Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [201,2,Mod(1,201)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(201, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("201.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 201 = 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 201.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: | \(1.60499308063\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.17009\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 201.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.53919 | 1.08837 | 0.544185 | − | 0.838965i | \(-0.316839\pi\) | ||||
0.544185 | + | 0.838965i | \(0.316839\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.369102 | 0.184551 | ||||||||
\(5\) | 2.17009 | 0.970492 | 0.485246 | − | 0.874378i | \(-0.338730\pi\) | ||||
0.485246 | + | 0.874378i | \(0.338730\pi\) | |||||||
\(6\) | −1.53919 | −0.628371 | ||||||||
\(7\) | 2.70928 | 1.02401 | 0.512005 | − | 0.858983i | \(-0.328903\pi\) | ||||
0.512005 | + | 0.858983i | \(0.328903\pi\) | |||||||
\(8\) | −2.51026 | −0.887511 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.34017 | 1.05626 | ||||||||
\(11\) | 4.63090 | 1.39627 | 0.698134 | − | 0.715967i | \(-0.254014\pi\) | ||||
0.698134 | + | 0.715967i | \(0.254014\pi\) | |||||||
\(12\) | −0.369102 | −0.106551 | ||||||||
\(13\) | −1.36910 | −0.379721 | −0.189860 | − | 0.981811i | \(-0.560804\pi\) | ||||
−0.189860 | + | 0.981811i | \(0.560804\pi\) | |||||||
\(14\) | 4.17009 | 1.11450 | ||||||||
\(15\) | −2.17009 | −0.560314 | ||||||||
\(16\) | −4.60197 | −1.15049 | ||||||||
\(17\) | −6.04945 | −1.46721 | −0.733603 | − | 0.679578i | \(-0.762163\pi\) | ||||
−0.733603 | + | 0.679578i | \(0.762163\pi\) | |||||||
\(18\) | 1.53919 | 0.362790 | ||||||||
\(19\) | −0.447480 | −0.102659 | −0.0513295 | − | 0.998682i | \(-0.516346\pi\) | ||||
−0.0513295 | + | 0.998682i | \(0.516346\pi\) | |||||||
\(20\) | 0.800984 | 0.179105 | ||||||||
\(21\) | −2.70928 | −0.591212 | ||||||||
\(22\) | 7.12783 | 1.51966 | ||||||||
\(23\) | −5.58864 | −1.16531 | −0.582656 | − | 0.812719i | \(-0.697986\pi\) | ||||
−0.582656 | + | 0.812719i | \(0.697986\pi\) | |||||||
\(24\) | 2.51026 | 0.512405 | ||||||||
\(25\) | −0.290725 | −0.0581449 | ||||||||
\(26\) | −2.10731 | −0.413277 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 8.68035 | 1.61190 | 0.805950 | − | 0.591984i | \(-0.201655\pi\) | ||||
0.805950 | + | 0.591984i | \(0.201655\pi\) | |||||||
\(30\) | −3.34017 | −0.609829 | ||||||||
\(31\) | −4.75872 | −0.854692 | −0.427346 | − | 0.904088i | \(-0.640551\pi\) | ||||
−0.427346 | + | 0.904088i | \(0.640551\pi\) | |||||||
\(32\) | −2.06278 | −0.364651 | ||||||||
\(33\) | −4.63090 | −0.806136 | ||||||||
\(34\) | −9.31124 | −1.59687 | ||||||||
\(35\) | 5.87936 | 0.993794 | ||||||||
\(36\) | 0.369102 | 0.0615171 | ||||||||
\(37\) | −7.97107 | −1.31044 | −0.655218 | − | 0.755440i | \(-0.727423\pi\) | ||||
−0.655218 | + | 0.755440i | \(0.727423\pi\) | |||||||
\(38\) | −0.688756 | −0.111731 | ||||||||
\(39\) | 1.36910 | 0.219232 | ||||||||
\(40\) | −5.44748 | −0.861322 | ||||||||
\(41\) | −1.72261 | −0.269026 | −0.134513 | − | 0.990912i | \(-0.542947\pi\) | ||||
−0.134513 | + | 0.990912i | \(0.542947\pi\) | |||||||
\(42\) | −4.17009 | −0.643458 | ||||||||
\(43\) | −1.00000 | −0.152499 | −0.0762493 | − | 0.997089i | \(-0.524294\pi\) | ||||
−0.0762493 | + | 0.997089i | \(0.524294\pi\) | |||||||
\(44\) | 1.70928 | 0.257683 | ||||||||
\(45\) | 2.17009 | 0.323497 | ||||||||
\(46\) | −8.60197 | −1.26829 | ||||||||
\(47\) | 13.1278 | 1.91489 | 0.957445 | − | 0.288615i | \(-0.0931949\pi\) | ||||
0.957445 | + | 0.288615i | \(0.0931949\pi\) | |||||||
\(48\) | 4.60197 | 0.664237 | ||||||||
\(49\) | 0.340173 | 0.0485961 | ||||||||
\(50\) | −0.447480 | −0.0632832 | ||||||||
\(51\) | 6.04945 | 0.847092 | ||||||||
\(52\) | −0.505339 | −0.0700779 | ||||||||
\(53\) | −4.03612 | −0.554403 | −0.277202 | − | 0.960812i | \(-0.589407\pi\) | ||||
−0.277202 | + | 0.960812i | \(0.589407\pi\) | |||||||
\(54\) | −1.53919 | −0.209457 | ||||||||
\(55\) | 10.0494 | 1.35507 | ||||||||
\(56\) | −6.80098 | −0.908820 | ||||||||
\(57\) | 0.447480 | 0.0592702 | ||||||||
\(58\) | 13.3607 | 1.75434 | ||||||||
\(59\) | 7.69594 | 1.00193 | 0.500963 | − | 0.865469i | \(-0.332979\pi\) | ||||
0.500963 | + | 0.865469i | \(0.332979\pi\) | |||||||
\(60\) | −0.800984 | −0.103407 | ||||||||
\(61\) | −10.3896 | −1.33025 | −0.665127 | − | 0.746730i | \(-0.731623\pi\) | ||||
−0.665127 | + | 0.746730i | \(0.731623\pi\) | |||||||
\(62\) | −7.32457 | −0.930222 | ||||||||
\(63\) | 2.70928 | 0.341337 | ||||||||
\(64\) | 6.02893 | 0.753616 | ||||||||
\(65\) | −2.97107 | −0.368516 | ||||||||
\(66\) | −7.12783 | −0.877375 | ||||||||
\(67\) | 1.00000 | 0.122169 | ||||||||
\(68\) | −2.23287 | −0.270775 | ||||||||
\(69\) | 5.58864 | 0.672793 | ||||||||
\(70\) | 9.04945 | 1.08162 | ||||||||
\(71\) | 10.9711 | 1.30203 | 0.651013 | − | 0.759066i | \(-0.274344\pi\) | ||||
0.651013 | + | 0.759066i | \(0.274344\pi\) | |||||||
\(72\) | −2.51026 | −0.295837 | ||||||||
\(73\) | −3.73820 | −0.437524 | −0.218762 | − | 0.975778i | \(-0.570202\pi\) | ||||
−0.218762 | + | 0.975778i | \(0.570202\pi\) | |||||||
\(74\) | −12.2690 | −1.42624 | ||||||||
\(75\) | 0.290725 | 0.0335700 | ||||||||
\(76\) | −0.165166 | −0.0189458 | ||||||||
\(77\) | 12.5464 | 1.42979 | ||||||||
\(78\) | 2.10731 | 0.238606 | ||||||||
\(79\) | 5.65983 | 0.636780 | 0.318390 | − | 0.947960i | \(-0.396858\pi\) | ||||
0.318390 | + | 0.947960i | \(0.396858\pi\) | |||||||
\(80\) | −9.98667 | −1.11654 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.65142 | −0.292800 | ||||||||
\(83\) | 2.95774 | 0.324654 | 0.162327 | − | 0.986737i | \(-0.448100\pi\) | ||||
0.162327 | + | 0.986737i | \(0.448100\pi\) | |||||||
\(84\) | −1.00000 | −0.109109 | ||||||||
\(85\) | −13.1278 | −1.42391 | ||||||||
\(86\) | −1.53919 | −0.165975 | ||||||||
\(87\) | −8.68035 | −0.930631 | ||||||||
\(88\) | −11.6248 | −1.23920 | ||||||||
\(89\) | 0.814315 | 0.0863172 | 0.0431586 | − | 0.999068i | \(-0.486258\pi\) | ||||
0.0431586 | + | 0.999068i | \(0.486258\pi\) | |||||||
\(90\) | 3.34017 | 0.352085 | ||||||||
\(91\) | −3.70928 | −0.388838 | ||||||||
\(92\) | −2.06278 | −0.215060 | ||||||||
\(93\) | 4.75872 | 0.493457 | ||||||||
\(94\) | 20.2062 | 2.08411 | ||||||||
\(95\) | −0.971071 | −0.0996297 | ||||||||
\(96\) | 2.06278 | 0.210532 | ||||||||
\(97\) | 13.9649 | 1.41792 | 0.708962 | − | 0.705247i | \(-0.249164\pi\) | ||||
0.708962 | + | 0.705247i | \(0.249164\pi\) | |||||||
\(98\) | 0.523590 | 0.0528906 | ||||||||
\(99\) | 4.63090 | 0.465423 | ||||||||
\(100\) | −0.107307 | −0.0107307 | ||||||||
\(101\) | −17.5669 | −1.74797 | −0.873986 | − | 0.485952i | \(-0.838473\pi\) | ||||
−0.873986 | + | 0.485952i | \(0.838473\pi\) | |||||||
\(102\) | 9.31124 | 0.921950 | ||||||||
\(103\) | −10.5464 | −1.03917 | −0.519583 | − | 0.854420i | \(-0.673913\pi\) | ||||
−0.519583 | + | 0.854420i | \(0.673913\pi\) | |||||||
\(104\) | 3.43680 | 0.337006 | ||||||||
\(105\) | −5.87936 | −0.573767 | ||||||||
\(106\) | −6.21235 | −0.603396 | ||||||||
\(107\) | 0.630898 | 0.0609912 | 0.0304956 | − | 0.999535i | \(-0.490291\pi\) | ||||
0.0304956 | + | 0.999535i | \(0.490291\pi\) | |||||||
