Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3525,2,Mod(1,3525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3525, 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("3525.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3525 = 3 \cdot 5^{2} \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3525.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: | \(28.1472667125\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 3 x^{12} - 17 x^{11} + 51 x^{10} + 106 x^{9} - 316 x^{8} - 288 x^{7} + 852 x^{6} + 309 x^{5} - 923 x^{4} - 107 x^{3} + 293 x^{2} + 12 x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 705) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(-2.24873\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3525.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.24873 | 1.59009 | 0.795045 | − | 0.606550i | \(-0.207447\pi\) | ||||
0.795045 | + | 0.606550i | \(0.207447\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.05678 | 1.52839 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.24873 | −0.918039 | ||||||||
\(7\) | 1.38491 | 0.523447 | 0.261723 | − | 0.965143i | \(-0.415709\pi\) | ||||
0.261723 | + | 0.965143i | \(0.415709\pi\) | |||||||
\(8\) | 2.37640 | 0.840185 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.19292 | 1.56572 | 0.782862 | − | 0.622196i | \(-0.213759\pi\) | ||||
0.782862 | + | 0.622196i | \(0.213759\pi\) | |||||||
\(12\) | −3.05678 | −0.882415 | ||||||||
\(13\) | −2.59916 | −0.720876 | −0.360438 | − | 0.932783i | \(-0.617373\pi\) | ||||
−0.360438 | + | 0.932783i | \(0.617373\pi\) | |||||||
\(14\) | 3.11429 | 0.832328 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.769670 | −0.192417 | ||||||||
\(17\) | 3.45174 | 0.837171 | 0.418585 | − | 0.908177i | \(-0.362526\pi\) | ||||
0.418585 | + | 0.908177i | \(0.362526\pi\) | |||||||
\(18\) | 2.24873 | 0.530030 | ||||||||
\(19\) | 1.01677 | 0.233262 | 0.116631 | − | 0.993175i | \(-0.462790\pi\) | ||||
0.116631 | + | 0.993175i | \(0.462790\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.38491 | −0.302212 | ||||||||
\(22\) | 11.6775 | 2.48964 | ||||||||
\(23\) | 2.00367 | 0.417794 | 0.208897 | − | 0.977938i | \(-0.433013\pi\) | ||||
0.208897 | + | 0.977938i | \(0.433013\pi\) | |||||||
\(24\) | −2.37640 | −0.485081 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5.84480 | −1.14626 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 4.23336 | 0.800030 | ||||||||
\(29\) | 7.23539 | 1.34358 | 0.671789 | − | 0.740742i | \(-0.265526\pi\) | ||||
0.671789 | + | 0.740742i | \(0.265526\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.286932 | −0.0515345 | −0.0257673 | − | 0.999668i | \(-0.508203\pi\) | ||||
−0.0257673 | + | 0.999668i | \(0.508203\pi\) | |||||||
\(32\) | −6.48358 | −1.14615 | ||||||||
\(33\) | −5.19292 | −0.903971 | ||||||||
\(34\) | 7.76203 | 1.33118 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.05678 | 0.509463 | ||||||||
\(37\) | −4.63981 | −0.762780 | −0.381390 | − | 0.924414i | \(-0.624555\pi\) | ||||
−0.381390 | + | 0.924414i | \(0.624555\pi\) | |||||||
\(38\) | 2.28643 | 0.370908 | ||||||||
\(39\) | 2.59916 | 0.416198 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.775913 | −0.121177 | −0.0605886 | − | 0.998163i | \(-0.519298\pi\) | ||||
−0.0605886 | + | 0.998163i | \(0.519298\pi\) | |||||||
\(42\) | −3.11429 | −0.480545 | ||||||||
\(43\) | −2.06895 | −0.315511 | −0.157756 | − | 0.987478i | \(-0.550426\pi\) | ||||
−0.157756 | + | 0.987478i | \(0.550426\pi\) | |||||||
\(44\) | 15.8736 | 2.39303 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.50571 | 0.664330 | ||||||||
\(47\) | −1.00000 | −0.145865 | ||||||||
\(48\) | 0.769670 | 0.111092 | ||||||||
\(49\) | −5.08202 | −0.726003 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.45174 | −0.483341 | ||||||||
\(52\) | −7.94504 | −1.10178 | ||||||||
\(53\) | −0.703311 | −0.0966072 | −0.0483036 | − | 0.998833i | \(-0.515382\pi\) | ||||
−0.0483036 | + | 0.998833i | \(0.515382\pi\) | |||||||
\(54\) | −2.24873 | −0.306013 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.29111 | 0.439792 | ||||||||
\(57\) | −1.01677 | −0.134674 | ||||||||
\(58\) | 16.2704 | 2.13641 | ||||||||
\(59\) | 10.9167 | 1.42123 | 0.710616 | − | 0.703580i | \(-0.248416\pi\) | ||||
0.710616 | + | 0.703580i | \(0.248416\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.46158 | 0.955358 | 0.477679 | − | 0.878535i | \(-0.341478\pi\) | ||||
0.477679 | + | 0.878535i | \(0.341478\pi\) | |||||||
\(62\) | −0.645232 | −0.0819445 | ||||||||
\(63\) | 1.38491 | 0.174482 | ||||||||
\(64\) | −13.0405 | −1.63006 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −11.6775 | −1.43740 | ||||||||
\(67\) | 3.36130 | 0.410648 | 0.205324 | − | 0.978694i | \(-0.434175\pi\) | ||||
0.205324 | + | 0.978694i | \(0.434175\pi\) | |||||||
\(68\) | 10.5512 | 1.27952 | ||||||||
\(69\) | −2.00367 | −0.241213 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.94927 | 0.468692 | 0.234346 | − | 0.972153i | \(-0.424705\pi\) | ||||
0.234346 | + | 0.972153i | \(0.424705\pi\) | |||||||
\(72\) | 2.37640 | 0.280062 | ||||||||
\(73\) | 15.0178 | 1.75770 | 0.878852 | − | 0.477094i | \(-0.158310\pi\) | ||||
0.878852 | + | 0.477094i | \(0.158310\pi\) | |||||||
\(74\) | −10.4337 | −1.21289 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.10803 | 0.356515 | ||||||||
\(77\) | 7.19173 | 0.819573 | ||||||||
\(78\) | 5.84480 | 0.661793 | ||||||||
\(79\) | −6.69906 | −0.753703 | −0.376851 | − | 0.926274i | \(-0.622993\pi\) | ||||
−0.376851 | + | 0.926274i | \(0.622993\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.74482 | −0.192683 | ||||||||
\(83\) | 10.4990 | 1.15241 | 0.576207 | − | 0.817304i | \(-0.304532\pi\) | ||||
0.576207 | + | 0.817304i | \(0.304532\pi\) | |||||||
\(84\) | −4.23336 | −0.461898 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.65249 | −0.501691 | ||||||||
\(87\) | −7.23539 | −0.775715 | ||||||||
\(88\) | 12.3405 | 1.31550 | ||||||||
\(89\) | 15.4868 | 1.64160 | 0.820798 | − | 0.571218i | \(-0.193529\pi\) | ||||
0.820798 | + | 0.571218i | \(0.193529\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.59960 | −0.377341 | ||||||||
\(92\) | 6.12477 | 0.638551 | ||||||||
\(93\) | 0.286932 | 0.0297535 | ||||||||
\(94\) | −2.24873 | −0.231939 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 6.48358 | 0.661728 | ||||||||
\(97\) | 10.9476 | 1.11156 | 0.555781 | − | 0.831328i | \(-0.312419\pi\) | ||||
0.555781 | + | 0.831328i | \(0.312419\pi\) | |||||||
\(98\) | −11.4281 | −1.15441 | ||||||||
\(99\) | 5.19292 | 0.521908 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.5503 | 1.64682 | 0.823408 | − | 0.567451i | \(-0.192070\pi\) | ||||
0.823408 | + | 0.567451i | \(0.192070\pi\) | |||||||
\(102\) | −7.76203 | −0.768556 | ||||||||
\(103\) | −4.90157 | −0.482966 | −0.241483 | − | 0.970405i | \(-0.577634\pi\) | ||||
−0.241483 | + | 0.970405i | \(0.577634\pi\) | |||||||
\(104\) | −6.17664 | −0.605670 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.58156 | −0.153614 | ||||||||
