Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [845,2,Mod(1,845)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(845, 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("845.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 845 = 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 845.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: | \(6.74735897080\) |
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 | 1.3 | ||
Root | \(1.21969\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 845.1 |
$q$-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 | \(-0.358082\pi\) | ||||
0.431224 | + | 0.902245i | \(0.358082\pi\) | |||||||
\(3\) | 2.33225 | 1.34652 | 0.673262 | − | 0.739404i | \(-0.264893\pi\) | ||||
0.673262 | + | 0.739404i | \(0.264893\pi\) | |||||||
\(4\) | −0.512364 | −0.256182 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 2.84461 | 1.16131 | ||||||||
\(7\) | 3.60020 | 1.36075 | 0.680373 | − | 0.732866i | \(-0.261818\pi\) | ||||
0.680373 | + | 0.732866i | \(0.261818\pi\) | |||||||
\(8\) | −3.06430 | −1.08339 | ||||||||
\(9\) | 2.43937 | 0.813125 | ||||||||
\(10\) | −1.21969 | −0.385699 | ||||||||
\(11\) | 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 | ||||||||
\(15\) | −2.33225 | −0.602183 | ||||||||
\(16\) | −2.71276 | −0.678189 | ||||||||
\(17\) | −1.13186 | −0.274515 | −0.137258 | − | 0.990535i | \(-0.543829\pi\) | ||||
−0.137258 | + | 0.990535i | \(0.543829\pi\) | |||||||
\(18\) | 2.97527 | 0.701278 | ||||||||
\(19\) | 2.26795 | 0.520303 | 0.260152 | − | 0.965568i | \(-0.416227\pi\) | ||||
0.260152 | + | 0.965568i | \(0.416227\pi\) | |||||||
\(20\) | 0.512364 | 0.114568 | ||||||||
\(21\) | 8.39654 | 1.83228 | ||||||||
\(22\) | 6.55193 | 1.39688 | ||||||||
\(23\) | −3.89287 | −0.811720 | −0.405860 | − | 0.913935i | \(-0.633028\pi\) | ||||
−0.405860 | + | 0.913935i | \(0.633028\pi\) | |||||||
\(24\) | −7.14670 | −1.45881 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 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 | \(0.500731\pi\) | |||||||
\(30\) | −2.84461 | −0.519352 | ||||||||
\(31\) | 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 | ||||||||
\(35\) | −3.60020 | −0.608544 | ||||||||
\(36\) | −1.24985 | −0.208308 | ||||||||
\(37\) | −8.70406 | −1.43094 | −0.715470 | − | 0.698644i | \(-0.753787\pi\) | ||||
−0.715470 | + | 0.698644i | \(0.753787\pi\) | |||||||
\(38\) | 2.76619 | 0.448735 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.06430 | 0.484508 | ||||||||
\(41\) | 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 | \(-0.527505\pi\) | ||||
−0.0863031 | + | 0.996269i | \(0.527505\pi\) | |||||||
\(44\) | −2.75232 | −0.414929 | ||||||||
\(45\) | −2.43937 | −0.363640 | ||||||||
\(46\) | −4.74809 | −0.700067 | ||||||||
\(47\) | 2.58535 | 0.377113 | 0.188556 | − | 0.982062i | \(-0.439619\pi\) | ||||
0.188556 | + | 0.982062i | \(0.439619\pi\) | |||||||
\(48\) | −6.32681 | −0.913197 | ||||||||
\(49\) | 5.96141 | 0.851630 | ||||||||
\(50\) | 1.21969 | 0.172490 | ||||||||
\(51\) | −2.63977 | −0.369641 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.43937 | −0.609795 | −0.304897 | − | 0.952385i | \(-0.598622\pi\) | ||||
−0.304897 | + | 0.952385i | \(0.598622\pi\) | |||||||
\(54\) | −1.59476 | −0.217020 | ||||||||
\(55\) | −5.37182 | −0.724336 | ||||||||
\(56\) | −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 | \(0.503552\pi\) | |||||||
\(60\) | 1.19496 | 0.154269 | ||||||||
\(61\) | 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 | \(-0.372153\pi\) | ||||
0.390930 | + | 0.920420i | \(0.372153\pi\) | |||||||
\(68\) | 0.579922 | 0.0703258 | ||||||||
\(69\) | −9.07914 | −1.09300 | ||||||||
\(70\) | −4.39111 | −0.524838 | ||||||||
\(71\) | −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 | \(-0.588753\pi\) | ||||
−0.275227 | + | 0.961379i | \(0.588753\pi\) | |||||||
\(74\) | −10.6162 | −1.23411 | ||||||||
\(75\) | 2.33225 | 0.269305 | ||||||||
\(76\) | −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 | \(0.735457\pi\) | |||||||
\(80\) | 2.71276 | 0.303295 | ||||||||
\(81\) | −10.3676 | −1.15195 | ||||||||
\(82\) | 4.55193 | 0.502677 | ||||||||
\(83\) | −12.1286 | −1.33129 | −0.665643 | − | 0.746270i | \(-0.731843\pi\) | ||||
−0.665643 | + | 0.746270i | \(0.731843\pi\) | |||||||
\(84\) | −4.30209 | −0.469396 | ||||||||
\(85\) | 1.13186 | 0.122767 | ||||||||
\(86\) | −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 | \(0.827158\pi\) | |||||||
\(90\) | −2.97527 | −0.313621 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.99457 | 0.207948 | ||||||||
\(93\) | 12.7436 | 1.32145 | ||||||||
\(94\) | 3.15332 | 0.325240 | ||||||||
\(95\) | −2.26795 | −0.232687 | ||||||||
\(96\) | 6.57666 | 0.671228 | ||||||||
\(97\) | 12.1682 | 1.23549 | 0.617745 | − | 0.786379i | \(-0.288046\pi\) | ||||
0.617745 | + | 0.786379i | \(0.288046\pi\) | |||||||
\(98\) | 7.27105 | 0.734487 | ||||||||
\(99\) | 13.1039 | 1.31699 | ||||||||
\(100\) | −0.512364 | −0.0512364 | ||||||||
\(101\) | −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 | \(-0.843831\pi\) | ||||
−0.882041 | + | 0.471173i | \(0.843831\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.39654 | −0.819419 | ||||||||
\(106\) | −5.41465 | −0.525917 | ||||||||
\(107\) | −9.13186 | −0.882810 | −0.441405 | − | 0.897308i | \(-0.645520\pi\) | ||||
−0.441405 | + | 0.897308i | \(0.645520\pi\) | |||||||
\(108\) | 0.669925 | 0.0644636 | ||||||||
\(109\) | 7.37605 | 0.706498 | 0.353249 | − | 0.935529i | \(-0.385077\pi\) | ||||
0.353249 | + | 0.935529i | \(0.385077\pi\) | |||||||
