Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(1322,1323)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1323, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.1322");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.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: | \(10.5642081874\) |
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: | \( x^{16} - 12x^{14} + 106x^{12} - 384x^{10} + 1005x^{8} - 1200x^{6} + 1030x^{4} - 252x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1322.16 | ||
Root | \(2.38976 + 1.37973i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1323.1322 |
Dual form | 1323.2.c.e.1322.2 |
$q$-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 \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.75946i | 1.95123i | 0.219481 | + | 0.975617i | \(0.429564\pi\) | ||||
−0.219481 | + | 0.975617i | \(0.570436\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −5.61463 | −2.80731 | ||||||||
\(5\) | 2.24426 | 1.00366 | 0.501831 | − | 0.864966i | \(-0.332660\pi\) | ||||
0.501831 | + | 0.864966i | \(0.332660\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − 9.97442i | − 3.52649i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.19294i | 1.95838i | ||||||||
\(11\) | 0.797407i | 0.240427i | 0.992748 | + | 0.120214i | \(0.0383579\pi\) | ||||
−0.992748 | + | 0.120214i | \(0.961642\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.06262i | 1.40412i | 0.712119 | + | 0.702058i | \(0.247736\pi\) | ||||
−0.712119 | + | 0.702058i | \(0.752264\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.2948 | 4.07369 | ||||||||
\(17\) | −4.46023 | −1.08177 | −0.540883 | − | 0.841098i | \(-0.681910\pi\) | ||||
−0.540883 | + | 0.841098i | \(0.681910\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 1.25139i | − 0.287088i | −0.989644 | − | 0.143544i | \(-0.954150\pi\) | ||||
0.989644 | − | 0.143544i | \(-0.0458499\pi\) | |||||||
\(20\) | −12.6007 | −2.81759 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.20041 | −0.469130 | ||||||||
\(23\) | 3.78594i | 0.789423i | 0.918805 | + | 0.394712i | \(0.129155\pi\) | ||||
−0.918805 | + | 0.394712i | \(0.870845\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.0366824 | 0.00733649 | ||||||||
\(26\) | −13.9701 | −2.73976 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.04562i | 0.751253i | 0.926771 | + | 0.375626i | \(0.122572\pi\) | ||||
−0.926771 | + | 0.375626i | \(0.877428\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.35979i | 0.962646i | 0.876543 | + | 0.481323i | \(0.159844\pi\) | ||||
−0.876543 | + | 0.481323i | \(0.840156\pi\) | |||||||
\(32\) | 25.0160i | 4.42224i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − 12.3078i | − 2.11078i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.33120 | −0.876444 | −0.438222 | − | 0.898867i | \(-0.644392\pi\) | ||||
−0.438222 | + | 0.898867i | \(0.644392\pi\) | |||||||
\(38\) | 3.45316 | 0.560177 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − 22.3851i | − 3.53940i | ||||||||
\(41\) | −4.50330 | −0.703298 | −0.351649 | − | 0.936132i | \(-0.614379\pi\) | ||||
−0.351649 | + | 0.936132i | \(0.614379\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.390920 | 0.0596147 | 0.0298073 | − | 0.999556i | \(-0.490511\pi\) | ||||
0.0298073 | + | 0.999556i | \(0.490511\pi\) | |||||||
\(44\) | − 4.47714i | − 0.674954i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −10.4472 | −1.54035 | ||||||||
\(47\) | −6.60051 | −0.962783 | −0.481392 | − | 0.876506i | \(-0.659869\pi\) | ||||
−0.481392 | + | 0.876506i | \(0.659869\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.101224i | 0.0143152i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 28.4247i | − 3.94180i | ||||||||
\(53\) | − 6.67723i | − 0.917188i | −0.888646 | − | 0.458594i | \(-0.848353\pi\) | ||||
0.888646 | − | 0.458594i | \(-0.151647\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.78958i | 0.241307i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −11.1637 | −1.46587 | ||||||||
\(59\) | −13.3598 | −1.73930 | −0.869648 | − | 0.493673i | \(-0.835654\pi\) | ||||
−0.869648 | + | 0.493673i | \(0.835654\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.12408i | 1.04018i | 0.854111 | + | 0.520091i | \(0.174102\pi\) | ||||
−0.854111 | + | 0.520091i | \(0.825898\pi\) | |||||||
\(62\) | −14.7901 | −1.87835 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −36.4410 | −4.55513 | ||||||||
\(65\) | 11.3618i | 1.40926i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.8939 | 1.57525 | 0.787623 | − | 0.616157i | \(-0.211311\pi\) | ||||
0.787623 | + | 0.616157i | \(0.211311\pi\) | |||||||
\(68\) | 25.0425 | 3.03686 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.19597i | 0.379291i | 0.981853 | + | 0.189646i | \(0.0607339\pi\) | ||||
−0.981853 | + | 0.189646i | \(0.939266\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 9.03259i | − 1.05718i | −0.848876 | − | 0.528592i | \(-0.822720\pi\) | ||||
0.848876 | − | 0.528592i | \(-0.177280\pi\) | |||||||
\(74\) | − 14.7112i | − 1.71015i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.02608i | 0.805947i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.14069 | 0.578373 | 0.289187 | − | 0.957273i | \(-0.406615\pi\) | ||||
0.289187 | + | 0.957273i | \(0.406615\pi\) | |||||||
\(80\) | 36.5696 | 4.08861 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 12.4267i | − 1.37230i | ||||||||
\(83\) | 9.29454 | 1.02021 | 0.510104 | − | 0.860113i | \(-0.329607\pi\) | ||||
0.510104 | + | 0.860113i | \(0.329607\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.0099 | −1.08573 | ||||||||
\(86\) | 1.07873i | 0.116322i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 7.95367 | 0.847864 | ||||||||
\(89\) | 10.6640 | 1.13038 | 0.565190 | − | 0.824961i | \(-0.308803\pi\) | ||||
0.565190 | + | 0.824961i | \(0.308803\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − 21.2566i | − 2.21616i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − 18.2139i | − 1.87862i | ||||||||
\(95\) | − 2.80844i | − 0.288140i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 1.93337i | − 0.196304i | −0.995171 | − | 0.0981519i | \(-0.968707\pi\) | ||||
0.995171 | − | 0.0981519i | \(-0.0312931\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.205958 | −0.0205958 | ||||||||
\(101\) | −10.5034 | −1.04513 | −0.522566 | − | 0.852599i | \(-0.675025\pi\) | ||||
