Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [572,2,Mod(309,572)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(572, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("572.309");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 572 = 2^{2} \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 572.p (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: | \(4.56744299562\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 485.6 | ||
Character | \(\chi\) | \(=\) | 572.485 |
Dual form | 572.2.p.a.309.6 |
$q$-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 \(\left(\mathbb{Z}/572\mathbb{Z}\right)^\times\).
\(n\) | \(287\) | \(353\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −0.308986 | + | 0.535180i | −0.178393 | + | 0.308986i | −0.941330 | − | 0.337486i | \(-0.890423\pi\) |
0.762937 | + | 0.646473i | \(0.223757\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.59217i | 1.60647i | 0.595665 | + | 0.803233i | \(0.296889\pi\) | ||||
−0.595665 | + | 0.803233i | \(0.703111\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.27174 | + | 0.734239i | −0.480672 | + | 0.277516i | −0.720697 | − | 0.693251i | \(-0.756178\pi\) |
0.240024 | + | 0.970767i | \(0.422845\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.30905 | + | 2.26735i | 0.436352 | + | 0.755783i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.866025 | − | 0.500000i | −0.261116 | − | 0.150756i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.34121 | − | 1.35512i | 0.926684 | − | 0.375842i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.92246 | − | 1.10993i | −0.496376 | − | 0.286583i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.71480 | − | 6.43423i | −0.900972 | − | 1.56053i | −0.826235 | − | 0.563326i | \(-0.809522\pi\) |
−0.0747372 | − | 0.997203i | \(-0.523812\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.72329 | + | 3.30435i | −1.31301 | + | 0.758069i | −0.982594 | − | 0.185765i | \(-0.940524\pi\) |
−0.330420 | + | 0.943834i | \(0.607190\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 0.907479i | − | 0.198028i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.07847 | + | 5.33207i | −0.641906 | + | 1.11181i | 0.343101 | + | 0.939299i | \(0.388523\pi\) |
−0.985007 | + | 0.172515i | \(0.944811\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.90366 | −1.58073 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.47184 | −0.668156 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.37531 | − | 2.38211i | 0.255389 | − | 0.442347i | −0.709612 | − | 0.704593i | \(-0.751130\pi\) |
0.965001 | + | 0.262245i | \(0.0844630\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.07233i | 0.731412i | 0.930730 | + | 0.365706i | \(0.119172\pi\) | ||||
−0.930730 | + | 0.365706i | \(0.880828\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.535180 | − | 0.308986i | 0.0931629 | − | 0.0537876i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.63751 | − | 4.56830i | −0.445820 | − | 0.772183i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.03139 | + | 5.21428i | 1.48475 | + | 0.857222i | 0.999850 | − | 0.0173470i | \(-0.00552200\pi\) |
0.484902 | + | 0.874569i | \(0.338855\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.307155 | + | 2.20686i | −0.0491842 | + | 0.353380i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.15608 | + | 2.97686i | 0.805244 | + | 0.464908i | 0.845302 | − | 0.534289i | \(-0.179421\pi\) |
−0.0400573 | + | 0.999197i | \(0.512754\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.23482 | + | 2.13877i | 0.188308 | + | 0.326160i | 0.944686 | − | 0.327975i | \(-0.106366\pi\) |
−0.756378 | + | 0.654135i | \(0.773033\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −8.14470 | + | 4.70234i | −1.21414 | + | 0.700984i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 10.6258i | − | 1.54994i | −0.631999 | − | 0.774969i | \(-0.717765\pi\) | ||
0.631999 | − | 0.774969i | \(-0.282235\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.42179 | + | 4.19466i | −0.345969 | + | 0.599237i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.59129 | 0.642910 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.18535 | −0.574902 | −0.287451 | − | 0.957795i | \(-0.592808\pi\) | ||||
−0.287451 | + | 0.957795i | \(0.592808\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.79608 | − | 3.11091i | 0.242184 | − | 0.419475i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 4.08399i | − | 0.540938i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.01791 | − | 0.587690i | 0.132520 | − | 0.0765107i | −0.432274 | − | 0.901742i | \(-0.642289\pi\) |
0.564795 | + | 0.825232i | \(0.308955\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.509296 | − | 0.882126i | −0.0652087 | − | 0.112945i | 0.831578 | − | 0.555408i | \(-0.187438\pi\) |
−0.896787 | + | 0.442463i | \(0.854105\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.32955 | − | 1.92232i | −0.419484 | − | 0.242189i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.86781 | + | 12.0022i | 0.603777 | + | 1.48869i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.14619 | + | 3.54850i | 0.750876 | + | 0.433518i | 0.826010 | − | 0.563655i | \(-0.190605\pi\) |
−0.0751343 | + | 0.997173i | \(0.523939\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.90241 | − | 3.29508i | −0.229024 | − | 0.396680i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.15016 | − | 0.664048i | 0.136499 | − | 0.0788080i | −0.430195 | − | 0.902736i | \(-0.641555\pi\) |
0.566695 | + | 0.823928i | \(0.308222\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.6727i | 1.24915i | 0.780965 | + | 0.624575i | \(0.214728\pi\) | ||||
−0.780965 | + | 0.624575i | \(0.785272\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.44212 | − | 4.22988i | 0.281992 | − | 0.488425i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.46848 | 0.167349 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.3896 | −1.28143 | −0.640717 | − | 0.767777i | \(-0.721363\pi\) | ||||
−0.640717 | + | 0.767777i | \(0.721363\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.85441 | + | 4.94399i | −0.317157 | + | 0.549332i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 1.48873i | − | 0.163410i | −0.996657 | − | 0.0817048i | \(-0.973964\pi\) | ||
0.996657 | − | 0.0817048i | \(-0.0260365\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 23.1128 | − | 13.3442i | 2.50694 | − | 1.44738i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.849907 | + | 1.47208i | 0.0911196 | + | 0.157824i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.53139 | + | 4.34825i | 0.798326 | + | 0.460914i | 0.842885 | − | 0.538093i | \(-0.180855\pi\) |
−0.0445596 | + | 0.999007i | \(0.514188\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.25416 | + | 4.17660i | −0.341129 | + | 0.437827i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.17943 | − | 1.25829i | −0.225996 | − | 0.130479i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −11.8698 | − | 20.5590i | −1.21781 | − | 2.10931i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.07905 | + | 1.20034i | −0.211096 | + | 0.121876i | −0.601820 | − | 0.798631i | \(-0.705558\pi\) |
0.390725 | + | 0.920508i | \(0.372224\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 2.61811i | − | 0.263130i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.07520 | − | 7.05845i | 0.405498 | − | 0.702342i | −0.588882 | − | 0.808219i | \(-0.700432\pi\) |
0.994379 | + | 0.105877i | \(0.0337649\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.6538 | 1.83801 | 0.919004 | − | 0.394247i | \(-0.128995\pi\) | ||||
0.919004 | + | 0.394247i | \(0.128995\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.25982 | 0.318126 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.37610 | − | 7.57962i | 0.423053 | − | 0.732750i | −0.573183 | − | 0.819427i | \(-0.694292\pi\) |
