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 | 1057.10 | ||
Character | \(\chi\) | \(=\) | 1380.1057 |
Dual form | 1380.2.t.a.1333.10 |
$q$-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 \(\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(691\) | \(1201\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) | \(-1\) |
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 | \(-0.749002\pi\) |
0.709320 | + | 0.704887i | \(0.249002\pi\) | |||||||
\(8\) | 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 | −0.954889 | − | 0.296963i | \(-0.904026\pi\) |
0.296963 | + | 0.954889i | \(0.404026\pi\) | |||||||
\(14\) | 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 | \(-0.842222\pi\) |
0.475625 | + | 0.879648i | \(0.342222\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.73367 | 1.54481 | 0.772405 | − | 0.635131i | \(-0.219054\pi\) | ||||
0.772405 | + | 0.635131i | \(0.219054\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.0165866i | 0.00361948i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.79553 | + | 0.0541507i | 0.999936 | + | 0.0112912i | ||||
\(24\) | 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 | \(-0.973534\pi\) | ||
0.996545 | − | 0.0830506i | \(-0.0264663\pi\) | |||||||
\(30\) | 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 | \(-0.747872\pi\) |
0.711819 | + | 0.702363i | \(0.247872\pi\) | |||||||
\(38\) | 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 | \(-0.404203\pi\) |
−0.955054 | + | 0.296432i | \(0.904203\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.768407 | − | 2.09989i | −0.114547 | − | 0.313034i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.61450 | − | 7.61450i | −1.11069 | − | 1.11069i | −0.993057 | − | 0.117632i | \(-0.962470\pi\) |
−0.117632 | − | 0.993057i | \(-0.537530\pi\) | |||||||
\(48\) | 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 | 0.909671 | + | 0.415329i | \(0.136334\pi\) |
0.415329 | + | 0.909671i | \(0.363666\pi\) | |||||||
\(54\) | 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 | \(-0.554573\pi\) | ||
0.170607 | − | 0.985339i | \(-0.445427\pi\) | |||||||
\(60\) | 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 | \(-0.694989\pi\) |
0.818169 | + | 0.574978i | \(0.194989\pi\) | |||||||
\(68\) | 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 | −0.109745 | − | 0.993960i | \(-0.535003\pi\) |
0.993960 | + | 0.109745i | \(0.0350034\pi\) | |||||||
\(74\) | 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 | \(-0.570688\pi\) | ||||
−0.220251 | + | 0.975443i | \(0.570688\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.2961 | + | 12.2961i | 1.34967 | + | 1.34967i | 0.886014 | + | 0.463659i | \(0.153464\pi\) |
0.463659 | + | 0.886014i | \(0.346536\pi\) | |||||||
\(84\) | 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 | \(-0.386046\pi\) | ||||
0.350400 | + | 0.936600i | \(0.386046\pi\) | |||||||
\(90\) | 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 | \(-0.998498\pi\) |
0.00471962 | + | 0.999989i | \(0.498498\pi\) | |||||||
\(98\) | 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 | 0.991873 | + | 0.127232i | \(0.0406092\pi\) |
0.127232 | + | 0.991873i | \(0.459391\pi\) | |||||||
\(104\) | 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 | \(-0.567205\pi\) |
0.977795 | + | 0.209565i | \(0.0672047\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.3003 | −0.986589 | −0.493295 | − | 0.869862i | \(-0.664208\pi\) | ||||
−0.493295 | + | 0.869862i | \(0.664208\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.0813454i | 0.00772096i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.53608 | − | 6.53608i | −0.614863 | − | 0.614863i | 0.329346 | − | 0.944209i | \(-0.393172\pi\) |
−0.944209 | + | 0.329346i | \(0.893172\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.1117 | − | 3.57120i | 0.942921 | − | 0.333016i | ||||
\(116\) | 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 | 0.575026 | − | 0.818135i | \(-0.304992\pi\) |
−0.818135 | + | 0.575026i | \(0.804992\pi\) | |||||||
