Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,2,Mod(46,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.46");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.h (of order \(5\), degree \(4\), 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: | \(1.79663404548\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.26265625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 2x^{6} + x^{4} + 8x^{2} - 24x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 181.2 | ||
Root | \(1.40799 + 0.132563i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.181 |
Dual form | 225.2.h.c.46.2 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.346820 | + | 1.06740i | 0.245239 | + | 0.754768i | 0.995597 | + | 0.0937362i | \(0.0298810\pi\) |
−0.750358 | + | 0.661031i | \(0.770119\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.598970 | − | 0.435177i | 0.299485 | − | 0.217589i | ||||
\(5\) | −0.407987 | + | 2.19853i | −0.182457 | + | 0.983214i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.11373 | 0.420952 | 0.210476 | − | 0.977599i | \(-0.432499\pi\) | ||||
0.210476 | + | 0.977599i | \(0.432499\pi\) | |||||||
\(8\) | 2.48822 | + | 1.80780i | 0.879718 | + | 0.639152i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.48822 | + | 0.327009i | −0.786844 | + | 0.103409i | ||||
\(11\) | −1.13412 | − | 3.49045i | −0.341949 | − | 1.05241i | −0.963197 | − | 0.268796i | \(-0.913374\pi\) |
0.621248 | − | 0.783614i | \(-0.286626\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.25215 | + | 3.85372i | −0.347284 | + | 1.06883i | 0.613066 | + | 0.790032i | \(0.289936\pi\) |
−0.960350 | + | 0.278798i | \(0.910064\pi\) | |||||||
\(14\) | 0.386266 | + | 1.18880i | 0.103234 | + | 0.317721i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.609110 | + | 1.87465i | −0.152277 | + | 0.468662i | ||||
\(17\) | 1.71700 | + | 1.24748i | 0.416435 | + | 0.302557i | 0.776202 | − | 0.630485i | \(-0.217144\pi\) |
−0.359767 | + | 0.933042i | \(0.617144\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.28513 | + | 2.38678i | 0.753660 | + | 0.547566i | 0.896959 | − | 0.442113i | \(-0.145771\pi\) |
−0.143299 | + | 0.989679i | \(0.545771\pi\) | |||||||
\(20\) | 0.712379 | + | 1.49440i | 0.159293 | + | 0.334158i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.33238 | − | 2.42112i | 0.710466 | − | 0.516184i | ||||
\(23\) | −1.90799 | − | 5.87218i | −0.397843 | − | 1.22443i | −0.926725 | − | 0.375739i | \(-0.877389\pi\) |
0.528883 | − | 0.848695i | \(-0.322611\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.66709 | − | 1.79395i | −0.933419 | − | 0.358789i | ||||
\(26\) | −4.54774 | −0.891886 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.667093 | − | 0.484672i | 0.126069 | − | 0.0915943i | ||||
\(29\) | −1.82808 | + | 1.32818i | −0.339466 | + | 0.246637i | −0.744437 | − | 0.667693i | \(-0.767282\pi\) |
0.404970 | + | 0.914330i | \(0.367282\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.13227 | − | 5.90844i | −1.46060 | − | 1.06119i | −0.983206 | − | 0.182498i | \(-0.941582\pi\) |
−0.477393 | − | 0.878690i | \(-0.658418\pi\) | |||||||
\(32\) | 3.93896 | 0.696316 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.736068 | + | 2.26538i | −0.126235 | + | 0.388510i | ||||
\(35\) | −0.454389 | + | 2.44858i | −0.0768058 | + | 0.413886i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.27817 | − | 7.01149i | 0.374529 | − | 1.15268i | −0.569267 | − | 0.822153i | \(-0.692773\pi\) |
0.943796 | − | 0.330529i | \(-0.107227\pi\) | |||||||
\(38\) | −1.40831 | + | 4.33434i | −0.228458 | + | 0.703123i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.98966 | + | 4.73287i | −0.788934 | + | 0.748333i | ||||
\(41\) | 2.30902 | − | 7.10642i | 0.360608 | − | 1.10984i | −0.592078 | − | 0.805881i | \(-0.701692\pi\) |
0.952686 | − | 0.303956i | \(-0.0983077\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.24998 | 1.41061 | 0.705304 | − | 0.708905i | \(-0.250810\pi\) | ||||
0.705304 | + | 0.708905i | \(0.250810\pi\) | |||||||
\(44\) | −2.19826 | − | 1.59713i | −0.331401 | − | 0.240777i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.60625 | − | 4.07318i | 0.826597 | − | 0.600558i | ||||
\(47\) | −2.53032 | + | 1.83839i | −0.369085 | + | 0.268156i | −0.756831 | − | 0.653610i | \(-0.773254\pi\) |
0.387746 | + | 0.921766i | \(0.373254\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.75960 | −0.822799 | ||||||||
\(50\) | 0.296220 | − | 5.60384i | 0.0418918 | − | 0.792503i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.927051 | + | 2.85317i | 0.128559 | + | 0.395663i | ||||
\(53\) | −2.83934 | + | 2.06290i | −0.390013 | + | 0.283361i | −0.765461 | − | 0.643483i | \(-0.777489\pi\) |
0.375448 | + | 0.926844i | \(0.377489\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.13657 | − | 1.06933i | 1.09714 | − | 0.144189i | ||||
\(56\) | 2.77121 | + | 2.01340i | 0.370319 | + | 0.269053i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.05172 | − | 1.49066i | −0.269404 | − | 0.195733i | ||||
\(59\) | 2.03760 | − | 6.27109i | 0.265273 | − | 0.816427i | −0.726357 | − | 0.687317i | \(-0.758788\pi\) |
0.991630 | − | 0.129110i | \(-0.0412119\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.81332 | − | 8.65850i | −0.360208 | − | 1.10861i | −0.952928 | − | 0.303198i | \(-0.901946\pi\) |
0.592719 | − | 0.805409i | \(-0.298054\pi\) | |||||||
\(62\) | 3.48625 | − | 10.7296i | 0.442754 | − | 1.36266i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.58433 | + | 7.95375i | 0.323041 | + | 0.994219i | ||||
\(65\) | −7.96167 | − | 4.32516i | −0.987524 | − | 0.536470i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.12499 | − | 1.54390i | −0.259609 | − | 0.188617i | 0.450366 | − | 0.892844i | \(-0.351294\pi\) |
−0.709975 | + | 0.704227i | \(0.751294\pi\) | |||||||
\(68\) | 1.57131 | 0.190549 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.77121 | + | 0.364201i | −0.331223 | + | 0.0435304i | ||||
\(71\) | 0.534620 | − | 0.388424i | 0.0634477 | − | 0.0460975i | −0.555609 | − | 0.831443i | \(-0.687515\pi\) |
0.619057 | + | 0.785346i | \(0.287515\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.31003 | + | 7.10955i | 0.270369 | + | 0.832110i | 0.990408 | + | 0.138176i | \(0.0441239\pi\) |
−0.720039 | + | 0.693934i | \(0.755876\pi\) | |||||||
\(74\) | 8.27420 | 0.961856 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.00637 | 0.344854 | ||||||||
\(77\) | −1.26310 | − | 3.88743i | −0.143944 | − | 0.443014i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.90667 | + | 5.01799i | −0.777061 | + | 0.564568i | −0.904096 | − | 0.427330i | \(-0.859454\pi\) |
0.127034 | + | 0.991898i | \(0.459454\pi\) | |||||||
\(80\) | −3.87297 | − | 2.10398i | −0.433011 | − | 0.235232i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 8.38623 | 0.926104 | ||||||||
\(83\) | 9.92170 | + | 7.20854i | 1.08905 | + | 0.791240i | 0.979238 | − | 0.202713i | \(-0.0649758\pi\) |
0.109810 | + | 0.993953i | \(0.464976\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.44313 | + | 3.26594i | −0.373460 | + | 0.354240i | ||||
\(86\) | 3.20808 | + | 9.87345i | 0.345936 | + | 1.06468i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.48809 | − | 10.7352i | 0.371832 | − | 1.14438i | ||||
\(89\) | 4.72429 | + | 14.5399i | 0.500773 | + | 1.54122i | 0.807762 | + | 0.589509i | \(0.200679\pi\) |
−0.306989 | + | 0.951713i | \(0.599321\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.39456 | + | 4.29202i | −0.146190 | + | 0.449926i | ||||
\(92\) | −3.69826 | − | 2.68695i | −0.385571 | − | 0.280134i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.83986 | − | 2.06328i | −0.292910 | − | 0.212811i | ||||
\(95\) | −6.58771 | + | 6.24868i | −0.675885 | + | 0.641101i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.9217 | + | 7.93508i | −1.10893 | + | 0.805685i | −0.982495 | − | 0.186290i | \(-0.940354\pi\) |
−0.126436 | + | 0.991975i | \(0.540354\pi\) | |||||||
\(98\) | −1.99754 | − | 6.14781i | −0.201782 | − | 0.621022i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.57613 | + | 0.956493i | −0.357613 | + | 0.0956493i | ||||
\(101\) | −7.22642 | −0.719055 | −0.359528 | − | 0.933134i | \(-0.617062\pi\) | ||||
−0.359528 | + | 0.933134i | \(0.617062\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.26957 | + | 3.10203i | −0.420693 | + | 0.305652i | −0.777917 | − | 0.628367i | \(-0.783723\pi\) |
0.357223 | + | 0.934019i | \(0.383723\pi\) | |||||||
\(104\) | −10.0824 | + | 7.32526i | −0.988657 | + | 0.718301i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.18668 | − | 2.31526i | −0.309518 | − | 0.224878i | ||||
\(107\) | −5.46682 | −0.528498 | −0.264249 | − | 0.964455i | \(-0.585124\pi\) | ||||
−0.264249 | + | 0.964455i | \(0.585124\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.50410 | − | 10.7845i | 0.335632 | − | 1.03297i | −0.630778 | − | 0.775963i | \(-0.717264\pi\) |
0.966410 | − | 0.257005i | \(-0.0827358\pi\) | |||||||
