Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [130,2,Mod(61,130)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(130, 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("130.61");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 130 = 2 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 130.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: | \(1.03805522628\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 81.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 130.81 |
Dual form | 130.2.e.b.61.1 |
$q$-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 \(\left(\mathbb{Z}/130\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(41\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | 1.00000 | + | 1.73205i | 0.577350 | + | 1.00000i | 0.995782 | + | 0.0917517i | \(0.0292466\pi\) |
−0.418432 | + | 0.908248i | \(0.637420\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.00000 | + | 1.73205i | −0.408248 | + | 0.707107i | ||||
\(7\) | 0.500000 | − | 0.866025i | 0.188982 | − | 0.327327i | −0.755929 | − | 0.654654i | \(-0.772814\pi\) |
0.944911 | + | 0.327327i | \(0.106148\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −0.500000 | − | 0.866025i | −0.158114 | − | 0.273861i | ||||
\(11\) | −1.50000 | − | 2.59808i | −0.452267 | − | 0.783349i | 0.546259 | − | 0.837616i | \(-0.316051\pi\) |
−0.998526 | + | 0.0542666i | \(0.982718\pi\) | |||||||
\(12\) | −2.00000 | −0.577350 | ||||||||
\(13\) | 2.50000 | + | 2.59808i | 0.693375 | + | 0.720577i | ||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −1.00000 | − | 1.73205i | −0.258199 | − | 0.447214i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 3.00000 | − | 5.19615i | 0.727607 | − | 1.26025i | −0.230285 | − | 0.973123i | \(-0.573966\pi\) |
0.957892 | − | 0.287129i | \(-0.0927008\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −2.50000 | + | 4.33013i | −0.573539 | + | 0.993399i | 0.422659 | + | 0.906289i | \(0.361097\pi\) |
−0.996199 | + | 0.0871106i | \(0.972237\pi\) | |||||||
\(20\) | 0.500000 | − | 0.866025i | 0.111803 | − | 0.193649i | ||||
\(21\) | 2.00000 | 0.436436 | ||||||||
\(22\) | 1.50000 | − | 2.59808i | 0.319801 | − | 0.553912i | ||||
\(23\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(24\) | −1.00000 | − | 1.73205i | −0.204124 | − | 0.353553i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.00000 | + | 3.46410i | −0.196116 | + | 0.679366i | ||||
\(27\) | 4.00000 | 0.769800 | ||||||||
\(28\) | 0.500000 | + | 0.866025i | 0.0944911 | + | 0.163663i | ||||
\(29\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(30\) | 1.00000 | − | 1.73205i | 0.182574 | − | 0.316228i | ||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 3.00000 | − | 5.19615i | 0.522233 | − | 0.904534i | ||||
\(34\) | 6.00000 | 1.02899 | ||||||||
\(35\) | −0.500000 | + | 0.866025i | −0.0845154 | + | 0.146385i | ||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | −5.50000 | − | 9.52628i | −0.904194 | − | 1.56611i | −0.821995 | − | 0.569495i | \(-0.807139\pi\) |
−0.0821995 | − | 0.996616i | \(-0.526194\pi\) | |||||||
\(38\) | −5.00000 | −0.811107 | ||||||||
\(39\) | −2.00000 | + | 6.92820i | −0.320256 | + | 1.10940i | ||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −3.00000 | − | 5.19615i | −0.468521 | − | 0.811503i | 0.530831 | − | 0.847477i | \(-0.321880\pi\) |
−0.999353 | + | 0.0359748i | \(0.988546\pi\) | |||||||
\(42\) | 1.00000 | + | 1.73205i | 0.154303 | + | 0.267261i | ||||
\(43\) | −1.00000 | + | 1.73205i | −0.152499 | + | 0.264135i | −0.932145 | − | 0.362084i | \(-0.882065\pi\) |
0.779647 | + | 0.626219i | \(0.215399\pi\) | |||||||
\(44\) | 3.00000 | 0.452267 | ||||||||
\(45\) | 0.500000 | − | 0.866025i | 0.0745356 | − | 0.129099i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.00000 | −0.437595 | −0.218797 | − | 0.975770i | \(-0.570213\pi\) | ||||
−0.218797 | + | 0.975770i | \(0.570213\pi\) | |||||||
\(48\) | 1.00000 | − | 1.73205i | 0.144338 | − | 0.250000i | ||||
\(49\) | 3.00000 | + | 5.19615i | 0.428571 | + | 0.742307i | ||||
\(50\) | 0.500000 | + | 0.866025i | 0.0707107 | + | 0.122474i | ||||
\(51\) | 12.0000 | 1.68034 | ||||||||
\(52\) | −3.50000 | + | 0.866025i | −0.485363 | + | 0.120096i | ||||
\(53\) | −9.00000 | −1.23625 | −0.618123 | − | 0.786082i | \(-0.712106\pi\) | ||||
−0.618123 | + | 0.786082i | \(0.712106\pi\) | |||||||
\(54\) | 2.00000 | + | 3.46410i | 0.272166 | + | 0.471405i | ||||
\(55\) | 1.50000 | + | 2.59808i | 0.202260 | + | 0.350325i | ||||
\(56\) | −0.500000 | + | 0.866025i | −0.0668153 | + | 0.115728i | ||||
\(57\) | −10.0000 | −1.32453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(60\) | 2.00000 | 0.258199 | ||||||||
\(61\) | −4.00000 | + | 6.92820i | −0.512148 | + | 0.887066i | 0.487753 | + | 0.872982i | \(0.337817\pi\) |
−0.999901 | + | 0.0140840i | \(0.995517\pi\) | |||||||
\(62\) | −2.00000 | − | 3.46410i | −0.254000 | − | 0.439941i | ||||
\(63\) | 0.500000 | + | 0.866025i | 0.0629941 | + | 0.109109i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.50000 | − | 2.59808i | −0.310087 | − | 0.322252i | ||||
\(66\) | 6.00000 | 0.738549 | ||||||||
\(67\) | 8.00000 | + | 13.8564i | 0.977356 | + | 1.69283i | 0.671932 | + | 0.740613i | \(0.265465\pi\) |
0.305424 | + | 0.952217i | \(0.401202\pi\) | |||||||
\(68\) | 3.00000 | + | 5.19615i | 0.363803 | + | 0.630126i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | −3.00000 | + | 5.19615i | −0.356034 | + | 0.616670i | −0.987294 | − | 0.158901i | \(-0.949205\pi\) |
0.631260 | + | 0.775571i | \(0.282538\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | 14.0000 | 1.63858 | 0.819288 | − | 0.573382i | \(-0.194369\pi\) | ||||
0.819288 | + | 0.573382i | \(0.194369\pi\) | |||||||
\(74\) | 5.50000 | − | 9.52628i | 0.639362 | − | 1.10741i | ||||
\(75\) | 1.00000 | + | 1.73205i | 0.115470 | + | 0.200000i | ||||
\(76\) | −2.50000 | − | 4.33013i | −0.286770 | − | 0.496700i | ||||
\(77\) | −3.00000 | −0.341882 | ||||||||
\(78\) | −7.00000 | + | 1.73205i | −0.792594 | + | 0.196116i | ||||
\(79\) | −16.0000 | −1.80014 | −0.900070 | − | 0.435745i | \(-0.856485\pi\) | ||||
−0.900070 | + | 0.435745i | \(0.856485\pi\) | |||||||
\(80\) | 0.500000 | + | 0.866025i | 0.0559017 | + | 0.0968246i | ||||
\(81\) | 5.50000 | + | 9.52628i | 0.611111 | + | 1.05848i | ||||
\(82\) | 3.00000 | − | 5.19615i | 0.331295 | − | 0.573819i | ||||
\(83\) | −6.00000 | −0.658586 | −0.329293 | − | 0.944228i | \(-0.606810\pi\) | ||||
−0.329293 | + | 0.944228i | \(0.606810\pi\) | |||||||
\(84\) | −1.00000 | + | 1.73205i | −0.109109 | + | 0.188982i | ||||
\(85\) | −3.00000 | + | 5.19615i | −0.325396 | + | 0.563602i | ||||
\(86\) | −2.00000 | −0.215666 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.50000 | + | 2.59808i | 0.159901 | + | 0.276956i | ||||
\(89\) | −4.50000 | − | 7.79423i | −0.476999 | − | 0.826187i | 0.522654 | − | 0.852545i | \(-0.324942\pi\) |
−0.999653 | + | 0.0263586i | \(0.991609\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 3.50000 | − | 0.866025i | 0.366900 | − | 0.0907841i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.00000 | − | 6.92820i | −0.414781 | − | 0.718421i | ||||
\(94\) | −1.50000 | − | 2.59808i | −0.154713 | − | 0.267971i | ||||
\(95\) | 2.50000 | − | 4.33013i | 0.256495 | − | 0.444262i | ||||
\(96\) | 2.00000 | 0.204124 | ||||||||
\(97\) | 5.00000 | − | 8.66025i | 0.507673 | − | 0.879316i | −0.492287 | − | 0.870433i | \(-0.663839\pi\) |
0.999961 | − | 0.00888289i | \(-0.00282755\pi\) | |||||||
\(98\) | −3.00000 | + | 5.19615i | −0.303046 | + | 0.524891i | ||||
\(99\) | 3.00000 | 0.301511 | ||||||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | 3.00000 | + | 5.19615i | 0.298511 | + | 0.517036i | 0.975796 | − | 0.218685i | \(-0.0701767\pi\) |
−0.677284 | + | 0.735721i | \(0.736843\pi\) | |||||||
\(102\) | 6.00000 | + | 10.3923i | 0.594089 | + | 1.02899i | ||||
\(103\) | 5.00000 | 0.492665 | 0.246332 | − | 0.969185i | \(-0.420775\pi\) | ||||
0.246332 | + | 0.969185i | \(0.420775\pi\) | |||||||
\(104\) | −2.50000 | − | 2.59808i | −0.245145 | − | 0.254762i | ||||
\(105\) | −2.00000 | −0.195180 | ||||||||
\(106\) | −4.50000 | − | 7.79423i | −0.437079 | − | 0.757042i | ||||
\(107\) | 6.00000 | + | 10.3923i | 0.580042 | + | 1.00466i | 0.995474 | + | 0.0950377i | \(0.0302972\pi\) |
−0.415432 | + | 0.909624i | \(0.636370\pi\) | |||||||
\(108\) | −2.00000 | + | 3.46410i | −0.192450 | + | 0.333333i | ||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | −1.50000 | + | 2.59808i | −0.143019 | + | 0.247717i | ||||
\(111\) | 11.0000 | − | 19.0526i | 1.04407 | − | 1.80839i | ||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 6.00000 | − | 10.3923i | 0.564433 | − | 0.977626i | −0.432670 | − | 0.901553i | \(-0.642428\pi\) |
0.997102 | − | 0.0760733i | \(-0.0242383\pi\) | |||||||
\(114\) | −5.00000 | − | 8.66025i | −0.468293 | − | 0.811107i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.50000 | + | 0.866025i | −0.323575 | + | 0.0800641i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.00000 | − | 5.19615i | −0.275010 | − | 0.476331i | ||||
\(120\) | 1.00000 | + | 1.73205i | 0.0912871 | + | 0.158114i | ||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | −8.00000 | −0.724286 | ||||||||