0.996236 | + | 0.0866777i | \(0.0276250\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 9.88343i | − | 0.946661i | −0.880885 | − | 0.473331i | \(-0.843052\pi\) | ||
0.880885 | − | 0.473331i | \(-0.156948\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.58115 | + | 3.22228i | −0.529740 | + | 0.305845i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.42305 | + | 2.46480i | 0.133869 | + | 0.231869i | 0.925165 | − | 0.379565i | \(-0.123926\pi\) |
−0.791296 | + | 0.611434i | \(0.790593\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −19.1537 | − | 11.0584i | −1.78609 | − | 1.03120i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.44635 | + | 5.80176i | 0.688415 | + | 0.536373i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.44852 | + | 5.45511i | 0.866144 | + | 0.500069i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.500000 | + | 0.866025i | 0.0454545 | + | 0.0787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.18632 | + | 1.83962i | −0.287301 | + | 0.165873i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 10.4304i | − | 0.932926i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.74628 | + | 3.02465i | −0.154957 | + | 0.268394i | −0.933044 | − | 0.359763i | \(-0.882857\pi\) |
0.778086 | + | 0.628158i | \(0.216191\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.52617 | −0.134372 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.7087 | 1.72195 | 0.860977 | − | 0.508644i | \(-0.169853\pi\) | ||||
0.860977 | + | 0.508644i | \(0.169853\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.85236 | − | 8.40453i | 0.420753 | − | 0.728765i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 12.4714i | − | 1.07337i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.0911 | + | 5.82613i | −0.862145 | + | 0.497760i | −0.864730 | − | 0.502237i | \(-0.832510\pi\) |
0.00258506 | + | 0.999997i | \(0.499177\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.33648 | + | 4.04691i | 0.198178 | + | 0.343254i | 0.947938 | − | 0.318456i | \(-0.103164\pi\) |
−0.749760 | + | 0.661710i | \(0.769831\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.68674 | + | 3.28324i | 0.478910 | + | 0.276499i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.57113 | − | 0.497036i | −0.298633 | − | 0.0415643i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.55695 | + | 4.94036i | 0.710616 | + | 0.410274i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.49660 | − | 2.59218i | −0.123437 | − | 0.213800i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.7149 | + | 10.2277i | −1.45126 | + | 0.837885i | −0.998553 | − | 0.0537753i | \(-0.982875\pi\) |
−0.452706 | + | 0.891660i | \(0.649541\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.5794i | 1.59335i | 0.604408 | + | 0.796675i | \(0.293410\pi\) | ||||
−0.604408 | + | 0.796675i | \(0.706590\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.72576 | − | 16.8455i | 0.786281 | − | 1.36188i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −14.6285 | −1.17499 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.9554 | 1.35319 | 0.676594 | − | 0.736357i | \(-0.263455\pi\) | ||||
0.676594 | + | 0.736357i | \(0.263455\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.29322 | − | 2.23992i | 0.102559 | − | 0.177637i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 9.04134i | − | 0.712558i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.5196 | − | 11.8470i | 1.60722 | − | 0.927929i | 0.617232 | − | 0.786782i | \(-0.288254\pi\) |
0.989989 | − | 0.141147i | \(-0.0450792\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.10993 | + | 1.92246i | 0.0864080 | + | 0.149663i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.45956 | + | 5.46148i | 0.732003 | + | 0.422622i | 0.819154 | − | 0.573573i | \(-0.194443\pi\) |
−0.0871516 | + | 0.996195i | \(0.527776\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.32731 | − | 9.05545i | 0.717485 | − | 0.696573i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −14.9842 | − | 8.65114i | −1.14587 | − | 0.661569i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.69744 | − | 4.67210i | −0.205083 | − | 0.355214i | 0.745076 | − | 0.666979i | \(-0.232413\pi\) |
−0.950159 | + | 0.311766i | \(0.899080\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.0514 | − | 5.80317i | 0.759814 | − | 0.438679i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.726353i | 0.0545960i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.2109 | + | 19.4179i | −0.837944 | + | 1.45136i | 0.0536663 | + | 0.998559i | \(0.482909\pi\) |
−0.891611 | + | 0.452803i | \(0.850424\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.61937 | 0.417684 | 0.208842 | − | 0.977949i | \(-0.433030\pi\) | ||||
0.208842 | + | 0.977949i | \(0.433030\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.629462 | 0.0465312 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −18.7305 | + | 32.4423i | −1.37710 | + | 2.38520i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.42960i | 0.543307i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.41527 | − | 2.54916i | 0.321164 | − | 0.185424i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.07987 | − | 10.5306i | −0.439924 | − | 0.761971i | 0.557759 | − | 0.830003i | \(-0.311661\pi\) |
−0.997683 | + | 0.0680320i | \(0.978328\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.3554 | + | 8.28808i | 1.03332 | + | 0.596589i | 0.917935 | − | 0.396731i | \(-0.129856\pi\) |
0.115388 | + | 0.993320i | \(0.463189\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7.92741 | − | 1.10335i | −0.567693 | − | 0.0790127i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.83822 | + | 5.68010i | 0.700944 | + | 0.404690i | 0.807699 | − | 0.589595i | \(-0.200713\pi\) |
−0.106755 | + | 0.994285i | \(0.534046\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.559399 | − | 0.968908i | −0.0396548 | − | 0.0686841i | 0.845517 | − | 0.533949i | \(-0.179292\pi\) |
−0.885172 | + | 0.465265i | \(0.845959\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.79817 | + | 2.19288i | −0.267903 | + | 0.154674i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.03924i | 0.283499i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.6934 | + | 18.5215i | −0.746859 | + | 1.29360i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −16.1196 | −1.12039 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.60869 | 0.457133 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.25639 | + | 10.8364i | −0.430708 | + | 0.746008i | −0.996934 | − | 0.0782419i | \(-0.975069\pi\) |
0.566227 | + | 0.824250i | \(0.308403\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.820727i | 0.0562353i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.68282 | + | 4.43568i | −0.523964 | + | 0.302511i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.99006 | − | 5.17894i | −0.202979 | − | 0.351569i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.71184 | − | 3.29773i | −0.385970 | − | 0.222840i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −21.1311 | − | 16.4641i | −1.42143 | − | 1.10749i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.49158 | + | 3.74792i | 0.434708 | + | 0.250979i | 0.701350 | − | 0.712817i | \(-0.252581\pi\) |
−0.266642 | + | 0.963796i | \(0.585914\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −10.3463 | − | 17.9204i | −0.689755 | − | 1.19469i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.7364 | − | 9.66276i | 1.11083 | − | 0.641340i | 0.171788 | − | 0.985134i | \(-0.445046\pi\) |
0.939045 | + | 0.343794i | \(0.111712\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 18.8527i | − | 1.24582i | −0.782293 | − | 0.622910i | \(-0.785950\pi\) | ||
0.782293 | − | 0.622910i | \(-0.214050\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.453740 | + | 0.785900i | −0.0298539 | + | 0.0517084i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.8404 | −1.03774 | −0.518868 | − | 0.854854i | \(-0.673646\pi\) | ||||
