Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [896,2,Mod(703,896)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(896, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("896.703");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 896 = 2^{7} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 896.q (of order \(6\), 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: | \(7.15459602111\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 24x^{14} + 226x^{12} - 972x^{10} + 1575x^{8} + 252x^{6} + 550x^{4} + 156x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 703.8 | ||
Root | \(-2.65282 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 896.703 |
Dual form | 896.2.q.a.831.8 |
$q$-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 \(\left(\mathbb{Z}/896\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(645\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 | 0 | ||||||||
\(3\) | 1.54741 | + | 0.893397i | 0.893397 | + | 0.515803i | 0.875052 | − | 0.484028i | \(-0.160827\pi\) |
0.0183452 | + | 0.999832i | \(0.494160\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.581841 | + | 1.00778i | 0.260207 | + | 0.450692i | 0.966297 | − | 0.257430i | \(-0.0828757\pi\) |
−0.706090 | + | 0.708123i | \(0.749542\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.23781 | + | 1.41146i | 0.845811 | + | 0.533482i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.0963180 | + | 0.166828i | 0.0321060 | + | 0.0556092i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.13595 | − | 1.96752i | 0.342502 | − | 0.593230i | −0.642395 | − | 0.766374i | \(-0.722059\pi\) |
0.984897 | + | 0.173144i | \(0.0553925\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.57988 | −0.438180 | −0.219090 | − | 0.975705i | \(-0.570309\pi\) | ||||
−0.219090 | + | 0.975705i | \(0.570309\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.07926i | 0.536863i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.96304 | + | 3.44276i | 1.44625 | + | 0.834992i | 0.998255 | − | 0.0590449i | \(-0.0188055\pi\) |
0.447993 | + | 0.894037i | \(0.352139\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.671415 | − | 0.387642i | 0.154033 | − | 0.0889311i | −0.421002 | − | 0.907060i | \(-0.638322\pi\) |
0.575035 | + | 0.818128i | \(0.304988\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.20181 | + | 4.18336i | 0.480474 | + | 0.912884i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.11497 | + | 0.643728i | −0.232487 | + | 0.134227i | −0.611719 | − | 0.791075i | \(-0.709522\pi\) |
0.379232 | + | 0.925302i | \(0.376188\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.82292 | − | 3.15739i | 0.364584 | − | 0.631478i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.01618i | − | 0.965365i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.38228i | 1.55655i | 0.627924 | + | 0.778275i | \(0.283905\pi\) | ||||
−0.627924 | + | 0.778275i | \(0.716095\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.554469 | + | 0.960369i | −0.0995856 | + | 0.172487i | −0.911513 | − | 0.411271i | \(-0.865085\pi\) |
0.811928 | + | 0.583758i | \(0.198418\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.51556 | − | 2.02971i | 0.611980 | − | 0.353327i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.120392 | + | 3.07646i | −0.0203499 | + | 0.520017i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.84739 | + | 3.37599i | −0.961306 | + | 0.555010i | −0.896575 | − | 0.442893i | \(-0.853952\pi\) |
−0.0647311 | + | 0.997903i | \(0.520619\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.44472 | − | 1.41146i | −0.391469 | − | 0.226015i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.99371i | − | 0.311365i | −0.987807 | − | 0.155683i | \(-0.950242\pi\) | ||
0.987807 | − | 0.155683i | \(-0.0497577\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.64584 | −0.860983 | −0.430491 | − | 0.902595i | \(-0.641660\pi\) | ||||
−0.430491 | + | 0.902595i | \(0.641660\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.112084 | + | 0.194134i | −0.0167084 | + | 0.0289399i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.90963 | − | 5.03963i | −0.424413 | − | 0.735106i | 0.571952 | − | 0.820287i | \(-0.306186\pi\) |
−0.996365 | + | 0.0851814i | \(0.972853\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.01556 | + | 6.31715i | 0.430794 | + | 0.902450i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.15151 | + | 10.6547i | 0.861383 | + | 1.49196i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.317587 | − | 0.183359i | −0.0436239 | − | 0.0251863i | 0.478029 | − | 0.878344i | \(-0.341351\pi\) |
−0.521653 | + | 0.853158i | \(0.674685\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.64377 | 0.356486 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.38527 | 0.183484 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.6422 | − | 6.14429i | −1.38550 | − | 0.799919i | −0.392696 | − | 0.919668i | \(-0.628458\pi\) |
−0.992804 | + | 0.119749i | \(0.961791\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.93386 | + | 6.81364i | 0.503679 | + | 0.872398i | 0.999991 | + | 0.00425345i | \(0.00135392\pi\) |
−0.496312 | + | 0.868144i | \(0.665313\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.0199296 | + | 0.509277i | −0.00251090 | + | 0.0641629i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.919239 | − | 1.59217i | −0.114018 | − | 0.197484i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.01194 | + | 6.94889i | −0.490137 | + | 0.848942i | −0.999936 | − | 0.0113517i | \(-0.996387\pi\) |
0.509799 | + | 0.860294i | \(0.329720\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.30042 | −0.276938 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 12.7646i | − | 1.51487i | −0.652909 | − | 0.757437i | \(-0.726451\pi\) | ||
0.652909 | − | 0.757437i | \(-0.273549\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.70520 | + | 5.60330i | 1.13591 | + | 0.655816i | 0.945414 | − | 0.325872i | \(-0.105658\pi\) |
0.190493 | + | 0.981688i | \(0.438991\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.64161 | − | 3.25719i | 0.651437 | − | 0.376108i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.31911 | − | 2.79959i | 0.606169 | − | 0.319042i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.6446 | − | 6.72299i | 1.31012 | − | 0.756395i | 0.328000 | − | 0.944678i | \(-0.393625\pi\) |
0.982115 | + | 0.188282i | \(0.0602919\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.77040 | − | 8.26257i | 0.530044 | − | 0.918064i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.15976i | 0.346829i | 0.984849 | + | 0.173414i | \(0.0554800\pi\) | ||||
−0.984849 | + | 0.173414i | \(0.944520\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.01256i | 0.869084i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.48870 | + | 12.9708i | −0.802873 | + | 1.39062i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.53111 | + | 1.46134i | −0.268298 | + | 0.154902i | −0.628114 | − | 0.778122i | \(-0.716173\pi\) |
0.359816 | + | 0.933023i | \(0.382839\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.53547 | − | 2.22994i | −0.370618 | − | 0.233761i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.71598 | + | 0.990723i | −0.177939 | + | 0.102733i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.781314 | + | 0.451092i | 0.0801611 | + | 0.0462810i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.333655i | 0.0338776i | 0.999857 | + | 0.0169388i | \(0.00539204\pi\) | ||||
−0.999857 | + | 0.0169388i | \(0.994608\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.437649 | 0.0439854 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.61953 | − | 13.1974i | 0.758172 | − | 1.31319i | −0.185610 | − | 0.982623i | \(-0.559426\pi\) |
0.943782 | − | 0.330569i | \(-0.107241\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.46329 | − | 11.1948i | −0.636847 | − | 1.10305i | −0.986121 | − | 0.166031i | \(-0.946905\pi\) |
