Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [750,2,Mod(151,750)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(750, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("750.151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 750 = 2 \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 750.g (of order \(5\), degree \(4\), not 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: | \(5.98878015160\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 24 x^{14} + 94 x^{13} + 262 x^{12} - 936 x^{11} - 1584 x^{10} + 4642 x^{9} + \cdots + 11105 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 5^{6} \) |
Twist minimal: | no (minimal twist has level 150) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 151.4 | ||
Root | \(2.32349 + 0.309017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 750.151 |
Dual form | 750.2.g.f.601.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{2}{5}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.309017 | + | 0.951057i | 0.218508 | + | 0.672499i | ||||
\(3\) | −0.809017 | + | 0.587785i | −0.467086 | + | 0.339358i | ||||
\(4\) | −0.809017 | + | 0.587785i | −0.404508 | + | 0.293893i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.809017 | − | 0.587785i | −0.330280 | − | 0.239962i | ||||
\(7\) | 3.23143 | 1.22136 | 0.610682 | − | 0.791876i | \(-0.290895\pi\) | ||||
0.610682 | + | 0.791876i | \(0.290895\pi\) | |||||||
\(8\) | −0.809017 | − | 0.587785i | −0.286031 | − | 0.207813i | ||||
\(9\) | 0.309017 | − | 0.951057i | 0.103006 | − | 0.317019i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.63788 | + | 5.04087i | 0.493839 | + | 1.51988i | 0.818758 | + | 0.574138i | \(0.194663\pi\) |
−0.324920 | + | 0.945742i | \(0.605337\pi\) | |||||||
\(12\) | 0.309017 | − | 0.951057i | 0.0892055 | − | 0.274546i | ||||
\(13\) | 1.82456 | − | 5.61543i | 0.506043 | − | 1.55744i | −0.292967 | − | 0.956122i | \(-0.594643\pi\) |
0.799010 | − | 0.601318i | \(-0.205357\pi\) | |||||||
\(14\) | 0.998566 | + | 3.07327i | 0.266878 | + | 0.821366i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.309017 | − | 0.951057i | 0.0772542 | − | 0.237764i | ||||
\(17\) | −0.828995 | − | 0.602300i | −0.201061 | − | 0.146079i | 0.482699 | − | 0.875786i | \(-0.339656\pi\) |
−0.683760 | + | 0.729707i | \(0.739656\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 3.64639 | + | 2.64926i | 0.836539 | + | 0.607781i | 0.921402 | − | 0.388611i | \(-0.127045\pi\) |
−0.0848627 | + | 0.996393i | \(0.527045\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.61428 | + | 1.89939i | −0.570483 | + | 0.414480i | ||||
\(22\) | −4.28802 | + | 3.11543i | −0.914209 | + | 0.664212i | ||||
\(23\) | 0.595870 | + | 1.83390i | 0.124247 | + | 0.382394i | 0.993763 | − | 0.111511i | \(-0.0355690\pi\) |
−0.869516 | + | 0.493905i | \(0.835569\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 5.90441 | 1.15795 | ||||||||
\(27\) | 0.309017 | + | 0.951057i | 0.0594703 | + | 0.183031i | ||||
\(28\) | −2.61428 | + | 1.89939i | −0.494053 | + | 0.358950i | ||||
\(29\) | 0.210961 | − | 0.153272i | 0.0391744 | − | 0.0284619i | −0.568026 | − | 0.823011i | \(-0.692293\pi\) |
0.607200 | + | 0.794549i | \(0.292293\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.81386 | + | 1.31784i | 0.325778 | + | 0.236692i | 0.738637 | − | 0.674103i | \(-0.235470\pi\) |
−0.412859 | + | 0.910795i | \(0.635470\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −4.28802 | − | 3.11543i | −0.746449 | − | 0.542327i | ||||
\(34\) | 0.316648 | − | 0.974542i | 0.0543046 | − | 0.167133i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.309017 | + | 0.951057i | 0.0515028 | + | 0.158509i | ||||
\(37\) | −2.95221 | + | 9.08596i | −0.485340 | + | 1.49372i | 0.346149 | + | 0.938180i | \(0.387489\pi\) |
−0.831488 | + | 0.555542i | \(0.812511\pi\) | |||||||
\(38\) | −1.39280 | + | 4.28659i | −0.225941 | + | 0.695376i | ||||
\(39\) | 1.82456 | + | 5.61543i | 0.292164 | + | 0.899188i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.07816 | + | 9.47359i | −0.480727 | + | 1.47953i | 0.357348 | + | 0.933971i | \(0.383681\pi\) |
−0.838075 | + | 0.545555i | \(0.816319\pi\) | |||||||
\(42\) | −2.61428 | − | 1.89939i | −0.403392 | − | 0.293082i | ||||
\(43\) | −5.30164 | −0.808492 | −0.404246 | − | 0.914650i | \(-0.632466\pi\) | ||||
−0.404246 | + | 0.914650i | \(0.632466\pi\) | |||||||
\(44\) | −4.28802 | − | 3.11543i | −0.646444 | − | 0.469669i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.56001 | + | 1.13341i | −0.230010 | + | 0.167112i | ||||
\(47\) | 8.51747 | − | 6.18830i | 1.24240 | − | 0.902657i | 0.244644 | − | 0.969613i | \(-0.421329\pi\) |
0.997756 | + | 0.0669561i | \(0.0213288\pi\) | |||||||
\(48\) | 0.309017 | + | 0.951057i | 0.0446028 | + | 0.137273i | ||||
\(49\) | 3.44213 | 0.491732 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.02469 | 0.143486 | ||||||||
\(52\) | 1.82456 | + | 5.61543i | 0.253021 | + | 0.778720i | ||||
\(53\) | 1.86970 | − | 1.35841i | 0.256823 | − | 0.186593i | −0.451923 | − | 0.892057i | \(-0.649262\pi\) |
0.708745 | + | 0.705465i | \(0.249262\pi\) | |||||||
\(54\) | −0.809017 | + | 0.587785i | −0.110093 | + | 0.0799874i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.61428 | − | 1.89939i | −0.349348 | − | 0.253816i | ||||
\(57\) | −4.50718 | −0.596991 | ||||||||
\(58\) | 0.210961 | + | 0.153272i | 0.0277005 | + | 0.0201256i | ||||
\(59\) | −2.00615 | + | 6.17428i | −0.261178 | + | 0.803823i | 0.731371 | + | 0.681979i | \(0.238881\pi\) |
−0.992549 | + | 0.121844i | \(0.961119\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.21905 | − | 3.75186i | −0.156084 | − | 0.480376i | 0.842185 | − | 0.539188i | \(-0.181269\pi\) |
−0.998269 | + | 0.0588118i | \(0.981269\pi\) | |||||||
\(62\) | −0.692831 | + | 2.13232i | −0.0879897 | + | 0.270804i | ||||
\(63\) | 0.998566 | − | 3.07327i | 0.125808 | − | 0.387196i | ||||
\(64\) | 0.309017 | + | 0.951057i | 0.0386271 | + | 0.118882i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.63788 | − | 5.04087i | 0.201609 | − | 0.620488i | ||||
\(67\) | −7.51747 | − | 5.46176i | −0.918405 | − | 0.667260i | 0.0247216 | − | 0.999694i | \(-0.492130\pi\) |
−0.943126 | + | 0.332434i | \(0.892130\pi\) | |||||||
\(68\) | 1.02469 | 0.124262 | ||||||||
\(69\) | −1.56001 | − | 1.13341i | −0.187803 | − | 0.136447i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.90715 | + | 5.01834i | −0.819728 | + | 0.595567i | −0.916635 | − | 0.399726i | \(-0.869105\pi\) |
0.0969066 | + | 0.995293i | \(0.469105\pi\) | |||||||
\(72\) | −0.809017 | + | 0.587785i | −0.0953436 | + | 0.0692712i | ||||
\(73\) | 1.22192 | + | 3.76068i | 0.143015 | + | 0.440155i | 0.996750 | − | 0.0805522i | \(-0.0256684\pi\) |
−0.853735 | + | 0.520707i | \(0.825668\pi\) | |||||||
\(74\) | −9.55354 | −1.11058 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.50718 | −0.517010 | ||||||||
\(77\) | 5.29269 | + | 16.2892i | 0.603158 | + | 1.85633i | ||||
\(78\) | −4.77677 | + | 3.47053i | −0.540863 | + | 0.392960i | ||||
\(79\) | 10.8177 | − | 7.85950i | 1.21708 | − | 0.884263i | 0.221229 | − | 0.975222i | \(-0.428993\pi\) |
0.995855 | + | 0.0909589i | \(0.0289932\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | − | 0.587785i | −0.0898908 | − | 0.0653095i | ||||
\(82\) | −9.96112 | −1.10002 | ||||||||
\(83\) | −6.05709 | − | 4.40074i | −0.664852 | − | 0.483044i | 0.203446 | − | 0.979086i | \(-0.434786\pi\) |
−0.868298 | + | 0.496043i | \(0.834786\pi\) | |||||||
\(84\) | 0.998566 | − | 3.07327i | 0.108952 | − | 0.335321i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.63830 | − | 5.04216i | −0.176662 | − | 0.543710i | ||||
\(87\) | −0.0805798 | + | 0.247999i | −0.00863906 | + | 0.0265883i | ||||
\(88\) | 1.63788 | − | 5.04087i | 0.174598 | − | 0.537359i | ||||
\(89\) | −0.226687 | − | 0.697671i | −0.0240288 | − | 0.0739529i | 0.938323 | − | 0.345760i | \(-0.112379\pi\) |
−0.962352 | + | 0.271807i | \(0.912379\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.89595 | − | 18.1459i | 0.618063 | − | 1.90220i | ||||
\(92\) | −1.56001 | − | 1.13341i | −0.162642 | − | 0.118166i | ||||
\(93\) | −2.24205 | −0.232490 | ||||||||
\(94\) | 8.51747 | + | 6.18830i | 0.878510 | + | 0.638275i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.809017 | + | 0.587785i | −0.0825700 | + | 0.0599906i | ||||
\(97\) | 13.9610 | − | 10.1432i | 1.41752 | − | 1.02989i | 0.425345 | − | 0.905031i | \(-0.360153\pi\) |
0.992175 | − | 0.124857i | \(-0.0398473\pi\) | |||||||
\(98\) | 1.06368 | + | 3.27366i | 0.107447 | + | 0.330689i | ||||
\(99\) | 5.30029 | 0.532699 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.8454 | 1.17866 | 0.589331 | − | 0.807892i | \(-0.299391\pi\) | ||||
0.589331 | + | 0.807892i | \(0.299391\pi\) | |||||||
\(102\) | 0.316648 | + | 0.974542i | 0.0313528 | + | 0.0964940i | ||||
\(103\) | 5.78515 | − | 4.20316i | 0.570028 | − | 0.414150i | −0.265087 | − | 0.964224i | \(-0.585401\pi\) |
0.835115 | + | 0.550075i | \(0.185401\pi\) | |||||||
\(104\) | −4.77677 | + | 3.47053i | −0.468401 | + | 0.340313i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.86970 | + | 1.35841i | 0.181601 | + | 0.131941i | ||||
\(107\) | 3.20058 | 0.309412 | 0.154706 | − | 0.987961i | \(-0.450557\pi\) | ||||
0.154706 | + | 0.987961i | \(0.450557\pi\) | |||||||
\(108\) | −0.809017 | − | 0.587785i | −0.0778477 | − | 0.0565597i | ||||
