||||
\(149\) | 9.56745 | − | 5.52377i | 0.783796 | − | 0.452525i | −0.0539779 | − | 0.998542i | \(-0.517190\pi\) |
0.837774 | + | 0.546017i | \(0.183857\pi\) | |||||||
\(150\) | 3.45501 | − | 1.62807i | 0.282101 | − | 0.132932i | ||||
\(151\) | −9.19950 | + | 15.9340i | −0.748645 | + | 1.29669i | 0.199828 | + | 0.979831i | \(0.435962\pi\) |
−0.948472 | + | 0.316859i | \(0.897372\pi\) | |||||||
\(152\) | −0.0471251 | + | 0.175873i | −0.00382235 | + | 0.0142652i | ||||
\(153\) | −1.49007 | + | 1.49007i | −0.120465 | + | 0.120465i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.74873 | − | 2.48420i | 0.381428 | − | 0.199536i | ||||
\(156\) | 3.67407 | + | 6.36367i | 0.294161 | + | 0.509502i | ||||
\(157\) | −1.43425 | + | 0.384306i | −0.114465 | + | 0.0306709i | −0.315597 | − | 0.948893i | \(-0.602205\pi\) |
0.201132 | + | 0.979564i | \(0.435538\pi\) | |||||||
\(158\) | −7.27763 | + | 1.95003i | −0.578977 | + | 0.155136i | ||||
\(159\) | 4.34039 | + | 7.51777i | 0.344215 | + | 0.596198i | ||||
\(160\) | −12.5065 | − | 3.91560i | −0.988724 | − | 0.309555i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.540143 | + | 0.540143i | −0.0424377 | + | 0.0424377i | ||||
\(163\) | 2.01511 | − | 7.52050i | 0.157836 | − | 0.589051i | −0.841010 | − | 0.541020i | \(-0.818038\pi\) |
0.998846 | − | 0.0480317i | \(-0.0152948\pi\) | |||||||
\(164\) | 6.14812 | − | 10.6488i | 0.480087 | − | 0.831535i | ||||
\(165\) | −6.33763 | + | 5.83089i | −0.493384 | + | 0.453935i | ||||
\(166\) | 1.53028 | − | 0.883510i | 0.118773 | − | 0.0685737i | ||||
\(167\) | −1.88968 | − | 1.88968i | −0.146228 | − | 0.146228i | 0.630203 | − | 0.776431i | \(-0.282972\pi\) |
−0.776431 | + | 0.630203i | \(0.782972\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 13.9108i | − | 1.07006i | ||||||
\(170\) | −1.92784 | + | 3.03960i | −0.147859 | + | 0.233127i | ||||
\(171\) | −0.0604203 | − | 0.0348837i | −0.00462046 | − | 0.00266762i | ||||
\(172\) | 1.43672 | + | 5.36192i | 0.109549 | + | 0.408843i | ||||
\(173\) | −6.70378 | − | 1.79627i | −0.509679 | − | 0.136568i | −0.00519041 | − | 0.999987i | \(-0.501652\pi\) |
−0.504488 | + | 0.863419i | \(0.668319\pi\) | |||||||
\(174\) | 2.11676 | 0.160471 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.23294 | 0.243692 | ||||||||
\(177\) | 6.73676 | + | 1.80511i | 0.506366 | + | 0.135680i | ||||
\(178\) | 0.999035 | + | 3.72845i | 0.0748808 | + | 0.279459i | ||||
\(179\) | 16.0957 | + | 9.29284i | 1.20305 | + | 0.694579i | 0.961231 | − | 0.275743i | \(-0.0889239\pi\) |
0.241815 | + | 0.970322i | \(0.422257\pi\) | |||||||
\(180\) | 1.69644 | − | 2.67475i | 0.126445 | − | 0.199364i | ||||
\(181\) | 8.48528i | 0.630706i | 0.948974 | + | 0.315353i | \(0.102123\pi\) | ||||
−0.948974 | + | 0.315353i | \(0.897877\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.1192 | − | 10.1192i | −0.748034 | − | 0.748034i | ||||
\(184\) | −1.70740 | + | 0.985766i | −0.125871 | + | 0.0726716i | ||||
\(185\) | −14.3995 | + | 13.2482i | −1.05867 | + | 0.974025i | ||||
\(186\) | −0.915407 | + | 1.58553i | −0.0671209 | + | 0.116257i | ||||
\(187\) | 2.10055 | − | 7.83935i | 0.153607 | − | 0.573270i | ||||
\(188\) | 7.77713 | − | 7.77713i | 0.567206 | − | 0.567206i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.113725 | − | 0.0356057i | −0.00825047 | − | 0.00258311i | ||||
\(191\) | 2.69676 | + | 4.67092i | 0.195130 | + | 0.337976i | 0.946943 | − | 0.321401i | \(-0.104154\pi\) |
−0.751813 | + | 0.659377i | \(0.770820\pi\) | |||||||
\(192\) | 2.70273 | − | 0.724193i | 0.195052 | − | 0.0522641i | ||||
\(193\) | 6.56510 | − | 1.75911i | 0.472566 | − | 0.126624i | −0.0146728 | − | 0.999892i | \(-0.504671\pi\) |
0.487239 | + | 0.873269i | \(0.338004\pi\) | |||||||
\(194\) | 3.70458 | + | 6.41652i | 0.265973 | + | 0.460679i | ||||
\(195\) | −10.2783 | + | 5.37688i | −0.736044 | + | 0.385046i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.6739 | − | 12.6739i | 0.902981 | − | 0.902981i | −0.0927124 | − | 0.995693i | \(-0.529554\pi\) |
0.995693 | + | 0.0927124i | \(0.0295537\pi\) | |||||||
\(198\) | 0.761438 | − | 2.84172i | 0.0541130 | − | 0.201953i | ||||
\(199\) | −1.33556 | + | 2.31325i | −0.0946750 | + | 0.163982i | −0.909473 | − | 0.415763i | \(-0.863515\pi\) |
0.814798 | + | 0.579745i | \(0.196848\pi\) | |||||||
\(200\) | 4.41356 | − | 12.2798i | 0.312086 | − | 0.868316i | ||||
\(201\) | 0.510095 | − | 0.294503i | 0.0359793 | − | 0.0207727i | ||||
\(202\) | −10.3682 | − | 10.3682i | −0.729503 | − | 0.729503i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 2.98494i | 0.208988i | ||||||||
\(205\) | 16.3919 | + | 10.3964i | 1.14486 | + | 0.726117i | ||||
\(206\) | −2.18756 | − | 1.26299i | −0.152414 | − | 0.0879965i | ||||
\(207\) | −0.195522 | − | 0.729698i | −0.0135897 | − | 0.0507175i | ||||
\(208\) | 4.20621 | + | 1.12705i | 0.291648 | + | 0.0781468i | ||||
\(209\) | 0.268699 | 0.0185863 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0239 | −0.827757 | −0.413879 | − | 0.910332i | \(-0.635826\pi\) | ||||
−0.413879 | + | 0.910332i | \(0.635826\pi\) | |||||||
\(212\) | 11.8772 | + | 3.18250i | 0.815733 | + | 0.218575i | ||||
\(213\) | 2.10364 | + | 7.85088i | 0.144139 | + | 0.537933i | ||||
\(214\) | −5.98519 | − | 3.45555i | −0.409139 | − | 0.236217i | ||||
\(215\) | −8.55135 | + | 1.91387i | −0.583198 | + | 0.130525i | ||||
\(216\) | 2.60978i | 0.177573i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.16702 | + | 1.16702i | 0.0790405 | + | 0.0790405i | ||||
\(219\) | −11.6989 | + | 6.75436i | −0.790538 | + | 0.456417i | ||||
\(220\) | −0.507553 | + | 12.1881i | −0.0342192 | + | 0.821723i | ||||
\(221\) | 5.46582 | − | 9.46708i | 0.367671 | − | 0.636825i | ||||
\(222\) | 1.73004 | − | 6.45658i | 0.116112 | − | 0.433337i | ||||
\(223\) | 11.6925 | − | 11.6925i | 0.782988 | − | 0.782988i | −0.197346 | − | 0.980334i | \(-0.563232\pi\) |
0.980334 | + | 0.197346i | \(0.0632321\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.10728 | + | 2.85136i | 0.273819 | + | 0.190091i | ||||
\(226\) | 2.23524 | + | 3.87155i | 0.148686 | + | 0.257531i | ||||
\(227\) | 1.50971 | − | 0.404524i | 0.100203 | − | 0.0268492i | −0.208369 | − | 0.978050i | \(-0.566816\pi\) |
0.308572 | + | 0.951201i | \(0.400149\pi\) | |||||||
\(228\) | −0.0954574 | + | 0.0255777i | −0.00632182 | + | 0.00169393i | ||||
\(229\) | 3.91654 | + | 6.78365i | 0.258812 | + | 0.448276i | 0.965924 | − | 0.258826i | \(-0.0833355\pi\) |
−0.707112 | + | 0.707102i | \(0.750002\pi\) | |||||||
\(230\) | −0.598123 | − | 1.14335i | −0.0394390 | − | 0.0753906i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.11372 | − | 5.11372i | 0.335732 | − | 0.335732i | ||||
\(233\) | 0.368944 | − | 1.37692i | 0.0241703 | − | 0.0902048i | −0.952787 | − | 0.303639i | \(-0.901798\pi\) |
0.976957 | + | 0.213434i | \(0.0684649\pi\) | |||||||
\(234\) | 1.98133 | − | 3.43177i | 0.129524 | − | 0.224342i | ||||
\(235\) | 11.7555 | + | 12.7771i | 0.766845 | + | 0.833488i | ||||
\(236\) | 8.55562 | − | 4.93959i | 0.556923 | − | 0.321540i | ||||
\(237\) | −6.97440 | − | 6.97440i | −0.453036 | − | 0.453036i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.2805i | 1.31183i | 0.754833 | + | 0.655917i | \(0.227718\pi\) | ||||
−0.754833 | + | 0.655917i | \(0.772282\pi\) | |||||||
\(240\) | −0.409951 | − | 1.83170i | −0.0264622 | − | 0.118236i | ||||
\(241\) | −2.39883 | − | 1.38497i | −0.154522 | − | 0.0892136i | 0.420745 | − | 0.907179i | \(-0.361769\pi\) |
−0.575268 | + | 0.817965i | \(0.695102\pi\) | |||||||
\(242\) | 0.757804 | + | 2.82816i | 0.0487135 | + | 0.181801i | ||||
\(243\) | −0.965926 | − | 0.258819i | −0.0619642 | − | 0.0166032i | ||||
\(244\) | −20.2710 | −1.29772 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.63105 | −0.422780 | ||||||||
\(247\) | 0.349590 | + | 0.0936725i | 0.0222439 | + | 0.00596024i | ||||
\(248\) | 1.61890 | + | 6.04183i | 0.102800 | + | 0.383656i | ||||
\(249\) | 2.00331 | + | 1.15661i | 0.126955 | + | 0.0732973i | ||||
\(250\) | 7.90992 | + | 3.22054i | 0.500267 | + | 0.203685i | ||||
\(251\) | − | 6.09982i | − | 0.385017i | −0.981295 | − | 0.192509i | \(-0.938338\pi\) | ||
0.981295 | − | 0.192509i | \(-0.0616623\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.05731 | + | 2.05731i | 0.129342 | + | 0.129342i | ||||
\(254\) | 4.52152 | − | 2.61050i | 0.283706 | − | 0.163797i | ||||
