Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4225,2,Mod(1,4225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4225.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4225 = 5^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4225.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: | \(33.7367948540\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.4752.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 3x^{2} + 4x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 65) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.21969\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.21969 | −0.862449 | −0.431224 | − | 0.902245i | \(-0.641918\pi\) | ||||
−0.431224 | + | 0.902245i | \(0.641918\pi\) | |||||||
\(3\) | −2.33225 | −1.34652 | −0.673262 | − | 0.739404i | \(-0.735107\pi\) | ||||
−0.673262 | + | 0.739404i | \(0.735107\pi\) | |||||||
\(4\) | −0.512364 | −0.256182 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.84461 | 1.16131 | ||||||||
\(7\) | −3.60020 | −1.36075 | −0.680373 | − | 0.732866i | \(-0.738182\pi\) | ||||
−0.680373 | + | 0.732866i | \(0.738182\pi\) | |||||||
\(8\) | 3.06430 | 1.08339 | ||||||||
\(9\) | 2.43937 | 0.813125 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.37182 | 1.61966 | 0.809832 | − | 0.586662i | \(-0.199558\pi\) | ||||
0.809832 | + | 0.586662i | \(0.199558\pi\) | |||||||
\(12\) | 1.19496 | 0.344955 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 4.39111 | 1.17357 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.71276 | −0.678189 | ||||||||
\(17\) | 1.13186 | 0.274515 | 0.137258 | − | 0.990535i | \(-0.456171\pi\) | ||||
0.137258 | + | 0.990535i | \(0.456171\pi\) | |||||||
\(18\) | −2.97527 | −0.701278 | ||||||||
\(19\) | 2.26795 | 0.520303 | 0.260152 | − | 0.965568i | \(-0.416227\pi\) | ||||
0.260152 | + | 0.965568i | \(0.416227\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.39654 | 1.83228 | ||||||||
\(22\) | −6.55193 | −1.39688 | ||||||||
\(23\) | 3.89287 | 0.811720 | 0.405860 | − | 0.913935i | \(-0.366972\pi\) | ||||
0.405860 | + | 0.913935i | \(0.366972\pi\) | |||||||
\(24\) | −7.14670 | −1.45881 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.30752 | 0.251632 | ||||||||
\(28\) | 1.84461 | 0.348599 | ||||||||
\(29\) | −0.0247279 | −0.00459185 | −0.00229593 | − | 0.999997i | \(-0.500731\pi\) | ||||
−0.00229593 | + | 0.999997i | \(0.500731\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.46410 | 0.981382 | 0.490691 | − | 0.871334i | \(-0.336744\pi\) | ||||
0.490691 | + | 0.871334i | \(0.336744\pi\) | |||||||
\(32\) | −2.81988 | −0.498490 | ||||||||
\(33\) | −12.5284 | −2.18091 | ||||||||
\(34\) | −1.38051 | −0.236755 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.24985 | −0.208308 | ||||||||
\(37\) | 8.70406 | 1.43094 | 0.715470 | − | 0.698644i | \(-0.246213\pi\) | ||||
0.715470 | + | 0.698644i | \(0.246213\pi\) | |||||||
\(38\) | −2.76619 | −0.448735 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.73205 | 0.582848 | 0.291424 | − | 0.956594i | \(-0.405871\pi\) | ||||
0.291424 | + | 0.956594i | \(0.405871\pi\) | |||||||
\(42\) | −10.2412 | −1.58024 | ||||||||
\(43\) | 1.13186 | 0.172606 | 0.0863031 | − | 0.996269i | \(-0.472495\pi\) | ||||
0.0863031 | + | 0.996269i | \(0.472495\pi\) | |||||||
\(44\) | −2.75232 | −0.414929 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.74809 | −0.700067 | ||||||||
\(47\) | −2.58535 | −0.377113 | −0.188556 | − | 0.982062i | \(-0.560381\pi\) | ||||
−0.188556 | + | 0.982062i | \(0.560381\pi\) | |||||||
\(48\) | 6.32681 | 0.913197 | ||||||||
\(49\) | 5.96141 | 0.851630 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.63977 | −0.369641 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.43937 | 0.609795 | 0.304897 | − | 0.952385i | \(-0.401378\pi\) | ||||
0.304897 | + | 0.952385i | \(0.401378\pi\) | |||||||
\(54\) | −1.59476 | −0.217020 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −11.0321 | −1.47422 | ||||||||
\(57\) | −5.28942 | −0.700600 | ||||||||
\(58\) | 0.0301603 | 0.00396024 | ||||||||
\(59\) | −0.171425 | −0.0223176 | −0.0111588 | − | 0.999938i | \(-0.503552\pi\) | ||||
−0.0111588 | + | 0.999938i | \(0.503552\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.36023 | 0.430234 | 0.215117 | − | 0.976588i | \(-0.430987\pi\) | ||||
0.215117 | + | 0.976588i | \(0.430987\pi\) | |||||||
\(62\) | −6.66449 | −0.846391 | ||||||||
\(63\) | −8.78222 | −1.10646 | ||||||||
\(64\) | 8.86488 | 1.10811 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 15.2807 | 1.88093 | ||||||||
\(67\) | −6.39980 | −0.781861 | −0.390930 | − | 0.920420i | \(-0.627847\pi\) | ||||
−0.390930 | + | 0.920420i | \(0.627847\pi\) | |||||||
\(68\) | −0.579922 | −0.0703258 | ||||||||
\(69\) | −9.07914 | −1.09300 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.7973 | −1.28141 | −0.640703 | − | 0.767788i | \(-0.721357\pi\) | ||||
−0.640703 | + | 0.767788i | \(0.721357\pi\) | |||||||
\(72\) | 7.47497 | 0.880933 | ||||||||
\(73\) | 4.70308 | 0.550454 | 0.275227 | − | 0.961379i | \(-0.411247\pi\) | ||||
0.275227 | + | 0.961379i | \(0.411247\pi\) | |||||||
\(74\) | −10.6162 | −1.23411 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.16202 | −0.133292 | ||||||||
\(77\) | −19.3396 | −2.20395 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.9826 | −1.34815 | −0.674075 | − | 0.738663i | \(-0.735457\pi\) | ||||
−0.674075 | + | 0.738663i | \(0.735457\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.3676 | −1.15195 | ||||||||
\(82\) | −4.55193 | −0.502677 | ||||||||
\(83\) | 12.1286 | 1.33129 | 0.665643 | − | 0.746270i | \(-0.268157\pi\) | ||||
0.665643 | + | 0.746270i | \(0.268157\pi\) | |||||||
\(84\) | −4.30209 | −0.469396 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.38051 | −0.148864 | ||||||||
\(87\) | 0.0576715 | 0.00618303 | ||||||||
\(88\) | 16.4608 | 1.75473 | ||||||||
\(89\) | −16.1540 | −1.71232 | −0.856162 | − | 0.516707i | \(-0.827158\pi\) | ||||
−0.856162 | + | 0.516707i | \(0.827158\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.99457 | −0.207948 | ||||||||
\(93\) | −12.7436 | −1.32145 | ||||||||
\(94\) | 3.15332 | 0.325240 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 6.57666 | 0.671228 | ||||||||
\(97\) | −12.1682 | −1.23549 | −0.617745 | − | 0.786379i | \(-0.711954\pi\) | ||||
−0.617745 | + | 0.786379i | \(0.711954\pi\) | |||||||
\(98\) | −7.27105 | −0.734487 | ||||||||
\(99\) | 13.1039 | 1.31699 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.05441 | −0.403429 | −0.201714 | − | 0.979444i | \(-0.564651\pi\) | ||||
−0.201714 | + | 0.979444i | \(0.564651\pi\) | |||||||
\(102\) | 3.21969 | 0.318797 | ||||||||
\(103\) | 17.9035 | 1.76408 | 0.882041 | − | 0.471173i | \(-0.156169\pi\) | ||||
0.882041 | + | 0.471173i | \(0.156169\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.41465 | −0.525917 | ||||||||
\(107\) | 9.13186 | 0.882810 | 0.441405 | − | 0.897308i | \(-0.354480\pi\) | ||||
0.441405 | + | 0.897308i | \(0.354480\pi\) | |||||||
\(108\) | −0.669925 | −0.0644636 | ||||||||
