Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4031,2,Mod(1,4031)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4031, 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("4031.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4031 = 29 \cdot 139 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4031.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1876970548\) |
Analytic rank: | \(0\) |
Dimension: | \(103\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 4031.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.68510 | −1.89865 | −0.949326 | − | 0.314293i | \(-0.898232\pi\) | ||||
−0.949326 | + | 0.314293i | \(0.898232\pi\) | |||||||
\(3\) | −0.634380 | −0.366260 | −0.183130 | − | 0.983089i | \(-0.558623\pi\) | ||||
−0.183130 | + | 0.983089i | \(0.558623\pi\) | |||||||
\(4\) | 5.20976 | 2.60488 | ||||||||
\(5\) | 1.13239 | 0.506420 | 0.253210 | − | 0.967411i | \(-0.418514\pi\) | ||||
0.253210 | + | 0.967411i | \(0.418514\pi\) | |||||||
\(6\) | 1.70337 | 0.695399 | ||||||||
\(7\) | 4.26000 | 1.61013 | 0.805065 | − | 0.593186i | \(-0.202130\pi\) | ||||
0.805065 | + | 0.593186i | \(0.202130\pi\) | |||||||
\(8\) | −8.61852 | −3.04711 | ||||||||
\(9\) | −2.59756 | −0.865854 | ||||||||
\(10\) | −3.04058 | −0.961515 | ||||||||
\(11\) | −6.04290 | −1.82200 | −0.911002 | − | 0.412402i | \(-0.864690\pi\) | ||||
−0.911002 | + | 0.412402i | \(0.864690\pi\) | |||||||
\(12\) | −3.30497 | −0.954062 | ||||||||
\(13\) | 5.71769 | 1.58580 | 0.792901 | − | 0.609351i | \(-0.208570\pi\) | ||||
0.792901 | + | 0.609351i | \(0.208570\pi\) | |||||||
\(14\) | −11.4385 | −3.05708 | ||||||||
\(15\) | −0.718365 | −0.185481 | ||||||||
\(16\) | 12.7221 | 3.18051 | ||||||||
\(17\) | 3.90610 | 0.947368 | 0.473684 | − | 0.880695i | \(-0.342924\pi\) | ||||
0.473684 | + | 0.880695i | \(0.342924\pi\) | |||||||
\(18\) | 6.97471 | 1.64396 | ||||||||
\(19\) | −0.321001 | −0.0736428 | −0.0368214 | − | 0.999322i | \(-0.511723\pi\) | ||||
−0.0368214 | + | 0.999322i | \(0.511723\pi\) | |||||||
\(20\) | 5.89947 | 1.31916 | ||||||||
\(21\) | −2.70246 | −0.589726 | ||||||||
\(22\) | 16.2258 | 3.45935 | ||||||||
\(23\) | 0.470194 | 0.0980422 | 0.0490211 | − | 0.998798i | \(-0.484390\pi\) | ||||
0.0490211 | + | 0.998798i | \(0.484390\pi\) | |||||||
\(24\) | 5.46742 | 1.11603 | ||||||||
\(25\) | −3.71770 | −0.743539 | ||||||||
\(26\) | −15.3526 | −3.01088 | ||||||||
\(27\) | 3.55098 | 0.683387 | ||||||||
\(28\) | 22.1936 | 4.19419 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 1.92888 | 0.352164 | ||||||||
\(31\) | −10.0857 | −1.81145 | −0.905725 | − | 0.423867i | \(-0.860673\pi\) | ||||
−0.905725 | + | 0.423867i | \(0.860673\pi\) | |||||||
\(32\) | −16.9229 | −2.99158 | ||||||||
\(33\) | 3.83350 | 0.667326 | ||||||||
\(34\) | −10.4883 | −1.79872 | ||||||||
\(35\) | 4.82398 | 0.815402 | ||||||||
\(36\) | −13.5327 | −2.25544 | ||||||||
\(37\) | 8.59551 | 1.41309 | 0.706546 | − | 0.707667i | \(-0.250252\pi\) | ||||
0.706546 | + | 0.707667i | \(0.250252\pi\) | |||||||
\(38\) | 0.861921 | 0.139822 | ||||||||
\(39\) | −3.62719 | −0.580815 | ||||||||
\(40\) | −9.75951 | −1.54311 | ||||||||
\(41\) | −4.43703 | −0.692948 | −0.346474 | − | 0.938060i | \(-0.612621\pi\) | ||||
−0.346474 | + | 0.938060i | \(0.612621\pi\) | |||||||
\(42\) | 7.25638 | 1.11968 | ||||||||
\(43\) | −3.34993 | −0.510860 | −0.255430 | − | 0.966828i | \(-0.582217\pi\) | ||||
−0.255430 | + | 0.966828i | \(0.582217\pi\) | |||||||
\(44\) | −31.4821 | −4.74610 | ||||||||
\(45\) | −2.94145 | −0.438485 | ||||||||
\(46\) | −1.26252 | −0.186148 | ||||||||
\(47\) | −1.52974 | −0.223136 | −0.111568 | − | 0.993757i | \(-0.535587\pi\) | ||||
−0.111568 | + | 0.993757i | \(0.535587\pi\) | |||||||
\(48\) | −8.07062 | −1.16489 | ||||||||
\(49\) | 11.1476 | 1.59252 | ||||||||
\(50\) | 9.98238 | 1.41172 | ||||||||
\(51\) | −2.47795 | −0.346983 | ||||||||
\(52\) | 29.7878 | 4.13082 | ||||||||
\(53\) | 7.29192 | 1.00162 | 0.500811 | − | 0.865556i | \(-0.333035\pi\) | ||||
0.500811 | + | 0.865556i | \(0.333035\pi\) | |||||||
\(54\) | −9.53474 | −1.29751 | ||||||||
\(55\) | −6.84291 | −0.922698 | ||||||||
\(56\) | −36.7149 | −4.90624 | ||||||||
\(57\) | 0.203637 | 0.0269724 | ||||||||
\(58\) | 2.68510 | 0.352571 | ||||||||
\(59\) | 7.45661 | 0.970768 | 0.485384 | − | 0.874301i | \(-0.338680\pi\) | ||||
0.485384 | + | 0.874301i | \(0.338680\pi\) | |||||||
\(60\) | −3.74251 | −0.483156 | ||||||||
\(61\) | −4.27509 | −0.547370 | −0.273685 | − | 0.961819i | \(-0.588243\pi\) | ||||
−0.273685 | + | 0.961819i | \(0.588243\pi\) | |||||||
\(62\) | 27.0812 | 3.43931 | ||||||||
\(63\) | −11.0656 | −1.39414 | ||||||||
\(64\) | 19.9957 | 2.49946 | ||||||||
\(65\) | 6.47465 | 0.803081 | ||||||||
\(66\) | −10.2933 | −1.26702 | ||||||||
\(67\) | 8.21626 | 1.00378 | 0.501888 | − | 0.864933i | \(-0.332639\pi\) | ||||
0.501888 | + | 0.864933i | \(0.332639\pi\) | |||||||
\(68\) | 20.3498 | 2.46778 | ||||||||
\(69\) | −0.298282 | −0.0359089 | ||||||||
\(70\) | −12.9529 | −1.54816 | ||||||||
\(71\) | −12.4356 | −1.47583 | −0.737915 | − | 0.674894i | \(-0.764189\pi\) | ||||
−0.737915 | + | 0.674894i | \(0.764189\pi\) | |||||||
\(72\) | 22.3871 | 2.63835 | ||||||||
\(73\) | 1.46047 | 0.170935 | 0.0854677 | − | 0.996341i | \(-0.472762\pi\) | ||||
0.0854677 | + | 0.996341i | \(0.472762\pi\) | |||||||
\(74\) | −23.0798 | −2.68297 | ||||||||
\(75\) | 2.35843 | 0.272328 | ||||||||
\(76\) | −1.67234 | −0.191830 | ||||||||
\(77\) | −25.7428 | −2.93366 | ||||||||
\(78\) | 9.73936 | 1.10277 | ||||||||
\(79\) | 17.3013 | 1.94655 | 0.973274 | − | 0.229647i | \(-0.0737573\pi\) | ||||
0.973274 | + | 0.229647i | \(0.0737573\pi\) | |||||||
\(80\) | 14.4063 | 1.61067 | ||||||||
\(81\) | 5.54001 | 0.615557 | ||||||||
\(82\) | 11.9139 | 1.31567 | ||||||||
\(83\) | 5.68429 | 0.623931 | 0.311966 | − | 0.950093i | \(-0.399013\pi\) | ||||
0.311966 | + | 0.950093i | \(0.399013\pi\) | |||||||
\(84\) | −14.0792 | −1.53616 | ||||||||
\(85\) | 4.42322 | 0.479766 | ||||||||
\(86\) | 8.99489 | 0.969944 | ||||||||
\(87\) | 0.634380 | 0.0680127 | ||||||||
\(88\) | 52.0808 | 5.55184 | ||||||||
\(89\) | 14.6303 | 1.55081 | 0.775405 | − | 0.631465i | \(-0.217546\pi\) | ||||
0.775405 | + | 0.631465i | \(0.217546\pi\) | |||||||
\(90\) | 7.89808 | 0.832531 | ||||||||
\(91\) | 24.3574 | 2.55335 | ||||||||
\(92\) | 2.44960 | 0.255388 | ||||||||
\(93\) | 6.39818 | 0.663461 | ||||||||
\(94\) | 4.10751 | 0.423658 | ||||||||
\(95\) | −0.363498 | −0.0372941 | ||||||||
\(96\) | 10.7356 | 1.09570 | ||||||||
\(97\) | −3.29050 | −0.334099 | −0.167050 | − | 0.985948i | \(-0.553424\pi\) | ||||
−0.167050 | + | 0.985948i | \(0.553424\pi\) | |||||||
\(98\) | −29.9325 | −3.02364 | ||||||||
\(99\) | 15.6968 | 1.57759 | ||||||||
\(100\) | −19.3683 | −1.93683 | ||||||||
\(101\) | 8.21401 | 0.817324 | 0.408662 | − | 0.912686i | \(-0.365995\pi\) | ||||
0.408662 | + | 0.912686i | \(0.365995\pi\) | |||||||
\(102\) | 6.65355 | 0.658799 | ||||||||
\(103\) | −4.17813 | −0.411683 | −0.205842 | − | 0.978585i | \(-0.565993\pi\) | ||||
−0.205842 | + | 0.978585i | \(0.565993\pi\) | |||||||
\(104\) | −49.2780 | −4.83210 | ||||||||
\(105\) | −3.06024 | −0.298649 | ||||||||
