Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,2,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1849.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.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: | \(14.7643393337\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\Q(\zeta_{44})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 11x^{8} + 44x^{6} - 77x^{4} + 55x^{2} - 11 \) |
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 | \(-1.81926\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.81926 | −1.28641 | −0.643207 | − | 0.765692i | \(-0.722397\pi\) | ||||
−0.643207 | + | 0.765692i | \(0.722397\pi\) | |||||||
\(3\) | −1.25580 | −0.725036 | −0.362518 | − | 0.931977i | \(-0.618083\pi\) | ||||
−0.362518 | + | 0.931977i | \(0.618083\pi\) | |||||||
\(4\) | 1.30972 | 0.654861 | ||||||||
\(5\) | −0.160379 | −0.0717236 | −0.0358618 | − | 0.999357i | \(-0.511418\pi\) | ||||
−0.0358618 | + | 0.999357i | \(0.511418\pi\) | |||||||
\(6\) | 2.28463 | 0.932696 | ||||||||
\(7\) | 4.31672 | 1.63157 | 0.815784 | − | 0.578357i | \(-0.196306\pi\) | ||||
0.815784 | + | 0.578357i | \(0.196306\pi\) | |||||||
\(8\) | 1.25580 | 0.443992 | ||||||||
\(9\) | −1.42297 | −0.474323 | ||||||||
\(10\) | 0.291772 | 0.0922663 | ||||||||
\(11\) | −0.148323 | −0.0447211 | −0.0223605 | − | 0.999750i | \(-0.507118\pi\) | ||||
−0.0223605 | + | 0.999750i | \(0.507118\pi\) | |||||||
\(12\) | −1.64475 | −0.474797 | ||||||||
\(13\) | 1.68675 | 0.467821 | 0.233910 | − | 0.972258i | \(-0.424848\pi\) | ||||
0.233910 | + | 0.972258i | \(0.424848\pi\) | |||||||
\(14\) | −7.85326 | −2.09887 | ||||||||
\(15\) | 0.201404 | 0.0520022 | ||||||||
\(16\) | −4.90407 | −1.22602 | ||||||||
\(17\) | −5.73187 | −1.39018 | −0.695091 | − | 0.718922i | \(-0.744636\pi\) | ||||
−0.695091 | + | 0.718922i | \(0.744636\pi\) | |||||||
\(18\) | 2.58876 | 0.610176 | ||||||||
\(19\) | 4.22912 | 0.970228 | 0.485114 | − | 0.874451i | \(-0.338778\pi\) | ||||
0.485114 | + | 0.874451i | \(0.338778\pi\) | |||||||
\(20\) | −0.210052 | −0.0469690 | ||||||||
\(21\) | −5.42094 | −1.18295 | ||||||||
\(22\) | 0.269839 | 0.0575298 | ||||||||
\(23\) | −3.75285 | −0.782524 | −0.391262 | − | 0.920279i | \(-0.627961\pi\) | ||||
−0.391262 | + | 0.920279i | \(0.627961\pi\) | |||||||
\(24\) | −1.57703 | −0.321910 | ||||||||
\(25\) | −4.97428 | −0.994856 | ||||||||
\(26\) | −3.06865 | −0.601811 | ||||||||
\(27\) | 5.55436 | 1.06894 | ||||||||
\(28\) | 5.65371 | 1.06845 | ||||||||
\(29\) | −8.83708 | −1.64101 | −0.820503 | − | 0.571643i | \(-0.806306\pi\) | ||||
−0.820503 | + | 0.571643i | \(0.806306\pi\) | |||||||
\(30\) | −0.366406 | −0.0668963 | ||||||||
\(31\) | 8.64308 | 1.55234 | 0.776172 | − | 0.630522i | \(-0.217159\pi\) | ||||
0.776172 | + | 0.630522i | \(0.217159\pi\) | |||||||
\(32\) | 6.41020 | 1.13317 | ||||||||
\(33\) | 0.186264 | 0.0324244 | ||||||||
\(34\) | 10.4278 | 1.78835 | ||||||||
\(35\) | −0.692311 | −0.117022 | ||||||||
\(36\) | −1.86369 | −0.310616 | ||||||||
\(37\) | −7.19452 | −1.18277 | −0.591386 | − | 0.806389i | \(-0.701419\pi\) | ||||
−0.591386 | + | 0.806389i | \(0.701419\pi\) | |||||||
\(38\) | −7.69389 | −1.24811 | ||||||||
\(39\) | −2.11822 | −0.339187 | ||||||||
\(40\) | −0.201404 | −0.0318447 | ||||||||
\(41\) | −3.67049 | −0.573234 | −0.286617 | − | 0.958045i | \(-0.592531\pi\) | ||||
−0.286617 | + | 0.958045i | \(0.592531\pi\) | |||||||
\(42\) | 9.86211 | 1.52176 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | −0.194262 | −0.0292861 | ||||||||
\(45\) | 0.228214 | 0.0340202 | ||||||||
\(46\) | 6.82743 | 1.00665 | ||||||||
\(47\) | −2.13120 | −0.310867 | −0.155434 | − | 0.987846i | \(-0.549677\pi\) | ||||
−0.155434 | + | 0.987846i | \(0.549677\pi\) | |||||||
\(48\) | 6.15853 | 0.888907 | ||||||||
\(49\) | 11.6341 | 1.66201 | ||||||||
\(50\) | 9.04953 | 1.27980 | ||||||||
\(51\) | 7.19807 | 1.00793 | ||||||||
\(52\) | 2.20918 | 0.306357 | ||||||||
\(53\) | 1.98798 | 0.273071 | 0.136535 | − | 0.990635i | \(-0.456403\pi\) | ||||
0.136535 | + | 0.990635i | \(0.456403\pi\) | |||||||
\(54\) | −10.1048 | −1.37510 | ||||||||
\(55\) | 0.0237879 | 0.00320756 | ||||||||
\(56\) | 5.42094 | 0.724403 | ||||||||
\(57\) | −5.31093 | −0.703450 | ||||||||
\(58\) | 16.0770 | 2.11101 | ||||||||
\(59\) | 11.3627 | 1.47930 | 0.739648 | − | 0.672993i | \(-0.234992\pi\) | ||||
0.739648 | + | 0.672993i | \(0.234992\pi\) | |||||||
\(60\) | 0.263783 | 0.0340542 | ||||||||
\(61\) | −5.65302 | −0.723796 | −0.361898 | − | 0.932218i | \(-0.617871\pi\) | ||||
−0.361898 | + | 0.932218i | \(0.617871\pi\) | |||||||
\(62\) | −15.7240 | −1.99696 | ||||||||
\(63\) | −6.14256 | −0.773890 | ||||||||
\(64\) | −1.85371 | −0.231714 | ||||||||
\(65\) | −0.270519 | −0.0335538 | ||||||||
\(66\) | −0.338863 | −0.0417112 | ||||||||
\(67\) | −1.42587 | −0.174197 | −0.0870986 | − | 0.996200i | \(-0.527760\pi\) | ||||
−0.0870986 | + | 0.996200i | \(0.527760\pi\) | |||||||
\(68\) | −7.50715 | −0.910375 | ||||||||
\(69\) | 4.71283 | 0.567358 | ||||||||
\(70\) | 1.25950 | 0.150539 | ||||||||
\(71\) | 7.56187 | 0.897429 | 0.448715 | − | 0.893675i | \(-0.351882\pi\) | ||||
0.448715 | + | 0.893675i | \(0.351882\pi\) | |||||||
\(72\) | −1.78696 | −0.210596 | ||||||||
\(73\) | 4.99089 | 0.584140 | 0.292070 | − | 0.956397i | \(-0.405656\pi\) | ||||
0.292070 | + | 0.956397i | \(0.405656\pi\) | |||||||
\(74\) | 13.0887 | 1.52153 | ||||||||
\(75\) | 6.24669 | 0.721306 | ||||||||
\(76\) | 5.53898 | 0.635364 | ||||||||
\(77\) | −0.640269 | −0.0729654 | ||||||||
\(78\) | 3.85360 | 0.436335 | ||||||||
\(79\) | −14.8660 | −1.67255 | −0.836277 | − | 0.548306i | \(-0.815273\pi\) | ||||
−0.836277 | + | 0.548306i | \(0.815273\pi\) | |||||||
\(80\) | 0.786510 | 0.0879345 | ||||||||
\(81\) | −2.70625 | −0.300695 | ||||||||
\(82\) | 6.67759 | 0.737417 | ||||||||
\(83\) | −6.11970 | −0.671725 | −0.335862 | − | 0.941911i | \(-0.609028\pi\) | ||||
−0.335862 | + | 0.941911i | \(0.609028\pi\) | |||||||
\(84\) | −7.09992 | −0.774664 | ||||||||
\(85\) | 0.919270 | 0.0997089 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 11.0976 | 1.18979 | ||||||||
\(88\) | −0.186264 | −0.0198558 | ||||||||
\(89\) | 8.33340 | 0.883339 | 0.441670 | − | 0.897178i | \(-0.354386\pi\) | ||||
0.441670 | + | 0.897178i | \(0.354386\pi\) | |||||||
\(90\) | −0.415182 | −0.0437640 | ||||||||
\(91\) | 7.28124 | 0.763281 | ||||||||
\(92\) | −4.91519 | −0.512444 | ||||||||
\(93\) | −10.8540 | −1.12550 | ||||||||
\(94\) | 3.87721 | 0.399904 | ||||||||
\(95\) | −0.678262 | −0.0695882 | ||||||||
\(96\) | −8.04993 | −0.821592 | ||||||||
\(97\) | 2.10967 | 0.214204 | 0.107102 | − | 0.994248i | \(-0.465843\pi\) | ||||
0.107102 | + | 0.994248i | \(0.465843\pi\) | |||||||
\(98\) | −21.1655 | −2.13804 | ||||||||
\(99\) | 0.211059 | 0.0212122 | ||||||||
\(100\) | −6.51492 | −0.651492 | ||||||||
\(101\) | −9.16261 | −0.911713 | −0.455857 | − | 0.890053i | \(-0.650667\pi\) | ||||
−0.455857 | + | 0.890053i | \(0.650667\pi\) | |||||||
\(102\) | −13.0952 | −1.29662 | ||||||||
\(103\) | 4.29602 | 0.423299 | 0.211650 | − | 0.977346i | \(-0.432116\pi\) | ||||
0.211650 | + | 0.977346i | \(0.432116\pi\) | |||||||
\(104\) | 2.11822 | 0.207709 | ||||||||
\(105\) | 0.869404 | 0.0848451 | ||||||||
