Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1400,2,Mod(657,1400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1400, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1400.657");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1400.x (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.1790562830\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | 16.0.29960650073923649536.7 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 7x^{12} + 40x^{8} - 112x^{4} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{22} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 993.6 | ||
Root | \(-0.481610 + 1.32968i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1400.993 |
Dual form | 1400.2.x.a.657.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(701\) | \(801\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.848071 | − | 0.848071i | 0.489634 | − | 0.489634i | −0.418557 | − | 0.908191i | \(-0.637464\pi\) |
0.908191 | + | 0.418557i | \(0.137464\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.406039 | − | 2.61441i | −0.153468 | − | 0.988154i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.56155i | 0.520518i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.56155 | −0.772337 | −0.386169 | − | 0.922428i | \(-0.626202\pi\) | ||||
−0.386169 | + | 0.922428i | \(0.626202\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.17238 | + | 2.17238i | −0.602509 | + | 0.602509i | −0.940978 | − | 0.338469i | \(-0.890091\pi\) |
0.338469 | + | 0.940978i | \(0.390091\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.17238 | − | 2.17238i | −0.526879 | − | 0.526879i | 0.392761 | − | 0.919640i | \(-0.371520\pi\) |
−0.919640 | + | 0.392761i | \(0.871520\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.54312 | −1.95993 | −0.979963 | − | 0.199181i | \(-0.936172\pi\) | ||||
−0.979963 | + | 0.199181i | \(0.936172\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.56155 | − | 1.87285i | −0.558977 | − | 0.408690i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.03680 | − | 5.03680i | −1.05024 | − | 1.05024i | −0.998669 | − | 0.0515755i | \(-0.983576\pi\) |
−0.0515755 | − | 0.998669i | \(-0.516424\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.86852 | + | 3.86852i | 0.744497 | + | 0.744497i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.68466i | 1.05561i | 0.849364 | + | 0.527807i | \(0.176986\pi\) | ||||
−0.849364 | + | 0.527807i | \(0.823014\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4.79741i | − | 0.861641i | −0.902438 | − | 0.430820i | \(-0.858224\pi\) | ||
0.902438 | − | 0.430820i | \(-0.141776\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.17238 | + | 2.17238i | −0.378162 | + | 0.378162i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.82843 | − | 2.82843i | 0.464991 | − | 0.464991i | −0.435297 | − | 0.900287i | \(-0.643356\pi\) |
0.900287 | + | 0.435297i | \(0.143356\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.68466i | 0.590018i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 8.54312i | − | 1.33421i | −0.744963 | − | 0.667105i | \(-0.767533\pi\) | ||
0.744963 | − | 0.667105i | \(-0.232467\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.620058 | + | 0.620058i | 0.0945580 | + | 0.0945580i | 0.752803 | − | 0.658245i | \(-0.228701\pi\) |
−0.658245 | + | 0.752803i | \(0.728701\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.848071 | + | 0.848071i | 0.123704 | + | 0.123704i | 0.766248 | − | 0.642545i | \(-0.222121\pi\) |
−0.642545 | + | 0.766248i | \(0.722121\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.67026 | + | 2.12311i | −0.952895 | + | 0.303301i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.68466 | −0.515955 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.41674 | + | 4.41674i | 0.606686 | + | 0.606686i | 0.942078 | − | 0.335393i | \(-0.108869\pi\) |
−0.335393 | + | 0.942078i | \(0.608869\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.24517 | + | 7.24517i | −0.959646 | + | 0.959646i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.74571 | −0.487649 | −0.243825 | − | 0.969819i | \(-0.578402\pi\) | ||||
−0.243825 | + | 0.969819i | \(0.578402\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.79741i | 0.614246i | 0.951670 | + | 0.307123i | \(0.0993662\pi\) | ||||
−0.951670 | + | 0.307123i | \(0.900634\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.08254 | − | 0.634052i | 0.514351 | − | 0.0798830i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.20837 | − | 2.20837i | 0.269795 | − | 0.269795i | −0.559222 | − | 0.829018i | \(-0.688900\pi\) |
0.829018 | + | 0.559222i | \(0.188900\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.54312 | −1.02847 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.2462 | −1.21600 | −0.608001 | − | 0.793936i | \(-0.708028\pi\) | ||||
−0.608001 | + | 0.793936i | \(0.708028\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.39228 | + | 3.39228i | −0.397037 | + | 0.397037i | −0.877186 | − | 0.480150i | \(-0.840582\pi\) |
0.480150 | + | 0.877186i | \(0.340582\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.04009 | + | 6.69695i | 0.118529 | + | 0.763188i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.80776i | 0.990951i | 0.868622 | + | 0.495475i | \(0.165006\pi\) | ||||
−0.868622 | + | 0.495475i | \(0.834994\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.87689 | 0.208544 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.66906 | − | 5.66906i | 0.622260 | − | 0.622260i | −0.323849 | − | 0.946109i | \(-0.604977\pi\) |
0.946109 | + | 0.323849i | \(0.104977\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.82099 | + | 4.82099i | 0.516865 | + | 0.516865i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.79741 | −0.508525 | −0.254262 | − | 0.967135i | \(-0.581833\pi\) | ||||
−0.254262 | + | 0.967135i | \(0.581833\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.56155 | + | 4.79741i | 0.687838 | + | 0.502905i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.06854 | − | 4.06854i | −0.421888 | − | 0.421888i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.3017 | − | 13.3017i | −1.35058 | − | 1.35058i | −0.885009 | − | 0.465573i | \(-0.845848\pi\) |
−0.465573 | − | 0.885009i | \(-0.654152\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 4.00000i | − | 0.402015i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 18.1379i | − | 1.80479i | −0.430907 | − | 0.902396i | \(-0.641806\pi\) | ||
0.430907 | − | 0.902396i | \(-0.358194\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.53758 | − | 9.53758i | 0.939766 | − | 0.939766i | −0.0585205 | − | 0.998286i | \(-0.518638\pi\) |
