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 | \(1.80194\) 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 | ||||||||
\(7\) | 1.19806 | 0.452825 | 0.226412 | − | 0.974032i | \(-0.427300\pi\) | ||||
0.226412 | + | 0.974032i | \(0.427300\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0.554958 | 0.167326 | 0.0836631 | − | 0.996494i | \(-0.473338\pi\) | ||||
0.0836631 | + | 0.996494i | \(0.473338\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.19806 | −0.320196 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.45473 | −1.56550 | −0.782751 | − | 0.622335i | \(-0.786184\pi\) | ||||
−0.782751 | + | 0.622335i | \(0.786184\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −5.40581 | −1.24018 | −0.620089 | − | 0.784531i | \(-0.712904\pi\) | ||||
−0.620089 | + | 0.784531i | \(0.712904\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −1.19806 | −0.261439 | ||||||||
\(22\) | −0.554958 | −0.118317 | ||||||||
\(23\) | 7.96077 | 1.65994 | 0.829968 | − | 0.557811i | \(-0.188359\pi\) | ||||
0.829968 | + | 0.557811i | \(0.188359\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.19806 | 0.226412 | ||||||||
\(29\) | −6.89977 | −1.28126 | −0.640628 | − | 0.767852i | \(-0.721326\pi\) | ||||
−0.640628 | + | 0.767852i | \(0.721326\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | 3.04892 | 0.547602 | 0.273801 | − | 0.961786i | \(-0.411719\pi\) | ||||
0.273801 | + | 0.961786i | \(0.411719\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.554958 | −0.0966058 | ||||||||
\(34\) | 6.45473 | 1.10698 | ||||||||
\(35\) | 1.19806 | 0.202509 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −7.96615 | −1.30963 | −0.654813 | − | 0.755791i | \(-0.727253\pi\) | ||||
−0.654813 | + | 0.755791i | \(0.727253\pi\) | |||||||
\(38\) | 5.40581 | 0.876939 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 3.08815 | 0.482287 | 0.241144 | − | 0.970489i | \(-0.422477\pi\) | ||||
0.241144 | + | 0.970489i | \(0.422477\pi\) | |||||||
\(42\) | 1.19806 | 0.184865 | ||||||||
\(43\) | 1.15883 | 0.176720 | 0.0883602 | − | 0.996089i | \(-0.471837\pi\) | ||||
0.0883602 | + | 0.996089i | \(0.471837\pi\) | |||||||
\(44\) | 0.554958 | 0.0836631 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | −7.96077 | −1.17375 | ||||||||
\(47\) | 12.2620 | 1.78860 | 0.894302 | − | 0.447465i | \(-0.147673\pi\) | ||||
0.894302 | + | 0.447465i | \(0.147673\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −5.56465 | −0.794950 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 6.45473 | 0.903843 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.47219 | 1.16374 | 0.581872 | − | 0.813280i | \(-0.302320\pi\) | ||||
0.581872 | + | 0.813280i | \(0.302320\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0.554958 | 0.0748305 | ||||||||
\(56\) | −1.19806 | −0.160098 | ||||||||
\(57\) | 5.40581 | 0.716017 | ||||||||
\(58\) | 6.89977 | 0.905985 | ||||||||
\(59\) | 1.45712 | 0.189701 | 0.0948507 | − | 0.995492i | \(-0.469763\pi\) | ||||
0.0948507 | + | 0.995492i | \(0.469763\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | 2.76271 | 0.353729 | 0.176864 | − | 0.984235i | \(-0.443405\pi\) | ||||
0.176864 | + | 0.984235i | \(0.443405\pi\) | |||||||
\(62\) | −3.04892 | −0.387213 | ||||||||
\(63\) | 1.19806 | 0.150942 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.554958 | 0.0683106 | ||||||||
\(67\) | −3.34481 | −0.408634 | −0.204317 | − | 0.978905i | \(-0.565497\pi\) | ||||
−0.204317 | + | 0.978905i | \(0.565497\pi\) | |||||||
\(68\) | −6.45473 | −0.782751 | ||||||||
\(69\) | −7.96077 | −0.958364 | ||||||||
\(70\) | −1.19806 | −0.143196 | ||||||||
\(71\) | 2.35690 | 0.279712 | 0.139856 | − | 0.990172i | \(-0.455336\pi\) | ||||
0.139856 | + | 0.990172i | \(0.455336\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 13.3448 | 1.56189 | 0.780946 | − | 0.624598i | \(-0.214737\pi\) | ||||
0.780946 | + | 0.624598i | \(0.214737\pi\) | |||||||
\(74\) | 7.96615 | 0.926046 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | −5.40581 | −0.620089 | ||||||||
\(77\) | 0.664874 | 0.0757695 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.990311 | −0.111419 | −0.0557094 | − | 0.998447i | \(-0.517742\pi\) | ||||
−0.0557094 | + | 0.998447i | \(0.517742\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −3.08815 | −0.341029 | ||||||||
\(83\) | 5.88471 | 0.645931 | 0.322965 | − | 0.946411i | \(-0.395320\pi\) | ||||
0.322965 | + | 0.946411i | \(0.395320\pi\) | |||||||
\(84\) | −1.19806 | −0.130719 | ||||||||
\(85\) | −6.45473 | −0.700114 | ||||||||
\(86\) | −1.15883 | −0.124960 | ||||||||
\(87\) | 6.89977 | 0.739733 | ||||||||
\(88\) | −0.554958 | −0.0591587 | ||||||||
\(89\) | 13.7845 | 1.46115 | 0.730576 | − | 0.682831i | \(-0.239252\pi\) | ||||
0.730576 | + | 0.682831i | \(0.239252\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 7.96077 | 0.829968 | ||||||||
\(93\) | −3.04892 | −0.316158 | ||||||||
\(94\) | −12.2620 | −1.26473 | ||||||||
\(95\) | −5.40581 | −0.554625 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 7.07606 | 0.718465 | 0.359233 | − | 0.933248i | \(-0.383038\pi\) | ||||
0.359233 | + | 0.933248i | \(0.383038\pi\) | |||||||
\(98\) | 5.56465 | 0.562114 | ||||||||
\(99\) | 0.554958 | 0.0557754 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 4.09783 | 0.407750 | 0.203875 | − | 0.978997i | \(-0.434646\pi\) | ||||
0.203875 | + | 0.978997i | \(0.434646\pi\) | |||||||
\(102\) | −6.45473 | −0.639114 | ||||||||
\(103\) | −4.16421 | −0.410312 | −0.205156 | − | 0.978729i | \(-0.565770\pi\) | ||||
−0.205156 | + | 0.978729i | \(0.565770\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.19806 | −0.116919 | ||||||||
\(106\) | −8.47219 | −0.822892 | ||||||||
\(107\) | −4.98254 | −0.481680 | −0.240840 | − | 0.970565i | \(-0.577423\pi\) | ||||
−0.240840 | + | 0.970565i | \(0.577423\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 1.31336 | 0.125797 | 0.0628983 | − | 0.998020i | \(-0.479966\pi\) | ||||
0.0628983 | + | 0.998020i | \(0.479966\pi\) | |||||||
\(110\) | −0.554958 | −0.0529132 | ||||||||
\(111\) | 7.96615 | 0.756113 | ||||||||
\(112\) | 1.19806 | 0.113206 | ||||||||
\(113\) | 3.55496 | 0.334422 | 0.167211 | − | 0.985921i | \(-0.446524\pi\) | ||||
0.167211 | + | 0.985921i | \(0.446524\pi\) | |||||||
\(114\) | −5.40581 | −0.506301 | ||||||||
\(115\) | 7.96077 | 0.742346 | ||||||||
\(116\) | −6.89977 | −0.640628 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.45712 | −0.134139 | ||||||||
\(119\) | −7.73317 | −0.708898 | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | −10.6920 | −0.972002 | ||||||||
\(122\) | −2.76271 | −0.250124 | ||||||||
\(123\) | −3.08815 | −0.278449 | ||||||||
\(124\) | 3.04892 | 0.273801 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −1.19806 | −0.106732 | ||||||||
\(127\) | 21.8756 | 1.94115 | 0.970573 | − | 0.240806i | \(-0.0774118\pi\) | ||||
