Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [625,2,Mod(1,625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(625, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("625.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 625 = 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 625.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: | \(4.99065012633\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.6152203125.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} - 8x^{6} + 20x^{5} + 26x^{4} - 35x^{3} - 27x^{2} + 16x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(1.32675\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 625.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.326751 | 0.231048 | 0.115524 | − | 0.993305i | \(-0.463145\pi\) | ||||
0.115524 | + | 0.993305i | \(0.463145\pi\) | |||||||
\(3\) | 1.71538 | 0.990374 | 0.495187 | − | 0.868786i | \(-0.335100\pi\) | ||||
0.495187 | + | 0.868786i | \(0.335100\pi\) | |||||||
\(4\) | −1.89323 | −0.946617 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.560502 | 0.228824 | ||||||||
\(7\) | −3.42409 | −1.29419 | −0.647093 | − | 0.762411i | \(-0.724016\pi\) | ||||
−0.647093 | + | 0.762411i | \(0.724016\pi\) | |||||||
\(8\) | −1.27212 | −0.449762 | ||||||||
\(9\) | −0.0574791 | −0.0191597 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.34111 | −1.61041 | −0.805203 | − | 0.592999i | \(-0.797944\pi\) | ||||
−0.805203 | + | 0.592999i | \(0.797944\pi\) | |||||||
\(12\) | −3.24761 | −0.937505 | ||||||||
\(13\) | 3.52114 | 0.976588 | 0.488294 | − | 0.872679i | \(-0.337619\pi\) | ||||
0.488294 | + | 0.872679i | \(0.337619\pi\) | |||||||
\(14\) | −1.11883 | −0.299019 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.37080 | 0.842700 | ||||||||
\(17\) | −2.55787 | −0.620375 | −0.310188 | − | 0.950675i | \(-0.600392\pi\) | ||||
−0.310188 | + | 0.950675i | \(0.600392\pi\) | |||||||
\(18\) | −0.0187814 | −0.00442681 | ||||||||
\(19\) | −2.02579 | −0.464748 | −0.232374 | − | 0.972626i | \(-0.574649\pi\) | ||||
−0.232374 | + | 0.972626i | \(0.574649\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.87362 | −1.28173 | ||||||||
\(22\) | −1.74522 | −0.372081 | ||||||||
\(23\) | −7.57082 | −1.57863 | −0.789313 | − | 0.613991i | \(-0.789563\pi\) | ||||
−0.789313 | + | 0.613991i | \(0.789563\pi\) | |||||||
\(24\) | −2.18216 | −0.445432 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.15054 | 0.225639 | ||||||||
\(27\) | −5.24473 | −1.00935 | ||||||||
\(28\) | 6.48261 | 1.22510 | ||||||||
\(29\) | 4.74270 | 0.880697 | 0.440348 | − | 0.897827i | \(-0.354855\pi\) | ||||
0.440348 | + | 0.897827i | \(0.354855\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.62421 | 0.291716 | 0.145858 | − | 0.989306i | \(-0.453406\pi\) | ||||
0.145858 | + | 0.989306i | \(0.453406\pi\) | |||||||
\(32\) | 3.64565 | 0.644466 | ||||||||
\(33\) | −9.16203 | −1.59490 | ||||||||
\(34\) | −0.835788 | −0.143336 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.108821 | 0.0181369 | ||||||||
\(37\) | 0.0134290 | 0.00220771 | 0.00110385 | − | 0.999999i | \(-0.499649\pi\) | ||||
0.00110385 | + | 0.999999i | \(0.499649\pi\) | |||||||
\(38\) | −0.661929 | −0.107379 | ||||||||
\(39\) | 6.04008 | 0.967187 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.67740 | 1.51136 | 0.755678 | − | 0.654943i | \(-0.227307\pi\) | ||||
0.755678 | + | 0.654943i | \(0.227307\pi\) | |||||||
\(42\) | −1.91921 | −0.296141 | ||||||||
\(43\) | −2.32645 | −0.354780 | −0.177390 | − | 0.984141i | \(-0.556765\pi\) | ||||
−0.177390 | + | 0.984141i | \(0.556765\pi\) | |||||||
\(44\) | 10.1120 | 1.52444 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.47377 | −0.364738 | ||||||||
\(47\) | −6.94647 | −1.01325 | −0.506624 | − | 0.862167i | \(-0.669107\pi\) | ||||
−0.506624 | + | 0.862167i | \(0.669107\pi\) | |||||||
\(48\) | 5.78220 | 0.834588 | ||||||||
\(49\) | 4.72443 | 0.674918 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.38772 | −0.614403 | ||||||||
\(52\) | −6.66634 | −0.924454 | ||||||||
\(53\) | −1.72246 | −0.236598 | −0.118299 | − | 0.992978i | \(-0.537744\pi\) | ||||
−0.118299 | + | 0.992978i | \(0.537744\pi\) | |||||||
\(54\) | −1.71372 | −0.233208 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.35585 | 0.582075 | ||||||||
\(57\) | −3.47500 | −0.460275 | ||||||||
\(58\) | 1.54968 | 0.203483 | ||||||||
\(59\) | −0.0221830 | −0.00288798 | −0.00144399 | − | 0.999999i | \(-0.500460\pi\) | ||||
−0.00144399 | + | 0.999999i | \(0.500460\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.91768 | 0.501607 | 0.250804 | − | 0.968038i | \(-0.419305\pi\) | ||||
0.250804 | + | 0.968038i | \(0.419305\pi\) | |||||||
\(62\) | 0.530712 | 0.0674004 | ||||||||
\(63\) | 0.196814 | 0.0247962 | ||||||||
\(64\) | −5.55038 | −0.693798 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.99370 | −0.368499 | ||||||||
\(67\) | −4.11832 | −0.503133 | −0.251566 | − | 0.967840i | \(-0.580946\pi\) | ||||
−0.251566 | + | 0.967840i | \(0.580946\pi\) | |||||||
\(68\) | 4.84265 | 0.587258 | ||||||||
\(69\) | −12.9868 | −1.56343 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.33894 | 0.277581 | 0.138790 | − | 0.990322i | \(-0.455679\pi\) | ||||
0.138790 | + | 0.990322i | \(0.455679\pi\) | |||||||
\(72\) | 0.0731202 | 0.00861730 | ||||||||
\(73\) | −1.51373 | −0.177169 | −0.0885843 | − | 0.996069i | \(-0.528234\pi\) | ||||
−0.0885843 | + | 0.996069i | \(0.528234\pi\) | |||||||
\(74\) | 0.00438793 | 0.000510086 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.83530 | 0.439939 | ||||||||
\(77\) | 18.2885 | 2.08417 | ||||||||
\(78\) | 1.97360 | 0.223467 | ||||||||
\(79\) | 0.426831 | 0.0480222 | 0.0240111 | − | 0.999712i | \(-0.492356\pi\) | ||||
0.0240111 | + | 0.999712i | \(0.492356\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.82426 | −0.980473 | ||||||||
\(82\) | 3.16210 | 0.349196 | ||||||||
\(83\) | 6.04187 | 0.663181 | 0.331591 | − | 0.943423i | \(-0.392415\pi\) | ||||
0.331591 | + | 0.943423i | \(0.392415\pi\) | |||||||
\(84\) | 11.1201 | 1.21331 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.760170 | −0.0819712 | ||||||||
\(87\) | 8.13552 | 0.872219 | ||||||||
\(88\) | 6.79453 | 0.724299 | ||||||||
\(89\) | −6.09362 | −0.645922 | −0.322961 | − | 0.946412i | \(-0.604678\pi\) | ||||
−0.322961 | + | 0.946412i | \(0.604678\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.0567 | −1.26389 | ||||||||
\(92\) | 14.3333 | 1.49435 | ||||||||
\(93\) | 2.78613 | 0.288908 | ||||||||
\(94\) | −2.26977 | −0.234109 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 6.25367 | 0.638262 | ||||||||
\(97\) | 16.0018 | 1.62474 | 0.812370 | − | 0.583143i | \(-0.198177\pi\) | ||||
0.812370 | + | 0.583143i | \(0.198177\pi\) | |||||||
\(98\) | 1.54371 | 0.155938 | ||||||||
\(99\) | 0.307002 | 0.0308549 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.44418 | 0.143701 | 0.0718505 | − | 0.997415i | \(-0.477110\pi\) | ||||
0.0718505 | + | 0.997415i | \(0.477110\pi\) | |||||||
\(102\) | −1.43369 | −0.141957 | ||||||||
\(103\) | −14.6657 | −1.44506 | −0.722529 | − | 0.691341i | \(-0.757020\pi\) | ||||
−0.722529 | + | 0.691341i | \(0.757020\pi\) | |||||||
\(104\) | −4.47930 | −0.439232 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.562816 | −0.0546655 | ||||||||
