Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [143,2,Mod(100,143)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(143, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("143.100");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 143 = 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 143.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: | \(1.14186074890\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.3518667.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 7x^{4} - 8x^{3} + 43x^{2} - 42x + 49 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 100.1 | ||
Root | \(-1.25351 + 2.17114i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 143.100 |
Dual form | 143.2.e.b.133.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/143\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.25351 | + | 2.17114i | −0.886365 | + | 1.53523i | −0.0422238 | + | 0.999108i | \(0.513444\pi\) |
−0.844141 | + | 0.536121i | \(0.819889\pi\) | |||||||
\(3\) | −1.14257 | + | 1.97899i | −0.659664 | + | 1.14257i | 0.321039 | + | 0.947066i | \(0.395968\pi\) |
−0.980703 | + | 0.195505i | \(0.937365\pi\) | |||||||
\(4\) | −2.14257 | − | 3.71104i | −1.07129 | − | 1.85552i | ||||
\(5\) | −1.22188 | −0.546440 | −0.273220 | − | 0.961952i | \(-0.588089\pi\) | ||||
−0.273220 | + | 0.961952i | \(0.588089\pi\) | |||||||
\(6\) | −2.86445 | − | 4.96137i | −1.16941 | − | 2.02547i | ||||
\(7\) | −0.389062 | − | 0.673875i | −0.147052 | − | 0.254701i | 0.783085 | − | 0.621915i | \(-0.213645\pi\) |
−0.930136 | + | 0.367214i | \(0.880312\pi\) | |||||||
\(8\) | 5.72889 | 2.02547 | ||||||||
\(9\) | −1.11094 | − | 1.92420i | −0.370313 | − | 0.641400i | ||||
\(10\) | 1.53163 | − | 2.65287i | 0.484345 | − | 0.838910i | ||||
\(11\) | −0.500000 | + | 0.866025i | −0.150756 | + | 0.261116i | ||||
\(12\) | 9.79216 | 2.82675 | ||||||||
\(13\) | −2.50000 | + | 2.59808i | −0.693375 | + | 0.720577i | ||||
\(14\) | 1.95077 | 0.521365 | ||||||||
\(15\) | 1.39608 | − | 2.41808i | 0.360466 | − | 0.624346i | ||||
\(16\) | −2.89608 | + | 5.01616i | −0.724020 | + | 1.25404i | ||||
\(17\) | 2.14257 | + | 3.71104i | 0.519650 | + | 0.900060i | 0.999739 | + | 0.0228403i | \(0.00727093\pi\) |
−0.480089 | + | 0.877220i | \(0.659396\pi\) | |||||||
\(18\) | 5.57028 | 1.31293 | ||||||||
\(19\) | −4.14959 | − | 7.18730i | −0.951981 | − | 1.64888i | −0.741130 | − | 0.671362i | \(-0.765710\pi\) |
−0.210851 | − | 0.977518i | \(-0.567624\pi\) | |||||||
\(20\) | 2.61796 | + | 4.53443i | 0.585393 | + | 1.01393i | ||||
\(21\) | 1.77812 | 0.388018 | ||||||||
\(22\) | −1.25351 | − | 2.17114i | −0.267249 | − | 0.462889i | ||||
\(23\) | 1.36445 | − | 2.36329i | 0.284507 | − | 0.492780i | −0.687983 | − | 0.725727i | \(-0.741503\pi\) |
0.972489 | + | 0.232947i | \(0.0748368\pi\) | |||||||
\(24\) | −6.54567 | + | 11.3374i | −1.33613 | + | 2.31424i | ||||
\(25\) | −3.50702 | −0.701404 | ||||||||
\(26\) | −2.50702 | − | 8.68457i | −0.491667 | − | 1.70318i | ||||
\(27\) | −1.77812 | −0.342200 | ||||||||
\(28\) | −1.66719 | + | 2.88765i | −0.315068 | + | 0.545715i | ||||
\(29\) | −3.68122 | + | 6.37607i | −0.683586 | + | 1.18401i | 0.290293 | + | 0.956938i | \(0.406247\pi\) |
−0.973879 | + | 0.227068i | \(0.927086\pi\) | |||||||
\(30\) | 3.50000 | + | 6.06218i | 0.639010 | + | 1.10680i | ||||
\(31\) | −1.44375 | −0.259306 | −0.129653 | − | 0.991559i | \(-0.541386\pi\) | ||||
−0.129653 | + | 0.991559i | \(0.541386\pi\) | |||||||
\(32\) | −1.53163 | − | 2.65287i | −0.270757 | − | 0.468965i | ||||
\(33\) | −1.14257 | − | 1.97899i | −0.198896 | − | 0.344498i | ||||
\(34\) | −10.7429 | −1.84240 | ||||||||
\(35\) | 0.475385 | + | 0.823392i | 0.0803548 | + | 0.139179i | ||||
\(36\) | −4.76053 | + | 8.24548i | −0.793421 | + | 1.37425i | ||||
\(37\) | 0.396081 | − | 0.686032i | 0.0651152 | − | 0.112783i | −0.831630 | − | 0.555330i | \(-0.812592\pi\) |
0.896745 | + | 0.442547i | \(0.145925\pi\) | |||||||
\(38\) | 20.8062 | 3.37521 | ||||||||
\(39\) | −2.28514 | − | 7.91597i | −0.365916 | − | 1.26757i | ||||
\(40\) | −7.00000 | −1.10680 | ||||||||
\(41\) | −4.87147 | + | 8.43763i | −0.760795 | + | 1.31774i | 0.181646 | + | 0.983364i | \(0.441857\pi\) |
−0.942441 | + | 0.334372i | \(0.891476\pi\) | |||||||
\(42\) | −2.22889 | + | 3.86056i | −0.343926 | + | 0.595697i | ||||
\(43\) | 4.83983 | + | 8.38284i | 0.738068 | + | 1.27837i | 0.953364 | + | 0.301822i | \(0.0975948\pi\) |
−0.215297 | + | 0.976549i | \(0.569072\pi\) | |||||||
\(44\) | 4.28514 | 0.646010 | ||||||||
\(45\) | 1.35743 | + | 2.35114i | 0.202354 | + | 0.350487i | ||||
\(46\) | 3.42070 | + | 5.92482i | 0.504354 | + | 0.873567i | ||||
\(47\) | −3.38049 | −0.493095 | −0.246547 | − | 0.969131i | \(-0.579296\pi\) | ||||
−0.246547 | + | 0.969131i | \(0.579296\pi\) | |||||||
\(48\) | −6.61796 | − | 11.4626i | −0.955220 | − | 1.65449i | ||||
\(49\) | 3.19726 | − | 5.53782i | 0.456752 | − | 0.791117i | ||||
\(50\) | 4.39608 | − | 7.61423i | 0.621700 | − | 1.07682i | ||||
\(51\) | −9.79216 | −1.37118 | ||||||||
\(52\) | 14.9980 | + | 3.71104i | 2.07985 | + | 0.514629i | ||||
\(53\) | 1.79216 | 0.246172 | 0.123086 | − | 0.992396i | \(-0.460721\pi\) | ||||
0.123086 | + | 0.992396i | \(0.460721\pi\) | |||||||
\(54\) | 2.22889 | − | 3.86056i | 0.303314 | − | 0.525356i | ||||
\(55\) | 0.610938 | − | 1.05818i | 0.0823789 | − | 0.142684i | ||||
\(56\) | −2.22889 | − | 3.86056i | −0.297849 | − | 0.515889i | ||||
\(57\) | 18.9648 | 2.51195 | ||||||||
\(58\) | −9.22889 | − | 15.9849i | −1.21181 | − | 2.09892i | ||||
\(59\) | −2.60392 | − | 4.51012i | −0.339001 | − | 0.587168i | 0.645244 | − | 0.763977i | \(-0.276756\pi\) |
−0.984245 | + | 0.176809i | \(0.943422\pi\) | |||||||
\(60\) | −11.9648 | −1.54465 | ||||||||
\(61\) | 7.26053 | + | 12.5756i | 0.929615 | + | 1.61014i | 0.783965 | + | 0.620805i | \(0.213194\pi\) |
0.145650 | + | 0.989336i | \(0.453473\pi\) | |||||||
\(62\) | 1.80976 | − | 3.13459i | 0.229839 | − | 0.398093i | ||||
\(63\) | −0.864447 | + | 1.49727i | −0.108910 | + | 0.188638i | ||||
\(64\) | −3.90466 | −0.488082 | ||||||||
\(65\) | 3.05469 | − | 3.17453i | 0.378888 | − | 0.393752i | ||||
\(66\) | 5.72889 | 0.705178 | ||||||||
\(67\) | −3.03163 | + | 5.25094i | −0.370373 | + | 0.641505i | −0.989623 | − | 0.143689i | \(-0.954103\pi\) |
0.619250 | + | 0.785194i | \(0.287437\pi\) | |||||||
\(68\) | 9.18122 | − | 15.9023i | 1.11339 | − | 1.92844i | ||||
\(69\) | 3.11796 | + | 5.40046i | 0.375358 | + | 0.650139i | ||||
\(70\) | −2.38360 | −0.284895 | ||||||||
\(71\) | 3.25351 | + | 5.63524i | 0.386121 | + | 0.668780i | 0.991924 | − | 0.126834i | \(-0.0404815\pi\) |
−0.605803 | + | 0.795614i | \(0.707148\pi\) | |||||||
\(72\) | −6.36445 | − | 11.0235i | −0.750057 | − | 1.29914i | ||||
\(73\) | −2.00000 | −0.234082 | −0.117041 | − | 0.993127i | \(-0.537341\pi\) | ||||
−0.117041 | + | 0.993127i | \(0.537341\pi\) | |||||||
\(74\) | 0.992981 | + | 1.71989i | 0.115432 | + | 0.199934i | ||||
\(75\) | 4.00702 | − | 6.94036i | 0.462691 | − | 0.801404i | ||||
\(76\) | −17.7816 | + | 30.7986i | −2.03969 | + | 3.53284i | ||||
\(77\) | 0.778124 | 0.0886754 | ||||||||
\(78\) | 20.0511 | + | 4.96137i | 2.27034 | + | 0.561764i | ||||
\(79\) | 13.5843 | 1.52836 | 0.764178 | − | 0.645006i | \(-0.223145\pi\) | ||||
0.764178 | + | 0.645006i | \(0.223145\pi\) | |||||||
\(80\) | 3.53865 | − | 6.12912i | 0.395633 | − | 0.685257i | ||||
\(81\) | 5.36445 | − | 9.29150i | 0.596050 | − | 1.03239i | ||||
\(82\) | −12.2129 | − | 21.1533i | −1.34868 | − | 2.33599i | ||||
\(83\) | −13.3624 | −1.46672 | −0.733360 | − | 0.679841i | \(-0.762049\pi\) | ||||
−0.733360 | + | 0.679841i | \(0.762049\pi\) | |||||||
\(84\) | −3.80976 | − | 6.59869i | −0.415679 | − | 0.719976i | ||||
\(85\) | −2.61796 | − | 4.53443i | −0.283957 | − | 0.491828i | ||||
\(86\) | −24.2671 | −2.61679 | ||||||||
\(87\) | −8.41212 | − | 14.5702i | −0.901874 | − | 1.56209i | ||||
\(88\) | −2.86445 | + | 4.96137i | −0.305351 | + | 0.528884i | ||||
\(89\) | 2.38906 | − | 4.13798i | 0.253240 | − | 0.438625i | −0.711176 | − | 0.703014i | \(-0.751837\pi\) |
0.964416 | + | 0.264389i | \(0.0851704\pi\) | |||||||
\(90\) | −6.80620 | −0.717436 | ||||||||
\(91\) | 2.72343 | + | 0.673875i | 0.285493 | + | 0.0706413i | ||||
\(92\) | −11.6937 | −1.21915 | ||||||||
\(93\) | 1.64959 | − | 2.85717i | 0.171055 | − | 0.296275i | ||||
\(94\) | 4.23747 | − | 7.33951i | 0.437062 | − | 0.757013i | ||||
\(95\) | 5.07028 | + | 8.78199i | 0.520200 | + | 0.901013i | ||||
\(96\) | 7.00000 | 0.714435 | ||||||||
\(97\) | 2.07028 | + | 3.58584i | 0.210206 | + | 0.364087i | 0.951779 | − | 0.306785i | \(-0.0992533\pi\) |
−0.741573 | + | 0.670872i | \(0.765920\pi\) | |||||||
\(98\) | 8.01559 | + | 13.8834i | 0.809697 | + | 1.40244i | ||||
\(99\) | 2.22188 | 0.223307 | ||||||||
\(100\) | 7.51404 | + | 13.0147i | 0.751404 | + | 1.30147i | ||||
\(101\) | −2.41212 | + | 4.17791i | −0.240015 | + | 0.415718i | −0.960718 | − | 0.277526i | \(-0.910486\pi\) |
0.720703 | + | 0.693244i | \(0.243819\pi\) | |||||||
\(102\) | 12.2746 | − | 21.2602i | 1.21536 | − | 2.10507i | ||||
\(103\) | 9.76008 | 0.961690 | 0.480845 | − | 0.876806i | \(-0.340330\pi\) | ||||
0.480845 | + | 0.876806i | \(0.340330\pi\) | |||||||
\(104\) | −14.3222 | + | 14.8841i | −1.40441 | + | 1.45951i | ||||
\(105\) | −2.17265 | −0.212029 | ||||||||
\(106\) | −2.24649 | + | 3.89104i | −0.218198 | + | 0.377931i | ||||
\(107\) | −1.18122 | + | 2.04594i | −0.114193 | + | 0.197788i | −0.917457 | − | 0.397835i | \(-0.869762\pi\) |
0.803264 | + | 0.595623i | \(0.203095\pi\) | |||||||
\(108\) | 3.80976 | + | 6.59869i | 0.366594 | + | 0.634959i | ||||