−0.522566 | + | 0.852599i | \(0.675025\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.24301i | 0.713675i | 0.934167 | + | 0.356837i | \(0.116145\pi\) | ||||
−0.934167 | + | 0.356837i | \(0.883855\pi\) | |||||||
\(104\) | 50.4967 | 4.95160 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 18.4256 | 1.78965 | ||||||||
\(107\) | 14.0640i | 1.35962i | 0.733388 | + | 0.679811i | \(0.237938\pi\) | ||||
−0.733388 | + | 0.679811i | \(0.762062\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.88056 | 0.467473 | 0.233736 | − | 0.972300i | \(-0.424905\pi\) | ||||
0.233736 | + | 0.972300i | \(0.424905\pi\) | |||||||
\(110\) | −4.93829 | −0.470847 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.2757i | 1.15480i | 0.816460 | + | 0.577402i | \(0.195933\pi\) | ||||
−0.816460 | + | 0.577402i | \(0.804067\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.49662i | 0.792314i | ||||||||
\(116\) | − 22.7146i | − 2.10900i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 36.8658i | − 3.39377i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.3641 | 0.942195 | ||||||||
\(122\) | −22.4181 | −2.02964 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − 30.0932i | − 2.70245i | ||||||||
\(125\) | −11.1390 | −0.996298 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.79030 | 0.158864 | 0.0794318 | − | 0.996840i | \(-0.474689\pi\) | ||||
0.0794318 | + | 0.996840i | \(0.474689\pi\) | |||||||
\(128\) | − 50.5256i | − 4.46588i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −31.3525 | −2.74979 | ||||||||
\(131\) | −3.03602 | −0.265258 | −0.132629 | − | 0.991166i | \(-0.542342\pi\) | ||||
−0.132629 | + | 0.991166i | \(0.542342\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 35.5804i | 3.07367i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 44.4883i | 3.81484i | ||||||||
\(137\) | − 5.79063i | − 0.494727i | −0.968923 | − | 0.247364i | \(-0.920436\pi\) | ||||
0.968923 | − | 0.247364i | \(-0.0795642\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.34617i | 0.283819i | 0.989880 | + | 0.141909i | \(0.0453241\pi\) | ||||
−0.989880 | + | 0.141909i | \(0.954676\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −8.81914 | −0.740086 | ||||||||
\(143\) | −4.03696 | −0.337588 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.07940i | 0.754003i | ||||||||
\(146\) | 24.9251 | 2.06281 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 29.9327 | 2.46045 | ||||||||
\(149\) | − 18.7199i | − 1.53360i | −0.641889 | − | 0.766798i | \(-0.721849\pi\) | ||||
0.641889 | − | 0.766798i | \(-0.278151\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.41011 | −0.114753 | −0.0573766 | − | 0.998353i | \(-0.518274\pi\) | ||||
−0.0573766 | + | 0.998353i | \(0.518274\pi\) | |||||||
\(152\) | −12.4819 | −1.01241 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.0287i | 0.966171i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.06147i | 0.244332i | 0.992510 | + | 0.122166i | \(0.0389840\pi\) | ||||
−0.992510 | + | 0.122166i | \(0.961016\pi\) | |||||||
\(158\) | 14.1855i | 1.12854i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 56.1422i | 4.43843i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.8480 | 1.39796 | 0.698981 | − | 0.715140i | \(-0.253637\pi\) | ||||
0.698981 | + | 0.715140i | \(0.253637\pi\) | |||||||
\(164\) | 25.2844 | 1.97438 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 25.6479i | 1.99067i | ||||||||
\(167\) | −13.7738 | −1.06585 | −0.532926 | − | 0.846162i | \(-0.678908\pi\) | ||||
−0.532926 | + | 0.846162i | \(0.678908\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6301 | −0.971544 | ||||||||
\(170\) | − 27.6219i | − 2.11851i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.19487 | −0.167357 | ||||||||
\(173\) | −22.3867 | −1.70203 | −0.851016 | − | 0.525140i | \(-0.824013\pi\) | ||||
−0.851016 | + | 0.525140i | \(0.824013\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 12.9936i | 0.979426i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 29.4268i | 2.20563i | ||||||||
\(179\) | − 20.5388i | − 1.53514i | −0.640963 | − | 0.767572i | \(-0.721465\pi\) | ||||
0.640963 | − | 0.767572i | \(-0.278535\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.5428i | 1.45261i | 0.687374 | + | 0.726303i | \(0.258763\pi\) | ||||
−0.687374 | + | 0.726303i | \(0.741237\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 37.7626 | 2.78389 | ||||||||
\(185\) | −11.9646 | −0.879653 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 3.55662i | − 0.260086i | ||||||||
\(188\) | 37.0594 | 2.70283 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.74977 | 0.562228 | ||||||||
\(191\) | 27.1791i | 1.96661i | 0.181963 | + | 0.983305i | \(0.441755\pi\) | ||||
−0.181963 | + | 0.983305i | \(0.558245\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.0985 | 1.01483 | 0.507415 | − | 0.861702i | \(-0.330601\pi\) | ||||
0.507415 | + | 0.861702i | \(0.330601\pi\) | |||||||
\(194\) | 5.33505 | 0.383035 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 15.0415i | − 1.07167i | −0.844324 | − | 0.535833i | \(-0.819998\pi\) | ||||
0.844324 | − | 0.535833i | \(-0.180002\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 1.34725i | − 0.0955037i | −0.998859 | − | 0.0477518i | \(-0.984794\pi\) | ||||
0.998859 | − | 0.0477518i | \(-0.0152057\pi\) | |||||||
\(200\) | − 0.365886i | − 0.0258721i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 28.9839i | − 2.03930i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.1066 | −0.705873 | ||||||||
\(206\) | −19.9868 | −1.39255 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 82.4942i | 5.71994i | ||||||||
\(209\) | 0.997866 | 0.0690238 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.42941 | 0.511462 | 0.255731 | − | 0.966748i | \(-0.417684\pi\) | ||||
0.255731 | + | 0.966748i | \(0.417684\pi\) | |||||||
\(212\) | 37.4902i | 2.57483i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −38.8092 | −2.65294 | ||||||||
\(215\) | 0.877323 | 0.0598329 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 13.4677i | 0.912149i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − 10.0478i | − 0.677426i | ||||||||
\(221\) | − 22.5805i | − 1.51893i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.6135i | 1.64824i | 0.566415 | + | 0.824120i | \(0.308330\pi\) | ||||
−0.566415 | + | 0.824120i | \(0.691670\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −33.8744 | −2.25329 | ||||||||
\(227\) | 20.1800 | 1.33939 | 0.669696 | − | 0.742636i | \(-0.266425\pi\) | ||||