\(107\) | −12.2169 | −1.18106 | −0.590528 | − | 0.807017i | \(-0.701081\pi\) | ||||
−0.590528 | + | 0.807017i | \(0.701081\pi\) | |||||||
\(108\) | 9.92950 | 0.955467 | ||||||||
\(109\) | −15.3516 | −1.47041 | −0.735207 | − | 0.677843i | \(-0.762915\pi\) | ||||
−0.735207 | + | 0.677843i | \(0.762915\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.0230357 | 0.00218646 | ||||||||
\(112\) | −11.5419 | −1.09061 | ||||||||
\(113\) | −18.5544 | −1.74545 | −0.872727 | − | 0.488209i | \(-0.837650\pi\) | ||||
−0.872727 | + | 0.488209i | \(0.837650\pi\) | |||||||
\(114\) | −1.13546 | −0.106345 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −8.97904 | −0.833683 | ||||||||
\(117\) | −0.202392 | −0.0187111 | ||||||||
\(118\) | −0.00724831 | −0.000667261 0 | ||||||||
\(119\) | 8.75840 | 0.802881 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.5275 | 1.59341 | ||||||||
\(122\) | 1.28011 | 0.115895 | ||||||||
\(123\) | 16.6004 | 1.49681 | ||||||||
\(124\) | −3.07500 | −0.276144 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.0643092 | 0.00572911 | ||||||||
\(127\) | −0.677902 | −0.0601541 | −0.0300771 | − | 0.999548i | \(-0.509575\pi\) | ||||
−0.0300771 | + | 0.999548i | \(0.509575\pi\) | |||||||
\(128\) | −9.10489 | −0.804766 | ||||||||
\(129\) | −3.99074 | −0.351365 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.05058 | 0.616012 | 0.308006 | − | 0.951384i | \(-0.400338\pi\) | ||||
0.308006 | + | 0.951384i | \(0.400338\pi\) | |||||||
\(132\) | 17.3459 | 1.50976 | ||||||||
\(133\) | 6.93650 | 0.601471 | ||||||||
\(134\) | −1.34567 | −0.116248 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.25392 | 0.279021 | ||||||||
\(137\) | 10.9186 | 0.932837 | 0.466418 | − | 0.884564i | \(-0.345544\pi\) | ||||
0.466418 | + | 0.884564i | \(0.345544\pi\) | |||||||
\(138\) | −4.24346 | −0.361227 | ||||||||
\(139\) | 19.5102 | 1.65483 | 0.827416 | − | 0.561589i | \(-0.189810\pi\) | ||||
0.827416 | + | 0.561589i | \(0.189810\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.9158 | −1.00349 | ||||||||
\(142\) | 0.764251 | 0.0641345 | ||||||||
\(143\) | −18.8068 | −1.57270 | ||||||||
\(144\) | −0.193751 | −0.0161459 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.494613 | −0.0409345 | ||||||||
\(147\) | 8.10418 | 0.668421 | ||||||||
\(148\) | −0.0254242 | −0.00208985 | ||||||||
\(149\) | −12.7945 | −1.04817 | −0.524085 | − | 0.851666i | \(-0.675593\pi\) | ||||
−0.524085 | + | 0.851666i | \(0.675593\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.15617 | 0.175466 | 0.0877331 | − | 0.996144i | \(-0.472038\pi\) | ||||
0.0877331 | + | 0.996144i | \(0.472038\pi\) | |||||||
\(152\) | 2.57705 | 0.209026 | ||||||||
\(153\) | 0.147024 | 0.0118862 | ||||||||
\(154\) | 5.97578 | 0.481542 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −11.4353 | −0.915556 | ||||||||
\(157\) | 15.7474 | 1.25678 | 0.628389 | − | 0.777899i | \(-0.283715\pi\) | ||||
0.628389 | + | 0.777899i | \(0.283715\pi\) | |||||||
\(158\) | 0.139467 | 0.0110954 | ||||||||
\(159\) | −2.95467 | −0.234321 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 25.9232 | 2.04304 | ||||||||
\(162\) | −2.88334 | −0.226536 | ||||||||
\(163\) | −7.39219 | −0.579001 | −0.289500 | − | 0.957178i | \(-0.593489\pi\) | ||||
−0.289500 | + | 0.957178i | \(0.593489\pi\) | |||||||
\(164\) | −18.3216 | −1.43068 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.97419 | 0.153227 | ||||||||
\(167\) | 10.8165 | 0.837007 | 0.418504 | − | 0.908215i | \(-0.362555\pi\) | ||||
0.418504 | + | 0.908215i | \(0.362555\pi\) | |||||||
\(168\) | 7.47194 | 0.576472 | ||||||||
\(169\) | −0.601591 | −0.0462762 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.116441 | 0.00890444 | ||||||||
\(172\) | 4.40451 | 0.335841 | ||||||||
\(173\) | −14.9983 | −1.14030 | −0.570149 | − | 0.821541i | \(-0.693115\pi\) | ||||
−0.570149 | + | 0.821541i | \(0.693115\pi\) | |||||||
\(174\) | 2.65829 | 0.201524 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −18.0038 | −1.35709 | ||||||||
\(177\) | −0.0380522 | −0.00286018 | ||||||||
\(178\) | −1.99110 | −0.149239 | ||||||||
\(179\) | 7.39841 | 0.552983 | 0.276492 | − | 0.961016i | \(-0.410828\pi\) | ||||
0.276492 | + | 0.961016i | \(0.410828\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.9177 | −0.811503 | −0.405752 | − | 0.913983i | \(-0.632990\pi\) | ||||
−0.405752 | + | 0.913983i | \(0.632990\pi\) | |||||||
\(182\) | −3.93954 | −0.292018 | ||||||||
\(183\) | 6.72030 | 0.496779 | ||||||||
\(184\) | 9.63098 | 0.710006 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.910371 | 0.0667516 | ||||||||
\(187\) | 13.6619 | 0.999056 | ||||||||
\(188\) | 13.1513 | 0.959157 | ||||||||
\(189\) | 17.9585 | 1.30629 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.75142 | −0.126728 | −0.0633642 | − | 0.997990i | \(-0.520183\pi\) | ||||
−0.0633642 | + | 0.997990i | \(0.520183\pi\) | |||||||
\(192\) | −9.52100 | −0.687119 | ||||||||
\(193\) | 9.53146 | 0.686089 | 0.343045 | − | 0.939319i | \(-0.388542\pi\) | ||||
0.343045 | + | 0.939319i | \(0.388542\pi\) | |||||||
\(194\) | 5.22862 | 0.375393 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.94444 | −0.638889 | ||||||||
\(197\) | −23.9169 | −1.70401 | −0.852004 | − | 0.523535i | \(-0.824613\pi\) | ||||
−0.852004 | + | 0.523535i | \(0.824613\pi\) | |||||||
\(198\) | 0.100313 | 0.00712896 | ||||||||
\(199\) | 23.8281 | 1.68913 | 0.844566 | − | 0.535451i | \(-0.179858\pi\) | ||||
0.844566 | + | 0.535451i | \(0.179858\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.06448 | −0.498290 | ||||||||
\(202\) | 0.471886 | 0.0332018 | ||||||||
\(203\) | −16.2394 | −1.13979 | ||||||||
\(204\) | 8.30697 | 0.581605 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.79204 | −0.333878 | ||||||||
\(207\) | 0.435164 | 0.0302460 | ||||||||
\(208\) | 11.8691 | 0.822971 | ||||||||
\(209\) | 10.8200 | 0.748434 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.3923 | −1.05965 | −0.529826 | − | 0.848107i | \(-0.677743\pi\) | ||||
−0.529826 | + | 0.848107i | \(0.677743\pi\) | |||||||
\(212\) | 3.26102 | 0.223968 | ||||||||
\(213\) | 4.01216 | 0.274909 | ||||||||
\(214\) | −3.99190 | −0.272881 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 6.67192 | 0.453967 | ||||||||
\(217\) | −5.56144 | −0.377535 | ||||||||
\(218\) | −5.01614 | −0.339736 | ||||||||
\(219\) | −2.59662 | −0.175463 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.00662 | −0.605851 | ||||||||
\(222\) | 0.00752696 | 0.000505176 0 | ||||||||
\(223\) | 19.5753 | 1.31086 | 0.655429 | − | 0.755257i | \(-0.272488\pi\) | ||||
0.655429 | + | 0.755257i | \(0.272488\pi\) | |||||||
\(224\) | −12.4831 | −0.834059 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.06268 | −0.403283 | ||||||||
\(227\) | −1.34207 | −0.0890760 | −0.0445380 | − | 0.999008i | \(-0.514182\pi\) | ||||
−0.0445380 | + | 0.999008i | \(0.514182\pi\) | |||||||
\(228\) | 6.57898 | 0.435704 | ||||||||
\(229\) | −22.3702 | −1.47827 | −0.739133 | − | 0.673560i | \(-0.764764\pi\) | ||||
−0.739133 | + | 0.673560i | \(0.764764\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 31.3717 | 2.06410 | ||||||||
\(232\) | −6.03327 | −0.396104 | ||||||||
\(233\) | −18.3651 | −1.20314 | −0.601568 | − | 0.798822i | \(-0.705457\pi\) | ||||
−0.601568 | + | 0.798822i | \(0.705457\pi\) | |||||||