0.998286 | + | 0.0585205i | \(0.0186383\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.86522 | − | 7.86522i | 0.760360 | − | 0.760360i | −0.216027 | − | 0.976387i | \(-0.569310\pi\) |
0.976387 | + | 0.216027i | \(0.0693101\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.68466i | 0.927622i | 0.885934 | + | 0.463811i | \(0.153518\pi\) | ||||
−0.885934 | + | 0.463811i | \(0.846482\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 4.79741i | − | 0.455350i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.9020 | + | 12.9020i | 1.21372 | + | 1.21372i | 0.969794 | + | 0.243926i | \(0.0784354\pi\) |
0.243926 | + | 0.969794i | \(0.421565\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.39228 | − | 3.39228i | −0.313617 | − | 0.313617i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.79741 | + | 6.56155i | −0.439778 | + | 0.601497i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.43845 | −0.403495 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.24517 | − | 7.24517i | −0.653275 | − | 0.653275i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.44849 | + | 3.44849i | −0.306004 | + | 0.306004i | −0.843357 | − | 0.537354i | \(-0.819424\pi\) |
0.537354 | + | 0.843357i | \(0.319424\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.05171 | 0.0925975 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.05171i | 0.0918880i | 0.998944 | + | 0.0459440i | \(0.0146296\pi\) | ||||
−0.998944 | + | 0.0459440i | \(0.985370\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.46884 | + | 22.3352i | 0.300787 | + | 1.93671i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.58831 | + | 1.58831i | −0.135699 | + | 0.135699i | −0.771693 | − | 0.635995i | \(-0.780590\pi\) |
0.635995 | + | 0.771693i | \(0.280590\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.74571 | −0.317707 | −0.158853 | − | 0.987302i | \(-0.550780\pi\) | ||||
−0.158853 | + | 0.987302i | \(0.550780\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.43845 | 0.121139 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.56466 | − | 5.56466i | 0.465340 | − | 0.465340i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.85631 | + | 7.45740i | −0.318063 | + | 0.615076i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 12.2462i | − | 1.00325i | −0.865086 | − | 0.501624i | \(-0.832736\pi\) | ||
0.865086 | − | 0.501624i | \(-0.167264\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.31534 | −0.351178 | −0.175589 | − | 0.984464i | \(-0.556183\pi\) | ||||
−0.175589 | + | 0.984464i | \(0.556183\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.39228 | − | 3.39228i | 0.274250 | − | 0.274250i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.78456 | + | 6.78456i | 0.541467 | + | 0.541467i | 0.923959 | − | 0.382492i | \(-0.124934\pi\) |
−0.382492 | + | 0.923959i | \(0.624934\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.49141 | 0.594108 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.1231 | + | 15.2134i | −0.876624 | + | 1.19898i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.5221 | − | 13.5221i | −1.05913 | − | 1.05913i | −0.998138 | − | 0.0609926i | \(-0.980573\pi\) |
−0.0609926 | − | 0.998138i | \(-0.519427\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.63263 | + | 7.63263i | 0.590631 | + | 0.590631i | 0.937802 | − | 0.347171i | \(-0.112858\pi\) |
−0.347171 | + | 0.937802i | \(0.612858\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.56155i | 0.273966i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 13.3405i | − | 1.02018i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.90941 | + | 9.90941i | −0.753399 | + | 0.753399i | −0.975112 | − | 0.221713i | \(-0.928835\pi\) |
0.221713 | + | 0.975112i | \(0.428835\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.17662 | + | 3.17662i | −0.238770 | + | 0.238770i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 14.2462i | − | 1.06481i | −0.846489 | − | 0.532406i | \(-0.821288\pi\) | ||
0.846489 | − | 0.532406i | \(-0.178712\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.8319i | 1.54843i | 0.632925 | + | 0.774213i | \(0.281854\pi\) | ||||
−0.632925 | + | 0.774213i | \(0.718146\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.06854 | + | 4.06854i | 0.300755 | + | 0.300755i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.56466 | + | 5.56466i | 0.406928 | + | 0.406928i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.54312 | − | 11.6847i | 0.621420 | − | 0.849934i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.5616 | 1.05364 | 0.526818 | − | 0.849978i | \(-0.323385\pi\) | ||||
0.526818 | + | 0.849978i | \(0.323385\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.9020 | − | 12.9020i | −0.928708 | − | 0.928708i | 0.0689148 | − | 0.997623i | \(-0.478046\pi\) |
−0.997623 | + | 0.0689148i | \(0.978046\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.00505 | − | 6.00505i | 0.427842 | − | 0.427842i | −0.460051 | − | 0.887893i | \(-0.652169\pi\) |
0.887893 | + | 0.460051i | \(0.152169\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.0862 | 1.21121 | 0.605605 | − | 0.795765i | \(-0.292931\pi\) | ||||
0.605605 | + | 0.795765i | \(0.292931\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 3.74571i | − | 0.264202i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14.8620 | − | 2.30820i | 1.04311 | − | 0.162004i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.86522 | − | 7.86522i | 0.546671 | − | 0.546671i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 21.8836 | 1.51372 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.1771 | 1.38905 | 0.694524 | − | 0.719470i | \(-0.255615\pi\) | ||||
0.694524 | + | 0.719470i | \(0.255615\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.68951 | + | 8.68951i | −0.595395 | + | 0.595395i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.5424 | + | 1.94794i | −0.851433 | + | 0.132235i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.75379i | 0.388805i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.43845 | 0.634899 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.9299 | + | 12.9299i | −0.865848 | + | 0.865848i | −0.992010 | − | 0.126162i | \(-0.959734\pi\) |
0.126162 | + | 0.992010i | \(0.459734\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.6260 | − | 14.6260i | −0.970762 | − | 0.970762i | 0.0288226 | − | 0.999585i | \(-0.490824\pi\) |
−0.999585 | + | 0.0288226i | \(0.990824\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.54312 | −0.564545 | −0.282273 | − | 0.959334i | \(-0.591088\pi\) | ||||
