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 | 793.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1386.793 |
Dual form | 1386.2.k.b.991.1 |
$q$-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 \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||
\(5\) | −1.50000 | + | 2.59808i | −0.670820 | + | 1.16190i | 0.306851 | + | 0.951757i | \(0.400725\pi\) |
−0.977672 | + | 0.210138i | \(0.932609\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | − | 2.59808i | −0.188982 | − | 0.981981i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.50000 | − | 2.59808i | −0.474342 | − | 0.821584i | ||||
\(11\) | 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 | \(0.410544\pi\) | |||||||
\(14\) | 2.50000 | + | 0.866025i | 0.668153 | + | 0.231455i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.50000 | + | 2.59808i | 0.363803 | + | 0.630126i | 0.988583 | − | 0.150675i | \(-0.0481447\pi\) |
−0.624780 | + | 0.780801i | \(0.714811\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | + | 1.73205i | −0.229416 | + | 0.397360i | −0.957635 | − | 0.287984i | \(-0.907015\pi\) |
0.728219 | + | 0.685344i | \(0.240348\pi\) | |||||||
\(20\) | 3.00000 | 0.670820 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −1.50000 | + | 2.59808i | −0.312772 | + | 0.541736i | −0.978961 | − | 0.204046i | \(-0.934591\pi\) |
0.666190 | + | 0.745782i | \(0.267924\pi\) | |||||||
\(24\) | 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 | ||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | − | 1.73205i | −0.179605 | − | 0.311086i | 0.762140 | − | 0.647412i | \(-0.224149\pi\) |
−0.941745 | + | 0.336327i | \(0.890815\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.00000 | −0.514496 | ||||||||
\(35\) | 7.50000 | + | 2.59808i | 1.26773 | + | 0.439155i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | + | 6.92820i | −0.657596 | + | 1.13899i | 0.323640 | + | 0.946180i | \(0.395093\pi\) |
−0.981236 | + | 0.192809i | \(0.938240\pi\) | |||||||
\(38\) | −1.00000 | − | 1.73205i | −0.162221 | − | 0.280976i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.50000 | + | 2.59808i | −0.237171 | + | 0.410792i | ||||
\(41\) | −9.00000 | −1.40556 | −0.702782 | − | 0.711405i | \(-0.748059\pi\) | ||||
−0.702782 | + | 0.711405i | \(0.748059\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 0.500000 | − | 0.866025i | 0.0753778 | − | 0.130558i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.50000 | − | 2.59808i | −0.221163 | − | 0.383065i | ||||
\(47\) | −1.50000 | + | 2.59808i | −0.218797 | + | 0.378968i | −0.954441 | − | 0.298401i | \(-0.903547\pi\) |
0.735643 | + | 0.677369i | \(0.236880\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.50000 | + | 2.59808i | −0.928571 | + | 0.371154i | ||||
\(50\) | 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 | 0.583036 | − | 0.812447i | \(-0.301865\pi\) |
−0.995117 | + | 0.0987002i | \(0.968532\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.00000 | −0.404520 | ||||||||
\(56\) | −0.500000 | − | 2.59808i | −0.0668153 | − | 0.347183i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.00000 | − | 5.19615i | −0.390567 | − | 0.676481i | 0.601958 | − | 0.798528i | \(-0.294388\pi\) |
−0.992524 | + | 0.122047i | \(0.961054\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.50000 | + | 4.33013i | −0.320092 | + | 0.554416i | −0.980507 | − | 0.196485i | \(-0.937047\pi\) |
0.660415 | + | 0.750901i | \(0.270381\pi\) | |||||||
\(62\) | 2.00000 | 0.254000 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.00000 | + | 5.19615i | −0.372104 | + | 0.644503i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.50000 | − | 9.52628i | −0.671932 | − | 1.16382i | −0.977356 | − | 0.211604i | \(-0.932131\pi\) |
0.305424 | − | 0.952217i | \(-0.401202\pi\) | |||||||
\(68\) | 1.50000 | − | 2.59808i | 0.181902 | − | 0.315063i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −6.00000 | + | 5.19615i | −0.717137 | + | 0.621059i | ||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.00000 | − | 1.73205i | −0.117041 | − | 0.202721i | 0.801553 | − | 0.597924i | \(-0.204008\pi\) |
−0.918594 | + | 0.395203i | \(0.870674\pi\) | |||||||
\(74\) | −4.00000 | − | 6.92820i | −0.464991 | − | 0.805387i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00000 | 0.229416 | ||||||||
\(77\) | 2.00000 | − | 1.73205i | 0.227921 | − | 0.197386i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.50000 | − | 11.2583i | 0.731307 | − | 1.26666i | −0.225018 | − | 0.974355i | \(-0.572244\pi\) |
0.956325 | − | 0.292306i | \(-0.0944227\pi\) | |||||||
\(80\) | −1.50000 | − | 2.59808i | −0.167705 | − | 0.290474i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.50000 | − | 7.79423i | 0.496942 | − | 0.860729i | ||||
\(83\) | 9.00000 | 0.987878 | 0.493939 | − | 0.869496i | \(-0.335557\pi\) | ||||
0.493939 | + | 0.869496i | \(0.335557\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.00000 | −0.976187 | ||||||||
\(86\) | 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 | 0.350304 | + | 0.936636i | \(0.386078\pi\) |
−0.986303 | + | 0.164946i | \(0.947255\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | − | 5.19615i | −0.104828 | − | 0.544705i | ||||
\(92\) | 3.00000 | 0.312772 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.50000 | − | 2.59808i | −0.154713 | − | 0.267971i | ||||
\(95\) | −3.00000 | − | 5.19615i | −0.307794 | − | 0.533114i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.00000 | 0.507673 | 0.253837 | − | 0.967247i | \(-0.418307\pi\) | ||||
0.253837 | + | 0.967247i | \(0.418307\pi\) | |||||||
\(98\) | 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 | 0.993258 | + | 0.115924i | \(0.0369830\pi\) |
−0.396236 | + | 0.918149i | \(0.629684\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.0000 | + | 17.3205i | −0.985329 | + | 1.70664i | −0.344865 | + | 0.938652i | \(0.612075\pi\) |
−0.640464 | + | 0.767988i | \(0.721258\pi\) | |||||||
\(104\) | 2.00000 | 0.196116 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.00000 | 0.582772 | ||||||||
\(107\) | −1.50000 | + | 2.59808i | −0.145010 | + | 0.251166i | −0.929377 | − | 0.369132i | \(-0.879655\pi\) |
0.784366 | + | 0.620298i | \(0.212988\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.500000 | + | 0.866025i | 0.0478913 | + | 0.0829502i | 0.888977 | − | 0.457951i | \(-0.151417\pi\) |
−0.841086 | + | 0.540901i | \(0.818083\pi\) | |||||||
\(110\) | 1.50000 | − | 2.59808i | 0.143019 | − | 0.247717i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.50000 | + | 0.866025i | 0.236228 | + | 0.0818317i | ||||
\(113\) | −18.0000 | −1.69330 | −0.846649 | − | 0.532152i | \(-0.821383\pi\) | ||||
−0.846649 | + | 0.532152i | \(0.821383\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.50000 | − | 7.79423i | −0.419627 | − | 0.726816i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.00000 | 0.552345 | ||||||||
\(119\) | 6.00000 | − | 5.19615i | 0.550019 | − | 0.476331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | + | 0.866025i | −0.0454545 | + | 0.0787296i | ||||
\(122\) | −2.50000 | − | 4.33013i | −0.226339 | − | 0.392031i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.00000 | + | 1.73205i | −0.0898027 | + | 0.155543i | ||||
\(125\) | −3.00000 | −0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.0000 | −1.68598 | −0.842989 | − | 0.537931i | \(-0.819206\pi\) | ||||
−0.842989 | + | 0.537931i | \(0.819206\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.00000 | − | 5.19615i | −0.263117 | − | 0.455733i | ||||
\(131\) | −6.00000 | + | 10.3923i | −0.524222 | + | 0.907980i | 0.475380 | + | 0.879781i | \(0.342311\pi\) |
−0.999602 | + | 0.0281993i | \(0.991023\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.00000 | + | 1.73205i | 0.433555 | + | 0.150188i | ||||
