Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(1457,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3150.1457");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.m (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: | \(25.1528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.1698758656.6 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 630) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 2843.2 | ||
Root | \(-0.692297i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3150.2843 |
Dual form | 3150.2.m.j.1457.1 |
$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.707107 | + | 0.707107i | −0.267261 | + | 0.267261i | ||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.77786i | 0.536046i | 0.963412 | + | 0.268023i | \(0.0863704\pi\) | ||||
−0.963412 | + | 0.268023i | \(0.913630\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.692297 | − | 0.692297i | −0.192009 | − | 0.192009i | 0.604555 | − | 0.796564i | \(-0.293351\pi\) |
−0.796564 | + | 0.604555i | \(0.793351\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −2.39327 | − | 2.39327i | −0.580453 | − | 0.580453i | 0.354575 | − | 0.935028i | \(-0.384626\pi\) |
−0.935028 | + | 0.354575i | \(0.884626\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.25714 | − | 1.25714i | 0.268023 | − | 0.268023i | ||||
\(23\) | 3.38459 | − | 3.38459i | 0.705737 | − | 0.705737i | −0.259899 | − | 0.965636i | \(-0.583689\pi\) |
0.965636 | + | 0.259899i | \(0.0836893\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.979056i | 0.192009i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.707107 | − | 0.707107i | −0.133631 | − | 0.133631i | ||||
\(29\) | 4.42289 | 0.821310 | 0.410655 | − | 0.911791i | \(-0.365300\pi\) | ||||
0.410655 | + | 0.911791i | \(0.365300\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.77786 | −1.03774 | −0.518868 | − | 0.854855i | \(-0.673646\pi\) | ||||
−0.518868 | + | 0.854855i | \(0.673646\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.38459i | 0.580453i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.91399 | + | 5.91399i | −0.972255 | + | 0.972255i | −0.999625 | − | 0.0273707i | \(-0.991287\pi\) |
0.0273707 | + | 0.999625i | \(0.491287\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 0.807922i | − | 0.126176i | −0.998008 | − | 0.0630881i | \(-0.979905\pi\) | ||
0.998008 | − | 0.0630881i | \(-0.0200949\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.64173 | + | 4.64173i | 0.707858 | + | 0.707858i | 0.966084 | − | 0.258227i | \(-0.0831381\pi\) |
−0.258227 | + | 0.966084i | \(0.583138\pi\) | |||||||
\(44\) | −1.77786 | −0.268023 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.78654 | −0.705737 | ||||||||
\(47\) | −7.47016 | − | 7.47016i | −1.08964 | − | 1.08964i | −0.995566 | − | 0.0940694i | \(-0.970012\pi\) |
−0.0940694 | − | 0.995566i | \(-0.529988\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.692297 | − | 0.692297i | 0.0960044 | − | 0.0960044i | ||||
\(53\) | 3.56484 | − | 3.56484i | 0.489669 | − | 0.489669i | −0.418533 | − | 0.908202i | \(-0.637456\pi\) |
0.908202 | + | 0.418533i | \(0.137456\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000i | 0.133631i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.12745 | − | 3.12745i | −0.410655 | − | 0.410655i | ||||
\(59\) | 5.89887 | 0.767968 | 0.383984 | − | 0.923340i | \(-0.374552\pi\) | ||||
0.383984 | + | 0.923340i | \(0.374552\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.39327 | 0.306427 | 0.153213 | − | 0.988193i | \(-0.451038\pi\) | ||||
0.153213 | + | 0.988193i | \(0.451038\pi\) | |||||||
\(62\) | 4.08557 | + | 4.08557i | 0.518868 | + | 0.518868i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.641735 | − | 0.641735i | 0.0784004 | − | 0.0784004i | −0.666819 | − | 0.745220i | \(-0.732345\pi\) |
0.745220 | + | 0.666819i | \(0.232345\pi\) | |||||||
\(68\) | 2.39327 | − | 2.39327i | 0.290227 | − | 0.290227i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 10.6854i | − | 1.26813i | −0.773282 | − | 0.634063i | \(-0.781386\pi\) | ||
0.773282 | − | 0.634063i | \(-0.218614\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.70097 | − | 5.70097i | −0.667248 | − | 0.667248i | 0.289830 | − | 0.957078i | \(-0.406401\pi\) |
−0.957078 | + | 0.289830i | \(0.906401\pi\) | |||||||
\(74\) | 8.36365 | 0.972255 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.25714 | − | 1.25714i | −0.143264 | − | 0.143264i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 16.3423i | − | 1.83865i | −0.393500 | − | 0.919324i | \(-0.628736\pi\) | ||
0.393500 | − | 0.919324i | \(-0.371264\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.571287 | + | 0.571287i | −0.0630881 | + | 0.0630881i | ||||
\(83\) | −0.171134 | + | 0.171134i | −0.0187844 | + | 0.0187844i | −0.716437 | − | 0.697652i | \(-0.754228\pi\) |
0.697652 | + | 0.716437i | \(0.254228\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 6.56440i | − | 0.707858i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.25714 | + | 1.25714i | 0.134012 | + | 0.134012i | ||||
\(89\) | 13.2340 | 1.40280 | 0.701399 | − | 0.712769i | \(-0.252559\pi\) | ||||
0.701399 | + | 0.712769i | \(0.252559\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.979056 | 0.102633 | ||||||||
\(92\) | 3.38459 | + | 3.38459i | 0.352868 | + | 0.352868i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 10.5644i | 1.08964i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.6413 | + | 12.6413i | −1.28353 | + | 1.28353i | −0.344884 | + | 0.938645i | \(0.612082\pi\) |
−0.938645 | + | 0.344884i | \(0.887918\pi\) | |||||||
\(98\) | −0.707107 | + | 0.707107i | −0.0714286 | + | 0.0714286i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 12.6778i | − | 1.26149i | −0.775991 | − | 0.630744i | \(-0.782750\pi\) | ||
0.775991 | − | 0.630744i | \(-0.217250\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.43472 | − | 7.43472i | −0.732565 | − | 0.732565i | 0.238563 | − | 0.971127i | \(-0.423324\pi\) |
−0.971127 | + | 0.238563i | \(0.923324\pi\) | |||||||
\(104\) | −0.979056 | −0.0960044 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.04145 | −0.489669 | ||||||||
\(107\) | 13.5138 | + | 13.5138i | 1.30643 | + | 1.30643i | 0.923972 | + | 0.382461i | \(0.124923\pi\) |
0.382461 | + | 0.923972i | \(0.375077\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.30082i | 0.316161i | 0.987426 | + | 0.158081i | \(0.0505306\pi\) | ||||
−0.987426 | + | 0.158081i | \(0.949469\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.707107 | − | 0.707107i | 0.0668153 | − | 0.0668153i | ||||
\(113\) | 5.84937 | − | 5.84937i | 0.550263 | − | 0.550263i | −0.376254 | − | 0.926517i | \(-0.622788\pi\) |
0.926517 | + | 0.376254i | \(0.122788\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.42289i | 0.410655i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.17113 | − | 4.17113i | −0.383984 | − | 0.383984i | ||||