\(106\) | −3.61667 | −0.351282 | ||||||||
\(107\) | −10.2188 | −0.987888 | −0.493944 | − | 0.869494i | \(-0.664445\pi\) | ||||
−0.493944 | + | 0.869494i | \(0.664445\pi\) | |||||||
\(108\) | 7.27466 | 0.700005 | ||||||||
\(109\) | −13.8777 | −1.32924 | −0.664622 | − | 0.747179i | \(-0.731408\pi\) | ||||
−0.664622 | + | 0.747179i | \(0.731408\pi\) | |||||||
\(110\) | −0.0432764 | −0.00412624 | ||||||||
\(111\) | 9.03487 | 0.857552 | ||||||||
\(112\) | −21.1695 | −2.00033 | ||||||||
\(113\) | −9.56571 | −0.899866 | −0.449933 | − | 0.893062i | \(-0.648552\pi\) | ||||
−0.449933 | + | 0.893062i | \(0.648552\pi\) | |||||||
\(114\) | 9.66198 | 0.904928 | ||||||||
\(115\) | 0.601878 | 0.0561254 | ||||||||
\(116\) | −11.5741 | −1.07463 | ||||||||
\(117\) | −2.40020 | −0.221898 | ||||||||
\(118\) | −20.6717 | −1.90299 | ||||||||
\(119\) | −24.7429 | −2.26818 | ||||||||
\(120\) | 0.252922 | 0.0230886 | ||||||||
\(121\) | −10.9780 | −0.998000 | ||||||||
\(122\) | 10.2843 | 0.931101 | ||||||||
\(123\) | 4.60940 | 0.415615 | ||||||||
\(124\) | 11.3200 | 1.01657 | ||||||||
\(125\) | 1.59966 | 0.143078 | ||||||||
\(126\) | 11.1749 | 0.995543 | ||||||||
\(127\) | 6.98124 | 0.619485 | 0.309742 | − | 0.950820i | \(-0.399757\pi\) | ||||
0.309742 | + | 0.950820i | \(0.399757\pi\) | |||||||
\(128\) | −9.44802 | −0.835095 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.492146 | 0.0431641 | ||||||||
\(131\) | 7.19432 | 0.628571 | 0.314285 | − | 0.949329i | \(-0.398235\pi\) | ||||
0.314285 | + | 0.949329i | \(0.398235\pi\) | |||||||
\(132\) | 0.243954 | 0.0212334 | ||||||||
\(133\) | 18.2560 | 1.58299 | ||||||||
\(134\) | 2.59403 | 0.224090 | ||||||||
\(135\) | −0.890802 | −0.0766680 | ||||||||
\(136\) | −7.19807 | −0.617229 | ||||||||
\(137\) | −4.78323 | −0.408659 | −0.204330 | − | 0.978902i | \(-0.565501\pi\) | ||||
−0.204330 | + | 0.978902i | \(0.565501\pi\) | |||||||
\(138\) | −8.57388 | −0.729857 | ||||||||
\(139\) | −2.42056 | −0.205309 | −0.102655 | − | 0.994717i | \(-0.532734\pi\) | ||||
−0.102655 | + | 0.994717i | \(0.532734\pi\) | |||||||
\(140\) | −0.906735 | −0.0766331 | ||||||||
\(141\) | 2.67636 | 0.225390 | ||||||||
\(142\) | −13.7570 | −1.15447 | ||||||||
\(143\) | −0.250184 | −0.0209214 | ||||||||
\(144\) | 6.97834 | 0.581529 | ||||||||
\(145\) | 1.41728 | 0.117699 | ||||||||
\(146\) | −9.07975 | −0.751446 | ||||||||
\(147\) | −14.6101 | −1.20502 | ||||||||
\(148\) | −9.42281 | −0.774550 | ||||||||
\(149\) | −3.68350 | −0.301764 | −0.150882 | − | 0.988552i | \(-0.548211\pi\) | ||||
−0.150882 | + | 0.988552i | \(0.548211\pi\) | |||||||
\(150\) | −11.3644 | −0.927898 | ||||||||
\(151\) | 8.15480 | 0.663628 | 0.331814 | − | 0.943345i | \(-0.392339\pi\) | ||||
0.331814 | + | 0.943345i | \(0.392339\pi\) | |||||||
\(152\) | 5.31093 | 0.430773 | ||||||||
\(153\) | 8.15627 | 0.659395 | ||||||||
\(154\) | 1.16482 | 0.0938638 | ||||||||
\(155\) | −1.38617 | −0.111340 | ||||||||
\(156\) | −2.77428 | −0.222120 | ||||||||
\(157\) | −4.84998 | −0.387071 | −0.193535 | − | 0.981093i | \(-0.561995\pi\) | ||||
−0.193535 | + | 0.981093i | \(0.561995\pi\) | |||||||
\(158\) | 27.0452 | 2.15160 | ||||||||
\(159\) | −2.49651 | −0.197986 | ||||||||
\(160\) | −1.02806 | −0.0812754 | ||||||||
\(161\) | −16.2000 | −1.27674 | ||||||||
\(162\) | 4.92339 | 0.386818 | ||||||||
\(163\) | −12.4423 | −0.974554 | −0.487277 | − | 0.873247i | \(-0.662010\pi\) | ||||
−0.487277 | + | 0.873247i | \(0.662010\pi\) | |||||||
\(164\) | −4.80732 | −0.375389 | ||||||||
\(165\) | −0.0298728 | −0.00232559 | ||||||||
\(166\) | 11.1334 | 0.864116 | ||||||||
\(167\) | −15.6217 | −1.20884 | −0.604420 | − | 0.796666i | \(-0.706595\pi\) | ||||
−0.604420 | + | 0.796666i | \(0.706595\pi\) | |||||||
\(168\) | −6.80761 | −0.525218 | ||||||||
\(169\) | −10.1549 | −0.781144 | ||||||||
\(170\) | −1.67240 | −0.128267 | ||||||||
\(171\) | −6.01791 | −0.460201 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.5555 | 0.802518 | 0.401259 | − | 0.915965i | \(-0.368573\pi\) | ||||
0.401259 | + | 0.915965i | \(0.368573\pi\) | |||||||
\(174\) | −20.1895 | −1.53056 | ||||||||
\(175\) | −21.4726 | −1.62317 | ||||||||
\(176\) | 0.727387 | 0.0548288 | ||||||||
\(177\) | −14.2693 | −1.07254 | ||||||||
\(178\) | −15.1607 | −1.13634 | ||||||||
\(179\) | 6.10540 | 0.456339 | 0.228169 | − | 0.973621i | \(-0.426726\pi\) | ||||
0.228169 | + | 0.973621i | \(0.426726\pi\) | |||||||
\(180\) | 0.298897 | 0.0222785 | ||||||||
\(181\) | −23.6663 | −1.75910 | −0.879552 | − | 0.475802i | \(-0.842158\pi\) | ||||
−0.879552 | + | 0.475802i | \(0.842158\pi\) | |||||||
\(182\) | −13.2465 | −0.981896 | ||||||||
\(183\) | 7.09906 | 0.524778 | ||||||||
\(184\) | −4.71283 | −0.347434 | ||||||||
\(185\) | 1.15385 | 0.0848326 | ||||||||
\(186\) | 19.7462 | 1.44786 | ||||||||
\(187\) | 0.850167 | 0.0621704 | ||||||||
\(188\) | −2.79128 | −0.203575 | ||||||||
\(189\) | 23.9766 | 1.74404 | ||||||||
\(190\) | 1.23394 | 0.0895193 | ||||||||
\(191\) | −15.7807 | −1.14185 | −0.570925 | − | 0.821002i | \(-0.693415\pi\) | ||||
−0.570925 | + | 0.821002i | \(0.693415\pi\) | |||||||
\(192\) | 2.32789 | 0.168001 | ||||||||
\(193\) | 21.4398 | 1.54327 | 0.771637 | − | 0.636064i | \(-0.219438\pi\) | ||||
0.771637 | + | 0.636064i | \(0.219438\pi\) | |||||||
\(194\) | −3.83804 | −0.275555 | ||||||||
\(195\) | 0.339718 | 0.0243277 | ||||||||
\(196\) | 15.2374 | 1.08839 | ||||||||
\(197\) | −15.5242 | −1.10606 | −0.553028 | − | 0.833163i | \(-0.686528\pi\) | ||||
−0.553028 | + | 0.833163i | \(0.686528\pi\) | |||||||
\(198\) | −0.383972 | −0.0272877 | ||||||||
\(199\) | −8.14166 | −0.577147 | −0.288573 | − | 0.957458i | \(-0.593181\pi\) | ||||
−0.288573 | + | 0.957458i | \(0.593181\pi\) | |||||||
\(200\) | −6.24669 | −0.441708 | ||||||||
\(201\) | 1.79060 | 0.126299 | ||||||||
\(202\) | 16.6692 | 1.17284 | ||||||||
\(203\) | −38.1472 | −2.67741 | ||||||||
\(204\) | 9.42747 | 0.660055 | ||||||||
\(205\) | 0.588669 | 0.0411144 | ||||||||
\(206\) | −7.81559 | −0.544538 | ||||||||
\(207\) | 5.34019 | 0.371169 | ||||||||
\(208\) | −8.27195 | −0.573557 | ||||||||
\(209\) | −0.627276 | −0.0433896 | ||||||||
\(210\) | −1.58167 | −0.109146 | ||||||||
\(211\) | 6.35814 | 0.437712 | 0.218856 | − | 0.975757i | \(-0.429767\pi\) | ||||
0.218856 | + | 0.975757i | \(0.429767\pi\) | |||||||
\(212\) | 2.60371 | 0.178823 | ||||||||
\(213\) | −9.49619 | −0.650668 | ||||||||
\(214\) | 18.5907 | 1.27083 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 6.97516 | 0.474599 | ||||||||
\(217\) | 37.3098 | 2.53275 | ||||||||
\(218\) | 25.2472 | 1.70996 | ||||||||
\(219\) | −6.26756 | −0.423522 | ||||||||
\(220\) | 0.0311555 | 0.00210050 | ||||||||
\(221\) | −9.66824 | −0.650356 | ||||||||
\(222\) | −16.4368 | −1.10317 | ||||||||
\(223\) | 11.8266 | 0.791969 | 0.395984 | − | 0.918257i | \(-0.370403\pi\) | ||||
0.395984 | + | 0.918257i | \(0.370403\pi\) | |||||||
\(224\) | 27.6711 | 1.84885 | ||||||||
\(225\) | 7.07825 | 0.471883 | ||||||||
\(226\) | 17.4026 | 1.15760 | ||||||||
\(227\) | 23.9172 | 1.58744 | 0.793720 | − | 0.608283i | \(-0.208141\pi\) | ||||
0.793720 | + | 0.608283i | \(0.208141\pi\) | |||||||
\(228\) | −6.95584 | −0.460662 | ||||||||
\(229\) | 6.12429 | 0.404705 | 0.202352 | − | 0.979313i | \(-0.435141\pi\) | ||||
