Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6034,2,Mod(1,6034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6034, 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("6034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6034 = 2 \cdot 7 \cdot 431 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6034.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: | \(48.1817325796\) |
Analytic rank: | \(1\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 6034.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0.402295 | 0.232265 | 0.116132 | − | 0.993234i | \(-0.462950\pi\) | ||||
0.116132 | + | 0.993234i | \(0.462950\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.29038 | 0.577075 | 0.288538 | − | 0.957469i | \(-0.406831\pi\) | ||||
0.288538 | + | 0.957469i | \(0.406831\pi\) | |||||||
\(6\) | 0.402295 | 0.164236 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.83816 | −0.946053 | ||||||||
\(10\) | 1.29038 | 0.408054 | ||||||||
\(11\) | −4.26945 | −1.28729 | −0.643644 | − | 0.765325i | \(-0.722578\pi\) | ||||
−0.643644 | + | 0.765325i | \(0.722578\pi\) | |||||||
\(12\) | 0.402295 | 0.116132 | ||||||||
\(13\) | 4.48732 | 1.24456 | 0.622279 | − | 0.782795i | \(-0.286207\pi\) | ||||
0.622279 | + | 0.782795i | \(0.286207\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0.519113 | 0.134034 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.29141 | −1.28336 | −0.641678 | − | 0.766975i | \(-0.721761\pi\) | ||||
−0.641678 | + | 0.766975i | \(0.721761\pi\) | |||||||
\(18\) | −2.83816 | −0.668960 | ||||||||
\(19\) | −4.09738 | −0.940004 | −0.470002 | − | 0.882665i | \(-0.655747\pi\) | ||||
−0.470002 | + | 0.882665i | \(0.655747\pi\) | |||||||
\(20\) | 1.29038 | 0.288538 | ||||||||
\(21\) | 0.402295 | 0.0877879 | ||||||||
\(22\) | −4.26945 | −0.910250 | ||||||||
\(23\) | 1.57271 | 0.327934 | 0.163967 | − | 0.986466i | \(-0.447571\pi\) | ||||
0.163967 | + | 0.986466i | \(0.447571\pi\) | |||||||
\(24\) | 0.402295 | 0.0821181 | ||||||||
\(25\) | −3.33492 | −0.666984 | ||||||||
\(26\) | 4.48732 | 0.880036 | ||||||||
\(27\) | −2.34866 | −0.452000 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −6.89951 | −1.28121 | −0.640603 | − | 0.767872i | \(-0.721316\pi\) | ||||
−0.640603 | + | 0.767872i | \(0.721316\pi\) | |||||||
\(30\) | 0.519113 | 0.0947766 | ||||||||
\(31\) | 4.91518 | 0.882792 | 0.441396 | − | 0.897313i | \(-0.354483\pi\) | ||||
0.441396 | + | 0.897313i | \(0.354483\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.71758 | −0.298992 | ||||||||
\(34\) | −5.29141 | −0.907469 | ||||||||
\(35\) | 1.29038 | 0.218114 | ||||||||
\(36\) | −2.83816 | −0.473026 | ||||||||
\(37\) | 1.33586 | 0.219614 | 0.109807 | − | 0.993953i | \(-0.464977\pi\) | ||||
0.109807 | + | 0.993953i | \(0.464977\pi\) | |||||||
\(38\) | −4.09738 | −0.664684 | ||||||||
\(39\) | 1.80523 | 0.289067 | ||||||||
\(40\) | 1.29038 | 0.204027 | ||||||||
\(41\) | −12.7678 | −1.99400 | −0.997001 | − | 0.0773897i | \(-0.975341\pi\) | ||||
−0.997001 | + | 0.0773897i | \(0.975341\pi\) | |||||||
\(42\) | 0.402295 | 0.0620754 | ||||||||
\(43\) | −10.1930 | −1.55441 | −0.777206 | − | 0.629246i | \(-0.783364\pi\) | ||||
−0.777206 | + | 0.629246i | \(0.783364\pi\) | |||||||
\(44\) | −4.26945 | −0.643644 | ||||||||
\(45\) | −3.66230 | −0.545944 | ||||||||
\(46\) | 1.57271 | 0.231884 | ||||||||
\(47\) | −10.9210 | −1.59299 | −0.796495 | − | 0.604646i | \(-0.793315\pi\) | ||||
−0.796495 | + | 0.604646i | \(0.793315\pi\) | |||||||
\(48\) | 0.402295 | 0.0580662 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −3.33492 | −0.471629 | ||||||||
\(51\) | −2.12871 | −0.298078 | ||||||||
\(52\) | 4.48732 | 0.622279 | ||||||||
\(53\) | 5.46626 | 0.750849 | 0.375424 | − | 0.926853i | \(-0.377497\pi\) | ||||
0.375424 | + | 0.926853i | \(0.377497\pi\) | |||||||
\(54\) | −2.34866 | −0.319612 | ||||||||
\(55\) | −5.50921 | −0.742862 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −1.64836 | −0.218330 | ||||||||
\(58\) | −6.89951 | −0.905949 | ||||||||
\(59\) | −8.89097 | −1.15751 | −0.578753 | − | 0.815503i | \(-0.696460\pi\) | ||||
−0.578753 | + | 0.815503i | \(0.696460\pi\) | |||||||
\(60\) | 0.519113 | 0.0670172 | ||||||||
\(61\) | 3.53783 | 0.452973 | 0.226487 | − | 0.974014i | \(-0.427276\pi\) | ||||
0.226487 | + | 0.974014i | \(0.427276\pi\) | |||||||
\(62\) | 4.91518 | 0.624228 | ||||||||
\(63\) | −2.83816 | −0.357574 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.79035 | 0.718204 | ||||||||
\(66\) | −1.71758 | −0.211419 | ||||||||
\(67\) | 6.08722 | 0.743672 | 0.371836 | − | 0.928298i | \(-0.378728\pi\) | ||||
