Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [845,2,Mod(316,845)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(845, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("845.316");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 845 = 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 845.m (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.74735897080\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 65) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 316.4 | ||
Root | \(0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 845.316 |
Dual form | 845.2.m.f.361.4 |
$q$-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 \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).
\(n\) | \(171\) | \(677\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.09077 | + | 1.20711i | 1.47840 | + | 0.853553i | 0.999702 | − | 0.0244272i | \(-0.00777619\pi\) |
0.478696 | + | 0.877981i | \(0.341110\pi\) | |||||||
\(3\) | 0.707107 | − | 1.22474i | 0.408248 | − | 0.707107i | −0.586445 | − | 0.809989i | \(-0.699473\pi\) |
0.994694 | + | 0.102882i | \(0.0328064\pi\) | |||||||
\(4\) | 1.91421 | + | 3.31552i | 0.957107 | + | 1.65776i | ||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 2.95680 | − | 1.70711i | 1.20711 | − | 0.696923i | ||||
\(7\) | −4.18154 | + | 2.41421i | −1.58047 | + | 0.912487i | −0.585684 | + | 0.810539i | \(0.699174\pi\) |
−0.994790 | + | 0.101947i | \(0.967493\pi\) | |||||||
\(8\) | 4.41421i | 1.56066i | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | −1.20711 | + | 2.09077i | −0.381721 | + | 0.661160i | ||||
\(11\) | 2.95680 | + | 1.70711i | 0.891507 | + | 0.514712i | 0.874435 | − | 0.485142i | \(-0.161232\pi\) |
0.0170722 | + | 0.999854i | \(0.494565\pi\) | |||||||
\(12\) | 5.41421 | 1.56295 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −11.6569 | −3.11543 | ||||||||
\(15\) | 1.22474 | + | 0.707107i | 0.316228 | + | 0.182574i | ||||
\(16\) | −1.50000 | + | 2.59808i | −0.375000 | + | 0.649519i | ||||
\(17\) | 0.414214 | + | 0.717439i | 0.100462 | + | 0.174005i | 0.911875 | − | 0.410468i | \(-0.134635\pi\) |
−0.811413 | + | 0.584473i | \(0.801301\pi\) | |||||||
\(18\) | 2.41421i | 0.569036i | ||||||||
\(19\) | 0.507306 | − | 0.292893i | 0.116384 | − | 0.0671943i | −0.440678 | − | 0.897665i | \(-0.645262\pi\) |
0.557062 | + | 0.830471i | \(0.311929\pi\) | |||||||
\(20\) | −3.31552 | + | 1.91421i | −0.741372 | + | 0.428031i | ||||
\(21\) | 6.82843i | 1.49008i | ||||||||
\(22\) | 4.12132 | + | 7.13834i | 0.878668 | + | 1.52190i | ||||
\(23\) | 0.707107 | − | 1.22474i | 0.147442 | − | 0.255377i | −0.782839 | − | 0.622224i | \(-0.786229\pi\) |
0.930281 | + | 0.366847i | \(0.119563\pi\) | |||||||
\(24\) | 5.40629 | + | 3.12132i | 1.10355 | + | 0.637137i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.65685 | 1.08866 | ||||||||
\(28\) | −16.0087 | − | 9.24264i | −3.02536 | − | 1.74669i | ||||
\(29\) | 2.82843 | − | 4.89898i | 0.525226 | − | 0.909718i | −0.474343 | − | 0.880340i | \(-0.657314\pi\) |
0.999568 | − | 0.0293774i | \(-0.00935245\pi\) | |||||||
\(30\) | 1.70711 | + | 2.95680i | 0.311674 | + | 0.539835i | ||||
\(31\) | 1.75736i | 0.315631i | 0.987469 | + | 0.157816i | \(0.0504451\pi\) | ||||
−0.987469 | + | 0.157816i | \(0.949555\pi\) | |||||||
\(32\) | 1.37333 | − | 0.792893i | 0.242773 | − | 0.140165i | ||||
\(33\) | 4.18154 | − | 2.41421i | 0.727913 | − | 0.420261i | ||||
\(34\) | 2.00000i | 0.342997i | ||||||||
\(35\) | −2.41421 | − | 4.18154i | −0.408077 | − | 0.706809i | ||||
\(36\) | −1.91421 | + | 3.31552i | −0.319036 | + | 0.552586i | ||||
\(37\) | −7.34847 | − | 4.24264i | −1.20808 | − | 0.697486i | −0.245741 | − | 0.969335i | \(-0.579031\pi\) |
−0.962340 | + | 0.271850i | \(0.912365\pi\) | |||||||
\(38\) | 1.41421 | 0.229416 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.41421 | −0.697948 | ||||||||
\(41\) | 2.74666 | + | 1.58579i | 0.428957 | + | 0.247658i | 0.698902 | − | 0.715217i | \(-0.253672\pi\) |
−0.269945 | + | 0.962876i | \(0.587006\pi\) | |||||||
\(42\) | −8.24264 | + | 14.2767i | −1.27187 | + | 2.20294i | ||||
\(43\) | −5.53553 | − | 9.58783i | −0.844161 | − | 1.46213i | −0.886348 | − | 0.463020i | \(-0.846766\pi\) |
0.0421868 | − | 0.999110i | \(-0.486568\pi\) | |||||||
\(44\) | 13.0711i | 1.97054i | ||||||||
\(45\) | −0.866025 | + | 0.500000i | −0.129099 | + | 0.0745356i | ||||
\(46\) | 2.95680 | − | 1.70711i | 0.435956 | − | 0.251699i | ||||
\(47\) | 4.82843i | 0.704298i | 0.935944 | + | 0.352149i | \(0.114549\pi\) | ||||
−0.935944 | + | 0.352149i | \(0.885451\pi\) | |||||||
\(48\) | 2.12132 | + | 3.67423i | 0.306186 | + | 0.530330i | ||||
\(49\) | 8.15685 | − | 14.1281i | 1.16526 | − | 2.01830i | ||||
\(50\) | −2.09077 | − | 1.20711i | −0.295680 | − | 0.170711i | ||||
\(51\) | 1.17157 | 0.164053 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.48528 | 0.341380 | 0.170690 | − | 0.985325i | \(-0.445400\pi\) | ||||
0.170690 | + | 0.985325i | \(0.445400\pi\) | |||||||
\(54\) | 11.8272 | + | 6.82843i | 1.60948 | + | 0.929231i | ||||
\(55\) | −1.70711 | + | 2.95680i | −0.230186 | + | 0.398694i | ||||
\(56\) | −10.6569 | − | 18.4582i | −1.42408 | − | 2.46658i | ||||
\(57\) | − | 0.828427i | − | 0.109728i | ||||||
\(58\) | 11.8272 | − | 6.82843i | 1.55299 | − | 0.896616i | ||||
\(59\) | −1.52192 | + | 0.878680i | −0.198137 | + | 0.114394i | −0.595786 | − | 0.803143i | \(-0.703159\pi\) |
0.397649 | + | 0.917537i | \(0.369826\pi\) | |||||||
\(60\) | 5.41421i | 0.698972i | ||||||||
\(61\) | 4.00000 | + | 6.92820i | 0.512148 | + | 0.887066i | 0.999901 | + | 0.0140840i | \(0.00448323\pi\) |
−0.487753 | + | 0.872982i | \(0.662183\pi\) | |||||||
\(62\) | −2.12132 | + | 3.67423i | −0.269408 | + | 0.466628i | ||||
\(63\) | −4.18154 | − | 2.41421i | −0.526825 | − | 0.304162i | ||||
\(64\) | 9.82843 | 1.22855 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 11.6569 | 1.43486 | ||||||||
\(67\) | 1.73205 | + | 1.00000i | 0.211604 | + | 0.122169i | 0.602056 | − | 0.798454i | \(-0.294348\pi\) |
−0.390453 | + | 0.920623i | \(0.627682\pi\) | |||||||
\(68\) | −1.58579 | + | 2.74666i | −0.192305 | + | 0.333082i | ||||
\(69\) | −1.00000 | − | 1.73205i | −0.120386 | − | 0.208514i | ||||
\(70\) | − | 11.6569i | − | 1.39326i | ||||||
\(71\) | 10.3053 | − | 5.94975i | 1.22301 | − | 0.706105i | 0.257451 | − | 0.966291i | \(-0.417117\pi\) |
0.965558 | + | 0.260186i | \(0.0837839\pi\) | |||||||
\(72\) | −3.82282 | + | 2.20711i | −0.450524 | + | 0.260110i | ||||
\(73\) | − | 8.48528i | − | 0.993127i | −0.868000 | − | 0.496564i | \(-0.834595\pi\) | ||
0.868000 | − | 0.496564i | \(-0.165405\pi\) | |||||||
\(74\) | −10.2426 | − | 17.7408i | −1.19068 | − | 2.06232i | ||||
\(75\) | −0.707107 | + | 1.22474i | −0.0816497 | + | 0.141421i | ||||
\(76\) | 1.94218 | + | 1.12132i | 0.222784 | + | 0.128624i | ||||
\(77\) | −16.4853 | −1.87867 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.48528 | −0.954669 | −0.477334 | − | 0.878722i | \(-0.658397\pi\) | ||||
−0.477334 | + | 0.878722i | \(0.658397\pi\) | |||||||
\(80\) | −2.59808 | − | 1.50000i | −0.290474 | − | 0.167705i | ||||
\(81\) | 2.50000 | − | 4.33013i | 0.277778 | − | 0.481125i | ||||
\(82\) | 3.82843 | + | 6.63103i | 0.422779 | + | 0.732275i | ||||
\(83\) | − | 3.17157i | − | 0.348125i | −0.984735 | − | 0.174063i | \(-0.944310\pi\) | ||
0.984735 | − | 0.174063i | \(-0.0556895\pi\) | |||||||
\(84\) | −22.6398 | + | 13.0711i | −2.47020 | + | 1.42617i | ||||
\(85\) | −0.717439 | + | 0.414214i | −0.0778172 | + | 0.0449278i | ||||
\(86\) | − | 26.7279i | − | 2.88215i | ||||||
\(87\) | −4.00000 | − | 6.92820i | −0.428845 | − | 0.742781i | ||||
\(88\) | −7.53553 | + | 13.0519i | −0.803291 | + | 1.39134i | ||||
\(89\) | 5.19615 | + | 3.00000i | 0.550791 | + | 0.317999i | 0.749441 | − | 0.662071i | \(-0.230322\pi\) |
−0.198650 | + | 0.980071i | \(0.563656\pi\) | |||||||
\(90\) | −2.41421 | −0.254480 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.41421 | 0.564471 | ||||||||
\(93\) | 2.15232 | + | 1.24264i | 0.223185 | + | 0.128856i | ||||
\(94\) | −5.82843 | + | 10.0951i | −0.601156 | + | 1.04123i | ||||
\(95\) | 0.292893 | + | 0.507306i | 0.0300502 | + | 0.0520485i | ||||
\(96\) | − | 2.24264i | − | 0.228889i | ||||||
\(97\) | −6.63103 | + | 3.82843i | −0.673279 | + | 0.388718i | −0.797318 | − | 0.603559i | \(-0.793749\pi\) |
0.124039 | + | 0.992277i | \(0.460415\pi\) | |||||||
\(98\) | 34.1082 | − | 19.6924i | 3.44545 | − | 1.98923i | ||||
\(99\) | 3.41421i | 0.343141i | ||||||||
\(100\) | −1.91421 | − | 3.31552i | −0.191421 | − | 0.331552i | ||||
\(101\) | −1.82843 | + | 3.16693i | −0.181935 | + | 0.315121i | −0.942540 | − | 0.334095i | \(-0.891569\pi\) |
0.760604 | + | 0.649216i | \(0.224903\pi\) | |||||||
\(102\) | 2.44949 | + | 1.41421i | 0.242536 | + | 0.140028i | ||||
\(103\) | −14.5858 | −1.43718 | −0.718590 | − | 0.695434i | \(-0.755212\pi\) | ||||
−0.718590 | + | 0.695434i | \(0.755212\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.82843 | −0.666386 | ||||||||
\(106\) | 5.19615 | + | 3.00000i | 0.504695 | + | 0.291386i | ||||
\(107\) | 4.70711 | − | 8.15295i | 0.455053 | − | 0.788175i | −0.543638 | − | 0.839320i | \(-0.682954\pi\) |
0.998691 | + | 0.0511445i | \(0.0162869\pi\) | |||||||
\(108\) | 10.8284 | + | 18.7554i | 1.04197 | + | 1.80474i | ||||
\(109\) | − | 2.00000i | − | 0.191565i | −0.995402 | − | 0.0957826i | \(-0.969465\pi\) | ||
0.995402 | − | 0.0957826i | \(-0.0305354\pi\) | |||||||
\(110\) | −7.13834 | + | 4.12132i | −0.680614 | + | 0.392952i | ||||