\(234\) | −0.0661317 | −0.00432317 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.0419976 | 0.00273381 | ||||||||
\(237\) | 0.732176 | 0.0475600 | ||||||||
\(238\) | 2.86182 | 0.185504 | ||||||||
\(239\) | −12.0037 | −0.776458 | −0.388229 | − | 0.921563i | \(-0.626913\pi\) | ||||
−0.388229 | + | 0.921563i | \(0.626913\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.1170 | 0.651692 | 0.325846 | − | 0.945423i | \(-0.394351\pi\) | ||||
0.325846 | + | 0.945423i | \(0.394351\pi\) | |||||||
\(242\) | 5.72713 | 0.368154 | ||||||||
\(243\) | 0.597258 | 0.0383141 | ||||||||
\(244\) | −7.41708 | −0.474830 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.42420 | 0.345834 | ||||||||
\(247\) | −7.13309 | −0.453867 | ||||||||
\(248\) | −2.06618 | −0.131203 | ||||||||
\(249\) | 10.3641 | 0.656797 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.7258 | 1.05573 | 0.527863 | − | 0.849330i | \(-0.322994\pi\) | ||||
0.527863 | + | 0.849330i | \(0.322994\pi\) | |||||||
\(252\) | −0.372615 | −0.0234725 | ||||||||
\(253\) | 40.4366 | 2.54223 | ||||||||
\(254\) | −0.221505 | −0.0138985 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.12573 | 0.507858 | ||||||||
\(257\) | −15.0170 | −0.936732 | −0.468366 | − | 0.883535i | \(-0.655157\pi\) | ||||
−0.468366 | + | 0.883535i | \(0.655157\pi\) | |||||||
\(258\) | −1.30398 | −0.0811822 | ||||||||
\(259\) | −0.0459821 | −0.00285719 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.272606 | −0.0168739 | ||||||||
\(262\) | 2.30379 | 0.142328 | ||||||||
\(263\) | −6.17182 | −0.380571 | −0.190285 | − | 0.981729i | \(-0.560941\pi\) | ||||
−0.190285 | + | 0.981729i | \(0.560941\pi\) | |||||||
\(264\) | 11.6552 | 0.717327 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.26651 | 0.138969 | ||||||||
\(267\) | −10.4529 | −0.639704 | ||||||||
\(268\) | 7.79694 | 0.476274 | ||||||||
\(269\) | 11.1052 | 0.677098 | 0.338549 | − | 0.940949i | \(-0.390064\pi\) | ||||
0.338549 | + | 0.940949i | \(0.390064\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.16149 | −0.0705554 | −0.0352777 | − | 0.999378i | \(-0.511232\pi\) | ||||
−0.0352777 | + | 0.999378i | \(0.511232\pi\) | |||||||
\(272\) | −8.62208 | −0.522790 | ||||||||
\(273\) | −20.6818 | −1.25172 | ||||||||
\(274\) | 3.56766 | 0.215530 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 24.5871 | 1.47997 | ||||||||
\(277\) | 2.17486 | 0.130675 | 0.0653374 | − | 0.997863i | \(-0.479188\pi\) | ||||
0.0653374 | + | 0.997863i | \(0.479188\pi\) | |||||||
\(278\) | 6.37497 | 0.382346 | ||||||||
\(279\) | −0.0933580 | −0.00558920 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.1177 | −1.43874 | −0.719370 | − | 0.694627i | \(-0.755569\pi\) | ||||
−0.719370 | + | 0.694627i | \(0.755569\pi\) | |||||||
\(282\) | −3.89351 | −0.231855 | ||||||||
\(283\) | −16.2144 | −0.963845 | −0.481923 | − | 0.876214i | \(-0.660061\pi\) | ||||
−0.481923 | + | 0.876214i | \(0.660061\pi\) | |||||||
\(284\) | −4.42816 | −0.262763 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.14514 | −0.363370 | ||||||||
\(287\) | −33.1363 | −1.95598 | ||||||||
\(288\) | −0.209549 | −0.0123478 | ||||||||
\(289\) | −10.4573 | −0.615135 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 27.4492 | 1.60910 | ||||||||
\(292\) | 2.86584 | 0.167711 | ||||||||
\(293\) | −3.48929 | −0.203846 | −0.101923 | − | 0.994792i | \(-0.532500\pi\) | ||||
−0.101923 | + | 0.994792i | \(0.532500\pi\) | |||||||
\(294\) | 2.64805 | 0.154437 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.0170832 | −0.000992943 0 | ||||||||
\(297\) | 28.0127 | 1.62546 | ||||||||
\(298\) | −4.18063 | −0.242178 | ||||||||
\(299\) | −26.6579 | −1.54167 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.96599 | 0.459152 | ||||||||
\(302\) | 0.704529 | 0.0405411 | ||||||||
\(303\) | 2.47731 | 0.142318 | ||||||||
\(304\) | −6.82854 | −0.391644 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.0480403 | 0.00274628 | ||||||||
\(307\) | −8.92690 | −0.509485 | −0.254742 | − | 0.967009i | \(-0.581991\pi\) | ||||
−0.254742 | + | 0.967009i | \(0.581991\pi\) | |||||||
\(308\) | −34.6244 | −1.97291 | ||||||||
\(309\) | −25.1573 | −1.43115 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.1101 | −1.53727 | −0.768635 | − | 0.639687i | \(-0.779064\pi\) | ||||
−0.768635 | + | 0.639687i | \(0.779064\pi\) | |||||||
\(312\) | −7.68370 | −0.435004 | ||||||||
\(313\) | 20.1073 | 1.13653 | 0.568267 | − | 0.822844i | \(-0.307614\pi\) | ||||
0.568267 | + | 0.822844i | \(0.307614\pi\) | |||||||
\(314\) | 5.14548 | 0.290376 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.808091 | −0.0454587 | ||||||||
\(317\) | −9.67993 | −0.543679 | −0.271840 | − | 0.962343i | \(-0.587632\pi\) | ||||
−0.271840 | + | 0.962343i | \(0.587632\pi\) | |||||||
\(318\) | −0.965442 | −0.0541393 | ||||||||
\(319\) | −25.3313 | −1.41828 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −20.9567 | −1.16969 | ||||||||
\(322\) | 8.47044 | 0.472039 | ||||||||
\(323\) | 5.18171 | 0.288318 | ||||||||
\(324\) | 16.7064 | 0.928132 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.41540 | −0.133777 | ||||||||
\(327\) | −26.3337 | −1.45626 | ||||||||
\(328\) | −12.3108 | −0.679750 | ||||||||
\(329\) | 23.7854 | 1.31133 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.6759 | 1.08148 | 0.540742 | − | 0.841189i | \(-0.318144\pi\) | ||||
0.540742 | + | 0.841189i | \(0.318144\pi\) | |||||||
\(332\) | −11.4387 | −0.627778 | ||||||||
\(333\) | −0.000771885 0 | −4.22990e−5 0 | ||||||||
\(334\) | 3.53431 | 0.193389 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −19.7988 | −1.08011 | ||||||||
\(337\) | −18.8552 | −1.02711 | −0.513554 | − | 0.858057i | \(-0.671671\pi\) | ||||
−0.513554 | + | 0.858057i | \(0.671671\pi\) | |||||||
\(338\) | −0.196571 | −0.0106920 | ||||||||
\(339\) | −31.8279 | −1.72865 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.67508 | −0.469782 | ||||||||
\(342\) | 0.0380471 | 0.00205735 | ||||||||
\(343\) | 7.79178 | 0.420717 | ||||||||
\(344\) | 2.95952 | 0.159567 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.90071 | −0.263464 | ||||||||
\(347\) | −25.9753 | −1.39442 | −0.697212 | − | 0.716865i | \(-0.745577\pi\) | ||||
−0.697212 | + | 0.716865i | \(0.745577\pi\) | |||||||
\(348\) | −15.4024 | −0.825657 | ||||||||
\(349\) | −26.1490 | −1.39972 | −0.699861 | − | 0.714279i | \(-0.746755\pi\) | ||||
−0.699861 | + | 0.714279i | \(0.746755\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −18.4674 | −0.985718 | ||||||||
\(352\) | −19.4718 | −1.03785 | ||||||||
\(353\) | 5.32892 | 0.283630 | 0.141815 | − | 0.989893i | \(-0.454706\pi\) | ||||
0.141815 | + | 0.989893i | \(0.454706\pi\) | |||||||
\(354\) | −0.0124336 | −0.000660838 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 11.5366 | 0.611441 | ||||||||
\(357\) | 15.0240 | 0.795152 | ||||||||
\(358\) | 2.41744 | 0.127766 | ||||||||
\(359\) | 9.89929 | 0.522465 | 0.261232 | − | 0.965276i | \(-0.415871\pi\) | ||||
0.261232 | + | 0.965276i | \(0.415871\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.8962 | −0.784009 | ||||||||
\(362\) | −3.56736 | −0.187496 | ||||||||
\(363\) | 30.0663 | 1.57807 | ||||||||
\(364\) | 22.8262 | 1.19642 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.19587 | 0.114780 | ||||||||