0.371836 | + | 0.928298i | \(0.378728\pi\) | |||||||
\(68\) | −5.29141 | −0.641678 | ||||||||
\(69\) | 0.632695 | 0.0761675 | ||||||||
\(70\) | 1.29038 | 0.154230 | ||||||||
\(71\) | 7.41357 | 0.879829 | 0.439915 | − | 0.898040i | \(-0.355009\pi\) | ||||
0.439915 | + | 0.898040i | \(0.355009\pi\) | |||||||
\(72\) | −2.83816 | −0.334480 | ||||||||
\(73\) | 16.8789 | 1.97553 | 0.987763 | − | 0.155964i | \(-0.0498485\pi\) | ||||
0.987763 | + | 0.155964i | \(0.0498485\pi\) | |||||||
\(74\) | 1.33586 | 0.155291 | ||||||||
\(75\) | −1.34162 | −0.154917 | ||||||||
\(76\) | −4.09738 | −0.470002 | ||||||||
\(77\) | −4.26945 | −0.486549 | ||||||||
\(78\) | 1.80523 | 0.204402 | ||||||||
\(79\) | 4.63855 | 0.521877 | 0.260939 | − | 0.965355i | \(-0.415968\pi\) | ||||
0.260939 | + | 0.965355i | \(0.415968\pi\) | |||||||
\(80\) | 1.29038 | 0.144269 | ||||||||
\(81\) | 7.56962 | 0.841069 | ||||||||
\(82\) | −12.7678 | −1.40997 | ||||||||
\(83\) | 13.3622 | 1.46670 | 0.733348 | − | 0.679854i | \(-0.237957\pi\) | ||||
0.733348 | + | 0.679854i | \(0.237957\pi\) | |||||||
\(84\) | 0.402295 | 0.0438940 | ||||||||
\(85\) | −6.82793 | −0.740593 | ||||||||
\(86\) | −10.1930 | −1.09914 | ||||||||
\(87\) | −2.77563 | −0.297579 | ||||||||
\(88\) | −4.26945 | −0.455125 | ||||||||
\(89\) | −13.1678 | −1.39578 | −0.697890 | − | 0.716205i | \(-0.745878\pi\) | ||||
−0.697890 | + | 0.716205i | \(0.745878\pi\) | |||||||
\(90\) | −3.66230 | −0.386041 | ||||||||
\(91\) | 4.48732 | 0.470399 | ||||||||
\(92\) | 1.57271 | 0.163967 | ||||||||
\(93\) | 1.97735 | 0.205042 | ||||||||
\(94\) | −10.9210 | −1.12641 | ||||||||
\(95\) | −5.28718 | −0.542454 | ||||||||
\(96\) | 0.402295 | 0.0410590 | ||||||||
\(97\) | −11.1611 | −1.13323 | −0.566617 | − | 0.823981i | \(-0.691748\pi\) | ||||
−0.566617 | + | 0.823981i | \(0.691748\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 12.1174 | 1.21784 | ||||||||
\(100\) | −3.33492 | −0.333492 | ||||||||
\(101\) | −14.1440 | −1.40739 | −0.703693 | − | 0.710505i | \(-0.748467\pi\) | ||||
−0.703693 | + | 0.710505i | \(0.748467\pi\) | |||||||
\(102\) | −2.12871 | −0.210773 | ||||||||
\(103\) | 8.10218 | 0.798331 | 0.399166 | − | 0.916879i | \(-0.369300\pi\) | ||||
0.399166 | + | 0.916879i | \(0.369300\pi\) | |||||||
\(104\) | 4.48732 | 0.440018 | ||||||||
\(105\) | 0.519113 | 0.0506602 | ||||||||
\(106\) | 5.46626 | 0.530930 | ||||||||
\(107\) | −8.03379 | −0.776656 | −0.388328 | − | 0.921521i | \(-0.626947\pi\) | ||||
−0.388328 | + | 0.921521i | \(0.626947\pi\) | |||||||
\(108\) | −2.34866 | −0.226000 | ||||||||
\(109\) | −0.168957 | −0.0161831 | −0.00809155 | − | 0.999967i | \(-0.502576\pi\) | ||||
−0.00809155 | + | 0.999967i | \(0.502576\pi\) | |||||||
\(110\) | −5.50921 | −0.525283 | ||||||||
\(111\) | 0.537410 | 0.0510087 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 17.0693 | 1.60574 | 0.802872 | − | 0.596152i | \(-0.203304\pi\) | ||||
0.802872 | + | 0.596152i | \(0.203304\pi\) | |||||||
\(114\) | −1.64836 | −0.154383 | ||||||||
\(115\) | 2.02940 | 0.189242 | ||||||||
\(116\) | −6.89951 | −0.640603 | ||||||||
\(117\) | −12.7357 | −1.17742 | ||||||||
\(118\) | −8.89097 | −0.818480 | ||||||||
\(119\) | −5.29141 | −0.485063 | ||||||||
\(120\) | 0.519113 | 0.0473883 | ||||||||
\(121\) | 7.22821 | 0.657110 | ||||||||
\(122\) | 3.53783 | 0.320301 | ||||||||
\(123\) | −5.13644 | −0.463137 | ||||||||
\(124\) | 4.91518 | 0.441396 | ||||||||
\(125\) | −10.7552 | −0.961976 | ||||||||
\(126\) | −2.83816 | −0.252843 | ||||||||
\(127\) | −17.2185 | −1.52789 | −0.763947 | − | 0.645279i | \(-0.776741\pi\) | ||||
−0.763947 | + | 0.645279i | \(0.776741\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −4.10058 | −0.361036 | ||||||||
\(130\) | 5.79035 | 0.507847 | ||||||||
\(131\) | −14.2327 | −1.24352 | −0.621759 | − | 0.783209i | \(-0.713582\pi\) | ||||
−0.621759 | + | 0.783209i | \(0.713582\pi\) | |||||||
\(132\) | −1.71758 | −0.149496 | ||||||||
\(133\) | −4.09738 | −0.355288 | ||||||||
\(134\) | 6.08722 | 0.525855 | ||||||||
\(135\) | −3.03066 | −0.260838 | ||||||||
\(136\) | −5.29141 | −0.453735 | ||||||||
\(137\) | −10.4057 | −0.889019 | −0.444510 | − | 0.895774i | \(-0.646622\pi\) | ||||
−0.444510 | + | 0.895774i | \(0.646622\pi\) | |||||||
\(138\) | 0.632695 | 0.0538585 | ||||||||
\(139\) | 0.839150 | 0.0711757 | 0.0355879 | − | 0.999367i | \(-0.488670\pi\) | ||||
0.0355879 | + | 0.999367i | \(0.488670\pi\) | |||||||
\(140\) | 1.29038 | 0.109057 | ||||||||
\(141\) | −4.39345 | −0.369996 | ||||||||
\(142\) | 7.41357 | 0.622133 | ||||||||
\(143\) | −19.1584 | −1.60211 | ||||||||