\(109\) | 3.05789 | − | 9.41123i | 0.292893 | − | 0.901432i | −0.691028 | − | 0.722828i | \(-0.742842\pi\) |
0.983921 | − | 0.178604i | \(-0.0571581\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.95221 | − | 9.08596i | −0.280211 | − | 0.862401i | ||||
\(112\) | 0.998566 | − | 3.07327i | 0.0943556 | − | 0.290397i | ||||
\(113\) | −1.31201 | + | 4.03794i | −0.123423 | + | 0.379858i | −0.993611 | − | 0.112863i | \(-0.963998\pi\) |
0.870187 | + | 0.492721i | \(0.163998\pi\) | |||||||
\(114\) | −1.39280 | − | 4.28659i | −0.130447 | − | 0.401476i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.0805798 | + | 0.247999i | −0.00748165 | + | 0.0230261i | ||||
\(117\) | −4.77677 | − | 3.47053i | −0.441613 | − | 0.320850i | ||||
\(118\) | −6.49202 | −0.597639 | ||||||||
\(119\) | −2.67884 | − | 1.94629i | −0.245569 | − | 0.178416i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13.8285 | + | 10.0470i | −1.25714 | + | 0.913366i | ||||
\(122\) | 3.19152 | − | 2.31878i | 0.288947 | − | 0.209932i | ||||
\(123\) | −3.07816 | − | 9.47359i | −0.277548 | − | 0.854205i | ||||
\(124\) | −2.24205 | −0.201342 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.23143 | 0.287878 | ||||||||
\(127\) | −2.85868 | − | 8.79813i | −0.253667 | − | 0.780708i | −0.994089 | − | 0.108565i | \(-0.965374\pi\) |
0.740422 | − | 0.672142i | \(-0.234626\pi\) | |||||||
\(128\) | −0.809017 | + | 0.587785i | −0.0715077 | + | 0.0519534i | ||||
\(129\) | 4.28912 | − | 3.11623i | 0.377636 | − | 0.274368i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.93584 | + | 2.85956i | 0.343876 | + | 0.249841i | 0.746296 | − | 0.665615i | \(-0.231831\pi\) |
−0.402419 | + | 0.915455i | \(0.631831\pi\) | |||||||
\(132\) | 5.30029 | 0.461331 | ||||||||
\(133\) | 11.7830 | + | 8.56088i | 1.02172 | + | 0.742323i | ||||
\(134\) | 2.87142 | − | 8.83731i | 0.248053 | − | 0.763428i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.316648 | + | 0.974542i | 0.0271523 | + | 0.0835663i | ||||
\(137\) | 1.85925 | − | 5.72219i | 0.158847 | − | 0.488879i | −0.839684 | − | 0.543076i | \(-0.817260\pi\) |
0.998530 | + | 0.0541963i | \(0.0172597\pi\) | |||||||
\(138\) | 0.595870 | − | 1.83390i | 0.0507238 | − | 0.156112i | ||||
\(139\) | −1.73890 | − | 5.35178i | −0.147492 | − | 0.453932i | 0.849831 | − | 0.527055i | \(-0.176704\pi\) |
−0.997323 | + | 0.0731222i | \(0.976704\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.25338 | + | 10.0129i | −0.273984 | + | 0.843237i | ||||
\(142\) | −6.90715 | − | 5.01834i | −0.579635 | − | 0.421130i | ||||
\(143\) | 31.2951 | 2.61703 | ||||||||
\(144\) | −0.809017 | − | 0.587785i | −0.0674181 | − | 0.0489821i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.19903 | + | 2.32423i | −0.264754 | + | 0.192355i | ||||
\(147\) | −2.78474 | + | 2.02323i | −0.229681 | + | 0.166873i | ||||
\(148\) | −2.95221 | − | 9.08596i | −0.242670 | − | 0.746861i | ||||
\(149\) | −11.6556 | −0.954863 | −0.477432 | − | 0.878669i | \(-0.658432\pi\) | ||||
−0.477432 | + | 0.878669i | \(0.658432\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.52354 | 0.449499 | 0.224750 | − | 0.974417i | \(-0.427844\pi\) | ||||
0.224750 | + | 0.974417i | \(0.427844\pi\) | |||||||
\(152\) | −1.39280 | − | 4.28659i | −0.112971 | − | 0.347688i | ||||
\(153\) | −0.828995 | + | 0.602300i | −0.0670202 | + | 0.0486931i | ||||
\(154\) | −13.8564 | + | 10.0673i | −1.11658 | + | 0.811245i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −4.77677 | − | 3.47053i | −0.382448 | − | 0.277864i | ||||
\(157\) | −6.84307 | −0.546136 | −0.273068 | − | 0.961995i | \(-0.588038\pi\) | ||||
−0.273068 | + | 0.961995i | \(0.588038\pi\) | |||||||
\(158\) | 10.8177 | + | 7.85950i | 0.860608 | + | 0.625268i | ||||
\(159\) | −0.714161 | + | 2.19796i | −0.0566366 | + | 0.174310i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.92551 | + | 5.92611i | 0.151751 | + | 0.467043i | ||||
\(162\) | 0.309017 | − | 0.951057i | 0.0242787 | − | 0.0747221i | ||||
\(163\) | −2.90080 | + | 8.92773i | −0.227208 | + | 0.699274i | 0.770852 | + | 0.637014i | \(0.219831\pi\) |
−0.998060 | + | 0.0622597i | \(0.980169\pi\) | |||||||
\(164\) | −3.07816 | − | 9.47359i | −0.240364 | − | 0.739763i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.31360 | − | 7.12054i | 0.179570 | − | 0.552661i | ||||
\(167\) | −5.52464 | − | 4.01388i | −0.427509 | − | 0.310604i | 0.353143 | − | 0.935569i | \(-0.385113\pi\) |
−0.780652 | + | 0.624966i | \(0.785113\pi\) | |||||||
\(168\) | 3.23143 | 0.249310 | ||||||||
\(169\) | −17.6868 | − | 12.8502i | −1.36052 | − | 0.988478i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.64639 | − | 2.64926i | 0.278846 | − | 0.202594i | ||||
\(172\) | 4.28912 | − | 3.11623i | 0.327042 | − | 0.237610i | ||||
\(173\) | 5.82820 | + | 17.9373i | 0.443110 | + | 1.36375i | 0.884544 | + | 0.466457i | \(0.154470\pi\) |
−0.441434 | + | 0.897294i | \(0.645530\pi\) | |||||||
\(174\) | −0.260762 | −0.0197683 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.30029 | 0.399524 | ||||||||
\(177\) | −2.00615 | − | 6.17428i | −0.150791 | − | 0.464087i | ||||
\(178\) | 0.593474 | − | 0.431184i | 0.0444828 | − | 0.0323186i | ||||
\(179\) | −0.761557 | + | 0.553303i | −0.0569214 | + | 0.0413558i | −0.615882 | − | 0.787838i | \(-0.711200\pi\) |
0.558961 | + | 0.829194i | \(0.311200\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.4118 | − | 8.29114i | −0.848231 | − | 0.616276i | 0.0764270 | − | 0.997075i | \(-0.475649\pi\) |
−0.924658 | + | 0.380800i | \(0.875649\pi\) | |||||||
\(182\) | 19.0797 | 1.41428 | ||||||||
\(183\) | 3.19152 | + | 2.31878i | 0.235924 | + | 0.171409i | ||||
\(184\) | 0.595870 | − | 1.83390i | 0.0439281 | − | 0.135197i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.692831 | − | 2.13232i | −0.0508009 | − | 0.156349i | ||||
\(187\) | 1.67832 | − | 5.16535i | 0.122731 | − | 0.377728i | ||||
\(188\) | −3.25338 | + | 10.0129i | −0.237277 | + | 0.730265i | ||||
\(189\) | 0.998566 | + | 3.07327i | 0.0726350 | + | 0.223548i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.87125 | − | 24.2252i | 0.569544 | − | 1.75288i | −0.0845047 | − | 0.996423i | \(-0.526931\pi\) |
0.654049 | − | 0.756453i | \(-0.273069\pi\) | |||||||
\(192\) | −0.809017 | − | 0.587785i | −0.0583858 | − | 0.0424197i | ||||
\(193\) | −6.63439 | −0.477554 | −0.238777 | − | 0.971074i | \(-0.576746\pi\) | ||||
−0.238777 | + | 0.971074i | \(0.576746\pi\) | |||||||
\(194\) | 13.9610 | + | 10.1432i | 1.00234 | + | 0.728241i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.78474 | + | 2.02323i | −0.198910 | + | 0.144517i | ||||
\(197\) | 8.23396 | − | 5.98232i | 0.586645 | − | 0.426223i | −0.254468 | − | 0.967081i | \(-0.581900\pi\) |
0.841114 | + | 0.540858i | \(0.181900\pi\) | |||||||
\(198\) | 1.63788 | + | 5.04087i | 0.116399 | + | 0.358239i | ||||
\(199\) | −2.52238 | −0.178807 | −0.0894035 | − | 0.995995i | \(-0.528496\pi\) | ||||
−0.0894035 | + | 0.995995i | \(0.528496\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.29210 | 0.655414 | ||||||||
\(202\) | 3.66043 | + | 11.2656i | 0.257547 | + | 0.792648i | ||||
\(203\) | 0.681704 | − | 0.495287i | 0.0478463 | − | 0.0347623i | ||||
\(204\) | −0.828995 | + | 0.602300i | −0.0580412 | + | 0.0421694i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.78515 | + | 4.20316i | 0.403071 | + | 0.292848i | ||||
\(207\) | 1.92827 | 0.134024 | ||||||||
\(208\) | −4.77677 | − | 3.47053i | −0.331209 | − | 0.240638i | ||||
\(209\) | −7.38222 | + | 22.7201i | −0.510639 | + | 1.57158i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.87129 | + | 14.9923i | 0.335353 | + | 1.03211i | 0.966548 | + | 0.256487i | \(0.0825650\pi\) |
−0.631194 | + | 0.775625i | \(0.717435\pi\) | |||||||
\(212\) | −0.714161 | + | 2.19796i | −0.0490487 | + | 0.150957i | ||||
\(213\) | 2.63830 | − | 8.11984i | 0.180773 | − | 0.556362i | ||||
\(214\) | 0.989034 | + | 3.04393i | 0.0676090 | + | 0.208079i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.309017 | − | 0.951057i | 0.0210259 | − | 0.0647112i | ||||
\(217\) | 5.86135 | + | 4.25852i | 0.397894 | + | 0.289087i | ||||
\(218\) | 9.89555 | 0.670211 | ||||||||
\(219\) | −3.19903 | − | 2.32423i | −0.216170 | − | 0.157057i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.89473 | + | 3.55623i | −0.329255 | + | 0.239218i | ||||
\(222\) | 7.72898 | − | 5.61543i | 0.518735 | − | 0.376883i | ||||
\(223\) | −2.87242 | − | 8.84040i | −0.192351 | − | 0.591997i | −0.999997 | − | 0.00232890i | \(-0.999259\pi\) |
0.807646 | − | 0.589668i | \(-0.200741\pi\) | |||||||
\(224\) | 3.23143 | 0.215909 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.24575 | −0.282423 | ||||||||
\(227\) | −1.12423 | − | 3.46003i | −0.0746178 | − | 0.229650i | 0.906791 | − | 0.421582i | \(-0.138525\pi\) |
−0.981408 | + | 0.191931i | \(0.938525\pi\) | |||||||
\(228\) | 3.64639 | − | 2.64926i | 0.241488 | − | 0.175451i | ||||
\(229\) | −8.03500 | + | 5.83777i | −0.530968 | + | 0.385771i | −0.820720 | − | 0.571331i | \(-0.806427\pi\) |
0.289752 | + | 0.957102i | \(0.406427\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −13.8564 | − | 10.0673i | −0.911686 | − | 0.662379i | ||||
\(232\) | −0.260762 | −0.0171198 | ||||||||
\(233\) | −15.2009 | − | 11.0441i | −0.995844 | − | 0.723523i | −0.0346507 | − | 0.999399i | \(-0.511032\pi\) |
−0.961193 | + | 0.275877i | \(0.911032\pi\) | |||||||
