Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2475,2,Mod(199,2475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2475, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2475.199");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2475.c (of order \(2\), degree \(1\), 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: | \(19.7629745003\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.2 | ||
Root | \(-1.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2475.199 |
Dual form | 2475.2.c.i.199.3 |
$q$-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 \(\left(\mathbb{Z}/2475\mathbb{Z}\right)^\times\).
\(n\) | \(551\) | \(2026\) | \(2377\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.56155i | − 1.10418i | −0.833783 | − | 0.552092i | \(-0.813830\pi\) | ||||
0.833783 | − | 0.552092i | \(-0.186170\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.438447 | −0.219224 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | 0.981981 | + | 0.188982i | \(0.0605189\pi\) | ||||
−0.981981 | + | 0.188982i | \(0.939481\pi\) | |||||||
\(8\) | − 2.43845i | − 0.862121i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.56155i | 1.26515i | 0.774500 | + | 0.632574i | \(0.218001\pi\) | ||||
−0.774500 | + | 0.632574i | \(0.781999\pi\) | |||||||
\(14\) | 1.56155 | 0.417343 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.68466 | −1.17116 | ||||||||
\(17\) | 5.56155i | 1.34887i | 0.738332 | + | 0.674437i | \(0.235614\pi\) | ||||
−0.738332 | + | 0.674437i | \(0.764386\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.00000 | −0.688247 | −0.344124 | − | 0.938924i | \(-0.611824\pi\) | ||||
−0.344124 | + | 0.938924i | \(0.611824\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.56155i | 0.332924i | ||||||||
\(23\) | − 2.43845i | − 0.508451i | −0.967145 | − | 0.254226i | \(-0.918179\pi\) | ||||
0.967145 | − | 0.254226i | \(-0.0818206\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 7.12311 | 1.39696 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − 0.438447i | − 0.0828587i | ||||||||
\(29\) | 3.12311 | 0.579946 | 0.289973 | − | 0.957035i | \(-0.406354\pi\) | ||||
0.289973 | + | 0.957035i | \(0.406354\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.68466 | −1.38021 | −0.690103 | − | 0.723711i | \(-0.742435\pi\) | ||||
−0.690103 | + | 0.723711i | \(0.742435\pi\) | |||||||
\(32\) | 2.43845i | 0.431061i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 8.68466 | 1.48941 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.80776i | 1.61239i | 0.591652 | + | 0.806193i | \(0.298476\pi\) | ||||
−0.591652 | + | 0.806193i | \(0.701524\pi\) | |||||||
\(38\) | 4.68466i | 0.759952i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.68466 | 0.731621 | 0.365810 | − | 0.930689i | \(-0.380792\pi\) | ||||
0.365810 | + | 0.930689i | \(0.380792\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.68466i | 1.17190i | 0.810347 | + | 0.585950i | \(0.199278\pi\) | ||||
−0.810347 | + | 0.585950i | \(0.800722\pi\) | |||||||
\(44\) | 0.438447 | 0.0660984 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.80776 | −0.561424 | ||||||||
\(47\) | 9.56155i | 1.39470i | 0.716733 | + | 0.697348i | \(0.245637\pi\) | ||||
−0.716733 | + | 0.697348i | \(0.754363\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.00000 | 0.857143 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 2.00000i | − 0.277350i | ||||||||
\(53\) | − 7.12311i | − 0.978434i | −0.872162 | − | 0.489217i | \(-0.837283\pi\) | ||||
0.872162 | − | 0.489217i | \(-0.162717\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.43845 | 0.325851 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − 4.87689i | − 0.640368i | ||||||||
\(59\) | −6.43845 | −0.838214 | −0.419107 | − | 0.907937i | \(-0.637657\pi\) | ||||
−0.419107 | + | 0.907937i | \(0.637657\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.43845 | −0.440248 | −0.220124 | − | 0.975472i | \(-0.570646\pi\) | ||||
−0.220124 | + | 0.975472i | \(0.570646\pi\) | |||||||
\(62\) | 12.0000i | 1.52400i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.56155 | −0.695194 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.68466i | 0.694492i | 0.937774 | + | 0.347246i | \(0.112883\pi\) | ||||
−0.937774 | + | 0.347246i | \(0.887117\pi\) | |||||||
\(68\) | − 2.43845i | − 0.295705i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.8078 | −1.40132 | −0.700662 | − | 0.713493i | \(-0.747112\pi\) | ||||
−0.700662 | + | 0.713493i | \(0.747112\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.246211i | 0.0288168i | 0.999896 | + | 0.0144084i | \(0.00458650\pi\) | ||||
−0.999896 | + | 0.0144084i | \(0.995413\pi\) | |||||||
\(74\) | 15.3153 | 1.78037 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.31534 | 0.150880 | ||||||||
\(77\) | − 1.00000i | − 0.113961i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.31534 | 0.373005 | 0.186503 | − | 0.982454i | \(-0.440285\pi\) | ||||
0.186503 | + | 0.982454i | \(0.440285\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 7.31534i | − 0.807844i | ||||||||
\(83\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 12.0000 | 1.29399 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.43845i | 0.259939i | ||||||||
\(89\) | 8.87689 | 0.940949 | 0.470474 | − | 0.882414i | \(-0.344083\pi\) | ||||
0.470474 | + | 0.882414i | \(0.344083\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.56155 | −0.478181 | ||||||||
\(92\) | 1.06913i | 0.111465i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 14.9309 | 1.54000 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 6.12311i | − 0.621707i | −0.950458 | − | 0.310854i | \(-0.899385\pi\) | ||||
0.950458 | − | 0.310854i | \(-0.100615\pi\) | |||||||
\(98\) | − 9.36932i | − 0.946444i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.56155 | 0.553395 | 0.276698 | − | 0.960957i | \(-0.410760\pi\) | ||||
0.276698 | + | 0.960957i | \(0.410760\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.876894i | 0.0864030i | 0.999066 | + | 0.0432015i | \(0.0137557\pi\) | ||||
−0.999066 | + | 0.0432015i | \(0.986244\pi\) | |||||||
\(104\) | 11.1231 | 1.09071 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11.1231 | −1.08037 | ||||||||