\(255\) | −4.70794 | − | 0.196054i | −0.294823 | − | 0.0122774i | ||||
\(256\) | 6.45864 | − | 11.1867i | 0.403665 | − | 0.699168i | ||||
\(257\) | 0.738795 | − | 2.75722i | 0.0460848 | − | 0.171991i | −0.939048 | − | 0.343787i | \(-0.888290\pi\) |
0.985133 | + | 0.171796i | \(0.0549570\pi\) | |||||||
\(258\) | 2.11676 | − | 2.11676i | 0.131784 | − | 0.131784i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −4.90931 | + | 15.6804i | −0.304462 | + | 0.972456i | ||||
\(261\) | 1.38554 | + | 2.39982i | 0.0857626 | + | 0.148545i | ||||
\(262\) | −0.477756 | + | 0.128014i | −0.0295159 | + | 0.00790876i | ||||
\(263\) | −22.9063 | + | 6.13773i | −1.41246 | + | 0.378469i | −0.882804 | − | 0.469741i | \(-0.844347\pi\) |
−0.529660 | + | 0.848210i | \(0.677681\pi\) | |||||||
\(264\) | −5.02561 | − | 8.70460i | −0.309305 | − | 0.535731i | ||||
\(265\) | −5.79964 | + | 18.5241i | −0.356269 | + | 1.13793i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.57310 | + | 3.57310i | −0.218670 | + | 0.218670i | ||||
\(268\) | 0.215939 | − | 0.805894i | 0.0131905 | − | 0.0492278i | ||||
\(269\) | 12.3676 | − | 21.4213i | 0.754064 | − | 1.30608i | −0.191774 | − | 0.981439i | \(-0.561424\pi\) |
0.945838 | − | 0.324638i | \(-0.105242\pi\) | |||||||
\(270\) | −1.70660 | − | 0.0710685i | −0.103861 | − | 0.00432509i | ||||
\(271\) | 3.58076 | − | 2.06735i | 0.217515 | − | 0.125583i | −0.387284 | − | 0.921961i | \(-0.626587\pi\) |
0.604799 | + | 0.796378i | \(0.293253\pi\) | |||||||
\(272\) | 1.25081 | + | 1.25081i | 0.0758413 | + | 0.0758413i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 11.0588i | − | 0.668085i | ||||||
\(275\) | −19.1901 | − | 1.60106i | −1.15721 | − | 0.0965473i | ||||
\(276\) | −0.926710 | − | 0.535036i | −0.0557814 | − | 0.0322054i | ||||
\(277\) | −4.43358 | − | 16.5463i | −0.266388 | − | 0.994174i | −0.961395 | − | 0.275171i | \(-0.911266\pi\) |
0.695007 | − | 0.719003i | \(-0.255401\pi\) | |||||||
\(278\) | −16.3554 | − | 4.38241i | −0.980931 | − | 0.262840i | ||||
\(279\) | −2.39674 | −0.143489 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.25279 | 0.313355 | 0.156678 | − | 0.987650i | \(-0.449922\pi\) | ||||
0.156678 | + | 0.987650i | \(0.449922\pi\) | |||||||
\(282\) | −5.72913 | − | 1.53511i | −0.341164 | − | 0.0914147i | ||||
\(283\) | 0.610271 | + | 2.27756i | 0.0362768 | + | 0.135387i | 0.981689 | − | 0.190489i | \(-0.0610074\pi\) |
−0.945412 | + | 0.325876i | \(0.894341\pi\) | |||||||
\(284\) | 9.97054 | + | 5.75649i | 0.591643 | + | 0.341585i | ||||
\(285\) | −0.0340722 | − | 0.152238i | −0.00201827 | − | 0.00901782i | ||||
\(286\) | 15.2617i | 0.902441i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 4.14420 | + | 4.14420i | 0.244199 | + | 0.244199i | ||||
\(289\) | −10.8767 | + | 6.27969i | −0.639808 | + | 0.369393i | ||||
\(290\) | 3.20474 | + | 3.48325i | 0.188189 | + | 0.204544i | ||||
\(291\) | −4.84970 | + | 8.39993i | −0.284294 | + | 0.492412i | ||||
\(292\) | −4.95249 | + | 18.4830i | −0.289823 | + | 1.08163i | ||||
\(293\) | 15.2556 | − | 15.2556i | 0.891240 | − | 0.891240i | −0.103400 | − | 0.994640i | \(-0.532972\pi\) |
0.994640 | + | 0.103400i | \(0.0329722\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.22893 | + | 13.8186i | 0.420884 | + | 0.804551i | ||||
\(296\) | −11.4185 | − | 19.7774i | −0.663687 | − | 1.14954i | ||||
\(297\) | 3.72013 | − | 0.996806i | 0.215864 | − | 0.0578405i | ||||
\(298\) | −8.15142 | + | 2.18417i | −0.472199 | + | 0.126525i | ||||
\(299\) | 1.95945 | + | 3.39386i | 0.113318 | + | 0.196272i | ||||
\(300\) | 6.96984 | − | 1.25794i | 0.402404 | − | 0.0726272i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 9.93809 | − | 9.93809i | 0.571873 | − | 0.571873i | ||||
\(303\) | 4.96810 | − | 18.5412i | 0.285410 | − | 1.06516i | ||||
\(304\) | −0.0292823 | + | 0.0507184i | −0.00167946 | + | 0.00290890i | ||||
\(305\) | 1.33142 | − | 31.9720i | 0.0762369 | − | 1.83071i | ||||
\(306\) | 1.39404 | − | 0.804852i | 0.0796922 | − | 0.0460103i | ||||
\(307\) | 14.6198 | + | 14.6198i | 0.834394 | + | 0.834394i | 0.988114 | − | 0.153721i | \(-0.0491256\pi\) |
−0.153721 | + | 0.988114i | \(0.549126\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 3.30678i | − | 0.188116i | ||||||
\(310\) | −3.99499 | + | 0.894114i | −0.226900 | + | 0.0507823i | ||||
\(311\) | −2.47872 | − | 1.43109i | −0.140555 | − | 0.0811497i | 0.428073 | − | 0.903744i | \(-0.359193\pi\) |
−0.568629 | + | 0.822594i | \(0.692526\pi\) | |||||||
\(312\) | −3.50400 | − | 13.0771i | −0.198375 | − | 0.740345i | ||||
\(313\) | −12.8656 | − | 3.44732i | −0.727204 | − | 0.194854i | −0.123820 | − | 0.992305i | \(-0.539515\pi\) |
−0.603384 | + | 0.797451i | \(0.706181\pi\) | |||||||
\(314\) | 1.13424 | 0.0640088 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13.9713 | −0.785945 | ||||||||
\(317\) | −10.0855 | − | 2.70240i | −0.566459 | − | 0.151782i | −0.0357866 | − | 0.999359i | \(-0.511394\pi\) |
−0.530672 | + | 0.847577i | \(0.678060\pi\) | |||||||
\(318\) | −1.71624 | − | 6.40510i | −0.0962421 | − | 0.359180i | ||||
\(319\) | −9.24258 | − | 5.33620i | −0.517485 | − | 0.298770i | ||||
\(320\) | 5.28358 | + | 3.35107i | 0.295361 | + | 0.187331i | ||||
\(321\) | − | 9.04739i | − | 0.504976i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.103958 | + | 0.103958i | 0.00578440 | + | 0.00578440i | ||||
\(324\) | −1.22672 | + | 0.708245i | −0.0681509 | + | 0.0393470i | ||||
\(325\) | −24.4091 | − | 8.77301i | −1.35397 | − | 0.486639i | ||||
\(326\) | −2.97370 | + | 5.15060i | −0.164698 | + | 0.285265i | ||||
\(327\) | −0.559197 | + | 2.08695i | −0.0309237 | + | 0.115409i | ||||
\(328\) | −16.0194 | + | 16.0194i | −0.884526 | + | 0.884526i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 5.82902 | − | 3.04933i | 0.320877 | − | 0.167860i | ||||
\(331\) | −11.8100 | − | 20.4555i | −0.649136 | − | 1.12434i | −0.983330 | − | 0.181833i | \(-0.941797\pi\) |
0.334193 | − | 0.942505i | \(-0.391536\pi\) | |||||||
\(332\) | 3.16501 | − | 0.848062i | 0.173703 | − | 0.0465435i | ||||
\(333\) | 8.45237 | − | 2.26481i | 0.463187 | − | 0.124111i | ||||
\(334\) | 1.02070 | + | 1.76790i | 0.0558500 | + | 0.0967351i | ||||
\(335\) | 1.25690 | + | 0.393517i | 0.0686716 | + | 0.0215001i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.93809 | + | 4.93809i | −0.268995 | + | 0.268995i | −0.828695 | − | 0.559700i | \(-0.810916\pi\) |
0.559700 | + | 0.828695i | \(0.310916\pi\) | |||||||
\(338\) | −2.75026 | + | 10.2641i | −0.149594 | + | 0.558293i | ||||
\(339\) | −2.92617 | + | 5.06828i | −0.158928 | + | 0.275271i | ||||
\(340\) | −4.91189 | + | 4.51915i | −0.266385 | + | 0.245085i | ||||
\(341\) | 7.99402 | − | 4.61535i | 0.432900 | − | 0.249935i | ||||
\(342\) | 0.0376844 | + | 0.0376844i | 0.00203774 | + | 0.00203774i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 10.2274i | − | 0.551427i | ||||||
\(345\) | 0.904743 | − | 1.42649i | 0.0487097 | − | 0.0767998i | ||||
\(346\) | 4.59124 | + | 2.65076i | 0.246827 | + | 0.142505i | ||||
\(347\) | 2.13647 | + | 7.97341i | 0.114692 | + | 0.428035i | 0.999264 | − | 0.0383685i | \(-0.0122161\pi\) |
−0.884572 | + | 0.466404i | \(0.845549\pi\) | |||||||
\(348\) | 3.79145 | + | 1.01592i | 0.203243 | + | 0.0544589i | ||||
\(349\) | 16.9121 | 0.905282 | 0.452641 | − | 0.891693i | \(-0.350482\pi\) | ||||
0.452641 | + | 0.891693i | \(0.350482\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.18757 | 0.276892 | ||||||||
\(352\) | −21.8029 | − | 5.84206i | −1.16210 | − | 0.311383i | ||||
\(353\) | 4.07257 | + | 15.1990i | 0.216761 | + | 0.808963i | 0.985539 | + | 0.169448i | \(0.0541984\pi\) |
−0.768778 | + | 0.639516i | \(0.779135\pi\) | |||||||
\(354\) | −4.61383 | − | 2.66380i | −0.245222 | − | 0.141579i | ||||
\(355\) | −9.73419 | + | 15.3477i | −0.516637 | + | 0.814574i | ||||
\(356\) | 7.15771i | 0.379358i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.0389 | − | 10.0389i | −0.530574 | − | 0.530574i | ||||
\(359\) | 7.05693 | − | 4.07432i | 0.372450 | − | 0.215034i | −0.302078 | − | 0.953283i | \(-0.597680\pi\) |
0.674528 | + | 0.738249i | \(0.264347\pi\) | |||||||
\(360\) | −4.29454 | + | 3.95116i | −0.226342 | + | 0.208245i | ||||
\(361\) | 9.49757 | − | 16.4503i | 0.499872 | − | 0.865804i | ||||
\(362\) | 1.67759 | − | 6.26086i | 0.0881723 | − | 0.329063i | ||||