\(123\) | 6.00000 | − | 10.3923i | 0.541002 | − | 0.937043i | ||||
\(124\) | 2.00000 | − | 3.46410i | 0.179605 | − | 0.311086i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −0.500000 | + | 0.866025i | −0.0445435 | + | 0.0771517i | ||||
\(127\) | 0.500000 | + | 0.866025i | 0.0443678 | + | 0.0768473i | 0.887357 | − | 0.461084i | \(-0.152539\pi\) |
−0.842989 | + | 0.537931i | \(0.819206\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | −4.00000 | −0.352180 | ||||||||
\(130\) | 1.00000 | − | 3.46410i | 0.0877058 | − | 0.303822i | ||||
\(131\) | −9.00000 | −0.786334 | −0.393167 | − | 0.919467i | \(-0.628621\pi\) | ||||
−0.393167 | + | 0.919467i | \(0.628621\pi\) | |||||||
\(132\) | 3.00000 | + | 5.19615i | 0.261116 | + | 0.452267i | ||||
\(133\) | 2.50000 | + | 4.33013i | 0.216777 | + | 0.375470i | ||||
\(134\) | −8.00000 | + | 13.8564i | −0.691095 | + | 1.19701i | ||||
\(135\) | −4.00000 | −0.344265 | ||||||||
\(136\) | −3.00000 | + | 5.19615i | −0.257248 | + | 0.445566i | ||||
\(137\) | −3.00000 | + | 5.19615i | −0.256307 | + | 0.443937i | −0.965250 | − | 0.261329i | \(-0.915839\pi\) |
0.708942 | + | 0.705266i | \(0.249173\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.50000 | − | 16.4545i | 0.805779 | − | 1.39565i | −0.109984 | − | 0.993933i | \(-0.535080\pi\) |
0.915764 | − | 0.401718i | \(-0.131587\pi\) | |||||||
\(140\) | −0.500000 | − | 0.866025i | −0.0422577 | − | 0.0731925i | ||||
\(141\) | −3.00000 | − | 5.19615i | −0.252646 | − | 0.437595i | ||||
\(142\) | −6.00000 | −0.503509 | ||||||||
\(143\) | 3.00000 | − | 10.3923i | 0.250873 | − | 0.869048i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 7.00000 | + | 12.1244i | 0.579324 | + | 1.00342i | ||||
\(147\) | −6.00000 | + | 10.3923i | −0.494872 | + | 0.857143i | ||||
\(148\) | 11.0000 | 0.904194 | ||||||||
\(149\) | 9.00000 | − | 15.5885i | 0.737309 | − | 1.27706i | −0.216394 | − | 0.976306i | \(-0.569430\pi\) |
0.953703 | − | 0.300750i | \(-0.0972370\pi\) | |||||||
\(150\) | −1.00000 | + | 1.73205i | −0.0816497 | + | 0.141421i | ||||
\(151\) | −16.0000 | −1.30206 | −0.651031 | − | 0.759051i | \(-0.725663\pi\) | ||||
−0.651031 | + | 0.759051i | \(0.725663\pi\) | |||||||
\(152\) | 2.50000 | − | 4.33013i | 0.202777 | − | 0.351220i | ||||
\(153\) | 3.00000 | + | 5.19615i | 0.242536 | + | 0.420084i | ||||
\(154\) | −1.50000 | − | 2.59808i | −0.120873 | − | 0.209359i | ||||
\(155\) | 4.00000 | 0.321288 | ||||||||
\(156\) | −5.00000 | − | 5.19615i | −0.400320 | − | 0.416025i | ||||
\(157\) | 17.0000 | 1.35675 | 0.678374 | − | 0.734717i | \(-0.262685\pi\) | ||||
0.678374 | + | 0.734717i | \(0.262685\pi\) | |||||||
\(158\) | −8.00000 | − | 13.8564i | −0.636446 | − | 1.10236i | ||||
\(159\) | −9.00000 | − | 15.5885i | −0.713746 | − | 1.23625i | ||||
\(160\) | −0.500000 | + | 0.866025i | −0.0395285 | + | 0.0684653i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −5.50000 | + | 9.52628i | −0.432121 | + | 0.748455i | ||||
\(163\) | −1.00000 | + | 1.73205i | −0.0783260 | + | 0.135665i | −0.902528 | − | 0.430632i | \(-0.858291\pi\) |
0.824202 | + | 0.566296i | \(0.191624\pi\) | |||||||
\(164\) | 6.00000 | 0.468521 | ||||||||
\(165\) | −3.00000 | + | 5.19615i | −0.233550 | + | 0.404520i | ||||
\(166\) | −3.00000 | − | 5.19615i | −0.232845 | − | 0.403300i | ||||
\(167\) | 7.50000 | + | 12.9904i | 0.580367 | + | 1.00523i | 0.995436 | + | 0.0954356i | \(0.0304244\pi\) |
−0.415068 | + | 0.909790i | \(0.636242\pi\) | |||||||
\(168\) | −2.00000 | −0.154303 | ||||||||
\(169\) | −0.500000 | + | 12.9904i | −0.0384615 | + | 0.999260i | ||||
\(170\) | −6.00000 | −0.460179 | ||||||||
\(171\) | −2.50000 | − | 4.33013i | −0.191180 | − | 0.331133i | ||||
\(172\) | −1.00000 | − | 1.73205i | −0.0762493 | − | 0.132068i | ||||
\(173\) | −7.50000 | + | 12.9904i | −0.570214 | + | 0.987640i | 0.426329 | + | 0.904568i | \(0.359807\pi\) |
−0.996544 | + | 0.0830722i | \(0.973527\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.500000 | − | 0.866025i | 0.0377964 | − | 0.0654654i | ||||
\(176\) | −1.50000 | + | 2.59808i | −0.113067 | + | 0.195837i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.50000 | − | 7.79423i | 0.337289 | − | 0.584202i | ||||
\(179\) | 12.0000 | + | 20.7846i | 0.896922 | + | 1.55351i | 0.831408 | + | 0.555663i | \(0.187536\pi\) |
0.0655145 | + | 0.997852i | \(0.479131\pi\) | |||||||
\(180\) | 0.500000 | + | 0.866025i | 0.0372678 | + | 0.0645497i | ||||
\(181\) | 8.00000 | 0.594635 | 0.297318 | − | 0.954779i | \(-0.403908\pi\) | ||||
0.297318 | + | 0.954779i | \(0.403908\pi\) | |||||||
\(182\) | 2.50000 | + | 2.59808i | 0.185312 | + | 0.192582i | ||||
\(183\) | −16.0000 | −1.18275 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.50000 | + | 9.52628i | 0.404368 | + | 0.700386i | ||||
\(186\) | 4.00000 | − | 6.92820i | 0.293294 | − | 0.508001i | ||||
\(187\) | −18.0000 | −1.31629 | ||||||||
\(188\) | 1.50000 | − | 2.59808i | 0.109399 | − | 0.189484i | ||||
\(189\) | 2.00000 | − | 3.46410i | 0.145479 | − | 0.251976i | ||||
\(190\) | 5.00000 | 0.362738 | ||||||||
\(191\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(192\) | 1.00000 | + | 1.73205i | 0.0721688 | + | 0.125000i | ||||
\(193\) | 2.00000 | + | 3.46410i | 0.143963 | + | 0.249351i | 0.928986 | − | 0.370116i | \(-0.120682\pi\) |
−0.785022 | + | 0.619467i | \(0.787349\pi\) | |||||||
\(194\) | 10.0000 | 0.717958 | ||||||||
\(195\) | 2.00000 | − | 6.92820i | 0.143223 | − | 0.496139i | ||||
\(196\) | −6.00000 | −0.428571 | ||||||||
\(197\) | 13.5000 | + | 23.3827i | 0.961835 | + | 1.66595i | 0.717888 | + | 0.696159i | \(0.245109\pi\) |
0.243947 | + | 0.969788i | \(0.421558\pi\) | |||||||
\(198\) | 1.50000 | + | 2.59808i | 0.106600 | + | 0.184637i | ||||
\(199\) | 5.00000 | − | 8.66025i | 0.354441 | − | 0.613909i | −0.632581 | − | 0.774494i | \(-0.718005\pi\) |
0.987022 | + | 0.160585i | \(0.0513380\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −16.0000 | + | 27.7128i | −1.12855 | + | 1.95471i | ||||
\(202\) | −3.00000 | + | 5.19615i | −0.211079 | + | 0.365600i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −6.00000 | + | 10.3923i | −0.420084 | + | 0.727607i | ||||
\(205\) | 3.00000 | + | 5.19615i | 0.209529 | + | 0.362915i | ||||
\(206\) | 2.50000 | + | 4.33013i | 0.174183 | + | 0.301694i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.00000 | − | 3.46410i | 0.0693375 | − | 0.240192i | ||||
\(209\) | 15.0000 | 1.03757 | ||||||||
\(210\) | −1.00000 | − | 1.73205i | −0.0690066 | − | 0.119523i | ||||
\(211\) | −11.5000 | − | 19.9186i | −0.791693 | − | 1.37125i | −0.924918 | − | 0.380166i | \(-0.875867\pi\) |
0.133226 | − | 0.991086i | \(-0.457467\pi\) | |||||||
\(212\) | 4.50000 | − | 7.79423i | 0.309061 | − | 0.535310i | ||||
\(213\) | −12.0000 | −0.822226 | ||||||||
\(214\) | −6.00000 | + | 10.3923i | −0.410152 | + | 0.710403i | ||||
\(215\) | 1.00000 | − | 1.73205i | 0.0681994 | − | 0.118125i | ||||
\(216\) | −4.00000 | −0.272166 | ||||||||
\(217\) | −2.00000 | + | 3.46410i | −0.135769 | + | 0.235159i | ||||
\(218\) | 1.00000 | + | 1.73205i | 0.0677285 | + | 0.117309i | ||||
\(219\) | 14.0000 | + | 24.2487i | 0.946032 | + | 1.63858i | ||||
\(220\) | −3.00000 | −0.202260 | ||||||||
\(221\) | 21.0000 | − | 5.19615i | 1.41261 | − | 0.349531i | ||||
\(222\) | 22.0000 | 1.47654 | ||||||||
\(223\) | 9.50000 | + | 16.4545i | 0.636167 | + | 1.10187i | 0.986267 | + | 0.165161i | \(0.0528144\pi\) |
−0.350100 | + | 0.936713i | \(0.613852\pi\) | |||||||
\(224\) | −0.500000 | − | 0.866025i | −0.0334077 | − | 0.0578638i | ||||
\(225\) | −0.500000 | + | 0.866025i | −0.0333333 | + | 0.0577350i | ||||
\(226\) | 12.0000 | 0.798228 | ||||||||
\(227\) | 12.0000 | − | 20.7846i | 0.796468 | − | 1.37952i | −0.125435 | − | 0.992102i | \(-0.540033\pi\) |
0.921903 | − | 0.387421i | \(-0.126634\pi\) | |||||||
\(228\) | 5.00000 | − | 8.66025i | 0.331133 | − | 0.573539i | ||||
\(229\) | −4.00000 | −0.264327 | −0.132164 | − | 0.991228i | \(-0.542192\pi\) | ||||
−0.132164 | + | 0.991228i | \(0.542192\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.00000 | − | 5.19615i | −0.197386 | − | 0.341882i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −24.0000 | −1.57229 | −0.786146 | − | 0.618041i | \(-0.787927\pi\) | ||||
−0.786146 | + | 0.618041i | \(0.787927\pi\) | |||||||
\(234\) | −2.50000 | − | 2.59808i | −0.163430 | − | 0.169842i | ||||
\(235\) | 3.00000 | 0.195698 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −16.0000 | − | 27.7128i | −1.03931 | − | 1.80014i | ||||
\(238\) | 3.00000 | − | 5.19615i | 0.194461 | − | 0.336817i | ||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | −1.00000 | + | 1.73205i | −0.0645497 | + | 0.111803i | ||||
\(241\) | −11.5000 | + | 19.9186i | −0.740780 | + | 1.28307i | 0.211360 | + | 0.977408i | \(0.432211\pi\) |
−0.952141 | + | 0.305661i | \(0.901123\pi\) | |||||||
\(242\) | 2.00000 | 0.128565 | ||||||||
\(243\) | −5.00000 | + | 8.66025i | −0.320750 | + | 0.555556i | ||||
\(244\) | −4.00000 | − | 6.92820i | −0.256074 | − | 0.443533i | ||||
\(245\) | −3.00000 | − | 5.19615i | −0.191663 | − | 0.331970i | ||||
\(246\) | 12.0000 | 0.765092 | ||||||||
\(247\) | −17.5000 | + | 4.33013i | −1.11350 | + | 0.275519i | ||||
\(248\) | 4.00000 | 0.254000 | ||||||||
