Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1260,2,Mod(811,1260)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1260, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1260.811");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1260.c (of order \(2\), degree \(1\), 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: | \(10.0611506547\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 3 x^{12} + 2 x^{11} - 7 x^{10} + 12 x^{9} - 28 x^{8} + 24 x^{7} - 28 x^{6} + 16 x^{5} + 48 x^{4} - 128 x^{3} + 192 x^{2} - 256 x + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 420) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 811.13 | ||
Root | \(-0.947441 - 1.04993i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1260.811 |
Dual form | 1260.2.c.d.811.14 |
$q$-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 \(\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times\).
\(n\) | \(281\) | \(631\) | \(757\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.947441 | − | 1.04993i | 0.669942 | − | 0.742413i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.204711 | − | 1.98950i | −0.102355 | − | 0.994748i | ||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.29670 | − | 1.31346i | −0.868070 | − | 0.496442i | ||||
\(8\) | −2.28279 | − | 1.67000i | −0.807086 | − | 0.590433i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.04993 | + | 0.947441i | 0.332017 | + | 0.299607i | ||||
\(11\) | − | 0.477147i | − | 0.143865i | −0.997409 | − | 0.0719326i | \(-0.977083\pi\) | ||
0.997409 | − | 0.0719326i | \(-0.0229167\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.96271i | 0.821708i | 0.911701 | + | 0.410854i | \(0.134769\pi\) | ||||
−0.911701 | + | 0.410854i | \(0.865231\pi\) | |||||||
\(14\) | −3.55503 | + | 1.16694i | −0.950122 | + | 0.311879i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.91619 | + | 0.814543i | −0.979047 | + | 0.203636i | ||||
\(17\) | − | 3.83353i | − | 0.929767i | −0.885372 | − | 0.464883i | \(-0.846096\pi\) | ||
0.885372 | − | 0.464883i | \(-0.153904\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.31262 | −1.21880 | −0.609399 | − | 0.792864i | \(-0.708589\pi\) | ||||
−0.609399 | + | 0.792864i | \(0.708589\pi\) | |||||||
\(20\) | 1.98950 | − | 0.204711i | 0.444865 | − | 0.0457747i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.500972 | − | 0.452069i | −0.106808 | − | 0.0963814i | ||||
\(23\) | − | 7.60808i | − | 1.58639i | −0.608965 | − | 0.793197i | \(-0.708415\pi\) | ||
0.608965 | − | 0.793197i | \(-0.291585\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 3.11064 | + | 2.80699i | 0.610047 | + | 0.550497i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.14297 | + | 4.83815i | −0.404983 | + | 0.914324i | ||||
\(29\) | −6.17752 | −1.14714 | −0.573569 | − | 0.819158i | \(-0.694441\pi\) | ||||
−0.573569 | + | 0.819158i | \(0.694441\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.38789 | −0.608482 | −0.304241 | − | 0.952595i | \(-0.598403\pi\) | ||||
−0.304241 | + | 0.952595i | \(0.598403\pi\) | |||||||
\(32\) | −2.85514 | + | 4.88346i | −0.504723 | + | 0.863282i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.02494 | − | 3.63204i | −0.690271 | − | 0.622890i | ||||
\(35\) | 1.31346 | − | 2.29670i | 0.222016 | − | 0.388213i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.62867 | −1.41854 | −0.709272 | − | 0.704935i | \(-0.750976\pi\) | ||||
−0.709272 | + | 0.704935i | \(0.750976\pi\) | |||||||
\(38\) | −5.03339 | + | 5.57788i | −0.816524 | + | 0.904852i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.67000 | − | 2.28279i | 0.264050 | − | 0.360940i | ||||
\(41\) | 1.01125i | 0.157930i | 0.996877 | + | 0.0789651i | \(0.0251616\pi\) | ||||
−0.996877 | + | 0.0789651i | \(0.974838\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.85412i | 1.04524i | 0.852565 | + | 0.522622i | \(0.175046\pi\) | ||||
−0.852565 | + | 0.522622i | \(0.824954\pi\) | |||||||
\(44\) | −0.949282 | + | 0.0976772i | −0.143110 | + | 0.0147254i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.98796 | − | 7.20820i | −1.17776 | − | 1.06279i | ||||
\(47\) | 6.21838 | 0.907043 | 0.453522 | − | 0.891245i | \(-0.350167\pi\) | ||||
0.453522 | + | 0.891245i | \(0.350167\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.54963 | + | 6.03325i | 0.507090 | + | 0.861893i | ||||
\(50\) | −0.947441 | + | 1.04993i | −0.133988 | + | 0.148483i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.89430 | − | 0.606499i | 0.817392 | − | 0.0841063i | ||||
\(53\) | 9.30380 | 1.27797 | 0.638987 | − | 0.769217i | \(-0.279354\pi\) | ||||
0.638987 | + | 0.769217i | \(0.279354\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.477147 | 0.0643385 | ||||||||
\(56\) | 3.04938 | + | 6.83383i | 0.407491 | + | 0.913209i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.85284 | + | 6.48597i | −0.768515 | + | 0.851650i | ||||
\(59\) | −4.88854 | −0.636433 | −0.318217 | − | 0.948018i | \(-0.603084\pi\) | ||||
−0.318217 | + | 0.948018i | \(0.603084\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 4.75818i | − | 0.609222i | −0.952477 | − | 0.304611i | \(-0.901474\pi\) | ||
0.952477 | − | 0.304611i | \(-0.0985264\pi\) | |||||||
\(62\) | −3.20982 | + | 3.55705i | −0.407648 | + | 0.451745i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.42221 | + | 7.62449i | 0.302777 | + | 0.953061i | ||||
\(65\) | −2.96271 | −0.367479 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 1.30610i | − | 0.159565i | −0.996812 | − | 0.0797826i | \(-0.974577\pi\) | ||
0.996812 | − | 0.0797826i | \(-0.0254226\pi\) | |||||||
\(68\) | −7.62679 | + | 0.784764i | −0.924884 | + | 0.0951667i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.16694 | − | 3.55503i | −0.139477 | − | 0.424907i | ||||
\(71\) | − | 9.18700i | − | 1.09030i | −0.838340 | − | 0.545148i | \(-0.816473\pi\) | ||
0.838340 | − | 0.545148i | \(-0.183527\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.49766i | 0.526411i | 0.964740 | + | 0.263206i | \(0.0847797\pi\) | ||||
−0.964740 | + | 0.263206i | \(0.915220\pi\) | |||||||
\(74\) | −8.17516 | + | 9.05951i | −0.950343 | + | 1.05315i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.08755 | + | 10.5694i | 0.124751 | + | 1.21240i | ||||
\(77\) | −0.626715 | + | 1.09586i | −0.0714208 | + | 0.124885i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 8.80833i | − | 0.991015i | −0.868604 | − | 0.495507i | \(-0.834982\pi\) | ||
0.868604 | − | 0.495507i | \(-0.165018\pi\) | |||||||
\(80\) | −0.814543 | − | 3.91619i | −0.0910686 | − | 0.437843i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.06174 | + | 0.958097i | 0.117249 | + | 0.105804i | ||||
\(83\) | −10.9520 | −1.20214 | −0.601068 | − | 0.799198i | \(-0.705258\pi\) | ||||
−0.601068 | + | 0.799198i | \(0.705258\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.83353 | 0.415804 | ||||||||
\(86\) | 7.19635 | + | 6.49388i | 0.776003 | + | 0.700253i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.796835 | + | 1.08922i | −0.0849429 | + | 0.116112i | ||||
\(89\) | − | 13.1208i | − | 1.39080i | −0.718621 | − | 0.695402i | \(-0.755226\pi\) | ||
0.718621 | − | 0.695402i | \(-0.244774\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.89141 | − | 6.80445i | 0.407931 | − | 0.713300i | ||||
\(92\) | −15.1362 | + | 1.55746i | −1.57806 | + | 0.162376i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.89154 | − | 6.52887i | 0.607666 | − | 0.673401i | ||||
\(95\) | − | 5.31262i | − | 0.545063i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.60612i | 0.163077i | 0.996670 | + | 0.0815384i | \(0.0259833\pi\) | ||||
−0.996670 | + | 0.0815384i | \(0.974017\pi\) | |||||||
\(98\) | 9.69756 | + | 1.98928i | 0.979602 | + | 0.200948i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.204711 | + | 1.98950i | 0.0204711 | + | 0.198950i | ||||
\(101\) | − | 6.17664i | − | 0.614599i | −0.951613 | − | 0.307299i | \(-0.900575\pi\) | ||
0.951613 | − | 0.307299i | \(-0.0994253\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.8145 | 1.65678 | 0.828390 | − | 0.560151i | \(-0.189257\pi\) | ||||
0.828390 | + | 0.560151i | \(0.189257\pi\) | |||||||
\(104\) | 4.94772 | − | 6.76323i | 0.485164 | − | 0.663189i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.81480 | − | 9.76835i | 0.856169 | − | 0.948786i | ||||
