Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,2,Mod(81,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("320.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.l (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.55521286468\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 4 x^{14} + 7 x^{12} - 8 x^{11} - 28 x^{10} + 28 x^{9} + 17 x^{8} + 56 x^{7} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | no (minimal twist has level 80) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 81.6 | ||
Root | \(1.26868 + 0.624862i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 320.81 |
Dual form | 320.2.l.a.241.6 |
$q$-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 \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(257\) | \(261\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | 0.720673 | + | 0.720673i | 0.416081 | + | 0.416081i | 0.883850 | − | 0.467770i | \(-0.154942\pi\) |
−0.467770 | + | 0.883850i | \(0.654942\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.707107 | − | 0.707107i | 0.316228 | − | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.02840i | 1.52259i | 0.648405 | + | 0.761296i | \(0.275437\pi\) | ||||
−0.648405 | + | 0.761296i | \(0.724563\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.96126i | − | 0.653754i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.646837 | − | 0.646837i | 0.195029 | − | 0.195029i | −0.602836 | − | 0.797865i | \(-0.705963\pi\) |
0.797865 | + | 0.602836i | \(0.205963\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.91492 | + | 4.91492i | 1.36315 | + | 1.36315i | 0.869867 | + | 0.493286i | \(0.164204\pi\) |
0.493286 | + | 0.869867i | \(0.335796\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.01919 | 0.263153 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.70862 | −0.656938 | −0.328469 | − | 0.944515i | \(-0.606533\pi\) | ||||
−0.328469 | + | 0.944515i | \(0.606533\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.438397 | + | 0.438397i | 0.100575 | + | 0.100575i | 0.755604 | − | 0.655029i | \(-0.227344\pi\) |
−0.655029 | + | 0.755604i | \(0.727344\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.90316 | + | 2.90316i | −0.633521 | + | 0.633521i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 3.60080i | − | 0.750819i | −0.926859 | − | 0.375410i | \(-0.877502\pi\) | ||
0.926859 | − | 0.375410i | \(-0.122498\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 1.00000i | − | 0.200000i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.57545 | − | 3.57545i | 0.688095 | − | 0.688095i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00921 | + | 2.00921i | 0.373102 | + | 0.373102i | 0.868606 | − | 0.495504i | \(-0.165017\pi\) |
−0.495504 | + | 0.868606i | \(0.665017\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.30994 | −0.774087 | −0.387044 | − | 0.922061i | \(-0.626504\pi\) | ||||
−0.387044 | + | 0.922061i | \(0.626504\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.932316 | 0.162295 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.84851 | + | 2.84851i | 0.481486 | + | 0.481486i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.743961 | + | 0.743961i | −0.122306 | + | 0.122306i | −0.765611 | − | 0.643304i | \(-0.777563\pi\) |
0.643304 | + | 0.765611i | \(0.277563\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.08410i | 1.13436i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 0.603979i | − | 0.0943256i | −0.998887 | − | 0.0471628i | \(-0.984982\pi\) | ||
0.998887 | − | 0.0471628i | \(-0.0150180\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.03010 | − | 5.03010i | 0.767083 | − | 0.767083i | −0.210509 | − | 0.977592i | \(-0.567512\pi\) |
0.977592 | + | 0.210509i | \(0.0675121\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.38682 | − | 1.38682i | −0.206735 | − | 0.206735i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.8177 | −1.57793 | −0.788963 | − | 0.614440i | \(-0.789382\pi\) | ||||
−0.788963 | + | 0.614440i | \(0.789382\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9.22800 | −1.31829 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.95203 | − | 1.95203i | −0.273339 | − | 0.273339i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.07420 | − | 4.07420i | 0.559634 | − | 0.559634i | −0.369569 | − | 0.929203i | \(-0.620495\pi\) |
0.929203 | + | 0.369569i | \(0.120495\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.914766i | − | 0.123347i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.631882i | 0.0836948i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.22845 | + | 1.22845i | −0.159931 | + | 0.159931i | −0.782536 | − | 0.622605i | \(-0.786074\pi\) |
0.622605 | + | 0.782536i | \(0.286074\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.98912 | − | 6.98912i | −0.894865 | − | 0.894865i | 0.100112 | − | 0.994976i | \(-0.468080\pi\) |
−0.994976 | + | 0.100112i | \(0.968080\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.90074 | 0.995400 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.95074 | 0.862134 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.24219 | − | 5.24219i | −0.640435 | − | 0.640435i | 0.310227 | − | 0.950662i | \(-0.399595\pi\) |
−0.950662 | + | 0.310227i | \(0.899595\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.59500 | − | 2.59500i | 0.312401 | − | 0.312401i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 13.7940i | − | 1.63704i | −0.574475 | − | 0.818522i | \(-0.694794\pi\) | ||
0.574475 | − | 0.818522i | \(-0.305206\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1.30876i | − | 0.153179i | −0.997063 | − | 0.0765895i | \(-0.975597\pi\) | ||
0.997063 | − | 0.0765895i | \(-0.0244031\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.720673 | − | 0.720673i | 0.0832162 | − | 0.0832162i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.60572 | + | 2.60572i | 0.296949 | + | 0.296949i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.611127 | −0.0687571 | −0.0343786 | − | 0.999409i | \(-0.510945\pi\) | ||||
−0.0343786 | + | 0.999409i | \(0.510945\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.730326 | −0.0811473 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.29471 | − | 1.29471i | −0.142113 | − | 0.142113i | 0.632471 | − | 0.774584i | \(-0.282041\pi\) |
−0.774584 | + | 0.632471i | \(0.782041\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.91529 | + | 1.91529i | −0.207742 | + | 0.207742i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.89597i | 0.310481i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 10.9236i | − | 1.15790i | −0.815363 | − | 0.578950i | \(-0.803463\pi\) | ||
0.815363 | − | 0.578950i | \(-0.196537\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −19.7993 | + | 19.7993i | −2.07553 | + | 2.07553i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.10606 | − | 3.10606i | −0.322083 | − | 0.322083i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.619987 | 0.0636093 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.7571 | −1.29528 | −0.647642 | − | 0.761945i | \(-0.724245\pi\) | ||||
−0.647642 | + | 0.761945i | \(0.724245\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.26862 | − | 1.26862i | −0.127501 | − | 0.127501i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.59804 | + | 8.59804i | −0.855537 | + | 0.855537i | −0.990809 | − | 0.135272i | \(-0.956809\pi\) |
0.135272 | + | 0.990809i | \(0.456809\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.0328i | 1.18563i | 0.805338 | + | 0.592815i | \(0.201984\pi\) | ||||
−0.805338 | + | 0.592815i | \(0.798016\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.10569i | 0.400674i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.37309 | − | 2.37309i | 0.229415 | − | 0.229415i | −0.583033 | − | 0.812448i | \(-0.698134\pi\) |
