Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4025,2,Mod(1,4025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4025, 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("4025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4025 = 5^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4025.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: | \(32.1397868136\) |
Analytic rank: | \(0\) |
Dimension: | \(21\) |
Twist minimal: | no (minimal twist has level 805) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 4025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.35921 | 1.66822 | 0.834108 | − | 0.551601i | \(-0.185983\pi\) | ||||
0.834108 | + | 0.551601i | \(0.185983\pi\) | |||||||
\(3\) | 2.50751 | 1.44771 | 0.723856 | − | 0.689952i | \(-0.242368\pi\) | ||||
0.723856 | + | 0.689952i | \(0.242368\pi\) | |||||||
\(4\) | 3.56589 | 1.78294 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 5.91575 | 2.41509 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 3.69426 | 1.30612 | ||||||||
\(9\) | 3.28760 | 1.09587 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.70134 | 0.814486 | 0.407243 | − | 0.913320i | \(-0.366490\pi\) | ||||
0.407243 | + | 0.913320i | \(0.366490\pi\) | |||||||
\(12\) | 8.94150 | 2.58119 | ||||||||
\(13\) | 2.80434 | 0.777783 | 0.388892 | − | 0.921283i | \(-0.372858\pi\) | ||||
0.388892 | + | 0.921283i | \(0.372858\pi\) | |||||||
\(14\) | 2.35921 | 0.630526 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.58378 | 0.395944 | ||||||||
\(17\) | −1.99885 | −0.484792 | −0.242396 | − | 0.970177i | \(-0.577933\pi\) | ||||
−0.242396 | + | 0.970177i | \(0.577933\pi\) | |||||||
\(18\) | 7.75616 | 1.82814 | ||||||||
\(19\) | −1.11683 | −0.256219 | −0.128110 | − | 0.991760i | \(-0.540891\pi\) | ||||
−0.128110 | + | 0.991760i | \(0.540891\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.50751 | 0.547183 | ||||||||
\(22\) | 6.37305 | 1.35874 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 9.26340 | 1.89088 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.61603 | 1.29751 | ||||||||
\(27\) | 0.721167 | 0.138789 | ||||||||
\(28\) | 3.56589 | 0.673889 | ||||||||
\(29\) | −8.42950 | −1.56532 | −0.782659 | − | 0.622450i | \(-0.786137\pi\) | ||||
−0.782659 | + | 0.622450i | \(0.786137\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.48252 | 0.445875 | 0.222937 | − | 0.974833i | \(-0.428435\pi\) | ||||
0.222937 | + | 0.974833i | \(0.428435\pi\) | |||||||
\(32\) | −3.65206 | −0.645598 | ||||||||
\(33\) | 6.77365 | 1.17914 | ||||||||
\(34\) | −4.71571 | −0.808738 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 11.7232 | 1.95387 | ||||||||
\(37\) | 0.807977 | 0.132831 | 0.0664153 | − | 0.997792i | \(-0.478844\pi\) | ||||
0.0664153 | + | 0.997792i | \(0.478844\pi\) | |||||||
\(38\) | −2.63485 | −0.427429 | ||||||||
\(39\) | 7.03190 | 1.12601 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.79798 | 1.06167 | 0.530833 | − | 0.847477i | \(-0.321879\pi\) | ||||
0.530833 | + | 0.847477i | \(0.321879\pi\) | |||||||
\(42\) | 5.91575 | 0.912820 | ||||||||
\(43\) | 3.15924 | 0.481780 | 0.240890 | − | 0.970552i | \(-0.422561\pi\) | ||||
0.240890 | + | 0.970552i | \(0.422561\pi\) | |||||||
\(44\) | 9.63269 | 1.45218 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.35921 | 0.347847 | ||||||||
\(47\) | −10.0740 | −1.46945 | −0.734724 | − | 0.678366i | \(-0.762688\pi\) | ||||
−0.734724 | + | 0.678366i | \(0.762688\pi\) | |||||||
\(48\) | 3.97133 | 0.573213 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.01213 | −0.701839 | ||||||||
\(52\) | 9.99995 | 1.38674 | ||||||||
\(53\) | −4.86545 | −0.668322 | −0.334161 | − | 0.942516i | \(-0.608453\pi\) | ||||
−0.334161 | + | 0.942516i | \(0.608453\pi\) | |||||||
\(54\) | 1.70139 | 0.231530 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.69426 | 0.493666 | ||||||||
\(57\) | −2.80047 | −0.370931 | ||||||||
\(58\) | −19.8870 | −2.61129 | ||||||||
\(59\) | −12.1768 | −1.58528 | −0.792642 | − | 0.609688i | \(-0.791295\pi\) | ||||
−0.792642 | + | 0.609688i | \(0.791295\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.43038 | 1.20744 | 0.603718 | − | 0.797198i | \(-0.293685\pi\) | ||||
0.603718 | + | 0.797198i | \(0.293685\pi\) | |||||||
\(62\) | 5.85680 | 0.743815 | ||||||||
\(63\) | 3.28760 | 0.414199 | ||||||||
\(64\) | −11.7835 | −1.47294 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 15.9805 | 1.96706 | ||||||||
\(67\) | 7.25984 | 0.886930 | 0.443465 | − | 0.896292i | \(-0.353749\pi\) | ||||
0.443465 | + | 0.896292i | \(0.353749\pi\) | |||||||
\(68\) | −7.12767 | −0.864357 | ||||||||
\(69\) | 2.50751 | 0.301869 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.44213 | −0.289828 | −0.144914 | − | 0.989444i | \(-0.546290\pi\) | ||||
−0.144914 | + | 0.989444i | \(0.546290\pi\) | |||||||
\(72\) | 12.1453 | 1.43133 | ||||||||
\(73\) | 1.70335 | 0.199362 | 0.0996808 | − | 0.995019i | \(-0.468218\pi\) | ||||
0.0996808 | + | 0.995019i | \(0.468218\pi\) | |||||||
\(74\) | 1.90619 | 0.221590 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.98250 | −0.456824 | ||||||||
\(77\) | 2.70134 | 0.307847 | ||||||||
\(78\) | 16.5898 | 1.87842 | ||||||||
\(79\) | 15.4751 | 1.74108 | 0.870540 | − | 0.492098i | \(-0.163770\pi\) | ||||
0.870540 | + | 0.492098i | \(0.163770\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.05448 | −0.894942 | ||||||||
\(82\) | 16.0379 | 1.77109 | ||||||||
\(83\) | 10.7887 | 1.18421 | 0.592107 | − | 0.805860i | \(-0.298296\pi\) | ||||
0.592107 | + | 0.805860i | \(0.298296\pi\) | |||||||
\(84\) | 8.94150 | 0.975597 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.45333 | 0.803713 | ||||||||
\(87\) | −21.1371 | −2.26613 | ||||||||
\(88\) | 9.97947 | 1.06382 | ||||||||
\(89\) | −8.27944 | −0.877619 | −0.438809 | − | 0.898580i | \(-0.644600\pi\) | ||||
−0.438809 | + | 0.898580i | \(0.644600\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.80434 | 0.293974 | ||||||||
\(92\) | 3.56589 | 0.371769 | ||||||||
\(93\) | 6.22495 | 0.645498 | ||||||||
\(94\) | −23.7668 | −2.45136 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −9.15757 | −0.934640 | ||||||||
\(97\) | −13.2465 | −1.34498 | −0.672491 | − | 0.740106i | \(-0.734776\pi\) | ||||
−0.672491 | + | 0.740106i | \(0.734776\pi\) | |||||||
\(98\) | 2.35921 | 0.238317 | ||||||||
\(99\) | 8.88095 | 0.892569 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.4521 | −1.33854 | −0.669268 | − | 0.743021i | \(-0.733392\pi\) | ||||
−0.669268 | + | 0.743021i | \(0.733392\pi\) | |||||||
\(102\) | −11.8247 | −1.17082 | ||||||||
\(103\) | −6.77042 | −0.667109 | −0.333554 | − | 0.942731i | \(-0.608248\pi\) | ||||
−0.333554 | + | 0.942731i | \(0.608248\pi\) | |||||||
\(104\) | 10.3600 | 1.01588 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11.4786 | −1.11490 | ||||||||
\(107\) | −10.0195 | −0.968619 | −0.484309 | − | 0.874897i | \(-0.660929\pi\) | ||||
−0.484309 | + | 0.874897i | \(0.660929\pi\) | |||||||