\(110\) | 3.96334 | + | 8.31413i | 0.377889 | + | 0.792721i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.678387 | + | 2.08786i | −0.0641015 | + | 0.197284i | ||||
\(113\) | −1.49416 | + | 4.59855i | −0.140559 | + | 0.432595i | −0.996413 | − | 0.0846215i | \(-0.973032\pi\) |
0.855854 | + | 0.517217i | \(0.173032\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.6886 | − | 1.79900i | 1.27647 | − | 0.167758i | ||||
\(116\) | −0.516973 | + | 1.59108i | −0.0479997 | + | 0.147728i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.40046 | 0.681268 | ||||||||
\(119\) | 1.91229 | + | 1.38936i | 0.175299 | + | 0.127362i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.99783 | + | 1.45151i | −0.181621 | + | 0.131955i | ||||
\(122\) | 8.26639 | − | 6.00588i | 0.748404 | − | 0.543747i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.44220 | −0.668330 | ||||||||
\(125\) | 5.84816 | − | 9.52885i | 0.523075 | − | 0.852286i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.234728 | + | 0.722418i | 0.0208287 | + | 0.0641043i | 0.960931 | − | 0.276789i | \(-0.0892704\pi\) |
−0.940102 | + | 0.340894i | \(0.889270\pi\) | |||||||
\(128\) | −1.22019 | + | 0.886518i | −0.107850 | + | 0.0783578i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.85542 | − | 9.99836i | 0.162731 | − | 0.876914i | ||||
\(131\) | 11.8562 | + | 8.61406i | 1.03588 | + | 0.752614i | 0.969478 | − | 0.245179i | \(-0.0788467\pi\) |
0.0664061 | + | 0.997793i | \(0.478847\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.65876 | + | 2.65824i | 0.317255 | + | 0.230499i | ||||
\(134\) | 0.910969 | − | 2.80367i | 0.0786958 | − | 0.242201i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.01710 | + | 6.20799i | 0.172965 | + | 0.532330i | ||||
\(137\) | −3.79825 | + | 11.6898i | −0.324506 | + | 0.998728i | 0.647157 | + | 0.762357i | \(0.275958\pi\) |
−0.971663 | + | 0.236371i | \(0.924042\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.55306 | + | 14.0129i | 0.386185 | + | 1.18856i | 0.935617 | + | 0.353017i | \(0.114844\pi\) |
−0.549432 | + | 0.835539i | \(0.685156\pi\) | |||||||
\(140\) | 0.793401 | + | 1.66437i | 0.0670547 | + | 0.140665i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.600022 | + | 0.435941i | 0.0503527 | + | 0.0365834i | ||||
\(143\) | 14.8713 | 1.24360 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.17421 | − | 4.56098i | −0.180558 | − | 0.378768i | ||||
\(146\) | −6.78758 | + | 4.93147i | −0.561744 | + | 0.408131i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.68668 | − | 5.19108i | −0.138645 | − | 0.426704i | ||||
\(149\) | −15.6498 | −1.28208 | −0.641041 | − | 0.767507i | \(-0.721497\pi\) | ||||
−0.641041 | + | 0.767507i | \(0.721497\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.95819 | 0.322113 | 0.161056 | − | 0.986945i | \(-0.448510\pi\) | ||||
0.161056 | + | 0.986945i | \(0.448510\pi\) | |||||||
\(152\) | 3.85929 | + | 11.8777i | 0.313030 | + | 0.963407i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.71139 | − | 2.69648i | 0.299072 | − | 0.217289i | ||||
\(155\) | 16.3078 | − | 15.4685i | 1.30987 | − | 1.24246i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.50061 | −0.359188 | −0.179594 | − | 0.983741i | \(-0.557478\pi\) | ||||
−0.179594 | + | 0.983741i | \(0.557478\pi\) | |||||||
\(158\) | −7.75159 | − | 5.63186i | −0.616683 | − | 0.448047i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.60704 | + | 8.65993i | −0.127048 | + | 0.684627i | ||||
\(161\) | −2.12499 | − | 6.54005i | −0.167473 | − | 0.515428i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.758292 | + | 2.33378i | −0.0593940 | + | 0.182796i | −0.976352 | − | 0.216189i | \(-0.930637\pi\) |
0.916958 | + | 0.398985i | \(0.130637\pi\) | |||||||
\(164\) | −1.70952 | − | 5.26137i | −0.133491 | − | 0.410844i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.25337 | + | 13.0905i | −0.330125 | + | 1.01602i | ||||
\(167\) | −2.47824 | − | 1.80055i | −0.191772 | − | 0.139331i | 0.487756 | − | 0.872980i | \(-0.337816\pi\) |
−0.679528 | + | 0.733649i | \(0.737816\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.76606 | − | 2.00966i | −0.212774 | − | 0.154589i | ||||
\(170\) | −4.68022 | − | 2.54252i | −0.358956 | − | 0.195002i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.54046 | − | 4.02538i | 0.422456 | − | 0.306932i | ||||
\(173\) | −3.47942 | − | 10.7085i | −0.264535 | − | 0.814156i | −0.991800 | − | 0.127799i | \(-0.959209\pi\) |
0.727265 | − | 0.686357i | \(-0.240791\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.19790 | − | 1.99798i | −0.392925 | − | 0.151033i | ||||
\(176\) | 7.23416 | 0.545296 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −13.8814 | + | 10.0854i | −1.04046 | + | 0.755935i | ||||
\(179\) | 8.13657 | − | 5.91157i | 0.608156 | − | 0.441851i | −0.240609 | − | 0.970622i | \(-0.577347\pi\) |
0.848764 | + | 0.528771i | \(0.177347\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.7503 | + | 11.4433i | 1.17071 | + | 0.850571i | 0.991094 | − | 0.133165i | \(-0.0425141\pi\) |
0.179617 | + | 0.983737i | \(0.442514\pi\) | |||||||
\(182\) | −5.06498 | −0.375441 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5.86822 | − | 18.0605i | 0.432611 | − | 1.33144i | ||||
\(185\) | 14.4855 | + | 7.86923i | 1.06500 | + | 0.578557i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.40697 | − | 7.40790i | 0.176015 | − | 0.541719i | ||||
\(188\) | −0.715563 | + | 2.20227i | −0.0521878 | + | 0.160617i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −8.95461 | − | 4.86457i | −0.649636 | − | 0.352913i | ||||
\(191\) | 3.58739 | − | 11.0408i | 0.259574 | − | 0.798888i | −0.733320 | − | 0.679884i | \(-0.762030\pi\) |
0.992894 | − | 0.119003i | \(-0.0379700\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.38156 | −0.243410 | −0.121705 | − | 0.992566i | \(-0.538836\pi\) | ||||
−0.121705 | + | 0.992566i | \(0.538836\pi\) | |||||||
\(194\) | −12.2578 | − | 8.90581i | −0.880058 | − | 0.639400i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.44982 | + | 2.50644i | −0.246416 | + | 0.179032i | ||||
\(197\) | −14.2291 | + | 10.3380i | −1.01378 | + | 0.736554i | −0.964998 | − | 0.262256i | \(-0.915534\pi\) |
−0.0487811 | + | 0.998809i | \(0.515534\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.0102 | 1.41849 | 0.709244 | − | 0.704963i | \(-0.249037\pi\) | ||||
0.709244 | + | 0.704963i | \(0.249037\pi\) | |||||||
\(200\) | −8.36966 | − | 12.9009i | −0.591824 | − | 0.912230i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.50627 | − | 7.71350i | −0.176340 | − | 0.542720i | ||||
\(203\) | −2.03600 | + | 1.47924i | −0.142899 | + | 0.103822i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.6817 | + | 7.97578i | 1.02541 | + | 0.557052i | ||||
\(206\) | −4.79188 | − | 3.48151i | −0.333866 | − | 0.242568i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.46167 | − | 4.69468i | −0.448036 | − | 0.325517i | ||||
\(209\) | 4.60524 | − | 14.1735i | 0.318551 | − | 0.980399i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.754807 | + | 2.32306i | 0.0519631 | + | 0.159926i | 0.973671 | − | 0.227960i | \(-0.0732055\pi\) |
−0.921707 | + | 0.387886i | \(0.873206\pi\) | |||||||
\(212\) | −0.802951 | + | 2.47123i | −0.0551469 | + | 0.169725i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.89600 | − | 5.83530i | −0.129608 | − | 0.398893i | ||||
\(215\) | −3.77387 | + | 20.3364i | −0.257376 | + | 1.38693i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.05719 | − | 6.58044i | −0.614842 | − | 0.446709i | ||||
\(218\) | 12.7267 | 0.861961 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.40821 | − | 4.18135i | 0.297202 | − | 0.281906i | ||||
\(221\) | −6.95737 | + | 5.05483i | −0.468003 | + | 0.340024i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.92223 | − | 24.3821i | −0.530511 | − | 1.63275i | −0.753153 | − | 0.657846i | \(-0.771468\pi\) |
0.222641 | − | 0.974900i | \(-0.428532\pi\) | |||||||
\(224\) | 4.38695 | 0.293116 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.42671 | −0.360979 | ||||||||
\(227\) | −2.02819 | − | 6.24212i | −0.134616 | − | 0.414304i | 0.860914 | − | 0.508750i | \(-0.169892\pi\) |
−0.995530 | + | 0.0944455i | \(0.969892\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.44293 | − | 4.68106i | 0.425761 | − | 0.309333i | −0.354191 | − | 0.935173i | \(-0.615244\pi\) |
0.779952 | + | 0.625840i | \(0.215244\pi\) | |||||||
\(230\) | 6.66774 | + | 13.9873i | 0.439658 | + | 0.922297i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.94974 | −0.456273 | ||||||||
\(233\) | −7.62181 | − | 5.53757i | −0.499321 | − | 0.362778i | 0.309436 | − | 0.950920i | \(-0.399860\pi\) |
−0.808758 | + | 0.588142i | \(0.799860\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.00941 | − | 6.31303i | −0.196312 | − | 0.411817i | ||||
\(236\) | −1.50857 | − | 4.64291i | −0.0981998 | − | 0.302228i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.819784 | + | 2.52304i | −0.0531387 | + | 0.163544i | ||||