\(107\) | − 0.876894i | − 0.0847726i | −0.999101 | − | 0.0423863i | \(-0.986504\pi\) | ||||
0.999101 | − | 0.0423863i | \(-0.0134960\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.8078 | −1.22676 | −0.613381 | − | 0.789787i | \(-0.710191\pi\) | ||||
−0.613381 | + | 0.789787i | \(0.710191\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 4.68466i | − 0.442659i | ||||||||
\(113\) | 0.876894i | 0.0824913i | 0.999149 | + | 0.0412456i | \(0.0131326\pi\) | ||||
−0.999149 | + | 0.0412456i | \(0.986867\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.36932 | −0.127138 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.0540i | 0.925543i | ||||||||
\(119\) | −5.56155 | −0.509827 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 5.36932i | 0.486115i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.36932 | 0.302574 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.8078i | 1.40271i | 0.712811 | + | 0.701356i | \(0.247422\pi\) | ||||
−0.712811 | + | 0.701356i | \(0.752578\pi\) | |||||||
\(128\) | 13.5616i | 1.19868i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.4924 | 1.44095 | 0.720475 | − | 0.693481i | \(-0.243924\pi\) | ||||
0.720475 | + | 0.693481i | \(0.243924\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 3.00000i | − 0.260133i | ||||||||
\(134\) | 8.87689 | 0.766847 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 13.5616 | 1.16289 | ||||||||
\(137\) | 21.3693i | 1.82570i | 0.408291 | + | 0.912852i | \(0.366125\pi\) | ||||
−0.408291 | + | 0.912852i | \(0.633875\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.00000 | −0.678551 | −0.339276 | − | 0.940687i | \(-0.610182\pi\) | ||||
−0.339276 | + | 0.940687i | \(0.610182\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 18.4384i | 1.54732i | ||||||||
\(143\) | − 4.56155i | − 0.381456i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.384472 | 0.0318191 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − 4.30019i | − 0.353473i | ||||||||
\(149\) | 11.8078 | 0.967330 | 0.483665 | − | 0.875253i | \(-0.339305\pi\) | ||||
0.483665 | + | 0.875253i | \(0.339305\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.31534 | −0.351178 | −0.175589 | − | 0.984464i | \(-0.556183\pi\) | ||||
−0.175589 | + | 0.984464i | \(0.556183\pi\) | |||||||
\(152\) | 7.31534i | 0.593353i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.56155 | −0.125834 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 9.68466i | − 0.772920i | −0.922306 | − | 0.386460i | \(-0.873698\pi\) | ||||
0.922306 | − | 0.386460i | \(-0.126302\pi\) | |||||||
\(158\) | − 5.17708i | − 0.411866i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.43845 | 0.192177 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.6847i | 1.38517i | 0.721337 | + | 0.692585i | \(0.243528\pi\) | ||||
−0.721337 | + | 0.692585i | \(0.756472\pi\) | |||||||
\(164\) | −2.05398 | −0.160389 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.36932i | 0.725020i | 0.931980 | + | 0.362510i | \(0.118080\pi\) | ||||
−0.931980 | + | 0.362510i | \(0.881920\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.80776 | −0.600597 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − 3.36932i | − 0.256908i | ||||||||
\(173\) | − 17.5616i | − 1.33518i | −0.744529 | − | 0.667590i | \(-0.767326\pi\) | ||||
0.744529 | − | 0.667590i | \(-0.232674\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.68466 | 0.353119 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 13.8617i | − 1.03898i | ||||||||
\(179\) | −10.4384 | −0.780206 | −0.390103 | − | 0.920771i | \(-0.627561\pi\) | ||||
−0.390103 | + | 0.920771i | \(0.627561\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.1231 | 1.49574 | 0.747869 | − | 0.663846i | \(-0.231077\pi\) | ||||
0.747869 | + | 0.663846i | \(0.231077\pi\) | |||||||
\(182\) | 7.12311i | 0.528000i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.94602 | −0.438347 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 5.56155i | − 0.406701i | ||||||||
\(188\) | − 4.19224i | − 0.305750i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 26.9309 | 1.94865 | 0.974325 | − | 0.225148i | \(-0.0722864\pi\) | ||||
0.974325 | + | 0.225148i | \(0.0722864\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 13.4384i | − 0.967321i | −0.875256 | − | 0.483660i | \(-0.839307\pi\) | ||||
0.875256 | − | 0.483660i | \(-0.160693\pi\) | |||||||
\(194\) | −9.56155 | −0.686479 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.63068 | −0.187906 | ||||||||
\(197\) | − 10.9309i | − 0.778792i | −0.921070 | − | 0.389396i | \(-0.872684\pi\) | ||||
0.921070 | − | 0.389396i | \(-0.127316\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.80776 | −0.482590 | −0.241295 | − | 0.970452i | \(-0.577572\pi\) | ||||
−0.241295 | + | 0.970452i | \(0.577572\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 8.68466i | − 0.611050i | ||||||||
\(203\) | 3.12311i | 0.219199i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.36932 | 0.0954048 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 21.3693i | − 1.48170i | ||||||||
\(209\) | 3.00000 | 0.207514 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.6847 | 1.07978 | 0.539888 | − | 0.841737i | \(-0.318467\pi\) | ||||
0.539888 | + | 0.841737i | \(0.318467\pi\) | |||||||
\(212\) | 3.12311i | 0.214496i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.36932 | −0.0936046 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 7.68466i | − 0.521669i | ||||||||
\(218\) | 20.0000i | 1.35457i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −25.3693 | −1.70652 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 1.19224i | − 0.0798380i | −0.999203 | − | 0.0399190i | \(-0.987290\pi\) | ||||
0.999203 | − | 0.0399190i | \(-0.0127100\pi\) | |||||||
\(224\) | −2.43845 | −0.162926 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.36932 | 0.0910856 | ||||||||
\(227\) | − 12.4924i | − 0.829151i | −0.910015 | − | 0.414576i | \(-0.863930\pi\) | ||||
0.910015 | − | 0.414576i | \(-0.136070\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.123106 | −0.00813505 | −0.00406752 | − | 0.999992i | \(-0.501295\pi\) | ||||