\(119\) | 3.38459 | 0.310265 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.83920 | 0.712654 | ||||||||
\(122\) | −1.69230 | − | 1.69230i | −0.153213 | − | 0.153213i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 5.77786i | − | 0.518868i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.615405 | − | 0.615405i | 0.0546084 | − | 0.0546084i | −0.679275 | − | 0.733884i | \(-0.737706\pi\) |
0.733884 | + | 0.679275i | \(0.237706\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 6.52717i | − | 0.570281i | −0.958486 | − | 0.285141i | \(-0.907960\pi\) | ||
0.958486 | − | 0.285141i | \(-0.0920403\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.907550 | −0.0784004 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.38459 | −0.290227 | ||||||||
\(137\) | −0.192517 | − | 0.192517i | −0.0164478 | − | 0.0164478i | 0.698835 | − | 0.715283i | \(-0.253702\pi\) |
−0.715283 | + | 0.698835i | \(0.753702\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 14.8694i | − | 1.26121i | −0.776104 | − | 0.630605i | \(-0.782807\pi\) | ||
0.776104 | − | 0.630605i | \(-0.217193\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.55573 | + | 7.55573i | −0.634063 | + | 0.634063i | ||||
\(143\) | 1.23081 | − | 1.23081i | 0.102926 | − | 0.102926i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 8.06239i | 0.667248i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.91399 | − | 5.91399i | −0.486127 | − | 0.486127i | ||||
\(149\) | −20.6467 | −1.69144 | −0.845721 | − | 0.533625i | \(-0.820829\pi\) | ||||
−0.845721 | + | 0.533625i | \(0.820829\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.01735 | 0.489685 | 0.244843 | − | 0.969563i | \(-0.421264\pi\) | ||||
0.244843 | + | 0.969563i | \(0.421264\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.77786i | 0.143264i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.608522 | − | 0.608522i | 0.0485654 | − | 0.0485654i | −0.682407 | − | 0.730972i | \(-0.739067\pi\) |
0.730972 | + | 0.682407i | \(0.239067\pi\) | |||||||
\(158\) | −11.5557 | + | 11.5557i | −0.919324 | + | 0.919324i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.78654i | 0.377232i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.12745 | − | 6.12745i | −0.479939 | − | 0.479939i | 0.425173 | − | 0.905112i | \(-0.360213\pi\) |
−0.905112 | + | 0.425173i | \(0.860213\pi\) | |||||||
\(164\) | 0.807922 | 0.0630881 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.242020 | 0.0187844 | ||||||||
\(167\) | −6.18669 | − | 6.18669i | −0.478741 | − | 0.478741i | 0.425988 | − | 0.904729i | \(-0.359927\pi\) |
−0.904729 | + | 0.425988i | \(0.859927\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 12.0414i | − | 0.926265i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.64173 | + | 4.64173i | −0.353929 | + | 0.353929i | ||||
\(173\) | 15.7720 | − | 15.7720i | 1.19913 | − | 1.19913i | 0.224697 | − | 0.974429i | \(-0.427861\pi\) |
0.974429 | − | 0.224697i | \(-0.0721394\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 1.77786i | − | 0.134012i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −9.35783 | − | 9.35783i | −0.701399 | − | 0.701399i | ||||
\(179\) | −3.87899 | −0.289929 | −0.144965 | − | 0.989437i | \(-0.546307\pi\) | ||||
−0.144965 | + | 0.989437i | \(0.546307\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.6896 | 1.76084 | 0.880418 | − | 0.474198i | \(-0.157262\pi\) | ||||
0.880418 | + | 0.474198i | \(0.157262\pi\) | |||||||
\(182\) | −0.692297 | − | 0.692297i | −0.0513165 | − | 0.0513165i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 4.78654i | − | 0.352868i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.25491 | − | 4.25491i | 0.311150 | − | 0.311150i | ||||
\(188\) | 7.47016 | − | 7.47016i | 0.544818 | − | 0.544818i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 23.4720i | − | 1.69837i | −0.528095 | − | 0.849185i | \(-0.677093\pi\) | ||
0.528095 | − | 0.849185i | \(-0.322907\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.1288 | − | 18.1288i | −1.30494 | − | 1.30494i | −0.925019 | − | 0.379921i | \(-0.875951\pi\) |
−0.379921 | − | 0.925019i | \(-0.624049\pi\) | |||||||
\(194\) | 17.8775 | 1.28353 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 9.58535 | + | 9.58535i | 0.682928 | + | 0.682928i | 0.960659 | − | 0.277731i | \(-0.0895824\pi\) |
−0.277731 | + | 0.960659i | \(0.589582\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.46416i | 0.174679i | 0.996179 | + | 0.0873397i | \(0.0278366\pi\) | ||||
−0.996179 | + | 0.0873397i | \(0.972163\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8.96456 | + | 8.96456i | −0.630744 | + | 0.630744i | ||||
\(203\) | −3.12745 | + | 3.12745i | −0.219504 | + | 0.219504i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 10.5143i | 0.732565i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.692297 | + | 0.692297i | 0.0480022 | + | 0.0480022i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.57308 | −0.383667 | −0.191833 | − | 0.981428i | \(-0.561443\pi\) | ||||
−0.191833 | + | 0.981428i | \(0.561443\pi\) | |||||||
\(212\) | 3.56484 | + | 3.56484i | 0.244834 | + | 0.244834i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 19.1115i | − | 1.30643i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.08557 | − | 4.08557i | 0.277346 | − | 0.277346i | ||||
\(218\) | 2.33403 | − | 2.33403i | 0.158081 | − | 0.158081i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.31371i | 0.222904i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.6854 | + | 14.6854i | 0.983408 | + | 0.983408i | 0.999865 | − | 0.0164565i | \(-0.00523851\pi\) |
−0.0164565 | + | 0.999865i | \(0.505239\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.27226 | −0.550263 | ||||||||
\(227\) | −19.5557 | − | 19.5557i | −1.29796 | − | 1.29796i | −0.929738 | − | 0.368221i | \(-0.879967\pi\) |
−0.368221 | − | 0.929738i | \(-0.620033\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.3622i | 1.60990i | 0.593345 | + | 0.804948i | \(0.297807\pi\) | ||||
−0.593345 | + | 0.804948i | \(0.702193\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.12745 | − | 3.12745i | 0.205327 | − | 0.205327i | ||||
\(233\) | 14.7692 | − | 14.7692i | 0.967562 | − | 0.967562i | −0.0319284 | − | 0.999490i | \(-0.510165\pi\) |
0.999490 | + | 0.0319284i | \(0.0101649\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 5.89887i | 0.383984i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.39327 | − | 2.39327i | −0.155133 | − | 0.155133i | ||||
\(239\) | −1.47283 | −0.0952695 | −0.0476348 | − | 0.998865i | \(-0.515168\pi\) | ||||
−0.0476348 | + | 0.998865i | \(0.515168\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.5557 | −1.38853 | −0.694263 | − | 0.719721i | \(-0.744270\pi\) | ||||
