Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{24})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.93185\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.41421 | −1.39385 | −0.696923 | − | 0.717146i | \(-0.745448\pi\) | ||||
−0.696923 | + | 0.717146i | \(0.745448\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 2.41421 | 0.985599 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.82843 | 0.942809 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −2.41421 | −0.696923 | ||||||||
\(13\) | 5.59575 | 1.55198 | 0.775991 | − | 0.630743i | \(-0.217250\pi\) | ||||
0.775991 | + | 0.630743i | \(0.217250\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −2.41421 | −0.623347 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.449490 | 0.109017 | 0.0545086 | − | 0.998513i | \(-0.482641\pi\) | ||||
0.0545086 | + | 0.998513i | \(0.482641\pi\) | |||||||
\(18\) | −2.82843 | −0.666667 | ||||||||
\(19\) | −2.27792 | −0.522590 | −0.261295 | − | 0.965259i | \(-0.584150\pi\) | ||||
−0.261295 | + | 0.965259i | \(0.584150\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −2.41421 | −0.526825 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.110988 | 0.0231426 | 0.0115713 | − | 0.999933i | \(-0.496317\pi\) | ||||
0.0115713 | + | 0.999933i | \(0.496317\pi\) | |||||||
\(24\) | 2.41421 | 0.492799 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −5.59575 | −1.09742 | ||||||||
\(27\) | 0.414214 | 0.0797154 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −2.49938 | −0.464123 | −0.232061 | − | 0.972701i | \(-0.574547\pi\) | ||||
−0.232061 | + | 0.972701i | \(0.574547\pi\) | |||||||
\(30\) | 2.41421 | 0.440773 | ||||||||
\(31\) | 4.52004 | 0.811824 | 0.405912 | − | 0.913912i | \(-0.366954\pi\) | ||||
0.405912 | + | 0.913912i | \(0.366954\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.449490 | −0.0770869 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 2.82843 | 0.471405 | ||||||||
\(37\) | −6.42883 | −1.05689 | −0.528446 | − | 0.848967i | \(-0.677225\pi\) | ||||
−0.528446 | + | 0.848967i | \(0.677225\pi\) | |||||||
\(38\) | 2.27792 | 0.369527 | ||||||||
\(39\) | −13.5093 | −2.16323 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −7.67752 | −1.19903 | −0.599513 | − | 0.800365i | \(-0.704639\pi\) | ||||
−0.599513 | + | 0.800365i | \(0.704639\pi\) | |||||||
\(42\) | 2.41421 | 0.372521 | ||||||||
\(43\) | 1.34366 | 0.204906 | 0.102453 | − | 0.994738i | \(-0.467331\pi\) | ||||
0.102453 | + | 0.994738i | \(0.467331\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.82843 | 0.421637 | ||||||||
\(46\) | −0.110988 | −0.0163643 | ||||||||
\(47\) | 1.51399 | 0.220838 | 0.110419 | − | 0.993885i | \(-0.464781\pi\) | ||||
0.110419 | + | 0.993885i | \(0.464781\pi\) | |||||||
\(48\) | −2.41421 | −0.348462 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −1.08516 | −0.151953 | ||||||||
\(52\) | 5.59575 | 0.775991 | ||||||||
\(53\) | −6.94887 | −0.954500 | −0.477250 | − | 0.878767i | \(-0.658366\pi\) | ||||
−0.477250 | + | 0.878767i | \(0.658366\pi\) | |||||||
\(54\) | −0.414214 | −0.0563673 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 5.49938 | 0.728410 | ||||||||
\(58\) | 2.49938 | 0.328184 | ||||||||
\(59\) | 3.97469 | 0.517461 | 0.258730 | − | 0.965950i | \(-0.416696\pi\) | ||||
0.258730 | + | 0.965950i | \(0.416696\pi\) | |||||||
\(60\) | −2.41421 | −0.311674 | ||||||||
\(61\) | −4.29253 | −0.549602 | −0.274801 | − | 0.961501i | \(-0.588612\pi\) | ||||
−0.274801 | + | 0.961501i | \(0.588612\pi\) | |||||||
\(62\) | −4.52004 | −0.574046 | ||||||||
\(63\) | 2.82843 | 0.356348 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.59575 | 0.694068 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.1708 | −1.36474 | −0.682368 | − | 0.731009i | \(-0.739050\pi\) | ||||
−0.682368 | + | 0.731009i | \(0.739050\pi\) | |||||||
\(68\) | 0.449490 | 0.0545086 | ||||||||
\(69\) | −0.267949 | −0.0322573 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | −1.87780 | −0.222854 | −0.111427 | − | 0.993773i | \(-0.535542\pi\) | ||||
−0.111427 | + | 0.993773i | \(0.535542\pi\) | |||||||
\(72\) | −2.82843 | −0.333333 | ||||||||
\(73\) | −3.41421 | −0.399603 | −0.199802 | − | 0.979836i | \(-0.564030\pi\) | ||||
−0.199802 | + | 0.979836i | \(0.564030\pi\) | |||||||
\(74\) | 6.42883 | 0.747336 | ||||||||
\(75\) | −2.41421 | −0.278769 | ||||||||
\(76\) | −2.27792 | −0.261295 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 13.5093 | 1.52963 | ||||||||
\(79\) | 11.2168 | 1.26199 | 0.630995 | − | 0.775787i | \(-0.282647\pi\) | ||||
0.630995 | + | 0.775787i | \(0.282647\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −9.48528 | −1.05392 | ||||||||
\(82\) | 7.67752 | 0.847840 | ||||||||
\(83\) | −16.6960 | −1.83263 | −0.916315 | − | 0.400459i | \(-0.868851\pi\) | ||||
−0.916315 | + | 0.400459i | \(0.868851\pi\) | |||||||
\(84\) | −2.41421 | −0.263412 | ||||||||
\(85\) | 0.449490 | 0.0487540 | ||||||||
\(86\) | −1.34366 | −0.144891 | ||||||||
\(87\) | 6.03403 | 0.646916 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.17209 | 0.230241 | 0.115120 | − | 0.993352i | \(-0.463275\pi\) | ||||
0.115120 | + | 0.993352i | \(0.463275\pi\) | |||||||
\(90\) | −2.82843 | −0.298142 | ||||||||
\(91\) | 5.59575 | 0.586594 | ||||||||
\(92\) | 0.110988 | 0.0115713 | ||||||||
\(93\) | −10.9123 | −1.13156 | ||||||||
\(94\) | −1.51399 | −0.156156 | ||||||||
\(95\) | −2.27792 | −0.233709 | ||||||||
\(96\) | 2.41421 | 0.246400 | ||||||||
\(97\) | −10.1270 | −1.02824 | −0.514121 | − | 0.857718i | \(-0.671882\pi\) | ||||
−0.514121 | + | 0.857718i | \(0.671882\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −6.46410 | −0.643202 | −0.321601 | − | 0.946875i | \(-0.604221\pi\) | ||||
−0.321601 | + | 0.946875i | \(0.604221\pi\) | |||||||
\(102\) | 1.08516 | 0.107447 | ||||||||
\(103\) | −7.55051 | −0.743974 | −0.371987 | − | 0.928238i | \(-0.621323\pi\) | ||||
−0.371987 | + | 0.928238i | \(0.621323\pi\) | |||||||
\(104\) | −5.59575 | −0.548709 | ||||||||
\(105\) | −2.41421 | −0.235603 | ||||||||
\(106\) | 6.94887 | 0.674934 | ||||||||
\(107\) | 6.00481 | 0.580507 | 0.290253 | − | 0.956950i | \(-0.406260\pi\) | ||||
0.290253 | + | 0.956950i | \(0.406260\pi\) | |||||||
\(108\) | 0.414214 | 0.0398577 | ||||||||
\(109\) | 1.01461 | 0.0971822 | 0.0485911 | − | 0.998819i | \(-0.484527\pi\) | ||||
0.0485911 | + | 0.998819i | \(0.484527\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 15.5206 | 1.47315 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −5.83912 | −0.549299 | −0.274649 | − | 0.961544i | \(-0.588562\pi\) | ||||
−0.274649 | + | 0.961544i | \(0.588562\pi\) | |||||||
\(114\) | −5.49938 | −0.515064 | ||||||||
\(115\) | 0.110988 | 0.0103497 | ||||||||
\(116\) | −2.49938 | −0.232061 | ||||||||
\(117\) | 15.8272 | 1.46322 | ||||||||
\(118\) | −3.97469 | −0.365900 | ||||||||
\(119\) | 0.449490 | 0.0412047 | ||||||||
\(120\) | 2.41421 | 0.220387 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 4.29253 | 0.388627 | ||||||||
