Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2013,2,Mod(1,2013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2013, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2013 = 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2013.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: | \(16.0738859269\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - x^{13} - 21 x^{12} + 20 x^{11} + 167 x^{10} - 148 x^{9} - 627 x^{8} + 497 x^{7} + 1123 x^{6} - 745 x^{5} - 802 x^{4} + 386 x^{3} + 74 x^{2} - 15 x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.93923\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2013.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.93923 | −1.37124 | −0.685621 | − | 0.727959i | \(-0.740469\pi\) | ||||
−0.685621 | + | 0.727959i | \(0.740469\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.76061 | 0.880304 | ||||||||
\(5\) | 3.07794 | 1.37650 | 0.688248 | − | 0.725475i | \(-0.258380\pi\) | ||||
0.688248 | + | 0.725475i | \(0.258380\pi\) | |||||||
\(6\) | 1.93923 | 0.791687 | ||||||||
\(7\) | −3.15900 | −1.19399 | −0.596994 | − | 0.802246i | \(-0.703638\pi\) | ||||
−0.596994 | + | 0.802246i | \(0.703638\pi\) | |||||||
\(8\) | 0.464237 | 0.164132 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −5.96883 | −1.88751 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −1.76061 | −0.508244 | ||||||||
\(13\) | −4.31016 | −1.19542 | −0.597711 | − | 0.801711i | \(-0.703923\pi\) | ||||
−0.597711 | + | 0.801711i | \(0.703923\pi\) | |||||||
\(14\) | 6.12601 | 1.63725 | ||||||||
\(15\) | −3.07794 | −0.794720 | ||||||||
\(16\) | −4.42148 | −1.10537 | ||||||||
\(17\) | −3.81369 | −0.924956 | −0.462478 | − | 0.886631i | \(-0.653040\pi\) | ||||
−0.462478 | + | 0.886631i | \(0.653040\pi\) | |||||||
\(18\) | −1.93923 | −0.457081 | ||||||||
\(19\) | −4.23281 | −0.971073 | −0.485537 | − | 0.874216i | \(-0.661376\pi\) | ||||
−0.485537 | + | 0.874216i | \(0.661376\pi\) | |||||||
\(20\) | 5.41904 | 1.21173 | ||||||||
\(21\) | 3.15900 | 0.689349 | ||||||||
\(22\) | 1.93923 | 0.413445 | ||||||||
\(23\) | 6.48918 | 1.35309 | 0.676544 | − | 0.736402i | \(-0.263477\pi\) | ||||
0.676544 | + | 0.736402i | \(0.263477\pi\) | |||||||
\(24\) | −0.464237 | −0.0947619 | ||||||||
\(25\) | 4.47371 | 0.894742 | ||||||||
\(26\) | 8.35838 | 1.63921 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −5.56175 | −1.05107 | ||||||||
\(29\) | −3.27479 | −0.608113 | −0.304056 | − | 0.952654i | \(-0.598341\pi\) | ||||
−0.304056 | + | 0.952654i | \(0.598341\pi\) | |||||||
\(30\) | 5.96883 | 1.08975 | ||||||||
\(31\) | 10.0842 | 1.81117 | 0.905585 | − | 0.424164i | \(-0.139432\pi\) | ||||
0.905585 | + | 0.424164i | \(0.139432\pi\) | |||||||
\(32\) | 7.64578 | 1.35160 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 7.39562 | 1.26834 | ||||||||
\(35\) | −9.72319 | −1.64352 | ||||||||
\(36\) | 1.76061 | 0.293435 | ||||||||
\(37\) | −1.85262 | −0.304569 | −0.152284 | − | 0.988337i | \(-0.548663\pi\) | ||||
−0.152284 | + | 0.988337i | \(0.548663\pi\) | |||||||
\(38\) | 8.20839 | 1.33158 | ||||||||
\(39\) | 4.31016 | 0.690178 | ||||||||
\(40\) | 1.42889 | 0.225928 | ||||||||
\(41\) | −10.7788 | −1.68337 | −0.841685 | − | 0.539969i | \(-0.818436\pi\) | ||||
−0.841685 | + | 0.539969i | \(0.818436\pi\) | |||||||
\(42\) | −6.12601 | −0.945264 | ||||||||
\(43\) | 10.4003 | 1.58603 | 0.793013 | − | 0.609205i | \(-0.208511\pi\) | ||||
0.793013 | + | 0.609205i | \(0.208511\pi\) | |||||||
\(44\) | −1.76061 | −0.265422 | ||||||||
\(45\) | 3.07794 | 0.458832 | ||||||||
\(46\) | −12.5840 | −1.85541 | ||||||||
\(47\) | 10.3730 | 1.51305 | 0.756527 | − | 0.653962i | \(-0.226894\pi\) | ||||
0.756527 | + | 0.653962i | \(0.226894\pi\) | |||||||
\(48\) | 4.42148 | 0.638185 | ||||||||
\(49\) | 2.97925 | 0.425607 | ||||||||
\(50\) | −8.67555 | −1.22691 | ||||||||
\(51\) | 3.81369 | 0.534024 | ||||||||
\(52\) | −7.58850 | −1.05234 | ||||||||
\(53\) | 8.28262 | 1.13771 | 0.568853 | − | 0.822439i | \(-0.307387\pi\) | ||||
0.568853 | + | 0.822439i | \(0.307387\pi\) | |||||||
\(54\) | 1.93923 | 0.263896 | ||||||||
\(55\) | −3.07794 | −0.415029 | ||||||||
\(56\) | −1.46652 | −0.195972 | ||||||||
\(57\) | 4.23281 | 0.560649 | ||||||||
\(58\) | 6.35056 | 0.833869 | ||||||||
\(59\) | −10.0151 | −1.30385 | −0.651925 | − | 0.758283i | \(-0.726038\pi\) | ||||
−0.651925 | + | 0.758283i | \(0.726038\pi\) | |||||||
\(60\) | −5.41904 | −0.699595 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | −19.5555 | −2.48355 | ||||||||
\(63\) | −3.15900 | −0.397996 | ||||||||
\(64\) | −5.98396 | −0.747995 | ||||||||
\(65\) | −13.2664 | −1.64550 | ||||||||
\(66\) | −1.93923 | −0.238703 | ||||||||
\(67\) | −5.80576 | −0.709287 | −0.354643 | − | 0.935002i | \(-0.615398\pi\) | ||||
−0.354643 | + | 0.935002i | \(0.615398\pi\) | |||||||
\(68\) | −6.71441 | −0.814242 | ||||||||
\(69\) | −6.48918 | −0.781205 | ||||||||
\(70\) | 18.8555 | 2.25366 | ||||||||
\(71\) | −3.40168 | −0.403705 | −0.201853 | − | 0.979416i | \(-0.564696\pi\) | ||||
−0.201853 | + | 0.979416i | \(0.564696\pi\) | |||||||
\(72\) | 0.464237 | 0.0547108 | ||||||||
\(73\) | 11.2828 | 1.32055 | 0.660276 | − | 0.751023i | \(-0.270439\pi\) | ||||
0.660276 | + | 0.751023i | \(0.270439\pi\) | |||||||
\(74\) | 3.59265 | 0.417638 | ||||||||
\(75\) | −4.47371 | −0.516580 | ||||||||
\(76\) | −7.45232 | −0.854840 | ||||||||
\(77\) | 3.15900 | 0.360001 | ||||||||
\(78\) | −8.35838 | −0.946400 | ||||||||
\(79\) | 4.26886 | 0.480284 | 0.240142 | − | 0.970738i | \(-0.422806\pi\) | ||||
0.240142 | + | 0.970738i | \(0.422806\pi\) | |||||||
\(80\) | −13.6090 | −1.52154 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 20.9026 | 2.30831 | ||||||||
\(83\) | 17.4095 | 1.91094 | 0.955469 | − | 0.295092i | \(-0.0953505\pi\) | ||||
0.955469 | + | 0.295092i | \(0.0953505\pi\) | |||||||
\(84\) | 5.56175 | 0.606837 | ||||||||
\(85\) | −11.7383 | −1.27320 | ||||||||
\(86\) | −20.1685 | −2.17483 | ||||||||
\(87\) | 3.27479 | 0.351094 | ||||||||
\(88\) | −0.464237 | −0.0494878 | ||||||||
\(89\) | −9.75884 | −1.03444 | −0.517218 | − | 0.855854i | \(-0.673032\pi\) | ||||
−0.517218 | + | 0.855854i | \(0.673032\pi\) | |||||||
\(90\) | −5.96883 | −0.629170 | ||||||||
\(91\) | 13.6158 | 1.42732 | ||||||||
\(92\) | 11.4249 | 1.19113 | ||||||||
\(93\) | −10.0842 | −1.04568 | ||||||||
\(94\) | −20.1156 | −2.07476 | ||||||||
\(95\) | −13.0283 | −1.33668 | ||||||||
\(96\) | −7.64578 | −0.780344 | ||||||||
\(97\) | 0.814992 | 0.0827499 | 0.0413749 | − | 0.999144i | \(-0.486826\pi\) | ||||
0.0413749 | + | 0.999144i | \(0.486826\pi\) | |||||||
\(98\) | −5.77745 | −0.583610 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 7.87645 | 0.787645 | ||||||||
\(101\) | 8.64218 | 0.859929 | 0.429965 | − | 0.902846i | \(-0.358526\pi\) | ||||
0.429965 | + | 0.902846i | \(0.358526\pi\) | |||||||
\(102\) | −7.39562 | −0.732275 | ||||||||
\(103\) | 1.53886 | 0.151629 | 0.0758143 | − | 0.997122i | \(-0.475844\pi\) | ||||
0.0758143 | + | 0.997122i | \(0.475844\pi\) | |||||||
\(104\) | −2.00093 | −0.196208 | ||||||||
\(105\) | 9.72319 | 0.948887 | ||||||||
\(106\) | −16.0619 | −1.56007 | ||||||||
\(107\) | −1.27301 | −0.123067 | −0.0615333 | − | 0.998105i | \(-0.519599\pi\) | ||||
