Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1380,2,Mod(1057,1380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1380, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1380.1057");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1380.t (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.0193554789\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1333.9 | ||
Character | \(\chi\) | \(=\) | 1380.1333 |
Dual form | 1380.2.t.a.1057.9 |
$q$-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 \(\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(691\) | \(1201\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −0.707107 | − | 0.707107i | −0.408248 | − | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.09989 | − | 0.768407i | −0.939101 | − | 0.343642i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.0117285 | − | 0.0117285i | −0.00443294 | − | 0.00443294i | 0.704887 | − | 0.709320i | \(-0.250998\pi\) |
−0.709320 | + | 0.704887i | \(0.750998\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.72770i | − | 0.520920i | −0.965485 | − | 0.260460i | \(-0.916126\pi\) | ||
0.965485 | − | 0.260460i | \(-0.0838742\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.37219 | − | 2.37219i | −0.657926 | − | 0.657926i | 0.296963 | − | 0.954889i | \(-0.404026\pi\) |
−0.954889 | + | 0.296963i | \(0.904026\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.941503 | + | 2.02819i | 0.243095 | + | 0.523678i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.66583 | + | 1.66583i | 0.404023 | + | 0.404023i | 0.879648 | − | 0.475625i | \(-0.157778\pi\) |
−0.475625 | + | 0.879648i | \(0.657778\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.73367 | −1.54481 | −0.772405 | − | 0.635131i | \(-0.780946\pi\) | ||||
−0.772405 | + | 0.635131i | \(0.780946\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.0165866i | 0.00361948i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.0541507 | + | 4.79553i | −0.0112912 | + | 0.999936i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.81910 | + | 3.22714i | 0.763820 | + | 0.645429i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.707107 | − | 0.707107i | 0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.894482i | 0.166101i | 0.996545 | + | 0.0830506i | \(0.0264663\pi\) | ||||
−0.996545 | + | 0.0830506i | \(0.973534\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.90064 | 1.23939 | 0.619696 | − | 0.784842i | \(-0.287256\pi\) | ||||
0.619696 | + | 0.784842i | \(0.287256\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.22167 | + | 1.22167i | −0.212665 | + | 0.212665i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.0156163 | + | 0.0336408i | 0.00263963 | + | 0.00568633i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.0575199 | − | 0.0575199i | −0.00945621 | − | 0.00945621i | 0.702363 | − | 0.711819i | \(-0.252128\pi\) |
−0.711819 | + | 0.702363i | \(0.752128\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.35478i | 0.537194i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.278794 | 0.0435403 | 0.0217702 | − | 0.999763i | \(-0.493070\pi\) | ||||
0.0217702 | + | 0.999763i | \(0.493070\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.31887 | − | 4.31887i | 0.658622 | − | 0.658622i | −0.296432 | − | 0.955054i | \(-0.595797\pi\) |
0.955054 | + | 0.296432i | \(0.0957969\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.768407 | − | 2.09989i | 0.114547 | − | 0.313034i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.61450 | + | 7.61450i | −1.11069 | + | 1.11069i | −0.117632 | + | 0.993057i | \(0.537530\pi\) |
−0.993057 | + | 0.117632i | \(0.962470\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 6.99972i | − | 0.999961i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 2.35584i | − | 0.329883i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.64615 | + | 9.64615i | −1.32500 | + | 1.32500i | −0.415329 | + | 0.909671i | \(0.636334\pi\) |
−0.909671 | + | 0.415329i | \(0.863666\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.32757 | + | 3.62798i | −0.179010 | + | 0.489196i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.76142 | + | 4.76142i | 0.630666 | + | 0.630666i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 15.1371i | 1.97068i | 0.170607 | + | 0.985339i | \(0.445427\pi\) | ||||
−0.170607 | + | 0.985339i | \(0.554573\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.91692i | 0.757584i | 0.925482 | + | 0.378792i | \(0.123660\pi\) | ||||
−0.925482 | + | 0.378792i | \(0.876340\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.0117285 | − | 0.0117285i | 0.00147765 | − | 0.00147765i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.15853 | + | 6.80414i | 0.391768 | + | 0.843950i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.99060 | − | 1.99060i | −0.243191 | − | 0.243191i | 0.574978 | − | 0.818169i | \(-0.305011\pi\) |
−0.818169 | + | 0.574978i | \(0.805011\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.42924 | − | 3.35266i | 0.412832 | − | 0.403613i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.6488 | 1.50113 | 0.750567 | − | 0.660795i | \(-0.229781\pi\) | ||||
0.750567 | + | 0.660795i | \(0.229781\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.55474 | + | 7.55474i | 0.884215 | + | 0.884215i | 0.993960 | − | 0.109745i | \(-0.0350034\pi\) |
−0.109745 | + | 0.993960i | \(0.535003\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.418577 | − | 4.98245i | −0.0483331 | − | 0.575324i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.0202632 | + | 0.0202632i | −0.00230921 | + | 0.00230921i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.91526 | 0.440502 | 0.220251 | − | 0.975443i | \(-0.429312\pi\) | ||||
0.220251 | + | 0.975443i | \(0.429312\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.2961 | + | 12.2961i | −1.34967 | + | 1.34967i | −0.463659 | + | 0.886014i | \(0.653464\pi\) |
−0.886014 | + | 0.463659i | \(0.846536\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.21803 | − | 4.77810i | −0.240579 | − | 0.518257i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.632494 | − | 0.632494i | 0.0678105 | − | 0.0678105i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.61134 | −0.700800 | −0.350400 | − | 0.936600i | \(-0.613954\pi\) | ||||
−0.350400 | + | 0.936600i | \(0.613954\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0556442i | 0.00583310i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.87949 | − | 4.87949i | −0.505979 | − | 0.505979i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 14.1400 | + | 5.17420i | 1.45073 | + | 0.530861i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.80227 | + | 9.80227i | 0.995269 | + | 0.995269i | 0.999989 | − | 0.00471962i | \(-0.00150231\pi\) |
−0.00471962 | + | 0.999989i | \(0.501502\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.72770 | 0.173640 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.42053 | 0.837874 | 0.418937 | − | 0.908015i | \(-0.362403\pi\) | ||||
0.418937 | + | 0.908015i | \(0.362403\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.3577 | + | 11.3577i | −1.11910 | + | 1.11910i | −0.127232 | + | 0.991873i | \(0.540609\pi\) |
−0.991873 | + | 0.127232i | \(0.959391\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.0127452 | − | 0.0348300i | 0.00124381 | − | 0.00339906i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.94663 | − | 7.94663i | −0.768230 | − | 0.768230i | 0.209565 | − | 0.977795i | \(-0.432795\pi\) |
−0.977795 | + | 0.209565i | \(0.932795\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.3003 | 0.986589 | 0.493295 | − | 0.869862i | \(-0.335792\pi\) | ||||
