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.i.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 | ||||
\(5\) | 1.00000 | + | 1.73205i | 0.447214 | + | 0.774597i | 0.998203 | − | 0.0599153i | \(-0.0190830\pi\) |
−0.550990 | + | 0.834512i | \(0.685750\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | − | 1.73205i | 0.755929 | − | 0.654654i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | − | 1.73205i | 0.316228 | − | 0.547723i | ||||
\(11\) | 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 | −0.624780 | − | 0.780801i | \(-0.714811\pi\) |
0.988583 | + | 0.150675i | \(0.0481447\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.50000 | − | 6.06218i | −0.802955 | − | 1.39076i | −0.917663 | − | 0.397360i | \(-0.869927\pi\) |
0.114708 | − | 0.993399i | \(-0.463407\pi\) | |||||||
\(20\) | −2.00000 | −0.447214 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 3.50000 | + | 6.06218i | 0.729800 | + | 1.26405i | 0.956967 | + | 0.290196i | \(0.0937204\pi\) |
−0.227167 | + | 0.973856i | \(0.572946\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | −1.00000 | − | 1.73205i | −0.196116 | − | 0.339683i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.500000 | + | 2.59808i | 0.0944911 | + | 0.490990i | ||||
\(29\) | −5.00000 | −0.928477 | −0.464238 | − | 0.885710i | \(-0.653672\pi\) | ||||
−0.464238 | + | 0.885710i | \(0.653672\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | + | 1.73205i | −0.179605 | + | 0.311086i | −0.941745 | − | 0.336327i | \(-0.890815\pi\) |
0.762140 | + | 0.647412i | \(0.224149\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.00000 | −0.514496 | ||||||||
\(35\) | 5.00000 | + | 1.73205i | 0.845154 | + | 0.292770i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.50000 | − | 2.59808i | −0.246598 | − | 0.427121i | 0.715981 | − | 0.698119i | \(-0.245980\pi\) |
−0.962580 | + | 0.270998i | \(0.912646\pi\) | |||||||
\(38\) | −3.50000 | + | 6.06218i | −0.567775 | + | 0.983415i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | + | 1.73205i | 0.158114 | + | 0.273861i | ||||
\(41\) | 6.00000 | 0.937043 | 0.468521 | − | 0.883452i | \(-0.344787\pi\) | ||||
0.468521 | + | 0.883452i | \(0.344787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.0000 | 1.67748 | 0.838742 | − | 0.544529i | \(-0.183292\pi\) | ||||
0.838742 | + | 0.544529i | \(0.183292\pi\) | |||||||
\(44\) | 0.500000 | + | 0.866025i | 0.0753778 | + | 0.130558i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.50000 | − | 6.06218i | 0.516047 | − | 0.893819i | ||||
\(47\) | 3.50000 | + | 6.06218i | 0.510527 | + | 0.884260i | 0.999926 | + | 0.0121990i | \(0.00388317\pi\) |
−0.489398 | + | 0.872060i | \(0.662783\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | − | 6.92820i | 0.142857 | − | 0.989743i | ||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.00000 | + | 1.73205i | −0.138675 | + | 0.240192i | ||||
\(53\) | 2.00000 | − | 3.46410i | 0.274721 | − | 0.475831i | −0.695344 | − | 0.718677i | \(-0.744748\pi\) |
0.970065 | + | 0.242846i | \(0.0780811\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.00000 | 0.269680 | ||||||||
\(56\) | 2.00000 | − | 1.73205i | 0.267261 | − | 0.231455i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.50000 | + | 4.33013i | 0.328266 | + | 0.568574i | ||||
\(59\) | −5.50000 | + | 9.52628i | −0.716039 | + | 1.24022i | 0.246518 | + | 0.969138i | \(0.420713\pi\) |
−0.962557 | + | 0.271078i | \(0.912620\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.00000 | − | 8.66025i | −0.640184 | − | 1.10883i | −0.985391 | − | 0.170305i | \(-0.945525\pi\) |
0.345207 | − | 0.938527i | \(-0.387809\pi\) | |||||||
\(62\) | 2.00000 | 0.254000 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.00000 | + | 3.46410i | 0.248069 | + | 0.429669i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.00000 | − | 3.46410i | 0.244339 | − | 0.423207i | −0.717607 | − | 0.696449i | \(-0.754762\pi\) |
0.961946 | + | 0.273241i | \(0.0880957\pi\) | |||||||
\(68\) | 1.50000 | + | 2.59808i | 0.181902 | + | 0.315063i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.00000 | − | 5.19615i | −0.119523 | − | 0.621059i | ||||
\(71\) | −5.00000 | −0.593391 | −0.296695 | − | 0.954972i | \(-0.595885\pi\) | ||||
−0.296695 | + | 0.954972i | \(0.595885\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.00000 | − | 6.92820i | 0.468165 | − | 0.810885i | −0.531174 | − | 0.847263i | \(-0.678249\pi\) |
0.999338 | + | 0.0363782i | \(0.0115821\pi\) | |||||||
\(74\) | −1.50000 | + | 2.59808i | −0.174371 | + | 0.302020i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.00000 | 0.802955 | ||||||||
\(77\) | −0.500000 | − | 2.59808i | −0.0569803 | − | 0.296078i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000 | + | 6.92820i | 0.450035 | + | 0.779484i | 0.998388 | − | 0.0567635i | \(-0.0180781\pi\) |
−0.548352 | + | 0.836247i | \(0.684745\pi\) | |||||||
\(80\) | 1.00000 | − | 1.73205i | 0.111803 | − | 0.193649i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.00000 | − | 5.19615i | −0.331295 | − | 0.573819i | ||||
\(83\) | 14.0000 | 1.53670 | 0.768350 | − | 0.640030i | \(-0.221078\pi\) | ||||
0.768350 | + | 0.640030i | \(0.221078\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.00000 | 0.650791 | ||||||||
\(86\) | −5.50000 | − | 9.52628i | −0.593080 | − | 1.02725i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.500000 | − | 0.866025i | 0.0533002 | − | 0.0923186i | ||||
\(89\) | −1.00000 | − | 1.73205i | −0.106000 | − | 0.183597i | 0.808146 | − | 0.588982i | \(-0.200471\pi\) |
−0.914146 | + | 0.405385i | \(0.867138\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.00000 | − | 3.46410i | 0.419314 | − | 0.363137i | ||||
\(92\) | −7.00000 | −0.729800 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.50000 | − | 6.06218i | 0.360997 | − | 0.625266i | ||||
\(95\) | 7.00000 | − | 12.1244i | 0.718185 | − | 1.24393i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.0000 | 1.52302 | 0.761510 | − | 0.648154i | \(-0.224459\pi\) | ||||
0.761510 | + | 0.648154i | \(0.224459\pi\) | |||||||
\(98\) | −6.50000 | + | 2.59808i | −0.656599 | + | 0.262445i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.500000 | + | 0.866025i | 0.0500000 | + | 0.0866025i | ||||
\(101\) | −1.50000 | + | 2.59808i | −0.149256 | + | 0.258518i | −0.930953 | − | 0.365140i | \(-0.881021\pi\) |
0.781697 | + | 0.623658i | \(0.214354\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.00000 | + | 8.66025i | 0.492665 | + | 0.853320i | 0.999964 | − | 0.00844953i | \(-0.00268960\pi\) |
−0.507300 | + | 0.861770i | \(0.669356\pi\) | |||||||
\(104\) | 2.00000 | 0.196116 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.00000 | −0.388514 | ||||||||
\(107\) | −9.00000 | − | 15.5885i | −0.870063 | − | 1.50699i | −0.861931 | − | 0.507026i | \(-0.830745\pi\) |
−0.00813215 | − | 0.999967i | \(-0.502589\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.00000 | + | 3.46410i | −0.191565 | + | 0.331801i | −0.945769 | − | 0.324840i | \(-0.894690\pi\) |
0.754204 | + | 0.656640i | \(0.228023\pi\) | |||||||
\(110\) | −1.00000 | − | 1.73205i | −0.0953463 | − | 0.165145i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.50000 | − | 0.866025i | −0.236228 | − | 0.0818317i | ||||
\(113\) | 2.00000 | 0.188144 | 0.0940721 | − | 0.995565i | \(-0.470012\pi\) | ||||
0.0940721 | + | 0.995565i | \(0.470012\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.00000 | + | 12.1244i | −0.652753 | + | 1.13060i | ||||
\(116\) | 2.50000 | − | 4.33013i | 0.232119 | − | 0.402042i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 11.0000 | 1.01263 | ||||||||
\(119\) | −1.50000 | − | 7.79423i | −0.137505 | − | 0.714496i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | −5.00000 | + | 8.66025i | −0.452679 | + | 0.784063i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.00000 | − | 1.73205i | −0.0898027 | − | 0.155543i | ||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | 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 | ||||||||
\(130\) | 2.00000 | − | 3.46410i | 0.175412 | − | 0.303822i | ||||