\(249\) | −6.00000 | − | 10.3923i | −0.380235 | − | 0.658586i | ||||
\(250\) | −0.500000 | − | 0.866025i | −0.0316228 | − | 0.0547723i | ||||
\(251\) | 7.50000 | − | 12.9904i | 0.473396 | − | 0.819946i | −0.526140 | − | 0.850398i | \(-0.676361\pi\) |
0.999536 | + | 0.0304521i | \(0.00969471\pi\) | |||||||
\(252\) | −1.00000 | −0.0629941 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −0.500000 | + | 0.866025i | −0.0313728 | + | 0.0543393i | ||||
\(255\) | −12.0000 | −0.751469 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −6.00000 | − | 10.3923i | −0.374270 | − | 0.648254i | 0.615948 | − | 0.787787i | \(-0.288773\pi\) |
−0.990217 | + | 0.139533i | \(0.955440\pi\) | |||||||
\(258\) | −2.00000 | − | 3.46410i | −0.124515 | − | 0.215666i | ||||
\(259\) | −11.0000 | −0.683507 | ||||||||
\(260\) | 3.50000 | − | 0.866025i | 0.217061 | − | 0.0537086i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.50000 | − | 7.79423i | −0.278011 | − | 0.481529i | ||||
\(263\) | −4.50000 | − | 7.79423i | −0.277482 | − | 0.480613i | 0.693276 | − | 0.720672i | \(-0.256167\pi\) |
−0.970758 | + | 0.240059i | \(0.922833\pi\) | |||||||
\(264\) | −3.00000 | + | 5.19615i | −0.184637 | + | 0.319801i | ||||
\(265\) | 9.00000 | 0.552866 | ||||||||
\(266\) | −2.50000 | + | 4.33013i | −0.153285 | + | 0.265497i | ||||
\(267\) | 9.00000 | − | 15.5885i | 0.550791 | − | 0.953998i | ||||
\(268\) | −16.0000 | −0.977356 | ||||||||
\(269\) | −3.00000 | + | 5.19615i | −0.182913 | + | 0.316815i | −0.942871 | − | 0.333157i | \(-0.891886\pi\) |
0.759958 | + | 0.649972i | \(0.225219\pi\) | |||||||
\(270\) | −2.00000 | − | 3.46410i | −0.121716 | − | 0.210819i | ||||
\(271\) | −10.0000 | − | 17.3205i | −0.607457 | − | 1.05215i | −0.991658 | − | 0.128897i | \(-0.958856\pi\) |
0.384201 | − | 0.923249i | \(-0.374477\pi\) | |||||||
\(272\) | −6.00000 | −0.363803 | ||||||||
\(273\) | 5.00000 | + | 5.19615i | 0.302614 | + | 0.314485i | ||||
\(274\) | −6.00000 | −0.362473 | ||||||||
\(275\) | −1.50000 | − | 2.59808i | −0.0904534 | − | 0.156670i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.500000 | − | 0.866025i | 0.0300421 | − | 0.0520344i | −0.850613 | − | 0.525792i | \(-0.823769\pi\) |
0.880656 | + | 0.473757i | \(0.157103\pi\) | |||||||
\(278\) | 19.0000 | 1.13954 | ||||||||
\(279\) | 2.00000 | − | 3.46410i | 0.119737 | − | 0.207390i | ||||
\(280\) | 0.500000 | − | 0.866025i | 0.0298807 | − | 0.0517549i | ||||
\(281\) | −6.00000 | −0.357930 | −0.178965 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178965 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(282\) | 3.00000 | − | 5.19615i | 0.178647 | − | 0.309426i | ||||
\(283\) | −7.00000 | − | 12.1244i | −0.416107 | − | 0.720718i | 0.579437 | − | 0.815017i | \(-0.303272\pi\) |
−0.995544 | + | 0.0942988i | \(0.969939\pi\) | |||||||
\(284\) | −3.00000 | − | 5.19615i | −0.178017 | − | 0.308335i | ||||
\(285\) | 10.0000 | 0.592349 | ||||||||
\(286\) | 10.5000 | − | 2.59808i | 0.620878 | − | 0.153627i | ||||
\(287\) | −6.00000 | −0.354169 | ||||||||
\(288\) | 0.500000 | + | 0.866025i | 0.0294628 | + | 0.0510310i | ||||
\(289\) | −9.50000 | − | 16.4545i | −0.558824 | − | 0.967911i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 20.0000 | 1.17242 | ||||||||
\(292\) | −7.00000 | + | 12.1244i | −0.409644 | + | 0.709524i | ||||
\(293\) | −4.50000 | + | 7.79423i | −0.262893 | + | 0.455344i | −0.967009 | − | 0.254741i | \(-0.918010\pi\) |
0.704117 | + | 0.710084i | \(0.251343\pi\) | |||||||
\(294\) | −12.0000 | −0.699854 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.50000 | + | 9.52628i | 0.319681 | + | 0.553704i | ||||
\(297\) | −6.00000 | − | 10.3923i | −0.348155 | − | 0.603023i | ||||
\(298\) | 18.0000 | 1.04271 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −2.00000 | −0.115470 | ||||||||
\(301\) | 1.00000 | + | 1.73205i | 0.0576390 | + | 0.0998337i | ||||
\(302\) | −8.00000 | − | 13.8564i | −0.460348 | − | 0.797347i | ||||
\(303\) | −6.00000 | + | 10.3923i | −0.344691 | + | 0.597022i | ||||
\(304\) | 5.00000 | 0.286770 | ||||||||
\(305\) | 4.00000 | − | 6.92820i | 0.229039 | − | 0.396708i | ||||
\(306\) | −3.00000 | + | 5.19615i | −0.171499 | + | 0.297044i | ||||
\(307\) | 2.00000 | 0.114146 | 0.0570730 | − | 0.998370i | \(-0.481823\pi\) | ||||
0.0570730 | + | 0.998370i | \(0.481823\pi\) | |||||||
\(308\) | 1.50000 | − | 2.59808i | 0.0854704 | − | 0.148039i | ||||
\(309\) | 5.00000 | + | 8.66025i | 0.284440 | + | 0.492665i | ||||
\(310\) | 2.00000 | + | 3.46410i | 0.113592 | + | 0.196748i | ||||
\(311\) | 30.0000 | 1.70114 | 0.850572 | − | 0.525859i | \(-0.176256\pi\) | ||||
0.850572 | + | 0.525859i | \(0.176256\pi\) | |||||||
\(312\) | 2.00000 | − | 6.92820i | 0.113228 | − | 0.392232i | ||||
\(313\) | 14.0000 | 0.791327 | 0.395663 | − | 0.918396i | \(-0.370515\pi\) | ||||
0.395663 | + | 0.918396i | \(0.370515\pi\) | |||||||
\(314\) | 8.50000 | + | 14.7224i | 0.479683 | + | 0.830835i | ||||
\(315\) | −0.500000 | − | 0.866025i | −0.0281718 | − | 0.0487950i | ||||
\(316\) | 8.00000 | − | 13.8564i | 0.450035 | − | 0.779484i | ||||
\(317\) | 15.0000 | 0.842484 | 0.421242 | − | 0.906948i | \(-0.361594\pi\) | ||||
0.421242 | + | 0.906948i | \(0.361594\pi\) | |||||||
\(318\) | 9.00000 | − | 15.5885i | 0.504695 | − | 0.874157i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −12.0000 | + | 20.7846i | −0.669775 | + | 1.16008i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.0000 | + | 25.9808i | 0.834622 | + | 1.44561i | ||||
\(324\) | −11.0000 | −0.611111 | ||||||||
\(325\) | 2.50000 | + | 2.59808i | 0.138675 | + | 0.144115i | ||||
\(326\) | −2.00000 | −0.110770 | ||||||||
\(327\) | 2.00000 | + | 3.46410i | 0.110600 | + | 0.191565i | ||||
\(328\) | 3.00000 | + | 5.19615i | 0.165647 | + | 0.286910i | ||||
\(329\) | −1.50000 | + | 2.59808i | −0.0826977 | + | 0.143237i | ||||
\(330\) | −6.00000 | −0.330289 | ||||||||
\(331\) | −10.0000 | + | 17.3205i | −0.549650 | + | 0.952021i | 0.448649 | + | 0.893708i | \(0.351905\pi\) |
−0.998298 | + | 0.0583130i | \(0.981428\pi\) | |||||||
\(332\) | 3.00000 | − | 5.19615i | 0.164646 | − | 0.285176i | ||||
\(333\) | 11.0000 | 0.602796 | ||||||||
\(334\) | −7.50000 | + | 12.9904i | −0.410382 | + | 0.710802i | ||||
\(335\) | −8.00000 | − | 13.8564i | −0.437087 | − | 0.757056i | ||||
\(336\) | −1.00000 | − | 1.73205i | −0.0545545 | − | 0.0944911i | ||||
\(337\) | −16.0000 | −0.871576 | −0.435788 | − | 0.900049i | \(-0.643530\pi\) | ||||
−0.435788 | + | 0.900049i | \(0.643530\pi\) | |||||||
\(338\) | −11.5000 | + | 6.06218i | −0.625518 | + | 0.329739i | ||||
\(339\) | 24.0000 | 1.30350 | ||||||||
\(340\) | −3.00000 | − | 5.19615i | −0.162698 | − | 0.281801i | ||||
\(341\) | 6.00000 | + | 10.3923i | 0.324918 | + | 0.562775i | ||||
\(342\) | 2.50000 | − | 4.33013i | 0.135185 | − | 0.234146i | ||||
\(343\) | 13.0000 | 0.701934 | ||||||||
\(344\) | 1.00000 | − | 1.73205i | 0.0539164 | − | 0.0933859i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15.0000 | −0.806405 | ||||||||
\(347\) | −3.00000 | + | 5.19615i | −0.161048 | + | 0.278944i | −0.935245 | − | 0.354001i | \(-0.884821\pi\) |
0.774197 | + | 0.632945i | \(0.218154\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.00000 | − | 1.73205i | −0.0535288 | − | 0.0927146i | 0.838019 | − | 0.545640i | \(-0.183714\pi\) |
−0.891548 | + | 0.452926i | \(0.850380\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | 10.0000 | + | 10.3923i | 0.533761 | + | 0.554700i | ||||
\(352\) | −3.00000 | −0.159901 | ||||||||
\(353\) | −3.00000 | − | 5.19615i | −0.159674 | − | 0.276563i | 0.775077 | − | 0.631867i | \(-0.217711\pi\) |
−0.934751 | + | 0.355303i | \(0.884378\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.00000 | − | 5.19615i | 0.159223 | − | 0.275783i | ||||
\(356\) | 9.00000 | 0.476999 | ||||||||
\(357\) | 6.00000 | − | 10.3923i | 0.317554 | − | 0.550019i | ||||
\(358\) | −12.0000 | + | 20.7846i | −0.634220 | + | 1.09850i | ||||
\(359\) | −6.00000 | −0.316668 | −0.158334 | − | 0.987386i | \(-0.550612\pi\) | ||||
−0.158334 | + | 0.987386i | \(0.550612\pi\) | |||||||
\(360\) | −0.500000 | + | 0.866025i | −0.0263523 | + | 0.0456435i | ||||
\(361\) | −3.00000 | − | 5.19615i | −0.157895 | − | 0.273482i | ||||
\(362\) | 4.00000 | + | 6.92820i | 0.210235 | + | 0.364138i | ||||
\(363\) | 4.00000 | 0.209946 | ||||||||
\(364\) | −1.00000 | + | 3.46410i | −0.0524142 | + | 0.181568i | ||||
\(365\) | −14.0000 | −0.732793 | ||||||||
\(366\) | −8.00000 | − | 13.8564i | −0.418167 | − | 0.724286i | ||||
\(367\) | −16.0000 | − | 27.7128i | −0.835193 | − | 1.44660i | −0.893873 | − | 0.448320i | \(-0.852022\pi\) |
0.0586798 | − | 0.998277i | \(-0.481311\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.00000 | 0.312348 | ||||||||
\(370\) | −5.50000 | + | 9.52628i | −0.285931 | + | 0.495248i | ||||
\(371\) | −4.50000 | + | 7.79423i | −0.233628 | + | 0.404656i | ||||
\(372\) | 8.00000 | 0.414781 | ||||||||
\(373\) | −7.00000 | + | 12.1244i | −0.362446 | + | 0.627775i | −0.988363 | − | 0.152115i | \(-0.951392\pi\) |
0.625917 | + | 0.779890i | \(0.284725\pi\) | |||||||
\(374\) | −9.00000 | − | 15.5885i | −0.465379 | − | 0.806060i | ||||
\(375\) | −1.00000 | − | 1.73205i | −0.0516398 | − | 0.0894427i | ||||