0.202352 | + | 0.979313i | \(0.435141\pi\) | |||||||
\(230\) | −1.09498 | −0.0722006 | ||||||||
\(231\) | 0.804049 | 0.0529026 | ||||||||
\(232\) | −11.0976 | −0.728593 | ||||||||
\(233\) | −11.7698 | −0.771066 | −0.385533 | − | 0.922694i | \(-0.625982\pi\) | ||||
−0.385533 | + | 0.922694i | \(0.625982\pi\) | |||||||
\(234\) | 4.36659 | 0.285453 | ||||||||
\(235\) | 0.341799 | 0.0222965 | ||||||||
\(236\) | 14.8820 | 0.968733 | ||||||||
\(237\) | 18.6687 | 1.21266 | ||||||||
\(238\) | 45.0138 | 2.91781 | ||||||||
\(239\) | −16.6746 | −1.07859 | −0.539294 | − | 0.842118i | \(-0.681309\pi\) | ||||
−0.539294 | + | 0.842118i | \(0.681309\pi\) | |||||||
\(240\) | −0.987698 | −0.0637556 | ||||||||
\(241\) | −1.75804 | −0.113245 | −0.0566226 | − | 0.998396i | \(-0.518033\pi\) | ||||
−0.0566226 | + | 0.998396i | \(0.518033\pi\) | |||||||
\(242\) | 19.9719 | 1.28384 | ||||||||
\(243\) | −13.2646 | −0.850923 | ||||||||
\(244\) | −7.40389 | −0.473985 | ||||||||
\(245\) | −1.86586 | −0.119206 | ||||||||
\(246\) | −8.38571 | −0.534653 | ||||||||
\(247\) | 7.13348 | 0.453893 | ||||||||
\(248\) | 10.8540 | 0.689228 | ||||||||
\(249\) | 7.68512 | 0.487025 | ||||||||
\(250\) | −2.91021 | −0.184058 | ||||||||
\(251\) | 1.53584 | 0.0969415 | 0.0484708 | − | 0.998825i | \(-0.484565\pi\) | ||||
0.0484708 | + | 0.998825i | \(0.484565\pi\) | |||||||
\(252\) | −8.04505 | −0.506790 | ||||||||
\(253\) | 0.556634 | 0.0349953 | ||||||||
\(254\) | −12.7007 | −0.796914 | ||||||||
\(255\) | −1.15442 | −0.0722925 | ||||||||
\(256\) | 20.8959 | 1.30599 | ||||||||
\(257\) | −29.4257 | −1.83552 | −0.917761 | − | 0.397133i | \(-0.870005\pi\) | ||||
−0.917761 | + | 0.397133i | \(0.870005\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −31.0567 | −1.92977 | ||||||||
\(260\) | −0.354305 | −0.0219731 | ||||||||
\(261\) | 12.5749 | 0.778367 | ||||||||
\(262\) | −13.0884 | −0.808602 | ||||||||
\(263\) | −7.93106 | −0.489050 | −0.244525 | − | 0.969643i | \(-0.578632\pi\) | ||||
−0.244525 | + | 0.969643i | \(0.578632\pi\) | |||||||
\(264\) | 0.233910 | 0.0143962 | ||||||||
\(265\) | −0.318831 | −0.0195856 | ||||||||
\(266\) | −33.2124 | −2.03638 | ||||||||
\(267\) | −10.4651 | −0.640452 | ||||||||
\(268\) | −1.86749 | −0.114075 | ||||||||
\(269\) | 1.25644 | 0.0766066 | 0.0383033 | − | 0.999266i | \(-0.487805\pi\) | ||||
0.0383033 | + | 0.999266i | \(0.487805\pi\) | |||||||
\(270\) | 1.62060 | 0.0986268 | ||||||||
\(271\) | −28.0838 | −1.70597 | −0.852983 | − | 0.521938i | \(-0.825209\pi\) | ||||
−0.852983 | + | 0.521938i | \(0.825209\pi\) | |||||||
\(272\) | 28.1095 | 1.70439 | ||||||||
\(273\) | −9.14377 | −0.553406 | ||||||||
\(274\) | 8.70197 | 0.525705 | ||||||||
\(275\) | 0.737800 | 0.0444910 | ||||||||
\(276\) | 6.17249 | 0.371540 | ||||||||
\(277\) | 13.0713 | 0.785379 | 0.392690 | − | 0.919671i | \(-0.371545\pi\) | ||||
0.392690 | + | 0.919671i | \(0.371545\pi\) | |||||||
\(278\) | 4.40364 | 0.264113 | ||||||||
\(279\) | −12.2988 | −0.736312 | ||||||||
\(280\) | −0.869404 | −0.0519568 | ||||||||
\(281\) | −13.2238 | −0.788868 | −0.394434 | − | 0.918924i | \(-0.629059\pi\) | ||||
−0.394434 | + | 0.918924i | \(0.629059\pi\) | |||||||
\(282\) | −4.86900 | −0.289945 | ||||||||
\(283\) | 17.0833 | 1.01550 | 0.507748 | − | 0.861506i | \(-0.330478\pi\) | ||||
0.507748 | + | 0.861506i | \(0.330478\pi\) | |||||||
\(284\) | 9.90395 | 0.587691 | ||||||||
\(285\) | 0.851761 | 0.0504540 | ||||||||
\(286\) | 0.455151 | 0.0269136 | ||||||||
\(287\) | −15.8445 | −0.935271 | ||||||||
\(288\) | −9.12152 | −0.537491 | ||||||||
\(289\) | 15.8543 | 0.932605 | ||||||||
\(290\) | −2.57841 | −0.151409 | ||||||||
\(291\) | −2.64932 | −0.155306 | ||||||||
\(292\) | 6.53668 | 0.382530 | ||||||||
\(293\) | 25.8110 | 1.50790 | 0.753949 | − | 0.656933i | \(-0.228147\pi\) | ||||
0.753949 | + | 0.656933i | \(0.228147\pi\) | |||||||
\(294\) | 26.5796 | 1.55015 | ||||||||
\(295\) | −1.82234 | −0.106101 | ||||||||
\(296\) | −9.03487 | −0.525141 | ||||||||
\(297\) | −0.823839 | −0.0478040 | ||||||||
\(298\) | 6.70125 | 0.388193 | ||||||||
\(299\) | −6.33013 | −0.366081 | ||||||||
\(300\) | 8.18143 | 0.472355 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −14.8357 | −0.853701 | ||||||||
\(303\) | 11.5064 | 0.661025 | ||||||||
\(304\) | −20.7399 | −1.18952 | ||||||||
\(305\) | 0.906626 | 0.0519132 | ||||||||
\(306\) | −14.8384 | −0.848255 | ||||||||
\(307\) | −8.06495 | −0.460291 | −0.230145 | − | 0.973156i | \(-0.573920\pi\) | ||||
−0.230145 | + | 0.973156i | \(0.573920\pi\) | |||||||
\(308\) | −0.838574 | −0.0477822 | ||||||||
\(309\) | −5.39493 | −0.306907 | ||||||||
\(310\) | 2.52180 | 0.143229 | ||||||||
\(311\) | −2.25085 | −0.127634 | −0.0638171 | − | 0.997962i | \(-0.520327\pi\) | ||||
−0.0638171 | + | 0.997962i | \(0.520327\pi\) | |||||||
\(312\) | −2.66006 | −0.150596 | ||||||||
\(313\) | 21.6275 | 1.22246 | 0.611229 | − | 0.791454i | \(-0.290675\pi\) | ||||
0.611229 | + | 0.791454i | \(0.290675\pi\) | |||||||
\(314\) | 8.82340 | 0.497933 | ||||||||
\(315\) | 0.985138 | 0.0555062 | ||||||||
\(316\) | −19.4703 | −1.09529 | ||||||||
\(317\) | −4.66235 | −0.261864 | −0.130932 | − | 0.991391i | \(-0.541797\pi\) | ||||
−0.130932 | + | 0.991391i | \(0.541797\pi\) | |||||||
\(318\) | 4.54181 | 0.254692 | ||||||||
\(319\) | 1.31074 | 0.0733875 | ||||||||
\(320\) | 0.297296 | 0.0166193 | ||||||||
\(321\) | 12.8328 | 0.716254 | ||||||||
\(322\) | 29.4721 | 1.64242 | ||||||||
\(323\) | −24.2408 | −1.34879 | ||||||||
\(324\) | −3.54444 | −0.196913 | ||||||||
\(325\) | −8.39037 | −0.465414 | ||||||||
\(326\) | 22.6358 | 1.25368 | ||||||||
\(327\) | 17.4276 | 0.963750 | ||||||||
\(328\) | −4.60940 | −0.254511 | ||||||||
\(329\) | −9.19979 | −0.507201 | ||||||||
\(330\) | 0.0543465 | 0.00299168 | ||||||||
\(331\) | −6.77060 | −0.372146 | −0.186073 | − | 0.982536i | \(-0.559576\pi\) | ||||
−0.186073 | + | 0.982536i | \(0.559576\pi\) | |||||||
\(332\) | −8.01511 | −0.439886 | ||||||||
\(333\) | 10.2376 | 0.561016 | ||||||||
\(334\) | 28.4199 | 1.55507 | ||||||||
\(335\) | 0.228679 | 0.0124941 | ||||||||
\(336\) | 26.5847 | 1.45031 | ||||||||
\(337\) | −14.1869 | −0.772808 | −0.386404 | − | 0.922330i | \(-0.626283\pi\) | ||||
−0.386404 | + | 0.922330i | \(0.626283\pi\) | |||||||
\(338\) | 18.4744 | 1.00487 | ||||||||
\(339\) | 12.0126 | 0.652435 | ||||||||
\(340\) | 1.20399 | 0.0652954 | ||||||||
\(341\) | −1.28197 | −0.0694224 | ||||||||
\(342\) | 10.9482 | 0.592009 | ||||||||
\(343\) | 20.0041 | 1.08012 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.755838 | −0.0406930 | ||||||||
\(346\) | −19.2032 | −1.03237 | ||||||||
\(347\) | −24.8725 | −1.33523 | −0.667614 | − | 0.744508i | \(-0.732684\pi\) | ||||
−0.667614 | + | 0.744508i | \(0.732684\pi\) | |||||||
\(348\) | 14.5348 | 0.779145 | ||||||||
\(349\) | −11.2707 | −0.603307 | −0.301654 | − | 0.953418i | \(-0.597539\pi\) | ||||
−0.301654 | + | 0.953418i | \(0.597539\pi\) | |||||||
\(350\) | 39.0643 | 2.08807 | ||||||||
\(351\) | 9.36883 | 0.500071 | ||||||||
\(352\) | −0.950781 | −0.0506768 | ||||||||
\(353\) | 19.5266 | 1.03930 | 0.519648 | − | 0.854380i | \(-0.326063\pi\) | ||||
0.519648 | + | 0.854380i | \(0.326063\pi\) | |||||||