\(144\) | −2.83816 | −0.236513 | ||||||||
\(145\) | −8.90298 | −0.739353 | ||||||||
\(146\) | 16.8789 | 1.39691 | ||||||||
\(147\) | 0.402295 | 0.0331807 | ||||||||
\(148\) | 1.33586 | 0.109807 | ||||||||
\(149\) | 7.11269 | 0.582694 | 0.291347 | − | 0.956617i | \(-0.405897\pi\) | ||||
0.291347 | + | 0.956617i | \(0.405897\pi\) | |||||||
\(150\) | −1.34162 | −0.109543 | ||||||||
\(151\) | 4.13649 | 0.336622 | 0.168311 | − | 0.985734i | \(-0.446169\pi\) | ||||
0.168311 | + | 0.985734i | \(0.446169\pi\) | |||||||
\(152\) | −4.09738 | −0.332342 | ||||||||
\(153\) | 15.0179 | 1.21412 | ||||||||
\(154\) | −4.26945 | −0.344042 | ||||||||
\(155\) | 6.34244 | 0.509437 | ||||||||
\(156\) | 1.80523 | 0.144534 | ||||||||
\(157\) | −20.8366 | −1.66294 | −0.831472 | − | 0.555566i | \(-0.812502\pi\) | ||||
−0.831472 | + | 0.555566i | \(0.812502\pi\) | |||||||
\(158\) | 4.63855 | 0.369023 | ||||||||
\(159\) | 2.19905 | 0.174396 | ||||||||
\(160\) | 1.29038 | 0.102013 | ||||||||
\(161\) | 1.57271 | 0.123947 | ||||||||
\(162\) | 7.56962 | 0.594726 | ||||||||
\(163\) | −10.3606 | −0.811503 | −0.405752 | − | 0.913983i | \(-0.632990\pi\) | ||||
−0.405752 | + | 0.913983i | \(0.632990\pi\) | |||||||
\(164\) | −12.7678 | −0.997001 | ||||||||
\(165\) | −2.21633 | −0.172541 | ||||||||
\(166\) | 13.3622 | 1.03711 | ||||||||
\(167\) | 6.98350 | 0.540400 | 0.270200 | − | 0.962804i | \(-0.412910\pi\) | ||||
0.270200 | + | 0.962804i | \(0.412910\pi\) | |||||||
\(168\) | 0.402295 | 0.0310377 | ||||||||
\(169\) | 7.13604 | 0.548926 | ||||||||
\(170\) | −6.82793 | −0.523678 | ||||||||
\(171\) | 11.6290 | 0.889294 | ||||||||
\(172\) | −10.1930 | −0.777206 | ||||||||
\(173\) | 8.61652 | 0.655102 | 0.327551 | − | 0.944833i | \(-0.393777\pi\) | ||||
0.327551 | + | 0.944833i | \(0.393777\pi\) | |||||||
\(174\) | −2.77563 | −0.210420 | ||||||||
\(175\) | −3.33492 | −0.252096 | ||||||||
\(176\) | −4.26945 | −0.321822 | ||||||||
\(177\) | −3.57679 | −0.268848 | ||||||||
\(178\) | −13.1678 | −0.986966 | ||||||||
\(179\) | 6.07710 | 0.454224 | 0.227112 | − | 0.973869i | \(-0.427072\pi\) | ||||
0.227112 | + | 0.973869i | \(0.427072\pi\) | |||||||
\(180\) | −3.66230 | −0.272972 | ||||||||
\(181\) | 24.2041 | 1.79907 | 0.899537 | − | 0.436844i | \(-0.143904\pi\) | ||||
0.899537 | + | 0.436844i | \(0.143904\pi\) | |||||||
\(182\) | 4.48732 | 0.332622 | ||||||||
\(183\) | 1.42325 | 0.105210 | ||||||||
\(184\) | 1.57271 | 0.115942 | ||||||||
\(185\) | 1.72377 | 0.126734 | ||||||||
\(186\) | 1.97735 | 0.144986 | ||||||||
\(187\) | 22.5914 | 1.65205 | ||||||||
\(188\) | −10.9210 | −0.796495 | ||||||||
\(189\) | −2.34866 | −0.170840 | ||||||||
\(190\) | −5.28718 | −0.383573 | ||||||||
\(191\) | −18.9466 | −1.37093 | −0.685464 | − | 0.728106i | \(-0.740401\pi\) | ||||
−0.685464 | + | 0.728106i | \(0.740401\pi\) | |||||||
\(192\) | 0.402295 | 0.0290331 | ||||||||
\(193\) | 7.10269 | 0.511263 | 0.255631 | − | 0.966774i | \(-0.417717\pi\) | ||||
0.255631 | + | 0.966774i | \(0.417717\pi\) | |||||||
\(194\) | −11.1611 | −0.801317 | ||||||||
\(195\) | 2.32943 | 0.166814 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 18.6519 | 1.32889 | 0.664447 | − | 0.747336i | \(-0.268667\pi\) | ||||
0.664447 | + | 0.747336i | \(0.268667\pi\) | |||||||
\(198\) | 12.1174 | 0.861145 | ||||||||
\(199\) | 18.6356 | 1.32104 | 0.660520 | − | 0.750808i | \(-0.270336\pi\) | ||||
0.660520 | + | 0.750808i | \(0.270336\pi\) | |||||||
\(200\) | −3.33492 | −0.235814 | ||||||||
\(201\) | 2.44885 | 0.172729 | ||||||||
\(202\) | −14.1440 | −0.995172 | ||||||||
\(203\) | −6.89951 | −0.484250 | ||||||||
\(204\) | −2.12871 | −0.149039 | ||||||||
\(205\) | −16.4754 | −1.15069 | ||||||||
\(206\) | 8.10218 | 0.564506 | ||||||||
\(207\) | −4.46361 | −0.310243 | ||||||||
\(208\) | 4.48732 | 0.311140 | ||||||||
\(209\) | 17.4936 | 1.21006 | ||||||||
\(210\) | 0.519113 | 0.0358222 | ||||||||
\(211\) | 15.4689 | 1.06493 | 0.532463 | − | 0.846454i | \(-0.321267\pi\) | ||||
0.532463 | + | 0.846454i | \(0.321267\pi\) | |||||||
\(212\) | 5.46626 | 0.375424 | ||||||||
\(213\) | 2.98244 | 0.204354 | ||||||||
\(214\) | −8.03379 | −0.549179 | ||||||||
\(215\) | −13.1528 | −0.897013 | ||||||||
\(216\) | −2.34866 | −0.159806 | ||||||||
\(217\) | 4.91518 | 0.333664 | ||||||||
\(218\) | −0.168957 | −0.0114432 | ||||||||
\(219\) | 6.79029 | 0.458845 | ||||||||
\(220\) | −5.50921 | −0.371431 | ||||||||
\(221\) | −23.7442 | −1.59721 | ||||||||
\(222\) | 0.537410 | 0.0360686 | ||||||||
\(223\) | 12.2261 | 0.818718 | 0.409359 | − | 0.912373i | \(-0.365752\pi\) | ||||
