Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(1,1183)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, 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("1183.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.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: | \(9.44630255912\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 15 x^{10} + 46 x^{9} + 80 x^{8} - 246 x^{7} - 199 x^{6} + 562 x^{5} + 262 x^{4} - 542 x^{3} - 157 x^{2} + 183 x + 29 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(0.983820\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1183.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.983820 | 0.695666 | 0.347833 | − | 0.937557i | \(-0.386918\pi\) | ||||
0.347833 | + | 0.937557i | \(0.386918\pi\) | |||||||
\(3\) | −1.57171 | −0.907427 | −0.453713 | − | 0.891148i | \(-0.649901\pi\) | ||||
−0.453713 | + | 0.891148i | \(0.649901\pi\) | |||||||
\(4\) | −1.03210 | −0.516049 | ||||||||
\(5\) | 0.398447 | 0.178191 | 0.0890954 | − | 0.996023i | \(-0.471602\pi\) | ||||
0.0890954 | + | 0.996023i | \(0.471602\pi\) | |||||||
\(6\) | −1.54628 | −0.631265 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −2.98304 | −1.05466 | ||||||||
\(9\) | −0.529731 | −0.176577 | ||||||||
\(10\) | 0.392000 | 0.123961 | ||||||||
\(11\) | 4.24206 | 1.27903 | 0.639515 | − | 0.768779i | \(-0.279135\pi\) | ||||
0.639515 | + | 0.768779i | \(0.279135\pi\) | |||||||
\(12\) | 1.62216 | 0.468277 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0.983820 | 0.262937 | ||||||||
\(15\) | −0.626242 | −0.161695 | ||||||||
\(16\) | −0.870575 | −0.217644 | ||||||||
\(17\) | −5.10528 | −1.23821 | −0.619106 | − | 0.785307i | \(-0.712505\pi\) | ||||
−0.619106 | + | 0.785307i | \(0.712505\pi\) | |||||||
\(18\) | −0.521160 | −0.122838 | ||||||||
\(19\) | 2.12698 | 0.487962 | 0.243981 | − | 0.969780i | \(-0.421546\pi\) | ||||
0.243981 | + | 0.969780i | \(0.421546\pi\) | |||||||
\(20\) | −0.411236 | −0.0919553 | ||||||||
\(21\) | −1.57171 | −0.342975 | ||||||||
\(22\) | 4.17342 | 0.889777 | ||||||||
\(23\) | 2.19449 | 0.457583 | 0.228792 | − | 0.973475i | \(-0.426523\pi\) | ||||
0.228792 | + | 0.973475i | \(0.426523\pi\) | |||||||
\(24\) | 4.68847 | 0.957030 | ||||||||
\(25\) | −4.84124 | −0.968248 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.54771 | 1.06766 | ||||||||
\(28\) | −1.03210 | −0.195048 | ||||||||
\(29\) | 2.90902 | 0.540191 | 0.270095 | − | 0.962834i | \(-0.412945\pi\) | ||||
0.270095 | + | 0.962834i | \(0.412945\pi\) | |||||||
\(30\) | −0.616110 | −0.112486 | ||||||||
\(31\) | 2.20466 | 0.395968 | 0.197984 | − | 0.980205i | \(-0.436561\pi\) | ||||
0.197984 | + | 0.980205i | \(0.436561\pi\) | |||||||
\(32\) | 5.10959 | 0.903256 | ||||||||
\(33\) | −6.66728 | −1.16063 | ||||||||
\(34\) | −5.02268 | −0.861382 | ||||||||
\(35\) | 0.398447 | 0.0673498 | ||||||||
\(36\) | 0.546734 | 0.0911224 | ||||||||
\(37\) | 11.4227 | 1.87788 | 0.938941 | − | 0.344077i | \(-0.111808\pi\) | ||||
0.938941 | + | 0.344077i | \(0.111808\pi\) | |||||||
\(38\) | 2.09256 | 0.339459 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.18858 | −0.187931 | ||||||||
\(41\) | 5.07633 | 0.792790 | 0.396395 | − | 0.918080i | \(-0.370261\pi\) | ||||
0.396395 | + | 0.918080i | \(0.370261\pi\) | |||||||
\(42\) | −1.54628 | −0.238596 | ||||||||
\(43\) | −0.328195 | −0.0500492 | −0.0250246 | − | 0.999687i | \(-0.507966\pi\) | ||||
−0.0250246 | + | 0.999687i | \(0.507966\pi\) | |||||||
\(44\) | −4.37822 | −0.660042 | ||||||||
\(45\) | −0.211070 | −0.0314644 | ||||||||
\(46\) | 2.15899 | 0.318325 | ||||||||
\(47\) | 6.62722 | 0.966679 | 0.483340 | − | 0.875433i | \(-0.339424\pi\) | ||||
0.483340 | + | 0.875433i | \(0.339424\pi\) | |||||||
\(48\) | 1.36829 | 0.197496 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −4.76291 | −0.673577 | ||||||||
\(51\) | 8.02401 | 1.12359 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.9423 | 1.50304 | 0.751518 | − | 0.659712i | \(-0.229322\pi\) | ||||
0.751518 | + | 0.659712i | \(0.229322\pi\) | |||||||
\(54\) | 5.45795 | 0.742732 | ||||||||
\(55\) | 1.69024 | 0.227911 | ||||||||
\(56\) | −2.98304 | −0.398625 | ||||||||
\(57\) | −3.34299 | −0.442790 | ||||||||
\(58\) | 2.86195 | 0.375792 | ||||||||
\(59\) | −7.70620 | −1.00326 | −0.501631 | − | 0.865082i | \(-0.667266\pi\) | ||||
−0.501631 | + | 0.865082i | \(0.667266\pi\) | |||||||
\(60\) | 0.646344 | 0.0834427 | ||||||||
\(61\) | 14.6039 | 1.86984 | 0.934921 | − | 0.354857i | \(-0.115470\pi\) | ||||
0.934921 | + | 0.354857i | \(0.115470\pi\) | |||||||
\(62\) | 2.16899 | 0.275462 | ||||||||
\(63\) | −0.529731 | −0.0667398 | ||||||||
\(64\) | 6.76806 | 0.846008 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.55941 | −0.807407 | ||||||||
\(67\) | 1.22074 | 0.149137 | 0.0745685 | − | 0.997216i | \(-0.476242\pi\) | ||||
0.0745685 | + | 0.997216i | \(0.476242\pi\) | |||||||
\(68\) | 5.26915 | 0.638979 | ||||||||
\(69\) | −3.44910 | −0.415223 | ||||||||
\(70\) | 0.392000 | 0.0468529 | ||||||||
\(71\) | −1.75019 | −0.207709 | −0.103854 | − | 0.994593i | \(-0.533118\pi\) | ||||
−0.103854 | + | 0.994593i | \(0.533118\pi\) | |||||||
\(72\) | 1.58021 | 0.186229 | ||||||||
\(73\) | −6.11791 | −0.716047 | −0.358023 | − | 0.933713i | \(-0.616549\pi\) | ||||
−0.358023 | + | 0.933713i | \(0.616549\pi\) | |||||||
\(74\) | 11.2379 | 1.30638 | ||||||||
\(75\) | 7.60902 | 0.878614 | ||||||||
\(76\) | −2.19525 | −0.251813 | ||||||||
\(77\) | 4.24206 | 0.483428 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.20871 | 0.473517 | 0.236759 | − | 0.971569i | \(-0.423915\pi\) | ||||
0.236759 | + | 0.971569i | \(0.423915\pi\) | |||||||
\(80\) | −0.346878 | −0.0387821 | ||||||||
\(81\) | −7.13019 | −0.792244 | ||||||||
\(82\) | 4.99419 | 0.551517 | ||||||||
\(83\) | 10.8154 | 1.18714 | 0.593571 | − | 0.804782i | \(-0.297718\pi\) | ||||
0.593571 | + | 0.804782i | \(0.297718\pi\) | |||||||
\(84\) | 1.62216 | 0.176992 | ||||||||
\(85\) | −2.03418 | −0.220638 | ||||||||
\(86\) | −0.322884 | −0.0348175 | ||||||||
\(87\) | −4.57213 | −0.490183 | ||||||||
\(88\) | −12.6542 | −1.34895 | ||||||||
\(89\) | −15.6973 | −1.66392 | −0.831958 | − | 0.554839i | \(-0.812780\pi\) | ||||
−0.831958 | + | 0.554839i | \(0.812780\pi\) | |||||||
\(90\) | −0.207654 | −0.0218887 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.26493 | −0.236136 | ||||||||
\(93\) | −3.46508 | −0.359312 | ||||||||
\(94\) | 6.51999 | 0.672485 | ||||||||
\(95\) | 0.847488 | 0.0869504 | ||||||||
\(96\) | −8.03079 | −0.819639 | ||||||||
\(97\) | −14.4763 | −1.46985 | −0.734924 | − | 0.678149i | \(-0.762782\pi\) | ||||
−0.734924 | + | 0.678149i | \(0.762782\pi\) | |||||||
\(98\) | 0.983820 | 0.0993808 | ||||||||
\(99\) | −2.24715 | −0.225847 | ||||||||
\(100\) | 4.99664 | 0.499664 | ||||||||
\(101\) | 7.31830 | 0.728198 | 0.364099 | − | 0.931360i | \(-0.381377\pi\) | ||||
0.364099 | + | 0.931360i | \(0.381377\pi\) | |||||||
\(102\) | 7.89418 | 0.781641 | ||||||||
\(103\) | −12.7643 | −1.25770 | −0.628851 | − | 0.777526i | \(-0.716474\pi\) | ||||
−0.628851 | + | 0.777526i | \(0.716474\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.626242 | −0.0611150 | ||||||||
\(106\) | 10.7652 | 1.04561 | ||||||||