0.493295 | + | 0.869862i | \(0.335792\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.0813454i | 0.00772096i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.53608 | − | 6.53608i | 0.614863 | − | 0.614863i | −0.329346 | − | 0.944209i | \(-0.606828\pi\) |
0.944209 | + | 0.329346i | \(0.106828\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.79863 | − | 10.0285i | 0.354224 | − | 0.935161i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.37219 | − | 2.37219i | 0.219309 | − | 0.219309i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 0.0390752i | − | 0.00358202i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.01507 | 0.728642 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.197137 | − | 0.197137i | −0.0177753 | − | 0.0177753i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.53995 | − | 9.71128i | −0.495508 | − | 0.868603i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.73971 | + | 2.73971i | −0.243110 | + | 0.243110i | −0.818135 | − | 0.575026i | \(-0.804992\pi\) |
0.575026 | + | 0.818135i | \(0.304992\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.10781 | −0.537762 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.6163 | −1.01492 | −0.507458 | − | 0.861676i | \(-0.669415\pi\) | ||||
−0.507458 | + | 0.861676i | \(0.669415\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.0789756 | + | 0.0789756i | 0.00684805 | + | 0.00684805i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.02819 | + | 0.941503i | −0.174559 | + | 0.0810317i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.80967 | + | 1.80967i | 0.154611 | + | 0.154611i | 0.780174 | − | 0.625563i | \(-0.215131\pi\) |
−0.625563 | + | 0.780174i | \(0.715131\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.50003i | 0.466507i | 0.972416 | + | 0.233253i | \(0.0749371\pi\) | ||||
−0.972416 | + | 0.233253i | \(0.925063\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.7685 | 0.906874 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.09842 | + | 4.09842i | −0.342727 | + | 0.342727i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.687326 | − | 1.87832i | 0.0570793 | − | 0.155986i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.94955 | + | 4.94955i | −0.408232 | + | 0.408232i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.57524 | 0.129049 | 0.0645243 | − | 0.997916i | \(-0.479447\pi\) | ||||
0.0645243 | + | 0.997916i | \(0.479447\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.0184 | −1.38494 | −0.692469 | − | 0.721448i | \(-0.743477\pi\) | ||||
−0.692469 | + | 0.721448i | \(0.743477\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.66583 | + | 1.66583i | −0.134674 | + | 0.134674i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −14.4906 | − | 5.30250i | −1.16391 | − | 0.425907i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.29982 | + | 8.29982i | 0.662398 | + | 0.662398i | 0.955945 | − | 0.293547i | \(-0.0948357\pi\) |
−0.293547 | + | 0.955945i | \(0.594836\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.6417 | 1.08186 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.0568793 | − | 0.0556091i | 0.00448271 | − | 0.00438261i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.4524 | − | 16.4524i | −1.28865 | − | 1.28865i | −0.935607 | − | 0.353044i | \(-0.885147\pi\) |
−0.353044 | − | 0.935607i | \(-0.614853\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.50410 | − | 1.62663i | 0.272794 | − | 0.126633i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.26933 | + | 3.26933i | −0.252989 | + | 0.252989i | −0.822195 | − | 0.569206i | \(-0.807251\pi\) |
0.569206 | + | 0.822195i | \(0.307251\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 1.74546i | − | 0.134266i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 6.73367i | − | 0.514936i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.37850 | + | 3.37850i | 0.256862 | + | 0.256862i | 0.823777 | − | 0.566914i | \(-0.191863\pi\) |
−0.566914 | + | 0.823777i | \(0.691863\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.00694275 | − | 0.0826417i | −0.000524823 | − | 0.00624712i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.7035 | − | 10.7035i | 0.804526 | − | 0.804526i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 2.90634i | − | 0.217230i | −0.994084 | − | 0.108615i | \(-0.965358\pi\) | ||
0.994084 | − | 0.108615i | \(-0.0346416\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 4.39491i | − | 0.326671i | −0.986571 | − | 0.163336i | \(-0.947775\pi\) | ||
0.986571 | − | 0.163336i | \(-0.0522254\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.18390 | − | 4.18390i | 0.309283 | − | 0.309283i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.0765869 | + | 0.164984i | 0.00563078 | + | 0.0121299i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.87805 | − | 2.87805i | 0.210464 | − | 0.210464i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.0165866 | −0.00120649 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 7.01334i | − | 0.507467i | −0.967274 | − | 0.253734i | \(-0.918341\pi\) | ||
0.967274 | − | 0.253734i | \(-0.0816587\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.7410 | − | 10.7410i | −0.773151 | − | 0.773151i | 0.205505 | − | 0.978656i | \(-0.434116\pi\) |
−0.978656 | + | 0.205505i | \(0.934116\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.57783 | − | 7.04468i | 0.184603 | − | 0.504480i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.15071 | + | 1.15071i | −0.0819848 | + | 0.0819848i | −0.746910 | − | 0.664925i | \(-0.768463\pi\) |
0.664925 | + | 0.746910i | \(0.268463\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.6728 | −1.25279 | −0.626397 | − | 0.779504i | \(-0.715471\pi\) | ||||
−0.626397 | + | 0.779504i | \(0.715471\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.81513i | 0.198564i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.0104909 | − | 0.0104909i | 0.000736317 | − | 0.000736317i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.585438 | − | 0.214227i | −0.0408888 | − | 0.0149623i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.79553 | − | 0.0541507i | −0.333312 | − | 0.00376374i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.6337i | 0.804722i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.29187 | 0.433150 | 0.216575 | − | 0.976266i | \(-0.430511\pi\) | ||||
0.216575 | + | 0.976266i | \(0.430511\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.94403 | − | 8.94403i | −0.612835 | − | 0.612835i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.3878 | + | 5.75052i | −0.844842 | + | 0.392182i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.0809339 | − | 0.0809339i | −0.00549415 | − | 0.00549415i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 10.6840i | − | 0.721958i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 7.90331i | − | 0.531634i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.61400 | − | 6.61400i | −0.442906 | − | 0.442906i | 0.450081 | − | 0.892988i | \(-0.351395\pi\) |
−0.892988 | + | 0.450081i | \(0.851395\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.22714 | + | 3.81910i | −0.215143 | + | 0.254607i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.842807 | − | 0.842807i | −0.0559391 | − | 0.0559391i | 0.678584 | − | 0.734523i | \(-0.262594\pi\) |
−0.734523 | + | 0.678584i | \(0.762594\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.3773 | 1.34657 | 0.673285 | − | 0.739383i | \(-0.264883\pi\) | ||||
0.673285 | + | 0.739383i | \(0.264883\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.0286565 | 0.00188546 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.0006 | − | 15.0006i | −0.982722 | − | 0.982722i | 0.0171312 | − | 0.999853i | \(-0.494547\pi\) |