\(134\) | 11.0000 | 0.950255 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.50000 | + | 2.59808i | 0.128624 | + | 0.222783i | ||||
\(137\) | −3.00000 | − | 5.19615i | −0.256307 | − | 0.443937i | 0.708942 | − | 0.705266i | \(-0.249173\pi\) |
−0.965250 | + | 0.261329i | \(0.915839\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.00000 | 0.169638 | 0.0848189 | − | 0.996396i | \(-0.472969\pi\) | ||||
0.0848189 | + | 0.996396i | \(0.472969\pi\) | |||||||
\(140\) | −1.50000 | − | 7.79423i | −0.126773 | − | 0.658733i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | + | 1.73205i | 0.0836242 | + | 0.144841i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.00000 | 0.165521 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.00000 | 0.657596 | ||||||||
\(149\) | −6.00000 | + | 10.3923i | −0.491539 | + | 0.851371i | −0.999953 | − | 0.00974235i | \(-0.996899\pi\) |
0.508413 | + | 0.861113i | \(0.330232\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.50000 | − | 4.33013i | −0.203447 | − | 0.352381i | 0.746190 | − | 0.665733i | \(-0.231881\pi\) |
−0.949637 | + | 0.313353i | \(0.898548\pi\) | |||||||
\(152\) | −1.00000 | + | 1.73205i | −0.0811107 | + | 0.140488i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.500000 | + | 2.59808i | 0.0402911 | + | 0.209359i | ||||
\(155\) | 6.00000 | 0.481932 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.00000 | + | 3.46410i | 0.159617 | + | 0.276465i | 0.934731 | − | 0.355357i | \(-0.115641\pi\) |
−0.775113 | + | 0.631822i | \(0.782307\pi\) | |||||||
\(158\) | 6.50000 | + | 11.2583i | 0.517112 | + | 0.895665i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.00000 | 0.237171 | ||||||||
\(161\) | 7.50000 | + | 2.59808i | 0.591083 | + | 0.204757i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.50000 | − | 16.4545i | 0.744097 | − | 1.28881i | −0.206518 | − | 0.978443i | \(-0.566213\pi\) |
0.950615 | − | 0.310372i | \(-0.100454\pi\) | |||||||
\(164\) | 4.50000 | + | 7.79423i | 0.351391 | + | 0.608627i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.50000 | + | 7.79423i | −0.349268 | + | 0.604949i | ||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 4.50000 | − | 7.79423i | 0.345134 | − | 0.597790i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.00000 | + | 3.46410i | 0.152499 | + | 0.264135i | ||||
\(173\) | 3.00000 | − | 5.19615i | 0.228086 | − | 0.395056i | −0.729155 | − | 0.684349i | \(-0.760087\pi\) |
0.957241 | + | 0.289292i | \(0.0934200\pi\) | |||||||
\(174\) | 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 | ||||
\(179\) | −3.00000 | − | 5.19615i | −0.224231 | − | 0.388379i | 0.731858 | − | 0.681457i | \(-0.238654\pi\) |
−0.956088 | + | 0.293079i | \(0.905320\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.0000 | 1.48659 | 0.743294 | − | 0.668965i | \(-0.233262\pi\) | ||||
0.743294 | + | 0.668965i | \(0.233262\pi\) | |||||||
\(182\) | 5.00000 | + | 1.73205i | 0.370625 | + | 0.128388i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.50000 | + | 2.59808i | −0.110581 | + | 0.191533i | ||||
\(185\) | −12.0000 | − | 20.7846i | −0.882258 | − | 1.52811i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.50000 | + | 2.59808i | −0.109691 | + | 0.189990i | ||||
\(188\) | 3.00000 | 0.218797 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.00000 | 0.435286 | ||||||||
\(191\) | −6.00000 | + | 10.3923i | −0.434145 | + | 0.751961i | −0.997225 | − | 0.0744412i | \(-0.976283\pi\) |
0.563081 | + | 0.826402i | \(0.309616\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.00000 | + | 13.8564i | 0.575853 | + | 0.997406i | 0.995948 | + | 0.0899262i | \(0.0286631\pi\) |
−0.420096 | + | 0.907480i | \(0.638004\pi\) | |||||||
\(194\) | −2.50000 | + | 4.33013i | −0.179490 | + | 0.310885i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.50000 | + | 4.33013i | 0.392857 | + | 0.309295i | ||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.00000 | + | 8.66025i | 0.354441 | + | 0.613909i | 0.987022 | − | 0.160585i | \(-0.0513380\pi\) |
−0.632581 | + | 0.774494i | \(0.718005\pi\) | |||||||
\(200\) | −2.00000 | − | 3.46410i | −0.141421 | − | 0.244949i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −12.0000 | −0.844317 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.5000 | − | 23.3827i | 0.942881 | − | 1.63312i | ||||
\(206\) | −10.0000 | − | 17.3205i | −0.696733 | − | 1.20678i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.00000 | + | 1.73205i | −0.0693375 | + | 0.120096i | ||||
\(209\) | −2.00000 | −0.138343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.0000 | 1.37686 | 0.688428 | − | 0.725304i | \(-0.258301\pi\) | ||||
0.688428 | + | 0.725304i | \(0.258301\pi\) | |||||||
\(212\) | −3.00000 | + | 5.19615i | −0.206041 | + | 0.356873i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.50000 | − | 2.59808i | −0.102538 | − | 0.177601i | ||||
\(215\) | 6.00000 | − | 10.3923i | 0.409197 | − | 0.708749i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.00000 | + | 3.46410i | −0.271538 | + | 0.235159i | ||||
\(218\) | −1.00000 | −0.0677285 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.50000 | + | 2.59808i | 0.101130 | + | 0.175162i | ||||
\(221\) | 3.00000 | + | 5.19615i | 0.201802 | + | 0.349531i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.0000 | 1.74109 | 0.870544 | − | 0.492090i | \(-0.163767\pi\) | ||||
0.870544 | + | 0.492090i | \(0.163767\pi\) | |||||||
\(224\) | −2.00000 | + | 1.73205i | −0.133631 | + | 0.115728i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.00000 | − | 15.5885i | 0.598671 | − | 1.03693i | ||||
\(227\) | −7.50000 | − | 12.9904i | −0.497792 | − | 0.862202i | 0.502204 | − | 0.864749i | \(-0.332523\pi\) |
−0.999997 | + | 0.00254715i | \(0.999189\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.0000 | + | 17.3205i | −0.660819 | + | 1.14457i | 0.319582 | + | 0.947559i | \(0.396457\pi\) |
−0.980401 | + | 0.197013i | \(0.936876\pi\) | |||||||
\(230\) | 9.00000 | 0.593442 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.5000 | + | 18.1865i | −0.687878 | + | 1.19144i | 0.284645 | + | 0.958633i | \(0.408124\pi\) |
−0.972523 | + | 0.232806i | \(0.925209\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.50000 | − | 7.79423i | −0.293548 | − | 0.508439i | ||||
\(236\) | −3.00000 | + | 5.19615i | −0.195283 | + | 0.338241i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.50000 | + | 7.79423i | 0.0972306 | + | 0.505225i | ||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.00000 | + | 3.46410i | 0.128831 | + | 0.223142i | 0.923224 | − | 0.384262i | \(-0.125544\pi\) |
−0.794393 | + | 0.607404i | \(0.792211\pi\) | |||||||
\(242\) | −0.500000 | − | 0.866025i | −0.0321412 | − | 0.0556702i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.00000 | 0.320092 | ||||||||
\(245\) | 3.00000 | − | 20.7846i | 0.191663 | − | 1.32788i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.00000 | + | 3.46410i | −0.127257 | + | 0.220416i | ||||
\(248\) | −1.00000 | − | 1.73205i | −0.0635001 | − | 0.109985i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.50000 | − | 2.59808i | 0.0948683 | − | 0.164317i | ||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.00000 | −0.188608 | ||||||||
\(254\) | 9.50000 | − | 16.4545i | 0.596083 | − | 1.03245i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 12.0000 | − | 20.7846i | 0.748539 | − | 1.29651i | −0.199983 | − | 0.979799i | \(-0.564089\pi\) |
0.948523 | − | 0.316709i | \(-0.102578\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.0000 | + | 6.92820i | 1.24274 | + | 0.430498i | ||||
\(260\) | 6.00000 | 0.372104 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.00000 | − | 10.3923i | −0.370681 | − | 0.642039i | ||||
\(263\) | 15.0000 | + | 25.9808i | 0.924940 | + | 1.60204i | 0.791658 | + | 0.610964i | \(0.209218\pi\) |