\(107\) | 9.06986 | 0.876816 | 0.438408 | − | 0.898776i | \(-0.355542\pi\) | ||||
0.438408 | + | 0.898776i | \(0.355542\pi\) | |||||||
\(108\) | −5.72578 | −0.550964 | ||||||||
\(109\) | −4.95091 | −0.474211 | −0.237106 | − | 0.971484i | \(-0.576199\pi\) | ||||
−0.237106 | + | 0.971484i | \(0.576199\pi\) | |||||||
\(110\) | 1.66289 | 0.158550 | ||||||||
\(111\) | −17.9532 | −1.70404 | ||||||||
\(112\) | −0.870575 | −0.0822616 | ||||||||
\(113\) | 2.39270 | 0.225086 | 0.112543 | − | 0.993647i | \(-0.464100\pi\) | ||||
0.112543 | + | 0.993647i | \(0.464100\pi\) | |||||||
\(114\) | −3.28890 | −0.308034 | ||||||||
\(115\) | 0.874389 | 0.0815372 | ||||||||
\(116\) | −3.00239 | −0.278765 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.58151 | −0.697935 | ||||||||
\(119\) | −5.10528 | −0.468000 | ||||||||
\(120\) | 1.86811 | 0.170534 | ||||||||
\(121\) | 6.99507 | 0.635915 | ||||||||
\(122\) | 14.3676 | 1.30078 | ||||||||
\(123\) | −7.97852 | −0.719398 | ||||||||
\(124\) | −2.27543 | −0.204339 | ||||||||
\(125\) | −3.92121 | −0.350724 | ||||||||
\(126\) | −0.521160 | −0.0464286 | ||||||||
\(127\) | 15.0587 | 1.33625 | 0.668123 | − | 0.744051i | \(-0.267098\pi\) | ||||
0.668123 | + | 0.744051i | \(0.267098\pi\) | |||||||
\(128\) | −3.56062 | −0.314718 | ||||||||
\(129\) | 0.515826 | 0.0454160 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.6011 | −1.01359 | −0.506796 | − | 0.862066i | \(-0.669170\pi\) | ||||
−0.506796 | + | 0.862066i | \(0.669170\pi\) | |||||||
\(132\) | 6.88129 | 0.598940 | ||||||||
\(133\) | 2.12698 | 0.184432 | ||||||||
\(134\) | 1.20099 | 0.103750 | ||||||||
\(135\) | 2.21047 | 0.190247 | ||||||||
\(136\) | 15.2292 | 1.30590 | ||||||||
\(137\) | 0.410279 | 0.0350525 | 0.0175263 | − | 0.999846i | \(-0.494421\pi\) | ||||
0.0175263 | + | 0.999846i | \(0.494421\pi\) | |||||||
\(138\) | −3.39330 | −0.288857 | ||||||||
\(139\) | −18.1715 | −1.54129 | −0.770644 | − | 0.637266i | \(-0.780065\pi\) | ||||
−0.770644 | + | 0.637266i | \(0.780065\pi\) | |||||||
\(140\) | −0.411236 | −0.0347558 | ||||||||
\(141\) | −10.4161 | −0.877190 | ||||||||
\(142\) | −1.72187 | −0.144496 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.461170 | 0.0384309 | ||||||||
\(145\) | 1.15909 | 0.0962570 | ||||||||
\(146\) | −6.01892 | −0.498129 | ||||||||
\(147\) | −1.57171 | −0.129632 | ||||||||
\(148\) | −11.7894 | −0.969080 | ||||||||
\(149\) | 10.9195 | 0.894561 | 0.447280 | − | 0.894394i | \(-0.352393\pi\) | ||||
0.447280 | + | 0.894394i | \(0.352393\pi\) | |||||||
\(150\) | 7.48590 | 0.611222 | ||||||||
\(151\) | 20.3174 | 1.65341 | 0.826703 | − | 0.562639i | \(-0.190214\pi\) | ||||
0.826703 | + | 0.562639i | \(0.190214\pi\) | |||||||
\(152\) | −6.34486 | −0.514636 | ||||||||
\(153\) | 2.70442 | 0.218640 | ||||||||
\(154\) | 4.17342 | 0.336304 | ||||||||
\(155\) | 0.878439 | 0.0705579 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 23.4474 | 1.87131 | 0.935653 | − | 0.352922i | \(-0.114812\pi\) | ||||
0.935653 | + | 0.352922i | \(0.114812\pi\) | |||||||
\(158\) | 4.14062 | 0.329410 | ||||||||
\(159\) | −17.1981 | −1.36390 | ||||||||
\(160\) | 2.03590 | 0.160952 | ||||||||
\(161\) | 2.19449 | 0.172950 | ||||||||
\(162\) | −7.01482 | −0.551137 | ||||||||
\(163\) | 12.7006 | 0.994791 | 0.497396 | − | 0.867524i | \(-0.334290\pi\) | ||||
0.497396 | + | 0.867524i | \(0.334290\pi\) | |||||||
\(164\) | −5.23927 | −0.409119 | ||||||||
\(165\) | −2.65656 | −0.206813 | ||||||||
\(166\) | 10.6404 | 0.825853 | ||||||||
\(167\) | −10.0996 | −0.781531 | −0.390765 | − | 0.920490i | \(-0.627790\pi\) | ||||
−0.390765 | + | 0.920490i | \(0.627790\pi\) | |||||||
\(168\) | 4.68847 | 0.361723 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −2.00127 | −0.153490 | ||||||||
\(171\) | −1.12673 | −0.0861629 | ||||||||
\(172\) | 0.338729 | 0.0258279 | ||||||||
\(173\) | 16.5810 | 1.26063 | 0.630316 | − | 0.776339i | \(-0.282925\pi\) | ||||
0.630316 | + | 0.776339i | \(0.282925\pi\) | |||||||
\(174\) | −4.49815 | −0.341004 | ||||||||
\(175\) | −4.84124 | −0.365963 | ||||||||
\(176\) | −3.69303 | −0.278373 | ||||||||
\(177\) | 12.1119 | 0.910386 | ||||||||
\(178\) | −15.4434 | −1.15753 | ||||||||
\(179\) | −23.5863 | −1.76292 | −0.881461 | − | 0.472257i | \(-0.843439\pi\) | ||||
−0.881461 | + | 0.472257i | \(0.843439\pi\) | |||||||
\(180\) | 0.217845 | 0.0162372 | ||||||||
\(181\) | −23.7219 | −1.76324 | −0.881619 | − | 0.471962i | \(-0.843546\pi\) | ||||
−0.881619 | + | 0.471962i | \(0.843546\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −22.9531 | −1.69674 | ||||||||
\(184\) | −6.54626 | −0.482596 | ||||||||
\(185\) | 4.55134 | 0.334621 | ||||||||
\(186\) | −3.40902 | −0.249961 | ||||||||
\(187\) | −21.6569 | −1.58371 | ||||||||
\(188\) | −6.83994 | −0.498854 | ||||||||
\(189\) | 5.54771 | 0.403537 | ||||||||
\(190\) | 0.833775 | 0.0604884 | ||||||||
\(191\) | 2.18467 | 0.158077 | 0.0790385 | − | 0.996872i | \(-0.474815\pi\) | ||||
0.0790385 | + | 0.996872i | \(0.474815\pi\) | |||||||
\(192\) | −10.6374 | −0.767690 | ||||||||
\(193\) | 18.6395 | 1.34170 | 0.670851 | − | 0.741592i | \(-0.265929\pi\) | ||||
0.670851 | + | 0.741592i | \(0.265929\pi\) | |||||||
\(194\) | −14.2421 | −1.02252 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.03210 | −0.0737213 | ||||||||
\(197\) | −14.9820 | −1.06743 | −0.533713 | − | 0.845666i | \(-0.679204\pi\) | ||||
−0.533713 | + | 0.845666i | \(0.679204\pi\) | |||||||
\(198\) | −2.21079 | −0.157114 | ||||||||
\(199\) | 8.58624 | 0.608662 | 0.304331 | − | 0.952566i | \(-0.401567\pi\) | ||||
0.304331 | + | 0.952566i | \(0.401567\pi\) | |||||||
\(200\) | 14.4416 | 1.02118 | ||||||||
\(201\) | −1.91865 | −0.135331 | ||||||||
\(202\) | 7.19989 | 0.506583 | ||||||||
\(203\) | 2.90902 | 0.204173 | ||||||||
\(204\) | −8.28157 | −0.579826 | ||||||||
\(205\) | 2.02265 | 0.141268 | ||||||||
\(206\) | −12.5578 | −0.874940 | ||||||||
\(207\) | −1.16249 | −0.0807987 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.02277 | 0.624118 | ||||||||
\(210\) | −0.616110 | −0.0425156 | ||||||||
\(211\) | −28.3478 | −1.95155 | −0.975773 | − | 0.218785i | \(-0.929791\pi\) | ||||
−0.975773 | + | 0.218785i | \(0.929791\pi\) | |||||||
\(212\) | −11.2935 | −0.775641 | ||||||||
\(213\) | 2.75078 | 0.188481 | ||||||||
\(214\) | 8.92310 | 0.609971 | ||||||||
\(215\) | −0.130768 | −0.00891831 | ||||||||
\(216\) | −16.5490 | −1.12602 | ||||||||
\(217\) | 2.20466 | 0.149662 | ||||||||
\(218\) | −4.87080 | −0.329892 | ||||||||
\(219\) | 9.61557 | 0.649760 | ||||||||
\(220\) | −1.74449 | −0.117613 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −17.6627 | −1.18544 | ||||||||
\(223\) | −14.1295 | −0.946181 | −0.473091 | − | 0.881014i | \(-0.656862\pi\) | ||||
−0.473091 | + | 0.881014i | \(0.656862\pi\) | |||||||
\(224\) | 5.10959 | 0.341399 | ||||||||
\(225\) | 2.56455 | 0.170970 | ||||||||
\(226\) | 2.35399 | 0.156585 | ||||||||
\(227\) | −18.7325 | −1.24332 | −0.621661 | − | 0.783286i | \(-0.713542\pi\) | ||||
−0.621661 | + | 0.783286i | \(0.713542\pi\) | |||||||
\(228\) | 3.45030 | 0.228502 | ||||||||
\(229\) | −3.24595 | −0.214499 | −0.107249 | − | 0.994232i | \(-0.534204\pi\) | ||||
−0.107249 | + | 0.994232i | \(0.534204\pi\) | |||||||