\(106\) | −19.5795 | −1.90173 | ||||||||
\(107\) | 3.29478 | 0.318518 | 0.159259 | − | 0.987237i | \(-0.449089\pi\) | ||||
0.159259 | + | 0.987237i | \(0.449089\pi\) | |||||||
\(108\) | 18.4998 | 1.78014 | ||||||||
\(109\) | 6.35842 | 0.609026 | 0.304513 | − | 0.952508i | \(-0.401506\pi\) | ||||
0.304513 | + | 0.952508i | \(0.401506\pi\) | |||||||
\(110\) | 18.3739 | 1.75188 | ||||||||
\(111\) | −5.45282 | −0.517559 | ||||||||
\(112\) | 54.1960 | 5.12104 | ||||||||
\(113\) | 7.01170 | 0.659605 | 0.329803 | − | 0.944050i | \(-0.393018\pi\) | ||||
0.329803 | + | 0.944050i | \(0.393018\pi\) | |||||||
\(114\) | −0.546785 | −0.0512111 | ||||||||
\(115\) | 0.532442 | 0.0496505 | ||||||||
\(116\) | −5.20976 | −0.483714 | ||||||||
\(117\) | −14.8520 | −1.37307 | ||||||||
\(118\) | −20.0217 | −1.84315 | ||||||||
\(119\) | 16.6400 | 1.52539 | ||||||||
\(120\) | 6.19124 | 0.565180 | ||||||||
\(121\) | 25.5167 | 2.31970 | ||||||||
\(122\) | 11.4791 | 1.03926 | ||||||||
\(123\) | 2.81477 | 0.253799 | ||||||||
\(124\) | −52.5442 | −4.71861 | ||||||||
\(125\) | −9.87182 | −0.882962 | ||||||||
\(126\) | 29.7123 | 2.64698 | ||||||||
\(127\) | 6.93898 | 0.615734 | 0.307867 | − | 0.951429i | \(-0.400385\pi\) | ||||
0.307867 | + | 0.951429i | \(0.400385\pi\) | |||||||
\(128\) | −19.8445 | −1.75402 | ||||||||
\(129\) | 2.12513 | 0.187107 | ||||||||
\(130\) | −17.3851 | −1.52477 | ||||||||
\(131\) | −10.2913 | −0.899154 | −0.449577 | − | 0.893242i | \(-0.648425\pi\) | ||||
−0.449577 | + | 0.893242i | \(0.648425\pi\) | |||||||
\(132\) | 19.9716 | 1.73830 | ||||||||
\(133\) | −1.36747 | −0.118574 | ||||||||
\(134\) | −22.0615 | −1.90582 | ||||||||
\(135\) | 4.02109 | 0.346081 | ||||||||
\(136\) | −33.6648 | −2.88673 | ||||||||
\(137\) | 13.9411 | 1.19107 | 0.595536 | − | 0.803329i | \(-0.296940\pi\) | ||||
0.595536 | + | 0.803329i | \(0.296940\pi\) | |||||||
\(138\) | 0.800916 | 0.0681785 | ||||||||
\(139\) | 1.00000 | 0.0848189 | ||||||||
\(140\) | 25.1318 | 2.12402 | ||||||||
\(141\) | 0.970439 | 0.0817257 | ||||||||
\(142\) | 33.3907 | 2.80209 | ||||||||
\(143\) | −34.5514 | −2.88934 | ||||||||
\(144\) | −33.0463 | −2.75386 | ||||||||
\(145\) | −1.13239 | −0.0940398 | ||||||||
\(146\) | −3.92151 | −0.324547 | ||||||||
\(147\) | −7.07184 | −0.583276 | ||||||||
\(148\) | 44.7805 | 3.68093 | ||||||||
\(149\) | −17.5661 | −1.43907 | −0.719535 | − | 0.694456i | \(-0.755645\pi\) | ||||
−0.719535 | + | 0.694456i | \(0.755645\pi\) | |||||||
\(150\) | −6.33263 | −0.517057 | ||||||||
\(151\) | −17.1209 | −1.39328 | −0.696639 | − | 0.717422i | \(-0.745322\pi\) | ||||
−0.696639 | + | 0.717422i | \(0.745322\pi\) | |||||||
\(152\) | 2.76656 | 0.224397 | ||||||||
\(153\) | −10.1463 | −0.820282 | ||||||||
\(154\) | 69.1219 | 5.57000 | ||||||||
\(155\) | −11.4210 | −0.917353 | ||||||||
\(156\) | −18.8968 | −1.51295 | ||||||||
\(157\) | 1.62185 | 0.129438 | 0.0647188 | − | 0.997904i | \(-0.479385\pi\) | ||||
0.0647188 | + | 0.997904i | \(0.479385\pi\) | |||||||
\(158\) | −46.4557 | −3.69582 | ||||||||
\(159\) | −4.62585 | −0.366854 | ||||||||
\(160\) | −19.1634 | −1.51500 | ||||||||
\(161\) | 2.00303 | 0.157861 | ||||||||
\(162\) | −14.8755 | −1.16873 | ||||||||
\(163\) | 7.83518 | 0.613699 | 0.306849 | − | 0.951758i | \(-0.400725\pi\) | ||||
0.306849 | + | 0.951758i | \(0.400725\pi\) | |||||||
\(164\) | −23.1159 | −1.80505 | ||||||||
\(165\) | 4.34101 | 0.337947 | ||||||||
\(166\) | −15.2629 | −1.18463 | ||||||||
\(167\) | −20.9838 | −1.62377 | −0.811887 | − | 0.583815i | \(-0.801560\pi\) | ||||
−0.811887 | + | 0.583815i | \(0.801560\pi\) | |||||||
\(168\) | 23.2912 | 1.79696 | ||||||||
\(169\) | 19.6920 | 1.51477 | ||||||||
\(170\) | −11.8768 | −0.910908 | ||||||||
\(171\) | 0.833821 | 0.0637639 | ||||||||
\(172\) | −17.4523 | −1.33073 | ||||||||
\(173\) | −3.13875 | −0.238634 | −0.119317 | − | 0.992856i | \(-0.538071\pi\) | ||||
−0.119317 | + | 0.992856i | \(0.538071\pi\) | |||||||
\(174\) | −1.70337 | −0.129132 | ||||||||
\(175\) | −15.8374 | −1.19719 | ||||||||
\(176\) | −76.8781 | −5.79491 | ||||||||
\(177\) | −4.73033 | −0.355553 | ||||||||
\(178\) | −39.2838 | −2.94445 | ||||||||
\(179\) | −2.63246 | −0.196760 | −0.0983798 | − | 0.995149i | \(-0.531366\pi\) | ||||
−0.0983798 | + | 0.995149i | \(0.531366\pi\) | |||||||
\(180\) | −15.3242 | −1.14220 | ||||||||
\(181\) | 10.2405 | 0.761170 | 0.380585 | − | 0.924746i | \(-0.375723\pi\) | ||||
0.380585 | + | 0.924746i | \(0.375723\pi\) | |||||||
\(182\) | −65.4020 | −4.84792 | ||||||||
\(183\) | 2.71204 | 0.200479 | ||||||||
\(184\) | −4.05237 | −0.298745 | ||||||||
\(185\) | 9.73345 | 0.715618 | ||||||||
\(186\) | −17.1798 | −1.25968 | ||||||||
\(187\) | −23.6042 | −1.72611 | ||||||||
\(188\) | −7.96959 | −0.581242 | ||||||||
\(189\) | 15.1272 | 1.10034 | ||||||||
\(190\) | 0.976029 | 0.0708086 | ||||||||
\(191\) | 16.3101 | 1.18016 | 0.590078 | − | 0.807346i | \(-0.299097\pi\) | ||||
0.590078 | + | 0.807346i | \(0.299097\pi\) | |||||||
\(192\) | −12.6849 | −0.915451 | ||||||||
\(193\) | 23.1364 | 1.66539 | 0.832697 | − | 0.553730i | \(-0.186796\pi\) | ||||
0.832697 | + | 0.553730i | \(0.186796\pi\) | |||||||
\(194\) | 8.83531 | 0.634338 | ||||||||
\(195\) | −4.10739 | −0.294136 | ||||||||
\(196\) | 58.0765 | 4.14832 | ||||||||
\(197\) | 7.70316 | 0.548827 | 0.274414 | − | 0.961612i | \(-0.411516\pi\) | ||||
0.274414 | + | 0.961612i | \(0.411516\pi\) | |||||||
\(198\) | −42.1475 | −2.99529 | ||||||||
\(199\) | −18.8108 | −1.33346 | −0.666731 | − | 0.745299i | \(-0.732307\pi\) | ||||
−0.666731 | + | 0.745299i | \(0.732307\pi\) | |||||||
\(200\) | 32.0410 | 2.26564 | ||||||||
\(201\) | −5.21223 | −0.367643 | ||||||||
\(202\) | −22.0554 | −1.55181 | ||||||||
\(203\) | −4.26000 | −0.298994 | ||||||||
\(204\) | −12.9095 | −0.903848 | ||||||||
\(205\) | −5.02444 | −0.350922 | ||||||||
\(206\) | 11.2187 | 0.781643 | ||||||||
\(207\) | −1.22136 | −0.0848902 | ||||||||
\(208\) | 72.7408 | 5.04366 | ||||||||
\(209\) | 1.93978 | 0.134177 | ||||||||
\(210\) | 8.21704 | 0.567030 | ||||||||
\(211\) | −4.76369 | −0.327946 | −0.163973 | − | 0.986465i | \(-0.552431\pi\) | ||||
−0.163973 | + | 0.986465i | \(0.552431\pi\) | |||||||
\(212\) | 37.9892 | 2.60911 | ||||||||
\(213\) | 7.88888 | 0.540537 | ||||||||
\(214\) | −8.84681 | −0.604756 | ||||||||
\(215\) | −3.79342 | −0.258709 | ||||||||
\(216\) | −30.6042 | −2.08235 | ||||||||
\(217\) | −42.9652 | −2.91667 | ||||||||
\(218\) | −17.0730 | −1.15633 | ||||||||
\(219\) | −0.926495 | −0.0626067 | ||||||||
\(220\) | −35.6499 | −2.40352 | ||||||||
\(221\) | 22.3339 | 1.50234 | ||||||||
\(222\) | 14.6414 | 0.982664 | ||||||||
\(223\) | −0.485916 | −0.0325393 | −0.0162697 | − | 0.999868i | \(-0.505179\pi\) | ||||
−0.0162697 | + | 0.999868i | \(0.505179\pi\) | |||||||
\(224\) | −72.0918 | −4.81684 | ||||||||
\(225\) | 9.65694 | 0.643796 | ||||||||
\(226\) | −18.8271 | −1.25236 | ||||||||
\(227\) | 24.8926 | 1.65218 | 0.826089 | − | 0.563540i | \(-0.190561\pi\) | ||||
0.826089 | + | 0.563540i | \(0.190561\pi\) | |||||||
\(228\) | 1.06090 | 0.0702598 | ||||||||
\(229\) | 23.0702 | 1.52452 | 0.762261 | − | 0.647270i | \(-0.224089\pi\) | ||||
