Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [390,2,Mod(121,390)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(390, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("390.121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 390.bb (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.11416567883\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.17284886784.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 2x^{6} + 30x^{5} + 185x^{4} + 36x^{3} + 8x^{2} + 208x + 2704 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 121.1 | ||
Root | \(3.17270 + 3.17270i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 390.121 |
Dual form | 390.2.bb.c.361.1 |
$q$-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 \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).
\(n\) | \(131\) | \(157\) | \(301\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0.866025 | − | 0.500000i | 0.353553 | − | 0.204124i | ||||
\(7\) | −2.01141 | + | 1.16129i | −0.760243 | + | 0.438926i | −0.829383 | − | 0.558681i | \(-0.811308\pi\) |
0.0691402 | + | 0.997607i | \(0.477974\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −0.500000 | + | 0.866025i | −0.158114 | + | 0.273861i | ||||
\(11\) | 4.62926 | + | 2.67270i | 1.39577 | + | 0.805850i | 0.993946 | − | 0.109865i | \(-0.0350420\pi\) |
0.401827 | + | 0.915716i | \(0.368375\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −3.60194 | + | 0.161290i | −0.998999 | + | 0.0447338i | ||||
\(14\) | 2.32258 | 0.620736 | ||||||||
\(15\) | 0.866025 | + | 0.500000i | 0.223607 | + | 0.129099i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 2.00000 | + | 3.46410i | 0.485071 | + | 0.840168i | 0.999853 | − | 0.0171533i | \(-0.00546033\pi\) |
−0.514782 | + | 0.857321i | \(0.672127\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | −3.48387 | + | 2.01141i | −0.799254 | + | 0.461450i | −0.843210 | − | 0.537584i | \(-0.819337\pi\) |
0.0439559 | + | 0.999033i | \(0.486004\pi\) | |||||||
\(20\) | 0.866025 | − | 0.500000i | 0.193649 | − | 0.111803i | ||||
\(21\) | − | 2.32258i | − | 0.506828i | ||||||
\(22\) | −2.67270 | − | 4.62926i | −0.569822 | − | 0.986961i | ||||
\(23\) | −2.46797 | + | 4.27464i | −0.514607 | + | 0.891325i | 0.485250 | + | 0.874376i | \(0.338729\pi\) |
−0.999856 | + | 0.0169494i | \(0.994605\pi\) | |||||||
\(24\) | 0.866025 | + | 0.500000i | 0.176777 | + | 0.102062i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 3.20002 | + | 1.66129i | 0.627575 | + | 0.325806i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.01141 | − | 1.16129i | −0.380121 | − | 0.219463i | ||||
\(29\) | −2.14539 | + | 3.71592i | −0.398388 | + | 0.690029i | −0.993527 | − | 0.113594i | \(-0.963764\pi\) |
0.595139 | + | 0.803623i | \(0.297097\pi\) | |||||||
\(30\) | −0.500000 | − | 0.866025i | −0.0912871 | − | 0.158114i | ||||
\(31\) | 3.47183i | 0.623560i | 0.950154 | + | 0.311780i | \(0.100925\pi\) | ||||
−0.950154 | + | 0.311780i | \(0.899075\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | −4.62926 | + | 2.67270i | −0.805850 | + | 0.465258i | ||||
\(34\) | − | 4.00000i | − | 0.685994i | ||||||
\(35\) | 1.16129 | + | 2.01141i | 0.196294 | + | 0.339991i | ||||
\(36\) | 0.500000 | − | 0.866025i | 0.0833333 | − | 0.144338i | ||||
\(37\) | −2.72733 | − | 1.57463i | −0.448371 | − | 0.258867i | 0.258771 | − | 0.965939i | \(-0.416682\pi\) |
−0.707142 | + | 0.707072i | \(0.750016\pi\) | |||||||
\(38\) | 4.02283 | 0.652589 | ||||||||
\(39\) | 1.66129 | − | 3.20002i | 0.266019 | − | 0.512413i | ||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 2.29078 | + | 1.32258i | 0.357759 | + | 0.206552i | 0.668097 | − | 0.744074i | \(-0.267109\pi\) |
−0.310338 | + | 0.950626i | \(0.600442\pi\) | |||||||
\(42\) | −1.16129 | + | 2.01141i | −0.179191 | + | 0.310368i | ||||
\(43\) | 6.12539 | + | 10.6095i | 0.934113 | + | 1.61793i | 0.776207 | + | 0.630478i | \(0.217141\pi\) |
0.157906 | + | 0.987454i | \(0.449526\pi\) | |||||||
\(44\) | 5.34541i | 0.805850i | ||||||||
\(45\) | −0.866025 | + | 0.500000i | −0.129099 | + | 0.0745356i | ||||
\(46\) | 4.27464 | − | 2.46797i | 0.630262 | − | 0.363882i | ||||
\(47\) | − | 1.81894i | − | 0.265320i | −0.991162 | − | 0.132660i | \(-0.957648\pi\) | ||
0.991162 | − | 0.132660i | \(-0.0423518\pi\) | |||||||
\(48\) | −0.500000 | − | 0.866025i | −0.0721688 | − | 0.125000i | ||||
\(49\) | −0.802812 | + | 1.39051i | −0.114687 | + | 0.198644i | ||||
\(50\) | 0.866025 | + | 0.500000i | 0.122474 | + | 0.0707107i | ||||
\(51\) | −4.00000 | −0.560112 | ||||||||
\(52\) | −1.94065 | − | 3.03873i | −0.269120 | − | 0.421396i | ||||
\(53\) | −5.48693 | −0.753687 | −0.376844 | − | 0.926277i | \(-0.622991\pi\) | ||||
−0.376844 | + | 0.926277i | \(0.622991\pi\) | |||||||
\(54\) | −0.866025 | − | 0.500000i | −0.117851 | − | 0.0680414i | ||||
\(55\) | 2.67270 | − | 4.62926i | 0.360387 | − | 0.624209i | ||||
\(56\) | 1.16129 | + | 2.01141i | 0.155184 | + | 0.268786i | ||||
\(57\) | − | 4.02283i | − | 0.532836i | ||||||
\(58\) | 3.71592 | − | 2.14539i | 0.487924 | − | 0.281703i | ||||
\(59\) | 5.87744 | − | 3.39334i | 0.765177 | − | 0.441775i | −0.0659742 | − | 0.997821i | \(-0.521016\pi\) |
0.831152 | + | 0.556046i | \(0.187682\pi\) | |||||||
\(60\) | 1.00000i | 0.129099i | ||||||||
\(61\) | −0.267949 | − | 0.464102i | −0.0343074 | − | 0.0594221i | 0.848362 | − | 0.529417i | \(-0.177589\pi\) |
−0.882669 | + | 0.469995i | \(0.844256\pi\) | |||||||
\(62\) | 1.73592 | − | 3.00670i | 0.220462 | − | 0.381851i | ||||
\(63\) | 2.01141 | + | 1.16129i | 0.253414 | + | 0.146309i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0.161290 | + | 3.60194i | 0.0200055 | + | 0.446766i | ||||
\(66\) | 5.34541 | 0.657974 | ||||||||
\(67\) | 3.55872 | + | 2.05463i | 0.434767 | + | 0.251013i | 0.701376 | − | 0.712792i | \(-0.252570\pi\) |
−0.266608 | + | 0.963805i | \(0.585903\pi\) | |||||||
\(68\) | −2.00000 | + | 3.46410i | −0.242536 | + | 0.420084i | ||||
\(69\) | −2.46797 | − | 4.27464i | −0.297108 | − | 0.514607i | ||||
\(70\) | − | 2.32258i | − | 0.277601i | ||||||
\(71\) | 13.7454 | − | 7.93593i | 1.63128 | − | 0.941822i | 0.647586 | − | 0.761992i | \(-0.275779\pi\) |
0.983698 | − | 0.179830i | \(-0.0575547\pi\) | |||||||
\(72\) | −0.866025 | + | 0.500000i | −0.102062 | + | 0.0589256i | ||||
\(73\) | − | 13.5734i | − | 1.58864i | −0.607498 | − | 0.794321i | \(-0.707827\pi\) | ||
0.607498 | − | 0.794321i | \(-0.292173\pi\) | |||||||
\(74\) | 1.57463 | + | 2.72733i | 0.183047 | + | 0.317046i | ||||
\(75\) | 0.500000 | − | 0.866025i | 0.0577350 | − | 0.100000i | ||||
\(76\) | −3.48387 | − | 2.01141i | −0.399627 | − | 0.230725i | ||||
\(77\) | −12.4151 | −1.41484 | ||||||||
\(78\) | −3.03873 | + | 1.94065i | −0.344068 | + | 0.219736i | ||||
\(79\) | −7.96774 | −0.896441 | −0.448220 | − | 0.893923i | \(-0.647942\pi\) | ||||
−0.448220 | + | 0.893923i | \(0.647942\pi\) | |||||||
\(80\) | 0.866025 | + | 0.500000i | 0.0968246 | + | 0.0559017i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −1.32258 | − | 2.29078i | −0.146054 | − | 0.252974i | ||||
\(83\) | − | 11.3360i | − | 1.24428i | −0.782904 | − | 0.622142i | \(-0.786263\pi\) | ||
0.782904 | − | 0.622142i | \(-0.213737\pi\) | |||||||
\(84\) | 2.01141 | − | 1.16129i | 0.219463 | − | 0.126707i | ||||
\(85\) | 3.46410 | − | 2.00000i | 0.375735 | − | 0.216930i | ||||
\(86\) | − | 12.2508i | − | 1.32104i | ||||||
\(87\) | −2.14539 | − | 3.71592i | −0.230010 | − | 0.398388i | ||||
\(88\) | 2.67270 | − | 4.62926i | 0.284911 | − | 0.493480i | ||||
\(89\) | −1.50670 | − | 0.869891i | −0.159709 | − | 0.0922083i | 0.418015 | − | 0.908440i | \(-0.362726\pi\) |
−0.577725 | + | 0.816232i | \(0.696059\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 7.05769 | − | 4.50732i | 0.739847 | − | 0.472495i | ||||
\(92\) | −4.93593 | −0.514607 | ||||||||
\(93\) | −3.00670 | − | 1.73592i | −0.311780 | − | 0.180006i | ||||
\(94\) | −0.909471 | + | 1.57525i | −0.0938048 | + | 0.162475i | ||||
\(95\) | 2.01141 | + | 3.48387i | 0.206367 | + | 0.357437i | ||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | −13.9510 | + | 8.05463i | −1.41651 | + | 0.817824i | −0.995991 | − | 0.0894586i | \(-0.971486\pi\) |
−0.420522 | + | 0.907282i | \(0.638153\pi\) | |||||||
\(98\) | 1.39051 | − | 0.802812i | 0.140463 | − | 0.0810962i | ||||
\(99\) | − | 5.34541i | − | 0.537233i | ||||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | 6.34541 | − | 10.9906i | 0.631391 | − | 1.09360i | −0.355876 | − | 0.934533i | \(-0.615817\pi\) |
0.987267 | − | 0.159069i | \(-0.0508492\pi\) | |||||||
\(102\) | 3.46410 | + | 2.00000i | 0.342997 | + | 0.198030i | ||||
\(103\) | −4.79612 | −0.472575 | −0.236288 | − | 0.971683i | \(-0.575931\pi\) | ||||
−0.236288 | + | 0.971683i | \(0.575931\pi\) | |||||||
\(104\) | 0.161290 | + | 3.60194i | 0.0158158 | + | 0.353199i | ||||
\(105\) | −2.32258 | −0.226661 | ||||||||
\(106\) | 4.75182 | + | 2.74346i | 0.461537 | + | 0.266469i | ||||
\(107\) | −1.53590 | + | 2.66025i | −0.148481 | + | 0.257176i | −0.930666 | − | 0.365869i | \(-0.880772\pi\) |
0.782185 | + | 0.623046i | \(0.214105\pi\) | |||||||
\(108\) | 0.500000 | + | 0.866025i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | − | 6.69081i | − | 0.640864i | −0.947272 | − | 0.320432i | \(-0.896172\pi\) | ||
0.947272 | − | 0.320432i | \(-0.103828\pi\) | |||||||
\(110\) | −4.62926 | + | 2.67270i | −0.441382 | + | 0.254832i | ||||
\(111\) | 2.72733 | − | 1.57463i | 0.258867 | − | 0.149457i | ||||
\(112\) | − | 2.32258i | − | 0.219463i | ||||||
\(113\) | 3.55486 | + | 6.15720i | 0.334413 | + | 0.579220i | 0.983372 | − | 0.181603i | \(-0.0581286\pi\) |
−0.648959 | + | 0.760823i | \(0.724795\pi\) | |||||||
\(114\) | −2.01141 | + | 3.48387i | −0.188386 | + | 0.326294i | ||||