−0.518868 | + | 0.854854i | \(0.673646\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 38.1698 | 2.48992 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.51924 | − | 6.09550i | 0.228599 | − | 0.395945i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.3455i | 0.863246i | 0.902054 | + | 0.431623i | \(0.142059\pi\) | ||||
−0.902054 | + | 0.431623i | \(0.857941\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.7823 | − | 8.53454i | 0.952209 | − | 0.549758i | 0.0584428 | − | 0.998291i | \(-0.481386\pi\) |
0.893767 | + | 0.448532i | \(0.148053\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.97171 | − | 12.0754i | −0.447235 | − | 0.774634i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −15.0679 | − | 8.69946i | −0.962653 | − | 0.555788i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.6449 | + | 18.7962i | −0.931834 | + | 1.19598i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.796740 | + | 0.459998i | 0.0504913 | + | 0.0291512i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.13738 | − | 10.6303i | −0.387388 | − | 0.670976i | 0.604709 | − | 0.796446i | \(-0.293289\pi\) |
−0.992097 | + | 0.125470i | \(0.959956\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.33207 | − | 3.07847i | 0.335225 | − | 0.193542i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 16.4927i | 1.03281i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.1767 | + | 22.8226i | −0.821937 | + | 1.42364i | 0.0823006 | + | 0.996608i | \(0.473773\pi\) |
−0.904238 | + | 0.427029i | \(0.859560\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −15.3141 | −0.951572 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.20145 | 0.445758 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.24704 | − | 9.08814i | 0.323546 | − | 0.560399i | −0.657671 | − | 0.753306i | \(-0.728458\pi\) |
0.981217 | + | 0.192907i | \(0.0617915\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 15.0345i | − | 0.923560i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.65419 | + | 2.68710i | −0.284832 | + | 0.164448i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.24887 | − | 16.0195i | −0.563914 | − | 0.976727i | −0.997150 | − | 0.0754468i | \(-0.975962\pi\) |
0.433236 | − | 0.901280i | \(-0.357372\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.1061 | − | 9.29886i | −0.978376 | − | 0.564865i | −0.0765963 | − | 0.997062i | \(-0.524405\pi\) |
−0.901779 | + | 0.432197i | \(0.857739\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.22974 | − | 3.03207i | −0.0744273 | − | 0.183510i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.84477 | + | 3.95183i | 0.412755 | + | 0.238304i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.47146 | + | 11.2089i | 0.388832 | + | 0.673477i | 0.992293 | − | 0.123916i | \(-0.0395452\pi\) |
−0.603461 | + | 0.797393i | \(0.706212\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.23339 | + | 5.33090i | −0.552789 | + | 0.319153i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.19174i | 0.488678i | 0.969690 | + | 0.244339i | \(0.0785710\pi\) | ||||
−0.969690 | + | 0.244339i | \(0.921429\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.13215 | − | 3.69299i | 0.126743 | − | 0.219525i | −0.795670 | − | 0.605731i | \(-0.792881\pi\) |
0.922413 | + | 0.386205i | \(0.126214\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 14.6704 | 0.868998 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.74292 | −0.516078 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −19.0995 | + | 33.0813i | −1.12350 | + | 1.94596i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 1.48356i | − | 0.0869676i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.23456 | − | 2.44482i | 0.247386 | − | 0.142828i | −0.371181 | − | 0.928561i | \(-0.621047\pi\) |
0.618567 | + | 0.785732i | \(0.287714\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.11108 | + | 3.65650i | 0.122912 | + | 0.212890i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.00670 | + | 1.73592i | 0.174466 | + | 0.100728i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.06023 | + | 21.9872i | −0.176978 | + | 1.27156i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.14074 | − | 1.81331i | −0.181029 | − | 0.104517i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.51836 | + | 4.36193i | 0.144676 | + | 0.250586i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.16874 | − | 1.82948i | 0.181442 | − | 0.104755i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.7105i | 1.06787i | 0.845526 | + | 0.533933i | \(0.179287\pi\) | ||||
−0.845526 | + | 0.533933i | \(0.820713\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.76375 | + | 9.98312i | −0.327889 | + | 0.567920i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.84936 | −0.501801 | −0.250901 | − | 0.968013i | \(-0.580727\pi\) | ||||
−0.250901 | + | 0.968013i | \(0.580727\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.52830 | 0.199431 | 0.0997157 | − | 0.995016i | \(-0.468207\pi\) | ||||
0.0997157 | + | 0.995016i | \(0.468207\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.90529 | − | 11.9603i | 0.389069 | − | 0.673887i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 23.1339i | − | 1.29933i | −0.760222 | − | 0.649664i | \(-0.774910\pi\) | ||
0.760222 | − | 0.649664i | \(-0.225090\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.38211 | + | 1.37531i | −0.133373 | + | 0.0770028i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.70431 | + | 4.68400i | 0.150940 | + | 0.261435i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 42.5218 | + | 24.5500i | 2.36598 | + | 1.36600i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −26.4078 | + | 10.7104i | −1.46484 | + | 0.594106i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.28942 | + | 3.05385i | 0.292505 | + | 0.168878i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.80191 | + | 13.5133i | 0.430133 | + | 0.745013i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.2579 | + | 7.65443i | −0.728718 | + | 0.420725i | −0.817953 | − | 0.575285i | \(-0.804891\pi\) |
0.0892351 | + | 0.996011i | \(0.471558\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 27.3031i | 1.49620i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.7468 | + | 22.0781i | −0.696433 | + | 1.20626i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.8616 | −1.02746 | −0.513729 | − | 0.857952i | \(-0.671736\pi\) | ||||
−0.513729 | + | 0.857952i | \(0.671736\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.75881 | −0.0955256 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.03616 | − | 3.52674i | 0.110265 | − | 0.190984i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 17.3920i | − | 0.939081i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 11.8365 | − | 6.83378i | 0.637254 | − | 0.367919i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.57133 | − | 11.3819i | −0.352768 | − | 0.611012i | 0.633966 | − | 0.773361i | \(-0.281426\pi\) |
−0.986733 | + | 0.162350i | \(0.948093\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.67289 | + | 0.965846i | 0.0895480 | + | 0.0517005i | 0.544105 | − | 0.839017i | \(-0.316869\pi\) |
−0.454557 | + | 0.890717i | \(0.650203\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.6001 | + | 4.70475i | −0.619169 | + | 0.251121i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.08923 | + | 4.67032i | 0.430546 | + | 0.248576i | 0.699579 | − | 0.714555i | \(-0.253371\pi\) |
−0.269033 | + | 0.963131i | \(0.586704\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.38537 | + | 4.13158i | 0.126602 | + | 0.219282i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.83893 | + | 3.37111i | −0.309029 | + | 0.178418i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.11468i | 0.322720i | 0.986896 | + | 0.161360i | \(0.0515881\pi\) | ||||