\(128\) | 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 | \(-0.784869\pi\) |
0.625563 | + | 0.780174i | \(0.284869\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 5.50003i | − | 0.466507i | −0.972416 | − | 0.233253i | \(-0.925063\pi\) | ||
0.972416 | − | 0.233253i | \(-0.0749371\pi\) | |||||||
\(140\) | 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 | \(-0.520553\pi\) | ||||
−0.0645243 | + | 0.997916i | \(0.520553\pi\) | |||||||
\(150\) | 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 | \(-0.905164\pi\) |
0.293547 | + | 0.955945i | \(0.405164\pi\) | |||||||
\(158\) | 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 | −0.353044 | + | 0.935607i | \(0.614853\pi\) |
−0.935607 | + | 0.353044i | \(0.885147\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.50410 | + | 1.62663i | 0.272794 | + | 0.126633i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.26933 | − | 3.26933i | −0.252989 | − | 0.252989i | 0.569206 | − | 0.822195i | \(-0.307251\pi\) |
−0.822195 | + | 0.569206i | \(0.807251\pi\) | |||||||
\(168\) | 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 | −0.566914 | − | 0.823777i | \(-0.691863\pi\) |
0.823777 | + | 0.566914i | \(0.191863\pi\) | |||||||
\(174\) | 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 | \(0.0346416\pi\) | ||||
−0.994084 | + | 0.108615i | \(0.965358\pi\) | |||||||
\(180\) | 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 | −0.978656 | − | 0.205505i | \(-0.934116\pi\) |
0.205505 | + | 0.978656i | \(0.434116\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.57783 | − | 7.04468i | −0.184603 | − | 0.504480i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.15071 | − | 1.15071i | −0.0819848 | − | 0.0819848i | 0.664925 | − | 0.746910i | \(-0.268463\pi\) |
−0.746910 | + | 0.664925i | \(0.768463\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.6728 | 1.25279 | 0.626397 | − | 0.779504i | \(-0.284529\pi\) | ||||
0.626397 | + | 0.779504i | \(0.284529\pi\) | |||||||
\(200\) | 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 | ||||||||
\(207\) | 0.0541507 | − | 4.79553i | 0.00376374 | − | 0.333312i | ||||
\(208\) | 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 | −0.892988 | − | 0.450081i | \(-0.851395\pi\) |
0.450081 | + | 0.892988i | \(0.351395\pi\) | |||||||
\(224\) | 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 | \(-0.737406\pi\) |
0.734523 | + | 0.678584i | \(0.237406\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.3773 | −1.34657 | −0.673285 | − | 0.739383i | \(-0.735117\pi\) | ||||
−0.673285 | + | 0.739383i | \(0.735117\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.0286565 | 0.00188546 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.0006 | + | 15.0006i | −0.982722 | + | 0.982722i | −0.999853 | − | 0.0171312i | \(-0.994547\pi\) |
0.0171312 | + | 0.999853i | \(0.494547\pi\) | |||||||
\(234\) | 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 | \(-0.813940\pi\) | ||
0.833974 | − | 0.551804i | \(-0.186060\pi\) | |||||||
\(240\) | 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 | ||||||||
\(253\) | 0.0935560 | − | 8.28521i | 0.00588181 | − | 0.520887i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.81024 | − | 4.94701i | −0.113362 | − | 0.309794i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.64897 | − | 1.64897i | −0.102860 | − | 0.102860i | 0.653804 | − | 0.756664i | \(-0.273172\pi\) |
−0.756664 | + | 0.653804i | \(0.773172\pi\) | |||||||
\(258\) | 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 | \(-0.275762\pi\) |
−0.761959 | + | 0.647625i | \(0.775762\pi\) | |||||||
\(264\) | 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 | \(-0.814814\pi\) | ||
0.835486 | − | 0.549511i | \(-0.185186\pi\) | |||||||
\(270\) | 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 | −0.999336 | − | 0.0364415i | \(-0.988398\pi\) |
−0.0364415 | − | 0.999336i | \(-0.511602\pi\) | |||||||
\(278\) | 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 | \(-0.228048\pi\) |
−0.656699 | + | 0.754153i | \(0.728048\pi\) | |||||||