0.812448 | + | 0.583033i | \(0.198134\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.24479 | − | 3.24479i | −0.310794 | − | 0.310794i | 0.534423 | − | 0.845217i | \(-0.320529\pi\) |
−0.845217 | + | 0.534423i | \(0.820529\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.07230 | −0.101779 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.3173 | 1.62907 | 0.814536 | − | 0.580114i | \(-0.196992\pi\) | ||||
0.814536 | + | 0.580114i | \(0.196992\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.54615 | − | 2.54615i | −0.237430 | − | 0.237430i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.63944 | − | 9.63944i | 0.891166 | − | 0.891166i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 10.9114i | − | 1.00025i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.1632i | 0.923928i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.435271 | − | 0.435271i | 0.0392471 | − | 0.0392471i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.707107 | − | 0.707107i | −0.0632456 | − | 0.0632456i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.5438 | 1.37929 | 0.689645 | − | 0.724147i | \(-0.257766\pi\) | ||||
0.689645 | + | 0.724147i | \(0.257766\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.25011 | 0.638337 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.2770 | + | 11.2770i | 0.985280 | + | 0.985280i | 0.999893 | − | 0.0146129i | \(-0.00465160\pi\) |
−0.0146129 | + | 0.999893i | \(0.504652\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.76604 | + | 1.76604i | −0.153135 | + | 0.153135i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 5.05645i | − | 0.435190i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.67273i | 0.313782i | 0.987616 | + | 0.156891i | \(0.0501472\pi\) | ||||
−0.987616 | + | 0.156891i | \(0.949853\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.23552 | − | 5.23552i | 0.444071 | − | 0.444071i | −0.449307 | − | 0.893378i | \(-0.648329\pi\) |
0.893378 | + | 0.449307i | \(0.148329\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.79604 | − | 7.79604i | −0.656545 | − | 0.656545i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.35830 | 0.531708 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.84146 | 0.235970 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.65037 | − | 6.65037i | −0.548514 | − | 0.548514i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.29391 | + | 3.29391i | −0.269848 | + | 0.269848i | −0.829039 | − | 0.559191i | \(-0.811112\pi\) |
0.559191 | + | 0.829039i | \(0.311112\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 6.93206i | − | 0.564123i | −0.959396 | − | 0.282061i | \(-0.908982\pi\) | ||
0.959396 | − | 0.282061i | \(-0.0910182\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.31232i | 0.429475i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.04759 | + | 3.04759i | −0.244788 | + | 0.244788i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.65633 | + | 5.65633i | 0.451425 | + | 0.451425i | 0.895827 | − | 0.444403i | \(-0.146584\pi\) |
−0.444403 | + | 0.895827i | \(0.646584\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.87233 | 0.465706 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 14.5055 | 1.14319 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.9746 | + | 10.9746i | 0.859593 | + | 0.859593i | 0.991290 | − | 0.131697i | \(-0.0420425\pi\) |
−0.131697 | + | 0.991290i | \(0.542043\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.659247 | − | 0.659247i | 0.0513223 | − | 0.0513223i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.7686i | 0.910685i | 0.890316 | + | 0.455343i | \(0.150483\pi\) | ||||
−0.890316 | + | 0.455343i | \(0.849517\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 35.3128i | 2.71637i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.859811 | − | 0.859811i | 0.0657514 | − | 0.0657514i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.40225 | − | 1.40225i | −0.106611 | − | 0.106611i | 0.651789 | − | 0.758400i | \(-0.274019\pi\) |
−0.758400 | + | 0.651789i | \(0.774019\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.02840 | 0.304518 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.77063 | −0.133088 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.66131 | − | 9.66131i | −0.722120 | − | 0.722120i | 0.246917 | − | 0.969037i | \(-0.420583\pi\) |
−0.969037 | + | 0.246917i | \(0.920583\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.294844 | − | 0.294844i | 0.0219156 | − | 0.0219156i | −0.696064 | − | 0.717980i | \(-0.745067\pi\) |
0.717980 | + | 0.696064i | \(0.245067\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 10.0737i | − | 0.744672i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.05212i | 0.0773533i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.75204 | + | 1.75204i | −0.128122 | + | 0.128122i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 14.4033 | + | 14.4033i | 1.04769 | + | 1.04769i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.9352 | 1.22539 | 0.612694 | − | 0.790320i | \(-0.290086\pi\) | ||||
0.612694 | + | 0.790320i | \(0.290086\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.5927 | −1.19437 | −0.597185 | − | 0.802103i | \(-0.703714\pi\) | ||||
−0.597185 | + | 0.802103i | \(0.703714\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.00921 | + | 5.00921i | 0.358717 | + | 0.358717i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.38392 | + | 2.38392i | −0.169847 | + | 0.169847i | −0.786912 | − | 0.617065i | \(-0.788322\pi\) |
0.617065 | + | 0.786912i | \(0.288322\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.1411i | 0.718883i | 0.933168 | + | 0.359442i | \(0.117033\pi\) | ||||
−0.933168 | + | 0.359442i | \(0.882967\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 7.55581i | − | 0.532946i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.09392 | + | 8.09392i | −0.568082 | + | 0.568082i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.427078 | − | 0.427078i | −0.0298284 | − | 0.0298284i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.06211 | −0.490851 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.567143 | 0.0392301 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.81171 | + | 2.81171i | 0.193566 | + | 0.193566i | 0.797235 | − | 0.603669i | \(-0.206295\pi\) |
−0.603669 | + | 0.797235i | \(0.706295\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.94095 | − | 9.94095i | 0.681143 | − | 0.681143i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 7.11363i | − | 0.485146i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 17.3621i | − | 1.17862i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.943190 | − | 0.943190i | 0.0637349 | − | 0.0637349i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.3127 | − | 13.3127i | −0.895507 | − | 0.895507i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.0502 | −0.940871 | −0.470436 | − | 0.882434i | \(-0.655903\pi\) | ||||
−0.470436 | + | 0.882434i | \(0.655903\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.96126 | −0.130751 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.3495 | + | 13.3495i | 0.886037 | + | 0.886037i | 0.994140 | − | 0.108103i | \(-0.0344776\pi\) |
−0.108103 | + | 0.994140i | \(0.534478\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.78589 | − | 8.78589i | 0.580588 | − | 0.580588i | −0.354477 | − | 0.935065i | \(-0.615341\pi\) |
0.935065 | + | 0.354477i | \(0.115341\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.75574i | 0.247110i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 15.1472i | − | 0.992329i | −0.868229 | − | 0.496165i | \(-0.834741\pi\) | ||
0.868229 | − | 0.496165i | \(-0.165259\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.64928 | + | 7.64928i | −0.498984 | + | 0.498984i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.440423 | − | 0.440423i | −0.0286085 | − | 0.0286085i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.9151 | −1.15883 | −0.579414 | − | 0.815033i | \(-0.696719\pi\) | ||||
