Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(793,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1386.793");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.k (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: | \(11.0672657201\) |
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 | 991.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1386.991 |
Dual form | 1386.2.k.g.793.1 |
$q$-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 \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | 0.955901 | − | 0.293691i | \(-0.0948835\pi\) |
−0.732294 | + | 0.680989i | \(0.761550\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.50000 | − | 0.866025i | −0.944911 | − | 0.327327i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.500000 | − | 0.866025i | 0.158114 | − | 0.273861i | ||||
\(11\) | 0.500000 | − | 0.866025i | 0.150756 | − | 0.261116i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0.500000 | + | 2.59808i | 0.133631 | + | 0.694365i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −2.50000 | + | 4.33013i | −0.606339 | + | 1.05021i | 0.385499 | + | 0.922708i | \(0.374029\pi\) |
−0.991838 | + | 0.127502i | \(0.959304\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.00000 | + | 5.19615i | 0.688247 | + | 1.19208i | 0.972404 | + | 0.233301i | \(0.0749529\pi\) |
−0.284157 | + | 0.958778i | \(0.591714\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −3.50000 | − | 6.06218i | −0.729800 | − | 1.26405i | −0.956967 | − | 0.290196i | \(-0.906280\pi\) |
0.227167 | − | 0.973856i | \(-0.427054\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00000 | − | 3.46410i | 0.400000 | − | 0.692820i | ||||
\(26\) | −1.00000 | − | 1.73205i | −0.196116 | − | 0.339683i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.00000 | − | 1.73205i | 0.377964 | − | 0.327327i | ||||
\(29\) | −8.00000 | −1.48556 | −0.742781 | − | 0.669534i | \(-0.766494\pi\) | ||||
−0.742781 | + | 0.669534i | \(0.766494\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.00000 | + | 8.66025i | −0.898027 | + | 1.55543i | −0.0680129 | + | 0.997684i | \(0.521666\pi\) |
−0.830014 | + | 0.557743i | \(0.811667\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.00000 | 0.857493 | ||||||||
\(35\) | −0.500000 | − | 2.59808i | −0.0845154 | − | 0.439155i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.00000 | + | 6.92820i | 0.657596 | + | 1.13899i | 0.981236 | + | 0.192809i | \(0.0617599\pi\) |
−0.323640 | + | 0.946180i | \(0.604907\pi\) | |||||||
\(38\) | 3.00000 | − | 5.19615i | 0.486664 | − | 0.842927i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.500000 | + | 0.866025i | 0.0790569 | + | 0.136931i | ||||
\(41\) | 7.00000 | 1.09322 | 0.546608 | − | 0.837389i | \(-0.315919\pi\) | ||||
0.546608 | + | 0.837389i | \(0.315919\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000 | 0.609994 | 0.304997 | − | 0.952353i | \(-0.401344\pi\) | ||||
0.304997 | + | 0.952353i | \(0.401344\pi\) | |||||||
\(44\) | 0.500000 | + | 0.866025i | 0.0753778 | + | 0.130558i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.50000 | + | 6.06218i | −0.516047 | + | 0.893819i | ||||
\(47\) | 0.500000 | + | 0.866025i | 0.0729325 | + | 0.126323i | 0.900185 | − | 0.435507i | \(-0.143431\pi\) |
−0.827253 | + | 0.561830i | \(0.810098\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.50000 | + | 4.33013i | 0.785714 | + | 0.618590i | ||||
\(50\) | −4.00000 | −0.565685 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.00000 | + | 1.73205i | −0.138675 | + | 0.240192i | ||||
\(53\) | −3.00000 | + | 5.19615i | −0.412082 | + | 0.713746i | −0.995117 | − | 0.0987002i | \(-0.968532\pi\) |
0.583036 | + | 0.812447i | \(0.301865\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | −2.50000 | − | 0.866025i | −0.334077 | − | 0.115728i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.00000 | + | 6.92820i | 0.525226 | + | 0.909718i | ||||
\(59\) | −3.00000 | + | 5.19615i | −0.390567 | + | 0.676481i | −0.992524 | − | 0.122047i | \(-0.961054\pi\) |
0.601958 | + | 0.798528i | \(0.294388\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.500000 | − | 0.866025i | −0.0640184 | − | 0.110883i | 0.832240 | − | 0.554416i | \(-0.187058\pi\) |
−0.896258 | + | 0.443533i | \(0.853725\pi\) | |||||||
\(62\) | 10.0000 | 1.27000 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.00000 | + | 1.73205i | 0.124035 | + | 0.214834i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.50000 | + | 2.59808i | −0.183254 | + | 0.317406i | −0.942987 | − | 0.332830i | \(-0.891996\pi\) |
0.759733 | + | 0.650236i | \(0.225330\pi\) | |||||||
\(68\) | −2.50000 | − | 4.33013i | −0.303170 | − | 0.525105i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.00000 | + | 1.73205i | −0.239046 | + | 0.207020i | ||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.00000 | + | 8.66025i | −0.585206 | + | 1.01361i | 0.409644 | + | 0.912245i | \(0.365653\pi\) |
−0.994850 | + | 0.101361i | \(0.967680\pi\) | |||||||
\(74\) | 4.00000 | − | 6.92820i | 0.464991 | − | 0.805387i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.00000 | −0.688247 | ||||||||
\(77\) | −2.00000 | + | 1.73205i | −0.227921 | + | 0.197386i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.50000 | + | 7.79423i | 0.506290 | + | 0.876919i | 0.999974 | + | 0.00727784i | \(0.00231663\pi\) |
−0.493684 | + | 0.869641i | \(0.664350\pi\) | |||||||
\(80\) | 0.500000 | − | 0.866025i | 0.0559017 | − | 0.0968246i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.50000 | − | 6.06218i | −0.386510 | − | 0.669456i | ||||
\(83\) | −15.0000 | −1.64646 | −0.823232 | − | 0.567705i | \(-0.807831\pi\) | ||||
−0.823232 | + | 0.567705i | \(0.807831\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.00000 | −0.542326 | ||||||||
\(86\) | −2.00000 | − | 3.46410i | −0.215666 | − | 0.373544i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.500000 | − | 0.866025i | 0.0533002 | − | 0.0923186i | ||||
\(89\) | 6.00000 | + | 10.3923i | 0.635999 | + | 1.10158i | 0.986303 | + | 0.164946i | \(0.0527450\pi\) |
−0.350304 | + | 0.936636i | \(0.613922\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.00000 | − | 1.73205i | −0.524142 | − | 0.181568i | ||||
\(92\) | 7.00000 | 0.729800 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.500000 | − | 0.866025i | 0.0515711 | − | 0.0893237i | ||||
\(95\) | −3.00000 | + | 5.19615i | −0.307794 | + | 0.533114i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.0000 | 1.31995 | 0.659975 | − | 0.751288i | \(-0.270567\pi\) | ||||
0.659975 | + | 0.751288i | \(0.270567\pi\) | |||||||
\(98\) | 1.00000 | − | 6.92820i | 0.101015 | − | 0.699854i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.00000 | + | 3.46410i | 0.200000 | + | 0.346410i | ||||
\(101\) | −6.00000 | + | 10.3923i | −0.597022 | + | 1.03407i | 0.396236 | + | 0.918149i | \(0.370316\pi\) |
−0.993258 | + | 0.115924i | \(0.963017\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.00000 | − | 10.3923i | −0.591198 | − | 1.02398i | −0.994071 | − | 0.108729i | \(-0.965322\pi\) |
0.402874 | − | 0.915255i | \(-0.368011\pi\) | |||||||
\(104\) | 2.00000 | 0.196116 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.00000 | 0.582772 | ||||||||
\(107\) | 6.50000 | + | 11.2583i | 0.628379 | + | 1.08838i | 0.987877 | + | 0.155238i | \(0.0496145\pi\) |
−0.359498 | + | 0.933146i | \(0.617052\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.50000 | + | 16.4545i | −0.909935 | + | 1.57605i | −0.0957826 | + | 0.995402i | \(0.530535\pi\) |
−0.814152 | + | 0.580651i | \(0.802798\pi\) | |||||||
\(110\) | −0.500000 | − | 0.866025i | −0.0476731 | − | 0.0825723i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.500000 | + | 2.59808i | 0.0472456 | + | 0.245495i | ||||
\(113\) | 14.0000 | 1.31701 | 0.658505 | − | 0.752577i | \(-0.271189\pi\) | ||||
0.658505 | + | 0.752577i | \(0.271189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.50000 | − | 6.06218i | 0.326377 | − | 0.565301i | ||||
\(116\) | 4.00000 | − | 6.92820i | 0.371391 | − | 0.643268i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.00000 | 0.552345 | ||||||||
\(119\) | 10.0000 | − | 8.66025i | 0.916698 | − | 0.793884i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | −0.500000 | + | 0.866025i | −0.0452679 | + | 0.0784063i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.00000 | − | 8.66025i | −0.449013 | − | 0.777714i | ||||
