Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,2,Mod(2255,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2352.2255");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.h (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: | \(18.7808145554\) |
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: | \( x^{16} - 12x^{14} + 97x^{12} - 432x^{10} + 1392x^{8} - 2502x^{6} + 3181x^{4} - 1650x^{2} + 625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{16}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2255.1 | ||
Root | \(2.01367 + 1.16260i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.2255 |
Dual form | 2352.2.h.p.2255.4 |
$q$-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 \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1471\) | \(1765\) | \(2257\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
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 | 0 | ||||||||
\(3\) | −1.70166 | − | 0.323042i | −0.982453 | − | 0.186508i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.55481i | − | 0.695331i | −0.937619 | − | 0.347665i | \(-0.886975\pi\) | ||
0.937619 | − | 0.347665i | \(-0.113025\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.79129 | + | 1.09941i | 0.930429 | + | 0.366471i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.53326 | −0.702601 | −0.351300 | − | 0.936263i | \(-0.614260\pi\) | ||||
−0.351300 | + | 0.936263i | \(0.614260\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.502268 | + | 2.64575i | −0.129685 | + | 0.683130i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.33991i | − | 1.05258i | −0.850304 | − | 0.526292i | \(-0.823582\pi\) | ||
0.850304 | − | 0.526292i | \(-0.176418\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.83723i | 1.56857i | 0.620402 | + | 0.784284i | \(0.286970\pi\) | ||||
−0.620402 | + | 0.784284i | \(0.713030\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.80848 | 0.794124 | 0.397062 | − | 0.917792i | \(-0.370030\pi\) | ||||
0.397062 | + | 0.917792i | \(0.370030\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.58258 | 0.516515 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.39466 | − | 2.77253i | −0.845753 | − | 0.533574i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 8.33639i | − | 1.54803i | −0.633168 | − | 0.774015i | \(-0.718246\pi\) | ||
0.633168 | − | 0.774015i | \(-0.281754\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4.89898i | − | 0.879883i | −0.898027 | − | 0.439941i | \(-0.854999\pi\) | ||
0.898027 | − | 0.439941i | \(-0.145001\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.58258 | 0.260174 | 0.130087 | − | 0.991503i | \(-0.458474\pi\) | ||||
0.130087 | + | 0.991503i | \(0.458474\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.31075 | + | 0.818350i | 0.690273 | + | 0.131041i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 7.44953i | − | 1.16342i | −0.813396 | − | 0.581710i | \(-0.802384\pi\) | ||
0.813396 | − | 0.581710i | \(-0.197616\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.20520i | 0.946285i | 0.880986 | + | 0.473142i | \(0.156880\pi\) | ||||
−0.880986 | + | 0.473142i | \(0.843120\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.70938 | − | 4.33991i | 0.254819 | − | 0.646956i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.38601 | 0.785630 | 0.392815 | − | 0.919617i | \(-0.371501\pi\) | ||||
0.392815 | + | 0.919617i | \(0.371501\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.40197 | + | 7.38505i | −0.196316 | + | 1.03411i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.5352i | 1.44712i | 0.690259 | + | 0.723562i | \(0.257496\pi\) | ||||
−0.690259 | + | 0.723562i | \(0.742504\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.20871 | − | 11.6346i | 0.292551 | − | 1.54105i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.2100 | −1.32922 | −0.664611 | − | 0.747189i | \(-0.731403\pi\) | ||||
−0.664611 | + | 0.747189i | \(0.731403\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.19012 | 1.04864 | 0.524319 | − | 0.851522i | \(-0.324320\pi\) | ||||
0.524319 | + | 0.851522i | \(0.324320\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.93874i | 0.488540i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 3.46410i | − | 0.423207i | −0.977356 | − | 0.211604i | \(-0.932131\pi\) | ||
0.977356 | − | 0.211604i | \(-0.0678686\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.48074 | − | 1.23030i | −0.780189 | − | 0.148111i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.4391 | −1.71360 | −0.856800 | − | 0.515648i | \(-0.827551\pi\) | ||||
−0.856800 | + | 0.515648i | \(0.827551\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.5473 | −1.35151 | −0.675753 | − | 0.737128i | \(-0.736181\pi\) | ||||
−0.675753 | + | 0.737128i | \(0.736181\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.39466 | − | 0.834280i | −0.507452 | − | 0.0963344i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 6.92820i | − | 0.779484i | −0.920924 | − | 0.389742i | \(-0.872564\pi\) | ||
0.920924 | − | 0.389742i | \(-0.127436\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.58258 | + | 6.13756i | 0.731397 | + | 0.681952i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.82395 | −0.529497 | −0.264748 | − | 0.964318i | \(-0.585289\pi\) | ||||
−0.264748 | + | 0.964318i | \(0.585289\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.74773 | −0.731894 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.69300 | + | 14.1857i | −0.288720 | + | 1.52087i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 4.33991i | − | 0.460030i | −0.973187 | − | 0.230015i | \(-0.926122\pi\) | ||
0.973187 | − | 0.230015i | \(-0.0738775\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.58258 | + | 8.33639i | −0.164105 | + | 0.864444i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10.6306 | 1.09067 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.89949 | 1.00514 | 0.502571 | − | 0.864536i | \(-0.332388\pi\) | ||||
0.502571 | + | 0.864536i | \(0.332388\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 19.5635i | − | 1.94664i | −0.229455 | − | 0.973319i | \(-0.573694\pi\) | ||