0.349273 | − | 0.937021i | \(-0.386428\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.93480 | + | 4.65299i | −0.286407 | + | 0.454085i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.423405 | − | 0.733358i | −0.0409321 | − | 0.0708964i | 0.844834 | − | 0.535029i | \(-0.179699\pi\) |
−0.885766 | + | 0.464133i | \(0.846366\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.9692 | − | 10.3745i | −1.72113 | − | 0.993697i | −0.916618 | − | 0.399764i | \(-0.869092\pi\) |
−0.804515 | − | 0.593933i | \(-0.797575\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.0644 | −1.14510 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.5719 | −1.37081 | −0.685405 | − | 0.728162i | \(-0.740375\pi\) | ||||
−0.685405 | + | 0.728162i | \(0.740375\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.29747 | − | 0.749095i | −0.120990 | − | 0.0698535i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.152171 | − | 0.263568i | −0.0140682 | − | 0.0243668i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.48480 | + | 16.1208i | 0.777800 | + | 1.47779i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.91924 | + | 5.05627i | 0.265385 | + | 0.459661i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.78118 | − | 3.08509i | 0.160603 | − | 0.278173i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.0610 | 0.899885 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.7646i | 1.48761i | 0.668395 | + | 0.743807i | \(0.266982\pi\) | ||||
−0.668395 | + | 0.743807i | \(0.733018\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.73643 | − | 5.04398i | −0.769200 | − | 0.444098i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.5630 | − | 7.25323i | 1.09763 | − | 0.633718i | 0.162034 | − | 0.986785i | \(-0.448195\pi\) |
0.935598 | + | 0.353067i | \(0.114861\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.04964 | + | 0.0802088i | 0.177726 | + | 0.00695499i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.05520 | − | 2.91862i | 0.435083 | − | 0.251195i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.15567 | − | 8.92989i | 0.440479 | − | 0.762932i | −0.557246 | − | 0.830347i | \(-0.688142\pi\) |
0.997725 | + | 0.0674157i | \(0.0214754\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 15.2121i | − | 1.29028i | −0.764066 | − | 0.645138i | \(-0.776800\pi\) | ||
0.764066 | − | 0.645138i | \(-0.223200\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 10.3978i | − | 0.875655i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.79466 | + | 3.10845i | −0.150077 | + | 0.259941i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.44748 | + | 4.87715i | −0.701525 | + | 0.405026i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.977425 | + | 12.4693i | −0.0806166 | + | 1.02845i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.48516 | − | 3.74421i | 0.531285 | − | 0.306738i | −0.210254 | − | 0.977647i | \(-0.567429\pi\) |
0.741540 | + | 0.670909i | \(0.234096\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.60529 | − | 1.50417i | −0.212016 | − | 0.122407i | 0.390232 | − | 0.920716i | \(-0.372395\pi\) |
−0.602248 | + | 0.798309i | \(0.705728\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.32640i | 0.107233i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.29045 | −0.103652 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.66069 | + | 4.60845i | −0.212346 | + | 0.367794i | −0.952448 | − | 0.304700i | \(-0.901444\pi\) |
0.740102 | + | 0.672494i | \(0.234777\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.327625 | − | 0.567463i | −0.0259823 | − | 0.0450027i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.40368 | − | 0.133197i | −0.268248 | − | 0.0104974i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.54741 | + | 13.0725i | 0.591159 | + | 1.02392i | 0.994077 | + | 0.108681i | \(0.0346627\pi\) |
−0.402918 | + | 0.915236i | \(0.632004\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.09099 | + | 2.36194i | 0.318483 | + | 0.183876i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.99109 | 0.695751 | 0.347876 | − | 0.937541i | \(-0.386903\pi\) | ||||
0.347876 | + | 0.937541i | \(0.386903\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.5040 | −0.807998 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.129339 | + | 0.0746737i | 0.00989078 | + | 0.00571044i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.36549 | − | 5.82920i | −0.255874 | − | 0.443186i | 0.709259 | − | 0.704948i | \(-0.249030\pi\) |
−0.965132 | + | 0.261762i | \(0.915696\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.53588 | − | 4.49265i | 0.645252 | − | 0.339613i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.9786 | − | 19.0155i | −0.825202 | − | 1.42929i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.50267 | − | 14.7271i | 0.635519 | − | 1.10075i | −0.350886 | − | 0.936418i | \(-0.614119\pi\) |
0.986405 | − | 0.164333i | \(-0.0525472\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.8668 | −1.47669 | −0.738346 | − | 0.674422i | \(-0.764393\pi\) | ||||
−0.738346 | + | 0.674422i | \(0.764393\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.0580i | 1.03920i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.80451 | − | 3.92859i | −0.500278 | − | 0.288835i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.5474 | − | 7.82160i | 0.990685 | − | 0.571972i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 7.08015 | − | 11.2252i | 0.515005 | − | 0.816517i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.9064 | − | 8.60621i | 1.07859 | − | 0.622724i | 0.148074 | − | 0.988976i | \(-0.452693\pi\) |
0.930515 | + | 0.366253i | \(0.119359\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.97859 | + | 13.8193i | −0.574312 | + | 0.994737i | 0.421804 | + | 0.906687i | \(0.361397\pi\) |
−0.996116 | + | 0.0880502i | \(0.971936\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 3.28498i | − | 0.235243i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 7.29468i | − | 0.519725i | −0.965646 | − | 0.259862i | \(-0.916323\pi\) | ||
0.965646 | − | 0.259862i | \(-0.0836772\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.14586 | − | 5.44879i | 0.223004 | − | 0.386255i | −0.732715 | − | 0.680536i | \(-0.761747\pi\) |
0.955719 | + | 0.294281i | \(0.0950803\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.4162 | + | 7.16852i | −0.875774 | + | 0.505628i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −11.8313 | + | 18.7579i | −0.830391 | + | 1.31655i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.00922 | − | 1.16002i | 0.140330 | − | 0.0810195i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.214783 | − | 0.124005i | −0.0149285 | − | 0.00861895i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 1.76136i | − | 0.121836i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.15852 | −0.561656 | −0.280828 | − | 0.959758i | \(-0.590609\pi\) | ||||
−0.280828 | + | 0.959758i | \(0.590609\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.4038 | − | 19.7520i | 0.781377 | − | 1.35338i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.28498 | − | 5.68976i | −0.224034 | − | 0.388038i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.59632 | + | 1.36651i | −0.176250 | + | 0.0927646i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.0119 | + | 17.3412i | 0.676544 | + | 1.17181i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.42088 | − | 5.43915i | −0.633717 | − | 0.365877i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −26.6002 | −1.78128 | −0.890641 | − | 0.454708i | \(-0.849744\pi\) | ||||
−0.890641 | + | 0.454708i | \(0.849744\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.702321 | 0.0468214 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.1402 | − | 8.74119i | −1.00489 | − | 0.580173i | −0.0951978 | − | 0.995458i | \(-0.530348\pi\) |
−0.909691 | + | 0.415285i | \(0.863682\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.1014 | − | 17.4962i | −0.667522 | − | 1.15618i | −0.978595 | − | 0.205796i | \(-0.934022\pi\) |