\(239\) | 3.46814 | + | 10.6738i | 0.224335 | + | 0.690433i | 0.998358 | + | 0.0572756i | \(0.0182414\pi\) |
−0.774023 | + | 0.633157i | \(0.781759\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.00879 | − | 21.5708i | 0.451476 | − | 1.38950i | −0.423748 | − | 0.905780i | \(-0.639286\pi\) |
0.875223 | − | 0.483719i | \(-0.160714\pi\) | |||||||
\(242\) | −2.24223 | − | 1.62908i | −0.144136 | − | 0.104721i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.45307 | − | 3.96189i | −0.349097 | − | 0.253634i | ||||
\(245\) | 2.34984 | − | 12.6627i | 0.150126 | − | 0.808988i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.3115 | + | 9.67135i | −0.846989 | + | 0.615373i | ||||
\(248\) | −9.55361 | − | 29.4030i | −0.606655 | − | 1.86709i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 12.1994 | + | 2.93754i | 0.771557 | + | 0.185787i | ||||
\(251\) | 6.76819 | 0.427205 | 0.213602 | − | 0.976921i | \(-0.431480\pi\) | ||||
0.213602 | + | 0.976921i | \(0.431480\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −18.3327 | + | 13.3195i | −1.15257 | + | 0.837387i | ||||
\(254\) | −0.689703 | + | 0.501098i | −0.0432758 | + | 0.0314417i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 12.1623 | + | 8.83640i | 0.760142 | + | 0.552275i | ||||
\(257\) | 14.7934 | 0.922786 | 0.461393 | − | 0.887196i | \(-0.347350\pi\) | ||||
0.461393 | + | 0.887196i | \(0.347350\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.53728 | − | 7.80894i | 0.157659 | − | 0.485224i | ||||
\(260\) | −6.65101 | + | 0.874096i | −0.412478 | + | 0.0542092i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5.08269 | + | 15.6429i | −0.314009 | + | 0.966422i | ||||
\(263\) | −6.17070 | + | 18.9915i | −0.380502 | + | 1.17106i | 0.559189 | + | 0.829040i | \(0.311113\pi\) |
−0.939691 | + | 0.342024i | \(0.888887\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.37694 | − | 7.08401i | −0.207444 | − | 0.435167i | ||||
\(266\) | −1.56849 | + | 4.82730i | −0.0961700 | + | 0.295981i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.94467 | −0.118790 | ||||||||
\(269\) | −8.28280 | − | 6.01780i | −0.505011 | − | 0.366912i | 0.305917 | − | 0.952058i | \(-0.401037\pi\) |
−0.810928 | + | 0.585146i | \(0.801037\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.95701 | + | 7.23419i | −0.604845 | + | 0.439446i | −0.847595 | − | 0.530643i | \(-0.821950\pi\) |
0.242750 | + | 0.970089i | \(0.421950\pi\) | |||||||
\(272\) | −3.38442 | + | 2.45893i | −0.205211 | + | 0.149094i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −13.7950 | −0.833389 | ||||||||
\(275\) | −0.968651 | + | 18.3248i | −0.0584118 | + | 1.10503i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.75011 | + | 30.0077i | 0.585827 | + | 1.80299i | 0.595923 | + | 0.803041i | \(0.296786\pi\) |
−0.0100963 | + | 0.999949i | \(0.503214\pi\) | |||||||
\(278\) | −13.3783 | + | 9.71989i | −0.802376 | + | 0.582960i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.55716 | + | 5.27116i | −0.332104 | + | 0.315012i | ||||
\(281\) | −17.2417 | − | 12.5268i | −1.02855 | − | 0.747288i | −0.0605353 | − | 0.998166i | \(-0.519281\pi\) |
−0.968019 | + | 0.250878i | \(0.919281\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.699317 | + | 0.508083i | 0.0415701 | + | 0.0302024i | 0.608376 | − | 0.793649i | \(-0.291821\pi\) |
−0.566806 | + | 0.823851i | \(0.691821\pi\) | |||||||
\(284\) | 0.151188 | − | 0.465309i | 0.00897135 | − | 0.0276110i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.15767 | + | 15.8737i | 0.304979 | + | 0.938629i | ||||
\(287\) | 2.57163 | − | 7.91467i | 0.151799 | − | 0.467188i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.86138 | − | 11.8841i | −0.227140 | − | 0.699066i | ||||
\(290\) | 4.11434 | − | 3.90260i | 0.241602 | − | 0.229168i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.47755 | + | 3.25313i | 0.262029 | + | 0.190375i | ||||
\(293\) | −3.17701 | −0.185603 | −0.0928014 | − | 0.995685i | \(-0.529582\pi\) | ||||
−0.0928014 | + | 0.995685i | \(0.529582\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.9559 | + | 7.03826i | 0.754321 | + | 0.409783i | ||||
\(296\) | 18.3439 | − | 13.3276i | 1.06622 | − | 0.774653i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.42766 | − | 16.7046i | −0.314416 | − | 0.967673i | ||||
\(299\) | 25.0188 | 1.44688 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.3020 | 0.593799 | ||||||||
\(302\) | 1.37278 | + | 4.22498i | 0.0789945 | + | 0.243120i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.47538 | + | 4.70464i | −0.371389 | + | 0.269830i | ||||
\(305\) | 20.1838 | − | 2.65262i | 1.15572 | − | 0.151888i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.507986 | −0.0289923 | −0.0144961 | − | 0.999895i | \(-0.504614\pi\) | ||||
−0.0144961 | + | 0.999895i | \(0.504614\pi\) | |||||||
\(308\) | −2.44828 | − | 1.77878i | −0.139504 | − | 0.101356i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 22.1670 | + | 12.0422i | 1.25900 | + | 0.683949i | ||||
\(311\) | 4.52519 | + | 13.9271i | 0.256600 | + | 0.789734i | 0.993510 | + | 0.113743i | \(0.0362841\pi\) |
−0.736910 | + | 0.675991i | \(0.763716\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.62171 | + | 14.2241i | −0.261234 | + | 0.803996i | 0.731303 | + | 0.682053i | \(0.238913\pi\) |
−0.992537 | + | 0.121943i | \(0.961087\pi\) | |||||||
\(314\) | −1.56090 | − | 4.80397i | −0.0880869 | − | 0.271103i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.95317 | + | 6.01125i | −0.109875 | + | 0.338159i | ||||
\(317\) | 14.6586 | + | 10.6501i | 0.823310 | + | 0.598170i | 0.917659 | − | 0.397369i | \(-0.130077\pi\) |
−0.0943487 | + | 0.995539i | \(0.530077\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.70920 | + | 4.87452i | 0.375643 | + | 0.272921i | ||||
\(320\) | −18.5409 | + | 2.43671i | −1.03647 | + | 0.136216i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.24388 | − | 4.53644i | 0.347958 | − | 0.252806i | ||||
\(323\) | 2.66312 | + | 8.19624i | 0.148180 | + | 0.456051i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.7573 | − | 15.7394i | 0.707646 | − | 0.873064i | ||||
\(326\) | −2.75408 | −0.152534 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 18.5923 | − | 13.5081i | 1.02659 | − | 0.745860i | ||||
\(329\) | −2.81811 | + | 2.04747i | −0.155367 | + | 0.112881i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.3188 | − | 15.4890i | −1.17178 | − | 0.851351i | −0.180563 | − | 0.983563i | \(-0.557792\pi\) |
−0.991221 | + | 0.132212i | \(0.957792\pi\) | |||||||
\(332\) | 9.07979 | 0.498318 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.06241 | − | 3.26975i | 0.0581322 | − | 0.178913i | ||||
\(335\) | 4.26127 | − | 4.04197i | 0.232818 | − | 0.220837i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.30488 | + | 10.1714i | −0.180028 | + | 0.554070i | −0.999827 | − | 0.0185811i | \(-0.994085\pi\) |
0.819799 | + | 0.572651i | \(0.194085\pi\) | |||||||
\(338\) | 1.18579 | − | 3.64949i | 0.0644986 | − | 0.198506i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.641073 | + | 3.45457i | −0.0347670 | + | 0.187350i | ||||
\(341\) | −11.4002 | + | 35.0861i | −0.617354 | + | 1.90002i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.2108 | −0.767311 | ||||||||
\(344\) | 23.0160 | + | 16.7221i | 1.24094 | + | 0.901594i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.2236 | − | 7.42788i | 0.549624 | − | 0.399325i | ||||
\(347\) | 13.0850 | − | 9.50682i | 0.702441 | − | 0.510353i | −0.178286 | − | 0.983979i | \(-0.557055\pi\) |
0.880726 | + | 0.473626i | \(0.157055\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.2383 | 0.815688 | 0.407844 | − | 0.913052i | \(-0.366281\pi\) | ||||
0.407844 | + | 0.913052i | \(0.366281\pi\) | |||||||
\(350\) | 0.329910 | − | 6.24119i | 0.0176344 | − | 0.333606i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.46723 | − | 13.7487i | −0.238104 | − | 0.732810i | ||||
\(353\) | −23.8970 | + | 17.3622i | −1.27191 | + | 0.924097i | −0.999277 | − | 0.0380214i | \(-0.987894\pi\) |
−0.272633 | + | 0.962118i | \(0.587894\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.635845 | + | 1.33385i | 0.0337472 | + | 0.0707935i | ||||
\(356\) | 9.15712 | + | 6.65304i | 0.485326 | + | 0.352610i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.13195 | + | 6.63475i | 0.482638 | + | 0.350657i | ||||
\(359\) | 4.06875 | − | 12.5223i | 0.214740 | − | 0.660903i | −0.784431 | − | 0.620216i | \(-0.787045\pi\) |
0.999172 | − | 0.0406876i | \(-0.0129549\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.776002 | − | 2.38829i | −0.0408422 | − | 0.125699i | ||||
\(362\) | −6.75205 | + | 20.7807i | −0.354880 | + | 1.09221i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.03249 | + | 3.17767i | 0.0541171 | + | 0.166555i | ||||
