Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5070,2,Mod(1351,5070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5070, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("5070.1351");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5070.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(40.4841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.153664.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 5x^{4} + 6x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1351.1 | ||
Root | \(-0.445042i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5070.1351 |
Dual form | 5070.2.b.t.1351.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5070\mathbb{Z}\right)^\times\).
\(n\) | \(1691\) | \(1861\) | \(4057\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.707107i | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − 1.00000i | − 0.447214i | ||||||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | − 1.69202i | − 0.639524i | −0.947498 | − | 0.319762i | \(-0.896397\pi\) | ||||
0.947498 | − | 0.319762i | \(-0.103603\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 2.15883i | 0.650913i | 0.945557 | + | 0.325456i | \(0.105518\pi\) | ||||
−0.945557 | + | 0.325456i | \(0.894482\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.69202 | −0.452212 | ||||||||
\(15\) | 1.00000i | 0.258199i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.35690 | −0.571631 | −0.285816 | − | 0.958285i | \(-0.592264\pi\) | ||||
−0.285816 | + | 0.958285i | \(0.592264\pi\) | |||||||
\(18\) | − 1.00000i | − 0.235702i | ||||||||
\(19\) | − 0.198062i | − 0.0454386i | −0.999742 | − | 0.0227193i | \(-0.992768\pi\) | ||||
0.999742 | − | 0.0227193i | \(-0.00723240\pi\) | |||||||
\(20\) | 1.00000i | 0.223607i | ||||||||
\(21\) | 1.69202i | 0.369229i | ||||||||
\(22\) | 2.15883 | 0.460265 | ||||||||
\(23\) | 3.74094 | 0.780040 | 0.390020 | − | 0.920806i | \(-0.372468\pi\) | ||||
0.390020 | + | 0.920806i | \(0.372468\pi\) | |||||||
\(24\) | − 1.00000i | − 0.204124i | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.69202i | 0.319762i | ||||||||
\(29\) | 1.29590 | 0.240642 | 0.120321 | − | 0.992735i | \(-0.461608\pi\) | ||||
0.120321 | + | 0.992735i | \(0.461608\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | − 1.44504i | − 0.259537i | −0.991544 | − | 0.129769i | \(-0.958577\pi\) | ||||
0.991544 | − | 0.129769i | \(-0.0414234\pi\) | |||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | − 2.15883i | − 0.375805i | ||||||||
\(34\) | 2.35690i | 0.404204i | ||||||||
\(35\) | −1.69202 | −0.286004 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 0.801938i | 0.131838i | 0.997825 | + | 0.0659189i | \(0.0209979\pi\) | ||||
−0.997825 | + | 0.0659189i | \(0.979002\pi\) | |||||||
\(38\) | −0.198062 | −0.0321299 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 1.89977i | 0.296695i | 0.988935 | + | 0.148347i | \(0.0473953\pi\) | ||||
−0.988935 | + | 0.148347i | \(0.952605\pi\) | |||||||
\(42\) | 1.69202 | 0.261085 | ||||||||
\(43\) | −12.5429 | −1.91277 | −0.956385 | − | 0.292108i | \(-0.905643\pi\) | ||||
−0.956385 | + | 0.292108i | \(0.905643\pi\) | |||||||
\(44\) | − 2.15883i | − 0.325456i | ||||||||
\(45\) | − 1.00000i | − 0.149071i | ||||||||
\(46\) | − 3.74094i | − 0.551571i | ||||||||
\(47\) | 8.87800i | 1.29499i | 0.762070 | + | 0.647495i | \(0.224183\pi\) | ||||
−0.762070 | + | 0.647495i | \(0.775817\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 4.13706 | 0.591009 | ||||||||
\(50\) | 1.00000i | 0.141421i | ||||||||
\(51\) | 2.35690 | 0.330031 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.00969 | −0.138691 | −0.0693457 | − | 0.997593i | \(-0.522091\pi\) | ||||
−0.0693457 | + | 0.997593i | \(0.522091\pi\) | |||||||
\(54\) | 1.00000i | 0.136083i | ||||||||
\(55\) | 2.15883 | 0.291097 | ||||||||
\(56\) | 1.69202 | 0.226106 | ||||||||
\(57\) | 0.198062i | 0.0262340i | ||||||||
\(58\) | − 1.29590i | − 0.170160i | ||||||||
\(59\) | 3.73125i | 0.485767i | 0.970055 | + | 0.242884i | \(0.0780933\pi\) | ||||
−0.970055 | + | 0.242884i | \(0.921907\pi\) | |||||||
\(60\) | − 1.00000i | − 0.129099i | ||||||||
\(61\) | −6.32304 | −0.809583 | −0.404791 | − | 0.914409i | \(-0.632656\pi\) | ||||
−0.404791 | + | 0.914409i | \(0.632656\pi\) | |||||||
\(62\) | −1.44504 | −0.183521 | ||||||||
\(63\) | − 1.69202i | − 0.213175i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.15883 | −0.265734 | ||||||||
\(67\) | 7.56465i | 0.924169i | 0.886836 | + | 0.462084i | \(0.152898\pi\) | ||||
−0.886836 | + | 0.462084i | \(0.847102\pi\) | |||||||
\(68\) | 2.35690 | 0.285816 | ||||||||
\(69\) | −3.74094 | −0.450356 | ||||||||
\(70\) | 1.69202i | 0.202235i | ||||||||
\(71\) | 4.18060i | 0.496146i | 0.968741 | + | 0.248073i | \(0.0797974\pi\) | ||||
−0.968741 | + | 0.248073i | \(0.920203\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | 11.9366i | 1.39707i | 0.715574 | + | 0.698537i | \(0.246165\pi\) | ||||
−0.715574 | + | 0.698537i | \(0.753835\pi\) | |||||||
\(74\) | 0.801938 | 0.0932234 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0.198062i | 0.0227193i | ||||||||
\(77\) | 3.65279 | 0.416274 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.40581 | 1.05824 | 0.529118 | − | 0.848548i | \(-0.322523\pi\) | ||||
0.529118 | + | 0.848548i | \(0.322523\pi\) | |||||||
\(80\) | − 1.00000i | − 0.111803i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.89977 | 0.209795 | ||||||||
\(83\) | − 8.43296i | − 0.925638i | −0.886453 | − | 0.462819i | \(-0.846838\pi\) | ||||
0.886453 | − | 0.462819i | \(-0.153162\pi\) | |||||||
\(84\) | − 1.69202i | − 0.184615i | ||||||||
\(85\) | 2.35690i | 0.255641i | ||||||||
\(86\) | 12.5429i | 1.35253i | ||||||||
\(87\) | −1.29590 | −0.138935 | ||||||||
\(88\) | −2.15883 | −0.230132 | ||||||||
\(89\) | − 2.41119i | − 0.255586i | −0.991801 | − | 0.127793i | \(-0.959211\pi\) | ||||
0.991801 | − | 0.127793i | \(-0.0407893\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.74094 | −0.390020 | ||||||||
\(93\) | 1.44504i | 0.149844i | ||||||||
\(94\) | 8.87800 | 0.915696 | ||||||||
\(95\) | −0.198062 | −0.0203208 | ||||||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | 0.0881460i | 0.00894987i | 0.999990 | + | 0.00447494i | \(0.00142442\pi\) | ||||
−0.999990 | + | 0.00447494i | \(0.998576\pi\) | |||||||
\(98\) | − 4.13706i | − 0.417907i | ||||||||
\(99\) | 2.15883i | 0.216971i | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 11.1099 | 1.10548 | 0.552739 | − | 0.833354i | \(-0.313583\pi\) | ||||
0.552739 | + | 0.833354i | \(0.313583\pi\) | |||||||
\(102\) | − 2.35690i | − 0.233367i | ||||||||
\(103\) | −9.54825 | −0.940817 | −0.470409 | − | 0.882449i | \(-0.655893\pi\) | ||||
−0.470409 | + | 0.882449i | \(0.655893\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.69202 | 0.165124 | ||||||||
\(106\) | 1.00969i | 0.0980696i | ||||||||
\(107\) | 18.1468 | 1.75431 | 0.877156 | − | 0.480205i | \(-0.159438\pi\) | ||||
0.877156 | + | 0.480205i | \(0.159438\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 2.24698i | 0.215222i | 0.994193 | + | 0.107611i | \(0.0343200\pi\) | ||||
−0.994193 | + | 0.107611i | \(0.965680\pi\) | |||||||
\(110\) | − 2.15883i | − 0.205837i | ||||||||
\(111\) | − 0.801938i | − 0.0761166i | ||||||||