\(109\) | 7.37605 | 0.706498 | 0.353249 | − | 0.935529i | \(-0.385077\pi\) | ||||
0.353249 | + | 0.935529i | \(0.385077\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −20.3000 | −1.92679 | ||||||||
\(112\) | 9.76645 | 0.922843 | ||||||||
\(113\) | −7.07588 | −0.665643 | −0.332821 | − | 0.942990i | \(-0.608001\pi\) | ||||
−0.332821 | + | 0.942990i | \(0.608001\pi\) | |||||||
\(114\) | 6.45143 | 0.604232 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.0126697 | 0.00117635 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.209084 | 0.0192478 | ||||||||
\(119\) | −4.07490 | −0.373545 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.8564 | 1.62331 | ||||||||
\(122\) | −4.09843 | −0.371055 | ||||||||
\(123\) | −8.70406 | −0.784819 | ||||||||
\(124\) | −2.79961 | −0.251412 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 10.7116 | 0.954262 | ||||||||
\(127\) | 11.4361 | 1.01479 | 0.507395 | − | 0.861713i | \(-0.330608\pi\) | ||||
0.507395 | + | 0.861713i | \(0.330608\pi\) | |||||||
\(128\) | −5.17262 | −0.457199 | ||||||||
\(129\) | −2.63977 | −0.232418 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.5680 | −0.923328 | −0.461664 | − | 0.887055i | \(-0.652747\pi\) | ||||
−0.461664 | + | 0.887055i | \(0.652747\pi\) | |||||||
\(132\) | 6.41910 | 0.558711 | ||||||||
\(133\) | −8.16506 | −0.708001 | ||||||||
\(134\) | 7.80576 | 0.674315 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.46834 | 0.297408 | ||||||||
\(137\) | −3.78672 | −0.323522 | −0.161761 | − | 0.986830i | \(-0.551717\pi\) | ||||
−0.161761 | + | 0.986830i | \(0.551717\pi\) | |||||||
\(138\) | 11.0737 | 0.942656 | ||||||||
\(139\) | 2.01386 | 0.170814 | 0.0854068 | − | 0.996346i | \(-0.472781\pi\) | ||||
0.0854068 | + | 0.996346i | \(0.472781\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.02968 | 0.507791 | ||||||||
\(142\) | 13.1694 | 1.10515 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −6.61742 | −0.551452 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5.73629 | −0.474739 | ||||||||
\(147\) | −13.9035 | −1.14674 | ||||||||
\(148\) | −4.45965 | −0.366581 | ||||||||
\(149\) | −5.51780 | −0.452035 | −0.226018 | − | 0.974123i | \(-0.572571\pi\) | ||||
−0.226018 | + | 0.974123i | \(0.572571\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.88961 | −0.397911 | −0.198956 | − | 0.980009i | \(-0.563755\pi\) | ||||
−0.198956 | + | 0.980009i | \(0.563755\pi\) | |||||||
\(152\) | 6.94967 | 0.563693 | ||||||||
\(153\) | 2.76102 | 0.223215 | ||||||||
\(154\) | 23.5882 | 1.90079 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.0405 | −0.801323 | −0.400661 | − | 0.916226i | \(-0.631220\pi\) | ||||
−0.400661 | + | 0.916226i | \(0.631220\pi\) | |||||||
\(158\) | 14.6150 | 1.16271 | ||||||||
\(159\) | −10.3537 | −0.821103 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.0151 | −1.10454 | ||||||||
\(162\) | 12.6452 | 0.993501 | ||||||||
\(163\) | −6.78124 | −0.531148 | −0.265574 | − | 0.964090i | \(-0.585561\pi\) | ||||
−0.265574 | + | 0.964090i | \(0.585561\pi\) | |||||||
\(164\) | −1.91217 | −0.149315 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.7931 | −1.14817 | ||||||||
\(167\) | −10.4898 | −0.811726 | −0.405863 | − | 0.913934i | \(-0.633029\pi\) | ||||
−0.405863 | + | 0.913934i | \(0.633029\pi\) | |||||||
\(168\) | 25.7295 | 1.98507 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.53238 | 0.423071 | ||||||||
\(172\) | −0.579922 | −0.0442186 | ||||||||
\(173\) | 4.45845 | 0.338970 | 0.169485 | − | 0.985533i | \(-0.445790\pi\) | ||||
0.169485 | + | 0.985533i | \(0.445790\pi\) | |||||||
\(174\) | −0.0703412 | −0.00533255 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −14.5724 | −1.09844 | ||||||||
\(177\) | 0.399804 | 0.0300511 | ||||||||
\(178\) | 19.7029 | 1.47679 | ||||||||
\(179\) | 18.6313 | 1.39257 | 0.696284 | − | 0.717766i | \(-0.254835\pi\) | ||||
0.696284 | + | 0.717766i | \(0.254835\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.0900 | 1.34462 | 0.672310 | − | 0.740270i | \(-0.265302\pi\) | ||||
0.672310 | + | 0.740270i | \(0.265302\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.83690 | −0.579320 | ||||||||
\(184\) | 11.9289 | 0.879412 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 15.5432 | 1.13969 | ||||||||
\(187\) | 6.08012 | 0.444622 | ||||||||
\(188\) | 1.32464 | 0.0966095 | ||||||||
\(189\) | −4.70732 | −0.342407 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 27.3363 | 1.97799 | 0.988994 | − | 0.147958i | \(-0.0472701\pi\) | ||||
0.988994 | + | 0.147958i | \(0.0472701\pi\) | |||||||
\(192\) | −20.6751 | −1.49210 | ||||||||
\(193\) | −21.7674 | −1.56685 | −0.783425 | − | 0.621486i | \(-0.786529\pi\) | ||||
−0.783425 | + | 0.621486i | \(0.786529\pi\) | |||||||
\(194\) | 14.8413 | 1.06555 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.05441 | −0.218172 | ||||||||
\(197\) | 1.69672 | 0.120886 | 0.0604432 | − | 0.998172i | \(-0.480749\pi\) | ||||
0.0604432 | + | 0.998172i | \(0.480749\pi\) | |||||||
\(198\) | −15.9826 | −1.13583 | ||||||||
\(199\) | 25.3255 | 1.79527 | 0.897637 | − | 0.440735i | \(-0.145282\pi\) | ||||
0.897637 | + | 0.440735i | \(0.145282\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.9259 | 1.05279 | ||||||||
\(202\) | 4.94511 | 0.347937 | ||||||||
\(203\) | 0.0890252 | 0.00624834 | ||||||||
\(204\) | 1.35252 | 0.0946954 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −21.8366 | −1.52143 | ||||||||
\(207\) | 9.49617 | 0.660030 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.1830 | 0.842716 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.335507 | −0.0230973 | −0.0115486 | − | 0.999933i | \(-0.503676\pi\) | ||||
−0.0115486 | + | 0.999933i | \(0.503676\pi\) | |||||||
\(212\) | −2.27458 | −0.156218 | ||||||||
\(213\) | 25.1820 | 1.72544 | ||||||||
\(214\) | −11.1380 | −0.761378 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 4.00663 | 0.272616 | ||||||||
\(217\) | −19.6718 | −1.33541 | ||||||||
\(218\) | −8.99648 | −0.609318 | ||||||||
\(219\) | −10.9688 | −0.741200 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 24.7597 | 1.66176 | ||||||||
\(223\) | 12.2968 | 0.823452 | 0.411726 | − | 0.911308i | \(-0.364926\pi\) | ||||
0.411726 | + | 0.911308i | \(0.364926\pi\) | |||||||
\(224\) | 10.1521 | 0.678318 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.63036 | 0.574083 | ||||||||
\(227\) | 7.63227 | 0.506571 | 0.253286 | − | 0.967392i | \(-0.418489\pi\) | ||||
0.253286 | + | 0.967392i | \(0.418489\pi\) | |||||||
\(228\) | 2.71011 | 0.179481 | ||||||||
\(229\) | −14.4008 | −0.951631 | −0.475815 | − | 0.879545i | \(-0.657847\pi\) | ||||
−0.475815 | + | 0.879545i | \(0.657847\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 45.1047 | 2.96767 | ||||||||
\(232\) | −0.0757736 | −0.00497478 | ||||||||
\(233\) | −9.49617 | −0.622115 | −0.311057 | − | 0.950391i | \(-0.600683\pi\) | ||||
−0.311057 | + | 0.950391i | \(0.600683\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.0878318 | 0.00571736 | ||||||||
\(237\) | 27.9464 | 1.81531 | ||||||||
\(238\) | 4.97010 | 0.322164 | ||||||||