\(234\) | 1.82456 | − | 5.61543i | 0.119275 | − | 0.367092i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.00615 | − | 6.17428i | −0.130589 | − | 0.401912i | ||||
\(237\) | −4.13198 | + | 12.7169i | −0.268401 | + | 0.826054i | ||||
\(238\) | 1.02322 | − | 3.14916i | 0.0663258 | − | 0.204130i | ||||
\(239\) | −3.01349 | − | 9.27457i | −0.194926 | − | 0.599922i | −0.999977 | − | 0.00671626i | \(-0.997862\pi\) |
0.805051 | − | 0.593206i | \(-0.202138\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.84694 | − | 17.9950i | 0.376634 | − | 1.15916i | −0.565735 | − | 0.824587i | \(-0.691408\pi\) |
0.942369 | − | 0.334574i | \(-0.108592\pi\) | |||||||
\(242\) | −13.8285 | − | 10.0470i | −0.888933 | − | 0.645848i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 3.19152 | + | 2.31878i | 0.204316 | + | 0.148444i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 8.05872 | − | 5.85500i | 0.513805 | − | 0.373301i | ||||
\(247\) | 21.5298 | − | 15.6423i | 1.36991 | − | 0.995296i | ||||
\(248\) | −0.692831 | − | 2.13232i | −0.0439948 | − | 0.135402i | ||||
\(249\) | 7.48698 | 0.474468 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.98608 | −0.125360 | −0.0626801 | − | 0.998034i | \(-0.519965\pi\) | ||||
−0.0626801 | + | 0.998034i | \(0.519965\pi\) | |||||||
\(252\) | 0.998566 | + | 3.07327i | 0.0629038 | + | 0.193598i | ||||
\(253\) | −8.26848 | + | 6.00740i | −0.519835 | + | 0.377682i | ||||
\(254\) | 7.48413 | − | 5.43754i | 0.469596 | − | 0.341182i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.809017 | − | 0.587785i | −0.0505636 | − | 0.0367366i | ||||
\(257\) | −19.2797 | −1.20263 | −0.601317 | − | 0.799010i | \(-0.705357\pi\) | ||||
−0.601317 | + | 0.799010i | \(0.705357\pi\) | |||||||
\(258\) | 4.28912 | + | 3.11623i | 0.267029 | + | 0.194008i | ||||
\(259\) | −9.53984 | + | 29.3606i | −0.592777 | + | 1.82438i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.0805798 | − | 0.247999i | −0.00498777 | − | 0.0153508i | ||||
\(262\) | −1.50336 | + | 4.62686i | −0.0928778 | + | 0.285848i | ||||
\(263\) | 3.87188 | − | 11.9164i | 0.238751 | − | 0.734799i | −0.757851 | − | 0.652428i | \(-0.773751\pi\) |
0.996602 | − | 0.0823713i | \(-0.0262493\pi\) | |||||||
\(264\) | 1.63788 | + | 5.04087i | 0.100804 | + | 0.310244i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.50072 | + | 13.8518i | −0.275957 | + | 0.849308i | ||||
\(267\) | 0.593474 | + | 0.431184i | 0.0363200 | + | 0.0263880i | ||||
\(268\) | 9.29210 | 0.567605 | ||||||||
\(269\) | −10.9160 | − | 7.93096i | −0.665562 | − | 0.483559i | 0.202975 | − | 0.979184i | \(-0.434939\pi\) |
−0.868537 | + | 0.495625i | \(0.834939\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.6926 | − | 15.7606i | 1.31773 | − | 0.957387i | 0.317773 | − | 0.948167i | \(-0.397065\pi\) |
0.999957 | − | 0.00922023i | \(-0.00293493\pi\) | |||||||
\(272\) | −0.828995 | + | 0.602300i | −0.0502652 | + | 0.0365198i | ||||
\(273\) | 5.89595 | + | 18.1459i | 0.356839 | + | 1.09824i | ||||
\(274\) | 6.01666 | 0.363480 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.92827 | 0.116068 | ||||||||
\(277\) | 2.52382 | + | 7.76751i | 0.151641 | + | 0.466704i | 0.997805 | − | 0.0662188i | \(-0.0210935\pi\) |
−0.846164 | + | 0.532923i | \(0.821094\pi\) | |||||||
\(278\) | 4.55250 | − | 3.30758i | 0.273041 | − | 0.198376i | ||||
\(279\) | 1.81386 | − | 1.31784i | 0.108593 | − | 0.0788972i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −25.3561 | − | 18.4223i | −1.51262 | − | 1.09898i | −0.965000 | − | 0.262249i | \(-0.915536\pi\) |
−0.547615 | − | 0.836730i | \(-0.684464\pi\) | |||||||
\(282\) | −10.5282 | −0.626943 | ||||||||
\(283\) | 13.2277 | + | 9.61049i | 0.786306 | + | 0.571284i | 0.906865 | − | 0.421422i | \(-0.138469\pi\) |
−0.120559 | + | 0.992706i | \(0.538469\pi\) | |||||||
\(284\) | 2.63830 | − | 8.11984i | 0.156554 | − | 0.481824i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.67071 | + | 29.7634i | 0.571841 | + | 1.75995i | ||||
\(287\) | −9.94684 | + | 30.6132i | −0.587143 | + | 1.80704i | ||||
\(288\) | 0.309017 | − | 0.951057i | 0.0182090 | − | 0.0560415i | ||||
\(289\) | −4.92882 | − | 15.1694i | −0.289931 | − | 0.892315i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.33261 | + | 16.4121i | −0.312603 | + | 0.962093i | ||||
\(292\) | −3.19903 | − | 2.32423i | −0.187209 | − | 0.136015i | ||||
\(293\) | −28.1867 | −1.64669 | −0.823343 | − | 0.567545i | \(-0.807893\pi\) | ||||
−0.823343 | + | 0.567545i | \(0.807893\pi\) | |||||||
\(294\) | −2.78474 | − | 2.02323i | −0.162409 | − | 0.117997i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 7.72898 | − | 5.61543i | 0.449238 | − | 0.326390i | ||||
\(297\) | −4.28802 | + | 3.11543i | −0.248816 | + | 0.180776i | ||||
\(298\) | −3.60178 | − | 11.0851i | −0.208645 | − | 0.642144i | ||||
\(299\) | 11.3853 | 0.658431 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.1319 | −0.987464 | ||||||||
\(302\) | 1.70687 | + | 5.25320i | 0.0982192 | + | 0.302288i | ||||
\(303\) | −9.58313 | + | 6.96255i | −0.550537 | + | 0.399988i | ||||
\(304\) | 3.64639 | − | 2.64926i | 0.209135 | − | 0.151945i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.828995 | − | 0.602300i | −0.0473905 | − | 0.0344312i | ||||
\(307\) | −14.5372 | −0.829680 | −0.414840 | − | 0.909894i | \(-0.636163\pi\) | ||||
−0.414840 | + | 0.909894i | \(0.636163\pi\) | |||||||
\(308\) | −13.8564 | − | 10.0673i | −0.789543 | − | 0.573637i | ||||
\(309\) | −2.20973 | + | 6.80085i | −0.125707 | + | 0.386887i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.47841 | + | 13.7831i | 0.253947 | + | 0.781570i | 0.994035 | + | 0.109060i | \(0.0347839\pi\) |
−0.740088 | + | 0.672510i | \(0.765216\pi\) | |||||||
\(312\) | 1.82456 | − | 5.61543i | 0.103296 | − | 0.317911i | ||||
\(313\) | −9.74294 | + | 29.9857i | −0.550703 | + | 1.69489i | 0.156325 | + | 0.987706i | \(0.450035\pi\) |
−0.707029 | + | 0.707185i | \(0.749965\pi\) | |||||||
\(314\) | −2.11462 | − | 6.50814i | −0.119335 | − | 0.367276i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.13198 | + | 12.7169i | −0.232442 | + | 0.715384i | ||||
\(317\) | 12.1199 | + | 8.80564i | 0.680722 | + | 0.494574i | 0.873597 | − | 0.486650i | \(-0.161781\pi\) |
−0.192875 | + | 0.981223i | \(0.561781\pi\) | |||||||
\(318\) | −2.31107 | −0.129598 | ||||||||
\(319\) | 1.11815 | + | 0.812385i | 0.0626045 | + | 0.0454848i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.58932 | + | 1.88125i | −0.144522 | + | 0.105001i | ||||
\(322\) | −5.04105 | + | 3.66254i | −0.280927 | + | 0.204105i | ||||
\(323\) | −1.42719 | − | 4.39244i | −0.0794110 | − | 0.244402i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9.38717 | −0.519907 | ||||||||
\(327\) | 3.05789 | + | 9.41123i | 0.169102 | + | 0.520442i | ||||
\(328\) | 8.05872 | − | 5.85500i | 0.444968 | − | 0.323288i | ||||
\(329\) | 27.5236 | − | 19.9971i | 1.51742 | − | 1.10247i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.4888 | + | 12.7064i | 0.961273 | + | 0.698406i | 0.953446 | − | 0.301563i | \(-0.0975085\pi\) |
0.00782724 | + | 0.999969i | \(0.497508\pi\) | |||||||
\(332\) | 7.48698 | 0.410901 | ||||||||
\(333\) | 7.72898 | + | 5.61543i | 0.423545 | + | 0.307724i | ||||
\(334\) | 2.11022 | − | 6.49460i | 0.115466 | − | 0.355369i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.998566 | + | 3.07327i | 0.0544762 | + | 0.167661i | ||||
\(337\) | −2.34697 | + | 7.22323i | −0.127848 | + | 0.393474i | −0.994409 | − | 0.105596i | \(-0.966325\pi\) |
0.866562 | + | 0.499070i | \(0.166325\pi\) | |||||||
\(338\) | 6.75576 | − | 20.7921i | 0.367465 | − | 1.13094i | ||||
\(339\) | −1.31201 | − | 4.03794i | −0.0712585 | − | 0.219311i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.67220 | + | 11.3019i | −0.198861 | + | 0.612031i | ||||
\(342\) | 3.64639 | + | 2.64926i | 0.197174 | + | 0.143255i | ||||
\(343\) | −11.4970 | −0.620780 | ||||||||
\(344\) | 4.28912 | + | 3.11623i | 0.231254 | + | 0.168016i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15.2584 | + | 11.0859i | −0.820298 | + | 0.595981i | ||||
\(347\) | 6.09436 | − | 4.42781i | 0.327162 | − | 0.237697i | −0.412063 | − | 0.911155i | \(-0.635192\pi\) |
0.739226 | + | 0.673458i | \(0.235192\pi\) | |||||||
\(348\) | −0.0805798 | − | 0.247999i | −0.00431953 | − | 0.0132942i | ||||
\(349\) | 18.7527 | 1.00381 | 0.501904 | − | 0.864923i | \(-0.332633\pi\) | ||||
0.501904 | + | 0.864923i | \(0.332633\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.90441 | 0.315154 | ||||||||
\(352\) | 1.63788 | + | 5.04087i | 0.0872992 | + | 0.268679i | ||||
\(353\) | −3.53223 | + | 2.56631i | −0.188001 | + | 0.136591i | −0.677805 | − | 0.735242i | \(-0.737069\pi\) |
0.489803 | + | 0.871833i | \(0.337069\pi\) | |||||||
\(354\) | 5.25216 | − | 3.81592i | 0.279149 | − | 0.202814i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.593474 | + | 0.431184i | 0.0314541 | + | 0.0228527i | ||||
\(357\) | 3.31122 | 0.175249 | ||||||||
\(358\) | −0.761557 | − | 0.553303i | −0.0402495 | − | 0.0292430i | ||||
\(359\) | 0.227811 | − | 0.701130i | 0.0120234 | − | 0.0370042i | −0.944865 | − | 0.327461i | \(-0.893807\pi\) |
0.956888 | + | 0.290456i | \(0.0938071\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.406269 | + | 1.25037i | 0.0213826 | + | 0.0658088i | ||||
\(362\) | 4.35891 | − | 13.4153i | 0.229099 | − | 0.705095i | ||||
\(363\) | 5.28204 | − | 16.2564i | 0.277235 | − | 0.853242i | ||||
