Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5070,2,Mod(1,5070)]
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, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5070.1");
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.a (trivial) |
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: | yes |
Analytic conductor: | \(40.4841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.445042\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5070.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −1.69202 | −0.639524 | −0.319762 | − | 0.947498i | \(-0.603603\pi\) | ||||
−0.319762 | + | 0.947498i | \(0.603603\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 2.15883 | 0.650913 | 0.325456 | − | 0.945557i | \(-0.394482\pi\) | ||||
0.325456 | + | 0.945557i | \(0.394482\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.69202 | −0.452212 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.35690 | 0.571631 | 0.285816 | − | 0.958285i | \(-0.407736\pi\) | ||||
0.285816 | + | 0.958285i | \(0.407736\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 0.198062 | 0.0454386 | 0.0227193 | − | 0.999742i | \(-0.492768\pi\) | ||||
0.0227193 | + | 0.999742i | \(0.492768\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 1.69202 | 0.369229 | ||||||||
\(22\) | 2.15883 | 0.460265 | ||||||||
\(23\) | −3.74094 | −0.780040 | −0.390020 | − | 0.920806i | \(-0.627532\pi\) | ||||
−0.390020 | + | 0.920806i | \(0.627532\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.69202 | −0.319762 | ||||||||
\(29\) | 1.29590 | 0.240642 | 0.120321 | − | 0.992735i | \(-0.461608\pi\) | ||||
0.120321 | + | 0.992735i | \(0.461608\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | 1.44504 | 0.259537 | 0.129769 | − | 0.991544i | \(-0.458577\pi\) | ||||
0.129769 | + | 0.991544i | \(0.458577\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −2.15883 | −0.375805 | ||||||||
\(34\) | 2.35690 | 0.404204 | ||||||||
\(35\) | −1.69202 | −0.286004 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 0.801938 | 0.131838 | 0.0659189 | − | 0.997825i | \(-0.479002\pi\) | ||||
0.0659189 | + | 0.997825i | \(0.479002\pi\) | |||||||
\(38\) | 0.198062 | 0.0321299 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −1.89977 | −0.296695 | −0.148347 | − | 0.988935i | \(-0.547395\pi\) | ||||
−0.148347 | + | 0.988935i | \(0.547395\pi\) | |||||||
\(42\) | 1.69202 | 0.261085 | ||||||||
\(43\) | 12.5429 | 1.91277 | 0.956385 | − | 0.292108i | \(-0.0943566\pi\) | ||||
0.956385 | + | 0.292108i | \(0.0943566\pi\) | |||||||
\(44\) | 2.15883 | 0.325456 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | −3.74094 | −0.551571 | ||||||||
\(47\) | 8.87800 | 1.29499 | 0.647495 | − | 0.762070i | \(-0.275817\pi\) | ||||
0.647495 | + | 0.762070i | \(0.275817\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −4.13706 | −0.591009 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −2.35690 | −0.330031 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.00969 | −0.138691 | −0.0693457 | − | 0.997593i | \(-0.522091\pi\) | ||||
−0.0693457 | + | 0.997593i | \(0.522091\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 2.15883 | 0.291097 | ||||||||
\(56\) | −1.69202 | −0.226106 | ||||||||
\(57\) | −0.198062 | −0.0262340 | ||||||||
\(58\) | 1.29590 | 0.170160 | ||||||||
\(59\) | 3.73125 | 0.485767 | 0.242884 | − | 0.970055i | \(-0.421907\pi\) | ||||
0.242884 | + | 0.970055i | \(0.421907\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | −6.32304 | −0.809583 | −0.404791 | − | 0.914409i | \(-0.632656\pi\) | ||||
−0.404791 | + | 0.914409i | \(0.632656\pi\) | |||||||
\(62\) | 1.44504 | 0.183521 | ||||||||
\(63\) | −1.69202 | −0.213175 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.15883 | −0.265734 | ||||||||
\(67\) | −7.56465 | −0.924169 | −0.462084 | − | 0.886836i | \(-0.652898\pi\) | ||||
−0.462084 | + | 0.886836i | \(0.652898\pi\) | |||||||
\(68\) | 2.35690 | 0.285816 | ||||||||
\(69\) | 3.74094 | 0.450356 | ||||||||
\(70\) | −1.69202 | −0.202235 | ||||||||
\(71\) | −4.18060 | −0.496146 | −0.248073 | − | 0.968741i | \(-0.579797\pi\) | ||||
−0.248073 | + | 0.968741i | \(0.579797\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 11.9366 | 1.39707 | 0.698537 | − | 0.715574i | \(-0.253835\pi\) | ||||
0.698537 | + | 0.715574i | \(0.253835\pi\) | |||||||
\(74\) | 0.801938 | 0.0932234 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0.198062 | 0.0227193 | ||||||||
\(77\) | −3.65279 | −0.416274 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.40581 | 1.05824 | 0.529118 | − | 0.848548i | \(-0.322523\pi\) | ||||
0.529118 | + | 0.848548i | \(0.322523\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.89977 | −0.209795 | ||||||||
\(83\) | 8.43296 | 0.925638 | 0.462819 | − | 0.886453i | \(-0.346838\pi\) | ||||
0.462819 | + | 0.886453i | \(0.346838\pi\) | |||||||
\(84\) | 1.69202 | 0.184615 | ||||||||
\(85\) | 2.35690 | 0.255641 | ||||||||
\(86\) | 12.5429 | 1.35253 | ||||||||
\(87\) | −1.29590 | −0.138935 | ||||||||
\(88\) | 2.15883 | 0.230132 | ||||||||
\(89\) | −2.41119 | −0.255586 | −0.127793 | − | 0.991801i | \(-0.540789\pi\) | ||||
−0.127793 | + | 0.991801i | \(0.540789\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.74094 | −0.390020 | ||||||||
\(93\) | −1.44504 | −0.149844 | ||||||||
\(94\) | 8.87800 | 0.915696 | ||||||||
\(95\) | 0.198062 | 0.0203208 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −0.0881460 | −0.00894987 | −0.00447494 | − | 0.999990i | \(-0.501424\pi\) | ||||
−0.00447494 | + | 0.999990i | \(0.501424\pi\) | |||||||
\(98\) | −4.13706 | −0.417907 | ||||||||
\(99\) | 2.15883 | 0.216971 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −11.1099 | −1.10548 | −0.552739 | − | 0.833354i | \(-0.686417\pi\) | ||||
−0.552739 | + | 0.833354i | \(0.686417\pi\) | |||||||
\(102\) | −2.35690 | −0.233367 | ||||||||
\(103\) | 9.54825 | 0.940817 | 0.470409 | − | 0.882449i | \(-0.344107\pi\) | ||||
0.470409 | + | 0.882449i | \(0.344107\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.69202 | 0.165124 | ||||||||
\(106\) | −1.00969 | −0.0980696 | ||||||||
\(107\) | 18.1468 | 1.75431 | 0.877156 | − | 0.480205i | \(-0.159438\pi\) | ||||
0.877156 | + | 0.480205i | \(0.159438\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −2.24698 | −0.215222 | −0.107611 | − | 0.994193i | \(-0.534320\pi\) | ||||
−0.107611 | + | 0.994193i | \(0.534320\pi\) | |||||||
\(110\) | 2.15883 | 0.205837 | ||||||||
\(111\) | −0.801938 | −0.0761166 | ||||||||
\(112\) | −1.69202 | −0.159881 | ||||||||
\(113\) | −11.8726 | −1.11688 | −0.558441 | − | 0.829544i | \(-0.688600\pi\) | ||||
−0.558441 | + | 0.829544i | \(0.688600\pi\) | |||||||
\(114\) | −0.198062 | −0.0185502 | ||||||||
\(115\) | −3.74094 | −0.348844 | ||||||||
\(116\) | 1.29590 | 0.120321 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.73125 | 0.343489 | ||||||||
\(119\) | −3.98792 | −0.365572 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | −6.33944 | −0.576312 | ||||||||
