Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [117,2,Mod(43,117)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(117, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("117.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 117 = 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 117.r (of order \(6\), 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: | \(0.934249703649\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 43.8 | ||
Character | \(\chi\) | \(=\) | 117.43 |
Dual form | 117.2.r.b.49.8 |
$q$-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 \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(92\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.677814 | − | 0.391336i | 0.479287 | − | 0.276716i | −0.240832 | − | 0.970567i | \(-0.577420\pi\) |
0.720119 | + | 0.693850i | \(0.244087\pi\) | |||||||
\(3\) | 1.22535 | + | 1.22414i | 0.707454 | + | 0.706760i | ||||
\(4\) | −0.693712 | + | 1.20154i | −0.346856 | + | 0.600772i | ||||
\(5\) | −0.0536139 | + | 0.0309540i | −0.0239769 | + | 0.0138431i | −0.511941 | − | 0.859021i | \(-0.671073\pi\) |
0.487964 | + | 0.872864i | \(0.337740\pi\) | |||||||
\(6\) | 1.30961 | + | 0.350219i | 0.534645 | + | 0.142976i | ||||
\(7\) | − | 3.75567i | − | 1.41951i | −0.704449 | − | 0.709754i | \(-0.748806\pi\) | ||
0.704449 | − | 0.709754i | \(-0.251194\pi\) | |||||||
\(8\) | 2.65124i | 0.937356i | ||||||||
\(9\) | 0.00294547 | + | 3.00000i | 0.000981824 | + | 1.00000i | ||||
\(10\) | −0.0242268 | + | 0.0419621i | −0.00766120 | + | 0.0132696i | ||||
\(11\) | −1.11071 | + | 0.641267i | −0.334891 | + | 0.193349i | −0.658010 | − | 0.753009i | \(-0.728602\pi\) |
0.323120 | + | 0.946358i | \(0.395268\pi\) | |||||||
\(12\) | −2.32090 | + | 0.623105i | −0.669986 | + | 0.179875i | ||||
\(13\) | 1.65180 | − | 3.20493i | 0.458127 | − | 0.888887i | ||||
\(14\) | −1.46973 | − | 2.54564i | −0.392801 | − | 0.680352i | ||||
\(15\) | −0.103588 | − | 0.0277018i | −0.0267462 | − | 0.00715256i | ||||
\(16\) | −0.349898 | − | 0.606041i | −0.0874746 | − | 0.151510i | ||||
\(17\) | −2.74383 | − | 4.75245i | −0.665476 | − | 1.15264i | −0.979156 | − | 0.203109i | \(-0.934895\pi\) |
0.313681 | − | 0.949529i | \(-0.398438\pi\) | |||||||
\(18\) | 1.17600 | + | 2.03229i | 0.277187 | + | 0.479015i | ||||
\(19\) | 2.72231 | − | 1.57173i | 0.624540 | − | 0.360579i | −0.154094 | − | 0.988056i | \(-0.549246\pi\) |
0.778635 | + | 0.627478i | \(0.215913\pi\) | |||||||
\(20\) | − | 0.0858927i | − | 0.0192062i | ||||||
\(21\) | 4.59748 | − | 4.60199i | 1.00325 | − | 1.00424i | ||||
\(22\) | −0.501902 | + | 0.869319i | −0.107006 | + | 0.185339i | ||||
\(23\) | −5.65979 | −1.18015 | −0.590074 | − | 0.807349i | \(-0.700901\pi\) | ||||
−0.590074 | + | 0.807349i | \(0.700901\pi\) | |||||||
\(24\) | −3.24550 | + | 3.24869i | −0.662485 | + | 0.663136i | ||||
\(25\) | −2.49808 | + | 4.32681i | −0.499617 | + | 0.865362i | ||||
\(26\) | −0.134590 | − | 2.81875i | −0.0263953 | − | 0.552803i | ||||
\(27\) | −3.66882 | + | 3.67964i | −0.706065 | + | 0.708147i | ||||
\(28\) | 4.51260 | + | 2.60535i | 0.852802 | + | 0.492365i | ||||
\(29\) | 3.56722 | + | 6.17860i | 0.662416 | + | 1.14734i | 0.979979 | + | 0.199101i | \(0.0638021\pi\) |
−0.317563 | + | 0.948237i | \(0.602865\pi\) | |||||||
\(30\) | −0.0810539 | + | 0.0217610i | −0.0147983 | + | 0.00397299i | ||||
\(31\) | 3.62246 | − | 2.09143i | 0.650613 | − | 0.375632i | −0.138078 | − | 0.990421i | \(-0.544092\pi\) |
0.788691 | + | 0.614790i | \(0.210759\pi\) | |||||||
\(32\) | −5.06642 | − | 2.92510i | −0.895625 | − | 0.517089i | ||||
\(33\) | −2.14600 | − | 0.573891i | −0.373571 | − | 0.0999015i | ||||
\(34\) | −3.71961 | − | 2.14752i | −0.637907 | − | 0.368296i | ||||
\(35\) | 0.116253 | + | 0.201356i | 0.0196503 | + | 0.0340354i | ||||
\(36\) | −3.60668 | − | 2.07760i | −0.601113 | − | 0.346266i | ||||
\(37\) | −4.03923 | − | 2.33205i | −0.664045 | − | 0.383386i | 0.129772 | − | 0.991544i | \(-0.458576\pi\) |
−0.793816 | + | 0.608158i | \(0.791909\pi\) | |||||||
\(38\) | 1.23015 | − | 2.13067i | 0.199556 | − | 0.345641i | ||||
\(39\) | 5.94732 | − | 1.90510i | 0.952333 | − | 0.305061i | ||||
\(40\) | −0.0820666 | − | 0.142143i | −0.0129759 | − | 0.0224749i | ||||
\(41\) | 9.88981i | 1.54453i | 0.635302 | + | 0.772264i | \(0.280876\pi\) | ||||
−0.635302 | + | 0.772264i | \(0.719124\pi\) | |||||||
\(42\) | 1.31531 | − | 4.91845i | 0.202956 | − | 0.758934i | ||||
\(43\) | 4.22761 | 0.644704 | 0.322352 | − | 0.946620i | \(-0.395526\pi\) | ||||
0.322352 | + | 0.946620i | \(0.395526\pi\) | |||||||
\(44\) | − | 1.77942i | − | 0.268257i | ||||||
\(45\) | −0.0930199 | − | 0.160750i | −0.0138666 | − | 0.0239633i | ||||
\(46\) | −3.83628 | + | 2.21488i | −0.565629 | + | 0.326566i | ||||
\(47\) | 2.73495 | + | 1.57902i | 0.398933 | + | 0.230324i | 0.686024 | − | 0.727579i | \(-0.259355\pi\) |
−0.287090 | + | 0.957904i | \(0.592688\pi\) | |||||||
\(48\) | 0.313135 | − | 1.17094i | 0.0451972 | − | 0.169010i | ||||
\(49\) | −7.10504 | −1.01501 | ||||||||
\(50\) | 3.91036i | 0.553008i | ||||||||
\(51\) | 2.45554 | − | 9.18223i | 0.343844 | − | 1.28577i | ||||
\(52\) | 2.70499 | + | 4.20801i | 0.375115 | + | 0.583546i | ||||
\(53\) | −0.752963 | −0.103427 | −0.0517137 | − | 0.998662i | \(-0.516468\pi\) | ||||
−0.0517137 | + | 0.998662i | \(0.516468\pi\) | |||||||
\(54\) | −1.04680 | + | 3.92985i | −0.142451 | + | 0.534785i | ||||
\(55\) | 0.0396996 | − | 0.0687616i | 0.00535309 | − | 0.00927182i | ||||
\(56\) | 9.95718 | 1.33058 | ||||||||
\(57\) | 5.25979 | + | 1.40659i | 0.696676 | + | 0.186307i | ||||
\(58\) | 4.83582 | + | 2.79196i | 0.634974 | + | 0.366602i | ||||
\(59\) | −0.310908 | − | 0.179503i | −0.0404767 | − | 0.0233692i | 0.479625 | − | 0.877474i | \(-0.340773\pi\) |
−0.520102 | + | 0.854104i | \(0.674106\pi\) | |||||||
\(60\) | 0.105145 | − | 0.105248i | 0.0135742 | − | 0.0135875i | ||||
\(61\) | 1.65095 | 0.211382 | 0.105691 | − | 0.994399i | \(-0.466295\pi\) | ||||
0.105691 | + | 0.994399i | \(0.466295\pi\) | |||||||
\(62\) | 1.63690 | − | 2.83520i | 0.207887 | − | 0.360071i | ||||
\(63\) | 11.2670 | − | 0.0110622i | 1.41951 | − | 0.00139371i | ||||
\(64\) | −3.17919 | −0.397399 | ||||||||
\(65\) | 0.0106459 | + | 0.222958i | 0.00132046 | + | 0.0276546i | ||||
\(66\) | −1.67917 | + | 0.450817i | −0.206692 | + | 0.0554917i | ||||
\(67\) | 1.65785i | 0.202539i | 0.994859 | + | 0.101269i | \(0.0322904\pi\) | ||||
−0.994859 | + | 0.101269i | \(0.967710\pi\) | |||||||
\(68\) | 7.61370 | 0.923297 | ||||||||
\(69\) | −6.93520 | − | 6.92840i | −0.834900 | − | 0.834081i | ||||
\(70\) | 0.157596 | + | 0.0909879i | 0.0188363 | + | 0.0108751i | ||||
\(71\) | 11.3838 | − | 6.57246i | 1.35101 | − | 0.780008i | 0.362622 | − | 0.931936i | \(-0.381882\pi\) |
0.988391 | + | 0.151929i | \(0.0485484\pi\) | |||||||
\(72\) | −7.95372 | + | 0.00780916i | −0.937355 | + | 0.000920319i | ||||
\(73\) | 6.09030i | 0.712816i | 0.934330 | + | 0.356408i | \(0.115999\pi\) | ||||
−0.934330 | + | 0.356408i | \(0.884001\pi\) | |||||||
\(74\) | −3.65046 | −0.424357 | ||||||||
\(75\) | −8.35765 | + | 2.24382i | −0.965058 | + | 0.259094i | ||||
\(76\) | 4.36130i | 0.500276i | ||||||||
\(77\) | 2.40838 | + | 4.17145i | 0.274461 | + | 0.475380i | ||||
\(78\) | 3.28564 | − | 3.61870i | 0.372025 | − | 0.409738i | ||||
\(79\) | −0.616191 | + | 1.06727i | −0.0693269 | + | 0.120078i | −0.898605 | − | 0.438758i | \(-0.855418\pi\) |
0.829278 | + | 0.558836i | \(0.188752\pi\) | |||||||
\(80\) | 0.0375188 | + | 0.0216615i | 0.00419473 | + | 0.00242183i | ||||
\(81\) | −8.99998 | + | 0.0176728i | −0.999998 | + | 0.00196365i | ||||
\(82\) | 3.87024 | + | 6.70345i | 0.427396 | + | 0.740272i | ||||
\(83\) | −11.0538 | − | 6.38193i | −1.21332 | − | 0.700508i | −0.249835 | − | 0.968288i | \(-0.580376\pi\) |
−0.963480 | + | 0.267781i | \(0.913710\pi\) | |||||||
\(84\) | 2.34017 | + | 8.71653i | 0.255334 | + | 0.951052i | ||||
\(85\) | 0.294215 | + | 0.169865i | 0.0319120 | + | 0.0184244i | ||||
\(86\) | 2.86553 | − | 1.65442i | 0.308998 | − | 0.178400i | ||||
\(87\) | −3.19242 | + | 11.9377i | −0.342263 | + | 1.27986i | ||||
\(88\) | −1.70015 | − | 2.94475i | −0.181237 | − | 0.313912i | ||||
\(89\) | 1.30142 | + | 0.751374i | 0.137950 | + | 0.0796455i | 0.567387 | − | 0.823452i | \(-0.307955\pi\) |
−0.429437 | + | 0.903097i | \(0.641288\pi\) | |||||||
\(90\) | −0.125958 | − | 0.0725569i | −0.0132771 | − | 0.00764816i | ||||
\(91\) | −12.0366 | − | 6.20361i | −1.26178 | − | 0.650315i | ||||
\(92\) | 3.92627 | − | 6.80049i | 0.409342 | − | 0.709000i | ||||
\(93\) | 6.99898 | + | 1.87169i | 0.725760 | + | 0.194085i | ||||
\(94\) | 2.47172 | 0.254938 | ||||||||
\(95\) | −0.0973024 | + | 0.168533i | −0.00998301 | + | 0.0172911i | ||||
\(96\) | −2.62738 | − | 9.78628i | −0.268155 | − | 0.998808i | ||||
\(97\) | 10.0235i | 1.01773i | 0.860847 | + | 0.508865i | \(0.169935\pi\) | ||||
−0.860847 | + | 0.508865i | \(0.830065\pi\) | |||||||
\(98\) | −4.81589 | + | 2.78046i | −0.486479 | + | 0.280869i | ||||
\(99\) | −1.92707 | − | 3.33023i | −0.193678 | − | 0.334701i | ||||
\(100\) | −3.46590 | − | 6.00312i | −0.346590 | − | 0.600312i | ||||
\(101\) | 8.60026 | + | 14.8961i | 0.855758 | + | 1.48222i | 0.875940 | + | 0.482420i | \(0.160242\pi\) |
−0.0201819 | + | 0.999796i | \(0.506425\pi\) | |||||||
\(102\) | −1.92894 | − | 7.18478i | −0.190993 | − | 0.711399i | ||||
\(103\) | −8.82611 | − | 15.2873i | −0.869662 | − | 1.50630i | −0.862342 | − | 0.506326i | \(-0.831003\pi\) |
−0.00732055 | − | 0.999973i | \(-0.502330\pi\) | |||||||
\(104\) | 8.49704 | + | 4.37932i | 0.833203 | + | 0.429428i | ||||
\(105\) | −0.104039 | + | 0.389041i | −0.0101531 | + | 0.0379665i | ||||
\(106\) | −0.510369 | + | 0.294661i | −0.0495714 | + | 0.0286201i | ||||
\(107\) | 5.14019 | − | 8.90307i | 0.496921 | − | 0.860692i | −0.503073 | − | 0.864244i | \(-0.667797\pi\) |
0.999994 | + | 0.00355197i | \(0.00113063\pi\) | |||||||
\(108\) | −1.87615 | − | 6.96086i | −0.180533 | − | 0.669809i | ||||
\(109\) | − | 7.16152i | − | 0.685949i | −0.939345 | − | 0.342975i | \(-0.888566\pi\) | ||
0.939345 | − | 0.342975i | \(-0.111434\pi\) | |||||||