\(364\) | 5.89595 | + | 18.1459i | 0.309032 | + | 0.951101i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.21905 | + | 3.75186i | −0.0637209 | + | 0.196113i | ||||
\(367\) | −15.2581 | − | 11.0856i | −0.796466 | − | 0.578666i | 0.113410 | − | 0.993548i | \(-0.463823\pi\) |
−0.909875 | + | 0.414882i | \(0.863823\pi\) | |||||||
\(368\) | 1.92827 | 0.100518 | ||||||||
\(369\) | 8.05872 | + | 5.85500i | 0.419520 | + | 0.304799i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.04179 | − | 4.38962i | 0.313674 | − | 0.227898i | ||||
\(372\) | 1.81386 | − | 1.31784i | 0.0940441 | − | 0.0683270i | ||||
\(373\) | −9.22003 | − | 28.3763i | −0.477395 | − | 1.46927i | −0.842700 | − | 0.538383i | \(-0.819035\pi\) |
0.365305 | − | 0.930888i | \(-0.380965\pi\) | |||||||
\(374\) | 5.43117 | 0.280839 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.5282 | −0.542949 | ||||||||
\(377\) | −0.475776 | − | 1.46429i | −0.0245037 | − | 0.0754147i | ||||
\(378\) | −2.61428 | + | 1.89939i | −0.134464 | + | 0.0976939i | ||||
\(379\) | −20.6159 | + | 14.9783i | −1.05897 | + | 0.769384i | −0.973897 | − | 0.226991i | \(-0.927111\pi\) |
−0.0850692 | + | 0.996375i | \(0.527111\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.48413 | + | 5.43754i | 0.383424 | + | 0.278574i | ||||
\(382\) | 25.4719 | 1.30326 | ||||||||
\(383\) | −25.6000 | − | 18.5995i | −1.30810 | − | 0.950389i | −0.308098 | − | 0.951354i | \(-0.599693\pi\) |
−1.00000 | 0.000965638i | \(0.999693\pi\) | ||||||||
\(384\) | 0.309017 | − | 0.951057i | 0.0157695 | − | 0.0485334i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.05014 | − | 6.30968i | −0.104349 | − | 0.321154i | ||||
\(387\) | −1.63830 | + | 5.04216i | −0.0832793 | + | 0.256307i | ||||
\(388\) | −5.33261 | + | 16.4121i | −0.270722 | + | 0.833197i | ||||
\(389\) | 3.72304 | + | 11.4583i | 0.188766 | + | 0.580961i | 0.999993 | − | 0.00377022i | \(-0.00120010\pi\) |
−0.811227 | + | 0.584731i | \(0.801200\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.610584 | − | 1.87918i | 0.0308786 | − | 0.0950344i | ||||
\(392\) | −2.78474 | − | 2.02323i | −0.140651 | − | 0.102189i | ||||
\(393\) | −4.86497 | −0.245405 | ||||||||
\(394\) | 8.23396 | + | 5.98232i | 0.414821 | + | 0.301385i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −4.28802 | + | 3.11543i | −0.215481 | + | 0.156556i | ||||
\(397\) | −20.8374 | + | 15.1393i | −1.04580 | + | 0.759819i | −0.971410 | − | 0.237410i | \(-0.923702\pi\) |
−0.0743920 | + | 0.997229i | \(0.523702\pi\) | |||||||
\(398\) | −0.779460 | − | 2.39893i | −0.0390708 | − | 0.120247i | ||||
\(399\) | −14.5646 | −0.729144 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.3196 | 1.31434 | 0.657169 | − | 0.753743i | \(-0.271754\pi\) | ||||
0.657169 | + | 0.753743i | \(0.271754\pi\) | |||||||
\(402\) | 2.87142 | + | 8.83731i | 0.143213 | + | 0.440765i | ||||
\(403\) | 10.7098 | − | 7.78109i | 0.533491 | − | 0.387604i | ||||
\(404\) | −9.58313 | + | 6.96255i | −0.476779 | + | 0.346400i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.681704 | + | 0.495287i | 0.0338324 | + | 0.0245807i | ||||
\(407\) | −50.6365 | −2.50996 | ||||||||
\(408\) | −0.828995 | − | 0.602300i | −0.0410414 | − | 0.0298183i | ||||
\(409\) | 11.3630 | − | 34.9716i | 0.561863 | − | 1.72924i | −0.115230 | − | 0.993339i | \(-0.536761\pi\) |
0.677093 | − | 0.735897i | \(-0.263239\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.85925 | + | 5.72219i | 0.0917101 | + | 0.282255i | ||||
\(412\) | −2.20973 | + | 6.80085i | −0.108866 | + | 0.335054i | ||||
\(413\) | −6.48272 | + | 19.9517i | −0.318994 | + | 0.981761i | ||||
\(414\) | 0.595870 | + | 1.83390i | 0.0292854 | + | 0.0901312i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.82456 | − | 5.61543i | 0.0894566 | − | 0.275319i | ||||
\(417\) | 4.55250 | + | 3.30758i | 0.222937 | + | 0.161973i | ||||
\(418\) | −23.8894 | −1.16847 | ||||||||
\(419\) | 25.6657 | + | 18.6472i | 1.25385 | + | 0.910975i | 0.998439 | − | 0.0558572i | \(-0.0177891\pi\) |
0.255411 | + | 0.966833i | \(0.417789\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.13332 | + | 5.18266i | −0.347657 | + | 0.252587i | −0.747885 | − | 0.663828i | \(-0.768931\pi\) |
0.400229 | + | 0.916415i | \(0.368931\pi\) | |||||||
\(422\) | −12.7532 | + | 9.26574i | −0.620816 | + | 0.451049i | ||||
\(423\) | −3.25338 | − | 10.0129i | −0.158185 | − | 0.486843i | ||||
\(424\) | −2.31107 | −0.112236 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 8.53771 | 0.413653 | ||||||||
\(427\) | −3.93928 | − | 12.1239i | −0.190635 | − | 0.586715i | ||||
\(428\) | −2.58932 | + | 1.88125i | −0.125160 | + | 0.0909339i | ||||
\(429\) | −25.3182 | + | 18.3948i | −1.22238 | + | 0.888108i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.0172 | − | 13.8168i | −0.916026 | − | 0.665532i | 0.0265058 | − | 0.999649i | \(-0.491562\pi\) |
−0.942532 | + | 0.334117i | \(0.891562\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 6.79827 | + | 4.93923i | 0.326704 | + | 0.237364i | 0.739031 | − | 0.673672i | \(-0.235284\pi\) |
−0.412327 | + | 0.911036i | \(0.635284\pi\) | |||||||
\(434\) | −2.23883 | + | 6.89042i | −0.107468 | + | 0.330751i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.05789 | + | 9.41123i | 0.146447 | + | 0.450716i | ||||
\(437\) | −2.68569 | + | 8.26572i | −0.128474 | + | 0.395403i | ||||
\(438\) | 1.22192 | − | 3.76068i | 0.0583856 | − | 0.179692i | ||||
\(439\) | 11.0111 | + | 33.8885i | 0.525529 | + | 1.61741i | 0.763268 | + | 0.646083i | \(0.223594\pi\) |
−0.237739 | + | 0.971329i | \(0.576406\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.06368 | − | 3.27366i | 0.0506512 | − | 0.155888i | ||||
\(442\) | −4.89473 | − | 3.55623i | −0.232818 | − | 0.169152i | ||||
\(443\) | −6.79550 | −0.322864 | −0.161432 | − | 0.986884i | \(-0.551611\pi\) | ||||
−0.161432 | + | 0.986884i | \(0.551611\pi\) | |||||||
\(444\) | 7.72898 | + | 5.61543i | 0.366801 | + | 0.266497i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 7.52009 | − | 5.46366i | 0.356087 | − | 0.258712i | ||||
\(447\) | 9.42957 | − | 6.85098i | 0.446003 | − | 0.324040i | ||||
\(448\) | 0.998566 | + | 3.07327i | 0.0471778 | + | 0.145198i | ||||
\(449\) | 8.75011 | 0.412943 | 0.206472 | − | 0.978453i | \(-0.433802\pi\) | ||||
0.206472 | + | 0.978453i | \(0.433802\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −52.7968 | −2.48610 | ||||||||
\(452\) | −1.31201 | − | 4.03794i | −0.0617117 | − | 0.189929i | ||||
\(453\) | −4.46864 | + | 3.24666i | −0.209955 | + | 0.152541i | ||||
\(454\) | 2.94327 | − | 2.13841i | 0.138135 | − | 0.100361i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.64639 | + | 2.64926i | 0.170758 | + | 0.124063i | ||||
\(457\) | 38.1474 | 1.78446 | 0.892230 | − | 0.451581i | \(-0.149140\pi\) | ||||
0.892230 | + | 0.451581i | \(0.149140\pi\) | |||||||
\(458\) | −8.03500 | − | 5.83777i | −0.375451 | − | 0.272781i | ||||
\(459\) | 0.316648 | − | 0.974542i | 0.0147799 | − | 0.0454877i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.392689 | − | 1.20857i | −0.0182893 | − | 0.0562888i | 0.941495 | − | 0.337026i | \(-0.109421\pi\) |
−0.959785 | + | 0.280737i | \(0.909421\pi\) | |||||||
\(462\) | 5.29269 | − | 16.2892i | 0.246238 | − | 0.757843i | ||||
\(463\) | −2.76060 | + | 8.49626i | −0.128296 | + | 0.394855i | −0.994487 | − | 0.104858i | \(-0.966561\pi\) |
0.866191 | + | 0.499713i | \(0.166561\pi\) | |||||||
\(464\) | −0.0805798 | − | 0.247999i | −0.00374082 | − | 0.0115131i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.80623 | − | 17.8697i | 0.268968 | − | 0.827799i | ||||
\(467\) | −4.65737 | − | 3.38378i | −0.215517 | − | 0.156582i | 0.474789 | − | 0.880100i | \(-0.342524\pi\) |
−0.690306 | + | 0.723517i | \(0.742524\pi\) | |||||||
\(468\) | 5.90441 | 0.272932 | ||||||||
\(469\) | −24.2922 | − | 17.6493i | −1.12171 | − | 0.814968i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.53616 | − | 4.02225i | 0.255093 | − | 0.185336i | ||||
\(472\) | 5.25216 | − | 3.81592i | 0.241750 | − | 0.175642i | ||||
\(473\) | −8.68344 | − | 26.7249i | −0.399265 | − | 1.22881i | ||||
\(474\) | −13.3714 | −0.614168 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.31122 | 0.151770 | ||||||||
\(477\) | −0.714161 | − | 2.19796i | −0.0326992 | − | 0.100638i | ||||
\(478\) | 7.88942 | − | 5.73200i | 0.360854 | − | 0.262175i | ||||
\(479\) | 3.74616 | − | 2.72175i | 0.171167 | − | 0.124360i | −0.498904 | − | 0.866657i | \(-0.666264\pi\) |
0.670070 | + | 0.742298i | \(0.266264\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 45.6351 | + | 33.1558i | 2.08078 | + | 1.51177i | ||||
\(482\) | 18.9211 | 0.861832 | ||||||||
\(483\) | −5.04105 | − | 3.66254i | −0.229376 | − | 0.166651i | ||||
\(484\) | 5.28204 | − | 16.2564i | 0.240093 | − | 0.738929i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.309017 | + | 0.951057i | 0.0140173 | + | 0.0431408i | ||||
\(487\) | −4.92064 | + | 15.1442i | −0.222975 | + | 0.686248i | 0.775515 | + | 0.631329i | \(0.217490\pi\) |
−0.998491 | + | 0.0549192i | \(0.982510\pi\) | |||||||
\(488\) | −1.21905 | + | 3.75186i | −0.0551839 | + | 0.169839i | ||||
\(489\) | −2.90080 | − | 8.92773i | −0.131178 | − | 0.403726i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.97176 | + | 6.06846i | −0.0889844 | + | 0.273866i | −0.985639 | − | 0.168864i | \(-0.945990\pi\) |