\(109\) | −2.86946 | −0.274845 | −0.137422 | − | 0.990513i | \(-0.543882\pi\) | ||||
−0.137422 | + | 0.990513i | \(0.543882\pi\) | |||||||
\(110\) | 1.53163 | + | 2.65287i | 0.146035 | + | 0.252941i | ||||
\(111\) | 0.905101 | + | 1.56768i | 0.0859083 | + | 0.148798i | ||||
\(112\) | 4.50702 | 0.425873 | ||||||||
\(113\) | 2.80118 | + | 4.85179i | 0.263513 | + | 0.456418i | 0.967173 | − | 0.254119i | \(-0.0817855\pi\) |
−0.703660 | + | 0.710537i | \(0.748452\pi\) | |||||||
\(114\) | −23.7726 | + | 41.1753i | −2.22650 | + | 3.85642i | ||||
\(115\) | −1.66719 | + | 2.88765i | −0.155466 | + | 0.269275i | ||||
\(116\) | 31.5491 | 2.92926 | ||||||||
\(117\) | 7.77657 | + | 1.92420i | 0.718944 | + | 0.177892i | ||||
\(118\) | 13.0561 | 1.20192 | ||||||||
\(119\) | 1.66719 | − | 2.88765i | 0.152831 | − | 0.264710i | ||||
\(120\) | 7.99800 | − | 13.8529i | 0.730114 | − | 1.26459i | ||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | −36.4046 | −3.29591 | ||||||||
\(123\) | −11.1320 | − | 19.2812i | −1.00374 | − | 1.73853i | ||||
\(124\) | 3.09334 | + | 5.35783i | 0.277790 | + | 0.481147i | ||||
\(125\) | 10.3945 | 0.929714 | ||||||||
\(126\) | −2.16719 | − | 3.75368i | −0.193068 | − | 0.334404i | ||||
\(127\) | −3.61796 | + | 6.26648i | −0.321042 | + | 0.556061i | −0.980703 | − | 0.195502i | \(-0.937366\pi\) |
0.659662 | + | 0.751563i | \(0.270700\pi\) | |||||||
\(128\) | 7.95779 | − | 13.7833i | 0.703376 | − | 1.21828i | ||||
\(129\) | −22.1194 | −1.94751 | ||||||||
\(130\) | 3.06327 | + | 10.6115i | 0.268666 | + | 0.930687i | ||||
\(131\) | −10.3484 | −0.904145 | −0.452072 | − | 0.891981i | \(-0.649315\pi\) | ||||
−0.452072 | + | 0.891981i | \(0.649315\pi\) | |||||||
\(132\) | −4.89608 | + | 8.48026i | −0.426149 | + | 0.738112i | ||||
\(133\) | −3.22889 | + | 5.59261i | −0.279981 | + | 0.484941i | ||||
\(134\) | −7.60036 | − | 13.1642i | −0.656571 | − | 1.13721i | ||||
\(135\) | 2.17265 | 0.186992 | ||||||||
\(136\) | 12.2746 | + | 21.2602i | 1.05254 | + | 1.82304i | ||||
\(137\) | 2.46837 | + | 4.27534i | 0.210887 | + | 0.365267i | 0.951992 | − | 0.306122i | \(-0.0990315\pi\) |
−0.741106 | + | 0.671389i | \(0.765698\pi\) | |||||||
\(138\) | −15.6336 | −1.33082 | ||||||||
\(139\) | −8.23591 | − | 14.2650i | −0.698561 | − | 1.20994i | −0.968965 | − | 0.247196i | \(-0.920491\pi\) |
0.270404 | − | 0.962747i | \(-0.412843\pi\) | |||||||
\(140\) | 2.03709 | − | 3.52835i | 0.172166 | − | 0.298200i | ||||
\(141\) | 3.86245 | − | 6.68995i | 0.325277 | − | 0.563396i | ||||
\(142\) | −16.3132 | −1.36897 | ||||||||
\(143\) | −1.00000 | − | 3.46410i | −0.0836242 | − | 0.289683i | ||||
\(144\) | 12.8695 | 1.07246 | ||||||||
\(145\) | 4.49800 | − | 7.79076i | 0.373538 | − | 0.646988i | ||||
\(146\) | 2.50702 | − | 4.34228i | 0.207482 | − | 0.359370i | ||||
\(147\) | 7.30620 | + | 12.6547i | 0.602605 | + | 1.04374i | ||||
\(148\) | −3.39452 | −0.279028 | ||||||||
\(149\) | 0.952328 | + | 1.64948i | 0.0780178 | + | 0.135131i | 0.902395 | − | 0.430911i | \(-0.141808\pi\) |
−0.824377 | + | 0.566041i | \(0.808474\pi\) | |||||||
\(150\) | 10.0457 | + | 17.3996i | 0.820226 | + | 1.42067i | ||||
\(151\) | 18.4086 | 1.49807 | 0.749034 | − | 0.662532i | \(-0.230518\pi\) | ||||
0.749034 | + | 0.662532i | \(0.230518\pi\) | |||||||
\(152\) | −23.7726 | − | 41.1753i | −1.92821 | − | 3.33976i | ||||
\(153\) | 4.76053 | − | 8.24548i | 0.384866 | − | 0.666607i | ||||
\(154\) | −0.975385 | + | 1.68942i | −0.0785988 | + | 0.136137i | ||||
\(155\) | 1.76409 | 0.141695 | ||||||||
\(156\) | −24.4804 | + | 25.4408i | −1.96000 | + | 2.03689i | ||||
\(157\) | −12.1054 | −0.966114 | −0.483057 | − | 0.875589i | \(-0.660474\pi\) | ||||
−0.483057 | + | 0.875589i | \(0.660474\pi\) | |||||||
\(158\) | −17.0281 | + | 29.4935i | −1.35468 | + | 2.34638i | ||||
\(159\) | −2.04767 | + | 3.54667i | −0.162391 | + | 0.281269i | ||||
\(160\) | 1.87147 | + | 3.24147i | 0.147952 | + | 0.256261i | ||||
\(161\) | −2.12342 | −0.167349 | ||||||||
\(162\) | 13.4488 | + | 23.2940i | 1.05664 | + | 1.83015i | ||||
\(163\) | −0.959347 | − | 1.66164i | −0.0751418 | − | 0.130149i | 0.826006 | − | 0.563661i | \(-0.190608\pi\) |
−0.901148 | + | 0.433512i | \(0.857274\pi\) | |||||||
\(164\) | 41.7499 | 3.26012 | ||||||||
\(165\) | 1.39608 | + | 2.41808i | 0.108685 | + | 0.188247i | ||||
\(166\) | 16.7500 | − | 29.0118i | 1.30005 | − | 2.25175i | ||||
\(167\) | 3.53008 | − | 6.11427i | 0.273165 | − | 0.473136i | −0.696505 | − | 0.717552i | \(-0.745263\pi\) |
0.969671 | + | 0.244415i | \(0.0785960\pi\) | |||||||
\(168\) | 10.1867 | 0.785920 | ||||||||
\(169\) | −0.500000 | − | 12.9904i | −0.0384615 | − | 0.999260i | ||||
\(170\) | 13.1265 | 1.00676 | ||||||||
\(171\) | −9.21987 | + | 15.9693i | −0.705061 | + | 1.22120i | ||||
\(172\) | 20.7394 | − | 35.9216i | 1.58136 | − | 2.73900i | ||||
\(173\) | −0.823794 | − | 1.42685i | −0.0626319 | − | 0.108482i | 0.833009 | − | 0.553259i | \(-0.186616\pi\) |
−0.895641 | + | 0.444778i | \(0.853283\pi\) | |||||||
\(174\) | 42.1787 | 3.19756 | ||||||||
\(175\) | 1.36445 | + | 2.36329i | 0.103143 | + | 0.178648i | ||||
\(176\) | −2.89608 | − | 5.01616i | −0.218300 | − | 0.378107i | ||||
\(177\) | 11.9007 | 0.894508 | ||||||||
\(178\) | 5.98942 | + | 10.3740i | 0.448926 | + | 0.777563i | ||||
\(179\) | −3.66719 | + | 6.35175i | −0.274098 | + | 0.474752i | −0.969907 | − | 0.243475i | \(-0.921713\pi\) |
0.695809 | + | 0.718227i | \(0.255046\pi\) | |||||||
\(180\) | 5.81678 | − | 10.0750i | 0.433557 | − | 0.750943i | ||||
\(181\) | 11.7750 | 0.875230 | 0.437615 | − | 0.899163i | \(-0.355823\pi\) | ||||
0.437615 | + | 0.899163i | \(0.355823\pi\) | |||||||
\(182\) | −4.87693 | + | 5.06825i | −0.361502 | + | 0.375684i | ||||
\(183\) | −33.1827 | −2.45293 | ||||||||
\(184\) | 7.81678 | − | 13.5391i | 0.576260 | − | 0.998112i | ||||
\(185\) | −0.483961 | + | 0.838246i | −0.0355815 | + | 0.0616291i | ||||
\(186\) | 4.13555 | + | 7.16299i | 0.303233 | + | 0.525216i | ||||
\(187\) | −4.28514 | −0.313361 | ||||||||
\(188\) | 7.24293 | + | 12.5451i | 0.528245 | + | 0.914947i | ||||
\(189\) | 0.691800 | + | 1.19823i | 0.0503211 | + | 0.0871586i | ||||
\(190\) | −25.4226 | −1.84435 | ||||||||
\(191\) | −7.37147 | − | 12.7678i | −0.533381 | − | 0.923842i | −0.999240 | − | 0.0389834i | \(-0.987588\pi\) |
0.465859 | − | 0.884859i | \(-0.345745\pi\) | |||||||
\(192\) | 4.46135 | − | 7.72728i | 0.321970 | − | 0.557669i | ||||
\(193\) | 4.45077 | − | 7.70896i | 0.320374 | − | 0.554903i | −0.660192 | − | 0.751097i | \(-0.729525\pi\) |
0.980565 | + | 0.196194i | \(0.0628583\pi\) | |||||||
\(194\) | −10.3805 | −0.745275 | ||||||||
\(195\) | 2.79216 | + | 9.67233i | 0.199951 | + | 0.692650i | ||||
\(196\) | −27.4014 | −1.95725 | ||||||||
\(197\) | 3.05625 | − | 5.29358i | 0.217749 | − | 0.377152i | −0.736371 | − | 0.676578i | \(-0.763462\pi\) |
0.954119 | + | 0.299427i | \(0.0967954\pi\) | |||||||
\(198\) | −2.78514 | + | 4.82401i | −0.197931 | + | 0.342827i | ||||
\(199\) | −4.67265 | − | 8.09326i | −0.331235 | − | 0.573716i | 0.651519 | − | 0.758632i | \(-0.274132\pi\) |
−0.982754 | + | 0.184916i | \(0.940799\pi\) | |||||||
\(200\) | −20.0913 | −1.42067 | ||||||||
\(201\) | −6.92771 | − | 11.9992i | −0.488643 | − | 0.846355i | ||||
\(202\) | −6.04723 | − | 10.4741i | −0.425481 | − | 0.736956i | ||||
\(203\) | 5.72889 | 0.402090 | ||||||||
\(204\) | 20.9804 | + | 36.3391i | 1.46892 | + | 2.54425i | ||||
\(205\) | 5.95233 | − | 10.3097i | 0.415729 | − | 0.720063i | ||||
\(206\) | −12.2344 | + | 21.1905i | −0.852408 | + | 1.47641i | ||||
\(207\) | −6.06327 | −0.421426 | ||||||||
\(208\) | −5.79216 | − | 20.0646i | −0.401614 | − | 1.39123i | ||||
\(209\) | 8.29918 | 0.574066 | ||||||||
\(210\) | 2.72343 | − | 4.71713i | 0.187935 | − | 0.325513i | ||||
\(211\) | 2.59334 | − | 4.49180i | 0.178533 | − | 0.309228i | −0.762845 | − | 0.646581i | \(-0.776198\pi\) |
0.941378 | + | 0.337353i | \(0.109532\pi\) | |||||||
\(212\) | −3.83983 | − | 6.65079i | −0.263721 | − | 0.456778i | ||||
\(213\) | −14.8695 | −1.01884 | ||||||||
\(214\) | −2.96135 | − | 5.12921i | −0.202434 | − | 0.350625i | ||||
\(215\) | −5.91368 | − | 10.2428i | −0.403309 | − | 0.698552i | ||||
\(216\) | −10.1867 | −0.693116 | ||||||||
\(217\) | 0.561709 | + | 0.972909i | 0.0381313 | + | 0.0660453i | ||||
\(218\) | 3.59690 | − | 6.23001i | 0.243613 | − | 0.421950i | ||||
\(219\) | 2.28514 | − | 3.95798i | 0.154416 | − | 0.267456i | ||||
\(220\) | −5.23591 | −0.353005 | ||||||||
\(221\) | −14.9980 | − | 3.71104i | −1.00887 | − | 0.249632i | ||||
\(222\) | −4.53821 | −0.304585 | ||||||||
\(223\) | −8.41714 | + | 14.5789i | −0.563653 | + | 0.976276i | 0.433520 | + | 0.901144i | \(0.357271\pi\) |
−0.997174 | + | 0.0751322i | \(0.976062\pi\) | |||||||
\(224\) | −1.19180 | + | 2.06426i | −0.0796305 | + | 0.137924i | ||||
\(225\) | 3.89608 | + | 6.74821i | 0.259739 | + | 0.449881i | ||||
\(226\) | −14.0452 | −0.934275 | ||||||||
\(227\) | 8.80820 | + | 15.2562i | 0.584621 | + | 1.01259i | 0.994923 | + | 0.100643i | \(0.0320900\pi\) |
−0.410302 | + | 0.911950i | \(0.634577\pi\) | |||||||
\(228\) | −40.6335 | − | 70.3792i | −2.69102 | − | 4.66098i | ||||
\(229\) | 26.8554 | 1.77466 | 0.887328 | − | 0.461138i | \(-0.152559\pi\) | ||||
0.887328 | + | 0.461138i | \(0.152559\pi\) | |||||||
\(230\) | −4.17967 | − | 7.23939i | −0.275599 | − | 0.477351i | ||||
\(231\) | −0.889062 | + | 1.53990i | −0.0584960 | + | 0.101318i | ||||
\(232\) | −21.0893 | + | 36.5278i | −1.38458 | + | 2.39817i | ||||
\(233\) | −27.1406 | −1.77804 | −0.889019 | − | 0.457870i | \(-0.848612\pi\) | ||||
