Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1134,2,Mod(1133,1134)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1134, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1134.1133");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1134 = 2 \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1134.d (of order \(2\), degree \(1\), 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: | \(9.05503558921\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 56 x^{14} - 252 x^{13} + 962 x^{12} - 2860 x^{11} + 7240 x^{10} - 15036 x^{9} + 26533 x^{8} - 38796 x^{7} + 47500 x^{6} - 47396 x^{5} + 38144 x^{4} + \cdots + 457 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1133.11 | ||
Root | \(0.500000 - 1.61238i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1134.1133 |
Dual form | 1134.2.d.b.1133.3 |
$q$-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 \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.57315 | −0.703534 | −0.351767 | − | 0.936088i | \(-0.614419\pi\) | ||||
−0.351767 | + | 0.936088i | \(0.614419\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.858719 | + | 2.50252i | 0.324565 | + | 0.945863i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 1.57315i | − | 0.497473i | ||||||
\(11\) | 0.835475i | 0.251905i | 0.992036 | + | 0.125953i | \(0.0401987\pi\) | ||||
−0.992036 | + | 0.125953i | \(0.959801\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.55675i | 1.26381i | 0.775044 | + | 0.631907i | \(0.217727\pi\) | ||||
−0.775044 | + | 0.631907i | \(0.782273\pi\) | |||||||
\(14\) | −2.50252 | + | 0.858719i | −0.668826 | + | 0.229502i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.258822 | −0.0627735 | −0.0313868 | − | 0.999507i | \(-0.509992\pi\) | ||||
−0.0313868 | + | 0.999507i | \(0.509992\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.46595i | − | 0.565728i | −0.959160 | − | 0.282864i | \(-0.908715\pi\) | ||
0.959160 | − | 0.282864i | \(-0.0912846\pi\) | |||||||
\(20\) | 1.57315 | 0.351767 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.835475 | −0.178124 | ||||||||
\(23\) | − | 5.07812i | − | 1.05886i | −0.848354 | − | 0.529430i | \(-0.822406\pi\) | ||
0.848354 | − | 0.529430i | \(-0.177594\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.52520 | −0.505040 | ||||||||
\(26\) | −4.55675 | −0.893651 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.858719 | − | 2.50252i | −0.162283 | − | 0.472932i | ||||
\(29\) | − | 2.91359i | − | 0.541040i | −0.962714 | − | 0.270520i | \(-0.912804\pi\) | ||
0.962714 | − | 0.270520i | \(-0.0871957\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.98331i | 1.79305i | 0.442988 | + | 0.896527i | \(0.353918\pi\) | ||||
−0.442988 | + | 0.896527i | \(0.646082\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 0.258822i | − | 0.0443876i | ||||||
\(35\) | −1.35089 | − | 3.93684i | −0.228343 | − | 0.665447i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.400597 | 0.0658578 | 0.0329289 | − | 0.999458i | \(-0.489517\pi\) | ||||
0.0329289 | + | 0.999458i | \(0.489517\pi\) | |||||||
\(38\) | 2.46595 | 0.400030 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.57315i | 0.248737i | ||||||||
\(41\) | −9.82060 | −1.53372 | −0.766860 | − | 0.641814i | \(-0.778182\pi\) | ||||
−0.766860 | + | 0.641814i | \(0.778182\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.15623 | −0.938817 | −0.469408 | − | 0.882981i | \(-0.655533\pi\) | ||||
−0.469408 | + | 0.882981i | \(0.655533\pi\) | |||||||
\(44\) | − | 0.835475i | − | 0.125953i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.07812 | 0.748727 | ||||||||
\(47\) | −10.6904 | −1.55936 | −0.779679 | − | 0.626179i | \(-0.784618\pi\) | ||||
−0.779679 | + | 0.626179i | \(0.784618\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.52520 | + | 4.29792i | −0.789315 | + | 0.613989i | ||||
\(50\) | − | 2.52520i | − | 0.357117i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 4.55675i | − | 0.631907i | ||||||
\(53\) | 8.19615i | 1.12583i | 0.826515 | + | 0.562914i | \(0.190320\pi\) | ||||
−0.826515 | + | 0.562914i | \(0.809680\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.31433i | − | 0.177224i | ||||||
\(56\) | 2.50252 | − | 0.858719i | 0.334413 | − | 0.114751i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.91359 | 0.382573 | ||||||||
\(59\) | −1.83197 | −0.238502 | −0.119251 | − | 0.992864i | \(-0.538049\pi\) | ||||
−0.119251 | + | 0.992864i | \(0.538049\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 0.703333i | − | 0.0900525i | −0.998986 | − | 0.0450263i | \(-0.985663\pi\) | ||
0.998986 | − | 0.0450263i | \(-0.0143371\pi\) | |||||||
\(62\) | −9.98331 | −1.26788 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − | 7.16844i | − | 0.889136i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.46651 | −1.03435 | −0.517174 | − | 0.855880i | \(-0.673016\pi\) | ||||
−0.517174 | + | 0.855880i | \(0.673016\pi\) | |||||||
\(68\) | 0.258822 | 0.0313868 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.93684 | − | 1.35089i | 0.470542 | − | 0.161463i | ||||
\(71\) | − | 4.76784i | − | 0.565839i | −0.959144 | − | 0.282919i | \(-0.908697\pi\) | ||
0.959144 | − | 0.282919i | \(-0.0913029\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 7.72981i | − | 0.904706i | −0.891839 | − | 0.452353i | \(-0.850585\pi\) | ||
0.891839 | − | 0.452353i | \(-0.149415\pi\) | |||||||
\(74\) | 0.400597i | 0.0465685i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.46595i | 0.282864i | ||||||||
\(77\) | −2.09079 | + | 0.717439i | −0.238268 | + | 0.0817598i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.9917 | 1.46168 | 0.730841 | − | 0.682548i | \(-0.239128\pi\) | ||||
0.730841 | + | 0.682548i | \(0.239128\pi\) | |||||||
\(80\) | −1.57315 | −0.175883 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 9.82060i | − | 1.08450i | ||||||
\(83\) | −5.42278 | −0.595227 | −0.297614 | − | 0.954686i | \(-0.596191\pi\) | ||||
−0.297614 | + | 0.954686i | \(0.596191\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.407165 | 0.0441633 | ||||||||
\(86\) | − | 6.15623i | − | 0.663844i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.835475 | 0.0890620 | ||||||||
\(89\) | 6.03377 | 0.639579 | 0.319789 | − | 0.947489i | \(-0.396388\pi\) | ||||
0.319789 | + | 0.947489i | \(0.396388\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.4033 | + | 3.91297i | −1.19539 | + | 0.410190i | ||||
\(92\) | 5.07812i | 0.529430i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 10.6904i | − | 1.10263i | ||||||
\(95\) | 3.87931i | 0.398009i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.15163i | 0.116930i | 0.998289 | + | 0.0584649i | \(0.0186206\pi\) | ||||
−0.998289 | + | 0.0584649i | \(0.981379\pi\) | |||||||
\(98\) | −4.29792 | − | 5.52520i | −0.434156 | − | 0.558130i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.52520 | 0.252520 | ||||||||
\(101\) | −18.6059 | −1.85136 | −0.925679 | − | 0.378309i | \(-0.876506\pi\) | ||||
−0.925679 | + | 0.378309i | \(0.876506\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.66394i | 0.361019i | 0.983573 | + | 0.180509i | \(0.0577746\pi\) | ||||
−0.983573 | + | 0.180509i | \(0.942225\pi\) | |||||||
\(104\) | 4.55675 | 0.446826 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.19615 | −0.796081 | ||||||||
\(107\) | 3.48137i | 0.336556i | 0.985740 | + | 0.168278i | \(0.0538207\pi\) | ||||