0.970573 | + | 0.240806i | \(0.0774118\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −1.15883 | −0.102030 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −21.6528 | −1.89181 | −0.945907 | − | 0.324439i | \(-0.894825\pi\) | ||||
−0.945907 | + | 0.324439i | \(0.894825\pi\) | |||||||
\(132\) | −0.554958 | −0.0483029 | ||||||||
\(133\) | −6.47650 | −0.561584 | ||||||||
\(134\) | 3.34481 | 0.288948 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 6.45473 | 0.553489 | ||||||||
\(137\) | 7.08815 | 0.605581 | 0.302791 | − | 0.953057i | \(-0.402082\pi\) | ||||
0.302791 | + | 0.953057i | \(0.402082\pi\) | |||||||
\(138\) | 7.96077 | 0.677666 | ||||||||
\(139\) | 0.340502 | 0.0288810 | 0.0144405 | − | 0.999896i | \(-0.495403\pi\) | ||||
0.0144405 | + | 0.999896i | \(0.495403\pi\) | |||||||
\(140\) | 1.19806 | 0.101255 | ||||||||
\(141\) | −12.2620 | −1.03265 | ||||||||
\(142\) | −2.35690 | −0.197786 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −6.89977 | −0.572995 | ||||||||
\(146\) | −13.3448 | −1.10442 | ||||||||
\(147\) | 5.56465 | 0.458964 | ||||||||
\(148\) | −7.96615 | −0.654813 | ||||||||
\(149\) | 7.40581 | 0.606708 | 0.303354 | − | 0.952878i | \(-0.401894\pi\) | ||||
0.303354 | + | 0.952878i | \(0.401894\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | 10.4209 | 0.848039 | 0.424020 | − | 0.905653i | \(-0.360619\pi\) | ||||
0.424020 | + | 0.905653i | \(0.360619\pi\) | |||||||
\(152\) | 5.40581 | 0.438469 | ||||||||
\(153\) | −6.45473 | −0.521834 | ||||||||
\(154\) | −0.664874 | −0.0535771 | ||||||||
\(155\) | 3.04892 | 0.244895 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.0151 | −1.51757 | −0.758784 | − | 0.651343i | \(-0.774206\pi\) | ||||
−0.758784 | + | 0.651343i | \(0.774206\pi\) | |||||||
\(158\) | 0.990311 | 0.0787849 | ||||||||
\(159\) | −8.47219 | −0.671888 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 9.53750 | 0.751660 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 5.65279 | 0.442761 | 0.221380 | − | 0.975188i | \(-0.428944\pi\) | ||||
0.221380 | + | 0.975188i | \(0.428944\pi\) | |||||||
\(164\) | 3.08815 | 0.241144 | ||||||||
\(165\) | −0.554958 | −0.0432034 | ||||||||
\(166\) | −5.88471 | −0.456742 | ||||||||
\(167\) | 2.15883 | 0.167056 | 0.0835278 | − | 0.996505i | \(-0.473381\pi\) | ||||
0.0835278 | + | 0.996505i | \(0.473381\pi\) | |||||||
\(168\) | 1.19806 | 0.0924325 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 6.45473 | 0.495055 | ||||||||
\(171\) | −5.40581 | −0.413393 | ||||||||
\(172\) | 1.15883 | 0.0883602 | ||||||||
\(173\) | 21.6722 | 1.64770 | 0.823852 | − | 0.566805i | \(-0.191821\pi\) | ||||
0.823852 | + | 0.566805i | \(0.191821\pi\) | |||||||
\(174\) | −6.89977 | −0.523070 | ||||||||
\(175\) | 1.19806 | 0.0905650 | ||||||||
\(176\) | 0.554958 | 0.0418315 | ||||||||
\(177\) | −1.45712 | −0.109524 | ||||||||
\(178\) | −13.7845 | −1.03319 | ||||||||
\(179\) | −0.956459 | −0.0714891 | −0.0357446 | − | 0.999361i | \(-0.511380\pi\) | ||||
−0.0357446 | + | 0.999361i | \(0.511380\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | 0.405813 | 0.0301639 | 0.0150819 | − | 0.999886i | \(-0.495199\pi\) | ||||
0.0150819 | + | 0.999886i | \(0.495199\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.76271 | −0.204225 | ||||||||
\(184\) | −7.96077 | −0.586876 | ||||||||
\(185\) | −7.96615 | −0.585683 | ||||||||
\(186\) | 3.04892 | 0.223557 | ||||||||
\(187\) | −3.58211 | −0.261949 | ||||||||
\(188\) | 12.2620 | 0.894302 | ||||||||
\(189\) | −1.19806 | −0.0871462 | ||||||||
\(190\) | 5.40581 | 0.392179 | ||||||||
\(191\) | −19.0097 | −1.37549 | −0.687746 | − | 0.725951i | \(-0.741400\pi\) | ||||
−0.687746 | + | 0.725951i | \(0.741400\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 0.599564 | 0.0431575 | 0.0215788 | − | 0.999767i | \(-0.493131\pi\) | ||||
0.0215788 | + | 0.999767i | \(0.493131\pi\) | |||||||
\(194\) | −7.07606 | −0.508032 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.56465 | −0.397475 | ||||||||
\(197\) | 3.78448 | 0.269633 | 0.134816 | − | 0.990871i | \(-0.456956\pi\) | ||||
0.134816 | + | 0.990871i | \(0.456956\pi\) | |||||||
\(198\) | −0.554958 | −0.0394392 | ||||||||
\(199\) | −10.2349 | −0.725533 | −0.362766 | − | 0.931880i | \(-0.618168\pi\) | ||||
−0.362766 | + | 0.931880i | \(0.618168\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 3.34481 | 0.235925 | ||||||||
\(202\) | −4.09783 | −0.288323 | ||||||||
\(203\) | −8.26636 | −0.580185 | ||||||||
\(204\) | 6.45473 | 0.451922 | ||||||||
\(205\) | 3.08815 | 0.215685 | ||||||||
\(206\) | 4.16421 | 0.290134 | ||||||||
\(207\) | 7.96077 | 0.553312 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.00000 | −0.207514 | ||||||||
\(210\) | 1.19806 | 0.0826742 | ||||||||
\(211\) | −8.71379 | −0.599882 | −0.299941 | − | 0.953958i | \(-0.596967\pi\) | ||||
−0.299941 | + | 0.953958i | \(0.596967\pi\) | |||||||
\(212\) | 8.47219 | 0.581872 | ||||||||
\(213\) | −2.35690 | −0.161492 | ||||||||
\(214\) | 4.98254 | 0.340600 | ||||||||
\(215\) | 1.15883 | 0.0790318 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 3.65279 | 0.247968 | ||||||||
\(218\) | −1.31336 | −0.0889516 | ||||||||
\(219\) | −13.3448 | −0.901759 | ||||||||
\(220\) | 0.554958 | 0.0374153 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −7.96615 | −0.534653 | ||||||||
\(223\) | −15.0694 | −1.00912 | −0.504559 | − | 0.863377i | \(-0.668345\pi\) | ||||
−0.504559 | + | 0.863377i | \(0.668345\pi\) | |||||||
\(224\) | −1.19806 | −0.0800489 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −3.55496 | −0.236472 | ||||||||
\(227\) | −20.4577 | −1.35783 | −0.678913 | − | 0.734219i | \(-0.737549\pi\) | ||||
−0.678913 | + | 0.734219i | \(0.737549\pi\) | |||||||
\(228\) | 5.40581 | 0.358009 | ||||||||
\(229\) | 18.7657 | 1.24007 | 0.620036 | − | 0.784573i | \(-0.287118\pi\) | ||||
0.620036 | + | 0.784573i | \(0.287118\pi\) | |||||||
\(230\) | −7.96077 | −0.524918 | ||||||||
\(231\) | −0.664874 | −0.0437455 | ||||||||
\(232\) | 6.89977 | 0.452992 | ||||||||
\(233\) | 23.6353 | 1.54840 | 0.774201 | − | 0.632940i | \(-0.218152\pi\) | ||||
0.774201 | + | 0.632940i | \(0.218152\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.2620 | 0.799888 | ||||||||
\(236\) | 1.45712 | 0.0948507 | ||||||||
\(237\) | 0.990311 | 0.0643276 | ||||||||
\(238\) | 7.73317 | 0.501267 | ||||||||
\(239\) | 28.7506 | 1.85972 | 0.929862 | − | 0.367909i | \(-0.119926\pi\) | ||||
0.929862 | + | 0.367909i | \(0.119926\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | −3.89440 | −0.250860 | −0.125430 | − | 0.992102i | \(-0.540031\pi\) | ||||
−0.125430 | + | 0.992102i | \(0.540031\pi\) | |||||||
\(242\) | 10.6920 | 0.687309 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 2.76271 | 0.176864 | ||||||||
\(245\) | −5.56465 | −0.355512 | ||||||||
\(246\) | 3.08815 | 0.196893 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −3.04892 | −0.193606 | ||||||||