−0.889019 | + | 0.457870i | \(0.848612\pi\) | |||||||
\(234\) | −13.9257 | + | 14.4720i | −0.910352 | + | 0.946066i | ||||
\(235\) | 4.13054 | 0.269446 | ||||||||
\(236\) | −11.1582 | + | 19.3265i | −0.726335 | + | 1.25805i | ||||
\(237\) | −15.5211 | + | 26.8833i | −1.00820 | + | 1.74626i | ||||
\(238\) | 4.17967 | + | 7.23939i | 0.270927 | + | 0.469260i | ||||
\(239\) | 0.746047 | 0.0482577 | 0.0241289 | − | 0.999709i | \(-0.492319\pi\) | ||||
0.0241289 | + | 0.999709i | \(0.492319\pi\) | |||||||
\(240\) | 8.08632 | + | 14.0059i | 0.521970 | + | 0.904078i | ||||
\(241\) | −8.08632 | − | 14.0059i | −0.520886 | − | 0.902201i | −0.999705 | − | 0.0242873i | \(-0.992268\pi\) |
0.478819 | − | 0.877914i | \(-0.341065\pi\) | |||||||
\(242\) | 2.50702 | 0.161157 | ||||||||
\(243\) | 9.59134 | + | 16.6127i | 0.615285 | + | 1.06570i | ||||
\(244\) | 31.1124 | − | 53.8883i | 1.99177 | − | 3.44984i | ||||
\(245\) | −3.90666 | + | 6.76653i | −0.249587 | + | 0.432298i | ||||
\(246\) | 55.8162 | 3.55871 | ||||||||
\(247\) | 29.0471 | + | 7.18730i | 1.84822 | + | 0.457317i | ||||
\(248\) | −8.27111 | −0.525216 | ||||||||
\(249\) | 15.2675 | − | 26.4442i | 0.967541 | − | 1.67583i | ||||
\(250\) | −13.0296 | + | 22.5680i | −0.824066 | + | 1.42732i | ||||
\(251\) | 5.51404 | + | 9.55059i | 0.348043 | + | 0.602828i | 0.985902 | − | 0.167325i | \(-0.0535130\pi\) |
−0.637859 | + | 0.770153i | \(0.720180\pi\) | |||||||
\(252\) | 7.40856 | 0.466695 | ||||||||
\(253\) | 1.36445 | + | 2.36329i | 0.0857821 | + | 0.148579i | ||||
\(254\) | −9.07028 | − | 15.7102i | −0.569120 | − | 0.985745i | ||||
\(255\) | 11.9648 | 0.749265 | ||||||||
\(256\) | 16.0457 | + | 27.7919i | 1.00285 | + | 1.73699i | ||||
\(257\) | −9.42616 | + | 16.3266i | −0.587987 | + | 1.01842i | 0.406508 | + | 0.913647i | \(0.366746\pi\) |
−0.994496 | + | 0.104777i | \(0.966587\pi\) | |||||||
\(258\) | 27.7269 | − | 48.0244i | 1.72620 | − | 2.98987i | ||||
\(259\) | −0.616399 | −0.0383012 | ||||||||
\(260\) | −18.3257 | − | 4.53443i | −1.13651 | − | 0.281214i | ||||
\(261\) | 16.3584 | 1.01256 | ||||||||
\(262\) | 12.9718 | − | 22.4679i | 0.801402 | − | 1.38807i | ||||
\(263\) | 7.77612 | − | 13.4686i | 0.479496 | − | 0.830512i | −0.520227 | − | 0.854028i | \(-0.674153\pi\) |
0.999723 | + | 0.0235160i | \(0.00748607\pi\) | |||||||
\(264\) | −6.54567 | − | 11.3374i | −0.402858 | − | 0.697771i | ||||
\(265\) | −2.18980 | −0.134518 | ||||||||
\(266\) | −8.09490 | − | 14.0208i | −0.496330 | − | 0.859669i | ||||
\(267\) | 5.45935 | + | 9.45587i | 0.334107 | + | 0.578690i | ||||
\(268\) | 25.9820 | 1.58710 | ||||||||
\(269\) | 2.61094 | + | 4.52228i | 0.159192 | + | 0.275728i | 0.934577 | − | 0.355760i | \(-0.115778\pi\) |
−0.775386 | + | 0.631488i | \(0.782445\pi\) | |||||||
\(270\) | −2.72343 | + | 4.71713i | −0.165743 | + | 0.287075i | ||||
\(271\) | −12.9684 | + | 22.4619i | −0.787772 | + | 1.36446i | 0.139557 | + | 0.990214i | \(0.455432\pi\) |
−0.927329 | + | 0.374247i | \(0.877901\pi\) | |||||||
\(272\) | −24.8202 | −1.50495 | ||||||||
\(273\) | −4.44531 | + | 4.61970i | −0.269042 | + | 0.279597i | ||||
\(274\) | −12.3765 | −0.747691 | ||||||||
\(275\) | 1.75351 | − | 3.03717i | 0.105741 | − | 0.183148i | ||||
\(276\) | 13.3609 | − | 23.1417i | 0.804231 | − | 1.39297i | ||||
\(277\) | 8.88706 | + | 15.3928i | 0.533972 | + | 0.924866i | 0.999212 | + | 0.0396819i | \(0.0126345\pi\) |
−0.465241 | + | 0.885184i | \(0.654032\pi\) | |||||||
\(278\) | 41.2952 | 2.47672 | ||||||||
\(279\) | 1.60392 | + | 2.77807i | 0.0960241 | + | 0.166319i | ||||
\(280\) | 2.72343 | + | 4.71713i | 0.162756 | + | 0.281902i | ||||
\(281\) | 7.41168 | 0.442143 | 0.221072 | − | 0.975258i | \(-0.429045\pi\) | ||||
0.221072 | + | 0.975258i | \(0.429045\pi\) | |||||||
\(282\) | 9.68322 | + | 16.7718i | 0.576628 | + | 0.998748i | ||||
\(283\) | −4.65861 | + | 8.06895i | −0.276926 | + | 0.479649i | −0.970619 | − | 0.240621i | \(-0.922649\pi\) |
0.693694 | + | 0.720270i | \(0.255982\pi\) | |||||||
\(284\) | 13.9418 | − | 24.1478i | 0.827291 | − | 1.43291i | ||||
\(285\) | −23.1726 | −1.37263 | ||||||||
\(286\) | 8.77457 | + | 2.17114i | 0.518851 | + | 0.128382i | ||||
\(287\) | 7.58121 | 0.447505 | ||||||||
\(288\) | −3.40310 | + | 5.89434i | −0.200530 | + | 0.347327i | ||||
\(289\) | −0.681223 | + | 1.17991i | −0.0400719 | + | 0.0694066i | ||||
\(290\) | 11.2766 | + | 19.5316i | 0.662183 | + | 1.14693i | ||||
\(291\) | −9.46179 | −0.554660 | ||||||||
\(292\) | 4.28514 | + | 7.42208i | 0.250769 | + | 0.434345i | ||||
\(293\) | 14.3765 | + | 24.9008i | 0.839883 | + | 1.45472i | 0.889992 | + | 0.455976i | \(0.150710\pi\) |
−0.0501087 | + | 0.998744i | \(0.515957\pi\) | |||||||
\(294\) | −36.6336 | −2.13651 | ||||||||
\(295\) | 3.18167 | + | 5.51081i | 0.185244 | + | 0.320852i | ||||
\(296\) | 2.26910 | − | 3.93020i | 0.131889 | − | 0.228438i | ||||
\(297\) | 0.889062 | − | 1.53990i | 0.0515886 | − | 0.0893541i | ||||
\(298\) | −4.77501 | −0.276609 | ||||||||
\(299\) | 2.72889 | + | 9.45317i | 0.157816 | + | 0.546691i | ||||
\(300\) | −34.3413 | −1.98270 | ||||||||
\(301\) | 3.76599 | − | 6.52288i | 0.217068 | − | 0.375973i | ||||
\(302\) | −23.0753 | + | 39.9676i | −1.32783 | + | 2.29988i | ||||
\(303\) | −5.51204 | − | 9.54713i | −0.316658 | − | 0.548468i | ||||
\(304\) | 48.0702 | 2.75701 | ||||||||
\(305\) | −8.87147 | − | 15.3658i | −0.507979 | − | 0.879845i | ||||
\(306\) | 11.9347 | + | 20.6716i | 0.682263 | + | 1.18171i | ||||
\(307\) | −0.792161 | −0.0452110 | −0.0226055 | − | 0.999744i | \(-0.507196\pi\) | ||||
−0.0226055 | + | 0.999744i | \(0.507196\pi\) | |||||||
\(308\) | −1.66719 | − | 2.88765i | −0.0949967 | − | 0.164539i | ||||
\(309\) | −11.1516 | + | 19.3151i | −0.634392 | + | 1.09880i | ||||
\(310\) | −2.21130 | + | 3.83008i | −0.125593 | + | 0.217534i | ||||
\(311\) | 25.8022 | 1.46311 | 0.731554 | − | 0.681783i | \(-0.238795\pi\) | ||||
0.731554 | + | 0.681783i | \(0.238795\pi\) | |||||||
\(312\) | −13.0913 | − | 45.3497i | −0.741151 | − | 2.56742i | ||||
\(313\) | −26.2780 | −1.48532 | −0.742661 | − | 0.669668i | \(-0.766437\pi\) | ||||
−0.742661 | + | 0.669668i | \(0.766437\pi\) | |||||||
\(314\) | 15.1742 | − | 26.2825i | 0.856330 | − | 1.48321i | ||||
\(315\) | 1.05625 | − | 1.82947i | 0.0595128 | − | 0.103079i | ||||
\(316\) | −29.1054 | − | 50.4120i | −1.63731 | − | 2.83590i | ||||
\(317\) | 10.9788 | 0.616633 | 0.308317 | − | 0.951284i | \(-0.400234\pi\) | ||||
0.308317 | + | 0.951284i | \(0.400234\pi\) | |||||||
\(318\) | −5.13355 | − | 8.89157i | −0.287875 | − | 0.498615i | ||||
\(319\) | −3.68122 | − | 6.37607i | −0.206109 | − | 0.356991i | ||||
\(320\) | 4.77101 | 0.266707 | ||||||||
\(321\) | −2.69926 | − | 4.67526i | −0.150658 | − | 0.260948i | ||||
\(322\) | 2.66172 | − | 4.61024i | 0.148332 | − | 0.256919i | ||||
\(323\) | 17.7816 | − | 30.7986i | 0.989394 | − | 1.71368i | ||||
\(324\) | −45.9748 | −2.55416 | ||||||||
\(325\) | 8.76755 | − | 9.11150i | 0.486336 | − | 0.505415i | ||||
\(326\) | 4.81020 | 0.266412 | ||||||||
\(327\) | 3.27857 | − | 5.67865i | 0.181305 | − | 0.314030i | ||||
\(328\) | −27.9081 | + | 48.3383i | −1.54097 | + | 2.66903i | ||||
\(329\) | 1.31522 | + | 2.27803i | 0.0725103 | + | 0.125592i | ||||
\(330\) | −7.00000 | −0.385337 | ||||||||
\(331\) | −5.02807 | − | 8.70888i | −0.276368 | − | 0.478683i | 0.694111 | − | 0.719868i | \(-0.255798\pi\) |
−0.970479 | + | 0.241184i | \(0.922464\pi\) | |||||||
\(332\) | 28.6300 | + | 49.5886i | 1.57127 | + | 2.72153i | ||||
\(333\) | −1.76008 | −0.0964520 | ||||||||
\(334\) | 8.84997 | + | 15.3286i | 0.484249 | + | 0.838743i | ||||
\(335\) | 3.70428 | − | 6.41600i | 0.202386 | − | 0.350544i | ||||
\(336\) | −5.14959 | + | 8.91935i | −0.280933 | + | 0.486591i | ||||
\(337\) | 19.7398 | 1.07530 | 0.537648 | − | 0.843169i | \(-0.319313\pi\) | ||||
0.537648 | + | 0.843169i | \(0.319313\pi\) | |||||||
\(338\) | 28.8307 | + | 15.1980i | 1.56818 | + | 0.826662i | ||||
\(339\) | −12.8022 | −0.695320 | ||||||||
\(340\) | −11.2183 | + | 19.4307i | −0.608399 | + | 1.05378i | ||||
\(341\) | 0.721876 | − | 1.25033i | 0.0390918 | − | 0.0677090i | ||||
\(342\) | −23.1144 | − | 40.0353i | −1.24988 | − | 2.16486i | ||||
\(343\) | −10.4226 | −0.562767 | ||||||||
\(344\) | 27.7269 | + | 48.0244i | 1.49493 | + | 2.58930i | ||||
\(345\) | −3.80976 | − | 6.59869i | −0.205110 | − | 0.355262i | ||||
\(346\) | 4.13054 | 0.222059 | ||||||||
\(347\) | −9.15661 | − | 15.8597i | −0.491553 | − | 0.851394i | 0.508400 | − | 0.861121i | \(-0.330237\pi\) |
−0.999953 | + | 0.00972702i | \(0.996904\pi\) | |||||||
\(348\) | −36.0471 | + | 62.4355i | −1.93233 | + | 3.34689i | ||||
\(349\) | −8.68824 | + | 15.0485i | −0.465071 | + | 0.805526i | −0.999205 | − | 0.0398735i | \(-0.987305\pi\) |
0.534134 | + | 0.845400i | \(0.320638\pi\) | |||||||
\(350\) | −6.84139 | −0.365688 | ||||||||
\(351\) | 4.44531 | − | 4.61970i | 0.237273 | − | 0.246581i | ||||
\(352\) | 3.06327 | 0.163273 | ||||||||
\(353\) | −16.8835 | + | 29.2431i | −0.898618 | + | 1.55645i | −0.0693563 | + | 0.997592i | \(0.522095\pi\) |
−0.829262 | + | 0.558860i | \(0.811239\pi\) | |||||||
\(354\) | −14.9176 | + | 25.8380i | −0.792860 | + | 1.37327i | ||||
\(355\) | −3.97539 | − | 6.88557i | −0.210992 | − | 0.365448i | ||||
\(356\) | −20.4749 | −1.08517 | ||||||||
\(357\) | 3.80976 | + | 6.59869i | 0.201634 | + | 0.349240i | ||||
\(358\) | −9.19370 | − | 15.9240i | −0.485902 | − | 0.841607i | ||||
\(359\) | −4.72889 | −0.249582 | −0.124791 | − | 0.992183i | \(-0.539826\pi\) | ||||
−0.124791 | + | 0.992183i | \(0.539826\pi\) | |||||||