−0.985740 | + | 0.168278i | \(0.946179\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.6692 | 1.69240 | 0.846202 | − | 0.532862i | \(-0.178883\pi\) | ||||
0.846202 | + | 0.532862i | \(0.178883\pi\) | |||||||
\(110\) | 1.31433 | 0.125316 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.858719 | + | 2.50252i | 0.0811414 | + | 0.236466i | ||||
\(113\) | 14.2808i | 1.34343i | 0.740811 | + | 0.671714i | \(0.234442\pi\) | ||||
−0.740811 | + | 0.671714i | \(0.765558\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.98863i | 0.744944i | ||||||||
\(116\) | 2.91359i | 0.270520i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 1.83197i | − | 0.168647i | ||||||
\(119\) | −0.222255 | − | 0.647707i | −0.0203741 | − | 0.0593752i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.3020 | 0.936544 | ||||||||
\(122\) | 0.703333 | 0.0636767 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 9.98331i | − | 0.896527i | ||||||
\(125\) | 11.8383 | 1.05885 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.82327 | 0.250524 | 0.125262 | − | 0.992124i | \(-0.460023\pi\) | ||||
0.125262 | + | 0.992124i | \(0.460023\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.16844 | 0.628714 | ||||||||
\(131\) | 18.6059 | 1.62561 | 0.812803 | − | 0.582538i | \(-0.197940\pi\) | ||||
0.812803 | + | 0.582538i | \(0.197940\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.17109 | − | 2.11756i | 0.535102 | − | 0.183616i | ||||
\(134\) | − | 8.46651i | − | 0.731395i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.258822i | 0.0221938i | ||||||||
\(137\) | 17.6227i | 1.50561i | 0.658242 | + | 0.752806i | \(0.271300\pi\) | ||||
−0.658242 | + | 0.752806i | \(0.728700\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.02144i | 0.171456i | 0.996319 | + | 0.0857282i | \(0.0273217\pi\) | ||||
−0.996319 | + | 0.0857282i | \(0.972678\pi\) | |||||||
\(140\) | 1.35089 | + | 3.93684i | 0.114171 | + | 0.332723i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.76784 | 0.400108 | ||||||||
\(143\) | −3.80705 | −0.318361 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.58351i | 0.380640i | ||||||||
\(146\) | 7.72981 | 0.639724 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.400597 | −0.0329289 | ||||||||
\(149\) | − | 21.6505i | − | 1.77367i | −0.462082 | − | 0.886837i | \(-0.652898\pi\) | ||
0.462082 | − | 0.886837i | \(-0.347102\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.5235 | −1.42604 | −0.713020 | − | 0.701144i | \(-0.752673\pi\) | ||||
−0.713020 | + | 0.701144i | \(0.752673\pi\) | |||||||
\(152\) | −2.46595 | −0.200015 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.717439 | − | 2.09079i | −0.0578129 | − | 0.168481i | ||||
\(155\) | − | 15.7052i | − | 1.26147i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 10.8493i | − | 0.865872i | −0.901425 | − | 0.432936i | \(-0.857478\pi\) | ||
0.901425 | − | 0.432936i | \(-0.142522\pi\) | |||||||
\(158\) | 12.9917i | 1.03356i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 1.57315i | − | 0.124368i | ||||||
\(161\) | 12.7081 | − | 4.36068i | 1.00154 | − | 0.343669i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.6376 | −0.911527 | −0.455764 | − | 0.890101i | \(-0.650634\pi\) | ||||
−0.455764 | + | 0.890101i | \(0.650634\pi\) | |||||||
\(164\) | 9.82060 | 0.766860 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 5.42278i | − | 0.420889i | ||||||
\(167\) | 11.1349 | 0.861647 | 0.430823 | − | 0.902436i | \(-0.358223\pi\) | ||||
0.430823 | + | 0.902436i | \(0.358223\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.76393 | −0.597225 | ||||||||
\(170\) | 0.407165i | 0.0312282i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.15623 | 0.469408 | ||||||||
\(173\) | 7.80295 | 0.593247 | 0.296623 | − | 0.954995i | \(-0.404139\pi\) | ||||
0.296623 | + | 0.954995i | \(0.404139\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.16844 | − | 6.31937i | −0.163919 | − | 0.477699i | ||||
\(176\) | 0.835475i | 0.0629763i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.03377i | 0.452251i | ||||||||
\(179\) | 15.9956i | 1.19557i | 0.801657 | + | 0.597784i | \(0.203952\pi\) | ||||
−0.801657 | + | 0.597784i | \(0.796048\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.92154i | 0.142827i | 0.997447 | + | 0.0714135i | \(0.0227510\pi\) | ||||
−0.997447 | + | 0.0714135i | \(0.977249\pi\) | |||||||
\(182\) | −3.91297 | − | 11.4033i | −0.290048 | − | 0.845272i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.07812 | −0.374364 | ||||||||
\(185\) | −0.630200 | −0.0463332 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 0.216239i | − | 0.0158130i | ||||||
\(188\) | 10.6904 | 0.779679 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.87931 | −0.281435 | ||||||||
\(191\) | − | 5.92580i | − | 0.428776i | −0.976749 | − | 0.214388i | \(-0.931224\pi\) | ||
0.976749 | − | 0.214388i | \(-0.0687757\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.98450 | 0.214829 | 0.107414 | − | 0.994214i | \(-0.465743\pi\) | ||||
0.107414 | + | 0.994214i | \(0.465743\pi\) | |||||||
\(194\) | −1.15163 | −0.0826819 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.52520 | − | 4.29792i | 0.394657 | − | 0.306995i | ||||
\(197\) | − | 1.00657i | − | 0.0717150i | −0.999357 | − | 0.0358575i | \(-0.988584\pi\) | ||
0.999357 | − | 0.0358575i | \(-0.0114162\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.6170i | 1.24884i | 0.781090 | + | 0.624418i | \(0.214664\pi\) | ||||
−0.781090 | + | 0.624418i | \(0.785336\pi\) | |||||||
\(200\) | 2.52520i | 0.178559i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 18.6059i | − | 1.30911i | ||||||
\(203\) | 7.29132 | − | 2.50196i | 0.511750 | − | 0.175603i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.4493 | 1.07902 | ||||||||
\(206\) | −3.66394 | −0.255279 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.55675i | 0.315953i | ||||||||
\(209\) | 2.06024 | 0.142510 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.87540 | 0.197950 | 0.0989752 | − | 0.995090i | \(-0.468444\pi\) | ||||
0.0989752 | + | 0.995090i | \(0.468444\pi\) | |||||||
\(212\) | − | 8.19615i | − | 0.562914i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.48137 | −0.237981 | ||||||||
\(215\) | 9.68467 | 0.660489 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −24.9834 | + | 8.57286i | −1.69598 | + | 0.581964i | ||||
\(218\) | 17.6692i | 1.19671i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.31433i | 0.0886119i | ||||||||
\(221\) | − | 1.17939i | − | 0.0793340i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.3380i | 1.16104i | 0.814248 | + | 0.580518i | \(0.197150\pi\) | ||||
−0.814248 | + | 0.580518i | \(0.802850\pi\) | |||||||
\(224\) | −2.50252 | + | 0.858719i | −0.167207 | + | 0.0573756i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.2808 | −0.949947 | ||||||||
\(227\) | 15.0151 | 0.996588 | 0.498294 | − | 0.867008i | \(-0.333960\pi\) | ||||
0.498294 | + | 0.867008i | \(0.333960\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 18.7484i | − | 1.23893i | −0.785024 | − | 0.619465i | \(-0.787350\pi\) | ||
0.785024 | − | 0.619465i | \(-0.212650\pi\) | |||||||
\(230\) | −7.98863 | −0.526755 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.91359 | −0.191287 | ||||||||
\(233\) | 12.6099i | 0.826101i | 0.910708 | + | 0.413051i | \(0.135537\pi\) | ||||
