Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(100,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.100");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 10.0.7965937851507.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} + 8x^{8} - 6x^{7} + 28x^{6} - 23x^{5} + 51x^{4} - 10x^{3} + 25x^{2} - 6x + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 100.1 | ||
Root | \(1.19780 + 2.07464i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 429.100 |
Dual form | 429.2.i.c.133.1 |
$q$-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 \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.19780 | + | 2.07464i | −0.846970 | + | 1.46700i | 0.0369290 | + | 0.999318i | \(0.488242\pi\) |
−0.883899 | + | 0.467678i | \(0.845091\pi\) | |||||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | −1.86943 | − | 3.23795i | −0.934717 | − | 1.61898i | ||||
\(5\) | 3.82235 | 1.70941 | 0.854703 | − | 0.519118i | \(-0.173739\pi\) | ||||
0.854703 | + | 0.519118i | \(0.173739\pi\) | |||||||
\(6\) | −1.19780 | − | 2.07464i | −0.488998 | − | 0.846970i | ||||
\(7\) | −2.02991 | − | 3.51590i | −0.767233 | − | 1.32889i | −0.939058 | − | 0.343759i | \(-0.888300\pi\) |
0.171825 | − | 0.985128i | \(-0.445034\pi\) | |||||||
\(8\) | 4.16562 | 1.47277 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −4.57839 | + | 7.93001i | −1.44782 | + | 2.50769i | ||||
\(11\) | 0.500000 | − | 0.866025i | 0.150756 | − | 0.261116i | ||||
\(12\) | 3.73887 | 1.07932 | ||||||||
\(13\) | 1.95068 | + | 3.03230i | 0.541021 | + | 0.841009i | ||||
\(14\) | 9.72567 | 2.59929 | ||||||||
\(15\) | −1.91117 | + | 3.31025i | −0.493463 | + | 0.854703i | ||||
\(16\) | −1.25070 | + | 2.16628i | −0.312675 | + | 0.541569i | ||||
\(17\) | 2.90676 | + | 5.03465i | 0.704992 | + | 1.22108i | 0.966694 | + | 0.255934i | \(0.0823828\pi\) |
−0.261702 | + | 0.965149i | \(0.584284\pi\) | |||||||
\(18\) | 2.39559 | 0.564647 | ||||||||
\(19\) | 2.85444 | + | 4.94403i | 0.654853 | + | 1.13424i | 0.981931 | + | 0.189241i | \(0.0606028\pi\) |
−0.327078 | + | 0.944997i | \(0.606064\pi\) | |||||||
\(20\) | −7.14563 | − | 12.3766i | −1.59781 | − | 2.76749i | ||||
\(21\) | 4.05982 | 0.885924 | ||||||||
\(22\) | 1.19780 | + | 2.07464i | 0.255371 | + | 0.442316i | ||||
\(23\) | 2.62232 | − | 4.54199i | 0.546791 | − | 0.947070i | −0.451701 | − | 0.892169i | \(-0.649183\pi\) |
0.998492 | − | 0.0549003i | \(-0.0174841\pi\) | |||||||
\(24\) | −2.08281 | + | 3.60753i | −0.425152 | + | 0.736385i | ||||
\(25\) | 9.61033 | 1.92207 | ||||||||
\(26\) | −8.62747 | + | 0.414889i | −1.69199 | + | 0.0813663i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −7.58956 | + | 13.1455i | −1.43429 | + | 2.48427i | ||||
\(29\) | −1.68222 | + | 2.91369i | −0.312380 | + | 0.541058i | −0.978877 | − | 0.204450i | \(-0.934459\pi\) |
0.666497 | + | 0.745508i | \(0.267793\pi\) | |||||||
\(30\) | −4.57839 | − | 7.93001i | −0.835897 | − | 1.44782i | ||||
\(31\) | −1.05349 | −0.189212 | −0.0946059 | − | 0.995515i | \(-0.530159\pi\) | ||||
−0.0946059 | + | 0.995515i | \(0.530159\pi\) | |||||||
\(32\) | 1.16945 | + | 2.02555i | 0.206732 | + | 0.358071i | ||||
\(33\) | 0.500000 | + | 0.866025i | 0.0870388 | + | 0.150756i | ||||
\(34\) | −13.9268 | −2.38843 | ||||||||
\(35\) | −7.75901 | − | 13.4390i | −1.31151 | − | 2.27161i | ||||
\(36\) | −1.86943 | + | 3.23795i | −0.311572 | + | 0.539659i | ||||
\(37\) | −0.752883 | + | 1.30403i | −0.123773 | + | 0.214382i | −0.921253 | − | 0.388964i | \(-0.872833\pi\) |
0.797479 | + | 0.603346i | \(0.206166\pi\) | |||||||
\(38\) | −13.6761 | −2.21856 | ||||||||
\(39\) | −3.60139 | + | 0.173188i | −0.576684 | + | 0.0277323i | ||||
\(40\) | 15.9224 | 2.51756 | ||||||||
\(41\) | 2.74945 | − | 4.76218i | 0.429392 | − | 0.743728i | −0.567428 | − | 0.823423i | \(-0.692061\pi\) |
0.996819 | + | 0.0796952i | \(0.0253947\pi\) | |||||||
\(42\) | −4.86283 | + | 8.42268i | −0.750352 | + | 1.29965i | ||||
\(43\) | 1.55825 | + | 2.69897i | 0.237631 | + | 0.411589i | 0.960034 | − | 0.279883i | \(-0.0902957\pi\) |
−0.722403 | + | 0.691472i | \(0.756962\pi\) | |||||||
\(44\) | −3.73887 | −0.563656 | ||||||||
\(45\) | −1.91117 | − | 3.31025i | −0.284901 | − | 0.493463i | ||||
\(46\) | 6.28201 | + | 10.8808i | 0.926231 | + | 1.60428i | ||||
\(47\) | 4.97001 | 0.724950 | 0.362475 | − | 0.931993i | \(-0.381932\pi\) | ||||
0.362475 | + | 0.931993i | \(0.381932\pi\) | |||||||
\(48\) | −1.25070 | − | 2.16628i | −0.180523 | − | 0.312675i | ||||
\(49\) | −4.74105 | + | 8.21174i | −0.677293 | + | 1.17311i | ||||
\(50\) | −11.5112 | + | 19.9380i | −1.62793 | + | 2.81966i | ||||
\(51\) | −5.81351 | −0.814055 | ||||||||
\(52\) | 6.17178 | − | 11.9849i | 0.855873 | − | 1.66201i | ||||
\(53\) | 4.56558 | 0.627131 | 0.313565 | − | 0.949567i | \(-0.398476\pi\) | ||||
0.313565 | + | 0.949567i | \(0.398476\pi\) | |||||||
\(54\) | −1.19780 | + | 2.07464i | −0.162999 | + | 0.282323i | ||||
\(55\) | 1.91117 | − | 3.31025i | 0.257703 | − | 0.446354i | ||||
\(56\) | −8.45583 | − | 14.6459i | −1.12996 | − | 1.95714i | ||||
\(57\) | −5.70888 | −0.756159 | ||||||||
\(58\) | −4.02991 | − | 6.98001i | −0.529153 | − | 0.916520i | ||||
\(59\) | −2.01276 | − | 3.48621i | −0.262039 | − | 0.453866i | 0.704744 | − | 0.709461i | \(-0.251062\pi\) |
−0.966784 | + | 0.255596i | \(0.917728\pi\) | |||||||
\(60\) | 14.2913 | 1.84499 | ||||||||
\(61\) | −7.27717 | − | 12.6044i | −0.931746 | − | 1.61383i | −0.780335 | − | 0.625361i | \(-0.784952\pi\) |
−0.151411 | − | 0.988471i | \(-0.548382\pi\) | |||||||
\(62\) | 1.26186 | − | 2.18561i | 0.160257 | − | 0.277573i | ||||
\(63\) | −2.02991 | + | 3.51590i | −0.255744 | + | 0.442962i | ||||
\(64\) | −10.6059 | −1.32573 | ||||||||
\(65\) | 7.45618 | + | 11.5905i | 0.924825 | + | 1.43763i | ||||
\(66\) | −2.39559 | −0.294877 | ||||||||
\(67\) | 1.68264 | − | 2.91441i | 0.205567 | − | 0.356052i | −0.744746 | − | 0.667347i | \(-0.767430\pi\) |
0.950313 | + | 0.311296i | \(0.100763\pi\) | |||||||
\(68\) | 10.8680 | − | 18.8239i | 1.31794 | − | 2.28273i | ||||
\(69\) | 2.62232 | + | 4.54199i | 0.315690 | + | 0.546791i | ||||
\(70\) | 37.1749 | 4.44325 | ||||||||
\(71\) | −1.82895 | − | 3.16783i | −0.217056 | − | 0.375952i | 0.736851 | − | 0.676056i | \(-0.236312\pi\) |
−0.953907 | + | 0.300104i | \(0.902979\pi\) | |||||||
\(72\) | −2.08281 | − | 3.60753i | −0.245462 | − | 0.425152i | ||||
\(73\) | −0.00632885 | −0.000740735 | −0.000370368 | − | 1.00000i | \(-0.500118\pi\) | ||||
−0.000370368 | 1.00000i | \(0.500118\pi\) | ||||||||
\(74\) | −1.80360 | − | 3.12393i | −0.209665 | − | 0.363150i | ||||
\(75\) | −4.80517 | + | 8.32279i | −0.554853 | + | 0.961033i | ||||
\(76\) | 10.6724 | − | 18.4851i | 1.22420 | − | 2.12038i | ||||
\(77\) | −4.05982 | −0.462659 | ||||||||
\(78\) | 3.95443 | − | 7.67905i | 0.447751 | − | 0.869481i | ||||
\(79\) | −3.36756 | −0.378880 | −0.189440 | − | 0.981892i | \(-0.560667\pi\) | ||||
−0.189440 | + | 0.981892i | \(0.560667\pi\) | |||||||
\(80\) | −4.78061 | + | 8.28026i | −0.534488 | + | 0.925761i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 6.58656 | + | 11.4083i | 0.727364 | + | 1.25983i | ||||
\(83\) | 8.92689 | 0.979853 | 0.489927 | − | 0.871764i | \(-0.337024\pi\) | ||||
0.489927 | + | 0.871764i | \(0.337024\pi\) | |||||||
\(84\) | −7.58956 | − | 13.1455i | −0.828089 | − | 1.43429i | ||||
\(85\) | 11.1106 | + | 19.2442i | 1.20512 | + | 2.08732i | ||||
\(86\) | −7.46587 | −0.805066 | ||||||||
\(87\) | −1.68222 | − | 2.91369i | −0.180353 | − | 0.312380i | ||||
\(88\) | 2.08281 | − | 3.60753i | 0.222028 | − | 0.384564i | ||||
\(89\) | 6.51256 | − | 11.2801i | 0.690330 | − | 1.19569i | −0.281399 | − | 0.959591i | \(-0.590799\pi\) |
0.971730 | − | 0.236096i | \(-0.0758681\pi\) | |||||||
\(90\) | 9.15679 | 0.965210 | ||||||||
\(91\) | 6.70158 | − | 13.0137i | 0.702516 | − | 1.36421i | ||||
\(92\) | −19.6090 | −2.04438 | ||||||||
\(93\) | 0.526743 | − | 0.912346i | 0.0546208 | − | 0.0946059i | ||||
\(94\) | −5.95306 | + | 10.3110i | −0.614011 | + | 1.06350i | ||||
\(95\) | 10.9107 | + | 18.8978i | 1.11941 | + | 1.93887i | ||||
\(96\) | −2.33891 | −0.238714 | ||||||||
\(97\) | 9.68010 | + | 16.7664i | 0.982865 | + | 1.70237i | 0.651065 | + | 0.759022i | \(0.274323\pi\) |
0.331800 | + | 0.943350i | \(0.392344\pi\) | |||||||
\(98\) | −11.3576 | − | 19.6720i | −1.14729 | − | 1.98717i | ||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | −17.9659 | − | 31.1178i | −1.79659 | − | 3.11178i | ||||
\(101\) | −1.19042 | + | 2.06186i | −0.118451 | + | 0.205163i | −0.919154 | − | 0.393898i | \(-0.871126\pi\) |
0.800703 | + | 0.599061i | \(0.204459\pi\) | |||||||
\(102\) | 6.96341 | − | 12.0610i | 0.689480 | − | 1.19421i | ||||
\(103\) | −10.6841 | −1.05274 | −0.526370 | − | 0.850256i | \(-0.676447\pi\) | ||||
−0.526370 | + | 0.850256i | \(0.676447\pi\) | |||||||
\(104\) | 8.12579 | + | 12.6314i | 0.796800 | + | 1.23861i | ||||
\(105\) | 15.5180 | 1.51440 | ||||||||
\(106\) | −5.46864 | + | 9.47196i | −0.531161 | + | 0.919998i | ||||
\(107\) | −6.71509 | + | 11.6309i | −0.649172 | + | 1.12440i | 0.334149 | + | 0.942520i | \(0.391551\pi\) |
−0.983321 | + | 0.181879i | \(0.941782\pi\) | |||||||
\(108\) | −1.86943 | − | 3.23795i | −0.179886 | − | 0.311572i | ||||
\(109\) | −13.0924 | −1.25403 | −0.627014 | − | 0.779008i | \(-0.715723\pi\) | ||||
−0.627014 | + | 0.779008i | \(0.715723\pi\) | |||||||
\(110\) | 4.57839 | + | 7.93001i | 0.436533 | + | 0.756097i | ||||
\(111\) | −0.752883 | − | 1.30403i | −0.0714605 | − | 0.123773i | ||||
\(112\) | 10.1552 | 0.959578 | ||||||||