\(110\) | − | 0.0621435i | − | 0.00592515i | ||||||
\(111\) | −2.09469 | − | 7.80216i | −0.198819 | − | 0.740548i | ||||
\(112\) | −2.27609 | + | 1.31410i | −0.215070 | + | 0.124171i | ||||
\(113\) | −1.65216 | + | 2.86162i | −0.155422 | + | 0.269199i | −0.933213 | − | 0.359325i | \(-0.883007\pi\) |
0.777791 | + | 0.628523i | \(0.216340\pi\) | |||||||
\(114\) | 4.11560 | − | 1.10494i | 0.385462 | − | 0.103487i | ||||
\(115\) | 0.303443 | − | 0.175193i | 0.0282963 | − | 0.0163368i | ||||
\(116\) | −9.89849 | −0.919052 | ||||||||
\(117\) | 9.61964 | + | 4.94596i | 0.889336 | + | 0.457254i | ||||
\(118\) | −0.280983 | −0.0258666 | ||||||||
\(119\) | −17.8486 | + | 10.3049i | −1.63618 | + | 0.944649i | ||||
\(120\) | 0.0734441 | − | 0.274636i | 0.00670449 | − | 0.0250707i | ||||
\(121\) | −4.67755 | + | 8.10176i | −0.425232 | + | 0.736524i | ||||
\(122\) | 1.11903 | − | 0.646075i | 0.101313 | − | 0.0584929i | ||||
\(123\) | −12.1065 | + | 12.1184i | −1.09161 | + | 1.09268i | ||||
\(124\) | 5.80340i | 0.521161i | ||||||||
\(125\) | − | 0.618843i | − | 0.0553510i | ||||||
\(126\) | 7.63260 | − | 4.41668i | 0.679966 | − | 0.393469i | ||||
\(127\) | −3.56802 | + | 6.18000i | −0.316611 | + | 0.548386i | −0.979779 | − | 0.200085i | \(-0.935878\pi\) |
0.663168 | + | 0.748471i | \(0.269212\pi\) | |||||||
\(128\) | 7.97794 | − | 4.60606i | 0.705157 | − | 0.407122i | ||||
\(129\) | 5.18028 | + | 5.17520i | 0.456099 | + | 0.455651i | ||||
\(130\) | 0.0944676 | + | 0.146958i | 0.00828536 | + | 0.0128891i | ||||
\(131\) | −9.76000 | − | 16.9048i | −0.852735 | − | 1.47698i | −0.878730 | − | 0.477319i | \(-0.841609\pi\) |
0.0259946 | − | 0.999662i | \(-0.491725\pi\) | |||||||
\(132\) | 2.17826 | − | 2.18040i | 0.189594 | − | 0.189780i | ||||
\(133\) | −5.90288 | − | 10.2241i | −0.511844 | − | 0.886541i | ||||
\(134\) | 0.648777 | + | 1.12372i | 0.0560458 | + | 0.0970742i | ||||
\(135\) | 0.0828001 | − | 0.310845i | 0.00712630 | − | 0.0267532i | ||||
\(136\) | 12.5999 | − | 7.27455i | 1.08043 | − | 0.623787i | ||||
\(137\) | − | 8.32371i | − | 0.711143i | −0.934649 | − | 0.355571i | \(-0.884286\pi\) | ||
0.934649 | − | 0.355571i | \(-0.115714\pi\) | |||||||
\(138\) | −7.41211 | − | 1.98217i | −0.630960 | − | 0.168733i | ||||
\(139\) | −1.91239 | + | 3.31236i | −0.162207 | + | 0.280951i | −0.935660 | − | 0.352903i | \(-0.885195\pi\) |
0.773453 | + | 0.633854i | \(0.218528\pi\) | |||||||
\(140\) | −0.322584 | −0.0272634 | ||||||||
\(141\) | 1.41831 | + | 5.28282i | 0.119443 | + | 0.444894i | ||||
\(142\) | 5.14408 | − | 8.90981i | 0.431682 | − | 0.747695i | ||||
\(143\) | 0.220548 | + | 4.61898i | 0.0184431 | + | 0.386258i | ||||
\(144\) | 1.81709 | − | 1.05148i | 0.151424 | − | 0.0876233i | ||||
\(145\) | −0.382505 | − | 0.220839i | −0.0317653 | − | 0.0183397i | ||||
\(146\) | 2.38335 | + | 4.12809i | 0.197248 | + | 0.341643i | ||||
\(147\) | −8.70613 | − | 8.69759i | −0.718070 | − | 0.717365i | ||||
\(148\) | 5.60412 | − | 3.23554i | 0.460656 | − | 0.265960i | ||||
\(149\) | −17.3709 | − | 10.0291i | −1.42308 | − | 0.821614i | −0.426517 | − | 0.904480i | \(-0.640260\pi\) |
−0.996561 | + | 0.0828653i | \(0.973593\pi\) | |||||||
\(150\) | −4.78684 | + | 4.79154i | −0.390844 | + | 0.391228i | ||||
\(151\) | 12.0273 | + | 6.94396i | 0.978767 | + | 0.565092i | 0.901898 | − | 0.431950i | \(-0.142174\pi\) |
0.0768696 | + | 0.997041i | \(0.475507\pi\) | |||||||
\(152\) | 4.16702 | + | 7.21750i | 0.337990 | + | 0.585416i | ||||
\(153\) | 14.2493 | − | 8.24547i | 1.15198 | − | 0.666607i | ||||
\(154\) | 3.26487 | + | 1.88498i | 0.263091 | + | 0.151896i | ||||
\(155\) | −0.129476 | + | 0.224259i | −0.0103998 | + | 0.0180129i | ||||
\(156\) | −1.83666 | + | 8.46756i | −0.147050 | + | 0.677948i | ||||
\(157\) | 7.95334 | + | 13.7756i | 0.634746 | + | 1.09941i | 0.986569 | + | 0.163346i | \(0.0522286\pi\) |
−0.351823 | + | 0.936067i | \(0.614438\pi\) | |||||||
\(158\) | 0.964551i | 0.0767355i | ||||||||
\(159\) | −0.922640 | − | 0.921735i | −0.0731701 | − | 0.0730983i | ||||
\(160\) | 0.362174 | 0.0286324 | ||||||||
\(161\) | 21.2563i | 1.67523i | ||||||||
\(162\) | −6.09340 | + | 3.53400i | −0.478742 | + | 0.277657i | ||||
\(163\) | 11.4205 | − | 6.59365i | 0.894525 | − | 0.516454i | 0.0191051 | − | 0.999817i | \(-0.493918\pi\) |
0.875420 | + | 0.483363i | \(0.160585\pi\) | |||||||
\(164\) | −11.8830 | − | 6.86068i | −0.927910 | − | 0.535729i | ||||
\(165\) | 0.132820 | − | 0.0356589i | 0.0103400 | − | 0.00277604i | ||||
\(166\) | −9.98991 | −0.775368 | ||||||||
\(167\) | − | 1.34960i | − | 0.104435i | −0.998636 | − | 0.0522177i | \(-0.983371\pi\) | ||
0.998636 | − | 0.0522177i | \(-0.0166290\pi\) | |||||||
\(168\) | 12.2010 | + | 12.1890i | 0.941327 | + | 0.940403i | ||||
\(169\) | −7.54311 | − | 10.5878i | −0.580239 | − | 0.814446i | ||||
\(170\) | 0.265897 | 0.0203934 | ||||||||
\(171\) | 4.72319 | + | 8.16229i | 0.361192 | + | 0.624186i | ||||
\(172\) | −2.93274 | + | 5.07966i | −0.223620 | + | 0.387321i | ||||
\(173\) | 14.7144 | 1.11871 | 0.559356 | − | 0.828927i | \(-0.311048\pi\) | ||||
0.559356 | + | 0.828927i | \(0.311048\pi\) | |||||||
\(174\) | 2.50779 | + | 9.34085i | 0.190115 | + | 0.708128i | ||||
\(175\) | 16.2501 | + | 9.38197i | 1.22839 | + | 0.709210i | ||||
\(176\) | 0.777269 | + | 0.448756i | 0.0585888 | + | 0.0338263i | ||||
\(177\) | −0.161232 | − | 0.600548i | −0.0121190 | − | 0.0451400i | ||||
\(178\) | 1.17616 | 0.0881568 | ||||||||
\(179\) | −2.60130 | + | 4.50559i | −0.194431 | + | 0.336764i | −0.946714 | − | 0.322076i | \(-0.895619\pi\) |
0.752283 | + | 0.658840i | \(0.228953\pi\) | |||||||
\(180\) | 0.257678 | 0.000252995i | 0.0192062 | 1.88571e-5i | ||||||
\(181\) | 10.0948 | 0.750340 | 0.375170 | − | 0.926956i | \(-0.377584\pi\) | ||||
0.375170 | + | 0.926956i | \(0.377584\pi\) | |||||||
\(182\) | −10.5863 | + | 0.505476i | −0.784709 | + | 0.0374684i | ||||
\(183\) | 2.02298 | + | 2.02100i | 0.149543 | + | 0.149396i | ||||
\(184\) | − | 15.0055i | − | 1.10622i | ||||||
\(185\) | 0.288745 | 0.0212289 | ||||||||
\(186\) | 5.47646 | − | 1.47030i | 0.401554 | − | 0.107807i | ||||
\(187\) | 6.09517 | + | 3.51905i | 0.445723 | + | 0.257338i | ||||
\(188\) | −3.79454 | + | 2.19078i | −0.276745 | + | 0.159779i | ||||
\(189\) | 13.8195 | + | 13.7789i | 1.00522 | + | 1.00227i | ||||
\(190\) | 0.152312i | 0.0110499i | ||||||||
\(191\) | −2.71789 | −0.196659 | −0.0983297 | − | 0.995154i | \(-0.531350\pi\) | ||||
−0.0983297 | + | 0.995154i | \(0.531350\pi\) | |||||||
\(192\) | −3.89561 | − | 3.89179i | −0.281141 | − | 0.280865i | ||||
\(193\) | − | 19.0863i | − | 1.37386i | −0.726723 | − | 0.686930i | \(-0.758958\pi\) | ||
0.726723 | − | 0.686930i | \(-0.241042\pi\) | |||||||
\(194\) | 3.92254 | + | 6.79405i | 0.281622 | + | 0.487784i | ||||
\(195\) | −0.259888 | + | 0.286233i | −0.0186110 | + | 0.0204976i | ||||
\(196\) | 4.92885 | − | 8.53702i | 0.352061 | − | 0.609787i | ||||
\(197\) | 1.87976 | + | 1.08528i | 0.133927 | + | 0.0773230i | 0.565467 | − | 0.824771i | \(-0.308696\pi\) |
−0.431539 | + | 0.902094i | \(0.642029\pi\) | |||||||
\(198\) | −2.60943 | − | 1.50314i | −0.185444 | − | 0.106824i | ||||
\(199\) | 5.21774 | + | 9.03739i | 0.369876 | + | 0.640644i | 0.989546 | − | 0.144219i | \(-0.0460669\pi\) |
−0.619670 | + | 0.784862i | \(0.712734\pi\) | |||||||
\(200\) | −11.4714 | − | 6.62302i | −0.811152 | − | 0.468319i | ||||
\(201\) | −2.02945 | + | 2.03144i | −0.143146 | + | 0.143287i | ||||
\(202\) | 11.6588 | + | 6.73118i | 0.820307 | + | 0.473604i | ||||
\(203\) | 23.2048 | − | 13.3973i | 1.62866 | − | 0.940305i | ||||
\(204\) | 9.32942 | + | 9.32027i | 0.653190 | + | 0.652549i | ||||
\(205\) | −0.306129 | − | 0.530231i | −0.0213810 | − | 0.0370330i | ||||
\(206\) | −11.9649 | − | 6.90795i | −0.833635 | − | 0.481300i | ||||
\(207\) | −0.0166708 | − | 16.9794i | −0.00115870 | − | 1.18015i | ||||
\(208\) | −2.52028 | + | 0.120339i | −0.174750 | + | 0.00834399i | ||||
\(209\) | −2.01579 | + | 3.49145i | −0.139435 | + | 0.241509i | ||||
\(210\) | 0.0817270 | + | 0.304411i | 0.00563970 | + | 0.0210064i | ||||
\(211\) | 0.386502 | 0.0266079 | 0.0133039 | − | 0.999911i | \(-0.495765\pi\) | ||||
0.0133039 | + | 0.999911i | \(0.495765\pi\) | |||||||
\(212\) | 0.522340 | − | 0.904719i | 0.0358744 | − | 0.0621363i | ||||
\(213\) | 21.9948 | + | 5.88191i | 1.50706 | + | 0.403022i | ||||
\(214\) | − | 8.04616i | − | 0.550024i | ||||||
\(215\) | −0.226659 | + | 0.130861i | −0.0154580 | + | 0.00892467i | ||||
\(216\) | −9.75562 | − | 9.72693i | −0.663786 | − | 0.661834i | ||||
\(217\) | −7.85471 | − | 13.6048i | −0.533213 | − | 0.923551i | ||||
\(218\) | −2.80256 | − | 4.85418i | −0.189813 | − | 0.328766i | ||||
\(219\) | −7.45540 | + | 7.46272i | −0.503789 | + | 0.504284i | ||||
\(220\) | 0.0550801 | + | 0.0954016i | 0.00371350 | + | 0.00643197i | ||||
\(221\) | −19.7635 | + | 0.943671i | −1.32944 | + | 0.0634782i | ||||
\(222\) | −4.47307 | − | 4.46868i | −0.300213 | − | 0.299918i | ||||
\(223\) | 1.75987 | − | 1.01606i | 0.117850 | − | 0.0680405i | −0.439916 | − | 0.898039i | \(-0.644992\pi\) |
0.557766 | + | 0.829998i | \(0.311659\pi\) | |||||||
\(224\) | −10.9857 | + | 19.0278i | −0.734013 | + | 1.27135i | ||||
\(225\) | −12.9878 | − | 7.48150i | −0.865852 | − | 0.498767i | ||||
\(226\) | 2.58620i | 0.172031i | ||||||||
\(227\) | − | 26.3044i | − | 1.74588i | −0.487826 | − | 0.872941i | \(-0.662210\pi\) | ||
0.487826 | − | 0.872941i | \(-0.337790\pi\) | |||||||
\(228\) | −5.33886 | + | 5.34410i | −0.353575 | + | 0.353922i | ||||
\(229\) | −23.2482 | + | 13.4224i | −1.53629 | + | 0.886976i | −0.537236 | + | 0.843432i | \(0.680531\pi\) |
−0.999052 | + | 0.0435436i | \(0.986135\pi\) | |||||||
\(230\) | 0.137119 | − | 0.237497i | 0.00904134 | − | 0.0156601i | ||||
\(231\) | −2.15534 | + | 8.05967i | −0.141811 | + | 0.530287i | ||||
\(232\) | −16.3810 | + | 9.45756i | −1.07546 | + | 0.620919i | ||||
\(233\) | −8.15619 | −0.534330 | −0.267165 | − | 0.963651i | \(-0.586087\pi\) | ||||
−0.267165 | + | 0.963651i | \(0.586087\pi\) | |||||||
\(234\) | 8.45586 | − | 0.412073i | 0.552777 | − | 0.0269381i | ||||
\(235\) | −0.195508 | −0.0127536 | ||||||||