−0.0615333 | + | 0.998105i | \(0.519599\pi\) | |||||||
\(108\) | −1.76061 | −0.169415 | ||||||||
\(109\) | 10.8977 | 1.04381 | 0.521905 | − | 0.853004i | \(-0.325222\pi\) | ||||
0.521905 | + | 0.853004i | \(0.325222\pi\) | |||||||
\(110\) | 5.96883 | 0.569105 | ||||||||
\(111\) | 1.85262 | 0.175843 | ||||||||
\(112\) | 13.9674 | 1.31980 | ||||||||
\(113\) | −12.6330 | −1.18841 | −0.594206 | − | 0.804313i | \(-0.702534\pi\) | ||||
−0.594206 | + | 0.804313i | \(0.702534\pi\) | |||||||
\(114\) | −8.20839 | −0.768786 | ||||||||
\(115\) | 19.9733 | 1.86252 | ||||||||
\(116\) | −5.76561 | −0.535324 | ||||||||
\(117\) | −4.31016 | −0.398474 | ||||||||
\(118\) | 19.4215 | 1.78789 | ||||||||
\(119\) | 12.0474 | 1.10439 | ||||||||
\(120\) | −1.42889 | −0.130439 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −1.93923 | −0.175570 | ||||||||
\(123\) | 10.7788 | 0.971894 | ||||||||
\(124\) | 17.7543 | 1.59438 | ||||||||
\(125\) | −1.61989 | −0.144887 | ||||||||
\(126\) | 6.12601 | 0.545749 | ||||||||
\(127\) | 12.4848 | 1.10784 | 0.553921 | − | 0.832569i | \(-0.313131\pi\) | ||||
0.553921 | + | 0.832569i | \(0.313131\pi\) | |||||||
\(128\) | −3.68729 | −0.325913 | ||||||||
\(129\) | −10.4003 | −0.915693 | ||||||||
\(130\) | 25.7266 | 2.25637 | ||||||||
\(131\) | 0.0498953 | 0.00435938 | 0.00217969 | − | 0.999998i | \(-0.499306\pi\) | ||||
0.00217969 | + | 0.999998i | \(0.499306\pi\) | |||||||
\(132\) | 1.76061 | 0.153241 | ||||||||
\(133\) | 13.3714 | 1.15945 | ||||||||
\(134\) | 11.2587 | 0.972604 | ||||||||
\(135\) | −3.07794 | −0.264907 | ||||||||
\(136\) | −1.77045 | −0.151815 | ||||||||
\(137\) | 0.243742 | 0.0208243 | 0.0104121 | − | 0.999946i | \(-0.496686\pi\) | ||||
0.0104121 | + | 0.999946i | \(0.496686\pi\) | |||||||
\(138\) | 12.5840 | 1.07122 | ||||||||
\(139\) | −21.1871 | −1.79706 | −0.898531 | − | 0.438910i | \(-0.855365\pi\) | ||||
−0.898531 | + | 0.438910i | \(0.855365\pi\) | |||||||
\(140\) | −17.1187 | −1.44680 | ||||||||
\(141\) | −10.3730 | −0.873562 | ||||||||
\(142\) | 6.59664 | 0.553578 | ||||||||
\(143\) | 4.31016 | 0.360434 | ||||||||
\(144\) | −4.42148 | −0.368456 | ||||||||
\(145\) | −10.0796 | −0.837065 | ||||||||
\(146\) | −21.8799 | −1.81080 | ||||||||
\(147\) | −2.97925 | −0.245724 | ||||||||
\(148\) | −3.26174 | −0.268113 | ||||||||
\(149\) | 13.4964 | 1.10567 | 0.552834 | − | 0.833291i | \(-0.313546\pi\) | ||||
0.552834 | + | 0.833291i | \(0.313546\pi\) | |||||||
\(150\) | 8.67555 | 0.708355 | ||||||||
\(151\) | 2.14503 | 0.174560 | 0.0872801 | − | 0.996184i | \(-0.472182\pi\) | ||||
0.0872801 | + | 0.996184i | \(0.472182\pi\) | |||||||
\(152\) | −1.96503 | −0.159385 | ||||||||
\(153\) | −3.81369 | −0.308319 | ||||||||
\(154\) | −6.12601 | −0.493648 | ||||||||
\(155\) | 31.0385 | 2.49307 | ||||||||
\(156\) | 7.58850 | 0.607566 | ||||||||
\(157\) | −2.78006 | −0.221873 | −0.110936 | − | 0.993828i | \(-0.535385\pi\) | ||||
−0.110936 | + | 0.993828i | \(0.535385\pi\) | |||||||
\(158\) | −8.27830 | −0.658586 | ||||||||
\(159\) | −8.28262 | −0.656855 | ||||||||
\(160\) | 23.5332 | 1.86047 | ||||||||
\(161\) | −20.4993 | −1.61557 | ||||||||
\(162\) | −1.93923 | −0.152360 | ||||||||
\(163\) | 16.8129 | 1.31689 | 0.658444 | − | 0.752630i | \(-0.271215\pi\) | ||||
0.658444 | + | 0.752630i | \(0.271215\pi\) | |||||||
\(164\) | −18.9773 | −1.48188 | ||||||||
\(165\) | 3.07794 | 0.239617 | ||||||||
\(166\) | −33.7609 | −2.62036 | ||||||||
\(167\) | 14.1771 | 1.09706 | 0.548529 | − | 0.836132i | \(-0.315188\pi\) | ||||
0.548529 | + | 0.836132i | \(0.315188\pi\) | |||||||
\(168\) | 1.46652 | 0.113145 | ||||||||
\(169\) | 5.57746 | 0.429036 | ||||||||
\(170\) | 22.7633 | 1.74586 | ||||||||
\(171\) | −4.23281 | −0.323691 | ||||||||
\(172\) | 18.3108 | 1.39618 | ||||||||
\(173\) | 19.2019 | 1.45989 | 0.729945 | − | 0.683505i | \(-0.239545\pi\) | ||||
0.729945 | + | 0.683505i | \(0.239545\pi\) | |||||||
\(174\) | −6.35056 | −0.481435 | ||||||||
\(175\) | −14.1324 | −1.06831 | ||||||||
\(176\) | 4.42148 | 0.333281 | ||||||||
\(177\) | 10.0151 | 0.752778 | ||||||||
\(178\) | 18.9246 | 1.41846 | ||||||||
\(179\) | −6.27478 | −0.468999 | −0.234500 | − | 0.972116i | \(-0.575345\pi\) | ||||
−0.234500 | + | 0.972116i | \(0.575345\pi\) | |||||||
\(180\) | 5.41904 | 0.403912 | ||||||||
\(181\) | 14.9701 | 1.11272 | 0.556359 | − | 0.830942i | \(-0.312198\pi\) | ||||
0.556359 | + | 0.830942i | \(0.312198\pi\) | |||||||
\(182\) | −26.4041 | −1.95720 | ||||||||
\(183\) | −1.00000 | −0.0739221 | ||||||||
\(184\) | 3.01251 | 0.222085 | ||||||||
\(185\) | −5.70225 | −0.419238 | ||||||||
\(186\) | 19.5555 | 1.43388 | ||||||||
\(187\) | 3.81369 | 0.278885 | ||||||||
\(188\) | 18.2627 | 1.33195 | ||||||||
\(189\) | 3.15900 | 0.229783 | ||||||||
\(190\) | 25.2649 | 1.83291 | ||||||||
\(191\) | −1.11274 | −0.0805152 | −0.0402576 | − | 0.999189i | \(-0.512818\pi\) | ||||
−0.0402576 | + | 0.999189i | \(0.512818\pi\) | |||||||
\(192\) | 5.98396 | 0.431855 | ||||||||
\(193\) | −16.4747 | −1.18587 | −0.592937 | − | 0.805249i | \(-0.702032\pi\) | ||||
−0.592937 | + | 0.805249i | \(0.702032\pi\) | |||||||
\(194\) | −1.58046 | −0.113470 | ||||||||
\(195\) | 13.2664 | 0.950027 | ||||||||
\(196\) | 5.24529 | 0.374664 | ||||||||
\(197\) | 25.4239 | 1.81138 | 0.905690 | − | 0.423941i | \(-0.139354\pi\) | ||||
0.905690 | + | 0.423941i | \(0.139354\pi\) | |||||||
\(198\) | 1.93923 | 0.137815 | ||||||||
\(199\) | −8.05688 | −0.571137 | −0.285569 | − | 0.958358i | \(-0.592182\pi\) | ||||
−0.285569 | + | 0.958358i | \(0.592182\pi\) | |||||||
\(200\) | 2.07686 | 0.146856 | ||||||||
\(201\) | 5.80576 | 0.409507 | ||||||||
\(202\) | −16.7592 | −1.17917 | ||||||||
\(203\) | 10.3450 | 0.726079 | ||||||||
\(204\) | 6.71441 | 0.470103 | ||||||||
\(205\) | −33.1766 | −2.31715 | ||||||||
\(206\) | −2.98420 | −0.207919 | ||||||||
\(207\) | 6.48918 | 0.451029 | ||||||||
\(208\) | 19.0573 | 1.32138 | ||||||||
\(209\) | 4.23281 | 0.292790 | ||||||||
\(210\) | −18.8555 | −1.30115 | ||||||||
\(211\) | 21.8405 | 1.50356 | 0.751780 | − | 0.659414i | \(-0.229196\pi\) | ||||
0.751780 | + | 0.659414i | \(0.229196\pi\) | |||||||
\(212\) | 14.5825 | 1.00153 | ||||||||
\(213\) | 3.40168 | 0.233079 | ||||||||
\(214\) | 2.46866 | 0.168754 | ||||||||
\(215\) | 32.0114 | 2.18316 | ||||||||
\(216\) | −0.464237 | −0.0315873 | ||||||||
\(217\) | −31.8559 | −2.16252 | ||||||||
\(218\) | −21.1331 | −1.43132 | ||||||||
\(219\) | −11.2828 | −0.762422 | ||||||||
\(220\) | −5.41904 | −0.365352 | ||||||||
\(221\) | 16.4376 | 1.10571 | ||||||||
\(222\) | −3.59265 | −0.241123 | ||||||||
\(223\) | 12.6761 | 0.848852 | 0.424426 | − | 0.905463i | \(-0.360476\pi\) | ||||
0.424426 | + | 0.905463i | \(0.360476\pi\) | |||||||
\(224\) | −24.1530 | −1.61379 | ||||||||
\(225\) | 4.47371 | 0.298247 | ||||||||
\(226\) | 24.4983 | 1.62960 | ||||||||
\(227\) | 18.0164 | 1.19579 | 0.597897 | − | 0.801573i | \(-0.296003\pi\) | ||||
0.597897 | + | 0.801573i | \(0.296003\pi\) | |||||||
\(228\) | 7.45232 | 0.493542 | ||||||||
\(229\) | 21.1854 | 1.39997 | 0.699984 | − | 0.714159i | \(-0.253191\pi\) | ||||
0.699984 | + | 0.714159i | \(0.253191\pi\) | |||||||
\(230\) | −38.7328 | −2.55397 | ||||||||