\(365\) | −16.5730 | + | 2.17808i | −0.867472 | + | 0.114006i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.14622 | + | 2.28586i | 0.164232 | + | 0.119321i | 0.666865 | − | 0.745178i | \(-0.267636\pi\) |
−0.502634 | + | 0.864499i | \(0.667636\pi\) | |||||||
\(368\) | 12.1704 | 0.634428 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.37576 | + | 18.1911i | −0.175498 | + | 0.945710i | ||||
\(371\) | −3.16227 | + | 2.29752i | −0.164177 | + | 0.119281i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.51641 | − | 7.74470i | −0.130295 | − | 0.401006i | 0.864534 | − | 0.502575i | \(-0.167614\pi\) |
−0.994829 | + | 0.101569i | \(0.967614\pi\) | |||||||
\(374\) | 8.74200 | 0.452038 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.61941 | −0.496083 | ||||||||
\(377\) | −2.82940 | − | 8.70799i | −0.145721 | − | 0.448484i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.01509 | + | 5.82330i | −0.411708 | + | 0.299123i | −0.774293 | − | 0.632828i | \(-0.781894\pi\) |
0.362585 | + | 0.931951i | \(0.381894\pi\) | |||||||
\(380\) | −1.22656 | + | 6.60960i | −0.0629211 | + | 0.339065i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 13.0292 | 0.666632 | ||||||||
\(383\) | −4.22481 | − | 3.06951i | −0.215878 | − | 0.156844i | 0.474591 | − | 0.880206i | \(-0.342596\pi\) |
−0.690469 | + | 0.723362i | \(0.742596\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.06198 | − | 1.19095i | 0.461841 | − | 0.0606966i | ||||
\(386\) | −1.17279 | − | 3.60949i | −0.0596937 | − | 0.183718i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.08860 | + | 9.50575i | −0.156800 | + | 0.482581i | ||||
\(389\) | 1.15255 | + | 3.54719i | 0.0584367 | + | 0.179850i | 0.976014 | − | 0.217708i | \(-0.0698579\pi\) |
−0.917577 | + | 0.397557i | \(0.869858\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.04938 | − | 12.4627i | 0.204786 | − | 0.630267i | ||||
\(392\) | −14.3311 | − | 10.4122i | −0.723831 | − | 0.525894i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −15.9698 | − | 11.6027i | −0.804545 | − | 0.584536i | ||||
\(395\) | −8.21438 | − | 17.2318i | −0.413310 | − | 0.867027i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.24870 | + | 2.36032i | −0.163048 | + | 0.118461i | −0.666317 | − | 0.745668i | \(-0.732130\pi\) |
0.503270 | + | 0.864130i | \(0.332130\pi\) | |||||||
\(398\) | 6.93995 | + | 21.3590i | 0.347868 | + | 1.07063i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.20579 | − | 7.65645i | 0.310289 | − | 0.382822i | ||||
\(401\) | 24.9890 | 1.24789 | 0.623945 | − | 0.781468i | \(-0.285529\pi\) | ||||
0.623945 | + | 0.781468i | \(0.285529\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 32.9523 | − | 23.9413i | 1.64147 | − | 1.19260i | ||||
\(404\) | −4.32841 | + | 3.14477i | −0.215346 | + | 0.156458i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.28507 | − | 1.66020i | −0.113406 | − | 0.0823943i | ||||
\(407\) | −27.0570 | −1.34116 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.84186 | + | 24.1348i | −0.387755 | + | 1.19339i | 0.546707 | + | 0.837324i | \(0.315881\pi\) |
−0.934462 | + | 0.356063i | \(0.884119\pi\) | |||||||
\(410\) | −3.42147 | + | 18.4374i | −0.168974 | + | 0.910558i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.20741 | + | 3.71604i | −0.0594850 | + | 0.183076i | ||||
\(413\) | 2.26935 | − | 6.98433i | 0.111667 | − | 0.343677i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −19.8961 | + | 18.8722i | −0.976663 | + | 0.926400i | ||||
\(416\) | −4.93216 | + | 15.1796i | −0.241819 | + | 0.744243i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 16.7260 | 0.818094 | ||||||||
\(419\) | −24.9354 | − | 18.1166i | −1.21817 | − | 0.885056i | −0.222227 | − | 0.974995i | \(-0.571333\pi\) |
−0.995947 | + | 0.0899392i | \(0.971333\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.91425 | + | 5.02350i | −0.336980 | + | 0.244830i | −0.743387 | − | 0.668862i | \(-0.766782\pi\) |
0.406406 | + | 0.913692i | \(0.366782\pi\) | |||||||
\(422\) | −2.21785 | + | 1.61137i | −0.107963 | + | 0.0784401i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −10.7942 | −0.524212 | ||||||||
\(425\) | −5.77551 | − | 8.90230i | −0.280154 | − | 0.431825i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.13329 | − | 9.64327i | −0.151630 | − | 0.466670i | ||||
\(428\) | −3.27446 | + | 2.37904i | −0.158277 | + | 0.114995i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −23.0160 | + | 3.02483i | −1.10993 | + | 0.145870i | ||||
\(431\) | −21.3431 | − | 15.5067i | −1.02806 | − | 0.746929i | −0.0601403 | − | 0.998190i | \(-0.519155\pi\) |
−0.967919 | + | 0.251261i | \(0.919155\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.58269 | + | 5.50914i | 0.364401 | + | 0.264753i | 0.754885 | − | 0.655857i | \(-0.227693\pi\) |
−0.390485 | + | 0.920609i | \(0.627693\pi\) | |||||||
\(434\) | 3.88276 | − | 11.9499i | 0.186378 | − | 0.573613i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.59432 | − | 7.98450i | −0.124245 | − | 0.382388i | ||||
\(437\) | 7.74765 | − | 23.8448i | 0.370620 | − | 1.14065i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.159447 | − | 0.490727i | −0.00760998 | − | 0.0234211i | 0.947179 | − | 0.320704i | \(-0.103920\pi\) |
−0.954789 | + | 0.297283i | \(0.903920\pi\) | |||||||
\(440\) | 22.1787 | + | 12.0485i | 1.05733 | + | 0.574391i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −7.80849 | − | 5.67320i | −0.371412 | − | 0.269847i | ||||
\(443\) | 17.8348 | 0.847357 | 0.423678 | − | 0.905813i | \(-0.360739\pi\) | ||||
0.423678 | + | 0.905813i | \(0.360739\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −33.8938 | + | 4.45443i | −1.60672 | + | 0.211160i | ||||
\(446\) | 23.2779 | − | 16.9124i | 1.10224 | − | 0.800826i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.87826 | + | 8.85836i | 0.135985 | + | 0.418518i | ||||
\(449\) | 4.16533 | 0.196574 | 0.0982870 | − | 0.995158i | \(-0.468664\pi\) | ||||
0.0982870 | + | 0.995158i | \(0.468664\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −27.4233 | −1.29131 | ||||||||
\(452\) | 1.10623 | + | 3.40462i | 0.0520325 | + | 0.160140i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.95944 | − | 4.32979i | 0.279691 | − | 0.203207i | ||||
\(455\) | −8.86719 | − | 4.81708i | −0.415700 | − | 0.225828i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.6734 | −0.826725 | −0.413362 | − | 0.910567i | \(-0.635646\pi\) | ||||
−0.413362 | + | 0.910567i | \(0.635646\pi\) | |||||||
\(458\) | 7.23112 | + | 5.25371i | 0.337888 | + | 0.245490i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 7.41618 | − | 7.03452i | 0.345781 | − | 0.327986i | ||||
\(461\) | 0.0633350 | + | 0.194925i | 0.00294981 | + | 0.00907857i | 0.952521 | − | 0.304474i | \(-0.0984807\pi\) |
−0.949571 | + | 0.313553i | \(0.898481\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.96084 | + | 12.1902i | −0.184076 | + | 0.566528i | −0.999931 | − | 0.0117286i | \(-0.996267\pi\) |
0.815855 | + | 0.578256i | \(0.196267\pi\) | |||||||
\(464\) | −1.37636 | − | 4.23601i | −0.0638961 | − | 0.196652i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.26742 | − | 10.0561i | 0.151360 | − | 0.465839i | ||||
\(467\) | 0.901030 | + | 0.654637i | 0.0416947 | + | 0.0302930i | 0.608437 | − | 0.793602i | \(-0.291797\pi\) |
−0.566743 | + | 0.823895i | \(0.691797\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.36668 | − | 1.71949i | −0.109283 | − | 0.0793987i | ||||
\(470\) | 5.69482 | − | 5.40174i | 0.262682 | − | 0.249164i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 16.4069 | − | 11.9203i | 0.755187 | − | 0.548675i | ||||
\(473\) | −10.4905 | − | 32.2866i | −0.482356 | − | 1.48454i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.0502 | − | 17.0327i | −0.507020 | − | 0.781513i | ||||
\(476\) | 1.75002 | 0.0802120 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −10.1905 | + | 7.40380i | −0.466101 | + | 0.338642i | ||||
\(479\) | −20.3670 | + | 14.7975i | −0.930590 | + | 0.676113i | −0.946137 | − | 0.323766i | \(-0.895051\pi\) |
0.0155470 | + | 0.999879i | \(0.495051\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.1677 | + | 17.5589i | 1.10195 | + | 0.800615i | ||||
\(482\) | 25.4555 | 1.15947 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.564977 | + | 1.73882i | −0.0256808 | + | 0.0790373i | ||||
\(485\) | −12.9896 | − | 27.2491i | −0.589828 | − | 1.23732i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.20135 | − | 9.85274i | 0.145067 | − | 0.446470i | −0.851953 | − | 0.523619i | \(-0.824582\pi\) |
0.997020 | + | 0.0771487i | \(0.0245816\pi\) | |||||||
\(488\) | 8.65265 | − | 26.6301i | 0.391687 | − | 1.20549i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 14.3311 | − | 1.88344i | 0.647414 | − | 0.0850852i | ||||
\(491\) | 4.83831 | − | 14.8908i | 0.218350 | − | 0.672012i | −0.780549 | − | 0.625095i | \(-0.785060\pi\) |
0.998899 | − | 0.0469170i | \(-0.0149396\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.79569 | −0.215987 | ||||||||