0.762261 | + | 0.647270i | \(0.224089\pi\) | |||||||
\(230\) | −1.42966 | −0.0942690 | ||||||||
\(231\) | 16.3307 | 1.07448 | ||||||||
\(232\) | 8.61852 | 0.565833 | ||||||||
\(233\) | 18.9799 | 1.24341 | 0.621706 | − | 0.783251i | \(-0.286440\pi\) | ||||
0.621706 | + | 0.783251i | \(0.286440\pi\) | |||||||
\(234\) | 39.8792 | 2.60699 | ||||||||
\(235\) | −1.73226 | −0.113000 | ||||||||
\(236\) | 38.8471 | 2.52873 | ||||||||
\(237\) | −10.9756 | −0.712942 | ||||||||
\(238\) | −44.6800 | −2.89618 | ||||||||
\(239\) | 5.26823 | 0.340773 | 0.170387 | − | 0.985377i | \(-0.445498\pi\) | ||||
0.170387 | + | 0.985377i | \(0.445498\pi\) | |||||||
\(240\) | −9.13908 | −0.589925 | ||||||||
\(241\) | −27.2067 | −1.75254 | −0.876268 | − | 0.481824i | \(-0.839974\pi\) | ||||
−0.876268 | + | 0.481824i | \(0.839974\pi\) | |||||||
\(242\) | −68.5148 | −4.40430 | ||||||||
\(243\) | −14.1674 | −0.908841 | ||||||||
\(244\) | −22.2722 | −1.42583 | ||||||||
\(245\) | 12.6235 | 0.806483 | ||||||||
\(246\) | −7.55792 | −0.481876 | ||||||||
\(247\) | −1.83539 | −0.116783 | ||||||||
\(248\) | 86.9240 | 5.51968 | ||||||||
\(249\) | −3.60600 | −0.228521 | ||||||||
\(250\) | 26.5068 | 1.67644 | ||||||||
\(251\) | 13.3232 | 0.840956 | 0.420478 | − | 0.907303i | \(-0.361862\pi\) | ||||
0.420478 | + | 0.907303i | \(0.361862\pi\) | |||||||
\(252\) | −57.6492 | −3.63156 | ||||||||
\(253\) | −2.84133 | −0.178633 | ||||||||
\(254\) | −18.6318 | −1.16907 | ||||||||
\(255\) | −2.80601 | −0.175719 | ||||||||
\(256\) | 13.2930 | 0.830816 | ||||||||
\(257\) | 0.666973 | 0.0416046 | 0.0208023 | − | 0.999784i | \(-0.493378\pi\) | ||||
0.0208023 | + | 0.999784i | \(0.493378\pi\) | |||||||
\(258\) | −5.70618 | −0.355251 | ||||||||
\(259\) | 36.6169 | 2.27526 | ||||||||
\(260\) | 33.7313 | 2.09193 | ||||||||
\(261\) | 2.59756 | 0.160785 | ||||||||
\(262\) | 27.6331 | 1.70718 | ||||||||
\(263\) | 18.4823 | 1.13967 | 0.569833 | − | 0.821761i | \(-0.307008\pi\) | ||||
0.569833 | + | 0.821761i | \(0.307008\pi\) | |||||||
\(264\) | −33.0391 | −2.03341 | ||||||||
\(265\) | 8.25729 | 0.507241 | ||||||||
\(266\) | 3.67179 | 0.225132 | ||||||||
\(267\) | −9.28118 | −0.567999 | ||||||||
\(268\) | 42.8047 | 2.61471 | ||||||||
\(269\) | 3.25871 | 0.198687 | 0.0993435 | − | 0.995053i | \(-0.468326\pi\) | ||||
0.0993435 | + | 0.995053i | \(0.468326\pi\) | |||||||
\(270\) | −10.7970 | −0.657086 | ||||||||
\(271\) | −30.4341 | −1.84874 | −0.924369 | − | 0.381501i | \(-0.875407\pi\) | ||||
−0.924369 | + | 0.381501i | \(0.875407\pi\) | |||||||
\(272\) | 49.6936 | 3.01312 | ||||||||
\(273\) | −15.4518 | −0.935188 | ||||||||
\(274\) | −37.4333 | −2.26143 | ||||||||
\(275\) | 22.4657 | 1.35473 | ||||||||
\(276\) | −1.55397 | −0.0935383 | ||||||||
\(277\) | −2.17481 | −0.130672 | −0.0653359 | − | 0.997863i | \(-0.520812\pi\) | ||||
−0.0653359 | + | 0.997863i | \(0.520812\pi\) | |||||||
\(278\) | −2.68510 | −0.161042 | ||||||||
\(279\) | 26.1983 | 1.56845 | ||||||||
\(280\) | −41.5756 | −2.48461 | ||||||||
\(281\) | 15.8763 | 0.947101 | 0.473551 | − | 0.880767i | \(-0.342972\pi\) | ||||
0.473551 | + | 0.880767i | \(0.342972\pi\) | |||||||
\(282\) | −2.60572 | −0.155169 | ||||||||
\(283\) | 6.08870 | 0.361936 | 0.180968 | − | 0.983489i | \(-0.442077\pi\) | ||||
0.180968 | + | 0.983489i | \(0.442077\pi\) | |||||||
\(284\) | −64.7863 | −3.84436 | ||||||||
\(285\) | 0.230596 | 0.0136593 | ||||||||
\(286\) | 92.7740 | 5.48584 | ||||||||
\(287\) | −18.9018 | −1.11574 | ||||||||
\(288\) | 43.9584 | 2.59027 | ||||||||
\(289\) | −1.74239 | −0.102493 | ||||||||
\(290\) | 3.04058 | 0.178549 | ||||||||
\(291\) | 2.08743 | 0.122367 | ||||||||
\(292\) | 7.60871 | 0.445266 | ||||||||
\(293\) | −27.9492 | −1.63281 | −0.816403 | − | 0.577482i | \(-0.804035\pi\) | ||||
−0.816403 | + | 0.577482i | \(0.804035\pi\) | |||||||
\(294\) | 18.9886 | 1.10744 | ||||||||
\(295\) | 8.44378 | 0.491616 | ||||||||
\(296\) | −74.0805 | −4.30584 | ||||||||
\(297\) | −21.4582 | −1.24513 | ||||||||
\(298\) | 47.1667 | 2.73229 | ||||||||
\(299\) | 2.68842 | 0.155475 | ||||||||
\(300\) | 12.2869 | 0.709382 | ||||||||
\(301\) | −14.2707 | −0.822550 | ||||||||
\(302\) | 45.9713 | 2.64535 | ||||||||
\(303\) | −5.21080 | −0.299353 | ||||||||
\(304\) | −4.08380 | −0.234222 | ||||||||
\(305\) | −4.84107 | −0.277199 | ||||||||
\(306\) | 27.2439 | 1.55743 | ||||||||
\(307\) | 5.10355 | 0.291275 | 0.145638 | − | 0.989338i | \(-0.453477\pi\) | ||||
0.145638 | + | 0.989338i | \(0.453477\pi\) | |||||||
\(308\) | −134.114 | −7.64184 | ||||||||
\(309\) | 2.65052 | 0.150783 | ||||||||
\(310\) | 30.6664 | 1.74173 | ||||||||
\(311\) | 9.25161 | 0.524610 | 0.262305 | − | 0.964985i | \(-0.415517\pi\) | ||||
0.262305 | + | 0.964985i | \(0.415517\pi\) | |||||||
\(312\) | 31.2610 | 1.76980 | ||||||||
\(313\) | 12.6099 | 0.712755 | 0.356378 | − | 0.934342i | \(-0.384012\pi\) | ||||
0.356378 | + | 0.934342i | \(0.384012\pi\) | |||||||
\(314\) | −4.35482 | −0.245757 | ||||||||
\(315\) | −12.5306 | −0.706019 | ||||||||
\(316\) | 90.1355 | 5.07052 | ||||||||
\(317\) | −9.55673 | −0.536759 | −0.268380 | − | 0.963313i | \(-0.586488\pi\) | ||||
−0.268380 | + | 0.963313i | \(0.586488\pi\) | |||||||
\(318\) | 12.4209 | 0.696528 | ||||||||
\(319\) | 6.04290 | 0.338338 | ||||||||
\(320\) | 22.6429 | 1.26578 | ||||||||
\(321\) | −2.09014 | −0.116660 | ||||||||
\(322\) | −5.37833 | −0.299722 | ||||||||
\(323\) | −1.25386 | −0.0697668 | ||||||||
\(324\) | 28.8621 | 1.60345 | ||||||||
\(325\) | −21.2566 | −1.17911 | ||||||||
\(326\) | −21.0382 | −1.16520 | ||||||||
\(327\) | −4.03365 | −0.223062 | ||||||||
\(328\) | 38.2406 | 2.11149 | ||||||||
\(329\) | −6.51671 | −0.359278 | ||||||||
\(330\) | −11.6560 | −0.641644 | ||||||||
\(331\) | −17.9599 | −0.987166 | −0.493583 | − | 0.869699i | \(-0.664313\pi\) | ||||
−0.493583 | + | 0.869699i | \(0.664313\pi\) | |||||||
\(332\) | 29.6137 | 1.62527 | ||||||||
\(333\) | −22.3274 | −1.22353 | ||||||||
\(334\) | 56.3435 | 3.08298 | ||||||||
\(335\) | 9.30400 | 0.508332 | ||||||||
\(336\) | −34.3809 | −1.87563 | ||||||||
\(337\) | 0.231403 | 0.0126053 | 0.00630267 | − | 0.999980i | \(-0.497994\pi\) | ||||
0.00630267 | + | 0.999980i | \(0.497994\pi\) | |||||||
\(338\) | −52.8749 | −2.87601 | ||||||||
\(339\) | −4.44808 | −0.241587 | ||||||||
\(340\) | 23.0439 | 1.24973 | ||||||||
\(341\) | 60.9470 | 3.30047 | ||||||||
\(342\) | −2.23889 | −0.121065 | ||||||||
\(343\) | 17.6690 | 0.954034 | ||||||||
\(344\) | 28.8714 | 1.55664 | ||||||||
\(345\) | −0.337771 | −0.0181850 | ||||||||
\(346\) | 8.42784 | 0.453084 | ||||||||
\(347\) | −7.26342 | −0.389921 | −0.194960 | − | 0.980811i | \(-0.562458\pi\) | ||||
−0.194960 | + | 0.980811i | \(0.562458\pi\) | |||||||
\(348\) | 3.30497 | 0.177165 | ||||||||
\(349\) | −21.2600 | −1.13802 | −0.569012 | − | 0.822329i | \(-0.692674\pi\) | ||||
−0.569012 | + | 0.822329i | \(0.692674\pi\) | |||||||
\(350\) | 42.5250 | 2.27306 | ||||||||
\(351\) | 20.3034 | 1.08372 | ||||||||
\(352\) | 102.264 | 5.45067 | ||||||||
\(353\) | −6.98241 | −0.371636 | −0.185818 | − | 0.982584i | \(-0.559494\pi\) | ||||
−0.185818 | + | 0.982584i | \(0.559494\pi\) | |||||||
\(354\) | 12.7014 | 0.675072 | ||||||||