\(112\) | − 1.69202i | − 0.159881i | ||||||||
\(113\) | −11.8726 | −1.11688 | −0.558441 | − | 0.829544i | \(-0.688600\pi\) | ||||
−0.558441 | + | 0.829544i | \(0.688600\pi\) | |||||||
\(114\) | 0.198062 | 0.0185502 | ||||||||
\(115\) | − 3.74094i | − 0.348844i | ||||||||
\(116\) | −1.29590 | −0.120321 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.73125 | 0.343489 | ||||||||
\(119\) | 3.98792i | 0.365572i | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | 6.33944 | 0.576312 | ||||||||
\(122\) | 6.32304i | 0.572462i | ||||||||
\(123\) | − 1.89977i | − 0.171297i | ||||||||
\(124\) | 1.44504i | 0.129769i | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −1.69202 | −0.150737 | ||||||||
\(127\) | −13.0097 | −1.15442 | −0.577212 | − | 0.816595i | \(-0.695859\pi\) | ||||
−0.577212 | + | 0.816595i | \(0.695859\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 12.5429 | 1.10434 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.82908 | −0.684030 | −0.342015 | − | 0.939694i | \(-0.611109\pi\) | ||||
−0.342015 | + | 0.939694i | \(0.611109\pi\) | |||||||
\(132\) | 2.15883i | 0.187902i | ||||||||
\(133\) | −0.335126 | −0.0290591 | ||||||||
\(134\) | 7.56465 | 0.653486 | ||||||||
\(135\) | 1.00000i | 0.0860663i | ||||||||
\(136\) | − 2.35690i | − 0.202102i | ||||||||
\(137\) | 5.36227i | 0.458130i | 0.973411 | + | 0.229065i | \(0.0735668\pi\) | ||||
−0.973411 | + | 0.229065i | \(0.926433\pi\) | |||||||
\(138\) | 3.74094i | 0.318450i | ||||||||
\(139\) | 3.12200 | 0.264804 | 0.132402 | − | 0.991196i | \(-0.457731\pi\) | ||||
0.132402 | + | 0.991196i | \(0.457731\pi\) | |||||||
\(140\) | 1.69202 | 0.143002 | ||||||||
\(141\) | − 8.87800i | − 0.747663i | ||||||||
\(142\) | 4.18060 | 0.350828 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | − 1.29590i | − 0.107618i | ||||||||
\(146\) | 11.9366 | 0.987881 | ||||||||
\(147\) | −4.13706 | −0.341219 | ||||||||
\(148\) | − 0.801938i | − 0.0659189i | ||||||||
\(149\) | − 4.24160i | − 0.347486i | −0.984791 | − | 0.173743i | \(-0.944414\pi\) | ||||
0.984791 | − | 0.173743i | \(-0.0555861\pi\) | |||||||
\(150\) | − 1.00000i | − 0.0816497i | ||||||||
\(151\) | 22.9148i | 1.86478i | 0.361450 | + | 0.932392i | \(0.382282\pi\) | ||||
−0.361450 | + | 0.932392i | \(0.617718\pi\) | |||||||
\(152\) | 0.198062 | 0.0160650 | ||||||||
\(153\) | −2.35690 | −0.190544 | ||||||||
\(154\) | − 3.65279i | − 0.294350i | ||||||||
\(155\) | −1.44504 | −0.116069 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.0707 | 1.28258 | 0.641290 | − | 0.767298i | \(-0.278399\pi\) | ||||
0.641290 | + | 0.767298i | \(0.278399\pi\) | |||||||
\(158\) | − 9.40581i | − 0.748286i | ||||||||
\(159\) | 1.00969 | 0.0800735 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | − 6.32975i | − 0.498854i | ||||||||
\(162\) | − 1.00000i | − 0.0785674i | ||||||||
\(163\) | − 0.488582i | − 0.0382687i | −0.999817 | − | 0.0191344i | \(-0.993909\pi\) | ||||
0.999817 | − | 0.0191344i | \(-0.00609103\pi\) | |||||||
\(164\) | − 1.89977i | − 0.148347i | ||||||||
\(165\) | −2.15883 | −0.168065 | ||||||||
\(166\) | −8.43296 | −0.654525 | ||||||||
\(167\) | 14.0610i | 1.08807i | 0.839062 | + | 0.544036i | \(0.183105\pi\) | ||||
−0.839062 | + | 0.544036i | \(0.816895\pi\) | |||||||
\(168\) | −1.69202 | −0.130542 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 2.35690 | 0.180766 | ||||||||
\(171\) | − 0.198062i | − 0.0151462i | ||||||||
\(172\) | 12.5429 | 0.956385 | ||||||||
\(173\) | −21.7942 | −1.65698 | −0.828490 | − | 0.560004i | \(-0.810800\pi\) | ||||
−0.828490 | + | 0.560004i | \(0.810800\pi\) | |||||||
\(174\) | 1.29590i | 0.0982417i | ||||||||
\(175\) | 1.69202i | 0.127905i | ||||||||
\(176\) | 2.15883i | 0.162728i | ||||||||
\(177\) | − 3.73125i | − 0.280458i | ||||||||
\(178\) | −2.41119 | −0.180726 | ||||||||
\(179\) | 14.1293 | 1.05607 | 0.528036 | − | 0.849222i | \(-0.322928\pi\) | ||||
0.528036 | + | 0.849222i | \(0.322928\pi\) | |||||||
\(180\) | 1.00000i | 0.0745356i | ||||||||
\(181\) | 5.63773 | 0.419049 | 0.209524 | − | 0.977803i | \(-0.432808\pi\) | ||||
0.209524 | + | 0.977803i | \(0.432808\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.32304 | 0.467413 | ||||||||
\(184\) | 3.74094i | 0.275786i | ||||||||
\(185\) | 0.801938 | 0.0589596 | ||||||||
\(186\) | 1.44504 | 0.105956 | ||||||||
\(187\) | − 5.08815i | − 0.372082i | ||||||||
\(188\) | − 8.87800i | − 0.647495i | ||||||||
\(189\) | 1.69202i | 0.123076i | ||||||||
\(190\) | 0.198062i | 0.0143689i | ||||||||
\(191\) | −2.59419 | −0.187709 | −0.0938544 | − | 0.995586i | \(-0.529919\pi\) | ||||
−0.0938544 | + | 0.995586i | \(0.529919\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | − 3.98361i | − 0.286746i | −0.989669 | − | 0.143373i | \(-0.954205\pi\) | ||||
0.989669 | − | 0.143373i | \(-0.0457949\pi\) | |||||||
\(194\) | 0.0881460 | 0.00632851 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.13706 | −0.295505 | ||||||||
\(197\) | 6.65040i | 0.473821i | 0.971531 | + | 0.236911i | \(0.0761349\pi\) | ||||
−0.971531 | + | 0.236911i | \(0.923865\pi\) | |||||||
\(198\) | 2.15883 | 0.153422 | ||||||||
\(199\) | 1.01639 | 0.0720502 | 0.0360251 | − | 0.999351i | \(-0.488530\pi\) | ||||
0.0360251 | + | 0.999351i | \(0.488530\pi\) | |||||||
\(200\) | − 1.00000i | − 0.0707107i | ||||||||
\(201\) | − 7.56465i | − 0.533569i | ||||||||
\(202\) | − 11.1099i | − 0.781691i | ||||||||
\(203\) | − 2.19269i | − 0.153896i | ||||||||
\(204\) | −2.35690 | −0.165016 | ||||||||
\(205\) | 1.89977 | 0.132686 | ||||||||
\(206\) | 9.54825i | 0.665258i | ||||||||
\(207\) | 3.74094 | 0.260013 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.427583 | 0.0295766 | ||||||||
\(210\) | − 1.69202i | − 0.116761i | ||||||||
\(211\) | 10.1414 | 0.698161 | 0.349081 | − | 0.937093i | \(-0.386494\pi\) | ||||
0.349081 | + | 0.937093i | \(0.386494\pi\) | |||||||
\(212\) | 1.00969 | 0.0693457 | ||||||||
\(213\) | − 4.18060i | − 0.286450i | ||||||||
\(214\) | − 18.1468i | − 1.24049i | ||||||||
\(215\) | 12.5429i | 0.855417i | ||||||||
\(216\) | − 1.00000i | − 0.0680414i | ||||||||
\(217\) | −2.44504 | −0.165980 | ||||||||
\(218\) | 2.24698 | 0.152185 | ||||||||
\(219\) | − 11.9366i | − 0.806601i | ||||||||
\(220\) | −2.15883 | −0.145549 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −0.801938 | −0.0538225 | ||||||||
\(223\) | 16.8388i | 1.12761i | 0.825909 | + | 0.563804i | \(0.190663\pi\) | ||||
−0.825909 | + | 0.563804i | \(0.809337\pi\) | |||||||
\(224\) | −1.69202 | −0.113053 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 11.8726i | 0.789755i | ||||||||
\(227\) | − 18.3056i | − 1.21498i | −0.794326 | − | 0.607492i | \(-0.792176\pi\) | ||||
0.794326 | − | 0.607492i | \(-0.207824\pi\) | |||||||
\(228\) | − 0.198062i | − 0.0131170i | ||||||||
\(229\) | 5.14244i | 0.339822i | 0.985459 | + | 0.169911i | \(0.0543480\pi\) | ||||
−0.985459 | + | 0.169911i | \(0.945652\pi\) | |||||||
\(230\) | −3.74094 | −0.246670 | ||||||||
\(231\) | −3.65279 | −0.240336 | ||||||||
\(232\) | 1.29590i | 0.0850798i | ||||||||
\(233\) | 10.9215 | 0.715494 | 0.357747 | − | 0.933819i | \(-0.383545\pi\) | ||||
0.357747 | + | 0.933819i | \(0.383545\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.87800 | 0.579137 | ||||||||