\(110\) | −6.55193 | −0.624702 | ||||||||
\(111\) | −20.3000 | −1.92679 | ||||||||
\(112\) | −9.76645 | −0.922843 | ||||||||
\(113\) | 7.07588 | 0.665643 | 0.332821 | − | 0.942990i | \(-0.391999\pi\) | ||||
0.332821 | + | 0.942990i | \(0.391999\pi\) | |||||||
\(114\) | 6.45143 | 0.604232 | ||||||||
\(115\) | 3.89287 | 0.363012 | ||||||||
\(116\) | 0.0126697 | 0.00117635 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.209084 | −0.0192478 | ||||||||
\(119\) | −4.07490 | −0.373545 | ||||||||
\(120\) | 7.14670 | 0.652401 | ||||||||
\(121\) | 17.8564 | 1.62331 | ||||||||
\(122\) | 4.09843 | 0.371055 | ||||||||
\(123\) | 8.70406 | 0.784819 | ||||||||
\(124\) | −2.79961 | −0.251412 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 10.7116 | 0.954262 | ||||||||
\(127\) | −11.4361 | −1.01479 | −0.507395 | − | 0.861713i | \(-0.669392\pi\) | ||||
−0.507395 | + | 0.861713i | \(0.669392\pi\) | |||||||
\(128\) | 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 | ||||||||
\(135\) | 1.30752 | 0.112533 | ||||||||
\(136\) | 3.46834 | 0.297408 | ||||||||
\(137\) | 3.78672 | 0.323522 | 0.161761 | − | 0.986830i | \(-0.448283\pi\) | ||||
0.161761 | + | 0.986830i | \(0.448283\pi\) | |||||||
\(138\) | −11.0737 | −0.942656 | ||||||||
\(139\) | 2.01386 | 0.170814 | 0.0854068 | − | 0.996346i | \(-0.472781\pi\) | ||||
0.0854068 | + | 0.996346i | \(0.472781\pi\) | |||||||
\(140\) | 1.84461 | 0.155898 | ||||||||
\(141\) | 6.02968 | 0.507791 | ||||||||
\(142\) | −13.1694 | −1.10515 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −6.61742 | −0.551452 | ||||||||
\(145\) | 0.0247279 | 0.00205354 | ||||||||
\(146\) | −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 | \(0.572571\pi\) | |||||||
\(150\) | 2.84461 | 0.232261 | ||||||||
\(151\) | −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 | ||||||||
\(155\) | −5.46410 | −0.438887 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.0405 | 0.801323 | 0.400661 | − | 0.916226i | \(-0.368780\pi\) | ||||
0.400661 | + | 0.916226i | \(0.368780\pi\) | |||||||
\(158\) | −14.6150 | −1.16271 | ||||||||
\(159\) | −10.3537 | −0.821103 | ||||||||
\(160\) | −2.81988 | −0.222931 | ||||||||
\(161\) | −14.0151 | −1.10454 | ||||||||
\(162\) | −12.6452 | −0.993501 | ||||||||
\(163\) | 6.78124 | 0.531148 | 0.265574 | − | 0.964090i | \(-0.414439\pi\) | ||||
0.265574 | + | 0.964090i | \(0.414439\pi\) | |||||||
\(164\) | −1.91217 | −0.149315 | ||||||||
\(165\) | −12.5284 | −0.975335 | ||||||||
\(166\) | −14.7931 | −1.14817 | ||||||||
\(167\) | 10.4898 | 0.811726 | 0.405863 | − | 0.913934i | \(-0.366971\pi\) | ||||
0.405863 | + | 0.913934i | \(0.366971\pi\) | |||||||
\(168\) | −25.7295 | −1.98507 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 1.38051 | 0.105880 | ||||||||
\(171\) | 5.53238 | 0.423071 | ||||||||
\(172\) | 0.579922 | 0.0442186 | ||||||||
\(173\) | −4.45845 | −0.338970 | −0.169485 | − | 0.985533i | \(-0.554210\pi\) | ||||
−0.169485 | + | 0.985533i | \(0.554210\pi\) | |||||||
\(174\) | −0.0703412 | −0.00533255 | ||||||||
\(175\) | 3.60020 | 0.272149 | ||||||||
\(176\) | −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 | \(0.254835\pi\) | |||||||
\(180\) | 1.24985 | 0.0931581 | ||||||||
\(181\) | 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 | ||||||||
\(185\) | 8.70406 | 0.639935 | ||||||||
\(186\) | 15.5432 | 1.13969 | ||||||||
\(187\) | −6.08012 | −0.444622 | ||||||||
\(188\) | −1.32464 | −0.0966095 | ||||||||
\(189\) | −4.70732 | −0.342407 | ||||||||
\(190\) | −2.76619 | −0.200680 | ||||||||
\(191\) | 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 | \(-0.213471\pi\) | ||||
0.783425 | + | 0.621486i | \(0.213471\pi\) | |||||||
\(194\) | 14.8413 | 1.06555 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.05441 | −0.218172 | ||||||||
\(197\) | −1.69672 | −0.120886 | −0.0604432 | − | 0.998172i | \(-0.519251\pi\) | ||||
−0.0604432 | + | 0.998172i | \(0.519251\pi\) | |||||||
\(198\) | 15.9826 | 1.13583 | ||||||||
\(199\) | 25.3255 | 1.79527 | 0.897637 | − | 0.440735i | \(-0.145282\pi\) | ||||
0.897637 | + | 0.440735i | \(0.145282\pi\) | |||||||
\(200\) | −3.06430 | −0.216679 | ||||||||
\(201\) | 14.9259 | 1.05279 | ||||||||
\(202\) | −4.94511 | −0.347937 | ||||||||
\(203\) | −0.0890252 | −0.00624834 | ||||||||
\(204\) | 1.35252 | 0.0946954 | ||||||||
\(205\) | −3.73205 | −0.260658 | ||||||||
\(206\) | −21.8366 | −1.52143 | ||||||||
\(207\) | −9.49617 | −0.660030 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.1830 | 0.842716 | ||||||||
\(210\) | −10.2412 | −0.706707 | ||||||||
\(211\) | −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 | ||||||||
\(215\) | 1.13186 | 0.0771919 | ||||||||
\(216\) | 4.00663 | 0.272616 | ||||||||
\(217\) | 19.6718 | 1.33541 | ||||||||
\(218\) | 8.99648 | 0.609318 | ||||||||
\(219\) | −10.9688 | −0.741200 | ||||||||
\(220\) | 2.75232 | 0.185562 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −24.7597 | −1.66176 | ||||||||
\(223\) | −12.2968 | −0.823452 | −0.411726 | − | 0.911308i | \(-0.635074\pi\) | ||||
−0.411726 | + | 0.911308i | \(0.635074\pi\) | |||||||
\(224\) | 10.1521 | 0.678318 | ||||||||
\(225\) | 2.43937 | 0.162625 | ||||||||
\(226\) | 8.63036 | 0.574083 | ||||||||
\(227\) | −7.63227 | −0.506571 | −0.253286 | − | 0.967392i | \(-0.581511\pi\) | ||||
−0.253286 | + | 0.967392i | \(0.581511\pi\) | |||||||
\(228\) | −2.71011 | −0.179481 | ||||||||
\(229\) | −14.4008 | −0.951631 | −0.475815 | − | 0.879545i | \(-0.657847\pi\) | ||||
−0.475815 | + | 0.879545i | \(0.657847\pi\) | |||||||