\(131\) | 4.00000 | + | 6.92820i | 0.349482 | + | 0.605320i | 0.986157 | − | 0.165812i | \(-0.0530244\pi\) |
−0.636676 | + | 0.771132i | \(0.719691\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −17.5000 | − | 6.06218i | −1.51744 | − | 0.525657i | ||||
\(134\) | −4.00000 | −0.345547 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.50000 | − | 2.59808i | 0.128624 | − | 0.222783i | ||||
\(137\) | −3.00000 | + | 5.19615i | −0.256307 | + | 0.443937i | −0.965250 | − | 0.261329i | \(-0.915839\pi\) |
0.708942 | + | 0.705266i | \(0.249173\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.0000 | 1.44192 | 0.720961 | − | 0.692976i | \(-0.243701\pi\) | ||||
0.720961 | + | 0.692976i | \(0.243701\pi\) | |||||||
\(140\) | −4.00000 | + | 3.46410i | −0.338062 | + | 0.292770i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.50000 | + | 4.33013i | 0.209795 | + | 0.363376i | ||||
\(143\) | 1.00000 | − | 1.73205i | 0.0836242 | − | 0.144841i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.00000 | − | 8.66025i | −0.415227 | − | 0.719195i | ||||
\(146\) | −8.00000 | −0.662085 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.00000 | 0.246598 | ||||||||
\(149\) | −8.50000 | − | 14.7224i | −0.696347 | − | 1.20611i | −0.969724 | − | 0.244202i | \(-0.921474\pi\) |
0.273377 | − | 0.961907i | \(-0.411859\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.50000 | − | 4.33013i | 0.203447 | − | 0.352381i | −0.746190 | − | 0.665733i | \(-0.768119\pi\) |
0.949637 | + | 0.313353i | \(0.101452\pi\) | |||||||
\(152\) | −3.50000 | − | 6.06218i | −0.283887 | − | 0.491708i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.00000 | + | 1.73205i | −0.161165 | + | 0.139573i | ||||
\(155\) | −4.00000 | −0.321288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.500000 | + | 0.866025i | −0.0399043 | + | 0.0691164i | −0.885288 | − | 0.465044i | \(-0.846039\pi\) |
0.845383 | + | 0.534160i | \(0.179372\pi\) | |||||||
\(158\) | 4.00000 | − | 6.92820i | 0.318223 | − | 0.551178i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.00000 | −0.158114 | ||||||||
\(161\) | 17.5000 | + | 6.06218i | 1.37919 | + | 0.477767i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.00000 | − | 5.19615i | −0.234978 | − | 0.406994i | 0.724288 | − | 0.689497i | \(-0.242169\pi\) |
−0.959266 | + | 0.282503i | \(0.908835\pi\) | |||||||
\(164\) | −3.00000 | + | 5.19615i | −0.234261 | + | 0.405751i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.00000 | − | 12.1244i | −0.543305 | − | 0.941033i | ||||
\(167\) | −10.0000 | −0.773823 | −0.386912 | − | 0.922117i | \(-0.626458\pi\) | ||||
−0.386912 | + | 0.922117i | \(0.626458\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | −3.00000 | − | 5.19615i | −0.230089 | − | 0.398527i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.50000 | + | 9.52628i | −0.419371 | + | 0.726372i | ||||
\(173\) | −7.00000 | − | 12.1244i | −0.532200 | − | 0.921798i | −0.999293 | − | 0.0375896i | \(-0.988032\pi\) |
0.467093 | − | 0.884208i | \(-0.345301\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.500000 | − | 2.59808i | −0.0377964 | − | 0.196396i | ||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.00000 | + | 1.73205i | −0.0749532 | + | 0.129823i | ||||
\(179\) | 4.50000 | − | 7.79423i | 0.336346 | − | 0.582568i | −0.647397 | − | 0.762153i | \(-0.724142\pi\) |
0.983742 | + | 0.179585i | \(0.0574756\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | −5.00000 | − | 1.73205i | −0.370625 | − | 0.128388i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.50000 | + | 6.06218i | 0.258023 | + | 0.446910i | ||||
\(185\) | 3.00000 | − | 5.19615i | 0.220564 | − | 0.382029i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.50000 | − | 2.59808i | −0.109691 | − | 0.189990i | ||||
\(188\) | −7.00000 | −0.510527 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −14.0000 | −1.01567 | ||||||||
\(191\) | 4.00000 | + | 6.92820i | 0.289430 | + | 0.501307i | 0.973674 | − | 0.227946i | \(-0.0732010\pi\) |
−0.684244 | + | 0.729253i | \(0.739868\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.0000 | + | 20.7846i | −0.863779 | + | 1.49611i | 0.00447566 | + | 0.999990i | \(0.498575\pi\) |
−0.868255 | + | 0.496119i | \(0.834758\pi\) | |||||||
\(194\) | −7.50000 | − | 12.9904i | −0.538469 | − | 0.932655i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.50000 | + | 4.33013i | 0.392857 | + | 0.309295i | ||||
\(197\) | 15.0000 | 1.06871 | 0.534353 | − | 0.845262i | \(-0.320555\pi\) | ||||
0.534353 | + | 0.845262i | \(0.320555\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.00000 | + | 8.66025i | −0.354441 | + | 0.613909i | −0.987022 | − | 0.160585i | \(-0.948662\pi\) |
0.632581 | + | 0.774494i | \(0.281995\pi\) | |||||||
\(200\) | 0.500000 | − | 0.866025i | 0.0353553 | − | 0.0612372i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.00000 | 0.211079 | ||||||||
\(203\) | −10.0000 | + | 8.66025i | −0.701862 | + | 0.607831i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.00000 | + | 10.3923i | 0.419058 | + | 0.725830i | ||||
\(206\) | 5.00000 | − | 8.66025i | 0.348367 | − | 0.603388i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.00000 | − | 1.73205i | −0.0693375 | − | 0.120096i | ||||
\(209\) | −7.00000 | −0.484200 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.0000 | 1.37686 | 0.688428 | − | 0.725304i | \(-0.258301\pi\) | ||||
0.688428 | + | 0.725304i | \(0.258301\pi\) | |||||||
\(212\) | 2.00000 | + | 3.46410i | 0.137361 | + | 0.237915i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −9.00000 | + | 15.5885i | −0.615227 | + | 1.06561i | ||||
\(215\) | 11.0000 | + | 19.0526i | 0.750194 | + | 1.29937i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.00000 | + | 5.19615i | 0.0678844 | + | 0.352738i | ||||
\(218\) | 4.00000 | 0.270914 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.00000 | + | 1.73205i | −0.0674200 | + | 0.116775i | ||||
\(221\) | 3.00000 | − | 5.19615i | 0.201802 | − | 0.349531i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.0000 | −0.937509 | −0.468755 | − | 0.883328i | \(-0.655297\pi\) | ||||
−0.468755 | + | 0.883328i | \(0.655297\pi\) | |||||||
\(224\) | 0.500000 | + | 2.59808i | 0.0334077 | + | 0.173591i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.00000 | − | 1.73205i | −0.0665190 | − | 0.115214i | ||||
\(227\) | −5.00000 | + | 8.66025i | −0.331862 | + | 0.574801i | −0.982877 | − | 0.184263i | \(-0.941010\pi\) |
0.651015 | + | 0.759065i | \(0.274343\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.00000 | + | 8.66025i | 0.330409 | + | 0.572286i | 0.982592 | − | 0.185776i | \(-0.0594799\pi\) |
−0.652183 | + | 0.758062i | \(0.726147\pi\) | |||||||
\(230\) | 14.0000 | 0.923133 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.00000 | −0.328266 | ||||||||
\(233\) | 4.50000 | + | 7.79423i | 0.294805 | + | 0.510617i | 0.974939 | − | 0.222470i | \(-0.0714120\pi\) |
−0.680135 | + | 0.733087i | \(0.738079\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.00000 | + | 12.1244i | −0.456630 | + | 0.790906i | ||||
\(236\) | −5.50000 | − | 9.52628i | −0.358020 | − | 0.620108i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −6.00000 | + | 5.19615i | −0.388922 | + | 0.336817i | ||||
\(239\) | −10.0000 | −0.646846 | −0.323423 | − | 0.946254i | \(-0.604834\pi\) | ||||
−0.323423 | + | 0.946254i | \(0.604834\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.00000 | − | 3.46410i | 0.128831 | − | 0.223142i | −0.794393 | − | 0.607404i | \(-0.792211\pi\) |
0.923224 | + | 0.384262i | \(0.125544\pi\) | |||||||
\(242\) | −0.500000 | + | 0.866025i | −0.0321412 | + | 0.0556702i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 10.0000 | 0.640184 | ||||||||
\(245\) | 13.0000 | − | 5.19615i | 0.830540 | − | 0.331970i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.00000 | − | 12.1244i | −0.445399 | − | 0.771454i | ||||
\(248\) | −1.00000 | + | 1.73205i | −0.0635001 | + | 0.109985i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.00000 | − | 10.3923i | −0.379473 | − | 0.657267i | ||||
\(251\) | 5.00000 | 0.315597 | 0.157799 | − | 0.987471i | \(-0.449560\pi\) | ||||
