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: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - x^{13} - 22 x^{12} + 18 x^{11} + 187 x^{10} - 118 x^{9} - 772 x^{8} + 346 x^{7} + 1581 x^{6} + \cdots - 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Root | \(2.79074\) of defining polynomial | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.79074 | 1.97335 | 0.986676 | − | 0.162699i | \(-0.0520198\pi\) | ||||
0.986676 | + | 0.162699i | \(0.0520198\pi\) | |||||||
\(3\) | 2.29281 | 1.32376 | 0.661879 | − | 0.749611i | \(-0.269759\pi\) | ||||
0.661879 | + | 0.749611i | \(0.269759\pi\) | |||||||
\(4\) | 5.78823 | 2.89412 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 6.39865 | 2.61224 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 10.5720 | 3.73776 | ||||||||
\(9\) | 2.25700 | 0.752333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.340565 | 0.102684 | 0.0513421 | − | 0.998681i | \(-0.483650\pi\) | ||||
0.0513421 | + | 0.998681i | \(0.483650\pi\) | |||||||
\(12\) | 13.2713 | 3.83111 | ||||||||
\(13\) | 1.30291 | 0.361362 | 0.180681 | − | 0.983542i | \(-0.442170\pi\) | ||||
0.180681 | + | 0.983542i | \(0.442170\pi\) | |||||||
\(14\) | 2.79074 | 0.745857 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 17.9272 | 4.48179 | ||||||||
\(17\) | −2.59659 | −0.629767 | −0.314883 | − | 0.949130i | \(-0.601965\pi\) | ||||
−0.314883 | + | 0.949130i | \(0.601965\pi\) | |||||||
\(18\) | 6.29870 | 1.48462 | ||||||||
\(19\) | −8.28544 | −1.90081 | −0.950405 | − | 0.311015i | \(-0.899331\pi\) | ||||
−0.950405 | + | 0.311015i | \(0.899331\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.29281 | 0.500333 | ||||||||
\(22\) | 0.950428 | 0.202632 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 24.2396 | 4.94788 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.63608 | 0.713095 | ||||||||
\(27\) | −1.70356 | −0.327851 | ||||||||
\(28\) | 5.78823 | 1.09387 | ||||||||
\(29\) | 3.78448 | 0.702760 | 0.351380 | − | 0.936233i | \(-0.385713\pi\) | ||||
0.351380 | + | 0.936233i | \(0.385713\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.08631 | −1.63195 | −0.815975 | − | 0.578088i | \(-0.803799\pi\) | ||||
−0.815975 | + | 0.578088i | \(0.803799\pi\) | |||||||
\(32\) | 28.8861 | 5.10640 | ||||||||
\(33\) | 0.780852 | 0.135929 | ||||||||
\(34\) | −7.24642 | −1.24275 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 13.0640 | 2.17734 | ||||||||
\(37\) | −6.40257 | −1.05258 | −0.526288 | − | 0.850306i | \(-0.676417\pi\) | ||||
−0.526288 | + | 0.850306i | \(0.676417\pi\) | |||||||
\(38\) | −23.1225 | −3.75097 | ||||||||
\(39\) | 2.98733 | 0.478356 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.841753 | 0.131460 | 0.0657299 | − | 0.997837i | \(-0.479062\pi\) | ||||
0.0657299 | + | 0.997837i | \(0.479062\pi\) | |||||||
\(42\) | 6.39865 | 0.987333 | ||||||||
\(43\) | −9.17532 | −1.39922 | −0.699612 | − | 0.714523i | \(-0.746644\pi\) | ||||
−0.699612 | + | 0.714523i | \(0.746644\pi\) | |||||||
\(44\) | 1.97127 | 0.297180 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.79074 | −0.411472 | ||||||||
\(47\) | −4.66829 | −0.680940 | −0.340470 | − | 0.940255i | \(-0.610586\pi\) | ||||
−0.340470 | + | 0.940255i | \(0.610586\pi\) | |||||||
\(48\) | 41.1037 | 5.93281 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.95351 | −0.833658 | ||||||||
\(52\) | 7.54155 | 1.04582 | ||||||||
\(53\) | −3.49781 | −0.480461 | −0.240230 | − | 0.970716i | \(-0.577223\pi\) | ||||
−0.240230 | + | 0.970716i | \(0.577223\pi\) | |||||||
\(54\) | −4.75420 | −0.646964 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 10.5720 | 1.41274 | ||||||||
\(57\) | −18.9970 | −2.51621 | ||||||||
\(58\) | 10.5615 | 1.38679 | ||||||||
\(59\) | −2.98127 | −0.388128 | −0.194064 | − | 0.980989i | \(-0.562167\pi\) | ||||
−0.194064 | + | 0.980989i | \(0.562167\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.00861 | −0.385213 | −0.192607 | − | 0.981276i | \(-0.561694\pi\) | ||||
−0.192607 | + | 0.981276i | \(0.561694\pi\) | |||||||
\(62\) | −25.3575 | −3.22041 | ||||||||
\(63\) | 2.25700 | 0.284355 | ||||||||
\(64\) | 44.7594 | 5.59492 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.17916 | 0.268236 | ||||||||
\(67\) | 11.6183 | 1.41940 | 0.709701 | − | 0.704503i | \(-0.248830\pi\) | ||||
0.709701 | + | 0.704503i | \(0.248830\pi\) | |||||||
\(68\) | −15.0297 | −1.82262 | ||||||||
\(69\) | −2.29281 | −0.276022 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.87205 | 0.696884 | 0.348442 | − | 0.937330i | \(-0.386711\pi\) | ||||
0.348442 | + | 0.937330i | \(0.386711\pi\) | |||||||
\(72\) | 23.8610 | 2.81204 | ||||||||
\(73\) | 7.81259 | 0.914395 | 0.457197 | − | 0.889365i | \(-0.348853\pi\) | ||||
0.457197 | + | 0.889365i | \(0.348853\pi\) | |||||||
\(74\) | −17.8679 | −2.07710 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −47.9581 | −5.50117 | ||||||||
\(77\) | 0.340565 | 0.0388110 | ||||||||
\(78\) | 8.33687 | 0.943964 | ||||||||
\(79\) | 4.35387 | 0.489848 | 0.244924 | − | 0.969542i | \(-0.421237\pi\) | ||||
0.244924 | + | 0.969542i | \(0.421237\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.6770 | −1.18633 | ||||||||
\(82\) | 2.34912 | 0.259416 | ||||||||
\(83\) | 9.31355 | 1.02229 | 0.511147 | − | 0.859493i | \(-0.329221\pi\) | ||||
0.511147 | + | 0.859493i | \(0.329221\pi\) | |||||||
\(84\) | 13.2713 | 1.44802 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −25.6059 | −2.76116 | ||||||||
\(87\) | 8.67710 | 0.930283 | ||||||||
\(88\) | 3.60044 | 0.383809 | ||||||||
\(89\) | 2.83424 | 0.300429 | 0.150214 | − | 0.988653i | \(-0.452004\pi\) | ||||
0.150214 | + | 0.988653i | \(0.452004\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.30291 | 0.136582 | ||||||||
\(92\) | −5.78823 | −0.603465 | ||||||||
\(93\) | −20.8332 | −2.16031 | ||||||||
\(94\) | −13.0280 | −1.34373 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 66.2306 | 6.75963 | ||||||||
\(97\) | −0.660946 | −0.0671089 | −0.0335545 | − | 0.999437i | \(-0.510683\pi\) | ||||
−0.0335545 | + | 0.999437i | \(0.510683\pi\) | |||||||
\(98\) | 2.79074 | 0.281907 | ||||||||
\(99\) | 0.768655 | 0.0772527 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.7434 | 1.26802 | 0.634010 | − | 0.773325i | \(-0.281408\pi\) | ||||
0.634010 | + | 0.773325i | \(0.281408\pi\) | |||||||
\(102\) | −16.6147 | −1.64510 | ||||||||
\(103\) | 12.2329 | 1.20534 | 0.602670 | − | 0.797991i | \(-0.294104\pi\) | ||||
0.602670 | + | 0.797991i | \(0.294104\pi\) | |||||||
\(104\) | 13.7743 | 1.35068 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.76148 | −0.948118 | ||||||||
\(107\) | 15.1269 | 1.46237 | 0.731186 | − | 0.682179i | \(-0.238967\pi\) | ||||
0.731186 | + | 0.682179i | \(0.238967\pi\) | |||||||
\(108\) | −9.86061 | −0.948838 | ||||||||
\(109\) | 9.13756 | 0.875219 | 0.437610 | − | 0.899165i | \(-0.355825\pi\) | ||||