\(249\) | −5.88471 | −0.372928 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −24.3327 | −1.53587 | −0.767934 | − | 0.640529i | \(-0.778715\pi\) | ||||
−0.767934 | + | 0.640529i | \(0.778715\pi\) | |||||||
\(252\) | 1.19806 | 0.0754708 | ||||||||
\(253\) | 4.41789 | 0.277751 | ||||||||
\(254\) | −21.8756 | −1.37260 | ||||||||
\(255\) | 6.45473 | 0.404211 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 30.4426 | 1.89896 | 0.949480 | − | 0.313827i | \(-0.101611\pi\) | ||||
0.949480 | + | 0.313827i | \(0.101611\pi\) | |||||||
\(258\) | 1.15883 | 0.0721458 | ||||||||
\(259\) | −9.54394 | −0.593032 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.89977 | −0.427085 | ||||||||
\(262\) | 21.6528 | 1.33771 | ||||||||
\(263\) | −9.33944 | −0.575894 | −0.287947 | − | 0.957646i | \(-0.592973\pi\) | ||||
−0.287947 | + | 0.957646i | \(0.592973\pi\) | |||||||
\(264\) | 0.554958 | 0.0341553 | ||||||||
\(265\) | 8.47219 | 0.520442 | ||||||||
\(266\) | 6.47650 | 0.397100 | ||||||||
\(267\) | −13.7845 | −0.843596 | ||||||||
\(268\) | −3.34481 | −0.204317 | ||||||||
\(269\) | 26.7821 | 1.63293 | 0.816466 | − | 0.577393i | \(-0.195930\pi\) | ||||
0.816466 | + | 0.577393i | \(0.195930\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | −2.58748 | −0.157178 | −0.0785892 | − | 0.996907i | \(-0.525042\pi\) | ||||
−0.0785892 | + | 0.996907i | \(0.525042\pi\) | |||||||
\(272\) | −6.45473 | −0.391376 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.08815 | −0.428211 | ||||||||
\(275\) | 0.554958 | 0.0334652 | ||||||||
\(276\) | −7.96077 | −0.479182 | ||||||||
\(277\) | 11.0532 | 0.664124 | 0.332062 | − | 0.943258i | \(-0.392256\pi\) | ||||
0.332062 | + | 0.943258i | \(0.392256\pi\) | |||||||
\(278\) | −0.340502 | −0.0204220 | ||||||||
\(279\) | 3.04892 | 0.182534 | ||||||||
\(280\) | −1.19806 | −0.0715979 | ||||||||
\(281\) | 10.5090 | 0.626916 | 0.313458 | − | 0.949602i | \(-0.398513\pi\) | ||||
0.313458 | + | 0.949602i | \(0.398513\pi\) | |||||||
\(282\) | 12.2620 | 0.730194 | ||||||||
\(283\) | −1.07069 | −0.0636458 | −0.0318229 | − | 0.999494i | \(-0.510131\pi\) | ||||
−0.0318229 | + | 0.999494i | \(0.510131\pi\) | |||||||
\(284\) | 2.35690 | 0.139856 | ||||||||
\(285\) | 5.40581 | 0.320213 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.69979 | 0.218392 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 24.6635 | 1.45080 | ||||||||
\(290\) | 6.89977 | 0.405169 | ||||||||
\(291\) | −7.07606 | −0.414806 | ||||||||
\(292\) | 13.3448 | 0.780946 | ||||||||
\(293\) | 27.4142 | 1.60155 | 0.800777 | − | 0.598963i | \(-0.204420\pi\) | ||||
0.800777 | + | 0.598963i | \(0.204420\pi\) | |||||||
\(294\) | −5.56465 | −0.324537 | ||||||||
\(295\) | 1.45712 | 0.0848370 | ||||||||
\(296\) | 7.96615 | 0.463023 | ||||||||
\(297\) | −0.554958 | −0.0322019 | ||||||||
\(298\) | −7.40581 | −0.429007 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 1.38835 | 0.0800234 | ||||||||
\(302\) | −10.4209 | −0.599654 | ||||||||
\(303\) | −4.09783 | −0.235414 | ||||||||
\(304\) | −5.40581 | −0.310045 | ||||||||
\(305\) | 2.76271 | 0.158192 | ||||||||
\(306\) | 6.45473 | 0.368992 | ||||||||
\(307\) | 24.4969 | 1.39811 | 0.699057 | − | 0.715066i | \(-0.253603\pi\) | ||||
0.699057 | + | 0.715066i | \(0.253603\pi\) | |||||||
\(308\) | 0.664874 | 0.0378847 | ||||||||
\(309\) | 4.16421 | 0.236894 | ||||||||
\(310\) | −3.04892 | −0.173167 | ||||||||
\(311\) | 16.4403 | 0.932241 | 0.466121 | − | 0.884721i | \(-0.345651\pi\) | ||||
0.466121 | + | 0.884721i | \(0.345651\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.0320 | −1.47142 | −0.735709 | − | 0.677298i | \(-0.763151\pi\) | ||||
−0.735709 | + | 0.677298i | \(0.763151\pi\) | |||||||
\(314\) | 19.0151 | 1.07308 | ||||||||
\(315\) | 1.19806 | 0.0675032 | ||||||||
\(316\) | −0.990311 | −0.0557094 | ||||||||
\(317\) | 19.3545 | 1.08706 | 0.543529 | − | 0.839391i | \(-0.317088\pi\) | ||||
0.543529 | + | 0.839391i | \(0.317088\pi\) | |||||||
\(318\) | 8.47219 | 0.475097 | ||||||||
\(319\) | −3.82908 | −0.214388 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 4.98254 | 0.278098 | ||||||||
\(322\) | −9.53750 | −0.531504 | ||||||||
\(323\) | 34.8931 | 1.94150 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −5.65279 | −0.313079 | ||||||||
\(327\) | −1.31336 | −0.0726287 | ||||||||
\(328\) | −3.08815 | −0.170514 | ||||||||
\(329\) | 14.6907 | 0.809924 | ||||||||
\(330\) | 0.554958 | 0.0305494 | ||||||||
\(331\) | −0.173899 | −0.00955836 | −0.00477918 | − | 0.999989i | \(-0.501521\pi\) | ||||
−0.00477918 | + | 0.999989i | \(0.501521\pi\) | |||||||
\(332\) | 5.88471 | 0.322965 | ||||||||
\(333\) | −7.96615 | −0.436542 | ||||||||
\(334\) | −2.15883 | −0.118126 | ||||||||
\(335\) | −3.34481 | −0.182747 | ||||||||
\(336\) | −1.19806 | −0.0653597 | ||||||||
\(337\) | −14.3793 | −0.783288 | −0.391644 | − | 0.920117i | \(-0.628094\pi\) | ||||
−0.391644 | + | 0.920117i | \(0.628094\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.55496 | −0.193079 | ||||||||
\(340\) | −6.45473 | −0.350057 | ||||||||
\(341\) | 1.69202 | 0.0916281 | ||||||||
\(342\) | 5.40581 | 0.292313 | ||||||||
\(343\) | −15.0532 | −0.812798 | ||||||||
\(344\) | −1.15883 | −0.0624801 | ||||||||
\(345\) | −7.96077 | −0.428594 | ||||||||
\(346\) | −21.6722 | −1.16510 | ||||||||
\(347\) | −26.3400 | −1.41401 | −0.707003 | − | 0.707210i | \(-0.749953\pi\) | ||||
−0.707003 | + | 0.707210i | \(0.749953\pi\) | |||||||
\(348\) | 6.89977 | 0.369867 | ||||||||
\(349\) | −8.44371 | −0.451982 | −0.225991 | − | 0.974129i | \(-0.572562\pi\) | ||||
−0.225991 | + | 0.974129i | \(0.572562\pi\) | |||||||
\(350\) | −1.19806 | −0.0640391 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.554958 | −0.0295794 | ||||||||
\(353\) | −10.9420 | −0.582383 | −0.291192 | − | 0.956665i | \(-0.594052\pi\) | ||||
−0.291192 | + | 0.956665i | \(0.594052\pi\) | |||||||
\(354\) | 1.45712 | 0.0774452 | ||||||||
\(355\) | 2.35690 | 0.125091 | ||||||||
\(356\) | 13.7845 | 0.730576 | ||||||||
\(357\) | 7.73317 | 0.409283 | ||||||||
\(358\) | 0.956459 | 0.0505505 | ||||||||
\(359\) | 8.07606 | 0.426238 | 0.213119 | − | 0.977026i | \(-0.431638\pi\) | ||||
0.213119 | + | 0.977026i | \(0.431638\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | 10.2228 | 0.538043 | ||||||||
\(362\) | −0.405813 | −0.0213291 | ||||||||
\(363\) | 10.6920 | 0.561186 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.3448 | 0.698500 | ||||||||
\(366\) | 2.76271 | 0.144409 | ||||||||
\(367\) | 17.1575 | 0.895615 | 0.447807 | − | 0.894130i | \(-0.352205\pi\) | ||||
0.447807 | + | 0.894130i | \(0.352205\pi\) | |||||||
\(368\) | 7.96077 | 0.414984 | ||||||||
\(369\) | 3.08815 | 0.160762 | ||||||||
\(370\) | 7.96615 | 0.414140 | ||||||||
\(371\) | 10.1502 | 0.526973 | ||||||||
\(372\) | −3.04892 | −0.158079 | ||||||||
\(373\) | 2.72455 | 0.141072 | 0.0705358 | − | 0.997509i | \(-0.477529\pi\) | ||||
0.0705358 | + | 0.997509i | \(0.477529\pi\) | |||||||