\(236\) | − 3.73125i | − 0.242884i | ||||||||
\(237\) | −9.40581 | −0.610973 | ||||||||
\(238\) | 3.98792 | 0.258498 | ||||||||
\(239\) | − 19.9041i | − 1.28749i | −0.765241 | − | 0.643744i | \(-0.777380\pi\) | ||||
0.765241 | − | 0.643744i | \(-0.222620\pi\) | |||||||
\(240\) | 1.00000i | 0.0645497i | ||||||||
\(241\) | 18.2228i | 1.17383i | 0.809647 | + | 0.586917i | \(0.199659\pi\) | ||||
−0.809647 | + | 0.586917i | \(0.800341\pi\) | |||||||
\(242\) | − 6.33944i | − 0.407514i | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 6.32304 | 0.404791 | ||||||||
\(245\) | − 4.13706i | − 0.264307i | ||||||||
\(246\) | −1.89977 | −0.121125 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1.44504 | 0.0917603 | ||||||||
\(249\) | 8.43296i | 0.534417i | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 17.0030 | 1.07322 | 0.536609 | − | 0.843831i | \(-0.319705\pi\) | ||||
0.536609 | + | 0.843831i | \(0.319705\pi\) | |||||||
\(252\) | 1.69202i | 0.106587i | ||||||||
\(253\) | 8.07606i | 0.507738i | ||||||||
\(254\) | 13.0097i | 0.816300i | ||||||||
\(255\) | − 2.35690i | − 0.147595i | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 7.65519 | 0.477517 | 0.238759 | − | 0.971079i | \(-0.423260\pi\) | ||||
0.238759 | + | 0.971079i | \(0.423260\pi\) | |||||||
\(258\) | − 12.5429i | − 0.780885i | ||||||||
\(259\) | 1.35690 | 0.0843134 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.29590 | 0.0802140 | ||||||||
\(262\) | 7.82908i | 0.483682i | ||||||||
\(263\) | 21.0411 | 1.29745 | 0.648726 | − | 0.761022i | \(-0.275302\pi\) | ||||
0.648726 | + | 0.761022i | \(0.275302\pi\) | |||||||
\(264\) | 2.15883 | 0.132867 | ||||||||
\(265\) | 1.00969i | 0.0620247i | ||||||||
\(266\) | 0.335126i | 0.0205479i | ||||||||
\(267\) | 2.41119i | 0.147562i | ||||||||
\(268\) | − 7.56465i | − 0.462084i | ||||||||
\(269\) | 24.3183 | 1.48271 | 0.741355 | − | 0.671113i | \(-0.234183\pi\) | ||||
0.741355 | + | 0.671113i | \(0.234183\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | 10.9922i | 0.667730i | 0.942621 | + | 0.333865i | \(0.108353\pi\) | ||||
−0.942621 | + | 0.333865i | \(0.891647\pi\) | |||||||
\(272\) | −2.35690 | −0.142908 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.36227 | 0.323947 | ||||||||
\(275\) | − 2.15883i | − 0.130183i | ||||||||
\(276\) | 3.74094 | 0.225178 | ||||||||
\(277\) | 11.4601 | 0.688571 | 0.344286 | − | 0.938865i | \(-0.388121\pi\) | ||||
0.344286 | + | 0.938865i | \(0.388121\pi\) | |||||||
\(278\) | − 3.12200i | − 0.187245i | ||||||||
\(279\) | − 1.44504i | − 0.0865124i | ||||||||
\(280\) | − 1.69202i | − 0.101118i | ||||||||
\(281\) | − 9.88231i | − 0.589529i | −0.955570 | − | 0.294765i | \(-0.904759\pi\) | ||||
0.955570 | − | 0.294765i | \(-0.0952413\pi\) | |||||||
\(282\) | −8.87800 | −0.528677 | ||||||||
\(283\) | 21.3207 | 1.26738 | 0.633691 | − | 0.773587i | \(-0.281539\pi\) | ||||
0.633691 | + | 0.773587i | \(0.281539\pi\) | |||||||
\(284\) | − 4.18060i | − 0.248073i | ||||||||
\(285\) | 0.198062 | 0.0117322 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.21446 | 0.189743 | ||||||||
\(288\) | − 1.00000i | − 0.0589256i | ||||||||
\(289\) | −11.4450 | −0.673238 | ||||||||
\(290\) | −1.29590 | −0.0760977 | ||||||||
\(291\) | − 0.0881460i | − 0.00516721i | ||||||||
\(292\) | − 11.9366i | − 0.698537i | ||||||||
\(293\) | − 18.7090i | − 1.09299i | −0.837462 | − | 0.546496i | \(-0.815961\pi\) | ||||
0.837462 | − | 0.546496i | \(-0.184039\pi\) | |||||||
\(294\) | 4.13706i | 0.241278i | ||||||||
\(295\) | 3.73125 | 0.217242 | ||||||||
\(296\) | −0.801938 | −0.0466117 | ||||||||
\(297\) | − 2.15883i | − 0.125268i | ||||||||
\(298\) | −4.24160 | −0.245709 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 21.2228i | 1.22326i | ||||||||
\(302\) | 22.9148 | 1.31860 | ||||||||
\(303\) | −11.1099 | −0.638248 | ||||||||
\(304\) | − 0.198062i | − 0.0113596i | ||||||||
\(305\) | 6.32304i | 0.362056i | ||||||||
\(306\) | 2.35690i | 0.134735i | ||||||||
\(307\) | 17.2241i | 0.983034i | 0.870868 | + | 0.491517i | \(0.163557\pi\) | ||||
−0.870868 | + | 0.491517i | \(0.836443\pi\) | |||||||
\(308\) | −3.65279 | −0.208137 | ||||||||
\(309\) | 9.54825 | 0.543181 | ||||||||
\(310\) | 1.44504i | 0.0820729i | ||||||||
\(311\) | 13.5200 | 0.766651 | 0.383326 | − | 0.923613i | \(-0.374779\pi\) | ||||
0.383326 | + | 0.923613i | \(0.374779\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.3303 | 1.37523 | 0.687616 | − | 0.726074i | \(-0.258657\pi\) | ||||
0.687616 | + | 0.726074i | \(0.258657\pi\) | |||||||
\(314\) | − 16.0707i | − 0.906921i | ||||||||
\(315\) | −1.69202 | −0.0953346 | ||||||||
\(316\) | −9.40581 | −0.529118 | ||||||||
\(317\) | − 34.7821i | − 1.95356i | −0.214253 | − | 0.976778i | \(-0.568732\pi\) | ||||
0.214253 | − | 0.976778i | \(-0.431268\pi\) | |||||||
\(318\) | − 1.00969i | − 0.0566205i | ||||||||
\(319\) | 2.79763i | 0.156637i | ||||||||
\(320\) | 1.00000i | 0.0559017i | ||||||||
\(321\) | −18.1468 | −1.01285 | ||||||||
\(322\) | −6.32975 | −0.352743 | ||||||||
\(323\) | 0.466812i | 0.0259741i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.488582 | −0.0270601 | ||||||||
\(327\) | − 2.24698i | − 0.124258i | ||||||||
\(328\) | −1.89977 | −0.104897 | ||||||||
\(329\) | 15.0218 | 0.828177 | ||||||||
\(330\) | 2.15883i | 0.118840i | ||||||||
\(331\) | 9.66919i | 0.531467i | 0.964047 | + | 0.265733i | \(0.0856140\pi\) | ||||
−0.964047 | + | 0.265733i | \(0.914386\pi\) | |||||||
\(332\) | 8.43296i | 0.462819i | ||||||||
\(333\) | 0.801938i | 0.0439459i | ||||||||
\(334\) | 14.0610 | 0.769384 | ||||||||
\(335\) | 7.56465 | 0.413301 | ||||||||
\(336\) | 1.69202i | 0.0923073i | ||||||||
\(337\) | 17.3612 | 0.945725 | 0.472863 | − | 0.881136i | \(-0.343221\pi\) | ||||
0.472863 | + | 0.881136i | \(0.343221\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.8726 | 0.644832 | ||||||||
\(340\) | − 2.35690i | − 0.127821i | ||||||||
\(341\) | 3.11960 | 0.168936 | ||||||||
\(342\) | −0.198062 | −0.0107100 | ||||||||
\(343\) | − 18.8442i | − 1.01749i | ||||||||
\(344\) | − 12.5429i | − 0.676267i | ||||||||
\(345\) | 3.74094i | 0.201405i | ||||||||
\(346\) | 21.7942i | 1.17166i | ||||||||
\(347\) | 8.86294 | 0.475787 | 0.237894 | − | 0.971291i | \(-0.423543\pi\) | ||||
0.237894 | + | 0.971291i | \(0.423543\pi\) | |||||||
\(348\) | 1.29590 | 0.0694674 | ||||||||
\(349\) | 2.78554i | 0.149107i | 0.997217 | + | 0.0745534i | \(0.0237531\pi\) | ||||
−0.997217 | + | 0.0745534i | \(0.976247\pi\) | |||||||
\(350\) | 1.69202 | 0.0904424 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.15883 | 0.115066 | ||||||||
\(353\) | − 21.0640i | − 1.12112i | −0.828113 | − | 0.560561i | \(-0.810585\pi\) | ||||
0.828113 | − | 0.560561i | \(-0.189415\pi\) | |||||||
\(354\) | −3.73125 | −0.198314 | ||||||||
\(355\) | 4.18060 | 0.221883 | ||||||||
\(356\) | 2.41119i | 0.127793i | ||||||||
\(357\) | − 3.98792i | − 0.211063i | ||||||||
\(358\) | − 14.1293i | − 0.746756i | ||||||||
\(359\) | 17.3274i | 0.914503i | 0.889337 | + | 0.457251i | \(0.151166\pi\) | ||||
−0.889337 | + | 0.457251i | \(0.848834\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | 18.9608 | 0.997935 | ||||||||
\(362\) | − 5.63773i | − 0.296312i | ||||||||
\(363\) | −6.33944 | −0.332734 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.9366 | 0.624791 | ||||||||