−0.986896 | + | 0.161360i | \(0.948412\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.3374 | − | 21.3690i | 0.649337 | − | 1.12468i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.617973 | −0.0324352 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −38.3383 | −2.00672 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.50143 | − | 14.7249i | 0.443771 | − | 0.768634i | −0.554195 | − | 0.832387i | \(-0.686974\pi\) |
0.997966 | + | 0.0637533i | \(0.0203071\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 15.5875i | 0.811454i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.32267 | − | 3.07305i | 0.276339 | − | 0.159545i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.23700 | − | 2.14254i | −0.0640493 | − | 0.110937i | 0.832223 | − | 0.554442i | \(-0.187068\pi\) |
−0.896272 | + | 0.443505i | \(0.853735\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.58216 | + | 3.22286i | 0.288261 | + | 0.166428i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.36716 | − | 9.82285i | 0.0704124 | − | 0.505902i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.6424 | − | 12.4952i | −1.11169 | − | 0.641837i | −0.172427 | − | 0.985022i | \(-0.555161\pi\) |
−0.939268 | + | 0.343185i | \(0.888494\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.07915 | − | 1.86915i | −0.0552868 | − | 0.0957595i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 25.6675 | − | 14.8192i | 1.31155 | − | 0.757224i | 0.329197 | − | 0.944261i | \(-0.393222\pi\) |
0.982353 | + | 0.187038i | \(0.0598886\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.27502i | 0.268840i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.23289 | + | 5.59954i | −0.164337 | + | 0.284641i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.9078 | −1.06007 | −0.530034 | − | 0.847977i | \(-0.677821\pi\) | ||||
−0.530034 | + | 0.847977i | \(0.677821\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 45.7437 | 2.31336 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.08971 | + | 10.5477i | −0.307185 | + | 0.532060i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 40.9134i | − | 2.05858i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.70414 | − | 0.983887i | 0.0855284 | − | 0.0493799i | −0.456626 | − | 0.889659i | \(-0.650942\pi\) |
0.542154 | + | 0.840279i | \(0.317609\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.99862 | + | 5.19377i | 0.150119 | + | 0.260014i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.65134 | + | 2.68545i | 0.232277 | + | 0.134105i | 0.611622 | − | 0.791150i | \(-0.290517\pi\) |
−0.379345 | + | 0.925255i | \(0.623851\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.51849 | + | 13.6065i | 0.274895 | + | 0.677788i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −17.7596 | − | 10.2535i | −0.882483 | − | 0.509502i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.21428 | − | 9.03139i | −0.258462 | − | 0.447669i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.4464 | − | 6.03123i | 0.516541 | − | 0.298225i | −0.218977 | − | 0.975730i | \(-0.570272\pi\) |
0.735518 | + | 0.677505i | \(0.236939\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 7.20077i | − | 0.355188i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.863010 | + | 1.49478i | −0.0424659 | + | 0.0735532i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.34777 | 0.262512 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.88777 | −0.141415 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.60502 | − | 6.24408i | 0.176117 | − | 0.305043i | −0.764430 | − | 0.644706i | \(-0.776980\pi\) |
0.940547 | + | 0.339663i | \(0.110313\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 14.3016i | − | 0.697018i | −0.937305 | − | 0.348509i | \(-0.886688\pi\) | ||
0.937305 | − | 0.348509i | \(-0.113312\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 24.0925 | − | 13.9098i | 1.17142 | − | 0.676318i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 29.3605 | + | 50.8539i | 1.42420 | + | 2.46678i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.29538 | + | 0.747890i | 0.0626880 | + | 0.0361929i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.36943 | − | 1.75762i | 0.0661169 | − | 0.0848586i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.8506 | + | 7.41932i | 0.618993 | + | 0.357376i | 0.776477 | − | 0.630146i | \(-0.217005\pi\) |
−0.157484 | + | 0.987522i | \(0.550338\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.25188 | − | 16.0247i | −0.444617 | − | 0.770099i | 0.553408 | − | 0.832910i | \(-0.313327\pi\) |
−0.998025 | + | 0.0628107i | \(0.979994\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.28796 | + | 3.05301i | −0.253538 | + | 0.146380i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 40.6894i | − | 1.94644i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.66147 | + | 9.80596i | −0.270207 | + | 0.468013i | −0.968915 | − | 0.247395i | \(-0.920426\pi\) |
0.698707 | + | 0.715408i | \(0.253759\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12.6810 | −0.603857 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.1660 | −1.24318 | −0.621592 | − | 0.783341i | \(-0.713514\pi\) | ||||
−0.621592 | + | 0.783341i | \(0.713514\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15.6196 | + | 27.0540i | −0.740442 | + | 1.28248i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 12.6409i | − | 0.597892i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.83139 | + | 2.78940i | −0.228007 | + | 0.131640i | −0.609652 | − | 0.792669i | \(-0.708691\pi\) |
0.381645 | + | 0.924309i | \(0.375358\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.97686 | − | 5.15608i | −0.140175 | − | 0.242790i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.4785 | − | 6.04977i | −0.492324 | − | 0.284243i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −15.0030 | − | 11.6895i | −0.703353 | − | 0.548012i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.6844 | − | 18.2930i | −1.48213 | − | 0.855711i | −0.482340 | − | 0.875984i | \(-0.660213\pi\) |
−0.999794 | + | 0.0202735i | \(0.993546\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 12.8972 | + | 22.3386i | 0.601989 | + | 1.04268i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.49797 | − | 2.01955i | 0.162917 | − | 0.0940599i | −0.416325 | − | 0.909216i | \(-0.636682\pi\) |
0.579242 | + | 0.815156i | \(0.303349\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 10.7499i | − | 0.499590i | −0.968299 | − | 0.249795i | \(-0.919637\pi\) | ||
0.968299 | − | 0.249795i | \(-0.0803632\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.52000 | − | 7.82887i | 0.209610 | − | 0.363055i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −27.8116 | −1.28697 | −0.643483 | − | 0.765460i | \(-0.722511\pi\) | ||||
−0.643483 | + | 0.765460i | \(0.722511\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.4218 | −0.481234 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.23898 | + | 9.07419i | −0.241400 | + | 0.418116i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 2.46964i | − | 0.113554i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 45.2350 | − | 26.1164i | 2.07552 | − | 1.19830i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.47885 | − | 9.48965i | −0.250859 | − | 0.434501i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.28513 | − | 4.20607i | −0.332866 | − | 0.192180i | 0.324247 | − | 0.945972i | \(-0.394889\pi\) |
−0.657113 | + | 0.753792i | \(0.728222\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 37.2417 | + | 5.18337i | 1.69807 | + | 0.236341i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.83875 | + | 2.79365i | 0.220171 | + | 0.127116i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.31182 | − | 7.46830i | −0.195790 | − | 0.339118i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.608545 | − | 0.351343i | 0.0275758 | − | 0.0159209i | −0.486149 | − | 0.873876i | \(-0.661599\pi\) |