0.311073 | − | 0.950386i | \(-0.399312\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 10.7320 | + | 0.419977i | 0.706113 | + | 0.0276325i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.14011 | − | 10.6350i | −0.402252 | − | 0.696721i | 0.591745 | − | 0.806125i | \(-0.298439\pi\) |
−0.993997 | + | 0.109404i | \(0.965106\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.38589 | − | 5.86453i | 0.220871 | − | 0.382560i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 24.0252 | 1.56060 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.46876i | 0.289060i | 0.989500 | + | 0.144530i | \(0.0461671\pi\) | ||||
−0.989500 | + | 0.144530i | \(0.953833\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.92209 | + | 3.99647i | 0.445891 | + | 0.257435i | 0.706093 | − | 0.708119i | \(-0.250456\pi\) |
−0.260202 | + | 0.965554i | \(0.583789\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.73110 | − | 0.999450i | 0.111050 | − | 0.0641148i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.61172 | + | 6.71459i | −0.294632 | + | 0.428980i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.06075 | + | 0.612427i | −0.0674942 | + | 0.0389678i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.82292 | + | 4.88944i | −0.178895 | + | 0.309856i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.0313i | 0.948767i | 0.880318 | + | 0.474384i | \(0.157329\pi\) | ||||
−0.880318 | + | 0.474384i | \(0.842671\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.92497i | 0.183891i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.15840 | + | 12.3987i | −0.448276 | + | 0.776438i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.50983 | − | 4.91315i | 0.530829 | − | 0.306474i | −0.210525 | − | 0.977588i | \(-0.567517\pi\) |
0.741354 | + | 0.671114i | \(0.234184\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −17.8504 | − | 0.698544i | −1.10917 | − | 0.0434054i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.39840 | + | 0.807364i | −0.0865585 | + | 0.0499746i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −17.4884 | − | 10.0969i | −1.07838 | − | 0.622604i | −0.147922 | − | 0.988999i | \(-0.547258\pi\) |
−0.930459 | + | 0.366395i | \(0.880592\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 0.426743i | − | 0.0262146i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.22223 | −0.319595 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.65440 | + | 8.06165i | −0.283784 | + | 0.491528i | −0.972313 | − | 0.233680i | \(-0.924923\pi\) |
0.688530 | + | 0.725208i | \(0.258256\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.1736 | − | 19.3533i | −0.678749 | − | 1.17563i | −0.975358 | − | 0.220629i | \(-0.929189\pi\) |
0.296609 | − | 0.954999i | \(-0.404144\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.47859 | − | 6.60920i | −0.210534 | − | 0.400007i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.14149 | − | 7.17327i | −0.249741 | − | 0.432565i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.4618 | + | 11.8136i | 1.22943 | + | 0.709813i | 0.966911 | − | 0.255113i | \(-0.0821127\pi\) |
0.262521 | + | 0.964926i | \(0.415446\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.213621 | −0.0127892 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.42209 | −0.323455 | −0.161727 | − | 0.986835i | \(-0.551707\pi\) | ||||
−0.161727 | + | 0.986835i | \(0.551707\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.6923 | − | 7.32791i | −0.754479 | − | 0.435599i | 0.0728308 | − | 0.997344i | \(-0.476797\pi\) |
−0.827310 | + | 0.561745i | \(0.810130\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.806008 | + | 1.39605i | 0.0477438 | + | 0.0826947i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.81404 | − | 4.46154i | 0.166108 | − | 0.263356i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.2052 | + | 26.3362i | 0.894423 | + | 1.54919i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.298087 | + | 0.516302i | −0.0174742 | + | 0.0302661i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.36928 | −0.488939 | −0.244469 | − | 0.969657i | \(-0.578614\pi\) | ||||
−0.244469 | + | 0.969657i | \(0.578614\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 14.3000i | − | 0.832579i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9.86945 | − | 5.69813i | −0.572684 | − | 0.330639i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.76152 | − | 1.01701i | 0.101871 | − | 0.0588154i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.6343 | − | 7.96889i | −0.728229 | − | 0.459319i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 23.5811 | − | 13.6145i | 1.35470 | − | 0.782135i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.57776 | + | 7.92892i | −0.262122 | + | 0.454009i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 12.3058i | − | 0.702331i | −0.936313 | − | 0.351166i | \(-0.885785\pi\) | ||
0.936313 | − | 0.351166i | \(-0.114215\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 23.0972i | − | 1.31395i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.6670 | + | 25.4040i | −0.831691 | + | 1.44053i | 0.0650050 | + | 0.997885i | \(0.479294\pi\) |
−0.896696 | + | 0.442646i | \(0.854040\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.39086 | − | 3.68976i | 0.361233 | − | 0.208558i | −0.308389 | − | 0.951260i | \(-0.599790\pi\) |
0.669621 | + | 0.742703i | \(0.266456\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.524835 | + | 0.276234i | −0.0295711 | + | 0.0155640i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.1821 | − | 11.6521i | 1.13354 | − | 0.654448i | 0.188716 | − | 0.982032i | \(-0.439568\pi\) |
0.944822 | + | 0.327583i | \(0.106234\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.4923 | + | 9.52184i | 0.923392 | + | 0.533121i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 1.51307i | − | 0.0844516i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.33823 | 0.297027 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.88000 | + | 4.98830i | −0.159753 | + | 0.276701i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −18.5371 | − | 32.1072i | −1.02510 | − | 1.77553i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.602046 | − | 15.3846i | 0.0331919 | − | 0.848178i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.0119 | + | 17.3412i | 0.550306 | + | 0.953158i | 0.998252 | + | 0.0590977i | \(0.0188223\pi\) |
−0.447946 | + | 0.894061i | \(0.647844\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.12642 | − | 0.650338i | −0.0617274 | − | 0.0356383i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.33726 | −0.510149 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.9883 | 1.47015 | 0.735073 | − | 0.677988i | \(-0.237148\pi\) | ||||
0.735073 | + | 0.677988i | \(0.237148\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −22.5487 | − | 13.0185i | −1.22468 | − | 0.707068i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.25970 | + | 2.18186i | 0.0682165 | + | 0.118154i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.16818 | + | 18.3929i | −0.117071 | + | 0.993124i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.33848 | − | 2.31831i | −0.0720613 | − | 0.124814i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.6972 | + | 25.4564i | −0.788989 | + | 1.36657i | 0.137598 | + | 0.990488i | \(0.456062\pi\) |
−0.926587 | + | 0.376080i | \(0.877272\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.8919 | −1.11832 | −0.559160 | − | 0.829060i | \(-0.688876\pi\) | ||||
−0.559160 | + | 0.829060i | \(0.688876\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.92497i | 0.423003i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.66425 | − | 4.42496i | −0.407927 | − | 0.235517i | 0.281972 | − | 0.959423i | \(-0.409012\pi\) |
−0.689899 | + | 0.723906i | \(0.742345\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.8638 | − | 7.42694i | 0.682742 | − | 0.394181i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.27284 | + | 32.5258i | −0.0673658 | + | 1.72145i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 27.3788 | − | 15.8072i | 1.44500 | − | 0.834271i | 0.446823 | − | 0.894623i | \(-0.352556\pi\) |