−0.910708 | + | 0.413051i | \(0.864463\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.8176 | 1.09706 | ||||||||
\(236\) | 1.83197 | 0.119251 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.647707 | − | 0.222255i | 0.0419846 | − | 0.0144067i | ||||
\(239\) | 24.5429i | 1.58755i | 0.608213 | + | 0.793774i | \(0.291887\pi\) | ||||
−0.608213 | + | 0.793774i | \(0.708113\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 18.0653i | − | 1.16369i | −0.813300 | − | 0.581844i | \(-0.802331\pi\) | ||
0.813300 | − | 0.581844i | \(-0.197669\pi\) | |||||||
\(242\) | 10.3020i | 0.662236i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.703333i | 0.0450263i | ||||||||
\(245\) | 8.69197 | − | 6.76127i | 0.555309 | − | 0.431962i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.2367 | 0.714975 | ||||||||
\(248\) | 9.98331 | 0.633941 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 11.8383i | 0.748718i | ||||||||
\(251\) | −17.7361 | −1.11949 | −0.559747 | − | 0.828664i | \(-0.689102\pi\) | ||||
−0.559747 | + | 0.828664i | \(0.689102\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.24264 | 0.266733 | ||||||||
\(254\) | 2.82327i | 0.177148i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −31.3140 | −1.95331 | −0.976657 | − | 0.214805i | \(-0.931088\pi\) | ||||
−0.976657 | + | 0.214805i | \(0.931088\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.344001 | + | 1.00250i | 0.0213752 | + | 0.0622925i | ||||
\(260\) | 7.16844i | 0.444568i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 18.6059i | 1.14948i | ||||||||
\(263\) | 24.1918i | 1.49173i | 0.666098 | + | 0.745864i | \(0.267963\pi\) | ||||
−0.666098 | + | 0.745864i | \(0.732037\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 12.8938i | − | 0.792058i | ||||||
\(266\) | 2.11756 | + | 6.17109i | 0.129836 | + | 0.378374i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.46651 | 0.517174 | ||||||||
\(269\) | 25.8912 | 1.57862 | 0.789308 | − | 0.613998i | \(-0.210440\pi\) | ||||
0.789308 | + | 0.613998i | \(0.210440\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 29.8768i | 1.81489i | 0.420176 | + | 0.907443i | \(0.361968\pi\) | ||||
−0.420176 | + | 0.907443i | \(0.638032\pi\) | |||||||
\(272\) | −0.258822 | −0.0156934 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −17.6227 | −1.06463 | ||||||||
\(275\) | − | 2.10974i | − | 0.127222i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.5113 | −1.53282 | −0.766412 | − | 0.642350i | \(-0.777960\pi\) | ||||
−0.766412 | + | 0.642350i | \(0.777960\pi\) | |||||||
\(278\) | −2.02144 | −0.121238 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.93684 | + | 1.35089i | −0.235271 | + | 0.0807313i | ||||
\(281\) | 9.01221i | 0.537623i | 0.963193 | + | 0.268812i | \(0.0866309\pi\) | ||||
−0.963193 | + | 0.268812i | \(0.913369\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.07817i | 0.301866i | 0.988544 | + | 0.150933i | \(0.0482278\pi\) | ||||
−0.988544 | + | 0.150933i | \(0.951772\pi\) | |||||||
\(284\) | 4.76784i | 0.282919i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 3.80705i | − | 0.225115i | ||||||
\(287\) | −8.43314 | − | 24.5762i | −0.497793 | − | 1.45069i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9330 | −0.996059 | ||||||||
\(290\) | −4.58351 | −0.269153 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.72981i | 0.452353i | ||||||||
\(293\) | 20.6339 | 1.20545 | 0.602723 | − | 0.797950i | \(-0.294082\pi\) | ||||
0.602723 | + | 0.797950i | \(0.294082\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.88196 | 0.167794 | ||||||||
\(296\) | − | 0.400597i | − | 0.0232843i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 21.6505 | 1.25418 | ||||||||
\(299\) | 23.1397 | 1.33820 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.28648 | − | 15.4061i | −0.304707 | − | 0.887992i | ||||
\(302\) | − | 17.5235i | − | 1.00836i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 2.46595i | − | 0.141432i | ||||||
\(305\) | 1.10645i | 0.0633550i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.8254i | 1.24564i | 0.782366 | + | 0.622819i | \(0.214013\pi\) | ||||
−0.782366 | + | 0.622819i | \(0.785987\pi\) | |||||||
\(308\) | 2.09079 | − | 0.717439i | 0.119134 | − | 0.0408799i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 15.7052 | 0.891997 | ||||||||
\(311\) | −0.289372 | −0.0164088 | −0.00820440 | − | 0.999966i | \(-0.502612\pi\) | ||||
−0.00820440 | + | 0.999966i | \(0.502612\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.8915i | 1.06781i | 0.845544 | + | 0.533906i | \(0.179276\pi\) | ||||
−0.845544 | + | 0.533906i | \(0.820724\pi\) | |||||||
\(314\) | 10.8493 | 0.612264 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.9917 | −0.730841 | ||||||||
\(317\) | − | 15.0299i | − | 0.844163i | −0.906558 | − | 0.422082i | \(-0.861300\pi\) | ||
0.906558 | − | 0.422082i | \(-0.138700\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.43423 | 0.136291 | ||||||||
\(320\) | 1.57315 | 0.0879417 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.36068 | + | 12.7081i | 0.243011 | + | 0.708194i | ||||
\(323\) | 0.638242i | 0.0355128i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 11.5067i | − | 0.638277i | ||||||
\(326\) | − | 11.6376i | − | 0.644547i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.82060i | 0.542252i | ||||||||
\(329\) | −9.18007 | − | 26.7530i | −0.506114 | − | 1.47494i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.8182 | 1.19924 | 0.599620 | − | 0.800285i | \(-0.295319\pi\) | ||||
0.599620 | + | 0.800285i | \(0.295319\pi\) | |||||||
\(332\) | 5.42278 | 0.297614 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 11.1349i | 0.609276i | ||||||||
\(335\) | 13.3191 | 0.727699 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.09032 | 0.495181 | 0.247591 | − | 0.968865i | \(-0.420361\pi\) | ||||
0.247591 | + | 0.968865i | \(0.420361\pi\) | |||||||
\(338\) | − | 7.76393i | − | 0.422302i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.407165 | −0.0220816 | ||||||||
\(341\) | −8.34081 | −0.451680 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.5002 | − | 10.1362i | −0.836934 | − | 0.547304i | ||||
\(344\) | 6.15623i | 0.331922i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.80295i | 0.419489i | ||||||||
\(347\) | 14.2826i | 0.766728i | 0.923597 | + | 0.383364i | \(0.125235\pi\) | ||||
−0.923597 | + | 0.383364i | \(0.874765\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 33.5047i | − | 1.79347i | −0.442573 | − | 0.896733i | \(-0.645934\pi\) | ||
0.442573 | − | 0.896733i | \(-0.354066\pi\) | |||||||
\(350\) | 6.31937 | − | 2.16844i | 0.337784 | − | 0.115908i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.835475 | −0.0445310 | ||||||||
\(353\) | 28.5625 | 1.52023 | 0.760113 | − | 0.649791i | \(-0.225143\pi\) | ||||
0.760113 | + | 0.649791i | \(0.225143\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.50053i | 0.398087i | ||||||||
\(356\) | −6.03377 | −0.319789 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −15.9956 | −0.845395 | ||||||||
\(359\) | − | 23.8272i | − | 1.25755i | −0.777587 | − | 0.628775i | \(-0.783557\pi\) | ||
0.777587 | − | 0.628775i | \(-0.216443\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.9191 | 0.679952 | ||||||||
\(362\) | −1.92154 | −0.100994 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 11.4033 | − | 3.91297i | 0.597697 | − | 0.205095i | ||||
