Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [406,2,Mod(233,406)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(406, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("406.233");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 406 = 2 \cdot 7 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 406.e (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: | \(3.24192632206\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 10.0.3118758597603.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 4x^{8} - 16x^{6} - 34x^{5} + 43x^{4} + 155x^{3} + 199x^{2} + 124x + 43 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 291.1 | ||
Root | \(-0.359001 - 0.701254i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 406.291 |
Dual form | 406.2.e.a.233.1 |
$q$-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 \(\left(\mathbb{Z}/406\mathbb{Z}\right)^\times\).
\(n\) | \(59\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | −1.61748 | + | 2.80156i | −0.933854 | + | 1.61748i | −0.157191 | + | 0.987568i | \(0.550244\pi\) |
−0.776664 | + | 0.629915i | \(0.783090\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −0.572197 | − | 0.991074i | −0.255894 | − | 0.443222i | 0.709244 | − | 0.704963i | \(-0.249037\pi\) |
−0.965138 | + | 0.261741i | \(0.915703\pi\) | |||||||
\(6\) | 3.23497 | 1.32067 | ||||||||
\(7\) | 0.469216 | − | 2.60381i | 0.177347 | − | 0.984148i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −3.73251 | − | 6.46489i | −1.24417 | − | 2.15496i | ||||
\(10\) | −0.572197 | + | 0.991074i | −0.180945 | + | 0.313405i | ||||
\(11\) | 0.425341 | − | 0.736713i | 0.128245 | − | 0.222127i | −0.794752 | − | 0.606935i | \(-0.792399\pi\) |
0.922997 | + | 0.384808i | \(0.125732\pi\) | |||||||
\(12\) | −1.61748 | − | 2.80156i | −0.466927 | − | 0.808742i | ||||
\(13\) | 3.66136 | 1.01548 | 0.507739 | − | 0.861511i | \(-0.330481\pi\) | ||||
0.507739 | + | 0.861511i | \(0.330481\pi\) | |||||||
\(14\) | −2.48958 | + | 0.895553i | −0.665367 | + | 0.239347i | ||||
\(15\) | 3.70208 | 0.955872 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −0.0971241 | + | 0.168224i | −0.0235561 | + | 0.0408003i | −0.877563 | − | 0.479461i | \(-0.840832\pi\) |
0.854007 | + | 0.520261i | \(0.174165\pi\) | |||||||
\(18\) | −3.73251 | + | 6.46489i | −0.879760 | + | 1.52379i | ||||
\(19\) | 3.49684 | + | 6.05671i | 0.802231 | + | 1.38950i | 0.918145 | + | 0.396246i | \(0.129687\pi\) |
−0.115913 | + | 0.993259i | \(0.536980\pi\) | |||||||
\(20\) | 1.14439 | 0.255894 | ||||||||
\(21\) | 6.53580 | + | 5.52616i | 1.42623 | + | 1.20591i | ||||
\(22\) | −0.850683 | −0.181366 | ||||||||
\(23\) | 1.73109 | + | 2.99834i | 0.360958 | + | 0.625197i | 0.988119 | − | 0.153692i | \(-0.0491165\pi\) |
−0.627161 | + | 0.778890i | \(0.715783\pi\) | |||||||
\(24\) | −1.61748 | + | 2.80156i | −0.330167 | + | 0.571867i | ||||
\(25\) | 1.84518 | − | 3.19595i | 0.369036 | − | 0.639190i | ||||
\(26\) | −1.83068 | − | 3.17083i | −0.359026 | − | 0.621851i | ||||
\(27\) | 14.4442 | 2.77978 | ||||||||
\(28\) | 2.02036 | + | 1.70826i | 0.381812 | + | 0.322831i | ||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | −1.85104 | − | 3.20609i | −0.337952 | − | 0.585350i | ||||
\(31\) | 1.98711 | − | 3.44178i | 0.356896 | − | 0.618162i | −0.630544 | − | 0.776153i | \(-0.717168\pi\) |
0.987441 | + | 0.157991i | \(0.0505017\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 1.37597 | + | 2.38324i | 0.239525 | + | 0.414869i | ||||
\(34\) | 0.194248 | 0.0333133 | ||||||||
\(35\) | −2.84905 | + | 1.02487i | −0.481578 | + | 0.173234i | ||||
\(36\) | 7.46501 | 1.24417 | ||||||||
\(37\) | −3.60460 | − | 6.24335i | −0.592592 | − | 1.02640i | −0.993882 | − | 0.110448i | \(-0.964771\pi\) |
0.401290 | − | 0.915951i | \(-0.368562\pi\) | |||||||
\(38\) | 3.49684 | − | 6.05671i | 0.567263 | − | 0.982528i | ||||
\(39\) | −5.92219 | + | 10.2575i | −0.948309 | + | 1.64252i | ||||
\(40\) | −0.572197 | − | 0.991074i | −0.0904723 | − | 0.156703i | ||||
\(41\) | 4.04493 | 0.631712 | 0.315856 | − | 0.948807i | \(-0.397708\pi\) | ||||
0.315856 | + | 0.948807i | \(0.397708\pi\) | |||||||
\(42\) | 1.51790 | − | 8.42325i | 0.234217 | − | 1.29973i | ||||
\(43\) | 9.77788 | 1.49111 | 0.745556 | − | 0.666443i | \(-0.232184\pi\) | ||||
0.745556 | + | 0.666443i | \(0.232184\pi\) | |||||||
\(44\) | 0.425341 | + | 0.736713i | 0.0641226 | + | 0.111064i | ||||
\(45\) | −4.27146 | + | 7.39838i | −0.636751 | + | 1.10289i | ||||
\(46\) | 1.73109 | − | 2.99834i | 0.255236 | − | 0.442081i | ||||
\(47\) | −0.0269105 | − | 0.0466104i | −0.00392531 | − | 0.00679883i | 0.864056 | − | 0.503396i | \(-0.167916\pi\) |
−0.867981 | + | 0.496597i | \(0.834583\pi\) | |||||||
\(48\) | 3.23497 | 0.466927 | ||||||||
\(49\) | −6.55967 | − | 2.44350i | −0.937096 | − | 0.349071i | ||||
\(50\) | −3.69036 | −0.521896 | ||||||||
\(51\) | −0.314193 | − | 0.544199i | −0.0439958 | − | 0.0762030i | ||||
\(52\) | −1.83068 | + | 3.17083i | −0.253869 | + | 0.439715i | ||||
\(53\) | 1.33549 | − | 2.31313i | 0.183443 | − | 0.317733i | −0.759608 | − | 0.650382i | \(-0.774609\pi\) |
0.943051 | + | 0.332649i | \(0.107942\pi\) | |||||||
\(54\) | −7.22208 | − | 12.5090i | −0.982801 | − | 1.70226i | ||||
\(55\) | −0.973516 | −0.131269 | ||||||||
\(56\) | 0.469216 | − | 2.60381i | 0.0627016 | − | 0.347949i | ||||
\(57\) | −22.6244 | −2.99667 | ||||||||
\(58\) | 0.500000 | + | 0.866025i | 0.0656532 | + | 0.113715i | ||||
\(59\) | 4.02177 | − | 6.96591i | 0.523590 | − | 0.906885i | −0.476033 | − | 0.879427i | \(-0.657926\pi\) |
0.999623 | − | 0.0274571i | \(-0.00874096\pi\) | |||||||
\(60\) | −1.85104 | + | 3.20609i | −0.238968 | + | 0.413905i | ||||
\(61\) | 2.54072 | + | 4.40065i | 0.325306 | + | 0.563446i | 0.981574 | − | 0.191081i | \(-0.0611995\pi\) |
−0.656268 | + | 0.754527i | \(0.727866\pi\) | |||||||
\(62\) | −3.97423 | −0.504727 | ||||||||
\(63\) | −18.5847 | + | 6.68531i | −2.34145 | + | 0.842270i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.09502 | − | 3.62868i | −0.259855 | − | 0.450082i | ||||
\(66\) | 1.37597 | − | 2.38324i | 0.169370 | − | 0.293357i | ||||
\(67\) | 5.80013 | − | 10.0461i | 0.708599 | − | 1.22733i | −0.256778 | − | 0.966471i | \(-0.582661\pi\) |
0.965377 | − | 0.260859i | \(-0.0840059\pi\) | |||||||
\(68\) | −0.0971241 | − | 0.168224i | −0.0117780 | − | 0.0204001i | ||||
\(69\) | −11.2001 | −1.34833 | ||||||||
\(70\) | 2.31209 | + | 1.95492i | 0.276347 | + | 0.233658i | ||||
\(71\) | −11.2825 | −1.33898 | −0.669492 | − | 0.742819i | \(-0.733488\pi\) | ||||
−0.669492 | + | 0.742819i | \(0.733488\pi\) | |||||||
\(72\) | −3.73251 | − | 6.46489i | −0.439880 | − | 0.761894i | ||||
\(73\) | 3.65539 | − | 6.33131i | 0.427830 | − | 0.741024i | −0.568850 | − | 0.822442i | \(-0.692611\pi\) |
0.996680 | + | 0.0814175i | \(0.0259447\pi\) | |||||||
\(74\) | −3.60460 | + | 6.24335i | −0.419026 | + | 0.725774i | ||||
\(75\) | 5.96910 | + | 10.3388i | 0.689252 | + | 1.19382i | ||||
\(76\) | −6.99369 | −0.802231 | ||||||||
\(77\) | −1.71868 | − | 1.45319i | −0.195862 | − | 0.165606i | ||||
\(78\) | 11.8444 | 1.34111 | ||||||||
\(79\) | 6.67821 | + | 11.5670i | 0.751357 | + | 1.30139i | 0.947165 | + | 0.320746i | \(0.103934\pi\) |
−0.195808 | + | 0.980642i | \(0.562733\pi\) | |||||||
\(80\) | −0.572197 | + | 0.991074i | −0.0639736 | + | 0.110805i | ||||
\(81\) | −12.1657 | + | 21.0716i | −1.35174 | + | 2.34129i | ||||
\(82\) | −2.02247 | − | 3.50301i | −0.223344 | − | 0.386843i | ||||
\(83\) | 9.04564 | 0.992888 | 0.496444 | − | 0.868069i | \(-0.334639\pi\) | ||||
0.496444 | + | 0.868069i | \(0.334639\pi\) | |||||||
\(84\) | −8.05369 | + | 2.89708i | −0.878730 | + | 0.316098i | ||||
\(85\) | 0.222296 | 0.0241114 | ||||||||
\(86\) | −4.88894 | − | 8.46789i | −0.527188 | − | 0.913116i | ||||
\(87\) | 1.61748 | − | 2.80156i | 0.173412 | − | 0.300359i | ||||
\(88\) | 0.425341 | − | 0.736713i | 0.0453415 | − | 0.0785339i | ||||
\(89\) | −7.11526 | − | 12.3240i | −0.754216 | − | 1.30634i | −0.945763 | − | 0.324857i | \(-0.894684\pi\) |
0.191547 | − | 0.981483i | \(-0.438650\pi\) | |||||||
\(90\) | 8.54291 | 0.900502 | ||||||||
\(91\) | 1.71797 | − | 9.53349i | 0.180092 | − | 0.999381i | ||||
\(92\) | −3.46219 | −0.360958 | ||||||||
\(93\) | 6.42825 | + | 11.1340i | 0.666578 | + | 1.15455i | ||||
\(94\) | −0.0269105 | + | 0.0466104i | −0.00277561 | + | 0.00480750i | ||||
\(95\) | 4.00177 | − | 6.93126i | 0.410573 | − | 0.711133i | ||||
\(96\) | −1.61748 | − | 2.80156i | −0.165084 | − | 0.285933i | ||||
\(97\) | 18.7779 | 1.90660 | 0.953302 | − | 0.302017i | \(-0.0976601\pi\) | ||||
0.953302 | + | 0.302017i | \(0.0976601\pi\) | |||||||
\(98\) | 1.16370 | + | 6.90259i | 0.117552 | + | 0.697267i | ||||
\(99\) | −6.35036 | −0.638235 | ||||||||
\(100\) | 1.84518 | + | 3.19595i | 0.184518 | + | 0.319595i | ||||
\(101\) | −6.85968 | + | 11.8813i | −0.682564 | + | 1.18224i | 0.291632 | + | 0.956531i | \(0.405802\pi\) |
−0.974196 | + | 0.225705i | \(0.927531\pi\) | |||||||
\(102\) | −0.314193 | + | 0.544199i | −0.0311098 | + | 0.0538837i | ||||
\(103\) | −0.590573 | − | 1.02290i | −0.0581909 | − | 0.100790i | 0.835462 | − | 0.549548i | \(-0.185200\pi\) |
−0.893653 | + | 0.448758i | \(0.851867\pi\) | |||||||
\(104\) | 3.66136 | 0.359026 | ||||||||
\(105\) | 1.73707 | − | 9.63951i | 0.169521 | − | 0.940720i | ||||
\(106\) | −2.67097 | −0.259428 | ||||||||
\(107\) | 0.896121 | + | 1.55213i | 0.0866313 | + | 0.150050i | 0.906085 | − | 0.423095i | \(-0.139056\pi\) |
−0.819454 | + | 0.573145i | \(0.805723\pi\) | |||||||
\(108\) | −7.22208 | + | 12.5090i | −0.694945 | + | 1.20368i | ||||
\(109\) | −1.82095 | + | 3.15397i | −0.174415 | + | 0.302096i | −0.939959 | − | 0.341288i | \(-0.889137\pi\) |