\(107\) | −10.6478 | −1.02936 | −0.514679 | − | 0.857383i | \(-0.672089\pi\) | ||||
−0.514679 | + | 0.857383i | \(0.672089\pi\) | |||||||
\(108\) | −3.05678 | −0.294138 | ||||||||
\(109\) | −8.60514 | −0.824223 | −0.412112 | − | 0.911133i | \(-0.635209\pi\) | ||||
−0.412112 | + | 0.911133i | \(0.635209\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.63981 | 0.440391 | ||||||||
\(112\) | −1.06592 | −0.100720 | ||||||||
\(113\) | −10.5128 | −0.988965 | −0.494482 | − | 0.869188i | \(-0.664642\pi\) | ||||
−0.494482 | + | 0.869188i | \(0.664642\pi\) | |||||||
\(114\) | −2.28643 | −0.214144 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 22.1170 | 2.05351 | ||||||||
\(117\) | −2.59916 | −0.240292 | ||||||||
\(118\) | 24.5487 | 2.25989 | ||||||||
\(119\) | 4.78036 | 0.438214 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.9664 | 1.45149 | ||||||||
\(122\) | 16.7791 | 1.51911 | ||||||||
\(123\) | 0.775913 | 0.0699617 | ||||||||
\(124\) | −0.877087 | −0.0787647 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.11429 | 0.277443 | ||||||||
\(127\) | −12.3634 | −1.09707 | −0.548535 | − | 0.836127i | \(-0.684814\pi\) | ||||
−0.548535 | + | 0.836127i | \(0.684814\pi\) | |||||||
\(128\) | −16.3573 | −1.44580 | ||||||||
\(129\) | 2.06895 | 0.182160 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.92428 | −0.692347 | −0.346174 | − | 0.938170i | \(-0.612519\pi\) | ||||
−0.346174 | + | 0.938170i | \(0.612519\pi\) | |||||||
\(132\) | −15.8736 | −1.38162 | ||||||||
\(133\) | 1.40813 | 0.122100 | ||||||||
\(134\) | 7.55865 | 0.652967 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.20273 | 0.703379 | ||||||||
\(137\) | 7.00433 | 0.598420 | 0.299210 | − | 0.954187i | \(-0.403277\pi\) | ||||
0.299210 | + | 0.954187i | \(0.403277\pi\) | |||||||
\(138\) | −4.50571 | −0.383551 | ||||||||
\(139\) | −2.33550 | −0.198094 | −0.0990472 | − | 0.995083i | \(-0.531579\pi\) | ||||
−0.0990472 | + | 0.995083i | \(0.531579\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.00000 | 0.0842152 | ||||||||
\(142\) | 8.88084 | 0.745263 | ||||||||
\(143\) | −13.4972 | −1.12869 | ||||||||
\(144\) | −0.769670 | −0.0641392 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 33.7710 | 2.79491 | ||||||||
\(147\) | 5.08202 | 0.419158 | ||||||||
\(148\) | −14.1829 | −1.16582 | ||||||||
\(149\) | −15.2887 | −1.25250 | −0.626248 | − | 0.779624i | \(-0.715410\pi\) | ||||
−0.626248 | + | 0.779624i | \(0.715410\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.2657 | −1.24231 | −0.621154 | − | 0.783689i | \(-0.713336\pi\) | ||||
−0.621154 | + | 0.783689i | \(0.713336\pi\) | |||||||
\(152\) | 2.41625 | 0.195983 | ||||||||
\(153\) | 3.45174 | 0.279057 | ||||||||
\(154\) | 16.1722 | 1.30320 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 7.94504 | 0.636113 | ||||||||
\(157\) | 17.7558 | 1.41707 | 0.708535 | − | 0.705676i | \(-0.249356\pi\) | ||||
0.708535 | + | 0.705676i | \(0.249356\pi\) | |||||||
\(158\) | −15.0644 | −1.19846 | ||||||||
\(159\) | 0.703311 | 0.0557762 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.77490 | 0.218693 | ||||||||
\(162\) | 2.24873 | 0.176677 | ||||||||
\(163\) | −9.71780 | −0.761156 | −0.380578 | − | 0.924749i | \(-0.624275\pi\) | ||||
−0.380578 | + | 0.924749i | \(0.624275\pi\) | |||||||
\(164\) | −2.37179 | −0.185206 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 23.6094 | 1.83244 | ||||||||
\(167\) | −13.8924 | −1.07503 | −0.537513 | − | 0.843256i | \(-0.680636\pi\) | ||||
−0.537513 | + | 0.843256i | \(0.680636\pi\) | |||||||
\(168\) | −3.29111 | −0.253914 | ||||||||
\(169\) | −6.24438 | −0.480337 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.01677 | 0.0777540 | ||||||||
\(172\) | −6.32430 | −0.482224 | ||||||||
\(173\) | −21.5086 | −1.63526 | −0.817632 | − | 0.575741i | \(-0.804714\pi\) | ||||
−0.817632 | + | 0.575741i | \(0.804714\pi\) | |||||||
\(174\) | −16.2704 | −1.23346 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.99683 | −0.301273 | ||||||||
\(177\) | −10.9167 | −0.820548 | ||||||||
\(178\) | 34.8256 | 2.61029 | ||||||||
\(179\) | −3.20665 | −0.239676 | −0.119838 | − | 0.992793i | \(-0.538238\pi\) | ||||
−0.119838 | + | 0.992793i | \(0.538238\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.05576 | 0.152803 | 0.0764017 | − | 0.997077i | \(-0.475657\pi\) | ||||
0.0764017 | + | 0.997077i | \(0.475657\pi\) | |||||||
\(182\) | −8.09452 | −0.600006 | ||||||||
\(183\) | −7.46158 | −0.551576 | ||||||||
\(184\) | 4.76153 | 0.351024 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.645232 | 0.0473107 | ||||||||
\(187\) | 17.9246 | 1.31078 | ||||||||
\(188\) | −3.05678 | −0.222938 | ||||||||
\(189\) | −1.38491 | −0.100737 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.25008 | −0.307525 | −0.153762 | − | 0.988108i | \(-0.549139\pi\) | ||||
−0.153762 | + | 0.988108i | \(0.549139\pi\) | |||||||
\(192\) | 13.0405 | 0.941115 | ||||||||
\(193\) | −18.3835 | −1.32327 | −0.661635 | − | 0.749826i | \(-0.730137\pi\) | ||||
−0.661635 | + | 0.749826i | \(0.730137\pi\) | |||||||
\(194\) | 24.6182 | 1.76749 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −15.5346 | −1.10961 | ||||||||
\(197\) | −9.01182 | −0.642065 | −0.321033 | − | 0.947068i | \(-0.604030\pi\) | ||||
−0.321033 | + | 0.947068i | \(0.604030\pi\) | |||||||
\(198\) | 11.6775 | 0.829881 | ||||||||
\(199\) | 24.9219 | 1.76666 | 0.883332 | − | 0.468749i | \(-0.155295\pi\) | ||||
0.883332 | + | 0.468749i | \(0.155295\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.36130 | −0.237088 | ||||||||
\(202\) | 37.2171 | 2.61859 | ||||||||
\(203\) | 10.0204 | 0.703292 | ||||||||
\(204\) | −10.5512 | −0.738732 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −11.0223 | −0.767960 | ||||||||
\(207\) | 2.00367 | 0.139265 | ||||||||
\(208\) | 2.00049 | 0.138709 | ||||||||
\(209\) | 5.27998 | 0.365224 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.2396 | 0.842610 | 0.421305 | − | 0.906919i | \(-0.361572\pi\) | ||||
0.421305 | + | 0.906919i | \(0.361572\pi\) | |||||||
\(212\) | −2.14987 | −0.147653 | ||||||||
\(213\) | −3.94927 | −0.270600 | ||||||||
\(214\) | −23.9439 | −1.63677 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.37640 | −0.161694 | ||||||||
\(217\) | −0.397375 | −0.0269756 | ||||||||
\(218\) | −19.3506 | −1.31059 | ||||||||
\(219\) | −15.0178 | −1.01481 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.97162 | −0.603497 | ||||||||
\(222\) | 10.4337 | 0.700262 | ||||||||
\(223\) | 21.4122 | 1.43387 | 0.716934 | − | 0.697141i | \(-0.245545\pi\) | ||||
0.716934 | + | 0.697141i | \(0.245545\pi\) | |||||||
\(224\) | −8.97918 | −0.599947 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −23.6405 | −1.57254 | ||||||||
\(227\) | −7.59972 | −0.504411 | −0.252206 | − | 0.967674i | \(-0.581156\pi\) | ||||
−0.252206 | + | 0.967674i | \(0.581156\pi\) | |||||||
\(228\) | −3.10803 | −0.205834 | ||||||||
\(229\) | −24.0119 | −1.58675 | −0.793374 | − | 0.608735i | \(-0.791677\pi\) | ||||