−0.00406752 | + | 0.999992i | \(0.501295\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 7.61553i | − 0.499984i | ||||||||
\(233\) | − 4.19224i | − 0.274643i | −0.990527 | − | 0.137321i | \(-0.956151\pi\) | ||||
0.990527 | − | 0.137321i | \(-0.0438493\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.82292 | 0.183756 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 8.68466i | 0.562943i | ||||||||
\(239\) | −16.4924 | −1.06681 | −0.533403 | − | 0.845861i | \(-0.679087\pi\) | ||||
−0.533403 | + | 0.845861i | \(0.679087\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.0540 | 1.48504 | 0.742519 | − | 0.669826i | \(-0.233631\pi\) | ||||
0.742519 | + | 0.669826i | \(0.233631\pi\) | |||||||
\(242\) | − 1.56155i | − 0.100380i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.50758 | 0.0965128 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 13.6847i | − 0.870734i | ||||||||
\(248\) | 18.7386i | 1.18990i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.43845i | 0.153304i | ||||||||
\(254\) | 24.6847 | 1.54885 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 10.0540 | 0.628373 | ||||||||
\(257\) | 1.75379i | 0.109398i | 0.998503 | + | 0.0546992i | \(0.0174200\pi\) | ||||
−0.998503 | + | 0.0546992i | \(0.982580\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.80776 | −0.609425 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − 25.7538i | − 1.59107i | ||||||||
\(263\) | − 21.3693i | − 1.31769i | −0.752279 | − | 0.658844i | \(-0.771046\pi\) | ||||
0.752279 | − | 0.658844i | \(-0.228954\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.68466 | −0.287235 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − 2.49242i | − 0.152249i | ||||||||
\(269\) | 4.49242 | 0.273908 | 0.136954 | − | 0.990577i | \(-0.456269\pi\) | ||||
0.136954 | + | 0.990577i | \(0.456269\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.1771 | 1.04343 | 0.521717 | − | 0.853119i | \(-0.325292\pi\) | ||||
0.521717 | + | 0.853119i | \(0.325292\pi\) | |||||||
\(272\) | − 26.0540i | − 1.57975i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 33.3693 | 2.01591 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.1771i | 1.33249i | 0.745732 | + | 0.666246i | \(0.232100\pi\) | ||||
−0.745732 | + | 0.666246i | \(0.767900\pi\) | |||||||
\(278\) | 12.4924i | 0.749246i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −23.8078 | −1.42025 | −0.710126 | − | 0.704075i | \(-0.751362\pi\) | ||||
−0.710126 | + | 0.704075i | \(0.751362\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 23.8769i | − 1.41933i | −0.704537 | − | 0.709667i | \(-0.748845\pi\) | ||||
0.704537 | − | 0.709667i | \(-0.251155\pi\) | |||||||
\(284\) | 5.17708 | 0.307203 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.12311 | −0.421198 | ||||||||
\(287\) | 4.68466i | 0.276527i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.9309 | −0.819463 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 0.107951i | − 0.00631733i | ||||||||
\(293\) | − 30.9309i | − 1.80700i | −0.428587 | − | 0.903500i | \(-0.640989\pi\) | ||||
0.428587 | − | 0.903500i | \(-0.359011\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 23.9157 | 1.39007 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − 18.4384i | − 1.06811i | ||||||||
\(299\) | 11.1231 | 0.643266 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.68466 | −0.442936 | ||||||||
\(302\) | 6.73863i | 0.387765i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 14.0540 | 0.806051 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.93087i | 0.338493i | 0.985574 | + | 0.169246i | \(0.0541333\pi\) | ||||
−0.985574 | + | 0.169246i | \(0.945867\pi\) | |||||||
\(308\) | 0.438447i | 0.0249828i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −30.2462 | −1.71511 | −0.857553 | − | 0.514396i | \(-0.828016\pi\) | ||||
−0.857553 | + | 0.514396i | \(0.828016\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.7538i | 0.833933i | 0.908922 | + | 0.416967i | \(0.136907\pi\) | ||||
−0.908922 | + | 0.416967i | \(0.863093\pi\) | |||||||
\(314\) | −15.1231 | −0.853446 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.45360 | −0.0817715 | ||||||||
\(317\) | 15.1231i | 0.849398i | 0.905335 | + | 0.424699i | \(0.139620\pi\) | ||||
−0.905335 | + | 0.424699i | \(0.860380\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.12311 | −0.174860 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − 3.80776i | − 0.212198i | ||||||||
\(323\) | − 16.6847i | − 0.928359i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 27.6155 | 1.52948 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 11.4233i | − 0.630746i | ||||||||
\(329\) | −9.56155 | −0.527145 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.24621 | 0.343323 | 0.171661 | − | 0.985156i | \(-0.445086\pi\) | ||||
0.171661 | + | 0.985156i | \(0.445086\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 14.6307 | 0.800555 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.68466i | 0.0917692i | 0.998947 | + | 0.0458846i | \(0.0146107\pi\) | ||||
−0.998947 | + | 0.0458846i | \(0.985389\pi\) | |||||||
\(338\) | 12.1922i | 0.663170i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.68466 | 0.416148 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.0000i | 0.701934i | ||||||||
\(344\) | 18.7386 | 1.01032 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −27.4233 | −1.47429 | ||||||||
\(347\) | − 2.63068i | − 0.141222i | −0.997504 | − | 0.0706112i | \(-0.977505\pi\) | ||||
0.997504 | − | 0.0706112i | \(-0.0224950\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −31.3693 | −1.67916 | −0.839581 | − | 0.543235i | \(-0.817199\pi\) | ||||
−0.839581 | + | 0.543235i | \(0.817199\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − 2.43845i | − 0.129970i | ||||||||
\(353\) | 29.8617i | 1.58938i | 0.607015 | + | 0.794690i | \(0.292367\pi\) | ||||
−0.607015 | + | 0.794690i | \(0.707633\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3.89205 | −0.206278 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 16.3002i | 0.861492i | ||||||||
\(359\) | −9.75379 | −0.514785 | −0.257393 | − | 0.966307i | \(-0.582863\pi\) | ||||