\(363\) | −2.71033 | + | 2.71033i | −0.142255 | + | 0.142255i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −28.8266 | − | 9.02520i | −1.50885 | − | 0.472401i | ||||
\(366\) | 5.46582 | + | 9.46708i | 0.285703 | + | 0.494852i | ||||
\(367\) | 20.1462 | − | 5.39815i | 1.05162 | − | 0.281781i | 0.308700 | − | 0.951160i | \(-0.400106\pi\) |
0.742922 | + | 0.669378i | \(0.233439\pi\) | |||||||
\(368\) | −0.612529 | + | 0.164127i | −0.0319303 | + | 0.00855569i | ||||
\(369\) | −4.34039 | − | 7.51777i | −0.225951 | − | 0.391359i | ||||
\(370\) | 13.2439 | − | 6.92828i | 0.688518 | − | 0.360184i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −2.40060 | + | 2.40060i | −0.124465 | + | 0.124465i | ||||
\(373\) | 0.547065 | − | 2.04168i | 0.0283260 | − | 0.105714i | −0.950316 | − | 0.311288i | \(-0.899240\pi\) |
0.978642 | + | 0.205574i | \(0.0659062\pi\) | |||||||
\(374\) | −3.09977 | + | 5.36897i | −0.160286 | + | 0.277623i | ||||
\(375\) | 1.52627 | + | 11.0757i | 0.0788165 | + | 0.571945i | ||||
\(376\) | −17.5491 | + | 10.1320i | −0.905027 | + | 0.522518i | ||||
\(377\) | −10.1648 | − | 10.1648i | −0.523511 | − | 0.523511i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.7135i | 0.961248i | 0.876927 | + | 0.480624i | \(0.159590\pi\) | ||||
−0.876927 | + | 0.480624i | \(0.840410\pi\) | |||||||
\(380\) | −0.186611 | − | 0.118356i | −0.00957292 | − | 0.00607155i | ||||
\(381\) | 5.91917 | + | 3.41743i | 0.303248 | + | 0.175080i | ||||
\(382\) | −1.06633 | − | 3.97960i | −0.0545582 | − | 0.203614i | ||||
\(383\) | 28.5983 | + | 7.66288i | 1.46130 | + | 0.391555i | 0.899940 | − | 0.436014i | \(-0.143610\pi\) |
0.561364 | + | 0.827569i | \(0.310277\pi\) | |||||||
\(384\) | 9.58418 | 0.489091 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.19184 | −0.264258 | ||||||||
\(387\) | 3.78536 | + | 1.01428i | 0.192421 | + | 0.0515589i | ||||
\(388\) | 3.55594 | + | 13.2710i | 0.180526 | + | 0.673731i | ||||
\(389\) | −22.2232 | − | 12.8305i | −1.12676 | − | 0.650535i | −0.183641 | − | 0.982993i | \(-0.558788\pi\) |
−0.943118 | + | 0.332459i | \(0.892122\pi\) | |||||||
\(390\) | 8.64687 | − | 1.93525i | 0.437852 | − | 0.0979949i | ||||
\(391\) | 1.59192i | 0.0805069i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.457851 | − | 0.457851i | −0.0230955 | − | 0.0230955i | ||||
\(394\) | −11.8572 | + | 6.84574i | −0.597356 | + | 0.344883i | ||||
\(395\) | 0.917646 | − | 22.0359i | 0.0461718 | − | 1.10875i | ||||
\(396\) | 2.72771 | − | 4.72453i | 0.137073 | − | 0.237417i | ||||
\(397\) | −2.46549 | + | 9.20135i | −0.123740 | + | 0.461802i | −0.999792 | − | 0.0204142i | \(-0.993502\pi\) |
0.876052 | + | 0.482217i | \(0.160168\pi\) | |||||||
\(398\) | 1.44278 | − | 1.44278i | 0.0723201 | − | 0.0723201i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.39351 | − | 3.44776i | 0.119676 | − | 0.172388i | ||||
\(401\) | −7.37513 | − | 12.7741i | −0.368296 | − | 0.637908i | 0.621003 | − | 0.783808i | \(-0.286726\pi\) |
−0.989299 | + | 0.145900i | \(0.953392\pi\) | |||||||
\(402\) | −0.434598 | + | 0.116450i | −0.0216758 | + | 0.00580801i | ||||
\(403\) | 12.0096 | − | 3.21796i | 0.598240 | − | 0.160298i | ||||
\(404\) | −13.5950 | − | 23.5472i | −0.676374 | − | 1.17151i | ||||
\(405\) | −1.03649 | − | 1.98133i | −0.0515038 | − | 0.0984532i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −23.8305 | + | 23.8305i | −1.18124 | + | 1.18124i | ||||
\(408\) | 1.42339 | − | 5.31215i | 0.0704681 | − | 0.262990i | ||||
\(409\) | 5.28021 | − | 9.14560i | 0.261090 | − | 0.452221i | −0.705442 | − | 0.708768i | \(-0.749251\pi\) |
0.966532 | + | 0.256547i | \(0.0825848\pi\) | |||||||
\(410\) | −10.0393 | − | 10.9118i | −0.495805 | − | 0.538894i | ||||
\(411\) | 12.5376 | − | 7.23858i | 0.618434 | − | 0.357053i | ||||
\(412\) | −3.31210 | − | 3.31210i | −0.163176 | − | 0.163176i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.577063i | 0.0283611i | ||||||||
\(415\) | 1.12971 | + | 5.04765i | 0.0554552 | + | 0.247779i | ||||
\(416\) | −26.3299 | − | 15.2016i | −1.29093 | − | 0.745320i | ||||
\(417\) | −5.73706 | − | 21.4110i | −0.280945 | − | 1.04850i | ||||
\(418\) | −0.198260 | − | 0.0531235i | −0.00969719 | − | 0.00259835i | ||||
\(419\) | −15.5472 | −0.759532 | −0.379766 | − | 0.925083i | \(-0.623996\pi\) | ||||
−0.379766 | + | 0.925083i | \(0.623996\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.29886 | 0.160776 | 0.0803882 | − | 0.996764i | \(-0.474384\pi\) | ||||
0.0803882 | + | 0.996764i | \(0.474384\pi\) | |||||||
\(422\) | 8.87180 | + | 2.37719i | 0.431873 | + | 0.115720i | ||||
\(423\) | −2.00963 | − | 7.50006i | −0.0977117 | − | 0.364665i | ||||
\(424\) | −19.6197 | − | 11.3275i | −0.952818 | − | 0.550110i | ||||
\(425\) | −6.80512 | − | 8.04400i | −0.330097 | − | 0.390191i | ||||
\(426\) | − | 6.20867i | − | 0.300811i | ||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −9.06196 | − | 9.06196i | −0.438026 | − | 0.438026i | ||||
\(429\) | −17.3025 | + | 9.98959i | −0.835372 | + | 0.482302i | ||||
\(430\) | 6.68799 | + | 0.278510i | 0.322524 | + | 0.0134309i | ||||
\(431\) | 7.04553 | − | 12.2032i | 0.339371 | − | 0.587809i | −0.644943 | − | 0.764230i | \(-0.723119\pi\) |
0.984315 | + | 0.176422i | \(0.0564523\pi\) | |||||||
\(432\) | −0.217260 | + | 0.810825i | −0.0104529 | + | 0.0390108i | ||||
\(433\) | 1.72650 | − | 1.72650i | 0.0829702 | − | 0.0829702i | −0.664404 | − | 0.747374i | \(-0.731314\pi\) |
0.747374 | + | 0.664404i | \(0.231314\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.85136 | + | 5.91327i | −0.0887660 | + | 0.283519i | ||||
\(436\) | 1.53022 | + | 2.65041i | 0.0732840 | + | 0.126932i | ||||
\(437\) | −0.0509091 | + | 0.0136411i | −0.00243531 | + | 0.000652540i | ||||
\(438\) | 9.96739 | − | 2.67075i | 0.476260 | − | 0.127614i | ||||
\(439\) | −13.5586 | − | 23.4841i | −0.647116 | − | 1.12084i | −0.983809 | − | 0.179223i | \(-0.942642\pi\) |
0.336693 | − | 0.941615i | \(-0.390692\pi\) | |||||||
\(440\) | 6.71524 | − | 21.4485i | 0.320136 | − | 1.02252i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.90465 | + | 5.90465i | −0.280856 | + | 0.280856i | ||||
\(443\) | −8.83957 | + | 32.9897i | −0.419981 | + | 1.56739i | 0.354664 | + | 0.934994i | \(0.384595\pi\) |
−0.774645 | + | 0.632396i | \(0.782072\pi\) | |||||||
\(444\) | 6.19753 | − | 10.7344i | 0.294122 | − | 0.509434i | ||||
\(445\) | −11.2894 | − | 0.470126i | −0.535167 | − | 0.0222861i | ||||
\(446\) | −10.9390 | + | 6.31563i | −0.517976 | + | 0.299054i | ||||
\(447\) | −7.81179 | − | 7.81179i | −0.369485 | − | 0.369485i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 9.80267i | − | 0.462617i | −0.972881 | − | 0.231308i | \(-0.925699\pi\) | ||
0.972881 | − | 0.231308i | \(-0.0743006\pi\) | |||||||
\(450\) | −2.46682 | − | 2.91591i | −0.116287 | − | 0.137457i | ||||
\(451\) | 28.9536 | + | 16.7164i | 1.36337 | + | 0.787144i | ||||
\(452\) | 2.14556 | + | 8.00732i | 0.100918 | + | 0.376633i | ||||
\(453\) | 17.7721 | + | 4.76201i | 0.835005 | + | 0.223739i | ||||
\(454\) | −1.19391 | −0.0560331 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.182078 | 0.00852656 | ||||||||
\(457\) | −0.751411 | − | 0.201340i | −0.0351495 | − | 0.00941828i | 0.241201 | − | 0.970475i | \(-0.422459\pi\) |
−0.276351 | + | 0.961057i | \(0.589125\pi\) | |||||||
\(458\) | −1.54865 | − | 5.77964i | −0.0723636 | − | 0.270065i | ||||
\(459\) | 1.82496 | + | 1.05364i | 0.0851817 | + | 0.0491797i | ||||
\(460\) | −0.522591 | − | 2.33499i | −0.0243659 | − | 0.108869i | ||||
\(461\) | 0.831786i | 0.0387401i | 0.999812 | + | 0.0193701i | \(0.00616607\pi\) | ||||
−0.999812 | + | 0.0193701i | \(0.993834\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.45140 | + | 5.45140i | 0.253348 | + | 0.253348i | 0.822342 | − | 0.568994i | \(-0.192667\pi\) |
−0.568994 | + | 0.822342i | \(0.692667\pi\) | |||||||
\(464\) | 2.01448 | − | 1.16306i | 0.0935197 | − | 0.0539936i | ||||
\(465\) | −3.62862 | − | 3.94397i | −0.168273 | − | 0.182897i | ||||
\(466\) | −0.544450 | + | 0.943015i | −0.0252211 | + | 0.0436843i | ||||
\(467\) | 8.52208 | − | 31.8048i | 0.394355 | − | 1.47175i | −0.428522 | − | 0.903531i | \(-0.640965\pi\) |
0.822876 | − | 0.568220i | \(-0.192368\pi\) | |||||||
\(468\) | 5.19592 | − | 5.19592i | 0.240181 | − | 0.240181i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −6.14768 | − | 11.7517i | −0.283571 | − | 0.542067i | ||||
\(471\) | 0.742422 | + | 1.28591i | 0.0342090 | + | 0.0592517i | ||||