\(365\) | 12.1601i | 0.636491i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.2709i | 0.588334i | 0.955754 | + | 0.294167i | \(0.0950423\pi\) | ||||
−0.955754 | + | 0.294167i | \(0.904958\pi\) | |||||||
\(368\) | − | 5.07812i | − | 0.264715i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 0.630200i | − | 0.0327625i | ||||||
\(371\) | −20.5110 | + | 7.03820i | −1.06488 | + | 0.365405i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.65153 | −0.137291 | −0.0686455 | − | 0.997641i | \(-0.521868\pi\) | ||||
−0.0686455 | + | 0.997641i | \(0.521868\pi\) | |||||||
\(374\) | 0.216239 | 0.0111815 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.6904i | 0.551316i | ||||||||
\(377\) | 13.2765 | 0.683774 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.0820 | 0.723345 | 0.361673 | − | 0.932305i | \(-0.382206\pi\) | ||||
0.361673 | + | 0.932305i | \(0.382206\pi\) | |||||||
\(380\) | − | 3.87931i | − | 0.199004i | ||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.92580 | 0.303190 | ||||||||
\(383\) | 16.6936 | 0.853005 | 0.426503 | − | 0.904486i | \(-0.359745\pi\) | ||||
0.426503 | + | 0.904486i | \(0.359745\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.28913 | − | 1.12864i | 0.167630 | − | 0.0575207i | ||||
\(386\) | 2.98450i | 0.151907i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 1.15163i | − | 0.0584649i | ||||||
\(389\) | 28.7203i | 1.45618i | 0.685484 | + | 0.728088i | \(0.259591\pi\) | ||||
−0.685484 | + | 0.728088i | \(0.740409\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.31433i | 0.0664684i | ||||||||
\(392\) | 4.29792 | + | 5.52520i | 0.217078 | + | 0.279065i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.00657 | 0.0507102 | ||||||||
\(395\) | −20.4379 | −1.02834 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 23.6343i | − | 1.18617i | −0.805139 | − | 0.593087i | \(-0.797909\pi\) | ||
0.805139 | − | 0.593087i | \(-0.202091\pi\) | |||||||
\(398\) | −17.6170 | −0.883060 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.52520 | −0.126260 | ||||||||
\(401\) | − | 9.07546i | − | 0.453207i | −0.973987 | − | 0.226604i | \(-0.927238\pi\) | ||
0.973987 | − | 0.226604i | \(-0.0727622\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −45.4914 | −2.26609 | ||||||||
\(404\) | 18.6059 | 0.925679 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.50196 | + | 7.29132i | 0.124170 | + | 0.361862i | ||||
\(407\) | 0.334689i | 0.0165899i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 3.36909i | − | 0.166591i | −0.996525 | − | 0.0832953i | \(-0.973456\pi\) | ||
0.996525 | − | 0.0832953i | \(-0.0265445\pi\) | |||||||
\(410\) | 15.4493i | 0.762985i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 3.66394i | − | 0.180509i | ||||||
\(413\) | −1.57315 | − | 4.58454i | −0.0774096 | − | 0.225591i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.53084 | 0.418763 | ||||||||
\(416\) | −4.55675 | −0.223413 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.06024i | 0.100770i | ||||||||
\(419\) | −8.64938 | −0.422550 | −0.211275 | − | 0.977427i | \(-0.567762\pi\) | ||||
−0.211275 | + | 0.977427i | \(0.567762\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.2112 | 1.56988 | 0.784939 | − | 0.619573i | \(-0.212694\pi\) | ||||
0.784939 | + | 0.619573i | \(0.212694\pi\) | |||||||
\(422\) | 2.87540i | 0.139972i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8.19615 | 0.398040 | ||||||||
\(425\) | 0.653577 | 0.0317032 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.76010 | − | 0.603965i | 0.0851774 | − | 0.0292279i | ||||
\(428\) | − | 3.48137i | − | 0.168278i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 9.68467i | 0.467036i | ||||||||
\(431\) | 27.0725i | 1.30404i | 0.758204 | + | 0.652018i | \(0.226077\pi\) | ||||
−0.758204 | + | 0.652018i | \(0.773923\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 23.3909i | − | 1.12410i | −0.827104 | − | 0.562048i | \(-0.810013\pi\) | ||
0.827104 | − | 0.562048i | \(-0.189987\pi\) | |||||||
\(434\) | −8.57286 | − | 24.9834i | −0.411510 | − | 1.19924i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −17.6692 | −0.846202 | ||||||||
\(437\) | −12.5224 | −0.599027 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 10.0297i | − | 0.478690i | −0.970935 | − | 0.239345i | \(-0.923067\pi\) | ||
0.970935 | − | 0.239345i | \(-0.0769327\pi\) | |||||||
\(440\) | −1.31433 | −0.0626581 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.17939 | 0.0560976 | ||||||||
\(443\) | − | 3.12697i | − | 0.148567i | −0.997237 | − | 0.0742835i | \(-0.976333\pi\) | ||
0.997237 | − | 0.0742835i | \(-0.0236670\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.49203 | −0.449965 | ||||||||
\(446\) | −17.3380 | −0.820976 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.858719 | − | 2.50252i | −0.0405707 | − | 0.118233i | ||||
\(449\) | 18.0633i | 0.852458i | 0.904615 | + | 0.426229i | \(0.140158\pi\) | ||||
−0.904615 | + | 0.426229i | \(0.859842\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 8.20487i | − | 0.386352i | ||||||
\(452\) | − | 14.2808i | − | 0.671714i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 15.0151i | 0.704694i | ||||||||
\(455\) | 17.9392 | − | 6.15568i | 0.841001 | − | 0.288583i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.1822 | 1.13120 | 0.565598 | − | 0.824681i | \(-0.308645\pi\) | ||||
0.565598 | + | 0.824681i | \(0.308645\pi\) | |||||||
\(458\) | 18.7484 | 0.876056 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 7.98863i | − | 0.372472i | ||||||
\(461\) | −16.7668 | −0.780907 | −0.390453 | − | 0.920623i | \(-0.627682\pi\) | ||||
−0.390453 | + | 0.920623i | \(0.627682\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.7052 | −0.636936 | −0.318468 | − | 0.947934i | \(-0.603168\pi\) | ||||
−0.318468 | + | 0.947934i | \(0.603168\pi\) | |||||||
\(464\) | − | 2.91359i | − | 0.135260i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.6099 | −0.584142 | ||||||||
\(467\) | −38.1548 | −1.76559 | −0.882797 | − | 0.469755i | \(-0.844342\pi\) | ||||
−0.882797 | + | 0.469755i | \(0.844342\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.27035 | − | 21.1876i | −0.335714 | − | 0.978352i | ||||
\(470\) | 16.8176i | 0.775739i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.83197i | 0.0843233i | ||||||||
\(473\) | − | 5.14338i | − | 0.236493i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.22703i | 0.285716i | ||||||||
\(476\) | 0.222255 | + | 0.647707i | 0.0101871 | + | 0.0296876i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −24.5429 | −1.12257 | ||||||||
\(479\) | −14.3544 | −0.655868 | −0.327934 | − | 0.944701i | \(-0.606352\pi\) | ||||
−0.327934 | + | 0.944701i | \(0.606352\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.82542i | 0.0832320i | ||||||||
\(482\) | 18.0653 | 0.822852 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.3020 | −0.468272 | ||||||||
\(485\) | − | 1.81168i | − | 0.0822641i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.3633 | 0.469607 | 0.234804 | − | 0.972043i | \(-0.424555\pi\) | ||||
0.234804 | + | 0.972043i | \(0.424555\pi\) | |||||||
\(488\) | −0.703333 | −0.0318384 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 6.76127 | + | 8.69197i | 0.305443 | + | 0.392663i | ||||
\(491\) | 28.3923i | 1.28133i | 0.767822 | + | 0.640663i | \(0.221341\pi\) | ||||