\(239\) | −19.9143 | −1.28815 | −0.644076 | − | 0.764962i | \(-0.722758\pi\) | ||||
−0.644076 | + | 0.764962i | \(0.722758\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.2664 | 1.49872 | 0.749360 | − | 0.662163i | \(-0.230361\pi\) | ||||
0.749360 | + | 0.662163i | \(0.230361\pi\) | |||||||
\(242\) | −21.7792 | −1.40002 | ||||||||
\(243\) | 20.2572 | 1.29950 | ||||||||
\(244\) | −1.72166 | −0.110218 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 10.6162 | 0.676866 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 16.7436 | 1.06322 | ||||||||
\(249\) | −28.2869 | −1.79261 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.8402 | 0.747344 | 0.373672 | − | 0.927561i | \(-0.378099\pi\) | ||||
0.373672 | + | 0.927561i | \(0.378099\pi\) | |||||||
\(252\) | 4.49969 | 0.283454 | ||||||||
\(253\) | 20.9118 | 1.31471 | ||||||||
\(254\) | −13.9485 | −0.875205 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −11.4208 | −0.713800 | ||||||||
\(257\) | 5.55002 | 0.346201 | 0.173100 | − | 0.984904i | \(-0.444621\pi\) | ||||
0.173100 | + | 0.984904i | \(0.444621\pi\) | |||||||
\(258\) | 3.21969 | 0.200449 | ||||||||
\(259\) | −31.3363 | −1.94714 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.0603205 | −0.00373375 | ||||||||
\(262\) | 12.8896 | 0.796323 | ||||||||
\(263\) | −6.85967 | −0.422985 | −0.211493 | − | 0.977380i | \(-0.567832\pi\) | ||||
−0.211493 | + | 0.977380i | \(0.567832\pi\) | |||||||
\(264\) | −38.3907 | −2.36279 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 9.95882 | 0.610614 | ||||||||
\(267\) | 37.6752 | 2.30568 | ||||||||
\(268\) | 3.27903 | 0.200299 | ||||||||
\(269\) | −1.42199 | −0.0867001 | −0.0433501 | − | 0.999060i | \(-0.513803\pi\) | ||||
−0.0433501 | + | 0.999060i | \(0.513803\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.96947 | −0.605602 | −0.302801 | − | 0.953054i | \(-0.597922\pi\) | ||||
−0.302801 | + | 0.953054i | \(0.597922\pi\) | |||||||
\(272\) | −3.07045 | −0.186173 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.61862 | 0.279021 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.65182 | 0.280007 | ||||||||
\(277\) | 17.5237 | 1.05290 | 0.526449 | − | 0.850206i | \(-0.323523\pi\) | ||||
0.526449 | + | 0.850206i | \(0.323523\pi\) | |||||||
\(278\) | −2.45628 | −0.147318 | ||||||||
\(279\) | 13.3290 | 0.797986 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.7352 | 0.640406 | 0.320203 | − | 0.947349i | \(-0.396249\pi\) | ||||
0.320203 | + | 0.947349i | \(0.396249\pi\) | |||||||
\(282\) | −7.35433 | −0.437944 | ||||||||
\(283\) | −1.31838 | −0.0783698 | −0.0391849 | − | 0.999232i | \(-0.512476\pi\) | ||||
−0.0391849 | + | 0.999232i | \(0.512476\pi\) | |||||||
\(284\) | 5.53216 | 0.328273 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.4361 | −0.793109 | ||||||||
\(288\) | −6.87875 | −0.405334 | ||||||||
\(289\) | −15.7189 | −0.924641 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 28.3792 | 1.66362 | ||||||||
\(292\) | −2.40969 | −0.141016 | ||||||||
\(293\) | −18.7427 | −1.09496 | −0.547479 | − | 0.836820i | \(-0.684412\pi\) | ||||
−0.547479 | + | 0.836820i | \(0.684412\pi\) | |||||||
\(294\) | 16.9579 | 0.989004 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 26.6718 | 1.55027 | ||||||||
\(297\) | 7.02375 | 0.407559 | ||||||||
\(298\) | 6.72998 | 0.389857 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.07490 | −0.234873 | ||||||||
\(302\) | 5.96380 | 0.343178 | ||||||||
\(303\) | 9.45589 | 0.543226 | ||||||||
\(304\) | −6.15239 | −0.352864 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.36758 | −0.192512 | ||||||||
\(307\) | −14.3043 | −0.816387 | −0.408194 | − | 0.912895i | \(-0.633841\pi\) | ||||
−0.408194 | + | 0.912895i | \(0.633841\pi\) | |||||||
\(308\) | 9.90891 | 0.564612 | ||||||||
\(309\) | −41.7553 | −2.37538 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.76102 | 0.156563 | 0.0782815 | − | 0.996931i | \(-0.475057\pi\) | ||||
0.0782815 | + | 0.996931i | \(0.475057\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.3858 | 0.926179 | 0.463090 | − | 0.886311i | \(-0.346741\pi\) | ||||
0.463090 | + | 0.886311i | \(0.346741\pi\) | |||||||
\(314\) | 12.2463 | 0.691100 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.13946 | 0.345372 | ||||||||
\(317\) | −1.78575 | −0.100297 | −0.0501487 | − | 0.998742i | \(-0.515970\pi\) | ||||
−0.0501487 | + | 0.998742i | \(0.515970\pi\) | |||||||
\(318\) | 12.6283 | 0.708159 | ||||||||
\(319\) | −0.132834 | −0.00743725 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −21.2977 | −1.18872 | ||||||||
\(322\) | 17.0940 | 0.952613 | ||||||||
\(323\) | 2.56699 | 0.142831 | ||||||||
\(324\) | 5.31197 | 0.295110 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8.27099 | 0.458088 | ||||||||
\(327\) | −17.2028 | −0.951316 | ||||||||
\(328\) | 11.4361 | 0.631454 | ||||||||
\(329\) | 9.30778 | 0.513155 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.22440 | 0.397089 | 0.198545 | − | 0.980092i | \(-0.436379\pi\) | ||||
0.198545 | + | 0.980092i | \(0.436379\pi\) | |||||||
\(332\) | −6.21425 | −0.341052 | ||||||||
\(333\) | 21.2325 | 1.16353 | ||||||||
\(334\) | 12.7943 | 0.700072 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −22.7778 | −1.24263 | ||||||||
\(337\) | 4.36219 | 0.237624 | 0.118812 | − | 0.992917i | \(-0.462091\pi\) | ||||
0.118812 | + | 0.992917i | \(0.462091\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.5027 | 0.896303 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 29.3521 | 1.58951 | ||||||||
\(342\) | −6.74777 | −0.364877 | ||||||||
\(343\) | 3.73913 | 0.201894 | ||||||||
\(344\) | 3.46834 | 0.187000 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.43792 | −0.292344 | ||||||||
\(347\) | 26.7072 | 1.43372 | 0.716858 | − | 0.697219i | \(-0.245580\pi\) | ||||
0.716858 | + | 0.697219i | \(0.245580\pi\) | |||||||
\(348\) | −0.0295488 | −0.00158398 | ||||||||
\(349\) | 23.5711 | 1.26173 | 0.630865 | − | 0.775892i | \(-0.282700\pi\) | ||||
0.630865 | + | 0.775892i | \(0.282700\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −15.1479 | −0.807385 | ||||||||
\(353\) | −5.73727 | −0.305364 | −0.152682 | − | 0.988275i | \(-0.548791\pi\) | ||||
−0.152682 | + | 0.988275i | \(0.548791\pi\) | |||||||
\(354\) | −0.487636 | −0.0259176 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 8.27675 | 0.438667 | ||||||||
\(357\) | 9.50367 | 0.502988 | ||||||||
\(358\) | −22.7243 | −1.20102 | ||||||||
\(359\) | −24.7583 | −1.30669 | −0.653347 | − | 0.757059i | \(-0.726636\pi\) | ||||
−0.653347 | + | 0.757059i | \(0.726636\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.8564 | −0.729285 | ||||||||
\(362\) | −22.0641 | −1.15967 | ||||||||
\(363\) | −41.6455 | −2.18582 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 9.55856 | 0.499634 | ||||||||
\(367\) | −26.0535 | −1.35998 | −0.679992 | − | 0.733220i | \(-0.738017\pi\) | ||||
−0.679992 | + | 0.733220i | \(0.738017\pi\) | |||||||
\(368\) | −10.5604 | −0.550499 | ||||||||
\(369\) | 9.10387 | 0.473928 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −15.9826 | −0.829776 | ||||||||