−0.999853 | + | 0.0171312i | \(0.994547\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 21.8407 | − | 10.1386i | 1.42473 | − | 0.661370i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.76851 | − | 2.76851i | −0.179834 | − | 0.179834i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.0614i | 1.10361i | 0.833974 | + | 0.551804i | \(0.186060\pi\) | ||||
−0.833974 | + | 0.551804i | \(0.813940\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 23.3681i | − | 1.50527i | −0.658438 | − | 0.752635i | \(-0.728783\pi\) | ||
0.658438 | − | 0.752635i | \(-0.271217\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.707107 | + | 0.707107i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.37864 | + | 14.6987i | −0.343628 | + | 0.939064i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 15.9735 | + | 15.9735i | 1.01637 | + | 1.01637i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 17.3893 | 1.10200 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.0277i | 0.696063i | 0.937483 | + | 0.348032i | \(0.113150\pi\) | ||||
−0.937483 | + | 0.348032i | \(0.886850\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.28521 | + | 0.0935560i | 0.520887 | + | 0.00588181i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.81024 | + | 4.94701i | −0.113362 | + | 0.309794i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.64897 | + | 1.64897i | −0.102860 | + | 0.102860i | −0.756664 | − | 0.653804i | \(-0.773172\pi\) |
0.653804 | + | 0.756664i | \(0.273172\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.00134924i | 8.38377e-5i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.894482 | −0.0553670 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.85419 | − | 1.85419i | 0.114334 | − | 0.114334i | −0.647625 | − | 0.761959i | \(-0.724238\pi\) |
0.761959 | + | 0.647625i | \(0.224238\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 27.6680 | − | 12.8437i | 1.69963 | − | 0.788983i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.67492 | + | 4.67492i | 0.286101 | + | 0.286101i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.0253i | 1.09902i | 0.835486 | + | 0.549511i | \(0.185186\pi\) | ||||
−0.835486 | + | 0.549511i | \(0.814814\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −31.0616 | −1.88686 | −0.943429 | − | 0.331574i | \(-0.892420\pi\) | ||||
−0.943429 | + | 0.331574i | \(0.892420\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.0393464 | − | 0.0393464i | 0.00238135 | − | 0.00238135i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.57552 | − | 6.59825i | 0.336217 | − | 0.397889i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.2388 | + | 17.2388i | −1.03578 | + | 1.03578i | −0.0364415 | + | 0.999336i | \(0.511602\pi\) |
−0.999336 | + | 0.0364415i | \(0.988398\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.90064i | 0.413130i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 28.7503i | − | 1.71510i | −0.514401 | − | 0.857550i | \(-0.671986\pi\) | ||
0.514401 | − | 0.857550i | \(-0.328014\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.63943 | + | 1.63943i | −0.0974541 | + | 0.0974541i | −0.754153 | − | 0.656699i | \(-0.771952\pi\) |
0.656699 | + | 0.754153i | \(0.271952\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.33977 | − | 13.6572i | −0.375535 | − | 0.808982i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.00326983 | − | 0.00326983i | −0.000193012 | − | 0.000193012i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 11.4500i | − | 0.673531i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 13.8625i | − | 0.812634i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.90209 | + | 2.90209i | −0.169542 | + | 0.169542i | −0.786778 | − | 0.617236i | \(-0.788252\pi\) |
0.617236 | + | 0.786778i | \(0.288252\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.6314 | − | 31.7862i | 0.677208 | − | 1.85067i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.22167 | − | 1.22167i | −0.0708882 | − | 0.0708882i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 11.5043 | − | 11.2474i | 0.665313 | − | 0.650455i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.101307 | −0.00583926 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.95421 | − | 5.95421i | −0.342060 | − | 0.342060i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.54660 | − | 12.4249i | 0.260338 | − | 0.711448i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.9933 | + | 20.9933i | −1.19815 | + | 1.19815i | −0.223434 | + | 0.974719i | \(0.571727\pi\) |
−0.974719 | + | 0.223434i | \(0.928273\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.0622 | 0.913745 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.0182 | 1.47536 | 0.737678 | − | 0.675153i | \(-0.235922\pi\) | ||||
0.737678 | + | 0.675153i | \(0.235922\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.7233 | + | 13.7233i | −0.775690 | + | 0.775690i | −0.979095 | − | 0.203405i | \(-0.934799\pi\) |
0.203405 | + | 0.979095i | \(0.434799\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.0336408 | + | 0.0156163i | −0.00189544 | + | 0.000879878i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.5746 | + | 18.5746i | −1.04325 | + | 1.04325i | −0.0442316 | + | 0.999021i | \(0.514084\pi\) |
−0.999021 | + | 0.0442316i | \(0.985916\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.54539 | 0.0865254 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.2382i | 0.627257i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −11.2171 | − | 11.2171i | −0.624138 | − | 0.624138i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.40423 | − | 16.7150i | −0.0778929 | − | 0.927182i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.28341 | − | 7.28341i | −0.402773 | − | 0.402773i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.178613 | 0.00984725 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.54938 | −0.469916 | −0.234958 | − | 0.972006i | \(-0.575495\pi\) | ||||
−0.234958 | + | 0.972006i | \(0.575495\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.0575199 | − | 0.0575199i | 0.00315207 | − | 0.00315207i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.65046 | + | 5.70964i | 0.144810 | + | 0.311951i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.7074 | + | 13.7074i | 0.746687 | + | 0.746687i | 0.973855 | − | 0.227168i | \(-0.0729468\pi\) |
−0.227168 | + | 0.973855i | \(0.572947\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.24341 | −0.502033 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 11.9222i | − | 0.645624i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.164195 | + | 0.164195i | −0.00886571 | + | 0.00886571i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.77724 | + | 4.40517i | −0.526389 | + | 0.237167i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.02177 | − | 7.02177i | 0.376949 | − | 0.376949i | −0.493052 | − | 0.870000i | \(-0.664119\pi\) |
0.870000 | + | 0.493052i | \(0.164119\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 21.7920i | − | 1.16650i | −0.812294 | − | 0.583249i | \(-0.801781\pi\) | ||
0.812294 | − | 0.583249i | \(-0.198219\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.35478 | −0.179065 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.0973 | − | 14.0973i | −0.750326 | − | 0.750326i | 0.224214 | − | 0.974540i | \(-0.428019\pi\) |
−0.974540 | + | 0.224214i | \(0.928019\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −26.5611 | − | 9.71940i | −1.40972 | − | 0.515852i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.0276304 | + | 0.0276304i | −0.00146235 | + | 0.00146235i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −21.4103 | −1.12999 | −0.564997 | − | 0.825093i | \(-0.691123\pi\) | ||||