0.998177 | + | 0.0603517i | \(0.0192222\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.19947 | + | 15.9339i | −0.484183 | + | 0.838629i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.4322i | 0.547547i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.0409i | 0.682593i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.437113 | − | 0.757102i | 0.0228171 | − | 0.0395204i | −0.854391 | − | 0.519630i | \(-0.826070\pi\) |
0.877208 | + | 0.480110i | \(0.159403\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.332606 | − | 0.192030i | 0.0173148 | − | 0.00999669i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.451894 | − | 0.858583i | −0.0234612 | − | 0.0445754i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.0441 | + | 12.7272i | −1.14140 | + | 0.658987i | −0.946777 | − | 0.321891i | \(-0.895682\pi\) |
−0.194622 | + | 0.980878i | \(0.562348\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 15.5685 | + | 8.98849i | 0.803955 | + | 0.464163i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 13.2430i | − | 0.682049i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.8082 | 1.53115 | 0.765573 | − | 0.643349i | \(-0.222456\pi\) | ||||
0.765573 | + | 0.643349i | \(0.222456\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.9774 | + | 25.9416i | −0.767316 | + | 1.32903i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.11806 | + | 5.40064i | 0.159326 | + | 0.275960i | 0.934626 | − | 0.355633i | \(-0.115735\pi\) |
−0.775300 | + | 0.631593i | \(0.782401\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.91624 | + | 3.73158i | 0.301520 | + | 0.190179i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.543796 | − | 0.941883i | −0.0276427 | − | 0.0478786i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 29.4531 | + | 17.0048i | 1.49333 | + | 0.862177i | 0.999971 | − | 0.00764684i | \(-0.00243409\pi\) |
0.493363 | + | 0.869824i | \(0.335767\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.86480 | −0.448312 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 25.9201 | 1.30749 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 13.5506 | + | 7.82343i | 0.681803 | + | 0.393639i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.3893 | + | 28.3871i | 0.822554 | + | 1.42471i | 0.903774 | + | 0.428009i | \(0.140785\pi\) |
−0.0812202 | + | 0.996696i | \(0.525882\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.09997 | + | 1.95526i | 0.155193 | + | 0.0978853i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.34531 | + | 9.25835i | 0.266932 | + | 0.462340i | 0.968068 | − | 0.250688i | \(-0.0806567\pi\) |
−0.701136 | + | 0.713028i | \(0.747323\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.875995 | − | 1.51727i | 0.0436364 | − | 0.0755805i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 11.1025 | 0.551686 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15.3398i | 0.760367i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.09919 | + | 2.94402i | 0.252139 | + | 0.145572i | 0.620743 | − | 0.784014i | \(-0.286831\pi\) |
−0.368604 | + | 0.929586i | \(0.620164\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 15.9559 | − | 9.21213i | 0.787045 | − | 0.454401i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −15.1428 | − | 28.7708i | −0.745130 | − | 1.41572i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.18434 | + | 1.83848i | −0.156313 | + | 0.0902474i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.5905 | − | 23.5394i | 0.665528 | − | 1.15273i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 28.4042i | − | 1.38764i | −0.720149 | − | 0.693819i | \(-0.755927\pi\) | ||
0.720149 | − | 0.693819i | \(-0.244073\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.29468i | 0.258047i | 0.991642 | + | 0.129024i | \(0.0411843\pi\) | ||||
−0.991642 | + | 0.129024i | \(0.958816\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.560500 | − | 0.970814i | 0.0272524 | − | 0.0472026i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 21.7403 | − | 12.5518i | 1.05456 | − | 0.608850i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.813974 | + | 20.8001i | −0.0393910 | + | 1.00659i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.55416 | + | 3.20669i | −0.268157 | + | 0.154821i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.5805 | − | 7.26338i | −0.605984 | − | 0.349865i | 0.165408 | − | 0.986225i | \(-0.447106\pi\) |
−0.771392 | + | 0.636360i | \(0.780439\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.5096i | 0.985628i | 0.870135 | + | 0.492814i | \(0.164032\pi\) | ||||
−0.870135 | + | 0.492814i | \(0.835968\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −17.4289 | −0.835654 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.499071 | + | 0.864417i | −0.0238738 | + | 0.0413507i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.6482 | + | 21.9073i | 0.603666 | + | 1.04558i | 0.992261 | + | 0.124171i | \(0.0396272\pi\) |
−0.388595 | + | 0.921409i | \(0.627039\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.763423 | + | 1.11153i | −0.0363535 | + | 0.0529302i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.4913 | + | 26.8318i | 0.736016 | + | 1.27482i | 0.954276 | + | 0.298926i | \(0.0966284\pi\) |
−0.218261 | + | 0.975891i | \(0.570038\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.94541 | − | 1.70054i | −0.139626 | − | 0.0806131i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13.3803 | 0.632865 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.63439 | −0.171517 | −0.0857586 | − | 0.996316i | \(-0.527331\pi\) | ||||
−0.0857586 | + | 0.996316i | \(0.527331\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.92267 | − | 2.26475i | −0.184711 | − | 0.106643i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.68763 | − | 4.65512i | −0.126276 | − | 0.218717i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.190204 | − | 4.86044i | 0.00891692 | − | 0.227861i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.1469 | + | 17.5750i | 0.474654 | + | 0.822125i | 0.999579 | − | 0.0290237i | \(-0.00923982\pi\) |
−0.524925 | + | 0.851149i | \(0.675906\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 17.2695 | − | 29.9117i | 0.806072 | − | 1.39616i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.3236 | 1.27259 | 0.636293 | − | 0.771448i | \(-0.280467\pi\) | ||||
0.636293 | + | 0.771448i | \(0.280467\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.51268i | 0.116774i | 0.998294 | + | 0.0583871i | \(0.0185958\pi\) | ||||
−0.998294 | + | 0.0583871i | \(0.981404\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.99686 | − | 1.15289i | −0.0926021 | − | 0.0534639i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 27.8982 | − | 16.1070i | 1.29097 | − | 0.745345i | 0.312148 | − | 0.950034i | \(-0.398952\pi\) |
0.978827 | + | 0.204689i | \(0.0656183\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −18.7860 | + | 9.88757i | −0.867459 | + | 0.456566i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.23435 | + | 4.75410i | −0.379419 | + | 0.219058i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.41339 | + | 11.1083i | −0.294888 | + | 0.510761i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 2.82656i | − | 0.129691i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 0.0706430i | − | 0.00323452i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.12964 | + | 10.6168i | −0.280070 | + | 0.485096i | −0.971402 | − | 0.237442i | \(-0.923691\pi\) |
0.691332 | + | 0.722538i | \(0.257024\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.23818 | − | 5.33367i | 0.421225 | − | 0.243194i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.14789 | − | 3.24695i | −0.234237 | − | 0.147741i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.336251 | + | 0.194134i | −0.0152684 | + | 0.00881519i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.72155 | + | 2.72599i | 0.213954 | + | 0.123526i | 0.603148 | − | 0.797630i | \(-0.293913\pi\) |