−0.793374 | + | 0.608735i | \(0.791677\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.19173 | −0.473181 | ||||||||
\(232\) | 17.1942 | 1.12886 | ||||||||
\(233\) | 13.8785 | 0.909211 | 0.454605 | − | 0.890693i | \(-0.349780\pi\) | ||||
0.454605 | + | 0.890693i | \(0.349780\pi\) | |||||||
\(234\) | −5.84480 | −0.382086 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 33.3699 | 2.17219 | ||||||||
\(237\) | 6.69906 | 0.435150 | ||||||||
\(238\) | 10.7497 | 0.696801 | ||||||||
\(239\) | 4.91814 | 0.318128 | 0.159064 | − | 0.987268i | \(-0.449152\pi\) | ||||
0.159064 | + | 0.987268i | \(0.449152\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.0191 | 1.41838 | 0.709188 | − | 0.705019i | \(-0.249062\pi\) | ||||
0.709188 | + | 0.705019i | \(0.249062\pi\) | |||||||
\(242\) | 35.9041 | 2.30800 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 22.8084 | 1.46016 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.74482 | 0.111245 | ||||||||
\(247\) | −2.64273 | −0.168153 | ||||||||
\(248\) | −0.681866 | −0.0432985 | ||||||||
\(249\) | −10.4990 | −0.665346 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.7608 | −1.24729 | −0.623644 | − | 0.781709i | \(-0.714348\pi\) | ||||
−0.623644 | + | 0.781709i | \(0.714348\pi\) | |||||||
\(252\) | 4.23336 | 0.266677 | ||||||||
\(253\) | 10.4049 | 0.654150 | ||||||||
\(254\) | −27.8018 | −1.74444 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.7022 | −0.668887 | ||||||||
\(257\) | −25.9677 | −1.61982 | −0.809911 | − | 0.586552i | \(-0.800485\pi\) | ||||
−0.809911 | + | 0.586552i | \(0.800485\pi\) | |||||||
\(258\) | 4.65249 | 0.289652 | ||||||||
\(259\) | −6.42572 | −0.399275 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.23539 | 0.447860 | ||||||||
\(262\) | −17.8195 | −1.10090 | ||||||||
\(263\) | 23.5775 | 1.45385 | 0.726926 | − | 0.686716i | \(-0.240948\pi\) | ||||
0.726926 | + | 0.686716i | \(0.240948\pi\) | |||||||
\(264\) | −12.3405 | −0.759503 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.16650 | 0.194151 | ||||||||
\(267\) | −15.4868 | −0.947776 | ||||||||
\(268\) | 10.2747 | 0.627630 | ||||||||
\(269\) | −12.3825 | −0.754977 | −0.377489 | − | 0.926014i | \(-0.623212\pi\) | ||||
−0.377489 | + | 0.926014i | \(0.623212\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.7346 | 1.13804 | 0.569022 | − | 0.822322i | \(-0.307322\pi\) | ||||
0.569022 | + | 0.822322i | \(0.307322\pi\) | |||||||
\(272\) | −2.65670 | −0.161086 | ||||||||
\(273\) | 3.59960 | 0.217858 | ||||||||
\(274\) | 15.7508 | 0.951543 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.12477 | −0.368668 | ||||||||
\(277\) | −8.15990 | −0.490281 | −0.245140 | − | 0.969488i | \(-0.578834\pi\) | ||||
−0.245140 | + | 0.969488i | \(0.578834\pi\) | |||||||
\(278\) | −5.25190 | −0.314988 | ||||||||
\(279\) | −0.286932 | −0.0171782 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.3677 | 1.15538 | 0.577689 | − | 0.816257i | \(-0.303954\pi\) | ||||
0.577689 | + | 0.816257i | \(0.303954\pi\) | |||||||
\(282\) | 2.24873 | 0.133910 | ||||||||
\(283\) | 11.1945 | 0.665446 | 0.332723 | − | 0.943025i | \(-0.392033\pi\) | ||||
0.332723 | + | 0.943025i | \(0.392033\pi\) | |||||||
\(284\) | 12.0720 | 0.716344 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −30.3515 | −1.79472 | ||||||||
\(287\) | −1.07457 | −0.0634298 | ||||||||
\(288\) | −6.48358 | −0.382049 | ||||||||
\(289\) | −5.08547 | −0.299145 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.9476 | −0.641761 | ||||||||
\(292\) | 45.9062 | 2.68645 | ||||||||
\(293\) | 13.7883 | 0.805522 | 0.402761 | − | 0.915305i | \(-0.368051\pi\) | ||||
0.402761 | + | 0.915305i | \(0.368051\pi\) | |||||||
\(294\) | 11.4281 | 0.666500 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −11.0261 | −0.640877 | ||||||||
\(297\) | −5.19292 | −0.301324 | ||||||||
\(298\) | −34.3800 | −1.99158 | ||||||||
\(299\) | −5.20785 | −0.301178 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.86530 | −0.165153 | ||||||||
\(302\) | −34.3285 | −1.97538 | ||||||||
\(303\) | −16.5503 | −0.950789 | ||||||||
\(304\) | −0.782574 | −0.0448837 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 7.76203 | 0.443726 | ||||||||
\(307\) | −14.4636 | −0.825483 | −0.412742 | − | 0.910848i | \(-0.635429\pi\) | ||||
−0.412742 | + | 0.910848i | \(0.635429\pi\) | |||||||
\(308\) | 21.9835 | 1.25263 | ||||||||
\(309\) | 4.90157 | 0.278841 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.67137 | −0.0947747 | −0.0473873 | − | 0.998877i | \(-0.515090\pi\) | ||||
−0.0473873 | + | 0.998877i | \(0.515090\pi\) | |||||||
\(312\) | 6.17664 | 0.349684 | ||||||||
\(313\) | −11.6450 | −0.658212 | −0.329106 | − | 0.944293i | \(-0.606747\pi\) | ||||
−0.329106 | + | 0.944293i | \(0.606747\pi\) | |||||||
\(314\) | 39.9280 | 2.25327 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −20.4775 | −1.15195 | ||||||||
\(317\) | −17.8715 | −1.00376 | −0.501882 | − | 0.864936i | \(-0.667359\pi\) | ||||
−0.501882 | + | 0.864936i | \(0.667359\pi\) | |||||||
\(318\) | 1.58156 | 0.0886892 | ||||||||
\(319\) | 37.5728 | 2.10367 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.6478 | 0.594300 | ||||||||
\(322\) | 6.24000 | 0.347742 | ||||||||
\(323\) | 3.50962 | 0.195280 | ||||||||
\(324\) | 3.05678 | 0.169821 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −21.8527 | −1.21031 | ||||||||
\(327\) | 8.60514 | 0.475865 | ||||||||
\(328\) | −1.84388 | −0.101811 | ||||||||
\(329\) | −1.38491 | −0.0763526 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.3796 | 0.845339 | 0.422669 | − | 0.906284i | \(-0.361093\pi\) | ||||
0.422669 | + | 0.906284i | \(0.361093\pi\) | |||||||
\(332\) | 32.0931 | 1.76134 | ||||||||
\(333\) | −4.63981 | −0.254260 | ||||||||
\(334\) | −31.2402 | −1.70939 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.06592 | 0.0581509 | ||||||||
\(337\) | −23.7793 | −1.29534 | −0.647669 | − | 0.761922i | \(-0.724256\pi\) | ||||
−0.647669 | + | 0.761922i | \(0.724256\pi\) | |||||||
\(338\) | −14.0419 | −0.763780 | ||||||||
\(339\) | 10.5128 | 0.570979 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.49001 | −0.0806888 | ||||||||
\(342\) | 2.28643 | 0.123636 | ||||||||
\(343\) | −16.7325 | −0.903471 | ||||||||
\(344\) | −4.91665 | −0.265088 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −48.3669 | −2.60022 | ||||||||
\(347\) | −0.909029 | −0.0487992 | −0.0243996 | − | 0.999702i | \(-0.507767\pi\) | ||||
−0.0243996 | + | 0.999702i | \(0.507767\pi\) | |||||||
\(348\) | −22.1170 | −1.18559 | ||||||||
\(349\) | −6.80159 | −0.364081 | −0.182041 | − | 0.983291i | \(-0.558270\pi\) | ||||
−0.182041 | + | 0.983291i | \(0.558270\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.59916 | 0.138733 | ||||||||
\(352\) | −33.6687 | −1.79455 | ||||||||
\(353\) | −36.2525 | −1.92952 | −0.964762 | − | 0.263123i | \(-0.915248\pi\) | ||||
−0.964762 | + | 0.263123i | \(0.915248\pi\) | |||||||
\(354\) | −24.5487 | −1.30475 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 47.3397 | 2.50900 | ||||||||