−0.694263 | + | 0.719721i | \(0.744270\pi\) | |||||||
\(242\) | −5.54315 | − | 5.54315i | −0.356327 | − | 0.356327i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.39327i | 0.153213i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −4.08557 | + | 4.08557i | −0.259434 | + | 0.259434i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 2.68541i | − | 0.169502i | −0.996402 | − | 0.0847509i | \(-0.972991\pi\) | ||
0.996402 | − | 0.0847509i | \(-0.0270095\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.01735 | + | 6.01735i | 0.378308 | + | 0.378308i | ||||
\(254\) | −0.870315 | −0.0546084 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −10.9873 | − | 10.9873i | −0.685368 | − | 0.685368i | 0.275836 | − | 0.961205i | \(-0.411045\pi\) |
−0.961205 | + | 0.275836i | \(0.911045\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 8.36365i | − | 0.519692i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.61541 | + | 4.61541i | −0.285141 | + | 0.285141i | ||||
\(263\) | −7.92911 | + | 7.92911i | −0.488930 | + | 0.488930i | −0.907969 | − | 0.419038i | \(-0.862367\pi\) |
0.419038 | + | 0.907969i | \(0.362367\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.641735 | + | 0.641735i | 0.0392002 | + | 0.0392002i | ||||
\(269\) | −7.26420 | −0.442906 | −0.221453 | − | 0.975171i | \(-0.571080\pi\) | ||||
−0.221453 | + | 0.975171i | \(0.571080\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.5756 | −1.06764 | −0.533821 | − | 0.845597i | \(-0.679244\pi\) | ||||
−0.533821 | + | 0.845597i | \(0.679244\pi\) | |||||||
\(272\) | 2.39327 | + | 2.39327i | 0.145113 | + | 0.145113i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.272260i | 0.0164478i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.81287 | − | 9.81287i | 0.589598 | − | 0.589598i | −0.347924 | − | 0.937523i | \(-0.613113\pi\) |
0.937523 | + | 0.347924i | \(0.113113\pi\) | |||||||
\(278\) | −10.5143 | + | 10.5143i | −0.630605 | + | 0.630605i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.5849i | 0.750753i | 0.926872 | + | 0.375376i | \(0.122487\pi\) | ||||
−0.926872 | + | 0.375376i | \(0.877513\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.69918 | − | 4.69918i | −0.279337 | − | 0.279337i | 0.553507 | − | 0.832844i | \(-0.313289\pi\) |
−0.832844 | + | 0.553507i | \(0.813289\pi\) | |||||||
\(284\) | 10.6854 | 0.634063 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.74063 | −0.102926 | ||||||||
\(287\) | 0.571287 | + | 0.571287i | 0.0337220 | + | 0.0337220i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 5.54452i | − | 0.326148i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.70097 | − | 5.70097i | 0.333624 | − | 0.333624i | ||||
\(293\) | 3.39866 | − | 3.39866i | 0.198552 | − | 0.198552i | −0.600827 | − | 0.799379i | \(-0.705162\pi\) |
0.799379 | + | 0.600827i | \(0.205162\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 8.36365i | 0.486127i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 14.5994 | + | 14.5994i | 0.845721 | + | 0.845721i | ||||
\(299\) | −4.68629 | −0.271015 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.56440 | −0.378366 | ||||||||
\(302\) | −4.25491 | − | 4.25491i | −0.244843 | − | 0.244843i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.5557 | − | 15.5557i | 0.887812 | − | 0.887812i | −0.106500 | − | 0.994313i | \(-0.533965\pi\) |
0.994313 | + | 0.106500i | \(0.0339645\pi\) | |||||||
\(308\) | 1.25714 | − | 1.25714i | 0.0716322 | − | 0.0716322i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.773651i | 0.0438697i | 0.999759 | + | 0.0219349i | \(0.00698264\pi\) | ||||
−0.999759 | + | 0.0219349i | \(0.993017\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.8548 | + | 11.8548i | 0.670070 | + | 0.670070i | 0.957732 | − | 0.287662i | \(-0.0928779\pi\) |
−0.287662 | + | 0.957732i | \(0.592878\pi\) | |||||||
\(314\) | −0.860580 | −0.0485654 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 16.3423 | 0.919324 | ||||||||
\(317\) | −0.00911383 | − | 0.00911383i | −0.000511884 | − | 0.000511884i | 0.706851 | − | 0.707363i | \(-0.250115\pi\) |
−0.707363 | + | 0.706851i | \(0.750115\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.86330i | 0.440260i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.38459 | − | 3.38459i | 0.188616 | − | 0.188616i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8.66553i | 0.479939i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.571287 | − | 0.571287i | −0.0315441 | − | 0.0315441i | ||||
\(329\) | 10.5644 | 0.582434 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.7977 | −1.30804 | −0.654021 | − | 0.756476i | \(-0.726919\pi\) | ||||
−0.654021 | + | 0.756476i | \(0.726919\pi\) | |||||||
\(332\) | −0.171134 | − | 0.171134i | −0.00939221 | − | 0.00939221i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.74930i | 0.478741i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.828866 | − | 0.828866i | 0.0451512 | − | 0.0451512i | −0.684171 | − | 0.729322i | \(-0.739836\pi\) |
0.729322 | + | 0.684171i | \(0.239836\pi\) | |||||||
\(338\) | −8.51459 | + | 8.51459i | −0.463133 | + | 0.463133i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 10.2723i | − | 0.556274i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.707107 | + | 0.707107i | 0.0381802 | + | 0.0381802i | ||||
\(344\) | 6.56440 | 0.353929 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −22.3050 | −1.19913 | ||||||||
\(347\) | −5.17157 | − | 5.17157i | −0.277625 | − | 0.277625i | 0.554535 | − | 0.832160i | \(-0.312896\pi\) |
−0.832160 | + | 0.554535i | \(0.812896\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 4.20837i | − | 0.225269i | −0.993636 | − | 0.112634i | \(-0.964071\pi\) | ||
0.993636 | − | 0.112634i | \(-0.0359289\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.25714 | + | 1.25714i | −0.0670058 | + | 0.0670058i | ||||
\(353\) | −2.22214 | + | 2.22214i | −0.118272 | + | 0.118272i | −0.763766 | − | 0.645493i | \(-0.776652\pi\) |
0.645493 | + | 0.763766i | \(0.276652\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 13.2340i | 0.701399i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.74286 | + | 2.74286i | 0.144965 | + | 0.144965i | ||||
\(359\) | −22.7692 | −1.20171 | −0.600856 | − | 0.799357i | \(-0.705173\pi\) | ||||
−0.600856 | + | 0.799357i | \(0.705173\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.0000 | 1.00000 | ||||||||
\(362\) | −16.7511 | − | 16.7511i | −0.880418 | − | 0.880418i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.979056i | 0.0513165i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.13836 | + | 2.13836i | −0.111622 | + | 0.111622i | −0.760712 | − | 0.649090i | \(-0.775150\pi\) |
0.649090 | + | 0.760712i | \(0.275150\pi\) | |||||||