−0.257393 | + | 0.966307i | \(0.582863\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.0000 | −0.526316 | ||||||||
\(362\) | − 31.4233i | − 1.65157i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.00000 | 0.104828 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 23.0540i | − 1.20341i | −0.798719 | − | 0.601704i | \(-0.794489\pi\) | ||||
0.798719 | − | 0.601704i | \(-0.205511\pi\) | |||||||
\(368\) | 11.4233i | 0.595480i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.12311 | 0.369813 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 6.80776i | − 0.352493i | −0.984346 | − | 0.176246i | \(-0.943604\pi\) | ||||
0.984346 | − | 0.176246i | \(-0.0563955\pi\) | |||||||
\(374\) | −8.68466 | −0.449073 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 23.3153 | 1.20240 | ||||||||
\(377\) | 14.2462i | 0.733717i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.3002 | −1.50505 | −0.752525 | − | 0.658564i | \(-0.771164\pi\) | ||||
−0.752525 | + | 0.658564i | \(0.771164\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − 42.0540i | − 2.15167i | ||||||||
\(383\) | − 5.75379i | − 0.294005i | −0.989136 | − | 0.147002i | \(-0.953037\pi\) | ||||
0.989136 | − | 0.147002i | \(-0.0469625\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −20.9848 | −1.06810 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.68466i | 0.136293i | ||||||||
\(389\) | −33.8617 | −1.71686 | −0.858429 | − | 0.512932i | \(-0.828559\pi\) | ||||
−0.858429 | + | 0.512932i | \(0.828559\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.5616 | 0.685837 | ||||||||
\(392\) | − 14.6307i | − 0.738961i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −17.0691 | −0.859930 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.5616i | 1.63422i | 0.576484 | + | 0.817109i | \(0.304424\pi\) | ||||
−0.576484 | + | 0.817109i | \(0.695576\pi\) | |||||||
\(398\) | 10.6307i | 0.532868i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −35.6155 | −1.77855 | −0.889277 | − | 0.457368i | \(-0.848792\pi\) | ||||
−0.889277 | + | 0.457368i | \(0.848792\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 35.0540i | − 1.74616i | ||||||||
\(404\) | −2.43845 | −0.121317 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.87689 | 0.242036 | ||||||||
\(407\) | − 9.80776i | − 0.486153i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.0540 | 1.43663 | 0.718313 | − | 0.695720i | \(-0.244914\pi\) | ||||
0.718313 | + | 0.695720i | \(0.244914\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 0.384472i | − 0.0189416i | ||||||||
\(413\) | − 6.43845i | − 0.316815i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −11.1231 | −0.545355 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 4.68466i | − 0.229134i | ||||||||
\(419\) | −29.5616 | −1.44418 | −0.722088 | − | 0.691801i | \(-0.756818\pi\) | ||||
−0.722088 | + | 0.691801i | \(0.756818\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.0540 | 0.977371 | 0.488685 | − | 0.872460i | \(-0.337477\pi\) | ||||
0.488685 | + | 0.872460i | \(0.337477\pi\) | |||||||
\(422\) | − 24.4924i | − 1.19227i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −17.3693 | −0.843529 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 3.43845i | − 0.166398i | ||||||||
\(428\) | 0.384472i | 0.0185841i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −38.2462 | −1.84226 | −0.921128 | − | 0.389261i | \(-0.872730\pi\) | ||||
−0.921128 | + | 0.389261i | \(0.872730\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.9309i | 0.573361i | 0.958026 | + | 0.286681i | \(0.0925518\pi\) | ||||
−0.958026 | + | 0.286681i | \(0.907448\pi\) | |||||||
\(434\) | −12.0000 | −0.576018 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.61553 | 0.268935 | ||||||||
\(437\) | 7.31534i | 0.349940i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 37.7386 | 1.80117 | 0.900583 | − | 0.434683i | \(-0.143140\pi\) | ||||
0.900583 | + | 0.434683i | \(0.143140\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 39.6155i | 1.88432i | ||||||||
\(443\) | 28.3002i | 1.34458i | 0.740287 | + | 0.672291i | \(0.234690\pi\) | ||||
−0.740287 | + | 0.672291i | \(0.765310\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.86174 | −0.0881559 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − 5.56155i | − 0.262759i | ||||||||
\(449\) | −4.49242 | −0.212011 | −0.106005 | − | 0.994366i | \(-0.533806\pi\) | ||||
−0.106005 | + | 0.994366i | \(0.533806\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.68466 | −0.220592 | ||||||||
\(452\) | − 0.384472i | − 0.0180840i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −19.5076 | −0.915536 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 11.3693i | − 0.531834i | −0.963996 | − | 0.265917i | \(-0.914325\pi\) | ||||
0.963996 | − | 0.265917i | \(-0.0856747\pi\) | |||||||
\(458\) | 0.192236i | 0.00898260i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 41.8617 | 1.94970 | 0.974848 | − | 0.222872i | \(-0.0715431\pi\) | ||||
0.974848 | + | 0.222872i | \(0.0715431\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.2462i | 0.847973i | 0.905668 | + | 0.423987i | \(0.139370\pi\) | ||||
−0.905668 | + | 0.423987i | \(0.860630\pi\) | |||||||
\(464\) | −14.6307 | −0.679212 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.54640 | −0.303256 | ||||||||
\(467\) | − 14.2462i | − 0.659236i | −0.944114 | − | 0.329618i | \(-0.893080\pi\) | ||||
0.944114 | − | 0.329618i | \(-0.106920\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.68466 | −0.262493 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 15.6998i | 0.722642i | ||||||||
\(473\) | − 7.68466i | − 0.353341i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.43845 | 0.111766 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 25.7538i | 1.17795i | ||||||||
\(479\) | 21.3693 | 0.976389 | 0.488195 | − | 0.872735i | \(-0.337656\pi\) | ||||
0.488195 | + | 0.872735i | \(0.337656\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −44.7386 | −2.03991 | ||||||||
\(482\) | − 36.0000i | − 1.63976i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.438447 | −0.0199294 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.0540i | 1.13530i | 0.823269 | + | 0.567652i | \(0.192148\pi\) | ||||