0.513725 | + | 0.857955i | \(0.328265\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 14.6423i | 0.662145i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.2907 | − | 36.8767i | 0.960838 | − | 1.66422i | 0.240434 | − | 0.970666i | \(-0.422710\pi\) |
0.720404 | − | 0.693554i | \(-0.243956\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −20.4361 | −0.920395 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9.40469 | 0.422709 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.975139 | + | 1.68899i | −0.0437410 | + | 0.0757616i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.6730i | 0.791154i | 0.918433 | + | 0.395577i | \(0.129455\pi\) | ||||
−0.918433 | + | 0.395577i | \(0.870545\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.84575 | + | 3.37505i | −0.261169 | + | 0.150786i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.15000 | − | 10.6521i | −0.274215 | − | 0.474954i | 0.695722 | − | 0.718311i | \(-0.255085\pi\) |
−0.969937 | + | 0.243357i | \(0.921751\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 25.3551 | + | 14.6388i | 1.12829 | + | 0.651418i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.96429 | + | 7.78980i | 0.0872370 | + | 0.345957i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.3876 | − | 8.88404i | −0.682044 | − | 0.393778i | 0.118581 | − | 0.992944i | \(-0.462166\pi\) |
−0.800625 | + | 0.599166i | \(0.795499\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.83635 | − | 13.5730i | −0.346660 | − | 0.600432i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 19.8704 | − | 11.4722i | 0.877297 | − | 0.506508i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 67.0074i | 2.95270i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.31292 | + | 9.20225i | −0.233662 | + | 0.404715i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.33389 | 0.146341 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 35.3705 | 1.54961 | 0.774806 | − | 0.632200i | \(-0.217848\pi\) | ||||
0.774806 | + | 0.632200i | \(0.217848\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.82895 | − | 17.0242i | 0.429790 | − | 0.744418i | −0.567065 | − | 0.823673i | \(-0.691921\pi\) |
0.996854 | + | 0.0792556i | \(0.0252543\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 7.17241i | 0.313030i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 26.2023 | − | 15.1279i | 1.14139 | − | 0.658982i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.45400 | − | 12.9107i | −0.324087 | − | 0.561335i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.66500 | + | 1.53864i | 0.115651 | + | 0.0667712i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 21.2615 | + | 2.95922i | 0.920939 | + | 0.128178i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 27.2273 | + | 15.7197i | 1.17714 | + | 0.679620i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.92805 | − | 11.9997i | −0.298967 | − | 0.517827i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.19466 | − | 2.42179i | 0.180677 | − | 0.104314i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 16.5141i | − | 0.709995i | −0.934867 | − | 0.354998i | \(-0.884482\pi\) | ||
0.934867 | − | 0.354998i | \(-0.115518\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.73631 | + | 3.00737i | −0.0745121 | + | 0.129059i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 35.5029 | 1.52078 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.4780 | 0.576278 | 0.288139 | − | 0.957589i | \(-0.406964\pi\) | ||||
0.288139 | + | 0.957589i | \(0.406964\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.33339 | − | 2.30950i | 0.0569078 | − | 0.0985672i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18.1781i | 0.774411i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.4846 | − | 8.36271i | 0.615949 | − | 0.355619i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −11.5750 | − | 20.0484i | −0.491330 | − | 0.851008i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.6588 | + | 9.61798i | 0.705857 | + | 0.407527i | 0.809525 | − | 0.587085i | \(-0.199725\pi\) |
−0.103668 | + | 0.994612i | \(0.533058\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.02408 | + | 5.47275i | 0.297087 | + | 0.231473i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.97618 | − | 2.29565i | −0.167874 | − | 0.0969223i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.0896 | − | 34.7962i | −0.846676 | − | 1.46649i | −0.884158 | − | 0.467188i | \(-0.845267\pi\) |
0.0374825 | − | 0.999297i | \(-0.488066\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.85396 | + | 5.11184i | −0.372489 | + | 0.215057i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 8.38329i | − | 0.352065i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.36255 | + | 7.55615i | −0.182887 | + | 0.316770i | −0.942863 | − | 0.333182i | \(-0.891878\pi\) |
0.759975 | + | 0.649952i | \(0.225211\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.2638 | 1.43389 | 0.716947 | − | 0.697128i | \(-0.245539\pi\) | ||||
0.716947 | + | 0.697128i | \(0.245539\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.51439 | 0.313918 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 24.3312 | − | 42.1429i | 1.01468 | − | 1.75748i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.1689i | 1.38084i | 0.723409 | + | 0.690420i | \(0.242574\pi\) | ||||
−0.723409 | + | 0.690420i | \(0.757426\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.87123 | + | 5.12181i | −0.368676 | + | 0.212855i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.09309 | + | 1.89328i | 0.0453488 | + | 0.0785464i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.62462 | + | 2.09267i | 0.150116 | + | 0.0866697i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −20.8409 | + | 26.7485i | −0.861664 | + | 1.10592i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.5975 | + | 12.4693i | 0.891424 | + | 0.514664i | 0.874408 | − | 0.485191i | \(-0.161250\pi\) |
0.0170158 | + | 0.999855i | \(0.494583\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.4564 | − | 23.3071i | −0.554461 | − | 0.960354i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.07975 | + | 3.51015i | −0.250088 | + | 0.144388i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.29002i | 0.258300i | 0.991625 | + | 0.129150i | \(0.0412249\pi\) | ||||
−0.991625 | + | 0.129150i | \(0.958775\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −19.5956 | + | 33.9407i | −0.803343 | + | 1.39143i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.691387 | 0.0282966 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 40.7583 | 1.66534 | 0.832670 | − | 0.553770i | \(-0.186811\pi\) | ||||
0.832670 | + | 0.553770i | \(0.186811\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.92944 | + | 17.1983i | −0.405030 | + | 0.701533i | −0.994325 | − | 0.106385i | \(-0.966072\pi\) |
0.589295 | + | 0.807918i | \(0.299406\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 18.5807i | 0.756666i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.11091 | + | 1.79608i | −0.126476 | + | 0.0730212i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.08744 | + | 14.0079i | 0.328259 | + | 0.568561i | 0.982166 | − | 0.188013i | \(-0.0602048\pi\) |
−0.653908 | + | 0.756574i | \(0.726871\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.16172 | − | 1.24807i | −0.0875973 | − | 0.0505743i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14.3993 | − | 35.5031i | −0.582532 | − | 1.43630i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.64700 | + | 0.950895i | 0.0665216 | + | 0.0384063i | 0.532892 | − | 0.846183i | \(-0.321105\pi\) |