\(123\) | 18.5352 | 1.67126 | ||||||||
\(124\) | 4.52004 | 0.405912 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −2.82843 | −0.251976 | ||||||||
\(127\) | −8.36257 | −0.742058 | −0.371029 | − | 0.928621i | \(-0.620995\pi\) | ||||
−0.371029 | + | 0.928621i | \(0.620995\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −3.24389 | −0.285608 | ||||||||
\(130\) | −5.59575 | −0.490780 | ||||||||
\(131\) | 10.5704 | 0.923544 | 0.461772 | − | 0.886999i | \(-0.347214\pi\) | ||||
0.461772 | + | 0.886999i | \(0.347214\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.27792 | −0.197520 | ||||||||
\(134\) | 11.1708 | 0.965014 | ||||||||
\(135\) | 0.414214 | 0.0356498 | ||||||||
\(136\) | −0.449490 | −0.0385434 | ||||||||
\(137\) | −10.8895 | −0.930355 | −0.465178 | − | 0.885217i | \(-0.654010\pi\) | ||||
−0.465178 | + | 0.885217i | \(0.654010\pi\) | |||||||
\(138\) | 0.267949 | 0.0228093 | ||||||||
\(139\) | 15.5493 | 1.31887 | 0.659436 | − | 0.751761i | \(-0.270795\pi\) | ||||
0.659436 | + | 0.751761i | \(0.270795\pi\) | |||||||
\(140\) | 1.00000 | 0.0845154 | ||||||||
\(141\) | −3.65509 | −0.307814 | ||||||||
\(142\) | 1.87780 | 0.157581 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.82843 | 0.235702 | ||||||||
\(145\) | −2.49938 | −0.207562 | ||||||||
\(146\) | 3.41421 | 0.282562 | ||||||||
\(147\) | −2.41421 | −0.199121 | ||||||||
\(148\) | −6.42883 | −0.528446 | ||||||||
\(149\) | −19.0552 | −1.56106 | −0.780532 | − | 0.625116i | \(-0.785052\pi\) | ||||
−0.780532 | + | 0.625116i | \(0.785052\pi\) | |||||||
\(150\) | 2.41421 | 0.197120 | ||||||||
\(151\) | 23.3590 | 1.90092 | 0.950462 | − | 0.310840i | \(-0.100610\pi\) | ||||
0.950462 | + | 0.310840i | \(0.100610\pi\) | |||||||
\(152\) | 2.27792 | 0.184763 | ||||||||
\(153\) | 1.27135 | 0.102782 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.52004 | 0.363059 | ||||||||
\(156\) | −13.5093 | −1.08161 | ||||||||
\(157\) | −16.6617 | −1.32975 | −0.664873 | − | 0.746957i | \(-0.731514\pi\) | ||||
−0.664873 | + | 0.746957i | \(0.731514\pi\) | |||||||
\(158\) | −11.2168 | −0.892362 | ||||||||
\(159\) | 16.7761 | 1.33043 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 0.110988 | 0.00874709 | ||||||||
\(162\) | 9.48528 | 0.745234 | ||||||||
\(163\) | 2.01994 | 0.158214 | 0.0791068 | − | 0.996866i | \(-0.474793\pi\) | ||||
0.0791068 | + | 0.996866i | \(0.474793\pi\) | |||||||
\(164\) | −7.67752 | −0.599513 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 16.6960 | 1.29586 | ||||||||
\(167\) | 22.4402 | 1.73647 | 0.868237 | − | 0.496149i | \(-0.165253\pi\) | ||||
0.868237 | + | 0.496149i | \(0.165253\pi\) | |||||||
\(168\) | 2.41421 | 0.186261 | ||||||||
\(169\) | 18.3125 | 1.40865 | ||||||||
\(170\) | −0.449490 | −0.0344743 | ||||||||
\(171\) | −6.44292 | −0.492703 | ||||||||
\(172\) | 1.34366 | 0.102453 | ||||||||
\(173\) | −20.2419 | −1.53896 | −0.769482 | − | 0.638668i | \(-0.779486\pi\) | ||||
−0.769482 | + | 0.638668i | \(0.779486\pi\) | |||||||
\(174\) | −6.03403 | −0.457439 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.59575 | −0.721261 | ||||||||
\(178\) | −2.17209 | −0.162805 | ||||||||
\(179\) | −16.3132 | −1.21931 | −0.609653 | − | 0.792669i | \(-0.708691\pi\) | ||||
−0.609653 | + | 0.792669i | \(0.708691\pi\) | |||||||
\(180\) | 2.82843 | 0.210819 | ||||||||
\(181\) | 10.0659 | 0.748193 | 0.374097 | − | 0.927390i | \(-0.377953\pi\) | ||||
0.374097 | + | 0.927390i | \(0.377953\pi\) | |||||||
\(182\) | −5.59575 | −0.414785 | ||||||||
\(183\) | 10.3631 | 0.766061 | ||||||||
\(184\) | −0.110988 | −0.00818216 | ||||||||
\(185\) | −6.42883 | −0.472657 | ||||||||
\(186\) | 10.9123 | 0.800132 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 1.51399 | 0.110419 | ||||||||
\(189\) | 0.414214 | 0.0301296 | ||||||||
\(190\) | 2.27792 | 0.165257 | ||||||||
\(191\) | −12.6211 | −0.913228 | −0.456614 | − | 0.889665i | \(-0.650938\pi\) | ||||
−0.456614 | + | 0.889665i | \(0.650938\pi\) | |||||||
\(192\) | −2.41421 | −0.174231 | ||||||||
\(193\) | −18.3984 | −1.32434 | −0.662171 | − | 0.749352i | \(-0.730365\pi\) | ||||
−0.662171 | + | 0.749352i | \(0.730365\pi\) | |||||||
\(194\) | 10.1270 | 0.727077 | ||||||||
\(195\) | −13.5093 | −0.967424 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 4.24921 | 0.302744 | 0.151372 | − | 0.988477i | \(-0.451631\pi\) | ||||
0.151372 | + | 0.988477i | \(0.451631\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.8211 | −1.19242 | −0.596209 | − | 0.802829i | \(-0.703327\pi\) | ||||
−0.596209 | + | 0.802829i | \(0.703327\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 26.9688 | 1.90223 | ||||||||
\(202\) | 6.46410 | 0.454813 | ||||||||
\(203\) | −2.49938 | −0.175422 | ||||||||
\(204\) | −1.08516 | −0.0759767 | ||||||||
\(205\) | −7.67752 | −0.536221 | ||||||||
\(206\) | 7.55051 | 0.526069 | ||||||||
\(207\) | 0.313922 | 0.0218191 | ||||||||
\(208\) | 5.59575 | 0.387996 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 2.41421 | 0.166597 | ||||||||
\(211\) | −0.762683 | −0.0525052 | −0.0262526 | − | 0.999655i | \(-0.508357\pi\) | ||||
−0.0262526 | + | 0.999655i | \(0.508357\pi\) | |||||||
\(212\) | −6.94887 | −0.477250 | ||||||||
\(213\) | 4.53341 | 0.310624 | ||||||||
\(214\) | −6.00481 | −0.410480 | ||||||||
\(215\) | 1.34366 | 0.0916369 | ||||||||
\(216\) | −0.414214 | −0.0281837 | ||||||||
\(217\) | 4.52004 | 0.306840 | ||||||||
\(218\) | −1.01461 | −0.0687182 | ||||||||
\(219\) | 8.24264 | 0.556986 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.51523 | 0.169193 | ||||||||
\(222\) | −15.5206 | −1.04167 | ||||||||
\(223\) | 9.00532 | 0.603041 | 0.301521 | − | 0.953460i | \(-0.402506\pi\) | ||||
0.301521 | + | 0.953460i | \(0.402506\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 2.82843 | 0.188562 | ||||||||
\(226\) | 5.83912 | 0.388413 | ||||||||
\(227\) | −20.9895 | −1.39312 | −0.696560 | − | 0.717499i | \(-0.745287\pi\) | ||||
−0.696560 | + | 0.717499i | \(0.745287\pi\) | |||||||
\(228\) | 5.49938 | 0.364205 | ||||||||
\(229\) | 29.9109 | 1.97657 | 0.988283 | − | 0.152633i | \(-0.0487751\pi\) | ||||
0.988283 | + | 0.152633i | \(0.0487751\pi\) | |||||||
\(230\) | −0.110988 | −0.00731834 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.49938 | 0.164092 | ||||||||
\(233\) | 11.8917 | 0.779050 | 0.389525 | − | 0.921016i | \(-0.372639\pi\) | ||||
0.389525 | + | 0.921016i | \(0.372639\pi\) | |||||||
\(234\) | −15.8272 | −1.03466 | ||||||||
\(235\) | 1.51399 | 0.0987618 | ||||||||
\(236\) | 3.97469 | 0.258730 | ||||||||
\(237\) | −27.0798 | −1.75902 | ||||||||
\(238\) | −0.449490 | −0.0291361 | ||||||||
\(239\) | 22.6819 | 1.46717 | 0.733587 | − | 0.679596i | \(-0.237845\pi\) | ||||
0.733587 | + | 0.679596i | \(0.237845\pi\) | |||||||
\(240\) | −2.41421 | −0.155837 | ||||||||
\(241\) | 8.72135 | 0.561792 | 0.280896 | − | 0.959738i | \(-0.409368\pi\) | ||||
0.280896 | + | 0.959738i | \(0.409368\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 21.6569 | 1.38929 | ||||||||