0.765544 | + | 0.643384i | \(0.222470\pi\) | |||||||
\(110\) | 0.486758 | + | 0.843090i | 0.0464106 | + | 0.0803855i | ||||
\(111\) | 23.3215 | 2.21358 | ||||||||
\(112\) | −2.48958 | + | 0.895553i | −0.235243 | + | 0.0846218i | ||||
\(113\) | −17.7718 | −1.67183 | −0.835915 | − | 0.548859i | \(-0.815063\pi\) | ||||
−0.835915 | + | 0.548859i | \(0.815063\pi\) | |||||||
\(114\) | 11.3122 | + | 19.5933i | 1.05948 | + | 1.83508i | ||||
\(115\) | 1.98105 | − | 3.43128i | 0.184734 | − | 0.319969i | ||||
\(116\) | 0.500000 | − | 0.866025i | 0.0464238 | − | 0.0804084i | ||||
\(117\) | −13.6660 | − | 23.6703i | −1.26343 | − | 2.18832i | ||||
\(118\) | −8.04354 | −0.740468 | ||||||||
\(119\) | 0.392451 | + | 0.331826i | 0.0359759 | + | 0.0304185i | ||||
\(120\) | 3.70208 | 0.337952 | ||||||||
\(121\) | 5.13817 | + | 8.89957i | 0.467106 | + | 0.809052i | ||||
\(122\) | 2.54072 | − | 4.40065i | 0.230026 | − | 0.398416i | ||||
\(123\) | −6.54261 | + | 11.3321i | −0.589927 | + | 1.02178i | ||||
\(124\) | 1.98711 | + | 3.44178i | 0.178448 | + | 0.309081i | ||||
\(125\) | −9.94520 | −0.889526 | ||||||||
\(126\) | 15.0820 | + | 12.7522i | 1.34361 | + | 1.13605i | ||||
\(127\) | −11.5789 | −1.02746 | −0.513732 | − | 0.857950i | \(-0.671738\pi\) | ||||
−0.513732 | + | 0.857950i | \(0.671738\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | −15.8156 | + | 27.3934i | −1.39248 | + | 2.41185i | ||||
\(130\) | −2.09502 | + | 3.62868i | −0.183745 | + | 0.318256i | ||||
\(131\) | 8.09878 | + | 14.0275i | 0.707593 | + | 1.22559i | 0.965747 | + | 0.259484i | \(0.0835524\pi\) |
−0.258154 | + | 0.966104i | \(0.583114\pi\) | |||||||
\(132\) | −2.75193 | −0.239525 | ||||||||
\(133\) | 17.4113 | − | 6.26322i | 1.50975 | − | 0.543090i | ||||
\(134\) | −11.6003 | −1.00211 | ||||||||
\(135\) | −8.26491 | − | 14.3152i | −0.711330 | − | 1.23206i | ||||
\(136\) | −0.0971241 | + | 0.168224i | −0.00832832 | + | 0.0144251i | ||||
\(137\) | 6.39212 | − | 11.0715i | 0.546116 | − | 0.945900i | −0.452420 | − | 0.891805i | \(-0.649439\pi\) |
0.998536 | − | 0.0540951i | \(-0.0172274\pi\) | |||||||
\(138\) | 5.60003 | + | 9.69954i | 0.476706 | + | 0.825679i | ||||
\(139\) | 0.170575 | 0.0144679 | 0.00723397 | − | 0.999974i | \(-0.497697\pi\) | ||||
0.00723397 | + | 0.999974i | \(0.497697\pi\) | |||||||
\(140\) | 0.536968 | − | 2.97979i | 0.0453821 | − | 0.251838i | ||||
\(141\) | 0.174109 | 0.0146627 | ||||||||
\(142\) | 5.64124 | + | 9.77091i | 0.473402 | + | 0.819957i | ||||
\(143\) | 1.55733 | − | 2.69737i | 0.130230 | − | 0.225565i | ||||
\(144\) | −3.73251 | + | 6.46489i | −0.311042 | + | 0.538741i | ||||
\(145\) | 0.572197 | + | 0.991074i | 0.0475184 | + | 0.0823042i | ||||
\(146\) | −7.31077 | −0.605044 | ||||||||
\(147\) | 17.4558 | − | 14.4250i | 1.43973 | − | 1.18976i | ||||
\(148\) | 7.20919 | 0.592592 | ||||||||
\(149\) | −7.02198 | − | 12.1624i | −0.575263 | − | 0.996384i | −0.996013 | − | 0.0892077i | \(-0.971567\pi\) |
0.420750 | − | 0.907176i | \(-0.361767\pi\) | |||||||
\(150\) | 5.96910 | − | 10.3388i | 0.487375 | − | 0.844158i | ||||
\(151\) | −6.09878 | + | 10.5634i | −0.496311 | + | 0.859636i | −0.999991 | − | 0.00425408i | \(-0.998646\pi\) |
0.503680 | + | 0.863891i | \(0.331979\pi\) | |||||||
\(152\) | 3.49684 | + | 6.05671i | 0.283632 | + | 0.491264i | ||||
\(153\) | 1.45006 | 0.117231 | ||||||||
\(154\) | −0.399154 | + | 2.21502i | −0.0321647 | + | 0.178491i | ||||
\(155\) | −4.54808 | −0.365311 | ||||||||
\(156\) | −5.92219 | − | 10.2575i | −0.474154 | − | 0.821259i | ||||
\(157\) | −7.19485 | + | 12.4618i | −0.574212 | + | 0.994564i | 0.421915 | + | 0.906635i | \(0.361358\pi\) |
−0.996127 | + | 0.0879283i | \(0.971975\pi\) | |||||||
\(158\) | 6.67821 | − | 11.5670i | 0.531290 | − | 0.920220i | ||||
\(159\) | 4.32025 | + | 7.48290i | 0.342618 | + | 0.593433i | ||||
\(160\) | 1.14439 | 0.0904723 | ||||||||
\(161\) | 8.61937 | − | 3.10057i | 0.679302 | − | 0.244359i | ||||
\(162\) | 24.3314 | 1.91165 | ||||||||
\(163\) | −8.38368 | − | 14.5210i | −0.656660 | − | 1.13737i | −0.981475 | − | 0.191591i | \(-0.938635\pi\) |
0.324814 | − | 0.945778i | \(-0.394698\pi\) | |||||||
\(164\) | −2.02247 | + | 3.50301i | −0.157928 | + | 0.273539i | ||||
\(165\) | 1.57465 | − | 2.72737i | 0.122586 | − | 0.212325i | ||||
\(166\) | −4.52282 | − | 7.83376i | −0.351039 | − | 0.608017i | ||||
\(167\) | −10.6555 | −0.824544 | −0.412272 | − | 0.911061i | \(-0.635265\pi\) | ||||
−0.412272 | + | 0.911061i | \(0.635265\pi\) | |||||||
\(168\) | 6.53580 | + | 5.52616i | 0.504248 | + | 0.426353i | ||||
\(169\) | 0.405541 | 0.0311955 | ||||||||
\(170\) | −0.111148 | − | 0.192514i | −0.00852468 | − | 0.0147652i | ||||
\(171\) | 26.1040 | − | 45.2134i | 1.99622 | − | 3.45756i | ||||
\(172\) | −4.88894 | + | 8.46789i | −0.372778 | + | 0.645671i | ||||
\(173\) | −8.96254 | − | 15.5236i | −0.681409 | − | 1.18024i | −0.974551 | − | 0.224167i | \(-0.928034\pi\) |
0.293141 | − | 0.956069i | \(-0.405299\pi\) | |||||||
\(174\) | −3.23497 | −0.245242 | ||||||||
\(175\) | −7.45586 | − | 6.30409i | −0.563610 | − | 0.476545i | ||||
\(176\) | −0.850683 | −0.0641226 | ||||||||
\(177\) | 13.0103 | + | 22.5345i | 0.977914 | + | 1.69380i | ||||
\(178\) | −7.11526 | + | 12.3240i | −0.533311 | + | 0.923722i | ||||
\(179\) | −2.64460 | + | 4.58058i | −0.197667 | + | 0.342368i | −0.947771 | − | 0.318950i | \(-0.896670\pi\) |
0.750105 | + | 0.661319i | \(0.230003\pi\) | |||||||
\(180\) | −4.27146 | − | 7.39838i | −0.318376 | − | 0.551443i | ||||
\(181\) | 13.1711 | 0.978997 | 0.489498 | − | 0.872004i | \(-0.337180\pi\) | ||||
0.489498 | + | 0.872004i | \(0.337180\pi\) | |||||||
\(182\) | −9.11523 | + | 3.27894i | −0.675665 | + | 0.243051i | ||||
\(183\) | −16.4383 | −1.21515 | ||||||||
\(184\) | 1.73109 | + | 2.99834i | 0.127618 | + | 0.221041i | ||||
\(185\) | −4.12508 | + | 7.14485i | −0.303282 | + | 0.525300i | ||||
\(186\) | 6.42825 | − | 11.1340i | 0.471342 | − | 0.816388i | ||||
\(187\) | 0.0826218 | + | 0.143105i | 0.00604190 | + | 0.0104649i | ||||
\(188\) | 0.0538211 | 0.00392531 | ||||||||
\(189\) | 6.77743 | − | 37.6099i | 0.492985 | − | 2.73572i | ||||
\(190\) | −8.00353 | −0.580637 | ||||||||
\(191\) | −4.95435 | − | 8.58118i | −0.358484 | − | 0.620912i | 0.629224 | − | 0.777224i | \(-0.283373\pi\) |
−0.987708 | + | 0.156312i | \(0.950040\pi\) | |||||||
\(192\) | −1.61748 | + | 2.80156i | −0.116732 | + | 0.202185i | ||||
\(193\) | 8.69752 | − | 15.0645i | 0.626061 | − | 1.08437i | −0.362274 | − | 0.932072i | \(-0.617999\pi\) |
0.988335 | − | 0.152298i | \(-0.0486672\pi\) | |||||||
\(194\) | −9.38894 | − | 16.2621i | −0.674087 | − | 1.16755i | ||||
\(195\) | 13.5546 | 0.970667 | ||||||||
\(196\) | 5.39597 | − | 4.45909i | 0.385426 | − | 0.318507i | ||||
\(197\) | 17.5961 | 1.25367 | 0.626834 | − | 0.779153i | \(-0.284350\pi\) | ||||
0.626834 | + | 0.779153i | \(0.284350\pi\) | |||||||
\(198\) | 3.17518 | + | 5.49957i | 0.225650 | + | 0.390837i | ||||
\(199\) | −5.64229 | + | 9.77274i | −0.399972 | + | 0.692771i | −0.993722 | − | 0.111878i | \(-0.964313\pi\) |
0.593750 | + | 0.804649i | \(0.297647\pi\) | |||||||
\(200\) | 1.84518 | − | 3.19595i | 0.130474 | − | 0.225988i | ||||
\(201\) | 18.7632 | + | 32.4989i | 1.32346 | + | 2.29229i | ||||
\(202\) | 13.7194 | 0.965291 | ||||||||
\(203\) | −0.469216 | + | 2.60381i | −0.0329325 | + | 0.182752i | ||||
\(204\) | 0.628386 | 0.0439958 | ||||||||
\(205\) | −2.31450 | − | 4.00883i | −0.161652 | − | 0.279989i | ||||
\(206\) | −0.590573 | + | 1.02290i | −0.0411472 | + | 0.0712690i | ||||
\(207\) | 12.9226 | − | 22.3827i | 0.898185 | − | 1.55570i | ||||
\(208\) | −1.83068 | − | 3.17083i | −0.126935 | − | 0.219857i | ||||
\(209\) | 5.94941 | 0.411529 | ||||||||
\(210\) | −9.21660 | + | 3.31541i | −0.636006 | + | 0.228785i | ||||
\(211\) | −9.87572 | −0.679873 | −0.339936 | − | 0.940448i | \(-0.610406\pi\) | ||||
−0.339936 | + | 0.940448i | \(0.610406\pi\) | |||||||
\(212\) | 1.33549 | + | 2.31313i | 0.0917216 | + | 0.158866i | ||||
\(213\) | 18.2492 | − | 31.6086i | 1.25042 | − | 2.16578i | ||||
\(214\) | 0.896121 | − | 1.55213i | 0.0612576 | − | 0.106101i | ||||
\(215\) | −5.59487 | − | 9.69060i | −0.381567 | − | 0.660894i | ||||
\(216\) | 14.4442 | 0.982801 | ||||||||
\(217\) | −8.02937 | − | 6.78901i | −0.545069 | − | 0.460868i | ||||
\(218\) | 3.64190 | 0.246660 | ||||||||
\(219\) | 11.8250 | + | 20.4816i | 0.799063 | + | 1.38402i | ||||
\(220\) | 0.486758 | − | 0.843090i | 0.0328172 | − | 0.0568411i | ||||
\(221\) | −0.355606 | + | 0.615928i | −0.0239207 | + | 0.0414318i | ||||
\(222\) | −11.6608 | − | 20.1970i | −0.782618 | − | 1.35553i | ||||
\(223\) | −16.5982 | −1.11150 | −0.555748 | − | 0.831351i | \(-0.687568\pi\) | ||||
−0.555748 | + | 0.831351i | \(0.687568\pi\) | |||||||
\(224\) | 2.02036 | + | 1.70826i | 0.134991 | + | 0.114138i | ||||
\(225\) | −27.5486 | −1.83657 | ||||||||
\(226\) | 8.88590 | + | 15.3908i | 0.591081 | + | 1.02378i | ||||
\(227\) | −8.99651 | + | 15.5824i | −0.597120 | + | 1.03424i | 0.396125 | + | 0.918197i | \(0.370355\pi\) |
−0.993244 | + | 0.116045i | \(0.962978\pi\) | |||||||
\(228\) | 11.3122 | − | 19.5933i | 0.749167 | − | 1.29760i | ||||
\(229\) | 1.01911 | + | 1.76514i | 0.0673444 | + | 0.116644i | 0.897732 | − | 0.440543i | \(-0.145214\pi\) |
−0.830387 | + | 0.557187i | \(0.811881\pi\) | |||||||
\(230\) | −3.96211 | −0.261253 | ||||||||
\(231\) | 6.85114 | − | 2.46450i | 0.450772 | − | 0.162152i | ||||
\(232\) | −1.00000 | −0.0656532 | ||||||||
\(233\) | 8.24947 | + | 14.2885i | 0.540441 | + | 0.936071i | 0.998879 | + | 0.0473443i | \(0.0150758\pi\) |
−0.458438 | + | 0.888726i | \(0.651591\pi\) | |||||||
\(234\) | −13.6660 | + | 23.6703i | −0.893377 | + | 1.54737i | ||||