\(115\) | 4.27464 | + | 2.46797i | 0.398613 | + | 0.230139i | ||||
\(116\) | −4.29078 | −0.398388 | ||||||||
\(117\) | 1.94065 | + | 3.03873i | 0.179413 | + | 0.280931i | ||||
\(118\) | −6.78668 | −0.624765 | ||||||||
\(119\) | −8.04565 | − | 4.64516i | −0.737544 | − | 0.425821i | ||||
\(120\) | 0.500000 | − | 0.866025i | 0.0456435 | − | 0.0790569i | ||||
\(121\) | 8.78668 | + | 15.2190i | 0.798789 | + | 1.38354i | ||||
\(122\) | 0.535898i | 0.0485180i | ||||||||
\(123\) | −2.29078 | + | 1.32258i | −0.206552 | + | 0.119253i | ||||
\(124\) | −3.00670 | + | 1.73592i | −0.270009 | + | 0.155890i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −1.16129 | − | 2.01141i | −0.103456 | − | 0.179191i | ||||
\(127\) | −1.06604 | + | 1.84644i | −0.0945961 | + | 0.163845i | −0.909440 | − | 0.415835i | \(-0.863489\pi\) |
0.814844 | + | 0.579680i | \(0.196823\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | −12.2508 | −1.07862 | ||||||||
\(130\) | 1.66129 | − | 3.20002i | 0.145705 | − | 0.280660i | ||||
\(131\) | 1.25851 | 0.109957 | 0.0549785 | − | 0.998488i | \(-0.482491\pi\) | ||||
0.0549785 | + | 0.998488i | \(0.482491\pi\) | |||||||
\(132\) | −4.62926 | − | 2.67270i | −0.402925 | − | 0.232629i | ||||
\(133\) | 4.67167 | − | 8.09156i | 0.405085 | − | 0.701628i | ||||
\(134\) | −2.05463 | − | 3.55872i | −0.177493 | − | 0.307427i | ||||
\(135\) | − | 1.00000i | − | 0.0860663i | ||||||
\(136\) | 3.46410 | − | 2.00000i | 0.297044 | − | 0.171499i | ||||
\(137\) | 17.0736 | − | 9.85744i | 1.45870 | − | 0.842178i | 0.459748 | − | 0.888049i | \(-0.347940\pi\) |
0.998947 | + | 0.0458713i | \(0.0146064\pi\) | |||||||
\(138\) | 4.93593i | 0.420175i | ||||||||
\(139\) | −2.83871 | − | 4.91679i | −0.240776 | − | 0.417037i | 0.720159 | − | 0.693809i | \(-0.244069\pi\) |
−0.960936 | + | 0.276772i | \(0.910735\pi\) | |||||||
\(140\) | −1.16129 | + | 2.01141i | −0.0981469 | + | 0.169995i | ||||
\(141\) | 1.57525 | + | 0.909471i | 0.132660 | + | 0.0765913i | ||||
\(142\) | −15.8719 | −1.33194 | ||||||||
\(143\) | −17.1054 | − | 8.88027i | −1.43043 | − | 0.742605i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 3.71592 | + | 2.14539i | 0.308590 | + | 0.178165i | ||||
\(146\) | −6.78668 | + | 11.7549i | −0.561670 | + | 0.972841i | ||||
\(147\) | −0.802812 | − | 1.39051i | −0.0662148 | − | 0.114687i | ||||
\(148\) | − | 3.14925i | − | 0.258867i | ||||||
\(149\) | −16.8680 | + | 9.73875i | −1.38188 | + | 0.797829i | −0.992382 | − | 0.123198i | \(-0.960685\pi\) |
−0.389499 | + | 0.921027i | \(0.627352\pi\) | |||||||
\(150\) | −0.866025 | + | 0.500000i | −0.0707107 | + | 0.0408248i | ||||
\(151\) | 14.5170i | 1.18138i | 0.806899 | + | 0.590690i | \(0.201144\pi\) | ||||
−0.806899 | + | 0.590690i | \(0.798856\pi\) | |||||||
\(152\) | 2.01141 | + | 3.48387i | 0.163147 | + | 0.282579i | ||||
\(153\) | 2.00000 | − | 3.46410i | 0.161690 | − | 0.280056i | ||||
\(154\) | 10.7518 | + | 6.20757i | 0.866406 | + | 0.500220i | ||||
\(155\) | 3.47183 | 0.278864 | ||||||||
\(156\) | 3.60194 | − | 0.161290i | 0.288386 | − | 0.0129135i | ||||
\(157\) | 24.3829 | 1.94596 | 0.972982 | − | 0.230879i | \(-0.0741602\pi\) | ||||
0.972982 | + | 0.230879i | \(0.0741602\pi\) | |||||||
\(158\) | 6.90026 | + | 3.98387i | 0.548956 | + | 0.316940i | ||||
\(159\) | 2.74346 | − | 4.75182i | 0.217571 | − | 0.376844i | ||||
\(160\) | −0.500000 | − | 0.866025i | −0.0395285 | − | 0.0684653i | ||||
\(161\) | − | 11.4641i | − | 0.903498i | ||||||
\(162\) | 0.866025 | − | 0.500000i | 0.0680414 | − | 0.0392837i | ||||
\(163\) | 20.4614 | − | 11.8134i | 1.60266 | − | 0.925295i | 0.611704 | − | 0.791086i | \(-0.290484\pi\) |
0.990953 | − | 0.134208i | \(-0.0428492\pi\) | |||||||
\(164\) | 2.64516i | 0.206552i | ||||||||
\(165\) | 2.67270 | + | 4.62926i | 0.208070 | + | 0.360387i | ||||
\(166\) | −5.66799 | + | 9.81724i | −0.439921 | + | 0.761966i | ||||
\(167\) | 14.5035 | + | 8.37357i | 1.12231 | + | 0.647967i | 0.941990 | − | 0.335641i | \(-0.108953\pi\) |
0.180321 | + | 0.983608i | \(0.442286\pi\) | |||||||
\(168\) | −2.32258 | −0.179191 | ||||||||
\(169\) | 12.9480 | − | 1.16191i | 0.995998 | − | 0.0893780i | ||||
\(170\) | −4.00000 | −0.306786 | ||||||||
\(171\) | 3.48387 | + | 2.01141i | 0.266418 | + | 0.153817i | ||||
\(172\) | −6.12539 | + | 10.6095i | −0.467057 | + | 0.808966i | ||||
\(173\) | 8.06604 | + | 13.9708i | 0.613250 | + | 1.06218i | 0.990689 | + | 0.136146i | \(0.0434715\pi\) |
−0.377439 | + | 0.926034i | \(0.623195\pi\) | |||||||
\(174\) | 4.29078i | 0.325283i | ||||||||
\(175\) | 2.01141 | − | 1.16129i | 0.152049 | − | 0.0877853i | ||||
\(176\) | −4.62926 | + | 2.67270i | −0.348943 | + | 0.201463i | ||||
\(177\) | 6.78668i | 0.510118i | ||||||||
\(178\) | 0.869891 | + | 1.50670i | 0.0652011 | + | 0.112932i | ||||
\(179\) | 3.66412 | − | 6.34644i | 0.273869 | − | 0.474355i | −0.695980 | − | 0.718061i | \(-0.745030\pi\) |
0.969849 | + | 0.243706i | \(0.0783631\pi\) | |||||||
\(180\) | −0.866025 | − | 0.500000i | −0.0645497 | − | 0.0372678i | ||||
\(181\) | −19.5734 | −1.45488 | −0.727438 | − | 0.686173i | \(-0.759289\pi\) | ||||
−0.727438 | + | 0.686173i | \(0.759289\pi\) | |||||||
\(182\) | −8.36580 | + | 0.374609i | −0.620114 | + | 0.0277678i | ||||
\(183\) | 0.535898 | 0.0396147 | ||||||||
\(184\) | 4.27464 | + | 2.46797i | 0.315131 | + | 0.181941i | ||||
\(185\) | −1.57463 | + | 2.72733i | −0.115769 | + | 0.200518i | ||||
\(186\) | 1.73592 | + | 3.00670i | 0.127284 | + | 0.220462i | ||||
\(187\) | 21.3816i | 1.56358i | ||||||||
\(188\) | 1.57525 | − | 0.909471i | 0.114887 | − | 0.0663300i | ||||
\(189\) | −2.01141 | + | 1.16129i | −0.146309 | + | 0.0844714i | ||||
\(190\) | − | 4.02283i | − | 0.291846i | ||||||
\(191\) | 8.51873 | + | 14.7549i | 0.616394 | + | 1.06763i | 0.990138 | + | 0.140094i | \(0.0447404\pi\) |
−0.373744 | + | 0.927532i | \(0.621926\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | 5.33031 | + | 3.07746i | 0.383684 | + | 0.221520i | 0.679420 | − | 0.733750i | \(-0.262231\pi\) |
−0.295736 | + | 0.955270i | \(0.595565\pi\) | |||||||
\(194\) | 16.1093 | 1.15658 | ||||||||
\(195\) | −3.20002 | − | 1.66129i | −0.229158 | − | 0.118967i | ||||
\(196\) | −1.60562 | −0.114687 | ||||||||
\(197\) | −11.9396 | − | 6.89334i | −0.850662 | − | 0.491130i | 0.0102119 | − | 0.999948i | \(-0.496749\pi\) |
−0.860874 | + | 0.508818i | \(0.830083\pi\) | |||||||
\(198\) | −2.67270 | + | 4.62926i | −0.189941 | + | 0.328987i | ||||
\(199\) | 1.14152 | + | 1.97717i | 0.0809203 | + | 0.140158i | 0.903646 | − | 0.428281i | \(-0.140881\pi\) |
−0.822725 | + | 0.568439i | \(0.807547\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | −3.55872 | + | 2.05463i | −0.251013 | + | 0.144922i | ||||
\(202\) | −10.9906 | + | 6.34541i | −0.773293 | + | 0.446461i | ||||
\(203\) | − | 9.96567i | − | 0.699453i | ||||||
\(204\) | −2.00000 | − | 3.46410i | −0.140028 | − | 0.242536i | ||||
\(205\) | 1.32258 | − | 2.29078i | 0.0923730 | − | 0.159995i | ||||
\(206\) | 4.15356 | + | 2.39806i | 0.289392 | + | 0.167081i | ||||
\(207\) | 4.93593 | 0.343071 | ||||||||
\(208\) | 1.66129 | − | 3.20002i | 0.115190 | − | 0.221881i | ||||
\(209\) | −21.5036 | −1.48744 | ||||||||
\(210\) | 2.01141 | + | 1.16129i | 0.138801 | + | 0.0801366i | ||||
\(211\) | −11.2387 | + | 19.4661i | −0.773707 | + | 1.34010i | 0.161811 | + | 0.986822i | \(0.448267\pi\) |
−0.935518 | + | 0.353278i | \(0.885067\pi\) | |||||||
\(212\) | −2.74346 | − | 4.75182i | −0.188422 | − | 0.326356i | ||||
\(213\) | 15.8719i | 1.08752i | ||||||||
\(214\) | 2.66025 | − | 1.53590i | 0.181851 | − | 0.104992i | ||||
\(215\) | 10.6095 | − | 6.12539i | 0.723561 | − | 0.417748i | ||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | −4.03180 | − | 6.98329i | −0.273697 | − | 0.474057i | ||||
\(218\) | −3.34541 | + | 5.79441i | −0.226579 | + | 0.392447i | ||||
\(219\) | 11.7549 | + | 6.78668i | 0.794321 | + | 0.458601i | ||||
\(220\) | 5.34541 | 0.360387 | ||||||||
\(221\) | −7.76261 | − | 12.1549i | −0.522170 | − | 0.817628i | ||||
\(222\) | −3.14925 | −0.211364 | ||||||||
\(223\) | 1.19417 | + | 0.689457i | 0.0799678 | + | 0.0461694i | 0.539451 | − | 0.842017i | \(-0.318632\pi\) |
−0.459483 | + | 0.888187i | \(0.651965\pi\) | |||||||
\(224\) | −1.16129 | + | 2.01141i | −0.0775919 | + | 0.134393i | ||||
\(225\) | 0.500000 | + | 0.866025i | 0.0333333 | + | 0.0577350i | ||||
\(226\) | − | 7.10972i | − | 0.472931i | ||||||
\(227\) | −16.7321 | + | 9.66025i | −1.11055 | + | 0.641174i | −0.938971 | − | 0.343998i | \(-0.888219\pi\) |
−0.171575 | + | 0.985171i | \(0.554885\pi\) | |||||||
\(228\) | 3.48387 | − | 2.01141i | 0.230725 | − | 0.133209i | ||||
\(229\) | − | 15.7626i | − | 1.04162i | −0.853672 | − | 0.520811i | \(-0.825630\pi\) | ||
0.853672 | − | 0.520811i | \(-0.174370\pi\) | |||||||
\(230\) | −2.46797 | − | 4.27464i | −0.162733 | − | 0.281862i | ||||
\(231\) | 6.20757 | − | 10.7518i | 0.408428 | − | 0.707418i | ||||
\(232\) | 3.71592 | + | 2.14539i | 0.243962 | + | 0.140852i | ||||
\(233\) | −16.5549 | −1.08455 | −0.542275 | − | 0.840201i | \(-0.682437\pi\) | ||||
−0.542275 | + | 0.840201i | \(0.682437\pi\) | |||||||
\(234\) | −0.161290 | − | 3.60194i | −0.0105438 | − | 0.235466i | ||||
\(235\) | −1.81894 | −0.118655 | ||||||||
\(236\) | 5.87744 | + | 3.39334i | 0.382589 | + | 0.220888i | ||||
\(237\) | 3.98387 | − | 6.90026i | 0.258780 | − | 0.448220i | ||||
\(238\) | 4.64516 | + | 8.04565i | 0.301101 | + | 0.521522i | ||||
\(239\) | 26.2006i | 1.69477i | 0.530976 | + | 0.847387i | \(0.321825\pi\) | ||||
−0.530976 | + | 0.847387i | \(0.678175\pi\) | |||||||
\(240\) | −0.866025 | + | 0.500000i | −0.0559017 | + | 0.0322749i | ||||
\(241\) | −13.5529 | + | 7.82479i | −0.873021 | + | 0.504039i | −0.868351 | − | 0.495950i | \(-0.834820\pi\) |
−0.00466988 | + | 0.999989i | \(0.501486\pi\) | |||||||