\(111\) | −10.3923 | + | 6.00000i | −0.986394 | + | 0.569495i | ||||
\(112\) | − | 14.4853i | − | 1.36873i | ||||||
\(113\) | 4.41421 | + | 7.64564i | 0.415254 | + | 0.719242i | 0.995455 | − | 0.0952319i | \(-0.0303593\pi\) |
−0.580201 | + | 0.814473i | \(0.697026\pi\) | |||||||
\(114\) | 1.00000 | − | 1.73205i | 0.0936586 | − | 0.162221i | ||||
\(115\) | 1.22474 | + | 0.707107i | 0.114208 | + | 0.0659380i | ||||
\(116\) | 21.6569 | 2.01079 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.24264 | −0.390567 | ||||||||
\(119\) | −3.46410 | − | 2.00000i | −0.317554 | − | 0.183340i | ||||
\(120\) | −3.12132 | + | 5.40629i | −0.284936 | + | 0.493524i | ||||
\(121\) | 0.328427 | + | 0.568852i | 0.0298570 | + | 0.0517139i | ||||
\(122\) | 19.3137i | 1.74858i | ||||||||
\(123\) | 3.88437 | − | 2.24264i | 0.350242 | − | 0.202212i | ||||
\(124\) | −5.82655 | + | 3.36396i | −0.523240 | + | 0.302093i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | −5.82843 | − | 10.0951i | −0.519238 | − | 0.899346i | ||||
\(127\) | −3.29289 | + | 5.70346i | −0.292197 | + | 0.506100i | −0.974329 | − | 0.225129i | \(-0.927720\pi\) |
0.682132 | + | 0.731229i | \(0.261053\pi\) | |||||||
\(128\) | 17.8023 | + | 10.2782i | 1.57352 | + | 0.908471i | ||||
\(129\) | −15.6569 | −1.37851 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.9706 | −1.48272 | −0.741362 | − | 0.671105i | \(-0.765820\pi\) | ||||
−0.741362 | + | 0.671105i | \(0.765820\pi\) | |||||||
\(132\) | 16.0087 | + | 9.24264i | 1.39338 | + | 0.804469i | ||||
\(133\) | −1.41421 | + | 2.44949i | −0.122628 | + | 0.212398i | ||||
\(134\) | 2.41421 | + | 4.18154i | 0.208556 | + | 0.361230i | ||||
\(135\) | 5.65685i | 0.486864i | ||||||||
\(136\) | −3.16693 | + | 1.82843i | −0.271562 | + | 0.156786i | ||||
\(137\) | 14.9941 | − | 8.65685i | 1.28103 | − | 0.739605i | 0.303996 | − | 0.952673i | \(-0.401679\pi\) |
0.977037 | + | 0.213068i | \(0.0683457\pi\) | |||||||
\(138\) | − | 4.82843i | − | 0.411023i | ||||||
\(139\) | −2.24264 | − | 3.88437i | −0.190218 | − | 0.329468i | 0.755104 | − | 0.655605i | \(-0.227586\pi\) |
−0.945323 | + | 0.326137i | \(0.894253\pi\) | |||||||
\(140\) | 9.24264 | − | 16.0087i | 0.781146 | − | 1.35298i | ||||
\(141\) | 5.91359 | + | 3.41421i | 0.498014 | + | 0.287529i | ||||
\(142\) | 28.7279 | 2.41079 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −3.00000 | −0.250000 | ||||||||
\(145\) | 4.89898 | + | 2.82843i | 0.406838 | + | 0.234888i | ||||
\(146\) | 10.2426 | − | 17.7408i | 0.847687 | − | 1.46824i | ||||
\(147\) | −11.5355 | − | 19.9801i | −0.951435 | − | 1.64793i | ||||
\(148\) | − | 32.4853i | − | 2.67027i | ||||||
\(149\) | −10.0951 | + | 5.82843i | −0.827025 | + | 0.477483i | −0.852833 | − | 0.522184i | \(-0.825118\pi\) |
0.0258077 | + | 0.999667i | \(0.491784\pi\) | |||||||
\(150\) | −2.95680 | + | 1.70711i | −0.241421 | + | 0.139385i | ||||
\(151\) | − | 9.75736i | − | 0.794043i | −0.917809 | − | 0.397021i | \(-0.870044\pi\) | ||
0.917809 | − | 0.397021i | \(-0.129956\pi\) | |||||||
\(152\) | 1.29289 | + | 2.23936i | 0.104867 | + | 0.181636i | ||||
\(153\) | −0.414214 | + | 0.717439i | −0.0334872 | + | 0.0580015i | ||||
\(154\) | −34.4669 | − | 19.8995i | −2.77742 | − | 1.60355i | ||||
\(155\) | −1.75736 | −0.141154 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.0000 | 1.43656 | 0.718278 | − | 0.695756i | \(-0.244931\pi\) | ||||
0.718278 | + | 0.695756i | \(0.244931\pi\) | |||||||
\(158\) | −17.7408 | − | 10.2426i | −1.41138 | − | 0.814861i | ||||
\(159\) | 1.75736 | − | 3.04384i | 0.139368 | − | 0.241392i | ||||
\(160\) | 0.792893 | + | 1.37333i | 0.0626837 | + | 0.108571i | ||||
\(161\) | 6.82843i | 0.538155i | ||||||||
\(162\) | 10.4539 | − | 6.03553i | 0.821332 | − | 0.474196i | ||||
\(163\) | −16.4290 | + | 9.48528i | −1.28682 | + | 0.742945i | −0.978085 | − | 0.208204i | \(-0.933238\pi\) |
−0.308732 | + | 0.951149i | \(0.599905\pi\) | |||||||
\(164\) | 12.1421i | 0.948141i | ||||||||
\(165\) | 2.41421 | + | 4.18154i | 0.187946 | + | 0.325532i | ||||
\(166\) | 3.82843 | − | 6.63103i | 0.297144 | − | 0.514668i | ||||
\(167\) | −2.74666 | − | 1.58579i | −0.212543 | − | 0.122712i | 0.389950 | − | 0.920836i | \(-0.372492\pi\) |
−0.602493 | + | 0.798124i | \(0.705826\pi\) | |||||||
\(168\) | −30.1421 | −2.32552 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −2.00000 | −0.153393 | ||||||||
\(171\) | 0.507306 | + | 0.292893i | 0.0387947 | + | 0.0223981i | ||||
\(172\) | 21.1924 | − | 36.7063i | 1.61590 | − | 2.79883i | ||||
\(173\) | 8.41421 | + | 14.5738i | 0.639721 | + | 1.10803i | 0.985494 | + | 0.169711i | \(0.0542834\pi\) |
−0.345773 | + | 0.938318i | \(0.612383\pi\) | |||||||
\(174\) | − | 19.3137i | − | 1.46417i | ||||||
\(175\) | 4.18154 | − | 2.41421i | 0.316095 | − | 0.182497i | ||||
\(176\) | −8.87039 | + | 5.12132i | −0.668631 | + | 0.386034i | ||||
\(177\) | 2.48528i | 0.186805i | ||||||||
\(178\) | 7.24264 | + | 12.5446i | 0.542859 | + | 0.940259i | ||||
\(179\) | 2.82843 | − | 4.89898i | 0.211407 | − | 0.366167i | −0.740748 | − | 0.671783i | \(-0.765529\pi\) |
0.952155 | + | 0.305616i | \(0.0988623\pi\) | |||||||
\(180\) | −3.31552 | − | 1.91421i | −0.247124 | − | 0.142677i | ||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.3137 | 0.836333 | ||||||||
\(184\) | 5.40629 | + | 3.12132i | 0.398557 | + | 0.230107i | ||||
\(185\) | 4.24264 | − | 7.34847i | 0.311925 | − | 0.540270i | ||||
\(186\) | 3.00000 | + | 5.19615i | 0.219971 | + | 0.381000i | ||||
\(187\) | 2.82843i | 0.206835i | ||||||||
\(188\) | −16.0087 | + | 9.24264i | −1.16756 | + | 0.674089i | ||||
\(189\) | −23.6544 | + | 13.6569i | −1.72060 | + | 0.993390i | ||||
\(190\) | 1.41421i | 0.102598i | ||||||||
\(191\) | −1.17157 | − | 2.02922i | −0.0847720 | − | 0.146829i | 0.820522 | − | 0.571615i | \(-0.193683\pi\) |
−0.905294 | + | 0.424785i | \(0.860350\pi\) | |||||||
\(192\) | 6.94975 | − | 12.0373i | 0.501555 | − | 0.868718i | ||||
\(193\) | 3.76127 | + | 2.17157i | 0.270742 | + | 0.156313i | 0.629225 | − | 0.777223i | \(-0.283372\pi\) |
−0.358483 | + | 0.933536i | \(0.616706\pi\) | |||||||
\(194\) | −18.4853 | −1.32717 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 62.4558 | 4.46113 | ||||||||
\(197\) | −9.50079 | − | 5.48528i | −0.676903 | − | 0.390810i | 0.121784 | − | 0.992557i | \(-0.461138\pi\) |
−0.798687 | + | 0.601746i | \(0.794472\pi\) | |||||||
\(198\) | −4.12132 | + | 7.13834i | −0.292889 | + | 0.507299i | ||||
\(199\) | 2.00000 | + | 3.46410i | 0.141776 | + | 0.245564i | 0.928166 | − | 0.372168i | \(-0.121385\pi\) |
−0.786389 | + | 0.617731i | \(0.788052\pi\) | |||||||
\(200\) | − | 4.41421i | − | 0.312132i | ||||||
\(201\) | 2.44949 | − | 1.41421i | 0.172774 | − | 0.0997509i | ||||
\(202\) | −7.64564 | + | 4.41421i | −0.537946 | + | 0.310583i | ||||
\(203\) | 27.3137i | 1.91705i | ||||||||
\(204\) | 2.24264 | + | 3.88437i | 0.157016 | + | 0.271960i | ||||
\(205\) | −1.58579 | + | 2.74666i | −0.110756 | + | 0.191835i | ||||
\(206\) | −30.4955 | − | 17.6066i | −2.12472 | − | 1.22671i | ||||
\(207\) | 1.41421 | 0.0982946 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.00000 | 0.138343 | ||||||||
\(210\) | −14.2767 | − | 8.24264i | −0.985184 | − | 0.568796i | ||||
\(211\) | −1.65685 | + | 2.86976i | −0.114063 | + | 0.197562i | −0.917405 | − | 0.397956i | \(-0.869720\pi\) |
0.803342 | + | 0.595518i | \(0.203053\pi\) | |||||||
\(212\) | 4.75736 | + | 8.23999i | 0.326737 | + | 0.565925i | ||||
\(213\) | − | 16.8284i | − | 1.15306i | ||||||
\(214\) | 19.6830 | − | 11.3640i | 1.34550 | − | 0.776824i | ||||
\(215\) | 9.58783 | − | 5.53553i | 0.653884 | − | 0.377520i | ||||
\(216\) | 24.9706i | 1.69903i | ||||||||
\(217\) | −4.24264 | − | 7.34847i | −0.288009 | − | 0.498847i | ||||
\(218\) | 2.41421 | − | 4.18154i | 0.163511 | − | 0.283210i | ||||
\(219\) | −10.3923 | − | 6.00000i | −0.702247 | − | 0.405442i | ||||
\(220\) | −13.0711 | −0.881251 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −28.9706 | −1.94438 | ||||||||
\(223\) | −8.23999 | − | 4.75736i | −0.551790 | − | 0.318576i | 0.198053 | − | 0.980191i | \(-0.436538\pi\) |
−0.749844 | + | 0.661615i | \(0.769871\pi\) | |||||||
\(224\) | −3.82843 | + | 6.63103i | −0.255798 | + | 0.443054i | ||||
\(225\) | −0.500000 | − | 0.866025i | −0.0333333 | − | 0.0577350i | ||||
\(226\) | 21.3137i | 1.41777i | ||||||||
\(227\) | −14.1536 | + | 8.17157i | −0.939406 | + | 0.542366i | −0.889774 | − | 0.456401i | \(-0.849138\pi\) |
−0.0496320 | + | 0.998768i | \(0.515805\pi\) | |||||||
\(228\) | 2.74666 | − | 1.58579i | 0.181902 | − | 0.105021i | ||||
\(229\) | 4.82843i | 0.319071i | 0.987192 | + | 0.159536i | \(0.0509997\pi\) | ||||
−0.987192 | + | 0.159536i | \(0.949000\pi\) | |||||||
\(230\) | 1.70711 | + | 2.95680i | 0.112563 | + | 0.194965i | ||||
\(231\) | −11.6569 | + | 20.1903i | −0.766965 | + | 1.32842i | ||||
\(232\) | 21.6251 | + | 12.4853i | 1.41976 | + | 0.819699i | ||||
\(233\) | 20.6274 | 1.35135 | 0.675674 | − | 0.737201i | \(-0.263853\pi\) | ||||
0.675674 | + | 0.737201i | \(0.263853\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.82843 | −0.314972 | ||||||||
\(236\) | −5.82655 | − | 3.36396i | −0.379276 | − | 0.218975i | ||||
\(237\) | −6.00000 | + | 10.3923i | −0.389742 | + | 0.675053i | ||||
\(238\) | −4.82843 | − | 8.36308i | −0.312980 | − | 0.542098i | ||||
\(239\) | − | 3.41421i | − | 0.220847i | −0.993885 | − | 0.110424i | \(-0.964779\pi\) | ||
0.993885 | − | 0.110424i | \(-0.0352207\pi\) | |||||||
\(240\) | −3.67423 | + | 2.12132i | −0.237171 | + | 0.136931i | ||||