\(125\) | 9.00000 | 0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.0000 | 1.50851 | 0.754253 | − | 0.656584i | \(-0.227999\pi\) | ||||
0.754253 | + | 0.656584i | \(0.227999\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.00000 | − | 1.73205i | 0.0877058 | − | 0.151911i | ||||
\(131\) | −6.00000 | − | 10.3923i | −0.524222 | − | 0.907980i | −0.999602 | − | 0.0281993i | \(-0.991023\pi\) |
0.475380 | − | 0.879781i | \(-0.342311\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.00000 | − | 15.5885i | −0.260133 | − | 1.35169i | ||||
\(134\) | 3.00000 | 0.259161 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.50000 | + | 4.33013i | −0.214373 | + | 0.371305i | ||||
\(137\) | 9.00000 | − | 15.5885i | 0.768922 | − | 1.33181i | −0.169226 | − | 0.985577i | \(-0.554127\pi\) |
0.938148 | − | 0.346235i | \(-0.112540\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.00000 | 0.169638 | 0.0848189 | − | 0.996396i | \(-0.472969\pi\) | ||||
0.0848189 | + | 0.996396i | \(0.472969\pi\) | |||||||
\(140\) | 2.50000 | + | 0.866025i | 0.211289 | + | 0.0731925i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.00000 | + | 6.92820i | 0.335673 | + | 0.581402i | ||||
\(143\) | 1.00000 | − | 1.73205i | 0.0836242 | − | 0.144841i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.00000 | − | 6.92820i | −0.332182 | − | 0.575356i | ||||
\(146\) | 10.0000 | 0.827606 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.00000 | −0.657596 | ||||||||
\(149\) | 2.00000 | + | 3.46410i | 0.163846 | + | 0.283790i | 0.936245 | − | 0.351348i | \(-0.114277\pi\) |
−0.772399 | + | 0.635138i | \(0.780943\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.50000 | + | 7.79423i | −0.366205 | + | 0.634285i | −0.988969 | − | 0.148124i | \(-0.952676\pi\) |
0.622764 | + | 0.782410i | \(0.286010\pi\) | |||||||
\(152\) | 3.00000 | + | 5.19615i | 0.243332 | + | 0.421464i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.50000 | + | 0.866025i | 0.201456 | + | 0.0697863i | ||||
\(155\) | −10.0000 | −0.803219 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.00000 | + | 3.46410i | −0.159617 | + | 0.276465i | −0.934731 | − | 0.355357i | \(-0.884359\pi\) |
0.775113 | + | 0.631822i | \(0.217693\pi\) | |||||||
\(158\) | 4.50000 | − | 7.79423i | 0.358001 | − | 0.620076i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 3.50000 | + | 18.1865i | 0.275839 | + | 1.43330i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.50000 | − | 11.2583i | −0.509119 | − | 0.881820i | −0.999944 | − | 0.0105623i | \(-0.996638\pi\) |
0.490825 | − | 0.871258i | \(-0.336695\pi\) | |||||||
\(164\) | −3.50000 | + | 6.06218i | −0.273304 | + | 0.473377i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.50000 | + | 12.9904i | 0.582113 | + | 1.00825i | ||||
\(167\) | −8.00000 | −0.619059 | −0.309529 | − | 0.950890i | \(-0.600171\pi\) | ||||
−0.309529 | + | 0.950890i | \(0.600171\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 2.50000 | + | 4.33013i | 0.191741 | + | 0.332106i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.00000 | + | 3.46410i | −0.152499 | + | 0.264135i | ||||
\(173\) | 7.00000 | + | 12.1244i | 0.532200 | + | 0.921798i | 0.999293 | + | 0.0375896i | \(0.0119679\pi\) |
−0.467093 | + | 0.884208i | \(0.654699\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.00000 | + | 6.92820i | −0.604743 | + | 0.523723i | ||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.00000 | − | 10.3923i | 0.449719 | − | 0.778936i | ||||
\(179\) | 1.00000 | − | 1.73205i | 0.0747435 | − | 0.129460i | −0.826231 | − | 0.563331i | \(-0.809520\pi\) |
0.900975 | + | 0.433872i | \(0.142853\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.0000 | 1.48659 | 0.743294 | − | 0.668965i | \(-0.233262\pi\) | ||||
0.743294 | + | 0.668965i | \(0.233262\pi\) | |||||||
\(182\) | 1.00000 | + | 5.19615i | 0.0741249 | + | 0.385164i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.50000 | − | 6.06218i | −0.258023 | − | 0.446910i | ||||
\(185\) | −4.00000 | + | 6.92820i | −0.294086 | + | 0.509372i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.50000 | + | 4.33013i | 0.182818 | + | 0.316650i | ||||
\(188\) | −1.00000 | −0.0729325 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.00000 | 0.435286 | ||||||||
\(191\) | −10.0000 | − | 17.3205i | −0.723575 | − | 1.25327i | −0.959558 | − | 0.281511i | \(-0.909164\pi\) |
0.235983 | − | 0.971757i | \(-0.424169\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.00000 | + | 6.92820i | −0.287926 | + | 0.498703i | −0.973315 | − | 0.229475i | \(-0.926299\pi\) |
0.685388 | + | 0.728178i | \(0.259632\pi\) | |||||||
\(194\) | −6.50000 | − | 11.2583i | −0.466673 | − | 0.808301i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.50000 | + | 2.59808i | −0.464286 | + | 0.185577i | ||||
\(197\) | −24.0000 | −1.70993 | −0.854965 | − | 0.518686i | \(-0.826421\pi\) | ||||
−0.854965 | + | 0.518686i | \(0.826421\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.0000 | − | 22.5167i | 0.921546 | − | 1.59616i | 0.124521 | − | 0.992217i | \(-0.460261\pi\) |
0.797025 | − | 0.603947i | \(-0.206406\pi\) | |||||||
\(200\) | 2.00000 | − | 3.46410i | 0.141421 | − | 0.244949i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.0000 | 0.844317 | ||||||||
\(203\) | 20.0000 | + | 6.92820i | 1.40372 | + | 0.486265i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.50000 | + | 6.06218i | 0.244451 | + | 0.423401i | ||||
\(206\) | −6.00000 | + | 10.3923i | −0.418040 | + | 0.724066i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.00000 | − | 1.73205i | −0.0693375 | − | 0.120096i | ||||
\(209\) | 6.00000 | 0.415029 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.0000 | −1.37686 | −0.688428 | − | 0.725304i | \(-0.741699\pi\) | ||||
−0.688428 | + | 0.725304i | \(0.741699\pi\) | |||||||
\(212\) | −3.00000 | − | 5.19615i | −0.206041 | − | 0.356873i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.50000 | − | 11.2583i | 0.444331 | − | 0.769604i | ||||
\(215\) | 2.00000 | + | 3.46410i | 0.136399 | + | 0.236250i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 20.0000 | − | 17.3205i | 1.35769 | − | 1.17579i | ||||
\(218\) | 19.0000 | 1.28684 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.500000 | + | 0.866025i | −0.0337100 | + | 0.0583874i | ||||
\(221\) | −5.00000 | + | 8.66025i | −0.336336 | + | 0.582552i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.0000 | 0.669650 | 0.334825 | − | 0.942280i | \(-0.391323\pi\) | ||||
0.334825 | + | 0.942280i | \(0.391323\pi\) | |||||||
\(224\) | 2.00000 | − | 1.73205i | 0.133631 | − | 0.115728i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.00000 | − | 12.1244i | −0.465633 | − | 0.806500i | ||||
\(227\) | 8.50000 | − | 14.7224i | 0.564165 | − | 0.977162i | −0.432962 | − | 0.901412i | \(-0.642532\pi\) |
0.997127 | − | 0.0757500i | \(-0.0241351\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.0000 | − | 17.3205i | −0.660819 | − | 1.14457i | −0.980401 | − | 0.197013i | \(-0.936876\pi\) |
0.319582 | − | 0.947559i | \(-0.396457\pi\) | |||||||
\(230\) | −7.00000 | −0.461566 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.00000 | −0.525226 | ||||||||
\(233\) | −10.5000 | − | 18.1865i | −0.687878 | − | 1.19144i | −0.972523 | − | 0.232806i | \(-0.925209\pi\) |
0.284645 | − | 0.958633i | \(-0.408124\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.500000 | + | 0.866025i | −0.0326164 | + | 0.0564933i | ||||
\(236\) | −3.00000 | − | 5.19615i | −0.195283 | − | 0.338241i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −12.5000 | − | 4.33013i | −0.810255 | − | 0.280680i | ||||
\(239\) | 16.0000 | 1.03495 | 0.517477 | − | 0.855697i | \(-0.326871\pi\) | ||||
0.517477 | + | 0.855697i | \(0.326871\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.00000 | + | 10.3923i | −0.386494 | + | 0.669427i | −0.991975 | − | 0.126432i | \(-0.959647\pi\) |
0.605481 | + | 0.795860i | \(0.292981\pi\) | |||||||
\(242\) | −0.500000 | + | 0.866025i | −0.0321412 | + | 0.0556702i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.00000 | 0.0640184 | ||||||||
\(245\) | −1.00000 | + | 6.92820i | −0.0638877 | + | 0.442627i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.00000 | + | 10.3923i | 0.381771 | + | 0.661247i | ||||