\(242\) | − | 17.5734i | − | 1.12966i | ||||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 0.267949 | − | 0.464102i | 0.0171537 | − | 0.0297111i | ||||
\(245\) | 1.39051 | + | 0.802812i | 0.0888365 | + | 0.0512898i | ||||
\(246\) | 2.64516 | 0.168649 | ||||||||
\(247\) | 12.2243 | − | 7.80691i | 0.777812 | − | 0.496742i | ||||
\(248\) | 3.47183 | 0.220462 | ||||||||
\(249\) | 9.81724 | + | 5.66799i | 0.622142 | + | 0.359194i | ||||
\(250\) | 0.500000 | − | 0.866025i | 0.0316228 | − | 0.0547723i | ||||
\(251\) | −14.1708 | − | 24.5446i | −0.894454 | − | 1.54924i | −0.834479 | − | 0.551040i | \(-0.814231\pi\) |
−0.0599750 | − | 0.998200i | \(-0.519102\pi\) | |||||||
\(252\) | 2.32258i | 0.146309i | ||||||||
\(253\) | −22.8497 | + | 13.1923i | −1.43655 | + | 0.829392i | ||||
\(254\) | 1.84644 | − | 1.06604i | 0.115856 | − | 0.0668895i | ||||
\(255\) | 4.00000i | 0.250490i | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −6.25465 | + | 10.8334i | −0.390154 | + | 0.675767i | −0.992470 | − | 0.122491i | \(-0.960912\pi\) |
0.602315 | + | 0.798258i | \(0.294245\pi\) | |||||||
\(258\) | 10.6095 | + | 6.12539i | 0.660518 | + | 0.381350i | ||||
\(259\) | 7.31439 | 0.454494 | ||||||||
\(260\) | −3.03873 | + | 1.94065i | −0.188454 | + | 0.120354i | ||||
\(261\) | 4.29078 | 0.265592 | ||||||||
\(262\) | −1.08991 | − | 0.629257i | −0.0673346 | − | 0.0388756i | ||||
\(263\) | 5.35295 | − | 9.27159i | 0.330077 | − | 0.571711i | −0.652449 | − | 0.757832i | \(-0.726259\pi\) |
0.982527 | + | 0.186122i | \(0.0595919\pi\) | |||||||
\(264\) | 2.67270 | + | 4.62926i | 0.164493 | + | 0.284911i | ||||
\(265\) | 5.48693i | 0.337059i | ||||||||
\(266\) | −8.09156 | + | 4.67167i | −0.496126 | + | 0.286438i | ||||
\(267\) | 1.50670 | − | 0.869891i | 0.0922083 | − | 0.0532365i | ||||
\(268\) | 4.10926i | 0.251013i | ||||||||
\(269\) | −3.76261 | − | 6.51703i | −0.229410 | − | 0.397350i | 0.728223 | − | 0.685340i | \(-0.240346\pi\) |
−0.957633 | + | 0.287990i | \(0.907013\pi\) | |||||||
\(270\) | −0.500000 | + | 0.866025i | −0.0304290 | + | 0.0527046i | ||||
\(271\) | 8.52920 | + | 4.92434i | 0.518112 | + | 0.299132i | 0.736162 | − | 0.676805i | \(-0.236636\pi\) |
−0.218050 | + | 0.975938i | \(0.569970\pi\) | |||||||
\(272\) | −4.00000 | −0.242536 | ||||||||
\(273\) | 0.374609 | + | 8.36580i | 0.0226723 | + | 0.506321i | ||||
\(274\) | −19.7149 | −1.19102 | ||||||||
\(275\) | −4.62926 | − | 2.67270i | −0.279155 | − | 0.161170i | ||||
\(276\) | 2.46797 | − | 4.27464i | 0.148554 | − | 0.257303i | ||||
\(277\) | 0.476550 | + | 0.825410i | 0.0286331 | + | 0.0495941i | 0.879987 | − | 0.474998i | \(-0.157551\pi\) |
−0.851354 | + | 0.524592i | \(0.824218\pi\) | |||||||
\(278\) | 5.67742i | 0.340509i | ||||||||
\(279\) | 3.00670 | − | 1.73592i | 0.180006 | − | 0.103927i | ||||
\(280\) | 2.01141 | − | 1.16129i | 0.120205 | − | 0.0694003i | ||||
\(281\) | − | 5.57336i | − | 0.332479i | −0.986085 | − | 0.166239i | \(-0.946838\pi\) | ||
0.986085 | − | 0.166239i | \(-0.0531625\pi\) | |||||||
\(282\) | −0.909471 | − | 1.57525i | −0.0541582 | − | 0.0938048i | ||||
\(283\) | 11.0067 | − | 19.0642i | 0.654280 | − | 1.13325i | −0.327794 | − | 0.944749i | \(-0.606305\pi\) |
0.982074 | − | 0.188497i | \(-0.0603616\pi\) | |||||||
\(284\) | 13.7454 | + | 7.93593i | 0.815642 | + | 0.470911i | ||||
\(285\) | −4.02283 | −0.238292 | ||||||||
\(286\) | 10.3736 | + | 16.2432i | 0.613402 | + | 0.960483i | ||||
\(287\) | −6.14359 | −0.362645 | ||||||||
\(288\) | −0.866025 | − | 0.500000i | −0.0510310 | − | 0.0294628i | ||||
\(289\) | 0.500000 | − | 0.866025i | 0.0294118 | − | 0.0509427i | ||||
\(290\) | −2.14539 | − | 3.71592i | −0.125981 | − | 0.218206i | ||||
\(291\) | − | 16.1093i | − | 0.944342i | ||||||
\(292\) | 11.7549 | − | 6.78668i | 0.687902 | − | 0.397160i | ||||
\(293\) | 5.92623 | − | 3.42151i | 0.346214 | − | 0.199887i | −0.316803 | − | 0.948491i | \(-0.602609\pi\) |
0.663016 | + | 0.748605i | \(0.269276\pi\) | |||||||
\(294\) | 1.60562i | 0.0936419i | ||||||||
\(295\) | −3.39334 | − | 5.87744i | −0.197568 | − | 0.342198i | ||||
\(296\) | −1.57463 | + | 2.72733i | −0.0915233 | + | 0.158523i | ||||
\(297\) | 4.62926 | + | 2.67270i | 0.268617 | + | 0.155086i | ||||
\(298\) | 19.4775 | 1.12830 | ||||||||
\(299\) | 8.20002 | − | 15.7951i | 0.474219 | − | 0.913453i | ||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | −24.6414 | − | 14.2267i | −1.42031 | − | 0.820014i | ||||
\(302\) | 7.25851 | − | 12.5721i | 0.417681 | − | 0.723444i | ||||
\(303\) | 6.34541 | + | 10.9906i | 0.364534 | + | 0.631391i | ||||
\(304\) | − | 4.02283i | − | 0.230725i | ||||||
\(305\) | −0.464102 | + | 0.267949i | −0.0265744 | + | 0.0153427i | ||||
\(306\) | −3.46410 | + | 2.00000i | −0.198030 | + | 0.114332i | ||||
\(307\) | − | 4.75442i | − | 0.271349i | −0.990753 | − | 0.135675i | \(-0.956680\pi\) | ||
0.990753 | − | 0.135675i | \(-0.0433202\pi\) | |||||||
\(308\) | −6.20757 | − | 10.7518i | −0.353709 | − | 0.612642i | ||||
\(309\) | 2.39806 | − | 4.15356i | 0.136421 | − | 0.236288i | ||||
\(310\) | −3.00670 | − | 1.73592i | −0.170769 | − | 0.0985934i | ||||
\(311\) | 1.93639 | 0.109803 | 0.0549013 | − | 0.998492i | \(-0.482516\pi\) | ||||
0.0549013 | + | 0.998492i | \(0.482516\pi\) | |||||||
\(312\) | −3.20002 | − | 1.66129i | −0.181165 | − | 0.0940520i | ||||
\(313\) | 25.5545 | 1.44443 | 0.722213 | − | 0.691671i | \(-0.243125\pi\) | ||||
0.722213 | + | 0.691671i | \(0.243125\pi\) | |||||||
\(314\) | −21.1162 | − | 12.1914i | −1.19166 | − | 0.688002i | ||||
\(315\) | 1.16129 | − | 2.01141i | 0.0654313 | − | 0.113330i | ||||
\(316\) | −3.98387 | − | 6.90026i | −0.224110 | − | 0.388170i | ||||
\(317\) | − | 12.6667i | − | 0.711435i | −0.934594 | − | 0.355717i | \(-0.884237\pi\) | ||
0.934594 | − | 0.355717i | \(-0.115763\pi\) | |||||||
\(318\) | −4.75182 | + | 2.74346i | −0.266469 | + | 0.153846i | ||||
\(319\) | −19.8631 | + | 11.4680i | −1.11212 | + | 0.642083i | ||||
\(320\) | 1.00000i | 0.0559017i | ||||||||
\(321\) | −1.53590 | − | 2.66025i | −0.0857255 | − | 0.148481i | ||||
\(322\) | −5.73205 | + | 9.92820i | −0.319435 | + | 0.553277i | ||||
\(323\) | −13.9355 | − | 8.04565i | −0.775391 | − | 0.447672i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 3.60194 | − | 0.161290i | 0.199800 | − | 0.00894675i | ||||
\(326\) | −23.6267 | −1.30856 | ||||||||
\(327\) | 5.79441 | + | 3.34541i | 0.320432 | + | 0.185001i | ||||
\(328\) | 1.32258 | − | 2.29078i | 0.0730272 | − | 0.126487i | ||||
\(329\) | 2.11232 | + | 3.65864i | 0.116456 | + | 0.201708i | ||||
\(330\) | − | 5.34541i | − | 0.294255i | ||||||
\(331\) | −20.5231 | + | 11.8490i | −1.12805 | + | 0.651282i | −0.943445 | − | 0.331530i | \(-0.892435\pi\) |
−0.184609 | + | 0.982812i | \(0.559102\pi\) | |||||||
\(332\) | 9.81724 | − | 5.66799i | 0.538791 | − | 0.311071i | ||||
\(333\) | 3.14925i | 0.172578i | ||||||||
\(334\) | −8.37357 | − | 14.5035i | −0.458182 | − | 0.793594i | ||||
\(335\) | 2.05463 | − | 3.55872i | 0.112256 | − | 0.194434i | ||||
\(336\) | 2.01141 | + | 1.16129i | 0.109732 | + | 0.0633536i | ||||
\(337\) | 19.5554 | 1.06525 | 0.532625 | − | 0.846351i | \(-0.321205\pi\) | ||||
0.532625 | + | 0.846351i | \(0.321205\pi\) | |||||||
\(338\) | −11.7942 | − | 5.46774i | −0.641521 | − | 0.297406i | ||||
\(339\) | −7.10972 | −0.386147 | ||||||||
\(340\) | 3.46410 | + | 2.00000i | 0.187867 | + | 0.108465i | ||||
\(341\) | −9.27918 | + | 16.0720i | −0.502496 | + | 0.870348i | ||||
\(342\) | −2.01141 | − | 3.48387i | −0.108765 | − | 0.188386i | ||||
\(343\) | − | 19.9872i | − | 1.07921i | ||||||
\(344\) | 10.6095 | − | 6.12539i | 0.572025 | − | 0.330259i | ||||
\(345\) | −4.27464 | + | 2.46797i | −0.230139 | + | 0.132871i | ||||
\(346\) | − | 16.1321i | − | 0.867266i | ||||||
\(347\) | 11.5187 | + | 19.9510i | 0.618358 | + | 1.07103i | 0.989785 | + | 0.142565i | \(0.0455351\pi\) |
−0.371427 | + | 0.928462i | \(0.621132\pi\) | |||||||
\(348\) | 2.14539 | − | 3.71592i | 0.115005 | − | 0.199194i | ||||
\(349\) | 13.2679 | + | 7.66025i | 0.710217 | + | 0.410044i | 0.811141 | − | 0.584850i | \(-0.198847\pi\) |
−0.100924 | + | 0.994894i | \(0.532180\pi\) | |||||||
\(350\) | −2.32258 | −0.124147 | ||||||||
\(351\) | −3.60194 | + | 0.161290i | −0.192257 | + | 0.00860902i | ||||
\(352\) | 5.34541 | 0.284911 | ||||||||
\(353\) | 24.6018 | + | 14.2039i | 1.30942 | + | 0.755996i | 0.982000 | − | 0.188881i | \(-0.0604860\pi\) |
0.327424 | + | 0.944877i | \(0.393819\pi\) | |||||||
\(354\) | 3.39334 | − | 5.87744i | 0.180354 | − | 0.312382i | ||||
\(355\) | −7.93593 | − | 13.7454i | −0.421196 | − | 0.729532i | ||||
\(356\) | − | 1.73978i | − | 0.0922083i | ||||||
\(357\) | 8.04565 | − | 4.64516i | 0.425821 | − | 0.245848i | ||||
\(358\) | −6.34644 | + | 3.66412i | −0.335420 | + | 0.193655i | ||||
\(359\) | 23.5734i | 1.24415i | 0.782956 | + | 0.622077i | \(0.213711\pi\) | ||||
−0.782956 | + | 0.622077i | \(0.786289\pi\) | |||||||
\(360\) | 0.500000 | + | 0.866025i | 0.0263523 | + | 0.0456435i | ||||
\(361\) | −1.40844 | + | 2.43948i | −0.0741282 | + | 0.128394i | ||||
\(362\) | 16.9510 | + | 9.78668i | 0.890926 | + | 0.514377i | ||||
\(363\) | −17.5734 | −0.922362 | ||||||||
\(364\) | 7.43230 | + | 3.85848i | 0.389558 | + | 0.202239i | ||||
\(365\) | −13.5734 | −0.710462 | ||||||||
\(366\) | −0.464102 | − | 0.267949i | −0.0242590 | − | 0.0140059i | ||||
\(367\) | −13.7454 | + | 23.8078i | −0.717506 | + | 1.24276i | 0.244479 | + | 0.969655i | \(0.421383\pi\) |
−0.961985 | + | 0.273103i | \(0.911950\pi\) | |||||||
\(368\) | −2.46797 | − | 4.27464i | −0.128652 | − | 0.222831i | ||||
\(369\) | − | 2.64516i | − | 0.137701i | ||||||
\(370\) | 2.72733 | − | 1.57463i | 0.141787 | − | 0.0818609i | ||||
\(371\) | 11.0365 | − | 6.37191i | 0.572985 | − | 0.330813i | ||||