\(235\) | −0.0307963 | + | 0.0533407i | −0.00200893 | + | 0.00347956i | ||||
\(236\) | 4.02177 | + | 6.96591i | 0.261795 | + | 0.453442i | ||||
\(237\) | −43.2075 | −2.80663 | ||||||||
\(238\) | 0.0911443 | − | 0.505786i | 0.00590801 | − | 0.0327852i | ||||
\(239\) | 18.7414 | 1.21228 | 0.606141 | − | 0.795357i | \(-0.292717\pi\) | ||||
0.606141 | + | 0.795357i | \(0.292717\pi\) | |||||||
\(240\) | −1.85104 | − | 3.20609i | −0.119484 | − | 0.206952i | ||||
\(241\) | −8.93903 | + | 15.4828i | −0.575813 | + | 0.997338i | 0.420139 | + | 0.907460i | \(0.361981\pi\) |
−0.995953 | + | 0.0898784i | \(0.971352\pi\) | |||||||
\(242\) | 5.13817 | − | 8.89957i | 0.330294 | − | 0.572086i | ||||
\(243\) | −17.6893 | − | 30.6388i | −1.13477 | − | 1.96548i | ||||
\(244\) | −5.08144 | −0.325306 | ||||||||
\(245\) | 1.33174 | + | 7.89929i | 0.0850815 | + | 0.504667i | ||||
\(246\) | 13.0852 | 0.834283 | ||||||||
\(247\) | 12.8032 | + | 22.1758i | 0.814648 | + | 1.41101i | ||||
\(248\) | 1.98711 | − | 3.44178i | 0.126182 | − | 0.218553i | ||||
\(249\) | −14.6312 | + | 25.3419i | −0.927213 | + | 1.60598i | ||||
\(250\) | 4.97260 | + | 8.61279i | 0.314495 | + | 0.544721i | ||||
\(251\) | −1.69249 | −0.106829 | −0.0534144 | − | 0.998572i | \(-0.517010\pi\) | ||||
−0.0534144 | + | 0.998572i | \(0.517010\pi\) | |||||||
\(252\) | 3.50270 | − | 19.4375i | 0.220649 | − | 1.22445i | ||||
\(253\) | 2.94522 | 0.185165 | ||||||||
\(254\) | 5.78947 | + | 10.0277i | 0.363264 | + | 0.629191i | ||||
\(255\) | −0.359561 | + | 0.622778i | −0.0225166 | + | 0.0389998i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −1.77662 | − | 3.07719i | −0.110822 | − | 0.191950i | 0.805280 | − | 0.592895i | \(-0.202015\pi\) |
−0.916102 | + | 0.400945i | \(0.868682\pi\) | |||||||
\(258\) | 31.6311 | 1.96927 | ||||||||
\(259\) | −17.9478 | + | 6.45622i | −1.11522 | + | 0.401170i | ||||
\(260\) | 4.19004 | 0.259855 | ||||||||
\(261\) | 3.73251 | + | 6.46489i | 0.231036 | + | 0.400167i | ||||
\(262\) | 8.09878 | − | 14.0275i | 0.500344 | − | 0.866621i | ||||
\(263\) | 9.18136 | − | 15.9026i | 0.566147 | − | 0.980595i | −0.430795 | − | 0.902450i | \(-0.641767\pi\) |
0.996942 | − | 0.0781456i | \(-0.0248999\pi\) | |||||||
\(264\) | 1.37597 | + | 2.38324i | 0.0846848 | + | 0.146678i | ||||
\(265\) | −3.05665 | −0.187768 | ||||||||
\(266\) | −14.1298 | − | 11.9470i | −0.866351 | − | 0.732519i | ||||
\(267\) | 46.0353 | 2.81731 | ||||||||
\(268\) | 5.80013 | + | 10.0461i | 0.354300 | + | 0.613665i | ||||
\(269\) | −9.09102 | + | 15.7461i | −0.554289 | + | 0.960057i | 0.443669 | + | 0.896191i | \(0.353676\pi\) |
−0.997958 | + | 0.0638663i | \(0.979657\pi\) | |||||||
\(270\) | −8.26491 | + | 14.3152i | −0.502986 | + | 0.871198i | ||||
\(271\) | 3.65352 | + | 6.32808i | 0.221935 | + | 0.384403i | 0.955396 | − | 0.295329i | \(-0.0954293\pi\) |
−0.733460 | + | 0.679732i | \(0.762096\pi\) | |||||||
\(272\) | 0.194248 | 0.0117780 | ||||||||
\(273\) | 23.9299 | + | 20.2333i | 1.44830 | + | 1.22457i | ||||
\(274\) | −12.7842 | −0.772324 | ||||||||
\(275\) | −1.56966 | − | 2.71874i | −0.0946543 | − | 0.163946i | ||||
\(276\) | 5.60003 | − | 9.69954i | 0.337082 | − | 0.583843i | ||||
\(277\) | 8.32098 | − | 14.4124i | 0.499959 | − | 0.865955i | −0.500041 | − | 0.866002i | \(-0.666682\pi\) |
1.00000 | 4.71482e-5i | \(1.50077e-5\pi\) | ||||||||
\(278\) | −0.0852873 | − | 0.147722i | −0.00511519 | − | 0.00885977i | ||||
\(279\) | −29.6676 | −1.77616 | ||||||||
\(280\) | −2.84905 | + | 1.02487i | −0.170264 | + | 0.0612474i | ||||
\(281\) | 13.2562 | 0.790800 | 0.395400 | − | 0.918509i | \(-0.370606\pi\) | ||||
0.395400 | + | 0.918509i | \(0.370606\pi\) | |||||||
\(282\) | −0.0870547 | − | 0.150783i | −0.00518403 | − | 0.00897901i | ||||
\(283\) | 7.63929 | − | 13.2316i | 0.454109 | − | 0.786539i | −0.544528 | − | 0.838743i | \(-0.683291\pi\) |
0.998636 | + | 0.0522035i | \(0.0166244\pi\) | |||||||
\(284\) | 5.64124 | − | 9.77091i | 0.334746 | − | 0.579797i | ||||
\(285\) | 12.9456 | + | 22.4224i | 0.766830 | + | 1.32819i | ||||
\(286\) | −3.11465 | −0.184173 | ||||||||
\(287\) | 1.89795 | − | 10.5322i | 0.112032 | − | 0.621698i | ||||
\(288\) | 7.46501 | 0.439880 | ||||||||
\(289\) | 8.48113 | + | 14.6898i | 0.498890 | + | 0.864103i | ||||
\(290\) | 0.572197 | − | 0.991074i | 0.0336006 | − | 0.0581979i | ||||
\(291\) | −30.3729 | + | 52.6074i | −1.78049 | + | 3.08390i | ||||
\(292\) | 3.65539 | + | 6.33131i | 0.213915 | + | 0.370512i | ||||
\(293\) | −15.5191 | −0.906637 | −0.453318 | − | 0.891349i | \(-0.649760\pi\) | ||||
−0.453318 | + | 0.891349i | \(0.649760\pi\) | |||||||
\(294\) | −21.2203 | − | 7.90464i | −1.23759 | − | 0.461008i | ||||
\(295\) | −9.20498 | −0.535935 | ||||||||
\(296\) | −3.60460 | − | 6.24335i | −0.209513 | − | 0.362887i | ||||
\(297\) | 6.14370 | − | 10.6412i | 0.356494 | − | 0.617465i | ||||
\(298\) | −7.02198 | + | 12.1624i | −0.406772 | + | 0.704550i | ||||
\(299\) | 6.33815 | + | 10.9780i | 0.366545 | + | 0.634874i | ||||
\(300\) | −11.9382 | −0.689252 | ||||||||
\(301\) | 4.58794 | − | 25.4598i | 0.264444 | − | 1.46748i | ||||
\(302\) | 12.1976 | 0.701890 | ||||||||
\(303\) | −22.1908 | − | 38.4357i | −1.27483 | − | 2.20807i | ||||
\(304\) | 3.49684 | − | 6.05671i | 0.200558 | − | 0.347376i | ||||
\(305\) | 2.90758 | − | 5.03608i | 0.166488 | − | 0.288365i | ||||
\(306\) | −0.725032 | − | 1.25579i | −0.0414473 | − | 0.0717889i | ||||
\(307\) | 3.14277 | 0.179368 | 0.0896838 | − | 0.995970i | \(-0.471414\pi\) | ||||
0.0896838 | + | 0.995970i | \(0.471414\pi\) | |||||||
\(308\) | 2.11784 | − | 0.761832i | 0.120675 | − | 0.0434094i | ||||
\(309\) | 3.82097 | 0.217367 | ||||||||
\(310\) | 2.27404 | + | 3.93875i | 0.129157 | + | 0.223706i | ||||
\(311\) | −12.1080 | + | 20.9717i | −0.686581 | + | 1.18919i | 0.286356 | + | 0.958123i | \(0.407556\pi\) |
−0.972937 | + | 0.231070i | \(0.925777\pi\) | |||||||
\(312\) | −5.92219 | + | 10.2575i | −0.335278 | + | 0.580718i | ||||
\(313\) | 5.17640 | + | 8.96579i | 0.292588 | + | 0.506777i | 0.974421 | − | 0.224731i | \(-0.0721504\pi\) |
−0.681833 | + | 0.731508i | \(0.738817\pi\) | |||||||
\(314\) | 14.3897 | 0.812058 | ||||||||
\(315\) | 17.2598 | + | 14.5935i | 0.972477 | + | 0.822251i | ||||
\(316\) | −13.3564 | −0.751357 | ||||||||
\(317\) | 17.2664 | + | 29.9063i | 0.969780 | + | 1.67971i | 0.696185 | + | 0.717862i | \(0.254879\pi\) |
0.273594 | + | 0.961845i | \(0.411787\pi\) | |||||||
\(318\) | 4.32025 | − | 7.48290i | 0.242268 | − | 0.419620i | ||||
\(319\) | −0.425341 | + | 0.736713i | −0.0238145 | + | 0.0412480i | ||||
\(320\) | −0.572197 | − | 0.991074i | −0.0319868 | − | 0.0554027i | ||||
\(321\) | −5.79784 | −0.323604 | ||||||||
\(322\) | −6.99486 | − | 5.91431i | −0.389808 | − | 0.329592i | ||||
\(323\) | −1.35851 | −0.0755896 | ||||||||
\(324\) | −12.1657 | − | 21.0716i | −0.675871 | − | 1.17064i | ||||
\(325\) | 6.75587 | − | 11.7015i | 0.374748 | − | 0.649083i | ||||
\(326\) | −8.38368 | + | 14.5210i | −0.464329 | + | 0.804241i | ||||
\(327\) | −5.89071 | − | 10.2030i | −0.325757 | − | 0.564227i | ||||
\(328\) | 4.04493 | 0.223344 | ||||||||
\(329\) | −0.133992 | + | 0.0481996i | −0.00738720 | + | 0.00265733i | ||||
\(330\) | −3.14929 | −0.173363 | ||||||||
\(331\) | −2.55022 | − | 4.41710i | −0.140173 | − | 0.242786i | 0.787389 | − | 0.616457i | \(-0.211432\pi\) |
−0.927562 | + | 0.373671i | \(0.878099\pi\) | |||||||
\(332\) | −4.52282 | + | 7.83376i | −0.248222 | + | 0.429933i | ||||
\(333\) | −26.9084 | + | 46.6066i | −1.47457 | + | 2.55403i | ||||
\(334\) | 5.32773 | + | 9.22789i | 0.291520 | + | 0.504928i | ||||
\(335\) | −13.2753 | −0.725306 | ||||||||
\(336\) | 1.51790 | − | 8.42325i | 0.0828081 | − | 0.459526i | ||||
\(337\) | 24.7613 | 1.34884 | 0.674418 | − | 0.738350i | \(-0.264394\pi\) | ||||
0.674418 | + | 0.738350i | \(0.264394\pi\) | |||||||
\(338\) | −0.202771 | − | 0.351209i | −0.0110293 | − | 0.0191033i | ||||
\(339\) | 28.7456 | − | 49.7888i | 1.56125 | − | 2.70416i | ||||
\(340\) | −0.111148 | + | 0.192514i | −0.00602786 | + | 0.0104406i | ||||
\(341\) | −1.69040 | − | 2.92786i | −0.0915405 | − | 0.158553i | ||||
\(342\) | −52.2080 | −2.82308 | ||||||||
\(343\) | −9.44032 | + | 15.9336i | −0.509729 | + | 0.860335i | ||||
\(344\) | 9.77788 | 0.527188 | ||||||||
\(345\) | 6.40864 | + | 11.1001i | 0.345030 | + | 0.597609i | ||||
\(346\) | −8.96254 | + | 15.5236i | −0.481829 | + | 0.834553i | ||||
\(347\) | −3.21016 | + | 5.56016i | −0.172331 | + | 0.298485i | −0.939234 | − | 0.343277i | \(-0.888463\pi\) |
0.766904 | + | 0.641762i | \(0.221796\pi\) | |||||||
\(348\) | 1.61748 | + | 2.80156i | 0.0867062 | + | 0.150180i | ||||
\(349\) | −2.54039 | −0.135984 | −0.0679920 | − | 0.997686i | \(-0.521659\pi\) | ||||
−0.0679920 | + | 0.997686i | \(0.521659\pi\) | |||||||
\(350\) | −1.73158 | + | 9.60901i | −0.0925567 | + | 0.513623i | ||||
\(351\) | 52.8852 | 2.82281 | ||||||||
\(352\) | 0.425341 | + | 0.736713i | 0.0226708 | + | 0.0392669i | ||||
\(353\) | 0.603140 | − | 1.04467i | 0.0321019 | − | 0.0556021i | −0.849528 | − | 0.527543i | \(-0.823113\pi\) |
0.881630 | + | 0.471941i | \(0.156447\pi\) | |||||||
\(354\) | 13.0103 | − | 22.5345i | 0.691489 | − | 1.19769i | ||||
\(355\) | 6.45580 | + | 11.1818i | 0.342638 | + | 0.593467i | ||||
\(356\) | 14.2305 | 0.754216 | ||||||||
\(357\) | −1.56442 | + | 0.562753i | −0.0827976 | + | 0.0297841i | ||||
\(358\) | 5.28920 | 0.279543 | ||||||||
\(359\) | −0.157998 | − | 0.273661i | −0.00833883 | − | 0.0144433i | 0.861826 | − | 0.507204i | \(-0.169321\pi\) |
−0.870165 | + | 0.492761i | \(0.835988\pi\) | |||||||
\(360\) | −4.27146 | + | 7.39838i | −0.225126 | + | 0.389929i | ||||
\(361\) | −14.9558 | + | 25.9043i | −0.787149 | + | 1.36338i | ||||