0.409359 | + | 0.912373i | \(0.365752\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 9.46503 | 0.631002 | ||||||||
\(226\) | 17.0693 | 1.13543 | ||||||||
\(227\) | 13.0966 | 0.869253 | 0.434626 | − | 0.900611i | \(-0.356880\pi\) | ||||
0.434626 | + | 0.900611i | \(0.356880\pi\) | |||||||
\(228\) | −1.64836 | −0.109165 | ||||||||
\(229\) | 19.3324 | 1.27752 | 0.638760 | − | 0.769406i | \(-0.279448\pi\) | ||||
0.638760 | + | 0.769406i | \(0.279448\pi\) | |||||||
\(230\) | 2.02940 | 0.133815 | ||||||||
\(231\) | −1.71758 | −0.113008 | ||||||||
\(232\) | −6.89951 | −0.452975 | ||||||||
\(233\) | −17.6137 | −1.15392 | −0.576958 | − | 0.816774i | \(-0.695760\pi\) | ||||
−0.576958 | + | 0.816774i | \(0.695760\pi\) | |||||||
\(234\) | −12.7357 | −0.832561 | ||||||||
\(235\) | −14.0922 | −0.919275 | ||||||||
\(236\) | −8.89097 | −0.578753 | ||||||||
\(237\) | 1.86606 | 0.121214 | ||||||||
\(238\) | −5.29141 | −0.342991 | ||||||||
\(239\) | 13.4662 | 0.871057 | 0.435529 | − | 0.900175i | \(-0.356561\pi\) | ||||
0.435529 | + | 0.900175i | \(0.356561\pi\) | |||||||
\(240\) | 0.519113 | 0.0335086 | ||||||||
\(241\) | −25.3288 | −1.63157 | −0.815785 | − | 0.578355i | \(-0.803695\pi\) | ||||
−0.815785 | + | 0.578355i | \(0.803695\pi\) | |||||||
\(242\) | 7.22821 | 0.464647 | ||||||||
\(243\) | 10.0912 | 0.647351 | ||||||||
\(244\) | 3.53783 | 0.226487 | ||||||||
\(245\) | 1.29038 | 0.0824394 | ||||||||
\(246\) | −5.13644 | −0.327487 | ||||||||
\(247\) | −18.3863 | −1.16989 | ||||||||
\(248\) | 4.91518 | 0.312114 | ||||||||
\(249\) | 5.37555 | 0.340662 | ||||||||
\(250\) | −10.7552 | −0.680219 | ||||||||
\(251\) | −1.58647 | −0.100137 | −0.0500684 | − | 0.998746i | \(-0.515944\pi\) | ||||
−0.0500684 | + | 0.998746i | \(0.515944\pi\) | |||||||
\(252\) | −2.83816 | −0.178787 | ||||||||
\(253\) | −6.71463 | −0.422145 | ||||||||
\(254\) | −17.2185 | −1.08038 | ||||||||
\(255\) | −2.74684 | −0.172014 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 12.7615 | 0.796042 | 0.398021 | − | 0.917376i | \(-0.369697\pi\) | ||||
0.398021 | + | 0.917376i | \(0.369697\pi\) | |||||||
\(258\) | −4.10058 | −0.255291 | ||||||||
\(259\) | 1.33586 | 0.0830065 | ||||||||
\(260\) | 5.79035 | 0.359102 | ||||||||
\(261\) | 19.5819 | 1.21209 | ||||||||
\(262\) | −14.2327 | −0.879300 | ||||||||
\(263\) | −5.94191 | −0.366394 | −0.183197 | − | 0.983076i | \(-0.558645\pi\) | ||||
−0.183197 | + | 0.983076i | \(0.558645\pi\) | |||||||
\(264\) | −1.71758 | −0.105710 | ||||||||
\(265\) | 7.05355 | 0.433296 | ||||||||
\(266\) | −4.09738 | −0.251227 | ||||||||
\(267\) | −5.29732 | −0.324191 | ||||||||
\(268\) | 6.08722 | 0.371836 | ||||||||
\(269\) | −22.8417 | −1.39268 | −0.696341 | − | 0.717711i | \(-0.745190\pi\) | ||||
−0.696341 | + | 0.717711i | \(0.745190\pi\) | |||||||
\(270\) | −3.03066 | −0.184440 | ||||||||
\(271\) | 4.28619 | 0.260368 | 0.130184 | − | 0.991490i | \(-0.458443\pi\) | ||||
0.130184 | + | 0.991490i | \(0.458443\pi\) | |||||||
\(272\) | −5.29141 | −0.320839 | ||||||||
\(273\) | 1.80523 | 0.109257 | ||||||||
\(274\) | −10.4057 | −0.628631 | ||||||||
\(275\) | 14.2383 | 0.858600 | ||||||||
\(276\) | 0.632695 | 0.0380837 | ||||||||
\(277\) | −26.8331 | −1.61224 | −0.806122 | − | 0.591749i | \(-0.798438\pi\) | ||||
−0.806122 | + | 0.591749i | \(0.798438\pi\) | |||||||
\(278\) | 0.839150 | 0.0503289 | ||||||||
\(279\) | −13.9500 | −0.835168 | ||||||||
\(280\) | 1.29038 | 0.0771150 | ||||||||
\(281\) | 5.11611 | 0.305202 | 0.152601 | − | 0.988288i | \(-0.451235\pi\) | ||||
0.152601 | + | 0.988288i | \(0.451235\pi\) | |||||||
\(282\) | −4.39345 | −0.261626 | ||||||||
\(283\) | −26.1743 | −1.55590 | −0.777950 | − | 0.628326i | \(-0.783740\pi\) | ||||
−0.777950 | + | 0.628326i | \(0.783740\pi\) | |||||||
\(284\) | 7.41357 | 0.439915 | ||||||||
\(285\) | −2.12701 | −0.125993 | ||||||||
\(286\) | −19.1584 | −1.13286 | ||||||||
\(287\) | −12.7678 | −0.753662 | ||||||||
\(288\) | −2.83816 | −0.167240 | ||||||||
\(289\) | 10.9990 | 0.647000 | ||||||||
\(290\) | −8.90298 | −0.522801 | ||||||||
\(291\) | −4.49004 | −0.263211 | ||||||||
\(292\) | 16.8789 | 0.987763 | ||||||||
\(293\) | −13.5050 | −0.788968 | −0.394484 | − | 0.918903i | \(-0.629077\pi\) | ||||
−0.394484 | + | 0.918903i | \(0.629077\pi\) | |||||||
\(294\) | 0.402295 | 0.0234623 | ||||||||
\(295\) | −11.4727 | −0.667968 | ||||||||
\(296\) | 1.33586 | 0.0776454 | ||||||||
\(297\) | 10.0275 | 0.581854 | ||||||||
\(298\) | 7.11269 | 0.412027 | ||||||||
\(299\) | 7.05727 | 0.408133 | ||||||||
\(300\) | −1.34162 | −0.0774585 | ||||||||
\(301\) | −10.1930 | −0.587513 | ||||||||