−0.579414 | + | 0.815033i | \(0.696719\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25.6594 | 1.65287 | 0.826433 | − | 0.563035i | \(-0.190366\pi\) | ||||
0.826433 | + | 0.563035i | \(0.190366\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.2527 | − | 11.2527i | −0.721859 | − | 0.721859i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.52518 | + | 6.52518i | −0.416879 | + | 0.416879i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.30937i | 0.274199i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 1.86613i | − | 0.118261i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.95195 | − | 5.95195i | 0.375684 | − | 0.375684i | −0.493858 | − | 0.869542i | \(-0.664414\pi\) |
0.869542 | + | 0.493858i | \(0.164414\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.32913 | − | 2.32913i | −0.146431 | − | 0.146431i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.76059 | −0.172875 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.17369 | −0.260348 | −0.130174 | − | 0.991491i | \(-0.541554\pi\) | ||||
−0.130174 | + | 0.991491i | \(0.541554\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.99697 | − | 2.99697i | −0.186223 | − | 0.186223i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.94059 | − | 3.94059i | 0.243917 | − | 0.243917i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.14469i | 0.563885i | 0.959431 | + | 0.281943i | \(0.0909788\pi\) | ||||
−0.959431 | + | 0.281943i | \(0.909021\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 5.76178i | − | 0.353944i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.87234 | − | 7.87234i | 0.481780 | − | 0.481780i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.40029 | − | 8.40029i | −0.512175 | − | 0.512175i | 0.403017 | − | 0.915192i | \(-0.367961\pi\) |
−0.915192 | + | 0.403017i | \(0.867961\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.7794 | −1.14077 | −0.570383 | − | 0.821379i | \(-0.693205\pi\) | ||||
−0.570383 | + | 0.821379i | \(0.693205\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −28.5376 | −1.72717 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.646837 | − | 0.646837i | −0.0390057 | − | 0.0390057i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.54167 | + | 3.54167i | −0.212798 | + | 0.212798i | −0.805455 | − | 0.592657i | \(-0.798079\pi\) |
0.592657 | + | 0.805455i | \(0.298079\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.45291i | 0.506062i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.31811i | 0.138287i | 0.997607 | + | 0.0691433i | \(0.0220266\pi\) | ||||
−0.997607 | + | 0.0691433i | \(0.977973\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.63197 | − | 1.63197i | 0.0970108 | − | 0.0970108i | −0.656936 | − | 0.753947i | \(-0.728148\pi\) |
0.753947 | + | 0.656936i | \(0.228148\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.446808 | + | 0.446808i | 0.0264666 | + | 0.0264666i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.43307 | 0.143619 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.66335 | −0.568433 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.19367 | − | 9.19367i | −0.538943 | − | 0.538943i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.5789 | + | 11.5789i | −0.676444 | + | 0.676444i | −0.959194 | − | 0.282750i | \(-0.908753\pi\) |
0.282750 | + | 0.959194i | \(0.408753\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.73729i | 0.101149i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 4.62546i | − | 0.268397i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17.6976 | − | 17.6976i | 1.02348 | − | 1.02348i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.2632 | + | 20.2632i | 1.16795 | + | 1.16795i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12.3927 | −0.711945 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.88410 | −0.565962 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.7116 | − | 11.7116i | −0.668415 | − | 0.668415i | 0.288934 | − | 0.957349i | \(-0.406699\pi\) |
−0.957349 | + | 0.288934i | \(0.906699\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.67174 | + | 8.67174i | −0.493318 | + | 0.493318i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 11.2068i | − | 0.635477i | −0.948178 | − | 0.317739i | \(-0.897077\pi\) | ||
0.948178 | − | 0.317739i | \(-0.102923\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.50635i | 0.424284i | 0.977239 | + | 0.212142i | \(0.0680439\pi\) | ||||
−0.977239 | + | 0.212142i | \(0.931956\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.58667 | − | 5.58667i | 0.314773 | − | 0.314773i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.2854 | + | 16.2854i | 0.914680 | + | 0.914680i | 0.996636 | − | 0.0819564i | \(-0.0261168\pi\) |
−0.0819564 | + | 0.996636i | \(0.526117\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.59927 | 0.145531 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.42044 | 0.190910 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.18745 | − | 1.18745i | −0.0660716 | − | 0.0660716i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.91492 | − | 4.91492i | 0.272631 | − | 0.272631i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 4.67686i | − | 0.258631i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 43.5781i | − | 2.40254i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.3846 | − | 19.3846i | 1.06547 | − | 1.06547i | 0.0677707 | − | 0.997701i | \(-0.478411\pi\) |
0.997701 | − | 0.0677707i | \(-0.0215886\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.45910 | + | 1.45910i | 0.0799582 | + | 0.0799582i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.41357 | −0.405047 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.82991 | −0.426522 | −0.213261 | − | 0.976995i | \(-0.568408\pi\) | ||||
−0.213261 | + | 0.976995i | \(0.568408\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.4801 | + | 12.4801i | 0.677825 | + | 0.677825i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.78783 | + | 2.78783i | −0.150969 | + | 0.150969i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 8.97529i | − | 0.484620i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 3.66988i | − | 0.197580i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.91753 | + | 8.91753i | −0.478718 | + | 0.478718i | −0.904721 | − | 0.426004i | \(-0.859921\pi\) |
0.426004 | + | 0.904721i | \(0.359921\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.69072 | − | 6.69072i | −0.358146 | − | 0.358146i | 0.504983 | − | 0.863129i | \(-0.331499\pi\) |
−0.863129 | + | 0.504983i | \(0.831499\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 35.1461 | 1.87596 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.05215 | −0.109225 | −0.0546126 | − | 0.998508i | \(-0.517392\pi\) | ||||
−0.0546126 | + | 0.998508i | \(0.517392\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.75382 | − | 9.75382i | −0.517679 | − | 0.517679i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.86357 | − | 7.86357i | 0.416184 | − | 0.416184i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 9.52634i | − | 0.502781i | −0.967886 | − | 0.251391i | \(-0.919112\pi\) | ||
0.967886 | − | 0.251391i | \(-0.0808879\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 18.6156i | − | 0.979769i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.32435 | + | 7.32435i | −0.384429 | + | 0.384429i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.925435 | − | 0.925435i | −0.0484395 | − | 0.0484395i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.39736 | 0.177341 | 0.0886703 | − | 0.996061i | \(-0.471738\pi\) | ||||