\(472\) | −17.5815 | + | 4.71094i | −0.809252 | + | 0.216838i | ||||
\(473\) | −14.5788 | + | 3.90637i | −0.670333 | + | 0.179615i | ||||
\(474\) | 3.76718 | + | 6.52494i | 0.173032 | + | 0.299700i | ||||
\(475\) | 0.198932 | − | 0.286554i | 0.00912762 | − | 0.0131480i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.13823 | − | 6.13823i | 0.281050 | − | 0.281050i | ||||
\(478\) | 4.00957 | − | 14.9639i | 0.183394 | − | 0.684434i | ||||
\(479\) | −20.2160 | + | 35.0151i | −0.923691 | + | 1.59988i | −0.130038 | + | 0.991509i | \(0.541510\pi\) |
−0.793653 | + | 0.608371i | \(0.791823\pi\) | |||||||
\(480\) | −0.545267 | + | 13.0938i | −0.0248879 | + | 0.597646i | ||||
\(481\) | −39.3123 | + | 22.6970i | −1.79249 | + | 1.03489i | ||||
\(482\) | 1.49616 | + | 1.49616i | 0.0681483 | + | 0.0681483i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.42938i | 0.246790i | ||||||||
\(485\) | −21.1649 | + | 4.73689i | −0.961049 | + | 0.215091i | ||||
\(486\) | 0.661538 | + | 0.381939i | 0.0300080 | + | 0.0173251i | ||||
\(487\) | −2.64597 | − | 9.87490i | −0.119900 | − | 0.447474i | 0.879706 | − | 0.475517i | \(-0.157739\pi\) |
−0.999607 | + | 0.0280431i | \(0.991072\pi\) | |||||||
\(488\) | 36.0753 | + | 9.66634i | 1.63305 | + | 0.437575i | ||||
\(489\) | −7.78580 | −0.352086 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.1040 | 0.907279 | 0.453639 | − | 0.891185i | \(-0.350125\pi\) | ||||
0.453639 | + | 0.891185i | \(0.350125\pi\) | |||||||
\(492\) | −11.8772 | − | 3.18250i | −0.535468 | − | 0.143478i | ||||
\(493\) | −1.51135 | − | 5.64045i | −0.0680680 | − | 0.254033i | ||||
\(494\) | −0.239425 | − | 0.138232i | −0.0107723 | − | 0.00621937i | ||||
\(495\) | 7.27251 | + | 4.61254i | 0.326875 | + | 0.207318i | ||||
\(496\) | 2.01189i | 0.0903364i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.24947 | − | 1.24947i | −0.0559902 | − | 0.0559902i | ||||
\(499\) | 13.3564 | − | 7.71133i | 0.597916 | − | 0.345207i | −0.170306 | − | 0.985391i | \(-0.554475\pi\) |
0.768221 | + | 0.640185i | \(0.221142\pi\) | |||||||
\(500\) | 12.6222 | + | 9.56477i | 0.564484 | + | 0.427750i | ||||
\(501\) | −1.33620 | + | 2.31437i | −0.0596972 | + | 0.103399i | ||||
\(502\) | −1.20597 | + | 4.50075i | −0.0538252 | + | 0.200878i | ||||
\(503\) | −25.9985 | + | 25.9985i | −1.15922 | + | 1.15922i | −0.174573 | + | 0.984644i | \(0.555855\pi\) |
−0.984644 | + | 0.174573i | \(0.944145\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 38.0322 | − | 19.8958i | 1.69241 | − | 0.885350i | ||||
\(506\) | −1.11124 | − | 1.92472i | −0.0494006 | − | 0.0855644i | ||||
\(507\) | −13.4368 | + | 3.60039i | −0.596751 | + | 0.159899i | ||||
\(508\) | 9.35164 | − | 2.50576i | 0.414912 | − | 0.111175i | ||||
\(509\) | 18.5636 | + | 32.1530i | 0.822816 | + | 1.42516i | 0.903577 | + | 0.428425i | \(0.140931\pi\) |
−0.0807619 | + | 0.996733i | \(0.525735\pi\) | |||||||
\(510\) | 3.43499 | + | 1.07545i | 0.152104 | + | 0.0476216i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 6.57690 | − | 6.57690i | 0.290661 | − | 0.290661i | ||||
\(513\) | −0.0180571 | + | 0.0673901i | −0.000797241 | + | 0.00297535i | ||||
\(514\) | −1.09024 | + | 1.88835i | −0.0480884 | + | 0.0832915i | ||||
\(515\) | 5.44149 | − | 5.00641i | 0.239781 | − | 0.220609i | ||||
\(516\) | 4.80737 | − | 2.77554i | 0.211633 | − | 0.122186i | ||||
\(517\) | 21.1456 | + | 21.1456i | 0.929982 | + | 0.929982i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.94026i | 0.304644i | ||||||||
\(520\) | 16.2141 | − | 25.5645i | 0.711036 | − | 1.12108i | ||||
\(521\) | 2.24415 | + | 1.29566i | 0.0983180 | + | 0.0567639i | 0.548353 | − | 0.836247i | \(-0.315255\pi\) |
−0.450035 | + | 0.893011i | \(0.648588\pi\) | |||||||
\(522\) | −0.547858 | − | 2.04464i | −0.0239791 | − | 0.0894913i | ||||
\(523\) | −8.31711 | − | 2.22856i | −0.363682 | − | 0.0974482i | 0.0723506 | − | 0.997379i | \(-0.476950\pi\) |
−0.436032 | + | 0.899931i | \(0.643617\pi\) | |||||||
\(524\) | −0.917176 | −0.0400670 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 18.1149 | 0.789846 | ||||||||
\(527\) | 4.87850 | + | 1.30719i | 0.212511 | + | 0.0569421i | ||||
\(528\) | −0.836746 | − | 3.12278i | −0.0364147 | − | 0.135901i | ||||
\(529\) | 19.4244 | + | 11.2147i | 0.844537 | + | 0.487594i | ||||
\(530\) | 7.94159 | − | 12.5214i | 0.344961 | − | 0.543894i | ||||
\(531\) | − | 6.97440i | − | 0.302663i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 31.8425 | + | 31.8425i | 1.37925 | + | 1.37925i | ||||
\(534\) | 3.34284 | − | 1.92999i | 0.144659 | − | 0.0835187i | ||||
\(535\) | 14.8880 | − | 13.6976i | 0.643664 | − | 0.592199i | ||||
\(536\) | −0.768589 | + | 1.33124i | −0.0331980 | + | 0.0575006i | ||||
\(537\) | 4.81033 | − | 17.9524i | 0.207581 | − | 0.774703i | ||||
\(538\) | −13.3605 | + | 13.3605i | −0.576013 | + | 0.576013i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3.02269 | − | 0.946361i | −0.130076 | − | 0.0407249i | ||||
\(541\) | 16.7319 | + | 28.9805i | 0.719360 | + | 1.24597i | 0.961254 | + | 0.275665i | \(0.0888980\pi\) |
−0.241894 | + | 0.970303i | \(0.577769\pi\) | |||||||
\(542\) | −3.05079 | + | 0.817456i | −0.131042 | + | 0.0351127i | ||||
\(543\) | 8.19615 | − | 2.19615i | 0.351731 | − | 0.0942459i | ||||
\(544\) | −6.17515 | − | 10.6957i | −0.264757 | − | 0.458573i | ||||
\(545\) | −4.28081 | + | 2.23942i | −0.183370 | + | 0.0959262i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.828381 | + | 0.828381i | −0.0354190 | + | 0.0354190i | −0.724594 | − | 0.689175i | \(-0.757973\pi\) |
0.689175 | + | 0.724594i | \(0.257973\pi\) | |||||||
\(548\) | 5.30754 | − | 19.8080i | 0.226727 | − | 0.846156i | ||||
\(549\) | −7.15536 | + | 12.3935i | −0.305383 | + | 0.528940i | ||||
\(550\) | 13.8429 | + | 4.97534i | 0.590263 | + | 0.212149i | ||||
\(551\) | 0.167429 | − | 0.0966653i | 0.00713272 | − | 0.00411808i | ||||
\(552\) | 1.39408 | + | 1.39408i | 0.0593361 | + | 0.0593361i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 13.0853i | 0.555939i | ||||||||
\(555\) | 16.5236 | + | 10.4800i | 0.701388 | + | 0.444850i | ||||
\(556\) | −27.1918 | − | 15.6992i | −1.15319 | − | 0.665793i | ||||
\(557\) | 5.38496 | + | 20.0969i | 0.228168 | + | 0.851534i | 0.981111 | + | 0.193448i | \(0.0619671\pi\) |
−0.752943 | + | 0.658086i | \(0.771366\pi\) | |||||||
\(558\) | 1.76843 | + | 0.473850i | 0.0748636 | + | 0.0200597i | ||||
\(559\) | −20.3295 | −0.859846 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.11589 | −0.342653 | ||||||||
\(562\) | −3.87577 | − | 1.03851i | −0.163489 | − | 0.0438069i | ||||
\(563\) | 8.77338 | + | 32.7427i | 0.369754 | + | 1.37994i | 0.860860 | + | 0.508841i | \(0.169926\pi\) |
−0.491106 | + | 0.871100i | \(0.663407\pi\) | |||||||
\(564\) | −9.52500 | − | 5.49926i | −0.401075 | − | 0.231561i | ||||
\(565\) | −12.7703 | + | 2.85811i | −0.537251 | + | 0.120241i | ||||
\(566\) | − | 1.80115i | − | 0.0757080i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −14.9990 | − | 14.9990i | −0.629346 | − | 0.629346i | ||||
\(569\) | 13.5671 | − | 7.83298i | 0.568763 | − | 0.328376i | −0.187892 | − | 0.982190i | \(-0.560165\pi\) |
0.756655 | + | 0.653814i | \(0.226832\pi\) | |||||||
\(570\) | −0.00495826 | + | 0.119065i | −0.000207679 | + | 0.00498709i | ||||
\(571\) | −18.4943 | + | 32.0331i | −0.773964 | + | 1.34055i | 0.161411 | + | 0.986887i | \(0.448396\pi\) |
−0.935375 | + | 0.353658i | \(0.884938\pi\) | |||||||
\(572\) | −7.32466 | + | 27.3360i | −0.306260 | + | 1.14298i | ||||
\(573\) | 3.81379 | − | 3.81379i | 0.159323 | − | 0.159323i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.71714 | − | 0.670882i | 0.155015 | − | 0.0279777i | ||||
\(576\) | −1.39903 | − | 2.42320i | −0.0582931 | − | 0.100967i | ||||
\(577\) | 21.2536 | − | 5.69488i | 0.884798 | − | 0.237081i | 0.212322 | − | 0.977200i | \(-0.431897\pi\) |
0.672476 | + | 0.740119i | \(0.265231\pi\) | |||||||
\(578\) | 9.26693 | − | 2.48307i | 0.385453 | − | 0.103282i | ||||
\(579\) | −3.39835 | − | 5.88611i | −0.141230 | − | 0.244618i | ||||
\(580\) | 4.06845 | + | 7.77713i | 0.168933 | + | 0.322928i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 5.23907 | − | 5.23907i | 0.217166 | − | 0.217166i | ||||
\(583\) | −8.65304 | + | 32.2936i | −0.358372 | + | 1.33746i | ||||
\(584\) | 17.6274 | − | 30.5315i | 0.729427 | − | 1.26340i | ||||