0.896655 | + | 0.442730i | \(0.145990\pi\) | |||||||
\(492\) | 8.05872 | + | 5.85500i | 0.363315 | + | 0.263964i | ||||
\(493\) | −0.267201 | −0.0120341 | ||||||||
\(494\) | 21.5298 | + | 15.6423i | 0.968671 | + | 0.703780i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.81386 | − | 1.31784i | 0.0814445 | − | 0.0591729i | ||||
\(497\) | −22.3200 | + | 16.2164i | −1.00119 | + | 0.727405i | ||||
\(498\) | 2.31360 | + | 7.12054i | 0.103675 | + | 0.319079i | ||||
\(499\) | 12.9135 | 0.578087 | 0.289044 | − | 0.957316i | \(-0.406663\pi\) | ||||
0.289044 | + | 0.957316i | \(0.406663\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.82883 | 0.305090 | ||||||||
\(502\) | −0.613732 | − | 1.88887i | −0.0273922 | − | 0.0843046i | ||||
\(503\) | −1.17472 | + | 0.853483i | −0.0523781 | + | 0.0380549i | −0.613666 | − | 0.789566i | \(-0.710306\pi\) |
0.561288 | + | 0.827620i | \(0.310306\pi\) | |||||||
\(504\) | −2.61428 | + | 1.89939i | −0.116449 | + | 0.0846054i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −8.26848 | − | 6.00740i | −0.367579 | − | 0.267062i | ||||
\(507\) | 21.8621 | 0.970929 | ||||||||
\(508\) | 7.48413 | + | 5.43754i | 0.332055 | + | 0.241252i | ||||
\(509\) | −3.83481 | + | 11.8023i | −0.169975 | + | 0.523130i | −0.999368 | − | 0.0355355i | \(-0.988686\pi\) |
0.829393 | + | 0.558665i | \(0.188686\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.94855 | + | 12.1524i | 0.174673 | + | 0.537590i | ||||
\(512\) | 0.309017 | − | 0.951057i | 0.0136568 | − | 0.0420312i | ||||
\(513\) | −1.39280 | + | 4.28659i | −0.0614935 | + | 0.189257i | ||||
\(514\) | −5.95775 | − | 18.3361i | −0.262785 | − | 0.808770i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.63830 | + | 5.04216i | −0.0721220 | + | 0.221969i | ||||
\(517\) | 45.1450 | + | 32.7998i | 1.98548 | + | 1.44253i | ||||
\(518\) | −30.8716 | −1.35642 | ||||||||
\(519\) | −15.2584 | − | 11.0859i | −0.669770 | − | 0.486617i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.42857 | + | 4.67063i | −0.281641 | + | 0.204624i | −0.719633 | − | 0.694355i | \(-0.755690\pi\) |
0.437992 | + | 0.898979i | \(0.355690\pi\) | |||||||
\(522\) | 0.210961 | − | 0.153272i | 0.00923350 | − | 0.00670853i | ||||
\(523\) | 10.7632 | + | 33.1258i | 0.470643 | + | 1.44849i | 0.851745 | + | 0.523957i | \(0.175545\pi\) |
−0.381101 | + | 0.924533i | \(0.624455\pi\) | |||||||
\(524\) | −4.86497 | −0.212527 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.5297 | 0.546320 | ||||||||
\(527\) | −0.709940 | − | 2.18497i | −0.0309255 | − | 0.0951788i | ||||
\(528\) | −4.28802 | + | 3.11543i | −0.186612 | + | 0.135582i | ||||
\(529\) | 15.5993 | − | 11.3335i | 0.678229 | − | 0.492762i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.25216 | + | 3.81592i | 0.227924 | + | 0.165597i | ||||
\(532\) | −14.5646 | −0.631457 | ||||||||
\(533\) | 47.5820 | + | 34.5703i | 2.06100 | + | 1.49741i | ||||
\(534\) | −0.226687 | + | 0.697671i | −0.00980970 | + | 0.0301912i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.87142 | + | 8.83731i | 0.124026 | + | 0.381714i | ||||
\(537\) | 0.290889 | − | 0.895264i | 0.0125528 | − | 0.0386335i | ||||
\(538\) | 4.16955 | − | 12.8326i | 0.179762 | − | 0.553251i | ||||
\(539\) | 5.63778 | + | 17.3513i | 0.242837 | + | 0.747374i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.70571 | − | 26.7934i | 0.374288 | − | 1.15194i | −0.569670 | − | 0.821873i | \(-0.692929\pi\) |
0.943958 | − | 0.330065i | \(-0.107071\pi\) | |||||||
\(542\) | 21.6926 | + | 15.7606i | 0.931776 | + | 0.676975i | ||||
\(543\) | 14.1057 | 0.605335 | ||||||||
\(544\) | −0.828995 | − | 0.602300i | −0.0355429 | − | 0.0258234i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −15.4358 | + | 11.2148i | −0.660591 | + | 0.479947i | ||||
\(547\) | −21.9873 | + | 15.9747i | −0.940108 | + | 0.683029i | −0.948447 | − | 0.316937i | \(-0.897346\pi\) |
0.00833839 | + | 0.999965i | \(0.497346\pi\) | |||||||
\(548\) | 1.85925 | + | 5.72219i | 0.0794233 | + | 0.244440i | ||||
\(549\) | −3.94494 | −0.168366 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.17530 | 0.0500695 | ||||||||
\(552\) | 0.595870 | + | 1.83390i | 0.0253619 | + | 0.0780559i | ||||
\(553\) | 34.9565 | − | 25.3974i | 1.48650 | − | 1.08001i | ||||
\(554\) | −6.60744 | + | 4.80058i | −0.280723 | + | 0.203957i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.55250 | + | 3.30758i | 0.193069 | + | 0.140273i | ||||
\(557\) | −6.74857 | −0.285946 | −0.142973 | − | 0.989727i | \(-0.545666\pi\) | ||||
−0.142973 | + | 0.989727i | \(0.545666\pi\) | |||||||
\(558\) | 1.81386 | + | 1.31784i | 0.0767867 | + | 0.0557888i | ||||
\(559\) | −9.67318 | + | 29.7710i | −0.409132 | + | 1.25918i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.67832 | + | 5.16535i | 0.0708589 | + | 0.218081i | ||||
\(562\) | 9.68515 | − | 29.8078i | 0.408543 | − | 1.25737i | ||||
\(563\) | 3.49426 | − | 10.7542i | 0.147265 | − | 0.453236i | −0.850030 | − | 0.526734i | \(-0.823416\pi\) |
0.997295 | + | 0.0734982i | \(0.0234163\pi\) | |||||||
\(564\) | −3.25338 | − | 10.0129i | −0.136992 | − | 0.421618i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −5.05253 | + | 15.5501i | −0.212374 | + | 0.653620i | ||||
\(567\) | −2.61428 | − | 1.89939i | −0.109789 | − | 0.0797667i | ||||
\(568\) | 8.53771 | 0.358234 | ||||||||
\(569\) | −20.4022 | − | 14.8231i | −0.855304 | − | 0.621415i | 0.0712991 | − | 0.997455i | \(-0.477286\pi\) |
−0.926603 | + | 0.376040i | \(0.877286\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.4908 | − | 16.3405i | 0.941209 | − | 0.683828i | −0.00750262 | − | 0.999972i | \(-0.502388\pi\) |
0.948711 | + | 0.316144i | \(0.102388\pi\) | |||||||
\(572\) | −25.3182 | + | 18.3948i | −1.05861 | + | 0.769124i | ||||
\(573\) | 7.87125 | + | 24.2252i | 0.328826 | + | 1.01202i | ||||
\(574\) | −32.1886 | −1.34353 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −3.55168 | − | 10.9309i | −0.147858 | − | 0.455061i | 0.849509 | − | 0.527574i | \(-0.176898\pi\) |
−0.997367 | + | 0.0725129i | \(0.976898\pi\) | |||||||
\(578\) | 12.9038 | − | 9.37518i | 0.536728 | − | 0.389956i | ||||
\(579\) | 5.36734 | − | 3.89960i | 0.223059 | − | 0.162062i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −19.5731 | − | 14.2207i | −0.812027 | − | 0.589972i | ||||
\(582\) | −17.2567 | −0.715313 | ||||||||
\(583\) | 9.90993 | + | 7.19998i | 0.410427 | + | 0.298193i | ||||
\(584\) | 1.22192 | − | 3.76068i | 0.0505634 | − | 0.155618i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.71017 | − | 26.8072i | −0.359814 | − | 1.10739i | ||||
\(587\) | 13.0492 | − | 40.1613i | 0.538598 | − | 1.65763i | −0.197147 | − | 0.980374i | \(-0.563168\pi\) |
0.735745 | − | 0.677259i | \(-0.236832\pi\) | |||||||
\(588\) | 1.06368 | − | 3.27366i | 0.0438652 | − | 0.135003i | ||||
\(589\) | 3.12272 | + | 9.61074i | 0.128669 | + | 0.396004i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.14509 | + | 9.67960i | −0.129372 | + | 0.398166i | ||||
\(592\) | 7.72898 | + | 5.61543i | 0.317659 | + | 0.230793i | ||||
\(593\) | −0.0131121 | −0.000538451 | −0.000269225 | − | 1.00000i | \(-0.500086\pi\) | ||||
−0.000269225 | 1.00000i | \(0.500086\pi\) | ||||||||
\(594\) | −4.28802 | − | 3.11543i | −0.175940 | − | 0.127828i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.42957 | − | 6.85098i | 0.386250 | − | 0.280627i | ||||
\(597\) | 2.04065 | − | 1.48262i | 0.0835183 | − | 0.0606796i | ||||
\(598\) | 3.51826 | + | 10.8281i | 0.143872 | + | 0.442794i | ||||
\(599\) | 2.38072 | 0.0972738 | 0.0486369 | − | 0.998817i | \(-0.484512\pi\) | ||||
0.0486369 | + | 0.998817i | \(0.484512\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.6020 | −0.799581 | −0.399790 | − | 0.916607i | \(-0.630917\pi\) | ||||
−0.399790 | + | 0.916607i | \(0.630917\pi\) | |||||||
\(602\) | −5.29404 | − | 16.2934i | −0.215769 | − | 0.664068i | ||||
\(603\) | −7.51747 | + | 5.46176i | −0.306135 | + | 0.222420i | ||||
\(604\) | −4.46864 | + | 3.24666i | −0.181826 | + | 0.132105i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −9.58313 | − | 6.96255i | −0.389288 | − | 0.282834i | ||||
\(607\) | 10.7155 | 0.434930 | 0.217465 | − | 0.976068i | \(-0.430221\pi\) | ||||
0.217465 | + | 0.976068i | \(0.430221\pi\) | |||||||
\(608\) | 3.64639 | + | 2.64926i | 0.147881 | + | 0.107442i | ||||
\(609\) | −0.260388 | + | 0.801391i | −0.0105514 | + | 0.0324740i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −19.2093 | − | 59.1202i | −0.777126 | − | 2.39175i | ||||
\(612\) | 0.316648 | − | 0.974542i | 0.0127997 | − | 0.0393935i | ||||
\(613\) | 0.359801 | − | 1.10735i | 0.0145322 | − | 0.0447256i | −0.943527 | − | 0.331294i | \(-0.892515\pi\) |
0.958060 | + | 0.286569i | \(0.0925147\pi\) | |||||||
\(614\) | −4.49223 | − | 13.8257i | −0.181292 | − | 0.557959i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.29269 | − | 16.2892i | 0.213248 | − | 0.656311i | ||||
\(617\) | −18.3190 | − | 13.3095i | −0.737495 | − | 0.535821i | 0.154431 | − | 0.988004i | \(-0.450646\pi\) |
−0.891926 | + | 0.452182i | \(0.850646\pi\) | |||||||
\(618\) | −7.15084 | −0.287649 | ||||||||
\(619\) | −20.0413 | − | 14.5609i | −0.805529 | − | 0.585251i | 0.107002 | − | 0.994259i | \(-0.465875\pi\) |
−0.912531 | + | 0.409008i | \(0.865875\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.56001 | + | 1.13341i | −0.0626009 | + | 0.0454822i | ||||