\(367\) | −16.4392 | −0.858118 | −0.429059 | − | 0.903276i | \(-0.641155\pi\) | ||||
−0.429059 | + | 0.903276i | \(0.641155\pi\) | |||||||
\(368\) | −25.5197 | −1.33031 | ||||||||
\(369\) | −0.556248 | −0.0289571 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.89787 | 0.306202 | ||||||||
\(372\) | −5.27479 | −0.273485 | ||||||||
\(373\) | −22.9933 | −1.19055 | −0.595273 | − | 0.803524i | \(-0.702956\pi\) | ||||
−0.595273 | + | 0.803524i | \(0.702956\pi\) | |||||||
\(374\) | 4.46404 | 0.230830 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.83674 | 0.455720 | ||||||||
\(377\) | 16.6997 | 0.860078 | ||||||||
\(378\) | 5.86795 | 0.301815 | ||||||||
\(379\) | 16.4246 | 0.843674 | 0.421837 | − | 0.906672i | \(-0.361385\pi\) | ||||
0.421837 | + | 0.906672i | \(0.361385\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.16286 | −0.0595751 | ||||||||
\(382\) | −0.572279 | −0.0292803 | ||||||||
\(383\) | −4.70503 | −0.240416 | −0.120208 | − | 0.992749i | \(-0.538356\pi\) | ||||
−0.120208 | + | 0.992749i | \(0.538356\pi\) | |||||||
\(384\) | −15.6183 | −0.797020 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.11441 | 0.158520 | ||||||||
\(387\) | 0.133722 | 0.00679748 | ||||||||
\(388\) | −30.2952 | −1.53801 | ||||||||
\(389\) | 3.53865 | 0.179417 | 0.0897083 | − | 0.995968i | \(-0.471407\pi\) | ||||
0.0897083 | + | 0.995968i | \(0.471407\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.3652 | 0.979340 | ||||||||
\(392\) | −6.01003 | −0.303552 | ||||||||
\(393\) | 12.0944 | 0.610082 | ||||||||
\(394\) | −7.81487 | −0.393707 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.581227 | −0.0292078 | ||||||||
\(397\) | 8.76374 | 0.439839 | 0.219920 | − | 0.975518i | \(-0.429420\pi\) | ||||
0.219920 | + | 0.975518i | \(0.429420\pi\) | |||||||
\(398\) | 7.78587 | 0.390270 | ||||||||
\(399\) | 11.8987 | 0.595681 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.7677 | 1.13697 | 0.568483 | − | 0.822695i | \(-0.307531\pi\) | ||||
0.568483 | + | 0.822695i | \(0.307531\pi\) | |||||||
\(402\) | −2.30833 | −0.115129 | ||||||||
\(403\) | 5.71906 | 0.284887 | ||||||||
\(404\) | −2.73416 | −0.136030 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.30626 | −0.263345 | ||||||||
\(407\) | −0.0717256 | −0.00355531 | ||||||||
\(408\) | 5.58170 | 0.276335 | ||||||||
\(409\) | 28.0426 | 1.38662 | 0.693309 | − | 0.720640i | \(-0.256152\pi\) | ||||
0.693309 | + | 0.720640i | \(0.256152\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18.7295 | 0.923857 | ||||||||
\(412\) | 27.7657 | 1.36792 | ||||||||
\(413\) | 0.0759566 | 0.00373758 | ||||||||
\(414\) | 0.142190 | 0.00698827 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 12.8368 | 0.629378 | ||||||||
\(417\) | 33.4673 | 1.63890 | ||||||||
\(418\) | 3.53544 | 0.172924 | ||||||||
\(419\) | 34.0901 | 1.66541 | 0.832705 | − | 0.553717i | \(-0.186791\pi\) | ||||
0.832705 | + | 0.553717i | \(0.186791\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −32.1390 | −1.56636 | −0.783180 | − | 0.621796i | \(-0.786403\pi\) | ||||
−0.783180 | + | 0.621796i | \(0.786403\pi\) | |||||||
\(422\) | −5.02946 | −0.244830 | ||||||||
\(423\) | 0.399277 | 0.0194135 | ||||||||
\(424\) | 2.19117 | 0.106413 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.31098 | 0.0635171 | ||||||||
\(427\) | −13.4145 | −0.649173 | ||||||||
\(428\) | 23.1295 | 1.11801 | ||||||||
\(429\) | −32.2608 | −1.55756 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.7549 | −0.855222 | −0.427611 | − | 0.903963i | \(-0.640645\pi\) | ||||
−0.427611 | + | 0.903963i | \(0.640645\pi\) | |||||||
\(432\) | −17.6789 | −0.850579 | ||||||||
\(433\) | −3.06764 | −0.147421 | −0.0737107 | − | 0.997280i | \(-0.523484\pi\) | ||||
−0.0737107 | + | 0.997280i | \(0.523484\pi\) | |||||||
\(434\) | −1.81721 | −0.0872287 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 29.0641 | 1.39192 | ||||||||
\(437\) | 15.3369 | 0.733664 | ||||||||
\(438\) | −0.848448 | −0.0405404 | ||||||||
\(439\) | 14.7475 | 0.703861 | 0.351931 | − | 0.936026i | \(-0.385525\pi\) | ||||
0.351931 | + | 0.936026i | \(0.385525\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.271556 | −0.0129312 | ||||||||
\(442\) | −2.94292 | −0.139981 | ||||||||
\(443\) | 10.1857 | 0.483935 | 0.241968 | − | 0.970284i | \(-0.422207\pi\) | ||||
0.241968 | + | 0.970284i | \(0.422207\pi\) | |||||||
\(444\) | −0.0436121 | −0.00206974 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 6.39624 | 0.302871 | ||||||||
\(447\) | −21.9475 | −1.03808 | ||||||||
\(448\) | 19.0050 | 0.897904 | ||||||||
\(449\) | 18.9484 | 0.894230 | 0.447115 | − | 0.894477i | \(-0.352451\pi\) | ||||
0.447115 | + | 0.894477i | \(0.352451\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −51.6881 | −2.43390 | ||||||||
\(452\) | 35.1279 | 1.65228 | ||||||||
\(453\) | 3.69864 | 0.173777 | ||||||||
\(454\) | −0.438522 | −0.0205808 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.42061 | 0.207014 | ||||||||
\(457\) | 30.4392 | 1.42389 | 0.711943 | − | 0.702237i | \(-0.247815\pi\) | ||||
0.711943 | + | 0.702237i | \(0.247815\pi\) | |||||||
\(458\) | −7.30949 | −0.341550 | ||||||||
\(459\) | 13.4154 | 0.626175 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.36972 | 0.110369 | 0.0551844 | − | 0.998476i | \(-0.482425\pi\) | ||||
0.0551844 | + | 0.998476i | \(0.482425\pi\) | |||||||
\(462\) | 10.2507 | 0.476907 | ||||||||
\(463\) | −0.320982 | −0.0149173 | −0.00745865 | − | 0.999972i | \(-0.502374\pi\) | ||||
−0.00745865 | + | 0.999972i | \(0.502374\pi\) | |||||||
\(464\) | 15.9867 | 0.742164 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.00081 | −0.277982 | ||||||||
\(467\) | −12.8071 | −0.592644 | −0.296322 | − | 0.955088i | \(-0.595760\pi\) | ||||
−0.296322 | + | 0.955088i | \(0.595760\pi\) | |||||||
\(468\) | 0.383175 | 0.0177123 | ||||||||
\(469\) | 14.1015 | 0.651148 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 27.0127 | 1.24468 | ||||||||
\(472\) | 0.0282194 | 0.00129890 | ||||||||
\(473\) | 12.4258 | 0.571341 | ||||||||
\(474\) | 0.239239 | 0.0109886 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −16.5817 | −0.760021 | ||||||||
\(477\) | 0.0990055 | 0.00453315 | ||||||||
\(478\) | −3.92224 | −0.179399 | ||||||||
\(479\) | −20.3446 | −0.929569 | −0.464784 | − | 0.885424i | \(-0.653868\pi\) | ||||
−0.464784 | + | 0.885424i | \(0.653868\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.0472852 | 0.00215602 | ||||||||
\(482\) | 3.30573 | 0.150572 | ||||||||
\(483\) | 44.4681 | 2.02337 | ||||||||
\(484\) | −33.1837 | −1.50835 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.195155 | 0.00885239 | ||||||||
\(487\) | −15.4919 | −0.702003 | −0.351002 | − | 0.936375i | \(-0.614159\pi\) | ||||
−0.351002 | + | 0.936375i | \(0.614159\pi\) | |||||||
\(488\) | −4.98375 | −0.225604 | ||||||||
\(489\) | −12.6804 | −0.573427 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −27.5085 | −1.24144 | −0.620722 | − | 0.784031i | \(-0.713160\pi\) | ||||
−0.620722 | + | 0.784031i | \(0.713160\pi\) | |||||||
\(492\) | −31.4284 | −1.41690 | ||||||||
\(493\) | −12.1312 | −0.546362 | ||||||||
\(494\) | −2.33074 | −0.104865 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.47488 | 0.245829 | ||||||||
\(497\) | −8.00875 | −0.359241 | ||||||||
\(498\) | 3.38648 | 0.151752 | ||||||||