\(230\) | 4.74809 | 0.313080 | ||||||||
\(231\) | 45.1047 | 2.96767 | ||||||||
\(232\) | 0.0757736 | 0.00497478 | ||||||||
\(233\) | 9.49617 | 0.622115 | 0.311057 | − | 0.950391i | \(-0.399317\pi\) | ||||
0.311057 | + | 0.950391i | \(0.399317\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.58535 | −0.168650 | ||||||||
\(236\) | 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 | \(0.722758\pi\) | |||||||
\(240\) | 6.32681 | 0.408394 | ||||||||
\(241\) | 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 | ||||||||
\(245\) | −5.96141 | −0.380860 | ||||||||
\(246\) | 10.6162 | 0.676866 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −16.7436 | −1.06322 | ||||||||
\(249\) | −28.2869 | −1.79261 | ||||||||
\(250\) | −1.21969 | −0.0771398 | ||||||||
\(251\) | 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 | ||||||||
\(255\) | 2.63977 | 0.165309 | ||||||||
\(256\) | −11.4208 | −0.713800 | ||||||||
\(257\) | −5.55002 | −0.346201 | −0.173100 | − | 0.984904i | \(-0.555379\pi\) | ||||
−0.173100 | + | 0.984904i | \(0.555379\pi\) | |||||||
\(258\) | −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 | \(-0.432168\pi\) | ||||
0.211493 | + | 0.977380i | \(0.432168\pi\) | |||||||
\(264\) | −38.3907 | −2.36279 | ||||||||
\(265\) | 4.43937 | 0.272709 | ||||||||
\(266\) | 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 | \(0.513803\pi\) | |||||||
\(270\) | 1.59476 | 0.0970542 | ||||||||
\(271\) | −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 | ||||||||
\(275\) | 5.37182 | 0.323933 | ||||||||
\(276\) | 4.65182 | 0.280007 | ||||||||
\(277\) | −17.5237 | −1.05290 | −0.526449 | − | 0.850206i | \(-0.676477\pi\) | ||||
−0.526449 | + | 0.850206i | \(0.676477\pi\) | |||||||
\(278\) | 2.45628 | 0.147318 | ||||||||
\(279\) | 13.3290 | 0.797986 | ||||||||
\(280\) | 11.0321 | 0.659292 | ||||||||
\(281\) | 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 | \(-0.487524\pi\) | ||||
0.0391849 | + | 0.999232i | \(0.487524\pi\) | |||||||
\(284\) | 5.53216 | 0.328273 | ||||||||
\(285\) | −5.28942 | −0.313318 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 13.4361 | 0.793109 | ||||||||
\(288\) | 6.87875 | 0.405334 | ||||||||
\(289\) | −15.7189 | −0.924641 | ||||||||
\(290\) | 0.0301603 | 0.00177107 | ||||||||
\(291\) | 28.3792 | 1.66362 | ||||||||
\(292\) | 2.40969 | 0.141016 | ||||||||
\(293\) | 18.7427 | 1.09496 | 0.547479 | − | 0.836820i | \(-0.315588\pi\) | ||||
0.547479 | + | 0.836820i | \(0.315588\pi\) | |||||||
\(294\) | 16.9579 | 0.989004 | ||||||||
\(295\) | 0.171425 | 0.00998072 | ||||||||
\(296\) | 26.6718 | 1.55027 | ||||||||
\(297\) | −7.02375 | −0.407559 | ||||||||
\(298\) | −6.72998 | −0.389857 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.19496 | −0.0689910 | ||||||||
\(301\) | −4.07490 | −0.234873 | ||||||||
\(302\) | −5.96380 | −0.343178 | ||||||||
\(303\) | −9.45589 | −0.543226 | ||||||||
\(304\) | −6.15239 | −0.352864 | ||||||||
\(305\) | −3.36023 | −0.192406 | ||||||||
\(306\) | −3.36758 | −0.192512 | ||||||||
\(307\) | 14.3043 | 0.816387 | 0.408194 | − | 0.912895i | \(-0.366159\pi\) | ||||
0.408194 | + | 0.912895i | \(0.366159\pi\) | |||||||
\(308\) | −9.90891 | −0.564612 | ||||||||
\(309\) | −41.7553 | −2.37538 | ||||||||
\(310\) | −6.66449 | −0.378518 | ||||||||
\(311\) | 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 | \(-0.653259\pi\) | ||||
−0.463090 | + | 0.886311i | \(0.653259\pi\) | |||||||
\(314\) | 12.2463 | 0.691100 | ||||||||
\(315\) | −8.78222 | −0.494822 | ||||||||
\(316\) | 6.13946 | 0.345372 | ||||||||
\(317\) | 1.78575 | 0.100297 | 0.0501487 | − | 0.998742i | \(-0.484030\pi\) | ||||
0.0501487 | + | 0.998742i | \(0.484030\pi\) | |||||||
\(318\) | −12.6283 | −0.708159 | ||||||||
\(319\) | −0.132834 | −0.00743725 | ||||||||
\(320\) | −8.86488 | −0.495562 | ||||||||
\(321\) | −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 | ||||||||
\(330\) | −15.2807 | −0.841176 | ||||||||
\(331\) | 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 | ||||||||
\(335\) | −6.39980 | −0.349659 | ||||||||
\(336\) | −22.7778 | −1.24263 | ||||||||
\(337\) | −4.36219 | −0.237624 | −0.118812 | − | 0.992917i | \(-0.537909\pi\) | ||||
−0.118812 | + | 0.992917i | \(0.537909\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.5027 | 0.896303 | ||||||||
\(340\) | −0.579922 | −0.0314507 | ||||||||
\(341\) | 29.3521 | 1.58951 | ||||||||
\(342\) | 6.74777 | 0.364877 | ||||||||
\(343\) | −3.73913 | −0.201894 | ||||||||
\(344\) | 3.46834 | 0.187000 | ||||||||
\(345\) | 9.07914 | 0.488804 | ||||||||
\(346\) | −5.43792 | −0.292344 | ||||||||
\(347\) | −26.7072 | −1.43372 | −0.716858 | − | 0.697219i | \(-0.754420\pi\) | ||||
−0.716858 | + | 0.697219i | \(0.754420\pi\) | |||||||
\(348\) | 0.0295488 | 0.00158398 | ||||||||
\(349\) | 23.5711 | 1.26173 | 0.630865 | − | 0.775892i | \(-0.282700\pi\) | ||||
0.630865 | + | 0.775892i | \(0.282700\pi\) | |||||||
\(350\) | 4.39111 | 0.234715 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 15.1479 | 0.807385 | ||||||||
\(353\) | 5.73727 | 0.305364 | 0.152682 | − | 0.988275i | \(-0.451209\pi\) | ||||
0.152682 | + | 0.988275i | \(0.451209\pi\) | |||||||
\(354\) | −0.487636 | −0.0259176 | ||||||||
\(355\) | 10.7973 | 0.573063 | ||||||||
\(356\) | 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 | \(0.726636\pi\) | |||||||
\(360\) | 7.47497 | 0.393965 | ||||||||
\(361\) | −13.8564 | −0.729285 | ||||||||
\(362\) | 22.0641 | 1.15967 | ||||||||
\(363\) | 41.6455 | 2.18582 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.70308 | 0.246171 | ||||||||