\(248\) | −5.00000 | + | 8.66025i | −0.317500 | + | 0.549927i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4.50000 | − | 7.79423i | −0.284605 | − | 0.492950i | ||||
\(251\) | 24.0000 | 1.51487 | 0.757433 | − | 0.652913i | \(-0.226453\pi\) | ||||
0.757433 | + | 0.652913i | \(0.226453\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.00000 | −0.440086 | ||||||||
\(254\) | −8.50000 | − | 14.7224i | −0.533337 | − | 0.923768i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.00000 | − | 20.7846i | −0.248548 | − | 1.29149i | ||||
\(260\) | −2.00000 | −0.124035 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.00000 | + | 10.3923i | −0.370681 | + | 0.642039i | ||||
\(263\) | −9.00000 | + | 15.5885i | −0.554964 | + | 0.961225i | 0.442943 | + | 0.896550i | \(0.353935\pi\) |
−0.997906 | + | 0.0646755i | \(0.979399\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.00000 | −0.368577 | ||||||||
\(266\) | −12.0000 | + | 10.3923i | −0.735767 | + | 0.637193i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.50000 | − | 2.59808i | −0.0916271 | − | 0.158703i | ||||
\(269\) | −1.50000 | + | 2.59808i | −0.0914566 | + | 0.158408i | −0.908124 | − | 0.418701i | \(-0.862486\pi\) |
0.816668 | + | 0.577108i | \(0.195819\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.00000 | − | 13.8564i | −0.485965 | − | 0.841717i | 0.513905 | − | 0.857847i | \(-0.328199\pi\) |
−0.999870 | + | 0.0161307i | \(0.994865\pi\) | |||||||
\(272\) | 5.00000 | 0.303170 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −18.0000 | −1.08742 | ||||||||
\(275\) | −2.00000 | − | 3.46410i | −0.120605 | − | 0.208893i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.00000 | − | 15.5885i | 0.540758 | − | 0.936620i | −0.458103 | − | 0.888899i | \(-0.651471\pi\) |
0.998861 | − | 0.0477206i | \(-0.0151957\pi\) | |||||||
\(278\) | −1.00000 | − | 1.73205i | −0.0599760 | − | 0.103882i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.500000 | − | 2.59808i | −0.0298807 | − | 0.155265i | ||||
\(281\) | −19.0000 | −1.13344 | −0.566722 | − | 0.823909i | \(-0.691789\pi\) | ||||
−0.566722 | + | 0.823909i | \(0.691789\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.0000 | + | 20.7846i | −0.713326 | + | 1.23552i | 0.250276 | + | 0.968175i | \(0.419479\pi\) |
−0.963602 | + | 0.267342i | \(0.913855\pi\) | |||||||
\(284\) | 4.00000 | − | 6.92820i | 0.237356 | − | 0.411113i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.00000 | −0.118262 | ||||||||
\(287\) | −17.5000 | − | 6.06218i | −1.03299 | − | 0.357839i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.00000 | − | 6.92820i | −0.235294 | − | 0.407541i | ||||
\(290\) | −4.00000 | + | 6.92820i | −0.234888 | + | 0.406838i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.00000 | − | 8.66025i | −0.292603 | − | 0.506803i | ||||
\(293\) | 6.00000 | 0.350524 | 0.175262 | − | 0.984522i | \(-0.443923\pi\) | ||||
0.175262 | + | 0.984522i | \(0.443923\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.00000 | −0.349334 | ||||||||
\(296\) | 4.00000 | + | 6.92820i | 0.232495 | + | 0.402694i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.00000 | − | 3.46410i | 0.115857 | − | 0.200670i | ||||
\(299\) | −7.00000 | − | 12.1244i | −0.404820 | − | 0.701170i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.0000 | − | 3.46410i | −0.576390 | − | 0.199667i | ||||
\(302\) | 9.00000 | 0.517892 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.00000 | − | 5.19615i | 0.172062 | − | 0.298020i | ||||
\(305\) | 0.500000 | − | 0.866025i | 0.0286299 | − | 0.0495885i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.00000 | 0.456584 | 0.228292 | − | 0.973593i | \(-0.426686\pi\) | ||||
0.228292 | + | 0.973593i | \(0.426686\pi\) | |||||||
\(308\) | −0.500000 | − | 2.59808i | −0.0284901 | − | 0.148039i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 5.00000 | + | 8.66025i | 0.283981 | + | 0.491869i | ||||
\(311\) | −8.50000 | + | 14.7224i | −0.481991 | + | 0.834833i | −0.999786 | − | 0.0206719i | \(-0.993419\pi\) |
0.517796 | + | 0.855504i | \(0.326753\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.0000 | − | 19.0526i | −0.621757 | − | 1.07691i | −0.989158 | − | 0.146852i | \(-0.953086\pi\) |
0.367402 | − | 0.930062i | \(-0.380247\pi\) | |||||||
\(314\) | 4.00000 | 0.225733 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.00000 | −0.506290 | ||||||||
\(317\) | 1.50000 | + | 2.59808i | 0.0842484 | + | 0.145922i | 0.905071 | − | 0.425261i | \(-0.139818\pi\) |
−0.820822 | + | 0.571184i | \(0.806484\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.00000 | + | 6.92820i | −0.223957 | + | 0.387905i | ||||
\(320\) | 0.500000 | + | 0.866025i | 0.0279508 | + | 0.0484123i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 14.0000 | − | 12.1244i | 0.780189 | − | 0.675664i | ||||
\(323\) | −30.0000 | −1.66924 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.00000 | − | 6.92820i | 0.221880 | − | 0.384308i | ||||
\(326\) | −6.50000 | + | 11.2583i | −0.360002 | + | 0.623541i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.00000 | 0.386510 | ||||||||
\(329\) | −0.500000 | − | 2.59808i | −0.0275659 | − | 0.143237i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.50000 | − | 11.2583i | −0.357272 | − | 0.618814i | 0.630232 | − | 0.776407i | \(-0.282960\pi\) |
−0.987504 | + | 0.157593i | \(0.949627\pi\) | |||||||
\(332\) | 7.50000 | − | 12.9904i | 0.411616 | − | 0.712940i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4.00000 | + | 6.92820i | 0.218870 | + | 0.379094i | ||||
\(335\) | −3.00000 | −0.163908 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.0000 | 0.980522 | 0.490261 | − | 0.871576i | \(-0.336901\pi\) | ||||
0.490261 | + | 0.871576i | \(0.336901\pi\) | |||||||
\(338\) | 4.50000 | + | 7.79423i | 0.244768 | + | 0.423950i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.50000 | − | 4.33013i | 0.135582 | − | 0.234834i | ||||
\(341\) | 5.00000 | + | 8.66025i | 0.270765 | + | 0.468979i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | − | 15.5885i | −0.539949 | − | 0.841698i | ||||
\(344\) | 4.00000 | 0.215666 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.00000 | − | 12.1244i | 0.376322 | − | 0.651809i | ||||
\(347\) | 6.50000 | − | 11.2583i | 0.348938 | − | 0.604379i | −0.637123 | − | 0.770762i | \(-0.719876\pi\) |
0.986061 | + | 0.166383i | \(0.0532089\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.0000 | −0.695874 | −0.347937 | − | 0.937518i | \(-0.613118\pi\) | ||||
−0.347937 | + | 0.937518i | \(0.613118\pi\) | |||||||
\(350\) | 10.0000 | + | 3.46410i | 0.534522 | + | 0.185164i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.500000 | + | 0.866025i | 0.0266501 | + | 0.0461593i | ||||
\(353\) | 3.00000 | − | 5.19615i | 0.159674 | − | 0.276563i | −0.775077 | − | 0.631867i | \(-0.782289\pi\) |
0.934751 | + | 0.355303i | \(0.115622\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.00000 | − | 6.92820i | −0.212298 | − | 0.367711i | ||||
\(356\) | −12.0000 | −0.635999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.00000 | −0.105703 | ||||||||
\(359\) | −10.0000 | − | 17.3205i | −0.527780 | − | 0.914141i | −0.999476 | − | 0.0323801i | \(-0.989691\pi\) |
0.471696 | − | 0.881761i | \(-0.343642\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.50000 | + | 14.7224i | −0.447368 | + | 0.774865i | ||||
\(362\) | −10.0000 | − | 17.3205i | −0.525588 | − | 0.910346i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.00000 | − | 3.46410i | 0.209657 | − | 0.181568i | ||||
\(365\) | −10.0000 | −0.523424 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.00000 | − | 1.73205i | 0.0521996 | − | 0.0904123i | −0.838745 | − | 0.544524i | \(-0.816710\pi\) |
0.890945 | + | 0.454112i | \(0.150043\pi\) | |||||||
\(368\) | −3.50000 | + | 6.06218i | −0.182450 | + | 0.316013i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 8.00000 | 0.415900 | ||||||||
\(371\) | 12.0000 | − | 10.3923i | 0.623009 | − | 0.539542i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.50000 | + | 11.2583i | 0.336557 | + | 0.582934i | 0.983783 | − | 0.179364i | \(-0.0574041\pi\) |
−0.647225 | + | 0.762299i | \(0.724071\pi\) | |||||||