0.669696 | + | 0.742636i | \(0.266425\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 27.4274i | − 1.81246i | −0.422789 | − | 0.906228i | \(-0.638949\pi\) | ||||
0.422789 | − | 0.906228i | \(-0.361051\pi\) | |||||||
\(230\) | −23.4461 | −1.54599 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 40.3527 | 2.64929 | ||||||||
\(233\) | − 7.38680i | − 0.483925i | −0.970286 | − | 0.241963i | \(-0.922209\pi\) | ||||
0.970286 | − | 0.241963i | \(-0.0777912\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.8132 | −0.966309 | ||||||||
\(236\) | 75.0102 | 4.88275 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 4.83804i | − 0.312947i | −0.987682 | − | 0.156473i | \(-0.949987\pi\) | ||||
0.987682 | − | 0.156473i | \(-0.0500126\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 14.2513i | − 0.918005i | −0.888435 | − | 0.459002i | \(-0.848207\pi\) | ||||
0.888435 | − | 0.459002i | \(-0.151793\pi\) | |||||||
\(242\) | 28.5994i | 1.83844i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − 45.6137i | − 2.92012i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.33530 | 0.403106 | ||||||||
\(248\) | 53.4608 | 3.39476 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − 30.7375i | − 1.94401i | ||||||||
\(251\) | 2.83977 | 0.179245 | 0.0896224 | − | 0.995976i | \(-0.471434\pi\) | ||||
0.0896224 | + | 0.995976i | \(0.471434\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.01893 | −0.189799 | ||||||||
\(254\) | 4.94027i | 0.309980i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 66.5415 | 4.15885 | ||||||||
\(257\) | 20.4218 | 1.27388 | 0.636938 | − | 0.770915i | \(-0.280201\pi\) | ||||
0.636938 | + | 0.770915i | \(0.280201\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − 63.7923i | − 3.95623i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − 8.37777i | − 0.517580i | ||||||||
\(263\) | 12.2388i | 0.754676i | 0.926076 | + | 0.377338i | \(0.123161\pi\) | ||||
−0.926076 | + | 0.377338i | \(0.876839\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 14.9854i | − 0.920547i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −72.3947 | −4.42221 | ||||||||
\(269\) | −13.8987 | −0.847421 | −0.423711 | − | 0.905798i | \(-0.639273\pi\) | ||||
−0.423711 | + | 0.905798i | \(0.639273\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 1.55881i | − 0.0946909i | −0.998879 | − | 0.0473455i | \(-0.984924\pi\) | ||||
0.998879 | − | 0.0473455i | \(-0.0150762\pi\) | |||||||
\(272\) | −72.6785 | −4.40678 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 15.9790 | 0.965328 | ||||||||
\(275\) | 0.0292508i | 0.00176389i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.1195 | 1.26895 | 0.634473 | − | 0.772945i | \(-0.281217\pi\) | ||||
0.634473 | + | 0.772945i | \(0.281217\pi\) | |||||||
\(278\) | −9.23363 | −0.553797 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.38090i | 0.261343i | 0.991426 | + | 0.130671i | \(0.0417132\pi\) | ||||
−0.991426 | + | 0.130671i | \(0.958287\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.1453i | 0.900293i | 0.892955 | + | 0.450147i | \(0.148628\pi\) | ||||
−0.892955 | + | 0.450147i | \(0.851372\pi\) | |||||||
\(284\) | − 17.9441i | − 1.06479i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − 11.1398i | − 0.658713i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.89369 | 0.170217 | ||||||||
\(290\) | −25.0543 | −1.47124 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 50.7146i | 2.96785i | ||||||||
\(293\) | −1.34729 | −0.0787094 | −0.0393547 | − | 0.999225i | \(-0.512530\pi\) | ||||
−0.0393547 | + | 0.999225i | \(0.512530\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −29.9828 | −1.74566 | ||||||||
\(296\) | 53.1756i | 3.09077i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 51.6569 | 2.99240 | ||||||||
\(299\) | −19.1668 | −1.10844 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − 3.89115i | − 0.223910i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − 20.3911i | − 1.16951i | ||||||||
\(305\) | 18.2325i | 1.04399i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.9640i | 1.53891i | 0.638698 | + | 0.769457i | \(0.279473\pi\) | ||||
−0.638698 | + | 0.769457i | \(0.720527\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −33.1928 | −1.88523 | ||||||||
\(311\) | 6.06228 | 0.343760 | 0.171880 | − | 0.985118i | \(-0.445016\pi\) | ||||
0.171880 | + | 0.985118i | \(0.445016\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.24917i | 0.0706072i | 0.999377 | + | 0.0353036i | \(0.0112398\pi\) | ||||
−0.999377 | + | 0.0353036i | \(0.988760\pi\) | |||||||
\(314\) | −8.44800 | −0.476748 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −28.8631 | −1.62367 | ||||||||
\(317\) | 16.3340i | 0.917411i | 0.888588 | + | 0.458705i | \(0.151687\pi\) | ||||
−0.888588 | + | 0.458705i | \(0.848313\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.22600 | −0.180622 | ||||||||
\(320\) | −81.7829 | −4.57181 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.58149i | 0.310562i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.185709i | 0.0103013i | ||||||||
\(326\) | 49.2508i | 2.72775i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 44.9178i | 2.48017i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.73806 | −0.0955325 | −0.0477663 | − | 0.998859i | \(-0.515210\pi\) | ||||
−0.0477663 | + | 0.998859i | \(0.515210\pi\) | |||||||
\(332\) | −52.1854 | −2.86405 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − 38.0084i | − 2.07973i | ||||||||
\(335\) | 28.9373 | 1.58101 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.3682 | −0.946109 | −0.473054 | − | 0.881033i | \(-0.656849\pi\) | ||||
−0.473054 | + | 0.881033i | \(0.656849\pi\) | |||||||
\(338\) | − 34.8522i | − 1.89571i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 56.2019 | 3.04797 | ||||||||
\(341\) | −4.27393 | −0.231446 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − 3.89920i | − 0.210231i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − 61.7753i | − 3.32106i | ||||||||
\(347\) | 11.0499i | 0.593188i | 0.955004 | + | 0.296594i | \(0.0958509\pi\) | ||||
−0.955004 | + | 0.296594i | \(0.904149\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.60574i | 0.139482i | 0.997565 | + | 0.0697411i | \(0.0222173\pi\) | ||||
−0.997565 | + | 0.0697411i | \(0.977783\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −19.9479 | −1.06323 | ||||||||