\(366\) | 9.55856 | 0.499634 | ||||||||
\(367\) | 26.0535 | 1.35998 | 0.679992 | − | 0.733220i | \(-0.261983\pi\) | ||||
0.679992 | + | 0.733220i | \(0.261983\pi\) | |||||||
\(368\) | 10.5604 | 0.550499 | ||||||||
\(369\) | 9.10387 | 0.473928 | ||||||||
\(370\) | 10.6162 | 0.551912 | ||||||||
\(371\) | −15.9826 | −0.829776 | ||||||||
\(372\) | −6.52938 | −0.338532 | ||||||||
\(373\) | 13.2045 | 0.683702 | 0.341851 | − | 0.939754i | \(-0.388946\pi\) | ||||
0.341851 | + | 0.939754i | \(0.388946\pi\) | |||||||
\(374\) | −7.41584 | −0.383464 | ||||||||
\(375\) | −2.33225 | −0.120437 | ||||||||
\(376\) | −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 | \(0.267276\pi\) | |||||||
\(380\) | 1.16202 | 0.0596101 | ||||||||
\(381\) | −26.6718 | −1.36644 | ||||||||
\(382\) | 33.3418 | 1.70591 | ||||||||
\(383\) | −9.60020 | −0.490547 | −0.245274 | − | 0.969454i | \(-0.578878\pi\) | ||||
−0.245274 | + | 0.969454i | \(0.578878\pi\) | |||||||
\(384\) | 12.0638 | 0.615629 | ||||||||
\(385\) | −19.3396 | −0.985637 | ||||||||
\(386\) | 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 | ||||||||
\(395\) | 11.9826 | 0.602911 | ||||||||
\(396\) | −6.71395 | −0.337389 | ||||||||
\(397\) | −16.7658 | −0.841452 | −0.420726 | − | 0.907188i | \(-0.638225\pi\) | ||||
−0.420726 | + | 0.907188i | \(0.638225\pi\) | |||||||
\(398\) | 30.8891 | 1.54833 | ||||||||
\(399\) | 19.0429 | 0.953339 | ||||||||
\(400\) | −2.71276 | −0.135638 | ||||||||
\(401\) | −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 | ||||||||
\(405\) | 10.3676 | 0.515169 | ||||||||
\(406\) | −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 | \(0.240687\pi\) | |||||||
\(410\) | −4.55193 | −0.224804 | ||||||||
\(411\) | 8.83157 | 0.435629 | ||||||||
\(412\) | 9.17310 | 0.451926 | ||||||||
\(413\) | −0.617162 | −0.0303686 | ||||||||
\(414\) | −11.5824 | −0.569242 | ||||||||
\(415\) | 12.1286 | 0.595369 | ||||||||
\(416\) | 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 | \(0.445558\pi\) | |||||||
\(420\) | 4.30209 | 0.209920 | ||||||||
\(421\) | 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 | ||||||||
\(425\) | −1.13186 | −0.0549030 | ||||||||
\(426\) | −30.7142 | −1.48811 | ||||||||
\(427\) | 12.0975 | 0.585439 | ||||||||
\(428\) | 4.67883 | 0.226160 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.38051 | 0.0665740 | ||||||||
\(431\) | 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 | \(-0.490820\pi\) | ||||
0.0288373 | + | 0.999584i | \(0.490820\pi\) | |||||||
\(434\) | 23.9935 | 1.15172 | ||||||||
\(435\) | 0.0576715 | 0.00276514 | ||||||||
\(436\) | −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 | \(0.629270\pi\) | |||||||
\(440\) | 16.4608 | 0.784740 | ||||||||
\(441\) | 14.5421 | 0.692481 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.55949 | 0.216628 | 0.108314 | − | 0.994117i | \(-0.465455\pi\) | ||||
0.108314 | + | 0.994117i | \(0.465455\pi\) | |||||||
\(444\) | 10.4010 | 0.493610 | ||||||||
\(445\) | 16.1540 | 0.765775 | ||||||||
\(446\) | −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 | \(0.394009\pi\) | |||||||
\(450\) | 2.97527 | 0.140256 | ||||||||
\(451\) | 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 | \(-0.112455\pi\) | ||||
0.938240 | + | 0.345984i | \(0.112455\pi\) | |||||||
\(458\) | −17.5644 | −0.820733 | ||||||||
\(459\) | 1.47992 | 0.0690768 | ||||||||
\(460\) | −1.99457 | −0.0929972 | ||||||||
\(461\) | −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 | \(-0.317859\pi\) | ||||
0.541494 | + | 0.840705i | \(0.317859\pi\) | |||||||
\(464\) | 0.0670807 | 0.00311414 | ||||||||
\(465\) | −12.7436 | −0.590972 | ||||||||
\(466\) | 11.5824 | 0.536542 | ||||||||
\(467\) | −22.6297 | −1.04718 | −0.523589 | − | 0.851971i | \(-0.675407\pi\) | ||||
−0.523589 | + | 0.851971i | \(0.675407\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23.0405 | 1.06391 | ||||||||
\(470\) | −3.15332 | −0.145452 | ||||||||
\(471\) | 23.4170 | 1.07900 | ||||||||
\(472\) | 0.525296 | 0.0241787 | ||||||||
\(473\) | −6.08012 | −0.279564 | ||||||||
\(474\) | −34.0859 | −1.56562 | ||||||||
\(475\) | 2.26795 | 0.104061 | ||||||||
\(476\) | 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 | \(0.343661\pi\) | |||||||
\(480\) | −6.57666 | −0.300182 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 28.3777 | 1.29257 | ||||||||
\(483\) | −32.6867 | −1.48730 | ||||||||
\(484\) | −9.14898 | −0.415863 | ||||||||
\(485\) | −12.1682 | −0.552528 | ||||||||
\(486\) | −24.7074 | −1.12075 | ||||||||
\(487\) | 3.03605 | 0.137576 | 0.0687882 | − | 0.997631i | \(-0.478087\pi\) | ||||
0.0687882 | + | 0.997631i | \(0.478087\pi\) | |||||||
\(488\) | −10.2968 | −0.466112 | ||||||||
\(489\) | 15.8155 | 0.715203 | ||||||||
\(490\) | −7.27105 | −0.328473 | ||||||||
\(491\) | 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 | ||||||||
\(495\) | −13.1039 | −0.588975 | ||||||||
\(496\) | −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 | \(0.225636\pi\) | |||||||
\(500\) | 0.512364 | 0.0229136 | ||||||||
\(501\) | 24.4648 | 1.09301 | ||||||||
\(502\) | 14.4413 | 0.644546 | ||||||||
\(503\) | −12.6276 | −0.563037 | −0.281518 | − | 0.959556i | \(-0.590838\pi\) | ||||
−0.281518 | + | 0.959556i | \(0.590838\pi\) | |||||||
\(504\) | −26.9113 | −1.19873 | ||||||||
\(505\) | 4.05441 | 0.180419 | ||||||||
\(506\) | −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 | \(0.679791\pi\) | |||||||
\(510\) | 3.21969 | 0.142570 | ||||||||
\(511\) | −16.9320 | −0.749029 | ||||||||