\(230\) | 0.860241 | 0.0567226 | ||||||||
\(231\) | −6.66728 | −0.438675 | ||||||||
\(232\) | −8.67771 | −0.569719 | ||||||||
\(233\) | 17.4275 | 1.14171 | 0.570856 | − | 0.821050i | \(-0.306612\pi\) | ||||
0.570856 | + | 0.821050i | \(0.306612\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.64059 | 0.172253 | ||||||||
\(236\) | 7.95356 | 0.517732 | ||||||||
\(237\) | −6.61487 | −0.429682 | ||||||||
\(238\) | −5.02268 | −0.325572 | ||||||||
\(239\) | −3.89803 | −0.252142 | −0.126071 | − | 0.992021i | \(-0.540237\pi\) | ||||
−0.126071 | + | 0.992021i | \(0.540237\pi\) | |||||||
\(240\) | 0.545191 | 0.0351919 | ||||||||
\(241\) | 17.6973 | 1.13998 | 0.569990 | − | 0.821652i | \(-0.306947\pi\) | ||||
0.569990 | + | 0.821652i | \(0.306947\pi\) | |||||||
\(242\) | 6.88189 | 0.442385 | ||||||||
\(243\) | −5.43654 | −0.348754 | ||||||||
\(244\) | −15.0727 | −0.964930 | ||||||||
\(245\) | 0.398447 | 0.0254558 | ||||||||
\(246\) | −7.84942 | −0.500461 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −6.57658 | −0.417613 | ||||||||
\(249\) | −16.9986 | −1.07724 | ||||||||
\(250\) | −3.85776 | −0.243986 | ||||||||
\(251\) | −1.70708 | −0.107750 | −0.0538750 | − | 0.998548i | \(-0.517157\pi\) | ||||
−0.0538750 | + | 0.998548i | \(0.517157\pi\) | |||||||
\(252\) | 0.546734 | 0.0344410 | ||||||||
\(253\) | 9.30917 | 0.585262 | ||||||||
\(254\) | 14.8151 | 0.929581 | ||||||||
\(255\) | 3.19714 | 0.200213 | ||||||||
\(256\) | −17.0391 | −1.06495 | ||||||||
\(257\) | 23.2726 | 1.45171 | 0.725853 | − | 0.687849i | \(-0.241445\pi\) | ||||
0.725853 | + | 0.687849i | \(0.241445\pi\) | |||||||
\(258\) | 0.507480 | 0.0315943 | ||||||||
\(259\) | 11.4227 | 0.709773 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.54100 | −0.0953852 | ||||||||
\(262\) | −11.4134 | −0.705121 | ||||||||
\(263\) | 14.0596 | 0.866949 | 0.433475 | − | 0.901166i | \(-0.357287\pi\) | ||||
0.433475 | + | 0.901166i | \(0.357287\pi\) | |||||||
\(264\) | 19.8888 | 1.22407 | ||||||||
\(265\) | 4.35991 | 0.267827 | ||||||||
\(266\) | 2.09256 | 0.128303 | ||||||||
\(267\) | 24.6717 | 1.50988 | ||||||||
\(268\) | −1.25992 | −0.0769621 | ||||||||
\(269\) | 3.44689 | 0.210161 | 0.105080 | − | 0.994464i | \(-0.466490\pi\) | ||||
0.105080 | + | 0.994464i | \(0.466490\pi\) | |||||||
\(270\) | 2.17470 | 0.132348 | ||||||||
\(271\) | −21.2277 | −1.28949 | −0.644744 | − | 0.764399i | \(-0.723036\pi\) | ||||
−0.644744 | + | 0.764399i | \(0.723036\pi\) | |||||||
\(272\) | 4.44453 | 0.269489 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.403641 | 0.0243848 | ||||||||
\(275\) | −20.5368 | −1.23842 | ||||||||
\(276\) | 3.55982 | 0.214276 | ||||||||
\(277\) | 7.06655 | 0.424588 | 0.212294 | − | 0.977206i | \(-0.431907\pi\) | ||||
0.212294 | + | 0.977206i | \(0.431907\pi\) | |||||||
\(278\) | −17.8775 | −1.07222 | ||||||||
\(279\) | −1.16788 | −0.0699189 | ||||||||
\(280\) | −1.18858 | −0.0710314 | ||||||||
\(281\) | 2.37834 | 0.141880 | 0.0709398 | − | 0.997481i | \(-0.477400\pi\) | ||||
0.0709398 | + | 0.997481i | \(0.477400\pi\) | |||||||
\(282\) | −10.2475 | −0.610231 | ||||||||
\(283\) | −14.2529 | −0.847248 | −0.423624 | − | 0.905838i | \(-0.639242\pi\) | ||||
−0.423624 | + | 0.905838i | \(0.639242\pi\) | |||||||
\(284\) | 1.80636 | 0.107188 | ||||||||
\(285\) | −1.33200 | −0.0789011 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.07633 | 0.299646 | ||||||||
\(288\) | −2.70671 | −0.159494 | ||||||||
\(289\) | 9.06388 | 0.533169 | ||||||||
\(290\) | 1.14033 | 0.0669627 | ||||||||
\(291\) | 22.7526 | 1.33378 | ||||||||
\(292\) | 6.31428 | 0.369515 | ||||||||
\(293\) | −7.15874 | −0.418218 | −0.209109 | − | 0.977892i | \(-0.567056\pi\) | ||||
−0.209109 | + | 0.977892i | \(0.567056\pi\) | |||||||
\(294\) | −1.54628 | −0.0901808 | ||||||||
\(295\) | −3.07051 | −0.178772 | ||||||||
\(296\) | −34.0744 | −1.98053 | ||||||||
\(297\) | 23.5337 | 1.36556 | ||||||||
\(298\) | 10.7428 | 0.622315 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −7.85326 | −0.453408 | ||||||||
\(301\) | −0.328195 | −0.0189168 | ||||||||
\(302\) | 19.9887 | 1.15022 | ||||||||
\(303\) | −11.5022 | −0.660787 | ||||||||
\(304\) | −1.85169 | −0.106202 | ||||||||
\(305\) | 5.81889 | 0.333189 | ||||||||
\(306\) | 2.66067 | 0.152100 | ||||||||
\(307\) | 24.4217 | 1.39382 | 0.696910 | − | 0.717159i | \(-0.254558\pi\) | ||||
0.696910 | + | 0.717159i | \(0.254558\pi\) | |||||||
\(308\) | −4.37822 | −0.249472 | ||||||||
\(309\) | 20.0617 | 1.14127 | ||||||||
\(310\) | 0.864226 | 0.0490847 | ||||||||
\(311\) | 23.7212 | 1.34510 | 0.672552 | − | 0.740050i | \(-0.265198\pi\) | ||||
0.672552 | + | 0.740050i | \(0.265198\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.0876 | −0.852803 | −0.426401 | − | 0.904534i | \(-0.640219\pi\) | ||||
−0.426401 | + | 0.904534i | \(0.640219\pi\) | |||||||
\(314\) | 23.0680 | 1.30180 | ||||||||
\(315\) | −0.211070 | −0.0118924 | ||||||||
\(316\) | −4.34381 | −0.244358 | ||||||||
\(317\) | 31.5913 | 1.77434 | 0.887172 | − | 0.461440i | \(-0.152667\pi\) | ||||
0.887172 | + | 0.461440i | \(0.152667\pi\) | |||||||
\(318\) | −16.9198 | −0.948815 | ||||||||
\(319\) | 12.3402 | 0.690920 | ||||||||
\(320\) | 2.69671 | 0.150751 | ||||||||
\(321\) | −14.2552 | −0.795646 | ||||||||
\(322\) | 2.15899 | 0.120316 | ||||||||
\(323\) | −10.8588 | −0.604201 | ||||||||
\(324\) | 7.35906 | 0.408837 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 12.4951 | 0.692042 | ||||||||
\(327\) | 7.78139 | 0.430312 | ||||||||
\(328\) | −15.1429 | −0.836126 | ||||||||
\(329\) | 6.62722 | 0.365370 | ||||||||
\(330\) | −2.61357 | −0.143873 | ||||||||
\(331\) | 19.8976 | 1.09367 | 0.546835 | − | 0.837240i | \(-0.315832\pi\) | ||||
0.546835 | + | 0.837240i | \(0.315832\pi\) | |||||||
\(332\) | −11.1625 | −0.612623 | ||||||||
\(333\) | −6.05096 | −0.331591 | ||||||||
\(334\) | −9.93619 | −0.543684 | ||||||||
\(335\) | 0.486400 | 0.0265749 | ||||||||
\(336\) | 1.36829 | 0.0746464 | ||||||||
\(337\) | −2.71943 | −0.148137 | −0.0740685 | − | 0.997253i | \(-0.523598\pi\) | ||||
−0.0740685 | + | 0.997253i | \(0.523598\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.76063 | −0.204249 | ||||||||
\(340\) | 2.09948 | 0.113860 | ||||||||
\(341\) | 9.35229 | 0.506455 | ||||||||
\(342\) | −1.10850 | −0.0599406 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0.979017 | 0.0527851 | ||||||||
\(345\) | −1.37428 | −0.0739890 | ||||||||
\(346\) | 16.3127 | 0.876978 | ||||||||
\(347\) | −12.8135 | −0.687865 | −0.343932 | − | 0.938994i | \(-0.611759\pi\) | ||||
−0.343932 | + | 0.938994i | \(0.611759\pi\) | |||||||
\(348\) | 4.71889 | 0.252959 | ||||||||
\(349\) | −9.05354 | −0.484625 | −0.242312 | − | 0.970198i | \(-0.577906\pi\) | ||||
−0.242312 | + | 0.970198i | \(0.577906\pi\) | |||||||
\(350\) | −4.76291 | −0.254588 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 21.6752 | 1.15529 | ||||||||
\(353\) | −9.43537 | −0.502194 | −0.251097 | − | 0.967962i | \(-0.580791\pi\) | ||||
−0.251097 | + | 0.967962i | \(0.580791\pi\) | |||||||
\(354\) | 11.9159 | 0.633324 | ||||||||
\(355\) | −0.697356 | −0.0370118 | ||||||||
\(356\) | 16.2012 | 0.858662 | ||||||||
\(357\) | 8.02401 | 0.424676 | ||||||||