0.133281 | + | 0.991078i | \(0.457449\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.0000 | 1.10573 | ||||||||
\(266\) | −4.00000 | + | 3.46410i | −0.245256 | + | 0.212398i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.50000 | + | 9.52628i | −0.335966 | + | 0.581910i | ||||
\(269\) | −7.50000 | − | 12.9904i | −0.457283 | − | 0.792038i | 0.541533 | − | 0.840679i | \(-0.317844\pi\) |
−0.998816 | + | 0.0486418i | \(0.984511\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.00000 | + | 6.92820i | −0.242983 | + | 0.420858i | −0.961563 | − | 0.274586i | \(-0.911459\pi\) |
0.718580 | + | 0.695444i | \(0.244792\pi\) | |||||||
\(272\) | −3.00000 | −0.181902 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.00000 | 0.362473 | ||||||||
\(275\) | 2.00000 | − | 3.46410i | 0.120605 | − | 0.208893i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.00000 | − | 12.1244i | −0.420589 | − | 0.728482i | 0.575408 | − | 0.817867i | \(-0.304843\pi\) |
−0.995997 | + | 0.0893846i | \(0.971510\pi\) | |||||||
\(278\) | −1.00000 | + | 1.73205i | −0.0599760 | + | 0.103882i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 7.50000 | + | 2.59808i | 0.448211 | + | 0.155265i | ||||
\(281\) | −27.0000 | −1.61068 | −0.805342 | − | 0.592810i | \(-0.798019\pi\) | ||||
−0.805342 | + | 0.592810i | \(0.798019\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.00000 | + | 13.8564i | 0.475551 | + | 0.823678i | 0.999608 | − | 0.0280052i | \(-0.00891551\pi\) |
−0.524057 | + | 0.851683i | \(0.675582\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.00000 | −0.118262 | ||||||||
\(287\) | 4.50000 | + | 23.3827i | 0.265627 | + | 1.38024i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.00000 | − | 6.92820i | 0.235294 | − | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.00000 | + | 1.73205i | −0.0585206 | + | 0.101361i | ||||
\(293\) | −18.0000 | −1.05157 | −0.525786 | − | 0.850617i | \(-0.676229\pi\) | ||||
−0.525786 | + | 0.850617i | \(0.676229\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 18.0000 | 1.04800 | ||||||||
\(296\) | −4.00000 | + | 6.92820i | −0.232495 | + | 0.402694i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.00000 | − | 10.3923i | −0.347571 | − | 0.602010i | ||||
\(299\) | −3.00000 | + | 5.19615i | −0.173494 | + | 0.300501i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.00000 | + | 10.3923i | 0.115278 | + | 0.599002i | ||||
\(302\) | 5.00000 | 0.287718 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.00000 | − | 1.73205i | −0.0573539 | − | 0.0993399i | ||||
\(305\) | −7.50000 | − | 12.9904i | −0.429449 | − | 0.743827i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.00000 | 0.456584 | 0.228292 | − | 0.973593i | \(-0.426686\pi\) | ||||
0.228292 | + | 0.973593i | \(0.426686\pi\) | |||||||
\(308\) | −2.50000 | − | 0.866025i | −0.142451 | − | 0.0493464i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.00000 | + | 5.19615i | −0.170389 | + | 0.295122i | ||||
\(311\) | 1.50000 | + | 2.59808i | 0.0850572 | + | 0.147323i | 0.905416 | − | 0.424526i | \(-0.139559\pi\) |
−0.820358 | + | 0.571850i | \(0.806226\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.00000 | − | 8.66025i | 0.282617 | − | 0.489506i | −0.689412 | − | 0.724370i | \(-0.742131\pi\) |
0.972028 | + | 0.234863i | \(0.0754642\pi\) | |||||||
\(314\) | −4.00000 | −0.225733 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13.0000 | −0.731307 | ||||||||
\(317\) | 7.50000 | − | 12.9904i | 0.421242 | − | 0.729612i | −0.574819 | − | 0.818280i | \(-0.694928\pi\) |
0.996061 | + | 0.0886679i | \(0.0282610\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.50000 | + | 2.59808i | −0.0838525 | + | 0.145237i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.00000 | + | 5.19615i | −0.334367 | + | 0.289570i | ||||
\(323\) | −6.00000 | −0.333849 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.00000 | − | 6.92820i | −0.221880 | − | 0.384308i | ||||
\(326\) | 9.50000 | + | 16.4545i | 0.526156 | + | 0.911330i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −9.00000 | −0.496942 | ||||||||
\(329\) | 7.50000 | + | 2.59808i | 0.413488 | + | 0.143237i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.50000 | − | 16.4545i | 0.522167 | − | 0.904420i | −0.477500 | − | 0.878632i | \(-0.658457\pi\) |
0.999667 | − | 0.0257885i | \(-0.00820965\pi\) | |||||||
\(332\) | −4.50000 | − | 7.79423i | −0.246970 | − | 0.427764i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 33.0000 | 1.80298 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.0000 | −1.19842 | −0.599208 | − | 0.800593i | \(-0.704518\pi\) | ||||
−0.599208 | + | 0.800593i | \(0.704518\pi\) | |||||||
\(338\) | 4.50000 | − | 7.79423i | 0.244768 | − | 0.423950i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.50000 | + | 7.79423i | 0.244047 | + | 0.422701i | ||||
\(341\) | 1.00000 | − | 1.73205i | 0.0541530 | − | 0.0937958i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | + | 15.5885i | 0.539949 | + | 0.841698i | ||||
\(344\) | −4.00000 | −0.215666 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.00000 | + | 5.19615i | 0.161281 | + | 0.279347i | ||||
\(347\) | 10.5000 | + | 18.1865i | 0.563670 | + | 0.976304i | 0.997172 | + | 0.0751519i | \(0.0239442\pi\) |
−0.433503 | + | 0.901152i | \(0.642722\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.0000 | 1.23116 | 0.615581 | − | 0.788074i | \(-0.288921\pi\) | ||||
0.615581 | + | 0.788074i | \(0.288921\pi\) | |||||||
\(350\) | −2.00000 | − | 10.3923i | −0.106904 | − | 0.555492i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.500000 | − | 0.866025i | 0.0266501 | − | 0.0461593i | ||||
\(353\) | 15.0000 | + | 25.9808i | 0.798369 | + | 1.38282i | 0.920677 | + | 0.390324i | \(0.127637\pi\) |
−0.122308 | + | 0.992492i | \(0.539030\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 12.0000 | 0.635999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.00000 | 0.317110 | ||||||||
\(359\) | −6.00000 | + | 10.3923i | −0.316668 | + | 0.548485i | −0.979791 | − | 0.200026i | \(-0.935897\pi\) |
0.663123 | + | 0.748511i | \(0.269231\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.50000 | + | 12.9904i | 0.394737 | + | 0.683704i | ||||
\(362\) | −10.0000 | + | 17.3205i | −0.525588 | + | 0.910346i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.00000 | + | 3.46410i | −0.209657 | + | 0.181568i | ||||
\(365\) | 6.00000 | 0.314054 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.00000 | + | 8.66025i | 0.260998 | + | 0.452062i | 0.966507 | − | 0.256639i | \(-0.0826151\pi\) |
−0.705509 | + | 0.708700i | \(0.749282\pi\) | |||||||
\(368\) | −1.50000 | − | 2.59808i | −0.0781929 | − | 0.135434i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 24.0000 | 1.24770 | ||||||||
\(371\) | −12.0000 | + | 10.3923i | −0.623009 | + | 0.539542i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.5000 | + | 19.9186i | −0.595447 | + | 1.03135i | 0.398036 | + | 0.917370i | \(0.369692\pi\) |
−0.993484 | + | 0.113975i | \(0.963641\pi\) | |||||||
\(374\) | −1.50000 | − | 2.59808i | −0.0775632 | − | 0.134343i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.50000 | + | 2.59808i | −0.0773566 | + | 0.133986i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.00000 | −0.0513665 | −0.0256833 | − | 0.999670i | \(-0.508176\pi\) | ||||
−0.0256833 | + | 0.999670i | \(0.508176\pi\) | |||||||
\(380\) | −3.00000 | + | 5.19615i | −0.153897 | + | 0.266557i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.00000 | − | 10.3923i | −0.306987 | − | 0.531717i | ||||
\(383\) | 12.0000 | − | 20.7846i | 0.613171 | − | 1.06204i | −0.377531 | − | 0.925997i | \(-0.623227\pi\) |