\(376\) | 3.00000 | 0.154713 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 4.00000 | 0.205738 | ||||||||
\(379\) | 9.50000 | + | 16.4545i | 0.487982 | + | 0.845210i | 0.999904 | − | 0.0138218i | \(-0.00439975\pi\) |
−0.511922 | + | 0.859032i | \(0.671066\pi\) | |||||||
\(380\) | 2.50000 | + | 4.33013i | 0.128247 | + | 0.222131i | ||||
\(381\) | −1.00000 | + | 1.73205i | −0.0512316 | + | 0.0887357i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(384\) | −1.00000 | + | 1.73205i | −0.0510310 | + | 0.0883883i | ||||
\(385\) | 3.00000 | 0.152894 | ||||||||
\(386\) | −2.00000 | + | 3.46410i | −0.101797 | + | 0.176318i | ||||
\(387\) | −1.00000 | − | 1.73205i | −0.0508329 | − | 0.0880451i | ||||
\(388\) | 5.00000 | + | 8.66025i | 0.253837 | + | 0.439658i | ||||
\(389\) | −30.0000 | −1.52106 | −0.760530 | − | 0.649303i | \(-0.775061\pi\) | ||||
−0.760530 | + | 0.649303i | \(0.775061\pi\) | |||||||
\(390\) | 7.00000 | − | 1.73205i | 0.354459 | − | 0.0877058i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −3.00000 | − | 5.19615i | −0.151523 | − | 0.262445i | ||||
\(393\) | −9.00000 | − | 15.5885i | −0.453990 | − | 0.786334i | ||||
\(394\) | −13.5000 | + | 23.3827i | −0.680120 | + | 1.17800i | ||||
\(395\) | 16.0000 | 0.805047 | ||||||||
\(396\) | −1.50000 | + | 2.59808i | −0.0753778 | + | 0.130558i | ||||
\(397\) | 6.50000 | − | 11.2583i | 0.326226 | − | 0.565039i | −0.655534 | − | 0.755166i | \(-0.727556\pi\) |
0.981760 | + | 0.190126i | \(0.0608897\pi\) | |||||||
\(398\) | 10.0000 | 0.501255 | ||||||||
\(399\) | −5.00000 | + | 8.66025i | −0.250313 | + | 0.433555i | ||||
\(400\) | −0.500000 | − | 0.866025i | −0.0250000 | − | 0.0433013i | ||||
\(401\) | 7.50000 | + | 12.9904i | 0.374532 | + | 0.648709i | 0.990257 | − | 0.139253i | \(-0.0444700\pi\) |
−0.615725 | + | 0.787961i | \(0.711137\pi\) | |||||||
\(402\) | −32.0000 | −1.59601 | ||||||||
\(403\) | −10.0000 | − | 10.3923i | −0.498135 | − | 0.517678i | ||||
\(404\) | −6.00000 | −0.298511 | ||||||||
\(405\) | −5.50000 | − | 9.52628i | −0.273297 | − | 0.473365i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16.5000 | + | 28.5788i | −0.817875 | + | 1.41660i | ||||
\(408\) | −12.0000 | −0.594089 | ||||||||
\(409\) | −2.50000 | + | 4.33013i | −0.123617 | + | 0.214111i | −0.921192 | − | 0.389109i | \(-0.872783\pi\) |
0.797574 | + | 0.603220i | \(0.206116\pi\) | |||||||
\(410\) | −3.00000 | + | 5.19615i | −0.148159 | + | 0.256620i | ||||
\(411\) | −12.0000 | −0.591916 | ||||||||
\(412\) | −2.50000 | + | 4.33013i | −0.123166 | + | 0.213330i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.00000 | 0.294528 | ||||||||
\(416\) | 3.50000 | − | 0.866025i | 0.171602 | − | 0.0424604i | ||||
\(417\) | 38.0000 | 1.86087 | ||||||||
\(418\) | 7.50000 | + | 12.9904i | 0.366837 | + | 0.635380i | ||||
\(419\) | 18.0000 | + | 31.1769i | 0.879358 | + | 1.52309i | 0.852047 | + | 0.523465i | \(0.175361\pi\) |
0.0273103 | + | 0.999627i | \(0.491306\pi\) | |||||||
\(420\) | 1.00000 | − | 1.73205i | 0.0487950 | − | 0.0845154i | ||||
\(421\) | −10.0000 | −0.487370 | −0.243685 | − | 0.969854i | \(-0.578356\pi\) | ||||
−0.243685 | + | 0.969854i | \(0.578356\pi\) | |||||||
\(422\) | 11.5000 | − | 19.9186i | 0.559811 | − | 0.969622i | ||||
\(423\) | 1.50000 | − | 2.59808i | 0.0729325 | − | 0.126323i | ||||
\(424\) | 9.00000 | 0.437079 | ||||||||
\(425\) | 3.00000 | − | 5.19615i | 0.145521 | − | 0.252050i | ||||
\(426\) | −6.00000 | − | 10.3923i | −0.290701 | − | 0.503509i | ||||
\(427\) | 4.00000 | + | 6.92820i | 0.193574 | + | 0.335279i | ||||
\(428\) | −12.0000 | −0.580042 | ||||||||
\(429\) | 21.0000 | − | 5.19615i | 1.01389 | − | 0.250873i | ||||
\(430\) | 2.00000 | 0.0964486 | ||||||||
\(431\) | −15.0000 | − | 25.9808i | −0.722525 | − | 1.25145i | −0.959985 | − | 0.280052i | \(-0.909648\pi\) |
0.237460 | − | 0.971397i | \(-0.423685\pi\) | |||||||
\(432\) | −2.00000 | − | 3.46410i | −0.0962250 | − | 0.166667i | ||||
\(433\) | 8.00000 | − | 13.8564i | 0.384455 | − | 0.665896i | −0.607238 | − | 0.794520i | \(-0.707723\pi\) |
0.991693 | + | 0.128624i | \(0.0410559\pi\) | |||||||
\(434\) | −4.00000 | −0.192006 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.00000 | + | 1.73205i | −0.0478913 | + | 0.0829502i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −14.0000 | + | 24.2487i | −0.668946 | + | 1.15865i | ||||
\(439\) | −10.0000 | − | 17.3205i | −0.477274 | − | 0.826663i | 0.522387 | − | 0.852709i | \(-0.325042\pi\) |
−0.999661 | + | 0.0260459i | \(0.991708\pi\) | |||||||
\(440\) | −1.50000 | − | 2.59808i | −0.0715097 | − | 0.123858i | ||||
\(441\) | −6.00000 | −0.285714 | ||||||||
\(442\) | 15.0000 | + | 15.5885i | 0.713477 | + | 0.741467i | ||||
\(443\) | −18.0000 | −0.855206 | −0.427603 | − | 0.903967i | \(-0.640642\pi\) | ||||
−0.427603 | + | 0.903967i | \(0.640642\pi\) | |||||||
\(444\) | 11.0000 | + | 19.0526i | 0.522037 | + | 0.904194i | ||||
\(445\) | 4.50000 | + | 7.79423i | 0.213320 | + | 0.369482i | ||||
\(446\) | −9.50000 | + | 16.4545i | −0.449838 | + | 0.779142i | ||||
\(447\) | 36.0000 | 1.70274 | ||||||||
\(448\) | 0.500000 | − | 0.866025i | 0.0236228 | − | 0.0409159i | ||||
\(449\) | −4.50000 | + | 7.79423i | −0.212368 | + | 0.367832i | −0.952455 | − | 0.304679i | \(-0.901451\pi\) |
0.740087 | + | 0.672511i | \(0.234784\pi\) | |||||||
\(450\) | −1.00000 | −0.0471405 | ||||||||
\(451\) | −9.00000 | + | 15.5885i | −0.423793 | + | 0.734032i | ||||
\(452\) | 6.00000 | + | 10.3923i | 0.282216 | + | 0.488813i | ||||
\(453\) | −16.0000 | − | 27.7128i | −0.751746 | − | 1.30206i | ||||
\(454\) | 24.0000 | 1.12638 | ||||||||
\(455\) | −3.50000 | + | 0.866025i | −0.164083 | + | 0.0405999i | ||||
\(456\) | 10.0000 | 0.468293 | ||||||||
\(457\) | 2.00000 | + | 3.46410i | 0.0935561 | + | 0.162044i | 0.909005 | − | 0.416785i | \(-0.136843\pi\) |
−0.815449 | + | 0.578829i | \(0.803510\pi\) | |||||||
\(458\) | −2.00000 | − | 3.46410i | −0.0934539 | − | 0.161867i | ||||
\(459\) | 12.0000 | − | 20.7846i | 0.560112 | − | 0.970143i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.0000 | − | 36.3731i | 0.978068 | − | 1.69406i | 0.308651 | − | 0.951175i | \(-0.400123\pi\) |
0.669417 | − | 0.742887i | \(-0.266544\pi\) | |||||||
\(462\) | 3.00000 | − | 5.19615i | 0.139573 | − | 0.241747i | ||||
\(463\) | 8.00000 | 0.371792 | 0.185896 | − | 0.982569i | \(-0.440481\pi\) | ||||
0.185896 | + | 0.982569i | \(0.440481\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.00000 | + | 6.92820i | 0.185496 | + | 0.321288i | ||||
\(466\) | −12.0000 | − | 20.7846i | −0.555889 | − | 0.962828i | ||||
\(467\) | −12.0000 | −0.555294 | −0.277647 | − | 0.960683i | \(-0.589555\pi\) | ||||
−0.277647 | + | 0.960683i | \(0.589555\pi\) | |||||||
\(468\) | 1.00000 | − | 3.46410i | 0.0462250 | − | 0.160128i | ||||
\(469\) | 16.0000 | 0.738811 | ||||||||
\(470\) | 1.50000 | + | 2.59808i | 0.0691898 | + | 0.119840i | ||||
\(471\) | 17.0000 | + | 29.4449i | 0.783319 | + | 1.35675i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.00000 | 0.275880 | ||||||||
\(474\) | 16.0000 | − | 27.7128i | 0.734904 | − | 1.27289i | ||||
\(475\) | −2.50000 | + | 4.33013i | −0.114708 | + | 0.198680i | ||||
\(476\) | 6.00000 | 0.275010 | ||||||||
\(477\) | 4.50000 | − | 7.79423i | 0.206041 | − | 0.356873i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.0000 | + | 25.9808i | 0.685367 | + | 1.18709i | 0.973321 | + | 0.229447i | \(0.0736918\pi\) |
−0.287954 | + | 0.957644i | \(0.592975\pi\) | |||||||
\(480\) | −2.00000 | −0.0912871 | ||||||||
\(481\) | 11.0000 | − | 38.1051i | 0.501557 | − | 1.73744i | ||||
\(482\) | −23.0000 | −1.04762 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | + | 1.73205i | 0.0454545 | + | 0.0787296i | ||||
\(485\) | −5.00000 | + | 8.66025i | −0.227038 | + | 0.393242i | ||||
\(486\) | −10.0000 | −0.453609 | ||||||||
\(487\) | 9.50000 | − | 16.4545i | 0.430486 | − | 0.745624i | −0.566429 | − | 0.824110i | \(-0.691675\pi\) |
0.996915 | + | 0.0784867i | \(0.0250088\pi\) | |||||||
\(488\) | 4.00000 | − | 6.92820i | 0.181071 | − | 0.313625i | ||||
\(489\) | −4.00000 | −0.180886 | ||||||||
\(490\) | 3.00000 | − | 5.19615i | 0.135526 | − | 0.234738i | ||||
\(491\) | −13.5000 | − | 23.3827i | −0.609246 | − | 1.05525i | −0.991365 | − | 0.131132i | \(-0.958139\pi\) |
0.382118 | − | 0.924113i | \(-0.375195\pi\) | |||||||
\(492\) | 6.00000 | + | 10.3923i | 0.270501 | + | 0.468521i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −12.5000 | − | 12.9904i | −0.562402 | − | 0.584465i | ||||
\(495\) | −3.00000 | −0.134840 | ||||||||
\(496\) | 2.00000 | + | 3.46410i | 0.0898027 | + | 0.155543i | ||||
\(497\) | 3.00000 | + | 5.19615i | 0.134568 | + | 0.233079i | ||||
\(498\) | 6.00000 | − | 10.3923i | 0.268866 | − | 0.465690i | ||||
\(499\) | −4.00000 | −0.179065 | −0.0895323 | − | 0.995984i | \(-0.528537\pi\) | ||||
−0.0895323 | + | 0.995984i | \(0.528537\pi\) | |||||||
\(500\) | 0.500000 | − | 0.866025i | 0.0223607 | − | 0.0387298i | ||||
\(501\) | −15.0000 | + | 25.9808i | −0.670151 | + | 1.16073i | ||||
\(502\) | 15.0000 | 0.669483 | ||||||||
\(503\) | −4.50000 | + | 7.79423i | −0.200645 | + | 0.347527i | −0.948736 | − | 0.316068i | \(-0.897637\pi\) |
0.748091 | + | 0.663596i | \(0.230970\pi\) | |||||||