\(244\) | −4.29253 | −0.274801 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | −18.5352 | −1.18176 | ||||||||
\(247\) | −12.7467 | −0.811051 | ||||||||
\(248\) | −4.52004 | −0.287023 | ||||||||
\(249\) | 40.3078 | 2.55440 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 0.728651 | 0.0459920 | 0.0229960 | − | 0.999736i | \(-0.492679\pi\) | ||||
0.0229960 | + | 0.999736i | \(0.492679\pi\) | |||||||
\(252\) | 2.82843 | 0.178174 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 8.36257 | 0.524714 | ||||||||
\(255\) | −1.08516 | −0.0679556 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 10.4203 | 0.649998 | 0.324999 | − | 0.945714i | \(-0.394636\pi\) | ||||
0.324999 | + | 0.945714i | \(0.394636\pi\) | |||||||
\(258\) | 3.24389 | 0.201955 | ||||||||
\(259\) | −6.42883 | −0.399468 | ||||||||
\(260\) | 5.59575 | 0.347034 | ||||||||
\(261\) | −7.06931 | −0.437579 | ||||||||
\(262\) | −10.5704 | −0.653044 | ||||||||
\(263\) | −0.150909 | −0.00930542 | −0.00465271 | − | 0.999989i | \(-0.501481\pi\) | ||||
−0.00465271 | + | 0.999989i | \(0.501481\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.94887 | −0.426866 | ||||||||
\(266\) | 2.27792 | 0.139668 | ||||||||
\(267\) | −5.24389 | −0.320921 | ||||||||
\(268\) | −11.1708 | −0.682368 | ||||||||
\(269\) | 1.33726 | 0.0815340 | 0.0407670 | − | 0.999169i | \(-0.487020\pi\) | ||||
0.0407670 | + | 0.999169i | \(0.487020\pi\) | |||||||
\(270\) | −0.414214 | −0.0252082 | ||||||||
\(271\) | 25.2500 | 1.53383 | 0.766913 | − | 0.641751i | \(-0.221792\pi\) | ||||
0.766913 | + | 0.641751i | \(0.221792\pi\) | |||||||
\(272\) | 0.449490 | 0.0272543 | ||||||||
\(273\) | −13.5093 | −0.817623 | ||||||||
\(274\) | 10.8895 | 0.657860 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.267949 | −0.0161286 | ||||||||
\(277\) | 4.14286 | 0.248921 | 0.124460 | − | 0.992225i | \(-0.460280\pi\) | ||||
0.124460 | + | 0.992225i | \(0.460280\pi\) | |||||||
\(278\) | −15.5493 | −0.932583 | ||||||||
\(279\) | 12.7846 | 0.765395 | ||||||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | 9.33046 | 0.556608 | 0.278304 | − | 0.960493i | \(-0.410228\pi\) | ||||
0.278304 | + | 0.960493i | \(0.410228\pi\) | |||||||
\(282\) | 3.65509 | 0.217658 | ||||||||
\(283\) | 0.839639 | 0.0499114 | 0.0249557 | − | 0.999689i | \(-0.492056\pi\) | ||||
0.0249557 | + | 0.999689i | \(0.492056\pi\) | |||||||
\(284\) | −1.87780 | −0.111427 | ||||||||
\(285\) | 5.49938 | 0.325755 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.67752 | −0.453190 | ||||||||
\(288\) | −2.82843 | −0.166667 | ||||||||
\(289\) | −16.7980 | −0.988115 | ||||||||
\(290\) | 2.49938 | 0.146769 | ||||||||
\(291\) | 24.4488 | 1.43321 | ||||||||
\(292\) | −3.41421 | −0.199802 | ||||||||
\(293\) | −14.6968 | −0.858595 | −0.429297 | − | 0.903163i | \(-0.641239\pi\) | ||||
−0.429297 | + | 0.903163i | \(0.641239\pi\) | |||||||
\(294\) | 2.41421 | 0.140800 | ||||||||
\(295\) | 3.97469 | 0.231415 | ||||||||
\(296\) | 6.42883 | 0.373668 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 19.0552 | 1.10384 | ||||||||
\(299\) | 0.621063 | 0.0359170 | ||||||||
\(300\) | −2.41421 | −0.139385 | ||||||||
\(301\) | 1.34366 | 0.0774473 | ||||||||
\(302\) | −23.3590 | −1.34416 | ||||||||
\(303\) | 15.6057 | 0.896525 | ||||||||
\(304\) | −2.27792 | −0.130647 | ||||||||
\(305\) | −4.29253 | −0.245789 | ||||||||
\(306\) | −1.27135 | −0.0726782 | ||||||||
\(307\) | 21.2724 | 1.21408 | 0.607039 | − | 0.794672i | \(-0.292357\pi\) | ||||
0.607039 | + | 0.794672i | \(0.292357\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.2285 | 1.03699 | ||||||||
\(310\) | −4.52004 | −0.256721 | ||||||||
\(311\) | −15.4623 | −0.876789 | −0.438394 | − | 0.898783i | \(-0.644453\pi\) | ||||
−0.438394 | + | 0.898783i | \(0.644453\pi\) | |||||||
\(312\) | 13.5093 | 0.764816 | ||||||||
\(313\) | −10.0613 | −0.568696 | −0.284348 | − | 0.958721i | \(-0.591777\pi\) | ||||
−0.284348 | + | 0.958721i | \(0.591777\pi\) | |||||||
\(314\) | 16.6617 | 0.940272 | ||||||||
\(315\) | 2.82843 | 0.159364 | ||||||||
\(316\) | 11.2168 | 0.630995 | ||||||||
\(317\) | 12.3764 | 0.695131 | 0.347565 | − | 0.937656i | \(-0.387008\pi\) | ||||
0.347565 | + | 0.937656i | \(0.387008\pi\) | |||||||
\(318\) | −16.7761 | −0.940754 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −14.4969 | −0.809137 | ||||||||
\(322\) | −0.110988 | −0.00618513 | ||||||||
\(323\) | −1.02390 | −0.0569713 | ||||||||
\(324\) | −9.48528 | −0.526960 | ||||||||
\(325\) | 5.59575 | 0.310397 | ||||||||
\(326\) | −2.01994 | −0.111874 | ||||||||
\(327\) | −2.44949 | −0.135457 | ||||||||
\(328\) | 7.67752 | 0.423920 | ||||||||
\(329\) | 1.51399 | 0.0834690 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.80776 | 0.374188 | 0.187094 | − | 0.982342i | \(-0.440093\pi\) | ||||
0.187094 | + | 0.982342i | \(0.440093\pi\) | |||||||
\(332\) | −16.6960 | −0.916315 | ||||||||
\(333\) | −18.1835 | −0.996448 | ||||||||
\(334\) | −22.4402 | −1.22787 | ||||||||
\(335\) | −11.1708 | −0.610328 | ||||||||
\(336\) | −2.41421 | −0.131706 | ||||||||
\(337\) | 4.48852 | 0.244505 | 0.122253 | − | 0.992499i | \(-0.460988\pi\) | ||||
0.122253 | + | 0.992499i | \(0.460988\pi\) | |||||||
\(338\) | −18.3125 | −0.996067 | ||||||||
\(339\) | 14.0969 | 0.765638 | ||||||||
\(340\) | 0.449490 | 0.0243770 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 6.44292 | 0.348393 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −1.34366 | −0.0724454 | ||||||||
\(345\) | −0.267949 | −0.0144259 | ||||||||
\(346\) | 20.2419 | 1.08821 | ||||||||
\(347\) | 24.7899 | 1.33079 | 0.665396 | − | 0.746490i | \(-0.268263\pi\) | ||||
0.665396 | + | 0.746490i | \(0.268263\pi\) | |||||||
\(348\) | 6.03403 | 0.323458 | ||||||||
\(349\) | 5.59716 | 0.299609 | 0.149805 | − | 0.988716i | \(-0.452136\pi\) | ||||
0.149805 | + | 0.988716i | \(0.452136\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | 2.31784 | 0.123717 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.32956 | −0.177215 | −0.0886074 | − | 0.996067i | \(-0.528242\pi\) | ||||
−0.0886074 | + | 0.996067i | \(0.528242\pi\) | |||||||
\(354\) | 9.59575 | 0.510009 | ||||||||
\(355\) | −1.87780 | −0.0996633 | ||||||||
\(356\) | 2.17209 | 0.115120 | ||||||||
\(357\) | −1.08516 | −0.0574330 | ||||||||
\(358\) | 16.3132 | 0.862179 | ||||||||
\(359\) | −27.2046 | −1.43581 | −0.717903 | − | 0.696143i | \(-0.754898\pi\) | ||||
−0.717903 | + | 0.696143i | \(0.754898\pi\) | |||||||
\(360\) | −2.82843 | −0.149071 | ||||||||
\(361\) | −13.8111 | −0.726900 | ||||||||
\(362\) | −10.0659 | −0.529052 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.59575 | 0.293297 | ||||||||
\(365\) | −3.41421 | −0.178708 | ||||||||
\(366\) | −10.3631 | −0.541687 | ||||||||
\(367\) | −36.2016 | −1.88971 | −0.944855 | − | 0.327489i | \(-0.893798\pi\) | ||||
−0.944855 | + | 0.327489i | \(0.893798\pi\) | |||||||
\(368\) | 0.110988 | 0.00578566 | ||||||||