\(284\) | 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 | \(-0.211748\pi\) |
−0.617236 | + | 0.786778i | \(0.711748\pi\) | |||||||
\(294\) | 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 | −0.974719 | − | 0.223434i | \(-0.928273\pi\) |
−0.223434 | − | 0.974719i | \(-0.571727\pi\) | |||||||
\(308\) | 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 | \(-0.0652008\pi\) |
−0.203405 | + | 0.979095i | \(0.565201\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.0336408 | − | 0.0156163i | −0.00189544 | − | 0.000879878i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.5746 | − | 18.5746i | −1.04325 | − | 1.04325i | −0.999021 | − | 0.0442316i | \(-0.985916\pi\) |
−0.0442316 | − | 0.999021i | \(-0.514084\pi\) | |||||||
\(318\) | 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 | \(-0.927053\pi\) |
0.227168 | + | 0.973855i | \(0.427053\pi\) | |||||||
\(338\) | 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 | ||||||||
\(345\) | −4.62483 | + | 9.67528i | −0.248992 | + | 0.520899i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.02177 | + | 7.02177i | 0.376949 | + | 0.376949i | 0.870000 | − | 0.493052i | \(-0.164119\pi\) |
−0.493052 | + | 0.870000i | \(0.664119\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.7920i | 1.16650i | 0.812294 | + | 0.583249i | \(0.198219\pi\) | ||||
−0.812294 | + | 0.583249i | \(0.801781\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.35478 | −0.179065 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.0973 | + | 14.0973i | −0.750326 | + | 0.750326i | −0.974540 | − | 0.224214i | \(-0.928019\pi\) |
0.224214 | + | 0.974540i | \(0.428019\pi\) | |||||||
\(354\) | 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 | \(-0.308877\pi\) | ||||
0.564997 | + | 0.825093i | \(0.308877\pi\) | |||||||
\(360\) | 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 | \(-0.586283\pi\) |
0.963486 | + | 0.267760i | \(0.0862834\pi\) | |||||||
\(368\) | 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 | −0.942331 | − | 0.334681i | \(-0.891371\pi\) |
−0.334681 | − | 0.942331i | \(-0.608629\pi\) | |||||||
\(374\) | 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 | \(-0.598488\pi\) | ||||
−0.304497 | + | 0.952513i | \(0.598488\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.87453 | 0.198498 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.5598 | + | 11.5598i | 0.590679 | + | 0.590679i | 0.937815 | − | 0.347136i | \(-0.112846\pi\) |
−0.347136 | + | 0.937815i | \(0.612846\pi\) | |||||||
\(384\) | 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 | \(-0.597004\pi\) | ||||
−0.300053 | + | 0.953923i | \(0.597004\pi\) | |||||||
\(390\) | 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 | 0.790247 | − | 0.612789i | \(-0.209952\pi\) |
−0.612789 | + | 0.790247i | \(0.709952\pi\) | |||||||
\(398\) | 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 | \(-0.978570\pi\) | ||
0.997734 | − | 0.0672750i | \(-0.0214305\pi\) | |||||||
\(410\) | 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 | \(-0.758174\pi\) | ||||
−0.725030 | + | 0.688717i | \(0.758174\pi\) | |||||||
\(420\) | 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 | \(-0.147586\pi\) |
−0.447220 | + | 0.894424i | \(0.647586\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.81418 | + | 0.842157i | 0.0869834 | + | 0.0403784i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 32.2915 | + | 0.364633i | 1.54471 | + | 0.0174428i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 2.67753i | − | 0.127791i | −0.997957 | − | 0.0638957i | \(-0.979648\pi\) | ||
0.997957 | − | 0.0638957i | \(-0.0203525\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.99972 | 0.333320 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.8957 | − | 14.8957i | 0.707717 | − | 0.707717i | −0.258338 | − | 0.966055i | \(-0.583175\pi\) |
0.966055 | + | 0.258338i | \(0.0831748\pi\) | |||||||
\(444\) | 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 | \(-0.804631\pi\) | ||
0.817482 | − | 0.575954i | \(-0.195369\pi\) | |||||||
\(450\) | 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 | \(-0.786930\pi\) |