0.157799 | + | 0.987471i | \(0.449560\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.00000 | 0.440086 | ||||||||
\(254\) | 9.50000 | + | 16.4545i | 0.596083 | + | 1.03245i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 7.00000 | + | 12.1244i | 0.436648 | + | 0.756297i | 0.997429 | − | 0.0716680i | \(-0.0228322\pi\) |
−0.560781 | + | 0.827964i | \(0.689499\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.50000 | − | 2.59808i | −0.466027 | − | 0.161437i | ||||
\(260\) | −4.00000 | −0.248069 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.00000 | − | 6.92820i | 0.247121 | − | 0.428026i | ||||
\(263\) | −15.0000 | + | 25.9808i | −0.924940 | + | 1.60204i | −0.133281 | + | 0.991078i | \(0.542551\pi\) |
−0.791658 | + | 0.610964i | \(0.790782\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.00000 | 0.491436 | ||||||||
\(266\) | 3.50000 | + | 18.1865i | 0.214599 | + | 1.11509i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.00000 | + | 3.46410i | 0.122169 | + | 0.211604i | ||||
\(269\) | 10.0000 | − | 17.3205i | 0.609711 | − | 1.05605i | −0.381577 | − | 0.924337i | \(-0.624619\pi\) |
0.991288 | − | 0.131713i | \(-0.0420477\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.00000 | − | 6.92820i | −0.242983 | − | 0.420858i | 0.718580 | − | 0.695444i | \(-0.244792\pi\) |
−0.961563 | + | 0.274586i | \(0.911459\pi\) | |||||||
\(272\) | −3.00000 | −0.181902 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.00000 | 0.362473 | ||||||||
\(275\) | −0.500000 | − | 0.866025i | −0.0301511 | − | 0.0522233i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.0000 | + | 20.7846i | −0.721010 | + | 1.24883i | 0.239585 | + | 0.970875i | \(0.422989\pi\) |
−0.960595 | + | 0.277951i | \(0.910345\pi\) | |||||||
\(278\) | −8.50000 | − | 14.7224i | −0.509796 | − | 0.882993i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.00000 | + | 1.73205i | 0.298807 | + | 0.103510i | ||||
\(281\) | 3.00000 | 0.178965 | 0.0894825 | − | 0.995988i | \(-0.471479\pi\) | ||||
0.0894825 | + | 0.995988i | \(0.471479\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.0000 | + | 20.7846i | −0.713326 | + | 1.23552i | 0.250276 | + | 0.968175i | \(0.419479\pi\) |
−0.963602 | + | 0.267342i | \(0.913855\pi\) | |||||||
\(284\) | 2.50000 | − | 4.33013i | 0.148348 | − | 0.256946i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.00000 | −0.118262 | ||||||||
\(287\) | 12.0000 | − | 10.3923i | 0.708338 | − | 0.613438i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.00000 | + | 6.92820i | 0.235294 | + | 0.407541i | ||||
\(290\) | −5.00000 | + | 8.66025i | −0.293610 | + | 0.508548i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.00000 | + | 6.92820i | 0.234082 | + | 0.405442i | ||||
\(293\) | −3.00000 | −0.175262 | −0.0876309 | − | 0.996153i | \(-0.527930\pi\) | ||||
−0.0876309 | + | 0.996153i | \(0.527930\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −22.0000 | −1.28089 | ||||||||
\(296\) | −1.50000 | − | 2.59808i | −0.0871857 | − | 0.151010i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −8.50000 | + | 14.7224i | −0.492392 | + | 0.852848i | ||||
\(299\) | 7.00000 | + | 12.1244i | 0.404820 | + | 0.701170i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 22.0000 | − | 19.0526i | 1.26806 | − | 1.09817i | ||||
\(302\) | −5.00000 | −0.287718 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.50000 | + | 6.06218i | −0.200739 | + | 0.347690i | ||||
\(305\) | 10.0000 | − | 17.3205i | 0.572598 | − | 0.991769i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.0000 | 1.59804 | 0.799022 | − | 0.601302i | \(-0.205351\pi\) | ||||
0.799022 | + | 0.601302i | \(0.205351\pi\) | |||||||
\(308\) | 2.50000 | + | 0.866025i | 0.142451 | + | 0.0493464i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.00000 | + | 3.46410i | 0.113592 | + | 0.196748i | ||||
\(311\) | −13.5000 | + | 23.3827i | −0.765515 | + | 1.32591i | 0.174459 | + | 0.984664i | \(0.444182\pi\) |
−0.939974 | + | 0.341246i | \(0.889151\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.50000 | − | 12.9904i | −0.423925 | − | 0.734260i | 0.572394 | − | 0.819979i | \(-0.306015\pi\) |
−0.996319 | + | 0.0857188i | \(0.972681\pi\) | |||||||
\(314\) | 1.00000 | 0.0564333 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.00000 | −0.450035 | ||||||||
\(317\) | −15.0000 | − | 25.9808i | −0.842484 | − | 1.45922i | −0.887788 | − | 0.460252i | \(-0.847759\pi\) |
0.0453045 | − | 0.998973i | \(-0.485574\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.50000 | + | 4.33013i | −0.139973 | + | 0.242441i | ||||
\(320\) | 1.00000 | + | 1.73205i | 0.0559017 | + | 0.0968246i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.50000 | − | 18.1865i | −0.195047 | − | 1.01350i | ||||
\(323\) | −21.0000 | −1.16847 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000 | − | 1.73205i | 0.0554700 | − | 0.0960769i | ||||
\(326\) | −3.00000 | + | 5.19615i | −0.166155 | + | 0.287788i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.00000 | 0.331295 | ||||||||
\(329\) | 17.5000 | + | 6.06218i | 0.964806 | + | 0.334219i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.00000 | + | 12.1244i | 0.384755 | + | 0.666415i | 0.991735 | − | 0.128302i | \(-0.0409527\pi\) |
−0.606980 | + | 0.794717i | \(0.707619\pi\) | |||||||
\(332\) | −7.00000 | + | 12.1244i | −0.384175 | + | 0.665410i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.00000 | + | 8.66025i | 0.273588 | + | 0.473868i | ||||
\(335\) | 8.00000 | 0.437087 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.00000 | 0.435788 | 0.217894 | − | 0.975972i | \(-0.430081\pi\) | ||||
0.217894 | + | 0.975972i | \(0.430081\pi\) | |||||||
\(338\) | 4.50000 | + | 7.79423i | 0.244768 | + | 0.423950i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.00000 | + | 5.19615i | −0.162698 | + | 0.281801i | ||||
\(341\) | 1.00000 | + | 1.73205i | 0.0541530 | + | 0.0937958i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | − | 15.5885i | −0.539949 | − | 0.841698i | ||||
\(344\) | 11.0000 | 0.593080 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.00000 | + | 12.1244i | −0.376322 | + | 0.651809i | ||||
\(347\) | −12.0000 | + | 20.7846i | −0.644194 | + | 1.11578i | 0.340293 | + | 0.940319i | \(0.389474\pi\) |
−0.984487 | + | 0.175457i | \(0.943860\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.00000 | 0.428230 | 0.214115 | − | 0.976808i | \(-0.431313\pi\) | ||||
0.214115 | + | 0.976808i | \(0.431313\pi\) | |||||||
\(350\) | −2.00000 | + | 1.73205i | −0.106904 | + | 0.0925820i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.500000 | + | 0.866025i | 0.0266501 | + | 0.0461593i | ||||
\(353\) | −5.00000 | + | 8.66025i | −0.266123 | + | 0.460939i | −0.967857 | − | 0.251500i | \(-0.919076\pi\) |
0.701734 | + | 0.712439i | \(0.252409\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.00000 | − | 8.66025i | −0.265372 | − | 0.459639i | ||||
\(356\) | 2.00000 | 0.106000 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.00000 | −0.475665 | ||||||||
\(359\) | 9.00000 | + | 15.5885i | 0.475002 | + | 0.822727i | 0.999590 | − | 0.0286287i | \(-0.00911406\pi\) |
−0.524588 | + | 0.851356i | \(0.675781\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | + | 25.9808i | −0.789474 | + | 1.36741i | ||||
\(362\) | 5.00000 | + | 8.66025i | 0.262794 | + | 0.455173i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.00000 | + | 5.19615i | 0.0524142 | + | 0.272352i | ||||
\(365\) | 16.0000 | 0.837478 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(368\) | 3.50000 | − | 6.06218i | 0.182450 | − | 0.316013i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.00000 | −0.311925 | ||||||||
\(371\) | −2.00000 | − | 10.3923i | −0.103835 | − | 0.539542i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.0000 | + | 19.0526i | 0.569558 | + | 0.986504i | 0.996610 | + | 0.0822766i | \(0.0262191\pi\) |
−0.427051 | + | 0.904227i | \(0.640448\pi\) | |||||||
\(374\) | −1.50000 | + | 2.59808i | −0.0775632 | + | 0.134343i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.50000 | + | 6.06218i | 0.180499 | + | 0.312633i | ||||