0.229455 | − | 0.973319i | \(-0.426306\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 3.87650i | − | 0.381963i | −0.981594 | − | 0.190982i | \(-0.938833\pi\) | ||
0.981594 | − | 0.190982i | \(-0.0611671\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.4391 | 1.39588 | 0.697938 | − | 0.716158i | \(-0.254101\pi\) | ||||
0.697938 | + | 0.716158i | \(0.254101\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.5826 | −1.30097 | −0.650487 | − | 0.759517i | \(-0.725435\pi\) | ||||
−0.650487 | + | 0.759517i | \(0.725435\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.69300 | − | 0.511238i | −0.255609 | − | 0.0485246i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 14.4740i | − | 1.36160i | −0.732471 | − | 0.680798i | \(-0.761633\pi\) | ||
0.732471 | − | 0.680798i | \(-0.238367\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 5.92146i | − | 0.552179i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.07107 | − | 2.78511i | −0.653720 | − | 0.257483i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.40651 | + | 12.6766i | −0.216988 | + | 1.14301i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 11.7894i | − | 1.05448i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 10.3923i | − | 0.922168i | −0.887357 | − | 0.461084i | \(-0.847461\pi\) | ||
0.887357 | − | 0.461084i | \(-0.152539\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.00454 | − | 10.5591i | 0.176490 | − | 0.929681i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.5960 | −1.36263 | −0.681313 | − | 0.731992i | \(-0.738591\pi\) | ||||
−0.681313 | + | 0.731992i | \(0.738591\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.31075 | + | 6.83285i | −0.371010 | + | 0.588078i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.73991i | 0.148650i | 0.997234 | + | 0.0743251i | \(0.0236803\pi\) | ||||
−0.997234 | + | 0.0743251i | \(0.976320\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.7362i | 0.995452i | 0.867334 | + | 0.497726i | \(0.165832\pi\) | ||||
−0.867334 | + | 0.497726i | \(0.834168\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.16515 | − | 1.73991i | −0.771845 | − | 0.146527i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.9615 | −1.07639 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.5352i | 0.863079i | 0.902094 | + | 0.431540i | \(0.142029\pi\) | ||||
−0.902094 | + | 0.431540i | \(0.857971\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 15.8745i | − | 1.29185i | −0.763401 | − | 0.645925i | \(-0.776472\pi\) | ||
0.763401 | − | 0.645925i | \(-0.223528\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.77136 | − | 12.1139i | 0.385742 | − | 0.979355i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.61697 | −0.611809 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.19012 | −0.653643 | −0.326821 | − | 0.945086i | \(-0.605978\pi\) | ||||
−0.326821 | + | 0.945086i | \(0.605978\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.40332 | − | 17.9274i | 0.269901 | − | 1.42173i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 20.0616i | − | 1.57135i | −0.618642 | − | 0.785673i | \(-0.712317\pi\) | ||
0.618642 | − | 0.785673i | \(-0.287683\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.58258 | −0.506352 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.51695 | + | 19.0847i | −0.574836 | + | 1.45944i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 1.55481i | − | 0.118210i | −0.998252 | − | 0.0591049i | \(-0.981175\pi\) | ||
0.998252 | − | 0.0591049i | \(-0.0188246\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 17.3739 | + | 3.29824i | 1.30590 | + | 0.247911i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.4391 | −1.07923 | −0.539613 | − | 0.841913i | \(-0.681429\pi\) | ||||
−0.539613 | + | 0.841913i | \(0.681429\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.4282 | −0.775123 | −0.387562 | − | 0.921844i | \(-0.626683\pi\) | ||||
−0.387562 | + | 0.921844i | \(0.626683\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.9368 | − | 2.64575i | −1.03024 | − | 0.195580i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 2.46060i | − | 0.180907i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.0560 | −1.59592 | −0.797959 | − | 0.602712i | \(-0.794087\pi\) | ||||
−0.797959 | + | 0.602712i | \(0.794087\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.74773 | 0.629675 | 0.314838 | − | 0.949146i | \(-0.398050\pi\) | ||||
0.314838 | + | 0.949146i | \(0.398050\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.27238 | − | 6.70239i | 0.0911168 | − | 0.479968i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 10.5352i | − | 0.750604i | −0.926903 | − | 0.375302i | \(-0.877539\pi\) | ||
0.926903 | − | 0.375302i | \(-0.122461\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 9.79796i | − | 0.694559i | −0.937762 | − | 0.347279i | \(-0.887106\pi\) | ||
0.937762 | − | 0.347279i | \(-0.112894\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.11905 | + | 5.89472i | −0.0789317 | + | 0.415782i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.5826 | −0.808962 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 10.6306 | + | 4.18710i | 0.738876 | + | 0.291024i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 15.8745i | − | 1.09285i | −0.837509 | − | 0.546423i | \(-0.815989\pi\) | ||
0.837509 | − | 0.546423i | \(-0.184011\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 24.5704 | + | 4.66442i | 1.68353 | + | 0.319601i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.64789 | 0.657981 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 19.6495 | + | 3.73025i | 1.32779 | + | 0.252067i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.9941i | 0.739546i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.4724i | 1.57183i | 0.618335 | + | 0.785915i | \(0.287808\pi\) | ||||
−0.618335 | + | 0.785915i | \(0.712192\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.20871 | + | 2.83932i | 0.480581 | + | 0.189288i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.82395 | −0.320177 | −0.160088 | − | 0.987103i | \(-0.551178\pi\) | ||||
−0.160088 | + | 0.987103i | \(0.551178\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.78044 | 0.580228 | 0.290114 | − | 0.956992i | \(-0.406307\pi\) | ||||