\(302\) | 4.13649 | 0.238028 | ||||||||
\(303\) | −5.69008 | −0.326886 | ||||||||
\(304\) | −4.09738 | −0.235001 | ||||||||
\(305\) | 4.56515 | 0.261400 | ||||||||
\(306\) | 15.0179 | 0.858514 | ||||||||
\(307\) | 18.7583 | 1.07059 | 0.535297 | − | 0.844664i | \(-0.320200\pi\) | ||||
0.535297 | + | 0.844664i | \(0.320200\pi\) | |||||||
\(308\) | −4.26945 | −0.243275 | ||||||||
\(309\) | 3.25946 | 0.185424 | ||||||||
\(310\) | 6.34244 | 0.360227 | ||||||||
\(311\) | −3.76364 | −0.213416 | −0.106708 | − | 0.994290i | \(-0.534031\pi\) | ||||
−0.106708 | + | 0.994290i | \(0.534031\pi\) | |||||||
\(312\) | 1.80523 | 0.102201 | ||||||||
\(313\) | 14.3209 | 0.809466 | 0.404733 | − | 0.914435i | \(-0.367365\pi\) | ||||
0.404733 | + | 0.914435i | \(0.367365\pi\) | |||||||
\(314\) | −20.8366 | −1.17588 | ||||||||
\(315\) | −3.66230 | −0.206347 | ||||||||
\(316\) | 4.63855 | 0.260939 | ||||||||
\(317\) | −0.961763 | −0.0540180 | −0.0270090 | − | 0.999635i | \(-0.508598\pi\) | ||||
−0.0270090 | + | 0.999635i | \(0.508598\pi\) | |||||||
\(318\) | 2.19905 | 0.123316 | ||||||||
\(319\) | 29.4571 | 1.64928 | ||||||||
\(320\) | 1.29038 | 0.0721344 | ||||||||
\(321\) | −3.23195 | −0.180390 | ||||||||
\(322\) | 1.57271 | 0.0876439 | ||||||||
\(323\) | 21.6809 | 1.20636 | ||||||||
\(324\) | 7.56962 | 0.420535 | ||||||||
\(325\) | −14.9649 | −0.830101 | ||||||||
\(326\) | −10.3606 | −0.573819 | ||||||||
\(327\) | −0.0679703 | −0.00375877 | ||||||||
\(328\) | −12.7678 | −0.704986 | ||||||||
\(329\) | −10.9210 | −0.602093 | ||||||||
\(330\) | −2.21633 | −0.122005 | ||||||||
\(331\) | 17.1265 | 0.941360 | 0.470680 | − | 0.882304i | \(-0.344009\pi\) | ||||
0.470680 | + | 0.882304i | \(0.344009\pi\) | |||||||
\(332\) | 13.3622 | 0.733348 | ||||||||
\(333\) | −3.79139 | −0.207767 | ||||||||
\(334\) | 6.98350 | 0.382120 | ||||||||
\(335\) | 7.85482 | 0.429155 | ||||||||
\(336\) | 0.402295 | 0.0219470 | ||||||||
\(337\) | −11.3371 | −0.617570 | −0.308785 | − | 0.951132i | \(-0.599922\pi\) | ||||
−0.308785 | + | 0.951132i | \(0.599922\pi\) | |||||||
\(338\) | 7.13604 | 0.388150 | ||||||||
\(339\) | 6.86688 | 0.372958 | ||||||||
\(340\) | −6.82793 | −0.370296 | ||||||||
\(341\) | −20.9851 | −1.13641 | ||||||||
\(342\) | 11.6290 | 0.628826 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −10.1930 | −0.549568 | ||||||||
\(345\) | 0.816416 | 0.0439544 | ||||||||
\(346\) | 8.61652 | 0.463227 | ||||||||
\(347\) | −18.6999 | −1.00386 | −0.501931 | − | 0.864908i | \(-0.667377\pi\) | ||||
−0.501931 | + | 0.864908i | \(0.667377\pi\) | |||||||
\(348\) | −2.77563 | −0.148790 | ||||||||
\(349\) | 23.4872 | 1.25724 | 0.628620 | − | 0.777713i | \(-0.283620\pi\) | ||||
0.628620 | + | 0.777713i | \(0.283620\pi\) | |||||||
\(350\) | −3.33492 | −0.178259 | ||||||||
\(351\) | −10.5392 | −0.562540 | ||||||||
\(352\) | −4.26945 | −0.227563 | ||||||||
\(353\) | 19.2863 | 1.02650 | 0.513252 | − | 0.858238i | \(-0.328441\pi\) | ||||
0.513252 | + | 0.858238i | \(0.328441\pi\) | |||||||
\(354\) | −3.57679 | −0.190104 | ||||||||
\(355\) | 9.56633 | 0.507728 | ||||||||
\(356\) | −13.1678 | −0.697890 | ||||||||
\(357\) | −2.12871 | −0.112663 | ||||||||
\(358\) | 6.07710 | 0.321185 | ||||||||
\(359\) | 8.66200 | 0.457163 | 0.228581 | − | 0.973525i | \(-0.426591\pi\) | ||||
0.228581 | + | 0.973525i | \(0.426591\pi\) | |||||||
\(360\) | −3.66230 | −0.193020 | ||||||||
\(361\) | −2.21144 | −0.116392 | ||||||||
\(362\) | 24.2041 | 1.27214 | ||||||||
\(363\) | 2.90787 | 0.152624 | ||||||||
\(364\) | 4.48732 | 0.235199 | ||||||||
\(365\) | 21.7802 | 1.14003 | ||||||||
\(366\) | 1.42325 | 0.0743946 | ||||||||
\(367\) | −0.608611 | −0.0317692 | −0.0158846 | − | 0.999874i | \(-0.505056\pi\) | ||||
−0.0158846 | + | 0.999874i | \(0.505056\pi\) | |||||||
\(368\) | 1.57271 | 0.0819834 | ||||||||
\(369\) | 36.2372 | 1.88643 | ||||||||
\(370\) | 1.72377 | 0.0896146 | ||||||||
\(371\) | 5.46626 | 0.283794 | ||||||||
\(372\) | 1.97735 | 0.102521 | ||||||||
\(373\) | −28.4115 | −1.47109 | −0.735546 | − | 0.677475i | \(-0.763074\pi\) | ||||
−0.735546 | + | 0.677475i | \(0.763074\pi\) | |||||||
\(374\) | 22.5914 | 1.16817 | ||||||||
\(375\) | −4.32677 | −0.223433 | ||||||||
\(376\) | −10.9210 | −0.563207 | ||||||||
\(377\) | −30.9603 | −1.59454 | ||||||||
\(378\) | −2.34866 | −0.120802 | ||||||||
\(379\) | 13.6763 | 0.702504 | 0.351252 | − | 0.936281i | \(-0.385756\pi\) | ||||
0.351252 | + | 0.936281i | \(0.385756\pi\) | |||||||
\(380\) | −5.28718 | −0.271227 | ||||||||
\(381\) | −6.92691 | −0.354876 | ||||||||
\(382\) | −18.9466 | −0.969393 | ||||||||