\(354\) | 25.9596 | 1.37973 | ||||||||
\(355\) | −1.21277 | −0.0643669 | ||||||||
\(356\) | 10.9144 | 0.578464 | ||||||||
\(357\) | 31.0721 | 1.64451 | ||||||||
\(358\) | −11.1073 | −0.587041 | ||||||||
\(359\) | −8.98116 | −0.474008 | −0.237004 | − | 0.971509i | \(-0.576165\pi\) | ||||
−0.237004 | + | 0.971509i | \(0.576165\pi\) | |||||||
\(360\) | 0.286591 | 0.0151047 | ||||||||
\(361\) | −1.11451 | −0.0586583 | ||||||||
\(362\) | 43.0553 | 2.26294 | ||||||||
\(363\) | 13.7862 | 0.723586 | ||||||||
\(364\) | 9.53640 | 0.499843 | ||||||||
\(365\) | −0.800434 | −0.0418966 | ||||||||
\(366\) | −12.9151 | −0.675081 | ||||||||
\(367\) | 8.93222 | 0.466258 | 0.233129 | − | 0.972446i | \(-0.425104\pi\) | ||||
0.233129 | + | 0.972446i | \(0.425104\pi\) | |||||||
\(368\) | 18.4043 | 0.959388 | ||||||||
\(369\) | 5.22300 | 0.271898 | ||||||||
\(370\) | −2.09916 | −0.109130 | ||||||||
\(371\) | 8.58158 | 0.445533 | ||||||||
\(372\) | −14.2157 | −0.737049 | ||||||||
\(373\) | 15.3197 | 0.793224 | 0.396612 | − | 0.917986i | \(-0.370186\pi\) | ||||
0.396612 | + | 0.917986i | \(0.370186\pi\) | |||||||
\(374\) | −1.54668 | −0.0799769 | ||||||||
\(375\) | −2.00886 | −0.103737 | ||||||||
\(376\) | −2.67636 | −0.138023 | ||||||||
\(377\) | −14.9060 | −0.767696 | ||||||||
\(378\) | −43.6198 | −2.24356 | ||||||||
\(379\) | −30.2720 | −1.55497 | −0.777484 | − | 0.628903i | \(-0.783504\pi\) | ||||
−0.777484 | + | 0.628903i | \(0.783504\pi\) | |||||||
\(380\) | −0.888335 | −0.0455706 | ||||||||
\(381\) | −8.76703 | −0.449149 | ||||||||
\(382\) | 28.7092 | 1.46889 | ||||||||
\(383\) | −1.02239 | −0.0522415 | −0.0261208 | − | 0.999659i | \(-0.508315\pi\) | ||||
−0.0261208 | + | 0.999659i | \(0.508315\pi\) | |||||||
\(384\) | 11.8648 | 0.605474 | ||||||||
\(385\) | 0.102686 | 0.00523335 | ||||||||
\(386\) | −39.0047 | −1.98529 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.76307 | 0.140274 | ||||||||
\(389\) | −32.6968 | −1.65780 | −0.828898 | − | 0.559400i | \(-0.811031\pi\) | ||||
−0.828898 | + | 0.559400i | \(0.811031\pi\) | |||||||
\(390\) | −0.618037 | −0.0312955 | ||||||||
\(391\) | 21.5108 | 1.08785 | ||||||||
\(392\) | 14.6101 | 0.737921 | ||||||||
\(393\) | −9.03462 | −0.455736 | ||||||||
\(394\) | 28.2427 | 1.42285 | ||||||||
\(395\) | 2.38419 | 0.119962 | ||||||||
\(396\) | 0.276429 | 0.0138911 | ||||||||
\(397\) | 17.6659 | 0.886625 | 0.443312 | − | 0.896367i | \(-0.353803\pi\) | ||||
0.443312 | + | 0.896367i | \(0.353803\pi\) | |||||||
\(398\) | 14.8118 | 0.742450 | ||||||||
\(399\) | −22.9258 | −1.14773 | ||||||||
\(400\) | 24.3942 | 1.21971 | ||||||||
\(401\) | −35.2016 | −1.75788 | −0.878942 | − | 0.476929i | \(-0.841750\pi\) | ||||
−0.878942 | + | 0.476929i | \(0.841750\pi\) | |||||||
\(402\) | −3.25758 | −0.162473 | ||||||||
\(403\) | 14.5787 | 0.726218 | ||||||||
\(404\) | −12.0005 | −0.597045 | ||||||||
\(405\) | 0.434026 | 0.0215669 | ||||||||
\(406\) | 69.3999 | 3.44426 | ||||||||
\(407\) | 1.06711 | 0.0528948 | ||||||||
\(408\) | 9.03933 | 0.447513 | ||||||||
\(409\) | −23.8017 | −1.17692 | −0.588459 | − | 0.808527i | \(-0.700265\pi\) | ||||
−0.588459 | + | 0.808527i | \(0.700265\pi\) | |||||||
\(410\) | −1.07094 | −0.0528902 | ||||||||
\(411\) | 6.00678 | 0.296293 | ||||||||
\(412\) | 5.62658 | 0.277202 | ||||||||
\(413\) | 49.0496 | 2.41357 | ||||||||
\(414\) | −9.71522 | −0.477477 | ||||||||
\(415\) | 0.981471 | 0.0481785 | ||||||||
\(416\) | 10.8124 | 0.530123 | ||||||||
\(417\) | 3.03974 | 0.148857 | ||||||||
\(418\) | 1.14118 | 0.0558170 | ||||||||
\(419\) | 21.1878 | 1.03509 | 0.517546 | − | 0.855656i | \(-0.326846\pi\) | ||||
0.517546 | + | 0.855656i | \(0.326846\pi\) | |||||||
\(420\) | 1.13868 | 0.0555617 | ||||||||
\(421\) | 1.36811 | 0.0666774 | 0.0333387 | − | 0.999444i | \(-0.489386\pi\) | ||||
0.0333387 | + | 0.999444i | \(0.489386\pi\) | |||||||
\(422\) | −11.5671 | −0.563079 | ||||||||
\(423\) | 3.03263 | 0.147451 | ||||||||
\(424\) | 2.49651 | 0.121241 | ||||||||
\(425\) | 28.5119 | 1.38303 | ||||||||
\(426\) | 17.2761 | 0.837029 | ||||||||
\(427\) | −24.4025 | −1.18092 | ||||||||
\(428\) | −13.3838 | −0.646929 | ||||||||
\(429\) | 0.314181 | 0.0151688 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.95981 | −0.190737 | −0.0953687 | − | 0.995442i | \(-0.530403\pi\) | ||||
−0.0953687 | + | 0.995442i | \(0.530403\pi\) | |||||||
\(432\) | −27.2390 | −1.31054 | ||||||||
\(433\) | 0.859593 | 0.0413094 | 0.0206547 | − | 0.999787i | \(-0.493425\pi\) | ||||
0.0206547 | + | 0.999787i | \(0.493425\pi\) | |||||||
\(434\) | −67.8764 | −3.25817 | ||||||||
\(435\) | −1.77982 | −0.0853359 | ||||||||
\(436\) | −18.1759 | −0.870470 | ||||||||
\(437\) | −15.8713 | −0.759226 | ||||||||
\(438\) | 11.4023 | 0.544825 | ||||||||
\(439\) | 16.0673 | 0.766850 | 0.383425 | − | 0.923572i | \(-0.374745\pi\) | ||||
0.383425 | + | 0.923572i | \(0.374745\pi\) | |||||||
\(440\) | 0.0298728 | 0.00142413 | ||||||||
\(441\) | −16.5550 | −0.788332 | ||||||||
\(442\) | 17.5891 | 0.836627 | ||||||||
\(443\) | −7.12994 | −0.338754 | −0.169377 | − | 0.985551i | \(-0.554175\pi\) | ||||
−0.169377 | + | 0.985551i | \(0.554175\pi\) | |||||||
\(444\) | 11.8332 | 0.561577 | ||||||||
\(445\) | −1.33650 | −0.0633563 | ||||||||
\(446\) | −21.5157 | −1.01880 | ||||||||
\(447\) | 4.62573 | 0.218790 | ||||||||
\(448\) | −8.00195 | −0.378057 | ||||||||
\(449\) | 22.0200 | 1.03919 | 0.519594 | − | 0.854413i | \(-0.326083\pi\) | ||||
0.519594 | + | 0.854413i | \(0.326083\pi\) | |||||||
\(450\) | −12.8772 | −0.607037 | ||||||||
\(451\) | 0.544418 | 0.0256356 | ||||||||
\(452\) | −12.5284 | −0.589287 | ||||||||
\(453\) | −10.2408 | −0.481154 | ||||||||
\(454\) | −43.5117 | −2.04211 | ||||||||
\(455\) | −1.16776 | −0.0547453 | ||||||||
\(456\) | −6.66946 | −0.312326 | ||||||||
\(457\) | −18.1341 | −0.848277 | −0.424138 | − | 0.905597i | \(-0.639423\pi\) | ||||
−0.424138 | + | 0.905597i | \(0.639423\pi\) | |||||||
\(458\) | −11.1417 | −0.520618 | ||||||||
\(459\) | −31.8368 | −1.48602 | ||||||||
\(460\) | 0.788293 | 0.0367543 | ||||||||
\(461\) | 9.59608 | 0.446934 | 0.223467 | − | 0.974712i | \(-0.428263\pi\) | ||||
0.223467 | + | 0.974712i | \(0.428263\pi\) | |||||||
\(462\) | −1.46278 | −0.0680546 | ||||||||
\(463\) | −4.05803 | −0.188593 | −0.0942964 | − | 0.995544i | \(-0.530060\pi\) | ||||
−0.0942964 | + | 0.995544i | \(0.530060\pi\) | |||||||
\(464\) | 43.3377 | 2.01190 | ||||||||
\(465\) | 1.74075 | 0.0807252 | ||||||||
\(466\) | 21.4124 | 0.991910 | ||||||||
\(467\) | 10.5710 | 0.489170 | 0.244585 | − | 0.969628i | \(-0.421348\pi\) | ||||
0.244585 | + | 0.969628i | \(0.421348\pi\) | |||||||
\(468\) | −3.14359 | −0.145312 | ||||||||
\(469\) | −6.15507 | −0.284215 | ||||||||
\(470\) | −0.621823 | −0.0286825 | ||||||||
\(471\) | 6.09061 | 0.280640 | ||||||||
\(472\) | 14.2693 | 0.656796 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −33.9633 | −1.55999 | ||||||||
\(475\) | −21.0368 | −0.965237 | ||||||||
\(476\) | −32.4063 | −1.48534 | ||||||||
\(477\) | −2.82884 | −0.129524 | ||||||||
\(478\) | 30.3354 | 1.38751 | ||||||||
\(479\) | 25.8866 | 1.18279 | 0.591395 | − | 0.806382i | \(-0.298577\pi\) | ||||
0.591395 | + | 0.806382i | \(0.298577\pi\) | |||||||
\(480\) | 1.29104 | 0.0589276 | ||||||||