−0.466370 | + | 0.884590i | \(0.654439\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.60822 | − | 11.4458i | −0.266469 | − | 0.461538i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.4208 | − | 7.17115i | 0.500043 | − | 0.288700i | −0.228689 | − | 0.973500i | \(-0.573444\pi\) |
0.728731 | + | 0.684800i | \(0.240110\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 5.40168i | − | 0.217112i | −0.994090 | − | 0.108556i | \(-0.965377\pi\) | ||
0.994090 | − | 0.108556i | \(-0.0346226\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.6880 | − | 18.5121i | 0.428893 | − | 0.742865i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.7706 | −0.511644 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.05046 | −0.0820184 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.04200 | + | 3.53684i | −0.0815494 | + | 0.141248i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 77.4800i | − | 3.08933i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.6314 | + | 12.4889i | −0.861131 | + | 0.497174i | −0.864391 | − | 0.502821i | \(-0.832296\pi\) |
0.00325992 | + | 0.999995i | \(0.498962\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.86628 | − | 6.69659i | −0.153671 | − | 0.266166i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.8650 | − | 6.27293i | −0.431166 | − | 0.248934i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.40743 | + | 17.2970i | −0.0953859 | + | 0.685333i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.01126 | + | 1.73855i | 0.119123 | + | 0.0687760i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.5883 | − | 20.0716i | −0.457711 | − | 0.792779i | 0.541128 | − | 0.840940i | \(-0.317997\pi\) |
−0.998840 | + | 0.0481607i | \(0.984664\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −33.3510 | + | 19.2552i | −1.31524 | + | 0.759352i | −0.982958 | − | 0.183830i | \(-0.941150\pi\) |
−0.332278 | + | 0.943182i | \(0.607817\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 5.48226i | − | 0.215864i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.24614 | − | 12.5507i | 0.284875 | − | 0.493418i | −0.687704 | − | 0.725991i | \(-0.741381\pi\) |
0.972579 | + | 0.232573i | \(0.0747145\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.17538 | −0.0461377 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.69555 | 0.144840 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.9699 | − | 39.7851i | 0.898882 | − | 1.55691i | 0.0699567 | − | 0.997550i | \(-0.477714\pi\) |
0.828925 | − | 0.559359i | \(-0.188953\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 70.7968i | 2.76626i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −24.1988 | + | 13.9712i | −0.944087 | + | 0.545069i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.6798 | + | 30.6223i | 0.688707 | + | 1.19288i | 0.972256 | + | 0.233918i | \(0.0751549\pi\) |
−0.283549 | + | 0.958958i | \(0.591512\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.0952 | + | 5.82848i | 0.392659 | + | 0.226702i | 0.683311 | − | 0.730127i | \(-0.260539\pi\) |
−0.290653 | + | 0.956829i | \(0.593872\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 15.3405 | − | 6.22174i | 0.595774 | − | 0.241632i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 30.1905 | + | 17.4305i | 1.17074 | + | 0.675925i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.46774 | + | 14.6666i | 0.327872 | + | 0.567891i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.01162 | + | 2.31611i | −0.155098 | + | 0.0895460i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.01859i | 0.0393223i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.2170 | − | 29.8207i | 0.663666 | − | 1.14950i | −0.315979 | − | 0.948766i | \(-0.602333\pi\) |
0.979645 | − | 0.200738i | \(-0.0643339\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 27.4402 | 1.05617 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.03487 | −0.116640 | −0.0583198 | − | 0.998298i | \(-0.518574\pi\) | ||||
−0.0583198 | + | 0.998298i | \(0.518574\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.76267 | − | 3.05304i | 0.0676452 | − | 0.117165i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.9426i | 0.457643i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.9798 | + | 8.07126i | −0.534923 | + | 0.308838i | −0.743019 | − | 0.669270i | \(-0.766607\pi\) |
0.208096 | + | 0.978108i | \(0.433273\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20.9284 | − | 36.2491i | −0.799634 | − | 1.38501i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.0896 | + | 5.82522i | 0.384942 | + | 0.222246i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13.9841 | + | 5.67164i | −0.532752 | + | 0.216072i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.0825 | + | 22.5643i | 1.48677 | + | 0.858387i | 0.999886 | − | 0.0150798i | \(-0.00480022\pi\) |
0.486884 | + | 0.873467i | \(0.338134\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.92232 | + | 3.32955i | 0.0730228 | + | 0.126479i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14.5372 | + | 8.39304i | −0.551426 | + | 0.318366i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 44.2339i | − | 1.67548i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.89445 | − | 8.47744i | 0.185125 | − | 0.320646i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.5529 | −0.965121 | −0.482561 | − | 0.875863i | \(-0.660293\pi\) | ||||
−0.482561 | + | 0.875863i | \(0.660293\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −68.9191 | −2.59933 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −11.7939 | + | 20.4277i | −0.444186 | + | 0.769352i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.9687i | 0.450129i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.0192 | + | 5.78456i | −0.376277 | + | 0.217244i | −0.676197 | − | 0.736721i | \(-0.736373\pi\) |
0.299920 | + | 0.953964i | \(0.403040\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.9096 | − | 25.8243i | −0.559156 | − | 0.968486i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −21.7140 | − | 12.5366i | −0.813194 | − | 0.469498i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.78544 | − | 12.8281i | 0.0667716 | − | 0.479743i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.14222 | − | 4.12357i | −0.266731 | − | 0.153997i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.53709 | − | 4.39438i | −0.0946176 | − | 0.163883i | 0.814831 | − | 0.579698i | \(-0.196830\pi\) |
−0.909449 | + | 0.415816i | \(0.863496\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23.7227 | + | 13.6963i | −0.883480 | + | 0.510077i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.5482i | 0.392293i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10.8700 | + | 18.8274i | −0.403702 | + | 0.699233i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 44.7840 | 1.66095 | 0.830474 | − | 0.557058i | \(-0.188070\pi\) | ||||
0.830474 | + | 0.557058i | \(0.188070\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.50983 | −0.315179 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.17423 | − | 15.8902i | 0.339321 | − | 0.587721i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 36.9408i | − | 1.36444i | −0.731147 | − | 0.682220i | \(-0.761015\pi\) | ||
0.731147 | − | 0.682220i | \(-0.238985\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9.31155 | − | 5.37603i | 0.343462 | − | 0.198298i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.54850 | − | 6.14619i | −0.130711 | − | 0.226398i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.39244 | − | 3.11333i | −0.198364 | − | 0.114526i | 0.397528 | − | 0.917590i | \(-0.369868\pi\) |
−0.595892 | + | 0.803064i | \(0.703201\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.53429 | − | 13.6455i | −0.203307 | − | 0.501278i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.0738 | − | 8.70285i | −0.553003 | − | 0.319277i | 0.197329 | − | 0.980337i | \(-0.436773\pi\) |