\(357\) | −4.78036 | −0.253003 | ||||||||
\(358\) | −7.21088 | −0.381107 | ||||||||
\(359\) | 16.1026 | 0.849863 | 0.424931 | − | 0.905226i | \(-0.360298\pi\) | ||||
0.424931 | + | 0.905226i | \(0.360298\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.9662 | −0.945589 | ||||||||
\(362\) | 4.62285 | 0.242971 | ||||||||
\(363\) | −15.9664 | −0.838018 | ||||||||
\(364\) | −11.0032 | −0.576723 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −16.7791 | −0.877056 | ||||||||
\(367\) | −16.3763 | −0.854835 | −0.427417 | − | 0.904054i | \(-0.640577\pi\) | ||||
−0.427417 | + | 0.904054i | \(0.640577\pi\) | |||||||
\(368\) | −1.54216 | −0.0803909 | ||||||||
\(369\) | −0.775913 | −0.0403924 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.974023 | −0.0505688 | ||||||||
\(372\) | 0.877087 | 0.0454748 | ||||||||
\(373\) | −15.9249 | −0.824561 | −0.412281 | − | 0.911057i | \(-0.635268\pi\) | ||||
−0.412281 | + | 0.911057i | \(0.635268\pi\) | |||||||
\(374\) | 40.3076 | 2.08426 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.37640 | −0.122554 | ||||||||
\(377\) | −18.8059 | −0.968554 | ||||||||
\(378\) | −3.11429 | −0.160182 | ||||||||
\(379\) | −6.41058 | −0.329289 | −0.164645 | − | 0.986353i | \(-0.552648\pi\) | ||||
−0.164645 | + | 0.986353i | \(0.552648\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.3634 | 0.633394 | ||||||||
\(382\) | −9.55727 | −0.488992 | ||||||||
\(383\) | −37.6109 | −1.92183 | −0.960913 | − | 0.276851i | \(-0.910709\pi\) | ||||
−0.960913 | + | 0.276851i | \(0.910709\pi\) | |||||||
\(384\) | 16.3573 | 0.834731 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −41.3394 | −2.10412 | ||||||||
\(387\) | −2.06895 | −0.105170 | ||||||||
\(388\) | 33.4644 | 1.69890 | ||||||||
\(389\) | 16.4422 | 0.833650 | 0.416825 | − | 0.908987i | \(-0.363143\pi\) | ||||
0.416825 | + | 0.908987i | \(0.363143\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.91615 | 0.349765 | ||||||||
\(392\) | −12.0769 | −0.609977 | ||||||||
\(393\) | 7.92428 | 0.399727 | ||||||||
\(394\) | −20.2651 | −1.02094 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 15.8736 | 0.797678 | ||||||||
\(397\) | −2.48769 | −0.124854 | −0.0624269 | − | 0.998050i | \(-0.519884\pi\) | ||||
−0.0624269 | + | 0.998050i | \(0.519884\pi\) | |||||||
\(398\) | 56.0425 | 2.80915 | ||||||||
\(399\) | −1.40813 | −0.0704947 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −21.0039 | −1.04889 | −0.524443 | − | 0.851445i | \(-0.675726\pi\) | ||||
−0.524443 | + | 0.851445i | \(0.675726\pi\) | |||||||
\(402\) | −7.55865 | −0.376991 | ||||||||
\(403\) | 0.745781 | 0.0371500 | ||||||||
\(404\) | 50.5905 | 2.51697 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 22.5331 | 1.11830 | ||||||||
\(407\) | −24.0942 | −1.19430 | ||||||||
\(408\) | −8.20273 | −0.406096 | ||||||||
\(409\) | 33.9322 | 1.67784 | 0.838920 | − | 0.544254i | \(-0.183187\pi\) | ||||
0.838920 | + | 0.544254i | \(0.183187\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.00433 | −0.345498 | ||||||||
\(412\) | −14.9830 | −0.738160 | ||||||||
\(413\) | 15.1186 | 0.743939 | ||||||||
\(414\) | 4.50571 | 0.221443 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 16.8519 | 0.826230 | ||||||||
\(417\) | 2.33550 | 0.114370 | ||||||||
\(418\) | 11.8732 | 0.580739 | ||||||||
\(419\) | 28.4851 | 1.39159 | 0.695794 | − | 0.718241i | \(-0.255052\pi\) | ||||
0.695794 | + | 0.718241i | \(0.255052\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.1675 | −0.739219 | −0.369610 | − | 0.929187i | \(-0.620509\pi\) | ||||
−0.369610 | + | 0.929187i | \(0.620509\pi\) | |||||||
\(422\) | 27.5236 | 1.33983 | ||||||||
\(423\) | −1.00000 | −0.0486217 | ||||||||
\(424\) | −1.67135 | −0.0811680 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −8.88084 | −0.430278 | ||||||||
\(427\) | 10.3336 | 0.500079 | ||||||||
\(428\) | −32.5478 | −1.57326 | ||||||||
\(429\) | 13.4972 | 0.651651 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −26.7117 | −1.28666 | −0.643328 | − | 0.765591i | \(-0.722447\pi\) | ||||
−0.643328 | + | 0.765591i | \(0.722447\pi\) | |||||||
\(432\) | 0.769670 | 0.0370308 | ||||||||
\(433\) | −6.84811 | −0.329099 | −0.164550 | − | 0.986369i | \(-0.552617\pi\) | ||||
−0.164550 | + | 0.986369i | \(0.552617\pi\) | |||||||
\(434\) | −0.893589 | −0.0428936 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −26.3040 | −1.25973 | ||||||||
\(437\) | 2.03726 | 0.0974555 | ||||||||
\(438\) | −33.7710 | −1.61364 | ||||||||
\(439\) | −29.4001 | −1.40319 | −0.701594 | − | 0.712577i | \(-0.747528\pi\) | ||||
−0.701594 | + | 0.712577i | \(0.747528\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.08202 | −0.242001 | ||||||||
\(442\) | −20.1747 | −0.959615 | ||||||||
\(443\) | 13.5666 | 0.644569 | 0.322285 | − | 0.946643i | \(-0.395549\pi\) | ||||
0.322285 | + | 0.946643i | \(0.395549\pi\) | |||||||
\(444\) | 14.1829 | 0.673089 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 48.1502 | 2.27998 | ||||||||
\(447\) | 15.2887 | 0.723129 | ||||||||
\(448\) | −18.0599 | −0.853250 | ||||||||
\(449\) | −0.690194 | −0.0325723 | −0.0162861 | − | 0.999867i | \(-0.505184\pi\) | ||||
−0.0162861 | + | 0.999867i | \(0.505184\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.02925 | −0.189730 | ||||||||
\(452\) | −32.1354 | −1.51152 | ||||||||
\(453\) | 15.2657 | 0.717246 | ||||||||
\(454\) | −17.0897 | −0.802059 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.41625 | −0.113151 | ||||||||
\(457\) | −20.0644 | −0.938574 | −0.469287 | − | 0.883046i | \(-0.655489\pi\) | ||||
−0.469287 | + | 0.883046i | \(0.655489\pi\) | |||||||
\(458\) | −53.9961 | −2.52307 | ||||||||
\(459\) | −3.45174 | −0.161114 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.0748678 | −0.00348694 | −0.00174347 | − | 0.999998i | \(-0.500555\pi\) | ||||
−0.00174347 | + | 0.999998i | \(0.500555\pi\) | |||||||
\(462\) | −16.1722 | −0.752400 | ||||||||
\(463\) | −13.1562 | −0.611423 | −0.305711 | − | 0.952124i | \(-0.598894\pi\) | ||||
−0.305711 | + | 0.952124i | \(0.598894\pi\) | |||||||
\(464\) | −5.56886 | −0.258528 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 31.2090 | 1.44573 | ||||||||
\(467\) | −24.1841 | −1.11911 | −0.559553 | − | 0.828795i | \(-0.689027\pi\) | ||||
−0.559553 | + | 0.828795i | \(0.689027\pi\) | |||||||
\(468\) | −7.94504 | −0.367260 | ||||||||
\(469\) | 4.65510 | 0.214952 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.7558 | −0.818146 | ||||||||
\(472\) | 25.9424 | 1.19410 | ||||||||
\(473\) | −10.7439 | −0.494003 | ||||||||
\(474\) | 15.0644 | 0.691929 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 14.6125 | 0.669762 | ||||||||
\(477\) | −0.703311 | −0.0322024 | ||||||||
\(478\) | 11.0596 | 0.505852 | ||||||||
\(479\) | −37.3687 | −1.70742 | −0.853709 | − | 0.520751i | \(-0.825652\pi\) | ||||
−0.853709 | + | 0.520751i | \(0.825652\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.0596 | 0.549870 | ||||||||