\(368\) | −3.38459 | + | 3.38459i | −0.176434 | + | 0.176434i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.04145i | 0.261739i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.0263 | − | 13.0263i | −0.674478 | − | 0.674478i | 0.284267 | − | 0.958745i | \(-0.408250\pi\) |
−0.958745 | + | 0.284267i | \(0.908250\pi\) | |||||||
\(374\) | −6.01735 | −0.311150 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.5644 | −0.544818 | ||||||||
\(377\) | −3.06195 | − | 3.06195i | −0.157699 | − | 0.157699i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 27.4011i | − | 1.40750i | −0.710449 | − | 0.703749i | \(-0.751508\pi\) | ||
0.710449 | − | 0.703749i | \(-0.248492\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −16.5972 | + | 16.5972i | −0.849185 | + | 0.849185i | ||||
\(383\) | 17.6715 | − | 17.6715i | 0.902973 | − | 0.902973i | −0.0927190 | − | 0.995692i | \(-0.529556\pi\) |
0.995692 | + | 0.0927190i | \(0.0295558\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 25.6380i | 1.30494i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −12.6413 | − | 12.6413i | −0.641765 | − | 0.641765i | ||||
\(389\) | −15.8356 | −0.802897 | −0.401449 | − | 0.915882i | \(-0.631493\pi\) | ||||
−0.401449 | + | 0.915882i | \(0.631493\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.2005 | −0.819294 | ||||||||
\(392\) | −0.707107 | − | 0.707107i | −0.0357143 | − | 0.0357143i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 13.5557i | − | 0.682928i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.5575 | − | 14.5575i | 0.730621 | − | 0.730621i | −0.240122 | − | 0.970743i | \(-0.577187\pi\) |
0.970743 | + | 0.240122i | \(0.0771874\pi\) | |||||||
\(398\) | 1.74242 | − | 1.74242i | 0.0873397 | − | 0.0873397i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.78102i | 0.488441i | 0.969720 | + | 0.244220i | \(0.0785320\pi\) | ||||
−0.969720 | + | 0.244220i | \(0.921468\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.00000 | + | 4.00000i | 0.199254 | + | 0.199254i | ||||
\(404\) | 12.6778 | 0.630744 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.42289 | 0.219504 | ||||||||
\(407\) | −10.5143 | − | 10.5143i | −0.521174 | − | 0.521174i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.3907i | 0.513789i | 0.966439 | + | 0.256894i | \(0.0826993\pi\) | ||||
−0.966439 | + | 0.256894i | \(0.917301\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7.43472 | − | 7.43472i | 0.366282 | − | 0.366282i | ||||
\(413\) | −4.17113 | + | 4.17113i | −0.205248 | + | 0.205248i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 0.979056i | − | 0.0480022i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −32.8521 | −1.60493 | −0.802465 | − | 0.596700i | \(-0.796478\pi\) | ||||
−0.802465 | + | 0.596700i | \(0.796478\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.6560 | 1.64029 | 0.820146 | − | 0.572154i | \(-0.193892\pi\) | ||||
0.820146 | + | 0.572154i | \(0.193892\pi\) | |||||||
\(422\) | 3.94076 | + | 3.94076i | 0.191833 | + | 0.191833i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 5.04145i | − | 0.244834i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.69230 | + | 1.69230i | −0.0818960 | + | 0.0818960i | ||||
\(428\) | −13.5138 | + | 13.5138i | −0.653216 | + | 0.653216i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.4260i | 1.36923i | 0.728903 | + | 0.684617i | \(0.240031\pi\) | ||||
−0.728903 | + | 0.684617i | \(0.759969\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.84355 | + | 8.84355i | 0.424994 | + | 0.424994i | 0.886919 | − | 0.461925i | \(-0.152841\pi\) |
−0.461925 | + | 0.886919i | \(0.652841\pi\) | |||||||
\(434\) | −5.77786 | −0.277346 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.30082 | −0.158081 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.481506i | 0.0229810i | 0.999934 | + | 0.0114905i | \(0.00365763\pi\) | ||||
−0.999934 | + | 0.0114905i | \(0.996342\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.34315 | − | 2.34315i | 0.111452 | − | 0.111452i | ||||
\(443\) | −15.8570 | + | 15.8570i | −0.753388 | + | 0.753388i | −0.975110 | − | 0.221722i | \(-0.928832\pi\) |
0.221722 | + | 0.975110i | \(0.428832\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 20.7683i | − | 0.983408i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.707107 | + | 0.707107i | 0.0334077 | + | 0.0334077i | ||||
\(449\) | 31.8986 | 1.50539 | 0.752694 | − | 0.658370i | \(-0.228754\pi\) | ||||
0.752694 | + | 0.658370i | \(0.228754\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.43638 | 0.0676363 | ||||||||
\(452\) | 5.84937 | + | 5.84937i | 0.275131 | + | 0.275131i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 27.6560i | 1.29796i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.5557 | + | 20.5557i | −0.961556 | + | 0.961556i | −0.999288 | − | 0.0377315i | \(-0.987987\pi\) |
0.0377315 | + | 0.999288i | \(0.487987\pi\) | |||||||
\(458\) | 17.2266 | − | 17.2266i | 0.804948 | − | 0.804948i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 35.9849i | − | 1.67599i | −0.545682 | − | 0.837993i | \(-0.683729\pi\) | ||
0.545682 | − | 0.837993i | \(-0.316271\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.8703 | + | 12.8703i | 0.598134 | + | 0.598134i | 0.939816 | − | 0.341682i | \(-0.110996\pi\) |
−0.341682 | + | 0.939816i | \(0.610996\pi\) | |||||||
\(464\) | −4.42289 | −0.205327 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20.8868 | −0.967562 | ||||||||
\(467\) | 0.531630 | + | 0.531630i | 0.0246009 | + | 0.0246009i | 0.719300 | − | 0.694699i | \(-0.244463\pi\) |
−0.694699 | + | 0.719300i | \(0.744463\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.907550i | 0.0419068i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.17113 | − | 4.17113i | 0.191992 | − | 0.191992i | ||||
\(473\) | −8.25237 | + | 8.25237i | −0.379445 | + | 0.379445i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.38459i | 0.155133i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.04145 | + | 1.04145i | 0.0476348 | + | 0.0476348i | ||||
\(479\) | −23.0588 | −1.05358 | −0.526792 | − | 0.849994i | \(-0.676605\pi\) | ||||
−0.526792 | + | 0.849994i | \(0.676605\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.18848 | 0.373363 | ||||||||
\(482\) | 15.2422 | + | 15.2422i | 0.694263 | + | 0.694263i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.83920i | 0.356327i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.9291 | − | 15.9291i | 0.721817 | − | 0.721817i | −0.247158 | − | 0.968975i | \(-0.579497\pi\) |
0.968975 | + | 0.247158i | \(0.0794967\pi\) | |||||||
\(488\) | 1.69230 | − | 1.69230i | 0.0766067 | − | 0.0766067i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.3509i | 0.512261i | 0.966642 | + | 0.256130i | \(0.0824477\pi\) | ||||
−0.966642 | + | 0.256130i | \(0.917552\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.5852 | − | 10.5852i | −0.476732 | − | 0.476732i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.77786 | 0.259434 | ||||||||