\(377\) | −10.0000 | −0.515026 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.0000 | −0.821865 | −0.410932 | − | 0.911666i | \(-0.634797\pi\) | ||||
−0.410932 | + | 0.911666i | \(0.634797\pi\) | |||||||
\(380\) | 7.00000 | + | 12.1244i | 0.359092 | + | 0.621966i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.00000 | − | 6.92820i | 0.204658 | − | 0.354478i | ||||
\(383\) | −15.5000 | − | 26.8468i | −0.792013 | − | 1.37181i | −0.924719 | − | 0.380651i | \(-0.875700\pi\) |
0.132706 | − | 0.991155i | \(-0.457633\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.00000 | − | 3.46410i | 0.203859 | − | 0.176547i | ||||
\(386\) | 24.0000 | 1.22157 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7.50000 | + | 12.9904i | −0.380755 | + | 0.659487i | ||||
\(389\) | 3.00000 | − | 5.19615i | 0.152106 | − | 0.263455i | −0.779895 | − | 0.625910i | \(-0.784728\pi\) |
0.932002 | + | 0.362454i | \(0.118061\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.0000 | 1.06202 | ||||||||
\(392\) | 1.00000 | − | 6.92820i | 0.0505076 | − | 0.349927i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7.50000 | − | 12.9904i | −0.377845 | − | 0.654446i | ||||
\(395\) | −8.00000 | + | 13.8564i | −0.402524 | + | 0.697191i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.50000 | + | 2.59808i | 0.0752828 | + | 0.130394i | 0.901209 | − | 0.433384i | \(-0.142681\pi\) |
−0.825926 | + | 0.563778i | \(0.809347\pi\) | |||||||
\(398\) | 10.0000 | 0.501255 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | −16.0000 | − | 27.7128i | −0.799002 | − | 1.38391i | −0.920267 | − | 0.391292i | \(-0.872028\pi\) |
0.121265 | − | 0.992620i | \(-0.461305\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.00000 | + | 3.46410i | −0.0996271 | + | 0.172559i | ||||
\(404\) | −1.50000 | − | 2.59808i | −0.0746278 | − | 0.129259i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 12.5000 | + | 4.33013i | 0.620365 | + | 0.214901i | ||||
\(407\) | −3.00000 | −0.148704 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.0000 | + | 27.7128i | −0.791149 | + | 1.37031i | 0.134107 | + | 0.990967i | \(0.457183\pi\) |
−0.925256 | + | 0.379344i | \(0.876150\pi\) | |||||||
\(410\) | 6.00000 | − | 10.3923i | 0.296319 | − | 0.513239i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −10.0000 | −0.492665 | ||||||||
\(413\) | 5.50000 | + | 28.5788i | 0.270637 | + | 1.40627i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.0000 | + | 24.2487i | 0.687233 | + | 1.19032i | ||||
\(416\) | −1.00000 | + | 1.73205i | −0.0490290 | + | 0.0849208i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.50000 | + | 6.06218i | 0.171191 | + | 0.296511i | ||||
\(419\) | 3.00000 | 0.146560 | 0.0732798 | − | 0.997311i | \(-0.476653\pi\) | ||||
0.0732798 | + | 0.997311i | \(0.476653\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.0000 | −0.828529 | −0.414265 | − | 0.910156i | \(-0.635961\pi\) | ||||
−0.414265 | + | 0.910156i | \(0.635961\pi\) | |||||||
\(422\) | −10.0000 | − | 17.3205i | −0.486792 | − | 0.843149i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.00000 | − | 3.46410i | 0.0971286 | − | 0.168232i | ||||
\(425\) | −1.50000 | − | 2.59808i | −0.0727607 | − | 0.126025i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −25.0000 | − | 8.66025i | −1.20983 | − | 0.419099i | ||||
\(428\) | 18.0000 | 0.870063 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 11.0000 | − | 19.0526i | 0.530467 | − | 0.918796i | ||||
\(431\) | −20.0000 | + | 34.6410i | −0.963366 | + | 1.66860i | −0.249424 | + | 0.968394i | \(0.580241\pi\) |
−0.713942 | + | 0.700205i | \(0.753092\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.00000 | 0.240285 | 0.120142 | − | 0.992757i | \(-0.461665\pi\) | ||||
0.120142 | + | 0.992757i | \(0.461665\pi\) | |||||||
\(434\) | 4.00000 | − | 3.46410i | 0.192006 | − | 0.166282i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.00000 | − | 3.46410i | −0.0957826 | − | 0.165900i | ||||
\(437\) | 24.5000 | − | 42.4352i | 1.17199 | − | 2.02995i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.50000 | − | 4.33013i | −0.119318 | − | 0.206666i | 0.800179 | − | 0.599761i | \(-0.204738\pi\) |
−0.919498 | + | 0.393095i | \(0.871404\pi\) | |||||||
\(440\) | 2.00000 | 0.0953463 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.00000 | −0.285391 | ||||||||
\(443\) | −20.5000 | − | 35.5070i | −0.973984 | − | 1.68699i | −0.683247 | − | 0.730188i | \(-0.739433\pi\) |
−0.290738 | − | 0.956803i | \(-0.593901\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.00000 | − | 3.46410i | 0.0948091 | − | 0.164214i | ||||
\(446\) | 7.00000 | + | 12.1244i | 0.331460 | + | 0.574105i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.00000 | − | 1.73205i | 0.0944911 | − | 0.0818317i | ||||
\(449\) | −36.0000 | −1.69895 | −0.849473 | − | 0.527633i | \(-0.823080\pi\) | ||||
−0.849473 | + | 0.527633i | \(0.823080\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.00000 | − | 5.19615i | 0.141264 | − | 0.244677i | ||||
\(452\) | −1.00000 | + | 1.73205i | −0.0470360 | + | 0.0814688i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 10.0000 | 0.469323 | ||||||||
\(455\) | 10.0000 | + | 3.46410i | 0.468807 | + | 0.162400i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.0000 | − | 34.6410i | −0.935561 | − | 1.62044i | −0.773631 | − | 0.633636i | \(-0.781562\pi\) |
−0.161929 | − | 0.986802i | \(-0.551772\pi\) | |||||||
\(458\) | 5.00000 | − | 8.66025i | 0.233635 | − | 0.404667i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −7.00000 | − | 12.1244i | −0.326377 | − | 0.565301i | ||||
\(461\) | 13.0000 | 0.605470 | 0.302735 | − | 0.953075i | \(-0.402100\pi\) | ||||
0.302735 | + | 0.953075i | \(0.402100\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.0000 | −1.11537 | −0.557687 | − | 0.830051i | \(-0.688311\pi\) | ||||
−0.557687 | + | 0.830051i | \(0.688311\pi\) | |||||||
\(464\) | 2.50000 | + | 4.33013i | 0.116060 | + | 0.201021i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.50000 | − | 7.79423i | 0.208458 | − | 0.361061i | ||||
\(467\) | −6.50000 | − | 11.2583i | −0.300784 | − | 0.520973i | 0.675530 | − | 0.737333i | \(-0.263915\pi\) |
−0.976314 | + | 0.216359i | \(0.930582\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.00000 | − | 10.3923i | −0.0923514 | − | 0.479872i | ||||
\(470\) | 14.0000 | 0.645772 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.50000 | + | 9.52628i | −0.253158 | + | 0.438483i | ||||
\(473\) | 5.50000 | − | 9.52628i | 0.252890 | − | 0.438019i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.00000 | −0.321182 | ||||||||
\(476\) | 7.50000 | + | 2.59808i | 0.343762 | + | 0.119083i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.00000 | + | 8.66025i | 0.228695 | + | 0.396111i | ||||
\(479\) | −9.00000 | + | 15.5885i | −0.411220 | + | 0.712255i | −0.995023 | − | 0.0996406i | \(-0.968231\pi\) |
0.583803 | + | 0.811895i | \(0.301564\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.00000 | − | 5.19615i | −0.136788 | − | 0.236924i | ||||
\(482\) | −4.00000 | −0.182195 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 15.0000 | + | 25.9808i | 0.681115 | + | 1.17973i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.00000 | + | 15.5885i | −0.407829 | + | 0.706380i | −0.994646 | − | 0.103339i | \(-0.967047\pi\) |
0.586817 | + | 0.809719i | \(0.300381\pi\) | |||||||
\(488\) | −5.00000 | − | 8.66025i | −0.226339 | − | 0.392031i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −11.0000 | − | 8.66025i | −0.496929 | − | 0.391230i | ||||
\(491\) | −26.0000 | −1.17336 | −0.586682 | − | 0.809818i | \(-0.699566\pi\) | ||||
−0.586682 | + | 0.809818i | \(0.699566\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.50000 | + | 12.9904i | −0.337783 | + | 0.585057i | ||||
\(494\) | −7.00000 | + | 12.1244i | −0.314945 | + | 0.545501i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.00000 | 0.0898027 | ||||||||
\(497\) | −10.0000 | + | 8.66025i | −0.448561 | + | 0.388465i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.0000 | + | 34.6410i | 0.895323 | + | 1.55074i | 0.833404 | + | 0.552664i | \(0.186389\pi\) |
0.0619186 | + | 0.998081i | \(0.480278\pi\) | |||||||