\(494\) | −14.9399 | − | 10.8545i | −0.672178 | − | 0.488366i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 16.0297 | − | 11.6463i | 0.719754 | − | 0.522932i | ||||
\(497\) | 0.595425 | − | 0.432601i | 0.0267084 | − | 0.0194048i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 35.7864 | 1.60202 | 0.801010 | − | 0.598651i | \(-0.204296\pi\) | ||||
0.801010 | + | 0.598651i | \(0.204296\pi\) | |||||||
\(500\) | −0.643866 | − | 8.25248i | −0.0287946 | − | 0.369062i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.34735 | + | 7.22439i | 0.104767 | + | 0.322440i | ||||
\(503\) | −9.52947 | + | 6.92356i | −0.424898 | + | 0.308706i | −0.779606 | − | 0.626271i | \(-0.784580\pi\) |
0.354708 | + | 0.934977i | \(0.384580\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.94828 | − | 15.8875i | 0.131197 | − | 0.706985i | ||||
\(506\) | −20.5754 | − | 14.9489i | −0.914687 | − | 0.664559i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.454975 | + | 0.330559i | 0.0201862 | + | 0.0146662i | ||||
\(509\) | −10.3986 | + | 32.0037i | −0.460912 | + | 1.41854i | 0.403141 | + | 0.915138i | \(0.367918\pi\) |
−0.864052 | + | 0.503402i | \(0.832082\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.57276 | + | 7.91815i | 0.113812 | + | 0.350278i | ||||
\(512\) | −6.14602 | + | 18.9155i | −0.271618 | + | 0.835955i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.13064 | + | 15.7905i | 0.226303 | + | 0.696489i | ||||
\(515\) | −5.07798 | − | 10.6524i | −0.223762 | − | 0.469400i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.28647 | + | 6.74701i | 0.408418 | + | 0.296733i | ||||
\(518\) | 9.21526 | 0.404895 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −11.9914 | − | 25.1550i | −0.525856 | − | 1.10312i | ||||
\(521\) | −9.58263 | + | 6.96219i | −0.419823 | + | 0.305019i | −0.777566 | − | 0.628801i | \(-0.783546\pi\) |
0.357744 | + | 0.933820i | \(0.383546\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.26602 | + | 3.89642i | 0.0553593 | + | 0.170379i | 0.974913 | − | 0.222586i | \(-0.0714497\pi\) |
−0.919554 | + | 0.392964i | \(0.871450\pi\) | |||||||
\(524\) | 10.8502 | 0.473992 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −22.4117 | −0.977195 | ||||||||
\(527\) | −6.59250 | − | 20.2896i | −0.287174 | − | 0.883830i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.2347 | + | 8.88902i | −0.531943 | + | 0.386479i | ||||
\(530\) | 6.39030 | − | 6.06143i | 0.277577 | − | 0.263292i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.34829 | 0.145167 | ||||||||
\(533\) | 24.4949 | + | 17.7966i | 1.06099 | + | 0.770857i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.23039 | − | 12.0190i | 0.0964282 | − | 0.519626i | ||||
\(536\) | −2.49639 | − | 7.68310i | −0.107828 | − | 0.331859i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.55078 | − | 10.9282i | 0.153085 | − | 0.471147i | ||||
\(539\) | 6.53205 | + | 20.1036i | 0.281355 | + | 0.865922i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.31332 | − | 13.2750i | 0.185444 | − | 0.570738i | −0.814512 | − | 0.580147i | \(-0.802995\pi\) |
0.999956 | + | 0.00940920i | \(0.00299509\pi\) | |||||||
\(542\) | −11.1751 | − | 8.11917i | −0.480011 | − | 0.348748i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.76321 | + | 4.91376i | 0.289970 | + | 0.210676i | ||||
\(545\) | 22.2805 | + | 12.1038i | 0.954390 | + | 0.518470i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.4426 | − | 15.5789i | 0.916818 | − | 0.666107i | −0.0259119 | − | 0.999664i | \(-0.508249\pi\) |
0.942730 | + | 0.333557i | \(0.108249\pi\) | |||||||
\(548\) | 2.81210 | + | 8.65476i | 0.120127 | + | 0.369713i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −19.8959 | + | 5.32147i | −0.848363 | + | 0.226908i | ||||
\(551\) | −9.17556 | −0.390892 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.69220 | + | 5.58871i | −0.327105 | + | 0.237656i | ||||
\(554\) | −28.6488 | + | 20.8146i | −1.21717 | + | 0.884327i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.82522 | + | 6.41190i | 0.374273 | + | 0.271925i | ||||
\(557\) | −10.6860 | −0.452781 | −0.226391 | − | 0.974037i | \(-0.572693\pi\) | ||||
−0.226391 | + | 0.974037i | \(0.572693\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.5824 | + | 35.6468i | −0.489882 | + | 1.50770i | ||||
\(560\) | −4.31345 | − | 2.34327i | −0.182277 | − | 0.0990214i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.39140 | − | 22.7484i | 0.311788 | − | 0.959583i | ||||
\(563\) | 7.90310 | − | 24.3232i | 0.333076 | − | 1.02510i | −0.634586 | − | 0.772852i | \(-0.718829\pi\) |
0.967662 | − | 0.252250i | \(-0.0811706\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.50047 | − | 5.16111i | −0.399688 | − | 0.217129i | ||||
\(566\) | −0.299792 | + | 0.922666i | −0.0126012 | + | 0.0387825i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.03244 | 0.0852794 | ||||||||
\(569\) | 4.93670 | + | 3.58672i | 0.206957 | + | 0.150363i | 0.686436 | − | 0.727190i | \(-0.259174\pi\) |
−0.479479 | + | 0.877554i | \(0.659174\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.2058 | + | 13.9538i | −0.803737 | + | 0.583949i | −0.912008 | − | 0.410173i | \(-0.865468\pi\) |
0.108271 | + | 0.994121i | \(0.465468\pi\) | |||||||
\(572\) | 8.90746 | − | 6.47165i | 0.372440 | − | 0.270593i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 9.34003 | 0.389845 | ||||||||
\(575\) | −1.62962 | + | 30.8288i | −0.0679597 | + | 1.28565i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.6474 | − | 42.0024i | −0.568149 | − | 1.74858i | −0.658405 | − | 0.752664i | \(-0.728769\pi\) |
0.0902565 | − | 0.995919i | \(-0.471231\pi\) | |||||||
\(578\) | 11.3459 | − | 8.24330i | 0.471929 | − | 0.342876i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.28712 | − | 1.78572i | −0.136490 | − | 0.0741480i | ||||
\(581\) | 11.0501 | + | 8.02840i | 0.458437 | + | 0.333074i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.4206 | + | 7.57100i | 0.431576 | + | 0.313559i | ||||
\(584\) | −7.10475 | + | 21.8662i | −0.293997 | + | 0.904828i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.10185 | − | 3.39115i | −0.0455170 | − | 0.140087i | ||||
\(587\) | −0.158206 | + | 0.486909i | −0.00652987 | + | 0.0200969i | −0.954268 | − | 0.298951i | \(-0.903363\pi\) |
0.947738 | + | 0.319048i | \(0.103363\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.6134 | − | 38.8200i | −0.519725 | − | 1.59955i | ||||
\(590\) | −3.01929 | + | 16.2702i | −0.124302 | + | 0.669832i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 11.7564 | + | 8.54153i | 0.483186 | + | 0.351055i | ||||
\(593\) | 18.8405 | 0.773687 | 0.386844 | − | 0.922145i | \(-0.373565\pi\) | ||||
0.386844 | + | 0.922145i | \(0.373565\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.83474 | + | 3.63738i | −0.157209 | + | 0.149118i | ||||
\(596\) | −9.37376 | + | 6.81043i | −0.383964 | + | 0.278966i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 8.67703 | + | 26.7052i | 0.354830 | + | 1.09206i | ||||
\(599\) | −6.20712 | −0.253616 | −0.126808 | − | 0.991927i | \(-0.540473\pi\) | ||||
−0.126808 | + | 0.991927i | \(0.540473\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.0303 | 1.38813 | 0.694063 | − | 0.719915i | \(-0.255819\pi\) | ||||
0.694063 | + | 0.719915i | \(0.255819\pi\) | |||||||
\(602\) | 3.57295 | + | 10.9964i | 0.145623 | + | 0.448180i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.37083 | − | 1.72251i | 0.0964679 | − | 0.0700880i | ||||
\(605\) | −2.37610 | − | 4.98450i | −0.0966023 | − | 0.202649i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.2488 | 0.659518 | 0.329759 | − | 0.944065i | \(-0.393032\pi\) | ||||
0.329759 | + | 0.944065i | \(0.393032\pi\) | |||||||
\(608\) | 12.9400 | + | 9.40144i | 0.524785 | + | 0.381279i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9.83155 | + | 20.6242i | 0.398068 | + | 0.835051i | ||||
\(611\) | −3.91628 | − | 12.0531i | −0.158436 | − | 0.487615i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.0210086 | + | 0.0646578i | −0.000848529 | + | 0.00261150i | −0.951480 | − | 0.307711i | \(-0.900437\pi\) |
0.950631 | + | 0.310322i | \(0.100437\pi\) | |||||||
\(614\) | −0.176180 | − | 0.542225i | −0.00711004 | − | 0.0218824i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.88481 | − | 11.9562i | 0.156523 | − | 0.481730i | ||||
\(617\) | 26.5445 | + | 19.2857i | 1.06864 | + | 0.776413i | 0.975667 | − | 0.219256i | \(-0.0703629\pi\) |
0.0929733 | + | 0.995669i | \(0.470363\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.48280 | + | 3.98349i | 0.220372 | + | 0.160110i | 0.692494 | − | 0.721423i | \(-0.256512\pi\) |
−0.472122 | + | 0.881533i | \(0.656512\pi\) | |||||||
\(620\) | 3.03632 | − | 16.3619i | 0.121942 | − | 0.657111i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −13.2964 | + | 9.66040i | −0.533137 | + | 0.387347i | ||||
\(623\) | 5.26160 | + | 16.1935i | 0.210802 | + | 0.648780i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.5635 | + | 16.7450i | 0.742541 | + | 0.669801i | ||||