0.620498 | + | 0.784208i | \(0.286930\pi\) | |||||||
\(458\) | 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 | −0.0709131 | − | 0.997482i | \(-0.522591\pi\) |
0.997482 | + | 0.0709131i | \(0.0225913\pi\) | |||||||
\(464\) | 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 | \(-0.794924\pi\) |
0.600612 | + | 0.799541i | \(0.294924\pi\) | |||||||
\(468\) | 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 | \(-0.701897\pi\) | ||||
−0.592596 | + | 0.805500i | \(0.701897\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.272896i | 0.0124430i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.000898174 | 0.0795412i | −4.08683e−5 | 0.00361925i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.0516 | + | 28.1158i | −0.592642 | + | 1.27667i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.3525 | + | 11.3525i | 0.514430 | + | 0.514430i | 0.915881 | − | 0.401451i | \(-0.131494\pi\) |
−0.401451 | + | 0.915881i | \(0.631494\pi\) | |||||||
\(488\) | 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 | \(0.0546886\pi\) | ||||
−0.985277 | + | 0.170965i | \(0.945311\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.62353 | 0.206564 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10.4184 | + | 10.4184i | 0.464535 | + | 0.464535i | 0.900139 | − | 0.435603i | \(-0.143465\pi\) |
−0.435603 | + | 0.900139i | \(0.643465\pi\) | |||||||
\(504\) | 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 | \(-0.901791\pi\) | ||
0.952780 | − | 0.303660i | \(-0.0982088\pi\) | |||||||
\(510\) | 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 | \(-0.460667\pi\) |
−0.992375 | + | 0.123255i | \(0.960667\pi\) | |||||||
\(524\) | 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 | 0.754183 | − | 0.656665i | \(-0.228033\pi\) |
−0.656665 | + | 0.754183i | \(0.728033\pi\) | |||||||
\(548\) | 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 | −0.110588 | + | 0.993866i | \(0.535273\pi\) |
−0.993866 | + | 0.110588i | \(0.964727\pi\) | |||||||
\(558\) | 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 | \(-0.380227\pi\) |
−0.930039 | + | 0.367461i | \(0.880227\pi\) | |||||||
\(564\) | 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 | \(-0.671070\pi\) | ||||
−0.511932 | + | 0.859026i | \(0.671070\pi\) | |||||||
\(570\) | 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 | ||||||||
\(575\) | 18.4894 | − | 15.2690i | 0.771059 | − | 0.636763i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.01040 | − | 5.01040i | −0.208586 | − | 0.208586i | 0.595081 | − | 0.803666i | \(-0.297120\pi\) |
−0.803666 | + | 0.595081i | \(0.797120\pi\) | |||||||
\(578\) | 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 | 0.903134 | − | 0.429358i | \(-0.141260\pi\) |
−0.429358 | + | 0.903134i | \(0.641260\pi\) | |||||||
\(588\) | 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 | −0.456905 | − | 0.889515i | \(-0.651042\pi\) |
0.889515 | + | 0.456905i | \(0.151042\pi\) | |||||||
\(594\) | 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 | \(-0.911463\pi\) | ||
0.961566 | − | 0.274573i | \(-0.0885365\pi\) | |||||||
\(600\) | 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 | 0.432080 | − | 0.901835i | \(-0.357780\pi\) |
−0.901835 | + | 0.432080i | \(0.857780\pi\) | |||||||
\(608\) | 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 | 0.990083 | + | 0.140486i | \(0.0448664\pi\) |
0.140486 | + | 0.990083i | \(0.455134\pi\) | |||||||
\(614\) | 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 | \(-0.812671\pi\) |
0.555122 | + | 0.831769i | \(0.312671\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −43.3388 | −1.74193 | −0.870967 | − | 0.491342i | \(-0.836506\pi\) | ||||
−0.870967 | + | 0.491342i | \(0.836506\pi\) | |||||||
\(620\) | 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 | \(-0.324072\pi\) |
−0.851114 | + | 0.524981i | \(0.824072\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12.8257 | − | 4.69328i | 0.505013 | − | 0.184798i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.77391 | − | 2.77391i | −0.109054 | − | 0.109054i | 0.650475 | − | 0.759528i | \(-0.274570\pi\) |