\(358\) | −23.2047 | −1.22640 | ||||||||
\(359\) | 9.68118 | 0.510953 | 0.255477 | − | 0.966815i | \(-0.417768\pi\) | ||||
0.255477 | + | 0.966815i | \(0.417768\pi\) | |||||||
\(360\) | 0.629629 | 0.0331843 | ||||||||
\(361\) | −14.4760 | −0.761893 | ||||||||
\(362\) | −23.3381 | −1.22662 | ||||||||
\(363\) | −10.9942 | −0.577047 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.43766 | −0.127593 | ||||||||
\(366\) | −22.5817 | −1.18037 | ||||||||
\(367\) | −15.3650 | −0.802047 | −0.401023 | − | 0.916068i | \(-0.631345\pi\) | ||||
−0.401023 | + | 0.916068i | \(0.631345\pi\) | |||||||
\(368\) | −1.91047 | −0.0995901 | ||||||||
\(369\) | −2.68909 | −0.139988 | ||||||||
\(370\) | 4.47770 | 0.232785 | ||||||||
\(371\) | 10.9423 | 0.568094 | ||||||||
\(372\) | 3.57631 | 0.185423 | ||||||||
\(373\) | 12.6878 | 0.656948 | 0.328474 | − | 0.944513i | \(-0.393466\pi\) | ||||
0.328474 | + | 0.944513i | \(0.393466\pi\) | |||||||
\(374\) | −21.3065 | −1.10173 | ||||||||
\(375\) | 6.16300 | 0.318256 | ||||||||
\(376\) | −19.7692 | −1.01952 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 5.45795 | 0.280726 | ||||||||
\(379\) | 6.59026 | 0.338519 | 0.169259 | − | 0.985572i | \(-0.445862\pi\) | ||||
0.169259 | + | 0.985572i | \(0.445862\pi\) | |||||||
\(380\) | −0.874691 | −0.0448707 | ||||||||
\(381\) | −23.6679 | −1.21255 | ||||||||
\(382\) | 2.14932 | 0.109969 | ||||||||
\(383\) | −31.3776 | −1.60332 | −0.801660 | − | 0.597781i | \(-0.796049\pi\) | ||||
−0.801660 | + | 0.597781i | \(0.796049\pi\) | |||||||
\(384\) | 5.59626 | 0.285583 | ||||||||
\(385\) | 1.69024 | 0.0861424 | ||||||||
\(386\) | 18.3379 | 0.933376 | ||||||||
\(387\) | 0.173855 | 0.00883754 | ||||||||
\(388\) | 14.9410 | 0.758514 | ||||||||
\(389\) | 16.4265 | 0.832857 | 0.416428 | − | 0.909169i | \(-0.363282\pi\) | ||||
0.416428 | + | 0.909169i | \(0.363282\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.2035 | −0.566585 | ||||||||
\(392\) | −2.98304 | −0.150666 | ||||||||
\(393\) | 18.2335 | 0.919760 | ||||||||
\(394\) | −14.7396 | −0.742572 | ||||||||
\(395\) | 1.67695 | 0.0843764 | ||||||||
\(396\) | 2.31928 | 0.116548 | ||||||||
\(397\) | −6.94037 | −0.348327 | −0.174163 | − | 0.984717i | \(-0.555722\pi\) | ||||
−0.174163 | + | 0.984717i | \(0.555722\pi\) | |||||||
\(398\) | 8.44731 | 0.423425 | ||||||||
\(399\) | −3.34299 | −0.167359 | ||||||||
\(400\) | 4.21466 | 0.210733 | ||||||||
\(401\) | −0.890125 | −0.0444507 | −0.0222254 | − | 0.999753i | \(-0.507075\pi\) | ||||
−0.0222254 | + | 0.999753i | \(0.507075\pi\) | |||||||
\(402\) | −1.88760 | −0.0941451 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −7.55321 | −0.375786 | ||||||||
\(405\) | −2.84100 | −0.141171 | ||||||||
\(406\) | 2.86195 | 0.142036 | ||||||||
\(407\) | 48.4558 | 2.40187 | ||||||||
\(408\) | −23.9359 | −1.18501 | ||||||||
\(409\) | 2.00173 | 0.0989793 | 0.0494897 | − | 0.998775i | \(-0.484241\pi\) | ||||
0.0494897 | + | 0.998775i | \(0.484241\pi\) | |||||||
\(410\) | 1.98992 | 0.0982752 | ||||||||
\(411\) | −0.644840 | −0.0318076 | ||||||||
\(412\) | 13.1740 | 0.649036 | ||||||||
\(413\) | −7.70620 | −0.379197 | ||||||||
\(414\) | −1.14368 | −0.0562088 | ||||||||
\(415\) | 4.30935 | 0.211538 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 28.5603 | 1.39861 | ||||||||
\(418\) | 8.87678 | 0.434178 | ||||||||
\(419\) | 32.3340 | 1.57962 | 0.789809 | − | 0.613353i | \(-0.210180\pi\) | ||||
0.789809 | + | 0.613353i | \(0.210180\pi\) | |||||||
\(420\) | 0.646344 | 0.0315384 | ||||||||
\(421\) | 9.10353 | 0.443679 | 0.221839 | − | 0.975083i | \(-0.428794\pi\) | ||||
0.221839 | + | 0.975083i | \(0.428794\pi\) | |||||||
\(422\) | −27.8892 | −1.35762 | ||||||||
\(423\) | −3.51064 | −0.170693 | ||||||||
\(424\) | −32.6412 | −1.58520 | ||||||||
\(425\) | 24.7159 | 1.19890 | ||||||||
\(426\) | 2.70627 | 0.131119 | ||||||||
\(427\) | 14.6039 | 0.706734 | ||||||||
\(428\) | −9.36099 | −0.452480 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.128652 | −0.00620416 | ||||||||
\(431\) | −15.8655 | −0.764216 | −0.382108 | − | 0.924118i | \(-0.624802\pi\) | ||||
−0.382108 | + | 0.924118i | \(0.624802\pi\) | |||||||
\(432\) | −4.82970 | −0.232369 | ||||||||
\(433\) | 15.8736 | 0.762835 | 0.381418 | − | 0.924403i | \(-0.375436\pi\) | ||||
0.381418 | + | 0.924403i | \(0.375436\pi\) | |||||||
\(434\) | 2.16899 | 0.104115 | ||||||||
\(435\) | −1.82175 | −0.0873462 | ||||||||
\(436\) | 5.10983 | 0.244716 | ||||||||
\(437\) | 4.66764 | 0.223283 | ||||||||
\(438\) | 9.45999 | 0.452016 | ||||||||
\(439\) | 5.37687 | 0.256624 | 0.128312 | − | 0.991734i | \(-0.459044\pi\) | ||||
0.128312 | + | 0.991734i | \(0.459044\pi\) | |||||||
\(440\) | −5.04204 | −0.240370 | ||||||||
\(441\) | −0.529731 | −0.0252253 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −25.4188 | −1.20768 | −0.603841 | − | 0.797105i | \(-0.706364\pi\) | ||||
−0.603841 | + | 0.797105i | \(0.706364\pi\) | |||||||
\(444\) | 18.5295 | 0.879369 | ||||||||
\(445\) | −6.25456 | −0.296494 | ||||||||
\(446\) | −13.9009 | −0.658226 | ||||||||
\(447\) | −17.1623 | −0.811748 | ||||||||
\(448\) | 6.76806 | 0.319761 | ||||||||
\(449\) | −15.4369 | −0.728512 | −0.364256 | − | 0.931299i | \(-0.618677\pi\) | ||||
−0.364256 | + | 0.931299i | \(0.618677\pi\) | |||||||
\(450\) | 2.52306 | 0.118938 | ||||||||
\(451\) | 21.5341 | 1.01400 | ||||||||
\(452\) | −2.46950 | −0.116156 | ||||||||
\(453\) | −31.9330 | −1.50034 | ||||||||
\(454\) | −18.4294 | −0.864936 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 9.97227 | 0.466995 | ||||||||
\(457\) | 30.2784 | 1.41636 | 0.708181 | − | 0.706031i | \(-0.249516\pi\) | ||||
0.708181 | + | 0.706031i | \(0.249516\pi\) | |||||||
\(458\) | −3.19343 | −0.149219 | ||||||||
\(459\) | −28.3226 | −1.32199 | ||||||||
\(460\) | −0.902455 | −0.0420772 | ||||||||
\(461\) | 25.3431 | 1.18035 | 0.590173 | − | 0.807276i | \(-0.299059\pi\) | ||||
0.590173 | + | 0.807276i | \(0.299059\pi\) | |||||||
\(462\) | −6.55941 | −0.305171 | ||||||||
\(463\) | −2.93975 | −0.136622 | −0.0683109 | − | 0.997664i | \(-0.521761\pi\) | ||||
−0.0683109 | + | 0.997664i | \(0.521761\pi\) | |||||||
\(464\) | −2.53252 | −0.117569 | ||||||||
\(465\) | −1.38065 | −0.0640262 | ||||||||
\(466\) | 17.1455 | 0.794250 | ||||||||
\(467\) | 24.0967 | 1.11506 | 0.557531 | − | 0.830156i | \(-0.311749\pi\) | ||||
0.557531 | + | 0.830156i | \(0.311749\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.22074 | 0.0563685 | ||||||||
\(470\) | 2.59787 | 0.119831 | ||||||||
\(471\) | −36.8525 | −1.69807 | ||||||||
\(472\) | 22.9879 | 1.05810 | ||||||||
\(473\) | −1.39222 | −0.0640144 | ||||||||
\(474\) | −6.50784 | −0.298915 | ||||||||
\(475\) | −10.2972 | −0.472469 | ||||||||
\(476\) | 5.26915 | 0.241511 | ||||||||
\(477\) | −5.79646 | −0.265402 | ||||||||
\(478\) | −3.83495 | −0.175407 | ||||||||
\(479\) | 11.1069 | 0.507488 | 0.253744 | − | 0.967271i | \(-0.418338\pi\) | ||||
0.253744 | + | 0.967271i | \(0.418338\pi\) | |||||||
\(480\) | −3.19984 | −0.146052 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 17.4109 | 0.793045 | ||||||||
\(483\) | −3.44910 | −0.156940 | ||||||||
\(484\) | −7.21960 | −0.328164 | ||||||||
\(485\) | −5.76805 | −0.261913 | ||||||||