\(372\) | − | 3.47183i | − | 0.180006i | ||||||
\(373\) | −13.1710 | − | 22.8129i | −0.681971 | − | 1.18121i | −0.974379 | − | 0.224914i | \(-0.927790\pi\) |
0.292408 | − | 0.956294i | \(-0.405544\pi\) | |||||||
\(374\) | 10.6908 | − | 18.5170i | 0.552809 | − | 0.957493i | ||||
\(375\) | −0.866025 | − | 0.500000i | −0.0447214 | − | 0.0258199i | ||||
\(376\) | −1.81894 | −0.0938048 | ||||||||
\(377\) | 7.12822 | − | 13.7306i | 0.367122 | − | 0.707160i | ||||
\(378\) | 2.32258 | 0.119461 | ||||||||
\(379\) | 0.388456 | + | 0.224275i | 0.0199537 | + | 0.0115202i | 0.509944 | − | 0.860208i | \(-0.329666\pi\) |
−0.489990 | + | 0.871728i | \(0.663000\pi\) | |||||||
\(380\) | −2.01141 | + | 3.48387i | −0.103183 | + | 0.178719i | ||||
\(381\) | −1.06604 | − | 1.84644i | −0.0546151 | − | 0.0945961i | ||||
\(382\) | − | 17.0375i | − | 0.871713i | ||||||
\(383\) | 10.4985 | − | 6.06133i | 0.536450 | − | 0.309719i | −0.207189 | − | 0.978301i | \(-0.566432\pi\) |
0.743639 | + | 0.668582i | \(0.233098\pi\) | |||||||
\(384\) | −0.866025 | + | 0.500000i | −0.0441942 | + | 0.0255155i | ||||
\(385\) | 12.4151i | 0.632734i | ||||||||
\(386\) | −3.07746 | − | 5.33031i | −0.156638 | − | 0.271306i | ||||
\(387\) | 6.12539 | − | 10.6095i | 0.311371 | − | 0.539311i | ||||
\(388\) | −13.9510 | − | 8.05463i | −0.708256 | − | 0.408912i | ||||
\(389\) | 18.6195 | 0.944045 | 0.472022 | − | 0.881587i | \(-0.343524\pi\) | ||||
0.472022 | + | 0.881587i | \(0.343524\pi\) | |||||||
\(390\) | 1.94065 | + | 3.03873i | 0.0982687 | + | 0.153872i | ||||
\(391\) | −19.7437 | −0.998484 | ||||||||
\(392\) | 1.39051 | + | 0.802812i | 0.0702314 | + | 0.0405481i | ||||
\(393\) | −0.629257 | + | 1.08991i | −0.0317418 | + | 0.0549785i | ||||
\(394\) | 6.89334 | + | 11.9396i | 0.347281 | + | 0.601509i | ||||
\(395\) | 7.96774i | 0.400900i | ||||||||
\(396\) | 4.62926 | − | 2.67270i | 0.232629 | − | 0.134308i | ||||
\(397\) | 9.78970 | − | 5.65208i | 0.491331 | − | 0.283670i | −0.233796 | − | 0.972286i | \(-0.575115\pi\) |
0.725126 | + | 0.688616i | \(0.241781\pi\) | |||||||
\(398\) | − | 2.28304i | − | 0.114439i | ||||||
\(399\) | 4.67167 | + | 8.09156i | 0.233876 | + | 0.405085i | ||||
\(400\) | 0.500000 | − | 0.866025i | 0.0250000 | − | 0.0433013i | ||||
\(401\) | −1.30406 | − | 0.752899i | −0.0651216 | − | 0.0375980i | 0.467086 | − | 0.884212i | \(-0.345304\pi\) |
−0.532207 | + | 0.846614i | \(0.678637\pi\) | |||||||
\(402\) | 4.10926 | 0.204951 | ||||||||
\(403\) | −0.559971 | − | 12.5053i | −0.0278942 | − | 0.622935i | ||||
\(404\) | 12.6908 | 0.631391 | ||||||||
\(405\) | 0.866025 | + | 0.500000i | 0.0430331 | + | 0.0248452i | ||||
\(406\) | −4.98283 | + | 8.63052i | −0.247294 | + | 0.428326i | ||||
\(407\) | −8.41702 | − | 14.5787i | −0.417216 | − | 0.722640i | ||||
\(408\) | 4.00000i | 0.198030i | ||||||||
\(409\) | 9.64697 | − | 5.56968i | 0.477012 | − | 0.275403i | −0.242158 | − | 0.970237i | \(-0.577855\pi\) |
0.719170 | + | 0.694834i | \(0.244522\pi\) | |||||||
\(410\) | −2.29078 | + | 1.32258i | −0.113133 | + | 0.0653176i | ||||
\(411\) | 19.7149i | 0.972464i | ||||||||
\(412\) | −2.39806 | − | 4.15356i | −0.118144 | − | 0.204631i | ||||
\(413\) | −7.88130 | + | 13.6508i | −0.387814 | + | 0.671713i | ||||
\(414\) | −4.27464 | − | 2.46797i | −0.210087 | − | 0.121294i | ||||
\(415\) | −11.3360 | −0.556461 | ||||||||
\(416\) | −3.03873 | + | 1.94065i | −0.148986 | + | 0.0951483i | ||||
\(417\) | 5.67742 | 0.278024 | ||||||||
\(418\) | 18.6227 | + | 10.7518i | 0.910866 | + | 0.525889i | ||||
\(419\) | 7.75488 | − | 13.4318i | 0.378851 | − | 0.656188i | −0.612045 | − | 0.790823i | \(-0.709653\pi\) |
0.990895 | + | 0.134635i | \(0.0429861\pi\) | |||||||
\(420\) | −1.16129 | − | 2.01141i | −0.0566651 | − | 0.0981469i | ||||
\(421\) | − | 39.4452i | − | 1.92244i | −0.275778 | − | 0.961221i | \(-0.588935\pi\) | ||
0.275778 | − | 0.961221i | \(-0.411065\pi\) | |||||||
\(422\) | 19.4661 | − | 11.2387i | 0.947594 | − | 0.547094i | ||||
\(423\) | −1.57525 | + | 0.909471i | −0.0765913 | + | 0.0442200i | ||||
\(424\) | 5.48693i | 0.266469i | ||||||||
\(425\) | −2.00000 | − | 3.46410i | −0.0970143 | − | 0.168034i | ||||
\(426\) | 7.93593 | − | 13.7454i | 0.384497 | − | 0.665969i | ||||
\(427\) | 1.07791 | + | 0.622333i | 0.0521639 | + | 0.0301168i | ||||
\(428\) | −3.07180 | −0.148481 | ||||||||
\(429\) | 16.2432 | − | 10.3736i | 0.784231 | − | 0.500841i | ||||
\(430\) | −12.2508 | −0.590785 | ||||||||
\(431\) | 1.86621 | + | 1.07746i | 0.0898921 | + | 0.0518993i | 0.544272 | − | 0.838909i | \(-0.316806\pi\) |
−0.454380 | + | 0.890808i | \(0.650139\pi\) | |||||||
\(432\) | −0.500000 | + | 0.866025i | −0.0240563 | + | 0.0416667i | ||||
\(433\) | 0.669689 | + | 1.15994i | 0.0321832 | + | 0.0557429i | 0.881668 | − | 0.471870i | \(-0.156421\pi\) |
−0.849485 | + | 0.527612i | \(0.823087\pi\) | |||||||
\(434\) | 8.06361i | 0.387066i | ||||||||
\(435\) | −3.71592 | + | 2.14539i | −0.178165 | + | 0.102863i | ||||
\(436\) | 5.79441 | − | 3.34541i | 0.277502 | − | 0.160216i | ||||
\(437\) | − | 19.8564i | − | 0.949861i | ||||||
\(438\) | −6.78668 | − | 11.7549i | −0.324280 | − | 0.561670i | ||||
\(439\) | −15.8490 | + | 27.4513i | −0.756434 | + | 1.31018i | 0.188225 | + | 0.982126i | \(0.439727\pi\) |
−0.944658 | + | 0.328055i | \(0.893607\pi\) | |||||||
\(440\) | −4.62926 | − | 2.67270i | −0.220691 | − | 0.127416i | ||||
\(441\) | 1.60562 | 0.0764583 | ||||||||
\(442\) | 0.645159 | + | 14.4078i | 0.0306871 | + | 0.685308i | ||||
\(443\) | −28.0904 | −1.33461 | −0.667307 | − | 0.744782i | \(-0.732553\pi\) | ||||
−0.667307 | + | 0.744782i | \(0.732553\pi\) | |||||||
\(444\) | 2.72733 | + | 1.57463i | 0.129434 | + | 0.0747285i | ||||
\(445\) | −0.869891 | + | 1.50670i | −0.0412368 | + | 0.0714242i | ||||
\(446\) | −0.689457 | − | 1.19417i | −0.0326467 | − | 0.0565458i | ||||
\(447\) | − | 19.4775i | − | 0.921254i | ||||||
\(448\) | 2.01141 | − | 1.16129i | 0.0950303 | − | 0.0548658i | ||||
\(449\) | 25.0426 | − | 14.4583i | 1.18183 | − | 0.682332i | 0.225395 | − | 0.974267i | \(-0.427633\pi\) |
0.956438 | + | 0.291936i | \(0.0942994\pi\) | |||||||
\(450\) | − | 1.00000i | − | 0.0471405i | ||||||
\(451\) | 7.06973 | + | 12.2451i | 0.332900 | + | 0.576600i | ||||
\(452\) | −3.55486 | + | 6.15720i | −0.167206 | + | 0.289610i | ||||
\(453\) | −12.5721 | − | 7.25851i | −0.590690 | − | 0.341035i | ||||
\(454\) | 19.3205 | 0.906756 | ||||||||
\(455\) | −4.50732 | − | 7.05769i | −0.211306 | − | 0.330870i | ||||
\(456\) | −4.02283 | −0.188386 | ||||||||
\(457\) | 8.39958 | + | 4.84950i | 0.392916 | + | 0.226850i | 0.683423 | − | 0.730023i | \(-0.260491\pi\) |
−0.290507 | + | 0.956873i | \(0.593824\pi\) | |||||||
\(458\) | −7.88130 | + | 13.6508i | −0.368269 | + | 0.637861i | ||||
\(459\) | 2.00000 | + | 3.46410i | 0.0933520 | + | 0.161690i | ||||
\(460\) | 4.93593i | 0.230139i | ||||||||
\(461\) | 10.3905 | − | 5.99896i | 0.483934 | − | 0.279400i | −0.238120 | − | 0.971236i | \(-0.576531\pi\) |
0.722055 | + | 0.691836i | \(0.243198\pi\) | |||||||
\(462\) | −10.7518 | + | 6.20757i | −0.500220 | + | 0.288802i | ||||
\(463\) | 6.42664i | 0.298671i | 0.988787 | + | 0.149336i | \(0.0477135\pi\) | ||||
−0.988787 | + | 0.149336i | \(0.952287\pi\) | |||||||
\(464\) | −2.14539 | − | 3.71592i | −0.0995971 | − | 0.172507i | ||||
\(465\) | −1.73592 | + | 3.00670i | −0.0805012 | + | 0.139432i | ||||
\(466\) | 14.3370 | + | 8.27747i | 0.664149 | + | 0.383447i | ||||
\(467\) | 26.2642 | 1.21536 | 0.607681 | − | 0.794182i | \(-0.292100\pi\) | ||||
0.607681 | + | 0.794182i | \(0.292100\pi\) | |||||||
\(468\) | −1.66129 | + | 3.20002i | −0.0767932 | + | 0.147921i | ||||
\(469\) | −9.54409 | −0.440705 | ||||||||
\(470\) | 1.57525 | + | 0.909471i | 0.0726609 | + | 0.0419508i | ||||
\(471\) | −12.1914 | + | 21.1162i | −0.561752 | + | 0.972982i | ||||
\(472\) | −3.39334 | − | 5.87744i | −0.156191 | − | 0.270531i | ||||
\(473\) | 65.4854i | 3.01102i | ||||||||
\(474\) | −6.90026 | + | 3.98387i | −0.316940 | + | 0.182985i | ||||
\(475\) | 3.48387 | − | 2.01141i | 0.159851 | − | 0.0922900i | ||||
\(476\) | − | 9.29032i | − | 0.425821i | ||||||
\(477\) | 2.74346 | + | 4.75182i | 0.125615 | + | 0.217571i | ||||
\(478\) | 13.1003 | − | 22.6904i | 0.599193 | − | 1.03783i | ||||
\(479\) | −22.2418 | − | 12.8413i | −1.01625 | − | 0.586735i | −0.103237 | − | 0.994657i | \(-0.532920\pi\) |
−0.913017 | + | 0.407922i | \(0.866253\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | 10.0777 | + | 5.23182i | 0.459502 | + | 0.238551i | ||||
\(482\) | 15.6496 | 0.712818 | ||||||||
\(483\) | 9.92820 | + | 5.73205i | 0.451749 | + | 0.260817i | ||||
\(484\) | −8.78668 | + | 15.2190i | −0.399395 | + | 0.691772i | ||||
\(485\) | 8.05463 | + | 13.9510i | 0.365742 | + | 0.633484i | ||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | −8.12238 | + | 4.68946i | −0.368060 | + | 0.212500i | −0.672611 | − | 0.739997i | \(-0.734827\pi\) |
0.304551 | + | 0.952496i | \(0.401494\pi\) | |||||||
\(488\) | −0.464102 | + | 0.267949i | −0.0210089 | + | 0.0121295i | ||||
\(489\) | 23.6267i | 1.06844i | ||||||||
\(490\) | −0.802812 | − | 1.39051i | −0.0362673 | − | 0.0628169i | ||||
\(491\) | −3.86927 | + | 6.70177i | −0.174618 | + | 0.302447i | −0.940029 | − | 0.341095i | \(-0.889202\pi\) |
0.765411 | + | 0.643541i | \(0.222536\pi\) | |||||||
\(492\) | −2.29078 | − | 1.32258i | −0.103276 | − | 0.0596265i | ||||
\(493\) | −17.1631 | −0.772987 | ||||||||
\(494\) | −14.4900 | + | 0.648841i | −0.651935 | + | 0.0291927i | ||||
\(495\) | −5.34541 | −0.240258 | ||||||||
\(496\) | −3.00670 | − | 1.73592i | −0.135005 | − | 0.0779450i | ||||
\(497\) | −18.4318 | + | 31.9249i | −0.826781 | + | 1.43203i | ||||
\(498\) | −5.66799 | − | 9.81724i | −0.253989 | − | 0.439921i | ||||