\(372\) | 6.52938 | 0.338532 | ||||||||
\(373\) | −13.2045 | −0.683702 | −0.341851 | − | 0.939754i | \(-0.611054\pi\) | ||||
−0.341851 | + | 0.939754i | \(0.611054\pi\) | |||||||
\(374\) | −7.41584 | −0.383464 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.92229 | −0.408561 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 5.74146 | 0.295309 | ||||||||
\(379\) | 25.9977 | 1.33541 | 0.667707 | − | 0.744425i | \(-0.267276\pi\) | ||||
0.667707 | + | 0.744425i | \(0.267276\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −26.6718 | −1.36644 | ||||||||
\(382\) | −33.3418 | −1.70591 | ||||||||
\(383\) | 9.60020 | 0.490547 | 0.245274 | − | 0.969454i | \(-0.421122\pi\) | ||||
0.245274 | + | 0.969454i | \(0.421122\pi\) | |||||||
\(384\) | 12.0638 | 0.615629 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 26.5494 | 1.35133 | ||||||||
\(387\) | 2.76102 | 0.140350 | ||||||||
\(388\) | 6.23453 | 0.316510 | ||||||||
\(389\) | 5.63129 | 0.285518 | 0.142759 | − | 0.989758i | \(-0.454403\pi\) | ||||
0.142759 | + | 0.989758i | \(0.454403\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.40617 | 0.222829 | ||||||||
\(392\) | 18.2675 | 0.922650 | ||||||||
\(393\) | 24.6471 | 1.24328 | ||||||||
\(394\) | −2.06947 | −0.104258 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −6.71395 | −0.337389 | ||||||||
\(397\) | 16.7658 | 0.841452 | 0.420726 | − | 0.907188i | \(-0.361775\pi\) | ||||
0.420726 | + | 0.907188i | \(0.361775\pi\) | |||||||
\(398\) | −30.8891 | −1.54833 | ||||||||
\(399\) | 19.0429 | 0.953339 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.8780 | −0.693036 | −0.346518 | − | 0.938043i | \(-0.612636\pi\) | ||||
−0.346518 | + | 0.938043i | \(0.612636\pi\) | |||||||
\(402\) | −18.2050 | −0.907980 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 2.07733 | 0.103351 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.108583 | −0.00538888 | ||||||||
\(407\) | 46.7566 | 2.31764 | ||||||||
\(408\) | −8.08903 | −0.400466 | ||||||||
\(409\) | 29.4251 | 1.45498 | 0.727489 | − | 0.686120i | \(-0.240687\pi\) | ||||
0.727489 | + | 0.686120i | \(0.240687\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.83157 | 0.435629 | ||||||||
\(412\) | −9.17310 | −0.451926 | ||||||||
\(413\) | 0.617162 | 0.0303686 | ||||||||
\(414\) | −11.5824 | −0.569242 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.69683 | −0.230005 | ||||||||
\(418\) | −14.8595 | −0.726800 | ||||||||
\(419\) | 6.96793 | 0.340406 | 0.170203 | − | 0.985409i | \(-0.445558\pi\) | ||||
0.170203 | + | 0.985409i | \(0.445558\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.12125 | 0.347069 | 0.173534 | − | 0.984828i | \(-0.444481\pi\) | ||||
0.173534 | + | 0.984828i | \(0.444481\pi\) | |||||||
\(422\) | 0.409213 | 0.0199202 | ||||||||
\(423\) | −6.30664 | −0.306640 | ||||||||
\(424\) | 13.6036 | 0.660647 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −30.7142 | −1.48811 | ||||||||
\(427\) | −12.0975 | −0.585439 | ||||||||
\(428\) | −4.67883 | −0.226160 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.2144 | 1.45537 | 0.727687 | − | 0.685909i | \(-0.240595\pi\) | ||||
0.727687 | + | 0.685909i | \(0.240595\pi\) | |||||||
\(432\) | −3.54698 | −0.170654 | ||||||||
\(433\) | −1.20013 | −0.0576745 | −0.0288373 | − | 0.999584i | \(-0.509180\pi\) | ||||
−0.0288373 | + | 0.999584i | \(0.509180\pi\) | |||||||
\(434\) | 23.9935 | 1.15172 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.77922 | −0.180992 | ||||||||
\(437\) | 8.82884 | 0.422341 | ||||||||
\(438\) | 13.3784 | 0.639247 | ||||||||
\(439\) | −16.5541 | −0.790084 | −0.395042 | − | 0.918663i | \(-0.629270\pi\) | ||||
−0.395042 | + | 0.918663i | \(0.629270\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.5421 | 0.692481 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.55949 | −0.216628 | −0.108314 | − | 0.994117i | \(-0.534545\pi\) | ||||
−0.108314 | + | 0.994117i | \(0.534545\pi\) | |||||||
\(444\) | 10.4010 | 0.493610 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −14.9982 | −0.710185 | ||||||||
\(447\) | 12.8689 | 0.608676 | ||||||||
\(448\) | −31.9153 | −1.50786 | ||||||||
\(449\) | 13.8522 | 0.653724 | 0.326862 | − | 0.945072i | \(-0.394009\pi\) | ||||
0.326862 | + | 0.945072i | \(0.394009\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.0479 | 0.944018 | ||||||||
\(452\) | 3.62542 | 0.170526 | ||||||||
\(453\) | 11.4038 | 0.535796 | ||||||||
\(454\) | −9.30897 | −0.436892 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −16.2083 | −0.759025 | ||||||||
\(457\) | −40.1146 | −1.87648 | −0.938240 | − | 0.345984i | \(-0.887545\pi\) | ||||
−0.938240 | + | 0.345984i | \(0.887545\pi\) | |||||||
\(458\) | 17.5644 | 0.820733 | ||||||||
\(459\) | 1.47992 | 0.0690768 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.53900 | −0.351126 | −0.175563 | − | 0.984468i | \(-0.556175\pi\) | ||||
−0.175563 | + | 0.984468i | \(0.556175\pi\) | |||||||
\(462\) | −55.0136 | −2.55946 | ||||||||
\(463\) | −23.3031 | −1.08299 | −0.541494 | − | 0.840705i | \(-0.682141\pi\) | ||||
−0.541494 | + | 0.840705i | \(0.682141\pi\) | |||||||
\(464\) | 0.0670807 | 0.00311414 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.5824 | 0.536542 | ||||||||
\(467\) | 22.6297 | 1.04718 | 0.523589 | − | 0.851971i | \(-0.324593\pi\) | ||||
0.523589 | + | 0.851971i | \(0.324593\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23.0405 | 1.06391 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 23.4170 | 1.07900 | ||||||||
\(472\) | −0.525296 | −0.0241787 | ||||||||
\(473\) | 6.08012 | 0.279564 | ||||||||
\(474\) | −34.0859 | −1.56562 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.08783 | 0.0956956 | ||||||||
\(477\) | 10.8293 | 0.495839 | ||||||||
\(478\) | 24.2893 | 1.11096 | ||||||||
\(479\) | 20.6448 | 0.943286 | 0.471643 | − | 0.881790i | \(-0.343661\pi\) | ||||
0.471643 | + | 0.881790i | \(0.343661\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −28.3777 | −1.29257 | ||||||||
\(483\) | 32.6867 | 1.48730 | ||||||||
\(484\) | −9.14898 | −0.415863 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −24.7074 | −1.12075 | ||||||||
\(487\) | −3.03605 | −0.137576 | −0.0687882 | − | 0.997631i | \(-0.521913\pi\) | ||||
−0.0687882 | + | 0.997631i | \(0.521913\pi\) | |||||||
\(488\) | 10.2968 | 0.466112 | ||||||||
\(489\) | 15.8155 | 0.715203 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.6680 | 0.481441 | 0.240720 | − | 0.970595i | \(-0.422616\pi\) | ||||
0.240720 | + | 0.970595i | \(0.422616\pi\) | |||||||
\(492\) | 4.45965 | 0.201056 | ||||||||
\(493\) | −0.0279884 | −0.00126053 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −14.8228 | −0.665562 | ||||||||
\(497\) | 38.8725 | 1.74367 | ||||||||
\(498\) | 34.5011 | 1.54603 | ||||||||
\(499\) | 33.9143 | 1.51821 | 0.759107 | − | 0.650966i | \(-0.225636\pi\) | ||||
0.759107 | + | 0.650966i | \(0.225636\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 24.4648 | 1.09301 | ||||||||
\(502\) | −14.4413 | −0.644546 | ||||||||