\(360\) | 7.77657 | + | 13.4694i | 0.409861 | + | 0.709900i | ||||
\(361\) | −24.9382 | + | 43.1942i | −1.31254 | + | 2.27338i | ||||
\(362\) | −14.7601 | + | 25.5652i | −0.775773 | + | 1.34368i | ||||
\(363\) | 2.28514 | 0.119939 | ||||||||
\(364\) | −3.33437 | − | 11.5506i | −0.174769 | − | 0.605416i | ||||
\(365\) | 2.44375 | 0.127912 | ||||||||
\(366\) | 41.5948 | − | 72.0443i | 2.17420 | − | 3.76582i | ||||
\(367\) | −3.21330 | + | 5.56560i | −0.167733 | + | 0.290522i | −0.937622 | − | 0.347655i | \(-0.886978\pi\) |
0.769890 | + | 0.638177i | \(0.220311\pi\) | |||||||
\(368\) | 7.90310 | + | 13.6886i | 0.411978 | + | 0.713566i | ||||
\(369\) | 21.6476 | 1.12693 | ||||||||
\(370\) | −1.21330 | − | 2.10150i | −0.0630765 | − | 0.109252i | ||||
\(371\) | −0.697262 | − | 1.20769i | −0.0362000 | − | 0.0627003i | ||||
\(372\) | −14.1375 | −0.732993 | ||||||||
\(373\) | 2.20584 | + | 3.82062i | 0.114214 | + | 0.197824i | 0.917465 | − | 0.397816i | \(-0.130232\pi\) |
−0.803251 | + | 0.595640i | \(0.796898\pi\) | |||||||
\(374\) | 5.37147 | − | 9.30365i | 0.277752 | − | 0.481080i | ||||
\(375\) | −11.8765 | + | 20.5707i | −0.613299 | + | 1.06226i | ||||
\(376\) | −19.3664 | −0.998748 | ||||||||
\(377\) | −7.36245 | − | 25.5043i | −0.379185 | − | 1.31354i | ||||
\(378\) | −3.46871 | −0.178411 | ||||||||
\(379\) | −9.75351 | + | 16.8936i | −0.501004 | + | 0.867765i | 0.498995 | + | 0.866605i | \(0.333703\pi\) |
−0.999999 | + | 0.00115985i | \(0.999631\pi\) | |||||||
\(380\) | 21.7269 | − | 37.6321i | 1.11457 | − | 1.93049i | ||||
\(381\) | −8.26755 | − | 14.3198i | −0.423559 | − | 0.733626i | ||||
\(382\) | 36.9608 | 1.89108 | ||||||||
\(383\) | −13.8152 | − | 23.9287i | −0.705925 | − | 1.22270i | −0.966357 | − | 0.257205i | \(-0.917198\pi\) |
0.260432 | − | 0.965492i | \(-0.416135\pi\) | |||||||
\(384\) | 18.1847 | + | 31.4968i | 0.927983 | + | 1.60731i | ||||
\(385\) | −0.950771 | −0.0484558 | ||||||||
\(386\) | 11.1582 | + | 19.3265i | 0.567936 | + | 0.983693i | ||||
\(387\) | 10.7535 | − | 18.6256i | 0.546632 | − | 0.946794i | ||||
\(388\) | 8.87147 | − | 15.3658i | 0.450380 | − | 0.780082i | ||||
\(389\) | −28.9960 | −1.47016 | −0.735078 | − | 0.677983i | \(-0.762854\pi\) | ||||
−0.735078 | + | 0.677983i | \(0.762854\pi\) | |||||||
\(390\) | −24.5000 | − | 6.06218i | −1.24061 | − | 0.306970i | ||||
\(391\) | 11.6937 | 0.591376 | ||||||||
\(392\) | 18.3168 | − | 31.7256i | 0.925137 | − | 1.60238i | ||||
\(393\) | 11.8238 | − | 20.4794i | 0.596432 | − | 1.03305i | ||||
\(394\) | 7.66207 | + | 13.2711i | 0.386010 | + | 0.668588i | ||||
\(395\) | −16.5984 | −0.835154 | ||||||||
\(396\) | −4.76053 | − | 8.24548i | −0.239226 | − | 0.414351i | ||||
\(397\) | −17.3293 | − | 30.0152i | −0.869730 | − | 1.50642i | −0.862272 | − | 0.506445i | \(-0.830959\pi\) |
−0.00745819 | − | 0.999972i | \(-0.502374\pi\) | |||||||
\(398\) | 23.4288 | 1.17438 | ||||||||
\(399\) | −7.37848 | − | 12.7799i | −0.369386 | − | 0.639796i | ||||
\(400\) | 10.1566 | − | 17.5918i | 0.507830 | − | 0.879588i | ||||
\(401\) | 7.29372 | − | 12.6331i | 0.364231 | − | 0.630866i | −0.624422 | − | 0.781088i | \(-0.714665\pi\) |
0.988652 | + | 0.150221i | \(0.0479986\pi\) | |||||||
\(402\) | 34.7358 | 1.73246 | ||||||||
\(403\) | 3.60938 | − | 3.75098i | 0.179796 | − | 0.186850i | ||||
\(404\) | 20.6725 | 1.02850 | ||||||||
\(405\) | −6.55469 | + | 11.3531i | −0.325705 | + | 0.564138i | ||||
\(406\) | −7.18122 | + | 12.4382i | −0.356398 | + | 0.617300i | ||||
\(407\) | 0.396081 | + | 0.686032i | 0.0196330 | + | 0.0340053i | ||||
\(408\) | −56.0983 | −2.77728 | ||||||||
\(409\) | −8.30074 | − | 14.3773i | −0.410445 | − | 0.710912i | 0.584493 | − | 0.811398i | \(-0.301293\pi\) |
−0.994938 | + | 0.100487i | \(0.967960\pi\) | |||||||
\(410\) | 14.9226 | + | 25.8467i | 0.736975 | + | 1.27648i | ||||
\(411\) | −11.2811 | −0.556458 | ||||||||
\(412\) | −20.9117 | − | 36.2201i | −1.03024 | − | 1.78444i | ||||
\(413\) | −2.02617 | + | 3.50943i | −0.0997014 | + | 0.172688i | ||||
\(414\) | 7.60036 | − | 13.1642i | 0.373537 | − | 0.646986i | ||||
\(415\) | 16.3273 | 0.801473 | ||||||||
\(416\) | 10.7214 | + | 2.65287i | 0.525661 | + | 0.130067i | ||||
\(417\) | 37.6405 | 1.84326 | ||||||||
\(418\) | −10.4031 | + | 18.0187i | −0.508832 | + | 0.881323i | ||||
\(419\) | 11.1476 | − | 19.3082i | 0.544595 | − | 0.943267i | −0.454037 | − | 0.890983i | \(-0.650017\pi\) |
0.998632 | − | 0.0522839i | \(-0.0166501\pi\) | |||||||
\(420\) | 4.65505 | + | 8.06279i | 0.227143 | + | 0.393424i | ||||
\(421\) | −3.45779 | −0.168522 | −0.0842612 | − | 0.996444i | \(-0.526853\pi\) | ||||
−0.0842612 | + | 0.996444i | \(0.526853\pi\) | |||||||
\(422\) | 6.50156 | + | 11.2610i | 0.316491 | + | 0.548178i | ||||
\(423\) | 3.75551 | + | 6.50474i | 0.182599 | + | 0.316271i | ||||
\(424\) | 10.2671 | 0.498615 | ||||||||
\(425\) | −7.51404 | − | 13.0147i | −0.364484 | − | 0.631305i | ||||
\(426\) | 18.6390 | − | 32.2837i | 0.903063 | − | 1.56415i | ||||
\(427\) | 5.64959 | − | 9.78538i | 0.273403 | − | 0.473548i | ||||
\(428\) | 10.1234 | 0.489334 | ||||||||
\(429\) | 7.99800 | + | 1.97899i | 0.386147 | + | 0.0955466i | ||||
\(430\) | 29.6514 | 1.42992 | ||||||||
\(431\) | −12.9402 | + | 22.4131i | −0.623307 | + | 1.07960i | 0.365558 | + | 0.930788i | \(0.380878\pi\) |
−0.988866 | + | 0.148811i | \(0.952455\pi\) | |||||||
\(432\) | 5.14959 | − | 8.91935i | 0.247760 | − | 0.429132i | ||||
\(433\) | −7.19024 | − | 12.4539i | −0.345541 | − | 0.598495i | 0.639911 | − | 0.768449i | \(-0.278971\pi\) |
−0.985452 | + | 0.169955i | \(0.945638\pi\) | |||||||
\(434\) | −2.81643 | −0.135193 | ||||||||
\(435\) | 10.2786 | + | 17.8030i | 0.492820 | + | 0.853589i | ||||
\(436\) | 6.14803 | + | 10.6487i | 0.294437 | + | 0.509980i | ||||
\(437\) | −22.6476 | −1.08338 | ||||||||
\(438\) | 5.72889 | + | 9.92274i | 0.273737 | + | 0.474127i | ||||
\(439\) | −2.28314 | + | 3.95452i | −0.108968 | + | 0.188739i | −0.915353 | − | 0.402653i | \(-0.868088\pi\) |
0.806384 | + | 0.591392i | \(0.201421\pi\) | |||||||
\(440\) | 3.50000 | − | 6.06218i | 0.166856 | − | 0.289003i | ||||
\(441\) | −14.2078 | −0.676564 | ||||||||
\(442\) | 26.8573 | − | 27.9110i | 1.27747 | − | 1.32759i | ||||
\(443\) | 18.1718 | 0.863366 | 0.431683 | − | 0.902025i | \(-0.357920\pi\) | ||||
0.431683 | + | 0.902025i | \(0.357920\pi\) | |||||||
\(444\) | 3.87848 | − | 6.71773i | 0.184065 | − | 0.318809i | ||||
\(445\) | −2.91914 | + | 5.05609i | −0.138380 | + | 0.239682i | ||||
\(446\) | −21.1019 | − | 36.5496i | −0.999205 | − | 1.73067i | ||||
\(447\) | −4.35241 | −0.205862 | ||||||||
\(448\) | 1.51915 | + | 2.63125i | 0.0717732 | + | 0.124315i | ||||
\(449\) | 6.31477 | + | 10.9375i | 0.298013 | + | 0.516173i | 0.975681 | − | 0.219194i | \(-0.0703429\pi\) |
−0.677669 | + | 0.735367i | \(0.737010\pi\) | |||||||
\(450\) | −19.5351 | −0.920893 | ||||||||
\(451\) | −4.87147 | − | 8.43763i | −0.229388 | − | 0.397312i | ||||
\(452\) | 12.0035 | − | 20.7906i | 0.564595 | − | 0.977908i | ||||
\(453\) | −21.0331 | + | 36.4304i | −0.988221 | + | 1.71165i | ||||
\(454\) | −44.1646 | −2.07275 | ||||||||
\(455\) | −3.32770 | − | 0.823392i | −0.156005 | − | 0.0386012i | ||||
\(456\) | 108.647 | 5.08788 | ||||||||
\(457\) | 12.8941 | − | 22.3332i | 0.603160 | − | 1.04470i | −0.389180 | − | 0.921162i | \(-0.627242\pi\) |
0.992339 | − | 0.123541i | \(-0.0394251\pi\) | |||||||
\(458\) | −33.6635 | + | 58.3069i | −1.57299 | + | 2.72450i | ||||
\(459\) | −3.80976 | − | 6.59869i | −0.177824 | − | 0.308001i | ||||
\(460\) | 14.2883 | 0.666193 | ||||||||
\(461\) | 6.31678 | + | 10.9410i | 0.294202 | + | 0.509572i | 0.974799 | − | 0.223086i | \(-0.0716130\pi\) |
−0.680597 | + | 0.732658i | \(0.738280\pi\) | |||||||
\(462\) | −2.22889 | − | 3.86056i | −0.103698 | − | 0.179609i | ||||
\(463\) | −3.47494 | −0.161494 | −0.0807471 | − | 0.996735i | \(-0.525731\pi\) | ||||
−0.0807471 | + | 0.996735i | \(0.525731\pi\) | |||||||
\(464\) | −21.3222 | − | 36.9312i | −0.989860 | − | 1.71449i | ||||
\(465\) | −2.01559 | + | 3.49111i | −0.0934710 | + | 0.161896i | ||||
\(466\) | 34.0210 | − | 58.9260i | 1.57599 | − | 2.72970i | ||||
\(467\) | −18.7258 | −0.866526 | −0.433263 | − | 0.901268i | \(-0.642638\pi\) | ||||
−0.433263 | + | 0.901268i | \(0.642638\pi\) | |||||||
\(468\) | −9.52106 | − | 32.9819i | −0.440111 | − | 1.52459i | ||||
\(469\) | 4.71797 | 0.217856 | ||||||||
\(470\) | −5.17766 | + | 8.96798i | −0.238828 | + | 0.413662i | ||||
\(471\) | 13.8313 | − | 23.9564i | 0.637311 | − | 1.10385i | ||||
\(472\) | −14.9176 | − | 25.8380i | −0.686637 | − | 1.18929i | ||||
\(473\) | −9.67967 | −0.445072 | ||||||||
\(474\) | −38.9116 | − | 67.3968i | −1.78727 | − | 3.09564i | ||||
\(475\) | 14.5527 | + | 25.2060i | 0.667723 | + | 1.15653i | ||||
\(476\) | −14.2883 | −0.654901 | ||||||||
\(477\) | −1.99098 | − | 3.44848i | −0.0911607 | − | 0.157895i | ||||
\(478\) | −0.935176 | + | 1.61977i | −0.0427740 | + | 0.0740867i | ||||
\(479\) | −4.64257 | + | 8.04117i | −0.212124 | + | 0.367410i | −0.952379 | − | 0.304916i | \(-0.901372\pi\) |
0.740255 | + | 0.672327i | \(0.234705\pi\) | |||||||
\(480\) | −8.55313 | −0.390395 | ||||||||
\(481\) | 0.792161 | + | 2.74413i | 0.0361194 | + | 0.125121i | ||||
\(482\) | 40.5451 | 1.84678 | ||||||||
\(483\) | 2.42616 | − | 4.20223i | 0.110394 | − | 0.191208i | ||||
\(484\) | −2.14257 | + | 3.71104i | −0.0973896 | + | 0.168684i | ||||
\(485\) | −2.52963 | − | 4.38145i | −0.114865 | − | 0.198951i | ||||
\(486\) | −48.0913 | −2.18147 | ||||||||
\(487\) | 19.9648 | + | 34.5801i | 0.904692 | + | 1.56697i | 0.821330 | + | 0.570453i | \(0.193232\pi\) |