\(353\) | 23.7919 | 1.26631 | 0.633157 | − | 0.774023i | \(-0.281759\pi\) | ||||
0.633157 | + | 0.774023i | \(0.281759\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.17256i | 0.380680i | ||||||||
\(356\) | −59.8743 | −3.17333 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 56.6761 | 2.99542 | ||||||||
\(359\) | − 31.0060i | − 1.63643i | −0.574911 | − | 0.818216i | \(-0.694963\pi\) | ||||
0.574911 | − | 0.818216i | \(-0.305037\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.4340 | 0.917580 | ||||||||
\(362\) | −53.9277 | −2.83438 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 20.2714i | − 1.06106i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.8336i | 0.669907i | 0.942235 | + | 0.334953i | \(0.108721\pi\) | ||||
−0.942235 | + | 0.334953i | \(0.891279\pi\) | |||||||
\(368\) | 61.6910i | 3.21587i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − 33.0158i | − 1.71641i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −26.7014 | −1.38255 | −0.691273 | − | 0.722594i | \(-0.742950\pi\) | ||||
−0.691273 | + | 0.722594i | \(0.742950\pi\) | |||||||
\(374\) | 9.81436 | 0.507488 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 65.8363i | 3.39525i | ||||||||
\(377\) | −20.4814 | −1.05485 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.1788 | −0.933783 | −0.466892 | − | 0.884315i | \(-0.654626\pi\) | ||||
−0.466892 | + | 0.884315i | \(0.654626\pi\) | |||||||
\(380\) | 15.7683i | 0.808898i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −74.9997 | −3.83732 | ||||||||
\(383\) | 5.47829 | 0.279927 | 0.139964 | − | 0.990157i | \(-0.455301\pi\) | ||||
0.139964 | + | 0.990157i | \(0.455301\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 38.9042i | 1.98017i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 10.8551i | 0.551086i | ||||||||
\(389\) | 14.7845i | 0.749603i | 0.927105 | + | 0.374802i | \(0.122289\pi\) | ||||
−0.927105 | + | 0.374802i | \(0.877711\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 16.8862i | − 0.853971i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 41.5065 | 2.09107 | ||||||||
\(395\) | 11.5370 | 0.580491 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.32834i | 0.167045i | 0.996506 | + | 0.0835224i | \(0.0266170\pi\) | ||||
−0.996506 | + | 0.0835224i | \(0.973383\pi\) | |||||||
\(398\) | 3.71767 | 0.186350 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.597732 | 0.0298866 | ||||||||
\(401\) | − 24.0773i | − 1.20236i | −0.799112 | − | 0.601182i | \(-0.794697\pi\) | ||||
0.799112 | − | 0.601182i | \(-0.205303\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −27.1345 | −1.35167 | ||||||||
\(404\) | 58.9729 | 2.93401 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 4.25113i | − 0.210721i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 7.60844i | − 0.376213i | −0.982149 | − | 0.188106i | \(-0.939765\pi\) | ||||
0.982149 | − | 0.188106i | \(-0.0602350\pi\) | |||||||
\(410\) | − 27.8887i | − 1.37732i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 40.6668i | − 2.00351i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.8593 | 1.02394 | ||||||||
\(416\) | −126.646 | −6.20934 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.75357i | 0.134682i | ||||||||
\(419\) | −28.1468 | −1.37506 | −0.687531 | − | 0.726155i | \(-0.741306\pi\) | ||||
−0.687531 | + | 0.726155i | \(0.741306\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.14273 | 0.299378 | 0.149689 | − | 0.988733i | \(-0.452173\pi\) | ||||
0.149689 | + | 0.988733i | \(0.452173\pi\) | |||||||
\(422\) | 20.5012i | 0.997981i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −66.6015 | −3.23446 | ||||||||
\(425\) | −0.163612 | −0.00793636 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − 78.9643i | − 3.81688i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.42094i | 0.116748i | ||||||||
\(431\) | 3.95970i | 0.190732i | 0.995442 | + | 0.0953660i | \(0.0304021\pi\) | ||||
−0.995442 | + | 0.0953660i | \(0.969598\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.409544i | 0.0196814i | 0.999952 | + | 0.00984072i | \(0.00313245\pi\) | ||||
−0.999952 | + | 0.00984072i | \(0.996868\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −27.4025 | −1.31234 | ||||||||
\(437\) | 4.73769 | 0.226634 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.7978i | 0.849444i | 0.905324 | + | 0.424722i | \(0.139628\pi\) | ||||
−0.905324 | + | 0.424722i | \(0.860372\pi\) | |||||||
\(440\) | 17.8501 | 0.850968 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 62.3099 | 2.96378 | ||||||||
\(443\) | − 2.22743i | − 0.105828i | −0.998599 | − | 0.0529141i | \(-0.983149\pi\) | ||||
0.998599 | − | 0.0529141i | \(-0.0168510\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 23.9327 | 1.13452 | ||||||||
\(446\) | −67.9199 | −3.21610 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.25376i | 0.200747i | 0.994950 | + | 0.100374i | \(0.0320038\pi\) | ||||
−0.994950 | + | 0.100374i | \(0.967996\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 3.59096i | − 0.169092i | ||||||||
\(452\) | − 68.9237i | − 3.24190i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 55.6858i | 2.61347i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 37.6032 | 1.75900 | 0.879502 | − | 0.475896i | \(-0.157876\pi\) | ||||
0.879502 | + | 0.475896i | \(0.157876\pi\) | |||||||
\(458\) | 75.6849 | 3.53653 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − 47.7053i | − 2.22427i | ||||||||
\(461\) | 27.0807 | 1.26127 | 0.630637 | − | 0.776078i | \(-0.282794\pi\) | ||||
0.630637 | + | 0.776078i | \(0.282794\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 36.6047 | 1.70117 | 0.850583 | − | 0.525840i | \(-0.176249\pi\) | ||||
0.850583 | + | 0.525840i | \(0.176249\pi\) | |||||||
\(464\) | 65.9225i | 3.06037i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 20.3836 | 0.944252 | ||||||||
\(467\) | 27.9285 | 1.29238 | 0.646188 | − | 0.763178i | \(-0.276362\pi\) | ||||
0.646188 | + | 0.763178i | \(0.276362\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − 40.8765i | − 1.88549i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 133.256i | 6.13361i | ||||||||
\(473\) | 0.311722i | 0.0143330i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 0.0459040i | − 0.00210622i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 13.3504 | 0.610633 | ||||||||
\(479\) | 14.5600 | 0.665264 | 0.332632 | − | 0.943057i | \(-0.392063\pi\) | ||||