\(585\) | 7.85389 | + | 8.53643i | 0.324718 | + | 0.352938i | ||||
\(586\) | −14.2724 | + | 8.24019i | −0.589589 | + | 0.340399i | ||||
\(587\) | 15.7111 | + | 15.7111i | 0.648468 | + | 0.648468i | 0.952623 | − | 0.304155i | \(-0.0983740\pi\) |
−0.304155 | + | 0.952623i | \(0.598374\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.167214i | 0.00688993i | ||||||||
\(590\) | −2.60183 | − | 11.6253i | −0.107116 | − | 0.478604i | ||||
\(591\) | −15.5223 | − | 8.96183i | −0.638504 | − | 0.368640i | ||||
\(592\) | −1.90114 | − | 7.09515i | −0.0781364 | − | 0.291609i | ||||
\(593\) | −2.52987 | − | 0.677877i | −0.103889 | − | 0.0278371i | 0.206500 | − | 0.978447i | \(-0.433793\pi\) |
−0.310389 | + | 0.950610i | \(0.600459\pi\) | |||||||
\(594\) | −2.94197 | −0.120710 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −15.6487 | −0.640997 | ||||||||
\(597\) | 2.58009 | + | 0.691334i | 0.105596 | + | 0.0282944i | ||||
\(598\) | −0.774789 | − | 2.89155i | −0.0316835 | − | 0.118244i | ||||
\(599\) | 40.9761 | + | 23.6576i | 1.67424 | + | 0.966622i | 0.965223 | + | 0.261429i | \(0.0841936\pi\) |
0.709015 | + | 0.705193i | \(0.249140\pi\) | |||||||
\(600\) | −13.0037 | − | 1.08492i | −0.530875 | − | 0.0442915i | ||||
\(601\) | − | 11.0819i | − | 0.452041i | −0.974123 | − | 0.226021i | \(-0.927428\pi\) | ||
0.974123 | − | 0.226021i | \(-0.0725717\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.416491 | − | 0.416491i | −0.0169608 | − | 0.0169608i | ||||
\(604\) | 22.5704 | − | 13.0310i | 0.918375 | − | 0.530224i | ||||
\(605\) | −8.56339 | − | 0.356607i | −0.348151 | − | 0.0144981i | ||||
\(606\) | −7.33142 | + | 12.6984i | −0.297819 | + | 0.515837i | ||||
\(607\) | −2.76222 | + | 10.3088i | −0.112115 | + | 0.418419i | −0.999055 | − | 0.0434656i | \(-0.986160\pi\) |
0.886940 | + | 0.461885i | \(0.152827\pi\) | |||||||
\(608\) | 0.289130 | − | 0.289130i | 0.0117258 | − | 0.0117258i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.30346 | + | 23.3273i | −0.295708 | + | 0.944496i | ||||
\(611\) | 20.1398 | + | 34.8831i | 0.814767 | + | 1.41122i | ||||
\(612\) | 2.88323 | − | 0.772560i | 0.116548 | − | 0.0312289i | ||||
\(613\) | 3.58564 | − | 0.960769i | 0.144823 | − | 0.0388051i | −0.185679 | − | 0.982610i | \(-0.559449\pi\) |
0.330502 | + | 0.943805i | \(0.392782\pi\) | |||||||
\(614\) | −7.89676 | − | 13.6776i | −0.318687 | − | 0.551983i | ||||
\(615\) | 5.79964 | − | 18.5241i | 0.233864 | − | 0.746965i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.3212 | − | 11.3212i | 0.455774 | − | 0.455774i | −0.441491 | − | 0.897266i | \(-0.645550\pi\) |
0.897266 | + | 0.441491i | \(0.145550\pi\) | |||||||
\(618\) | −0.653770 | + | 2.43990i | −0.0262985 | + | 0.0981473i | ||||
\(619\) | −4.53385 | + | 7.85287i | −0.182231 | + | 0.315633i | −0.942640 | − | 0.333811i | \(-0.891665\pi\) |
0.760409 | + | 0.649445i | \(0.224999\pi\) | |||||||
\(620\) | −7.58478 | − | 0.315855i | −0.304612 | − | 0.0126850i | ||||
\(621\) | −0.654230 | + | 0.377720i | −0.0262533 | + | 0.0151574i | ||||
\(622\) | 1.54599 | + | 1.54599i | 0.0619884 | + | 0.0619884i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 4.35458i | − | 0.174323i | ||||||
\(625\) | −15.9149 | + | 19.2799i | −0.636595 | + | 0.771198i | ||||
\(626\) | 8.81129 | + | 5.08720i | 0.352170 | + | 0.203325i | ||||
\(627\) | −0.0695445 | − | 0.259544i | −0.00277734 | − | 0.0103652i | ||||
\(628\) | 2.03160 | + | 0.544366i | 0.0810697 | + | 0.0217225i | ||||
\(629\) | −18.4398 | −0.735244 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.67260 | −0.385060 | −0.192530 | − | 0.981291i | \(-0.561669\pi\) | ||||
−0.192530 | + | 0.981291i | \(0.561669\pi\) | |||||||
\(632\) | 24.8639 | + | 6.66227i | 0.989034 | + | 0.265011i | ||||
\(633\) | 3.11201 | + | 11.6142i | 0.123691 | + | 0.461622i | ||||
\(634\) | 6.90730 | + | 3.98793i | 0.274324 | + | 0.158381i | ||||
\(635\) | 3.33794 | + | 14.9143i | 0.132462 | + | 0.591854i | ||||
\(636\) | − | 12.2962i | − | 0.487577i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 5.76463 | + | 5.76463i | 0.228224 | + | 0.228224i | ||||
\(639\) | 7.03890 | − | 4.06391i | 0.278455 | − | 0.160766i | ||||
\(640\) | 14.5103 | + | 15.7713i | 0.573570 | + | 0.623416i | ||||
\(641\) | 20.2924 | − | 35.1474i | 0.801500 | − | 1.38824i | −0.117129 | − | 0.993117i | \(-0.537369\pi\) |
0.918629 | − | 0.395122i | \(-0.129298\pi\) | |||||||
\(642\) | −1.78872 | + | 6.67561i | −0.0705953 | + | 0.263465i | ||||
\(643\) | −3.89544 | + | 3.89544i | −0.153621 | + | 0.153621i | −0.779733 | − | 0.626112i | \(-0.784645\pi\) |
0.626112 | + | 0.779733i | \(0.284645\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.06191 | + | 7.76463i | 0.159937 | + | 0.305732i | ||||
\(646\) | −0.0561524 | − | 0.0972588i | −0.00220929 | − | 0.00382660i | ||||
\(647\) | 23.0058 | − | 6.16438i | 0.904450 | − | 0.242347i | 0.223524 | − | 0.974698i | \(-0.428244\pi\) |
0.680927 | + | 0.732352i | \(0.261577\pi\) | |||||||
\(648\) | 2.52086 | − | 0.675461i | 0.0990285 | − | 0.0265346i | ||||
\(649\) | 13.4305 | + | 23.2623i | 0.527192 | + | 0.913123i | ||||
\(650\) | 16.2758 | + | 11.2990i | 0.638388 | + | 0.443183i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.79833 | + | 7.79833i | −0.305406 | + | 0.305406i | ||||
\(653\) | −8.41678 | + | 31.4119i | −0.329374 | + | 1.22924i | 0.580467 | + | 0.814284i | \(0.302870\pi\) |
−0.909841 | + | 0.414957i | \(0.863797\pi\) | |||||||
\(654\) | 0.825207 | − | 1.42930i | 0.0322681 | − | 0.0558901i | ||||
\(655\) | 0.0602410 | − | 1.44660i | 0.00235381 | − | 0.0565232i | ||||
\(656\) | −6.31062 | + | 3.64344i | −0.246388 | + | 0.142252i | ||||
\(657\) | 9.55210 | + | 9.55210i | 0.372663 | + | 0.372663i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 32.7543i | − | 1.27593i | −0.770067 | − | 0.637963i | \(-0.779777\pi\) | ||
0.770067 | − | 0.637963i | \(-0.220223\pi\) | |||||||
\(660\) | 11.9042 | − | 2.66426i | 0.463370 | − | 0.103706i | ||||
\(661\) | −28.1609 | − | 16.2587i | −1.09533 | − | 0.632391i | −0.160341 | − | 0.987062i | \(-0.551260\pi\) |
−0.934991 | + | 0.354671i | \(0.884593\pi\) | |||||||
\(662\) | 4.66982 | + | 17.4280i | 0.181498 | + | 0.677359i | ||||
\(663\) | −10.5592 | − | 2.82932i | −0.410084 | − | 0.109882i | ||||
\(664\) | −6.03701 | −0.234281 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6.68434 | −0.259013 | ||||||||
\(667\) | 2.02205 | + | 0.541806i | 0.0782940 | + | 0.0209788i | ||||
\(668\) | 0.979744 | + | 3.65646i | 0.0379075 | + | 0.141473i | ||||
\(669\) | −14.3203 | − | 8.26785i | −0.553656 | − | 0.319654i | ||||
\(670\) | −0.849600 | − | 0.538852i | −0.0328229 | − | 0.0208177i | ||||
\(671\) | − | 55.1158i | − | 2.12772i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.7534 | − | 16.7534i | −0.645796 | − | 0.645796i | 0.306179 | − | 0.951974i | \(-0.400950\pi\) |
−0.951974 | + | 0.306179i | \(0.900950\pi\) | |||||||
\(674\) | 4.61986 | − | 2.66728i | 0.177950 | − | 0.102740i | ||||
\(675\) | 1.69116 | − | 4.70531i | 0.0650928 | − | 0.181108i | ||||
\(676\) | −9.85228 | + | 17.0647i | −0.378934 | + | 0.656333i | ||||
\(677\) | 2.50935 | − | 9.36503i | 0.0964422 | − | 0.359927i | −0.900792 | − | 0.434251i | \(-0.857013\pi\) |
0.997234 | + | 0.0743237i | \(0.0236798\pi\) | |||||||
\(678\) | 3.16110 | − | 3.16110i | 0.121401 | − | 0.121401i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 10.8964 | − | 5.70024i | 0.417858 | − | 0.218594i | ||||
\(681\) | −0.781481 | − | 1.35357i | −0.0299464 | − | 0.0518687i | ||||
\(682\) | −6.81087 | + | 1.82497i | −0.260802 | + | 0.0698816i | ||||
\(683\) | −31.7389 | + | 8.50440i | −1.21445 | + | 0.325412i | −0.808508 | − | 0.588485i | \(-0.799725\pi\) |
−0.405946 | + | 0.913897i | \(0.633058\pi\) | |||||||
\(684\) | 0.0494124 | + | 0.0855848i | 0.00188933 | + | 0.00327242i | ||||
\(685\) | 30.8932 | + | 9.67222i | 1.18037 | + | 0.369557i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.53883 | − | 5.53883i | 0.211319 | − | 0.211319i | ||||
\(688\) | 0.851417 | − | 3.17753i | 0.0324600 | − | 0.121142i | ||||
\(689\) | −22.5160 | + | 38.9989i | −0.857793 | + | 1.48574i | ||||
\(690\) | −0.949590 | + | 0.873664i | −0.0361503 | + | 0.0332598i | ||||
\(691\) | 36.7813 | − | 21.2357i | 1.39923 | − | 0.807845i | 0.404916 | − | 0.914354i | \(-0.367301\pi\) |
0.994312 | + | 0.106509i | \(0.0339673\pi\) | |||||||