\(108\) | −0.369102 | −0.0355169 | ||||||||
\(109\) | −3.86603 | −0.370299 | −0.185149 | − | 0.982710i | \(-0.559277\pi\) | ||||
−0.185149 | + | 0.982710i | \(0.559277\pi\) | |||||||
\(110\) | 15.4680 | 1.47482 | ||||||||
\(111\) | 7.97107 | 0.756581 | ||||||||
\(112\) | −12.4680 | −1.17812 | ||||||||
\(113\) | 10.5464 | 0.992120 | 0.496060 | − | 0.868288i | \(-0.334780\pi\) | ||||
0.496060 | + | 0.868288i | \(0.334780\pi\) | |||||||
\(114\) | 0.688756 | 0.0645080 | ||||||||
\(115\) | −12.1278 | −1.13093 | ||||||||
\(116\) | 3.20394 | 0.297478 | ||||||||
\(117\) | −1.36910 | −0.126574 | ||||||||
\(118\) | 11.8455 | 1.09047 | ||||||||
\(119\) | −16.3896 | −1.50243 | ||||||||
\(120\) | 5.44748 | 0.497285 | ||||||||
\(121\) | 10.4452 | 0.949565 | ||||||||
\(122\) | −15.9916 | −1.44781 | ||||||||
\(123\) | 1.72261 | 0.155322 | ||||||||
\(124\) | −1.75646 | −0.157734 | ||||||||
\(125\) | −11.4813 | −1.02692 | ||||||||
\(126\) | 4.17009 | 0.371501 | ||||||||
\(127\) | 19.8082 | 1.75769 | 0.878846 | − | 0.477106i | \(-0.158314\pi\) | ||||
0.878846 | + | 0.477106i | \(0.158314\pi\) | |||||||
\(128\) | 13.4052 | 1.18487 | ||||||||
\(129\) | 1.00000 | 0.0880451 | ||||||||
\(130\) | −4.57304 | −0.401082 | ||||||||
\(131\) | 0.326842 | 0.0285563 | 0.0142782 | − | 0.999898i | \(-0.495455\pi\) | ||||
0.0142782 | + | 0.999898i | \(0.495455\pi\) | |||||||
\(132\) | −1.70928 | −0.148773 | ||||||||
\(133\) | −1.21235 | −0.105124 | ||||||||
\(134\) | 1.53919 | 0.132966 | ||||||||
\(135\) | −2.17009 | −0.186771 | ||||||||
\(136\) | 15.1857 | 1.30216 | ||||||||
\(137\) | 8.40295 | 0.717913 | 0.358956 | − | 0.933354i | \(-0.383133\pi\) | ||||
0.358956 | + | 0.933354i | \(0.383133\pi\) | |||||||
\(138\) | 8.60197 | 0.732248 | ||||||||
\(139\) | −0.735937 | −0.0624214 | −0.0312107 | − | 0.999513i | \(-0.509936\pi\) | ||||
−0.0312107 | + | 0.999513i | \(0.509936\pi\) | |||||||
\(140\) | 2.17009 | 0.183406 | ||||||||
\(141\) | −13.1278 | −1.10556 | ||||||||
\(142\) | 16.8865 | 1.41709 | ||||||||
\(143\) | −6.34017 | −0.530192 | ||||||||
\(144\) | −4.60197 | −0.383497 | ||||||||
\(145\) | 18.8371 | 1.56434 | ||||||||
\(146\) | −5.75380 | −0.476188 | ||||||||
\(147\) | −0.340173 | −0.0280570 | ||||||||
\(148\) | −2.94214 | −0.241843 | ||||||||
\(149\) | 13.5753 | 1.11213 | 0.556066 | − | 0.831138i | \(-0.312310\pi\) | ||||
0.556066 | + | 0.831138i | \(0.312310\pi\) | |||||||
\(150\) | 0.447480 | 0.0365366 | ||||||||
\(151\) | 21.0433 | 1.71248 | 0.856240 | − | 0.516578i | \(-0.172794\pi\) | ||||
0.856240 | + | 0.516578i | \(0.172794\pi\) | |||||||
\(152\) | 1.12329 | 0.0911110 | ||||||||
\(153\) | −6.04945 | −0.489069 | ||||||||
\(154\) | 19.3112 | 1.55614 | ||||||||
\(155\) | −10.3268 | −0.829472 | ||||||||
\(156\) | 0.505339 | 0.0404595 | ||||||||
\(157\) | −7.24128 | −0.577917 | −0.288958 | − | 0.957342i | \(-0.593309\pi\) | ||||
−0.288958 | + | 0.957342i | \(0.593309\pi\) | |||||||
\(158\) | 8.71154 | 0.693053 | ||||||||
\(159\) | 4.03612 | 0.320085 | ||||||||
\(160\) | −4.47641 | −0.353891 | ||||||||
\(161\) | −15.1412 | −1.19329 | ||||||||
\(162\) | 1.53919 | 0.120930 | ||||||||
\(163\) | −18.3402 | −1.43651 | −0.718257 | − | 0.695778i | \(-0.755060\pi\) | ||||
−0.718257 | + | 0.695778i | \(0.755060\pi\) | |||||||
\(164\) | −0.635818 | −0.0496491 | ||||||||
\(165\) | −10.0494 | −0.782348 | ||||||||
\(166\) | 4.55252 | 0.353344 | ||||||||
\(167\) | −17.7454 | −1.37318 | −0.686590 | − | 0.727045i | \(-0.740893\pi\) | ||||
−0.686590 | + | 0.727045i | \(0.740893\pi\) | |||||||
\(168\) | 6.80098 | 0.524707 | ||||||||
\(169\) | −11.1256 | −0.855812 | ||||||||
\(170\) | −20.2062 | −1.54975 | ||||||||
\(171\) | −0.447480 | −0.0342197 | ||||||||
\(172\) | −0.369102 | −0.0281438 | ||||||||
\(173\) | −7.89269 | −0.600070 | −0.300035 | − | 0.953928i | \(-0.596998\pi\) | ||||
−0.300035 | + | 0.953928i | \(0.596998\pi\) | |||||||
\(174\) | −13.3607 | −1.01287 | ||||||||
\(175\) | −0.787653 | −0.0595410 | ||||||||
\(176\) | −21.3112 | −1.60640 | ||||||||
\(177\) | −7.69594 | −0.578463 | ||||||||
\(178\) | 1.25338 | 0.0939452 | ||||||||
\(179\) | 1.55252 | 0.116041 | 0.0580204 | − | 0.998315i | \(-0.481521\pi\) | ||||
0.0580204 | + | 0.998315i | \(0.481521\pi\) | |||||||
\(180\) | 0.800984 | 0.0597018 | ||||||||
\(181\) | 9.72979 | 0.723210 | 0.361605 | − | 0.932331i | \(-0.382229\pi\) | ||||
0.361605 | + | 0.932331i | \(0.382229\pi\) | |||||||
\(182\) | −5.70928 | −0.423200 | ||||||||
\(183\) | 10.3896 | 0.768023 | ||||||||
\(184\) | 14.0289 | 1.03423 | ||||||||
\(185\) | −17.2979 | −1.27177 | ||||||||
\(186\) | 7.32457 | 0.537064 | ||||||||
\(187\) | −28.0144 | −2.04861 | ||||||||
\(188\) | 4.84551 | 0.353395 | ||||||||
\(189\) | −2.70928 | −0.197071 | ||||||||
\(190\) | −1.49466 | −0.108434 | ||||||||
\(191\) | 12.0989 | 0.875445 | 0.437723 | − | 0.899110i | \(-0.355785\pi\) | ||||
0.437723 | + | 0.899110i | \(0.355785\pi\) | |||||||
\(192\) | −6.02893 | −0.435101 | ||||||||
\(193\) | 12.6020 | 0.907110 | 0.453555 | − | 0.891228i | \(-0.350156\pi\) | ||||
0.453555 | + | 0.891228i | \(0.350156\pi\) | |||||||
\(194\) | 21.4947 | 1.54323 | ||||||||
\(195\) | 2.97107 | 0.212763 | ||||||||
\(196\) | 0.125559 | 0.00896848 | ||||||||
\(197\) | −4.46081 | −0.317820 | −0.158910 | − | 0.987293i | \(-0.550798\pi\) | ||||
−0.158910 | + | 0.987293i | \(0.550798\pi\) | |||||||
\(198\) | 7.12783 | 0.506553 | ||||||||
\(199\) | −9.07838 | −0.643549 | −0.321775 | − | 0.946816i | \(-0.604279\pi\) | ||||
−0.321775 | + | 0.946816i | \(0.604279\pi\) | |||||||
\(200\) | 0.729794 | 0.0516042 | ||||||||
\(201\) | −1.00000 | −0.0705346 | ||||||||
\(202\) | −27.0388 | −1.90244 | ||||||||
\(203\) | 23.5174 | 1.65060 | ||||||||
\(204\) | 2.23287 | 0.156332 | ||||||||
\(205\) | −3.73820 | −0.261088 | ||||||||
\(206\) | −16.2329 | −1.13100 | ||||||||
\(207\) | −5.58864 | −0.388437 | ||||||||
\(208\) | 6.30057 | 0.436866 | ||||||||
\(209\) | −2.07223 | −0.143339 | ||||||||
\(210\) | −9.04945 | −0.624471 | ||||||||
\(211\) | 15.3919 | 1.05962 | 0.529811 | − | 0.848116i | \(-0.322263\pi\) | ||||
0.529811 | + | 0.848116i | \(0.322263\pi\) | |||||||
\(212\) | −1.48974 | −0.102316 | ||||||||
\(213\) | −10.9711 | −0.751725 | ||||||||
\(214\) | 0.971071 | 0.0663810 | ||||||||
\(215\) | −2.17009 | −0.147999 | ||||||||
\(216\) | 2.51026 | 0.170802 | ||||||||
\(217\) | −12.8927 | −0.875213 | ||||||||
\(218\) | −5.95055 | −0.403022 | ||||||||
\(219\) | 3.73820 | 0.252604 | ||||||||
\(220\) | 3.70928 | 0.250079 | ||||||||
\(221\) | 8.28231 | 0.557129 | ||||||||
\(222\) | 12.2690 | 0.823440 | ||||||||
\(223\) | −25.5174 | −1.70877 | −0.854387 | − | 0.519637i | \(-0.826067\pi\) | ||||
−0.854387 | + | 0.519637i | \(0.826067\pi\) | |||||||
\(224\) | −5.58864 | −0.373407 | ||||||||
\(225\) | −0.290725 | −0.0193816 | ||||||||
\(226\) | 16.2329 | 1.07979 | ||||||||
\(227\) | −23.6381 | −1.56891 | −0.784457 | − | 0.620183i | \(-0.787058\pi\) | ||||
−0.784457 | + | 0.620183i | \(0.787058\pi\) | |||||||
\(228\) | 0.165166 | 0.0109384 | ||||||||
\(229\) | 3.75872 | 0.248383 | 0.124192 | − | 0.992258i | \(-0.460366\pi\) | ||||
0.124192 | + | 0.992258i | \(0.460366\pi\) | |||||||
\(230\) | −18.6670 | −1.23087 | ||||||||
\(231\) | −12.5464 | −0.825491 | ||||||||
\(232\) | −21.7899 | −1.43058 | ||||||||