\(231\) | −3.15900 | −0.207847 | ||||||||
\(232\) | −1.52028 | −0.0998110 | ||||||||
\(233\) | −28.3068 | −1.85444 | −0.927221 | − | 0.374516i | \(-0.877809\pi\) | ||||
−0.927221 | + | 0.374516i | \(0.877809\pi\) | |||||||
\(234\) | 8.35838 | 0.546405 | ||||||||
\(235\) | 31.9274 | 2.08271 | ||||||||
\(236\) | −17.6326 | −1.14778 | ||||||||
\(237\) | −4.26886 | −0.277292 | ||||||||
\(238\) | −23.3627 | −1.51438 | ||||||||
\(239\) | 4.89918 | 0.316902 | 0.158451 | − | 0.987367i | \(-0.449350\pi\) | ||||
0.158451 | + | 0.987367i | \(0.449350\pi\) | |||||||
\(240\) | 13.6090 | 0.878459 | ||||||||
\(241\) | 27.3485 | 1.76167 | 0.880836 | − | 0.473422i | \(-0.156981\pi\) | ||||
0.880836 | + | 0.473422i | \(0.156981\pi\) | |||||||
\(242\) | −1.93923 | −0.124658 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 1.76061 | 0.112711 | ||||||||
\(245\) | 9.16995 | 0.585847 | ||||||||
\(246\) | −20.9026 | −1.33270 | ||||||||
\(247\) | 18.2441 | 1.16084 | ||||||||
\(248\) | 4.68144 | 0.297272 | ||||||||
\(249\) | −17.4095 | −1.10328 | ||||||||
\(250\) | 3.14134 | 0.198676 | ||||||||
\(251\) | 2.95590 | 0.186575 | 0.0932874 | − | 0.995639i | \(-0.470262\pi\) | ||||
0.0932874 | + | 0.995639i | \(0.470262\pi\) | |||||||
\(252\) | −5.56175 | −0.350357 | ||||||||
\(253\) | −6.48918 | −0.407971 | ||||||||
\(254\) | −24.2108 | −1.51912 | ||||||||
\(255\) | 11.7383 | 0.735082 | ||||||||
\(256\) | 19.1184 | 1.19490 | ||||||||
\(257\) | 8.57140 | 0.534669 | 0.267335 | − | 0.963604i | \(-0.413857\pi\) | ||||
0.267335 | + | 0.963604i | \(0.413857\pi\) | |||||||
\(258\) | 20.1685 | 1.25564 | ||||||||
\(259\) | 5.85242 | 0.363652 | ||||||||
\(260\) | −23.3569 | −1.44854 | ||||||||
\(261\) | −3.27479 | −0.202704 | ||||||||
\(262\) | −0.0967585 | −0.00597776 | ||||||||
\(263\) | −1.84001 | −0.113460 | −0.0567300 | − | 0.998390i | \(-0.518067\pi\) | ||||
−0.0567300 | + | 0.998390i | \(0.518067\pi\) | |||||||
\(264\) | 0.464237 | 0.0285718 | ||||||||
\(265\) | 25.4934 | 1.56605 | ||||||||
\(266\) | −25.9303 | −1.58989 | ||||||||
\(267\) | 9.75884 | 0.597232 | ||||||||
\(268\) | −10.2217 | −0.624388 | ||||||||
\(269\) | −8.65480 | −0.527692 | −0.263846 | − | 0.964565i | \(-0.584991\pi\) | ||||
−0.263846 | + | 0.964565i | \(0.584991\pi\) | |||||||
\(270\) | 5.96883 | 0.363251 | ||||||||
\(271\) | 18.4447 | 1.12044 | 0.560219 | − | 0.828344i | \(-0.310717\pi\) | ||||
0.560219 | + | 0.828344i | \(0.310717\pi\) | |||||||
\(272\) | 16.8621 | 1.02242 | ||||||||
\(273\) | −13.6158 | −0.824064 | ||||||||
\(274\) | −0.472671 | −0.0285551 | ||||||||
\(275\) | −4.47371 | −0.269775 | ||||||||
\(276\) | −11.4249 | −0.687698 | ||||||||
\(277\) | 8.09606 | 0.486445 | 0.243223 | − | 0.969971i | \(-0.421795\pi\) | ||||
0.243223 | + | 0.969971i | \(0.421795\pi\) | |||||||
\(278\) | 41.0865 | 2.46421 | ||||||||
\(279\) | 10.0842 | 0.603724 | ||||||||
\(280\) | −4.51386 | −0.269755 | ||||||||
\(281\) | −17.8764 | −1.06642 | −0.533208 | − | 0.845984i | \(-0.679014\pi\) | ||||
−0.533208 | + | 0.845984i | \(0.679014\pi\) | |||||||
\(282\) | 20.1156 | 1.19787 | ||||||||
\(283\) | 17.7034 | 1.05236 | 0.526179 | − | 0.850374i | \(-0.323624\pi\) | ||||
0.526179 | + | 0.850374i | \(0.323624\pi\) | |||||||
\(284\) | −5.98903 | −0.355383 | ||||||||
\(285\) | 13.0283 | 0.771732 | ||||||||
\(286\) | −8.35838 | −0.494241 | ||||||||
\(287\) | 34.0503 | 2.00992 | ||||||||
\(288\) | 7.64578 | 0.450532 | ||||||||
\(289\) | −2.45576 | −0.144456 | ||||||||
\(290\) | 19.5466 | 1.14782 | ||||||||
\(291\) | −0.814992 | −0.0477757 | ||||||||
\(292\) | 19.8646 | 1.16249 | ||||||||
\(293\) | −13.3362 | −0.779109 | −0.389554 | − | 0.921003i | \(-0.627371\pi\) | ||||
−0.389554 | + | 0.921003i | \(0.627371\pi\) | |||||||
\(294\) | 5.77745 | 0.336948 | ||||||||
\(295\) | −30.8258 | −1.79474 | ||||||||
\(296\) | −0.860054 | −0.0499896 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | −26.1726 | −1.51614 | ||||||||
\(299\) | −27.9694 | −1.61751 | ||||||||
\(300\) | −7.87645 | −0.454747 | ||||||||
\(301\) | −32.8544 | −1.89370 | ||||||||
\(302\) | −4.15971 | −0.239364 | ||||||||
\(303\) | −8.64218 | −0.496480 | ||||||||
\(304\) | 18.7153 | 1.07339 | ||||||||
\(305\) | 3.07794 | 0.176242 | ||||||||
\(306\) | 7.39562 | 0.422779 | ||||||||
\(307\) | −32.1020 | −1.83216 | −0.916080 | − | 0.400996i | \(-0.868664\pi\) | ||||
−0.916080 | + | 0.400996i | \(0.868664\pi\) | |||||||
\(308\) | 5.56175 | 0.316910 | ||||||||
\(309\) | −1.53886 | −0.0875428 | ||||||||
\(310\) | −60.1907 | −3.41860 | ||||||||
\(311\) | 19.1427 | 1.08548 | 0.542742 | − | 0.839899i | \(-0.317386\pi\) | ||||
0.542742 | + | 0.839899i | \(0.317386\pi\) | |||||||
\(312\) | 2.00093 | 0.113281 | ||||||||
\(313\) | 7.12592 | 0.402781 | 0.201390 | − | 0.979511i | \(-0.435454\pi\) | ||||
0.201390 | + | 0.979511i | \(0.435454\pi\) | |||||||
\(314\) | 5.39117 | 0.304241 | ||||||||
\(315\) | −9.72319 | −0.547840 | ||||||||
\(316\) | 7.51579 | 0.422796 | ||||||||
\(317\) | −30.7643 | −1.72789 | −0.863947 | − | 0.503584i | \(-0.832015\pi\) | ||||
−0.863947 | + | 0.503584i | \(0.832015\pi\) | |||||||
\(318\) | 16.0619 | 0.900707 | ||||||||
\(319\) | 3.27479 | 0.183353 | ||||||||
\(320\) | −18.4183 | −1.02961 | ||||||||
\(321\) | 1.27301 | 0.0710525 | ||||||||
\(322\) | 39.7528 | 2.21534 | ||||||||
\(323\) | 16.1426 | 0.898200 | ||||||||
\(324\) | 1.76061 | 0.0978115 | ||||||||
\(325\) | −19.2824 | −1.06959 | ||||||||
\(326\) | −32.6040 | −1.80577 | ||||||||
\(327\) | −10.8977 | −0.602644 | ||||||||
\(328\) | −5.00393 | −0.276296 | ||||||||
\(329\) | −32.7682 | −1.80657 | ||||||||
\(330\) | −5.96883 | −0.328573 | ||||||||
\(331\) | −1.20244 | −0.0660920 | −0.0330460 | − | 0.999454i | \(-0.510521\pi\) | ||||
−0.0330460 | + | 0.999454i | \(0.510521\pi\) | |||||||
\(332\) | 30.6512 | 1.68221 | ||||||||
\(333\) | −1.85262 | −0.101523 | ||||||||
\(334\) | −27.4926 | −1.50433 | ||||||||
\(335\) | −17.8698 | −0.976331 | ||||||||
\(336\) | −13.9674 | −0.761985 | ||||||||
\(337\) | −27.8849 | −1.51898 | −0.759492 | − | 0.650516i | \(-0.774553\pi\) | ||||
−0.759492 | + | 0.650516i | \(0.774553\pi\) | |||||||
\(338\) | −10.8160 | −0.588312 | ||||||||
\(339\) | 12.6330 | 0.686131 | ||||||||
\(340\) | −20.6666 | −1.12080 | ||||||||
\(341\) | −10.0842 | −0.546089 | ||||||||
\(342\) | 8.20839 | 0.443859 | ||||||||
\(343\) | 12.7015 | 0.685818 | ||||||||
\(344\) | 4.82818 | 0.260318 | ||||||||
\(345\) | −19.9733 | −1.07533 | ||||||||
\(346\) | −37.2368 | −2.00186 | ||||||||
\(347\) | 8.66808 | 0.465327 | 0.232663 | − | 0.972557i | \(-0.425256\pi\) | ||||
0.232663 | + | 0.972557i | \(0.425256\pi\) | |||||||
\(348\) | 5.76561 | 0.309069 | ||||||||
\(349\) | −3.27364 | −0.175234 | −0.0876170 | − | 0.996154i | \(-0.527925\pi\) | ||||
−0.0876170 | + | 0.996154i | \(0.527925\pi\) | |||||||
\(350\) | 27.4060 | 1.46491 | ||||||||
\(351\) | 4.31016 | 0.230059 | ||||||||
\(352\) | −7.64578 | −0.407521 | ||||||||
\(353\) | 23.4498 | 1.24811 | 0.624054 | − | 0.781381i | \(-0.285485\pi\) | ||||
0.624054 | + | 0.781381i | \(0.285485\pi\) | |||||||
\(354\) | −19.4215 | −1.03224 | ||||||||
\(355\) | −10.4702 | −0.555699 | ||||||||
\(356\) | −17.1815 | −0.910617 | ||||||||