0.990702 | − | 0.136047i | \(-0.0434398\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.50000 | + | 7.79423i | 0.0764471 | + | 0.397231i | ||||
\(386\) | −16.0000 | −0.814379 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.50000 | − | 4.33013i | −0.126918 | − | 0.219829i | ||||
\(389\) | 10.5000 | + | 18.1865i | 0.532371 | + | 0.922094i | 0.999286 | + | 0.0377914i | \(0.0120322\pi\) |
−0.466915 | + | 0.884302i | \(0.654634\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.00000 | −0.455150 | ||||||||
\(392\) | −6.50000 | + | 2.59808i | −0.328300 | + | 0.131223i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 19.5000 | + | 33.7750i | 0.981151 | + | 1.69940i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.0000 | − | 24.2487i | 0.702640 | − | 1.21701i | −0.264897 | − | 0.964277i | \(-0.585338\pi\) |
0.967537 | − | 0.252731i | \(-0.0813288\pi\) | |||||||
\(398\) | −10.0000 | −0.501255 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.00000 | 0.200000 | ||||||||
\(401\) | −6.00000 | + | 10.3923i | −0.299626 | + | 0.518967i | −0.976050 | − | 0.217545i | \(-0.930195\pi\) |
0.676425 | + | 0.736512i | \(0.263528\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.00000 | − | 3.46410i | −0.0996271 | − | 0.172559i | ||||
\(404\) | 6.00000 | − | 10.3923i | 0.298511 | − | 0.517036i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.00000 | −0.396545 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.00000 | − | 1.73205i | −0.0494468 | − | 0.0856444i | 0.840243 | − | 0.542211i | \(-0.182412\pi\) |
−0.889689 | + | 0.456566i | \(0.849079\pi\) | |||||||
\(410\) | 13.5000 | + | 23.3827i | 0.666717 | + | 1.15479i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 20.0000 | 0.985329 | ||||||||
\(413\) | −12.0000 | + | 10.3923i | −0.590481 | + | 0.511372i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.5000 | + | 23.3827i | −0.662689 | + | 1.14781i | ||||
\(416\) | −1.00000 | − | 1.73205i | −0.0490290 | − | 0.0849208i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.00000 | − | 1.73205i | 0.0489116 | − | 0.0847174i | ||||
\(419\) | 18.0000 | 0.879358 | 0.439679 | − | 0.898155i | \(-0.355092\pi\) | ||||
0.439679 | + | 0.898155i | \(0.355092\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.00000 | 0.389896 | 0.194948 | − | 0.980814i | \(-0.437546\pi\) | ||||
0.194948 | + | 0.980814i | \(0.437546\pi\) | |||||||
\(422\) | −10.0000 | + | 17.3205i | −0.486792 | + | 0.843149i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.00000 | − | 5.19615i | −0.145693 | − | 0.252347i | ||||
\(425\) | 6.00000 | − | 10.3923i | 0.291043 | − | 0.504101i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.5000 | + | 4.33013i | 0.604917 | + | 0.209550i | ||||
\(428\) | 3.00000 | 0.145010 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.00000 | + | 10.3923i | 0.289346 | + | 0.501161i | ||||
\(431\) | 15.0000 | + | 25.9808i | 0.722525 | + | 1.25145i | 0.959985 | + | 0.280052i | \(0.0903517\pi\) |
−0.237460 | + | 0.971397i | \(0.576315\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 35.0000 | 1.68199 | 0.840996 | − | 0.541041i | \(-0.181970\pi\) | ||||
0.840996 | + | 0.541041i | \(0.181970\pi\) | |||||||
\(434\) | −1.00000 | − | 5.19615i | −0.0480015 | − | 0.249423i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.500000 | − | 0.866025i | 0.0239457 | − | 0.0414751i | ||||
\(437\) | −3.00000 | − | 5.19615i | −0.143509 | − | 0.248566i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.5000 | + | 30.3109i | −0.835229 | + | 1.44666i | 0.0586141 | + | 0.998281i | \(0.481332\pi\) |
−0.893843 | + | 0.448379i | \(0.852001\pi\) | |||||||
\(440\) | −3.00000 | −0.143019 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.00000 | −0.285391 | ||||||||
\(443\) | 12.0000 | − | 20.7846i | 0.570137 | − | 0.987507i | −0.426414 | − | 0.904528i | \(-0.640223\pi\) |
0.996551 | − | 0.0829786i | \(-0.0264433\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.0000 | − | 31.1769i | −0.853282 | − | 1.47793i | ||||
\(446\) | −13.0000 | + | 22.5167i | −0.615568 | + | 1.06619i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.500000 | − | 2.59808i | −0.0236228 | − | 0.122748i | ||||
\(449\) | −36.0000 | −1.69895 | −0.849473 | − | 0.527633i | \(-0.823080\pi\) | ||||
−0.849473 | + | 0.527633i | \(0.823080\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.50000 | − | 7.79423i | −0.211897 | − | 0.367016i | ||||
\(452\) | 9.00000 | + | 15.5885i | 0.423324 | + | 0.733219i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 15.0000 | 0.703985 | ||||||||
\(455\) | 15.0000 | + | 5.19615i | 0.703211 | + | 0.243599i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.0000 | − | 34.6410i | 0.935561 | − | 1.62044i | 0.161929 | − | 0.986802i | \(-0.448228\pi\) |
0.773631 | − | 0.633636i | \(-0.218438\pi\) | |||||||
\(458\) | −10.0000 | − | 17.3205i | −0.467269 | − | 0.809334i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.50000 | + | 7.79423i | −0.209814 | + | 0.363408i | ||||
\(461\) | 18.0000 | 0.838344 | 0.419172 | − | 0.907907i | \(-0.362320\pi\) | ||||
0.419172 | + | 0.907907i | \(0.362320\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.00000 | −0.185896 | −0.0929479 | − | 0.995671i | \(-0.529629\pi\) | ||||
−0.0929479 | + | 0.995671i | \(0.529629\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.5000 | − | 18.1865i | −0.486403 | − | 0.842475i | ||||
\(467\) | 21.0000 | − | 36.3731i | 0.971764 | − | 1.68314i | 0.281539 | − | 0.959550i | \(-0.409155\pi\) |
0.690225 | − | 0.723595i | \(-0.257512\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −22.0000 | + | 19.0526i | −1.01587 | + | 0.879765i | ||||
\(470\) | 9.00000 | 0.415139 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.00000 | − | 5.19615i | −0.138086 | − | 0.239172i | ||||
\(473\) | −2.00000 | − | 3.46410i | −0.0919601 | − | 0.159280i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.00000 | 0.367065 | ||||||||
\(476\) | −7.50000 | − | 2.59808i | −0.343762 | − | 0.119083i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.00000 | + | 10.3923i | 0.274147 | + | 0.474837i | 0.969920 | − | 0.243426i | \(-0.0782712\pi\) |
−0.695773 | + | 0.718262i | \(0.744938\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.00000 | + | 13.8564i | −0.364769 | + | 0.631798i | ||||
\(482\) | −4.00000 | −0.182195 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −7.50000 | + | 12.9904i | −0.340557 | + | 0.589863i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.0000 | − | 32.9090i | −0.860972 | − | 1.49125i | −0.870992 | − | 0.491298i | \(-0.836523\pi\) |
0.0100195 | − | 0.999950i | \(-0.496811\pi\) | |||||||
\(488\) | −2.50000 | + | 4.33013i | −0.113170 | + | 0.196016i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 16.5000 | + | 12.9904i | 0.745394 | + | 0.586846i | ||||
\(491\) | 9.00000 | 0.406164 | 0.203082 | − | 0.979162i | \(-0.434904\pi\) | ||||
0.203082 | + | 0.979162i | \(0.434904\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −2.00000 | − | 3.46410i | −0.0899843 | − | 0.155857i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.00000 | 0.0898027 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.0000 | + | 17.3205i | −0.447661 | + | 0.775372i | −0.998233 | − | 0.0594153i | \(-0.981076\pi\) |
0.550572 | + | 0.834788i | \(0.314410\pi\) | |||||||
\(500\) | 1.50000 | + | 2.59808i | 0.0670820 | + | 0.116190i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −36.0000 | −1.60198 | ||||||||
\(506\) | 1.50000 | − | 2.59808i | 0.0666831 | − | 0.115499i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.50000 | + | 16.4545i | 0.421494 | + | 0.730050i | ||||
\(509\) | 3.00000 | − | 5.19615i | 0.132973 | − | 0.230315i | −0.791849 | − | 0.610718i | \(-0.790881\pi\) |