\(622\) | −11.7246 | + | 8.51844i | −0.470115 | + | 0.341559i | ||||
\(623\) | −0.732522 | − | 2.25447i | −0.0293479 | − | 0.0903235i | ||||
\(624\) | 5.90441 | 0.236366 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −31.5288 | −1.26014 | ||||||||
\(627\) | −7.38222 | − | 22.7201i | −0.294817 | − | 0.907355i | ||||
\(628\) | 5.53616 | − | 4.02225i | 0.220917 | − | 0.160505i | ||||
\(629\) | 7.91983 | − | 5.75410i | 0.315784 | − | 0.229431i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.4156 | + | 19.1920i | 1.05159 | + | 0.764023i | 0.972514 | − | 0.232845i | \(-0.0748036\pi\) |
0.0790740 | + | 0.996869i | \(0.474804\pi\) | |||||||
\(632\) | −13.3714 | −0.531885 | ||||||||
\(633\) | −12.7532 | − | 9.26574i | −0.506894 | − | 0.368280i | ||||
\(634\) | −4.62940 | + | 14.2478i | −0.183857 | + | 0.565853i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.714161 | − | 2.19796i | −0.0283183 | − | 0.0871548i | ||||
\(637\) | 6.28038 | − | 19.3290i | 0.248838 | − | 0.765844i | ||||
\(638\) | −0.427096 | + | 1.31447i | −0.0169089 | + | 0.0520402i | ||||
\(639\) | 2.63830 | + | 8.11984i | 0.104369 | + | 0.321216i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.29842 | + | 25.5399i | −0.327768 | + | 1.00877i | 0.642408 | + | 0.766363i | \(0.277936\pi\) |
−0.970176 | + | 0.242403i | \(0.922064\pi\) | |||||||
\(642\) | −2.58932 | − | 1.88125i | −0.102193 | − | 0.0742472i | ||||
\(643\) | 17.1051 | 0.674559 | 0.337279 | − | 0.941405i | \(-0.390493\pi\) | ||||
0.337279 | + | 0.941405i | \(0.390493\pi\) | |||||||
\(644\) | −5.04105 | − | 3.66254i | −0.198645 | − | 0.144324i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.73643 | − | 2.71468i | 0.147008 | − | 0.106808i | ||||
\(647\) | 37.0639 | − | 26.9285i | 1.45713 | − | 1.05867i | 0.473036 | − | 0.881043i | \(-0.343158\pi\) |
0.984098 | − | 0.177626i | \(-0.0568418\pi\) | |||||||
\(648\) | 0.309017 | + | 0.951057i | 0.0121393 | + | 0.0373610i | ||||
\(649\) | −34.4096 | −1.35069 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.24502 | −0.283955 | ||||||||
\(652\) | −2.90080 | − | 8.92773i | −0.113604 | − | 0.349637i | ||||
\(653\) | 9.26769 | − | 6.73337i | 0.362673 | − | 0.263497i | −0.391493 | − | 0.920181i | \(-0.628041\pi\) |
0.754166 | + | 0.656684i | \(0.228041\pi\) | |||||||
\(654\) | −8.00567 | + | 5.81646i | −0.313046 | + | 0.227442i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 8.05872 | + | 5.85500i | 0.314640 | + | 0.228599i | ||||
\(657\) | 3.95422 | 0.154269 | ||||||||
\(658\) | 27.5236 | + | 19.9971i | 1.07298 | + | 0.779566i | ||||
\(659\) | 12.3601 | − | 38.0405i | 0.481482 | − | 1.48185i | −0.355531 | − | 0.934664i | \(-0.615700\pi\) |
0.837013 | − | 0.547183i | \(-0.184300\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.75871 | − | 5.41276i | −0.0684060 | − | 0.210532i | 0.911010 | − | 0.412384i | \(-0.135304\pi\) |
−0.979416 | + | 0.201852i | \(0.935304\pi\) | |||||||
\(662\) | −6.68014 | + | 20.5594i | −0.259631 | + | 0.799062i | ||||
\(663\) | 1.86962 | − | 5.75410i | 0.0726100 | − | 0.223471i | ||||
\(664\) | 2.31360 | + | 7.12054i | 0.0897852 | + | 0.276331i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.95221 | + | 9.08596i | −0.114396 | + | 0.352074i | ||||
\(667\) | 0.406790 | + | 0.295550i | 0.0157510 | + | 0.0114438i | ||||
\(668\) | 6.82883 | 0.264215 | ||||||||
\(669\) | 7.52009 | + | 5.46366i | 0.290743 | + | 0.211237i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.9160 | − | 12.2902i | 0.653034 | − | 0.474457i | ||||
\(672\) | −2.61428 | + | 1.89939i | −0.100848 | + | 0.0732704i | ||||
\(673\) | −14.9727 | − | 46.0813i | −0.577156 | − | 1.77630i | −0.628719 | − | 0.777633i | \(-0.716420\pi\) |
0.0515628 | − | 0.998670i | \(-0.483580\pi\) | |||||||
\(674\) | −7.59495 | −0.292547 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 21.8621 | 0.840849 | ||||||||
\(677\) | −5.71966 | − | 17.6033i | −0.219824 | − | 0.676550i | −0.998776 | − | 0.0494656i | \(-0.984248\pi\) |
0.778951 | − | 0.627084i | \(-0.215752\pi\) | |||||||
\(678\) | 3.43488 | − | 2.49559i | 0.131916 | − | 0.0958424i | ||||
\(679\) | 45.1138 | − | 32.7771i | 1.73131 | − | 1.25787i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.94327 | + | 2.13841i | 0.112787 | + | 0.0819442i | ||||
\(682\) | −11.8835 | −0.455043 | ||||||||
\(683\) | −29.1442 | − | 21.1745i | −1.11517 | − | 0.810219i | −0.131701 | − | 0.991289i | \(-0.542044\pi\) |
−0.983470 | + | 0.181070i | \(0.942044\pi\) | |||||||
\(684\) | −1.39280 | + | 4.28659i | −0.0532549 | + | 0.163902i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −3.55277 | − | 10.9343i | −0.135645 | − | 0.417474i | ||||
\(687\) | 3.06910 | − | 9.44571i | 0.117093 | − | 0.360376i | ||||
\(688\) | −1.63830 | + | 5.04216i | −0.0624595 | + | 0.192231i | ||||
\(689\) | −4.21670 | − | 12.9777i | −0.160643 | − | 0.494410i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.47133 | + | 13.7613i | −0.170097 | + | 0.523506i | −0.999376 | − | 0.0353301i | \(-0.988752\pi\) |
0.829278 | + | 0.558836i | \(0.188752\pi\) | |||||||
\(692\) | −15.2584 | − | 11.0859i | −0.580038 | − | 0.421422i | ||||
\(693\) | 17.1275 | 0.650620 | ||||||||
\(694\) | 6.09436 | + | 4.42781i | 0.231339 | + | 0.168077i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.210961 | − | 0.153272i | 0.00799644 | − | 0.00580976i | ||||
\(697\) | 8.25772 | − | 5.99958i | 0.312783 | − | 0.227250i | ||||
\(698\) | 5.79489 | + | 17.8349i | 0.219340 | + | 0.675059i | ||||
\(699\) | 18.7893 | 0.710678 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.31284 | 0.313972 | 0.156986 | − | 0.987601i | \(-0.449822\pi\) | ||||
0.156986 | + | 0.987601i | \(0.449822\pi\) | |||||||
\(702\) | 1.82456 | + | 5.61543i | 0.0688637 | + | 0.211941i | ||||
\(703\) | −34.8359 | + | 25.3098i | −1.31386 | + | 0.954576i | ||||
\(704\) | −4.28802 | + | 3.11543i | −0.161611 | + | 0.117417i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.53223 | − | 2.56631i | −0.132937 | − | 0.0965845i | ||||
\(707\) | 38.2776 | 1.43958 | ||||||||
\(708\) | 5.25216 | + | 3.81592i | 0.197388 | + | 0.143411i | ||||
\(709\) | −2.77255 | + | 8.53302i | −0.104125 | + | 0.320464i | −0.989524 | − | 0.144368i | \(-0.953885\pi\) |
0.885399 | + | 0.464832i | \(0.153885\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.13198 | − | 12.7169i | −0.154962 | − | 0.476923i | ||||
\(712\) | −0.226687 | + | 0.697671i | −0.00849545 | + | 0.0261463i | ||||
\(713\) | −1.33597 | + | 4.11169i | −0.0500324 | + | 0.153984i | ||||
\(714\) | 1.02322 | + | 3.14916i | 0.0382932 | + | 0.117854i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.290889 | − | 0.895264i | 0.0108710 | − | 0.0334576i | ||||
\(717\) | 7.88942 | + | 5.73200i | 0.294636 | + | 0.214065i | ||||
\(718\) | 0.737212 | 0.0275125 | ||||||||
\(719\) | −22.7445 | − | 16.5249i | −0.848228 | − | 0.616274i | 0.0764289 | − | 0.997075i | \(-0.475648\pi\) |
−0.924657 | + | 0.380801i | \(0.875648\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.6943 | − | 13.5822i | 0.696212 | − | 0.505828i | ||||
\(722\) | −1.06363 | + | 0.772769i | −0.0395840 | + | 0.0287595i | ||||
\(723\) | 5.84694 | + | 17.9950i | 0.217450 | + | 0.669242i | ||||
\(724\) | 14.1057 | 0.524235 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 17.0930 | 0.634382 | ||||||||
\(727\) | 7.68734 | + | 23.6592i | 0.285108 | + | 0.877471i | 0.986366 | + | 0.164564i | \(0.0526217\pi\) |
−0.701259 | + | 0.712907i | \(0.747378\pi\) | |||||||
\(728\) | −15.4358 | + | 11.2148i | −0.572088 | + | 0.415647i | ||||
\(729\) | −0.809017 | + | 0.587785i | −0.0299636 | + | 0.0217698i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.39503 | + | 3.19318i | 0.162556 | + | 0.118104i | ||||
\(732\) | −3.94494 | −0.145809 | ||||||||
\(733\) | 5.46572 | + | 3.97108i | 0.201881 | + | 0.146675i | 0.684133 | − | 0.729358i | \(-0.260181\pi\) |
−0.482252 | + | 0.876033i | \(0.660181\pi\) | |||||||
\(734\) | 5.82807 | − | 17.9370i | 0.215118 | − | 0.662065i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.595870 | + | 1.83390i | 0.0219640 | + | 0.0675984i | ||||
\(737\) | 15.2193 | − | 46.8403i | 0.560611 | − | 1.72538i | ||||
\(738\) | −3.07816 | + | 9.47359i | −0.113308 | + | 0.348728i | ||||
\(739\) | −1.57339 | − | 4.84241i | −0.0578783 | − | 0.178131i | 0.917938 | − | 0.396724i | \(-0.129853\pi\) |
−0.975816 | + | 0.218593i | \(0.929853\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.22365 | + | 25.3098i | −0.302103 | + | 0.929778i | ||||
\(742\) | 6.04179 | + | 4.38962i | 0.221801 | + | 0.161148i | ||||
\(743\) | 16.0999 | 0.590647 | 0.295324 | − | 0.955397i | \(-0.404573\pi\) | ||||
0.295324 | + | 0.955397i | \(0.404573\pi\) | |||||||
\(744\) | 1.81386 | + | 1.31784i | 0.0664992 | + | 0.0483145i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 24.1383 | − | 17.5375i | 0.883768 | − | 0.642095i | ||||
\(747\) | −6.05709 | + | 4.40074i | −0.221617 | + | 0.161015i | ||||
\(748\) | 1.67832 | + | 5.16535i | 0.0613656 | + | 0.188864i | ||||
\(749\) | 10.3424 | 0.377905 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.4366 | −0.928196 | −0.464098 | − | 0.885784i | \(-0.653622\pi\) | ||||
−0.464098 | + | 0.885784i | \(0.653622\pi\) | |||||||
\(752\) | −3.25338 | − | 10.0129i | −0.118639 | − | 0.365132i | ||||
\(753\) | 1.60677 | − | 1.16739i | 0.0585540 | − | 0.0425420i | ||||