\(504\) | −0.500000 | − | 0.866025i | −0.0222718 | − | 0.0385758i | ||||
\(505\) | −3.00000 | − | 5.19615i | −0.133498 | − | 0.231226i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −23.0000 | + | 12.1244i | −1.02147 | + | 0.538462i | ||||
\(508\) | −1.00000 | −0.0443678 | ||||||||
\(509\) | −3.00000 | − | 5.19615i | −0.132973 | − | 0.230315i | 0.791849 | − | 0.610718i | \(-0.209119\pi\) |
−0.924821 | + | 0.380402i | \(0.875786\pi\) | |||||||
\(510\) | −6.00000 | − | 10.3923i | −0.265684 | − | 0.460179i | ||||
\(511\) | 7.00000 | − | 12.1244i | 0.309662 | − | 0.536350i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −10.0000 | + | 17.3205i | −0.441511 | + | 0.764719i | ||||
\(514\) | 6.00000 | − | 10.3923i | 0.264649 | − | 0.458385i | ||||
\(515\) | −5.00000 | −0.220326 | ||||||||
\(516\) | 2.00000 | − | 3.46410i | 0.0880451 | − | 0.152499i | ||||
\(517\) | 4.50000 | + | 7.79423i | 0.197910 | + | 0.342790i | ||||
\(518\) | −5.50000 | − | 9.52628i | −0.241656 | − | 0.418561i | ||||
\(519\) | −30.0000 | −1.31685 | ||||||||
\(520\) | 2.50000 | + | 2.59808i | 0.109632 | + | 0.113933i | ||||
\(521\) | −27.0000 | −1.18289 | −0.591446 | − | 0.806345i | \(-0.701443\pi\) | ||||
−0.591446 | + | 0.806345i | \(0.701443\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.00000 | − | 12.1244i | −0.306089 | − | 0.530161i | 0.671414 | − | 0.741082i | \(-0.265687\pi\) |
−0.977503 | + | 0.210921i | \(0.932354\pi\) | |||||||
\(524\) | 4.50000 | − | 7.79423i | 0.196583 | − | 0.340492i | ||||
\(525\) | 2.00000 | 0.0872872 | ||||||||
\(526\) | 4.50000 | − | 7.79423i | 0.196209 | − | 0.339845i | ||||
\(527\) | −12.0000 | + | 20.7846i | −0.522728 | + | 0.905392i | ||||
\(528\) | −6.00000 | −0.261116 | ||||||||
\(529\) | 11.5000 | − | 19.9186i | 0.500000 | − | 0.866025i | ||||
\(530\) | 4.50000 | + | 7.79423i | 0.195468 | + | 0.338560i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.00000 | −0.216777 | ||||||||
\(533\) | 6.00000 | − | 20.7846i | 0.259889 | − | 0.900281i | ||||
\(534\) | 18.0000 | 0.778936 | ||||||||
\(535\) | −6.00000 | − | 10.3923i | −0.259403 | − | 0.449299i | ||||
\(536\) | −8.00000 | − | 13.8564i | −0.345547 | − | 0.598506i | ||||
\(537\) | −24.0000 | + | 41.5692i | −1.03568 | + | 1.79384i | ||||
\(538\) | −6.00000 | −0.258678 | ||||||||
\(539\) | 9.00000 | − | 15.5885i | 0.387657 | − | 0.671442i | ||||
\(540\) | 2.00000 | − | 3.46410i | 0.0860663 | − | 0.149071i | ||||
\(541\) | 20.0000 | 0.859867 | 0.429934 | − | 0.902861i | \(-0.358537\pi\) | ||||
0.429934 | + | 0.902861i | \(0.358537\pi\) | |||||||
\(542\) | 10.0000 | − | 17.3205i | 0.429537 | − | 0.743980i | ||||
\(543\) | 8.00000 | + | 13.8564i | 0.343313 | + | 0.594635i | ||||
\(544\) | −3.00000 | − | 5.19615i | −0.128624 | − | 0.222783i | ||||
\(545\) | −2.00000 | −0.0856706 | ||||||||
\(546\) | −2.00000 | + | 6.92820i | −0.0855921 | + | 0.296500i | ||||
\(547\) | −34.0000 | −1.45374 | −0.726868 | − | 0.686778i | \(-0.759025\pi\) | ||||
−0.726868 | + | 0.686778i | \(0.759025\pi\) | |||||||
\(548\) | −3.00000 | − | 5.19615i | −0.128154 | − | 0.221969i | ||||
\(549\) | −4.00000 | − | 6.92820i | −0.170716 | − | 0.295689i | ||||
\(550\) | 1.50000 | − | 2.59808i | 0.0639602 | − | 0.110782i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.00000 | + | 13.8564i | −0.340195 | + | 0.589234i | ||||
\(554\) | 1.00000 | 0.0424859 | ||||||||
\(555\) | −11.0000 | + | 19.0526i | −0.466924 | + | 0.808736i | ||||
\(556\) | 9.50000 | + | 16.4545i | 0.402890 | + | 0.697826i | ||||
\(557\) | −10.5000 | − | 18.1865i | −0.444899 | − | 0.770588i | 0.553146 | − | 0.833084i | \(-0.313427\pi\) |
−0.998045 | + | 0.0624962i | \(0.980094\pi\) | |||||||
\(558\) | 4.00000 | 0.169334 | ||||||||
\(559\) | −7.00000 | + | 1.73205i | −0.296068 | + | 0.0732579i | ||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | −18.0000 | − | 31.1769i | −0.759961 | − | 1.31629i | ||||
\(562\) | −3.00000 | − | 5.19615i | −0.126547 | − | 0.219186i | ||||
\(563\) | 18.0000 | − | 31.1769i | 0.758610 | − | 1.31395i | −0.184950 | − | 0.982748i | \(-0.559212\pi\) |
0.943560 | − | 0.331202i | \(-0.107454\pi\) | |||||||
\(564\) | 6.00000 | 0.252646 | ||||||||
\(565\) | −6.00000 | + | 10.3923i | −0.252422 | + | 0.437208i | ||||
\(566\) | 7.00000 | − | 12.1244i | 0.294232 | − | 0.509625i | ||||
\(567\) | 11.0000 | 0.461957 | ||||||||
\(568\) | 3.00000 | − | 5.19615i | 0.125877 | − | 0.218026i | ||||
\(569\) | −4.50000 | − | 7.79423i | −0.188650 | − | 0.326751i | 0.756151 | − | 0.654398i | \(-0.227078\pi\) |
−0.944800 | + | 0.327647i | \(0.893744\pi\) | |||||||
\(570\) | 5.00000 | + | 8.66025i | 0.209427 | + | 0.362738i | ||||
\(571\) | 17.0000 | 0.711428 | 0.355714 | − | 0.934595i | \(-0.384238\pi\) | ||||
0.355714 | + | 0.934595i | \(0.384238\pi\) | |||||||
\(572\) | 7.50000 | + | 7.79423i | 0.313591 | + | 0.325893i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.00000 | − | 5.19615i | −0.125218 | − | 0.216883i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 32.0000 | 1.33218 | 0.666089 | − | 0.745873i | \(-0.267967\pi\) | ||||
0.666089 | + | 0.745873i | \(0.267967\pi\) | |||||||
\(578\) | 9.50000 | − | 16.4545i | 0.395148 | − | 0.684416i | ||||
\(579\) | −4.00000 | + | 6.92820i | −0.166234 | + | 0.287926i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.00000 | + | 5.19615i | −0.124461 | + | 0.215573i | ||||
\(582\) | 10.0000 | + | 17.3205i | 0.414513 | + | 0.717958i | ||||
\(583\) | 13.5000 | + | 23.3827i | 0.559113 | + | 0.968412i | ||||
\(584\) | −14.0000 | −0.579324 | ||||||||
\(585\) | 3.50000 | − | 0.866025i | 0.144707 | − | 0.0358057i | ||||
\(586\) | −9.00000 | −0.371787 | ||||||||
\(587\) | 3.00000 | + | 5.19615i | 0.123823 | + | 0.214468i | 0.921272 | − | 0.388918i | \(-0.127151\pi\) |
−0.797449 | + | 0.603386i | \(0.793818\pi\) | |||||||
\(588\) | −6.00000 | − | 10.3923i | −0.247436 | − | 0.428571i | ||||
\(589\) | 10.0000 | − | 17.3205i | 0.412043 | − | 0.713679i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −27.0000 | + | 46.7654i | −1.11063 | + | 1.92367i | ||||
\(592\) | −5.50000 | + | 9.52628i | −0.226049 | + | 0.391528i | ||||
\(593\) | 24.0000 | 0.985562 | 0.492781 | − | 0.870153i | \(-0.335980\pi\) | ||||
0.492781 | + | 0.870153i | \(0.335980\pi\) | |||||||
\(594\) | 6.00000 | − | 10.3923i | 0.246183 | − | 0.426401i | ||||
\(595\) | 3.00000 | + | 5.19615i | 0.122988 | + | 0.213021i | ||||
\(596\) | 9.00000 | + | 15.5885i | 0.368654 | + | 0.638528i | ||||
\(597\) | 20.0000 | 0.818546 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.0000 | −0.735460 | −0.367730 | − | 0.929933i | \(-0.619865\pi\) | ||||
−0.367730 | + | 0.929933i | \(0.619865\pi\) | |||||||
\(600\) | −1.00000 | − | 1.73205i | −0.0408248 | − | 0.0707107i | ||||
\(601\) | 9.50000 | + | 16.4545i | 0.387513 | + | 0.671192i | 0.992114 | − | 0.125336i | \(-0.0400009\pi\) |
−0.604601 | + | 0.796528i | \(0.706668\pi\) | |||||||
\(602\) | −1.00000 | + | 1.73205i | −0.0407570 | + | 0.0705931i | ||||
\(603\) | −16.0000 | −0.651570 | ||||||||
\(604\) | 8.00000 | − | 13.8564i | 0.325515 | − | 0.563809i | ||||
\(605\) | −1.00000 | + | 1.73205i | −0.0406558 | + | 0.0704179i | ||||
\(606\) | −12.0000 | −0.487467 | ||||||||
\(607\) | 6.50000 | − | 11.2583i | 0.263827 | − | 0.456962i | −0.703429 | − | 0.710766i | \(-0.748349\pi\) |
0.967256 | + | 0.253804i | \(0.0816819\pi\) | |||||||
\(608\) | 2.50000 | + | 4.33013i | 0.101388 | + | 0.175610i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.00000 | 0.323911 | ||||||||
\(611\) | −7.50000 | − | 7.79423i | −0.303418 | − | 0.315321i | ||||
\(612\) | −6.00000 | −0.242536 | ||||||||
\(613\) | 6.50000 | + | 11.2583i | 0.262533 | + | 0.454720i | 0.966914 | − | 0.255102i | \(-0.0821090\pi\) |
−0.704382 | + | 0.709821i | \(0.748776\pi\) | |||||||
\(614\) | 1.00000 | + | 1.73205i | 0.0403567 | + | 0.0698999i | ||||
\(615\) | −6.00000 | + | 10.3923i | −0.241943 | + | 0.419058i | ||||
\(616\) | 3.00000 | 0.120873 | ||||||||
\(617\) | −9.00000 | + | 15.5885i | −0.362326 | + | 0.627568i | −0.988343 | − | 0.152242i | \(-0.951351\pi\) |
0.626017 | + | 0.779809i | \(0.284684\pi\) | |||||||
\(618\) | −5.00000 | + | 8.66025i | −0.201129 | + | 0.348367i | ||||
\(619\) | −1.00000 | −0.0401934 | −0.0200967 | − | 0.999798i | \(-0.506397\pi\) | ||||
−0.0200967 | + | 0.999798i | \(0.506397\pi\) | |||||||
\(620\) | −2.00000 | + | 3.46410i | −0.0803219 | + | 0.139122i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 15.0000 | + | 25.9808i | 0.601445 | + | 1.04173i | ||||
\(623\) | −9.00000 | −0.360577 | ||||||||
\(624\) | 7.00000 | − | 1.73205i | 0.280224 | − | 0.0693375i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 7.00000 | + | 12.1244i | 0.279776 | + | 0.484587i | ||||
\(627\) | 15.0000 | + | 25.9808i | 0.599042 | + | 1.03757i | ||||
\(628\) | −8.50000 | + | 14.7224i | −0.339187 | + | 0.587489i | ||||
\(629\) | −66.0000 | −2.63159 | ||||||||
\(630\) | 0.500000 | − | 0.866025i | 0.0199205 | − | 0.0345033i | ||||
\(631\) | 14.0000 | − | 24.2487i | 0.557331 | − | 0.965326i | −0.440387 | − | 0.897808i | \(-0.645159\pi\) |
0.997718 | − | 0.0675178i | \(-0.0215080\pi\) | |||||||
\(632\) | 16.0000 | 0.636446 | ||||||||
\(633\) | 23.0000 | − | 39.8372i | 0.914168 | − | 1.58339i | ||||