\(241\) | 12.5446 | − | 7.24264i | 0.808070 | − | 0.466539i | −0.0382151 | − | 0.999270i | \(-0.512167\pi\) |
0.846285 | + | 0.532730i | \(0.178834\pi\) | |||||||
\(242\) | 1.58579i | 0.101938i | ||||||||
\(243\) | 4.94975 | + | 8.57321i | 0.317526 | + | 0.549972i | ||||
\(244\) | −15.3137 | + | 26.5241i | −0.980360 | + | 1.69803i | ||||
\(245\) | 14.1281 | + | 8.15685i | 0.902610 | + | 0.521122i | ||||
\(246\) | 10.8284 | 0.690395 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −7.75736 | −0.492593 | ||||||||
\(249\) | −3.88437 | − | 2.24264i | −0.246162 | − | 0.142122i | ||||
\(250\) | 1.20711 | − | 2.09077i | 0.0763441 | − | 0.132232i | ||||
\(251\) | 9.89949 | + | 17.1464i | 0.624851 | + | 1.08227i | 0.988570 | + | 0.150764i | \(0.0481735\pi\) |
−0.363719 | + | 0.931509i | \(0.618493\pi\) | |||||||
\(252\) | − | 18.4853i | − | 1.16446i | ||||||
\(253\) | 4.18154 | − | 2.41421i | 0.262891 | − | 0.151780i | ||||
\(254\) | −13.7694 | + | 7.94975i | −0.863967 | + | 0.498812i | ||||
\(255\) | 1.17157i | 0.0733667i | ||||||||
\(256\) | 14.9853 | + | 25.9553i | 0.936580 | + | 1.62220i | ||||
\(257\) | 13.8284 | − | 23.9515i | 0.862594 | − | 1.49406i | −0.00682332 | − | 0.999977i | \(-0.502172\pi\) |
0.869417 | − | 0.494079i | \(-0.164495\pi\) | |||||||
\(258\) | −32.7349 | − | 18.8995i | −2.03798 | − | 1.17663i | ||||
\(259\) | 40.9706 | 2.54579 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.65685 | 0.350150 | ||||||||
\(262\) | −35.4815 | − | 20.4853i | −2.19206 | − | 1.26558i | ||||
\(263\) | 5.29289 | − | 9.16756i | 0.326374 | − | 0.565296i | −0.655416 | − | 0.755268i | \(-0.727507\pi\) |
0.981789 | + | 0.189972i | \(0.0608399\pi\) | |||||||
\(264\) | 10.6569 | + | 18.4582i | 0.655884 | + | 1.13602i | ||||
\(265\) | 2.48528i | 0.152670i | ||||||||
\(266\) | −5.91359 | + | 3.41421i | −0.362586 | + | 0.209339i | ||||
\(267\) | 7.34847 | − | 4.24264i | 0.449719 | − | 0.259645i | ||||
\(268\) | 7.65685i | 0.467717i | ||||||||
\(269\) | 12.6569 | + | 21.9223i | 0.771702 | + | 1.33663i | 0.936630 | + | 0.350321i | \(0.113928\pi\) |
−0.164928 | + | 0.986306i | \(0.552739\pi\) | |||||||
\(270\) | −6.82843 | + | 11.8272i | −0.415565 | + | 0.719779i | ||||
\(271\) | 23.1471 | + | 13.3640i | 1.40608 | + | 0.811803i | 0.995008 | − | 0.0997982i | \(-0.0318197\pi\) |
0.411076 | + | 0.911601i | \(0.365153\pi\) | |||||||
\(272\) | −2.48528 | −0.150692 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 41.7990 | 2.52517 | ||||||||
\(275\) | −2.95680 | − | 1.70711i | −0.178301 | − | 0.102942i | ||||
\(276\) | 3.82843 | − | 6.63103i | 0.230444 | − | 0.399141i | ||||
\(277\) | −6.41421 | − | 11.1097i | −0.385393 | − | 0.667520i | 0.606431 | − | 0.795136i | \(-0.292601\pi\) |
−0.991824 | + | 0.127616i | \(0.959267\pi\) | |||||||
\(278\) | − | 10.8284i | − | 0.649446i | ||||||
\(279\) | −1.52192 | + | 0.878680i | −0.0911148 | + | 0.0526052i | ||||
\(280\) | 18.4582 | − | 10.6569i | 1.10309 | − | 0.636869i | ||||
\(281\) | − | 21.7990i | − | 1.30042i | −0.759755 | − | 0.650209i | \(-0.774681\pi\) | ||
0.759755 | − | 0.650209i | \(-0.225319\pi\) | |||||||
\(282\) | 8.24264 | + | 14.2767i | 0.490842 | + | 0.850163i | ||||
\(283\) | −8.36396 | + | 14.4868i | −0.497186 | + | 0.861151i | −0.999995 | − | 0.00324643i | \(-0.998967\pi\) |
0.502809 | + | 0.864398i | \(0.332300\pi\) | |||||||
\(284\) | 39.4530 | + | 22.7782i | 2.34110 | + | 1.35164i | ||||
\(285\) | 0.828427 | 0.0490718 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −15.3137 | −0.903940 | ||||||||
\(288\) | 1.37333 | + | 0.792893i | 0.0809243 | + | 0.0467217i | ||||
\(289\) | 8.15685 | − | 14.1281i | 0.479815 | − | 0.831064i | ||||
\(290\) | 6.82843 | + | 11.8272i | 0.400979 | + | 0.694516i | ||||
\(291\) | 10.8284i | 0.634774i | ||||||||
\(292\) | 28.1331 | − | 16.2426i | 1.64636 | − | 0.950529i | ||||
\(293\) | −22.6398 | + | 13.0711i | −1.32263 | + | 0.763620i | −0.984147 | − | 0.177353i | \(-0.943247\pi\) |
−0.338481 | + | 0.940973i | \(0.609913\pi\) | |||||||
\(294\) | − | 55.6985i | − | 3.24840i | ||||||
\(295\) | −0.878680 | − | 1.52192i | −0.0511587 | − | 0.0886095i | ||||
\(296\) | 18.7279 | − | 32.4377i | 1.08854 | − | 1.88540i | ||||
\(297\) | 16.7262 | + | 9.65685i | 0.970550 | + | 0.560348i | ||||
\(298\) | −28.1421 | −1.63023 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −5.41421 | −0.312590 | ||||||||
\(301\) | 46.2941 | + | 26.7279i | 2.66835 | + | 1.54057i | ||||
\(302\) | 11.7782 | − | 20.4004i | 0.677758 | − | 1.17391i | ||||
\(303\) | 2.58579 | + | 4.47871i | 0.148550 | + | 0.257295i | ||||
\(304\) | 1.75736i | 0.100791i | ||||||||
\(305\) | −6.92820 | + | 4.00000i | −0.396708 | + | 0.229039i | ||||
\(306\) | −1.73205 | + | 1.00000i | −0.0990148 | + | 0.0571662i | ||||
\(307\) | − | 24.8284i | − | 1.41703i | −0.705694 | − | 0.708517i | \(-0.749365\pi\) | ||
0.705694 | − | 0.708517i | \(-0.250635\pi\) | |||||||
\(308\) | −31.5563 | − | 54.6572i | −1.79809 | − | 3.11438i | ||||
\(309\) | −10.3137 | + | 17.8639i | −0.586726 | + | 1.01624i | ||||
\(310\) | −3.67423 | − | 2.12132i | −0.208683 | − | 0.120483i | ||||
\(311\) | −8.48528 | −0.481156 | −0.240578 | − | 0.970630i | \(-0.577337\pi\) | ||||
−0.240578 | + | 0.970630i | \(0.577337\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.82843 | −0.272919 | −0.136459 | − | 0.990646i | \(-0.543572\pi\) | ||||
−0.136459 | + | 0.990646i | \(0.543572\pi\) | |||||||
\(314\) | 37.6339 | + | 21.7279i | 2.12380 | + | 1.22618i | ||||
\(315\) | 2.41421 | − | 4.18154i | 0.136026 | − | 0.235603i | ||||
\(316\) | −16.2426 | − | 28.1331i | −0.913720 | − | 1.58261i | ||||
\(317\) | − | 2.14214i | − | 0.120314i | −0.998189 | − | 0.0601572i | \(-0.980840\pi\) | ||
0.998189 | − | 0.0601572i | \(-0.0191602\pi\) | |||||||
\(318\) | 7.34847 | − | 4.24264i | 0.412082 | − | 0.237915i | ||||
\(319\) | 16.7262 | − | 9.65685i | 0.936485 | − | 0.540680i | ||||
\(320\) | 9.82843i | 0.549426i | ||||||||
\(321\) | −6.65685 | − | 11.5300i | −0.371549 | − | 0.643542i | ||||
\(322\) | −8.24264 | + | 14.2767i | −0.459344 | + | 0.795608i | ||||
\(323\) | 0.420266 | + | 0.242641i | 0.0233842 | + | 0.0135009i | ||||
\(324\) | 19.1421 | 1.06345 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −45.7990 | −2.53657 | ||||||||
\(327\) | −2.44949 | − | 1.41421i | −0.135457 | − | 0.0782062i | ||||
\(328\) | −7.00000 | + | 12.1244i | −0.386510 | + | 0.669456i | ||||
\(329\) | −11.6569 | − | 20.1903i | −0.642663 | − | 1.11313i | ||||
\(330\) | 11.6569i | 0.641689i | ||||||||
\(331\) | −22.5527 | + | 13.0208i | −1.23961 | + | 0.715689i | −0.969014 | − | 0.247005i | \(-0.920554\pi\) |
−0.270595 | + | 0.962693i | \(0.587220\pi\) | |||||||
\(332\) | 10.5154 | − | 6.07107i | 0.577107 | − | 0.333193i | ||||
\(333\) | − | 8.48528i | − | 0.464991i | ||||||
\(334\) | −3.82843 | − | 6.63103i | −0.209482 | − | 0.362834i | ||||
\(335\) | −1.00000 | + | 1.73205i | −0.0546358 | + | 0.0946320i | ||||
\(336\) | −17.7408 | − | 10.2426i | −0.967839 | − | 0.558782i | ||||
\(337\) | −12.8284 | −0.698809 | −0.349404 | − | 0.936972i | \(-0.613616\pi\) | ||||
−0.349404 | + | 0.936972i | \(0.613616\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.4853 | 0.678107 | ||||||||
\(340\) | −2.74666 | − | 1.58579i | −0.148959 | − | 0.0860013i | ||||
\(341\) | −3.00000 | + | 5.19615i | −0.162459 | + | 0.281387i | ||||
\(342\) | 0.707107 | + | 1.22474i | 0.0382360 | + | 0.0662266i | ||||
\(343\) | 44.9706i | 2.42818i | ||||||||
\(344\) | 42.3227 | − | 24.4350i | 2.28189 | − | 1.31745i | ||||
\(345\) | 1.73205 | − | 1.00000i | 0.0932505 | − | 0.0538382i | ||||
\(346\) | 40.6274i | 2.18414i | ||||||||
\(347\) | 2.12132 | + | 3.67423i | 0.113878 | + | 0.197243i | 0.917331 | − | 0.398126i | \(-0.130339\pi\) |
−0.803452 | + | 0.595369i | \(0.797006\pi\) | |||||||
\(348\) | 15.3137 | − | 26.5241i | 0.820901 | − | 1.42184i | ||||
\(349\) | 16.0087 | + | 9.24264i | 0.856927 | + | 0.494747i | 0.862982 | − | 0.505234i | \(-0.168594\pi\) |
−0.00605481 | + | 0.999982i | \(0.501927\pi\) | |||||||
\(350\) | 11.6569 | 0.623085 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.41421 | 0.288579 | ||||||||
\(353\) | −12.8418 | − | 7.41421i | −0.683500 | − | 0.394619i | 0.117673 | − | 0.993052i | \(-0.462457\pi\) |
−0.801172 | + | 0.598434i | \(0.795790\pi\) | |||||||
\(354\) | −3.00000 | + | 5.19615i | −0.159448 | + | 0.276172i | ||||
\(355\) | 5.94975 | + | 10.3053i | 0.315780 | + | 0.546947i | ||||
\(356\) | 22.9706i | 1.21744i | ||||||||
\(357\) | −4.89898 | + | 2.82843i | −0.259281 | + | 0.149696i | ||||
\(358\) | 11.8272 | − | 6.82843i | 0.625086 | − | 0.360894i | ||||
\(359\) | 8.10051i | 0.427528i | 0.976885 | + | 0.213764i | \(0.0685724\pi\) | ||||
−0.976885 | + | 0.213764i | \(0.931428\pi\) | |||||||
\(360\) | −2.20711 | − | 3.82282i | −0.116325 | − | 0.201480i | ||||
\(361\) | −9.32843 | + | 16.1573i | −0.490970 | + | 0.850385i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.928932 | 0.0487563 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.48528 | 0.444140 | ||||||||
\(366\) | 23.6544 | + | 13.6569i | 1.23643 | + | 0.713855i | ||||
\(367\) | −17.7782 | + | 30.7927i | −0.928013 | + | 1.60737i | −0.141371 | + | 0.989957i | \(0.545151\pi\) |
−0.786642 | + | 0.617409i | \(0.788182\pi\) | |||||||
\(368\) | 2.12132 | + | 3.67423i | 0.110581 | + | 0.191533i | ||||
\(369\) | 3.17157i | 0.165105i | ||||||||
\(370\) | 17.7408 | − | 10.2426i | 0.922299 | − | 0.532490i | ||||
\(371\) | −10.3923 | + | 6.00000i | −0.539542 | + | 0.311504i | ||||
\(372\) | 9.51472i | 0.493315i | ||||||||