0.290114 | + | 0.956992i | \(0.406307\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 1.73991i | − | 0.113985i | −0.998375 | − | 0.0569925i | \(-0.981849\pi\) | ||
0.998375 | − | 0.0569925i | \(-0.0181511\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 8.37420i | − | 0.546273i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.23810 | + | 11.7894i | −0.145380 | + | 0.765806i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.80848 | 0.246350 | 0.123175 | − | 0.992385i | \(-0.460692\pi\) | ||||
0.123175 | + | 0.992385i | \(0.460692\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.06199 | 0.197240 | 0.0986199 | − | 0.995125i | \(-0.468557\pi\) | ||||
0.0986199 | + | 0.995125i | \(0.468557\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −9.21861 | − | 12.5705i | −0.591374 | − | 0.806397i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 17.3205i | − | 1.10208i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.20871 | + | 1.55834i | 0.520206 | + | 0.0987556i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.562063 | −0.0354771 | −0.0177385 | − | 0.999843i | \(-0.505647\pi\) | ||||
−0.0177385 | + | 0.999843i | \(0.505647\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 11.4823 | + | 2.17980i | 0.719052 | + | 0.136504i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.6688i | 0.852633i | 0.904574 | + | 0.426317i | \(0.140189\pi\) | ||||
−0.904574 | + | 0.426317i | \(0.859811\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.16515 | − | 23.2693i | 0.567309 | − | 1.44033i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 29.6730 | 1.82971 | 0.914857 | − | 0.403777i | \(-0.132303\pi\) | ||||
0.914857 | + | 0.403777i | \(0.132303\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.3802 | 1.00623 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.40197 | + | 7.38505i | −0.0857994 | + | 0.451958i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.55481i | 0.0947982i | 0.998876 | + | 0.0473991i | \(0.0150933\pi\) | ||||
−0.998876 | + | 0.0473991i | \(0.984907\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.5959i | 1.19037i | 0.803590 | + | 0.595184i | \(0.202921\pi\) | ||||
−0.803590 | + | 0.595184i | \(0.797079\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.00000 | 0.120168 | 0.0600842 | − | 0.998193i | \(-0.480863\pi\) | ||||
0.0600842 | + | 0.998193i | \(0.480863\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.38601 | − | 13.6745i | 0.322452 | − | 0.818669i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.9329i | 0.890821i | 0.895326 | + | 0.445410i | \(0.146942\pi\) | ||||
−0.895326 | + | 0.445410i | \(0.853058\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 26.4331i | − | 1.57129i | −0.618679 | − | 0.785644i | \(-0.712332\pi\) | ||
0.618679 | − | 0.785644i | \(-0.287668\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −18.0896 | − | 3.43412i | −1.07154 | − | 0.203420i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.83485 | −0.107932 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −16.8456 | − | 3.19795i | −0.987505 | − | 0.187467i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.3442i | 0.779579i | 0.920904 | + | 0.389790i | \(0.127452\pi\) | ||||
−0.920904 | + | 0.389790i | \(0.872548\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.8745i | 0.924250i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.64789 | −0.557952 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.31982 | + | 33.2904i | −0.363064 | + | 1.91248i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 12.7341i | − | 0.729150i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 11.7362i | − | 0.669821i | −0.942250 | − | 0.334910i | \(-0.891294\pi\) | ||
0.942250 | − | 0.334910i | \(-0.108706\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.25227 | + | 6.59649i | −0.0712393 | + | 0.375261i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.0339 | 0.852494 | 0.426247 | − | 0.904607i | \(-0.359835\pi\) | ||||
0.426247 | + | 0.904607i | \(0.359835\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.89041 | 0.332946 | 0.166473 | − | 0.986046i | \(-0.446762\pi\) | ||||
0.166473 | + | 0.986046i | \(0.446762\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.65775i | 0.149274i | 0.997211 | + | 0.0746371i | \(0.0237798\pi\) | ||||
−0.997211 | + | 0.0746371i | \(0.976220\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −24.5704 | − | 4.66442i | −1.37138 | − | 0.260343i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 29.6730 | 1.65105 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.54234 | −0.362904 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 23.1129 | + | 4.38774i | 1.27815 | + | 0.242643i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 13.1334i | − | 0.721877i | −0.932590 | − | 0.360939i | \(-0.882456\pi\) | ||
0.932590 | − | 0.360939i | \(-0.117544\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.41742 | + | 1.73991i | 0.242073 | + | 0.0953463i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.38601 | −0.294269 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.25227 | −0.0682157 | −0.0341078 | − | 0.999418i | \(-0.510859\pi\) | ||||
−0.0341078 | + | 0.999418i | \(0.510859\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.67569 | + | 24.6297i | −0.253949 | + | 1.33770i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.91288 | + | 10.0763i | −0.102986 | + | 0.542490i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −36.4951 | −1.95916 | −0.979579 | − | 0.201058i | \(-0.935562\pi\) | ||||
−0.979579 | + | 0.201058i | \(0.935562\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.77136 | 0.255405 | 0.127703 | − | 0.991813i | \(-0.459240\pi\) | ||||
0.127703 | + | 0.991813i | \(0.459240\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.1328 | + | 7.02355i | 0.594227 | + | 0.374890i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 27.9188i | 1.48597i | 0.669309 | + | 0.742984i | \(0.266590\pi\) | ||||
−0.669309 | + | 0.742984i | \(0.733410\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 22.4499i | 1.19152i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.80848 | −0.201004 | −0.100502 | − | 0.994937i | \(-0.532045\pi\) | ||||