\(355\) | −14.0819 | −0.747389 | ||||||||
\(356\) | 76.2203 | 4.03967 | ||||||||
\(357\) | −10.5561 | −0.558687 | ||||||||
\(358\) | 7.06843 | 0.373578 | ||||||||
\(359\) | 18.7846 | 0.991413 | 0.495707 | − | 0.868490i | \(-0.334909\pi\) | ||||
0.495707 | + | 0.868490i | \(0.334909\pi\) | |||||||
\(360\) | 25.3509 | 1.33611 | ||||||||
\(361\) | −18.8970 | −0.994577 | ||||||||
\(362\) | −27.4968 | −1.44520 | ||||||||
\(363\) | −16.1873 | −0.849611 | ||||||||
\(364\) | 126.896 | 6.65116 | ||||||||
\(365\) | 1.65382 | 0.0865650 | ||||||||
\(366\) | −7.28208 | −0.380641 | ||||||||
\(367\) | 23.8213 | 1.24346 | 0.621730 | − | 0.783232i | \(-0.286430\pi\) | ||||
0.621730 | + | 0.783232i | \(0.286430\pi\) | |||||||
\(368\) | 5.98183 | 0.311824 | ||||||||
\(369\) | 11.5255 | 0.599992 | ||||||||
\(370\) | −26.1353 | −1.35871 | ||||||||
\(371\) | 31.0636 | 1.61274 | ||||||||
\(372\) | 33.3330 | 1.72823 | ||||||||
\(373\) | −19.4035 | −1.00467 | −0.502337 | − | 0.864672i | \(-0.667526\pi\) | ||||
−0.502337 | + | 0.864672i | \(0.667526\pi\) | |||||||
\(374\) | 63.3796 | 3.27728 | ||||||||
\(375\) | 6.26249 | 0.323393 | ||||||||
\(376\) | 13.1841 | 0.679919 | ||||||||
\(377\) | −5.71769 | −0.294476 | ||||||||
\(378\) | −40.6180 | −2.08917 | ||||||||
\(379\) | 13.8163 | 0.709695 | 0.354848 | − | 0.934924i | \(-0.384533\pi\) | ||||
0.354848 | + | 0.934924i | \(0.384533\pi\) | |||||||
\(380\) | −1.89374 | −0.0971467 | ||||||||
\(381\) | −4.40195 | −0.225519 | ||||||||
\(382\) | −43.7942 | −2.24070 | ||||||||
\(383\) | 7.20712 | 0.368266 | 0.184133 | − | 0.982901i | \(-0.441052\pi\) | ||||
0.184133 | + | 0.982901i | \(0.441052\pi\) | |||||||
\(384\) | 12.5889 | 0.642427 | ||||||||
\(385\) | −29.1508 | −1.48566 | ||||||||
\(386\) | −62.1235 | −3.16200 | ||||||||
\(387\) | 8.70165 | 0.442330 | ||||||||
\(388\) | −17.1427 | −0.870288 | ||||||||
\(389\) | −5.19326 | −0.263309 | −0.131654 | − | 0.991296i | \(-0.542029\pi\) | ||||
−0.131654 | + | 0.991296i | \(0.542029\pi\) | |||||||
\(390\) | 11.0287 | 0.558462 | ||||||||
\(391\) | 1.83662 | 0.0928820 | ||||||||
\(392\) | −96.0761 | −4.85258 | ||||||||
\(393\) | 6.52859 | 0.329324 | ||||||||
\(394\) | −20.6837 | −1.04203 | ||||||||
\(395\) | 19.5918 | 0.985770 | ||||||||
\(396\) | 81.7766 | 4.10943 | ||||||||
\(397\) | 13.8072 | 0.692961 | 0.346481 | − | 0.938057i | \(-0.387377\pi\) | ||||
0.346481 | + | 0.938057i | \(0.387377\pi\) | |||||||
\(398\) | 50.5088 | 2.53178 | ||||||||
\(399\) | 0.867494 | 0.0434290 | ||||||||
\(400\) | −47.2967 | −2.36484 | ||||||||
\(401\) | −25.6728 | −1.28204 | −0.641020 | − | 0.767524i | \(-0.721488\pi\) | ||||
−0.641020 | + | 0.767524i | \(0.721488\pi\) | |||||||
\(402\) | 13.9954 | 0.698025 | ||||||||
\(403\) | −57.6670 | −2.87260 | ||||||||
\(404\) | 42.7930 | 2.12903 | ||||||||
\(405\) | 6.27345 | 0.311730 | ||||||||
\(406\) | 11.4385 | 0.567685 | ||||||||
\(407\) | −51.9418 | −2.57466 | ||||||||
\(408\) | 21.3563 | 1.05729 | ||||||||
\(409\) | 9.19424 | 0.454626 | 0.227313 | − | 0.973822i | \(-0.427006\pi\) | ||||
0.227313 | + | 0.973822i | \(0.427006\pi\) | |||||||
\(410\) | 13.4911 | 0.666279 | ||||||||
\(411\) | −8.84398 | −0.436241 | ||||||||
\(412\) | −21.7670 | −1.07239 | ||||||||
\(413\) | 31.7652 | 1.56306 | ||||||||
\(414\) | 3.27947 | 0.161177 | ||||||||
\(415\) | 6.43682 | 0.315971 | ||||||||
\(416\) | −96.7601 | −4.74406 | ||||||||
\(417\) | −0.634380 | −0.0310657 | ||||||||
\(418\) | −5.20850 | −0.254756 | ||||||||
\(419\) | 8.35548 | 0.408192 | 0.204096 | − | 0.978951i | \(-0.434575\pi\) | ||||
0.204096 | + | 0.978951i | \(0.434575\pi\) | |||||||
\(420\) | −15.9431 | −0.777944 | ||||||||
\(421\) | −5.80266 | −0.282804 | −0.141402 | − | 0.989952i | \(-0.545161\pi\) | ||||
−0.141402 | + | 0.989952i | \(0.545161\pi\) | |||||||
\(422\) | 12.7910 | 0.622655 | ||||||||
\(423\) | 3.97360 | 0.193203 | ||||||||
\(424\) | −62.8456 | −3.05205 | ||||||||
\(425\) | −14.5217 | −0.704405 | ||||||||
\(426\) | −21.1824 | −1.02629 | ||||||||
\(427\) | −18.2119 | −0.881336 | ||||||||
\(428\) | 17.1650 | 0.829702 | ||||||||
\(429\) | 21.9187 | 1.05825 | ||||||||
\(430\) | 10.1857 | 0.491199 | ||||||||
\(431\) | 0.647192 | 0.0311741 | 0.0155871 | − | 0.999879i | \(-0.495038\pi\) | ||||
0.0155871 | + | 0.999879i | \(0.495038\pi\) | |||||||
\(432\) | 45.1758 | 2.17352 | ||||||||
\(433\) | 1.91751 | 0.0921499 | 0.0460749 | − | 0.998938i | \(-0.485329\pi\) | ||||
0.0460749 | + | 0.998938i | \(0.485329\pi\) | |||||||
\(434\) | 115.366 | 5.53774 | ||||||||
\(435\) | 0.718365 | 0.0344430 | ||||||||
\(436\) | 33.1258 | 1.58644 | ||||||||
\(437\) | −0.150933 | −0.00722010 | ||||||||
\(438\) | 2.48773 | 0.118868 | ||||||||
\(439\) | 26.5405 | 1.26671 | 0.633354 | − | 0.773862i | \(-0.281678\pi\) | ||||
0.633354 | + | 0.773862i | \(0.281678\pi\) | |||||||
\(440\) | 58.9758 | 2.81156 | ||||||||
\(441\) | −28.9567 | −1.37889 | ||||||||
\(442\) | −59.9686 | −2.85242 | ||||||||
\(443\) | 18.3116 | 0.870011 | 0.435006 | − | 0.900428i | \(-0.356746\pi\) | ||||
0.435006 | + | 0.900428i | \(0.356746\pi\) | |||||||
\(444\) | −28.4079 | −1.34818 | ||||||||
\(445\) | 16.5672 | 0.785360 | ||||||||
\(446\) | 1.30473 | 0.0617808 | ||||||||
\(447\) | 11.1436 | 0.527073 | ||||||||
\(448\) | 85.1817 | 4.02446 | ||||||||
\(449\) | 18.2634 | 0.861905 | 0.430952 | − | 0.902375i | \(-0.358178\pi\) | ||||
0.430952 | + | 0.902375i | \(0.358178\pi\) | |||||||
\(450\) | −25.9299 | −1.22234 | ||||||||
\(451\) | 26.8125 | 1.26255 | ||||||||
\(452\) | 36.5293 | 1.71819 | ||||||||
\(453\) | 10.8612 | 0.510301 | ||||||||
\(454\) | −66.8390 | −3.13691 | ||||||||
\(455\) | 27.5820 | 1.29307 | ||||||||
\(456\) | −1.75505 | −0.0821877 | ||||||||
\(457\) | 35.4383 | 1.65773 | 0.828866 | − | 0.559447i | \(-0.188987\pi\) | ||||
0.828866 | + | 0.559447i | \(0.188987\pi\) | |||||||
\(458\) | −61.9458 | −2.89454 | ||||||||
\(459\) | 13.8705 | 0.647419 | ||||||||
\(460\) | 2.77389 | 0.129333 | ||||||||
\(461\) | 13.6366 | 0.635121 | 0.317560 | − | 0.948238i | \(-0.397136\pi\) | ||||
0.317560 | + | 0.948238i | \(0.397136\pi\) | |||||||
\(462\) | −43.8496 | −2.04007 | ||||||||
\(463\) | 25.5791 | 1.18876 | 0.594381 | − | 0.804183i | \(-0.297397\pi\) | ||||
0.594381 | + | 0.804183i | \(0.297397\pi\) | |||||||
\(464\) | −12.7221 | −0.590607 | ||||||||
\(465\) | 7.24523 | 0.335990 | ||||||||
\(466\) | −50.9628 | −2.36081 | ||||||||
\(467\) | 20.1031 | 0.930261 | 0.465131 | − | 0.885242i | \(-0.346007\pi\) | ||||
0.465131 | + | 0.885242i | \(0.346007\pi\) | |||||||
\(468\) | −77.3756 | −3.57669 | ||||||||
\(469\) | 35.0013 | 1.61621 | ||||||||
\(470\) | 4.65130 | 0.214548 | ||||||||
\(471\) | −1.02887 | −0.0474078 | ||||||||
\(472\) | −64.2649 | −2.95803 | ||||||||
\(473\) | 20.2433 | 0.930788 | ||||||||
\(474\) | 29.4706 | 1.35363 | ||||||||
\(475\) | 1.19339 | 0.0547563 | ||||||||
\(476\) | 86.6904 | 3.97345 | ||||||||
\(477\) | −18.9412 | −0.867259 | ||||||||
\(478\) | −14.1457 | −0.647010 | ||||||||
\(479\) | −15.3045 | −0.699281 | −0.349640 | − | 0.936884i | \(-0.613696\pi\) | ||||
−0.349640 | + | 0.936884i | \(0.613696\pi\) | |||||||
\(480\) | 12.1569 | 0.554882 | ||||||||
\(481\) | 49.1464 | 2.24088 | ||||||||