\(113\) | 4.86232 | + | 8.42179i | 0.457409 | + | 0.792255i | 0.998823 | − | 0.0485008i | \(-0.0154443\pi\) |
−0.541414 | + | 0.840756i | \(0.682111\pi\) | |||||||
\(114\) | 6.83807 | − | 11.8439i | 0.640444 | − | 1.10928i | ||||
\(115\) | 10.0234 | − | 17.3610i | 0.934687 | − | 1.61893i | ||||
\(116\) | 12.5792 | 1.16795 | ||||||||
\(117\) | 1.65071 | − | 3.20549i | 0.152608 | − | 0.296348i | ||||
\(118\) | 9.64353 | 0.887758 | ||||||||
\(119\) | 11.8009 | − | 20.4398i | 1.08179 | − | 1.87371i | ||||
\(120\) | −7.96122 | + | 13.7892i | −0.726757 | + | 1.25878i | ||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | 34.8663 | 3.15665 | ||||||||
\(123\) | 2.74945 | + | 4.76218i | 0.247909 | + | 0.429392i | ||||
\(124\) | 1.96942 | + | 3.41114i | 0.176860 | + | 0.306330i | ||||
\(125\) | 17.6223 | 1.57619 | ||||||||
\(126\) | −4.86283 | − | 8.42268i | −0.433216 | − | 0.750352i | ||||
\(127\) | −6.45966 | + | 11.1885i | −0.573202 | + | 0.992815i | 0.423032 | + | 0.906115i | \(0.360966\pi\) |
−0.996234 | + | 0.0867006i | \(0.972368\pi\) | |||||||
\(128\) | 10.3648 | − | 17.9523i | 0.916125 | − | 1.58677i | ||||
\(129\) | −3.11650 | −0.274393 | ||||||||
\(130\) | −32.9772 | + | 1.58585i | −2.89229 | + | 0.139088i | ||||
\(131\) | −4.98647 | −0.435670 | −0.217835 | − | 0.975986i | \(-0.569899\pi\) | ||||
−0.217835 | + | 0.975986i | \(0.569899\pi\) | |||||||
\(132\) | 1.86943 | − | 3.23795i | 0.162713 | − | 0.281828i | ||||
\(133\) | 11.5885 | − | 20.0719i | 1.00485 | − | 1.74045i | ||||
\(134\) | 4.03091 | + | 6.98174i | 0.348218 | + | 0.603131i | ||||
\(135\) | 3.82235 | 0.328975 | ||||||||
\(136\) | 12.1084 | + | 20.9725i | 1.03829 | + | 1.79837i | ||||
\(137\) | 4.80727 | + | 8.32643i | 0.410713 | + | 0.711375i | 0.994968 | − | 0.100195i | \(-0.0319466\pi\) |
−0.584255 | + | 0.811570i | \(0.698613\pi\) | |||||||
\(138\) | −12.5640 | −1.06952 | ||||||||
\(139\) | −8.29759 | − | 14.3718i | −0.703792 | − | 1.21900i | −0.967126 | − | 0.254299i | \(-0.918155\pi\) |
0.263334 | − | 0.964705i | \(-0.415178\pi\) | |||||||
\(140\) | −29.0099 | + | 50.2467i | −2.45179 | + | 4.24662i | ||||
\(141\) | −2.48500 | + | 4.30415i | −0.209275 | + | 0.362475i | ||||
\(142\) | 8.76283 | 0.735360 | ||||||||
\(143\) | 3.60139 | − | 0.173188i | 0.301163 | − | 0.0144827i | ||||
\(144\) | 2.50140 | 0.208450 | ||||||||
\(145\) | −6.43002 | + | 11.1371i | −0.533984 | + | 0.924887i | ||||
\(146\) | 0.00758067 | − | 0.0131301i | 0.000627381 | − | 0.00108666i | ||||
\(147\) | −4.74105 | − | 8.21174i | −0.391035 | − | 0.677293i | ||||
\(148\) | 5.62986 | 0.462772 | ||||||||
\(149\) | −8.09070 | − | 14.0135i | −0.662816 | − | 1.14803i | −0.979872 | − | 0.199625i | \(-0.936028\pi\) |
0.317056 | − | 0.948407i | \(-0.397306\pi\) | |||||||
\(150\) | −11.5112 | − | 19.9380i | −0.939888 | − | 1.62793i | ||||
\(151\) | −2.02312 | −0.164639 | −0.0823196 | − | 0.996606i | \(-0.526233\pi\) | ||||
−0.0823196 | + | 0.996606i | \(0.526233\pi\) | |||||||
\(152\) | 11.8905 | + | 20.5950i | 0.964448 | + | 1.67047i | ||||
\(153\) | 2.90676 | − | 5.03465i | 0.234997 | − | 0.407027i | ||||
\(154\) | 4.86283 | − | 8.42268i | 0.391858 | − | 0.678719i | ||||
\(155\) | −4.02679 | −0.323440 | ||||||||
\(156\) | 7.29334 | + | 11.3374i | 0.583934 | + | 0.907716i | ||||
\(157\) | −18.3521 | −1.46465 | −0.732327 | − | 0.680953i | \(-0.761566\pi\) | ||||
−0.732327 | + | 0.680953i | \(0.761566\pi\) | |||||||
\(158\) | 4.03366 | − | 6.98650i | 0.320900 | − | 0.555816i | ||||
\(159\) | −2.28279 | + | 3.95391i | −0.181037 | + | 0.313565i | ||||
\(160\) | 4.47006 | + | 7.74237i | 0.353389 | + | 0.612088i | ||||
\(161\) | −21.2923 | −1.67806 | ||||||||
\(162\) | −1.19780 | − | 2.07464i | −0.0941078 | − | 0.162999i | ||||
\(163\) | −10.0722 | − | 17.4456i | −0.788917 | − | 1.36644i | −0.926631 | − | 0.375972i | \(-0.877309\pi\) |
0.137715 | − | 0.990472i | \(-0.456024\pi\) | |||||||
\(164\) | −20.5596 | −1.60544 | ||||||||
\(165\) | 1.91117 | + | 3.31025i | 0.148785 | + | 0.257703i | ||||
\(166\) | −10.6926 | + | 18.5201i | −0.829906 | + | 1.43744i | ||||
\(167\) | −0.519947 | + | 0.900575i | −0.0402347 | + | 0.0696886i | −0.885442 | − | 0.464751i | \(-0.846144\pi\) |
0.845207 | + | 0.534439i | \(0.179477\pi\) | |||||||
\(168\) | 16.9117 | 1.30476 | ||||||||
\(169\) | −5.38969 | + | 11.8301i | −0.414592 | + | 0.910007i | ||||
\(170\) | −53.2331 | −4.08279 | ||||||||
\(171\) | 2.85444 | − | 4.94403i | 0.218284 | − | 0.378080i | ||||
\(172\) | 5.82610 | − | 10.0911i | 0.444236 | − | 0.769439i | ||||
\(173\) | −8.03064 | − | 13.9095i | −0.610558 | − | 1.05752i | −0.991146 | − | 0.132773i | \(-0.957612\pi\) |
0.380588 | − | 0.924745i | \(-0.375722\pi\) | |||||||
\(174\) | 8.05982 | 0.611013 | ||||||||
\(175\) | −19.5081 | − | 33.7890i | −1.47467 | − | 2.55421i | ||||
\(176\) | 1.25070 | + | 2.16628i | 0.0942750 | + | 0.163289i | ||||
\(177\) | 4.02553 | 0.302577 | ||||||||
\(178\) | 15.6015 | + | 27.0225i | 1.16938 | + | 2.02542i | ||||
\(179\) | −0.473091 | + | 0.819418i | −0.0353605 | + | 0.0612461i | −0.883164 | − | 0.469064i | \(-0.844591\pi\) |
0.847804 | + | 0.530310i | \(0.177925\pi\) | |||||||
\(180\) | −7.14563 | + | 12.3766i | −0.532603 | + | 0.922496i | ||||
\(181\) | −11.7118 | −0.870534 | −0.435267 | − | 0.900301i | \(-0.643346\pi\) | ||||
−0.435267 | + | 0.900301i | \(0.643346\pi\) | |||||||
\(182\) | 18.9717 | + | 29.4912i | 1.40627 | + | 2.18603i | ||||
\(183\) | 14.5543 | 1.07589 | ||||||||
\(184\) | 10.9236 | − | 18.9202i | 0.805297 | − | 1.39482i | ||||
\(185\) | −2.87778 | + | 4.98446i | −0.211579 | + | 0.366465i | ||||
\(186\) | 1.26186 | + | 2.18561i | 0.0925243 | + | 0.160257i | ||||
\(187\) | 5.81351 | 0.425126 | ||||||||
\(188\) | −9.29110 | − | 16.0927i | −0.677623 | − | 1.17368i | ||||
\(189\) | −2.02991 | − | 3.51590i | −0.147654 | − | 0.255744i | ||||
\(190\) | −52.2750 | −3.79243 | ||||||||
\(191\) | 5.31376 | + | 9.20371i | 0.384490 | + | 0.665957i | 0.991698 | − | 0.128586i | \(-0.0410438\pi\) |
−0.607208 | + | 0.794543i | \(0.707711\pi\) | |||||||
\(192\) | 5.30293 | − | 9.18495i | 0.382706 | − | 0.662867i | ||||
\(193\) | 11.9830 | − | 20.7551i | 0.862553 | − | 1.49399i | −0.00690373 | − | 0.999976i | \(-0.502198\pi\) |
0.869457 | − | 0.494009i | \(-0.164469\pi\) | |||||||
\(194\) | −46.3792 | −3.32983 | ||||||||
\(195\) | −13.7658 | + | 0.661985i | −0.985786 | + | 0.0474058i | ||||
\(196\) | 35.4523 | 2.53231 | ||||||||
\(197\) | −7.80117 | + | 13.5120i | −0.555810 | + | 0.962692i | 0.442030 | + | 0.897000i | \(0.354259\pi\) |
−0.997840 | + | 0.0656913i | \(0.979075\pi\) | |||||||
\(198\) | 1.19780 | − | 2.07464i | 0.0851237 | − | 0.147439i | ||||
\(199\) | 3.39892 | + | 5.88711i | 0.240943 | + | 0.417326i | 0.960983 | − | 0.276607i | \(-0.0892099\pi\) |
−0.720040 | + | 0.693933i | \(0.755877\pi\) | |||||||
\(200\) | 40.0330 | 2.83076 | ||||||||
\(201\) | 1.68264 | + | 2.91441i | 0.118684 | + | 0.205567i | ||||
\(202\) | −2.85175 | − | 4.93938i | −0.200649 | − | 0.347534i | ||||
\(203\) | 13.6590 | 0.958673 | ||||||||
\(204\) | 10.8680 | + | 18.8239i | 0.760911 | + | 1.31794i | ||||
\(205\) | 10.5093 | − | 18.2027i | 0.734004 | − | 1.27133i | ||||
\(206\) | 12.7974 | − | 22.1658i | 0.891639 | − | 1.54436i | ||||
\(207\) | −5.24463 | −0.364527 | ||||||||
\(208\) | −9.00851 | + | 0.433213i | −0.624628 | + | 0.0300379i | ||||
\(209\) | 5.70888 | 0.394891 | ||||||||
\(210\) | −18.5874 | + | 32.1944i | −1.28266 | + | 2.22162i | ||||
\(211\) | 7.62151 | − | 13.2008i | 0.524686 | − | 0.908784i | −0.474900 | − | 0.880040i | \(-0.657516\pi\) |
0.999587 | − | 0.0287440i | \(-0.00915077\pi\) | |||||||
\(212\) | −8.53506 | − | 14.7831i | −0.586190 | − | 1.01531i | ||||
\(213\) | 3.65789 | 0.250635 | ||||||||
\(214\) | −16.0866 | − | 27.8628i | −1.09966 | − | 1.90467i | ||||
\(215\) | 5.95618 | + | 10.3164i | 0.406208 | + | 0.703573i | ||||
\(216\) | 4.16562 | 0.283435 | ||||||||
\(217\) | 2.13848 | + | 3.70396i | 0.145170 | + | 0.251441i | ||||
\(218\) | 15.6821 | − | 27.1622i | 1.06212 | − | 1.83965i | ||||
\(219\) | 0.00316442 | − | 0.00548094i | 0.000213832 | − | 0.000370368i | ||||
\(220\) | −14.2913 | −0.963516 | ||||||||
\(221\) | −9.59642 | + | 18.6352i | −0.645525 | + | 1.25354i | ||||
\(222\) | 3.60720 | 0.242100 | ||||||||
\(223\) | −1.70108 | + | 2.94635i | −0.113913 | + | 0.197302i | −0.917345 | − | 0.398094i | \(-0.869672\pi\) |
0.803432 | + | 0.595397i | \(0.203005\pi\) | |||||||
\(224\) | 4.74777 | − | 8.22337i | 0.317223 | − | 0.549447i | ||||
\(225\) | −4.80517 | − | 8.32279i | −0.320344 | − | 0.554853i | ||||
\(226\) | −23.2963 | −1.54965 | ||||||||
\(227\) | 1.98497 | + | 3.43807i | 0.131747 | + | 0.228193i | 0.924350 | − | 0.381545i | \(-0.124608\pi\) |
−0.792603 | + | 0.609738i | \(0.791275\pi\) | |||||||
\(228\) | 10.6724 | + | 18.4851i | 0.706795 | + | 1.22420i | ||||
\(229\) | 0.989162 | 0.0653657 | 0.0326828 | − | 0.999466i | \(-0.489595\pi\) | ||||
0.0326828 | + | 0.999466i | \(0.489595\pi\) | |||||||
\(230\) | 24.0120 | + | 41.5900i | 1.58330 | + | 2.74236i | ||||
\(231\) | 2.02991 | − | 3.51590i | 0.133558 | − | 0.231329i | ||||
\(232\) | −7.00748 | + | 12.1373i | −0.460064 | + | 0.796853i | ||||
\(233\) | −14.9645 | −0.980355 | −0.490178 | − | 0.871623i | \(-0.663068\pi\) | ||||
−0.490178 | + | 0.871623i | \(0.663068\pi\) | |||||||
\(234\) | 4.67304 | + | 7.26416i | 0.305486 | + | 0.474873i | ||||
\(235\) | 18.9971 | 1.23923 | ||||||||
\(236\) | −7.52546 | + | 13.0345i | −0.489866 | + | 0.848472i | ||||
\(237\) | 1.68378 | − | 2.91640i | 0.109373 | − | 0.189440i | ||||