−0.389194 | + | 0.921156i | \(0.627246\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 26.9713i | 1.21969i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.0205 | −1.35481 | −0.677404 | − | 0.735612i | \(-0.736895\pi\) | ||||
−0.677404 | + | 0.735612i | \(0.736895\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −28.8582 | + | 49.9838i | −1.29971 | + | 2.25116i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.254642 | + | 0.441054i | 0.0114453 | + | 0.0198239i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 18.0167 | − | 28.5646i | 0.808158 | − | 1.28130i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.17347 | − | 3.76455i | −0.0972977 | − | 0.168524i | 0.813268 | − | 0.581890i | \(-0.197687\pi\) |
−0.910565 | + | 0.413365i | \(0.864353\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.9129 | + | 8.03261i | 0.621582 | + | 0.358871i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.75385 | −0.434903 | −0.217451 | − | 0.976071i | \(-0.569774\pi\) | ||||
−0.217451 | + | 0.976071i | \(0.569774\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.7334 | 0.789128 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −16.2540 | − | 9.38423i | −0.721864 | − | 0.416768i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.998039 | − | 1.72865i | −0.0442373 | − | 0.0766212i | 0.843059 | − | 0.537821i | \(-0.180752\pi\) |
−0.887296 | + | 0.461200i | \(0.847419\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.8095 | + | 26.2376i | 0.610897 | + | 1.16068i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.94448 | − | 3.36794i | −0.0858510 | − | 0.148698i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.52122 | − | 13.0271i | 0.331425 | − | 0.574044i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.2208 | −0.581449 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 12.0269i | − | 0.527922i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.45719 | − | 3.15071i | −0.239084 | − | 0.138035i | 0.375672 | − | 0.926753i | \(-0.377412\pi\) |
−0.614756 | + | 0.788718i | \(0.710745\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.98699 | + | 1.14719i | −0.0868849 | + | 0.0501630i | −0.542813 | − | 0.839854i | \(-0.682641\pi\) |
0.455928 | + | 0.890017i | \(0.349307\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 17.2222 | + | 0.673961i | 0.751640 | + | 0.0294141i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.61264 | + | 3.81781i | −0.288051 | + | 0.166306i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.6712 | + | 18.4831i | −0.463966 | + | 0.803614i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 2.36722i | − | 0.102729i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.14982i | 0.136434i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.492709 | − | 0.853396i | 0.0213017 | − | 0.0368955i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 26.3142 | − | 15.1925i | 1.13554 | − | 0.655606i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.8547 | + | 1.24279i | 0.682908 | + | 0.0535307i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.00219 | − | 5.19742i | 0.387034 | − | 0.223454i | −0.293840 | − | 0.955855i | \(-0.594933\pi\) |
0.680874 | + | 0.732400i | \(0.261600\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −30.7422 | − | 17.7490i | −1.31927 | − | 0.761682i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 24.1452i | − | 1.03427i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.13726 | −0.262410 | −0.131205 | − | 0.991355i | \(-0.541885\pi\) | ||||
−0.131205 | + | 0.991355i | \(0.541885\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.757803 | + | 1.31255i | −0.0323422 | + | 0.0560184i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.24932 | + | 5.62798i | 0.138426 | + | 0.239760i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 35.5475 | + | 1.39109i | 1.51163 | + | 0.0591550i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.01958 | − | 12.1583i | −0.297965 | − | 0.516090i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.675593 | + | 0.390054i | 0.0286258 | + | 0.0165271i | 0.514245 | − | 0.857644i | \(-0.328072\pi\) |
−0.485619 | + | 0.874171i | \(0.661406\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.91975 | 0.377265 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 27.9512 | 1.18010 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.8515 | + | 7.41983i | 0.541627 | + | 0.312709i | 0.745738 | − | 0.666239i | \(-0.232097\pi\) |
−0.204111 | + | 0.978948i | \(0.565430\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.47854 | − | 14.6853i | −0.356695 | − | 0.617814i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 22.3375 | − | 11.7568i | 0.938088 | − | 0.493740i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.67408 | + | 15.0240i | 0.363636 | + | 0.629837i | 0.988556 | − | 0.150852i | \(-0.0482017\pi\) |
−0.624920 | + | 0.780689i | \(0.714868\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.6684 | + | 18.4782i | −0.446459 | + | 0.773290i | −0.998153 | − | 0.0607568i | \(-0.980649\pi\) |
0.551693 | + | 0.834047i | \(0.313982\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 30.7551 | 1.28481 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.69386i | 0.195748i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.02714 | − | 2.90242i | −0.209282 | − | 0.120829i | 0.391695 | − | 0.920095i | \(-0.371889\pi\) |
−0.600978 | + | 0.799266i | \(0.705222\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −24.6923 | + | 14.2561i | −1.02618 | + | 0.592464i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.45988 | + | 7.07093i | −0.185027 | + | 0.293352i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.721525 | + | 0.416573i | −0.0298825 | + | 0.0172527i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.177079 | − | 0.306709i | 0.00732130 | − | 0.0126809i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.98632i | 0.247082i | 0.992339 | + | 0.123541i | \(0.0394250\pi\) | ||||
−0.992339 | + | 0.123541i | \(0.960575\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.859741i | 0.0354250i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.51705 | − | 11.2879i | 0.268076 | − | 0.464321i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −28.9786 | + | 16.7308i | −1.19001 | + | 0.687052i | −0.958308 | − | 0.285736i | \(-0.907762\pi\) |
−0.231700 | + | 0.972787i | \(0.574429\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.3094 | + | 17.9306i | −0.463641 | + | 0.735081i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.73587 | − | 5.62101i | 0.398463 | − | 0.230053i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.2940 | − | 11.1394i | −0.788330 | − | 0.455143i | 0.0510442 | − | 0.998696i | \(-0.483745\pi\) |
−0.839374 | + | 0.543554i | \(0.817078\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.75431i | 0.397887i | 0.980011 | + | 0.198943i | \(0.0637509\pi\) | ||||
−0.980011 | + | 0.198943i | \(0.936249\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.54569 | −0.0629454 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.39707 | + | 5.88389i | −0.138110 | + | 0.239214i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.3810 | − | 35.3009i | −0.827239 | − | 1.43282i | −0.900196 | − | 0.435486i | \(-0.856577\pi\) |
0.0729563 | − | 0.997335i | \(-0.476757\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −35.0661 | + | 18.4562i | −1.42095 | + | 0.747882i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.59687 | + | 7.96201i | 0.185969 | + | 0.322109i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.5353 | + | 7.23723i | 0.506294 | + | 0.292309i | 0.731309 | − | 0.682046i | \(-0.238910\pi\) |
−0.225015 | + | 0.974355i | \(0.572243\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.14545 | 0.167160 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.01966 | 0.322859 | 0.161430 | − | 0.986884i | \(-0.448390\pi\) | ||||