0.437610 | + | 0.899165i | \(0.355825\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −14.6799 | −1.39336 | ||||||||
\(112\) | 17.9272 | 1.69396 | ||||||||
\(113\) | 5.87183 | 0.552375 | 0.276188 | − | 0.961104i | \(-0.410929\pi\) | ||||
0.276188 | + | 0.961104i | \(0.410929\pi\) | |||||||
\(114\) | −53.0156 | −4.96537 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 21.9054 | 2.03387 | ||||||||
\(117\) | 2.94067 | 0.271865 | ||||||||
\(118\) | −8.31994 | −0.765913 | ||||||||
\(119\) | −2.59659 | −0.238029 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8840 | −0.989456 | ||||||||
\(122\) | −8.39625 | −0.760161 | ||||||||
\(123\) | 1.92998 | 0.174021 | ||||||||
\(124\) | −52.5937 | −4.72305 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 6.29870 | 0.561133 | ||||||||
\(127\) | −16.8289 | −1.49332 | −0.746662 | − | 0.665204i | \(-0.768345\pi\) | ||||
−0.746662 | + | 0.665204i | \(0.768345\pi\) | |||||||
\(128\) | 67.1396 | 5.93435 | ||||||||
\(129\) | −21.0373 | −1.85223 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.5076 | 1.79175 | 0.895877 | − | 0.444302i | \(-0.146548\pi\) | ||||
0.895877 | + | 0.444302i | \(0.146548\pi\) | |||||||
\(132\) | 4.51976 | 0.393394 | ||||||||
\(133\) | −8.28544 | −0.718439 | ||||||||
\(134\) | 32.4237 | 2.80098 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −27.4511 | −2.35392 | ||||||||
\(137\) | −19.2523 | −1.64484 | −0.822418 | − | 0.568883i | \(-0.807376\pi\) | ||||
−0.822418 | + | 0.568883i | \(0.807376\pi\) | |||||||
\(138\) | −6.39865 | −0.544689 | ||||||||
\(139\) | 5.86865 | 0.497772 | 0.248886 | − | 0.968533i | \(-0.419935\pi\) | ||||
0.248886 | + | 0.968533i | \(0.419935\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.7035 | −0.901399 | ||||||||
\(142\) | 16.3874 | 1.37520 | ||||||||
\(143\) | 0.443725 | 0.0371062 | ||||||||
\(144\) | 40.4616 | 3.37180 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 21.8029 | 1.80442 | ||||||||
\(147\) | 2.29281 | 0.189108 | ||||||||
\(148\) | −37.0596 | −3.04628 | ||||||||
\(149\) | 21.2884 | 1.74401 | 0.872006 | − | 0.489495i | \(-0.162819\pi\) | ||||
0.872006 | + | 0.489495i | \(0.162819\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.74934 | 0.712011 | 0.356006 | − | 0.934484i | \(-0.384138\pi\) | ||||
0.356006 | + | 0.934484i | \(0.384138\pi\) | |||||||
\(152\) | −87.5935 | −7.10477 | ||||||||
\(153\) | −5.86051 | −0.473794 | ||||||||
\(154\) | 0.950428 | 0.0765877 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 17.2914 | 1.38442 | ||||||||
\(157\) | −17.6262 | −1.40672 | −0.703360 | − | 0.710833i | \(-0.748318\pi\) | ||||
−0.703360 | + | 0.710833i | \(0.748318\pi\) | |||||||
\(158\) | 12.1505 | 0.966643 | ||||||||
\(159\) | −8.01983 | −0.636014 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | −29.7966 | −2.34104 | ||||||||
\(163\) | 19.4546 | 1.52380 | 0.761900 | − | 0.647695i | \(-0.224267\pi\) | ||||
0.761900 | + | 0.647695i | \(0.224267\pi\) | |||||||
\(164\) | 4.87226 | 0.380460 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 25.9917 | 2.01735 | ||||||||
\(167\) | −23.2552 | −1.79954 | −0.899769 | − | 0.436367i | \(-0.856265\pi\) | ||||
−0.899769 | + | 0.436367i | \(0.856265\pi\) | |||||||
\(168\) | 24.2396 | 1.87012 | ||||||||
\(169\) | −11.3024 | −0.869417 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −18.7002 | −1.43004 | ||||||||
\(172\) | −53.1089 | −4.04952 | ||||||||
\(173\) | 11.4043 | 0.867055 | 0.433528 | − | 0.901140i | \(-0.357269\pi\) | ||||
0.433528 | + | 0.901140i | \(0.357269\pi\) | |||||||
\(174\) | 24.2155 | 1.83578 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.10537 | 0.460209 | ||||||||
\(177\) | −6.83549 | −0.513787 | ||||||||
\(178\) | 7.90963 | 0.592852 | ||||||||
\(179\) | −2.41652 | −0.180619 | −0.0903096 | − | 0.995914i | \(-0.528786\pi\) | ||||
−0.0903096 | + | 0.995914i | \(0.528786\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.54238 | −0.263303 | −0.131651 | − | 0.991296i | \(-0.542028\pi\) | ||||
−0.131651 | + | 0.991296i | \(0.542028\pi\) | |||||||
\(182\) | 3.63608 | 0.269524 | ||||||||
\(183\) | −6.89819 | −0.509929 | ||||||||
\(184\) | −10.5720 | −0.779376 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −58.1401 | −4.26304 | ||||||||
\(187\) | −0.884309 | −0.0646671 | ||||||||
\(188\) | −27.0211 | −1.97072 | ||||||||
\(189\) | −1.70356 | −0.123916 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.78907 | 0.274168 | 0.137084 | − | 0.990559i | \(-0.456227\pi\) | ||||
0.137084 | + | 0.990559i | \(0.456227\pi\) | |||||||
\(192\) | 102.625 | 7.40632 | ||||||||
\(193\) | 19.3042 | 1.38955 | 0.694774 | − | 0.719229i | \(-0.255505\pi\) | ||||
0.694774 | + | 0.719229i | \(0.255505\pi\) | |||||||
\(194\) | −1.84453 | −0.132429 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.78823 | 0.413445 | ||||||||
\(197\) | −17.3149 | −1.23364 | −0.616818 | − | 0.787106i | \(-0.711579\pi\) | ||||
−0.616818 | + | 0.787106i | \(0.711579\pi\) | |||||||
\(198\) | 2.14512 | 0.152447 | ||||||||
\(199\) | 11.8403 | 0.839338 | 0.419669 | − | 0.907677i | \(-0.362146\pi\) | ||||
0.419669 | + | 0.907677i | \(0.362146\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 26.6386 | 1.87894 | ||||||||
\(202\) | 35.5637 | 2.50225 | ||||||||
\(203\) | 3.78448 | 0.265618 | ||||||||
\(204\) | −34.4603 | −2.41270 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 34.1387 | 2.37856 | ||||||||
\(207\) | −2.25700 | −0.156872 | ||||||||
\(208\) | 23.3575 | 1.61955 | ||||||||
\(209\) | −2.82173 | −0.195183 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.7747 | 0.741760 | 0.370880 | − | 0.928681i | \(-0.379056\pi\) | ||||
0.370880 | + | 0.928681i | \(0.379056\pi\) | |||||||
\(212\) | −20.2461 | −1.39051 | ||||||||
\(213\) | 13.4635 | 0.922506 | ||||||||
\(214\) | 42.2152 | 2.88577 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −18.0100 | −1.22543 | ||||||||
\(217\) | −9.08631 | −0.616819 | ||||||||
\(218\) | 25.5006 | 1.72712 | ||||||||
\(219\) | 17.9128 | 1.21044 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.38313 | −0.227574 | ||||||||
\(222\) | −40.9678 | −2.74958 | ||||||||
\(223\) | 17.0655 | 1.14279 | 0.571395 | − | 0.820675i | \(-0.306402\pi\) | ||||
0.571395 | + | 0.820675i | \(0.306402\pi\) | |||||||
\(224\) | 28.8861 | 1.93004 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 16.3867 | 1.09003 | ||||||||
\(227\) | 15.7713 | 1.04678 | 0.523390 | − | 0.852093i | \(-0.324667\pi\) | ||||
0.523390 | + | 0.852093i | \(0.324667\pi\) | |||||||
\(228\) | −109.959 | −7.28221 | ||||||||
\(229\) | −18.1881 | −1.20191 | −0.600953 | − | 0.799285i | \(-0.705212\pi\) | ||||
−0.600953 | + | 0.799285i | \(0.705212\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.780852 | 0.0513763 | ||||||||
\(232\) | 40.0094 | 2.62675 | ||||||||
\(233\) | −19.4957 | −1.27721 | −0.638604 | − | 0.769535i | \(-0.720488\pi\) | ||||
−0.638604 | + | 0.769535i | \(0.720488\pi\) | |||||||