\(482\) | 49.5150 | 2.25535 | ||||||||
\(483\) | −2.77490 | −0.126262 | ||||||||
\(484\) | 48.8057 | 2.21844 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.24873 | −0.102004 | ||||||||
\(487\) | 2.66731 | 0.120867 | 0.0604337 | − | 0.998172i | \(-0.480752\pi\) | ||||
0.0604337 | + | 0.998172i | \(0.480752\pi\) | |||||||
\(488\) | 17.7317 | 0.802678 | ||||||||
\(489\) | 9.71780 | 0.439454 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.9997 | −1.03796 | −0.518981 | − | 0.854786i | \(-0.673689\pi\) | ||||
−0.518981 | + | 0.854786i | \(0.673689\pi\) | |||||||
\(492\) | 2.37179 | 0.106929 | ||||||||
\(493\) | 24.9747 | 1.12480 | ||||||||
\(494\) | −5.94279 | −0.267379 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.220843 | 0.00991614 | ||||||||
\(497\) | 5.46939 | 0.245336 | ||||||||
\(498\) | −23.6094 | −1.05796 | ||||||||
\(499\) | 32.9237 | 1.47387 | 0.736933 | − | 0.675965i | \(-0.236273\pi\) | ||||
0.736933 | + | 0.675965i | \(0.236273\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.8924 | 0.620666 | ||||||||
\(502\) | −44.4366 | −1.98330 | ||||||||
\(503\) | 27.2034 | 1.21294 | 0.606469 | − | 0.795107i | \(-0.292585\pi\) | ||||
0.606469 | + | 0.795107i | \(0.292585\pi\) | |||||||
\(504\) | 3.29111 | 0.146597 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 23.3978 | 1.04016 | ||||||||
\(507\) | 6.24438 | 0.277323 | ||||||||
\(508\) | −37.7920 | −1.67675 | ||||||||
\(509\) | 18.2534 | 0.809068 | 0.404534 | − | 0.914523i | \(-0.367434\pi\) | ||||
0.404534 | + | 0.914523i | \(0.367434\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.7984 | 0.920065 | ||||||||
\(512\) | 8.64831 | 0.382205 | ||||||||
\(513\) | −1.01677 | −0.0448913 | ||||||||
\(514\) | −58.3944 | −2.57566 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 6.32430 | 0.278412 | ||||||||
\(517\) | −5.19292 | −0.228384 | ||||||||
\(518\) | −14.4497 | −0.634884 | ||||||||
\(519\) | 21.5086 | 0.944121 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −28.6237 | −1.25403 | −0.627013 | − | 0.779009i | \(-0.715723\pi\) | ||||
−0.627013 | + | 0.779009i | \(0.715723\pi\) | |||||||
\(522\) | 16.2704 | 0.712137 | ||||||||
\(523\) | −40.7455 | −1.78168 | −0.890838 | − | 0.454320i | \(-0.849882\pi\) | ||||
−0.890838 | + | 0.454320i | \(0.849882\pi\) | |||||||
\(524\) | −24.2227 | −1.05818 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 53.0194 | 2.31176 | ||||||||
\(527\) | −0.990416 | −0.0431432 | ||||||||
\(528\) | 3.99683 | 0.173940 | ||||||||
\(529\) | −18.9853 | −0.825448 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.9167 | 0.473744 | ||||||||
\(532\) | 4.30434 | 0.186617 | ||||||||
\(533\) | 2.01672 | 0.0873538 | ||||||||
\(534\) | −34.8256 | −1.50705 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 7.98780 | 0.345020 | ||||||||
\(537\) | 3.20665 | 0.138377 | ||||||||
\(538\) | −27.8450 | −1.20048 | ||||||||
\(539\) | −26.3905 | −1.13672 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.5428 | −0.711231 | −0.355615 | − | 0.934632i | \(-0.615729\pi\) | ||||
−0.355615 | + | 0.934632i | \(0.615729\pi\) | |||||||
\(542\) | 42.1289 | 1.80959 | ||||||||
\(543\) | −2.05576 | −0.0882211 | ||||||||
\(544\) | −22.3797 | −0.959520 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 8.09452 | 0.346414 | ||||||||
\(547\) | 27.4024 | 1.17164 | 0.585820 | − | 0.810441i | \(-0.300772\pi\) | ||||
0.585820 | + | 0.810441i | \(0.300772\pi\) | |||||||
\(548\) | 21.4107 | 0.914619 | ||||||||
\(549\) | 7.46158 | 0.318453 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.35670 | 0.313406 | ||||||||
\(552\) | −4.76153 | −0.202664 | ||||||||
\(553\) | −9.27759 | −0.394523 | ||||||||
\(554\) | −18.3494 | −0.779591 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.13910 | −0.302765 | ||||||||
\(557\) | −0.716768 | −0.0303704 | −0.0151852 | − | 0.999885i | \(-0.504834\pi\) | ||||
−0.0151852 | + | 0.999885i | \(0.504834\pi\) | |||||||
\(558\) | −0.645232 | −0.0273148 | ||||||||
\(559\) | 5.37751 | 0.227445 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −17.9246 | −0.756778 | ||||||||
\(562\) | 43.5526 | 1.83716 | ||||||||
\(563\) | −25.7954 | −1.08715 | −0.543573 | − | 0.839362i | \(-0.682929\pi\) | ||||
−0.543573 | + | 0.839362i | \(0.682929\pi\) | |||||||
\(564\) | 3.05678 | 0.128714 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 25.1735 | 1.05812 | ||||||||
\(567\) | 1.38491 | 0.0581608 | ||||||||
\(568\) | 9.38506 | 0.393788 | ||||||||
\(569\) | 45.3234 | 1.90005 | 0.950027 | − | 0.312167i | \(-0.101055\pi\) | ||||
0.950027 | + | 0.312167i | \(0.101055\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.7434 | 1.32842 | 0.664209 | − | 0.747547i | \(-0.268768\pi\) | ||||
0.664209 | + | 0.747547i | \(0.268768\pi\) | |||||||
\(572\) | −41.2580 | −1.72508 | ||||||||
\(573\) | 4.25008 | 0.177550 | ||||||||
\(574\) | −2.41641 | −0.100859 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −13.0405 | −0.543353 | ||||||||
\(577\) | 2.06921 | 0.0861425 | 0.0430713 | − | 0.999072i | \(-0.486286\pi\) | ||||
0.0430713 | + | 0.999072i | \(0.486286\pi\) | |||||||
\(578\) | −11.4358 | −0.475668 | ||||||||
\(579\) | 18.3835 | 0.763991 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.5402 | 0.603227 | ||||||||
\(582\) | −24.6182 | −1.02046 | ||||||||
\(583\) | −3.65224 | −0.151260 | ||||||||
\(584\) | 35.6884 | 1.47680 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 31.0062 | 1.28085 | ||||||||
\(587\) | 46.6127 | 1.92391 | 0.961957 | − | 0.273202i | \(-0.0880826\pi\) | ||||
0.961957 | + | 0.273202i | \(0.0880826\pi\) | |||||||
\(588\) | 15.5346 | 0.640636 | ||||||||
\(589\) | −0.291743 | −0.0120210 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.01182 | 0.370697 | ||||||||
\(592\) | 3.57112 | 0.146772 | ||||||||
\(593\) | −37.7442 | −1.54997 | −0.774985 | − | 0.631980i | \(-0.782243\pi\) | ||||
−0.774985 | + | 0.631980i | \(0.782243\pi\) | |||||||
\(594\) | −11.6775 | −0.479132 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −46.7340 | −1.91430 | ||||||||
\(597\) | −24.9219 | −1.01998 | ||||||||
\(598\) | −11.7110 | −0.478900 | ||||||||
\(599\) | −16.6614 | −0.680765 | −0.340382 | − | 0.940287i | \(-0.610556\pi\) | ||||
−0.340382 | + | 0.940287i | \(0.610556\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.6432 | 0.842052 | 0.421026 | − | 0.907049i | \(-0.361670\pi\) | ||||
0.421026 | + | 0.907049i | \(0.361670\pi\) | |||||||
\(602\) | −6.44329 | −0.262609 | ||||||||
\(603\) | 3.36130 | 0.136883 | ||||||||
\(604\) | −46.6639 | −1.89873 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −37.2171 | −1.51184 | ||||||||
\(607\) | −11.5930 | −0.470545 | −0.235273 | − | 0.971929i | \(-0.575598\pi\) | ||||
−0.235273 | + | 0.971929i | \(0.575598\pi\) | |||||||
\(608\) | −6.59229 | −0.267353 | ||||||||
\(609\) | −10.0204 | −0.406046 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.59916 | 0.105151 | ||||||||
\(612\) | 10.5512 | 0.426507 | ||||||||
\(613\) | 14.6236 | 0.590642 | 0.295321 | − | 0.955398i | \(-0.404573\pi\) | ||||