\(233\) | 24.6670 | 1.61599 | 0.807995 | − | 0.589189i | \(-0.200553\pi\) | ||||
0.807995 | + | 0.589189i | \(0.200553\pi\) | |||||||
\(234\) | −2.10731 | −0.137759 | ||||||||
\(235\) | 28.4885 | 1.85839 | ||||||||
\(236\) | 2.84059 | 0.184907 | ||||||||
\(237\) | −5.65983 | −0.367645 | ||||||||
\(238\) | −25.2267 | −1.63521 | ||||||||
\(239\) | 2.08452 | 0.134836 | 0.0674182 | − | 0.997725i | \(-0.478524\pi\) | ||||
0.0674182 | + | 0.997725i | \(0.478524\pi\) | |||||||
\(240\) | 9.98667 | 0.644637 | ||||||||
\(241\) | −10.1012 | −0.650673 | −0.325337 | − | 0.945598i | \(-0.605478\pi\) | ||||
−0.325337 | + | 0.945598i | \(0.605478\pi\) | |||||||
\(242\) | 16.0772 | 1.03348 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −3.83483 | −0.245500 | ||||||||
\(245\) | 0.738205 | 0.0471622 | ||||||||
\(246\) | 2.65142 | 0.169048 | ||||||||
\(247\) | 0.612646 | 0.0389817 | ||||||||
\(248\) | 11.9456 | 0.758548 | ||||||||
\(249\) | −2.95774 | −0.187439 | ||||||||
\(250\) | −17.6719 | −1.11767 | ||||||||
\(251\) | −10.8371 | −0.684032 | −0.342016 | − | 0.939694i | \(-0.611110\pi\) | ||||
−0.342016 | + | 0.939694i | \(0.611110\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | −25.8804 | −1.62709 | ||||||||
\(254\) | 30.4885 | 1.91302 | ||||||||
\(255\) | 13.1278 | 0.822096 | ||||||||
\(256\) | 8.57531 | 0.535957 | ||||||||
\(257\) | 25.3607 | 1.58196 | 0.790978 | − | 0.611844i | \(-0.209572\pi\) | ||||
0.790978 | + | 0.611844i | \(0.209572\pi\) | |||||||
\(258\) | 1.53919 | 0.0958257 | ||||||||
\(259\) | −21.5958 | −1.34190 | ||||||||
\(260\) | −1.09663 | −0.0680101 | ||||||||
\(261\) | 8.68035 | 0.537300 | ||||||||
\(262\) | 0.503072 | 0.0310799 | ||||||||
\(263\) | −12.9311 | −0.797364 | −0.398682 | − | 0.917089i | \(-0.630532\pi\) | ||||
−0.398682 | + | 0.917089i | \(0.630532\pi\) | |||||||
\(264\) | 11.6248 | 0.715454 | ||||||||
\(265\) | −8.75872 | −0.538044 | ||||||||
\(266\) | −1.86603 | −0.114414 | ||||||||
\(267\) | −0.814315 | −0.0498353 | ||||||||
\(268\) | 0.369102 | 0.0225465 | ||||||||
\(269\) | 22.0638 | 1.34526 | 0.672628 | − | 0.739981i | \(-0.265166\pi\) | ||||
0.672628 | + | 0.739981i | \(0.265166\pi\) | |||||||
\(270\) | −3.34017 | −0.203276 | ||||||||
\(271\) | 16.1834 | 0.983073 | 0.491536 | − | 0.870857i | \(-0.336436\pi\) | ||||
0.491536 | + | 0.870857i | \(0.336436\pi\) | |||||||
\(272\) | 27.8394 | 1.68801 | ||||||||
\(273\) | 3.70928 | 0.224496 | ||||||||
\(274\) | 12.9337 | 0.781355 | ||||||||
\(275\) | −1.34632 | −0.0811859 | ||||||||
\(276\) | 2.06278 | 0.124165 | ||||||||
\(277\) | −2.86991 | −0.172436 | −0.0862180 | − | 0.996276i | \(-0.527478\pi\) | ||||
−0.0862180 | + | 0.996276i | \(0.527478\pi\) | |||||||
\(278\) | −1.13275 | −0.0679376 | ||||||||
\(279\) | −4.75872 | −0.284897 | ||||||||
\(280\) | −14.7587 | −0.882002 | ||||||||
\(281\) | −6.63090 | −0.395566 | −0.197783 | − | 0.980246i | \(-0.563374\pi\) | ||||
−0.197783 | + | 0.980246i | \(0.563374\pi\) | |||||||
\(282\) | −20.2062 | −1.20326 | ||||||||
\(283\) | 16.2329 | 0.964944 | 0.482472 | − | 0.875911i | \(-0.339739\pi\) | ||||
0.482472 | + | 0.875911i | \(0.339739\pi\) | |||||||
\(284\) | 4.04945 | 0.240291 | ||||||||
\(285\) | 0.971071 | 0.0575213 | ||||||||
\(286\) | −9.75872 | −0.577045 | ||||||||
\(287\) | −4.66701 | −0.275485 | ||||||||
\(288\) | −2.06278 | −0.121550 | ||||||||
\(289\) | 19.5958 | 1.15270 | ||||||||
\(290\) | 28.9939 | 1.70258 | ||||||||
\(291\) | −13.9649 | −0.818639 | ||||||||
\(292\) | −1.37978 | −0.0807455 | ||||||||
\(293\) | 33.3340 | 1.94739 | 0.973697 | − | 0.227845i | \(-0.0731680\pi\) | ||||
0.973697 | + | 0.227845i | \(0.0731680\pi\) | |||||||
\(294\) | −0.523590 | −0.0305364 | ||||||||
\(295\) | 16.7009 | 0.972362 | ||||||||
\(296\) | 20.0095 | 1.16303 | ||||||||
\(297\) | −4.63090 | −0.268712 | ||||||||
\(298\) | 20.8950 | 1.21041 | ||||||||
\(299\) | 7.65142 | 0.442493 | ||||||||
\(300\) | 0.107307 | 0.00619538 | ||||||||
\(301\) | −2.70928 | −0.156160 | ||||||||
\(302\) | 32.3896 | 1.86381 | ||||||||
\(303\) | 17.5669 | 1.00919 | ||||||||
\(304\) | 2.05929 | 0.118108 | ||||||||
\(305\) | −22.5464 | −1.29100 | ||||||||
\(306\) | −9.31124 | −0.532288 | ||||||||
\(307\) | 24.5113 | 1.39893 | 0.699467 | − | 0.714665i | \(-0.253421\pi\) | ||||
0.699467 | + | 0.714665i | \(0.253421\pi\) | |||||||
\(308\) | 4.63090 | 0.263870 | ||||||||
\(309\) | 10.5464 | 0.599962 | ||||||||
\(310\) | −15.8950 | −0.902773 | ||||||||
\(311\) | −3.21235 | −0.182155 | −0.0910777 | − | 0.995844i | \(-0.529031\pi\) | ||||
−0.0910777 | + | 0.995844i | \(0.529031\pi\) | |||||||
\(312\) | −3.43680 | −0.194571 | ||||||||
\(313\) | 7.55252 | 0.426894 | 0.213447 | − | 0.976955i | \(-0.431531\pi\) | ||||
0.213447 | + | 0.976955i | \(0.431531\pi\) | |||||||
\(314\) | −11.1457 | −0.628988 | ||||||||
\(315\) | 5.87936 | 0.331265 | ||||||||
\(316\) | 2.08906 | 0.117519 | ||||||||
\(317\) | −6.72979 | −0.377983 | −0.188991 | − | 0.981979i | \(-0.560522\pi\) | ||||
−0.188991 | + | 0.981979i | \(0.560522\pi\) | |||||||
\(318\) | 6.21235 | 0.348371 | ||||||||
\(319\) | 40.1978 | 2.25064 | ||||||||
\(320\) | 13.0833 | 0.731379 | ||||||||
\(321\) | −0.630898 | −0.0352133 | ||||||||
\(322\) | −23.3051 | −1.29874 | ||||||||
\(323\) | 2.70701 | 0.150622 | ||||||||
\(324\) | 0.369102 | 0.0205057 | ||||||||
\(325\) | 0.398032 | 0.0220788 | ||||||||
\(326\) | −28.2290 | −1.56346 | ||||||||
\(327\) | 3.86603 | 0.213792 | ||||||||
\(328\) | 4.32419 | 0.238763 | ||||||||
\(329\) | 35.5669 | 1.96087 | ||||||||
\(330\) | −15.4680 | −0.851485 | ||||||||
\(331\) | 1.49693 | 0.0822786 | 0.0411393 | − | 0.999153i | \(-0.486901\pi\) | ||||
0.0411393 | + | 0.999153i | \(0.486901\pi\) | |||||||
\(332\) | 1.09171 | 0.0599153 | ||||||||
\(333\) | −7.97107 | −0.436812 | ||||||||
\(334\) | −27.3135 | −1.49453 | ||||||||
\(335\) | 2.17009 | 0.118564 | ||||||||
\(336\) | 12.4680 | 0.680185 | ||||||||
\(337\) | −19.7503 | −1.07587 | −0.537934 | − | 0.842987i | \(-0.680795\pi\) | ||||
−0.537934 | + | 0.842987i | \(0.680795\pi\) | |||||||
\(338\) | −17.1243 | −0.931441 | ||||||||
\(339\) | −10.5464 | −0.572801 | ||||||||
\(340\) | −4.84551 | −0.262785 | ||||||||
\(341\) | −22.0372 | −1.19338 | ||||||||
\(342\) | −0.688756 | −0.0372437 | ||||||||
\(343\) | −18.0433 | −0.974247 | ||||||||
\(344\) | 2.51026 | 0.135344 | ||||||||
\(345\) | 12.1278 | 0.652940 | ||||||||
\(346\) | −12.1483 | −0.653099 | ||||||||
\(347\) | −23.2495 | −1.24810 | −0.624050 | − | 0.781385i | \(-0.714514\pi\) | ||||
−0.624050 | + | 0.781385i | \(0.714514\pi\) | |||||||
\(348\) | −3.20394 | −0.171749 | ||||||||
\(349\) | −9.25953 | −0.495651 | −0.247826 | − | 0.968805i | \(-0.579716\pi\) | ||||
−0.247826 | + | 0.968805i | \(0.579716\pi\) | |||||||
\(350\) | −1.21235 | −0.0648027 | ||||||||
\(351\) | 1.36910 | 0.0730773 | ||||||||
\(352\) | −9.55252 | −0.509151 | ||||||||
\(353\) | −16.1701 | −0.860647 | −0.430323 | − | 0.902675i | \(-0.641600\pi\) | ||||
−0.430323 | + | 0.902675i | \(0.641600\pi\) | |||||||
\(354\) | −11.8455 | −0.629582 | ||||||||
\(355\) | 23.8082 | 1.26361 | ||||||||
\(356\) | 0.300566 | 0.0159299 | ||||||||
\(357\) | 16.3896 | 0.867431 | ||||||||
\(358\) | 2.38962 | 0.126295 | ||||||||
\(359\) | 4.30018 | 0.226955 | 0.113477 | − | 0.993541i | \(-0.463801\pi\) | ||||