\(369\) | −21.7153 | −1.13045 | ||||||||
\(370\) | 6.42883 | 0.334219 | ||||||||
\(371\) | −6.94887 | −0.360767 | ||||||||
\(372\) | −10.9123 | −0.565779 | ||||||||
\(373\) | −3.02848 | −0.156809 | −0.0784043 | − | 0.996922i | \(-0.524983\pi\) | ||||
−0.0784043 | + | 0.996922i | \(0.524983\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.41421 | −0.124669 | ||||||||
\(376\) | −1.51399 | −0.0780781 | ||||||||
\(377\) | −13.9859 | −0.720311 | ||||||||
\(378\) | −0.414214 | −0.0213048 | ||||||||
\(379\) | 11.6617 | 0.599019 | 0.299510 | − | 0.954093i | \(-0.403177\pi\) | ||||
0.299510 | + | 0.954093i | \(0.403177\pi\) | |||||||
\(380\) | −2.27792 | −0.116855 | ||||||||
\(381\) | 20.1890 | 1.03431 | ||||||||
\(382\) | 12.6211 | 0.645750 | ||||||||
\(383\) | −8.46943 | −0.432767 | −0.216384 | − | 0.976308i | \(-0.569426\pi\) | ||||
−0.216384 | + | 0.976308i | \(0.569426\pi\) | |||||||
\(384\) | 2.41421 | 0.123200 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 18.3984 | 0.936452 | ||||||||
\(387\) | 3.80045 | 0.193188 | ||||||||
\(388\) | −10.1270 | −0.514121 | ||||||||
\(389\) | 10.5400 | 0.534398 | 0.267199 | − | 0.963641i | \(-0.413902\pi\) | ||||
0.267199 | + | 0.963641i | \(0.413902\pi\) | |||||||
\(390\) | 13.5093 | 0.684072 | ||||||||
\(391\) | 0.0498881 | 0.00252295 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −25.5193 | −1.28728 | ||||||||
\(394\) | −4.24921 | −0.214072 | ||||||||
\(395\) | 11.2168 | 0.564379 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.9280 | −1.30129 | −0.650644 | − | 0.759383i | \(-0.725501\pi\) | ||||
−0.650644 | + | 0.759383i | \(0.725501\pi\) | |||||||
\(398\) | 16.8211 | 0.843167 | ||||||||
\(399\) | 5.49938 | 0.275313 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 3.06251 | 0.152934 | 0.0764672 | − | 0.997072i | \(-0.475636\pi\) | ||||
0.0764672 | + | 0.997072i | \(0.475636\pi\) | |||||||
\(402\) | −26.9688 | −1.34508 | ||||||||
\(403\) | 25.2930 | 1.25994 | ||||||||
\(404\) | −6.46410 | −0.321601 | ||||||||
\(405\) | −9.48528 | −0.471327 | ||||||||
\(406\) | 2.49938 | 0.124042 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 1.08516 | 0.0537236 | ||||||||
\(409\) | −14.8635 | −0.734952 | −0.367476 | − | 0.930033i | \(-0.619778\pi\) | ||||
−0.367476 | + | 0.930033i | \(0.619778\pi\) | |||||||
\(410\) | 7.67752 | 0.379166 | ||||||||
\(411\) | 26.2896 | 1.29677 | ||||||||
\(412\) | −7.55051 | −0.371987 | ||||||||
\(413\) | 3.97469 | 0.195582 | ||||||||
\(414\) | −0.313922 | −0.0154284 | ||||||||
\(415\) | −16.6960 | −0.819577 | ||||||||
\(416\) | −5.59575 | −0.274354 | ||||||||
\(417\) | −37.5392 | −1.83830 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −30.5280 | −1.49139 | −0.745696 | − | 0.666286i | \(-0.767883\pi\) | ||||
−0.745696 | + | 0.666286i | \(0.767883\pi\) | |||||||
\(420\) | −2.41421 | −0.117802 | ||||||||
\(421\) | 21.5425 | 1.04992 | 0.524958 | − | 0.851128i | \(-0.324081\pi\) | ||||
0.524958 | + | 0.851128i | \(0.324081\pi\) | |||||||
\(422\) | 0.762683 | 0.0371268 | ||||||||
\(423\) | 4.28221 | 0.208208 | ||||||||
\(424\) | 6.94887 | 0.337467 | ||||||||
\(425\) | 0.449490 | 0.0218035 | ||||||||
\(426\) | −4.53341 | −0.219644 | ||||||||
\(427\) | −4.29253 | −0.207730 | ||||||||
\(428\) | 6.00481 | 0.290253 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.34366 | −0.0647971 | ||||||||
\(431\) | −2.31784 | −0.111646 | −0.0558231 | − | 0.998441i | \(-0.517778\pi\) | ||||
−0.0558231 | + | 0.998441i | \(0.517778\pi\) | |||||||
\(432\) | 0.414214 | 0.0199289 | ||||||||
\(433\) | −15.3870 | −0.739451 | −0.369726 | − | 0.929141i | \(-0.620548\pi\) | ||||
−0.369726 | + | 0.929141i | \(0.620548\pi\) | |||||||
\(434\) | −4.52004 | −0.216969 | ||||||||
\(435\) | 6.03403 | 0.289310 | ||||||||
\(436\) | 1.01461 | 0.0485911 | ||||||||
\(437\) | −0.252822 | −0.0120941 | ||||||||
\(438\) | −8.24264 | −0.393849 | ||||||||
\(439\) | −19.8045 | −0.945218 | −0.472609 | − | 0.881272i | \(-0.656688\pi\) | ||||
−0.472609 | + | 0.881272i | \(0.656688\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.82843 | 0.134687 | ||||||||
\(442\) | −2.51523 | −0.119637 | ||||||||
\(443\) | 15.4203 | 0.732640 | 0.366320 | − | 0.930489i | \(-0.380618\pi\) | ||||
0.366320 | + | 0.930489i | \(0.380618\pi\) | |||||||
\(444\) | 15.5206 | 0.736573 | ||||||||
\(445\) | 2.17209 | 0.102967 | ||||||||
\(446\) | −9.00532 | −0.426414 | ||||||||
\(447\) | 46.0034 | 2.17588 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −18.2046 | −0.859130 | −0.429565 | − | 0.903036i | \(-0.641333\pi\) | ||||
−0.429565 | + | 0.903036i | \(0.641333\pi\) | |||||||
\(450\) | −2.82843 | −0.133333 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −5.83912 | −0.274649 | ||||||||
\(453\) | −56.3935 | −2.64960 | ||||||||
\(454\) | 20.9895 | 0.985085 | ||||||||
\(455\) | 5.59575 | 0.262333 | ||||||||
\(456\) | −5.49938 | −0.257532 | ||||||||
\(457\) | 27.6216 | 1.29208 | 0.646041 | − | 0.763302i | \(-0.276423\pi\) | ||||
0.646041 | + | 0.763302i | \(0.276423\pi\) | |||||||
\(458\) | −29.9109 | −1.39764 | ||||||||
\(459\) | 0.186185 | 0.00869036 | ||||||||
\(460\) | 0.110988 | 0.00517485 | ||||||||
\(461\) | 31.6027 | 1.47189 | 0.735943 | − | 0.677044i | \(-0.236739\pi\) | ||||
0.735943 | + | 0.677044i | \(0.236739\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.02990 | 0.140812 | 0.0704058 | − | 0.997518i | \(-0.477571\pi\) | ||||
0.0704058 | + | 0.997518i | \(0.477571\pi\) | |||||||
\(464\) | −2.49938 | −0.116031 | ||||||||
\(465\) | −10.9123 | −0.506048 | ||||||||
\(466\) | −11.8917 | −0.550872 | ||||||||
\(467\) | −3.45679 | −0.159961 | −0.0799805 | − | 0.996796i | \(-0.525486\pi\) | ||||
−0.0799805 | + | 0.996796i | \(0.525486\pi\) | |||||||
\(468\) | 15.8272 | 0.731612 | ||||||||
\(469\) | −11.1708 | −0.515822 | ||||||||
\(470\) | −1.51399 | −0.0698351 | ||||||||
\(471\) | 40.2248 | 1.85346 | ||||||||
\(472\) | −3.97469 | −0.182950 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 27.0798 | 1.24382 | ||||||||
\(475\) | −2.27792 | −0.104518 | ||||||||
\(476\) | 0.449490 | 0.0206023 | ||||||||
\(477\) | −19.6544 | −0.899912 | ||||||||
\(478\) | −22.6819 | −1.03745 | ||||||||
\(479\) | 2.92067 | 0.133449 | 0.0667245 | − | 0.997771i | \(-0.478745\pi\) | ||||
0.0667245 | + | 0.997771i | \(0.478745\pi\) | |||||||
\(480\) | 2.41421 | 0.110193 | ||||||||
\(481\) | −35.9741 | −1.64028 | ||||||||
\(482\) | −8.72135 | −0.397247 | ||||||||
\(483\) | −0.267949 | −0.0121921 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.1270 | −0.459844 | ||||||||
\(486\) | −21.6569 | −0.982375 | ||||||||
\(487\) | −4.24248 | −0.192245 | −0.0961225 | − | 0.995370i | \(-0.530644\pi\) | ||||
−0.0961225 | + | 0.995370i | \(0.530644\pi\) | |||||||
\(488\) | 4.29253 | 0.194314 | ||||||||
\(489\) | −4.87656 | −0.220525 | ||||||||
\(490\) | −1.00000 | −0.0451754 | ||||||||
\(491\) | 30.8597 | 1.39268 | 0.696340 | − | 0.717712i | \(-0.254810\pi\) | ||||
0.696340 | + | 0.717712i | \(0.254810\pi\) | |||||||