0.0886703 | + | 0.996061i | \(0.471738\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.18456 | −0.0616657 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.4125 | + | 16.4125i | 0.852094 | + | 0.852094i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.4895 | + | 22.4895i | −1.16446 | + | 1.16446i | −0.180971 | + | 0.983488i | \(0.557924\pi\) |
−0.983488 | + | 0.180971i | \(0.942076\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 1.01919i | − | 0.0526305i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 19.7502i | 1.01719i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.9819 | + | 14.9819i | −0.769567 | + | 0.769567i | −0.978030 | − | 0.208463i | \(-0.933154\pi\) |
0.208463 | + | 0.978030i | \(0.433154\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.2020 | + | 11.2020i | 0.573896 | + | 0.573896i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −26.1197 | −1.33466 | −0.667328 | − | 0.744764i | \(-0.732562\pi\) | ||||
−0.667328 | + | 0.744764i | \(0.732562\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.68504 | 0.187807 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.86534 | − | 9.86534i | −0.501483 | − | 0.501483i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.08395 | + | 2.08395i | −0.105660 | + | 0.105660i | −0.757961 | − | 0.652300i | \(-0.773804\pi\) |
0.652300 | + | 0.757961i | \(0.273804\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.75322i | 0.493241i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16.2541i | 0.819912i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.432132 | + | 0.432132i | −0.0217429 | + | 0.0217429i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.43282 | + | 1.43282i | 0.0719114 | + | 0.0719114i | 0.742148 | − | 0.670236i | \(-0.233807\pi\) |
−0.670236 | + | 0.742148i | \(0.733807\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.54547 | −0.127433 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −29.9853 | −1.49739 | −0.748697 | − | 0.662912i | \(-0.769320\pi\) | ||||
−0.748697 | + | 0.662912i | \(0.769320\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −21.1830 | − | 21.1830i | −1.05520 | − | 1.05520i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.516418 | + | 0.516418i | −0.0256610 | + | 0.0256610i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.962443i | 0.0477065i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 4.17833i | − | 0.206605i | −0.994650 | − | 0.103302i | \(-0.967059\pi\) | ||
0.994650 | − | 0.103302i | \(-0.0329410\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.64684 | + | 2.64684i | −0.130559 | + | 0.130559i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.94870 | − | 4.94870i | −0.243510 | − | 0.243510i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.83100 | −0.0898801 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.54620 | 0.369539 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.4667 | + | 24.4667i | 1.19528 | + | 1.19528i | 0.975565 | + | 0.219712i | \(0.0705119\pi\) |
0.219712 | + | 0.975565i | \(0.429488\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.6017 | − | 25.6017i | 1.24775 | − | 1.24775i | 0.291039 | − | 0.956711i | \(-0.405999\pi\) |
0.956711 | − | 0.291039i | \(-0.0940008\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 21.2164i | 1.03158i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.70862i | 0.131388i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 28.1550 | − | 28.1550i | 1.36251 | − | 1.36251i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.58226 | + | 4.58226i | 0.221233 | + | 0.221233i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.6126 | −0.848367 | −0.424184 | − | 0.905576i | \(-0.639439\pi\) | ||||
−0.424184 | + | 0.905576i | \(0.639439\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.0568 | 1.30027 | 0.650133 | − | 0.759820i | \(-0.274713\pi\) | ||||
0.650133 | + | 0.759820i | \(0.274713\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.04776 | + | 2.04776i | 0.0981827 | + | 0.0981827i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.57858 | − | 1.57858i | 0.0755138 | − | 0.0755138i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.9965i | 1.09756i | 0.835967 | + | 0.548780i | \(0.184908\pi\) | ||||
−0.835967 | + | 0.548780i | \(0.815092\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.0985i | 0.861834i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.7715 | − | 13.7715i | 0.654303 | − | 0.654303i | −0.299723 | − | 0.954026i | \(-0.596894\pi\) |
0.954026 | + | 0.299723i | \(0.0968943\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.72415 | − | 7.72415i | −0.366160 | − | 0.366160i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.74766 | −0.224557 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.88838 | 0.325083 | 0.162541 | − | 0.986702i | \(-0.448031\pi\) | ||||
0.162541 | + | 0.986702i | \(0.448031\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.390676 | − | 0.390676i | −0.0183962 | − | 0.0183962i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.99575 | − | 4.99575i | 0.234721 | − | 0.234721i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 28.0004i | 1.31268i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.52622i | 0.118171i | 0.998253 | + | 0.0590857i | \(0.0188185\pi\) | ||||
−0.998253 | + | 0.0590857i | \(0.981181\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −9.68454 | + | 9.68454i | −0.452036 | + | 0.452036i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.23502 | + | 9.23502i | 0.430118 | + | 0.430118i | 0.888668 | − | 0.458550i | \(-0.151631\pi\) |
−0.458550 | + | 0.888668i | \(0.651631\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.2676 | 0.523652 | 0.261826 | − | 0.965115i | \(-0.415675\pi\) | ||||
0.261826 | + | 0.965115i | \(0.415675\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.39263 | −0.203703 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.8291 | + | 25.8291i | 1.19523 | + | 1.19523i | 0.975579 | + | 0.219650i | \(0.0704916\pi\) |
0.219650 | + | 0.975579i | \(0.429508\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 21.1176 | − | 21.1176i | 0.975122 | − | 0.975122i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.15273i | 0.375658i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 6.50731i | − | 0.299206i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.438397 | − | 0.438397i | 0.0201150 | − | 0.0201150i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.99056 | − | 7.99056i | −0.365863 | − | 0.365863i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.7261 | 0.718545 | 0.359273 | − | 0.933233i | \(-0.383025\pi\) | ||||
0.359273 | + | 0.933233i | \(0.383025\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.31301 | −0.333445 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.4537 | + | 10.4537i | 0.475660 | + | 0.475660i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.02061 | + | 9.02061i | −0.409605 | + | 0.409605i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 35.3717i | − | 1.60284i | −0.598100 | − | 0.801422i | \(-0.704077\pi\) | ||
0.598100 | − | 0.801422i | \(-0.295923\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 15.8181i | 0.715320i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.95703 | + | 7.95703i | −0.359096 | + | 0.359096i | −0.863480 | − | 0.504384i | \(-0.831720\pi\) |
0.504384 | + | 0.863480i | \(0.331720\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.44221 | − | 5.44221i | −0.245105 | − | 0.245105i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.79409 | −0.0806385 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 55.5677 | 2.49255 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.5864 | − | 11.5864i | −0.518677 | − | 0.518677i | 0.398494 | − | 0.917171i | \(-0.369533\pi\) |