\(692\) | 6.95144 | + | 6.95144i | 0.264254 | + | 0.264254i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 6.30557i | − | 0.239356i | ||||||
\(695\) | 26.5472 | − | 41.8565i | 1.00699 | − | 1.58771i | ||||
\(696\) | −6.26301 | − | 3.61595i | −0.237399 | − | 0.137062i | ||||
\(697\) | 4.73453 | + | 17.6695i | 0.179333 | + | 0.669280i | ||||
\(698\) | −12.4786 | − | 3.34362i | −0.472320 | − | 0.126558i | ||||
\(699\) | −1.42549 | −0.0539169 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.0793 | 0.645077 | 0.322539 | − | 0.946556i | \(-0.395464\pi\) | ||||
0.322539 | + | 0.946556i | \(0.395464\pi\) | |||||||
\(702\) | −3.82764 | − | 1.02561i | −0.144465 | − | 0.0387093i | ||||
\(703\) | −0.158010 | − | 0.589700i | −0.00595944 | − | 0.0222409i | ||||
\(704\) | 9.33261 | + | 5.38818i | 0.351736 | + | 0.203075i | ||||
\(705\) | 9.29921 | − | 14.6619i | 0.350229 | − | 0.552200i | ||||
\(706\) | − | 12.0198i | − | 0.452370i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −6.98563 | − | 6.98563i | −0.262536 | − | 0.262536i | ||||
\(709\) | −28.2967 | + | 16.3371i | −1.06270 | + | 0.613552i | −0.926179 | − | 0.377084i | \(-0.876927\pi\) |
−0.136525 | + | 0.990637i | \(0.543593\pi\) | |||||||
\(710\) | 10.2167 | − | 9.39981i | 0.383426 | − | 0.352769i | ||||
\(711\) | −4.93165 | + | 8.54186i | −0.184951 | + | 0.320345i | ||||
\(712\) | 3.41319 | − | 12.7382i | 0.127915 | − | 0.477385i | ||||
\(713\) | −1.28028 | + | 1.28028i | −0.0479469 | + | 0.0479469i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −42.6341 | − | 13.3481i | −1.59443 | − | 0.499192i | ||||
\(716\) | −13.1632 | − | 22.7994i | −0.491933 | − | 0.852052i | ||||
\(717\) | 19.5894 | − | 5.24897i | 0.731581 | − | 0.196027i | ||||
\(718\) | −6.01247 | + | 1.61104i | −0.224383 | + | 0.0601233i | ||||
\(719\) | −9.66239 | − | 16.7357i | −0.360346 | − | 0.624138i | 0.627671 | − | 0.778478i | \(-0.284008\pi\) |
−0.988018 | + | 0.154340i | \(0.950675\pi\) | |||||||
\(720\) | −1.66319 | + | 0.870061i | −0.0619832 | + | 0.0324253i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −10.2601 | + | 10.2601i | −0.381841 | + | 0.381841i | ||||
\(723\) | −0.716912 | + | 2.67555i | −0.0266622 | + | 0.0995048i | ||||
\(724\) | 6.00966 | − | 10.4090i | 0.223347 | − | 0.386849i | ||||
\(725\) | −12.5335 | + | 5.90607i | −0.465484 | + | 0.219346i | ||||
\(726\) | 2.53566 | − | 1.46396i | 0.0941072 | − | 0.0543328i | ||||
\(727\) | −2.71795 | − | 2.71795i | −0.100803 | − | 0.100803i | 0.654907 | − | 0.755710i | \(-0.272708\pi\) |
−0.755710 | + | 0.654907i | \(0.772708\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 19.4853 | + | 12.3584i | 0.721185 | + | 0.457406i | ||||
\(731\) | −7.15181 | − | 4.12910i | −0.264519 | − | 0.152720i | ||||
\(732\) | 5.24652 | + | 19.5803i | 0.193917 | + | 0.723709i | ||||
\(733\) | −3.25711 | − | 0.872739i | −0.120304 | − | 0.0322354i | 0.198165 | − | 0.980169i | \(-0.436502\pi\) |
−0.318469 | + | 0.947933i | \(0.603169\pi\) | |||||||
\(734\) | −15.9321 | −0.588064 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.42747 | 0.163199 | ||||||||
\(737\) | 2.19118 | + | 0.587125i | 0.0807132 | + | 0.0216270i | ||||
\(738\) | 1.71624 | + | 6.40510i | 0.0631757 | + | 0.235775i | ||||
\(739\) | 4.29271 | + | 2.47840i | 0.157910 | + | 0.0911693i | 0.576873 | − | 0.816834i | \(-0.304273\pi\) |
−0.418963 | + | 0.908003i | \(0.637606\pi\) | |||||||
\(740\) | 27.0471 | − | 6.05337i | 0.994270 | − | 0.222526i | ||||
\(741\) | − | 0.361923i | − | 0.0132956i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.6556 | + | 15.6556i | 0.574347 | + | 0.574347i | 0.933340 | − | 0.358993i | \(-0.116880\pi\) |
−0.358993 | + | 0.933340i | \(0.616880\pi\) | |||||||
\(744\) | 5.41695 | − | 3.12748i | 0.198595 | − | 0.114659i | ||||
\(745\) | 1.02782 | − | 24.6817i | 0.0376566 | − | 0.904266i | ||||
\(746\) | −0.807303 | + | 1.39829i | −0.0295575 | + | 0.0511950i | ||||
\(747\) | 0.598706 | − | 2.23440i | 0.0219055 | − | 0.0817525i | ||||
\(748\) | −8.12896 | + | 8.12896i | −0.297224 | + | 0.297224i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.06357 | − | 8.47393i | 0.0388360 | − | 0.309424i | ||||
\(751\) | 5.59544 | + | 9.69159i | 0.204181 | + | 0.353651i | 0.949871 | − | 0.312641i | \(-0.101214\pi\) |
−0.745691 | + | 0.666292i | \(0.767880\pi\) | |||||||
\(752\) | −6.29575 | + | 1.68694i | −0.229582 | + | 0.0615164i | ||||
\(753\) | −5.89197 | + | 1.57875i | −0.214715 | + | 0.0575328i | ||||
\(754\) | 5.49042 | + | 9.50969i | 0.199949 | + | 0.346322i | ||||
\(755\) | 19.0704 | + | 36.4545i | 0.694045 | + | 1.32672i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.4977 | − | 29.4977i | 1.07211 | − | 1.07211i | 0.0749214 | − | 0.997189i | \(-0.476129\pi\) |
0.997189 | − | 0.0749214i | \(-0.0238706\pi\) | |||||||
\(758\) | 3.69977 | − | 13.8077i | 0.134382 | − | 0.501520i | ||||
\(759\) | 1.45473 | − | 2.51967i | 0.0528035 | − | 0.0914584i | ||||
\(760\) | 0.275662 | + | 0.299619i | 0.00999932 | + | 0.0108683i | ||||
\(761\) | 24.3504 | − | 14.0587i | 0.882703 | − | 0.509629i | 0.0111541 | − | 0.999938i | \(-0.496449\pi\) |
0.871549 | + | 0.490309i | \(0.163116\pi\) | |||||||
\(762\) | −3.69181 | − | 3.69181i | −0.133740 | − | 0.133740i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 7.63986i | − | 0.276400i | ||||||
\(765\) | 1.02913 | + | 4.59826i | 0.0372083 | + | 0.166251i | ||||
\(766\) | −19.5862 | − | 11.3081i | −0.707679 | − | 0.408579i | ||||
\(767\) | 9.36412 | + | 34.9474i | 0.338119 | + | 1.26188i | ||||
\(768\) | −12.4771 | − | 3.34324i | −0.450230 | − | 0.120639i | ||||
\(769\) | −6.61248 | −0.238452 | −0.119226 | − | 0.992867i | \(-0.538041\pi\) | ||||
−0.119226 | + | 0.992867i | \(0.538041\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.85449 | −0.102802 | ||||||||
\(772\) | −9.29941 | − | 2.49177i | −0.334693 | − | 0.0896807i | ||||
\(773\) | −11.6120 | − | 43.3367i | −0.417656 | − | 1.55871i | −0.779456 | − | 0.626457i | \(-0.784504\pi\) |
0.361800 | − | 0.932256i | \(-0.382162\pi\) | |||||||
\(774\) | −2.59249 | − | 1.49678i | −0.0931853 | − | 0.0538005i | ||||
\(775\) | 0.996351 | − | 11.9422i | 0.0357900 | − | 0.428976i | ||||
\(776\) | − | 25.3133i | − | 0.908695i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 13.8607 | + | 13.8607i | 0.496929 | + | 0.496929i | ||||
\(779\) | −0.524495 | + | 0.302817i | −0.0187920 | + | 0.0108496i | ||||
\(780\) | 16.4167 | + | 0.683645i | 0.587812 | + | 0.0244784i | ||||
\(781\) | −15.6516 | + | 27.1094i | −0.560058 | + | 0.970049i | ||||
\(782\) | 0.314733 | − | 1.17460i | 0.0112548 | − | 0.0420035i | ||||
\(783\) | 1.95945 | − | 1.95945i | 0.0700249 | − | 0.0700249i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.992027 | + | 3.16855i | −0.0354070 | + | 0.113090i | ||||
\(786\) | 0.247305 | + | 0.428345i | 0.00882108 | + | 0.0152786i | ||||
\(787\) | 30.6634 | − | 8.21624i | 1.09303 | − | 0.292877i | 0.333108 | − | 0.942889i | \(-0.391903\pi\) |
0.759924 | + | 0.650011i | \(0.225236\pi\) | |||||||
\(788\) | −24.5236 | + | 6.57108i | −0.873617 | + | 0.234085i | ||||
\(789\) | 11.8572 | + | 20.5372i | 0.422127 | + | 0.731145i | ||||
\(790\) | −5.03372 | + | 16.0777i | −0.179092 | + | 0.572021i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −7.10728 | + | 7.10728i | −0.252546 | + | 0.252546i | ||||
\(793\) | 19.2142 | − | 71.7082i | 0.682315 | − | 2.54643i | ||||
\(794\) | 3.63833 | − | 6.30177i | 0.129119 | − | 0.223641i | ||||
\(795\) | 19.3940 | + | 0.807629i | 0.687834 | + | 0.0286436i | ||||
\(796\) | 3.27670 | − | 1.89180i | 0.116139 | − | 0.0670531i | ||||
\(797\) | −5.14677 | − | 5.14677i | −0.182308 | − | 0.182308i | 0.610053 | − | 0.792361i | \(-0.291148\pi\) |
−0.792361 | + | 0.610053i | \(0.791148\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.3622i | 0.578854i | ||||||||
\(800\) | −22.3720 | + | 18.9265i | −0.790971 | + | 0.669151i | ||||
\(801\) | 4.37614 | + | 2.52657i | 0.154623 | + | 0.0892718i | ||||
\(802\) | 2.91622 | + | 10.8835i | 0.102975 | + | 0.384309i | ||||
\(803\) | −50.2541 | − | 13.4656i | −1.77343 | − | 0.475189i | ||||
\(804\) | −0.834323 | −0.0294243 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9.49747 | −0.334534 | ||||||||
\(807\) | −23.8923 | − | 6.40192i | −0.841049 | − | 0.225358i | ||||
\(808\) | 12.9657 | + | 48.3885i | 0.456130 | + | 1.70230i | ||||
\(809\) | 19.5042 | + | 11.2608i | 0.685732 | + | 0.395907i | 0.802011 | − | 0.597309i | \(-0.203763\pi\) |