\(238\) | 28.2702 | + | 48.9653i | 1.83248 | + | 3.17395i | ||||
\(239\) | 19.6498 | 1.27104 | 0.635519 | − | 0.772085i | \(-0.280786\pi\) | ||||
0.635519 | + | 0.772085i | \(0.280786\pi\) | |||||||
\(240\) | −4.78061 | − | 8.28026i | −0.308587 | − | 0.534488i | ||||
\(241\) | 4.60933 | + | 7.98360i | 0.296913 | + | 0.514269i | 0.975428 | − | 0.220318i | \(-0.0707095\pi\) |
−0.678515 | + | 0.734587i | \(0.737376\pi\) | |||||||
\(242\) | 2.39559 | 0.153995 | ||||||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | −27.2084 | + | 47.1263i | −1.74184 | + | 3.01695i | ||||
\(245\) | −18.1219 | + | 31.3881i | −1.15777 | + | 2.00531i | ||||
\(246\) | −13.1731 | −0.839887 | ||||||||
\(247\) | −9.42370 | + | 18.2997i | −0.599615 | + | 1.16438i | ||||
\(248\) | −4.38843 | −0.278665 | ||||||||
\(249\) | −4.46344 | + | 7.73091i | −0.282859 | + | 0.489927i | ||||
\(250\) | −21.1079 | + | 36.5600i | −1.33498 | + | 2.31226i | ||||
\(251\) | −10.6460 | − | 18.4394i | −0.671968 | − | 1.16388i | −0.977345 | − | 0.211651i | \(-0.932116\pi\) |
0.305377 | − | 0.952231i | \(-0.401217\pi\) | |||||||
\(252\) | 15.1791 | 0.956194 | ||||||||
\(253\) | −2.62232 | − | 4.54199i | −0.164864 | − | 0.285552i | ||||
\(254\) | −15.4747 | − | 26.8030i | −0.970970 | − | 1.68177i | ||||
\(255\) | −22.2213 | −1.39155 | ||||||||
\(256\) | 14.2239 | + | 24.6365i | 0.888994 | + | 1.53978i | ||||
\(257\) | 4.28045 | − | 7.41396i | 0.267007 | − | 0.462470i | −0.701080 | − | 0.713082i | \(-0.747299\pi\) |
0.968088 | + | 0.250612i | \(0.0806319\pi\) | |||||||
\(258\) | 3.73294 | − | 6.46563i | 0.232402 | − | 0.402533i | ||||
\(259\) | 6.11314 | 0.379852 | ||||||||
\(260\) | 23.5907 | − | 45.8104i | 1.46303 | − | 2.84104i | ||||
\(261\) | 3.36443 | 0.208253 | ||||||||
\(262\) | 5.97278 | − | 10.3452i | 0.368999 | − | 0.639126i | ||||
\(263\) | −14.0654 | + | 24.3619i | −0.867307 | + | 1.50222i | −0.00256942 | + | 0.999997i | \(0.500818\pi\) |
−0.864738 | + | 0.502224i | \(0.832515\pi\) | |||||||
\(264\) | 2.08281 | + | 3.60753i | 0.128188 | + | 0.222028i | ||||
\(265\) | 17.4512 | 1.07202 | ||||||||
\(266\) | 27.7613 | + | 48.0840i | 1.70216 | + | 2.94822i | ||||
\(267\) | 6.51256 | + | 11.2801i | 0.398562 | + | 0.690330i | ||||
\(268\) | −12.5823 | −0.768587 | ||||||||
\(269\) | 8.88225 | + | 15.3845i | 0.541560 | + | 0.938010i | 0.998815 | + | 0.0486738i | \(0.0154995\pi\) |
−0.457255 | + | 0.889336i | \(0.651167\pi\) | |||||||
\(270\) | −4.57839 | + | 7.93001i | −0.278632 | + | 0.482605i | ||||
\(271\) | −1.21986 | + | 2.11286i | −0.0741012 | + | 0.128347i | −0.900695 | − | 0.434452i | \(-0.856942\pi\) |
0.826594 | + | 0.562799i | \(0.190275\pi\) | |||||||
\(272\) | −14.5419 | −0.881733 | ||||||||
\(273\) | 7.91940 | + | 12.3106i | 0.479304 | + | 0.745070i | ||||
\(274\) | −23.0325 | −1.39145 | ||||||||
\(275\) | 4.80517 | − | 8.32279i | 0.289762 | − | 0.501883i | ||||
\(276\) | 9.80450 | − | 16.9819i | 0.590162 | − | 1.02219i | ||||
\(277\) | −7.85092 | − | 13.5982i | −0.471716 | − | 0.817036i | 0.527760 | − | 0.849393i | \(-0.323032\pi\) |
−0.999476 | + | 0.0323572i | \(0.989699\pi\) | |||||||
\(278\) | 39.7553 | 2.38436 | ||||||||
\(279\) | 0.526743 | + | 0.912346i | 0.0315353 | + | 0.0546208i | ||||
\(280\) | −32.3211 | − | 55.9818i | −1.93156 | − | 3.34555i | ||||
\(281\) | 30.5093 | 1.82003 | 0.910017 | − | 0.414571i | \(-0.136068\pi\) | ||||
0.910017 | + | 0.414571i | \(0.136068\pi\) | |||||||
\(282\) | −5.95306 | − | 10.3110i | −0.354500 | − | 0.614011i | ||||
\(283\) | 7.98355 | − | 13.8279i | 0.474573 | − | 0.821984i | −0.525003 | − | 0.851100i | \(-0.675936\pi\) |
0.999576 | + | 0.0291159i | \(0.00926919\pi\) | |||||||
\(284\) | −6.83819 | + | 11.8441i | −0.405772 | + | 0.702818i | ||||
\(285\) | −21.8213 | −1.29258 | ||||||||
\(286\) | −3.95443 | + | 7.67905i | −0.233830 | + | 0.454072i | ||||
\(287\) | −22.3245 | −1.31777 | ||||||||
\(288\) | 1.16945 | − | 2.02555i | 0.0689107 | − | 0.119357i | ||||
\(289\) | −8.39847 | + | 14.5466i | −0.494028 | + | 0.855681i | ||||
\(290\) | −15.4037 | − | 26.6800i | −0.904537 | − | 1.56670i | ||||
\(291\) | −19.3602 | −1.13491 | ||||||||
\(292\) | 0.0118314 | + | 0.0204925i | 0.000692378 | + | 0.00119923i | ||||
\(293\) | −9.94864 | − | 17.2316i | −0.581206 | − | 1.00668i | −0.995337 | − | 0.0964609i | \(-0.969248\pi\) |
0.414131 | − | 0.910217i | \(-0.364086\pi\) | |||||||
\(294\) | 22.7153 | 1.32478 | ||||||||
\(295\) | −7.69348 | − | 13.3255i | −0.447932 | − | 0.775840i | ||||
\(296\) | −3.13623 | + | 5.43210i | −0.182289 | + | 0.315735i | ||||
\(297\) | 0.500000 | − | 0.866025i | 0.0290129 | − | 0.0502519i | ||||
\(298\) | 38.7641 | 2.24554 | ||||||||
\(299\) | 18.8880 | − | 0.908309i | 1.09232 | − | 0.0525289i | ||||
\(300\) | 35.9318 | 2.07452 | ||||||||
\(301\) | 6.32621 | − | 10.9573i | 0.364637 | − | 0.631569i | ||||
\(302\) | 2.42329 | − | 4.19726i | 0.139445 | − | 0.241525i | ||||
\(303\) | −1.19042 | − | 2.06186i | −0.0683876 | − | 0.118451i | ||||
\(304\) | −14.2802 | −0.819024 | ||||||||
\(305\) | −27.8159 | − | 48.1785i | −1.59273 | − | 2.75869i | ||||
\(306\) | 6.96341 | + | 12.0610i | 0.398072 | + | 0.689480i | ||||
\(307\) | 10.3458 | 0.590464 | 0.295232 | − | 0.955426i | \(-0.404603\pi\) | ||||
0.295232 | + | 0.955426i | \(0.404603\pi\) | |||||||
\(308\) | 7.58956 | + | 13.1455i | 0.432455 | + | 0.749034i | ||||
\(309\) | 5.34207 | − | 9.25274i | 0.303900 | − | 0.526370i | ||||
\(310\) | 4.82328 | − | 8.35416i | 0.273944 | − | 0.474485i | ||||
\(311\) | −19.6627 | −1.11497 | −0.557484 | − | 0.830187i | \(-0.688233\pi\) | ||||
−0.557484 | + | 0.830187i | \(0.688233\pi\) | |||||||
\(312\) | −15.0020 | + | 0.721436i | −0.849322 | + | 0.0408433i | ||||
\(313\) | −17.2708 | −0.976204 | −0.488102 | − | 0.872787i | \(-0.662311\pi\) | ||||
−0.488102 | + | 0.872787i | \(0.662311\pi\) | |||||||
\(314\) | 21.9820 | − | 38.0740i | 1.24052 | − | 2.14864i | ||||
\(315\) | −7.75901 | + | 13.4390i | −0.437171 | + | 0.757202i | ||||
\(316\) | 6.29544 | + | 10.9040i | 0.354146 | + | 0.613399i | ||||
\(317\) | 8.93735 | 0.501972 | 0.250986 | − | 0.967991i | \(-0.419245\pi\) | ||||
0.250986 | + | 0.967991i | \(0.419245\pi\) | |||||||
\(318\) | −5.46864 | − | 9.47196i | −0.306666 | − | 0.531161i | ||||
\(319\) | 1.68222 | + | 2.91369i | 0.0941861 | + | 0.163135i | ||||
\(320\) | −40.5393 | −2.26622 | ||||||||
\(321\) | −6.71509 | − | 11.6309i | −0.374800 | − | 0.649172i | ||||
\(322\) | 25.5038 | − | 44.1739i | 1.42127 | − | 2.46171i | ||||
\(323\) | −16.5943 | + | 28.7422i | −0.923333 | + | 1.59926i | ||||
\(324\) | 3.73887 | 0.207715 | ||||||||
\(325\) | 18.7467 | + | 29.1414i | 1.03988 | + | 1.61648i | ||||
\(326\) | 48.2579 | 2.67276 | ||||||||
\(327\) | 6.54622 | − | 11.3384i | 0.362007 | − | 0.627014i | ||||
\(328\) | 11.4532 | − | 19.8375i | 0.632395 | − | 1.09534i | ||||
\(329\) | −10.0887 | − | 17.4741i | −0.556206 | − | 0.963377i | ||||
\(330\) | −9.15679 | −0.504065 | ||||||||
\(331\) | 6.90466 | + | 11.9592i | 0.379514 | + | 0.657338i | 0.990992 | − | 0.133924i | \(-0.0427578\pi\) |
−0.611477 | + | 0.791262i | \(0.709424\pi\) | |||||||
\(332\) | −16.6882 | − | 28.9049i | −0.915885 | − | 1.58636i | ||||
\(333\) | 1.50577 | 0.0825155 | ||||||||
\(334\) | −1.24558 | − | 2.15741i | −0.0681552 | − | 0.118048i | ||||
\(335\) | 6.43162 | − | 11.1399i | 0.351397 | − | 0.608637i | ||||
\(336\) | −5.07761 | + | 8.79468i | −0.277006 | + | 0.479789i | ||||
\(337\) | 10.7973 | 0.588165 | 0.294083 | − | 0.955780i | \(-0.404986\pi\) | ||||
0.294083 | + | 0.955780i | \(0.404986\pi\) | |||||||
\(338\) | −18.0875 | − | 25.3518i | −0.983830 | − | 1.37895i | ||||
\(339\) | −9.72464 | −0.528170 | ||||||||
\(340\) | 41.5412 | − | 71.9515i | 2.25289 | − | 3.90212i | ||||
\(341\) | −0.526743 | + | 0.912346i | −0.0285248 | + | 0.0494063i | ||||
\(342\) | 6.83807 | + | 11.8439i | 0.369761 | + | 0.640444i | ||||
\(343\) | 10.0769 | 0.544101 | ||||||||
\(344\) | 6.49108 | + | 11.2429i | 0.349976 | + | 0.606176i | ||||
\(345\) | 10.0234 | + | 17.3610i | 0.539642 | + | 0.934687i | ||||
\(346\) | 38.4763 | 2.06850 | ||||||||
\(347\) | −5.02081 | − | 8.69630i | −0.269531 | − | 0.466842i | 0.699210 | − | 0.714917i | \(-0.253535\pi\) |
−0.968741 | + | 0.248075i | \(0.920202\pi\) | |||||||
\(348\) | −6.28959 | + | 10.8939i | −0.337157 | + | 0.583974i | ||||
\(349\) | −14.7807 | + | 25.6010i | −0.791194 | + | 1.37039i | 0.134034 | + | 0.990977i | \(0.457207\pi\) |
−0.925228 | + | 0.379411i | \(0.876127\pi\) | |||||||
\(350\) | 93.4669 | 4.99602 | ||||||||
\(351\) | 1.95068 | + | 3.03230i | 0.104120 | + | 0.161852i | ||||
\(352\) | 2.33891 | 0.124664 | ||||||||
\(353\) | 13.0890 | − | 22.6707i | 0.696655 | − | 1.20664i | −0.272965 | − | 0.962024i | \(-0.588004\pi\) |
0.969620 | − | 0.244618i | \(-0.0786624\pi\) | |||||||
\(354\) | −4.82176 | + | 8.35154i | −0.256274 | + | 0.443879i | ||||
\(355\) | −6.99087 | − | 12.1085i | −0.371037 | − | 0.642655i | ||||
\(356\) | −48.6992 | −2.58105 | ||||||||
\(357\) | 11.8009 | + | 20.4398i | 0.624570 | + | 1.08179i | ||||
\(358\) | −1.13333 | − | 1.96299i | −0.0598985 | − | 0.103747i | ||||
\(359\) | −33.2680 | −1.75582 | −0.877910 | − | 0.478825i | \(-0.841063\pi\) | ||||
−0.877910 | + | 0.478825i | \(0.841063\pi\) | |||||||
\(360\) | −7.96122 | − | 13.7892i | −0.419593 | − | 0.726757i | ||||
\(361\) | −6.79564 | + | 11.7704i | −0.357665 | + | 0.619494i | ||||
\(362\) | 14.0284 | − | 24.2979i | 0.737317 | − | 1.27707i | ||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | −54.6659 | + | 2.62884i | −2.86527 | + | 0.137789i | ||||
