Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [375,2,Mod(76,375)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(375, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("375.76");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 375 = 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 375.g (of order \(5\), 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: | \(2.99439007580\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 151.2 | ||
Root | \(1.40799 + 0.132563i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 375.151 |
Dual form | 375.2.g.b.226.2 |
$q$-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 \(\left(\mathbb{Z}/375\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{2}{5}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.346820 | + | 1.06740i | 0.245239 | + | 0.754768i | 0.995597 | + | 0.0937362i | \(0.0298810\pi\) |
−0.750358 | + | 0.661031i | \(0.770119\pi\) | |||||||
\(3\) | 0.809017 | − | 0.587785i | 0.467086 | − | 0.339358i | ||||
\(4\) | 0.598970 | − | 0.435177i | 0.299485 | − | 0.217589i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.907987 | + | 0.659691i | 0.370684 | + | 0.269318i | ||||
\(7\) | −1.11373 | −0.420952 | −0.210476 | − | 0.977599i | \(-0.567501\pi\) | ||||
−0.210476 | + | 0.977599i | \(0.567501\pi\) | |||||||
\(8\) | 2.48822 | + | 1.80780i | 0.879718 | + | 0.639152i | ||||
\(9\) | 0.309017 | − | 0.951057i | 0.103006 | − | 0.317019i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.13412 | + | 3.49045i | 0.341949 | + | 1.05241i | 0.963197 | + | 0.268796i | \(0.0866258\pi\) |
−0.621248 | + | 0.783614i | \(0.713374\pi\) | |||||||
\(12\) | 0.228786 | − | 0.704131i | 0.0660449 | − | 0.203265i | ||||
\(13\) | 1.25215 | − | 3.85372i | 0.347284 | − | 1.06883i | −0.613066 | − | 0.790032i | \(-0.710064\pi\) |
0.960350 | − | 0.278798i | \(-0.0899360\pi\) | |||||||
\(14\) | −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 | \(0.617144\pi\) | |||||||
\(18\) | 1.12233 | 0.264537 | ||||||||
\(19\) | 3.28513 | + | 2.38678i | 0.753660 | + | 0.547566i | 0.896959 | − | 0.442113i | \(-0.145771\pi\) |
−0.143299 | + | 0.989679i | \(0.545771\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.901030 | + | 0.654637i | −0.196621 | + | 0.142853i | ||||
\(22\) | −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 | \(-0.322611\pi\) | |||||||
\(24\) | 3.07561 | 0.627806 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.54774 | 0.891886 | ||||||||
\(27\) | −0.309017 | − | 0.951057i | −0.0594703 | − | 0.183031i | ||||
\(28\) | −0.667093 | + | 0.484672i | −0.126069 | + | 0.0915943i | ||||
\(29\) | 1.82808 | − | 1.32818i | 0.339466 | − | 0.246637i | −0.404970 | − | 0.914330i | \(-0.632718\pi\) |
0.744437 | + | 0.667693i | \(0.232718\pi\) | |||||||
\(30\) | 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 | ||||||||
\(33\) | 2.96915 | + | 2.15722i | 0.516863 | + | 0.375523i | ||||
\(34\) | −0.736068 | + | 2.26538i | −0.126235 | + | 0.388510i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.228786 | − | 0.704131i | −0.0381310 | − | 0.117355i | ||||
\(37\) | −2.27817 | + | 7.01149i | −0.374529 | + | 1.15268i | 0.569267 | + | 0.822153i | \(0.307227\pi\) |
−0.943796 | + | 0.330529i | \(0.892773\pi\) | |||||||
\(38\) | −1.40831 | + | 4.33434i | −0.228458 | + | 0.703123i | ||||
\(39\) | −1.25215 | − | 3.85372i | −0.200504 | − | 0.617089i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.30902 | + | 7.10642i | −0.360608 | + | 1.10984i | 0.592078 | + | 0.805881i | \(0.298308\pi\) |
−0.952686 | + | 0.303956i | \(0.901692\pi\) | |||||||
\(42\) | −1.01126 | − | 0.734721i | −0.156040 | − | 0.113370i | ||||
\(43\) | −9.24998 | −1.41061 | −0.705304 | − | 0.708905i | \(-0.749190\pi\) | ||||
−0.705304 | + | 0.708905i | \(0.749190\pi\) | |||||||
\(44\) | 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 | \(0.373254\pi\) | |||||||
\(48\) | 0.609110 | + | 1.87465i | 0.0879174 | + | 0.270582i | ||||
\(49\) | −5.75960 | −0.822799 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.12233 | 0.297186 | ||||||||
\(52\) | −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 | \(0.377489\pi\) | |||||||
\(54\) | 0.907987 | − | 0.659691i | 0.123561 | − | 0.0897726i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.77121 | − | 2.01340i | −0.370319 | − | 0.269053i | ||||
\(57\) | 4.06064 | 0.537845 | ||||||||
\(58\) | 2.05172 | + | 1.49066i | 0.269404 | + | 0.195733i | ||||
\(59\) | −2.03760 | + | 6.27109i | −0.265273 | + | 0.816427i | 0.726357 | + | 0.687317i | \(0.241212\pi\) |
−0.991630 | + | 0.129110i | \(0.958788\pi\) | |||||||
\(60\) | 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 | ||||
\(63\) | −0.344163 | + | 1.05922i | −0.0433604 | + | 0.133450i | ||||
\(64\) | 2.58433 | + | 7.95375i | 0.323041 | + | 0.994219i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.27286 | + | 3.91745i | −0.156678 | + | 0.482205i | ||||
\(67\) | 2.12499 | + | 1.54390i | 0.259609 | + | 0.188617i | 0.709975 | − | 0.704227i | \(-0.248706\pi\) |
−0.450366 | + | 0.892844i | \(0.648706\pi\) | |||||||
\(68\) | 1.57131 | 0.190549 | ||||||||
\(69\) | −4.99517 | − | 3.62921i | −0.601348 | − | 0.436905i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.534620 | + | 0.388424i | −0.0634477 | + | 0.0460975i | −0.619057 | − | 0.785346i | \(-0.712485\pi\) |
0.555609 | + | 0.831443i | \(0.312485\pi\) | |||||||
\(72\) | 2.48822 | − | 1.80780i | 0.293239 | − | 0.213051i | ||||
\(73\) | −2.31003 | − | 7.10955i | −0.270369 | − | 0.832110i | −0.990408 | − | 0.138176i | \(-0.955876\pi\) |
0.720039 | − | 0.693934i | \(-0.244124\pi\) | |||||||
\(74\) | −8.27420 | −0.961856 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.00637 | 0.344854 | ||||||||
\(77\) | −1.26310 | − | 3.88743i | −0.143944 | − | 0.443014i | ||||
\(78\) | 3.67920 | − | 2.67310i | 0.416587 | − | 0.302668i | ||||
\(79\) | −6.90667 | + | 5.01799i | −0.777061 | + | 0.564568i | −0.904096 | − | 0.427330i | \(-0.859454\pi\) |
0.127034 | + | 0.991898i | \(0.459454\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | − | 0.587785i | −0.0898908 | − | 0.0653095i | ||||
\(82\) | −8.38623 | −0.926104 | ||||||||
\(83\) | 9.92170 | + | 7.20854i | 1.08905 | + | 0.791240i | 0.979238 | − | 0.202713i | \(-0.0649758\pi\) |
0.109810 | + | 0.993953i | \(0.464976\pi\) | |||||||
\(84\) | −0.254807 | + | 0.784215i | −0.0278017 | + | 0.0855649i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.20808 | − | 9.87345i | −0.345936 | − | 1.06468i | ||||
\(87\) | 0.698265 | − | 2.14904i | 0.0748618 | − | 0.230401i | ||||
\(88\) | −3.48809 | + | 10.7352i | −0.371832 | + | 1.14438i | ||||
\(89\) | −4.72429 | − | 14.5399i | −0.500773 | − | 1.54122i | −0.807762 | − | 0.589509i | \(-0.799321\pi\) |
0.306989 | − | 0.951713i | \(-0.400679\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.39456 | + | 4.29202i | −0.146190 | + | 0.449926i | ||||
\(92\) | −3.69826 | − | 2.68695i | −0.385571 | − | 0.280134i | ||||
\(93\) | −10.0520 | −1.04235 | ||||||||
\(94\) | −2.83986 | − | 2.06328i | −0.292910 | − | 0.212811i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.18668 | − | 2.31526i | 0.325240 | − | 0.236300i | ||||
\(97\) | 10.9217 | − | 7.93508i | 1.10893 | − | 0.805685i | 0.126436 | − | 0.991975i | \(-0.459646\pi\) |
0.982495 | + | 0.186290i | \(0.0596463\pi\) | |||||||
\(98\) | −1.99754 | − | 6.14781i | −0.201782 | − | 0.621022i | ||||
\(99\) | 3.67008 | 0.368856 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.22642 | 0.719055 | 0.359528 | − | 0.933134i | \(-0.382938\pi\) | ||||
0.359528 | + | 0.933134i | \(0.382938\pi\) | |||||||
\(102\) | 0.736068 | + | 2.26538i | 0.0728816 | + | 0.224306i | ||||