−0.750332 | + | 0.661061i | \(0.770107\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −36.7395 | − | 63.6348i | −1.34603 | − | 2.33140i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.37548 | − | 1.94883i | 0.123502 | − | 0.0713040i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.8524i | 0.469616i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.3057 | + | 21.3140i | −0.449040 | + | 0.777759i | −0.998324 | − | 0.0578762i | \(-0.981567\pi\) |
0.549284 | + | 0.835636i | \(0.314900\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.58547 | 0.276430 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −70.3325 | −2.55966 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.5596 | − | 23.4859i | 0.492832 | − | 0.853610i | −0.507134 | − | 0.861867i | \(-0.669295\pi\) |
0.999966 | + | 0.00825749i | \(0.00262847\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.80483i | 0.138106i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −46.6440 | + | 26.9299i | −1.69084 | + | 0.976209i | −0.737006 | + | 0.675886i | \(0.763761\pi\) |
−0.953838 | + | 0.300323i | \(0.902906\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.25680 | + | 12.5692i | 0.262714 | + | 0.455034i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 60.5119 | + | 34.9366i | 2.18781 | + | 1.26313i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.60465 | − | 3.34298i | 0.0940486 | − | 0.120708i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35.9602 | − | 20.7616i | −1.29676 | − | 0.748683i | −0.316914 | − | 0.948454i | \(-0.602647\pi\) |
−0.979842 | + | 0.199772i | \(0.935980\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.14281 | − | 14.1038i | −0.293256 | − | 0.507935i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.7613 | − | 10.8318i | 0.674796 | − | 0.389594i | −0.123095 | − | 0.992395i | \(-0.539282\pi\) |
0.797891 | + | 0.602801i | \(0.205949\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 32.1863i | − | 1.15617i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.73185 | − | 8.19580i | 0.169754 | − | 0.294023i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −39.3464 | −1.40973 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.32810 | −0.0475230 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.77487 | + | 8.27031i | −0.170640 | + | 0.295557i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 60.9066i | 2.17385i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.109582 | + | 0.0632672i | −0.00390618 | + | 0.00225523i | −0.501952 | − | 0.864896i | \(-0.667385\pi\) |
0.498046 | + | 0.867151i | \(0.334051\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.24253 | + | 5.61622i | 0.115437 | + | 0.199943i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.61950 | − | 2.08972i | −0.128695 | − | 0.0743019i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.89705 | − | 2.25721i | −0.102877 | − | 0.0801559i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.04615 | + | 4.64545i | 0.285367 | + | 0.164757i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13.5318 | + | 23.4378i | 0.479322 | + | 0.830211i | 0.999719 | − | 0.0237140i | \(-0.00754911\pi\) |
−0.520396 | + | 0.853925i | \(0.674216\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −68.3691 | + | 39.4729i | −2.41872 | + | 1.39645i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 22.7684i | 0.804482i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.33637 | − | 9.24287i | 0.188317 | − | 0.326174i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 32.4780 | 1.14470 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.4311 | 0.402394 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.18619 | + | 7.25069i | −0.147179 | + | 0.254921i | −0.930184 | − | 0.367095i | \(-0.880353\pi\) |
0.783005 | + | 0.622015i | \(0.213686\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.13534i | 0.110097i | 0.998484 | + | 0.0550483i | \(0.0175313\pi\) | ||||
−0.998484 | + | 0.0550483i | \(0.982469\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.95313 | − | 5.74644i | 0.349071 | − | 0.201536i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 42.5564 | + | 73.7099i | 1.49069 | + | 2.58194i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.1345 | − | 8.16054i | −0.494503 | − | 0.285501i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −13.7297 | − | 1.91092i | −0.479754 | − | 0.0667731i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 45.7774 | + | 26.4296i | 1.59764 | + | 0.922399i | 0.991940 | + | 0.126707i | \(0.0404409\pi\) |
0.605702 | + | 0.795692i | \(0.292892\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.73749 | + | 15.1338i | 0.304570 | + | 0.527530i | 0.977165 | − | 0.212480i | \(-0.0681540\pi\) |
−0.672596 | + | 0.740010i | \(0.734821\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.22988 | + | 2.44212i | −0.147266 | + | 0.0850238i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.40361i | 0.118355i | 0.998247 | + | 0.0591776i | \(0.0188478\pi\) | ||||
−0.998247 | + | 0.0591776i | \(0.981152\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.3166 | + | 21.3330i | −0.427774 | + | 0.740926i | −0.996675 | − | 0.0814801i | \(-0.974035\pi\) |
0.568901 | + | 0.822406i | \(0.307369\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.99837 | −0.277460 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 35.9858 | 1.24684 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19.6185 | + | 33.9803i | −0.678928 | + | 1.17594i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 14.1385i | − | 0.488697i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.1012 | − | 6.40930i | 0.383257 | − | 0.221274i | −0.295977 | − | 0.955195i | \(-0.595645\pi\) |
0.679235 | + | 0.733921i | \(0.262312\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.7170 | + | 18.5624i | 0.369552 | + | 0.640084i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.38406 | − | 2.53114i | −0.150995 | − | 0.0871770i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 32.5287 | + | 33.5053i | 1.11902 | + | 1.15262i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.27174 | − | 0.734239i | −0.0436975 | − | 0.0252287i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.31761 | + | 2.28217i | 0.0452202 | + | 0.0783238i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −55.6058 | + | 32.1040i | −1.90614 | + | 1.10051i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 10.7738i | − | 0.368887i | −0.982843 | − | 0.184443i | \(-0.940952\pi\) | ||
0.982843 | − | 0.184443i | \(-0.0590482\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 31.0763 | − | 53.8258i | 1.06279 | − | 1.84080i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −19.3011 | −0.659313 | −0.329656 | − | 0.944101i | \(-0.606933\pi\) | ||||
−0.329656 | + | 0.944101i | \(0.606933\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.64223 | 0.260749 | 0.130375 | − | 0.991465i | \(-0.458382\pi\) | ||||
0.130375 | + | 0.991465i | \(0.458382\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.70144 | − | 4.67904i | 0.0920649 | − | 0.159461i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 11.0181i | − | 0.375061i | −0.982259 | − | 0.187531i | \(-0.939952\pi\) | ||
0.982259 | − | 0.187531i | \(-0.0600484\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.7830 | − | 9.68966i | 0.570638 | − | 0.329458i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.8030 | − | 20.4434i | −0.400850 | − | 0.694293i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.86371 | + | 5.69481i | 0.334603 | + | 0.193183i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 25.3443 | + | 3.52747i | 0.858759 | + | 0.119524i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.44318 | − | 3.14262i | −0.184224 | − | 0.106362i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.65843 | + | 13.2648i | 0.258902 | + | 0.448432i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.08586 | + | 5.24573i | −0.306808 | + | 0.177136i | −0.645497 | − | 0.763763i | \(-0.723350\pi\) |