\(365\) | −0.0241910 | −0.00126622 | ||||||||
\(366\) | −17.4331 | + | 30.1951i | −0.911245 | + | 1.57832i | ||||
\(367\) | −1.69733 | + | 2.93985i | −0.0885996 | + | 0.153459i | −0.906919 | − | 0.421304i | \(-0.861573\pi\) |
0.818320 | + | 0.574763i | \(0.194906\pi\) | |||||||
\(368\) | 6.55946 | + | 11.3613i | 0.341936 | + | 0.592250i | ||||
\(369\) | −5.49890 | −0.286261 | ||||||||
\(370\) | −6.89399 | − | 11.9407i | −0.358402 | − | 0.620770i | ||||
\(371\) | −9.26771 | − | 16.0521i | −0.481156 | − | 0.833386i | ||||
\(372\) | −3.93885 | −0.204220 | ||||||||
\(373\) | −4.44352 | − | 7.69640i | −0.230077 | − | 0.398504i | 0.727754 | − | 0.685838i | \(-0.240564\pi\) |
−0.957830 | + | 0.287334i | \(0.907231\pi\) | |||||||
\(374\) | −6.96341 | + | 12.0610i | −0.360069 | + | 0.623658i | ||||
\(375\) | −8.81115 | + | 15.2614i | −0.455006 | + | 0.788093i | ||||
\(376\) | 20.7032 | 1.06768 | ||||||||
\(377\) | −12.1166 | + | 0.582680i | −0.624039 | + | 0.0300096i | ||||
\(378\) | 9.72567 | 0.500234 | ||||||||
\(379\) | −16.1501 | + | 27.9727i | −0.829573 | + | 1.43686i | 0.0687999 | + | 0.997630i | \(0.478083\pi\) |
−0.898373 | + | 0.439233i | \(0.855250\pi\) | |||||||
\(380\) | 40.7935 | − | 70.6564i | 2.09266 | − | 3.62460i | ||||
\(381\) | −6.45966 | − | 11.1885i | −0.330938 | − | 0.573202i | ||||
\(382\) | −25.4592 | −1.30261 | ||||||||
\(383\) | 6.17721 | + | 10.6992i | 0.315641 | + | 0.546706i | 0.979574 | − | 0.201086i | \(-0.0644472\pi\) |
−0.663933 | + | 0.747792i | \(0.731114\pi\) | |||||||
\(384\) | 10.3648 | + | 17.9523i | 0.528925 | + | 0.916125i | ||||
\(385\) | −15.5180 | −0.790872 | ||||||||
\(386\) | 28.7063 | + | 49.7208i | 1.46111 | + | 2.53072i | ||||
\(387\) | 1.55825 | − | 2.69897i | 0.0792104 | − | 0.137196i | ||||
\(388\) | 36.1926 | − | 62.6874i | 1.83740 | − | 3.18247i | ||||
\(389\) | −5.42849 | −0.275235 | −0.137618 | − | 0.990485i | \(-0.543945\pi\) | ||||
−0.137618 | + | 0.990485i | \(0.543945\pi\) | |||||||
\(390\) | 15.1152 | − | 29.3520i | 0.765388 | − | 1.48630i | ||||
\(391\) | 30.4898 | 1.54193 | ||||||||
\(392\) | −19.7494 | + | 34.2070i | −0.997497 | + | 1.72772i | ||||
\(393\) | 2.49323 | − | 4.31841i | 0.125767 | − | 0.217835i | ||||
\(394\) | −18.6884 | − | 32.3693i | −0.941510 | − | 1.63074i | ||||
\(395\) | −12.8720 | −0.647660 | ||||||||
\(396\) | 1.86943 | + | 3.23795i | 0.0939426 | + | 0.162713i | ||||
\(397\) | −5.63771 | − | 9.76480i | −0.282949 | − | 0.490081i | 0.689161 | − | 0.724608i | \(-0.257979\pi\) |
−0.972110 | + | 0.234527i | \(0.924646\pi\) | |||||||
\(398\) | −16.2849 | −0.816287 | ||||||||
\(399\) | 11.5885 | + | 20.0719i | 0.580150 | + | 1.00485i | ||||
\(400\) | −12.0196 | + | 20.8186i | −0.600982 | + | 1.04093i | ||||
\(401\) | 1.23687 | − | 2.14233i | 0.0617664 | − | 0.106983i | −0.833489 | − | 0.552537i | \(-0.813660\pi\) |
0.895255 | + | 0.445554i | \(0.146993\pi\) | |||||||
\(402\) | −8.06182 | −0.402087 | ||||||||
\(403\) | −2.05502 | − | 3.19449i | −0.102368 | − | 0.159129i | ||||
\(404\) | 8.90162 | 0.442872 | ||||||||
\(405\) | −1.91117 | + | 3.31025i | −0.0949670 | + | 0.164488i | ||||
\(406\) | −16.3607 | + | 28.3375i | −0.811967 | + | 1.40637i | ||||
\(407\) | 0.752883 | + | 1.30403i | 0.0373190 | + | 0.0646385i | ||||
\(408\) | −24.2169 | −1.19892 | ||||||||
\(409\) | −5.67503 | − | 9.82945i | −0.280612 | − | 0.486035i | 0.690923 | − | 0.722928i | \(-0.257204\pi\) |
−0.971536 | + | 0.236893i | \(0.923871\pi\) | |||||||
\(410\) | 25.1761 | + | 43.6063i | 1.24336 | + | 2.15356i | ||||
\(411\) | −9.61453 | −0.474250 | ||||||||
\(412\) | 19.9733 | + | 34.5948i | 0.984014 | + | 1.70436i | ||||
\(413\) | −8.17145 | + | 14.1534i | −0.402091 | + | 0.696441i | ||||
\(414\) | 6.28201 | − | 10.8808i | 0.308744 | − | 0.534760i | ||||
\(415\) | 34.1217 | 1.67497 | ||||||||
\(416\) | −3.86086 | + | 7.49734i | −0.189294 | + | 0.367587i | ||||
\(417\) | 16.5952 | 0.812669 | ||||||||
\(418\) | −6.83807 | + | 11.8439i | −0.334461 | + | 0.579304i | ||||
\(419\) | −3.71606 | + | 6.43641i | −0.181542 | + | 0.314439i | −0.942406 | − | 0.334472i | \(-0.891442\pi\) |
0.760864 | + | 0.648911i | \(0.224775\pi\) | |||||||
\(420\) | −29.0099 | − | 50.2467i | −1.41554 | − | 2.45179i | ||||
\(421\) | −17.6143 | −0.858468 | −0.429234 | − | 0.903193i | \(-0.641217\pi\) | ||||
−0.429234 | + | 0.903193i | \(0.641217\pi\) | |||||||
\(422\) | 18.2580 | + | 31.6239i | 0.888788 | + | 1.53943i | ||||
\(423\) | −2.48500 | − | 4.30415i | −0.120825 | − | 0.209275i | ||||
\(424\) | 19.0185 | 0.923619 | ||||||||
\(425\) | 27.9349 | + | 48.3847i | 1.35504 | + | 2.34700i | ||||
\(426\) | −4.38141 | + | 7.58883i | −0.212280 | + | 0.367680i | ||||
\(427\) | −29.5440 | + | 51.1717i | −1.42973 | + | 2.47637i | ||||
\(428\) | 50.2137 | 2.42717 | ||||||||
\(429\) | −1.65071 | + | 3.20549i | −0.0796970 | + | 0.154762i | ||||
\(430\) | −28.5372 | −1.37618 | ||||||||
\(431\) | −7.76179 | + | 13.4438i | −0.373872 | + | 0.647566i | −0.990158 | − | 0.139957i | \(-0.955304\pi\) |
0.616285 | + | 0.787523i | \(0.288637\pi\) | |||||||
\(432\) | −1.25070 | + | 2.16628i | −0.0601743 | + | 0.104225i | ||||
\(433\) | −1.70511 | − | 2.95333i | −0.0819422 | − | 0.141928i | 0.822142 | − | 0.569283i | \(-0.192779\pi\) |
−0.904084 | + | 0.427355i | \(0.859446\pi\) | |||||||
\(434\) | −10.2459 | −0.491817 | ||||||||
\(435\) | −6.43002 | − | 11.1371i | −0.308296 | − | 0.533984i | ||||
\(436\) | 24.4755 | + | 42.3927i | 1.17216 | + | 2.03024i | ||||
\(437\) | 29.9410 | 1.43227 | ||||||||
\(438\) | 0.00758067 | + | 0.0131301i | 0.000362219 | + | 0.000627381i | ||||
\(439\) | 4.83467 | − | 8.37390i | 0.230746 | − | 0.399664i | −0.727282 | − | 0.686339i | \(-0.759217\pi\) |
0.958028 | + | 0.286675i | \(0.0925499\pi\) | |||||||
\(440\) | 7.96122 | − | 13.7892i | 0.379536 | − | 0.657376i | ||||
\(441\) | 9.48210 | 0.451529 | ||||||||
\(442\) | −27.1668 | − | 42.2303i | −1.29219 | − | 2.00869i | ||||
\(443\) | −1.23707 | −0.0587749 | −0.0293874 | − | 0.999568i | \(-0.509356\pi\) | ||||
−0.0293874 | + | 0.999568i | \(0.509356\pi\) | |||||||
\(444\) | −2.81493 | + | 4.87560i | −0.133591 | + | 0.231386i | ||||
\(445\) | 24.8933 | − | 43.1164i | 1.18005 | − | 2.04391i | ||||
\(446\) | −4.07509 | − | 7.05827i | −0.192961 | − | 0.334219i | ||||
\(447\) | 16.1814 | 0.765354 | ||||||||
\(448\) | 21.5289 | + | 37.2892i | 1.01715 | + | 1.76175i | ||||
\(449\) | 1.08768 | + | 1.88392i | 0.0513308 | + | 0.0889076i | 0.890549 | − | 0.454887i | \(-0.150320\pi\) |
−0.839218 | + | 0.543795i | \(0.816987\pi\) | |||||||
\(450\) | 23.0225 | 1.08529 | ||||||||
\(451\) | −2.74945 | − | 4.76218i | −0.129466 | − | 0.224242i | ||||
\(452\) | 18.1796 | − | 31.4880i | 0.855095 | − | 1.48107i | ||||
\(453\) | 1.01156 | − | 1.75207i | 0.0475272 | − | 0.0823196i | ||||
\(454\) | −9.51036 | −0.446343 | ||||||||
\(455\) | 25.6157 | − | 49.7429i | 1.20088 | − | 2.33198i | ||||
\(456\) | −23.7810 | −1.11365 | ||||||||
\(457\) | 11.7328 | − | 20.3218i | 0.548836 | − | 0.950611i | −0.449519 | − | 0.893271i | \(-0.648405\pi\) |
0.998355 | − | 0.0573406i | \(-0.0182621\pi\) | |||||||
\(458\) | −1.18482 | + | 2.05216i | −0.0553628 | + | 0.0958912i | ||||
\(459\) | 2.90676 | + | 5.03465i | 0.135676 | + | 0.234997i | ||||
\(460\) | −74.9524 | −3.49467 | ||||||||
\(461\) | −5.75680 | − | 9.97107i | −0.268121 | − | 0.464399i | 0.700256 | − | 0.713892i | \(-0.253069\pi\) |
−0.968377 | + | 0.249493i | \(0.919736\pi\) | |||||||
\(462\) | 4.86283 | + | 8.42268i | 0.226240 | + | 0.391858i | ||||
\(463\) | −11.5553 | −0.537022 | −0.268511 | − | 0.963277i | \(-0.586532\pi\) | ||||
−0.268511 | + | 0.963277i | \(0.586532\pi\) | |||||||
\(464\) | −4.20790 | − | 7.28829i | −0.195347 | − | 0.338350i | ||||
\(465\) | 2.01340 | − | 3.48730i | 0.0933690 | − | 0.161720i | ||||
\(466\) | 17.9244 | − | 31.0460i | 0.830332 | − | 1.43818i | ||||
\(467\) | −0.875475 | −0.0405121 | −0.0202561 | − | 0.999795i | \(-0.506448\pi\) | ||||
−0.0202561 | + | 0.999795i | \(0.506448\pi\) | |||||||
\(468\) | −13.4651 | + | 0.647528i | −0.622425 | + | 0.0299320i | ||||
\(469\) | −13.6624 | −0.630870 | ||||||||
\(470\) | −22.7547 | + | 39.4122i | −1.04959 | + | 1.81795i | ||||
\(471\) | 9.17603 | − | 15.8934i | 0.422809 | − | 0.732327i | ||||
\(472\) | −8.38441 | − | 14.5222i | −0.385924 | − | 0.668440i | ||||
\(473\) | 3.11650 | 0.143297 | ||||||||
\(474\) | 4.03366 | + | 6.98650i | 0.185272 | + | 0.320900i | ||||
\(475\) | 27.4321 | + | 47.5138i | 1.25867 | + | 2.18008i | ||||
\(476\) | −88.2440 | −4.04466 | ||||||||
\(477\) | −2.28279 | − | 3.95391i | −0.104522 | − | 0.181037i | ||||
\(478\) | −23.5364 | + | 40.7663i | −1.07653 | + | 1.86461i | ||||
\(479\) | 11.6197 | − | 20.1259i | 0.530917 | − | 0.919575i | −0.468432 | − | 0.883499i | \(-0.655181\pi\) |
0.999349 | − | 0.0360756i | \(-0.0114857\pi\) | |||||||
\(480\) | −8.94011 | −0.408059 | ||||||||
\(481\) | −5.42285 | + | 0.260781i | −0.247261 | + | 0.0118906i | ||||
\(482\) | −22.0842 | −1.00591 | ||||||||
\(483\) | 10.6461 | − | 18.4396i | 0.484415 | − | 0.839032i | ||||
\(484\) | −1.86943 | + | 3.23795i | −0.0849743 | + | 0.147180i | ||||
\(485\) | 37.0007 | + | 64.0871i | 1.68011 | + | 2.91004i | ||||
\(486\) | 2.39559 | 0.108666 | ||||||||
\(487\) | −15.7535 | − | 27.2859i | −0.713861 | − | 1.23644i | −0.963397 | − | 0.268078i | \(-0.913611\pi\) |
0.249536 | − | 0.968366i | \(-0.419722\pi\) | |||||||
\(488\) | −30.3139 | − | 52.5053i | −1.37225 | − | 2.37680i | ||||