\(362\) | −6.58553 | − | 11.4065i | −0.346128 | − | 0.599511i | ||||
\(363\) | −33.2436 | −1.74484 | ||||||||
\(364\) | 7.39726 | + | 6.25455i | 0.387722 | + | 0.327827i | ||||
\(365\) | −8.36640 | −0.437917 | ||||||||
\(366\) | 8.21914 | + | 14.2360i | 0.429621 | + | 0.744126i | ||||
\(367\) | −12.1499 | + | 21.0442i | −0.634217 | + | 1.09850i | 0.352463 | + | 0.935826i | \(0.385344\pi\) |
−0.986680 | + | 0.162671i | \(0.947989\pi\) | |||||||
\(368\) | 1.73109 | − | 2.99834i | 0.0902395 | − | 0.156299i | ||||
\(369\) | −15.0977 | − | 26.1500i | −0.785956 | − | 1.36132i | ||||
\(370\) | 8.25016 | 0.428905 | ||||||||
\(371\) | −5.39632 | − | 4.56271i | −0.280163 | − | 0.236884i | ||||
\(372\) | −12.8565 | −0.666578 | ||||||||
\(373\) | 4.99255 | + | 8.64735i | 0.258504 | + | 0.447743i | 0.965841 | − | 0.259134i | \(-0.0834370\pi\) |
−0.707337 | + | 0.706876i | \(0.750104\pi\) | |||||||
\(374\) | 0.0826218 | − | 0.143105i | 0.00427227 | − | 0.00739979i | ||||
\(375\) | 16.0862 | − | 27.8621i | 0.830687 | − | 1.43879i | ||||
\(376\) | −0.0269105 | − | 0.0466104i | −0.00138781 | − | 0.00240375i | ||||
\(377\) | −3.66136 | −0.188570 | ||||||||
\(378\) | −35.9598 | + | 12.9355i | −1.84957 | + | 0.665331i | ||||
\(379\) | −13.0891 | −0.672343 | −0.336172 | − | 0.941801i | \(-0.609132\pi\) | ||||
−0.336172 | + | 0.941801i | \(0.609132\pi\) | |||||||
\(380\) | 4.00177 | + | 6.93126i | 0.205286 | + | 0.355566i | ||||
\(381\) | 18.7287 | − | 32.4391i | 0.959503 | − | 1.66191i | ||||
\(382\) | −4.95435 | + | 8.58118i | −0.253486 | + | 0.439051i | ||||
\(383\) | 1.48195 | + | 2.56681i | 0.0757241 | + | 0.131158i | 0.901401 | − | 0.432985i | \(-0.142540\pi\) |
−0.825677 | + | 0.564143i | \(0.809206\pi\) | |||||||
\(384\) | 3.23497 | 0.165084 | ||||||||
\(385\) | −0.456789 | + | 2.53485i | −0.0232801 | + | 0.129188i | ||||
\(386\) | −17.3950 | −0.885384 | ||||||||
\(387\) | −36.4960 | − | 63.2129i | −1.85520 | − | 3.21329i | ||||
\(388\) | −9.38894 | + | 16.2621i | −0.476651 | + | 0.825584i | ||||
\(389\) | 17.4557 | − | 30.2342i | 0.885040 | − | 1.53293i | 0.0393729 | − | 0.999225i | \(-0.487464\pi\) |
0.845667 | − | 0.533710i | \(-0.179203\pi\) | |||||||
\(390\) | −6.77731 | − | 11.7387i | −0.343183 | − | 0.594410i | ||||
\(391\) | −0.672523 | −0.0340110 | ||||||||
\(392\) | −6.55967 | − | 2.44350i | −0.331314 | − | 0.123415i | ||||
\(393\) | −52.3985 | −2.64316 | ||||||||
\(394\) | −8.79804 | − | 15.2386i | −0.443239 | − | 0.767712i | ||||
\(395\) | 7.64250 | − | 13.2372i | 0.384536 | − | 0.666036i | ||||
\(396\) | 3.17518 | − | 5.49957i | 0.159559 | − | 0.276364i | ||||
\(397\) | −7.70778 | − | 13.3503i | −0.386842 | − | 0.670031i | 0.605180 | − | 0.796088i | \(-0.293101\pi\) |
−0.992023 | + | 0.126057i | \(0.959768\pi\) | |||||||
\(398\) | 11.2846 | 0.565645 | ||||||||
\(399\) | −10.6157 | + | 58.9096i | −0.531450 | + | 2.94917i | ||||
\(400\) | −3.69036 | −0.184518 | ||||||||
\(401\) | −19.0183 | − | 32.9406i | −0.949728 | − | 1.64498i | −0.745996 | − | 0.665950i | \(-0.768026\pi\) |
−0.203731 | − | 0.979027i | \(-0.565307\pi\) | |||||||
\(402\) | 18.7632 | − | 32.4989i | 0.935825 | − | 1.62090i | ||||
\(403\) | 7.27553 | − | 12.6016i | 0.362420 | − | 0.627730i | ||||
\(404\) | −6.85968 | − | 11.8813i | −0.341282 | − | 0.591118i | ||||
\(405\) | 27.8447 | 1.38361 | ||||||||
\(406\) | 2.48958 | − | 0.895553i | 0.123556 | − | 0.0444456i | ||||
\(407\) | −6.13274 | −0.303989 | ||||||||
\(408\) | −0.314193 | − | 0.544199i | −0.0155549 | − | 0.0269418i | ||||
\(409\) | 14.6428 | − | 25.3621i | 0.724041 | − | 1.25408i | −0.235327 | − | 0.971916i | \(-0.575616\pi\) |
0.959368 | − | 0.282159i | \(-0.0910506\pi\) | |||||||
\(410\) | −2.31450 | + | 4.00883i | −0.114305 | + | 0.197982i | ||||
\(411\) | 20.6783 | + | 35.8159i | 1.01999 | + | 1.76667i | ||||
\(412\) | 1.18115 | 0.0581909 | ||||||||
\(413\) | −16.2508 | − | 13.7405i | −0.799652 | − | 0.676123i | ||||
\(414\) | −25.8453 | −1.27023 | ||||||||
\(415\) | −5.17589 | − | 8.96490i | −0.254074 | − | 0.440070i | ||||
\(416\) | −1.83068 | + | 3.17083i | −0.0897564 | + | 0.155463i | ||||
\(417\) | −0.275902 | + | 0.477875i | −0.0135110 | + | 0.0234017i | ||||
\(418\) | −2.97471 | − | 5.15234i | −0.145498 | − | 0.252009i | ||||
\(419\) | −6.29412 | −0.307488 | −0.153744 | − | 0.988111i | \(-0.549133\pi\) | ||||
−0.153744 | + | 0.988111i | \(0.549133\pi\) | |||||||
\(420\) | 7.47952 | + | 6.32410i | 0.364963 | + | 0.308585i | ||||
\(421\) | 2.94479 | 0.143520 | 0.0717602 | − | 0.997422i | \(-0.477138\pi\) | ||||
0.0717602 | + | 0.997422i | \(0.477138\pi\) | |||||||
\(422\) | 4.93786 | + | 8.55262i | 0.240371 | + | 0.416335i | ||||
\(423\) | −0.200887 | + | 0.347947i | −0.00976748 | + | 0.0169178i | ||||
\(424\) | 1.33549 | − | 2.31313i | 0.0648570 | − | 0.112336i | ||||
\(425\) | 0.358423 | + | 0.620807i | 0.0173861 | + | 0.0301136i | ||||
\(426\) | −36.4984 | −1.76836 | ||||||||
\(427\) | 12.6506 | − | 4.55070i | 0.612206 | − | 0.220224i | ||||
\(428\) | −1.79224 | −0.0866313 | ||||||||
\(429\) | 5.03790 | + | 8.72590i | 0.243232 | + | 0.421290i | ||||
\(430\) | −5.59487 | + | 9.69060i | −0.269809 | + | 0.467322i | ||||
\(431\) | −2.72971 | + | 4.72800i | −0.131486 | + | 0.227740i | −0.924249 | − | 0.381789i | \(-0.875308\pi\) |
0.792764 | + | 0.609529i | \(0.208641\pi\) | |||||||
\(432\) | −7.22208 | − | 12.5090i | −0.347473 | − | 0.601840i | ||||
\(433\) | −16.9899 | −0.816482 | −0.408241 | − | 0.912874i | \(-0.633858\pi\) | ||||
−0.408241 | + | 0.912874i | \(0.633858\pi\) | |||||||
\(434\) | −1.86477 | + | 10.3481i | −0.0895118 | + | 0.496727i | ||||
\(435\) | −3.70208 | −0.177501 | ||||||||
\(436\) | −1.82095 | − | 3.15397i | −0.0872076 | − | 0.151048i | ||||
\(437\) | −12.1067 | + | 20.9695i | −0.579143 | + | 1.00311i | ||||
\(438\) | 11.8250 | − | 20.4816i | 0.565023 | − | 0.978648i | ||||
\(439\) | 11.3210 | + | 19.6085i | 0.540321 | + | 0.935863i | 0.998885 | + | 0.0472016i | \(0.0150303\pi\) |
−0.458565 | + | 0.888661i | \(0.651636\pi\) | |||||||
\(440\) | −0.973516 | −0.0464106 | ||||||||
\(441\) | 8.68706 | + | 51.5279i | 0.413670 | + | 2.45371i | ||||
\(442\) | 0.711212 | 0.0338289 | ||||||||
\(443\) | 8.56936 | + | 14.8426i | 0.407143 | + | 0.705192i | 0.994568 | − | 0.104086i | \(-0.0331919\pi\) |
−0.587426 | + | 0.809278i | \(0.699859\pi\) | |||||||
\(444\) | −11.6608 | + | 20.1970i | −0.553395 | + | 0.958508i | ||||
\(445\) | −8.14266 | + | 14.1035i | −0.385999 | + | 0.668570i | ||||
\(446\) | 8.29908 | + | 14.3744i | 0.392973 | + | 0.680649i | ||||
\(447\) | 45.4317 | 2.14885 | ||||||||
\(448\) | 0.469216 | − | 2.60381i | 0.0221684 | − | 0.123019i | ||||
\(449\) | −12.1802 | −0.574818 | −0.287409 | − | 0.957808i | \(-0.592794\pi\) | ||||
−0.287409 | + | 0.957808i | \(0.592794\pi\) | |||||||
\(450\) | 13.7743 | + | 23.8578i | 0.649327 | + | 1.12467i | ||||
\(451\) | 1.72048 | − | 2.97995i | 0.0810141 | − | 0.140321i | ||||
\(452\) | 8.88590 | − | 15.3908i | 0.417958 | − | 0.723924i | ||||
\(453\) | −19.7293 | − | 34.1722i | −0.926965 | − | 1.60555i | ||||
\(454\) | 17.9930 | 0.844455 | ||||||||
\(455\) | −10.4314 | + | 3.75240i | −0.489032 | + | 0.175915i | ||||
\(456\) | −22.6244 | −1.05948 | ||||||||
\(457\) | −15.7551 | − | 27.2886i | −0.736991 | − | 1.27651i | −0.953844 | − | 0.300302i | \(-0.902912\pi\) |
0.216853 | − | 0.976204i | \(-0.430421\pi\) | |||||||
\(458\) | 1.01911 | − | 1.76514i | 0.0476197 | − | 0.0824797i | ||||
\(459\) | −1.40288 | + | 2.42985i | −0.0654806 | + | 0.113416i | ||||
\(460\) | 1.98105 | + | 3.43128i | 0.0923671 | + | 0.159984i | ||||
\(461\) | −6.40796 | −0.298448 | −0.149224 | − | 0.988803i | \(-0.547678\pi\) | ||||
−0.149224 | + | 0.988803i | \(0.547678\pi\) | |||||||
\(462\) | −5.55989 | − | 4.70101i | −0.258669 | − | 0.218711i | ||||
\(463\) | −0.902939 | −0.0419632 | −0.0209816 | − | 0.999780i | \(-0.506679\pi\) | ||||
−0.0209816 | + | 0.999780i | \(0.506679\pi\) | |||||||
\(464\) | 0.500000 | + | 0.866025i | 0.0232119 | + | 0.0402042i | ||||
\(465\) | 7.35645 | − | 12.7417i | 0.341147 | − | 0.590884i | ||||
\(466\) | 8.24947 | − | 14.2885i | 0.382149 | − | 0.661902i | ||||
\(467\) | 18.2056 | + | 31.5330i | 0.842454 | + | 1.45917i | 0.887814 | + | 0.460202i | \(0.152223\pi\) |
−0.0453601 | + | 0.998971i | \(0.514444\pi\) | |||||||
\(468\) | 27.3321 | 1.26343 | ||||||||
\(469\) | −23.4367 | − | 19.8163i | −1.08221 | − | 0.915030i | ||||
\(470\) | 0.0615925 | 0.00284105 | ||||||||
\(471\) | −23.2751 | − | 40.3137i | −1.07246 | − | 1.85756i | ||||
\(472\) | 4.02177 | − | 6.96591i | 0.185117 | − | 0.320632i | ||||
\(473\) | 4.15894 | − | 7.20349i | 0.191228 | − | 0.331217i | ||||
\(474\) | 21.6038 | + | 37.4188i | 0.992294 | + | 1.71870i | ||||
\(475\) | 25.8092 | 1.18421 | ||||||||
\(476\) | −0.483595 | + | 0.173960i | −0.0221656 | + | 0.00797342i | ||||
\(477\) | −19.9388 | −0.912937 | ||||||||
\(478\) | −9.37071 | − | 16.2305i | −0.428606 | − | 0.742368i | ||||
\(479\) | −15.7142 | + | 27.2177i | −0.717998 | + | 1.24361i | 0.243794 | + | 0.969827i | \(0.421608\pi\) |
−0.961792 | + | 0.273782i | \(0.911725\pi\) | |||||||
\(480\) | −1.85104 | + | 3.20609i | −0.0844880 | + | 0.146337i | ||||
\(481\) | −13.1977 | − | 22.8591i | −0.601764 | − | 1.04229i | ||||
\(482\) | 17.8781 | 0.814323 | ||||||||
\(483\) | −5.25525 | + | 29.1628i | −0.239122 | + | 1.32696i | ||||
\(484\) | −10.2763 | −0.467106 | ||||||||
\(485\) | −10.7446 | − | 18.6103i | −0.487889 | − | 0.845049i | ||||
\(486\) | −17.6893 | + | 30.6388i | −0.802404 | + | 1.38980i | ||||
\(487\) | −7.22298 | + | 12.5106i | −0.327304 | + | 0.566908i | −0.981976 | − | 0.189006i | \(-0.939474\pi\) |