\(634\) | 7.50000 | + | 12.9904i | 0.297863 | + | 0.515914i | ||||
\(635\) | −0.500000 | − | 0.866025i | −0.0198419 | − | 0.0343672i | ||||
\(636\) | 18.0000 | 0.713746 | ||||||||
\(637\) | −6.00000 | + | 20.7846i | −0.237729 | + | 0.823516i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.00000 | − | 5.19615i | −0.118678 | − | 0.205557i | ||||
\(640\) | −0.500000 | − | 0.866025i | −0.0197642 | − | 0.0342327i | ||||
\(641\) | 4.50000 | − | 7.79423i | 0.177739 | − | 0.307854i | −0.763367 | − | 0.645966i | \(-0.776455\pi\) |
0.941106 | + | 0.338112i | \(0.109788\pi\) | |||||||
\(642\) | −24.0000 | −0.947204 | ||||||||
\(643\) | −1.00000 | + | 1.73205i | −0.0394362 | + | 0.0683054i | −0.885070 | − | 0.465458i | \(-0.845890\pi\) |
0.845634 | + | 0.533764i | \(0.179223\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.00000 | 0.157500 | ||||||||
\(646\) | −15.0000 | + | 25.9808i | −0.590167 | + | 1.02220i | ||||
\(647\) | 4.50000 | + | 7.79423i | 0.176913 | + | 0.306423i | 0.940822 | − | 0.338902i | \(-0.110055\pi\) |
−0.763908 | + | 0.645325i | \(0.776722\pi\) | |||||||
\(648\) | −5.50000 | − | 9.52628i | −0.216060 | − | 0.374228i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −1.00000 | + | 3.46410i | −0.0392232 | + | 0.135873i | ||||
\(651\) | −8.00000 | −0.313545 | ||||||||
\(652\) | −1.00000 | − | 1.73205i | −0.0391630 | − | 0.0678323i | ||||
\(653\) | 13.5000 | + | 23.3827i | 0.528296 | + | 0.915035i | 0.999456 | + | 0.0329874i | \(0.0105021\pi\) |
−0.471160 | + | 0.882048i | \(0.656165\pi\) | |||||||
\(654\) | −2.00000 | + | 3.46410i | −0.0782062 | + | 0.135457i | ||||
\(655\) | 9.00000 | 0.351659 | ||||||||
\(656\) | −3.00000 | + | 5.19615i | −0.117130 | + | 0.202876i | ||||
\(657\) | −7.00000 | + | 12.1244i | −0.273096 | + | 0.473016i | ||||
\(658\) | −3.00000 | −0.116952 | ||||||||
\(659\) | −6.00000 | + | 10.3923i | −0.233727 | + | 0.404827i | −0.958902 | − | 0.283738i | \(-0.908425\pi\) |
0.725175 | + | 0.688565i | \(0.241759\pi\) | |||||||
\(660\) | −3.00000 | − | 5.19615i | −0.116775 | − | 0.202260i | ||||
\(661\) | 2.00000 | + | 3.46410i | 0.0777910 | + | 0.134738i | 0.902297 | − | 0.431116i | \(-0.141880\pi\) |
−0.824506 | + | 0.565854i | \(0.808547\pi\) | |||||||
\(662\) | −20.0000 | −0.777322 | ||||||||
\(663\) | 30.0000 | + | 31.1769i | 1.16510 | + | 1.21081i | ||||
\(664\) | 6.00000 | 0.232845 | ||||||||
\(665\) | −2.50000 | − | 4.33013i | −0.0969458 | − | 0.167915i | ||||
\(666\) | 5.50000 | + | 9.52628i | 0.213121 | + | 0.369136i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −15.0000 | −0.580367 | ||||||||
\(669\) | −19.0000 | + | 32.9090i | −0.734582 | + | 1.27233i | ||||
\(670\) | 8.00000 | − | 13.8564i | 0.309067 | − | 0.535320i | ||||
\(671\) | 24.0000 | 0.926510 | ||||||||
\(672\) | 1.00000 | − | 1.73205i | 0.0385758 | − | 0.0668153i | ||||
\(673\) | −10.0000 | − | 17.3205i | −0.385472 | − | 0.667657i | 0.606363 | − | 0.795188i | \(-0.292628\pi\) |
−0.991835 | + | 0.127532i | \(0.959295\pi\) | |||||||
\(674\) | −8.00000 | − | 13.8564i | −0.308148 | − | 0.533729i | ||||
\(675\) | 4.00000 | 0.153960 | ||||||||
\(676\) | −11.0000 | − | 6.92820i | −0.423077 | − | 0.266469i | ||||
\(677\) | −18.0000 | −0.691796 | −0.345898 | − | 0.938272i | \(-0.612426\pi\) | ||||
−0.345898 | + | 0.938272i | \(0.612426\pi\) | |||||||
\(678\) | 12.0000 | + | 20.7846i | 0.460857 | + | 0.798228i | ||||
\(679\) | −5.00000 | − | 8.66025i | −0.191882 | − | 0.332350i | ||||
\(680\) | 3.00000 | − | 5.19615i | 0.115045 | − | 0.199263i | ||||
\(681\) | 48.0000 | 1.83936 | ||||||||
\(682\) | −6.00000 | + | 10.3923i | −0.229752 | + | 0.397942i | ||||
\(683\) | 3.00000 | − | 5.19615i | 0.114792 | − | 0.198825i | −0.802905 | − | 0.596107i | \(-0.796713\pi\) |
0.917697 | + | 0.397282i | \(0.130047\pi\) | |||||||
\(684\) | 5.00000 | 0.191180 | ||||||||
\(685\) | 3.00000 | − | 5.19615i | 0.114624 | − | 0.198535i | ||||
\(686\) | 6.50000 | + | 11.2583i | 0.248171 | + | 0.429845i | ||||
\(687\) | −4.00000 | − | 6.92820i | −0.152610 | − | 0.264327i | ||||
\(688\) | 2.00000 | 0.0762493 | ||||||||
\(689\) | −22.5000 | − | 23.3827i | −0.857182 | − | 0.890809i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.50000 | + | 11.2583i | 0.247272 | + | 0.428287i | 0.962768 | − | 0.270330i | \(-0.0871327\pi\) |
−0.715496 | + | 0.698617i | \(0.753799\pi\) | |||||||
\(692\) | −7.50000 | − | 12.9904i | −0.285107 | − | 0.493820i | ||||
\(693\) | 1.50000 | − | 2.59808i | 0.0569803 | − | 0.0986928i | ||||
\(694\) | −6.00000 | −0.227757 | ||||||||
\(695\) | −9.50000 | + | 16.4545i | −0.360356 | + | 0.624154i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −36.0000 | −1.36360 | ||||||||
\(698\) | 1.00000 | − | 1.73205i | 0.0378506 | − | 0.0655591i | ||||
\(699\) | −24.0000 | − | 41.5692i | −0.907763 | − | 1.57229i | ||||
\(700\) | 0.500000 | + | 0.866025i | 0.0188982 | + | 0.0327327i | ||||
\(701\) | 6.00000 | 0.226617 | 0.113308 | − | 0.993560i | \(-0.463855\pi\) | ||||
0.113308 | + | 0.993560i | \(0.463855\pi\) | |||||||
\(702\) | −4.00000 | + | 13.8564i | −0.150970 | + | 0.522976i | ||||
\(703\) | 55.0000 | 2.07436 | ||||||||
\(704\) | −1.50000 | − | 2.59808i | −0.0565334 | − | 0.0979187i | ||||
\(705\) | 3.00000 | + | 5.19615i | 0.112987 | + | 0.195698i | ||||
\(706\) | 3.00000 | − | 5.19615i | 0.112906 | − | 0.195560i | ||||
\(707\) | 6.00000 | 0.225653 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.00000 | − | 8.66025i | 0.187779 | − | 0.325243i | −0.756730 | − | 0.653727i | \(-0.773204\pi\) |
0.944509 | + | 0.328484i | \(0.106538\pi\) | |||||||
\(710\) | 6.00000 | 0.225176 | ||||||||
\(711\) | 8.00000 | − | 13.8564i | 0.300023 | − | 0.519656i | ||||
\(712\) | 4.50000 | + | 7.79423i | 0.168645 | + | 0.292101i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 12.0000 | 0.449089 | ||||||||
\(715\) | −3.00000 | + | 10.3923i | −0.112194 | + | 0.388650i | ||||
\(716\) | −24.0000 | −0.896922 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.00000 | − | 5.19615i | −0.111959 | − | 0.193919i | ||||
\(719\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | 2.50000 | − | 4.33013i | 0.0931049 | − | 0.161262i | ||||
\(722\) | 3.00000 | − | 5.19615i | 0.111648 | − | 0.193381i | ||||
\(723\) | −46.0000 | −1.71076 | ||||||||
\(724\) | −4.00000 | + | 6.92820i | −0.148659 | + | 0.257485i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.00000 | + | 3.46410i | 0.0742270 | + | 0.128565i | ||||
\(727\) | 29.0000 | 1.07555 | 0.537775 | − | 0.843088i | \(-0.319265\pi\) | ||||
0.537775 | + | 0.843088i | \(0.319265\pi\) | |||||||
\(728\) | −3.50000 | + | 0.866025i | −0.129719 | + | 0.0320970i | ||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | −7.00000 | − | 12.1244i | −0.259082 | − | 0.448743i | ||||
\(731\) | 6.00000 | + | 10.3923i | 0.221918 | + | 0.384373i | ||||
\(732\) | 8.00000 | − | 13.8564i | 0.295689 | − | 0.512148i | ||||
\(733\) | −25.0000 | −0.923396 | −0.461698 | − | 0.887037i | \(-0.652760\pi\) | ||||
−0.461698 | + | 0.887037i | \(0.652760\pi\) | |||||||
\(734\) | 16.0000 | − | 27.7128i | 0.590571 | − | 1.02290i | ||||
\(735\) | 6.00000 | − | 10.3923i | 0.221313 | − | 0.383326i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 24.0000 | − | 41.5692i | 0.884051 | − | 1.53122i | ||||
\(738\) | 3.00000 | + | 5.19615i | 0.110432 | + | 0.191273i | ||||
\(739\) | 3.50000 | + | 6.06218i | 0.128750 | + | 0.223001i | 0.923192 | − | 0.384338i | \(-0.125570\pi\) |
−0.794443 | + | 0.607339i | \(0.792237\pi\) | |||||||
\(740\) | −11.0000 | −0.404368 | ||||||||
\(741\) | −25.0000 | − | 25.9808i | −0.918398 | − | 0.954427i | ||||
\(742\) | −9.00000 | −0.330400 | ||||||||
\(743\) | −6.00000 | − | 10.3923i | −0.220119 | − | 0.381257i | 0.734725 | − | 0.678365i | \(-0.237311\pi\) |
−0.954844 | + | 0.297108i | \(0.903978\pi\) | |||||||
\(744\) | 4.00000 | + | 6.92820i | 0.146647 | + | 0.254000i | ||||
\(745\) | −9.00000 | + | 15.5885i | −0.329734 | + | 0.571117i | ||||
\(746\) | −14.0000 | −0.512576 | ||||||||
\(747\) | 3.00000 | − | 5.19615i | 0.109764 | − | 0.190117i | ||||
\(748\) | 9.00000 | − | 15.5885i | 0.329073 | − | 0.569970i | ||||
\(749\) | 12.0000 | 0.438470 | ||||||||
\(750\) | 1.00000 | − | 1.73205i | 0.0365148 | − | 0.0632456i | ||||
\(751\) | 20.0000 | + | 34.6410i | 0.729810 | + | 1.26407i | 0.956963 | + | 0.290209i | \(0.0937250\pi\) |
−0.227153 | + | 0.973859i | \(0.572942\pi\) | |||||||
\(752\) | 1.50000 | + | 2.59808i | 0.0546994 | + | 0.0947421i | ||||
\(753\) | 30.0000 | 1.09326 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.0000 | 0.582300 | ||||||||
\(756\) | 2.00000 | + | 3.46410i | 0.0727393 | + | 0.125988i | ||||
\(757\) | −11.5000 | − | 19.9186i | −0.417975 | − | 0.723953i | 0.577761 | − | 0.816206i | \(-0.303927\pi\) |
−0.995736 | + | 0.0922527i | \(0.970593\pi\) | |||||||
\(758\) | −9.50000 | + | 16.4545i | −0.345056 | + | 0.597654i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.50000 | + | 4.33013i | −0.0906845 | + | 0.157070i | ||||
\(761\) | 1.50000 | − | 2.59808i | 0.0543750 | − | 0.0941802i | −0.837557 | − | 0.546350i | \(-0.816017\pi\) |
0.891932 | + | 0.452170i | \(0.149350\pi\) | |||||||
\(762\) | −2.00000 | −0.0724524 | ||||||||