\(489\) | 20.1444 | 0.910962 | ||||||||
\(490\) | −43.4128 | − | 75.1932i | −1.96119 | − | 3.39688i | ||||
\(491\) | 3.70134 | − | 6.41091i | 0.167039 | − | 0.289320i | −0.770338 | − | 0.637635i | \(-0.779913\pi\) |
0.937378 | + | 0.348315i | \(0.113246\pi\) | |||||||
\(492\) | 10.2798 | − | 17.8052i | 0.463450 | − | 0.802719i | ||||
\(493\) | −19.5592 | −0.880901 | ||||||||
\(494\) | −26.6778 | − | 41.4702i | −1.20029 | − | 1.86583i | ||||
\(495\) | −3.82235 | −0.171802 | ||||||||
\(496\) | 1.31760 | − | 2.28214i | 0.0591618 | − | 0.102471i | ||||
\(497\) | −7.42519 | + | 12.8608i | −0.333065 | + | 0.576886i | ||||
\(498\) | −10.6926 | − | 18.5201i | −0.479147 | − | 0.829906i | ||||
\(499\) | 39.9472 | 1.78828 | 0.894140 | − | 0.447787i | \(-0.147788\pi\) | ||||
0.894140 | + | 0.447787i | \(0.147788\pi\) | |||||||
\(500\) | −32.9437 | − | 57.0602i | −1.47329 | − | 2.55181i | ||||
\(501\) | −0.519947 | − | 0.900575i | −0.0232295 | − | 0.0402347i | ||||
\(502\) | 51.0068 | 2.27655 | ||||||||
\(503\) | 0.995247 | + | 1.72382i | 0.0443759 | + | 0.0768613i | 0.887360 | − | 0.461077i | \(-0.152537\pi\) |
−0.842984 | + | 0.537938i | \(0.819203\pi\) | |||||||
\(504\) | −8.45583 | + | 14.6459i | −0.376653 | + | 0.652381i | ||||
\(505\) | −4.55018 | + | 7.88115i | −0.202481 | + | 0.350707i | ||||
\(506\) | 12.5640 | 0.558539 | ||||||||
\(507\) | −7.55032 | − | 10.5827i | −0.335321 | − | 0.469992i | ||||
\(508\) | 48.3036 | 2.14313 | ||||||||
\(509\) | −8.10896 | + | 14.0451i | −0.359423 | + | 0.622539i | −0.987865 | − | 0.155318i | \(-0.950360\pi\) |
0.628441 | + | 0.777857i | \(0.283693\pi\) | |||||||
\(510\) | 26.6166 | − | 46.1012i | 1.17860 | − | 2.04140i | ||||
\(511\) | 0.0128470 | + | 0.0222516i | 0.000568317 | + | 0.000984353i | ||||
\(512\) | −26.6903 | −1.17956 | ||||||||
\(513\) | 2.85444 | + | 4.94403i | 0.126027 | + | 0.218284i | ||||
\(514\) | 10.2542 | + | 17.7608i | 0.452295 | + | 0.783397i | ||||
\(515\) | −40.8385 | −1.79956 | ||||||||
\(516\) | 5.82610 | + | 10.0911i | 0.256480 | + | 0.444236i | ||||
\(517\) | 2.48500 | − | 4.30415i | 0.109290 | − | 0.189296i | ||||
\(518\) | −7.32229 | + | 12.6826i | −0.321723 | + | 0.557241i | ||||
\(519\) | 16.0613 | 0.705012 | ||||||||
\(520\) | 31.0596 | + | 48.2817i | 1.36205 | + | 2.11729i | ||||
\(521\) | 17.9249 | 0.785306 | 0.392653 | − | 0.919687i | \(-0.371557\pi\) | ||||
0.392653 | + | 0.919687i | \(0.371557\pi\) | |||||||
\(522\) | −4.02991 | + | 6.98001i | −0.176384 | + | 0.305507i | ||||
\(523\) | −15.1137 | + | 26.1778i | −0.660878 | + | 1.14467i | 0.319507 | + | 0.947584i | \(0.396483\pi\) |
−0.980385 | + | 0.197090i | \(0.936851\pi\) | |||||||
\(524\) | 9.32188 | + | 16.1460i | 0.407228 | + | 0.705340i | ||||
\(525\) | 39.0162 | 1.70281 | ||||||||
\(526\) | −33.6949 | − | 58.3613i | −1.46917 | − | 2.54467i | ||||
\(527\) | −3.06223 | − | 5.30394i | −0.133393 | − | 0.231043i | ||||
\(528\) | −2.50140 | −0.108859 | ||||||||
\(529\) | −2.25310 | − | 3.90248i | −0.0979608 | − | 0.169673i | ||||
\(530\) | −20.9030 | + | 36.2051i | −0.907970 | + | 1.57265i | ||||
\(531\) | −2.01276 | + | 3.48621i | −0.0873465 | + | 0.151289i | ||||
\(532\) | −86.6557 | −3.75700 | ||||||||
\(533\) | 19.8037 | − | 0.952344i | 0.857792 | − | 0.0412506i | ||||
\(534\) | −31.2029 | −1.35028 | ||||||||
\(535\) | −25.6674 | + | 44.4572i | −1.10970 | + | 1.92205i | ||||
\(536\) | 7.00922 | − | 12.1403i | 0.302752 | − | 0.524382i | ||||
\(537\) | −0.473091 | − | 0.819418i | −0.0204154 | − | 0.0353605i | ||||
\(538\) | −42.5565 | −1.83474 | ||||||||
\(539\) | 4.74105 | + | 8.21174i | 0.204212 | + | 0.353705i | ||||
\(540\) | −7.14563 | − | 12.3766i | −0.307499 | − | 0.532603i | ||||
\(541\) | 16.5223 | 0.710347 | 0.355174 | − | 0.934800i | \(-0.384422\pi\) | ||||
0.355174 | + | 0.934800i | \(0.384422\pi\) | |||||||
\(542\) | −2.92229 | − | 5.06155i | −0.125523 | − | 0.217412i | ||||
\(543\) | 5.85592 | − | 10.1428i | 0.251302 | − | 0.435267i | ||||
\(544\) | −6.79864 | + | 11.7756i | −0.291489 | + | 0.504874i | ||||
\(545\) | −50.0438 | −2.14364 | ||||||||
\(546\) | −35.0259 | + | 1.68437i | −1.49897 | + | 0.0720844i | ||||
\(547\) | −28.2565 | −1.20816 | −0.604080 | − | 0.796924i | \(-0.706459\pi\) | ||||
−0.604080 | + | 0.796924i | \(0.706459\pi\) | |||||||
\(548\) | 17.9737 | − | 31.1314i | 0.767800 | − | 1.32987i | ||||
\(549\) | −7.27717 | + | 12.6044i | −0.310582 | + | 0.537944i | ||||
\(550\) | 11.5112 | + | 19.9380i | 0.490840 | + | 0.850160i | ||||
\(551\) | −19.2071 | −0.818252 | ||||||||
\(552\) | 10.9236 | + | 18.9202i | 0.464939 | + | 0.805297i | ||||
\(553\) | 6.83584 | + | 11.8400i | 0.290690 | + | 0.503489i | ||||
\(554\) | 37.6152 | 1.59812 | ||||||||
\(555\) | −2.87778 | − | 4.98446i | −0.122155 | − | 0.211579i | ||||
\(556\) | −31.0236 | + | 53.7344i | −1.31569 | + | 2.27885i | ||||
\(557\) | 0.873661 | − | 1.51323i | 0.0370182 | − | 0.0641174i | −0.846923 | − | 0.531716i | \(-0.821547\pi\) |
0.883941 | + | 0.467599i | \(0.154881\pi\) | |||||||
\(558\) | −2.52373 | −0.106838 | ||||||||
\(559\) | −5.14444 | + | 9.98991i | −0.217587 | + | 0.422528i | ||||
\(560\) | 38.8168 | 1.64031 | ||||||||
\(561\) | −2.90676 | + | 5.03465i | −0.122723 | + | 0.212563i | ||||
\(562\) | −36.5440 | + | 63.2960i | −1.54151 | + | 2.66998i | ||||
\(563\) | −1.57810 | − | 2.73335i | −0.0665089 | − | 0.115197i | 0.830853 | − | 0.556491i | \(-0.187853\pi\) |
−0.897362 | + | 0.441295i | \(0.854519\pi\) | |||||||
\(564\) | 18.5822 | 0.782452 | ||||||||
\(565\) | 18.5855 | + | 32.1910i | 0.781897 | + | 1.35429i | ||||
\(566\) | 19.1253 | + | 33.1261i | 0.803898 | + | 1.39239i | ||||
\(567\) | 4.05982 | 0.170496 | ||||||||
\(568\) | −7.61870 | − | 13.1960i | −0.319674 | − | 0.553691i | ||||
\(569\) | 3.92754 | − | 6.80270i | 0.164651 | − | 0.285184i | −0.771880 | − | 0.635768i | \(-0.780684\pi\) |
0.936531 | + | 0.350584i | \(0.114017\pi\) | |||||||
\(570\) | 26.1375 | − | 45.2715i | 1.09478 | − | 1.89621i | ||||
\(571\) | −23.8772 | −0.999231 | −0.499615 | − | 0.866247i | \(-0.666525\pi\) | ||||
−0.499615 | + | 0.866247i | \(0.666525\pi\) | |||||||
\(572\) | −7.29334 | − | 11.3374i | −0.304950 | − | 0.474039i | ||||
\(573\) | −10.6275 | −0.443971 | ||||||||
\(574\) | 26.7402 | − | 46.3154i | 1.11612 | − | 1.93317i | ||||
\(575\) | 25.2013 | − | 43.6500i | 1.05097 | − | 1.82033i | ||||
\(576\) | 5.30293 | + | 9.18495i | 0.220956 | + | 0.382706i | ||||
\(577\) | 28.9230 | 1.20408 | 0.602041 | − | 0.798465i | \(-0.294354\pi\) | ||||
0.602041 | + | 0.798465i | \(0.294354\pi\) | |||||||
\(578\) | −20.1193 | − | 34.8477i | −0.836854 | − | 1.44947i | ||||
\(579\) | 11.9830 | + | 20.7551i | 0.497995 | + | 0.862553i | ||||
\(580\) | 48.0820 | 1.99650 | ||||||||
\(581\) | −18.1208 | − | 31.3861i | −0.751776 | − | 1.30211i | ||||
\(582\) | 23.1896 | − | 40.1655i | 0.961239 | − | 1.66491i | ||||
\(583\) | 2.28279 | − | 3.95391i | 0.0945436 | − | 0.163754i | ||||
\(584\) | −0.0263636 | −0.00109093 | ||||||||
\(585\) | 6.30958 | − | 12.2525i | 0.260869 | − | 0.506578i | ||||
\(586\) | 47.6658 | 1.96906 | ||||||||
\(587\) | −15.1861 | + | 26.3032i | −0.626799 | + | 1.08565i | 0.361391 | + | 0.932414i | \(0.382302\pi\) |
−0.988190 | + | 0.153233i | \(0.951031\pi\) | |||||||
\(588\) | −17.7262 | + | 30.7026i | −0.731015 | + | 1.26615i | ||||
\(589\) | −3.00711 | − | 5.20847i | −0.123906 | − | 0.214611i | ||||
\(590\) | 36.8609 | 1.51754 | ||||||||
\(591\) | −7.80117 | − | 13.5120i | −0.320897 | − | 0.555810i | ||||
\(592\) | −1.88326 | − | 3.26191i | −0.0774016 | − | 0.134063i | ||||
\(593\) | 41.8447 | 1.71836 | 0.859178 | − | 0.511676i | \(-0.170975\pi\) | ||||
0.859178 | + | 0.511676i | \(0.170975\pi\) | |||||||
\(594\) | 1.19780 | + | 2.07464i | 0.0491462 | + | 0.0851237i | ||||
\(595\) | 45.1071 | − | 78.1278i | 1.84921 | − | 3.20293i | ||||
\(596\) | −30.2501 | + | 52.3947i | −1.23909 | + | 2.14617i | ||||
\(597\) | −6.79785 | −0.278217 | ||||||||
\(598\) | −20.7395 | + | 40.2738i | −0.848103 | + | 1.64692i | ||||
\(599\) | −10.2426 | −0.418501 | −0.209251 | − | 0.977862i | \(-0.567102\pi\) | ||||
−0.209251 | + | 0.977862i | \(0.567102\pi\) | |||||||
\(600\) | −20.0165 | + | 34.6696i | −0.817170 | + | 1.41538i | ||||
\(601\) | 9.29155 | − | 16.0934i | 0.379010 | − | 0.656465i | −0.611908 | − | 0.790929i | \(-0.709598\pi\) |
0.990919 | + | 0.134464i | \(0.0429312\pi\) | |||||||
\(602\) | 15.1550 | + | 26.2493i | 0.617673 | + | 1.06984i | ||||
\(603\) | −3.36527 | −0.137044 | ||||||||
\(604\) | 3.78209 | + | 6.55077i | 0.153891 | + | 0.266547i | ||||
\(605\) | −1.91117 | − | 3.31025i | −0.0777002 | − | 0.134581i | ||||
\(606\) | 5.70351 | 0.231689 | ||||||||
\(607\) | −0.539012 | − | 0.933595i | −0.0218778 | − | 0.0378935i | 0.854879 | − | 0.518827i | \(-0.173631\pi\) |
−0.876757 | + | 0.480934i | \(0.840298\pi\) | |||||||
\(608\) | −6.67627 | + | 11.5636i | −0.270758 | + | 0.468967i | ||||
\(609\) | −6.82949 | + | 11.8290i | −0.276745 | + | 0.479336i | ||||
\(610\) | 133.271 | 5.39599 | ||||||||
\(611\) | 9.69490 | + | 15.0706i | 0.392214 | + | 0.609690i | ||||
\(612\) | −21.7360 | −0.878624 | ||||||||
\(613\) | 5.97314 | − | 10.3458i | 0.241253 | − | 0.417862i | −0.719819 | − | 0.694162i | \(-0.755775\pi\) |
0.961071 | + | 0.276300i | \(0.0891084\pi\) | |||||||
\(614\) | −12.3921 | + | 21.4638i | −0.500105 | + | 0.866208i | ||||
\(615\) | 10.5093 | + | 18.2027i | 0.423778 | + | 0.734004i | ||||
\(616\) | −16.9117 | −0.681390 | ||||||||
\(617\) | 12.6732 | + | 21.9506i | 0.510202 | + | 0.883696i | 0.999930 | + | 0.0118207i | \(0.00376273\pi\) |