0.113477 | + | 0.993541i | \(0.463801\pi\) | |||||||
\(360\) | −5.44748 | −0.287107 | ||||||||
\(361\) | −18.7998 | −0.989461 | ||||||||
\(362\) | 14.9760 | 0.787121 | ||||||||
\(363\) | −10.4452 | −0.548231 | ||||||||
\(364\) | −1.36910 | −0.0717605 | ||||||||
\(365\) | −8.11223 | −0.424613 | ||||||||
\(366\) | 15.9916 | 0.835894 | ||||||||
\(367\) | 35.4329 | 1.84958 | 0.924792 | − | 0.380473i | \(-0.124239\pi\) | ||||
0.924792 | + | 0.380473i | \(0.124239\pi\) | |||||||
\(368\) | 25.7187 | 1.34068 | ||||||||
\(369\) | −1.72261 | −0.0896753 | ||||||||
\(370\) | −26.6248 | −1.38416 | ||||||||
\(371\) | −10.9350 | −0.567714 | ||||||||
\(372\) | 1.75646 | 0.0910680 | ||||||||
\(373\) | −15.2846 | −0.791406 | −0.395703 | − | 0.918379i | \(-0.629499\pi\) | ||||
−0.395703 | + | 0.918379i | \(0.629499\pi\) | |||||||
\(374\) | −43.1194 | −2.22965 | ||||||||
\(375\) | 11.4813 | 0.592893 | ||||||||
\(376\) | −32.9542 | −1.69949 | ||||||||
\(377\) | −11.8843 | −0.612072 | ||||||||
\(378\) | −4.17009 | −0.214486 | ||||||||
\(379\) | −14.5402 | −0.746882 | −0.373441 | − | 0.927654i | \(-0.621822\pi\) | ||||
−0.373441 | + | 0.927654i | \(0.621822\pi\) | |||||||
\(380\) | −0.358424 | −0.0183868 | ||||||||
\(381\) | −19.8082 | −1.01480 | ||||||||
\(382\) | 18.6225 | 0.952809 | ||||||||
\(383\) | 3.13624 | 0.160254 | 0.0801271 | − | 0.996785i | \(-0.474467\pi\) | ||||
0.0801271 | + | 0.996785i | \(0.474467\pi\) | |||||||
\(384\) | −13.4052 | −0.684082 | ||||||||
\(385\) | 27.2267 | 1.38760 | ||||||||
\(386\) | 19.3968 | 0.987272 | ||||||||
\(387\) | −1.00000 | −0.0508329 | ||||||||
\(388\) | 5.15449 | 0.261679 | ||||||||
\(389\) | 26.9399 | 1.36591 | 0.682953 | − | 0.730462i | \(-0.260695\pi\) | ||||
0.682953 | + | 0.730462i | \(0.260695\pi\) | |||||||
\(390\) | 4.57304 | 0.231565 | ||||||||
\(391\) | 33.8082 | 1.70975 | ||||||||
\(392\) | −0.853922 | −0.0431296 | ||||||||
\(393\) | −0.326842 | −0.0164870 | ||||||||
\(394\) | −6.86603 | −0.345906 | ||||||||
\(395\) | 12.2823 | 0.617990 | ||||||||
\(396\) | 1.70928 | 0.0858943 | ||||||||
\(397\) | −17.7854 | −0.892623 | −0.446311 | − | 0.894878i | \(-0.647263\pi\) | ||||
−0.446311 | + | 0.894878i | \(0.647263\pi\) | |||||||
\(398\) | −13.9733 | −0.700420 | ||||||||
\(399\) | 1.21235 | 0.0606933 | ||||||||
\(400\) | 1.33791 | 0.0668953 | ||||||||
\(401\) | 9.93722 | 0.496241 | 0.248121 | − | 0.968729i | \(-0.420187\pi\) | ||||
0.248121 | + | 0.968729i | \(0.420187\pi\) | |||||||
\(402\) | −1.53919 | −0.0767678 | ||||||||
\(403\) | 6.51518 | 0.324544 | ||||||||
\(404\) | −6.48398 | −0.322590 | ||||||||
\(405\) | 2.17009 | 0.107832 | ||||||||
\(406\) | 36.1978 | 1.79647 | ||||||||
\(407\) | −36.9132 | −1.82972 | ||||||||
\(408\) | −15.1857 | −0.751803 | ||||||||
\(409\) | −18.3090 | −0.905321 | −0.452660 | − | 0.891683i | \(-0.649525\pi\) | ||||
−0.452660 | + | 0.891683i | \(0.649525\pi\) | |||||||
\(410\) | −5.75380 | −0.284160 | ||||||||
\(411\) | −8.40295 | −0.414487 | ||||||||
\(412\) | −3.89269 | −0.191779 | ||||||||
\(413\) | 20.8504 | 1.02598 | ||||||||
\(414\) | −8.60197 | −0.422764 | ||||||||
\(415\) | 6.41855 | 0.315074 | ||||||||
\(416\) | 2.82416 | 0.138466 | ||||||||
\(417\) | 0.735937 | 0.0360390 | ||||||||
\(418\) | −3.18956 | −0.156007 | ||||||||
\(419\) | −15.9821 | −0.780778 | −0.390389 | − | 0.920650i | \(-0.627660\pi\) | ||||
−0.390389 | + | 0.920650i | \(0.627660\pi\) | |||||||
\(420\) | −2.17009 | −0.105889 | ||||||||
\(421\) | 36.7731 | 1.79221 | 0.896106 | − | 0.443841i | \(-0.146384\pi\) | ||||
0.896106 | + | 0.443841i | \(0.146384\pi\) | |||||||
\(422\) | 23.6910 | 1.15326 | ||||||||
\(423\) | 13.1278 | 0.638297 | ||||||||
\(424\) | 10.1317 | 0.492039 | ||||||||
\(425\) | 1.75872 | 0.0853106 | ||||||||
\(426\) | −16.8865 | −0.818156 | ||||||||
\(427\) | −28.1483 | −1.36219 | ||||||||
\(428\) | 0.232866 | 0.0112560 | ||||||||
\(429\) | 6.34017 | 0.306106 | ||||||||
\(430\) | −3.34017 | −0.161077 | ||||||||
\(431\) | 21.1412 | 1.01833 | 0.509167 | − | 0.860668i | \(-0.329954\pi\) | ||||
0.509167 | + | 0.860668i | \(0.329954\pi\) | |||||||
\(432\) | 4.60197 | 0.221412 | ||||||||
\(433\) | 13.3607 | 0.642074 | 0.321037 | − | 0.947067i | \(-0.395969\pi\) | ||||
0.321037 | + | 0.947067i | \(0.395969\pi\) | |||||||
\(434\) | −19.8443 | −0.952556 | ||||||||
\(435\) | −18.8371 | −0.903170 | ||||||||
\(436\) | −1.42696 | −0.0683390 | ||||||||
\(437\) | 2.50080 | 0.119630 | ||||||||
\(438\) | 5.75380 | 0.274927 | ||||||||
\(439\) | −25.5441 | −1.21915 | −0.609577 | − | 0.792727i | \(-0.708661\pi\) | ||||
−0.609577 | + | 0.792727i | \(0.708661\pi\) | |||||||
\(440\) | −25.2267 | −1.20264 | ||||||||
\(441\) | 0.340173 | 0.0161987 | ||||||||
\(442\) | 12.7480 | 0.606363 | ||||||||
\(443\) | −19.3958 | −0.921521 | −0.460760 | − | 0.887525i | \(-0.652423\pi\) | ||||
−0.460760 | + | 0.887525i | \(0.652423\pi\) | |||||||
\(444\) | 2.94214 | 0.139628 | ||||||||
\(445\) | 1.76713 | 0.0837702 | ||||||||
\(446\) | −39.2762 | −1.85978 | ||||||||
\(447\) | −13.5753 | −0.642090 | ||||||||
\(448\) | 16.3340 | 0.771710 | ||||||||
\(449\) | −21.3112 | −1.00574 | −0.502870 | − | 0.864362i | \(-0.667723\pi\) | ||||
−0.502870 | + | 0.864362i | \(0.667723\pi\) | |||||||
\(450\) | −0.447480 | −0.0210944 | ||||||||
\(451\) | −7.97721 | −0.375632 | ||||||||
\(452\) | 3.89269 | 0.183097 | ||||||||
\(453\) | −21.0433 | −0.988701 | ||||||||
\(454\) | −36.3835 | −1.70756 | ||||||||
\(455\) | −8.04945 | −0.377364 | ||||||||
\(456\) | −1.12329 | −0.0526029 | ||||||||
\(457\) | −24.6681 | −1.15392 | −0.576962 | − | 0.816771i | \(-0.695762\pi\) | ||||
−0.576962 | + | 0.816771i | \(0.695762\pi\) | |||||||
\(458\) | 5.78539 | 0.270333 | ||||||||
\(459\) | 6.04945 | 0.282364 | ||||||||
\(460\) | −4.47641 | −0.208714 | ||||||||
\(461\) | 24.5958 | 1.14554 | 0.572771 | − | 0.819716i | \(-0.305868\pi\) | ||||
0.572771 | + | 0.819716i | \(0.305868\pi\) | |||||||
\(462\) | −19.3112 | −0.898440 | ||||||||
\(463\) | 0.793796 | 0.0368908 | 0.0184454 | − | 0.999830i | \(-0.494128\pi\) | ||||
0.0184454 | + | 0.999830i | \(0.494128\pi\) | |||||||
\(464\) | −39.9467 | −1.85448 | ||||||||
\(465\) | 10.3268 | 0.478896 | ||||||||
\(466\) | 37.9672 | 1.75880 | ||||||||
\(467\) | 5.80817 | 0.268770 | 0.134385 | − | 0.990929i | \(-0.457094\pi\) | ||||
0.134385 | + | 0.990929i | \(0.457094\pi\) | |||||||
\(468\) | −0.505339 | −0.0233593 | ||||||||
\(469\) | 2.70928 | 0.125103 | ||||||||
\(470\) | 43.8492 | 2.02261 | ||||||||
\(471\) | 7.24128 | 0.333660 | ||||||||
\(472\) | −19.3188 | −0.889221 | ||||||||
\(473\) | −4.63090 | −0.212929 | ||||||||
\(474\) | −8.71154 | −0.400134 | ||||||||
\(475\) | 0.130094 | 0.00596910 | ||||||||
\(476\) | −6.04945 | −0.277276 | ||||||||
\(477\) | −4.03612 | −0.184801 | ||||||||
\(478\) | 3.20847 | 0.146752 | ||||||||
\(479\) | 6.27739 | 0.286821 | 0.143411 | − | 0.989663i | \(-0.454193\pi\) | ||||
0.143411 | + | 0.989663i | \(0.454193\pi\) | |||||||
\(480\) | 4.47641 | 0.204319 | ||||||||
\(481\) | 10.9132 | 0.497600 | ||||||||
\(482\) | −15.5476 | −0.708174 | ||||||||
\(483\) | 15.1412 | 0.688947 | ||||||||
\(484\) | 3.85535 | 0.175243 | ||||||||
\(485\) | 30.3051 | 1.37608 | ||||||||
\(486\) | −1.53919 | −0.0698190 | ||||||||