−0.282273 | + | 0.959334i | \(0.591088\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.56155 | + | 4.79741i | 0.431718 | + | 0.315646i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.9706 | − | 16.9706i | −1.11178 | − | 1.11178i | −0.992910 | − | 0.118869i | \(-0.962073\pi\) |
−0.118869 | − | 0.992910i | \(-0.537927\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.46960 | + | 7.46960i | 0.485203 | + | 0.485203i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 0.807764i | − | 0.0522499i | −0.999659 | − | 0.0261250i | \(-0.991683\pi\) | ||
0.999659 | − | 0.0261250i | \(-0.00831678\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.0345i | 1.03287i | 0.856325 | + | 0.516437i | \(0.172742\pi\) | ||||
−0.856325 | + | 0.516437i | \(0.827258\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.0138 | + | 10.0138i | −0.642387 | + | 0.642387i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.5589 | − | 18.5589i | 1.18087 | − | 1.18087i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 9.61553i | − | 0.609359i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 3.74571i | − | 0.236427i | −0.992988 | − | 0.118213i | \(-0.962283\pi\) | ||
0.992988 | − | 0.118213i | \(-0.0377167\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.9020 | + | 12.9020i | 0.811143 | + | 0.811143i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.68951 | − | 8.68951i | −0.542037 | − | 0.542037i | 0.382089 | − | 0.924126i | \(-0.375205\pi\) |
−0.924126 | + | 0.382089i | \(0.875205\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.54312 | − | 6.24621i | −0.530843 | − | 0.388121i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.87689 | −0.549466 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.2820 | − | 12.2820i | −0.757338 | − | 0.757338i | 0.218499 | − | 0.975837i | \(-0.429884\pi\) |
−0.975837 | + | 0.218499i | \(0.929884\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.06854 | + | 4.06854i | −0.248991 | + | 0.248991i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.0862 | 1.04177 | 0.520883 | − | 0.853628i | \(-0.325603\pi\) | ||||
0.520883 | + | 0.853628i | \(0.325603\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.8836i | 1.32934i | 0.747139 | + | 0.664668i | \(0.231427\pi\) | ||||
−0.747139 | + | 0.664668i | \(0.768573\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.63320 | − | 1.49612i | 0.583028 | − | 0.0905491i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.41674 | − | 4.41674i | 0.265376 | − | 0.265376i | −0.561858 | − | 0.827234i | \(-0.689913\pi\) |
0.827234 | + | 0.561858i | \(0.189913\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.49141 | 0.448499 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.56155 | 0.272119 | 0.136060 | − | 0.990701i | \(-0.456556\pi\) | ||||
0.136060 | + | 0.990701i | \(0.456556\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.9299 | − | 12.9299i | 0.768601 | − | 0.768601i | −0.209260 | − | 0.977860i | \(-0.567105\pi\) |
0.977860 | + | 0.209260i | \(0.0671054\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −22.3352 | + | 3.46884i | −1.31841 | + | 0.204759i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 7.56155i | − | 0.444797i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −22.5616 | −1.32258 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.12485 | + | 3.12485i | −0.182556 | + | 0.182556i | −0.792469 | − | 0.609913i | \(-0.791204\pi\) |
0.609913 | + | 0.792469i | \(0.291204\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9.90941 | − | 9.90941i | −0.575003 | − | 0.575003i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 21.8836 | 1.26556 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.36932 | − | 1.87285i | 0.0789261 | − | 0.107949i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −15.3823 | − | 15.3823i | −0.883687 | − | 0.883687i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.32878 | + | 9.32878i | 0.532421 | + | 0.532421i | 0.921292 | − | 0.388871i | \(-0.127135\pi\) |
−0.388871 | + | 0.921292i | \(0.627135\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 16.1771i | − | 0.920282i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.2888i | 0.696835i | 0.937339 | + | 0.348418i | \(0.113281\pi\) | ||||
−0.937339 | + | 0.348418i | \(0.886719\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.0387 | − | 21.0387i | 1.18918 | − | 1.18918i | 0.211885 | − | 0.977295i | \(-0.432040\pi\) |
0.977295 | − | 0.211885i | \(-0.0679602\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 24.5639 | − | 24.5639i | 1.37965 | − | 1.37965i | 0.534443 | − | 0.845205i | \(-0.320522\pi\) |
0.845205 | − | 0.534443i | \(-0.179478\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 14.5616i | − | 0.815290i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 13.3405i | − | 0.744596i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 18.5589 | + | 18.5589i | 1.03264 | + | 1.03264i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.21327 | + | 8.21327i | 0.454195 | + | 0.454195i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.87285 | − | 2.56155i | 0.103254 | − | 0.141223i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.7386 | 1.46969 | 0.734844 | − | 0.678236i | \(-0.237255\pi\) | ||||
0.734844 | + | 0.678236i | \(0.237255\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.41674 | + | 4.41674i | 0.242036 | + | 0.242036i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.1472 | + | 20.1472i | −1.09749 | + | 1.09749i | −0.102783 | + | 0.994704i | \(0.532775\pi\) |
−0.994704 | + | 0.102783i | \(0.967225\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 21.8836 | 1.18856 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.2888i | 0.665477i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.25906 | + | 16.5767i | 0.445947 | + | 0.895059i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.79668 | + | 3.79668i | −0.203816 | + | 0.203816i | −0.801633 | − | 0.597816i | \(-0.796035\pi\) |
0.597816 | + | 0.801633i | \(0.296035\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.54312 | 0.457303 | 0.228651 | − | 0.973508i | \(-0.426568\pi\) | ||||
0.228651 | + | 0.973508i | \(0.426568\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −16.8078 | −0.897132 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.00447 | + | 8.00447i | −0.426035 | + | 0.426035i | −0.887275 | − | 0.461240i | \(-0.847405\pi\) |