\(366\) | − 6.32304i | − 0.330511i | ||||||||
\(367\) | −30.8049 | −1.60800 | −0.804002 | − | 0.594627i | \(-0.797300\pi\) | ||||
−0.804002 | + | 0.594627i | \(0.797300\pi\) | |||||||
\(368\) | 3.74094 | 0.195010 | ||||||||
\(369\) | 1.89977i | 0.0988982i | ||||||||
\(370\) | − 0.801938i | − 0.0416908i | ||||||||
\(371\) | 1.70841i | 0.0886965i | ||||||||
\(372\) | − 1.44504i | − 0.0749219i | ||||||||
\(373\) | −25.6668 | −1.32898 | −0.664488 | − | 0.747299i | \(-0.731350\pi\) | ||||
−0.664488 | + | 0.747299i | \(0.731350\pi\) | |||||||
\(374\) | −5.08815 | −0.263102 | ||||||||
\(375\) | − 1.00000i | − 0.0516398i | ||||||||
\(376\) | −8.87800 | −0.457848 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.69202 | 0.0870282 | ||||||||
\(379\) | − 5.46144i | − 0.280535i | −0.990114 | − | 0.140268i | \(-0.955204\pi\) | ||||
0.990114 | − | 0.140268i | \(-0.0447963\pi\) | |||||||
\(380\) | 0.198062 | 0.0101604 | ||||||||
\(381\) | 13.0097 | 0.666507 | ||||||||
\(382\) | 2.59419i | 0.132730i | ||||||||
\(383\) | 25.9221i | 1.32456i | 0.749257 | + | 0.662280i | \(0.230411\pi\) | ||||
−0.749257 | + | 0.662280i | \(0.769589\pi\) | |||||||
\(384\) | − 1.00000i | − 0.0510310i | ||||||||
\(385\) | − 3.65279i | − 0.186164i | ||||||||
\(386\) | −3.98361 | −0.202760 | ||||||||
\(387\) | −12.5429 | −0.637590 | ||||||||
\(388\) | − 0.0881460i | − 0.00447494i | ||||||||
\(389\) | 32.0006 | 1.62249 | 0.811247 | − | 0.584703i | \(-0.198789\pi\) | ||||
0.811247 | + | 0.584703i | \(0.198789\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.81700 | −0.445895 | ||||||||
\(392\) | 4.13706i | 0.208953i | ||||||||
\(393\) | 7.82908 | 0.394925 | ||||||||
\(394\) | 6.65040 | 0.335042 | ||||||||
\(395\) | − 9.40581i | − 0.473258i | ||||||||
\(396\) | − 2.15883i | − 0.108485i | ||||||||
\(397\) | 0.457123i | 0.0229424i | 0.999934 | + | 0.0114712i | \(0.00365147\pi\) | ||||
−0.999934 | + | 0.0114712i | \(0.996349\pi\) | |||||||
\(398\) | − 1.01639i | − 0.0509472i | ||||||||
\(399\) | 0.335126 | 0.0167773 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 23.2553i | 1.16132i | 0.814147 | + | 0.580658i | \(0.197205\pi\) | ||||
−0.814147 | + | 0.580658i | \(0.802795\pi\) | |||||||
\(402\) | −7.56465 | −0.377290 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −11.1099 | −0.552739 | ||||||||
\(405\) | − 1.00000i | − 0.0496904i | ||||||||
\(406\) | −2.19269 | −0.108821 | ||||||||
\(407\) | −1.73125 | −0.0858149 | ||||||||
\(408\) | 2.35690i | 0.116684i | ||||||||
\(409\) | − 39.0629i | − 1.93154i | −0.259406 | − | 0.965768i | \(-0.583527\pi\) | ||||
0.259406 | − | 0.965768i | \(-0.416473\pi\) | |||||||
\(410\) | − 1.89977i | − 0.0938231i | ||||||||
\(411\) | − 5.36227i | − 0.264501i | ||||||||
\(412\) | 9.54825 | 0.470409 | ||||||||
\(413\) | 6.31336 | 0.310660 | ||||||||
\(414\) | − 3.74094i | − 0.183857i | ||||||||
\(415\) | −8.43296 | −0.413958 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.12200 | −0.152885 | ||||||||
\(418\) | − 0.427583i | − 0.0209138i | ||||||||
\(419\) | −18.1269 | −0.885557 | −0.442779 | − | 0.896631i | \(-0.646007\pi\) | ||||
−0.442779 | + | 0.896631i | \(0.646007\pi\) | |||||||
\(420\) | −1.69202 | −0.0825622 | ||||||||
\(421\) | 20.4916i | 0.998698i | 0.866401 | + | 0.499349i | \(0.166427\pi\) | ||||
−0.866401 | + | 0.499349i | \(0.833573\pi\) | |||||||
\(422\) | − 10.1414i | − 0.493674i | ||||||||
\(423\) | 8.87800i | 0.431663i | ||||||||
\(424\) | − 1.00969i | − 0.0490348i | ||||||||
\(425\) | 2.35690 | 0.114326 | ||||||||
\(426\) | −4.18060 | −0.202551 | ||||||||
\(427\) | 10.6987i | 0.517748i | ||||||||
\(428\) | −18.1468 | −0.877156 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 12.5429 | 0.604871 | ||||||||
\(431\) | 22.2989i | 1.07410i | 0.843551 | + | 0.537050i | \(0.180461\pi\) | ||||
−0.843551 | + | 0.537050i | \(0.819539\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −7.47650 | −0.359298 | −0.179649 | − | 0.983731i | \(-0.557496\pi\) | ||||
−0.179649 | + | 0.983731i | \(0.557496\pi\) | |||||||
\(434\) | 2.44504i | 0.117366i | ||||||||
\(435\) | 1.29590i | 0.0621335i | ||||||||
\(436\) | − 2.24698i | − 0.107611i | ||||||||
\(437\) | − 0.740939i | − 0.0354439i | ||||||||
\(438\) | −11.9366 | −0.570353 | ||||||||
\(439\) | 19.3924 | 0.925549 | 0.462774 | − | 0.886476i | \(-0.346854\pi\) | ||||
0.462774 | + | 0.886476i | \(0.346854\pi\) | |||||||
\(440\) | 2.15883i | 0.102918i | ||||||||
\(441\) | 4.13706 | 0.197003 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.0935 | 0.479558 | 0.239779 | − | 0.970828i | \(-0.422925\pi\) | ||||
0.239779 | + | 0.970828i | \(0.422925\pi\) | |||||||
\(444\) | 0.801938i | 0.0380583i | ||||||||
\(445\) | −2.41119 | −0.114301 | ||||||||
\(446\) | 16.8388 | 0.797339 | ||||||||
\(447\) | 4.24160i | 0.200621i | ||||||||
\(448\) | 1.69202i | 0.0799405i | ||||||||
\(449\) | − 2.78448i | − 0.131408i | −0.997839 | − | 0.0657039i | \(-0.979071\pi\) | ||||
0.997839 | − | 0.0657039i | \(-0.0209293\pi\) | |||||||
\(450\) | 1.00000i | 0.0471405i | ||||||||
\(451\) | −4.10129 | −0.193122 | ||||||||
\(452\) | 11.8726 | 0.558441 | ||||||||
\(453\) | − 22.9148i | − 1.07663i | ||||||||
\(454\) | −18.3056 | −0.859124 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.198062 | −0.00927512 | ||||||||
\(457\) | 13.1056i | 0.613054i | 0.951862 | + | 0.306527i | \(0.0991670\pi\) | ||||
−0.951862 | + | 0.306527i | \(0.900833\pi\) | |||||||
\(458\) | 5.14244 | 0.240290 | ||||||||
\(459\) | 2.35690 | 0.110010 | ||||||||
\(460\) | 3.74094i | 0.174422i | ||||||||
\(461\) | − 16.2174i | − 0.755321i | −0.925944 | − | 0.377661i | \(-0.876729\pi\) | ||||
0.925944 | − | 0.377661i | \(-0.123271\pi\) | |||||||
\(462\) | 3.65279i | 0.169943i | ||||||||
\(463\) | 15.5415i | 0.722277i | 0.932512 | + | 0.361139i | \(0.117612\pi\) | ||||
−0.932512 | + | 0.361139i | \(0.882388\pi\) | |||||||
\(464\) | 1.29590 | 0.0601605 | ||||||||
\(465\) | 1.44504 | 0.0670122 | ||||||||
\(466\) | − 10.9215i | − 0.505931i | ||||||||
\(467\) | 10.1578 | 0.470045 | 0.235023 | − | 0.971990i | \(-0.424484\pi\) | ||||
0.235023 | + | 0.971990i | \(0.424484\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.7995 | 0.591028 | ||||||||
\(470\) | − 8.87800i | − 0.409512i | ||||||||
\(471\) | −16.0707 | −0.740498 | ||||||||
\(472\) | −3.73125 | −0.171745 | ||||||||
\(473\) | − 27.0780i | − 1.24505i | ||||||||
\(474\) | 9.40581i | 0.432023i | ||||||||
\(475\) | 0.198062i | 0.00908772i | ||||||||
\(476\) | − 3.98792i | − 0.182786i | ||||||||
\(477\) | −1.00969 | −0.0462305 | ||||||||
\(478\) | −19.9041 | −0.910392 | ||||||||
\(479\) | 31.4263i | 1.43590i | 0.696094 | + | 0.717951i | \(0.254920\pi\) | ||||
−0.696094 | + | 0.717951i | \(0.745080\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 18.2228 | 0.830027 | ||||||||
\(483\) | 6.32975i | 0.288014i | ||||||||
\(484\) | −6.33944 | −0.288156 | ||||||||
\(485\) | 0.0881460 | 0.00400250 | ||||||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | 24.1323i | 1.09354i | 0.837284 | + | 0.546769i | \(0.184142\pi\) | ||||
−0.837284 | + | 0.546769i | \(0.815858\pi\) | |||||||
\(488\) | − 6.32304i | − 0.286231i | ||||||||
\(489\) | 0.488582i | 0.0220945i | ||||||||