\(503\) | 12.6276 | 0.563037 | 0.281518 | − | 0.959556i | \(-0.409162\pi\) | ||||
0.281518 | + | 0.959556i | \(0.409162\pi\) | |||||||
\(504\) | −26.9113 | −1.19873 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −25.5058 | −1.13387 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.85945 | −0.259971 | ||||||||
\(509\) | −24.1526 | −1.07055 | −0.535273 | − | 0.844679i | \(-0.679791\pi\) | ||||
−0.535273 | + | 0.844679i | \(0.679791\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.9320 | −0.749029 | ||||||||
\(512\) | 24.2750 | 1.07281 | ||||||||
\(513\) | 2.96539 | 0.130925 | ||||||||
\(514\) | −6.76929 | −0.298581 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.35252 | 0.0595414 | ||||||||
\(517\) | −13.8880 | −0.610796 | ||||||||
\(518\) | 38.2205 | 1.67931 | ||||||||
\(519\) | −10.3982 | −0.456431 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.7521 | −1.08441 | −0.542205 | − | 0.840246i | \(-0.682410\pi\) | ||||
−0.542205 | + | 0.840246i | \(0.682410\pi\) | |||||||
\(522\) | 0.0735722 | 0.00322017 | ||||||||
\(523\) | −37.0326 | −1.61932 | −0.809662 | − | 0.586897i | \(-0.800350\pi\) | ||||
−0.809662 | + | 0.586897i | \(0.800350\pi\) | |||||||
\(524\) | 5.41465 | 0.236540 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.36665 | 0.364803 | ||||||||
\(527\) | 6.18457 | 0.269404 | ||||||||
\(528\) | 33.9865 | 1.47907 | ||||||||
\(529\) | −7.84554 | −0.341111 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.418169 | −0.0181470 | ||||||||
\(532\) | 4.18348 | 0.181377 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −45.9519 | −1.98854 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −19.6109 | −0.847062 | ||||||||
\(537\) | −43.4528 | −1.87512 | ||||||||
\(538\) | 1.73438 | 0.0747744 | ||||||||
\(539\) | 32.0236 | 1.37935 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.38144 | −0.360346 | −0.180173 | − | 0.983635i | \(-0.557666\pi\) | ||||
−0.180173 | + | 0.983635i | \(0.557666\pi\) | |||||||
\(542\) | 12.1596 | 0.522301 | ||||||||
\(543\) | −42.1903 | −1.81056 | ||||||||
\(544\) | −3.19170 | −0.136843 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.7842 | 0.974181 | 0.487091 | − | 0.873351i | \(-0.338058\pi\) | ||||
0.487091 | + | 0.873351i | \(0.338058\pi\) | |||||||
\(548\) | 1.94018 | 0.0828804 | ||||||||
\(549\) | 8.19687 | 0.349834 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.0560816 | −0.00238915 | ||||||||
\(552\) | −27.8212 | −1.18415 | ||||||||
\(553\) | 43.1398 | 1.83449 | ||||||||
\(554\) | −21.3735 | −0.908071 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.03183 | −0.0437594 | ||||||||
\(557\) | 28.1527 | 1.19287 | 0.596435 | − | 0.802662i | \(-0.296583\pi\) | ||||
0.596435 | + | 0.802662i | \(0.296583\pi\) | |||||||
\(558\) | −16.2572 | −0.688222 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.1803 | −0.598694 | ||||||||
\(562\) | −13.0935 | −0.552317 | ||||||||
\(563\) | 18.1303 | 0.764101 | 0.382050 | − | 0.924142i | \(-0.375218\pi\) | ||||
0.382050 | + | 0.924142i | \(0.375218\pi\) | |||||||
\(564\) | −3.08939 | −0.130087 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.60801 | 0.0675899 | ||||||||
\(567\) | 37.3253 | 1.56752 | ||||||||
\(568\) | −33.0862 | −1.38827 | ||||||||
\(569\) | 40.5985 | 1.70198 | 0.850988 | − | 0.525185i | \(-0.176004\pi\) | ||||
0.850988 | + | 0.525185i | \(0.176004\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.7159 | 1.03433 | 0.517164 | − | 0.855886i | \(-0.326988\pi\) | ||||
0.517164 | + | 0.855886i | \(0.326988\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −63.7551 | −2.66341 | ||||||||
\(574\) | 16.3879 | 0.684016 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 21.6248 | 0.901032 | ||||||||
\(577\) | −23.0691 | −0.960379 | −0.480189 | − | 0.877165i | \(-0.659432\pi\) | ||||
−0.480189 | + | 0.877165i | \(0.659432\pi\) | |||||||
\(578\) | 19.1721 | 0.797456 | ||||||||
\(579\) | 50.7669 | 2.10980 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −43.6653 | −1.81154 | ||||||||
\(582\) | −34.6137 | −1.43478 | ||||||||
\(583\) | 23.8475 | 0.987662 | ||||||||
\(584\) | 14.4116 | 0.596358 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 22.8602 | 0.944345 | ||||||||
\(587\) | 20.3523 | 0.840030 | 0.420015 | − | 0.907517i | \(-0.362025\pi\) | ||||
0.420015 | + | 0.907517i | \(0.362025\pi\) | |||||||
\(588\) | 7.12364 | 0.293774 | ||||||||
\(589\) | 12.3923 | 0.510616 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.95717 | −0.162776 | ||||||||
\(592\) | −23.6120 | −0.970447 | ||||||||
\(593\) | −10.3834 | −0.426395 | −0.213198 | − | 0.977009i | \(-0.568388\pi\) | ||||
−0.213198 | + | 0.977009i | \(0.568388\pi\) | |||||||
\(594\) | −8.56677 | −0.351499 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.82712 | 0.115803 | ||||||||
\(597\) | −59.0652 | −2.41738 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −31.5965 | −1.29100 | −0.645499 | − | 0.763761i | \(-0.723351\pi\) | ||||
−0.645499 | + | 0.763761i | \(0.723351\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −43.8845 | −1.79009 | −0.895044 | − | 0.445979i | \(-0.852856\pi\) | ||||
−0.895044 | + | 0.445979i | \(0.852856\pi\) | |||||||
\(602\) | 4.97010 | 0.202566 | ||||||||
\(603\) | −15.6115 | −0.635750 | ||||||||
\(604\) | 2.50526 | 0.101938 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −11.5332 | −0.468505 | ||||||||
\(607\) | −2.17540 | −0.0882968 | −0.0441484 | − | 0.999025i | \(-0.514057\pi\) | ||||
−0.0441484 | + | 0.999025i | \(0.514057\pi\) | |||||||
\(608\) | −6.39535 | −0.259366 | ||||||||
\(609\) | −0.207629 | −0.00841354 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −1.41465 | −0.0571837 | ||||||||
\(613\) | 14.7620 | 0.596231 | 0.298116 | − | 0.954530i | \(-0.403642\pi\) | ||||
0.298116 | + | 0.954530i | \(0.403642\pi\) | |||||||
\(614\) | 17.4467 | 0.704092 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −59.2622 | −2.38774 | ||||||||
\(617\) | 20.2972 | 0.817134 | 0.408567 | − | 0.912728i | \(-0.366029\pi\) | ||||
0.408567 | + | 0.912728i | \(0.366029\pi\) | |||||||
\(618\) | 50.9284 | 2.04864 | ||||||||
\(619\) | 9.94207 | 0.399605 | 0.199803 | − | 0.979836i | \(-0.435970\pi\) | ||||
0.199803 | + | 0.979836i | \(0.435970\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.09000 | 0.204255 | ||||||||
\(622\) | −3.36758 | −0.135028 | ||||||||
\(623\) | 58.1577 | 2.33004 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −19.9855 | −0.798782 | ||||||||
\(627\) | −28.4138 | −1.13474 | ||||||||
\(628\) | 5.14441 | 0.205284 | ||||||||
\(629\) | 9.85174 | 0.392815 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.973420 | 0.0387512 | 0.0193756 | − | 0.999812i | \(-0.493832\pi\) | ||||
0.0193756 | + | 0.999812i | \(0.493832\pi\) | |||||||
\(632\) | −36.7183 | −1.46058 | ||||||||
\(633\) | 0.782485 | 0.0311010 | ||||||||
\(634\) | 2.17805 | 0.0865014 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 5.30487 | 0.210352 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.162015 | 0.00641425 | ||||||||