\(500\) | −6.00000 | + | 10.3923i | −0.268328 | + | 0.464758i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.50000 | − | 4.33013i | −0.111580 | − | 0.193263i | ||||
\(503\) | −30.0000 | −1.33763 | −0.668817 | − | 0.743427i | \(-0.733199\pi\) | ||||
−0.668817 | + | 0.743427i | \(0.733199\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.00000 | −0.266996 | ||||||||
\(506\) | −3.50000 | − | 6.06218i | −0.155594 | − | 0.269497i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.50000 | − | 16.4545i | 0.421494 | − | 0.730050i | ||||
\(509\) | −2.00000 | − | 3.46410i | −0.0886484 | − | 0.153544i | 0.818292 | − | 0.574803i | \(-0.194921\pi\) |
−0.906940 | + | 0.421260i | \(0.861588\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.00000 | − | 20.7846i | −0.176950 | − | 0.919457i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7.00000 | − | 12.1244i | 0.308757 | − | 0.534782i | ||||
\(515\) | −10.0000 | + | 17.3205i | −0.440653 | + | 0.763233i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.00000 | 0.307860 | ||||||||
\(518\) | 1.50000 | + | 7.79423i | 0.0659062 | + | 0.342459i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.00000 | + | 3.46410i | 0.0877058 | + | 0.151911i | ||||
\(521\) | 9.00000 | − | 15.5885i | 0.394297 | − | 0.682943i | −0.598714 | − | 0.800963i | \(-0.704321\pi\) |
0.993011 | + | 0.118020i | \(0.0376547\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.0000 | + | 17.3205i | 0.437269 | + | 0.757373i | 0.997478 | − | 0.0709788i | \(-0.0226123\pi\) |
−0.560208 | + | 0.828352i | \(0.689279\pi\) | |||||||
\(524\) | −8.00000 | −0.349482 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 30.0000 | 1.30806 | ||||||||
\(527\) | 3.00000 | + | 5.19615i | 0.130682 | + | 0.226348i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.0000 | + | 22.5167i | −0.565217 | + | 0.978985i | ||||
\(530\) | −4.00000 | − | 6.92820i | −0.173749 | − | 0.300942i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 14.0000 | − | 12.1244i | 0.606977 | − | 0.525657i | ||||
\(533\) | 12.0000 | 0.519778 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.0000 | − | 31.1769i | 0.778208 | − | 1.34790i | ||||
\(536\) | 2.00000 | − | 3.46410i | 0.0863868 | − | 0.149626i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −20.0000 | −0.862261 | ||||||||
\(539\) | −5.50000 | − | 4.33013i | −0.236902 | − | 0.186512i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.00000 | − | 13.8564i | −0.343947 | − | 0.595733i | 0.641215 | − | 0.767361i | \(-0.278431\pi\) |
−0.985162 | + | 0.171628i | \(0.945097\pi\) | |||||||
\(542\) | −4.00000 | + | 6.92820i | −0.171815 | + | 0.297592i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.50000 | + | 2.59808i | 0.0643120 | + | 0.111392i | ||||
\(545\) | −8.00000 | −0.342682 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.0000 | −0.470326 | −0.235163 | − | 0.971956i | \(-0.575562\pi\) | ||||
−0.235163 | + | 0.971956i | \(0.575562\pi\) | |||||||
\(548\) | −3.00000 | − | 5.19615i | −0.128154 | − | 0.221969i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.500000 | + | 0.866025i | −0.0213201 | + | 0.0369274i | ||||
\(551\) | 17.5000 | + | 30.3109i | 0.745525 | + | 1.29129i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 20.0000 | + | 6.92820i | 0.850487 | + | 0.294617i | ||||
\(554\) | 24.0000 | 1.01966 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.50000 | + | 14.7224i | −0.360480 | + | 0.624370i | ||||
\(557\) | −4.50000 | + | 7.79423i | −0.190671 | + | 0.330252i | −0.945473 | − | 0.325701i | \(-0.894400\pi\) |
0.754802 | + | 0.655953i | \(0.227733\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22.0000 | 0.930501 | ||||||||
\(560\) | −1.00000 | − | 5.19615i | −0.0422577 | − | 0.219578i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.50000 | − | 2.59808i | −0.0632737 | − | 0.109593i | ||||
\(563\) | 21.0000 | − | 36.3731i | 0.885044 | − | 1.53294i | 0.0393818 | − | 0.999224i | \(-0.487461\pi\) |
0.845663 | − | 0.533718i | \(-0.179206\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.00000 | + | 3.46410i | 0.0841406 | + | 0.145736i | ||||
\(566\) | 24.0000 | 1.00880 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.00000 | −0.209795 | ||||||||
\(569\) | −6.50000 | − | 11.2583i | −0.272494 | − | 0.471974i | 0.697006 | − | 0.717066i | \(-0.254515\pi\) |
−0.969500 | + | 0.245092i | \(0.921182\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.5000 | − | 37.2391i | 0.899747 | − | 1.55841i | 0.0719297 | − | 0.997410i | \(-0.477084\pi\) |
0.827817 | − | 0.560998i | \(-0.189582\pi\) | |||||||
\(572\) | 1.00000 | + | 1.73205i | 0.0418121 | + | 0.0724207i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −15.0000 | − | 5.19615i | −0.626088 | − | 0.216883i | ||||
\(575\) | 7.00000 | 0.291920 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.00000 | − | 15.5885i | 0.374675 | − | 0.648956i | −0.615603 | − | 0.788056i | \(-0.711088\pi\) |
0.990278 | + | 0.139100i | \(0.0444210\pi\) | |||||||
\(578\) | 4.00000 | − | 6.92820i | 0.166378 | − | 0.288175i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 10.0000 | 0.415227 | ||||||||
\(581\) | 28.0000 | − | 24.2487i | 1.16164 | − | 1.00601i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.00000 | − | 3.46410i | −0.0828315 | − | 0.143468i | ||||
\(584\) | 4.00000 | − | 6.92820i | 0.165521 | − | 0.286691i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.50000 | + | 2.59808i | 0.0619644 | + | 0.107326i | ||||
\(587\) | −12.0000 | −0.495293 | −0.247647 | − | 0.968850i | \(-0.579657\pi\) | ||||
−0.247647 | + | 0.968850i | \(0.579657\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.0000 | 0.576860 | ||||||||
\(590\) | 11.0000 | + | 19.0526i | 0.452863 | + | 0.784381i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.50000 | + | 2.59808i | −0.0616496 | + | 0.106780i | ||||
\(593\) | 10.5000 | + | 18.1865i | 0.431183 | + | 0.746831i | 0.996976 | − | 0.0777165i | \(-0.0247629\pi\) |
−0.565792 | + | 0.824548i | \(0.691430\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.0000 | − | 10.3923i | 0.491952 | − | 0.426043i | ||||
\(596\) | 17.0000 | 0.696347 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7.00000 | − | 12.1244i | 0.286251 | − | 0.495802i | ||||
\(599\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(602\) | −27.5000 | − | 9.52628i | −1.12082 | − | 0.388262i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.50000 | + | 4.33013i | 0.101724 | + | 0.176190i | ||||
\(605\) | 1.00000 | − | 1.73205i | 0.0406558 | − | 0.0704179i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.0000 | − | 31.1769i | −0.730597 | − | 1.26543i | −0.956628 | − | 0.291312i | \(-0.905908\pi\) |
0.226031 | − | 0.974120i | \(-0.427425\pi\) | |||||||
\(608\) | 7.00000 | 0.283887 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −20.0000 | −0.809776 | ||||||||
\(611\) | 7.00000 | + | 12.1244i | 0.283190 | + | 0.490499i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.00000 | + | 1.73205i | −0.0403896 | + | 0.0699569i | −0.885514 | − | 0.464614i | \(-0.846193\pi\) |
0.845124 | + | 0.534570i | \(0.179527\pi\) | |||||||
\(614\) | −14.0000 | − | 24.2487i | −0.564994 | − | 0.978598i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.500000 | − | 2.59808i | −0.0201456 | − | 0.104679i | ||||
\(617\) | −20.0000 | −0.805170 | −0.402585 | − | 0.915383i | \(-0.631888\pi\) | ||||
−0.402585 | + | 0.915383i | \(0.631888\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.0000 | − | 22.5167i | 0.522514 | − | 0.905021i | −0.477143 | − | 0.878826i | \(-0.658328\pi\) |
0.999657 | − | 0.0261952i | \(-0.00833914\pi\) | |||||||
\(620\) | 2.00000 | − | 3.46410i | 0.0803219 | − | 0.139122i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 27.0000 | 1.08260 | ||||||||
\(623\) | −5.00000 | − | 1.73205i | −0.200321 | − | 0.0693932i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.50000 | + | 16.4545i | 0.380000 | + | 0.658179i | ||||
\(626\) | −7.50000 | + | 12.9904i | −0.299760 | + | 0.519200i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.500000 | − | 0.866025i | −0.0199522 | − | 0.0345582i | ||||