\(383\) | −17.9619 | −0.917810 | −0.458905 | − | 0.888485i | \(-0.651758\pi\) | ||||
−0.458905 | + | 0.888485i | \(0.651758\pi\) | |||||||
\(384\) | 0.402295 | 0.0205295 | ||||||||
\(385\) | −5.50921 | −0.280776 | ||||||||
\(386\) | 7.10269 | 0.361517 | ||||||||
\(387\) | 28.9293 | 1.47056 | ||||||||
\(388\) | −11.1611 | −0.566617 | ||||||||
\(389\) | −5.82184 | −0.295179 | −0.147590 | − | 0.989049i | \(-0.547151\pi\) | ||||
−0.147590 | + | 0.989049i | \(0.547151\pi\) | |||||||
\(390\) | 2.32943 | 0.117955 | ||||||||
\(391\) | −8.32187 | −0.420855 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −5.72574 | −0.288826 | ||||||||
\(394\) | 18.6519 | 0.939670 | ||||||||
\(395\) | 5.98549 | 0.301163 | ||||||||
\(396\) | 12.1174 | 0.608921 | ||||||||
\(397\) | −33.0817 | −1.66032 | −0.830162 | − | 0.557522i | \(-0.811752\pi\) | ||||
−0.830162 | + | 0.557522i | \(0.811752\pi\) | |||||||
\(398\) | 18.6356 | 0.934117 | ||||||||
\(399\) | −1.64836 | −0.0825210 | ||||||||
\(400\) | −3.33492 | −0.166746 | ||||||||
\(401\) | −32.8107 | −1.63849 | −0.819245 | − | 0.573444i | \(-0.805607\pi\) | ||||
−0.819245 | + | 0.573444i | \(0.805607\pi\) | |||||||
\(402\) | 2.44885 | 0.122138 | ||||||||
\(403\) | 22.0560 | 1.09869 | ||||||||
\(404\) | −14.1440 | −0.703693 | ||||||||
\(405\) | 9.76769 | 0.485360 | ||||||||
\(406\) | −6.89951 | −0.342417 | ||||||||
\(407\) | −5.70340 | −0.282707 | ||||||||
\(408\) | −2.12871 | −0.105387 | ||||||||
\(409\) | 24.4040 | 1.20670 | 0.603349 | − | 0.797477i | \(-0.293833\pi\) | ||||
0.603349 | + | 0.797477i | \(0.293833\pi\) | |||||||
\(410\) | −16.4754 | −0.813660 | ||||||||
\(411\) | −4.18616 | −0.206488 | ||||||||
\(412\) | 8.10218 | 0.399166 | ||||||||
\(413\) | −8.89097 | −0.437496 | ||||||||
\(414\) | −4.46361 | −0.219375 | ||||||||
\(415\) | 17.2424 | 0.846394 | ||||||||
\(416\) | 4.48732 | 0.220009 | ||||||||
\(417\) | 0.337585 | 0.0165316 | ||||||||
\(418\) | 17.4936 | 0.855639 | ||||||||
\(419\) | −32.2470 | −1.57537 | −0.787685 | − | 0.616078i | \(-0.788720\pi\) | ||||
−0.787685 | + | 0.616078i | \(0.788720\pi\) | |||||||
\(420\) | 0.519113 | 0.0253301 | ||||||||
\(421\) | −19.6786 | −0.959076 | −0.479538 | − | 0.877521i | \(-0.659196\pi\) | ||||
−0.479538 | + | 0.877521i | \(0.659196\pi\) | |||||||
\(422\) | 15.4689 | 0.753016 | ||||||||
\(423\) | 30.9955 | 1.50705 | ||||||||
\(424\) | 5.46626 | 0.265465 | ||||||||
\(425\) | 17.6464 | 0.855977 | ||||||||
\(426\) | 2.98244 | 0.144500 | ||||||||
\(427\) | 3.53783 | 0.171208 | ||||||||
\(428\) | −8.03379 | −0.388328 | ||||||||
\(429\) | −7.70732 | −0.372113 | ||||||||
\(430\) | −13.1528 | −0.634284 | ||||||||
\(431\) | −1.00000 | −0.0481683 | ||||||||
\(432\) | −2.34866 | −0.113000 | ||||||||
\(433\) | −1.99480 | −0.0958640 | −0.0479320 | − | 0.998851i | \(-0.515263\pi\) | ||||
−0.0479320 | + | 0.998851i | \(0.515263\pi\) | |||||||
\(434\) | 4.91518 | 0.235936 | ||||||||
\(435\) | −3.58162 | −0.171726 | ||||||||
\(436\) | −0.168957 | −0.00809155 | ||||||||
\(437\) | −6.44401 | −0.308259 | ||||||||
\(438\) | 6.79029 | 0.324453 | ||||||||
\(439\) | −35.9660 | −1.71656 | −0.858281 | − | 0.513180i | \(-0.828467\pi\) | ||||
−0.858281 | + | 0.513180i | \(0.828467\pi\) | |||||||
\(440\) | −5.50921 | −0.262641 | ||||||||
\(441\) | −2.83816 | −0.135150 | ||||||||
\(442\) | −23.7442 | −1.12940 | ||||||||
\(443\) | −34.2598 | −1.62773 | −0.813866 | − | 0.581053i | \(-0.802641\pi\) | ||||
−0.813866 | + | 0.581053i | \(0.802641\pi\) | |||||||
\(444\) | 0.537410 | 0.0255044 | ||||||||
\(445\) | −16.9914 | −0.805471 | ||||||||
\(446\) | 12.2261 | 0.578921 | ||||||||
\(447\) | 2.86140 | 0.135339 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | 3.00677 | 0.141898 | 0.0709492 | − | 0.997480i | \(-0.477397\pi\) | ||||
0.0709492 | + | 0.997480i | \(0.477397\pi\) | |||||||
\(450\) | 9.46503 | 0.446186 | ||||||||
\(451\) | 54.5117 | 2.56685 | ||||||||
\(452\) | 17.0693 | 0.802872 | ||||||||
\(453\) | 1.66409 | 0.0781856 | ||||||||
\(454\) | 13.0966 | 0.614654 | ||||||||
\(455\) | 5.79035 | 0.271456 | ||||||||
\(456\) | −1.64836 | −0.0771913 | ||||||||
\(457\) | −19.5362 | −0.913863 | −0.456931 | − | 0.889502i | \(-0.651052\pi\) | ||||
−0.456931 | + | 0.889502i | \(0.651052\pi\) | |||||||
\(458\) | 19.3324 | 0.903343 | ||||||||
\(459\) | 12.4277 | 0.580076 | ||||||||
\(460\) | 2.02940 | 0.0946212 | ||||||||
\(461\) | 24.2117 | 1.12765 | 0.563825 | − | 0.825895i | \(-0.309329\pi\) | ||||
0.563825 | + | 0.825895i | \(0.309329\pi\) | |||||||
\(462\) | −1.71758 | −0.0799089 | ||||||||
\(463\) | 35.4816 | 1.64897 | 0.824486 | − | 0.565883i | \(-0.191465\pi\) | ||||