\(236\) | 0.431361 | − | 0.249046i | 0.0280792 | − | 0.0162115i | ||||
\(237\) | −2.06154 | + | 0.553474i | −0.133912 | + | 0.0359520i | ||||
\(238\) | −8.06536 | + | 13.9696i | −0.522799 | + | 0.905515i | ||||
\(239\) | 11.8525 | − | 6.84307i | 0.766677 | − | 0.442641i | −0.0650107 | − | 0.997885i | \(-0.520708\pi\) |
0.831688 | + | 0.555243i | \(0.187375\pi\) | |||||||
\(240\) | 0.0194568 | + | 0.0724713i | 0.00125593 | + | 0.00467800i | ||||
\(241\) | − | 13.2782i | − | 0.855325i | −0.903938 | − | 0.427663i | \(-0.859337\pi\) | ||
0.903938 | − | 0.427663i | \(-0.140663\pi\) | |||||||
\(242\) | 7.32198i | 0.470675i | ||||||||
\(243\) | −11.0497 | − | 10.9956i | −0.708840 | − | 0.705369i | ||||
\(244\) | −1.14528 | + | 1.98369i | −0.0733192 | + | 0.126993i | ||||
\(245\) | 0.380929 | − | 0.219929i | 0.0243367 | − | 0.0140508i | ||||
\(246\) | −3.46360 | + | 12.9518i | −0.220831 | + | 0.825774i | ||||
\(247\) | −0.540556 | − | 11.3210i | −0.0343947 | − | 0.720336i | ||||
\(248\) | 5.54488 | + | 9.60402i | 0.352101 | + | 0.609856i | ||||
\(249\) | −5.73236 | − | 21.3515i | −0.363274 | − | 1.35310i | ||||
\(250\) | −0.242175 | − | 0.419460i | −0.0153165 | − | 0.0265290i | ||||
\(251\) | −2.59137 | − | 4.48838i | −0.163566 | − | 0.283304i | 0.772579 | − | 0.634918i | \(-0.218966\pi\) |
−0.936145 | + | 0.351614i | \(0.885633\pi\) | |||||||
\(252\) | −7.80276 | + | 13.5455i | −0.491528 | + | 0.853285i | ||||
\(253\) | 6.28637 | − | 3.62944i | 0.395220 | − | 0.228181i | ||||
\(254\) | 5.58518i | 0.350446i | ||||||||
\(255\) | 0.152576 | + | 0.568304i | 0.00955466 | + | 0.0355886i | ||||
\(256\) | 6.78423 | − | 11.7506i | 0.424014 | − | 0.734414i | ||||
\(257\) | 29.2021 | 1.82158 | 0.910789 | − | 0.412873i | \(-0.135475\pi\) | ||||
0.910789 | + | 0.412873i | \(0.135475\pi\) | |||||||
\(258\) | 5.53651 | + | 1.48059i | 0.344688 | + | 0.0921775i | ||||
\(259\) | −8.75840 | + | 15.1700i | −0.544220 | + | 0.942617i | ||||
\(260\) | −0.275280 | − | 0.141878i | −0.0170721 | − | 0.00879887i | ||||
\(261\) | −18.5253 | + | 10.7198i | −1.14669 | + | 0.663542i | ||||
\(262\) | −13.2309 | − | 7.63888i | −0.817410 | − | 0.471932i | ||||
\(263\) | −2.71399 | − | 4.70077i | −0.167352 | − | 0.289862i | 0.770136 | − | 0.637880i | \(-0.220188\pi\) |
−0.937488 | + | 0.348018i | \(0.886855\pi\) | |||||||
\(264\) | 1.52152 | − | 5.68957i | 0.0936433 | − | 0.350169i | ||||
\(265\) | 0.0403693 | − | 0.0233072i | 0.00247987 | − | 0.00143175i | ||||
\(266\) | −8.00210 | − | 4.62002i | −0.490640 | − | 0.283271i | ||||
\(267\) | 0.674898 | + | 2.51382i | 0.0413031 | + | 0.153843i | ||||
\(268\) | −1.99198 | − | 1.15007i | −0.121680 | − | 0.0702519i | ||||
\(269\) | −6.85146 | − | 11.8671i | −0.417741 | − | 0.723549i | 0.577971 | − | 0.816057i | \(-0.303845\pi\) |
−0.995712 | + | 0.0925087i | \(0.970511\pi\) | |||||||
\(270\) | −0.0655216 | − | 0.243097i | −0.00398752 | − | 0.0147944i | ||||
\(271\) | 10.5946 | + | 6.11677i | 0.643573 | + | 0.371567i | 0.785990 | − | 0.618240i | \(-0.212154\pi\) |
−0.142416 | + | 0.989807i | \(0.545487\pi\) | |||||||
\(272\) | −1.92012 | + | 3.32575i | −0.116424 | + | 0.201653i | ||||
\(273\) | −7.15494 | − | 22.3361i | −0.433036 | − | 1.35185i | ||||
\(274\) | −3.25737 | − | 5.64193i | −0.196785 | − | 0.340841i | ||||
\(275\) | − | 6.40775i | − | 0.386402i | ||||||
\(276\) | 13.1358 | − | 3.52664i | 0.790683 | − | 0.212279i | ||||
\(277\) | −14.0400 | −0.843582 | −0.421791 | − | 0.906693i | \(-0.638598\pi\) | ||||
−0.421791 | + | 0.906693i | \(0.638598\pi\) | |||||||
\(278\) | 2.99355i | 0.179541i | ||||||||
\(279\) | 6.28495 | + | 10.8612i | 0.376270 | + | 0.650244i | ||||
\(280\) | −0.533844 | + | 0.308215i | −0.0319033 | + | 0.0184194i | ||||
\(281\) | 18.6400 | + | 10.7618i | 1.11197 | + | 0.641997i | 0.939339 | − | 0.342990i | \(-0.111440\pi\) |
0.172632 | + | 0.984986i | \(0.444773\pi\) | |||||||
\(282\) | 3.02871 | + | 3.02573i | 0.180357 | + | 0.180180i | ||||
\(283\) | 23.1108 | 1.37379 | 0.686897 | − | 0.726755i | \(-0.258972\pi\) | ||||
0.686897 | + | 0.726755i | \(0.258972\pi\) | |||||||
\(284\) | 18.2376i | 1.08220i | ||||||||
\(285\) | −0.325537 | + | 0.0873988i | −0.0192832 | + | 0.00517706i | ||||
\(286\) | 1.95706 | + | 3.04450i | 0.115724 | + | 0.180025i | ||||
\(287\) | 37.1428 | 2.19247 | ||||||||
\(288\) | 8.76037 | − | 15.2079i | 0.516210 | − | 0.896132i | ||||
\(289\) | −6.55717 | + | 11.3573i | −0.385716 | + | 0.668079i | ||||
\(290\) | −0.345690 | −0.0202996 | ||||||||
\(291\) | −12.2702 | + | 12.2822i | −0.719290 | + | 0.719996i | ||||
\(292\) | −7.31777 | − | 4.22492i | −0.428240 | − | 0.247245i | ||||
\(293\) | 0.259773 | + | 0.149980i | 0.0151761 | + | 0.00876193i | 0.507569 | − | 0.861611i | \(-0.330544\pi\) |
−0.492393 | + | 0.870373i | \(0.663878\pi\) | |||||||
\(294\) | −9.30481 | − | 2.48832i | −0.542668 | − | 0.145122i | ||||
\(295\) | 0.0222253 | 0.00129401 | ||||||||
\(296\) | 6.18282 | − | 10.7090i | 0.359369 | − | 0.622446i | ||||
\(297\) | 1.71535 | − | 6.43969i | 0.0995347 | − | 0.373669i | ||||
\(298\) | −15.6990 | −0.909416 | ||||||||
\(299\) | −9.34884 | + | 18.1392i | −0.540658 | + | 1.04902i | ||||
\(300\) | 3.10175 | − | 11.5987i | 0.179080 | − | 0.669649i | ||||
\(301\) | − | 15.8775i | − | 0.915163i | ||||||
\(302\) | 10.8697 | 0.625480 | ||||||||
\(303\) | −7.69666 | + | 28.7808i | −0.442161 | + | 1.65341i | ||||
\(304\) | −1.90506 | − | 1.09989i | −0.109263 | − | 0.0630829i | ||||
\(305\) | −0.0885137 | + | 0.0511034i | −0.00506828 | + | 0.00292617i | ||||
\(306\) | 6.43159 | − | 11.1651i | 0.367669 | − | 0.638269i | ||||
\(307\) | 13.4090i | 0.765291i | 0.923895 | + | 0.382646i | \(0.124987\pi\) | ||||
−0.923895 | + | 0.382646i | \(0.875013\pi\) | |||||||
\(308\) | −6.68291 | −0.380794 | ||||||||
\(309\) | 7.89877 | − | 29.5366i | 0.449346 | − | 1.68028i | ||||
\(310\) | 0.202675i | 0.0115112i | ||||||||
\(311\) | 6.66305 | + | 11.5407i | 0.377827 | + | 0.654415i | 0.990746 | − | 0.135731i | \(-0.0433382\pi\) |
−0.612919 | + | 0.790146i | \(0.710005\pi\) | |||||||
\(312\) | 5.05089 | + | 15.7678i | 0.285950 | + | 0.892675i | ||||
\(313\) | −7.54812 | + | 13.0737i | −0.426645 | + | 0.738971i | −0.996572 | − | 0.0827243i | \(-0.973638\pi\) |
0.569928 | + | 0.821695i | \(0.306971\pi\) | |||||||
\(314\) | 10.7818 | + | 6.22486i | 0.608451 | + | 0.351289i | ||||
\(315\) | −0.603725 | + | 0.349352i | −0.0340161 | + | 0.0196837i | ||||
\(316\) | −0.854918 | − | 1.48076i | −0.0480929 | − | 0.0832994i | ||||
\(317\) | −16.1108 | − | 9.30158i | −0.904873 | − | 0.522429i | −0.0260952 | − | 0.999659i | \(-0.508307\pi\) |
−0.878778 | + | 0.477231i | \(0.841641\pi\) | |||||||
\(318\) | −0.986086 | − | 0.263702i | −0.0552970 | − | 0.0147877i | ||||
\(319\) | −7.92427 | − | 4.57508i | −0.443674 | − | 0.256155i | ||||
\(320\) | 0.170449 | − | 0.0984087i | 0.00952838 | − | 0.00550121i | ||||
\(321\) | 17.1971 | − | 4.61701i | 0.959851 | − | 0.257696i | ||||
\(322\) | 8.31835 | + | 14.4078i | 0.463564 | + | 0.802916i | ||||
\(323\) | −14.9391 | − | 8.62508i | −0.831233 | − | 0.479912i | ||||
\(324\) | 6.22216 | − | 10.8261i | 0.345676 | − | 0.601452i | ||||
\(325\) | 9.74077 | + | 15.1532i | 0.540321 | + | 0.840548i | ||||
\(326\) | 5.16066 | − | 8.93853i | 0.285823 | − | 0.495059i | ||||
\(327\) | 8.76673 | − | 8.77534i | 0.484801 | − | 0.485277i | ||||
\(328\) | −26.2203 | −1.44777 | ||||||||
\(329\) | 5.93029 | − | 10.2716i | 0.326947 | − | 0.566290i | ||||
\(330\) | 0.0760725 | − | 0.0761472i | 0.00418765 | − | 0.00419177i | ||||
\(331\) | 5.69806i | 0.313194i | 0.987663 | + | 0.156597i | \(0.0500524\pi\) | ||||
−0.987663 | + | 0.156597i | \(0.949948\pi\) | |||||||
\(332\) | 15.3364 | − | 8.85445i | 0.841692 | − | 0.485951i | ||||
\(333\) | 6.98424 | − | 12.1245i | 0.382734 | − | 0.664421i | ||||
\(334\) | −0.528149 | − | 0.914780i | −0.0288990 | − | 0.0500545i | ||||
\(335\) | −0.0513172 | − | 0.0888840i | −0.00280376 | − | 0.00485625i | ||||
\(336\) | −4.39765 | − | 1.17603i | −0.239911 | − | 0.0641578i | ||||
\(337\) | 16.0839 | + | 27.8581i | 0.876146 | + | 1.51753i | 0.855537 | + | 0.517741i | \(0.173227\pi\) |
0.0206081 | + | 0.999788i | \(0.493440\pi\) | |||||||
\(338\) | −9.25621 | − | 4.22466i | −0.503472 | − | 0.229791i | ||||
\(339\) | −5.52750 | + | 1.48400i | −0.300213 | + | 0.0805997i | ||||
\(340\) | −0.408200 | + | 0.235675i | −0.0221378 | + | 0.0127813i | ||||
\(341\) | −2.68233 | + | 4.64593i | −0.145256 | + | 0.251591i | ||||
\(342\) | 6.39564 | + | 3.68416i | 0.345837 | + | 0.199216i | ||||
\(343\) | 0.394490i | 0.0213005i | ||||||||
\(344\) | 11.2084i | 0.604317i | ||||||||
\(345\) | 0.586285 | + | 0.156786i | 0.0315645 | + | 0.00844108i | ||||
\(346\) | 9.97360 | − | 5.75826i | 0.536184 | − | 0.309566i | ||||
\(347\) | −8.02447 | + | 13.8988i | −0.430776 | + | 0.746127i | −0.996940 | − | 0.0781661i | \(-0.975094\pi\) |
0.566164 | + | 0.824293i | \(0.308427\pi\) | |||||||
\(348\) | −12.1291 | − | 12.1172i | −0.650187 | − | 0.649549i | ||||
\(349\) | 23.5647 | − | 13.6051i | 1.26139 | − | 0.728262i | 0.288045 | − | 0.957617i | \(-0.406995\pi\) |
0.973343 | + | 0.229355i | \(0.0736615\pi\) | |||||||
\(350\) | 14.6860 | 0.785000 | ||||||||
\(351\) | 5.73283 | + | 17.8363i | 0.305996 | + | 0.952033i | ||||
\(352\) | 7.50307 | 0.399915 | ||||||||
\(353\) | 4.01185 | − | 2.31624i | 0.213529 | − | 0.123281i | −0.389421 | − | 0.921060i | \(-0.627325\pi\) |
0.602951 | + | 0.797779i | \(0.293992\pi\) | |||||||
\(354\) | −0.344302 | − | 0.343964i | −0.0182994 | − | 0.0182815i | ||||
\(355\) | −0.406888 | + | 0.704751i | −0.0215954 | + | 0.0374043i | ||||
\(356\) | −1.80562 | + | 1.04248i | −0.0956977 | + | 0.0552511i | ||||
\(357\) | −34.4854 | − | 9.22219i | −1.82516 | − | 0.488090i | ||||
\(358\) | 4.07194i | 0.215208i | ||||||||
\(359\) | 16.1406i | 0.851870i | 0.904754 | + | 0.425935i | \(0.140055\pi\) | ||||
−0.904754 | + | 0.425935i | \(0.859945\pi\) | |||||||
\(360\) | 0.426188 | − | 0.246618i | 0.0224621 | − | 0.0129979i | ||||
\(361\) | −4.55936 | + | 7.89704i | −0.239966 | + | 0.415634i | ||||
\(362\) | 6.84239 | − | 3.95046i | 0.359628 | − | 0.207631i | ||||
\(363\) | −15.6493 | + | 4.20146i | −0.821377 | + | 0.220520i | ||||