\(107\) | 9.15824i | 0.885360i | 0.896680 | + | 0.442680i | \(0.145972\pi\) | ||||
−0.896680 | + | 0.442680i | \(0.854028\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.2477 | −1.46046 | −0.730230 | − | 0.683201i | \(-0.760587\pi\) | ||||
−0.730230 | + | 0.683201i | \(0.760587\pi\) | |||||||
\(110\) | 0.452069 | − | 0.500972i | 0.0431031 | − | 0.0477658i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 10.0642 | + | 3.27301i | 0.950974 | + | 0.309270i | ||||
\(113\) | 4.04995 | 0.380987 | 0.190493 | − | 0.981688i | \(-0.438991\pi\) | ||||
0.190493 | + | 0.981688i | \(0.438991\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.60808 | 0.709457 | ||||||||
\(116\) | 1.26461 | + | 12.2902i | 0.117416 | + | 1.14111i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.63160 | + | 5.13263i | −0.426373 | + | 0.472496i | ||||
\(119\) | −5.03519 | + | 8.80445i | −0.461576 | + | 0.807102i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.7723 | 0.979303 | ||||||||
\(122\) | −4.99576 | − | 4.50809i | −0.452295 | − | 0.408143i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.693537 | + | 6.74018i | 0.0622814 | + | 0.605286i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 12.9949i | − | 1.15311i | −0.817059 | − | 0.576554i | \(-0.804397\pi\) | ||
0.817059 | − | 0.576554i | \(-0.195603\pi\) | |||||||
\(128\) | 10.3001 | + | 4.68060i | 0.910409 | + | 0.413710i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.80699 | + | 3.11064i | −0.246190 | + | 0.272821i | ||||
\(131\) | 1.77552 | 0.155128 | 0.0775640 | − | 0.996987i | \(-0.475286\pi\) | ||||
0.0775640 | + | 0.996987i | \(0.475286\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.2015 | + | 6.97792i | 1.05800 | + | 0.605063i | ||||
\(134\) | −1.37131 | − | 1.23745i | −0.118463 | − | 0.106899i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.40198 | + | 8.75112i | −0.548965 | + | 0.750402i | ||||
\(137\) | 15.1622 | 1.29539 | 0.647695 | − | 0.761900i | \(-0.275733\pi\) | ||||
0.647695 | + | 0.761900i | \(0.275733\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.8544 | −1.59921 | −0.799607 | − | 0.600524i | \(-0.794959\pi\) | ||||
−0.799607 | + | 0.600524i | \(0.794959\pi\) | |||||||
\(140\) | −4.83815 | − | 2.14297i | −0.408898 | − | 0.181114i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −9.64571 | − | 8.70414i | −0.809450 | − | 0.730435i | ||||
\(143\) | 1.41365 | 0.118215 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 6.17752i | − | 0.513015i | ||||||
\(146\) | 4.72223 | + | 4.26127i | 0.390815 | + | 0.352665i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.76638 | + | 17.1667i | 0.145196 | + | 1.41109i | ||||
\(149\) | 18.8439 | 1.54376 | 0.771878 | − | 0.635771i | \(-0.219318\pi\) | ||||
0.771878 | + | 0.635771i | \(0.219318\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.6462i | 1.51741i | 0.651435 | + | 0.758704i | \(0.274167\pi\) | ||||
−0.651435 | + | 0.758704i | \(0.725833\pi\) | |||||||
\(152\) | 12.1276 | + | 8.87206i | 0.983675 | + | 0.719619i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.556804 | + | 1.69627i | 0.0448686 | + | 0.136690i | ||||
\(155\) | − | 3.38789i | − | 0.272121i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 22.6941i | − | 1.81118i | −0.424149 | − | 0.905592i | \(-0.639427\pi\) | ||
0.424149 | − | 0.905592i | \(-0.360573\pi\) | |||||||
\(158\) | −9.24814 | − | 8.34538i | −0.735743 | − | 0.663922i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.88346 | − | 2.85514i | −0.386071 | − | 0.225719i | ||||
\(161\) | −9.99293 | + | 17.4734i | −0.787553 | + | 1.37710i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 9.17980i | − | 0.719017i | −0.933142 | − | 0.359509i | \(-0.882944\pi\) | ||
0.933142 | − | 0.359509i | \(-0.117056\pi\) | |||||||
\(164\) | 2.01187 | − | 0.207013i | 0.157101 | − | 0.0161650i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −10.3764 | + | 11.4988i | −0.805362 | + | 0.892483i | ||||
\(167\) | −14.8751 | −1.15107 | −0.575535 | − | 0.817777i | \(-0.695206\pi\) | ||||
−0.575535 | + | 0.817777i | \(0.695206\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.22235 | 0.324796 | ||||||||
\(170\) | 3.63204 | − | 4.02494i | 0.278565 | − | 0.308699i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 13.6362 | − | 1.40311i | 1.03975 | − | 0.106986i | ||||
\(173\) | 18.2211i | 1.38532i | 0.721262 | + | 0.692662i | \(0.243562\pi\) | ||||
−0.721262 | + | 0.692662i | \(0.756438\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.29670 | + | 1.31346i | 0.173614 | + | 0.0992885i | ||||
\(176\) | 0.388657 | + | 1.86860i | 0.0292961 | + | 0.140851i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −13.7760 | − | 12.4312i | −1.03255 | − | 0.931758i | ||||
\(179\) | − | 5.02780i | − | 0.375796i | −0.982189 | − | 0.187898i | \(-0.939833\pi\) | ||
0.982189 | − | 0.187898i | \(-0.0601674\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 14.6503i | − | 1.08895i | −0.838777 | − | 0.544476i | \(-0.816729\pi\) | ||
0.838777 | − | 0.544476i | \(-0.183271\pi\) | |||||||
\(182\) | −3.45732 | − | 10.5325i | −0.256274 | − | 0.780723i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −12.7055 | + | 17.3676i | −0.936660 | + | 1.28036i | ||||
\(185\) | − | 8.62867i | − | 0.634393i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.82916 | −0.133761 | ||||||||
\(188\) | −1.27297 | − | 12.3714i | −0.0928408 | − | 0.902279i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.57788 | − | 5.03339i | −0.404662 | − | 0.365161i | ||||
\(191\) | 6.84692i | 0.495426i | 0.968833 | + | 0.247713i | \(0.0796790\pi\) | ||||
−0.968833 | + | 0.247713i | \(0.920321\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.47575 | 0.538116 | 0.269058 | − | 0.963124i | \(-0.413288\pi\) | ||||
0.269058 | + | 0.963124i | \(0.413288\pi\) | |||||||
\(194\) | 1.68632 | + | 1.52170i | 0.121070 | + | 0.109252i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11.2765 | − | 8.29705i | 0.805463 | − | 0.592646i | ||||
\(197\) | 14.2749 | 1.01705 | 0.508523 | − | 0.861048i | \(-0.330192\pi\) | ||||
0.508523 | + | 0.861048i | \(0.330192\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.60743 | 0.113948 | 0.0569739 | − | 0.998376i | \(-0.481855\pi\) | ||||
0.0569739 | + | 0.998376i | \(0.481855\pi\) | |||||||
\(200\) | 2.28279 | + | 1.67000i | 0.161417 | + | 0.118087i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.48505 | − | 5.85200i | −0.456286 | − | 0.411745i | ||||
\(203\) | 14.1879 | + | 8.11395i | 0.995795 | + | 0.569487i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.01125 | −0.0706285 | ||||||||
\(206\) | 15.9307 | − | 17.6541i | 1.10995 | − | 1.23002i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.41325 | − | 11.6025i | −0.167329 | − | 0.804491i | ||||
\(209\) | 2.53490i | 0.175343i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.32588i | 0.0912770i | 0.998958 | + | 0.0456385i | \(0.0145322\pi\) | ||||
−0.998958 | + | 0.0456385i | \(0.985468\pi\) | |||||||
\(212\) | −1.90459 | − | 18.5099i | −0.130808 | − | 1.27126i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 9.61552 | + | 8.67689i | 0.657303 | + | 0.593140i | ||||
\(215\) | −6.85412 | −0.467447 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.78094 | + | 4.44986i | 0.528205 | + | 0.302076i | ||||
\(218\) | −14.4463 | + | 16.0090i | −0.978424 | + | 1.08427i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.0976772 | − | 0.949282i | −0.00658539 | − | 0.0640006i | ||||
\(221\) | 11.3576 | 0.763997 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.5307 | −1.44180 | −0.720902 | − | 0.693037i | \(-0.756272\pi\) | ||||
−0.720902 | + | 0.693037i | \(0.756272\pi\) | |||||||
\(224\) | 12.9716 | − | 7.46570i | 0.866704 | − | 0.498823i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.83709 | − | 4.25216i | 0.255239 | − | 0.282850i | ||||
\(227\) | 14.0514 | 0.932625 | 0.466313 | − | 0.884620i | \(-0.345582\pi\) | ||||
0.466313 | + | 0.884620i | \(0.345582\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 17.1949i | − | 1.13627i | −0.822934 | − | 0.568136i | \(-0.807665\pi\) | ||
0.822934 | − | 0.568136i | \(-0.192335\pi\) | |||||||
\(230\) | 7.20820 | − | 7.98796i | 0.475295 | − | 0.526710i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 14.1020 | + | 10.3164i | 0.925839 | + | 0.677308i | ||||