0.332632 | + | 0.943057i | \(0.392063\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 26.9898i | − 1.23063i | ||||||||
\(482\) | 39.3258 | 1.79124 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −58.1908 | −2.64504 | ||||||||
\(485\) | − 4.33897i | − 0.197023i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.7378 | −0.577206 | −0.288603 | − | 0.957449i | \(-0.593191\pi\) | ||||
−0.288603 | + | 0.957449i | \(0.593191\pi\) | |||||||
\(488\) | 81.0330 | 3.66819 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 15.7391i | − 0.710294i | −0.934810 | − | 0.355147i | \(-0.884431\pi\) | ||||
0.934810 | − | 0.355147i | \(-0.115569\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 18.0444i | − 0.812679i | ||||||||
\(494\) | 17.4820i | 0.786553i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 87.3365i | 3.92153i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 37.0868 | 1.66023 | 0.830116 | − | 0.557591i | \(-0.188274\pi\) | ||||
0.830116 | + | 0.557591i | \(0.188274\pi\) | |||||||
\(500\) | 62.5411 | 2.79692 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7.83624i | 0.349748i | ||||||||
\(503\) | 12.5405 | 0.559152 | 0.279576 | − | 0.960124i | \(-0.409806\pi\) | ||||
0.279576 | + | 0.960124i | \(0.409806\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23.5724 | −1.04896 | ||||||||
\(506\) | − 8.33063i | − 0.370342i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −10.0519 | −0.445980 | ||||||||
\(509\) | 5.99402 | 0.265680 | 0.132840 | − | 0.991137i | \(-0.457590\pi\) | ||||
0.132840 | + | 0.991137i | \(0.457590\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 82.5675i | 3.64900i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 56.3531i | 2.48563i | ||||||||
\(515\) | 16.2552i | 0.716288i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 5.26329i | − 0.231479i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 113.327 | 4.96974 | ||||||||
\(521\) | 17.5334 | 0.768150 | 0.384075 | − | 0.923302i | \(-0.374520\pi\) | ||||
0.384075 | + | 0.923302i | \(0.374520\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 40.0001i | 1.74908i | 0.484950 | + | 0.874542i | \(0.338838\pi\) | ||||
−0.484950 | + | 0.874542i | \(0.661162\pi\) | |||||||
\(524\) | 17.0461 | 0.744662 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −33.7725 | −1.47255 | ||||||||
\(527\) | − 23.9059i | − 1.04136i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.66665 | 0.376811 | ||||||||
\(530\) | 41.3517 | 1.79620 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 22.7985i | − 0.987513i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 31.5633i | 1.36460i | ||||||||
\(536\) | − 128.610i | − 5.55509i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 38.3530i | − 1.65352i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.3970 | −1.47884 | −0.739421 | − | 0.673244i | \(-0.764901\pi\) | ||||
−0.739421 | + | 0.673244i | \(0.764901\pi\) | |||||||
\(542\) | 4.30147 | 0.184764 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − 111.577i | − 4.78383i | ||||||||
\(545\) | 10.9532 | 0.469185 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.3009 | 1.50936 | 0.754680 | − | 0.656094i | \(-0.227792\pi\) | ||||
0.754680 | + | 0.656094i | \(0.227792\pi\) | |||||||
\(548\) | 32.5122i | 1.38885i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.0807165 | −0.00344176 | ||||||||
\(551\) | 5.06264 | 0.215676 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 58.2783i | 2.47601i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − 18.7875i | − 0.796768i | ||||||||
\(557\) | 14.4115i | 0.610637i | 0.952250 | + | 0.305318i | \(0.0987629\pi\) | ||||
−0.952250 | + | 0.305318i | \(0.901237\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.97908i | 0.0837060i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −12.0889 | −0.509940 | ||||||||
\(563\) | −13.5455 | −0.570875 | −0.285438 | − | 0.958397i | \(-0.592139\pi\) | ||||
−0.285438 | + | 0.958397i | \(0.592139\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 27.5499i | 1.15903i | ||||||||
\(566\) | −41.7928 | −1.75668 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 31.8779 | 1.33757 | ||||||||
\(569\) | 10.2750i | 0.430751i | 0.976531 | + | 0.215376i | \(0.0690976\pi\) | ||||
−0.976531 | + | 0.215376i | \(0.930902\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.5872 | 0.652305 | 0.326153 | − | 0.945317i | \(-0.394248\pi\) | ||||
0.326153 | + | 0.945317i | \(0.394248\pi\) | |||||||
\(572\) | 22.6660 | 0.947715 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.138878i | 0.00579160i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 26.0495i | − 1.08445i | −0.840232 | − | 0.542227i | \(-0.817581\pi\) | ||||
0.840232 | − | 0.542227i | \(-0.182419\pi\) | |||||||
\(578\) | 7.98503i | 0.332134i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − 50.9775i | − 2.11672i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.32447 | 0.220517 | ||||||||
\(584\) | −90.0949 | −3.72815 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − 3.71779i | − 0.153580i | ||||||||
\(587\) | 32.3864 | 1.33673 | 0.668364 | − | 0.743834i | \(-0.266995\pi\) | ||||
0.668364 | + | 0.743834i | \(0.266995\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.70718 | 0.276365 | ||||||||
\(590\) | − 82.7363i | − 3.40620i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −86.8707 | −3.57036 | ||||||||
\(593\) | 5.21887 | 0.214313 | 0.107157 | − | 0.994242i | \(-0.465825\pi\) | ||||
0.107157 | + | 0.994242i | \(0.465825\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 105.105i | 4.30528i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 52.8899i | − 2.16283i | ||||||||
\(599\) | 32.7107i | 1.33652i | 0.743926 | + | 0.668262i | \(0.232961\pi\) | ||||
−0.743926 | + | 0.668262i | \(0.767039\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 20.5762i | − 0.839319i | −0.907682 | − | 0.419659i | \(-0.862150\pi\) | ||||
0.907682 | − | 0.419659i | \(-0.137850\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7.91724 | 0.322148 | ||||||||
\(605\) | 23.2598 | 0.945645 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 21.3300i | − 0.865758i | −0.901452 | − | 0.432879i | \(-0.857498\pi\) | ||||
0.901452 | − | 0.432879i | \(-0.142502\pi\) | |||||||
\(608\) | 31.3047 | 1.26957 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −50.3119 | −2.03707 | ||||||||
\(611\) | − 33.4159i | − 1.35186i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.3388 | −0.659918 | −0.329959 | − | 0.943995i | \(-0.607035\pi\) | ||||