0.0833614 | + | 0.996519i | \(0.473434\pi\) | |||||||
\(488\) | 41.5948 | + | 72.0443i | 1.88291 | + | 3.26129i | ||||
\(489\) | 4.38449 | 0.198273 | ||||||||
\(490\) | −9.79406 | − | 16.9638i | −0.442451 | − | 0.766347i | ||||
\(491\) | 20.5913 | − | 35.6652i | 0.929274 | − | 1.60955i | 0.144735 | − | 0.989470i | \(-0.453767\pi\) |
0.784539 | − | 0.620080i | \(-0.212900\pi\) | |||||||
\(492\) | −47.7022 | + | 82.6226i | −2.15058 | + | 3.72491i | ||||
\(493\) | −31.5491 | −1.42090 | ||||||||
\(494\) | −52.0155 | + | 54.0561i | −2.34029 | + | 2.43210i | ||||
\(495\) | −2.71486 | −0.122024 | ||||||||
\(496\) | 4.18122 | − | 7.24209i | 0.187742 | − | 0.325179i | ||||
\(497\) | 2.53163 | − | 4.38492i | 0.113559 | − | 0.196690i | ||||
\(498\) | 38.2760 | + | 66.2960i | 1.71519 | + | 2.97080i | ||||
\(499\) | 19.3132 | 0.864578 | 0.432289 | − | 0.901735i | \(-0.357706\pi\) | ||||
0.432289 | + | 0.901735i | \(0.357706\pi\) | |||||||
\(500\) | −22.2710 | − | 38.5745i | −0.995990 | − | 1.72510i | ||||
\(501\) | 8.06673 | + | 13.9720i | 0.360395 | + | 0.624222i | ||||
\(502\) | −27.6476 | −1.23397 | ||||||||
\(503\) | −9.84485 | − | 17.0518i | −0.438960 | − | 0.760301i | 0.558649 | − | 0.829404i | \(-0.311320\pi\) |
−0.997610 | + | 0.0691026i | \(0.977986\pi\) | |||||||
\(504\) | −4.95233 | + | 8.57768i | −0.220594 | + | 0.382080i | ||||
\(505\) | 2.94731 | − | 5.10489i | 0.131154 | − | 0.227165i | ||||
\(506\) | −6.84139 | −0.304137 | ||||||||
\(507\) | 26.2791 | + | 13.8529i | 1.16710 | + | 0.615231i | ||||
\(508\) | 31.0069 | 1.37571 | ||||||||
\(509\) | −6.73747 | + | 11.6696i | −0.298633 | + | 0.517248i | −0.975823 | − | 0.218560i | \(-0.929864\pi\) |
0.677190 | + | 0.735808i | \(0.263197\pi\) | |||||||
\(510\) | −14.9980 | + | 25.9773i | −0.664123 | + | 1.15029i | ||||
\(511\) | 0.778124 | + | 1.34775i | 0.0344222 | + | 0.0596210i | ||||
\(512\) | −48.6224 | −2.14883 | ||||||||
\(513\) | 7.37848 | + | 12.7799i | 0.325768 | + | 0.564247i | ||||
\(514\) | −23.6315 | − | 40.9310i | −1.04234 | − | 1.80539i | ||||
\(515\) | −11.9256 | −0.525505 | ||||||||
\(516\) | 47.3924 | + | 82.0861i | 2.08634 | + | 3.61364i | ||||
\(517\) | 1.69024 | − | 2.92759i | 0.0743368 | − | 0.128755i | ||||
\(518\) | 0.772662 | − | 1.33829i | 0.0339488 | − | 0.0588011i | ||||
\(519\) | 3.76497 | 0.165264 | ||||||||
\(520\) | 17.5000 | − | 18.1865i | 0.767426 | − | 0.797532i | ||||
\(521\) | 19.4266 | 0.851095 | 0.425547 | − | 0.904936i | \(-0.360082\pi\) | ||||
0.425547 | + | 0.904936i | \(0.360082\pi\) | |||||||
\(522\) | −20.5055 | + | 35.5165i | −0.897500 | + | 1.55452i | ||||
\(523\) | −5.46135 | + | 9.45933i | −0.238808 | + | 0.413628i | −0.960373 | − | 0.278720i | \(-0.910090\pi\) |
0.721564 | + | 0.692347i | \(0.243423\pi\) | |||||||
\(524\) | 22.1722 | + | 38.4034i | 0.968597 | + | 1.67766i | ||||
\(525\) | −6.23591 | −0.272158 | ||||||||
\(526\) | 19.4949 | + | 33.7661i | 0.850017 | + | 1.47227i | ||||
\(527\) | −3.09334 | − | 5.35783i | −0.134748 | − | 0.233391i | ||||
\(528\) | 13.2359 | 0.576019 | ||||||||
\(529\) | 7.77657 | + | 13.4694i | 0.338112 | + | 0.585626i | ||||
\(530\) | 2.74493 | − | 4.75436i | 0.119232 | − | 0.206516i | ||||
\(531\) | −5.78559 | + | 10.0209i | −0.251073 | + | 0.434871i | ||||
\(532\) | 27.6725 | 1.19976 | ||||||||
\(533\) | −9.74293 | − | 33.7505i | −0.422013 | − | 1.46190i | ||||
\(534\) | −27.3734 | −1.18456 | ||||||||
\(535\) | 1.44331 | − | 2.49988i | 0.0623997 | − | 0.108079i | ||||
\(536\) | −17.3679 | + | 30.0821i | −0.750179 | + | 1.29935i | ||||
\(537\) | −8.38004 | − | 14.5147i | −0.361626 | − | 0.626354i | ||||
\(538\) | −13.0913 | −0.564408 | ||||||||
\(539\) | 3.19726 | + | 5.53782i | 0.137716 | + | 0.238531i | ||||
\(540\) | −4.65505 | − | 8.06279i | −0.200322 | − | 0.346967i | ||||
\(541\) | −16.9820 | −0.730111 | −0.365056 | − | 0.930986i | \(-0.618950\pi\) | ||||
−0.365056 | + | 0.930986i | \(0.618950\pi\) | |||||||
\(542\) | −32.5119 | − | 56.3123i | −1.39651 | − | 2.41882i | ||||
\(543\) | −13.4538 | + | 23.3026i | −0.577357 | + | 1.00001i | ||||
\(544\) | 6.56327 | − | 11.3679i | 0.281398 | − | 0.487395i | ||||
\(545\) | 3.50613 | 0.150186 | ||||||||
\(546\) | −4.45779 | − | 15.4422i | −0.190776 | − | 0.660867i | ||||
\(547\) | 1.13345 | 0.0484629 | 0.0242315 | − | 0.999706i | \(-0.492286\pi\) | ||||
0.0242315 | + | 0.999706i | \(0.492286\pi\) | |||||||
\(548\) | 10.5773 | − | 18.3204i | 0.451840 | − | 0.782610i | ||||
\(549\) | 16.1320 | − | 27.9414i | 0.688497 | − | 1.19251i | ||||
\(550\) | 4.39608 | + | 7.61423i | 0.187450 | + | 0.324672i | ||||
\(551\) | 61.1023 | 2.60304 | ||||||||
\(552\) | 17.8624 | + | 30.9387i | 0.760276 | + | 1.31684i | ||||
\(553\) | −5.28514 | − | 9.15414i | −0.224747 | − | 0.389273i | ||||
\(554\) | −44.5601 | −1.89318 | ||||||||
\(555\) | −1.10592 | − | 1.91551i | −0.0469437 | − | 0.0813089i | ||||
\(556\) | −35.2921 | + | 61.1276i | −1.49672 | + | 2.59239i | ||||
\(557\) | 10.1336 | − | 17.5518i | 0.429372 | − | 0.743695i | −0.567445 | − | 0.823411i | \(-0.692068\pi\) |
0.996818 | + | 0.0797164i | \(0.0254015\pi\) | |||||||
\(558\) | −8.04211 | −0.340450 | ||||||||
\(559\) | −33.8788 | − | 8.38284i | −1.43292 | − | 0.354556i | ||||
\(560\) | −5.50702 | −0.232714 | ||||||||
\(561\) | 4.89608 | − | 8.48026i | 0.206713 | − | 0.358037i | ||||
\(562\) | −9.29060 | + | 16.0918i | −0.391900 | + | 0.678792i | ||||
\(563\) | −0.156609 | − | 0.271254i | −0.00660026 | − | 0.0114320i | 0.862706 | − | 0.505705i | \(-0.168768\pi\) |
−0.869307 | + | 0.494273i | \(0.835434\pi\) | |||||||
\(564\) | −33.1023 | −1.39386 | ||||||||
\(565\) | −3.42270 | − | 5.92828i | −0.143994 | − | 0.249405i | ||||
\(566\) | −11.6792 | − | 20.2290i | −0.490914 | − | 0.850289i | ||||
\(567\) | −8.34841 | −0.350600 | ||||||||
\(568\) | 18.6390 | + | 32.2837i | 0.782076 | + | 1.35459i | ||||
\(569\) | 5.54211 | − | 9.59922i | 0.232337 | − | 0.402420i | −0.726158 | − | 0.687528i | \(-0.758696\pi\) |
0.958496 | + | 0.285108i | \(0.0920293\pi\) | |||||||
\(570\) | 29.0471 | − | 50.3111i | 1.21665 | − | 2.10730i | ||||
\(571\) | 41.7037 | 1.74525 | 0.872624 | − | 0.488393i | \(-0.162417\pi\) | ||||
0.872624 | + | 0.488393i | \(0.162417\pi\) | |||||||
\(572\) | −10.7129 | + | 11.1331i | −0.447927 | + | 0.465499i | ||||
\(573\) | 33.6897 | 1.40741 | ||||||||
\(574\) | −9.50311 | + | 16.4599i | −0.396652 | + | 0.687022i | ||||
\(575\) | −4.78514 | + | 8.28811i | −0.199554 | + | 0.345638i | ||||
\(576\) | 4.33783 | + | 7.51334i | 0.180743 | + | 0.313056i | ||||
\(577\) | 19.1867 | 0.798752 | 0.399376 | − | 0.916787i | \(-0.369227\pi\) | ||||
0.399376 | + | 0.916787i | \(0.369227\pi\) | |||||||
\(578\) | −1.70784 | − | 2.95806i | −0.0710367 | − | 0.123039i | ||||
\(579\) | 10.1706 | + | 17.6161i | 0.422678 | + | 0.732099i | ||||
\(580\) | −38.5491 | −1.60067 | ||||||||
\(581\) | 5.19882 | + | 9.00462i | 0.215683 | + | 0.373575i | ||||
\(582\) | 11.8604 | − | 20.5429i | 0.491631 | − | 0.851530i | ||||
\(583\) | −0.896081 | + | 1.55206i | −0.0371119 | + | 0.0642796i | ||||
\(584\) | −11.4578 | −0.474127 | ||||||||
\(585\) | −9.50200 | − | 2.35114i | −0.392859 | − | 0.0972075i | ||||
\(586\) | −72.0842 | −2.97777 | ||||||||
\(587\) | 6.29216 | − | 10.8983i | 0.259705 | − | 0.449823i | −0.706458 | − | 0.707755i | \(-0.749708\pi\) |
0.966163 | + | 0.257933i | \(0.0830412\pi\) | |||||||
\(588\) | 31.3081 | − | 54.2272i | 1.29112 | − | 2.23629i | ||||
\(589\) | 5.99098 | + | 10.3767i | 0.246854 | + | 0.427564i | ||||
\(590\) | −15.9530 | −0.656775 | ||||||||
\(591\) | 6.98396 | + | 12.0966i | 0.287282 | + | 0.497587i | ||||
\(592\) | 2.29416 | + | 3.97361i | 0.0942895 | + | 0.163314i | ||||
\(593\) | −13.7117 | −0.563074 | −0.281537 | − | 0.959550i | \(-0.590844\pi\) | ||||
−0.281537 | + | 0.959550i | \(0.590844\pi\) | |||||||
\(594\) | 2.22889 | + | 3.86056i | 0.0914527 | + | 0.158401i | ||||
\(595\) | −2.03709 | + | 3.52835i | −0.0835127 | + | 0.144648i | ||||
\(596\) | 4.08086 | − | 7.06826i | 0.167159 | − | 0.289527i | ||||
\(597\) | 21.3553 | 0.874015 | ||||||||
\(598\) | −23.9449 | − | 5.92482i | −0.979178 | − | 0.242284i | ||||
\(599\) | −15.3905 | −0.628840 | −0.314420 | − | 0.949284i | \(-0.601810\pi\) | ||||
−0.314420 | + | 0.949284i | \(0.601810\pi\) | |||||||
\(600\) | 22.9558 | − | 39.7606i | 0.937166 | − | 1.62322i | ||||
\(601\) | 8.10738 | − | 14.0424i | 0.330707 | − | 0.572801i | −0.651944 | − | 0.758267i | \(-0.726046\pi\) |
0.982651 | + | 0.185466i | \(0.0593795\pi\) | |||||||
\(602\) | 9.44141 | + | 16.3530i | 0.384803 | + | 0.666498i | ||||
\(603\) | 13.4718 | 0.548615 | ||||||||
\(604\) | −39.4417 | − | 68.3149i | −1.60486 | − | 2.77970i | ||||
\(605\) | 0.610938 | + | 1.05818i | 0.0248382 | + | 0.0430210i | ||||
\(606\) | 27.6376 | 1.12270 | ||||||||
\(607\) | −1.34139 | − | 2.32336i | −0.0544453 | − | 0.0943021i | 0.837518 | − | 0.546409i | \(-0.184006\pi\) |
−0.891964 | + | 0.452107i | \(0.850672\pi\) | |||||||
\(608\) | −12.7113 | + | 22.0166i | −0.515511 | + | 0.892892i | ||||
\(609\) | −6.54567 | + | 11.3374i | −0.265244 | + | 0.459416i | ||||
\(610\) | 44.4819 | 1.80102 | ||||||||
\(611\) | 8.45122 | − | 8.78276i | 0.341900 | − | 0.355312i | ||||
\(612\) | −40.7991 | −1.64921 | ||||||||
\(613\) | 18.0457 | − | 31.2560i | 0.728858 | − | 1.26242i | −0.228509 | − | 0.973542i | \(-0.573385\pi\) |
0.957366 | − | 0.288877i | \(-0.0932818\pi\) | |||||||
\(614\) | 0.992981 | − | 1.71989i | 0.0400735 | − | 0.0694093i | ||||
\(615\) | 13.6019 | + | 23.5592i | 0.548482 | + | 0.949999i | ||||