0.338689 | + | 0.940898i | \(0.390016\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.02167i | 0.101918i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.00874 | + | 6.94334i | −0.135058 | + | 0.233927i | −0.925620 | − | 0.378455i | \(-0.876455\pi\) |
0.790562 | + | 0.612382i | \(0.209789\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.9068 | 0.501652 | 0.250826 | − | 0.968032i | \(-0.419298\pi\) | ||||
0.250826 | + | 0.968032i | \(0.419298\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.60918 | −0.0877066 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.4948 | + | 18.1776i | −0.352381 | + | 0.610342i | −0.986666 | − | 0.162757i | \(-0.947961\pi\) |
0.634285 | + | 0.773099i | \(0.281295\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 5.12875i | − | 0.172013i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.94399 | − | 2.85441i | 0.165630 | − | 0.0956265i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 35.1115 | + | 60.8148i | 1.17496 | + | 2.03509i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −69.7523 | − | 40.2715i | −2.33156 | − | 1.34613i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −10.8216 | − | 8.43153i | −0.361322 | − | 0.281521i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.70075 | + | 5.60073i | 0.323538 | + | 0.186795i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.5477 | + | 26.9295i | 0.517970 | + | 0.897151i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.94089 | − | 1.12057i | 0.0645888 | − | 0.0372904i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20.1857i | 0.670996i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.13273 | − | 15.8183i | 0.303247 | − | 0.525240i | −0.673622 | − | 0.739076i | \(-0.735263\pi\) |
0.976870 | + | 0.213836i | \(0.0685959\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 21.3386 | 0.707758 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.4866 | −1.20885 | −0.604427 | − | 0.796660i | \(-0.706598\pi\) | ||||
−0.604427 | + | 0.796660i | \(0.706598\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.744366 | + | 1.28928i | −0.0246349 | + | 0.0426689i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.26113i | 0.0747507i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −25.0643 | + | 14.4709i | −0.827696 | + | 0.477870i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.4739 | − | 19.8734i | −0.378490 | − | 0.655564i | 0.612353 | − | 0.790585i | \(-0.290223\pi\) |
−0.990843 | + | 0.135021i | \(0.956890\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.0135 | − | 5.78130i | −0.329956 | − | 0.190500i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.94307 | − | 3.77733i | 0.0968724 | − | 0.124332i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −71.3810 | − | 41.2119i | −2.34699 | − | 1.35504i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 24.4188 | + | 42.2946i | 0.802018 | + | 1.38914i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.19533 | + | 3.57687i | −0.203262 | + | 0.117353i | −0.598176 | − | 0.801365i | \(-0.704108\pi\) |
0.394914 | + | 0.918718i | \(0.370774\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 32.0097i | − | 1.04907i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.73433 | − | 4.73600i | 0.0895180 | − | 0.155050i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −26.6884 | −0.872803 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −42.3673 | −1.38408 | −0.692039 | − | 0.721860i | \(-0.743287\pi\) | ||||
−0.692039 | + | 0.721860i | \(0.743287\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.09020 | + | 1.88828i | −0.0355772 | + | 0.0616216i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 43.6192i | − | 1.42194i | −0.703220 | − | 0.710972i | \(-0.748255\pi\) | ||
0.703220 | − | 0.710972i | \(-0.251745\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −31.7457 | + | 18.3284i | −1.03378 | + | 0.596855i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9.15700 | + | 15.8604i | 0.297877 | + | 0.515939i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 32.3522 | + | 18.6785i | 1.05130 | + | 0.606971i | 0.923014 | − | 0.384766i | \(-0.125718\pi\) |
0.128290 | + | 0.991737i | \(0.459051\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.4628 | + | 35.6598i | 0.469483 | + | 1.15757i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12.3808 | + | 7.14805i | 0.401474 | + | 0.231791i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.63581 | + | 6.29741i | 0.117776 | + | 0.203993i | 0.918886 | − | 0.394523i | \(-0.129090\pi\) |
−0.801110 | + | 0.598517i | \(0.795757\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 37.8278 | − | 21.8399i | 1.22408 | − | 0.706723i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 1.69981i | − | 0.0549472i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.55554 | − | 14.8186i | 0.276273 | − | 0.478518i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.4161 | 0.465036 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 22.9142 | 0.738400 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −29.7722 | + | 51.5669i | −0.958400 | + | 1.66000i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 61.2301i | − | 1.96903i | −0.175308 | − | 0.984514i | \(-0.556092\pi\) | ||
0.175308 | − | 0.984514i | \(-0.443908\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −26.2773 | + | 15.1712i | −0.844149 | + | 0.487370i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.460539 | − | 0.797677i | −0.0147794 | − | 0.0255987i | 0.858541 | − | 0.512745i | \(-0.171371\pi\) |
−0.873321 | + | 0.487146i | \(0.838038\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.94280 | − | 3.43108i | −0.190517 | − | 0.109995i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.42765 | − | 17.4423i | 0.0777470 | − | 0.558600i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.3273 | + | 7.69450i | 0.426377 | + | 0.246169i | 0.697802 | − | 0.716291i | \(-0.254162\pi\) |
−0.271425 | + | 0.962460i | \(0.587495\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.34825 | − | 7.53139i | −0.138971 | − | 0.240704i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 22.4092 | − | 12.9380i | 0.715471 | − | 0.413077i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.6056i | 0.402056i | 0.979585 | + | 0.201028i | \(0.0644283\pi\) | ||||
−0.979585 | + | 0.201028i | \(0.935572\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.4039 | + | 35.3405i | −0.650121 | + | 1.12604i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −9.64273 | −0.306932 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15.2054 | −0.483505 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.2602 | − | 48.9482i | 0.897716 | − | 1.55489i | 0.0673094 | − | 0.997732i | \(-0.478559\pi\) |
0.830407 | − | 0.557158i | \(-0.188108\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 9.46045i | − | 0.300218i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.48048 | − | 2.00946i | 0.110339 | − | 0.0637040i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.251412 | + | 0.435459i | 0.00796230 | + | 0.0137911i | 0.869979 | − | 0.493089i | \(-0.164132\pi\) |
−0.862017 | + | 0.506880i | \(0.830799\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −31.3555 | − | 18.1031i | −0.992045 | − | 0.572757i |
(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 | 572.2.p.a.485.6 | yes | 24 | |
13.6 | odd | 12 | 7436.2.a.u.1.7 | 12 | |||
13.7 | odd | 12 | 7436.2.a.v.1.7 | 12 | |||
13.10 | even | 6 | inner | 572.2.p.a.309.6 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
572.2.p.a.309.6 | ✓ | 24 | 13.10 | even | 6 | inner | |
572.2.p.a.485.6 | yes | 24 | 1.1 | even | 1 | trivial | |
7436.2.a.u.1.7 | 12 | 13.6 | odd | 12 | |||
7436.2.a.v.1.7 | 12 | 13.7 | odd | 12 |