0.824486 | + | 0.565883i | \(0.191465\pi\) | |||||||
\(464\) | −6.89951 | −0.320301 | ||||||||
\(465\) | 2.55153 | 0.118324 | ||||||||
\(466\) | −17.6137 | −0.815941 | ||||||||
\(467\) | 25.0107 | 1.15736 | 0.578679 | − | 0.815555i | \(-0.303568\pi\) | ||||
0.578679 | + | 0.815555i | \(0.303568\pi\) | |||||||
\(468\) | −12.7357 | −0.588709 | ||||||||
\(469\) | 6.08722 | 0.281082 | ||||||||
\(470\) | −14.0922 | −0.650026 | ||||||||
\(471\) | −8.38247 | −0.386244 | ||||||||
\(472\) | −8.89097 | −0.409240 | ||||||||
\(473\) | 43.5184 | 2.00098 | ||||||||
\(474\) | 1.86606 | 0.0857111 | ||||||||
\(475\) | 13.6644 | 0.626968 | ||||||||
\(476\) | −5.29141 | −0.242531 | ||||||||
\(477\) | −15.5141 | −0.710343 | ||||||||
\(478\) | 13.4662 | 0.615930 | ||||||||
\(479\) | 2.45113 | 0.111995 | 0.0559974 | − | 0.998431i | \(-0.482166\pi\) | ||||
0.0559974 | + | 0.998431i | \(0.482166\pi\) | |||||||
\(480\) | 0.519113 | 0.0236942 | ||||||||
\(481\) | 5.99444 | 0.273323 | ||||||||
\(482\) | −25.3288 | −1.15369 | ||||||||
\(483\) | 0.632695 | 0.0287886 | ||||||||
\(484\) | 7.22821 | 0.328555 | ||||||||
\(485\) | −14.4020 | −0.653962 | ||||||||
\(486\) | 10.0912 | 0.457746 | ||||||||
\(487\) | −32.6827 | −1.48099 | −0.740497 | − | 0.672060i | \(-0.765410\pi\) | ||||
−0.740497 | + | 0.672060i | \(0.765410\pi\) | |||||||
\(488\) | 3.53783 | 0.160150 | ||||||||
\(489\) | −4.16801 | −0.188484 | ||||||||
\(490\) | 1.29038 | 0.0582934 | ||||||||
\(491\) | 40.8488 | 1.84348 | 0.921741 | − | 0.387805i | \(-0.126767\pi\) | ||||
0.921741 | + | 0.387805i | \(0.126767\pi\) | |||||||
\(492\) | −5.13644 | −0.231568 | ||||||||
\(493\) | 36.5081 | 1.64424 | ||||||||
\(494\) | −18.3863 | −0.827238 | ||||||||
\(495\) | 15.6360 | 0.702787 | ||||||||
\(496\) | 4.91518 | 0.220698 | ||||||||
\(497\) | 7.41357 | 0.332544 | ||||||||
\(498\) | 5.37555 | 0.240884 | ||||||||
\(499\) | 21.8637 | 0.978753 | 0.489376 | − | 0.872073i | \(-0.337224\pi\) | ||||
0.489376 | + | 0.872073i | \(0.337224\pi\) | |||||||
\(500\) | −10.7552 | −0.480988 | ||||||||
\(501\) | 2.80943 | 0.125516 | ||||||||
\(502\) | −1.58647 | −0.0708074 | ||||||||
\(503\) | −20.5702 | −0.917182 | −0.458591 | − | 0.888648i | \(-0.651646\pi\) | ||||
−0.458591 | + | 0.888648i | \(0.651646\pi\) | |||||||
\(504\) | −2.83816 | −0.126422 | ||||||||
\(505\) | −18.2512 | −0.812168 | ||||||||
\(506\) | −6.71463 | −0.298502 | ||||||||
\(507\) | 2.87079 | 0.127496 | ||||||||
\(508\) | −17.2185 | −0.763947 | ||||||||
\(509\) | −28.1182 | −1.24632 | −0.623158 | − | 0.782096i | \(-0.714151\pi\) | ||||
−0.623158 | + | 0.782096i | \(0.714151\pi\) | |||||||
\(510\) | −2.74684 | −0.121632 | ||||||||
\(511\) | 16.8789 | 0.746678 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 9.62336 | 0.424882 | ||||||||
\(514\) | 12.7615 | 0.562887 | ||||||||
\(515\) | 10.4549 | 0.460697 | ||||||||
\(516\) | −4.10058 | −0.180518 | ||||||||
\(517\) | 46.6266 | 2.05064 | ||||||||
\(518\) | 1.33586 | 0.0586944 | ||||||||
\(519\) | 3.46638 | 0.152157 | ||||||||
\(520\) | 5.79035 | 0.253924 | ||||||||
\(521\) | −20.0445 | −0.878167 | −0.439083 | − | 0.898446i | \(-0.644697\pi\) | ||||
−0.439083 | + | 0.898446i | \(0.644697\pi\) | |||||||
\(522\) | 19.5819 | 0.857076 | ||||||||
\(523\) | 32.6174 | 1.42626 | 0.713131 | − | 0.701031i | \(-0.247277\pi\) | ||||
0.713131 | + | 0.701031i | \(0.247277\pi\) | |||||||
\(524\) | −14.2327 | −0.621759 | ||||||||
\(525\) | −1.34162 | −0.0585531 | ||||||||
\(526\) | −5.94191 | −0.259079 | ||||||||
\(527\) | −26.0082 | −1.13293 | ||||||||
\(528\) | −1.71758 | −0.0747480 | ||||||||
\(529\) | −20.5266 | −0.892460 | ||||||||
\(530\) | 7.05355 | 0.306387 | ||||||||
\(531\) | 25.2340 | 1.09506 | ||||||||
\(532\) | −4.09738 | −0.177644 | ||||||||
\(533\) | −57.2934 | −2.48165 | ||||||||
\(534\) | −5.29732 | −0.229238 | ||||||||
\(535\) | −10.3666 | −0.448189 | ||||||||
\(536\) | 6.08722 | 0.262928 | ||||||||
\(537\) | 2.44478 | 0.105500 | ||||||||
\(538\) | −22.8417 | −0.984775 | ||||||||
\(539\) | −4.26945 | −0.183898 | ||||||||
\(540\) | −3.03066 | −0.130419 | ||||||||
\(541\) | −45.8958 | −1.97322 | −0.986608 | − | 0.163112i | \(-0.947847\pi\) | ||||
−0.986608 | + | 0.163112i | \(0.947847\pi\) | |||||||
\(542\) | 4.28619 | 0.184108 | ||||||||
\(543\) | 9.73717 | 0.417862 | ||||||||
\(544\) | −5.29141 | −0.226867 | ||||||||
\(545\) | −0.218018 | −0.00933887 | ||||||||
\(546\) | 1.80523 | 0.0772565 | ||||||||
\(547\) | 7.14405 | 0.305457 | 0.152729 | − | 0.988268i | \(-0.451194\pi\) | ||||
0.152729 | + | 0.988268i | \(0.451194\pi\) | |||||||