0.461240 | + | 0.887275i | \(0.347405\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.49612 | + | 9.63320i | 0.0791829 | + | 0.509843i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 22.7386i | − | 1.20010i | −0.799963 | − | 0.600050i | \(-0.795148\pi\) | ||
0.799963 | − | 0.600050i | \(-0.204852\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 53.9848 | 2.84131 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.76412 | + | 3.76412i | −0.197565 | + | 0.197565i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.24035 | − | 4.24035i | −0.221345 | − | 0.221345i | 0.587720 | − | 0.809064i | \(-0.300026\pi\) |
−0.809064 | + | 0.587720i | \(0.800026\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 13.3405 | 0.694480 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.75379 | − | 13.3405i | 0.506391 | − | 0.692606i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.1421 | − | 14.1421i | −0.732252 | − | 0.732252i | 0.238813 | − | 0.971065i | \(-0.423242\pi\) |
−0.971065 | + | 0.238813i | \(0.923242\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.3492 | − | 12.3492i | −0.636017 | − | 0.636017i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 9.75379i | − | 0.501018i | −0.968114 | − | 0.250509i | \(-0.919402\pi\) | ||
0.968114 | − | 0.250509i | \(-0.0805980\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.84912i | 0.299659i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.76412 | + | 3.76412i | −0.192337 | + | 0.192337i | −0.796705 | − | 0.604368i | \(-0.793426\pi\) |
0.604368 | + | 0.796705i | \(0.293426\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.968253 | + | 0.968253i | −0.0492191 | + | 0.0492191i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 24.5616i | 1.24532i | 0.782492 | + | 0.622660i | \(0.213948\pi\) | ||||
−0.782492 | + | 0.622660i | \(0.786052\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.8836i | 1.10670i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.891921 | + | 0.891921i | 0.0449914 | + | 0.0449914i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.8619 | + | 10.8619i | 0.545142 | + | 0.545142i | 0.925032 | − | 0.379889i | \(-0.124038\pi\) |
−0.379889 | + | 0.925032i | \(0.624038\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 21.8836 | + | 16.0000i | 1.09555 | + | 0.801002i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −27.9309 | −1.39480 | −0.697401 | − | 0.716682i | \(-0.745660\pi\) | ||||
−0.697401 | + | 0.716682i | \(0.745660\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.4218 | + | 10.4218i | 0.519146 | + | 0.519146i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.24517 | + | 7.24517i | −0.359130 | + | 0.359130i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.84912 | −0.289220 | −0.144610 | − | 0.989489i | \(-0.546193\pi\) | ||||
−0.144610 | + | 0.989489i | \(0.546193\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.69400i | 0.132885i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.52090 | + | 9.79280i | 0.0748388 | + | 0.481872i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.17662 | + | 3.17662i | −0.155560 | + | 0.155560i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.3405 | 0.651727 | 0.325864 | − | 0.945417i | \(-0.394345\pi\) | ||||
0.325864 | + | 0.945417i | \(0.394345\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.68466 | 0.0821052 | 0.0410526 | − | 0.999157i | \(-0.486929\pi\) | ||||
0.0410526 | + | 0.999157i | \(0.486929\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.32431 | + | 1.32431i | −0.0643900 | + | 0.0643900i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.5424 | − | 1.94794i | 0.606969 | − | 0.0942673i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 9.43845i | − | 0.455693i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.5616 | −1.08675 | −0.543376 | − | 0.839490i | \(-0.682854\pi\) | ||||
−0.543376 | + | 0.839490i | \(0.682854\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.7713 | − | 20.7713i | 0.998205 | − | 0.998205i | −0.00179335 | − | 0.999998i | \(-0.500571\pi\) |
0.999998 | + | 0.00179335i | \(0.000570843\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 43.0299 | + | 43.0299i | 2.05840 | + | 2.05840i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.5776 | −1.17303 | −0.586513 | − | 0.809939i | \(-0.699500\pi\) | ||||
−0.586513 | + | 0.809939i | \(0.699500\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.31534 | − | 10.4160i | −0.157873 | − | 0.495999i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.0074 | − | 22.0074i | −1.04560 | − | 1.04560i | −0.998909 | − | 0.0466918i | \(-0.985132\pi\) |
−0.0466918 | − | 0.998909i | \(-0.514868\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.3857 | − | 10.3857i | −0.491224 | − | 0.491224i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 17.0540i | − | 0.804827i | −0.915458 | − | 0.402413i | \(-0.868171\pi\) | ||
0.915458 | − | 0.402413i | \(-0.131829\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.8836i | 1.03046i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.65971 | + | 3.65971i | −0.171948 | + | 0.171948i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.3823 | − | 15.3823i | 0.719551 | − | 0.719551i | −0.248962 | − | 0.968513i | \(-0.580089\pi\) |
0.968513 | + | 0.248962i | \(0.0800894\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 16.8078i | − | 0.784519i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 11.2371i | − | 0.523365i | −0.965154 | − | 0.261682i | \(-0.915723\pi\) | ||
0.965154 | − | 0.261682i | \(-0.0842773\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.1840 | + | 25.1840i | 1.17040 | + | 1.17040i | 0.982115 | + | 0.188284i | \(0.0602926\pi\) |
0.188284 | + | 0.982115i | \(0.439707\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.6260 | − | 14.6260i | −0.676811 | − | 0.676811i | 0.282466 | − | 0.959277i | \(-0.408847\pi\) |
−0.959277 | + | 0.282466i | \(0.908847\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.67026 | − | 4.87689i | −0.308004 | − | 0.225194i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.5076 | 0.530241 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.58831 | − | 1.58831i | −0.0730306 | − | 0.0730306i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.89697 | + | 6.89697i | −0.315791 | + | 0.315791i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −38.9699 | −1.78058 | −0.890290 | − | 0.455395i | \(-0.849498\pi\) | ||||
−0.890290 | + | 0.455395i | \(0.849498\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.2888i | 0.560322i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.46884 | + | 22.3352i | 0.157838 | + | 1.01629i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.5221 | + | 13.5221i | −0.612744 | + | 0.612744i | −0.943660 | − | 0.330916i | \(-0.892642\pi\) |