\(629\) | −9.00000 | −0.358854 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.0000 | −0.398094 | −0.199047 | − | 0.979990i | \(-0.563785\pi\) | ||||
−0.199047 | + | 0.979990i | \(0.563785\pi\) | |||||||
\(632\) | 4.00000 | + | 6.92820i | 0.159111 | + | 0.275589i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −15.0000 | + | 25.9808i | −0.595726 | + | 1.03183i | ||||
\(635\) | −19.0000 | − | 32.9090i | −0.753992 | − | 1.30595i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.00000 | − | 13.8564i | 0.0792429 | − | 0.549011i | ||||
\(638\) | 5.00000 | 0.197952 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | − | 1.73205i | 0.0395285 | − | 0.0684653i | ||||
\(641\) | 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 | ||||||||
\(643\) | 40.0000 | 1.57745 | 0.788723 | − | 0.614749i | \(-0.210743\pi\) | ||||
0.788723 | + | 0.614749i | \(0.210743\pi\) | |||||||
\(644\) | −14.0000 | + | 12.1244i | −0.551677 | + | 0.477767i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 10.5000 | + | 18.1865i | 0.413117 | + | 0.715540i | ||||
\(647\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.50000 | + | 9.52628i | 0.215894 | + | 0.373939i | ||||
\(650\) | −2.00000 | −0.0784465 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.00000 | 0.234978 | ||||||||
\(653\) | 5.00000 | + | 8.66025i | 0.195665 | + | 0.338902i | 0.947118 | − | 0.320884i | \(-0.103980\pi\) |
−0.751453 | + | 0.659786i | \(0.770647\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.00000 | + | 13.8564i | −0.312586 | + | 0.541415i | ||||
\(656\) | −3.00000 | − | 5.19615i | −0.117130 | − | 0.202876i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.50000 | − | 18.1865i | −0.136444 | − | 0.708985i | ||||
\(659\) | −20.0000 | −0.779089 | −0.389545 | − | 0.921008i | \(-0.627368\pi\) | ||||
−0.389545 | + | 0.921008i | \(0.627368\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.50000 | − | 9.52628i | 0.213925 | − | 0.370529i | −0.739014 | − | 0.673690i | \(-0.764708\pi\) |
0.952940 | + | 0.303160i | \(0.0980418\pi\) | |||||||
\(662\) | 7.00000 | − | 12.1244i | 0.272063 | − | 0.471226i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14.0000 | 0.543305 | ||||||||
\(665\) | −7.00000 | − | 36.3731i | −0.271448 | − | 1.41049i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17.5000 | − | 30.3109i | −0.677603 | − | 1.17364i | ||||
\(668\) | 5.00000 | − | 8.66025i | 0.193456 | − | 0.335075i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4.00000 | − | 6.92820i | −0.154533 | − | 0.267660i | ||||
\(671\) | −10.0000 | −0.386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.0000 | −0.385472 | −0.192736 | − | 0.981251i | \(-0.561736\pi\) | ||||
−0.192736 | + | 0.981251i | \(0.561736\pi\) | |||||||
\(674\) | −4.00000 | − | 6.92820i | −0.154074 | − | 0.266864i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.50000 | − | 7.79423i | 0.173077 | − | 0.299778i | ||||
\(677\) | 10.5000 | + | 18.1865i | 0.403548 | + | 0.698965i | 0.994151 | − | 0.107997i | \(-0.0344436\pi\) |
−0.590603 | + | 0.806962i | \(0.701110\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 30.0000 | − | 25.9808i | 1.15129 | − | 0.997050i | ||||
\(680\) | 6.00000 | 0.230089 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.00000 | − | 1.73205i | 0.0382920 | − | 0.0663237i | ||||
\(683\) | −19.5000 | + | 33.7750i | −0.746147 | + | 1.29236i | 0.203510 | + | 0.979073i | \(0.434765\pi\) |
−0.949657 | + | 0.313291i | \(0.898568\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.0000 | −0.458496 | ||||||||
\(686\) | −8.50000 | + | 16.4545i | −0.324532 | + | 0.628235i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.50000 | − | 9.52628i | −0.209686 | − | 0.363186i | ||||
\(689\) | 4.00000 | − | 6.92820i | 0.152388 | − | 0.263944i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.00000 | − | 15.5885i | −0.342376 | − | 0.593013i | 0.642497 | − | 0.766288i | \(-0.277898\pi\) |
−0.984873 | + | 0.173275i | \(0.944565\pi\) | |||||||
\(692\) | 14.0000 | 0.532200 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 24.0000 | 0.911028 | ||||||||
\(695\) | 17.0000 | + | 29.4449i | 0.644847 | + | 1.11691i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.00000 | − | 15.5885i | 0.340899 | − | 0.590455i | ||||
\(698\) | −4.00000 | − | 6.92820i | −0.151402 | − | 0.262236i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.50000 | + | 0.866025i | 0.0944911 | + | 0.0327327i | ||||
\(701\) | −27.0000 | −1.01978 | −0.509888 | − | 0.860241i | \(-0.670313\pi\) | ||||
−0.509888 | + | 0.860241i | \(0.670313\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.5000 | + | 18.1865i | −0.396015 | + | 0.685918i | ||||
\(704\) | 0.500000 | − | 0.866025i | 0.0188445 | − | 0.0326396i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10.0000 | 0.376355 | ||||||||
\(707\) | 1.50000 | + | 7.79423i | 0.0564133 | + | 0.293132i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.5000 | + | 26.8468i | 0.582115 | + | 1.00825i | 0.995228 | + | 0.0975728i | \(0.0311079\pi\) |
−0.413114 | + | 0.910679i | \(0.635559\pi\) | |||||||
\(710\) | −5.00000 | + | 8.66025i | −0.187647 | + | 0.325014i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.00000 | − | 1.73205i | −0.0374766 | − | 0.0649113i | ||||
\(713\) | −14.0000 | −0.524304 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.00000 | 0.149592 | ||||||||
\(716\) | 4.50000 | + | 7.79423i | 0.168173 | + | 0.291284i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9.00000 | − | 15.5885i | 0.335877 | − | 0.581756i | ||||
\(719\) | −4.50000 | − | 7.79423i | −0.167822 | − | 0.290676i | 0.769832 | − | 0.638247i | \(-0.220340\pi\) |
−0.937654 | + | 0.347571i | \(0.887007\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 25.0000 | + | 8.66025i | 0.931049 | + | 0.322525i | ||||
\(722\) | 30.0000 | 1.11648 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.00000 | − | 8.66025i | 0.185824 | − | 0.321856i | ||||
\(725\) | −2.50000 | + | 4.33013i | −0.0928477 | + | 0.160817i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.0000 | −0.519231 | −0.259616 | − | 0.965712i | \(-0.583596\pi\) | ||||
−0.259616 | + | 0.965712i | \(0.583596\pi\) | |||||||
\(728\) | 4.00000 | − | 3.46410i | 0.148250 | − | 0.128388i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −8.00000 | − | 13.8564i | −0.296093 | − | 0.512849i | ||||
\(731\) | 16.5000 | − | 28.5788i | 0.610275 | − | 1.05703i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.0000 | − | 19.0526i | −0.406294 | − | 0.703722i | 0.588177 | − | 0.808732i | \(-0.299846\pi\) |
−0.994471 | + | 0.105010i | \(0.966513\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.00000 | −0.258023 | ||||||||
\(737\) | −2.00000 | − | 3.46410i | −0.0736709 | − | 0.127602i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.0000 | + | 17.3205i | −0.367856 | + | 0.637145i | −0.989230 | − | 0.146369i | \(-0.953241\pi\) |
0.621374 | + | 0.783514i | \(0.286575\pi\) | |||||||
\(740\) | 3.00000 | + | 5.19615i | 0.110282 | + | 0.191014i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.00000 | + | 6.92820i | −0.293689 | + | 0.254342i | ||||
\(743\) | −4.00000 | −0.146746 | −0.0733729 | − | 0.997305i | \(-0.523376\pi\) | ||||
−0.0733729 | + | 0.997305i | \(0.523376\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.0000 | − | 29.4449i | 0.622832 | − | 1.07878i | ||||
\(746\) | 11.0000 | − | 19.0526i | 0.402739 | − | 0.697564i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.00000 | 0.109691 | ||||||||
\(749\) | −45.0000 | − | 15.5885i | −1.64426 | − | 0.569590i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.0000 | + | 34.6410i | 0.729810 | + | 1.26407i | 0.956963 | + | 0.290209i | \(0.0937250\pi\) |
−0.227153 | + | 0.973859i | \(0.572942\pi\) | |||||||
\(752\) | 3.50000 | − | 6.06218i | 0.127632 | − | 0.221065i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.00000 | + | 8.66025i | 0.182089 | + | 0.315388i | ||||
\(755\) | 10.0000 | 0.363937 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.0000 | 0.545184 | 0.272592 | − | 0.962130i | \(-0.412119\pi\) | ||||
0.272592 | + | 0.962130i | \(0.412119\pi\) | |||||||