0.295321 | + | 0.955398i | \(0.404573\pi\) | |||||||
\(614\) | −32.5248 | −1.31259 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 17.0904 | 0.688593 | ||||||||
\(617\) | −18.7899 | −0.756452 | −0.378226 | − | 0.925713i | \(-0.623466\pi\) | ||||
−0.378226 | + | 0.925713i | \(0.623466\pi\) | |||||||
\(618\) | 11.0223 | 0.443382 | ||||||||
\(619\) | 18.5086 | 0.743923 | 0.371961 | − | 0.928248i | \(-0.378685\pi\) | ||||
0.371961 | + | 0.928248i | \(0.378685\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.00367 | −0.0804045 | ||||||||
\(622\) | −3.75845 | −0.150700 | ||||||||
\(623\) | 21.4478 | 0.859289 | ||||||||
\(624\) | −2.00049 | −0.0800838 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −26.1863 | −1.04662 | ||||||||
\(627\) | −5.27998 | −0.210862 | ||||||||
\(628\) | 54.2756 | 2.16583 | ||||||||
\(629\) | −16.0154 | −0.638577 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.28725 | 0.210482 | 0.105241 | − | 0.994447i | \(-0.466439\pi\) | ||||
0.105241 | + | 0.994447i | \(0.466439\pi\) | |||||||
\(632\) | −15.9197 | −0.633250 | ||||||||
\(633\) | −12.2396 | −0.486481 | ||||||||
\(634\) | −40.1881 | −1.59607 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.14987 | 0.0852477 | ||||||||
\(637\) | 13.2090 | 0.523359 | ||||||||
\(638\) | 84.4910 | 3.34503 | ||||||||
\(639\) | 3.94927 | 0.156231 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.4627 | −0.966217 | −0.483108 | − | 0.875561i | \(-0.660492\pi\) | ||||
−0.483108 | + | 0.875561i | \(0.660492\pi\) | |||||||
\(642\) | 23.9439 | 0.944990 | ||||||||
\(643\) | −11.0093 | −0.434166 | −0.217083 | − | 0.976153i | \(-0.569654\pi\) | ||||
−0.217083 | + | 0.976153i | \(0.569654\pi\) | |||||||
\(644\) | 8.48226 | 0.334248 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.89217 | 0.310513 | ||||||||
\(647\) | 6.22989 | 0.244922 | 0.122461 | − | 0.992473i | \(-0.460921\pi\) | ||||
0.122461 | + | 0.992473i | \(0.460921\pi\) | |||||||
\(648\) | 2.37640 | 0.0933539 | ||||||||
\(649\) | 56.6895 | 2.22526 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.397375 | 0.0155744 | ||||||||
\(652\) | −29.7051 | −1.16334 | ||||||||
\(653\) | 31.9087 | 1.24868 | 0.624342 | − | 0.781151i | \(-0.285367\pi\) | ||||
0.624342 | + | 0.781151i | \(0.285367\pi\) | |||||||
\(654\) | 19.3506 | 0.756669 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.597197 | 0.0233166 | ||||||||
\(657\) | 15.0178 | 0.585901 | ||||||||
\(658\) | −3.11429 | −0.121408 | ||||||||
\(659\) | 40.4861 | 1.57712 | 0.788558 | − | 0.614961i | \(-0.210828\pi\) | ||||
0.788558 | + | 0.614961i | \(0.210828\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −48.1092 | −1.87123 | −0.935616 | − | 0.353019i | \(-0.885155\pi\) | ||||
−0.935616 | + | 0.353019i | \(0.885155\pi\) | |||||||
\(662\) | 34.5845 | 1.34417 | ||||||||
\(663\) | 8.97162 | 0.348429 | ||||||||
\(664\) | 24.9498 | 0.968241 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −10.4337 | −0.404297 | ||||||||
\(667\) | 14.4973 | 0.561339 | ||||||||
\(668\) | −42.4659 | −1.64306 | ||||||||
\(669\) | −21.4122 | −0.827844 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 38.7474 | 1.49583 | ||||||||
\(672\) | 8.97918 | 0.346380 | ||||||||
\(673\) | 41.7722 | 1.61020 | 0.805100 | − | 0.593140i | \(-0.202112\pi\) | ||||
0.805100 | + | 0.593140i | \(0.202112\pi\) | |||||||
\(674\) | −53.4731 | −2.05971 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −19.0877 | −0.734142 | ||||||||
\(677\) | 4.47192 | 0.171870 | 0.0859350 | − | 0.996301i | \(-0.472612\pi\) | ||||
0.0859350 | + | 0.996301i | \(0.472612\pi\) | |||||||
\(678\) | 23.6405 | 0.907909 | ||||||||
\(679\) | 15.1615 | 0.581844 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.59972 | 0.291222 | ||||||||
\(682\) | −3.35064 | −0.128303 | ||||||||
\(683\) | 39.7016 | 1.51914 | 0.759570 | − | 0.650425i | \(-0.225409\pi\) | ||||
0.759570 | + | 0.650425i | \(0.225409\pi\) | |||||||
\(684\) | 3.10803 | 0.118838 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −37.6269 | −1.43660 | ||||||||
\(687\) | 24.0119 | 0.916109 | ||||||||
\(688\) | 1.59240 | 0.0607099 | ||||||||
\(689\) | 1.82802 | 0.0696419 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33.1679 | −1.26177 | −0.630883 | − | 0.775878i | \(-0.717307\pi\) | ||||
−0.630883 | + | 0.775878i | \(0.717307\pi\) | |||||||
\(692\) | −65.7468 | −2.49932 | ||||||||
\(693\) | 7.19173 | 0.273191 | ||||||||
\(694\) | −2.04416 | −0.0775952 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −17.1942 | −0.651745 | ||||||||
\(697\) | −2.67825 | −0.101446 | ||||||||
\(698\) | −15.2949 | −0.578922 | ||||||||
\(699\) | −13.8785 | −0.524933 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.4394 | −0.545367 | −0.272683 | − | 0.962104i | \(-0.587911\pi\) | ||||
−0.272683 | + | 0.962104i | \(0.587911\pi\) | |||||||
\(702\) | 5.84480 | 0.220598 | ||||||||
\(703\) | −4.71760 | −0.177928 | ||||||||
\(704\) | −67.7181 | −2.55222 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −81.5220 | −3.06812 | ||||||||
\(707\) | 22.9207 | 0.862020 | ||||||||
\(708\) | −33.3699 | −1.25412 | ||||||||
\(709\) | −20.0737 | −0.753885 | −0.376943 | − | 0.926237i | \(-0.623025\pi\) | ||||
−0.376943 | + | 0.926237i | \(0.623025\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.69906 | −0.251234 | ||||||||
\(712\) | 36.8029 | 1.37925 | ||||||||
\(713\) | −0.574917 | −0.0215308 | ||||||||
\(714\) | −10.7497 | −0.402298 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −9.80201 | −0.366318 | ||||||||
\(717\) | −4.91814 | −0.183671 | ||||||||
\(718\) | 36.2104 | 1.35136 | ||||||||
\(719\) | −13.6562 | −0.509288 | −0.254644 | − | 0.967035i | \(-0.581958\pi\) | ||||
−0.254644 | + | 0.967035i | \(0.581958\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.78824 | −0.252807 | ||||||||
\(722\) | −40.4011 | −1.50357 | ||||||||
\(723\) | −22.0191 | −0.818900 | ||||||||
\(724\) | 6.28400 | 0.233543 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −35.9041 | −1.33253 | ||||||||
\(727\) | −12.6002 | −0.467315 | −0.233658 | − | 0.972319i | \(-0.575069\pi\) | ||||
−0.233658 | + | 0.972319i | \(0.575069\pi\) | |||||||
\(728\) | −8.55410 | −0.317036 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.14147 | −0.264137 | ||||||||
\(732\) | −22.8084 | −0.843022 | ||||||||
\(733\) | −41.9299 | −1.54872 | −0.774359 | − | 0.632747i | \(-0.781927\pi\) | ||||
−0.774359 | + | 0.632747i | \(0.781927\pi\) | |||||||
\(734\) | −36.8258 | −1.35926 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −12.9910 | −0.478853 | ||||||||
\(737\) | 17.4549 | 0.642961 | ||||||||
\(738\) | −1.74482 | −0.0642276 | ||||||||
\(739\) | 28.3150 | 1.04158 | 0.520792 | − | 0.853683i | \(-0.325637\pi\) | ||||
0.520792 | + | 0.853683i | \(0.325637\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.64273 | 0.0970833 | ||||||||
\(742\) | −2.19031 | −0.0804089 | ||||||||
\(743\) | −19.5904 | −0.718702 | −0.359351 | − | 0.933202i | \(-0.617002\pi\) | ||||