\(497\) | 7.55573 | + | 7.55573i | 0.338921 | + | 0.338921i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.6319i | 0.923610i | 0.886982 | + | 0.461805i | \(0.152798\pi\) | ||||
−0.886982 | + | 0.461805i | \(0.847202\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.89887 | + | 1.89887i | −0.0847509 | + | 0.0847509i | ||||
\(503\) | −21.2982 | + | 21.2982i | −0.949638 | + | 0.949638i | −0.998791 | − | 0.0491536i | \(-0.984348\pi\) |
0.0491536 | + | 0.998791i | \(0.484348\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 8.50982i | − | 0.378308i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.615405 | + | 0.615405i | 0.0273042 | + | 0.0273042i | ||||
\(509\) | −8.13328 | −0.360501 | −0.180251 | − | 0.983621i | \(-0.557691\pi\) | ||||
−0.180251 | + | 0.983621i | \(0.557691\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.06239 | 0.356659 | ||||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 15.5384i | 0.685368i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.2809 | − | 13.2809i | 0.584095 | − | 0.584095i | ||||
\(518\) | −5.91399 | + | 5.91399i | −0.259846 | + | 0.259846i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 19.2331i | − | 0.842617i | −0.906917 | − | 0.421308i | \(-0.861571\pi\) | ||
0.906917 | − | 0.421308i | \(-0.138429\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.22635 | + | 3.22635i | 0.141078 | + | 0.141078i | 0.774119 | − | 0.633040i | \(-0.218193\pi\) |
−0.633040 | + | 0.774119i | \(0.718193\pi\) | |||||||
\(524\) | 6.52717 | 0.285141 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.2135 | 0.488930 | ||||||||
\(527\) | 13.8280 | + | 13.8280i | 0.602357 | + | 0.602357i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.0890385i | 0.00387124i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.559322 | + | 0.559322i | −0.0242269 | + | 0.0242269i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 0.907550i | − | 0.0392002i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.13657 | + | 5.13657i | 0.221453 | + | 0.221453i | ||||
\(539\) | 1.77786 | 0.0765780 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.9412 | −0.556386 | −0.278193 | − | 0.960525i | \(-0.589735\pi\) | ||||
−0.278193 | + | 0.960525i | \(0.589735\pi\) | |||||||
\(542\) | 12.4278 | + | 12.4278i | 0.533821 | + | 0.533821i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 3.38459i | − | 0.145113i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.15601 | + | 7.15601i | −0.305969 | + | 0.305969i | −0.843344 | − | 0.537375i | \(-0.819416\pi\) |
0.537375 | + | 0.843344i | \(0.319416\pi\) | |||||||
\(548\) | 0.192517 | − | 0.192517i | 0.00822390 | − | 0.00822390i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.5557 | + | 11.5557i | 0.491400 | + | 0.491400i | ||||
\(554\) | −13.8775 | −0.589598 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 14.8694 | 0.630605 | ||||||||
\(557\) | 19.5648 | + | 19.5648i | 0.828989 | + | 0.828989i | 0.987377 | − | 0.158388i | \(-0.0506297\pi\) |
−0.158388 | + | 0.987377i | \(0.550630\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 6.42692i | − | 0.271830i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.89887 | − | 8.89887i | 0.375376 | − | 0.375376i | ||||
\(563\) | −0.0708861 | + | 0.0708861i | −0.00298749 | + | 0.00298749i | −0.708599 | − | 0.705611i | \(-0.750672\pi\) |
0.705611 | + | 0.708599i | \(0.250672\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 6.64564i | 0.279337i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.55573 | − | 7.55573i | −0.317031 | − | 0.317031i | ||||
\(569\) | 20.2232 | 0.847799 | 0.423900 | − | 0.905709i | \(-0.360661\pi\) | ||||
0.423900 | + | 0.905709i | \(0.360661\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.9439 | 1.46236 | 0.731179 | − | 0.682186i | \(-0.238971\pi\) | ||||
0.731179 | + | 0.682186i | \(0.238971\pi\) | |||||||
\(572\) | 1.23081 | + | 1.23081i | 0.0514628 | + | 0.0514628i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 0.807922i | − | 0.0337220i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −32.2853 | + | 32.2853i | −1.34405 | + | 1.34405i | −0.452071 | + | 0.891982i | \(0.649315\pi\) |
−0.891982 | + | 0.452071i | \(0.850685\pi\) | |||||||
\(578\) | −3.92057 | + | 3.92057i | −0.163074 | + | 0.163074i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 0.242020i | − | 0.0100407i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.33781 | + | 6.33781i | 0.262485 | + | 0.262485i | ||||
\(584\) | −8.06239 | −0.333624 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.80642 | −0.198552 | ||||||||
\(587\) | −9.40194 | − | 9.40194i | −0.388060 | − | 0.388060i | 0.485935 | − | 0.873995i | \(-0.338479\pi\) |
−0.873995 | + | 0.485935i | \(0.838479\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.91399 | − | 5.91399i | 0.243064 | − | 0.243064i | ||||
\(593\) | 0.326416 | − | 0.326416i | 0.0134043 | − | 0.0134043i | −0.700373 | − | 0.713777i | \(-0.746983\pi\) |
0.713777 | + | 0.700373i | \(0.246983\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 20.6467i | − | 0.845721i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.31371 | + | 3.31371i | 0.135508 | + | 0.135508i | ||||
\(599\) | −29.1288 | −1.19017 | −0.595085 | − | 0.803662i | \(-0.702882\pi\) | ||||
−0.595085 | + | 0.803662i | \(0.702882\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 45.0579 | 1.83795 | 0.918975 | − | 0.394315i | \(-0.129018\pi\) | ||||
0.918975 | + | 0.394315i | \(0.129018\pi\) | |||||||
\(602\) | 4.64173 | + | 4.64173i | 0.189183 | + | 0.189183i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6.01735i | 0.244843i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.68541 | + | 6.68541i | −0.271353 | + | 0.271353i | −0.829645 | − | 0.558292i | \(-0.811457\pi\) |
0.558292 | + | 0.829645i | \(0.311457\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.3431i | 0.418439i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.5112 | + | 20.5112i | 0.828438 | + | 0.828438i | 0.987301 | − | 0.158862i | \(-0.0507826\pi\) |
−0.158862 | + | 0.987301i | \(0.550783\pi\) | |||||||
\(614\) | −21.9991 | −0.887812 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.77786 | −0.0716322 | ||||||||
\(617\) | −4.29214 | − | 4.29214i | −0.172795 | − | 0.172795i | 0.615411 | − | 0.788206i | \(-0.288990\pi\) |
−0.788206 | + | 0.615411i | \(0.788990\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.16755i | 0.328282i | 0.986437 | + | 0.164141i | \(0.0524851\pi\) | ||||
−0.986437 | + | 0.164141i | \(0.947515\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0.547054 | − | 0.547054i | 0.0219349 | − | 0.0219349i | ||||