\(754\) | 1.24560 | − | 0.904981i | 0.0453620 | − | 0.0329575i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.61428 | − | 1.89939i | −0.0950804 | − | 0.0690800i | ||||
\(757\) | −12.4947 | −0.454129 | −0.227064 | − | 0.973880i | \(-0.572913\pi\) | ||||
−0.227064 | + | 0.973880i | \(0.572913\pi\) | |||||||
\(758\) | −20.6159 | − | 14.9783i | −0.748802 | − | 0.544037i | ||||
\(759\) | 3.15828 | − | 9.72018i | 0.114638 | − | 0.352820i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.58120 | − | 11.0218i | −0.129818 | − | 0.399540i | 0.864930 | − | 0.501893i | \(-0.167363\pi\) |
−0.994748 | + | 0.102353i | \(0.967363\pi\) | |||||||
\(762\) | −2.85868 | + | 8.79813i | −0.103559 | + | 0.318723i | ||||
\(763\) | 9.88136 | − | 30.4117i | 0.357729 | − | 1.10098i | ||||
\(764\) | 7.87125 | + | 24.2252i | 0.284772 | + | 0.876438i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.77832 | − | 30.0946i | 0.353305 | − | 1.08736i | ||||
\(767\) | 31.0109 | + | 22.5307i | 1.11974 | + | 0.813538i | ||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 19.2155 | + | 13.9609i | 0.692927 | + | 0.503441i | 0.877621 | − | 0.479355i | \(-0.159129\pi\) |
−0.184694 | + | 0.982796i | \(0.559129\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.5976 | − | 11.3323i | 0.561734 | − | 0.408124i | ||||
\(772\) | 5.36734 | − | 3.89960i | 0.193175 | − | 0.140350i | ||||
\(773\) | −3.73754 | − | 11.5030i | −0.134430 | − | 0.413732i | 0.861071 | − | 0.508485i | \(-0.169794\pi\) |
−0.995501 | + | 0.0947521i | \(0.969794\pi\) | |||||||
\(774\) | −5.30164 | −0.190564 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −17.2567 | −0.619479 | ||||||||
\(777\) | −9.53984 | − | 29.3606i | −0.342240 | − | 1.05331i | ||||
\(778\) | −9.74704 | + | 7.08164i | −0.349448 | + | 0.253889i | ||||
\(779\) | −36.3221 | + | 26.3896i | −1.30138 | + | 0.945504i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −36.6099 | − | 26.5986i | −1.31000 | − | 0.951774i | ||||
\(782\) | 1.97589 | 0.0706577 | ||||||||
\(783\) | 0.210961 | + | 0.153272i | 0.00753912 | + | 0.00547749i | ||||
\(784\) | 1.06368 | − | 3.27366i | 0.0379884 | − | 0.116916i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.50336 | − | 4.62686i | −0.0536230 | − | 0.165035i | ||||
\(787\) | 6.27371 | − | 19.3085i | 0.223634 | − | 0.688274i | −0.774794 | − | 0.632214i | \(-0.782146\pi\) |
0.998427 | − | 0.0560597i | \(-0.0178537\pi\) | |||||||
\(788\) | −3.14509 | + | 9.67960i | −0.112039 | + | 0.344821i | ||||
\(789\) | 3.87188 | + | 11.9164i | 0.137843 | + | 0.424236i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.23966 | + | 13.0483i | −0.150745 | + | 0.463945i | ||||
\(792\) | −4.28802 | − | 3.11543i | −0.152368 | − | 0.110702i | ||||
\(793\) | −23.2925 | −0.827142 | ||||||||
\(794\) | −20.8374 | − | 15.1393i | −0.739493 | − | 0.537273i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.04065 | − | 1.48262i | 0.0723290 | − | 0.0525501i | ||||
\(797\) | −25.6479 | + | 18.6343i | −0.908493 | + | 0.660059i | −0.940633 | − | 0.339424i | \(-0.889768\pi\) |
0.0321399 | + | 0.999483i | \(0.489768\pi\) | |||||||
\(798\) | −4.50072 | − | 13.8518i | −0.159324 | − | 0.490348i | ||||
\(799\) | −10.7881 | −0.381657 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.733574 | −0.0259196 | ||||||||
\(802\) | 8.13321 | + | 25.0314i | 0.287194 | + | 0.883891i | ||||
\(803\) | −16.9558 | + | 12.3191i | −0.598356 | + | 0.434731i | ||||
\(804\) | −7.51747 | + | 5.46176i | −0.265121 | + | 0.192621i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 10.7098 | + | 7.78109i | 0.377235 | + | 0.274077i | ||||
\(807\) | 13.4929 | 0.474974 | ||||||||
\(808\) | −9.58313 | − | 6.96255i | −0.337133 | − | 0.244942i | ||||
\(809\) | 2.69637 | − | 8.29856i | 0.0947992 | − | 0.291762i | −0.892402 | − | 0.451241i | \(-0.850981\pi\) |
0.987201 | + | 0.159479i | \(0.0509815\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.69774 | + | 14.4581i | 0.164960 | + | 0.507694i | 0.999033 | − | 0.0439592i | \(-0.0139972\pi\) |
−0.834074 | + | 0.551653i | \(0.813997\pi\) | |||||||
\(812\) | −0.260388 | + | 0.801391i | −0.00913782 | + | 0.0281233i | ||||
\(813\) | −8.28583 | + | 25.5012i | −0.290597 | + | 0.894365i | ||||
\(814\) | −15.6475 | − | 48.1582i | −0.548446 | − | 1.68794i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.316648 | − | 0.974542i | 0.0110849 | − | 0.0341158i | ||||
\(817\) | −19.3318 | − | 14.0454i | −0.676336 | − | 0.491387i | ||||
\(818\) | 36.7714 | 1.28568 | ||||||||
\(819\) | −15.4358 | − | 11.2148i | −0.539370 | − | 0.391875i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.3160 | + | 9.67465i | −0.464732 | + | 0.337648i | −0.795385 | − | 0.606105i | \(-0.792731\pi\) |
0.330653 | + | 0.943753i | \(0.392731\pi\) | |||||||
\(822\) | −4.86758 | + | 3.53651i | −0.169776 | + | 0.123350i | ||||
\(823\) | 7.10692 | + | 21.8728i | 0.247732 | + | 0.762439i | 0.995175 | + | 0.0981141i | \(0.0312810\pi\) |
−0.747444 | + | 0.664325i | \(0.768719\pi\) | |||||||
\(824\) | −7.15084 | −0.249111 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −20.9785 | −0.729936 | ||||||||
\(827\) | 7.64257 | + | 23.5214i | 0.265758 | + | 0.817919i | 0.991518 | + | 0.129971i | \(0.0414884\pi\) |
−0.725760 | + | 0.687948i | \(0.758512\pi\) | |||||||
\(828\) | −1.56001 | + | 1.13341i | −0.0542140 | + | 0.0393888i | ||||
\(829\) | −16.8789 | + | 12.2632i | −0.586227 | + | 0.425919i | −0.840964 | − | 0.541091i | \(-0.818011\pi\) |
0.254736 | + | 0.967011i | \(0.418011\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.60744 | − | 4.80058i | −0.229209 | − | 0.166530i | ||||
\(832\) | 5.90441 | 0.204699 | ||||||||
\(833\) | −2.85350 | − | 2.07319i | −0.0988681 | − | 0.0718319i | ||||
\(834\) | −1.73890 | + | 5.35178i | −0.0602132 | + | 0.185317i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −7.38222 | − | 22.7201i | −0.255319 | − | 0.785792i | ||||
\(837\) | −0.692831 | + | 2.13232i | −0.0239478 | + | 0.0737036i | ||||
\(838\) | −9.80341 | + | 30.1718i | −0.338653 | + | 1.04227i | ||||
\(839\) | −7.29166 | − | 22.4414i | −0.251736 | − | 0.774764i | −0.994455 | − | 0.105161i | \(-0.966464\pi\) |
0.742719 | − | 0.669603i | \(-0.233536\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.94048 | + | 27.5160i | −0.308292 | + | 0.948827i | ||||
\(842\) | −7.13332 | − | 5.18266i | −0.245830 | − | 0.178606i | ||||
\(843\) | 31.3418 | 1.07947 | ||||||||
\(844\) | −12.7532 | − | 9.26574i | −0.438983 | − | 0.318940i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 8.51747 | − | 6.18830i | 0.292837 | − | 0.212758i | ||||
\(847\) | −44.6860 | + | 32.4663i | −1.53543 | + | 1.11555i | ||||
\(848\) | −0.714161 | − | 2.19796i | −0.0245244 | − | 0.0754783i | ||||
\(849\) | −16.3503 | −0.561142 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.4218 | −0.631493 | ||||||||
\(852\) | 2.63830 | + | 8.11984i | 0.0903866 | + | 0.278181i | ||||
\(853\) | 21.3280 | − | 15.4957i | 0.730257 | − | 0.530563i | −0.159388 | − | 0.987216i | \(-0.550952\pi\) |
0.889645 | + | 0.456653i | \(0.150952\pi\) | |||||||
\(854\) | 10.3132 | − | 7.49296i | 0.352910 | − | 0.256404i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.58932 | − | 1.88125i | −0.0885013 | − | 0.0643000i | ||||
\(857\) | −16.0891 | −0.549593 | −0.274797 | − | 0.961502i | \(-0.588611\pi\) | ||||
−0.274797 | + | 0.961502i | \(0.588611\pi\) | |||||||
\(858\) | −25.3182 | − | 18.3948i | −0.864351 | − | 0.627987i | ||||
\(859\) | 3.26846 | − | 10.0593i | 0.111519 | − | 0.343219i | −0.879686 | − | 0.475554i | \(-0.842248\pi\) |
0.991205 | + | 0.132335i | \(0.0422476\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.94684 | − | 30.6132i | −0.338987 | − | 1.04330i | ||||
\(862\) | 7.26392 | − | 22.3560i | 0.247410 | − | 0.761450i | ||||
\(863\) | 12.9051 | − | 39.7177i | 0.439293 | − | 1.35201i | −0.449329 | − | 0.893366i | \(-0.648337\pi\) |
0.888622 | − | 0.458640i | \(-0.151663\pi\) | |||||||
\(864\) | 0.309017 | + | 0.951057i | 0.0105130 | + | 0.0323556i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.59671 | + | 7.99185i | −0.0882397 | + | 0.271574i | ||||
\(867\) | 12.9038 | + | 9.37518i | 0.438237 | + | 0.318398i | ||||
\(868\) | −7.24502 | −0.245912 | ||||||||
\(869\) | 57.3368 | + | 41.6576i | 1.94502 | + | 1.41314i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −44.3862 | + | 32.2485i | −1.50397 | + | 1.09270i | ||||
\(872\) | −8.00567 | + | 5.81646i | −0.271106 | + | 0.196970i | ||||
\(873\) | −5.33261 | − | 16.4121i | −0.180481 | − | 0.555465i | ||||
\(874\) | −8.69109 | −0.293980 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.95422 | 0.133601 | ||||||||
\(877\) | −9.83498 | − | 30.2690i | −0.332104 | − | 1.02211i | −0.968131 | − | 0.250444i | \(-0.919423\pi\) |
0.636027 | − | 0.771667i | \(-0.280577\pi\) | |||||||
\(878\) | −28.8273 | + | 20.9443i | −0.972875 | + | 0.706835i | ||||
\(879\) | 22.8035 | − | 16.5677i | 0.769144 | − | 0.558816i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.1535 | + | 29.1732i | 1.35280 | + | 0.982870i | 0.998866 | + | 0.0476012i | \(0.0151577\pi\) |
0.353938 | + | 0.935269i | \(0.384842\pi\) | |||||||
\(882\) | 3.44213 | 0.115902 | ||||||||
\(883\) | 4.09442 | + | 2.97477i | 0.137788 | + | 0.100109i | 0.654544 | − | 0.756024i | \(-0.272861\pi\) |
−0.516756 | + | 0.856133i | \(0.672861\pi\) | |||||||
\(884\) | 1.86962 | − | 5.75410i | 0.0628821 | − | 0.193531i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.09992 | − | 6.46290i | −0.0705483 | − | 0.217125i | ||||