\(364\) | 15.8039 | − | 10.1590i | 0.828349 | − | 0.532478i | ||||
\(365\) | −0.188519 | − | 0.326525i | −0.00986754 | − | 0.0170911i | ||||
\(366\) | 2.16209 | + | 0.578194i | 0.113014 | + | 0.0302227i | ||||
\(367\) | 10.3833 | + | 17.9845i | 0.542005 | + | 0.938781i | 0.998789 | + | 0.0492028i | \(0.0156681\pi\) |
−0.456783 | + | 0.889578i | \(0.650999\pi\) | |||||||
\(368\) | 1.98035 | + | 3.43007i | 0.103233 | + | 0.178805i | ||||
\(369\) | −29.6694 | + | 0.0291302i | −1.54453 | + | 0.00151646i | ||||
\(370\) | 0.195715 | − | 0.112996i | 0.0101748 | − | 0.00587440i | ||||
\(371\) | 2.82788i | 0.146816i | ||||||||
\(372\) | −7.10419 | + | 7.11117i | −0.368335 | + | 0.368697i | ||||
\(373\) | −3.03953 | + | 5.26462i | −0.157381 | + | 0.272592i | −0.933923 | − | 0.357473i | \(-0.883638\pi\) |
0.776543 | + | 0.630065i | \(0.216972\pi\) | |||||||
\(374\) | 5.50852 | 0.284839 | ||||||||
\(375\) | 0.757552 | − | 0.758297i | 0.0391198 | − | 0.0391583i | ||||
\(376\) | −4.18638 | + | 7.25101i | −0.215896 | + | 0.373943i | ||||
\(377\) | 25.6943 | − | 1.22686i | 1.32332 | − | 0.0631863i | ||||
\(378\) | 14.7592 | + | 3.93143i | 0.759132 | + | 0.202211i | ||||
\(379\) | −13.7130 | − | 7.91718i | −0.704388 | − | 0.406678i | 0.104592 | − | 0.994515i | \(-0.466646\pi\) |
−0.808979 | + | 0.587837i | \(0.799980\pi\) | |||||||
\(380\) | −0.135000 | − | 0.233826i | −0.00692534 | − | 0.0119950i | ||||
\(381\) | −11.9373 | + | 3.20486i | −0.611565 | + | 0.164190i | ||||
\(382\) | −1.84222 | + | 1.06361i | −0.0942563 | + | 0.0544189i | ||||
\(383\) | −12.9901 | − | 7.49986i | −0.663765 | − | 0.383225i | 0.129945 | − | 0.991521i | \(-0.458520\pi\) |
−0.793710 | + | 0.608296i | \(0.791853\pi\) | |||||||
\(384\) | 15.4142 | + | 4.12212i | 0.786603 | + | 0.210356i | ||||
\(385\) | −0.258246 | − | 0.149098i | −0.0131614 | − | 0.00759875i | ||||
\(386\) | −7.46915 | − | 12.9369i | −0.380170 | − | 0.658473i | ||||
\(387\) | 0.0124523 | + | 12.6828i | 0.000632986 | + | 0.644704i | ||||
\(388\) | −12.0436 | − | 6.95340i | −0.611424 | − | 0.353006i | ||||
\(389\) | 8.69825 | − | 15.0658i | 0.441019 | − | 0.763867i | −0.556747 | − | 0.830682i | \(-0.687951\pi\) |
0.997765 | + | 0.0668155i | \(0.0212839\pi\) | |||||||
\(390\) | −0.0641425 | + | 0.295717i | −0.00324798 | + | 0.0149742i | ||||
\(391\) | 15.5295 | + | 26.8979i | 0.785360 | + | 1.36028i | ||||
\(392\) | − | 18.8372i | − | 0.951421i | ||||||
\(393\) | 8.73455 | − | 32.6619i | 0.440600 | − | 1.64757i | ||||
\(394\) | 1.69884 | 0.0855861 | ||||||||
\(395\) | − | 0.0762943i | − | 0.00383878i | ||||||
\(396\) | 5.33825 | − | 0.00524123i | 0.268257 | − | 0.000263382i | ||||
\(397\) | −9.89799 | + | 5.71461i | −0.496766 | + | 0.286808i | −0.727377 | − | 0.686238i | \(-0.759261\pi\) |
0.230611 | + | 0.973046i | \(0.425928\pi\) | |||||||
\(398\) | 7.07331 | + | 4.08378i | 0.354553 | + | 0.204701i | ||||
\(399\) | 5.28268 | − | 19.7540i | 0.264465 | − | 0.988937i | ||||
\(400\) | 3.49630 | 0.174815 | ||||||||
\(401\) | 12.7790i | 0.638151i | 0.947729 | + | 0.319075i | \(0.103372\pi\) | ||||
−0.947729 | + | 0.319075i | \(0.896628\pi\) | |||||||
\(402\) | −0.580612 | + | 2.17114i | −0.0289583 | + | 0.108286i | ||||
\(403\) | −0.719295 | − | 15.0643i | −0.0358306 | − | 0.750409i | ||||
\(404\) | −23.8644 | −1.18730 | ||||||||
\(405\) | 0.481977 | − | 0.279533i | 0.0239496 | − | 0.0138901i | ||||
\(406\) | 10.4857 | − | 18.1617i | 0.520395 | − | 0.901351i | ||||
\(407\) | 5.98186 | 0.296510 | ||||||||
\(408\) | 24.3443 | + | 6.51023i | 1.20522 | + | 0.322304i | ||||
\(409\) | −17.1272 | − | 9.88837i | −0.846884 | − | 0.488949i | 0.0127143 | − | 0.999919i | \(-0.495953\pi\) |
−0.859598 | + | 0.510971i | \(0.829286\pi\) | |||||||
\(410\) | −0.414997 | − | 0.239599i | −0.0204952 | − | 0.0118329i | ||||
\(411\) | 10.1894 | − | 10.1994i | 0.502607 | − | 0.503101i | ||||
\(412\) | 24.4911 | 1.20659 | ||||||||
\(413\) | −0.674152 | + | 1.16767i | −0.0331728 | + | 0.0574571i | ||||
\(414\) | −6.65593 | − | 11.5023i | −0.327121 | − | 0.565308i | ||||
\(415\) | 0.790185 | 0.0387887 | ||||||||
\(416\) | −17.7434 | + | 11.4058i | −0.869943 | + | 0.559216i | ||||
\(417\) | −6.39814 | + | 1.71774i | −0.313318 | + | 0.0841183i | ||||
\(418\) | 3.15541i | 0.154336i | ||||||||
\(419\) | 1.02767 | 0.0502051 | 0.0251025 | − | 0.999685i | \(-0.492009\pi\) | ||||
0.0251025 | + | 0.999685i | \(0.492009\pi\) | |||||||
\(420\) | −0.395278 | − | 0.394890i | −0.0192876 | − | 0.0192686i | ||||
\(421\) | −19.3455 | − | 11.1691i | −0.942843 | − | 0.544351i | −0.0519927 | − | 0.998647i | \(-0.516557\pi\) |
−0.890850 | + | 0.454297i | \(0.849891\pi\) | |||||||
\(422\) | 0.261976 | − | 0.151252i | 0.0127528 | − | 0.00736283i | ||||
\(423\) | −4.72901 | + | 8.20950i | −0.229933 | + | 0.399159i | ||||
\(424\) | − | 1.99629i | − | 0.0969483i | ||||||
\(425\) | 27.4172 | 1.32993 | ||||||||
\(426\) | 17.2102 | − | 4.62051i | 0.833835 | − | 0.223864i | ||||
\(427\) | − | 6.20041i | − | 0.300059i | ||||||
\(428\) | 7.13162 | + | 12.3523i | 0.344720 | + | 0.597073i | ||||
\(429\) | −5.38404 | + | 5.92983i | −0.259944 | + | 0.286295i | ||||
\(430\) | −0.102422 | + | 0.177399i | −0.00493921 | + | 0.00855496i | ||||
\(431\) | −6.38655 | − | 3.68727i | −0.307629 | − | 0.177610i | 0.338236 | − | 0.941061i | \(-0.390170\pi\) |
−0.645865 | + | 0.763452i | \(0.723503\pi\) | |||||||
\(432\) | 3.51373 | + | 0.935957i | 0.169054 | + | 0.0450312i | ||||
\(433\) | 2.96921 | + | 5.14283i | 0.142691 | + | 0.247148i | 0.928509 | − | 0.371309i | \(-0.121091\pi\) |
−0.785818 | + | 0.618458i | \(0.787758\pi\) | |||||||
\(434\) | −10.6481 | − | 6.14766i | −0.511123 | − | 0.295097i | ||||
\(435\) | −0.198362 | − | 0.738846i | −0.00951072 | − | 0.0354249i | ||||
\(436\) | 8.60489 | + | 4.96804i | 0.412099 | + | 0.237926i | ||||
\(437\) | −15.4077 | + | 8.89564i | −0.737050 | + | 0.425536i | ||||
\(438\) | −2.13294 | + | 7.97590i | −0.101916 | + | 0.381103i | ||||
\(439\) | −11.8461 | − | 20.5180i | −0.565382 | − | 0.979270i | −0.997014 | − | 0.0772203i | \(-0.975396\pi\) |
0.431632 | − | 0.902050i | \(-0.357938\pi\) | |||||||
\(440\) | 0.182304 | + | 0.105253i | 0.00869099 | + | 0.00501775i | ||||
\(441\) | −0.0209277 | − | 21.3151i | −0.000996557 | − | 1.01501i | ||||
\(442\) | −13.0267 | + | 8.37380i | −0.619616 | + | 0.398301i | ||||
\(443\) | −19.8468 | + | 34.3756i | −0.942948 | + | 1.63323i | −0.183138 | + | 0.983087i | \(0.558626\pi\) |
−0.759809 | + | 0.650146i | \(0.774708\pi\) | |||||||
\(444\) | 10.8278 | + | 2.89559i | 0.513862 | + | 0.137419i | ||||
\(445\) | −0.0930322 | −0.00441015 | ||||||||
\(446\) | 0.795243 | − | 1.37740i | 0.0376558 | − | 0.0652218i | ||||
\(447\) | −9.00830 | − | 33.5535i | −0.426078 | − | 1.58703i | ||||
\(448\) | 11.9400i | 0.564111i | ||||||||
\(449\) | −7.64958 | + | 4.41649i | −0.361006 | + | 0.208427i | −0.669522 | − | 0.742792i | \(-0.733501\pi\) |
0.308516 | + | 0.951219i | \(0.400168\pi\) | |||||||
\(450\) | −11.7311 | + | 0.0115179i | −0.553008 | + | 0.000542957i | ||||
\(451\) | −6.34200 | − | 10.9847i | −0.298633 | − | 0.517248i | ||||
\(452\) | −2.29225 | − | 3.97028i | −0.107818 | − | 0.186746i | ||||
\(453\) | 6.23719 | + | 23.2319i | 0.293049 | + | 1.09153i | ||||
\(454\) | −10.2938 | − | 17.8295i | −0.483114 | − | 0.836778i | ||||
\(455\) | 0.837358 | − | 0.0399823i | 0.0392559 | − | 0.00187440i | ||||
\(456\) | −3.72921 | + | 13.9450i | −0.174636 | + | 0.653033i | ||||
\(457\) | −17.9905 | + | 10.3868i | −0.841559 | + | 0.485874i | −0.857794 | − | 0.513994i | \(-0.828165\pi\) |
0.0162349 | + | 0.999868i | \(0.494832\pi\) | |||||||
\(458\) | −10.5053 | + | 18.1957i | −0.490881 | + | 0.850231i | ||||
\(459\) | 27.5539 | + | 7.33957i | 1.28611 | + | 0.342582i | ||||
\(460\) | 0.486135i | 0.0226661i | ||||||||
\(461\) | 10.4811i | 0.488152i | 0.969756 | + | 0.244076i | \(0.0784847\pi\) | ||||
−0.969756 | + | 0.244076i | \(0.921515\pi\) | |||||||
\(462\) | 1.69312 | + | 6.30642i | 0.0787710 | + | 0.293401i | ||||
\(463\) | −17.5850 | + | 10.1527i | −0.817243 | + | 0.471835i | −0.849465 | − | 0.527645i | \(-0.823075\pi\) |
0.0322220 | + | 0.999481i | \(0.489742\pi\) | |||||||
\(464\) | 2.49633 | − | 4.32376i | 0.115889 | − | 0.200726i | ||||
\(465\) | −0.433179 | + | 0.116298i | −0.0200882 | + | 0.00539318i | ||||
\(466\) | −5.52838 | + | 3.19181i | −0.256097 | + | 0.147858i | ||||
\(467\) | −14.0228 | −0.648897 | −0.324448 | − | 0.945903i | \(-0.605179\pi\) | ||||
−0.324448 | + | 0.945903i | \(0.605179\pi\) | |||||||
\(468\) | −12.6161 | + | 8.12736i | −0.583177 | + | 0.375687i | ||||
\(469\) | 6.22634 | 0.287506 | ||||||||
\(470\) | −0.132518 | + | 0.0765095i | −0.00611261 | + | 0.00352912i | ||||
\(471\) | −7.11771 | + | 26.6159i | −0.327967 | + | 1.22640i | ||||
\(472\) | 0.475905 | − | 0.824291i | 0.0219053 | − | 0.0379411i | ||||
\(473\) | −4.69563 | + | 2.71103i | −0.215905 | + | 0.124653i | ||||
\(474\) | −1.18075 | + | 1.18191i | −0.0542336 | + | 0.0542868i | ||||
\(475\) | 15.7052i | 0.720604i | ||||||||
\(476\) | − | 28.5945i | − | 1.31063i | ||||||
\(477\) | −0.00221783 | − | 2.25889i | −0.000101548 | − | 0.103427i | ||||
\(478\) | 5.35588 | − | 9.27665i | 0.244972 | − | 0.424304i | ||||
\(479\) | 8.56760 | − | 4.94650i | 0.391464 | − | 0.226012i | −0.291331 | − | 0.956622i | \(-0.594098\pi\) |
0.682794 | + | 0.730611i | \(0.260765\pi\) | |||||||
\(480\) | 0.443788 | + | 0.443353i | 0.0202561 | + | 0.0202362i | ||||
\(481\) | −14.1460 | + | 9.09335i | −0.645004 | + | 0.414621i | ||||
\(482\) | −5.19624 | − | 9.00016i | −0.236682 | − | 0.409946i | ||||
\(483\) | −26.0207 | + | 26.0463i | −1.18399 | + | 1.18515i | ||||
\(484\) | −6.48975 | − | 11.2406i | −0.294989 | − | 0.510936i | ||||
\(485\) | −0.310267 | − | 0.537397i | −0.0140885 | − | 0.0244020i | ||||
\(486\) | −11.7926 | − | 3.12882i | −0.534925 | − | 0.141926i | ||||
\(487\) | 35.6312 | − | 20.5717i | 1.61460 | − | 0.932192i | 0.626320 | − | 0.779566i | \(-0.284560\pi\) |
0.988284 | − | 0.152626i | \(-0.0487731\pi\) | |||||||
\(488\) | 4.37706i | 0.198140i | ||||||||
\(489\) | 22.0657 | + | 5.90087i | 0.997844 | + | 0.266847i | ||||