\(103\) | 4.26957 | − | 3.10203i | 0.420693 | − | 0.305652i | −0.357223 | − | 0.934019i | \(-0.616277\pi\) |
0.777917 | + | 0.628367i | \(0.216277\pi\) | |||||||
\(104\) | 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 | \(0.585124\pi\) | |||||||
\(108\) | −0.598970 | − | 0.435177i | −0.0576359 | − | 0.0418749i | ||||
\(109\) | 3.50410 | − | 10.7845i | 0.335632 | − | 1.03297i | −0.630778 | − | 0.775963i | \(-0.717264\pi\) |
0.966410 | − | 0.257005i | \(-0.0827358\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.27817 | + | 7.01149i | 0.216234 | + | 0.665501i | ||||
\(112\) | 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 | \(0.173032\pi\) | |||||||
\(114\) | 1.40831 | + | 4.33434i | 0.131900 | + | 0.405948i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.516973 | − | 1.59108i | 0.0479997 | − | 0.147728i | ||||
\(117\) | −3.27817 | − | 2.38173i | −0.303067 | − | 0.220191i | ||||
\(118\) | −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 | ||||
\(123\) | 2.30902 | + | 7.10642i | 0.208197 | + | 0.640765i | ||||
\(124\) | −7.44220 | −0.668330 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.24998 | −0.111357 | ||||||||
\(127\) | −0.234728 | − | 0.722418i | −0.0208287 | − | 0.0641043i | 0.940102 | − | 0.340894i | \(-0.110730\pi\) |
−0.960931 | + | 0.276789i | \(0.910730\pi\) | |||||||
\(128\) | −1.22019 | + | 0.886518i | −0.107850 | + | 0.0783578i | ||||
\(129\) | −7.48339 | + | 5.43700i | −0.658876 | + | 0.478701i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.8562 | − | 8.61406i | −1.03588 | − | 0.752614i | −0.0664061 | − | 0.997793i | \(-0.521153\pi\) |
−0.969478 | + | 0.245179i | \(0.921153\pi\) | |||||||
\(132\) | 2.71720 | 0.236502 | ||||||||
\(133\) | −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 | \(0.924042\pi\) | |||||||
\(138\) | 2.14140 | − | 6.59054i | 0.182288 | − | 0.561024i | ||||
\(139\) | 4.55306 | + | 14.0129i | 0.386185 | + | 1.18856i | 0.935617 | + | 0.353017i | \(0.114844\pi\) |
−0.549432 | + | 0.835539i | \(0.685156\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.966496 | + | 2.97457i | −0.0813937 | + | 0.250504i | ||||
\(142\) | −0.600022 | − | 0.435941i | −0.0503527 | − | 0.0365834i | ||||
\(143\) | 14.8713 | 1.24360 | ||||||||
\(144\) | 1.59467 | + | 1.15860i | 0.132889 | + | 0.0965497i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.78758 | − | 4.93147i | 0.561744 | − | 0.408131i | ||||
\(147\) | −4.65961 | + | 3.38541i | −0.384318 | + | 0.279224i | ||||
\(148\) | 1.68668 | + | 5.19108i | 0.138645 | + | 0.426704i | ||||
\(149\) | 15.6498 | 1.28208 | 0.641041 | − | 0.767507i | \(-0.278503\pi\) | ||||
0.641041 | + | 0.767507i | \(0.278503\pi\) | |||||||
\(150\) | 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 | ||||
\(153\) | 1.71700 | − | 1.24748i | 0.138812 | − | 0.100852i | ||||
\(154\) | 3.71139 | − | 2.69648i | 0.299072 | − | 0.217289i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.42705 | − | 1.76336i | −0.194320 | − | 0.141181i | ||||
\(157\) | 4.50061 | 0.359188 | 0.179594 | − | 0.983741i | \(-0.442522\pi\) | ||||
0.179594 | + | 0.983741i | \(0.442522\pi\) | |||||||
\(158\) | −7.75159 | − | 5.63186i | −0.616683 | − | 0.448047i | ||||
\(159\) | −1.08453 | + | 3.33784i | −0.0860089 | + | 0.264708i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.12499 | + | 6.54005i | 0.167473 | + | 0.515428i | ||||
\(162\) | 0.346820 | − | 1.06740i | 0.0272488 | − | 0.0838631i | ||||
\(163\) | 0.758292 | − | 2.33378i | 0.0593940 | − | 0.182796i | −0.916958 | − | 0.398985i | \(-0.869363\pi\) |
0.976352 | + | 0.216189i | \(0.0693626\pi\) | |||||||
\(164\) | 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 | \(0.737816\pi\) | |||||||
\(168\) | −3.42541 | −0.264276 | ||||||||
\(169\) | −2.76606 | − | 2.00966i | −0.212774 | − | 0.154589i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.28513 | − | 2.38678i | 0.251220 | − | 0.182522i | ||||
\(172\) | −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 | \(-0.240791\pi\) | |||||||
\(174\) | 2.53606 | 0.192258 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −7.23416 | −0.545296 | ||||||||
\(177\) | 2.03760 | + | 6.27109i | 0.153156 | + | 0.471364i | ||||
\(178\) | 13.8814 | − | 10.0854i | 1.04046 | − | 0.755935i | ||||
\(179\) | −8.13657 | + | 5.91157i | −0.608156 | + | 0.441851i | −0.848764 | − | 0.528771i | \(-0.822653\pi\) |
0.240609 | + | 0.970622i | \(0.422653\pi\) | |||||||
\(180\) | 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 | ||||||||
\(183\) | −7.36536 | − | 5.35125i | −0.544463 | − | 0.395575i | ||||
\(184\) | 5.86822 | − | 18.0605i | 0.432611 | − | 1.33144i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3.48625 | − | 10.7296i | −0.255624 | − | 0.786731i | ||||
\(187\) | −2.40697 | + | 7.40790i | −0.176015 | + | 0.541719i | ||||
\(188\) | −0.715563 | + | 2.20227i | −0.0521878 | + | 0.160617i | ||||
\(189\) | 0.344163 | + | 1.05922i | 0.0250342 | + | 0.0770472i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.58739 | + | 11.0408i | −0.259574 | + | 0.798888i | 0.733320 | + | 0.679884i | \(0.237970\pi\) |
−0.992894 | + | 0.119003i | \(0.962030\pi\) | |||||||
\(192\) | 6.76586 | + | 4.91569i | 0.488284 | + | 0.354759i | ||||
\(193\) | 3.38156 | 0.243410 | 0.121705 | − | 0.992566i | \(-0.461164\pi\) | ||||
0.121705 | + | 0.992566i | \(0.461164\pi\) | |||||||
\(194\) | 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 | \(0.515534\pi\) | |||||||
\(198\) | 1.27286 | + | 3.91745i | 0.0904579 | + | 0.278401i | ||||
\(199\) | 20.0102 | 1.41849 | 0.709244 | − | 0.704963i | \(-0.249037\pi\) | ||||
0.709244 | + | 0.704963i | \(0.249037\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.62663 | 0.185268 | ||||||||
\(202\) | 2.50627 | + | 7.71350i | 0.176340 | + | 0.542720i | ||||
\(203\) | −2.03600 | + | 1.47924i | −0.142899 | + | 0.103822i | ||||
\(204\) | 1.27121 | − | 0.923591i | 0.0890028 | − | 0.0646643i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.79188 | + | 3.48151i | 0.333866 | + | 0.242568i | ||||
\(207\) | −6.17438 | −0.429149 | ||||||||
\(208\) | 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 | ||||
\(213\) | −0.204207 | + | 0.628483i | −0.0139920 | + | 0.0430630i | ||||
\(214\) | −1.89600 | − | 5.83530i | −0.129608 | − | 0.398893i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.950415 | − | 2.92508i | 0.0646675 | − | 0.199026i | ||||
\(217\) | 9.05719 | + | 6.58044i | 0.614842 | + | 0.446709i | ||||
\(218\) | 12.7267 | 0.861961 | ||||||||
\(219\) | −6.04774 | − | 4.39394i | −0.408669 | − | 0.296915i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.95737 | − | 5.05483i | 0.468003 | − | 0.340024i | ||||
\(222\) | −6.69397 | + | 4.86345i | −0.449270 | + | 0.326413i | ||||
\(223\) | 7.92223 | + | 24.3821i | 0.530511 | + | 1.63275i | 0.753153 | + | 0.657846i | \(0.228532\pi\) |
−0.222641 | + | 0.974900i | \(0.571468\pi\) | |||||||
\(224\) | −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 | \(0.969892\pi\) | |||||||
\(228\) | 2.43220 | − | 1.76710i | 0.161076 | − | 0.117029i | ||||
\(229\) | 6.44293 | − | 4.68106i | 0.425761 | − | 0.309333i | −0.354191 | − | 0.935173i | \(-0.615244\pi\) |
0.779952 | + | 0.625840i | \(0.215244\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.30685 | − | 2.40257i | −0.217575 | − | 0.158077i | ||||
\(232\) | 6.94974 | 0.456273 | ||||||||
\(233\) | −7.62181 | − | 5.53757i | −0.499321 | − | 0.362778i | 0.309436 | − | 0.950920i | \(-0.399860\pi\) |
−0.808758 | + | 0.588142i | \(0.799860\pi\) | |||||||