\(887\) | 3.41594 | − | 10.5132i | 0.114696 | − | 0.352998i | −0.877187 | − | 0.480148i | \(-0.840583\pi\) |
0.991884 | + | 0.127150i | \(0.0405829\pi\) | |||||||
\(888\) | −2.95221 | + | 9.08596i | −0.0990696 | + | 0.304905i | ||||
\(889\) | −9.23763 | − | 28.4305i | −0.309820 | − | 0.953529i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.63788 | − | 5.04087i | 0.0548710 | − | 0.168876i | ||||
\(892\) | 7.52009 | + | 5.46366i | 0.251791 | + | 0.182937i | ||||
\(893\) | 47.4524 | 1.58793 | ||||||||
\(894\) | 9.42957 | + | 6.85098i | 0.315372 | + | 0.229131i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.61428 | + | 1.89939i | −0.0873370 | + | 0.0634540i | ||||
\(897\) | −9.21092 | + | 6.69213i | −0.307544 | + | 0.223444i | ||||
\(898\) | 2.70393 | + | 8.32185i | 0.0902314 | + | 0.277704i | ||||
\(899\) | 0.584641 | 0.0194989 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.36814 | −0.0788942 | ||||||||
\(902\) | −16.3151 | − | 50.2127i | −0.543234 | − | 1.67190i | ||||
\(903\) | 13.8600 | − | 10.0699i | 0.461231 | − | 0.335104i | ||||
\(904\) | 3.43488 | − | 2.49559i | 0.114242 | − | 0.0830020i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −4.46864 | − | 3.24666i | −0.148461 | − | 0.107863i | ||||
\(907\) | −7.57086 | −0.251386 | −0.125693 | − | 0.992069i | \(-0.540115\pi\) | ||||
−0.125693 | + | 0.992069i | \(0.540115\pi\) | |||||||
\(908\) | 2.94327 | + | 2.13841i | 0.0976760 | + | 0.0709658i | ||||
\(909\) | 3.66043 | − | 11.2656i | 0.121409 | − | 0.373658i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.0530 | + | 34.0177i | 0.366203 | + | 1.12706i | 0.949224 | + | 0.314601i | \(0.101871\pi\) |
−0.583021 | + | 0.812457i | \(0.698129\pi\) | |||||||
\(912\) | −1.39280 | + | 4.28659i | −0.0461201 | + | 0.141943i | ||||
\(913\) | 12.2628 | − | 37.7409i | 0.405838 | − | 1.24904i | ||||
\(914\) | 11.7882 | + | 36.2803i | 0.389919 | + | 1.20005i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.06910 | − | 9.44571i | 0.101406 | − | 0.312095i | ||||
\(917\) | 12.7184 | + | 9.24046i | 0.419998 | + | 0.305147i | ||||
\(918\) | 1.02469 | 0.0338199 | ||||||||
\(919\) | 40.1464 | + | 29.1680i | 1.32431 | + | 0.962165i | 0.999868 | + | 0.0162579i | \(0.00517529\pi\) |
0.324438 | + | 0.945907i | \(0.394825\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.7608 | − | 8.54474i | 0.387532 | − | 0.281559i | ||||
\(922\) | 1.02807 | − | 0.746939i | 0.0338578 | − | 0.0245991i | ||||
\(923\) | 15.5776 | + | 47.9429i | 0.512743 | + | 1.57806i | ||||
\(924\) | 17.1275 | 0.563453 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −8.93349 | −0.293573 | ||||||||
\(927\) | −2.20973 | − | 6.80085i | −0.0725771 | − | 0.223369i | ||||
\(928\) | 0.210961 | − | 0.153272i | 0.00692512 | − | 0.00503140i | ||||
\(929\) | 13.1559 | − | 9.55836i | 0.431633 | − | 0.313599i | −0.350669 | − | 0.936500i | \(-0.614046\pi\) |
0.782301 | + | 0.622900i | \(0.214046\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.5513 | + | 9.11908i | 0.411353 | + | 0.298866i | ||||
\(932\) | 18.7893 | 0.615465 | ||||||||
\(933\) | −11.7246 | − | 8.51844i | −0.383847 | − | 0.278881i | ||||
\(934\) | 1.77896 | − | 5.47507i | 0.0582092 | − | 0.179150i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.82456 | + | 5.61543i | 0.0596377 | + | 0.183546i | ||||
\(937\) | 0.176101 | − | 0.541982i | 0.00575296 | − | 0.0177058i | −0.948139 | − | 0.317857i | \(-0.897037\pi\) |
0.953892 | + | 0.300151i | \(0.0970370\pi\) | |||||||
\(938\) | 9.27878 | − | 28.5571i | 0.302963 | − | 0.932424i | ||||
\(939\) | −9.74294 | − | 29.9857i | −0.317949 | − | 0.978545i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.16169 | − | 6.65300i | 0.0704691 | − | 0.216882i | −0.909619 | − | 0.415443i | \(-0.863627\pi\) |
0.980089 | + | 0.198561i | \(0.0636267\pi\) | |||||||
\(942\) | 5.53616 | + | 4.02225i | 0.180378 | + | 0.131052i | ||||
\(943\) | −19.2078 | −0.625491 | ||||||||
\(944\) | 5.25216 | + | 3.81592i | 0.170943 | + | 0.124198i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 22.7335 | − | 16.5169i | 0.739131 | − | 0.537010i | ||||
\(947\) | −27.8804 | + | 20.2563i | −0.905991 | + | 0.658241i | −0.939998 | − | 0.341181i | \(-0.889173\pi\) |
0.0340070 | + | 0.999422i | \(0.489173\pi\) | |||||||
\(948\) | −4.13198 | − | 12.7169i | −0.134201 | − | 0.413027i | ||||
\(949\) | 23.3473 | 0.757886 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.9810 | −0.485794 | ||||||||
\(952\) | 1.02322 | + | 3.14916i | 0.0331629 | + | 0.102065i | ||||
\(953\) | −34.0081 | + | 24.7083i | −1.10163 | + | 0.800382i | −0.981325 | − | 0.192355i | \(-0.938387\pi\) |
−0.120305 | + | 0.992737i | \(0.538387\pi\) | |||||||
\(954\) | 1.86970 | − | 1.35841i | 0.0605337 | − | 0.0439803i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 7.88942 | + | 5.73200i | 0.255162 | + | 0.185386i | ||||
\(957\) | −1.38211 | −0.0446773 | ||||||||
\(958\) | 3.74616 | + | 2.72175i | 0.121033 | + | 0.0879356i | ||||
\(959\) | 6.00804 | − | 18.4908i | 0.194010 | − | 0.597100i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.02616 | − | 24.7020i | −0.258909 | − | 0.796839i | ||||
\(962\) | −17.4310 | + | 53.6472i | −0.561999 | + | 1.72966i | ||||
\(963\) | 0.989034 | − | 3.04393i | 0.0318712 | − | 0.0980894i | ||||
\(964\) | 5.84694 | + | 17.9950i | 0.188317 | + | 0.579580i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.92551 | − | 5.92611i | 0.0619523 | − | 0.190669i | ||||
\(967\) | 9.68283 | + | 7.03499i | 0.311379 | + | 0.226230i | 0.732488 | − | 0.680780i | \(-0.238359\pi\) |
−0.421109 | + | 0.907010i | \(0.638359\pi\) | |||||||
\(968\) | 17.0930 | 0.549391 | ||||||||
\(969\) | 3.73643 | + | 2.71468i | 0.120031 | + | 0.0872080i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.09374 | + | 0.794651i | −0.0350999 | + | 0.0255016i | −0.605197 | − | 0.796076i | \(-0.706906\pi\) |
0.570097 | + | 0.821577i | \(0.306906\pi\) | |||||||
\(972\) | −0.809017 | + | 0.587785i | −0.0259492 | + | 0.0188532i | ||||
\(973\) | −5.61913 | − | 17.2939i | −0.180141 | − | 0.554417i | ||||
\(974\) | −15.9235 | −0.510223 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.94494 | −0.126274 | ||||||||
\(977\) | 5.73065 | + | 17.6371i | 0.183340 | + | 0.564262i | 0.999916 | − | 0.0129761i | \(-0.00413053\pi\) |
−0.816576 | + | 0.577238i | \(0.804131\pi\) | |||||||
\(978\) | 7.59438 | − | 5.51764i | 0.242842 | − | 0.176435i | ||||
\(979\) | 3.14558 | − | 2.28540i | 0.100533 | − | 0.0730417i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.00567 | − | 5.81646i | −0.255601 | − | 0.185705i | ||||
\(982\) | −6.38076 | −0.203618 | ||||||||
\(983\) | 13.2534 | + | 9.62915i | 0.422718 | + | 0.307122i | 0.778730 | − | 0.627359i | \(-0.215864\pi\) |
−0.356013 | + | 0.934481i | \(0.615864\pi\) | |||||||
\(984\) | −3.07816 | + | 9.47359i | −0.0981280 | + | 0.302007i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.0825696 | − | 0.254123i | −0.00262955 | − | 0.00809293i | ||||
\(987\) | −10.5131 | + | 32.3559i | −0.334635 | + | 1.02990i | ||||
\(988\) | −8.22365 | + | 25.3098i | −0.261629 | + | 0.805211i | ||||
\(989\) | −3.15909 | − | 9.72267i | −0.100453 | − | 0.309163i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.12790 | − | 18.8597i | 0.194659 | − | 0.599099i | −0.805321 | − | 0.592839i | \(-0.798007\pi\) |
0.999980 | − | 0.00626045i | \(-0.00199278\pi\) | |||||||
\(992\) | 1.81386 | + | 1.31784i | 0.0575900 | + | 0.0418416i | ||||
\(993\) | −21.6174 | −0.686007 | ||||||||
\(994\) | −22.3200 | − | 16.2164i | −0.707946 | − | 0.514353i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −6.05709 | + | 4.40074i | −0.191926 | + | 0.139443i | ||||
\(997\) | 8.46835 | − | 6.15262i | 0.268195 | − | 0.194855i | −0.445557 | − | 0.895254i | \(-0.646994\pi\) |
0.713752 | + | 0.700398i | \(0.246994\pi\) | |||||||
\(998\) | 3.99049 | + | 12.2815i | 0.126317 | + | 0.388763i | ||||
\(999\) | −9.55354 | −0.302261 |
(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 | 750.2.g.f.151.4 | 16 | ||
5.2 | odd | 4 | 750.2.h.d.349.2 | 16 | |||
5.3 | odd | 4 | 150.2.h.b.19.3 | ✓ | 16 | ||
5.4 | even | 2 | 750.2.g.g.151.1 | 16 | |||
15.8 | even | 4 | 450.2.l.c.19.2 | 16 | |||
25.2 | odd | 20 | 3750.2.c.k.1249.15 | 16 | |||
25.3 | odd | 20 | 750.2.h.d.649.1 | 16 | |||
25.4 | even | 10 | 750.2.g.g.601.1 | 16 | |||
25.11 | even | 5 | 3750.2.a.v.1.7 | 8 | |||
25.14 | even | 10 | 3750.2.a.u.1.2 | 8 | |||
25.21 | even | 5 | inner | 750.2.g.f.601.4 | 16 | ||
25.22 | odd | 20 | 150.2.h.b.79.3 | yes | 16 | ||
25.23 | odd | 20 | 3750.2.c.k.1249.2 | 16 | |||
75.47 | even | 20 | 450.2.l.c.379.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.2.h.b.19.3 | ✓ | 16 | 5.3 | odd | 4 | ||
150.2.h.b.79.3 | yes | 16 | 25.22 | odd | 20 | ||
450.2.l.c.19.2 | 16 | 15.8 | even | 4 | |||
450.2.l.c.379.2 | 16 | 75.47 | even | 20 | |||
750.2.g.f.151.4 | 16 | 1.1 | even | 1 | trivial | ||
750.2.g.f.601.4 | 16 | 25.21 | even | 5 | inner | ||
750.2.g.g.151.1 | 16 | 5.4 | even | 2 | |||
750.2.g.g.601.1 | 16 | 25.4 | even | 10 | |||
750.2.h.d.349.2 | 16 | 5.2 | odd | 4 | |||
750.2.h.d.649.1 | 16 | 25.3 | odd | 20 | |||
3750.2.a.u.1.2 | 8 | 25.14 | even | 10 | |||
3750.2.a.v.1.7 | 8 | 25.11 | even | 5 | |||
3750.2.c.k.1249.2 | 16 | 25.23 | odd | 20 | |||
3750.2.c.k.1249.15 | 16 | 25.2 | odd | 20 |