0.161430 | + | 0.986884i | \(0.448390\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 35.0723 | + | 20.2490i | 1.40967 | + | 0.813876i | 0.995357 | − | 0.0962568i | \(-0.0306870\pi\) |
0.414317 | + | 0.910132i | \(0.364020\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.22906 | + | 5.59289i | 0.129578 | + | 0.224435i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.72677 | − | 0.302373i | −0.309566 | − | 0.0121143i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.26069 | − | 5.64768i | −0.130428 | − | 0.225907i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.57360 | − | 2.72555i | 0.0628435 | − | 0.108848i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −46.4910 | −1.85372 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.80166i | 0.270770i | 0.990793 | + | 0.135385i | \(0.0432271\pi\) | ||||
−0.990793 | + | 0.135385i | \(0.956773\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.6246 | − | 7.28880i | −0.501782 | − | 0.289704i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.8950 | + | 9.75431i | −0.670456 | + | 0.387088i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.76422 | − | 9.98034i | −0.188765 | − | 0.395436i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.12948 | − | 1.22946i | 0.0842409 | − | 0.0486365i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.07491 | − | 15.7182i | 0.358437 | − | 0.620832i | −0.629263 | − | 0.777193i | \(-0.716643\pi\) |
0.987700 | + | 0.156361i | \(0.0499763\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.1896i | 0.559583i | 0.960061 | + | 0.279792i | \(0.0902654\pi\) | ||||
−0.960061 | + | 0.279792i | \(0.909735\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 11.7392i | − | 0.462230i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.56278 | − | 9.63503i | 0.218696 | − | 0.378792i | −0.735714 | − | 0.677293i | \(-0.763153\pi\) |
0.954409 | + | 0.298501i | \(0.0964865\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.1781 | + | 13.9592i | −0.949072 | + | 0.547947i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.23840 | − | 0.204995i | −0.205309 | − | 0.00803440i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.295831 | − | 0.170798i | 0.0115768 | − | 0.00668386i | −0.494200 | − | 0.869348i | \(-0.664539\pi\) |
0.505777 | + | 0.862664i | \(0.331206\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.6193 | + | 8.44046i | 0.571224 | + | 0.329796i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.15879i | 0.0842226i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.86660 | −0.228530 | −0.114265 | − | 0.993450i | \(-0.536451\pi\) | ||||
−0.114265 | + | 0.993450i | \(0.536451\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.7756 | − | 22.1280i | 0.496913 | − | 0.860679i | −0.503080 | − | 0.864240i | \(-0.667800\pi\) |
0.999994 | + | 0.00356071i | \(0.00113341\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.71864 | − | 16.8332i | −0.377441 | − | 0.653747i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.11173 | + | 2.11225i | 0.0431111 | + | 0.0819095i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.39590 | − | 9.34598i | −0.208930 | − | 0.361878i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −41.1614 | − | 23.7646i | −1.59139 | − | 0.918791i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.8747 | 0.690043 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.2431 | −1.20433 | −0.602167 | − | 0.798370i | \(-0.705696\pi\) | ||||
−0.602167 | + | 0.798370i | \(0.705696\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −15.8381 | − | 9.14411i | −0.609607 | − | 0.351957i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.71455 | + | 16.8261i | 0.373361 | + | 0.646679i | 0.990080 | − | 0.140503i | \(-0.0448721\pi\) |
−0.616720 | + | 0.787183i | \(0.711539\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.470941 | + | 0.746656i | −0.0180731 | + | 0.0286540i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.6187 | − | 27.0524i | −0.598510 | − | 1.03665i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.43063 | + | 4.20998i | −0.0930055 | + | 0.161090i | −0.908774 | − | 0.417288i | \(-0.862981\pi\) |
0.815769 | + | 0.578378i | \(0.196314\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.9991 | 0.458463 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 36.0984i | − | 1.37724i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.501749 | + | 0.289685i | 0.0191151 | + | 0.0110361i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.0723 | + | 13.3208i | −0.877711 | + | 0.506747i | −0.869903 | − | 0.493223i | \(-0.835819\pi\) |
−0.00780793 | + | 0.999970i | \(0.502485\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.979375 | + | 0.617725i | 0.0372034 | + | 0.0234654i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15.3304 | − | 8.85104i | 0.581517 | − | 0.335739i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.86387 | − | 11.8886i | 0.259987 | − | 0.450311i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 21.9422i | − | 0.829932i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 6.56046i | − | 0.247785i | −0.992296 | − | 0.123893i | \(-0.960462\pi\) | ||
0.992296 | − | 0.123893i | \(-0.0395378\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.61735 | + | 4.53339i | −0.0987153 | + | 0.170980i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.4787 | − | 6.04989i | 0.394651 | − | 0.227852i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 35.6787 | − | 18.7786i | 1.34183 | − | 0.706242i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.70421 | − | 4.44803i | 0.289338 | − | 0.167049i | −0.348305 | − | 0.937381i | \(-0.613243\pi\) |
0.637643 | + | 0.770332i | \(0.279909\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.24316 | + | 1.29509i | 0.0841251 | + | 0.0485697i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1.42771i | − | 0.0534681i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.17684 | −0.156205 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.99238 | + | 6.91501i | −0.149098 | + | 0.258246i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.23335 | + | 7.33238i | 0.157877 | + | 0.273452i | 0.934103 | − | 0.357003i | \(-0.116202\pi\) |
−0.776226 | + | 0.630455i | \(0.782868\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.33735 | − | 34.1744i | 0.0498056 | − | 1.27272i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.14088 | + | 12.3684i | 0.265572 | + | 0.459984i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 26.4661 | + | 15.2802i | 0.982927 | + | 0.567493i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27.4279 | −1.01724 | −0.508621 | − | 0.860990i | \(-0.669845\pi\) | ||||
−0.508621 | + | 0.860990i | \(0.669845\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.0508 | −0.927806 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −33.6664 | − | 19.4373i | −1.24520 | − | 0.718914i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.27274 | − | 12.5967i | −0.268625 | − | 0.465272i | 0.699882 | − | 0.714258i | \(-0.253236\pi\) |
−0.968507 | + | 0.248987i | \(0.919902\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −13.1350 | + | 6.27013i | −0.484492 | + | 0.231277i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.11473 | + | 15.7872i | 0.335745 | + | 0.581528i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21.0055 | + | 36.3827i | −0.772701 | + | 1.33836i | 0.163376 | + | 0.986564i | \(0.447762\pi\) |
−0.936077 | + | 0.351794i | \(0.885572\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.18856 | −0.0803989 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.2063i | 0.741297i | 0.928773 | + | 0.370649i | \(0.120865\pi\) | ||||
−0.928773 | + | 0.370649i | \(0.879135\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.54667 | + | 4.35707i | 0.276489 | + | 0.159631i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.527135 | + | 0.304342i | −0.0192869 | + | 0.0111353i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.0876088 | − | 2.23873i | 0.00320115 | − | 0.0818015i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35.0599 | + | 20.2418i | −1.27935 | + | 0.738635i | −0.976729 | − | 0.214475i | \(-0.931196\pi\) |