\(499\) | 4.91044 | 0.219821 | 0.109911 | − | 0.993941i | \(-0.464943\pi\) | ||||
0.109911 | + | 0.993941i | \(0.464943\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.5544 | 0.828950 | ||||||||
\(502\) | 5.46518 | 0.243923 | ||||||||
\(503\) | −41.0454 | −1.83012 | −0.915062 | − | 0.403314i | \(-0.867858\pi\) | ||||
−0.915062 | + | 0.403314i | \(0.867858\pi\) | |||||||
\(504\) | −0.250371 | −0.0111524 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 13.2127 | 0.587377 | ||||||||
\(507\) | −1.03196 | −0.0458308 | ||||||||
\(508\) | 1.28343 | 0.0569429 | ||||||||
\(509\) | 41.4404 | 1.83681 | 0.918407 | − | 0.395637i | \(-0.129476\pi\) | ||||
0.918407 | + | 0.395637i | \(0.129476\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.18315 | 0.229289 | ||||||||
\(512\) | 20.8649 | 0.922106 | ||||||||
\(513\) | 10.6247 | 0.469093 | ||||||||
\(514\) | −4.90681 | −0.216430 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 7.55540 | 0.332608 | ||||||||
\(517\) | 37.1019 | 1.63174 | ||||||||
\(518\) | −0.0150247 | −0.000660147 0 | ||||||||
\(519\) | −25.7277 | −1.12932 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.62447 | −0.0711691 | −0.0355846 | − | 0.999367i | \(-0.511329\pi\) | ||||
−0.0355846 | + | 0.999367i | \(0.511329\pi\) | |||||||
\(522\) | −0.0890743 | −0.00389868 | ||||||||
\(523\) | 19.0009 | 0.830853 | 0.415427 | − | 0.909627i | \(-0.363632\pi\) | ||||
0.415427 | + | 0.909627i | \(0.363632\pi\) | |||||||
\(524\) | −13.3484 | −0.583128 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.01665 | −0.0879301 | ||||||||
\(527\) | −4.15451 | −0.180973 | ||||||||
\(528\) | −30.8834 | −1.34403 | ||||||||
\(529\) | 34.3174 | 1.49206 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.00127506 | 5.53328e−5 0 | ||||||||
\(532\) | −13.1324 | −0.569362 | ||||||||
\(533\) | 34.0755 | 1.47597 | ||||||||
\(534\) | −3.41548 | −0.147802 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.23899 | 0.226290 | ||||||||
\(537\) | 12.6911 | 0.547660 | ||||||||
\(538\) | 3.62865 | 0.156442 | ||||||||
\(539\) | −25.2337 | −1.08689 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −33.5195 | −1.44112 | −0.720558 | − | 0.693394i | \(-0.756114\pi\) | ||||
−0.720558 | + | 0.693394i | \(0.756114\pi\) | |||||||
\(542\) | −0.379518 | −0.0163017 | ||||||||
\(543\) | −18.7279 | −0.803691 | ||||||||
\(544\) | −9.32511 | −0.399811 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −6.75780 | −0.289207 | ||||||||
\(547\) | 17.4258 | 0.745072 | 0.372536 | − | 0.928018i | \(-0.378488\pi\) | ||||
0.372536 | + | 0.928018i | \(0.378488\pi\) | |||||||
\(548\) | −20.6714 | −0.883039 | ||||||||
\(549\) | −0.225185 | −0.00961065 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.60771 | −0.409302 | ||||||||
\(552\) | 16.5208 | 0.703171 | ||||||||
\(553\) | −1.46151 | −0.0621497 | ||||||||
\(554\) | 0.710638 | 0.0301921 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −36.9373 | −1.56649 | ||||||||
\(557\) | 16.2929 | 0.690351 | 0.345175 | − | 0.938538i | \(-0.387819\pi\) | ||||
0.345175 | + | 0.938538i | \(0.387819\pi\) | |||||||
\(558\) | −0.0305048 | −0.00129137 | ||||||||
\(559\) | −8.19175 | −0.346474 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 23.4353 | 0.989439 | ||||||||
\(562\) | −7.88048 | −0.332418 | ||||||||
\(563\) | −23.0999 | −0.973545 | −0.486773 | − | 0.873529i | \(-0.661826\pi\) | ||||
−0.486773 | + | 0.873529i | \(0.661826\pi\) | |||||||
\(564\) | 22.5594 | 0.949924 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −5.29807 | −0.222694 | ||||||||
\(567\) | 30.2151 | 1.26891 | ||||||||
\(568\) | −2.97541 | −0.124845 | ||||||||
\(569\) | −9.28334 | −0.389178 | −0.194589 | − | 0.980885i | \(-0.562337\pi\) | ||||
−0.194589 | + | 0.980885i | \(0.562337\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.2143 | 0.929640 | 0.464820 | − | 0.885405i | \(-0.346119\pi\) | ||||
0.464820 | + | 0.885405i | \(0.346119\pi\) | |||||||
\(572\) | 35.6057 | 1.48875 | ||||||||
\(573\) | −3.00435 | −0.125509 | ||||||||
\(574\) | −10.8273 | −0.451924 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.319031 | 0.0132930 | ||||||||
\(577\) | −14.6093 | −0.608192 | −0.304096 | − | 0.952641i | \(-0.598354\pi\) | ||||
−0.304096 | + | 0.952641i | \(0.598354\pi\) | |||||||
\(578\) | −3.41693 | −0.142126 | ||||||||
\(579\) | 16.3500 | 0.679485 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −20.6879 | −0.858280 | ||||||||
\(582\) | 8.96905 | 0.371779 | ||||||||
\(583\) | 9.19986 | 0.381019 | ||||||||
\(584\) | 1.92564 | 0.0796837 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.14013 | −0.0470983 | ||||||||
\(587\) | −23.3435 | −0.963489 | −0.481744 | − | 0.876312i | \(-0.659997\pi\) | ||||
−0.481744 | + | 0.876312i | \(0.659997\pi\) | |||||||
\(588\) | −15.3431 | −0.632739 | ||||||||
\(589\) | −3.29030 | −0.135575 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −41.0265 | −1.68760 | ||||||||
\(592\) | 0.0452664 | 0.00186044 | ||||||||
\(593\) | 41.9815 | 1.72397 | 0.861986 | − | 0.506932i | \(-0.169220\pi\) | ||||
0.861986 | + | 0.506932i | \(0.169220\pi\) | |||||||
\(594\) | 9.15319 | 0.375560 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 24.2231 | 0.992215 | ||||||||
\(597\) | 40.8743 | 1.67287 | ||||||||
\(598\) | −8.71050 | −0.356199 | ||||||||
\(599\) | −25.4160 | −1.03847 | −0.519236 | − | 0.854631i | \(-0.673783\pi\) | ||||
−0.519236 | + | 0.854631i | \(0.673783\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.1379 | 1.51489 | 0.757444 | − | 0.652900i | \(-0.226448\pi\) | ||||
0.757444 | + | 0.652900i | \(0.226448\pi\) | |||||||
\(602\) | 2.60289 | 0.106086 | ||||||||
\(603\) | 0.236717 | 0.00963988 | ||||||||
\(604\) | −4.08213 | −0.166099 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.809463 | 0.0328822 | ||||||||
\(607\) | 18.9242 | 0.768109 | 0.384054 | − | 0.923310i | \(-0.374527\pi\) | ||||
0.384054 | + | 0.923310i | \(0.374527\pi\) | |||||||
\(608\) | −7.38532 | −0.299514 | ||||||||
\(609\) | −27.8568 | −1.12881 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −24.4595 | −0.989525 | ||||||||
\(612\) | −0.278351 | −0.0112517 | ||||||||
\(613\) | −9.20317 | −0.371713 | −0.185856 | − | 0.982577i | \(-0.559506\pi\) | ||||
−0.185856 | + | 0.982577i | \(0.559506\pi\) | |||||||
\(614\) | −2.91687 | −0.117715 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −23.2651 | −0.937378 | ||||||||
\(617\) | 32.7375 | 1.31796 | 0.658981 | − | 0.752159i | \(-0.270988\pi\) | ||||
0.658981 | + | 0.752159i | \(0.270988\pi\) | |||||||
\(618\) | −8.22017 | −0.330664 | ||||||||
\(619\) | 36.3952 | 1.46285 | 0.731424 | − | 0.681923i | \(-0.238856\pi\) | ||||
0.731424 | + | 0.681923i | \(0.238856\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 39.7069 | 1.59338 | ||||||||
\(622\) | −8.85824 | −0.355183 | ||||||||
\(623\) | 20.8651 | 0.835943 | ||||||||
\(624\) | 20.3599 | 0.815049 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 6.57010 | 0.262594 | ||||||||
\(627\) | 18.5604 | 0.741229 | ||||||||
\(628\) | −29.8135 | −1.18969 | ||||||||
\(629\) | −0.0343496 | −0.00136961 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.1083 | 0.482024 | 0.241012 | − | 0.970522i | \(-0.422521\pi\) | ||||
0.241012 | + | 0.970522i | \(0.422521\pi\) | |||||||