\(512\) | −24.2750 | −1.07281 | ||||||||
\(513\) | −2.96539 | −0.130925 | ||||||||
\(514\) | −6.76929 | −0.298581 | ||||||||
\(515\) | 17.9035 | 0.788921 | ||||||||
\(516\) | 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 | \(-0.199650\pi\) | ||||
0.809662 | + | 0.586897i | \(0.199650\pi\) | |||||||
\(524\) | 5.41465 | 0.236540 | ||||||||
\(525\) | 8.39654 | 0.366455 | ||||||||
\(526\) | 8.36665 | 0.364803 | ||||||||
\(527\) | −6.18457 | −0.269404 | ||||||||
\(528\) | −33.9865 | −1.47907 | ||||||||
\(529\) | −7.84554 | −0.341111 | ||||||||
\(530\) | 5.41465 | 0.235197 | ||||||||
\(531\) | −0.418169 | −0.0181470 | ||||||||
\(532\) | −4.18348 | −0.181377 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −45.9519 | −1.98854 | ||||||||
\(535\) | 9.13186 | 0.394805 | ||||||||
\(536\) | −19.6109 | −0.847062 | ||||||||
\(537\) | 43.4528 | 1.87512 | ||||||||
\(538\) | −1.73438 | −0.0747744 | ||||||||
\(539\) | 32.0236 | 1.37935 | ||||||||
\(540\) | −0.669925 | −0.0288290 | ||||||||
\(541\) | −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 | ||||||||
\(545\) | −7.37605 | −0.315955 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.7842 | −0.974181 | −0.487091 | − | 0.873351i | \(-0.661942\pi\) | ||||
−0.487091 | + | 0.873351i | \(0.661942\pi\) | |||||||
\(548\) | −1.94018 | −0.0828804 | ||||||||
\(549\) | 8.19687 | 0.349834 | ||||||||
\(550\) | 6.55193 | 0.279375 | ||||||||
\(551\) | −0.0560816 | −0.00238915 | ||||||||
\(552\) | 27.8212 | 1.18415 | ||||||||
\(553\) | −43.1398 | −1.83449 | ||||||||
\(554\) | −21.3735 | −0.908071 | ||||||||
\(555\) | 20.3000 | 0.861688 | ||||||||
\(556\) | −1.03183 | −0.0437594 | ||||||||
\(557\) | −28.1527 | −1.19287 | −0.596435 | − | 0.802662i | \(-0.703417\pi\) | ||||
−0.596435 | + | 0.802662i | \(0.703417\pi\) | |||||||
\(558\) | 16.2572 | 0.688222 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 9.76645 | 0.412708 | ||||||||
\(561\) | −14.1803 | −0.598694 | ||||||||
\(562\) | 13.0935 | 0.552317 | ||||||||
\(563\) | −18.1303 | −0.764101 | −0.382050 | − | 0.924142i | \(-0.624782\pi\) | ||||
−0.382050 | + | 0.924142i | \(0.624782\pi\) | |||||||
\(564\) | −3.08939 | −0.130087 | ||||||||
\(565\) | −7.07588 | −0.297684 | ||||||||
\(566\) | 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 | \(0.176004\pi\) | |||||||
\(570\) | −6.45143 | −0.270221 | ||||||||
\(571\) | 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 | ||||||||
\(575\) | −3.89287 | −0.162344 | ||||||||
\(576\) | 21.6248 | 0.901032 | ||||||||
\(577\) | 23.0691 | 0.960379 | 0.480189 | − | 0.877165i | \(-0.340568\pi\) | ||||
0.480189 | + | 0.877165i | \(0.340568\pi\) | |||||||
\(578\) | −19.1721 | −0.797456 | ||||||||
\(579\) | 50.7669 | 2.10980 | ||||||||
\(580\) | −0.0126697 | −0.000526079 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 | \(-0.637975\pi\) | ||||
−0.420015 | + | 0.907517i | \(0.637975\pi\) | |||||||
\(588\) | −7.12364 | −0.293774 | ||||||||
\(589\) | 12.3923 | 0.510616 | ||||||||
\(590\) | 0.209084 | 0.00860786 | ||||||||
\(591\) | −3.95717 | −0.162776 | ||||||||
\(592\) | 23.6120 | 0.970447 | ||||||||
\(593\) | 10.3834 | 0.426395 | 0.213198 | − | 0.977009i | \(-0.431612\pi\) | ||||
0.213198 | + | 0.977009i | \(0.431612\pi\) | |||||||
\(594\) | −8.56677 | −0.351499 | ||||||||
\(595\) | 4.07490 | 0.167055 | ||||||||
\(596\) | 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 | \(0.723351\pi\) | |||||||
\(600\) | −7.14670 | −0.291763 | ||||||||
\(601\) | −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 | ||||||||
\(605\) | −17.8564 | −0.725966 | ||||||||
\(606\) | −11.5332 | −0.468505 | ||||||||
\(607\) | 2.17540 | 0.0882968 | 0.0441484 | − | 0.999025i | \(-0.485943\pi\) | ||||
0.0441484 | + | 0.999025i | \(0.485943\pi\) | |||||||
\(608\) | 6.39535 | 0.259366 | ||||||||
\(609\) | −0.207629 | −0.00841354 | ||||||||
\(610\) | −4.09843 | −0.165941 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 1.41465 | 0.0571837 | ||||||||
\(613\) | −14.7620 | −0.596231 | −0.298116 | − | 0.954530i | \(-0.596358\pi\) | ||||
−0.298116 | + | 0.954530i | \(0.596358\pi\) | |||||||
\(614\) | 17.4467 | 0.704092 | ||||||||
\(615\) | −8.70406 | −0.350982 | ||||||||
\(616\) | −59.2622 | −2.38774 | ||||||||
\(617\) | −20.2972 | −0.817134 | −0.408567 | − | 0.912728i | \(-0.633971\pi\) | ||||
−0.408567 | + | 0.912728i | \(0.633971\pi\) | |||||||
\(618\) | −50.9284 | −2.04864 | ||||||||
\(619\) | 9.94207 | 0.399605 | 0.199803 | − | 0.979836i | \(-0.435970\pi\) | ||||
0.199803 | + | 0.979836i | \(0.435970\pi\) | |||||||
\(620\) | 2.79961 | 0.112435 | ||||||||
\(621\) | 5.09000 | 0.204255 | ||||||||
\(622\) | 3.36758 | 0.135028 | ||||||||
\(623\) | −58.1577 | −2.33004 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −19.9855 | −0.798782 | ||||||||
\(627\) | 28.4138 | 1.13474 | ||||||||
\(628\) | −5.14441 | −0.205284 | ||||||||
\(629\) | 9.85174 | 0.392815 | ||||||||
\(630\) | −10.7116 | −0.426759 | ||||||||
\(631\) | 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 | ||||||||
\(635\) | 11.4361 | 0.453828 | ||||||||
\(636\) | 5.30487 | 0.210352 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.162015 | −0.00641425 | ||||||||
\(639\) | −26.3387 | −1.04194 | ||||||||
\(640\) | −5.17262 | −0.204466 | ||||||||
\(641\) | −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 | \(-0.437075\pi\) | ||||
0.196401 | + | 0.980524i | \(0.437075\pi\) | |||||||
\(644\) | 7.18083 | 0.282964 | ||||||||
\(645\) | 2.63977 | 0.103941 | ||||||||
\(646\) | −3.13092 | −0.123185 | ||||||||