\(233\) | 11.5500 | 0.756668 | 0.378334 | − | 0.925669i | \(-0.376497\pi\) | ||||
0.378334 | + | 0.925669i | \(0.376497\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.21838i | 0.405642i | ||||||||
\(236\) | 1.00074 | + | 9.72572i | 0.0651424 | + | 0.633091i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.47351 | + | 13.6283i | 0.289975 | + | 0.883392i | ||||
\(239\) | − | 13.5047i | − | 0.873549i | −0.899571 | − | 0.436774i | \(-0.856121\pi\) | ||
0.899571 | − | 0.436774i | \(-0.143879\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.07807i | 0.391523i | 0.980652 | + | 0.195761i | \(0.0627178\pi\) | ||||
−0.980652 | + | 0.195761i | \(0.937282\pi\) | |||||||
\(242\) | 10.2061 | − | 11.3102i | 0.656076 | − | 0.727048i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −9.46637 | + | 0.974050i | −0.606022 | + | 0.0623572i | ||||
\(245\) | −6.03325 | + | 3.54963i | −0.385450 | + | 0.226778i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 15.7397i | − | 1.00150i | ||||||
\(248\) | 7.73381 | + | 5.65776i | 0.491098 | + | 0.359268i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.04993 | − | 0.947441i | −0.0664035 | − | 0.0599214i | ||||
\(251\) | −25.9947 | −1.64077 | −0.820385 | − | 0.571812i | \(-0.806241\pi\) | ||||
−0.820385 | + | 0.571812i | \(0.806241\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.63017 | −0.228227 | ||||||||
\(254\) | −13.6437 | − | 12.3119i | −0.856083 | − | 0.772516i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 14.6730 | − | 6.37980i | 0.917065 | − | 0.398738i | ||||
\(257\) | − | 26.1382i | − | 1.63045i | −0.579141 | − | 0.815227i | \(-0.696612\pi\) | ||
0.579141 | − | 0.815227i | \(-0.303388\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 19.8174 | + | 11.3334i | 1.23140 | + | 0.704226i | ||||
\(260\) | 0.606499 | + | 5.89430i | 0.0376135 | + | 0.365549i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.68220 | − | 1.86417i | 0.103927 | − | 0.115169i | ||||
\(263\) | − | 20.1419i | − | 1.24200i | −0.783809 | − | 0.621001i | \(-0.786726\pi\) | ||
0.783809 | − | 0.621001i | \(-0.213274\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.30380i | 0.571528i | ||||||||
\(266\) | 18.8865 | − | 6.19953i | 1.15801 | − | 0.380118i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.59848 | + | 0.267372i | −0.158727 | + | 0.0163324i | ||||
\(269\) | − | 25.1731i | − | 1.53483i | −0.641151 | − | 0.767415i | \(-0.721543\pi\) | ||
0.641151 | − | 0.767415i | \(-0.278457\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.13276 | −0.554776 | −0.277388 | − | 0.960758i | \(-0.589469\pi\) | ||||
−0.277388 | + | 0.960758i | \(0.589469\pi\) | |||||||
\(272\) | 3.12257 | + | 15.0128i | 0.189334 | + | 0.910285i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14.3652 | − | 15.9192i | 0.867836 | − | 0.961715i | ||||
\(275\) | 0.477147i | 0.0287731i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.2069 | −1.03386 | −0.516931 | − | 0.856027i | \(-0.672926\pi\) | ||||
−0.516931 | + | 0.856027i | \(0.672926\pi\) | |||||||
\(278\) | −17.8635 | + | 19.7959i | −1.07138 | + | 1.18728i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6.83383 | + | 3.04938i | −0.408400 | + | 0.182236i | ||||
\(281\) | −10.6360 | −0.634490 | −0.317245 | − | 0.948344i | \(-0.602758\pi\) | ||||
−0.317245 | + | 0.948344i | \(0.602758\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.3615 | 1.15092 | 0.575462 | − | 0.817828i | \(-0.304822\pi\) | ||||
0.575462 | + | 0.817828i | \(0.304822\pi\) | |||||||
\(284\) | −18.2775 | + | 1.88068i | −1.08457 | + | 0.111598i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.33935 | − | 1.48423i | 0.0791974 | − | 0.0877646i | ||||
\(287\) | 1.32823 | − | 2.32253i | 0.0784032 | − | 0.137094i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.30407 | 0.135534 | ||||||||
\(290\) | −6.48597 | − | 5.85284i | −0.380869 | − | 0.343690i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8.94807 | − | 0.920719i | 0.523646 | − | 0.0538810i | ||||
\(293\) | 24.5856i | 1.43631i | 0.695885 | + | 0.718153i | \(0.255012\pi\) | ||||
−0.695885 | + | 0.718153i | \(0.744988\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 4.88854i | − | 0.284622i | ||||||
\(296\) | 19.6974 | + | 14.4099i | 1.14489 | + | 0.837556i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 17.8535 | − | 19.7848i | 1.03423 | − | 1.14611i | ||||
\(299\) | 22.5405 | 1.30355 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.00263 | − | 15.7418i | 0.518903 | − | 0.907344i | ||||
\(302\) | 19.5773 | + | 17.6662i | 1.12654 | + | 1.01658i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 20.8052 | − | 4.32735i | 1.19326 | − | 0.248191i | ||||
\(305\) | 4.75818 | 0.272452 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.23094 | −0.184399 | −0.0921997 | − | 0.995741i | \(-0.529390\pi\) | ||||
−0.0921997 | + | 0.995741i | \(0.529390\pi\) | |||||||
\(308\) | 2.30851 | + | 1.02251i | 0.131539 | + | 0.0582630i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.55705 | − | 3.20982i | −0.202027 | − | 0.182306i | ||||
\(311\) | −9.34597 | −0.529962 | −0.264981 | − | 0.964254i | \(-0.585366\pi\) | ||||
−0.264981 | + | 0.964254i | \(0.585366\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.6495i | 0.941085i | 0.882377 | + | 0.470543i | \(0.155942\pi\) | ||||
−0.882377 | + | 0.470543i | \(0.844058\pi\) | |||||||
\(314\) | −23.8272 | − | 21.5013i | −1.34465 | − | 1.21339i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −17.5241 | + | 1.80316i | −0.985810 | + | 0.101436i | ||||
\(317\) | −25.7874 | −1.44836 | −0.724182 | − | 0.689609i | \(-0.757782\pi\) | ||||
−0.724182 | + | 0.689609i | \(0.757782\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.94759i | 0.165033i | ||||||||
\(320\) | −7.62449 | + | 2.42221i | −0.426222 | + | 0.135406i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.87821 | + | 27.0469i | 0.494763 | + | 1.50727i | ||||
\(323\) | 20.3661i | 1.13320i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 2.96271i | − | 0.164342i | ||||||
\(326\) | −9.63816 | − | 8.69732i | −0.533808 | − | 0.481700i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.68878 | − | 2.30846i | 0.0932473 | − | 0.127463i | ||||
\(329\) | −14.2817 | − | 8.16760i | −0.787377 | − | 0.450295i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 33.4834i | 1.84041i | 0.391432 | + | 0.920207i | \(0.371980\pi\) | ||||
−0.391432 | + | 0.920207i | \(0.628020\pi\) | |||||||
\(332\) | 2.24199 | + | 21.7889i | 0.123045 | + | 1.19582i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −14.0933 | + | 15.6178i | −0.771151 | + | 0.854571i | ||||
\(335\) | 1.30610 | 0.0713598 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.98366 | −0.271477 | −0.135739 | − | 0.990745i | \(-0.543341\pi\) | ||||
−0.135739 | + | 0.990745i | \(0.543341\pi\) | |||||||
\(338\) | 4.00042 | − | 4.43317i | 0.217594 | − | 0.241133i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.784764 | − | 7.62679i | −0.0425598 | − | 0.413620i | ||||
\(341\) | 1.61652i | 0.0875395i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.227975 | − | 18.5189i | −0.0123095 | − | 0.999924i | ||||
\(344\) | 11.4464 | − | 15.6465i | 0.617147 | − | 0.843602i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 19.1309 | + | 17.2634i | 1.02848 | + | 0.928087i | ||||
\(347\) | − | 2.96693i | − | 0.159273i | −0.996824 | − | 0.0796367i | \(-0.974624\pi\) | ||
0.996824 | − | 0.0796367i | \(-0.0253760\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 15.7698i | − | 0.844139i | −0.906563 | − | 0.422070i | \(-0.861304\pi\) | ||
0.906563 | − | 0.422070i | \(-0.138696\pi\) | |||||||
\(350\) | 3.55503 | − | 1.16694i | 0.190024 | − | 0.0623758i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.33013 | + | 1.36232i | 0.124196 | + | 0.0726121i | ||||
\(353\) | 9.20491i | 0.489928i | 0.969532 | + | 0.244964i | \(0.0787761\pi\) | ||||
−0.969532 | + | 0.244964i | \(0.921224\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.18700 | 0.487595 | ||||||||
\(356\) | −26.1038 | + | 2.68597i | −1.38350 | + | 0.142356i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.27885 | − | 4.76355i | −0.278996 | − | 0.251761i | ||||
\(359\) | 20.9031i | 1.10322i | 0.834102 | + | 0.551611i | \(0.185987\pi\) | ||||