\(490\) | −4.13706 | −0.186893 | ||||||||
\(491\) | 19.1099 | 0.862418 | 0.431209 | − | 0.902252i | \(-0.358087\pi\) | ||||
0.431209 | + | 0.902252i | \(0.358087\pi\) | |||||||
\(492\) | 1.89977i | 0.0856484i | ||||||||
\(493\) | −3.05429 | −0.137558 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.15883 | 0.0970324 | ||||||||
\(496\) | − 1.44504i | − 0.0648843i | ||||||||
\(497\) | 7.07367 | 0.317298 | ||||||||
\(498\) | 8.43296 | 0.377890 | ||||||||
\(499\) | 34.9724i | 1.56558i | 0.622287 | + | 0.782789i | \(0.286204\pi\) | ||||
−0.622287 | + | 0.782789i | \(0.713796\pi\) | |||||||
\(500\) | − 1.00000i | − 0.0447214i | ||||||||
\(501\) | − 14.0610i | − 0.628199i | ||||||||
\(502\) | − 17.0030i | − 0.758880i | ||||||||
\(503\) | 29.5579 | 1.31792 | 0.658962 | − | 0.752176i | \(-0.270996\pi\) | ||||
0.658962 | + | 0.752176i | \(0.270996\pi\) | |||||||
\(504\) | 1.69202 | 0.0753686 | ||||||||
\(505\) | − 11.1099i | − 0.494385i | ||||||||
\(506\) | 8.07606 | 0.359025 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.0097 | 0.577212 | ||||||||
\(509\) | − 24.4838i | − 1.08523i | −0.839983 | − | 0.542613i | \(-0.817435\pi\) | ||||
0.839983 | − | 0.542613i | \(-0.182565\pi\) | |||||||
\(510\) | −2.35690 | −0.104365 | ||||||||
\(511\) | 20.1970 | 0.893463 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | 0.198062i | 0.00874466i | ||||||||
\(514\) | − 7.65519i | − 0.337656i | ||||||||
\(515\) | 9.54825i | 0.420746i | ||||||||
\(516\) | −12.5429 | −0.552169 | ||||||||
\(517\) | −19.1661 | −0.842925 | ||||||||
\(518\) | − 1.35690i | − 0.0596186i | ||||||||
\(519\) | 21.7942 | 0.956658 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −33.8713 | −1.48393 | −0.741964 | − | 0.670439i | \(-0.766106\pi\) | ||||
−0.741964 | + | 0.670439i | \(0.766106\pi\) | |||||||
\(522\) | − 1.29590i | − 0.0567199i | ||||||||
\(523\) | −42.5870 | −1.86220 | −0.931100 | − | 0.364764i | \(-0.881150\pi\) | ||||
−0.931100 | + | 0.364764i | \(0.881150\pi\) | |||||||
\(524\) | 7.82908 | 0.342015 | ||||||||
\(525\) | − 1.69202i | − 0.0738459i | ||||||||
\(526\) | − 21.0411i | − 0.917438i | ||||||||
\(527\) | 3.40581i | 0.148360i | ||||||||
\(528\) | − 2.15883i | − 0.0939512i | ||||||||
\(529\) | −9.00538 | −0.391538 | ||||||||
\(530\) | 1.00969 | 0.0438581 | ||||||||
\(531\) | 3.73125i | 0.161922i | ||||||||
\(532\) | 0.335126 | 0.0145295 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 2.41119 | 0.104342 | ||||||||
\(535\) | − 18.1468i | − 0.784553i | ||||||||
\(536\) | −7.56465 | −0.326743 | ||||||||
\(537\) | −14.1293 | −0.609724 | ||||||||
\(538\) | − 24.3183i | − 1.04843i | ||||||||
\(539\) | 8.93123i | 0.384695i | ||||||||
\(540\) | − 1.00000i | − 0.0430331i | ||||||||
\(541\) | − 3.23298i | − 0.138997i | −0.997582 | − | 0.0694983i | \(-0.977860\pi\) | ||||
0.997582 | − | 0.0694983i | \(-0.0221398\pi\) | |||||||
\(542\) | 10.9922 | 0.472157 | ||||||||
\(543\) | −5.63773 | −0.241938 | ||||||||
\(544\) | 2.35690i | 0.101051i | ||||||||
\(545\) | 2.24698 | 0.0962500 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.51573 | −0.235836 | −0.117918 | − | 0.993023i | \(-0.537622\pi\) | ||||
−0.117918 | + | 0.993023i | \(0.537622\pi\) | |||||||
\(548\) | − 5.36227i | − 0.229065i | ||||||||
\(549\) | −6.32304 | −0.269861 | ||||||||
\(550\) | −2.15883 | −0.0920530 | ||||||||
\(551\) | − 0.256668i | − 0.0109344i | ||||||||
\(552\) | − 3.74094i | − 0.159225i | ||||||||
\(553\) | − 15.9148i | − 0.676768i | ||||||||
\(554\) | − 11.4601i | − 0.486893i | ||||||||
\(555\) | −0.801938 | −0.0340404 | ||||||||
\(556\) | −3.12200 | −0.132402 | ||||||||
\(557\) | 30.3502i | 1.28598i | 0.765875 | + | 0.642989i | \(0.222306\pi\) | ||||
−0.765875 | + | 0.642989i | \(0.777694\pi\) | |||||||
\(558\) | −1.44504 | −0.0611735 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1.69202 | −0.0715010 | ||||||||
\(561\) | 5.08815i | 0.214822i | ||||||||
\(562\) | −9.88231 | −0.416860 | ||||||||
\(563\) | −6.34375 | −0.267357 | −0.133679 | − | 0.991025i | \(-0.542679\pi\) | ||||
−0.133679 | + | 0.991025i | \(0.542679\pi\) | |||||||
\(564\) | 8.87800i | 0.373831i | ||||||||
\(565\) | 11.8726i | 0.499485i | ||||||||
\(566\) | − 21.3207i | − 0.896174i | ||||||||
\(567\) | − 1.69202i | − 0.0710582i | ||||||||
\(568\) | −4.18060 | −0.175414 | ||||||||
\(569\) | −24.7275 | −1.03663 | −0.518316 | − | 0.855189i | \(-0.673441\pi\) | ||||
−0.518316 | + | 0.855189i | \(0.673441\pi\) | |||||||
\(570\) | − 0.198062i | − 0.00829592i | ||||||||
\(571\) | −13.6262 | −0.570240 | −0.285120 | − | 0.958492i | \(-0.592033\pi\) | ||||
−0.285120 | + | 0.958492i | \(0.592033\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.59419 | 0.108374 | ||||||||
\(574\) | − 3.21446i | − 0.134169i | ||||||||
\(575\) | −3.74094 | −0.156008 | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | 16.2828i | 0.677860i | 0.940812 | + | 0.338930i | \(0.110065\pi\) | ||||
−0.940812 | + | 0.338930i | \(0.889935\pi\) | |||||||
\(578\) | 11.4450i | 0.476051i | ||||||||
\(579\) | 3.98361i | 0.165553i | ||||||||
\(580\) | 1.29590i | 0.0538092i | ||||||||
\(581\) | −14.2687 | −0.591967 | ||||||||
\(582\) | −0.0881460 | −0.00365377 | ||||||||
\(583\) | − 2.17975i | − 0.0902760i | ||||||||
\(584\) | −11.9366 | −0.493940 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −18.7090 | −0.772862 | ||||||||
\(587\) | 11.0344i | 0.455440i | 0.973727 | + | 0.227720i | \(0.0731271\pi\) | ||||
−0.973727 | + | 0.227720i | \(0.926873\pi\) | |||||||
\(588\) | 4.13706 | 0.170610 | ||||||||
\(589\) | −0.286208 | −0.0117930 | ||||||||
\(590\) | − 3.73125i | − 0.153613i | ||||||||
\(591\) | − 6.65040i | − 0.273561i | ||||||||
\(592\) | 0.801938i | 0.0329594i | ||||||||
\(593\) | − 25.4905i | − 1.04677i | −0.852096 | − | 0.523385i | \(-0.824669\pi\) | ||||
0.852096 | − | 0.523385i | \(-0.175331\pi\) | |||||||
\(594\) | −2.15883 | −0.0885780 | ||||||||
\(595\) | 3.98792 | 0.163489 | ||||||||
\(596\) | 4.24160i | 0.173743i | ||||||||
\(597\) | −1.01639 | −0.0415982 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.501729 | −0.0205001 | −0.0102500 | − | 0.999947i | \(-0.503263\pi\) | ||||
−0.0102500 | + | 0.999947i | \(0.503263\pi\) | |||||||
\(600\) | 1.00000i | 0.0408248i | ||||||||
\(601\) | −18.3744 | −0.749506 | −0.374753 | − | 0.927125i | \(-0.622272\pi\) | ||||
−0.374753 | + | 0.927125i | \(0.622272\pi\) | |||||||
\(602\) | 21.2228 | 0.864977 | ||||||||
\(603\) | 7.56465i | 0.308056i | ||||||||
\(604\) | − 22.9148i | − 0.932392i | ||||||||
\(605\) | − 6.33944i | − 0.257735i | ||||||||
\(606\) | 11.1099i | 0.451309i | ||||||||
\(607\) | −17.1395 | −0.695669 | −0.347835 | − | 0.937556i | \(-0.613083\pi\) | ||||
−0.347835 | + | 0.937556i | \(0.613083\pi\) | |||||||
\(608\) | −0.198062 | −0.00803249 | ||||||||
\(609\) | 2.19269i | 0.0888521i | ||||||||
\(610\) | 6.32304 | 0.256013 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 2.35690 | 0.0952719 | ||||||||
\(613\) | − 1.15751i | − 0.0467512i | −0.999727 | − | 0.0233756i | \(-0.992559\pi\) | ||||
0.999727 | − | 0.0233756i | \(-0.00744136\pi\) | |||||||
\(614\) | 17.2241 | 0.695110 | ||||||||
\(615\) | −1.89977 | −0.0766062 | ||||||||
\(616\) | 3.65279i | 0.147175i | ||||||||
\(617\) | − 7.71618i | − 0.310642i | −0.987864 | − | 0.155321i | \(-0.950359\pi\) | ||||