\(374\) | 3.58211 | 0.185226 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | −12.2620 | −0.632367 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.19806 | 0.0616217 | ||||||||
\(379\) | −26.8998 | −1.38175 | −0.690874 | − | 0.722975i | \(-0.742774\pi\) | ||||
−0.690874 | + | 0.722975i | \(0.742774\pi\) | |||||||
\(380\) | −5.40581 | −0.277312 | ||||||||
\(381\) | −21.8756 | −1.12072 | ||||||||
\(382\) | 19.0097 | 0.972620 | ||||||||
\(383\) | 29.9511 | 1.53043 | 0.765214 | − | 0.643776i | \(-0.222633\pi\) | ||||
0.765214 | + | 0.643776i | \(0.222633\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0.664874 | 0.0338851 | ||||||||
\(386\) | −0.599564 | −0.0305170 | ||||||||
\(387\) | 1.15883 | 0.0589068 | ||||||||
\(388\) | 7.07606 | 0.359233 | ||||||||
\(389\) | 10.0140 | 0.507730 | 0.253865 | − | 0.967240i | \(-0.418298\pi\) | ||||
0.253865 | + | 0.967240i | \(0.418298\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −51.3846 | −2.59863 | ||||||||
\(392\) | 5.56465 | 0.281057 | ||||||||
\(393\) | 21.6528 | 1.09224 | ||||||||
\(394\) | −3.78448 | −0.190659 | ||||||||
\(395\) | −0.990311 | −0.0498280 | ||||||||
\(396\) | 0.554958 | 0.0278877 | ||||||||
\(397\) | 17.0489 | 0.855661 | 0.427830 | − | 0.903859i | \(-0.359278\pi\) | ||||
0.427830 | + | 0.903859i | \(0.359278\pi\) | |||||||
\(398\) | 10.2349 | 0.513029 | ||||||||
\(399\) | 6.47650 | 0.324231 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 0.975246 | 0.0487015 | 0.0243507 | − | 0.999703i | \(-0.492248\pi\) | ||||
0.0243507 | + | 0.999703i | \(0.492248\pi\) | |||||||
\(402\) | −3.34481 | −0.166824 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 4.09783 | 0.203875 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 8.26636 | 0.410252 | ||||||||
\(407\) | −4.42088 | −0.219135 | ||||||||
\(408\) | −6.45473 | −0.319557 | ||||||||
\(409\) | −37.7439 | −1.86632 | −0.933158 | − | 0.359465i | \(-0.882959\pi\) | ||||
−0.933158 | + | 0.359465i | \(0.882959\pi\) | |||||||
\(410\) | −3.08815 | −0.152513 | ||||||||
\(411\) | −7.08815 | −0.349632 | ||||||||
\(412\) | −4.16421 | −0.205156 | ||||||||
\(413\) | 1.74572 | 0.0859015 | ||||||||
\(414\) | −7.96077 | −0.391251 | ||||||||
\(415\) | 5.88471 | 0.288869 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.340502 | −0.0166745 | ||||||||
\(418\) | 3.00000 | 0.146735 | ||||||||
\(419\) | −21.5700 | −1.05376 | −0.526882 | − | 0.849938i | \(-0.676639\pi\) | ||||
−0.526882 | + | 0.849938i | \(0.676639\pi\) | |||||||
\(420\) | −1.19806 | −0.0584595 | ||||||||
\(421\) | 33.2403 | 1.62003 | 0.810016 | − | 0.586408i | \(-0.199458\pi\) | ||||
0.810016 | + | 0.586408i | \(0.199458\pi\) | |||||||
\(422\) | 8.71379 | 0.424181 | ||||||||
\(423\) | 12.2620 | 0.596201 | ||||||||
\(424\) | −8.47219 | −0.411446 | ||||||||
\(425\) | −6.45473 | −0.313100 | ||||||||
\(426\) | 2.35690 | 0.114192 | ||||||||
\(427\) | 3.30990 | 0.160177 | ||||||||
\(428\) | −4.98254 | −0.240840 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.15883 | −0.0558839 | ||||||||
\(431\) | 20.9041 | 1.00691 | 0.503457 | − | 0.864020i | \(-0.332061\pi\) | ||||
0.503457 | + | 0.864020i | \(0.332061\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 36.5864 | 1.75823 | 0.879115 | − | 0.476609i | \(-0.158134\pi\) | ||||
0.879115 | + | 0.476609i | \(0.158134\pi\) | |||||||
\(434\) | −3.65279 | −0.175340 | ||||||||
\(435\) | 6.89977 | 0.330819 | ||||||||
\(436\) | 1.31336 | 0.0628983 | ||||||||
\(437\) | −43.0344 | −2.05862 | ||||||||
\(438\) | 13.3448 | 0.637640 | ||||||||
\(439\) | 27.5036 | 1.31268 | 0.656339 | − | 0.754466i | \(-0.272104\pi\) | ||||
0.656339 | + | 0.754466i | \(0.272104\pi\) | |||||||
\(440\) | −0.554958 | −0.0264566 | ||||||||
\(441\) | −5.56465 | −0.264983 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.34614 | −0.206491 | −0.103246 | − | 0.994656i | \(-0.532923\pi\) | ||||
−0.103246 | + | 0.994656i | \(0.532923\pi\) | |||||||
\(444\) | 7.96615 | 0.378057 | ||||||||
\(445\) | 13.7845 | 0.653447 | ||||||||
\(446\) | 15.0694 | 0.713555 | ||||||||
\(447\) | −7.40581 | −0.350283 | ||||||||
\(448\) | 1.19806 | 0.0566031 | ||||||||
\(449\) | 0.423272 | 0.0199754 | 0.00998771 | − | 0.999950i | \(-0.496821\pi\) | ||||
0.00998771 | + | 0.999950i | \(0.496821\pi\) | |||||||
\(450\) | −1.00000 | −0.0471405 | ||||||||
\(451\) | 1.71379 | 0.0806993 | ||||||||
\(452\) | 3.55496 | 0.167211 | ||||||||
\(453\) | −10.4209 | −0.489616 | ||||||||
\(454\) | 20.4577 | 0.960128 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.40581 | −0.253150 | ||||||||
\(457\) | −18.6396 | −0.871926 | −0.435963 | − | 0.899965i | \(-0.643592\pi\) | ||||
−0.435963 | + | 0.899965i | \(0.643592\pi\) | |||||||
\(458\) | −18.7657 | −0.876863 | ||||||||
\(459\) | 6.45473 | 0.301281 | ||||||||
\(460\) | 7.96077 | 0.371173 | ||||||||
\(461\) | 8.22223 | 0.382947 | 0.191474 | − | 0.981498i | \(-0.438673\pi\) | ||||
0.191474 | + | 0.981498i | \(0.438673\pi\) | |||||||
\(462\) | 0.664874 | 0.0309328 | ||||||||
\(463\) | 34.1118 | 1.58531 | 0.792656 | − | 0.609670i | \(-0.208698\pi\) | ||||
0.792656 | + | 0.609670i | \(0.208698\pi\) | |||||||
\(464\) | −6.89977 | −0.320314 | ||||||||
\(465\) | −3.04892 | −0.141390 | ||||||||
\(466\) | −23.6353 | −1.09489 | ||||||||
\(467\) | 13.9245 | 0.644350 | 0.322175 | − | 0.946680i | \(-0.395586\pi\) | ||||
0.322175 | + | 0.946680i | \(0.395586\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.00730 | −0.185040 | ||||||||
\(470\) | −12.2620 | −0.565606 | ||||||||
\(471\) | 19.0151 | 0.876168 | ||||||||
\(472\) | −1.45712 | −0.0670695 | ||||||||
\(473\) | 0.643104 | 0.0295700 | ||||||||
\(474\) | −0.990311 | −0.0454865 | ||||||||
\(475\) | −5.40581 | −0.248036 | ||||||||
\(476\) | −7.73317 | −0.354449 | ||||||||
\(477\) | 8.47219 | 0.387915 | ||||||||
\(478\) | −28.7506 | −1.31502 | ||||||||
\(479\) | 1.79225 | 0.0818899 | 0.0409450 | − | 0.999161i | \(-0.486963\pi\) | ||||
0.0409450 | + | 0.999161i | \(0.486963\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 3.89440 | 0.177385 | ||||||||
\(483\) | −9.53750 | −0.433971 | ||||||||
\(484\) | −10.6920 | −0.486001 | ||||||||
\(485\) | 7.07606 | 0.321308 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −0.126310 | −0.00572364 | −0.00286182 | − | 0.999996i | \(-0.500911\pi\) | ||||
−0.00286182 | + | 0.999996i | \(0.500911\pi\) | |||||||
\(488\) | −2.76271 | −0.125062 | ||||||||
\(489\) | −5.65279 | −0.255628 | ||||||||
\(490\) | 5.56465 | 0.251385 | ||||||||
\(491\) | −17.6823 | −0.797993 | −0.398996 | − | 0.916953i | \(-0.630641\pi\) | ||||
−0.398996 | + | 0.916953i | \(0.630641\pi\) | |||||||
\(492\) | −3.08815 | −0.139224 | ||||||||
\(493\) | 44.5362 | 2.00581 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.554958 | 0.0249435 | ||||||||
\(496\) | 3.04892 | 0.136900 | ||||||||
\(497\) | 2.82371 | 0.126661 | ||||||||
\(498\) | 5.88471 | 0.263700 | ||||||||