0.330916 | + | 0.943660i | \(0.392642\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −22.9354 | −1.03717 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.68466 | −0.346804 | −0.173402 | − | 0.984851i | \(-0.555476\pi\) | ||||
−0.173402 | + | 0.984851i | \(0.555476\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.3492 | − | 12.3492i | 0.556181 | − | 0.556181i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.16037 | + | 26.7878i | 0.186618 | + | 1.20160i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 36.8078i | 1.64774i | 0.566777 | + | 0.823871i | \(0.308190\pi\) | ||||
−0.566777 | + | 0.823871i | \(0.691810\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.9460 | 0.578386 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.84144 | − | 7.84144i | 0.349632 | − | 0.349632i | −0.510340 | − | 0.859973i | \(-0.670480\pi\) |
0.859973 | + | 0.510340i | \(0.170480\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.02045 | + | 3.02045i | 0.134143 | + | 0.134143i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.8319 | 0.923359 | 0.461680 | − | 0.887047i | \(-0.347247\pi\) | ||||
0.461680 | + | 0.887047i | \(0.347247\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.2462 | + | 7.49141i | 0.453266 | + | 0.331401i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −33.0492 | − | 33.0492i | −1.45916 | − | 1.45916i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.17238 | − | 2.17238i | −0.0955410 | − | 0.0955410i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.8078i | 0.737779i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 19.7802i | − | 0.866588i | −0.901253 | − | 0.433294i | \(-0.857351\pi\) | ||
0.901253 | − | 0.433294i | \(-0.142649\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.4536 | + | 12.4536i | −0.544559 | + | 0.544559i | −0.924862 | − | 0.380303i | \(-0.875820\pi\) |
0.380303 | + | 0.924862i | \(0.375820\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.4218 | + | 10.4218i | −0.453980 | + | 0.453980i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27.7386i | 1.20603i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 5.84912i | − | 0.253830i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 18.5589 | + | 18.5589i | 0.803874 | + | 0.803874i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.0818 | − | 12.0818i | −0.521368 | − | 0.521368i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 17.0862 | − | 5.43845i | 0.735956 | − | 0.234251i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.0691303 | −0.00297214 | −0.00148607 | − | 0.999999i | \(-0.500473\pi\) | ||||
−0.00148607 | + | 0.999999i | \(0.500473\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17.6670 | + | 17.6670i | 0.758162 | + | 0.758162i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.5271 | + | 19.5271i | −0.834920 | + | 0.834920i | −0.988185 | − | 0.153265i | \(-0.951021\pi\) |
0.153265 | + | 0.988185i | \(0.451021\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.49141 | −0.319726 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 48.5647i | − | 2.06893i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 23.0271 | − | 3.57630i | 0.979212 | − | 0.152080i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.7405 | − | 27.7405i | 1.17540 | − | 1.17540i | 0.194503 | − | 0.980902i | \(-0.437691\pi\) |
0.980902 | − | 0.194503i | \(-0.0623093\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.69400 | −0.113944 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.43845 | 0.398492 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −23.7917 | + | 23.7917i | −1.00270 | + | 1.00270i | −0.00270634 | + | 0.999996i | \(0.500861\pi\) |
−0.999996 | + | 0.00270634i | \(0.999139\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.762093 | − | 4.90697i | −0.0320049 | − | 0.206073i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.7386i | 0.534031i | 0.963692 | + | 0.267016i | \(0.0860375\pi\) | ||||
−0.963692 | + | 0.267016i | \(0.913962\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −38.2462 | −1.60055 | −0.800277 | − | 0.599630i | \(-0.795314\pi\) | ||||
−0.800277 | + | 0.599630i | \(0.795314\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.3492 | − | 12.3492i | 0.515896 | − | 0.515896i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.6940 | − | 16.6940i | −0.694979 | − | 0.694979i | 0.268344 | − | 0.963323i | \(-0.413524\pi\) |
−0.963323 | + | 0.268344i | \(0.913524\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −21.8836 | −0.909453 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17.1231 | − | 12.5194i | −0.710386 | − | 0.519391i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.3137 | − | 11.3137i | −0.468566 | − | 0.468566i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.41273 | − | 6.41273i | −0.264682 | − | 0.264682i | 0.562271 | − | 0.826953i | \(-0.309928\pi\) |
−0.826953 | + | 0.562271i | \(0.809928\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 40.9848i | 1.68875i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 10.1854i | − | 0.418972i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.1338 | − | 19.1338i | 0.785730 | − | 0.785730i | −0.195061 | − | 0.980791i | \(-0.562490\pi\) |
0.980791 | + | 0.195061i | \(0.0624904\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.4903 | − | 14.4903i | 0.593050 | − | 0.593050i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 35.6847i | − | 1.45804i | −0.684495 | − | 0.729018i | \(-0.739977\pi\) | ||
0.684495 | − | 0.729018i | \(-0.260023\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.9354i | 0.935552i | 0.883847 | + | 0.467776i | \(0.154945\pi\) | ||||
−0.883847 | + | 0.467776i | \(0.845055\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.44849 | + | 3.44849i | 0.140433 | + | 0.140433i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.84144 | − | 7.84144i | −0.318274 | − | 0.318274i | 0.529830 | − | 0.848104i | \(-0.322256\pi\) |
−0.848104 | + | 0.529830i | \(0.822256\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.6465 | − | 14.5616i | 0.431419 | − | 0.590064i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.68466 | −0.149065 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.3873 | − | 21.3873i | −0.863825 | − | 0.863825i | 0.127955 | − | 0.991780i | \(-0.459159\pi\) |
−0.991780 | + | 0.127955i | \(0.959159\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −44.8190 | −1.80143 | −0.900714 | − | 0.434413i | \(-0.856956\pi\) | ||||