\(626\) | −16.7858 | −0.670895 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.69573 | + | 1.95856i | −0.107571 | + | 0.0781552i | ||||
\(629\) | 12.6583 | − | 9.19679i | 0.504719 | − | 0.366700i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.20352 | + | 4.50712i | 0.246958 | + | 0.179426i | 0.704378 | − | 0.709825i | \(-0.251226\pi\) |
−0.457419 | + | 0.889251i | \(0.651226\pi\) | |||||||
\(632\) | −26.2568 | −1.04444 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6.28405 | + | 19.3403i | −0.249572 | + | 0.768102i | ||||
\(635\) | −1.68403 | + | 0.221320i | −0.0668285 | + | 0.00878281i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.21188 | − | 22.1959i | 0.285745 | − | 0.879432i | ||||
\(638\) | −2.87619 | + | 8.85199i | −0.113869 | + | 0.350454i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.45122 | − | 3.04431i | −0.0573644 | − | 0.120337i | ||||
\(641\) | 7.32096 | − | 22.5316i | 0.289161 | − | 0.889945i | −0.695960 | − | 0.718081i | \(-0.745021\pi\) |
0.985121 | − | 0.171864i | \(-0.0549791\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.16861 | 0.0855218 | 0.0427609 | − | 0.999085i | \(-0.486385\pi\) | ||||
0.0427609 | + | 0.999085i | \(0.486385\pi\) | |||||||
\(644\) | −4.11889 | − | 2.99255i | −0.162307 | − | 0.117923i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.82506 | + | 5.68524i | −0.307873 | + | 0.223683i | ||||
\(647\) | 2.06737 | − | 1.50203i | 0.0812767 | − | 0.0590510i | −0.546405 | − | 0.837521i | \(-0.684004\pi\) |
0.627682 | + | 0.778470i | \(0.284004\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.1998 | −0.949926 | ||||||||
\(650\) | 21.2247 | + | 8.15840i | 0.832503 | + | 0.319999i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.561415 | + | 1.72786i | 0.0219867 | + | 0.0676681i | ||||
\(653\) | 26.2233 | − | 19.0523i | 1.02620 | − | 0.745575i | 0.0586517 | − | 0.998279i | \(-0.481320\pi\) |
0.967544 | + | 0.252704i | \(0.0813199\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −23.7755 | + | 22.5519i | −0.928985 | + | 0.881175i | ||||
\(656\) | 11.9156 | + | 8.65719i | 0.465226 | + | 0.338006i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.16285 | − | 2.29795i | −0.123301 | − | 0.0895833i | ||||
\(659\) | −0.139043 | + | 0.427929i | −0.00541633 | + | 0.0166697i | −0.953728 | − | 0.300670i | \(-0.902790\pi\) |
0.948312 | + | 0.317340i | \(0.102790\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.33812 | − | 25.6621i | −0.324315 | − | 0.998140i | −0.971749 | − | 0.236018i | \(-0.924158\pi\) |
0.647433 | − | 0.762122i | \(-0.275842\pi\) | |||||||
\(662\) | 9.13921 | − | 28.1276i | 0.355205 | − | 1.09321i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 11.6558 | + | 35.8728i | 0.452332 | + | 1.39214i | ||||
\(665\) | −7.33696 | + | 6.95937i | −0.284515 | + | 0.269873i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.2873 | + | 8.20067i | 0.437044 | + | 0.317531i | ||||
\(668\) | −2.26795 | −0.0877496 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 5.79231 | + | 3.14666i | 0.223776 | + | 0.121566i | ||||
\(671\) | −27.0314 | + | 19.6395i | −1.04354 | + | 0.758174i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.44561 | + | 16.7599i | 0.209913 | + | 0.646046i | 0.999476 | + | 0.0323758i | \(0.0103073\pi\) |
−0.789563 | + | 0.613670i | \(0.789693\pi\) | |||||||
\(674\) | −12.0032 | −0.462344 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.53135 | −0.0973595 | ||||||||
\(677\) | 5.97899 | + | 18.4014i | 0.229791 | + | 0.707225i | 0.997770 | + | 0.0667494i | \(0.0212628\pi\) |
−0.767978 | + | 0.640476i | \(0.778737\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.1639 | + | 8.83757i | −0.466807 | + | 0.339155i | ||||
\(680\) | −14.4714 | + | 1.90188i | −0.554953 | + | 0.0729336i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −41.4049 | −1.58547 | ||||||||
\(683\) | −24.2268 | − | 17.6018i | −0.927015 | − | 0.673515i | 0.0182455 | − | 0.999834i | \(-0.494192\pi\) |
−0.945260 | + | 0.326318i | \(0.894192\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −24.1508 | − | 13.1199i | −0.922755 | − | 0.501284i | ||||
\(686\) | −4.92859 | − | 15.1686i | −0.188175 | − | 0.579142i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.63426 | + | 17.3405i | −0.214804 | + | 0.661099i | ||||
\(689\) | −4.39456 | − | 13.5251i | −0.167419 | − | 0.515264i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.16024 | + | 18.9593i | −0.234346 | + | 0.721244i | 0.762861 | + | 0.646563i | \(0.223794\pi\) |
−0.997207 | + | 0.0746817i | \(0.976206\pi\) | |||||||
\(692\) | −6.74418 | − | 4.89993i | −0.256375 | − | 0.186268i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.6858 | + | 10.6698i | 0.557464 | + | 0.405021i | ||||
\(695\) | −32.6653 | + | 4.29298i | −1.23907 | + | 0.162842i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.8297 | − | 9.32131i | 0.485959 | − | 0.353070i | ||||
\(698\) | 5.28495 | + | 16.2654i | 0.200038 | + | 0.615655i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.98286 | + | 1.06528i | −0.150538 | + | 0.0402638i | ||||
\(701\) | 49.0150 | 1.85127 | 0.925636 | − | 0.378415i | \(-0.123531\pi\) | ||||
0.925636 | + | 0.378415i | \(0.123531\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.2190 | − | 17.5961i | 0.913437 | − | 0.663651i | ||||
\(704\) | 24.8312 | − | 18.0409i | 0.935862 | − | 0.679944i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −26.8204 | − | 19.4862i | −1.00940 | − | 0.733372i | ||||
\(707\) | −8.04831 | −0.302688 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.48744 | + | 4.57788i | −0.0558621 | + | 0.171926i | −0.975095 | − | 0.221789i | \(-0.928810\pi\) |
0.919233 | + | 0.393715i | \(0.128810\pi\) | |||||||
\(710\) | −1.20323 | + | 1.14131i | −0.0451565 | + | 0.0428326i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −14.5300 | + | 44.7189i | −0.544536 | + | 1.67591i | ||||
\(713\) | −19.1792 | + | 59.0274i | −0.718265 | + | 2.21059i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.06730 | + | 32.6950i | −0.226904 | + | 1.22273i | ||||
\(716\) | 2.30098 | − | 7.08170i | 0.0859918 | − | 0.264656i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 14.7775 | 0.551491 | ||||||||
\(719\) | 26.0917 | + | 18.9568i | 0.973058 | + | 0.706968i | 0.956146 | − | 0.292889i | \(-0.0946167\pi\) |
0.0169113 | + | 0.999857i | \(0.494617\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.75517 | + | 3.45483i | −0.177092 | + | 0.128665i | ||||
\(722\) | 2.28013 | − | 1.65661i | 0.0848578 | − | 0.0616528i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 14.4138 | 0.535685 | ||||||||
\(725\) | 10.9145 | − | 2.91926i | 0.405355 | − | 0.108418i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.01548 | − | 27.7468i | −0.334366 | − | 1.02907i | −0.967034 | − | 0.254648i | \(-0.918040\pi\) |
0.632668 | − | 0.774423i | \(-0.281960\pi\) | |||||||
\(728\) | −11.2291 | + | 8.15840i | −0.416177 | + | 0.302370i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −8.07275 | − | 16.9347i | −0.298786 | − | 0.626781i | ||||
\(731\) | 15.8823 | + | 11.5391i | 0.587426 | + | 0.426790i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.20771 | − | 3.05708i | −0.155415 | − | 0.112916i | 0.507360 | − | 0.861734i | \(-0.330622\pi\) |
−0.662775 | + | 0.748818i | \(0.730622\pi\) | |||||||
\(734\) | −1.34876 | + | 4.15107i | −0.0497838 | + | 0.153219i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.51548 | − | 23.1303i | −0.277024 | − | 0.852593i | ||||
\(737\) | −2.97891 | + | 9.16813i | −0.109729 | + | 0.337712i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.04334 | − | 15.5218i | −0.185522 | − | 0.570979i | 0.814435 | − | 0.580255i | \(-0.197047\pi\) |
−0.999957 | + | 0.00927620i | \(0.997047\pi\) | |||||||
\(740\) | 12.1009 | − | 1.59034i | 0.444838 | − | 0.0584620i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.54912 | − | 2.57859i | −0.130292 | − | 0.0946629i | ||||
\(743\) | −53.4487 | −1.96084 | −0.980421 | − | 0.196914i | \(-0.936908\pi\) | ||||
−0.980421 | + | 0.196914i | \(0.936908\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.38491 | − | 34.4066i | 0.233925 | − | 1.26056i | ||||
\(746\) | 7.39398 | − | 5.37204i | 0.270713 | − | 0.196684i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.78204 | − | 5.48457i | −0.0651580 | − | 0.200536i | ||||
\(749\) | −6.08859 | −0.222472 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.566970 | −0.0206890 | −0.0103445 | − | 0.999946i | \(-0.503293\pi\) | ||||
−0.0103445 | + | 0.999946i | \(0.503293\pi\) | |||||||
\(752\) | −1.90508 | − | 5.86324i | −0.0694712 | − | 0.213810i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.31364 | − | 6.04021i | 0.302765 | − | 0.219972i | ||||
\(755\) | −1.61489 | + | 8.70220i | −0.0587718 | + | 0.316706i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 53.0708 | 1.92889 | 0.964445 | − | 0.264282i | \(-0.0851350\pi\) | ||||