−0.834102 | + | 0.551611i | \(0.814013\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.22390 | 0.485468 | ||||||||
\(362\) | −15.3819 | − | 13.8803i | −0.808452 | − | 0.729534i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −14.3340 | − | 6.34900i | −0.751308 | − | 0.332778i | ||||
\(365\) | −4.49766 | −0.235418 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.79845 | 0.250477 | 0.125239 | − | 0.992127i | \(-0.460030\pi\) | ||||
0.125239 | + | 0.992127i | \(0.460030\pi\) | |||||||
\(368\) | 6.19710 | + | 29.7947i | 0.323046 | + | 1.55315i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −9.05951 | − | 8.17516i | −0.470982 | − | 0.425006i | ||||
\(371\) | −21.3680 | − | 12.2202i | −1.10937 | − | 0.634441i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.9408 | 1.49850 | 0.749250 | − | 0.662287i | \(-0.230414\pi\) | ||||
0.749250 | + | 0.662287i | \(0.230414\pi\) | |||||||
\(374\) | −1.73302 | + | 1.92049i | −0.0896122 | + | 0.0993061i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −14.1952 | − | 10.3847i | −0.732062 | − | 0.535549i | ||||
\(377\) | − | 18.3022i | − | 0.942612i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.73908i | 0.243430i | 0.992565 | + | 0.121715i | \(0.0388394\pi\) | ||||
−0.992565 | + | 0.121715i | \(0.961161\pi\) | |||||||
\(380\) | −10.5694 | + | 1.08755i | −0.542200 | + | 0.0557901i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 7.18880 | + | 6.48706i | 0.367811 | + | 0.331907i | ||||
\(383\) | 11.9795 | 0.612125 | 0.306063 | − | 0.952011i | \(-0.400988\pi\) | ||||
0.306063 | + | 0.952011i | \(0.400988\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.09586 | − | 0.626715i | −0.0558503 | − | 0.0319404i | ||||
\(386\) | 7.08283 | − | 7.84902i | 0.360507 | − | 0.399505i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.19537 | − | 0.328790i | 0.162220 | − | 0.0166918i | ||||
\(389\) | −24.1871 | −1.22633 | −0.613167 | − | 0.789953i | \(-0.710105\pi\) | ||||
−0.613167 | + | 0.789953i | \(0.710105\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −29.1658 | −1.47498 | ||||||||
\(392\) | 1.97247 | − | 19.7005i | 0.0996249 | − | 0.995025i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 13.5246 | − | 14.9877i | 0.681362 | − | 0.755069i | ||||
\(395\) | 8.80833 | 0.443195 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 37.1405i | 1.86403i | 0.362420 | + | 0.932015i | \(0.381951\pi\) | ||||
−0.362420 | + | 0.932015i | \(0.618049\pi\) | |||||||
\(398\) | 1.52295 | − | 1.68769i | 0.0763384 | − | 0.0845964i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.91619 | − | 0.814543i | 0.195809 | − | 0.0407271i | ||||
\(401\) | −20.4040 | −1.01893 | −0.509464 | − | 0.860492i | \(-0.670156\pi\) | ||||
−0.509464 | + | 0.860492i | \(0.670156\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 10.0373i | − | 0.499995i | ||||||
\(404\) | −12.2884 | + | 1.26442i | −0.611371 | + | 0.0629075i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 21.9613 | − | 7.20883i | 1.08992 | − | 0.357768i | ||||
\(407\) | 4.11715i | 0.204079i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 4.69204i | − | 0.232007i | −0.993249 | − | 0.116003i | \(-0.962992\pi\) | ||
0.993249 | − | 0.116003i | \(-0.0370083\pi\) | |||||||
\(410\) | −0.958097 | + | 1.06174i | −0.0473170 | + | 0.0524356i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.44211 | − | 33.4523i | −0.169580 | − | 1.64808i | ||||
\(413\) | 11.2275 | + | 6.42091i | 0.552468 | + | 0.315952i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 10.9520i | − | 0.537612i | ||||||
\(416\) | −14.4683 | − | 8.45896i | −0.709365 | − | 0.414735i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.66147 | + | 2.40167i | 0.130177 | + | 0.117469i | ||||
\(419\) | 10.4551 | 0.510766 | 0.255383 | − | 0.966840i | \(-0.417798\pi\) | ||||
0.255383 | + | 0.966840i | \(0.417798\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.0598 | −1.41629 | −0.708144 | − | 0.706068i | \(-0.750467\pi\) | ||||
−0.708144 | + | 0.706068i | \(0.750467\pi\) | |||||||
\(422\) | 1.39208 | + | 1.25619i | 0.0677653 | + | 0.0611503i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −21.2386 | − | 15.5373i | −1.03144 | − | 0.754559i | ||||
\(425\) | 3.83353i | 0.185953i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.24969 | + | 10.9281i | −0.302444 | + | 0.528847i | ||||
\(428\) | 18.2203 | − | 1.87479i | 0.880710 | − | 0.0906214i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.49388 | + | 7.19635i | −0.313162 | + | 0.347039i | ||||
\(431\) | − | 11.8497i | − | 0.570779i | −0.958412 | − | 0.285389i | \(-0.907877\pi\) | ||
0.958412 | − | 0.285389i | \(-0.0921229\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 37.2566i | 1.79044i | 0.445625 | + | 0.895220i | \(0.352981\pi\) | ||||
−0.445625 | + | 0.895220i | \(0.647019\pi\) | |||||||
\(434\) | 12.0440 | − | 3.95347i | 0.578132 | − | 0.189773i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.12136 | + | 30.3352i | 0.149486 | + | 1.45279i | ||||
\(437\) | 40.4188i | 1.93349i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.20068 | 0.105033 | 0.0525163 | − | 0.998620i | \(-0.483276\pi\) | ||||
0.0525163 | + | 0.998620i | \(0.483276\pi\) | |||||||
\(440\) | −1.08922 | − | 0.796835i | −0.0519267 | − | 0.0379876i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 10.7607 | − | 11.9247i | 0.511834 | − | 0.567202i | ||||
\(443\) | − | 5.86101i | − | 0.278465i | −0.990260 | − | 0.139233i | \(-0.955536\pi\) | ||
0.990260 | − | 0.139233i | \(-0.0444636\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.1208 | 0.621987 | ||||||||
\(446\) | −20.3991 | + | 22.6058i | −0.965925 | + | 1.07041i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.45139 | − | 20.6926i | 0.210309 | − | 0.977635i | ||||
\(449\) | 11.2784 | 0.532259 | 0.266129 | − | 0.963937i | \(-0.414255\pi\) | ||||
0.266129 | + | 0.963937i | \(0.414255\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.482513 | 0.0227207 | ||||||||
\(452\) | −0.829068 | − | 8.05735i | −0.0389961 | − | 0.378986i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 13.3129 | − | 14.7530i | 0.624805 | − | 0.692394i | ||||
\(455\) | 6.80445 | + | 3.89141i | 0.318997 | + | 0.182432i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.5671 | 0.494307 | 0.247153 | − | 0.968976i | \(-0.420505\pi\) | ||||
0.247153 | + | 0.968976i | \(0.420505\pi\) | |||||||
\(458\) | −18.0535 | − | 16.2912i | −0.843584 | − | 0.761237i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.55746 | − | 15.1362i | −0.0726167 | − | 0.705731i | ||||
\(461\) | − | 0.502682i | − | 0.0234122i | −0.999931 | − | 0.0117061i | \(-0.996274\pi\) | ||
0.999931 | − | 0.0117061i | \(-0.00372626\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 16.5694i | − | 0.770044i | −0.922907 | − | 0.385022i | \(-0.874194\pi\) | ||
0.922907 | − | 0.385022i | \(-0.125806\pi\) | |||||||
\(464\) | 24.1923 | − | 5.03185i | 1.12310 | − | 0.233598i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.9430 | − | 12.1267i | 0.506924 | − | 0.561761i | ||||
\(467\) | 17.1182 | 0.792137 | 0.396069 | − | 0.918221i | \(-0.370374\pi\) | ||||
0.396069 | + | 0.918221i | \(0.370374\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.71551 | + | 2.99971i | −0.0792149 | + | 0.138514i | ||||
\(470\) | 6.52887 | + | 5.89154i | 0.301154 | + | 0.271757i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 11.1595 | + | 8.16384i | 0.513657 | + | 0.375771i | ||||
\(473\) | 3.27042 | 0.150374 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.31262 | 0.243760 | ||||||||
\(476\) | 18.5472 | + | 8.21513i | 0.850108 | + | 0.376540i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −14.1790 | − | 12.7949i | −0.648534 | − | 0.585227i | ||||
\(479\) | −7.51289 | −0.343272 | −0.171636 | − | 0.985160i | \(-0.554905\pi\) | ||||
−0.171636 | + | 0.985160i | \(0.554905\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 25.5643i | − | 1.16563i | ||||||
\(482\) | 6.38155 | + | 5.75861i | 0.290672 | + | 0.262298i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.20521 | − | 21.4315i | −0.100237 | − | 0.974159i | ||||
\(485\) | −1.60612 | −0.0729302 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.3725i | 0.832537i | 0.909242 | + | 0.416269i | \(0.136662\pi\) | ||||
−0.909242 | + | 0.416269i | \(0.863338\pi\) | |||||||