−0.823269 | + | 0.567652i | \(0.807852\pi\) | |||||||
\(488\) | 8.38447i | 0.379547i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.4924 | −0.744293 | −0.372146 | − | 0.928174i | \(-0.621378\pi\) | ||||
−0.372146 | + | 0.928174i | \(0.621378\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.3693i | 0.782275i | ||||||||
\(494\) | −21.3693 | −0.961451 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 36.0000 | 1.61645 | ||||||||
\(497\) | − 11.8078i | − 0.529651i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.8078 | 0.752419 | 0.376209 | − | 0.926535i | \(-0.377227\pi\) | ||||
0.376209 | + | 0.926535i | \(0.377227\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 18.7386i | 0.836346i | ||||||||
\(503\) | − 16.4924i | − 0.735361i | −0.929952 | − | 0.367680i | \(-0.880152\pi\) | ||||
0.929952 | − | 0.367680i | \(-0.119848\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.80776 | 0.169276 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − 6.93087i | − 0.307508i | ||||||||
\(509\) | 8.87689 | 0.393461 | 0.196731 | − | 0.980458i | \(-0.436968\pi\) | ||||
0.196731 | + | 0.980458i | \(0.436968\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.246211 | −0.0108917 | ||||||||
\(512\) | 11.4233i | 0.504843i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.73863 | 0.120796 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 9.56155i | − 0.420517i | ||||||||
\(518\) | 15.3153i | 0.672917i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.6155 | 0.684129 | 0.342064 | − | 0.939677i | \(-0.388874\pi\) | ||||
0.342064 | + | 0.939677i | \(0.388874\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.24621i | 0.316855i | 0.987371 | + | 0.158427i | \(0.0506424\pi\) | ||||
−0.987371 | + | 0.158427i | \(0.949358\pi\) | |||||||
\(524\) | −7.23106 | −0.315890 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −33.3693 | −1.45497 | ||||||||
\(527\) | − 42.7386i | − 1.86172i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.0540 | 0.741477 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.31534i | 0.0570273i | ||||||||
\(533\) | 21.3693i | 0.925608i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 13.8617 | 0.598736 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 7.01515i | − 0.302445i | ||||||||
\(539\) | −6.00000 | −0.258438 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.6847 | −0.846310 | −0.423155 | − | 0.906057i | \(-0.639077\pi\) | ||||
−0.423155 | + | 0.906057i | \(0.639077\pi\) | |||||||
\(542\) | − 26.8229i | − 1.15214i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −13.5616 | −0.581447 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 8.68466i | − 0.371329i | −0.982613 | − | 0.185665i | \(-0.940556\pi\) | ||||
0.982613 | − | 0.185665i | \(-0.0594438\pi\) | |||||||
\(548\) | − 9.36932i | − 0.400237i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.36932 | −0.399146 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.31534i | 0.140983i | ||||||||
\(554\) | 34.6307 | 1.47132 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.50758 | 0.148754 | ||||||||
\(557\) | − 7.12311i | − 0.301816i | −0.988548 | − | 0.150908i | \(-0.951780\pi\) | ||||
0.988548 | − | 0.150908i | \(-0.0482197\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −35.0540 | −1.48263 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 37.1771i | 1.56822i | ||||||||
\(563\) | 19.1231i | 0.805943i | 0.915213 | + | 0.402971i | \(0.132023\pi\) | ||||
−0.915213 | + | 0.402971i | \(0.867977\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −37.2850 | −1.56721 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 28.7926i | 1.20811i | ||||||||
\(569\) | −9.06913 | −0.380198 | −0.190099 | − | 0.981765i | \(-0.560881\pi\) | ||||
−0.190099 | + | 0.981765i | \(0.560881\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.946025 | 0.0395899 | 0.0197950 | − | 0.999804i | \(-0.493699\pi\) | ||||
0.0197950 | + | 0.999804i | \(0.493699\pi\) | |||||||
\(572\) | 2.00000i | 0.0836242i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7.31534 | 0.305336 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 3.63068i | − 0.151147i | −0.997140 | − | 0.0755737i | \(-0.975921\pi\) | ||||
0.997140 | − | 0.0755737i | \(-0.0240788\pi\) | |||||||
\(578\) | 21.7538i | 0.904838i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.12311i | 0.295009i | ||||||||
\(584\) | 0.600373 | 0.0248436 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −48.3002 | −1.99526 | ||||||||
\(587\) | − 47.8078i | − 1.97324i | −0.163044 | − | 0.986619i | \(-0.552131\pi\) | ||||
0.163044 | − | 0.986619i | \(-0.447869\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.0540 | 0.949923 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − 45.9460i | − 1.88837i | ||||||||
\(593\) | − 40.1080i | − 1.64704i | −0.567290 | − | 0.823518i | \(-0.692008\pi\) | ||||
0.567290 | − | 0.823518i | \(-0.307992\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.17708 | −0.212061 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 17.3693i | − 0.710284i | ||||||||
\(599\) | 21.1771 | 0.865272 | 0.432636 | − | 0.901569i | \(-0.357584\pi\) | ||||
0.432636 | + | 0.901569i | \(0.357584\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.4233 | −0.996247 | −0.498123 | − | 0.867106i | \(-0.665977\pi\) | ||||
−0.498123 | + | 0.867106i | \(0.665977\pi\) | |||||||
\(602\) | 12.0000i | 0.489083i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.89205 | 0.0769864 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 10.2462i | − 0.415881i | −0.978141 | − | 0.207940i | \(-0.933324\pi\) | ||||
0.978141 | − | 0.207940i | \(-0.0666760\pi\) | |||||||
\(608\) | − 7.31534i | − 0.296676i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −43.6155 | −1.76450 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 46.1080i | 1.86228i | 0.364659 | + | 0.931141i | \(0.381186\pi\) | ||||
−0.364659 | + | 0.931141i | \(0.618814\pi\) | |||||||
\(614\) | 9.26137 | 0.373758 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.43845 | −0.0982478 | ||||||||
\(617\) | 38.2462i | 1.53973i | 0.638204 | + | 0.769867i | \(0.279678\pi\) | ||||