−0.329959 | + | 0.943995i | \(0.607035\pi\) | |||||||
\(614\) | −74.4060 | −3.00278 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.8105i | 0.837800i | 0.908032 | + | 0.418900i | \(0.137584\pi\) | ||||
−0.908032 | + | 0.418900i | \(0.862416\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.84787i | 0.114465i | 0.998361 | + | 0.0572327i | \(0.0182277\pi\) | ||||
−0.998361 | + | 0.0572327i | \(0.981772\pi\) | |||||||
\(620\) | − 67.5368i | − 2.71235i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 16.7286i | 0.670757i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.1821 | −1.00728 | ||||||||
\(626\) | −3.44703 | −0.137771 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 17.1890i | − 0.685916i | ||||||||
\(629\) | 23.7784 | 0.948107 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.5713 | 0.978167 | 0.489084 | − | 0.872237i | \(-0.337331\pi\) | ||||
0.489084 | + | 0.872237i | \(0.337331\pi\) | |||||||
\(632\) | − 51.2754i | − 2.03963i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −45.0731 | −1.79008 | ||||||||
\(635\) | 4.01790 | 0.159445 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − 8.90203i | − 0.352435i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − 113.392i | − 4.48223i | ||||||||
\(641\) | 37.6347i | 1.48648i | 0.669025 | + | 0.743240i | \(0.266712\pi\) | ||||
−0.669025 | + | 0.743240i | \(0.733288\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.4783i | 0.531534i | 0.964037 | + | 0.265767i | \(0.0856252\pi\) | ||||
−0.964037 | + | 0.265767i | \(0.914375\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −15.4019 | −0.605980 | ||||||||
\(647\) | −4.47576 | −0.175960 | −0.0879802 | − | 0.996122i | \(-0.528041\pi\) | ||||
−0.0879802 | + | 0.996122i | \(0.528041\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 10.6532i | − 0.418174i | ||||||||
\(650\) | −0.512457 | −0.0201002 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −100.210 | −3.92452 | ||||||||
\(653\) | − 28.3537i | − 1.10957i | −0.831995 | − | 0.554783i | \(-0.812801\pi\) | ||||
0.831995 | − | 0.554783i | \(-0.187199\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.81360 | −0.266229 | ||||||||
\(656\) | −73.3803 | −2.86502 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 9.66270i | − 0.376405i | −0.982130 | − | 0.188203i | \(-0.939734\pi\) | ||||
0.982130 | − | 0.188203i | \(-0.0602662\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.68551i | 0.298932i | 0.988767 | + | 0.149466i | \(0.0477554\pi\) | ||||
−0.988767 | + | 0.149466i | \(0.952245\pi\) | |||||||
\(662\) | − 4.79611i | − 0.186406i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − 92.7077i | − 3.59776i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.3165 | −0.593056 | ||||||||
\(668\) | 77.3350 | 2.99218 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 79.8514i | 3.08493i | ||||||||
\(671\) | −6.47820 | −0.250088 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.4935 | −0.558683 | −0.279341 | − | 0.960192i | \(-0.590116\pi\) | ||||
−0.279341 | + | 0.960192i | \(0.590116\pi\) | |||||||
\(674\) | − 47.9270i | − 1.84608i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 70.9132 | 2.72743 | ||||||||
\(677\) | 20.4462 | 0.785813 | 0.392907 | − | 0.919578i | \(-0.371470\pi\) | ||||
0.392907 | + | 0.919578i | \(0.371470\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 99.8430i | 3.82880i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 11.7937i | − 0.451606i | ||||||||
\(683\) | 22.0854i | 0.845073i | 0.906346 | + | 0.422536i | \(0.138860\pi\) | ||||
−0.906346 | + | 0.422536i | \(0.861140\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 12.9957i | − 0.496539i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.36995 | 0.242852 | ||||||||
\(689\) | 33.8043 | 1.28784 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 31.4512i | − 1.19646i | −0.801325 | − | 0.598230i | \(-0.795871\pi\) | ||||
0.801325 | − | 0.598230i | \(-0.204129\pi\) | |||||||
\(692\) | 125.693 | 4.77814 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −30.4917 | −1.15745 | ||||||||
\(695\) | 7.50967i | 0.284858i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.0858 | 0.760804 | ||||||||
\(698\) | −7.19044 | −0.272162 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 4.78252i | − 0.180633i | −0.995913 | − | 0.0903167i | \(-0.971212\pi\) | ||||
0.995913 | − | 0.0903167i | \(-0.0287879\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.67141i | 0.251617i | ||||||||
\(704\) | − 29.0583i | − 1.09518i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 65.6528i | 2.47088i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −37.4050 | −1.40477 | −0.702386 | − | 0.711796i | \(-0.747882\pi\) | ||||
−0.702386 | + | 0.711796i | \(0.747882\pi\) | |||||||
\(710\) | −19.7924 | −0.742796 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 106.367i | − 3.98627i | ||||||||
\(713\) | −20.2918 | −0.759935 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.05998 | −0.338824 | ||||||||
\(716\) | 115.318i | 4.30963i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 85.5598 | 3.19306 | ||||||||
\(719\) | −35.4881 | −1.32348 | −0.661742 | − | 0.749732i | \(-0.730183\pi\) | ||||
−0.661742 | + | 0.749732i | \(0.730183\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 48.1085i | 1.79041i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − 109.726i | − 4.07792i | ||||||||
\(725\) | 0.148403i | 0.00551156i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.7768i | 1.28980i | 0.764267 | + | 0.644900i | \(0.223101\pi\) | ||||
−0.764267 | + | 0.644900i | \(0.776899\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 55.9383 | 2.07037 | ||||||||
\(731\) | −1.74359 | −0.0644891 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.4602i | 0.607971i | 0.952677 | + | 0.303986i | \(0.0983175\pi\) | ||||
−0.952677 | + | 0.303986i | \(0.901683\pi\) | |||||||
\(734\) | −35.4137 | −1.30715 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −94.7089 | −3.49102 | ||||||||
\(737\) | 10.2817i | 0.378732i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.37549 | −0.271312 | −0.135656 | − | 0.990756i | \(-0.543314\pi\) | ||||
−0.135656 | + | 0.990756i | \(0.543314\pi\) | |||||||
\(740\) | 67.1766 | 2.46946 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 25.9252i | − 0.951103i | −0.879688 | − | 0.475552i | \(-0.842248\pi\) | ||||