0.924821 | + | 0.380402i | \(0.124214\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.00000 | + | 3.46410i | −0.176950 | + | 0.153243i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 12.0000 | + | 20.7846i | 0.529297 | + | 0.916770i | ||||
\(515\) | −30.0000 | − | 51.9615i | −1.32196 | − | 2.28970i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.00000 | −0.131940 | ||||||||
\(518\) | −16.0000 | + | 13.8564i | −0.703000 | + | 0.608816i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.00000 | + | 5.19615i | −0.131559 | + | 0.227866i | ||||
\(521\) | −21.0000 | − | 36.3731i | −0.920027 | − | 1.59353i | −0.799370 | − | 0.600839i | \(-0.794833\pi\) |
−0.120656 | − | 0.992694i | \(-0.538500\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.00000 | − | 8.66025i | 0.218635 | − | 0.378686i | −0.735756 | − | 0.677247i | \(-0.763173\pi\) |
0.954391 | + | 0.298560i | \(0.0965063\pi\) | |||||||
\(524\) | 12.0000 | 0.524222 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −30.0000 | −1.30806 | ||||||||
\(527\) | 3.00000 | − | 5.19615i | 0.130682 | − | 0.226348i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | + | 12.1244i | 0.304348 | + | 0.527146i | ||||
\(530\) | −9.00000 | + | 15.5885i | −0.390935 | + | 0.677119i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.00000 | − | 5.19615i | −0.0433555 | − | 0.225282i | ||||
\(533\) | −18.0000 | −0.779667 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.50000 | − | 7.79423i | −0.194552 | − | 0.336974i | ||||
\(536\) | −5.50000 | − | 9.52628i | −0.237564 | − | 0.411473i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 15.0000 | 0.646696 | ||||||||
\(539\) | −5.50000 | − | 4.33013i | −0.236902 | − | 0.186512i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.50000 | + | 9.52628i | −0.236463 | + | 0.409567i | −0.959697 | − | 0.281037i | \(-0.909322\pi\) |
0.723234 | + | 0.690604i | \(0.242655\pi\) | |||||||
\(542\) | −4.00000 | − | 6.92820i | −0.171815 | − | 0.297592i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.50000 | − | 2.59808i | 0.0643120 | − | 0.111392i | ||||
\(545\) | −3.00000 | −0.128506 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.0000 | 0.598597 | 0.299298 | − | 0.954160i | \(-0.403247\pi\) | ||||
0.299298 | + | 0.954160i | \(0.403247\pi\) | |||||||
\(548\) | −3.00000 | + | 5.19615i | −0.128154 | + | 0.221969i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.00000 | + | 3.46410i | 0.0852803 | + | 0.147710i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −32.5000 | − | 11.2583i | −1.38204 | − | 0.478753i | ||||
\(554\) | 14.0000 | 0.594803 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.00000 | − | 1.73205i | −0.0424094 | − | 0.0734553i | ||||
\(557\) | −12.0000 | − | 20.7846i | −0.508456 | − | 0.880672i | −0.999952 | − | 0.00979220i | \(-0.996883\pi\) |
0.491496 | − | 0.870880i | \(-0.336450\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.00000 | −0.338364 | ||||||||
\(560\) | −6.00000 | + | 5.19615i | −0.253546 | + | 0.219578i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 13.5000 | − | 23.3827i | 0.569463 | − | 0.986339i | ||||
\(563\) | 6.00000 | + | 10.3923i | 0.252870 | + | 0.437983i | 0.964315 | − | 0.264758i | \(-0.0852922\pi\) |
−0.711445 | + | 0.702742i | \(0.751959\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 27.0000 | − | 46.7654i | 1.13590 | − | 1.96743i | ||||
\(566\) | −16.0000 | −0.672530 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.0000 | − | 36.3731i | 0.880366 | − | 1.52484i | 0.0294311 | − | 0.999567i | \(-0.490630\pi\) |
0.850935 | − | 0.525271i | \(-0.176036\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.0000 | − | 27.7128i | −0.669579 | − | 1.15975i | −0.978022 | − | 0.208502i | \(-0.933141\pi\) |
0.308443 | − | 0.951243i | \(-0.400192\pi\) | |||||||
\(572\) | 1.00000 | − | 1.73205i | 0.0418121 | − | 0.0724207i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −22.5000 | − | 7.79423i | −0.939132 | − | 0.325325i | ||||
\(575\) | 12.0000 | 0.500435 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.50000 | − | 14.7224i | −0.353860 | − | 0.612903i | 0.633062 | − | 0.774101i | \(-0.281798\pi\) |
−0.986922 | + | 0.161198i | \(0.948464\pi\) | |||||||
\(578\) | 4.00000 | + | 6.92820i | 0.166378 | + | 0.288175i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.50000 | − | 23.3827i | −0.186691 | − | 0.970077i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.00000 | − | 5.19615i | 0.124247 | − | 0.215203i | ||||
\(584\) | −1.00000 | − | 1.73205i | −0.0413803 | − | 0.0716728i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.00000 | − | 15.5885i | 0.371787 | − | 0.643953i | ||||
\(587\) | 18.0000 | 0.742940 | 0.371470 | − | 0.928445i | \(-0.378854\pi\) | ||||
0.371470 | + | 0.928445i | \(0.378854\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.00000 | 0.164817 | ||||||||
\(590\) | −9.00000 | + | 15.5885i | −0.370524 | + | 0.641767i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.00000 | − | 6.92820i | −0.164399 | − | 0.284747i | ||||
\(593\) | 3.00000 | − | 5.19615i | 0.123195 | − | 0.213380i | −0.797831 | − | 0.602881i | \(-0.794019\pi\) |
0.921026 | + | 0.389501i | \(0.127353\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.50000 | + | 23.3827i | 0.184482 | + | 0.958597i | ||||
\(596\) | 12.0000 | 0.491539 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.00000 | − | 5.19615i | −0.122679 | − | 0.212486i | ||||
\(599\) | −7.50000 | − | 12.9904i | −0.306442 | − | 0.530773i | 0.671140 | − | 0.741331i | \(-0.265805\pi\) |
−0.977581 | + | 0.210558i | \(0.932472\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −40.0000 | −1.63163 | −0.815817 | − | 0.578310i | \(-0.803712\pi\) | ||||
−0.815817 | + | 0.578310i | \(0.803712\pi\) | |||||||
\(602\) | −10.0000 | − | 3.46410i | −0.407570 | − | 0.141186i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.50000 | + | 4.33013i | −0.101724 | + | 0.176190i | ||||
\(605\) | −1.50000 | − | 2.59808i | −0.0609837 | − | 0.105627i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.5000 | + | 35.5070i | −0.832069 | + | 1.44119i | 0.0643251 | + | 0.997929i | \(0.479511\pi\) |
−0.896394 | + | 0.443257i | \(0.853823\pi\) | |||||||
\(608\) | 2.00000 | 0.0811107 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 15.0000 | 0.607332 | ||||||||
\(611\) | −3.00000 | + | 5.19615i | −0.121367 | + | 0.210214i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.50000 | − | 14.7224i | −0.343312 | − | 0.594633i | 0.641734 | − | 0.766927i | \(-0.278215\pi\) |
−0.985046 | + | 0.172294i | \(0.944882\pi\) | |||||||
\(614\) | −4.00000 | + | 6.92820i | −0.161427 | + | 0.279600i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.00000 | − | 1.73205i | 0.0805823 | − | 0.0697863i | ||||
\(617\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.5000 | + | 26.8468i | 0.622998 | + | 1.07906i | 0.988924 | + | 0.148420i | \(0.0474187\pi\) |
−0.365927 | + | 0.930644i | \(0.619248\pi\) | |||||||
\(620\) | −3.00000 | − | 5.19615i | −0.120483 | − | 0.208683i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3.00000 | −0.120289 | ||||||||
\(623\) | 30.0000 | + | 10.3923i | 1.20192 | + | 0.416359i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | − | 25.1147i | 0.580000 | − | 1.00459i | ||||
\(626\) | 5.00000 | + | 8.66025i | 0.199840 | + | 0.346133i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.00000 | − | 3.46410i | 0.0798087 | − | 0.138233i | ||||
\(629\) | −24.0000 | −0.956943 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.0000 | −0.398094 | −0.199047 | − | 0.979990i | \(-0.563785\pi\) | ||||
−0.199047 | + | 0.979990i | \(0.563785\pi\) | |||||||
\(632\) | 6.50000 | − | 11.2583i | 0.258556 | − | 0.447832i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7.50000 | + | 12.9904i | 0.297863 | + | 0.515914i | ||||