−0.564997 | + | 0.825093i | \(0.691123\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.3423 | 1.38644 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.66751 | − | 5.66751i | −0.297467 | − | 0.297467i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.0590 | − | 21.6692i | −0.526514 | − | 1.13422i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.3282 | − | 13.3282i | −0.695726 | − | 0.695726i | 0.267760 | − | 0.963486i | \(-0.413717\pi\) |
−0.963486 | + | 0.267760i | \(0.913717\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.278794i | 0.0145134i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.226269 | 0.0117473 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.6632 | − | 24.6632i | 1.27701 | − | 1.27701i | 0.334681 | − | 0.942331i | \(-0.391371\pi\) |
0.942331 | − | 0.334681i | \(-0.108629\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.94958 | + | 10.7842i | −0.152316 | + | 0.556896i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.12188 | − | 2.12188i | 0.109282 | − | 0.109282i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.8558 | 0.608994 | 0.304497 | − | 0.952513i | \(-0.401512\pi\) | ||||
0.304497 | + | 0.952513i | \(0.401512\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.87453 | 0.198498 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.5598 | + | 11.5598i | −0.590679 | + | 0.590679i | −0.937815 | − | 0.347136i | \(-0.887154\pi\) |
0.347136 | + | 0.937815i | \(0.387154\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.0581210 | − | 0.0269802i | 0.00296212 | − | 0.00137504i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.31887 | + | 4.31887i | 0.219541 | + | 0.219541i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.8359 | 0.600106 | 0.300053 | − | 0.953923i | \(-0.402996\pi\) | ||||
0.300053 | + | 0.953923i | \(0.402996\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.07873 | + | 7.89832i | −0.408559 | + | 0.399435i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.21393 | + | 8.21393i | 0.414338 | + | 0.414338i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.22164 | − | 3.00852i | −0.413675 | − | 0.151375i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.53582 | − | 3.53582i | 0.177458 | − | 0.177458i | −0.612789 | − | 0.790247i | \(-0.709952\pi\) |
0.790247 | + | 0.612789i | \(0.209952\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 0.111688i | − | 0.00559141i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.6536i | 1.13127i | 0.824657 | + | 0.565633i | \(0.191368\pi\) | ||||
−0.824657 | + | 0.565633i | \(0.808632\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.3696 | − | 16.3696i | −0.815428 | − | 0.815428i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.09989 | + | 0.768407i | 0.104345 | + | 0.0381824i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.0993769 | + | 0.0993769i | −0.00492593 | + | 0.00492593i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.72111i | 0.134550i | 0.997734 | + | 0.0672750i | \(0.0214305\pi\) | ||||
−0.997734 | + | 0.0672750i | \(0.978570\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 2.55927i | − | 0.126239i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.177535 | − | 0.177535i | 0.00873590 | − | 0.00873590i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 35.2689 | − | 16.3721i | 1.73128 | − | 0.803675i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.88911 | − | 3.88911i | 0.190451 | − | 0.190451i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 29.6820 | 1.45006 | 0.725030 | − | 0.688717i | \(-0.241826\pi\) | ||||
0.725030 | + | 0.688717i | \(0.241826\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.9116i | 0.629271i | 0.949213 | + | 0.314636i | \(0.101882\pi\) | ||||
−0.949213 | + | 0.314636i | \(0.898118\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.61450 | − | 7.61450i | −0.370230 | − | 0.370230i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.986100 | + | 11.7378i | 0.0478329 | + | 0.569369i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.0693964 | − | 0.0693964i | 0.00335833 | − | 0.00335833i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.79604 | 0.279835 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.6210i | 0.848772i | 0.905481 | + | 0.424386i | \(0.139510\pi\) | ||||
−0.905481 | + | 0.424386i | \(0.860490\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.30573 | + | 9.30573i | −0.447205 | + | 0.447205i | −0.894424 | − | 0.447220i | \(-0.852414\pi\) |
0.447220 | + | 0.894424i | \(0.352414\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.81418 | + | 0.842157i | −0.0869834 | + | 0.0403784i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.364633 | − | 32.2915i | 0.0174428 | − | 1.54471i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.67753i | 0.127791i | 0.997957 | + | 0.0638957i | \(0.0203525\pi\) | ||||
−0.997957 | + | 0.0638957i | \(0.979648\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.99972 | 0.333320 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.8957 | + | 14.8957i | 0.707717 | + | 0.707717i | 0.966055 | − | 0.258338i | \(-0.0831748\pi\) |
−0.258338 | + | 0.966055i | \(0.583175\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.8831 | + | 5.08020i | 0.658122 | + | 0.240824i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.11386 | − | 1.11386i | −0.0526839 | − | 0.0526839i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.4085i | 1.15191i | 0.817482 | + | 0.575954i | \(0.195369\pi\) | ||||
−0.817482 | + | 0.575954i | \(0.804631\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 0.481672i | − | 0.0226810i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.0338 | + | 12.0338i | 0.565398 | + | 0.565398i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.0427574 | − | 0.116847i | 0.00200450 | − | 0.00547787i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.49970 | + | 3.49970i | 0.163709 | + | 0.163709i | 0.784208 | − | 0.620498i | \(-0.213070\pi\) |
−0.620498 | + | 0.784208i | \(0.713070\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.35584 | 0.109961 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.6454 | −0.728680 | −0.364340 | − | 0.931266i | \(-0.618705\pi\) | ||||
−0.364340 | + | 0.931266i | \(0.618705\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.9374 | + | 19.9374i | 0.926569 | + | 0.926569i | 0.997482 | − | 0.0709131i | \(-0.0225913\pi\) |
−0.0709131 | + | 0.997482i | \(0.522591\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.49697 | + | 13.9958i | 0.301290 | + | 0.649041i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.29888 | + | 4.29888i | 0.198929 | + | 0.198929i | 0.799541 | − | 0.600612i | \(-0.205076\pi\) |
−0.600612 | + | 0.799541i | \(0.705076\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.0466934i | 0.00215610i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 11.7377i | − | 0.540845i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.46169 | − | 7.46169i | −0.343089 | − | 0.343089i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −25.7166 | − | 21.7305i | −1.17996 | − | 0.997065i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.64615 | − | 9.64615i | −0.441667 | − | 0.441667i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 25.9392 | 1.18519 | 0.592596 | − | 0.805500i | \(-0.298103\pi\) | ||||
0.592596 | + | 0.805500i | \(0.298103\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.272896i | 0.0124430i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.0795412 | 0.000898174i | −0.00361925 | 4.08683e-5i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.0516 | − | 28.1158i | −0.592642 | − | 1.27667i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.3525 | − | 11.3525i | 0.514430 | − | 0.514430i | −0.401451 | − | 0.915881i | \(-0.631494\pi\) |