\(234\) | 1.40533 | − | 4.32516i | 0.0918693 | − | 0.282745i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.50857 | + | 4.64291i | 0.0981998 | + | 0.302228i | ||||
\(237\) | −2.63811 | + | 8.11928i | −0.171364 | + | 0.527404i | ||||
\(238\) | 0.819784 | − | 2.52304i | 0.0531387 | − | 0.163544i | ||||
\(239\) | −3.46814 | − | 10.6738i | −0.224335 | − | 0.690433i | −0.998358 | − | 0.0572756i | \(-0.981759\pi\) |
0.774023 | − | 0.633157i | \(-0.218241\pi\) | |||||||
\(240\) | 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 | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −5.45307 | − | 3.96189i | −0.349097 | − | 0.253634i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.78460 | + | 4.92930i | −0.432570 | + | 0.314281i | ||||
\(247\) | 13.3115 | − | 9.67135i | 0.846989 | − | 0.615373i | ||||
\(248\) | −9.55361 | − | 29.4030i | −0.606655 | − | 1.86709i | ||||
\(249\) | 12.2639 | 0.777193 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.76819 | −0.427205 | −0.213602 | − | 0.976921i | \(-0.568520\pi\) | ||||
−0.213602 | + | 0.976921i | \(0.568520\pi\) | |||||||
\(252\) | 0.254807 | + | 0.784215i | 0.0160513 | + | 0.0494009i | ||||
\(253\) | 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 | \(0.347350\pi\) | |||||||
\(258\) | −8.39886 | − | 6.10213i | −0.522890 | − | 0.379902i | ||||
\(259\) | 2.53728 | − | 7.80894i | 0.157659 | − | 0.485224i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.698265 | − | 2.14904i | −0.0432215 | − | 0.133022i | ||||
\(262\) | 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 | \(0.888887\pi\) | |||||||
\(264\) | 3.48809 | + | 10.7352i | 0.214677 | + | 0.660709i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.56849 | − | 4.82730i | 0.0961700 | − | 0.295981i | ||||
\(267\) | −12.3683 | − | 8.98613i | −0.756930 | − | 0.549942i | ||||
\(268\) | 1.94467 | 0.118790 | ||||||||
\(269\) | 8.28280 | + | 6.01780i | 0.505011 | + | 0.366912i | 0.810928 | − | 0.585146i | \(-0.198963\pi\) |
−0.305917 | + | 0.952058i | \(0.598963\pi\) | |||||||
\(270\) | 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 | ||||
\(273\) | 1.39456 | + | 4.29202i | 0.0844028 | + | 0.259765i | ||||
\(274\) | −13.7950 | −0.833389 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.57131 | −0.275160 | ||||||||
\(277\) | −9.75011 | − | 30.0077i | −0.585827 | − | 1.80299i | −0.595923 | − | 0.803041i | \(-0.703214\pi\) |
0.0100963 | − | 0.999949i | \(-0.496786\pi\) | |||||||
\(278\) | −13.3783 | + | 9.71989i | −0.802376 | + | 0.582960i | ||||
\(279\) | −8.13227 | + | 5.90844i | −0.486866 | + | 0.353729i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.2417 | + | 12.5268i | 1.02855 | + | 0.747288i | 0.968019 | − | 0.250878i | \(-0.0807192\pi\) |
0.0605353 | + | 0.998166i | \(0.480719\pi\) | |||||||
\(282\) | −3.51026 | −0.209033 | ||||||||
\(283\) | −0.699317 | − | 0.508083i | −0.0415701 | − | 0.0302024i | 0.566806 | − | 0.823851i | \(-0.308179\pi\) |
−0.608376 | + | 0.793649i | \(0.708179\pi\) | |||||||
\(284\) | −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 | ||||
\(288\) | 1.21720 | − | 3.74617i | 0.0717245 | − | 0.220745i | ||||
\(289\) | −3.86138 | − | 11.8841i | −0.227140 | − | 0.699066i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.17172 | − | 12.8392i | 0.244550 | − | 0.752649i | ||||
\(292\) | −4.47755 | − | 3.25313i | −0.262029 | − | 0.190375i | ||||
\(293\) | −3.17701 | −0.185603 | −0.0928014 | − | 0.995685i | \(-0.529582\pi\) | ||||
−0.0928014 | + | 0.995685i | \(0.529582\pi\) | |||||||
\(294\) | −5.22964 | − | 3.79955i | −0.304999 | − | 0.221594i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −18.3439 | + | 13.3276i | −1.06622 | + | 0.774653i | ||||
\(297\) | 2.96915 | − | 2.15722i | 0.172288 | − | 0.125174i | ||||
\(298\) | 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 | ||||
\(303\) | 5.84629 | − | 4.24758i | 0.335861 | − | 0.244017i | ||||
\(304\) | −6.47538 | + | 4.70464i | −0.371389 | + | 0.269830i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.92705 | + | 1.40008i | 0.110162 | + | 0.0800375i | ||||
\(307\) | 0.507986 | 0.0289923 | 0.0144961 | − | 0.999895i | \(-0.495386\pi\) | ||||
0.0144961 | + | 0.999895i | \(0.495386\pi\) | |||||||
\(308\) | −2.44828 | − | 1.77878i | −0.139504 | − | 0.101356i | ||||
\(309\) | 1.63083 | − | 5.01918i | 0.0927747 | − | 0.285531i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.52519 | − | 13.9271i | −0.256600 | − | 0.789734i | −0.993510 | − | 0.113743i | \(-0.963716\pi\) |
0.736910 | − | 0.675991i | \(-0.236284\pi\) | |||||||
\(312\) | 3.85112 | − | 11.8525i | 0.218027 | − | 0.671017i | ||||
\(313\) | 4.62171 | − | 14.2241i | 0.261234 | − | 0.803996i | −0.731303 | − | 0.682053i | \(-0.761087\pi\) |
0.992537 | − | 0.121943i | \(-0.0389127\pi\) | |||||||
\(314\) | 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 | \(0.530077\pi\) | |||||||
\(318\) | −3.93896 | −0.220886 | ||||||||
\(319\) | 6.70920 | + | 4.87452i | 0.375643 | + | 0.272921i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.42275 | + | 3.21332i | −0.246854 | + | 0.179350i | ||||
\(322\) | −6.24388 | + | 4.53644i | −0.347958 | + | 0.252806i | ||||
\(323\) | 2.66312 | + | 8.19624i | 0.148180 | + | 0.456051i | ||||
\(324\) | −0.740367 | −0.0411315 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.75408 | 0.152534 | ||||||||
\(327\) | −3.50410 | − | 10.7845i | −0.193777 | − | 0.596385i | ||||
\(328\) | −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 | ||||||||
\(333\) | 5.96433 | + | 4.33334i | 0.326843 | + | 0.237465i | ||||
\(334\) | 1.06241 | − | 3.26975i | 0.0581322 | − | 0.178913i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.678387 | − | 2.08786i | −0.0370090 | − | 0.113902i | ||||
\(337\) | 3.30488 | − | 10.1714i | 0.180028 | − | 0.554070i | −0.819799 | − | 0.572651i | \(-0.805915\pi\) |
0.999827 | + | 0.0185811i | \(0.00591487\pi\) | |||||||
\(338\) | 1.18579 | − | 3.64949i | 0.0644986 | − | 0.198506i | ||||
\(339\) | 1.49416 | + | 4.59855i | 0.0811516 | + | 0.249759i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.4002 | − | 35.0861i | 0.617354 | − | 1.90002i | ||||
\(342\) | 3.68701 | + | 2.67877i | 0.199371 | + | 0.144851i | ||||
\(343\) | 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 | \(0.157055\pi\) | |||||||
\(348\) | −0.516973 | − | 1.59108i | −0.0277126 | − | 0.0852907i | ||||
\(349\) | 15.2383 | 0.815688 | 0.407844 | − | 0.913052i | \(-0.366281\pi\) | ||||
0.407844 | + | 0.913052i | \(0.366281\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.05204 | −0.216282 | ||||||||
\(352\) | 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 | \(0.587894\pi\) | |||||||
\(354\) | −5.98710 | + | 4.34988i | −0.318211 | + | 0.231194i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −9.15712 | − | 6.65304i | −0.485326 | − | 0.352610i | ||||
\(357\) | −2.36372 | −0.125101 | ||||||||
\(358\) | −9.13195 | − | 6.63475i | −0.482638 | − | 0.350657i | ||||
\(359\) | −4.06875 | + | 12.5223i | −0.214740 | + | 0.660903i | 0.784431 | + | 0.620216i | \(0.212955\pi\) |
−0.999172 | + | 0.0406876i | \(0.987045\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.776002 | − | 2.38829i | −0.0408422 | − | 0.125699i | ||||
\(362\) | −6.75205 | + | 20.7807i | −0.354880 | + | 1.09221i | ||||
\(363\) | −0.763104 | + | 2.34859i | −0.0400526 | + | 0.123269i | ||||
\(364\) | 1.03249 | + | 3.17767i | 0.0541171 | + | 0.166555i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3.15748 | − | 9.71772i | 0.165044 | − | 0.507953i | ||||
\(367\) | −3.14622 | − | 2.28586i | −0.164232 | − | 0.119321i | 0.502634 | − | 0.864499i | \(-0.332364\pi\) |
−0.666865 | + | 0.745178i | \(0.732364\pi\) | |||||||
\(368\) | 12.1704 | 0.634428 | ||||||||