\(632\) | −0.542980 | −0.0215986 | ||||||||
\(633\) | −26.4037 | −1.04945 | ||||||||
\(634\) | −3.16293 | −0.125616 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 5.59388 | 0.221812 | ||||||||
\(637\) | 16.6354 | 0.659117 | ||||||||
\(638\) | −8.27703 | −0.327691 | ||||||||
\(639\) | −0.134440 | −0.00531837 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.75177 | 0.385172 | 0.192586 | − | 0.981280i | \(-0.438313\pi\) | ||||
0.192586 | + | 0.981280i | \(0.438313\pi\) | |||||||
\(642\) | −6.84762 | −0.270254 | ||||||||
\(643\) | −6.77862 | −0.267323 | −0.133661 | − | 0.991027i | \(-0.542673\pi\) | ||||
−0.133661 | + | 0.991027i | \(0.542673\pi\) | |||||||
\(644\) | −49.0787 | −1.93397 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.69313 | 0.0666153 | ||||||||
\(647\) | 40.1188 | 1.57723 | 0.788616 | − | 0.614886i | \(-0.210798\pi\) | ||||
0.788616 | + | 0.614886i | \(0.210798\pi\) | |||||||
\(648\) | 11.2255 | 0.440979 | ||||||||
\(649\) | 0.118482 | 0.00465082 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.53997 | −0.373901 | ||||||||
\(652\) | 13.9951 | 0.548092 | ||||||||
\(653\) | −6.14210 | −0.240359 | −0.120179 | − | 0.992752i | \(-0.538347\pi\) | ||||
−0.120179 | + | 0.992752i | \(0.538347\pi\) | |||||||
\(654\) | −8.60458 | −0.336466 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 32.6206 | 1.27362 | ||||||||
\(657\) | 0.0870078 | 0.00339450 | ||||||||
\(658\) | 7.77190 | 0.302980 | ||||||||
\(659\) | −44.1645 | −1.72040 | −0.860202 | − | 0.509954i | \(-0.829662\pi\) | ||||
−0.860202 | + | 0.509954i | \(0.829662\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.7447 | 1.07915 | 0.539573 | − | 0.841939i | \(-0.318586\pi\) | ||||
0.539573 | + | 0.841939i | \(0.318586\pi\) | |||||||
\(662\) | 6.42911 | 0.249875 | ||||||||
\(663\) | −15.4498 | −0.600019 | ||||||||
\(664\) | −7.68597 | −0.298274 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.000252214 0 | −9.77310e−6 0 | ||||||||
\(667\) | −35.9061 | −1.39029 | ||||||||
\(668\) | −20.4782 | −0.792325 | ||||||||
\(669\) | 33.5790 | 1.29824 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −20.9248 | −0.807792 | ||||||||
\(672\) | −21.4131 | −0.826030 | ||||||||
\(673\) | 41.8324 | 1.61252 | 0.806259 | − | 0.591562i | \(-0.201489\pi\) | ||||
0.806259 | + | 0.591562i | \(0.201489\pi\) | |||||||
\(674\) | −6.16096 | −0.237311 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.13895 | 0.0438059 | ||||||||
\(677\) | −22.6274 | −0.869643 | −0.434821 | − | 0.900517i | \(-0.643188\pi\) | ||||
−0.434821 | + | 0.900517i | \(0.643188\pi\) | |||||||
\(678\) | −10.3998 | −0.399401 | ||||||||
\(679\) | −54.7918 | −2.10272 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.30215 | −0.0882186 | ||||||||
\(682\) | −2.83459 | −0.108542 | ||||||||
\(683\) | 49.0024 | 1.87502 | 0.937512 | − | 0.347953i | \(-0.113123\pi\) | ||||
0.937512 | + | 0.347953i | \(0.113123\pi\) | |||||||
\(684\) | −0.220449 | −0.00842909 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.54597 | 0.0972057 | ||||||||
\(687\) | −38.3734 | −1.46404 | ||||||||
\(688\) | −7.84200 | −0.298973 | ||||||||
\(689\) | −6.06502 | −0.231059 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.2583 | 1.37933 | 0.689665 | − | 0.724128i | \(-0.257758\pi\) | ||||
0.689665 | + | 0.724128i | \(0.257758\pi\) | |||||||
\(692\) | 28.3953 | 1.07943 | ||||||||
\(693\) | −1.05121 | −0.0399320 | ||||||||
\(694\) | −8.48744 | −0.322179 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −10.3493 | −0.392291 | ||||||||
\(697\) | −24.7536 | −0.937608 | ||||||||
\(698\) | −8.54421 | −0.323403 | ||||||||
\(699\) | −31.5030 | −1.19155 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.32362 | −0.314379 | −0.157189 | − | 0.987568i | \(-0.550243\pi\) | ||||
−0.157189 | + | 0.987568i | \(0.550243\pi\) | |||||||
\(702\) | −6.03425 | −0.227748 | ||||||||
\(703\) | −0.0272043 | −0.00102603 | ||||||||
\(704\) | 29.6452 | 1.11730 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.74123 | 0.0655321 | ||||||||
\(707\) | −4.94500 | −0.185976 | ||||||||
\(708\) | 0.0720417 | 0.00270749 | ||||||||
\(709\) | 37.3097 | 1.40119 | 0.700597 | − | 0.713557i | \(-0.252917\pi\) | ||||
0.700597 | + | 0.713557i | \(0.252917\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.0245339 | −0.000920092 0 | ||||||||
\(712\) | 7.75180 | 0.290511 | ||||||||
\(713\) | −12.2966 | −0.460511 | ||||||||
\(714\) | 4.90910 | 0.183718 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −14.0069 | −0.523463 | ||||||||
\(717\) | −20.5910 | −0.768983 | ||||||||
\(718\) | 3.23460 | 0.120714 | ||||||||
\(719\) | −7.66524 | −0.285865 | −0.142933 | − | 0.989732i | \(-0.545653\pi\) | ||||
−0.142933 | + | 0.989732i | \(0.545653\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 50.2169 | 1.87017 | ||||||||
\(722\) | −4.86734 | −0.181144 | ||||||||
\(723\) | 17.3544 | 0.645419 | ||||||||
\(724\) | 20.6697 | 0.768183 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 9.82419 | 0.364610 | ||||||||
\(727\) | 45.9089 | 1.70267 | 0.851334 | − | 0.524624i | \(-0.175794\pi\) | ||||
0.851334 | + | 0.524624i | \(0.175794\pi\) | |||||||
\(728\) | 15.3376 | 0.568448 | ||||||||
\(729\) | 27.4973 | 1.01842 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.95076 | 0.220097 | ||||||||
\(732\) | −12.7231 | −0.470259 | ||||||||
\(733\) | −23.7131 | −0.875864 | −0.437932 | − | 0.899008i | \(-0.644289\pi\) | ||||
−0.437932 | + | 0.899008i | \(0.644289\pi\) | |||||||
\(734\) | −5.37152 | −0.198266 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −27.6006 | −1.01737 | ||||||||
\(737\) | 21.9964 | 0.810249 | ||||||||
\(738\) | −0.181755 | −0.00669048 | ||||||||
\(739\) | −3.53683 | −0.130104 | −0.0650522 | − | 0.997882i | \(-0.520721\pi\) | ||||
−0.0650522 | + | 0.997882i | \(0.520721\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12.2359 | −0.449498 | ||||||||
\(742\) | 1.92714 | 0.0707474 | ||||||||
\(743\) | 15.7201 | 0.576715 | 0.288358 | − | 0.957523i | \(-0.406891\pi\) | ||||
0.288358 | + | 0.957523i | \(0.406891\pi\) | |||||||
\(744\) | −3.54429 | −0.129940 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −7.51307 | −0.275073 | ||||||||
\(747\) | −0.347281 | −0.0127063 | ||||||||
\(748\) | −25.8651 | −0.945724 | ||||||||
\(749\) | 41.8320 | 1.52851 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.1856 | −0.517642 | −0.258821 | − | 0.965925i | \(-0.583334\pi\) | ||||
−0.258821 | + | 0.965925i | \(0.583334\pi\) | |||||||
\(752\) | −23.4152 | −0.853864 | ||||||||
\(753\) | 28.6911 | 1.04556 | ||||||||
\(754\) | 5.45664 | 0.198719 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −33.9996 | −1.23655 | ||||||||
\(757\) | −12.7388 | −0.463000 | −0.231500 | − | 0.972835i | \(-0.574363\pi\) | ||||
−0.231500 | + | 0.972835i | \(0.574363\pi\) | |||||||
\(758\) | 5.36675 | 0.194929 | ||||||||
\(759\) | 69.3641 | 2.51776 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32.2299 | 1.16833 | 0.584167 | − | 0.811633i | \(-0.301421\pi\) | ||||
0.584167 | + | 0.811633i | \(0.301421\pi\) | |||||||
\(762\) | −0.379965 | −0.0137647 | ||||||||
\(763\) | 52.5652 | 1.90299 | ||||||||
\(764\) | 3.31585 | 0.119963 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.53737 | −0.0555476 | ||||||||
\(767\) | −0.0781093 | −0.00282036 | ||||||||