−0.917171 | + | 0.398494i | \(0.869533\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.48135 | + | 8.48135i | −0.378919 | + | 0.378919i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 23.5051i | − | 1.04804i | −0.851706 | − | 0.524020i | \(-0.824432\pi\) | ||
0.851706 | − | 0.524020i | \(-0.175568\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.1595i | 0.541089i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −25.4490 | + | 25.4490i | −1.13023 | + | 1.13023i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.08381 | − | 3.08381i | −0.136687 | − | 0.136687i | 0.635452 | − | 0.772140i | \(-0.280814\pi\) |
−0.772140 | + | 0.635452i | \(0.780814\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.27222 | 0.233229 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.13493 | 0.138411 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.50850 | + | 8.50850i | 0.374929 | + | 0.374929i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.99730 | + | 6.99730i | −0.307741 | + | 0.307741i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 2.02113i | − | 0.0887178i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.5762i | 0.507161i | 0.967314 | + | 0.253580i | \(0.0816083\pi\) | ||||
−0.967314 | + | 0.253580i | \(0.918392\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.97900 | + | 3.97900i | −0.173990 | + | 0.173990i | −0.788730 | − | 0.614740i | \(-0.789261\pi\) |
0.614740 | + | 0.788730i | \(0.289261\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.90316 | + | 2.90316i | 0.126704 | + | 0.126704i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11.6740 | 0.508527 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.0342 | 0.436271 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.40932 | + | 2.40932i | 0.104555 | + | 0.104555i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.96851 | − | 2.96851i | 0.128580 | − | 0.128580i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 3.35605i | − | 0.145095i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 13.9253i | − | 0.600921i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.96902 | + | 5.96902i | −0.257104 | + | 0.257104i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.2148 | + | 17.2148i | 0.740123 | + | 0.740123i | 0.972602 | − | 0.232478i | \(-0.0746835\pi\) |
−0.232478 | + | 0.972602i | \(0.574684\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.424973 | 0.0182373 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.58882 | −0.196564 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.3610 | + | 20.3610i | 0.870573 | + | 0.870573i | 0.992535 | − | 0.121962i | \(-0.0389187\pi\) |
−0.121962 | + | 0.992535i | \(0.538919\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −13.7075 | + | 13.7075i | −0.585021 | + | 0.585021i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.76167i | 0.0750495i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 2.46186i | − | 0.104689i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.758234 | + | 0.758234i | −0.0321852 | + | 0.0321852i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22.7029 | − | 22.7029i | −0.961954 | − | 0.961954i | 0.0373478 | − | 0.999302i | \(-0.488109\pi\) |
−0.999302 | + | 0.0373478i | \(0.988109\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 49.4451 | 2.09130 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.52529 | −0.106618 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.4153 | − | 15.4153i | −0.649676 | − | 0.649676i | 0.303238 | − | 0.952915i | \(-0.401932\pi\) |
−0.952915 | + | 0.303238i | \(0.901932\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.2452 | − | 12.2452i | 0.515158 | − | 0.515158i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 2.94204i | − | 0.123554i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22.6529i | 0.949660i | 0.880078 | + | 0.474830i | \(0.157490\pi\) | ||||
−0.880078 | + | 0.474830i | \(0.842510\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.4941 | − | 13.4941i | 0.564710 | − | 0.564710i | −0.365931 | − | 0.930642i | \(-0.619250\pi\) |
0.930642 | + | 0.365931i | \(0.119250\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.2047 | + | 12.2047i | 0.509860 | + | 0.509860i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.60080 | −0.150164 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.08684 | 0.253398 | 0.126699 | − | 0.991941i | \(-0.459562\pi\) | ||||
0.126699 | + | 0.991941i | \(0.459562\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.9579 | − | 11.9579i | −0.496955 | − | 0.496955i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.21561 | − | 5.21561i | 0.216380 | − | 0.216380i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 5.27068i | − | 0.218289i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 13.6322i | − | 0.563623i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21.4418 | + | 21.4418i | −0.884999 | + | 0.884999i | −0.994038 | − | 0.109039i | \(-0.965223\pi\) |
0.109039 | + | 0.994038i | \(0.465223\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.88946 | − | 1.88946i | −0.0778540 | − | 0.0778540i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.43605 | −0.141340 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −28.2005 | −1.15806 | −0.579028 | − | 0.815308i | \(-0.696568\pi\) | ||||
−0.579028 | + | 0.815308i | \(0.696568\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.71554 | − | 7.71554i | −0.316306 | − | 0.316306i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.30841 | + | 7.30841i | −0.299113 | + | 0.299113i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 38.0516i | − | 1.55475i | −0.629039 | − | 0.777374i | \(-0.716551\pi\) | ||
0.629039 | − | 0.777374i | \(-0.283449\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 19.0716i | − | 0.777947i | −0.921249 | − | 0.388974i | \(-0.872830\pi\) | ||
0.921249 | − | 0.388974i | \(-0.127170\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.2813 | + | 10.2813i | −0.418687 | + | 0.418687i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.18647 | + | 7.18647i | 0.292172 | + | 0.292172i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.73433 | −0.232749 | −0.116375 | − | 0.993205i | \(-0.537127\pi\) | ||||
−0.116375 | + | 0.993205i | \(0.537127\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −11.6661 | −0.472736 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −53.1682 | − | 53.1682i | −2.15096 | − | 2.15096i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.36917 | − | 5.36917i | 0.216859 | − | 0.216859i | −0.590315 | − | 0.807173i | \(-0.700996\pi\) |
0.807173 | + | 0.590315i | \(0.200996\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 0.615566i | − | 0.0248220i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.2915i | 1.13897i | 0.822000 | + | 0.569487i | \(0.192858\pi\) | ||||
−0.822000 | + | 0.569487i | \(0.807142\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.9669 | + | 18.9669i | −0.762345 | + | 0.762345i | −0.976746 | − | 0.214401i | \(-0.931220\pi\) |
0.214401 | + | 0.976746i | \(0.431220\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −12.8745 | − | 12.8745i | −0.516635 | − | 0.516635i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 44.0046 | 1.76301 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.408725 | + | 0.408725i | 0.0163229 | + | 0.0163229i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.01511 | − | 2.01511i | 0.0803477 | − | 0.0803477i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 41.7662i | 1.66269i | 0.555758 | + | 0.831344i | \(0.312428\pi\) | ||||
−0.555758 | + | 0.831344i | \(0.687572\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.05265i | 0.161078i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.9911 | − | 10.9911i | 0.436170 | − | 0.436170i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −45.3549 | − | 45.3549i | −1.79703 | − | 1.79703i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −27.0536 | −1.07022 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.85195 | −0.112645 | −0.0563227 | − | 0.998413i | \(-0.517938\pi\) | ||||