\(492\) | 18.5352 | 0.835630 | ||||||||
\(493\) | −1.12344 | −0.0505974 | ||||||||
\(494\) | 12.7467 | 0.573499 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.52004 | 0.202956 | ||||||||
\(497\) | −1.87780 | −0.0842308 | ||||||||
\(498\) | −40.3078 | −1.80624 | ||||||||
\(499\) | −38.3475 | −1.71667 | −0.858336 | − | 0.513089i | \(-0.828501\pi\) | ||||
−0.858336 | + | 0.513089i | \(0.828501\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −54.1754 | −2.42038 | ||||||||
\(502\) | −0.728651 | −0.0325213 | ||||||||
\(503\) | −21.7360 | −0.969159 | −0.484579 | − | 0.874747i | \(-0.661027\pi\) | ||||
−0.484579 | + | 0.874747i | \(0.661027\pi\) | |||||||
\(504\) | −2.82843 | −0.125988 | ||||||||
\(505\) | −6.46410 | −0.287649 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −44.2102 | −1.96344 | ||||||||
\(508\) | −8.36257 | −0.371029 | ||||||||
\(509\) | −25.7306 | −1.14049 | −0.570244 | − | 0.821475i | \(-0.693151\pi\) | ||||
−0.570244 | + | 0.821475i | \(0.693151\pi\) | |||||||
\(510\) | 1.08516 | 0.0480519 | ||||||||
\(511\) | −3.41421 | −0.151036 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −0.943544 | −0.0416585 | ||||||||
\(514\) | −10.4203 | −0.459618 | ||||||||
\(515\) | −7.55051 | −0.332715 | ||||||||
\(516\) | −3.24389 | −0.142804 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 6.42883 | 0.282466 | ||||||||
\(519\) | 48.8683 | 2.14508 | ||||||||
\(520\) | −5.59575 | −0.245390 | ||||||||
\(521\) | −6.74378 | −0.295450 | −0.147725 | − | 0.989028i | \(-0.547195\pi\) | ||||
−0.147725 | + | 0.989028i | \(0.547195\pi\) | |||||||
\(522\) | 7.06931 | 0.309415 | ||||||||
\(523\) | 2.58595 | 0.113076 | 0.0565379 | − | 0.998400i | \(-0.481994\pi\) | ||||
0.0565379 | + | 0.998400i | \(0.481994\pi\) | |||||||
\(524\) | 10.5704 | 0.461772 | ||||||||
\(525\) | −2.41421 | −0.105365 | ||||||||
\(526\) | 0.150909 | 0.00657993 | ||||||||
\(527\) | 2.03171 | 0.0885028 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9877 | −0.999464 | ||||||||
\(530\) | 6.94887 | 0.301840 | ||||||||
\(531\) | 11.2421 | 0.487867 | ||||||||
\(532\) | −2.27792 | −0.0987602 | ||||||||
\(533\) | −42.9615 | −1.86087 | ||||||||
\(534\) | 5.24389 | 0.226925 | ||||||||
\(535\) | 6.00481 | 0.259610 | ||||||||
\(536\) | 11.1708 | 0.482507 | ||||||||
\(537\) | 39.3835 | 1.69952 | ||||||||
\(538\) | −1.33726 | −0.0576532 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.414214 | 0.0178249 | ||||||||
\(541\) | −42.4707 | −1.82596 | −0.912979 | − | 0.408007i | \(-0.866224\pi\) | ||||
−0.912979 | + | 0.408007i | \(0.866224\pi\) | |||||||
\(542\) | −25.2500 | −1.08458 | ||||||||
\(543\) | −24.3013 | −1.04287 | ||||||||
\(544\) | −0.449490 | −0.0192717 | ||||||||
\(545\) | 1.01461 | 0.0434612 | ||||||||
\(546\) | 13.5093 | 0.578147 | ||||||||
\(547\) | 29.6629 | 1.26830 | 0.634148 | − | 0.773212i | \(-0.281351\pi\) | ||||
0.634148 | + | 0.773212i | \(0.281351\pi\) | |||||||
\(548\) | −10.8895 | −0.465178 | ||||||||
\(549\) | −12.1411 | −0.518170 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.69337 | 0.242546 | ||||||||
\(552\) | 0.267949 | 0.0114047 | ||||||||
\(553\) | 11.2168 | 0.476988 | ||||||||
\(554\) | −4.14286 | −0.176013 | ||||||||
\(555\) | 15.5206 | 0.658811 | ||||||||
\(556\) | 15.5493 | 0.659436 | ||||||||
\(557\) | 1.64299 | 0.0696157 | 0.0348079 | − | 0.999394i | \(-0.488918\pi\) | ||||
0.0348079 | + | 0.999394i | \(0.488918\pi\) | |||||||
\(558\) | −12.7846 | −0.541216 | ||||||||
\(559\) | 7.51880 | 0.318011 | ||||||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9.33046 | −0.393582 | ||||||||
\(563\) | −6.29591 | −0.265341 | −0.132670 | − | 0.991160i | \(-0.542355\pi\) | ||||
−0.132670 | + | 0.991160i | \(0.542355\pi\) | |||||||
\(564\) | −3.65509 | −0.153907 | ||||||||
\(565\) | −5.83912 | −0.245654 | ||||||||
\(566\) | −0.839639 | −0.0352927 | ||||||||
\(567\) | −9.48528 | −0.398344 | ||||||||
\(568\) | 1.87780 | 0.0787907 | ||||||||
\(569\) | −19.7613 | −0.828436 | −0.414218 | − | 0.910178i | \(-0.635945\pi\) | ||||
−0.414218 | + | 0.910178i | \(0.635945\pi\) | |||||||
\(570\) | −5.49938 | −0.230344 | ||||||||
\(571\) | 15.9882 | 0.669086 | 0.334543 | − | 0.942380i | \(-0.391418\pi\) | ||||
0.334543 | + | 0.942380i | \(0.391418\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 30.4699 | 1.27290 | ||||||||
\(574\) | 7.67752 | 0.320453 | ||||||||
\(575\) | 0.110988 | 0.00462853 | ||||||||
\(576\) | 2.82843 | 0.117851 | ||||||||
\(577\) | −35.5977 | −1.48195 | −0.740975 | − | 0.671532i | \(-0.765636\pi\) | ||||
−0.740975 | + | 0.671532i | \(0.765636\pi\) | |||||||
\(578\) | 16.7980 | 0.698703 | ||||||||
\(579\) | 44.4176 | 1.84593 | ||||||||
\(580\) | −2.49938 | −0.103781 | ||||||||
\(581\) | −16.6960 | −0.692669 | ||||||||
\(582\) | −24.4488 | −1.01343 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 3.41421 | 0.141281 | ||||||||
\(585\) | 15.8272 | 0.654373 | ||||||||
\(586\) | 14.6968 | 0.607118 | ||||||||
\(587\) | −39.2344 | −1.61938 | −0.809688 | − | 0.586860i | \(-0.800364\pi\) | ||||
−0.809688 | + | 0.586860i | \(0.800364\pi\) | |||||||
\(588\) | −2.41421 | −0.0995605 | ||||||||
\(589\) | −10.2963 | −0.424251 | ||||||||
\(590\) | −3.97469 | −0.163635 | ||||||||
\(591\) | −10.2585 | −0.421978 | ||||||||
\(592\) | −6.42883 | −0.264223 | ||||||||
\(593\) | −24.7544 | −1.01654 | −0.508270 | − | 0.861198i | \(-0.669715\pi\) | ||||
−0.508270 | + | 0.861198i | \(0.669715\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.449490 | 0.0184273 | ||||||||
\(596\) | −19.0552 | −0.780532 | ||||||||
\(597\) | 40.6098 | 1.66205 | ||||||||
\(598\) | −0.621063 | −0.0253971 | ||||||||
\(599\) | −35.5118 | −1.45097 | −0.725486 | − | 0.688237i | \(-0.758385\pi\) | ||||
−0.725486 | + | 0.688237i | \(0.758385\pi\) | |||||||
\(600\) | 2.41421 | 0.0985599 | ||||||||
\(601\) | 31.5173 | 1.28562 | 0.642810 | − | 0.766026i | \(-0.277769\pi\) | ||||
0.642810 | + | 0.766026i | \(0.277769\pi\) | |||||||
\(602\) | −1.34366 | −0.0547635 | ||||||||
\(603\) | −31.5959 | −1.28669 | ||||||||
\(604\) | 23.3590 | 0.950462 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −15.6057 | −0.633939 | ||||||||
\(607\) | 11.0849 | 0.449924 | 0.224962 | − | 0.974368i | \(-0.427774\pi\) | ||||
0.224962 | + | 0.974368i | \(0.427774\pi\) | |||||||
\(608\) | 2.27792 | 0.0923817 | ||||||||
\(609\) | 6.03403 | 0.244511 | ||||||||
\(610\) | 4.29253 | 0.173799 | ||||||||
\(611\) | 8.47191 | 0.342737 | ||||||||
\(612\) | 1.27135 | 0.0513912 | ||||||||
\(613\) | 19.3616 | 0.782008 | 0.391004 | − | 0.920389i | \(-0.372128\pi\) | ||||
0.391004 | + | 0.920389i | \(0.372128\pi\) | |||||||
\(614\) | −21.2724 | −0.858483 | ||||||||
\(615\) | 18.5352 | 0.747410 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 39.7449 | 1.60007 | 0.800034 | − | 0.599955i | \(-0.204815\pi\) | ||||
0.800034 | + | 0.599955i | \(0.204815\pi\) | |||||||
\(618\) | −18.2285 | −0.733260 | ||||||||