\(490\) | 0.172133 | − | 0.298142i | 0.00777616 | − | 0.0134687i | ||||
\(491\) | −17.7119 | −0.799326 | −0.399663 | − | 0.916662i | \(-0.630873\pi\) | ||||
−0.399663 | + | 0.916662i | \(0.630873\pi\) | |||||||
\(492\) | −6.16239 | − | 22.9533i | −0.277822 | − | 1.03481i | ||||
\(493\) | 19.5757 | − | 33.9060i | 0.881643 | − | 1.52705i | ||||
\(494\) | −4.79670 | − | 7.46197i | −0.215814 | − | 0.335730i | ||||
\(495\) | 0.206402 | + | 0.118896i | 0.00927707 | + | 0.00534398i | ||||
\(496\) | −2.53499 | − | 1.46357i | −0.113824 | − | 0.0657164i | ||||
\(497\) | −24.6840 | − | 42.7539i | −1.10723 | − | 1.91778i | ||||
\(498\) | −12.2411 | − | 12.2291i | −0.548537 | − | 0.547999i | ||||
\(499\) | 16.2710 | − | 9.39408i | 0.728391 | − | 0.420537i | −0.0894423 | − | 0.995992i | \(-0.528508\pi\) |
0.817833 | + | 0.575455i | \(0.195175\pi\) | |||||||
\(500\) | 0.743568 | + | 0.429299i | 0.0332534 | + | 0.0191988i | ||||
\(501\) | 1.65211 | − | 1.65373i | 0.0738108 | − | 0.0738833i | ||||
\(502\) | −3.51293 | − | 2.02819i | −0.156790 | − | 0.0905226i | ||||
\(503\) | −7.83131 | − | 13.5642i | −0.349181 | − | 0.604799i | 0.636923 | − | 0.770927i | \(-0.280207\pi\) |
−0.986104 | + | 0.166128i | \(0.946873\pi\) | |||||||
\(504\) | 0.0293286 | + | 29.8715i | 0.00130640 | + | 1.33058i | ||||
\(505\) | −0.922187 | − | 0.532425i | −0.0410368 | − | 0.0236926i | ||||
\(506\) | 2.84066 | − | 4.92016i | 0.126283 | − | 0.218728i | ||||
\(507\) | 3.71806 | − | 22.2076i | 0.165125 | − | 0.986273i | ||||
\(508\) | −4.95036 | − | 8.57428i | −0.219637 | − | 0.380422i | ||||
\(509\) | − | 37.6313i | − | 1.66798i | −0.551781 | − | 0.833989i | \(-0.686052\pi\) | ||
0.551781 | − | 0.833989i | \(-0.313948\pi\) | |||||||
\(510\) | 0.325816 | + | 0.325496i | 0.0144274 | + | 0.0144132i | ||||
\(511\) | 22.8731 | 1.01185 | ||||||||
\(512\) | 7.80461i | 0.344918i | ||||||||
\(513\) | −4.20427 | + | 15.7835i | −0.185623 | + | 0.696858i | ||||
\(514\) | 19.7936 | − | 11.4278i | 0.873058 | − | 0.504060i | ||||
\(515\) | 0.946405 | + | 0.546407i | 0.0417036 | + | 0.0240776i | ||||
\(516\) | −9.81186 | + | 2.63424i | −0.431943 | + | 0.115966i | ||||
\(517\) | −4.05030 | −0.178132 | ||||||||
\(518\) | 13.7099i | 0.602379i | ||||||||
\(519\) | 18.0302 | + | 18.0125i | 0.791438 | + | 0.790661i | ||||
\(520\) | −0.591117 | + | 0.0282247i | −0.0259222 | + | 0.00123774i | ||||
\(521\) | 3.84164 | 0.168305 | 0.0841526 | − | 0.996453i | \(-0.473182\pi\) | ||||
0.0841526 | + | 0.996453i | \(0.473182\pi\) | |||||||
\(522\) | −8.36164 | + | 14.5157i | −0.365979 | + | 0.635334i | ||||
\(523\) | −19.6605 | + | 34.0529i | −0.859692 | + | 1.48903i | 0.0125300 | + | 0.999921i | \(0.496011\pi\) |
−0.872222 | + | 0.489109i | \(0.837322\pi\) | |||||||
\(524\) | 27.0825 | 1.18311 | ||||||||
\(525\) | 8.42706 | + | 31.3886i | 0.367787 | + | 1.36991i | ||||
\(526\) | −3.67916 | − | 2.12417i | −0.160419 | − | 0.0926181i | ||||
\(527\) | −19.8788 | − | 11.4770i | −0.865935 | − | 0.499948i | ||||
\(528\) | 0.403081 | + | 1.50137i | 0.0175418 | + | 0.0653387i | ||||
\(529\) | 9.03323 | 0.392749 | ||||||||
\(530\) | 0.0182419 | − | 0.0315959i | 0.000792378 | − | 0.00137244i | ||||
\(531\) | 0.537592 | − | 0.933251i | 0.0233295 | − | 0.0404996i | ||||
\(532\) | 16.3796 | 0.710146 | ||||||||
\(533\) | 31.6961 | + | 16.3360i | 1.37291 | + | 0.707590i | ||||
\(534\) | 1.44120 | + | 1.43979i | 0.0623669 | + | 0.0623057i | ||||
\(535\) | 0.636438i | 0.0275156i | ||||||||
\(536\) | −4.39537 | −0.189851 | ||||||||
\(537\) | −8.70299 | + | 2.33654i | −0.375562 | + | 0.100829i | ||||
\(538\) | −9.28803 | − | 5.36245i | −0.400436 | − | 0.231192i | ||||
\(539\) | 7.89161 | − | 4.55623i | 0.339916 | − | 0.196251i | ||||
\(540\) | 0.316054 | + | 0.315125i | 0.0136008 | + | 0.0135608i | ||||
\(541\) | − | 45.4115i | − | 1.95239i | −0.216885 | − | 0.976197i | \(-0.569590\pi\) | ||
0.216885 | − | 0.976197i | \(-0.430410\pi\) | |||||||
\(542\) | 9.57485 | 0.411275 | ||||||||
\(543\) | 12.3696 | + | 12.3575i | 0.530831 | + | 0.530310i | ||||
\(544\) | 32.1038i | 1.37644i | ||||||||
\(545\) | 0.221678 | + | 0.383957i | 0.00949563 | + | 0.0164469i | ||||
\(546\) | −13.5907 | − | 12.3398i | −0.581626 | − | 0.528093i | ||||
\(547\) | 7.70865 | − | 13.3518i | 0.329598 | − | 0.570881i | −0.652834 | − | 0.757501i | \(-0.726420\pi\) |
0.982432 | + | 0.186620i | \(0.0597534\pi\) | |||||||
\(548\) | 10.0013 | + | 5.77426i | 0.427235 | + | 0.246664i | ||||
\(549\) | 0.00486282 | + | 4.95284i | 0.000207540 | + | 0.211382i | ||||
\(550\) | −2.50758 | − | 4.34326i | −0.106924 | − | 0.185197i | ||||
\(551\) | 19.4221 | + | 11.2134i | 0.827411 | + | 0.477706i | ||||
\(552\) | 18.3689 | − | 18.3869i | 0.781830 | − | 0.782598i | ||||
\(553\) | 4.00833 | + | 2.31421i | 0.170451 | + | 0.0984101i | ||||
\(554\) | −9.51650 | + | 5.49436i | −0.404317 | + | 0.233433i | ||||
\(555\) | 0.353812 | + | 0.353465i | 0.0150185 | + | 0.0150038i | ||||
\(556\) | −2.65330 | − | 4.59565i | −0.112525 | − | 0.194899i | ||||
\(557\) | −24.1319 | − | 13.9325i | −1.02250 | − | 0.590341i | −0.107673 | − | 0.994186i | \(-0.534340\pi\) |
−0.914827 | + | 0.403846i | \(0.867673\pi\) | |||||||
\(558\) | 8.51041 | + | 4.90236i | 0.360275 | + | 0.207533i | ||||
\(559\) | 6.98316 | − | 13.5492i | 0.295356 | − | 0.573069i | ||||
\(560\) | 0.0813534 | − | 0.140908i | 0.00343781 | − | 0.00595446i | ||||
\(561\) | 3.16087 | + | 11.7734i | 0.133452 | + | 0.497074i | ||||
\(562\) | 16.8460 | 0.710604 | ||||||||
\(563\) | −13.3491 | + | 23.1214i | −0.562599 | + | 0.974450i | 0.434669 | + | 0.900590i | \(0.356865\pi\) |
−0.997269 | + | 0.0738603i | \(0.976468\pi\) | |||||||
\(564\) | −7.33145 | − | 1.96060i | −0.308710 | − | 0.0825561i | ||||
\(565\) | − | 0.204564i | − | 0.00860606i | ||||||
\(566\) | 15.6648 | − | 9.04408i | 0.658441 | − | 0.380151i | ||||
\(567\) | 0.0663733 | + | 33.8009i | 0.00278742 | + | 1.41951i | ||||
\(568\) | 17.4252 | + | 30.1813i | 0.731145 | + | 1.26638i | ||||
\(569\) | 7.92670 | + | 13.7294i | 0.332305 | + | 0.575568i | 0.982963 | − | 0.183802i | \(-0.0588405\pi\) |
−0.650659 | + | 0.759370i | \(0.725507\pi\) | |||||||
\(570\) | −0.186451 | + | 0.186635i | −0.00780959 | + | 0.00781726i | ||||
\(571\) | −5.89230 | − | 10.2058i | −0.246585 | − | 0.427098i | 0.715991 | − | 0.698109i | \(-0.245975\pi\) |
−0.962576 | + | 0.271012i | \(0.912642\pi\) | |||||||
\(572\) | −5.70291 | − | 2.93924i | −0.238451 | − | 0.122896i | ||||
\(573\) | −3.33035 | − | 3.32709i | −0.139128 | − | 0.138991i | ||||
\(574\) | 25.1759 | − | 14.5353i | 1.05082 | − | 0.606693i | ||||
\(575\) | 14.1386 | − | 24.4888i | 0.589622 | − | 1.02125i | ||||
\(576\) | −0.00936422 | − | 9.53757i | −0.000390176 | − | 0.397399i | ||||
\(577\) | − | 3.85716i | − | 0.160576i | −0.996772 | − | 0.0802879i | \(-0.974416\pi\) | ||
0.996772 | − | 0.0802879i | \(-0.0255840\pi\) | |||||||
\(578\) | 10.2642i | 0.426935i | ||||||||
\(579\) | 23.3643 | − | 23.3873i | 0.970989 | − | 0.971943i | ||||
\(580\) | 0.530697 | − | 0.306398i | 0.0220360 | − | 0.0127225i | ||||
\(581\) | −23.9684 | + | 41.5145i | −0.994377 | + | 1.72231i | ||||
\(582\) | −3.51041 | + | 13.1268i | −0.145511 | + | 0.544124i | ||||
\(583\) | 0.836321 | − | 0.482850i | 0.0346369 | − | 0.0199976i | ||||
\(584\) | −16.1469 | −0.668162 | ||||||||
\(585\) | −0.668844 | + | 0.0325943i | −0.0276533 | + | 0.00134761i | ||||
\(586\) | 0.234771 | 0.00969828 | ||||||||
\(587\) | −22.1887 | + | 12.8107i | −0.915827 | + | 0.528753i | −0.882301 | − | 0.470685i | \(-0.844007\pi\) |
−0.0335257 | + | 0.999438i | \(0.510674\pi\) | |||||||
\(588\) | 16.4901 | − | 4.42718i | 0.680040 | − | 0.182574i | ||||
\(589\) | 6.57430 | − | 11.3870i | 0.270889 | − | 0.469194i | ||||
\(590\) | 0.0150646 | − | 0.00869756i | 0.000620200 | − | 0.000358073i | ||||
\(591\) | 0.974818 | + | 3.63094i | 0.0400986 | + | 0.149357i | ||||
\(592\) | 3.26392i | 0.134146i | ||||||||
\(593\) | − | 10.1922i | − | 0.418543i | −0.977858 | − | 0.209272i | \(-0.932891\pi\) | ||
0.977858 | − | 0.209272i | \(-0.0671093\pi\) | |||||||
\(594\) | −1.35740 | − | 5.03619i | −0.0556946 | − | 0.206637i | ||||
\(595\) | 0.637956 | − | 1.10497i | 0.0261536 | − | 0.0452994i | ||||
\(596\) | 24.1008 | − | 13.9146i | 0.987206 | − | 0.569964i | ||||
\(597\) | −4.66953 | + | 17.4612i | −0.191111 | + | 0.714639i | ||||
\(598\) | 0.761752 | + | 15.9535i | 0.0311504 | + | 0.652389i | ||||
\(599\) | −6.90176 | − | 11.9542i | −0.281998 | − | 0.488435i | 0.689878 | − | 0.723925i | \(-0.257664\pi\) |
−0.971877 | + | 0.235490i | \(0.924331\pi\) | |||||||
\(600\) | −5.94892 | − | 22.1582i | −0.242864 | − | 0.904603i | ||||
\(601\) | 5.66423 | + | 9.81073i | 0.231049 | + | 0.400188i | 0.958117 | − | 0.286377i | \(-0.0924510\pi\) |
−0.727068 | + | 0.686565i | \(0.759118\pi\) | |||||||
\(602\) | −6.21343 | − | 10.7620i | −0.253241 | − | 0.438626i | ||||
\(603\) | −4.97356 | + | 0.00488316i | −0.202539 | + | 0.000198858i | ||||
\(604\) | −16.6870 | + | 9.63422i | −0.678983 | + | 0.392011i | ||||
\(605\) | − | 0.579156i | − | 0.0235460i | ||||||
\(606\) | 6.04607 | + | 22.5200i | 0.245605 | + | 0.914813i | ||||
\(607\) | −5.44652 | + | 9.43365i | −0.221067 | + | 0.382900i | −0.955132 | − | 0.296179i | \(-0.904287\pi\) |
0.734065 | + | 0.679079i | \(0.237621\pi\) | |||||||
\(608\) | −18.3898 | −0.745805 | ||||||||
\(609\) | 44.8341 | + | 11.9897i | 1.81677 | + | 0.485846i | ||||
\(610\) | −0.0399972 | + | 0.0692772i | −0.00161944 | + | 0.00280495i | ||||
\(611\) | 9.57825 | − | 6.15708i | 0.387494 | − | 0.249089i | ||||
\(612\) | 0.0224260 | + | 22.8411i | 0.000906516 | + | 0.923297i | ||||
\(613\) | 27.0132 | + | 15.5961i | 1.09105 | + | 0.629920i | 0.933857 | − | 0.357647i | \(-0.116421\pi\) |
0.157197 | + | 0.987567i | \(0.449754\pi\) | |||||||
\(614\) | 5.24742 | + | 9.08880i | 0.211769 | + | 0.366794i | ||||
\(615\) | 0.273965 | − | 1.02446i | 0.0110473 | − | 0.0413103i | ||||
\(616\) | −11.0595 | + | 6.38521i | −0.445600 | + | 0.257268i | ||||
\(617\) | 29.4907 | + | 17.0265i | 1.18725 | + | 0.685460i | 0.957681 | − | 0.287831i | \(-0.0929343\pi\) |
0.229571 | + | 0.973292i | \(0.426268\pi\) | |||||||