−0.900714 | + | 0.434413i | \(0.856956\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 38.9699i | − | 1.56381i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.94794 | + | 12.5424i | 0.0780425 | + | 0.502500i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 18.5589 | − | 18.5589i | 0.741170 | − | 0.741170i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.2888 | −0.489987 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.807764 | 0.0321566 | 0.0160783 | − | 0.999871i | \(-0.494882\pi\) | ||||
0.0160783 | + | 0.999871i | \(0.494882\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 17.1116 | − | 17.1116i | 0.680125 | − | 0.680125i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.87814 | − | 19.1025i | 0.391386 | − | 0.756869i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 16.0000i | − | 0.632950i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.73863 | −0.187165 | −0.0935824 | − | 0.995612i | \(-0.529832\pi\) | ||||
−0.0935824 | + | 0.995612i | \(0.529832\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.9232 | + | 19.9232i | −0.785696 | + | 0.785696i | −0.980785 | − | 0.195090i | \(-0.937500\pi\) |
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −21.1431 | − | 21.1431i | −0.831222 | − | 0.831222i | 0.156462 | − | 0.987684i | \(-0.449991\pi\) |
−0.987684 | + | 0.156462i | \(0.949991\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.59482 | 0.376630 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.98485 | + | 12.2888i | −0.352144 | + | 0.481637i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.1421 | − | 14.1421i | −0.553425 | − | 0.553425i | 0.374003 | − | 0.927428i | \(-0.377985\pi\) |
−0.927428 | + | 0.374003i | \(0.877985\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.29723 | − | 5.29723i | −0.206665 | − | 0.206665i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.93087i | 0.0752160i | 0.999293 | + | 0.0376080i | \(0.0119738\pi\) | ||||
−0.999293 | + | 0.0376080i | \(0.988026\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.7673i | 1.70235i | 0.524882 | + | 0.851175i | \(0.324110\pi\) | ||||
−0.524882 | + | 0.851175i | \(0.675890\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.00447 | − | 8.00447i | 0.310868 | − | 0.310868i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 28.6325 | − | 28.6325i | 1.10865 | − | 1.10865i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 21.9309i | 0.847896i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 12.2888i | − | 0.474405i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.9121 | − | 24.9121i | −0.960292 | − | 0.960292i | 0.0389496 | − | 0.999241i | \(-0.487599\pi\) |
−0.999241 | + | 0.0389496i | \(0.987599\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30.6807 | + | 30.6807i | 1.17916 | + | 1.17916i | 0.979960 | + | 0.199196i | \(0.0638330\pi\) |
0.199196 | + | 0.979960i | \(0.436167\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −29.3751 | + | 40.1771i | −1.12731 | + | 1.54185i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −24.8078 | −0.950636 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.8703 | − | 13.8703i | −0.530731 | − | 0.530731i | 0.390059 | − | 0.920790i | \(-0.372455\pi\) |
−0.920790 | + | 0.390059i | \(0.872455\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.24517 | + | 7.24517i | −0.276420 | + | 0.276420i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −19.1896 | −0.731067 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 13.3405i | − | 0.507498i | −0.967270 | − | 0.253749i | \(-0.918336\pi\) | ||
0.967270 | − | 0.253749i | \(-0.0816637\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10.4576 | + | 1.62416i | −0.397253 | + | 0.0616966i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.5589 | + | 18.5589i | −0.702967 | + | 0.702967i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −28.7845 | −1.08873 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.0691 | 0.455845 | 0.227922 | − | 0.973679i | \(-0.426807\pi\) | ||||
0.227922 | + | 0.973679i | \(0.426807\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24.1636 | + | 24.1636i | −0.911347 | + | 0.911347i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −47.4200 | + | 7.36472i | −1.78341 | + | 0.276979i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 9.19224i | − | 0.345222i | −0.984990 | − | 0.172611i | \(-0.944780\pi\) | ||
0.984990 | − | 0.172611i | \(-0.0552203\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.7538 | −0.515807 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −24.1636 | + | 24.1636i | −0.904933 | + | 0.904933i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.685041 | − | 0.685041i | −0.0255833 | − | 0.0255833i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14.3922 | 0.536740 | 0.268370 | − | 0.963316i | \(-0.413515\pi\) | ||||
0.268370 | + | 0.963316i | \(0.413515\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −28.8078 | − | 21.0625i | −1.07286 | − | 0.784408i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13.5984 | + | 13.5984i | 0.505730 | + | 0.505730i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.1431 | + | 21.1431i | 0.784155 | + | 0.784155i | 0.980529 | − | 0.196374i | \(-0.0629166\pi\) |
−0.196374 | + | 0.980529i | \(0.562917\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 22.6155i | 0.837612i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 2.69400i | − | 0.0996412i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.7282 | + | 29.7282i | −1.09804 | + | 1.09804i | −0.103398 | + | 0.994640i | \(0.532971\pi\) |
−0.994640 | + | 0.103398i | \(0.967029\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.65685 | + | 5.65685i | −0.208373 | + | 0.208373i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.4233i | 0.824854i | 0.910991 | + | 0.412427i | \(0.135319\pi\) | ||||
−0.910991 | + | 0.412427i | \(0.864681\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 31.4785i | − | 1.15639i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.968253 | − | 0.968253i | −0.0355218 | − | 0.0355218i | 0.689123 | − | 0.724645i | \(-0.257996\pi\) |
−0.724645 | + | 0.689123i | \(0.757996\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.85254 | + | 8.85254i | 0.323897 | + | 0.323897i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −23.7565 | − | 17.3693i | −0.868044 | − | 0.634661i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38.5616 | 1.40713 | 0.703566 | − | 0.710630i | \(-0.251590\pi\) | ||||