\(619\) | −35.5001 | −1.42687 | −0.713434 | − | 0.700723i | \(-0.752861\pi\) | ||||
−0.713434 | + | 0.700723i | \(0.752861\pi\) | |||||||
\(620\) | 4.52004 | 0.181529 | ||||||||
\(621\) | 0.0459728 | 0.00184483 | ||||||||
\(622\) | 15.4623 | 0.619983 | ||||||||
\(623\) | 2.17209 | 0.0870229 | ||||||||
\(624\) | −13.5093 | −0.540807 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 10.0613 | 0.402129 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −16.6617 | −0.664873 | ||||||||
\(629\) | −2.88969 | −0.115220 | ||||||||
\(630\) | −2.82843 | −0.112687 | ||||||||
\(631\) | 31.7687 | 1.26469 | 0.632347 | − | 0.774686i | \(-0.282092\pi\) | ||||
0.632347 | + | 0.774686i | \(0.282092\pi\) | |||||||
\(632\) | −11.2168 | −0.446181 | ||||||||
\(633\) | 1.84128 | 0.0731843 | ||||||||
\(634\) | −12.3764 | −0.491532 | ||||||||
\(635\) | −8.36257 | −0.331858 | ||||||||
\(636\) | 16.7761 | 0.665214 | ||||||||
\(637\) | 5.59575 | 0.221712 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.31122 | −0.210109 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 48.4441 | 1.91343 | 0.956713 | − | 0.291034i | \(-0.0939992\pi\) | ||||
0.956713 | + | 0.291034i | \(0.0939992\pi\) | |||||||
\(642\) | 14.4969 | 0.572147 | ||||||||
\(643\) | −5.25526 | −0.207247 | −0.103624 | − | 0.994617i | \(-0.533044\pi\) | ||||
−0.103624 | + | 0.994617i | \(0.533044\pi\) | |||||||
\(644\) | 0.110988 | 0.00437355 | ||||||||
\(645\) | −3.24389 | −0.127728 | ||||||||
\(646\) | 1.02390 | 0.0402848 | ||||||||
\(647\) | 49.1639 | 1.93283 | 0.966416 | − | 0.256984i | \(-0.0827287\pi\) | ||||
0.966416 | + | 0.256984i | \(0.0827287\pi\) | |||||||
\(648\) | 9.48528 | 0.372617 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −5.59575 | −0.219484 | ||||||||
\(651\) | −10.9123 | −0.427689 | ||||||||
\(652\) | 2.01994 | 0.0791068 | ||||||||
\(653\) | −35.4550 | −1.38746 | −0.693732 | − | 0.720234i | \(-0.744035\pi\) | ||||
−0.693732 | + | 0.720234i | \(0.744035\pi\) | |||||||
\(654\) | 2.44949 | 0.0957826 | ||||||||
\(655\) | 10.5704 | 0.413021 | ||||||||
\(656\) | −7.67752 | −0.299757 | ||||||||
\(657\) | −9.65685 | −0.376750 | ||||||||
\(658\) | −1.51399 | −0.0590215 | ||||||||
\(659\) | −15.5831 | −0.607031 | −0.303515 | − | 0.952827i | \(-0.598160\pi\) | ||||
−0.303515 | + | 0.952827i | \(0.598160\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.5419 | −0.876778 | −0.438389 | − | 0.898785i | \(-0.644451\pi\) | ||||
−0.438389 | + | 0.898785i | \(0.644451\pi\) | |||||||
\(662\) | −6.80776 | −0.264591 | ||||||||
\(663\) | −6.07231 | −0.235829 | ||||||||
\(664\) | 16.6960 | 0.647932 | ||||||||
\(665\) | −2.27792 | −0.0883338 | ||||||||
\(666\) | 18.1835 | 0.704595 | ||||||||
\(667\) | −0.277401 | −0.0107410 | ||||||||
\(668\) | 22.4402 | 0.868237 | ||||||||
\(669\) | −21.7408 | −0.840547 | ||||||||
\(670\) | 11.1708 | 0.431567 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 2.41421 | 0.0931303 | ||||||||
\(673\) | 42.2397 | 1.62822 | 0.814111 | − | 0.580710i | \(-0.197225\pi\) | ||||
0.814111 | + | 0.580710i | \(0.197225\pi\) | |||||||
\(674\) | −4.48852 | −0.172891 | ||||||||
\(675\) | 0.414214 | 0.0159431 | ||||||||
\(676\) | 18.3125 | 0.704326 | ||||||||
\(677\) | 27.2287 | 1.04648 | 0.523242 | − | 0.852184i | \(-0.324722\pi\) | ||||
0.523242 | + | 0.852184i | \(0.324722\pi\) | |||||||
\(678\) | −14.0969 | −0.541388 | ||||||||
\(679\) | −10.1270 | −0.388639 | ||||||||
\(680\) | −0.449490 | −0.0172371 | ||||||||
\(681\) | 50.6731 | 1.94180 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.2266 | −1.27138 | −0.635690 | − | 0.771945i | \(-0.719284\pi\) | ||||
−0.635690 | + | 0.771945i | \(0.719284\pi\) | |||||||
\(684\) | −6.44292 | −0.246351 | ||||||||
\(685\) | −10.8895 | −0.416067 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | −72.2112 | −2.75503 | ||||||||
\(688\) | 1.34366 | 0.0512266 | ||||||||
\(689\) | −38.8842 | −1.48137 | ||||||||
\(690\) | 0.267949 | 0.0102007 | ||||||||
\(691\) | 3.12921 | 0.119041 | 0.0595204 | − | 0.998227i | \(-0.481043\pi\) | ||||
0.0595204 | + | 0.998227i | \(0.481043\pi\) | |||||||
\(692\) | −20.2419 | −0.769482 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −24.7899 | −0.941012 | ||||||||
\(695\) | 15.5493 | 0.589817 | ||||||||
\(696\) | −6.03403 | −0.228719 | ||||||||
\(697\) | −3.45097 | −0.130715 | ||||||||
\(698\) | −5.59716 | −0.211856 | ||||||||
\(699\) | −28.7091 | −1.08588 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | −8.48402 | −0.320437 | −0.160218 | − | 0.987082i | \(-0.551220\pi\) | ||||
−0.160218 | + | 0.987082i | \(0.551220\pi\) | |||||||
\(702\) | −2.31784 | −0.0874811 | ||||||||
\(703\) | 14.6443 | 0.552321 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.65509 | −0.137659 | ||||||||
\(706\) | 3.32956 | 0.125310 | ||||||||
\(707\) | −6.46410 | −0.243108 | ||||||||
\(708\) | −9.59575 | −0.360631 | ||||||||
\(709\) | 1.62962 | 0.0612017 | 0.0306009 | − | 0.999532i | \(-0.490258\pi\) | ||||
0.0306009 | + | 0.999532i | \(0.490258\pi\) | |||||||
\(710\) | 1.87780 | 0.0704726 | ||||||||
\(711\) | 31.7259 | 1.18982 | ||||||||
\(712\) | −2.17209 | −0.0814025 | ||||||||
\(713\) | 0.501671 | 0.0187877 | ||||||||
\(714\) | 1.08516 | 0.0406113 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −16.3132 | −0.609653 | ||||||||
\(717\) | −54.7591 | −2.04501 | ||||||||
\(718\) | 27.2046 | 1.01527 | ||||||||
\(719\) | −23.4644 | −0.875076 | −0.437538 | − | 0.899200i | \(-0.644149\pi\) | ||||
−0.437538 | + | 0.899200i | \(0.644149\pi\) | |||||||
\(720\) | 2.82843 | 0.105409 | ||||||||
\(721\) | −7.55051 | −0.281196 | ||||||||
\(722\) | 13.8111 | 0.513996 | ||||||||
\(723\) | −21.0552 | −0.783052 | ||||||||
\(724\) | 10.0659 | 0.374097 | ||||||||
\(725\) | −2.49938 | −0.0928246 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.87175 | −0.254859 | −0.127429 | − | 0.991848i | \(-0.540673\pi\) | ||||
−0.127429 | + | 0.991848i | \(0.540673\pi\) | |||||||
\(728\) | −5.59575 | −0.207392 | ||||||||
\(729\) | −23.8284 | −0.882534 | ||||||||
\(730\) | 3.41421 | 0.126366 | ||||||||
\(731\) | 0.603962 | 0.0223383 | ||||||||
\(732\) | 10.3631 | 0.383030 | ||||||||
\(733\) | −33.9730 | −1.25482 | −0.627411 | − | 0.778688i | \(-0.715885\pi\) | ||||
−0.627411 | + | 0.778688i | \(0.715885\pi\) | |||||||
\(734\) | 36.2016 | 1.33623 | ||||||||
\(735\) | −2.41421 | −0.0890496 | ||||||||
\(736\) | −0.110988 | −0.00409108 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 21.7153 | 0.799351 | ||||||||
\(739\) | −29.0301 | −1.06789 | −0.533944 | − | 0.845520i | \(-0.679291\pi\) | ||||
−0.533944 | + | 0.845520i | \(0.679291\pi\) | |||||||
\(740\) | −6.42883 | −0.236328 | ||||||||
\(741\) | 30.7732 | 1.13048 | ||||||||
\(742\) | 6.94887 | 0.255101 | ||||||||
\(743\) | −47.1515 | −1.72982 | −0.864911 | − | 0.501925i | \(-0.832625\pi\) | ||||
−0.864911 | + | 0.501925i | \(0.832625\pi\) | |||||||
\(744\) | 10.9123 | 0.400066 | ||||||||
\(745\) | −19.0552 | −0.698129 | ||||||||
\(746\) | 3.02848 | 0.110880 | ||||||||