\(369\) | 6.04508 | + | 4.39201i | 0.314695 | + | 0.228639i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.16227 | − | 2.29752i | 0.164177 | − | 0.119281i | ||||
\(372\) | −6.02087 | + | 4.37442i | −0.312168 | + | 0.226803i | ||||
\(373\) | 2.51641 | + | 7.74470i | 0.130295 | + | 0.401006i | 0.994829 | − | 0.101569i | \(-0.0323862\pi\) |
−0.864534 | + | 0.502575i | \(0.832386\pi\) | |||||||
\(374\) | −8.74200 | −0.452038 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.61941 | −0.496083 | ||||||||
\(377\) | −2.82940 | − | 8.70799i | −0.145721 | − | 0.448484i | ||||
\(378\) | −1.01126 | + | 0.734721i | −0.0520134 | + | 0.0377900i | ||||
\(379\) | −8.01509 | + | 5.82330i | −0.411708 | + | 0.299123i | −0.774293 | − | 0.632828i | \(-0.781894\pi\) |
0.362585 | + | 0.931951i | \(0.381894\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.614526 | − | 0.446479i | −0.0314831 | − | 0.0228738i | ||||
\(382\) | −13.0292 | −0.666632 | ||||||||
\(383\) | −4.22481 | − | 3.06951i | −0.215878 | − | 0.156844i | 0.474591 | − | 0.880206i | \(-0.342596\pi\) |
−0.690469 | + | 0.723362i | \(0.742596\pi\) | |||||||
\(384\) | −0.466070 | + | 1.43442i | −0.0237840 | + | 0.0731997i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.17279 | + | 3.60949i | 0.0596937 | + | 0.183718i | ||||
\(387\) | −2.85840 | + | 8.79726i | −0.145301 | + | 0.447190i | ||||
\(388\) | 3.08860 | − | 9.50575i | 0.156800 | − | 0.482581i | ||||
\(389\) | −1.15255 | − | 3.54719i | −0.0584367 | − | 0.179850i | 0.917577 | − | 0.397557i | \(-0.130142\pi\) |
−0.976014 | + | 0.217708i | \(0.930142\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.04938 | − | 12.4627i | 0.204786 | − | 0.630267i | ||||
\(392\) | −14.3311 | − | 10.4122i | −0.723831 | − | 0.525894i | ||||
\(393\) | −14.6551 | −0.739253 | ||||||||
\(394\) | −15.9698 | − | 11.6027i | −0.804545 | − | 0.584536i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.19826 | − | 1.59713i | 0.110467 | − | 0.0802589i | ||||
\(397\) | 3.24870 | − | 2.36032i | 0.163048 | − | 0.118461i | −0.503270 | − | 0.864130i | \(-0.667870\pi\) |
0.666317 | + | 0.745668i | \(0.267870\pi\) | |||||||
\(398\) | 6.93995 | + | 21.3590i | 0.347868 | + | 1.07063i | ||||
\(399\) | −4.52248 | −0.226407 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.9890 | −1.24789 | −0.623945 | − | 0.781468i | \(-0.714471\pi\) | ||||
−0.623945 | + | 0.781468i | \(0.714471\pi\) | |||||||
\(402\) | 0.910969 | + | 2.80367i | 0.0454350 | + | 0.139835i | ||||
\(403\) | −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 | ||||||||
\(408\) | 5.28083 | + | 3.83675i | 0.261440 | + | 0.189947i | ||||
\(409\) | −7.84186 | + | 24.1348i | −0.387755 | + | 1.19339i | 0.546707 | + | 0.837324i | \(0.315881\pi\) |
−0.934462 | + | 0.356063i | \(0.884119\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.79825 | + | 11.6898i | 0.187354 | + | 0.576616i | ||||
\(412\) | 1.20741 | − | 3.71604i | 0.0594850 | − | 0.183076i | ||||
\(413\) | 2.26935 | − | 6.98433i | 0.111667 | − | 0.343677i | ||||
\(414\) | −2.14140 | − | 6.59054i | −0.105244 | − | 0.323908i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.93216 | − | 15.1796i | 0.241819 | − | 0.744243i | ||||
\(417\) | 11.9201 | + | 8.66043i | 0.583728 | + | 0.424103i | ||||
\(418\) | −16.7260 | −0.818094 | ||||||||
\(419\) | 24.9354 | + | 18.1166i | 1.21817 | + | 0.885056i | 0.995947 | − | 0.0899392i | \(-0.0286673\pi\) |
0.222227 | + | 0.974995i | \(0.428667\pi\) | |||||||
\(420\) | 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 | ||||
\(423\) | 0.966496 | + | 2.97457i | 0.0469927 | + | 0.144629i | ||||
\(424\) | −10.7942 | −0.524212 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.741668 | −0.0359339 | ||||||||
\(427\) | 3.13329 | + | 9.64327i | 0.151630 | + | 0.466670i | ||||
\(428\) | −3.27446 | + | 2.37904i | −0.158277 | + | 0.114995i | ||||
\(429\) | 12.0311 | − | 8.74113i | 0.580869 | − | 0.422026i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.3431 | + | 15.5067i | 1.02806 | + | 0.746929i | 0.967919 | − | 0.251261i | \(-0.0808452\pi\) |
0.0601403 | + | 0.998190i | \(0.480845\pi\) | |||||||
\(432\) | 1.97112 | 0.0948356 | ||||||||
\(433\) | −7.58269 | − | 5.50914i | −0.364401 | − | 0.264753i | 0.390485 | − | 0.920609i | \(-0.372307\pi\) |
−0.754885 | + | 0.655857i | \(0.772307\pi\) | |||||||
\(434\) | −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 | ||||
\(438\) | 2.59263 | − | 7.97928i | 0.123880 | − | 0.381265i | ||||
\(439\) | −0.159447 | − | 0.490727i | −0.00760998 | − | 0.0234211i | 0.947179 | − | 0.320704i | \(-0.103920\pi\) |
−0.954789 | + | 0.297283i | \(0.903920\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.77981 | + | 5.47770i | −0.0847530 | + | 0.260843i | ||||
\(442\) | 7.80849 | + | 5.67320i | 0.371412 | + | 0.269847i | ||||
\(443\) | 17.8348 | 0.847357 | 0.423678 | − | 0.905813i | \(-0.360739\pi\) | ||||
0.423678 | + | 0.905813i | \(0.360739\pi\) | |||||||
\(444\) | 4.41579 | + | 3.20826i | 0.209564 | + | 0.152257i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −23.2779 | + | 16.9124i | −1.10224 | + | 0.800826i | ||||
\(447\) | 12.6610 | − | 9.19872i | 0.598842 | − | 0.435084i | ||||
\(448\) | −2.87826 | − | 8.85836i | −0.135985 | − | 0.418518i | ||||
\(449\) | −4.16533 | −0.196574 | −0.0982870 | − | 0.995158i | \(-0.531336\pi\) | ||||
−0.0982870 | + | 0.995158i | \(0.531336\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −27.4233 | −1.29131 | ||||||||
\(452\) | 1.10623 | + | 3.40462i | 0.0520325 | + | 0.160140i | ||||
\(453\) | 3.20224 | − | 2.32656i | 0.150454 | − | 0.109311i | ||||
\(454\) | 5.95944 | − | 4.32979i | 0.279691 | − | 0.203207i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 10.1038 | + | 7.34081i | 0.473152 | + | 0.343765i | ||||
\(457\) | 17.6734 | 0.826725 | 0.413362 | − | 0.910567i | \(-0.364354\pi\) | ||||
0.413362 | + | 0.910567i | \(0.364354\pi\) | |||||||
\(458\) | 7.23112 | + | 5.25371i | 0.337888 | + | 0.245490i | ||||
\(459\) | 0.655837 | − | 2.01846i | 0.0306119 | − | 0.0942136i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.0633350 | − | 0.194925i | −0.00294981 | − | 0.00907857i | 0.949571 | − | 0.313553i | \(-0.101519\pi\) |
−0.952521 | + | 0.304474i | \(0.901519\pi\) | |||||||
\(462\) | 1.41762 | − | 4.36300i | 0.0659538 | − | 0.202985i | ||||
\(463\) | 3.96084 | − | 12.1902i | 0.184076 | − | 0.566528i | −0.815855 | − | 0.578256i | \(-0.803733\pi\) |
0.999931 | + | 0.0117286i | \(0.00373342\pi\) | |||||||
\(464\) | 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 | \(0.691797\pi\) | |||||||
\(468\) | −3.00000 | −0.138675 | ||||||||
\(469\) | −2.36668 | − | 1.71949i | −0.109283 | − | 0.0793987i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.64107 | − | 2.64539i | 0.167772 | − | 0.121893i | ||||
\(472\) | −16.4069 | + | 11.9203i | −0.755187 | + | 0.548675i | ||||
\(473\) | −10.4905 | − | 32.2866i | −0.482356 | − | 1.48454i | ||||
\(474\) | −9.58149 | −0.440092 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.75002 | −0.0802120 | ||||||||
\(477\) | 1.08453 | + | 3.33784i | 0.0496572 | + | 0.152829i | ||||
\(478\) | 10.1905 | − | 7.40380i | 0.466101 | − | 0.338642i | ||||
\(479\) | 20.3670 | − | 14.7975i | 0.930590 | − | 0.676113i | −0.0155470 | − | 0.999879i | \(-0.504949\pi\) |
0.946137 | + | 0.323766i | \(0.104949\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.1677 | + | 17.5589i | 1.10195 | + | 0.800615i | ||||
\(482\) | 25.4555 | 1.15947 | ||||||||
\(483\) | 5.56330 | + | 4.04197i | 0.253139 | + | 0.183916i | ||||