0.703566 | + | 0.710630i | \(0.251590\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.17662 | − | 3.17662i | −0.115763 | − | 0.115763i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.24012 | + | 1.24012i | −0.0450728 | + | 0.0450728i | −0.729284 | − | 0.684211i | \(-0.760147\pi\) |
0.684211 | + | 0.729284i | \(0.260147\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 21.8836 | 0.794326 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 21.8836i | − | 0.793282i | −0.917974 | − | 0.396641i | \(-0.870176\pi\) | ||
0.917974 | − | 0.396641i | \(-0.129824\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 25.3197 | − | 3.93235i | 0.916633 | − | 0.142361i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.13709 | − | 8.13709i | 0.293813 | − | 0.293813i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −41.6639 | −1.50244 | −0.751219 | − | 0.660053i | \(-0.770534\pi\) | ||||
−0.751219 | + | 0.660053i | \(0.770534\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.7386 | −0.530799 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 26.8708 | − | 26.8708i | 0.966476 | − | 0.966476i | −0.0329796 | − | 0.999456i | \(-0.510500\pi\) |
0.999456 | + | 0.0329796i | \(0.0104996\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −12.5424 | + | 1.94794i | −0.449956 | + | 0.0698819i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 72.9848i | 2.61495i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 26.2462 | 0.939163 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −21.9912 | + | 21.9912i | −0.785902 | + | 0.785902i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.14530 | + | 6.14530i | 0.219056 | + | 0.219056i | 0.808101 | − | 0.589044i | \(-0.200496\pi\) |
−0.589044 | + | 0.808101i | \(0.700496\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −20.8319 | −0.741637 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 28.4924 | − | 38.9699i | 1.01307 | − | 1.38561i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.4218 | − | 10.4218i | −0.370089 | − | 0.370089i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 37.4653 | + | 37.4653i | 1.32709 | + | 1.32709i | 0.907899 | + | 0.419190i | \(0.137686\pi\) |
0.419190 | + | 0.907899i | \(0.362314\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 3.68466i | − | 0.130354i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 7.49141i | − | 0.264696i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.68951 | − | 8.68951i | 0.306646 | − | 0.306646i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.4903 | − | 14.4903i | 0.510084 | − | 0.510084i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 22.3153i | 0.784566i | 0.919845 | + | 0.392283i | \(0.128315\pi\) | ||||
−0.919845 | + | 0.392283i | \(0.871685\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.9354i | 0.805369i | 0.915339 | + | 0.402685i | \(0.131923\pi\) | ||||
−0.915339 | + | 0.402685i | \(0.868077\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18.5589 | + | 18.5589i | 0.650888 | + | 0.650888i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.29723 | − | 5.29723i | −0.185327 | − | 0.185327i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.49141 | + | 10.2462i | −0.261771 | + | 0.358032i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −49.5464 | −1.72918 | −0.864591 | − | 0.502477i | \(-0.832422\pi\) | ||||
−0.864591 | + | 0.502477i | \(0.832422\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.7672 | − | 20.7672i | −0.723901 | − | 0.723901i | 0.245497 | − | 0.969397i | \(-0.421049\pi\) |
−0.969397 | + | 0.245497i | \(0.921049\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.86522 | + | 7.86522i | −0.273501 | + | 0.273501i | −0.830508 | − | 0.557007i | \(-0.811950\pi\) |
0.557007 | + | 0.830508i | \(0.311950\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −48.5647 | −1.68672 | −0.843361 | − | 0.537348i | \(-0.819426\pi\) | ||||
−0.843361 | + | 0.537348i | \(0.819426\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 7.49141i | − | 0.259874i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 19.1025 | + | 9.87814i | 0.661863 | + | 0.342257i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 18.5589 | − | 18.5589i | 0.641489 | − | 0.641489i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.7802 | −0.682889 | −0.341445 | − | 0.939902i | \(-0.610916\pi\) | ||||
−0.341445 | + | 0.939902i | \(0.610916\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.31534 | −0.114322 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.86852 | − | 3.86852i | 0.133239 | − | 0.133239i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.80218 | + | 11.6039i | 0.0619238 | + | 0.398715i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 21.9309i | − | 0.752665i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −28.4924 | −0.976708 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.29723 | − | 5.29723i | 0.181374 | − | 0.181374i | −0.610581 | − | 0.791954i | \(-0.709064\pi\) |
0.791954 | + | 0.610581i | \(0.209064\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.2586 | − | 22.2586i | −0.760341 | − | 0.760341i | 0.216043 | − | 0.976384i | \(-0.430685\pi\) |
−0.976384 | + | 0.216043i | \(0.930685\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.8319 | 0.710777 | 0.355388 | − | 0.934719i | \(-0.384349\pi\) | ||||
0.355388 | + | 0.934719i | \(0.384349\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −16.0000 | + | 21.8836i | −0.545279 | + | 0.745793i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.620058 | − | 0.620058i | −0.0211070 | − | 0.0211070i | 0.696475 | − | 0.717582i | \(-0.254751\pi\) |
−0.717582 | + | 0.696475i | \(0.754751\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.41273 | − | 6.41273i | −0.217788 | − | 0.217788i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 22.5616i | − | 0.765348i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.59482i | 0.325108i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 20.7713 | − | 20.7713i | 0.703002 | − | 0.703002i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.00505 | + | 6.00505i | −0.202776 | + | 0.202776i | −0.801188 | − | 0.598412i | \(-0.795799\pi\) |
0.598412 | + | 0.801188i | \(0.295799\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.30019i | 0.178771i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 45.4096i | 1.52989i | 0.644097 | + | 0.764944i | \(0.277233\pi\) | ||||
−0.644097 | + | 0.764944i | \(0.722767\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.21342 | + | 8.21342i | 0.276404 | + | 0.276404i | 0.831672 | − | 0.555268i | \(-0.187384\pi\) |