\(373\) | 1.34315 | + | 2.32640i | 0.0695455 | + | 0.120456i | 0.898701 | − | 0.438561i | \(-0.144512\pi\) |
−0.829156 | + | 0.559018i | \(0.811178\pi\) | |||||||
\(374\) | −3.41421 | + | 5.91359i | −0.176545 | + | 0.305785i | ||||
\(375\) | −1.22474 | − | 0.707107i | −0.0632456 | − | 0.0365148i | ||||
\(376\) | −21.3137 | −1.09917 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −65.9411 | −3.39165 | ||||||||
\(379\) | −25.1763 | − | 14.5355i | −1.29322 | − | 0.746640i | −0.313995 | − | 0.949425i | \(-0.601668\pi\) |
−0.979223 | + | 0.202784i | \(0.935001\pi\) | |||||||
\(380\) | −1.12132 | + | 1.94218i | −0.0575225 | + | 0.0996319i | ||||
\(381\) | 4.65685 | + | 8.06591i | 0.238578 | + | 0.413229i | ||||
\(382\) | − | 5.65685i | − | 0.289430i | ||||||
\(383\) | −25.2123 | + | 14.5563i | −1.28829 | + | 0.743795i | −0.978349 | − | 0.206961i | \(-0.933643\pi\) |
−0.309941 | + | 0.950756i | \(0.600309\pi\) | |||||||
\(384\) | 25.1763 | − | 14.5355i | 1.28477 | − | 0.741763i | ||||
\(385\) | − | 16.4853i | − | 0.840168i | ||||||
\(386\) | 5.24264 | + | 9.08052i | 0.266843 | + | 0.462186i | ||||
\(387\) | 5.53553 | − | 9.58783i | 0.281387 | − | 0.487377i | ||||
\(388\) | −25.3864 | − | 14.6569i | −1.28880 | − | 0.744089i | ||||
\(389\) | −28.6274 | −1.45147 | −0.725734 | − | 0.687976i | \(-0.758500\pi\) | ||||
−0.725734 | + | 0.687976i | \(0.758500\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.17157 | 0.0592490 | ||||||||
\(392\) | 62.3644 | + | 36.0061i | 3.14988 | + | 1.81858i | ||||
\(393\) | −12.0000 | + | 20.7846i | −0.605320 | + | 1.04844i | ||||
\(394\) | −13.2426 | − | 22.9369i | −0.667155 | − | 1.15555i | ||||
\(395\) | − | 8.48528i | − | 0.426941i | ||||||
\(396\) | −11.3199 | + | 6.53553i | −0.568845 | + | 0.328423i | ||||
\(397\) | −10.2182 | + | 5.89949i | −0.512838 | + | 0.296087i | −0.733999 | − | 0.679150i | \(-0.762349\pi\) |
0.221161 | + | 0.975237i | \(0.429015\pi\) | |||||||
\(398\) | 9.65685i | 0.484054i | ||||||||
\(399\) | 2.00000 | + | 3.46410i | 0.100125 | + | 0.173422i | ||||
\(400\) | 1.50000 | − | 2.59808i | 0.0750000 | − | 0.129904i | ||||
\(401\) | −4.60181 | − | 2.65685i | −0.229803 | − | 0.132677i | 0.380678 | − | 0.924708i | \(-0.375691\pi\) |
−0.610481 | + | 0.792031i | \(0.709024\pi\) | |||||||
\(402\) | 6.82843 | 0.340571 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −14.0000 | −0.696526 | ||||||||
\(405\) | 4.33013 | + | 2.50000i | 0.215166 | + | 0.124226i | ||||
\(406\) | −32.9706 | + | 57.1067i | −1.63630 | + | 2.83416i | ||||
\(407\) | −14.4853 | − | 25.0892i | −0.718009 | − | 1.24363i | ||||
\(408\) | 5.17157i | 0.256031i | ||||||||
\(409\) | 6.21076 | − | 3.58579i | 0.307103 | − | 0.177306i | −0.338527 | − | 0.940957i | \(-0.609929\pi\) |
0.645629 | + | 0.763651i | \(0.276595\pi\) | |||||||
\(410\) | −6.63103 | + | 3.82843i | −0.327483 | + | 0.189073i | ||||
\(411\) | − | 24.4853i | − | 1.20777i | ||||||
\(412\) | −27.9203 | − | 48.3594i | −1.37553 | − | 2.38250i | ||||
\(413\) | 4.24264 | − | 7.34847i | 0.208767 | − | 0.361595i | ||||
\(414\) | 2.95680 | + | 1.70711i | 0.145319 | + | 0.0838997i | ||||
\(415\) | 3.17157 | 0.155686 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.34315 | −0.310625 | ||||||||
\(418\) | 4.18154 | + | 2.41421i | 0.204526 | + | 0.118083i | ||||
\(419\) | −5.41421 | + | 9.37769i | −0.264502 | + | 0.458130i | −0.967433 | − | 0.253127i | \(-0.918541\pi\) |
0.702931 | + | 0.711258i | \(0.251874\pi\) | |||||||
\(420\) | −13.0711 | − | 22.6398i | −0.637803 | − | 1.10471i | ||||
\(421\) | − | 34.9706i | − | 1.70436i | −0.523248 | − | 0.852180i | \(-0.675280\pi\) | ||
0.523248 | − | 0.852180i | \(-0.324720\pi\) | |||||||
\(422\) | −6.92820 | + | 4.00000i | −0.337260 | + | 0.194717i | ||||
\(423\) | −4.18154 | + | 2.41421i | −0.203313 | + | 0.117383i | ||||
\(424\) | 10.9706i | 0.532778i | ||||||||
\(425\) | −0.414214 | − | 0.717439i | −0.0200923 | − | 0.0348009i | ||||
\(426\) | 20.3137 | − | 35.1844i | 0.984202 | − | 1.70469i | ||||
\(427\) | −33.4523 | − | 19.3137i | −1.61887 | − | 0.934656i | ||||
\(428\) | 36.0416 | 1.74214 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 26.7279 | 1.28893 | ||||||||
\(431\) | −34.9742 | − | 20.1924i | −1.68465 | − | 0.972633i | −0.958498 | − | 0.285099i | \(-0.907974\pi\) |
−0.726152 | − | 0.687534i | \(-0.758693\pi\) | |||||||
\(432\) | −8.48528 | + | 14.6969i | −0.408248 | + | 0.707107i | ||||
\(433\) | 3.82843 | + | 6.63103i | 0.183982 | + | 0.318667i | 0.943233 | − | 0.332131i | \(-0.107768\pi\) |
−0.759251 | + | 0.650798i | \(0.774434\pi\) | |||||||
\(434\) | − | 20.4853i | − | 0.983325i | ||||||
\(435\) | 6.92820 | − | 4.00000i | 0.332182 | − | 0.191785i | ||||
\(436\) | 6.63103 | − | 3.82843i | 0.317569 | − | 0.183348i | ||||
\(437\) | − | 0.828427i | − | 0.0396290i | ||||||
\(438\) | −14.4853 | − | 25.0892i | −0.692134 | − | 1.19881i | ||||
\(439\) | 0.485281 | − | 0.840532i | 0.0231612 | − | 0.0401164i | −0.854212 | − | 0.519924i | \(-0.825960\pi\) |
0.877374 | + | 0.479808i | \(0.159294\pi\) | |||||||
\(440\) | −13.0519 | − | 7.53553i | −0.622226 | − | 0.359242i | ||||
\(441\) | 16.3137 | 0.776843 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.41421 | −0.447283 | −0.223641 | − | 0.974671i | \(-0.571794\pi\) | ||||
−0.223641 | + | 0.974671i | \(0.571794\pi\) | |||||||
\(444\) | −39.7862 | − | 22.9706i | −1.88817 | − | 1.09013i | ||||
\(445\) | −3.00000 | + | 5.19615i | −0.142214 | + | 0.246321i | ||||
\(446\) | −11.4853 | − | 19.8931i | −0.543844 | − | 0.941965i | ||||
\(447\) | 16.4853i | 0.779727i | ||||||||
\(448\) | −41.0980 | + | 23.7279i | −1.94170 | + | 1.12104i | ||||
\(449\) | 28.6764 | − | 16.5563i | 1.35332 | − | 0.781342i | 0.364611 | − | 0.931160i | \(-0.381202\pi\) |
0.988714 | + | 0.149817i | \(0.0478686\pi\) | |||||||
\(450\) | − | 2.41421i | − | 0.113807i | ||||||
\(451\) | 5.41421 | + | 9.37769i | 0.254945 | + | 0.441578i | ||||
\(452\) | −16.8995 | + | 29.2708i | −0.794885 | + | 1.37678i | ||||
\(453\) | −11.9503 | − | 6.89949i | −0.561473 | − | 0.324167i | ||||
\(454\) | −39.4558 | −1.85175 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.65685 | 0.171248 | ||||||||
\(457\) | 15.5885 | + | 9.00000i | 0.729197 | + | 0.421002i | 0.818128 | − | 0.575036i | \(-0.195012\pi\) |
−0.0889312 | + | 0.996038i | \(0.528345\pi\) | |||||||
\(458\) | −5.82843 | + | 10.0951i | −0.272345 | + | 0.471715i | ||||
\(459\) | 2.34315 | + | 4.05845i | 0.109369 | + | 0.189432i | ||||
\(460\) | 5.41421i | 0.252439i | ||||||||
\(461\) | 8.23999 | − | 4.75736i | 0.383775 | − | 0.221572i | −0.295685 | − | 0.955286i | \(-0.595548\pi\) |
0.679459 | + | 0.733713i | \(0.262214\pi\) | |||||||
\(462\) | −48.7436 | + | 28.1421i | −2.26776 | + | 1.30929i | ||||
\(463\) | 4.34315i | 0.201843i | 0.994894 | + | 0.100922i | \(0.0321791\pi\) | ||||
−0.994894 | + | 0.100922i | \(0.967821\pi\) | |||||||
\(464\) | 8.48528 | + | 14.6969i | 0.393919 | + | 0.682288i | ||||
\(465\) | −1.24264 | + | 2.15232i | −0.0576261 | + | 0.0998113i | ||||
\(466\) | 43.1272 | + | 24.8995i | 1.99783 | + | 1.15345i | ||||
\(467\) | 13.4142 | 0.620736 | 0.310368 | − | 0.950617i | \(-0.399548\pi\) | ||||
0.310368 | + | 0.950617i | \(0.399548\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.65685 | −0.445912 | ||||||||
\(470\) | −10.0951 | − | 5.82843i | −0.465654 | − | 0.268845i | ||||
\(471\) | 12.7279 | − | 22.0454i | 0.586472 | − | 1.01580i | ||||
\(472\) | −3.87868 | − | 6.71807i | −0.178531 | − | 0.309224i | ||||
\(473\) | − | 37.7990i | − | 1.73800i | ||||||
\(474\) | −25.0892 | + | 14.4853i | −1.15239 | + | 0.665331i | ||||
\(475\) | −0.507306 | + | 0.292893i | −0.0232768 | + | 0.0134389i | ||||
\(476\) | − | 15.3137i | − | 0.701903i | ||||||
\(477\) | 1.24264 | + | 2.15232i | 0.0568966 | + | 0.0985478i | ||||
\(478\) | 4.12132 | − | 7.13834i | 0.188505 | − | 0.326500i | ||||
\(479\) | −26.6112 | − | 15.3640i | −1.21589 | − | 0.701997i | −0.251858 | − | 0.967764i | \(-0.581041\pi\) |
−0.964037 | + | 0.265767i | \(0.914375\pi\) | |||||||
\(480\) | 2.24264 | 0.102362 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 34.9706 | 1.59287 | ||||||||
\(483\) | 8.36308 | + | 4.82843i | 0.380533 | + | 0.219701i | ||||
\(484\) | −1.25736 | + | 2.17781i | −0.0571527 | + | 0.0989914i | ||||
\(485\) | −3.82843 | − | 6.63103i | −0.173840 | − | 0.301100i | ||||
\(486\) | 23.8995i | 1.08410i | ||||||||
\(487\) | −9.50079 | + | 5.48528i | −0.430522 | + | 0.248562i | −0.699569 | − | 0.714565i | \(-0.746625\pi\) |
0.269047 | + | 0.963127i | \(0.413291\pi\) | |||||||
\(488\) | −30.5826 | + | 17.6569i | −1.38441 | + | 0.799288i | ||||
\(489\) | 26.8284i | 1.21322i | ||||||||
\(490\) | 19.6924 | + | 34.1082i | 0.889611 | + | 1.54085i | ||||
\(491\) | 2.58579 | − | 4.47871i | 0.116695 | − | 0.202122i | −0.801761 | − | 0.597645i | \(-0.796103\pi\) |
0.918456 | + | 0.395523i | \(0.129437\pi\) | |||||||
\(492\) | 14.8710 | + | 8.58579i | 0.670437 | + | 0.387077i | ||||
\(493\) | 4.68629 | 0.211060 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.41421 | −0.153457 | ||||||||
\(496\) | −4.56575 | − | 2.63604i | −0.205008 | − | 0.118362i | ||||
\(497\) | −28.7279 | + | 49.7582i | −1.28862 | + | 2.23196i | ||||
\(498\) | −5.41421 | − | 9.37769i | −0.242617 | − | 0.420224i | ||||
\(499\) | 41.5563i | 1.86032i | 0.367157 | + | 0.930159i | \(0.380331\pi\) | ||||
−0.367157 | + | 0.930159i | \(0.619669\pi\) | |||||||
\(500\) | 3.31552 | − | 1.91421i | 0.148274 | − | 0.0856062i | ||||
\(501\) | −3.88437 | + | 2.24264i | −0.173541 | + | 0.100194i | ||||
\(502\) | 47.7990i | 2.13337i | ||||||||