\(482\) | 73.0526 | 3.32746 | ||||||||
\(483\) | −1.27068 | −0.0578180 | ||||||||
\(484\) | 132.936 | 6.04253 | ||||||||
\(485\) | −3.72612 | −0.169194 | ||||||||
\(486\) | 38.0409 | 1.72557 | ||||||||
\(487\) | −15.8113 | −0.716480 | −0.358240 | − | 0.933630i | \(-0.616623\pi\) | ||||
−0.358240 | + | 0.933630i | \(0.616623\pi\) | |||||||
\(488\) | 36.8450 | 1.66789 | ||||||||
\(489\) | −4.97048 | −0.224773 | ||||||||
\(490\) | −33.8952 | −1.53123 | ||||||||
\(491\) | −20.4391 | −0.922404 | −0.461202 | − | 0.887295i | \(-0.652582\pi\) | ||||
−0.461202 | + | 0.887295i | \(0.652582\pi\) | |||||||
\(492\) | 14.6642 | 0.661115 | ||||||||
\(493\) | −3.90610 | −0.175922 | ||||||||
\(494\) | 4.92819 | 0.221730 | ||||||||
\(495\) | 17.7749 | 0.798922 | ||||||||
\(496\) | −128.311 | −5.76134 | ||||||||
\(497\) | −52.9756 | −2.37628 | ||||||||
\(498\) | 9.68246 | 0.433882 | ||||||||
\(499\) | 26.2082 | 1.17324 | 0.586620 | − | 0.809862i | \(-0.300458\pi\) | ||||
0.586620 | + | 0.809862i | \(0.300458\pi\) | |||||||
\(500\) | −51.4298 | −2.30001 | ||||||||
\(501\) | 13.3117 | 0.594723 | ||||||||
\(502\) | −35.7742 | −1.59668 | ||||||||
\(503\) | 25.3318 | 1.12949 | 0.564744 | − | 0.825266i | \(-0.308975\pi\) | ||||
0.564744 | + | 0.825266i | \(0.308975\pi\) | |||||||
\(504\) | 95.3693 | 4.24808 | ||||||||
\(505\) | 9.30145 | 0.413909 | ||||||||
\(506\) | 7.62927 | 0.339162 | ||||||||
\(507\) | −12.4922 | −0.554798 | ||||||||
\(508\) | 36.1504 | 1.60391 | ||||||||
\(509\) | 38.0122 | 1.68486 | 0.842431 | − | 0.538805i | \(-0.181124\pi\) | ||||
0.842431 | + | 0.538805i | \(0.181124\pi\) | |||||||
\(510\) | 7.53440 | 0.333629 | ||||||||
\(511\) | 6.22162 | 0.275228 | ||||||||
\(512\) | 3.99581 | 0.176592 | ||||||||
\(513\) | −1.13987 | −0.0503265 | ||||||||
\(514\) | −1.79089 | −0.0789927 | ||||||||
\(515\) | −4.73127 | −0.208485 | ||||||||
\(516\) | 11.0714 | 0.487392 | ||||||||
\(517\) | 9.24409 | 0.406555 | ||||||||
\(518\) | −98.3200 | −4.31993 | ||||||||
\(519\) | 1.99116 | 0.0874022 | ||||||||
\(520\) | −55.8018 | −2.44707 | ||||||||
\(521\) | −33.5830 | −1.47130 | −0.735648 | − | 0.677364i | \(-0.763122\pi\) | ||||
−0.735648 | + | 0.677364i | \(0.763122\pi\) | |||||||
\(522\) | −6.97471 | −0.305275 | ||||||||
\(523\) | −14.5752 | −0.637331 | −0.318666 | − | 0.947867i | \(-0.603235\pi\) | ||||
−0.318666 | + | 0.947867i | \(0.603235\pi\) | |||||||
\(524\) | −53.6151 | −2.34219 | ||||||||
\(525\) | 10.0469 | 0.438484 | ||||||||
\(526\) | −49.6267 | −2.16383 | ||||||||
\(527\) | −39.3958 | −1.71611 | ||||||||
\(528\) | 48.7700 | 2.12244 | ||||||||
\(529\) | −22.7789 | −0.990388 | ||||||||
\(530\) | −22.1716 | −0.963075 | ||||||||
\(531\) | −19.3690 | −0.840543 | ||||||||
\(532\) | −7.12417 | −0.308872 | ||||||||
\(533\) | −25.3696 | −1.09888 | ||||||||
\(534\) | 24.9209 | 1.07843 | ||||||||
\(535\) | 3.73097 | 0.161304 | ||||||||
\(536\) | −70.8120 | −3.05861 | ||||||||
\(537\) | 1.66998 | 0.0720651 | ||||||||
\(538\) | −8.74996 | −0.377237 | ||||||||
\(539\) | −67.3641 | −2.90158 | ||||||||
\(540\) | 20.9489 | 0.901498 | ||||||||
\(541\) | 21.4791 | 0.923460 | 0.461730 | − | 0.887021i | \(-0.347229\pi\) | ||||
0.461730 | + | 0.887021i | \(0.347229\pi\) | |||||||
\(542\) | 81.7184 | 3.51011 | ||||||||
\(543\) | −6.49637 | −0.278786 | ||||||||
\(544\) | −66.1027 | −2.83413 | ||||||||
\(545\) | 7.20020 | 0.308423 | ||||||||
\(546\) | 41.4897 | 1.77560 | ||||||||
\(547\) | −40.4651 | −1.73016 | −0.865081 | − | 0.501632i | \(-0.832733\pi\) | ||||
−0.865081 | + | 0.501632i | \(0.832733\pi\) | |||||||
\(548\) | 72.6299 | 3.10260 | ||||||||
\(549\) | 11.1048 | 0.473942 | ||||||||
\(550\) | −60.3226 | −2.57216 | ||||||||
\(551\) | 0.321001 | 0.0136751 | ||||||||
\(552\) | 2.57074 | 0.109418 | ||||||||
\(553\) | 73.7036 | 3.13420 | ||||||||
\(554\) | 5.83959 | 0.248100 | ||||||||
\(555\) | −6.17471 | −0.262102 | ||||||||
\(556\) | 5.20976 | 0.220943 | ||||||||
\(557\) | −23.5219 | −0.996654 | −0.498327 | − | 0.866989i | \(-0.666052\pi\) | ||||
−0.498327 | + | 0.866989i | \(0.666052\pi\) | |||||||
\(558\) | −70.3450 | −2.97794 | ||||||||
\(559\) | −19.1539 | −0.810122 | ||||||||
\(560\) | 61.3709 | 2.59340 | ||||||||
\(561\) | 14.9740 | 0.632204 | ||||||||
\(562\) | −42.6295 | −1.79822 | ||||||||
\(563\) | 1.99192 | 0.0839494 | 0.0419747 | − | 0.999119i | \(-0.486635\pi\) | ||||
0.0419747 | + | 0.999119i | \(0.486635\pi\) | |||||||
\(564\) | 5.05575 | 0.212886 | ||||||||
\(565\) | 7.93997 | 0.334037 | ||||||||
\(566\) | −16.3488 | −0.687190 | ||||||||
\(567\) | 23.6005 | 0.991127 | ||||||||
\(568\) | 107.176 | 4.49701 | ||||||||
\(569\) | −16.2491 | −0.681196 | −0.340598 | − | 0.940209i | \(-0.610630\pi\) | ||||
−0.340598 | + | 0.940209i | \(0.610630\pi\) | |||||||
\(570\) | −0.619174 | −0.0259343 | ||||||||
\(571\) | 20.4182 | 0.854476 | 0.427238 | − | 0.904139i | \(-0.359487\pi\) | ||||
0.427238 | + | 0.904139i | \(0.359487\pi\) | |||||||
\(572\) | −180.005 | −7.52637 | ||||||||
\(573\) | −10.3468 | −0.432243 | ||||||||
\(574\) | 50.7531 | 2.11839 | ||||||||
\(575\) | −1.74804 | −0.0728982 | ||||||||
\(576\) | −51.9400 | −2.16417 | ||||||||
\(577\) | −47.9364 | −1.99562 | −0.997810 | − | 0.0661520i | \(-0.978928\pi\) | ||||
−0.997810 | + | 0.0661520i | \(0.978928\pi\) | |||||||
\(578\) | 4.67849 | 0.194599 | ||||||||
\(579\) | −14.6773 | −0.609966 | ||||||||
\(580\) | −5.89947 | −0.244962 | ||||||||
\(581\) | 24.2151 | 1.00461 | ||||||||
\(582\) | −5.60494 | −0.232332 | ||||||||
\(583\) | −44.0644 | −1.82496 | ||||||||
\(584\) | −12.5871 | −0.520858 | ||||||||
\(585\) | −16.8183 | −0.695351 | ||||||||
\(586\) | 75.0462 | 3.10013 | ||||||||
\(587\) | 14.8599 | 0.613332 | 0.306666 | − | 0.951817i | \(-0.400787\pi\) | ||||
0.306666 | + | 0.951817i | \(0.400787\pi\) | |||||||
\(588\) | −36.8426 | −1.51936 | ||||||||
\(589\) | 3.23753 | 0.133400 | ||||||||
\(590\) | −22.6724 | −0.933408 | ||||||||
\(591\) | −4.88673 | −0.201013 | ||||||||
\(592\) | 109.353 | 4.49436 | ||||||||
\(593\) | 16.4235 | 0.674432 | 0.337216 | − | 0.941427i | \(-0.390515\pi\) | ||||
0.337216 | + | 0.941427i | \(0.390515\pi\) | |||||||
\(594\) | 57.6175 | 2.36407 | ||||||||
\(595\) | 18.8429 | 0.772486 | ||||||||
\(596\) | −91.5151 | −3.74860 | ||||||||
\(597\) | 11.9332 | 0.488393 | ||||||||
\(598\) | −7.21868 | −0.295194 | ||||||||
\(599\) | 17.0152 | 0.695222 | 0.347611 | − | 0.937639i | \(-0.386993\pi\) | ||||
0.347611 | + | 0.937639i | \(0.386993\pi\) | |||||||
\(600\) | −20.3262 | −0.829813 | ||||||||
\(601\) | −26.2279 | −1.06986 | −0.534930 | − | 0.844896i | \(-0.679662\pi\) | ||||
−0.534930 | + | 0.844896i | \(0.679662\pi\) | |||||||
\(602\) | 38.3183 | 1.56174 | ||||||||
\(603\) | −21.3422 | −0.869123 | ||||||||
\(604\) | −89.1956 | −3.62932 | ||||||||
\(605\) | 28.8948 | 1.17474 | ||||||||
\(606\) | 13.9915 | 0.568367 | ||||||||
\(607\) | 40.8876 | 1.65958 | 0.829789 | − | 0.558078i | \(-0.188461\pi\) | ||||
0.829789 | + | 0.558078i | \(0.188461\pi\) | |||||||
\(608\) | 5.43229 | 0.220308 | ||||||||
\(609\) | 2.70246 | 0.109509 | ||||||||
\(610\) | 12.9987 | 0.526304 | ||||||||
\(611\) | −8.74660 | −0.353849 | ||||||||
\(612\) | −52.8599 | −2.13674 | ||||||||