−0.100502 | + | 0.994937i | \(0.532045\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −27.7477 | −1.46041 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 18.7183 | + | 3.55346i | 0.982453 | + | 0.186508i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 17.9538i | 0.939743i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 23.4724i | − | 1.22525i | −0.790374 | − | 0.612625i | \(-0.790114\pi\) | ||
0.790374 | − | 0.612625i | \(-0.209886\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.19012 | − | 20.7938i | 0.426361 | − | 1.08248i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.0000 | 0.517780 | 0.258890 | − | 0.965907i | \(-0.416643\pi\) | ||||
0.258890 | + | 0.965907i | \(0.416643\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.80848 | + | 20.0616i | −0.196669 | + | 1.03598i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 21.1183i | 1.08765i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 6.20520i | − | 0.318740i | −0.987219 | − | 0.159370i | \(-0.949054\pi\) | ||
0.987219 | − | 0.159370i | \(-0.0509463\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.35715 | + | 17.6842i | −0.171992 | + | 0.905987i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.0339 | 0.768196 | 0.384098 | − | 0.923292i | \(-0.374512\pi\) | ||||
0.384098 | + | 0.923292i | \(0.374512\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.82209 | + | 17.3205i | −0.346786 | + | 0.880451i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 38.2022i | − | 1.93693i | −0.249157 | − | 0.968463i | \(-0.580154\pi\) | ||
0.249157 | − | 0.968463i | \(-0.419846\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 16.5285i | − | 0.835882i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 26.5390 | + | 5.03815i | 1.33872 | + | 0.254141i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.7720 | −0.541999 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 38.1222 | 1.91330 | 0.956648 | − | 0.291246i | \(-0.0940698\pi\) | ||||
0.956648 | + | 0.291246i | \(0.0940698\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 21.5294i | − | 1.07513i | −0.843224 | − | 0.537563i | \(-0.819345\pi\) | ||
0.843224 | − | 0.537563i | \(-0.180655\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.4104i | 0.618206i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.54273 | − | 10.2346i | 0.474182 | − | 0.508563i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.7944 | −0.879879 | −0.439939 | − | 0.898027i | \(-0.645000\pi\) | ||||
−0.439939 | + | 0.898027i | \(0.645000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.562063 | − | 2.96073i | 0.0277245 | − | 0.146042i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.50030i | 0.368175i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.79129 | − | 19.9710i | 0.185660 | − | 0.977986i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.5960 | −0.761913 | −0.380956 | − | 0.924593i | \(-0.624405\pi\) | ||||
−0.380956 | + | 0.924593i | \(0.624405\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 35.4955 | 1.72994 | 0.864971 | − | 0.501821i | \(-0.167337\pi\) | ||||
0.864971 | + | 0.501821i | \(0.167337\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 15.0339 | + | 5.92146i | 0.730973 | + | 0.287911i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 11.2082i | − | 0.543675i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.4527 | 0.840665 | 0.420333 | − | 0.907370i | \(-0.361913\pi\) | ||||
0.420333 | + | 0.907370i | \(0.361913\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.823886 | 0.0395935 | 0.0197967 | − | 0.999804i | \(-0.493698\pi\) | ||||
0.0197967 | + | 0.999804i | \(0.493698\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 22.0560 | + | 4.18710i | 1.05751 | + | 0.200756i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 26.0395i | 1.24564i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.6969i | 0.701447i | 0.936479 | + | 0.350723i | \(0.114064\pi\) | ||||
−0.936479 | + | 0.350723i | \(0.885936\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.82209 | 0.324127 | 0.162064 | − | 0.986780i | \(-0.448185\pi\) | ||||
0.162064 | + | 0.986780i | \(0.448185\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.74773 | −0.319873 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.40332 | − | 17.9274i | 0.160971 | − | 0.847935i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 28.9479i | 1.36614i | 0.730355 | + | 0.683068i | \(0.239355\pi\) | ||||
−0.730355 | + | 0.683068i | \(0.760645\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.12813 | + | 27.0130i | −0.240941 | + | 1.26918i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.7477 | −1.15765 | −0.578825 | − | 0.815452i | \(-0.696489\pi\) | ||||
−0.578825 | + | 0.815452i | \(0.696489\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −12.0325 | + | 19.0725i | −0.561631 | + | 0.890226i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.2346i | 0.476674i | 0.971182 | + | 0.238337i | \(0.0766023\pi\) | ||||
−0.971182 | + | 0.238337i | \(0.923398\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.2668i | 1.22072i | 0.792123 | + | 0.610361i | \(0.208976\pi\) | ||||
−0.792123 | + | 0.610361i | \(0.791024\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 12.9615 | + | 2.46060i | 0.601074 | + | 0.114108i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −25.2439 | −1.16815 | −0.584073 | − | 0.811701i | \(-0.698542\pi\) | ||||
−0.584073 | + | 0.811701i | \(0.698542\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.9368 | + | 2.64575i | 0.642173 | + | 0.121910i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 17.6577i | 0.810189i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −11.5826 | + | 29.4068i | −0.530330 | + | 1.34645i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 31.1919 | 1.42520 | 0.712598 | − | 0.701573i | \(-0.247518\pi\) | ||||
0.712598 | + | 0.701573i | \(0.247518\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.00908 | −0.182798 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 15.3918i | − | 0.698906i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 36.6591i | − | 1.66118i | −0.556882 | − | 0.830592i | \(-0.688002\pi\) | ||