\(635\) | 28.5000 | − | 49.3634i | 1.13099 | − | 1.95893i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.0000 | + | 5.19615i | −0.515079 | + | 0.205879i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.50000 | − | 2.59808i | −0.0592927 | − | 0.102698i | ||||
\(641\) | 6.00000 | + | 10.3923i | 0.236986 | + | 0.410471i | 0.959848 | − | 0.280521i | \(-0.0905072\pi\) |
−0.722862 | + | 0.690992i | \(0.757174\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.0000 | 0.788723 | 0.394362 | − | 0.918955i | \(-0.370966\pi\) | ||||
0.394362 | + | 0.918955i | \(0.370966\pi\) | |||||||
\(644\) | −1.50000 | − | 7.79423i | −0.0591083 | − | 0.307136i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.00000 | − | 5.19615i | 0.118033 | − | 0.204440i | ||||
\(647\) | −7.50000 | − | 12.9904i | −0.294855 | − | 0.510705i | 0.680096 | − | 0.733123i | \(-0.261938\pi\) |
−0.974951 | + | 0.222419i | \(0.928605\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.00000 | − | 5.19615i | 0.117760 | − | 0.203967i | ||||
\(650\) | 8.00000 | 0.313786 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −19.0000 | −0.744097 | ||||||||
\(653\) | 7.50000 | − | 12.9904i | 0.293498 | − | 0.508353i | −0.681137 | − | 0.732156i | \(-0.738514\pi\) |
0.974634 | + | 0.223803i | \(0.0718474\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.0000 | − | 31.1769i | −0.703318 | − | 1.21818i | ||||
\(656\) | 4.50000 | − | 7.79423i | 0.175695 | − | 0.304314i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6.00000 | + | 5.19615i | −0.233904 | + | 0.202567i | ||||
\(659\) | −45.0000 | −1.75295 | −0.876476 | − | 0.481446i | \(-0.840112\pi\) | ||||
−0.876476 | + | 0.481446i | \(0.840112\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.00000 | − | 12.1244i | −0.272268 | − | 0.471583i | 0.697174 | − | 0.716902i | \(-0.254441\pi\) |
−0.969442 | + | 0.245319i | \(0.921107\pi\) | |||||||
\(662\) | 9.50000 | + | 16.4545i | 0.369228 | + | 0.639522i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.00000 | 0.349268 | ||||||||
\(665\) | −12.0000 | + | 10.3923i | −0.465340 | + | 0.402996i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −16.5000 | + | 28.5788i | −0.637451 | + | 1.10410i | ||||
\(671\) | −5.00000 | −0.193023 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.0000 | −0.385472 | −0.192736 | − | 0.981251i | \(-0.561736\pi\) | ||||
−0.192736 | + | 0.981251i | \(0.561736\pi\) | |||||||
\(674\) | 11.0000 | − | 19.0526i | 0.423704 | − | 0.733877i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.50000 | + | 7.79423i | 0.173077 | + | 0.299778i | ||||
\(677\) | 3.00000 | − | 5.19615i | 0.115299 | − | 0.199704i | −0.802600 | − | 0.596518i | \(-0.796551\pi\) |
0.917899 | + | 0.396813i | \(0.129884\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.50000 | − | 12.9904i | −0.0959412 | − | 0.498525i | ||||
\(680\) | −9.00000 | −0.345134 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.00000 | + | 1.73205i | 0.0382920 | + | 0.0663237i | ||||
\(683\) | −12.0000 | − | 20.7846i | −0.459167 | − | 0.795301i | 0.539750 | − | 0.841825i | \(-0.318519\pi\) |
−0.998917 | + | 0.0465244i | \(0.985185\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 18.0000 | 0.687745 | ||||||||
\(686\) | −18.5000 | + | 0.866025i | −0.706333 | + | 0.0330650i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.00000 | − | 3.46410i | 0.0762493 | − | 0.132068i | ||||
\(689\) | −6.00000 | − | 10.3923i | −0.228582 | − | 0.395915i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.5000 | + | 19.9186i | −0.437481 | + | 0.757739i | −0.997494 | − | 0.0707446i | \(-0.977462\pi\) |
0.560014 | + | 0.828483i | \(0.310796\pi\) | |||||||
\(692\) | −6.00000 | −0.228086 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −21.0000 | −0.797149 | ||||||||
\(695\) | −3.00000 | + | 5.19615i | −0.113796 | + | 0.197101i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.5000 | − | 23.3827i | −0.511349 | − | 0.885682i | ||||
\(698\) | −11.5000 | + | 19.9186i | −0.435281 | + | 0.753930i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 10.0000 | + | 3.46410i | 0.377964 | + | 0.130931i | ||||
\(701\) | 18.0000 | 0.679851 | 0.339925 | − | 0.940452i | \(-0.389598\pi\) | ||||
0.339925 | + | 0.940452i | \(0.389598\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.00000 | − | 13.8564i | −0.301726 | − | 0.522604i | ||||
\(704\) | 0.500000 | + | 0.866025i | 0.0188445 | + | 0.0326396i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −30.0000 | −1.12906 | ||||||||
\(707\) | 24.0000 | − | 20.7846i | 0.902613 | − | 0.781686i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.00000 | + | 12.1244i | −0.262891 | + | 0.455340i | −0.967009 | − | 0.254743i | \(-0.918009\pi\) |
0.704118 | + | 0.710083i | \(0.251342\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.00000 | + | 10.3923i | −0.224860 | + | 0.389468i | ||||
\(713\) | 6.00000 | 0.224702 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.00000 | −0.224387 | ||||||||
\(716\) | −3.00000 | + | 5.19615i | −0.112115 | + | 0.194189i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −6.00000 | − | 10.3923i | −0.223918 | − | 0.387837i | ||||
\(719\) | −19.5000 | + | 33.7750i | −0.727227 | + | 1.25959i | 0.230823 | + | 0.972996i | \(0.425858\pi\) |
−0.958051 | + | 0.286599i | \(0.907475\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 50.0000 | + | 17.3205i | 1.86210 | + | 0.645049i | ||||
\(722\) | −15.0000 | −0.558242 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −10.0000 | − | 17.3205i | −0.371647 | − | 0.643712i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.00000 | −0.148352 | −0.0741759 | − | 0.997245i | \(-0.523633\pi\) | ||||
−0.0741759 | + | 0.997245i | \(0.523633\pi\) | |||||||
\(728\) | −1.00000 | − | 5.19615i | −0.0370625 | − | 0.192582i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3.00000 | + | 5.19615i | −0.111035 | + | 0.192318i | ||||
\(731\) | −6.00000 | − | 10.3923i | −0.221918 | − | 0.384373i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.5000 | + | 40.7032i | −0.867992 | + | 1.50341i | −0.00394730 | + | 0.999992i | \(0.501256\pi\) |
−0.864045 | + | 0.503415i | \(0.832077\pi\) | |||||||
\(734\) | −10.0000 | −0.369107 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.00000 | 0.110581 | ||||||||
\(737\) | 5.50000 | − | 9.52628i | 0.202595 | − | 0.350905i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.00000 | + | 8.66025i | 0.183928 | + | 0.318573i | 0.943215 | − | 0.332184i | \(-0.107785\pi\) |
−0.759287 | + | 0.650756i | \(0.774452\pi\) | |||||||
\(740\) | −12.0000 | + | 20.7846i | −0.441129 | + | 0.764057i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.00000 | − | 15.5885i | −0.110133 | − | 0.572270i | ||||
\(743\) | 36.0000 | 1.32071 | 0.660356 | − | 0.750953i | \(-0.270405\pi\) | ||||
0.660356 | + | 0.750953i | \(0.270405\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.0000 | − | 31.1769i | −0.659469 | − | 1.14223i | ||||
\(746\) | −11.5000 | − | 19.9186i | −0.421045 | − | 0.729271i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.00000 | 0.109691 | ||||||||
\(749\) | 7.50000 | + | 2.59808i | 0.274044 | + | 0.0949316i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.0000 | + | 43.3013i | −0.912263 | + | 1.58009i | −0.101403 | + | 0.994845i | \(0.532333\pi\) |
−0.810860 | + | 0.585240i | \(0.801000\pi\) | |||||||
\(752\) | −1.50000 | − | 2.59808i | −0.0546994 | − | 0.0947421i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.0000 | 0.545906 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.0000 | −0.363456 | −0.181728 | − | 0.983349i | \(-0.558169\pi\) | ||||
−0.181728 | + | 0.983349i | \(0.558169\pi\) | |||||||
\(758\) | 0.500000 | − | 0.866025i | 0.0181608 | − | 0.0314555i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.00000 | − | 5.19615i | −0.108821 | − | 0.188484i | ||||