\(122\) | −6.32304 | −0.572462 | ||||||||
\(123\) | 1.89977 | 0.171297 | ||||||||
\(124\) | 1.44504 | 0.129769 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −1.69202 | −0.150737 | ||||||||
\(127\) | 13.0097 | 1.15442 | 0.577212 | − | 0.816595i | \(-0.304141\pi\) | ||||
0.577212 | + | 0.816595i | \(0.304141\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −12.5429 | −1.10434 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.82908 | −0.684030 | −0.342015 | − | 0.939694i | \(-0.611109\pi\) | ||||
−0.342015 | + | 0.939694i | \(0.611109\pi\) | |||||||
\(132\) | −2.15883 | −0.187902 | ||||||||
\(133\) | −0.335126 | −0.0290591 | ||||||||
\(134\) | −7.56465 | −0.653486 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 2.35690 | 0.202102 | ||||||||
\(137\) | 5.36227 | 0.458130 | 0.229065 | − | 0.973411i | \(-0.426433\pi\) | ||||
0.229065 | + | 0.973411i | \(0.426433\pi\) | |||||||
\(138\) | 3.74094 | 0.318450 | ||||||||
\(139\) | 3.12200 | 0.264804 | 0.132402 | − | 0.991196i | \(-0.457731\pi\) | ||||
0.132402 | + | 0.991196i | \(0.457731\pi\) | |||||||
\(140\) | −1.69202 | −0.143002 | ||||||||
\(141\) | −8.87800 | −0.747663 | ||||||||
\(142\) | −4.18060 | −0.350828 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 1.29590 | 0.107618 | ||||||||
\(146\) | 11.9366 | 0.987881 | ||||||||
\(147\) | 4.13706 | 0.341219 | ||||||||
\(148\) | 0.801938 | 0.0659189 | ||||||||
\(149\) | 4.24160 | 0.347486 | 0.173743 | − | 0.984791i | \(-0.444414\pi\) | ||||
0.173743 | + | 0.984791i | \(0.444414\pi\) | |||||||
\(150\) | −1.00000 | −0.0816497 | ||||||||
\(151\) | 22.9148 | 1.86478 | 0.932392 | − | 0.361450i | \(-0.117718\pi\) | ||||
0.932392 | + | 0.361450i | \(0.117718\pi\) | |||||||
\(152\) | 0.198062 | 0.0160650 | ||||||||
\(153\) | 2.35690 | 0.190544 | ||||||||
\(154\) | −3.65279 | −0.294350 | ||||||||
\(155\) | 1.44504 | 0.116069 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.0707 | 1.28258 | 0.641290 | − | 0.767298i | \(-0.278399\pi\) | ||||
0.641290 | + | 0.767298i | \(0.278399\pi\) | |||||||
\(158\) | 9.40581 | 0.748286 | ||||||||
\(159\) | 1.00969 | 0.0800735 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 6.32975 | 0.498854 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −0.488582 | −0.0382687 | −0.0191344 | − | 0.999817i | \(-0.506091\pi\) | ||||
−0.0191344 | + | 0.999817i | \(0.506091\pi\) | |||||||
\(164\) | −1.89977 | −0.148347 | ||||||||
\(165\) | −2.15883 | −0.168065 | ||||||||
\(166\) | 8.43296 | 0.654525 | ||||||||
\(167\) | 14.0610 | 1.08807 | 0.544036 | − | 0.839062i | \(-0.316895\pi\) | ||||
0.544036 | + | 0.839062i | \(0.316895\pi\) | |||||||
\(168\) | 1.69202 | 0.130542 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 2.35690 | 0.180766 | ||||||||
\(171\) | 0.198062 | 0.0151462 | ||||||||
\(172\) | 12.5429 | 0.956385 | ||||||||
\(173\) | 21.7942 | 1.65698 | 0.828490 | − | 0.560004i | \(-0.189200\pi\) | ||||
0.828490 | + | 0.560004i | \(0.189200\pi\) | |||||||
\(174\) | −1.29590 | −0.0982417 | ||||||||
\(175\) | −1.69202 | −0.127905 | ||||||||
\(176\) | 2.15883 | 0.162728 | ||||||||
\(177\) | −3.73125 | −0.280458 | ||||||||
\(178\) | −2.41119 | −0.180726 | ||||||||
\(179\) | −14.1293 | −1.05607 | −0.528036 | − | 0.849222i | \(-0.677072\pi\) | ||||
−0.528036 | + | 0.849222i | \(0.677072\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | −5.63773 | −0.419049 | −0.209524 | − | 0.977803i | \(-0.567192\pi\) | ||||
−0.209524 | + | 0.977803i | \(0.567192\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.32304 | 0.467413 | ||||||||
\(184\) | −3.74094 | −0.275786 | ||||||||
\(185\) | 0.801938 | 0.0589596 | ||||||||
\(186\) | −1.44504 | −0.105956 | ||||||||
\(187\) | 5.08815 | 0.372082 | ||||||||
\(188\) | 8.87800 | 0.647495 | ||||||||
\(189\) | 1.69202 | 0.123076 | ||||||||
\(190\) | 0.198062 | 0.0143689 | ||||||||
\(191\) | −2.59419 | −0.187709 | −0.0938544 | − | 0.995586i | \(-0.529919\pi\) | ||||
−0.0938544 | + | 0.995586i | \(0.529919\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −3.98361 | −0.286746 | −0.143373 | − | 0.989669i | \(-0.545795\pi\) | ||||
−0.143373 | + | 0.989669i | \(0.545795\pi\) | |||||||
\(194\) | −0.0881460 | −0.00632851 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.13706 | −0.295505 | ||||||||
\(197\) | −6.65040 | −0.473821 | −0.236911 | − | 0.971531i | \(-0.576135\pi\) | ||||
−0.236911 | + | 0.971531i | \(0.576135\pi\) | |||||||
\(198\) | 2.15883 | 0.153422 | ||||||||
\(199\) | −1.01639 | −0.0720502 | −0.0360251 | − | 0.999351i | \(-0.511470\pi\) | ||||
−0.0360251 | + | 0.999351i | \(0.511470\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 7.56465 | 0.533569 | ||||||||
\(202\) | −11.1099 | −0.781691 | ||||||||
\(203\) | −2.19269 | −0.153896 | ||||||||
\(204\) | −2.35690 | −0.165016 | ||||||||
\(205\) | −1.89977 | −0.132686 | ||||||||
\(206\) | 9.54825 | 0.665258 | ||||||||
\(207\) | −3.74094 | −0.260013 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.427583 | 0.0295766 | ||||||||
\(210\) | 1.69202 | 0.116761 | ||||||||
\(211\) | 10.1414 | 0.698161 | 0.349081 | − | 0.937093i | \(-0.386494\pi\) | ||||
0.349081 | + | 0.937093i | \(0.386494\pi\) | |||||||
\(212\) | −1.00969 | −0.0693457 | ||||||||
\(213\) | 4.18060 | 0.286450 | ||||||||
\(214\) | 18.1468 | 1.24049 | ||||||||
\(215\) | 12.5429 | 0.855417 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −2.44504 | −0.165980 | ||||||||
\(218\) | −2.24698 | −0.152185 | ||||||||
\(219\) | −11.9366 | −0.806601 | ||||||||
\(220\) | 2.15883 | 0.145549 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −0.801938 | −0.0538225 | ||||||||
\(223\) | −16.8388 | −1.12761 | −0.563804 | − | 0.825909i | \(-0.690663\pi\) | ||||
−0.563804 | + | 0.825909i | \(0.690663\pi\) | |||||||
\(224\) | −1.69202 | −0.113053 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −11.8726 | −0.789755 | ||||||||
\(227\) | 18.3056 | 1.21498 | 0.607492 | − | 0.794326i | \(-0.292176\pi\) | ||||
0.607492 | + | 0.794326i | \(0.292176\pi\) | |||||||
\(228\) | −0.198062 | −0.0131170 | ||||||||
\(229\) | 5.14244 | 0.339822 | 0.169911 | − | 0.985459i | \(-0.445652\pi\) | ||||
0.169911 | + | 0.985459i | \(0.445652\pi\) | |||||||
\(230\) | −3.74094 | −0.246670 | ||||||||
\(231\) | 3.65279 | 0.240336 | ||||||||
\(232\) | 1.29590 | 0.0850798 | ||||||||
\(233\) | −10.9215 | −0.715494 | −0.357747 | − | 0.933819i | \(-0.616455\pi\) | ||||
−0.357747 | + | 0.933819i | \(0.616455\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.87800 | 0.579137 | ||||||||
\(236\) | 3.73125 | 0.242884 | ||||||||
\(237\) | −9.40581 | −0.610973 | ||||||||
\(238\) | −3.98792 | −0.258498 | ||||||||
\(239\) | 19.9041 | 1.28749 | 0.643744 | − | 0.765241i | \(-0.277380\pi\) | ||||
0.643744 | + | 0.765241i | \(0.277380\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | 18.2228 | 1.17383 | 0.586917 | − | 0.809647i | \(-0.300341\pi\) | ||||
0.586917 | + | 0.809647i | \(0.300341\pi\) | |||||||