\(768\) | 13.9387 | 0.502969 | ||||||||
\(769\) | −11.3687 | −0.409965 | −0.204983 | − | 0.978766i | \(-0.565714\pi\) | ||||
−0.204983 | + | 0.978766i | \(0.565714\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −25.7597 | −0.927715 | ||||||||
\(772\) | −18.0453 | −0.649464 | ||||||||
\(773\) | −27.1994 | −0.978295 | −0.489147 | − | 0.872201i | \(-0.662692\pi\) | ||||
−0.489147 | + | 0.872201i | \(0.662692\pi\) | |||||||
\(774\) | 0.0436939 | 0.00157054 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −20.3562 | −0.730746 | ||||||||
\(777\) | −0.0788766 | −0.00282968 | ||||||||
\(778\) | 1.15626 | 0.0414538 | ||||||||
\(779\) | −19.6044 | −0.702400 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.4925 | −0.447018 | ||||||||
\(782\) | 6.32760 | 0.226275 | ||||||||
\(783\) | −24.8742 | −0.888931 | ||||||||
\(784\) | 15.9251 | 0.568754 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3.95186 | 0.140958 | ||||||||
\(787\) | 25.7266 | 0.917054 | 0.458527 | − | 0.888680i | \(-0.348377\pi\) | ||||
0.458527 | + | 0.888680i | \(0.348377\pi\) | |||||||
\(788\) | 45.2803 | 1.61304 | ||||||||
\(789\) | −10.5870 | −0.376908 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 63.5321 | 2.25894 | ||||||||
\(792\) | −0.390543 | −0.0138774 | ||||||||
\(793\) | 13.7947 | 0.489864 | ||||||||
\(794\) | 2.86356 | 0.101624 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −45.1122 | −1.59896 | ||||||||
\(797\) | −17.6713 | −0.625951 | −0.312975 | − | 0.949761i | \(-0.601326\pi\) | ||||
−0.312975 | + | 0.949761i | \(0.601326\pi\) | |||||||
\(798\) | 3.88792 | 0.137631 | ||||||||
\(799\) | 17.7682 | 0.628593 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.350256 | 0.0123757 | ||||||||
\(802\) | 7.43938 | 0.262694 | ||||||||
\(803\) | 8.08500 | 0.285314 | ||||||||
\(804\) | 13.3747 | 0.471689 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.86871 | 0.0658224 | ||||||||
\(807\) | 19.0497 | 0.670580 | ||||||||
\(808\) | −1.83716 | −0.0646312 | ||||||||
\(809\) | −40.8576 | −1.43648 | −0.718238 | − | 0.695798i | \(-0.755051\pi\) | ||||
−0.718238 | + | 0.695798i | \(0.755051\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.6214 | 0.583656 | 0.291828 | − | 0.956471i | \(-0.405737\pi\) | ||||
0.291828 | + | 0.956471i | \(0.405737\pi\) | |||||||
\(812\) | 30.7451 | 1.07894 | ||||||||
\(813\) | −1.99239 | −0.0698763 | ||||||||
\(814\) | −0.0234364 | −0.000821447 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −14.7901 | −0.517758 | ||||||||
\(817\) | 4.71290 | 0.164884 | ||||||||
\(818\) | 9.16296 | 0.320375 | ||||||||
\(819\) | 0.693009 | 0.0242157 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −43.8983 | −1.53206 | −0.766031 | − | 0.642803i | \(-0.777771\pi\) | ||||
−0.766031 | + | 0.642803i | \(0.777771\pi\) | |||||||
\(822\) | 6.11988 | 0.213455 | ||||||||
\(823\) | −26.1962 | −0.913143 | −0.456571 | − | 0.889687i | \(-0.650923\pi\) | ||||
−0.456571 | + | 0.889687i | \(0.650923\pi\) | |||||||
\(824\) | 18.6565 | 0.649932 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.0248189 | 0.000863561 0 | ||||||||
\(827\) | −22.3827 | −0.778321 | −0.389161 | − | 0.921170i | \(-0.627235\pi\) | ||||
−0.389161 | + | 0.921170i | \(0.627235\pi\) | |||||||
\(828\) | −0.823867 | −0.0286314 | ||||||||
\(829\) | 0.841282 | 0.0292189 | 0.0146095 | − | 0.999893i | \(-0.495349\pi\) | ||||
0.0146095 | + | 0.999893i | \(0.495349\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.73071 | 0.129417 | ||||||||
\(832\) | −19.5437 | −0.677554 | ||||||||
\(833\) | −12.0845 | −0.418702 | ||||||||
\(834\) | 10.9355 | 0.378665 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −20.4848 | −0.708480 | ||||||||
\(837\) | −8.51853 | −0.294444 | ||||||||
\(838\) | 11.1390 | 0.384790 | ||||||||
\(839\) | 35.5528 | 1.22742 | 0.613710 | − | 0.789532i | \(-0.289677\pi\) | ||||
0.613710 | + | 0.789532i | \(0.289677\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.50681 | −0.224373 | ||||||||
\(842\) | −10.5015 | −0.361904 | ||||||||
\(843\) | −41.3709 | −1.42489 | ||||||||
\(844\) | 29.1413 | 1.00308 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.130464 | 0.00448545 | ||||||||
\(847\) | −60.0158 | −2.06217 | ||||||||
\(848\) | −5.80608 | −0.199381 | ||||||||
\(849\) | −27.8138 | −0.954567 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.101668 | −0.00348515 | ||||||||
\(852\) | −7.59596 | −0.260233 | ||||||||
\(853\) | 19.5406 | 0.669058 | 0.334529 | − | 0.942386i | \(-0.391423\pi\) | ||||
0.334529 | + | 0.942386i | \(0.391423\pi\) | |||||||
\(854\) | −4.38320 | −0.149990 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.5414 | 0.531194 | ||||||||
\(857\) | 0.570622 | 0.0194921 | 0.00974604 | − | 0.999953i | \(-0.496898\pi\) | ||||
0.00974604 | + | 0.999953i | \(0.496898\pi\) | |||||||
\(858\) | −10.5412 | −0.359872 | ||||||||
\(859\) | −20.0983 | −0.685744 | −0.342872 | − | 0.939382i | \(-0.611400\pi\) | ||||
−0.342872 | + | 0.939382i | \(0.611400\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −56.8413 | −1.93715 | ||||||||
\(862\) | −5.80142 | −0.197597 | ||||||||
\(863\) | −13.9645 | −0.475358 | −0.237679 | − | 0.971344i | \(-0.576387\pi\) | ||||
−0.237679 | + | 0.971344i | \(0.576387\pi\) | |||||||
\(864\) | −19.1205 | −0.650491 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.00236 | −0.0340614 | ||||||||
\(867\) | −17.9382 | −0.609213 | ||||||||
\(868\) | 10.5291 | 0.357381 | ||||||||
\(869\) | −2.27975 | −0.0773353 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.5012 | −0.491353 | ||||||||
\(872\) | 19.5290 | 0.661336 | ||||||||
\(873\) | −0.919771 | −0.0311295 | ||||||||
\(874\) | 5.01135 | 0.169511 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.91601 | 0.166096 | ||||||||
\(877\) | −23.4512 | −0.791891 | −0.395946 | − | 0.918274i | \(-0.629583\pi\) | ||||
−0.395946 | + | 0.918274i | \(0.629583\pi\) | |||||||
\(878\) | 4.81877 | 0.162626 | ||||||||
\(879\) | −5.98545 | −0.201884 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.4714 | 1.49828 | 0.749139 | − | 0.662412i | \(-0.230467\pi\) | ||||
0.749139 | + | 0.662412i | \(0.230467\pi\) | |||||||
\(882\) | −0.0887311 | −0.00298773 | ||||||||
\(883\) | 0.758169 | 0.0255144 | 0.0127572 | − | 0.999919i | \(-0.495939\pi\) | ||||
0.0127572 | + | 0.999919i | \(0.495939\pi\) | |||||||
\(884\) | 17.0516 | 0.573509 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.32818 | 0.111812 | ||||||||
\(887\) | −55.4695 | −1.86248 | −0.931242 | − | 0.364402i | \(-0.881273\pi\) | ||||
−0.931242 | + | 0.364402i | \(0.881273\pi\) | |||||||
\(888\) | −0.0293042 | −0.000983385 0 | ||||||||
\(889\) | 2.32120 | 0.0778506 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 47.1314 | 1.57896 | ||||||||
\(892\) | −37.0606 | −1.24088 | ||||||||
\(893\) | 14.0721 | 0.470905 | ||||||||
\(894\) | −7.17136 | −0.239846 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 31.1760 | 1.04152 | ||||||||
\(897\) | −45.7284 | −1.52683 | ||||||||
\(898\) | 6.19141 | 0.206610 | ||||||||
\(899\) | 7.70312 | 0.256914 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.40584 | 0.146780 | ||||||||
\(902\) | −16.8891 | −0.562347 | ||||||||
\(903\) | 13.6647 | 0.454732 | ||||||||
\(904\) | 23.6034 | 0.785038 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.20853 | 0.0401509 | ||||||||