0.915881 | + | 0.401451i | \(0.131494\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 23.2672i | 1.05218i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −33.9816 | −1.53357 | −0.766784 | − | 0.641906i | \(-0.778144\pi\) | ||||
−0.766784 | + | 0.641906i | \(0.778144\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.49005 | + | 1.49005i | −0.0671086 | + | 0.0671086i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.62798 | − | 1.32757i | −0.163065 | − | 0.0596700i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.148351 | − | 0.148351i | −0.00665444 | − | 0.00665444i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 7.63815i | − | 0.341930i | −0.985277 | − | 0.170965i | \(-0.945311\pi\) | ||
0.985277 | − | 0.170965i | \(-0.0546886\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.62353 | 0.206564 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.4184 | + | 10.4184i | −0.464535 | + | 0.464535i | −0.900139 | − | 0.435603i | \(-0.856535\pi\) |
0.435603 | + | 0.900139i | \(0.356535\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.6822 | − | 6.47039i | −0.786848 | − | 0.287929i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.23423 | + | 1.23423i | −0.0548140 | + | 0.0548140i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.7018i | 0.607320i | 0.952780 | + | 0.303660i | \(0.0982088\pi\) | ||||
−0.952780 | + | 0.303660i | \(0.901791\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 0.177211i | − | 0.00783935i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.76142 | + | 4.76142i | −0.210222 | + | 0.210222i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 32.5772 | − | 15.1226i | 1.43552 | − | 0.666381i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.1555 | + | 13.1555i | 0.578580 | + | 0.578580i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 4.77792i | − | 0.209727i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 10.4040i | − | 0.455806i | −0.973684 | − | 0.227903i | \(-0.926813\pi\) | ||
0.973684 | − | 0.227903i | \(-0.0731870\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.8761 | − | 19.8761i | 0.869120 | − | 0.869120i | −0.123255 | − | 0.992375i | \(-0.539333\pi\) |
0.992375 | + | 0.123255i | \(0.0393333\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.0535272 | + | 0.0633457i | −0.00233612 | + | 0.00276463i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11.4953 | + | 11.4953i | 0.500742 | + | 0.500742i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9941 | − | 0.519362i | −0.999745 | − | 0.0225810i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −15.1371 | −0.656893 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.661352 | − | 0.661352i | −0.0286463 | − | 0.0286463i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.5808 | + | 22.7933i | 0.457449 | + | 0.985441i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.05510 | + | 2.05510i | −0.0886839 | + | 0.0886839i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −12.0934 | −0.520899 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.70430 | 0.159260 | 0.0796302 | − | 0.996824i | \(-0.474626\pi\) | ||||
0.0796302 | + | 0.996824i | \(0.474626\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.10767 | + | 3.10767i | −0.133363 | + | 0.133363i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −21.6295 | − | 7.91481i | −0.926506 | − | 0.339033i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.28076 | − | 2.28076i | 0.0975182 | − | 0.0975182i | −0.656665 | − | 0.754183i | \(-0.728033\pi\) |
0.754183 | + | 0.656665i | \(0.228033\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.91692 | −0.252528 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 6.02314i | − | 0.256595i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.0459200 | − | 0.0459200i | −0.00195272 | − | 0.00195272i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.0625064 | − | 0.170817i | 0.00265325 | − | 0.00725076i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 26.0661 | + | 26.0661i | 1.10445 | + | 1.10445i | 0.993866 | + | 0.110588i | \(0.0352734\pi\) |
0.110588 | + | 0.993866i | \(0.464727\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20.4903 | −0.866649 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.07017 | −0.171843 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.3486 | − | 13.3486i | 0.562578 | − | 0.562578i | −0.367461 | − | 0.930039i | \(-0.619773\pi\) |
0.930039 | + | 0.367461i | \(0.119773\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18.7474 | + | 8.70270i | −0.788711 | + | 0.366125i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.0117285 | + | 0.0117285i | 0.000492549 | + | 0.000492549i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.4230 | 1.02386 | 0.511932 | − | 0.859026i | \(-0.328930\pi\) | ||||
0.511932 | + | 0.859026i | \(0.328930\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.36696i | 0.266449i | 0.991086 | + | 0.133225i | \(0.0425332\pi\) | ||||
−0.991086 | + | 0.133225i | \(0.957467\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.95918 | + | 4.95918i | −0.207173 | + | 0.207173i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −15.6827 | + | 18.1398i | −0.654012 | + | 0.756484i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.01040 | + | 5.01040i | −0.208586 | + | 0.208586i | −0.803666 | − | 0.595081i | \(-0.797120\pi\) |
0.595081 | + | 0.803666i | \(0.297120\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 15.1900i | 0.631275i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.288429 | 0.0119660 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.6656 | + | 16.6656i | 0.690219 | + | 0.690219i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.80414 | + | 3.15853i | −0.281317 | + | 0.130589i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.4787 | − | 11.4787i | 0.473776 | − | 0.473776i | −0.429358 | − | 0.903134i | \(-0.641260\pi\) |
0.903134 | + | 0.429358i | \(0.141260\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −46.4666 | −1.91462 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.62735 | 0.0669403 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.5347 | + | 10.5347i | 0.432610 | + | 0.432610i | 0.889515 | − | 0.456905i | \(-0.151042\pi\) |
−0.456905 | + | 0.889515i | \(0.651042\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.0300257 | + | 0.0820538i | −0.00123093 | + | 0.00336388i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.4966 | + | 12.4966i | 0.511451 | + | 0.511451i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.4401i | 0.549146i | 0.961566 | + | 0.274573i | \(0.0885365\pi\) | ||||
−0.961566 | + | 0.274573i | \(0.911463\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.20348 | 0.334627 | 0.167313 | − | 0.985904i | \(-0.446491\pi\) | ||||
0.167313 | + | 0.985904i | \(0.446491\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.99060 | − | 1.99060i | 0.0810635 | − | 0.0810635i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −16.8308 | − | 6.15883i | −0.684269 | − | 0.250392i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.5736 | + | 11.5736i | −0.469756 | + | 0.469756i | −0.901835 | − | 0.432080i | \(-0.857780\pi\) |
0.432080 | + | 0.901835i | \(0.357780\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.0148364 | −0.000601200 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 36.1260 | 1.46150 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −27.9916 | + | 27.9916i | −1.13057 | + | 1.13057i | −0.140486 | + | 0.990083i | \(0.544866\pi\) |
−0.990083 | + | 0.140486i | \(0.955134\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.262486 | + | 0.565449i | 0.0105844 | + | 0.0228011i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.87175 | + | 6.87175i | 0.276646 | + | 0.276646i | 0.831769 | − | 0.555122i | \(-0.187329\pi\) |