−0.0563227 | + | 0.998413i | \(0.517938\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.8921 | + | 31.8921i | 1.25770 | + | 1.25770i | 0.952187 | + | 0.305516i | \(0.0988288\pi\) |
0.305516 | + | 0.952187i | \(0.401171\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.12660 | − | 5.12660i | 0.201860 | − | 0.201860i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.83402i | 0.307987i | 0.988072 | + | 0.153994i | \(0.0492135\pi\) | ||||
−0.988072 | + | 0.153994i | \(0.950786\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.58922i | 0.0623823i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.5124 | − | 12.5124i | 0.490401 | − | 0.490401i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.6822 | − | 12.6822i | −0.496292 | − | 0.496292i | 0.413989 | − | 0.910282i | \(-0.364135\pi\) |
−0.910282 | + | 0.413989i | \(0.864135\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15.9482 | 0.623146 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.56682 | −0.100141 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.9694 | − | 12.9694i | −0.505217 | − | 0.505217i | 0.407837 | − | 0.913055i | \(-0.366283\pi\) |
−0.913055 | + | 0.407837i | \(0.866283\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.85796 | + | 6.85796i | −0.266744 | + | 0.266744i | −0.827787 | − | 0.561043i | \(-0.810400\pi\) |
0.561043 | + | 0.827787i | \(0.310400\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 19.1882i | − | 0.745206i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.49756i | 0.0968511i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.23478 | − | 7.23478i | 0.280132 | − | 0.280132i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −10.1256 | − | 10.1256i | −0.391478 | − | 0.391478i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.04164 | −0.349049 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.1277 | 0.891508 | 0.445754 | − | 0.895155i | \(-0.352936\pi\) | ||||
0.445754 | + | 0.895155i | \(0.352936\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.57545 | − | 3.57545i | −0.137619 | − | 0.137619i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20.2521 | + | 20.2521i | −0.778352 | + | 0.778352i | −0.979550 | − | 0.201199i | \(-0.935516\pi\) |
0.201199 | + | 0.979550i | \(0.435516\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 51.3905i | − | 1.97219i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.2412i | 0.737326i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26.2957 | + | 26.2957i | −1.00618 | + | 1.00618i | −0.00619708 | + | 0.999981i | \(0.501973\pi\) |
−0.999981 | + | 0.00619708i | \(0.998027\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.59701 | + | 2.59701i | 0.0992267 | + | 0.0992267i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.6635 | 0.483143 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 40.0487 | 1.52573 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.91230 | + | 4.91230i | 0.186873 | + | 0.186873i | 0.794343 | − | 0.607470i | \(-0.207815\pi\) |
−0.607470 | + | 0.794343i | \(0.707815\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.11049 | − | 5.11049i | 0.194132 | − | 0.194132i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 7.40414i | − | 0.280855i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.63595i | 0.0619661i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.9162 | − | 10.9162i | 0.412889 | − | 0.412889i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.3598 | − | 12.3598i | −0.466824 | − | 0.466824i | 0.434060 | − | 0.900884i | \(-0.357081\pi\) |
−0.900884 | + | 0.434060i | \(0.857081\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.652300 | −0.0246020 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −11.0253 | −0.415235 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −34.6363 | − | 34.6363i | −1.30263 | − | 1.30263i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26.6076 | + | 26.6076i | −0.999270 | + | 0.999270i | −1.00000 | 0.000729493i | \(-0.999768\pi\) | |
0.000729493 | 1.00000i | \(0.499768\pi\) | ||||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.19858i | 0.0449502i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 15.5192i | 0.581200i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.49600 | − | 4.49600i | 0.168141 | − | 0.168141i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −12.9109 | − | 12.9109i | −0.482166 | − | 0.482166i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −50.9765 | −1.90110 | −0.950551 | − | 0.310570i | \(-0.899480\pi\) | ||||
−0.950551 | + | 0.310570i | \(0.899480\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −48.4731 | −1.80523 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 18.4920 | + | 18.4920i | 0.687726 | + | 0.687726i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.00921 | − | 2.00921i | 0.0746203 | − | 0.0746203i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 13.2824i | − | 0.492616i | −0.969192 | − | 0.246308i | \(-0.920782\pi\) | ||
0.969192 | − | 0.246308i | \(-0.0792175\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 14.0280i | − | 0.519556i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.6246 | + | 13.6246i | −0.503926 | + | 0.503926i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.3075 | + | 21.3075i | 0.787012 | + | 0.787012i | 0.981003 | − | 0.193991i | \(-0.0621434\pi\) |
−0.193991 | + | 0.981003i | \(0.562143\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9.40505 | −0.346910 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.78168 | −0.249807 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.83841 | − | 5.83841i | −0.214769 | − | 0.214769i | 0.591521 | − | 0.806290i | \(-0.298528\pi\) |
−0.806290 | + | 0.591521i | \(0.798528\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.10565 | + | 3.10565i | −0.114089 | + | 0.114089i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.25778i | 0.119516i | 0.998213 | + | 0.0597582i | \(0.0190330\pi\) | ||||
−0.998213 | + | 0.0597582i | \(0.980967\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.65829i | 0.170667i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.53926 | + | 2.53926i | −0.0929068 | + | 0.0929068i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.55975 | + | 9.55975i | 0.349306 | + | 0.349306i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.7322 | −0.756530 | −0.378265 | − | 0.925697i | \(-0.623479\pi\) | ||||
−0.378265 | + | 0.925697i | \(0.623479\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.57882 | 0.312630 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.90171 | − | 4.90171i | −0.178391 | − | 0.178391i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.3278 | − | 23.3278i | 0.847862 | − | 0.847862i | −0.142004 | − | 0.989866i | \(-0.545355\pi\) |
0.989866 | + | 0.142004i | \(0.0453547\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 3.35709i | − | 0.121854i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 24.0242i | − | 0.870878i | −0.900218 | − | 0.435439i | \(-0.856593\pi\) | ||
0.900218 | − | 0.435439i | \(-0.143407\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.0713 | − | 13.0713i | 0.473213 | − | 0.473213i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.75638 | + | 3.75638i | 0.135812 | + | 0.135812i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.0755 | −0.436021 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.70862 | −0.0976754 | −0.0488377 | − | 0.998807i | \(-0.515552\pi\) | ||||