\(499\) | −21.1535 | −0.946959 | −0.473479 | − | 0.880805i | \(-0.657002\pi\) | ||||
−0.473479 | + | 0.880805i | \(0.657002\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −2.15883 | −0.0964496 | ||||||||
\(502\) | 24.3327 | 1.08602 | ||||||||
\(503\) | −29.7187 | −1.32509 | −0.662546 | − | 0.749022i | \(-0.730524\pi\) | ||||
−0.662546 | + | 0.749022i | \(0.730524\pi\) | |||||||
\(504\) | −1.19806 | −0.0533659 | ||||||||
\(505\) | 4.09783 | 0.182351 | ||||||||
\(506\) | −4.41789 | −0.196399 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 21.8756 | 0.970573 | ||||||||
\(509\) | 0.786872 | 0.0348775 | 0.0174387 | − | 0.999848i | \(-0.494449\pi\) | ||||
0.0174387 | + | 0.999848i | \(0.494449\pi\) | |||||||
\(510\) | −6.45473 | −0.285820 | ||||||||
\(511\) | 15.9879 | 0.707264 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 5.40581 | 0.238672 | ||||||||
\(514\) | −30.4426 | −1.34277 | ||||||||
\(515\) | −4.16421 | −0.183497 | ||||||||
\(516\) | −1.15883 | −0.0510148 | ||||||||
\(517\) | 6.80492 | 0.299280 | ||||||||
\(518\) | 9.54394 | 0.419337 | ||||||||
\(519\) | −21.6722 | −0.951303 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.1782 | 1.05927 | 0.529633 | − | 0.848227i | \(-0.322330\pi\) | ||||
0.529633 | + | 0.848227i | \(0.322330\pi\) | |||||||
\(522\) | 6.89977 | 0.301995 | ||||||||
\(523\) | 23.0750 | 1.00900 | 0.504500 | − | 0.863412i | \(-0.331677\pi\) | ||||
0.504500 | + | 0.863412i | \(0.331677\pi\) | |||||||
\(524\) | −21.6528 | −0.945907 | ||||||||
\(525\) | −1.19806 | −0.0522877 | ||||||||
\(526\) | 9.33944 | 0.407219 | ||||||||
\(527\) | −19.6799 | −0.857272 | ||||||||
\(528\) | −0.554958 | −0.0241515 | ||||||||
\(529\) | 40.3739 | 1.75539 | ||||||||
\(530\) | −8.47219 | −0.368008 | ||||||||
\(531\) | 1.45712 | 0.0632338 | ||||||||
\(532\) | −6.47650 | −0.280792 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 13.7845 | 0.596513 | ||||||||
\(535\) | −4.98254 | −0.215414 | ||||||||
\(536\) | 3.34481 | 0.144474 | ||||||||
\(537\) | 0.956459 | 0.0412743 | ||||||||
\(538\) | −26.7821 | −1.15466 | ||||||||
\(539\) | −3.08815 | −0.133016 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | −24.6122 | −1.05816 | −0.529081 | − | 0.848571i | \(-0.677463\pi\) | ||||
−0.529081 | + | 0.848571i | \(0.677463\pi\) | |||||||
\(542\) | 2.58748 | 0.111142 | ||||||||
\(543\) | −0.405813 | −0.0174151 | ||||||||
\(544\) | 6.45473 | 0.276744 | ||||||||
\(545\) | 1.31336 | 0.0562580 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.492894 | −0.0210746 | −0.0105373 | − | 0.999944i | \(-0.503354\pi\) | ||||
−0.0105373 | + | 0.999944i | \(0.503354\pi\) | |||||||
\(548\) | 7.08815 | 0.302791 | ||||||||
\(549\) | 2.76271 | 0.117910 | ||||||||
\(550\) | −0.554958 | −0.0236635 | ||||||||
\(551\) | 37.2989 | 1.58899 | ||||||||
\(552\) | 7.96077 | 0.338833 | ||||||||
\(553\) | −1.18645 | −0.0504532 | ||||||||
\(554\) | −11.0532 | −0.469607 | ||||||||
\(555\) | 7.96615 | 0.338144 | ||||||||
\(556\) | 0.340502 | 0.0144405 | ||||||||
\(557\) | −12.6028 | −0.533998 | −0.266999 | − | 0.963697i | \(-0.586032\pi\) | ||||
−0.266999 | + | 0.963697i | \(0.586032\pi\) | |||||||
\(558\) | −3.04892 | −0.129071 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 1.19806 | 0.0506274 | ||||||||
\(561\) | 3.58211 | 0.151237 | ||||||||
\(562\) | −10.5090 | −0.443296 | ||||||||
\(563\) | 24.5743 | 1.03568 | 0.517842 | − | 0.855476i | \(-0.326735\pi\) | ||||
0.517842 | + | 0.855476i | \(0.326735\pi\) | |||||||
\(564\) | −12.2620 | −0.516325 | ||||||||
\(565\) | 3.55496 | 0.149558 | ||||||||
\(566\) | 1.07069 | 0.0450044 | ||||||||
\(567\) | 1.19806 | 0.0503139 | ||||||||
\(568\) | −2.35690 | −0.0988932 | ||||||||
\(569\) | 18.9414 | 0.794065 | 0.397032 | − | 0.917805i | \(-0.370040\pi\) | ||||
0.397032 | + | 0.917805i | \(0.370040\pi\) | |||||||
\(570\) | −5.40581 | −0.226425 | ||||||||
\(571\) | −17.2978 | −0.723891 | −0.361946 | − | 0.932199i | \(-0.617887\pi\) | ||||
−0.361946 | + | 0.932199i | \(0.617887\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19.0097 | 0.794141 | ||||||||
\(574\) | −3.69979 | −0.154426 | ||||||||
\(575\) | 7.96077 | 0.331987 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −42.5628 | −1.77191 | −0.885957 | − | 0.463767i | \(-0.846497\pi\) | ||||
−0.885957 | + | 0.463767i | \(0.846497\pi\) | |||||||
\(578\) | −24.6635 | −1.02587 | ||||||||
\(579\) | −0.599564 | −0.0249170 | ||||||||
\(580\) | −6.89977 | −0.286497 | ||||||||
\(581\) | 7.05025 | 0.292493 | ||||||||
\(582\) | 7.07606 | 0.293312 | ||||||||
\(583\) | 4.70171 | 0.194725 | ||||||||
\(584\) | −13.3448 | −0.552212 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −27.4142 | −1.13247 | ||||||||
\(587\) | 43.2737 | 1.78609 | 0.893047 | − | 0.449963i | \(-0.148563\pi\) | ||||
0.893047 | + | 0.449963i | \(0.148563\pi\) | |||||||
\(588\) | 5.56465 | 0.229482 | ||||||||
\(589\) | −16.4819 | −0.679124 | ||||||||
\(590\) | −1.45712 | −0.0599888 | ||||||||
\(591\) | −3.78448 | −0.155673 | ||||||||
\(592\) | −7.96615 | −0.327407 | ||||||||
\(593\) | 19.8672 | 0.815850 | 0.407925 | − | 0.913015i | \(-0.366252\pi\) | ||||
0.407925 | + | 0.913015i | \(0.366252\pi\) | |||||||
\(594\) | 0.554958 | 0.0227702 | ||||||||
\(595\) | −7.73317 | −0.317029 | ||||||||
\(596\) | 7.40581 | 0.303354 | ||||||||
\(597\) | 10.2349 | 0.418886 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.3448 | 0.912984 | 0.456492 | − | 0.889727i | \(-0.349106\pi\) | ||||
0.456492 | + | 0.889727i | \(0.349106\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | 38.3696 | 1.56513 | 0.782564 | − | 0.622571i | \(-0.213912\pi\) | ||||
0.782564 | + | 0.622571i | \(0.213912\pi\) | |||||||
\(602\) | −1.38835 | −0.0565851 | ||||||||
\(603\) | −3.34481 | −0.136211 | ||||||||
\(604\) | 10.4209 | 0.424020 | ||||||||
\(605\) | −10.6920 | −0.434692 | ||||||||
\(606\) | 4.09783 | 0.166463 | ||||||||
\(607\) | 34.9778 | 1.41970 | 0.709852 | − | 0.704351i | \(-0.248762\pi\) | ||||
0.709852 | + | 0.704351i | \(0.248762\pi\) | |||||||
\(608\) | 5.40581 | 0.219235 | ||||||||
\(609\) | 8.26636 | 0.334970 | ||||||||
\(610\) | −2.76271 | −0.111859 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −6.45473 | −0.260917 | ||||||||
\(613\) | 28.1648 | 1.13757 | 0.568783 | − | 0.822488i | \(-0.307414\pi\) | ||||
0.568783 | + | 0.822488i | \(0.307414\pi\) | |||||||
\(614\) | −24.4969 | −0.988616 | ||||||||
\(615\) | −3.08815 | −0.124526 | ||||||||
\(616\) | −0.664874 | −0.0267886 | ||||||||
\(617\) | −24.0640 | −0.968779 | −0.484390 | − | 0.874852i | \(-0.660958\pi\) | ||||
−0.484390 | + | 0.874852i | \(0.660958\pi\) | |||||||
\(618\) | −4.16421 | −0.167509 | ||||||||
\(619\) | −14.7651 | −0.593460 | −0.296730 | − | 0.954961i | \(-0.595896\pi\) | ||||
−0.296730 | + | 0.954961i | \(0.595896\pi\) | |||||||
\(620\) | 3.04892 | 0.122447 | ||||||||
\(621\) | −7.96077 | −0.319455 | ||||||||
\(622\) | −16.4403 | −0.659194 | ||||||||