\(488\) | −7.94614 | + | 10.8619i | −0.359705 | + | 0.491695i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.98928 | + | 9.69756i | −0.0898666 | + | 0.438091i | ||||
\(491\) | 12.3732i | 0.558395i | 0.960234 | + | 0.279197i | \(0.0900684\pi\) | ||||
−0.960234 | + | 0.279197i | \(0.909932\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 23.6817i | 1.06657i | ||||||||
\(494\) | −16.5257 | − | 14.9125i | −0.743524 | − | 0.670944i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 13.2676 | − | 2.75958i | 0.595732 | − | 0.123909i | ||||
\(497\) | −12.0668 | + | 21.0997i | −0.541269 | + | 0.946453i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 3.90928i | − | 0.175003i | −0.996164 | − | 0.0875017i | \(-0.972112\pi\) | ||
0.996164 | − | 0.0875017i | \(-0.0278883\pi\) | |||||||
\(500\) | −1.98950 | + | 0.204711i | −0.0889730 | + | 0.00915495i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −24.6284 | + | 27.2926i | −1.09922 | + | 1.21813i | ||||
\(503\) | 20.7397 | 0.924738 | 0.462369 | − | 0.886688i | \(-0.347000\pi\) | ||||
0.462369 | + | 0.886688i | \(0.347000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.17664 | 0.274857 | ||||||||
\(506\) | −3.43937 | + | 3.81143i | −0.152899 | + | 0.169439i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −25.8532 | + | 2.66019i | −1.14705 | + | 0.118027i | ||||
\(509\) | − | 19.9445i | − | 0.884025i | −0.897009 | − | 0.442012i | \(-0.854265\pi\) | ||
0.897009 | − | 0.442012i | \(-0.145735\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.90751 | − | 10.3298i | 0.261333 | − | 0.456962i | ||||
\(512\) | 7.20349 | − | 21.4502i | 0.318352 | − | 0.947972i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −27.4433 | − | 24.7644i | −1.21047 | − | 1.09231i | ||||
\(515\) | 16.8145i | 0.740935i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 2.96708i | − | 0.130492i | ||||||
\(518\) | 30.6752 | − | 10.0692i | 1.34779 | − | 0.442414i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6.76323 | + | 4.94772i | 0.296587 | + | 0.216972i | ||||
\(521\) | − | 37.8103i | − | 1.65650i | −0.560361 | − | 0.828249i | \(-0.689338\pi\) | ||
0.560361 | − | 0.828249i | \(-0.310662\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.5206 | 0.722398 | 0.361199 | − | 0.932489i | \(-0.382368\pi\) | ||||
0.361199 | + | 0.932489i | \(0.382368\pi\) | |||||||
\(524\) | −0.363468 | − | 3.53239i | −0.0158782 | − | 0.154313i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −21.1476 | − | 19.0833i | −0.922080 | − | 0.832070i | ||||
\(527\) | 12.9875i | 0.565746i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −34.8828 | −1.51664 | ||||||||
\(530\) | 9.76835 | + | 8.81480i | 0.424310 | + | 0.382890i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 11.3848 | − | 25.7032i | 0.493593 | − | 1.11438i | ||||
\(533\) | −2.99603 | −0.129773 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.15824 | −0.395945 | ||||||||
\(536\) | −2.18118 | + | 2.98154i | −0.0942127 | + | 0.128783i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −26.4300 | − | 23.8500i | −1.13948 | − | 1.02825i | ||||
\(539\) | 2.87875 | − | 1.69370i | 0.123996 | − | 0.0729527i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.6251 | −1.40266 | −0.701331 | − | 0.712836i | \(-0.747411\pi\) | ||||
−0.701331 | + | 0.712836i | \(0.747411\pi\) | |||||||
\(542\) | −8.65275 | + | 9.58877i | −0.371668 | + | 0.411873i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 18.7209 | + | 10.9453i | 0.802650 | + | 0.469274i | ||||
\(545\) | − | 15.2477i | − | 0.653138i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.9526i | 1.53722i | 0.639716 | + | 0.768612i | \(0.279052\pi\) | ||||
−0.639716 | + | 0.768612i | \(0.720948\pi\) | |||||||
\(548\) | −3.10386 | − | 30.1650i | −0.132590 | − | 1.28859i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.500972 | + | 0.452069i | 0.0213615 | + | 0.0192763i | ||||
\(551\) | 32.8188 | 1.39813 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.5694 | + | 20.2301i | −0.491982 | + | 0.860270i | ||||
\(554\) | −16.3025 | + | 18.0661i | −0.692628 | + | 0.767553i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.85971 | + | 37.5108i | 0.163688 | + | 1.59081i | ||||
\(557\) | 8.84229 | 0.374660 | 0.187330 | − | 0.982297i | \(-0.440017\pi\) | ||||
0.187330 | + | 0.982297i | \(0.440017\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20.3068 | −0.858885 | ||||||||
\(560\) | −3.27301 | + | 10.0642i | −0.138310 | + | 0.425289i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −10.0770 | + | 11.1671i | −0.425072 | + | 0.471054i | ||||
\(563\) | 17.7594 | 0.748471 | 0.374235 | − | 0.927334i | \(-0.377905\pi\) | ||||
0.374235 | + | 0.927334i | \(0.377905\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.04995i | 0.170383i | ||||||||
\(566\) | 18.3439 | − | 20.3283i | 0.771052 | − | 0.854462i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −15.3423 | + | 20.9719i | −0.643747 | + | 0.879963i | ||||
\(569\) | −36.7269 | −1.53967 | −0.769835 | − | 0.638243i | \(-0.779661\pi\) | ||||
−0.769835 | + | 0.638243i | \(0.779661\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.1069i | 0.715902i | 0.933740 | + | 0.357951i | \(0.116524\pi\) | ||||
−0.933740 | + | 0.357951i | \(0.883476\pi\) | |||||||
\(572\) | −0.289389 | − | 2.81245i | −0.0121000 | − | 0.117594i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.18007 | − | 3.59501i | −0.0492551 | − | 0.150053i | ||||
\(575\) | 7.60808i | 0.317279i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 37.9794i | − | 1.58110i | −0.612395 | − | 0.790552i | \(-0.709794\pi\) | ||
0.612395 | − | 0.790552i | \(-0.290206\pi\) | |||||||
\(578\) | 2.18297 | − | 2.41912i | 0.0907998 | − | 0.100622i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −12.2902 | + | 1.26461i | −0.510321 | + | 0.0525099i | ||||
\(581\) | 25.1534 | + | 14.3850i | 1.04354 | + | 0.596792i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 4.43928i | − | 0.183856i | ||||||
\(584\) | 7.51108 | − | 10.2672i | 0.310811 | − | 0.424859i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 25.8132 | + | 23.2934i | 1.06633 | + | 0.962242i | ||||
\(587\) | −40.1743 | −1.65817 | −0.829085 | − | 0.559122i | \(-0.811138\pi\) | ||||
−0.829085 | + | 0.559122i | \(0.811138\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.9985 | 0.741617 | ||||||||
\(590\) | −5.13263 | − | 4.63160i | −0.211307 | − | 0.190680i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 33.7915 | − | 7.02842i | 1.38882 | − | 0.288866i | ||||
\(593\) | − | 2.80855i | − | 0.115333i | −0.998336 | − | 0.0576667i | \(-0.981634\pi\) | ||
0.998336 | − | 0.0576667i | \(-0.0183661\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.80445 | − | 5.03519i | −0.360947 | − | 0.206423i | ||||
\(596\) | −3.85756 | − | 37.4899i | −0.158012 | − | 1.53565i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 21.3558 | − | 23.6660i | 0.873305 | − | 0.967775i | ||||
\(599\) | 10.0933i | 0.412399i | 0.978510 | + | 0.206200i | \(0.0661097\pi\) | ||||
−0.978510 | + | 0.206200i | \(0.933890\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.17083i | 0.333295i | 0.986017 | + | 0.166648i | \(0.0532942\pi\) | ||||
−0.986017 | + | 0.166648i | \(0.946706\pi\) | |||||||
\(602\) | −7.99838 | − | 24.3666i | −0.325990 | − | 0.993109i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 37.0966 | − | 3.81708i | 1.50944 | − | 0.155315i | ||||
\(605\) | 10.7723i | 0.437958i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.7112 | −0.840642 | −0.420321 | − | 0.907375i | \(-0.638083\pi\) | ||||
−0.420321 | + | 0.907375i | \(0.638083\pi\) | |||||||
\(608\) | 15.1683 | − | 25.9439i | 0.615155 | − | 1.05217i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.50809 | − | 4.99576i | 0.182527 | − | 0.202272i | ||||
\(611\) | 18.4232i | 0.745325i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.61369 | 0.186345 | 0.0931726 | − | 0.995650i | \(-0.470299\pi\) | ||||
0.0931726 | + | 0.995650i | \(0.470299\pi\) | |||||||
\(614\) | −3.06112 | + | 3.39226i | −0.123537 | + | 0.136901i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.26074 | − | 1.45501i | 0.131379 | − | 0.0586238i | ||||
\(617\) | −13.3799 | −0.538655 | −0.269328 | − | 0.963049i | \(-0.586801\pi\) | ||||