0.654672 | + | 0.755913i | \(0.272807\pi\) | |||||||
\(488\) | 2.54072 | + | 4.40065i | 0.115013 | + | 0.199208i | ||||
\(489\) | 54.2418 | 2.45290 | ||||||||
\(490\) | 6.17511 | − | 5.10296i | 0.278963 | − | 0.230528i | ||||
\(491\) | 29.2405 | 1.31961 | 0.659803 | − | 0.751439i | \(-0.270640\pi\) | ||||
0.659803 | + | 0.751439i | \(0.270640\pi\) | |||||||
\(492\) | −6.54261 | − | 11.3321i | −0.294964 | − | 0.510892i | ||||
\(493\) | 0.0971241 | − | 0.168224i | 0.00437425 | − | 0.00757642i | ||||
\(494\) | 12.8032 | − | 22.1758i | 0.576043 | − | 0.997736i | ||||
\(495\) | 3.63365 | + | 6.29367i | 0.163321 | + | 0.282880i | ||||
\(496\) | −3.97423 | −0.178448 | ||||||||
\(497\) | −5.29392 | + | 29.3774i | −0.237465 | + | 1.31776i | ||||
\(498\) | 29.2624 | 1.31128 | ||||||||
\(499\) | −14.2452 | − | 24.6735i | −0.637704 | − | 1.10454i | −0.985935 | − | 0.167127i | \(-0.946551\pi\) |
0.348231 | − | 0.937409i | \(-0.386782\pi\) | |||||||
\(500\) | 4.97260 | − | 8.61279i | 0.222381 | − | 0.385176i | ||||
\(501\) | 17.2350 | − | 29.8519i | 0.770004 | − | 1.33369i | ||||
\(502\) | 0.846243 | + | 1.46574i | 0.0377697 | + | 0.0654190i | ||||
\(503\) | 19.9091 | 0.887701 | 0.443850 | − | 0.896101i | \(-0.353612\pi\) | ||||
0.443850 | + | 0.896101i | \(0.353612\pi\) | |||||||
\(504\) | −18.5847 | + | 6.68531i | −0.827829 | + | 0.297788i | ||||
\(505\) | 15.7004 | 0.698657 | ||||||||
\(506\) | −1.47261 | − | 2.55064i | −0.0654656 | − | 0.113390i | ||||
\(507\) | −0.655956 | + | 1.13615i | −0.0291321 | + | 0.0504582i | ||||
\(508\) | 5.78947 | − | 10.0277i | 0.256866 | − | 0.444905i | ||||
\(509\) | −1.78599 | − | 3.09343i | −0.0791628 | − | 0.137114i | 0.823726 | − | 0.566988i | \(-0.191891\pi\) |
−0.902889 | + | 0.429874i | \(0.858558\pi\) | |||||||
\(510\) | 0.719122 | 0.0318432 | ||||||||
\(511\) | −14.7704 | − | 12.4887i | −0.653403 | − | 0.552467i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 50.5090 | + | 87.4841i | 2.23003 | + | 3.86252i | ||||
\(514\) | −1.77662 | + | 3.07719i | −0.0783633 | + | 0.135729i | ||||
\(515\) | −0.675848 | + | 1.17060i | −0.0297814 | + | 0.0515829i | ||||
\(516\) | −15.8156 | − | 27.3934i | −0.696241 | − | 1.20593i | ||||
\(517\) | −0.0457847 | −0.00201361 | ||||||||
\(518\) | 14.5652 | + | 12.3152i | 0.639956 | + | 0.541097i | ||||
\(519\) | 57.9871 | 2.54535 | ||||||||
\(520\) | −2.09502 | − | 3.62868i | −0.0918726 | − | 0.159128i | ||||
\(521\) | 4.68438 | − | 8.11359i | 0.205227 | − | 0.355463i | −0.744978 | − | 0.667089i | \(-0.767540\pi\) |
0.950205 | + | 0.311626i | \(0.100874\pi\) | |||||||
\(522\) | 3.73251 | − | 6.46489i | 0.163367 | − | 0.282960i | ||||
\(523\) | 6.80794 | + | 11.7917i | 0.297690 | + | 0.515615i | 0.975607 | − | 0.219524i | \(-0.0704504\pi\) |
−0.677917 | + | 0.735139i | \(0.737117\pi\) | |||||||
\(524\) | −16.1976 | −0.707593 | ||||||||
\(525\) | 29.7210 | − | 10.6913i | 1.29713 | − | 0.466606i | ||||
\(526\) | −18.3627 | −0.800653 | ||||||||
\(527\) | 0.385993 | + | 0.668560i | 0.0168141 | + | 0.0291229i | ||||
\(528\) | 1.37597 | − | 2.38324i | 0.0598812 | − | 0.103717i | ||||
\(529\) | 5.50663 | − | 9.53777i | 0.239419 | − | 0.414686i | ||||
\(530\) | 1.52832 | + | 2.64713i | 0.0663861 | + | 0.114984i | ||||
\(531\) | −60.0451 | −2.60574 | ||||||||
\(532\) | −3.28155 | + | 18.2102i | −0.142273 | + | 0.789514i | ||||
\(533\) | 14.8099 | 0.641490 | ||||||||
\(534\) | −23.0176 | − | 39.8677i | −0.996070 | − | 1.72524i | ||||
\(535\) | 1.02552 | − | 1.77624i | 0.0443369 | − | 0.0767937i | ||||
\(536\) | 5.80013 | − | 10.0461i | 0.250528 | − | 0.433927i | ||||
\(537\) | −8.55519 | − | 14.8180i | −0.369184 | − | 0.639445i | ||||
\(538\) | 18.1820 | 0.783883 | ||||||||
\(539\) | −4.59026 | + | 3.79327i | −0.197716 | + | 0.163388i | ||||
\(540\) | 16.5298 | 0.711330 | ||||||||
\(541\) | −5.34851 | − | 9.26389i | −0.229951 | − | 0.398286i | 0.727843 | − | 0.685744i | \(-0.240523\pi\) |
−0.957793 | + | 0.287458i | \(0.907190\pi\) | |||||||
\(542\) | 3.65352 | − | 6.32808i | 0.156932 | − | 0.271814i | ||||
\(543\) | −21.3040 | + | 36.8995i | −0.914240 | + | 1.58351i | ||||
\(544\) | −0.0971241 | − | 0.168224i | −0.00416416 | − | 0.00721254i | ||||
\(545\) | 4.16776 | 0.178527 | ||||||||
\(546\) | 5.55757 | − | 30.8405i | 0.237842 | − | 1.31985i | ||||
\(547\) | −23.6925 | −1.01302 | −0.506509 | − | 0.862235i | \(-0.669064\pi\) | ||||
−0.506509 | + | 0.862235i | \(0.669064\pi\) | |||||||
\(548\) | 6.39212 | + | 11.0715i | 0.273058 | + | 0.472950i | ||||
\(549\) | 18.9665 | − | 32.8509i | 0.809470 | − | 1.40204i | ||||
\(550\) | −1.56966 | + | 2.71874i | −0.0669307 | + | 0.115927i | ||||
\(551\) | −3.49684 | − | 6.05671i | −0.148971 | − | 0.258025i | ||||
\(552\) | −11.2001 | −0.476706 | ||||||||
\(553\) | 33.2518 | − | 11.9614i | 1.41401 | − | 0.508649i | ||||
\(554\) | −16.6420 | −0.707049 | ||||||||
\(555\) | −13.3445 | − | 23.1133i | −0.566442 | − | 0.981107i | ||||
\(556\) | −0.0852873 | + | 0.147722i | −0.00361699 | + | 0.00626480i | ||||
\(557\) | −6.13907 | + | 10.6332i | −0.260121 | + | 0.450543i | −0.966274 | − | 0.257517i | \(-0.917096\pi\) |
0.706153 | + | 0.708059i | \(0.250429\pi\) | |||||||
\(558\) | 14.8338 | + | 25.6929i | 0.627966 | + | 1.08767i | ||||
\(559\) | 35.8003 | 1.51419 | ||||||||
\(560\) | 2.31209 | + | 1.95492i | 0.0977035 | + | 0.0826105i | ||||
\(561\) | −0.534558 | −0.0225690 | ||||||||
\(562\) | −6.62811 | − | 11.4802i | −0.279590 | − | 0.484264i | ||||
\(563\) | −18.6915 | + | 32.3747i | −0.787755 | + | 1.36443i | 0.139585 | + | 0.990210i | \(0.455423\pi\) |
−0.927340 | + | 0.374221i | \(0.877910\pi\) | |||||||
\(564\) | −0.0870547 | + | 0.150783i | −0.00366566 | + | 0.00634912i | ||||
\(565\) | 10.1690 | + | 17.6132i | 0.427812 | + | 0.740992i | ||||
\(566\) | −15.2786 | −0.642207 | ||||||||
\(567\) | 49.1581 | + | 41.5642i | 2.06444 | + | 1.74553i | ||||
\(568\) | −11.2825 | −0.473402 | ||||||||
\(569\) | 7.12391 | + | 12.3390i | 0.298650 | + | 0.517277i | 0.975827 | − | 0.218543i | \(-0.0701304\pi\) |
−0.677177 | + | 0.735820i | \(0.736797\pi\) | |||||||
\(570\) | 12.9456 | − | 22.4224i | 0.542231 | − | 0.939171i | ||||
\(571\) | 3.29932 | − | 5.71460i | 0.138072 | − | 0.239148i | −0.788695 | − | 0.614785i | \(-0.789243\pi\) |
0.926767 | + | 0.375637i | \(0.122576\pi\) | |||||||
\(572\) | 1.55733 | + | 2.69737i | 0.0651151 | + | 0.112783i | ||||
\(573\) | 32.0543 | 1.33909 | ||||||||
\(574\) | −10.0702 | + | 3.62245i | −0.420320 | + | 0.151198i | ||||
\(575\) | 12.7767 | 0.532826 | ||||||||
\(576\) | −3.73251 | − | 6.46489i | −0.155521 | − | 0.269370i | ||||
\(577\) | 10.5455 | − | 18.2654i | 0.439016 | − | 0.760398i | −0.558598 | − | 0.829439i | \(-0.688660\pi\) |
0.997614 | + | 0.0690406i | \(0.0219938\pi\) | |||||||
\(578\) | 8.48113 | − | 14.6898i | 0.352769 | − | 0.611013i | ||||
\(579\) | 28.1362 | + | 48.7333i | 1.16930 | + | 2.02529i | ||||
\(580\) | −1.14439 | −0.0475184 | ||||||||
\(581\) | 4.24436 | − | 23.5532i | 0.176086 | − | 0.977149i | ||||
\(582\) | 60.7458 | 2.51800 | ||||||||
\(583\) | −1.13608 | − | 1.96774i | −0.0470514 | − | 0.0814955i | ||||
\(584\) | 3.65539 | − | 6.33131i | 0.151261 | − | 0.261992i | ||||
\(585\) | −15.6393 | + | 27.0881i | −0.646607 | + | 1.11996i | ||||
\(586\) | 7.75956 | + | 13.4400i | 0.320545 | + | 0.555199i | ||||
\(587\) | 23.5851 | 0.973459 | 0.486730 | − | 0.873553i | \(-0.338190\pi\) | ||||
0.486730 | + | 0.873553i | \(0.338190\pi\) | |||||||
\(588\) | 3.76454 | + | 22.3297i | 0.155247 | + | 0.920860i | ||||
\(589\) | 27.7945 | 1.14525 | ||||||||
\(590\) | 4.60249 | + | 7.97175i | 0.189482 | + | 0.328192i | ||||
\(591\) | −28.4614 | + | 49.2965i | −1.17074 | + | 2.02779i | ||||
\(592\) | −3.60460 | + | 6.24335i | −0.148148 | + | 0.256600i | ||||
\(593\) | 12.4404 | + | 21.5474i | 0.510865 | + | 0.884844i | 0.999921 | + | 0.0125916i | \(0.00400813\pi\) |
−0.489056 | + | 0.872253i | \(0.662659\pi\) | |||||||
\(594\) | −12.2874 | −0.504158 | ||||||||
\(595\) | 0.104305 | − | 0.578818i | 0.00427609 | − | 0.0237292i | ||||
\(596\) | 14.0440 | 0.575263 | ||||||||
\(597\) | −18.2526 | − | 31.6145i | −0.747031 | − | 1.29390i | ||||
\(598\) | 6.33815 | − | 10.9780i | 0.259186 | − | 0.448924i | ||||
\(599\) | −2.38954 | + | 4.13880i | −0.0976338 | + | 0.169107i | −0.910705 | − | 0.413058i | \(-0.864461\pi\) |
0.813071 | + | 0.582165i | \(0.197794\pi\) | |||||||
\(600\) | 5.96910 | + | 10.3388i | 0.243687 | + | 0.422079i | ||||
\(601\) | −44.3292 | −1.80823 | −0.904113 | − | 0.427292i | \(-0.859467\pi\) | ||||
−0.904113 | + | 0.427292i | \(0.859467\pi\) | |||||||
\(602\) | −24.3428 | + | 8.75661i | −0.992137 | + | 0.356893i | ||||
\(603\) | −86.5961 | −3.52647 | ||||||||
\(604\) | −6.09878 | − | 10.5634i | −0.248156 | − | 0.429818i | ||||
\(605\) | 5.88009 | − | 10.1846i | 0.239060 | − | 0.414063i | ||||
\(606\) | −22.1908 | + | 38.4357i | −0.901442 | + | 1.56134i | ||||
\(607\) | −21.4496 | − | 37.1518i | −0.870613 | − | 1.50795i | −0.861364 | − | 0.507989i | \(-0.830389\pi\) |
−0.00924938 | − | 0.999957i | \(-0.502944\pi\) | |||||||
\(608\) | −6.99369 | −0.283632 | ||||||||
\(609\) | −6.53580 | − | 5.52616i | −0.264844 | − | 0.223931i | ||||
\(610\) | −5.81517 | −0.235449 | ||||||||
\(611\) | −0.0985291 | − | 0.170657i | −0.00398606 | − | 0.00690406i | ||||
\(612\) | −0.725032 | + | 1.25579i | −0.0293077 | + | 0.0507624i | ||||
\(613\) | −13.0203 | + | 22.5518i | −0.525884 | + | 0.910857i | 0.473662 | + | 0.880707i | \(0.342932\pi\) |
−0.999545 | + | 0.0301503i | \(0.990401\pi\) | |||||||
\(614\) | −1.57139 | − | 2.72172i | −0.0634160 | − | 0.109840i | ||||
\(615\) | 14.9746 | 0.603836 | ||||||||
\(616\) | −1.71868 | − | 1.45319i | −0.0692478 | − | 0.0585505i | ||||