\(623\) | 16.5147 | 0.661646 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 26.0320 | 1.04045 | ||||||||
\(627\) | 3.00000 | 0.119808 | ||||||||
\(628\) | −19.0151 | −0.758784 | ||||||||
\(629\) | 51.4193 | 2.05022 | ||||||||
\(630\) | −1.19806 | −0.0477319 | ||||||||
\(631\) | −22.9788 | −0.914772 | −0.457386 | − | 0.889268i | \(-0.651214\pi\) | ||||
−0.457386 | + | 0.889268i | \(0.651214\pi\) | |||||||
\(632\) | 0.990311 | 0.0393925 | ||||||||
\(633\) | 8.71379 | 0.346342 | ||||||||
\(634\) | −19.3545 | −0.768666 | ||||||||
\(635\) | 21.8756 | 0.868107 | ||||||||
\(636\) | −8.47219 | −0.335944 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.82908 | 0.151595 | ||||||||
\(639\) | 2.35690 | 0.0932374 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −5.34913 | −0.211278 | −0.105639 | − | 0.994405i | \(-0.533689\pi\) | ||||
−0.105639 | + | 0.994405i | \(0.533689\pi\) | |||||||
\(642\) | −4.98254 | −0.196645 | ||||||||
\(643\) | 39.2984 | 1.54978 | 0.774889 | − | 0.632097i | \(-0.217806\pi\) | ||||
0.774889 | + | 0.632097i | \(0.217806\pi\) | |||||||
\(644\) | 9.53750 | 0.375830 | ||||||||
\(645\) | −1.15883 | −0.0456290 | ||||||||
\(646\) | −34.8931 | −1.37285 | ||||||||
\(647\) | 0.328684 | 0.0129219 | 0.00646095 | − | 0.999979i | \(-0.497943\pi\) | ||||
0.00646095 | + | 0.999979i | \(0.497943\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 0.808643 | 0.0317420 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.65279 | −0.143164 | ||||||||
\(652\) | 5.65279 | 0.221380 | ||||||||
\(653\) | 41.6426 | 1.62960 | 0.814801 | − | 0.579741i | \(-0.196846\pi\) | ||||
0.814801 | + | 0.579741i | \(0.196846\pi\) | |||||||
\(654\) | 1.31336 | 0.0513563 | ||||||||
\(655\) | −21.6528 | −0.846045 | ||||||||
\(656\) | 3.08815 | 0.120572 | ||||||||
\(657\) | 13.3448 | 0.520631 | ||||||||
\(658\) | −14.6907 | −0.572703 | ||||||||
\(659\) | −4.24698 | −0.165439 | −0.0827194 | − | 0.996573i | \(-0.526361\pi\) | ||||
−0.0827194 | + | 0.996573i | \(0.526361\pi\) | |||||||
\(660\) | −0.554958 | −0.0216017 | ||||||||
\(661\) | 29.7071 | 1.15547 | 0.577736 | − | 0.816224i | \(-0.303936\pi\) | ||||
0.577736 | + | 0.816224i | \(0.303936\pi\) | |||||||
\(662\) | 0.173899 | 0.00675878 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.88471 | −0.228371 | ||||||||
\(665\) | −6.47650 | −0.251148 | ||||||||
\(666\) | 7.96615 | 0.308682 | ||||||||
\(667\) | −54.9275 | −2.12680 | ||||||||
\(668\) | 2.15883 | 0.0835278 | ||||||||
\(669\) | 15.0694 | 0.582615 | ||||||||
\(670\) | 3.34481 | 0.129221 | ||||||||
\(671\) | 1.53319 | 0.0591881 | ||||||||
\(672\) | 1.19806 | 0.0462163 | ||||||||
\(673\) | −21.7004 | −0.836488 | −0.418244 | − | 0.908335i | \(-0.637354\pi\) | ||||
−0.418244 | + | 0.908335i | \(0.637354\pi\) | |||||||
\(674\) | 14.3793 | 0.553868 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.5168 | −0.481059 | −0.240530 | − | 0.970642i | \(-0.577321\pi\) | ||||
−0.240530 | + | 0.970642i | \(0.577321\pi\) | |||||||
\(678\) | 3.55496 | 0.136527 | ||||||||
\(679\) | 8.47757 | 0.325339 | ||||||||
\(680\) | 6.45473 | 0.247528 | ||||||||
\(681\) | 20.4577 | 0.783941 | ||||||||
\(682\) | −1.69202 | −0.0647909 | ||||||||
\(683\) | −3.82908 | −0.146516 | −0.0732579 | − | 0.997313i | \(-0.523340\pi\) | ||||
−0.0732579 | + | 0.997313i | \(0.523340\pi\) | |||||||
\(684\) | −5.40581 | −0.206696 | ||||||||
\(685\) | 7.08815 | 0.270824 | ||||||||
\(686\) | 15.0532 | 0.574735 | ||||||||
\(687\) | −18.7657 | −0.715956 | ||||||||
\(688\) | 1.15883 | 0.0441801 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 7.96077 | 0.303061 | ||||||||
\(691\) | 27.4239 | 1.04325 | 0.521626 | − | 0.853174i | \(-0.325325\pi\) | ||||
0.521626 | + | 0.853174i | \(0.325325\pi\) | |||||||
\(692\) | 21.6722 | 0.823852 | ||||||||
\(693\) | 0.664874 | 0.0252565 | ||||||||
\(694\) | 26.3400 | 0.999854 | ||||||||
\(695\) | 0.340502 | 0.0129160 | ||||||||
\(696\) | −6.89977 | −0.261535 | ||||||||
\(697\) | −19.9332 | −0.755022 | ||||||||
\(698\) | 8.44371 | 0.319599 | ||||||||
\(699\) | −23.6353 | −0.893970 | ||||||||
\(700\) | 1.19806 | 0.0452825 | ||||||||
\(701\) | 31.5803 | 1.19277 | 0.596386 | − | 0.802698i | \(-0.296603\pi\) | ||||
0.596386 | + | 0.802698i | \(0.296603\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 43.0635 | 1.62417 | ||||||||
\(704\) | 0.554958 | 0.0209158 | ||||||||
\(705\) | −12.2620 | −0.461815 | ||||||||
\(706\) | 10.9420 | 0.411807 | ||||||||
\(707\) | 4.90946 | 0.184639 | ||||||||
\(708\) | −1.45712 | −0.0547621 | ||||||||
\(709\) | 28.9788 | 1.08832 | 0.544161 | − | 0.838981i | \(-0.316848\pi\) | ||||
0.544161 | + | 0.838981i | \(0.316848\pi\) | |||||||
\(710\) | −2.35690 | −0.0884527 | ||||||||
\(711\) | −0.990311 | −0.0371396 | ||||||||
\(712\) | −13.7845 | −0.516595 | ||||||||
\(713\) | 24.2717 | 0.908984 | ||||||||
\(714\) | −7.73317 | −0.289407 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.956459 | −0.0357446 | ||||||||
\(717\) | −28.7506 | −1.07371 | ||||||||
\(718\) | −8.07606 | −0.301396 | ||||||||
\(719\) | 27.0670 | 1.00943 | 0.504714 | − | 0.863287i | \(-0.331598\pi\) | ||||
0.504714 | + | 0.863287i | \(0.331598\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | −4.98898 | −0.185799 | ||||||||
\(722\) | −10.2228 | −0.380454 | ||||||||
\(723\) | 3.89440 | 0.144834 | ||||||||
\(724\) | 0.405813 | 0.0150819 | ||||||||
\(725\) | −6.89977 | −0.256251 | ||||||||
\(726\) | −10.6920 | −0.396818 | ||||||||
\(727\) | −26.6612 | −0.988807 | −0.494404 | − | 0.869232i | \(-0.664614\pi\) | ||||
−0.494404 | + | 0.869232i | \(0.664614\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −13.3448 | −0.493914 | ||||||||
\(731\) | −7.47996 | −0.276656 | ||||||||
\(732\) | −2.76271 | −0.102113 | ||||||||
\(733\) | −51.2984 | −1.89475 | −0.947375 | − | 0.320126i | \(-0.896275\pi\) | ||||
−0.947375 | + | 0.320126i | \(0.896275\pi\) | |||||||
\(734\) | −17.1575 | −0.633295 | ||||||||
\(735\) | 5.56465 | 0.205255 | ||||||||
\(736\) | −7.96077 | −0.293438 | ||||||||
\(737\) | −1.85623 | −0.0683752 | ||||||||
\(738\) | −3.08815 | −0.113676 | ||||||||
\(739\) | 28.6456 | 1.05375 | 0.526873 | − | 0.849944i | \(-0.323364\pi\) | ||||
0.526873 | + | 0.849944i | \(0.323364\pi\) | |||||||
\(740\) | −7.96615 | −0.292841 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −10.1502 | −0.372626 | ||||||||
\(743\) | −43.6674 | −1.60200 | −0.801000 | − | 0.598664i | \(-0.795699\pi\) | ||||
−0.801000 | + | 0.598664i | \(0.795699\pi\) | |||||||
\(744\) | 3.04892 | 0.111779 | ||||||||
\(745\) | 7.40581 | 0.271328 | ||||||||
\(746\) | −2.72455 | −0.0997527 | ||||||||
\(747\) | 5.88471 | 0.215310 | ||||||||
\(748\) | −3.58211 | −0.130975 | ||||||||
\(749\) | −5.96940 | −0.218117 | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | −20.1535 | −0.735410 | −0.367705 | − | 0.929942i | \(-0.619856\pi\) | ||||
−0.367705 | + | 0.929942i | \(0.619856\pi\) | |||||||