−0.638204 | + | 0.769867i | \(0.720322\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 38.1771 | 1.53447 | 0.767233 | − | 0.641368i | \(-0.221633\pi\) | ||||
0.767233 | + | 0.641368i | \(0.221633\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 47.2311i | 1.89379i | ||||||||
\(623\) | 8.87689i | 0.355645i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 23.0388 | 0.920816 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.24621i | 0.169442i | ||||||||
\(629\) | −54.5464 | −2.17491 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.3153 | −0.410647 | −0.205324 | − | 0.978694i | \(-0.565825\pi\) | ||||
−0.205324 | + | 0.978694i | \(0.565825\pi\) | |||||||
\(632\) | − 8.08429i | − 0.321576i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 23.6155 | 0.937892 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 27.3693i | 1.08441i | ||||||||
\(638\) | 4.87689i | 0.193078i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.73863 | −0.266160 | −0.133080 | − | 0.991105i | \(-0.542487\pi\) | ||||
−0.133080 | + | 0.991105i | \(0.542487\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.36932i | 0.369490i | 0.982787 | + | 0.184745i | \(0.0591459\pi\) | ||||
−0.982787 | + | 0.184745i | \(0.940854\pi\) | |||||||
\(644\) | −1.06913 | −0.0421296 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −26.0540 | −1.02508 | ||||||||
\(647\) | − 20.1922i | − 0.793839i | −0.917853 | − | 0.396919i | \(-0.870079\pi\) | ||||
0.917853 | − | 0.396919i | \(-0.129921\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.43845 | 0.252731 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 7.75379i | − 0.303662i | ||||||||
\(653\) | − 40.4924i | − 1.58459i | −0.610138 | − | 0.792295i | \(-0.708886\pi\) | ||||
0.610138 | − | 0.792295i | \(-0.291114\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −21.9460 | −0.856848 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 14.9309i | 0.582066i | ||||||||
\(659\) | −33.3693 | −1.29988 | −0.649942 | − | 0.759984i | \(-0.725207\pi\) | ||||
−0.649942 | + | 0.759984i | \(0.725207\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.8078 | −0.537060 | −0.268530 | − | 0.963271i | \(-0.586538\pi\) | ||||
−0.268530 | + | 0.963271i | \(0.586538\pi\) | |||||||
\(662\) | − 9.75379i | − 0.379092i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 7.61553i | − 0.294874i | ||||||||
\(668\) | − 4.10795i | − 0.158941i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.43845 | 0.132740 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 35.3693i | − 1.36339i | −0.731638 | − | 0.681693i | \(-0.761244\pi\) | ||||
0.731638 | − | 0.681693i | \(-0.238756\pi\) | |||||||
\(674\) | 2.63068 | 0.101330 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.42329 | 0.131665 | ||||||||
\(677\) | 20.8769i | 0.802364i | 0.915998 | + | 0.401182i | \(0.131401\pi\) | ||||
−0.915998 | + | 0.401182i | \(0.868599\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.12311 | 0.234983 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 12.0000i | − 0.459504i | ||||||||
\(683\) | 0.192236i | 0.00735570i | 0.999993 | + | 0.00367785i | \(0.00117070\pi\) | ||||
−0.999993 | + | 0.00367785i | \(0.998829\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 20.3002 | 0.775065 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − 36.0000i | − 1.37249i | ||||||||
\(689\) | 32.4924 | 1.23786 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.4924 | −0.779568 | −0.389784 | − | 0.920906i | \(-0.627450\pi\) | ||||
−0.389784 | + | 0.920906i | \(0.627450\pi\) | |||||||
\(692\) | 7.69981i | 0.292703i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.10795 | −0.155936 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 26.0540i | 0.986865i | ||||||||
\(698\) | 48.9848i | 1.85410i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.9309 | 1.01716 | 0.508582 | − | 0.861013i | \(-0.330170\pi\) | ||||
0.508582 | + | 0.861013i | \(0.330170\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 29.4233i | − 1.10972i | ||||||||
\(704\) | 5.56155 | 0.209609 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 46.6307 | 1.75497 | ||||||||
\(707\) | 5.56155i | 0.209164i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.12311 | 0.0797349 | 0.0398675 | − | 0.999205i | \(-0.487306\pi\) | ||||
0.0398675 | + | 0.999205i | \(0.487306\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 21.6458i | − 0.811212i | ||||||||
\(713\) | 18.7386i | 0.701767i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.57671 | 0.171040 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 15.2311i | 0.568418i | ||||||||
\(719\) | −32.9848 | −1.23013 | −0.615064 | − | 0.788478i | \(-0.710870\pi\) | ||||
−0.615064 | + | 0.788478i | \(0.710870\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.876894 | −0.0326573 | ||||||||
\(722\) | 15.6155i | 0.581150i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8.82292 | −0.327901 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.05398i | 0.261617i | 0.991408 | + | 0.130809i | \(0.0417574\pi\) | ||||
−0.991408 | + | 0.130809i | \(0.958243\pi\) | |||||||
\(728\) | 11.1231i | 0.412250i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −42.7386 | −1.58075 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 2.00000i | − 0.0738717i | −0.999318 | − | 0.0369358i | \(-0.988240\pi\) | ||||
0.999318 | − | 0.0369358i | \(-0.0117597\pi\) | |||||||
\(734\) | −36.0000 | −1.32878 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.94602 | 0.219173 | ||||||||
\(737\) | − 5.68466i | − 0.209397i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.684658 | −0.0251856 | −0.0125928 | − | 0.999921i | \(-0.504009\pi\) | ||||
−0.0125928 | + | 0.999921i | \(0.504009\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − 11.1231i | − 0.408342i | ||||||||
\(743\) | 9.86174i | 0.361792i | 0.983502 | + | 0.180896i | \(0.0578998\pi\) | ||||
−0.983502 | + | 0.180896i | \(0.942100\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −10.6307 | −0.389217 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.43845i | 0.0891585i | ||||||||
\(749\) | 0.876894 | 0.0320410 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.7386 | −0.829745 | −0.414872 | − | 0.909880i | \(-0.636174\pi\) | ||||