−0.759528 | + | 0.650475i | \(0.774570\pi\) | |||||||
\(648\) | 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 | −0.536368 | − | 0.843984i | \(-0.680204\pi\) |
0.843984 | + | 0.536368i | \(0.180204\pi\) | |||||||
\(654\) | 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 | \(-0.325246\pi\) | ||||
0.521839 | + | 0.853044i | \(0.325246\pi\) | |||||||
\(660\) | 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 | ||||||||
\(667\) | 0.0484368 | − | 4.28951i | 0.00187548 | − | 0.166091i | ||||
\(668\) | 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 | −0.893703 | − | 0.448659i | \(-0.851902\pi\) |
0.448659 | + | 0.893703i | \(0.351902\pi\) | |||||||
\(674\) | 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 | \(-0.568172\pi\) |
0.977153 | + | 0.212535i | \(0.0681719\pi\) | |||||||
\(678\) | 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 | −0.972479 | − | 0.232991i | \(-0.925149\pi\) |
0.232991 | + | 0.972479i | \(0.425149\pi\) | |||||||
\(684\) | 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 | \(-0.367641\pi\) | ||||
0.403938 | + | 0.914786i | \(0.367641\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.91526i | 0.146834i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 33.0922 | + | 0.373675i | 1.23931 | + | 0.0139942i | ||||
\(714\) | 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 | \(0.0882594\pi\) | ||||
−0.961805 | + | 0.273736i | \(0.911741\pi\) | |||||||
\(720\) | 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 | 0.178277 | − | 0.983980i | \(-0.442948\pi\) |
0.983980 | − | 0.178277i | \(-0.0570522\pi\) | |||||||
\(728\) | 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 | \(-0.134426\pi\) |
−0.409870 | + | 0.912144i | \(0.634426\pi\) | |||||||
\(734\) | 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 | \(-0.803199\pi\) | ||
0.814883 | − | 0.579625i | \(-0.196801\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 22.5900i | − | 0.829863i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 33.9355 | + | 33.9355i | 1.24497 | + | 1.24497i | 0.957912 | + | 0.287061i | \(0.0926781\pi\) |
0.287061 | + | 0.957912i | \(0.407322\pi\) | |||||||
\(744\) | 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 | \(-0.960378\pi\) |
0.124154 | + | 0.992263i | \(0.460378\pi\) | |||||||
\(758\) | 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 | \(-0.103402\pi\) | ||||
0.947699 | + | 0.319165i | \(0.103402\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.33200 | 0.0839849 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.7819 | + | 11.7819i | 0.423764 | + | 0.423764i | 0.886497 | − | 0.462734i | \(-0.153131\pi\) |
−0.462734 | + | 0.886497i | \(0.653131\pi\) | |||||||
\(774\) | 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 | \(-0.829948\pi\) |
0.509182 | + | 0.860659i | \(0.329948\pi\) | |||||||
\(788\) | 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 | \(-0.553560\pi\) |
0.985877 | + | 0.167471i | \(0.0535601\pi\) | |||||||
\(798\) | 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 | ||||||||
\(805\) | 0.0767100 | − | 0.160479i | 0.00270367 | − | 0.00565616i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.7458 | + | 12.7458i | 0.448674 | + | 0.448674i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 54.7553i | 1.92509i | 0.271116 | + | 0.962547i | \(0.412607\pi\) | ||||
−0.271116 | + | 0.962547i | \(0.587393\pi\) | |||||||
\(810\) | 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 | 0.0660840 | − | 0.997814i | \(-0.478949\pi\) |
0.997814 | − | 0.0660840i | \(-0.0210505\pi\) | |||||||
\(824\) | 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 | \(-0.776200\pi\) |
0.646578 | + | 0.762848i | \(0.276200\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.28008i | 0.148653i | 0.997234 | + | 0.0743266i | \(0.0236807\pi\) | ||||
−0.997234 | + | 0.0743266i | \(0.976319\pi\) | |||||||
\(830\) | 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 | \(-0.410423\pi\) | ||||