\(242\) | −6.33944 | −0.407514 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −6.32304 | −0.404791 | ||||||||
\(245\) | −4.13706 | −0.264307 | ||||||||
\(246\) | 1.89977 | 0.121125 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1.44504 | 0.0917603 | ||||||||
\(249\) | −8.43296 | −0.534417 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −17.0030 | −1.07322 | −0.536609 | − | 0.843831i | \(-0.680295\pi\) | ||||
−0.536609 | + | 0.843831i | \(0.680295\pi\) | |||||||
\(252\) | −1.69202 | −0.106587 | ||||||||
\(253\) | −8.07606 | −0.507738 | ||||||||
\(254\) | 13.0097 | 0.816300 | ||||||||
\(255\) | −2.35690 | −0.147595 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −7.65519 | −0.477517 | −0.238759 | − | 0.971079i | \(-0.576740\pi\) | ||||
−0.238759 | + | 0.971079i | \(0.576740\pi\) | |||||||
\(258\) | −12.5429 | −0.780885 | ||||||||
\(259\) | −1.35690 | −0.0843134 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.29590 | 0.0802140 | ||||||||
\(262\) | −7.82908 | −0.483682 | ||||||||
\(263\) | 21.0411 | 1.29745 | 0.648726 | − | 0.761022i | \(-0.275302\pi\) | ||||
0.648726 | + | 0.761022i | \(0.275302\pi\) | |||||||
\(264\) | −2.15883 | −0.132867 | ||||||||
\(265\) | −1.00969 | −0.0620247 | ||||||||
\(266\) | −0.335126 | −0.0205479 | ||||||||
\(267\) | 2.41119 | 0.147562 | ||||||||
\(268\) | −7.56465 | −0.462084 | ||||||||
\(269\) | 24.3183 | 1.48271 | 0.741355 | − | 0.671113i | \(-0.234183\pi\) | ||||
0.741355 | + | 0.671113i | \(0.234183\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | 10.9922 | 0.667730 | 0.333865 | − | 0.942621i | \(-0.391647\pi\) | ||||
0.333865 | + | 0.942621i | \(0.391647\pi\) | |||||||
\(272\) | 2.35690 | 0.142908 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.36227 | 0.323947 | ||||||||
\(275\) | 2.15883 | 0.130183 | ||||||||
\(276\) | 3.74094 | 0.225178 | ||||||||
\(277\) | −11.4601 | −0.688571 | −0.344286 | − | 0.938865i | \(-0.611879\pi\) | ||||
−0.344286 | + | 0.938865i | \(0.611879\pi\) | |||||||
\(278\) | 3.12200 | 0.187245 | ||||||||
\(279\) | 1.44504 | 0.0865124 | ||||||||
\(280\) | −1.69202 | −0.101118 | ||||||||
\(281\) | −9.88231 | −0.589529 | −0.294765 | − | 0.955570i | \(-0.595241\pi\) | ||||
−0.294765 | + | 0.955570i | \(0.595241\pi\) | |||||||
\(282\) | −8.87800 | −0.528677 | ||||||||
\(283\) | −21.3207 | −1.26738 | −0.633691 | − | 0.773587i | \(-0.718461\pi\) | ||||
−0.633691 | + | 0.773587i | \(0.718461\pi\) | |||||||
\(284\) | −4.18060 | −0.248073 | ||||||||
\(285\) | −0.198062 | −0.0117322 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.21446 | 0.189743 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −11.4450 | −0.673238 | ||||||||
\(290\) | 1.29590 | 0.0760977 | ||||||||
\(291\) | 0.0881460 | 0.00516721 | ||||||||
\(292\) | 11.9366 | 0.698537 | ||||||||
\(293\) | −18.7090 | −1.09299 | −0.546496 | − | 0.837462i | \(-0.684039\pi\) | ||||
−0.546496 | + | 0.837462i | \(0.684039\pi\) | |||||||
\(294\) | 4.13706 | 0.241278 | ||||||||
\(295\) | 3.73125 | 0.217242 | ||||||||
\(296\) | 0.801938 | 0.0466117 | ||||||||
\(297\) | −2.15883 | −0.125268 | ||||||||
\(298\) | 4.24160 | 0.245709 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | −21.2228 | −1.22326 | ||||||||
\(302\) | 22.9148 | 1.31860 | ||||||||
\(303\) | 11.1099 | 0.638248 | ||||||||
\(304\) | 0.198062 | 0.0113596 | ||||||||
\(305\) | −6.32304 | −0.362056 | ||||||||
\(306\) | 2.35690 | 0.134735 | ||||||||
\(307\) | 17.2241 | 0.983034 | 0.491517 | − | 0.870868i | \(-0.336443\pi\) | ||||
0.491517 | + | 0.870868i | \(0.336443\pi\) | |||||||
\(308\) | −3.65279 | −0.208137 | ||||||||
\(309\) | −9.54825 | −0.543181 | ||||||||
\(310\) | 1.44504 | 0.0820729 | ||||||||
\(311\) | −13.5200 | −0.766651 | −0.383326 | − | 0.923613i | \(-0.625221\pi\) | ||||
−0.383326 | + | 0.923613i | \(0.625221\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.3303 | 1.37523 | 0.687616 | − | 0.726074i | \(-0.258657\pi\) | ||||
0.687616 | + | 0.726074i | \(0.258657\pi\) | |||||||
\(314\) | 16.0707 | 0.906921 | ||||||||
\(315\) | −1.69202 | −0.0953346 | ||||||||
\(316\) | 9.40581 | 0.529118 | ||||||||
\(317\) | 34.7821 | 1.95356 | 0.976778 | − | 0.214253i | \(-0.0687316\pi\) | ||||
0.976778 | + | 0.214253i | \(0.0687316\pi\) | |||||||
\(318\) | 1.00969 | 0.0566205 | ||||||||
\(319\) | 2.79763 | 0.156637 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −18.1468 | −1.01285 | ||||||||
\(322\) | 6.32975 | 0.352743 | ||||||||
\(323\) | 0.466812 | 0.0259741 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.488582 | −0.0270601 | ||||||||
\(327\) | 2.24698 | 0.124258 | ||||||||
\(328\) | −1.89977 | −0.104897 | ||||||||
\(329\) | −15.0218 | −0.828177 | ||||||||
\(330\) | −2.15883 | −0.118840 | ||||||||
\(331\) | −9.66919 | −0.531467 | −0.265733 | − | 0.964047i | \(-0.585614\pi\) | ||||
−0.265733 | + | 0.964047i | \(0.585614\pi\) | |||||||
\(332\) | 8.43296 | 0.462819 | ||||||||
\(333\) | 0.801938 | 0.0439459 | ||||||||
\(334\) | 14.0610 | 0.769384 | ||||||||
\(335\) | −7.56465 | −0.413301 | ||||||||
\(336\) | 1.69202 | 0.0923073 | ||||||||
\(337\) | −17.3612 | −0.945725 | −0.472863 | − | 0.881136i | \(-0.656779\pi\) | ||||
−0.472863 | + | 0.881136i | \(0.656779\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.8726 | 0.644832 | ||||||||
\(340\) | 2.35690 | 0.127821 | ||||||||
\(341\) | 3.11960 | 0.168936 | ||||||||
\(342\) | 0.198062 | 0.0107100 | ||||||||
\(343\) | 18.8442 | 1.01749 | ||||||||
\(344\) | 12.5429 | 0.676267 | ||||||||
\(345\) | 3.74094 | 0.201405 | ||||||||
\(346\) | 21.7942 | 1.17166 | ||||||||
\(347\) | 8.86294 | 0.475787 | 0.237894 | − | 0.971291i | \(-0.423543\pi\) | ||||
0.237894 | + | 0.971291i | \(0.423543\pi\) | |||||||
\(348\) | −1.29590 | −0.0694674 | ||||||||
\(349\) | 2.78554 | 0.149107 | 0.0745534 | − | 0.997217i | \(-0.476247\pi\) | ||||
0.0745534 | + | 0.997217i | \(0.476247\pi\) | |||||||
\(350\) | −1.69202 | −0.0904424 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.15883 | 0.115066 | ||||||||
\(353\) | 21.0640 | 1.12112 | 0.560561 | − | 0.828113i | \(-0.310585\pi\) | ||||
0.560561 | + | 0.828113i | \(0.310585\pi\) | |||||||
\(354\) | −3.73125 | −0.198314 | ||||||||
\(355\) | −4.18060 | −0.221883 | ||||||||
\(356\) | −2.41119 | −0.127793 | ||||||||
\(357\) | 3.98792 | 0.211063 | ||||||||
\(358\) | −14.1293 | −0.746756 | ||||||||
\(359\) | 17.3274 | 0.914503 | 0.457251 | − | 0.889337i | \(-0.348834\pi\) | ||||
0.457251 | + | 0.889337i | \(0.348834\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | −18.9608 | −0.997935 | ||||||||
\(362\) | −5.63773 | −0.296312 | ||||||||
\(363\) | 6.33944 | 0.332734 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.9366 | 0.624791 | ||||||||
\(366\) | 6.32304 | 0.330511 | ||||||||
\(367\) | −30.8049 | −1.60800 | −0.804002 | − | 0.594627i | \(-0.797300\pi\) | ||||
−0.804002 | + | 0.594627i | \(0.797300\pi\) | |||||||
\(368\) | −3.74094 | −0.195010 | ||||||||
\(369\) | −1.89977 | −0.0988982 | ||||||||
\(370\) | 0.801938 | 0.0416908 | ||||||||