\(481\) | −12.1354 | −0.553325 | ||||||||
\(482\) | 3.19833 | 0.145680 | ||||||||
\(483\) | 20.3440 | 0.925683 | ||||||||
\(484\) | −14.3781 | −0.653551 | ||||||||
\(485\) | −0.338346 | −0.0153635 | ||||||||
\(486\) | 24.1318 | 1.09464 | ||||||||
\(487\) | 3.65177 | 0.165477 | 0.0827387 | − | 0.996571i | \(-0.473633\pi\) | ||||
0.0827387 | + | 0.996571i | \(0.473633\pi\) | |||||||
\(488\) | −7.09906 | −0.321359 | ||||||||
\(489\) | 15.6250 | 0.706587 | ||||||||
\(490\) | 3.39450 | 0.153348 | ||||||||
\(491\) | 32.0540 | 1.44658 | 0.723289 | − | 0.690545i | \(-0.242629\pi\) | ||||
0.723289 | + | 0.690545i | \(0.242629\pi\) | |||||||
\(492\) | 6.03703 | 0.272170 | ||||||||
\(493\) | 50.6530 | 2.28130 | ||||||||
\(494\) | −12.9777 | −0.583894 | ||||||||
\(495\) | −0.0338494 | −0.00152142 | ||||||||
\(496\) | −42.3863 | −1.90320 | ||||||||
\(497\) | 32.6425 | 1.46422 | ||||||||
\(498\) | −13.9813 | −0.626515 | ||||||||
\(499\) | −16.0927 | −0.720407 | −0.360204 | − | 0.932874i | \(-0.617293\pi\) | ||||
−0.360204 | + | 0.932874i | \(0.617293\pi\) | |||||||
\(500\) | 2.09511 | 0.0936963 | ||||||||
\(501\) | 19.6177 | 0.876452 | ||||||||
\(502\) | −2.79410 | −0.124707 | ||||||||
\(503\) | 13.4838 | 0.601212 | 0.300606 | − | 0.953748i | \(-0.402811\pi\) | ||||
0.300606 | + | 0.953748i | \(0.402811\pi\) | |||||||
\(504\) | −7.71383 | −0.343601 | ||||||||
\(505\) | 1.46949 | 0.0653914 | ||||||||
\(506\) | −1.01266 | −0.0450184 | ||||||||
\(507\) | 12.7525 | 0.566357 | ||||||||
\(508\) | 9.14348 | 0.405676 | ||||||||
\(509\) | 26.2654 | 1.16419 | 0.582097 | − | 0.813120i | \(-0.302232\pi\) | ||||
0.582097 | + | 0.813120i | \(0.302232\pi\) | |||||||
\(510\) | 2.10019 | 0.0929981 | ||||||||
\(511\) | 21.5443 | 0.953064 | ||||||||
\(512\) | −19.1191 | −0.844951 | ||||||||
\(513\) | 23.4901 | 1.03711 | ||||||||
\(514\) | 53.5330 | 2.36124 | ||||||||
\(515\) | −0.688990 | −0.0303605 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.316106 | 0.0139023 | ||||||||
\(518\) | 56.5004 | 2.48249 | ||||||||
\(519\) | −13.2556 | −0.581854 | ||||||||
\(520\) | −0.339718 | −0.0148976 | ||||||||
\(521\) | −11.0938 | −0.486027 | −0.243013 | − | 0.970023i | \(-0.578136\pi\) | ||||
−0.243013 | + | 0.970023i | \(0.578136\pi\) | |||||||
\(522\) | −22.8771 | −1.00130 | ||||||||
\(523\) | −0.981100 | −0.0429005 | −0.0214502 | − | 0.999770i | \(-0.506828\pi\) | ||||
−0.0214502 | + | 0.999770i | \(0.506828\pi\) | |||||||
\(524\) | 9.42256 | 0.411626 | ||||||||
\(525\) | 26.9652 | 1.17686 | ||||||||
\(526\) | 14.4287 | 0.629121 | ||||||||
\(527\) | −49.5410 | −2.15804 | ||||||||
\(528\) | −0.913451 | −0.0397529 | ||||||||
\(529\) | −8.91610 | −0.387656 | ||||||||
\(530\) | 0.580037 | 0.0251952 | ||||||||
\(531\) | −16.1688 | −0.701665 | ||||||||
\(532\) | 23.9102 | 1.03664 | ||||||||
\(533\) | −6.19121 | −0.268171 | ||||||||
\(534\) | 19.0387 | 0.823887 | ||||||||
\(535\) | 1.63888 | 0.0708549 | ||||||||
\(536\) | −1.79060 | −0.0773422 | ||||||||
\(537\) | −7.66715 | −0.330862 | ||||||||
\(538\) | −2.28580 | −0.0985477 | ||||||||
\(539\) | −1.72560 | −0.0743270 | ||||||||
\(540\) | −1.16670 | −0.0502069 | ||||||||
\(541\) | −9.12256 | −0.392209 | −0.196105 | − | 0.980583i | \(-0.562829\pi\) | ||||
−0.196105 | + | 0.980583i | \(0.562829\pi\) | |||||||
\(542\) | 51.0918 | 2.19458 | ||||||||
\(543\) | 29.7202 | 1.27541 | ||||||||
\(544\) | −36.7424 | −1.57532 | ||||||||
\(545\) | 2.22569 | 0.0953382 | ||||||||
\(546\) | 16.6349 | 0.711910 | ||||||||
\(547\) | 43.4839 | 1.85924 | 0.929618 | − | 0.368524i | \(-0.120137\pi\) | ||||
0.929618 | + | 0.368524i | \(0.120137\pi\) | |||||||
\(548\) | −6.26471 | −0.267615 | ||||||||
\(549\) | 8.04408 | 0.343313 | ||||||||
\(550\) | −1.34225 | −0.0572338 | ||||||||
\(551\) | −37.3731 | −1.59215 | ||||||||
\(552\) | 5.91836 | 0.251902 | ||||||||
\(553\) | −64.1724 | −2.72889 | ||||||||
\(554\) | −23.7802 | −1.01032 | ||||||||
\(555\) | −1.44900 | −0.0615067 | ||||||||
\(556\) | −3.17026 | −0.134449 | ||||||||
\(557\) | −19.6219 | −0.831406 | −0.415703 | − | 0.909500i | \(-0.636464\pi\) | ||||
−0.415703 | + | 0.909500i | \(0.636464\pi\) | |||||||
\(558\) | 22.3748 | 0.947202 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 3.39514 | 0.143471 | ||||||||
\(561\) | −1.06764 | −0.0450758 | ||||||||
\(562\) | 24.0576 | 1.01481 | ||||||||
\(563\) | −14.5633 | −0.613769 | −0.306885 | − | 0.951747i | \(-0.599287\pi\) | ||||
−0.306885 | + | 0.951747i | \(0.599287\pi\) | |||||||
\(564\) | 3.50528 | 0.147599 | ||||||||
\(565\) | 1.53414 | 0.0645417 | ||||||||
\(566\) | −31.0790 | −1.30635 | ||||||||
\(567\) | −11.6821 | −0.490604 | ||||||||
\(568\) | 9.49619 | 0.398451 | ||||||||
\(569\) | −40.0828 | −1.68036 | −0.840179 | − | 0.542310i | \(-0.817550\pi\) | ||||
−0.840179 | + | 0.542310i | \(0.817550\pi\) | |||||||
\(570\) | −1.54958 | −0.0649047 | ||||||||
\(571\) | 4.38952 | 0.183696 | 0.0918479 | − | 0.995773i | \(-0.470723\pi\) | ||||
0.0918479 | + | 0.995773i | \(0.470723\pi\) | |||||||
\(572\) | −0.327671 | −0.0137006 | ||||||||
\(573\) | 19.8174 | 0.827882 | ||||||||
\(574\) | 28.8253 | 1.20315 | ||||||||
\(575\) | 18.6677 | 0.778498 | ||||||||
\(576\) | 2.63777 | 0.109907 | ||||||||
\(577\) | −21.1471 | −0.880367 | −0.440184 | − | 0.897908i | \(-0.645087\pi\) | ||||
−0.440184 | + | 0.897908i | \(0.645087\pi\) | |||||||
\(578\) | −28.8431 | −1.19972 | ||||||||
\(579\) | −26.9241 | −1.11893 | ||||||||
\(580\) | 1.85624 | 0.0770763 | ||||||||
\(581\) | −26.4171 | −1.09596 | ||||||||
\(582\) | 4.81980 | 0.199787 | ||||||||
\(583\) | −0.294864 | −0.0122120 | ||||||||
\(584\) | 6.26756 | 0.259353 | ||||||||
\(585\) | 0.384941 | 0.0159153 | ||||||||
\(586\) | −46.9571 | −1.93978 | ||||||||
\(587\) | 16.7484 | 0.691280 | 0.345640 | − | 0.938367i | \(-0.387662\pi\) | ||||
0.345640 | + | 0.938367i | \(0.387662\pi\) | |||||||
\(588\) | −19.1351 | −0.789120 | ||||||||
\(589\) | 36.5527 | 1.50613 | ||||||||
\(590\) | 3.31531 | 0.136489 | ||||||||
\(591\) | 19.4953 | 0.801930 | ||||||||
\(592\) | 35.2824 | 1.45010 | ||||||||
\(593\) | −28.2891 | −1.16170 | −0.580848 | − | 0.814012i | \(-0.697279\pi\) | ||||
−0.580848 | + | 0.814012i | \(0.697279\pi\) | |||||||
\(594\) | 1.49878 | 0.0614957 | ||||||||
\(595\) | 3.96824 | 0.162682 | ||||||||
\(596\) | −4.82435 | −0.197613 | ||||||||
\(597\) | 10.2243 | 0.418452 | ||||||||
\(598\) | 11.5162 | 0.470932 | ||||||||
\(599\) | 12.1871 | 0.497951 | 0.248975 | − | 0.968510i | \(-0.419906\pi\) | ||||
0.248975 | + | 0.968510i | \(0.419906\pi\) | |||||||
\(600\) | 7.84459 | 0.320254 | ||||||||
\(601\) | 13.5029 | 0.550793 | 0.275397 | − | 0.961331i | \(-0.411191\pi\) | ||||
0.275397 | + | 0.961331i | \(0.411191\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.02896 | 0.0826258 | ||||||||
\(604\) | 10.6805 | 0.434584 | ||||||||
\(605\) | 1.76064 | 0.0715802 | ||||||||
\(606\) | −20.9332 | −0.850352 | ||||||||
\(607\) | 3.28555 | 0.133356 | 0.0666781 | − | 0.997775i | \(-0.478760\pi\) | ||||
0.0666781 | + | 0.997775i | \(0.478760\pi\) | |||||||
\(608\) | 27.1096 | 1.09944 | ||||||||
\(609\) | 47.9053 | 1.94122 | ||||||||
\(610\) | −1.64939 | −0.0667819 | ||||||||
\(611\) | −3.59480 | −0.145430 | ||||||||
\(612\) | 10.6824 | 0.431812 | ||||||||