−0.767822 | + | 0.640663i | \(0.778659\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.754101i | 0.0339630i | ||||||||
\(494\) | 11.2367i | 0.505564i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.98331i | 0.448264i | ||||||||
\(497\) | 11.9316 | − | 4.09424i | 0.535206 | − | 0.183652i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.40717 | −0.242058 | −0.121029 | − | 0.992649i | \(-0.538619\pi\) | ||||
−0.121029 | + | 0.992649i | \(0.538619\pi\) | |||||||
\(500\) | −11.8383 | −0.529423 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 17.7361i | − | 0.791601i | ||||||
\(503\) | −32.3695 | −1.44329 | −0.721643 | − | 0.692266i | \(-0.756613\pi\) | ||||
−0.721643 | + | 0.692266i | \(0.756613\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 29.2699 | 1.30249 | ||||||||
\(506\) | 4.24264i | 0.188608i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.82327 | −0.125262 | ||||||||
\(509\) | −5.07061 | −0.224751 | −0.112375 | − | 0.993666i | \(-0.535846\pi\) | ||||
−0.112375 | + | 0.993666i | \(0.535846\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.3440 | − | 6.63774i | 0.855728 | − | 0.293636i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 31.3140i | − | 1.38120i | ||||||
\(515\) | − | 5.76393i | − | 0.253989i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 8.93158i | − | 0.392811i | ||||||
\(518\) | −1.00250 | + | 0.344001i | −0.0440474 | + | 0.0151145i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −7.16844 | −0.314357 | ||||||||
\(521\) | −28.1911 | −1.23507 | −0.617537 | − | 0.786542i | \(-0.711869\pi\) | ||||
−0.617537 | + | 0.786542i | \(0.711869\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 29.4515i | − | 1.28782i | −0.765100 | − | 0.643912i | \(-0.777310\pi\) | ||
0.765100 | − | 0.643912i | \(-0.222690\pi\) | |||||||
\(524\) | −18.6059 | −0.812803 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24.1918 | −1.05481 | ||||||||
\(527\) | − | 2.58390i | − | 0.112556i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.78726 | −0.121185 | ||||||||
\(530\) | 12.8938 | 0.560070 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6.17109 | + | 2.11756i | −0.267551 | + | 0.0918079i | ||||
\(533\) | − | 44.7500i | − | 1.93834i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 5.47671i | − | 0.236779i | ||||||
\(536\) | 8.46651i | 0.365697i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 25.8912i | 1.11625i | ||||||||
\(539\) | −3.59081 | − | 4.61617i | −0.154667 | − | 0.198833i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.7052 | −0.976174 | −0.488087 | − | 0.872795i | \(-0.662305\pi\) | ||||
−0.488087 | + | 0.872795i | \(0.662305\pi\) | |||||||
\(542\) | −29.8768 | −1.28332 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 0.258822i | − | 0.0110969i | ||||||
\(545\) | −27.7963 | −1.19066 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.70258 | 0.286582 | 0.143291 | − | 0.989681i | \(-0.454232\pi\) | ||||
0.143291 | + | 0.989681i | \(0.454232\pi\) | |||||||
\(548\) | − | 17.6227i | − | 0.752806i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.10974 | 0.0899598 | ||||||||
\(551\) | −7.18478 | −0.306082 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.1562 | + | 32.5120i | 0.474411 | + | 1.38255i | ||||
\(554\) | − | 25.5113i | − | 1.08387i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 2.02144i | − | 0.0857282i | ||||||
\(557\) | − | 22.4015i | − | 0.949183i | −0.880206 | − | 0.474592i | \(-0.842596\pi\) | ||
0.880206 | − | 0.474592i | \(-0.157404\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 28.0524i | − | 1.18649i | ||||||
\(560\) | −1.35089 | − | 3.93684i | −0.0570857 | − | 0.166362i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9.01221 | −0.380157 | ||||||||
\(563\) | 38.1740 | 1.60884 | 0.804421 | − | 0.594059i | \(-0.202476\pi\) | ||||
0.804421 | + | 0.594059i | \(0.202476\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 22.4659i | − | 0.945147i | ||||||
\(566\) | −5.07817 | −0.213451 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.76784 | −0.200054 | ||||||||
\(569\) | − | 6.75955i | − | 0.283375i | −0.989911 | − | 0.141688i | \(-0.954747\pi\) | ||
0.989911 | − | 0.141688i | \(-0.0452528\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.0484 | −0.713453 | −0.356727 | − | 0.934209i | \(-0.616107\pi\) | ||||
−0.356727 | + | 0.934209i | \(0.616107\pi\) | |||||||
\(572\) | 3.80705 | 0.159181 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 24.5762 | − | 8.43314i | 1.02579 | − | 0.351993i | ||||
\(575\) | 12.8233i | 0.534767i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 0.919572i | − | 0.0382823i | −0.999817 | − | 0.0191411i | \(-0.993907\pi\) | ||
0.999817 | − | 0.0191411i | \(-0.00609319\pi\) | |||||||
\(578\) | − | 16.9330i | − | 0.704320i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 4.58351i | − | 0.190320i | ||||||
\(581\) | −4.65665 | − | 13.5706i | −0.193190 | − | 0.563004i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.84768 | −0.283602 | ||||||||
\(584\) | −7.72981 | −0.319862 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 20.6339i | 0.852379i | ||||||||
\(587\) | −17.8824 | −0.738084 | −0.369042 | − | 0.929413i | \(-0.620314\pi\) | ||||
−0.369042 | + | 0.929413i | \(0.620314\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24.6184 | 1.01438 | ||||||||
\(590\) | 2.88196i | 0.118649i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.400597 | 0.0164645 | ||||||||
\(593\) | 9.75882 | 0.400747 | 0.200373 | − | 0.979720i | \(-0.435785\pi\) | ||||
0.200373 | + | 0.979720i | \(0.435785\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.349641 | + | 1.01894i | 0.0143339 | + | 0.0417724i | ||||
\(596\) | 21.6505i | 0.886837i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 23.1397i | 0.946252i | ||||||||
\(599\) | − | 20.1506i | − | 0.823331i | −0.911335 | − | 0.411665i | \(-0.864947\pi\) | ||
0.911335 | − | 0.411665i | \(-0.135053\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 15.3831i | − | 0.627490i | −0.949507 | − | 0.313745i | \(-0.898416\pi\) | ||
0.949507 | − | 0.313745i | \(-0.101584\pi\) | |||||||
\(602\) | 15.4061 | − | 5.28648i | 0.627905 | − | 0.215461i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 17.5235 | 0.713020 | ||||||||
\(605\) | −16.2066 | −0.658890 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 46.3793i | 1.88248i | 0.337744 | + | 0.941238i | \(0.390336\pi\) | ||||
−0.337744 | + | 0.941238i | \(0.609664\pi\) | |||||||
\(608\) | 2.46595 | 0.100008 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.10645 | −0.0447987 | ||||||||
\(611\) | − | 48.7135i | − | 1.97074i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 42.7977 | 1.72858 | 0.864292 | − | 0.502990i | \(-0.167767\pi\) | ||||
0.864292 | + | 0.502990i | \(0.167767\pi\) | |||||||
\(614\) | −21.8254 | −0.880800 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.717439 | + | 2.09079i | 0.0289064 | + | 0.0842404i | ||||
\(617\) | − | 10.7464i | − | 0.432634i | −0.976323 | − | 0.216317i | \(-0.930595\pi\) | ||
0.976323 | − | 0.216317i | \(-0.0694045\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 14.0650i | − | 0.565320i | −0.959220 | − | 0.282660i | \(-0.908783\pi\) | ||
0.959220 | − | 0.282660i | \(-0.0912168\pi\) | |||||||
\(620\) | 15.7052i | 0.630737i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 0.289372i | − | 0.0116028i | ||||||