\(108\) | 2.57160 | 0.247452 | ||||||||
\(109\) | 15.5089 | 1.48548 | 0.742740 | − | 0.669580i | \(-0.233526\pi\) | ||||
0.742740 | + | 0.669580i | \(0.233526\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.02601 | 0.192300 | ||||||||
\(112\) | 1.58378 | 0.149653 | ||||||||
\(113\) | −0.178511 | −0.0167929 | −0.00839645 | − | 0.999965i | \(-0.502673\pi\) | ||||
−0.00839645 | + | 0.999965i | \(0.502673\pi\) | |||||||
\(114\) | −6.60690 | −0.618793 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −30.0586 | −2.79088 | ||||||||
\(117\) | 9.21955 | 0.852348 | ||||||||
\(118\) | −28.7277 | −2.64460 | ||||||||
\(119\) | −1.99885 | −0.183234 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.70274 | −0.336613 | ||||||||
\(122\) | 22.2483 | 2.01426 | ||||||||
\(123\) | 17.0460 | 1.53698 | ||||||||
\(124\) | 8.85240 | 0.794969 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 7.75616 | 0.690973 | ||||||||
\(127\) | 4.36340 | 0.387190 | 0.193595 | − | 0.981082i | \(-0.437985\pi\) | ||||
0.193595 | + | 0.981082i | \(0.437985\pi\) | |||||||
\(128\) | −20.4958 | −1.81159 | ||||||||
\(129\) | 7.92183 | 0.697479 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.35393 | −0.380405 | −0.190202 | − | 0.981745i | \(-0.560914\pi\) | ||||
−0.190202 | + | 0.981745i | \(0.560914\pi\) | |||||||
\(132\) | 24.1541 | 2.10234 | ||||||||
\(133\) | −1.11683 | −0.0968417 | ||||||||
\(134\) | 17.1275 | 1.47959 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.38427 | −0.633196 | ||||||||
\(137\) | 10.7306 | 0.916780 | 0.458390 | − | 0.888751i | \(-0.348426\pi\) | ||||
0.458390 | + | 0.888751i | \(0.348426\pi\) | |||||||
\(138\) | 5.91575 | 0.503582 | ||||||||
\(139\) | 6.30819 | 0.535053 | 0.267527 | − | 0.963550i | \(-0.413794\pi\) | ||||
0.267527 | + | 0.963550i | \(0.413794\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −25.2607 | −2.12734 | ||||||||
\(142\) | −5.76151 | −0.483495 | ||||||||
\(143\) | 7.57548 | 0.633494 | ||||||||
\(144\) | 5.20683 | 0.433902 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.01856 | 0.332578 | ||||||||
\(147\) | 2.50751 | 0.206816 | ||||||||
\(148\) | 2.88116 | 0.236830 | ||||||||
\(149\) | −12.4249 | −1.01789 | −0.508943 | − | 0.860800i | \(-0.669964\pi\) | ||||
−0.508943 | + | 0.860800i | \(0.669964\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.9899 | −0.975727 | −0.487864 | − | 0.872920i | \(-0.662224\pi\) | ||||
−0.487864 | + | 0.872920i | \(0.662224\pi\) | |||||||
\(152\) | −4.12587 | −0.334653 | ||||||||
\(153\) | −6.57142 | −0.531268 | ||||||||
\(154\) | 6.37305 | 0.513555 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 25.0750 | 2.00760 | ||||||||
\(157\) | 15.0216 | 1.19885 | 0.599427 | − | 0.800430i | \(-0.295395\pi\) | ||||
0.599427 | + | 0.800430i | \(0.295395\pi\) | |||||||
\(158\) | 36.5090 | 2.90450 | ||||||||
\(159\) | −12.2002 | −0.967537 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | −19.0022 | −1.49296 | ||||||||
\(163\) | 5.77178 | 0.452080 | 0.226040 | − | 0.974118i | \(-0.427422\pi\) | ||||
0.226040 | + | 0.974118i | \(0.427422\pi\) | |||||||
\(164\) | 24.2408 | 1.89289 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 25.4528 | 1.97552 | ||||||||
\(167\) | −0.00532684 | −0.000412203 0 | −0.000206101 | − | 1.00000i | \(-0.500066\pi\) | ||||
−0.000206101 | 1.00000i | \(0.500066\pi\) | ||||||||
\(168\) | 9.26340 | 0.714686 | ||||||||
\(169\) | −5.13569 | −0.395053 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.67170 | −0.280782 | ||||||||
\(172\) | 11.2655 | 0.858987 | ||||||||
\(173\) | 20.7072 | 1.57434 | 0.787168 | − | 0.616739i | \(-0.211546\pi\) | ||||
0.787168 | + | 0.616739i | \(0.211546\pi\) | |||||||
\(174\) | −49.8668 | −3.78039 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.27833 | 0.322491 | ||||||||
\(177\) | −30.5334 | −2.29503 | ||||||||
\(178\) | −19.5330 | −1.46406 | ||||||||
\(179\) | −12.1561 | −0.908586 | −0.454293 | − | 0.890852i | \(-0.650108\pi\) | ||||
−0.454293 | + | 0.890852i | \(0.650108\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.8574 | −0.955683 | −0.477842 | − | 0.878446i | \(-0.658581\pi\) | ||||
−0.477842 | + | 0.878446i | \(0.658581\pi\) | |||||||
\(182\) | 6.61603 | 0.490413 | ||||||||
\(183\) | 23.6468 | 1.74802 | ||||||||
\(184\) | 3.69426 | 0.272345 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 14.6860 | 1.07683 | ||||||||
\(187\) | −5.39958 | −0.394856 | ||||||||
\(188\) | −35.9228 | −2.61994 | ||||||||
\(189\) | 0.721167 | 0.0524572 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.9308 | 0.935639 | 0.467820 | − | 0.883824i | \(-0.345040\pi\) | ||||
0.467820 | + | 0.883824i | \(0.345040\pi\) | |||||||
\(192\) | −29.5473 | −2.13239 | ||||||||
\(193\) | −0.302842 | −0.0217991 | −0.0108995 | − | 0.999941i | \(-0.503469\pi\) | ||||
−0.0108995 | + | 0.999941i | \(0.503469\pi\) | |||||||
\(194\) | −31.2514 | −2.24372 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.56589 | 0.254706 | ||||||||
\(197\) | 10.3678 | 0.738672 | 0.369336 | − | 0.929296i | \(-0.379585\pi\) | ||||
0.369336 | + | 0.929296i | \(0.379585\pi\) | |||||||
\(198\) | 20.9520 | 1.48900 | ||||||||
\(199\) | −11.9825 | −0.849414 | −0.424707 | − | 0.905331i | \(-0.639623\pi\) | ||||
−0.424707 | + | 0.905331i | \(0.639623\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 18.2041 | 1.28402 | ||||||||
\(202\) | −31.7364 | −2.23297 | ||||||||
\(203\) | −8.42950 | −0.591635 | ||||||||
\(204\) | −17.8727 | −1.25134 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −15.9729 | −1.11288 | ||||||||
\(207\) | 3.28760 | 0.228504 | ||||||||
\(208\) | 4.44144 | 0.307959 | ||||||||
\(209\) | −3.01695 | −0.208687 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 28.1068 | 1.93495 | 0.967477 | − | 0.252960i | \(-0.0814039\pi\) | ||||
0.967477 | + | 0.252960i | \(0.0814039\pi\) | |||||||
\(212\) | −17.3497 | −1.19158 | ||||||||
\(213\) | −6.12366 | −0.419587 | ||||||||
\(214\) | −23.6381 | −1.61586 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.66418 | 0.181275 | ||||||||
\(217\) | 2.48252 | 0.168525 | ||||||||
\(218\) | 36.5887 | 2.47810 | ||||||||
\(219\) | 4.27116 | 0.288618 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.60545 | −0.377063 | ||||||||
\(222\) | 4.77979 | 0.320799 | ||||||||
\(223\) | −12.7655 | −0.854844 | −0.427422 | − | 0.904052i | \(-0.640578\pi\) | ||||
−0.427422 | + | 0.904052i | \(0.640578\pi\) | |||||||
\(224\) | −3.65206 | −0.244013 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.421145 | −0.0280142 | ||||||||
\(227\) | −1.81853 | −0.120700 | −0.0603499 | − | 0.998177i | \(-0.519222\pi\) | ||||
−0.0603499 | + | 0.998177i | \(0.519222\pi\) | |||||||
\(228\) | −9.98616 | −0.661349 | ||||||||
\(229\) | 5.42321 | 0.358376 | 0.179188 | − | 0.983815i | \(-0.442653\pi\) | ||||
0.179188 | + | 0.983815i | \(0.442653\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.77365 | 0.445673 | ||||||||
\(232\) | −31.1408 | −2.04449 | ||||||||