\(613\) | 41.4735 | 1.67510 | 0.837549 | − | 0.546362i | \(-0.183988\pi\) | ||||
0.837549 | + | 0.546362i | \(0.183988\pi\) | |||||||
\(614\) | 14.6723 | 0.592125 | ||||||||
\(615\) | −0.739250 | −0.0298094 | ||||||||
\(616\) | −0.804049 | −0.0323961 | ||||||||
\(617\) | 34.7109 | 1.39741 | 0.698704 | − | 0.715411i | \(-0.253760\pi\) | ||||
0.698704 | + | 0.715411i | \(0.253760\pi\) | |||||||
\(618\) | 9.81481 | 0.394809 | ||||||||
\(619\) | 8.57623 | 0.344708 | 0.172354 | − | 0.985035i | \(-0.444863\pi\) | ||||
0.172354 | + | 0.985035i | \(0.444863\pi\) | |||||||
\(620\) | −1.81549 | −0.0729120 | ||||||||
\(621\) | −20.8447 | −0.836469 | ||||||||
\(622\) | 4.09490 | 0.164190 | ||||||||
\(623\) | 35.9730 | 1.44123 | ||||||||
\(624\) | 10.3879 | 0.415849 | ||||||||
\(625\) | 24.6148 | 0.984594 | ||||||||
\(626\) | −39.3461 | −1.57259 | ||||||||
\(627\) | 0.787733 | 0.0314590 | ||||||||
\(628\) | −6.35213 | −0.253478 | ||||||||
\(629\) | 41.2380 | 1.64427 | ||||||||
\(630\) | −1.79223 | −0.0714040 | ||||||||
\(631\) | −0.378009 | −0.0150483 | −0.00752415 | − | 0.999972i | \(-0.502395\pi\) | ||||
−0.00752415 | + | 0.999972i | \(0.502395\pi\) | |||||||
\(632\) | −18.6687 | −0.742601 | ||||||||
\(633\) | −7.98455 | −0.317357 | ||||||||
\(634\) | 8.48205 | 0.336865 | ||||||||
\(635\) | −1.11964 | −0.0444317 | ||||||||
\(636\) | −3.26973 | −0.129653 | ||||||||
\(637\) | 19.6238 | 0.777525 | ||||||||
\(638\) | −2.38459 | −0.0944067 | ||||||||
\(639\) | −10.7603 | −0.425671 | ||||||||
\(640\) | 1.51526 | 0.0598960 | ||||||||
\(641\) | 23.7922 | 0.939734 | 0.469867 | − | 0.882737i | \(-0.344302\pi\) | ||||
0.469867 | + | 0.882737i | \(0.344302\pi\) | |||||||
\(642\) | −23.3462 | −0.921400 | ||||||||
\(643\) | −47.4615 | −1.87170 | −0.935849 | − | 0.352403i | \(-0.885365\pi\) | ||||
−0.935849 | + | 0.352403i | \(0.885365\pi\) | |||||||
\(644\) | −21.2175 | −0.836088 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 44.1004 | 1.73511 | ||||||||
\(647\) | −1.66417 | −0.0654254 | −0.0327127 | − | 0.999465i | \(-0.510415\pi\) | ||||
−0.0327127 | + | 0.999465i | \(0.510415\pi\) | |||||||
\(648\) | −3.39851 | −0.133506 | ||||||||
\(649\) | −1.68535 | −0.0661557 | ||||||||
\(650\) | 15.2643 | 0.598715 | ||||||||
\(651\) | −46.8536 | −1.83634 | ||||||||
\(652\) | −16.2959 | −0.638197 | ||||||||
\(653\) | 16.6432 | 0.651299 | 0.325650 | − | 0.945491i | \(-0.394417\pi\) | ||||
0.325650 | + | 0.945491i | \(0.394417\pi\) | |||||||
\(654\) | −31.7055 | −1.23978 | ||||||||
\(655\) | −1.15382 | −0.0450834 | ||||||||
\(656\) | 18.0004 | 0.702796 | ||||||||
\(657\) | −7.10189 | −0.277071 | ||||||||
\(658\) | 16.7368 | 0.652470 | ||||||||
\(659\) | 4.15199 | 0.161739 | 0.0808693 | − | 0.996725i | \(-0.474230\pi\) | ||||
0.0808693 | + | 0.996725i | \(0.474230\pi\) | |||||||
\(660\) | −0.0391250 | −0.00152294 | ||||||||
\(661\) | −48.7851 | −1.89752 | −0.948761 | − | 0.315995i | \(-0.897662\pi\) | ||||
−0.948761 | + | 0.315995i | \(0.897662\pi\) | |||||||
\(662\) | 12.3175 | 0.478734 | ||||||||
\(663\) | 12.1414 | 0.471531 | ||||||||
\(664\) | −7.68512 | −0.298240 | ||||||||
\(665\) | −2.92787 | −0.113538 | ||||||||
\(666\) | −18.6249 | −0.721698 | ||||||||
\(667\) | 33.1643 | 1.28413 | ||||||||
\(668\) | −20.4600 | −0.791622 | ||||||||
\(669\) | −14.8518 | −0.574206 | ||||||||
\(670\) | −0.416027 | −0.0160725 | ||||||||
\(671\) | 0.838473 | 0.0323689 | ||||||||
\(672\) | −34.7493 | −1.34048 | ||||||||
\(673\) | −27.6667 | −1.06647 | −0.533236 | − | 0.845967i | \(-0.679024\pi\) | ||||
−0.533236 | + | 0.845967i | \(0.679024\pi\) | |||||||
\(674\) | 25.8097 | 0.994151 | ||||||||
\(675\) | −27.6289 | −1.06344 | ||||||||
\(676\) | −13.3000 | −0.511540 | ||||||||
\(677\) | 12.8622 | 0.494336 | 0.247168 | − | 0.968973i | \(-0.420500\pi\) | ||||
0.247168 | + | 0.968973i | \(0.420500\pi\) | |||||||
\(678\) | −21.8541 | −0.839302 | ||||||||
\(679\) | 9.10684 | 0.349489 | ||||||||
\(680\) | 1.15442 | 0.0442699 | ||||||||
\(681\) | −30.0352 | −1.15095 | ||||||||
\(682\) | 2.33224 | 0.0893060 | ||||||||
\(683\) | 23.5818 | 0.902333 | 0.451167 | − | 0.892440i | \(-0.351008\pi\) | ||||
0.451167 | + | 0.892440i | \(0.351008\pi\) | |||||||
\(684\) | −7.88179 | −0.301368 | ||||||||
\(685\) | 0.767130 | 0.0293105 | ||||||||
\(686\) | −36.3928 | −1.38948 | ||||||||
\(687\) | −7.69088 | −0.293425 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.35324 | 0.127748 | ||||||||
\(690\) | 1.37507 | 0.0523480 | ||||||||
\(691\) | 1.26897 | 0.0482738 | 0.0241369 | − | 0.999709i | \(-0.492316\pi\) | ||||
0.0241369 | + | 0.999709i | \(0.492316\pi\) | |||||||
\(692\) | 13.8247 | 0.525538 | ||||||||
\(693\) | 0.911083 | 0.0346092 | ||||||||
\(694\) | 45.2497 | 1.71766 | ||||||||
\(695\) | 0.388207 | 0.0147255 | ||||||||
\(696\) | 13.9364 | 0.528256 | ||||||||
\(697\) | 21.0388 | 0.796900 | ||||||||
\(698\) | 20.5044 | 0.776103 | ||||||||
\(699\) | 14.7805 | 0.559051 | ||||||||
\(700\) | −28.1231 | −1.06295 | ||||||||
\(701\) | −40.4042 | −1.52604 | −0.763022 | − | 0.646372i | \(-0.776285\pi\) | ||||
−0.763022 | + | 0.646372i | \(0.776285\pi\) | |||||||
\(702\) | −17.0444 | −0.643298 | ||||||||
\(703\) | −30.4265 | −1.14756 | ||||||||
\(704\) | 0.274948 | 0.0103625 | ||||||||
\(705\) | −0.429231 | −0.0161658 | ||||||||
\(706\) | −35.5240 | −1.33697 | ||||||||
\(707\) | −39.5524 | −1.48752 | ||||||||
\(708\) | −18.6888 | −0.702366 | ||||||||
\(709\) | −41.6968 | −1.56596 | −0.782978 | − | 0.622050i | \(-0.786300\pi\) | ||||
−0.782978 | + | 0.622050i | \(0.786300\pi\) | |||||||
\(710\) | 2.20634 | 0.0828025 | ||||||||
\(711\) | 21.1539 | 0.793331 | ||||||||
\(712\) | 10.4651 | 0.392195 | ||||||||
\(713\) | −32.4362 | −1.21475 | ||||||||
\(714\) | −56.5283 | −2.11552 | ||||||||
\(715\) | 0.0401242 | 0.00150056 | ||||||||
\(716\) | 7.99637 | 0.298838 | ||||||||
\(717\) | 20.9399 | 0.782014 | ||||||||
\(718\) | 16.3391 | 0.609770 | ||||||||
\(719\) | −32.8441 | −1.22488 | −0.612439 | − | 0.790518i | \(-0.709812\pi\) | ||||
−0.612439 | + | 0.790518i | \(0.709812\pi\) | |||||||
\(720\) | −1.11918 | −0.0417093 | ||||||||
\(721\) | 18.5447 | 0.690641 | ||||||||
\(722\) | 2.02758 | 0.0754588 | ||||||||
\(723\) | 2.20774 | 0.0821068 | ||||||||
\(724\) | −30.9963 | −1.15197 | ||||||||
\(725\) | 43.9581 | 1.63256 | ||||||||
\(726\) | −25.0807 | −0.930831 | ||||||||
\(727\) | 9.89017 | 0.366806 | 0.183403 | − | 0.983038i | \(-0.441289\pi\) | ||||
0.183403 | + | 0.983038i | \(0.441289\pi\) | |||||||
\(728\) | 9.14377 | 0.338891 | ||||||||
\(729\) | 24.7764 | 0.917644 | ||||||||
\(730\) | 1.45620 | 0.0538964 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 9.29779 | 0.343656 | ||||||||
\(733\) | 8.65503 | 0.319681 | 0.159840 | − | 0.987143i | \(-0.448902\pi\) | ||||
0.159840 | + | 0.987143i | \(0.448902\pi\) | |||||||
\(734\) | −16.2501 | −0.599801 | ||||||||
\(735\) | 2.34315 | 0.0864284 | ||||||||
\(736\) | −24.0566 | −0.886736 | ||||||||
\(737\) | 0.211489 | 0.00779029 | ||||||||
\(738\) | −9.50201 | −0.349774 | ||||||||
\(739\) | −11.4741 | −0.422082 | −0.211041 | − | 0.977477i | \(-0.567685\pi\) | ||||
−0.211041 | + | 0.977477i | \(0.567685\pi\) | |||||||
\(740\) | 1.51122 | 0.0555536 | ||||||||
\(741\) | −8.95822 | −0.329088 | ||||||||