\(623\) | 5.18132 | + | 15.0996i | 0.207585 | + | 0.604954i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.99735 | −0.239894 | ||||||||
\(626\) | −18.8915 | −0.755057 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10.8493i | 0.432936i | ||||||||
\(629\) | −0.103683 | −0.00413413 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.27818 | 0.329549 | 0.164775 | − | 0.986331i | \(-0.447310\pi\) | ||||
0.164775 | + | 0.986331i | \(0.447310\pi\) | |||||||
\(632\) | − | 12.9917i | − | 0.516782i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 15.0299 | 0.596914 | ||||||||
\(635\) | −4.44142 | −0.176252 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19.5845 | − | 25.1769i | −0.775968 | − | 0.997547i | ||||
\(638\) | 2.43423i | 0.0963722i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.57315i | 0.0621842i | ||||||||
\(641\) | 31.0188i | 1.22517i | 0.790406 | + | 0.612584i | \(0.209870\pi\) | ||||
−0.790406 | + | 0.612584i | \(0.790130\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.33672i | 0.171024i | 0.996337 | + | 0.0855119i | \(0.0272525\pi\) | ||||
−0.996337 | + | 0.0855119i | \(0.972747\pi\) | |||||||
\(644\) | −12.7081 | + | 4.36068i | −0.500769 | + | 0.171835i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.638242 | −0.0251113 | ||||||||
\(647\) | −13.6205 | −0.535476 | −0.267738 | − | 0.963492i | \(-0.586276\pi\) | ||||
−0.267738 | + | 0.963492i | \(0.586276\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1.53057i | − | 0.0600800i | ||||||
\(650\) | 11.5067 | 0.451330 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11.6376 | 0.455764 | ||||||||
\(653\) | 38.6016i | 1.51060i | 0.655381 | + | 0.755299i | \(0.272508\pi\) | ||||
−0.655381 | + | 0.755299i | \(0.727492\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −29.2699 | −1.14367 | ||||||||
\(656\) | −9.82060 | −0.383430 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 26.7530 | − | 9.18007i | 1.04294 | − | 0.357877i | ||||
\(659\) | − | 3.29961i | − | 0.128535i | −0.997933 | − | 0.0642673i | \(-0.979529\pi\) | ||
0.997933 | − | 0.0642673i | \(-0.0204710\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 10.2885i | − | 0.400176i | −0.979778 | − | 0.200088i | \(-0.935877\pi\) | ||
0.979778 | − | 0.200088i | \(-0.0641228\pi\) | |||||||
\(662\) | 21.8182i | 0.847990i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.42278i | 0.210445i | ||||||||
\(665\) | −9.70805 | + | 3.33124i | −0.376462 | + | 0.129180i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.7956 | −0.572886 | ||||||||
\(668\) | −11.1349 | −0.430823 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 13.3191i | 0.514561i | ||||||||
\(671\) | 0.587617 | 0.0226847 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.58063 | 0.138023 | 0.0690115 | − | 0.997616i | \(-0.478015\pi\) | ||||
0.0690115 | + | 0.997616i | \(0.478015\pi\) | |||||||
\(674\) | 9.09032i | 0.350146i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.76393 | 0.298613 | ||||||||
\(677\) | −31.1283 | −1.19636 | −0.598179 | − | 0.801362i | \(-0.704109\pi\) | ||||
−0.598179 | + | 0.801362i | \(0.704109\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.88196 | + | 0.988923i | −0.110600 | + | 0.0379514i | ||||
\(680\) | − | 0.407165i | − | 0.0156141i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 8.34081i | − | 0.319386i | ||||||
\(683\) | − | 3.51472i | − | 0.134487i | −0.997737 | − | 0.0672435i | \(-0.978580\pi\) | ||
0.997737 | − | 0.0672435i | \(-0.0214204\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 27.7232i | − | 1.05925i | ||||||
\(686\) | 10.1362 | − | 15.5002i | 0.387002 | − | 0.591802i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.15623 | −0.234704 | ||||||||
\(689\) | −37.3478 | −1.42284 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 25.2239i | − | 0.959563i | −0.877388 | − | 0.479782i | \(-0.840716\pi\) | ||
0.877388 | − | 0.479782i | \(-0.159284\pi\) | |||||||
\(692\) | −7.80295 | −0.296623 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −14.2826 | −0.542159 | ||||||||
\(695\) | − | 3.18003i | − | 0.120625i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.54179 | 0.0962770 | ||||||||
\(698\) | 33.5047 | 1.26817 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.16844 | + | 6.31937i | 0.0819593 | + | 0.238850i | ||||
\(701\) | − | 20.5291i | − | 0.775374i | −0.921791 | − | 0.387687i | \(-0.873274\pi\) | ||
0.921791 | − | 0.387687i | \(-0.126726\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 0.987854i | − | 0.0372576i | ||||||
\(704\) | − | 0.835475i | − | 0.0314882i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 28.5625i | 1.07496i | ||||||||
\(707\) | −15.9773 | − | 46.5617i | −0.600887 | − | 1.75113i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.79821 | 0.330424 | 0.165212 | − | 0.986258i | \(-0.447169\pi\) | ||||
0.165212 | + | 0.986258i | \(0.447169\pi\) | |||||||
\(710\) | −7.50053 | −0.281490 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 6.03377i | − | 0.226125i | ||||||
\(713\) | 50.6964 | 1.89859 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.98905 | 0.223978 | ||||||||
\(716\) | − | 15.9956i | − | 0.597784i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 23.8272 | 0.889223 | ||||||||
\(719\) | 1.14886 | 0.0428451 | 0.0214226 | − | 0.999771i | \(-0.493180\pi\) | ||||
0.0214226 | + | 0.999771i | \(0.493180\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.16908 | + | 3.14630i | −0.341475 | + | 0.117174i | ||||
\(722\) | 12.9191i | 0.480798i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 1.92154i | − | 0.0714135i | ||||||
\(725\) | 7.35741i | 0.273247i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.7200i | 0.397581i | 0.980042 | + | 0.198791i | \(0.0637014\pi\) | ||||
−0.980042 | + | 0.198791i | \(0.936299\pi\) | |||||||
\(728\) | 3.91297 | + | 11.4033i | 0.145024 | + | 0.422636i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −12.1601 | −0.450067 | ||||||||
\(731\) | 1.59337 | 0.0589328 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 26.1768i | − | 0.966863i | −0.875382 | − | 0.483431i | \(-0.839390\pi\) | ||
0.875382 | − | 0.483431i | \(-0.160610\pi\) | |||||||
\(734\) | −11.2709 | −0.416015 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.07812 | 0.187182 | ||||||||
\(737\) | − | 7.07356i | − | 0.260558i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −41.6267 | −1.53126 | −0.765631 | − | 0.643280i | \(-0.777573\pi\) | ||||
−0.765631 | + | 0.643280i | \(0.777573\pi\) | |||||||
\(740\) | 0.630200 | 0.0231666 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.03820 | − | 20.5110i | −0.258380 | − | 0.752983i | ||||
\(743\) | 0.602674i | 0.0221100i | 0.999939 | + | 0.0110550i | \(0.00351898\pi\) | ||||
−0.999939 | + | 0.0110550i | \(0.996481\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 34.0594i | 1.24784i | ||||||||
\(746\) | − | 2.65153i | − | 0.0970794i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.216239i | 0.00790649i | ||||||||
\(749\) | −8.71218 | + | 2.98952i | −0.318336 | + | 0.109235i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.3550 | 0.560313 | 0.280157 | − | 0.959954i | \(-0.409614\pi\) | ||||
0.280157 | + | 0.959954i | \(0.409614\pi\) | |||||||
\(752\) | −10.6904 | −0.389840 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 13.2765i | 0.483501i | ||||||||