\(371\) | 1.70841 | 0.0886965 | ||||||||
\(372\) | −1.44504 | −0.0749219 | ||||||||
\(373\) | −25.6668 | −1.32898 | −0.664488 | − | 0.747299i | \(-0.731350\pi\) | ||||
−0.664488 | + | 0.747299i | \(0.731350\pi\) | |||||||
\(374\) | 5.08815 | 0.263102 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 8.87800 | 0.457848 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.69202 | 0.0870282 | ||||||||
\(379\) | 5.46144 | 0.280535 | 0.140268 | − | 0.990114i | \(-0.455204\pi\) | ||||
0.140268 | + | 0.990114i | \(0.455204\pi\) | |||||||
\(380\) | 0.198062 | 0.0101604 | ||||||||
\(381\) | −13.0097 | −0.666507 | ||||||||
\(382\) | −2.59419 | −0.132730 | ||||||||
\(383\) | −25.9221 | −1.32456 | −0.662280 | − | 0.749257i | \(-0.730411\pi\) | ||||
−0.662280 | + | 0.749257i | \(0.730411\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −3.65279 | −0.186164 | ||||||||
\(386\) | −3.98361 | −0.202760 | ||||||||
\(387\) | 12.5429 | 0.637590 | ||||||||
\(388\) | −0.0881460 | −0.00447494 | ||||||||
\(389\) | −32.0006 | −1.62249 | −0.811247 | − | 0.584703i | \(-0.801211\pi\) | ||||
−0.811247 | + | 0.584703i | \(0.801211\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.81700 | −0.445895 | ||||||||
\(392\) | −4.13706 | −0.208953 | ||||||||
\(393\) | 7.82908 | 0.394925 | ||||||||
\(394\) | −6.65040 | −0.335042 | ||||||||
\(395\) | 9.40581 | 0.473258 | ||||||||
\(396\) | 2.15883 | 0.108485 | ||||||||
\(397\) | 0.457123 | 0.0229424 | 0.0114712 | − | 0.999934i | \(-0.496349\pi\) | ||||
0.0114712 | + | 0.999934i | \(0.496349\pi\) | |||||||
\(398\) | −1.01639 | −0.0509472 | ||||||||
\(399\) | 0.335126 | 0.0167773 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 23.2553 | 1.16132 | 0.580658 | − | 0.814147i | \(-0.302795\pi\) | ||||
0.580658 | + | 0.814147i | \(0.302795\pi\) | |||||||
\(402\) | 7.56465 | 0.377290 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −11.1099 | −0.552739 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −2.19269 | −0.108821 | ||||||||
\(407\) | 1.73125 | 0.0858149 | ||||||||
\(408\) | −2.35690 | −0.116684 | ||||||||
\(409\) | 39.0629 | 1.93154 | 0.965768 | − | 0.259406i | \(-0.0835266\pi\) | ||||
0.965768 | + | 0.259406i | \(0.0835266\pi\) | |||||||
\(410\) | −1.89977 | −0.0938231 | ||||||||
\(411\) | −5.36227 | −0.264501 | ||||||||
\(412\) | 9.54825 | 0.470409 | ||||||||
\(413\) | −6.31336 | −0.310660 | ||||||||
\(414\) | −3.74094 | −0.183857 | ||||||||
\(415\) | 8.43296 | 0.413958 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.12200 | −0.152885 | ||||||||
\(418\) | 0.427583 | 0.0209138 | ||||||||
\(419\) | −18.1269 | −0.885557 | −0.442779 | − | 0.896631i | \(-0.646007\pi\) | ||||
−0.442779 | + | 0.896631i | \(0.646007\pi\) | |||||||
\(420\) | 1.69202 | 0.0825622 | ||||||||
\(421\) | −20.4916 | −0.998698 | −0.499349 | − | 0.866401i | \(-0.666427\pi\) | ||||
−0.499349 | + | 0.866401i | \(0.666427\pi\) | |||||||
\(422\) | 10.1414 | 0.493674 | ||||||||
\(423\) | 8.87800 | 0.431663 | ||||||||
\(424\) | −1.00969 | −0.0490348 | ||||||||
\(425\) | 2.35690 | 0.114326 | ||||||||
\(426\) | 4.18060 | 0.202551 | ||||||||
\(427\) | 10.6987 | 0.517748 | ||||||||
\(428\) | 18.1468 | 0.877156 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 12.5429 | 0.604871 | ||||||||
\(431\) | −22.2989 | −1.07410 | −0.537050 | − | 0.843551i | \(-0.680461\pi\) | ||||
−0.537050 | + | 0.843551i | \(0.680461\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 7.47650 | 0.359298 | 0.179649 | − | 0.983731i | \(-0.442504\pi\) | ||||
0.179649 | + | 0.983731i | \(0.442504\pi\) | |||||||
\(434\) | −2.44504 | −0.117366 | ||||||||
\(435\) | −1.29590 | −0.0621335 | ||||||||
\(436\) | −2.24698 | −0.107611 | ||||||||
\(437\) | −0.740939 | −0.0354439 | ||||||||
\(438\) | −11.9366 | −0.570353 | ||||||||
\(439\) | −19.3924 | −0.925549 | −0.462774 | − | 0.886476i | \(-0.653146\pi\) | ||||
−0.462774 | + | 0.886476i | \(0.653146\pi\) | |||||||
\(440\) | 2.15883 | 0.102918 | ||||||||
\(441\) | −4.13706 | −0.197003 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.0935 | 0.479558 | 0.239779 | − | 0.970828i | \(-0.422925\pi\) | ||||
0.239779 | + | 0.970828i | \(0.422925\pi\) | |||||||
\(444\) | −0.801938 | −0.0380583 | ||||||||
\(445\) | −2.41119 | −0.114301 | ||||||||
\(446\) | −16.8388 | −0.797339 | ||||||||
\(447\) | −4.24160 | −0.200621 | ||||||||
\(448\) | −1.69202 | −0.0799405 | ||||||||
\(449\) | −2.78448 | −0.131408 | −0.0657039 | − | 0.997839i | \(-0.520929\pi\) | ||||
−0.0657039 | + | 0.997839i | \(0.520929\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | −4.10129 | −0.193122 | ||||||||
\(452\) | −11.8726 | −0.558441 | ||||||||
\(453\) | −22.9148 | −1.07663 | ||||||||
\(454\) | 18.3056 | 0.859124 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.198062 | −0.00927512 | ||||||||
\(457\) | −13.1056 | −0.613054 | −0.306527 | − | 0.951862i | \(-0.599167\pi\) | ||||
−0.306527 | + | 0.951862i | \(0.599167\pi\) | |||||||
\(458\) | 5.14244 | 0.240290 | ||||||||
\(459\) | −2.35690 | −0.110010 | ||||||||
\(460\) | −3.74094 | −0.174422 | ||||||||
\(461\) | 16.2174 | 0.755321 | 0.377661 | − | 0.925944i | \(-0.376729\pi\) | ||||
0.377661 | + | 0.925944i | \(0.376729\pi\) | |||||||
\(462\) | 3.65279 | 0.169943 | ||||||||
\(463\) | 15.5415 | 0.722277 | 0.361139 | − | 0.932512i | \(-0.382388\pi\) | ||||
0.361139 | + | 0.932512i | \(0.382388\pi\) | |||||||
\(464\) | 1.29590 | 0.0601605 | ||||||||
\(465\) | −1.44504 | −0.0670122 | ||||||||
\(466\) | −10.9215 | −0.505931 | ||||||||
\(467\) | −10.1578 | −0.470045 | −0.235023 | − | 0.971990i | \(-0.575516\pi\) | ||||
−0.235023 | + | 0.971990i | \(0.575516\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.7995 | 0.591028 | ||||||||
\(470\) | 8.87800 | 0.409512 | ||||||||
\(471\) | −16.0707 | −0.740498 | ||||||||
\(472\) | 3.73125 | 0.171745 | ||||||||
\(473\) | 27.0780 | 1.24505 | ||||||||
\(474\) | −9.40581 | −0.432023 | ||||||||
\(475\) | 0.198062 | 0.00908772 | ||||||||
\(476\) | −3.98792 | −0.182786 | ||||||||
\(477\) | −1.00969 | −0.0462305 | ||||||||
\(478\) | 19.9041 | 0.910392 | ||||||||
\(479\) | 31.4263 | 1.43590 | 0.717951 | − | 0.696094i | \(-0.245080\pi\) | ||||
0.717951 | + | 0.696094i | \(0.245080\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 18.2228 | 0.830027 | ||||||||
\(483\) | −6.32975 | −0.288014 | ||||||||
\(484\) | −6.33944 | −0.288156 | ||||||||
\(485\) | −0.0881460 | −0.00400250 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −24.1323 | −1.09354 | −0.546769 | − | 0.837284i | \(-0.684142\pi\) | ||||
−0.546769 | + | 0.837284i | \(0.684142\pi\) | |||||||
\(488\) | −6.32304 | −0.286231 | ||||||||
\(489\) | 0.488582 | 0.0220945 | ||||||||
\(490\) | −4.13706 | −0.186893 | ||||||||
\(491\) | −19.1099 | −0.862418 | −0.431209 | − | 0.902252i | \(-0.641913\pi\) | ||||
−0.431209 | + | 0.902252i | \(0.641913\pi\) | |||||||
\(492\) | 1.89977 | 0.0856484 | ||||||||
\(493\) | 3.05429 | 0.137558 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.15883 | 0.0970324 | ||||||||