\(484\) | −0.564977 | + | 1.73882i | −0.0256808 | + | 0.0790373i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.346820 | − | 1.06740i | −0.0157321 | − | 0.0484184i | ||||
\(487\) | −3.20135 | + | 9.85274i | −0.145067 | + | 0.446470i | −0.997020 | − | 0.0771487i | \(-0.975418\pi\) |
0.851953 | + | 0.523619i | \(0.175418\pi\) | |||||||
\(488\) | 8.65265 | − | 26.6301i | 0.391687 | − | 1.20549i | ||||
\(489\) | −0.758292 | − | 2.33378i | −0.0342912 | − | 0.105537i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.83831 | + | 14.8908i | −0.218350 | + | 0.672012i | 0.780549 | + | 0.625095i | \(0.214940\pi\) |
−0.998899 | + | 0.0469170i | \(0.985060\pi\) | |||||||
\(492\) | 4.47558 | + | 3.25170i | 0.201775 | + | 0.146598i | ||||
\(493\) | 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 | ||||
\(498\) | 4.25337 | + | 13.0905i | 0.190598 | + | 0.586600i | ||||
\(499\) | 35.7864 | 1.60202 | 0.801010 | − | 0.598651i | \(-0.204296\pi\) | ||||
0.801010 | + | 0.598651i | \(0.204296\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.06328 | −0.136857 | ||||||||
\(502\) | −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 | \(0.384580\pi\) | |||||||
\(504\) | −2.77121 | + | 2.01340i | −0.123440 | + | 0.0896842i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 20.5754 | + | 14.9489i | 0.914687 | + | 0.664559i | ||||
\(507\) | −3.41904 | −0.151845 | ||||||||
\(508\) | −0.454975 | − | 0.330559i | −0.0201862 | − | 0.0146662i | ||||
\(509\) | 10.3986 | − | 32.0037i | 0.460912 | − | 1.41854i | −0.403141 | − | 0.915138i | \(-0.632082\pi\) |
0.864052 | − | 0.503402i | \(-0.167918\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.57276 | + | 7.91815i | 0.113812 | + | 0.350278i | ||||
\(512\) | −6.14602 | + | 18.9155i | −0.271618 | + | 0.835955i | ||||
\(513\) | 1.25481 | − | 3.86190i | 0.0554011 | − | 0.170507i | ||||
\(514\) | 5.13064 | + | 15.7905i | 0.226303 | + | 0.696489i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.11627 | + | 6.51320i | −0.0931635 | + | 0.286728i | ||||
\(517\) | −9.28647 | − | 6.74701i | −0.408418 | − | 0.296733i | ||||
\(518\) | 9.21526 | 0.404895 | ||||||||
\(519\) | −9.10923 | − | 6.61825i | −0.399851 | − | 0.290509i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.58263 | − | 6.96219i | 0.419823 | − | 0.305019i | −0.357744 | − | 0.933820i | \(-0.616454\pi\) |
0.777566 | + | 0.628801i | \(0.216454\pi\) | |||||||
\(522\) | 2.05172 | − | 1.49066i | 0.0898012 | − | 0.0652444i | ||||
\(523\) | −1.26602 | − | 3.89642i | −0.0553593 | − | 0.170379i | 0.919554 | − | 0.392964i | \(-0.128550\pi\) |
−0.974913 | + | 0.222586i | \(0.928550\pi\) | |||||||
\(524\) | −10.8502 | −0.473992 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −22.4117 | −0.977195 | ||||||||
\(527\) | −6.59250 | − | 20.2896i | −0.287174 | − | 0.883830i | ||||
\(528\) | −5.85256 | + | 4.25213i | −0.254700 | + | 0.185050i | ||||
\(529\) | −12.2347 | + | 8.88902i | −0.531943 | + | 0.386479i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.33451 | + | 3.87575i | 0.231498 | + | 0.168193i | ||||
\(532\) | −3.34829 | −0.145167 | ||||||||
\(533\) | 24.4949 | + | 17.7966i | 1.06099 | + | 0.770857i | ||||
\(534\) | 5.30222 | − | 16.3186i | 0.229450 | − | 0.706174i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.49639 | + | 7.68310i | 0.107828 | + | 0.331859i | ||||
\(537\) | −3.10789 | + | 9.56511i | −0.134116 | + | 0.412765i | ||||
\(538\) | −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 | ||||
\(543\) | 19.4684 | 0.835471 | ||||||||
\(544\) | 6.76321 | + | 4.91376i | 0.289970 | + | 0.210676i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4.09765 | + | 2.97712i | −0.175363 | + | 0.127409i | ||||
\(547\) | −21.4426 | + | 15.5789i | −0.916818 | + | 0.666107i | −0.942730 | − | 0.333557i | \(-0.891751\pi\) |
0.0259119 | + | 0.999664i | \(0.491751\pi\) | |||||||
\(548\) | 2.81210 | + | 8.65476i | 0.120127 | + | 0.369713i | ||||
\(549\) | −9.10408 | −0.388553 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.17556 | 0.390892 | ||||||||
\(552\) | −5.86822 | − | 18.0605i | −0.249768 | − | 0.768706i | ||||
\(553\) | 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 | \(0.572693\pi\) | |||||||
\(558\) | −9.12712 | − | 6.63124i | −0.386382 | − | 0.280723i | ||||
\(559\) | −11.5824 | + | 35.6468i | −0.489882 | + | 1.50770i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.40697 | + | 7.40790i | 0.101622 | + | 0.312762i | ||||
\(562\) | −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 | \(-0.0811706\pi\) | |||||||
\(564\) | 0.715563 | + | 2.20227i | 0.0301306 | + | 0.0927325i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.299792 | − | 0.922666i | 0.0126012 | − | 0.0387825i | ||||
\(567\) | 0.901030 | + | 0.654637i | 0.0378397 | + | 0.0274922i | ||||
\(568\) | −2.03244 | −0.0852794 | ||||||||
\(569\) | −4.93670 | − | 3.58672i | −0.206957 | − | 0.150363i | 0.479479 | − | 0.877554i | \(-0.340826\pi\) |
−0.686436 | + | 0.727190i | \(0.740826\pi\) | |||||||
\(570\) | 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 | ||||
\(573\) | 3.58739 | + | 11.0408i | 0.149865 | + | 0.461238i | ||||
\(574\) | 9.34003 | 0.389845 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 8.36307 | 0.348461 | ||||||||
\(577\) | 13.6474 | + | 42.0024i | 0.568149 | + | 1.74858i | 0.658405 | + | 0.752664i | \(0.271231\pi\) |
−0.0902565 | + | 0.995919i | \(0.528769\pi\) | |||||||
\(578\) | 11.3459 | − | 8.24330i | 0.471929 | − | 0.342876i | ||||
\(579\) | 2.73574 | − | 1.98763i | 0.113694 | − | 0.0826032i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.0501 | − | 8.02840i | −0.458437 | − | 0.333074i | ||||
\(582\) | 15.1515 | 0.628048 | ||||||||
\(583\) | −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 | \(0.103363\pi\) | |||||||
\(588\) | −1.31772 | + | 4.05551i | −0.0543417 | + | 0.167246i | ||||
\(589\) | −12.6134 | − | 38.8200i | −0.519725 | − | 1.59955i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.43502 | + | 16.7273i | −0.223567 | + | 0.688068i | ||||
\(592\) | −11.7564 | − | 8.54153i | −0.483186 | − | 0.351055i | ||||
\(593\) | 18.8405 | 0.773687 | 0.386844 | − | 0.922145i | \(-0.373565\pi\) | ||||
0.386844 | + | 0.922145i | \(0.373565\pi\) | |||||||
\(594\) | 3.33238 | + | 2.42112i | 0.136729 | + | 0.0993396i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.37376 | − | 6.81043i | 0.383964 | − | 0.278966i | ||||
\(597\) | 16.1886 | − | 11.7617i | 0.662556 | − | 0.481375i | ||||
\(598\) | −8.67703 | − | 26.7052i | −0.354830 | − | 1.09206i | ||||
\(599\) | 6.20712 | 0.253616 | 0.126808 | − | 0.991927i | \(-0.459527\pi\) | ||||
0.126808 | + | 0.991927i | \(0.459527\pi\) | |||||||
\(600\) | 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 | ||||
\(603\) | 2.12499 | − | 1.54390i | 0.0865363 | − | 0.0628723i | ||||
\(604\) | 2.37083 | − | 1.72251i | 0.0964679 | − | 0.0700880i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 6.56149 | + | 4.76720i | 0.266542 | + | 0.193654i | ||||
\(607\) | −16.2488 | −0.659518 | −0.329759 | − | 0.944065i | \(-0.606968\pi\) | ||||
−0.329759 | + | 0.944065i | \(0.606968\pi\) | |||||||
\(608\) | 12.9400 | + | 9.40144i | 0.524785 | + | 0.381279i | ||||
\(609\) | −0.777682 | + | 2.39346i | −0.0315132 | + | 0.0969878i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.91628 | + | 12.0531i | 0.158436 | + | 0.487615i | ||||
\(612\) | 0.485560 | − | 1.49440i | 0.0196276 | − | 0.0604076i | ||||
\(613\) | 0.0210086 | − | 0.0646578i | 0.000848529 | − | 0.00261150i | −0.950631 | − | 0.310322i | \(-0.899563\pi\) |
0.951480 | + | 0.307711i | \(0.0995630\pi\) | |||||||
\(614\) | 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 | \(0.470363\pi\) | |||||||