\(234\) | 8.20664 | 0.536485 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −17.2563 | −1.12329 | ||||||||
\(237\) | 9.98261 | 0.648440 | ||||||||
\(238\) | −7.24642 | −0.469716 | ||||||||
\(239\) | 22.0911 | 1.42896 | 0.714478 | − | 0.699658i | \(-0.246664\pi\) | ||||
0.714478 | + | 0.699658i | \(0.246664\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.30479 | 0.599374 | 0.299687 | − | 0.954038i | \(-0.403118\pi\) | ||||
0.299687 | + | 0.954038i | \(0.403118\pi\) | |||||||
\(242\) | −30.3745 | −1.95254 | ||||||||
\(243\) | −19.3696 | −1.24256 | ||||||||
\(244\) | −17.4145 | −1.11485 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.38609 | 0.343404 | ||||||||
\(247\) | −10.7952 | −0.686881 | ||||||||
\(248\) | −96.0603 | −6.09983 | ||||||||
\(249\) | 21.3542 | 1.35327 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.4581 | −1.10195 | −0.550974 | − | 0.834522i | \(-0.685744\pi\) | ||||
−0.550974 | + | 0.834522i | \(0.685744\pi\) | |||||||
\(252\) | 13.0640 | 0.822957 | ||||||||
\(253\) | −0.340565 | −0.0214111 | ||||||||
\(254\) | −46.9651 | −2.94685 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 97.8503 | 6.11564 | ||||||||
\(257\) | 15.9658 | 0.995918 | 0.497959 | − | 0.867200i | \(-0.334083\pi\) | ||||
0.497959 | + | 0.867200i | \(0.334083\pi\) | |||||||
\(258\) | −58.7097 | −3.65510 | ||||||||
\(259\) | −6.40257 | −0.397836 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.54156 | 0.528709 | ||||||||
\(262\) | 57.2313 | 3.53576 | ||||||||
\(263\) | 14.5099 | 0.894722 | 0.447361 | − | 0.894354i | \(-0.352364\pi\) | ||||
0.447361 | + | 0.894354i | \(0.352364\pi\) | |||||||
\(264\) | 8.25515 | 0.508069 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −23.1225 | −1.41773 | ||||||||
\(267\) | 6.49839 | 0.397695 | ||||||||
\(268\) | 67.2495 | 4.10792 | ||||||||
\(269\) | 1.69801 | 0.103530 | 0.0517649 | − | 0.998659i | \(-0.483515\pi\) | ||||
0.0517649 | + | 0.998659i | \(0.483515\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.9797 | −0.666970 | −0.333485 | − | 0.942755i | \(-0.608225\pi\) | ||||
−0.333485 | + | 0.942755i | \(0.608225\pi\) | |||||||
\(272\) | −46.5496 | −2.82248 | ||||||||
\(273\) | 2.98733 | 0.180802 | ||||||||
\(274\) | −53.7282 | −3.24584 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −13.2713 | −0.798841 | ||||||||
\(277\) | −2.28492 | −0.137287 | −0.0686437 | − | 0.997641i | \(-0.521867\pi\) | ||||
−0.0686437 | + | 0.997641i | \(0.521867\pi\) | |||||||
\(278\) | 16.3779 | 0.982280 | ||||||||
\(279\) | −20.5078 | −1.22777 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.74870 | −0.462249 | −0.231124 | − | 0.972924i | \(-0.574240\pi\) | ||||
−0.231124 | + | 0.972924i | \(0.574240\pi\) | |||||||
\(282\) | −29.8707 | −1.77878 | ||||||||
\(283\) | 4.22375 | 0.251076 | 0.125538 | − | 0.992089i | \(-0.459934\pi\) | ||||
0.125538 | + | 0.992089i | \(0.459934\pi\) | |||||||
\(284\) | 33.9888 | 2.01686 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.23832 | 0.0732235 | ||||||||
\(287\) | 0.841753 | 0.0496871 | ||||||||
\(288\) | 65.1960 | 3.84171 | ||||||||
\(289\) | −10.2577 | −0.603394 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.51543 | −0.0888359 | ||||||||
\(292\) | 45.2211 | 2.64636 | ||||||||
\(293\) | −20.7133 | −1.21008 | −0.605042 | − | 0.796193i | \(-0.706844\pi\) | ||||
−0.605042 | + | 0.796193i | \(0.706844\pi\) | |||||||
\(294\) | 6.39865 | 0.373177 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −67.6878 | −3.93428 | ||||||||
\(297\) | −0.580173 | −0.0336651 | ||||||||
\(298\) | 59.4104 | 3.44155 | ||||||||
\(299\) | −1.30291 | −0.0753492 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.17532 | −0.528857 | ||||||||
\(302\) | 24.4171 | 1.40505 | ||||||||
\(303\) | 29.2184 | 1.67855 | ||||||||
\(304\) | −148.535 | −8.51904 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −16.3552 | −0.934963 | ||||||||
\(307\) | −25.5218 | −1.45661 | −0.728303 | − | 0.685255i | \(-0.759691\pi\) | ||||
−0.728303 | + | 0.685255i | \(0.759691\pi\) | |||||||
\(308\) | 1.97127 | 0.112323 | ||||||||
\(309\) | 28.0477 | 1.59558 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.8893 | −1.35464 | −0.677320 | − | 0.735689i | \(-0.736859\pi\) | ||||
−0.677320 | + | 0.735689i | \(0.736859\pi\) | |||||||
\(312\) | 31.5820 | 1.78798 | ||||||||
\(313\) | −20.1080 | −1.13657 | −0.568287 | − | 0.822831i | \(-0.692394\pi\) | ||||
−0.568287 | + | 0.822831i | \(0.692394\pi\) | |||||||
\(314\) | −49.1900 | −2.77596 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 25.2012 | 1.41768 | ||||||||
\(317\) | 5.99196 | 0.336542 | 0.168271 | − | 0.985741i | \(-0.446182\pi\) | ||||
0.168271 | + | 0.985741i | \(0.446182\pi\) | |||||||
\(318\) | −22.3813 | −1.25508 | ||||||||
\(319\) | 1.28886 | 0.0721623 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 34.6831 | 1.93582 | ||||||||
\(322\) | −2.79074 | −0.155522 | ||||||||
\(323\) | 21.5139 | 1.19707 | ||||||||
\(324\) | −61.8007 | −3.43337 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 54.2927 | 3.00699 | ||||||||
\(327\) | 20.9507 | 1.15858 | ||||||||
\(328\) | 8.89900 | 0.491365 | ||||||||
\(329\) | −4.66829 | −0.257371 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30.8960 | −1.69820 | −0.849098 | − | 0.528235i | \(-0.822854\pi\) | ||||
−0.849098 | + | 0.528235i | \(0.822854\pi\) | |||||||
\(332\) | 53.9090 | 2.95864 | ||||||||
\(333\) | −14.4506 | −0.791888 | ||||||||
\(334\) | −64.8991 | −3.55112 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 41.1037 | 2.24239 | ||||||||
\(337\) | 17.4157 | 0.948691 | 0.474346 | − | 0.880339i | \(-0.342685\pi\) | ||||
0.474346 | + | 0.880339i | \(0.342685\pi\) | |||||||
\(338\) | −31.5421 | −1.71567 | ||||||||
\(339\) | 13.4630 | 0.731210 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.09448 | −0.167575 | ||||||||
\(342\) | −52.1875 | −2.82198 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −97.0013 | −5.22996 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 31.8265 | 1.71100 | ||||||||
\(347\) | −3.91958 | −0.210414 | −0.105207 | − | 0.994450i | \(-0.533551\pi\) | ||||
−0.105207 | + | 0.994450i | \(0.533551\pi\) | |||||||
\(348\) | 50.2251 | 2.69235 | ||||||||
\(349\) | −20.2285 | −1.08281 | −0.541404 | − | 0.840762i | \(-0.682107\pi\) | ||||
−0.541404 | + | 0.840762i | \(0.682107\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.21959 | −0.118473 | ||||||||
\(352\) | 9.83761 | 0.524346 | ||||||||
\(353\) | 10.7111 | 0.570092 | 0.285046 | − | 0.958514i | \(-0.407991\pi\) | ||||
0.285046 | + | 0.958514i | \(0.407991\pi\) | |||||||
\(354\) | −19.0761 | −1.01388 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 16.4052 | 0.869476 | ||||||||
\(357\) | −5.95351 | −0.315093 | ||||||||
\(358\) | −6.74388 | −0.356425 | ||||||||
\(359\) | −0.848230 | −0.0447679 | −0.0223839 | − | 0.999749i | \(-0.507126\pi\) | ||||