0.556882 | − | 0.830592i | \(-0.311998\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.48074 | + | 34.1380i | −0.293069 | + | 1.54377i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.0560 | 0.995374 | 0.497687 | − | 0.867357i | \(-0.334183\pi\) | ||||
0.497687 | + | 0.867357i | \(0.334183\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −36.1792 | −1.62943 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.94630i | 0.400492i | 0.979746 | + | 0.200246i | \(0.0641741\pi\) | ||||
−0.979746 | + | 0.200246i | \(0.935826\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 31.1919 | 1.39078 | 0.695390 | − | 0.718633i | \(-0.255232\pi\) | ||||
0.695390 | + | 0.718633i | \(0.255232\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −30.4174 | −1.35356 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.2013 | + | 2.12645i | 0.497467 | + | 0.0944389i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 0.905793i | − | 0.0401486i | −0.999798 | − | 0.0200743i | \(-0.993610\pi\) | ||
0.999798 | − | 0.0200743i | \(-0.00639027\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 18.9564 | − | 30.0473i | 0.836947 | − | 1.32662i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.02721 | −0.265591 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.502268 | + | 2.64575i | −0.0220471 | + | 0.116136i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.9188i | 1.22314i | 0.791189 | + | 0.611572i | \(0.209463\pi\) | ||||
−0.791189 | + | 0.611572i | \(0.790537\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 0.915775i | − | 0.0400440i | −0.999800 | − | 0.0200220i | \(-0.993626\pi\) | ||
0.999800 | − | 0.0200220i | \(-0.00637363\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −21.2611 | −0.926150 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.49545 | −0.369368 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −28.4989 | − | 11.2250i | −1.23675 | − | 0.487122i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 18.8716i | 0.817420i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 22.4499i | − | 0.970596i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 24.5704 | + | 4.66442i | 1.06029 | + | 0.201285i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.4955 | −1.01015 | −0.505074 | − | 0.863076i | \(-0.668535\pi\) | ||||
−0.505074 | + | 0.863076i | \(0.668535\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17.7453 | + | 3.36875i | 0.761523 | + | 0.144567i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 21.1183i | 0.904608i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 11.6874i | − | 0.499717i | −0.968282 | − | 0.249859i | \(-0.919616\pi\) | ||
0.968282 | − | 0.249859i | \(-0.0803842\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 22.8610 | + | 9.00433i | 0.975683 | + | 0.384296i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 56.9978 | 2.42819 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.794877 | + | 4.18710i | −0.0337406 | + | 0.177733i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.65775i | 0.112613i | 0.998414 | + | 0.0563063i | \(0.0179323\pi\) | ||||
−0.998414 | + | 0.0563063i | \(0.982068\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 15.7194i | − | 0.664860i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.562063 | −0.0236881 | −0.0118441 | − | 0.999930i | \(-0.503770\pi\) | ||||
−0.0118441 | + | 0.999930i | \(0.503770\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −22.5042 | −0.946759 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.85658i | 0.203598i | 0.994805 | + | 0.101799i | \(0.0324599\pi\) | ||||
−0.994805 | + | 0.101799i | \(0.967540\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 0.723000i | − | 0.0302566i | −0.999886 | − | 0.0151283i | \(-0.995184\pi\) | ||
0.999886 | − | 0.0151283i | \(-0.00481567\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 37.5318 | + | 7.12502i | 1.56791 | + | 0.297652i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.83570 | 0.410177 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 43.7174 | 1.81998 | 0.909990 | − | 0.414631i | \(-0.136089\pi\) | ||||
0.909990 | + | 0.414631i | \(0.136089\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −14.8856 | − | 2.82588i | −0.618627 | − | 0.117440i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.33030 | + | 10.9941i | −0.179036 | + | 0.454552i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 36.0159 | 1.48653 | 0.743267 | − | 0.668995i | \(-0.233275\pi\) | ||||
0.743267 | + | 0.668995i | \(0.233275\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 33.4955 | 1.38016 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.40332 | + | 17.9274i | −0.139994 | + | 0.737433i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 28.5678i | 1.17314i | 0.809899 | + | 0.586570i | \(0.199522\pi\) | ||||
−0.809899 | + | 0.586570i | \(0.800478\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.16515 | + | 16.6728i | −0.129541 | + | 0.682372i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −29.6730 | −1.21241 | −0.606203 | − | 0.795310i | \(-0.707308\pi\) | ||||
−0.606203 | + | 0.795310i | \(0.707308\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.823886 | −0.0336070 | −0.0168035 | − | 0.999859i | \(-0.505349\pi\) | ||||
−0.0168035 | + | 0.999859i | \(0.505349\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.80848 | − | 9.66930i | 0.155093 | − | 0.393765i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 17.1029i | 0.695331i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 18.5734i | − | 0.753873i | −0.926239 | − | 0.376936i | \(-0.876978\pi\) | ||
0.926239 | − | 0.376936i | \(-0.123022\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.6442 | −0.551984 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 38.2432 | 1.54463 | 0.772314 | − | 0.635241i | \(-0.219099\pi\) | ||||
0.772314 | + | 0.635241i | \(0.219099\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 19.7096 | + | 3.74166i | 0.794768 | + | 0.150878i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.5294i | 0.866740i | 0.901216 | + | 0.433370i | \(0.142676\pi\) | ||||