\(639\) | −26.3387 | −1.04194 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.6209 | −0.498497 | −0.249249 | − | 0.968440i | \(-0.580184\pi\) | ||||
−0.249249 | + | 0.968440i | \(0.580184\pi\) | |||||||
\(642\) | 25.9766 | 1.02521 | ||||||||
\(643\) | −9.96043 | −0.392801 | −0.196401 | − | 0.980524i | \(-0.562925\pi\) | ||||
−0.196401 | + | 0.980524i | \(0.562925\pi\) | |||||||
\(644\) | 7.18083 | 0.282964 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.13092 | −0.123185 | ||||||||
\(647\) | 36.2763 | 1.42617 | 0.713084 | − | 0.701079i | \(-0.247298\pi\) | ||||
0.713084 | + | 0.701079i | \(0.247298\pi\) | |||||||
\(648\) | −31.7693 | −1.24802 | ||||||||
\(649\) | −0.920861 | −0.0361470 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 45.8796 | 1.79816 | ||||||||
\(652\) | 3.47447 | 0.136071 | ||||||||
\(653\) | −13.7554 | −0.538289 | −0.269145 | − | 0.963100i | \(-0.586741\pi\) | ||||
−0.269145 | + | 0.963100i | \(0.586741\pi\) | |||||||
\(654\) | 20.9820 | 0.820461 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −10.1241 | −0.395281 | ||||||||
\(657\) | 11.4726 | 0.447588 | ||||||||
\(658\) | −11.3526 | −0.442570 | ||||||||
\(659\) | −2.58183 | −0.100574 | −0.0502869 | − | 0.998735i | \(-0.516014\pi\) | ||||
−0.0502869 | + | 0.998735i | \(0.516014\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.8765 | 0.967582 | 0.483791 | − | 0.875183i | \(-0.339259\pi\) | ||||
0.483791 | + | 0.875183i | \(0.339259\pi\) | |||||||
\(662\) | −8.81151 | −0.342469 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 37.1656 | 1.44231 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −25.8970 | −1.00349 | ||||||||
\(667\) | −0.0962625 | −0.00372730 | ||||||||
\(668\) | 5.37460 | 0.207949 | ||||||||
\(669\) | −28.6791 | −1.10880 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.0506 | 0.696834 | ||||||||
\(672\) | −23.6773 | −0.913370 | ||||||||
\(673\) | −43.3222 | −1.66995 | −0.834974 | − | 0.550289i | \(-0.814517\pi\) | ||||
−0.834974 | + | 0.550289i | \(0.814517\pi\) | |||||||
\(674\) | −5.32051 | −0.204938 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 41.3625 | 1.58969 | 0.794845 | − | 0.606813i | \(-0.207552\pi\) | ||||
0.794845 | + | 0.606813i | \(0.207552\pi\) | |||||||
\(678\) | −20.1281 | −0.773016 | ||||||||
\(679\) | 43.8078 | 1.68119 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17.8003 | −0.682110 | ||||||||
\(682\) | −35.8004 | −1.37087 | ||||||||
\(683\) | −2.62688 | −0.100515 | −0.0502574 | − | 0.998736i | \(-0.516004\pi\) | ||||
−0.0502574 | + | 0.998736i | \(0.516004\pi\) | |||||||
\(684\) | −2.83459 | −0.108383 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −4.56057 | −0.174123 | ||||||||
\(687\) | 33.5862 | 1.28139 | ||||||||
\(688\) | −3.07045 | −0.117060 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.2753 | −0.581099 | −0.290550 | − | 0.956860i | \(-0.593838\pi\) | ||||
−0.290550 | + | 0.956860i | \(0.593838\pi\) | |||||||
\(692\) | −2.28435 | −0.0868380 | ||||||||
\(693\) | −47.1765 | −1.79209 | ||||||||
\(694\) | −32.5744 | −1.23651 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.176723 | 0.00669865 | ||||||||
\(697\) | 4.22414 | 0.160001 | ||||||||
\(698\) | −28.7493 | −1.08818 | ||||||||
\(699\) | 22.1474 | 0.837692 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −48.1947 | −1.82029 | −0.910144 | − | 0.414292i | \(-0.864029\pi\) | ||||
−0.910144 | + | 0.414292i | \(0.864029\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.7404 | 0.744522 | ||||||||
\(704\) | 47.6205 | 1.79477 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.99767 | 0.263361 | ||||||||
\(707\) | 14.5967 | 0.548964 | ||||||||
\(708\) | −0.204845 | −0.00769856 | ||||||||
\(709\) | −38.8699 | −1.45979 | −0.729896 | − | 0.683559i | \(-0.760431\pi\) | ||||
−0.729896 | + | 0.683559i | \(0.760431\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −29.2301 | −1.09621 | ||||||||
\(712\) | −49.5008 | −1.85512 | ||||||||
\(713\) | 21.2711 | 0.796607 | ||||||||
\(714\) | −11.5915 | −0.433801 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −9.54600 | −0.356751 | ||||||||
\(717\) | 46.4452 | 1.73453 | ||||||||
\(718\) | 30.1974 | 1.12696 | ||||||||
\(719\) | 6.61660 | 0.246758 | 0.123379 | − | 0.992360i | \(-0.460627\pi\) | ||||
0.123379 | + | 0.992360i | \(0.460627\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −64.4560 | −2.40047 | ||||||||
\(722\) | 16.9005 | 0.628971 | ||||||||
\(723\) | −54.2629 | −2.01806 | ||||||||
\(724\) | −9.26867 | −0.344467 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 50.7945 | 1.88516 | ||||||||
\(727\) | 18.3735 | 0.681435 | 0.340717 | − | 0.940166i | \(-0.389330\pi\) | ||||
0.340717 | + | 0.940166i | \(0.389330\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −16.1420 | −0.597853 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.28110 | 0.0473830 | ||||||||
\(732\) | 4.01534 | 0.148411 | ||||||||
\(733\) | −0.791131 | −0.0292211 | −0.0146105 | − | 0.999893i | \(-0.504651\pi\) | ||||
−0.0146105 | + | 0.999893i | \(0.504651\pi\) | |||||||
\(734\) | 31.7772 | 1.17292 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −10.9774 | −0.404634 | ||||||||
\(737\) | −34.3786 | −1.26635 | ||||||||
\(738\) | −11.1039 | −0.408739 | ||||||||
\(739\) | 31.1853 | 1.14717 | 0.573585 | − | 0.819146i | \(-0.305552\pi\) | ||||
0.573585 | + | 0.819146i | \(0.305552\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 19.4938 | 0.715639 | ||||||||
\(743\) | −5.56304 | −0.204088 | −0.102044 | − | 0.994780i | \(-0.532538\pi\) | ||||
−0.102044 | + | 0.994780i | \(0.532538\pi\) | |||||||
\(744\) | −39.0503 | −1.43165 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 16.1053 | 0.589658 | ||||||||
\(747\) | 29.5862 | 1.08250 | ||||||||
\(748\) | −3.11523 | −0.113904 | ||||||||
\(749\) | −32.8765 | −1.20128 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35.2097 | −1.28482 | −0.642410 | − | 0.766361i | \(-0.722065\pi\) | ||||
−0.642410 | + | 0.766361i | \(0.722065\pi\) | |||||||
\(752\) | 7.01343 | 0.255754 | ||||||||
\(753\) | −27.6142 | −1.00632 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.41186 | 0.0877186 | ||||||||
\(757\) | −50.0446 | −1.81890 | −0.909451 | − | 0.415810i | \(-0.863498\pi\) | ||||
−0.909451 | + | 0.415810i | \(0.863498\pi\) | |||||||
\(758\) | −31.7091 | −1.15173 | ||||||||
\(759\) | −48.7715 | −1.77029 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 44.8209 | 1.62476 | 0.812379 | − | 0.583130i | \(-0.198172\pi\) | ||||
0.812379 | + | 0.583130i | \(0.198172\pi\) | |||||||
\(762\) | 32.5313 | 1.17848 | ||||||||
\(763\) | −26.5552 | −0.961364 | ||||||||
\(764\) | −14.0061 | −0.506725 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −11.7092 | −0.423072 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 26.6361 | 0.961148 | ||||||||
\(769\) | −39.3633 | −1.41948 | −0.709739 | − | 0.704465i | \(-0.751187\pi\) | ||||
−0.709739 | + | 0.704465i | \(0.751187\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.9440 | −0.466168 | ||||||||
\(772\) | 11.1528 | 0.401399 | ||||||||