0.879688 | − | 0.475552i | \(-0.157752\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 42.0123i | − 1.53921i | ||||||||
\(746\) | − 73.6815i | − 2.69767i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 19.9691i | 0.730142i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.4705 | 0.819958 | 0.409979 | − | 0.912095i | \(-0.365536\pi\) | ||||
0.409979 | + | 0.912095i | \(0.365536\pi\) | |||||||
\(752\) | −107.554 | −3.92208 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − 56.5177i | − 2.05825i | ||||||||
\(755\) | −3.16465 | −0.115173 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.00011 | −0.181732 | −0.0908660 | − | 0.995863i | \(-0.528963\pi\) | ||||
−0.0908660 | + | 0.995863i | \(0.528963\pi\) | |||||||
\(758\) | − 50.1637i | − 1.82203i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −28.0125 | −1.01612 | ||||||||
\(761\) | 4.87680 | 0.176784 | 0.0883920 | − | 0.996086i | \(-0.471827\pi\) | ||||
0.0883920 | + | 0.996086i | \(0.471827\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − 152.601i | − 5.52089i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15.1171i | 0.546204i | ||||||||
\(767\) | − 67.6354i | − 2.44217i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.9517i | 0.791600i | 0.918337 | + | 0.395800i | \(0.129533\pi\) | ||||
−0.918337 | + | 0.395800i | \(0.870467\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −79.1576 | −2.84894 | ||||||||
\(773\) | 13.6225 | 0.489968 | 0.244984 | − | 0.969527i | \(-0.421217\pi\) | ||||
0.244984 | + | 0.969527i | \(0.421217\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.196610i | 0.00706245i | ||||||||
\(776\) | −19.2842 | −0.692263 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −40.7972 | −1.46265 | ||||||||
\(779\) | 5.63539i | 0.201909i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.54848 | −0.0911919 | ||||||||
\(782\) | 46.5968 | 1.66630 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.87071i | 0.245226i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.1804i | 0.826293i | 0.910665 | + | 0.413146i | \(0.135570\pi\) | ||||
−0.910665 | + | 0.413146i | \(0.864430\pi\) | |||||||
\(788\) | 84.4526i | 3.00850i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 31.8360i | 1.13267i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −41.1291 | −1.46054 | ||||||||
\(794\) | −9.18444 | −0.325943 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.56428i | 0.268109i | ||||||||
\(797\) | 29.1588 | 1.03286 | 0.516428 | − | 0.856331i | \(-0.327261\pi\) | ||||
0.516428 | + | 0.856331i | \(0.327261\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 29.4398 | 1.04151 | ||||||||
\(800\) | 0.917647i | 0.0324437i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 66.4404 | 2.34609 | ||||||||
\(803\) | 7.20265 | 0.254176 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − 74.8767i | − 2.63742i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 104.766i | 3.68565i | ||||||||
\(809\) | 5.69368i | 0.200179i | 0.994978 | + | 0.100090i | \(0.0319130\pi\) | ||||
−0.994978 | + | 0.100090i | \(0.968087\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 45.3695i | − 1.59314i | −0.604547 | − | 0.796570i | \(-0.706646\pi\) | ||||
0.604547 | − | 0.796570i | \(-0.293354\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 11.7308 | 0.411166 | ||||||||
\(815\) | 40.0554 | 1.40308 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 0.489192i | − 0.0171147i | ||||||||
\(818\) | 20.9952 | 0.734079 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 56.7446 | 1.98161 | ||||||||
\(821\) | 2.41885i | 0.0844183i | 0.999109 | + | 0.0422091i | \(0.0134396\pi\) | ||||
−0.999109 | + | 0.0422091i | \(0.986560\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.82407 | 0.272730 | 0.136365 | − | 0.990659i | \(-0.456458\pi\) | ||||
0.136365 | + | 0.990659i | \(0.456458\pi\) | |||||||
\(824\) | 72.2448 | 2.51677 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 23.3143i | − 0.810717i | −0.914158 | − | 0.405359i | \(-0.867147\pi\) | ||||
0.914158 | − | 0.405359i | \(-0.132853\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 28.2751i | − 0.982034i | −0.871150 | − | 0.491017i | \(-0.836625\pi\) | ||||
0.871150 | − | 0.491017i | \(-0.163375\pi\) | |||||||
\(830\) | 57.5605i | 1.99795i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 184.487i | − 6.39593i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −30.9120 | −1.06975 | ||||||||
\(836\) | −5.60264 | −0.193772 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 77.6701i | − 2.68307i | ||||||||
\(839\) | −32.3512 | −1.11689 | −0.558444 | − | 0.829542i | \(-0.688601\pi\) | ||||
−0.558444 | + | 0.829542i | \(0.688601\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.6330 | 0.435619 | ||||||||
\(842\) | 16.9506i | 0.584157i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −41.7133 | −1.43583 | ||||||||
\(845\) | −28.3451 | −0.975102 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − 108.804i | − 3.73634i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − 0.451482i | − 0.0154857i | ||||||||
\(851\) | − 20.1836i | − 0.691885i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 14.1269i | − 0.483694i | −0.970314 | − | 0.241847i | \(-0.922247\pi\) | ||||
0.970314 | − | 0.241847i | \(-0.0777533\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 140.281 | 4.79469 | ||||||||
\(857\) | 29.5897 | 1.01076 | 0.505382 | − | 0.862896i | \(-0.331352\pi\) | ||||
0.505382 | + | 0.862896i | \(0.331352\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 11.3240i | − 0.386370i | −0.981162 | − | 0.193185i | \(-0.938118\pi\) | ||||
0.981162 | − | 0.193185i | \(-0.0618818\pi\) | |||||||
\(860\) | −4.92584 | −0.167970 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −10.9266 | −0.372163 | ||||||||
\(863\) | − 30.6289i | − 1.04262i | −0.853368 | − | 0.521309i | \(-0.825444\pi\) | ||||
0.853368 | − | 0.521309i | \(-0.174556\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −50.2416 | −1.70826 | ||||||||
\(866\) | −1.13012 | −0.0384031 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.09922i | 0.139057i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 65.2771i | 2.21183i | ||||||||
\(872\) | − 48.6808i | − 1.64854i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 13.0735i | 0.442216i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.5491 | −0.558824 | −0.279412 | − | 0.960171i | \(-0.590140\pi\) | ||||