\(617\) | −38.2301 | −1.53909 | −0.769543 | − | 0.638595i | \(-0.779516\pi\) | ||||
−0.769543 | + | 0.638595i | \(0.779516\pi\) | |||||||
\(618\) | −1.91048 | − | 3.30905i | −0.0768509 | − | 0.133110i | ||||
\(619\) | −16.9206 | + | 29.3074i | −0.680098 | + | 1.17796i | 0.294853 | + | 0.955543i | \(0.404729\pi\) |
−0.974951 | + | 0.222421i | \(0.928604\pi\) | |||||||
\(620\) | 2.27404 | − | 3.93875i | 0.0913277 | − | 0.158184i | ||||
\(621\) | 25.0042 | + | 43.3085i | 1.00338 | + | 1.73791i | ||||
\(622\) | 24.2160 | 0.970973 | ||||||||
\(623\) | −35.4280 | + | 12.7442i | −1.41939 | + | 0.510585i | ||||
\(624\) | 11.8444 | 0.474154 | ||||||||
\(625\) | −3.53529 | − | 6.12331i | −0.141412 | − | 0.244932i | ||||
\(626\) | 5.17640 | − | 8.96579i | 0.206891 | − | 0.358345i | ||||
\(627\) | −9.62307 | + | 16.6677i | −0.384309 | + | 0.665642i | ||||
\(628\) | −7.19485 | − | 12.4618i | −0.287106 | − | 0.497282i | ||||
\(629\) | 1.40037 | 0.0558365 | ||||||||
\(630\) | 4.00847 | − | 22.2441i | 0.159701 | − | 0.886228i | ||||
\(631\) | −36.3237 | −1.44602 | −0.723012 | − | 0.690835i | \(-0.757243\pi\) | ||||
−0.723012 | + | 0.690835i | \(0.757243\pi\) | |||||||
\(632\) | 6.67821 | + | 11.5670i | 0.265645 | + | 0.460110i | ||||
\(633\) | 15.9738 | − | 27.6675i | 0.634902 | − | 1.09968i | ||||
\(634\) | 17.2664 | − | 29.9063i | 0.685738 | − | 1.18773i | ||||
\(635\) | 6.62543 | + | 11.4756i | 0.262922 | + | 0.455395i | ||||
\(636\) | −8.64051 | −0.342618 | ||||||||
\(637\) | −24.0173 | − | 8.94653i | −0.951600 | − | 0.354474i | ||||
\(638\) | 0.850683 | 0.0336789 | ||||||||
\(639\) | 42.1119 | + | 72.9400i | 1.66592 | + | 2.88546i | ||||
\(640\) | −0.572197 | + | 0.991074i | −0.0226181 | + | 0.0391756i | ||||
\(641\) | 2.50688 | − | 4.34204i | 0.0990157 | − | 0.171500i | −0.812262 | − | 0.583293i | \(-0.801764\pi\) |
0.911278 | + | 0.411793i | \(0.135097\pi\) | |||||||
\(642\) | 2.89892 | + | 5.02108i | 0.114411 | + | 0.198166i | ||||
\(643\) | −21.6758 | −0.854811 | −0.427406 | − | 0.904060i | \(-0.640572\pi\) | ||||
−0.427406 | + | 0.904060i | \(0.640572\pi\) | |||||||
\(644\) | −1.62451 | + | 9.01488i | −0.0640148 | + | 0.355236i | ||||
\(645\) | 36.1985 | 1.42531 | ||||||||
\(646\) | 0.679256 | + | 1.17651i | 0.0267250 | + | 0.0462890i | ||||
\(647\) | 11.5473 | − | 20.0005i | 0.453970 | − | 0.786299i | −0.544658 | − | 0.838658i | \(-0.683341\pi\) |
0.998628 | + | 0.0523591i | \(0.0166740\pi\) | |||||||
\(648\) | −12.1657 | + | 21.0716i | −0.477913 | + | 0.827769i | ||||
\(649\) | −3.42125 | − | 5.92578i | −0.134296 | − | 0.232607i | ||||
\(650\) | −13.5117 | −0.529974 | ||||||||
\(651\) | 32.0072 | − | 11.5137i | 1.25446 | − | 0.451256i | ||||
\(652\) | 16.7674 | 0.656660 | ||||||||
\(653\) | 16.9620 | + | 29.3790i | 0.663774 | + | 1.14969i | 0.979616 | + | 0.200879i | \(0.0643798\pi\) |
−0.315842 | + | 0.948812i | \(0.602287\pi\) | |||||||
\(654\) | −5.89071 | + | 10.2030i | −0.230345 | + | 0.398969i | ||||
\(655\) | 9.26819 | − | 16.0530i | 0.362138 | − | 0.627242i | ||||
\(656\) | −2.02247 | − | 3.50301i | −0.0789640 | − | 0.136770i | ||||
\(657\) | −54.5750 | −2.12917 | ||||||||
\(658\) | 0.108738 | + | 0.0919403i | 0.00423905 | + | 0.00358421i | ||||
\(659\) | −5.52520 | −0.215231 | −0.107616 | − | 0.994193i | \(-0.534322\pi\) | ||||
−0.107616 | + | 0.994193i | \(0.534322\pi\) | |||||||
\(660\) | 1.57465 | + | 2.72737i | 0.0612930 | + | 0.106163i | ||||
\(661\) | 0.811825 | − | 1.40612i | 0.0315763 | − | 0.0546918i | −0.849805 | − | 0.527097i | \(-0.823281\pi\) |
0.881382 | + | 0.472405i | \(0.156614\pi\) | |||||||
\(662\) | −2.55022 | + | 4.41710i | −0.0991170 | + | 0.171676i | ||||
\(663\) | −1.15037 | − | 1.99251i | −0.0446768 | − | 0.0773825i | ||||
\(664\) | 9.04564 | 0.351039 | ||||||||
\(665\) | −16.1700 | − | 13.6721i | −0.627046 | − | 0.530182i | ||||
\(666\) | 53.8167 | 2.08536 | ||||||||
\(667\) | −1.73109 | − | 2.99834i | −0.0670282 | − | 0.116096i | ||||
\(668\) | 5.32773 | − | 9.22789i | 0.206136 | − | 0.357038i | ||||
\(669\) | 26.8473 | − | 46.5008i | 1.03798 | − | 1.79783i | ||||
\(670\) | 6.63764 | + | 11.4967i | 0.256434 | + | 0.444157i | ||||
\(671\) | 4.32269 | 0.166876 | ||||||||
\(672\) | −8.05369 | + | 2.89708i | −0.310678 | + | 0.111757i | ||||
\(673\) | −1.69886 | −0.0654862 | −0.0327431 | − | 0.999464i | \(-0.510424\pi\) | ||||
−0.0327431 | + | 0.999464i | \(0.510424\pi\) | |||||||
\(674\) | −12.3807 | − | 21.4440i | −0.476886 | − | 0.825990i | ||||
\(675\) | 26.6521 | − | 46.1628i | 1.02584 | − | 1.77681i | ||||
\(676\) | −0.202771 | + | 0.351209i | −0.00779887 | + | 0.0135080i | ||||
\(677\) | −10.3638 | − | 17.9507i | −0.398314 | − | 0.689900i | 0.595204 | − | 0.803575i | \(-0.297071\pi\) |
−0.993518 | + | 0.113674i | \(0.963738\pi\) | |||||||
\(678\) | −57.4912 | −2.20794 | ||||||||
\(679\) | 8.81088 | − | 48.8941i | 0.338130 | − | 1.87638i | ||||
\(680\) | 0.222296 | 0.00852468 | ||||||||
\(681\) | −29.1034 | − | 50.4086i | −1.11525 | − | 1.93166i | ||||
\(682\) | −1.69040 | + | 2.92786i | −0.0647289 | + | 0.112114i | ||||
\(683\) | 15.1908 | − | 26.3113i | 0.581261 | − | 1.00677i | −0.414069 | − | 0.910246i | \(-0.635893\pi\) |
0.995330 | − | 0.0965286i | \(-0.0307739\pi\) | |||||||
\(684\) | 26.1040 | + | 45.2134i | 0.998111 | + | 1.72878i | ||||
\(685\) | −14.6302 | −0.558991 | ||||||||
\(686\) | 18.5191 | + | 0.208741i | 0.707062 | + | 0.00796975i | ||||
\(687\) | −6.59355 | −0.251560 | ||||||||
\(688\) | −4.88894 | − | 8.46789i | −0.186389 | − | 0.322835i | ||||
\(689\) | 4.88969 | − | 8.46920i | 0.186282 | − | 0.322651i | ||||
\(690\) | 6.40864 | − | 11.1001i | 0.243973 | − | 0.422573i | ||||
\(691\) | 2.31023 | + | 4.00144i | 0.0878853 | + | 0.152222i | 0.906617 | − | 0.421954i | \(-0.138656\pi\) |
−0.818732 | + | 0.574176i | \(0.805322\pi\) | |||||||
\(692\) | 17.9251 | 0.681409 | ||||||||
\(693\) | −2.97969 | + | 16.5351i | −0.113189 | + | 0.628118i | ||||
\(694\) | 6.42032 | 0.243712 | ||||||||
\(695\) | −0.0976022 | − | 0.169052i | −0.00370226 | − | 0.00641251i | ||||
\(696\) | 1.61748 | − | 2.80156i | 0.0613106 | − | 0.106193i | ||||
\(697\) | −0.392860 | + | 0.680454i | −0.0148806 | + | 0.0257740i | ||||
\(698\) | 1.27020 | + | 2.20004i | 0.0480776 | + | 0.0832729i | ||||
\(699\) | −53.3735 | −2.01877 | ||||||||
\(700\) | 9.18743 | − | 3.30492i | 0.347252 | − | 0.124914i | ||||
\(701\) | 36.9179 | 1.39437 | 0.697186 | − | 0.716890i | \(-0.254435\pi\) | ||||
0.697186 | + | 0.716890i | \(0.254435\pi\) | |||||||
\(702\) | −26.4426 | − | 45.8000i | −0.998012 | − | 1.72861i | ||||
\(703\) | 25.2094 | − | 43.6640i | 0.950792 | − | 1.64682i | ||||
\(704\) | 0.425341 | − | 0.736713i | 0.0160307 | − | 0.0277659i | ||||
\(705\) | −0.0996249 | − | 0.172555i | −0.00375209 | − | 0.00649881i | ||||
\(706\) | −1.20628 | −0.0453989 | ||||||||
\(707\) | 27.7181 | + | 23.4362i | 1.04244 | + | 0.881410i | ||||
\(708\) | −26.0206 | −0.977914 | ||||||||
\(709\) | 16.0371 | + | 27.7771i | 0.602286 | + | 1.04319i | 0.992474 | + | 0.122454i | \(0.0390765\pi\) |
−0.390189 | + | 0.920735i | \(0.627590\pi\) | |||||||
\(710\) | 6.45580 | − | 11.1818i | 0.242282 | − | 0.419644i | ||||
\(711\) | 49.8529 | − | 86.3477i | 1.86963 | − | 3.23829i | ||||
\(712\) | −7.11526 | − | 12.3240i | −0.266656 | − | 0.461861i | ||||
\(713\) | 13.7595 | 0.515298 | ||||||||
\(714\) | 1.26957 | + | 1.07345i | 0.0475123 | + | 0.0401727i | ||||
\(715\) | −3.56439 | −0.133301 | ||||||||
\(716\) | −2.64460 | − | 4.58058i | −0.0988333 | − | 0.171184i | ||||
\(717\) | −30.3139 | + | 52.5053i | −1.13209 | + | 1.96085i | ||||
\(718\) | −0.157998 | + | 0.273661i | −0.00589644 | + | 0.0102129i | ||||
\(719\) | −17.9177 | − | 31.0344i | −0.668218 | − | 1.15739i | −0.978402 | − | 0.206711i | \(-0.933724\pi\) |
0.310184 | − | 0.950676i | \(-0.399609\pi\) | |||||||
\(720\) | 8.54291 | 0.318376 | ||||||||
\(721\) | −2.94055 | + | 1.05778i | −0.109512 | + | 0.0393937i | ||||
\(722\) | 29.9117 | 1.11320 | ||||||||
\(723\) | −28.9175 | − | 50.0865i | −1.07545 | − | 1.86274i | ||||
\(724\) | −6.58553 | + | 11.4065i | −0.244749 | + | 0.423918i | ||||
\(725\) | −1.84518 | + | 3.19595i | −0.0685283 | + | 0.118695i | ||||
\(726\) | 16.6218 | + | 28.7898i | 0.616893 | + | 1.06849i | ||||
\(727\) | −12.8401 | −0.476215 | −0.238107 | − | 0.971239i | \(-0.576527\pi\) | ||||
−0.238107 | + | 0.971239i | \(0.576527\pi\) | |||||||
\(728\) | 1.71797 | − | 9.53349i | 0.0636721 | − | 0.353335i | ||||
\(729\) | 41.4546 | 1.53536 | ||||||||
\(730\) | 4.18320 | + | 7.24552i | 0.154827 | + | 0.268169i | ||||
\(731\) | −0.949668 | + | 1.64487i | −0.0351247 | + | 0.0608378i | ||||
\(732\) | 8.21914 | − | 14.2360i | 0.303788 | − | 0.526177i | ||||
\(733\) | 4.56646 | + | 7.90935i | 0.168666 | + | 0.292138i | 0.937951 | − | 0.346767i | \(-0.112721\pi\) |
−0.769285 | + | 0.638906i | \(0.779387\pi\) | |||||||
\(734\) | 24.2997 | 0.896919 | ||||||||
\(735\) | −24.2844 | − | 9.04602i | −0.895744 | − | 0.333668i | ||||
\(736\) | −3.46219 | −0.127618 | ||||||||
\(737\) | −4.93407 | − | 8.54607i | −0.181749 | − | 0.314798i | ||||
\(738\) | −15.0977 | + | 26.1500i | −0.555755 | + | 0.962596i | ||||
\(739\) | −3.16227 | + | 5.47721i | −0.116326 | + | 0.201482i | −0.918309 | − | 0.395864i | \(-0.870445\pi\) |
0.801983 | + | 0.597347i | \(0.203778\pi\) | |||||||
\(740\) | −4.12508 | − | 7.14485i | −0.151641 | − | 0.262650i | ||||
\(741\) | −82.8358 | −3.04305 | ||||||||
\(742\) | −1.25326 | + | 6.95471i | −0.0460087 | + | 0.255315i | ||||
\(743\) | 32.2973 | 1.18487 | 0.592436 | − | 0.805618i | \(-0.298166\pi\) | ||||
0.592436 | + | 0.805618i | \(0.298166\pi\) | |||||||
\(744\) | 6.42825 | + | 11.1340i | 0.235671 | + | 0.408194i | ||||