\(499\) | 3.18106i | 0.142404i | 0.997462 | + | 0.0712019i | \(0.0226834\pi\) | ||||
−0.997462 | + | 0.0712019i | \(0.977317\pi\) | |||||||
\(500\) | −0.866025 | + | 0.500000i | −0.0387298 | + | 0.0223607i | ||||
\(501\) | −14.5035 | + | 8.37357i | −0.647967 | + | 0.374104i | ||||
\(502\) | 28.3416i | 1.26495i | ||||||||
\(503\) | 17.5379 | + | 30.3765i | 0.781975 | + | 1.35442i | 0.930789 | + | 0.365556i | \(0.119121\pi\) |
−0.148814 | + | 0.988865i | \(0.547546\pi\) | |||||||
\(504\) | 1.16129 | − | 2.01141i | 0.0517280 | − | 0.0895955i | ||||
\(505\) | −10.9906 | − | 6.34541i | −0.489074 | − | 0.282367i | ||||
\(506\) | 26.3846 | 1.17294 | ||||||||
\(507\) | −5.46774 | + | 11.7942i | −0.242831 | + | 0.523800i | ||||
\(508\) | −2.13209 | −0.0945961 | ||||||||
\(509\) | −16.2697 | − | 9.39334i | −0.721144 | − | 0.416353i | 0.0940298 | − | 0.995569i | \(-0.470025\pi\) |
−0.815173 | + | 0.579217i | \(0.803358\pi\) | |||||||
\(510\) | 2.00000 | − | 3.46410i | 0.0885615 | − | 0.153393i | ||||
\(511\) | 15.7626 | + | 27.3016i | 0.697297 | + | 1.20775i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −3.48387 | + | 2.01141i | −0.153817 | + | 0.0888061i | ||||
\(514\) | 10.8334 | − | 6.25465i | 0.477839 | − | 0.275881i | ||||
\(515\) | 4.79612i | 0.211342i | ||||||||
\(516\) | −6.12539 | − | 10.6095i | −0.269655 | − | 0.467057i | ||||
\(517\) | 4.86149 | − | 8.42035i | 0.213808 | − | 0.370327i | ||||
\(518\) | −6.33445 | − | 3.65720i | −0.278320 | − | 0.160688i | ||||
\(519\) | −16.1321 | −0.708120 | ||||||||
\(520\) | 3.60194 | − | 0.161290i | 0.157956 | − | 0.00707303i | ||||
\(521\) | 5.28512 | 0.231545 | 0.115773 | − | 0.993276i | \(-0.463066\pi\) | ||||
0.115773 | + | 0.993276i | \(0.463066\pi\) | |||||||
\(522\) | −3.71592 | − | 2.14539i | −0.162641 | − | 0.0939011i | ||||
\(523\) | 10.3762 | − | 17.9721i | 0.453718 | − | 0.785863i | −0.544895 | − | 0.838504i | \(-0.683431\pi\) |
0.998614 | + | 0.0526409i | \(0.0167639\pi\) | |||||||
\(524\) | 0.629257 | + | 1.08991i | 0.0274892 | + | 0.0476127i | ||||
\(525\) | 2.32258i | 0.101366i | ||||||||
\(526\) | −9.27159 | + | 5.35295i | −0.404260 | + | 0.233400i | ||||
\(527\) | −12.0268 | + | 6.94367i | −0.523895 | + | 0.302471i | ||||
\(528\) | − | 5.34541i | − | 0.232629i | ||||||
\(529\) | −0.681725 | − | 1.18078i | −0.0296402 | − | 0.0513384i | ||||
\(530\) | 2.74346 | − | 4.75182i | 0.119168 | − | 0.206406i | ||||
\(531\) | −5.87744 | − | 3.39334i | −0.255059 | − | 0.147258i | ||||
\(532\) | 9.34333 | 0.405085 | ||||||||
\(533\) | −8.46456 | − | 4.39438i | −0.366641 | − | 0.190342i | ||||
\(534\) | −1.73978 | −0.0752877 | ||||||||
\(535\) | 2.66025 | + | 1.53590i | 0.115013 | + | 0.0664027i | ||||
\(536\) | 2.05463 | − | 3.55872i | 0.0887465 | − | 0.153713i | ||||
\(537\) | 3.66412 | + | 6.34644i | 0.158118 | + | 0.273869i | ||||
\(538\) | 7.52522i | 0.324435i | ||||||||
\(539\) | −7.43284 | + | 4.29135i | −0.320155 | + | 0.184842i | ||||
\(540\) | 0.866025 | − | 0.500000i | 0.0372678 | − | 0.0215166i | ||||
\(541\) | − | 28.7365i | − | 1.23548i | −0.786384 | − | 0.617739i | \(-0.788049\pi\) | ||
0.786384 | − | 0.617739i | \(-0.211951\pi\) | |||||||
\(542\) | −4.92434 | − | 8.52920i | −0.211518 | − | 0.366361i | ||||
\(543\) | 9.78668 | − | 16.9510i | 0.419987 | − | 0.727438i | ||||
\(544\) | 3.46410 | + | 2.00000i | 0.148522 | + | 0.0857493i | ||||
\(545\) | −6.69081 | −0.286603 | ||||||||
\(546\) | 3.85848 | − | 7.43230i | 0.165128 | − | 0.318073i | ||||
\(547\) | 18.3768 | 0.785737 | 0.392869 | − | 0.919595i | \(-0.371483\pi\) | ||||
0.392869 | + | 0.919595i | \(0.371483\pi\) | |||||||
\(548\) | 17.0736 | + | 9.85744i | 0.729348 | + | 0.421089i | ||||
\(549\) | −0.267949 | + | 0.464102i | −0.0114358 | + | 0.0198074i | ||||
\(550\) | 2.67270 | + | 4.62926i | 0.113964 | + | 0.197392i | ||||
\(551\) | − | 17.2610i | − | 0.735345i | ||||||
\(552\) | −4.27464 | + | 2.46797i | −0.181941 | + | 0.105044i | ||||
\(553\) | 16.0264 | − | 9.25285i | 0.681512 | − | 0.393471i | ||||
\(554\) | − | 0.953101i | − | 0.0404934i | ||||||
\(555\) | −1.57463 | − | 2.72733i | −0.0668392 | − | 0.115769i | ||||
\(556\) | 2.83871 | − | 4.91679i | 0.120388 | − | 0.208518i | ||||
\(557\) | 22.9831 | + | 13.2693i | 0.973826 | + | 0.562238i | 0.900400 | − | 0.435062i | \(-0.143274\pi\) |
0.0734252 | + | 0.997301i | \(0.476607\pi\) | |||||||
\(558\) | −3.47183 | −0.146974 | ||||||||
\(559\) | −23.7745 | − | 37.2268i | −1.00555 | − | 1.57453i | ||||
\(560\) | −2.32258 | −0.0981469 | ||||||||
\(561\) | −18.5170 | − | 10.6908i | −0.781790 | − | 0.451366i | ||||
\(562\) | −2.78668 | + | 4.82667i | −0.117549 | + | 0.203601i | ||||
\(563\) | −3.03056 | − | 5.24908i | −0.127723 | − | 0.221222i | 0.795071 | − | 0.606516i | \(-0.207433\pi\) |
−0.922794 | + | 0.385294i | \(0.874100\pi\) | |||||||
\(564\) | 1.81894i | 0.0765913i | ||||||||
\(565\) | 6.15720 | − | 3.55486i | 0.259035 | − | 0.149554i | ||||
\(566\) | −19.0642 | + | 11.0067i | −0.801326 | + | 0.462646i | ||||
\(567\) | − | 2.32258i | − | 0.0975392i | ||||||
\(568\) | −7.93593 | − | 13.7454i | −0.332984 | − | 0.576746i | ||||
\(569\) | −7.24818 | + | 12.5542i | −0.303860 | + | 0.526300i | −0.977007 | − | 0.213208i | \(-0.931609\pi\) |
0.673147 | + | 0.739509i | \(0.264942\pi\) | |||||||
\(570\) | 3.48387 | + | 2.01141i | 0.145923 | + | 0.0842488i | ||||
\(571\) | −2.90413 | −0.121534 | −0.0607670 | − | 0.998152i | \(-0.519355\pi\) | ||||
−0.0607670 | + | 0.998152i | \(0.519355\pi\) | |||||||
\(572\) | −0.862160 | − | 19.2538i | −0.0360487 | − | 0.805044i | ||||
\(573\) | −17.0375 | −0.711750 | ||||||||
\(574\) | 5.32051 | + | 3.07180i | 0.222074 | + | 0.128214i | ||||
\(575\) | 2.46797 | − | 4.27464i | 0.102921 | − | 0.178265i | ||||
\(576\) | 0.500000 | + | 0.866025i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | − | 18.8180i | − | 0.783405i | −0.920092 | − | 0.391702i | \(-0.871886\pi\) | ||
0.920092 | − | 0.391702i | \(-0.128114\pi\) | |||||||
\(578\) | −0.866025 | + | 0.500000i | −0.0360219 | + | 0.0207973i | ||||
\(579\) | −5.33031 | + | 3.07746i | −0.221520 | + | 0.127895i | ||||
\(580\) | 4.29078i | 0.178165i | ||||||||
\(581\) | 13.1643 | + | 22.8013i | 0.546149 | + | 0.945958i | ||||
\(582\) | −8.05463 | + | 13.9510i | −0.333875 | + | 0.578289i | ||||
\(583\) | −25.4004 | − | 14.6649i | −1.05198 | − | 0.607359i | ||||
\(584\) | −13.5734 | −0.561670 | ||||||||
\(585\) | 3.03873 | − | 1.94065i | 0.125636 | − | 0.0802361i | ||||
\(586\) | −6.84302 | −0.282682 | ||||||||
\(587\) | −3.40901 | − | 1.96820i | −0.140705 | − | 0.0812361i | 0.427995 | − | 0.903781i | \(-0.359220\pi\) |
−0.568700 | + | 0.822545i | \(0.692553\pi\) | |||||||
\(588\) | 0.802812 | − | 1.39051i | 0.0331074 | − | 0.0573437i | ||||
\(589\) | −6.98329 | − | 12.0954i | −0.287741 | − | 0.498383i | ||||
\(590\) | 6.78668i | 0.279403i | ||||||||
\(591\) | 11.9396 | − | 6.89334i | 0.491130 | − | 0.283554i | ||||
\(592\) | 2.72733 | − | 1.57463i | 0.112093 | − | 0.0647168i | ||||
\(593\) | 20.1227i | 0.826338i | 0.910654 | + | 0.413169i | \(0.135578\pi\) | ||||
−0.910654 | + | 0.413169i | \(0.864422\pi\) | |||||||
\(594\) | −2.67270 | − | 4.62926i | −0.109662 | − | 0.189941i | ||||
\(595\) | −4.64516 | + | 8.04565i | −0.190433 | + | 0.329840i | ||||
\(596\) | −16.8680 | − | 9.73875i | −0.690940 | − | 0.398915i | ||||
\(597\) | −2.28304 | −0.0934388 | ||||||||
\(598\) | −14.9990 | + | 9.57893i | −0.613353 | + | 0.391712i | ||||
\(599\) | 48.1172 | 1.96601 | 0.983007 | − | 0.183567i | \(-0.0587644\pi\) | ||||
0.983007 | + | 0.183567i | \(0.0587644\pi\) | |||||||
\(600\) | −0.866025 | − | 0.500000i | −0.0353553 | − | 0.0204124i | ||||
\(601\) | 2.12109 | − | 3.67383i | 0.0865209 | − | 0.149859i | −0.819517 | − | 0.573054i | \(-0.805758\pi\) |
0.906038 | + | 0.423196i | \(0.139092\pi\) | |||||||
\(602\) | 14.2267 | + | 24.6414i | 0.579837 | + | 1.00431i | ||||
\(603\) | − | 4.10926i | − | 0.167342i | ||||||
\(604\) | −12.5721 | + | 7.25851i | −0.511552 | + | 0.295345i | ||||
\(605\) | 15.2190 | − | 8.78668i | 0.618739 | − | 0.357229i | ||||
\(606\) | − | 12.6908i | − | 0.515529i | ||||||
\(607\) | −6.03424 | − | 10.4516i | −0.244922 | − | 0.424218i | 0.717188 | − | 0.696880i | \(-0.245429\pi\) |
−0.962110 | + | 0.272663i | \(0.912096\pi\) | |||||||
\(608\) | −2.01141 | + | 3.48387i | −0.0815736 | + | 0.141290i | ||||
\(609\) | 8.63052 | + | 4.98283i | 0.349726 | + | 0.201915i | ||||
\(610\) | 0.535898 | 0.0216979 | ||||||||
\(611\) | 0.293377 | + | 6.55172i | 0.0118688 | + | 0.265054i | ||||
\(612\) | 4.00000 | 0.161690 | ||||||||
\(613\) | 36.1497 | + | 20.8711i | 1.46007 | + | 0.842974i | 0.999014 | − | 0.0443946i | \(-0.0141359\pi\) |
0.461060 | + | 0.887369i | \(0.347469\pi\) | |||||||
\(614\) | −2.37721 | + | 4.11745i | −0.0959364 | + | 0.166167i | ||||
\(615\) | 1.32258 | + | 2.29078i | 0.0533316 | + | 0.0923730i | ||||
\(616\) | 12.4151i | 0.500220i | ||||||||
\(617\) | −28.9760 | + | 16.7293i | −1.16653 | + | 0.673497i | −0.952860 | − | 0.303409i | \(-0.901875\pi\) |
−0.213670 | + | 0.976906i | \(0.568542\pi\) | |||||||
\(618\) | −4.15356 | + | 2.39806i | −0.167081 | + | 0.0964640i | ||||
\(619\) | 38.0978i | 1.53128i | 0.643270 | + | 0.765639i | \(0.277577\pi\) | ||||
−0.643270 | + | 0.765639i | \(0.722423\pi\) | |||||||
\(620\) | 1.73592 | + | 3.00670i | 0.0697161 | + | 0.120752i | ||||
\(621\) | −2.46797 | + | 4.27464i | −0.0990361 | + | 0.171536i | ||||
\(622\) | −1.67696 | − | 0.968196i | −0.0672401 | − | 0.0388211i | ||||
\(623\) | 4.04078 | 0.161891 | ||||||||
\(624\) | 1.94065 | + | 3.03873i | 0.0776883 | + | 0.121646i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −22.1308 | − | 12.7772i | −0.884526 | − | 0.510681i | ||||