−0.269328 | + | 0.963049i | \(0.586801\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 36.4215 | 1.46390 | 0.731951 | − | 0.681357i | \(-0.238610\pi\) | ||||
0.731951 | + | 0.681357i | \(0.238610\pi\) | |||||||
\(620\) | −6.74018 | + | 0.693537i | −0.270692 | + | 0.0278531i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −8.85476 | + | 9.81263i | −0.355044 | + | 0.393451i | ||||
\(623\) | −17.2337 | + | 30.1345i | −0.690454 | + | 1.20732i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 17.4808 | + | 15.7744i | 0.698674 | + | 0.630473i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −45.1498 | + | 4.64572i | −1.80167 | + | 0.185385i | ||||
\(629\) | 33.0782i | 1.31892i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.3976i | 0.931442i | 0.884932 | + | 0.465721i | \(0.154205\pi\) | ||||
−0.884932 | + | 0.465721i | \(0.845795\pi\) | |||||||
\(632\) | −14.7099 | + | 20.1075i | −0.585128 | + | 0.799835i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −24.4320 | + | 27.0750i | −0.970320 | + | 1.07528i | ||||
\(635\) | 12.9949 | 0.515686 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17.8748 | + | 10.5165i | −0.708224 | + | 0.416680i | ||||
\(638\) | 3.09476 | + | 2.79267i | 0.122523 | + | 0.110563i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −4.68060 | + | 10.3001i | −0.185017 | + | 0.407147i | ||||
\(641\) | −14.4482 | −0.570668 | −0.285334 | − | 0.958428i | \(-0.592104\pi\) | ||||
−0.285334 | + | 0.958428i | \(0.592104\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.1004 | −0.556065 | −0.278033 | − | 0.960572i | \(-0.589682\pi\) | ||||
−0.278033 | + | 0.960572i | \(0.589682\pi\) | |||||||
\(644\) | 36.8090 | + | 16.3039i | 1.45048 | + | 0.642463i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 21.3830 | + | 19.2956i | 0.841301 | + | 0.759177i | ||||
\(647\) | 13.1557 | 0.517205 | 0.258602 | − | 0.965984i | \(-0.416738\pi\) | ||||
0.258602 | + | 0.965984i | \(0.416738\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.33255i | 0.0915606i | ||||||||
\(650\) | −3.11064 | − | 2.80699i | −0.122009 | − | 0.110099i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −18.2632 | + | 1.87920i | −0.715241 | + | 0.0735953i | ||||
\(653\) | −34.5944 | −1.35378 | −0.676892 | − | 0.736083i | \(-0.736673\pi\) | ||||
−0.676892 | + | 0.736083i | \(0.736673\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.77552i | 0.0693753i | ||||||||
\(656\) | −0.823703 | − | 3.96023i | −0.0321602 | − | 0.154621i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −22.1065 | + | 7.25650i | −0.861802 | + | 0.282888i | ||||
\(659\) | − | 8.35962i | − | 0.325644i | −0.986655 | − | 0.162822i | \(-0.947940\pi\) | ||
0.986655 | − | 0.162822i | \(-0.0520597\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 45.6469i | 1.77546i | 0.460366 | + | 0.887729i | \(0.347718\pi\) | ||||
−0.460366 | + | 0.887729i | \(0.652282\pi\) | |||||||
\(662\) | 35.1553 | + | 31.7235i | 1.36635 | + | 1.23297i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 25.0010 | + | 18.2898i | 0.970228 | + | 0.709782i | ||||
\(665\) | −6.97792 | + | 12.2015i | −0.270592 | + | 0.473153i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 46.9991i | 1.81981i | ||||||||
\(668\) | 3.04510 | + | 29.5940i | 0.117818 | + | 1.14503i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.23745 | − | 1.37131i | 0.0478069 | − | 0.0529784i | ||||
\(671\) | −2.27035 | −0.0876459 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −39.4155 | −1.51936 | −0.759678 | − | 0.650299i | \(-0.774644\pi\) | ||||
−0.759678 | + | 0.650299i | \(0.774644\pi\) | |||||||
\(674\) | −4.72173 | + | 5.23250i | −0.181874 | + | 0.201548i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.864360 | − | 8.40034i | −0.0332446 | − | 0.323090i | ||||
\(677\) | − | 19.6704i | − | 0.755995i | −0.925807 | − | 0.377997i | \(-0.876613\pi\) | ||
0.925807 | − | 0.377997i | \(-0.123387\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.10958 | − | 3.68877i | 0.0809582 | − | 0.141562i | ||||
\(680\) | −8.75112 | − | 6.40198i | −0.335590 | − | 0.245505i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.69723 | + | 1.53156i | 0.0649905 | + | 0.0586464i | ||||
\(683\) | 5.27739i | 0.201934i | 0.994890 | + | 0.100967i | \(0.0321936\pi\) | ||||
−0.994890 | + | 0.100967i | \(0.967806\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.1622i | 0.579316i | ||||||||
\(686\) | −19.6595 | − | 17.3062i | −0.750604 | − | 0.660753i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.58297 | − | 26.8420i | −0.212849 | − | 1.02334i | ||||
\(689\) | 27.5645i | 1.05012i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.48775 | −0.322889 | −0.161445 | − | 0.986882i | \(-0.551615\pi\) | ||||
−0.161445 | + | 0.986882i | \(0.551615\pi\) | |||||||
\(692\) | 36.2508 | − | 3.73005i | 1.37805 | − | 0.141795i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.11508 | − | 2.81100i | −0.118247 | − | 0.106704i | ||||
\(695\) | − | 18.8544i | − | 0.715190i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.87664 | 0.146838 | ||||||||
\(698\) | −16.5572 | − | 14.9410i | −0.626700 | − | 0.565524i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.14297 | − | 4.83815i | 0.0809967 | − | 0.182865i | ||||
\(701\) | 10.1888 | 0.384825 | 0.192412 | − | 0.981314i | \(-0.438369\pi\) | ||||
0.192412 | + | 0.981314i | \(0.438369\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 45.8408 | 1.72892 | ||||||||
\(704\) | 3.63800 | − | 1.15575i | 0.137112 | − | 0.0435591i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.66452 | + | 8.72111i | 0.363729 | + | 0.328223i | ||||
\(707\) | −8.11279 | + | 14.1859i | −0.305113 | + | 0.533514i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.99960 | 0.150208 | 0.0751041 | − | 0.997176i | \(-0.476071\pi\) | ||||
0.0751041 | + | 0.997176i | \(0.476071\pi\) | |||||||
\(710\) | 8.70414 | − | 9.64571i | 0.326660 | − | 0.361997i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −21.9117 | + | 29.9520i | −0.821177 | + | 1.12250i | ||||
\(713\) | 25.7753i | 0.965292i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.41365i | 0.0528675i | ||||||||
\(716\) | −10.0028 | + | 1.02925i | −0.373822 | + | 0.0384647i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 21.9468 | + | 19.8044i | 0.819046 | + | 0.739094i | ||||
\(719\) | 8.22659 | 0.306800 | 0.153400 | − | 0.988164i | \(-0.450978\pi\) | ||||
0.153400 | + | 0.988164i | \(0.450978\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −38.6178 | − | 22.0852i | −1.43820 | − | 0.822496i | ||||
\(722\) | 8.73910 | − | 9.68446i | 0.325236 | − | 0.360418i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −29.1468 | + | 2.99908i | −1.08323 | + | 0.111460i | ||||
\(725\) | 6.17752 | 0.229427 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.05684 | 0.0762839 | 0.0381419 | − | 0.999272i | \(-0.487856\pi\) | ||||
0.0381419 | + | 0.999272i | \(0.487856\pi\) | |||||||
\(728\) | −20.2467 | + | 9.03444i | −0.750391 | + | 0.334839i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4.26127 | + | 4.72223i | −0.157717 | + | 0.174778i | ||||
\(731\) | 26.2755 | 0.971833 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 24.8578i | − | 0.918145i | −0.888399 | − | 0.459072i | \(-0.848182\pi\) | ||
0.888399 | − | 0.459072i | \(-0.151818\pi\) | |||||||
\(734\) | 4.54625 | − | 5.03804i | 0.167805 | − | 0.185958i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 37.1537 | + | 21.7221i | 1.36950 | + | 0.800689i | ||||
\(737\) | −0.623201 | −0.0229559 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.48614i | 0.0546686i | 0.999626 | + | 0.0273343i | \(0.00870186\pi\) | ||||
−0.999626 | + | 0.0273343i | \(0.991298\pi\) | |||||||
\(740\) | −17.1667 | + | 1.76638i | −0.631061 | + | 0.0649335i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −33.0753 | + | 10.8570i | −1.21423 | + | 0.398574i | ||||
\(743\) | 4.73363i | 0.173660i | 0.996223 | + | 0.0868299i | \(0.0276737\pi\) | ||||
−0.996223 | + | 0.0868299i | \(0.972326\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.8439i | 0.690389i | ||||||||
\(746\) | 27.4197 | − | 30.3859i | 1.00391 | − | 1.11251i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.374448 | + | 3.63910i | 0.0136912 | + | 0.133059i | ||||