\(496\) | 1.44504 | 0.0648843 | ||||||||
\(497\) | 7.07367 | 0.317298 | ||||||||
\(498\) | −8.43296 | −0.377890 | ||||||||
\(499\) | −34.9724 | −1.56558 | −0.782789 | − | 0.622287i | \(-0.786204\pi\) | ||||
−0.782789 | + | 0.622287i | \(0.786204\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −14.0610 | −0.628199 | ||||||||
\(502\) | −17.0030 | −0.758880 | ||||||||
\(503\) | 29.5579 | 1.31792 | 0.658962 | − | 0.752176i | \(-0.270996\pi\) | ||||
0.658962 | + | 0.752176i | \(0.270996\pi\) | |||||||
\(504\) | −1.69202 | −0.0753686 | ||||||||
\(505\) | −11.1099 | −0.494385 | ||||||||
\(506\) | −8.07606 | −0.359025 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.0097 | 0.577212 | ||||||||
\(509\) | 24.4838 | 1.08523 | 0.542613 | − | 0.839983i | \(-0.317435\pi\) | ||||
0.542613 | + | 0.839983i | \(0.317435\pi\) | |||||||
\(510\) | −2.35690 | −0.104365 | ||||||||
\(511\) | −20.1970 | −0.893463 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −0.198062 | −0.00874466 | ||||||||
\(514\) | −7.65519 | −0.337656 | ||||||||
\(515\) | 9.54825 | 0.420746 | ||||||||
\(516\) | −12.5429 | −0.552169 | ||||||||
\(517\) | 19.1661 | 0.842925 | ||||||||
\(518\) | −1.35690 | −0.0596186 | ||||||||
\(519\) | −21.7942 | −0.956658 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −33.8713 | −1.48393 | −0.741964 | − | 0.670439i | \(-0.766106\pi\) | ||||
−0.741964 | + | 0.670439i | \(0.766106\pi\) | |||||||
\(522\) | 1.29590 | 0.0567199 | ||||||||
\(523\) | −42.5870 | −1.86220 | −0.931100 | − | 0.364764i | \(-0.881150\pi\) | ||||
−0.931100 | + | 0.364764i | \(0.881150\pi\) | |||||||
\(524\) | −7.82908 | −0.342015 | ||||||||
\(525\) | 1.69202 | 0.0738459 | ||||||||
\(526\) | 21.0411 | 0.917438 | ||||||||
\(527\) | 3.40581 | 0.148360 | ||||||||
\(528\) | −2.15883 | −0.0939512 | ||||||||
\(529\) | −9.00538 | −0.391538 | ||||||||
\(530\) | −1.00969 | −0.0438581 | ||||||||
\(531\) | 3.73125 | 0.161922 | ||||||||
\(532\) | −0.335126 | −0.0145295 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 2.41119 | 0.104342 | ||||||||
\(535\) | 18.1468 | 0.784553 | ||||||||
\(536\) | −7.56465 | −0.326743 | ||||||||
\(537\) | 14.1293 | 0.609724 | ||||||||
\(538\) | 24.3183 | 1.04843 | ||||||||
\(539\) | −8.93123 | −0.384695 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | −3.23298 | −0.138997 | −0.0694983 | − | 0.997582i | \(-0.522140\pi\) | ||||
−0.0694983 | + | 0.997582i | \(0.522140\pi\) | |||||||
\(542\) | 10.9922 | 0.472157 | ||||||||
\(543\) | 5.63773 | 0.241938 | ||||||||
\(544\) | 2.35690 | 0.101051 | ||||||||
\(545\) | −2.24698 | −0.0962500 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.51573 | −0.235836 | −0.117918 | − | 0.993023i | \(-0.537622\pi\) | ||||
−0.117918 | + | 0.993023i | \(0.537622\pi\) | |||||||
\(548\) | 5.36227 | 0.229065 | ||||||||
\(549\) | −6.32304 | −0.269861 | ||||||||
\(550\) | 2.15883 | 0.0920530 | ||||||||
\(551\) | 0.256668 | 0.0109344 | ||||||||
\(552\) | 3.74094 | 0.159225 | ||||||||
\(553\) | −15.9148 | −0.676768 | ||||||||
\(554\) | −11.4601 | −0.486893 | ||||||||
\(555\) | −0.801938 | −0.0340404 | ||||||||
\(556\) | 3.12200 | 0.132402 | ||||||||
\(557\) | 30.3502 | 1.28598 | 0.642989 | − | 0.765875i | \(-0.277694\pi\) | ||||
0.642989 | + | 0.765875i | \(0.277694\pi\) | |||||||
\(558\) | 1.44504 | 0.0611735 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1.69202 | −0.0715010 | ||||||||
\(561\) | −5.08815 | −0.214822 | ||||||||
\(562\) | −9.88231 | −0.416860 | ||||||||
\(563\) | 6.34375 | 0.267357 | 0.133679 | − | 0.991025i | \(-0.457321\pi\) | ||||
0.133679 | + | 0.991025i | \(0.457321\pi\) | |||||||
\(564\) | −8.87800 | −0.373831 | ||||||||
\(565\) | −11.8726 | −0.499485 | ||||||||
\(566\) | −21.3207 | −0.896174 | ||||||||
\(567\) | −1.69202 | −0.0710582 | ||||||||
\(568\) | −4.18060 | −0.175414 | ||||||||
\(569\) | 24.7275 | 1.03663 | 0.518316 | − | 0.855189i | \(-0.326559\pi\) | ||||
0.518316 | + | 0.855189i | \(0.326559\pi\) | |||||||
\(570\) | −0.198062 | −0.00829592 | ||||||||
\(571\) | 13.6262 | 0.570240 | 0.285120 | − | 0.958492i | \(-0.407967\pi\) | ||||
0.285120 | + | 0.958492i | \(0.407967\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.59419 | 0.108374 | ||||||||
\(574\) | 3.21446 | 0.134169 | ||||||||
\(575\) | −3.74094 | −0.156008 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −16.2828 | −0.677860 | −0.338930 | − | 0.940812i | \(-0.610065\pi\) | ||||
−0.338930 | + | 0.940812i | \(0.610065\pi\) | |||||||
\(578\) | −11.4450 | −0.476051 | ||||||||
\(579\) | 3.98361 | 0.165553 | ||||||||
\(580\) | 1.29590 | 0.0538092 | ||||||||
\(581\) | −14.2687 | −0.591967 | ||||||||
\(582\) | 0.0881460 | 0.00365377 | ||||||||
\(583\) | −2.17975 | −0.0902760 | ||||||||
\(584\) | 11.9366 | 0.493940 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −18.7090 | −0.772862 | ||||||||
\(587\) | −11.0344 | −0.455440 | −0.227720 | − | 0.973727i | \(-0.573127\pi\) | ||||
−0.227720 | + | 0.973727i | \(0.573127\pi\) | |||||||
\(588\) | 4.13706 | 0.170610 | ||||||||
\(589\) | 0.286208 | 0.0117930 | ||||||||
\(590\) | 3.73125 | 0.153613 | ||||||||
\(591\) | 6.65040 | 0.273561 | ||||||||
\(592\) | 0.801938 | 0.0329594 | ||||||||
\(593\) | −25.4905 | −1.04677 | −0.523385 | − | 0.852096i | \(-0.675331\pi\) | ||||
−0.523385 | + | 0.852096i | \(0.675331\pi\) | |||||||
\(594\) | −2.15883 | −0.0885780 | ||||||||
\(595\) | −3.98792 | −0.163489 | ||||||||
\(596\) | 4.24160 | 0.173743 | ||||||||
\(597\) | 1.01639 | 0.0415982 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.501729 | −0.0205001 | −0.0102500 | − | 0.999947i | \(-0.503263\pi\) | ||||
−0.0102500 | + | 0.999947i | \(0.503263\pi\) | |||||||
\(600\) | −1.00000 | −0.0408248 | ||||||||
\(601\) | −18.3744 | −0.749506 | −0.374753 | − | 0.927125i | \(-0.622272\pi\) | ||||
−0.374753 | + | 0.927125i | \(0.622272\pi\) | |||||||
\(602\) | −21.2228 | −0.864977 | ||||||||
\(603\) | −7.56465 | −0.308056 | ||||||||
\(604\) | 22.9148 | 0.932392 | ||||||||
\(605\) | −6.33944 | −0.257735 | ||||||||
\(606\) | 11.1099 | 0.451309 | ||||||||
\(607\) | −17.1395 | −0.695669 | −0.347835 | − | 0.937556i | \(-0.613083\pi\) | ||||
−0.347835 | + | 0.937556i | \(0.613083\pi\) | |||||||
\(608\) | 0.198062 | 0.00803249 | ||||||||
\(609\) | 2.19269 | 0.0888521 | ||||||||
\(610\) | −6.32304 | −0.256013 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 2.35690 | 0.0952719 | ||||||||
\(613\) | 1.15751 | 0.0467512 | 0.0233756 | − | 0.999727i | \(-0.492559\pi\) | ||||
0.0233756 | + | 0.999727i | \(0.492559\pi\) | |||||||
\(614\) | 17.2241 | 0.695110 | ||||||||
\(615\) | 1.89977 | 0.0766062 | ||||||||
\(616\) | −3.65279 | −0.147175 | ||||||||
\(617\) | 7.71618 | 0.310642 | 0.155321 | − | 0.987864i | \(-0.450359\pi\) | ||||
0.155321 | + | 0.987864i | \(0.450359\pi\) | |||||||
\(618\) | −9.54825 | −0.384087 | ||||||||
\(619\) | 16.1142 | 0.647686 | 0.323843 | − | 0.946111i | \(-0.395025\pi\) | ||||
0.323843 | + | 0.946111i | \(0.395025\pi\) | |||||||