0.964445 | + | 0.264282i | \(0.0851350\pi\) | |||||||
\(758\) | −8.99560 | − | 6.53569i | −0.326735 | − | 0.237387i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −27.6880 | + | 3.63884i | −1.00435 | + | 0.131995i | ||||
\(761\) | 8.49970 | + | 26.1594i | 0.308114 | + | 0.948277i | 0.978497 | + | 0.206262i | \(0.0661298\pi\) |
−0.670383 | + | 0.742015i | \(0.733870\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.90264 | − | 12.0111i | 0.141285 | − | 0.434830i | ||||
\(764\) | −2.65599 | − | 8.17428i | −0.0960902 | − | 0.295735i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.81115 | − | 5.57414i | 0.0654394 | − | 0.201402i | ||||
\(767\) | 21.6157 | + | 15.7047i | 0.780496 | + | 0.567064i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.1123 | − | 8.80007i | −0.436779 | − | 0.317339i | 0.347575 | − | 0.937652i | \(-0.387005\pi\) |
−0.784354 | + | 0.620314i | \(0.787005\pi\) | |||||||
\(770\) | 4.41410 | + | 9.25974i | 0.159073 | + | 0.333698i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.02546 | + | 1.47158i | −0.0728977 | + | 0.0529633i | ||||
\(773\) | 0.634806 | + | 1.95373i | 0.0228324 | + | 0.0702708i | 0.961823 | − | 0.273671i | \(-0.0882378\pi\) |
−0.938991 | + | 0.343941i | \(0.888238\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 27.3547 | + | 42.1641i | 0.982608 | + | 1.51458i | ||||
\(776\) | −41.5206 | −1.49050 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.38655 | + | 2.46048i | −0.121414 | + | 0.0882123i | ||||
\(779\) | 24.5469 | − | 17.8344i | 0.879485 | − | 0.638983i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.96210 | − | 1.42555i | −0.0702093 | − | 0.0510100i | ||||
\(782\) | 14.7072 | 0.525927 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.50823 | − | 10.7972i | 0.125294 | − | 0.385615i | ||||
\(785\) | 1.83619 | − | 9.89475i | 0.0655365 | − | 0.353159i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.19981 | + | 16.0034i | −0.185353 | + | 0.570458i | −0.999954 | − | 0.00956327i | \(-0.996956\pi\) |
0.814601 | + | 0.580022i | \(0.196956\pi\) | |||||||
\(788\) | −4.02391 | + | 12.3843i | −0.143346 | + | 0.441174i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 15.5444 | − | 14.7444i | 0.553044 | − | 0.524582i | ||||
\(791\) | −1.66410 | + | 5.12156i | −0.0591685 | + | 0.182102i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 36.8901 | 1.31001 | ||||||||
\(794\) | −3.64613 | − | 2.64907i | −0.129396 | − | 0.0940118i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.9855 | − | 8.70799i | 0.424816 | − | 0.308647i | ||||
\(797\) | −0.168996 | + | 0.122783i | −0.00598616 | + | 0.00434920i | −0.590774 | − | 0.806837i | \(-0.701178\pi\) |
0.584788 | + | 0.811186i | \(0.301178\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.63791 | −0.234832 | ||||||||
\(800\) | −18.3835 | − | 7.06627i | −0.649954 | − | 0.249830i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 8.66668 | + | 26.6733i | 0.306031 | + | 0.941867i | ||||
\(803\) | 22.1957 | − | 16.1261i | 0.783268 | − | 0.569078i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.2455 | − | 2.00361i | 0.537333 | − | 0.0706179i | ||||
\(806\) | 36.9835 | + | 26.8701i | 1.30269 | + | 0.946458i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −17.9809 | − | 13.0639i | −0.632566 | − | 0.459586i | ||||
\(809\) | 5.24264 | − | 16.1352i | 0.184321 | − | 0.567283i | −0.815615 | − | 0.578595i | \(-0.803601\pi\) |
0.999936 | + | 0.0113128i | \(0.00360104\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.32508 | − | 19.4666i | −0.222103 | − | 0.683564i | −0.998573 | − | 0.0534090i | \(-0.982991\pi\) |
0.776469 | − | 0.630155i | \(-0.217009\pi\) | |||||||
\(812\) | −0.575770 | + | 1.77204i | −0.0202056 | + | 0.0621864i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −9.38390 | − | 28.8807i | −0.328905 | − | 1.01227i | ||||
\(815\) | −4.82153 | − | 2.61928i | −0.168891 | − | 0.0917495i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 30.3874 | + | 22.0777i | 1.06312 | + | 0.772401i | ||||
\(818\) | −28.4812 | −0.995822 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 12.2647 | − | 1.61187i | 0.428304 | − | 0.0562890i | ||||
\(821\) | 31.0368 | − | 22.5496i | 1.08319 | − | 0.786985i | 0.104955 | − | 0.994477i | \(-0.466530\pi\) |
0.978237 | + | 0.207492i | \(0.0665301\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.96451 | − | 27.5899i | −0.312483 | − | 0.961725i | −0.976778 | − | 0.214254i | \(-0.931268\pi\) |
0.664295 | − | 0.747471i | \(-0.268732\pi\) | |||||||
\(824\) | −16.2315 | −0.565449 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.24215 | 0.286781 | ||||||||
\(827\) | −4.43648 | − | 13.6541i | −0.154271 | − | 0.474799i | 0.843815 | − | 0.536634i | \(-0.180305\pi\) |
−0.998086 | + | 0.0618356i | \(0.980305\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.75031 | + | 2.72476i | −0.130254 | + | 0.0946347i | −0.651004 | − | 0.759074i | \(-0.725652\pi\) |
0.520751 | + | 0.853709i | \(0.325652\pi\) | |||||||
\(830\) | −27.0446 | − | 14.6919i | −0.938732 | − | 0.509964i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −33.8875 | −1.17484 | ||||||||
\(833\) | −9.88925 | − | 7.18496i | −0.342642 | − | 0.248944i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.96965 | − | 4.71390i | 0.171982 | − | 0.163131i | ||||
\(836\) | −3.40957 | − | 10.4936i | −0.117922 | − | 0.362928i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 10.6896 | − | 32.8993i | 0.369268 | − | 1.13649i | ||||
\(839\) | −1.52235 | − | 4.68531i | −0.0525573 | − | 0.161755i | 0.921333 | − | 0.388775i | \(-0.127102\pi\) |
−0.973890 | + | 0.227020i | \(0.927102\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.38367 | + | 22.7246i | −0.254609 | + | 0.783607i | ||||
\(842\) | −7.76010 | − | 5.63804i | −0.267431 | − | 0.194300i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.46305 | + | 1.06297i | 0.0503602 | + | 0.0365888i | ||||
\(845\) | 5.54683 | − | 5.26137i | 0.190817 | − | 0.180996i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.22505 | + | 1.61660i | −0.0764538 | + | 0.0555469i | ||||
\(848\) | −2.13774 | − | 6.57929i | −0.0734103 | − | 0.225934i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 7.49927 | − | 9.25229i | 0.257223 | − | 0.317351i | ||||
\(851\) | −45.5194 | −1.56039 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −43.4018 | + | 31.5333i | −1.48605 | + | 1.07968i | −0.510507 | + | 0.859874i | \(0.670542\pi\) |
−0.975544 | + | 0.219805i | \(0.929458\pi\) | |||||||
\(854\) | 9.20656 | − | 6.68896i | 0.315042 | − | 0.228891i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −13.6026 | − | 9.88290i | −0.464929 | − | 0.337790i | ||||
\(857\) | 27.1144 | 0.926210 | 0.463105 | − | 0.886303i | \(-0.346735\pi\) | ||||
0.463105 | + | 0.886303i | \(0.346735\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.21966 | − | 9.90910i | 0.109853 | − | 0.338094i | −0.880985 | − | 0.473143i | \(-0.843119\pi\) |
0.990839 | + | 0.135049i | \(0.0431193\pi\) | |||||||
\(860\) | 6.58950 | + | 13.8232i | 0.224700 | + | 0.471367i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9.14963 | − | 28.1597i | 0.311638 | − | 0.959122i | ||||
\(863\) | 13.4865 | − | 41.5072i | 0.459086 | − | 1.41292i | −0.407185 | − | 0.913346i | \(-0.633490\pi\) |
0.866271 | − | 0.499575i | \(-0.166510\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24.9626 | − | 3.28067i | 0.848756 | − | 0.111546i | ||||
\(866\) | −3.25065 | + | 10.0045i | −0.110461 | + | 0.339965i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −8.28864 | −0.281335 | ||||||||
\(869\) | 25.3480 | + | 18.4164i | 0.859872 | + | 0.624734i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.61055 | − | 6.25593i | 0.291757 | − | 0.211974i | ||||
\(872\) | 28.2151 | − | 20.4995i | 0.955485 | − | 0.694201i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 28.1391 | 0.951818 | ||||||||
\(875\) | 6.51330 | − | 10.6126i | 0.220190 | − | 0.358772i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.5767 | + | 51.0180i | 0.559757 | + | 1.72275i | 0.683038 | + | 0.730383i | \(0.260658\pi\) |
−0.123281 | + | 0.992372i | \(0.539342\pi\) | |||||||
\(878\) | 0.468503 | − | 0.340388i | 0.0158112 | − | 0.0114875i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.95144 | + | 15.9045i | −0.0994931 | + | 0.536142i | ||||
\(881\) | −44.4110 | − | 32.2665i | −1.49625 | − | 1.08709i | −0.971847 | − | 0.235613i | \(-0.924290\pi\) |
−0.524398 | − | 0.851473i | \(-0.675710\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.4483 | + | 11.2239i | 0.519877 | + | 0.377713i | 0.816558 | − | 0.577264i | \(-0.195880\pi\) |
−0.296681 | + | 0.954977i | \(0.595880\pi\) | |||||||
\(884\) | −1.96751 | + | 6.05538i | −0.0661746 | + | 0.203664i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.18547 | + | 19.0369i | 0.207805 | + | 0.639558i | ||||
\(887\) | 3.46598 | − | 10.6672i | 0.116376 | − | 0.358170i | −0.875855 | − | 0.482574i | \(-0.839702\pi\) |