\(752\) | 12.2620 | 0.447151 | ||||||||
\(753\) | 24.3327 | 0.886734 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.4209 | 0.379255 | ||||||||
\(756\) | −1.19806 | −0.0435731 | ||||||||
\(757\) | −41.8562 | −1.52129 | −0.760645 | − | 0.649168i | \(-0.775117\pi\) | ||||
−0.760645 | + | 0.649168i | \(0.775117\pi\) | |||||||
\(758\) | 26.8998 | 0.977044 | ||||||||
\(759\) | −4.41789 | −0.160359 | ||||||||
\(760\) | 5.40581 | 0.196089 | ||||||||
\(761\) | −32.8665 | −1.19141 | −0.595705 | − | 0.803203i | \(-0.703127\pi\) | ||||
−0.595705 | + | 0.803203i | \(0.703127\pi\) | |||||||
\(762\) | 21.8756 | 0.792470 | ||||||||
\(763\) | 1.57348 | 0.0569639 | ||||||||
\(764\) | −19.0097 | −0.687746 | ||||||||
\(765\) | −6.45473 | −0.233371 | ||||||||
\(766\) | −29.9511 | −1.08218 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −37.8877 | −1.36627 | −0.683133 | − | 0.730294i | \(-0.739383\pi\) | ||||
−0.683133 | + | 0.730294i | \(0.739383\pi\) | |||||||
\(770\) | −0.664874 | −0.0239604 | ||||||||
\(771\) | −30.4426 | −1.09637 | ||||||||
\(772\) | 0.599564 | 0.0215788 | ||||||||
\(773\) | −12.4523 | −0.447879 | −0.223940 | − | 0.974603i | \(-0.571892\pi\) | ||||
−0.223940 | + | 0.974603i | \(0.571892\pi\) | |||||||
\(774\) | −1.15883 | −0.0416534 | ||||||||
\(775\) | 3.04892 | 0.109520 | ||||||||
\(776\) | −7.07606 | −0.254016 | ||||||||
\(777\) | 9.54394 | 0.342387 | ||||||||
\(778\) | −10.0140 | −0.359019 | ||||||||
\(779\) | −16.6939 | −0.598122 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.30798 | 0.0468032 | ||||||||
\(782\) | 51.3846 | 1.83751 | ||||||||
\(783\) | 6.89977 | 0.246578 | ||||||||
\(784\) | −5.56465 | −0.198737 | ||||||||
\(785\) | −19.0151 | −0.678677 | ||||||||
\(786\) | −21.6528 | −0.772330 | ||||||||
\(787\) | −6.20536 | −0.221197 | −0.110599 | − | 0.993865i | \(-0.535277\pi\) | ||||
−0.110599 | + | 0.993865i | \(0.535277\pi\) | |||||||
\(788\) | 3.78448 | 0.134816 | ||||||||
\(789\) | 9.33944 | 0.332493 | ||||||||
\(790\) | 0.990311 | 0.0352337 | ||||||||
\(791\) | 4.25906 | 0.151435 | ||||||||
\(792\) | −0.554958 | −0.0197196 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −17.0489 | −0.605043 | ||||||||
\(795\) | −8.47219 | −0.300478 | ||||||||
\(796\) | −10.2349 | −0.362766 | ||||||||
\(797\) | 33.0627 | 1.17114 | 0.585570 | − | 0.810622i | \(-0.300871\pi\) | ||||
0.585570 | + | 0.810622i | \(0.300871\pi\) | |||||||
\(798\) | −6.47650 | −0.229266 | ||||||||
\(799\) | −79.1482 | −2.80006 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 13.7845 | 0.487051 | ||||||||
\(802\) | −0.975246 | −0.0344371 | ||||||||
\(803\) | 7.40581 | 0.261345 | ||||||||
\(804\) | 3.34481 | 0.117963 | ||||||||
\(805\) | 9.53750 | 0.336153 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −26.7821 | −0.942774 | ||||||||
\(808\) | −4.09783 | −0.144161 | ||||||||
\(809\) | −52.5454 | −1.84740 | −0.923699 | − | 0.383120i | \(-0.874850\pi\) | ||||
−0.923699 | + | 0.383120i | \(0.874850\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | −9.96508 | −0.349921 | −0.174961 | − | 0.984575i | \(-0.555980\pi\) | ||||
−0.174961 | + | 0.984575i | \(0.555980\pi\) | |||||||
\(812\) | −8.26636 | −0.290092 | ||||||||
\(813\) | 2.58748 | 0.0907470 | ||||||||
\(814\) | 4.42088 | 0.154952 | ||||||||
\(815\) | 5.65279 | 0.198009 | ||||||||
\(816\) | 6.45473 | 0.225961 | ||||||||
\(817\) | −6.26444 | −0.219165 | ||||||||
\(818\) | 37.7439 | 1.31969 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.08815 | 0.107843 | ||||||||
\(821\) | 28.6950 | 1.00146 | 0.500731 | − | 0.865603i | \(-0.333064\pi\) | ||||
0.500731 | + | 0.865603i | \(0.333064\pi\) | |||||||
\(822\) | 7.08815 | 0.247227 | ||||||||
\(823\) | 37.4053 | 1.30387 | 0.651934 | − | 0.758276i | \(-0.273958\pi\) | ||||
0.651934 | + | 0.758276i | \(0.273958\pi\) | |||||||
\(824\) | 4.16421 | 0.145067 | ||||||||
\(825\) | −0.554958 | −0.0193212 | ||||||||
\(826\) | −1.74572 | −0.0607415 | ||||||||
\(827\) | −36.3666 | −1.26459 | −0.632295 | − | 0.774728i | \(-0.717887\pi\) | ||||
−0.632295 | + | 0.774728i | \(0.717887\pi\) | |||||||
\(828\) | 7.96077 | 0.276656 | ||||||||
\(829\) | −32.6370 | −1.13353 | −0.566765 | − | 0.823880i | \(-0.691805\pi\) | ||||
−0.566765 | + | 0.823880i | \(0.691805\pi\) | |||||||
\(830\) | −5.88471 | −0.204261 | ||||||||
\(831\) | −11.0532 | −0.383432 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 35.9183 | 1.24450 | ||||||||
\(834\) | 0.340502 | 0.0117906 | ||||||||
\(835\) | 2.15883 | 0.0747095 | ||||||||
\(836\) | −3.00000 | −0.103757 | ||||||||
\(837\) | −3.04892 | −0.105386 | ||||||||
\(838\) | 21.5700 | 0.745124 | ||||||||
\(839\) | −11.6810 | −0.403273 | −0.201637 | − | 0.979460i | \(-0.564626\pi\) | ||||
−0.201637 | + | 0.979460i | \(0.564626\pi\) | |||||||
\(840\) | 1.19806 | 0.0413371 | ||||||||
\(841\) | 18.6069 | 0.641616 | ||||||||
\(842\) | −33.2403 | −1.14554 | ||||||||
\(843\) | −10.5090 | −0.361950 | ||||||||
\(844\) | −8.71379 | −0.299941 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −12.2620 | −0.421578 | ||||||||
\(847\) | −12.8097 | −0.440147 | ||||||||
\(848\) | 8.47219 | 0.290936 | ||||||||
\(849\) | 1.07069 | 0.0367459 | ||||||||
\(850\) | 6.45473 | 0.221395 | ||||||||
\(851\) | −63.4167 | −2.17390 | ||||||||
\(852\) | −2.35690 | −0.0807459 | ||||||||
\(853\) | −45.1756 | −1.54678 | −0.773391 | − | 0.633930i | \(-0.781441\pi\) | ||||
−0.773391 | + | 0.633930i | \(0.781441\pi\) | |||||||
\(854\) | −3.30990 | −0.113262 | ||||||||
\(855\) | −5.40581 | −0.184875 | ||||||||
\(856\) | 4.98254 | 0.170300 | ||||||||
\(857\) | −16.1602 | −0.552021 | −0.276010 | − | 0.961155i | \(-0.589012\pi\) | ||||
−0.276010 | + | 0.961155i | \(0.589012\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.9071 | 0.849818 | 0.424909 | − | 0.905236i | \(-0.360306\pi\) | ||||
0.424909 | + | 0.905236i | \(0.360306\pi\) | |||||||
\(860\) | 1.15883 | 0.0395159 | ||||||||
\(861\) | −3.69979 | −0.126089 | ||||||||
\(862\) | −20.9041 | −0.711996 | ||||||||
\(863\) | −25.9030 | −0.881749 | −0.440875 | − | 0.897569i | \(-0.645332\pi\) | ||||
−0.440875 | + | 0.897569i | \(0.645332\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 21.6722 | 0.736876 | ||||||||
\(866\) | −36.5864 | −1.24326 | ||||||||
\(867\) | −24.6635 | −0.837618 | ||||||||
\(868\) | 3.65279 | 0.123984 | ||||||||
\(869\) | −0.549581 | −0.0186433 | ||||||||
\(870\) | −6.89977 | −0.233924 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −1.31336 | −0.0444758 | ||||||||
\(873\) | 7.07606 | 0.239488 | ||||||||
\(874\) | 43.0344 | 1.45566 | ||||||||
\(875\) | 1.19806 | 0.0405019 | ||||||||
\(876\) | −13.3448 | −0.450879 | ||||||||
\(877\) | −21.5875 | −0.728957 | −0.364479 | − | 0.931212i | \(-0.618753\pi\) | ||||
−0.364479 | + | 0.931212i | \(0.618753\pi\) | |||||||
\(878\) | −27.5036 | −0.928203 | ||||||||
\(879\) | −27.4142 | −0.924657 | ||||||||
\(880\) | 0.554958 | 0.0187076 | ||||||||