−0.0223839 | + | 0.999749i | \(0.507126\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 49.6485 | 2.61308 | ||||||||
\(362\) | −9.88586 | −0.519589 | ||||||||
\(363\) | −24.9550 | −1.30980 | ||||||||
\(364\) | 7.54155 | 0.395284 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −19.2510 | −1.00627 | ||||||||
\(367\) | −7.32206 | −0.382209 | −0.191104 | − | 0.981570i | \(-0.561207\pi\) | ||||
−0.191104 | + | 0.981570i | \(0.561207\pi\) | |||||||
\(368\) | −17.9272 | −0.934519 | ||||||||
\(369\) | 1.89984 | 0.0989016 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.49781 | −0.181597 | ||||||||
\(372\) | −120.588 | −6.25217 | ||||||||
\(373\) | −5.42327 | −0.280806 | −0.140403 | − | 0.990094i | \(-0.544840\pi\) | ||||
−0.140403 | + | 0.990094i | \(0.544840\pi\) | |||||||
\(374\) | −2.46788 | −0.127611 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −49.3530 | −2.54519 | ||||||||
\(377\) | 4.93083 | 0.253951 | ||||||||
\(378\) | −4.75420 | −0.244530 | ||||||||
\(379\) | −4.81942 | −0.247557 | −0.123778 | − | 0.992310i | \(-0.539501\pi\) | ||||
−0.123778 | + | 0.992310i | \(0.539501\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −38.5855 | −1.97680 | ||||||||
\(382\) | 10.5743 | 0.541029 | ||||||||
\(383\) | −0.160218 | −0.00818675 | −0.00409338 | − | 0.999992i | \(-0.501303\pi\) | ||||
−0.00409338 | + | 0.999992i | \(0.501303\pi\) | |||||||
\(384\) | 153.939 | 7.85565 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 53.8730 | 2.74207 | ||||||||
\(387\) | −20.7087 | −1.05268 | ||||||||
\(388\) | −3.82571 | −0.194221 | ||||||||
\(389\) | 15.6916 | 0.795597 | 0.397798 | − | 0.917473i | \(-0.369774\pi\) | ||||
0.397798 | + | 0.917473i | \(0.369774\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.59659 | 0.131315 | ||||||||
\(392\) | 10.5720 | 0.533965 | ||||||||
\(393\) | 47.0201 | 2.37185 | ||||||||
\(394\) | −48.3214 | −2.43440 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.44915 | 0.223578 | ||||||||
\(397\) | 2.75070 | 0.138054 | 0.0690268 | − | 0.997615i | \(-0.478011\pi\) | ||||
0.0690268 | + | 0.997615i | \(0.478011\pi\) | |||||||
\(398\) | 33.0433 | 1.65631 | ||||||||
\(399\) | −18.9970 | −0.951038 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −35.3053 | −1.76306 | −0.881532 | − | 0.472125i | \(-0.843487\pi\) | ||||
−0.881532 | + | 0.472125i | \(0.843487\pi\) | |||||||
\(402\) | 74.3415 | 3.70782 | ||||||||
\(403\) | −11.8386 | −0.589725 | ||||||||
\(404\) | 73.7620 | 3.66980 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 10.5615 | 0.524158 | ||||||||
\(407\) | −2.18049 | −0.108083 | ||||||||
\(408\) | −62.9404 | −3.11601 | ||||||||
\(409\) | 30.1715 | 1.49188 | 0.745942 | − | 0.666010i | \(-0.231999\pi\) | ||||
0.745942 | + | 0.666010i | \(0.231999\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −44.1420 | −2.17736 | ||||||||
\(412\) | 70.8066 | 3.48839 | ||||||||
\(413\) | −2.98127 | −0.146699 | ||||||||
\(414\) | −6.29870 | −0.309564 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 37.6360 | 1.84526 | ||||||||
\(417\) | 13.4557 | 0.658930 | ||||||||
\(418\) | −7.87472 | −0.385165 | ||||||||
\(419\) | −6.01345 | −0.293776 | −0.146888 | − | 0.989153i | \(-0.546926\pi\) | ||||
−0.146888 | + | 0.989153i | \(0.546926\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.48581 | 0.267362 | 0.133681 | − | 0.991024i | \(-0.457320\pi\) | ||||
0.133681 | + | 0.991024i | \(0.457320\pi\) | |||||||
\(422\) | 30.0694 | 1.46375 | ||||||||
\(423\) | −10.5363 | −0.512294 | ||||||||
\(424\) | −36.9787 | −1.79585 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 37.5732 | 1.82043 | ||||||||
\(427\) | −3.00861 | −0.145597 | ||||||||
\(428\) | 87.5579 | 4.23227 | ||||||||
\(429\) | 1.01738 | 0.0491196 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.1380 | −0.777342 | −0.388671 | − | 0.921377i | \(-0.627066\pi\) | ||||
−0.388671 | + | 0.921377i | \(0.627066\pi\) | |||||||
\(432\) | −30.5400 | −1.46936 | ||||||||
\(433\) | −11.0995 | −0.533406 | −0.266703 | − | 0.963779i | \(-0.585934\pi\) | ||||
−0.266703 | + | 0.963779i | \(0.585934\pi\) | |||||||
\(434\) | −25.3575 | −1.21720 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 52.8903 | 2.53299 | ||||||||
\(437\) | 8.28544 | 0.396346 | ||||||||
\(438\) | 49.9900 | 2.38862 | ||||||||
\(439\) | 0.163841 | 0.00781971 | 0.00390986 | − | 0.999992i | \(-0.498755\pi\) | ||||
0.00390986 | + | 0.999992i | \(0.498755\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.25700 | 0.107476 | ||||||||
\(442\) | −9.44143 | −0.449083 | ||||||||
\(443\) | −11.2602 | −0.534991 | −0.267495 | − | 0.963559i | \(-0.586196\pi\) | ||||
−0.267495 | + | 0.963559i | \(0.586196\pi\) | |||||||
\(444\) | −84.9708 | −4.03253 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 47.6254 | 2.25513 | ||||||||
\(447\) | 48.8103 | 2.30865 | ||||||||
\(448\) | 44.7594 | 2.11468 | ||||||||
\(449\) | −10.9029 | −0.514537 | −0.257269 | − | 0.966340i | \(-0.582823\pi\) | ||||
−0.257269 | + | 0.966340i | \(0.582823\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.286672 | 0.0134988 | ||||||||
\(452\) | 33.9875 | 1.59864 | ||||||||
\(453\) | 20.0606 | 0.942530 | ||||||||
\(454\) | 44.0137 | 2.06566 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −200.836 | −9.40499 | ||||||||
\(457\) | 25.0195 | 1.17036 | 0.585182 | − | 0.810902i | \(-0.301023\pi\) | ||||
0.585182 | + | 0.810902i | \(0.301023\pi\) | |||||||
\(458\) | −50.7583 | −2.37178 | ||||||||
\(459\) | 4.42346 | 0.206469 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.0753 | −0.469253 | −0.234626 | − | 0.972086i | \(-0.575387\pi\) | ||||
−0.234626 | + | 0.972086i | \(0.575387\pi\) | |||||||
\(462\) | 2.17916 | 0.101384 | ||||||||
\(463\) | 42.3926 | 1.97015 | 0.985075 | − | 0.172123i | \(-0.0550628\pi\) | ||||
0.985075 | + | 0.172123i | \(0.0550628\pi\) | |||||||
\(464\) | 67.8450 | 3.14962 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −54.4076 | −2.52038 | ||||||||
\(467\) | 18.6945 | 0.865077 | 0.432539 | − | 0.901615i | \(-0.357618\pi\) | ||||
0.432539 | + | 0.901615i | \(0.357618\pi\) | |||||||
\(468\) | 17.0213 | 0.786808 | ||||||||
\(469\) | 11.6183 | 0.536484 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −40.4135 | −1.86216 | ||||||||
\(472\) | −31.5179 | −1.45073 | ||||||||
\(473\) | −3.12479 | −0.143678 | ||||||||
\(474\) | 27.8589 | 1.27960 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −15.0297 | −0.688885 | ||||||||
\(477\) | −7.89455 | −0.361467 | ||||||||
\(478\) | 61.6506 | 2.81983 | ||||||||
\(479\) | −8.00167 | −0.365606 | −0.182803 | − | 0.983150i | \(-0.558517\pi\) | ||||
−0.182803 | + | 0.983150i | \(0.558517\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.34198 | −0.380361 | ||||||||
\(482\) | 25.9672 | 1.18278 | ||||||||
\(483\) | −2.29281 | −0.104327 | ||||||||
\(484\) | −62.9992 | −2.86360 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −54.0555 | −2.45201 | ||||||||