\(616\) | 4.45779 | 0.179609 | ||||||||
\(617\) | 9.58588 | + | 16.6032i | 0.385913 | + | 0.668421i | 0.991895 | − | 0.127057i | \(-0.0405532\pi\) |
−0.605982 | + | 0.795478i | \(0.707220\pi\) | |||||||
\(618\) | −27.9572 | − | 48.4234i | −1.12461 | − | 1.94787i | ||||
\(619\) | 6.38049 | 0.256453 | 0.128227 | − | 0.991745i | \(-0.459071\pi\) | ||||
0.128227 | + | 0.991745i | \(0.459071\pi\) | |||||||
\(620\) | −3.77968 | − | 6.54660i | −0.151796 | − | 0.262918i | ||||
\(621\) | −2.42616 | + | 4.20223i | −0.0973583 | + | 0.168630i | ||||
\(622\) | −32.3433 | + | 56.0202i | −1.29685 | + | 2.24621i | ||||
\(623\) | −3.71797 | −0.148957 | ||||||||
\(624\) | 46.3257 | + | 11.4626i | 1.85451 | + | 0.458873i | ||||
\(625\) | 4.83427 | 0.193371 | ||||||||
\(626\) | 32.9397 | − | 57.0533i | 1.31654 | − | 2.28031i | ||||
\(627\) | −9.48240 | + | 16.4240i | −0.378691 | + | 0.655912i | ||||
\(628\) | 25.9366 | + | 44.9236i | 1.03498 | + | 1.79265i | ||||
\(629\) | 3.39452 | 0.135349 | ||||||||
\(630\) | 2.64803 | + | 4.58653i | 0.105500 | + | 0.182732i | ||||
\(631\) | 10.4503 | + | 18.1005i | 0.416021 | + | 0.720569i | 0.995535 | − | 0.0943928i | \(-0.0300910\pi\) |
−0.579514 | + | 0.814962i | \(0.696758\pi\) | |||||||
\(632\) | 77.8232 | 3.09564 | ||||||||
\(633\) | 5.92616 | + | 10.2644i | 0.235544 | + | 0.407973i | ||||
\(634\) | −13.7621 | + | 23.8366i | −0.546562 | + | 0.946674i | ||||
\(635\) | 4.42070 | − | 7.65687i | 0.175430 | − | 0.303854i | ||||
\(636\) | 17.5491 | 0.695868 | ||||||||
\(637\) | 6.39452 | + | 22.1513i | 0.253360 | + | 0.877666i | ||||
\(638\) | 18.4578 | 0.730751 | ||||||||
\(639\) | 7.22889 | − | 12.5208i | 0.285971 | − | 0.495316i | ||||
\(640\) | −9.72343 | + | 16.8415i | −0.384352 | + | 0.665718i | ||||
\(641\) | −9.55425 | − | 16.5484i | −0.377370 | − | 0.653624i | 0.613309 | − | 0.789843i | \(-0.289838\pi\) |
−0.990679 | + | 0.136219i | \(0.956505\pi\) | |||||||
\(642\) | 13.5342 | 0.534152 | ||||||||
\(643\) | 1.75351 | + | 3.03717i | 0.0691517 | + | 0.119774i | 0.898528 | − | 0.438916i | \(-0.144637\pi\) |
−0.829376 | + | 0.558690i | \(0.811304\pi\) | |||||||
\(644\) | 4.54957 | + | 7.88009i | 0.179278 | + | 0.310519i | ||||
\(645\) | 27.0272 | 1.06419 | ||||||||
\(646\) | 44.5788 | + | 77.2127i | 1.75393 | + | 3.03789i | ||||
\(647\) | −10.4171 | + | 18.0430i | −0.409540 | + | 0.709344i | −0.994838 | − | 0.101474i | \(-0.967644\pi\) |
0.585298 | + | 0.810818i | \(0.300977\pi\) | |||||||
\(648\) | 30.7324 | − | 53.2300i | 1.20728 | − | 2.09107i | ||||
\(649\) | 5.20784 | 0.204426 | ||||||||
\(650\) | 8.79216 | + | 30.4569i | 0.344857 | + | 1.19462i | ||||
\(651\) | −2.56717 | −0.100615 | ||||||||
\(652\) | −4.11094 | + | 7.12035i | −0.160997 | + | 0.278855i | ||||
\(653\) | 6.33783 | − | 10.9774i | 0.248019 | − | 0.429581i | −0.714957 | − | 0.699168i | \(-0.753554\pi\) |
0.962976 | + | 0.269587i | \(0.0868873\pi\) | |||||||
\(654\) | 8.21943 | + | 14.2365i | 0.321405 | + | 0.556690i | ||||
\(655\) | 12.6445 | 0.494060 | ||||||||
\(656\) | −28.2163 | − | 48.8721i | −1.10166 | − | 1.90813i | ||||
\(657\) | 2.22188 | + | 3.84840i | 0.0866836 | + | 0.150140i | ||||
\(658\) | −6.59455 | −0.257082 | ||||||||
\(659\) | −2.18980 | − | 3.79284i | −0.0853025 | − | 0.147748i | 0.820218 | − | 0.572052i | \(-0.193852\pi\) |
−0.905520 | + | 0.424303i | \(0.860519\pi\) | |||||||
\(660\) | 5.98240 | − | 10.3618i | 0.232865 | − | 0.403334i | ||||
\(661\) | 0.561265 | − | 0.972140i | 0.0218307 | − | 0.0378118i | −0.854904 | − | 0.518787i | \(-0.826384\pi\) |
0.876734 | + | 0.480975i | \(0.159717\pi\) | |||||||
\(662\) | 25.2110 | 0.979852 | ||||||||
\(663\) | 24.4804 | − | 25.4408i | 0.950740 | − | 0.988038i | ||||
\(664\) | −76.5520 | −2.97080 | ||||||||
\(665\) | 3.94531 | − | 6.83348i | 0.152993 | − | 0.264991i | ||||
\(666\) | 2.20628 | − | 3.82139i | 0.0854917 | − | 0.148076i | ||||
\(667\) | 10.0457 | + | 17.3996i | 0.388970 | + | 0.673716i | ||||
\(668\) | −30.2538 | −1.17055 | ||||||||
\(669\) | −19.2344 | − | 33.3149i | −0.743643 | − | 1.28803i | ||||
\(670\) | 9.28670 | + | 16.0850i | 0.358777 | + | 0.621419i | ||||
\(671\) | −14.5211 | −0.560579 | ||||||||
\(672\) | −2.72343 | − | 4.71713i | −0.105059 | − | 0.181967i | ||||
\(673\) | −9.02461 | + | 15.6311i | −0.347873 | + | 0.602534i | −0.985871 | − | 0.167504i | \(-0.946429\pi\) |
0.637998 | + | 0.770038i | \(0.279763\pi\) | |||||||
\(674\) | −24.7440 | + | 42.8579i | −0.953105 | + | 1.65083i | ||||
\(675\) | 6.23591 | 0.240020 | ||||||||
\(676\) | −47.1366 | + | 29.6883i | −1.81294 | + | 1.14186i | ||||
\(677\) | −26.7037 | −1.02631 | −0.513154 | − | 0.858297i | \(-0.671523\pi\) | ||||
−0.513154 | + | 0.858297i | \(0.671523\pi\) | |||||||
\(678\) | 16.0477 | − | 27.7954i | 0.616307 | − | 1.06748i | ||||
\(679\) | 1.61094 | − | 2.79023i | 0.0618221 | − | 0.107079i | ||||
\(680\) | −14.9980 | − | 25.9773i | −0.575147 | − | 0.996184i | ||||
\(681\) | −40.2560 | −1.54261 | ||||||||
\(682\) | 1.80976 | + | 3.13459i | 0.0692992 | + | 0.120030i | ||||
\(683\) | −15.4894 | − | 26.8285i | −0.592686 | − | 1.02656i | −0.993869 | − | 0.110565i | \(-0.964734\pi\) |
0.401183 | − | 0.915998i | \(-0.368599\pi\) | |||||||
\(684\) | 79.0170 | 3.02129 | ||||||||
\(685\) | −3.01604 | − | 5.22393i | −0.115237 | − | 0.199596i | ||||
\(686\) | 13.0648 | − | 22.6289i | 0.498817 | − | 0.863977i | ||||
\(687\) | −30.6842 | + | 53.1467i | −1.17068 | + | 2.02767i | ||||
\(688\) | −56.0662 | −2.13750 | ||||||||
\(689\) | −4.48040 | + | 4.65617i | −0.170690 | + | 0.177386i | ||||
\(690\) | 19.1023 | 0.727211 | ||||||||
\(691\) | 1.16563 | − | 2.01893i | 0.0443426 | − | 0.0768036i | −0.843002 | − | 0.537910i | \(-0.819214\pi\) |
0.887345 | + | 0.461106i | \(0.152547\pi\) | |||||||
\(692\) | −3.53008 | + | 6.11427i | −0.134193 | + | 0.232430i | ||||
\(693\) | −0.864447 | − | 1.49727i | −0.0328376 | − | 0.0568765i | ||||
\(694\) | 45.9116 | 1.74278 | ||||||||
\(695\) | 10.0633 | + | 17.4301i | 0.381721 | + | 0.661161i | ||||
\(696\) | −48.1921 | − | 83.4712i | −1.82672 | − | 3.16397i | ||||
\(697\) | −41.7499 | −1.58139 | ||||||||
\(698\) | −21.7816 | − | 37.7268i | −0.824445 | − | 1.42798i | ||||
\(699\) | 31.0100 | − | 53.7110i | 1.17291 | − | 2.03153i | ||||
\(700\) | 5.84685 | − | 10.1270i | 0.220990 | − | 0.382766i | ||||
\(701\) | −22.5834 | −0.852965 | −0.426482 | − | 0.904496i | \(-0.640247\pi\) | ||||
−0.426482 | + | 0.904496i | \(0.640247\pi\) | |||||||
\(702\) | 4.45779 | + | 15.4422i | 0.168248 | + | 0.582830i | ||||
\(703\) | −6.57429 | −0.247954 | ||||||||
\(704\) | 1.95233 | − | 3.38153i | 0.0735811 | − | 0.127446i | ||||
\(705\) | −4.71943 | + | 8.17429i | −0.177744 | + | 0.307862i | ||||
\(706\) | −42.3273 | − | 73.3130i | −1.59301 | − | 2.75917i | ||||
\(707\) | 3.75385 | 0.141178 | ||||||||
\(708\) | −25.4980 | − | 44.1638i | −0.958273 | − | 1.65978i | ||||
\(709\) | 7.86089 | + | 13.6155i | 0.295222 | + | 0.511339i | 0.975036 | − | 0.222045i | \(-0.0712731\pi\) |
−0.679815 | + | 0.733384i | \(0.737940\pi\) | |||||||
\(710\) | 19.9327 | 0.748062 | ||||||||
\(711\) | −15.0913 | − | 26.1390i | −0.565970 | − | 0.980288i | ||||
\(712\) | 13.6867 | − | 23.7060i | 0.512930 | − | 0.888421i | ||||
\(713\) | −1.96992 | + | 3.41201i | −0.0737742 | + | 0.127781i | ||||
\(714\) | −19.1023 | −0.714884 | ||||||||
\(715\) | 1.22188 | + | 4.23270i | 0.0456956 | + | 0.158294i | ||||
\(716\) | 31.4288 | 1.17455 | ||||||||
\(717\) | −0.852411 | + | 1.47642i | −0.0318339 | + | 0.0551379i | ||||
\(718\) | 5.92771 | − | 10.2671i | 0.221220 | − | 0.383165i | ||||
\(719\) | 14.9151 | + | 25.8338i | 0.556241 | + | 0.963437i | 0.997806 | + | 0.0662079i | \(0.0210901\pi\) |
−0.441565 | + | 0.897229i | \(0.645577\pi\) | |||||||
\(720\) | −15.7249 | −0.586032 | ||||||||
\(721\) | −3.79728 | − | 6.57708i | −0.141418 | − | 0.244943i | ||||
\(722\) | −62.5205 | − | 108.289i | −2.32677 | − | 4.03009i | ||||
\(723\) | 36.9568 | 1.37444 | ||||||||
\(724\) | −25.2288 | − | 43.6976i | −0.937621 | − | 1.62401i | ||||
\(725\) | 12.9101 | − | 22.3610i | 0.479470 | − | 0.830466i | ||||
\(726\) | −2.86445 | + | 4.96137i | −0.106310 | + | 0.184134i | ||||
\(727\) | −36.6053 | −1.35761 | −0.678807 | − | 0.734316i | \(-0.737503\pi\) | ||||
−0.678807 | + | 0.734316i | \(0.737503\pi\) | |||||||
\(728\) | 15.6023 | + | 3.86056i | 0.578258 | + | 0.143082i | ||||
\(729\) | −11.6485 | −0.431425 | ||||||||
\(730\) | −3.06327 | + | 5.30573i | −0.113377 | + | 0.196374i | ||||
\(731\) | −20.7394 | + | 35.9216i | −0.767073 | + | 1.32861i | ||||
\(732\) | 71.0963 | + | 123.142i | 2.62779 | + | 4.55147i | ||||
\(733\) | 29.8695 | 1.10325 | 0.551627 | − | 0.834091i | \(-0.314007\pi\) | ||||
0.551627 | + | 0.834091i | \(0.314007\pi\) | |||||||
\(734\) | −8.05580 | − | 13.9531i | −0.297345 | − | 0.515017i | ||||
\(735\) | −8.92727 | − | 15.4625i | −0.329287 | − | 0.570342i | ||||
\(736\) | −8.35933 | −0.308129 | ||||||||
\(737\) | −3.03163 | − | 5.25094i | −0.111672 | − | 0.193421i | ||||
\(738\) | −27.1355 | + | 47.0000i | −0.998870 | + | 1.73009i | ||||
\(739\) | −15.1284 | + | 26.2032i | −0.556508 | + | 0.963901i | 0.441276 | + | 0.897371i | \(0.354526\pi\) |
−0.997784 | + | 0.0665295i | \(0.978807\pi\) | |||||||
\(740\) | 4.14769 | 0.152472 | ||||||||
\(741\) | −47.4120 | + | 49.2720i | −1.74172 | + | 1.81005i | ||||
\(742\) | 3.49610 | 0.128346 | ||||||||
\(743\) | −19.6210 | + | 33.9845i | −0.719824 | + | 1.24677i | 0.241246 | + | 0.970464i | \(0.422444\pi\) |
−0.961069 | + | 0.276307i | \(0.910889\pi\) | |||||||
\(744\) | 9.45033 | − | 16.3684i | 0.346466 | − | 0.600096i | ||||