\(618\) | −6.20484 | − | 23.1114i | −0.249595 | − | 0.929677i | ||||
\(619\) | −7.48048 | − | 4.31886i | −0.300666 | − | 0.173589i | 0.342076 | − | 0.939672i | \(-0.388870\pi\) |
−0.642742 | + | 0.766083i | \(0.722203\pi\) | |||||||
\(620\) | −0.179638 | − | 0.311143i | −0.00721446 | − | 0.0124958i | ||||
\(621\) | 20.7647 | − | 20.8260i | 0.833261 | − | 0.835719i | ||||
\(622\) | 9.03261 | + | 5.21498i | 0.362175 | + | 0.209102i | ||||
\(623\) | 2.82191 | − | 4.88769i | 0.113057 | − | 0.195821i | ||||
\(624\) | −3.23553 | − | 2.93773i | −0.129525 | − | 0.117603i | ||||
\(625\) | −12.4713 | − | 21.6009i | −0.498851 | − | 0.864034i | ||||
\(626\) | 11.8154i | 0.472238i | ||||||||
\(627\) | −6.74408 | + | 1.81062i | −0.269333 | + | 0.0723092i | ||||
\(628\) | −22.0693 | −0.880662 | ||||||||
\(629\) | 25.5949i | 1.02054i | ||||||||
\(630\) | −0.272499 | + | 0.473055i | −0.0108566 | + | 0.0188470i | ||||
\(631\) | −34.8576 | + | 20.1250i | −1.38766 | + | 0.801165i | −0.993051 | − | 0.117684i | \(-0.962453\pi\) |
−0.394608 | + | 0.918850i | \(0.629120\pi\) | |||||||
\(632\) | −2.82960 | − | 1.63367i | −0.112555 | − | 0.0649839i | ||||
\(633\) | 0.473598 | + | 0.473133i | 0.0188238 | + | 0.0188054i | ||||
\(634\) | −14.5602 | −0.578258 | ||||||||
\(635\) | − | 0.441779i | − | 0.0175314i | ||||||
\(636\) | 1.74755 | − | 0.469175i | 0.0692950 | − | 0.0186040i | ||||
\(637\) | −11.7361 | + | 22.7711i | −0.465001 | + | 0.902225i | ||||
\(638\) | −7.16157 | −0.283529 | ||||||||
\(639\) | 19.7509 | + | 34.1321i | 0.781334 | + | 1.35025i | ||||
\(640\) | −0.285152 | + | 0.493898i | −0.0112716 | + | 0.0195230i | ||||
\(641\) | −25.7663 | −1.01771 | −0.508855 | − | 0.860852i | \(-0.669931\pi\) | ||||
−0.508855 | + | 0.860852i | \(0.669931\pi\) | |||||||
\(642\) | 9.84966 | − | 9.85933i | 0.388735 | − | 0.389117i | ||||
\(643\) | 3.85976 | + | 2.22843i | 0.152214 | + | 0.0878809i | 0.574173 | − | 0.818734i | \(-0.305324\pi\) |
−0.421958 | + | 0.906615i | \(0.638657\pi\) | |||||||
\(644\) | −25.5404 | − | 14.7458i | −1.00643 | − | 0.581064i | ||||
\(645\) | −0.437928 | − | 0.117112i | −0.0172434 | − | 0.00461129i | ||||
\(646\) | −13.5012 | −0.531198 | ||||||||
\(647\) | −4.35879 | + | 7.54964i | −0.171362 | + | 0.296807i | −0.938896 | − | 0.344201i | \(-0.888150\pi\) |
0.767535 | + | 0.641008i | \(0.221483\pi\) | |||||||
\(648\) | −0.0468549 | − | 23.8611i | −0.00184064 | − | 0.937354i | ||||
\(649\) | 0.460436 | 0.0180737 | ||||||||
\(650\) | 12.5324 | + | 6.45913i | 0.491562 | + | 0.253348i | ||||
\(651\) | 7.02944 | − | 26.2858i | 0.275505 | − | 1.03022i | ||||
\(652\) | 18.2964i | 0.716541i | ||||||||
\(653\) | 10.9850 | 0.429875 | 0.214938 | − | 0.976628i | \(-0.431045\pi\) | ||||
0.214938 | + | 0.976628i | \(0.431045\pi\) | |||||||
\(654\) | 2.50810 | − | 9.37878i | 0.0980746 | − | 0.366739i | ||||
\(655\) | 1.04654 | + | 0.604222i | 0.0408919 | + | 0.0236089i | ||||
\(656\) | 5.99363 | − | 3.46043i | 0.234012 | − | 0.135107i | ||||
\(657\) | −18.2709 | + | 0.0179388i | −0.712815 | + | 0.000699860i | ||||
\(658\) | − | 9.28294i | − | 0.361887i | ||||||
\(659\) | 18.2023 | 0.709062 | 0.354531 | − | 0.935044i | \(-0.384641\pi\) | ||||
0.354531 | + | 0.935044i | \(0.384641\pi\) | |||||||
\(660\) | −0.0492930 | + | 0.184326i | −0.00191873 | + | 0.00717488i | ||||
\(661\) | − | 10.4612i | − | 0.406894i | −0.979086 | − | 0.203447i | \(-0.934786\pi\) | ||
0.979086 | − | 0.203447i | \(-0.0652145\pi\) | |||||||
\(662\) | 2.22986 | + | 3.86223i | 0.0866659 | + | 0.150110i | ||||
\(663\) | −25.3723 | − | 23.0370i | −0.985379 | − | 0.894684i | ||||
\(664\) | 16.9200 | − | 29.3064i | 0.656625 | − | 1.13731i | ||||
\(665\) | 0.632953 | + | 0.365435i | 0.0245449 | + | 0.0141710i | ||||
\(666\) | −0.0107523 | − | 10.9514i | −0.000416644 | − | 0.424357i | ||||
\(667\) | −20.1897 | − | 34.9696i | −0.781749 | − | 1.35403i | ||||
\(668\) | 1.62161 | + | 0.936237i | 0.0627420 | + | 0.0362241i | ||||
\(669\) | 3.40025 | + | 0.909306i | 0.131461 | + | 0.0351558i | ||||
\(670\) | −0.0695670 | − | 0.0401645i | −0.00268761 | − | 0.00155169i | ||||
\(671\) | −1.83372 | + | 1.05870i | −0.0707899 | + | 0.0408706i | ||||
\(672\) | −36.7540 | + | 9.86755i | −1.41782 | + | 0.380649i | ||||
\(673\) | 7.31408 | + | 12.6684i | 0.281937 | + | 0.488329i | 0.971862 | − | 0.235552i | \(-0.0756898\pi\) |
−0.689925 | + | 0.723881i | \(0.742356\pi\) | |||||||
\(674\) | 21.8038 | + | 12.5884i | 0.839850 | + | 0.484888i | ||||
\(675\) | −6.75609 | − | 25.0663i | −0.260042 | − | 0.964803i | ||||
\(676\) | 17.9545 | − | 1.71850i | 0.690556 | − | 0.0660963i | ||||
\(677\) | 5.21183 | − | 9.02716i | 0.200307 | − | 0.346942i | −0.748320 | − | 0.663338i | \(-0.769139\pi\) |
0.948627 | + | 0.316396i | \(0.102473\pi\) | |||||||
\(678\) | −3.16587 | + | 3.16898i | −0.121585 | + | 0.121704i | ||||
\(679\) | 37.6448 | 1.44468 | ||||||||
\(680\) | −0.450353 | + | 0.780034i | −0.0172702 | + | 0.0299129i | ||||
\(681\) | 32.2003 | − | 32.2319i | 1.23392 | − | 1.23513i | ||||
\(682\) | 4.19877i | 0.160779i | ||||||||
\(683\) | 5.83030 | − | 3.36612i | 0.223090 | − | 0.128801i | −0.384290 | − | 0.923212i | \(-0.625554\pi\) |
0.607380 | + | 0.794411i | \(0.292220\pi\) | |||||||
\(684\) | −13.0839 | + | 0.0128461i | −0.500275 | + | 0.000491183i | ||||
\(685\) | 0.257652 | + | 0.446267i | 0.00984439 | + | 0.0170510i | ||||
\(686\) | 0.154378 | + | 0.267391i | 0.00589419 | + | 0.0102090i | ||||
\(687\) | −44.9181 | − | 12.0121i | −1.71373 | − | 0.458291i | ||||
\(688\) | −1.47923 | − | 2.56211i | −0.0563952 | − | 0.0976794i | ||||
\(689\) | −1.24374 | + | 2.41319i | −0.0473829 | + | 0.0919353i | ||||
\(690\) | 0.458748 | − | 0.123163i | 0.0174642 | − | 0.00468872i | ||||
\(691\) | −6.40388 | + | 3.69728i | −0.243615 | + | 0.140651i | −0.616837 | − | 0.787091i | \(-0.711586\pi\) |
0.373222 | + | 0.927742i | \(0.378253\pi\) | |||||||
\(692\) | −10.2075 | + | 17.6800i | −0.388032 | + | 0.672092i | ||||
\(693\) | −12.5072 | + | 7.23744i | −0.475111 | + | 0.274928i | ||||
\(694\) | 12.5611i | 0.476811i | ||||||||
\(695\) | − | 0.236785i | − | 0.00898176i | ||||||
\(696\) | −31.6498 | − | 8.46388i | −1.19968 | − | 0.320823i | ||||
\(697\) | 47.0008 | − | 27.1359i | 1.78028 | − | 1.02785i | ||||
\(698\) | 10.6483 | − | 18.4434i | 0.403044 | − | 0.698093i | ||||
\(699\) | −9.99415 | − | 9.98435i | −0.378014 | − | 0.377643i | ||||
\(700\) | −22.5457 | + | 13.0168i | −0.852148 | + | 0.491988i | ||||
\(701\) | −30.2665 | −1.14315 | −0.571576 | − | 0.820549i | \(-0.693668\pi\) | ||||
−0.571576 | + | 0.820549i | \(0.693668\pi\) | |||||||
\(702\) | 10.8658 | + | 9.84625i | 0.410103 | + | 0.371623i | ||||
\(703\) | −14.6614 | −0.552963 | ||||||||
\(704\) | 3.53115 | − | 2.03871i | 0.133085 | − | 0.0768368i | ||||
\(705\) | −0.239566 | − | 0.239330i | −0.00902256 | − | 0.00901371i | ||||
\(706\) | 1.81286 | − | 3.13996i | 0.0682278 | − | 0.118174i | ||||
\(707\) | 55.9448 | − | 32.2997i | 2.10402 | − | 1.21476i | ||||
\(708\) | 0.833435 | + | 0.222880i | 0.0313224 | + | 0.00837633i | ||||
\(709\) | − | 0.0660461i | − | 0.00248041i | −0.999999 | − | 0.00124021i | \(-0.999605\pi\) | ||
0.999999 | − | 0.00124021i | \(-0.000394770\pi\) | |||||||
\(710\) | 0.636920i | 0.0239032i | ||||||||
\(711\) | −3.20363 | − | 1.84543i | −0.120146 | − | 0.0692090i | ||||
\(712\) | −1.99207 | + | 3.45037i | −0.0746562 | + | 0.129308i | ||||
\(713\) | −20.5024 | + | 11.8370i | −0.767820 | + | 0.443301i | ||||
\(714\) | −26.9837 | + | 7.24445i | −1.00984 | + | 0.271117i | ||||
\(715\) | −0.154800 | − | 0.240815i | −0.00578920 | − | 0.00900596i | ||||
\(716\) | −3.60911 | − | 6.25117i | −0.134879 | − | 0.233617i | ||||
\(717\) | 22.9004 | + | 6.12409i | 0.855230 | + | 0.228708i | ||||
\(718\) | 6.31641 | + | 10.9403i | 0.235726 | + | 0.408290i | ||||
\(719\) | 1.90007 | + | 3.29102i | 0.0708607 | + | 0.122734i | 0.899279 | − | 0.437376i | \(-0.144092\pi\) |
−0.828418 | + | 0.560110i | \(0.810759\pi\) | |||||||
\(720\) | −0.0648740 | + | 0.112620i | −0.00241771 | + | 0.00419711i | ||||
\(721\) | −57.4139 | + | 33.1479i | −2.13821 | + | 1.23449i | ||||
\(722\) | 7.13696i | 0.265610i | ||||||||
\(723\) | 16.2544 | − | 16.2704i | 0.604509 | − | 0.605103i | ||||
\(724\) | −7.00289 | + | 12.1294i | −0.260260 | + | 0.450784i | ||||
\(725\) | −35.6448 | −1.32382 | ||||||||
\(726\) | −8.96315 | + | 8.97196i | −0.332654 | + | 0.332981i | ||||
\(727\) | −18.0132 | + | 31.1997i | −0.668071 | + | 1.15713i | 0.310372 | + | 0.950615i | \(0.399546\pi\) |
−0.978443 | + | 0.206518i | \(0.933787\pi\) | |||||||
\(728\) | 16.4473 | − | 31.9120i | 0.609577 | − | 1.18274i | ||||
\(729\) | −0.0795277 | − | 26.9999i | −0.00294547 | − | 0.999996i | ||||
\(730\) | −0.255562 | − | 0.147549i | −0.00945877 | − | 0.00546102i | ||||
\(731\) | −11.5998 | − | 20.0915i | −0.429035 | − | 0.743110i | ||||
\(732\) | −3.83168 | + | 1.02871i | −0.141623 | + | 0.0380223i | ||||
\(733\) | −6.90293 | + | 3.98541i | −0.254966 | + | 0.147204i | −0.622036 | − | 0.782989i | \(-0.713694\pi\) |
0.367070 | + | 0.930193i | \(0.380361\pi\) | |||||||
\(734\) | 14.0759 | + | 8.12674i | 0.519552 | + | 0.299963i | ||||
\(735\) | 0.735995 | + | 0.196822i | 0.0271476 | + | 0.00725989i | ||||
\(736\) | 28.6749 | + | 16.5554i | 1.05697 | + | 0.610242i | ||||
\(737\) | −1.06313 | − | 1.84139i | −0.0391607 | − | 0.0678284i | ||||
\(738\) | −20.0989 | + | 11.6304i | −0.739852 | + | 0.428123i | ||||
\(739\) | −8.98365 | − | 5.18671i | −0.330469 | − | 0.190796i | 0.325580 | − | 0.945514i | \(-0.394440\pi\) |
−0.656049 | + | 0.754718i | \(0.727774\pi\) | |||||||
\(740\) | −0.200306 | + | 0.346940i | −0.00736339 | + | 0.0127538i | ||||
\(741\) | 13.1961 | − | 14.5338i | 0.484772 | − | 0.533914i | ||||
\(742\) | 1.10665 | + | 1.91677i | 0.0406264 | + | 0.0703670i | ||||
\(743\) | 1.32175i | 0.0484904i | 0.999706 | + | 0.0242452i | \(0.00771824\pi\) | ||||
−0.999706 | + | 0.0242452i | \(0.992282\pi\) | |||||||
\(744\) | −4.96230 | + | 18.5560i | −0.181927 | + | 0.680295i | ||||
\(745\) | 1.24176 | 0.0454946 | ||||||||
\(746\) | 4.75791i | 0.174199i | ||||||||
\(747\) | 19.1132 | − | 33.1803i | 0.699316 | − | 1.21400i | ||||