\(357\) | −12.0474 | −0.637618 | ||||||||
\(358\) | 12.1682 | 0.643111 | ||||||||
\(359\) | −26.9502 | −1.42238 | −0.711188 | − | 0.703001i | \(-0.751843\pi\) | ||||
−0.711188 | + | 0.703001i | \(0.751843\pi\) | |||||||
\(360\) | 1.42889 | 0.0753092 | ||||||||
\(361\) | −1.08332 | −0.0570167 | ||||||||
\(362\) | −29.0304 | −1.52580 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 23.9720 | 1.25648 | ||||||||
\(365\) | 34.7278 | 1.81774 | ||||||||
\(366\) | 1.93923 | 0.101365 | ||||||||
\(367\) | −6.45575 | −0.336987 | −0.168494 | − | 0.985703i | \(-0.553890\pi\) | ||||
−0.168494 | + | 0.985703i | \(0.553890\pi\) | |||||||
\(368\) | −28.6918 | −1.49566 | ||||||||
\(369\) | −10.7788 | −0.561123 | ||||||||
\(370\) | 11.0580 | 0.574877 | ||||||||
\(371\) | −26.1648 | −1.35841 | ||||||||
\(372\) | −17.7543 | −0.920516 | ||||||||
\(373\) | 9.95114 | 0.515250 | 0.257625 | − | 0.966245i | \(-0.417060\pi\) | ||||
0.257625 | + | 0.966245i | \(0.417060\pi\) | |||||||
\(374\) | −7.39562 | −0.382418 | ||||||||
\(375\) | 1.61989 | 0.0836507 | ||||||||
\(376\) | 4.81552 | 0.248341 | ||||||||
\(377\) | 14.1148 | 0.726952 | ||||||||
\(378\) | −6.12601 | −0.315088 | ||||||||
\(379\) | −5.99448 | −0.307916 | −0.153958 | − | 0.988077i | \(-0.549202\pi\) | ||||
−0.153958 | + | 0.988077i | \(0.549202\pi\) | |||||||
\(380\) | −22.9378 | −1.17668 | ||||||||
\(381\) | −12.4848 | −0.639613 | ||||||||
\(382\) | 2.15786 | 0.110406 | ||||||||
\(383\) | 2.43976 | 0.124666 | 0.0623329 | − | 0.998055i | \(-0.480146\pi\) | ||||
0.0623329 | + | 0.998055i | \(0.480146\pi\) | |||||||
\(384\) | 3.68729 | 0.188166 | ||||||||
\(385\) | 9.72319 | 0.495540 | ||||||||
\(386\) | 31.9482 | 1.62612 | ||||||||
\(387\) | 10.4003 | 0.528675 | ||||||||
\(388\) | 1.43488 | 0.0728450 | ||||||||
\(389\) | −1.63009 | −0.0826491 | −0.0413245 | − | 0.999146i | \(-0.513158\pi\) | ||||
−0.0413245 | + | 0.999146i | \(0.513158\pi\) | |||||||
\(390\) | −25.7266 | −1.30272 | ||||||||
\(391\) | −24.7477 | −1.25155 | ||||||||
\(392\) | 1.38308 | 0.0698559 | ||||||||
\(393\) | −0.0498953 | −0.00251689 | ||||||||
\(394\) | −49.3028 | −2.48384 | ||||||||
\(395\) | 13.1393 | 0.661110 | ||||||||
\(396\) | −1.76061 | −0.0884739 | ||||||||
\(397\) | −29.1550 | −1.46325 | −0.731624 | − | 0.681709i | \(-0.761237\pi\) | ||||
−0.731624 | + | 0.681709i | \(0.761237\pi\) | |||||||
\(398\) | 15.6241 | 0.783167 | ||||||||
\(399\) | −13.3714 | −0.669409 | ||||||||
\(400\) | −19.7804 | −0.989020 | ||||||||
\(401\) | −28.8479 | −1.44059 | −0.720297 | − | 0.693666i | \(-0.755995\pi\) | ||||
−0.720297 | + | 0.693666i | \(0.755995\pi\) | |||||||
\(402\) | −11.2587 | −0.561533 | ||||||||
\(403\) | −43.4644 | −2.16512 | ||||||||
\(404\) | 15.2155 | 0.756999 | ||||||||
\(405\) | 3.07794 | 0.152944 | ||||||||
\(406\) | −20.0614 | −0.995630 | ||||||||
\(407\) | 1.85262 | 0.0918310 | ||||||||
\(408\) | 1.77045 | 0.0876506 | ||||||||
\(409\) | 19.7104 | 0.974619 | 0.487309 | − | 0.873229i | \(-0.337978\pi\) | ||||
0.487309 | + | 0.873229i | \(0.337978\pi\) | |||||||
\(410\) | 64.3370 | 3.17738 | ||||||||
\(411\) | −0.243742 | −0.0120229 | ||||||||
\(412\) | 2.70933 | 0.133479 | ||||||||
\(413\) | 31.6375 | 1.55678 | ||||||||
\(414\) | −12.5840 | −0.618470 | ||||||||
\(415\) | 53.5853 | 2.63040 | ||||||||
\(416\) | −32.9545 | −1.61573 | ||||||||
\(417\) | 21.1871 | 1.03753 | ||||||||
\(418\) | −8.20839 | −0.401485 | ||||||||
\(419\) | −6.33286 | −0.309381 | −0.154690 | − | 0.987963i | \(-0.549438\pi\) | ||||
−0.154690 | + | 0.987963i | \(0.549438\pi\) | |||||||
\(420\) | 17.1187 | 0.835309 | ||||||||
\(421\) | 30.9731 | 1.50954 | 0.754768 | − | 0.655992i | \(-0.227750\pi\) | ||||
0.754768 | + | 0.655992i | \(0.227750\pi\) | |||||||
\(422\) | −42.3537 | −2.06174 | ||||||||
\(423\) | 10.3730 | 0.504351 | ||||||||
\(424\) | 3.84510 | 0.186734 | ||||||||
\(425\) | −17.0613 | −0.827597 | ||||||||
\(426\) | −6.59664 | −0.319608 | ||||||||
\(427\) | −3.15900 | −0.152874 | ||||||||
\(428\) | −2.24127 | −0.108336 | ||||||||
\(429\) | −4.31016 | −0.208096 | ||||||||
\(430\) | −62.0774 | −2.99364 | ||||||||
\(431\) | −0.711680 | −0.0342804 | −0.0171402 | − | 0.999853i | \(-0.505456\pi\) | ||||
−0.0171402 | + | 0.999853i | \(0.505456\pi\) | |||||||
\(432\) | 4.42148 | 0.212728 | ||||||||
\(433\) | 38.6317 | 1.85652 | 0.928259 | − | 0.371934i | \(-0.121305\pi\) | ||||
0.928259 | + | 0.371934i | \(0.121305\pi\) | |||||||
\(434\) | 61.7758 | 2.96533 | ||||||||
\(435\) | 10.0796 | 0.483280 | ||||||||
\(436\) | 19.1866 | 0.918870 | ||||||||
\(437\) | −27.4675 | −1.31395 | ||||||||
\(438\) | 21.8799 | 1.04546 | ||||||||
\(439\) | 10.1209 | 0.483043 | 0.241522 | − | 0.970395i | \(-0.422353\pi\) | ||||
0.241522 | + | 0.970395i | \(0.422353\pi\) | |||||||
\(440\) | −1.42889 | −0.0681197 | ||||||||
\(441\) | 2.97925 | 0.141869 | ||||||||
\(442\) | −31.8763 | −1.51620 | ||||||||
\(443\) | −27.6987 | −1.31600 | −0.658002 | − | 0.753016i | \(-0.728598\pi\) | ||||
−0.658002 | + | 0.753016i | \(0.728598\pi\) | |||||||
\(444\) | 3.26174 | 0.154795 | ||||||||
\(445\) | −30.0371 | −1.42390 | ||||||||
\(446\) | −24.5818 | −1.16398 | ||||||||
\(447\) | −13.4964 | −0.638358 | ||||||||
\(448\) | 18.9033 | 0.893097 | ||||||||
\(449\) | 20.3574 | 0.960727 | 0.480364 | − | 0.877069i | \(-0.340505\pi\) | ||||
0.480364 | + | 0.877069i | \(0.340505\pi\) | |||||||
\(450\) | −8.67555 | −0.408969 | ||||||||
\(451\) | 10.7788 | 0.507555 | ||||||||
\(452\) | −22.2418 | −1.04616 | ||||||||
\(453\) | −2.14503 | −0.100782 | ||||||||
\(454\) | −34.9380 | −1.63972 | ||||||||
\(455\) | 41.9085 | 1.96470 | ||||||||
\(456\) | 1.96503 | 0.0920207 | ||||||||
\(457\) | −29.6278 | −1.38593 | −0.692964 | − | 0.720972i | \(-0.743696\pi\) | ||||
−0.692964 | + | 0.720972i | \(0.743696\pi\) | |||||||
\(458\) | −41.0832 | −1.91969 | ||||||||
\(459\) | 3.81369 | 0.178008 | ||||||||
\(460\) | 35.1651 | 1.63958 | ||||||||
\(461\) | 13.6161 | 0.634163 | 0.317081 | − | 0.948398i | \(-0.397297\pi\) | ||||
0.317081 | + | 0.948398i | \(0.397297\pi\) | |||||||
\(462\) | 6.12601 | 0.285008 | ||||||||
\(463\) | −16.1578 | −0.750914 | −0.375457 | − | 0.926840i | \(-0.622514\pi\) | ||||
−0.375457 | + | 0.926840i | \(0.622514\pi\) | |||||||
\(464\) | 14.4794 | 0.672189 | ||||||||
\(465\) | −31.0385 | −1.43937 | ||||||||
\(466\) | 54.8934 | 2.54289 | ||||||||
\(467\) | −12.4292 | −0.575155 | −0.287577 | − | 0.957757i | \(-0.592850\pi\) | ||||
−0.287577 | + | 0.957757i | \(0.592850\pi\) | |||||||
\(468\) | −7.58850 | −0.350778 | ||||||||
\(469\) | 18.3404 | 0.846880 | ||||||||
\(470\) | −61.9145 | −2.85590 | ||||||||
\(471\) | 2.78006 | 0.128098 | ||||||||
\(472\) | −4.64936 | −0.214004 | ||||||||
\(473\) | −10.4003 | −0.478205 | ||||||||
\(474\) | 8.27830 | 0.380235 | ||||||||
\(475\) | −18.9364 | −0.868860 | ||||||||
\(476\) | 21.2108 | 0.972196 | ||||||||
\(477\) | 8.28262 | 0.379235 | ||||||||
\(478\) | −9.50063 | −0.434549 | ||||||||
\(479\) | 29.1644 | 1.33255 | 0.666277 | − | 0.745704i | \(-0.267887\pi\) | ||||
0.666277 | + | 0.745704i | \(0.267887\pi\) | |||||||
\(480\) | −23.5332 | −1.07414 | ||||||||
\(481\) | 7.98509 | 0.364089 | ||||||||
\(482\) | −53.0350 | −2.41568 | ||||||||