\(613\) | 38.0298 | 1.53601 | 0.768005 | − | 0.640444i | \(-0.221250\pi\) | ||||
0.768005 | + | 0.640444i | \(0.221250\pi\) | |||||||
\(614\) | −13.7035 | −0.553030 | ||||||||
\(615\) | 3.18741 | 0.128529 | ||||||||
\(616\) | 221.865 | 8.93918 | ||||||||
\(617\) | 39.3160 | 1.58280 | 0.791401 | − | 0.611298i | \(-0.209352\pi\) | ||||
0.791401 | + | 0.611298i | \(0.209352\pi\) | |||||||
\(618\) | −7.11692 | −0.286284 | ||||||||
\(619\) | 24.6865 | 0.992234 | 0.496117 | − | 0.868256i | \(-0.334759\pi\) | ||||
0.496117 | + | 0.868256i | \(0.334759\pi\) | |||||||
\(620\) | −59.5004 | −2.38959 | ||||||||
\(621\) | 1.66965 | 0.0670007 | ||||||||
\(622\) | −24.8415 | −0.996053 | ||||||||
\(623\) | 62.3252 | 2.49700 | ||||||||
\(624\) | −46.1453 | −1.84729 | ||||||||
\(625\) | 7.40974 | 0.296390 | ||||||||
\(626\) | −33.8589 | −1.35327 | ||||||||
\(627\) | −1.23056 | −0.0491438 | ||||||||
\(628\) | 8.44944 | 0.337169 | ||||||||
\(629\) | 33.5749 | 1.33872 | ||||||||
\(630\) | 33.6459 | 1.34048 | ||||||||
\(631\) | −25.3344 | −1.00855 | −0.504274 | − | 0.863544i | \(-0.668240\pi\) | ||||
−0.504274 | + | 0.863544i | \(0.668240\pi\) | |||||||
\(632\) | −149.111 | −5.93134 | ||||||||
\(633\) | 3.02199 | 0.120113 | ||||||||
\(634\) | 25.6608 | 1.01912 | ||||||||
\(635\) | 7.85762 | 0.311820 | ||||||||
\(636\) | −24.0996 | −0.955610 | ||||||||
\(637\) | 63.7387 | 2.52542 | ||||||||
\(638\) | −16.2258 | −0.642385 | ||||||||
\(639\) | 32.3021 | 1.27785 | ||||||||
\(640\) | −22.4717 | −0.888271 | ||||||||
\(641\) | 23.6091 | 0.932502 | 0.466251 | − | 0.884653i | \(-0.345604\pi\) | ||||
0.466251 | + | 0.884653i | \(0.345604\pi\) | |||||||
\(642\) | 5.61224 | 0.221498 | ||||||||
\(643\) | −5.45055 | −0.214949 | −0.107474 | − | 0.994208i | \(-0.534276\pi\) | ||||
−0.107474 | + | 0.994208i | \(0.534276\pi\) | |||||||
\(644\) | 10.4353 | 0.411208 | ||||||||
\(645\) | 2.40647 | 0.0947548 | ||||||||
\(646\) | 3.36675 | 0.132463 | ||||||||
\(647\) | 18.6662 | 0.733845 | 0.366923 | − | 0.930252i | \(-0.380411\pi\) | ||||
0.366923 | + | 0.930252i | \(0.380411\pi\) | |||||||
\(648\) | −47.7467 | −1.87567 | ||||||||
\(649\) | −45.0596 | −1.76874 | ||||||||
\(650\) | 57.0762 | 2.23871 | ||||||||
\(651\) | 27.2563 | 1.06826 | ||||||||
\(652\) | 40.8194 | 1.59861 | ||||||||
\(653\) | −25.7106 | −1.00613 | −0.503066 | − | 0.864248i | \(-0.667795\pi\) | ||||
−0.503066 | + | 0.864248i | \(0.667795\pi\) | |||||||
\(654\) | 10.8308 | 0.423516 | ||||||||
\(655\) | −11.6537 | −0.455349 | ||||||||
\(656\) | −56.4482 | −2.20393 | ||||||||
\(657\) | −3.79367 | −0.148005 | ||||||||
\(658\) | 17.4980 | 0.682144 | ||||||||
\(659\) | 25.0477 | 0.975720 | 0.487860 | − | 0.872922i | \(-0.337778\pi\) | ||||
0.487860 | + | 0.872922i | \(0.337778\pi\) | |||||||
\(660\) | 22.6156 | 0.880311 | ||||||||
\(661\) | 50.5272 | 1.96528 | 0.982640 | − | 0.185523i | \(-0.0593981\pi\) | ||||
0.982640 | + | 0.185523i | \(0.0593981\pi\) | |||||||
\(662\) | 48.2241 | 1.87428 | ||||||||
\(663\) | −14.1682 | −0.550246 | ||||||||
\(664\) | −48.9901 | −1.90118 | ||||||||
\(665\) | −1.54850 | −0.0600484 | ||||||||
\(666\) | 59.9512 | 2.32306 | ||||||||
\(667\) | −0.470194 | −0.0182060 | ||||||||
\(668\) | −109.320 | −4.22973 | ||||||||
\(669\) | 0.308255 | 0.0119178 | ||||||||
\(670\) | −24.9822 | −0.965145 | ||||||||
\(671\) | 25.8340 | 0.997309 | ||||||||
\(672\) | 45.7336 | 1.76421 | ||||||||
\(673\) | 28.4760 | 1.09767 | 0.548835 | − | 0.835931i | \(-0.315072\pi\) | ||||
0.548835 | + | 0.835931i | \(0.315072\pi\) | |||||||
\(674\) | −0.621341 | −0.0239332 | ||||||||
\(675\) | −13.2015 | −0.508125 | ||||||||
\(676\) | 102.590 | 3.94578 | ||||||||
\(677\) | −11.0606 | −0.425092 | −0.212546 | − | 0.977151i | \(-0.568175\pi\) | ||||
−0.212546 | + | 0.977151i | \(0.568175\pi\) | |||||||
\(678\) | 11.9435 | 0.458689 | ||||||||
\(679\) | −14.0175 | −0.537943 | ||||||||
\(680\) | −38.1216 | −1.46190 | ||||||||
\(681\) | −15.7914 | −0.605126 | ||||||||
\(682\) | −163.649 | −6.26644 | ||||||||
\(683\) | 2.60973 | 0.0998584 | 0.0499292 | − | 0.998753i | \(-0.484100\pi\) | ||||
0.0499292 | + | 0.998753i | \(0.484100\pi\) | |||||||
\(684\) | 4.34401 | 0.166097 | ||||||||
\(685\) | 15.7868 | 0.603182 | ||||||||
\(686\) | −47.4429 | −1.81138 | ||||||||
\(687\) | −14.6353 | −0.558371 | ||||||||
\(688\) | −42.6180 | −1.62480 | ||||||||
\(689\) | 41.6930 | 1.58837 | ||||||||
\(690\) | 0.906948 | 0.0345269 | ||||||||
\(691\) | 9.76080 | 0.371318 | 0.185659 | − | 0.982614i | \(-0.440558\pi\) | ||||
0.185659 | + | 0.982614i | \(0.440558\pi\) | |||||||
\(692\) | −16.3521 | −0.621614 | ||||||||
\(693\) | 66.8685 | 2.54012 | ||||||||
\(694\) | 19.5030 | 0.740324 | ||||||||
\(695\) | 1.13239 | 0.0429540 | ||||||||
\(696\) | −5.46742 | −0.207242 | ||||||||
\(697\) | −17.3315 | −0.656477 | ||||||||
\(698\) | 57.0853 | 2.16071 | ||||||||
\(699\) | −12.0404 | −0.455412 | ||||||||
\(700\) | −82.5090 | −3.11855 | ||||||||
\(701\) | 34.5710 | 1.30573 | 0.652864 | − | 0.757475i | \(-0.273567\pi\) | ||||
0.652864 | + | 0.757475i | \(0.273567\pi\) | |||||||
\(702\) | −54.5167 | −2.05760 | ||||||||
\(703\) | −2.75917 | −0.104064 | ||||||||
\(704\) | −120.832 | −4.55402 | ||||||||
\(705\) | 1.09891 | 0.0413875 | ||||||||
\(706\) | 18.7485 | 0.705608 | ||||||||
\(707\) | 34.9917 | 1.31600 | ||||||||
\(708\) | −24.6439 | −0.926173 | ||||||||
\(709\) | −45.0495 | −1.69187 | −0.845934 | − | 0.533288i | \(-0.820956\pi\) | ||||
−0.845934 | + | 0.533288i | \(0.820956\pi\) | |||||||
\(710\) | 37.8113 | 1.41903 | ||||||||
\(711\) | −44.9412 | −1.68543 | ||||||||
\(712\) | −126.092 | −4.72548 | ||||||||
\(713\) | −4.74224 | −0.177598 | ||||||||
\(714\) | 28.3441 | 1.06075 | ||||||||
\(715\) | −39.1257 | −1.46322 | ||||||||
\(716\) | −13.7145 | −0.512535 | ||||||||
\(717\) | −3.34206 | −0.124811 | ||||||||
\(718\) | −50.4385 | −1.88235 | ||||||||
\(719\) | 21.8477 | 0.814781 | 0.407390 | − | 0.913254i | \(-0.366439\pi\) | ||||
0.407390 | + | 0.913254i | \(0.366439\pi\) | |||||||
\(720\) | −37.4213 | −1.39461 | ||||||||
\(721\) | −17.7989 | −0.662864 | ||||||||
\(722\) | 50.7402 | 1.88835 | ||||||||
\(723\) | 17.2594 | 0.641883 | ||||||||
\(724\) | 53.3505 | 1.98276 | ||||||||
\(725\) | 3.71770 | 0.138072 | ||||||||
\(726\) | 43.4644 | 1.61312 | ||||||||
\(727\) | −18.5984 | −0.689777 | −0.344889 | − | 0.938644i | \(-0.612083\pi\) | ||||
−0.344889 | + | 0.938644i | \(0.612083\pi\) | |||||||
\(728\) | −209.924 | −7.78032 | ||||||||
\(729\) | −7.63250 | −0.282685 | ||||||||
\(730\) | −4.44068 | −0.164357 | ||||||||
\(731\) | −13.0852 | −0.483972 | ||||||||
\(732\) | 14.1290 | 0.522224 | ||||||||
\(733\) | −15.1682 | −0.560252 | −0.280126 | − | 0.959963i | \(-0.590376\pi\) | ||||
−0.280126 | + | 0.959963i | \(0.590376\pi\) | |||||||
\(734\) | −63.9624 | −2.36090 | ||||||||
\(735\) | −8.00807 | −0.295382 | ||||||||
\(736\) | −7.95706 | −0.293301 | ||||||||
\(737\) | −49.6500 | −1.82888 | ||||||||
\(738\) | −30.9470 | −1.13918 | ||||||||
\(739\) | −2.01974 | −0.0742974 | −0.0371487 | − | 0.999310i | \(-0.511828\pi\) | ||||
−0.0371487 | + | 0.999310i | \(0.511828\pi\) | |||||||
\(740\) | 50.7089 | 1.86410 | ||||||||