\(623\) | −9.35783 | + | 9.35783i | −0.374913 | + | 0.374913i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 16.7652i | − | 0.670070i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.608522 | + | 0.608522i | 0.0242827 | + | 0.0242827i | ||||
\(629\) | 28.3076 | 1.12870 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.8694 | 1.54737 | 0.773684 | − | 0.633572i | \(-0.218412\pi\) | ||||
0.773684 | + | 0.633572i | \(0.218412\pi\) | |||||||
\(632\) | −11.5557 | − | 11.5557i | −0.459662 | − | 0.459662i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.0128889i | 0.000511884i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.692297 | + | 0.692297i | −0.0274298 | + | 0.0274298i | ||||
\(638\) | 5.56019 | − | 5.56019i | 0.220130 | − | 0.220130i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 20.0751i | − | 0.792918i | −0.918052 | − | 0.396459i | \(-0.870239\pi\) | ||
0.918052 | − | 0.396459i | \(-0.129761\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.6257 | + | 13.6257i | 0.537347 | + | 0.537347i | 0.922749 | − | 0.385402i | \(-0.125937\pi\) |
−0.385402 | + | 0.922749i | \(0.625937\pi\) | |||||||
\(644\) | −4.78654 | −0.188616 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.47104 | + | 1.47104i | 0.0578325 | + | 0.0578325i | 0.735432 | − | 0.677599i | \(-0.236979\pi\) |
−0.677599 | + | 0.735432i | \(0.736979\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.4874i | 0.411666i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.12745 | − | 6.12745i | 0.239970 | − | 0.239970i | ||||
\(653\) | 4.09647 | − | 4.09647i | 0.160307 | − | 0.160307i | −0.622396 | − | 0.782703i | \(-0.713840\pi\) |
0.782703 | + | 0.622396i | \(0.213840\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.807922i | 0.0315441i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −7.47016 | − | 7.47016i | −0.291217 | − | 0.291217i | ||||
\(659\) | −0.683757 | −0.0266354 | −0.0133177 | − | 0.999911i | \(-0.504239\pi\) | ||||
−0.0133177 | + | 0.999911i | \(0.504239\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −42.9776 | −1.67163 | −0.835817 | − | 0.549009i | \(-0.815005\pi\) | ||||
−0.835817 | + | 0.549009i | \(0.815005\pi\) | |||||||
\(662\) | 16.8275 | + | 16.8275i | 0.654021 | + | 0.654021i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.242020i | 0.00939221i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.9697 | − | 14.9697i | 0.579629 | − | 0.579629i | ||||
\(668\) | 6.18669 | − | 6.18669i | 0.239370 | − | 0.239370i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.25491i | 0.164259i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.6569 | + | 24.6569i | 0.950452 | + | 0.950452i | 0.998829 | − | 0.0483773i | \(-0.0154050\pi\) |
−0.0483773 | + | 0.998829i | \(0.515405\pi\) | |||||||
\(674\) | −1.17219 | −0.0451512 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 12.0414 | 0.463133 | ||||||||
\(677\) | 31.2343 | + | 31.2343i | 1.20043 | + | 1.20043i | 0.974036 | + | 0.226394i | \(0.0726938\pi\) |
0.226394 | + | 0.974036i | \(0.427306\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 17.8775i | − | 0.686075i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.26358 | + | 7.26358i | −0.278137 | + | 0.278137i | ||||
\(683\) | −7.92000 | + | 7.92000i | −0.303050 | + | 0.303050i | −0.842206 | − | 0.539156i | \(-0.818743\pi\) |
0.539156 | + | 0.842206i | \(0.318743\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 1.00000i | − | 0.0381802i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.64173 | − | 4.64173i | −0.176964 | − | 0.176964i | ||||
\(689\) | −4.93586 | −0.188041 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.1227 | 0.841586 | 0.420793 | − | 0.907157i | \(-0.361752\pi\) | ||||
0.420793 | + | 0.907157i | \(0.361752\pi\) | |||||||
\(692\) | 15.7720 | + | 15.7720i | 0.599563 | + | 0.599563i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.31371i | 0.277625i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.93358 | + | 1.93358i | −0.0732394 | + | 0.0732394i | ||||
\(698\) | −2.97577 | + | 2.97577i | −0.112634 | + | 0.112634i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.16352i | 0.232793i | 0.993203 | + | 0.116396i | \(0.0371343\pi\) | ||||
−0.993203 | + | 0.116396i | \(0.962866\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 1.77786 | 0.0670058 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.14257 | 0.118272 | ||||||||
\(707\) | 8.96456 | + | 8.96456i | 0.337147 | + | 0.337147i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 49.7215i | 1.86733i | 0.358146 | + | 0.933666i | \(0.383409\pi\) | ||||
−0.358146 | + | 0.933666i | \(0.616591\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9.35783 | − | 9.35783i | 0.350699 | − | 0.350699i | ||||
\(713\) | −19.5557 | + | 19.5557i | −0.732368 | + | 0.732368i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 3.87899i | − | 0.144965i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 16.1002 | + | 16.1002i | 0.600856 | + | 0.600856i | ||||
\(719\) | 16.9706 | 0.632895 | 0.316448 | − | 0.948610i | \(-0.397510\pi\) | ||||
0.316448 | + | 0.948610i | \(0.397510\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.5143 | 0.391572 | ||||||||
\(722\) | −13.4350 | − | 13.4350i | −0.500000 | − | 0.500000i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 23.6896i | 0.880418i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.9162 | − | 15.9162i | 0.590300 | − | 0.590300i | −0.347412 | − | 0.937712i | \(-0.612940\pi\) |
0.937712 | + | 0.347412i | \(0.112940\pi\) | |||||||
\(728\) | 0.692297 | − | 0.692297i | 0.0256582 | − | 0.0256582i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 22.2178i | − | 0.821757i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.3578 | + | 15.3578i | 0.567254 | + | 0.567254i | 0.931358 | − | 0.364104i | \(-0.118625\pi\) |
−0.364104 | + | 0.931358i | \(0.618625\pi\) | |||||||
\(734\) | 3.02410 | 0.111622 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.78654 | 0.176434 | ||||||||
\(737\) | 1.14092 | + | 1.14092i | 0.0420262 | + | 0.0420262i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 45.6515i | − | 1.67932i | −0.543114 | − | 0.839659i | \(-0.682755\pi\) | ||
0.543114 | − | 0.839659i | \(-0.317245\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.56484 | − | 3.56484i | 0.130869 | − | 0.130869i | ||||
\(743\) | −5.67508 | + | 5.67508i | −0.208199 | + | 0.208199i | −0.803501 | − | 0.595303i | \(-0.797032\pi\) |
0.595303 | + | 0.803501i | \(0.297032\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 18.4220i | 0.674478i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.25491 | + | 4.25491i | 0.155575 | + | 0.155575i | ||||
\(749\) | −19.1115 | −0.698317 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −41.4364 | −1.51203 | −0.756017 | − | 0.654552i | \(-0.772857\pi\) | ||||
−0.756017 | + | 0.654552i | \(0.772857\pi\) | |||||||