\(483\) | 20.4993 | 0.932750 | ||||||||
\(484\) | 1.76061 | 0.0800276 | ||||||||
\(485\) | 2.50850 | 0.113905 | ||||||||
\(486\) | 1.93923 | 0.0879652 | ||||||||
\(487\) | 36.8143 | 1.66822 | 0.834108 | − | 0.551601i | \(-0.185983\pi\) | ||||
0.834108 | + | 0.551601i | \(0.185983\pi\) | |||||||
\(488\) | 0.464237 | 0.0210150 | ||||||||
\(489\) | −16.8129 | −0.760305 | ||||||||
\(490\) | −17.7826 | −0.803337 | ||||||||
\(491\) | 38.5259 | 1.73865 | 0.869326 | − | 0.494239i | \(-0.164553\pi\) | ||||
0.869326 | + | 0.494239i | \(0.164553\pi\) | |||||||
\(492\) | 18.9773 | 0.855562 | ||||||||
\(493\) | 12.4890 | 0.562477 | ||||||||
\(494\) | −35.3794 | −1.59180 | ||||||||
\(495\) | −3.07794 | −0.138343 | ||||||||
\(496\) | −44.5869 | −2.00201 | ||||||||
\(497\) | 10.7459 | 0.482019 | ||||||||
\(498\) | 33.7609 | 1.51286 | ||||||||
\(499\) | 1.68198 | 0.0752959 | 0.0376480 | − | 0.999291i | \(-0.488013\pi\) | ||||
0.0376480 | + | 0.999291i | \(0.488013\pi\) | |||||||
\(500\) | −2.85199 | −0.127545 | ||||||||
\(501\) | −14.1771 | −0.633386 | ||||||||
\(502\) | −5.73217 | −0.255839 | ||||||||
\(503\) | 20.1033 | 0.896360 | 0.448180 | − | 0.893943i | \(-0.352072\pi\) | ||||
0.448180 | + | 0.893943i | \(0.352072\pi\) | |||||||
\(504\) | −1.46652 | −0.0653240 | ||||||||
\(505\) | 26.6001 | 1.18369 | ||||||||
\(506\) | 12.5840 | 0.559427 | ||||||||
\(507\) | −5.57746 | −0.247704 | ||||||||
\(508\) | 21.9807 | 0.975238 | ||||||||
\(509\) | 32.9375 | 1.45993 | 0.729964 | − | 0.683485i | \(-0.239537\pi\) | ||||
0.729964 | + | 0.683485i | \(0.239537\pi\) | |||||||
\(510\) | −22.7633 | −1.00797 | ||||||||
\(511\) | −35.6423 | −1.57672 | ||||||||
\(512\) | −29.7004 | −1.31259 | ||||||||
\(513\) | 4.23281 | 0.186883 | ||||||||
\(514\) | −16.6219 | −0.733161 | ||||||||
\(515\) | 4.73652 | 0.208716 | ||||||||
\(516\) | −18.3108 | −0.806088 | ||||||||
\(517\) | −10.3730 | −0.456203 | ||||||||
\(518\) | −11.3492 | −0.498654 | ||||||||
\(519\) | −19.2019 | −0.842868 | ||||||||
\(520\) | −6.15875 | −0.270079 | ||||||||
\(521\) | 6.18719 | 0.271066 | 0.135533 | − | 0.990773i | \(-0.456725\pi\) | ||||
0.135533 | + | 0.990773i | \(0.456725\pi\) | |||||||
\(522\) | 6.35056 | 0.277956 | ||||||||
\(523\) | 19.2567 | 0.842035 | 0.421017 | − | 0.907053i | \(-0.361673\pi\) | ||||
0.421017 | + | 0.907053i | \(0.361673\pi\) | |||||||
\(524\) | 0.0878461 | 0.00383757 | ||||||||
\(525\) | 14.1324 | 0.616790 | ||||||||
\(526\) | 3.56820 | 0.155581 | ||||||||
\(527\) | −38.4579 | −1.67525 | ||||||||
\(528\) | −4.42148 | −0.192420 | ||||||||
\(529\) | 19.1095 | 0.830846 | ||||||||
\(530\) | −49.4376 | −2.14743 | ||||||||
\(531\) | −10.0151 | −0.434617 | ||||||||
\(532\) | 23.5418 | 1.02067 | ||||||||
\(533\) | 46.4585 | 2.01234 | ||||||||
\(534\) | −18.9246 | −0.818949 | ||||||||
\(535\) | −3.91825 | −0.169401 | ||||||||
\(536\) | −2.69525 | −0.116417 | ||||||||
\(537\) | 6.27478 | 0.270777 | ||||||||
\(538\) | 16.7836 | 0.723594 | ||||||||
\(539\) | −2.97925 | −0.128325 | ||||||||
\(540\) | −5.41904 | −0.233198 | ||||||||
\(541\) | −32.4081 | −1.39333 | −0.696666 | − | 0.717395i | \(-0.745334\pi\) | ||||
−0.696666 | + | 0.717395i | \(0.745334\pi\) | |||||||
\(542\) | −35.7686 | −1.53639 | ||||||||
\(543\) | −14.9701 | −0.642427 | ||||||||
\(544\) | −29.1586 | −1.25017 | ||||||||
\(545\) | 33.5425 | 1.43680 | ||||||||
\(546\) | 26.4041 | 1.12999 | ||||||||
\(547\) | −10.6214 | −0.454140 | −0.227070 | − | 0.973878i | \(-0.572915\pi\) | ||||
−0.227070 | + | 0.973878i | \(0.572915\pi\) | |||||||
\(548\) | 0.429133 | 0.0183317 | ||||||||
\(549\) | 1.00000 | 0.0426790 | ||||||||
\(550\) | 8.67555 | 0.369927 | ||||||||
\(551\) | 13.8615 | 0.590522 | ||||||||
\(552\) | −3.01251 | −0.128221 | ||||||||
\(553\) | −13.4853 | −0.573454 | ||||||||
\(554\) | −15.7001 | −0.667034 | ||||||||
\(555\) | 5.70225 | 0.242047 | ||||||||
\(556\) | −37.3021 | −1.58196 | ||||||||
\(557\) | −33.3894 | −1.41475 | −0.707376 | − | 0.706837i | \(-0.750121\pi\) | ||||
−0.707376 | + | 0.706837i | \(0.750121\pi\) | |||||||
\(558\) | −19.5555 | −0.827851 | ||||||||
\(559\) | −44.8268 | −1.89597 | ||||||||
\(560\) | 42.9909 | 1.81670 | ||||||||
\(561\) | −3.81369 | −0.161014 | ||||||||
\(562\) | 34.6664 | 1.46231 | ||||||||
\(563\) | 8.93867 | 0.376720 | 0.188360 | − | 0.982100i | \(-0.439683\pi\) | ||||
0.188360 | + | 0.982100i | \(0.439683\pi\) | |||||||
\(564\) | −18.2627 | −0.769000 | ||||||||
\(565\) | −38.8836 | −1.63585 | ||||||||
\(566\) | −34.3309 | −1.44304 | ||||||||
\(567\) | −3.15900 | −0.132665 | ||||||||
\(568\) | −1.57918 | −0.0662611 | ||||||||
\(569\) | −2.35475 | −0.0987163 | −0.0493582 | − | 0.998781i | \(-0.515718\pi\) | ||||
−0.0493582 | + | 0.998781i | \(0.515718\pi\) | |||||||
\(570\) | −25.2649 | −1.05823 | ||||||||
\(571\) | 4.24507 | 0.177651 | 0.0888253 | − | 0.996047i | \(-0.471689\pi\) | ||||
0.0888253 | + | 0.996047i | \(0.471689\pi\) | |||||||
\(572\) | 7.58850 | 0.317291 | ||||||||
\(573\) | 1.11274 | 0.0464855 | ||||||||
\(574\) | −66.0313 | −2.75609 | ||||||||
\(575\) | 29.0307 | 1.21066 | ||||||||
\(576\) | −5.98396 | −0.249332 | ||||||||
\(577\) | −8.98406 | −0.374011 | −0.187006 | − | 0.982359i | \(-0.559878\pi\) | ||||
−0.187006 | + | 0.982359i | \(0.559878\pi\) | |||||||
\(578\) | 4.76227 | 0.198084 | ||||||||
\(579\) | 16.4747 | 0.684664 | ||||||||
\(580\) | −17.7462 | −0.736871 | ||||||||
\(581\) | −54.9964 | −2.28164 | ||||||||
\(582\) | 1.58046 | 0.0655120 | ||||||||
\(583\) | −8.28262 | −0.343031 | ||||||||
\(584\) | 5.23789 | 0.216745 | ||||||||
\(585\) | −13.2664 | −0.548498 | ||||||||
\(586\) | 25.8619 | 1.06835 | ||||||||
\(587\) | 0.0674569 | 0.00278424 | 0.00139212 | − | 0.999999i | \(-0.499557\pi\) | ||||
0.00139212 | + | 0.999999i | \(0.499557\pi\) | |||||||
\(588\) | −5.24529 | −0.216312 | ||||||||
\(589\) | −42.6844 | −1.75878 | ||||||||
\(590\) | 59.7782 | 2.46103 | ||||||||
\(591\) | −25.4239 | −1.04580 | ||||||||
\(592\) | 8.19132 | 0.336661 | ||||||||
\(593\) | −19.4214 | −0.797540 | −0.398770 | − | 0.917051i | \(-0.630563\pi\) | ||||
−0.398770 | + | 0.917051i | \(0.630563\pi\) | |||||||
\(594\) | −1.93923 | −0.0795675 | ||||||||
\(595\) | 37.0813 | 1.52018 | ||||||||
\(596\) | 23.7619 | 0.973324 | ||||||||
\(597\) | 8.05688 | 0.329746 | ||||||||
\(598\) | 54.2390 | 2.21800 | ||||||||
\(599\) | −19.6058 | −0.801070 | −0.400535 | − | 0.916282i | \(-0.631176\pi\) | ||||
−0.400535 | + | 0.916282i | \(0.631176\pi\) | |||||||
\(600\) | −2.07686 | −0.0847874 | ||||||||
\(601\) | 32.7244 | 1.33485 | 0.667427 | − | 0.744675i | \(-0.267395\pi\) | ||||
0.667427 | + | 0.744675i | \(0.267395\pi\) | |||||||
\(602\) | 63.7122 | 2.59672 | ||||||||
\(603\) | −5.80576 | −0.236429 | ||||||||
\(604\) | 3.77656 | 0.153666 | ||||||||
\(605\) | 3.07794 | 0.125136 | ||||||||
\(606\) | 16.7592 | 0.680795 | ||||||||
\(607\) | −6.92562 | −0.281102 | −0.140551 | − | 0.990073i | \(-0.544887\pi\) | ||||
−0.140551 | + | 0.990073i | \(0.544887\pi\) | |||||||
\(608\) | −32.3631 | −1.31250 | ||||||||
\(609\) | −10.3450 | −0.419202 | ||||||||
\(610\) | −5.96883 | −0.241671 | ||||||||
\(611\) | −44.7092 | −1.80874 | ||||||||
\(612\) | −6.71441 | −0.271414 | ||||||||