\(745\) | −1.16363 | − | 2.01546i | −0.0426320 | − | 0.0738408i | ||||
\(746\) | −11.0602 | −0.404941 | ||||||||
\(747\) | 14.8449 | + | 25.7120i | 0.543145 | + | 0.940754i | ||||
\(748\) | 9.18122 | + | 15.9023i | 0.335699 | + | 0.581447i | ||||
\(749\) | 1.83828 | 0.0671691 | ||||||||
\(750\) | −29.7746 | − | 51.5711i | −1.08721 | − | 1.88311i | ||||
\(751\) | −3.41168 | + | 5.90919i | −0.124494 | + | 0.215630i | −0.921535 | − | 0.388295i | \(-0.873064\pi\) |
0.797041 | + | 0.603925i | \(0.206397\pi\) | |||||||
\(752\) | 9.79016 | − | 16.9571i | 0.357010 | − | 0.618360i | ||||
\(753\) | −25.2007 | −0.918365 | ||||||||
\(754\) | 64.6023 | + | 15.9849i | 2.35268 | + | 0.582136i | ||||
\(755\) | −22.4930 | −0.818603 | ||||||||
\(756\) | 2.96446 | − | 5.13460i | 0.107816 | − | 0.186744i | ||||
\(757\) | 0.376483 | − | 0.652088i | 0.0136835 | − | 0.0237006i | −0.859103 | − | 0.511803i | \(-0.828978\pi\) |
0.872786 | + | 0.488103i | \(0.162311\pi\) | |||||||
\(758\) | −24.4522 | − | 42.3525i | −0.888145 | − | 1.53831i | ||||
\(759\) | −6.23591 | −0.226349 | ||||||||
\(760\) | 29.0471 | + | 50.3111i | 1.05365 | + | 1.82498i | ||||
\(761\) | −17.4874 | − | 30.2891i | −0.633919 | − | 1.09798i | −0.986743 | − | 0.162290i | \(-0.948112\pi\) |
0.352825 | − | 0.935689i | \(-0.385221\pi\) | |||||||
\(762\) | 41.4538 | 1.50171 | ||||||||
\(763\) | 1.11640 | + | 1.93366i | 0.0404164 | + | 0.0700032i | ||||
\(764\) | −31.5878 | + | 54.7116i | −1.14281 | + | 1.97940i | ||||
\(765\) | −5.81678 | + | 10.0750i | −0.210306 | + | 0.364261i | ||||
\(766\) | 69.2700 | 2.50283 | ||||||||
\(767\) | 18.2274 | + | 4.51012i | 0.658155 | + | 0.162851i | ||||
\(768\) | −73.3333 | −2.64619 | ||||||||
\(769\) | −7.73245 | + | 13.3930i | −0.278839 | + | 0.482964i | −0.971097 | − | 0.238687i | \(-0.923283\pi\) |
0.692257 | + | 0.721651i | \(0.256616\pi\) | |||||||
\(770\) | 1.19180 | − | 2.06426i | 0.0429495 | − | 0.0743907i | ||||
\(771\) | −21.5401 | − | 37.3086i | −0.775748 | − | 1.34364i | ||||
\(772\) | −38.1444 | −1.37285 | ||||||||
\(773\) | 18.0683 | + | 31.2952i | 0.649871 | + | 1.12561i | 0.983153 | + | 0.182783i | \(0.0585104\pi\) |
−0.333282 | + | 0.942827i | \(0.608156\pi\) | |||||||
\(774\) | 26.9592 | + | 46.6948i | 0.969030 | + | 1.67841i | ||||
\(775\) | 5.06327 | 0.181878 | ||||||||
\(776\) | 11.8604 | + | 20.5429i | 0.425765 | + | 0.737447i | ||||
\(777\) | 0.704280 | − | 1.21985i | 0.0252659 | − | 0.0437618i | ||||
\(778\) | 36.3468 | − | 62.9544i | 1.30309 | − | 2.25703i | ||||
\(779\) | 80.8583 | 2.89705 | ||||||||
\(780\) | 29.9120 | − | 31.0855i | 1.07102 | − | 1.11304i | ||||
\(781\) | −6.50702 | −0.232839 | ||||||||
\(782\) | −14.6582 | + | 25.3887i | −0.524175 | + | 0.907898i | ||||
\(783\) | 6.54567 | − | 11.3374i | 0.233923 | − | 0.405167i | ||||
\(784\) | 18.5191 | + | 32.0759i | 0.661395 | + | 1.14557i | ||||
\(785\) | 14.7913 | 0.527923 | ||||||||
\(786\) | 29.6425 | + | 51.3423i | 1.05731 | + | 1.83132i | ||||
\(787\) | 11.4749 | + | 19.8752i | 0.409037 | + | 0.708474i | 0.994782 | − | 0.102022i | \(-0.0325312\pi\) |
−0.585745 | + | 0.810496i | \(0.699198\pi\) | |||||||
\(788\) | −26.1929 | −0.933084 | ||||||||
\(789\) | 17.7695 | + | 30.7778i | 0.632613 | + | 1.09572i | ||||
\(790\) | 20.8062 | − | 36.0374i | 0.740251 | − | 1.28215i | ||||
\(791\) | 2.17967 | − | 3.77529i | 0.0775000 | − | 0.134234i | ||||
\(792\) | 12.7289 | 0.452302 | ||||||||
\(793\) | −50.8237 | − | 12.5756i | −1.80480 | − | 0.446573i | ||||
\(794\) | 86.8895 | 3.08359 | ||||||||
\(795\) | 2.50200 | − | 4.33359i | 0.0887368 | − | 0.153697i | ||||
\(796\) | −20.0230 | + | 34.6808i | −0.709695 | + | 1.22923i | ||||
\(797\) | −21.7249 | − | 37.6286i | −0.769535 | − | 1.33287i | −0.937815 | − | 0.347135i | \(-0.887155\pi\) |
0.168280 | − | 0.985739i | \(-0.446179\pi\) | |||||||
\(798\) | 36.9960 | 1.30964 | ||||||||
\(799\) | −7.24293 | − | 12.5451i | −0.256237 | − | 0.443815i | ||||
\(800\) | 5.37147 | + | 9.30365i | 0.189910 | + | 0.328934i | ||||
\(801\) | −10.6164 | −0.375112 | ||||||||
\(802\) | 18.2855 | + | 31.6714i | 0.645683 | + | 1.11836i | ||||
\(803\) | 1.00000 | − | 1.73205i | 0.0352892 | − | 0.0611227i | ||||
\(804\) | −29.6862 | + | 51.4181i | −1.04695 | + | 1.81338i | ||||
\(805\) | 2.59455 | 0.0914460 | ||||||||
\(806\) | 3.61951 | + | 12.5384i | 0.127492 | + | 0.441645i | ||||
\(807\) | −11.9327 | −0.420052 | ||||||||
\(808\) | −13.8188 | + | 23.9348i | −0.486143 | + | 0.842024i | ||||
\(809\) | 21.5547 | − | 37.3338i | 0.757823 | − | 1.31259i | −0.186136 | − | 0.982524i | \(-0.559597\pi\) |
0.943959 | − | 0.330063i | \(-0.107070\pi\) | |||||||
\(810\) | −16.4327 | − | 28.4623i | −0.577387 | − | 1.00006i | ||||
\(811\) | −17.9428 | −0.630056 | −0.315028 | − | 0.949082i | \(-0.602014\pi\) | ||||
−0.315028 | + | 0.949082i | \(0.602014\pi\) | |||||||
\(812\) | −12.2746 | − | 21.2602i | −0.430753 | − | 0.746086i | ||||
\(813\) | −29.6346 | − | 51.3286i | −1.03933 | − | 1.80017i | ||||
\(814\) | −1.98596 | −0.0696080 | ||||||||
\(815\) | 1.17220 | + | 2.03032i | 0.0410605 | + | 0.0711188i | ||||
\(816\) | 28.3589 | − | 49.1190i | 0.992760 | − | 1.71951i | ||||
\(817\) | 40.1666 | − | 69.5707i | 1.40525 | − | 2.43397i | ||||
\(818\) | 41.6202 | 1.45522 | ||||||||
\(819\) | −1.72889 | − | 5.98907i | −0.0604125 | − | 0.209275i | ||||
\(820\) | −51.0131 | −1.78146 | ||||||||
\(821\) | −7.83237 | + | 13.5661i | −0.273352 | + | 0.473459i | −0.969718 | − | 0.244228i | \(-0.921466\pi\) |
0.696366 | + | 0.717687i | \(0.254799\pi\) | |||||||
\(822\) | 14.1410 | − | 24.4930i | 0.493225 | − | 0.854290i | ||||
\(823\) | −1.84885 | − | 3.20231i | −0.0644470 | − | 0.111625i | 0.832002 | − | 0.554773i | \(-0.187195\pi\) |
−0.896449 | + | 0.443148i | \(0.853862\pi\) | |||||||
\(824\) | 55.9145 | 1.94787 | ||||||||
\(825\) | 4.00702 | + | 6.94036i | 0.139506 | + | 0.241632i | ||||
\(826\) | −5.07965 | − | 8.79821i | −0.176744 | − | 0.306129i | ||||
\(827\) | −42.3201 | −1.47162 | −0.735808 | − | 0.677191i | \(-0.763197\pi\) | ||||
−0.735808 | + | 0.677191i | \(0.763197\pi\) | |||||||
\(828\) | 12.9910 | + | 22.5010i | 0.451468 | + | 0.781965i | ||||
\(829\) | −3.57730 | + | 6.19607i | −0.124245 | + | 0.215198i | −0.921438 | − | 0.388527i | \(-0.872984\pi\) |
0.797193 | + | 0.603725i | \(0.206318\pi\) | |||||||
\(830\) | −20.4664 | + | 35.4488i | −0.710398 | + | 1.23045i | ||||
\(831\) | −40.6164 | −1.40897 | ||||||||
\(832\) | 9.76164 | − | 10.1446i | 0.338424 | − | 0.351701i | ||||
\(833\) | 27.4014 | 0.949404 | ||||||||
\(834\) | −47.1827 | + | 81.7228i | −1.63380 | + | 2.82983i | ||||
\(835\) | −4.31332 | + | 7.47088i | −0.149268 | + | 0.258541i | ||||
\(836\) | −17.7816 | − | 30.7986i | −0.614989 | − | 1.06519i | ||||
\(837\) | 2.56717 | 0.0887344 | ||||||||
\(838\) | 27.9472 | + | 48.4060i | 0.965420 | + | 1.67216i | ||||
\(839\) | −1.38004 | − | 2.39030i | −0.0476443 | − | 0.0825224i | 0.841220 | − | 0.540693i | \(-0.181838\pi\) |
−0.888864 | + | 0.458171i | \(0.848505\pi\) | |||||||
\(840\) | −12.4469 | −0.429458 | ||||||||
\(841\) | −12.6028 | − | 21.8287i | −0.434580 | − | 0.752714i | ||||
\(842\) | 4.33437 | − | 7.50735i | 0.149372 | − | 0.258720i | ||||
\(843\) | −8.46837 | + | 14.6676i | −0.291666 | + | 0.505180i | ||||
\(844\) | −22.2257 | −0.765040 | ||||||||
\(845\) | 0.610938 | + | 15.8726i | 0.0210169 | + | 0.546035i | ||||
\(846\) | −18.8303 | −0.647398 | ||||||||
\(847\) | −0.389062 | + | 0.673875i | −0.0133683 | + | 0.0231546i | ||||
\(848\) | −5.19024 | + | 8.98976i | −0.178234 | + | 0.308710i | ||||
\(849\) | −10.6456 | − | 18.4387i | −0.365356 | − | 0.632814i | ||||
\(850\) | 37.6757 | 1.29226 | ||||||||
\(851\) | −1.08086 | − | 1.87211i | −0.0370515 | − | 0.0641750i | ||||
\(852\) | 31.8589 | + | 55.1812i | 1.09147 | + | 1.89048i | ||||
\(853\) | 46.1615 | 1.58054 | 0.790270 | − | 0.612758i | \(-0.209940\pi\) | ||||
0.790270 | + | 0.612758i | \(0.209940\pi\) | |||||||
\(854\) | 14.1636 | + | 24.5321i | 0.484669 | + | 0.839472i | ||||
\(855\) | 11.2655 | − | 19.5125i | 0.385274 | − | 0.667313i | ||||
\(856\) | −6.76710 | + | 11.7210i | −0.231295 | + | 0.400614i | ||||
\(857\) | 26.2680 | 0.897297 | 0.448649 | − | 0.893708i | \(-0.351905\pi\) | ||||
0.448649 | + | 0.893708i | \(0.351905\pi\) | |||||||
\(858\) | −14.3222 | + | 14.8841i | −0.488953 | + | 0.508135i | ||||
\(859\) | −32.0381 | −1.09313 | −0.546563 | − | 0.837418i | \(-0.684064\pi\) | ||||
−0.546563 | + | 0.837418i | \(0.684064\pi\) | |||||||
\(860\) | −25.3409 | + | 43.8918i | −0.864119 | + | 1.49670i | ||||
\(861\) | −8.66207 | + | 15.0031i | −0.295203 | + | 0.511306i | ||||
\(862\) | −32.4413 | − | 56.1900i | −1.10496 | − | 1.91384i | ||||
\(863\) | −24.2078 | −0.824044 | −0.412022 | − | 0.911174i | \(-0.635177\pi\) | ||||
−0.412022 | + | 0.911174i | \(0.635177\pi\) | |||||||
\(864\) | 2.72343 | + | 4.71713i | 0.0926531 | + | 0.160480i | ||||
\(865\) | 1.00657 | + | 1.74344i | 0.0342246 | + | 0.0592787i | ||||
\(866\) | 36.0521 | 1.22510 | ||||||||
\(867\) | −1.55669 | − | 2.69627i | −0.0528680 | − | 0.0915701i | ||||
\(868\) | 2.40700 | − | 4.16905i | 0.0816990 | − | 0.141507i | ||||
\(869\) | −6.79216 | + | 11.7644i | −0.230408 | + | 0.399079i | ||||
\(870\) | −51.5371 | −1.74727 | ||||||||
\(871\) | −6.06327 | − | 21.0038i | −0.205446 | − | 0.711686i | ||||
\(872\) | −16.4389 | −0.556690 | ||||||||
\(873\) | 4.59992 | − | 7.96729i | 0.155684 | − | 0.269652i | ||||
\(874\) | 28.3890 | − | 49.1711i | 0.960271 | − | 1.66324i | ||||
\(875\) | −4.04411 | − | 7.00461i | −0.136716 | − | 0.236799i | ||||