−0.555122 | + | 0.831769i | \(0.687329\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 43.3388 | 1.74193 | 0.870967 | − | 0.491342i | \(-0.163494\pi\) | ||||
0.870967 | + | 0.491342i | \(0.163494\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.35266 | + | 3.42924i | 0.134538 | + | 0.137611i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.0775408 | + | 0.0775408i | 0.00310661 | + | 0.00310661i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.17108 | + | 24.6496i | 0.166843 | + | 0.985983i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.22629 | − | 8.22629i | 0.328526 | − | 0.328526i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 0.191637i | − | 0.00764105i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.6526i | 1.18045i | 0.807238 | + | 0.590225i | \(0.200961\pi\) | ||||
−0.807238 | + | 0.590225i | \(0.799039\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.44902 | − | 4.44902i | −0.176833 | − | 0.176833i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.85830 | − | 3.64788i | 0.311847 | − | 0.144762i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.6047 | + | 16.6047i | −0.657900 | + | 0.657900i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.6488i | 0.500378i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.85702i | 0.310333i | 0.987888 | + | 0.155167i | \(0.0495915\pi\) | ||||
−0.987888 | + | 0.155167i | \(0.950409\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.26989 | − | 8.26989i | 0.326133 | − | 0.326133i | −0.524981 | − | 0.851114i | \(-0.675928\pi\) |
0.851114 | + | 0.524981i | \(0.175928\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12.8257 | + | 4.69328i | 0.505013 | + | 0.184798i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.77391 | + | 2.77391i | −0.109054 | + | 0.109054i | −0.759528 | − | 0.650475i | \(-0.774570\pi\) |
0.650475 | + | 0.759528i | \(0.274570\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 26.1522 | 1.02657 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.114458i | 0.00448596i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.86077 | + | 7.86077i | 0.307616 | + | 0.307616i | 0.843984 | − | 0.536368i | \(-0.180204\pi\) |
−0.536368 | + | 0.843984i | \(0.680204\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 24.3929 | + | 8.92601i | 0.953109 | + | 0.348768i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7.55474 | + | 7.55474i | −0.294738 | + | 0.294738i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −26.7922 | −1.04368 | −0.521839 | − | 0.853044i | \(-0.674754\pi\) | ||||
−0.521839 | + | 0.853044i | \(0.674754\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 42.4339i | 1.65049i | 0.564777 | + | 0.825244i | \(0.308962\pi\) | ||||
−0.564777 | + | 0.825244i | \(0.691038\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.58849 | + | 5.58849i | −0.217039 | + | 0.217039i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.105155 | − | 0.226526i | −0.00407773 | − | 0.00878429i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.28951 | − | 0.0484368i | −0.166091 | − | 0.00187548i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.35361i | 0.361631i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.2226 | 0.394641 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.5454 | − | 11.5454i | −0.445043 | − | 0.445043i | 0.448659 | − | 0.893703i | \(-0.351902\pi\) |
−0.893703 | + | 0.448659i | \(0.851902\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.98245 | − | 0.418577i | 0.191775 | − | 0.0161110i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.8948 | − | 19.8948i | −0.764619 | − | 0.764619i | 0.212535 | − | 0.977153i | \(-0.431828\pi\) |
−0.977153 | + | 0.212535i | \(0.931828\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 0.229931i | − | 0.00882394i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.19191i | 0.0456741i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.3260 | − | 19.3260i | −0.739487 | − | 0.739487i | 0.232991 | − | 0.972479i | \(-0.425149\pi\) |
−0.972479 | + | 0.232991i | \(0.925149\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.40956 | − | 5.19069i | −0.0920644 | − | 0.198326i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.4089 | − | 14.4089i | −0.549735 | − | 0.549735i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 45.7649 | 1.74350 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.0154 | −0.837505 | −0.418752 | − | 0.908100i | \(-0.637532\pi\) | ||||
−0.418752 | + | 0.908100i | \(0.637532\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.0202632 | − | 0.0202632i | −0.000769736 | − | 0.000769736i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.22626 | − | 11.5495i | 0.160311 | − | 0.438097i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.464424 | + | 0.464424i | 0.0175913 | + | 0.0175913i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 21.2141i | 0.802389i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 33.7843i | − | 1.27602i | −0.770030 | − | 0.638008i | \(-0.779759\pi\) | ||
0.770030 | − | 0.638008i | \(-0.220241\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.387320 | + | 0.387320i | 0.0146080 | + | 0.0146080i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −22.6128 | − | 8.27462i | −0.851646 | − | 0.311640i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.0987598 | − | 0.0987598i | −0.00371425 | − | 0.00371425i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.5113 | −0.807876 | −0.403938 | − | 0.914786i | \(-0.632359\pi\) | ||||
−0.403938 | + | 0.914786i | \(0.632359\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.91526i | 0.146834i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.373675 | + | 33.0922i | −0.0139942 | + | 1.23931i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.7555 | − | 5.45699i | 0.439630 | − | 0.204080i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.0642 | − | 12.0642i | 0.450546 | − | 0.450546i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 14.6800i | − | 0.547472i | −0.961805 | − | 0.273736i | \(-0.911741\pi\) | ||
0.961805 | − | 0.273736i | \(-0.0882594\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.266416 | 0.00992186 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −16.5237 | + | 16.5237i | −0.614524 | + | 0.614524i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.88662 | + | 3.41612i | −0.107206 | + | 0.126871i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31.3379 | − | 31.3379i | −1.16226 | − | 1.16226i | −0.983980 | − | 0.178277i | \(-0.942948\pi\) |
−0.178277 | − | 0.983980i | \(-0.557052\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.3890 | 0.532196 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.5985 | + | 13.5985i | −0.502273 | + | 0.502273i | −0.912144 | − | 0.409870i | \(-0.865574\pi\) |
0.409870 | + | 0.912144i | \(0.365574\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 14.1968 | − | 6.59026i | 0.523657 | − | 0.243085i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.43915 | + | 3.43915i | −0.126683 | + | 0.126683i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.5137i | 1.15925i | 0.814883 | + | 0.579625i | \(0.196801\pi\) | ||||
−0.814883 | + | 0.579625i | \(0.803199\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 22.5900i | − | 0.829863i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.9355 | + | 33.9355i | −1.24497 | + | 1.24497i | −0.287061 | + | 0.957912i | \(0.592678\pi\) |
−0.957912 | + | 0.287061i | \(0.907322\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.30783 | − | 1.21042i | −0.121190 | − | 0.0443465i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.2961 | − | 12.2961i | −0.449891 | − | 0.449891i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.186404i | 0.00681104i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.9950i | 0.510686i | 0.966851 | + | 0.255343i | \(0.0821883\pi\) | ||||