\(503\) | −18.9497 | − | 32.8219i | −0.844927 | − | 1.46346i | −0.885684 | − | 0.464288i | \(-0.846310\pi\) |
0.0407567 | − | 0.999169i | \(-0.487023\pi\) | |||||||
\(504\) | 10.6569 | − | 18.4582i | 0.474694 | − | 0.822194i | ||||
\(505\) | −3.16693 | − | 1.82843i | −0.140926 | − | 0.0813639i | ||||
\(506\) | 11.6569 | 0.518210 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −25.2132 | −1.11866 | ||||||||
\(509\) | −35.6046 | − | 20.5563i | −1.57815 | − | 0.911144i | −0.995118 | − | 0.0986936i | \(-0.968534\pi\) |
−0.583030 | − | 0.812451i | \(-0.698133\pi\) | |||||||
\(510\) | −1.41421 | + | 2.44949i | −0.0626224 | + | 0.108465i | ||||
\(511\) | 20.4853 | + | 35.4815i | 0.906215 | + | 1.56961i | ||||
\(512\) | 31.2426i | 1.38074i | ||||||||
\(513\) | 2.86976 | − | 1.65685i | 0.126703 | − | 0.0731519i | ||||
\(514\) | 57.8241 | − | 33.3848i | 2.55051 | − | 1.47254i | ||||
\(515\) | − | 14.5858i | − | 0.642727i | ||||||
\(516\) | −29.9706 | − | 51.9105i | −1.31938 | − | 2.28523i | ||||
\(517\) | −8.24264 | + | 14.2767i | −0.362511 | + | 0.627887i | ||||
\(518\) | 85.6600 | + | 49.4558i | 3.76369 | + | 2.17297i | ||||
\(519\) | 23.7990 | 1.04466 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.6569 | −0.773561 | −0.386780 | − | 0.922172i | \(-0.626413\pi\) | ||||
−0.386780 | + | 0.922172i | \(0.626413\pi\) | |||||||
\(522\) | 11.8272 | + | 6.82843i | 0.517662 | + | 0.298872i | ||||
\(523\) | 9.87868 | − | 17.1104i | 0.431965 | − | 0.748184i | −0.565078 | − | 0.825038i | \(-0.691154\pi\) |
0.997042 | + | 0.0768531i | \(0.0244872\pi\) | |||||||
\(524\) | −32.4853 | − | 56.2662i | −1.41913 | − | 2.45800i | ||||
\(525\) | − | 6.82843i | − | 0.298017i | ||||||
\(526\) | 22.1324 | − | 12.7782i | 0.965021 | − | 0.557155i | ||||
\(527\) | −1.26080 | + | 0.727922i | −0.0549212 | + | 0.0317088i | ||||
\(528\) | 14.4853i | 0.630391i | ||||||||
\(529\) | 10.5000 | + | 18.1865i | 0.456522 | + | 0.790719i | ||||
\(530\) | −3.00000 | + | 5.19615i | −0.130312 | + | 0.225706i | ||||
\(531\) | −1.52192 | − | 0.878680i | −0.0660456 | − | 0.0381314i | ||||
\(532\) | −10.8284 | −0.469472 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 20.4853 | 0.886485 | ||||||||
\(535\) | 8.15295 | + | 4.70711i | 0.352483 | + | 0.203506i | ||||
\(536\) | −4.41421 | + | 7.64564i | −0.190665 | + | 0.330241i | ||||
\(537\) | −4.00000 | − | 6.92820i | −0.172613 | − | 0.298974i | ||||
\(538\) | 61.1127i | 2.63476i | ||||||||
\(539\) | 48.2363 | − | 27.8492i | 2.07768 | − | 1.19955i | ||||
\(540\) | −18.7554 | + | 10.8284i | −0.807103 | + | 0.465981i | ||||
\(541\) | 7.17157i | 0.308330i | 0.988045 | + | 0.154165i | \(0.0492687\pi\) | ||||
−0.988045 | + | 0.154165i | \(0.950731\pi\) | |||||||
\(542\) | 32.2635 | + | 55.8819i | 1.38583 | + | 2.40034i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.13770 | + | 0.656854i | 0.0487787 | + | 0.0281624i | ||||
\(545\) | 2.00000 | 0.0856706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.2132 | 0.564956 | 0.282478 | − | 0.959274i | \(-0.408844\pi\) | ||||
0.282478 | + | 0.959274i | \(0.408844\pi\) | |||||||
\(548\) | 57.4039 | + | 33.1421i | 2.45217 | + | 1.41576i | ||||
\(549\) | −4.00000 | + | 6.92820i | −0.170716 | + | 0.295689i | ||||
\(550\) | −4.12132 | − | 7.13834i | −0.175734 | − | 0.304380i | ||||
\(551\) | − | 3.31371i | − | 0.141169i | ||||||
\(552\) | 7.64564 | − | 4.41421i | 0.325420 | − | 0.187881i | ||||
\(553\) | 35.4815 | − | 20.4853i | 1.50883 | − | 0.871123i | ||||
\(554\) | − | 30.9706i | − | 1.31581i | ||||||
\(555\) | −6.00000 | − | 10.3923i | −0.254686 | − | 0.441129i | ||||
\(556\) | 8.58579 | − | 14.8710i | 0.364118 | − | 0.630672i | ||||
\(557\) | −31.0028 | − | 17.8995i | −1.31363 | − | 0.758426i | −0.330937 | − | 0.943653i | \(-0.607365\pi\) |
−0.982696 | + | 0.185227i | \(0.940698\pi\) | |||||||
\(558\) | −4.24264 | −0.179605 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 14.4853 | 0.612115 | ||||||||
\(561\) | 3.46410 | + | 2.00000i | 0.146254 | + | 0.0844401i | ||||
\(562\) | 26.3137 | − | 45.5767i | 1.10998 | − | 1.92254i | ||||
\(563\) | −3.87868 | − | 6.71807i | −0.163467 | − | 0.283133i | 0.772643 | − | 0.634841i | \(-0.218934\pi\) |
−0.936110 | + | 0.351708i | \(0.885601\pi\) | |||||||
\(564\) | 26.1421i | 1.10078i | ||||||||
\(565\) | −7.64564 | + | 4.41421i | −0.321655 | + | 0.185707i | ||||
\(566\) | −34.9742 | + | 20.1924i | −1.47008 | + | 0.848749i | ||||
\(567\) | 24.1421i | 1.01387i | ||||||||
\(568\) | 26.2635 | + | 45.4896i | 1.10199 | + | 1.90870i | ||||
\(569\) | −5.17157 | + | 8.95743i | −0.216804 | + | 0.375515i | −0.953829 | − | 0.300350i | \(-0.902896\pi\) |
0.737025 | + | 0.675865i | \(0.236230\pi\) | |||||||
\(570\) | 1.73205 | + | 1.00000i | 0.0725476 | + | 0.0418854i | ||||
\(571\) | 11.5147 | 0.481876 | 0.240938 | − | 0.970541i | \(-0.422545\pi\) | ||||
0.240938 | + | 0.970541i | \(0.422545\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.31371 | −0.138432 | ||||||||
\(574\) | −32.0174 | − | 18.4853i | −1.33638 | − | 0.771561i | ||||
\(575\) | −0.707107 | + | 1.22474i | −0.0294884 | + | 0.0510754i | ||||
\(576\) | 4.91421 | + | 8.51167i | 0.204759 | + | 0.354653i | ||||
\(577\) | − | 34.8284i | − | 1.44993i | −0.688788 | − | 0.724963i | \(-0.741857\pi\) | ||
0.688788 | − | 0.724963i | \(-0.258143\pi\) | |||||||
\(578\) | 34.1082 | − | 19.6924i | 1.41871 | − | 0.819095i | ||||
\(579\) | 5.31925 | − | 3.07107i | 0.221060 | − | 0.127629i | ||||
\(580\) | 21.6569i | 0.899252i | ||||||||
\(581\) | 7.65685 | + | 13.2621i | 0.317660 | + | 0.550203i | ||||
\(582\) | −13.0711 | + | 22.6398i | −0.541813 | + | 0.938448i | ||||
\(583\) | 7.34847 | + | 4.24264i | 0.304342 | + | 0.175712i | ||||
\(584\) | 37.4558 | 1.54993 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −63.1127 | −2.60716 | ||||||||
\(587\) | −17.6177 | − | 10.1716i | −0.727160 | − | 0.419826i | 0.0902226 | − | 0.995922i | \(-0.471242\pi\) |
−0.817382 | + | 0.576096i | \(0.804575\pi\) | |||||||
\(588\) | 44.1630 | − | 76.4925i | 1.82125 | − | 3.15450i | ||||
\(589\) | 0.514719 | + | 0.891519i | 0.0212086 | + | 0.0367344i | ||||
\(590\) | − | 4.24264i | − | 0.174667i | ||||||
\(591\) | −13.4361 | + | 7.75736i | −0.552689 | + | 0.319095i | ||||
\(592\) | 22.0454 | − | 12.7279i | 0.906061 | − | 0.523114i | ||||
\(593\) | 24.6274i | 1.01133i | 0.862731 | + | 0.505663i | \(0.168752\pi\) | ||||
−0.862731 | + | 0.505663i | \(0.831248\pi\) | |||||||
\(594\) | 23.3137 | + | 40.3805i | 0.956573 | + | 1.65683i | ||||
\(595\) | 2.00000 | − | 3.46410i | 0.0819920 | − | 0.142014i | ||||
\(596\) | −38.6485 | − | 22.3137i | −1.58310 | − | 0.914005i | ||||
\(597\) | 5.65685 | 0.231520 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.4558 | 1.04010 | 0.520049 | − | 0.854137i | \(-0.325914\pi\) | ||||
0.520049 | + | 0.854137i | \(0.325914\pi\) | |||||||
\(600\) | −5.40629 | − | 3.12132i | −0.220711 | − | 0.127427i | ||||
\(601\) | 22.3137 | − | 38.6485i | 0.910195 | − | 1.57650i | 0.0964075 | − | 0.995342i | \(-0.469265\pi\) |
0.813788 | − | 0.581162i | \(-0.197402\pi\) | |||||||
\(602\) | 64.5269 | + | 111.764i | 2.62992 | + | 4.55516i | ||||
\(603\) | 2.00000i | 0.0814463i | ||||||||
\(604\) | 32.3507 | − | 18.6777i | 1.31633 | − | 0.759984i | ||||
\(605\) | −0.568852 | + | 0.328427i | −0.0231271 | + | 0.0133525i | ||||
\(606\) | 12.4853i | 0.507180i | ||||||||
\(607\) | −15.8787 | − | 27.5027i | −0.644496 | − | 1.11630i | −0.984418 | − | 0.175846i | \(-0.943734\pi\) |
0.339922 | − | 0.940454i | \(-0.389599\pi\) | |||||||
\(608\) | 0.464466 | − | 0.804479i | 0.0188366 | − | 0.0326259i | ||||
\(609\) | 33.4523 | + | 19.3137i | 1.35556 | + | 0.782631i | ||||
\(610\) | −19.3137 | −0.781989 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −3.17157 | −0.128203 | ||||||||
\(613\) | 12.7187 | + | 7.34315i | 0.513704 | + | 0.296587i | 0.734355 | − | 0.678766i | \(-0.237485\pi\) |
−0.220651 | + | 0.975353i | \(0.570818\pi\) | |||||||
\(614\) | 29.9706 | − | 51.9105i | 1.20951 | − | 2.09494i | ||||
\(615\) | 2.24264 | + | 3.88437i | 0.0904320 | + | 0.156633i | ||||
\(616\) | − | 72.7696i | − | 2.93197i | ||||||
\(617\) | 9.50079 | − | 5.48528i | 0.382487 | − | 0.220829i | −0.296413 | − | 0.955060i | \(-0.595790\pi\) |
0.678900 | + | 0.734231i | \(0.262457\pi\) | |||||||
\(618\) | −43.1272 | + | 24.8995i | −1.73483 | + | 1.00160i | ||||
\(619\) | − | 1.75736i | − | 0.0706342i | −0.999376 | − | 0.0353171i | \(-0.988756\pi\) | ||
0.999376 | − | 0.0353171i | \(-0.0112441\pi\) | |||||||
\(620\) | −3.36396 | − | 5.82655i | −0.135100 | − | 0.234000i | ||||
\(621\) | 4.00000 | − | 6.92820i | 0.160514 | − | 0.278019i | ||||
\(622\) | −17.7408 | − | 10.2426i | −0.711340 | − | 0.410692i | ||||
\(623\) | −28.9706 | −1.16068 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −10.0951 | − | 5.82843i | −0.403483 | − | 0.232951i | ||||
\(627\) | 1.41421 | − | 2.44949i | 0.0564782 | − | 0.0978232i | ||||
\(628\) | 34.4558 | + | 59.6793i | 1.37494 | + | 2.38146i | ||||
\(629\) | − | 7.02944i | − | 0.280282i | ||||||
\(630\) | 10.0951 | − | 5.82843i | 0.402200 | − | 0.232210i | ||||
\(631\) | 8.45012 | − | 4.87868i | 0.336394 | − | 0.194217i | −0.322282 | − | 0.946644i | \(-0.604450\pi\) |
0.658676 | + | 0.752426i | \(0.271117\pi\) | |||||||
\(632\) | − | 37.4558i | − | 1.48991i | ||||||
\(633\) | 2.34315 | + | 4.05845i | 0.0931317 | + | 0.161309i | ||||
\(634\) | 2.58579 | − | 4.47871i | 0.102695 | − | 0.177872i | ||||
\(635\) | −5.70346 | − | 3.29289i | −0.226335 | − | 0.130674i | ||||