\(745\) | −8.03591 | + | 13.9186i | −0.294413 | + | 0.509938i | ||||
\(746\) | 4.99255 | − | 8.64735i | 0.182790 | − | 0.316602i | ||||
\(747\) | −33.7629 | − | 58.4791i | −1.23532 | − | 2.13964i | ||||
\(748\) | −0.165244 | −0.00604190 | ||||||||
\(749\) | 4.46192 | − | 1.60505i | 0.163035 | − | 0.0586472i | ||||
\(750\) | −32.1724 | −1.17477 | ||||||||
\(751\) | −9.93095 | − | 17.2009i | −0.362385 | − | 0.627670i | 0.625968 | − | 0.779849i | \(-0.284704\pi\) |
−0.988353 | + | 0.152179i | \(0.951371\pi\) | |||||||
\(752\) | −0.0269105 | + | 0.0466104i | −0.000981327 | + | 0.00169971i | ||||
\(753\) | 2.73757 | − | 4.74161i | 0.0997625 | − | 0.172794i | ||||
\(754\) | 1.83068 | + | 3.17083i | 0.0666694 | + | 0.115475i | ||||
\(755\) | 13.9588 | 0.508013 | ||||||||
\(756\) | 29.1824 | + | 24.6744i | 1.06135 | + | 0.897398i | ||||
\(757\) | 24.1136 | 0.876425 | 0.438213 | − | 0.898871i | \(-0.355612\pi\) | ||||
0.438213 | + | 0.898871i | \(0.355612\pi\) | |||||||
\(758\) | 6.54456 | + | 11.3355i | 0.237709 | + | 0.411725i | ||||
\(759\) | −4.76385 | + | 8.25123i | −0.172917 | + | 0.299501i | ||||
\(760\) | 4.00177 | − | 6.93126i | 0.145159 | − | 0.251423i | ||||
\(761\) | −19.8123 | − | 34.3158i | −0.718194 | − | 1.24395i | −0.961715 | − | 0.274052i | \(-0.911636\pi\) |
0.243521 | − | 0.969896i | \(-0.421697\pi\) | |||||||
\(762\) | −37.4575 | −1.35694 | ||||||||
\(763\) | 7.35794 | + | 6.22130i | 0.266375 | + | 0.225226i | ||||
\(764\) | 9.90869 | 0.358484 | ||||||||
\(765\) | −0.829723 | − | 1.43712i | −0.0299987 | − | 0.0519592i | ||||
\(766\) | 1.48195 | − | 2.56681i | 0.0535451 | − | 0.0927428i | ||||
\(767\) | 14.7251 | − | 25.5047i | 0.531694 | − | 0.920921i | ||||
\(768\) | −1.61748 | − | 2.80156i | −0.0583659 | − | 0.101093i | ||||
\(769\) | −11.8143 | −0.426034 | −0.213017 | − | 0.977049i | \(-0.568329\pi\) | ||||
−0.213017 | + | 0.977049i | \(0.568329\pi\) | |||||||
\(770\) | 2.42364 | − | 0.871836i | 0.0873420 | − | 0.0314188i | ||||
\(771\) | 11.4946 | 0.413968 | ||||||||
\(772\) | 8.69752 | + | 15.0645i | 0.313030 | + | 0.542185i | ||||
\(773\) | −9.01041 | + | 15.6065i | −0.324082 | + | 0.561327i | −0.981326 | − | 0.192351i | \(-0.938389\pi\) |
0.657244 | + | 0.753678i | \(0.271722\pi\) | |||||||
\(774\) | −36.4960 | + | 63.2129i | −1.31182 | + | 2.27214i | ||||
\(775\) | −7.33317 | − | 12.7014i | −0.263415 | − | 0.456249i | ||||
\(776\) | 18.7779 | 0.674087 | ||||||||
\(777\) | 10.9428 | − | 60.7248i | 0.392571 | − | 2.17849i | ||||
\(778\) | −34.9114 | −1.25164 | ||||||||
\(779\) | 14.1445 | + | 24.4990i | 0.506779 | + | 0.877767i | ||||
\(780\) | −6.77731 | + | 11.7387i | −0.242667 | + | 0.420311i | ||||
\(781\) | −4.79890 | + | 8.31195i | −0.171718 | + | 0.297425i | ||||
\(782\) | 0.336262 | + | 0.582422i | 0.0120247 | + | 0.0208274i | ||||
\(783\) | −14.4442 | −0.516192 | ||||||||
\(784\) | 1.16370 | + | 6.90259i | 0.0415608 | + | 0.246521i | ||||
\(785\) | 16.4675 | 0.587750 | ||||||||
\(786\) | 26.1993 | + | 45.3785i | 0.934497 | + | 1.61860i | ||||
\(787\) | 3.65922 | − | 6.33795i | 0.130437 | − | 0.225923i | −0.793408 | − | 0.608690i | \(-0.791695\pi\) |
0.923845 | + | 0.382767i | \(0.125029\pi\) | |||||||
\(788\) | −8.79804 | + | 15.2386i | −0.313417 | + | 0.542854i | ||||
\(789\) | 29.7014 | + | 51.4443i | 1.05740 | + | 1.83147i | ||||
\(790\) | −15.2850 | −0.543816 | ||||||||
\(791\) | −8.33881 | + | 46.2744i | −0.296494 | + | 1.64533i | ||||
\(792\) | −6.35036 | −0.225650 | ||||||||
\(793\) | 9.30248 | + | 16.1124i | 0.330341 | + | 0.572167i | ||||
\(794\) | −7.70778 | + | 13.3503i | −0.273539 | + | 0.473783i | ||||
\(795\) | 4.94407 | − | 8.56339i | 0.175348 | − | 0.303712i | ||||
\(796\) | −5.64229 | − | 9.77274i | −0.199986 | − | 0.346386i | ||||
\(797\) | 53.5394 | 1.89646 | 0.948232 | − | 0.317578i | \(-0.102869\pi\) | ||||
0.948232 | + | 0.317578i | \(0.102869\pi\) | |||||||
\(798\) | 56.3250 | − | 20.2613i | 1.99388 | − | 0.717242i | ||||
\(799\) | 0.0104546 | 0.000369859 | ||||||||
\(800\) | 1.84518 | + | 3.19595i | 0.0652370 | + | 0.112994i | ||||
\(801\) | −53.1155 | + | 91.9987i | −1.87674 | + | 3.25062i | ||||
\(802\) | −19.0183 | + | 32.9406i | −0.671559 | + | 1.16317i | ||||
\(803\) | −3.10957 | − | 5.38594i | −0.109734 | − | 0.190066i | ||||
\(804\) | −37.5265 | −1.32346 | ||||||||
\(805\) | −8.00488 | − | 6.76830i | −0.282135 | − | 0.238551i | ||||
\(806\) | −14.5511 | −0.512540 | ||||||||
\(807\) | −29.4091 | − | 50.9381i | −1.03525 | − | 1.79311i | ||||
\(808\) | −6.85968 | + | 11.8813i | −0.241323 | + | 0.417983i | ||||
\(809\) | −4.44663 | + | 7.70178i | −0.156335 | + | 0.270780i | −0.933544 | − | 0.358462i | \(-0.883301\pi\) |
0.777209 | + | 0.629242i | \(0.216635\pi\) | |||||||
\(810\) | −13.9223 | − | 24.1142i | −0.489181 | − | 0.847286i | ||||
\(811\) | 4.11053 | 0.144340 | 0.0721701 | − | 0.997392i | \(-0.477008\pi\) | ||||
0.0721701 | + | 0.997392i | \(0.477008\pi\) | |||||||
\(812\) | −2.02036 | − | 1.70826i | −0.0709007 | − | 0.0599481i | ||||
\(813\) | −23.6380 | −0.829021 | ||||||||
\(814\) | 3.06637 | + | 5.31111i | 0.107476 | + | 0.186154i | ||||
\(815\) | −9.59423 | + | 16.6177i | −0.336071 | + | 0.582092i | ||||
\(816\) | −0.314193 | + | 0.544199i | −0.0109990 | + | 0.0190508i | ||||
\(817\) | 34.1917 | + | 59.2218i | 1.19622 | + | 2.07191i | ||||
\(818\) | −29.2856 | −1.02395 | ||||||||
\(819\) | −68.0453 | + | 24.4773i | −2.37769 | + | 0.855307i | ||||
\(820\) | 4.62899 | 0.161652 | ||||||||
\(821\) | −7.10319 | − | 12.3031i | −0.247903 | − | 0.429381i | 0.715041 | − | 0.699083i | \(-0.246408\pi\) |
−0.962944 | + | 0.269702i | \(0.913075\pi\) | |||||||
\(822\) | 20.6783 | − | 35.8159i | 0.721238 | − | 1.24922i | ||||
\(823\) | −9.42010 | + | 16.3161i | −0.328364 | + | 0.568743i | −0.982187 | − | 0.187904i | \(-0.939831\pi\) |
0.653823 | + | 0.756647i | \(0.273164\pi\) | |||||||
\(824\) | −0.590573 | − | 1.02290i | −0.0205736 | − | 0.0356345i | ||||
\(825\) | 10.1556 | 0.353573 | ||||||||
\(826\) | −3.77416 | + | 20.9439i | −0.131320 | + | 0.728731i | ||||
\(827\) | 7.13405 | 0.248075 | 0.124038 | − | 0.992278i | \(-0.460416\pi\) | ||||
0.124038 | + | 0.992278i | \(0.460416\pi\) | |||||||
\(828\) | 12.9226 | + | 22.3827i | 0.449092 | + | 0.777851i | ||||
\(829\) | −0.606016 | + | 1.04965i | −0.0210478 | + | 0.0364559i | −0.876357 | − | 0.481661i | \(-0.840034\pi\) |
0.855310 | + | 0.518117i | \(0.173367\pi\) | |||||||
\(830\) | −5.17589 | + | 8.96490i | −0.179658 | + | 0.311176i | ||||
\(831\) | 26.9181 | + | 46.6235i | 0.933778 | + | 1.61735i | ||||
\(832\) | 3.66136 | 0.126935 | ||||||||
\(833\) | 1.04816 | − | 0.866171i | 0.0363165 | − | 0.0300110i | ||||
\(834\) | 0.551803 | 0.0191074 | ||||||||
\(835\) | 6.09702 | + | 10.5603i | 0.210996 | + | 0.365456i | ||||
\(836\) | −2.97471 | + | 5.15234i | −0.102882 | + | 0.178197i | ||||
\(837\) | 28.7022 | − | 49.7136i | 0.992093 | − | 1.71836i | ||||
\(838\) | 3.14706 | + | 5.45087i | 0.108713 | + | 0.188297i | ||||
\(839\) | 13.0004 | 0.448823 | 0.224412 | − | 0.974494i | \(-0.427954\pi\) | ||||
0.224412 | + | 0.974494i | \(0.427954\pi\) | |||||||
\(840\) | 1.73707 | − | 9.63951i | 0.0599347 | − | 0.332595i | ||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −1.47240 | − | 2.55026i | −0.0507421 | − | 0.0878879i | ||||
\(843\) | −21.4417 | + | 37.1382i | −0.738492 | + | 1.27911i | ||||
\(844\) | 4.93786 | − | 8.55262i | 0.169968 | − | 0.294393i | ||||
\(845\) | −0.232050 | − | 0.401922i | −0.00798275 | − | 0.0138265i | ||||
\(846\) | 0.401775 | 0.0138133 | ||||||||
\(847\) | 25.5837 | − | 9.20301i | 0.879067 | − | 0.316219i | ||||
\(848\) | −2.67097 | −0.0917216 | ||||||||
\(849\) | 24.7129 | + | 42.8039i | 0.848143 | + | 1.46903i | ||||
\(850\) | 0.358423 | − | 0.620807i | 0.0122938 | − | 0.0212935i | ||||
\(851\) | 12.4798 | − | 21.6156i | 0.427802 | − | 0.740974i | ||||
\(852\) | 18.2492 | + | 31.6086i | 0.625208 | + | 1.08289i | ||||
\(853\) | 23.8201 | 0.815584 | 0.407792 | − | 0.913075i | \(-0.366299\pi\) | ||||
0.407792 | + | 0.913075i | \(0.366299\pi\) | |||||||
\(854\) | −10.2663 | − | 8.68041i | −0.351307 | − | 0.297038i | ||||
\(855\) | −59.7465 | −2.04329 | ||||||||
\(856\) | 0.896121 | + | 1.55213i | 0.0306288 | + | 0.0530506i | ||||
\(857\) | 3.63570 | − | 6.29722i | 0.124193 | − | 0.215109i | −0.797224 | − | 0.603683i | \(-0.793699\pi\) |
0.921417 | + | 0.388575i | \(0.127032\pi\) | |||||||
\(858\) | 5.03790 | − | 8.72590i | 0.171991 | − | 0.297897i | ||||
\(859\) | −4.91631 | − | 8.51531i | −0.167742 | − | 0.290539i | 0.769883 | − | 0.638185i | \(-0.220314\pi\) |
−0.937626 | + | 0.347646i | \(0.886981\pi\) | |||||||
\(860\) | 11.1897 | 0.381567 | ||||||||
\(861\) | 26.4368 | + | 22.3529i | 0.900965 | + | 0.761786i | ||||
\(862\) | 5.45942 | 0.185949 | ||||||||
\(863\) | −10.9706 | − | 19.0017i | −0.373445 | − | 0.646826i | 0.616648 | − | 0.787239i | \(-0.288490\pi\) |
−0.990093 | + | 0.140413i | \(0.955157\pi\) | |||||||
\(864\) | −7.22208 | + | 12.5090i | −0.245700 | + | 0.425565i | ||||
\(865\) | −10.2567 | + | 17.7651i | −0.348738 | + | 0.604031i | ||||
\(866\) | 8.49495 | + | 14.7137i | 0.288670 | + | 0.499991i | ||||
\(867\) | −54.8724 | −1.86356 | ||||||||
\(868\) | 9.89414 | − | 3.55913i | 0.335829 | − | 0.120805i | ||||
\(869\) | 11.3621 | 0.385432 | ||||||||
\(870\) | 1.85104 | + | 3.20609i | 0.0627561 | + | 0.108697i | ||||
\(871\) | 21.2364 | − | 36.7825i | 0.719567 | − | 1.24633i | ||||
\(872\) | −1.82095 | + | 3.15397i | −0.0616651 | + | 0.106807i | ||||
\(873\) | −70.0885 | − | 121.397i | −2.37214 | − | 4.10866i | ||||
\(874\) | 24.2135 | 0.819032 | ||||||||
\(875\) | −4.66644 | + | 25.8954i | −0.157755 | + | 0.875425i | ||||
\(876\) | −23.6501 | −0.799063 | ||||||||