\(374\) | 2.50000 | − | 4.33013i | 0.129272 | − | 0.223906i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.500000 | + | 0.866025i | 0.0257855 | + | 0.0446619i | ||||
\(377\) | −16.0000 | −0.824042 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.0000 | −0.873231 | −0.436616 | − | 0.899648i | \(-0.643823\pi\) | ||||
−0.436616 | + | 0.899648i | \(0.643823\pi\) | |||||||
\(380\) | −3.00000 | − | 5.19615i | −0.153897 | − | 0.266557i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −10.0000 | + | 17.3205i | −0.511645 | + | 0.886194i | ||||
\(383\) | 8.00000 | + | 13.8564i | 0.408781 | + | 0.708029i | 0.994753 | − | 0.102302i | \(-0.0326207\pi\) |
−0.585973 | + | 0.810331i | \(0.699287\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.50000 | − | 0.866025i | −0.127412 | − | 0.0441367i | ||||
\(386\) | 8.00000 | 0.407189 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6.50000 | + | 11.2583i | −0.329988 | + | 0.571555i | ||||
\(389\) | −7.50000 | + | 12.9904i | −0.380265 | + | 0.658638i | −0.991100 | − | 0.133120i | \(-0.957501\pi\) |
0.610835 | + | 0.791758i | \(0.290834\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 35.0000 | 1.77003 | ||||||||
\(392\) | 5.50000 | + | 4.33013i | 0.277792 | + | 0.218704i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.0000 | + | 20.7846i | 0.604551 | + | 1.04711i | ||||
\(395\) | −4.50000 | + | 7.79423i | −0.226420 | + | 0.392170i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.00000 | − | 10.3923i | −0.301131 | − | 0.521575i | 0.675261 | − | 0.737579i | \(-0.264031\pi\) |
−0.976392 | + | 0.216004i | \(0.930698\pi\) | |||||||
\(398\) | −26.0000 | −1.30326 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.00000 | −0.200000 | ||||||||
\(401\) | 6.00000 | + | 10.3923i | 0.299626 | + | 0.518967i | 0.976050 | − | 0.217545i | \(-0.0698049\pi\) |
−0.676425 | + | 0.736512i | \(0.736472\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.0000 | + | 17.3205i | −0.498135 | + | 0.862796i | ||||
\(404\) | −6.00000 | − | 10.3923i | −0.298511 | − | 0.517036i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.00000 | − | 20.7846i | −0.198517 | − | 1.03152i | ||||
\(407\) | 8.00000 | 0.396545 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.00000 | + | 8.66025i | −0.247234 | + | 0.428222i | −0.962757 | − | 0.270367i | \(-0.912855\pi\) |
0.715523 | + | 0.698589i | \(0.246188\pi\) | |||||||
\(410\) | 3.50000 | − | 6.06218i | 0.172853 | − | 0.299390i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 12.0000 | 0.591198 | ||||||||
\(413\) | 12.0000 | − | 10.3923i | 0.590481 | − | 0.511372i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.50000 | − | 12.9904i | −0.368161 | − | 0.637673i | ||||
\(416\) | −1.00000 | + | 1.73205i | −0.0490290 | + | 0.0849208i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.00000 | − | 5.19615i | −0.146735 | − | 0.254152i | ||||
\(419\) | 10.0000 | 0.488532 | 0.244266 | − | 0.969708i | \(-0.421453\pi\) | ||||
0.244266 | + | 0.969708i | \(0.421453\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.0000 | 0.779792 | 0.389896 | − | 0.920859i | \(-0.372511\pi\) | ||||
0.389896 | + | 0.920859i | \(0.372511\pi\) | |||||||
\(422\) | 10.0000 | + | 17.3205i | 0.486792 | + | 0.843149i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.00000 | + | 5.19615i | −0.145693 | + | 0.252347i | ||||
\(425\) | 10.0000 | + | 17.3205i | 0.485071 | + | 0.840168i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.500000 | + | 2.59808i | 0.0241967 | + | 0.125730i | ||||
\(428\) | −13.0000 | −0.628379 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.00000 | − | 3.46410i | 0.0964486 | − | 0.167054i | ||||
\(431\) | −5.00000 | + | 8.66025i | −0.240842 | + | 0.417150i | −0.960954 | − | 0.276707i | \(-0.910757\pi\) |
0.720113 | + | 0.693857i | \(0.244090\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.0000 | −0.624740 | −0.312370 | − | 0.949960i | \(-0.601123\pi\) | ||||
−0.312370 | + | 0.949960i | \(0.601123\pi\) | |||||||
\(434\) | −25.0000 | − | 8.66025i | −1.20004 | − | 0.415705i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.50000 | − | 16.4545i | −0.454967 | − | 0.788027i | ||||
\(437\) | 21.0000 | − | 36.3731i | 1.00457 | − | 1.73996i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.50000 | − | 6.06218i | −0.167046 | − | 0.289332i | 0.770334 | − | 0.637641i | \(-0.220089\pi\) |
−0.937380 | + | 0.348309i | \(0.886756\pi\) | |||||||
\(440\) | 1.00000 | 0.0476731 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 10.0000 | 0.475651 | ||||||||
\(443\) | −12.0000 | − | 20.7846i | −0.570137 | − | 0.987507i | −0.996551 | − | 0.0829786i | \(-0.973557\pi\) |
0.426414 | − | 0.904528i | \(-0.359777\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.00000 | + | 10.3923i | −0.284427 | + | 0.492642i | ||||
\(446\) | −5.00000 | − | 8.66025i | −0.236757 | − | 0.410075i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.50000 | − | 0.866025i | −0.118114 | − | 0.0409159i | ||||
\(449\) | 36.0000 | 1.69895 | 0.849473 | − | 0.527633i | \(-0.176920\pi\) | ||||
0.849473 | + | 0.527633i | \(0.176920\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.50000 | − | 6.06218i | 0.164809 | − | 0.285457i | ||||
\(452\) | −7.00000 | + | 12.1244i | −0.329252 | + | 0.570282i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −17.0000 | −0.797850 | ||||||||
\(455\) | −1.00000 | − | 5.19615i | −0.0468807 | − | 0.243599i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.00000 | − | 6.92820i | −0.187112 | − | 0.324088i | 0.757174 | − | 0.653213i | \(-0.226579\pi\) |
−0.944286 | + | 0.329125i | \(0.893246\pi\) | |||||||
\(458\) | −10.0000 | + | 17.3205i | −0.467269 | + | 0.809334i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.50000 | + | 6.06218i | 0.163188 | + | 0.282650i | ||||
\(461\) | −30.0000 | −1.39724 | −0.698620 | − | 0.715493i | \(-0.746202\pi\) | ||||
−0.698620 | + | 0.715493i | \(0.746202\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.00000 | 0.185896 | 0.0929479 | − | 0.995671i | \(-0.470371\pi\) | ||||
0.0929479 | + | 0.995671i | \(0.470371\pi\) | |||||||
\(464\) | 4.00000 | + | 6.92820i | 0.185695 | + | 0.321634i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.5000 | + | 18.1865i | −0.486403 | + | 0.842475i | ||||
\(467\) | −3.00000 | − | 5.19615i | −0.138823 | − | 0.240449i | 0.788228 | − | 0.615383i | \(-0.210999\pi\) |
−0.927052 | + | 0.374934i | \(0.877665\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.00000 | − | 5.19615i | 0.277054 | − | 0.239936i | ||||
\(470\) | 1.00000 | 0.0461266 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.00000 | + | 5.19615i | −0.138086 | + | 0.239172i | ||||
\(473\) | 2.00000 | − | 3.46410i | 0.0919601 | − | 0.159280i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 24.0000 | 1.10120 | ||||||||
\(476\) | 2.50000 | + | 12.9904i | 0.114587 | + | 0.595413i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8.00000 | − | 13.8564i | −0.365911 | − | 0.633777i | ||||
\(479\) | 2.00000 | − | 3.46410i | 0.0913823 | − | 0.158279i | −0.816711 | − | 0.577047i | \(-0.804205\pi\) |
0.908093 | + | 0.418769i | \(0.137538\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.00000 | + | 13.8564i | 0.364769 | + | 0.631798i | ||||
\(482\) | 12.0000 | 0.546585 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 6.50000 | + | 11.2583i | 0.295150 | + | 0.511214i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.00000 | − | 8.66025i | 0.226572 | − | 0.392434i | −0.730218 | − | 0.683214i | \(-0.760582\pi\) |
0.956790 | + | 0.290780i | \(0.0939149\pi\) | |||||||
\(488\) | −0.500000 | − | 0.866025i | −0.0226339 | − | 0.0392031i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 6.50000 | − | 2.59808i | 0.293640 | − | 0.117369i | ||||
\(491\) | 9.00000 | 0.406164 | 0.203082 | − | 0.979162i | \(-0.434904\pi\) | ||||
0.203082 | + | 0.979162i | \(0.434904\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.0000 | − | 34.6410i | 0.900755 | − | 1.56015i | ||||
\(494\) | 6.00000 | − | 10.3923i | 0.269953 | − | 0.467572i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10.0000 | 0.449013 | ||||||||
\(497\) | 20.0000 | + | 6.92820i | 0.897123 | + | 0.310772i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.0000 | + | 24.2487i | 0.626726 | + | 1.08552i | 0.988204 | + | 0.153141i | \(0.0489388\pi\) |