\(773\) | −48.7805 | −1.75451 | −0.877256 | − | 0.480022i | \(-0.840629\pi\) | ||||
−0.877256 | + | 0.480022i | \(0.840629\pi\) | |||||||
\(774\) | −3.36758 | −0.121045 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −37.2869 | −1.33852 | ||||||||
\(777\) | 73.0840 | 2.62188 | ||||||||
\(778\) | −6.86841 | −0.246244 | ||||||||
\(779\) | 8.46410 | 0.303258 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −58.0013 | −2.07545 | ||||||||
\(782\) | −5.37415 | −0.192179 | ||||||||
\(783\) | −0.0323322 | −0.00115546 | ||||||||
\(784\) | −16.1718 | −0.577566 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −30.0618 | −1.07227 | ||||||||
\(787\) | −39.8608 | −1.42088 | −0.710442 | − | 0.703756i | \(-0.751505\pi\) | ||||
−0.710442 | + | 0.703756i | \(0.751505\pi\) | |||||||
\(788\) | −0.869338 | −0.0309689 | ||||||||
\(789\) | 15.9984 | 0.569559 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 25.4745 | 0.905771 | ||||||||
\(792\) | 40.1541 | 1.42682 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −20.4490 | −0.725709 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −12.9759 | −0.459917 | ||||||||
\(797\) | −26.2118 | −0.928470 | −0.464235 | − | 0.885712i | \(-0.653671\pi\) | ||||
−0.464235 | + | 0.885712i | \(0.653671\pi\) | |||||||
\(798\) | −23.2264 | −0.822206 | ||||||||
\(799\) | −2.92625 | −0.103523 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −39.4057 | −1.39233 | ||||||||
\(802\) | 16.9269 | 0.597708 | ||||||||
\(803\) | 25.2641 | 0.891551 | ||||||||
\(804\) | −7.64750 | −0.269707 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.31643 | 0.116744 | ||||||||
\(808\) | −12.4239 | −0.437072 | ||||||||
\(809\) | 22.2136 | 0.780990 | 0.390495 | − | 0.920605i | \(-0.372304\pi\) | ||||
0.390495 | + | 0.920605i | \(0.372304\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.0950 | 0.670515 | 0.335257 | − | 0.942127i | \(-0.391177\pi\) | ||||
0.335257 | + | 0.942127i | \(0.391177\pi\) | |||||||
\(812\) | −0.0456133 | −0.00160071 | ||||||||
\(813\) | 23.2513 | 0.815457 | ||||||||
\(814\) | −57.0284 | −1.99885 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 7.16104 | 0.250686 | ||||||||
\(817\) | 2.56699 | 0.0898076 | ||||||||
\(818\) | −35.8894 | −1.25484 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −34.1584 | −1.19214 | −0.596068 | − | 0.802934i | \(-0.703271\pi\) | ||||
−0.596068 | + | 0.802934i | \(0.703271\pi\) | |||||||
\(822\) | −10.7718 | −0.375708 | ||||||||
\(823\) | −4.07940 | −0.142199 | −0.0710995 | − | 0.997469i | \(-0.522651\pi\) | ||||
−0.0710995 | + | 0.997469i | \(0.522651\pi\) | |||||||
\(824\) | 54.8616 | 1.91119 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.752744 | −0.0261913 | ||||||||
\(827\) | 54.8780 | 1.90830 | 0.954148 | − | 0.299337i | \(-0.0967654\pi\) | ||||
0.954148 | + | 0.299337i | \(0.0967654\pi\) | |||||||
\(828\) | −4.86550 | −0.169088 | ||||||||
\(829\) | 8.14950 | 0.283044 | 0.141522 | − | 0.989935i | \(-0.454800\pi\) | ||||
0.141522 | + | 0.989935i | \(0.454800\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −40.8697 | −1.41775 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.74745 | 0.233785 | ||||||||
\(834\) | 5.72866 | 0.198367 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −6.24213 | −0.215889 | ||||||||
\(837\) | 7.14441 | 0.246947 | ||||||||
\(838\) | −8.49869 | −0.293582 | ||||||||
\(839\) | −21.8865 | −0.755606 | −0.377803 | − | 0.925886i | \(-0.623320\pi\) | ||||
−0.377803 | + | 0.925886i | \(0.623320\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9994 | −0.999979 | ||||||||
\(842\) | −8.68570 | −0.299329 | ||||||||
\(843\) | −25.0370 | −0.862321 | ||||||||
\(844\) | 0.171902 | 0.00591710 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 7.69213 | 0.264461 | ||||||||
\(847\) | −64.2866 | −2.20891 | ||||||||
\(848\) | −12.0429 | −0.413556 | ||||||||
\(849\) | 3.07480 | 0.105527 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 33.8838 | 1.16152 | ||||||||
\(852\) | −12.9024 | −0.442028 | ||||||||
\(853\) | 19.2240 | 0.658217 | 0.329108 | − | 0.944292i | \(-0.393252\pi\) | ||||
0.329108 | + | 0.944292i | \(0.393252\pi\) | |||||||
\(854\) | 14.7552 | 0.504911 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 27.9827 | 0.956430 | ||||||||
\(857\) | 27.8197 | 0.950302 | 0.475151 | − | 0.879904i | \(-0.342393\pi\) | ||||
0.475151 | + | 0.879904i | \(0.342393\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 45.7355 | 1.56048 | 0.780238 | − | 0.625482i | \(-0.215098\pi\) | ||||
0.780238 | + | 0.625482i | \(0.215098\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 31.3363 | 1.06794 | ||||||||
\(862\) | −36.8521 | −1.25519 | ||||||||
\(863\) | −54.8186 | −1.86605 | −0.933024 | − | 0.359814i | \(-0.882840\pi\) | ||||
−0.933024 | + | 0.359814i | \(0.882840\pi\) | |||||||
\(864\) | −3.68705 | −0.125436 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.46378 | 0.0497413 | ||||||||
\(867\) | 36.6604 | 1.24505 | ||||||||
\(868\) | 10.0791 | 0.342108 | ||||||||
\(869\) | −64.3684 | −2.18355 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 22.6024 | 0.765415 | ||||||||
\(873\) | −29.6827 | −1.00461 | ||||||||
\(874\) | −10.7684 | −0.364247 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 5.61999 | 0.189882 | ||||||||
\(877\) | 27.3794 | 0.924537 | 0.462269 | − | 0.886740i | \(-0.347036\pi\) | ||||
0.462269 | + | 0.886740i | \(0.347036\pi\) | |||||||
\(878\) | 20.1908 | 0.681407 | ||||||||
\(879\) | 43.7125 | 1.47439 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.4426 | −1.16040 | −0.580200 | − | 0.814474i | \(-0.697026\pi\) | ||||
−0.580200 | + | 0.814474i | \(0.697026\pi\) | |||||||
\(882\) | −17.7368 | −0.597230 | ||||||||
\(883\) | 17.3592 | 0.584183 | 0.292092 | − | 0.956390i | \(-0.405649\pi\) | ||||
0.292092 | + | 0.956390i | \(0.405649\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.56115 | 0.186831 | ||||||||
\(887\) | 31.1427 | 1.04567 | 0.522835 | − | 0.852434i | \(-0.324874\pi\) | ||||
0.522835 | + | 0.852434i | \(0.324874\pi\) | |||||||
\(888\) | −62.2053 | −2.08747 | ||||||||
\(889\) | −41.1722 | −1.38087 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −55.6927 | −1.86578 | ||||||||
\(892\) | −6.30042 | −0.210954 | ||||||||
\(893\) | −5.86345 | −0.196213 | ||||||||
\(894\) | −15.6960 | −0.524952 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 18.6224 | 0.622132 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −16.8953 | −0.563804 | ||||||||
\(899\) | −0.135116 | −0.00450636 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.02473 | 0.167398 | ||||||||
\(902\) | −24.4521 | −0.814167 | ||||||||
\(903\) | 9.50367 | 0.316262 | ||||||||
\(904\) | −21.6826 | −0.721152 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −13.9090 | −0.462097 | ||||||||
\(907\) | −17.6057 | −0.584587 | −0.292294 | − | 0.956329i | \(-0.594418\pi\) | ||||
−0.292294 | + | 0.956329i | \(0.594418\pi\) | |||||||
\(908\) | −3.91050 | −0.129774 | ||||||||
\(909\) | −9.89022 | −0.328038 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 50.0232 | 1.65734 | 0.828671 | − | 0.559737i | \(-0.189098\pi\) | ||||