\(647\) | −36.2763 | −1.42617 | −0.713084 | − | 0.701079i | \(-0.752702\pi\) | ||||
−0.713084 | + | 0.701079i | \(0.752702\pi\) | |||||||
\(648\) | 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 | \(-0.413259\pi\) | ||||
0.269145 | + | 0.963100i | \(0.413259\pi\) | |||||||
\(654\) | 20.9820 | 0.820461 | ||||||||
\(655\) | 10.5680 | 0.412925 | ||||||||
\(656\) | −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 | \(0.516014\pi\) | |||||||
\(660\) | 6.41910 | 0.249863 | ||||||||
\(661\) | 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 | ||||||||
\(665\) | −8.16506 | −0.316627 | ||||||||
\(666\) | −25.8970 | −1.00349 | ||||||||
\(667\) | 0.0962625 | 0.00372730 | ||||||||
\(668\) | −5.37460 | −0.207949 | ||||||||
\(669\) | −28.6791 | −1.10880 | ||||||||
\(670\) | −7.80576 | −0.301563 | ||||||||
\(671\) | 18.0506 | 0.696834 | ||||||||
\(672\) | 23.6773 | 0.913370 | ||||||||
\(673\) | 43.3222 | 1.66995 | 0.834974 | − | 0.550289i | \(-0.185483\pi\) | ||||
0.834974 | + | 0.550289i | \(0.185483\pi\) | |||||||
\(674\) | −5.32051 | −0.204938 | ||||||||
\(675\) | −1.30752 | −0.0503264 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −41.3625 | −1.58969 | −0.794845 | − | 0.606813i | \(-0.792448\pi\) | ||||
−0.794845 | + | 0.606813i | \(0.792448\pi\) | |||||||
\(678\) | 20.1281 | 0.773016 | ||||||||
\(679\) | 43.8078 | 1.68119 | ||||||||
\(680\) | −3.46834 | −0.133005 | ||||||||
\(681\) | −17.8003 | −0.682110 | ||||||||
\(682\) | 35.8004 | 1.37087 | ||||||||
\(683\) | 2.62688 | 0.100515 | 0.0502574 | − | 0.998736i | \(-0.483996\pi\) | ||||
0.0502574 | + | 0.998736i | \(0.483996\pi\) | |||||||
\(684\) | −2.83459 | −0.108383 | ||||||||
\(685\) | −3.78672 | −0.144683 | ||||||||
\(686\) | −4.56057 | −0.174123 | ||||||||
\(687\) | −33.5862 | −1.28139 | ||||||||
\(688\) | 3.07045 | 0.117060 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 11.0737 | 0.421569 | ||||||||
\(691\) | −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 | ||||||||
\(695\) | −2.01386 | −0.0763902 | ||||||||
\(696\) | 0.176723 | 0.00669865 | ||||||||
\(697\) | −4.22414 | −0.160001 | ||||||||
\(698\) | 28.7493 | 1.08818 | ||||||||
\(699\) | 22.1474 | 0.837692 | ||||||||
\(700\) | −1.84461 | −0.0697197 | ||||||||
\(701\) | −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 | ||||||||
\(705\) | −6.02968 | −0.227091 | ||||||||
\(706\) | 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 | \(0.760431\pi\) | |||||||
\(710\) | 13.1694 | 0.494237 | ||||||||
\(711\) | −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 | \(0.460627\pi\) | |||||||
\(720\) | 6.61742 | 0.246617 | ||||||||
\(721\) | −64.4560 | −2.40047 | ||||||||
\(722\) | −16.9005 | −0.628971 | ||||||||
\(723\) | 54.2629 | 2.01806 | ||||||||
\(724\) | −9.26867 | −0.344467 | ||||||||
\(725\) | −0.0247279 | −0.000918370 0 | ||||||||
\(726\) | 50.7945 | 1.88516 | ||||||||
\(727\) | −18.3735 | −0.681435 | −0.340717 | − | 0.940166i | \(-0.610670\pi\) | ||||
−0.340717 | + | 0.940166i | \(0.610670\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −16.1420 | −0.597853 | ||||||||
\(730\) | 5.73629 | 0.212310 | ||||||||
\(731\) | 1.28110 | 0.0473830 | ||||||||
\(732\) | −4.01534 | −0.148411 | ||||||||
\(733\) | 0.791131 | 0.0292211 | 0.0146105 | − | 0.999893i | \(-0.495349\pi\) | ||||
0.0146105 | + | 0.999893i | \(0.495349\pi\) | |||||||
\(734\) | 31.7772 | 1.17292 | ||||||||
\(735\) | −13.9035 | −0.512837 | ||||||||
\(736\) | −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 | \(0.305552\pi\) | |||||||
\(740\) | −4.45965 | −0.163940 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −19.4938 | −0.715639 | ||||||||
\(743\) | 5.56304 | 0.204088 | 0.102044 | − | 0.994780i | \(-0.467462\pi\) | ||||
0.102044 | + | 0.994780i | \(0.467462\pi\) | |||||||
\(744\) | −39.0503 | −1.43165 | ||||||||
\(745\) | 5.51780 | 0.202156 | ||||||||
\(746\) | 16.1053 | 0.589658 | ||||||||
\(747\) | −29.5862 | −1.08250 | ||||||||
\(748\) | 3.11523 | 0.113904 | ||||||||
\(749\) | −32.8765 | −1.20128 | ||||||||
\(750\) | −2.84461 | −0.103870 | ||||||||
\(751\) | −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 | ||||||||
\(755\) | 4.88961 | 0.177951 | ||||||||
\(756\) | 2.41186 | 0.0877186 | ||||||||
\(757\) | 50.0446 | 1.81890 | 0.909451 | − | 0.415810i | \(-0.136502\pi\) | ||||
0.909451 | + | 0.415810i | \(0.136502\pi\) | |||||||
\(758\) | 31.7091 | 1.15173 | ||||||||
\(759\) | −48.7715 | −1.77029 | ||||||||
\(760\) | 6.94967 | 0.252091 | ||||||||
\(761\) | 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 | ||||||||
\(765\) | 2.76102 | 0.0998248 | ||||||||
\(766\) | −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 | \(0.751187\pi\) | |||||||
\(770\) | −23.5882 | −0.850061 | ||||||||
\(771\) | −12.9440 | −0.466168 | ||||||||
\(772\) | −11.1528 | −0.401399 | ||||||||
\(773\) | 48.7805 | 1.75451 | 0.877256 | − | 0.480022i | \(-0.159371\pi\) | ||||
0.877256 | + | 0.480022i | \(0.159371\pi\) | |||||||
\(774\) | −3.36758 | −0.121045 | ||||||||
\(775\) | 5.46410 | 0.196276 | ||||||||
\(776\) | −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 | ||||||||
\(785\) | −10.0405 | −0.358363 | ||||||||
\(786\) | −30.0618 | −1.07227 | ||||||||
\(787\) | 39.8608 | 1.42088 | 0.710442 | − | 0.703756i | \(-0.248495\pi\) | ||||
0.710442 | + | 0.703756i | \(0.248495\pi\) | |||||||
\(788\) | 0.869338 | 0.0309689 | ||||||||
\(789\) | 15.9984 | 0.569559 | ||||||||
\(790\) | 14.6150 | 0.519980 | ||||||||
\(791\) | 25.4745 | 0.905771 | ||||||||
\(792\) | −40.1541 | −1.42682 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −20.4490 | −0.725709 | ||||||||