−0.966851 | + | 0.255343i | \(0.917812\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.79778 | − | 7.79778i | 0.284167 | − | 0.284167i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 35.7368 | + | 13.0771i | 1.30060 | + | 0.475923i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.8848 | + | 23.8848i | 0.868109 | + | 0.868109i | 0.992263 | − | 0.124154i | \(-0.0396216\pi\) |
−0.124154 | + | 0.992263i | \(0.539622\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.79237 | − | 5.92468i | −0.210250 | − | 0.215052i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27.0267 | 0.979718 | 0.489859 | − | 0.871802i | \(-0.337048\pi\) | ||||
0.489859 | + | 0.871802i | \(0.337048\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.120807 | − | 0.120807i | −0.00437349 | − | 0.00437349i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.77810 | − | 2.21803i | 0.172752 | − | 0.0801930i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 35.9079 | − | 35.9079i | 1.29656 | − | 1.29656i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −52.5610 | −1.89540 | −0.947699 | − | 0.319165i | \(-0.896598\pi\) | ||||
−0.947699 | + | 0.319165i | \(0.896598\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.33200 | 0.0839849 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.7819 | + | 11.7819i | −0.423764 | + | 0.423764i | −0.886497 | − | 0.462734i | \(-0.846869\pi\) |
0.462734 | + | 0.886497i | \(0.346869\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 26.3542 | + | 22.2694i | 0.946672 | + | 0.799939i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.000954057 | 0 | 0.000954057i | 3.42266e−5 | 0 | 3.42266e-5i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.87731 | −0.0672615 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 21.8532i | − | 0.781970i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.632494 | + | 0.632494i | 0.0226035 | + | 0.0226035i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11.0511 | − | 23.8064i | −0.394430 | − | 0.849686i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.86015 | + | 9.86015i | 0.351476 | + | 0.351476i | 0.860659 | − | 0.509182i | \(-0.170052\pi\) |
−0.509182 | + | 0.860659i | \(0.670052\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.62222 | −0.0933535 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.153316 | −0.00545130 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.0360 | − | 14.0360i | 0.498435 | − | 0.498435i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −28.6461 | − | 10.4824i | −1.01597 | − | 0.371772i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −23.1046 | − | 23.1046i | −0.818406 | − | 0.818406i | 0.167471 | − | 0.985877i | \(-0.446440\pi\) |
−0.985877 | + | 0.167471i | \(0.946440\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −25.3689 | −0.897488 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 6.61134i | − | 0.233600i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.0523 | − | 13.0523i | 0.460605 | − | 0.460605i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.162171 | + | 0.0730666i | −0.00571577 | + | 0.00257526i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.7458 | − | 12.7458i | 0.448674 | − | 0.448674i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 54.7553i | − | 1.92509i | −0.271116 | − | 0.962547i | \(-0.587393\pi\) | ||
0.271116 | − | 0.962547i | \(-0.412607\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.5346 | −1.35313 | −0.676567 | − | 0.736381i | \(-0.736533\pi\) | ||||
−0.676567 | + | 0.736381i | \(0.736533\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 21.9639 | + | 21.9639i | 0.770307 | + | 0.770307i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 21.9061 | + | 47.1904i | 0.767338 | + | 1.65301i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −29.0818 | + | 29.0818i | −1.01744 | + | 1.01744i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.0556442 | −0.00194437 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.82678 | 0.0637551 | 0.0318776 | − | 0.999492i | \(-0.489851\pi\) | ||||
0.0318776 | + | 0.999492i | \(0.489851\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 30.5211 | + | 30.5211i | 1.06390 | + | 1.06390i | 0.997814 | + | 0.0660840i | \(0.0210505\pi\) |
0.0660840 | + | 0.997814i | \(0.478949\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −8.60816 | + | 0.723174i | −0.299698 | + | 0.0251777i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.34366 | + | 3.34366i | 0.116270 | + | 0.116270i | 0.762848 | − | 0.646578i | \(-0.223800\pi\) |
−0.646578 | + | 0.762848i | \(0.723800\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 4.28008i | − | 0.148653i | −0.997234 | − | 0.0743266i | \(-0.976319\pi\) | ||
0.997234 | − | 0.0743266i | \(-0.0236807\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.3793 | 0.845709 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11.6603 | − | 11.6603i | 0.404007 | − | 0.404007i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.37743 | − | 4.35307i | 0.324519 | − | 0.150644i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.87949 | − | 4.87949i | 0.168660 | − | 0.168660i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.0883 | −0.555429 | −0.277714 | − | 0.960664i | \(-0.589577\pi\) | ||||
−0.277714 | + | 0.960664i | \(0.589577\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.1999 | 0.972410 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −20.3295 | + | 20.3295i | −0.700187 | + | 0.700187i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.34122 | + | 3.66528i | −0.0461395 | + | 0.126090i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.0940044 | − | 0.0940044i | −0.00323003 | − | 0.00323003i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.31851 | 0.0795709 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.278953 | − | 0.272723i | 0.00956238 | − | 0.00934884i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.6273 | + | 29.6273i | 1.01442 | + | 1.01442i | 0.999895 | + | 0.0145238i | \(0.00462323\pi\) |
0.0145238 | + | 0.999895i | \(0.495377\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.17420 | + | 14.1400i | −0.176954 | + | 0.483577i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.9180 | + | 22.9180i | −0.782865 | + | 0.782865i | −0.980313 | − | 0.197449i | \(-0.936734\pi\) |
0.197449 | + | 0.980313i | \(0.436734\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 44.9995i | − | 1.53536i | −0.640831 | − | 0.767682i | \(-0.721410\pi\) | ||
0.640831 | − | 0.767682i | \(-0.278590\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.00462424i | 0.000157594i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22.5165 | − | 22.5165i | −0.766469 | − | 0.766469i | 0.211014 | − | 0.977483i | \(-0.432324\pi\) |
−0.977483 | + | 0.211014i | \(0.932324\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.49842 | − | 9.69054i | −0.152951 | − | 0.329488i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.09639 | + | 8.09639i | −0.274968 | + | 0.274968i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 6.76439i | − | 0.229466i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.44415i | 0.320003i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.80227 | + | 9.80227i | −0.331756 | + | 0.331756i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.0489234 | + | 0.178873i | −0.00165391 | + | 0.00604703i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.130809 | + | 0.130809i | −0.00441710 | + | 0.00441710i | −0.709312 | − | 0.704895i | \(-0.750994\pi\) |