\(613\) | 10.1296 | 0.409131 | 0.204566 | − | 0.978853i | \(-0.434422\pi\) | ||||
0.204566 | + | 0.978853i | \(0.434422\pi\) | |||||||
\(614\) | 62.2532 | 2.51233 | ||||||||
\(615\) | 33.1766 | 1.33781 | ||||||||
\(616\) | 1.46652 | 0.0590878 | ||||||||
\(617\) | 3.90198 | 0.157088 | 0.0785439 | − | 0.996911i | \(-0.474973\pi\) | ||||
0.0785439 | + | 0.996911i | \(0.474973\pi\) | |||||||
\(618\) | 2.98420 | 0.120042 | ||||||||
\(619\) | 8.08612 | 0.325009 | 0.162504 | − | 0.986708i | \(-0.448043\pi\) | ||||
0.162504 | + | 0.986708i | \(0.448043\pi\) | |||||||
\(620\) | 54.6466 | 2.19466 | ||||||||
\(621\) | −6.48918 | −0.260402 | ||||||||
\(622\) | −37.1221 | −1.48846 | ||||||||
\(623\) | 30.8281 | 1.23510 | ||||||||
\(624\) | −19.0573 | −0.762901 | ||||||||
\(625\) | −27.3545 | −1.09418 | ||||||||
\(626\) | −13.8188 | −0.552310 | ||||||||
\(627\) | −4.23281 | −0.169042 | ||||||||
\(628\) | −4.89459 | −0.195315 | ||||||||
\(629\) | 7.06532 | 0.281713 | ||||||||
\(630\) | 18.8555 | 0.751221 | ||||||||
\(631\) | 14.8852 | 0.592569 | 0.296284 | − | 0.955100i | \(-0.404252\pi\) | ||||
0.296284 | + | 0.955100i | \(0.404252\pi\) | |||||||
\(632\) | 1.98176 | 0.0788302 | ||||||||
\(633\) | −21.8405 | −0.868081 | ||||||||
\(634\) | 59.6589 | 2.36936 | ||||||||
\(635\) | 38.4273 | 1.52494 | ||||||||
\(636\) | −14.5825 | −0.578232 | ||||||||
\(637\) | −12.8410 | −0.508780 | ||||||||
\(638\) | −6.35056 | −0.251421 | ||||||||
\(639\) | −3.40168 | −0.134568 | ||||||||
\(640\) | −11.3492 | −0.448618 | ||||||||
\(641\) | 6.49332 | 0.256471 | 0.128235 | − | 0.991744i | \(-0.459069\pi\) | ||||
0.128235 | + | 0.991744i | \(0.459069\pi\) | |||||||
\(642\) | −2.46866 | −0.0974301 | ||||||||
\(643\) | −0.679815 | −0.0268093 | −0.0134046 | − | 0.999910i | \(-0.504267\pi\) | ||||
−0.0134046 | + | 0.999910i | \(0.504267\pi\) | |||||||
\(644\) | −36.0912 | −1.42219 | ||||||||
\(645\) | −32.0114 | −1.26045 | ||||||||
\(646\) | −31.3043 | −1.23165 | ||||||||
\(647\) | 9.53160 | 0.374726 | 0.187363 | − | 0.982291i | \(-0.440006\pi\) | ||||
0.187363 | + | 0.982291i | \(0.440006\pi\) | |||||||
\(648\) | 0.464237 | 0.0182369 | ||||||||
\(649\) | 10.0151 | 0.393126 | ||||||||
\(650\) | 37.3930 | 1.46667 | ||||||||
\(651\) | 31.8559 | 1.24853 | ||||||||
\(652\) | 29.6009 | 1.15926 | ||||||||
\(653\) | −15.7563 | −0.616591 | −0.308296 | − | 0.951291i | \(-0.599759\pi\) | ||||
−0.308296 | + | 0.951291i | \(0.599759\pi\) | |||||||
\(654\) | 21.1331 | 0.826371 | ||||||||
\(655\) | 0.153575 | 0.00600066 | ||||||||
\(656\) | 47.6583 | 1.86075 | ||||||||
\(657\) | 11.2828 | 0.440184 | ||||||||
\(658\) | 63.5450 | 2.47724 | ||||||||
\(659\) | 22.5633 | 0.878941 | 0.439470 | − | 0.898257i | \(-0.355166\pi\) | ||||
0.439470 | + | 0.898257i | \(0.355166\pi\) | |||||||
\(660\) | 5.41904 | 0.210936 | ||||||||
\(661\) | −47.5006 | −1.84756 | −0.923779 | − | 0.382927i | \(-0.874916\pi\) | ||||
−0.923779 | + | 0.382927i | \(0.874916\pi\) | |||||||
\(662\) | 2.33180 | 0.0906281 | ||||||||
\(663\) | −16.4376 | −0.638384 | ||||||||
\(664\) | 8.08211 | 0.313647 | ||||||||
\(665\) | 41.1564 | 1.59598 | ||||||||
\(666\) | 3.59265 | 0.139213 | ||||||||
\(667\) | −21.2507 | −0.822830 | ||||||||
\(668\) | 24.9603 | 0.965744 | ||||||||
\(669\) | −12.6761 | −0.490085 | ||||||||
\(670\) | 34.6536 | 1.33879 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | 24.1530 | 0.931721 | ||||||||
\(673\) | 6.74671 | 0.260067 | 0.130033 | − | 0.991510i | \(-0.458492\pi\) | ||||
0.130033 | + | 0.991510i | \(0.458492\pi\) | |||||||
\(674\) | 54.0751 | 2.08290 | ||||||||
\(675\) | −4.47371 | −0.172193 | ||||||||
\(676\) | 9.81973 | 0.377682 | ||||||||
\(677\) | 31.7778 | 1.22132 | 0.610660 | − | 0.791893i | \(-0.290904\pi\) | ||||
0.610660 | + | 0.791893i | \(0.290904\pi\) | |||||||
\(678\) | −24.4983 | −0.940851 | ||||||||
\(679\) | −2.57456 | −0.0988024 | ||||||||
\(680\) | −5.44935 | −0.208973 | ||||||||
\(681\) | −18.0164 | −0.690392 | ||||||||
\(682\) | 19.5555 | 0.748819 | ||||||||
\(683\) | −4.24491 | −0.162427 | −0.0812135 | − | 0.996697i | \(-0.525880\pi\) | ||||
−0.0812135 | + | 0.996697i | \(0.525880\pi\) | |||||||
\(684\) | −7.45232 | −0.284947 | ||||||||
\(685\) | 0.750222 | 0.0286645 | ||||||||
\(686\) | −24.6312 | −0.940422 | ||||||||
\(687\) | −21.1854 | −0.808272 | ||||||||
\(688\) | −45.9845 | −1.75314 | ||||||||
\(689\) | −35.6994 | −1.36004 | ||||||||
\(690\) | 38.7328 | 1.47453 | ||||||||
\(691\) | 39.5060 | 1.50288 | 0.751440 | − | 0.659801i | \(-0.229359\pi\) | ||||
0.751440 | + | 0.659801i | \(0.229359\pi\) | |||||||
\(692\) | 33.8069 | 1.28515 | ||||||||
\(693\) | 3.15900 | 0.120000 | ||||||||
\(694\) | −16.8094 | −0.638076 | ||||||||
\(695\) | −65.2125 | −2.47365 | ||||||||
\(696\) | 1.52028 | 0.0576259 | ||||||||
\(697\) | 41.1071 | 1.55704 | ||||||||
\(698\) | 6.34834 | 0.240288 | ||||||||
\(699\) | 28.3068 | 1.07066 | ||||||||
\(700\) | −24.8817 | −0.940438 | ||||||||
\(701\) | −2.69413 | −0.101756 | −0.0508779 | − | 0.998705i | \(-0.516202\pi\) | ||||
−0.0508779 | + | 0.998705i | \(0.516202\pi\) | |||||||
\(702\) | −8.35838 | −0.315467 | ||||||||
\(703\) | 7.84179 | 0.295759 | ||||||||
\(704\) | 5.98396 | 0.225529 | ||||||||
\(705\) | −31.9274 | −1.20246 | ||||||||
\(706\) | −45.4746 | −1.71146 | ||||||||
\(707\) | −27.3006 | −1.02675 | ||||||||
\(708\) | 17.6326 | 0.662673 | ||||||||
\(709\) | 44.7755 | 1.68158 | 0.840790 | − | 0.541362i | \(-0.182091\pi\) | ||||
0.840790 | + | 0.541362i | \(0.182091\pi\) | |||||||
\(710\) | 20.3041 | 0.761997 | ||||||||
\(711\) | 4.26886 | 0.160095 | ||||||||
\(712\) | −4.53041 | −0.169784 | ||||||||
\(713\) | 65.4380 | 2.45067 | ||||||||
\(714\) | 23.3627 | 0.874328 | ||||||||
\(715\) | 13.2664 | 0.496135 | ||||||||
\(716\) | −11.0474 | −0.412862 | ||||||||
\(717\) | −4.89918 | −0.182963 | ||||||||
\(718\) | 52.2626 | 1.95042 | ||||||||
\(719\) | −28.5746 | −1.06565 | −0.532827 | − | 0.846224i | \(-0.678870\pi\) | ||||
−0.532827 | + | 0.846224i | \(0.678870\pi\) | |||||||
\(720\) | −13.6090 | −0.507179 | ||||||||
\(721\) | −4.86126 | −0.181043 | ||||||||
\(722\) | 2.10080 | 0.0781836 | ||||||||
\(723\) | −27.3485 | −1.01710 | ||||||||
\(724\) | 26.3564 | 0.979529 | ||||||||
\(725\) | −14.6504 | −0.544104 | ||||||||
\(726\) | 1.93923 | 0.0719715 | ||||||||
\(727\) | −25.0251 | −0.928130 | −0.464065 | − | 0.885801i | \(-0.653610\pi\) | ||||
−0.464065 | + | 0.885801i | \(0.653610\pi\) | |||||||
\(728\) | 6.32094 | 0.234270 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −67.3451 | −2.49256 | ||||||||
\(731\) | −39.6634 | −1.46700 | ||||||||
\(732\) | −1.76061 | −0.0650739 | ||||||||
\(733\) | −0.528034 | −0.0195034 | −0.00975169 | − | 0.999952i | \(-0.503104\pi\) | ||||
−0.00975169 | + | 0.999952i | \(0.503104\pi\) | |||||||
\(734\) | 12.5192 | 0.462091 | ||||||||
\(735\) | −9.16995 | −0.338239 | ||||||||
\(736\) | 49.6148 | 1.82883 | ||||||||
\(737\) | 5.80576 | 0.213858 | ||||||||
\(738\) | 20.9026 | 0.769436 | ||||||||
\(739\) | 20.9456 | 0.770496 | 0.385248 | − | 0.922813i | \(-0.374116\pi\) | ||||
0.385248 | + | 0.922813i | \(0.374116\pi\) | |||||||
\(740\) | −10.0394 | −0.369057 | ||||||||
\(741\) | −18.2441 | −0.670213 | ||||||||