\(487\) | 9.26794 | 0.419970 | 0.209985 | − | 0.977705i | \(-0.432658\pi\) | ||||
0.209985 | + | 0.977705i | \(0.432658\pi\) | |||||||
\(488\) | 26.0806 | 1.18062 | ||||||||
\(489\) | 18.3402 | 0.829371 | ||||||||
\(490\) | 1.13624 | 0.0513299 | ||||||||
\(491\) | −24.4608 | −1.10390 | −0.551950 | − | 0.833877i | \(-0.686116\pi\) | ||||
−0.551950 | + | 0.833877i | \(0.686116\pi\) | |||||||
\(492\) | 0.635818 | 0.0286649 | ||||||||
\(493\) | −52.5113 | −2.36499 | ||||||||
\(494\) | 0.942978 | 0.0424266 | ||||||||
\(495\) | 10.0494 | 0.451689 | ||||||||
\(496\) | 21.8995 | 0.983316 | ||||||||
\(497\) | 29.7237 | 1.33329 | ||||||||
\(498\) | −4.55252 | −0.204003 | ||||||||
\(499\) | 23.4329 | 1.04900 | 0.524501 | − | 0.851410i | \(-0.324252\pi\) | ||||
0.524501 | + | 0.851410i | \(0.324252\pi\) | |||||||
\(500\) | −4.23779 | −0.189520 | ||||||||
\(501\) | 17.7454 | 0.792806 | ||||||||
\(502\) | −16.6803 | −0.744480 | ||||||||
\(503\) | 15.9337 | 0.710450 | 0.355225 | − | 0.934781i | \(-0.384404\pi\) | ||||
0.355225 | + | 0.934781i | \(0.384404\pi\) | |||||||
\(504\) | −6.80098 | −0.302940 | ||||||||
\(505\) | −38.1217 | −1.69639 | ||||||||
\(506\) | −39.8348 | −1.77087 | ||||||||
\(507\) | 11.1256 | 0.494103 | ||||||||
\(508\) | 7.31124 | 0.324384 | ||||||||
\(509\) | −27.9071 | −1.23696 | −0.618480 | − | 0.785801i | \(-0.712251\pi\) | ||||
−0.618480 | + | 0.785801i | \(0.712251\pi\) | |||||||
\(510\) | 20.2062 | 0.894746 | ||||||||
\(511\) | −10.1278 | −0.448029 | ||||||||
\(512\) | −13.6114 | −0.601546 | ||||||||
\(513\) | 0.447480 | 0.0197567 | ||||||||
\(514\) | 39.0349 | 1.72176 | ||||||||
\(515\) | −22.8865 | −1.00850 | ||||||||
\(516\) | 0.369102 | 0.0162488 | ||||||||
\(517\) | 60.7936 | 2.67370 | ||||||||
\(518\) | −33.2401 | −1.46048 | ||||||||
\(519\) | 7.89269 | 0.346451 | ||||||||
\(520\) | 7.45816 | 0.327062 | ||||||||
\(521\) | 19.7237 | 0.864109 | 0.432054 | − | 0.901848i | \(-0.357789\pi\) | ||||
0.432054 | + | 0.901848i | \(0.357789\pi\) | |||||||
\(522\) | 13.3607 | 0.584782 | ||||||||
\(523\) | −24.2739 | −1.06142 | −0.530712 | − | 0.847552i | \(-0.678075\pi\) | ||||
−0.530712 | + | 0.847552i | \(0.678075\pi\) | |||||||
\(524\) | 0.120638 | 0.00527010 | ||||||||
\(525\) | 0.787653 | 0.0343760 | ||||||||
\(526\) | −19.9034 | −0.867828 | ||||||||
\(527\) | 28.7877 | 1.25401 | ||||||||
\(528\) | 21.3112 | 0.927453 | ||||||||
\(529\) | 8.23287 | 0.357951 | ||||||||
\(530\) | −13.4813 | −0.585592 | ||||||||
\(531\) | 7.69594 | 0.333976 | ||||||||
\(532\) | −0.447480 | −0.0194007 | ||||||||
\(533\) | 2.35842 | 0.102155 | ||||||||
\(534\) | −1.25338 | −0.0542393 | ||||||||
\(535\) | 1.36910 | 0.0591915 | ||||||||
\(536\) | −2.51026 | −0.108427 | ||||||||
\(537\) | −1.55252 | −0.0669962 | ||||||||
\(538\) | 33.9604 | 1.46414 | ||||||||
\(539\) | 1.57531 | 0.0678532 | ||||||||
\(540\) | −0.800984 | −0.0344689 | ||||||||
\(541\) | 37.1194 | 1.59589 | 0.797944 | − | 0.602731i | \(-0.205921\pi\) | ||||
0.797944 | + | 0.602731i | \(0.205921\pi\) | |||||||
\(542\) | 24.9093 | 1.06995 | ||||||||
\(543\) | −9.72979 | −0.417545 | ||||||||
\(544\) | 12.4787 | 0.535019 | ||||||||
\(545\) | −8.38962 | −0.359372 | ||||||||
\(546\) | 5.70928 | 0.244334 | ||||||||
\(547\) | 25.0494 | 1.07104 | 0.535519 | − | 0.844523i | \(-0.320116\pi\) | ||||
0.535519 | + | 0.844523i | \(0.320116\pi\) | |||||||
\(548\) | 3.10155 | 0.132492 | ||||||||
\(549\) | −10.3896 | −0.443418 | ||||||||
\(550\) | −2.07223 | −0.0883604 | ||||||||
\(551\) | −3.88428 | −0.165476 | ||||||||
\(552\) | −14.0289 | −0.597111 | ||||||||
\(553\) | 15.3340 | 0.652069 | ||||||||
\(554\) | −4.41733 | −0.187674 | ||||||||
\(555\) | 17.2979 | 0.734255 | ||||||||
\(556\) | −0.271636 | −0.0115199 | ||||||||
\(557\) | −23.0121 | −0.975054 | −0.487527 | − | 0.873108i | \(-0.662101\pi\) | ||||
−0.487527 | + | 0.873108i | \(0.662101\pi\) | |||||||
\(558\) | −7.32457 | −0.310074 | ||||||||
\(559\) | 1.36910 | 0.0579069 | ||||||||
\(560\) | −27.0566 | −1.14335 | ||||||||
\(561\) | 28.0144 | 1.18277 | ||||||||
\(562\) | −10.2062 | −0.430523 | ||||||||
\(563\) | −35.3835 | −1.49124 | −0.745618 | − | 0.666374i | \(-0.767846\pi\) | ||||
−0.745618 | + | 0.666374i | \(0.767846\pi\) | |||||||
\(564\) | −4.84551 | −0.204033 | ||||||||
\(565\) | 22.8865 | 0.962844 | ||||||||
\(566\) | 24.9854 | 1.05022 | ||||||||
\(567\) | 2.70928 | 0.113779 | ||||||||
\(568\) | −27.5402 | −1.15556 | ||||||||
\(569\) | −27.5136 | −1.15343 | −0.576714 | − | 0.816946i | \(-0.695665\pi\) | ||||
−0.576714 | + | 0.816946i | \(0.695665\pi\) | |||||||
\(570\) | 1.49466 | 0.0626045 | ||||||||
\(571\) | 25.2800 | 1.05794 | 0.528969 | − | 0.848641i | \(-0.322579\pi\) | ||||
0.528969 | + | 0.848641i | \(0.322579\pi\) | |||||||
\(572\) | −2.34017 | −0.0978475 | ||||||||
\(573\) | −12.0989 | −0.505439 | ||||||||
\(574\) | −7.18342 | −0.299830 | ||||||||
\(575\) | 1.62475 | 0.0677569 | ||||||||
\(576\) | 6.02893 | 0.251205 | ||||||||
\(577\) | −33.6475 | −1.40077 | −0.700383 | − | 0.713767i | \(-0.746987\pi\) | ||||
−0.700383 | + | 0.713767i | \(0.746987\pi\) | |||||||
\(578\) | 30.1617 | 1.25456 | ||||||||
\(579\) | −12.6020 | −0.523720 | ||||||||
\(580\) | 6.95282 | 0.288700 | ||||||||
\(581\) | 8.01333 | 0.332449 | ||||||||
\(582\) | −21.4947 | −0.890982 | ||||||||
\(583\) | −18.6908 | −0.774096 | ||||||||
\(584\) | 9.38386 | 0.388307 | ||||||||
\(585\) | −2.97107 | −0.122839 | ||||||||
\(586\) | 51.3074 | 2.11949 | ||||||||
\(587\) | −22.7838 | −0.940387 | −0.470194 | − | 0.882563i | \(-0.655816\pi\) | ||||
−0.470194 | + | 0.882563i | \(0.655816\pi\) | |||||||
\(588\) | −0.125559 | −0.00517795 | ||||||||
\(589\) | 2.12943 | 0.0877418 | ||||||||
\(590\) | 25.7058 | 1.05829 | ||||||||
\(591\) | 4.46081 | 0.183493 | ||||||||
\(592\) | 36.6826 | 1.50765 | ||||||||
\(593\) | −25.6647 | −1.05392 | −0.526962 | − | 0.849889i | \(-0.676669\pi\) | ||||
−0.526962 | + | 0.849889i | \(0.676669\pi\) | |||||||
\(594\) | −7.12783 | −0.292458 | ||||||||
\(595\) | −35.5669 | −1.45810 | ||||||||
\(596\) | 5.01068 | 0.205245 | ||||||||
\(597\) | 9.07838 | 0.371553 | ||||||||
\(598\) | 11.7770 | 0.481596 | ||||||||
\(599\) | 1.44134 | 0.0588914 | 0.0294457 | − | 0.999566i | \(-0.490626\pi\) | ||||
0.0294457 | + | 0.999566i | \(0.490626\pi\) | |||||||
\(600\) | −0.729794 | −0.0297937 | ||||||||
\(601\) | 28.4391 | 1.16005 | 0.580027 | − | 0.814597i | \(-0.303042\pi\) | ||||
0.580027 | + | 0.814597i | \(0.303042\pi\) | |||||||
\(602\) | −4.17009 | −0.169960 | ||||||||
\(603\) | 1.00000 | 0.0407231 | ||||||||
\(604\) | 7.76713 | 0.316040 | ||||||||
\(605\) | 22.6670 | 0.921545 | ||||||||
\(606\) | 27.0388 | 1.09837 | ||||||||
\(607\) | 1.97721 | 0.0802526 | 0.0401263 | − | 0.999195i | \(-0.487224\pi\) | ||||
0.0401263 | + | 0.999195i | \(0.487224\pi\) | |||||||
\(608\) | 0.923053 | 0.0374347 | ||||||||
\(609\) | −23.5174 | −0.952975 | ||||||||
\(610\) | −34.7031 | −1.40509 | ||||||||
\(611\) | −17.9733 | −0.727123 | ||||||||
\(612\) | −2.23287 | −0.0902583 | ||||||||
\(613\) | −30.6020 | −1.23600 | −0.618001 | − | 0.786177i | \(-0.712057\pi\) | ||||
−0.618001 | + | 0.786177i | \(0.712057\pi\) | |||||||
\(614\) | 37.7275 | 1.52256 | ||||||||
\(615\) | 3.73820 | 0.150739 | ||||||||
\(616\) | −31.4947 | −1.26896 | ||||||||