\(636\) | 13.4558 | 0.533559 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 46.6274 | 1.84600 | ||||||||
\(639\) | 10.3053 | + | 5.94975i | 0.407670 | + | 0.235368i | ||||
\(640\) | −10.2782 | + | 17.8023i | −0.406281 | + | 0.703699i | ||||
\(641\) | 23.8284 | + | 41.2720i | 0.941166 | + | 1.63015i | 0.763251 | + | 0.646102i | \(0.223602\pi\) |
0.177915 | + | 0.984046i | \(0.443065\pi\) | |||||||
\(642\) | − | 32.1421i | − | 1.26855i | ||||||
\(643\) | 8.23999 | − | 4.75736i | 0.324953 | − | 0.187612i | −0.328645 | − | 0.944454i | \(-0.606592\pi\) |
0.653598 | + | 0.756842i | \(0.273259\pi\) | |||||||
\(644\) | −22.6398 | + | 13.0711i | −0.892131 | + | 0.515072i | ||||
\(645\) | − | 15.6569i | − | 0.616488i | ||||||
\(646\) | 0.585786 | + | 1.01461i | 0.0230475 | + | 0.0399194i | ||||
\(647\) | 4.70711 | − | 8.15295i | 0.185055 | − | 0.320525i | −0.758540 | − | 0.651627i | \(-0.774087\pi\) |
0.943595 | + | 0.331101i | \(0.107420\pi\) | |||||||
\(648\) | 19.1141 | + | 11.0355i | 0.750873 | + | 0.433517i | ||||
\(649\) | −6.00000 | −0.235521 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.0000 | −0.470317 | ||||||||
\(652\) | −62.8972 | − | 36.3137i | −2.46324 | − | 1.42215i | ||||
\(653\) | −23.4853 | + | 40.6777i | −0.919050 | + | 1.59184i | −0.118189 | + | 0.992991i | \(0.537709\pi\) |
−0.800861 | + | 0.598850i | \(0.795624\pi\) | |||||||
\(654\) | −3.41421 | − | 5.91359i | −0.133506 | − | 0.231240i | ||||
\(655\) | − | 16.9706i | − | 0.663095i | ||||||
\(656\) | −8.23999 | + | 4.75736i | −0.321717 | + | 0.185744i | ||||
\(657\) | 7.34847 | − | 4.24264i | 0.286691 | − | 0.165521i | ||||
\(658\) | − | 56.2843i | − | 2.19419i | ||||||
\(659\) | −8.92893 | − | 15.4654i | −0.347822 | − | 0.602445i | 0.638040 | − | 0.770003i | \(-0.279745\pi\) |
−0.985862 | + | 0.167558i | \(0.946412\pi\) | |||||||
\(660\) | −9.24264 | + | 16.0087i | −0.359769 | + | 0.623139i | ||||
\(661\) | 25.6326 | + | 14.7990i | 0.996993 | + | 0.575614i | 0.907357 | − | 0.420361i | \(-0.138096\pi\) |
0.0896356 | + | 0.995975i | \(0.471430\pi\) | |||||||
\(662\) | −62.8701 | −2.44351 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14.0000 | 0.543305 | ||||||||
\(665\) | −2.44949 | − | 1.41421i | −0.0949871 | − | 0.0548408i | ||||
\(666\) | 10.2426 | − | 17.7408i | 0.396894 | − | 0.687441i | ||||
\(667\) | −4.00000 | − | 6.92820i | −0.154881 | − | 0.268261i | ||||
\(668\) | − | 12.1421i | − | 0.469793i | ||||||
\(669\) | −11.6531 | + | 6.72792i | −0.450535 | + | 0.260116i | ||||
\(670\) | −4.18154 | + | 2.41421i | −0.161547 | + | 0.0932692i | ||||
\(671\) | 27.3137i | 1.05443i | ||||||||
\(672\) | 5.41421 | + | 9.37769i | 0.208858 | + | 0.361752i | ||||
\(673\) | 3.24264 | − | 5.61642i | 0.124995 | − | 0.216497i | −0.796736 | − | 0.604327i | \(-0.793442\pi\) |
0.921731 | + | 0.387830i | \(0.126775\pi\) | |||||||
\(674\) | −26.8213 | − | 15.4853i | −1.03312 | − | 0.596471i | ||||
\(675\) | −5.65685 | −0.217732 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20.1421 | −0.774125 | −0.387063 | − | 0.922053i | \(-0.626510\pi\) | ||||
−0.387063 | + | 0.922053i | \(0.626510\pi\) | |||||||
\(678\) | 26.1039 | + | 15.0711i | 1.00251 | + | 0.578801i | ||||
\(679\) | 18.4853 | − | 32.0174i | 0.709400 | − | 1.22872i | ||||
\(680\) | −1.82843 | − | 3.16693i | −0.0701170 | − | 0.121446i | ||||
\(681\) | 23.1127i | 0.885681i | ||||||||
\(682\) | −12.5446 | + | 7.24264i | −0.480358 | + | 0.277335i | ||||
\(683\) | −9.25460 | + | 5.34315i | −0.354117 | + | 0.204450i | −0.666497 | − | 0.745507i | \(-0.732207\pi\) |
0.312380 | + | 0.949957i | \(0.398874\pi\) | |||||||
\(684\) | 2.24264i | 0.0857495i | ||||||||
\(685\) | 8.65685 | + | 14.9941i | 0.330761 | + | 0.572896i | ||||
\(686\) | −54.2843 | + | 94.0231i | −2.07258 | + | 3.58982i | ||||
\(687\) | 5.91359 | + | 3.41421i | 0.225618 | + | 0.130260i | ||||
\(688\) | 33.2132 | 1.26624 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 4.82843 | 0.183815 | ||||||||
\(691\) | −6.00063 | − | 3.46447i | −0.228275 | − | 0.131795i | 0.381501 | − | 0.924368i | \(-0.375407\pi\) |
−0.609776 | + | 0.792574i | \(0.708741\pi\) | |||||||
\(692\) | −32.2132 | + | 55.7949i | −1.22456 | + | 2.12100i | ||||
\(693\) | −8.24264 | − | 14.2767i | −0.313112 | − | 0.542326i | ||||
\(694\) | 10.2426i | 0.388805i | ||||||||
\(695\) | 3.88437 | − | 2.24264i | 0.147342 | − | 0.0850682i | ||||
\(696\) | 30.5826 | − | 17.6569i | 1.15923 | − | 0.669281i | ||||
\(697\) | 2.62742i | 0.0995205i | ||||||||
\(698\) | 22.3137 | + | 38.6485i | 0.844586 | + | 1.46287i | ||||
\(699\) | 14.5858 | − | 25.2633i | 0.551685 | − | 0.955547i | ||||
\(700\) | 16.0087 | + | 9.24264i | 0.605073 | + | 0.349339i | ||||
\(701\) | −14.6863 | −0.554694 | −0.277347 | − | 0.960770i | \(-0.589455\pi\) | ||||
−0.277347 | + | 0.960770i | \(0.589455\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.97056 | −0.187468 | ||||||||
\(704\) | 29.0607 | + | 16.7782i | 1.09526 | + | 0.632351i | ||||
\(705\) | −3.41421 | + | 5.91359i | −0.128587 | + | 0.222719i | ||||
\(706\) | −17.8995 | − | 31.0028i | −0.673656 | − | 1.16681i | ||||
\(707\) | − | 17.6569i | − | 0.664054i | ||||||
\(708\) | −8.23999 | + | 4.75736i | −0.309678 | + | 0.178793i | ||||
\(709\) | −39.0687 | + | 22.5563i | −1.46726 | + | 0.847121i | −0.999328 | − | 0.0366445i | \(-0.988333\pi\) |
−0.467929 | + | 0.883766i | \(0.655000\pi\) | |||||||
\(710\) | 28.7279i | 1.07814i | ||||||||
\(711\) | −4.24264 | − | 7.34847i | −0.159111 | − | 0.275589i | ||||
\(712\) | −13.2426 | + | 22.9369i | −0.496289 | + | 0.859598i | ||||
\(713\) | 2.15232 | + | 1.24264i | 0.0806049 | + | 0.0465373i | ||||
\(714\) | −13.6569 | −0.511095 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 21.6569 | 0.809355 | ||||||||
\(717\) | −4.18154 | − | 2.41421i | −0.156162 | − | 0.0901605i | ||||
\(718\) | −9.77817 | + | 16.9363i | −0.364918 | + | 0.632057i | ||||
\(719\) | 14.4853 | + | 25.0892i | 0.540210 | + | 0.935671i | 0.998892 | + | 0.0470703i | \(0.0149885\pi\) |
−0.458682 | + | 0.888601i | \(0.651678\pi\) | |||||||
\(720\) | − | 3.00000i | − | 0.111803i | ||||||
\(721\) | 60.9911 | − | 35.2132i | 2.27143 | − | 1.31141i | ||||
\(722\) | −39.0072 | + | 22.5208i | −1.45170 | + | 0.838138i | ||||
\(723\) | − | 20.4853i | − | 0.761856i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.82843 | + | 4.89898i | −0.105045 | + | 0.181944i | ||||
\(726\) | 1.94218 | + | 1.12132i | 0.0720812 | + | 0.0416161i | ||||
\(727\) | 51.3553 | 1.90466 | 0.952332 | − | 0.305063i | \(-0.0986777\pi\) | ||||
0.952332 | + | 0.305063i | \(0.0986777\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.0000 | 1.07407 | ||||||||
\(730\) | 17.7408 | + | 10.2426i | 0.656616 | + | 0.379097i | ||||
\(731\) | 4.58579 | − | 7.94282i | 0.169611 | − | 0.293776i | ||||
\(732\) | 21.6569 | + | 37.5108i | 0.800460 | + | 1.38644i | ||||
\(733\) | 21.3137i | 0.787240i | 0.919273 | + | 0.393620i | \(0.128777\pi\) | ||||
−0.919273 | + | 0.393620i | \(0.871223\pi\) | |||||||
\(734\) | −74.3402 | + | 42.9203i | −2.74395 | + | 1.58422i | ||||
\(735\) | 19.9801 | − | 11.5355i | 0.736978 | − | 0.425495i | ||||
\(736\) | − | 2.24264i | − | 0.0826648i | ||||||
\(737\) | 3.41421 | + | 5.91359i | 0.125764 | + | 0.217830i | ||||
\(738\) | −3.82843 | + | 6.63103i | −0.140926 | + | 0.244092i | ||||
\(739\) | 4.56575 | + | 2.63604i | 0.167954 | + | 0.0969683i | 0.581621 | − | 0.813460i | \(-0.302419\pi\) |
−0.413667 | + | 0.910428i | \(0.635752\pi\) | |||||||
\(740\) | 32.4853 | 1.19418 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −28.9706 | −1.06354 | ||||||||
\(743\) | 18.6323 | + | 10.7574i | 0.683553 | + | 0.394649i | 0.801192 | − | 0.598407i | \(-0.204199\pi\) |
−0.117640 | + | 0.993056i | \(0.537533\pi\) | |||||||
\(744\) | −5.48528 | + | 9.50079i | −0.201100 | + | 0.348316i | ||||
\(745\) | −5.82843 | − | 10.0951i | −0.213537 | − | 0.369857i | ||||
\(746\) | 6.48528i | 0.237443i | ||||||||
\(747\) | 2.74666 | − | 1.58579i | 0.100495 | − | 0.0580209i | ||||
\(748\) | −9.37769 | + | 5.41421i | −0.342882 | + | 0.197963i | ||||
\(749\) | 45.4558i | 1.66092i | ||||||||
\(750\) | −1.70711 | − | 2.95680i | −0.0623347 | − | 0.107967i | ||||
\(751\) | −13.7574 | + | 23.8284i | −0.502013 | + | 0.869512i | 0.497984 | + | 0.867186i | \(0.334074\pi\) |
−0.999997 | + | 0.00232617i | \(0.999260\pi\) | |||||||
\(752\) | −12.5446 | − | 7.24264i | −0.457455 | − | 0.264112i | ||||
\(753\) | 28.0000 | 1.02038 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.75736 | 0.355107 | ||||||||
\(756\) | −90.5590 | − | 52.2843i | −3.29360 | − | 1.90156i | ||||
\(757\) | 12.0711 | − | 20.9077i | 0.438730 | − | 0.759903i | −0.558861 | − | 0.829261i | \(-0.688762\pi\) |
0.997592 | + | 0.0693577i | \(0.0220950\pi\) | |||||||
\(758\) | −35.0919 | − | 60.7809i | −1.27459 | − | 2.20766i | ||||
\(759\) | − | 6.82843i | − | 0.247856i | ||||||
\(760\) | −2.23936 | + | 1.29289i | −0.0812300 | + | 0.0468982i | ||||
\(761\) | −7.47156 | + | 4.31371i | −0.270844 | + | 0.156372i | −0.629271 | − | 0.777186i | \(-0.716646\pi\) |
0.358427 | + | 0.933558i | \(0.383313\pi\) | |||||||
\(762\) | 22.4853i | 0.814556i | ||||||||
\(763\) | 4.82843 | + | 8.36308i | 0.174801 | + | 0.302764i | ||||
\(764\) | 4.48528 | − | 7.76874i | 0.162272 | − | 0.281063i | ||||
\(765\) | −0.717439 | − | 0.414214i | −0.0259391 | − | 0.0149759i | ||||
\(766\) | −70.2843 | −2.53947 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 42.3848 | 1.52943 | ||||||||
\(769\) | 19.8931 | + | 11.4853i | 0.717363 | + | 0.414170i | 0.813781 | − | 0.581171i | \(-0.197405\pi\) |