−0.901216 | + | 0.433370i | \(0.857324\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 7.85971i | − | 0.315908i | −0.987446 | − | 0.157954i | \(-0.949510\pi\) | ||
0.987446 | − | 0.157954i | \(-0.0504898\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −16.7370 | − | 10.5591i | −0.671633 | − | 0.423724i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.41742 | −0.216697 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 6.86824i | − | 0.273855i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 40.1232i | − | 1.59728i | −0.601809 | − | 0.798640i | \(-0.705553\pi\) | ||
0.601809 | − | 0.798640i | \(-0.294447\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.12813 | + | 27.0130i | −0.203825 | + | 1.07367i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.1580 | −0.641212 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −40.3036 | − | 15.8745i | −1.59438 | − | 0.627986i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.85658i | 0.191823i | 0.995390 | + | 0.0959117i | \(0.0305766\pi\) | ||||
−0.995390 | + | 0.0959117i | \(0.969423\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 39.0851i | 1.54137i | 0.637218 | + | 0.770684i | \(0.280085\pi\) | ||||
−0.637218 | + | 0.770684i | \(0.719915\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −16.4174 | − | 3.11667i | −0.646435 | − | 0.122719i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.8059 | 1.01454 | 0.507268 | − | 0.861789i | \(-0.330656\pi\) | ||||
0.507268 | + | 0.861789i | \(0.330656\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 25.0092i | − | 0.978685i | −0.872092 | − | 0.489342i | \(-0.837237\pi\) | ||
0.872092 | − | 0.489342i | \(-0.162763\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 24.2487i | 0.947476i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −32.2317 | − | 12.6952i | −1.25748 | − | 0.495288i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.6442 | 0.531502 | 0.265751 | − | 0.964042i | \(-0.414380\pi\) | ||||
0.265751 | + | 0.964042i | \(0.414380\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.24756 | 0.359689 | 0.179844 | − | 0.983695i | \(-0.442441\pi\) | ||||
0.179844 | + | 0.983695i | \(0.442441\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.55157 | − | 18.7083i | 0.137932 | − | 0.726570i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 31.7490i | − | 1.22933i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.58258 | − | 39.9421i | 0.293159 | − | 1.54425i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.1652 | −0.584574 | −0.292287 | − | 0.956331i | \(-0.594416\pi\) | ||||
−0.292287 | + | 0.956331i | \(0.594416\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −11.3496 | − | 7.16027i | −0.436844 | − | 0.275599i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0.905793i | 0.0348124i | 0.999849 | + | 0.0174062i | \(0.00554085\pi\) | ||||
−0.999849 | + | 0.0174062i | \(0.994459\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.20871 | + | 1.55834i | 0.314559 | + | 0.0597156i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22.0560 | −0.843950 | −0.421975 | − | 0.906607i | \(-0.638663\pi\) | ||||
−0.421975 | + | 0.906607i | \(0.638663\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.70522 | 0.103361 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.9413 | − | 2.83645i | −0.570047 | − | 0.108217i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 26.6885i | − | 1.01675i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 12.7587i | − | 0.485363i | −0.970106 | − | 0.242682i | \(-0.921973\pi\) | ||
0.970106 | − | 0.242682i | \(-0.0780270\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 18.2475 | 0.692169 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −32.3303 | −1.22460 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.562063 | + | 2.96073i | −0.0212592 | + | 0.111985i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.85658i | 0.183431i | 0.995785 | + | 0.0917153i | \(0.0292350\pi\) | ||||
−0.995785 | + | 0.0917153i | \(0.970765\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.8204i | 0.408100i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.70522 | + | 14.2500i | −0.101884 | + | 0.536688i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 47.0780 | 1.76805 | 0.884026 | − | 0.467437i | \(-0.154823\pi\) | ||||
0.884026 | + | 0.467437i | \(0.154823\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.61697 | − | 19.3386i | 0.285659 | − | 0.725255i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 18.6577i | − | 0.698736i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.48074 | − | 1.23030i | −0.242028 | − | 0.0459464i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.8059 | −0.962398 | −0.481199 | − | 0.876611i | \(-0.659799\pi\) | ||||
−0.481199 | + | 0.876611i | \(0.659799\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.21046 | − | 0.989150i | −0.193779 | − | 0.0367869i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 21.5294i | − | 0.799581i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.6184i | 0.764694i | 0.924019 | + | 0.382347i | \(0.124884\pi\) | ||||
−0.924019 | + | 0.382347i | \(0.875116\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 11.6261 | + | 24.3687i | 0.430598 | + | 0.902544i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 26.9300 | 0.996044 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.94294 | −0.0717640 | −0.0358820 | − | 0.999356i | \(-0.511424\pi\) | ||||
−0.0358820 | + | 0.999356i | \(0.511424\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 40.8462i | − | 1.50255i | −0.659988 | − | 0.751276i | \(-0.729439\pi\) | ||
0.659988 | − | 0.751276i | \(-0.270561\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.59525 | + | 29.4736i | −0.205547 | + | 1.08274i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.0696 | −0.919716 | −0.459858 | − | 0.887993i | \(-0.652100\pi\) | ||||
−0.459858 | + | 0.887993i | \(0.652100\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.3802 | 0.600125 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13.4650 | − | 5.30352i | −0.492659 | − | 0.194046i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 22.8027i | − | 0.832083i | −0.909346 | − | 0.416041i | \(-0.863417\pi\) | ||