0.987864 | − | 0.155321i | \(-0.0496412\pi\) | |||||||
\(618\) | − 9.54825i | − 0.384087i | ||||||||
\(619\) | 16.1142i | 0.647686i | 0.946111 | + | 0.323843i | \(0.104975\pi\) | ||||
−0.946111 | + | 0.323843i | \(0.895025\pi\) | |||||||
\(620\) | 1.44504 | 0.0580343 | ||||||||
\(621\) | −3.74094 | −0.150119 | ||||||||
\(622\) | − 13.5200i | − 0.542104i | ||||||||
\(623\) | −4.07979 | −0.163453 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | − 24.3303i | − 0.972436i | ||||||||
\(627\) | −0.427583 | −0.0170760 | ||||||||
\(628\) | −16.0707 | −0.641290 | ||||||||
\(629\) | − 1.89008i | − 0.0753626i | ||||||||
\(630\) | 1.69202i | 0.0674117i | ||||||||
\(631\) | − 7.77586i | − 0.309552i | −0.987950 | − | 0.154776i | \(-0.950534\pi\) | ||||
0.987950 | − | 0.154776i | \(-0.0494656\pi\) | |||||||
\(632\) | 9.40581i | 0.374143i | ||||||||
\(633\) | −10.1414 | −0.403083 | ||||||||
\(634\) | −34.7821 | −1.38137 | ||||||||
\(635\) | 13.0097i | 0.516274i | ||||||||
\(636\) | −1.00969 | −0.0400368 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.79763 | 0.110759 | ||||||||
\(639\) | 4.18060i | 0.165382i | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 35.1293 | 1.38752 | 0.693762 | − | 0.720204i | \(-0.255952\pi\) | ||||
0.693762 | + | 0.720204i | \(0.255952\pi\) | |||||||
\(642\) | 18.1468i | 0.716195i | ||||||||
\(643\) | 14.5459i | 0.573633i | 0.957986 | + | 0.286816i | \(0.0925970\pi\) | ||||
−0.957986 | + | 0.286816i | \(0.907403\pi\) | |||||||
\(644\) | 6.32975i | 0.249427i | ||||||||
\(645\) | − 12.5429i | − 0.493875i | ||||||||
\(646\) | 0.466812 | 0.0183665 | ||||||||
\(647\) | −36.2234 | −1.42409 | −0.712045 | − | 0.702134i | \(-0.752231\pi\) | ||||
−0.712045 | + | 0.702134i | \(0.752231\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | −8.05515 | −0.316192 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.44504 | 0.0958287 | ||||||||
\(652\) | 0.488582i | 0.0191344i | ||||||||
\(653\) | 19.4926 | 0.762806 | 0.381403 | − | 0.924409i | \(-0.375441\pi\) | ||||
0.381403 | + | 0.924409i | \(0.375441\pi\) | |||||||
\(654\) | −2.24698 | −0.0878639 | ||||||||
\(655\) | 7.82908i | 0.305908i | ||||||||
\(656\) | 1.89977i | 0.0741737i | ||||||||
\(657\) | 11.9366i | 0.465691i | ||||||||
\(658\) | − 15.0218i | − 0.585610i | ||||||||
\(659\) | 38.3400 | 1.49352 | 0.746758 | − | 0.665096i | \(-0.231609\pi\) | ||||
0.746758 | + | 0.665096i | \(0.231609\pi\) | |||||||
\(660\) | 2.15883 | 0.0840325 | ||||||||
\(661\) | 13.5985i | 0.528920i | 0.964397 | + | 0.264460i | \(0.0851938\pi\) | ||||
−0.964397 | + | 0.264460i | \(0.914806\pi\) | |||||||
\(662\) | 9.66919 | 0.375804 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.43296 | 0.327262 | ||||||||
\(665\) | 0.335126i | 0.0129956i | ||||||||
\(666\) | 0.801938 | 0.0310745 | ||||||||
\(667\) | 4.84787 | 0.187710 | ||||||||
\(668\) | − 14.0610i | − 0.544036i | ||||||||
\(669\) | − 16.8388i | − 0.651025i | ||||||||
\(670\) | − 7.56465i | − 0.292248i | ||||||||
\(671\) | − 13.6504i | − 0.526968i | ||||||||
\(672\) | 1.69202 | 0.0652711 | ||||||||
\(673\) | 49.7090 | 1.91614 | 0.958071 | − | 0.286532i | \(-0.0925025\pi\) | ||||
0.958071 | + | 0.286532i | \(0.0925025\pi\) | |||||||
\(674\) | − 17.3612i | − 0.668729i | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −50.2573 | −1.93154 | −0.965772 | − | 0.259394i | \(-0.916477\pi\) | ||||
−0.965772 | + | 0.259394i | \(0.916477\pi\) | |||||||
\(678\) | − 11.8726i | − 0.455965i | ||||||||
\(679\) | 0.149145 | 0.00572366 | ||||||||
\(680\) | −2.35690 | −0.0903828 | ||||||||
\(681\) | 18.3056i | 0.701472i | ||||||||
\(682\) | − 3.11960i | − 0.119456i | ||||||||
\(683\) | − 21.5415i | − 0.824264i | −0.911124 | − | 0.412132i | \(-0.864784\pi\) | ||||
0.911124 | − | 0.412132i | \(-0.135216\pi\) | |||||||
\(684\) | 0.198062i | 0.00757310i | ||||||||
\(685\) | 5.36227 | 0.204882 | ||||||||
\(686\) | −18.8442 | −0.719473 | ||||||||
\(687\) | − 5.14244i | − 0.196196i | ||||||||
\(688\) | −12.5429 | −0.478193 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 3.74094 | 0.142415 | ||||||||
\(691\) | 50.8165i | 1.93315i | 0.256380 | + | 0.966576i | \(0.417470\pi\) | ||||
−0.256380 | + | 0.966576i | \(0.582530\pi\) | |||||||
\(692\) | 21.7942 | 0.828490 | ||||||||
\(693\) | 3.65279 | 0.138758 | ||||||||
\(694\) | − 8.86294i | − 0.336432i | ||||||||
\(695\) | − 3.12200i | − 0.118424i | ||||||||
\(696\) | − 1.29590i | − 0.0491208i | ||||||||
\(697\) | − 4.47757i | − 0.169600i | ||||||||
\(698\) | 2.78554 | 0.105434 | ||||||||
\(699\) | −10.9215 | −0.413091 | ||||||||
\(700\) | − 1.69202i | − 0.0639524i | ||||||||
\(701\) | 13.2024 | 0.498647 | 0.249323 | − | 0.968420i | \(-0.419792\pi\) | ||||
0.249323 | + | 0.968420i | \(0.419792\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.158834 | 0.00599052 | ||||||||
\(704\) | − 2.15883i | − 0.0813641i | ||||||||
\(705\) | −8.87800 | −0.334365 | ||||||||
\(706\) | −21.0640 | −0.792753 | ||||||||
\(707\) | − 18.7982i | − 0.706980i | ||||||||
\(708\) | 3.73125i | 0.140229i | ||||||||
\(709\) | 0.430567i | 0.0161703i | 0.999967 | + | 0.00808515i | \(0.00257361\pi\) | ||||
−0.999967 | + | 0.00808515i | \(0.997426\pi\) | |||||||
\(710\) | − 4.18060i | − 0.156895i | ||||||||
\(711\) | 9.40581 | 0.352746 | ||||||||
\(712\) | 2.41119 | 0.0903632 | ||||||||
\(713\) | − 5.40581i | − 0.202449i | ||||||||
\(714\) | −3.98792 | −0.149244 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −14.1293 | −0.528036 | ||||||||
\(717\) | 19.9041i | 0.743332i | ||||||||
\(718\) | 17.3274 | 0.646651 | ||||||||
\(719\) | −8.24459 | −0.307471 | −0.153736 | − | 0.988112i | \(-0.549130\pi\) | ||||
−0.153736 | + | 0.988112i | \(0.549130\pi\) | |||||||
\(720\) | − 1.00000i | − 0.0372678i | ||||||||
\(721\) | 16.1558i | 0.601675i | ||||||||
\(722\) | − 18.9608i | − 0.705647i | ||||||||
\(723\) | − 18.2228i | − 0.677714i | ||||||||
\(724\) | −5.63773 | −0.209524 | ||||||||
\(725\) | −1.29590 | −0.0481284 | ||||||||
\(726\) | 6.33944i | 0.235279i | ||||||||
\(727\) | −21.2664 | −0.788726 | −0.394363 | − | 0.918955i | \(-0.629035\pi\) | ||||
−0.394363 | + | 0.918955i | \(0.629035\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | − 11.9366i | − 0.441794i | ||||||||
\(731\) | 29.5623 | 1.09340 | ||||||||
\(732\) | −6.32304 | −0.233706 | ||||||||
\(733\) | − 38.9178i | − 1.43746i | −0.695288 | − | 0.718731i | \(-0.744723\pi\) | ||||
0.695288 | − | 0.718731i | \(-0.255277\pi\) | |||||||
\(734\) | 30.8049i | 1.13703i | ||||||||
\(735\) | 4.13706i | 0.152598i | ||||||||
\(736\) | − 3.74094i | − 0.137893i | ||||||||
\(737\) | −16.3308 | −0.601553 | ||||||||
\(738\) | 1.89977 | 0.0699316 | ||||||||
\(739\) | 4.48486i | 0.164978i | 0.996592 | + | 0.0824891i | \(0.0262870\pi\) | ||||
−0.996592 | + | 0.0824891i | \(0.973713\pi\) | |||||||
\(740\) | −0.801938 | −0.0294798 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.70841 | 0.0627179 | ||||||||
\(743\) | − 26.8558i | − 0.985242i | −0.870244 | − | 0.492621i | \(-0.836039\pi\) | ||||
0.870244 | − | 0.492621i | \(-0.163961\pi\) | |||||||
\(744\) | −1.44504 | −0.0529778 | ||||||||
\(745\) | −4.24160 | −0.155400 | ||||||||
\(746\) | 25.6668i | 0.939728i | ||||||||
\(747\) | − 8.43296i | − 0.308546i | ||||||||