\(747\) | −47.2235 | −1.72782 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.00481 | 0.219411 | ||||||||
\(750\) | 2.41421 | 0.0881546 | ||||||||
\(751\) | −21.1160 | −0.770532 | −0.385266 | − | 0.922805i | \(-0.625890\pi\) | ||||
−0.385266 | + | 0.922805i | \(0.625890\pi\) | |||||||
\(752\) | 1.51399 | 0.0552095 | ||||||||
\(753\) | −1.75912 | −0.0641059 | ||||||||
\(754\) | 13.9859 | 0.509337 | ||||||||
\(755\) | 23.3590 | 0.850119 | ||||||||
\(756\) | 0.414214 | 0.0150648 | ||||||||
\(757\) | 11.2590 | 0.409216 | 0.204608 | − | 0.978844i | \(-0.434408\pi\) | ||||
0.204608 | + | 0.978844i | \(0.434408\pi\) | |||||||
\(758\) | −11.6617 | −0.423571 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.27792 | 0.0826287 | ||||||||
\(761\) | −10.2708 | −0.372317 | −0.186159 | − | 0.982520i | \(-0.559604\pi\) | ||||
−0.186159 | + | 0.982520i | \(0.559604\pi\) | |||||||
\(762\) | −20.1890 | −0.731371 | ||||||||
\(763\) | 1.01461 | 0.0367314 | ||||||||
\(764\) | −12.6211 | −0.456614 | ||||||||
\(765\) | 1.27135 | 0.0459657 | ||||||||
\(766\) | 8.46943 | 0.306013 | ||||||||
\(767\) | 22.2414 | 0.803090 | ||||||||
\(768\) | −2.41421 | −0.0871154 | ||||||||
\(769\) | 11.3560 | 0.409508 | 0.204754 | − | 0.978813i | \(-0.434361\pi\) | ||||
0.204754 | + | 0.978813i | \(0.434361\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −25.1567 | −0.905998 | ||||||||
\(772\) | −18.3984 | −0.662171 | ||||||||
\(773\) | −41.0116 | −1.47508 | −0.737542 | − | 0.675301i | \(-0.764014\pi\) | ||||
−0.737542 | + | 0.675301i | \(0.764014\pi\) | |||||||
\(774\) | −3.80045 | −0.136604 | ||||||||
\(775\) | 4.52004 | 0.162365 | ||||||||
\(776\) | 10.1270 | 0.363538 | ||||||||
\(777\) | 15.5206 | 0.556797 | ||||||||
\(778\) | −10.5400 | −0.377876 | ||||||||
\(779\) | 17.4887 | 0.626599 | ||||||||
\(780\) | −13.5093 | −0.483712 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −0.0498881 | −0.00178399 | ||||||||
\(783\) | −1.03528 | −0.0369978 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −16.6617 | −0.594680 | ||||||||
\(786\) | 25.5193 | 0.910244 | ||||||||
\(787\) | −45.1477 | −1.60934 | −0.804671 | − | 0.593721i | \(-0.797658\pi\) | ||||
−0.804671 | + | 0.593721i | \(0.797658\pi\) | |||||||
\(788\) | 4.24921 | 0.151372 | ||||||||
\(789\) | 0.364326 | 0.0129703 | ||||||||
\(790\) | −11.2168 | −0.399076 | ||||||||
\(791\) | −5.83912 | −0.207615 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24.0199 | −0.852973 | ||||||||
\(794\) | 25.9280 | 0.920150 | ||||||||
\(795\) | 16.7761 | 0.594985 | ||||||||
\(796\) | −16.8211 | −0.596209 | ||||||||
\(797\) | −34.8398 | −1.23409 | −0.617045 | − | 0.786928i | \(-0.711670\pi\) | ||||
−0.617045 | + | 0.786928i | \(0.711670\pi\) | |||||||
\(798\) | −5.49938 | −0.194676 | ||||||||
\(799\) | 0.680523 | 0.0240752 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 6.14359 | 0.217073 | ||||||||
\(802\) | −3.06251 | −0.108141 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 26.9688 | 0.951116 | ||||||||
\(805\) | 0.110988 | 0.00391182 | ||||||||
\(806\) | −25.2930 | −0.890909 | ||||||||
\(807\) | −3.22842 | −0.113646 | ||||||||
\(808\) | 6.46410 | 0.227406 | ||||||||
\(809\) | −23.5770 | −0.828924 | −0.414462 | − | 0.910067i | \(-0.636030\pi\) | ||||
−0.414462 | + | 0.910067i | \(0.636030\pi\) | |||||||
\(810\) | 9.48528 | 0.333279 | ||||||||
\(811\) | −14.9977 | −0.526641 | −0.263321 | − | 0.964708i | \(-0.584818\pi\) | ||||
−0.263321 | + | 0.964708i | \(0.584818\pi\) | |||||||
\(812\) | −2.49938 | −0.0877110 | ||||||||
\(813\) | −60.9588 | −2.13792 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.01994 | 0.0707552 | ||||||||
\(816\) | −1.08516 | −0.0379883 | ||||||||
\(817\) | −3.06075 | −0.107082 | ||||||||
\(818\) | 14.8635 | 0.519690 | ||||||||
\(819\) | 15.8272 | 0.553047 | ||||||||
\(820\) | −7.67752 | −0.268111 | ||||||||
\(821\) | −38.2540 | −1.33507 | −0.667537 | − | 0.744576i | \(-0.732651\pi\) | ||||
−0.667537 | + | 0.744576i | \(0.732651\pi\) | |||||||
\(822\) | −26.2896 | −0.916957 | ||||||||
\(823\) | −25.3006 | −0.881923 | −0.440961 | − | 0.897526i | \(-0.645362\pi\) | ||||
−0.440961 | + | 0.897526i | \(0.645362\pi\) | |||||||
\(824\) | 7.55051 | 0.263034 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.97469 | −0.138297 | ||||||||
\(827\) | −29.9973 | −1.04311 | −0.521554 | − | 0.853218i | \(-0.674647\pi\) | ||||
−0.521554 | + | 0.853218i | \(0.674647\pi\) | |||||||
\(828\) | 0.313922 | 0.0109095 | ||||||||
\(829\) | 44.3053 | 1.53879 | 0.769394 | − | 0.638775i | \(-0.220558\pi\) | ||||
0.769394 | + | 0.638775i | \(0.220558\pi\) | |||||||
\(830\) | 16.6960 | 0.579528 | ||||||||
\(831\) | −10.0018 | −0.346957 | ||||||||
\(832\) | 5.59575 | 0.193998 | ||||||||
\(833\) | 0.449490 | 0.0155739 | ||||||||
\(834\) | 37.5392 | 1.29988 | ||||||||
\(835\) | 22.4402 | 0.776575 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.87226 | 0.0647149 | ||||||||
\(838\) | 30.5280 | 1.05457 | ||||||||
\(839\) | 33.3319 | 1.15074 | 0.575372 | − | 0.817892i | \(-0.304857\pi\) | ||||
0.575372 | + | 0.817892i | \(0.304857\pi\) | |||||||
\(840\) | 2.41421 | 0.0832983 | ||||||||
\(841\) | −22.7531 | −0.784590 | ||||||||
\(842\) | −21.5425 | −0.742403 | ||||||||
\(843\) | −22.5257 | −0.775827 | ||||||||
\(844\) | −0.762683 | −0.0262526 | ||||||||
\(845\) | 18.3125 | 0.629968 | ||||||||
\(846\) | −4.28221 | −0.147225 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6.94887 | −0.238625 | ||||||||
\(849\) | −2.02707 | −0.0695688 | ||||||||
\(850\) | −0.449490 | −0.0154174 | ||||||||
\(851\) | −0.713524 | −0.0244593 | ||||||||
\(852\) | 4.53341 | 0.155312 | ||||||||
\(853\) | −11.3834 | −0.389760 | −0.194880 | − | 0.980827i | \(-0.562432\pi\) | ||||
−0.194880 | + | 0.980827i | \(0.562432\pi\) | |||||||
\(854\) | 4.29253 | 0.146887 | ||||||||
\(855\) | −6.44292 | −0.220343 | ||||||||
\(856\) | −6.00481 | −0.205240 | ||||||||
\(857\) | −37.8048 | −1.29139 | −0.645693 | − | 0.763597i | \(-0.723431\pi\) | ||||
−0.645693 | + | 0.763597i | \(0.723431\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −57.8457 | −1.97367 | −0.986834 | − | 0.161735i | \(-0.948291\pi\) | ||||
−0.986834 | + | 0.161735i | \(0.948291\pi\) | |||||||
\(860\) | 1.34366 | 0.0458185 | ||||||||
\(861\) | 18.5352 | 0.631677 | ||||||||
\(862\) | 2.31784 | 0.0789458 | ||||||||
\(863\) | 45.1248 | 1.53607 | 0.768033 | − | 0.640410i | \(-0.221236\pi\) | ||||
0.768033 | + | 0.640410i | \(0.221236\pi\) | |||||||
\(864\) | −0.414214 | −0.0140918 | ||||||||
\(865\) | −20.2419 | −0.688246 | ||||||||
\(866\) | 15.3870 | 0.522871 | ||||||||
\(867\) | 40.5539 | 1.37728 | ||||||||
\(868\) | 4.52004 | 0.153420 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −6.03403 | −0.204573 | ||||||||
\(871\) | −62.5093 | −2.11805 | ||||||||
\(872\) | −1.01461 | −0.0343591 | ||||||||
\(873\) | −28.6435 | −0.969436 | ||||||||
\(874\) | 0.252822 | 0.00855183 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 8.24264 | 0.278493 | ||||||||