\(742\) | −15.6122 | −0.573140 | ||||||||
\(743\) | −32.4692 | −1.19118 | −0.595590 | − | 0.803288i | \(-0.703082\pi\) | ||||
−0.595590 | + | 0.803288i | \(0.703082\pi\) | |||||||
\(744\) | −13.6304 | −0.499715 | ||||||||
\(745\) | 0.590755 | 0.0216436 | ||||||||
\(746\) | −27.8706 | −1.02041 | ||||||||
\(747\) | 8.70815 | 0.318615 | ||||||||
\(748\) | 1.11348 | 0.0407129 | ||||||||
\(749\) | −44.1117 | −1.61181 | ||||||||
\(750\) | 3.65464 | 0.133449 | ||||||||
\(751\) | −17.8947 | −0.652988 | −0.326494 | − | 0.945199i | \(-0.605867\pi\) | ||||
−0.326494 | + | 0.945199i | \(0.605867\pi\) | |||||||
\(752\) | 10.4515 | 0.381129 | ||||||||
\(753\) | −1.92871 | −0.0702861 | ||||||||
\(754\) | 27.1179 | 0.987575 | ||||||||
\(755\) | −1.30786 | −0.0475978 | ||||||||
\(756\) | 31.4027 | 1.14211 | ||||||||
\(757\) | −40.5848 | −1.47508 | −0.737539 | − | 0.675304i | \(-0.764012\pi\) | ||||
−0.737539 | + | 0.675304i | \(0.764012\pi\) | |||||||
\(758\) | 55.0727 | 2.00033 | ||||||||
\(759\) | −0.699021 | −0.0253728 | ||||||||
\(760\) | −0.851761 | −0.0308966 | ||||||||
\(761\) | −31.1825 | −1.13036 | −0.565182 | − | 0.824967i | \(-0.691194\pi\) | ||||
−0.565182 | + | 0.824967i | \(0.691194\pi\) | |||||||
\(762\) | 15.9496 | 0.577791 | ||||||||
\(763\) | −59.9063 | −2.16875 | ||||||||
\(764\) | −20.6683 | −0.747753 | ||||||||
\(765\) | −1.30809 | −0.0472942 | ||||||||
\(766\) | 1.85999 | 0.0672042 | ||||||||
\(767\) | 19.1660 | 0.692046 | ||||||||
\(768\) | −26.2410 | −0.946891 | ||||||||
\(769\) | −16.8244 | −0.606704 | −0.303352 | − | 0.952879i | \(-0.598106\pi\) | ||||
−0.303352 | + | 0.952879i | \(0.598106\pi\) | |||||||
\(770\) | −0.186812 | −0.00673225 | ||||||||
\(771\) | 36.9527 | 1.33082 | ||||||||
\(772\) | 28.0802 | 1.01063 | ||||||||
\(773\) | −1.36295 | −0.0490219 | −0.0245110 | − | 0.999700i | \(-0.507803\pi\) | ||||
−0.0245110 | + | 0.999700i | \(0.507803\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −42.9931 | −1.54436 | ||||||||
\(776\) | 2.64932 | 0.0951049 | ||||||||
\(777\) | 39.0010 | 1.39915 | ||||||||
\(778\) | 59.4842 | 2.13261 | ||||||||
\(779\) | −15.5230 | −0.556168 | ||||||||
\(780\) | 0.444936 | 0.0159313 | ||||||||
\(781\) | −1.12160 | −0.0401340 | ||||||||
\(782\) | −39.1339 | −1.39943 | ||||||||
\(783\) | −49.0843 | −1.75413 | ||||||||
\(784\) | −57.0545 | −2.03766 | ||||||||
\(785\) | 0.777835 | 0.0277621 | ||||||||
\(786\) | 16.4364 | 0.586266 | ||||||||
\(787\) | −10.8870 | −0.388081 | −0.194040 | − | 0.980994i | \(-0.562159\pi\) | ||||
−0.194040 | + | 0.980994i | \(0.562159\pi\) | |||||||
\(788\) | −20.3324 | −0.724313 | ||||||||
\(789\) | 9.95981 | 0.354579 | ||||||||
\(790\) | −4.33747 | −0.154320 | ||||||||
\(791\) | −41.2925 | −1.46819 | ||||||||
\(792\) | 0.265048 | 0.00941806 | ||||||||
\(793\) | −9.53525 | −0.338607 | ||||||||
\(794\) | −32.1389 | −1.14057 | ||||||||
\(795\) | 0.400387 | 0.0142003 | ||||||||
\(796\) | −10.6633 | −0.377951 | ||||||||
\(797\) | −40.5891 | −1.43774 | −0.718870 | − | 0.695145i | \(-0.755340\pi\) | ||||
−0.718870 | + | 0.695145i | \(0.755340\pi\) | |||||||
\(798\) | 41.7081 | 1.47645 | ||||||||
\(799\) | 12.2157 | 0.432162 | ||||||||
\(800\) | −31.8861 | −1.12735 | ||||||||
\(801\) | −11.8582 | −0.418988 | ||||||||
\(802\) | 64.0410 | 2.26137 | ||||||||
\(803\) | −0.740264 | −0.0261234 | ||||||||
\(804\) | 2.34519 | 0.0827084 | ||||||||
\(805\) | 2.59814 | 0.0915725 | ||||||||
\(806\) | −26.5226 | −0.934217 | ||||||||
\(807\) | −1.57784 | −0.0555425 | ||||||||
\(808\) | −11.5064 | −0.404793 | ||||||||
\(809\) | 3.98406 | 0.140072 | 0.0700361 | − | 0.997544i | \(-0.477689\pi\) | ||||
0.0700361 | + | 0.997544i | \(0.477689\pi\) | |||||||
\(810\) | −0.789607 | −0.0277440 | ||||||||
\(811\) | 35.9179 | 1.26125 | 0.630623 | − | 0.776089i | \(-0.282799\pi\) | ||||
0.630623 | + | 0.776089i | \(0.282799\pi\) | |||||||
\(812\) | −49.9623 | −1.75333 | ||||||||
\(813\) | 35.2675 | 1.23689 | ||||||||
\(814\) | −1.94136 | −0.0680446 | ||||||||
\(815\) | 1.99548 | 0.0698986 | ||||||||
\(816\) | −35.2999 | −1.23574 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 43.3016 | 1.51400 | ||||||||
\(819\) | −10.3610 | −0.362042 | ||||||||
\(820\) | 0.770993 | 0.0269242 | ||||||||
\(821\) | 25.7670 | 0.899276 | 0.449638 | − | 0.893211i | \(-0.351553\pi\) | ||||
0.449638 | + | 0.893211i | \(0.351553\pi\) | |||||||
\(822\) | −10.9279 | −0.381155 | ||||||||
\(823\) | −37.1671 | −1.29556 | −0.647782 | − | 0.761825i | \(-0.724303\pi\) | ||||
−0.647782 | + | 0.761825i | \(0.724303\pi\) | |||||||
\(824\) | 5.39493 | 0.187941 | ||||||||
\(825\) | −0.926528 | −0.0322576 | ||||||||
\(826\) | −89.2342 | −3.10485 | ||||||||
\(827\) | −14.5102 | −0.504568 | −0.252284 | − | 0.967653i | \(-0.581182\pi\) | ||||
−0.252284 | + | 0.967653i | \(0.581182\pi\) | |||||||
\(828\) | 6.99417 | 0.243064 | ||||||||
\(829\) | 22.2586 | 0.773074 | 0.386537 | − | 0.922274i | \(-0.373671\pi\) | ||||
0.386537 | + | 0.922274i | \(0.373671\pi\) | |||||||
\(830\) | −1.78556 | −0.0619775 | ||||||||
\(831\) | −16.4149 | −0.569428 | ||||||||
\(832\) | −3.12675 | −0.108400 | ||||||||
\(833\) | −66.6851 | −2.31050 | ||||||||
\(834\) | −5.53009 | −0.191491 | ||||||||
\(835\) | 2.50538 | 0.0867024 | ||||||||
\(836\) | −0.821557 | −0.0284141 | ||||||||
\(837\) | 48.0068 | 1.65936 | ||||||||
\(838\) | −38.5462 | −1.33156 | ||||||||
\(839\) | 51.0812 | 1.76352 | 0.881760 | − | 0.471699i | \(-0.156359\pi\) | ||||
0.881760 | + | 0.471699i | \(0.156359\pi\) | |||||||
\(840\) | 1.09180 | 0.0376706 | ||||||||
\(841\) | 49.0940 | 1.69290 | ||||||||
\(842\) | −2.48895 | −0.0857748 | ||||||||
\(843\) | 16.6065 | 0.571957 | ||||||||
\(844\) | 8.32739 | 0.286641 | ||||||||
\(845\) | 1.62863 | 0.0560265 | ||||||||
\(846\) | −5.51715 | −0.189684 | ||||||||
\(847\) | −47.3890 | −1.62830 | ||||||||
\(848\) | −9.74922 | −0.334789 | ||||||||
\(849\) | −21.4532 | −0.736271 | ||||||||
\(850\) | −51.8707 | −1.77915 | ||||||||
\(851\) | 27.0000 | 0.925547 | ||||||||
\(852\) | −12.4374 | −0.426097 | ||||||||
\(853\) | 12.8355 | 0.439478 | 0.219739 | − | 0.975559i | \(-0.429479\pi\) | ||||
0.219739 | + | 0.975559i | \(0.429479\pi\) | |||||||
\(854\) | 44.3947 | 1.51915 | ||||||||
\(855\) | 0.965146 | 0.0330073 | ||||||||
\(856\) | −12.8328 | −0.438614 | ||||||||
\(857\) | −38.8025 | −1.32547 | −0.662734 | − | 0.748855i | \(-0.730604\pi\) | ||||
−0.662734 | + | 0.748855i | \(0.730604\pi\) | |||||||
\(858\) | −0.571578 | −0.0195133 | ||||||||
\(859\) | 32.0864 | 1.09477 | 0.547387 | − | 0.836879i | \(-0.315622\pi\) | ||||
0.547387 | + | 0.836879i | \(0.315622\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 19.8975 | 0.678105 | ||||||||
\(862\) | 7.20394 | 0.245367 | ||||||||
\(863\) | 23.6312 | 0.804416 | 0.402208 | − | 0.915548i | \(-0.368243\pi\) | ||||
0.402208 | + | 0.915548i | \(0.368243\pi\) | |||||||
\(864\) | 35.6046 | 1.21129 | ||||||||
\(865\) | −1.69288 | −0.0575595 | ||||||||
\(866\) | −1.56383 | −0.0531410 | ||||||||
\(867\) | −19.9098 | −0.676172 | ||||||||
\(868\) | 48.8654 | 1.65860 | ||||||||
\(869\) | 2.20497 | 0.0747984 | ||||||||
\(870\) | 3.23796 | 0.109777 | ||||||||
\(871\) | −2.40508 | −0.0814931 | ||||||||
\(872\) | −17.4276 | −0.590174 | ||||||||