−0.489728 | + | 0.871875i | \(0.662904\pi\) | |||||||
\(618\) | 12.7974 | + | 22.1658i | 0.514788 | + | 0.891639i | ||||
\(619\) | 12.6835 | 0.509792 | 0.254896 | − | 0.966968i | \(-0.417959\pi\) | ||||
0.254896 | + | 0.966968i | \(0.417959\pi\) | |||||||
\(620\) | 7.52782 | + | 13.0386i | 0.302325 | + | 0.523642i | ||||
\(621\) | 2.62232 | − | 4.54199i | 0.105230 | − | 0.182264i | ||||
\(622\) | 23.5519 | − | 40.7931i | 0.944345 | − | 1.63565i | ||||
\(623\) | −52.8796 | −2.11858 | ||||||||
\(624\) | 4.12908 | − | 8.01821i | 0.165296 | − | 0.320985i | ||||
\(625\) | 19.3069 | 0.772274 | ||||||||
\(626\) | 20.6869 | − | 35.8308i | 0.826816 | − | 1.43209i | ||||
\(627\) | −2.85444 | + | 4.94403i | −0.113995 | + | 0.197446i | ||||
\(628\) | 34.3080 | + | 59.4232i | 1.36904 | + | 2.37124i | ||||
\(629\) | −8.75380 | −0.349037 | ||||||||
\(630\) | −18.5874 | − | 32.1944i | −0.740541 | − | 1.28266i | ||||
\(631\) | 1.09739 | + | 1.90074i | 0.0436865 | + | 0.0756672i | 0.887042 | − | 0.461689i | \(-0.152756\pi\) |
−0.843355 | + | 0.537356i | \(0.819423\pi\) | |||||||
\(632\) | −14.0280 | −0.558004 | ||||||||
\(633\) | 7.62151 | + | 13.2008i | 0.302928 | + | 0.524686i | ||||
\(634\) | −10.7051 | + | 18.5418i | −0.425155 | + | 0.736390i | ||||
\(635\) | −24.6911 | + | 42.7662i | −0.979835 | + | 1.69712i | ||||
\(636\) | 17.0701 | 0.676874 | ||||||||
\(637\) | −34.1487 | + | 1.64219i | −1.35302 | + | 0.0650659i | ||||
\(638\) | −8.05982 | −0.319091 | ||||||||
\(639\) | −1.82895 | + | 3.16783i | −0.0723520 | + | 0.125317i | ||||
\(640\) | 39.6177 | − | 68.6199i | 1.56603 | − | 2.71244i | ||||
\(641\) | −9.94043 | − | 17.2173i | −0.392623 | − | 0.680044i | 0.600171 | − | 0.799871i | \(-0.295099\pi\) |
−0.992795 | + | 0.119828i | \(0.961766\pi\) | |||||||
\(642\) | 32.1732 | 1.26978 | ||||||||
\(643\) | −16.5287 | − | 28.6285i | −0.651827 | − | 1.12900i | −0.982679 | − | 0.185315i | \(-0.940670\pi\) |
0.330852 | − | 0.943683i | \(-0.392664\pi\) | |||||||
\(644\) | 39.8045 | + | 68.9433i | 1.56852 | + | 2.71675i | ||||
\(645\) | −11.9124 | −0.469048 | ||||||||
\(646\) | −39.7532 | − | 68.8546i | −1.56407 | − | 2.70905i | ||||
\(647\) | −22.0707 | + | 38.2276i | −0.867690 | + | 1.50288i | −0.00333955 | + | 0.999994i | \(0.501063\pi\) |
−0.864351 | + | 0.502889i | \(0.832270\pi\) | |||||||
\(648\) | −2.08281 | + | 3.60753i | −0.0818205 | + | 0.141717i | ||||
\(649\) | −4.02553 | −0.158016 | ||||||||
\(650\) | −82.9128 | + | 3.98722i | −3.25211 | + | 0.156392i | ||||
\(651\) | −4.27696 | −0.167627 | ||||||||
\(652\) | −37.6587 | + | 65.2267i | −1.47483 | + | 2.55448i | ||||
\(653\) | −9.36032 | + | 16.2125i | −0.366298 | + | 0.634446i | −0.988983 | − | 0.148026i | \(-0.952708\pi\) |
0.622686 | + | 0.782472i | \(0.286041\pi\) | |||||||
\(654\) | 15.6821 | + | 27.1622i | 0.613218 | + | 1.06212i | ||||
\(655\) | −19.0600 | −0.744736 | ||||||||
\(656\) | 6.87747 | + | 11.9121i | 0.268520 | + | 0.465090i | ||||
\(657\) | 0.00316442 | + | 0.00548094i | 0.000123456 | + | 0.000213832i | ||||
\(658\) | 48.3367 | 1.88436 | ||||||||
\(659\) | 18.4498 | + | 31.9560i | 0.718703 | + | 1.24483i | 0.961514 | + | 0.274756i | \(0.0885971\pi\) |
−0.242811 | + | 0.970074i | \(0.578070\pi\) | |||||||
\(660\) | 7.14563 | − | 12.3766i | 0.278143 | − | 0.481758i | ||||
\(661\) | 9.36752 | − | 16.2250i | 0.364354 | − | 0.631080i | −0.624318 | − | 0.781170i | \(-0.714623\pi\) |
0.988672 | + | 0.150090i | \(0.0479564\pi\) | |||||||
\(662\) | −33.0815 | −1.28575 | ||||||||
\(663\) | −11.3403 | − | 17.6283i | −0.440421 | − | 0.684627i | ||||
\(664\) | 37.1860 | 1.44310 | ||||||||
\(665\) | 44.2952 | − | 76.7216i | 1.71770 | − | 2.97514i | ||||
\(666\) | −1.80360 | + | 3.12393i | −0.0698882 | + | 0.121050i | ||||
\(667\) | 8.82261 | + | 15.2812i | 0.341613 | + | 0.591691i | ||||
\(668\) | 3.88803 | 0.150432 | ||||||||
\(669\) | −1.70108 | − | 2.94635i | −0.0657675 | − | 0.113913i | ||||
\(670\) | 15.4075 | + | 26.6866i | 0.595245 | + | 1.03099i | ||||
\(671\) | −14.5543 | −0.561864 | ||||||||
\(672\) | 4.74777 | + | 8.22337i | 0.183149 | + | 0.317223i | ||||
\(673\) | −17.9325 | + | 31.0600i | −0.691246 | + | 1.19727i | 0.280183 | + | 0.959947i | \(0.409605\pi\) |
−0.971430 | + | 0.237328i | \(0.923729\pi\) | |||||||
\(674\) | −12.9329 | + | 22.4005i | −0.498158 | + | 0.862836i | ||||
\(675\) | 9.61033 | 0.369902 | ||||||||
\(676\) | 48.3810 | − | 4.66400i | 1.86081 | − | 0.179385i | ||||
\(677\) | −9.94933 | −0.382384 | −0.191192 | − | 0.981553i | \(-0.561235\pi\) | ||||
−0.191192 | + | 0.981553i | \(0.561235\pi\) | |||||||
\(678\) | 11.6481 | − | 20.1752i | 0.447344 | − | 0.774823i | ||||
\(679\) | 39.2994 | − | 68.0686i | 1.50817 | − | 2.61223i | ||||
\(680\) | 46.2827 | + | 80.1640i | 1.77486 | + | 3.07415i | ||||
\(681\) | −3.96994 | −0.152128 | ||||||||
\(682\) | −1.26186 | − | 2.18561i | −0.0483192 | − | 0.0836914i | ||||
\(683\) | 4.98562 | + | 8.63535i | 0.190769 | + | 0.330422i | 0.945505 | − | 0.325606i | \(-0.105568\pi\) |
−0.754736 | + | 0.656029i | \(0.772235\pi\) | |||||||
\(684\) | −21.3447 | −0.816136 | ||||||||
\(685\) | 18.3750 | + | 31.8265i | 0.702074 | + | 1.21603i | ||||
\(686\) | −12.0701 | + | 20.9060i | −0.460837 | + | 0.798193i | ||||
\(687\) | −0.494581 | + | 0.856640i | −0.0188694 | + | 0.0326828i | ||||
\(688\) | −7.79562 | −0.297205 | ||||||||
\(689\) | 8.90599 | + | 13.8442i | 0.339291 | + | 0.527423i | ||||
\(690\) | −48.0240 | −1.82824 | ||||||||
\(691\) | 5.83127 | − | 10.1001i | 0.221832 | − | 0.384224i | −0.733532 | − | 0.679655i | \(-0.762130\pi\) |
0.955364 | + | 0.295430i | \(0.0954630\pi\) | |||||||
\(692\) | −30.0255 | + | 52.0057i | −1.14140 | + | 1.97696i | ||||
\(693\) | 2.02991 | + | 3.51590i | 0.0771098 | + | 0.133558i | ||||
\(694\) | 24.0556 | 0.913139 | ||||||||
\(695\) | −31.7163 | − | 54.9342i | −1.20307 | − | 2.08377i | ||||
\(696\) | −7.00748 | − | 12.1373i | −0.265618 | − | 0.460064i | ||||
\(697\) | 31.9679 | 1.21087 | ||||||||
\(698\) | −35.4086 | − | 61.3295i | −1.34024 | − | 2.32136i | ||||
\(699\) | 7.48224 | − | 12.9596i | 0.283004 | − | 0.490178i | ||||
\(700\) | −72.9382 | + | 126.333i | −2.75680 | + | 4.77493i | ||||
\(701\) | 10.7213 | 0.404937 | 0.202468 | − | 0.979289i | \(-0.435104\pi\) | ||||
0.202468 | + | 0.979289i | \(0.435104\pi\) | |||||||
\(702\) | −8.62747 | + | 0.414889i | −0.325623 | + | 0.0156590i | ||||
\(703\) | −8.59624 | −0.324213 | ||||||||
\(704\) | −5.30293 | + | 9.18495i | −0.199862 | + | 0.346171i | ||||
\(705\) | −9.49855 | + | 16.4520i | −0.357736 | + | 0.619617i | ||||
\(706\) | 31.3558 | + | 54.3099i | 1.18009 | + | 2.04398i | ||||
\(707\) | 9.66574 | 0.363518 | ||||||||
\(708\) | −7.52546 | − | 13.0345i | −0.282824 | − | 0.489866i | ||||
\(709\) | −11.8838 | − | 20.5834i | −0.446307 | − | 0.773026i | 0.551836 | − | 0.833953i | \(-0.313928\pi\) |
−0.998142 | + | 0.0609271i | \(0.980594\pi\) | |||||||
\(710\) | 33.4946 | 1.25703 | ||||||||
\(711\) | 1.68378 | + | 2.91640i | 0.0631467 | + | 0.109373i | ||||
\(712\) | 27.1289 | − | 46.9886i | 1.01670 | − | 1.76097i | ||||
\(713\) | −2.76258 | + | 4.78492i | −0.103459 | + | 0.179197i | ||||
\(714\) | −56.5403 | −2.11597 | ||||||||
\(715\) | 13.7658 | − | 0.661985i | 0.514810 | − | 0.0247568i | ||||
\(716\) | 3.53765 | 0.132208 | ||||||||
\(717\) | −9.82489 | + | 17.0172i | −0.366917 | + | 0.635519i | ||||
\(718\) | 39.8484 | − | 69.0194i | 1.48713 | − | 2.57578i | ||||
\(719\) | 3.20607 | + | 5.55308i | 0.119566 | + | 0.207095i | 0.919596 | − | 0.392866i | \(-0.128516\pi\) |
−0.800030 | + | 0.599961i | \(0.795183\pi\) | |||||||
\(720\) | 9.56121 | 0.356325 | ||||||||
\(721\) | 21.6878 | + | 37.5644i | 0.807697 | + | 1.39897i | ||||
\(722\) | −16.2796 | − | 28.1971i | −0.605863 | − | 1.04939i | ||||
\(723\) | −9.21866 | −0.342846 | ||||||||
\(724\) | 21.8945 | + | 37.9224i | 0.813703 | + | 1.40938i | ||||
\(725\) | −16.1667 | + | 28.0015i | −0.600415 | + | 1.03995i | ||||
\(726\) | −1.19780 | + | 2.07464i | −0.0444544 | + | 0.0769973i | ||||
\(727\) | −42.2092 | −1.56545 | −0.782727 | − | 0.622365i | \(-0.786172\pi\) | ||||
−0.782727 | + | 0.622365i | \(0.786172\pi\) | |||||||
\(728\) | 27.9162 | − | 54.2101i | 1.03464 | − | 2.00916i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0.0289760 | − | 0.0501878i | 0.00107245 | − | 0.00185753i | ||||
\(731\) | −9.05891 | + | 15.6905i | −0.335056 | + | 0.580334i | ||||
\(732\) | −27.2084 | − | 47.1263i | −1.00565 | − | 1.74184i | ||||
\(733\) | −7.41443 | −0.273858 | −0.136929 | − | 0.990581i | \(-0.543723\pi\) | ||||
−0.136929 | + | 0.990581i | \(0.543723\pi\) | |||||||
\(734\) | −4.06610 | − | 7.04269i | −0.150083 | − | 0.259951i | ||||
\(735\) | −18.1219 | − | 31.3881i | −0.668438 | − | 1.15777i | ||||
\(736\) | 12.2667 | 0.452157 | ||||||||
\(737\) | −1.68264 | − | 2.91441i | −0.0619807 | − | 0.107354i | ||||
\(738\) | 6.58656 | − | 11.4083i | 0.242455 | − | 0.419944i | ||||
\(739\) | −5.65482 | + | 9.79444i | −0.208016 | + | 0.360294i | −0.951089 | − | 0.308916i | \(-0.900034\pi\) |
0.743073 | + | 0.669210i | \(0.233367\pi\) | |||||||
\(740\) | 21.5193 | 0.791065 | ||||||||
\(741\) | −11.1362 | − | 17.3110i | −0.409098 | − | 0.635937i | ||||
\(742\) | 44.4033 | 1.63010 | ||||||||
\(743\) | 10.5167 | − | 18.2155i | 0.385821 | − | 0.668262i | −0.606062 | − | 0.795418i | \(-0.707252\pi\) |
0.991883 | + | 0.127156i | \(0.0405848\pi\) | |||||||
\(744\) | 2.19421 | − | 3.80049i | 0.0804438 | − | 0.139333i | ||||
\(745\) | −30.9255 | − | 53.5645i | −1.13302 | − | 1.96245i | ||||