\(795\) | 10.3537 | 0.367208 | ||||||||
\(796\) | −12.9759 | −0.459917 | ||||||||
\(797\) | 26.2118 | 0.928470 | 0.464235 | − | 0.885712i | \(-0.346329\pi\) | ||||
0.464235 | + | 0.885712i | \(0.346329\pi\) | |||||||
\(798\) | 23.2264 | 0.822206 | ||||||||
\(799\) | −2.92625 | −0.103523 | ||||||||
\(800\) | 2.81988 | 0.0996979 | ||||||||
\(801\) | −39.4057 | −1.39233 | ||||||||
\(802\) | −16.9269 | −0.597708 | ||||||||
\(803\) | −25.2641 | −0.891551 | ||||||||
\(804\) | −7.64750 | −0.269707 | ||||||||
\(805\) | 14.0151 | 0.493968 | ||||||||
\(806\) | 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 | \(0.372304\pi\) | |||||||
\(810\) | 12.6452 | 0.444307 | ||||||||
\(811\) | 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 | ||||||||
\(815\) | −6.78124 | −0.237537 | ||||||||
\(816\) | 7.16104 | 0.250686 | ||||||||
\(817\) | −2.56699 | −0.0898076 | ||||||||
\(818\) | 35.8894 | 1.25484 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.91217 | 0.0667758 | ||||||||
\(821\) | −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 | \(-0.477349\pi\) | ||||
0.0710995 | + | 0.997469i | \(0.477349\pi\) | |||||||
\(824\) | 54.8616 | 1.91119 | ||||||||
\(825\) | 12.5284 | 0.436183 | ||||||||
\(826\) | −0.752744 | −0.0261913 | ||||||||
\(827\) | −54.8780 | −1.90830 | −0.954148 | − | 0.299337i | \(-0.903235\pi\) | ||||
−0.954148 | + | 0.299337i | \(0.903235\pi\) | |||||||
\(828\) | 4.86550 | 0.169088 | ||||||||
\(829\) | 8.14950 | 0.283044 | 0.141522 | − | 0.989935i | \(-0.454800\pi\) | ||||
0.141522 | + | 0.989935i | \(0.454800\pi\) | |||||||
\(830\) | 14.7931 | 0.513476 | ||||||||
\(831\) | −40.8697 | −1.41775 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.74745 | −0.233785 | ||||||||
\(834\) | 5.72866 | 0.198367 | ||||||||
\(835\) | −10.4898 | −0.363015 | ||||||||
\(836\) | −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 | \(0.623320\pi\) | |||||||
\(840\) | 25.7295 | 0.887752 | ||||||||
\(841\) | −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 | ||||||||
\(850\) | −1.38051 | −0.0473511 | ||||||||
\(851\) | 33.8838 | 1.16152 | ||||||||
\(852\) | 12.9024 | 0.442028 | ||||||||
\(853\) | −19.2240 | −0.658217 | −0.329108 | − | 0.944292i | \(-0.606748\pi\) | ||||
−0.329108 | + | 0.944292i | \(0.606748\pi\) | |||||||
\(854\) | 14.7552 | 0.504911 | ||||||||
\(855\) | −5.53238 | −0.189203 | ||||||||
\(856\) | 27.9827 | 0.956430 | ||||||||
\(857\) | −27.8197 | −0.950302 | −0.475151 | − | 0.879904i | \(-0.657607\pi\) | ||||
−0.475151 | + | 0.879904i | \(0.657607\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 45.7355 | 1.56048 | 0.780238 | − | 0.625482i | \(-0.215098\pi\) | ||||
0.780238 | + | 0.625482i | \(0.215098\pi\) | |||||||
\(860\) | −0.579922 | −0.0197752 | ||||||||
\(861\) | 31.3363 | 1.06794 | ||||||||
\(862\) | 36.8521 | 1.25519 | ||||||||
\(863\) | 54.8186 | 1.86605 | 0.933024 | − | 0.359814i | \(-0.117160\pi\) | ||||
0.933024 | + | 0.359814i | \(0.117160\pi\) | |||||||
\(864\) | −3.68705 | −0.125436 | ||||||||
\(865\) | 4.45845 | 0.151592 | ||||||||
\(866\) | 1.46378 | 0.0497413 | ||||||||
\(867\) | −36.6604 | −1.24505 | ||||||||
\(868\) | −10.0791 | −0.342108 | ||||||||
\(869\) | −64.3684 | −2.18355 | ||||||||
\(870\) | 0.0703412 | 0.00238479 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −22.6024 | −0.765415 | ||||||||
\(873\) | 29.6827 | 1.00461 | ||||||||
\(874\) | −10.7684 | −0.364247 | ||||||||
\(875\) | −3.60020 | −0.121709 | ||||||||
\(876\) | 5.61999 | 0.189882 | ||||||||
\(877\) | −27.3794 | −0.924537 | −0.462269 | − | 0.886740i | \(-0.652964\pi\) | ||||
−0.462269 | + | 0.886740i | \(0.652964\pi\) | |||||||
\(878\) | −20.1908 | −0.681407 | ||||||||
\(879\) | 43.7125 | 1.47439 | ||||||||
\(880\) | 14.5724 | 0.491236 | ||||||||
\(881\) | −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 | \(-0.594351\pi\) | ||||
−0.292092 | + | 0.956390i | \(0.594351\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.399804 | 0.0134393 | ||||||||
\(886\) | 5.56115 | 0.186831 | ||||||||
\(887\) | −31.1427 | −1.04567 | −0.522835 | − | 0.852434i | \(-0.675126\pi\) | ||||
−0.522835 | + | 0.852434i | \(0.675126\pi\) | |||||||
\(888\) | 62.2053 | 2.08747 | ||||||||
\(889\) | −41.1722 | −1.38087 | ||||||||
\(890\) | 19.7029 | 0.660442 | ||||||||
\(891\) | −55.6927 | −1.86578 | ||||||||
\(892\) | 6.30042 | 0.210954 | ||||||||
\(893\) | 5.86345 | 0.196213 | ||||||||
\(894\) | −15.6960 | −0.524952 | ||||||||
\(895\) | −18.6313 | −0.622775 | ||||||||
\(896\) | 18.6224 | 0.622132 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 16.8953 | 0.563804 | ||||||||
\(899\) | −0.135116 | −0.00450636 | ||||||||
\(900\) | −1.24985 | −0.0416616 | ||||||||
\(901\) | 5.02473 | 0.167398 | ||||||||
\(902\) | 24.4521 | 0.814167 | ||||||||
\(903\) | −9.50367 | −0.316262 | ||||||||
\(904\) | −21.6826 | −0.721152 | ||||||||
\(905\) | −18.0900 | −0.601332 | ||||||||
\(906\) | −13.9090 | −0.462097 | ||||||||
\(907\) | 17.6057 | 0.584587 | 0.292294 | − | 0.956329i | \(-0.405582\pi\) | ||||
0.292294 | + | 0.956329i | \(0.405582\pi\) | |||||||
\(908\) | 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 | ||||||||
\(915\) | −7.83690 | −0.259080 | ||||||||
\(916\) | 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 | \(0.540088\pi\) | |||||||
\(920\) | −11.9289 | −0.393285 | ||||||||
\(921\) | 33.3611 | 1.09928 | ||||||||
\(922\) | −9.19522 | −0.302828 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −23.1100 | −0.760264 | ||||||||
\(925\) | −8.70406 | −0.286188 | ||||||||