\(907\) | −15.8193 | −0.525271 | −0.262636 | − | 0.964895i | \(-0.584592\pi\) | ||||
−0.262636 | + | 0.964895i | \(0.584592\pi\) | |||||||
\(908\) | 2.54084 | 0.0843209 | ||||||||
\(909\) | −0.0830100 | −0.00275327 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.02411 | −0.265851 | −0.132925 | − | 0.991126i | \(-0.542437\pi\) | ||||
−0.132925 | + | 0.991126i | \(0.542437\pi\) | |||||||
\(912\) | −11.7135 | −0.387873 | ||||||||
\(913\) | −32.2703 | −1.06799 | ||||||||
\(914\) | 9.94605 | 0.328986 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 42.3520 | 1.39935 | ||||||||
\(917\) | −24.1419 | −0.797235 | ||||||||
\(918\) | 4.38348 | 0.144676 | ||||||||
\(919\) | 22.8402 | 0.753428 | 0.376714 | − | 0.926330i | \(-0.377054\pi\) | ||||
0.376714 | + | 0.926330i | \(0.377054\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.3130 | −0.504581 | ||||||||
\(922\) | 0.774308 | 0.0255005 | ||||||||
\(923\) | 8.23572 | 0.271082 | ||||||||
\(924\) | −59.3939 | −1.95392 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −0.104881 | −0.00344661 | ||||||||
\(927\) | 0.842973 | 0.0276869 | ||||||||
\(928\) | 17.2902 | 0.567579 | ||||||||
\(929\) | −39.7278 | −1.30343 | −0.651713 | − | 0.758465i | \(-0.725950\pi\) | ||||
−0.651713 | + | 0.758465i | \(0.725950\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.57070 | −0.313667 | ||||||||
\(932\) | 34.7694 | 1.13891 | ||||||||
\(933\) | −46.5040 | −1.52247 | ||||||||
\(934\) | −4.18475 | −0.136929 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.257466 | 0.00841555 | ||||||||
\(937\) | −30.4367 | −0.994325 | −0.497162 | − | 0.867658i | \(-0.665625\pi\) | ||||
−0.497162 | + | 0.867658i | \(0.665625\pi\) | |||||||
\(938\) | 4.60769 | 0.150446 | ||||||||
\(939\) | 34.4917 | 1.12559 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.6117 | 0.834916 | 0.417458 | − | 0.908696i | \(-0.362921\pi\) | ||||
0.417458 | + | 0.908696i | \(0.362921\pi\) | |||||||
\(942\) | 8.82643 | 0.287581 | ||||||||
\(943\) | −73.2659 | −2.38587 | ||||||||
\(944\) | −0.0747744 | −0.00243370 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.06016 | 0.132007 | ||||||||
\(947\) | 58.0741 | 1.88716 | 0.943578 | − | 0.331151i | \(-0.107437\pi\) | ||||
0.943578 | + | 0.331151i | \(0.107437\pi\) | |||||||
\(948\) | −1.38618 | −0.0450211 | ||||||||
\(949\) | −5.33005 | −0.173021 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16.6047 | −0.538446 | ||||||||
\(952\) | −11.1417 | −0.361105 | ||||||||
\(953\) | 45.6216 | 1.47783 | 0.738915 | − | 0.673799i | \(-0.235339\pi\) | ||||
0.738915 | + | 0.673799i | \(0.235339\pi\) | |||||||
\(954\) | 0.0323502 | 0.00104738 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 22.7259 | 0.735008 | ||||||||
\(957\) | −43.4527 | −1.40463 | ||||||||
\(958\) | −6.64762 | −0.214775 | ||||||||
\(959\) | −37.3862 | −1.20726 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.3620 | −0.914902 | ||||||||
\(962\) | 0.0154505 | 0.000498144 0 | ||||||||
\(963\) | 0.702219 | 0.0226287 | ||||||||
\(964\) | −19.1538 | −0.616903 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 14.5300 | 0.467495 | ||||||||
\(967\) | 42.4449 | 1.36494 | 0.682468 | − | 0.730916i | \(-0.260907\pi\) | ||||
0.682468 | + | 0.730916i | \(0.260907\pi\) | |||||||
\(968\) | −22.2971 | −0.716655 | ||||||||
\(969\) | 8.88860 | 0.285543 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.4332 | −0.463182 | −0.231591 | − | 0.972813i | \(-0.574393\pi\) | ||||
−0.231591 | + | 0.972813i | \(0.574393\pi\) | |||||||
\(972\) | −1.13075 | −0.0362688 | ||||||||
\(973\) | −66.8047 | −2.14166 | ||||||||
\(974\) | −5.06198 | −0.162196 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13.2057 | 0.422705 | ||||||||
\(977\) | −16.5748 | −0.530276 | −0.265138 | − | 0.964211i | \(-0.585417\pi\) | ||||
−0.265138 | + | 0.964211i | \(0.585417\pi\) | |||||||
\(978\) | −4.14333 | −0.132489 | ||||||||
\(979\) | 32.5467 | 1.04020 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.882394 | 0.0281727 | ||||||||
\(982\) | −8.98845 | −0.286833 | ||||||||
\(983\) | −33.3174 | −1.06266 | −0.531330 | − | 0.847165i | \(-0.678308\pi\) | ||||
−0.531330 | + | 0.847165i | \(0.678308\pi\) | |||||||
\(984\) | −21.1177 | −0.673207 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3.96389 | −0.126236 | ||||||||
\(987\) | 40.8009 | 1.29871 | ||||||||
\(988\) | 13.5046 | 0.429639 | ||||||||
\(989\) | 17.6131 | 0.560065 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.4962 | −0.778146 | −0.389073 | − | 0.921207i | \(-0.627205\pi\) | ||||
−0.389073 | + | 0.921207i | \(0.627205\pi\) | |||||||
\(992\) | 5.92129 | 0.188001 | ||||||||
\(993\) | 33.7516 | 1.07107 | ||||||||
\(994\) | −2.61687 | −0.0830020 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −19.6216 | −0.621735 | ||||||||
\(997\) | 59.8575 | 1.89571 | 0.947854 | − | 0.318706i | \(-0.103248\pi\) | ||||
0.947854 | + | 0.318706i | \(0.103248\pi\) | |||||||
\(998\) | 1.60449 | 0.0507893 | ||||||||
\(999\) | −0.0704313 | −0.00222835 |
(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 | 625.2.a.e.1.6 | ✓ | 8 | |
3.2 | odd | 2 | 5625.2.a.be.1.3 | 8 | |||
4.3 | odd | 2 | 10000.2.a.bn.1.2 | 8 | |||
5.2 | odd | 4 | 625.2.b.d.624.9 | 16 | |||
5.3 | odd | 4 | 625.2.b.d.624.8 | 16 | |||
5.4 | even | 2 | 625.2.a.g.1.3 | yes | 8 | ||
15.14 | odd | 2 | 5625.2.a.s.1.6 | 8 | |||
20.19 | odd | 2 | 10000.2.a.be.1.7 | 8 | |||
25.2 | odd | 20 | 625.2.e.j.124.5 | 32 | |||
25.3 | odd | 20 | 625.2.e.k.249.4 | 32 | |||
25.4 | even | 10 | 625.2.d.n.376.3 | 16 | |||
25.6 | even | 5 | 625.2.d.p.251.2 | 16 | |||
25.8 | odd | 20 | 625.2.e.k.374.5 | 32 | |||
25.9 | even | 10 | 625.2.d.m.126.2 | 16 | |||
25.11 | even | 5 | 625.2.d.q.501.3 | 16 | |||
25.12 | odd | 20 | 625.2.e.j.499.4 | 32 | |||
25.13 | odd | 20 | 625.2.e.j.499.5 | 32 | |||
25.14 | even | 10 | 625.2.d.m.501.2 | 16 | |||
25.16 | even | 5 | 625.2.d.q.126.3 | 16 | |||
25.17 | odd | 20 | 625.2.e.k.374.4 | 32 | |||
25.19 | even | 10 | 625.2.d.n.251.3 | 16 | |||
25.21 | even | 5 | 625.2.d.p.376.2 | 16 | |||
25.22 | odd | 20 | 625.2.e.k.249.5 | 32 | |||
25.23 | odd | 20 | 625.2.e.j.124.4 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
625.2.a.e.1.6 | ✓ | 8 | 1.1 | even | 1 | trivial | |
625.2.a.g.1.3 | yes | 8 | 5.4 | even | 2 | ||
625.2.b.d.624.8 | 16 | 5.3 | odd | 4 | |||
625.2.b.d.624.9 | 16 | 5.2 | odd | 4 | |||
625.2.d.m.126.2 | 16 | 25.9 | even | 10 | |||
625.2.d.m.501.2 | 16 | 25.14 | even | 10 | |||
625.2.d.n.251.3 | 16 | 25.19 | even | 10 | |||
625.2.d.n.376.3 | 16 | 25.4 | even | 10 | |||
625.2.d.p.251.2 | 16 | 25.6 | even | 5 | |||
625.2.d.p.376.2 | 16 | 25.21 | even | 5 | |||
625.2.d.q.126.3 | 16 | 25.16 | even | 5 | |||
625.2.d.q.501.3 | 16 | 25.11 | even | 5 | |||
625.2.e.j.124.4 | 32 | 25.23 | odd | 20 | |||
625.2.e.j.124.5 | 32 | 25.2 | odd | 20 | |||
625.2.e.j.499.4 | 32 | 25.12 | odd | 20 | |||
625.2.e.j.499.5 | 32 | 25.13 | odd | 20 | |||
625.2.e.k.249.4 | 32 | 25.3 | odd | 20 | |||
625.2.e.k.249.5 | 32 | 25.22 | odd | 20 | |||
625.2.e.k.374.4 | 32 | 25.17 | odd | 20 | |||
625.2.e.k.374.5 | 32 | 25.8 | odd | 20 | |||
5625.2.a.s.1.6 | 8 | 15.14 | odd | 2 | |||
5625.2.a.be.1.3 | 8 | 3.2 | odd | 2 | |||
10000.2.a.be.1.7 | 8 | 20.19 | odd | 2 | |||
10000.2.a.bn.1.2 | 8 | 4.3 | odd | 2 |