\(746\) | 21.2897 | 0.779472 | ||||||||
\(747\) | −4.46344 | − | 7.73091i | −0.163309 | − | 0.282859i | ||||
\(748\) | −10.8680 | − | 18.8239i | −0.397373 | − | 0.688270i | ||||
\(749\) | 54.5240 | 1.99227 | ||||||||
\(750\) | −21.1079 | − | 36.5600i | −0.770753 | − | 1.33498i | ||||
\(751\) | 21.9857 | − | 38.0804i | 0.802271 | − | 1.38957i | −0.115847 | − | 0.993267i | \(-0.536958\pi\) |
0.918118 | − | 0.396307i | \(-0.129708\pi\) | |||||||
\(752\) | −6.21599 | + | 10.7664i | −0.226674 | + | 0.392610i | ||||
\(753\) | 21.2919 | 0.775922 | ||||||||
\(754\) | 13.3044 | − | 25.8356i | 0.484518 | − | 0.940879i | ||||
\(755\) | −7.73307 | −0.281435 | ||||||||
\(756\) | −7.58956 | + | 13.1455i | −0.276030 | + | 0.478097i | ||||
\(757\) | 1.00491 | − | 1.74056i | 0.0365242 | − | 0.0632617i | −0.847185 | − | 0.531297i | \(-0.821705\pi\) |
0.883710 | + | 0.468036i | \(0.155038\pi\) | |||||||
\(758\) | −38.6890 | − | 67.0113i | −1.40525 | − | 2.43396i | ||||
\(759\) | 5.24463 | 0.190368 | ||||||||
\(760\) | 45.4496 | + | 78.7211i | 1.64863 | + | 2.85551i | ||||
\(761\) | 1.62429 | + | 2.81336i | 0.0588805 | + | 0.101984i | 0.893963 | − | 0.448140i | \(-0.147914\pi\) |
−0.835083 | + | 0.550125i | \(0.814580\pi\) | |||||||
\(762\) | 30.9494 | 1.12118 | ||||||||
\(763\) | 26.5764 | + | 46.0318i | 0.962132 | + | 1.66646i | ||||
\(764\) | 19.8675 | − | 34.4115i | 0.718780 | − | 1.24496i | ||||
\(765\) | 11.1106 | − | 19.2442i | 0.401706 | − | 0.695775i | ||||
\(766\) | −29.5962 | −1.06935 | ||||||||
\(767\) | 6.64497 | − | 12.9038i | 0.239936 | − | 0.465929i | ||||
\(768\) | −28.4478 | −1.02652 | ||||||||
\(769\) | −23.3040 | + | 40.3638i | −0.840365 | + | 1.45556i | 0.0492207 | + | 0.998788i | \(0.484326\pi\) |
−0.889586 | + | 0.456768i | \(0.849007\pi\) | |||||||
\(770\) | 18.5874 | − | 32.1944i | 0.669845 | − | 1.16021i | ||||
\(771\) | 4.28045 | + | 7.41396i | 0.154157 | + | 0.267007i | ||||
\(772\) | −89.6055 | −3.22497 | ||||||||
\(773\) | 13.0854 | + | 22.6647i | 0.470651 | + | 0.815191i | 0.999437 | − | 0.0335642i | \(-0.0106858\pi\) |
−0.528786 | + | 0.848755i | \(0.677353\pi\) | |||||||
\(774\) | 3.73294 | + | 6.46563i | 0.134178 | + | 0.232402i | ||||
\(775\) | −10.1244 | −0.363678 | ||||||||
\(776\) | 40.3236 | + | 69.8426i | 1.44753 | + | 2.50720i | ||||
\(777\) | −3.05657 | + | 5.29413i | −0.109654 | + | 0.189926i | ||||
\(778\) | 6.50223 | − | 11.2622i | 0.233116 | − | 0.403769i | ||||
\(779\) | 31.3925 | 1.12475 | ||||||||
\(780\) | 27.8777 | + | 43.3354i | 0.998180 | + | 1.55166i | ||||
\(781\) | −3.65789 | −0.130890 | ||||||||
\(782\) | −36.5205 | + | 63.2554i | −1.30597 | + | 2.26201i | ||||
\(783\) | −1.68222 | + | 2.91369i | −0.0601175 | + | 0.104127i | ||||
\(784\) | −11.8593 | − | 20.5408i | −0.423545 | − | 0.733602i | ||||
\(785\) | −70.1480 | −2.50369 | ||||||||
\(786\) | 5.97278 | + | 10.3452i | 0.213042 | + | 0.368999i | ||||
\(787\) | 1.47889 | + | 2.56151i | 0.0527167 | + | 0.0913080i | 0.891180 | − | 0.453651i | \(-0.149879\pi\) |
−0.838463 | + | 0.544959i | \(0.816545\pi\) | |||||||
\(788\) | 58.3351 | 2.07810 | ||||||||
\(789\) | −14.0654 | − | 24.3619i | −0.500740 | − | 0.867307i | ||||
\(790\) | 15.4180 | − | 26.7048i | 0.548549 | − | 0.950115i | ||||
\(791\) | 19.7401 | − | 34.1909i | 0.701878 | − | 1.21569i | ||||
\(792\) | −4.16562 | −0.148019 | ||||||||
\(793\) | 24.0250 | − | 46.6538i | 0.853152 | − | 1.65672i | ||||
\(794\) | 27.0113 | 0.958596 | ||||||||
\(795\) | −8.72562 | + | 15.1132i | −0.309466 | + | 0.536011i | ||||
\(796\) | 12.7081 | − | 22.0111i | 0.450428 | − | 0.780164i | ||||
\(797\) | 3.77378 | + | 6.53638i | 0.133674 | + | 0.231530i | 0.925090 | − | 0.379748i | \(-0.123989\pi\) |
−0.791416 | + | 0.611278i | \(0.790656\pi\) | |||||||
\(798\) | −55.5226 | −1.96548 | ||||||||
\(799\) | 14.4466 | + | 25.0223i | 0.511084 | + | 0.885224i | ||||
\(800\) | 11.2388 | + | 19.4662i | 0.397353 | + | 0.688236i | ||||
\(801\) | −13.0251 | −0.460220 | ||||||||
\(802\) | 2.96304 | + | 5.13214i | 0.104629 | + | 0.181222i | ||||
\(803\) | −0.00316442 | + | 0.00548094i | −0.000111670 | + | 0.000193418i | ||||
\(804\) | 6.29115 | − | 10.8966i | 0.221872 | − | 0.384293i | ||||
\(805\) | −81.3864 | −2.86849 | ||||||||
\(806\) | 9.08892 | − | 0.437080i | 0.320144 | − | 0.0153955i | ||||
\(807\) | −17.7645 | −0.625340 | ||||||||
\(808\) | −4.95882 | + | 8.58894i | −0.174451 | + | 0.302158i | ||||
\(809\) | 2.99247 | − | 5.18311i | 0.105210 | − | 0.182228i | −0.808614 | − | 0.588339i | \(-0.799782\pi\) |
0.913824 | + | 0.406111i | \(0.133115\pi\) | |||||||
\(810\) | −4.57839 | − | 7.93001i | −0.160868 | − | 0.278632i | ||||
\(811\) | −16.7015 | −0.586471 | −0.293235 | − | 0.956040i | \(-0.594732\pi\) | ||||
−0.293235 | + | 0.956040i | \(0.594732\pi\) | |||||||
\(812\) | −25.5346 | − | 44.2272i | −0.896088 | − | 1.55207i | ||||
\(813\) | −1.21986 | − | 2.11286i | −0.0427824 | − | 0.0741012i | ||||
\(814\) | −3.60720 | −0.126432 | ||||||||
\(815\) | −38.4995 | − | 66.6831i | −1.34858 | − | 2.33581i | ||||
\(816\) | 7.27096 | − | 12.5937i | 0.254535 | − | 0.440867i | ||||
\(817\) | −8.89586 | + | 15.4081i | −0.311227 | + | 0.539061i | ||||
\(818\) | 27.1901 | 0.950681 | ||||||||
\(819\) | −14.6210 | + | 0.703112i | −0.510898 | + | 0.0245687i | ||||
\(820\) | −78.5861 | −2.74435 | ||||||||
\(821\) | 24.1740 | − | 41.8706i | 0.843679 | − | 1.46130i | −0.0430838 | − | 0.999071i | \(-0.513718\pi\) |
0.886763 | − | 0.462224i | \(-0.152948\pi\) | |||||||
\(822\) | 11.5163 | − | 19.9467i | 0.401676 | − | 0.695723i | ||||
\(823\) | 9.21767 | + | 15.9655i | 0.321308 | + | 0.556522i | 0.980758 | − | 0.195227i | \(-0.0625442\pi\) |
−0.659450 | + | 0.751748i | \(0.729211\pi\) | |||||||
\(824\) | −44.5061 | −1.55044 | ||||||||
\(825\) | 4.80517 | + | 8.32279i | 0.167294 | + | 0.289762i | ||||
\(826\) | −19.5755 | − | 33.9057i | −0.681118 | − | 1.17973i | ||||
\(827\) | −44.1498 | −1.53524 | −0.767620 | − | 0.640906i | \(-0.778559\pi\) | ||||
−0.767620 | + | 0.640906i | \(0.778559\pi\) | |||||||
\(828\) | 9.80450 | + | 16.9819i | 0.340730 | + | 0.590162i | ||||
\(829\) | 6.33886 | − | 10.9792i | 0.220158 | − | 0.381324i | −0.734698 | − | 0.678394i | \(-0.762676\pi\) |
0.954856 | + | 0.297070i | \(0.0960095\pi\) | |||||||
\(830\) | −40.8708 | + | 70.7903i | −1.41865 | + | 2.45717i | ||||
\(831\) | 15.7018 | 0.544691 | ||||||||
\(832\) | −20.6887 | − | 32.1602i | −0.717250 | − | 1.11495i | ||||
\(833\) | −55.1243 | −1.90995 | ||||||||
\(834\) | −19.8776 | + | 34.4291i | −0.688307 | + | 1.19218i | ||||
\(835\) | −1.98742 | + | 3.44231i | −0.0687775 | + | 0.119126i | ||||
\(836\) | −10.6724 | − | 18.4851i | −0.369112 | − | 0.639320i | ||||
\(837\) | −1.05349 | −0.0364138 | ||||||||
\(838\) | −8.90218 | − | 15.4190i | −0.307521 | − | 0.532641i | ||||
\(839\) | 9.68136 | + | 16.7686i | 0.334238 | + | 0.578917i | 0.983338 | − | 0.181786i | \(-0.0581878\pi\) |
−0.649100 | + | 0.760703i | \(0.724854\pi\) | |||||||
\(840\) | 64.6422 | 2.23037 | ||||||||
\(841\) | 8.84029 | + | 15.3118i | 0.304838 | + | 0.527994i | ||||
\(842\) | 21.0984 | − | 36.5434i | 0.727097 | − | 1.25937i | ||||
\(843\) | −15.2547 | + | 26.4219i | −0.525399 | + | 0.910017i | ||||
\(844\) | −56.9917 | −1.96173 | ||||||||
\(845\) | −20.6013 | + | 45.2187i | −0.708706 | + | 1.55557i | ||||
\(846\) | 11.9061 | 0.409341 | ||||||||
\(847\) | −2.02991 | + | 3.51590i | −0.0697485 | + | 0.120808i | ||||
\(848\) | −5.71017 | + | 9.89031i | −0.196088 | + | 0.339635i | ||||
\(849\) | 7.98355 | + | 13.8279i | 0.273995 | + | 0.474573i | ||||
\(850\) | −133.841 | −4.59072 | ||||||||
\(851\) | 3.94860 | + | 6.83917i | 0.135356 | + | 0.234444i | ||||
\(852\) | −6.83819 | − | 11.8441i | −0.234273 | − | 0.405772i | ||||
\(853\) | −13.8312 | −0.473572 | −0.236786 | − | 0.971562i | \(-0.576094\pi\) | ||||
−0.236786 | + | 0.971562i | \(0.576094\pi\) | |||||||
\(854\) | −70.7754 | − | 122.587i | −2.42188 | − | 4.19482i | ||||
\(855\) | 10.9107 | − | 18.8978i | 0.373136 | − | 0.646291i | ||||
\(856\) | −27.9725 | + | 48.4498i | −0.956081 | + | 1.65598i | ||||
\(857\) | 43.9275 | 1.50054 | 0.750268 | − | 0.661134i | \(-0.229924\pi\) | ||||
0.750268 | + | 0.661134i | \(0.229924\pi\) | |||||||
\(858\) | −4.67304 | − | 7.26416i | −0.159535 | − | 0.247994i | ||||
\(859\) | 34.0142 | 1.16055 | 0.580275 | − | 0.814421i | \(-0.302945\pi\) | ||||
0.580275 | + | 0.814421i | \(0.302945\pi\) | |||||||
\(860\) | 22.2694 | − | 38.5717i | 0.759379 | − | 1.31528i | ||||
\(861\) | 11.1623 | − | 19.3336i | 0.380409 | − | 0.658887i | ||||
\(862\) | −18.5941 | − | 32.2059i | −0.633318 | − | 1.09694i | ||||
\(863\) | −11.8884 | −0.404686 | −0.202343 | − | 0.979315i | \(-0.564856\pi\) | ||||
−0.202343 | + | 0.979315i | \(0.564856\pi\) | |||||||
\(864\) | 1.16945 | + | 2.02555i | 0.0397856 | + | 0.0689107i | ||||
\(865\) | −30.6959 | − | 53.1668i | −1.04369 | − | 1.80773i | ||||
\(866\) | 8.16948 | 0.277610 | ||||||||
\(867\) | −8.39847 | − | 14.5466i | −0.285227 | − | 0.494028i | ||||
\(868\) | 7.99550 | − | 13.8486i | 0.271385 | − | 0.470053i | ||||
\(869\) | −1.68378 | + | 2.91640i | −0.0571184 | + | 0.0989319i | ||||
\(870\) | 30.8074 | 1.04447 | ||||||||
\(871\) | 12.1197 | − | 0.582825i | 0.410659 | − | 0.0197483i | ||||
\(872\) | −54.5381 | −1.84689 | ||||||||
\(873\) | 9.68010 | − | 16.7664i | 0.327622 | − | 0.567457i | ||||
\(874\) | −35.8632 | + | 62.1169i | −1.21309 | + | 2.10114i | ||||
\(875\) | −35.7716 | − | 61.9583i | −1.20930 | − | 2.09457i | ||||
\(876\) | −0.0236627 | −0.000799489 | ||||||||