\(926\) | 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 | \(0.574427\pi\) | |||||||
\(930\) | −15.5432 | −0.509683 | ||||||||
\(931\) | 13.5202 | 0.443106 | ||||||||
\(932\) | −4.86550 | −0.159375 | ||||||||
\(933\) | 6.43937 | 0.210816 | ||||||||
\(934\) | −27.6012 | −0.903138 | ||||||||
\(935\) | 6.08012 | 0.198841 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.9317 | −0.781815 | −0.390908 | − | 0.920430i | \(-0.627839\pi\) | ||||
−0.390908 | + | 0.920430i | \(0.627839\pi\) | |||||||
\(938\) | 28.1023 | 0.917571 | ||||||||
\(939\) | −38.2157 | −1.24712 | ||||||||
\(940\) | 1.32464 | 0.0432051 | ||||||||
\(941\) | −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 | ||||||||
\(945\) | 4.70732 | 0.153129 | ||||||||
\(946\) | −7.41584 | −0.241110 | ||||||||
\(947\) | 41.4223 | 1.34604 | 0.673021 | − | 0.739623i | \(-0.264996\pi\) | ||||
0.673021 | + | 0.739623i | \(0.264996\pi\) | |||||||
\(948\) | 14.3187 | 0.465051 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 2.76619 | 0.0897470 | ||||||||
\(951\) | 4.16480 | 0.135053 | ||||||||
\(952\) | 12.4867 | 0.404696 | ||||||||
\(953\) | 24.3026 | 0.787237 | 0.393619 | − | 0.919274i | \(-0.371223\pi\) | ||||
0.393619 | + | 0.919274i | \(0.371223\pi\) | |||||||
\(954\) | −13.2083 | −0.427636 | ||||||||
\(955\) | −27.3363 | −0.884583 | ||||||||
\(956\) | 10.2034 | 0.330001 | ||||||||
\(957\) | −0.309801 | −0.0100144 | ||||||||
\(958\) | 25.1802 | 0.813536 | ||||||||
\(959\) | 13.6329 | 0.440231 | ||||||||
\(960\) | −20.6751 | −0.667286 | ||||||||
\(961\) | −1.14359 | −0.0368901 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −22.2760 | −0.717834 | ||||||||
\(964\) | −11.9209 | −0.383945 | ||||||||
\(965\) | −21.7674 | −0.700717 | ||||||||
\(966\) | −39.8675 | −1.28272 | ||||||||
\(967\) | 23.6784 | 0.761445 | 0.380722 | − | 0.924689i | \(-0.375675\pi\) | ||||
0.380722 | + | 0.924689i | \(0.375675\pi\) | |||||||
\(968\) | −54.7173 | −1.75868 | ||||||||
\(969\) | −5.98685 | −0.192325 | ||||||||
\(970\) | −14.8413 | −0.476527 | ||||||||
\(971\) | −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 | \(-0.369044\pi\) | ||||
0.399901 | + | 0.916558i | \(0.369044\pi\) | |||||||
\(978\) | 19.2900 | 0.616826 | ||||||||
\(979\) | −86.7765 | −2.77339 | ||||||||
\(980\) | 3.05441 | 0.0975696 | ||||||||
\(981\) | 17.9930 | 0.574471 | ||||||||
\(982\) | 13.0116 | 0.415218 | ||||||||
\(983\) | −27.3418 | −0.872068 | −0.436034 | − | 0.899930i | \(-0.643617\pi\) | ||||
−0.436034 | + | 0.899930i | \(0.643617\pi\) | |||||||
\(984\) | −26.6718 | −0.850267 | ||||||||
\(985\) | 1.69672 | 0.0540620 | ||||||||
\(986\) | 0.0341370 | 0.00108715 | ||||||||
\(987\) | 21.7080 | 0.690975 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.40617 | 0.140108 | ||||||||
\(990\) | −15.9826 | −0.507961 | ||||||||
\(991\) | 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 | ||||||||
\(995\) | −25.3255 | −0.802871 | ||||||||
\(996\) | 14.4932 | 0.459234 | ||||||||
\(997\) | −34.5612 | −1.09456 | −0.547282 | − | 0.836948i | \(-0.684337\pi\) | ||||
−0.547282 | + | 0.836948i | \(0.684337\pi\) | |||||||
\(998\) | 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 | 845.2.a.m.1.3 | 4 | ||
3.2 | odd | 2 | 7605.2.a.cf.1.2 | 4 | |||
5.4 | even | 2 | 4225.2.a.bi.1.2 | 4 | |||
13.2 | odd | 12 | 65.2.m.a.56.3 | yes | 8 | ||
13.3 | even | 3 | 845.2.e.m.191.2 | 8 | |||
13.4 | even | 6 | 845.2.e.n.146.3 | 8 | |||
13.5 | odd | 4 | 845.2.c.g.506.3 | 8 | |||
13.6 | odd | 12 | 845.2.m.g.361.2 | 8 | |||
13.7 | odd | 12 | 65.2.m.a.36.3 | ✓ | 8 | ||
13.8 | odd | 4 | 845.2.c.g.506.6 | 8 | |||
13.9 | even | 3 | 845.2.e.m.146.2 | 8 | |||
13.10 | even | 6 | 845.2.e.n.191.3 | 8 | |||
13.11 | odd | 12 | 845.2.m.g.316.2 | 8 | |||
13.12 | even | 2 | 845.2.a.l.1.2 | 4 | |||
39.2 | even | 12 | 585.2.bu.c.316.2 | 8 | |||
39.20 | even | 12 | 585.2.bu.c.361.2 | 8 | |||
39.38 | odd | 2 | 7605.2.a.cj.1.3 | 4 | |||
52.7 | even | 12 | 1040.2.da.b.881.4 | 8 | |||
52.15 | even | 12 | 1040.2.da.b.641.4 | 8 | |||
65.2 | even | 12 | 325.2.m.b.199.2 | 8 | |||
65.7 | even | 12 | 325.2.m.c.49.3 | 8 | |||
65.28 | even | 12 | 325.2.m.c.199.3 | 8 | |||
65.33 | even | 12 | 325.2.m.b.49.2 | 8 | |||
65.54 | odd | 12 | 325.2.n.d.251.2 | 8 | |||
65.59 | odd | 12 | 325.2.n.d.101.2 | 8 | |||
65.64 | even | 2 | 4225.2.a.bl.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.2.m.a.36.3 | ✓ | 8 | 13.7 | odd | 12 | ||
65.2.m.a.56.3 | yes | 8 | 13.2 | odd | 12 | ||
325.2.m.b.49.2 | 8 | 65.33 | even | 12 | |||
325.2.m.b.199.2 | 8 | 65.2 | even | 12 | |||
325.2.m.c.49.3 | 8 | 65.7 | even | 12 | |||
325.2.m.c.199.3 | 8 | 65.28 | even | 12 | |||
325.2.n.d.101.2 | 8 | 65.59 | odd | 12 | |||
325.2.n.d.251.2 | 8 | 65.54 | odd | 12 | |||
585.2.bu.c.316.2 | 8 | 39.2 | even | 12 | |||
585.2.bu.c.361.2 | 8 | 39.20 | even | 12 | |||
845.2.a.l.1.2 | 4 | 13.12 | even | 2 | |||
845.2.a.m.1.3 | 4 | 1.1 | even | 1 | trivial | ||
845.2.c.g.506.3 | 8 | 13.5 | odd | 4 | |||
845.2.c.g.506.6 | 8 | 13.8 | odd | 4 | |||
845.2.e.m.146.2 | 8 | 13.9 | even | 3 | |||
845.2.e.m.191.2 | 8 | 13.3 | even | 3 | |||
845.2.e.n.146.3 | 8 | 13.4 | even | 6 | |||
845.2.e.n.191.3 | 8 | 13.10 | even | 6 | |||
845.2.m.g.316.2 | 8 | 13.11 | odd | 12 | |||
845.2.m.g.361.2 | 8 | 13.6 | odd | 12 | |||
1040.2.da.b.641.4 | 8 | 52.15 | even | 12 | |||
1040.2.da.b.881.4 | 8 | 52.7 | even | 12 | |||
4225.2.a.bi.1.2 | 4 | 5.4 | even | 2 | |||
4225.2.a.bl.1.3 | 4 | 65.64 | even | 2 | |||
7605.2.a.cf.1.2 | 4 | 3.2 | odd | 2 | |||
7605.2.a.cj.1.3 | 4 | 39.38 | odd | 2 |