\(748\) | 5.08815i | 0.186041i | ||||||||
\(749\) | − 30.7047i | − 1.12193i | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | 5.64012 | 0.205811 | 0.102905 | − | 0.994691i | \(-0.467186\pi\) | ||||
0.102905 | + | 0.994691i | \(0.467186\pi\) | |||||||
\(752\) | 8.87800i | 0.323747i | ||||||||
\(753\) | −17.0030 | −0.619623 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22.9148 | 0.833956 | ||||||||
\(756\) | − 1.69202i | − 0.0615382i | ||||||||
\(757\) | −35.6644 | −1.29624 | −0.648122 | − | 0.761536i | \(-0.724445\pi\) | ||||
−0.648122 | + | 0.761536i | \(0.724445\pi\) | |||||||
\(758\) | −5.46144 | −0.198368 | ||||||||
\(759\) | − 8.07606i | − 0.293143i | ||||||||
\(760\) | − 0.198062i | − 0.00718447i | ||||||||
\(761\) | 2.68425i | 0.0973041i | 0.998816 | + | 0.0486520i | \(0.0154925\pi\) | ||||
−0.998816 | + | 0.0486520i | \(0.984507\pi\) | |||||||
\(762\) | − 13.0097i | − 0.471291i | ||||||||
\(763\) | 3.80194 | 0.137639 | ||||||||
\(764\) | 2.59419 | 0.0938544 | ||||||||
\(765\) | 2.35690i | 0.0852137i | ||||||||
\(766\) | 25.9221 | 0.936605 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | − 48.7644i | − 1.75849i | −0.476372 | − | 0.879244i | \(-0.658048\pi\) | ||||
0.476372 | − | 0.879244i | \(-0.341952\pi\) | |||||||
\(770\) | −3.65279 | −0.131638 | ||||||||
\(771\) | −7.65519 | −0.275695 | ||||||||
\(772\) | 3.98361i | 0.143373i | ||||||||
\(773\) | 46.6152i | 1.67663i | 0.545184 | + | 0.838316i | \(0.316460\pi\) | ||||
−0.545184 | + | 0.838316i | \(0.683540\pi\) | |||||||
\(774\) | 12.5429i | 0.450844i | ||||||||
\(775\) | 1.44504i | 0.0519074i | ||||||||
\(776\) | −0.0881460 | −0.00316426 | ||||||||
\(777\) | −1.35690 | −0.0486784 | ||||||||
\(778\) | − 32.0006i | − 1.14728i | ||||||||
\(779\) | 0.376273 | 0.0134814 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.02523 | −0.322948 | ||||||||
\(782\) | 8.81700i | 0.315295i | ||||||||
\(783\) | −1.29590 | −0.0463116 | ||||||||
\(784\) | 4.13706 | 0.147752 | ||||||||
\(785\) | − 16.0707i | − 0.573587i | ||||||||
\(786\) | − 7.82908i | − 0.279254i | ||||||||
\(787\) | − 27.4045i | − 0.976864i | −0.872602 | − | 0.488432i | \(-0.837569\pi\) | ||||
0.872602 | − | 0.488432i | \(-0.162431\pi\) | |||||||
\(788\) | − 6.65040i | − 0.236911i | ||||||||
\(789\) | −21.0411 | −0.749085 | ||||||||
\(790\) | −9.40581 | −0.334644 | ||||||||
\(791\) | 20.0887i | 0.714273i | ||||||||
\(792\) | −2.15883 | −0.0767108 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0.457123 | 0.0162227 | ||||||||
\(795\) | − 1.00969i | − 0.0358100i | ||||||||
\(796\) | −1.01639 | −0.0360251 | ||||||||
\(797\) | 5.70278 | 0.202003 | 0.101001 | − | 0.994886i | \(-0.467795\pi\) | ||||
0.101001 | + | 0.994886i | \(0.467795\pi\) | |||||||
\(798\) | − 0.335126i | − 0.0118633i | ||||||||
\(799\) | − 20.9245i | − 0.740257i | ||||||||
\(800\) | 1.00000i | 0.0353553i | ||||||||
\(801\) | − 2.41119i | − 0.0851952i | ||||||||
\(802\) | 23.2553 | 0.821175 | ||||||||
\(803\) | −25.7692 | −0.909374 | ||||||||
\(804\) | 7.56465i | 0.266785i | ||||||||
\(805\) | −6.32975 | −0.223094 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −24.3183 | −0.856043 | ||||||||
\(808\) | 11.1099i | 0.390845i | ||||||||
\(809\) | −29.6165 | −1.04126 | −0.520631 | − | 0.853782i | \(-0.674303\pi\) | ||||
−0.520631 | + | 0.853782i | \(0.674303\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | 48.8901i | 1.71676i | 0.513012 | + | 0.858382i | \(0.328530\pi\) | ||||
−0.513012 | + | 0.858382i | \(0.671470\pi\) | |||||||
\(812\) | 2.19269i | 0.0769482i | ||||||||
\(813\) | − 10.9922i | − 0.385514i | ||||||||
\(814\) | 1.73125i | 0.0606803i | ||||||||
\(815\) | −0.488582 | −0.0171143 | ||||||||
\(816\) | 2.35690 | 0.0825079 | ||||||||
\(817\) | 2.48427i | 0.0869136i | ||||||||
\(818\) | −39.0629 | −1.36580 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.89977 | −0.0663429 | ||||||||
\(821\) | 19.7942i | 0.690821i | 0.938452 | + | 0.345411i | \(0.112260\pi\) | ||||
−0.938452 | + | 0.345411i | \(0.887740\pi\) | |||||||
\(822\) | −5.36227 | −0.187031 | ||||||||
\(823\) | −49.6118 | −1.72936 | −0.864679 | − | 0.502325i | \(-0.832478\pi\) | ||||
−0.864679 | + | 0.502325i | \(0.832478\pi\) | |||||||
\(824\) | − 9.54825i | − 0.332629i | ||||||||
\(825\) | 2.15883i | 0.0751609i | ||||||||
\(826\) | − 6.31336i | − 0.219670i | ||||||||
\(827\) | 26.0683i | 0.906483i | 0.891388 | + | 0.453242i | \(0.149733\pi\) | ||||
−0.891388 | + | 0.453242i | \(0.850267\pi\) | |||||||
\(828\) | −3.74094 | −0.130007 | ||||||||
\(829\) | −46.2215 | −1.60534 | −0.802669 | − | 0.596424i | \(-0.796588\pi\) | ||||
−0.802669 | + | 0.596424i | \(0.796588\pi\) | |||||||
\(830\) | 8.43296i | 0.292712i | ||||||||
\(831\) | −11.4601 | −0.397547 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.75063 | −0.337839 | ||||||||
\(834\) | 3.12200i | 0.108106i | ||||||||
\(835\) | 14.0610 | 0.486601 | ||||||||
\(836\) | −0.427583 | −0.0147883 | ||||||||
\(837\) | 1.44504i | 0.0499480i | ||||||||
\(838\) | 18.1269i | 0.626183i | ||||||||
\(839\) | 33.2693i | 1.14859i | 0.818650 | + | 0.574293i | \(0.194723\pi\) | ||||
−0.818650 | + | 0.574293i | \(0.805277\pi\) | |||||||
\(840\) | 1.69202i | 0.0583803i | ||||||||
\(841\) | −27.3207 | −0.942091 | ||||||||
\(842\) | 20.4916 | 0.706186 | ||||||||
\(843\) | 9.88231i | 0.340365i | ||||||||
\(844\) | −10.1414 | −0.349081 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 8.87800 | 0.305232 | ||||||||
\(847\) | − 10.7265i | − 0.368566i | ||||||||
\(848\) | −1.00969 | −0.0346729 | ||||||||
\(849\) | −21.3207 | −0.731723 | ||||||||
\(850\) | − 2.35690i | − 0.0808409i | ||||||||
\(851\) | 3.00000i | 0.102839i | ||||||||
\(852\) | 4.18060i | 0.143225i | ||||||||
\(853\) | − 39.3002i | − 1.34561i | −0.739818 | − | 0.672807i | \(-0.765089\pi\) | ||||
0.739818 | − | 0.672807i | \(-0.234911\pi\) | |||||||
\(854\) | 10.6987 | 0.366103 | ||||||||
\(855\) | −0.198062 | −0.00677359 | ||||||||
\(856\) | 18.1468i | 0.620243i | ||||||||
\(857\) | 39.7566 | 1.35806 | 0.679030 | − | 0.734111i | \(-0.262401\pi\) | ||||
0.679030 | + | 0.734111i | \(0.262401\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.43860 | −0.117324 | −0.0586618 | − | 0.998278i | \(-0.518683\pi\) | ||||
−0.0586618 | + | 0.998278i | \(0.518683\pi\) | |||||||
\(860\) | − 12.5429i | − 0.427709i | ||||||||
\(861\) | −3.21446 | −0.109548 | ||||||||
\(862\) | 22.2989 | 0.759503 | ||||||||
\(863\) | − 21.2301i | − 0.722681i | −0.932434 | − | 0.361341i | \(-0.882319\pi\) | ||||
0.932434 | − | 0.361341i | \(-0.117681\pi\) | |||||||
\(864\) | 1.00000i | 0.0340207i | ||||||||
\(865\) | 21.7942i | 0.741024i | ||||||||
\(866\) | 7.47650i | 0.254062i | ||||||||
\(867\) | 11.4450 | 0.388694 | ||||||||
\(868\) | 2.44504 | 0.0829901 | ||||||||
\(869\) | 20.3056i | 0.688820i | ||||||||
\(870\) | 1.29590 | 0.0439350 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −2.24698 | −0.0760923 | ||||||||
\(873\) | 0.0881460i | 0.00298329i | ||||||||
\(874\) | −0.740939 | −0.0250626 | ||||||||
\(875\) | 1.69202 | 0.0572008 | ||||||||
\(876\) | 11.9366i | 0.403301i | ||||||||
\(877\) | 5.74227i | 0.193903i | 0.995289 | + | 0.0969513i | \(0.0309091\pi\) | ||||
−0.995289 | + | 0.0969513i | \(0.969091\pi\) | |||||||