\(620\) | 1.44504 | 0.0580343 | ||||||||
\(621\) | 3.74094 | 0.150119 | ||||||||
\(622\) | −13.5200 | −0.542104 | ||||||||
\(623\) | 4.07979 | 0.163453 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 24.3303 | 0.972436 | ||||||||
\(627\) | −0.427583 | −0.0170760 | ||||||||
\(628\) | 16.0707 | 0.641290 | ||||||||
\(629\) | 1.89008 | 0.0753626 | ||||||||
\(630\) | −1.69202 | −0.0674117 | ||||||||
\(631\) | −7.77586 | −0.309552 | −0.154776 | − | 0.987950i | \(-0.549466\pi\) | ||||
−0.154776 | + | 0.987950i | \(0.549466\pi\) | |||||||
\(632\) | 9.40581 | 0.374143 | ||||||||
\(633\) | −10.1414 | −0.403083 | ||||||||
\(634\) | 34.7821 | 1.38137 | ||||||||
\(635\) | 13.0097 | 0.516274 | ||||||||
\(636\) | 1.00969 | 0.0400368 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.79763 | 0.110759 | ||||||||
\(639\) | −4.18060 | −0.165382 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −35.1293 | −1.38752 | −0.693762 | − | 0.720204i | \(-0.744048\pi\) | ||||
−0.693762 | + | 0.720204i | \(0.744048\pi\) | |||||||
\(642\) | −18.1468 | −0.716195 | ||||||||
\(643\) | −14.5459 | −0.573633 | −0.286816 | − | 0.957986i | \(-0.592597\pi\) | ||||
−0.286816 | + | 0.957986i | \(0.592597\pi\) | |||||||
\(644\) | 6.32975 | 0.249427 | ||||||||
\(645\) | −12.5429 | −0.493875 | ||||||||
\(646\) | 0.466812 | 0.0183665 | ||||||||
\(647\) | 36.2234 | 1.42409 | 0.712045 | − | 0.702134i | \(-0.247769\pi\) | ||||
0.712045 | + | 0.702134i | \(0.247769\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 8.05515 | 0.316192 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.44504 | 0.0958287 | ||||||||
\(652\) | −0.488582 | −0.0191344 | ||||||||
\(653\) | 19.4926 | 0.762806 | 0.381403 | − | 0.924409i | \(-0.375441\pi\) | ||||
0.381403 | + | 0.924409i | \(0.375441\pi\) | |||||||
\(654\) | 2.24698 | 0.0878639 | ||||||||
\(655\) | −7.82908 | −0.305908 | ||||||||
\(656\) | −1.89977 | −0.0741737 | ||||||||
\(657\) | 11.9366 | 0.465691 | ||||||||
\(658\) | −15.0218 | −0.585610 | ||||||||
\(659\) | 38.3400 | 1.49352 | 0.746758 | − | 0.665096i | \(-0.231609\pi\) | ||||
0.746758 | + | 0.665096i | \(0.231609\pi\) | |||||||
\(660\) | −2.15883 | −0.0840325 | ||||||||
\(661\) | 13.5985 | 0.528920 | 0.264460 | − | 0.964397i | \(-0.414806\pi\) | ||||
0.264460 | + | 0.964397i | \(0.414806\pi\) | |||||||
\(662\) | −9.66919 | −0.375804 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.43296 | 0.327262 | ||||||||
\(665\) | −0.335126 | −0.0129956 | ||||||||
\(666\) | 0.801938 | 0.0310745 | ||||||||
\(667\) | −4.84787 | −0.187710 | ||||||||
\(668\) | 14.0610 | 0.544036 | ||||||||
\(669\) | 16.8388 | 0.651025 | ||||||||
\(670\) | −7.56465 | −0.292248 | ||||||||
\(671\) | −13.6504 | −0.526968 | ||||||||
\(672\) | 1.69202 | 0.0652711 | ||||||||
\(673\) | −49.7090 | −1.91614 | −0.958071 | − | 0.286532i | \(-0.907498\pi\) | ||||
−0.958071 | + | 0.286532i | \(0.907498\pi\) | |||||||
\(674\) | −17.3612 | −0.668729 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −50.2573 | −1.93154 | −0.965772 | − | 0.259394i | \(-0.916477\pi\) | ||||
−0.965772 | + | 0.259394i | \(0.916477\pi\) | |||||||
\(678\) | 11.8726 | 0.455965 | ||||||||
\(679\) | 0.149145 | 0.00572366 | ||||||||
\(680\) | 2.35690 | 0.0903828 | ||||||||
\(681\) | −18.3056 | −0.701472 | ||||||||
\(682\) | 3.11960 | 0.119456 | ||||||||
\(683\) | −21.5415 | −0.824264 | −0.412132 | − | 0.911124i | \(-0.635216\pi\) | ||||
−0.412132 | + | 0.911124i | \(0.635216\pi\) | |||||||
\(684\) | 0.198062 | 0.00757310 | ||||||||
\(685\) | 5.36227 | 0.204882 | ||||||||
\(686\) | 18.8442 | 0.719473 | ||||||||
\(687\) | −5.14244 | −0.196196 | ||||||||
\(688\) | 12.5429 | 0.478193 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 3.74094 | 0.142415 | ||||||||
\(691\) | −50.8165 | −1.93315 | −0.966576 | − | 0.256380i | \(-0.917470\pi\) | ||||
−0.966576 | + | 0.256380i | \(0.917470\pi\) | |||||||
\(692\) | 21.7942 | 0.828490 | ||||||||
\(693\) | −3.65279 | −0.138758 | ||||||||
\(694\) | 8.86294 | 0.336432 | ||||||||
\(695\) | 3.12200 | 0.118424 | ||||||||
\(696\) | −1.29590 | −0.0491208 | ||||||||
\(697\) | −4.47757 | −0.169600 | ||||||||
\(698\) | 2.78554 | 0.105434 | ||||||||
\(699\) | 10.9215 | 0.413091 | ||||||||
\(700\) | −1.69202 | −0.0639524 | ||||||||
\(701\) | −13.2024 | −0.498647 | −0.249323 | − | 0.968420i | \(-0.580208\pi\) | ||||
−0.249323 | + | 0.968420i | \(0.580208\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.158834 | 0.00599052 | ||||||||
\(704\) | 2.15883 | 0.0813641 | ||||||||
\(705\) | −8.87800 | −0.334365 | ||||||||
\(706\) | 21.0640 | 0.792753 | ||||||||
\(707\) | 18.7982 | 0.706980 | ||||||||
\(708\) | −3.73125 | −0.140229 | ||||||||
\(709\) | 0.430567 | 0.0161703 | 0.00808515 | − | 0.999967i | \(-0.497426\pi\) | ||||
0.00808515 | + | 0.999967i | \(0.497426\pi\) | |||||||
\(710\) | −4.18060 | −0.156895 | ||||||||
\(711\) | 9.40581 | 0.352746 | ||||||||
\(712\) | −2.41119 | −0.0903632 | ||||||||
\(713\) | −5.40581 | −0.202449 | ||||||||
\(714\) | 3.98792 | 0.149244 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −14.1293 | −0.528036 | ||||||||
\(717\) | −19.9041 | −0.743332 | ||||||||
\(718\) | 17.3274 | 0.646651 | ||||||||
\(719\) | 8.24459 | 0.307471 | 0.153736 | − | 0.988112i | \(-0.450870\pi\) | ||||
0.153736 | + | 0.988112i | \(0.450870\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | −16.1558 | −0.601675 | ||||||||
\(722\) | −18.9608 | −0.705647 | ||||||||
\(723\) | −18.2228 | −0.677714 | ||||||||
\(724\) | −5.63773 | −0.209524 | ||||||||
\(725\) | 1.29590 | 0.0481284 | ||||||||
\(726\) | 6.33944 | 0.235279 | ||||||||
\(727\) | 21.2664 | 0.788726 | 0.394363 | − | 0.918955i | \(-0.370965\pi\) | ||||
0.394363 | + | 0.918955i | \(0.370965\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 11.9366 | 0.441794 | ||||||||
\(731\) | 29.5623 | 1.09340 | ||||||||
\(732\) | 6.32304 | 0.233706 | ||||||||
\(733\) | 38.9178 | 1.43746 | 0.718731 | − | 0.695288i | \(-0.244723\pi\) | ||||
0.718731 | + | 0.695288i | \(0.244723\pi\) | |||||||
\(734\) | −30.8049 | −1.13703 | ||||||||
\(735\) | 4.13706 | 0.152598 | ||||||||
\(736\) | −3.74094 | −0.137893 | ||||||||
\(737\) | −16.3308 | −0.601553 | ||||||||
\(738\) | −1.89977 | −0.0699316 | ||||||||
\(739\) | 4.48486 | 0.164978 | 0.0824891 | − | 0.996592i | \(-0.473713\pi\) | ||||
0.0824891 | + | 0.996592i | \(0.473713\pi\) | |||||||
\(740\) | 0.801938 | 0.0294798 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.70841 | 0.0627179 | ||||||||
\(743\) | 26.8558 | 0.985242 | 0.492621 | − | 0.870244i | \(-0.336039\pi\) | ||||
0.492621 | + | 0.870244i | \(0.336039\pi\) | |||||||
\(744\) | −1.44504 | −0.0529778 | ||||||||
\(745\) | 4.24160 | 0.155400 | ||||||||
\(746\) | −25.6668 | −0.939728 | ||||||||
\(747\) | 8.43296 | 0.308546 | ||||||||
\(748\) | 5.08815 | 0.186041 | ||||||||
\(749\) | −30.7047 | −1.12193 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | −5.64012 | −0.205811 | −0.102905 | − | 0.994691i | \(-0.532814\pi\) | ||||