\(617\) | −37.5981 | −1.51364 | −0.756821 | − | 0.653622i | \(-0.773249\pi\) | ||||
−0.756821 | + | 0.653622i | \(0.773249\pi\) | |||||||
\(618\) | 16.2329 | 0.652982 | ||||||||
\(619\) | −31.3568 | −1.26034 | −0.630168 | − | 0.776458i | \(-0.717014\pi\) | ||||
−0.630168 | + | 0.776458i | \(0.717014\pi\) | |||||||
\(620\) | −3.81166 | −0.153080 | ||||||||
\(621\) | 5.58864 | 0.224264 | ||||||||
\(622\) | −4.94441 | −0.198253 | ||||||||
\(623\) | 2.20620 | 0.0883897 | ||||||||
\(624\) | −6.30057 | −0.252224 | ||||||||
\(625\) | −23.4619 | −0.938474 | ||||||||
\(626\) | 11.6248 | 0.464619 | ||||||||
\(627\) | 2.07223 | 0.0827571 | ||||||||
\(628\) | −2.67277 | −0.106655 | ||||||||
\(629\) | 48.2206 | 1.92268 | ||||||||
\(630\) | 9.04945 | 0.360539 | ||||||||
\(631\) | −16.5814 | −0.660097 | −0.330049 | − | 0.943964i | \(-0.607065\pi\) | ||||
−0.330049 | + | 0.943964i | \(0.607065\pi\) | |||||||
\(632\) | −14.2076 | −0.565149 | ||||||||
\(633\) | −15.3919 | −0.611773 | ||||||||
\(634\) | −10.3584 | −0.411386 | ||||||||
\(635\) | 42.9854 | 1.70583 | ||||||||
\(636\) | 1.48974 | 0.0590721 | ||||||||
\(637\) | −0.465732 | −0.0184530 | ||||||||
\(638\) | 61.8720 | 2.44954 | ||||||||
\(639\) | 10.9711 | 0.434009 | ||||||||
\(640\) | 29.0905 | 1.14990 | ||||||||
\(641\) | −34.4524 | −1.36079 | −0.680394 | − | 0.732847i | \(-0.738191\pi\) | ||||
−0.680394 | + | 0.732847i | \(0.738191\pi\) | |||||||
\(642\) | −0.971071 | −0.0383251 | ||||||||
\(643\) | −22.6765 | −0.894273 | −0.447136 | − | 0.894466i | \(-0.647556\pi\) | ||||
−0.447136 | + | 0.894466i | \(0.647556\pi\) | |||||||
\(644\) | −5.58864 | −0.220223 | ||||||||
\(645\) | 2.17009 | 0.0854471 | ||||||||
\(646\) | 4.16660 | 0.163933 | ||||||||
\(647\) | 16.1399 | 0.634526 | 0.317263 | − | 0.948338i | \(-0.397236\pi\) | ||||
0.317263 | + | 0.948338i | \(0.397236\pi\) | |||||||
\(648\) | −2.51026 | −0.0986123 | ||||||||
\(649\) | 35.6391 | 1.39896 | ||||||||
\(650\) | 0.612646 | 0.0240300 | ||||||||
\(651\) | 12.8927 | 0.505304 | ||||||||
\(652\) | −6.76940 | −0.265110 | ||||||||
\(653\) | −14.6358 | −0.572744 | −0.286372 | − | 0.958119i | \(-0.592449\pi\) | ||||
−0.286372 | + | 0.958119i | \(0.592449\pi\) | |||||||
\(654\) | 5.95055 | 0.232685 | ||||||||
\(655\) | 0.709275 | 0.0277137 | ||||||||
\(656\) | 7.92738 | 0.309512 | ||||||||
\(657\) | −3.73820 | −0.145841 | ||||||||
\(658\) | 54.7442 | 2.13415 | ||||||||
\(659\) | −46.4934 | −1.81113 | −0.905564 | − | 0.424210i | \(-0.860552\pi\) | ||||
−0.905564 | + | 0.424210i | \(0.860552\pi\) | |||||||
\(660\) | −3.70928 | −0.144383 | ||||||||
\(661\) | −38.3812 | −1.49286 | −0.746428 | − | 0.665466i | \(-0.768233\pi\) | ||||
−0.746428 | + | 0.665466i | \(0.768233\pi\) | |||||||
\(662\) | 2.30406 | 0.0895497 | ||||||||
\(663\) | −8.28231 | −0.321658 | ||||||||
\(664\) | −7.42469 | −0.288134 | ||||||||
\(665\) | −2.63090 | −0.102022 | ||||||||
\(666\) | −12.2690 | −0.475413 | ||||||||
\(667\) | −48.5113 | −1.87837 | ||||||||
\(668\) | −6.54987 | −0.253422 | ||||||||
\(669\) | 25.5174 | 0.986562 | ||||||||
\(670\) | 3.34017 | 0.129042 | ||||||||
\(671\) | −48.1133 | −1.85739 | ||||||||
\(672\) | 5.58864 | 0.215586 | ||||||||
\(673\) | 41.6658 | 1.60610 | 0.803049 | − | 0.595913i | \(-0.203210\pi\) | ||||
0.803049 | + | 0.595913i | \(0.203210\pi\) | |||||||
\(674\) | −30.3995 | −1.17094 | ||||||||
\(675\) | 0.290725 | 0.0111900 | ||||||||
\(676\) | −4.10647 | −0.157941 | ||||||||
\(677\) | 43.6875 | 1.67905 | 0.839524 | − | 0.543322i | \(-0.182834\pi\) | ||||
0.839524 | + | 0.543322i | \(0.182834\pi\) | |||||||
\(678\) | −16.2329 | −0.623419 | ||||||||
\(679\) | 37.8348 | 1.45197 | ||||||||
\(680\) | 32.9542 | 1.26374 | ||||||||
\(681\) | 23.6381 | 0.905813 | ||||||||
\(682\) | −33.9194 | −1.29884 | ||||||||
\(683\) | −40.3584 | −1.54427 | −0.772136 | − | 0.635457i | \(-0.780812\pi\) | ||||
−0.772136 | + | 0.635457i | \(0.780812\pi\) | |||||||
\(684\) | −0.165166 | −0.00631528 | ||||||||
\(685\) | 18.2351 | 0.696729 | ||||||||
\(686\) | −27.7721 | −1.06034 | ||||||||
\(687\) | −3.75872 | −0.143404 | ||||||||
\(688\) | 4.60197 | 0.175448 | ||||||||
\(689\) | 5.52586 | 0.210518 | ||||||||
\(690\) | 18.6670 | 0.710641 | ||||||||
\(691\) | −0.255652 | −0.00972547 | −0.00486273 | − | 0.999988i | \(-0.501548\pi\) | ||||
−0.00486273 | + | 0.999988i | \(0.501548\pi\) | |||||||
\(692\) | −2.91321 | −0.110744 | ||||||||
\(693\) | 12.5464 | 0.476597 | ||||||||
\(694\) | −35.7854 | −1.35839 | ||||||||
\(695\) | −1.59705 | −0.0605795 | ||||||||
\(696\) | 21.7899 | 0.825945 | ||||||||
\(697\) | 10.4208 | 0.394717 | ||||||||
\(698\) | −14.2522 | −0.539452 | ||||||||
\(699\) | −24.6670 | −0.932992 | ||||||||
\(700\) | −0.290725 | −0.0109884 | ||||||||
\(701\) | 15.2218 | 0.574920 | 0.287460 | − | 0.957793i | \(-0.407189\pi\) | ||||
0.287460 | + | 0.957793i | \(0.407189\pi\) | |||||||
\(702\) | 2.10731 | 0.0795352 | ||||||||
\(703\) | 3.56690 | 0.134528 | ||||||||
\(704\) | 27.9194 | 1.05225 | ||||||||
\(705\) | −28.4885 | −1.07294 | ||||||||
\(706\) | −24.8888 | −0.936703 | ||||||||
\(707\) | −47.5936 | −1.78994 | ||||||||
\(708\) | −2.84059 | −0.106756 | ||||||||
\(709\) | −9.56916 | −0.359377 | −0.179689 | − | 0.983724i | \(-0.557509\pi\) | ||||
−0.179689 | + | 0.983724i | \(0.557509\pi\) | |||||||
\(710\) | 36.6453 | 1.37527 | ||||||||
\(711\) | 5.65983 | 0.212260 | ||||||||
\(712\) | −2.04414 | −0.0766075 | ||||||||
\(713\) | 26.5948 | 0.995982 | ||||||||
\(714\) | 25.2267 | 0.944086 | ||||||||
\(715\) | −13.7587 | −0.514547 | ||||||||
\(716\) | 0.573039 | 0.0214155 | ||||||||
\(717\) | −2.08452 | −0.0778479 | ||||||||
\(718\) | 6.61879 | 0.247011 | ||||||||
\(719\) | 21.9516 | 0.818656 | 0.409328 | − | 0.912387i | \(-0.365763\pi\) | ||||
0.409328 | + | 0.912387i | \(0.365763\pi\) | |||||||
\(720\) | −9.98667 | −0.372181 | ||||||||
\(721\) | −28.5730 | −1.06412 | ||||||||
\(722\) | −28.9364 | −1.07690 | ||||||||
\(723\) | 10.1012 | 0.375666 | ||||||||
\(724\) | 3.59129 | 0.133469 | ||||||||
\(725\) | −2.52359 | −0.0937238 | ||||||||
\(726\) | −16.0772 | −0.596679 | ||||||||
\(727\) | 6.70540 | 0.248690 | 0.124345 | − | 0.992239i | \(-0.460317\pi\) | ||||
0.124345 | + | 0.992239i | \(0.460317\pi\) | |||||||
\(728\) | 9.31124 | 0.345098 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −12.4863 | −0.462137 | ||||||||
\(731\) | 6.04945 | 0.223747 | ||||||||
\(732\) | 3.83483 | 0.141740 | ||||||||
\(733\) | −38.9939 | −1.44027 | −0.720135 | − | 0.693833i | \(-0.755920\pi\) | ||||
−0.720135 | + | 0.693833i | \(0.755920\pi\) | |||||||
\(734\) | 54.5380 | 2.01303 | ||||||||
\(735\) | −0.738205 | −0.0272291 | ||||||||
\(736\) | 11.5281 | 0.424932 | ||||||||
\(737\) | 4.63090 | 0.170581 | ||||||||
\(738\) | −2.65142 | −0.0976000 | ||||||||
\(739\) | 26.9565 | 0.991612 | 0.495806 | − | 0.868433i | \(-0.334873\pi\) | ||||
0.495806 | + | 0.868433i | \(0.334873\pi\) | |||||||
\(740\) | −6.38470 | −0.234706 | ||||||||
\(741\) | −0.612646 | −0.0225061 | ||||||||
\(742\) | −16.8310 | −0.617884 | ||||||||
\(743\) | 31.3428 | 1.14986 | 0.574928 | − | 0.818204i | \(-0.305030\pi\) | ||||
0.574928 | + | 0.818204i | \(0.305030\pi\) | |||||||
\(744\) | −11.9456 | −0.437948 | ||||||||
\(745\) | 29.4596 | 1.07932 | ||||||||
\(746\) | −23.5259 | −0.861343 | ||||||||