\(233\) | 9.74067 | 0.638133 | 0.319066 | − | 0.947732i | \(-0.396631\pi\) | ||||
0.319066 | + | 0.947732i | \(0.396631\pi\) | |||||||
\(234\) | 21.7509 | 1.42190 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −43.4211 | −2.82647 | ||||||||
\(237\) | 38.8039 | 2.52058 | ||||||||
\(238\) | −4.71571 | −0.305674 | ||||||||
\(239\) | −21.1865 | −1.37044 | −0.685220 | − | 0.728336i | \(-0.740294\pi\) | ||||
−0.685220 | + | 0.728336i | \(0.740294\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.8166 | 0.890008 | 0.445004 | − | 0.895529i | \(-0.353202\pi\) | ||||
0.445004 | + | 0.895529i | \(0.353202\pi\) | |||||||
\(242\) | −8.73555 | −0.561543 | ||||||||
\(243\) | −22.3602 | −1.43441 | ||||||||
\(244\) | 33.6277 | 2.15279 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 40.2151 | 2.56402 | ||||||||
\(247\) | −3.13198 | −0.199283 | ||||||||
\(248\) | 9.17110 | 0.582365 | ||||||||
\(249\) | 27.0528 | 1.71440 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.9432 | −0.753850 | −0.376925 | − | 0.926244i | \(-0.623019\pi\) | ||||
−0.376925 | + | 0.926244i | \(0.623019\pi\) | |||||||
\(252\) | 11.7232 | 0.738494 | ||||||||
\(253\) | 2.70134 | 0.169832 | ||||||||
\(254\) | 10.2942 | 0.645916 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −24.7868 | −1.54917 | ||||||||
\(257\) | −16.5580 | −1.03286 | −0.516431 | − | 0.856329i | \(-0.672740\pi\) | ||||
−0.516431 | + | 0.856329i | \(0.672740\pi\) | |||||||
\(258\) | 18.6893 | 1.16354 | ||||||||
\(259\) | 0.807977 | 0.0502053 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −27.7129 | −1.71538 | ||||||||
\(262\) | −10.2719 | −0.634597 | ||||||||
\(263\) | 17.5430 | 1.08175 | 0.540873 | − | 0.841104i | \(-0.318094\pi\) | ||||
0.540873 | + | 0.841104i | \(0.318094\pi\) | |||||||
\(264\) | 25.0236 | 1.54010 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.63485 | −0.161553 | ||||||||
\(267\) | −20.7608 | −1.27054 | ||||||||
\(268\) | 25.8878 | 1.58135 | ||||||||
\(269\) | 30.8143 | 1.87878 | 0.939389 | − | 0.342853i | \(-0.111393\pi\) | ||||
0.939389 | + | 0.342853i | \(0.111393\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.4786 | 1.24398 | 0.621992 | − | 0.783023i | \(-0.286324\pi\) | ||||
0.621992 | + | 0.783023i | \(0.286324\pi\) | |||||||
\(272\) | −3.16573 | −0.191951 | ||||||||
\(273\) | 7.03190 | 0.425590 | ||||||||
\(274\) | 25.3159 | 1.52939 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 8.94150 | 0.538215 | ||||||||
\(277\) | 31.9578 | 1.92016 | 0.960080 | − | 0.279727i | \(-0.0902438\pi\) | ||||
0.960080 | + | 0.279727i | \(0.0902438\pi\) | |||||||
\(278\) | 14.8824 | 0.892584 | ||||||||
\(279\) | 8.16156 | 0.488620 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.8548 | 0.766852 | 0.383426 | − | 0.923572i | \(-0.374744\pi\) | ||||
0.383426 | + | 0.923572i | \(0.374744\pi\) | |||||||
\(282\) | −59.5954 | −3.54885 | ||||||||
\(283\) | −25.7504 | −1.53070 | −0.765351 | − | 0.643613i | \(-0.777434\pi\) | ||||
−0.765351 | + | 0.643613i | \(0.777434\pi\) | |||||||
\(284\) | −8.70836 | −0.516746 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 17.8722 | 1.05680 | ||||||||
\(287\) | 6.79798 | 0.401272 | ||||||||
\(288\) | −12.0065 | −0.707491 | ||||||||
\(289\) | −13.0046 | −0.764977 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −33.2158 | −1.94714 | ||||||||
\(292\) | 6.07394 | 0.355451 | ||||||||
\(293\) | −14.9716 | −0.874651 | −0.437325 | − | 0.899303i | \(-0.644074\pi\) | ||||
−0.437325 | + | 0.899303i | \(0.644074\pi\) | |||||||
\(294\) | 5.91575 | 0.345014 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.98488 | 0.173493 | ||||||||
\(297\) | 1.94812 | 0.113041 | ||||||||
\(298\) | −29.3130 | −1.69805 | ||||||||
\(299\) | 2.80434 | 0.162179 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.15924 | 0.182096 | ||||||||
\(302\) | −28.2868 | −1.62772 | ||||||||
\(303\) | −33.7313 | −1.93781 | ||||||||
\(304\) | −1.76881 | −0.101448 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −15.5034 | −0.886270 | ||||||||
\(307\) | −29.1203 | −1.66198 | −0.830990 | − | 0.556287i | \(-0.812226\pi\) | ||||
−0.830990 | + | 0.556287i | \(0.812226\pi\) | |||||||
\(308\) | 9.63269 | 0.548873 | ||||||||
\(309\) | −16.9769 | −0.965781 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 27.9131 | 1.58281 | 0.791405 | − | 0.611293i | \(-0.209350\pi\) | ||||
0.791405 | + | 0.611293i | \(0.209350\pi\) | |||||||
\(312\) | 25.9777 | 1.47070 | ||||||||
\(313\) | −34.6962 | −1.96115 | −0.980573 | − | 0.196152i | \(-0.937155\pi\) | ||||
−0.980573 | + | 0.196152i | \(0.937155\pi\) | |||||||
\(314\) | 35.4391 | 1.99995 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 55.1823 | 3.10425 | ||||||||
\(317\) | −22.9724 | −1.29026 | −0.645130 | − | 0.764073i | \(-0.723197\pi\) | ||||
−0.645130 | + | 0.764073i | \(0.723197\pi\) | |||||||
\(318\) | −28.7828 | −1.61406 | ||||||||
\(319\) | −22.7710 | −1.27493 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −25.1239 | −1.40228 | ||||||||
\(322\) | 2.35921 | 0.131474 | ||||||||
\(323\) | 2.23238 | 0.124213 | ||||||||
\(324\) | −28.7213 | −1.59563 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 13.6168 | 0.754167 | ||||||||
\(327\) | 38.8886 | 2.15055 | ||||||||
\(328\) | 25.1135 | 1.38666 | ||||||||
\(329\) | −10.0740 | −0.555399 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.4248 | −0.792858 | −0.396429 | − | 0.918065i | \(-0.629751\pi\) | ||||
−0.396429 | + | 0.918065i | \(0.629751\pi\) | |||||||
\(332\) | 38.4713 | 2.11139 | ||||||||
\(333\) | 2.65631 | 0.145565 | ||||||||
\(334\) | −0.0125671 | −0.000687643 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.97133 | 0.216654 | ||||||||
\(337\) | −3.73562 | −0.203492 | −0.101746 | − | 0.994810i | \(-0.532443\pi\) | ||||
−0.101746 | + | 0.994810i | \(0.532443\pi\) | |||||||
\(338\) | −12.1162 | −0.659034 | ||||||||
\(339\) | −0.447618 | −0.0243113 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.70615 | 0.363159 | ||||||||
\(342\) | −8.66233 | −0.468405 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 11.6711 | 0.629262 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 48.8526 | 2.62633 | ||||||||
\(347\) | 15.9464 | 0.856045 | 0.428023 | − | 0.903768i | \(-0.359210\pi\) | ||||
0.428023 | + | 0.903768i | \(0.359210\pi\) | |||||||
\(348\) | −75.3723 | −4.04038 | ||||||||
\(349\) | 3.27234 | 0.175164 | 0.0875821 | − | 0.996157i | \(-0.472086\pi\) | ||||
0.0875821 | + | 0.996157i | \(0.472086\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.02240 | 0.107948 | ||||||||
\(352\) | −9.86546 | −0.525831 | ||||||||
\(353\) | 10.3265 | 0.549623 | 0.274812 | − | 0.961498i | \(-0.411385\pi\) | ||||
0.274812 | + | 0.961498i | \(0.411385\pi\) | |||||||
\(354\) | −72.0349 | −3.82861 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −29.5235 | −1.56474 | ||||||||
\(357\) | −5.01213 | −0.265270 | ||||||||
\(358\) | −28.6787 | −1.51572 | ||||||||