−0.361478 | + | 0.932381i | \(0.617728\pi\) | |||||||
\(500\) | −4.50000 | + | 7.79423i | −0.201246 | + | 0.348569i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −12.0000 | − | 20.7846i | −0.535586 | − | 0.927663i | ||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.0000 | −0.533993 | ||||||||
\(506\) | 3.50000 | + | 6.06218i | 0.155594 | + | 0.269497i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.50000 | + | 14.7224i | −0.377127 | + | 0.653202i | ||||
\(509\) | 11.0000 | + | 19.0526i | 0.487566 | + | 0.844490i | 0.999898 | − | 0.0142980i | \(-0.00455136\pi\) |
−0.512331 | + | 0.858788i | \(0.671218\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.0000 | − | 17.3205i | 0.884748 | − | 0.766214i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.00000 | − | 10.3923i | 0.264392 | − | 0.457940i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.00000 | 0.0439799 | ||||||||
\(518\) | −16.0000 | + | 13.8564i | −0.703000 | + | 0.608816i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.00000 | + | 1.73205i | 0.0438529 | + | 0.0759555i | ||||
\(521\) | −5.00000 | + | 8.66025i | −0.219054 | + | 0.379413i | −0.954519 | − | 0.298150i | \(-0.903630\pi\) |
0.735465 | + | 0.677563i | \(0.236964\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.0000 | + | 29.4449i | 0.743358 | + | 1.28753i | 0.950958 | + | 0.309320i | \(0.100101\pi\) |
−0.207600 | + | 0.978214i | \(0.566565\pi\) | |||||||
\(524\) | 12.0000 | 0.524222 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 18.0000 | 0.784837 | ||||||||
\(527\) | −25.0000 | − | 43.3013i | −1.08902 | − | 1.88623i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.0000 | + | 22.5167i | −0.565217 | + | 0.978985i | ||||
\(530\) | 3.00000 | + | 5.19615i | 0.130312 | + | 0.225706i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 15.0000 | + | 5.19615i | 0.650332 | + | 0.225282i | ||||
\(533\) | 14.0000 | 0.606407 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.50000 | + | 11.2583i | −0.281020 | + | 0.486740i | ||||
\(536\) | −1.50000 | + | 2.59808i | −0.0647901 | + | 0.112220i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.00000 | 0.129339 | ||||||||
\(539\) | 6.50000 | − | 2.59808i | 0.279975 | − | 0.111907i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.500000 | + | 0.866025i | 0.0214967 | + | 0.0372333i | 0.876574 | − | 0.481268i | \(-0.159824\pi\) |
−0.855077 | + | 0.518501i | \(0.826490\pi\) | |||||||
\(542\) | −8.00000 | + | 13.8564i | −0.343629 | + | 0.595184i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.50000 | − | 4.33013i | −0.107187 | − | 0.185653i | ||||
\(545\) | −19.0000 | −0.813871 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.00000 | 0.256541 | 0.128271 | − | 0.991739i | \(-0.459057\pi\) | ||||
0.128271 | + | 0.991739i | \(0.459057\pi\) | |||||||
\(548\) | 9.00000 | + | 15.5885i | 0.384461 | + | 0.665906i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.00000 | + | 3.46410i | −0.0852803 | + | 0.147710i | ||||
\(551\) | −24.0000 | − | 41.5692i | −1.02243 | − | 1.77091i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.50000 | − | 23.3827i | −0.191359 | − | 0.994333i | ||||
\(554\) | −18.0000 | −0.764747 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.00000 | + | 1.73205i | −0.0424094 | + | 0.0734553i | ||||
\(557\) | 8.00000 | − | 13.8564i | 0.338971 | − | 0.587115i | −0.645269 | − | 0.763956i | \(-0.723255\pi\) |
0.984239 | + | 0.176841i | \(0.0565879\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.00000 | 0.338364 | ||||||||
\(560\) | −2.00000 | + | 1.73205i | −0.0845154 | + | 0.0731925i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.50000 | + | 16.4545i | 0.400733 | + | 0.694090i | ||||
\(563\) | 14.0000 | − | 24.2487i | 0.590030 | − | 1.02196i | −0.404198 | − | 0.914671i | \(-0.632449\pi\) |
0.994228 | − | 0.107290i | \(-0.0342173\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.00000 | + | 12.1244i | 0.294492 | + | 0.510075i | ||||
\(566\) | 24.0000 | 1.00880 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.00000 | −0.335673 | ||||||||
\(569\) | 21.0000 | + | 36.3731i | 0.880366 | + | 1.52484i | 0.850935 | + | 0.525271i | \(0.176036\pi\) |
0.0294311 | + | 0.999567i | \(0.490630\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.00000 | + | 13.8564i | −0.334790 | + | 0.579873i | −0.983444 | − | 0.181210i | \(-0.941999\pi\) |
0.648655 | + | 0.761083i | \(0.275332\pi\) | |||||||
\(572\) | 1.00000 | + | 1.73205i | 0.0418121 | + | 0.0724207i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.50000 | + | 18.1865i | 0.146087 | + | 0.759091i | ||||
\(575\) | −28.0000 | −1.16768 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.50000 | − | 6.06218i | 0.145707 | − | 0.252372i | −0.783930 | − | 0.620850i | \(-0.786788\pi\) |
0.929636 | + | 0.368478i | \(0.120121\pi\) | |||||||
\(578\) | −4.00000 | + | 6.92820i | −0.166378 | + | 0.288175i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 8.00000 | 0.332182 | ||||||||
\(581\) | 37.5000 | + | 12.9904i | 1.55576 | + | 0.538932i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.00000 | + | 5.19615i | 0.124247 | + | 0.215203i | ||||
\(584\) | −5.00000 | + | 8.66025i | −0.206901 | + | 0.358364i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.00000 | − | 5.19615i | −0.123929 | − | 0.214651i | ||||
\(587\) | 42.0000 | 1.73353 | 0.866763 | − | 0.498721i | \(-0.166197\pi\) | ||||
0.866763 | + | 0.498721i | \(0.166197\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −60.0000 | −2.47226 | ||||||||
\(590\) | 3.00000 | + | 5.19615i | 0.123508 | + | 0.213922i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.00000 | − | 6.92820i | 0.164399 | − | 0.284747i | ||||
\(593\) | 3.00000 | + | 5.19615i | 0.123195 | + | 0.213380i | 0.921026 | − | 0.389501i | \(-0.127353\pi\) |
−0.797831 | + | 0.602881i | \(0.794019\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.5000 | + | 4.33013i | 0.512450 | + | 0.177518i | ||||
\(596\) | −4.00000 | −0.163846 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7.00000 | + | 12.1244i | −0.286251 | + | 0.495802i | ||||
\(599\) | −1.50000 | + | 2.59808i | −0.0612883 | + | 0.106155i | −0.895042 | − | 0.445983i | \(-0.852854\pi\) |
0.833753 | + | 0.552137i | \(0.186188\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.00000 | 0.326327 | 0.163163 | − | 0.986599i | \(-0.447830\pi\) | ||||
0.163163 | + | 0.986599i | \(0.447830\pi\) | |||||||
\(602\) | 2.00000 | + | 10.3923i | 0.0815139 | + | 0.423559i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.50000 | − | 7.79423i | −0.183102 | − | 0.317143i | ||||
\(605\) | 0.500000 | − | 0.866025i | 0.0203279 | − | 0.0352089i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.5000 | − | 25.1147i | −0.588537 | − | 1.01938i | −0.994424 | − | 0.105453i | \(-0.966371\pi\) |
0.405887 | − | 0.913923i | \(-0.366962\pi\) | |||||||
\(608\) | −6.00000 | −0.243332 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.00000 | −0.0404888 | ||||||||
\(611\) | 1.00000 | + | 1.73205i | 0.0404557 | + | 0.0700713i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.50000 | − | 9.52628i | 0.222143 | − | 0.384763i | −0.733316 | − | 0.679888i | \(-0.762028\pi\) |
0.955458 | + | 0.295126i | \(0.0953615\pi\) | |||||||
\(614\) | −4.00000 | − | 6.92820i | −0.161427 | − | 0.279600i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.00000 | + | 1.73205i | −0.0805823 | + | 0.0697863i | ||||
\(617\) | −24.0000 | −0.966204 | −0.483102 | − | 0.875564i | \(-0.660490\pi\) | ||||
−0.483102 | + | 0.875564i | \(0.660490\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.50000 | − | 6.06218i | 0.140677 | − | 0.243659i | −0.787075 | − | 0.616858i | \(-0.788405\pi\) |
0.927752 | + | 0.373198i | \(0.121739\pi\) | |||||||
\(620\) | 5.00000 | − | 8.66025i | 0.200805 | − | 0.347804i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 17.0000 | 0.681638 | ||||||||
\(623\) | −6.00000 | − | 31.1769i | −0.240385 | − | 1.24908i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.50000 | − | 9.52628i | −0.220000 | − | 0.381051i | ||||
\(626\) | −11.0000 | + | 19.0526i | −0.439648 | + | 0.761493i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.00000 | − | 3.46410i | −0.0798087 | − | 0.138233i | ||||