−0.0964182 | + | 0.995341i | \(0.530739\pi\) | |||||||
\(770\) | 19.8995 | − | 34.4669i | 0.717128 | − | 1.24210i | ||||
\(771\) | −19.5563 | − | 33.8726i | −0.704305 | − | 1.21989i | ||||
\(772\) | 16.6274i | 0.598434i | ||||||||
\(773\) | −19.1757 | + | 11.0711i | −0.689700 | + | 0.398199i | −0.803500 | − | 0.595305i | \(-0.797031\pi\) |
0.113799 | + | 0.993504i | \(0.463698\pi\) | |||||||
\(774\) | 23.1471 | − | 13.3640i | 0.832004 | − | 0.480358i | ||||
\(775\) | − | 1.75736i | − | 0.0631262i | ||||||
\(776\) | −16.8995 | − | 29.2708i | −0.606657 | − | 1.05076i | ||||
\(777\) | 28.9706 | − | 50.1785i | 1.03931 | − | 1.80014i | ||||
\(778\) | −59.8534 | − | 34.5563i | −2.14585 | − | 1.23891i | ||||
\(779\) | 1.85786 | 0.0665649 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 40.6274 | 1.45376 | ||||||||
\(782\) | 2.44949 | + | 1.41421i | 0.0875936 | + | 0.0505722i | ||||
\(783\) | 16.0000 | − | 27.7128i | 0.571793 | − | 0.990375i | ||||
\(784\) | 24.4706 | + | 42.3843i | 0.873949 | + | 1.51372i | ||||
\(785\) | 18.0000i | 0.642448i | ||||||||
\(786\) | −50.1785 | + | 28.9706i | −1.78981 | + | 1.03335i | ||||
\(787\) | −19.4728 | + | 11.2426i | −0.694131 | + | 0.400757i | −0.805158 | − | 0.593061i | \(-0.797919\pi\) |
0.111027 | + | 0.993817i | \(0.464586\pi\) | |||||||
\(788\) | − | 42.0000i | − | 1.49619i | ||||||
\(789\) | −7.48528 | − | 12.9649i | −0.266483 | − | 0.461562i | ||||
\(790\) | 10.2426 | − | 17.7408i | 0.364417 | − | 0.631188i | ||||
\(791\) | −36.9164 | − | 21.3137i | −1.31260 | − | 0.757828i | ||||
\(792\) | −15.0711 | −0.535527 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −28.4853 | −1.01090 | ||||||||
\(795\) | 3.04384 | + | 1.75736i | 0.107954 | + | 0.0623271i | ||||
\(796\) | −7.65685 | + | 13.2621i | −0.271390 | + | 0.470061i | ||||
\(797\) | −11.4853 | − | 19.8931i | −0.406830 | − | 0.704649i | 0.587703 | − | 0.809077i | \(-0.300032\pi\) |
−0.994533 | + | 0.104427i | \(0.966699\pi\) | |||||||
\(798\) | 9.65685i | 0.341849i | ||||||||
\(799\) | −3.46410 | + | 2.00000i | −0.122551 | + | 0.0707549i | ||||
\(800\) | −1.37333 | + | 0.792893i | −0.0485546 | + | 0.0280330i | ||||
\(801\) | 6.00000i | 0.212000i | ||||||||
\(802\) | −6.41421 | − | 11.1097i | −0.226494 | − | 0.392299i | ||||
\(803\) | 14.4853 | − | 25.0892i | 0.511174 | − | 0.885380i | ||||
\(804\) | 9.37769 | + | 5.41421i | 0.330726 | + | 0.190945i | ||||
\(805\) | −6.82843 | −0.240670 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 35.7990 | 1.26018 | ||||||||
\(808\) | −13.9795 | − | 8.07107i | −0.491797 | − | 0.283939i | ||||
\(809\) | −22.6274 | + | 39.1918i | −0.795538 | + | 1.37791i | 0.126960 | + | 0.991908i | \(0.459478\pi\) |
−0.922497 | + | 0.386004i | \(0.873855\pi\) | |||||||
\(810\) | 6.03553 | + | 10.4539i | 0.212067 | + | 0.367311i | ||||
\(811\) | − | 28.3848i | − | 0.996724i | −0.866969 | − | 0.498362i | \(-0.833935\pi\) | ||
0.866969 | − | 0.498362i | \(-0.166065\pi\) | |||||||
\(812\) | −90.5590 | + | 52.2843i | −3.17800 | + | 1.83482i | ||||
\(813\) | 32.7349 | − | 18.8995i | 1.14806 | − | 0.662834i | ||||
\(814\) | − | 69.9411i | − | 2.45144i | ||||||
\(815\) | −9.48528 | − | 16.4290i | −0.332255 | − | 0.575482i | ||||
\(816\) | −1.75736 | + | 3.04384i | −0.0615199 | + | 0.106556i | ||||
\(817\) | −5.61642 | − | 3.24264i | −0.196494 | − | 0.113446i | ||||
\(818\) | 17.3137 | 0.605360 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12.1421 | −0.424022 | ||||||||
\(821\) | 44.3880 | + | 25.6274i | 1.54915 | + | 0.894403i | 0.998207 | + | 0.0598613i | \(0.0190658\pi\) |
0.550945 | + | 0.834542i | \(0.314267\pi\) | |||||||
\(822\) | 29.5563 | − | 51.1931i | 1.03090 | − | 1.78556i | ||||
\(823\) | −1.19239 | − | 2.06528i | −0.0415640 | − | 0.0719910i | 0.844495 | − | 0.535563i | \(-0.179901\pi\) |
−0.886059 | + | 0.463572i | \(0.846567\pi\) | |||||||
\(824\) | − | 64.3848i | − | 2.24295i | ||||||
\(825\) | −4.18154 | + | 2.41421i | −0.145583 | + | 0.0840521i | ||||
\(826\) | 17.7408 | − | 10.2426i | 0.617280 | − | 0.356387i | ||||
\(827\) | − | 56.1421i | − | 1.95225i | −0.217202 | − | 0.976127i | \(-0.569693\pi\) | ||
0.217202 | − | 0.976127i | \(-0.430307\pi\) | |||||||
\(828\) | 2.70711 | + | 4.68885i | 0.0940785 | + | 0.162949i | ||||
\(829\) | 20.4853 | − | 35.4815i | 0.711483 | − | 1.23233i | −0.252817 | − | 0.967514i | \(-0.581357\pi\) |
0.964300 | − | 0.264811i | \(-0.0853096\pi\) | |||||||
\(830\) | 6.63103 | + | 3.82843i | 0.230166 | + | 0.132887i | ||||
\(831\) | −18.1421 | −0.629344 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 13.5147 | 0.468257 | ||||||||
\(834\) | −13.2621 | − | 7.65685i | −0.459228 | − | 0.265135i | ||||
\(835\) | 1.58579 | − | 2.74666i | 0.0548784 | − | 0.0950522i | ||||
\(836\) | 3.82843 | + | 6.63103i | 0.132409 | + | 0.229339i | ||||
\(837\) | 9.94113i | 0.343616i | ||||||||
\(838\) | −22.6398 | + | 13.0711i | −0.782077 | + | 0.451533i | ||||
\(839\) | −5.82655 | + | 3.36396i | −0.201155 | + | 0.116137i | −0.597194 | − | 0.802097i | \(-0.703718\pi\) |
0.396039 | + | 0.918234i | \(0.370384\pi\) | |||||||
\(840\) | − | 30.1421i | − | 1.04000i | ||||||
\(841\) | −1.50000 | − | 2.59808i | −0.0517241 | − | 0.0895888i | ||||
\(842\) | 42.2132 | − | 73.1154i | 1.45476 | − | 2.51972i | ||||
\(843\) | −26.6982 | − | 15.4142i | −0.919535 | − | 0.530894i | ||||
\(844\) | −12.6863 | −0.436680 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −11.6569 | −0.400771 | ||||||||
\(847\) | −2.74666 | − | 1.58579i | −0.0943764 | − | 0.0544883i | ||||
\(848\) | −3.72792 | + | 6.45695i | −0.128017 | + | 0.221733i | ||||
\(849\) | 11.8284 | + | 20.4874i | 0.405951 | + | 0.703127i | ||||
\(850\) | − | 2.00000i | − | 0.0685994i | ||||||
\(851\) | −10.3923 | + | 6.00000i | −0.356244 | + | 0.205677i | ||||
\(852\) | 55.7949 | − | 32.2132i | 1.91150 | − | 1.10361i | ||||
\(853\) | 13.4558i | 0.460719i | 0.973106 | + | 0.230360i | \(0.0739903\pi\) | ||||
−0.973106 | + | 0.230360i | \(0.926010\pi\) | |||||||
\(854\) | −46.6274 | − | 80.7611i | −1.59556 | − | 2.76359i | ||||
\(855\) | −0.292893 | + | 0.507306i | −0.0100167 | + | 0.0173495i | ||||
\(856\) | 35.9889 | + | 20.7782i | 1.23007 | + | 0.710183i | ||||
\(857\) | −11.6569 | −0.398191 | −0.199095 | − | 0.979980i | \(-0.563800\pi\) | ||||
−0.199095 | + | 0.979980i | \(0.563800\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −27.7990 | −0.948489 | −0.474245 | − | 0.880393i | \(-0.657279\pi\) | ||||
−0.474245 | + | 0.880393i | \(0.657279\pi\) | |||||||
\(860\) | 36.7063 | + | 21.1924i | 1.25167 | + | 0.722654i | ||||
\(861\) | −10.8284 | + | 18.7554i | −0.369032 | + | 0.639182i | ||||
\(862\) | −48.7487 | − | 84.4353i | −1.66039 | − | 2.87588i | ||||
\(863\) | − | 31.4558i | − | 1.07077i | −0.844608 | − | 0.535385i | \(-0.820167\pi\) | ||
0.844608 | − | 0.535385i | \(-0.179833\pi\) | |||||||
\(864\) | 7.76874 | − | 4.48528i | 0.264298 | − | 0.152592i | ||||
\(865\) | −14.5738 | + | 8.41421i | −0.495526 | + | 0.286092i | ||||
\(866\) | 18.4853i | 0.628155i | ||||||||
\(867\) | −11.5355 | − | 19.9801i | −0.391767 | − | 0.678561i | ||||
\(868\) | 16.2426 | − | 28.1331i | 0.551311 | − | 0.954899i | ||||
\(869\) | −25.0892 | − | 14.4853i | −0.851094 | − | 0.491380i | ||||
\(870\) | 19.3137 | 0.654796 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 8.82843 | 0.298968 | ||||||||
\(873\) | −6.63103 | − | 3.82843i | −0.224426 | − | 0.129573i | ||||
\(874\) | 1.00000 | − | 1.73205i | 0.0338255 | − | 0.0585875i | ||||
\(875\) | 2.41421 | + | 4.18154i | 0.0816153 | + | 0.141362i | ||||
\(876\) | − | 45.9411i | − | 1.55221i | ||||||
\(877\) | 21.9223 | − | 12.6569i | 0.740264 | − | 0.427392i | −0.0819013 | − | 0.996640i | \(-0.526099\pi\) |
0.822165 | + | 0.569249i | \(0.192766\pi\) | |||||||
\(878\) | 2.02922 | − | 1.17157i | 0.0684830 | − | 0.0395387i | ||||
\(879\) | 36.9706i | 1.24699i | ||||||||
\(880\) | −5.12132 | − | 8.87039i | −0.172640 | − | 0.299021i | ||||
\(881\) | 9.51472 | − | 16.4800i | 0.320559 | − | 0.555225i | −0.660044 | − | 0.751227i | \(-0.729463\pi\) |
0.980603 | + | 0.196002i | \(0.0627959\pi\) | |||||||
\(882\) | 34.1082 | + | 19.6924i | 1.14848 | + | 0.663077i | ||||
\(883\) | 23.7574 | 0.799499 | 0.399749 | − | 0.916624i | \(-0.369097\pi\) | ||||
0.399749 | + | 0.916624i | \(0.369097\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.48528 | −0.0835418 | ||||||||
\(886\) | −19.6830 | − | 11.3640i | −0.661262 | − | 0.381780i | ||||
\(887\) | 11.1924 | − | 19.3858i | 0.375804 | − | 0.650911i | −0.614643 | − | 0.788805i | \(-0.710700\pi\) |
0.990447 | + | 0.137894i | \(0.0440334\pi\) | |||||||
\(888\) | −26.4853 | − | 45.8739i | −0.888788 | − | 1.53943i | ||||
\(889\) | − | 31.7990i | − | 1.06650i | ||||||
\(890\) | −12.5446 | + | 7.24264i | −0.420497 | + | 0.242774i | ||||
\(891\) | 14.7840 | − | 8.53553i | 0.495282 | − | 0.285951i | ||||
\(892\) | − | 36.4264i | − | 1.21965i | ||||||
\(893\) | 1.41421 | + | 2.44949i | 0.0473249 | + | 0.0819690i | ||||
\(894\) | −19.8995 | + | 34.4669i | −0.665539 | + | 1.15275i | ||||
\(895\) | 4.89898 | + | 2.82843i | 0.163755 | + | 0.0945439i | ||||
\(896\) | −99.2548 | −3.31587 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 79.9411 | 2.66767 | ||||||||
\(899\) | 8.60927 | + | 4.97056i | 0.287135 | + | 0.165778i | ||||
\(900\) | 1.91421 | − | 3.31552i | 0.0638071 | − | 0.110517i | ||||
\(901\) | 1.02944 | + | 1.78304i | 0.0342955 | + | 0.0594016i | ||||
\(902\) | 26.1421i | 0.870438i | ||||||||
\(903\) | 65.4698 | − | 37.7990i | 2.17870 | − | 1.25787i | ||||