\(748\) | −8.45659 | + | 4.88242i | −0.309204 | + | 0.178519i | ||||
\(749\) | −33.4370 | − | 19.3048i | −1.22176 | − | 0.705383i | ||||
\(750\) | 0.216731 | − | 0.810441i | 0.00791389 | − | 0.0295931i | ||||
\(751\) | −13.8895 | −0.506834 | −0.253417 | − | 0.967357i | \(-0.581555\pi\) | ||||
−0.253417 | + | 0.967357i | \(0.581555\pi\) | |||||||
\(752\) | − | 2.20999i | − | 0.0805901i | ||||||
\(753\) | 2.31910 | − | 8.67202i | 0.0845127 | − | 0.316026i | ||||
\(754\) | 16.9358 | − | 10.8867i | 0.616767 | − | 0.396470i | ||||
\(755\) | −0.859774 | −0.0312904 | ||||||||
\(756\) | −26.1427 | + | 7.04620i | −0.950801 | + | 0.256268i | ||||
\(757\) | 15.7299 | − | 27.2450i | 0.571712 | − | 0.990235i | −0.424678 | − | 0.905344i | \(-0.639613\pi\) |
0.996390 | − | 0.0848903i | \(-0.0270540\pi\) | |||||||
\(758\) | −12.3931 | −0.450138 | ||||||||
\(759\) | 12.1459 | + | 3.24810i | 0.440869 | + | 0.117899i | ||||
\(760\) | −0.446821 | − | 0.257972i | −0.0162079 | − | 0.00935764i | ||||
\(761\) | 41.9973 | + | 24.2472i | 1.52240 | + | 0.878960i | 0.999649 | + | 0.0264754i | \(0.00842836\pi\) |
0.522753 | + | 0.852484i | \(0.324905\pi\) | |||||||
\(762\) | −6.83707 | + | 6.84378i | −0.247681 | + | 0.247924i | ||||
\(763\) | −26.8963 | −0.973711 | ||||||||
\(764\) | 1.88543 | − | 3.26567i | 0.0682126 | − | 0.118148i | ||||
\(765\) | −0.508728 | + | 0.883143i | −0.0183931 | + | 0.0319301i | ||||
\(766\) | −11.7399 | −0.424178 | ||||||||
\(767\) | −1.08885 | + | 0.699934i | −0.0393161 | + | 0.0252731i | ||||
\(768\) | 22.6975 | − | 6.09372i | 0.819025 | − | 0.219888i | ||||
\(769\) | 11.3355i | 0.408770i | 0.978891 | + | 0.204385i | \(0.0655194\pi\) | ||||
−0.978891 | + | 0.204385i | \(0.934481\pi\) | |||||||
\(770\) | −0.233390 | −0.00841080 | ||||||||
\(771\) | 35.7827 | + | 35.7476i | 1.28868 | + | 1.28742i | ||||
\(772\) | 22.9330 | + | 13.2404i | 0.825378 | + | 0.476532i | ||||
\(773\) | 6.57982 | − | 3.79886i | 0.236660 | − | 0.136635i | −0.376981 | − | 0.926221i | \(-0.623038\pi\) |
0.613640 | + | 0.789586i | \(0.289704\pi\) | |||||||
\(774\) | 4.97168 | + | 8.59172i | 0.178703 | + | 0.308823i | ||||
\(775\) | 20.8983i | 0.750688i | ||||||||
\(776\) | −26.5746 | −0.953974 | ||||||||
\(777\) | −29.3023 | + | 7.86695i | −1.05121 | + | 0.282225i | ||||
\(778\) | − | 13.6158i | − | 0.488148i | ||||||
\(779\) | 15.5441 | + | 26.9231i | 0.556924 | + | 0.964620i | ||||
\(780\) | −0.163635 | − | 0.510831i | −0.00585906 | − | 0.0182907i | ||||
\(781\) | −8.42940 | + | 14.6002i | −0.301628 | + | 0.522435i | ||||
\(782\) | 21.0522 | + | 12.1545i | 0.752825 | + | 0.434644i | ||||
\(783\) | −35.8225 | − | 9.54209i | −1.28019 | − | 0.341007i | ||||
\(784\) | 2.48604 | + | 4.30595i | 0.0887872 | + | 0.153784i | ||||
\(785\) | −0.852820 | − | 0.492376i | −0.0304384 | − | 0.0175736i | ||||
\(786\) | −6.86138 | − | 25.5568i | −0.244737 | − | 0.911582i | ||||
\(787\) | −32.1986 | − | 18.5899i | −1.14776 | − | 0.662658i | −0.199418 | − | 0.979915i | \(-0.563905\pi\) |
−0.948340 | + | 0.317256i | \(0.897238\pi\) | |||||||
\(788\) | −2.60802 | + | 1.50574i | −0.0929070 | + | 0.0536399i | ||||
\(789\) | 2.42884 | − | 9.08239i | 0.0864690 | − | 0.323342i | ||||
\(790\) | −0.0298567 | − | 0.0517133i | −0.00106225 | − | 0.00183988i | ||||
\(791\) | 10.7473 | + | 6.20496i | 0.382130 | + | 0.220623i | ||||
\(792\) | 8.82925 | − | 5.10913i | 0.313734 | − | 0.181545i | ||||
\(793\) | 2.72703 | − | 5.29116i | 0.0968398 | − | 0.187895i | ||||
\(794\) | −4.47266 | + | 7.74688i | −0.158729 | + | 0.274927i | ||||
\(795\) | 0.0779977 | + | 0.0208584i | 0.00276629 | + | 0.000739771i | ||||
\(796\) | −14.4784 | −0.513175 | ||||||||
\(797\) | 3.40431 | − | 5.89644i | 0.120587 | − | 0.208862i | −0.799412 | − | 0.600783i | \(-0.794856\pi\) |
0.919999 | + | 0.391920i | \(0.128189\pi\) | |||||||
\(798\) | −4.14978 | − | 15.4568i | −0.146901 | − | 0.547166i | ||||
\(799\) | − | 17.3303i | − | 0.613101i | ||||||
\(800\) | 25.3127 | − | 14.6143i | 0.894938 | − | 0.516693i | ||||
\(801\) | −2.25029 | + | 3.90647i | −0.0795100 | + | 0.138028i | ||||
\(802\) | 5.00086 | + | 8.66175i | 0.176587 | + | 0.305857i | ||||
\(803\) | −3.90551 | − | 6.76454i | −0.137822 | − | 0.238715i | ||||
\(804\) | −1.03302 | − | 3.84771i | −0.0364317 | − | 0.135698i | ||||
\(805\) | −0.657967 | − | 1.13963i | −0.0231903 | − | 0.0401668i | ||||
\(806\) | −6.38277 | − | 9.92934i | −0.224823 | − | 0.349746i | ||||
\(807\) | 6.13160 | − | 22.9285i | 0.215843 | − | 0.807120i | ||||
\(808\) | −39.4931 | + | 22.8014i | −1.38936 | + | 0.802150i | ||||
\(809\) | 8.57387 | − | 14.8504i | 0.301441 | − | 0.522112i | −0.675021 | − | 0.737798i | \(-0.735866\pi\) |
0.976463 | + | 0.215687i | \(0.0691989\pi\) | |||||||
\(810\) | 0.217299 | − | 0.378086i | 0.00763513 | − | 0.0132846i | ||||
\(811\) | 21.7276i | 0.762959i | 0.924377 | + | 0.381480i | \(0.124585\pi\) | ||||
−0.924377 | + | 0.381480i | \(0.875415\pi\) | |||||||
\(812\) | 37.1754i | 1.30460i | ||||||||
\(813\) | 5.49419 | + | 20.4644i | 0.192690 | + | 0.717718i | ||||
\(814\) | 4.05459 | − | 2.34092i | 0.142113 | − | 0.0820491i | ||||
\(815\) | −0.408200 | + | 0.707022i | −0.0142986 | + | 0.0247659i | ||||
\(816\) | −6.42400 | + | 1.72469i | −0.224885 | + | 0.0603761i | ||||
\(817\) | 11.5089 | − | 6.64464i | 0.402644 | − | 0.232467i | ||||
\(818\) | −15.4787 | −0.541200 | ||||||||
\(819\) | 18.5754 | − | 36.1282i | 0.649076 | − | 1.26242i | ||||
\(820\) | 0.849462 | 0.0296645 | ||||||||
\(821\) | 11.7354 | − | 6.77542i | 0.409567 | − | 0.236464i | −0.281036 | − | 0.959697i | \(-0.590678\pi\) |
0.690604 | + | 0.723233i | \(0.257345\pi\) | |||||||
\(822\) | 2.91513 | − | 10.9008i | 0.101677 | − | 0.380209i | ||||
\(823\) | 18.3870 | − | 31.8472i | 0.640931 | − | 1.11012i | −0.344295 | − | 0.938862i | \(-0.611882\pi\) |
0.985225 | − | 0.171263i | \(-0.0547847\pi\) | |||||||
\(824\) | 40.5303 | − | 23.4002i | 1.41194 | − | 0.815183i | ||||
\(825\) | 7.84401 | − | 7.85171i | 0.273093 | − | 0.273362i | ||||
\(826\) | 1.05528i | 0.0367179i | ||||||||
\(827\) | 46.7697i | 1.62634i | 0.582026 | + | 0.813170i | \(0.302260\pi\) | ||||
−0.582026 | + | 0.813170i | \(0.697740\pi\) | |||||||
\(828\) | 20.4130 | + | 11.7588i | 0.709402 | + | 0.408645i | ||||
\(829\) | 9.45842 | − | 16.3825i | 0.328505 | − | 0.568987i | −0.653711 | − | 0.756744i | \(-0.726789\pi\) |
0.982215 | + | 0.187758i | \(0.0601220\pi\) | |||||||
\(830\) | 0.535598 | − | 0.309228i | 0.0185909 | − | 0.0107335i | ||||
\(831\) | −17.2039 | − | 17.1870i | −0.596795 | − | 0.596209i | ||||
\(832\) | −5.25139 | + | 10.1891i | −0.182059 | + | 0.353243i | ||||
\(833\) | 19.4950 | + | 33.7663i | 0.675461 | + | 1.16993i | ||||
\(834\) | −3.66454 | + | 3.66813i | −0.126892 | + | 0.127017i | ||||
\(835\) | 0.0417757 | + | 0.0723576i | 0.00144571 | + | 0.00250404i | ||||
\(836\) | −2.79676 | − | 4.84413i | −0.0967279 | − | 0.167538i | ||||
\(837\) | −5.59445 | + | 21.0024i | −0.193372 | + | 0.725950i | ||||
\(838\) | 0.696571 | − | 0.402165i | 0.0240626 | − | 0.0138926i | ||||
\(839\) | 11.8603i | 0.409464i | 0.978818 | + | 0.204732i | \(0.0656323\pi\) | ||||
−0.978818 | + | 0.204732i | \(0.934368\pi\) | |||||||
\(840\) | −1.03144 | − | 0.275831i | −0.0355881 | − | 0.00951709i | ||||
\(841\) | −10.9501 | + | 18.9661i | −0.377589 | + | 0.654004i | ||||
\(842\) | −17.4836 | −0.602523 | ||||||||
\(843\) | 9.66647 | + | 36.0050i | 0.332931 | + | 1.24008i | ||||
\(844\) | −0.268121 | + | 0.464399i | −0.00922910 | + | 0.0159853i | ||||
\(845\) | 0.732150 | + | 0.334164i | 0.0251867 | + | 0.0114956i | ||||
\(846\) | 0.00728037 | + | 7.41514i | 0.000250304 | + | 0.254938i | ||||
\(847\) | 30.4275 | + | 17.5673i | 1.04550 | + | 0.603621i | ||||
\(848\) | 0.263460 | + | 0.456327i | 0.00904727 | + | 0.0156703i | ||||
\(849\) | 28.3187 | + | 28.2909i | 0.971896 | + | 0.970942i | ||||
\(850\) | 18.5838 | − | 10.7293i | 0.637418 | − | 0.368014i | ||||
\(851\) | 22.8612 | + | 13.1989i | 0.783671 | + | 0.452453i | ||||
\(852\) | −22.3254 | + | 22.3474i | −0.764857 | + | 0.765608i | ||||
\(853\) | −28.3691 | − | 16.3789i | −0.971340 | − | 0.560804i | −0.0716956 | − | 0.997427i | \(-0.522841\pi\) |
−0.899645 | + | 0.436623i | \(0.856174\pi\) | |||||||
\(854\) | −2.42644 | − | 4.20272i | −0.0830312 | − | 0.143814i | ||||
\(855\) | −0.505884 | − | 0.291411i | −0.0173009 | − | 0.00996603i | ||||
\(856\) | 23.6042 | + | 13.6279i | 0.806775 | + | 0.465791i | ||||
\(857\) | 27.4207 | − | 47.4941i | 0.936674 | − | 1.62237i | 0.165052 | − | 0.986285i | \(-0.447221\pi\) |
0.771622 | − | 0.636081i | \(-0.219446\pi\) | |||||||
\(858\) | −1.32882 | + | 6.12629i | −0.0453653 | + | 0.209148i | ||||
\(859\) | −17.3224 | − | 30.0032i | −0.591031 | − | 1.02370i | −0.994094 | − | 0.108524i | \(-0.965388\pi\) |
0.403063 | − | 0.915172i | \(-0.367946\pi\) | |||||||
\(860\) | − | 0.363121i | − | 0.0123823i | ||||||
\(861\) | 45.5128 | + | 45.4681i | 1.55107 | + | 1.54955i | ||||
\(862\) | −5.77185 | −0.196590 | ||||||||
\(863\) | 8.43673i | 0.287190i | 0.989637 | + | 0.143595i | \(0.0458662\pi\) | ||||
−0.989637 | + | 0.143595i | \(0.954134\pi\) | |||||||
\(864\) | 29.3511 | − | 7.91095i | 0.998544 | − | 0.269136i | ||||
\(865\) | −0.788895 | + | 0.455469i | −0.0268232 | + | 0.0154864i | ||||
\(866\) | 4.02515 | + | 2.32392i | 0.136780 | + | 0.0789700i | ||||
\(867\) | −21.9378 | + | 5.88976i | −0.745047 | + | 0.200027i | ||||
\(868\) | 21.7956 | 0.739792 | ||||||||
\(869\) | − | 1.58057i | − | 0.0536172i | ||||||
\(870\) | −0.423589 | − | 0.423174i | −0.0143610 | − | 0.0143469i | ||||
\(871\) | 5.31330 | + | 2.73844i | 0.180034 | + | 0.0927885i | ||||
\(872\) | 18.9869 | 0.642978 | ||||||||
\(873\) | −30.0704 | + | 0.0295239i | −1.01773 | + | 0.000999231i | ||||
\(874\) | −6.96236 | + | 12.0592i | −0.235505 | + | 0.407907i | ||||
\(875\) | −2.32417 | −0.0785712 | ||||||||
\(876\) | −3.79490 | − | 14.1350i | −0.128218 | − | 0.477577i | ||||
\(877\) | 8.48217 | + | 4.89718i | 0.286423 | + | 0.165366i | 0.636327 | − | 0.771419i | \(-0.280453\pi\) |
−0.349905 | + | 0.936785i | \(0.613786\pi\) | |||||||
\(878\) | −16.0589 | − | 9.27158i | −0.541960 | − | 0.312901i | ||||