−0.302624 | + | 0.953110i | \(0.597863\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13.4289 | + | 23.2596i | −0.489377 | + | 0.847626i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 3.50074i | − | 0.127405i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.0846i | 0.620950i | 0.950582 | + | 0.310475i | \(0.100488\pi\) | ||||
−0.950582 | + | 0.310475i | \(0.899512\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.61316 | + | 4.52612i | −0.0948517 | + | 0.164288i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.6059 | + | 10.7421i | −0.674463 | + | 0.389401i | −0.797765 | − | 0.602968i | \(-0.793985\pi\) |
0.123303 | + | 0.992369i | \(0.460651\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −25.5683 | − | 48.5789i | −0.925635 | − | 1.75867i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.33672 | + | 0.771754i | −0.0483291 | + | 0.0279028i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 16.8134 | + | 9.70725i | 0.607098 | + | 0.350508i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 10.3677i | − | 0.373870i | −0.982372 | − | 0.186935i | \(-0.940145\pi\) | ||
0.982372 | − | 0.186935i | \(-0.0598553\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.5576 | 0.632321 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22.1135 | − | 38.3017i | 0.795367 | − | 1.37762i | −0.127240 | − | 0.991872i | \(-0.540612\pi\) |
0.922606 | − | 0.385743i | \(-0.126055\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.02151 | + | 3.50135i | 0.0726147 | + | 0.125772i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −26.9978 | − | 17.0285i | −0.968542 | − | 0.610892i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.772845 | − | 1.33861i | −0.0276900 | − | 0.0479606i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −25.1145 | − | 14.4999i | −0.898668 | − | 0.518846i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 42.0470 | 1.50264 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.19239 | −0.221016 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 39.7993 | + | 22.9781i | 1.41869 | + | 0.819082i | 0.996184 | − | 0.0872780i | \(-0.0278168\pi\) |
0.422507 | + | 0.906360i | \(0.361150\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −18.0412 | − | 31.2482i | −0.642282 | − | 1.11247i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −32.6091 | − | 20.5677i | −1.15945 | − | 0.731303i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.21503 | − | 10.7647i | −0.220702 | − | 0.382267i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.381251 | − | 0.660346i | 0.0135216 | − | 0.0234201i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15.5217 | 0.549805 | 0.274903 | − | 0.961472i | \(-0.411354\pi\) | ||||
0.274903 | + | 0.961472i | \(0.411354\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 40.0687i | − | 1.41753i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.487584 | − | 0.281507i | −0.0172279 | − | 0.00994655i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 22.0492 | − | 12.7301i | 0.778100 | − | 0.449236i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.84617 | − | 3.50766i | −0.0650689 | − | 0.123629i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14.4045 | + | 8.31646i | −0.507063 | + | 0.292753i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13.5467 | + | 23.4635i | −0.476276 | + | 0.824934i | −0.999631 | − | 0.0271812i | \(-0.991347\pi\) |
0.523355 | + | 0.852115i | \(0.324680\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 35.5514i | − | 1.24838i | −0.781273 | − | 0.624190i | \(-0.785429\pi\) | ||
0.781273 | − | 0.624190i | \(-0.214571\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 39.9299i | − | 1.40040i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.78279 | + | 15.2122i | −0.307648 | + | 0.532861i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.79070 | + | 2.18856i | −0.132620 | + | 0.0765681i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.0314864 | − | 0.804597i | 0.00110022 | − | 0.0281149i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.32826 | − | 3.65362i | 0.220858 | − | 0.127512i | −0.385490 | − | 0.922712i | \(-0.625967\pi\) |
0.606347 | + | 0.795200i | \(0.292634\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39.7324 | + | 22.9395i | 1.38498 | + | 0.799621i | 0.992745 | − | 0.120242i | \(-0.0383670\pi\) |
0.392240 | + | 0.919863i | \(0.371700\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 14.8000i | − | 0.515270i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.96289 | 0.0682564 | 0.0341282 | − | 0.999417i | \(-0.489135\pi\) | ||||
0.0341282 | + | 0.999417i | \(0.489135\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.9828 | − | 20.7549i | 0.416181 | − | 0.720847i | −0.579371 | − | 0.815064i | \(-0.696702\pi\) |
0.995552 | + | 0.0942175i | \(0.0300349\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21.1086 | + | 36.5611i | 0.732248 | + | 1.26829i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.76656 | + | 48.0512i | −0.130504 | + | 1.66488i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.23139 | + | 9.06102i | 0.181040 | + | 0.313570i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.81739 | + | 2.78132i | 0.166513 | + | 0.0961365i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −28.1193 | −0.970786 | −0.485393 | − | 0.874296i | \(-0.661323\pi\) | ||||
−0.485393 | + | 0.874296i | \(0.661323\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −41.2625 | −1.42285 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8.39020 | − | 4.84408i | −0.288974 | − | 0.166839i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.11165 | − | 10.5857i | −0.210247 | − | 0.364159i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.604034 | + | 15.4353i | −0.0207549 | + | 0.530365i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −13.0935 | − | 22.6785i | −0.449367 | − | 0.778326i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.34644 | − | 7.52826i | 0.148994 | − | 0.258065i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.7019 | −0.571862 | −0.285931 | − | 0.958250i | \(-0.592303\pi\) | ||||
−0.285931 | + | 0.958250i | \(0.592303\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.173793i | 0.00594360i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.72835 | − | 2.15257i | −0.127358 | − | 0.0735302i | 0.434967 | − | 0.900446i | \(-0.356760\pi\) |
−0.562326 | + | 0.826916i | \(0.690093\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.1068 | − | 15.0728i | 0.890752 | − | 0.514276i | 0.0165639 | − | 0.999863i | \(-0.494727\pi\) |
0.874189 | + | 0.485587i | \(0.161394\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.34040 | − | 4.38977i | 0.284240 | − | 0.149603i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.5801 | + | 10.7272i | −0.632474 | + | 0.365159i | −0.781709 | − | 0.623643i | \(-0.785652\pi\) |
0.149236 | + | 0.988802i | \(0.452319\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.91636 | − | 6.78334i | 0.133160 | − | 0.230640i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 54.3371i | 1.84539i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 30.5479i | − | 1.03627i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.33839 | − | 10.9784i | 0.214768 | − | 0.371989i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.0556629 | + | 0.0321370i | −0.00188391 | + | 0.00108767i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 22.5146 | + | 14.2007i | 0.761133 | + | 0.480072i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.72762 | − | 5.03889i | 0.294711 | − | 0.170151i | −0.345354 | − | 0.938473i | \(-0.612241\pi\) |
0.640064 | + | 0.768321i | \(0.278908\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12.9507 | − | 7.47709i | −0.436817 | − | 0.252196i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.37180i | 0.248362i | 0.992260 | + | 0.124181i | \(0.0396304\pi\) | ||||