−0.116279 | + | 0.993217i | \(0.537097\pi\) | |||||||
\(810\) | 0.373055 | + | 1.66685i | 0.0131078 | + | 0.0585670i | ||||
\(811\) | − | 34.9145i | − | 1.22602i | −0.790077 | − | 0.613008i | \(-0.789960\pi\) | ||
0.790077 | − | 0.613008i | \(-0.210040\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.92367 | − | 2.92367i | −0.102538 | − | 0.102538i | ||||
\(814\) | 22.2948 | − | 12.8719i | 0.781432 | − | 0.451160i | ||||
\(815\) | −11.7876 | − | 12.8120i | −0.412900 | − | 0.448784i | ||||
\(816\) | 0.884454 | − | 1.53192i | 0.0309621 | − | 0.0536279i | ||||
\(817\) | 0.0707639 | − | 0.264094i | 0.00247572 | − | 0.00923949i | ||||
\(818\) | −5.70414 | + | 5.70414i | −0.199441 | + | 0.199441i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12.7450 | − | 24.3629i | −0.445074 | − | 0.850790i | ||||
\(821\) | −4.26320 | − | 7.38408i | −0.148787 | − | 0.257706i | 0.781993 | − | 0.623288i | \(-0.214203\pi\) |
−0.930779 | + | 0.365582i | \(0.880870\pi\) | |||||||
\(822\) | −10.6820 | + | 2.86222i | −0.372576 | + | 0.0998315i | ||||
\(823\) | 46.3143 | − | 12.4099i | 1.61441 | − | 0.432581i | 0.665060 | − | 0.746790i | \(-0.268406\pi\) |
0.949354 | + | 0.314209i | \(0.101739\pi\) | |||||||
\(824\) | 4.31498 | + | 7.47377i | 0.150320 | + | 0.260361i | ||||
\(825\) | 3.42027 | + | 18.9506i | 0.119079 | + | 0.659776i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −37.8440 | + | 37.8440i | −1.31597 | + | 1.31597i | −0.399025 | + | 0.916940i | \(0.630651\pi\) |
−0.916940 | + | 0.399025i | \(0.869349\pi\) | |||||||
\(828\) | −0.276955 | + | 1.03361i | −0.00962486 | + | 0.0359205i | ||||
\(829\) | −16.8570 | + | 29.1972i | −0.585469 | + | 1.01406i | 0.409348 | + | 0.912378i | \(0.365756\pi\) |
−0.994817 | + | 0.101683i | \(0.967577\pi\) | |||||||
\(830\) | 0.164397 | − | 3.94776i | 0.00570632 | − | 0.137029i | ||||
\(831\) | −14.8350 | + | 8.56502i | −0.514622 | + | 0.297117i | ||||
\(832\) | 10.2638 | + | 10.2638i | 0.355832 | + | 0.355832i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 16.9323i | 0.586319i | ||||||||
\(835\) | −5.83142 | + | 1.30512i | −0.201805 | + | 0.0451656i | ||||
\(836\) | −0.329618 | − | 0.190305i | −0.0114001 | − | 0.00658184i | ||||
\(837\) | 0.620321 | + | 2.31507i | 0.0214414 | + | 0.0800205i | ||||
\(838\) | 11.4715 | + | 3.07378i | 0.396277 | + | 0.106182i | ||||
\(839\) | 16.0665 | 0.554679 | 0.277339 | − | 0.960772i | \(-0.410547\pi\) | ||||
0.277339 | + | 0.960772i | \(0.410547\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.3211 | 0.735212 | ||||||||
\(842\) | −2.43406 | − | 0.652204i | −0.0838832 | − | 0.0224764i | ||||
\(843\) | −1.35952 | − | 5.07381i | −0.0468245 | − | 0.174751i | ||||
\(844\) | 14.7499 | + | 8.51585i | 0.507712 | + | 0.293128i | ||||
\(845\) | −26.2678 | − | 16.6601i | −0.903639 | − | 0.573126i | ||||
\(846\) | 5.93123i | 0.203920i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −5.15260 | − | 5.15260i | −0.176941 | − | 0.176941i | ||||
\(849\) | 2.04201 | − | 1.17895i | 0.0700814 | − | 0.0404615i | ||||
\(850\) | 3.43081 | + | 7.28067i | 0.117676 | + | 0.249725i | ||||
\(851\) | 3.30525 | − | 5.72486i | 0.113303 | − | 0.196246i | ||||
\(852\) | 2.97978 | − | 11.1207i | 0.102086 | − | 0.380989i | ||||
\(853\) | −5.14393 | + | 5.14393i | −0.176125 | + | 0.176125i | −0.789664 | − | 0.613539i | \(-0.789745\pi\) |
0.613539 | + | 0.789664i | \(0.289745\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.138232 | + | 0.0723134i | −0.00472745 | + | 0.00247307i | ||||
\(856\) | 11.8059 | + | 20.4483i | 0.403516 | + | 0.698910i | ||||
\(857\) | −7.71909 | + | 2.06832i | −0.263679 | + | 0.0706526i | −0.388236 | − | 0.921560i | \(-0.626916\pi\) |
0.124557 | + | 0.992212i | \(0.460249\pi\) | |||||||
\(858\) | 14.7416 | − | 3.95001i | 0.503271 | − | 0.134851i | ||||
\(859\) | 21.0400 | + | 36.4424i | 0.717877 | + | 1.24340i | 0.961839 | + | 0.273615i | \(0.0882193\pi\) |
−0.243963 | + | 0.969785i | \(0.578447\pi\) | |||||||
\(860\) | 11.8456 | + | 3.70868i | 0.403931 | + | 0.126465i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7.61119 | + | 7.61119i | −0.259238 | + | 0.259238i | ||||
\(863\) | −4.38413 | + | 16.3618i | −0.149237 | + | 0.556962i | 0.850293 | + | 0.526310i | \(0.176425\pi\) |
−0.999530 | + | 0.0306516i | \(0.990242\pi\) | |||||||
\(864\) | 2.93039 | − | 5.07559i | 0.0996939 | − | 0.172675i | ||||
\(865\) | −11.4206 | + | 10.5074i | −0.388312 | + | 0.357264i | ||||
\(866\) | −1.61524 | + | 0.932557i | −0.0548879 | + | 0.0316896i | ||||
\(867\) | 8.88082 | + | 8.88082i | 0.301608 | + | 0.301608i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 37.9871i | − | 1.28862i | ||||||
\(870\) | 2.53511 | − | 3.99708i | 0.0859484 | − | 0.135514i | ||||
\(871\) | 2.64615 | + | 1.52776i | 0.0896614 | + | 0.0517660i | ||||
\(872\) | −1.45938 | − | 5.44649i | −0.0494209 | − | 0.184441i | ||||
\(873\) | 9.36890 | + | 2.51039i | 0.317089 | + | 0.0849638i | ||||
\(874\) | 0.0402602 | 0.00136182 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 19.1350 | 0.646510 | ||||||||
\(877\) | 15.8208 | + | 4.23918i | 0.534232 | + | 0.143147i | 0.515842 | − | 0.856684i | \(-0.327479\pi\) |
0.0183902 | + | 0.999831i | \(0.494146\pi\) | |||||||
\(878\) | 5.36123 | + | 20.0084i | 0.180933 | + | 0.675250i | ||||
\(879\) | −18.6842 | − | 10.7873i | −0.630202 | − | 0.363847i | ||||
\(880\) | 3.87189 | − | 6.10474i | 0.130521 | − | 0.205791i | ||||
\(881\) | 8.72058i | 0.293804i | 0.989151 | + | 0.146902i | \(0.0469301\pi\) | ||||
−0.989151 | + | 0.146902i | \(0.953070\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.0876 | + | 17.0876i | 0.575044 | + | 0.575044i | 0.933534 | − | 0.358490i | \(-0.116708\pi\) |
−0.358490 | + | 0.933534i | \(0.616708\pi\) | |||||||
\(884\) | −13.4100 | + | 7.74229i | −0.451028 | + | 0.260401i | ||||
\(885\) | 11.4768 | − | 10.5591i | 0.385787 | − | 0.354941i | ||||
\(886\) | 13.0445 | − | 22.5938i | 0.438240 | − | 0.759054i | ||||
\(887\) | −9.66396 | + | 36.0664i | −0.324484 | + | 1.21099i | 0.590346 | + | 0.807151i | \(0.298991\pi\) |
−0.914830 | + | 0.403840i | \(0.867675\pi\) | |||||||
\(888\) | −16.1482 | + | 16.1482i | −0.541898 | + | 0.541898i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 8.23690 | + | 2.57886i | 0.276101 | + | 0.0864435i | ||||
\(891\) | −1.92568 | − | 3.33538i | −0.0645127 | − | 0.111739i | ||||
\(892\) | −22.6246 | + | 6.06223i | −0.757526 | + | 0.202979i | ||||
\(893\) | −0.523259 | + | 0.140207i | −0.0175102 | + | 0.00469184i | ||||
\(894\) | 4.21949 | + | 7.30836i | 0.141121 | + | 0.244428i | ||||
\(895\) | 36.8244 | − | 19.2639i | 1.23090 | − | 0.643922i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.77107 | − | 2.77107i | 0.0925235 | − | 0.0925235i | ||||
\(898\) | −1.93805 | + | 7.23289i | −0.0646735 | + | 0.241365i | ||||
\(899\) | 3.32077 | − | 5.75174i | 0.110754 | − | 0.191831i | ||||
\(900\) | −3.01901 | − | 6.40677i | −0.100634 | − | 0.213559i | ||||
\(901\) | −15.8420 | + | 9.14640i | −0.527775 | + | 0.304711i | ||||
\(902\) | −18.0585 | − | 18.0585i | −0.601282 | − | 0.601282i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 15.2733i | − | 0.507984i | ||||||
\(905\) | 16.0227 | + | 10.1623i | 0.532613 | + | 0.337806i | ||||
\(906\) | −12.1716 | − | 7.02729i | −0.404375 | − | 0.233466i | ||||
\(907\) | −8.65482 | − | 32.3002i | −0.287379 | − | 1.07251i | −0.947084 | − | 0.320987i | \(-0.895985\pi\) |
0.659705 | − | 0.751525i | \(-0.270681\pi\) | |||||||
\(908\) | −2.13848 | − | 0.573005i | −0.0709681 | − | 0.0190158i | ||||
\(909\) | −19.1953 | −0.636667 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17.8226 | −0.590490 | −0.295245 | − | 0.955422i | \(-0.595401\pi\) | ||||
−0.295245 | + | 0.955422i | \(0.595401\pi\) | |||||||
\(912\) | 0.0565691 | + | 0.0151576i | 0.00187319 | + | 0.000501920i | ||||
\(913\) | 2.30583 | + | 8.60549i | 0.0763120 | + | 0.284800i | ||||
\(914\) | 0.514622 | + | 0.297117i | 0.0170222 | + | 0.00982776i | ||||
\(915\) | −31.2272 | + | 6.98892i | −1.03234 | + | 0.231047i | ||||
\(916\) | − | 11.0955i | − | 0.366605i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −1.13823 | − | 1.13823i | −0.0375673 | − | 0.0375673i | ||||
\(919\) | −18.6847 | + | 10.7876i | −0.616351 | + | 0.355850i | −0.775447 | − | 0.631413i | \(-0.782475\pi\) |
0.159096 | + | 0.987263i | \(0.449142\pi\) | |||||||