\(629\) | −40.0000 | −1.59490 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −42.0000 | −1.67199 | −0.835997 | − | 0.548734i | \(-0.815110\pi\) | ||||
−0.835997 | + | 0.548734i | \(0.815110\pi\) | |||||||
\(632\) | 4.50000 | + | 7.79423i | 0.179000 | + | 0.310038i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.50000 | − | 2.59808i | 0.0595726 | − | 0.103183i | ||||
\(635\) | 8.50000 | + | 14.7224i | 0.337312 | + | 0.584242i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.0000 | + | 8.66025i | 0.435836 | + | 0.343132i | ||||
\(638\) | 8.00000 | 0.316723 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.500000 | − | 0.866025i | 0.0197642 | − | 0.0342327i | ||||
\(641\) | 6.00000 | − | 10.3923i | 0.236986 | − | 0.410471i | −0.722862 | − | 0.690992i | \(-0.757174\pi\) |
0.959848 | + | 0.280521i | \(0.0905072\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.00000 | 0.157745 | 0.0788723 | − | 0.996885i | \(-0.474868\pi\) | ||||
0.0788723 | + | 0.996885i | \(0.474868\pi\) | |||||||
\(644\) | −17.5000 | − | 6.06218i | −0.689597 | − | 0.238883i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 15.0000 | + | 25.9808i | 0.590167 | + | 1.02220i | ||||
\(647\) | 22.5000 | − | 38.9711i | 0.884566 | − | 1.53211i | 0.0383563 | − | 0.999264i | \(-0.487788\pi\) |
0.846210 | − | 0.532850i | \(-0.178879\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.00000 | + | 5.19615i | 0.117760 | + | 0.203967i | ||||
\(650\) | −8.00000 | −0.313786 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.0000 | 0.509119 | ||||||||
\(653\) | −6.50000 | − | 11.2583i | −0.254365 | − | 0.440573i | 0.710358 | − | 0.703840i | \(-0.248533\pi\) |
−0.964723 | + | 0.263268i | \(0.915200\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.00000 | − | 10.3923i | 0.234439 | − | 0.406061i | ||||
\(656\) | −3.50000 | − | 6.06218i | −0.136652 | − | 0.236688i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.00000 | + | 1.73205i | −0.0779681 | + | 0.0675224i | ||||
\(659\) | 19.0000 | 0.740135 | 0.370067 | − | 0.929005i | \(-0.379335\pi\) | ||||
0.370067 | + | 0.929005i | \(0.379335\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.00000 | + | 12.1244i | −0.272268 | + | 0.471583i | −0.969442 | − | 0.245319i | \(-0.921107\pi\) |
0.697174 | + | 0.716902i | \(0.254441\pi\) | |||||||
\(662\) | −6.50000 | + | 11.2583i | −0.252630 | + | 0.437567i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −15.0000 | −0.582113 | ||||||||
\(665\) | 12.0000 | − | 10.3923i | 0.465340 | − | 0.402996i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 28.0000 | + | 48.4974i | 1.08416 | + | 1.87783i | ||||
\(668\) | 4.00000 | − | 6.92820i | 0.154765 | − | 0.268060i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.50000 | + | 2.59808i | 0.0579501 | + | 0.100372i | ||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.0000 | 0.848038 | 0.424019 | − | 0.905653i | \(-0.360619\pi\) | ||||
0.424019 | + | 0.905653i | \(0.360619\pi\) | |||||||
\(674\) | −9.00000 | − | 15.5885i | −0.346667 | − | 0.600445i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.50000 | − | 7.79423i | 0.173077 | − | 0.299778i | ||||
\(677\) | −1.00000 | − | 1.73205i | −0.0384331 | − | 0.0665681i | 0.846169 | − | 0.532915i | \(-0.178903\pi\) |
−0.884602 | + | 0.466347i | \(0.845570\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −32.5000 | − | 11.2583i | −1.24724 | − | 0.432055i | ||||
\(680\) | −5.00000 | −0.191741 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5.00000 | − | 8.66025i | 0.191460 | − | 0.331618i | ||||
\(683\) | −12.0000 | + | 20.7846i | −0.459167 | + | 0.795301i | −0.998917 | − | 0.0465244i | \(-0.985185\pi\) |
0.539750 | + | 0.841825i | \(0.318519\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 18.0000 | 0.687745 | ||||||||
\(686\) | −8.50000 | + | 16.4545i | −0.324532 | + | 0.628235i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.00000 | − | 3.46410i | −0.0762493 | − | 0.132068i | ||||
\(689\) | −6.00000 | + | 10.3923i | −0.228582 | + | 0.395915i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.50000 | − | 12.9904i | −0.285313 | − | 0.494177i | 0.687372 | − | 0.726306i | \(-0.258764\pi\) |
−0.972685 | + | 0.232128i | \(0.925431\pi\) | |||||||
\(692\) | −14.0000 | −0.532200 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −13.0000 | −0.493473 | ||||||||
\(695\) | 1.00000 | + | 1.73205i | 0.0379322 | + | 0.0657004i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.5000 | + | 30.3109i | −0.662860 | + | 1.14811i | ||||
\(698\) | 6.50000 | + | 11.2583i | 0.246029 | + | 0.426134i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.00000 | − | 10.3923i | −0.0755929 | − | 0.392792i | ||||
\(701\) | 42.0000 | 1.58632 | 0.793159 | − | 0.609015i | \(-0.208435\pi\) | ||||
0.793159 | + | 0.609015i | \(0.208435\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24.0000 | + | 41.5692i | −0.905177 | + | 1.56781i | ||||
\(704\) | 0.500000 | − | 0.866025i | 0.0188445 | − | 0.0326396i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.00000 | −0.225813 | ||||||||
\(707\) | 24.0000 | − | 20.7846i | 0.902613 | − | 0.781686i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.0000 | + | 36.3731i | 0.788672 | + | 1.36602i | 0.926781 | + | 0.375602i | \(0.122564\pi\) |
−0.138109 | + | 0.990417i | \(0.544103\pi\) | |||||||
\(710\) | −4.00000 | + | 6.92820i | −0.150117 | + | 0.260011i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.00000 | + | 10.3923i | 0.224860 | + | 0.389468i | ||||
\(713\) | 70.0000 | 2.62152 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.00000 | 0.0747958 | ||||||||
\(716\) | 1.00000 | + | 1.73205i | 0.0373718 | + | 0.0647298i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −10.0000 | + | 17.3205i | −0.373197 | + | 0.646396i | ||||
\(719\) | 2.50000 | + | 4.33013i | 0.0932343 | + | 0.161486i | 0.908870 | − | 0.417079i | \(-0.136946\pi\) |
−0.815636 | + | 0.578565i | \(0.803613\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.00000 | + | 31.1769i | 0.223452 | + | 1.16109i | ||||
\(722\) | 17.0000 | 0.632674 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −10.0000 | + | 17.3205i | −0.371647 | + | 0.643712i | ||||
\(725\) | −16.0000 | + | 27.7128i | −0.594225 | + | 1.02923i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.0000 | 0.741759 | 0.370879 | − | 0.928681i | \(-0.379056\pi\) | ||||
0.370879 | + | 0.928681i | \(0.379056\pi\) | |||||||
\(728\) | −5.00000 | − | 1.73205i | −0.185312 | − | 0.0641941i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 5.00000 | + | 8.66025i | 0.185058 | + | 0.320530i | ||||
\(731\) | −10.0000 | + | 17.3205i | −0.369863 | + | 0.640622i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.5000 | + | 32.0429i | 0.683313 | + | 1.18353i | 0.973964 | + | 0.226704i | \(0.0727949\pi\) |
−0.290651 | + | 0.956829i | \(0.593872\pi\) | |||||||
\(734\) | −2.00000 | −0.0738213 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.00000 | 0.258023 | ||||||||
\(737\) | 1.50000 | + | 2.59808i | 0.0552532 | + | 0.0957014i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.00000 | + | 5.19615i | −0.110357 | + | 0.191144i | −0.915914 | − | 0.401374i | \(-0.868533\pi\) |
0.805557 | + | 0.592518i | \(0.201866\pi\) | |||||||
\(740\) | −4.00000 | − | 6.92820i | −0.147043 | − | 0.254686i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −15.0000 | − | 5.19615i | −0.550667 | − | 0.190757i | ||||
\(743\) | −12.0000 | −0.440237 | −0.220119 | − | 0.975473i | \(-0.570644\pi\) | ||||
−0.220119 | + | 0.975473i | \(0.570644\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.00000 | + | 3.46410i | −0.0732743 | + | 0.126915i | ||||
\(746\) | 6.50000 | − | 11.2583i | 0.237982 | − | 0.412197i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5.00000 | −0.182818 | ||||||||
\(749\) | −6.50000 | − | 33.7750i | −0.237505 | − | 1.23411i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.0000 | + | 32.9090i | 0.693320 | + | 1.20087i | 0.970744 | + | 0.240118i | \(0.0771860\pi\) |
−0.277424 | + | 0.960748i | \(0.589481\pi\) | |||||||
\(752\) | 0.500000 | − | 0.866025i | 0.0182331 | − | 0.0315807i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.00000 | + | 13.8564i | 0.291343 | + | 0.504621i | ||||
\(755\) | −9.00000 | −0.327544 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.0000 | −0.363456 | −0.181728 | − | 0.983349i | \(-0.558169\pi\) | ||||