\(747\) | 2.95774 | 0.108218 | ||||||||
\(748\) | −10.3402 | −0.378074 | ||||||||
\(749\) | 1.70928 | 0.0624556 | ||||||||
\(750\) | 17.6719 | 0.645288 | ||||||||
\(751\) | 6.01438 | 0.219468 | 0.109734 | − | 0.993961i | \(-0.465000\pi\) | ||||
0.109734 | + | 0.993961i | \(0.465000\pi\) | |||||||
\(752\) | −60.4138 | −2.20307 | ||||||||
\(753\) | 10.8371 | 0.394926 | ||||||||
\(754\) | −18.2922 | −0.666161 | ||||||||
\(755\) | 45.6658 | 1.66195 | ||||||||
\(756\) | −1.00000 | −0.0363696 | ||||||||
\(757\) | −3.57531 | −0.129947 | −0.0649734 | − | 0.997887i | \(-0.520696\pi\) | ||||
−0.0649734 | + | 0.997887i | \(0.520696\pi\) | |||||||
\(758\) | −22.3802 | −0.812884 | ||||||||
\(759\) | 25.8804 | 0.939399 | ||||||||
\(760\) | 2.43764 | 0.0884225 | ||||||||
\(761\) | −7.81205 | −0.283187 | −0.141593 | − | 0.989925i | \(-0.545223\pi\) | ||||
−0.141593 | + | 0.989925i | \(0.545223\pi\) | |||||||
\(762\) | −30.4885 | −1.10448 | ||||||||
\(763\) | −10.4741 | −0.379189 | ||||||||
\(764\) | 4.46573 | 0.161565 | ||||||||
\(765\) | −13.1278 | −0.474638 | ||||||||
\(766\) | 4.82726 | 0.174416 | ||||||||
\(767\) | −10.5365 | −0.380452 | ||||||||
\(768\) | −8.57531 | −0.309435 | ||||||||
\(769\) | −21.2990 | −0.768060 | −0.384030 | − | 0.923321i | \(-0.625464\pi\) | ||||
−0.384030 | + | 0.923321i | \(0.625464\pi\) | |||||||
\(770\) | 41.9071 | 1.51023 | ||||||||
\(771\) | −25.3607 | −0.913343 | ||||||||
\(772\) | 4.65142 | 0.167408 | ||||||||
\(773\) | −20.1522 | −0.724825 | −0.362412 | − | 0.932018i | \(-0.618047\pi\) | ||||
−0.362412 | + | 0.932018i | \(0.618047\pi\) | |||||||
\(774\) | −1.53919 | −0.0553250 | ||||||||
\(775\) | 1.38348 | 0.0496960 | ||||||||
\(776\) | −35.0556 | −1.25842 | ||||||||
\(777\) | 21.5958 | 0.774746 | ||||||||
\(778\) | 41.4656 | 1.48661 | ||||||||
\(779\) | 0.770832 | 0.0276179 | ||||||||
\(780\) | 1.09663 | 0.0392656 | ||||||||
\(781\) | 50.8059 | 1.81798 | ||||||||
\(782\) | 52.0372 | 1.86085 | ||||||||
\(783\) | −8.68035 | −0.310210 | ||||||||
\(784\) | −1.56547 | −0.0559095 | ||||||||
\(785\) | −15.7142 | −0.560864 | ||||||||
\(786\) | −0.503072 | −0.0179440 | ||||||||
\(787\) | 17.9048 | 0.638237 | 0.319119 | − | 0.947715i | \(-0.396613\pi\) | ||||
0.319119 | + | 0.947715i | \(0.396613\pi\) | |||||||
\(788\) | −1.64650 | −0.0586540 | ||||||||
\(789\) | 12.9311 | 0.460359 | ||||||||
\(790\) | 18.9048 | 0.672603 | ||||||||
\(791\) | 28.5730 | 1.01594 | ||||||||
\(792\) | −11.6248 | −0.413068 | ||||||||
\(793\) | 14.2245 | 0.505125 | ||||||||
\(794\) | −27.3751 | −0.971505 | ||||||||
\(795\) | 8.75872 | 0.310640 | ||||||||
\(796\) | −3.35085 | −0.118768 | ||||||||
\(797\) | 25.3958 | 0.899564 | 0.449782 | − | 0.893138i | \(-0.351502\pi\) | ||||
0.449782 | + | 0.893138i | \(0.351502\pi\) | |||||||
\(798\) | 1.86603 | 0.0660568 | ||||||||
\(799\) | −79.4161 | −2.80954 | ||||||||
\(800\) | 0.599701 | 0.0212026 | ||||||||
\(801\) | 0.814315 | 0.0287724 | ||||||||
\(802\) | 15.2953 | 0.540094 | ||||||||
\(803\) | −17.3112 | −0.610901 | ||||||||
\(804\) | −0.369102 | −0.0130172 | ||||||||
\(805\) | −32.8576 | −1.15808 | ||||||||
\(806\) | 10.0281 | 0.353224 | ||||||||
\(807\) | −22.0638 | −0.776683 | ||||||||
\(808\) | 44.0975 | 1.55134 | ||||||||
\(809\) | −13.8482 | −0.486876 | −0.243438 | − | 0.969917i | \(-0.578275\pi\) | ||||
−0.243438 | + | 0.969917i | \(0.578275\pi\) | |||||||
\(810\) | 3.34017 | 0.117362 | ||||||||
\(811\) | −15.4924 | −0.544012 | −0.272006 | − | 0.962296i | \(-0.587687\pi\) | ||||
−0.272006 | + | 0.962296i | \(0.587687\pi\) | |||||||
\(812\) | 8.68035 | 0.304620 | ||||||||
\(813\) | −16.1834 | −0.567577 | ||||||||
\(814\) | −56.8164 | −1.99141 | ||||||||
\(815\) | −39.7998 | −1.39412 | ||||||||
\(816\) | −27.8394 | −0.974573 | ||||||||
\(817\) | 0.447480 | 0.0156553 | ||||||||
\(818\) | −28.1810 | −0.985325 | ||||||||
\(819\) | −3.70928 | −0.129613 | ||||||||
\(820\) | −1.37978 | −0.0481840 | ||||||||
\(821\) | −34.7670 | −1.21338 | −0.606688 | − | 0.794940i | \(-0.707502\pi\) | ||||
−0.606688 | + | 0.794940i | \(0.707502\pi\) | |||||||
\(822\) | −12.9337 | −0.451116 | ||||||||
\(823\) | −42.4573 | −1.47997 | −0.739985 | − | 0.672624i | \(-0.765167\pi\) | ||||
−0.739985 | + | 0.672624i | \(0.765167\pi\) | |||||||
\(824\) | 26.4741 | 0.922270 | ||||||||
\(825\) | 1.34632 | 0.0468727 | ||||||||
\(826\) | 32.0928 | 1.11665 | ||||||||
\(827\) | −35.6802 | −1.24072 | −0.620361 | − | 0.784317i | \(-0.713014\pi\) | ||||
−0.620361 | + | 0.784317i | \(0.713014\pi\) | |||||||
\(828\) | −2.06278 | −0.0716865 | ||||||||
\(829\) | −26.2823 | −0.912823 | −0.456411 | − | 0.889769i | \(-0.650865\pi\) | ||||
−0.456411 | + | 0.889769i | \(0.650865\pi\) | |||||||
\(830\) | 9.87936 | 0.342918 | ||||||||
\(831\) | 2.86991 | 0.0995560 | ||||||||
\(832\) | −8.25422 | −0.286164 | ||||||||
\(833\) | −2.05786 | −0.0713006 | ||||||||
\(834\) | 1.13275 | 0.0392238 | ||||||||
\(835\) | −38.5090 | −1.33266 | ||||||||
\(836\) | −0.764867 | −0.0264535 | ||||||||
\(837\) | 4.75872 | 0.164486 | ||||||||
\(838\) | −24.5995 | −0.849776 | ||||||||
\(839\) | 12.0806 | 0.417070 | 0.208535 | − | 0.978015i | \(-0.433130\pi\) | ||||
0.208535 | + | 0.978015i | \(0.433130\pi\) | |||||||
\(840\) | 14.7587 | 0.509224 | ||||||||
\(841\) | 46.3484 | 1.59822 | ||||||||
\(842\) | 56.6007 | 1.95059 | ||||||||
\(843\) | 6.63090 | 0.228380 | ||||||||
\(844\) | 5.68118 | 0.195554 | ||||||||
\(845\) | −24.1434 | −0.830559 | ||||||||
\(846\) | 20.2062 | 0.694704 | ||||||||
\(847\) | 28.2990 | 0.972364 | ||||||||
\(848\) | 18.5741 | 0.637837 | ||||||||
\(849\) | −16.2329 | −0.557111 | ||||||||
\(850\) | 2.70701 | 0.0928496 | ||||||||
\(851\) | 44.5474 | 1.52707 | ||||||||
\(852\) | −4.04945 | −0.138732 | ||||||||
\(853\) | −27.0472 | −0.926078 | −0.463039 | − | 0.886338i | \(-0.653241\pi\) | ||||
−0.463039 | + | 0.886338i | \(0.653241\pi\) | |||||||
\(854\) | −43.3256 | −1.48257 | ||||||||
\(855\) | −0.971071 | −0.0332099 | ||||||||
\(856\) | −1.58372 | −0.0541303 | ||||||||
\(857\) | 44.2956 | 1.51311 | 0.756555 | − | 0.653930i | \(-0.226881\pi\) | ||||
0.756555 | + | 0.653930i | \(0.226881\pi\) | |||||||
\(858\) | 9.75872 | 0.333157 | ||||||||
\(859\) | 27.2990 | 0.931428 | 0.465714 | − | 0.884935i | \(-0.345797\pi\) | ||||
0.465714 | + | 0.884935i | \(0.345797\pi\) | |||||||
\(860\) | −0.800984 | −0.0273133 | ||||||||
\(861\) | 4.66701 | 0.159051 | ||||||||
\(862\) | 32.5402 | 1.10832 | ||||||||
\(863\) | 10.7477 | 0.365855 | 0.182927 | − | 0.983126i | \(-0.441443\pi\) | ||||
0.182927 | + | 0.983126i | \(0.441443\pi\) | |||||||
\(864\) | 2.06278 | 0.0701772 | ||||||||
\(865\) | −17.1278 | −0.582364 | ||||||||
\(866\) | 20.5646 | 0.698815 | ||||||||
\(867\) | −19.5958 | −0.665509 | ||||||||
\(868\) | −4.75872 | −0.161522 | ||||||||
\(869\) | 26.2101 | 0.889116 | ||||||||
\(870\) | −28.9939 | −0.982984 | ||||||||
\(871\) | −1.36910 | −0.0463903 | ||||||||
\(872\) | 9.70474 | 0.328644 | ||||||||
\(873\) | 13.9649 | 0.472641 | ||||||||
\(874\) | 3.84921 | 0.130201 | ||||||||
\(875\) | −31.1061 | −1.05158 | ||||||||
\(876\) | 1.37978 | 0.0466185 | ||||||||
\(877\) | 45.0349 | 1.52072 | 0.760360 | − | 0.649502i | \(-0.225022\pi\) | ||||
0.760360 | + | 0.649502i | \(0.225022\pi\) | |||||||