\(877\) | 16.4261 | + | 28.4509i | 0.554672 | + | 0.960719i | 0.997929 | + | 0.0643249i | \(0.0204894\pi\) |
−0.443257 | + | 0.896394i | \(0.646177\pi\) | |||||||
\(878\) | 11.5819 | + | 20.0605i | 0.390871 | + | 0.677008i | ||||
\(879\) | 19.8973 | 0.671119 | ||||||||
\(880\) | 4.78061 | + | 8.28026i | 0.161154 | + | 0.279127i | ||||
\(881\) | 7.75408 | − | 13.4305i | 0.261242 | − | 0.452484i | −0.705330 | − | 0.708879i | \(-0.749201\pi\) |
0.966572 | + | 0.256395i | \(0.0825347\pi\) | |||||||
\(882\) | −11.3576 | + | 19.6720i | −0.382431 | + | 0.662391i | ||||
\(883\) | 18.1363 | 0.610336 | 0.305168 | − | 0.952299i | \(-0.401287\pi\) | ||||
0.305168 | + | 0.952299i | \(0.401287\pi\) | |||||||
\(884\) | 78.2797 | − | 3.76441i | 2.63283 | − | 0.126611i | ||||
\(885\) | 15.3870 | 0.517227 | ||||||||
\(886\) | 1.48176 | − | 2.56648i | 0.0497806 | − | 0.0862225i | ||||
\(887\) | −14.3402 | + | 24.8379i | −0.481497 | + | 0.833977i | −0.999774 | − | 0.0212357i | \(-0.993240\pi\) |
0.518278 | + | 0.855212i | \(0.326573\pi\) | |||||||
\(888\) | −3.13623 | − | 5.43210i | −0.105245 | − | 0.182289i | ||||
\(889\) | 52.4501 | 1.75912 | ||||||||
\(890\) | 59.6342 | + | 103.289i | 1.99894 | + | 3.46227i | ||||
\(891\) | 0.500000 | + | 0.866025i | 0.0167506 | + | 0.0290129i | ||||
\(892\) | 12.7202 | 0.425904 | ||||||||
\(893\) | 14.1866 | + | 24.5719i | 0.474736 | + | 0.822267i | ||||
\(894\) | −19.3820 | + | 33.5707i | −0.648232 | + | 1.12277i | ||||
\(895\) | −1.80832 | + | 3.13210i | −0.0604454 | + | 0.104694i | ||||
\(896\) | −84.1581 | −2.81152 | ||||||||
\(897\) | −8.65737 | + | 16.8116i | −0.289061 | + | 0.561324i | ||||
\(898\) | −5.21128 | −0.173903 | ||||||||
\(899\) | 1.77219 | − | 3.06953i | 0.0591060 | − | 0.102375i | ||||
\(900\) | −17.9659 | + | 31.1178i | −0.598863 | + | 1.03726i | ||||
\(901\) | 13.2710 | + | 22.9861i | 0.442122 | + | 0.765778i | ||||
\(902\) | 13.1731 | 0.438617 | ||||||||
\(903\) | 6.32621 | + | 10.9573i | 0.210523 | + | 0.364637i | ||||
\(904\) | 20.2546 | + | 35.0820i | 0.673658 | + | 1.16681i | ||||
\(905\) | −44.7667 | −1.48810 | ||||||||
\(906\) | 2.42329 | + | 4.19726i | 0.0805083 | + | 0.139445i | ||||
\(907\) | 5.43056 | − | 9.40601i | 0.180319 | − | 0.312321i | −0.761670 | − | 0.647965i | \(-0.775620\pi\) |
0.941989 | + | 0.335643i | \(0.108954\pi\) | |||||||
\(908\) | 7.42154 | − | 12.8545i | 0.246292 | − | 0.426591i | ||||
\(909\) | 2.38083 | 0.0789673 | ||||||||
\(910\) | 72.5163 | + | 112.725i | 2.40389 | + | 3.73681i | ||||
\(911\) | 20.5377 | 0.680445 | 0.340223 | − | 0.940345i | \(-0.389498\pi\) | ||||
0.340223 | + | 0.940345i | \(0.389498\pi\) | |||||||
\(912\) | 7.14009 | − | 12.3670i | 0.236432 | − | 0.409512i | ||||
\(913\) | 4.46344 | − | 7.73091i | 0.147718 | − | 0.255856i | ||||
\(914\) | 28.1069 | + | 48.6827i | 0.929695 | + | 1.61028i | ||||
\(915\) | 55.6317 | 1.83913 | ||||||||
\(916\) | −1.84917 | − | 3.20286i | −0.0610984 | − | 0.105826i | ||||
\(917\) | 10.1221 | + | 17.5319i | 0.334260 | + | 0.578956i | ||||
\(918\) | −13.9268 | −0.459653 | ||||||||
\(919\) | −0.543417 | − | 0.941227i | −0.0179257 | − | 0.0310482i | 0.856923 | − | 0.515444i | \(-0.172373\pi\) |
−0.874849 | + | 0.484396i | \(0.839040\pi\) | |||||||
\(920\) | 41.7537 | − | 72.3196i | 1.37658 | − | 2.38431i | ||||
\(921\) | −5.17288 | + | 8.95969i | −0.170452 | + | 0.295232i | ||||
\(922\) | 27.5819 | 0.908362 | ||||||||
\(923\) | 6.03812 | − | 11.7253i | 0.198747 | − | 0.385944i | ||||
\(924\) | −15.1791 | −0.499356 | ||||||||
\(925\) | −7.23546 | + | 12.5322i | −0.237900 | + | 0.412056i | ||||
\(926\) | 13.8410 | − | 23.9732i | 0.454842 | − | 0.787809i | ||||
\(927\) | 5.34207 | + | 9.25274i | 0.175457 | + | 0.303900i | ||||
\(928\) | −7.86910 | −0.258316 | ||||||||
\(929\) | −24.7157 | − | 42.8089i | −0.810896 | − | 1.40451i | −0.912237 | − | 0.409662i | \(-0.865647\pi\) |
0.101341 | − | 0.994852i | \(-0.467687\pi\) | |||||||
\(930\) | 4.82328 | + | 8.35416i | 0.158162 | + | 0.273944i | ||||
\(931\) | −54.1322 | −1.77411 | ||||||||
\(932\) | 27.9751 | + | 48.4543i | 0.916355 | + | 1.58717i | ||||
\(933\) | 9.83134 | − | 17.0284i | 0.321864 | − | 0.557484i | ||||
\(934\) | 1.04864 | − | 1.81630i | 0.0343126 | − | 0.0594311i | ||||
\(935\) | 22.2213 | 0.726713 | ||||||||
\(936\) | 6.87623 | − | 13.3529i | 0.224757 | − | 0.436452i | ||||
\(937\) | 27.6967 | 0.904811 | 0.452405 | − | 0.891812i | \(-0.350566\pi\) | ||||
0.452405 | + | 0.891812i | \(0.350566\pi\) | |||||||
\(938\) | 16.3648 | − | 28.3446i | 0.534328 | − | 0.925484i | ||||
\(939\) | 8.63541 | − | 14.9570i | 0.281806 | − | 0.488102i | ||||
\(940\) | −35.5138 | − | 61.5117i | −1.15833 | − | 2.00629i | ||||
\(941\) | 35.6961 | 1.16366 | 0.581829 | − | 0.813311i | \(-0.302337\pi\) | ||||
0.581829 | + | 0.813311i | \(0.302337\pi\) | |||||||
\(942\) | 21.9820 | + | 38.0740i | 0.716214 | + | 1.24052i | ||||
\(943\) | −14.4198 | − | 24.9759i | −0.469575 | − | 0.813328i | ||||
\(944\) | 10.0694 | 0.327733 | ||||||||
\(945\) | −7.75901 | − | 13.4390i | −0.252401 | − | 0.437171i | ||||
\(946\) | −3.73294 | + | 6.46563i | −0.121368 | + | 0.210216i | ||||
\(947\) | −7.71754 | + | 13.3672i | −0.250786 | + | 0.434375i | −0.963743 | − | 0.266834i | \(-0.914023\pi\) |
0.712956 | + | 0.701209i | \(0.247356\pi\) | |||||||
\(948\) | −12.5909 | −0.408933 | ||||||||
\(949\) | −0.0123456 | − | 0.0191910i | −0.000400754 | − | 0.000622965i | ||||
\(950\) | −131.432 | −4.26423 | ||||||||
\(951\) | −4.46867 | + | 7.73997i | −0.144907 | + | 0.250986i | ||||
\(952\) | 49.1581 | − | 85.1443i | 1.59322 | − | 2.75954i | ||||
\(953\) | 8.11602 | + | 14.0574i | 0.262904 | + | 0.455363i | 0.967012 | − | 0.254730i | \(-0.0819865\pi\) |
−0.704109 | + | 0.710092i | \(0.748653\pi\) | |||||||
\(954\) | 10.9373 | 0.354108 | ||||||||
\(955\) | 20.3110 | + | 35.1798i | 0.657250 | + | 1.13839i | ||||
\(956\) | −36.7340 | − | 63.6251i | −1.18806 | − | 2.05778i | ||||
\(957\) | −3.36443 | −0.108757 | ||||||||
\(958\) | 27.8360 | + | 48.2134i | 0.899342 | + | 1.55771i | ||||
\(959\) | 19.5166 | − | 33.8038i | 0.630225 | − | 1.09158i | ||||
\(960\) | 20.2697 | − | 35.1081i | 0.654200 | − | 1.13311i | ||||
\(961\) | −29.8902 | −0.964199 | ||||||||
\(962\) | 5.95445 | − | 11.5629i | 0.191979 | − | 0.372801i | ||||
\(963\) | 13.4302 | 0.432781 | ||||||||
\(964\) | 17.2337 | − | 29.8496i | 0.555060 | − | 0.961391i | ||||
\(965\) | 45.8031 | − | 79.3332i | 1.47445 | − | 2.55383i | ||||
\(966\) | 25.5038 | + | 44.1739i | 0.820571 | + | 1.42127i | ||||
\(967\) | 49.6654 | 1.59713 | 0.798567 | − | 0.601907i | \(-0.205592\pi\) | ||||
0.798567 | + | 0.601907i | \(0.205592\pi\) | |||||||
\(968\) | −2.08281 | − | 3.60753i | −0.0669441 | − | 0.115951i | ||||
\(969\) | −16.5943 | − | 28.7422i | −0.533086 | − | 0.923333i | ||||
\(970\) | −177.277 | −5.69203 | ||||||||
\(971\) | −22.3511 | − | 38.7133i | −0.717282 | − | 1.24237i | −0.962073 | − | 0.272792i | \(-0.912053\pi\) |
0.244791 | − | 0.969576i | \(-0.421281\pi\) | |||||||
\(972\) | −1.86943 | + | 3.23795i | −0.0599621 | + | 0.103857i | ||||
\(973\) | −33.6867 | + | 58.3470i | −1.07995 | + | 1.87052i | ||||
\(974\) | 75.4782 | 2.41848 | ||||||||
\(975\) | −34.6106 | + | 1.66440i | −1.10842 | + | 0.0533033i | ||||
\(976\) | 36.4062 | 1.16533 | ||||||||
\(977\) | −17.5389 | + | 30.3783i | −0.561120 | + | 0.971889i | 0.436279 | + | 0.899812i | \(0.356296\pi\) |
−0.997399 | + | 0.0720772i | \(0.977037\pi\) | |||||||
\(978\) | −24.1289 | + | 41.7925i | −0.771558 | + | 1.33638i | ||||
\(979\) | −6.51256 | − | 11.2801i | −0.208142 | − | 0.360513i | ||||
\(980\) | 135.511 | 4.32874 | ||||||||
\(981\) | 6.54622 | + | 11.3384i | 0.209005 | + | 0.362007i | ||||
\(982\) | 8.86691 | + | 15.3579i | 0.282954 | + | 0.490091i | ||||
\(983\) | 24.6519 | 0.786272 | 0.393136 | − | 0.919480i | \(-0.371390\pi\) | ||||
0.393136 | + | 0.919480i | \(0.371390\pi\) | |||||||
\(984\) | 11.4532 | + | 19.8375i | 0.365113 | + | 0.632395i | ||||
\(985\) | −29.8188 | + | 51.6476i | −0.950105 | + | 1.64563i | ||||
\(986\) | 23.4279 | − | 40.5784i | 0.746097 | − | 1.29228i | ||||
\(987\) | 20.1773 | 0.642251 | ||||||||
\(988\) | 76.8707 | − | 3.69666i | 2.44558 | − | 0.117606i | ||||
\(989\) | 16.3449 | 0.519738 | ||||||||
\(990\) | 4.57839 | − | 7.93001i | 0.145511 | − | 0.252032i | ||||
\(991\) | −0.481199 | + | 0.833461i | −0.0152858 | + | 0.0264758i | −0.873567 | − | 0.486704i | \(-0.838199\pi\) |
0.858281 | + | 0.513179i | \(0.171532\pi\) | |||||||
\(992\) | −1.23200 | − | 2.13389i | −0.0391162 | − | 0.0677512i | ||||
\(993\) | −13.8093 | −0.438225 | ||||||||
\(994\) | −17.7877 | − | 30.8093i | −0.564192 | − | 0.977210i | ||||
\(995\) | 12.9919 | + | 22.5026i | 0.411870 | + | 0.713379i | ||||
\(996\) | 33.3765 | 1.05757 | ||||||||
\(997\) | −21.7284 | − | 37.6347i | −0.688145 | − | 1.19190i | −0.972437 | − | 0.233165i | \(-0.925092\pi\) |
0.284292 | − | 0.958738i | \(-0.408241\pi\) | |||||||
\(998\) | −47.8486 | + | 82.8762i | −1.51462 | + | 2.62340i | ||||
\(999\) | −0.752883 | + | 1.30403i | −0.0238202 | + | 0.0412578i |
(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 | 429.2.i.c.100.1 | ✓ | 10 | |
13.3 | even | 3 | inner | 429.2.i.c.133.1 | yes | 10 | |
13.4 | even | 6 | 5577.2.a.p.1.1 | 5 | |||
13.9 | even | 3 | 5577.2.a.v.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.i.c.100.1 | ✓ | 10 | 1.1 | even | 1 | trivial | |
429.2.i.c.133.1 | yes | 10 | 13.3 | even | 3 | inner | |
5577.2.a.p.1.1 | 5 | 13.4 | even | 6 | |||
5577.2.a.v.1.5 | 5 | 13.9 | even | 3 |