\(742\) | 50.7395 | 1.86270 | ||||||||
\(743\) | −17.0344 | −0.624932 | −0.312466 | − | 0.949929i | \(-0.601155\pi\) | ||||
−0.312466 | + | 0.949929i | \(0.601155\pi\) | |||||||
\(744\) | −4.68144 | −0.171630 | ||||||||
\(745\) | 41.5411 | 1.52195 | ||||||||
\(746\) | −19.2975 | −0.706533 | ||||||||
\(747\) | 17.4095 | 0.636979 | ||||||||
\(748\) | 6.71441 | 0.245503 | ||||||||
\(749\) | 4.02143 | 0.146940 | ||||||||
\(750\) | −3.14134 | −0.114705 | ||||||||
\(751\) | −10.2079 | −0.372491 | −0.186246 | − | 0.982503i | \(-0.559632\pi\) | ||||
−0.186246 | + | 0.982503i | \(0.559632\pi\) | |||||||
\(752\) | −45.8639 | −1.67248 | ||||||||
\(753\) | −2.95590 | −0.107719 | ||||||||
\(754\) | −27.3719 | −0.996826 | ||||||||
\(755\) | 6.60228 | 0.240281 | ||||||||
\(756\) | 5.56175 | 0.202279 | ||||||||
\(757\) | 18.2567 | 0.663549 | 0.331775 | − | 0.943359i | \(-0.392353\pi\) | ||||
0.331775 | + | 0.943359i | \(0.392353\pi\) | |||||||
\(758\) | 11.6247 | 0.422227 | ||||||||
\(759\) | 6.48918 | 0.235542 | ||||||||
\(760\) | −6.04823 | −0.219392 | ||||||||
\(761\) | 5.09224 | 0.184594 | 0.0922968 | − | 0.995732i | \(-0.470579\pi\) | ||||
0.0922968 | + | 0.995732i | \(0.470579\pi\) | |||||||
\(762\) | 24.2108 | 0.877064 | ||||||||
\(763\) | −34.4258 | −1.24630 | ||||||||
\(764\) | −1.95910 | −0.0708779 | ||||||||
\(765\) | −11.7383 | −0.424400 | ||||||||
\(766\) | −4.73125 | −0.170947 | ||||||||
\(767\) | 43.1665 | 1.55865 | ||||||||
\(768\) | −19.1184 | −0.689877 | ||||||||
\(769\) | −9.02962 | −0.325617 | −0.162808 | − | 0.986658i | \(-0.552055\pi\) | ||||
−0.162808 | + | 0.986658i | \(0.552055\pi\) | |||||||
\(770\) | −18.8555 | −0.679505 | ||||||||
\(771\) | −8.57140 | −0.308692 | ||||||||
\(772\) | −29.0054 | −1.04393 | ||||||||
\(773\) | −9.13122 | −0.328427 | −0.164214 | − | 0.986425i | \(-0.552509\pi\) | ||||
−0.164214 | + | 0.986425i | \(0.552509\pi\) | |||||||
\(774\) | −20.1685 | −0.724942 | ||||||||
\(775\) | 45.1137 | 1.62053 | ||||||||
\(776\) | 0.378349 | 0.0135819 | ||||||||
\(777\) | −5.85242 | −0.209954 | ||||||||
\(778\) | 3.16113 | 0.113332 | ||||||||
\(779\) | 45.6247 | 1.63468 | ||||||||
\(780\) | 23.3569 | 0.836312 | ||||||||
\(781\) | 3.40168 | 0.121722 | ||||||||
\(782\) | 47.9915 | 1.71617 | ||||||||
\(783\) | 3.27479 | 0.117031 | ||||||||
\(784\) | −13.1727 | −0.470453 | ||||||||
\(785\) | −8.55685 | −0.305407 | ||||||||
\(786\) | 0.0967585 | 0.00345126 | ||||||||
\(787\) | 28.3647 | 1.01109 | 0.505546 | − | 0.862800i | \(-0.331291\pi\) | ||||
0.505546 | + | 0.862800i | \(0.331291\pi\) | |||||||
\(788\) | 44.7615 | 1.59456 | ||||||||
\(789\) | 1.84001 | 0.0655062 | ||||||||
\(790\) | −25.4801 | −0.906541 | ||||||||
\(791\) | 39.9076 | 1.41895 | ||||||||
\(792\) | −0.464237 | −0.0164959 | ||||||||
\(793\) | −4.31016 | −0.153058 | ||||||||
\(794\) | 56.5382 | 2.00647 | ||||||||
\(795\) | −25.4934 | −0.904158 | ||||||||
\(796\) | −14.1850 | −0.502774 | ||||||||
\(797\) | 36.2460 | 1.28390 | 0.641950 | − | 0.766747i | \(-0.278126\pi\) | ||||
0.641950 | + | 0.766747i | \(0.278126\pi\) | |||||||
\(798\) | 25.9303 | 0.917921 | ||||||||
\(799\) | −39.5593 | −1.39951 | ||||||||
\(800\) | 34.2050 | 1.20933 | ||||||||
\(801\) | −9.75884 | −0.344812 | ||||||||
\(802\) | 55.9426 | 1.97540 | ||||||||
\(803\) | −11.2828 | −0.398162 | ||||||||
\(804\) | 10.2217 | 0.360491 | ||||||||
\(805\) | −63.0956 | −2.22383 | ||||||||
\(806\) | 84.2874 | 2.96890 | ||||||||
\(807\) | 8.65480 | 0.304663 | ||||||||
\(808\) | 4.01202 | 0.141142 | ||||||||
\(809\) | −53.3004 | −1.87394 | −0.936971 | − | 0.349408i | \(-0.886383\pi\) | ||||
−0.936971 | + | 0.349408i | \(0.886383\pi\) | |||||||
\(810\) | −5.96883 | −0.209723 | ||||||||
\(811\) | 13.8664 | 0.486914 | 0.243457 | − | 0.969912i | \(-0.421719\pi\) | ||||
0.243457 | + | 0.969912i | \(0.421719\pi\) | |||||||
\(812\) | 18.2135 | 0.639170 | ||||||||
\(813\) | −18.4447 | −0.646885 | ||||||||
\(814\) | −3.59265 | −0.125922 | ||||||||
\(815\) | 51.7491 | 1.81269 | ||||||||
\(816\) | −16.8621 | −0.590293 | ||||||||
\(817\) | −44.0224 | −1.54015 | ||||||||
\(818\) | −38.2231 | −1.33644 | ||||||||
\(819\) | 13.6158 | 0.475773 | ||||||||
\(820\) | −58.4109 | −2.03980 | ||||||||
\(821\) | −42.4160 | −1.48033 | −0.740164 | − | 0.672427i | \(-0.765252\pi\) | ||||
−0.740164 | + | 0.672427i | \(0.765252\pi\) | |||||||
\(822\) | 0.472671 | 0.0164863 | ||||||||
\(823\) | 35.8679 | 1.25028 | 0.625138 | − | 0.780514i | \(-0.285043\pi\) | ||||
0.625138 | + | 0.780514i | \(0.285043\pi\) | |||||||
\(824\) | 0.714396 | 0.0248871 | ||||||||
\(825\) | 4.47371 | 0.155755 | ||||||||
\(826\) | −61.3524 | −2.13472 | ||||||||
\(827\) | −7.27629 | −0.253022 | −0.126511 | − | 0.991965i | \(-0.540378\pi\) | ||||
−0.126511 | + | 0.991965i | \(0.540378\pi\) | |||||||
\(828\) | 11.4249 | 0.397043 | ||||||||
\(829\) | −21.2488 | −0.738000 | −0.369000 | − | 0.929429i | \(-0.620300\pi\) | ||||
−0.369000 | + | 0.929429i | \(0.620300\pi\) | |||||||
\(830\) | −103.914 | −3.60691 | ||||||||
\(831\) | −8.09606 | −0.280849 | ||||||||
\(832\) | 25.7918 | 0.894171 | ||||||||
\(833\) | −11.3619 | −0.393668 | ||||||||
\(834\) | −41.0865 | −1.42271 | ||||||||
\(835\) | 43.6363 | 1.51010 | ||||||||
\(836\) | 7.45232 | 0.257744 | ||||||||
\(837\) | −10.0842 | −0.348560 | ||||||||
\(838\) | 12.2809 | 0.424236 | ||||||||
\(839\) | 27.7675 | 0.958641 | 0.479320 | − | 0.877640i | \(-0.340883\pi\) | ||||
0.479320 | + | 0.877640i | \(0.340883\pi\) | |||||||
\(840\) | 4.51386 | 0.155743 | ||||||||
\(841\) | −18.2758 | −0.630199 | ||||||||
\(842\) | −60.0639 | −2.06994 | ||||||||
\(843\) | 17.8764 | 0.615695 | ||||||||
\(844\) | 38.4525 | 1.32359 | ||||||||
\(845\) | 17.1671 | 0.590566 | ||||||||
\(846\) | −20.1156 | −0.691588 | ||||||||
\(847\) | −3.15900 | −0.108544 | ||||||||
\(848\) | −36.6214 | −1.25758 | ||||||||
\(849\) | −17.7034 | −0.607579 | ||||||||
\(850\) | 33.0859 | 1.13484 | ||||||||
\(851\) | −12.0220 | −0.412108 | ||||||||
\(852\) | 5.98903 | 0.205181 | ||||||||
\(853\) | −7.41186 | −0.253777 | −0.126889 | − | 0.991917i | \(-0.540499\pi\) | ||||
−0.126889 | + | 0.991917i | \(0.540499\pi\) | |||||||
\(854\) | 6.12601 | 0.209628 | ||||||||
\(855\) | −13.0283 | −0.445560 | ||||||||
\(856\) | −0.590978 | −0.0201992 | ||||||||
\(857\) | −13.6447 | −0.466095 | −0.233047 | − | 0.972465i | \(-0.574870\pi\) | ||||
−0.233047 | + | 0.972465i | \(0.574870\pi\) | |||||||
\(858\) | 8.35838 | 0.285350 | ||||||||
\(859\) | −39.3829 | −1.34373 | −0.671864 | − | 0.740675i | \(-0.734506\pi\) | ||||
−0.671864 | + | 0.740675i | \(0.734506\pi\) | |||||||
\(860\) | 56.3595 | 1.92184 | ||||||||
\(861\) | −34.0503 | −1.16043 | ||||||||
\(862\) | 1.38011 | 0.0470068 | ||||||||
\(863\) | −48.1420 | −1.63877 | −0.819387 | − | 0.573241i | \(-0.805686\pi\) | ||||
−0.819387 | + | 0.573241i | \(0.805686\pi\) | |||||||
\(864\) | −7.64578 | −0.260115 | ||||||||
\(865\) | 59.1022 | 2.00953 | ||||||||
\(866\) | −74.9156 | −2.54574 | ||||||||
\(867\) | 2.45576 | 0.0834019 | ||||||||
\(868\) | −56.0857 | −1.90367 | ||||||||
\(869\) | −4.26886 | −0.144811 | ||||||||
\(870\) | −19.5466 | −0.662693 | ||||||||
\(871\) | 25.0238 | 0.847898 | ||||||||
\(872\) | 5.05911 | 0.171323 | ||||||||