\(487\) | 7.34483 | 0.332826 | 0.166413 | − | 0.986056i | \(-0.446781\pi\) | ||||
0.166413 | + | 0.986056i | \(0.446781\pi\) | |||||||
\(488\) | −31.8070 | −1.43983 | ||||||||
\(489\) | 44.6057 | 2.01714 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.48742 | 0.292773 | 0.146387 | − | 0.989227i | \(-0.453236\pi\) | ||||
0.146387 | + | 0.989227i | \(0.453236\pi\) | |||||||
\(492\) | 11.1712 | 0.503637 | ||||||||
\(493\) | −9.82675 | −0.442575 | ||||||||
\(494\) | −30.1266 | −1.35546 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −162.892 | −7.31406 | ||||||||
\(497\) | 5.87205 | 0.263398 | ||||||||
\(498\) | 59.5942 | 2.67048 | ||||||||
\(499\) | −16.9776 | −0.760023 | −0.380012 | − | 0.924982i | \(-0.624080\pi\) | ||||
−0.380012 | + | 0.924982i | \(0.624080\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −53.3198 | −2.38215 | ||||||||
\(502\) | −48.7212 | −2.17453 | ||||||||
\(503\) | −29.2073 | −1.30229 | −0.651145 | − | 0.758953i | \(-0.725711\pi\) | ||||
−0.651145 | + | 0.758953i | \(0.725711\pi\) | |||||||
\(504\) | 23.8610 | 1.06285 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.950428 | −0.0422517 | ||||||||
\(507\) | −25.9144 | −1.15090 | ||||||||
\(508\) | −97.4096 | −4.32185 | ||||||||
\(509\) | −10.9500 | −0.485351 | −0.242675 | − | 0.970108i | \(-0.578025\pi\) | ||||
−0.242675 | + | 0.970108i | \(0.578025\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.81259 | 0.345609 | ||||||||
\(512\) | 138.796 | 6.13396 | ||||||||
\(513\) | 14.1148 | 0.623182 | ||||||||
\(514\) | 44.5564 | 1.96530 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −121.769 | −5.36058 | ||||||||
\(517\) | −1.58985 | −0.0699217 | ||||||||
\(518\) | −17.8679 | −0.785071 | ||||||||
\(519\) | 26.1480 | 1.14777 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −39.7639 | −1.74209 | −0.871043 | − | 0.491206i | \(-0.836556\pi\) | ||||
−0.871043 | + | 0.491206i | \(0.836556\pi\) | |||||||
\(522\) | 23.8373 | 1.04333 | ||||||||
\(523\) | 20.1830 | 0.882541 | 0.441271 | − | 0.897374i | \(-0.354528\pi\) | ||||
0.441271 | + | 0.897374i | \(0.354528\pi\) | |||||||
\(524\) | 118.703 | 5.18555 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 40.4935 | 1.76560 | ||||||||
\(527\) | 23.5935 | 1.02775 | ||||||||
\(528\) | 13.9985 | 0.609206 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.72872 | −0.292001 | ||||||||
\(532\) | −47.9581 | −2.07925 | ||||||||
\(533\) | 1.09673 | 0.0475046 | ||||||||
\(534\) | 18.1353 | 0.784792 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 122.829 | 5.30538 | ||||||||
\(537\) | −5.54063 | −0.239096 | ||||||||
\(538\) | 4.73872 | 0.204301 | ||||||||
\(539\) | 0.340565 | 0.0146692 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.0445 | −0.947768 | −0.473884 | − | 0.880587i | \(-0.657148\pi\) | ||||
−0.473884 | + | 0.880587i | \(0.657148\pi\) | |||||||
\(542\) | −30.6415 | −1.31617 | ||||||||
\(543\) | −8.12202 | −0.348549 | ||||||||
\(544\) | −75.0056 | −3.21584 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 8.33687 | 0.356785 | ||||||||
\(547\) | −10.4538 | −0.446972 | −0.223486 | − | 0.974707i | \(-0.571744\pi\) | ||||
−0.223486 | + | 0.974707i | \(0.571744\pi\) | |||||||
\(548\) | −111.437 | −4.76035 | ||||||||
\(549\) | −6.79043 | −0.289809 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −31.3561 | −1.33581 | ||||||||
\(552\) | −24.2396 | −1.03171 | ||||||||
\(553\) | 4.35387 | 0.185145 | ||||||||
\(554\) | −6.37661 | −0.270916 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 33.9691 | 1.44061 | ||||||||
\(557\) | 10.0603 | 0.426270 | 0.213135 | − | 0.977023i | \(-0.431633\pi\) | ||||
0.213135 | + | 0.977023i | \(0.431633\pi\) | |||||||
\(558\) | −57.2320 | −2.42282 | ||||||||
\(559\) | −11.9546 | −0.505626 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.02756 | −0.0856035 | ||||||||
\(562\) | −21.6246 | −0.912179 | ||||||||
\(563\) | 5.15810 | 0.217388 | 0.108694 | − | 0.994075i | \(-0.465333\pi\) | ||||
0.108694 | + | 0.994075i | \(0.465333\pi\) | |||||||
\(564\) | −61.9545 | −2.60875 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 11.7874 | 0.495461 | ||||||||
\(567\) | −10.6770 | −0.448390 | ||||||||
\(568\) | 62.0792 | 2.60478 | ||||||||
\(569\) | −31.4681 | −1.31921 | −0.659605 | − | 0.751612i | \(-0.729277\pi\) | ||||
−0.659605 | + | 0.751612i | \(0.729277\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.9799 | −1.00353 | −0.501763 | − | 0.865005i | \(-0.667315\pi\) | ||||
−0.501763 | + | 0.865005i | \(0.667315\pi\) | |||||||
\(572\) | 2.56839 | 0.107390 | ||||||||
\(573\) | 8.68764 | 0.362931 | ||||||||
\(574\) | 2.34912 | 0.0980502 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 101.022 | 4.20925 | ||||||||
\(577\) | −22.1641 | −0.922702 | −0.461351 | − | 0.887218i | \(-0.652635\pi\) | ||||
−0.461351 | + | 0.887218i | \(0.652635\pi\) | |||||||
\(578\) | −28.6266 | −1.19071 | ||||||||
\(579\) | 44.2610 | 1.83942 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.31355 | 0.386391 | ||||||||
\(582\) | −4.22916 | −0.175304 | ||||||||
\(583\) | −1.19123 | −0.0493357 | ||||||||
\(584\) | 82.5945 | 3.41779 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −57.8055 | −2.38792 | ||||||||
\(587\) | −32.9841 | −1.36140 | −0.680700 | − | 0.732562i | \(-0.738324\pi\) | ||||
−0.680700 | + | 0.732562i | \(0.738324\pi\) | |||||||
\(588\) | 13.2713 | 0.547301 | ||||||||
\(589\) | 75.2841 | 3.10203 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −39.6999 | −1.63303 | ||||||||
\(592\) | −114.780 | −4.71743 | ||||||||
\(593\) | 20.0061 | 0.821551 | 0.410776 | − | 0.911736i | \(-0.365258\pi\) | ||||
0.410776 | + | 0.911736i | \(0.365258\pi\) | |||||||
\(594\) | −1.61911 | −0.0664330 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 123.222 | 5.04737 | ||||||||
\(597\) | 27.1477 | 1.11108 | ||||||||
\(598\) | −3.63608 | −0.148691 | ||||||||
\(599\) | −44.4511 | −1.81622 | −0.908111 | − | 0.418730i | \(-0.862475\pi\) | ||||
−0.908111 | + | 0.418730i | \(0.862475\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −37.7530 | −1.53998 | −0.769989 | − | 0.638057i | \(-0.779738\pi\) | ||||
−0.769989 | + | 0.638057i | \(0.779738\pi\) | |||||||
\(602\) | −25.6059 | −1.04362 | ||||||||
\(603\) | 26.2225 | 1.06786 | ||||||||
\(604\) | 50.6432 | 2.06064 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 81.5409 | 3.31237 | ||||||||
\(607\) | 29.5127 | 1.19788 | 0.598941 | − | 0.800793i | \(-0.295588\pi\) | ||||
0.598941 | + | 0.800793i | \(0.295588\pi\) | |||||||
\(608\) | −239.334 | −9.70629 | ||||||||
\(609\) | 8.67710 | 0.351614 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.08236 | −0.246066 | ||||||||
\(612\) | −33.9220 | −1.37122 | ||||||||
\(613\) | 24.5507 | 0.991593 | 0.495797 | − | 0.868439i | \(-0.334876\pi\) | ||||
0.495797 | + | 0.868439i | \(0.334876\pi\) | |||||||