−0.359351 | + | 0.933202i | \(0.617002\pi\) | |||||||
\(744\) | 0.681866 | 0.0249984 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −35.8108 | −1.31113 | ||||||||
\(747\) | 10.4990 | 0.384138 | ||||||||
\(748\) | 54.7916 | 2.00338 | ||||||||
\(749\) | −14.7462 | −0.538814 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.1807 | 0.699914 | 0.349957 | − | 0.936766i | \(-0.386196\pi\) | ||||
0.349957 | + | 0.936766i | \(0.386196\pi\) | |||||||
\(752\) | 0.769670 | 0.0280670 | ||||||||
\(753\) | 19.7608 | 0.720122 | ||||||||
\(754\) | −42.2894 | −1.54009 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.23336 | −0.153966 | ||||||||
\(757\) | 37.1406 | 1.34990 | 0.674948 | − | 0.737865i | \(-0.264166\pi\) | ||||
0.674948 | + | 0.737865i | \(0.264166\pi\) | |||||||
\(758\) | −14.4157 | −0.523600 | ||||||||
\(759\) | −10.4049 | −0.377674 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.66892 | 0.350498 | 0.175249 | − | 0.984524i | \(-0.443927\pi\) | ||||
0.175249 | + | 0.984524i | \(0.443927\pi\) | |||||||
\(762\) | 27.8018 | 1.00715 | ||||||||
\(763\) | −11.9174 | −0.431437 | ||||||||
\(764\) | −12.9915 | −0.470017 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −84.5766 | −3.05588 | ||||||||
\(767\) | −28.3742 | −1.02453 | ||||||||
\(768\) | 10.7022 | 0.386182 | ||||||||
\(769\) | 28.3930 | 1.02388 | 0.511938 | − | 0.859022i | \(-0.328928\pi\) | ||||
0.511938 | + | 0.859022i | \(0.328928\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 25.9677 | 0.935205 | ||||||||
\(772\) | −56.1941 | −2.02247 | ||||||||
\(773\) | 22.3138 | 0.802573 | 0.401286 | − | 0.915953i | \(-0.368563\pi\) | ||||
0.401286 | + | 0.915953i | \(0.368563\pi\) | |||||||
\(774\) | −4.65249 | −0.167230 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 26.0160 | 0.933919 | ||||||||
\(777\) | 6.42572 | 0.230522 | ||||||||
\(778\) | 36.9739 | 1.32558 | ||||||||
\(779\) | −0.788921 | −0.0282660 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.5082 | 0.733843 | ||||||||
\(782\) | 15.5525 | 0.556158 | ||||||||
\(783\) | −7.23539 | −0.258572 | ||||||||
\(784\) | 3.91148 | 0.139696 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 17.8195 | 0.635602 | ||||||||
\(787\) | −31.9455 | −1.13874 | −0.569368 | − | 0.822083i | \(-0.692812\pi\) | ||||
−0.569368 | + | 0.822083i | \(0.692812\pi\) | |||||||
\(788\) | −27.5471 | −0.981325 | ||||||||
\(789\) | −23.5775 | −0.839382 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.5593 | −0.517671 | ||||||||
\(792\) | 12.3405 | 0.438499 | ||||||||
\(793\) | −19.3938 | −0.688695 | ||||||||
\(794\) | −5.59414 | −0.198529 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 76.1805 | 2.70015 | ||||||||
\(797\) | −10.6664 | −0.377822 | −0.188911 | − | 0.981994i | \(-0.560496\pi\) | ||||
−0.188911 | + | 0.981994i | \(0.560496\pi\) | |||||||
\(798\) | −3.16650 | −0.112093 | ||||||||
\(799\) | −3.45174 | −0.122114 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.4868 | 0.547199 | ||||||||
\(802\) | −47.2321 | −1.66782 | ||||||||
\(803\) | 77.9864 | 2.75208 | ||||||||
\(804\) | −10.2747 | −0.362362 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.67706 | 0.0590719 | ||||||||
\(807\) | 12.3825 | 0.435886 | ||||||||
\(808\) | 39.3301 | 1.38363 | ||||||||
\(809\) | −38.8845 | −1.36711 | −0.683554 | − | 0.729900i | \(-0.739566\pi\) | ||||
−0.683554 | + | 0.729900i | \(0.739566\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.3259 | −0.362591 | −0.181296 | − | 0.983429i | \(-0.558029\pi\) | ||||
−0.181296 | + | 0.983429i | \(0.558029\pi\) | |||||||
\(812\) | 30.6300 | 1.07490 | ||||||||
\(813\) | −18.7346 | −0.657050 | ||||||||
\(814\) | −54.1812 | −1.89905 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.65670 | 0.0930032 | ||||||||
\(817\) | −2.10363 | −0.0735968 | ||||||||
\(818\) | 76.3043 | 2.66792 | ||||||||
\(819\) | −3.59960 | −0.125780 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.3767 | 0.397050 | 0.198525 | − | 0.980096i | \(-0.436385\pi\) | ||||
0.198525 | + | 0.980096i | \(0.436385\pi\) | |||||||
\(822\) | −15.7508 | −0.549373 | ||||||||
\(823\) | 12.9241 | 0.450506 | 0.225253 | − | 0.974300i | \(-0.427679\pi\) | ||||
0.225253 | + | 0.974300i | \(0.427679\pi\) | |||||||
\(824\) | −11.6481 | −0.405781 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 33.9977 | 1.18293 | ||||||||
\(827\) | −45.8003 | −1.59263 | −0.796316 | − | 0.604880i | \(-0.793221\pi\) | ||||
−0.796316 | + | 0.604880i | \(0.793221\pi\) | |||||||
\(828\) | 6.12477 | 0.212850 | ||||||||
\(829\) | 0.234799 | 0.00815491 | 0.00407746 | − | 0.999992i | \(-0.498702\pi\) | ||||
0.00407746 | + | 0.999992i | \(0.498702\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.15990 | 0.283064 | ||||||||
\(832\) | 33.8942 | 1.17507 | ||||||||
\(833\) | −17.5418 | −0.607789 | ||||||||
\(834\) | 5.25190 | 0.181858 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 16.1397 | 0.558204 | ||||||||
\(837\) | 0.286932 | 0.00991782 | ||||||||
\(838\) | 64.0553 | 2.21275 | ||||||||
\(839\) | 30.7648 | 1.06212 | 0.531060 | − | 0.847334i | \(-0.321794\pi\) | ||||
0.531060 | + | 0.847334i | \(0.321794\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.3509 | 0.805204 | ||||||||
\(842\) | −34.1076 | −1.17543 | ||||||||
\(843\) | −19.3677 | −0.667058 | ||||||||
\(844\) | 37.4138 | 1.28784 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.24873 | −0.0773129 | ||||||||
\(847\) | 22.1120 | 0.759778 | ||||||||
\(848\) | 0.541318 | 0.0185889 | ||||||||
\(849\) | −11.1945 | −0.384196 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.29665 | −0.318685 | ||||||||
\(852\) | −12.0720 | −0.413581 | ||||||||
\(853\) | 24.8759 | 0.851736 | 0.425868 | − | 0.904785i | \(-0.359969\pi\) | ||||
0.425868 | + | 0.904785i | \(0.359969\pi\) | |||||||
\(854\) | 23.2375 | 0.795171 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −25.3034 | −0.864851 | ||||||||
\(857\) | 49.5602 | 1.69294 | 0.846472 | − | 0.532433i | \(-0.178722\pi\) | ||||
0.846472 | + | 0.532433i | \(0.178722\pi\) | |||||||
\(858\) | 30.3515 | 1.03618 | ||||||||
\(859\) | 44.0603 | 1.50332 | 0.751658 | − | 0.659553i | \(-0.229254\pi\) | ||||
0.751658 | + | 0.659553i | \(0.229254\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.07457 | 0.0366212 | ||||||||
\(862\) | −60.0673 | −2.04590 | ||||||||
\(863\) | −30.8561 | −1.05035 | −0.525177 | − | 0.850993i | \(-0.676001\pi\) | ||||
−0.525177 | + | 0.850993i | \(0.676001\pi\) | |||||||
\(864\) | 6.48358 | 0.220576 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −15.3995 | −0.523298 | ||||||||
\(867\) | 5.08547 | 0.172712 | ||||||||
\(868\) | −1.21469 | −0.0412292 | ||||||||
\(869\) | −34.7876 | −1.18009 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.73654 | −0.296026 | ||||||||
\(872\) | −20.4493 | −0.692500 | ||||||||
\(873\) | 10.9476 | 0.370521 | ||||||||
\(874\) | 4.58125 | 0.154963 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −45.9062 | −1.55103 | ||||||||