\(755\) | 27.5670 | 1.00327 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.1331 | 0.949823 | 0.474911 | − | 0.880034i | \(-0.342480\pi\) | ||||
0.474911 | + | 0.880034i | \(0.342480\pi\) | |||||||
\(758\) | 14.0820i | 0.511482i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.87931 | 0.140717 | ||||||||
\(761\) | −16.2258 | −0.588183 | −0.294092 | − | 0.955777i | \(-0.595017\pi\) | ||||
−0.294092 | + | 0.955777i | \(0.595017\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.1729 | + | 44.2176i | 0.549296 | + | 1.60078i | ||||
\(764\) | 5.92580i | 0.214388i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 16.6936i | 0.603166i | ||||||||
\(767\) | − | 8.34783i | − | 0.301422i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36.9170i | 1.33126i | 0.746282 | + | 0.665630i | \(0.231837\pi\) | ||||
−0.746282 | + | 0.665630i | \(0.768163\pi\) | |||||||
\(770\) | 1.12864 | + | 3.28913i | 0.0406733 | + | 0.118532i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.98450 | −0.107414 | ||||||||
\(773\) | 18.8576 | 0.678260 | 0.339130 | − | 0.940740i | \(-0.389867\pi\) | ||||
0.339130 | + | 0.940740i | \(0.389867\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 25.2099i | − | 0.905565i | ||||||
\(776\) | 1.15163 | 0.0413409 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −28.7203 | −1.02967 | ||||||||
\(779\) | 24.2171i | 0.867669i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.98341 | 0.142538 | ||||||||
\(782\) | −1.31433 | −0.0470002 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.52520 | + | 4.29792i | −0.197329 | + | 0.153497i | ||||
\(785\) | 17.0676i | 0.609170i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.1760i | 0.469673i | 0.972035 | + | 0.234836i | \(0.0754554\pi\) | ||||
−0.972035 | + | 0.234836i | \(0.924545\pi\) | |||||||
\(788\) | 1.00657i | 0.0358575i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 20.4379i | − | 0.727148i | ||||||
\(791\) | −35.7381 | + | 12.2632i | −1.27070 | + | 0.436030i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.20491 | 0.113810 | ||||||||
\(794\) | 23.6343 | 0.838751 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 17.6170i | − | 0.624418i | ||||||
\(797\) | −7.80295 | −0.276394 | −0.138197 | − | 0.990405i | \(-0.544131\pi\) | ||||
−0.138197 | + | 0.990405i | \(0.544131\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.76691 | 0.0978864 | ||||||||
\(800\) | − | 2.52520i | − | 0.0892794i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.07546 | 0.320466 | ||||||||
\(803\) | 6.45807 | 0.227900 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −19.9917 | + | 6.86000i | −0.704615 | + | 0.241783i | ||||
\(806\) | − | 45.4914i | − | 1.60237i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 18.6059i | 0.654554i | ||||||||
\(809\) | 1.68815i | 0.0593523i | 0.999560 | + | 0.0296762i | \(0.00944761\pi\) | ||||
−0.999560 | + | 0.0296762i | \(0.990552\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.7131i | 1.42963i | 0.699314 | + | 0.714815i | \(0.253489\pi\) | ||||
−0.699314 | + | 0.714815i | \(0.746511\pi\) | |||||||
\(812\) | −7.29132 | + | 2.50196i | −0.255875 | + | 0.0878015i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.334689 | −0.0117309 | ||||||||
\(815\) | 18.3077 | 0.641290 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15.1810i | 0.531115i | ||||||||
\(818\) | 3.36909 | 0.117797 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −15.4493 | −0.539512 | ||||||||
\(821\) | − | 32.7408i | − | 1.14266i | −0.820720 | − | 0.571330i | \(-0.806427\pi\) | ||
0.820720 | − | 0.571330i | \(-0.193573\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −51.6210 | −1.79940 | −0.899698 | − | 0.436514i | \(-0.856213\pi\) | ||||
−0.899698 | + | 0.436514i | \(0.856213\pi\) | |||||||
\(824\) | 3.66394 | 0.127639 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.58454 | − | 1.57315i | 0.159517 | − | 0.0547369i | ||||
\(827\) | 28.5318i | 0.992147i | 0.868281 | + | 0.496073i | \(0.165225\pi\) | ||||
−0.868281 | + | 0.496073i | \(0.834775\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.1211i | 0.420983i | 0.977596 | + | 0.210491i | \(0.0675064\pi\) | ||||
−0.977596 | + | 0.210491i | \(0.932494\pi\) | |||||||
\(830\) | 8.53084i | 0.296110i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 4.55675i | − | 0.157977i | ||||||
\(833\) | 1.43004 | − | 1.11240i | 0.0495480 | − | 0.0385423i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17.5169 | −0.606198 | ||||||||
\(836\) | −2.06024 | −0.0712550 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 8.64938i | − | 0.298788i | ||||||
\(839\) | 17.4571 | 0.602685 | 0.301342 | − | 0.953516i | \(-0.402565\pi\) | ||||
0.301342 | + | 0.953516i | \(0.402565\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.5110 | 0.707275 | ||||||||
\(842\) | 32.2112i | 1.11007i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.87540 | −0.0989752 | ||||||||
\(845\) | 12.2138 | 0.420168 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.84651 | + | 25.7809i | 0.303970 | + | 0.885842i | ||||
\(848\) | 8.19615i | 0.281457i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.653577i | 0.0224175i | ||||||||
\(851\) | − | 2.03428i | − | 0.0697342i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.9338i | 0.990676i | 0.868700 | + | 0.495338i | \(0.164956\pi\) | ||||
−0.868700 | + | 0.495338i | \(0.835044\pi\) | |||||||
\(854\) | 0.603965 | + | 1.76010i | 0.0206673 | + | 0.0602295i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.48137 | 0.118991 | ||||||||
\(857\) | 23.0360 | 0.786895 | 0.393447 | − | 0.919347i | \(-0.371282\pi\) | ||||
0.393447 | + | 0.919347i | \(0.371282\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 25.3966i | − | 0.866520i | −0.901269 | − | 0.433260i | \(-0.857363\pi\) | ||
0.901269 | − | 0.433260i | \(-0.142637\pi\) | |||||||
\(860\) | −9.68467 | −0.330245 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −27.0725 | −0.922092 | ||||||||
\(863\) | − | 0.685811i | − | 0.0233453i | −0.999932 | − | 0.0116726i | \(-0.996284\pi\) | ||
0.999932 | − | 0.0116726i | \(-0.00371560\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.2752 | −0.417369 | ||||||||
\(866\) | 23.3909 | 0.794856 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 24.9834 | − | 8.57286i | 0.847992 | − | 0.290982i | ||||
\(869\) | 10.8543i | 0.368205i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 38.5797i | − | 1.30722i | ||||||
\(872\) | − | 17.6692i | − | 0.598355i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 12.5224i | − | 0.423576i | ||||||
\(875\) | 10.1657 | + | 29.6255i | 0.343665 | + | 1.00152i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −29.3236 | −0.990187 | −0.495094 | − | 0.868840i | \(-0.664866\pi\) | ||||
−0.495094 | + | 0.868840i | \(0.664866\pi\) | |||||||
\(878\) | 10.0297 | 0.338485 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 1.31433i | − | 0.0443060i | ||||||
\(881\) | −4.31752 | −0.145461 | −0.0727305 | − | 0.997352i | \(-0.523171\pi\) | ||||
−0.0727305 | + | 0.997352i | \(0.523171\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.9773 | 0.436721 | 0.218361 | − | 0.975868i | \(-0.429929\pi\) | ||||
0.218361 | + | 0.975868i | \(0.429929\pi\) | |||||||
\(884\) | 1.17939i | 0.0396670i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.12697 | 0.105053 | ||||||||