\(752\) | 7.47016 | + | 7.47016i | 0.272409 | + | 0.272409i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.33026i | 0.157699i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.4109 | − | 22.4109i | 0.814539 | − | 0.814539i | −0.170772 | − | 0.985311i | \(-0.554626\pi\) |
0.985311 | + | 0.170772i | \(0.0546261\pi\) | |||||||
\(758\) | −19.3755 | + | 19.3755i | −0.703749 | + | 0.703749i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 15.1675i | − | 0.549823i | −0.961470 | − | 0.274911i | \(-0.911351\pi\) | ||
0.961470 | − | 0.274911i | \(-0.0886485\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.33403 | − | 2.33403i | −0.0844976 | − | 0.0844976i | ||||
\(764\) | 23.4720 | 0.849185 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −24.9913 | −0.902973 | ||||||||
\(767\) | −4.08378 | − | 4.08378i | −0.147457 | − | 0.147457i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 19.8686i | − | 0.716481i | −0.933629 | − | 0.358241i | \(-0.883377\pi\) | ||
0.933629 | − | 0.358241i | \(-0.116623\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 18.1288 | − | 18.1288i | 0.652470 | − | 0.652470i | ||||
\(773\) | −0.293937 | + | 0.293937i | −0.0105722 | + | 0.0105722i | −0.712373 | − | 0.701801i | \(-0.752380\pi\) |
0.701801 | + | 0.712373i | \(0.252380\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 17.8775i | 0.641765i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 11.1975 | + | 11.1975i | 0.401449 | + | 0.401449i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.9972 | 0.679774 | ||||||||
\(782\) | 11.4555 | + | 11.4555i | 0.409647 | + | 0.409647i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000i | 0.0357143i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.3076 | + | 16.3076i | −0.581302 | + | 0.581302i | −0.935261 | − | 0.353959i | \(-0.884835\pi\) |
0.353959 | + | 0.935261i | \(0.384835\pi\) | |||||||
\(788\) | −9.58535 | + | 9.58535i | −0.341464 | + | 0.341464i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.27226i | 0.294128i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.65685 | − | 1.65685i | −0.0588366 | − | 0.0588366i | ||||
\(794\) | −20.5874 | −0.730621 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.46416 | −0.0873397 | ||||||||
\(797\) | −22.1562 | − | 22.1562i | −0.784813 | − | 0.784813i | 0.195826 | − | 0.980639i | \(-0.437261\pi\) |
−0.980639 | + | 0.195826i | \(0.937261\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 35.7562i | 1.26496i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6.91622 | − | 6.91622i | 0.244220 | − | 0.244220i | ||||
\(803\) | 10.1356 | − | 10.1356i | 0.357676 | − | 0.357676i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 5.65685i | − | 0.199254i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −8.96456 | − | 8.96456i | −0.315372 | − | 0.315372i | ||||
\(809\) | 17.0046 | 0.597851 | 0.298926 | − | 0.954276i | \(-0.403372\pi\) | ||||
0.298926 | + | 0.954276i | \(0.403372\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.7927 | 0.695015 | 0.347508 | − | 0.937677i | \(-0.387028\pi\) | ||||
0.347508 | + | 0.937677i | \(0.387028\pi\) | |||||||
\(812\) | −3.12745 | − | 3.12745i | −0.109752 | − | 0.109752i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 14.8694i | 0.521174i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 7.34736 | − | 7.34736i | 0.256894 | − | 0.256894i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.89887i | 0.310573i | 0.987870 | + | 0.155286i | \(0.0496300\pi\) | ||||
−0.987870 | + | 0.155286i | \(0.950370\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −31.0932 | − | 31.0932i | −1.08384 | − | 1.08384i | −0.996147 | − | 0.0876944i | \(-0.972050\pi\) |
−0.0876944 | − | 0.996147i | \(-0.527950\pi\) | |||||||
\(824\) | −10.5143 | −0.366282 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.89887 | 0.205248 | ||||||||
\(827\) | 25.5604 | + | 25.5604i | 0.888822 | + | 0.888822i | 0.994410 | − | 0.105588i | \(-0.0336726\pi\) |
−0.105588 | + | 0.994410i | \(0.533673\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.6067i | 0.472581i | 0.971682 | + | 0.236291i | \(0.0759317\pi\) | ||||
−0.971682 | + | 0.236291i | \(0.924068\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.692297 | + | 0.692297i | −0.0240011 | + | 0.0240011i | ||||
\(833\) | −2.39327 | + | 2.39327i | −0.0829219 | + | 0.0829219i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 23.2299 | + | 23.2299i | 0.802465 | + | 0.802465i | ||||
\(839\) | 45.4002 | 1.56739 | 0.783694 | − | 0.621147i | \(-0.213333\pi\) | ||||
0.783694 | + | 0.621147i | \(0.213333\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.43806 | −0.325450 | ||||||||
\(842\) | −23.7984 | − | 23.7984i | −0.820146 | − | 0.820146i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 5.57308i | − | 0.191833i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.54315 | + | 5.54315i | −0.190465 | + | 0.190465i | ||||
\(848\) | −3.56484 | + | 3.56484i | −0.122417 | + | 0.122417i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 40.0329i | 1.37231i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.62841 | − | 4.62841i | −0.158474 | − | 0.158474i | 0.623416 | − | 0.781890i | \(-0.285744\pi\) |
−0.781890 | + | 0.623416i | \(0.785744\pi\) | |||||||
\(854\) | 2.39327 | 0.0818960 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 19.1115 | 0.653216 | ||||||||
\(857\) | 23.4218 | + | 23.4218i | 0.800074 | + | 0.800074i | 0.983107 | − | 0.183032i | \(-0.0585913\pi\) |
−0.183032 | + | 0.983107i | \(0.558591\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29.8062i | 1.01697i | 0.861070 | + | 0.508487i | \(0.169795\pi\) | ||||
−0.861070 | + | 0.508487i | \(0.830205\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 20.1002 | − | 20.1002i | 0.684617 | − | 0.684617i | ||||
\(863\) | 12.8868 | − | 12.8868i | 0.438671 | − | 0.438671i | −0.452893 | − | 0.891565i | \(-0.649608\pi\) |
0.891565 | + | 0.452893i | \(0.149608\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 12.5067i | − | 0.424994i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4.08557 | + | 4.08557i | 0.138673 | + | 0.138673i | ||||
\(869\) | 29.0543 | 0.985601 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.888542 | −0.0301071 | ||||||||
\(872\) | 2.33403 | + | 2.33403i | 0.0790403 | + | 0.0790403i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.6479 | + | 10.6479i | −0.359553 | + | 0.359553i | −0.863648 | − | 0.504095i | \(-0.831826\pi\) |
0.504095 | + | 0.863648i | \(0.331826\pi\) | |||||||
\(878\) | 0.340476 | − | 0.340476i | 0.0114905 | − | 0.0114905i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 59.0706i | 1.99014i | 0.0991785 | + | 0.995070i | \(0.468379\pi\) | ||||
−0.0991785 | + | 0.995070i | \(0.531621\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.9269 | + | 14.9269i | 0.502330 | + | 0.502330i | 0.912161 | − | 0.409832i | \(-0.134413\pi\) |