−0.0488377 | + | 0.998807i | \(0.515552\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.00787 | − | 3.00787i | −0.108326 | − | 0.108326i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22.9473 | − | 22.9473i | 0.825358 | − | 0.825358i | −0.161513 | − | 0.986871i | \(-0.551637\pi\) |
0.986871 | + | 0.161513i | \(0.0516373\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.30994i | 0.154817i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 4.31967i | − | 0.154967i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.264783 | − | 0.264783i | 0.00948682 | − | 0.00948682i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.92246 | − | 8.92246i | −0.319271 | − | 0.319271i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 14.3677 | 0.513459 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.99926 | 0.285506 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.0592 | + | 14.0592i | 0.501157 | + | 0.501157i | 0.911797 | − | 0.410641i | \(-0.134695\pi\) |
−0.410641 | + | 0.911797i | \(0.634695\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.59033 | + | 6.59033i | −0.234622 | + | 0.234622i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 69.7609i | 2.48041i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 68.7019i | − | 2.43967i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.15236 | − | 4.15236i | 0.147269 | − | 0.147269i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35.4258 | + | 35.4258i | 1.25485 | + | 1.25485i | 0.953521 | + | 0.301326i | \(0.0974293\pi\) |
0.301326 | + | 0.953521i | \(0.402571\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 29.3011 | 1.03660 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −21.4240 | −0.756981 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.846556 | − | 0.846556i | −0.0298743 | − | 0.0298743i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.2569 | − | 10.2569i | 0.361509 | − | 0.361509i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 12.1077i | − | 0.426212i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 16.9217i | − | 0.594935i | −0.954732 | − | 0.297467i | \(-0.903858\pi\) | ||
0.954732 | − | 0.297467i | \(-0.0961420\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.4270 | − | 20.4270i | 0.717288 | − | 0.717288i | −0.250761 | − | 0.968049i | \(-0.580681\pi\) |
0.968049 | + | 0.250761i | \(0.0806807\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13.5338 | − | 13.5338i | −0.474651 | − | 0.474651i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15.5204 | 0.543655 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.41036 | 0.154299 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 38.8315 | + | 38.8315i | 1.35688 | + | 1.35688i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.4563 | − | 32.4563i | 1.13273 | − | 1.13273i | 0.143013 | − | 0.989721i | \(-0.454321\pi\) |
0.989721 | − | 0.143013i | \(-0.0456792\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.50705i | 0.226821i | 0.993548 | + | 0.113411i | \(0.0361776\pi\) | ||||
−0.993548 | + | 0.113411i | \(0.963822\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 0.932316i | − | 0.0324591i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.0528 | + | 27.0528i | −0.940718 | + | 0.940718i | −0.998339 | − | 0.0576204i | \(-0.981649\pi\) |
0.0576204 | + | 0.998339i | \(0.481649\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.54216 | − | 8.54216i | −0.296682 | − | 0.296682i | 0.543031 | − | 0.839713i | \(-0.317277\pi\) |
−0.839713 | + | 0.543031i | \(0.817277\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.10477 | −0.177083 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 24.9952 | 0.866032 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.32169 | + | 8.32169i | 0.287984 | + | 0.287984i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −15.4099 | + | 15.4099i | −0.532646 | + | 0.532646i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 24.4138i | 0.842860i | 0.906861 | + | 0.421430i | \(0.138472\pi\) | ||||
−0.906861 | + | 0.421430i | \(0.861528\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 20.9261i | − | 0.721590i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.67060 | + | 1.67060i | −0.0575384 | + | 0.0575384i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 24.9700 | + | 24.9700i | 0.858993 | + | 0.858993i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −40.9414 | −1.40676 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.35224 | 0.0807287 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.67885 | + | 2.67885i | 0.0918299 | + | 0.0918299i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.23270 | − | 8.23270i | 0.281882 | − | 0.281882i | −0.551977 | − | 0.833859i | \(-0.686126\pi\) |
0.833859 | + | 0.551977i | \(0.186126\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 1.21596i | − | 0.0415848i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.73909i | 0.161884i | 0.996719 | + | 0.0809421i | \(0.0257929\pi\) | ||||
−0.996719 | + | 0.0809421i | \(0.974207\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.65120 | − | 9.65120i | 0.329295 | − | 0.329295i | −0.523024 | − | 0.852318i | \(-0.675196\pi\) |
0.852318 | + | 0.523024i | \(0.175196\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.75345 | + | 1.75345i | 0.0597573 | + | 0.0597573i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.80368 | 0.129479 | 0.0647393 | − | 0.997902i | \(-0.479378\pi\) | ||||
0.0647393 | + | 0.997902i | \(0.479378\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.98309 | −0.0674269 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.96412 | − | 6.96412i | −0.236514 | − | 0.236514i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.395300 | + | 0.395300i | −0.0134096 | + | 0.0134096i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 51.5299i | − | 1.74602i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 25.0199i | 0.846796i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.84851 | − | 2.84851i | 0.0962972 | − | 0.0962972i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.38917 | + | 2.38917i | 0.0806765 | + | 0.0806765i | 0.746294 | − | 0.665617i | \(-0.231832\pi\) |
−0.665617 | + | 0.746294i | \(0.731832\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −16.6891 | −0.562911 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.6195 | −0.795762 | −0.397881 | − | 0.917437i | \(-0.630254\pi\) | ||||
−0.397881 | + | 0.917437i | \(0.630254\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.64752 | + | 9.64752i | 0.324665 | + | 0.324665i | 0.850553 | − | 0.525889i | \(-0.176267\pi\) |
−0.525889 | + | 0.850553i | \(0.676267\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.25202 | + | 1.25202i | −0.0420862 | + | 0.0420862i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.91140i | 0.299215i | 0.988745 | + | 0.149608i | \(0.0478011\pi\) | ||||
−0.988745 | + | 0.149608i | \(0.952199\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 62.6167i | 2.10010i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.472402 | + | 0.472402i | −0.0158261 | + | 0.0158261i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.74246 | − | 4.74246i | −0.158700 | − | 0.158700i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13.6632 | −0.456709 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 25.5084 | 0.851702 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.65959 | − | 8.65959i | −0.288813 | − | 0.288813i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.0355 | + | 11.0355i | −0.367645 | + | 0.367645i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 29.2064i | 0.971927i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 0.416973i | − | 0.0138606i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23.4874 | + | 23.4874i | −0.779886 | + | 0.779886i | −0.979811 | − | 0.199925i | \(-0.935930\pi\) |