\(359\) | 15.5797 | 0.822263 | 0.411131 | − | 0.911576i | \(-0.365134\pi\) | ||||
0.411131 | + | 0.911576i | \(0.365134\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.7527 | −0.934352 | ||||||||
\(362\) | −30.3334 | −1.59429 | ||||||||
\(363\) | −9.28466 | −0.487318 | ||||||||
\(364\) | 9.99995 | 0.524140 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 55.7878 | 2.91607 | ||||||||
\(367\) | −21.5509 | −1.12495 | −0.562475 | − | 0.826814i | \(-0.690151\pi\) | ||||
−0.562475 | + | 0.826814i | \(0.690151\pi\) | |||||||
\(368\) | 1.58378 | 0.0825601 | ||||||||
\(369\) | 22.3490 | 1.16344 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.86545 | −0.252602 | ||||||||
\(372\) | 22.1975 | 1.15089 | ||||||||
\(373\) | −20.5515 | −1.06412 | −0.532059 | − | 0.846707i | \(-0.678582\pi\) | ||||
−0.532059 | + | 0.846707i | \(0.678582\pi\) | |||||||
\(374\) | −12.7388 | −0.658706 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −37.2161 | −1.91927 | ||||||||
\(377\) | −23.6392 | −1.21748 | ||||||||
\(378\) | 1.70139 | 0.0875099 | ||||||||
\(379\) | 13.3073 | 0.683552 | 0.341776 | − | 0.939781i | \(-0.388972\pi\) | ||||
0.341776 | + | 0.939781i | \(0.388972\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.9413 | 0.560539 | ||||||||
\(382\) | 30.5065 | 1.56085 | ||||||||
\(383\) | 10.7300 | 0.548277 | 0.274139 | − | 0.961690i | \(-0.411607\pi\) | ||||
0.274139 | + | 0.961690i | \(0.411607\pi\) | |||||||
\(384\) | −51.3933 | −2.62265 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.714469 | −0.0363655 | ||||||||
\(387\) | 10.3863 | 0.527967 | ||||||||
\(388\) | −47.2356 | −2.39803 | ||||||||
\(389\) | −29.3543 | −1.48832 | −0.744161 | − | 0.668001i | \(-0.767150\pi\) | ||||
−0.744161 | + | 0.668001i | \(0.767150\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.99885 | −0.101086 | ||||||||
\(392\) | 3.69426 | 0.186588 | ||||||||
\(393\) | −10.9175 | −0.550716 | ||||||||
\(394\) | 24.4598 | 1.23226 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 31.6685 | 1.59140 | ||||||||
\(397\) | −7.32590 | −0.367676 | −0.183838 | − | 0.982957i | \(-0.558852\pi\) | ||||
−0.183838 | + | 0.982957i | \(0.558852\pi\) | |||||||
\(398\) | −28.2692 | −1.41701 | ||||||||
\(399\) | −2.80047 | −0.140199 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.7248 | 0.585510 | 0.292755 | − | 0.956187i | \(-0.405428\pi\) | ||||
0.292755 | + | 0.956187i | \(0.405428\pi\) | |||||||
\(402\) | 42.9474 | 2.14202 | ||||||||
\(403\) | 6.96184 | 0.346794 | ||||||||
\(404\) | −47.9688 | −2.38653 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −19.8870 | −0.986975 | ||||||||
\(407\) | 2.18262 | 0.108189 | ||||||||
\(408\) | −18.5161 | −0.916685 | ||||||||
\(409\) | 9.34310 | 0.461987 | 0.230993 | − | 0.972955i | \(-0.425802\pi\) | ||||
0.230993 | + | 0.972955i | \(0.425802\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 26.9072 | 1.32723 | ||||||||
\(412\) | −24.1425 | −1.18942 | ||||||||
\(413\) | −12.1768 | −0.599181 | ||||||||
\(414\) | 7.75616 | 0.381194 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −10.2416 | −0.502136 | ||||||||
\(417\) | 15.8178 | 0.774603 | ||||||||
\(418\) | −7.11763 | −0.348135 | ||||||||
\(419\) | 22.0474 | 1.07709 | 0.538543 | − | 0.842598i | \(-0.318975\pi\) | ||||
0.538543 | + | 0.842598i | \(0.318975\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.11313 | 0.249199 | 0.124599 | − | 0.992207i | \(-0.460235\pi\) | ||||
0.124599 | + | 0.992207i | \(0.460235\pi\) | |||||||
\(422\) | 66.3100 | 3.22792 | ||||||||
\(423\) | −33.1194 | −1.61032 | ||||||||
\(424\) | −17.9743 | −0.872907 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −14.4470 | −0.699961 | ||||||||
\(427\) | 9.43038 | 0.456368 | ||||||||
\(428\) | −35.7283 | −1.72699 | ||||||||
\(429\) | 18.9956 | 0.917116 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.08201 | 0.389296 | 0.194648 | − | 0.980873i | \(-0.437643\pi\) | ||||
0.194648 | + | 0.980873i | \(0.437643\pi\) | |||||||
\(432\) | 1.14217 | 0.0549526 | ||||||||
\(433\) | 38.6561 | 1.85769 | 0.928847 | − | 0.370464i | \(-0.120801\pi\) | ||||
0.928847 | + | 0.370464i | \(0.120801\pi\) | |||||||
\(434\) | 5.85680 | 0.281136 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 55.3028 | 2.64853 | ||||||||
\(437\) | −1.11683 | −0.0534254 | ||||||||
\(438\) | 10.0766 | 0.481477 | ||||||||
\(439\) | 2.29718 | 0.109638 | 0.0548192 | − | 0.998496i | \(-0.482542\pi\) | ||||
0.0548192 | + | 0.998496i | \(0.482542\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.28760 | 0.156553 | ||||||||
\(442\) | −13.2245 | −0.629023 | ||||||||
\(443\) | −29.1842 | −1.38658 | −0.693292 | − | 0.720657i | \(-0.743840\pi\) | ||||
−0.693292 | + | 0.720657i | \(0.743840\pi\) | |||||||
\(444\) | 7.22452 | 0.342861 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −30.1166 | −1.42606 | ||||||||
\(447\) | −31.1555 | −1.47361 | ||||||||
\(448\) | −11.7835 | −0.556720 | ||||||||
\(449\) | 20.8373 | 0.983374 | 0.491687 | − | 0.870772i | \(-0.336380\pi\) | ||||
0.491687 | + | 0.870772i | \(0.336380\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18.3637 | 0.864712 | ||||||||
\(452\) | −0.636550 | −0.0299408 | ||||||||
\(453\) | −30.0649 | −1.41257 | ||||||||
\(454\) | −4.29029 | −0.201353 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −10.3457 | −0.484480 | ||||||||
\(457\) | 13.4806 | 0.630596 | 0.315298 | − | 0.948993i | \(-0.397895\pi\) | ||||
0.315298 | + | 0.948993i | \(0.397895\pi\) | |||||||
\(458\) | 12.7945 | 0.597849 | ||||||||
\(459\) | −1.44151 | −0.0672837 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −34.2227 | −1.59391 | −0.796954 | − | 0.604040i | \(-0.793557\pi\) | ||||
−0.796954 | + | 0.604040i | \(0.793557\pi\) | |||||||
\(462\) | 15.9805 | 0.743479 | ||||||||
\(463\) | 28.0881 | 1.30536 | 0.652681 | − | 0.757632i | \(-0.273644\pi\) | ||||
0.652681 | + | 0.757632i | \(0.273644\pi\) | |||||||
\(464\) | −13.3504 | −0.619779 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 22.9803 | 1.06454 | ||||||||
\(467\) | −27.6544 | −1.27969 | −0.639846 | − | 0.768503i | \(-0.721002\pi\) | ||||
−0.639846 | + | 0.768503i | \(0.721002\pi\) | |||||||
\(468\) | 32.8759 | 1.51969 | ||||||||
\(469\) | 7.25984 | 0.335228 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 37.6668 | 1.73559 | ||||||||
\(472\) | −44.9843 | −2.07057 | ||||||||
\(473\) | 8.53421 | 0.392403 | ||||||||
\(474\) | 91.5466 | 4.20487 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −7.12767 | −0.326696 | ||||||||
\(477\) | −15.9957 | −0.732392 | ||||||||
\(478\) | −49.9834 | −2.28619 | ||||||||
\(479\) | −7.07484 | −0.323258 | −0.161629 | − | 0.986852i | \(-0.551675\pi\) | ||||
−0.161629 | + | 0.986852i | \(0.551675\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.26584 | 0.103313 | ||||||||
\(482\) | 32.5964 | 1.48473 | ||||||||
\(483\) | 2.50751 | 0.114096 | ||||||||
\(484\) | −13.2036 | −0.600162 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −52.7524 | −2.39290 | ||||||||