\(877\) | 20.5249 | 0.693075 | 0.346537 | − | 0.938036i | \(-0.387357\pi\) | ||||
0.346537 | + | 0.938036i | \(0.387357\pi\) | |||||||
\(878\) | 19.8045 | 0.668370 | ||||||||
\(879\) | 35.4812 | 1.19675 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.43131 | −0.284058 | −0.142029 | − | 0.989862i | \(-0.545363\pi\) | ||||
−0.142029 | + | 0.989862i | \(0.545363\pi\) | |||||||
\(882\) | −2.82843 | −0.0952381 | ||||||||
\(883\) | 51.5287 | 1.73408 | 0.867040 | − | 0.498239i | \(-0.166020\pi\) | ||||
0.867040 | + | 0.498239i | \(0.166020\pi\) | |||||||
\(884\) | 2.51523 | 0.0845965 | ||||||||
\(885\) | −9.59575 | −0.322558 | ||||||||
\(886\) | −15.4203 | −0.518055 | ||||||||
\(887\) | −28.9499 | −0.972042 | −0.486021 | − | 0.873947i | \(-0.661552\pi\) | ||||
−0.486021 | + | 0.873947i | \(0.661552\pi\) | |||||||
\(888\) | −15.5206 | −0.520836 | ||||||||
\(889\) | −8.36257 | −0.280471 | ||||||||
\(890\) | −2.17209 | −0.0728086 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 9.00532 | 0.301521 | ||||||||
\(893\) | −3.44874 | −0.115408 | ||||||||
\(894\) | −46.0034 | −1.53858 | ||||||||
\(895\) | −16.3132 | −0.545290 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −1.49938 | −0.0500628 | ||||||||
\(898\) | 18.2046 | 0.607497 | ||||||||
\(899\) | −11.2973 | −0.376786 | ||||||||
\(900\) | 2.82843 | 0.0942809 | ||||||||
\(901\) | −3.12344 | −0.104057 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.24389 | −0.107950 | ||||||||
\(904\) | 5.83912 | 0.194206 | ||||||||
\(905\) | 10.0659 | 0.334602 | ||||||||
\(906\) | 56.3935 | 1.87355 | ||||||||
\(907\) | −5.81255 | −0.193003 | −0.0965013 | − | 0.995333i | \(-0.530765\pi\) | ||||
−0.0965013 | + | 0.995333i | \(0.530765\pi\) | |||||||
\(908\) | −20.9895 | −0.696560 | ||||||||
\(909\) | −18.2832 | −0.606417 | ||||||||
\(910\) | −5.59575 | −0.185497 | ||||||||
\(911\) | 21.8126 | 0.722683 | 0.361341 | − | 0.932434i | \(-0.382319\pi\) | ||||
0.361341 | + | 0.932434i | \(0.382319\pi\) | |||||||
\(912\) | 5.49938 | 0.182103 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −27.6216 | −0.913641 | ||||||||
\(915\) | 10.3631 | 0.342593 | ||||||||
\(916\) | 29.9109 | 0.988283 | ||||||||
\(917\) | 10.5704 | 0.349067 | ||||||||
\(918\) | −0.186185 | −0.00614501 | ||||||||
\(919\) | 48.0456 | 1.58488 | 0.792440 | − | 0.609950i | \(-0.208811\pi\) | ||||
0.792440 | + | 0.609950i | \(0.208811\pi\) | |||||||
\(920\) | −0.110988 | −0.00365917 | ||||||||
\(921\) | −51.3561 | −1.69224 | ||||||||
\(922\) | −31.6027 | −1.04078 | ||||||||
\(923\) | −10.5077 | −0.345865 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.42883 | −0.211378 | ||||||||
\(926\) | −3.02990 | −0.0995688 | ||||||||
\(927\) | −21.3561 | −0.701425 | ||||||||
\(928\) | 2.49938 | 0.0820461 | ||||||||
\(929\) | 28.8259 | 0.945748 | 0.472874 | − | 0.881130i | \(-0.343217\pi\) | ||||
0.472874 | + | 0.881130i | \(0.343217\pi\) | |||||||
\(930\) | 10.9123 | 0.357830 | ||||||||
\(931\) | −2.27792 | −0.0746557 | ||||||||
\(932\) | 11.8917 | 0.389525 | ||||||||
\(933\) | 37.3294 | 1.22211 | ||||||||
\(934\) | 3.45679 | 0.113110 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −15.8272 | −0.517328 | ||||||||
\(937\) | 12.7627 | 0.416939 | 0.208469 | − | 0.978029i | \(-0.433152\pi\) | ||||
0.208469 | + | 0.978029i | \(0.433152\pi\) | |||||||
\(938\) | 11.1708 | 0.364741 | ||||||||
\(939\) | 24.2900 | 0.792675 | ||||||||
\(940\) | 1.51399 | 0.0493809 | ||||||||
\(941\) | −20.1593 | −0.657173 | −0.328586 | − | 0.944474i | \(-0.606572\pi\) | ||||
−0.328586 | + | 0.944474i | \(0.606572\pi\) | |||||||
\(942\) | −40.2248 | −1.31060 | ||||||||
\(943\) | −0.852114 | −0.0277486 | ||||||||
\(944\) | 3.97469 | 0.129365 | ||||||||
\(945\) | 0.414214 | 0.0134744 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.46868 | 0.0477256 | 0.0238628 | − | 0.999715i | \(-0.492404\pi\) | ||||
0.0238628 | + | 0.999715i | \(0.492404\pi\) | |||||||
\(948\) | −27.0798 | −0.879511 | ||||||||
\(949\) | −19.1051 | −0.620178 | ||||||||
\(950\) | 2.27792 | 0.0739054 | ||||||||
\(951\) | −29.8794 | −0.968906 | ||||||||
\(952\) | −0.449490 | −0.0145680 | ||||||||
\(953\) | −38.5687 | −1.24936 | −0.624681 | − | 0.780880i | \(-0.714771\pi\) | ||||
−0.624681 | + | 0.780880i | \(0.714771\pi\) | |||||||
\(954\) | 19.6544 | 0.636334 | ||||||||
\(955\) | −12.6211 | −0.408408 | ||||||||
\(956\) | 22.6819 | 0.733587 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.92067 | −0.0943627 | ||||||||
\(959\) | −10.8895 | −0.351641 | ||||||||
\(960\) | −2.41421 | −0.0779184 | ||||||||
\(961\) | −10.5692 | −0.340943 | ||||||||
\(962\) | 35.9741 | 1.15985 | ||||||||
\(963\) | 16.9842 | 0.547307 | ||||||||
\(964\) | 8.72135 | 0.280896 | ||||||||
\(965\) | −18.3984 | −0.592264 | ||||||||
\(966\) | 0.267949 | 0.00862112 | ||||||||
\(967\) | −44.4040 | −1.42794 | −0.713968 | − | 0.700178i | \(-0.753104\pi\) | ||||
−0.713968 | + | 0.700178i | \(0.753104\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.47191 | 0.0794093 | ||||||||
\(970\) | 10.1270 | 0.325159 | ||||||||
\(971\) | −17.4270 | −0.559260 | −0.279630 | − | 0.960108i | \(-0.590212\pi\) | ||||
−0.279630 | + | 0.960108i | \(0.590212\pi\) | |||||||
\(972\) | 21.6569 | 0.694644 | ||||||||
\(973\) | 15.5493 | 0.498487 | ||||||||
\(974\) | 4.24248 | 0.135938 | ||||||||
\(975\) | −13.5093 | −0.432645 | ||||||||
\(976\) | −4.29253 | −0.137400 | ||||||||
\(977\) | −1.26471 | −0.0404618 | −0.0202309 | − | 0.999795i | \(-0.506440\pi\) | ||||
−0.0202309 | + | 0.999795i | \(0.506440\pi\) | |||||||
\(978\) | 4.87656 | 0.155935 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | 2.86976 | 0.0916242 | ||||||||
\(982\) | −30.8597 | −0.984774 | ||||||||
\(983\) | −30.6312 | −0.976983 | −0.488492 | − | 0.872569i | \(-0.662453\pi\) | ||||
−0.488492 | + | 0.872569i | \(0.662453\pi\) | |||||||
\(984\) | −18.5352 | −0.590880 | ||||||||
\(985\) | 4.24921 | 0.135391 | ||||||||
\(986\) | 1.12344 | 0.0357778 | ||||||||
\(987\) | −3.65509 | −0.116343 | ||||||||
\(988\) | −12.7467 | −0.405525 | ||||||||
\(989\) | 0.149131 | 0.00474207 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.3840 | 0.838116 | 0.419058 | − | 0.907959i | \(-0.362360\pi\) | ||||
0.419058 | + | 0.907959i | \(0.362360\pi\) | |||||||
\(992\) | −4.52004 | −0.143511 | ||||||||
\(993\) | −16.4354 | −0.521561 | ||||||||
\(994\) | 1.87780 | 0.0595602 | ||||||||
\(995\) | −16.8211 | −0.533266 | ||||||||
\(996\) | 40.3078 | 1.27720 | ||||||||
\(997\) | −50.2403 | −1.59113 | −0.795563 | − | 0.605871i | \(-0.792825\pi\) | ||||
−0.795563 | + | 0.605871i | \(0.792825\pi\) | |||||||
\(998\) | 38.3475 | 1.21387 | ||||||||
\(999\) | −2.66291 | −0.0842506 |
(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 | 8470.2.a.cp.1.2 | ✓ | 4 | |
11.10 | odd | 2 | 8470.2.a.cr.1.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8470.2.a.cp.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
8470.2.a.cr.1.1 | yes | 4 | 11.10 | odd | 2 |