\(758\) | 8.00000 | + | 13.8564i | 0.290573 | + | 0.503287i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7.00000 | − | 12.1244i | 0.253917 | − | 0.439797i | ||||
\(761\) | 15.0000 | + | 25.9808i | 0.543750 | + | 0.941802i | 0.998684 | + | 0.0512772i | \(0.0163292\pi\) |
−0.454935 | + | 0.890525i | \(0.650337\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.00000 | + | 10.3923i | 0.0724049 | + | 0.376227i | ||||
\(764\) | −8.00000 | −0.289430 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −15.5000 | + | 26.8468i | −0.560038 | + | 0.970014i | ||||
\(767\) | −11.0000 | + | 19.0526i | −0.397187 | + | 0.687948i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28.0000 | 1.00971 | 0.504853 | − | 0.863205i | \(-0.331547\pi\) | ||||
0.504853 | + | 0.863205i | \(0.331547\pi\) | |||||||
\(770\) | −5.00000 | − | 1.73205i | −0.180187 | − | 0.0624188i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −12.0000 | − | 20.7846i | −0.431889 | − | 0.748054i | ||||
\(773\) | −2.00000 | + | 3.46410i | −0.0719350 | + | 0.124595i | −0.899749 | − | 0.436407i | \(-0.856251\pi\) |
0.827814 | + | 0.561002i | \(0.189584\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.00000 | + | 1.73205i | 0.0359211 | + | 0.0622171i | ||||
\(776\) | 15.0000 | 0.538469 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.00000 | −0.215110 | ||||||||
\(779\) | −21.0000 | − | 36.3731i | −0.752403 | − | 1.30320i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.50000 | + | 4.33013i | −0.0894570 | + | 0.154944i | ||||
\(782\) | −10.5000 | − | 18.1865i | −0.375479 | − | 0.650349i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.50000 | + | 2.59808i | −0.232143 | + | 0.0927884i | ||||
\(785\) | −2.00000 | −0.0713831 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.5000 | − | 32.0429i | 0.659454 | − | 1.14221i | −0.321303 | − | 0.946976i | \(-0.604121\pi\) |
0.980757 | − | 0.195231i | \(-0.0625457\pi\) | |||||||
\(788\) | −7.50000 | + | 12.9904i | −0.267176 | + | 0.462763i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 16.0000 | 0.569254 | ||||||||
\(791\) | 4.00000 | − | 3.46410i | 0.142224 | − | 0.123169i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.0000 | − | 17.3205i | −0.355110 | − | 0.615069i | ||||
\(794\) | 1.50000 | − | 2.59808i | 0.0532330 | − | 0.0922023i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.00000 | − | 8.66025i | −0.177220 | − | 0.306955i | ||||
\(797\) | −50.0000 | −1.77109 | −0.885545 | − | 0.464553i | \(-0.846215\pi\) | ||||
−0.885545 | + | 0.464553i | \(0.846215\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.0000 | 0.742927 | ||||||||
\(800\) | 0.500000 | + | 0.866025i | 0.0176777 | + | 0.0306186i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −16.0000 | + | 27.7128i | −0.564980 | + | 0.978573i | ||||
\(803\) | −4.00000 | − | 6.92820i | −0.141157 | − | 0.244491i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.00000 | + | 36.3731i | 0.246718 | + | 1.28198i | ||||
\(806\) | 4.00000 | 0.140894 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.50000 | + | 2.59808i | −0.0527698 | + | 0.0914000i | ||||
\(809\) | 7.00000 | − | 12.1244i | 0.246107 | − | 0.426270i | −0.716335 | − | 0.697756i | \(-0.754182\pi\) |
0.962442 | + | 0.271487i | \(0.0875152\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28.0000 | −0.983213 | −0.491606 | − | 0.870817i | \(-0.663590\pi\) | ||||
−0.491606 | + | 0.870817i | \(0.663590\pi\) | |||||||
\(812\) | −2.50000 | − | 12.9904i | −0.0877328 | − | 0.455873i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.50000 | + | 2.59808i | 0.0525750 | + | 0.0910625i | ||||
\(815\) | 6.00000 | − | 10.3923i | 0.210171 | − | 0.364027i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −38.5000 | − | 66.6840i | −1.34694 | − | 2.33298i | ||||
\(818\) | 32.0000 | 1.11885 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12.0000 | −0.419058 | ||||||||
\(821\) | −25.0000 | − | 43.3013i | −0.872506 | − | 1.51122i | −0.859396 | − | 0.511311i | \(-0.829160\pi\) |
−0.0131101 | − | 0.999914i | \(-0.504173\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.00000 | − | 3.46410i | 0.0697156 | − | 0.120751i | −0.829060 | − | 0.559159i | \(-0.811124\pi\) |
0.898776 | + | 0.438408i | \(0.144457\pi\) | |||||||
\(824\) | 5.00000 | + | 8.66025i | 0.174183 | + | 0.301694i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 22.0000 | − | 19.0526i | 0.765478 | − | 0.662923i | ||||
\(827\) | −10.0000 | −0.347734 | −0.173867 | − | 0.984769i | \(-0.555626\pi\) | ||||
−0.173867 | + | 0.984769i | \(0.555626\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.50000 | − | 14.7224i | 0.295217 | − | 0.511331i | −0.679818 | − | 0.733381i | \(-0.737941\pi\) |
0.975035 | + | 0.222049i | \(0.0712747\pi\) | |||||||
\(830\) | 14.0000 | − | 24.2487i | 0.485947 | − | 0.841685i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.00000 | 0.0693375 | ||||||||
\(833\) | −16.5000 | − | 12.9904i | −0.571691 | − | 0.450090i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.0000 | − | 17.3205i | −0.346064 | − | 0.599401i | ||||
\(836\) | 3.50000 | − | 6.06218i | 0.121050 | − | 0.209665i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.50000 | − | 2.59808i | −0.0518166 | − | 0.0897491i | ||||
\(839\) | 24.0000 | 0.828572 | 0.414286 | − | 0.910147i | \(-0.364031\pi\) | ||||
0.414286 | + | 0.910147i | \(0.364031\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.00000 | −0.137931 | ||||||||
\(842\) | 8.50000 | + | 14.7224i | 0.292929 | + | 0.507369i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10.0000 | + | 17.3205i | −0.344214 | + | 0.596196i | ||||
\(845\) | −9.00000 | − | 15.5885i | −0.309609 | − | 0.536259i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.50000 | − | 0.866025i | −0.0859010 | − | 0.0297570i | ||||
\(848\) | −4.00000 | −0.137361 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.50000 | + | 2.59808i | −0.0514496 | + | 0.0891133i | ||||
\(851\) | 10.5000 | − | 18.1865i | 0.359935 | − | 0.623426i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 46.0000 | 1.57501 | 0.787505 | − | 0.616308i | \(-0.211372\pi\) | ||||
0.787505 | + | 0.616308i | \(0.211372\pi\) | |||||||
\(854\) | 5.00000 | + | 25.9808i | 0.171096 | + | 0.889043i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.00000 | − | 15.5885i | −0.307614 | − | 0.532803i | ||||
\(857\) | −10.5000 | + | 18.1865i | −0.358673 | + | 0.621240i | −0.987739 | − | 0.156112i | \(-0.950104\pi\) |
0.629066 | + | 0.777352i | \(0.283437\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.0000 | + | 19.0526i | 0.375315 | + | 0.650065i | 0.990374 | − | 0.138416i | \(-0.0442012\pi\) |
−0.615059 | + | 0.788481i | \(0.710868\pi\) | |||||||
\(860\) | −22.0000 | −0.750194 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 40.0000 | 1.36241 | ||||||||
\(863\) | 14.0000 | + | 24.2487i | 0.476566 | + | 0.825436i | 0.999639 | − | 0.0268516i | \(-0.00854816\pi\) |
−0.523074 | + | 0.852287i | \(0.675215\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.0000 | − | 24.2487i | 0.476014 | − | 0.824481i | ||||
\(866\) | −2.50000 | − | 4.33013i | −0.0849535 | − | 0.147144i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5.00000 | − | 1.73205i | −0.169711 | − | 0.0587896i | ||||
\(869\) | 8.00000 | 0.271381 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.00000 | − | 6.92820i | 0.135535 | − | 0.234753i | ||||
\(872\) | −2.00000 | + | 3.46410i | −0.0677285 | + | 0.117309i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −49.0000 | −1.65745 | ||||||||
\(875\) | 24.0000 | − | 20.7846i | 0.811348 | − | 0.702648i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.0000 | − | 22.5167i | −0.438979 | − | 0.760334i | 0.558632 | − | 0.829416i | \(-0.311326\pi\) |
−0.997611 | + | 0.0690819i | \(0.977993\pi\) | |||||||
\(878\) | −2.50000 | + | 4.33013i | −0.0843709 | + | 0.146135i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.00000 | − | 1.73205i | −0.0337100 | − | 0.0583874i | ||||
\(881\) | 36.0000 | 1.21287 | 0.606435 | − | 0.795133i | \(-0.292599\pi\) | ||||
0.606435 | + | 0.795133i | \(0.292599\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.00000 | 0.269221 | 0.134611 | − | 0.990899i | \(-0.457022\pi\) | ||||