\(487\) | −41.7092 | −1.89002 | −0.945012 | − | 0.327037i | \(-0.893950\pi\) | ||||
−0.945012 | + | 0.327037i | \(0.893950\pi\) | |||||||
\(488\) | 34.8383 | 1.57706 | ||||||||
\(489\) | 14.4728 | 0.654482 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.60678 | 0.117642 | 0.0588212 | − | 0.998269i | \(-0.481266\pi\) | ||||
0.0588212 | + | 0.998269i | \(0.481266\pi\) | |||||||
\(492\) | 60.7841 | 2.74036 | ||||||||
\(493\) | 16.8493 | 0.758854 | ||||||||
\(494\) | −7.38900 | −0.332447 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.93176 | 0.176541 | ||||||||
\(497\) | −2.44213 | −0.109545 | ||||||||
\(498\) | 63.8232 | 2.85999 | ||||||||
\(499\) | 35.7391 | 1.59990 | 0.799951 | − | 0.600066i | \(-0.204859\pi\) | ||||
0.799951 | + | 0.600066i | \(0.204859\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.0133571 | −0.000596751 0 | ||||||||
\(502\) | −28.1766 | −1.25758 | ||||||||
\(503\) | −26.8250 | −1.19607 | −0.598033 | − | 0.801472i | \(-0.704051\pi\) | ||||
−0.598033 | + | 0.801472i | \(0.704051\pi\) | |||||||
\(504\) | 12.1453 | 0.540993 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6.37305 | 0.283316 | ||||||||
\(507\) | −12.8778 | −0.571923 | ||||||||
\(508\) | 15.5594 | 0.690337 | ||||||||
\(509\) | −10.6497 | −0.472038 | −0.236019 | − | 0.971748i | \(-0.575843\pi\) | ||||
−0.236019 | + | 0.971748i | \(0.575843\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.70335 | 0.0753516 | ||||||||
\(512\) | −17.4858 | −0.772771 | ||||||||
\(513\) | −0.805424 | −0.0355603 | ||||||||
\(514\) | −39.0639 | −1.72304 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 28.2484 | 1.24357 | ||||||||
\(517\) | −27.2134 | −1.19684 | ||||||||
\(518\) | 1.90619 | 0.0837532 | ||||||||
\(519\) | 51.9234 | 2.27918 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.9869 | −0.481346 | −0.240673 | − | 0.970606i | \(-0.577368\pi\) | ||||
−0.240673 | + | 0.970606i | \(0.577368\pi\) | |||||||
\(522\) | −65.3805 | −2.86163 | ||||||||
\(523\) | −28.5035 | −1.24637 | −0.623185 | − | 0.782074i | \(-0.714162\pi\) | ||||
−0.623185 | + | 0.782074i | \(0.714162\pi\) | |||||||
\(524\) | −15.5256 | −0.678240 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 41.3876 | 1.80459 | ||||||||
\(527\) | −4.96219 | −0.216157 | ||||||||
\(528\) | 10.7279 | 0.466874 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −40.0325 | −1.73726 | ||||||||
\(532\) | −3.98250 | −0.172663 | ||||||||
\(533\) | 19.0638 | 0.825746 | ||||||||
\(534\) | −48.9791 | −2.11953 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 26.8197 | 1.15844 | ||||||||
\(537\) | −30.4814 | −1.31537 | ||||||||
\(538\) | 72.6974 | 3.13421 | ||||||||
\(539\) | 2.70134 | 0.116355 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.2056 | −0.696735 | −0.348367 | − | 0.937358i | \(-0.613264\pi\) | ||||
−0.348367 | + | 0.937358i | \(0.613264\pi\) | |||||||
\(542\) | 48.3133 | 2.07523 | ||||||||
\(543\) | −32.2401 | −1.38355 | ||||||||
\(544\) | 7.29991 | 0.312981 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 16.5898 | 0.709976 | ||||||||
\(547\) | 1.49191 | 0.0637895 | 0.0318948 | − | 0.999491i | \(-0.489846\pi\) | ||||
0.0318948 | + | 0.999491i | \(0.489846\pi\) | |||||||
\(548\) | 38.2643 | 1.63457 | ||||||||
\(549\) | 31.0033 | 1.32319 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.41434 | 0.401065 | ||||||||
\(552\) | 9.26340 | 0.394276 | ||||||||
\(553\) | 15.4751 | 0.658066 | ||||||||
\(554\) | 75.3953 | 3.20324 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 22.4943 | 0.953970 | ||||||||
\(557\) | 21.1267 | 0.895167 | 0.447584 | − | 0.894242i | \(-0.352285\pi\) | ||||
0.447584 | + | 0.894242i | \(0.352285\pi\) | |||||||
\(558\) | 19.2548 | 0.815123 | ||||||||
\(559\) | 8.85959 | 0.374721 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13.5395 | −0.571638 | ||||||||
\(562\) | 30.3272 | 1.27927 | ||||||||
\(563\) | −11.4806 | −0.483851 | −0.241926 | − | 0.970295i | \(-0.577779\pi\) | ||||
−0.241926 | + | 0.970295i | \(0.577779\pi\) | |||||||
\(564\) | −90.0768 | −3.79292 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −60.7506 | −2.55354 | ||||||||
\(567\) | −8.05448 | −0.338256 | ||||||||
\(568\) | −9.02187 | −0.378549 | ||||||||
\(569\) | 19.7215 | 0.826768 | 0.413384 | − | 0.910557i | \(-0.364347\pi\) | ||||
0.413384 | + | 0.910557i | \(0.364347\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.6321 | 0.947126 | 0.473563 | − | 0.880760i | \(-0.342968\pi\) | ||||
0.473563 | + | 0.880760i | \(0.342968\pi\) | |||||||
\(572\) | 27.0133 | 1.12948 | ||||||||
\(573\) | 32.4241 | 1.35454 | ||||||||
\(574\) | 16.0379 | 0.669408 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −38.7396 | −1.61415 | ||||||||
\(577\) | −1.42011 | −0.0591199 | −0.0295599 | − | 0.999563i | \(-0.509411\pi\) | ||||
−0.0295599 | + | 0.999563i | \(0.509411\pi\) | |||||||
\(578\) | −30.6806 | −1.27615 | ||||||||
\(579\) | −0.759379 | −0.0315587 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.7887 | 0.447590 | ||||||||
\(582\) | −78.3632 | −3.24826 | ||||||||
\(583\) | −13.1433 | −0.544338 | ||||||||
\(584\) | 6.29261 | 0.260390 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −35.3212 | −1.45911 | ||||||||
\(587\) | −12.0482 | −0.497281 | −0.248640 | − | 0.968596i | \(-0.579984\pi\) | ||||
−0.248640 | + | 0.968596i | \(0.579984\pi\) | |||||||
\(588\) | 8.94150 | 0.368741 | ||||||||
\(589\) | −2.77257 | −0.114242 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 25.9973 | 1.06938 | ||||||||
\(592\) | 1.27966 | 0.0525935 | ||||||||
\(593\) | −13.4535 | −0.552471 | −0.276235 | − | 0.961090i | \(-0.589087\pi\) | ||||
−0.276235 | + | 0.961090i | \(0.589087\pi\) | |||||||
\(594\) | 4.59603 | 0.188578 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −44.3057 | −1.81483 | ||||||||
\(597\) | −30.0461 | −1.22971 | ||||||||
\(598\) | 6.61603 | 0.270550 | ||||||||
\(599\) | 43.1777 | 1.76419 | 0.882096 | − | 0.471069i | \(-0.156132\pi\) | ||||
0.882096 | + | 0.471069i | \(0.156132\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.3297 | −0.829266 | −0.414633 | − | 0.909989i | \(-0.636090\pi\) | ||||
−0.414633 | + | 0.909989i | \(0.636090\pi\) | |||||||
\(602\) | 7.45333 | 0.303775 | ||||||||
\(603\) | 23.8675 | 0.971958 | ||||||||
\(604\) | −42.7548 | −1.73967 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −79.5794 | −3.23269 | ||||||||
\(607\) | −0.793889 | −0.0322230 | −0.0161115 | − | 0.999870i | \(-0.505129\pi\) | ||||
−0.0161115 | + | 0.999870i | \(0.505129\pi\) | |||||||
\(608\) | 4.07874 | 0.165415 | ||||||||
\(609\) | −21.1371 | −0.856516 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −28.2510 | −1.14291 | ||||||||
\(612\) | −23.4330 | −0.947221 | ||||||||
\(613\) | 1.43440 | 0.0579349 | 0.0289674 | − | 0.999580i | \(-0.490778\pi\) | ||||
0.0289674 | + | 0.999580i | \(0.490778\pi\) | |||||||
\(614\) | −68.7009 | −2.77254 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9.97947 | 0.402084 | ||||||||