\(881\) | 0.468140 | 0.0157720 | 0.00788602 | − | 0.999969i | \(-0.497490\pi\) | ||||
0.00788602 | + | 0.999969i | \(0.497490\pi\) | |||||||
\(882\) | 5.56465 | 0.187371 | ||||||||
\(883\) | −43.6034 | −1.46737 | −0.733686 | − | 0.679489i | \(-0.762202\pi\) | ||||
−0.733686 | + | 0.679489i | \(0.762202\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.45712 | −0.0489807 | ||||||||
\(886\) | 4.34614 | 0.146012 | ||||||||
\(887\) | 24.1038 | 0.809326 | 0.404663 | − | 0.914466i | \(-0.367389\pi\) | ||||
0.404663 | + | 0.914466i | \(0.367389\pi\) | |||||||
\(888\) | −7.96615 | −0.267326 | ||||||||
\(889\) | 26.2083 | 0.879000 | ||||||||
\(890\) | −13.7845 | −0.462057 | ||||||||
\(891\) | 0.554958 | 0.0185918 | ||||||||
\(892\) | −15.0694 | −0.504559 | ||||||||
\(893\) | −66.2863 | −2.21819 | ||||||||
\(894\) | 7.40581 | 0.247687 | ||||||||
\(895\) | −0.956459 | −0.0319709 | ||||||||
\(896\) | −1.19806 | −0.0400245 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.423272 | −0.0141248 | ||||||||
\(899\) | −21.0368 | −0.701618 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −54.6857 | −1.82184 | ||||||||
\(902\) | −1.71379 | −0.0570630 | ||||||||
\(903\) | −1.38835 | −0.0462016 | ||||||||
\(904\) | −3.55496 | −0.118236 | ||||||||
\(905\) | 0.405813 | 0.0134897 | ||||||||
\(906\) | 10.4209 | 0.346211 | ||||||||
\(907\) | 55.0635 | 1.82835 | 0.914177 | − | 0.405315i | \(-0.132838\pi\) | ||||
0.914177 | + | 0.405315i | \(0.132838\pi\) | |||||||
\(908\) | −20.4577 | −0.678913 | ||||||||
\(909\) | 4.09783 | 0.135917 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.17151 | 0.237603 | 0.118801 | − | 0.992918i | \(-0.462095\pi\) | ||||
0.118801 | + | 0.992918i | \(0.462095\pi\) | |||||||
\(912\) | 5.40581 | 0.179004 | ||||||||
\(913\) | 3.26577 | 0.108081 | ||||||||
\(914\) | 18.6396 | 0.616545 | ||||||||
\(915\) | −2.76271 | −0.0913323 | ||||||||
\(916\) | 18.7657 | 0.620036 | ||||||||
\(917\) | −25.9414 | −0.856660 | ||||||||
\(918\) | −6.45473 | −0.213038 | ||||||||
\(919\) | −32.1081 | −1.05915 | −0.529574 | − | 0.848263i | \(-0.677648\pi\) | ||||
−0.529574 | + | 0.848263i | \(0.677648\pi\) | |||||||
\(920\) | −7.96077 | −0.262459 | ||||||||
\(921\) | −24.4969 | −0.807202 | ||||||||
\(922\) | −8.22223 | −0.270785 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −0.664874 | −0.0218728 | ||||||||
\(925\) | −7.96615 | −0.261925 | ||||||||
\(926\) | −34.1118 | −1.12098 | ||||||||
\(927\) | −4.16421 | −0.136771 | ||||||||
\(928\) | 6.89977 | 0.226496 | ||||||||
\(929\) | 3.46011 | 0.113522 | 0.0567612 | − | 0.998388i | \(-0.481923\pi\) | ||||
0.0567612 | + | 0.998388i | \(0.481923\pi\) | |||||||
\(930\) | 3.04892 | 0.0999779 | ||||||||
\(931\) | 30.0814 | 0.985879 | ||||||||
\(932\) | 23.6353 | 0.774201 | ||||||||
\(933\) | −16.4403 | −0.538230 | ||||||||
\(934\) | −13.9245 | −0.455624 | ||||||||
\(935\) | −3.58211 | −0.117147 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13.3918 | 0.437491 | 0.218746 | − | 0.975782i | \(-0.429803\pi\) | ||||
0.218746 | + | 0.975782i | \(0.429803\pi\) | |||||||
\(938\) | 4.00730 | 0.130843 | ||||||||
\(939\) | 26.0320 | 0.849524 | ||||||||
\(940\) | 12.2620 | 0.399944 | ||||||||
\(941\) | 47.0060 | 1.53235 | 0.766175 | − | 0.642632i | \(-0.222157\pi\) | ||||
0.766175 | + | 0.642632i | \(0.222157\pi\) | |||||||
\(942\) | −19.0151 | −0.619544 | ||||||||
\(943\) | 24.5840 | 0.800566 | ||||||||
\(944\) | 1.45712 | 0.0474253 | ||||||||
\(945\) | −1.19806 | −0.0389730 | ||||||||
\(946\) | −0.643104 | −0.0209091 | ||||||||
\(947\) | 44.9687 | 1.46129 | 0.730643 | − | 0.682760i | \(-0.239221\pi\) | ||||
0.730643 | + | 0.682760i | \(0.239221\pi\) | |||||||
\(948\) | 0.990311 | 0.0321638 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 5.40581 | 0.175388 | ||||||||
\(951\) | −19.3545 | −0.627613 | ||||||||
\(952\) | 7.73317 | 0.250633 | ||||||||
\(953\) | −12.1691 | −0.394196 | −0.197098 | − | 0.980384i | \(-0.563152\pi\) | ||||
−0.197098 | + | 0.980384i | \(0.563152\pi\) | |||||||
\(954\) | −8.47219 | −0.274297 | ||||||||
\(955\) | −19.0097 | −0.615139 | ||||||||
\(956\) | 28.7506 | 0.929862 | ||||||||
\(957\) | 3.82908 | 0.123777 | ||||||||
\(958\) | −1.79225 | −0.0579049 | ||||||||
\(959\) | 8.49204 | 0.274222 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | −21.7041 | −0.700132 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.98254 | −0.160560 | ||||||||
\(964\) | −3.89440 | −0.125430 | ||||||||
\(965\) | 0.599564 | 0.0193006 | ||||||||
\(966\) | 9.53750 | 0.306864 | ||||||||
\(967\) | 21.8799 | 0.703611 | 0.351805 | − | 0.936073i | \(-0.385568\pi\) | ||||
0.351805 | + | 0.936073i | \(0.385568\pi\) | |||||||
\(968\) | 10.6920 | 0.343655 | ||||||||
\(969\) | −34.8931 | −1.12093 | ||||||||
\(970\) | −7.07606 | −0.227199 | ||||||||
\(971\) | −36.6450 | −1.17599 | −0.587997 | − | 0.808863i | \(-0.700083\pi\) | ||||
−0.587997 | + | 0.808863i | \(0.700083\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0.407943 | 0.0130781 | ||||||||
\(974\) | 0.126310 | 0.00404722 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.76271 | 0.0884322 | ||||||||
\(977\) | 7.36957 | 0.235773 | 0.117887 | − | 0.993027i | \(-0.462388\pi\) | ||||
0.117887 | + | 0.993027i | \(0.462388\pi\) | |||||||
\(978\) | 5.65279 | 0.180756 | ||||||||
\(979\) | 7.64981 | 0.244489 | ||||||||
\(980\) | −5.56465 | −0.177756 | ||||||||
\(981\) | 1.31336 | 0.0419322 | ||||||||
\(982\) | 17.6823 | 0.564266 | ||||||||
\(983\) | 45.5612 | 1.45318 | 0.726588 | − | 0.687073i | \(-0.241105\pi\) | ||||
0.726588 | + | 0.687073i | \(0.241105\pi\) | |||||||
\(984\) | 3.08815 | 0.0984465 | ||||||||
\(985\) | 3.78448 | 0.120584 | ||||||||
\(986\) | −44.5362 | −1.41832 | ||||||||
\(987\) | −14.6907 | −0.467610 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.22521 | 0.293345 | ||||||||
\(990\) | −0.554958 | −0.0176377 | ||||||||
\(991\) | 35.4693 | 1.12672 | 0.563360 | − | 0.826211i | \(-0.309508\pi\) | ||||
0.563360 | + | 0.826211i | \(0.309508\pi\) | |||||||
\(992\) | −3.04892 | −0.0968032 | ||||||||
\(993\) | 0.173899 | 0.00551852 | ||||||||
\(994\) | −2.82371 | −0.0895626 | ||||||||
\(995\) | −10.2349 | −0.324468 | ||||||||
\(996\) | −5.88471 | −0.186464 | ||||||||
\(997\) | −3.74632 | −0.118647 | −0.0593235 | − | 0.998239i | \(-0.518894\pi\) | ||||
−0.0593235 | + | 0.998239i | \(0.518894\pi\) | |||||||
\(998\) | 21.1535 | 0.669601 | ||||||||
\(999\) | 7.96615 | 0.252038 |
(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.bm.1.1 | ✓ | 3 | |
13.5 | odd | 4 | 5070.2.b.u.1351.4 | 6 | |||
13.8 | odd | 4 | 5070.2.b.u.1351.3 | 6 | |||
13.12 | even | 2 | 5070.2.a.br.1.3 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5070.2.a.bm.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
5070.2.a.br.1.3 | yes | 3 | 13.12 | even | 2 | ||
5070.2.b.u.1351.3 | 6 | 13.8 | odd | 4 | |||
5070.2.b.u.1351.4 | 6 | 13.5 | odd | 4 |