\(614\) | −71.2247 | −2.87439 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.60044 | 0.145066 | ||||||||
\(617\) | 39.6302 | 1.59545 | 0.797727 | − | 0.603019i | \(-0.206036\pi\) | ||||
0.797727 | + | 0.603019i | \(0.206036\pi\) | |||||||
\(618\) | 78.2738 | 3.14863 | ||||||||
\(619\) | 15.5441 | 0.624770 | 0.312385 | − | 0.949956i | \(-0.398872\pi\) | ||||
0.312385 | + | 0.949956i | \(0.398872\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.70356 | 0.0683616 | ||||||||
\(622\) | −66.6689 | −2.67318 | ||||||||
\(623\) | 2.83424 | 0.113551 | ||||||||
\(624\) | 53.5544 | 2.14389 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −56.1163 | −2.24286 | ||||||||
\(627\) | −6.46970 | −0.258375 | ||||||||
\(628\) | −102.024 | −4.07121 | ||||||||
\(629\) | 16.6249 | 0.662878 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.4320 | 0.494908 | 0.247454 | − | 0.968900i | \(-0.420406\pi\) | ||||
0.247454 | + | 0.968900i | \(0.420406\pi\) | |||||||
\(632\) | 46.0290 | 1.83093 | ||||||||
\(633\) | 24.7044 | 0.981911 | ||||||||
\(634\) | 16.7220 | 0.664116 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −46.4206 | −1.84070 | ||||||||
\(637\) | 1.30291 | 0.0516232 | ||||||||
\(638\) | 3.59687 | 0.142402 | ||||||||
\(639\) | 13.2532 | 0.524289 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 31.6123 | 1.24861 | 0.624306 | − | 0.781180i | \(-0.285382\pi\) | ||||
0.624306 | + | 0.781180i | \(0.285382\pi\) | |||||||
\(642\) | 96.7917 | 3.82006 | ||||||||
\(643\) | 36.9408 | 1.45680 | 0.728401 | − | 0.685151i | \(-0.240264\pi\) | ||||
0.728401 | + | 0.685151i | \(0.240264\pi\) | |||||||
\(644\) | −5.78823 | −0.228088 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 60.0398 | 2.36223 | ||||||||
\(647\) | 9.98222 | 0.392441 | 0.196221 | − | 0.980560i | \(-0.437133\pi\) | ||||
0.196221 | + | 0.980560i | \(0.437133\pi\) | |||||||
\(648\) | −112.876 | −4.43421 | ||||||||
\(649\) | −1.01531 | −0.0398546 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −20.8332 | −0.816519 | ||||||||
\(652\) | 112.608 | 4.41005 | ||||||||
\(653\) | 10.6583 | 0.417091 | 0.208545 | − | 0.978013i | \(-0.433127\pi\) | ||||
0.208545 | + | 0.978013i | \(0.433127\pi\) | |||||||
\(654\) | 58.4680 | 2.28628 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 15.0903 | 0.589176 | ||||||||
\(657\) | 17.6330 | 0.687930 | ||||||||
\(658\) | −13.0280 | −0.507883 | ||||||||
\(659\) | 27.9875 | 1.09024 | 0.545119 | − | 0.838359i | \(-0.316485\pi\) | ||||
0.545119 | + | 0.838359i | \(0.316485\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 48.0644 | 1.86949 | 0.934745 | − | 0.355319i | \(-0.115628\pi\) | ||||
0.934745 | + | 0.355319i | \(0.115628\pi\) | |||||||
\(662\) | −86.2226 | −3.35114 | ||||||||
\(663\) | −7.75689 | −0.301253 | ||||||||
\(664\) | 98.4626 | 3.82109 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −40.3279 | −1.56267 | ||||||||
\(667\) | −3.78448 | −0.146536 | ||||||||
\(668\) | −134.606 | −5.20807 | ||||||||
\(669\) | 39.1280 | 1.51278 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.02463 | −0.0395553 | ||||||||
\(672\) | 66.2306 | 2.55490 | ||||||||
\(673\) | −35.1764 | −1.35595 | −0.677975 | − | 0.735085i | \(-0.737142\pi\) | ||||
−0.677975 | + | 0.735085i | \(0.737142\pi\) | |||||||
\(674\) | 48.6026 | 1.87210 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −65.4211 | −2.51620 | ||||||||
\(677\) | −27.9596 | −1.07457 | −0.537287 | − | 0.843399i | \(-0.680551\pi\) | ||||
−0.537287 | + | 0.843399i | \(0.680551\pi\) | |||||||
\(678\) | 37.5718 | 1.44294 | ||||||||
\(679\) | −0.660946 | −0.0253648 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 36.1607 | 1.38568 | ||||||||
\(682\) | −8.63589 | −0.330685 | ||||||||
\(683\) | 2.93123 | 0.112161 | 0.0560803 | − | 0.998426i | \(-0.482140\pi\) | ||||
0.0560803 | + | 0.998426i | \(0.482140\pi\) | |||||||
\(684\) | −108.241 | −4.13871 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.79074 | 0.106551 | ||||||||
\(687\) | −41.7020 | −1.59103 | ||||||||
\(688\) | −164.488 | −6.27103 | ||||||||
\(689\) | −4.55733 | −0.173620 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.4627 | 1.27298 | 0.636490 | − | 0.771285i | \(-0.280386\pi\) | ||||
0.636490 | + | 0.771285i | \(0.280386\pi\) | |||||||
\(692\) | 66.0109 | 2.50936 | ||||||||
\(693\) | 0.768655 | 0.0291988 | ||||||||
\(694\) | −10.9385 | −0.415221 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 91.7341 | 3.47717 | ||||||||
\(697\) | −2.18569 | −0.0827890 | ||||||||
\(698\) | −56.4526 | −2.13676 | ||||||||
\(699\) | −44.7001 | −1.69071 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.1388 | 0.798402 | 0.399201 | − | 0.916864i | \(-0.369288\pi\) | ||||
0.399201 | + | 0.916864i | \(0.369288\pi\) | |||||||
\(702\) | −6.19429 | −0.233788 | ||||||||
\(703\) | 53.0481 | 2.00075 | ||||||||
\(704\) | 15.2435 | 0.574510 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 29.8918 | 1.12499 | ||||||||
\(707\) | 12.7434 | 0.479267 | ||||||||
\(708\) | −39.5654 | −1.48696 | ||||||||
\(709\) | −41.7990 | −1.56979 | −0.784897 | − | 0.619627i | \(-0.787284\pi\) | ||||
−0.784897 | + | 0.619627i | \(0.787284\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.82667 | 0.368529 | ||||||||
\(712\) | 29.9635 | 1.12293 | ||||||||
\(713\) | 9.08631 | 0.340285 | ||||||||
\(714\) | −16.6147 | −0.621790 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −13.9874 | −0.522733 | ||||||||
\(717\) | 50.6509 | 1.89159 | ||||||||
\(718\) | −2.36719 | −0.0883428 | ||||||||
\(719\) | −35.8849 | −1.33828 | −0.669140 | − | 0.743136i | \(-0.733338\pi\) | ||||
−0.669140 | + | 0.743136i | \(0.733338\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.2329 | 0.455575 | ||||||||
\(722\) | 138.556 | 5.15652 | ||||||||
\(723\) | 21.3342 | 0.793426 | ||||||||
\(724\) | −20.5041 | −0.762030 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −69.6430 | −2.58470 | ||||||||
\(727\) | 43.5701 | 1.61592 | 0.807962 | − | 0.589234i | \(-0.200570\pi\) | ||||
0.807962 | + | 0.589234i | \(0.200570\pi\) | |||||||
\(728\) | 13.7743 | 0.510511 | ||||||||
\(729\) | −12.3800 | −0.458519 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 23.8246 | 0.881184 | ||||||||
\(732\) | −39.9283 | −1.47579 | ||||||||
\(733\) | −9.30801 | −0.343799 | −0.171900 | − | 0.985114i | \(-0.554990\pi\) | ||||
−0.171900 | + | 0.985114i | \(0.554990\pi\) | |||||||
\(734\) | −20.4340 | −0.754232 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −28.8861 | −1.06476 | ||||||||
\(737\) | 3.95679 | 0.145750 | ||||||||
\(738\) | 5.30195 | 0.195168 | ||||||||
\(739\) | 15.1965 | 0.559011 | 0.279505 | − | 0.960144i | \(-0.409830\pi\) | ||||
0.279505 | + | 0.960144i | \(0.409830\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −24.7514 | −0.909264 | ||||||||
\(742\) | −9.76148 | −0.358355 | ||||||||
\(743\) | −33.2864 | −1.22116 | −0.610579 | − | 0.791955i | \(-0.709063\pi\) | ||||