\(763\) | 1.00000 | − | 1.73205i | 0.0362024 | − | 0.0627044i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.00000 | − | 5.19615i | −0.108465 | − | 0.187867i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −2.00000 | −0.0721688 | ||||||||
\(769\) | 17.0000 | + | 29.4449i | 0.613036 | + | 1.06181i | 0.990726 | + | 0.135877i | \(0.0433852\pi\) |
−0.377690 | + | 0.925932i | \(0.623282\pi\) | |||||||
\(770\) | 1.50000 | + | 2.59808i | 0.0540562 | + | 0.0936282i | ||||
\(771\) | 12.0000 | − | 20.7846i | 0.432169 | − | 0.748539i | ||||
\(772\) | −4.00000 | −0.143963 | ||||||||
\(773\) | −19.5000 | + | 33.7750i | −0.701366 | + | 1.21480i | 0.266621 | + | 0.963802i | \(0.414093\pi\) |
−0.967987 | + | 0.251000i | \(0.919240\pi\) | |||||||
\(774\) | 1.00000 | − | 1.73205i | 0.0359443 | − | 0.0622573i | ||||
\(775\) | −4.00000 | −0.143684 | ||||||||
\(776\) | −5.00000 | + | 8.66025i | −0.179490 | + | 0.310885i | ||||
\(777\) | −11.0000 | − | 19.0526i | −0.394623 | − | 0.683507i | ||||
\(778\) | −15.0000 | − | 25.9808i | −0.537776 | − | 0.931455i | ||||
\(779\) | 30.0000 | 1.07486 | ||||||||
\(780\) | 5.00000 | + | 5.19615i | 0.179029 | + | 0.186052i | ||||
\(781\) | 18.0000 | 0.644091 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.00000 | − | 5.19615i | 0.107143 | − | 0.185577i | ||||
\(785\) | −17.0000 | −0.606756 | ||||||||
\(786\) | 9.00000 | − | 15.5885i | 0.321019 | − | 0.556022i | ||||
\(787\) | 11.0000 | − | 19.0526i | 0.392108 | − | 0.679150i | −0.600620 | − | 0.799535i | \(-0.705079\pi\) |
0.992727 | + | 0.120384i | \(0.0384127\pi\) | |||||||
\(788\) | −27.0000 | −0.961835 | ||||||||
\(789\) | 9.00000 | − | 15.5885i | 0.320408 | − | 0.554964i | ||||
\(790\) | 8.00000 | + | 13.8564i | 0.284627 | + | 0.492989i | ||||
\(791\) | −6.00000 | − | 10.3923i | −0.213335 | − | 0.369508i | ||||
\(792\) | −3.00000 | −0.106600 | ||||||||
\(793\) | −28.0000 | + | 6.92820i | −0.994309 | + | 0.246028i | ||||
\(794\) | 13.0000 | 0.461353 | ||||||||
\(795\) | 9.00000 | + | 15.5885i | 0.319197 | + | 0.552866i | ||||
\(796\) | 5.00000 | + | 8.66025i | 0.177220 | + | 0.306955i | ||||
\(797\) | −21.0000 | + | 36.3731i | −0.743858 | + | 1.28840i | 0.206868 | + | 0.978369i | \(0.433673\pi\) |
−0.950726 | + | 0.310031i | \(0.899660\pi\) | |||||||
\(798\) | −10.0000 | −0.353996 | ||||||||
\(799\) | −9.00000 | + | 15.5885i | −0.318397 | + | 0.551480i | ||||
\(800\) | 0.500000 | − | 0.866025i | 0.0176777 | − | 0.0306186i | ||||
\(801\) | 9.00000 | 0.317999 | ||||||||
\(802\) | −7.50000 | + | 12.9904i | −0.264834 | + | 0.458706i | ||||
\(803\) | −21.0000 | − | 36.3731i | −0.741074 | − | 1.28358i | ||||
\(804\) | −16.0000 | − | 27.7128i | −0.564276 | − | 0.977356i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.00000 | − | 13.8564i | 0.140894 | − | 0.488071i | ||||
\(807\) | −12.0000 | −0.422420 | ||||||||
\(808\) | −3.00000 | − | 5.19615i | −0.105540 | − | 0.182800i | ||||
\(809\) | 9.00000 | + | 15.5885i | 0.316423 | + | 0.548061i | 0.979739 | − | 0.200279i | \(-0.0641847\pi\) |
−0.663316 | + | 0.748340i | \(0.730851\pi\) | |||||||
\(810\) | 5.50000 | − | 9.52628i | 0.193250 | − | 0.334719i | ||||
\(811\) | −49.0000 | −1.72062 | −0.860311 | − | 0.509769i | \(-0.829731\pi\) | ||||
−0.860311 | + | 0.509769i | \(0.829731\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20.0000 | − | 34.6410i | 0.701431 | − | 1.21491i | ||||
\(814\) | −33.0000 | −1.15665 | ||||||||
\(815\) | 1.00000 | − | 1.73205i | 0.0350285 | − | 0.0606711i | ||||
\(816\) | −6.00000 | − | 10.3923i | −0.210042 | − | 0.363803i | ||||
\(817\) | −5.00000 | − | 8.66025i | −0.174928 | − | 0.302984i | ||||
\(818\) | −5.00000 | −0.174821 | ||||||||
\(819\) | −1.00000 | + | 3.46410i | −0.0349428 | + | 0.121046i | ||||
\(820\) | −6.00000 | −0.209529 | ||||||||
\(821\) | −18.0000 | − | 31.1769i | −0.628204 | − | 1.08808i | −0.987912 | − | 0.155017i | \(-0.950457\pi\) |
0.359708 | − | 0.933065i | \(-0.382876\pi\) | |||||||
\(822\) | −6.00000 | − | 10.3923i | −0.209274 | − | 0.362473i | ||||
\(823\) | 21.5000 | − | 37.2391i | 0.749443 | − | 1.29807i | −0.198647 | − | 0.980071i | \(-0.563655\pi\) |
0.948090 | − | 0.318002i | \(-0.103012\pi\) | |||||||
\(824\) | −5.00000 | −0.174183 | ||||||||
\(825\) | 3.00000 | − | 5.19615i | 0.104447 | − | 0.180907i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.0000 | 1.25184 | 0.625921 | − | 0.779886i | \(-0.284723\pi\) | ||||
0.625921 | + | 0.779886i | \(0.284723\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.0000 | + | 34.6410i | 0.694629 | + | 1.20313i | 0.970306 | + | 0.241882i | \(0.0777647\pi\) |
−0.275677 | + | 0.961250i | \(0.588902\pi\) | |||||||
\(830\) | 3.00000 | + | 5.19615i | 0.104132 | + | 0.180361i | ||||
\(831\) | 2.00000 | 0.0693792 | ||||||||
\(832\) | 2.50000 | + | 2.59808i | 0.0866719 | + | 0.0900721i | ||||
\(833\) | 36.0000 | 1.24733 | ||||||||
\(834\) | 19.0000 | + | 32.9090i | 0.657916 | + | 1.13954i | ||||
\(835\) | −7.50000 | − | 12.9904i | −0.259548 | − | 0.449551i | ||||
\(836\) | −7.50000 | + | 12.9904i | −0.259393 | + | 0.449282i | ||||
\(837\) | −16.0000 | −0.553041 | ||||||||
\(838\) | −18.0000 | + | 31.1769i | −0.621800 | + | 1.07699i | ||||
\(839\) | 12.0000 | − | 20.7846i | 0.414286 | − | 0.717564i | −0.581067 | − | 0.813856i | \(-0.697365\pi\) |
0.995353 | + | 0.0962912i | \(0.0306980\pi\) | |||||||
\(840\) | 2.00000 | 0.0690066 | ||||||||
\(841\) | 14.5000 | − | 25.1147i | 0.500000 | − | 0.866025i | ||||
\(842\) | −5.00000 | − | 8.66025i | −0.172311 | − | 0.298452i | ||||
\(843\) | −6.00000 | − | 10.3923i | −0.206651 | − | 0.357930i | ||||
\(844\) | 23.0000 | 0.791693 | ||||||||
\(845\) | 0.500000 | − | 12.9904i | 0.0172005 | − | 0.446883i | ||||
\(846\) | 3.00000 | 0.103142 | ||||||||
\(847\) | −1.00000 | − | 1.73205i | −0.0343604 | − | 0.0595140i | ||||
\(848\) | 4.50000 | + | 7.79423i | 0.154531 | + | 0.267655i | ||||
\(849\) | 14.0000 | − | 24.2487i | 0.480479 | − | 0.832214i | ||||
\(850\) | 6.00000 | 0.205798 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 6.00000 | − | 10.3923i | 0.205557 | − | 0.356034i | ||||
\(853\) | −46.0000 | −1.57501 | −0.787505 | − | 0.616308i | \(-0.788628\pi\) | ||||
−0.787505 | + | 0.616308i | \(0.788628\pi\) | |||||||
\(854\) | −4.00000 | + | 6.92820i | −0.136877 | + | 0.237078i | ||||
\(855\) | 2.50000 | + | 4.33013i | 0.0854982 | + | 0.148087i | ||||
\(856\) | −6.00000 | − | 10.3923i | −0.205076 | − | 0.355202i | ||||
\(857\) | −12.0000 | −0.409912 | −0.204956 | − | 0.978771i | \(-0.565705\pi\) | ||||
−0.204956 | + | 0.978771i | \(0.565705\pi\) | |||||||
\(858\) | 15.0000 | + | 15.5885i | 0.512092 | + | 0.532181i | ||||
\(859\) | −31.0000 | −1.05771 | −0.528853 | − | 0.848713i | \(-0.677378\pi\) | ||||
−0.528853 | + | 0.848713i | \(0.677378\pi\) | |||||||
\(860\) | 1.00000 | + | 1.73205i | 0.0340997 | + | 0.0590624i | ||||
\(861\) | −6.00000 | − | 10.3923i | −0.204479 | − | 0.354169i | ||||
\(862\) | 15.0000 | − | 25.9808i | 0.510902 | − | 0.884908i | ||||
\(863\) | 36.0000 | 1.22545 | 0.612727 | − | 0.790295i | \(-0.290072\pi\) | ||||
0.612727 | + | 0.790295i | \(0.290072\pi\) | |||||||
\(864\) | 2.00000 | − | 3.46410i | 0.0680414 | − | 0.117851i | ||||
\(865\) | 7.50000 | − | 12.9904i | 0.255008 | − | 0.441686i | ||||
\(866\) | 16.0000 | 0.543702 | ||||||||
\(867\) | 19.0000 | − | 32.9090i | 0.645274 | − | 1.11765i | ||||
\(868\) | −2.00000 | − | 3.46410i | −0.0678844 | − | 0.117579i | ||||
\(869\) | 24.0000 | + | 41.5692i | 0.814144 | + | 1.41014i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.0000 | + | 55.4256i | −0.542139 | + | 1.87803i | ||||
\(872\) | −2.00000 | −0.0677285 | ||||||||
\(873\) | 5.00000 | + | 8.66025i | 0.169224 | + | 0.293105i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.500000 | + | 0.866025i | −0.0169031 | + | 0.0292770i | ||||
\(876\) | −28.0000 | −0.946032 | ||||||||
\(877\) | 5.00000 | − | 8.66025i | 0.168838 | − | 0.292436i | −0.769174 | − | 0.639040i | \(-0.779332\pi\) |
0.938012 | + | 0.346604i | \(0.112665\pi\) | |||||||
\(878\) | 10.0000 | − | 17.3205i | 0.337484 | − | 0.584539i | ||||
\(879\) | −18.0000 | −0.607125 | ||||||||
\(880\) | 1.50000 | − | 2.59808i | 0.0505650 | − | 0.0875811i | ||||
\(881\) | 7.50000 | + | 12.9904i | 0.252681 | + | 0.437657i | 0.964263 | − | 0.264946i | \(-0.0853542\pi\) |
−0.711582 | + | 0.702603i | \(0.752021\pi\) | |||||||
\(882\) | −3.00000 | − | 5.19615i | −0.101015 | − | 0.174964i | ||||
\(883\) | −52.0000 | −1.74994 | −0.874970 | − | 0.484178i | \(-0.839119\pi\) | ||||
−0.874970 | + | 0.484178i | \(0.839119\pi\) | |||||||
\(884\) | −6.00000 | + | 20.7846i | −0.201802 | + | 0.699062i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −9.00000 | − | 15.5885i | −0.302361 | − | 0.523704i | ||||
\(887\) | 13.5000 | + | 23.3827i | 0.453286 | + | 0.785114i | 0.998588 | − | 0.0531258i | \(-0.0169184\pi\) |
−0.545302 | + | 0.838240i | \(0.683585\pi\) | |||||||
\(888\) | −11.0000 | + | 19.0526i | −0.369136 | + | 0.639362i | ||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | −4.50000 | + | 7.79423i | −0.150840 | + | 0.261263i | ||||
\(891\) | 16.5000 | − | 28.5788i | 0.552771 | − | 0.957427i | ||||
\(892\) | −19.0000 | −0.636167 | ||||||||
\(893\) | 7.50000 | − | 12.9904i | 0.250978 | − | 0.434707i | ||||