\(617\) | 46.1995 | 1.85992 | 0.929960 | − | 0.367660i | \(-0.119841\pi\) | ||||
0.929960 | + | 0.367660i | \(0.119841\pi\) | |||||||
\(618\) | −40.0521 | −1.61113 | ||||||||
\(619\) | 2.94224 | 0.118259 | 0.0591294 | − | 0.998250i | \(-0.481168\pi\) | ||||
0.0591294 | + | 0.998250i | \(0.481168\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.721167 | 0.0289395 | ||||||||
\(622\) | 65.8531 | 2.64047 | ||||||||
\(623\) | −8.27944 | −0.331709 | ||||||||
\(624\) | 11.1370 | 0.445835 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −81.8558 | −3.27162 | ||||||||
\(627\) | −7.56503 | −0.302118 | ||||||||
\(628\) | 53.5653 | 2.13749 | ||||||||
\(629\) | −1.61502 | −0.0643953 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.4317 | 1.13185 | 0.565924 | − | 0.824458i | \(-0.308520\pi\) | ||||
0.565924 | + | 0.824458i | \(0.308520\pi\) | |||||||
\(632\) | 57.1689 | 2.27406 | ||||||||
\(633\) | 70.4781 | 2.80125 | ||||||||
\(634\) | −54.1968 | −2.15243 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −43.5044 | −1.72506 | ||||||||
\(637\) | 2.80434 | 0.111112 | ||||||||
\(638\) | −53.7216 | −2.12686 | ||||||||
\(639\) | −8.02875 | −0.317613 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 44.8580 | 1.77178 | 0.885892 | − | 0.463892i | \(-0.153547\pi\) | ||||
0.885892 | + | 0.463892i | \(0.153547\pi\) | |||||||
\(642\) | −59.2727 | −2.33931 | ||||||||
\(643\) | −0.903492 | −0.0356302 | −0.0178151 | − | 0.999841i | \(-0.505671\pi\) | ||||
−0.0178151 | + | 0.999841i | \(0.505671\pi\) | |||||||
\(644\) | 3.56589 | 0.140516 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.26666 | 0.207214 | ||||||||
\(647\) | 17.0363 | 0.669765 | 0.334882 | − | 0.942260i | \(-0.391303\pi\) | ||||
0.334882 | + | 0.942260i | \(0.391303\pi\) | |||||||
\(648\) | −29.7553 | −1.16890 | ||||||||
\(649\) | −32.8937 | −1.29119 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.22495 | 0.243975 | ||||||||
\(652\) | 20.5815 | 0.806034 | ||||||||
\(653\) | −23.1721 | −0.906793 | −0.453397 | − | 0.891309i | \(-0.649788\pi\) | ||||
−0.453397 | + | 0.891309i | \(0.649788\pi\) | |||||||
\(654\) | 91.7465 | 3.58757 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 10.7665 | 0.420360 | ||||||||
\(657\) | 5.59993 | 0.218474 | ||||||||
\(658\) | −23.7668 | −0.926525 | ||||||||
\(659\) | −25.0481 | −0.975737 | −0.487868 | − | 0.872917i | \(-0.662225\pi\) | ||||
−0.487868 | + | 0.872917i | \(0.662225\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.53827 | −0.332100 | −0.166050 | − | 0.986117i | \(-0.553101\pi\) | ||||
−0.166050 | + | 0.986117i | \(0.553101\pi\) | |||||||
\(662\) | −34.0311 | −1.32266 | ||||||||
\(663\) | −14.0557 | −0.545879 | ||||||||
\(664\) | 39.8563 | 1.54672 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.26680 | 0.242833 | ||||||||
\(667\) | −8.42950 | −0.326392 | ||||||||
\(668\) | −0.0189949 | −0.000734934 0 | ||||||||
\(669\) | −32.0097 | −1.23757 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 25.4747 | 0.983440 | ||||||||
\(672\) | −9.15757 | −0.353261 | ||||||||
\(673\) | 23.9052 | 0.921477 | 0.460738 | − | 0.887536i | \(-0.347585\pi\) | ||||
0.460738 | + | 0.887536i | \(0.347585\pi\) | |||||||
\(674\) | −8.81313 | −0.339469 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −18.3133 | −0.704357 | ||||||||
\(677\) | 29.3023 | 1.12618 | 0.563090 | − | 0.826395i | \(-0.309612\pi\) | ||||
0.563090 | + | 0.826395i | \(0.309612\pi\) | |||||||
\(678\) | −1.05603 | −0.0405564 | ||||||||
\(679\) | −13.2465 | −0.508355 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.55997 | −0.174739 | ||||||||
\(682\) | 15.8212 | 0.605827 | ||||||||
\(683\) | 28.8697 | 1.10467 | 0.552334 | − | 0.833623i | \(-0.313737\pi\) | ||||
0.552334 | + | 0.833623i | \(0.313737\pi\) | |||||||
\(684\) | −13.0929 | −0.500619 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.35921 | 0.0900752 | ||||||||
\(687\) | 13.5988 | 0.518825 | ||||||||
\(688\) | 5.00354 | 0.190758 | ||||||||
\(689\) | −13.6444 | −0.519809 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.1773 | 0.501290 | 0.250645 | − | 0.968079i | \(-0.419357\pi\) | ||||
0.250645 | + | 0.968079i | \(0.419357\pi\) | |||||||
\(692\) | 73.8394 | 2.80695 | ||||||||
\(693\) | 8.88095 | 0.337359 | ||||||||
\(694\) | 37.6208 | 1.42807 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −78.0858 | −2.95983 | ||||||||
\(697\) | −13.5881 | −0.514687 | ||||||||
\(698\) | 7.72014 | 0.292212 | ||||||||
\(699\) | 24.4248 | 0.923832 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.1209 | 1.21319 | 0.606595 | − | 0.795011i | \(-0.292535\pi\) | ||||
0.606595 | + | 0.795011i | \(0.292535\pi\) | |||||||
\(702\) | 4.77127 | 0.180080 | ||||||||
\(703\) | −0.902376 | −0.0340337 | ||||||||
\(704\) | −31.8314 | −1.19969 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 24.3624 | 0.916890 | ||||||||
\(707\) | −13.4521 | −0.505919 | ||||||||
\(708\) | −108.879 | −4.09191 | ||||||||
\(709\) | 39.6975 | 1.49087 | 0.745435 | − | 0.666578i | \(-0.232242\pi\) | ||||
0.745435 | + | 0.666578i | \(0.232242\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 50.8758 | 1.90799 | ||||||||
\(712\) | −30.5864 | −1.14627 | ||||||||
\(713\) | 2.48252 | 0.0929713 | ||||||||
\(714\) | −11.8247 | −0.442528 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −43.3471 | −1.61996 | ||||||||
\(717\) | −53.1253 | −1.98400 | ||||||||
\(718\) | 36.7557 | 1.37171 | ||||||||
\(719\) | 28.5811 | 1.06590 | 0.532948 | − | 0.846148i | \(-0.321084\pi\) | ||||
0.532948 | + | 0.846148i | \(0.321084\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.77042 | −0.252143 | ||||||||
\(722\) | −41.8824 | −1.55870 | ||||||||
\(723\) | 34.6454 | 1.28847 | ||||||||
\(724\) | −45.8481 | −1.70393 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −21.9045 | −0.812952 | ||||||||
\(727\) | −9.67378 | −0.358781 | −0.179390 | − | 0.983778i | \(-0.557412\pi\) | ||||
−0.179390 | + | 0.983778i | \(0.557412\pi\) | |||||||
\(728\) | 10.3600 | 0.383966 | ||||||||
\(729\) | −31.9049 | −1.18166 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.31485 | −0.233563 | ||||||||
\(732\) | 84.3217 | 3.11662 | ||||||||
\(733\) | −23.1744 | −0.855966 | −0.427983 | − | 0.903787i | \(-0.640776\pi\) | ||||
−0.427983 | + | 0.903787i | \(0.640776\pi\) | |||||||
\(734\) | −50.8433 | −1.87666 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.65206 | −0.134617 | ||||||||
\(737\) | 19.6113 | 0.722392 | ||||||||
\(738\) | 52.7262 | 1.94088 | ||||||||
\(739\) | −29.2997 | −1.07781 | −0.538904 | − | 0.842367i | \(-0.681161\pi\) | ||||
−0.538904 | + | 0.842367i | \(0.681161\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.85346 | −0.288504 | ||||||||
\(742\) | −11.4786 | −0.421394 | ||||||||
\(743\) | 36.8301 | 1.35116 | 0.675582 | − | 0.737285i | \(-0.263892\pi\) | ||||
0.675582 | + | 0.737285i | \(0.263892\pi\) | |||||||