−0.181728 | + | 0.983349i | \(0.558169\pi\) | |||||||
\(758\) | 8.50000 | + | 14.7224i | 0.308734 | + | 0.534743i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.00000 | + | 5.19615i | −0.108821 | + | 0.188484i | ||||
\(761\) | 19.5000 | + | 33.7750i | 0.706874 | + | 1.22434i | 0.966011 | + | 0.258502i | \(0.0832288\pi\) |
−0.259136 | + | 0.965841i | \(0.583438\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 38.0000 | − | 32.9090i | 1.37569 | − | 1.19138i | ||||
\(764\) | 20.0000 | 0.723575 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.00000 | − | 13.8564i | 0.289052 | − | 0.500652i | ||||
\(767\) | −6.00000 | + | 10.3923i | −0.216647 | + | 0.375244i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.0000 | 1.22607 | 0.613036 | − | 0.790055i | \(-0.289948\pi\) | ||||
0.613036 | + | 0.790055i | \(0.289948\pi\) | |||||||
\(770\) | 0.500000 | + | 2.59808i | 0.0180187 | + | 0.0936282i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4.00000 | − | 6.92820i | −0.143963 | − | 0.249351i | ||||
\(773\) | 16.5000 | − | 28.5788i | 0.593464 | − | 1.02791i | −0.400298 | − | 0.916385i | \(-0.631093\pi\) |
0.993762 | − | 0.111524i | \(-0.0355733\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20.0000 | + | 34.6410i | 0.718421 | + | 1.24434i | ||||
\(776\) | 13.0000 | 0.466673 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 15.0000 | 0.537776 | ||||||||
\(779\) | 21.0000 | + | 36.3731i | 0.752403 | + | 1.30320i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.00000 | + | 6.92820i | −0.143131 | + | 0.247911i | ||||
\(782\) | −17.5000 | − | 30.3109i | −0.625799 | − | 1.08392i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | − | 6.92820i | 0.0357143 | − | 0.247436i | ||||
\(785\) | −4.00000 | −0.142766 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.00000 | + | 12.1244i | −0.249523 | + | 0.432187i | −0.963394 | − | 0.268091i | \(-0.913607\pi\) |
0.713871 | + | 0.700278i | \(0.246941\pi\) | |||||||
\(788\) | 12.0000 | − | 20.7846i | 0.427482 | − | 0.740421i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 9.00000 | 0.320206 | ||||||||
\(791\) | −35.0000 | − | 12.1244i | −1.24446 | − | 0.431092i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.00000 | − | 1.73205i | −0.0355110 | − | 0.0615069i | ||||
\(794\) | −6.00000 | + | 10.3923i | −0.212932 | + | 0.368809i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 13.0000 | + | 22.5167i | 0.460773 | + | 0.798082i | ||||
\(797\) | 23.0000 | 0.814702 | 0.407351 | − | 0.913272i | \(-0.366453\pi\) | ||||
0.407351 | + | 0.913272i | \(0.366453\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.00000 | −0.176887 | ||||||||
\(800\) | 2.00000 | + | 3.46410i | 0.0707107 | + | 0.122474i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6.00000 | − | 10.3923i | 0.211867 | − | 0.366965i | ||||
\(803\) | 5.00000 | + | 8.66025i | 0.176446 | + | 0.305614i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −14.0000 | + | 12.1244i | −0.493435 | + | 0.427327i | ||||
\(806\) | 20.0000 | 0.704470 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.00000 | + | 10.3923i | −0.211079 | + | 0.365600i | ||||
\(809\) | −4.50000 | + | 7.79423i | −0.158212 | + | 0.274030i | −0.934224 | − | 0.356687i | \(-0.883906\pi\) |
0.776012 | + | 0.630718i | \(0.217239\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.00000 | 0.0702295 | 0.0351147 | − | 0.999383i | \(-0.488820\pi\) | ||||
0.0351147 | + | 0.999383i | \(0.488820\pi\) | |||||||
\(812\) | −16.0000 | + | 13.8564i | −0.561490 | + | 0.486265i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.00000 | − | 6.92820i | −0.140200 | − | 0.242833i | ||||
\(815\) | 6.50000 | − | 11.2583i | 0.227685 | − | 0.394362i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.0000 | + | 20.7846i | 0.419827 | + | 0.727161i | ||||
\(818\) | 10.0000 | 0.349642 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.00000 | −0.244451 | ||||||||
\(821\) | −3.00000 | − | 5.19615i | −0.104701 | − | 0.181347i | 0.808915 | − | 0.587925i | \(-0.200055\pi\) |
−0.913616 | + | 0.406578i | \(0.866722\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.00000 | − | 8.66025i | 0.174289 | − | 0.301877i | −0.765626 | − | 0.643286i | \(-0.777571\pi\) |
0.939915 | + | 0.341409i | \(0.110904\pi\) | |||||||
\(824\) | −6.00000 | − | 10.3923i | −0.209020 | − | 0.362033i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −15.0000 | − | 5.19615i | −0.521917 | − | 0.180797i | ||||
\(827\) | −43.0000 | −1.49526 | −0.747628 | − | 0.664117i | \(-0.768807\pi\) | ||||
−0.747628 | + | 0.664117i | \(0.768807\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.0000 | − | 17.3205i | 0.347314 | − | 0.601566i | −0.638457 | − | 0.769657i | \(-0.720427\pi\) |
0.985771 | + | 0.168091i | \(0.0537604\pi\) | |||||||
\(830\) | −7.50000 | + | 12.9904i | −0.260329 | + | 0.450903i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.00000 | 0.0693375 | ||||||||
\(833\) | −32.5000 | + | 12.9904i | −1.12606 | + | 0.450090i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.00000 | − | 6.92820i | −0.138426 | − | 0.239760i | ||||
\(836\) | −3.00000 | + | 5.19615i | −0.103757 | + | 0.179713i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5.00000 | − | 8.66025i | −0.172722 | − | 0.299164i | ||||
\(839\) | 21.0000 | 0.725001 | 0.362500 | − | 0.931984i | \(-0.381923\pi\) | ||||
0.362500 | + | 0.931984i | \(0.381923\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 35.0000 | 1.20690 | ||||||||
\(842\) | −8.00000 | − | 13.8564i | −0.275698 | − | 0.477523i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 10.0000 | − | 17.3205i | 0.344214 | − | 0.596196i | ||||
\(845\) | −4.50000 | − | 7.79423i | −0.154805 | − | 0.268130i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.500000 | + | 2.59808i | 0.0171802 | + | 0.0892710i | ||||
\(848\) | 6.00000 | 0.206041 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 10.0000 | − | 17.3205i | 0.342997 | − | 0.594089i | ||||
\(851\) | 28.0000 | − | 48.4974i | 0.959828 | − | 1.66247i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.00000 | −0.239675 | −0.119838 | − | 0.992793i | \(-0.538237\pi\) | ||||
−0.119838 | + | 0.992793i | \(0.538237\pi\) | |||||||
\(854\) | 2.00000 | − | 1.73205i | 0.0684386 | − | 0.0592696i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.50000 | + | 11.2583i | 0.222165 | + | 0.384802i | ||||
\(857\) | 3.50000 | − | 6.06218i | 0.119558 | − | 0.207080i | −0.800035 | − | 0.599954i | \(-0.795186\pi\) |
0.919592 | + | 0.392874i | \(0.128519\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.5000 | − | 21.6506i | −0.426494 | − | 0.738710i | 0.570064 | − | 0.821600i | \(-0.306918\pi\) |
−0.996559 | + | 0.0828900i | \(0.973585\pi\) | |||||||
\(860\) | −4.00000 | −0.136399 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 10.0000 | 0.340601 | ||||||||
\(863\) | 2.50000 | + | 4.33013i | 0.0851010 | + | 0.147399i | 0.905434 | − | 0.424487i | \(-0.139545\pi\) |
−0.820333 | + | 0.571886i | \(0.806212\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.00000 | + | 12.1244i | −0.238007 | + | 0.412240i | ||||
\(866\) | 6.50000 | + | 11.2583i | 0.220879 | + | 0.382574i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5.00000 | + | 25.9808i | 0.169711 | + | 0.881845i | ||||
\(869\) | 9.00000 | 0.305304 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.00000 | + | 5.19615i | −0.101651 | + | 0.176065i | ||||
\(872\) | −9.50000 | + | 16.4545i | −0.321711 | + | 0.557219i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −42.0000 | −1.42067 | ||||||||
\(875\) | −22.5000 | − | 7.79423i | −0.760639 | − | 0.263493i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.5000 | + | 35.5070i | 0.692236 | + | 1.19899i | 0.971104 | + | 0.238658i | \(0.0767075\pi\) |
−0.278868 | + | 0.960329i | \(0.589959\pi\) | |||||||
\(878\) | −3.50000 | + | 6.06218i | −0.118119 | + | 0.204589i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.500000 | − | 0.866025i | −0.0168550 | − | 0.0291937i | ||||
\(881\) | −54.0000 | −1.81931 | −0.909653 | − | 0.415369i | \(-0.863653\pi\) | ||||
−0.909653 | + | 0.415369i | \(0.863653\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −47.0000 | −1.58168 | −0.790838 | − | 0.612026i | \(-0.790355\pi\) | ||||