\(873\) | 0.814992 | 0.0275833 | ||||||||
\(874\) | 53.2657 | 1.80174 | ||||||||
\(875\) | 5.11722 | 0.172994 | ||||||||
\(876\) | −19.8646 | −0.671163 | ||||||||
\(877\) | 37.6587 | 1.27164 | 0.635822 | − | 0.771836i | \(-0.280661\pi\) | ||||
0.635822 | + | 0.771836i | \(0.280661\pi\) | |||||||
\(878\) | −19.6267 | −0.662369 | ||||||||
\(879\) | 13.3362 | 0.449819 | ||||||||
\(880\) | 13.6090 | 0.458760 | ||||||||
\(881\) | 32.6783 | 1.10096 | 0.550480 | − | 0.834848i | \(-0.314445\pi\) | ||||
0.550480 | + | 0.834848i | \(0.314445\pi\) | |||||||
\(882\) | −5.77745 | −0.194537 | ||||||||
\(883\) | −2.47331 | −0.0832335 | −0.0416167 | − | 0.999134i | \(-0.513251\pi\) | ||||
−0.0416167 | + | 0.999134i | \(0.513251\pi\) | |||||||
\(884\) | 28.9402 | 0.973364 | ||||||||
\(885\) | 30.8258 | 1.03620 | ||||||||
\(886\) | 53.7141 | 1.80456 | ||||||||
\(887\) | 2.57792 | 0.0865580 | 0.0432790 | − | 0.999063i | \(-0.486220\pi\) | ||||
0.0432790 | + | 0.999063i | \(0.486220\pi\) | |||||||
\(888\) | 0.860054 | 0.0288615 | ||||||||
\(889\) | −39.4393 | −1.32275 | ||||||||
\(890\) | 58.2489 | 1.95251 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 22.3176 | 0.747248 | ||||||||
\(893\) | −43.9068 | −1.46929 | ||||||||
\(894\) | 26.1726 | 0.875343 | ||||||||
\(895\) | −19.3134 | −0.645576 | ||||||||
\(896\) | 11.6481 | 0.389136 | ||||||||
\(897\) | 27.9694 | 0.933871 | ||||||||
\(898\) | −39.4777 | −1.31739 | ||||||||
\(899\) | −33.0235 | −1.10140 | ||||||||
\(900\) | 7.87645 | 0.262548 | ||||||||
\(901\) | −31.5874 | −1.05233 | ||||||||
\(902\) | −20.9026 | −0.695981 | ||||||||
\(903\) | 32.8544 | 1.09333 | ||||||||
\(904\) | −5.86470 | −0.195057 | ||||||||
\(905\) | 46.0770 | 1.53165 | ||||||||
\(906\) | 4.15971 | 0.138197 | ||||||||
\(907\) | 8.34904 | 0.277225 | 0.138613 | − | 0.990347i | \(-0.455736\pi\) | ||||
0.138613 | + | 0.990347i | \(0.455736\pi\) | |||||||
\(908\) | 31.7199 | 1.05266 | ||||||||
\(909\) | 8.64218 | 0.286643 | ||||||||
\(910\) | −81.2702 | −2.69408 | ||||||||
\(911\) | −8.66605 | −0.287119 | −0.143560 | − | 0.989642i | \(-0.545855\pi\) | ||||
−0.143560 | + | 0.989642i | \(0.545855\pi\) | |||||||
\(912\) | −18.7153 | −0.619724 | ||||||||
\(913\) | −17.4095 | −0.576169 | ||||||||
\(914\) | 57.4550 | 1.90044 | ||||||||
\(915\) | −3.07794 | −0.101754 | ||||||||
\(916\) | 37.2991 | 1.23240 | ||||||||
\(917\) | −0.157619 | −0.00520504 | ||||||||
\(918\) | −7.39562 | −0.244092 | ||||||||
\(919\) | 17.4019 | 0.574035 | 0.287017 | − | 0.957925i | \(-0.407336\pi\) | ||||
0.287017 | + | 0.957925i | \(0.407336\pi\) | |||||||
\(920\) | 9.27234 | 0.305700 | ||||||||
\(921\) | 32.1020 | 1.05780 | ||||||||
\(922\) | −26.4046 | −0.869591 | ||||||||
\(923\) | 14.6618 | 0.482599 | ||||||||
\(924\) | −5.56175 | −0.182968 | ||||||||
\(925\) | −8.28809 | −0.272511 | ||||||||
\(926\) | 31.3336 | 1.02969 | ||||||||
\(927\) | 1.53886 | 0.0505428 | ||||||||
\(928\) | −25.0383 | −0.821922 | ||||||||
\(929\) | 7.38998 | 0.242458 | 0.121229 | − | 0.992625i | \(-0.461317\pi\) | ||||
0.121229 | + | 0.992625i | \(0.461317\pi\) | |||||||
\(930\) | 60.1907 | 1.97373 | ||||||||
\(931\) | −12.6106 | −0.413296 | ||||||||
\(932\) | −49.8372 | −1.63247 | ||||||||
\(933\) | −19.1427 | −0.626705 | ||||||||
\(934\) | 24.1031 | 0.788676 | ||||||||
\(935\) | 11.7383 | 0.383884 | ||||||||
\(936\) | −2.00093 | −0.0654025 | ||||||||
\(937\) | 41.9703 | 1.37111 | 0.685555 | − | 0.728021i | \(-0.259560\pi\) | ||||
0.685555 | + | 0.728021i | \(0.259560\pi\) | |||||||
\(938\) | −35.5662 | −1.16128 | ||||||||
\(939\) | −7.12592 | −0.232545 | ||||||||
\(940\) | 56.2116 | 1.83342 | ||||||||
\(941\) | −51.7763 | −1.68786 | −0.843929 | − | 0.536454i | \(-0.819763\pi\) | ||||
−0.843929 | + | 0.536454i | \(0.819763\pi\) | |||||||
\(942\) | −5.39117 | −0.175654 | ||||||||
\(943\) | −69.9458 | −2.27775 | ||||||||
\(944\) | 44.2814 | 1.44124 | ||||||||
\(945\) | 9.72319 | 0.316296 | ||||||||
\(946\) | 20.1685 | 0.655734 | ||||||||
\(947\) | 22.0964 | 0.718037 | 0.359019 | − | 0.933330i | \(-0.383111\pi\) | ||||
0.359019 | + | 0.933330i | \(0.383111\pi\) | |||||||
\(948\) | −7.51579 | −0.244101 | ||||||||
\(949\) | −48.6307 | −1.57862 | ||||||||
\(950\) | 36.7219 | 1.19142 | ||||||||
\(951\) | 30.7643 | 0.997600 | ||||||||
\(952\) | 5.59286 | 0.181266 | ||||||||
\(953\) | −36.4561 | −1.18093 | −0.590464 | − | 0.807064i | \(-0.701055\pi\) | ||||
−0.590464 | + | 0.807064i | \(0.701055\pi\) | |||||||
\(954\) | −16.0619 | −0.520023 | ||||||||
\(955\) | −3.42495 | −0.110829 | ||||||||
\(956\) | 8.62553 | 0.278970 | ||||||||
\(957\) | −3.27479 | −0.105859 | ||||||||
\(958\) | −56.5564 | −1.82725 | ||||||||
\(959\) | −0.769979 | −0.0248639 | ||||||||
\(960\) | 18.4183 | 0.594447 | ||||||||
\(961\) | 70.6905 | 2.28034 | ||||||||
\(962\) | −15.4849 | −0.499253 | ||||||||
\(963\) | −1.27301 | −0.0410222 | ||||||||
\(964\) | 48.1500 | 1.55081 | ||||||||
\(965\) | −50.7081 | −1.63235 | ||||||||
\(966\) | −39.7528 | −1.27903 | ||||||||
\(967\) | 1.95027 | 0.0627164 | 0.0313582 | − | 0.999508i | \(-0.490017\pi\) | ||||
0.0313582 | + | 0.999508i | \(0.490017\pi\) | |||||||
\(968\) | 0.464237 | 0.0149211 | ||||||||
\(969\) | −16.1426 | −0.518576 | ||||||||
\(970\) | −4.86455 | −0.156191 | ||||||||
\(971\) | −40.8271 | −1.31020 | −0.655102 | − | 0.755540i | \(-0.727374\pi\) | ||||
−0.655102 | + | 0.755540i | \(0.727374\pi\) | |||||||
\(972\) | −1.76061 | −0.0564715 | ||||||||
\(973\) | 66.9298 | 2.14567 | ||||||||
\(974\) | −71.3914 | −2.28753 | ||||||||
\(975\) | 19.2824 | 0.617531 | ||||||||
\(976\) | −4.42148 | −0.141528 | ||||||||
\(977\) | −29.4296 | −0.941535 | −0.470767 | − | 0.882257i | \(-0.656023\pi\) | ||||
−0.470767 | + | 0.882257i | \(0.656023\pi\) | |||||||
\(978\) | 32.6040 | 1.04256 | ||||||||
\(979\) | 9.75884 | 0.311894 | ||||||||
\(980\) | 16.1447 | 0.515723 | ||||||||
\(981\) | 10.8977 | 0.347937 | ||||||||
\(982\) | −74.7106 | −2.38411 | ||||||||
\(983\) | 12.2766 | 0.391562 | 0.195781 | − | 0.980648i | \(-0.437276\pi\) | ||||
0.195781 | + | 0.980648i | \(0.437276\pi\) | |||||||
\(984\) | 5.00393 | 0.159519 | ||||||||
\(985\) | 78.2533 | 2.49336 | ||||||||
\(986\) | −24.2191 | −0.771292 | ||||||||
\(987\) | 32.7682 | 1.04302 | ||||||||
\(988\) | 32.1207 | 1.02189 | ||||||||
\(989\) | 67.4892 | 2.14603 | ||||||||
\(990\) | 5.96883 | 0.189702 | ||||||||
\(991\) | −30.0821 | −0.955588 | −0.477794 | − | 0.878472i | \(-0.658563\pi\) | ||||
−0.477794 | + | 0.878472i | \(0.658563\pi\) | |||||||
\(992\) | 77.1014 | 2.44797 | ||||||||
\(993\) | 1.20244 | 0.0381582 | ||||||||
\(994\) | −20.8387 | −0.660965 | ||||||||
\(995\) | −24.7986 | −0.786168 | ||||||||
\(996\) | −30.6512 | −0.971222 | ||||||||
\(997\) | 28.9187 | 0.915866 | 0.457933 | − | 0.888987i | \(-0.348590\pi\) | ||||
0.457933 | + | 0.888987i | \(0.348590\pi\) | |||||||
\(998\) | −3.26175 | −0.103249 | ||||||||
\(999\) | 1.85262 | 0.0586143 |
(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 | 2013.2.a.h.1.3 | ✓ | 14 | |
3.2 | odd | 2 | 6039.2.a.j.1.12 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.2.a.h.1.3 | ✓ | 14 | 1.1 | even | 1 | trivial | |
6039.2.a.j.1.12 | 14 | 3.2 | odd | 2 |