\(744\) | 22.9966 | 0.843097 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −48.4855 | −1.77518 | ||||||||
\(747\) | 35.4689 | 1.29774 | ||||||||
\(748\) | −19.2543 | −0.704007 | ||||||||
\(749\) | −10.0195 | −0.366103 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 37.5423 | 1.36994 | 0.684969 | − | 0.728572i | \(-0.259816\pi\) | ||||
0.684969 | + | 0.728572i | \(0.259816\pi\) | |||||||
\(752\) | −15.9550 | −0.581819 | ||||||||
\(753\) | −29.9478 | −1.09136 | ||||||||
\(754\) | −55.7698 | −2.03102 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.57160 | 0.0935282 | ||||||||
\(757\) | 17.3405 | 0.630250 | 0.315125 | − | 0.949050i | \(-0.397954\pi\) | ||||
0.315125 | + | 0.949050i | \(0.397954\pi\) | |||||||
\(758\) | 31.3948 | 1.14031 | ||||||||
\(759\) | 6.77365 | 0.245868 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −44.6219 | −1.61754 | −0.808771 | − | 0.588123i | \(-0.799867\pi\) | ||||
−0.808771 | + | 0.588123i | \(0.799867\pi\) | |||||||
\(762\) | 25.8128 | 0.935099 | ||||||||
\(763\) | 15.5089 | 0.561458 | ||||||||
\(764\) | 46.1097 | 1.66819 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 25.3143 | 0.914644 | ||||||||
\(767\) | −34.1478 | −1.23301 | ||||||||
\(768\) | −62.1531 | −2.24276 | ||||||||
\(769\) | 38.4931 | 1.38810 | 0.694048 | − | 0.719929i | \(-0.255826\pi\) | ||||
0.694048 | + | 0.719929i | \(0.255826\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −41.5194 | −1.49528 | ||||||||
\(772\) | −1.07990 | −0.0388665 | ||||||||
\(773\) | −54.2437 | −1.95101 | −0.975505 | − | 0.219976i | \(-0.929402\pi\) | ||||
−0.975505 | + | 0.219976i | \(0.929402\pi\) | |||||||
\(774\) | 24.5036 | 0.880763 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −48.9362 | −1.75671 | ||||||||
\(777\) | 2.02601 | 0.0726827 | ||||||||
\(778\) | −69.2530 | −2.48284 | ||||||||
\(779\) | −7.59220 | −0.272019 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.59703 | −0.236060 | ||||||||
\(782\) | −4.71571 | −0.168634 | ||||||||
\(783\) | −6.07908 | −0.217249 | ||||||||
\(784\) | 1.58378 | 0.0565635 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −25.7568 | −0.918714 | ||||||||
\(787\) | 4.83401 | 0.172314 | 0.0861570 | − | 0.996282i | \(-0.472541\pi\) | ||||
0.0861570 | + | 0.996282i | \(0.472541\pi\) | |||||||
\(788\) | 36.9703 | 1.31701 | ||||||||
\(789\) | 43.9892 | 1.56606 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.178511 | −0.00634712 | ||||||||
\(792\) | 32.8085 | 1.16580 | ||||||||
\(793\) | 26.4460 | 0.939124 | ||||||||
\(794\) | −17.2834 | −0.613363 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −42.7281 | −1.51446 | ||||||||
\(797\) | 44.4895 | 1.57590 | 0.787950 | − | 0.615739i | \(-0.211143\pi\) | ||||
0.787950 | + | 0.615739i | \(0.211143\pi\) | |||||||
\(798\) | −6.60690 | −0.233882 | ||||||||
\(799\) | 20.1365 | 0.712377 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −27.2195 | −0.961754 | ||||||||
\(802\) | 27.6614 | 0.976757 | ||||||||
\(803\) | 4.60133 | 0.162377 | ||||||||
\(804\) | 64.9138 | 2.28933 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 16.4245 | 0.578527 | ||||||||
\(807\) | 77.2670 | 2.71993 | ||||||||
\(808\) | −49.6957 | −1.74829 | ||||||||
\(809\) | −19.7547 | −0.694540 | −0.347270 | − | 0.937765i | \(-0.612891\pi\) | ||||
−0.347270 | + | 0.937765i | \(0.612891\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.3167 | 0.397382 | 0.198691 | − | 0.980062i | \(-0.436331\pi\) | ||||
0.198691 | + | 0.980062i | \(0.436331\pi\) | |||||||
\(812\) | −30.0586 | −1.05485 | ||||||||
\(813\) | 51.3502 | 1.80093 | ||||||||
\(814\) | 5.14928 | 0.180482 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −7.93810 | −0.277889 | ||||||||
\(817\) | −3.52835 | −0.123441 | ||||||||
\(818\) | 22.0424 | 0.770694 | ||||||||
\(819\) | 9.21955 | 0.322157 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17.5446 | −0.612310 | −0.306155 | − | 0.951982i | \(-0.599043\pi\) | ||||
−0.306155 | + | 0.951982i | \(0.599043\pi\) | |||||||
\(822\) | 63.4798 | 2.21411 | ||||||||
\(823\) | −47.0147 | −1.63883 | −0.819415 | − | 0.573201i | \(-0.805701\pi\) | ||||
−0.819415 | + | 0.573201i | \(0.805701\pi\) | |||||||
\(824\) | −25.0117 | −0.871323 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −28.7277 | −0.999563 | ||||||||
\(827\) | 1.29703 | 0.0451022 | 0.0225511 | − | 0.999746i | \(-0.492821\pi\) | ||||
0.0225511 | + | 0.999746i | \(0.492821\pi\) | |||||||
\(828\) | 11.7232 | 0.407410 | ||||||||
\(829\) | 57.4555 | 1.99551 | 0.997757 | − | 0.0669420i | \(-0.0213243\pi\) | ||||
0.997757 | + | 0.0669420i | \(0.0213243\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 80.1345 | 2.77984 | ||||||||
\(832\) | −33.0450 | −1.14563 | ||||||||
\(833\) | −1.99885 | −0.0692560 | ||||||||
\(834\) | 37.3176 | 1.29220 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −10.7581 | −0.372077 | ||||||||
\(837\) | 1.79032 | 0.0618824 | ||||||||
\(838\) | 52.0145 | 1.79681 | ||||||||
\(839\) | −53.3764 | −1.84276 | −0.921379 | − | 0.388664i | \(-0.872937\pi\) | ||||
−0.921379 | + | 0.388664i | \(0.872937\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 42.0565 | 1.45022 | ||||||||
\(842\) | 12.0630 | 0.415717 | ||||||||
\(843\) | 32.2335 | 1.11018 | ||||||||
\(844\) | 100.226 | 3.44991 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −78.1357 | −2.68636 | ||||||||
\(847\) | −3.70274 | −0.127228 | ||||||||
\(848\) | −7.70579 | −0.264618 | ||||||||
\(849\) | −64.5693 | −2.21601 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.807977 | 0.0276971 | ||||||||
\(852\) | −21.8363 | −0.748099 | ||||||||
\(853\) | −20.9398 | −0.716966 | −0.358483 | − | 0.933536i | \(-0.616706\pi\) | ||||
−0.358483 | + | 0.933536i | \(0.616706\pi\) | |||||||
\(854\) | 22.2483 | 0.761320 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −37.0145 | −1.26513 | ||||||||
\(857\) | 12.5261 | 0.427883 | 0.213941 | − | 0.976846i | \(-0.431370\pi\) | ||||
0.213941 | + | 0.976846i | \(0.431370\pi\) | |||||||
\(858\) | 44.8147 | 1.52995 | ||||||||
\(859\) | 39.2473 | 1.33910 | 0.669550 | − | 0.742767i | \(-0.266487\pi\) | ||||
0.669550 | + | 0.742767i | \(0.266487\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 17.0460 | 0.580926 | ||||||||
\(862\) | 19.0672 | 0.649431 | ||||||||
\(863\) | −50.8955 | −1.73250 | −0.866251 | − | 0.499608i | \(-0.833477\pi\) | ||||
−0.866251 | + | 0.499608i | \(0.833477\pi\) | |||||||
\(864\) | −2.63374 | −0.0896018 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 91.1980 | 3.09903 | ||||||||
\(867\) | −32.6092 | −1.10747 | ||||||||
\(868\) | 8.85240 | 0.300470 | ||||||||
\(869\) | 41.8035 | 1.41809 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.3590 | 0.689840 | ||||||||
\(872\) | 57.2938 | 1.94021 | ||||||||
\(873\) | −43.5493 | −1.47392 | ||||||||
\(874\) | −2.63485 | −0.0891250 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 15.2305 | 0.514590 | ||||||||
\(877\) | 48.7836 | 1.64730 | 0.823652 | − | 0.567095i | \(-0.191933\pi\) | ||||