\(877\) | −7.78595 | −0.262913 | −0.131456 | − | 0.991322i | \(-0.541965\pi\) | ||||
−0.131456 | + | 0.991322i | \(0.541965\pi\) | |||||||
\(878\) | −66.1128 | −2.23120 | ||||||||
\(879\) | −13.7883 | −0.465068 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.5411 | −0.355139 | −0.177569 | − | 0.984108i | \(-0.556823\pi\) | ||||
−0.177569 | + | 0.984108i | \(0.556823\pi\) | |||||||
\(882\) | −11.4281 | −0.384804 | ||||||||
\(883\) | 12.9527 | 0.435893 | 0.217946 | − | 0.975961i | \(-0.430064\pi\) | ||||
0.217946 | + | 0.975961i | \(0.430064\pi\) | |||||||
\(884\) | −27.4243 | −0.922377 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 30.5076 | 1.02492 | ||||||||
\(887\) | −4.04891 | −0.135949 | −0.0679745 | − | 0.997687i | \(-0.521654\pi\) | ||||
−0.0679745 | + | 0.997687i | \(0.521654\pi\) | |||||||
\(888\) | 11.0261 | 0.370010 | ||||||||
\(889\) | −17.1221 | −0.574258 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.19292 | 0.173969 | ||||||||
\(892\) | 65.4523 | 2.19151 | ||||||||
\(893\) | −1.01677 | −0.0340248 | ||||||||
\(894\) | 34.3800 | 1.14984 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −22.6534 | −0.756797 | ||||||||
\(897\) | 5.20785 | 0.173885 | ||||||||
\(898\) | −1.55206 | −0.0517929 | ||||||||
\(899\) | −2.07607 | −0.0692407 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.42765 | −0.0808768 | ||||||||
\(902\) | −9.06069 | −0.301688 | ||||||||
\(903\) | 2.86530 | 0.0953513 | ||||||||
\(904\) | −24.9827 | −0.830914 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 34.3285 | 1.14049 | ||||||||
\(907\) | 20.8645 | 0.692794 | 0.346397 | − | 0.938088i | \(-0.387405\pi\) | ||||
0.346397 | + | 0.938088i | \(0.387405\pi\) | |||||||
\(908\) | −23.2306 | −0.770936 | ||||||||
\(909\) | 16.5503 | 0.548938 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.0423 | 0.498372 | 0.249186 | − | 0.968456i | \(-0.419837\pi\) | ||||
0.249186 | + | 0.968456i | \(0.419837\pi\) | |||||||
\(912\) | 0.782574 | 0.0259136 | ||||||||
\(913\) | 54.5204 | 1.80436 | ||||||||
\(914\) | −45.1194 | −1.49242 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −73.3989 | −2.42517 | ||||||||
\(917\) | −10.9744 | −0.362407 | ||||||||
\(918\) | −7.76203 | −0.256185 | ||||||||
\(919\) | −18.6661 | −0.615737 | −0.307869 | − | 0.951429i | \(-0.599616\pi\) | ||||
−0.307869 | + | 0.951429i | \(0.599616\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.4636 | 0.476593 | ||||||||
\(922\) | −0.168357 | −0.00554455 | ||||||||
\(923\) | −10.2648 | −0.337869 | ||||||||
\(924\) | −21.9835 | −0.723204 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −29.5848 | −0.972217 | ||||||||
\(927\) | −4.90157 | −0.160989 | ||||||||
\(928\) | −46.9113 | −1.53994 | ||||||||
\(929\) | −37.1223 | −1.21794 | −0.608971 | − | 0.793192i | \(-0.708418\pi\) | ||||
−0.608971 | + | 0.793192i | \(0.708418\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.16723 | −0.169349 | ||||||||
\(932\) | 42.4235 | 1.38963 | ||||||||
\(933\) | 1.67137 | 0.0547182 | ||||||||
\(934\) | −54.3834 | −1.77948 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6.17664 | −0.201890 | ||||||||
\(937\) | 39.0704 | 1.27638 | 0.638188 | − | 0.769881i | \(-0.279684\pi\) | ||||
0.638188 | + | 0.769881i | \(0.279684\pi\) | |||||||
\(938\) | 10.4680 | 0.341794 | ||||||||
\(939\) | 11.6450 | 0.380019 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −50.8417 | −1.65739 | −0.828697 | − | 0.559698i | \(-0.810917\pi\) | ||||
−0.828697 | + | 0.559698i | \(0.810917\pi\) | |||||||
\(942\) | −39.9280 | −1.30093 | ||||||||
\(943\) | −1.55467 | −0.0506271 | ||||||||
\(944\) | −8.40225 | −0.273470 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −24.1600 | −0.785510 | ||||||||
\(947\) | 2.25640 | 0.0733231 | 0.0366615 | − | 0.999328i | \(-0.488328\pi\) | ||||
0.0366615 | + | 0.999328i | \(0.488328\pi\) | |||||||
\(948\) | 20.4775 | 0.665079 | ||||||||
\(949\) | −39.0337 | −1.26709 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 17.8715 | 0.579523 | ||||||||
\(952\) | 11.3601 | 0.368181 | ||||||||
\(953\) | −22.2597 | −0.721064 | −0.360532 | − | 0.932747i | \(-0.617405\pi\) | ||||
−0.360532 | + | 0.932747i | \(0.617405\pi\) | |||||||
\(954\) | −1.58156 | −0.0512048 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 15.0336 | 0.486223 | ||||||||
\(957\) | −37.5728 | −1.21456 | ||||||||
\(958\) | −84.0319 | −2.71495 | ||||||||
\(959\) | 9.70037 | 0.313241 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9177 | −0.997344 | ||||||||
\(962\) | 27.1188 | 0.874344 | ||||||||
\(963\) | −10.6478 | −0.343119 | ||||||||
\(964\) | 67.3075 | 2.16783 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −6.24000 | −0.200769 | ||||||||
\(967\) | 54.3893 | 1.74904 | 0.874521 | − | 0.484988i | \(-0.161176\pi\) | ||||
0.874521 | + | 0.484988i | \(0.161176\pi\) | |||||||
\(968\) | 37.9426 | 1.21952 | ||||||||
\(969\) | −3.50962 | −0.112745 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.5812 | 0.692573 | 0.346286 | − | 0.938129i | \(-0.387443\pi\) | ||||
0.346286 | + | 0.938129i | \(0.387443\pi\) | |||||||
\(972\) | −3.05678 | −0.0980462 | ||||||||
\(973\) | −3.23446 | −0.103692 | ||||||||
\(974\) | 5.99805 | 0.192190 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.74296 | −0.183828 | ||||||||
\(977\) | −23.6500 | −0.756631 | −0.378315 | − | 0.925677i | \(-0.623497\pi\) | ||||
−0.378315 | + | 0.925677i | \(0.623497\pi\) | |||||||
\(978\) | 21.8527 | 0.698772 | ||||||||
\(979\) | 80.4216 | 2.57029 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.60514 | −0.274741 | ||||||||
\(982\) | −51.7201 | −1.65045 | ||||||||
\(983\) | −5.74522 | −0.183244 | −0.0916220 | − | 0.995794i | \(-0.529205\pi\) | ||||
−0.0916220 | + | 0.995794i | \(0.529205\pi\) | |||||||
\(984\) | 1.84388 | 0.0587808 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 56.1613 | 1.78854 | ||||||||
\(987\) | 1.38491 | 0.0440822 | ||||||||
\(988\) | −8.07825 | −0.257003 | ||||||||
\(989\) | −4.14548 | −0.131819 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −43.4775 | −1.38111 | −0.690555 | − | 0.723280i | \(-0.742634\pi\) | ||||
−0.690555 | + | 0.723280i | \(0.742634\pi\) | |||||||
\(992\) | 1.86035 | 0.0590661 | ||||||||
\(993\) | −15.3796 | −0.488057 | ||||||||
\(994\) | 12.2992 | 0.390106 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −32.0931 | −1.01691 | ||||||||
\(997\) | 34.3858 | 1.08901 | 0.544505 | − | 0.838758i | \(-0.316717\pi\) | ||||
0.544505 | + | 0.838758i | \(0.316717\pi\) | |||||||
\(998\) | 74.0364 | 2.34358 | ||||||||
\(999\) | 4.63981 | 0.146797 |
(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 | 3525.2.a.bh.1.12 | 13 | ||
5.2 | odd | 4 | 705.2.c.c.424.22 | yes | 26 | ||
5.3 | odd | 4 | 705.2.c.c.424.5 | ✓ | 26 | ||
5.4 | even | 2 | 3525.2.a.bi.1.2 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
705.2.c.c.424.5 | ✓ | 26 | 5.3 | odd | 4 | ||
705.2.c.c.424.22 | yes | 26 | 5.2 | odd | 4 | ||
3525.2.a.bh.1.12 | 13 | 1.1 | even | 1 | trivial | ||
3525.2.a.bi.1.2 | 13 | 5.4 | even | 2 |