\(618\) | 5.92309 | 0.238262 | ||||||||
\(619\) | 5.48280 | + | 3.98349i | 0.220372 | + | 0.160110i | 0.692494 | − | 0.721423i | \(-0.256512\pi\) |
−0.472122 | + | 0.881533i | \(0.656512\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.99517 | + | 3.62921i | −0.200449 | + | 0.145635i | ||||
\(622\) | 13.2964 | − | 9.66040i | 0.533137 | − | 0.387347i | ||||
\(623\) | 5.26160 | + | 16.1935i | 0.210802 | + | 0.648780i | ||||
\(624\) | 7.98706 | 0.319738 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 16.7858 | 0.670895 | ||||||||
\(627\) | 4.60524 | + | 14.1735i | 0.183915 | + | 0.566034i | ||||
\(628\) | 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 | ||||||||
\(633\) | 1.97611 | + | 1.43573i | 0.0785433 | + | 0.0570651i | ||||
\(634\) | −6.28405 | + | 19.3403i | −0.249572 | + | 0.768102i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.802951 | + | 2.47123i | 0.0318391 | + | 0.0979906i | ||||
\(637\) | −7.21188 | + | 22.1959i | −0.285745 | + | 0.879432i | ||||
\(638\) | −2.87619 | + | 8.85199i | −0.113869 | + | 0.350454i | ||||
\(639\) | 0.204207 | + | 0.628483i | 0.00807829 | + | 0.0248624i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.32096 | + | 22.5316i | −0.289161 | + | 0.889945i | 0.695960 | + | 0.718081i | \(0.254979\pi\) |
−0.985121 | + | 0.171864i | \(0.945021\pi\) | |||||||
\(642\) | −4.96380 | − | 3.60641i | −0.195906 | − | 0.142334i | ||||
\(643\) | −2.16861 | −0.0855218 | −0.0427609 | − | 0.999085i | \(-0.513615\pi\) | ||||
−0.0427609 | + | 0.999085i | \(0.513615\pi\) | |||||||
\(644\) | 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 | \(0.284004\pi\) | |||||||
\(648\) | −0.950415 | − | 2.92508i | −0.0373358 | − | 0.114908i | ||||
\(649\) | −24.1998 | −0.949926 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.1953 | 0.438779 | ||||||||
\(652\) | −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 | \(0.0813199\pi\) | |||||||
\(654\) | 10.2961 | − | 7.48057i | 0.402610 | − | 0.292513i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −11.9156 | − | 8.65719i | −0.465226 | − | 0.338006i | ||||
\(657\) | −7.47542 | −0.291644 | ||||||||
\(658\) | 3.16285 | + | 2.29795i | 0.123301 | + | 0.0895833i | ||||
\(659\) | 0.139043 | − | 0.427929i | 0.00541633 | − | 0.0166697i | −0.948312 | − | 0.317340i | \(-0.897210\pi\) |
0.953728 | + | 0.300670i | \(0.0972104\pi\) | |||||||
\(660\) | 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 | ||||
\(663\) | 2.65748 | − | 8.17888i | 0.103208 | − | 0.317641i | ||||
\(664\) | 11.6558 | + | 35.8728i | 0.452332 | + | 1.39214i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.55687 | + | 7.86923i | −0.0990766 | + | 0.304926i | ||||
\(667\) | −11.2873 | − | 8.20067i | −0.437044 | − | 0.317531i | ||||
\(668\) | −2.26795 | −0.0877496 | ||||||||
\(669\) | 20.7407 | + | 15.0690i | 0.801880 | + | 0.582600i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 27.0314 | − | 19.6395i | 1.04354 | − | 0.758174i | ||||
\(672\) | −3.54912 | + | 2.57859i | −0.136910 | + | 0.0994711i | ||||
\(673\) | −5.44561 | − | 16.7599i | −0.209913 | − | 0.646046i | −0.999476 | − | 0.0323758i | \(-0.989693\pi\) |
0.789563 | − | 0.613670i | \(-0.210307\pi\) | |||||||
\(674\) | 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 | \(0.778737\pi\) | |||||||
\(678\) | −4.39030 | + | 3.18974i | −0.168608 | + | 0.122501i | ||||
\(679\) | −12.1639 | + | 8.83757i | −0.466807 | + | 0.339155i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.30987 | − | 3.85784i | −0.203475 | − | 0.147833i | ||||
\(682\) | 41.4049 | 1.58547 | ||||||||
\(683\) | −24.2268 | − | 17.6018i | −0.927015 | − | 0.673515i | 0.0182455 | − | 0.999834i | \(-0.494192\pi\) |
−0.945260 | + | 0.326318i | \(0.894192\pi\) | |||||||
\(684\) | 0.929018 | − | 2.85922i | 0.0355219 | − | 0.109325i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 4.92859 | + | 15.1686i | 0.188175 | + | 0.579142i | ||||
\(687\) | 2.46098 | − | 7.57412i | 0.0938923 | − | 0.288971i | ||||
\(688\) | 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 | ||||
\(693\) | −4.08749 | −0.155271 | ||||||||
\(694\) | 14.6858 | + | 10.6698i | 0.557464 | + | 0.405021i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5.62246 | − | 4.08495i | 0.213119 | − | 0.154840i | ||||
\(697\) | −12.8297 | + | 9.32131i | −0.485959 | + | 0.353070i | ||||
\(698\) | 5.28495 | + | 16.2654i | 0.200038 | + | 0.615655i | ||||
\(699\) | −9.42107 | −0.356338 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −49.0150 | −1.85127 | −0.925636 | − | 0.378415i | \(-0.876469\pi\) | ||||
−0.925636 | + | 0.378415i | \(0.876469\pi\) | |||||||
\(702\) | −1.40533 | − | 4.32516i | −0.0530407 | − | 0.163243i | ||||
\(703\) | −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 | ||||||||
\(708\) | 3.94950 | + | 2.86948i | 0.148431 | + | 0.107842i | ||||
\(709\) | −1.48744 | + | 4.57788i | −0.0558621 | + | 0.171926i | −0.975095 | − | 0.221789i | \(-0.928810\pi\) |
0.919233 | + | 0.393715i | \(0.128810\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.63811 | + | 8.11928i | 0.0989370 | + | 0.304497i | ||||
\(712\) | 14.5300 | − | 44.7189i | 0.544536 | − | 1.67591i | ||||
\(713\) | −19.1792 | + | 59.0274i | −0.718265 | + | 2.21059i | ||||
\(714\) | −0.819784 | − | 2.52304i | −0.0306797 | − | 0.0944223i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.30098 | + | 7.08170i | −0.0859918 | + | 0.264656i | ||||
\(717\) | −9.07970 | − | 6.59679i | −0.339088 | − | 0.246362i | ||||
\(718\) | −14.7775 | −0.551491 | ||||||||
\(719\) | −26.0917 | − | 18.9568i | −0.973058 | − | 0.706968i | −0.0169113 | − | 0.999857i | \(-0.505383\pi\) |
−0.956146 | + | 0.292889i | \(0.905383\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.75517 | + | 3.45483i | −0.177092 | + | 0.128665i | ||||
\(722\) | 2.28013 | − | 1.65661i | 0.0848578 | − | 0.0616528i | ||||
\(723\) | −7.00879 | − | 21.5708i | −0.260660 | − | 0.802228i | ||||
\(724\) | 14.4138 | 0.535685 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.77155 | −0.102862 | ||||||||
\(727\) | 9.01548 | + | 27.7468i | 0.334366 | + | 1.02907i | 0.967034 | + | 0.254648i | \(0.0819598\pi\) |
−0.632668 | + | 0.774423i | \(0.718040\pi\) | |||||||
\(728\) | −11.2291 | + | 8.15840i | −0.416177 | + | 0.302370i | ||||
\(729\) | −0.809017 | + | 0.587785i | −0.0299636 | + | 0.0217698i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.8823 | − | 11.5391i | −0.587426 | − | 0.426790i | ||||
\(732\) | −6.74037 | −0.249131 | ||||||||
\(733\) | 4.20771 | + | 3.05708i | 0.155415 | + | 0.112916i | 0.662775 | − | 0.748818i | \(-0.269378\pi\) |
−0.507360 | + | 0.861734i | \(0.669378\pi\) | |||||||
\(734\) | 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 | ||||
\(738\) | −2.59149 | + | 7.97578i | −0.0953940 | + | 0.293592i | ||||
\(739\) | −5.04334 | − | 15.5218i | −0.185522 | − | 0.570979i | 0.814435 | − | 0.580255i | \(-0.197047\pi\) |
−0.999957 | + | 0.00927620i | \(0.997047\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.08453 | − | 15.6486i | 0.186785 | − | 0.574865i | ||||
\(742\) | 3.54912 | + | 2.57859i | 0.130292 | + | 0.0946629i | ||||
\(743\) | −53.4487 | −1.96084 | −0.980421 | − | 0.196914i | \(-0.936908\pi\) | ||||
−0.980421 | + | 0.196914i | \(0.936908\pi\) | |||||||
\(744\) | −25.0117 | − | 18.1720i | −0.916972 | − | 0.666219i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −7.39398 | + | 5.37204i | −0.270713 | + | 0.196684i | ||||
\(747\) | 9.92170 | − | 7.20854i | 0.363016 | − | 0.263747i | ||||
\(748\) | 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 | ||||
\(753\) | −5.47558 | + | 3.97824i | −0.199541 | + | 0.144975i | ||||