0.823652 | + | 0.567095i | \(0.191933\pi\) | |||||||
\(878\) | 5.41953 | 0.182900 | ||||||||
\(879\) | −37.5414 | −1.26624 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.7616 | 0.632093 | 0.316047 | − | 0.948744i | \(-0.397644\pi\) | ||||
0.316047 | + | 0.948744i | \(0.397644\pi\) | |||||||
\(882\) | 7.75616 | 0.261163 | ||||||||
\(883\) | 24.0146 | 0.808157 | 0.404078 | − | 0.914724i | \(-0.367592\pi\) | ||||
0.404078 | + | 0.914724i | \(0.367592\pi\) | |||||||
\(884\) | −19.9884 | −0.672283 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −68.8518 | −2.31312 | ||||||||
\(887\) | −1.47725 | −0.0496012 | −0.0248006 | − | 0.999692i | \(-0.507895\pi\) | ||||
−0.0248006 | + | 0.999692i | \(0.507895\pi\) | |||||||
\(888\) | 7.48461 | 0.251167 | ||||||||
\(889\) | 4.36340 | 0.146344 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −21.7579 | −0.728917 | ||||||||
\(892\) | −45.5205 | −1.52414 | ||||||||
\(893\) | 11.2510 | 0.376500 | ||||||||
\(894\) | −73.5025 | −2.45829 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −20.4958 | −0.684715 | ||||||||
\(897\) | 7.03190 | 0.234788 | ||||||||
\(898\) | 49.1597 | 1.64048 | ||||||||
\(899\) | −20.9264 | −0.697936 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.72531 | 0.323997 | ||||||||
\(902\) | 43.3238 | 1.44253 | ||||||||
\(903\) | 7.92183 | 0.263622 | ||||||||
\(904\) | −0.659466 | −0.0219335 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −70.9295 | −2.35647 | ||||||||
\(907\) | 17.3795 | 0.577077 | 0.288539 | − | 0.957468i | \(-0.406831\pi\) | ||||
0.288539 | + | 0.957468i | \(0.406831\pi\) | |||||||
\(908\) | −6.48466 | −0.215201 | ||||||||
\(909\) | −44.2252 | −1.46686 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −52.6898 | −1.74569 | −0.872846 | − | 0.487996i | \(-0.837728\pi\) | ||||
−0.872846 | + | 0.487996i | \(0.837728\pi\) | |||||||
\(912\) | −4.43532 | −0.146868 | ||||||||
\(913\) | 29.1440 | 0.964525 | ||||||||
\(914\) | 31.8036 | 1.05197 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 19.3386 | 0.638964 | ||||||||
\(917\) | −4.35393 | −0.143780 | ||||||||
\(918\) | −3.40082 | −0.112244 | ||||||||
\(919\) | −3.45752 | −0.114053 | −0.0570266 | − | 0.998373i | \(-0.518162\pi\) | ||||
−0.0570266 | + | 0.998373i | \(0.518162\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −73.0193 | −2.40607 | ||||||||
\(922\) | −80.7386 | −2.65898 | ||||||||
\(923\) | −6.84856 | −0.225423 | ||||||||
\(924\) | 24.1541 | 0.794610 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 66.2657 | 2.17763 | ||||||||
\(927\) | −22.2584 | −0.731063 | ||||||||
\(928\) | 30.7850 | 1.01057 | ||||||||
\(929\) | −12.8336 | −0.421057 | −0.210529 | − | 0.977588i | \(-0.567519\pi\) | ||||
−0.210529 | + | 0.977588i | \(0.567519\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.11683 | −0.0366027 | ||||||||
\(932\) | 34.7341 | 1.13775 | ||||||||
\(933\) | 69.9925 | 2.29145 | ||||||||
\(934\) | −65.2426 | −2.13480 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 34.0594 | 1.11327 | ||||||||
\(937\) | −32.5335 | −1.06282 | −0.531411 | − | 0.847114i | \(-0.678338\pi\) | ||||
−0.531411 | + | 0.847114i | \(0.678338\pi\) | |||||||
\(938\) | 17.1275 | 0.559233 | ||||||||
\(939\) | −87.0011 | −2.83917 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 44.7486 | 1.45876 | 0.729381 | − | 0.684108i | \(-0.239808\pi\) | ||||
0.729381 | + | 0.684108i | \(0.239808\pi\) | |||||||
\(942\) | 88.8640 | 2.89534 | ||||||||
\(943\) | 6.79798 | 0.221373 | ||||||||
\(944\) | −19.2853 | −0.627684 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 20.1340 | 0.654613 | ||||||||
\(947\) | −13.4275 | −0.436336 | −0.218168 | − | 0.975911i | \(-0.570008\pi\) | ||||
−0.218168 | + | 0.975911i | \(0.570008\pi\) | |||||||
\(948\) | 138.370 | 4.49405 | ||||||||
\(949\) | 4.77676 | 0.155060 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −57.6035 | −1.86792 | ||||||||
\(952\) | −7.38427 | −0.239326 | ||||||||
\(953\) | −7.99902 | −0.259114 | −0.129557 | − | 0.991572i | \(-0.541355\pi\) | ||||
−0.129557 | + | 0.991572i | \(0.541355\pi\) | |||||||
\(954\) | −37.7372 | −1.22179 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −75.5486 | −2.44342 | ||||||||
\(957\) | −57.0984 | −1.84573 | ||||||||
\(958\) | −16.6910 | −0.539263 | ||||||||
\(959\) | 10.7306 | 0.346510 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.8371 | −0.801196 | ||||||||
\(962\) | 5.34560 | 0.172349 | ||||||||
\(963\) | −32.9400 | −1.06148 | ||||||||
\(964\) | 49.2686 | 1.58683 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 5.91575 | 0.190336 | ||||||||
\(967\) | 43.6769 | 1.40455 | 0.702277 | − | 0.711904i | \(-0.252167\pi\) | ||||
0.702277 | + | 0.711904i | \(0.252167\pi\) | |||||||
\(968\) | −13.6789 | −0.439656 | ||||||||
\(969\) | 5.59772 | 0.179825 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.16184 | 0.229834 | 0.114917 | − | 0.993375i | \(-0.463340\pi\) | ||||
0.114917 | + | 0.993375i | \(0.463340\pi\) | |||||||
\(972\) | −79.7339 | −2.55746 | ||||||||
\(973\) | 6.30819 | 0.202231 | ||||||||
\(974\) | −98.4009 | −3.15297 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 14.9356 | 0.478077 | ||||||||
\(977\) | 15.6590 | 0.500977 | 0.250488 | − | 0.968120i | \(-0.419409\pi\) | ||||
0.250488 | + | 0.968120i | \(0.419409\pi\) | |||||||
\(978\) | 34.1444 | 1.09182 | ||||||||
\(979\) | −22.3656 | −0.714808 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 50.9870 | 1.62789 | ||||||||
\(982\) | 6.14996 | 0.196253 | ||||||||
\(983\) | −41.2674 | −1.31623 | −0.658113 | − | 0.752919i | \(-0.728645\pi\) | ||||
−0.658113 | + | 0.752919i | \(0.728645\pi\) | |||||||
\(984\) | 62.9723 | 2.00748 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 39.7511 | 1.26593 | ||||||||
\(987\) | −25.2607 | −0.804057 | ||||||||
\(988\) | −11.1683 | −0.355310 | ||||||||
\(989\) | 3.15924 | 0.100458 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 55.1091 | 1.75060 | 0.875300 | − | 0.483581i | \(-0.160664\pi\) | ||||
0.875300 | + | 0.483581i | \(0.160664\pi\) | |||||||
\(992\) | −9.06632 | −0.287856 | ||||||||
\(993\) | −36.1703 | −1.14783 | ||||||||
\(994\) | −5.76151 | −0.182744 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 96.4671 | 3.05668 | ||||||||
\(997\) | 4.56403 | 0.144544 | 0.0722721 | − | 0.997385i | \(-0.476975\pi\) | ||||
0.0722721 | + | 0.997385i | \(0.476975\pi\) | |||||||
\(998\) | 84.3161 | 2.66898 | ||||||||
\(999\) | 0.582687 | 0.0184354 |
(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 | 4025.2.a.be.1.18 | 21 | ||
5.2 | odd | 4 | 805.2.c.c.484.36 | yes | 42 | ||
5.3 | odd | 4 | 805.2.c.c.484.7 | ✓ | 42 | ||
5.4 | even | 2 | 4025.2.a.bd.1.4 | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
805.2.c.c.484.7 | ✓ | 42 | 5.3 | odd | 4 | ||
805.2.c.c.484.36 | yes | 42 | 5.2 | odd | 4 | ||
4025.2.a.bd.1.4 | 21 | 5.4 | even | 2 | |||
4025.2.a.be.1.18 | 21 | 1.1 | even | 1 | trivial |