0.277714 | + | 0.960664i | \(0.410423\pi\) | |||||||
\(840\) | 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 | 0.0145238 | − | 0.999895i | \(-0.495377\pi\) |
0.999895 | − | 0.0145238i | \(-0.00462323\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.17420 | − | 14.1400i | −0.176954 | − | 0.483577i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.9180 | − | 22.9180i | −0.782865 | − | 0.782865i | 0.197449 | − | 0.980313i | \(-0.436734\pi\) |
−0.980313 | + | 0.197449i | \(0.936734\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.9995i | 1.53536i | 0.640831 | + | 0.767682i | \(0.278590\pi\) | ||||
−0.640831 | + | 0.767682i | \(0.721410\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.00462424i | 0.000157594i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22.5165 | + | 22.5165i | −0.766469 | + | 0.766469i | −0.977483 | − | 0.211014i | \(-0.932324\pi\) |
0.211014 | + | 0.977483i | \(0.432324\pi\) | |||||||
\(864\) | 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 | 0.704895 | − | 0.709312i | \(-0.250994\pi\) |
−0.709312 | + | 0.704895i | \(0.750994\pi\) | |||||||
\(878\) | 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 | −0.406556 | − | 0.913626i | \(-0.633270\pi\) |
0.913626 | + | 0.406556i | \(0.133270\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 30.7009 | + | 14.2516i | 1.03200 | + | 0.479062i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.25851 | + | 4.25851i | 0.142987 | + | 0.142987i | 0.774977 | − | 0.631990i | \(-0.217762\pi\) |
−0.631990 | + | 0.774977i | \(0.717762\pi\) | |||||||
\(888\) | 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 | ||||||||
\(897\) | 0.181664 | − | 16.0879i | 0.00606557 | − | 0.537160i | ||||
\(898\) | 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 | \(-0.796783\pi\) |
0.595931 | + | 0.803035i | \(0.296783\pi\) | |||||||
\(908\) | 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 | \(-0.300762\pi\) | ||||
0.585848 | + | 0.810421i | \(0.300762\pi\) | |||||||
\(920\) | 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 | \(0.0805949\pi\) | ||||
−0.968117 | + | 0.250500i | \(0.919405\pi\) | |||||||
\(930\) | 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 | \(-0.955667\pi\) |
0.138826 | + | 0.990317i | \(0.455667\pi\) | |||||||
\(938\) | 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 | ||||||||
\(943\) | 1.33697 | + | 0.0150969i | 0.0435376 | + | 0.000491623i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.0348300 | − | 0.0127452i | 0.00113302 | − | 0.000414602i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −19.8343 | − | 19.8343i | −0.644528 | − | 0.644528i | 0.307137 | − | 0.951665i | \(-0.400629\pi\) |
−0.951665 | + | 0.307137i | \(0.900629\pi\) | |||||||
\(948\) | 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 | −0.999711 | − | 0.0240441i | \(-0.992346\pi\) |
−0.0240441 | − | 0.999711i | \(-0.507654\pi\) | |||||||
\(954\) | 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 | 0.873170 | − | 0.487416i | \(-0.162060\pi\) |
−0.487416 | + | 0.873170i | \(0.662060\pi\) | |||||||
\(968\) | 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 | \(-0.573550\pi\) |
0.973423 | + | 0.229013i | \(0.0735497\pi\) | |||||||
\(978\) | 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 | \(-0.192498\pi\) |
−0.568558 | + | 0.822643i | \(0.692498\pi\) | |||||||
\(984\) | 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 | 0.959097 | − | 0.283077i | \(-0.0913551\pi\) |
−0.283077 | + | 0.959097i | \(0.591355\pi\) | |||||||
\(998\) | 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.1057.10 | yes | 48 | |
5.3 | odd | 4 | inner | 1380.2.t.a.1333.9 | yes | 48 | |
23.22 | odd | 2 | inner | 1380.2.t.a.1057.9 | ✓ | 48 | |
115.68 | even | 4 | inner | 1380.2.t.a.1333.10 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1380.2.t.a.1057.9 | ✓ | 48 | 23.22 | odd | 2 | inner | |
1380.2.t.a.1057.10 | yes | 48 | 1.1 | even | 1 | trivial | |
1380.2.t.a.1333.9 | yes | 48 | 5.3 | odd | 4 | inner | |
1380.2.t.a.1333.10 | yes | 48 | 115.68 | even | 4 | inner |