\(920\) | −0.183424 | + | 4.40466i | −0.00604732 | + | 0.145217i | ||||
\(921\) | 10.3377 | − | 17.9055i | 0.340640 | − | 0.590005i | ||||
\(922\) | 0.164449 | − | 0.613733i | 0.00541585 | − | 0.0202122i | ||||
\(923\) | −29.8142 | + | 29.8142i | −0.981346 | + | 0.981346i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.77107 | + | 43.0570i | 0.255511 | + | 1.41571i | ||||
\(926\) | −2.94454 | − | 5.10009i | −0.0967636 | − | 0.167599i | ||||
\(927\) | −3.19410 | + | 0.855857i | −0.104908 | + | 0.0281100i | ||||
\(928\) | −15.6873 | + | 4.20339i | −0.514960 | + | 0.137983i | ||||
\(929\) | 19.1535 | + | 33.1748i | 0.628405 | + | 1.08843i | 0.987872 | + | 0.155272i | \(0.0496253\pi\) |
−0.359467 | + | 0.933158i | \(0.617041\pi\) | |||||||
\(930\) | 1.89763 | + | 3.62745i | 0.0622257 | + | 0.118949i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.42778 | + | 1.42778i | −0.0467686 | + | 0.0467686i | ||||
\(933\) | −0.740787 | + | 2.76465i | −0.0242523 | + | 0.0905107i | ||||
\(934\) | −12.5760 | + | 21.7823i | −0.411500 | + | 0.712739i | ||||
\(935\) | −12.2873 | − | 13.3552i | −0.401838 | − | 0.436760i | ||||
\(936\) | −11.7246 | + | 6.76921i | −0.383231 | + | 0.221258i | ||||
\(937\) | −13.2317 | − | 13.2317i | −0.432262 | − | 0.432262i | 0.457135 | − | 0.889397i | \(-0.348875\pi\) |
−0.889397 | + | 0.457135i | \(0.848875\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.3194i | 0.434662i | ||||||||
\(940\) | −5.37134 | − | 23.9997i | −0.175194 | − | 0.782784i | ||||
\(941\) | 2.23517 | + | 1.29048i | 0.0728645 | + | 0.0420683i | 0.535990 | − | 0.844225i | \(-0.319939\pi\) |
−0.463125 | + | 0.886293i | \(0.653272\pi\) | |||||||
\(942\) | −0.293563 | − | 1.09559i | −0.00956479 | − | 0.0356963i | ||||
\(943\) | −6.33435 | − | 1.69728i | −0.206275 | − | 0.0552711i | ||||
\(944\) | −5.85450 | −0.190548 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11.5293 | 0.374848 | ||||||||
\(947\) | −6.75097 | − | 1.80892i | −0.219377 | − | 0.0587819i | 0.147456 | − | 0.989069i | \(-0.452891\pi\) |
−0.366833 | + | 0.930287i | \(0.619558\pi\) | |||||||
\(948\) | 3.61603 | + | 13.4952i | 0.117443 | + | 0.438304i | ||||
\(949\) | −60.6887 | − | 35.0387i | −1.97004 | − | 1.13740i | ||||
\(950\) | −0.203435 | + | 0.172104i | −0.00660031 | + | 0.00558378i | ||||
\(951\) | 10.4413i | 0.338582i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.3558 | − | 16.3558i | −0.529818 | − | 0.529818i | 0.390700 | − | 0.920518i | \(-0.372233\pi\) |
−0.920518 | + | 0.390700i | \(0.872233\pi\) | |||||||
\(954\) | −5.74266 | + | 3.31552i | −0.185925 | + | 0.107344i | ||||
\(955\) | 12.0498 | + | 0.501793i | 0.389923 | + | 0.0162376i | ||||
\(956\) | 14.3636 | − | 24.8784i | 0.464551 | − | 0.804625i | ||||
\(957\) | −2.76222 | + | 10.3088i | −0.0892900 | + | 0.333235i | ||||
\(958\) | 21.8390 | − | 21.8390i | 0.705587 | − | 0.705587i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.86939 | − | 5.97087i | 0.0603345 | − | 0.192709i | ||||
\(961\) | −12.6278 | − | 21.8720i | −0.407349 | − | 0.705550i | ||||
\(962\) | 33.4939 | − | 8.97467i | 1.07989 | − | 0.289355i | ||||
\(963\) | −8.73911 | + | 2.34164i | −0.281614 | + | 0.0754582i | ||||
\(964\) | 1.96179 | + | 3.39793i | 0.0631851 | + | 0.109440i | ||||
\(965\) | 4.54089 | − | 14.5036i | 0.146176 | − | 0.466889i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.66781 | − | 8.66781i | 0.278738 | − | 0.278738i | −0.553867 | − | 0.832605i | \(-0.686848\pi\) |
0.832605 | + | 0.553867i | \(0.186848\pi\) | |||||||
\(968\) | 2.58903 | − | 9.66239i | 0.0832146 | − | 0.310561i | ||||
\(969\) | 0.0735096 | − | 0.127322i | 0.00236147 | − | 0.00409019i | ||||
\(970\) | 16.5530 | + | 0.689322i | 0.531486 | + | 0.0221328i | ||||
\(971\) | −11.4195 | + | 6.59307i | −0.366470 | + | 0.211582i | −0.671915 | − | 0.740628i | \(-0.734528\pi\) |
0.305445 | + | 0.952210i | \(0.401195\pi\) | |||||||
\(972\) | 1.00161 | + | 1.00161i | 0.0321267 | + | 0.0321267i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 7.80931i | 0.250226i | ||||||||
\(975\) | −2.15653 | + | 25.8480i | −0.0690643 | + | 0.827799i | ||||
\(976\) | 10.4034 | + | 6.00641i | 0.333005 | + | 0.192260i | ||||
\(977\) | −8.96490 | − | 33.4574i | −0.286812 | − | 1.07040i | −0.947505 | − | 0.319742i | \(-0.896404\pi\) |
0.660692 | − | 0.750657i | \(-0.270263\pi\) | |||||||
\(978\) | 5.74475 | + | 1.53930i | 0.183697 | + | 0.0492214i | ||||
\(979\) | −19.4614 | −0.621990 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.16057 | 0.0689818 | ||||||||
\(982\) | −14.8337 | − | 3.97468i | −0.473362 | − | 0.126837i | ||||
\(983\) | −5.75986 | − | 21.4961i | −0.183711 | − | 0.685618i | −0.994903 | − | 0.100838i | \(-0.967848\pi\) |
0.811192 | − | 0.584780i | \(-0.198819\pi\) | |||||||
\(984\) | 19.6197 | + | 11.3275i | 0.625454 | + | 0.361106i | ||||
\(985\) | −8.75336 | − | 39.1109i | −0.278905 | − | 1.24618i | ||||
\(986\) | 4.46061i | 0.142055i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.362505 | − | 0.362505i | −0.0115328 | − | 0.0115328i | ||||
\(989\) | 2.56386 | − | 1.48024i | 0.0815259 | − | 0.0470690i | ||||
\(990\) | −4.45409 | − | 4.84118i | −0.141560 | − | 0.153863i | ||||
\(991\) | 15.0516 | − | 26.0701i | 0.478128 | − | 0.828142i | −0.521557 | − | 0.853216i | \(-0.674649\pi\) |
0.999686 | + | 0.0250738i | \(0.00798206\pi\) | |||||||
\(992\) | 3.63557 | − | 13.5681i | 0.115429 | − | 0.430788i | ||||
\(993\) | −16.7019 | + | 16.7019i | −0.530018 | + | 0.530018i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.76859 | + | 5.29236i | 0.0877702 | + | 0.167779i | ||||
\(996\) | −1.63833 | − | 2.83767i | −0.0519125 | − | 0.0899150i | ||||
\(997\) | −31.2439 | + | 8.37177i | −0.989503 | + | 0.265137i | −0.717042 | − | 0.697030i | \(-0.754504\pi\) |
−0.272461 | + | 0.962167i | \(0.587838\pi\) | |||||||
\(998\) | −11.3796 | + | 3.04916i | −0.360215 | + | 0.0965194i | ||||
\(999\) | −4.37527 | − | 7.57819i | −0.138427 | − | 0.239763i |
(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 | 735.2.v.a.178.3 | 32 | ||
5.2 | odd | 4 | inner | 735.2.v.a.472.5 | 32 | ||
7.2 | even | 3 | inner | 735.2.v.a.313.6 | 32 | ||
7.3 | odd | 6 | 105.2.m.a.13.6 | yes | 16 | ||
7.4 | even | 3 | 105.2.m.a.13.5 | ✓ | 16 | ||
7.5 | odd | 6 | inner | 735.2.v.a.313.5 | 32 | ||
7.6 | odd | 2 | inner | 735.2.v.a.178.4 | 32 | ||
21.11 | odd | 6 | 315.2.p.e.118.3 | 16 | |||
21.17 | even | 6 | 315.2.p.e.118.4 | 16 | |||
28.3 | even | 6 | 1680.2.cz.d.433.2 | 16 | |||
28.11 | odd | 6 | 1680.2.cz.d.433.7 | 16 | |||
35.2 | odd | 12 | inner | 735.2.v.a.607.4 | 32 | ||
35.3 | even | 12 | 525.2.m.b.307.4 | 16 | |||
35.4 | even | 6 | 525.2.m.b.118.4 | 16 | |||
35.12 | even | 12 | inner | 735.2.v.a.607.3 | 32 | ||
35.17 | even | 12 | 105.2.m.a.97.5 | yes | 16 | ||
35.18 | odd | 12 | 525.2.m.b.307.3 | 16 | |||
35.24 | odd | 6 | 525.2.m.b.118.3 | 16 | |||
35.27 | even | 4 | inner | 735.2.v.a.472.6 | 32 | ||
35.32 | odd | 12 | 105.2.m.a.97.6 | yes | 16 | ||
105.17 | odd | 12 | 315.2.p.e.307.3 | 16 | |||
105.32 | even | 12 | 315.2.p.e.307.4 | 16 | |||
140.67 | even | 12 | 1680.2.cz.d.97.2 | 16 | |||
140.87 | odd | 12 | 1680.2.cz.d.97.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.m.a.13.5 | ✓ | 16 | 7.4 | even | 3 | ||
105.2.m.a.13.6 | yes | 16 | 7.3 | odd | 6 | ||
105.2.m.a.97.5 | yes | 16 | 35.17 | even | 12 | ||
105.2.m.a.97.6 | yes | 16 | 35.32 | odd | 12 | ||
315.2.p.e.118.3 | 16 | 21.11 | odd | 6 | |||
315.2.p.e.118.4 | 16 | 21.17 | even | 6 | |||
315.2.p.e.307.3 | 16 | 105.17 | odd | 12 | |||
315.2.p.e.307.4 | 16 | 105.32 | even | 12 | |||
525.2.m.b.118.3 | 16 | 35.24 | odd | 6 | |||
525.2.m.b.118.4 | 16 | 35.4 | even | 6 | |||
525.2.m.b.307.3 | 16 | 35.18 | odd | 12 | |||
525.2.m.b.307.4 | 16 | 35.3 | even | 12 | |||
735.2.v.a.178.3 | 32 | 1.1 | even | 1 | trivial | ||
735.2.v.a.178.4 | 32 | 7.6 | odd | 2 | inner | ||
735.2.v.a.313.5 | 32 | 7.5 | odd | 6 | inner | ||
735.2.v.a.313.6 | 32 | 7.2 | even | 3 | inner | ||
735.2.v.a.472.5 | 32 | 5.2 | odd | 4 | inner | ||
735.2.v.a.472.6 | 32 | 35.27 | even | 4 | inner | ||
735.2.v.a.607.3 | 32 | 35.12 | even | 12 | inner | ||
735.2.v.a.607.4 | 32 | 35.2 | odd | 12 | inner | ||
1680.2.cz.d.97.2 | 16 | 140.67 | even | 12 | |||
1680.2.cz.d.97.7 | 16 | 140.87 | odd | 12 | |||
1680.2.cz.d.433.2 | 16 | 28.3 | even | 6 | |||
1680.2.cz.d.433.7 | 16 | 28.11 | odd | 6 |