\(486\) | −5.34858 | −0.242616 | ||||||||
\(487\) | −29.1520 | −1.32100 | −0.660501 | − | 0.750825i | \(-0.729656\pi\) | ||||
−0.660501 | + | 0.750825i | \(0.729656\pi\) | |||||||
\(488\) | −43.5641 | −1.97205 | ||||||||
\(489\) | −19.9617 | −0.902700 | ||||||||
\(490\) | 0.392000 | 0.0177087 | ||||||||
\(491\) | 0.374507 | 0.0169013 | 0.00845063 | − | 0.999964i | \(-0.497310\pi\) | ||||
0.00845063 | + | 0.999964i | \(0.497310\pi\) | |||||||
\(492\) | 8.23462 | 0.371245 | ||||||||
\(493\) | −14.8513 | −0.668871 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.895370 | −0.0402439 | ||||||||
\(496\) | −1.91932 | −0.0861800 | ||||||||
\(497\) | −1.75019 | −0.0785066 | ||||||||
\(498\) | −16.7236 | −0.749401 | ||||||||
\(499\) | −0.402490 | −0.0180179 | −0.00900896 | − | 0.999959i | \(-0.502868\pi\) | ||||
−0.00900896 | + | 0.999959i | \(0.502868\pi\) | |||||||
\(500\) | 4.04708 | 0.180991 | ||||||||
\(501\) | 15.8736 | 0.709182 | ||||||||
\(502\) | −1.67946 | −0.0749580 | ||||||||
\(503\) | 14.1098 | 0.629124 | 0.314562 | − | 0.949237i | \(-0.398142\pi\) | ||||
0.314562 | + | 0.949237i | \(0.398142\pi\) | |||||||
\(504\) | 1.58021 | 0.0703880 | ||||||||
\(505\) | 2.91596 | 0.129758 | ||||||||
\(506\) | 9.15854 | 0.407147 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −15.5421 | −0.689569 | ||||||||
\(509\) | 37.0510 | 1.64225 | 0.821127 | − | 0.570745i | \(-0.193345\pi\) | ||||
0.821127 | + | 0.570745i | \(0.193345\pi\) | |||||||
\(510\) | 3.14541 | 0.139281 | ||||||||
\(511\) | −6.11791 | −0.270640 | ||||||||
\(512\) | −9.64220 | −0.426129 | ||||||||
\(513\) | 11.7999 | 0.520977 | ||||||||
\(514\) | 22.8961 | 1.00990 | ||||||||
\(515\) | −5.08589 | −0.224111 | ||||||||
\(516\) | −0.532384 | −0.0234369 | ||||||||
\(517\) | 28.1131 | 1.23641 | ||||||||
\(518\) | 11.2379 | 0.493765 | ||||||||
\(519\) | −26.0605 | −1.14393 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.5515 | 1.25086 | 0.625432 | − | 0.780279i | \(-0.284923\pi\) | ||||
0.625432 | + | 0.780279i | \(0.284923\pi\) | |||||||
\(522\) | −1.51606 | −0.0663562 | ||||||||
\(523\) | −7.85498 | −0.343474 | −0.171737 | − | 0.985143i | \(-0.554938\pi\) | ||||
−0.171737 | + | 0.985143i | \(0.554938\pi\) | |||||||
\(524\) | 11.9735 | 0.523063 | ||||||||
\(525\) | 7.60902 | 0.332085 | ||||||||
\(526\) | 13.8321 | 0.603107 | ||||||||
\(527\) | −11.2554 | −0.490293 | ||||||||
\(528\) | 5.80437 | 0.252603 | ||||||||
\(529\) | −18.1842 | −0.790617 | ||||||||
\(530\) | 4.28937 | 0.186318 | ||||||||
\(531\) | 4.08221 | 0.177153 | ||||||||
\(532\) | −2.19525 | −0.0951763 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 24.2725 | 1.05037 | ||||||||
\(535\) | 3.61386 | 0.156241 | ||||||||
\(536\) | −3.64151 | −0.157289 | ||||||||
\(537\) | 37.0708 | 1.59972 | ||||||||
\(538\) | 3.39112 | 0.146202 | ||||||||
\(539\) | 4.24206 | 0.182718 | ||||||||
\(540\) | −2.28142 | −0.0981767 | ||||||||
\(541\) | −36.0835 | −1.55135 | −0.775676 | − | 0.631131i | \(-0.782591\pi\) | ||||
−0.775676 | + | 0.631131i | \(0.782591\pi\) | |||||||
\(542\) | −20.8842 | −0.897052 | ||||||||
\(543\) | 37.2840 | 1.60001 | ||||||||
\(544\) | −26.0859 | −1.11842 | ||||||||
\(545\) | −1.97267 | −0.0845001 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −30.0255 | −1.28380 | −0.641899 | − | 0.766789i | \(-0.721853\pi\) | ||||
−0.641899 | + | 0.766789i | \(0.721853\pi\) | |||||||
\(548\) | −0.423449 | −0.0180888 | ||||||||
\(549\) | −7.73615 | −0.330171 | ||||||||
\(550\) | −20.2045 | −0.861524 | ||||||||
\(551\) | 6.18742 | 0.263593 | ||||||||
\(552\) | 10.2888 | 0.437921 | ||||||||
\(553\) | 4.20871 | 0.178973 | ||||||||
\(554\) | 6.95221 | 0.295371 | ||||||||
\(555\) | −7.15339 | −0.303644 | ||||||||
\(556\) | 18.7548 | 0.795380 | ||||||||
\(557\) | −11.6919 | −0.495400 | −0.247700 | − | 0.968837i | \(-0.579675\pi\) | ||||
−0.247700 | + | 0.968837i | \(0.579675\pi\) | |||||||
\(558\) | −1.14898 | −0.0486402 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −0.346878 | −0.0146583 | ||||||||
\(561\) | 34.0383 | 1.43710 | ||||||||
\(562\) | 2.33985 | 0.0987008 | ||||||||
\(563\) | −24.4062 | −1.02860 | −0.514300 | − | 0.857610i | \(-0.671948\pi\) | ||||
−0.514300 | + | 0.857610i | \(0.671948\pi\) | |||||||
\(564\) | 10.7504 | 0.452674 | ||||||||
\(565\) | 0.953364 | 0.0401083 | ||||||||
\(566\) | −14.0223 | −0.589401 | ||||||||
\(567\) | −7.13019 | −0.299440 | ||||||||
\(568\) | 5.22087 | 0.219063 | ||||||||
\(569\) | 21.2322 | 0.890099 | 0.445050 | − | 0.895506i | \(-0.353186\pi\) | ||||
0.445050 | + | 0.895506i | \(0.353186\pi\) | |||||||
\(570\) | −1.31045 | −0.0548888 | ||||||||
\(571\) | 29.0906 | 1.21741 | 0.608703 | − | 0.793398i | \(-0.291690\pi\) | ||||
0.608703 | + | 0.793398i | \(0.291690\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.43366 | −0.143443 | ||||||||
\(574\) | 4.99419 | 0.208454 | ||||||||
\(575\) | −10.6241 | −0.443054 | ||||||||
\(576\) | −3.58525 | −0.149385 | ||||||||
\(577\) | −25.1627 | −1.04754 | −0.523768 | − | 0.851861i | \(-0.675474\pi\) | ||||
−0.523768 | + | 0.851861i | \(0.675474\pi\) | |||||||
\(578\) | 8.91723 | 0.370908 | ||||||||
\(579\) | −29.2959 | −1.21750 | ||||||||
\(580\) | −1.19629 | −0.0496734 | ||||||||
\(581\) | 10.8154 | 0.448697 | ||||||||
\(582\) | 22.3844 | 0.927864 | ||||||||
\(583\) | 46.4178 | 1.92243 | ||||||||
\(584\) | 18.2499 | 0.755188 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.04291 | −0.290940 | ||||||||
\(587\) | 21.7327 | 0.897006 | 0.448503 | − | 0.893781i | \(-0.351957\pi\) | ||||
0.448503 | + | 0.893781i | \(0.351957\pi\) | |||||||
\(588\) | 1.62216 | 0.0668967 | ||||||||
\(589\) | 4.68926 | 0.193218 | ||||||||
\(590\) | −3.02083 | −0.124366 | ||||||||
\(591\) | 23.5474 | 0.968611 | ||||||||
\(592\) | −9.94433 | −0.408709 | ||||||||
\(593\) | −30.7678 | −1.26348 | −0.631741 | − | 0.775180i | \(-0.717659\pi\) | ||||
−0.631741 | + | 0.775180i | \(0.717659\pi\) | |||||||
\(594\) | 23.1529 | 0.949976 | ||||||||
\(595\) | −2.03418 | −0.0833934 | ||||||||
\(596\) | −11.2700 | −0.461637 | ||||||||
\(597\) | −13.4951 | −0.552316 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.7791 | −0.726436 | −0.363218 | − | 0.931704i | \(-0.618322\pi\) | ||||
−0.363218 | + | 0.931704i | \(0.618322\pi\) | |||||||
\(600\) | −22.6980 | −0.926642 | ||||||||
\(601\) | −7.17744 | −0.292774 | −0.146387 | − | 0.989227i | \(-0.546764\pi\) | ||||
−0.146387 | + | 0.989227i | \(0.546764\pi\) | |||||||
\(602\) | −0.322884 | −0.0131598 | ||||||||
\(603\) | −0.646663 | −0.0263342 | ||||||||
\(604\) | −20.9696 | −0.853239 | ||||||||
\(605\) | 2.78716 | 0.113314 | ||||||||
\(606\) | −11.3161 | −0.459687 | ||||||||
\(607\) | 27.2937 | 1.10782 | 0.553908 | − | 0.832578i | \(-0.313136\pi\) | ||||
0.553908 | + | 0.832578i | \(0.313136\pi\) | |||||||
\(608\) | 10.8680 | 0.440755 | ||||||||
\(609\) | −4.57213 | −0.185272 | ||||||||
\(610\) | 5.72474 | 0.231788 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −2.79123 | −0.112829 | ||||||||
\(613\) | −19.4824 | −0.786888 | −0.393444 | − | 0.919349i | \(-0.628716\pi\) | ||||
−0.393444 | + | 0.919349i | \(0.628716\pi\) | |||||||
\(614\) | 24.0265 | 0.969632 | ||||||||
\(615\) | −3.17901 | −0.128190 | ||||||||