−0.102905 | + | 0.994691i | \(0.532814\pi\) | |||||||
\(752\) | 8.87800 | 0.323747 | ||||||||
\(753\) | 17.0030 | 0.619623 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22.9148 | 0.833956 | ||||||||
\(756\) | 1.69202 | 0.0615382 | ||||||||
\(757\) | −35.6644 | −1.29624 | −0.648122 | − | 0.761536i | \(-0.724445\pi\) | ||||
−0.648122 | + | 0.761536i | \(0.724445\pi\) | |||||||
\(758\) | 5.46144 | 0.198368 | ||||||||
\(759\) | 8.07606 | 0.293143 | ||||||||
\(760\) | 0.198062 | 0.00718447 | ||||||||
\(761\) | 2.68425 | 0.0973041 | 0.0486520 | − | 0.998816i | \(-0.484507\pi\) | ||||
0.0486520 | + | 0.998816i | \(0.484507\pi\) | |||||||
\(762\) | −13.0097 | −0.471291 | ||||||||
\(763\) | 3.80194 | 0.137639 | ||||||||
\(764\) | −2.59419 | −0.0938544 | ||||||||
\(765\) | 2.35690 | 0.0852137 | ||||||||
\(766\) | −25.9221 | −0.936605 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 48.7644 | 1.75849 | 0.879244 | − | 0.476372i | \(-0.158048\pi\) | ||||
0.879244 | + | 0.476372i | \(0.158048\pi\) | |||||||
\(770\) | −3.65279 | −0.131638 | ||||||||
\(771\) | 7.65519 | 0.275695 | ||||||||
\(772\) | −3.98361 | −0.143373 | ||||||||
\(773\) | −46.6152 | −1.67663 | −0.838316 | − | 0.545184i | \(-0.816460\pi\) | ||||
−0.838316 | + | 0.545184i | \(0.816460\pi\) | |||||||
\(774\) | 12.5429 | 0.450844 | ||||||||
\(775\) | 1.44504 | 0.0519074 | ||||||||
\(776\) | −0.0881460 | −0.00316426 | ||||||||
\(777\) | 1.35690 | 0.0486784 | ||||||||
\(778\) | −32.0006 | −1.14728 | ||||||||
\(779\) | −0.376273 | −0.0134814 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.02523 | −0.322948 | ||||||||
\(782\) | −8.81700 | −0.315295 | ||||||||
\(783\) | −1.29590 | −0.0463116 | ||||||||
\(784\) | −4.13706 | −0.147752 | ||||||||
\(785\) | 16.0707 | 0.573587 | ||||||||
\(786\) | 7.82908 | 0.279254 | ||||||||
\(787\) | −27.4045 | −0.976864 | −0.488432 | − | 0.872602i | \(-0.662431\pi\) | ||||
−0.488432 | + | 0.872602i | \(0.662431\pi\) | |||||||
\(788\) | −6.65040 | −0.236911 | ||||||||
\(789\) | −21.0411 | −0.749085 | ||||||||
\(790\) | 9.40581 | 0.334644 | ||||||||
\(791\) | 20.0887 | 0.714273 | ||||||||
\(792\) | 2.15883 | 0.0767108 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0.457123 | 0.0162227 | ||||||||
\(795\) | 1.00969 | 0.0358100 | ||||||||
\(796\) | −1.01639 | −0.0360251 | ||||||||
\(797\) | −5.70278 | −0.202003 | −0.101001 | − | 0.994886i | \(-0.532205\pi\) | ||||
−0.101001 | + | 0.994886i | \(0.532205\pi\) | |||||||
\(798\) | 0.335126 | 0.0118633 | ||||||||
\(799\) | 20.9245 | 0.740257 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −2.41119 | −0.0851952 | ||||||||
\(802\) | 23.2553 | 0.821175 | ||||||||
\(803\) | 25.7692 | 0.909374 | ||||||||
\(804\) | 7.56465 | 0.266785 | ||||||||
\(805\) | 6.32975 | 0.223094 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −24.3183 | −0.856043 | ||||||||
\(808\) | −11.1099 | −0.390845 | ||||||||
\(809\) | −29.6165 | −1.04126 | −0.520631 | − | 0.853782i | \(-0.674303\pi\) | ||||
−0.520631 | + | 0.853782i | \(0.674303\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | −48.8901 | −1.71676 | −0.858382 | − | 0.513012i | \(-0.828530\pi\) | ||||
−0.858382 | + | 0.513012i | \(0.828530\pi\) | |||||||
\(812\) | −2.19269 | −0.0769482 | ||||||||
\(813\) | −10.9922 | −0.385514 | ||||||||
\(814\) | 1.73125 | 0.0606803 | ||||||||
\(815\) | −0.488582 | −0.0171143 | ||||||||
\(816\) | −2.35690 | −0.0825079 | ||||||||
\(817\) | 2.48427 | 0.0869136 | ||||||||
\(818\) | 39.0629 | 1.36580 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.89977 | −0.0663429 | ||||||||
\(821\) | −19.7942 | −0.690821 | −0.345411 | − | 0.938452i | \(-0.612260\pi\) | ||||
−0.345411 | + | 0.938452i | \(0.612260\pi\) | |||||||
\(822\) | −5.36227 | −0.187031 | ||||||||
\(823\) | 49.6118 | 1.72936 | 0.864679 | − | 0.502325i | \(-0.167522\pi\) | ||||
0.864679 | + | 0.502325i | \(0.167522\pi\) | |||||||
\(824\) | 9.54825 | 0.332629 | ||||||||
\(825\) | −2.15883 | −0.0751609 | ||||||||
\(826\) | −6.31336 | −0.219670 | ||||||||
\(827\) | 26.0683 | 0.906483 | 0.453242 | − | 0.891388i | \(-0.350267\pi\) | ||||
0.453242 | + | 0.891388i | \(0.350267\pi\) | |||||||
\(828\) | −3.74094 | −0.130007 | ||||||||
\(829\) | 46.2215 | 1.60534 | 0.802669 | − | 0.596424i | \(-0.203412\pi\) | ||||
0.802669 | + | 0.596424i | \(0.203412\pi\) | |||||||
\(830\) | 8.43296 | 0.292712 | ||||||||
\(831\) | 11.4601 | 0.397547 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.75063 | −0.337839 | ||||||||
\(834\) | −3.12200 | −0.108106 | ||||||||
\(835\) | 14.0610 | 0.486601 | ||||||||
\(836\) | 0.427583 | 0.0147883 | ||||||||
\(837\) | −1.44504 | −0.0499480 | ||||||||
\(838\) | −18.1269 | −0.626183 | ||||||||
\(839\) | 33.2693 | 1.14859 | 0.574293 | − | 0.818650i | \(-0.305277\pi\) | ||||
0.574293 | + | 0.818650i | \(0.305277\pi\) | |||||||
\(840\) | 1.69202 | 0.0583803 | ||||||||
\(841\) | −27.3207 | −0.942091 | ||||||||
\(842\) | −20.4916 | −0.706186 | ||||||||
\(843\) | 9.88231 | 0.340365 | ||||||||
\(844\) | 10.1414 | 0.349081 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 8.87800 | 0.305232 | ||||||||
\(847\) | 10.7265 | 0.368566 | ||||||||
\(848\) | −1.00969 | −0.0346729 | ||||||||
\(849\) | 21.3207 | 0.731723 | ||||||||
\(850\) | 2.35690 | 0.0808409 | ||||||||
\(851\) | −3.00000 | −0.102839 | ||||||||
\(852\) | 4.18060 | 0.143225 | ||||||||
\(853\) | −39.3002 | −1.34561 | −0.672807 | − | 0.739818i | \(-0.734911\pi\) | ||||
−0.672807 | + | 0.739818i | \(0.734911\pi\) | |||||||
\(854\) | 10.6987 | 0.366103 | ||||||||
\(855\) | 0.198062 | 0.00677359 | ||||||||
\(856\) | 18.1468 | 0.620243 | ||||||||
\(857\) | −39.7566 | −1.35806 | −0.679030 | − | 0.734111i | \(-0.737599\pi\) | ||||
−0.679030 | + | 0.734111i | \(0.737599\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.43860 | −0.117324 | −0.0586618 | − | 0.998278i | \(-0.518683\pi\) | ||||
−0.0586618 | + | 0.998278i | \(0.518683\pi\) | |||||||
\(860\) | 12.5429 | 0.427709 | ||||||||
\(861\) | −3.21446 | −0.109548 | ||||||||
\(862\) | −22.2989 | −0.759503 | ||||||||
\(863\) | 21.2301 | 0.722681 | 0.361341 | − | 0.932434i | \(-0.382319\pi\) | ||||
0.361341 | + | 0.932434i | \(0.382319\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 21.7942 | 0.741024 | ||||||||
\(866\) | 7.47650 | 0.254062 | ||||||||
\(867\) | 11.4450 | 0.388694 | ||||||||
\(868\) | −2.44504 | −0.0829901 | ||||||||
\(869\) | 20.3056 | 0.688820 | ||||||||
\(870\) | −1.29590 | −0.0439350 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −2.24698 | −0.0760923 | ||||||||
\(873\) | −0.0881460 | −0.00298329 | ||||||||
\(874\) | −0.740939 | −0.0250626 | ||||||||
\(875\) | −1.69202 | −0.0572008 | ||||||||
\(876\) | −11.9366 | −0.403301 | ||||||||
\(877\) | −5.74227 | −0.193903 | −0.0969513 | − | 0.995289i | \(-0.530909\pi\) | ||||
−0.0969513 | + | 0.995289i | \(0.530909\pi\) | |||||||
\(878\) | −19.3924 | −0.654462 | ||||||||
\(879\) | 18.7090 | 0.631039 | ||||||||