−0.279412 | + | 0.960171i | \(0.590140\pi\) | |||||||
\(878\) | −49.1124 | −1.65746 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 29.1609i | 0.983013i | ||||||||
\(881\) | −33.8234 | −1.13954 | −0.569770 | − | 0.821804i | \(-0.692968\pi\) | ||||
−0.569770 | + | 0.821804i | \(0.692968\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.8964 | 0.366691 | 0.183346 | − | 0.983048i | \(-0.441307\pi\) | ||||
0.183346 | + | 0.983048i | \(0.441307\pi\) | |||||||
\(884\) | 126.781i | 4.26410i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.14650 | 0.206496 | ||||||||
\(887\) | 55.7874 | 1.87316 | 0.936578 | − | 0.350459i | \(-0.113974\pi\) | ||||
0.936578 | + | 0.350459i | \(0.113974\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 66.0413i | 2.21371i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 138.195i | − 4.62712i | ||||||||
\(893\) | 8.25981i | 0.276404i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 46.0944i | − 1.54076i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −11.7381 | −0.391705 | ||||||||
\(899\) | −21.6837 | −0.723191 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 29.7820i | 0.992183i | ||||||||
\(902\) | 9.90913 | 0.329938 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 122.443 | 4.07241 | ||||||||
\(905\) | 43.8591i | 1.45793i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −52.8615 | −1.75524 | −0.877619 | − | 0.479358i | \(-0.840869\pi\) | ||||
−0.877619 | + | 0.479358i | \(0.840869\pi\) | |||||||
\(908\) | −113.303 | −3.76009 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.0952i | 0.334470i | 0.985917 | + | 0.167235i | \(0.0534838\pi\) | ||||
−0.985917 | + | 0.167235i | \(0.946516\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.41153i | 0.245286i | ||||||||
\(914\) | 103.765i | 3.43223i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 153.995i | 5.08813i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.74711 | 0.255554 | 0.127777 | − | 0.991803i | \(-0.459216\pi\) | ||||
0.127777 | + | 0.991803i | \(0.459216\pi\) | |||||||
\(920\) | 84.7488 | 2.79409 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 74.7281i | 2.46104i | ||||||||
\(923\) | −16.1799 | −0.532569 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.195561 | −0.00643002 | ||||||||
\(926\) | 101.009i | 3.31937i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −101.205 | −3.32222 | ||||||||
\(929\) | −46.5611 | −1.52762 | −0.763810 | − | 0.645441i | \(-0.776673\pi\) | ||||
−0.763810 | + | 0.645441i | \(0.776673\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 41.4741i | 1.35853i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 77.0675i | 2.52173i | ||||||||
\(935\) | − 7.98196i | − 0.261038i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 1.77445i | − 0.0579688i | −0.999580 | − | 0.0289844i | \(-0.990773\pi\) | ||||
0.999580 | − | 0.0289844i | \(-0.00922731\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 83.1708 | 2.71273 | ||||||||
\(941\) | −56.0365 | −1.82674 | −0.913370 | − | 0.407132i | \(-0.866529\pi\) | ||||
−0.913370 | + | 0.407132i | \(0.866529\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 17.0492i | − 0.555200i | ||||||||
\(944\) | −217.695 | −7.08536 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.860184 | −0.0279670 | ||||||||
\(947\) | − 22.2139i | − 0.721853i | −0.932594 | − | 0.360927i | \(-0.882460\pi\) | ||||
0.932594 | − | 0.360927i | \(-0.117540\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 45.7285 | 1.48441 | ||||||||
\(950\) | 0.126670 | 0.00410973 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.4738i | 0.954750i | 0.878700 | + | 0.477375i | \(0.158412\pi\) | ||||
−0.878700 | + | 0.477375i | \(0.841588\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 60.9969i | 1.97381i | ||||||||
\(956\) | 27.1638i | 0.878540i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 40.1778i | 1.29809i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.27267 | 0.0733118 | ||||||||
\(962\) | 74.4774 | 2.40125 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 80.0155i | 2.57713i | ||||||||
\(965\) | 31.6406 | 1.01855 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.5115 | −0.498815 | −0.249407 | − | 0.968399i | \(-0.580236\pi\) | ||||
−0.249407 | + | 0.968399i | \(0.580236\pi\) | |||||||
\(968\) | − 103.376i | − 3.32264i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 11.9732 | 0.384437 | ||||||||
\(971\) | 12.0421 | 0.386450 | 0.193225 | − | 0.981154i | \(-0.438105\pi\) | ||||
0.193225 | + | 0.981154i | \(0.438105\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − 35.1495i | − 1.12626i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 132.380i | 4.23738i | ||||||||
\(977\) | − 33.0576i | − 1.05761i | −0.848745 | − | 0.528803i | \(-0.822641\pi\) | ||||
0.848745 | − | 0.528803i | \(-0.177359\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.50353i | 0.271774i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 43.4314 | 1.38595 | ||||||||
\(983\) | −54.5392 | −1.73953 | −0.869765 | − | 0.493467i | \(-0.835729\pi\) | ||||
−0.869765 | + | 0.493467i | \(0.835729\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 33.7570i | − 1.07559i | ||||||||
\(986\) | 49.7929 | 1.58573 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −35.5704 | −1.13164 | ||||||||
\(989\) | 1.48000i | 0.0470612i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −44.9904 | −1.42917 | −0.714583 | − | 0.699550i | \(-0.753384\pi\) | ||||
−0.714583 | + | 0.699550i | \(0.753384\pi\) | |||||||
\(992\) | −134.080 | −4.25705 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 3.02356i | − 0.0958534i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 44.6129i | − 1.41290i | −0.707761 | − | 0.706452i | \(-0.750295\pi\) | ||||
0.707761 | − | 0.706452i | \(-0.249705\pi\) | |||||||
\(998\) | 102.340i | 3.23950i | ||||||||
\(999\) | 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 | 1323.2.c.e.1322.16 | yes | 16 | |
3.2 | odd | 2 | inner | 1323.2.c.e.1322.1 | ✓ | 16 | |
7.6 | odd | 2 | inner | 1323.2.c.e.1322.15 | yes | 16 | |
21.20 | even | 2 | inner | 1323.2.c.e.1322.2 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1323.2.c.e.1322.1 | ✓ | 16 | 3.2 | odd | 2 | inner | |
1323.2.c.e.1322.2 | yes | 16 | 21.20 | even | 2 | inner | |
1323.2.c.e.1322.15 | yes | 16 | 7.6 | odd | 2 | inner | |
1323.2.c.e.1322.16 | yes | 16 | 1.1 | even | 1 | trivial |