\(749\) | 12.0290 | − | 21.0337i | 0.439530 | − | 0.768555i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 49.1841i | − | 1.79475i | −0.441266 | − | 0.897376i | \(-0.645470\pi\) | ||
0.441266 | − | 0.897376i | \(-0.354530\pi\) | |||||||
\(752\) | −24.3523 | + | 5.06513i | −0.888038 | + | 0.184706i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −19.2161 | − | 17.3403i | −0.699808 | − | 0.631495i | ||||
\(755\) | −18.6462 | −0.678606 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.41551 | −0.233176 | −0.116588 | − | 0.993180i | \(-0.537196\pi\) | ||||
−0.116588 | + | 0.993180i | \(0.537196\pi\) | |||||||
\(758\) | 4.97571 | + | 4.49000i | 0.180726 | + | 0.163084i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −8.87206 | + | 12.1276i | −0.321823 | + | 0.439913i | ||||
\(761\) | − | 1.23026i | − | 0.0445970i | −0.999751 | − | 0.0222985i | \(-0.992902\pi\) | ||
0.999751 | − | 0.0222985i | \(-0.00709843\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 35.0192 | + | 20.0272i | 1.26778 | + | 0.725035i | ||||
\(764\) | 13.6219 | − | 1.40164i | 0.492824 | − | 0.0507095i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 11.3499 | − | 12.5777i | 0.410088 | − | 0.454450i | ||||
\(767\) | − | 14.4833i | − | 0.522962i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 28.9327i | − | 1.04334i | −0.853147 | − | 0.521670i | \(-0.825309\pi\) | ||
0.853147 | − | 0.521670i | \(-0.174691\pi\) | |||||||
\(770\) | −1.69627 | + | 0.556804i | −0.0611294 | + | 0.0200658i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.53037 | − | 14.8730i | −0.0550791 | − | 0.535290i | ||||
\(773\) | 12.9773i | 0.466761i | 0.972385 | + | 0.233380i | \(0.0749788\pi\) | ||||
−0.972385 | + | 0.233380i | \(0.925021\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.38789 | 0.121696 | ||||||||
\(776\) | 2.68222 | − | 3.66643i | 0.0962860 | − | 0.131617i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −22.9158 | + | 25.3948i | −0.821573 | + | 0.910447i | ||||
\(779\) | − | 5.37237i | − | 0.192485i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.38355 | −0.156856 | ||||||||
\(782\) | −27.6328 | + | 30.6220i | −0.988148 | + | 1.09504i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −18.8154 | − | 20.7360i | −0.671977 | − | 0.740572i | ||||
\(785\) | 22.6941 | 0.809986 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.7024 | −0.595377 | −0.297688 | − | 0.954663i | \(-0.596216\pi\) | ||||
−0.297688 | + | 0.954663i | \(0.596216\pi\) | |||||||
\(788\) | −2.92223 | − | 28.3999i | −0.104100 | − | 1.01170i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8.34538 | − | 9.24814i | 0.296915 | − | 0.329034i | ||||
\(791\) | −9.30150 | − | 5.31945i | −0.330723 | − | 0.189138i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.0971 | 0.500603 | ||||||||
\(794\) | 38.9950 | + | 35.1885i | 1.38388 | + | 1.24879i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.329059 | − | 3.19798i | −0.0116632 | − | 0.113349i | ||||
\(797\) | 7.59395i | 0.268992i | 0.990914 | + | 0.134496i | \(0.0429415\pi\) | ||||
−0.990914 | + | 0.134496i | \(0.957059\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 23.8383i | − | 0.843339i | ||||||
\(800\) | 2.85514 | − | 4.88346i | 0.100945 | − | 0.172656i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −19.3316 | + | 21.4228i | −0.682622 | + | 0.756465i | ||||
\(803\) | 2.14604 | 0.0757323 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17.4734 | − | 9.99293i | −0.615858 | − | 0.352204i | ||||
\(806\) | −10.5385 | − | 9.50977i | −0.371203 | − | 0.334967i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −10.3150 | + | 14.0999i | −0.362880 | + | 0.496034i | ||||
\(809\) | −26.4140 | −0.928665 | −0.464333 | − | 0.885661i | \(-0.653706\pi\) | ||||
−0.464333 | + | 0.885661i | \(0.653706\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.20334 | −0.0773697 | −0.0386848 | − | 0.999251i | \(-0.512317\pi\) | ||||
−0.0386848 | + | 0.999251i | \(0.512317\pi\) | |||||||
\(812\) | 13.2382 | − | 29.8878i | 0.464571 | − | 1.04886i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.32272 | + | 3.90075i | 0.151511 | + | 0.136721i | ||||
\(815\) | 9.17980 | 0.321554 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 36.4133i | − | 1.27394i | ||||||
\(818\) | −4.92632 | − | 4.44544i | −0.172245 | − | 0.155431i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.207013 | + | 2.01187i | 0.00722921 | + | 0.0702576i | ||||
\(821\) | −8.94895 | −0.312321 | −0.156160 | − | 0.987732i | \(-0.549912\pi\) | ||||
−0.156160 | + | 0.987732i | \(0.549912\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 40.8135i | − | 1.42267i | −0.702853 | − | 0.711335i | \(-0.748091\pi\) | ||
0.702853 | − | 0.711335i | \(-0.251909\pi\) | |||||||
\(824\) | −38.3839 | − | 28.0802i | −1.33716 | − | 0.978218i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 17.3789 | − | 5.70465i | 0.604689 | − | 0.198490i | ||||
\(827\) | − | 4.55874i | − | 0.158523i | −0.996854 | − | 0.0792615i | \(-0.974744\pi\) | ||
0.996854 | − | 0.0792615i | \(-0.0252562\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.872606i | 0.0303069i | 0.999885 | + | 0.0151534i | \(0.00482367\pi\) | ||||
−0.999885 | + | 0.0151534i | \(0.995176\pi\) | |||||||
\(830\) | −11.4988 | − | 10.3764i | −0.399130 | − | 0.360169i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −22.5892 | + | 7.17632i | −0.783138 | + | 0.248794i | ||||
\(833\) | 23.1286 | − | 13.6076i | 0.801359 | − | 0.471476i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 14.8751i | − | 0.514775i | ||||||
\(836\) | 5.04317 | − | 0.518921i | 0.174422 | − | 0.0179473i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 9.90561 | − | 10.9772i | 0.342184 | − | 0.379200i | ||||
\(839\) | −48.9005 | −1.68823 | −0.844117 | − | 0.536160i | \(-0.819874\pi\) | ||||
−0.844117 | + | 0.536160i | \(0.819874\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.16178 | 0.315923 | ||||||||
\(842\) | −27.5324 | + | 30.5108i | −0.948831 | + | 1.05147i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.63782 | − | 0.271421i | 0.0907976 | − | 0.00934270i | ||||
\(845\) | 4.22235i | 0.145253i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −24.7408 | − | 14.1491i | −0.850103 | − | 0.486167i | ||||
\(848\) | −36.4354 | + | 7.57834i | −1.25120 | + | 0.260241i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.02494 | + | 3.63204i | 0.138054 | + | 0.124578i | ||||
\(851\) | 65.6476i | 2.25037i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 46.6995i | − | 1.59896i | −0.600692 | − | 0.799480i | \(-0.705108\pi\) | ||
0.600692 | − | 0.799480i | \(-0.294892\pi\) | |||||||
\(854\) | 5.55253 | + | 16.9155i | 0.190004 | + | 0.578835i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.2942 | − | 20.9063i | 0.522746 | − | 0.714562i | ||||
\(857\) | 42.6029i | 1.45529i | 0.685955 | + | 0.727644i | \(0.259385\pi\) | ||||
−0.685955 | + | 0.727644i | \(0.740615\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.0255 | 1.12682 | 0.563408 | − | 0.826179i | \(-0.309490\pi\) | ||||
0.563408 | + | 0.826179i | \(0.309490\pi\) | |||||||
\(860\) | 1.40311 | + | 13.6362i | 0.0478457 | + | 0.464992i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −12.4413 | − | 11.2269i | −0.423754 | − | 0.382389i | ||||
\(863\) | − | 50.3282i | − | 1.71319i | −0.515989 | − | 0.856595i | \(-0.672575\pi\) | ||
0.515989 | − | 0.856595i | \(-0.327425\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.2211 | −0.619536 | ||||||||
\(866\) | 39.1169 | + | 35.2985i | 1.32925 | + | 1.19949i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 7.26014 | − | 16.3911i | 0.246425 | − | 0.556350i | ||||
\(869\) | −4.20287 | −0.142573 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.86959 | 0.131116 | ||||||||
\(872\) | 34.8071 | + | 25.4636i | 1.17872 | + | 0.862305i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 42.4370 | + | 38.2944i | 1.43545 | + | 1.29533i | ||||
\(875\) | −1.31346 | + | 2.29670i | −0.0444031 | + | 0.0776425i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.9157 | 0.638738 | 0.319369 | − | 0.947630i | \(-0.396529\pi\) | ||||
0.319369 | + | 0.947630i | \(0.396529\pi\) | |||||||
\(878\) | 2.08501 | − | 2.31056i | 0.0703658 | − | 0.0779776i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.86860 | + | 0.388657i | −0.0629904 | + | 0.0131016i | ||||