\(741\) | 1.16433 | 0.0427728 | ||||||||
\(742\) | −83.4089 | −3.06204 | ||||||||
\(743\) | −35.1505 | −1.28955 | −0.644773 | − | 0.764374i | \(-0.723048\pi\) | ||||
−0.644773 | + | 0.764374i | \(0.723048\pi\) | |||||||
\(744\) | −55.1428 | −2.02163 | ||||||||
\(745\) | −19.8916 | −0.728773 | ||||||||
\(746\) | 52.1003 | 1.90753 | ||||||||
\(747\) | −14.7653 | −0.540233 | ||||||||
\(748\) | −122.972 | −4.49630 | ||||||||
\(749\) | 14.0358 | 0.512856 | ||||||||
\(750\) | −16.8154 | −0.614012 | ||||||||
\(751\) | 4.09745 | 0.149518 | 0.0747590 | − | 0.997202i | \(-0.476181\pi\) | ||||
0.0747590 | + | 0.997202i | \(0.476181\pi\) | |||||||
\(752\) | −19.4615 | −0.709687 | ||||||||
\(753\) | −8.45200 | −0.308008 | ||||||||
\(754\) | 15.3526 | 0.559107 | ||||||||
\(755\) | −19.3875 | −0.705583 | ||||||||
\(756\) | 78.8090 | 2.86626 | ||||||||
\(757\) | 0.746758 | 0.0271414 | 0.0135707 | − | 0.999908i | \(-0.495680\pi\) | ||||
0.0135707 | + | 0.999908i | \(0.495680\pi\) | |||||||
\(758\) | −37.0981 | −1.34746 | ||||||||
\(759\) | 1.80249 | 0.0654261 | ||||||||
\(760\) | 3.13282 | 0.113639 | ||||||||
\(761\) | 43.5503 | 1.57870 | 0.789348 | − | 0.613946i | \(-0.210419\pi\) | ||||
0.789348 | + | 0.613946i | \(0.210419\pi\) | |||||||
\(762\) | 11.8197 | 0.428181 | ||||||||
\(763\) | 27.0869 | 0.980611 | ||||||||
\(764\) | 84.9715 | 3.07416 | ||||||||
\(765\) | −11.4896 | −0.415407 | ||||||||
\(766\) | −19.3518 | −0.699210 | ||||||||
\(767\) | 42.6346 | 1.53945 | ||||||||
\(768\) | −8.43285 | −0.304294 | ||||||||
\(769\) | 34.0282 | 1.22709 | 0.613544 | − | 0.789661i | \(-0.289743\pi\) | ||||
0.613544 | + | 0.789661i | \(0.289743\pi\) | |||||||
\(770\) | 78.2729 | 2.82076 | ||||||||
\(771\) | −0.423114 | −0.0152381 | ||||||||
\(772\) | 120.535 | 4.33815 | ||||||||
\(773\) | 8.61160 | 0.309738 | 0.154869 | − | 0.987935i | \(-0.450504\pi\) | ||||
0.154869 | + | 0.987935i | \(0.450504\pi\) | |||||||
\(774\) | −23.3648 | −0.839830 | ||||||||
\(775\) | 37.4956 | 1.34688 | ||||||||
\(776\) | 28.3592 | 1.01804 | ||||||||
\(777\) | −23.2290 | −0.833337 | ||||||||
\(778\) | 13.9444 | 0.499932 | ||||||||
\(779\) | 1.42429 | 0.0510306 | ||||||||
\(780\) | −21.3985 | −0.766189 | ||||||||
\(781\) | 75.1469 | 2.68897 | ||||||||
\(782\) | −4.93152 | −0.176351 | ||||||||
\(783\) | −3.55098 | −0.126902 | ||||||||
\(784\) | 141.821 | 5.06503 | ||||||||
\(785\) | 1.83656 | 0.0655497 | ||||||||
\(786\) | −17.5299 | −0.625271 | ||||||||
\(787\) | 47.3681 | 1.68849 | 0.844246 | − | 0.535956i | \(-0.180049\pi\) | ||||
0.844246 | + | 0.535956i | \(0.180049\pi\) | |||||||
\(788\) | 40.1316 | 1.42963 | ||||||||
\(789\) | −11.7248 | −0.417414 | ||||||||
\(790\) | −52.6059 | −1.87163 | ||||||||
\(791\) | 29.8699 | 1.06205 | ||||||||
\(792\) | −135.283 | −4.80708 | ||||||||
\(793\) | −24.4437 | −0.868020 | ||||||||
\(794\) | −37.0736 | −1.31569 | ||||||||
\(795\) | −5.23826 | −0.185782 | ||||||||
\(796\) | −97.9996 | −3.47350 | ||||||||
\(797\) | −20.8267 | −0.737720 | −0.368860 | − | 0.929485i | \(-0.620252\pi\) | ||||
−0.368860 | + | 0.929485i | \(0.620252\pi\) | |||||||
\(798\) | −2.32931 | −0.0824566 | ||||||||
\(799\) | −5.97533 | −0.211392 | ||||||||
\(800\) | 62.9144 | 2.22436 | ||||||||
\(801\) | −38.0031 | −1.34277 | ||||||||
\(802\) | 68.9341 | 2.43415 | ||||||||
\(803\) | −8.82549 | −0.311445 | ||||||||
\(804\) | −27.1545 | −0.957664 | ||||||||
\(805\) | 2.26821 | 0.0799437 | ||||||||
\(806\) | 154.842 | 5.45407 | ||||||||
\(807\) | −2.06726 | −0.0727710 | ||||||||
\(808\) | −70.7925 | −2.49047 | ||||||||
\(809\) | 2.88780 | 0.101530 | 0.0507648 | − | 0.998711i | \(-0.483834\pi\) | ||||
0.0507648 | + | 0.998711i | \(0.483834\pi\) | |||||||
\(810\) | −16.8448 | −0.591867 | ||||||||
\(811\) | −16.0209 | −0.562569 | −0.281285 | − | 0.959624i | \(-0.590761\pi\) | ||||
−0.281285 | + | 0.959624i | \(0.590761\pi\) | |||||||
\(812\) | −22.1936 | −0.778842 | ||||||||
\(813\) | 19.3068 | 0.677118 | ||||||||
\(814\) | 139.469 | 4.88838 | ||||||||
\(815\) | 8.87247 | 0.310789 | ||||||||
\(816\) | −31.5246 | −1.10358 | ||||||||
\(817\) | 1.07533 | 0.0376211 | ||||||||
\(818\) | −24.6874 | −0.863176 | ||||||||
\(819\) | −63.2698 | −2.21083 | ||||||||
\(820\) | −26.1761 | −0.914110 | ||||||||
\(821\) | −45.6331 | −1.59261 | −0.796303 | − | 0.604897i | \(-0.793214\pi\) | ||||
−0.796303 | + | 0.604897i | \(0.793214\pi\) | |||||||
\(822\) | 23.7470 | 0.828270 | ||||||||
\(823\) | 34.8963 | 1.21641 | 0.608205 | − | 0.793780i | \(-0.291890\pi\) | ||||
0.608205 | + | 0.793780i | \(0.291890\pi\) | |||||||
\(824\) | 36.0093 | 1.25444 | ||||||||
\(825\) | −14.2518 | −0.496183 | ||||||||
\(826\) | −85.2927 | −2.96771 | ||||||||
\(827\) | −53.7904 | −1.87047 | −0.935237 | − | 0.354022i | \(-0.884814\pi\) | ||||
−0.935237 | + | 0.354022i | \(0.884814\pi\) | |||||||
\(828\) | −6.36297 | −0.221129 | ||||||||
\(829\) | 20.6428 | 0.716954 | 0.358477 | − | 0.933539i | \(-0.383296\pi\) | ||||
0.358477 | + | 0.933539i | \(0.383296\pi\) | |||||||
\(830\) | −17.2835 | −0.599919 | ||||||||
\(831\) | 1.37966 | 0.0478598 | ||||||||
\(832\) | 114.329 | 3.96365 | ||||||||
\(833\) | 43.5438 | 1.50870 | ||||||||
\(834\) | 1.70337 | 0.0589830 | ||||||||
\(835\) | −23.7618 | −0.822311 | ||||||||
\(836\) | 10.1058 | 0.349516 | ||||||||
\(837\) | −35.8142 | −1.23792 | ||||||||
\(838\) | −22.4353 | −0.775014 | ||||||||
\(839\) | −36.3213 | −1.25395 | −0.626975 | − | 0.779039i | \(-0.715707\pi\) | ||||
−0.626975 | + | 0.779039i | \(0.715707\pi\) | |||||||
\(840\) | 26.3747 | 0.910014 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 15.5807 | 0.536947 | ||||||||
\(843\) | −10.0716 | −0.346885 | ||||||||
\(844\) | −24.8177 | −0.854259 | ||||||||
\(845\) | 22.2990 | 0.767108 | ||||||||
\(846\) | −10.6695 | −0.366826 | ||||||||
\(847\) | 108.701 | 3.73501 | ||||||||
\(848\) | 92.7683 | 3.18567 | ||||||||
\(849\) | −3.86255 | −0.132562 | ||||||||
\(850\) | 38.9922 | 1.33742 | ||||||||
\(851\) | 4.04155 | 0.138543 | ||||||||
\(852\) | 41.0991 | 1.40803 | ||||||||
\(853\) | −42.1635 | −1.44365 | −0.721825 | − | 0.692075i | \(-0.756697\pi\) | ||||
−0.721825 | + | 0.692075i | \(0.756697\pi\) | |||||||
\(854\) | 48.9008 | 1.67335 | ||||||||
\(855\) | 0.944210 | 0.0322913 | ||||||||
\(856\) | −28.3961 | −0.970559 | ||||||||
\(857\) | 28.5722 | 0.976007 | 0.488003 | − | 0.872842i | \(-0.337725\pi\) | ||||
0.488003 | + | 0.872842i | \(0.337725\pi\) | |||||||
\(858\) | −58.8540 | −2.00924 | ||||||||
\(859\) | −2.54750 | −0.0869196 | −0.0434598 | − | 0.999055i | \(-0.513838\pi\) | ||||
−0.0434598 | + | 0.999055i | \(0.513838\pi\) | |||||||
\(860\) | −19.7628 | −0.673906 | ||||||||
\(861\) | 11.9909 | 0.408649 | ||||||||
\(862\) | −1.73777 | −0.0591888 | ||||||||
\(863\) | −21.4878 | −0.731452 | −0.365726 | − | 0.930723i | \(-0.619179\pi\) | ||||
−0.365726 | + | 0.930723i | \(0.619179\pi\) | |||||||
\(864\) | −60.0931 | −2.04441 | ||||||||
\(865\) | −3.55428 | −0.120849 | ||||||||
\(866\) | −5.14872 | −0.174961 | ||||||||
\(867\) | 1.10534 | 0.0375392 | ||||||||
\(868\) | −223.838 | −7.59757 | ||||||||
\(869\) | −104.550 | −3.54662 | ||||||||
\(870\) | −1.92888 | −0.0653952 | ||||||||