0.909346 | − | 0.416041i | \(-0.136583\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.956439 | + | 0.181570i | 0.0348546 | + | 0.00661677i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −24.6818 | −0.898262 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.74773 | −0.172559 | −0.0862795 | − | 0.996271i | \(-0.527498\pi\) | ||||
−0.0862795 | + | 0.996271i | \(0.527498\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 13.6688i | − | 0.495492i | −0.968825 | − | 0.247746i | \(-0.920310\pi\) | ||
0.968825 | − | 0.247746i | \(-0.0796898\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −18.8348 | − | 7.41855i | −0.680975 | − | 0.268218i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 25.8645 | 0.933913 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.0801 | 0.399560 | 0.199780 | − | 0.979841i | \(-0.435977\pi\) | ||||
0.199780 | + | 0.979841i | \(0.435977\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.41558 | − | 23.2596i | 0.159023 | − | 0.837673i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 1.55481i | − | 0.0559225i | −0.999609 | − | 0.0279613i | \(-0.991098\pi\) | ||
0.999609 | − | 0.0279613i | \(-0.00890150\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 12.6520i | − | 0.454473i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 50.9341 | 1.82490 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −23.1129 | + | 36.6356i | −0.825988 | + | 1.30925i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.7341i | 0.454498i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.2872i | 1.04398i | 0.852953 | + | 0.521988i | \(0.174809\pi\) | ||||
−0.852953 | + | 0.521988i | \(0.825191\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −50.4933 | − | 9.58562i | −1.79761 | − | 0.341257i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.7477 | −0.736773 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −27.8736 | − | 5.29150i | −0.988574 | − | 0.187670i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 7.77403i | − | 0.275370i | −0.990476 | − | 0.137685i | \(-0.956034\pi\) | ||
0.990476 | − | 0.137685i | \(-0.0439662\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 23.3748i | − | 0.826941i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.77136 | − | 12.1139i | 0.168588 | − | 0.428025i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.502268 | − | 2.64575i | 0.0176807 | − | 0.0931349i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 22.3514i | − | 0.785834i | −0.919574 | − | 0.392917i | \(-0.871466\pi\) | ||
0.919574 | − | 0.392917i | \(-0.128534\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 54.8045i | − | 1.92445i | −0.272259 | − | 0.962224i | \(-0.587771\pi\) | ||
0.272259 | − | 0.962224i | \(-0.412229\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.33030 | − | 33.3456i | 0.222013 | − | 1.16948i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −31.1919 | −1.09261 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −42.4264 | −1.48431 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.65775i | 0.0927562i | 0.998924 | + | 0.0463781i | \(0.0147679\pi\) | ||||
−0.998924 | + | 0.0463781i | \(0.985232\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 40.1232i | 1.39861i | 0.714825 | + | 0.699304i | \(0.246507\pi\) | ||||
−0.714825 | + | 0.699304i | \(0.753493\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22.0560 | −0.766963 | −0.383482 | − | 0.923549i | \(-0.625275\pi\) | ||||
−0.383482 | + | 0.923549i | \(0.625275\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.71392 | 0.128990 | 0.0644948 | − | 0.997918i | \(-0.479456\pi\) | ||||
0.0644948 | + | 0.997918i | \(0.479456\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.40332 | − | 0.646084i | −0.118060 | − | 0.0224124i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −13.5826 | + | 21.5294i | −0.469482 | + | 0.744164i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 25.8059 | 0.890919 | 0.445460 | − | 0.895302i | \(-0.353040\pi\) | ||||
0.445460 | + | 0.895302i | \(0.353040\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −40.4955 | −1.39639 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.82395 | − | 25.4107i | 0.166146 | − | 0.875190i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.2346i | 0.352082i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.53901 | + | 44.9802i | −0.293058 | + | 1.54372i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.02721 | 0.206610 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.2272 | 1.03496 | 0.517480 | − | 0.855695i | \(-0.326870\pi\) | ||||
0.517480 | + | 0.855695i | \(0.326870\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 29.6730 | + | 11.6874i | 1.01479 | + | 0.399701i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 22.9976i | − | 0.785583i | −0.919628 | − | 0.392791i | \(-0.871509\pi\) | ||
0.919628 | − | 0.392791i | \(-0.128491\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.81475i | 0.198397i | 0.995068 | + | 0.0991984i | \(0.0316279\pi\) | ||||
−0.995068 | + | 0.0991984i | \(0.968372\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −35.7002 | −1.21525 | −0.607625 | − | 0.794224i | \(-0.707877\pi\) | ||||
−0.607625 | + | 0.794224i | \(0.707877\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.41742 | −0.0821949 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.12229 | + | 0.592733i | 0.106038 | + | 0.0201303i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.77548i | 0.297346i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 27.6323 | + | 10.8836i | 0.935213 | + | 0.368356i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.4174 | 0.351771 | 0.175886 | − | 0.984411i | \(-0.443721\pi\) | ||||
0.175886 | + | 0.984411i | \(0.443721\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.31075 | − | 22.7074i | 0.145398 | − | 0.765900i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.7784i | 0.565278i | 0.959226 | + | 0.282639i | \(0.0912098\pi\) | ||||