\(904\) | −33.7495 | + | 19.4853i | −1.12249 | + | 0.648071i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −16.6569 | − | 28.8505i | −0.553387 | − | 0.958494i | ||||
\(907\) | 4.60660 | − | 7.97887i | 0.152960 | − | 0.264934i | −0.779355 | − | 0.626583i | \(-0.784453\pi\) |
0.932314 | + | 0.361649i | \(0.117786\pi\) | |||||||
\(908\) | −54.1859 | − | 31.2843i | −1.79822 | − | 1.03821i | ||||
\(909\) | −3.65685 | −0.121290 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.0000 | −0.397578 | −0.198789 | − | 0.980042i | \(-0.563701\pi\) | ||||
−0.198789 | + | 0.980042i | \(0.563701\pi\) | |||||||
\(912\) | 2.15232 | + | 1.24264i | 0.0712703 | + | 0.0411479i | ||||
\(913\) | 5.41421 | − | 9.37769i | 0.179184 | − | 0.310356i | ||||
\(914\) | 21.7279 | + | 37.6339i | 0.718696 | + | 1.24482i | ||||
\(915\) | 11.3137i | 0.374020i | ||||||||
\(916\) | −16.0087 | + | 9.24264i | −0.528943 | + | 0.305385i | ||||
\(917\) | 70.9631 | − | 40.9706i | 2.34341 | − | 1.35297i | ||||
\(918\) | 11.3137i | 0.373408i | ||||||||
\(919\) | −0.242641 | − | 0.420266i | −0.00800398 | − | 0.0138633i | 0.861996 | − | 0.506916i | \(-0.169214\pi\) |
−0.870000 | + | 0.493052i | \(0.835881\pi\) | |||||||
\(920\) | −3.12132 | + | 5.40629i | −0.102907 | + | 0.178240i | ||||
\(921\) | −30.4085 | − | 17.5563i | −1.00199 | − | 0.578501i | ||||
\(922\) | 22.9706 | 0.756495 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −89.2548 | −2.93627 | ||||||||
\(925\) | 7.34847 | + | 4.24264i | 0.241616 | + | 0.139497i | ||||
\(926\) | −5.24264 | + | 9.08052i | −0.172284 | + | 0.298404i | ||||
\(927\) | −7.29289 | − | 12.6317i | −0.239530 | − | 0.414878i | ||||
\(928\) | − | 8.97056i | − | 0.294473i | ||||||
\(929\) | 14.5738 | − | 8.41421i | 0.478152 | − | 0.276061i | −0.241494 | − | 0.970402i | \(-0.577637\pi\) |
0.719646 | + | 0.694341i | \(0.244304\pi\) | |||||||
\(930\) | −5.19615 | + | 3.00000i | −0.170389 | + | 0.0983739i | ||||
\(931\) | − | 9.55635i | − | 0.313197i | ||||||
\(932\) | 39.4853 | + | 68.3905i | 1.29338 | + | 2.24021i | ||||
\(933\) | −6.00000 | + | 10.3923i | −0.196431 | + | 0.340229i | ||||
\(934\) | 28.0460 | + | 16.1924i | 0.917694 | + | 0.529831i | ||||
\(935\) | −2.82843 | −0.0924995 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.9706 | −0.750416 | −0.375208 | − | 0.926941i | \(-0.622429\pi\) | ||||
−0.375208 | + | 0.926941i | \(0.622429\pi\) | |||||||
\(938\) | −20.1903 | − | 11.6569i | −0.659235 | − | 0.380610i | ||||
\(939\) | −3.41421 | + | 5.91359i | −0.111419 | + | 0.192983i | ||||
\(940\) | −9.24264 | − | 16.0087i | −0.301462 | − | 0.522147i | ||||
\(941\) | 18.7696i | 0.611870i | 0.952052 | + | 0.305935i | \(0.0989690\pi\) | ||||
−0.952052 | + | 0.305935i | \(0.901031\pi\) | |||||||
\(942\) | 53.2223 | − | 30.7279i | 1.73408 | − | 1.00117i | ||||
\(943\) | 3.88437 | − | 2.24264i | 0.126492 | − | 0.0730304i | ||||
\(944\) | − | 5.27208i | − | 0.171592i | ||||||
\(945\) | −13.6569 | − | 23.6544i | −0.444258 | − | 0.769477i | ||||
\(946\) | 45.6274 | − | 79.0290i | 1.48348 | − | 2.56945i | ||||
\(947\) | 14.8200 | + | 8.55635i | 0.481586 | + | 0.278044i | 0.721077 | − | 0.692855i | \(-0.243647\pi\) |
−0.239491 | + | 0.970899i | \(0.576981\pi\) | |||||||
\(948\) | −45.9411 | −1.49210 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −1.41421 | −0.0458831 | ||||||||
\(951\) | −2.62357 | − | 1.51472i | −0.0850751 | − | 0.0491181i | ||||
\(952\) | 8.82843 | − | 15.2913i | 0.286131 | − | 0.495593i | ||||
\(953\) | 17.6274 | + | 30.5316i | 0.571008 | + | 0.989015i | 0.996463 | + | 0.0840352i | \(0.0267808\pi\) |
−0.425455 | + | 0.904980i | \(0.639886\pi\) | |||||||
\(954\) | 6.00000i | 0.194257i | ||||||||
\(955\) | 2.02922 | − | 1.17157i | 0.0656641 | − | 0.0379112i | ||||
\(956\) | 11.3199 | − | 6.53553i | 0.366111 | − | 0.211374i | ||||
\(957\) | − | 27.3137i | − | 0.882927i | ||||||
\(958\) | −37.0919 | − | 64.2450i | −1.19838 | − | 2.07566i | ||||
\(959\) | −41.7990 | + | 72.3980i | −1.34976 | + | 2.33785i | ||||
\(960\) | 12.0373 | + | 6.94975i | 0.388503 | + | 0.224302i | ||||
\(961\) | 27.9117 | 0.900377 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.41421 | 0.303369 | ||||||||
\(964\) | 48.0262 | + | 27.7279i | 1.54682 | + | 0.893056i | ||||
\(965\) | −2.17157 | + | 3.76127i | −0.0699054 | + | 0.121080i | ||||
\(966\) | 11.6569 | + | 20.1903i | 0.375053 | + | 0.649611i | ||||
\(967\) | 47.9411i | 1.54168i | 0.637027 | + | 0.770841i | \(0.280164\pi\) | ||||
−0.637027 | + | 0.770841i | \(0.719836\pi\) | |||||||
\(968\) | −2.51104 | + | 1.44975i | −0.0807078 | + | 0.0465966i | ||||
\(969\) | 0.594346 | − | 0.343146i | 0.0190931 | − | 0.0110234i | ||||
\(970\) | − | 18.4853i | − | 0.593527i | ||||||
\(971\) | −22.1421 | − | 38.3513i | −0.710575 | − | 1.23075i | −0.964642 | − | 0.263565i | \(-0.915102\pi\) |
0.254067 | − | 0.967187i | \(-0.418232\pi\) | |||||||
\(972\) | −18.9497 | + | 32.8219i | −0.607813 | + | 1.05276i | ||||
\(973\) | 18.7554 | + | 10.8284i | 0.601270 | + | 0.347143i | ||||
\(974\) | −26.4853 | −0.848643 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −24.0000 | −0.768221 | ||||||||
\(977\) | 34.2208 | + | 19.7574i | 1.09482 | + | 0.632094i | 0.934855 | − | 0.355029i | \(-0.115529\pi\) |
0.159964 | + | 0.987123i | \(0.448862\pi\) | |||||||
\(978\) | −32.3848 | + | 56.0921i | −1.03555 | + | 1.79363i | ||||
\(979\) | 10.2426 | + | 17.7408i | 0.327356 | + | 0.566998i | ||||
\(980\) | 62.4558i | 1.99508i | ||||||||
\(981\) | 1.73205 | − | 1.00000i | 0.0553001 | − | 0.0319275i | ||||
\(982\) | 10.8126 | − | 6.24264i | 0.345043 | − | 0.199211i | ||||
\(983\) | 1.02944i | 0.0328339i | 0.999865 | + | 0.0164170i | \(0.00522592\pi\) | ||||
−0.999865 | + | 0.0164170i | \(0.994774\pi\) | |||||||
\(984\) | 9.89949 | + | 17.1464i | 0.315584 | + | 0.546608i | ||||
\(985\) | 5.48528 | − | 9.50079i | 0.174776 | − | 0.302720i | ||||
\(986\) | 9.79796 | + | 5.65685i | 0.312031 | + | 0.180151i | ||||
\(987\) | −32.9706 | −1.04946 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15.6569 | −0.497859 | ||||||||
\(990\) | −7.13834 | − | 4.12132i | −0.226871 | − | 0.130984i | ||||
\(991\) | −24.4853 | + | 42.4098i | −0.777801 | + | 1.34719i | 0.155406 | + | 0.987851i | \(0.450331\pi\) |
−0.933207 | + | 0.359340i | \(0.883002\pi\) | |||||||
\(992\) | 1.39340 | + | 2.41344i | 0.0442404 | + | 0.0766267i | ||||
\(993\) | 36.8284i | 1.16871i | ||||||||
\(994\) | −120.127 | + | 69.3553i | −3.81020 | + | 2.19982i | ||||
\(995\) | −3.46410 | + | 2.00000i | −0.109819 | + | 0.0634043i | ||||
\(996\) | − | 17.1716i | − | 0.544102i | ||||||
\(997\) | −14.4142 | − | 24.9662i | −0.456503 | − | 0.790686i | 0.542271 | − | 0.840204i | \(-0.317565\pi\) |
−0.998773 | + | 0.0495181i | \(0.984231\pi\) | |||||||
\(998\) | −50.1630 | + | 86.8848i | −1.58788 | + | 2.75029i | ||||
\(999\) | −41.5692 | − | 24.0000i | −1.31519 | − | 0.759326i |
(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 | 845.2.m.f.316.4 | 8 | ||
13.2 | odd | 12 | 845.2.e.h.146.2 | 4 | |||
13.3 | even | 3 | inner | 845.2.m.f.361.1 | 8 | ||
13.4 | even | 6 | 845.2.c.b.506.4 | 4 | |||
13.5 | odd | 4 | 845.2.e.h.191.2 | 4 | |||
13.6 | odd | 12 | 65.2.a.b.1.1 | ✓ | 2 | ||
13.7 | odd | 12 | 845.2.a.g.1.2 | 2 | |||
13.8 | odd | 4 | 845.2.e.c.191.1 | 4 | |||
13.9 | even | 3 | 845.2.c.b.506.1 | 4 | |||
13.10 | even | 6 | inner | 845.2.m.f.361.4 | 8 | ||
13.11 | odd | 12 | 845.2.e.c.146.1 | 4 | |||
13.12 | even | 2 | inner | 845.2.m.f.316.1 | 8 | ||
39.20 | even | 12 | 7605.2.a.x.1.1 | 2 | |||
39.32 | even | 12 | 585.2.a.m.1.2 | 2 | |||
52.19 | even | 12 | 1040.2.a.j.1.2 | 2 | |||
65.19 | odd | 12 | 325.2.a.i.1.2 | 2 | |||
65.32 | even | 12 | 325.2.b.f.274.1 | 4 | |||
65.58 | even | 12 | 325.2.b.f.274.4 | 4 | |||
65.59 | odd | 12 | 4225.2.a.r.1.1 | 2 | |||
91.6 | even | 12 | 3185.2.a.j.1.1 | 2 | |||
104.19 | even | 12 | 4160.2.a.z.1.1 | 2 | |||
104.45 | odd | 12 | 4160.2.a.bf.1.2 | 2 | |||
143.32 | even | 12 | 7865.2.a.j.1.2 | 2 | |||
156.71 | odd | 12 | 9360.2.a.cd.1.1 | 2 | |||
195.32 | odd | 12 | 2925.2.c.r.2224.4 | 4 | |||
195.149 | even | 12 | 2925.2.a.u.1.1 | 2 | |||
195.188 | odd | 12 | 2925.2.c.r.2224.1 | 4 | |||
260.19 | even | 12 | 5200.2.a.bu.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.2.a.b.1.1 | ✓ | 2 | 13.6 | odd | 12 | ||
325.2.a.i.1.2 | 2 | 65.19 | odd | 12 | |||
325.2.b.f.274.1 | 4 | 65.32 | even | 12 | |||
325.2.b.f.274.4 | 4 | 65.58 | even | 12 | |||
585.2.a.m.1.2 | 2 | 39.32 | even | 12 | |||
845.2.a.g.1.2 | 2 | 13.7 | odd | 12 | |||
845.2.c.b.506.1 | 4 | 13.9 | even | 3 | |||
845.2.c.b.506.4 | 4 | 13.4 | even | 6 | |||
845.2.e.c.146.1 | 4 | 13.11 | odd | 12 | |||
845.2.e.c.191.1 | 4 | 13.8 | odd | 4 | |||
845.2.e.h.146.2 | 4 | 13.2 | odd | 12 | |||
845.2.e.h.191.2 | 4 | 13.5 | odd | 4 | |||
845.2.m.f.316.1 | 8 | 13.12 | even | 2 | inner | ||
845.2.m.f.316.4 | 8 | 1.1 | even | 1 | trivial | ||
845.2.m.f.361.1 | 8 | 13.3 | even | 3 | inner | ||
845.2.m.f.361.4 | 8 | 13.10 | even | 6 | inner | ||
1040.2.a.j.1.2 | 2 | 52.19 | even | 12 | |||
2925.2.a.u.1.1 | 2 | 195.149 | even | 12 | |||
2925.2.c.r.2224.1 | 4 | 195.188 | odd | 12 | |||
2925.2.c.r.2224.4 | 4 | 195.32 | odd | 12 | |||
3185.2.a.j.1.1 | 2 | 91.6 | even | 12 | |||
4160.2.a.z.1.1 | 2 | 104.19 | even | 12 | |||
4160.2.a.bf.1.2 | 2 | 104.45 | odd | 12 | |||
4225.2.a.r.1.1 | 2 | 65.59 | odd | 12 | |||
5200.2.a.bu.1.1 | 2 | 260.19 | even | 12 | |||
7605.2.a.x.1.1 | 2 | 39.20 | even | 12 | |||
7865.2.a.j.1.2 | 2 | 143.32 | even | 12 | |||
9360.2.a.cd.1.1 | 2 | 156.71 | odd | 12 |