−0.414872 | + | 0.909880i | \(0.636174\pi\) | |||||||
\(752\) | − 44.7926i | − 1.63342i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 22.2462 | 0.810159 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 47.3002i | − 1.71915i | −0.511006 | − | 0.859577i | \(-0.670727\pi\) | ||||
0.511006 | − | 0.859577i | \(-0.329273\pi\) | |||||||
\(758\) | 45.7538i | 1.66185i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 45.3693 | 1.64464 | 0.822318 | − | 0.569028i | \(-0.192680\pi\) | ||||
0.822318 | + | 0.569028i | \(0.192680\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 12.8078i | − 0.463672i | ||||||||
\(764\) | −11.8078 | −0.427190 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.98485 | −0.324636 | ||||||||
\(767\) | − 29.3693i | − 1.06046i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.0540 | 1.11983 | 0.559917 | − | 0.828548i | \(-0.310833\pi\) | ||||
0.559917 | + | 0.828548i | \(0.310833\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.89205i | 0.212059i | ||||||||
\(773\) | − 15.5076i | − 0.557769i | −0.960325 | − | 0.278884i | \(-0.910035\pi\) | ||||
0.960325 | − | 0.278884i | \(-0.0899646\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −14.9309 | −0.535987 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 52.8769i | 1.89573i | ||||||||
\(779\) | −14.0540 | −0.503536 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.8078 | 0.422515 | ||||||||
\(782\) | − 21.1771i | − 0.757291i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −28.1080 | −1.00386 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 53.7386i | 1.91558i | 0.287476 | + | 0.957788i | \(0.407184\pi\) | ||||
−0.287476 | + | 0.957788i | \(0.592816\pi\) | |||||||
\(788\) | 4.79261i | 0.170730i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.876894 | −0.0311788 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 15.6847i | − 0.556979i | ||||||||
\(794\) | 50.8466 | 1.80448 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.98485 | 0.105795 | ||||||||
\(797\) | 51.1231i | 1.81087i | 0.424481 | + | 0.905437i | \(0.360456\pi\) | ||||
−0.424481 | + | 0.905437i | \(0.639544\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −53.1771 | −1.88127 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 55.6155i | 1.96385i | ||||||||
\(803\) | − 0.246211i | − 0.00868861i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −54.7386 | −1.92809 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 13.5616i | − 0.477094i | ||||||||
\(809\) | −7.31534 | −0.257194 | −0.128597 | − | 0.991697i | \(-0.541047\pi\) | ||||
−0.128597 | + | 0.991697i | \(0.541047\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.00000 | −0.0351147 | −0.0175574 | − | 0.999846i | \(-0.505589\pi\) | ||||
−0.0175574 | + | 0.999846i | \(0.505589\pi\) | |||||||
\(812\) | − 1.36932i | − 0.0480536i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −15.3153 | −0.536802 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 23.0540i | − 0.806557i | ||||||||
\(818\) | − 45.3693i | − 1.58630i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.8769 | −0.589008 | −0.294504 | − | 0.955650i | \(-0.595154\pi\) | ||||
−0.294504 | + | 0.955650i | \(0.595154\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 37.0540i | 1.29162i | 0.763498 | + | 0.645810i | \(0.223480\pi\) | ||||
−0.763498 | + | 0.645810i | \(0.776520\pi\) | |||||||
\(824\) | 2.13826 | 0.0744898 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10.0540 | −0.349823 | ||||||||
\(827\) | 26.2462i | 0.912670i | 0.889808 | + | 0.456335i | \(0.150838\pi\) | ||||
−0.889808 | + | 0.456335i | \(0.849162\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.738634 | 0.0256538 | 0.0128269 | − | 0.999918i | \(-0.495917\pi\) | ||||
0.0128269 | + | 0.999918i | \(0.495917\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 25.3693i | − 0.879523i | ||||||||
\(833\) | 33.3693i | 1.15618i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.31534 | −0.0454920 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 46.1619i | 1.59464i | ||||||||
\(839\) | 12.4924 | 0.431286 | 0.215643 | − | 0.976472i | \(-0.430815\pi\) | ||||
0.215643 | + | 0.976472i | \(0.430815\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.2462 | −0.663662 | ||||||||
\(842\) | − 31.3153i | − 1.07920i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6.87689 | −0.236712 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000i | 0.0343604i | ||||||||
\(848\) | 33.3693i | 1.14591i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 23.9157 | 0.819820 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 26.4233i | − 0.904716i | −0.891836 | − | 0.452358i | \(-0.850583\pi\) | ||||
0.891836 | − | 0.452358i | \(-0.149417\pi\) | |||||||
\(854\) | −5.36932 | −0.183734 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.13826 | −0.0730842 | ||||||||
\(857\) | 9.56155i | 0.326616i | 0.986575 | + | 0.163308i | \(0.0522165\pi\) | ||||
−0.986575 | + | 0.163308i | \(0.947784\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34.3542 | 1.17215 | 0.586074 | − | 0.810257i | \(-0.300673\pi\) | ||||
0.586074 | + | 0.810257i | \(0.300673\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 59.7235i | 2.03419i | ||||||||
\(863\) | − 14.2462i | − 0.484947i | −0.970158 | − | 0.242473i | \(-0.922041\pi\) | ||||
0.970158 | − | 0.242473i | \(-0.0779587\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 18.6307 | 0.633096 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.36932i | 0.114362i | ||||||||
\(869\) | −3.31534 | −0.112465 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25.9309 | −0.878634 | ||||||||
\(872\) | 31.2311i | 1.05762i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 11.4233 | 0.386399 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 23.0540i | − 0.778477i | −0.921137 | − | 0.389239i | \(-0.872738\pi\) | ||||
0.921137 | − | 0.389239i | \(-0.127262\pi\) | |||||||
\(878\) | − 58.9309i | − 1.98882i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.2462 | −0.884257 | −0.442129 | − | 0.896952i | \(-0.645777\pi\) | ||||