−0.790838 | + | 0.612026i | \(0.790355\pi\) | |||||||
\(884\) | −5.00000 | − | 8.66025i | −0.168168 | − | 0.291276i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.0000 | + | 20.7846i | −0.403148 | + | 0.698273i | ||||
\(887\) | 1.00000 | + | 1.73205i | 0.0335767 | + | 0.0581566i | 0.882325 | − | 0.470640i | \(-0.155977\pi\) |
−0.848749 | + | 0.528796i | \(0.822644\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −42.5000 | − | 14.7224i | −1.42540 | − | 0.493775i | ||||
\(890\) | 12.0000 | 0.402241 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5.00000 | + | 8.66025i | −0.167412 | + | 0.289967i | ||||
\(893\) | −3.00000 | + | 5.19615i | −0.100391 | + | 0.173883i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.00000 | 0.0668526 | ||||||||
\(896\) | 0.500000 | + | 2.59808i | 0.0167038 | + | 0.0867956i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −18.0000 | − | 31.1769i | −0.600668 | − | 1.04039i | ||||
\(899\) | 40.0000 | − | 69.2820i | 1.33407 | − | 2.31069i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.0000 | − | 25.9808i | −0.499722 | − | 0.865545i | ||||
\(902\) | −7.00000 | −0.233075 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14.0000 | 0.465633 | ||||||||
\(905\) | 10.0000 | + | 17.3205i | 0.332411 | + | 0.575753i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.50000 | + | 14.7224i | −0.282238 | + | 0.488850i | −0.971936 | − | 0.235247i | \(-0.924410\pi\) |
0.689698 | + | 0.724097i | \(0.257743\pi\) | |||||||
\(908\) | 8.50000 | + | 14.7224i | 0.282082 | + | 0.488581i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.00000 | + | 3.46410i | −0.132599 | + | 0.114834i | ||||
\(911\) | −39.0000 | −1.29213 | −0.646064 | − | 0.763283i | \(-0.723586\pi\) | ||||
−0.646064 | + | 0.763283i | \(0.723586\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.50000 | + | 12.9904i | −0.248214 | + | 0.429919i | ||||
\(914\) | −4.00000 | + | 6.92820i | −0.132308 | + | 0.229165i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 20.0000 | 0.660819 | ||||||||
\(917\) | 6.00000 | + | 31.1769i | 0.198137 | + | 1.02955i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.5000 | − | 33.7750i | −0.643246 | − | 1.11413i | −0.984704 | − | 0.174237i | \(-0.944254\pi\) |
0.341458 | − | 0.939897i | \(-0.389079\pi\) | |||||||
\(920\) | 3.50000 | − | 6.06218i | 0.115392 | − | 0.199864i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 15.0000 | + | 25.9808i | 0.493999 | + | 0.855631i | ||||
\(923\) | −16.0000 | −0.526646 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 32.0000 | 1.05215 | ||||||||
\(926\) | −2.00000 | − | 3.46410i | −0.0657241 | − | 0.113837i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.00000 | − | 6.92820i | 0.131306 | − | 0.227429i | ||||
\(929\) | 15.0000 | + | 25.9808i | 0.492134 | + | 0.852401i | 0.999959 | − | 0.00905914i | \(-0.00288365\pi\) |
−0.507825 | + | 0.861460i | \(0.669550\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.00000 | + | 41.5692i | −0.196642 | + | 1.36238i | ||||
\(932\) | 21.0000 | 0.687878 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3.00000 | + | 5.19615i | −0.0981630 | + | 0.170023i | ||||
\(935\) | −2.50000 | + | 4.33013i | −0.0817587 | + | 0.141610i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42.0000 | 1.37208 | 0.686040 | − | 0.727564i | \(-0.259347\pi\) | ||||
0.686040 | + | 0.727564i | \(0.259347\pi\) | |||||||
\(938\) | −7.50000 | − | 2.59808i | −0.244884 | − | 0.0848302i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.500000 | − | 0.866025i | −0.0163082 | − | 0.0282466i | ||||
\(941\) | 7.00000 | − | 12.1244i | 0.228193 | − | 0.395243i | −0.729079 | − | 0.684429i | \(-0.760051\pi\) |
0.957273 | + | 0.289187i | \(0.0933848\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24.5000 | − | 42.4352i | −0.797830 | − | 1.38188i | ||||
\(944\) | 6.00000 | 0.195283 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.00000 | −0.130051 | ||||||||
\(947\) | 29.0000 | + | 50.2295i | 0.942373 | + | 1.63224i | 0.760927 | + | 0.648838i | \(0.224745\pi\) |
0.181447 | + | 0.983401i | \(0.441922\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.0000 | + | 17.3205i | −0.324614 | + | 0.562247i | ||||
\(950\) | −12.0000 | − | 20.7846i | −0.389331 | − | 0.674342i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 10.0000 | − | 8.66025i | 0.324102 | − | 0.280680i | ||||
\(953\) | −19.0000 | −0.615470 | −0.307735 | − | 0.951472i | \(-0.599571\pi\) | ||||
−0.307735 | + | 0.951472i | \(0.599571\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.0000 | − | 17.3205i | 0.323592 | − | 0.560478i | ||||
\(956\) | −8.00000 | + | 13.8564i | −0.258738 | + | 0.448148i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.00000 | −0.129234 | ||||||||
\(959\) | −36.0000 | + | 31.1769i | −1.16250 | + | 1.00676i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −34.5000 | − | 59.7558i | −1.11290 | − | 1.92760i | ||||
\(962\) | 8.00000 | − | 13.8564i | 0.257930 | − | 0.446748i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −6.00000 | − | 10.3923i | −0.193247 | − | 0.334714i | ||||
\(965\) | −8.00000 | −0.257529 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35.0000 | 1.12552 | 0.562762 | − | 0.826619i | \(-0.309739\pi\) | ||||
0.562762 | + | 0.826619i | \(0.309739\pi\) | |||||||
\(968\) | −0.500000 | − | 0.866025i | −0.0160706 | − | 0.0278351i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6.50000 | − | 11.2583i | 0.208702 | − | 0.361483i | ||||
\(971\) | 11.0000 | + | 19.0526i | 0.353007 | + | 0.611426i | 0.986775 | − | 0.162098i | \(-0.0518259\pi\) |
−0.633768 | + | 0.773523i | \(0.718493\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.00000 | − | 1.73205i | −0.160293 | − | 0.0555270i | ||||
\(974\) | −10.0000 | −0.320421 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.500000 | + | 0.866025i | −0.0160046 | + | 0.0277208i | ||||
\(977\) | 5.00000 | − | 8.66025i | 0.159964 | − | 0.277066i | −0.774891 | − | 0.632094i | \(-0.782195\pi\) |
0.934856 | + | 0.355028i | \(0.115529\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.0000 | 0.383522 | ||||||||
\(980\) | −5.50000 | − | 4.33013i | −0.175691 | − | 0.138321i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.50000 | − | 7.79423i | −0.143601 | − | 0.248724i | ||||
\(983\) | −7.50000 | + | 12.9904i | −0.239213 | + | 0.414329i | −0.960489 | − | 0.278319i | \(-0.910223\pi\) |
0.721276 | + | 0.692648i | \(0.243556\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.0000 | − | 20.7846i | −0.382352 | − | 0.662253i | ||||
\(986\) | −40.0000 | −1.27386 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −12.0000 | −0.381771 | ||||||||
\(989\) | −14.0000 | − | 24.2487i | −0.445174 | − | 0.771064i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.00000 | − | 6.92820i | 0.127064 | − | 0.220082i | −0.795474 | − | 0.605988i | \(-0.792778\pi\) |
0.922538 | + | 0.385906i | \(0.126111\pi\) | |||||||
\(992\) | −5.00000 | − | 8.66025i | −0.158750 | − | 0.274963i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.00000 | − | 20.7846i | −0.126872 | − | 0.659248i | ||||
\(995\) | 26.0000 | 0.824255 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.0000 | − | 25.9808i | 0.475055 | − | 0.822819i | −0.524537 | − | 0.851388i | \(-0.675762\pi\) |
0.999592 | + | 0.0285686i | \(0.00909491\pi\) | |||||||
\(998\) | 14.0000 | − | 24.2487i | 0.443162 | − | 0.767580i | ||||
\(999\) | 0 | 0 |
(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 | 1386.2.k.g.991.1 | yes | 2 | |
3.2 | odd | 2 | 1386.2.k.m.991.1 | yes | 2 | ||
7.2 | even | 3 | inner | 1386.2.k.g.793.1 | ✓ | 2 | |
7.3 | odd | 6 | 9702.2.a.bw.1.1 | 1 | |||
7.4 | even | 3 | 9702.2.a.bj.1.1 | 1 | |||
21.2 | odd | 6 | 1386.2.k.m.793.1 | yes | 2 | ||
21.11 | odd | 6 | 9702.2.a.p.1.1 | 1 | |||
21.17 | even | 6 | 9702.2.a.k.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1386.2.k.g.793.1 | ✓ | 2 | 7.2 | even | 3 | inner | |
1386.2.k.g.991.1 | yes | 2 | 1.1 | even | 1 | trivial | |
1386.2.k.m.793.1 | yes | 2 | 21.2 | odd | 6 | ||
1386.2.k.m.991.1 | yes | 2 | 3.2 | odd | 2 | ||
9702.2.a.k.1.1 | 1 | 21.17 | even | 6 | |||
9702.2.a.p.1.1 | 1 | 21.11 | odd | 6 | |||
9702.2.a.bj.1.1 | 1 | 7.4 | even | 3 | |||
9702.2.a.bw.1.1 | 1 | 7.3 | odd | 6 |