\(873\) | −3.00199 | −0.101602 | ||||||||
\(874\) | 28.8740 | 0.976679 | ||||||||
\(875\) | 6.90531 | 0.233442 | ||||||||
\(876\) | −8.20876 | −0.277348 | ||||||||
\(877\) | 18.7974 | 0.634743 | 0.317372 | − | 0.948301i | \(-0.397200\pi\) | ||||
0.317372 | + | 0.948301i | \(0.397200\pi\) | |||||||
\(878\) | −29.2306 | −0.986486 | ||||||||
\(879\) | −32.4135 | −1.09328 | ||||||||
\(880\) | −0.116657 | −0.00393252 | ||||||||
\(881\) | 8.12108 | 0.273606 | 0.136803 | − | 0.990598i | \(-0.456317\pi\) | ||||
0.136803 | + | 0.990598i | \(0.456317\pi\) | |||||||
\(882\) | 30.1179 | 1.01412 | ||||||||
\(883\) | 28.9422 | 0.973982 | 0.486991 | − | 0.873407i | \(-0.338094\pi\) | ||||
0.486991 | + | 0.873407i | \(0.338094\pi\) | |||||||
\(884\) | −12.6627 | −0.425893 | ||||||||
\(885\) | 2.28849 | 0.0769267 | ||||||||
\(886\) | 12.9712 | 0.435777 | ||||||||
\(887\) | −32.4245 | −1.08871 | −0.544353 | − | 0.838856i | \(-0.683225\pi\) | ||||
−0.544353 | + | 0.838856i | \(0.683225\pi\) | |||||||
\(888\) | 11.3460 | 0.380746 | ||||||||
\(889\) | 30.1361 | 1.01073 | ||||||||
\(890\) | 2.43145 | 0.0815024 | ||||||||
\(891\) | 0.401399 | 0.0134474 | ||||||||
\(892\) | 15.4896 | 0.518629 | ||||||||
\(893\) | −9.01310 | −0.301612 | ||||||||
\(894\) | −8.41542 | −0.281454 | ||||||||
\(895\) | −0.979177 | −0.0327303 | ||||||||
\(896\) | −40.7845 | −1.36251 | ||||||||
\(897\) | 7.94937 | 0.265422 | ||||||||
\(898\) | −40.0602 | −1.33683 | ||||||||
\(899\) | −76.3796 | −2.54740 | ||||||||
\(900\) | 9.27053 | 0.309018 | ||||||||
\(901\) | −11.3949 | −0.379618 | ||||||||
\(902\) | −0.990440 | −0.0329781 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12.0126 | −0.399533 | ||||||||
\(905\) | 3.79558 | 0.126169 | ||||||||
\(906\) | 18.6307 | 0.618964 | ||||||||
\(907\) | −8.15760 | −0.270869 | −0.135434 | − | 0.990786i | \(-0.543243\pi\) | ||||
−0.135434 | + | 0.990786i | \(0.543243\pi\) | |||||||
\(908\) | 31.3249 | 1.03955 | ||||||||
\(909\) | 13.0381 | 0.432447 | ||||||||
\(910\) | 2.12446 | 0.0704251 | ||||||||
\(911\) | 11.3023 | 0.374463 | 0.187231 | − | 0.982316i | \(-0.440049\pi\) | ||||
0.187231 | + | 0.982316i | \(0.440049\pi\) | |||||||
\(912\) | 26.0452 | 0.862442 | ||||||||
\(913\) | 0.907693 | 0.0300402 | ||||||||
\(914\) | 32.9907 | 1.09123 | ||||||||
\(915\) | −1.13854 | −0.0376390 | ||||||||
\(916\) | 8.02111 | 0.265025 | ||||||||
\(917\) | 31.0559 | 1.02556 | ||||||||
\(918\) | 57.9196 | 1.91163 | ||||||||
\(919\) | 17.7676 | 0.586098 | 0.293049 | − | 0.956097i | \(-0.405330\pi\) | ||||
0.293049 | + | 0.956097i | \(0.405330\pi\) | |||||||
\(920\) | 0.755838 | 0.0249192 | ||||||||
\(921\) | 10.1280 | 0.333727 | ||||||||
\(922\) | −17.4578 | −0.574942 | ||||||||
\(923\) | 12.7550 | 0.419836 | ||||||||
\(924\) | 1.05308 | 0.0346438 | ||||||||
\(925\) | 35.7875 | 1.17669 | ||||||||
\(926\) | 7.38264 | 0.242608 | ||||||||
\(927\) | −6.11310 | −0.200781 | ||||||||
\(928\) | −56.6475 | −1.85955 | ||||||||
\(929\) | −32.1876 | −1.05604 | −0.528020 | − | 0.849232i | \(-0.677065\pi\) | ||||
−0.528020 | + | 0.849232i | \(0.677065\pi\) | |||||||
\(930\) | −3.16688 | −0.103846 | ||||||||
\(931\) | 49.2021 | 1.61253 | ||||||||
\(932\) | −15.4152 | −0.504941 | ||||||||
\(933\) | 2.82662 | 0.0925394 | ||||||||
\(934\) | −19.2315 | −0.629275 | ||||||||
\(935\) | −0.136349 | −0.00445909 | ||||||||
\(936\) | −3.01416 | −0.0985210 | ||||||||
\(937\) | −19.4270 | −0.634652 | −0.317326 | − | 0.948316i | \(-0.602785\pi\) | ||||
−0.317326 | + | 0.948316i | \(0.602785\pi\) | |||||||
\(938\) | 11.1977 | 0.365618 | ||||||||
\(939\) | −27.1598 | −0.886326 | ||||||||
\(940\) | 0.447662 | 0.0146011 | ||||||||
\(941\) | −28.3881 | −0.925426 | −0.462713 | − | 0.886508i | \(-0.653124\pi\) | ||||
−0.462713 | + | 0.886508i | \(0.653124\pi\) | |||||||
\(942\) | −11.0804 | −0.361020 | ||||||||
\(943\) | 13.7748 | 0.448570 | ||||||||
\(944\) | −55.7235 | −1.81364 | ||||||||
\(945\) | −3.84535 | −0.125089 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25.9316 | 0.842664 | 0.421332 | − | 0.906906i | \(-0.361563\pi\) | ||||
0.421332 | + | 0.906906i | \(0.361563\pi\) | |||||||
\(948\) | 24.4508 | 0.794125 | ||||||||
\(949\) | 8.41840 | 0.273273 | ||||||||
\(950\) | 38.2716 | 1.24169 | ||||||||
\(951\) | 5.85498 | 0.189861 | ||||||||
\(952\) | −31.0721 | −1.00705 | ||||||||
\(953\) | 16.6331 | 0.538798 | 0.269399 | − | 0.963029i | \(-0.413175\pi\) | ||||
0.269399 | + | 0.963029i | \(0.413175\pi\) | |||||||
\(954\) | 5.14641 | 0.166621 | ||||||||
\(955\) | 2.53089 | 0.0818976 | ||||||||
\(956\) | −21.8390 | −0.706325 | ||||||||
\(957\) | −1.64603 | −0.0532085 | ||||||||
\(958\) | −47.0946 | −1.52156 | ||||||||
\(959\) | −20.6479 | −0.666756 | ||||||||
\(960\) | −0.373344 | −0.0120496 | ||||||||
\(961\) | 43.7028 | 1.40977 | ||||||||
\(962\) | 22.0774 | 0.711805 | ||||||||
\(963\) | 14.5410 | 0.468578 | ||||||||
\(964\) | −2.30254 | −0.0741598 | ||||||||
\(965\) | −3.43850 | −0.110689 | ||||||||
\(966\) | −37.0111 | −1.19081 | ||||||||
\(967\) | 37.5232 | 1.20667 | 0.603333 | − | 0.797489i | \(-0.293839\pi\) | ||||
0.603333 | + | 0.797489i | \(0.293839\pi\) | |||||||
\(968\) | −13.7862 | −0.443104 | ||||||||
\(969\) | 30.4415 | 0.977923 | ||||||||
\(970\) | 0.615540 | 0.0197638 | ||||||||
\(971\) | −14.6351 | −0.469662 | −0.234831 | − | 0.972036i | \(-0.575454\pi\) | ||||
−0.234831 | + | 0.972036i | \(0.575454\pi\) | |||||||
\(972\) | −17.3729 | −0.557236 | ||||||||
\(973\) | −10.4489 | −0.334976 | ||||||||
\(974\) | −6.64353 | −0.212872 | ||||||||
\(975\) | 10.5366 | 0.337442 | ||||||||
\(976\) | 27.7228 | 0.887387 | ||||||||
\(977\) | −3.59770 | −0.115101 | −0.0575503 | − | 0.998343i | \(-0.518329\pi\) | ||||
−0.0575503 | + | 0.998343i | \(0.518329\pi\) | |||||||
\(978\) | −28.4260 | −0.908963 | ||||||||
\(979\) | −1.23604 | −0.0395039 | ||||||||
\(980\) | −2.44376 | −0.0780631 | ||||||||
\(981\) | 19.7476 | 0.630491 | ||||||||
\(982\) | −58.3147 | −1.86090 | ||||||||
\(983\) | 25.2914 | 0.806670 | 0.403335 | − | 0.915052i | \(-0.367851\pi\) | ||||
0.403335 | + | 0.915052i | \(0.367851\pi\) | |||||||
\(984\) | 5.78848 | 0.184530 | ||||||||
\(985\) | 2.48976 | 0.0793303 | ||||||||
\(986\) | −92.1511 | −2.93469 | ||||||||
\(987\) | 11.5531 | 0.367739 | ||||||||
\(988\) | 9.34288 | 0.297236 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0.0615810 | 0.00195717 | ||||||||
\(991\) | −33.2741 | −1.05699 | −0.528494 | − | 0.848937i | \(-0.677243\pi\) | ||||
−0.528494 | + | 0.848937i | \(0.677243\pi\) | |||||||
\(992\) | 55.4039 | 1.75908 | ||||||||
\(993\) | 8.50251 | 0.269819 | ||||||||
\(994\) | −59.3854 | −1.88359 | ||||||||
\(995\) | 1.30575 | 0.0413951 | ||||||||
\(996\) | 10.0654 | 0.318933 | ||||||||
\(997\) | 18.2842 | 0.579067 | 0.289533 | − | 0.957168i | \(-0.406500\pi\) | ||||
0.289533 | + | 0.957168i | \(0.406500\pi\) | |||||||
\(998\) | 29.2768 | 0.926742 | ||||||||
\(999\) | −39.9609 | −1.26431 |
(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 | 1849.2.a.m.1.2 | ✓ | 10 | |
43.42 | odd | 2 | inner | 1849.2.a.m.1.9 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1849.2.a.m.1.2 | ✓ | 10 | 1.1 | even | 1 | trivial | |
1849.2.a.m.1.9 | yes | 10 | 43.42 | odd | 2 | inner |