−0.442129 | + | 0.896952i | \(0.645777\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.0691i | 0.540769i | 0.962752 | + | 0.270385i | \(0.0871509\pi\) | ||||
−0.962752 | + | 0.270385i | \(0.912849\pi\) | |||||||
\(884\) | 11.1231 | 0.374111 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 44.1922 | 1.48467 | ||||||||
\(887\) | − 29.8617i | − 1.00266i | −0.865256 | − | 0.501330i | \(-0.832844\pi\) | ||||
0.865256 | − | 0.501330i | \(-0.167156\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −15.8078 | −0.530175 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.522732i | 0.0175024i | ||||||||
\(893\) | − 28.6847i | − 0.959895i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −13.5616 | −0.453060 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 7.01515i | 0.234099i | ||||||||
\(899\) | −24.0000 | −0.800445 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 39.6155 | 1.31978 | ||||||||
\(902\) | 7.31534i | 0.243574i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.13826 | 0.0711175 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 28.1080i | − 0.933309i | −0.884440 | − | 0.466655i | \(-0.845459\pi\) | ||||
0.884440 | − | 0.466655i | \(-0.154541\pi\) | |||||||
\(908\) | 5.47727i | 0.181770i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 54.1619 | 1.79446 | 0.897232 | − | 0.441559i | \(-0.145574\pi\) | ||||
0.897232 | + | 0.441559i | \(0.145574\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −17.7538 | −0.587243 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.0539753 | 0.00178339 | ||||||||
\(917\) | 16.4924i | 0.544628i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.1080 | 1.09213 | 0.546065 | − | 0.837743i | \(-0.316125\pi\) | ||||
0.546065 | + | 0.837743i | \(0.316125\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 65.3693i | − 2.15282i | ||||||||
\(923\) | − 53.8617i | − 1.77288i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 28.4924 | 0.936319 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.61553i | 0.249992i | ||||||||
\(929\) | 59.2311 | 1.94331 | 0.971654 | − | 0.236408i | \(-0.0759701\pi\) | ||||
0.971654 | + | 0.236408i | \(0.0759701\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.0000 | −0.589926 | ||||||||
\(932\) | 1.83807i | 0.0602081i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −22.2462 | −0.727918 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.3153i | 0.729010i | 0.931201 | + | 0.364505i | \(0.118762\pi\) | ||||
−0.931201 | + | 0.364505i | \(0.881238\pi\) | |||||||
\(938\) | 8.87689i | 0.289841i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.8229 | 0.483213 | 0.241607 | − | 0.970374i | \(-0.422326\pi\) | ||||
0.241607 | + | 0.970374i | \(0.422326\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 11.4233i | − 0.371994i | ||||||||
\(944\) | 30.1619 | 0.981687 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.0000 | −0.390154 | ||||||||
\(947\) | 13.1771i | 0.428198i | 0.976812 | + | 0.214099i | \(0.0686815\pi\) | ||||
−0.976812 | + | 0.214099i | \(0.931319\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.12311 | −0.0364576 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 13.5616i | 0.439532i | ||||||||
\(953\) | − 15.8078i | − 0.512064i | −0.966668 | − | 0.256032i | \(-0.917585\pi\) | ||||
0.966668 | − | 0.256032i | \(-0.0824152\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 7.23106 | 0.233869 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 33.3693i | − 1.07811i | ||||||||
\(959\) | −21.3693 | −0.690051 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.0540 | 0.904967 | ||||||||
\(962\) | 69.8617i | 2.25243i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −10.1080 | −0.325555 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.0000i | 1.41494i | 0.706741 | + | 0.707472i | \(0.250165\pi\) | ||||
−0.706741 | + | 0.707472i | \(0.749835\pi\) | |||||||
\(968\) | − 2.43845i | − 0.0783747i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −37.1771 | −1.19307 | −0.596535 | − | 0.802587i | \(-0.703456\pi\) | ||||
−0.596535 | + | 0.802587i | \(0.703456\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 8.00000i | − 0.256468i | ||||||||
\(974\) | 39.1231 | 1.25359 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 16.1080 | 0.515603 | ||||||||
\(977\) | 15.6155i | 0.499585i | 0.968299 | + | 0.249793i | \(0.0803624\pi\) | ||||
−0.968299 | + | 0.249793i | \(0.919638\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.87689 | −0.283707 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 25.7538i | 0.821836i | ||||||||
\(983\) | 6.93087i | 0.221060i | 0.993873 | + | 0.110530i | \(0.0352549\pi\) | ||||
−0.993873 | + | 0.110530i | \(0.964745\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 27.1231 | 0.863776 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.00000i | 0.190885i | ||||||||
\(989\) | 18.7386 | 0.595854 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 49.6847 | 1.57829 | 0.789143 | − | 0.614210i | \(-0.210525\pi\) | ||||
0.789143 | + | 0.614210i | \(0.210525\pi\) | |||||||
\(992\) | − 18.7386i | − 0.594952i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −18.4384 | −0.584832 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 28.7386i | − 0.910162i | −0.890450 | − | 0.455081i | \(-0.849610\pi\) | ||||
0.890450 | − | 0.455081i | \(-0.150390\pi\) | |||||||
\(998\) | − 26.2462i | − 0.830809i | ||||||||
\(999\) | 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 | 2475.2.c.i.199.2 | 4 | ||
3.2 | odd | 2 | 2475.2.c.j.199.3 | 4 | |||
5.2 | odd | 4 | 2475.2.a.p.1.2 | ✓ | 2 | ||
5.3 | odd | 4 | 2475.2.a.v.1.1 | yes | 2 | ||
5.4 | even | 2 | inner | 2475.2.c.i.199.3 | 4 | ||
15.2 | even | 4 | 2475.2.a.u.1.1 | yes | 2 | ||
15.8 | even | 4 | 2475.2.a.q.1.2 | yes | 2 | ||
15.14 | odd | 2 | 2475.2.c.j.199.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2475.2.a.p.1.2 | ✓ | 2 | 5.2 | odd | 4 | ||
2475.2.a.q.1.2 | yes | 2 | 15.8 | even | 4 | ||
2475.2.a.u.1.1 | yes | 2 | 15.2 | even | 4 | ||
2475.2.a.v.1.1 | yes | 2 | 5.3 | odd | 4 | ||
2475.2.c.i.199.2 | 4 | 1.1 | even | 1 | trivial | ||
2475.2.c.i.199.3 | 4 | 5.4 | even | 2 | inner | ||
2475.2.c.j.199.2 | 4 | 15.14 | odd | 2 | |||
2475.2.c.j.199.3 | 4 | 3.2 | odd | 2 |