\(616\) | −12.6542 | −0.509853 | ||||||||
\(617\) | 7.14474 | 0.287636 | 0.143818 | − | 0.989604i | \(-0.454062\pi\) | ||||
0.143818 | + | 0.989604i | \(0.454062\pi\) | |||||||
\(618\) | 19.7371 | 0.793944 | ||||||||
\(619\) | −22.9703 | −0.923255 | −0.461628 | − | 0.887074i | \(-0.652734\pi\) | ||||
−0.461628 | + | 0.887074i | \(0.652734\pi\) | |||||||
\(620\) | −0.906636 | −0.0364114 | ||||||||
\(621\) | 12.1744 | 0.488542 | ||||||||
\(622\) | 23.3374 | 0.935743 | ||||||||
\(623\) | −15.6973 | −0.628901 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.6438 | 0.905752 | ||||||||
\(626\) | −14.8435 | −0.593266 | ||||||||
\(627\) | −14.1812 | −0.566341 | ||||||||
\(628\) | −24.2000 | −0.965686 | ||||||||
\(629\) | −58.3161 | −2.32522 | ||||||||
\(630\) | −0.207654 | −0.00827315 | ||||||||
\(631\) | −30.1524 | −1.20035 | −0.600173 | − | 0.799870i | \(-0.704902\pi\) | ||||
−0.600173 | + | 0.799870i | \(0.704902\pi\) | |||||||
\(632\) | −12.5548 | −0.499401 | ||||||||
\(633\) | 44.5546 | 1.77089 | ||||||||
\(634\) | 31.0801 | 1.23435 | ||||||||
\(635\) | 6.00010 | 0.238107 | ||||||||
\(636\) | 17.7501 | 0.703837 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 12.1406 | 0.480649 | ||||||||
\(639\) | 0.927127 | 0.0366766 | ||||||||
\(640\) | −1.41872 | −0.0560798 | ||||||||
\(641\) | −40.2705 | −1.59059 | −0.795295 | − | 0.606223i | \(-0.792684\pi\) | ||||
−0.795295 | + | 0.606223i | \(0.792684\pi\) | |||||||
\(642\) | −14.0245 | −0.553504 | ||||||||
\(643\) | −13.6321 | −0.537598 | −0.268799 | − | 0.963196i | \(-0.586627\pi\) | ||||
−0.268799 | + | 0.963196i | \(0.586627\pi\) | |||||||
\(644\) | −2.26493 | −0.0892509 | ||||||||
\(645\) | 0.205529 | 0.00809271 | ||||||||
\(646\) | −10.6831 | −0.420322 | ||||||||
\(647\) | −2.57274 | −0.101145 | −0.0505724 | − | 0.998720i | \(-0.516105\pi\) | ||||
−0.0505724 | + | 0.998720i | \(0.516105\pi\) | |||||||
\(648\) | 21.2696 | 0.835550 | ||||||||
\(649\) | −32.6902 | −1.28320 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.46508 | −0.135807 | ||||||||
\(652\) | −13.1083 | −0.513361 | ||||||||
\(653\) | 38.5454 | 1.50840 | 0.754198 | − | 0.656647i | \(-0.228026\pi\) | ||||
0.754198 | + | 0.656647i | \(0.228026\pi\) | |||||||
\(654\) | 7.65548 | 0.299353 | ||||||||
\(655\) | −4.62241 | −0.180613 | ||||||||
\(656\) | −4.41933 | −0.172546 | ||||||||
\(657\) | 3.24084 | 0.126437 | ||||||||
\(658\) | 6.51999 | 0.254176 | ||||||||
\(659\) | 15.1716 | 0.591000 | 0.295500 | − | 0.955343i | \(-0.404514\pi\) | ||||
0.295500 | + | 0.955343i | \(0.404514\pi\) | |||||||
\(660\) | 2.74183 | 0.106726 | ||||||||
\(661\) | −3.88736 | −0.151201 | −0.0756003 | − | 0.997138i | \(-0.524087\pi\) | ||||
−0.0756003 | + | 0.997138i | \(0.524087\pi\) | |||||||
\(662\) | 19.5756 | 0.760829 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −32.2627 | −1.25203 | ||||||||
\(665\) | 0.847488 | 0.0328642 | ||||||||
\(666\) | −5.95306 | −0.230676 | ||||||||
\(667\) | 6.38381 | 0.247182 | ||||||||
\(668\) | 10.4238 | 0.403308 | ||||||||
\(669\) | 22.2075 | 0.858590 | ||||||||
\(670\) | 0.478530 | 0.0184872 | ||||||||
\(671\) | 61.9507 | 2.39158 | ||||||||
\(672\) | −8.03079 | −0.309794 | ||||||||
\(673\) | −31.7515 | −1.22393 | −0.611965 | − | 0.790885i | \(-0.709621\pi\) | ||||
−0.611965 | + | 0.790885i | \(0.709621\pi\) | |||||||
\(674\) | −2.67543 | −0.103054 | ||||||||
\(675\) | −26.8578 | −1.03376 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.8303 | −0.454677 | −0.227338 | − | 0.973816i | \(-0.573002\pi\) | ||||
−0.227338 | + | 0.973816i | \(0.573002\pi\) | |||||||
\(678\) | −3.69978 | −0.142089 | ||||||||
\(679\) | −14.4763 | −0.555550 | ||||||||
\(680\) | 6.06804 | 0.232699 | ||||||||
\(681\) | 29.4421 | 1.12822 | ||||||||
\(682\) | 9.20097 | 0.352323 | ||||||||
\(683\) | −12.6451 | −0.483852 | −0.241926 | − | 0.970295i | \(-0.577779\pi\) | ||||
−0.241926 | + | 0.970295i | \(0.577779\pi\) | |||||||
\(684\) | 1.16289 | 0.0444643 | ||||||||
\(685\) | 0.163474 | 0.00624604 | ||||||||
\(686\) | 0.983820 | 0.0375624 | ||||||||
\(687\) | 5.10169 | 0.194642 | ||||||||
\(688\) | 0.285718 | 0.0108929 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −1.35205 | −0.0514716 | ||||||||
\(691\) | 14.6468 | 0.557190 | 0.278595 | − | 0.960409i | \(-0.410131\pi\) | ||||
0.278595 | + | 0.960409i | \(0.410131\pi\) | |||||||
\(692\) | −17.1132 | −0.650548 | ||||||||
\(693\) | −2.24715 | −0.0853622 | ||||||||
\(694\) | −12.6062 | −0.478524 | ||||||||
\(695\) | −7.24038 | −0.274643 | ||||||||
\(696\) | 13.6388 | 0.516979 | ||||||||
\(697\) | −25.9161 | −0.981642 | ||||||||
\(698\) | −8.90705 | −0.337137 | ||||||||
\(699\) | −27.3909 | −1.03602 | ||||||||
\(700\) | 4.99664 | 0.188855 | ||||||||
\(701\) | 7.16794 | 0.270729 | 0.135365 | − | 0.990796i | \(-0.456779\pi\) | ||||
0.135365 | + | 0.990796i | \(0.456779\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.2959 | 0.916336 | ||||||||
\(704\) | 28.7105 | 1.08207 | ||||||||
\(705\) | −4.15025 | −0.156307 | ||||||||
\(706\) | −9.28271 | −0.349359 | ||||||||
\(707\) | 7.31830 | 0.275233 | ||||||||
\(708\) | −12.5007 | −0.469804 | ||||||||
\(709\) | 2.14832 | 0.0806817 | 0.0403409 | − | 0.999186i | \(-0.487156\pi\) | ||||
0.0403409 | + | 0.999186i | \(0.487156\pi\) | |||||||
\(710\) | −0.686073 | −0.0257478 | ||||||||
\(711\) | −2.22948 | −0.0836122 | ||||||||
\(712\) | 46.8258 | 1.75487 | ||||||||
\(713\) | 4.83811 | 0.181189 | ||||||||
\(714\) | 7.89418 | 0.295432 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 24.3434 | 0.909755 | ||||||||
\(717\) | 6.12656 | 0.228801 | ||||||||
\(718\) | 9.52454 | 0.355453 | ||||||||
\(719\) | 9.34269 | 0.348424 | 0.174212 | − | 0.984708i | \(-0.444262\pi\) | ||||
0.174212 | + | 0.984708i | \(0.444262\pi\) | |||||||
\(720\) | 0.183752 | 0.00684803 | ||||||||
\(721\) | −12.7643 | −0.475367 | ||||||||
\(722\) | −14.2417 | −0.530023 | ||||||||
\(723\) | −27.8149 | −1.03445 | ||||||||
\(724\) | 24.4834 | 0.909918 | ||||||||
\(725\) | −14.0832 | −0.523039 | ||||||||
\(726\) | −10.8163 | −0.401432 | ||||||||
\(727\) | 41.2539 | 1.53002 | 0.765011 | − | 0.644017i | \(-0.222733\pi\) | ||||
0.765011 | + | 0.644017i | \(0.222733\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.9352 | 1.10871 | ||||||||
\(730\) | −2.39822 | −0.0887620 | ||||||||
\(731\) | 1.67553 | 0.0619715 | ||||||||
\(732\) | 23.6899 | 0.875604 | ||||||||
\(733\) | 11.6062 | 0.428686 | 0.214343 | − | 0.976758i | \(-0.431239\pi\) | ||||
0.214343 | + | 0.976758i | \(0.431239\pi\) | |||||||
\(734\) | −15.1164 | −0.557956 | ||||||||
\(735\) | −0.626242 | −0.0230993 | ||||||||
\(736\) | 11.2130 | 0.413315 | ||||||||
\(737\) | 5.17845 | 0.190751 | ||||||||
\(738\) | −2.64558 | −0.0973851 | ||||||||
\(739\) | −7.80551 | −0.287130 | −0.143565 | − | 0.989641i | \(-0.545857\pi\) | ||||
−0.143565 | + | 0.989641i | \(0.545857\pi\) | |||||||
\(740\) | −4.69744 | −0.172681 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 10.7652 | 0.395204 | ||||||||
\(743\) | 41.5158 | 1.52307 | 0.761533 | − | 0.648126i | \(-0.224447\pi\) | ||||
0.761533 | + | 0.648126i | \(0.224447\pi\) | |||||||
\(744\) | 10.3365 | 0.378954 | ||||||||
\(745\) | 4.35084 | 0.159402 | ||||||||