\(887\) | 3.24897 | 0.109090 | 0.0545448 | − | 0.998511i | \(-0.482629\pi\) | ||||
0.0545448 | + | 0.998511i | \(0.482629\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.42439 | + | 7.06528i | 0.0813116 | + | 0.236962i | ||||
\(890\) | − | 9.49203i | − | 0.318173i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 17.3380i | − | 0.580518i | ||||||
\(893\) | 26.3621i | 0.882173i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 25.1635i | − | 0.841123i | ||||||
\(896\) | 2.50252 | − | 0.858719i | 0.0836033 | − | 0.0286878i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −18.0633 | −0.602779 | ||||||||
\(899\) | 29.0873 | 0.970115 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 2.12134i | − | 0.0706722i | ||||||
\(902\) | 8.20487 | 0.273192 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14.2808 | 0.474974 | ||||||||
\(905\) | − | 3.02287i | − | 0.100484i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.1395 | 0.735129 | 0.367564 | − | 0.929998i | \(-0.380192\pi\) | ||||
0.367564 | + | 0.929998i | \(0.380192\pi\) | |||||||
\(908\) | −15.0151 | −0.498294 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 6.15568 | + | 17.9392i | 0.204059 | + | 0.594677i | ||||
\(911\) | − | 56.7602i | − | 1.88055i | −0.340417 | − | 0.940275i | \(-0.610568\pi\) | ||
0.340417 | − | 0.940275i | \(-0.389432\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 4.53060i | − | 0.149941i | ||||||
\(914\) | 24.1822i | 0.799877i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18.7484i | 0.619465i | ||||||||
\(917\) | 15.9773 | + | 46.5617i | 0.527616 | + | 1.53760i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.1180 | −0.564672 | −0.282336 | − | 0.959316i | \(-0.591109\pi\) | ||||
−0.282336 | + | 0.959316i | \(0.591109\pi\) | |||||||
\(920\) | 7.98863 | 0.263377 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 16.7668i | − | 0.552184i | ||||||
\(923\) | 21.7258 | 0.715115 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.01159 | −0.0332609 | ||||||||
\(926\) | − | 13.7052i | − | 0.450382i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.91359 | 0.0956433 | ||||||||
\(929\) | 8.61166 | 0.282539 | 0.141270 | − | 0.989971i | \(-0.454882\pi\) | ||||
0.141270 | + | 0.989971i | \(0.454882\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.5985 | + | 13.6249i | 0.347351 | + | 0.446538i | ||||
\(932\) | − | 12.6099i | − | 0.413051i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 38.1548i | − | 1.24846i | ||||||
\(935\) | 0.340177i | 0.0111250i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 59.3424i | 1.93863i | 0.245820 | + | 0.969316i | \(0.420943\pi\) | ||||
−0.245820 | + | 0.969316i | \(0.579057\pi\) | |||||||
\(938\) | 21.1876 | − | 7.27035i | 0.691799 | − | 0.237385i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −16.8176 | −0.548531 | ||||||||
\(941\) | 31.5199 | 1.02752 | 0.513760 | − | 0.857934i | \(-0.328252\pi\) | ||||
0.513760 | + | 0.857934i | \(0.328252\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 49.8702i | 1.62400i | ||||||||
\(944\) | −1.83197 | −0.0596256 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.14338 | 0.167226 | ||||||||
\(947\) | 19.2775i | 0.626436i | 0.949681 | + | 0.313218i | \(0.101407\pi\) | ||||
−0.949681 | + | 0.313218i | \(0.898593\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 35.2228 | 1.14338 | ||||||||
\(950\) | −6.22703 | −0.202031 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.647707 | + | 0.222255i | −0.0209923 | + | 0.00720334i | ||||
\(953\) | 24.1146i | 0.781148i | 0.920572 | + | 0.390574i | \(0.127723\pi\) | ||||
−0.920572 | + | 0.390574i | \(0.872277\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.32217i | 0.301658i | ||||||||
\(956\) | − | 24.5429i | − | 0.793774i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 14.3544i | − | 0.463768i | ||||||
\(959\) | −44.1012 | + | 15.1330i | −1.42410 | + | 0.488670i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −68.6664 | −2.21505 | ||||||||
\(962\) | −1.82542 | −0.0588539 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 18.0653i | 0.581844i | ||||||||
\(965\) | −4.69506 | −0.151139 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.5196 | 1.17439 | 0.587195 | − | 0.809446i | \(-0.300232\pi\) | ||||
0.587195 | + | 0.809446i | \(0.300232\pi\) | |||||||
\(968\) | − | 10.3020i | − | 0.331118i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.81168 | 0.0581695 | ||||||||
\(971\) | −0.597949 | −0.0191891 | −0.00959455 | − | 0.999954i | \(-0.503054\pi\) | ||||
−0.00959455 | + | 0.999954i | \(0.503054\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.05870 | + | 1.73585i | −0.162174 | + | 0.0556488i | ||||
\(974\) | 10.3633i | 0.332063i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 0.703333i | − | 0.0225131i | ||||||
\(977\) | − | 16.4167i | − | 0.525217i | −0.964902 | − | 0.262609i | \(-0.915417\pi\) | ||
0.964902 | − | 0.262609i | \(-0.0845828\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.04107i | 0.161113i | ||||||||
\(980\) | −8.69197 | + | 6.76127i | −0.277655 | + | 0.215981i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −28.3923 | −0.906035 | ||||||||
\(983\) | 6.88337 | 0.219546 | 0.109773 | − | 0.993957i | \(-0.464988\pi\) | ||||
0.109773 | + | 0.993957i | \(0.464988\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.58348i | 0.0504539i | ||||||||
\(986\) | −0.754101 | −0.0240155 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −11.2367 | −0.357488 | ||||||||
\(989\) | 31.2621i | 0.994076i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −40.6240 | −1.29046 | −0.645232 | − | 0.763987i | \(-0.723239\pi\) | ||||
−0.645232 | + | 0.763987i | \(0.723239\pi\) | |||||||
\(992\) | −9.98331 | −0.316970 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 4.09424 | + | 11.9316i | 0.129861 | + | 0.378448i | ||||
\(995\) | − | 27.7142i | − | 0.878598i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 32.9805i | − | 1.04450i | −0.852792 | − | 0.522252i | \(-0.825092\pi\) | ||
0.852792 | − | 0.522252i | \(-0.174908\pi\) | |||||||
\(998\) | − | 5.40717i | − | 0.171161i | ||||||
\(999\) | 0 | 0 |
(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 | 1134.2.d.b.1133.11 | yes | 16 | |
3.2 | odd | 2 | inner | 1134.2.d.b.1133.6 | yes | 16 | |
7.6 | odd | 2 | inner | 1134.2.d.b.1133.14 | yes | 16 | |
9.2 | odd | 6 | 1134.2.m.h.377.2 | 16 | |||
9.4 | even | 3 | 1134.2.m.h.755.3 | 16 | |||
9.5 | odd | 6 | 1134.2.m.i.755.6 | 16 | |||
9.7 | even | 3 | 1134.2.m.i.377.7 | 16 | |||
21.20 | even | 2 | inner | 1134.2.d.b.1133.3 | ✓ | 16 | |
63.13 | odd | 6 | 1134.2.m.h.755.2 | 16 | |||
63.20 | even | 6 | 1134.2.m.h.377.3 | 16 | |||
63.34 | odd | 6 | 1134.2.m.i.377.6 | 16 | |||
63.41 | even | 6 | 1134.2.m.i.755.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1134.2.d.b.1133.3 | ✓ | 16 | 21.20 | even | 2 | inner | |
1134.2.d.b.1133.6 | yes | 16 | 3.2 | odd | 2 | inner | |
1134.2.d.b.1133.11 | yes | 16 | 1.1 | even | 1 | trivial | |
1134.2.d.b.1133.14 | yes | 16 | 7.6 | odd | 2 | inner | |
1134.2.m.h.377.2 | 16 | 9.2 | odd | 6 | |||
1134.2.m.h.377.3 | 16 | 63.20 | even | 6 | |||
1134.2.m.h.755.2 | 16 | 63.13 | odd | 6 | |||
1134.2.m.h.755.3 | 16 | 9.4 | even | 3 | |||
1134.2.m.i.377.6 | 16 | 63.34 | odd | 6 | |||
1134.2.m.i.377.7 | 16 | 9.7 | even | 3 | |||
1134.2.m.i.755.6 | 16 | 9.5 | odd | 6 | |||
1134.2.m.i.755.7 | 16 | 63.41 | even | 6 |