−0.610579 | + | 0.791955i | \(0.709063\pi\) | |||||||
\(744\) | −220.248 | −8.07470 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −15.1349 | −0.554129 | ||||||||
\(747\) | 21.0207 | 0.769107 | ||||||||
\(748\) | −5.11859 | −0.187154 | ||||||||
\(749\) | 15.1269 | 0.552724 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.4114 | 1.00026 | 0.500128 | − | 0.865952i | \(-0.333286\pi\) | ||||
0.500128 | + | 0.865952i | \(0.333286\pi\) | |||||||
\(752\) | −83.6892 | −3.05183 | ||||||||
\(753\) | −40.0283 | −1.45871 | ||||||||
\(754\) | 13.7607 | 0.501134 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −9.86061 | −0.358627 | ||||||||
\(757\) | −40.1658 | −1.45985 | −0.729926 | − | 0.683526i | \(-0.760445\pi\) | ||||
−0.729926 | + | 0.683526i | \(0.760445\pi\) | |||||||
\(758\) | −13.4497 | −0.488517 | ||||||||
\(759\) | −0.780852 | −0.0283431 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.65834 | 0.0963646 | 0.0481823 | − | 0.998839i | \(-0.484657\pi\) | ||||
0.0481823 | + | 0.998839i | \(0.484657\pi\) | |||||||
\(762\) | −107.682 | −3.90092 | ||||||||
\(763\) | 9.13756 | 0.330802 | ||||||||
\(764\) | 21.9320 | 0.793473 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.447127 | −0.0161553 | ||||||||
\(767\) | −3.88432 | −0.140255 | ||||||||
\(768\) | 224.353 | 8.09563 | ||||||||
\(769\) | −53.4285 | −1.92668 | −0.963341 | − | 0.268281i | \(-0.913544\pi\) | ||||
−0.963341 | + | 0.268281i | \(0.913544\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 36.6066 | 1.31835 | ||||||||
\(772\) | 111.737 | 4.02151 | ||||||||
\(773\) | 43.0461 | 1.54826 | 0.774130 | − | 0.633026i | \(-0.218188\pi\) | ||||
0.774130 | + | 0.633026i | \(0.218188\pi\) | |||||||
\(774\) | −57.7926 | −2.07731 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6.98751 | −0.250837 | ||||||||
\(777\) | −14.6799 | −0.526639 | ||||||||
\(778\) | 43.7912 | 1.56999 | ||||||||
\(779\) | −6.97430 | −0.249880 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.99981 | 0.0715590 | ||||||||
\(782\) | 7.24642 | 0.259131 | ||||||||
\(783\) | −6.44709 | −0.230400 | ||||||||
\(784\) | 17.9272 | 0.640256 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 131.221 | 4.68049 | ||||||||
\(787\) | −1.48807 | −0.0530440 | −0.0265220 | − | 0.999648i | \(-0.508443\pi\) | ||||
−0.0265220 | + | 0.999648i | \(0.508443\pi\) | |||||||
\(788\) | −100.223 | −3.57029 | ||||||||
\(789\) | 33.2686 | 1.18439 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.87183 | 0.208778 | ||||||||
\(792\) | 8.12620 | 0.288752 | ||||||||
\(793\) | −3.91995 | −0.139201 | ||||||||
\(794\) | 7.67648 | 0.272428 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 68.5346 | 2.42914 | ||||||||
\(797\) | 10.0121 | 0.354648 | 0.177324 | − | 0.984153i | \(-0.443256\pi\) | ||||
0.177324 | + | 0.984153i | \(0.443256\pi\) | |||||||
\(798\) | −53.0156 | −1.87673 | ||||||||
\(799\) | 12.1216 | 0.428833 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.39688 | 0.226023 | ||||||||
\(802\) | −98.5280 | −3.47914 | ||||||||
\(803\) | 2.66069 | 0.0938939 | ||||||||
\(804\) | 154.191 | 5.43789 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −33.0386 | −1.16373 | ||||||||
\(807\) | 3.89323 | 0.137048 | ||||||||
\(808\) | 134.723 | 4.73955 | ||||||||
\(809\) | −11.4480 | −0.402491 | −0.201246 | − | 0.979541i | \(-0.564499\pi\) | ||||
−0.201246 | + | 0.979541i | \(0.564499\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.19686 | −0.0420274 | −0.0210137 | − | 0.999779i | \(-0.506689\pi\) | ||||
−0.0210137 | + | 0.999779i | \(0.506689\pi\) | |||||||
\(812\) | 21.9054 | 0.768730 | ||||||||
\(813\) | −25.1745 | −0.882907 | ||||||||
\(814\) | −6.08519 | −0.213286 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −106.730 | −3.73628 | ||||||||
\(817\) | 76.0216 | 2.65966 | ||||||||
\(818\) | 84.2008 | 2.94401 | ||||||||
\(819\) | 2.94067 | 0.102755 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −55.3711 | −1.93246 | −0.966232 | − | 0.257674i | \(-0.917044\pi\) | ||||
−0.966232 | + | 0.257674i | \(0.917044\pi\) | |||||||
\(822\) | −123.189 | −4.29671 | ||||||||
\(823\) | 29.2048 | 1.01802 | 0.509008 | − | 0.860762i | \(-0.330012\pi\) | ||||
0.509008 | + | 0.860762i | \(0.330012\pi\) | |||||||
\(824\) | 129.325 | 4.50527 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.31994 | −0.289488 | ||||||||
\(827\) | −3.53535 | −0.122936 | −0.0614681 | − | 0.998109i | \(-0.519578\pi\) | ||||
−0.0614681 | + | 0.998109i | \(0.519578\pi\) | |||||||
\(828\) | −13.0640 | −0.454007 | ||||||||
\(829\) | −9.17625 | −0.318704 | −0.159352 | − | 0.987222i | \(-0.550941\pi\) | ||||
−0.159352 | + | 0.987222i | \(0.550941\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.23889 | −0.181735 | ||||||||
\(832\) | 58.3175 | 2.02179 | ||||||||
\(833\) | −2.59659 | −0.0899667 | ||||||||
\(834\) | 37.5514 | 1.30030 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −16.3328 | −0.564883 | ||||||||
\(837\) | 15.4791 | 0.535036 | ||||||||
\(838\) | −16.7820 | −0.579724 | ||||||||
\(839\) | −9.35807 | −0.323077 | −0.161538 | − | 0.986866i | \(-0.551646\pi\) | ||||
−0.161538 | + | 0.986866i | \(0.551646\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.6777 | −0.506129 | ||||||||
\(842\) | 15.3095 | 0.527599 | ||||||||
\(843\) | −17.7663 | −0.611905 | ||||||||
\(844\) | 62.3664 | 2.14674 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −29.4041 | −1.01094 | ||||||||
\(847\) | −10.8840 | −0.373979 | ||||||||
\(848\) | −62.7058 | −2.15333 | ||||||||
\(849\) | 9.68428 | 0.332364 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.40257 | 0.219477 | ||||||||
\(852\) | 77.9300 | 2.66984 | ||||||||
\(853\) | −23.2096 | −0.794681 | −0.397340 | − | 0.917671i | \(-0.630067\pi\) | ||||
−0.397340 | + | 0.917671i | \(0.630067\pi\) | |||||||
\(854\) | −8.39625 | −0.287314 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 159.921 | 5.46599 | ||||||||
\(857\) | 52.8608 | 1.80569 | 0.902845 | − | 0.429965i | \(-0.141474\pi\) | ||||
0.902845 | + | 0.429965i | \(0.141474\pi\) | |||||||
\(858\) | 2.83924 | 0.0969302 | ||||||||
\(859\) | −17.9744 | −0.613278 | −0.306639 | − | 0.951826i | \(-0.599204\pi\) | ||||
−0.306639 | + | 0.951826i | \(0.599204\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.92998 | 0.0657737 | ||||||||
\(862\) | −45.0371 | −1.53397 | ||||||||
\(863\) | 50.2664 | 1.71109 | 0.855545 | − | 0.517729i | \(-0.173222\pi\) | ||||
0.855545 | + | 0.517729i | \(0.173222\pi\) | |||||||
\(864\) | −49.2093 | −1.67414 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −30.9757 | −1.05260 | ||||||||
\(867\) | −23.5190 | −0.798747 | ||||||||
\(868\) | −52.5937 | −1.78515 | ||||||||
\(869\) | 1.48277 | 0.0502997 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.1376 | 0.512919 | ||||||||
\(872\) | 96.6020 | 3.27136 | ||||||||
\(873\) | −1.49176 | −0.0504883 | ||||||||