\(627\) | 10.7518 | − | 18.6227i | 0.429386 | − | 0.743719i | ||||
\(628\) | 12.1914 | + | 21.1162i | 0.486491 | + | 0.842628i | ||||
\(629\) | − | 12.5970i | − | 0.502276i | ||||||
\(630\) | −2.01141 | + | 1.16129i | −0.0801366 | + | 0.0462669i | ||||
\(631\) | −21.4775 | + | 12.4000i | −0.855005 | + | 0.493638i | −0.862337 | − | 0.506335i | \(-0.831000\pi\) |
0.00733109 | + | 0.999973i | \(0.497666\pi\) | |||||||
\(632\) | 7.96774i | 0.316940i | ||||||||
\(633\) | −11.2387 | − | 19.4661i | −0.446700 | − | 0.773707i | ||||
\(634\) | −6.33337 | + | 10.9697i | −0.251530 | + | 0.435663i | ||||
\(635\) | 1.84644 | + | 1.06604i | 0.0732738 | + | 0.0423046i | ||||
\(636\) | 5.48693 | 0.217571 | ||||||||
\(637\) | 2.66741 | − | 5.13802i | 0.105686 | − | 0.203576i | ||||
\(638\) | 22.9359 | 0.908042 | ||||||||
\(639\) | −13.7454 | − | 7.93593i | −0.543761 | − | 0.313941i | ||||
\(640\) | 0.500000 | − | 0.866025i | 0.0197642 | − | 0.0342327i | ||||
\(641\) | 2.04259 | + | 3.53788i | 0.0806776 | + | 0.139738i | 0.903541 | − | 0.428501i | \(-0.140958\pi\) |
−0.822864 | + | 0.568239i | \(0.807625\pi\) | |||||||
\(642\) | 3.07180i | 0.121234i | ||||||||
\(643\) | −31.6806 | + | 18.2908i | −1.24936 | + | 0.721318i | −0.970982 | − | 0.239154i | \(-0.923130\pi\) |
−0.278377 | + | 0.960472i | \(0.589797\pi\) | |||||||
\(644\) | 9.92820 | − | 5.73205i | 0.391226 | − | 0.225874i | ||||
\(645\) | 12.2508i | 0.482374i | ||||||||
\(646\) | 8.04565 | + | 13.9355i | 0.316552 | + | 0.548284i | ||||
\(647\) | 8.61704 | − | 14.9251i | 0.338771 | − | 0.586768i | −0.645431 | − | 0.763818i | \(-0.723322\pi\) |
0.984202 | + | 0.177050i | \(0.0566556\pi\) | |||||||
\(648\) | 0.866025 | + | 0.500000i | 0.0340207 | + | 0.0196419i | ||||
\(649\) | 36.2776 | 1.42402 | ||||||||
\(650\) | −3.20002 | − | 1.66129i | −0.125515 | − | 0.0651611i | ||||
\(651\) | 8.06361 | 0.316038 | ||||||||
\(652\) | 20.4614 | + | 11.8134i | 0.801329 | + | 0.462647i | ||||
\(653\) | 10.9637 | − | 18.9897i | 0.429042 | − | 0.743123i | −0.567746 | − | 0.823204i | \(-0.692184\pi\) |
0.996788 | + | 0.0800806i | \(0.0255178\pi\) | |||||||
\(654\) | −3.34541 | − | 5.79441i | −0.130816 | − | 0.226579i | ||||
\(655\) | − | 1.25851i | − | 0.0491742i | ||||||
\(656\) | −2.29078 | + | 1.32258i | −0.0894397 | + | 0.0516381i | ||||
\(657\) | −11.7549 | + | 6.78668i | −0.458601 | + | 0.264774i | ||||
\(658\) | − | 4.22464i | − | 0.164694i | ||||||
\(659\) | 24.2379 | + | 41.9813i | 0.944176 | + | 1.63536i | 0.757393 | + | 0.652960i | \(0.226473\pi\) |
0.186783 | + | 0.982401i | \(0.440194\pi\) | |||||||
\(660\) | −2.67270 | + | 4.62926i | −0.104035 | + | 0.180194i | ||||
\(661\) | −25.8267 | − | 14.9110i | −1.00454 | − | 0.579972i | −0.0949524 | − | 0.995482i | \(-0.530270\pi\) |
−0.909589 | + | 0.415510i | \(0.863603\pi\) | |||||||
\(662\) | 23.6981 | 0.921052 | ||||||||
\(663\) | 14.4078 | − | 0.645159i | 0.559551 | − | 0.0250559i | ||||
\(664\) | −11.3360 | −0.439921 | ||||||||
\(665\) | −8.09156 | − | 4.67167i | −0.313777 | − | 0.181159i | ||||
\(666\) | 1.57463 | − | 2.72733i | 0.0610155 | − | 0.105682i | ||||
\(667\) | −10.5895 | − | 18.3415i | −0.410027 | − | 0.710187i | ||||
\(668\) | 16.7471i | 0.647967i | ||||||||
\(669\) | −1.19417 | + | 0.689457i | −0.0461694 | + | 0.0266559i | ||||
\(670\) | −3.55872 | + | 2.05463i | −0.137486 | + | 0.0793773i | ||||
\(671\) | − | 2.86459i | − | 0.110586i | ||||||
\(672\) | −1.16129 | − | 2.01141i | −0.0447977 | − | 0.0775919i | ||||
\(673\) | −15.3360 | + | 26.5627i | −0.591158 | + | 1.02392i | 0.402919 | + | 0.915236i | \(0.367996\pi\) |
−0.994077 | + | 0.108680i | \(0.965338\pi\) | |||||||
\(674\) | −16.9355 | − | 9.77770i | −0.652330 | − | 0.376623i | ||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 7.48023 | + | 10.6323i | 0.287701 | + | 0.408935i | ||||
\(677\) | 21.0831 | 0.810290 | 0.405145 | − | 0.914252i | \(-0.367221\pi\) | ||||
0.405145 | + | 0.914252i | \(0.367221\pi\) | |||||||
\(678\) | 6.15720 | + | 3.55486i | 0.236466 | + | 0.136524i | ||||
\(679\) | 18.7075 | − | 32.4024i | 0.717929 | − | 1.24349i | ||||
\(680\) | −2.00000 | − | 3.46410i | −0.0766965 | − | 0.132842i | ||||
\(681\) | − | 19.3205i | − | 0.740363i | ||||||
\(682\) | 16.0720 | − | 9.27918i | 0.615429 | − | 0.355318i | ||||
\(683\) | −11.5493 | + | 6.66799i | −0.441921 | + | 0.255143i | −0.704412 | − | 0.709791i | \(-0.748789\pi\) |
0.262491 | + | 0.964934i | \(0.415456\pi\) | |||||||
\(684\) | 4.02283i | 0.153817i | ||||||||
\(685\) | −9.85744 | − | 17.0736i | −0.376634 | − | 0.652348i | ||||
\(686\) | −9.99362 | + | 17.3095i | −0.381558 | + | 0.660878i | ||||
\(687\) | 13.6508 | + | 7.88130i | 0.520811 | + | 0.300691i | ||||
\(688\) | −12.2508 | −0.467057 | ||||||||
\(689\) | 19.7636 | − | 0.884986i | 0.752933 | − | 0.0337153i | ||||
\(690\) | 4.93593 | 0.187908 | ||||||||
\(691\) | −30.2289 | − | 17.4527i | −1.14996 | − | 0.663932i | −0.201085 | − | 0.979574i | \(-0.564447\pi\) |
−0.948878 | + | 0.315642i | \(0.897780\pi\) | |||||||
\(692\) | −8.06604 | + | 13.9708i | −0.306625 | + | 0.531090i | ||||
\(693\) | 6.20757 | + | 10.7518i | 0.235806 | + | 0.408428i | ||||
\(694\) | − | 23.0375i | − | 0.874490i | ||||||
\(695\) | −4.91679 | + | 2.83871i | −0.186504 | + | 0.107678i | ||||
\(696\) | −3.71592 | + | 2.14539i | −0.140852 | + | 0.0813207i | ||||
\(697\) | 10.5806i | 0.400770i | ||||||||
\(698\) | −7.66025 | − | 13.2679i | −0.289945 | − | 0.502199i | ||||
\(699\) | 8.27747 | − | 14.3370i | 0.313083 | − | 0.542275i | ||||
\(700\) | 2.01141 | + | 1.16129i | 0.0760243 | + | 0.0438926i | ||||
\(701\) | 39.6715 | 1.49837 | 0.749186 | − | 0.662360i | \(-0.230445\pi\) | ||||
0.749186 | + | 0.662360i | \(0.230445\pi\) | |||||||
\(702\) | 3.20002 | + | 1.66129i | 0.120777 | + | 0.0627013i | ||||
\(703\) | 12.6689 | 0.477817 | ||||||||
\(704\) | −4.62926 | − | 2.67270i | −0.174472 | − | 0.100731i | ||||
\(705\) | 0.909471 | − | 1.57525i | 0.0342527 | − | 0.0593274i | ||||
\(706\) | −14.2039 | − | 24.6018i | −0.534570 | − | 0.925903i | ||||
\(707\) | 29.4754i | 1.10854i | ||||||||
\(708\) | −5.87744 | + | 3.39334i | −0.220888 | + | 0.127530i | ||||
\(709\) | 2.45467 | − | 1.41720i | 0.0921869 | − | 0.0532242i | −0.453198 | − | 0.891410i | \(-0.649717\pi\) |
0.545385 | + | 0.838186i | \(0.316384\pi\) | |||||||
\(710\) | 15.8719i | 0.595661i | ||||||||
\(711\) | 3.98387 | + | 6.90026i | 0.149407 | + | 0.258780i | ||||
\(712\) | −0.869891 | + | 1.50670i | −0.0326005 | + | 0.0564658i | ||||
\(713\) | −14.8409 | − | 8.56837i | −0.555794 | − | 0.320888i | ||||
\(714\) | −9.29032 | −0.347681 | ||||||||
\(715\) | −8.88027 | + | 17.1054i | −0.332103 | + | 0.639706i | ||||
\(716\) | 7.32824 | 0.273869 | ||||||||
\(717\) | −22.6904 | − | 13.1003i | −0.847387 | − | 0.489239i | ||||
\(718\) | 11.7867 | − | 20.4151i | 0.439875 | − | 0.761886i | ||||
\(719\) | −21.8564 | − | 37.8564i | −0.815106 | − | 1.41181i | −0.909251 | − | 0.416247i | \(-0.863345\pi\) |
0.0941451 | − | 0.995558i | \(-0.469988\pi\) | |||||||
\(720\) | − | 1.00000i | − | 0.0372678i | ||||||
\(721\) | 9.64697 | − | 5.56968i | 0.359272 | − | 0.207426i | ||||
\(722\) | 2.43948 | − | 1.40844i | 0.0907881 | − | 0.0524165i | ||||
\(723\) | − | 15.6496i | − | 0.582014i | ||||||
\(724\) | −9.78668 | − | 16.9510i | −0.363719 | − | 0.629980i | ||||
\(725\) | 2.14539 | − | 3.71592i | 0.0796777 | − | 0.138006i | ||||
\(726\) | 15.2190 | + | 8.78668i | 0.564829 | + | 0.326104i | ||||
\(727\) | −16.2568 | −0.602932 | −0.301466 | − | 0.953477i | \(-0.597476\pi\) | ||||
−0.301466 | + | 0.953477i | \(0.597476\pi\) | |||||||
\(728\) | −4.50732 | − | 7.05769i | −0.167052 | − | 0.261575i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 11.7549 | + | 6.78668i | 0.435068 | + | 0.251186i | ||||
\(731\) | −24.5016 | + | 42.4380i | −0.906223 | + | 1.56962i | ||||
\(732\) | 0.267949 | + | 0.464102i | 0.00990369 | + | 0.0171537i | ||||
\(733\) | 4.96774i | 0.183488i | 0.995783 | + | 0.0917438i | \(0.0292441\pi\) | ||||
−0.995783 | + | 0.0917438i | \(0.970756\pi\) | |||||||
\(734\) | 23.8078 | − | 13.7454i | 0.878762 | − | 0.507354i | ||||
\(735\) | −1.39051 | + | 0.802812i | −0.0512898 | + | 0.0296122i | ||||
\(736\) | 4.93593i | 0.181941i | ||||||||
\(737\) | 10.9828 | + | 19.0228i | 0.404558 | + | 0.700715i | ||||
\(738\) | −1.32258 | + | 2.29078i | −0.0486848 | + | 0.0843246i | ||||
\(739\) | 43.0306 | + | 24.8437i | 1.58291 | + | 0.913892i | 0.994432 | + | 0.105377i | \(0.0336048\pi\) |
0.588475 | + | 0.808515i | \(0.299729\pi\) | |||||||
\(740\) | −3.14925 | −0.115769 | ||||||||
\(741\) | 0.648841 | + | 14.4900i | 0.0238358 | + | 0.532303i | ||||
\(742\) | −12.7438 | −0.467841 | ||||||||
\(743\) | 18.6559 | + | 10.7710i | 0.684420 | + | 0.395150i | 0.801518 | − | 0.597970i | \(-0.204026\pi\) |
−0.117098 | + | 0.993120i | \(0.537359\pi\) | |||||||
\(744\) | −1.73592 | + | 3.00670i | −0.0636418 | + | 0.110231i | ||||
\(745\) | 9.73875 | + | 16.8680i | 0.356800 | + | 0.617996i | ||||
\(746\) | 26.3421i | 0.964452i | ||||||||
\(747\) | −9.81724 | + | 5.66799i | −0.359194 | + | 0.207381i | ||||
\(748\) | −18.5170 | + | 10.6908i | −0.677050 | + | 0.390895i | ||||
\(749\) | − | 7.13449i | − | 0.260689i | ||||||
\(750\) | 0.500000 | + | 0.866025i | 0.0182574 | + | 0.0316228i | ||||
\(751\) | −3.17436 | + | 5.49816i | −0.115834 | + | 0.200631i | −0.918113 | − | 0.396319i | \(-0.870287\pi\) |
0.802279 | + | 0.596950i | \(0.203621\pi\) | |||||||
\(752\) | 1.57525 | + | 0.909471i | 0.0574435 | + | 0.0331650i | ||||
\(753\) | 28.3416 | 1.03283 | ||||||||
\(754\) | −13.0385 | + | 8.32690i | −0.474834 | + | 0.303248i | ||||
\(755\) | 14.5170 | 0.528329 | ||||||||
\(756\) | −2.01141 | − | 1.16129i | −0.0731544 | − | 0.0422357i | ||||
\(757\) | 24.0554 | − | 41.6651i | 0.874307 | − | 1.51434i | 0.0168078 | − | 0.999859i | \(-0.494650\pi\) |