\(880\) | 2.15883 | 0.0727743 | ||||||||
\(881\) | 12.6069 | 0.424736 | 0.212368 | − | 0.977190i | \(-0.431882\pi\) | ||||
0.212368 | + | 0.977190i | \(0.431882\pi\) | |||||||
\(882\) | −4.13706 | −0.139302 | ||||||||
\(883\) | 25.8086 | 0.868530 | 0.434265 | − | 0.900785i | \(-0.357008\pi\) | ||||
0.434265 | + | 0.900785i | \(0.357008\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.73125 | −0.125425 | ||||||||
\(886\) | 10.0935 | 0.339099 | ||||||||
\(887\) | −20.2392 | −0.679566 | −0.339783 | − | 0.940504i | \(-0.610354\pi\) | ||||
−0.339783 | + | 0.940504i | \(0.610354\pi\) | |||||||
\(888\) | −0.801938 | −0.0269113 | ||||||||
\(889\) | −22.0127 | −0.738281 | ||||||||
\(890\) | −2.41119 | −0.0808233 | ||||||||
\(891\) | 2.15883 | 0.0723236 | ||||||||
\(892\) | −16.8388 | −0.563804 | ||||||||
\(893\) | 1.75840 | 0.0588425 | ||||||||
\(894\) | −4.24160 | −0.141860 | ||||||||
\(895\) | −14.1293 | −0.472290 | ||||||||
\(896\) | −1.69202 | −0.0565265 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.78448 | −0.0929193 | ||||||||
\(899\) | 1.87263 | 0.0624556 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −2.37973 | −0.0792803 | ||||||||
\(902\) | −4.10129 | −0.136558 | ||||||||
\(903\) | 21.2228 | 0.706251 | ||||||||
\(904\) | −11.8726 | −0.394878 | ||||||||
\(905\) | −5.63773 | −0.187404 | ||||||||
\(906\) | −22.9148 | −0.761294 | ||||||||
\(907\) | −3.52350 | −0.116996 | −0.0584979 | − | 0.998288i | \(-0.518631\pi\) | ||||
−0.0584979 | + | 0.998288i | \(0.518631\pi\) | |||||||
\(908\) | 18.3056 | 0.607492 | ||||||||
\(909\) | −11.1099 | −0.368493 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.7426 | −1.15107 | −0.575537 | − | 0.817776i | \(-0.695207\pi\) | ||||
−0.575537 | + | 0.817776i | \(0.695207\pi\) | |||||||
\(912\) | −0.198062 | −0.00655850 | ||||||||
\(913\) | 18.2054 | 0.602509 | ||||||||
\(914\) | −13.1056 | −0.433495 | ||||||||
\(915\) | 6.32304 | 0.209033 | ||||||||
\(916\) | 5.14244 | 0.169911 | ||||||||
\(917\) | 13.2470 | 0.437454 | ||||||||
\(918\) | −2.35690 | −0.0777892 | ||||||||
\(919\) | −24.1430 | −0.796405 | −0.398203 | − | 0.917298i | \(-0.630366\pi\) | ||||
−0.398203 | + | 0.917298i | \(0.630366\pi\) | |||||||
\(920\) | −3.74094 | −0.123335 | ||||||||
\(921\) | −17.2241 | −0.567555 | ||||||||
\(922\) | 16.2174 | 0.534093 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 3.65279 | 0.120168 | ||||||||
\(925\) | 0.801938 | 0.0263676 | ||||||||
\(926\) | 15.5415 | 0.510727 | ||||||||
\(927\) | 9.54825 | 0.313606 | ||||||||
\(928\) | 1.29590 | 0.0425399 | ||||||||
\(929\) | −56.9700 | −1.86912 | −0.934562 | − | 0.355800i | \(-0.884209\pi\) | ||||
−0.934562 | + | 0.355800i | \(0.884209\pi\) | |||||||
\(930\) | −1.44504 | −0.0473848 | ||||||||
\(931\) | −0.819396 | −0.0268546 | ||||||||
\(932\) | −10.9215 | −0.357747 | ||||||||
\(933\) | 13.5200 | 0.442626 | ||||||||
\(934\) | −10.1578 | −0.332372 | ||||||||
\(935\) | 5.08815 | 0.166400 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −45.7966 | −1.49611 | −0.748054 | − | 0.663638i | \(-0.769012\pi\) | ||||
−0.748054 | + | 0.663638i | \(0.769012\pi\) | |||||||
\(938\) | 12.7995 | 0.417920 | ||||||||
\(939\) | −24.3303 | −0.793991 | ||||||||
\(940\) | 8.87800 | 0.289569 | ||||||||
\(941\) | −7.10262 | −0.231539 | −0.115769 | − | 0.993276i | \(-0.536933\pi\) | ||||
−0.115769 | + | 0.993276i | \(0.536933\pi\) | |||||||
\(942\) | −16.0707 | −0.523611 | ||||||||
\(943\) | 7.10693 | 0.231434 | ||||||||
\(944\) | 3.73125 | 0.121442 | ||||||||
\(945\) | 1.69202 | 0.0550415 | ||||||||
\(946\) | 27.0780 | 0.880381 | ||||||||
\(947\) | −11.2524 | −0.365652 | −0.182826 | − | 0.983145i | \(-0.558525\pi\) | ||||
−0.182826 | + | 0.983145i | \(0.558525\pi\) | |||||||
\(948\) | −9.40581 | −0.305487 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0.198062 | 0.00642599 | ||||||||
\(951\) | −34.7821 | −1.12789 | ||||||||
\(952\) | −3.98792 | −0.129249 | ||||||||
\(953\) | −1.61702 | −0.0523805 | −0.0261902 | − | 0.999657i | \(-0.508338\pi\) | ||||
−0.0261902 | + | 0.999657i | \(0.508338\pi\) | |||||||
\(954\) | −1.00969 | −0.0326899 | ||||||||
\(955\) | −2.59419 | −0.0839459 | ||||||||
\(956\) | 19.9041 | 0.643744 | ||||||||
\(957\) | −2.79763 | −0.0904344 | ||||||||
\(958\) | 31.4263 | 1.01534 | ||||||||
\(959\) | −9.07308 | −0.292985 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | −28.9119 | −0.932640 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 18.1468 | 0.584771 | ||||||||
\(964\) | 18.2228 | 0.586917 | ||||||||
\(965\) | −3.98361 | −0.128237 | ||||||||
\(966\) | −6.32975 | −0.203656 | ||||||||
\(967\) | −24.1588 | −0.776896 | −0.388448 | − | 0.921471i | \(-0.626989\pi\) | ||||
−0.388448 | + | 0.921471i | \(0.626989\pi\) | |||||||
\(968\) | −6.33944 | −0.203757 | ||||||||
\(969\) | −0.466812 | −0.0149962 | ||||||||
\(970\) | −0.0881460 | −0.00283020 | ||||||||
\(971\) | 43.2669 | 1.38850 | 0.694251 | − | 0.719733i | \(-0.255736\pi\) | ||||
0.694251 | + | 0.719733i | \(0.255736\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −5.28249 | −0.169349 | ||||||||
\(974\) | −24.1323 | −0.773248 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.32304 | −0.202396 | ||||||||
\(977\) | 24.9782 | 0.799124 | 0.399562 | − | 0.916706i | \(-0.369162\pi\) | ||||
0.399562 | + | 0.916706i | \(0.369162\pi\) | |||||||
\(978\) | 0.488582 | 0.0156231 | ||||||||
\(979\) | −5.20536 | −0.166364 | ||||||||
\(980\) | −4.13706 | −0.132154 | ||||||||
\(981\) | −2.24698 | −0.0717405 | ||||||||
\(982\) | −19.1099 | −0.609822 | ||||||||
\(983\) | −19.3134 | −0.616000 | −0.308000 | − | 0.951386i | \(-0.599660\pi\) | ||||
−0.308000 | + | 0.951386i | \(0.599660\pi\) | |||||||
\(984\) | 1.89977 | 0.0605625 | ||||||||
\(985\) | −6.65040 | −0.211899 | ||||||||
\(986\) | 3.05429 | 0.0972685 | ||||||||
\(987\) | 15.0218 | 0.478148 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −46.9221 | −1.49204 | ||||||||
\(990\) | 2.15883 | 0.0686122 | ||||||||
\(991\) | −27.5090 | −0.873853 | −0.436926 | − | 0.899497i | \(-0.643933\pi\) | ||||
−0.436926 | + | 0.899497i | \(0.643933\pi\) | |||||||
\(992\) | 1.44504 | 0.0458801 | ||||||||
\(993\) | 9.66919 | 0.306842 | ||||||||
\(994\) | 7.07367 | 0.224363 | ||||||||
\(995\) | −1.01639 | −0.0322218 | ||||||||
\(996\) | −8.43296 | −0.267209 | ||||||||
\(997\) | −23.1933 | −0.734538 | −0.367269 | − | 0.930115i | \(-0.619707\pi\) | ||||
−0.367269 | + | 0.930115i | \(0.619707\pi\) | |||||||
\(998\) | −34.9724 | −1.10703 | ||||||||
\(999\) | −0.801938 | −0.0253722 |
(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.a.bu.1.1 | yes | 3 | |
13.5 | odd | 4 | 5070.2.b.t.1351.1 | 6 | |||
13.8 | odd | 4 | 5070.2.b.t.1351.6 | 6 | |||
13.12 | even | 2 | 5070.2.a.bj.1.3 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5070.2.a.bj.1.3 | ✓ | 3 | 13.12 | even | 2 | ||
5070.2.a.bu.1.1 | yes | 3 | 1.1 | even | 1 | trivial | |
5070.2.b.t.1351.1 | 6 | 13.5 | odd | 4 | |||
5070.2.b.t.1351.6 | 6 | 13.8 | odd | 4 |