\(874\) | 23.1225 | 0.782131 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 103.684 | 3.50314 | ||||||||
\(877\) | −6.50538 | −0.219671 | −0.109836 | − | 0.993950i | \(-0.535032\pi\) | ||||
−0.109836 | + | 0.993950i | \(0.535032\pi\) | |||||||
\(878\) | 0.457238 | 0.0154310 | ||||||||
\(879\) | −47.4918 | −1.60186 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19.8310 | −0.668122 | −0.334061 | − | 0.942551i | \(-0.608419\pi\) | ||||
−0.334061 | + | 0.942551i | \(0.608419\pi\) | |||||||
\(882\) | 6.29870 | 0.212088 | ||||||||
\(883\) | 14.9867 | 0.504344 | 0.252172 | − | 0.967682i | \(-0.418855\pi\) | ||||
0.252172 | + | 0.967682i | \(0.418855\pi\) | |||||||
\(884\) | −19.5823 | −0.658625 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −31.4244 | −1.05572 | ||||||||
\(887\) | 3.22519 | 0.108291 | 0.0541457 | − | 0.998533i | \(-0.482756\pi\) | ||||
0.0541457 | + | 0.998533i | \(0.482756\pi\) | |||||||
\(888\) | −155.196 | −5.20803 | ||||||||
\(889\) | −16.8289 | −0.564423 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.63619 | −0.121817 | ||||||||
\(892\) | 98.7791 | 3.30737 | ||||||||
\(893\) | 38.6788 | 1.29434 | ||||||||
\(894\) | 136.217 | 4.55578 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 67.1396 | 2.24298 | ||||||||
\(897\) | −2.98733 | −0.0997441 | ||||||||
\(898\) | −30.4270 | −1.01536 | ||||||||
\(899\) | −34.3869 | −1.14687 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.08239 | 0.302578 | ||||||||
\(902\) | 0.800026 | 0.0266380 | ||||||||
\(903\) | −21.0373 | −0.700078 | ||||||||
\(904\) | 62.0768 | 2.06464 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 55.9840 | 1.85994 | ||||||||
\(907\) | −7.88833 | −0.261928 | −0.130964 | − | 0.991387i | \(-0.541807\pi\) | ||||
−0.130964 | + | 0.991387i | \(0.541807\pi\) | |||||||
\(908\) | 91.2881 | 3.02950 | ||||||||
\(909\) | 28.7620 | 0.953974 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.60435 | 0.285075 | 0.142537 | − | 0.989789i | \(-0.454474\pi\) | ||||
0.142537 | + | 0.989789i | \(0.454474\pi\) | |||||||
\(912\) | −340.562 | −11.2771 | ||||||||
\(913\) | 3.17187 | 0.104974 | ||||||||
\(914\) | 69.8230 | 2.30954 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −105.277 | −3.47845 | ||||||||
\(917\) | 20.5076 | 0.677220 | ||||||||
\(918\) | 12.3447 | 0.407437 | ||||||||
\(919\) | 25.8091 | 0.851364 | 0.425682 | − | 0.904873i | \(-0.360034\pi\) | ||||
0.425682 | + | 0.904873i | \(0.360034\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −58.5167 | −1.92819 | ||||||||
\(922\) | −28.1175 | −0.926000 | ||||||||
\(923\) | 7.65075 | 0.251828 | ||||||||
\(924\) | 4.51976 | 0.148689 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 118.307 | 3.88780 | ||||||||
\(927\) | 27.6096 | 0.906817 | ||||||||
\(928\) | 109.319 | 3.58857 | ||||||||
\(929\) | 22.4171 | 0.735483 | 0.367741 | − | 0.929928i | \(-0.380131\pi\) | ||||
0.367741 | + | 0.929928i | \(0.380131\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.28544 | −0.271544 | ||||||||
\(932\) | −112.846 | −3.69639 | ||||||||
\(933\) | −54.7738 | −1.79321 | ||||||||
\(934\) | 52.1714 | 1.70710 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 31.0887 | 1.01616 | ||||||||
\(937\) | −17.3093 | −0.565470 | −0.282735 | − | 0.959198i | \(-0.591242\pi\) | ||||
−0.282735 | + | 0.959198i | \(0.591242\pi\) | |||||||
\(938\) | 32.4237 | 1.05867 | ||||||||
\(939\) | −46.1040 | −1.50455 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −35.9965 | −1.17345 | −0.586727 | − | 0.809785i | \(-0.699584\pi\) | ||||
−0.586727 | + | 0.809785i | \(0.699584\pi\) | |||||||
\(942\) | −112.784 | −3.67469 | ||||||||
\(943\) | −0.841753 | −0.0274113 | ||||||||
\(944\) | −53.4457 | −1.73951 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.72048 | −0.283527 | ||||||||
\(947\) | −17.0281 | −0.553338 | −0.276669 | − | 0.960965i | \(-0.589231\pi\) | ||||
−0.276669 | + | 0.960965i | \(0.589231\pi\) | |||||||
\(948\) | 57.7817 | 1.87666 | ||||||||
\(949\) | 10.1791 | 0.330428 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.7385 | 0.445500 | ||||||||
\(952\) | −27.4511 | −0.889696 | ||||||||
\(953\) | 1.95658 | 0.0633799 | 0.0316899 | − | 0.999498i | \(-0.489911\pi\) | ||||
0.0316899 | + | 0.999498i | \(0.489911\pi\) | |||||||
\(954\) | −22.0316 | −0.713301 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 127.869 | 4.13557 | ||||||||
\(957\) | 2.95512 | 0.0955254 | ||||||||
\(958\) | −22.3306 | −0.721469 | ||||||||
\(959\) | −19.2523 | −0.621690 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 51.5610 | 1.66326 | ||||||||
\(962\) | −23.2803 | −0.750587 | ||||||||
\(963\) | 34.1414 | 1.10019 | ||||||||
\(964\) | 53.8583 | 1.73466 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −6.39865 | −0.205873 | ||||||||
\(967\) | −11.5841 | −0.372519 | −0.186259 | − | 0.982501i | \(-0.559636\pi\) | ||||
−0.186259 | + | 0.982501i | \(0.559636\pi\) | |||||||
\(968\) | −115.066 | −3.69835 | ||||||||
\(969\) | 49.3274 | 1.58463 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −43.0267 | −1.38079 | −0.690397 | − | 0.723431i | \(-0.742564\pi\) | ||||
−0.690397 | + | 0.723431i | \(0.742564\pi\) | |||||||
\(972\) | −112.116 | −3.59611 | ||||||||
\(973\) | 5.86865 | 0.188140 | ||||||||
\(974\) | 20.4975 | 0.656783 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −53.9359 | −1.72645 | ||||||||
\(977\) | −46.6160 | −1.49138 | −0.745689 | − | 0.666294i | \(-0.767879\pi\) | ||||
−0.745689 | + | 0.666294i | \(0.767879\pi\) | |||||||
\(978\) | 124.483 | 3.98053 | ||||||||
\(979\) | 0.965243 | 0.0308493 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 20.6235 | 0.658457 | ||||||||
\(982\) | 18.1047 | 0.577745 | ||||||||
\(983\) | −24.9615 | −0.796147 | −0.398073 | − | 0.917354i | \(-0.630321\pi\) | ||||
−0.398073 | + | 0.917354i | \(0.630321\pi\) | |||||||
\(984\) | 20.4037 | 0.650448 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −27.4239 | −0.873355 | ||||||||
\(987\) | −10.7035 | −0.340697 | ||||||||
\(988\) | −62.4850 | −1.98791 | ||||||||
\(989\) | 9.17532 | 0.291758 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.548307 | −0.0174175 | −0.00870877 | − | 0.999962i | \(-0.502772\pi\) | ||||
−0.00870877 | + | 0.999962i | \(0.502772\pi\) | |||||||
\(992\) | −262.469 | −8.33338 | ||||||||
\(993\) | −70.8387 | −2.24800 | ||||||||
\(994\) | 16.3874 | 0.519776 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 123.603 | 3.91652 | ||||||||
\(997\) | −1.96623 | −0.0622712 | −0.0311356 | − | 0.999515i | \(-0.509912\pi\) | ||||
−0.0311356 | + | 0.999515i | \(0.509912\pi\) | |||||||
\(998\) | −47.3802 | −1.49979 | ||||||||
\(999\) | 10.9072 | 0.345088 |
(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.bb.1.14 | yes | 14 | |
5.4 | even | 2 | 4025.2.a.ba.1.1 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4025.2.a.ba.1.1 | ✓ | 14 | 5.4 | even | 2 | ||
4025.2.a.bb.1.14 | yes | 14 | 1.1 | even | 1 | trivial |