\(754\) | 8.31364 | − | 6.04021i | 0.302765 | − | 0.219972i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.667093 | + | 0.484672i | 0.0242620 | + | 0.0176273i | ||||
\(757\) | −53.0708 | −1.92889 | −0.964445 | − | 0.264282i | \(-0.914865\pi\) | ||||
−0.964445 | + | 0.264282i | \(0.914865\pi\) | |||||||
\(758\) | −8.99560 | − | 6.53569i | −0.326735 | − | 0.237387i | ||||
\(759\) | 7.00246 | − | 21.5513i | 0.254173 | − | 0.782264i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.49970 | − | 26.1594i | −0.308114 | − | 0.948277i | −0.978497 | − | 0.206262i | \(-0.933870\pi\) |
0.670383 | − | 0.742015i | \(-0.266130\pi\) | |||||||
\(762\) | 0.263443 | − | 0.810794i | 0.00954353 | − | 0.0293720i | ||||
\(763\) | −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 | ||||
\(768\) | 15.0334 | 0.542471 | ||||||||
\(769\) | −12.1123 | − | 8.80007i | −0.436779 | − | 0.317339i | 0.347575 | − | 0.937652i | \(-0.387005\pi\) |
−0.784354 | + | 0.620314i | \(0.787005\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.9681 | − | 8.69533i | 0.431021 | − | 0.313155i | ||||
\(772\) | 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 | \(0.888238\pi\) | |||||||
\(774\) | −10.3816 | −0.373158 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 41.5206 | 1.49050 | ||||||||
\(777\) | −2.53728 | − | 7.80894i | −0.0910243 | − | 0.280144i | ||||
\(778\) | 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 | ||||||||
\(783\) | −1.82808 | − | 1.32818i | −0.0653303 | − | 0.0474652i | ||||
\(784\) | 3.50823 | − | 10.7972i | 0.125294 | − | 0.385615i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −5.08269 | − | 15.6429i | −0.181293 | − | 0.557964i | ||||
\(787\) | 5.19981 | − | 16.0034i | 0.185353 | − | 0.570458i | −0.814601 | − | 0.580022i | \(-0.803044\pi\) |
0.999954 | + | 0.00956327i | \(0.00304413\pi\) | |||||||
\(788\) | −4.02391 | + | 12.3843i | −0.143346 | + | 0.441174i | ||||
\(789\) | 6.17070 | + | 18.9915i | 0.219683 | + | 0.676114i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.66410 | − | 5.12156i | 0.0591685 | − | 0.182102i | ||||
\(792\) | 9.13195 | + | 6.63475i | 0.324490 | + | 0.235756i | ||||
\(793\) | −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 | \(0.301178\pi\) | |||||||
\(798\) | −1.56849 | − | 4.82730i | −0.0555238 | − | 0.170885i | ||||
\(799\) | −6.63791 | −0.234832 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.2881 | −0.540179 | ||||||||
\(802\) | −8.66668 | − | 26.6733i | −0.306031 | − | 0.941867i | ||||
\(803\) | 22.1957 | − | 16.1261i | 0.783268 | − | 0.569078i | ||||
\(804\) | 1.57327 | − | 1.14305i | 0.0554851 | − | 0.0403123i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −36.9835 | − | 26.8701i | −1.30269 | − | 0.946458i | ||||
\(807\) | 10.2381 | 0.360398 | ||||||||
\(808\) | 17.9809 | + | 13.0639i | 0.632566 | + | 0.459586i | ||||
\(809\) | −5.24264 | + | 16.1352i | −0.184321 | + | 0.567283i | −0.999936 | − | 0.0113128i | \(-0.996399\pi\) |
0.815615 | + | 0.578595i | \(0.196399\pi\) | |||||||
\(810\) | 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 | ||||
\(813\) | −3.80324 | + | 11.7052i | −0.133385 | + | 0.410518i | ||||
\(814\) | −9.38390 | − | 28.8807i | −0.328905 | − | 1.01227i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.29273 | + | 3.97863i | −0.0452548 | + | 0.139280i | ||||
\(817\) | −30.3874 | − | 22.0777i | −1.06312 | − | 0.772401i | ||||
\(818\) | −28.4812 | −0.995822 | ||||||||
\(819\) | 3.65101 | + | 2.65262i | 0.127577 | + | 0.0926899i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −31.0368 | + | 22.5496i | −1.08319 | + | 0.786985i | −0.978237 | − | 0.207492i | \(-0.933470\pi\) |
−0.104955 | + | 0.994477i | \(0.533470\pi\) | |||||||
\(822\) | −11.1604 | + | 8.10852i | −0.389265 | + | 0.282817i | ||||
\(823\) | 8.96451 | + | 27.5899i | 0.312483 | + | 0.961725i | 0.976778 | + | 0.214254i | \(0.0687320\pi\) |
−0.664295 | + | 0.747471i | \(0.731268\pi\) | |||||||
\(824\) | 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 | \(0.980305\pi\) | |||||||
\(828\) | −3.69826 | + | 2.68695i | −0.128524 | + | 0.0933779i | ||||
\(829\) | −3.75031 | + | 2.72476i | −0.130254 | + | 0.0946347i | −0.651004 | − | 0.759074i | \(-0.725652\pi\) |
0.520751 | + | 0.853709i | \(0.325652\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −25.5261 | − | 18.5458i | −0.885491 | − | 0.643347i | ||||
\(832\) | 33.8875 | 1.17484 | ||||||||
\(833\) | −9.88925 | − | 7.18496i | −0.342642 | − | 0.248944i | ||||
\(834\) | −5.11005 | + | 15.7271i | −0.176946 | + | 0.544585i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.40957 | + | 10.4936i | 0.117922 | + | 0.362928i | ||||
\(837\) | −3.10625 | + | 9.56006i | −0.107368 | + | 0.330444i | ||||
\(838\) | −10.6896 | + | 32.8993i | −0.369268 | + | 1.13649i | ||||
\(839\) | 1.52235 | + | 4.68531i | 0.0525573 | + | 0.161755i | 0.973890 | − | 0.227020i | \(-0.0728983\pi\) |
−0.921333 | + | 0.388775i | \(0.872898\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.38367 | + | 22.7246i | −0.254609 | + | 0.783607i | ||||
\(842\) | −7.76010 | − | 5.63804i | −0.267431 | − | 0.194300i | ||||
\(843\) | 21.3119 | 0.734022 | ||||||||
\(844\) | 1.46305 | + | 1.06297i | 0.0503602 | + | 0.0365888i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.83986 | + | 2.06328i | −0.0976365 | + | 0.0709371i | ||||
\(847\) | 2.22505 | − | 1.61660i | 0.0764538 | − | 0.0555469i | ||||
\(848\) | −2.13774 | − | 6.57929i | −0.0734103 | − | 0.225934i | ||||
\(849\) | −0.864403 | −0.0296662 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 45.5194 | 1.56039 | ||||||||
\(852\) | 0.151188 | + | 0.465309i | 0.00517961 | + | 0.0159412i | ||||
\(853\) | 43.4018 | − | 31.5333i | 1.48605 | − | 1.07968i | 0.510507 | − | 0.859874i | \(-0.329458\pi\) |
0.975544 | − | 0.219805i | \(-0.0705422\pi\) | |||||||
\(854\) | −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 | \(0.346735\pi\) | |||||||
\(858\) | 13.5029 | + | 9.81046i | 0.460983 | + | 0.334924i | ||||
\(859\) | 3.21966 | − | 9.90910i | 0.109853 | − | 0.338094i | −0.880985 | − | 0.473143i | \(-0.843119\pi\) |
0.990839 | + | 0.135049i | \(0.0431193\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.57163 | − | 7.91467i | −0.0876410 | − | 0.269731i | ||||
\(862\) | −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 | \(-0.166510\pi\) | |||||||
\(864\) | −1.21720 | − | 3.74617i | −0.0414101 | − | 0.127447i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 3.25065 | − | 10.0045i | 0.110461 | − | 0.339965i | ||||
\(867\) | −10.1092 | − | 7.34479i | −0.343328 | − | 0.249442i | ||||
\(868\) | 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 | ||||
\(873\) | −4.17172 | − | 12.8392i | −0.141191 | − | 0.434542i | ||||
\(874\) | 28.1391 | 0.951818 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.53456 | −0.186995 | ||||||||
\(877\) | −16.5767 | − | 51.0180i | −0.559757 | − | 1.72275i | −0.683038 | − | 0.730383i | \(-0.739342\pi\) |
0.123281 | − | 0.992372i | \(-0.460658\pi\) | |||||||
\(878\) | 0.468503 | − | 0.340388i | 0.0158112 | − | 0.0114875i | ||||
\(879\) | −2.57025 | + | 1.86740i | −0.0866925 | + | 0.0629858i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.4110 | + | 32.2665i | 1.49625 | + | 1.08709i | 0.971847 | + | 0.235613i | \(0.0757097\pi\) |
0.524398 | + | 0.851473i | \(0.324290\pi\) | |||||||
\(882\) | −6.46419 | −0.217661 | ||||||||
\(883\) | −15.4483 | − | 11.2239i | −0.519877 | − | 0.377713i | 0.296681 | − | 0.954977i | \(-0.404120\pi\) |
−0.816558 | + | 0.577264i | \(0.804120\pi\) | |||||||
\(884\) | 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 | \(0.0397020\pi\) | |||||||