\(871\) | 46.9780 | 1.59179 | ||||||||
\(872\) | −54.8001 | −1.85577 | ||||||||
\(873\) | 8.54727 | 0.289281 | ||||||||
\(874\) | 0.405270 | 0.0137085 | ||||||||
\(875\) | −42.0540 | −1.42168 | ||||||||
\(876\) | −4.82681 | −0.163083 | ||||||||
\(877\) | 4.34207 | 0.146621 | 0.0733106 | − | 0.997309i | \(-0.476644\pi\) | ||||
0.0733106 | + | 0.997309i | \(0.476644\pi\) | |||||||
\(878\) | −71.2638 | −2.40504 | ||||||||
\(879\) | 17.7304 | 0.598031 | ||||||||
\(880\) | −87.0559 | −2.93465 | ||||||||
\(881\) | −5.38871 | −0.181550 | −0.0907752 | − | 0.995871i | \(-0.528934\pi\) | ||||
−0.0907752 | + | 0.995871i | \(0.528934\pi\) | |||||||
\(882\) | 77.7515 | 2.61803 | ||||||||
\(883\) | 7.71472 | 0.259621 | 0.129810 | − | 0.991539i | \(-0.458563\pi\) | ||||
0.129810 | + | 0.991539i | \(0.458563\pi\) | |||||||
\(884\) | 116.354 | 3.91341 | ||||||||
\(885\) | −5.35657 | −0.180059 | ||||||||
\(886\) | −49.1685 | −1.65185 | ||||||||
\(887\) | 42.8186 | 1.43771 | 0.718854 | − | 0.695161i | \(-0.244667\pi\) | ||||
0.718854 | + | 0.695161i | \(0.244667\pi\) | |||||||
\(888\) | 46.9952 | 1.57706 | ||||||||
\(889\) | 29.5601 | 0.991413 | ||||||||
\(890\) | −44.4845 | −1.49113 | ||||||||
\(891\) | −33.4777 | −1.12155 | ||||||||
\(892\) | −2.53150 | −0.0847610 | ||||||||
\(893\) | 0.491050 | 0.0164324 | ||||||||
\(894\) | −29.9216 | −1.00073 | ||||||||
\(895\) | −2.98097 | −0.0996430 | ||||||||
\(896\) | −84.5376 | −2.82420 | ||||||||
\(897\) | −1.70548 | −0.0569444 | ||||||||
\(898\) | −49.0391 | −1.63646 | ||||||||
\(899\) | 10.0857 | 0.336378 | ||||||||
\(900\) | 50.3103 | 1.67701 | ||||||||
\(901\) | 28.4830 | 0.948906 | ||||||||
\(902\) | −71.9943 | −2.39715 | ||||||||
\(903\) | 9.05306 | 0.301267 | ||||||||
\(904\) | −60.4304 | −2.00989 | ||||||||
\(905\) | 11.5962 | 0.385472 | ||||||||
\(906\) | −29.1633 | −0.968885 | ||||||||
\(907\) | −40.7737 | −1.35387 | −0.676934 | − | 0.736044i | \(-0.736692\pi\) | ||||
−0.676934 | + | 0.736044i | \(0.736692\pi\) | |||||||
\(908\) | 129.684 | 4.30372 | ||||||||
\(909\) | −21.3364 | −0.707683 | ||||||||
\(910\) | −74.0605 | −2.45508 | ||||||||
\(911\) | −52.8775 | −1.75191 | −0.875955 | − | 0.482393i | \(-0.839768\pi\) | ||||
−0.875955 | + | 0.482393i | \(0.839768\pi\) | |||||||
\(912\) | 2.59068 | 0.0857860 | ||||||||
\(913\) | −34.3496 | −1.13681 | ||||||||
\(914\) | −95.1552 | −3.14746 | ||||||||
\(915\) | 3.07108 | 0.101527 | ||||||||
\(916\) | 120.190 | 3.97119 | ||||||||
\(917\) | −43.8409 | −1.44776 | ||||||||
\(918\) | −37.2436 | −1.22922 | ||||||||
\(919\) | 49.9161 | 1.64658 | 0.823290 | − | 0.567621i | \(-0.192136\pi\) | ||||
0.823290 | + | 0.567621i | \(0.192136\pi\) | |||||||
\(920\) | −4.58886 | −0.151290 | ||||||||
\(921\) | −3.23759 | −0.106682 | ||||||||
\(922\) | −36.6157 | −1.20587 | ||||||||
\(923\) | −71.1027 | −2.34037 | ||||||||
\(924\) | 85.0791 | 2.79890 | ||||||||
\(925\) | −31.9555 | −1.05069 | ||||||||
\(926\) | −68.6825 | −2.25705 | ||||||||
\(927\) | 10.8530 | 0.356458 | ||||||||
\(928\) | 16.9229 | 0.555523 | ||||||||
\(929\) | −29.5273 | −0.968760 | −0.484380 | − | 0.874858i | \(-0.660955\pi\) | ||||
−0.484380 | + | 0.874858i | \(0.660955\pi\) | |||||||
\(930\) | −19.4542 | −0.637927 | ||||||||
\(931\) | −3.57841 | −0.117278 | ||||||||
\(932\) | 98.8804 | 3.23894 | ||||||||
\(933\) | −5.86904 | −0.192144 | ||||||||
\(934\) | −53.9789 | −1.76624 | ||||||||
\(935\) | −26.7291 | −0.874135 | ||||||||
\(936\) | 128.003 | 4.18390 | ||||||||
\(937\) | 48.9587 | 1.59941 | 0.799705 | − | 0.600393i | \(-0.204989\pi\) | ||||
0.799705 | + | 0.600393i | \(0.204989\pi\) | |||||||
\(938\) | −93.9820 | −3.06862 | ||||||||
\(939\) | −7.99949 | −0.261053 | ||||||||
\(940\) | −9.02467 | −0.294352 | ||||||||
\(941\) | 28.9821 | 0.944789 | 0.472395 | − | 0.881387i | \(-0.343390\pi\) | ||||
0.472395 | + | 0.881387i | \(0.343390\pi\) | |||||||
\(942\) | 2.76261 | 0.0900108 | ||||||||
\(943\) | −2.08626 | −0.0679381 | ||||||||
\(944\) | 94.8634 | 3.08754 | ||||||||
\(945\) | 17.1299 | 0.557235 | ||||||||
\(946\) | −54.3553 | −1.76724 | ||||||||
\(947\) | 25.4621 | 0.827408 | 0.413704 | − | 0.910411i | \(-0.364235\pi\) | ||||
0.413704 | + | 0.910411i | \(0.364235\pi\) | |||||||
\(948\) | −57.1802 | −1.85713 | ||||||||
\(949\) | 8.35053 | 0.271070 | ||||||||
\(950\) | −3.20436 | −0.103963 | ||||||||
\(951\) | 6.06260 | 0.196593 | ||||||||
\(952\) | −143.412 | −4.64801 | ||||||||
\(953\) | 39.9532 | 1.29421 | 0.647105 | − | 0.762401i | \(-0.275980\pi\) | ||||
0.647105 | + | 0.762401i | \(0.275980\pi\) | |||||||
\(954\) | 50.8591 | 1.64662 | ||||||||
\(955\) | 18.4693 | 0.597654 | ||||||||
\(956\) | 27.4462 | 0.887673 | ||||||||
\(957\) | −3.83350 | −0.123919 | ||||||||
\(958\) | 41.0941 | 1.32769 | ||||||||
\(959\) | 59.3893 | 1.91778 | ||||||||
\(960\) | −14.3642 | −0.463602 | ||||||||
\(961\) | 70.7218 | 2.28135 | ||||||||
\(962\) | −131.963 | −4.25466 | ||||||||
\(963\) | −8.55840 | −0.275790 | ||||||||
\(964\) | −141.740 | −4.56514 | ||||||||
\(965\) | 26.1994 | 0.843388 | ||||||||
\(966\) | 3.41190 | 0.109776 | ||||||||
\(967\) | −11.6841 | −0.375736 | −0.187868 | − | 0.982194i | \(-0.560158\pi\) | ||||
−0.187868 | + | 0.982194i | \(0.560158\pi\) | |||||||
\(968\) | −219.916 | −7.06836 | ||||||||
\(969\) | 0.795426 | 0.0255528 | ||||||||
\(970\) | 10.0050 | 0.321241 | ||||||||
\(971\) | −35.2887 | −1.13247 | −0.566234 | − | 0.824245i | \(-0.691600\pi\) | ||||
−0.566234 | + | 0.824245i | \(0.691600\pi\) | |||||||
\(972\) | −73.8088 | −2.36742 | ||||||||
\(973\) | 4.26000 | 0.136569 | ||||||||
\(974\) | 42.4550 | 1.36035 | ||||||||
\(975\) | 13.4848 | 0.431859 | ||||||||
\(976\) | −54.3880 | −1.74092 | ||||||||
\(977\) | 52.4786 | 1.67894 | 0.839470 | − | 0.543407i | \(-0.182866\pi\) | ||||
0.839470 | + | 0.543407i | \(0.182866\pi\) | |||||||
\(978\) | 13.3462 | 0.426766 | ||||||||
\(979\) | −88.4095 | −2.82558 | ||||||||
\(980\) | 65.7652 | 2.10079 | ||||||||
\(981\) | −16.5164 | −0.527327 | ||||||||
\(982\) | 54.8811 | 1.75132 | ||||||||
\(983\) | −16.7031 | −0.532747 | −0.266374 | − | 0.963870i | \(-0.585826\pi\) | ||||
−0.266374 | + | 0.963870i | \(0.585826\pi\) | |||||||
\(984\) | −24.2591 | −0.773352 | ||||||||
\(985\) | 8.72297 | 0.277937 | ||||||||
\(986\) | 10.4883 | 0.334014 | ||||||||
\(987\) | 4.13407 | 0.131589 | ||||||||
\(988\) | −9.56192 | −0.304205 | ||||||||
\(989\) | −1.57512 | −0.0500858 | ||||||||
\(990\) | −47.7273 | −1.51687 | ||||||||
\(991\) | 18.7711 | 0.596284 | 0.298142 | − | 0.954522i | \(-0.403633\pi\) | ||||
0.298142 | + | 0.954522i | \(0.403633\pi\) | |||||||
\(992\) | 170.680 | 5.41910 | ||||||||
\(993\) | 11.3934 | 0.361559 | ||||||||
\(994\) | 142.245 | 4.51173 | ||||||||
\(995\) | −21.3011 | −0.675291 | ||||||||
\(996\) | −18.7864 | −0.595269 | ||||||||
\(997\) | 25.8249 | 0.817883 | 0.408942 | − | 0.912561i | \(-0.365898\pi\) | ||||
0.408942 | + | 0.912561i | \(0.365898\pi\) | |||||||
\(998\) | −70.3716 | −2.22757 | ||||||||
\(999\) | 30.5225 | 0.965689 |
(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 | 4031.2.a.e.1.5 | ✓ | 103 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4031.2.a.e.1.5 | ✓ | 103 | 1.1 | even | 1 | trivial |