0.992232 | + | 0.124404i | \(0.0397020\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.261425 | + | 0.804582i | 0.00876790 | + | 0.0269848i | ||||
\(890\) | −16.5097 | − | 34.6334i | −0.553407 | − | 1.16092i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −15.3557 | − | 11.1566i | −0.514147 | − | 0.373550i | ||||
\(893\) | −12.7003 | −0.424998 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.67716 | + | 20.3004i | 0.323472 | + | 0.678566i | ||||
\(896\) | −1.35896 | + | 0.987345i | −0.0453998 | + | 0.0329849i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.44462 | + | 4.44608i | 0.0482076 | + | 0.148368i | ||||
\(899\) | 22.7139 | 0.757552 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.44857 | −0.248148 | ||||||||
\(902\) | −9.51095 | − | 29.2717i | −0.316680 | − | 0.974641i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12.0310 | + | 8.74106i | −0.400146 | + | 0.290723i | ||||
\(905\) | −31.5843 | + | 29.9589i | −1.04990 | + | 0.995866i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36.4513 | −1.21034 | −0.605172 | − | 0.796095i | \(-0.706896\pi\) | ||||
−0.605172 | + | 0.796095i | \(0.706896\pi\) | |||||||
\(908\) | −3.93125 | − | 2.85622i | −0.130463 | − | 0.0947871i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.06644 | − | 11.1355i | 0.0685020 | − | 0.369139i | ||||
\(911\) | −0.360106 | − | 1.10829i | −0.0119309 | − | 0.0367194i | 0.944914 | − | 0.327319i | \(-0.106145\pi\) |
−0.956845 | + | 0.290600i | \(0.906145\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.9087 | − | 42.8065i | 0.460310 | − | 1.41669i | ||||
\(914\) | −6.12948 | − | 18.8646i | −0.202745 | − | 0.623985i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.82203 | − | 5.60763i | 0.0602016 | − | 0.185281i | ||||
\(917\) | 13.2047 | + | 9.59377i | 0.436057 | + | 0.316814i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −35.5543 | − | 25.8317i | −1.17283 | − | 0.852109i | −0.181482 | − | 0.983394i | \(-0.558089\pi\) |
−0.991345 | + | 0.131286i | \(0.958089\pi\) | |||||||
\(920\) | 37.3125 | + | 20.2699i | 1.23016 | + | 0.668279i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −0.186098 | + | 0.135208i | −0.00612880 | + | 0.00445283i | ||||
\(923\) | 0.827454 | + | 2.54664i | 0.0272360 | + | 0.0838237i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −23.2107 | + | 28.6364i | −0.763162 | + | 0.941558i | ||||
\(926\) | −14.3856 | −0.472739 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −7.20073 | + | 5.23164i | −0.236376 | + | 0.171737i | ||||
\(929\) | 25.2512 | − | 18.3460i | 0.828464 | − | 0.601914i | −0.0906606 | − | 0.995882i | \(-0.528898\pi\) |
0.919124 | + | 0.393968i | \(0.128898\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.9210 | − | 13.7469i | −0.620111 | − | 0.450537i | ||||
\(932\) | −6.97506 | −0.228476 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.386266 | + | 1.18880i | −0.0126390 | + | 0.0388988i | ||||
\(935\) | 15.3045 | + | 8.31413i | 0.500510 | + | 0.271901i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.9385 | + | 42.8983i | −0.455351 | + | 1.40143i | 0.415371 | + | 0.909652i | \(0.363652\pi\) |
−0.870722 | + | 0.491775i | \(0.836348\pi\) | |||||||
\(938\) | 1.01458 | − | 3.12255i | 0.0331271 | − | 0.101955i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.54983 | − | 2.47169i | −0.148399 | − | 0.0806175i | ||||
\(941\) | 12.0931 | − | 37.2187i | 0.394224 | − | 1.21330i | −0.535341 | − | 0.844636i | \(-0.679817\pi\) |
0.929565 | − | 0.368659i | \(-0.120183\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −46.1358 | −1.50239 | ||||||||
\(944\) | 10.5150 | + | 7.63957i | 0.342233 | + | 0.248647i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 30.8245 | − | 22.3953i | 1.00219 | − | 0.728133i | ||||
\(947\) | −39.5235 | + | 28.7155i | −1.28434 | + | 0.933128i | −0.999675 | − | 0.0254991i | \(-0.991883\pi\) |
−0.284665 | + | 0.958627i | \(0.591883\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −30.2907 | −0.983278 | ||||||||
\(950\) | 14.3483 | − | 17.7023i | 0.465520 | − | 0.574339i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.24651 | + | 6.91405i | 0.0728098 | + | 0.224086i | ||||
\(953\) | 18.4314 | − | 13.3912i | 0.597051 | − | 0.433783i | −0.247780 | − | 0.968816i | \(-0.579701\pi\) |
0.844831 | + | 0.535034i | \(0.179701\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.8101 | + | 12.3915i | 0.738116 | + | 0.400980i | ||||
\(956\) | 6.72232 | + | 4.88405i | 0.217415 | + | 0.157961i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −22.8585 | − | 16.6077i | −0.738525 | − | 0.536570i | ||||
\(959\) | −4.23024 | + | 13.0193i | −0.136602 | + | 0.420417i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.6446 | + | 66.6154i | 0.698214 | + | 2.14888i | ||||
\(962\) | −10.3605 | + | 31.8864i | −0.334037 | + | 1.02806i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.18908 | − | 15.9703i | −0.167129 | − | 0.514370i | ||||
\(965\) | 1.37963 | − | 7.43448i | 0.0444120 | − | 0.239324i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34.9436 | − | 25.3880i | −1.12371 | − | 0.816425i | −0.138944 | − | 0.990300i | \(-0.544371\pi\) |
−0.984768 | + | 0.173876i | \(0.944371\pi\) | |||||||
\(968\) | −7.59507 | −0.244115 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 24.5807 | − | 23.3157i | 0.789239 | − | 0.748622i | ||||
\(971\) | −25.9089 | + | 18.8239i | −0.831457 | + | 0.604089i | −0.919971 | − | 0.391986i | \(-0.871788\pi\) |
0.0885142 | + | 0.996075i | \(0.471788\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.07090 | + | 15.6066i | 0.162565 | + | 0.500325i | ||||
\(974\) | 11.6271 | 0.372557 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 17.9452 | 0.574413 | ||||||||
\(977\) | 2.24659 | + | 6.91428i | 0.0718747 | + | 0.221208i | 0.980541 | − | 0.196316i | \(-0.0628980\pi\) |
−0.908666 | + | 0.417524i | \(0.862898\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 45.3927 | − | 32.9798i | 1.45076 | − | 1.05404i | ||||
\(980\) | −4.10302 | − | 8.60715i | −0.131066 | − | 0.274945i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 17.5725 | 0.560760 | ||||||||
\(983\) | −4.11915 | − | 2.99274i | −0.131380 | − | 0.0954535i | 0.520154 | − | 0.854072i | \(-0.325874\pi\) |
−0.651535 | + | 0.758619i | \(0.725874\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.9232 | − | 35.5009i | −0.539219 | − | 1.13115i | ||||
\(986\) | −1.66324 | − | 5.11894i | −0.0529685 | − | 0.163020i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.76442 | + | 11.5857i | −0.119762 | + | 0.368590i | ||||
\(989\) | −17.6488 | − | 54.3176i | −0.561201 | − | 1.72720i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.1826 | + | 59.0380i | −0.609356 | + | 1.87540i | −0.145859 | + | 0.989305i | \(0.546594\pi\) |
−0.463497 | + | 0.886098i | \(0.653406\pi\) | |||||||
\(992\) | −32.0327 | − | 23.2731i | −1.01704 | − | 0.738922i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.668265 | + | 0.485523i | 0.0211961 | + | 0.0153999i | ||||
\(995\) | −8.16391 | + | 43.9931i | −0.258813 | + | 1.39468i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.07832 | + | 1.50999i | −0.0658212 | + | 0.0478219i | −0.620209 | − | 0.784436i | \(-0.712952\pi\) |
0.554388 | + | 0.832258i | \(0.312952\pi\) | |||||||
\(998\) | 12.4114 | + | 38.1985i | 0.392878 | + | 1.20915i | ||||
\(999\) | 0 | 0 |
(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 | 225.2.h.c.181.2 | 8 | ||
3.2 | odd | 2 | 75.2.g.b.31.1 | ✓ | 8 | ||
15.2 | even | 4 | 375.2.i.b.349.3 | 16 | |||
15.8 | even | 4 | 375.2.i.b.349.2 | 16 | |||
15.14 | odd | 2 | 375.2.g.b.151.2 | 8 | |||
25.11 | even | 5 | 5625.2.a.i.1.3 | 4 | |||
25.14 | even | 10 | 5625.2.a.n.1.2 | 4 | |||
25.21 | even | 5 | inner | 225.2.h.c.46.2 | 8 | ||
75.2 | even | 20 | 1875.2.b.c.1249.4 | 8 | |||
75.11 | odd | 10 | 1875.2.a.h.1.2 | 4 | |||
75.14 | odd | 10 | 1875.2.a.e.1.3 | 4 | |||
75.23 | even | 20 | 1875.2.b.c.1249.5 | 8 | |||
75.29 | odd | 10 | 375.2.g.b.226.2 | 8 | |||
75.47 | even | 20 | 375.2.i.b.274.2 | 16 | |||
75.53 | even | 20 | 375.2.i.b.274.3 | 16 | |||
75.71 | odd | 10 | 75.2.g.b.46.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.g.b.31.1 | ✓ | 8 | 3.2 | odd | 2 | ||
75.2.g.b.46.1 | yes | 8 | 75.71 | odd | 10 | ||
225.2.h.c.46.2 | 8 | 25.21 | even | 5 | inner | ||
225.2.h.c.181.2 | 8 | 1.1 | even | 1 | trivial | ||
375.2.g.b.151.2 | 8 | 15.14 | odd | 2 | |||
375.2.g.b.226.2 | 8 | 75.29 | odd | 10 | |||
375.2.i.b.274.2 | 16 | 75.47 | even | 20 | |||
375.2.i.b.274.3 | 16 | 75.53 | even | 20 | |||
375.2.i.b.349.2 | 16 | 15.8 | even | 4 | |||
375.2.i.b.349.3 | 16 | 15.2 | even | 4 | |||
1875.2.a.e.1.3 | 4 | 75.14 | odd | 10 | |||
1875.2.a.h.1.2 | 4 | 75.11 | odd | 10 | |||
1875.2.b.c.1249.4 | 8 | 75.2 | even | 20 | |||
1875.2.b.c.1249.5 | 8 | 75.23 | even | 20 | |||
5625.2.a.i.1.3 | 4 | 25.11 | even | 5 | |||
5625.2.a.n.1.2 | 4 | 25.14 | even | 10 |