−0.555268 | + | 0.831672i | \(0.687384\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.5487 | − | 10.5487i | −0.354190 | − | 0.354190i | 0.507476 | − | 0.861666i | \(-0.330579\pi\) |
−0.861666 | + | 0.507476i | \(0.830579\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.4160 | + | 7.61553i | 0.349340 | + | 0.255417i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.80776 | −0.161066 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.24517 | − | 7.24517i | −0.242450 | − | 0.242450i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 18.5589 | − | 18.5589i | 0.619663 | − | 0.619663i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 27.2716 | 0.909560 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 19.1896i | − | 0.639300i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.427034 | − | 2.74959i | −0.0142108 | − | 0.0915006i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.8307 | + | 18.8307i | −0.625264 | + | 0.625264i | −0.946873 | − | 0.321608i | \(-0.895777\pi\) |
0.321608 | + | 0.946873i | \(0.395777\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 28.3234 | 0.939426 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.2462 | −1.39968 | −0.699840 | − | 0.714300i | \(-0.746745\pi\) | ||||
−0.699840 | + | 0.714300i | \(0.746745\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14.5216 | + | 14.5216i | −0.480595 | + | 0.480595i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.74959 | − | 0.427034i | 0.0907994 | − | 0.0141019i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 18.0691i | − | 0.596046i | −0.954559 | − | 0.298023i | \(-0.903673\pi\) | ||
0.954559 | − | 0.298023i | \(-0.0963271\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.8229 | 0.521383 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 22.2586 | − | 22.2586i | 0.732652 | − | 0.732652i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.8934 | + | 14.8934i | 0.489165 | + | 0.489165i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −45.4096 | −1.48984 | −0.744920 | − | 0.667154i | \(-0.767512\pi\) | ||||
−0.744920 | + | 0.667154i | \(0.767512\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 56.9848 | − | 18.1379i | 1.86760 | − | 0.594447i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10.4218 | + | 10.4218i | 0.341194 | + | 0.341194i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.51713 | + | 6.51713i | 0.212905 | + | 0.212905i | 0.805501 | − | 0.592595i | \(-0.201897\pi\) |
−0.592595 | + | 0.805501i | \(0.701897\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 35.6847i | − | 1.16452i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.54312i | 0.278498i | 0.990257 | + | 0.139249i | \(0.0444688\pi\) | ||||
−0.990257 | + | 0.139249i | \(0.955531\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −43.0299 | + | 43.0299i | −1.40125 | + | 1.40125i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23.9439 | + | 23.9439i | −0.778071 | + | 0.778071i | −0.979503 | − | 0.201432i | \(-0.935441\pi\) |
0.201432 | + | 0.979503i | \(0.435441\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 14.7386i | − | 0.478436i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 41.6639i | − | 1.35104i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.76493 | + | 4.76493i | 0.154351 | + | 0.154351i | 0.780058 | − | 0.625707i | \(-0.215189\pi\) |
−0.625707 | + | 0.780058i | \(0.715189\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.3492 | − | 12.3492i | −0.399194 | − | 0.399194i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.79741 | + | 3.50758i | 0.154916 | + | 0.113266i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.98485 | 0.257576 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.2820 | + | 12.2820i | 0.395781 | + | 0.395781i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.14488 | − | 4.14488i | 0.133290 | − | 0.133290i | −0.637314 | − | 0.770604i | \(-0.719955\pi\) |
0.770604 | + | 0.637314i | \(0.219955\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 31.4785 | 1.01123 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.54312i | 0.274162i | 0.990560 | + | 0.137081i | \(0.0437720\pi\) | ||||
−0.990560 | + | 0.137081i | \(0.956228\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.52090 | + | 9.79280i | 0.0487579 | + | 0.313943i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.06854 | − | 4.06854i | 0.130164 | − | 0.130164i | −0.639023 | − | 0.769187i | \(-0.720661\pi\) |
0.769187 | + | 0.639023i | \(0.220661\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.2888 | 0.392752 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.1231 | −0.482844 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 30.3089 | − | 30.3089i | 0.966703 | − | 0.966703i | −0.0327601 | − | 0.999463i | \(-0.510430\pi\) |
0.999463 | + | 0.0327601i | \(0.0104297\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.584066 | − | 3.76069i | −0.0185910 | − | 0.119704i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 6.24621i | − | 0.198618i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.73863 | 0.214060 | 0.107030 | − | 0.994256i | \(-0.465866\pi\) | ||||
0.107030 | + | 0.994256i | \(0.465866\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 22.6762 | − | 22.6762i | 0.719609 | − | 0.719609i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.17238 | + | 2.17238i | 0.0687999 | + | 0.0687999i | 0.740669 | − | 0.671870i | \(-0.234508\pi\) |
−0.671870 | + | 0.740669i | \(0.734508\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 21.8836 | 0.692368 |
(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 | 1400.2.x.a.993.6 | yes | 16 | |
5.2 | odd | 4 | inner | 1400.2.x.a.657.4 | yes | 16 | |
5.3 | odd | 4 | inner | 1400.2.x.a.657.5 | yes | 16 | |
5.4 | even | 2 | inner | 1400.2.x.a.993.3 | yes | 16 | |
7.6 | odd | 2 | inner | 1400.2.x.a.993.4 | yes | 16 | |
35.13 | even | 4 | inner | 1400.2.x.a.657.3 | ✓ | 16 | |
35.27 | even | 4 | inner | 1400.2.x.a.657.6 | yes | 16 | |
35.34 | odd | 2 | inner | 1400.2.x.a.993.5 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1400.2.x.a.657.3 | ✓ | 16 | 35.13 | even | 4 | inner | |
1400.2.x.a.657.4 | yes | 16 | 5.2 | odd | 4 | inner | |
1400.2.x.a.657.5 | yes | 16 | 5.3 | odd | 4 | inner | |
1400.2.x.a.657.6 | yes | 16 | 35.27 | even | 4 | inner | |
1400.2.x.a.993.3 | yes | 16 | 5.4 | even | 2 | inner | |
1400.2.x.a.993.4 | yes | 16 | 7.6 | odd | 2 | inner | |
1400.2.x.a.993.5 | yes | 16 | 35.34 | odd | 2 | inner | |
1400.2.x.a.993.6 | yes | 16 | 1.1 | even | 1 | trivial |