0.828671 | + | 0.559737i | \(0.189098\pi\) | |||||||
\(912\) | 14.3489 | 0.475139 | ||||||||
\(913\) | 65.1526 | 2.15624 | ||||||||
\(914\) | 48.9272 | 1.61837 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.37844 | 0.243791 | ||||||||
\(917\) | 38.0468 | 1.25641 | ||||||||
\(918\) | −1.80504 | −0.0595752 | ||||||||
\(919\) | −7.61556 | −0.251214 | −0.125607 | − | 0.992080i | \(-0.540088\pi\) | ||||
−0.125607 | + | 0.992080i | \(0.540088\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 33.3611 | 1.09928 | ||||||||
\(922\) | 9.19522 | 0.302828 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −23.1100 | −0.760264 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 28.4225 | 0.934022 | ||||||||
\(927\) | 43.6733 | 1.43442 | ||||||||
\(928\) | 0.0697297 | 0.00228899 | ||||||||
\(929\) | −14.1239 | −0.463391 | −0.231695 | − | 0.972788i | \(-0.574427\pi\) | ||||
−0.231695 | + | 0.972788i | \(0.574427\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.5202 | 0.443106 | ||||||||
\(932\) | 4.86550 | 0.159375 | ||||||||
\(933\) | −6.43937 | −0.210816 | ||||||||
\(934\) | −27.6012 | −0.903138 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.9317 | 0.781815 | 0.390908 | − | 0.920430i | \(-0.372161\pi\) | ||||
0.390908 | + | 0.920430i | \(0.372161\pi\) | |||||||
\(938\) | −28.1023 | −0.917571 | ||||||||
\(939\) | −38.2157 | −1.24712 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25.3591 | −0.826683 | −0.413342 | − | 0.910576i | \(-0.635638\pi\) | ||||
−0.413342 | + | 0.910576i | \(0.635638\pi\) | |||||||
\(942\) | −28.5614 | −0.930582 | ||||||||
\(943\) | 14.5284 | 0.473110 | ||||||||
\(944\) | 0.465033 | 0.0151355 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.41584 | −0.241110 | ||||||||
\(947\) | −41.4223 | −1.34604 | −0.673021 | − | 0.739623i | \(-0.735004\pi\) | ||||
−0.673021 | + | 0.739623i | \(0.735004\pi\) | |||||||
\(948\) | −14.3187 | −0.465051 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.16480 | 0.135053 | ||||||||
\(952\) | −12.4867 | −0.404696 | ||||||||
\(953\) | −24.3026 | −0.787237 | −0.393619 | − | 0.919274i | \(-0.628777\pi\) | ||||
−0.393619 | + | 0.919274i | \(0.628777\pi\) | |||||||
\(954\) | −13.2083 | −0.427636 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 10.2034 | 0.330001 | ||||||||
\(957\) | 0.309801 | 0.0100144 | ||||||||
\(958\) | −25.1802 | −0.813536 | ||||||||
\(959\) | 13.6329 | 0.440231 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.14359 | −0.0368901 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 22.2760 | 0.717834 | ||||||||
\(964\) | −11.9209 | −0.383945 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −39.8675 | −1.28272 | ||||||||
\(967\) | −23.6784 | −0.761445 | −0.380722 | − | 0.924689i | \(-0.624325\pi\) | ||||
−0.380722 | + | 0.924689i | \(0.624325\pi\) | |||||||
\(968\) | 54.7173 | 1.75868 | ||||||||
\(969\) | −5.98685 | −0.192325 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.9722 | −0.544663 | −0.272332 | − | 0.962203i | \(-0.587795\pi\) | ||||
−0.272332 | + | 0.962203i | \(0.587795\pi\) | |||||||
\(972\) | −10.3791 | −0.332908 | ||||||||
\(973\) | −7.25030 | −0.232434 | ||||||||
\(974\) | 3.70303 | 0.118653 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.11550 | −0.291780 | ||||||||
\(977\) | −24.9994 | −0.799802 | −0.399901 | − | 0.916558i | \(-0.630956\pi\) | ||||
−0.399901 | + | 0.916558i | \(0.630956\pi\) | |||||||
\(978\) | −19.2900 | −0.616826 | ||||||||
\(979\) | −86.7765 | −2.77339 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.9930 | 0.574471 | ||||||||
\(982\) | −13.0116 | −0.415218 | ||||||||
\(983\) | 27.3418 | 0.872068 | 0.436034 | − | 0.899930i | \(-0.356383\pi\) | ||||
0.436034 | + | 0.899930i | \(0.356383\pi\) | |||||||
\(984\) | −26.6718 | −0.850267 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.0341370 | 0.00108715 | ||||||||
\(987\) | −21.7080 | −0.690975 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.40617 | 0.140108 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.0760 | 0.510672 | 0.255336 | − | 0.966852i | \(-0.417814\pi\) | ||||
0.255336 | + | 0.966852i | \(0.417814\pi\) | |||||||
\(992\) | −15.4081 | −0.489208 | ||||||||
\(993\) | −16.8491 | −0.534690 | ||||||||
\(994\) | −47.4123 | −1.50383 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 14.4932 | 0.459234 | ||||||||
\(997\) | 34.5612 | 1.09456 | 0.547282 | − | 0.836948i | \(-0.315663\pi\) | ||||
0.547282 | + | 0.836948i | \(0.315663\pi\) | |||||||
\(998\) | −41.3649 | −1.30938 | ||||||||
\(999\) | 11.3807 | 0.360070 |
(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 | 4225.2.a.bi.1.2 | 4 | ||
5.4 | even | 2 | 845.2.a.m.1.3 | 4 | |||
13.2 | odd | 12 | 325.2.n.d.251.2 | 8 | |||
13.7 | odd | 12 | 325.2.n.d.101.2 | 8 | |||
13.12 | even | 2 | 4225.2.a.bl.1.3 | 4 | |||
15.14 | odd | 2 | 7605.2.a.cf.1.2 | 4 | |||
65.2 | even | 12 | 325.2.m.c.199.3 | 8 | |||
65.4 | even | 6 | 845.2.e.n.146.3 | 8 | |||
65.7 | even | 12 | 325.2.m.b.49.2 | 8 | |||
65.9 | even | 6 | 845.2.e.m.146.2 | 8 | |||
65.19 | odd | 12 | 845.2.m.g.361.2 | 8 | |||
65.24 | odd | 12 | 845.2.m.g.316.2 | 8 | |||
65.28 | even | 12 | 325.2.m.b.199.2 | 8 | |||
65.29 | even | 6 | 845.2.e.m.191.2 | 8 | |||
65.33 | even | 12 | 325.2.m.c.49.3 | 8 | |||
65.34 | odd | 4 | 845.2.c.g.506.6 | 8 | |||
65.44 | odd | 4 | 845.2.c.g.506.3 | 8 | |||
65.49 | even | 6 | 845.2.e.n.191.3 | 8 | |||
65.54 | odd | 12 | 65.2.m.a.56.3 | yes | 8 | ||
65.59 | odd | 12 | 65.2.m.a.36.3 | ✓ | 8 | ||
65.64 | even | 2 | 845.2.a.l.1.2 | 4 | |||
195.59 | even | 12 | 585.2.bu.c.361.2 | 8 | |||
195.119 | even | 12 | 585.2.bu.c.316.2 | 8 | |||
195.194 | odd | 2 | 7605.2.a.cj.1.3 | 4 | |||
260.59 | even | 12 | 1040.2.da.b.881.4 | 8 | |||
260.119 | even | 12 | 1040.2.da.b.641.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.2.m.a.36.3 | ✓ | 8 | 65.59 | odd | 12 | ||
65.2.m.a.56.3 | yes | 8 | 65.54 | odd | 12 | ||
325.2.m.b.49.2 | 8 | 65.7 | even | 12 | |||
325.2.m.b.199.2 | 8 | 65.28 | even | 12 | |||
325.2.m.c.49.3 | 8 | 65.33 | even | 12 | |||
325.2.m.c.199.3 | 8 | 65.2 | even | 12 | |||
325.2.n.d.101.2 | 8 | 13.7 | odd | 12 | |||
325.2.n.d.251.2 | 8 | 13.2 | odd | 12 | |||
585.2.bu.c.316.2 | 8 | 195.119 | even | 12 | |||
585.2.bu.c.361.2 | 8 | 195.59 | even | 12 | |||
845.2.a.l.1.2 | 4 | 65.64 | even | 2 | |||
845.2.a.m.1.3 | 4 | 5.4 | even | 2 | |||
845.2.c.g.506.3 | 8 | 65.44 | odd | 4 | |||
845.2.c.g.506.6 | 8 | 65.34 | odd | 4 | |||
845.2.e.m.146.2 | 8 | 65.9 | even | 6 | |||
845.2.e.m.191.2 | 8 | 65.29 | even | 6 | |||
845.2.e.n.146.3 | 8 | 65.4 | even | 6 | |||
845.2.e.n.191.3 | 8 | 65.49 | even | 6 | |||
845.2.m.g.316.2 | 8 | 65.24 | odd | 12 | |||
845.2.m.g.361.2 | 8 | 65.19 | odd | 12 | |||
1040.2.da.b.641.4 | 8 | 260.119 | even | 12 | |||
1040.2.da.b.881.4 | 8 | 260.59 | even | 12 | |||
4225.2.a.bi.1.2 | 4 | 1.1 | even | 1 | trivial | ||
4225.2.a.bl.1.3 | 4 | 13.12 | even | 2 | |||
7605.2.a.cf.1.2 | 4 | 15.14 | odd | 2 | |||
7605.2.a.cj.1.3 | 4 | 195.194 | odd | 2 |