−0.409832 | + | 0.912161i | \(0.634413\pi\) | |||||||
\(884\) | −3.31371 | −0.111452 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 22.4252 | 0.753388 | ||||||||
\(887\) | −7.58864 | − | 7.58864i | −0.254802 | − | 0.254802i | 0.568134 | − | 0.822936i | \(-0.307665\pi\) |
−0.822936 | + | 0.568134i | \(0.807665\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.870315i | 0.0291894i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −14.6854 | + | 14.6854i | −0.491704 | + | 0.491704i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 1.00000i | − | 0.0334077i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −22.5557 | − | 22.5557i | −0.752694 | − | 0.752694i | ||||
\(899\) | −25.5549 | −0.852302 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.0633 | −0.568460 | ||||||||
\(902\) | −1.01567 | − | 1.01567i | −0.0338181 | − | 0.0338181i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 8.27226i | − | 0.275131i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.95544 | + | 7.95544i | −0.264156 | + | 0.264156i | −0.826740 | − | 0.562584i | \(-0.809807\pi\) |
0.562584 | + | 0.826740i | \(0.309807\pi\) | |||||||
\(908\) | 19.5557 | − | 19.5557i | 0.648980 | − | 0.648980i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 53.4969i | 1.77243i | 0.463274 | + | 0.886215i | \(0.346674\pi\) | ||||
−0.463274 | + | 0.886215i | \(0.653326\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.304253 | − | 0.304253i | −0.0100693 | − | 0.0100693i | ||||
\(914\) | 29.0702 | 0.961556 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −24.3622 | −0.804948 | ||||||||
\(917\) | 4.61541 | + | 4.61541i | 0.152414 | + | 0.152414i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 43.3882i | 1.43124i | 0.698488 | + | 0.715622i | \(0.253857\pi\) | ||||
−0.698488 | + | 0.715622i | \(0.746143\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −25.4452 | + | 25.4452i | −0.837993 | + | 0.837993i | ||||
\(923\) | −7.39748 | + | 7.39748i | −0.243491 | + | 0.243491i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 18.2014i | − | 0.598134i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.12745 | + | 3.12745i | 0.102664 | + | 0.102664i | ||||
\(929\) | −12.2024 | −0.400348 | −0.200174 | − | 0.979760i | \(-0.564151\pi\) | ||||
−0.200174 | + | 0.979760i | \(0.564151\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 14.7692 | + | 14.7692i | 0.483781 | + | 0.483781i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 0.751839i | − | 0.0246009i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.82978 | + | 2.82978i | −0.0924449 | + | 0.0924449i | −0.751817 | − | 0.659372i | \(-0.770822\pi\) |
0.659372 | + | 0.751817i | \(0.270822\pi\) | |||||||
\(938\) | 0.641735 | − | 0.641735i | 0.0209534 | − | 0.0209534i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 42.7478i | − | 1.39354i | −0.717295 | − | 0.696769i | \(-0.754620\pi\) | ||
0.717295 | − | 0.696769i | \(-0.245380\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.73449 | − | 2.73449i | −0.0890472 | − | 0.0890472i | ||||
\(944\) | −5.89887 | −0.191992 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11.6706 | 0.379445 | ||||||||
\(947\) | −35.5502 | − | 35.5502i | −1.15523 | − | 1.15523i | −0.985489 | − | 0.169737i | \(-0.945708\pi\) |
−0.169737 | − | 0.985489i | \(-0.554292\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.89354i | 0.256235i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.39327 | − | 2.39327i | 0.0775663 | − | 0.0775663i | ||||
\(953\) | 1.05372 | − | 1.05372i | 0.0341333 | − | 0.0341333i | −0.689834 | − | 0.723967i | \(-0.742317\pi\) |
0.723967 | + | 0.689834i | \(0.242317\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 1.47283i | − | 0.0476348i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 16.3050 | + | 16.3050i | 0.526792 | + | 0.526792i | ||||
\(959\) | 0.272260 | 0.00879172 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.38372 | 0.0768941 | ||||||||
\(962\) | −5.79013 | − | 5.79013i | −0.186681 | − | 0.186681i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 21.5557i | − | 0.694263i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.3414 | − | 26.3414i | 0.847082 | − | 0.847082i | −0.142686 | − | 0.989768i | \(-0.545574\pi\) |
0.989768 | + | 0.142686i | \(0.0455739\pi\) | |||||||
\(968\) | 5.54315 | − | 5.54315i | 0.178164 | − | 0.178164i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 30.7692i | 0.987430i | 0.869624 | + | 0.493715i | \(0.164361\pi\) | ||||
−0.869624 | + | 0.493715i | \(0.835639\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.5143 | + | 10.5143i | 0.337072 | + | 0.337072i | ||||
\(974\) | −22.5272 | −0.721817 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.39327 | −0.0766067 | ||||||||
\(977\) | 5.55661 | + | 5.55661i | 0.177772 | + | 0.177772i | 0.790384 | − | 0.612612i | \(-0.209881\pi\) |
−0.612612 | + | 0.790384i | \(0.709881\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23.5282i | 0.751964i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 8.02633 | − | 8.02633i | 0.256130 | − | 0.256130i | ||||
\(983\) | 40.8357 | − | 40.8357i | 1.30246 | − | 1.30246i | 0.375723 | − | 0.926732i | \(-0.377394\pi\) |
0.926732 | − | 0.375723i | \(-0.122606\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 14.9697i | 0.476732i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 31.4208 | 0.999123 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.67333 | −0.307283 | −0.153642 | − | 0.988127i | \(-0.549100\pi\) | ||||
−0.153642 | + | 0.988127i | \(0.549100\pi\) | |||||||
\(992\) | −4.08557 | − | 4.08557i | −0.129717 | − | 0.129717i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 10.6854i | − | 0.338921i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.1841 | − | 28.1841i | 0.892601 | − | 0.892601i | −0.102167 | − | 0.994767i | \(-0.532578\pi\) |
0.994767 | + | 0.102167i | \(0.0325775\pi\) | |||||||
\(998\) | 14.5889 | − | 14.5889i | 0.461805 | − | 0.461805i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3150.2.m.j.2843.2 | 8 | ||
3.2 | odd | 2 | 3150.2.m.i.2843.3 | 8 | |||
5.2 | odd | 4 | 3150.2.m.i.1457.4 | 8 | |||
5.3 | odd | 4 | 630.2.m.c.197.1 | ✓ | 8 | ||
5.4 | even | 2 | 630.2.m.d.323.4 | yes | 8 | ||
15.2 | even | 4 | inner | 3150.2.m.j.1457.1 | 8 | ||
15.8 | even | 4 | 630.2.m.d.197.4 | yes | 8 | ||
15.14 | odd | 2 | 630.2.m.c.323.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.m.c.197.1 | ✓ | 8 | 5.3 | odd | 4 | ||
630.2.m.c.323.1 | yes | 8 | 15.14 | odd | 2 | ||
630.2.m.d.197.4 | yes | 8 | 15.8 | even | 4 | ||
630.2.m.d.323.4 | yes | 8 | 5.4 | even | 2 | ||
3150.2.m.i.1457.4 | 8 | 5.2 | odd | 4 | |||
3150.2.m.i.2843.3 | 8 | 3.2 | odd | 2 | |||
3150.2.m.j.1457.1 | 8 | 15.2 | even | 4 | inner | ||
3150.2.m.j.2843.2 | 8 | 1.1 | even | 1 | trivial |