\(881\) | 18.9884i | 0.639736i | 0.947462 | + | 0.319868i | \(0.103639\pi\) | ||||
−0.947462 | + | 0.319868i | \(0.896361\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.4843i | 1.19414i | 0.802188 | + | 0.597072i | \(0.203669\pi\) | ||||
−0.802188 | + | 0.597072i | \(0.796331\pi\) | |||||||
\(884\) | −2.32503 | − | 22.5960i | −0.0781992 | − | 0.759984i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.15366 | − | 5.55296i | −0.206736 | − | 0.186555i | ||||
\(887\) | −53.4487 | −1.79463 | −0.897315 | − | 0.441390i | \(-0.854485\pi\) | ||||
−0.897315 | + | 0.441390i | \(0.854485\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.0683 | + | 29.8453i | −0.572452 | + | 1.00098i | ||||
\(890\) | 12.4312 | − | 13.7760i | 0.416695 | − | 0.461771i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.40757 | + | 42.8353i | 0.147576 | + | 1.43423i | ||||
\(893\) | −33.0358 | −1.10550 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.02780 | 0.168061 | ||||||||
\(896\) | −17.5084 | − | 24.2787i | −0.584915 | − | 0.811095i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10.6856 | − | 11.8415i | 0.356583 | − | 0.395156i | ||||
\(899\) | 20.9287 | 0.698012 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 35.6664i | − | 1.18822i | ||||||
\(902\) | 0.457153 | − | 0.506606i | 0.0152215 | − | 0.0168681i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.24516 | − | 6.76340i | −0.307489 | − | 0.224947i | ||||
\(905\) | 14.6503 | 0.486994 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 48.4656i | − | 1.60927i | −0.593768 | − | 0.804636i | \(-0.702360\pi\) | ||
0.593768 | − | 0.804636i | \(-0.297640\pi\) | |||||||
\(908\) | −2.87648 | − | 27.9552i | −0.0954592 | − | 0.927727i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 10.5325 | − | 3.45732i | 0.349150 | − | 0.114609i | ||||
\(911\) | 1.00067i | 0.0331538i | 0.999863 | + | 0.0165769i | \(0.00527684\pi\) | ||||
−0.999863 | + | 0.0165769i | \(0.994723\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.22571i | 0.172946i | ||||||||
\(914\) | 10.0117 | − | 11.0947i | 0.331157 | − | 0.366980i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −34.2092 | + | 3.51999i | −1.13030 | + | 0.116304i | ||||
\(917\) | −4.07783 | − | 2.33208i | −0.134662 | − | 0.0770121i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.71273i | 0.221433i | 0.993852 | + | 0.110716i | \(0.0353145\pi\) | ||||
−0.993852 | + | 0.110716i | \(0.964686\pi\) | |||||||
\(920\) | −17.3676 | − | 12.7055i | −0.572593 | − | 0.418887i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −0.527782 | − | 0.476262i | −0.0173816 | − | 0.0156848i | ||||
\(923\) | 27.2184 | 0.895905 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.62867 | 0.283709 | ||||||||
\(926\) | −17.3967 | − | 15.6985i | −0.571691 | − | 0.515885i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 17.6377 | − | 30.1677i | 0.578986 | − | 0.990302i | ||||
\(929\) | − | 12.9220i | − | 0.423957i | −0.977274 | − | 0.211979i | \(-0.932009\pi\) | ||
0.977274 | − | 0.211979i | \(-0.0679907\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.8578 | − | 32.0524i | −0.618040 | − | 1.05047i | ||||
\(932\) | −2.36442 | − | 22.9788i | −0.0774491 | − | 0.752694i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 16.2185 | − | 17.9730i | 0.530686 | − | 0.588093i | ||||
\(935\) | − | 1.82916i | − | 0.0598198i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 55.1955i | 1.80316i | 0.432615 | + | 0.901579i | \(0.357591\pi\) | ||||
−0.432615 | + | 0.901579i | \(0.642409\pi\) | |||||||
\(938\) | 1.52414 | + | 4.64322i | 0.0497651 | + | 0.151606i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 12.3714 | − | 1.27297i | 0.403512 | − | 0.0415197i | ||||
\(941\) | − | 41.8089i | − | 1.36293i | −0.731851 | − | 0.681465i | \(-0.761343\pi\) | ||
0.731851 | − | 0.681465i | \(-0.238657\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.69364 | 0.250539 | ||||||||
\(944\) | 19.1444 | − | 3.98192i | 0.623098 | − | 0.129600i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.09853 | − | 3.43372i | 0.100742 | − | 0.111640i | ||||
\(947\) | − | 29.9634i | − | 0.973679i | −0.873491 | − | 0.486839i | \(-0.838150\pi\) | ||
0.873491 | − | 0.486839i | \(-0.161850\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.3253 | −0.432556 | ||||||||
\(950\) | 5.03339 | − | 5.57788i | 0.163305 | − | 0.180970i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 26.1977 | − | 11.6899i | 0.849072 | − | 0.378872i | ||||
\(953\) | −4.49708 | −0.145675 | −0.0728373 | − | 0.997344i | \(-0.523205\pi\) | ||||
−0.0728373 | + | 0.997344i | \(0.523205\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.84692 | −0.221561 | ||||||||
\(956\) | −26.8676 | + | 2.76457i | −0.868961 | + | 0.0894125i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −7.11802 | + | 7.88801i | −0.229973 | + | 0.254850i | ||||
\(959\) | −34.8229 | − | 19.9149i | −1.12449 | − | 0.643086i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.5222 | −0.629749 | ||||||||
\(962\) | −26.8407 | − | 24.2206i | −0.865379 | − | 0.780904i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 12.0923 | − | 1.24425i | 0.389467 | − | 0.0400745i | ||||
\(965\) | 7.47575i | 0.240653i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 15.3198i | − | 0.492651i | −0.969187 | − | 0.246326i | \(-0.920777\pi\) | ||
0.969187 | − | 0.246326i | \(-0.0792232\pi\) | |||||||
\(968\) | −24.5909 | − | 17.9898i | −0.790382 | − | 0.578213i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.52170 | + | 1.68632i | −0.0488590 | + | 0.0541443i | ||||
\(971\) | −2.95293 | −0.0947641 | −0.0473821 | − | 0.998877i | \(-0.515088\pi\) | ||||
−0.0473821 | + | 0.998877i | \(0.515088\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 43.3029 | + | 24.7646i | 1.38823 | + | 0.793917i | ||||
\(974\) | 19.2899 | + | 17.4069i | 0.618087 | + | 0.557752i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.87574 | + | 18.6339i | 0.124059 | + | 0.596457i | ||||
\(977\) | −32.6707 | −1.04523 | −0.522615 | − | 0.852569i | \(-0.675043\pi\) | ||||
−0.522615 | + | 0.852569i | \(0.675043\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.26056 | −0.200088 | ||||||||
\(980\) | 8.29705 | + | 11.2765i | 0.265039 | + | 0.360214i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 12.9910 | + | 11.7229i | 0.414560 | + | 0.374092i | ||||
\(983\) | −12.7915 | −0.407986 | −0.203993 | − | 0.978972i | \(-0.565392\pi\) | ||||
−0.203993 | + | 0.978972i | \(0.565392\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.2749i | 0.454837i | ||||||||
\(986\) | 24.8641 | + | 22.4370i | 0.791836 | + | 0.714540i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −31.3142 | + | 3.22210i | −0.996236 | + | 0.102509i | ||||
\(989\) | 52.1467 | 1.65817 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 29.8437i | − | 0.948015i | −0.880521 | − | 0.474008i | \(-0.842807\pi\) | ||
0.880521 | − | 0.474008i | \(-0.157193\pi\) | |||||||
\(992\) | 9.67290 | − | 16.5446i | 0.307115 | − | 0.525291i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 10.7207 | + | 32.6601i | 0.340041 | + | 1.03591i | ||||
\(995\) | 1.60743i | 0.0509590i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 16.0457i | − | 0.508172i | −0.967182 | − | 0.254086i | \(-0.918225\pi\) | ||
0.967182 | − | 0.254086i | \(-0.0817746\pi\) | |||||||
\(998\) | −4.10448 | − | 3.70381i | −0.129925 | − | 0.117242i | ||||
\(999\) | 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 | 1260.2.c.d.811.13 | 16 | ||
3.2 | odd | 2 | 420.2.c.a.391.4 | yes | 16 | ||
4.3 | odd | 2 | 1260.2.c.e.811.14 | 16 | |||
7.6 | odd | 2 | 1260.2.c.e.811.13 | 16 | |||
12.11 | even | 2 | 420.2.c.b.391.3 | yes | 16 | ||
21.20 | even | 2 | 420.2.c.b.391.4 | yes | 16 | ||
28.27 | even | 2 | inner | 1260.2.c.d.811.14 | 16 | ||
84.83 | odd | 2 | 420.2.c.a.391.3 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.c.a.391.3 | ✓ | 16 | 84.83 | odd | 2 | ||
420.2.c.a.391.4 | yes | 16 | 3.2 | odd | 2 | ||
420.2.c.b.391.3 | yes | 16 | 12.11 | even | 2 | ||
420.2.c.b.391.4 | yes | 16 | 21.20 | even | 2 | ||
1260.2.c.d.811.13 | 16 | 1.1 | even | 1 | trivial | ||
1260.2.c.d.811.14 | 16 | 28.27 | even | 2 | inner | ||
1260.2.c.e.811.13 | 16 | 7.6 | odd | 2 | |||
1260.2.c.e.811.14 | 16 | 4.3 | odd | 2 |