\(877\) | −18.2830 | − | 31.6670i | −0.617372 | − | 1.06932i | −0.989963 | − | 0.141324i | \(-0.954864\pi\) |
0.372592 | − | 0.927995i | \(-0.378469\pi\) | |||||||
\(878\) | 11.3210 | − | 19.6085i | 0.382064 | − | 0.661755i | ||||
\(879\) | 25.1019 | − | 43.4778i | 0.846667 | − | 1.46647i | ||||
\(880\) | 0.486758 | + | 0.843090i | 0.0164086 | + | 0.0284206i | ||||
\(881\) | −33.4505 | −1.12698 | −0.563489 | − | 0.826124i | \(-0.690541\pi\) | ||||
−0.563489 | + | 0.826124i | \(0.690541\pi\) | |||||||
\(882\) | 40.2810 | − | 33.2872i | 1.35633 | − | 1.12084i | ||||
\(883\) | −23.9555 | −0.806166 | −0.403083 | − | 0.915163i | \(-0.632061\pi\) | ||||
−0.403083 | + | 0.915163i | \(0.632061\pi\) | |||||||
\(884\) | −0.355606 | − | 0.615928i | −0.0119603 | − | 0.0207159i | ||||
\(885\) | 14.8889 | − | 25.7883i | 0.500485 | − | 0.866866i | ||||
\(886\) | 8.56936 | − | 14.8426i | 0.287893 | − | 0.498646i | ||||
\(887\) | −3.69777 | − | 6.40472i | −0.124159 | − | 0.215049i | 0.797245 | − | 0.603656i | \(-0.206290\pi\) |
−0.921404 | + | 0.388606i | \(0.872957\pi\) | |||||||
\(888\) | 23.3215 | 0.782618 | ||||||||
\(889\) | −5.43302 | + | 30.1494i | −0.182218 | + | 1.01118i | ||||
\(890\) | 16.2853 | 0.545885 | ||||||||
\(891\) | 10.3491 | + | 17.9252i | 0.346709 | + | 0.600517i | ||||
\(892\) | 8.29908 | − | 14.3744i | 0.277874 | − | 0.481292i | ||||
\(893\) | 0.188204 | − | 0.325979i | 0.00629801 | − | 0.0109085i | ||||
\(894\) | −22.7159 | − | 39.3450i | −0.759732 | − | 1.31589i | ||||
\(895\) | 6.05292 | 0.202327 | ||||||||
\(896\) | −2.48958 | + | 0.895553i | −0.0831709 | + | 0.0299183i | ||||
\(897\) | −41.0074 | −1.36920 | ||||||||
\(898\) | 6.09008 | + | 10.5483i | 0.203229 | + | 0.352002i | ||||
\(899\) | −1.98711 | + | 3.44178i | −0.0662739 | + | 0.114790i | ||||
\(900\) | 13.7743 | − | 23.8578i | 0.459143 | − | 0.795259i | ||||
\(901\) | 0.259416 | + | 0.449321i | 0.00864239 | + | 0.0149691i | ||||
\(902\) | −3.44095 | −0.114571 | ||||||||
\(903\) | 63.9062 | + | 54.0341i | 2.12667 | + | 1.79814i | ||||
\(904\) | −17.7718 | −0.591081 | ||||||||
\(905\) | −7.53644 | − | 13.0535i | −0.250520 | − | 0.433913i | ||||
\(906\) | −19.7293 | + | 34.1722i | −0.655463 | + | 1.13530i | ||||
\(907\) | −14.2946 | + | 24.7590i | −0.474644 | + | 0.822108i | −0.999578 | − | 0.0290348i | \(-0.990757\pi\) |
0.524934 | + | 0.851143i | \(0.324090\pi\) | |||||||
\(908\) | −8.99651 | − | 15.5824i | −0.298560 | − | 0.517121i | ||||
\(909\) | 102.415 | 3.39690 | ||||||||
\(910\) | 8.46538 | + | 7.15767i | 0.280625 | + | 0.237274i | ||||
\(911\) | −15.2600 | −0.505587 | −0.252793 | − | 0.967520i | \(-0.581349\pi\) | ||||
−0.252793 | + | 0.967520i | \(0.581349\pi\) | |||||||
\(912\) | 11.3122 | + | 19.5933i | 0.374584 | + | 0.648798i | ||||
\(913\) | 3.84749 | − | 6.66404i | 0.127333 | − | 0.220548i | ||||
\(914\) | −15.7551 | + | 27.2886i | −0.521132 | + | 0.902626i | ||||
\(915\) | 9.40593 | + | 16.2916i | 0.310951 | + | 0.538582i | ||||
\(916\) | −2.03821 | −0.0673444 | ||||||||
\(917\) | 40.3250 | − | 14.5058i | 1.33165 | − | 0.479023i | ||||
\(918\) | 2.80575 | 0.0926036 | ||||||||
\(919\) | 11.1510 | + | 19.3140i | 0.367836 | + | 0.637111i | 0.989227 | − | 0.146390i | \(-0.0467654\pi\) |
−0.621391 | + | 0.783501i | \(0.713432\pi\) | |||||||
\(920\) | 1.98105 | − | 3.43128i | 0.0653134 | − | 0.113126i | ||||
\(921\) | −5.08339 | + | 8.80468i | −0.167503 | + | 0.290124i | ||||
\(922\) | 3.20398 | + | 5.54945i | 0.105517 | + | 0.182762i | ||||
\(923\) | −41.3092 | −1.35971 | ||||||||
\(924\) | −1.29125 | + | 7.16551i | −0.0424790 | + | 0.235728i | ||||
\(925\) | −26.6045 | −0.874752 | ||||||||
\(926\) | 0.451470 | + | 0.781968i | 0.0148362 | + | 0.0256971i | ||||
\(927\) | −4.40863 | + | 7.63598i | −0.144798 | + | 0.250798i | ||||
\(928\) | 0.500000 | − | 0.866025i | 0.0164133 | − | 0.0284287i | ||||
\(929\) | 22.4850 | + | 38.9452i | 0.737710 | + | 1.27775i | 0.953524 | + | 0.301316i | \(0.0974259\pi\) |
−0.215815 | + | 0.976434i | \(0.569241\pi\) | |||||||
\(930\) | −14.7129 | −0.482455 | ||||||||
\(931\) | −8.13858 | − | 48.2746i | −0.266731 | − | 1.58214i | ||||
\(932\) | −16.4989 | −0.540441 | ||||||||
\(933\) | −39.1690 | − | 67.8426i | −1.28233 | − | 2.22107i | ||||
\(934\) | 18.2056 | − | 31.5330i | 0.595705 | − | 1.03179i | ||||
\(935\) | 0.0945519 | − | 0.163769i | 0.00309218 | − | 0.00535581i | ||||
\(936\) | −13.6660 | − | 23.6703i | −0.446688 | − | 0.773687i | ||||
\(937\) | 20.6347 | 0.674105 | 0.337053 | − | 0.941486i | \(-0.390570\pi\) | ||||
0.337053 | + | 0.941486i | \(0.390570\pi\) | |||||||
\(938\) | −5.44303 | + | 30.2049i | −0.177721 | + | 0.986226i | ||||
\(939\) | −33.4910 | −1.09294 | ||||||||
\(940\) | −0.0307963 | − | 0.0533407i | −0.00100446 | − | 0.00173978i | ||||
\(941\) | −16.6294 | + | 28.8030i | −0.542103 | + | 0.938950i | 0.456680 | + | 0.889631i | \(0.349038\pi\) |
−0.998783 | + | 0.0493189i | \(0.984295\pi\) | |||||||
\(942\) | −23.2751 | + | 40.3137i | −0.758344 | + | 1.31349i | ||||
\(943\) | 7.00215 | + | 12.1281i | 0.228021 | + | 0.394945i | ||||
\(944\) | −8.04354 | −0.261795 | ||||||||
\(945\) | −41.1522 | + | 14.8033i | −1.33868 | + | 0.481552i | ||||
\(946\) | −8.31787 | −0.270437 | ||||||||
\(947\) | −0.0479947 | − | 0.0831292i | −0.00155962 | − | 0.00270134i | 0.865245 | − | 0.501350i | \(-0.167163\pi\) |
−0.866804 | + | 0.498649i | \(0.833830\pi\) | |||||||
\(948\) | 21.6038 | − | 37.4188i | 0.701658 | − | 1.21531i | ||||
\(949\) | 13.3837 | − | 23.1812i | 0.434452 | − | 0.752494i | ||||
\(950\) | −12.9046 | − | 22.3515i | −0.418681 | − | 0.725177i | ||||
\(951\) | −111.713 | −3.62253 | ||||||||
\(952\) | 0.392451 | + | 0.331826i | 0.0127194 | + | 0.0107545i | ||||
\(953\) | −11.4213 | −0.369974 | −0.184987 | − | 0.982741i | \(-0.559224\pi\) | ||||
−0.184987 | + | 0.982741i | \(0.559224\pi\) | |||||||
\(954\) | 9.96942 | + | 17.2675i | 0.322772 | + | 0.559057i | ||||
\(955\) | −5.66972 | + | 9.82025i | −0.183468 | + | 0.317776i | ||||
\(956\) | −9.37071 | + | 16.2305i | −0.303070 | + | 0.524933i | ||||
\(957\) | −1.37597 | − | 2.38324i | −0.0444786 | − | 0.0770393i | ||||
\(958\) | 31.4283 | 1.01540 | ||||||||
\(959\) | −25.8288 | − | 21.8388i | −0.834054 | − | 0.705211i | ||||
\(960\) | 3.70208 | 0.119484 | ||||||||
\(961\) | 7.60276 | + | 13.1684i | 0.245250 | + | 0.424786i | ||||
\(962\) | −13.1977 | + | 22.8591i | −0.425512 | + | 0.737008i | ||||
\(963\) | 6.68955 | − | 11.5866i | 0.215568 | − | 0.373374i | ||||
\(964\) | −8.93903 | − | 15.4828i | −0.287907 | − | 0.498669i | ||||
\(965\) | −19.9068 | −0.640822 | ||||||||
\(966\) | 27.8834 | − | 10.0302i | 0.897133 | − | 0.322718i | ||||
\(967\) | −9.43755 | −0.303491 | −0.151746 | − | 0.988420i | \(-0.548489\pi\) | ||||
−0.151746 | + | 0.988420i | \(0.548489\pi\) | |||||||
\(968\) | 5.13817 | + | 8.89957i | 0.165147 | + | 0.286043i | ||||
\(969\) | 2.19737 | − | 3.80596i | 0.0705897 | − | 0.122265i | ||||
\(970\) | −10.7446 | + | 18.6103i | −0.344990 | + | 0.597540i | ||||
\(971\) | 9.26400 | + | 16.0457i | 0.297296 | + | 0.514932i | 0.975516 | − | 0.219927i | \(-0.0705819\pi\) |
−0.678220 | + | 0.734859i | \(0.737249\pi\) | |||||||
\(972\) | 35.3786 | 1.13477 | ||||||||
\(973\) | 0.0800363 | − | 0.444144i | 0.00256585 | − | 0.0142386i | ||||
\(974\) | 14.4460 | 0.462878 | ||||||||
\(975\) | 21.8550 | + | 37.8540i | 0.699921 | + | 1.21230i | ||||
\(976\) | 2.54072 | − | 4.40065i | 0.0813264 | − | 0.140861i | ||||
\(977\) | 20.3383 | − | 35.2270i | 0.650680 | − | 1.12701i | −0.332279 | − | 0.943181i | \(-0.607817\pi\) |
0.982958 | − | 0.183829i | \(-0.0588492\pi\) | |||||||
\(978\) | −27.1209 | − | 46.9748i | −0.867231 | − | 1.50209i | ||||
\(979\) | −12.1057 | −0.386899 | ||||||||
\(980\) | −7.50685 | − | 2.79633i | −0.239798 | − | 0.0893254i | ||||
\(981\) | 27.1868 | 0.868008 | ||||||||
\(982\) | −14.6203 | − | 25.3230i | −0.466551 | − | 0.808090i | ||||
\(983\) | −26.3075 | + | 45.5659i | −0.839078 | + | 1.45332i | 0.0515893 | + | 0.998668i | \(0.483571\pi\) |
−0.890667 | + | 0.454657i | \(0.849762\pi\) | |||||||
\(984\) | −6.54261 | + | 11.3321i | −0.208571 | + | 0.361255i | ||||
\(985\) | −10.0684 | − | 17.4390i | −0.320806 | − | 0.555653i | ||||
\(986\) | −0.194248 | −0.00618612 | ||||||||
\(987\) | 0.0816949 | − | 0.453348i | 0.00260038 | − | 0.0144302i | ||||
\(988\) | −25.6064 | −0.814648 | ||||||||
\(989\) | 16.9264 | + | 29.3174i | 0.538229 | + | 0.932240i | ||||
\(990\) | 3.63365 | − | 6.29367i | 0.115485 | − | 0.200026i | ||||
\(991\) | 12.3917 | − | 21.4631i | 0.393637 | − | 0.681799i | −0.599290 | − | 0.800532i | \(-0.704550\pi\) |
0.992926 | + | 0.118734i | \(0.0378835\pi\) | |||||||
\(992\) | 1.98711 | + | 3.44178i | 0.0630909 | + | 0.109277i | ||||
\(993\) | 16.4997 | 0.523603 | ||||||||
\(994\) | 28.0886 | − | 10.1041i | 0.890915 | − | 0.320481i | ||||
\(995\) | 12.9140 | 0.409402 | ||||||||
\(996\) | −14.6312 | − | 25.3419i | −0.463607 | − | 0.802990i | ||||
\(997\) | −8.09453 | + | 14.0201i | −0.256356 | + | 0.444022i | −0.965263 | − | 0.261280i | \(-0.915855\pi\) |
0.708907 | + | 0.705302i | \(0.249189\pi\) | |||||||
\(998\) | −14.2452 | + | 24.6735i | −0.450925 | + | 0.781025i | ||||
\(999\) | −52.0654 | − | 90.1799i | −1.64728 | − | 2.85317i |
(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 | 406.2.e.a.291.1 | yes | 10 | |
7.2 | even | 3 | inner | 406.2.e.a.233.1 | ✓ | 10 | |
7.3 | odd | 6 | 2842.2.a.x.1.1 | 5 | |||
7.4 | even | 3 | 2842.2.a.z.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
406.2.e.a.233.1 | ✓ | 10 | 7.2 | even | 3 | inner | |
406.2.e.a.291.1 | yes | 10 | 1.1 | even | 1 | trivial | |
2842.2.a.x.1.1 | 5 | 7.3 | odd | 6 | |||
2842.2.a.z.1.5 | 5 | 7.4 | even | 3 |