−0.992260 | + | 0.124181i | \(0.960370\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.5124 | 0.925867 | 0.462934 | − | 0.886393i | \(-0.346797\pi\) | ||||
0.462934 | + | 0.886393i | \(0.346797\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12.7756 | − | 22.1280i | 0.429447 | − | 0.743824i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.6675 | + | 37.5293i | 0.727525 | + | 1.26011i | 0.957926 | + | 0.287014i | \(0.0926628\pi\) |
−0.230401 | + | 0.973096i | \(0.574004\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −23.6625 | + | 37.5158i | −0.793615 | + | 1.25824i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10.8379 | − | 18.7717i | −0.363082 | − | 0.628877i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.90714 | − | 2.25579i | −0.130747 | − | 0.0754871i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19.7888 | 0.661467 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.63439 | 0.121349 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.05008 | − | 4.64771i | −0.268485 | − | 0.155010i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.26252 | − | 2.18675i | −0.0420607 | − | 0.0728512i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12.4311 | − | 23.6186i | −0.413680 | − | 0.785977i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.5594 | − | 20.0214i | −0.384246 | − | 0.665533i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.9506 | − | 27.6272i | 0.529630 | − | 0.917346i | −0.469772 | − | 0.882788i | \(-0.655664\pi\) |
0.999403 | − | 0.0345589i | \(-0.0110026\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.93559 | 0.0973675 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.71677i | 0.156274i | 0.996943 | + | 0.0781369i | \(0.0248971\pi\) | ||||
−0.996943 | + | 0.0781369i | \(0.975103\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.21690 | + | 3.58933i | 0.205749 | + | 0.118789i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −14.1674 | + | 8.17952i | −0.468358 | + | 0.270407i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 38.3511 | + | 1.50080i | 1.26647 | + | 0.0495609i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.607906 | − | 0.350974i | 0.0200530 | − | 0.0115776i | −0.489940 | − | 0.871756i | \(-0.662981\pi\) |
0.509993 | + | 0.860179i | \(0.329648\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.9940 | − | 19.0422i | 0.362265 | − | 0.627461i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 20.1665i | 0.663787i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.6167i | 0.809392i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.24506 | − | 2.15651i | 0.0408932 | − | 0.0708292i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.5273 | − | 6.07791i | 0.345388 | − | 0.199410i | −0.317264 | − | 0.948337i | \(-0.602764\pi\) |
0.662652 | + | 0.748927i | \(0.269431\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.47348 | + | 3.07247i | 0.146612 | + | 0.100696i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −45.3918 | + | 26.2070i | −1.48606 | + | 0.857978i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 15.7649 | + | 9.10186i | 0.515567 | + | 0.297663i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 42.3926i | − | 1.38490i | −0.721464 | − | 0.692452i | \(-0.756530\pi\) | ||
0.721464 | − | 0.692452i | \(-0.243470\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.1857 | 0.430299 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.6455 | − | 23.6347i | 0.444830 | − | 0.770468i | −0.553210 | − | 0.833042i | \(-0.686597\pi\) |
0.998040 | + | 0.0625733i | \(0.0199307\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.28341 | + | 2.22293i | 0.0417935 | + | 0.0723884i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 15.4321 | + | 0.603907i | 0.502006 | + | 0.0196451i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.0119439 | + | 0.0206875i | 0.000388126 | + | 0.000672253i | 0.866219 | − | 0.499664i | \(-0.166543\pi\) |
−0.865831 | + | 0.500336i | \(0.833210\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.3330 | − | 8.85254i | −0.497732 | − | 0.287366i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 41.6399 | 1.35027 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29.1946 | −0.945706 | −0.472853 | − | 0.881141i | \(-0.656776\pi\) | ||||
−0.472853 | + | 0.881141i | \(0.656776\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.3463 | + | 10.0149i | 0.561314 | + | 0.324075i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 17.0136 | + | 29.4684i | 0.549971 | + | 0.952577i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 24.1416 | − | 12.7063i | 0.779572 | − | 0.410309i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.8851 | + | 25.7818i | 0.480165 | + | 0.831671i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.0815630 | − | 0.141271i | 0.00262833 | − | 0.00455240i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −18.5691 | −0.597760 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.9315i | 0.801744i | 0.916134 | + | 0.400872i | \(0.131293\pi\) | ||||
−0.916134 | + | 0.400872i | \(0.868707\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.26043 | + | 4.76916i | 0.265363 | + | 0.153207i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −36.3162 | + | 20.9672i | −1.16544 | + | 0.672868i | −0.952602 | − | 0.304219i | \(-0.901605\pi\) |
−0.212840 | + | 0.977087i | \(0.568271\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.4713 | − | 34.0418i | 0.688339 | − | 1.09133i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.91307 | + | 5.14596i | −0.285447 | + | 0.164803i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.0465 | − | 17.4011i | 0.321417 | − | 0.556710i | −0.659364 | − | 0.751824i | \(-0.729174\pi\) |
0.980781 | + | 0.195114i | \(0.0625076\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.64003i | 0.212216i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 3.99700i | − | 0.127614i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 21.9887 | − | 38.0855i | 0.701330 | − | 1.21474i | −0.266670 | − | 0.963788i | \(-0.585923\pi\) |
0.968000 | − | 0.250951i | \(-0.0807434\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.35143 | − | 4.24435i | 0.234236 | − | 0.135236i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 14.6761 | − | 23.2683i | 0.467146 | − | 0.740639i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.29494 | − | 3.63439i | 0.200167 | − | 0.115567i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.3615 | − | 7.71429i | −0.424443 | − | 0.245052i | 0.272533 | − | 0.962146i | \(-0.412139\pi\) |
−0.696977 | + | 0.717094i | \(0.745472\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 35.7786i | 1.13540i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.32157 | 0.232109 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.4335 | − | 42.3201i | 0.773817 | − | 1.34029i | −0.161640 | − | 0.986850i | \(-0.551678\pi\) |
0.935457 | − | 0.353441i | \(-0.114988\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 16.9346 | + | 29.3316i | 0.535787 | + | 0.928011i |
(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 | 896.2.q.a.703.8 | yes | 16 | |
4.3 | odd | 2 | 896.2.q.d.703.2 | yes | 16 | ||
7.5 | odd | 6 | inner | 896.2.q.a.831.7 | yes | 16 | |
8.3 | odd | 2 | inner | 896.2.q.a.703.7 | ✓ | 16 | |
8.5 | even | 2 | 896.2.q.d.703.1 | yes | 16 | ||
28.19 | even | 6 | 896.2.q.d.831.1 | yes | 16 | ||
56.5 | odd | 6 | 896.2.q.d.831.2 | yes | 16 | ||
56.19 | even | 6 | inner | 896.2.q.a.831.8 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
896.2.q.a.703.7 | ✓ | 16 | 8.3 | odd | 2 | inner | |
896.2.q.a.703.8 | yes | 16 | 1.1 | even | 1 | trivial | |
896.2.q.a.831.7 | yes | 16 | 7.5 | odd | 6 | inner | |
896.2.q.a.831.8 | yes | 16 | 56.19 | even | 6 | inner | |
896.2.q.d.703.1 | yes | 16 | 8.5 | even | 2 | ||
896.2.q.d.703.2 | yes | 16 | 4.3 | odd | 2 | ||
896.2.q.d.831.1 | yes | 16 | 28.19 | even | 6 | ||
896.2.q.d.831.2 | yes | 16 | 56.5 | odd | 6 |