0.704895 | + | 0.709312i | \(0.250994\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.10417 | 0.138430 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.93033i | 0.300871i | 0.988620 | + | 0.150435i | \(0.0480675\pi\) | ||||
−0.988620 | + | 0.150435i | \(0.951932\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.0677 | + | 15.0677i | 0.507070 | + | 0.507070i | 0.913626 | − | 0.406556i | \(-0.133270\pi\) |
−0.406556 | + | 0.913626i | \(0.633270\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −30.7009 | + | 14.2516i | −1.03200 | + | 0.479062i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.25851 | − | 4.25851i | 0.142987 | − | 0.142987i | −0.631990 | − | 0.774977i | \(-0.717762\pi\) |
0.774977 | + | 0.631990i | \(0.217762\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.0642651 | 0.00215538 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.72770i | 0.0578800i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 51.2735 | − | 51.2735i | 1.71580 | − | 1.71580i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.23325 | + | 6.10301i | −0.0746495 | + | 0.204001i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −16.0879 | − | 0.181664i | −0.537160 | − | 0.00606557i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.17250i | 0.205864i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −32.1377 | −1.07066 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.0716352 | + | 0.0716352i | 0.00238387 | + | 0.00238387i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.37708 | + | 9.22885i | −0.112258 | + | 0.306777i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.23724 | + | 6.23724i | 0.207104 | + | 0.207104i | 0.803035 | − | 0.595931i | \(-0.203217\pi\) |
−0.595931 | + | 0.803035i | \(0.703217\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.42053i | 0.279291i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 46.8771i | 1.55311i | 0.630050 | + | 0.776554i | \(0.283034\pi\) | ||||
−0.630050 | + | 0.776554i | \(0.716966\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.2439 | + | 21.2439i | 0.703071 | + | 0.703071i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −12.0007 | + | 5.57080i | −0.396730 | + | 0.184165i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.136241 | + | 0.136241i | 0.00449907 | + | 0.00449907i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −35.5200 | −1.17170 | −0.585848 | − | 0.810421i | \(-0.699238\pi\) | ||||
−0.585848 | + | 0.810421i | \(0.699238\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 29.6891 | 0.978288 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −30.0053 | − | 30.0053i | −0.987635 | − | 0.987635i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.0340493 | − | 0.405299i | −0.00111954 | − | 0.0133262i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11.3577 | − | 11.3577i | −0.373035 | − | 0.373035i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 15.2702i | − | 0.501000i | −0.968117 | − | 0.250500i | \(-0.919405\pi\) | ||
0.968117 | − | 0.250500i | \(-0.0805949\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 47.1338i | 1.54475i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −18.3976 | − | 18.3976i | −0.602311 | − | 0.602311i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.25510 | + | 3.83208i | −0.269971 | + | 0.125322i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.0645 | + | 26.0645i | 0.851491 | + | 0.851491i | 0.990317 | − | 0.138826i | \(-0.0443329\pi\) |
−0.138826 | + | 0.990317i | \(0.544333\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19.4077 | 0.633348 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 7.43783i | − | 0.242466i | −0.992624 | − | 0.121233i | \(-0.961315\pi\) | ||
0.992624 | − | 0.121233i | \(-0.0386849\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.0150969 | + | 1.33697i | −0.000491623 | + | 0.0435376i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.0348300 | + | 0.0127452i | 0.00113302 | + | 0.000414602i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −19.8343 | + | 19.8343i | −0.644528 | + | 0.644528i | −0.951665 | − | 0.307137i | \(-0.900629\pi\) |
0.307137 | + | 0.951665i | \(0.400629\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 35.8425i | − | 1.16350i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 26.2684 | 0.851812 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.6040 | − | 31.6040i | 1.02375 | − | 1.02375i | 0.0240441 | − | 0.999711i | \(-0.492346\pi\) |
0.999711 | − | 0.0240441i | \(-0.00765421\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.38910 | + | 14.7273i | −0.174387 | + | 0.476563i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.09276 | − | 1.09276i | −0.0353238 | − | 0.0353238i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 0.0424494i | − | 0.00137076i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16.6188 | 0.536091 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.94663 | − | 7.94663i | 0.256077 | − | 0.256077i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.3014 | + | 30.8083i | 0.460379 | + | 0.991753i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.9956 | − | 11.9956i | 0.385754 | − | 0.385754i | −0.487416 | − | 0.873170i | \(-0.662060\pi\) |
0.873170 | + | 0.487416i | \(0.162060\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 15.8634i | 0.509607i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 20.2973i | − | 0.651373i | −0.945478 | − | 0.325686i | \(-0.894405\pi\) | ||
0.945478 | − | 0.325686i | \(-0.105595\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.0645069 | − | 0.0645069i | 0.00206800 | − | 0.00206800i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −10.8264 | + | 12.8122i | −0.346721 | + | 0.410320i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −23.2680 | − | 23.2680i | −0.744411 | − | 0.744411i | 0.229013 | − | 0.973423i | \(-0.426450\pi\) |
−0.973423 | + | 0.229013i | \(0.926450\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.4224i | 0.365061i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.3003i | 0.328863i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.96631 | + | 7.96631i | −0.254086 | + | 0.254086i | −0.822643 | − | 0.568558i | \(-0.807502\pi\) |
0.568558 | + | 0.822643i | \(0.307502\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.30059 | − | 1.53216i | 0.105165 | − | 0.0488186i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.126298 | − | 0.126298i | −0.00402012 | − | 0.00402012i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 20.4774 | + | 20.9451i | 0.651143 | + | 0.666016i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.4553 | 0.395655 | 0.197827 | − | 0.980237i | \(-0.436611\pi\) | ||||
0.197827 | + | 0.980237i | \(0.436611\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.04532 | + | 6.04532i | 0.191842 | + | 0.191842i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 37.1111 | + | 13.5799i | 1.17650 | + | 0.430513i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.3456 | − | 21.3456i | 0.676021 | − | 0.676021i | −0.283077 | − | 0.959097i | \(-0.591355\pi\) |
0.959097 | + | 0.283077i | \(0.0913551\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.0813454 | −0.00257365 |
(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 | 1380.2.t.a.1333.9 | yes | 48 | |
5.2 | odd | 4 | inner | 1380.2.t.a.1057.10 | yes | 48 | |
23.22 | odd | 2 | inner | 1380.2.t.a.1333.10 | yes | 48 | |
115.22 | even | 4 | inner | 1380.2.t.a.1057.9 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1380.2.t.a.1057.9 | ✓ | 48 | 115.22 | even | 4 | inner | |
1380.2.t.a.1057.10 | yes | 48 | 5.2 | odd | 4 | inner | |
1380.2.t.a.1333.9 | yes | 48 | 1.1 | even | 1 | trivial | |
1380.2.t.a.1333.10 | yes | 48 | 23.22 | odd | 2 | inner |