\(878\) | −39.3172 | −1.32689 | ||||||||
\(879\) | −33.3340 | −1.12433 | ||||||||
\(880\) | −46.2472 | −1.55899 | ||||||||
\(881\) | −39.9155 | −1.34479 | −0.672393 | − | 0.740194i | \(-0.734734\pi\) | ||||
−0.672393 | + | 0.740194i | \(0.734734\pi\) | |||||||
\(882\) | 0.523590 | 0.0176302 | ||||||||
\(883\) | −7.94828 | −0.267481 | −0.133741 | − | 0.991016i | \(-0.542699\pi\) | ||||
−0.133741 | + | 0.991016i | \(0.542699\pi\) | |||||||
\(884\) | 3.05702 | 0.102819 | ||||||||
\(885\) | −16.7009 | −0.561393 | ||||||||
\(886\) | −29.8537 | −1.00296 | ||||||||
\(887\) | 31.2934 | 1.05073 | 0.525364 | − | 0.850877i | \(-0.323929\pi\) | ||||
0.525364 | + | 0.850877i | \(0.323929\pi\) | |||||||
\(888\) | −20.0095 | −0.671473 | ||||||||
\(889\) | 53.6658 | 1.79989 | ||||||||
\(890\) | 2.71995 | 0.0911730 | ||||||||
\(891\) | 4.63090 | 0.155141 | ||||||||
\(892\) | −9.41855 | −0.315356 | ||||||||
\(893\) | −5.87444 | −0.196581 | ||||||||
\(894\) | −20.8950 | −0.698832 | ||||||||
\(895\) | 3.36910 | 0.112617 | ||||||||
\(896\) | 36.3184 | 1.21331 | ||||||||
\(897\) | −7.65142 | −0.255473 | ||||||||
\(898\) | −32.8020 | −1.09462 | ||||||||
\(899\) | −41.3074 | −1.37768 | ||||||||
\(900\) | −0.107307 | −0.00357691 | ||||||||
\(901\) | 24.4163 | 0.813424 | ||||||||
\(902\) | −12.2784 | −0.408827 | ||||||||
\(903\) | 2.70928 | 0.0901590 | ||||||||
\(904\) | −26.4741 | −0.880517 | ||||||||
\(905\) | 21.1145 | 0.701870 | ||||||||
\(906\) | −32.3896 | −1.07607 | ||||||||
\(907\) | −17.9733 | −0.596795 | −0.298397 | − | 0.954442i | \(-0.596452\pi\) | ||||
−0.298397 | + | 0.954442i | \(0.596452\pi\) | |||||||
\(908\) | −8.72487 | −0.289545 | ||||||||
\(909\) | −17.5669 | −0.582657 | ||||||||
\(910\) | −12.3896 | −0.410712 | ||||||||
\(911\) | 49.0121 | 1.62384 | 0.811922 | − | 0.583766i | \(-0.198422\pi\) | ||||
0.811922 | + | 0.583766i | \(0.198422\pi\) | |||||||
\(912\) | −2.05929 | −0.0681899 | ||||||||
\(913\) | 13.6970 | 0.453304 | ||||||||
\(914\) | −37.9688 | −1.25590 | ||||||||
\(915\) | 22.5464 | 0.745360 | ||||||||
\(916\) | 1.38735 | 0.0458395 | ||||||||
\(917\) | 0.885505 | 0.0292419 | ||||||||
\(918\) | 9.31124 | 0.307317 | ||||||||
\(919\) | 46.6307 | 1.53821 | 0.769103 | − | 0.639125i | \(-0.220703\pi\) | ||||
0.769103 | + | 0.639125i | \(0.220703\pi\) | |||||||
\(920\) | 30.4440 | 1.00371 | ||||||||
\(921\) | −24.5113 | −0.807675 | ||||||||
\(922\) | 37.8576 | 1.24677 | ||||||||
\(923\) | −15.0205 | −0.494406 | ||||||||
\(924\) | −4.63090 | −0.152345 | ||||||||
\(925\) | 2.31739 | 0.0761952 | ||||||||
\(926\) | 1.22180 | 0.0401509 | ||||||||
\(927\) | −10.5464 | −0.346388 | ||||||||
\(928\) | −17.9056 | −0.587781 | ||||||||
\(929\) | 39.9214 | 1.30978 | 0.654890 | − | 0.755724i | \(-0.272715\pi\) | ||||
0.654890 | + | 0.755724i | \(0.272715\pi\) | |||||||
\(930\) | 15.8950 | 0.521216 | ||||||||
\(931\) | −0.152221 | −0.00498883 | ||||||||
\(932\) | 9.10465 | 0.298233 | ||||||||
\(933\) | 3.21235 | 0.105168 | ||||||||
\(934\) | 8.93987 | 0.292522 | ||||||||
\(935\) | −60.7936 | −1.98816 | ||||||||
\(936\) | 3.43680 | 0.112335 | ||||||||
\(937\) | 34.6888 | 1.13323 | 0.566616 | − | 0.823982i | \(-0.308252\pi\) | ||||
0.566616 | + | 0.823982i | \(0.308252\pi\) | |||||||
\(938\) | 4.17009 | 0.136158 | ||||||||
\(939\) | −7.55252 | −0.246467 | ||||||||
\(940\) | 10.5152 | 0.342967 | ||||||||
\(941\) | −15.6248 | −0.509352 | −0.254676 | − | 0.967026i | \(-0.581969\pi\) | ||||
−0.254676 | + | 0.967026i | \(0.581969\pi\) | |||||||
\(942\) | 11.1457 | 0.363146 | ||||||||
\(943\) | 9.62702 | 0.313499 | ||||||||
\(944\) | −35.4165 | −1.15271 | ||||||||
\(945\) | −5.87936 | −0.191256 | ||||||||
\(946\) | −7.12783 | −0.231746 | ||||||||
\(947\) | 29.9432 | 0.973023 | 0.486511 | − | 0.873674i | \(-0.338269\pi\) | ||||
0.486511 | + | 0.873674i | \(0.338269\pi\) | |||||||
\(948\) | −2.08906 | −0.0678494 | ||||||||
\(949\) | 5.11799 | 0.166137 | ||||||||
\(950\) | 0.200238 | 0.00649659 | ||||||||
\(951\) | 6.72979 | 0.218229 | ||||||||
\(952\) | 41.1422 | 1.33343 | ||||||||
\(953\) | 42.3234 | 1.37099 | 0.685494 | − | 0.728078i | \(-0.259586\pi\) | ||||
0.685494 | + | 0.728078i | \(0.259586\pi\) | |||||||
\(954\) | −6.21235 | −0.201132 | ||||||||
\(955\) | 26.2557 | 0.849613 | ||||||||
\(956\) | 0.769402 | 0.0248842 | ||||||||
\(957\) | −40.1978 | −1.29941 | ||||||||
\(958\) | 9.66209 | 0.312168 | ||||||||
\(959\) | 22.7659 | 0.735150 | ||||||||
\(960\) | −13.0833 | −0.422262 | ||||||||
\(961\) | −8.35455 | −0.269502 | ||||||||
\(962\) | 16.7975 | 0.541573 | ||||||||
\(963\) | 0.630898 | 0.0203304 | ||||||||
\(964\) | −3.72836 | −0.120083 | ||||||||
\(965\) | 27.3474 | 0.880343 | ||||||||
\(966\) | 23.3051 | 0.749829 | ||||||||
\(967\) | −15.4368 | −0.496414 | −0.248207 | − | 0.968707i | \(-0.579841\pi\) | ||||
−0.248207 | + | 0.968707i | \(0.579841\pi\) | |||||||
\(968\) | −26.2202 | −0.842749 | ||||||||
\(969\) | −2.70701 | −0.0869616 | ||||||||
\(970\) | 46.6453 | 1.49769 | ||||||||
\(971\) | 28.8143 | 0.924695 | 0.462348 | − | 0.886699i | \(-0.347007\pi\) | ||||
0.462348 | + | 0.886699i | \(0.347007\pi\) | |||||||
\(972\) | −0.369102 | −0.0118390 | ||||||||
\(973\) | −1.99386 | −0.0639201 | ||||||||
\(974\) | 14.2651 | 0.457084 | ||||||||
\(975\) | −0.398032 | −0.0127472 | ||||||||
\(976\) | 47.8127 | 1.53045 | ||||||||
\(977\) | 9.78539 | 0.313062 | 0.156531 | − | 0.987673i | \(-0.449969\pi\) | ||||
0.156531 | + | 0.987673i | \(0.449969\pi\) | |||||||
\(978\) | 28.2290 | 0.902664 | ||||||||
\(979\) | 3.77101 | 0.120522 | ||||||||
\(980\) | 0.272473 | 0.00870384 | ||||||||
\(981\) | −3.86603 | −0.123433 | ||||||||
\(982\) | −37.6498 | −1.20145 | ||||||||
\(983\) | −27.2495 | −0.869124 | −0.434562 | − | 0.900642i | \(-0.643097\pi\) | ||||
−0.434562 | + | 0.900642i | \(0.643097\pi\) | |||||||
\(984\) | −4.32419 | −0.137850 | ||||||||
\(985\) | −9.68035 | −0.308441 | ||||||||
\(986\) | −80.8248 | −2.57399 | ||||||||
\(987\) | −35.5669 | −1.13211 | ||||||||
\(988\) | 0.226129 | 0.00719413 | ||||||||
\(989\) | 5.58864 | 0.177708 | ||||||||
\(990\) | 15.4680 | 0.491605 | ||||||||
\(991\) | −41.6186 | −1.32206 | −0.661029 | − | 0.750360i | \(-0.729880\pi\) | ||||
−0.661029 | + | 0.750360i | \(0.729880\pi\) | |||||||
\(992\) | 9.81620 | 0.311665 | ||||||||
\(993\) | −1.49693 | −0.0475036 | ||||||||
\(994\) | 45.7503 | 1.45111 | ||||||||
\(995\) | −19.7009 | −0.624559 | ||||||||
\(996\) | −1.09171 | −0.0345921 | ||||||||
\(997\) | 1.03507 | 0.0327811 | 0.0163905 | − | 0.999866i | \(-0.494782\pi\) | ||||
0.0163905 | + | 0.999866i | \(0.494782\pi\) | |||||||
\(998\) | 36.0677 | 1.14170 | ||||||||
\(999\) | 7.97107 | 0.252194 |
(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 | 201.2.a.d.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 603.2.a.i.1.2 | 3 | |||
4.3 | odd | 2 | 3216.2.a.u.1.3 | 3 | |||
5.4 | even | 2 | 5025.2.a.m.1.2 | 3 | |||
7.6 | odd | 2 | 9849.2.a.ba.1.2 | 3 | |||
12.11 | even | 2 | 9648.2.a.bn.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
201.2.a.d.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
603.2.a.i.1.2 | 3 | 3.2 | odd | 2 | |||
3216.2.a.u.1.3 | 3 | 4.3 | odd | 2 | |||
5025.2.a.m.1.2 | 3 | 5.4 | even | 2 | |||
9648.2.a.bn.1.1 | 3 | 12.11 | even | 2 | |||
9849.2.a.ba.1.2 | 3 | 7.6 | odd | 2 |