\(761\) | 7.50000 | − | 12.9904i | 0.271875 | − | 0.470901i | −0.697467 | − | 0.716617i | \(-0.745690\pi\) |
0.969342 | + | 0.245716i | \(0.0790230\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.00000 | − | 1.73205i | 0.0724049 | − | 0.0627044i | ||||
\(764\) | 12.0000 | 0.434145 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.0000 | + | 20.7846i | 0.433578 | + | 0.750978i | ||||
\(767\) | −6.00000 | − | 10.3923i | −0.216647 | − | 0.375244i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.0000 | −0.793340 | −0.396670 | − | 0.917961i | \(-0.629834\pi\) | ||||
−0.396670 | + | 0.917961i | \(0.629834\pi\) | |||||||
\(770\) | −7.50000 | − | 2.59808i | −0.270281 | − | 0.0936282i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 8.00000 | − | 13.8564i | 0.287926 | − | 0.498703i | ||||
\(773\) | 10.5000 | + | 18.1865i | 0.377659 | + | 0.654124i | 0.990721 | − | 0.135910i | \(-0.0433959\pi\) |
−0.613062 | + | 0.790034i | \(0.710063\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.00000 | + | 6.92820i | −0.143684 | + | 0.248868i | ||||
\(776\) | 5.00000 | 0.179490 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −21.0000 | −0.752886 | ||||||||
\(779\) | 9.00000 | − | 15.5885i | 0.322458 | − | 0.558514i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 4.50000 | − | 7.79423i | 0.160920 | − | 0.278721i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | − | 6.92820i | 0.0357143 | − | 0.247436i | ||||
\(785\) | −12.0000 | −0.428298 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.0000 | − | 32.9090i | −0.677277 | − | 1.17308i | −0.975798 | − | 0.218675i | \(-0.929827\pi\) |
0.298521 | − | 0.954403i | \(-0.403507\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −39.0000 | −1.38756 | ||||||||
\(791\) | 9.00000 | + | 46.7654i | 0.320003 | + | 1.66279i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.00000 | + | 8.66025i | −0.177555 | + | 0.307535i | ||||
\(794\) | 14.0000 | + | 24.2487i | 0.496841 | + | 0.860555i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.00000 | − | 8.66025i | 0.177220 | − | 0.306955i | ||||
\(797\) | −45.0000 | −1.59398 | −0.796991 | − | 0.603991i | \(-0.793576\pi\) | ||||
−0.796991 | + | 0.603991i | \(0.793576\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.00000 | −0.318397 | ||||||||
\(800\) | −2.00000 | + | 3.46410i | −0.0707107 | + | 0.122474i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6.00000 | − | 10.3923i | −0.211867 | − | 0.366965i | ||||
\(803\) | 1.00000 | − | 1.73205i | 0.0352892 | − | 0.0611227i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −18.0000 | + | 15.5885i | −0.634417 | + | 0.549421i | ||||
\(806\) | 4.00000 | 0.140894 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.00000 | + | 10.3923i | 0.211079 | + | 0.365600i | ||||
\(809\) | 19.5000 | + | 33.7750i | 0.685583 | + | 1.18747i | 0.973253 | + | 0.229736i | \(0.0737862\pi\) |
−0.287670 | + | 0.957730i | \(0.592880\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.00000 | 0.0702295 | 0.0351147 | − | 0.999383i | \(-0.488820\pi\) | ||||
0.0351147 | + | 0.999383i | \(0.488820\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.00000 | − | 6.92820i | 0.140200 | − | 0.242833i | ||||
\(815\) | 28.5000 | + | 49.3634i | 0.998311 | + | 1.72913i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.00000 | − | 6.92820i | 0.139942 | − | 0.242387i | ||||
\(818\) | 2.00000 | 0.0699284 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −27.0000 | −0.942881 | ||||||||
\(821\) | −15.0000 | + | 25.9808i | −0.523504 | + | 0.906735i | 0.476122 | + | 0.879379i | \(0.342042\pi\) |
−0.999626 | + | 0.0273557i | \(0.991291\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.0000 | + | 29.4449i | 0.592583 | + | 1.02638i | 0.993883 | + | 0.110437i | \(0.0352250\pi\) |
−0.401300 | + | 0.915947i | \(0.631442\pi\) | |||||||
\(824\) | −10.0000 | + | 17.3205i | −0.348367 | + | 0.603388i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.00000 | − | 15.5885i | −0.104383 | − | 0.542392i | ||||
\(827\) | 45.0000 | 1.56480 | 0.782402 | − | 0.622774i | \(-0.213994\pi\) | ||||
0.782402 | + | 0.622774i | \(0.213994\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.0000 | + | 45.0333i | 0.903017 | + | 1.56407i | 0.823557 | + | 0.567234i | \(0.191986\pi\) |
0.0794606 | + | 0.996838i | \(0.474680\pi\) | |||||||
\(830\) | −13.5000 | − | 23.3827i | −0.468592 | − | 0.811625i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.00000 | 0.0693375 | ||||||||
\(833\) | −16.5000 | − | 12.9904i | −0.571691 | − | 0.450090i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.00000 | + | 1.73205i | 0.0345857 | + | 0.0599042i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −9.00000 | + | 15.5885i | −0.310900 | + | 0.538494i | ||||
\(839\) | 9.00000 | 0.310715 | 0.155357 | − | 0.987858i | \(-0.450347\pi\) | ||||
0.155357 | + | 0.987858i | \(0.450347\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | −4.00000 | + | 6.92820i | −0.137849 | + | 0.238762i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10.0000 | − | 17.3205i | −0.344214 | − | 0.596196i | ||||
\(845\) | 13.5000 | − | 23.3827i | 0.464414 | − | 0.804389i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.50000 | + | 0.866025i | 0.0859010 | + | 0.0297570i | ||||
\(848\) | 6.00000 | 0.206041 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.00000 | + | 10.3923i | 0.205798 | + | 0.356453i | ||||
\(851\) | −12.0000 | − | 20.7846i | −0.411355 | − | 0.712487i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.0000 | −0.650548 | −0.325274 | − | 0.945620i | \(-0.605456\pi\) | ||||
−0.325274 | + | 0.945620i | \(0.605456\pi\) | |||||||
\(854\) | −10.0000 | + | 8.66025i | −0.342193 | + | 0.296348i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.50000 | + | 2.59808i | −0.0512689 | + | 0.0888004i | ||||
\(857\) | 19.5000 | + | 33.7750i | 0.666107 | + | 1.15373i | 0.978984 | + | 0.203938i | \(0.0653741\pi\) |
−0.312877 | + | 0.949794i | \(0.601293\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.50000 | − | 6.06218i | 0.119418 | − | 0.206839i | −0.800119 | − | 0.599841i | \(-0.795230\pi\) |
0.919537 | + | 0.393003i | \(0.128564\pi\) | |||||||
\(860\) | −12.0000 | −0.409197 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −30.0000 | −1.02180 | ||||||||
\(863\) | 16.5000 | − | 28.5788i | 0.561667 | − | 0.972835i | −0.435685 | − | 0.900099i | \(-0.643494\pi\) |
0.997351 | − | 0.0727356i | \(-0.0231729\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.00000 | + | 15.5885i | 0.306009 | + | 0.530023i | ||||
\(866\) | −17.5000 | + | 30.3109i | −0.594674 | + | 1.03001i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5.00000 | + | 1.73205i | 0.169711 | + | 0.0587896i | ||||
\(869\) | 13.0000 | 0.440995 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.0000 | − | 19.0526i | −0.372721 | − | 0.645571i | ||||
\(872\) | 0.500000 | + | 0.866025i | 0.0169321 | + | 0.0293273i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6.00000 | 0.202953 | ||||||||
\(875\) | 1.50000 | + | 7.79423i | 0.0507093 | + | 0.263493i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.50000 | + | 9.52628i | −0.185722 | + | 0.321680i | −0.943820 | − | 0.330461i | \(-0.892796\pi\) |
0.758098 | + | 0.652141i | \(0.226129\pi\) | |||||||
\(878\) | −17.5000 | − | 30.3109i | −0.590596 | − | 1.02294i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.50000 | − | 2.59808i | 0.0505650 | − | 0.0875811i | ||||
\(881\) | −54.0000 | −1.81931 | −0.909653 | − | 0.415369i | \(-0.863653\pi\) | ||||
−0.909653 | + | 0.415369i | \(0.863653\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.00000 | −0.235569 | −0.117784 | − | 0.993039i | \(-0.537579\pi\) | ||||