0.857499 | − | 0.514485i | \(-0.172017\pi\) | |||||||
\(758\) | −0.224275 | − | 0.388456i | −0.00814604 | − | 0.0141094i | ||||
\(759\) | − | 26.3846i | − | 0.957699i | ||||||
\(760\) | 3.48387 | − | 2.01141i | 0.126373 | − | 0.0729616i | ||||
\(761\) | 29.1734 | − | 16.8433i | 1.05754 | − | 0.610569i | 0.132786 | − | 0.991145i | \(-0.457608\pi\) |
0.924750 | + | 0.380576i | \(0.124274\pi\) | |||||||
\(762\) | 2.13209i | 0.0772374i | ||||||||
\(763\) | 7.76997 | + | 13.4580i | 0.281292 | + | 0.487212i | ||||
\(764\) | −8.51873 | + | 14.7549i | −0.308197 | + | 0.533813i | ||||
\(765\) | −3.46410 | − | 2.00000i | −0.125245 | − | 0.0723102i | ||||
\(766\) | −12.1227 | −0.438009 | ||||||||
\(767\) | −20.6229 | + | 13.1706i | −0.744649 | + | 0.475562i | ||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −5.18651 | − | 2.99443i | −0.187030 | − | 0.107982i | 0.403561 | − | 0.914953i | \(-0.367772\pi\) |
−0.590592 | + | 0.806971i | \(0.701106\pi\) | |||||||
\(770\) | 6.20757 | − | 10.7518i | 0.223705 | − | 0.387469i | ||||
\(771\) | −6.25465 | − | 10.8334i | −0.225256 | − | 0.390154i | ||||
\(772\) | 6.15491i | 0.221520i | ||||||||
\(773\) | 11.6811 | − | 6.74409i | 0.420140 | − | 0.242568i | −0.274997 | − | 0.961445i | \(-0.588677\pi\) |
0.695137 | + | 0.718877i | \(0.255344\pi\) | |||||||
\(774\) | −10.6095 | + | 6.12539i | −0.381350 | + | 0.220173i | ||||
\(775\) | − | 3.47183i | − | 0.124712i | ||||||
\(776\) | 8.05463 | + | 13.9510i | 0.289144 | + | 0.500813i | ||||
\(777\) | −3.65720 | + | 6.33445i | −0.131201 | + | 0.227247i | ||||
\(778\) | −16.1249 | − | 9.30974i | −0.578107 | − | 0.333770i | ||||
\(779\) | −10.6410 | −0.381254 | ||||||||
\(780\) | −0.161290 | − | 3.60194i | −0.00577510 | − | 0.128970i | ||||
\(781\) | 84.8416 | 3.03587 | ||||||||
\(782\) | 17.0986 | + | 9.87187i | 0.611444 | + | 0.353017i | ||||
\(783\) | −2.14539 | + | 3.71592i | −0.0766699 | + | 0.132796i | ||||
\(784\) | −0.802812 | − | 1.39051i | −0.0286718 | − | 0.0496611i | ||||
\(785\) | − | 24.3829i | − | 0.870262i | ||||||
\(786\) | 1.08991 | − | 0.629257i | 0.0388756 | − | 0.0224449i | ||||
\(787\) | −47.3272 | + | 27.3244i | −1.68703 | + | 0.974009i | −0.730261 | + | 0.683168i | \(0.760602\pi\) |
−0.956772 | + | 0.290841i | \(0.906065\pi\) | |||||||
\(788\) | − | 13.7867i | − | 0.491130i | ||||||
\(789\) | 5.35295 | + | 9.27159i | 0.190570 | + | 0.330077i | ||||
\(790\) | 3.98387 | − | 6.90026i | 0.141740 | − | 0.245500i | ||||
\(791\) | −14.3006 | − | 8.25644i | −0.508470 | − | 0.293565i | ||||
\(792\) | −5.34541 | −0.189941 | ||||||||
\(793\) | 1.03999 | + | 1.62845i | 0.0369312 | + | 0.0578279i | ||||
\(794\) | −11.3042 | −0.401170 | ||||||||
\(795\) | −4.75182 | − | 2.74346i | −0.168530 | − | 0.0973006i | ||||
\(796\) | −1.14152 | + | 1.97717i | −0.0404602 | + | 0.0700791i | ||||
\(797\) | −19.1622 | − | 33.1899i | −0.678760 | − | 1.17565i | −0.975355 | − | 0.220643i | \(-0.929185\pi\) |
0.296595 | − | 0.955003i | \(-0.404149\pi\) | |||||||
\(798\) | − | 9.34333i | − | 0.330750i | ||||||
\(799\) | 6.30100 | − | 3.63788i | 0.222913 | − | 0.128699i | ||||
\(800\) | −0.866025 | + | 0.500000i | −0.0306186 | + | 0.0176777i | ||||
\(801\) | 1.73978i | 0.0614722i | ||||||||
\(802\) | 0.752899 | + | 1.30406i | 0.0265858 | + | 0.0460479i | ||||
\(803\) | 36.2776 | − | 62.8346i | 1.28021 | − | 2.21738i | ||||
\(804\) | −3.55872 | − | 2.05463i | −0.125507 | − | 0.0724612i | ||||
\(805\) | −11.4641 | −0.404056 | ||||||||
\(806\) | −5.76772 | + | 11.1099i | −0.203159 | + | 0.391331i | ||||
\(807\) | 7.52522 | 0.264900 | ||||||||
\(808\) | −10.9906 | − | 6.34541i | −0.386647 | − | 0.223231i | ||||
\(809\) | −5.69081 | + | 9.85677i | −0.200078 | + | 0.346546i | −0.948553 | − | 0.316617i | \(-0.897453\pi\) |
0.748475 | + | 0.663163i | \(0.230786\pi\) | |||||||
\(810\) | −0.500000 | − | 0.866025i | −0.0175682 | − | 0.0304290i | ||||
\(811\) | − | 10.8899i | − | 0.382397i | −0.981551 | − | 0.191198i | \(-0.938763\pi\) | ||
0.981551 | − | 0.191198i | \(-0.0612374\pi\) | |||||||
\(812\) | 8.63052 | − | 4.98283i | 0.302872 | − | 0.174863i | ||||
\(813\) | −8.52920 | + | 4.92434i | −0.299132 | + | 0.172704i | ||||
\(814\) | 16.8340i | 0.590033i | ||||||||
\(815\) | −11.8134 | − | 20.4614i | −0.413804 | − | 0.716730i | ||||
\(816\) | 2.00000 | − | 3.46410i | 0.0700140 | − | 0.121268i | ||||
\(817\) | −42.6801 | − | 24.6414i | −1.49319 | − | 0.862093i | ||||
\(818\) | −11.1394 | −0.389479 | ||||||||
\(819\) | −7.43230 | − | 3.85848i | −0.259705 | − | 0.134826i | ||||
\(820\) | 2.64516 | 0.0923730 | ||||||||
\(821\) | −1.46194 | − | 0.844051i | −0.0510220 | − | 0.0294576i | 0.474272 | − | 0.880378i | \(-0.342711\pi\) |
−0.525294 | + | 0.850921i | \(0.676045\pi\) | |||||||
\(822\) | 9.85744 | − | 17.0736i | 0.343818 | − | 0.595510i | ||||
\(823\) | 3.38908 | + | 5.87006i | 0.118136 | + | 0.204617i | 0.919029 | − | 0.394190i | \(-0.128975\pi\) |
−0.800893 | + | 0.598807i | \(0.795641\pi\) | |||||||
\(824\) | 4.79612i | 0.167081i | ||||||||
\(825\) | 4.62926 | − | 2.67270i | 0.161170 | − | 0.0930516i | ||||
\(826\) | 13.6508 | − | 7.88130i | 0.474973 | − | 0.274226i | ||||
\(827\) | − | 30.2298i | − | 1.05119i | −0.850733 | − | 0.525597i | \(-0.823842\pi\) | ||
0.850733 | − | 0.525597i | \(-0.176158\pi\) | |||||||
\(828\) | 2.46797 | + | 4.27464i | 0.0857678 | + | 0.148554i | ||||
\(829\) | −5.22023 | + | 9.04170i | −0.181306 | + | 0.314031i | −0.942326 | − | 0.334698i | \(-0.891366\pi\) |
0.761020 | + | 0.648729i | \(0.224699\pi\) | |||||||
\(830\) | 9.81724 | + | 5.66799i | 0.340761 | + | 0.196739i | ||||
\(831\) | −0.953101 | −0.0330627 | ||||||||
\(832\) | 3.60194 | − | 0.161290i | 0.124875 | − | 0.00559172i | ||||
\(833\) | −6.42249 | −0.222526 | ||||||||
\(834\) | −4.91679 | − | 2.83871i | −0.170255 | − | 0.0982965i | ||||
\(835\) | 8.37357 | − | 14.5035i | 0.289779 | − | 0.501913i | ||||
\(836\) | −10.7518 | − | 18.6227i | −0.371859 | − | 0.644079i | ||||
\(837\) | 3.47183i | 0.120004i | ||||||||
\(838\) | −13.4318 | + | 7.75488i | −0.463995 | + | 0.267888i | ||||
\(839\) | 9.69647 | − | 5.59826i | 0.334759 | − | 0.193273i | −0.323193 | − | 0.946333i | \(-0.604756\pi\) |
0.657952 | + | 0.753060i | \(0.271423\pi\) | |||||||
\(840\) | 2.32258i | 0.0801366i | ||||||||
\(841\) | 5.29462 | + | 9.17056i | 0.182573 | + | 0.316226i | ||||
\(842\) | −19.7226 | + | 34.1606i | −0.679686 | + | 1.17725i | ||||
\(843\) | 4.82667 | + | 2.78668i | 0.166239 | + | 0.0959784i | ||||
\(844\) | −22.4775 | −0.773707 | ||||||||
\(845\) | −1.16191 | − | 12.9480i | −0.0399710 | − | 0.445424i | ||||
\(846\) | 1.81894 | 0.0625365 | ||||||||
\(847\) | −35.3473 | − | 20.4078i | −1.21455 | − | 0.701219i | ||||
\(848\) | 2.74346 | − | 4.75182i | 0.0942109 | − | 0.163178i | ||||
\(849\) | 11.0067 | + | 19.0642i | 0.377749 | + | 0.654280i | ||||
\(850\) | 4.00000i | 0.137199i | ||||||||
\(851\) | 13.4619 | − | 7.77225i | 0.461469 | − | 0.266429i | ||||
\(852\) | −13.7454 | + | 7.93593i | −0.470911 | + | 0.271881i | ||||
\(853\) | 21.8185i | 0.747051i | 0.927620 | + | 0.373525i | \(0.121851\pi\) | ||||
−0.927620 | + | 0.373525i | \(0.878149\pi\) | |||||||
\(854\) | −0.622333 | − | 1.07791i | −0.0212958 | − | 0.0368854i | ||||
\(855\) | 2.01141 | − | 3.48387i | 0.0687889 | − | 0.119146i | ||||
\(856\) | 2.66025 | + | 1.53590i | 0.0909256 | + | 0.0524959i | ||||
\(857\) | −9.42369 | −0.321907 | −0.160954 | − | 0.986962i | \(-0.551457\pi\) | ||||
−0.160954 | + | 0.986962i | \(0.551457\pi\) | |||||||
\(858\) | −19.2538 | + | 0.862160i | −0.657315 | + | 0.0294336i | ||||
\(859\) | 24.4775 | 0.835161 | 0.417581 | − | 0.908640i | \(-0.362878\pi\) | ||||
0.417581 | + | 0.908640i | \(0.362878\pi\) | |||||||
\(860\) | 10.6095 | + | 6.12539i | 0.361781 | + | 0.208874i | ||||
\(861\) | 3.07180 | − | 5.32051i | 0.104687 | − | 0.181322i | ||||
\(862\) | −1.07746 | − | 1.86621i | −0.0366983 | − | 0.0635633i | ||||
\(863\) | − | 29.7873i | − | 1.01397i | −0.861954 | − | 0.506986i | \(-0.830760\pi\) | ||
0.861954 | − | 0.506986i | \(-0.169240\pi\) | |||||||
\(864\) | 0.866025 | − | 0.500000i | 0.0294628 | − | 0.0170103i | ||||
\(865\) | 13.9708 | − | 8.06604i | 0.475021 | − | 0.274254i | ||||
\(866\) | − | 1.33938i | − | 0.0455139i | ||||||
\(867\) | 0.500000 | + | 0.866025i | 0.0169809 | + | 0.0294118i | ||||
\(868\) | 4.03180 | − | 6.98329i | 0.136848 | − | 0.237028i | ||||
\(869\) | −36.8847 | − | 21.2954i | −1.25123 | − | 0.722397i | ||||
\(870\) | 4.29078 | 0.145471 | ||||||||
\(871\) | −13.1497 | − | 6.82667i | −0.445561 | − | 0.231313i | ||||
\(872\) | −6.69081 | −0.226579 | ||||||||
\(873\) | 13.9510 | + | 8.05463i | 0.472171 | + | 0.272608i | ||||
\(874\) | −9.92820 | + | 17.1962i | −0.335826 | + | 0.581669i | ||||
\(875\) | −1.16129 | − | 2.01141i | −0.0392588 | − | 0.0679982i | ||||
\(876\) | 13.5734i | 0.458601i | ||||||||
\(877\) | 1.65393 | − | 0.954895i | 0.0558491 | − | 0.0322445i | −0.471815 | − | 0.881697i | \(-0.656401\pi\) |
0.527665 | + | 0.849453i | \(0.323068\pi\) | |||||||
\(878\) | 27.4513 | − | 15.8490i | 0.926438 | − | 0.534879i | ||||
\(879\) | 6.84302i | 0.230809i | ||||||||
\(880\) | 2.67270 | + | 4.62926i | 0.0900968 | + | 0.156052i | ||||
\(881\) | 3.18412 | − | 5.51505i | 0.107276 | − | 0.185807i | −0.807390 | − | 0.590018i | \(-0.799121\pi\) |
0.914666 | + | 0.404211i | \(0.132454\pi\) | |||||||
\(882\) | −1.39051 | − | 0.802812i | −0.0468209 | − | 0.0270321i | ||||
\(883\) | −34.9897 | −1.17750 | −0.588749 | − | 0.808316i | \(-0.700379\pi\) | ||||
−0.588749 | + | 0.808316i | \(0.700379\pi\) | |||||||
\(884\) | 6.64516 | − | 12.8001i | 0.223501 | − | 0.430513i | ||||
\(885\) | 6.78668 | 0.228132 | ||||||||
\(886\) | 24.3270 | + | 14.0452i | 0.817281 | + | 0.471858i | ||||