\(879\) | 0.134715 | + | 0.501777i | 0.00454382 | + | 0.0169245i | ||||
\(880\) | −0.0555632 | −0.00187304 | ||||||||
\(881\) | 13.3270 | − | 23.0831i | 0.448999 | − | 0.777689i | −0.549322 | − | 0.835611i | \(-0.685114\pi\) |
0.998321 | + | 0.0579215i | \(0.0184473\pi\) | |||||||
\(882\) | −8.35555 | − | 14.4395i | −0.281346 | − | 0.486203i | ||||
\(883\) | 13.3367 | 0.448816 | 0.224408 | − | 0.974495i | \(-0.427955\pi\) | ||||
0.224408 | + | 0.974495i | \(0.427955\pi\) | |||||||
\(884\) | 12.5763 | − | 24.4014i | 0.422987 | − | 0.820707i | ||||
\(885\) | 0.0272337 | + | 0.0272069i | 0.000915450 | + | 0.000914551i | ||||
\(886\) | 31.0670i | 1.04372i | ||||||||
\(887\) | 22.5560 | 0.757355 | 0.378678 | − | 0.925529i | \(-0.376379\pi\) | ||||
0.378678 | + | 0.925529i | \(0.376379\pi\) | |||||||
\(888\) | 20.6854 | − | 5.55352i | 0.694157 | − | 0.186364i | ||||
\(889\) | 23.2100 | + | 13.4003i | 0.778439 | + | 0.449432i | ||||
\(890\) | −0.0630585 | + | 0.0364068i | −0.00211372 | + | 0.00122036i | ||||
\(891\) | 9.98501 | − | 5.79102i | 0.334510 | − | 0.194006i | ||||
\(892\) | 2.81942i | 0.0944011i | ||||||||
\(893\) | 9.92717 | 0.332200 | ||||||||
\(894\) | −19.2367 | − | 19.2178i | −0.643370 | − | 0.642739i | ||||
\(895\) | − | 0.322083i | − | 0.0107661i | ||||||
\(896\) | −17.2988 | − | 29.9625i | −0.577914 | − | 1.00098i | ||||
\(897\) | −33.6606 | + | 10.7825i | −1.12389 | + | 0.360017i | ||||
\(898\) | −3.45666 | + | 5.98711i | −0.115350 | + | 0.199793i | ||||
\(899\) | 25.8442 | + | 14.9212i | 0.861953 | + | 0.497649i | ||||
\(900\) | 17.9991 | − | 10.4154i | 0.599971 | − | 0.347180i | ||||
\(901\) | 2.06600 | + | 3.57842i | 0.0688284 | + | 0.119214i | ||||
\(902\) | −8.59740 | − | 4.96371i | −0.286262 | − | 0.165273i | ||||
\(903\) | 19.4363 | − | 19.4554i | 0.646801 | − | 0.647436i | ||||
\(904\) | −7.58685 | − | 4.38027i | −0.252335 | − | 0.145686i | ||||
\(905\) | −0.541222 | + | 0.312474i | −0.0179908 | + | 0.0103870i | ||||
\(906\) | 13.3191 | + | 13.3061i | 0.442498 | + | 0.442064i | ||||
\(907\) | 1.51436 | + | 2.62295i | 0.0502835 | + | 0.0870935i | 0.890072 | − | 0.455821i | \(-0.150654\pi\) |
−0.839788 | + | 0.542914i | \(0.817321\pi\) | |||||||
\(908\) | 31.6059 | + | 18.2477i | 1.04888 | + | 0.605570i | ||||
\(909\) | −44.6629 | + | 25.8447i | −1.48138 | + | 0.857213i | ||||
\(910\) | 0.551926 | − | 0.354789i | 0.0182962 | − | 0.0117611i | ||||
\(911\) | 8.08483 | − | 14.0033i | 0.267862 | − | 0.463951i | −0.700447 | − | 0.713704i | \(-0.747016\pi\) |
0.968310 | + | 0.249753i | \(0.0803494\pi\) | |||||||
\(912\) | −0.987939 | − | 3.67981i | −0.0327139 | − | 0.121851i | ||||
\(913\) | 16.3701 | 0.541770 | ||||||||
\(914\) | −8.12946 | + | 14.0806i | −0.268899 | + | 0.465746i | ||||
\(915\) | −0.171018 | − | 0.0457341i | −0.00565368 | − | 0.00151192i | ||||
\(916\) | − | 37.2451i | − | 1.23061i | ||||||
\(917\) | −63.4889 | + | 36.6553i | −2.09659 | + | 1.21047i | ||||
\(918\) | 21.5487 | − | 5.80797i | 0.711212 | − | 0.191692i | ||||
\(919\) | −1.41858 | − | 2.45706i | −0.0467947 | − | 0.0810509i | 0.841679 | − | 0.539978i | \(-0.181567\pi\) |
−0.888474 | + | 0.458927i | \(0.848234\pi\) | |||||||
\(920\) | 0.464480 | + | 0.804502i | 0.0153134 | + | 0.0265237i | ||||
\(921\) | −16.4145 | + | 16.4307i | −0.540877 | + | 0.541408i | ||||
\(922\) | 4.10162 | + | 7.10422i | 0.135080 | + | 0.233965i | ||||
\(923\) | −2.26043 | − | 47.3408i | −0.0744031 | − | 1.55824i | ||||
\(924\) | −8.18887 | − | 8.18083i | −0.269394 | − | 0.269130i | ||||
\(925\) | 20.1806 | − | 11.6513i | 0.663536 | − | 0.383092i | ||||
\(926\) | −7.94622 | + | 13.7633i | −0.261129 | + | 0.452289i | ||||
\(927\) | 45.8358 | − | 26.5233i | 1.50545 | − | 0.871141i | ||||
\(928\) | − | 41.7378i | − | 1.37011i | ||||||
\(929\) | 37.8966i | 1.24335i | 0.783276 | + | 0.621674i | \(0.213547\pi\) | ||||
−0.783276 | + | 0.621674i | \(0.786453\pi\) | |||||||
\(930\) | −0.248103 | + | 0.248347i | −0.00813562 | + | 0.00814361i | ||||
\(931\) | −19.3421 | + | 11.1672i | −0.633912 | + | 0.365989i | ||||
\(932\) | 5.65805 | − | 9.80003i | 0.185336 | − | 0.321011i | ||||
\(933\) | −5.96298 | + | 22.2979i | −0.195219 | + | 0.730001i | ||||
\(934\) | −9.50483 | + | 5.48762i | −0.311008 | + | 0.179560i | ||||
\(935\) | −0.435715 | −0.0142494 | ||||||||
\(936\) | −13.1129 | + | 25.5040i | −0.428610 | + | 0.833624i | ||||
\(937\) | −41.8330 | −1.36662 | −0.683312 | − | 0.730126i | \(-0.739461\pi\) | ||||
−0.683312 | + | 0.730126i | \(0.739461\pi\) | |||||||
\(938\) | 4.22030 | − | 2.43659i | 0.137798 | − | 0.0795576i | ||||
\(939\) | −25.2532 | + | 6.77986i | −0.824106 | + | 0.221252i | ||||
\(940\) | 0.135627 | − | 0.234912i | 0.00442365 | − | 0.00766199i | ||||
\(941\) | −1.89154 | + | 1.09208i | −0.0616623 | + | 0.0356008i | −0.530514 | − | 0.847676i | \(-0.678001\pi\) |
0.468852 | + | 0.883277i | \(0.344668\pi\) | |||||||
\(942\) | 5.59128 | + | 20.8260i | 0.182174 | + | 0.678549i | ||||
\(943\) | − | 55.9742i | − | 1.82277i | ||||||
\(944\) | 0.251230i | 0.00817686i | ||||||||
\(945\) | −1.16743 | − | 0.310970i | −0.0379765 | − | 0.0101158i | ||||
\(946\) | −2.12184 | + | 3.67514i | −0.0689871 | + | 0.119489i | ||||
\(947\) | −35.7338 | + | 20.6309i | −1.16119 | + | 0.670414i | −0.951589 | − | 0.307372i | \(-0.900550\pi\) |
−0.209603 | + | 0.977787i | \(0.567217\pi\) | |||||||
\(948\) | 0.765094 | − | 2.86099i | 0.0248491 | − | 0.0929206i | ||||
\(949\) | 19.5190 | + | 10.0600i | 0.633612 | + | 0.326560i | ||||
\(950\) | 6.14601 | + | 10.6452i | 0.199403 | + | 0.345376i | ||||
\(951\) | −8.35485 | − | 31.1196i | −0.270924 | − | 1.00912i | ||||
\(952\) | −27.3208 | − | 47.3210i | −0.885472 | − | 1.53368i | ||||
\(953\) | −24.5159 | − | 42.4627i | −0.794146 | − | 1.37550i | −0.923380 | − | 0.383888i | \(-0.874585\pi\) |
0.129233 | − | 0.991614i | \(-0.458748\pi\) | |||||||
\(954\) | −0.885487 | − | 1.53024i | −0.0286687 | − | 0.0495433i | ||||
\(955\) | 0.145717 | − | 0.0841295i | 0.00471528 | − | 0.00272237i | ||||
\(956\) | 18.9885i | 0.614132i | ||||||||
\(957\) | −4.10942 | − | 15.3065i | −0.132839 | − | 0.494789i | ||||
\(958\) | 3.87149 | − | 6.70562i | 0.125082 | − | 0.216649i | ||||
\(959\) | −31.2611 | −1.00947 | ||||||||
\(960\) | 0.329325 | + | 0.0880692i | 0.0106289 | + | 0.00284242i | ||||
\(961\) | −6.75185 | + | 11.6945i | −0.217802 | + | 0.377243i | ||||
\(962\) | −6.02983 | + | 11.6994i | −0.194409 | + | 0.377205i | ||||
\(963\) | 26.7243 | + | 15.3943i | 0.861179 | + | 0.496075i | ||||
\(964\) | 15.9544 | + | 9.21126i | 0.513856 | + | 0.296675i | ||||
\(965\) | 0.590797 | + | 1.02329i | 0.0190184 | + | 0.0329409i | ||||
\(966\) | −7.44436 | + | 27.8374i | −0.239519 | + | 0.895654i | ||||
\(967\) | −48.5763 | + | 28.0455i | −1.56211 | + | 0.901884i | −0.565064 | + | 0.825047i | \(0.691149\pi\) |
−0.997044 | + | 0.0768368i | \(0.975518\pi\) | |||||||
\(968\) | −21.4797 | − | 12.4013i | −0.690385 | − | 0.398594i | ||||
\(969\) | −7.74720 | − | 28.8563i | −0.248876 | − | 0.926998i | ||||
\(970\) | −0.420606 | − | 0.242837i | −0.0135048 | − | 0.00779702i | ||||
\(971\) | 16.5122 | + | 28.6000i | 0.529903 | + | 0.917819i | 0.999391 | + | 0.0348805i | \(0.0111051\pi\) |
−0.469488 | + | 0.882939i | \(0.655562\pi\) | |||||||
\(972\) | 20.8771 | − | 5.64895i | 0.669632 | − | 0.181190i | ||||
\(973\) | 12.4401 | + | 7.18231i | 0.398812 | + | 0.230254i | ||||
\(974\) | 16.1009 | − | 27.8875i | 0.515906 | − | 0.893575i | ||||
\(975\) | −6.61388 | + | 30.4920i | −0.211814 | + | 0.976526i | ||||
\(976\) | −0.577663 | − | 1.00054i | −0.0184906 | − | 0.0320266i | ||||
\(977\) | 33.4220i | 1.06927i | 0.845084 | + | 0.534633i | \(0.179550\pi\) | ||||
−0.845084 | + | 0.534633i | \(0.820450\pi\) | |||||||
\(978\) | 17.2656 | − | 4.63540i | 0.552094 | − | 0.148224i | ||||
\(979\) | −1.92733 | −0.0615976 | ||||||||
\(980\) | 0.610271i | 0.0194944i | ||||||||
\(981\) | 21.4846 | − | 0.0210941i | 0.685949 | − | 0.000673482i | ||||
\(982\) | −12.0054 | + | 6.93129i | −0.383106 | + | 0.221186i | ||||
\(983\) | −31.4108 | − | 18.1350i | −1.00185 | − | 0.578418i | −0.0930545 | − | 0.995661i | \(-0.529663\pi\) |
−0.908795 | + | 0.417243i | \(0.862996\pi\) | |||||||
\(984\) | −32.1289 | − | 32.0974i | −1.02423 | − | 1.02323i | ||||
\(985\) | −0.134375 | −0.00428154 | ||||||||
\(986\) | − | 30.6426i | − | 0.975860i | ||||||
\(987\) | 19.8405 | − | 5.32669i | 0.631531 | − | 0.169550i | ||||
\(988\) | 13.9777 | + | 7.20400i | 0.444688 | + | 0.229190i | ||||
\(989\) | −23.9274 | −0.760846 | ||||||||
\(990\) | 0.186430 | 0.000183042i | 0.00592514 | 5.81745e-6i | ||||||
\(991\) | 20.1550 | − | 34.9095i | 0.640244 | − | 1.10894i | −0.345134 | − | 0.938554i | \(-0.612166\pi\) |
0.985378 | − | 0.170382i | \(-0.0545003\pi\) | |||||||
\(992\) | −24.4705 | −0.776940 | ||||||||
\(993\) | −6.97525 | + | 6.98210i | −0.221353 | + | 0.221570i | ||||
\(994\) | −33.4623 | − | 19.3195i | −1.06136 | − | 0.612776i | ||||
\(995\) | −0.559487 | − | 0.323020i | −0.0177369 | − | 0.0102404i | ||||
\(996\) | 29.6314 | + | 7.92413i | 0.938908 | + | 0.251086i | ||||
\(997\) | 32.7202 | 1.03626 | 0.518129 | − | 0.855303i | \(-0.326629\pi\) | ||||
0.518129 | + | 0.855303i | \(0.326629\pi\) | |||||||
\(998\) | 7.35248 | − | 12.7349i | 0.232739 | − | 0.403115i | ||||
\(999\) | 23.4003 | − | 6.30704i | 0.740352 | − | 0.199546i |
(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 | 117.2.r.b.43.8 | yes | 22 | |
3.2 | odd | 2 | 351.2.r.b.316.4 | 22 | |||
9.4 | even | 3 | 117.2.l.b.4.8 | ✓ | 22 | ||
9.5 | odd | 6 | 351.2.l.b.199.4 | 22 | |||
13.10 | even | 6 | 117.2.l.b.88.4 | yes | 22 | ||
39.23 | odd | 6 | 351.2.l.b.127.8 | 22 | |||
117.23 | odd | 6 | 351.2.r.b.10.4 | 22 | |||
117.49 | even | 6 | inner | 117.2.r.b.49.8 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
117.2.l.b.4.8 | ✓ | 22 | 9.4 | even | 3 | ||
117.2.l.b.88.4 | yes | 22 | 13.10 | even | 6 | ||
117.2.r.b.43.8 | yes | 22 | 1.1 | even | 1 | trivial | |
117.2.r.b.49.8 | yes | 22 | 117.49 | even | 6 | inner | |
351.2.l.b.127.8 | 22 | 39.23 | odd | 6 | |||
351.2.l.b.199.4 | 22 | 9.5 | odd | 6 | |||
351.2.r.b.10.4 | 22 | 117.23 | odd | 6 | |||
351.2.r.b.316.4 | 22 | 3.2 | odd | 2 |