\(746\) | 12.4825 | 0.457016 | ||||||||
\(747\) | −5.72924 | −0.209622 | ||||||||
\(748\) | 22.3521 | 0.817272 | ||||||||
\(749\) | 9.06986 | 0.331405 | ||||||||
\(750\) | 6.06328 | 0.221400 | ||||||||
\(751\) | −22.7184 | −0.829005 | −0.414503 | − | 0.910048i | \(-0.636044\pi\) | ||||
−0.414503 | + | 0.910048i | \(0.636044\pi\) | |||||||
\(752\) | −5.76949 | −0.210392 | ||||||||
\(753\) | 2.68304 | 0.0977753 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.09540 | 0.294622 | ||||||||
\(756\) | −5.72578 | −0.208245 | ||||||||
\(757\) | −4.60782 | −0.167474 | −0.0837370 | − | 0.996488i | \(-0.526686\pi\) | ||||
−0.0837370 | + | 0.996488i | \(0.526686\pi\) | |||||||
\(758\) | 6.48362 | 0.235496 | ||||||||
\(759\) | −14.6313 | −0.531083 | ||||||||
\(760\) | −2.52809 | −0.0917034 | ||||||||
\(761\) | 21.2169 | 0.769112 | 0.384556 | − | 0.923102i | \(-0.374355\pi\) | ||||
0.384556 | + | 0.923102i | \(0.374355\pi\) | |||||||
\(762\) | −23.2850 | −0.843526 | ||||||||
\(763\) | −4.95091 | −0.179235 | ||||||||
\(764\) | −2.25479 | −0.0815755 | ||||||||
\(765\) | 1.07757 | 0.0389596 | ||||||||
\(766\) | −30.8699 | −1.11537 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 26.7806 | 0.966360 | ||||||||
\(769\) | −15.0781 | −0.543731 | −0.271865 | − | 0.962335i | \(-0.587641\pi\) | ||||
−0.271865 | + | 0.962335i | \(0.587641\pi\) | |||||||
\(770\) | 1.66289 | 0.0599263 | ||||||||
\(771\) | −36.5778 | −1.31732 | ||||||||
\(772\) | −19.2378 | −0.692385 | ||||||||
\(773\) | 4.39415 | 0.158047 | 0.0790233 | − | 0.996873i | \(-0.474820\pi\) | ||||
0.0790233 | + | 0.996873i | \(0.474820\pi\) | |||||||
\(774\) | 0.171042 | 0.00614797 | ||||||||
\(775\) | −10.6733 | −0.383396 | ||||||||
\(776\) | 43.1834 | 1.55020 | ||||||||
\(777\) | −17.9532 | −0.644067 | ||||||||
\(778\) | 16.1607 | 0.579390 | ||||||||
\(779\) | 10.7972 | 0.386852 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.42439 | −0.265666 | ||||||||
\(782\) | −11.0222 | −0.394154 | ||||||||
\(783\) | 16.1384 | 0.576739 | ||||||||
\(784\) | −0.870575 | −0.0310920 | ||||||||
\(785\) | 9.34254 | 0.333449 | ||||||||
\(786\) | 17.9385 | 0.639845 | ||||||||
\(787\) | −28.1360 | −1.00294 | −0.501470 | − | 0.865175i | \(-0.667207\pi\) | ||||
−0.501470 | + | 0.865175i | \(0.667207\pi\) | |||||||
\(788\) | 15.4629 | 0.550845 | ||||||||
\(789\) | −22.0975 | −0.786693 | ||||||||
\(790\) | 1.64982 | 0.0586978 | ||||||||
\(791\) | 2.39270 | 0.0850746 | ||||||||
\(792\) | 6.70333 | 0.238193 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −6.82807 | −0.242319 | ||||||||
\(795\) | −6.85251 | −0.243034 | ||||||||
\(796\) | −8.86185 | −0.314100 | ||||||||
\(797\) | 14.7844 | 0.523692 | 0.261846 | − | 0.965110i | \(-0.415669\pi\) | ||||
0.261846 | + | 0.965110i | \(0.415669\pi\) | |||||||
\(798\) | −3.28890 | −0.116426 | ||||||||
\(799\) | −33.8338 | −1.19695 | ||||||||
\(800\) | −24.7367 | −0.874576 | ||||||||
\(801\) | 8.31537 | 0.293809 | ||||||||
\(802\) | −0.875723 | −0.0309229 | ||||||||
\(803\) | −25.9525 | −0.915845 | ||||||||
\(804\) | 1.98023 | 0.0698375 | ||||||||
\(805\) | 0.874389 | 0.0308181 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.41751 | −0.190705 | ||||||||
\(808\) | −21.8308 | −0.768004 | ||||||||
\(809\) | 23.3097 | 0.819525 | 0.409763 | − | 0.912192i | \(-0.365612\pi\) | ||||
0.409763 | + | 0.912192i | \(0.365612\pi\) | |||||||
\(810\) | −2.79503 | −0.0982075 | ||||||||
\(811\) | −13.6662 | −0.479886 | −0.239943 | − | 0.970787i | \(-0.577129\pi\) | ||||
−0.239943 | + | 0.970787i | \(0.577129\pi\) | |||||||
\(812\) | −3.00239 | −0.105363 | ||||||||
\(813\) | 33.3637 | 1.17012 | ||||||||
\(814\) | 47.6718 | 1.67090 | ||||||||
\(815\) | 5.06053 | 0.177263 | ||||||||
\(816\) | −6.98550 | −0.244542 | ||||||||
\(817\) | −0.698063 | −0.0244221 | ||||||||
\(818\) | 1.96934 | 0.0688565 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.08757 | −0.0729012 | ||||||||
\(821\) | 11.8254 | 0.412708 | 0.206354 | − | 0.978477i | \(-0.433840\pi\) | ||||
0.206354 | + | 0.978477i | \(0.433840\pi\) | |||||||
\(822\) | −0.634406 | −0.0221274 | ||||||||
\(823\) | −12.6805 | −0.442015 | −0.221007 | − | 0.975272i | \(-0.570935\pi\) | ||||
−0.221007 | + | 0.975272i | \(0.570935\pi\) | |||||||
\(824\) | 38.0763 | 1.32645 | ||||||||
\(825\) | 32.2779 | 1.12377 | ||||||||
\(826\) | −7.58151 | −0.263794 | ||||||||
\(827\) | 19.7897 | 0.688156 | 0.344078 | − | 0.938941i | \(-0.388191\pi\) | ||||
0.344078 | + | 0.938941i | \(0.388191\pi\) | |||||||
\(828\) | 1.19980 | 0.0416961 | ||||||||
\(829\) | −15.7027 | −0.545378 | −0.272689 | − | 0.962102i | \(-0.587913\pi\) | ||||
−0.272689 | + | 0.962102i | \(0.587913\pi\) | |||||||
\(830\) | 4.23962 | 0.147160 | ||||||||
\(831\) | −11.1066 | −0.385282 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.10528 | −0.176887 | ||||||||
\(834\) | 28.0982 | 0.972962 | ||||||||
\(835\) | −4.02416 | −0.139262 | ||||||||
\(836\) | −9.31239 | −0.322076 | ||||||||
\(837\) | 12.2308 | 0.422759 | ||||||||
\(838\) | 31.8108 | 1.09889 | ||||||||
\(839\) | 18.8485 | 0.650722 | 0.325361 | − | 0.945590i | \(-0.394514\pi\) | ||||
0.325361 | + | 0.945590i | \(0.394514\pi\) | |||||||
\(840\) | 1.86811 | 0.0644558 | ||||||||
\(841\) | −20.5376 | −0.708194 | ||||||||
\(842\) | 8.95623 | 0.308652 | ||||||||
\(843\) | −3.73805 | −0.128745 | ||||||||
\(844\) | 29.2578 | 1.00709 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.45384 | −0.118745 | ||||||||
\(847\) | 6.99507 | 0.240353 | ||||||||
\(848\) | −9.52606 | −0.327126 | ||||||||
\(849\) | 22.4014 | 0.768815 | ||||||||
\(850\) | 24.3160 | 0.834031 | ||||||||
\(851\) | 25.0671 | 0.859288 | ||||||||
\(852\) | −2.83908 | −0.0972653 | ||||||||
\(853\) | −2.42144 | −0.0829084 | −0.0414542 | − | 0.999140i | \(-0.513199\pi\) | ||||
−0.0414542 | + | 0.999140i | \(0.513199\pi\) | |||||||
\(854\) | 14.3676 | 0.491650 | ||||||||
\(855\) | −0.448940 | −0.0153534 | ||||||||
\(856\) | −27.0557 | −0.924746 | ||||||||
\(857\) | 39.9800 | 1.36569 | 0.682845 | − | 0.730564i | \(-0.260743\pi\) | ||||
0.682845 | + | 0.730564i | \(0.260743\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.31038 | −0.0788292 | −0.0394146 | − | 0.999223i | \(-0.512549\pi\) | ||||
−0.0394146 | + | 0.999223i | \(0.512549\pi\) | |||||||
\(860\) | 0.134966 | 0.00460229 | ||||||||
\(861\) | −7.97852 | −0.271907 | ||||||||
\(862\) | −15.6088 | −0.531639 | ||||||||
\(863\) | 46.1232 | 1.57005 | 0.785027 | − | 0.619462i | \(-0.212649\pi\) | ||||
0.785027 | + | 0.619462i | \(0.212649\pi\) | |||||||
\(864\) | 28.3465 | 0.964368 | ||||||||
\(865\) | 6.60665 | 0.224633 | ||||||||
\(866\) | 15.6167 | 0.530678 | ||||||||
\(867\) | −14.2458 | −0.483812 | ||||||||
\(868\) | −2.27543 | −0.0772330 | ||||||||
\(869\) | 17.8536 | 0.605642 | ||||||||
\(870\) | −1.79227 | −0.0607637 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 14.7688 | 0.500133 | ||||||||
\(873\) | 7.66856 | 0.259541 | ||||||||
\(874\) | 4.59212 | 0.155331 | ||||||||
\(875\) | −3.92121 | −0.132561 | ||||||||
\(876\) | −9.92421 | −0.335308 | ||||||||
\(877\) | −22.7695 | −0.768870 | −0.384435 | − | 0.923152i | \(-0.625604\pi\) | ||||
−0.384435 | + | 0.923152i | \(0.625604\pi\) | |||||||
\(878\) | 5.28987 | 0.178524 | ||||||||