\(887\) | −10.7001 | + | 18.5331i | −0.359273 | + | 0.622279i | −0.987840 | − | 0.155477i | \(-0.950309\pi\) |
0.628567 | + | 0.777756i | \(0.283642\pi\) | |||||||
\(888\) | −1.57463 | − | 2.72733i | −0.0528410 | − | 0.0915233i | ||||
\(889\) | − | 4.95194i | − | 0.166083i | ||||||
\(890\) | 1.50670 | − | 0.869891i | 0.0505046 | − | 0.0291588i | ||||
\(891\) | −4.62926 | + | 2.67270i | −0.155086 | + | 0.0895389i | ||||
\(892\) | 1.37891i | 0.0461694i | ||||||||
\(893\) | 3.65864 | + | 6.33696i | 0.122432 | + | 0.212058i | ||||
\(894\) | −9.73875 | + | 16.8680i | −0.325712 | + | 0.564150i | ||||
\(895\) | −6.34644 | − | 3.66412i | −0.212138 | − | 0.122478i | ||||
\(896\) | −2.32258 | −0.0775919 | ||||||||
\(897\) | 9.57893 | + | 14.9990i | 0.319831 | + | 0.500801i | ||||
\(898\) | −28.9167 | −0.964963 | ||||||||
\(899\) | −12.9011 | − | 7.44843i | −0.430274 | − | 0.248419i | ||||
\(900\) | −0.500000 | + | 0.866025i | −0.0166667 | + | 0.0288675i | ||||
\(901\) | −10.9739 | − | 19.0073i | −0.365592 | − | 0.633224i | ||||
\(902\) | − | 14.1395i | − | 0.470792i | ||||||
\(903\) | 24.6414 | − | 14.2267i | 0.820014 | − | 0.473435i | ||||
\(904\) | 6.15720 | − | 3.55486i | 0.204785 | − | 0.118233i | ||||
\(905\) | 19.5734i | 0.650641i | ||||||||
\(906\) | 7.25851 | + | 12.5721i | 0.241148 | + | 0.417681i | ||||
\(907\) | 16.2347 | − | 28.1192i | 0.539063 | − | 0.933684i | −0.459892 | − | 0.887975i | \(-0.652112\pi\) |
0.998955 | − | 0.0457093i | \(-0.0145548\pi\) | |||||||
\(908\) | −16.7321 | − | 9.66025i | −0.555273 | − | 0.320587i | ||||
\(909\) | −12.6908 | −0.420928 | ||||||||
\(910\) | 0.374609 | + | 8.36580i | 0.0124182 | + | 0.277323i | ||||
\(911\) | 34.4380 | 1.14098 | 0.570490 | − | 0.821304i | \(-0.306753\pi\) | ||||
0.570490 | + | 0.821304i | \(0.306753\pi\) | |||||||
\(912\) | 3.48387 | + | 2.01141i | 0.115362 | + | 0.0666045i | ||||
\(913\) | 30.2977 | − | 52.4771i | 1.00271 | − | 1.73674i | ||||
\(914\) | −4.84950 | − | 8.39958i | −0.160407 | − | 0.277833i | ||||
\(915\) | − | 0.535898i | − | 0.0177163i | ||||||
\(916\) | 13.6508 | − | 7.88130i | 0.451036 | − | 0.260406i | ||||
\(917\) | −2.53139 | + | 1.46150i | −0.0835939 | + | 0.0482630i | ||||
\(918\) | − | 4.00000i | − | 0.132020i | ||||||
\(919\) | −18.2413 | − | 31.5949i | −0.601727 | − | 1.04222i | −0.992560 | − | 0.121759i | \(-0.961146\pi\) |
0.390833 | − | 0.920462i | \(-0.372187\pi\) | |||||||
\(920\) | 2.46797 | − | 4.27464i | 0.0813665 | − | 0.140931i | ||||
\(921\) | 4.11745 | + | 2.37721i | 0.135675 | + | 0.0783317i | ||||
\(922\) | −11.9979 | −0.395131 | ||||||||
\(923\) | −48.2303 | + | 30.8018i | −1.58752 | + | 1.01385i | ||||
\(924\) | 12.4151 | 0.408428 | ||||||||
\(925\) | 2.72733 | + | 1.57463i | 0.0896742 | + | 0.0517734i | ||||
\(926\) | 3.21332 | − | 5.56563i | 0.105596 | − | 0.182898i | ||||
\(927\) | 2.39806 | + | 4.15356i | 0.0787626 | + | 0.136421i | ||||
\(928\) | 4.29078i | 0.140852i | ||||||||
\(929\) | 43.2233 | − | 24.9550i | 1.41811 | − | 0.818747i | 0.421978 | − | 0.906606i | \(-0.361336\pi\) |
0.996133 | + | 0.0878597i | \(0.0280027\pi\) | |||||||
\(930\) | 3.00670 | − | 1.73592i | 0.0985934 | − | 0.0569229i | ||||
\(931\) | − | 6.45914i | − | 0.211690i | ||||||
\(932\) | −8.27747 | − | 14.3370i | −0.271138 | − | 0.469624i | ||||
\(933\) | −0.968196 | + | 1.67696i | −0.0316973 | + | 0.0549013i | ||||
\(934\) | −22.7454 | − | 13.1321i | −0.744254 | − | 0.429695i | ||||
\(935\) | 21.3816 | 0.699254 | ||||||||
\(936\) | 3.03873 | − | 1.94065i | 0.0993239 | − | 0.0634322i | ||||
\(937\) | −15.8873 | −0.519017 | −0.259508 | − | 0.965741i | \(-0.583560\pi\) | ||||
−0.259508 | + | 0.965741i | \(0.583560\pi\) | |||||||
\(938\) | 8.26542 | + | 4.77204i | 0.269876 | + | 0.155813i | ||||
\(939\) | −12.7772 | + | 22.1308i | −0.416970 | + | 0.722213i | ||||
\(940\) | −0.909471 | − | 1.57525i | −0.0296637 | − | 0.0513790i | ||||
\(941\) | 6.99273i | 0.227956i | 0.993483 | + | 0.113978i | \(0.0363594\pi\) | ||||
−0.993483 | + | 0.113978i | \(0.963641\pi\) | |||||||
\(942\) | 21.1162 | − | 12.1914i | 0.688002 | − | 0.397218i | ||||
\(943\) | −11.3071 | + | 6.52817i | −0.368210 | + | 0.212586i | ||||
\(944\) | 6.78668i | 0.220888i | ||||||||
\(945\) | 1.16129 | + | 2.01141i | 0.0377768 | + | 0.0654313i | ||||
\(946\) | 32.7427 | − | 56.7120i | 1.06456 | − | 1.84387i | ||||
\(947\) | −45.2987 | − | 26.1532i | −1.47201 | − | 0.849865i | −0.472505 | − | 0.881328i | \(-0.656650\pi\) |
−0.999505 | + | 0.0314631i | \(0.989983\pi\) | |||||||
\(948\) | 7.96774 | 0.258780 | ||||||||
\(949\) | 2.18925 | + | 48.8905i | 0.0710659 | + | 1.58705i | ||||
\(950\) | −4.02283 | −0.130518 | ||||||||
\(951\) | 10.9697 | + | 6.33337i | 0.355717 | + | 0.205374i | ||||
\(952\) | −4.64516 | + | 8.04565i | −0.150550 | + | 0.260761i | ||||
\(953\) | 14.4414 | + | 25.0132i | 0.467802 | + | 0.810256i | 0.999323 | − | 0.0367885i | \(-0.0117128\pi\) |
−0.531521 | + | 0.847045i | \(0.678379\pi\) | |||||||
\(954\) | − | 5.48693i | − | 0.177646i | ||||||
\(955\) | 14.7549 | − | 8.51873i | 0.477457 | − | 0.275660i | ||||
\(956\) | −22.6904 | + | 13.1003i | −0.733859 | + | 0.423693i | ||||
\(957\) | − | 22.9359i | − | 0.741413i | ||||||
\(958\) | 12.8413 | + | 22.2418i | 0.414884 | + | 0.718600i | ||||
\(959\) | −22.8947 | + | 39.6548i | −0.739308 | + | 1.28052i | ||||
\(960\) | −0.866025 | − | 0.500000i | −0.0279508 | − | 0.0161374i | ||||
\(961\) | 18.9464 | 0.611173 | ||||||||
\(962\) | −6.11160 | − | 9.56973i | −0.197046 | − | 0.308540i | ||||
\(963\) | 3.07180 | 0.0989873 | ||||||||
\(964\) | −13.5529 | − | 7.82479i | −0.436510 | − | 0.252019i | ||||
\(965\) | 3.07746 | − | 5.33031i | 0.0990668 | − | 0.171589i | ||||
\(966\) | −5.73205 | − | 9.92820i | −0.184426 | − | 0.319435i | ||||
\(967\) | 10.8610i | 0.349265i | 0.984634 | + | 0.174633i | \(0.0558738\pi\) | ||||
−0.984634 | + | 0.174633i | \(0.944126\pi\) | |||||||
\(968\) | 15.2190 | − | 8.78668i | 0.489156 | − | 0.282415i | ||||
\(969\) | 13.9355 | − | 8.04565i | 0.447672 | − | 0.258464i | ||||
\(970\) | − | 16.1093i | − | 0.517237i | ||||||
\(971\) | 12.4990 | + | 21.6488i | 0.401111 | + | 0.694744i | 0.993860 | − | 0.110643i | \(-0.0352909\pi\) |
−0.592749 | + | 0.805387i | \(0.701958\pi\) | |||||||
\(972\) | 0.500000 | − | 0.866025i | 0.0160375 | − | 0.0277778i | ||||
\(973\) | 11.4196 | + | 6.59313i | 0.366097 | + | 0.211366i | ||||
\(974\) | 9.37891 | 0.300520 | ||||||||
\(975\) | −1.66129 | + | 3.20002i | −0.0532039 | + | 0.102483i | ||||
\(976\) | 0.535898 | 0.0171537 | ||||||||
\(977\) | −37.0359 | − | 21.3827i | −1.18488 | − | 0.684092i | −0.227743 | − | 0.973721i | \(-0.573135\pi\) |
−0.957139 | + | 0.289629i | \(0.906468\pi\) | |||||||
\(978\) | 11.8134 | − | 20.4614i | 0.377750 | − | 0.654282i | ||||
\(979\) | −4.64992 | − | 8.05390i | −0.148612 | − | 0.257404i | ||||
\(980\) | 1.60562i | 0.0512898i | ||||||||
\(981\) | −5.79441 | + | 3.34541i | −0.185001 | + | 0.106811i | ||||
\(982\) | 6.70177 | − | 3.86927i | 0.213862 | − | 0.123473i | ||||
\(983\) | − | 10.1288i | − | 0.323058i | −0.986868 | − | 0.161529i | \(-0.948358\pi\) | ||
0.986868 | − | 0.161529i | \(-0.0516425\pi\) | |||||||
\(984\) | 1.32258 | + | 2.29078i | 0.0421623 | + | 0.0730272i | ||||
\(985\) | −6.89334 | + | 11.9396i | −0.219640 | + | 0.380428i | ||||
\(986\) | 14.8637 | + | 8.58155i | 0.473356 | + | 0.273292i | ||||
\(987\) | −4.22464 | −0.134472 | ||||||||
\(988\) | 12.8731 | + | 6.68308i | 0.409548 | + | 0.212617i | ||||
\(989\) | −60.4691 | −1.92280 | ||||||||
\(990\) | 4.62926 | + | 2.67270i | 0.147127 | + | 0.0849441i | ||||
\(991\) | −10.1241 | + | 17.5355i | −0.321604 | + | 0.557035i | −0.980819 | − | 0.194920i | \(-0.937555\pi\) |
0.659215 | + | 0.751954i | \(0.270889\pi\) | |||||||
\(992\) | 1.73592 | + | 3.00670i | 0.0551154 | + | 0.0954627i | ||||
\(993\) | − | 23.6981i | − | 0.752036i | ||||||
\(994\) | 31.9249 | − | 18.4318i | 1.01260 | − | 0.584622i | ||||
\(995\) | 1.97717 | − | 1.14152i | 0.0626806 | − | 0.0361887i | ||||
\(996\) | 11.3360i | 0.359194i | ||||||||
\(997\) | 10.3981 | + | 18.0100i | 0.329310 | + | 0.570381i | 0.982375 | − | 0.186920i | \(-0.0598506\pi\) |
−0.653065 | + | 0.757302i | \(0.726517\pi\) | |||||||
\(998\) | 1.59053 | − | 2.75488i | 0.0503473 | − | 0.0872041i | ||||
\(999\) | −2.72733 | − | 1.57463i | −0.0862890 | − | 0.0498190i |
(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 | 390.2.bb.c.121.1 | ✓ | 8 | |
3.2 | odd | 2 | 1170.2.bs.f.901.3 | 8 | |||
5.2 | odd | 4 | 1950.2.y.k.199.3 | 8 | |||
5.3 | odd | 4 | 1950.2.y.j.199.2 | 8 | |||
5.4 | even | 2 | 1950.2.bc.g.901.4 | 8 | |||
13.4 | even | 6 | 5070.2.b.ba.1351.3 | 8 | |||
13.6 | odd | 12 | 5070.2.a.ca.1.3 | 4 | |||
13.7 | odd | 12 | 5070.2.a.bz.1.2 | 4 | |||
13.9 | even | 3 | 5070.2.b.ba.1351.6 | 8 | |||
13.10 | even | 6 | inner | 390.2.bb.c.361.1 | yes | 8 | |
39.23 | odd | 6 | 1170.2.bs.f.361.3 | 8 | |||
65.23 | odd | 12 | 1950.2.y.k.49.3 | 8 | |||
65.49 | even | 6 | 1950.2.bc.g.751.4 | 8 | |||
65.62 | odd | 12 | 1950.2.y.j.49.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.bb.c.121.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
390.2.bb.c.361.1 | yes | 8 | 13.10 | even | 6 | inner | |
1170.2.bs.f.361.3 | 8 | 39.23 | odd | 6 | |||
1170.2.bs.f.901.3 | 8 | 3.2 | odd | 2 | |||
1950.2.y.j.49.2 | 8 | 65.62 | odd | 12 | |||
1950.2.y.j.199.2 | 8 | 5.3 | odd | 4 | |||
1950.2.y.k.49.3 | 8 | 65.23 | odd | 12 | |||
1950.2.y.k.199.3 | 8 | 5.2 | odd | 4 | |||
1950.2.bc.g.751.4 | 8 | 65.49 | even | 6 | |||
1950.2.bc.g.901.4 | 8 | 5.4 | even | 2 | |||
5070.2.a.bz.1.2 | 4 | 13.7 | odd | 12 | |||
5070.2.a.ca.1.3 | 4 | 13.6 | odd | 12 | |||
5070.2.b.ba.1351.3 | 8 | 13.4 | even | 6 | |||
5070.2.b.ba.1351.6 | 8 | 13.9 | even | 3 |