0.199925 | + | 0.979811i | \(0.435930\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16.8630 | + | 16.8630i | 0.559310 | + | 0.559310i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.77171 | 0.0586993 | 0.0293497 | − | 0.999569i | \(-0.490656\pi\) | ||||
0.0293497 | + | 0.999569i | \(0.490656\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.67493 | −0.0554322 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.12321 | − | 7.12321i | −0.235486 | − | 0.235486i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −45.4285 | + | 45.4285i | −1.50018 | + | 1.50018i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46.2001i | 1.52400i | 0.647576 | + | 0.762001i | \(0.275783\pi\) | ||||
−0.647576 | + | 0.762001i | \(0.724217\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 16.8804i | − | 0.556229i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 67.7963 | − | 67.7963i | 2.23154 | − | 2.23154i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.743961 | + | 0.743961i | 0.0244613 | + | 0.0244613i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 23.5995 | 0.775110 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −35.5011 | −1.16475 | −0.582376 | − | 0.812920i | \(-0.697877\pi\) | ||||
−0.582376 | + | 0.812920i | \(0.697877\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.04553 | − | 4.04553i | −0.132587 | − | 0.132587i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.07641 | − | 8.07641i | 0.264410 | − | 0.264410i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.47776i | 0.0810313i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.0385i | 0.327945i | 0.986465 | + | 0.163972i | \(0.0524308\pi\) | ||||
−0.986465 | + | 0.163972i | \(0.947569\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.40962 | + | 5.40962i | −0.176536 | + | 0.176536i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 42.3367 | + | 42.3367i | 1.38014 | + | 1.38014i | 0.844359 | + | 0.535777i | \(0.179981\pi\) |
0.535777 | + | 0.844359i | \(0.320019\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.17481 | −0.0708215 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 20.3694 | 0.662616 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 36.3384 | + | 36.3384i | 1.18084 | + | 1.18084i | 0.979527 | + | 0.201313i | \(0.0645209\pi\) |
0.201313 | + | 0.979527i | \(0.435479\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.43246 | − | 6.43246i | 0.208807 | − | 0.208807i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 23.4729i | 0.761161i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.7338i | 1.06035i | 0.847888 | + | 0.530176i | \(0.177874\pi\) | ||||
−0.847888 | + | 0.530176i | \(0.822126\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11.9750 | − | 11.9750i | 0.387502 | − | 0.387502i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.87322 | + | 1.87322i | 0.0605527 | + | 0.0605527i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14.7952 | −0.477762 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.4244 | −0.400789 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.65424 | − | 4.65424i | −0.149981 | − | 0.149981i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −11.7328 | + | 11.7328i | −0.377693 | + | 0.377693i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 49.7169i | − | 1.59879i | −0.600807 | − | 0.799394i | \(-0.705154\pi\) | ||
0.600807 | − | 0.799394i | \(-0.294846\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 1.71153i | − | 0.0549823i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.7937 | − | 24.7937i | 0.795667 | − | 0.795667i | −0.186742 | − | 0.982409i | \(-0.559793\pi\) |
0.982409 | + | 0.186742i | \(0.0597928\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.0908 | + | 21.0908i | 0.676139 | + | 0.676139i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.08410 | 0.226873 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −49.4546 | −1.58219 | −0.791096 | − | 0.611692i | \(-0.790489\pi\) | ||||
−0.791096 | + | 0.611692i | \(0.790489\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.06579 | − | 7.06579i | −0.225824 | − | 0.225824i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.36387 | + | 6.36387i | −0.203183 | + | 0.203183i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23.9656i | 0.764383i | 0.924083 | + | 0.382191i | \(0.124830\pi\) | ||||
−0.924083 | + | 0.382191i | \(0.875170\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.37137i | 0.107421i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 31.4056 | − | 31.4056i | 0.999650 | − | 0.999650i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18.1124 | − | 18.1124i | −0.575940 | − | 0.575940i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.8345 | −0.915957 | −0.457978 | − | 0.888963i | \(-0.651426\pi\) | ||||
−0.457978 | + | 0.888963i | \(0.651426\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 27.9399 | 0.886645 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.17084 | + | 7.17084i | 0.227331 | + | 0.227331i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.03212 | − | 6.03212i | 0.191039 | − | 0.191039i | −0.605106 | − | 0.796145i | \(-0.706869\pi\) |
0.796145 | + | 0.605106i | \(0.206869\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.31998i | 0.168317i |
(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 | 320.2.l.a.81.6 | 16 | ||
3.2 | odd | 2 | 2880.2.t.c.721.4 | 16 | |||
4.3 | odd | 2 | 80.2.l.a.61.1 | yes | 16 | ||
5.2 | odd | 4 | 1600.2.q.g.849.6 | 16 | |||
5.3 | odd | 4 | 1600.2.q.h.849.3 | 16 | |||
5.4 | even | 2 | 1600.2.l.i.401.3 | 16 | |||
8.3 | odd | 2 | 640.2.l.b.161.6 | 16 | |||
8.5 | even | 2 | 640.2.l.a.161.3 | 16 | |||
12.11 | even | 2 | 720.2.t.c.541.8 | 16 | |||
16.3 | odd | 4 | 640.2.l.b.481.6 | 16 | |||
16.5 | even | 4 | inner | 320.2.l.a.241.6 | 16 | ||
16.11 | odd | 4 | 80.2.l.a.21.1 | ✓ | 16 | ||
16.13 | even | 4 | 640.2.l.a.481.3 | 16 | |||
20.3 | even | 4 | 400.2.q.g.349.5 | 16 | |||
20.7 | even | 4 | 400.2.q.h.349.4 | 16 | |||
20.19 | odd | 2 | 400.2.l.h.301.8 | 16 | |||
32.5 | even | 8 | 5120.2.a.t.1.4 | 8 | |||
32.11 | odd | 8 | 5120.2.a.s.1.4 | 8 | |||
32.21 | even | 8 | 5120.2.a.u.1.5 | 8 | |||
32.27 | odd | 8 | 5120.2.a.v.1.5 | 8 | |||
48.5 | odd | 4 | 2880.2.t.c.2161.1 | 16 | |||
48.11 | even | 4 | 720.2.t.c.181.8 | 16 | |||
80.27 | even | 4 | 400.2.q.g.149.5 | 16 | |||
80.37 | odd | 4 | 1600.2.q.h.49.3 | 16 | |||
80.43 | even | 4 | 400.2.q.h.149.4 | 16 | |||
80.53 | odd | 4 | 1600.2.q.g.49.6 | 16 | |||
80.59 | odd | 4 | 400.2.l.h.101.8 | 16 | |||
80.69 | even | 4 | 1600.2.l.i.1201.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.2.l.a.21.1 | ✓ | 16 | 16.11 | odd | 4 | ||
80.2.l.a.61.1 | yes | 16 | 4.3 | odd | 2 | ||
320.2.l.a.81.6 | 16 | 1.1 | even | 1 | trivial | ||
320.2.l.a.241.6 | 16 | 16.5 | even | 4 | inner | ||
400.2.l.h.101.8 | 16 | 80.59 | odd | 4 | |||
400.2.l.h.301.8 | 16 | 20.19 | odd | 2 | |||
400.2.q.g.149.5 | 16 | 80.27 | even | 4 | |||
400.2.q.g.349.5 | 16 | 20.3 | even | 4 | |||
400.2.q.h.149.4 | 16 | 80.43 | even | 4 | |||
400.2.q.h.349.4 | 16 | 20.7 | even | 4 | |||
640.2.l.a.161.3 | 16 | 8.5 | even | 2 | |||
640.2.l.a.481.3 | 16 | 16.13 | even | 4 | |||
640.2.l.b.161.6 | 16 | 8.3 | odd | 2 | |||
640.2.l.b.481.6 | 16 | 16.3 | odd | 4 | |||
720.2.t.c.181.8 | 16 | 48.11 | even | 4 | |||
720.2.t.c.541.8 | 16 | 12.11 | even | 2 | |||
1600.2.l.i.401.3 | 16 | 5.4 | even | 2 | |||
1600.2.l.i.1201.3 | 16 | 80.69 | even | 4 | |||
1600.2.q.g.49.6 | 16 | 80.53 | odd | 4 | |||
1600.2.q.g.849.6 | 16 | 5.2 | odd | 4 | |||
1600.2.q.h.49.3 | 16 | 80.37 | odd | 4 | |||
1600.2.q.h.849.3 | 16 | 5.3 | odd | 4 | |||
2880.2.t.c.721.4 | 16 | 3.2 | odd | 2 | |||
2880.2.t.c.2161.1 | 16 | 48.5 | odd | 4 | |||
5120.2.a.s.1.4 | 8 | 32.11 | odd | 8 | |||
5120.2.a.t.1.4 | 8 | 32.5 | even | 8 | |||
5120.2.a.u.1.5 | 8 | 32.21 | even | 8 | |||
5120.2.a.v.1.5 | 8 | 32.27 | odd | 8 |