\(879\) | 11.2515 | 0.379502 | ||||||||
\(880\) | −1.47148 | −0.0496035 | ||||||||
\(881\) | 20.0984 | 0.677131 | 0.338566 | − | 0.940943i | \(-0.390058\pi\) | ||||
0.338566 | + | 0.940943i | \(0.390058\pi\) | |||||||
\(882\) | −0.521160 | −0.0175484 | ||||||||
\(883\) | −22.1650 | −0.745911 | −0.372956 | − | 0.927849i | \(-0.621656\pi\) | ||||
−0.372956 | + | 0.927849i | \(0.621656\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.82595 | 0.162222 | ||||||||
\(886\) | −25.0075 | −0.840143 | ||||||||
\(887\) | 6.35544 | 0.213395 | 0.106697 | − | 0.994292i | \(-0.465972\pi\) | ||||
0.106697 | + | 0.994292i | \(0.465972\pi\) | |||||||
\(888\) | 53.5550 | 1.79719 | ||||||||
\(889\) | 15.0587 | 0.505054 | ||||||||
\(890\) | −6.15336 | −0.206261 | ||||||||
\(891\) | −30.2467 | −1.01330 | ||||||||
\(892\) | 14.5830 | 0.488276 | ||||||||
\(893\) | 14.0960 | 0.471703 | ||||||||
\(894\) | −16.8846 | −0.564705 | ||||||||
\(895\) | −9.39788 | −0.314136 | ||||||||
\(896\) | −3.56062 | −0.118952 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −15.1871 | −0.506801 | ||||||||
\(899\) | 6.41339 | 0.213898 | ||||||||
\(900\) | −2.64687 | −0.0882291 | ||||||||
\(901\) | −55.8633 | −1.86108 | ||||||||
\(902\) | 21.1857 | 0.705406 | ||||||||
\(903\) | 0.515826 | 0.0171656 | ||||||||
\(904\) | −7.13752 | −0.237390 | ||||||||
\(905\) | −9.45193 | −0.314193 | ||||||||
\(906\) | −31.4163 | −1.04374 | ||||||||
\(907\) | −29.7539 | −0.987964 | −0.493982 | − | 0.869472i | \(-0.664459\pi\) | ||||
−0.493982 | + | 0.869472i | \(0.664459\pi\) | |||||||
\(908\) | 19.3338 | 0.641615 | ||||||||
\(909\) | −3.87673 | −0.128583 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.3649 | −1.13856 | −0.569279 | − | 0.822144i | \(-0.692778\pi\) | ||||
−0.569279 | + | 0.822144i | \(0.692778\pi\) | |||||||
\(912\) | 2.91032 | 0.0963705 | ||||||||
\(913\) | 45.8795 | 1.51839 | ||||||||
\(914\) | 29.7884 | 0.985314 | ||||||||
\(915\) | −9.14560 | −0.302344 | ||||||||
\(916\) | 3.35014 | 0.110692 | ||||||||
\(917\) | −11.6011 | −0.383101 | ||||||||
\(918\) | −27.8643 | −0.919660 | ||||||||
\(919\) | −44.0300 | −1.45241 | −0.726207 | − | 0.687476i | \(-0.758719\pi\) | ||||
−0.726207 | + | 0.687476i | \(0.758719\pi\) | |||||||
\(920\) | −2.60833 | −0.0859943 | ||||||||
\(921\) | −38.3838 | −1.26479 | ||||||||
\(922\) | 24.9331 | 0.821127 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 6.88129 | 0.226378 | ||||||||
\(925\) | −55.3001 | −1.81826 | ||||||||
\(926\) | −2.89218 | −0.0950430 | ||||||||
\(927\) | 6.76163 | 0.222081 | ||||||||
\(928\) | 14.8639 | 0.487931 | ||||||||
\(929\) | −33.8451 | −1.11042 | −0.555210 | − | 0.831710i | \(-0.687362\pi\) | ||||
−0.555210 | + | 0.831710i | \(0.687362\pi\) | |||||||
\(930\) | −1.35831 | −0.0445408 | ||||||||
\(931\) | 2.12698 | 0.0697089 | ||||||||
\(932\) | −17.9869 | −0.589180 | ||||||||
\(933\) | −37.2828 | −1.22058 | ||||||||
\(934\) | 23.7068 | 0.775710 | ||||||||
\(935\) | −8.62912 | −0.282203 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.0910 | 0.787017 | 0.393509 | − | 0.919321i | \(-0.371261\pi\) | ||||
0.393509 | + | 0.919321i | \(0.371261\pi\) | |||||||
\(938\) | 1.20099 | 0.0392136 | ||||||||
\(939\) | 23.7134 | 0.773856 | ||||||||
\(940\) | −2.72535 | −0.0888912 | ||||||||
\(941\) | 29.5369 | 0.962874 | 0.481437 | − | 0.876481i | \(-0.340115\pi\) | ||||
0.481437 | + | 0.876481i | \(0.340115\pi\) | |||||||
\(942\) | −36.2562 | −1.18129 | ||||||||
\(943\) | 11.1400 | 0.362767 | ||||||||
\(944\) | 6.70882 | 0.218354 | ||||||||
\(945\) | 2.21047 | 0.0719065 | ||||||||
\(946\) | −1.36969 | −0.0445326 | ||||||||
\(947\) | 22.6950 | 0.737490 | 0.368745 | − | 0.929531i | \(-0.379788\pi\) | ||||
0.368745 | + | 0.929531i | \(0.379788\pi\) | |||||||
\(948\) | 6.82720 | 0.221737 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −10.1306 | −0.328680 | ||||||||
\(951\) | −49.6523 | −1.61009 | ||||||||
\(952\) | 15.2292 | 0.493583 | ||||||||
\(953\) | 49.0720 | 1.58960 | 0.794799 | − | 0.606872i | \(-0.207576\pi\) | ||||
0.794799 | + | 0.606872i | \(0.207576\pi\) | |||||||
\(954\) | −5.70267 | −0.184631 | ||||||||
\(955\) | 0.870474 | 0.0281679 | ||||||||
\(956\) | 4.02315 | 0.130118 | ||||||||
\(957\) | −19.3952 | −0.626959 | ||||||||
\(958\) | 10.9272 | 0.353042 | ||||||||
\(959\) | 0.410279 | 0.0132486 | ||||||||
\(960\) | −4.23845 | −0.136795 | ||||||||
\(961\) | −26.1395 | −0.843209 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.80458 | −0.154825 | ||||||||
\(964\) | −18.2653 | −0.588286 | ||||||||
\(965\) | 7.42686 | 0.239079 | ||||||||
\(966\) | −3.39330 | −0.109178 | ||||||||
\(967\) | 23.1018 | 0.742905 | 0.371452 | − | 0.928452i | \(-0.378860\pi\) | ||||
0.371452 | + | 0.928452i | \(0.378860\pi\) | |||||||
\(968\) | −20.8666 | −0.670677 | ||||||||
\(969\) | 17.0669 | 0.548268 | ||||||||
\(970\) | −5.67472 | −0.182204 | ||||||||
\(971\) | −30.3111 | −0.972729 | −0.486365 | − | 0.873756i | \(-0.661677\pi\) | ||||
−0.486365 | + | 0.873756i | \(0.661677\pi\) | |||||||
\(972\) | 5.61105 | 0.179974 | ||||||||
\(973\) | −18.1715 | −0.582552 | ||||||||
\(974\) | −28.6803 | −0.918976 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12.7138 | −0.406959 | ||||||||
\(977\) | −2.18246 | −0.0698230 | −0.0349115 | − | 0.999390i | \(-0.511115\pi\) | ||||
−0.0349115 | + | 0.999390i | \(0.511115\pi\) | |||||||
\(978\) | −19.6387 | −0.627977 | ||||||||
\(979\) | −66.5891 | −2.12820 | ||||||||
\(980\) | −0.411236 | −0.0131365 | ||||||||
\(981\) | 2.62265 | 0.0837347 | ||||||||
\(982\) | 0.368447 | 0.0117576 | ||||||||
\(983\) | 2.60962 | 0.0832339 | 0.0416170 | − | 0.999134i | \(-0.486749\pi\) | ||||
0.0416170 | + | 0.999134i | \(0.486749\pi\) | |||||||
\(984\) | 23.8002 | 0.758723 | ||||||||
\(985\) | −5.96955 | −0.190206 | ||||||||
\(986\) | −14.6110 | −0.465310 | ||||||||
\(987\) | −10.4161 | −0.331547 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.720221 | −0.0229017 | ||||||||
\(990\) | −0.880882 | −0.0279963 | ||||||||
\(991\) | 12.5621 | 0.399048 | 0.199524 | − | 0.979893i | \(-0.436060\pi\) | ||||
0.199524 | + | 0.979893i | \(0.436060\pi\) | |||||||
\(992\) | 11.2649 | 0.357661 | ||||||||
\(993\) | −31.2732 | −0.992426 | ||||||||
\(994\) | −1.72187 | −0.0546143 | ||||||||
\(995\) | 3.42116 | 0.108458 | ||||||||
\(996\) | 17.5443 | 0.555911 | ||||||||
\(997\) | −32.9839 | −1.04461 | −0.522305 | − | 0.852759i | \(-0.674928\pi\) | ||||
−0.522305 | + | 0.852759i | \(0.674928\pi\) | |||||||
\(998\) | −0.395978 | −0.0125345 | ||||||||
\(999\) | 63.3699 | 2.00493 |
(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 | 1183.2.a.r.1.8 | yes | 12 | |
7.6 | odd | 2 | 8281.2.a.cq.1.8 | 12 | |||
13.5 | odd | 4 | 1183.2.c.j.337.9 | 24 | |||
13.8 | odd | 4 | 1183.2.c.j.337.16 | 24 | |||
13.12 | even | 2 | 1183.2.a.q.1.5 | ✓ | 12 | ||
91.90 | odd | 2 | 8281.2.a.cn.1.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1183.2.a.q.1.5 | ✓ | 12 | 13.12 | even | 2 | ||
1183.2.a.r.1.8 | yes | 12 | 1.1 | even | 1 | trivial | |
1183.2.c.j.337.9 | 24 | 13.5 | odd | 4 | |||
1183.2.c.j.337.16 | 24 | 13.8 | odd | 4 | |||
8281.2.a.cn.1.5 | 12 | 91.90 | odd | 2 | |||
8281.2.a.cq.1.8 | 12 | 7.6 | odd | 2 |