\(876\) | −19.5843 | −0.661693 | ||||||||
\(877\) | −0.528173 | − | 0.914823i | −0.0178351 | − | 0.0308914i | 0.856970 | − | 0.515366i | \(-0.172344\pi\) |
−0.874805 | + | 0.484475i | \(0.839011\pi\) | |||||||
\(878\) | −5.72388 | − | 9.91405i | −0.193172 | − | 0.334583i | ||||
\(879\) | −65.7046 | −2.21616 | ||||||||
\(880\) | 3.53865 | + | 6.12912i | 0.119288 | + | 0.206613i | ||||
\(881\) | 12.0828 | − | 20.9280i | 0.407079 | − | 0.705081i | −0.587482 | − | 0.809237i | \(-0.699881\pi\) |
0.994561 | + | 0.104156i | \(0.0332141\pi\) | |||||||
\(882\) | 17.8097 | − | 30.8472i | 0.599682 | − | 1.03868i | ||||
\(883\) | 5.84831 | 0.196811 | 0.0984057 | − | 0.995146i | \(-0.468626\pi\) | ||||
0.0984057 | + | 0.995146i | \(0.468626\pi\) | |||||||
\(884\) | 18.3624 | + | 63.6094i | 0.617596 | + | 2.13941i | ||||
\(885\) | −14.5411 | −0.488795 | ||||||||
\(886\) | −22.7785 | + | 39.4535i | −0.765258 | + | 1.32547i | ||||
\(887\) | 4.33783 | − | 7.51334i | 0.145650 | − | 0.252273i | −0.783965 | − | 0.620805i | \(-0.786806\pi\) |
0.929615 | + | 0.368531i | \(0.120139\pi\) | |||||||
\(888\) | 5.18523 | + | 8.98107i | 0.174005 | + | 0.301385i | ||||
\(889\) | 5.63044 | 0.188839 | ||||||||
\(890\) | −7.31833 | − | 12.6757i | −0.245311 | − | 0.424891i | ||||
\(891\) | 5.36445 | + | 9.29150i | 0.179716 | + | 0.311277i | ||||
\(892\) | 72.1373 | 2.41533 | ||||||||
\(893\) | 14.0276 | + | 24.2966i | 0.469417 | + | 0.813054i | ||||
\(894\) | 5.45579 | − | 9.44970i | 0.182469 | − | 0.316045i | ||||
\(895\) | 4.48085 | − | 7.76105i | 0.149778 | − | 0.259423i | ||||
\(896\) | −12.3843 | −0.413730 | ||||||||
\(897\) | −21.8257 | − | 5.40046i | −0.728739 | − | 0.180316i | ||||
\(898\) | −31.6625 | −1.05659 | ||||||||
\(899\) | 5.31477 | − | 9.20546i | 0.177258 | − | 0.307019i | ||||
\(900\) | 16.6953 | − | 28.9170i | 0.556509 | − | 0.963901i | ||||
\(901\) | 3.83983 | + | 6.65079i | 0.127923 | + | 0.221570i | ||||
\(902\) | 24.4257 | 0.813287 | ||||||||
\(903\) | 8.60582 | + | 14.9057i | 0.286384 | + | 0.496031i | ||||
\(904\) | 16.0477 | + | 27.7954i | 0.533738 | + | 0.924461i | ||||
\(905\) | −14.3876 | −0.478260 | ||||||||
\(906\) | −52.7304 | − | 91.3317i | −1.75185 | − | 3.03429i | ||||
\(907\) | 7.79762 | − | 13.5059i | 0.258916 | − | 0.448455i | −0.707036 | − | 0.707178i | \(-0.749968\pi\) |
0.965952 | + | 0.258722i | \(0.0833014\pi\) | |||||||
\(908\) | 37.7444 | − | 65.3752i | 1.25259 | − | 2.16955i | ||||
\(909\) | 10.7189 | 0.355522 | ||||||||
\(910\) | 5.95900 | − | 6.19278i | 0.197539 | − | 0.205289i | ||||
\(911\) | 24.5672 | 0.813947 | 0.406973 | − | 0.913440i | \(-0.366584\pi\) | ||||
0.406973 | + | 0.913440i | \(0.366584\pi\) | |||||||
\(912\) | −54.9236 | + | 95.1305i | −1.81870 | + | 3.15009i | ||||
\(913\) | 6.68122 | − | 11.5722i | 0.221116 | − | 0.382985i | ||||
\(914\) | 32.3257 | + | 55.9897i | 1.06924 | + | 1.85198i | ||||
\(915\) | 40.5451 | 1.34038 | ||||||||
\(916\) | −57.5397 | − | 99.6616i | −1.90116 | − | 3.29291i | ||||
\(917\) | 4.02617 | + | 6.97353i | 0.132956 | + | 0.230286i | ||||
\(918\) | 19.1023 | 0.630469 | ||||||||
\(919\) | −8.64057 | − | 14.9659i | −0.285026 | − | 0.493680i | 0.687589 | − | 0.726100i | \(-0.258669\pi\) |
−0.972616 | + | 0.232420i | \(0.925336\pi\) | |||||||
\(920\) | −9.55113 | + | 16.5430i | −0.314891 | + | 0.545408i | ||||
\(921\) | 0.905101 | − | 1.56768i | 0.0298241 | − | 0.0516568i | ||||
\(922\) | −31.6725 | −1.04308 | ||||||||
\(923\) | −22.7746 | − | 5.63524i | −0.749634 | − | 0.185486i | ||||
\(924\) | 7.61951 | 0.250664 | ||||||||
\(925\) | −1.38906 | + | 2.40593i | −0.0456721 | + | 0.0791064i | ||||
\(926\) | 4.35587 | − | 7.54459i | 0.143143 | − | 0.247931i | ||||
\(927\) | −10.8428 | − | 18.7804i | −0.356126 | − | 0.616828i | ||||
\(928\) | 22.5531 | 0.740343 | ||||||||
\(929\) | 24.1284 | + | 41.7917i | 0.791628 | + | 1.37114i | 0.924958 | + | 0.380069i | \(0.124100\pi\) |
−0.133330 | + | 0.991072i | \(0.542567\pi\) | |||||||
\(930\) | −5.05313 | − | 8.75228i | −0.165699 | − | 0.286999i | ||||
\(931\) | −53.0693 | −1.73928 | ||||||||
\(932\) | 58.1506 | + | 100.720i | 1.90479 | + | 3.29919i | ||||
\(933\) | −29.4808 | + | 51.0623i | −0.965160 | + | 1.67171i | ||||
\(934\) | 23.4729 | − | 40.6563i | 0.768058 | − | 1.33032i | ||||
\(935\) | 5.23591 | 0.171233 | ||||||||
\(936\) | 44.5511 | + | 11.0235i | 1.45620 | + | 0.360316i | ||||
\(937\) | −17.7209 | −0.578916 | −0.289458 | − | 0.957191i | \(-0.593475\pi\) | ||||
−0.289458 | + | 0.957191i | \(0.593475\pi\) | |||||||
\(938\) | −5.91402 | + | 10.2434i | −0.193100 | + | 0.334458i | ||||
\(939\) | 30.0245 | − | 52.0040i | 0.979813 | − | 1.69709i | ||||
\(940\) | −8.84997 | − | 15.3286i | −0.288654 | − | 0.499964i | ||||
\(941\) | 7.96392 | 0.259616 | 0.129808 | − | 0.991539i | \(-0.458564\pi\) | ||||
0.129808 | + | 0.991539i | \(0.458564\pi\) | |||||||
\(942\) | 34.6752 | + | 60.0592i | 1.12978 | + | 1.95684i | ||||
\(943\) | 13.2937 | + | 23.0254i | 0.432903 | + | 0.749810i | ||||
\(944\) | 30.1646 | 0.981775 | ||||||||
\(945\) | −0.845294 | − | 1.46409i | −0.0274974 | − | 0.0476269i | ||||
\(946\) | 12.1336 | − | 21.0159i | 0.394496 | − | 0.683287i | ||||
\(947\) | −7.78158 | + | 13.4781i | −0.252867 | + | 0.437979i | −0.964314 | − | 0.264761i | \(-0.914707\pi\) |
0.711447 | + | 0.702740i | \(0.248040\pi\) | |||||||
\(948\) | 133.020 | 4.32028 | ||||||||
\(949\) | 5.00000 | − | 5.19615i | 0.162307 | − | 0.168674i | ||||
\(950\) | −72.9677 | −2.36739 | ||||||||
\(951\) | −12.5441 | + | 21.7270i | −0.406771 | + | 0.704548i | ||||
\(952\) | 9.55113 | − | 16.5430i | 0.309554 | − | 0.536163i | ||||
\(953\) | 15.9242 | + | 27.5814i | 0.515834 | + | 0.893451i | 0.999831 | + | 0.0183810i | \(0.00585120\pi\) |
−0.483997 | + | 0.875070i | \(0.660815\pi\) | |||||||
\(954\) | 9.98285 | 0.323207 | ||||||||
\(955\) | 9.00702 | + | 15.6006i | 0.291460 | + | 0.504824i | ||||
\(956\) | −1.59846 | − | 2.76861i | −0.0516978 | − | 0.0895433i | ||||
\(957\) | 16.8242 | 0.543850 | ||||||||
\(958\) | −11.6390 | − | 20.1594i | −0.376039 | − | 0.651319i | ||||
\(959\) | 1.92070 | − | 3.32674i | 0.0620225 | − | 0.107426i | ||||
\(960\) | −5.45122 | + | 9.44178i | −0.175937 | + | 0.304732i | ||||
\(961\) | −28.9156 | −0.932761 | ||||||||
\(962\) | −6.95087 | − | 1.71989i | −0.224105 | − | 0.0554516i | ||||
\(963\) | 5.24906 | 0.169149 | ||||||||
\(964\) | −34.6510 | + | 60.0174i | −1.11604 | + | 1.93303i | ||||
\(965\) | −5.43829 | + | 9.41940i | −0.175065 | + | 0.303221i | ||||
\(966\) | 6.08242 | + | 10.5351i | 0.195699 | + | 0.338960i | ||||
\(967\) | −46.1023 | −1.48255 | −0.741274 | − | 0.671202i | \(-0.765778\pi\) | ||||
−0.741274 | + | 0.671202i | \(0.765778\pi\) | |||||||
\(968\) | −2.86445 | − | 4.96137i | −0.0920668 | − | 0.159464i | ||||
\(969\) | 40.6335 | + | 70.3792i | 1.30533 | + | 2.26091i | ||||
\(970\) | 12.6837 | 0.407248 | ||||||||
\(971\) | 7.39408 | + | 12.8069i | 0.237287 | + | 0.410994i | 0.959935 | − | 0.280223i | \(-0.0904084\pi\) |
−0.722648 | + | 0.691217i | \(0.757075\pi\) | |||||||
\(972\) | 41.1003 | − | 71.1877i | 1.31829 | − | 2.28335i | ||||
\(973\) | −6.40856 | + | 11.1000i | −0.205449 | + | 0.355848i | ||||
\(974\) | −100.104 | −3.20755 | ||||||||
\(975\) | 8.01404 | + | 27.7614i | 0.256655 | + | 0.889078i | ||||
\(976\) | −84.1083 | −2.69224 | ||||||||
\(977\) | −0.679666 | + | 1.17722i | −0.0217444 | + | 0.0376625i | −0.876693 | − | 0.481051i | \(-0.840255\pi\) |
0.854948 | + | 0.518713i | \(0.173589\pi\) | |||||||
\(978\) | −5.49600 | + | 9.51935i | −0.175743 | + | 0.304395i | ||||
\(979\) | 2.38906 | + | 4.13798i | 0.0763548 | + | 0.132250i | ||||
\(980\) | 33.4812 | 1.06952 | ||||||||
\(981\) | 3.18780 | + | 5.52143i | 0.101779 | + | 0.176286i | ||||
\(982\) | 51.6229 | + | 89.4134i | 1.64735 | + | 2.85330i | ||||
\(983\) | 27.4709 | 0.876187 | 0.438093 | − | 0.898929i | \(-0.355654\pi\) | ||||
0.438093 | + | 0.898929i | \(0.355654\pi\) | |||||||
\(984\) | −63.7740 | − | 110.460i | −2.03304 | − | 3.52133i | ||||
\(985\) | −3.73436 | + | 6.46809i | −0.118986 | + | 0.206091i | ||||
\(986\) | 39.5471 | − | 68.4976i | 1.25944 | − | 2.18141i | ||||
\(987\) | −6.01092 | −0.191330 | ||||||||
\(988\) | −35.5632 | − | 123.194i | −1.13142 | − | 3.91934i | ||||
\(989\) | 26.4148 | 0.839941 | ||||||||
\(990\) | 3.40310 | − | 5.89434i | 0.108158 | − | 0.187334i | ||||
\(991\) | −0.0867676 | + | 0.150286i | −0.00275626 | + | 0.00477399i | −0.867400 | − | 0.497611i | \(-0.834211\pi\) |
0.864644 | + | 0.502385i | \(0.167544\pi\) | |||||||
\(992\) | 2.21130 | + | 3.83008i | 0.0702088 | + | 0.121605i | ||||
\(993\) | 22.9797 | 0.729240 | ||||||||
\(994\) | 6.34685 | + | 10.9931i | 0.201310 | + | 0.348679i | ||||
\(995\) | 5.70940 | + | 9.88896i | 0.181000 | + | 0.313501i | ||||
\(996\) | −130.847 | −4.14605 | ||||||||
\(997\) | −22.0948 | − | 38.2693i | −0.699749 | − | 1.21200i | −0.968553 | − | 0.248807i | \(-0.919962\pi\) |
0.268804 | − | 0.963195i | \(-0.413372\pi\) | |||||||
\(998\) | −24.2093 | + | 41.9317i | −0.766332 | + | 1.32733i | ||||
\(999\) | −0.704280 | + | 1.21985i | −0.0222824 | + | 0.0385943i |
(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 | 143.2.e.b.100.1 | ✓ | 6 | |
13.3 | even | 3 | inner | 143.2.e.b.133.1 | yes | 6 | |
13.4 | even | 6 | 1859.2.a.g.1.1 | 3 | |||
13.9 | even | 3 | 1859.2.a.f.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
143.2.e.b.100.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
143.2.e.b.133.1 | yes | 6 | 13.3 | even | 3 | inner | |
1859.2.a.f.1.3 | 3 | 13.9 | even | 3 | |||
1859.2.a.g.1.1 | 3 | 13.4 | even | 6 |