−0.959226 | + | 0.282639i | \(0.908790\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.3567i | 0.718711i | 0.933201 | + | 0.359355i | \(0.117003\pi\) | ||||
−0.933201 | + | 0.359355i | \(0.882997\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.12813 | − | 27.0130i | 0.172380 | − | 0.908032i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 36.8254i | 1.23231i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.4499i | 0.750419i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16.4174 | + | 3.11667i | 0.548162 | + | 0.104063i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −40.8398 | −1.36208 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 45.7220 | 1.52322 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 16.2139i | 0.538967i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 43.5873i | 1.44729i | 0.690171 | + | 0.723647i | \(0.257535\pi\) | ||||
−0.690171 | + | 0.723647i | \(0.742465\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 21.5084 | − | 54.6073i | 0.713388 | − | 1.81121i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.0696 | −0.830594 | −0.415297 | − | 0.909686i | \(-0.636322\pi\) | ||||
−0.415297 | + | 0.909686i | \(0.636322\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.11363 | + | 21.6690i | −0.135992 | + | 0.716356i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.3024i | 0.504780i | 0.967626 | + | 0.252390i | \(0.0812166\pi\) | ||||
−0.967626 | + | 0.252390i | \(0.918783\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.79129 | + | 19.9710i | −0.124927 | + | 0.658068i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 36.5779 | 1.20398 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.08712 | 0.134384 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.26188 | − | 10.8204i | 0.139979 | − | 0.355390i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 51.4977i | − | 1.68958i | −0.535095 | − | 0.844792i | \(-0.679724\pi\) | ||
0.535095 | − | 0.844792i | \(-0.320276\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −25.5826 | − | 4.85658i | −0.837536 | − | 0.158997i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −37.0031 | −1.20884 | −0.604419 | − | 0.796666i | \(-0.706595\pi\) | ||||
−0.604419 | + | 0.796666i | \(0.706595\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.0235 | − | 1.90285i | −0.327104 | − | 0.0620972i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22.6731i | 0.739122i | 0.929207 | + | 0.369561i | \(0.120492\pi\) | ||||
−0.929207 | + | 0.369561i | \(0.879508\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 28.3714i | − | 0.923900i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.8509 | −0.742554 | −0.371277 | − | 0.928522i | \(-0.621080\pi\) | ||||
−0.371277 | + | 0.928522i | \(0.621080\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 29.2523 | 0.949569 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.858565 | − | 4.52259i | 0.0278409 | − | 0.146655i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 55.3339i | − | 1.79244i | −0.443610 | − | 0.896220i | \(-0.646303\pi\) | ||
0.443610 | − | 0.896220i | \(-0.353697\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 34.2929i | 1.10969i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.00000 | 0.225806 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 40.3036 | + | 15.8745i | 1.29876 | + | 0.511549i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 13.6010i | − | 0.437833i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.01810i | 0.0648978i | 0.999473 | + | 0.0324489i | \(0.0103306\pi\) | ||||
−0.999473 | + | 0.0324489i | \(0.989669\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −50.4933 | − | 9.58562i | −1.62208 | − | 0.307934i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36.0159 | 1.15580 | 0.577902 | − | 0.816106i | \(-0.303872\pi\) | ||||
0.577902 | + | 0.816106i | \(0.303872\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 11.1328 | + | 2.11345i | 0.356536 | + | 0.0676846i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 44.7986i | 1.43324i | 0.697466 | + | 0.716618i | \(0.254311\pi\) | ||||
−0.697466 | + | 0.716618i | \(0.745689\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −37.9129 | − | 14.9329i | −1.21047 | − | 0.476770i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.38601 | −0.171787 | −0.0858935 | − | 0.996304i | \(-0.527374\pi\) | ||||
−0.0858935 | + | 0.996304i | \(0.527374\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.3802 | −0.521918 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 23.6324i | 0.751467i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 59.4618i | − | 1.88887i | −0.328702 | − | 0.944434i | \(-0.606611\pi\) | ||
0.328702 | − | 0.944434i | \(-0.393389\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.24264 | + | 22.3486i | −0.134636 | + | 0.709211i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.2339 | −0.482948 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38.5893 | −1.22213 | −0.611067 | − | 0.791579i | \(-0.709260\pi\) | ||||
−0.611067 | + | 0.791579i | \(0.709260\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.95489 | − | 4.38774i | −0.220043 | − | 0.138822i |
(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 | 2352.2.h.p.2255.1 | ✓ | 16 | |
3.2 | odd | 2 | inner | 2352.2.h.p.2255.14 | yes | 16 | |
4.3 | odd | 2 | inner | 2352.2.h.p.2255.15 | yes | 16 | |
7.6 | odd | 2 | inner | 2352.2.h.p.2255.16 | yes | 16 | |
12.11 | even | 2 | inner | 2352.2.h.p.2255.4 | yes | 16 | |
21.20 | even | 2 | inner | 2352.2.h.p.2255.3 | yes | 16 | |
28.27 | even | 2 | inner | 2352.2.h.p.2255.2 | yes | 16 | |
84.83 | odd | 2 | inner | 2352.2.h.p.2255.13 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2352.2.h.p.2255.1 | ✓ | 16 | 1.1 | even | 1 | trivial | |
2352.2.h.p.2255.2 | yes | 16 | 28.27 | even | 2 | inner | |
2352.2.h.p.2255.3 | yes | 16 | 21.20 | even | 2 | inner | |
2352.2.h.p.2255.4 | yes | 16 | 12.11 | even | 2 | inner | |
2352.2.h.p.2255.13 | yes | 16 | 84.83 | odd | 2 | inner | |
2352.2.h.p.2255.14 | yes | 16 | 3.2 | odd | 2 | inner | |
2352.2.h.p.2255.15 | yes | 16 | 4.3 | odd | 2 | inner | |
2352.2.h.p.2255.16 | yes | 16 | 7.6 | odd | 2 | inner |