−0.117784 | + | 0.993039i | \(0.537579\pi\) | |||||||
\(884\) | 3.00000 | − | 5.19615i | 0.100901 | − | 0.174766i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12.0000 | + | 20.7846i | 0.403148 | + | 0.698273i | ||||
\(887\) | −15.0000 | + | 25.9808i | −0.503651 | + | 0.872349i | 0.496340 | + | 0.868128i | \(0.334677\pi\) |
−0.999991 | + | 0.00422062i | \(0.998657\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.50000 | + | 49.3634i | 0.318620 | + | 1.65560i | ||||
\(890\) | 36.0000 | 1.20672 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −13.0000 | − | 22.5167i | −0.435272 | − | 0.753914i | ||||
\(893\) | −3.00000 | − | 5.19615i | −0.100391 | − | 0.173883i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.0000 | 0.601674 | ||||||||
\(896\) | 2.50000 | + | 0.866025i | 0.0835191 | + | 0.0289319i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 18.0000 | − | 31.1769i | 0.600668 | − | 1.04039i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.00000 | − | 15.5885i | 0.299833 | − | 0.519327i | ||||
\(902\) | 9.00000 | 0.299667 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −18.0000 | −0.598671 | ||||||||
\(905\) | −30.0000 | + | 51.9615i | −0.997234 | + | 1.72726i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.5000 | − | 35.5070i | −0.680691 | − | 1.17899i | −0.974770 | − | 0.223211i | \(-0.928346\pi\) |
0.294079 | − | 0.955781i | \(-0.404987\pi\) | |||||||
\(908\) | −7.50000 | + | 12.9904i | −0.248896 | + | 0.431101i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −12.0000 | + | 10.3923i | −0.397796 | + | 0.344502i | ||||
\(911\) | −27.0000 | −0.894550 | −0.447275 | − | 0.894397i | \(-0.647605\pi\) | ||||
−0.447275 | + | 0.894397i | \(0.647605\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.50000 | + | 7.79423i | 0.148928 | + | 0.257951i | ||||
\(914\) | 20.0000 | + | 34.6410i | 0.661541 | + | 1.14582i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 20.0000 | 0.660819 | ||||||||
\(917\) | 30.0000 | + | 10.3923i | 0.990687 | + | 0.343184i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.5000 | − | 32.0429i | 0.610259 | − | 1.05700i | −0.380938 | − | 0.924601i | \(-0.624399\pi\) |
0.991197 | − | 0.132398i | \(-0.0422678\pi\) | |||||||
\(920\) | −4.50000 | − | 7.79423i | −0.148361 | − | 0.256968i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −9.00000 | + | 15.5885i | −0.296399 | + | 0.513378i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 32.0000 | 1.05215 | ||||||||
\(926\) | 2.00000 | − | 3.46410i | 0.0657241 | − | 0.113837i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.00000 | − | 5.19615i | 0.0984268 | − | 0.170480i | −0.812607 | − | 0.582812i | \(-0.801952\pi\) |
0.911034 | + | 0.412332i | \(0.135286\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.00000 | − | 13.8564i | 0.0655474 | − | 0.454125i | ||||
\(932\) | 21.0000 | 0.687878 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 21.0000 | + | 36.3731i | 0.687141 | + | 1.19016i | ||||
\(935\) | −4.50000 | − | 7.79423i | −0.147166 | − | 0.254899i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.0000 | 0.849383 | 0.424691 | − | 0.905338i | \(-0.360383\pi\) | ||||
0.424691 | + | 0.905338i | \(0.360383\pi\) | |||||||
\(938\) | −5.50000 | − | 28.5788i | −0.179581 | − | 0.933132i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.50000 | + | 7.79423i | −0.146774 | + | 0.254220i | ||||
\(941\) | 15.0000 | + | 25.9808i | 0.488986 | + | 0.846949i | 0.999920 | − | 0.0126715i | \(-0.00403357\pi\) |
−0.510934 | + | 0.859620i | \(0.670700\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.5000 | − | 23.3827i | 0.439620 | − | 0.761445i | ||||
\(944\) | 6.00000 | 0.195283 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.00000 | 0.130051 | ||||||||
\(947\) | 21.0000 | − | 36.3731i | 0.682408 | − | 1.18197i | −0.291835 | − | 0.956469i | \(-0.594266\pi\) |
0.974244 | − | 0.225497i | \(-0.0724007\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.00000 | − | 3.46410i | −0.0649227 | − | 0.112449i | ||||
\(950\) | −4.00000 | + | 6.92820i | −0.129777 | + | 0.224781i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6.00000 | − | 5.19615i | 0.194461 | − | 0.168408i | ||||
\(953\) | 45.0000 | 1.45769 | 0.728846 | − | 0.684677i | \(-0.240057\pi\) | ||||
0.728846 | + | 0.684677i | \(0.240057\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18.0000 | − | 31.1769i | −0.582466 | − | 1.00886i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −12.0000 | −0.387702 | ||||||||
\(959\) | −12.0000 | + | 10.3923i | −0.387500 | + | 0.335585i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.5000 | − | 23.3827i | 0.435484 | − | 0.754280i | ||||
\(962\) | −8.00000 | − | 13.8564i | −0.257930 | − | 0.446748i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.00000 | − | 3.46410i | 0.0644157 | − | 0.111571i | ||||
\(965\) | −48.0000 | −1.54517 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 47.0000 | 1.51142 | 0.755709 | − | 0.654907i | \(-0.227292\pi\) | ||||
0.755709 | + | 0.654907i | \(0.227292\pi\) | |||||||
\(968\) | −0.500000 | + | 0.866025i | −0.0160706 | + | 0.0278351i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −7.50000 | − | 12.9904i | −0.240810 | − | 0.417096i | ||||
\(971\) | 3.00000 | − | 5.19615i | 0.0962746 | − | 0.166752i | −0.813865 | − | 0.581054i | \(-0.802641\pi\) |
0.910140 | + | 0.414301i | \(0.135974\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.00000 | − | 5.19615i | −0.0320585 | − | 0.166581i | ||||
\(974\) | 38.0000 | 1.21760 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.50000 | − | 4.33013i | −0.0800230 | − | 0.138604i | ||||
\(977\) | −3.00000 | − | 5.19615i | −0.0959785 | − | 0.166240i | 0.814038 | − | 0.580812i | \(-0.197265\pi\) |
−0.910017 | + | 0.414572i | \(0.863931\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.0000 | −0.383522 | ||||||||
\(980\) | −19.5000 | + | 7.79423i | −0.622905 | + | 0.248978i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.50000 | + | 7.79423i | −0.143601 | + | 0.248724i | ||||
\(983\) | 10.5000 | + | 18.1865i | 0.334898 | + | 0.580060i | 0.983465 | − | 0.181097i | \(-0.0579648\pi\) |
−0.648567 | + | 0.761157i | \(0.724631\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.00000 | 0.127257 | ||||||||
\(989\) | 6.00000 | − | 10.3923i | 0.190789 | − | 0.330456i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.00000 | − | 6.92820i | −0.127064 | − | 0.220082i | 0.795474 | − | 0.605988i | \(-0.207222\pi\) |
−0.922538 | + | 0.385906i | \(0.873889\pi\) | |||||||
\(992\) | −1.00000 | + | 1.73205i | −0.0317500 | + | 0.0549927i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −30.0000 | −0.951064 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25.0000 | − | 43.3013i | −0.791758 | − | 1.37136i | −0.924878 | − | 0.380265i | \(-0.875833\pi\) |
0.133120 | − | 0.991100i | \(-0.457501\pi\) | |||||||
\(998\) | −10.0000 | − | 17.3205i | −0.316544 | − | 0.548271i | ||||
\(999\) | 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.b.793.1 | ✓ | 2 | |
3.2 | odd | 2 | 1386.2.k.p.793.1 | yes | 2 | ||
7.2 | even | 3 | 9702.2.a.cd.1.1 | 1 | |||
7.4 | even | 3 | inner | 1386.2.k.b.991.1 | yes | 2 | |
7.5 | odd | 6 | 9702.2.a.bc.1.1 | 1 | |||
21.2 | odd | 6 | 9702.2.a.c.1.1 | 1 | |||
21.5 | even | 6 | 9702.2.a.z.1.1 | 1 | |||
21.11 | odd | 6 | 1386.2.k.p.991.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1386.2.k.b.793.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1386.2.k.b.991.1 | yes | 2 | 7.4 | even | 3 | inner | |
1386.2.k.p.793.1 | yes | 2 | 3.2 | odd | 2 | ||
1386.2.k.p.991.1 | yes | 2 | 21.11 | odd | 6 | ||
9702.2.a.c.1.1 | 1 | 21.2 | odd | 6 | |||
9702.2.a.z.1.1 | 1 | 21.5 | even | 6 | |||
9702.2.a.bc.1.1 | 1 | 7.5 | odd | 6 | |||
9702.2.a.cd.1.1 | 1 | 7.2 | even | 3 |