0.134611 | + | 0.990899i | \(0.457022\pi\) | |||||||
\(884\) | 3.00000 | + | 5.19615i | 0.100901 | + | 0.174766i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −20.5000 | + | 35.5070i | −0.688711 | + | 1.19288i | ||||
\(887\) | 10.0000 | + | 17.3205i | 0.335767 | + | 0.581566i | 0.983632 | − | 0.180190i | \(-0.0576711\pi\) |
−0.647865 | + | 0.761755i | \(0.724338\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −38.0000 | + | 32.9090i | −1.27448 | + | 1.10373i | ||||
\(890\) | −4.00000 | −0.134080 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7.00000 | − | 12.1244i | 0.234377 | − | 0.405953i | ||||
\(893\) | 24.5000 | − | 42.4352i | 0.819861 | − | 1.42004i | ||||
\(894\) | 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 | ||||
\(899\) | 5.00000 | − | 8.66025i | 0.166759 | − | 0.288836i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.00000 | − | 10.3923i | −0.199889 | − | 0.346218i | ||||
\(902\) | −6.00000 | −0.199778 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.00000 | 0.0665190 | ||||||||
\(905\) | −10.0000 | − | 17.3205i | −0.332411 | − | 0.575753i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.0000 | − | 20.7846i | 0.398453 | − | 0.690142i | −0.595082 | − | 0.803665i | \(-0.702880\pi\) |
0.993535 | + | 0.113523i | \(0.0362137\pi\) | |||||||
\(908\) | −5.00000 | − | 8.66025i | −0.165931 | − | 0.287401i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.00000 | − | 10.3923i | −0.0662994 | − | 0.344502i | ||||
\(911\) | 13.0000 | 0.430709 | 0.215355 | − | 0.976536i | \(-0.430909\pi\) | ||||
0.215355 | + | 0.976536i | \(0.430909\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.00000 | − | 12.1244i | 0.231666 | − | 0.401258i | ||||
\(914\) | −20.0000 | + | 34.6410i | −0.661541 | + | 1.14582i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.0000 | −0.330409 | ||||||||
\(917\) | 20.0000 | + | 6.92820i | 0.660458 | + | 0.228789i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.5000 | − | 37.2391i | −0.709220 | − | 1.22840i | −0.965147 | − | 0.261708i | \(-0.915714\pi\) |
0.255927 | − | 0.966696i | \(-0.417619\pi\) | |||||||
\(920\) | −7.00000 | + | 12.1244i | −0.230783 | + | 0.399728i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −6.50000 | − | 11.2583i | −0.214066 | − | 0.370773i | ||||
\(923\) | −10.0000 | −0.329154 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.00000 | −0.0986394 | ||||||||
\(926\) | 12.0000 | + | 20.7846i | 0.394344 | + | 0.683025i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.50000 | − | 4.33013i | 0.0820665 | − | 0.142143i | ||||
\(929\) | −2.00000 | − | 3.46410i | −0.0656179 | − | 0.113653i | 0.831350 | − | 0.555749i | \(-0.187569\pi\) |
−0.896968 | + | 0.442096i | \(0.854235\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −45.5000 | + | 18.1865i | −1.49120 | + | 0.596040i | ||||
\(932\) | −9.00000 | −0.294805 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6.50000 | + | 11.2583i | −0.212686 | + | 0.368384i | ||||
\(935\) | 3.00000 | − | 5.19615i | 0.0981105 | − | 0.169932i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.0000 | 0.849383 | 0.424691 | − | 0.905338i | \(-0.360383\pi\) | ||||
0.424691 | + | 0.905338i | \(0.360383\pi\) | |||||||
\(938\) | −8.00000 | + | 6.92820i | −0.261209 | + | 0.226214i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −7.00000 | − | 12.1244i | −0.228315 | − | 0.395453i | ||||
\(941\) | −7.50000 | + | 12.9904i | −0.244493 | + | 0.423474i | −0.961989 | − | 0.273088i | \(-0.911955\pi\) |
0.717496 | + | 0.696563i | \(0.245288\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 21.0000 | + | 36.3731i | 0.683854 | + | 1.18447i | ||||
\(944\) | 11.0000 | 0.358020 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −11.0000 | −0.357641 | ||||||||
\(947\) | 13.5000 | + | 23.3827i | 0.438691 | + | 0.759835i | 0.997589 | − | 0.0694014i | \(-0.0221089\pi\) |
−0.558898 | + | 0.829237i | \(0.688776\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.00000 | − | 13.8564i | 0.259691 | − | 0.449798i | ||||
\(950\) | 3.50000 | + | 6.06218i | 0.113555 | + | 0.196683i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.50000 | − | 7.79423i | −0.0486153 | − | 0.252612i | ||||
\(953\) | −10.0000 | −0.323932 | −0.161966 | − | 0.986796i | \(-0.551783\pi\) | ||||
−0.161966 | + | 0.986796i | \(0.551783\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.00000 | + | 13.8564i | −0.258874 | + | 0.448383i | ||||
\(956\) | 5.00000 | − | 8.66025i | 0.161712 | − | 0.280093i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 18.0000 | 0.581554 | ||||||||
\(959\) | 3.00000 | + | 15.5885i | 0.0968751 | + | 0.503378i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.5000 | + | 23.3827i | 0.435484 | + | 0.754280i | ||||
\(962\) | −3.00000 | + | 5.19615i | −0.0967239 | + | 0.167531i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.00000 | + | 3.46410i | 0.0644157 | + | 0.111571i | ||||
\(965\) | −48.0000 | −1.54517 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.00000 | −0.0964735 | −0.0482367 | − | 0.998836i | \(-0.515360\pi\) | ||||
−0.0482367 | + | 0.998836i | \(0.515360\pi\) | |||||||
\(968\) | −0.500000 | − | 0.866025i | −0.0160706 | − | 0.0278351i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 15.0000 | − | 25.9808i | 0.481621 | − | 0.834192i | ||||
\(971\) | 18.0000 | + | 31.1769i | 0.577647 | + | 1.00051i | 0.995748 | + | 0.0921142i | \(0.0293625\pi\) |
−0.418101 | + | 0.908401i | \(0.637304\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 34.0000 | − | 29.4449i | 1.08999 | − | 0.943959i | ||||
\(974\) | 18.0000 | 0.576757 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.00000 | + | 8.66025i | −0.160046 | + | 0.277208i | ||||
\(977\) | 22.0000 | − | 38.1051i | 0.703842 | − | 1.21909i | −0.263265 | − | 0.964723i | \(-0.584799\pi\) |
0.967108 | − | 0.254367i | \(-0.0818672\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.00000 | −0.0639203 | ||||||||
\(980\) | −2.00000 | + | 13.8564i | −0.0638877 | + | 0.442627i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 13.0000 | + | 22.5167i | 0.414847 | + | 0.718536i | ||||
\(983\) | −24.5000 | + | 42.4352i | −0.781429 | + | 1.35347i | 0.149681 | + | 0.988734i | \(0.452175\pi\) |
−0.931110 | + | 0.364740i | \(0.881158\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.0000 | + | 25.9808i | 0.477940 | + | 0.827816i | ||||
\(986\) | 15.0000 | 0.477697 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 14.0000 | 0.445399 | ||||||||
\(989\) | 38.5000 | + | 66.6840i | 1.22423 | + | 2.12043i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.00000 | + | 6.92820i | −0.127064 | + | 0.220082i | −0.922538 | − | 0.385906i | \(-0.873889\pi\) |
0.795474 | + | 0.605988i | \(0.207222\pi\) | |||||||
\(992\) | −1.00000 | − | 1.73205i | −0.0317500 | − | 0.0549927i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 12.5000 | + | 4.33013i | 0.396476 | + | 0.137343i | ||||
\(995\) | −20.0000 | −0.634043 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15.0000 | + | 25.9808i | −0.475055 | + | 0.822819i | −0.999592 | − | 0.0285686i | \(-0.990905\pi\) |
0.524537 | + | 0.851388i | \(0.324238\pi\) | |||||||
\(998\) | 20.0000 | − | 34.6410i | 0.633089 | − | 1.09654i | ||||
\(999\) | 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.i.991.1 | yes | 2 | |
3.2 | odd | 2 | 1386.2.k.k.991.1 | yes | 2 | ||
7.2 | even | 3 | inner | 1386.2.k.i.793.1 | ✓ | 2 | |
7.3 | odd | 6 | 9702.2.a.bx.1.1 | 1 | |||
7.4 | even | 3 | 9702.2.a.bg.1.1 | 1 | |||
21.2 | odd | 6 | 1386.2.k.k.793.1 | yes | 2 | ||
21.11 | odd | 6 | 9702.2.a.w.1.1 | 1 | |||
21.17 | even | 6 | 9702.2.a.j.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1386.2.k.i.793.1 | ✓ | 2 | 7.2 | even | 3 | inner | |
1386.2.k.i.991.1 | yes | 2 | 1.1 | even | 1 | trivial | |
1386.2.k.k.793.1 | yes | 2 | 21.2 | odd | 6 | ||
1386.2.k.k.991.1 | yes | 2 | 3.2 | odd | 2 | ||
9702.2.a.j.1.1 | 1 | 21.17 | even | 6 | |||
9702.2.a.w.1.1 | 1 | 21.11 | odd | 6 | |||
9702.2.a.bg.1.1 | 1 | 7.4 | even | 3 | |||
9702.2.a.bx.1.1 | 1 | 7.3 | odd | 6 |