\(878\) | − 19.3924i | − 0.654462i | ||||||||
\(879\) | 18.7090i | 0.631039i | ||||||||
\(880\) | 2.15883 | 0.0727743 | ||||||||
\(881\) | −12.6069 | −0.424736 | −0.212368 | − | 0.977190i | \(-0.568118\pi\) | ||||
−0.212368 | + | 0.977190i | \(0.568118\pi\) | |||||||
\(882\) | − 4.13706i | − 0.139302i | ||||||||
\(883\) | −25.8086 | −0.868530 | −0.434265 | − | 0.900785i | \(-0.642992\pi\) | ||||
−0.434265 | + | 0.900785i | \(0.642992\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.73125 | −0.125425 | ||||||||
\(886\) | − 10.0935i | − 0.339099i | ||||||||
\(887\) | −20.2392 | −0.679566 | −0.339783 | − | 0.940504i | \(-0.610354\pi\) | ||||
−0.339783 | + | 0.940504i | \(0.610354\pi\) | |||||||
\(888\) | 0.801938 | 0.0269113 | ||||||||
\(889\) | 22.0127i | 0.738281i | ||||||||
\(890\) | 2.41119i | 0.0808233i | ||||||||
\(891\) | 2.15883i | 0.0723236i | ||||||||
\(892\) | − 16.8388i | − 0.563804i | ||||||||
\(893\) | 1.75840 | 0.0588425 | ||||||||
\(894\) | 4.24160 | 0.141860 | ||||||||
\(895\) | − 14.1293i | − 0.472290i | ||||||||
\(896\) | 1.69202 | 0.0565265 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.78448 | −0.0929193 | ||||||||
\(899\) | − 1.87263i | − 0.0624556i | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 2.37973 | 0.0792803 | ||||||||
\(902\) | 4.10129i | 0.136558i | ||||||||
\(903\) | − 21.2228i | − 0.706251i | ||||||||
\(904\) | − 11.8726i | − 0.394878i | ||||||||
\(905\) | − 5.63773i | − 0.187404i | ||||||||
\(906\) | −22.9148 | −0.761294 | ||||||||
\(907\) | 3.52350 | 0.116996 | 0.0584979 | − | 0.998288i | \(-0.481369\pi\) | ||||
0.0584979 | + | 0.998288i | \(0.481369\pi\) | |||||||
\(908\) | 18.3056i | 0.607492i | ||||||||
\(909\) | 11.1099 | 0.368493 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.7426 | −1.15107 | −0.575537 | − | 0.817776i | \(-0.695207\pi\) | ||||
−0.575537 | + | 0.817776i | \(0.695207\pi\) | |||||||
\(912\) | 0.198062i | 0.00655850i | ||||||||
\(913\) | 18.2054 | 0.602509 | ||||||||
\(914\) | 13.1056 | 0.433495 | ||||||||
\(915\) | − 6.32304i | − 0.209033i | ||||||||
\(916\) | − 5.14244i | − 0.169911i | ||||||||
\(917\) | 13.2470i | 0.437454i | ||||||||
\(918\) | − 2.35690i | − 0.0777892i | ||||||||
\(919\) | −24.1430 | −0.796405 | −0.398203 | − | 0.917298i | \(-0.630366\pi\) | ||||
−0.398203 | + | 0.917298i | \(0.630366\pi\) | |||||||
\(920\) | 3.74094 | 0.123335 | ||||||||
\(921\) | − 17.2241i | − 0.567555i | ||||||||
\(922\) | −16.2174 | −0.534093 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 3.65279 | 0.120168 | ||||||||
\(925\) | − 0.801938i | − 0.0263676i | ||||||||
\(926\) | 15.5415 | 0.510727 | ||||||||
\(927\) | −9.54825 | −0.313606 | ||||||||
\(928\) | − 1.29590i | − 0.0425399i | ||||||||
\(929\) | 56.9700i | 1.86912i | 0.355800 | + | 0.934562i | \(0.384209\pi\) | ||||
−0.355800 | + | 0.934562i | \(0.615791\pi\) | |||||||
\(930\) | − 1.44504i | − 0.0473848i | ||||||||
\(931\) | − 0.819396i | − 0.0268546i | ||||||||
\(932\) | −10.9215 | −0.357747 | ||||||||
\(933\) | −13.5200 | −0.442626 | ||||||||
\(934\) | − 10.1578i | − 0.332372i | ||||||||
\(935\) | −5.08815 | −0.166400 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −45.7966 | −1.49611 | −0.748054 | − | 0.663638i | \(-0.769012\pi\) | ||||
−0.748054 | + | 0.663638i | \(0.769012\pi\) | |||||||
\(938\) | − 12.7995i | − 0.417920i | ||||||||
\(939\) | −24.3303 | −0.793991 | ||||||||
\(940\) | −8.87800 | −0.289569 | ||||||||
\(941\) | 7.10262i | 0.231539i | 0.993276 | + | 0.115769i | \(0.0369334\pi\) | ||||
−0.993276 | + | 0.115769i | \(0.963067\pi\) | |||||||
\(942\) | 16.0707i | 0.523611i | ||||||||
\(943\) | 7.10693i | 0.231434i | ||||||||
\(944\) | 3.73125i | 0.121442i | ||||||||
\(945\) | 1.69202 | 0.0550415 | ||||||||
\(946\) | −27.0780 | −0.880381 | ||||||||
\(947\) | − 11.2524i | − 0.365652i | −0.983145 | − | 0.182826i | \(-0.941475\pi\) | ||||
0.983145 | − | 0.182826i | \(-0.0585246\pi\) | |||||||
\(948\) | 9.40581 | 0.305487 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0.198062 | 0.00642599 | ||||||||
\(951\) | 34.7821i | 1.12789i | ||||||||
\(952\) | −3.98792 | −0.129249 | ||||||||
\(953\) | 1.61702 | 0.0523805 | 0.0261902 | − | 0.999657i | \(-0.491662\pi\) | ||||
0.0261902 | + | 0.999657i | \(0.491662\pi\) | |||||||
\(954\) | 1.00969i | 0.0326899i | ||||||||
\(955\) | 2.59419i | 0.0839459i | ||||||||
\(956\) | 19.9041i | 0.643744i | ||||||||
\(957\) | − 2.79763i | − 0.0904344i | ||||||||
\(958\) | 31.4263 | 1.01534 | ||||||||
\(959\) | 9.07308 | 0.292985 | ||||||||
\(960\) | − 1.00000i | − 0.0322749i | ||||||||
\(961\) | 28.9119 | 0.932640 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 18.1468 | 0.584771 | ||||||||
\(964\) | − 18.2228i | − 0.586917i | ||||||||
\(965\) | −3.98361 | −0.128237 | ||||||||
\(966\) | 6.32975 | 0.203656 | ||||||||
\(967\) | 24.1588i | 0.776896i | 0.921471 | + | 0.388448i | \(0.126989\pi\) | ||||
−0.921471 | + | 0.388448i | \(0.873011\pi\) | |||||||
\(968\) | 6.33944i | 0.203757i | ||||||||
\(969\) | − 0.466812i | − 0.0149962i | ||||||||
\(970\) | − 0.0881460i | − 0.00283020i | ||||||||
\(971\) | 43.2669 | 1.38850 | 0.694251 | − | 0.719733i | \(-0.255736\pi\) | ||||
0.694251 | + | 0.719733i | \(0.255736\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | − 5.28249i | − 0.169349i | ||||||||
\(974\) | 24.1323 | 0.773248 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.32304 | −0.202396 | ||||||||
\(977\) | − 24.9782i | − 0.799124i | −0.916706 | − | 0.399562i | \(-0.869162\pi\) | ||||
0.916706 | − | 0.399562i | \(-0.130838\pi\) | |||||||
\(978\) | 0.488582 | 0.0156231 | ||||||||
\(979\) | 5.20536 | 0.166364 | ||||||||
\(980\) | 4.13706i | 0.132154i | ||||||||
\(981\) | 2.24698i | 0.0717405i | ||||||||
\(982\) | − 19.1099i | − 0.609822i | ||||||||
\(983\) | − 19.3134i | − 0.616000i | −0.951386 | − | 0.308000i | \(-0.900340\pi\) | ||||
0.951386 | − | 0.308000i | \(-0.0996597\pi\) | |||||||
\(984\) | 1.89977 | 0.0605625 | ||||||||
\(985\) | 6.65040 | 0.211899 | ||||||||
\(986\) | 3.05429i | 0.0972685i | ||||||||
\(987\) | −15.0218 | −0.478148 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −46.9221 | −1.49204 | ||||||||
\(990\) | − 2.15883i | − 0.0686122i | ||||||||
\(991\) | −27.5090 | −0.873853 | −0.436926 | − | 0.899497i | \(-0.643933\pi\) | ||||
−0.436926 | + | 0.899497i | \(0.643933\pi\) | |||||||
\(992\) | −1.44504 | −0.0458801 | ||||||||
\(993\) | − 9.66919i | − 0.306842i | ||||||||
\(994\) | − 7.07367i | − 0.224363i | ||||||||
\(995\) | − 1.01639i | − 0.0322218i | ||||||||
\(996\) | − 8.43296i | − 0.267209i | ||||||||
\(997\) | −23.1933 | −0.734538 | −0.367269 | − | 0.930115i | \(-0.619707\pi\) | ||||
−0.367269 | + | 0.930115i | \(0.619707\pi\) | |||||||
\(998\) | 34.9724 | 1.10703 | ||||||||
\(999\) | − 0.801938i | − 0.0253722i |
(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 | 5070.2.b.t.1351.1 | 6 | ||
13.5 | odd | 4 | 5070.2.a.bj.1.3 | ✓ | 3 | ||
13.8 | odd | 4 | 5070.2.a.bu.1.1 | yes | 3 | ||
13.12 | even | 2 | inner | 5070.2.b.t.1351.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5070.2.a.bj.1.3 | ✓ | 3 | 13.5 | odd | 4 | ||
5070.2.a.bu.1.1 | yes | 3 | 13.8 | odd | 4 | ||
5070.2.b.t.1351.1 | 6 | 1.1 | even | 1 | trivial | ||
5070.2.b.t.1351.6 | 6 | 13.12 | even | 2 | inner |