\(888\) | −7.00676 | + | 21.5646i | −0.235131 | + | 0.723660i | ||||
\(889\) | 0.261425 | + | 0.804582i | 0.00876790 | + | 0.0269848i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.13412 | − | 3.49045i | 0.0379943 | − | 0.116934i | ||||
\(892\) | 15.3557 | + | 11.1566i | 0.514147 | + | 0.373550i | ||||
\(893\) | −12.7003 | −0.424998 | ||||||||
\(894\) | 14.2098 | + | 10.3240i | 0.475247 | + | 0.345287i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.35896 | − | 0.987345i | 0.0453998 | − | 0.0329849i | ||||
\(897\) | −20.2407 | + | 14.7057i | −0.675816 | + | 0.491009i | ||||
\(898\) | −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 | ||||
\(903\) | 8.33451 | − | 6.05538i | 0.277355 | − | 0.201510i | ||||
\(904\) | −12.0310 | + | 8.74106i | −0.400146 | + | 0.290723i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3.59398 | + | 2.61118i | 0.119402 | + | 0.0867506i | ||||
\(907\) | 36.4513 | 1.21034 | 0.605172 | − | 0.796095i | \(-0.293104\pi\) | ||||
0.605172 | + | 0.796095i | \(0.293104\pi\) | |||||||
\(908\) | −3.93125 | − | 2.85622i | −0.130463 | − | 0.0947871i | ||||
\(909\) | 2.23309 | − | 6.87273i | 0.0740668 | − | 0.227954i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.360106 | + | 1.10829i | 0.0119309 | + | 0.0367194i | 0.956845 | − | 0.290600i | \(-0.0938548\pi\) |
−0.944914 | + | 0.327319i | \(0.893855\pi\) | |||||||
\(912\) | −2.47338 | + | 7.61227i | −0.0819017 | + | 0.252067i | ||||
\(913\) | −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 | ||||
\(918\) | 2.38197 | 0.0786166 | ||||||||
\(919\) | −35.5543 | − | 25.8317i | −1.17283 | − | 0.852109i | −0.181482 | − | 0.983394i | \(-0.558089\pi\) |
−0.991345 | + | 0.131286i | \(0.958089\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.410969 | − | 0.298587i | 0.0135419 | − | 0.00983876i | ||||
\(922\) | 0.186098 | − | 0.135208i | 0.00612880 | − | 0.00445283i | ||||
\(923\) | 0.827454 | + | 2.54664i | 0.0272360 | + | 0.0838237i | ||||
\(924\) | −3.02624 | −0.0995561 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 14.3856 | 0.472739 | ||||||||
\(927\) | −1.63083 | − | 5.01918i | −0.0535635 | − | 0.164852i | ||||
\(928\) | 7.20073 | − | 5.23164i | 0.236376 | − | 0.171737i | ||||
\(929\) | −25.2512 | + | 18.3460i | −0.828464 | + | 0.601914i | −0.919124 | − | 0.393968i | \(-0.871102\pi\) |
0.0906606 | + | 0.995882i | \(0.471102\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.9210 | − | 13.7469i | −0.620111 | − | 0.450537i | ||||
\(932\) | −6.97506 | −0.228476 | ||||||||
\(933\) | −11.8471 | − | 8.60743i | −0.387857 | − | 0.281795i | ||||
\(934\) | −0.386266 | + | 1.18880i | −0.0126390 | + | 0.0388988i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.85112 | − | 11.8525i | −0.125878 | − | 0.387412i | ||||
\(937\) | 13.9385 | − | 42.8983i | 0.455351 | − | 1.40143i | −0.415371 | − | 0.909652i | \(-0.636348\pi\) |
0.870722 | − | 0.491775i | \(-0.163652\pi\) | |||||||
\(938\) | 1.01458 | − | 3.12255i | 0.0331271 | − | 0.101955i | ||||
\(939\) | −4.62171 | − | 14.2241i | −0.150824 | − | 0.464188i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.0931 | + | 37.2187i | −0.394224 | + | 1.21330i | 0.535341 | + | 0.844636i | \(0.320183\pi\) |
−0.929565 | + | 0.368659i | \(0.879817\pi\) | |||||||
\(942\) | 4.08650 | + | 2.96901i | 0.133145 | + | 0.0967357i | ||||
\(943\) | 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 | \(0.591883\pi\) | |||||||
\(948\) | 1.95317 | + | 6.01125i | 0.0634361 | + | 0.195236i | ||||
\(949\) | −30.2907 | −0.983278 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 18.1190 | 0.587550 | ||||||||
\(952\) | −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 | \(0.179701\pi\) | |||||||
\(954\) | −3.18668 | + | 2.31526i | −0.103173 | + | 0.0749593i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −6.72232 | − | 4.88405i | −0.217415 | − | 0.157961i | ||||
\(957\) | 8.29302 | 0.268075 | ||||||||
\(958\) | 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 | ||||
\(963\) | −1.68934 | + | 5.19926i | −0.0544382 | + | 0.167544i | ||||
\(964\) | −5.18908 | − | 15.9703i | −0.167129 | − | 0.514370i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.38495 | + | 7.34012i | −0.0767345 | + | 0.236164i | ||||
\(967\) | 34.9436 | + | 25.3880i | 1.12371 | + | 0.816425i | 0.984768 | − | 0.173876i | \(-0.0556291\pi\) |
0.138944 | + | 0.990300i | \(0.455629\pi\) | |||||||
\(968\) | −7.59507 | −0.244115 | ||||||||
\(969\) | 6.97214 | + | 5.06555i | 0.223977 | + | 0.162729i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.9089 | − | 18.8239i | 0.831457 | − | 0.604089i | −0.0885142 | − | 0.996075i | \(-0.528212\pi\) |
0.919971 | + | 0.391986i | \(0.128212\pi\) | |||||||
\(972\) | −0.598970 | + | 0.435177i | −0.0192120 | + | 0.0139583i | ||||
\(973\) | −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 | \(0.862898\pi\) | |||||||
\(978\) | 2.22810 | − | 1.61881i | 0.0712467 | − | 0.0517637i | ||||
\(979\) | 45.3927 | − | 32.9798i | 1.45076 | − | 1.05404i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.17385 | − | 6.66519i | −0.292898 | − | 0.212803i | ||||
\(982\) | −17.5725 | −0.560760 | ||||||||
\(983\) | −4.11915 | − | 2.99274i | −0.131380 | − | 0.0954535i | 0.520154 | − | 0.854072i | \(-0.325874\pi\) |
−0.651535 | + | 0.758619i | \(0.725874\pi\) | |||||||
\(984\) | −7.10163 | + | 21.8566i | −0.226392 | + | 0.696762i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.66324 | + | 5.11894i | 0.0529685 | + | 0.163020i | ||||
\(987\) | 1.07642 | − | 3.31288i | 0.0342628 | − | 0.105450i | ||||
\(988\) | 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 | ||||
\(993\) | −26.3514 | −0.836237 | ||||||||
\(994\) | 0.668265 | + | 0.485523i | 0.0211961 | + | 0.0153999i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 7.34570 | − | 5.33697i | 0.232758 | − | 0.169108i | ||||
\(997\) | 2.07832 | − | 1.50999i | 0.0658212 | − | 0.0478219i | −0.554388 | − | 0.832258i | \(-0.687048\pi\) |
0.620209 | + | 0.784436i | \(0.287048\pi\) | |||||||
\(998\) | 12.4114 | + | 38.1985i | 0.392878 | + | 1.20915i | ||||
\(999\) | 7.37232 | 0.233250 |
(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 | 375.2.g.b.151.2 | 8 | ||
5.2 | odd | 4 | 375.2.i.b.349.2 | 16 | |||
5.3 | odd | 4 | 375.2.i.b.349.3 | 16 | |||
5.4 | even | 2 | 75.2.g.b.31.1 | ✓ | 8 | ||
15.14 | odd | 2 | 225.2.h.c.181.2 | 8 | |||
25.2 | odd | 20 | 1875.2.b.c.1249.5 | 8 | |||
25.3 | odd | 20 | 375.2.i.b.274.2 | 16 | |||
25.4 | even | 10 | 75.2.g.b.46.1 | yes | 8 | ||
25.11 | even | 5 | 1875.2.a.e.1.3 | 4 | |||
25.14 | even | 10 | 1875.2.a.h.1.2 | 4 | |||
25.21 | even | 5 | inner | 375.2.g.b.226.2 | 8 | ||
25.22 | odd | 20 | 375.2.i.b.274.3 | 16 | |||
25.23 | odd | 20 | 1875.2.b.c.1249.4 | 8 | |||
75.11 | odd | 10 | 5625.2.a.n.1.2 | 4 | |||
75.14 | odd | 10 | 5625.2.a.i.1.3 | 4 | |||
75.29 | odd | 10 | 225.2.h.c.46.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.g.b.31.1 | ✓ | 8 | 5.4 | even | 2 | ||
75.2.g.b.46.1 | yes | 8 | 25.4 | even | 10 | ||
225.2.h.c.46.2 | 8 | 75.29 | odd | 10 | |||
225.2.h.c.181.2 | 8 | 15.14 | odd | 2 | |||
375.2.g.b.151.2 | 8 | 1.1 | even | 1 | trivial | ||
375.2.g.b.226.2 | 8 | 25.21 | even | 5 | inner | ||
375.2.i.b.274.2 | 16 | 25.3 | odd | 20 | |||
375.2.i.b.274.3 | 16 | 25.22 | odd | 20 | |||
375.2.i.b.349.2 | 16 | 5.2 | odd | 4 | |||
375.2.i.b.349.3 | 16 | 5.3 | odd | 4 | |||
1875.2.a.e.1.3 | 4 | 25.11 | even | 5 | |||
1875.2.a.h.1.2 | 4 | 25.14 | even | 10 | |||
1875.2.b.c.1249.4 | 8 | 25.23 | odd | 20 | |||
1875.2.b.c.1249.5 | 8 | 25.2 | odd | 20 | |||
5625.2.a.i.1.3 | 4 | 75.14 | odd | 10 | |||
5625.2.a.n.1.2 | 4 | 75.11 | odd | 10 |