\(894\) | 18.0000 | + | 31.1769i | 0.602010 | + | 1.04271i | ||||
\(895\) | −12.0000 | − | 20.7846i | −0.401116 | − | 0.694753i | ||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −9.00000 | −0.300334 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.500000 | − | 0.866025i | −0.0166667 | − | 0.0288675i | ||||
\(901\) | −27.0000 | + | 46.7654i | −0.899500 | + | 1.55798i | ||||
\(902\) | −18.0000 | −0.599334 | ||||||||
\(903\) | −2.00000 | + | 3.46410i | −0.0665558 | + | 0.115278i | ||||
\(904\) | −6.00000 | + | 10.3923i | −0.199557 | + | 0.345643i | ||||
\(905\) | −8.00000 | −0.265929 | ||||||||
\(906\) | 16.0000 | − | 27.7128i | 0.531564 | − | 0.920697i | ||||
\(907\) | −4.00000 | − | 6.92820i | −0.132818 | − | 0.230047i | 0.791944 | − | 0.610594i | \(-0.209069\pi\) |
−0.924762 | + | 0.380547i | \(0.875736\pi\) | |||||||
\(908\) | 12.0000 | + | 20.7846i | 0.398234 | + | 0.689761i | ||||
\(909\) | −6.00000 | −0.199007 | ||||||||
\(910\) | −2.50000 | − | 2.59808i | −0.0828742 | − | 0.0861254i | ||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | 5.00000 | + | 8.66025i | 0.165567 | + | 0.286770i | ||||
\(913\) | 9.00000 | + | 15.5885i | 0.297857 | + | 0.515903i | ||||
\(914\) | −2.00000 | + | 3.46410i | −0.0661541 | + | 0.114582i | ||||
\(915\) | 16.0000 | 0.528944 | ||||||||
\(916\) | 2.00000 | − | 3.46410i | 0.0660819 | − | 0.114457i | ||||
\(917\) | −4.50000 | + | 7.79423i | −0.148603 | + | 0.257388i | ||||
\(918\) | 24.0000 | 0.792118 | ||||||||
\(919\) | 17.0000 | − | 29.4449i | 0.560778 | − | 0.971296i | −0.436650 | − | 0.899631i | \(-0.643835\pi\) |
0.997429 | − | 0.0716652i | \(-0.0228313\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.00000 | + | 3.46410i | 0.0659022 | + | 0.114146i | ||||
\(922\) | 42.0000 | 1.38320 | ||||||||
\(923\) | −21.0000 | + | 5.19615i | −0.691223 | + | 0.171033i | ||||
\(924\) | 6.00000 | 0.197386 | ||||||||
\(925\) | −5.50000 | − | 9.52628i | −0.180839 | − | 0.313222i | ||||
\(926\) | 4.00000 | + | 6.92820i | 0.131448 | + | 0.227675i | ||||
\(927\) | −2.50000 | + | 4.33013i | −0.0821108 | + | 0.142220i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21.0000 | + | 36.3731i | −0.688988 | + | 1.19336i | 0.283178 | + | 0.959067i | \(0.408611\pi\) |
−0.972166 | + | 0.234294i | \(0.924722\pi\) | |||||||
\(930\) | −4.00000 | + | 6.92820i | −0.131165 | + | 0.227185i | ||||
\(931\) | −30.0000 | −0.983210 | ||||||||
\(932\) | 12.0000 | − | 20.7846i | 0.393073 | − | 0.680823i | ||||
\(933\) | 30.0000 | + | 51.9615i | 0.982156 | + | 1.70114i | ||||
\(934\) | −6.00000 | − | 10.3923i | −0.196326 | − | 0.340047i | ||||
\(935\) | 18.0000 | 0.588663 | ||||||||
\(936\) | 3.50000 | − | 0.866025i | 0.114401 | − | 0.0283069i | ||||
\(937\) | 50.0000 | 1.63343 | 0.816714 | − | 0.577042i | \(-0.195793\pi\) | ||||
0.816714 | + | 0.577042i | \(0.195793\pi\) | |||||||
\(938\) | 8.00000 | + | 13.8564i | 0.261209 | + | 0.452428i | ||||
\(939\) | 14.0000 | + | 24.2487i | 0.456873 | + | 0.791327i | ||||
\(940\) | −1.50000 | + | 2.59808i | −0.0489246 | + | 0.0847399i | ||||
\(941\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(942\) | −17.0000 | + | 29.4449i | −0.553890 | + | 0.959366i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.00000 | + | 3.46410i | −0.0650600 | + | 0.112687i | ||||
\(946\) | 3.00000 | + | 5.19615i | 0.0975384 | + | 0.168941i | ||||
\(947\) | −24.0000 | − | 41.5692i | −0.779895 | − | 1.35082i | −0.932002 | − | 0.362454i | \(-0.881939\pi\) |
0.152106 | − | 0.988364i | \(-0.451394\pi\) | |||||||
\(948\) | 32.0000 | 1.03931 | ||||||||
\(949\) | 35.0000 | + | 36.3731i | 1.13615 | + | 1.18072i | ||||
\(950\) | −5.00000 | −0.162221 | ||||||||
\(951\) | 15.0000 | + | 25.9808i | 0.486408 | + | 0.842484i | ||||
\(952\) | 3.00000 | + | 5.19615i | 0.0972306 | + | 0.168408i | ||||
\(953\) | −12.0000 | + | 20.7846i | −0.388718 | + | 0.673280i | −0.992277 | − | 0.124039i | \(-0.960415\pi\) |
0.603559 | + | 0.797318i | \(0.293749\pi\) | |||||||
\(954\) | 9.00000 | 0.291386 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −15.0000 | + | 25.9808i | −0.484628 | + | 0.839400i | ||||
\(959\) | 3.00000 | + | 5.19615i | 0.0968751 | + | 0.167793i | ||||
\(960\) | −1.00000 | − | 1.73205i | −0.0322749 | − | 0.0559017i | ||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 38.5000 | − | 9.52628i | 1.24129 | − | 0.307140i | ||||
\(963\) | −12.0000 | −0.386695 | ||||||||
\(964\) | −11.5000 | − | 19.9186i | −0.370390 | − | 0.641534i | ||||
\(965\) | −2.00000 | − | 3.46410i | −0.0643823 | − | 0.111513i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.00000 | 0.160789 | 0.0803946 | − | 0.996763i | \(-0.474382\pi\) | ||||
0.0803946 | + | 0.996763i | \(0.474382\pi\) | |||||||
\(968\) | −1.00000 | + | 1.73205i | −0.0321412 | + | 0.0556702i | ||||
\(969\) | −30.0000 | + | 51.9615i | −0.963739 | + | 1.66924i | ||||
\(970\) | −10.0000 | −0.321081 | ||||||||
\(971\) | −16.5000 | + | 28.5788i | −0.529510 | + | 0.917139i | 0.469897 | + | 0.882721i | \(0.344291\pi\) |
−0.999408 | + | 0.0344175i | \(0.989042\pi\) | |||||||
\(972\) | −5.00000 | − | 8.66025i | −0.160375 | − | 0.277778i | ||||
\(973\) | −9.50000 | − | 16.4545i | −0.304556 | − | 0.527506i | ||||
\(974\) | 19.0000 | 0.608799 | ||||||||
\(975\) | −2.00000 | + | 6.92820i | −0.0640513 | + | 0.221880i | ||||
\(976\) | 8.00000 | 0.256074 | ||||||||
\(977\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(978\) | −2.00000 | − | 3.46410i | −0.0639529 | − | 0.110770i | ||||
\(979\) | −13.5000 | + | 23.3827i | −0.431462 | + | 0.747314i | ||||
\(980\) | 6.00000 | 0.191663 | ||||||||
\(981\) | −1.00000 | + | 1.73205i | −0.0319275 | + | 0.0553001i | ||||
\(982\) | 13.5000 | − | 23.3827i | 0.430802 | − | 0.746171i | ||||
\(983\) | 39.0000 | 1.24391 | 0.621953 | − | 0.783054i | \(-0.286339\pi\) | ||||
0.621953 | + | 0.783054i | \(0.286339\pi\) | |||||||
\(984\) | −6.00000 | + | 10.3923i | −0.191273 | + | 0.331295i | ||||
\(985\) | −13.5000 | − | 23.3827i | −0.430146 | − | 0.745034i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.00000 | −0.190982 | ||||||||
\(988\) | 5.00000 | − | 17.3205i | 0.159071 | − | 0.551039i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −1.50000 | − | 2.59808i | −0.0476731 | − | 0.0825723i | ||||
\(991\) | 11.0000 | + | 19.0526i | 0.349427 | + | 0.605224i | 0.986148 | − | 0.165870i | \(-0.0530431\pi\) |
−0.636721 | + | 0.771094i | \(0.719710\pi\) | |||||||
\(992\) | −2.00000 | + | 3.46410i | −0.0635001 | + | 0.109985i | ||||
\(993\) | −40.0000 | −1.26936 | ||||||||
\(994\) | −3.00000 | + | 5.19615i | −0.0951542 | + | 0.164812i | ||||
\(995\) | −5.00000 | + | 8.66025i | −0.158511 | + | 0.274549i | ||||
\(996\) | 12.0000 | 0.380235 | ||||||||
\(997\) | −20.5000 | + | 35.5070i | −0.649242 | + | 1.12452i | 0.334063 | + | 0.942551i | \(0.391580\pi\) |
−0.983304 | + | 0.181968i | \(0.941753\pi\) | |||||||
\(998\) | −2.00000 | − | 3.46410i | −0.0633089 | − | 0.109654i | ||||
\(999\) | −22.0000 | − | 38.1051i | −0.696049 | − | 1.20559i |
(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 | 130.2.e.b.81.1 | yes | 2 | |
3.2 | odd | 2 | 1170.2.i.f.991.1 | 2 | |||
4.3 | odd | 2 | 1040.2.q.c.81.1 | 2 | |||
5.2 | odd | 4 | 650.2.o.b.549.1 | 4 | |||
5.3 | odd | 4 | 650.2.o.b.549.2 | 4 | |||
5.4 | even | 2 | 650.2.e.a.601.1 | 2 | |||
13.2 | odd | 12 | 1690.2.d.a.1351.2 | 2 | |||
13.3 | even | 3 | 1690.2.a.a.1.1 | 1 | |||
13.4 | even | 6 | 1690.2.e.e.191.1 | 2 | |||
13.5 | odd | 4 | 1690.2.l.i.361.2 | 4 | |||
13.6 | odd | 12 | 1690.2.l.i.1161.1 | 4 | |||
13.7 | odd | 12 | 1690.2.l.i.1161.2 | 4 | |||
13.8 | odd | 4 | 1690.2.l.i.361.1 | 4 | |||
13.9 | even | 3 | inner | 130.2.e.b.61.1 | ✓ | 2 | |
13.10 | even | 6 | 1690.2.a.g.1.1 | 1 | |||
13.11 | odd | 12 | 1690.2.d.a.1351.1 | 2 | |||
13.12 | even | 2 | 1690.2.e.e.991.1 | 2 | |||
39.35 | odd | 6 | 1170.2.i.f.451.1 | 2 | |||
52.35 | odd | 6 | 1040.2.q.c.321.1 | 2 | |||
65.9 | even | 6 | 650.2.e.a.451.1 | 2 | |||
65.22 | odd | 12 | 650.2.o.b.399.2 | 4 | |||
65.29 | even | 6 | 8450.2.a.w.1.1 | 1 | |||
65.48 | odd | 12 | 650.2.o.b.399.1 | 4 | |||
65.49 | even | 6 | 8450.2.a.k.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
130.2.e.b.61.1 | ✓ | 2 | 13.9 | even | 3 | inner | |
130.2.e.b.81.1 | yes | 2 | 1.1 | even | 1 | trivial | |
650.2.e.a.451.1 | 2 | 65.9 | even | 6 | |||
650.2.e.a.601.1 | 2 | 5.4 | even | 2 | |||
650.2.o.b.399.1 | 4 | 65.48 | odd | 12 | |||
650.2.o.b.399.2 | 4 | 65.22 | odd | 12 | |||
650.2.o.b.549.1 | 4 | 5.2 | odd | 4 | |||
650.2.o.b.549.2 | 4 | 5.3 | odd | 4 | |||
1040.2.q.c.81.1 | 2 | 4.3 | odd | 2 | |||
1040.2.q.c.321.1 | 2 | 52.35 | odd | 6 | |||
1170.2.i.f.451.1 | 2 | 39.35 | odd | 6 | |||
1170.2.i.f.991.1 | 2 | 3.2 | odd | 2 | |||
1690.2.a.a.1.1 | 1 | 13.3 | even | 3 | |||
1690.2.a.g.1.1 | 1 | 13.10 | even | 6 | |||
1690.2.d.a.1351.1 | 2 | 13.11 | odd | 12 | |||
1690.2.d.a.1351.2 | 2 | 13.2 | odd | 12 | |||
1690.2.e.e.191.1 | 2 | 13.4 | even | 6 | |||
1690.2.e.e.991.1 | 2 | 13.12 | even | 2 | |||
1690.2.l.i.361.1 | 4 | 13.8 | odd | 4 | |||
1690.2.l.i.361.2 | 4 | 13.5 | odd | 4 | |||
1690.2.l.i.1161.1 | 4 | 13.6 | odd | 12 | |||
1690.2.l.i.1161.2 | 4 | 13.7 | odd | 12 | |||
8450.2.a.k.1.1 | 1 | 65.49 | even | 6 | |||
8450.2.a.w.1.1 | 1 | 65.29 | even | 6 |