\(548\) | −10.4057 | −0.444510 | ||||||||
\(549\) | −10.0409 | −0.428537 | ||||||||
\(550\) | 14.2383 | 0.607122 | ||||||||
\(551\) | 28.2699 | 1.20434 | ||||||||
\(552\) | 0.632695 | 0.0269293 | ||||||||
\(553\) | 4.63855 | 0.197251 | ||||||||
\(554\) | −26.8331 | −1.14003 | ||||||||
\(555\) | 0.693464 | 0.0294359 | ||||||||
\(556\) | 0.839150 | 0.0355879 | ||||||||
\(557\) | 43.0882 | 1.82570 | 0.912852 | − | 0.408290i | \(-0.133875\pi\) | ||||
0.912852 | + | 0.408290i | \(0.133875\pi\) | |||||||
\(558\) | −13.9500 | −0.590553 | ||||||||
\(559\) | −45.7391 | −1.93456 | ||||||||
\(560\) | 1.29038 | 0.0545285 | ||||||||
\(561\) | 9.08840 | 0.383713 | ||||||||
\(562\) | 5.11611 | 0.215810 | ||||||||
\(563\) | 0.116114 | 0.00489361 | 0.00244681 | − | 0.999997i | \(-0.499221\pi\) | ||||
0.00244681 | + | 0.999997i | \(0.499221\pi\) | |||||||
\(564\) | −4.39345 | −0.184998 | ||||||||
\(565\) | 22.0259 | 0.926635 | ||||||||
\(566\) | −26.1743 | −1.10019 | ||||||||
\(567\) | 7.56962 | 0.317894 | ||||||||
\(568\) | 7.41357 | 0.311067 | ||||||||
\(569\) | −7.70421 | −0.322977 | −0.161489 | − | 0.986875i | \(-0.551630\pi\) | ||||
−0.161489 | + | 0.986875i | \(0.551630\pi\) | |||||||
\(570\) | −2.12701 | −0.0890905 | ||||||||
\(571\) | 9.71404 | 0.406520 | 0.203260 | − | 0.979125i | \(-0.434846\pi\) | ||||
0.203260 | + | 0.979125i | \(0.434846\pi\) | |||||||
\(572\) | −19.1584 | −0.801053 | ||||||||
\(573\) | −7.62212 | −0.318419 | ||||||||
\(574\) | −12.7678 | −0.532919 | ||||||||
\(575\) | −5.24488 | −0.218726 | ||||||||
\(576\) | −2.83816 | −0.118257 | ||||||||
\(577\) | −38.7478 | −1.61309 | −0.806547 | − | 0.591170i | \(-0.798666\pi\) | ||||
−0.806547 | + | 0.591170i | \(0.798666\pi\) | |||||||
\(578\) | 10.9990 | 0.457498 | ||||||||
\(579\) | 2.85737 | 0.118748 | ||||||||
\(580\) | −8.90298 | −0.369676 | ||||||||
\(581\) | 13.3622 | 0.554359 | ||||||||
\(582\) | −4.49004 | −0.186118 | ||||||||
\(583\) | −23.3379 | −0.966558 | ||||||||
\(584\) | 16.8789 | 0.698454 | ||||||||
\(585\) | −16.4339 | −0.679459 | ||||||||
\(586\) | −13.5050 | −0.557885 | ||||||||
\(587\) | 16.5051 | 0.681240 | 0.340620 | − | 0.940201i | \(-0.389363\pi\) | ||||
0.340620 | + | 0.940201i | \(0.389363\pi\) | |||||||
\(588\) | 0.402295 | 0.0165904 | ||||||||
\(589\) | −20.1394 | −0.829828 | ||||||||
\(590\) | −11.4727 | −0.472325 | ||||||||
\(591\) | 7.50356 | 0.308655 | ||||||||
\(592\) | 1.33586 | 0.0549036 | ||||||||
\(593\) | 7.74850 | 0.318193 | 0.159096 | − | 0.987263i | \(-0.449142\pi\) | ||||
0.159096 | + | 0.987263i | \(0.449142\pi\) | |||||||
\(594\) | 10.0275 | 0.411433 | ||||||||
\(595\) | −6.82793 | −0.279918 | ||||||||
\(596\) | 7.11269 | 0.291347 | ||||||||
\(597\) | 7.49699 | 0.306831 | ||||||||
\(598\) | 7.05727 | 0.288593 | ||||||||
\(599\) | −1.24804 | −0.0509934 | −0.0254967 | − | 0.999675i | \(-0.508117\pi\) | ||||
−0.0254967 | + | 0.999675i | \(0.508117\pi\) | |||||||
\(600\) | −1.34162 | −0.0547714 | ||||||||
\(601\) | 18.1173 | 0.739018 | 0.369509 | − | 0.929227i | \(-0.379526\pi\) | ||||
0.369509 | + | 0.929227i | \(0.379526\pi\) | |||||||
\(602\) | −10.1930 | −0.415434 | ||||||||
\(603\) | −17.2765 | −0.703553 | ||||||||
\(604\) | 4.13649 | 0.168311 | ||||||||
\(605\) | 9.32714 | 0.379202 | ||||||||
\(606\) | −5.69008 | −0.231144 | ||||||||
\(607\) | 7.48701 | 0.303888 | 0.151944 | − | 0.988389i | \(-0.451447\pi\) | ||||
0.151944 | + | 0.988389i | \(0.451447\pi\) | |||||||
\(608\) | −4.09738 | −0.166171 | ||||||||
\(609\) | −2.77563 | −0.112474 | ||||||||
\(610\) | 4.56515 | 0.184838 | ||||||||
\(611\) | −49.0060 | −1.98257 | ||||||||
\(612\) | 15.0179 | 0.607061 | ||||||||
\(613\) | −22.1711 | −0.895484 | −0.447742 | − | 0.894163i | \(-0.647772\pi\) | ||||
−0.447742 | + | 0.894163i | \(0.647772\pi\) | |||||||
\(614\) | 18.7583 | 0.757024 | ||||||||
\(615\) | −6.62795 | −0.267265 | ||||||||
\(616\) | −4.26945 | −0.172021 | ||||||||
\(617\) | −27.2472 | −1.09693 | −0.548466 | − | 0.836173i | \(-0.684788\pi\) | ||||
−0.548466 | + | 0.836173i | \(0.684788\pi\) | |||||||
\(618\) | 3.25946 | 0.131115 | ||||||||
\(619\) | −26.9935 | −1.08496 | −0.542480 | − | 0.840069i | \(-0.682514\pi\) | ||||
−0.542480 | + | 0.840069i | \(0.682514\pi\) | |||||||
\(620\) | 6.34244 | 0.254719 | ||||||||
\(621\) | −3.69377 | −0.148226 | ||||||||
\(622\) | −3.76364 | −0.150908 | ||||||||
\(623\) | −13.1678 | −0.527556 | ||||||||
\(624\) | 1.80523 | 0.0722668 | ||||||||
\(625\) | 2.79629 | 0.111851 | ||||||||
\(626\) | 14.3209 | 0.572379 | ||||||||
\(627\) | 7.03758 | 0.281054 | ||||||||
\(628\) | −20.8366 | −0.831472 | ||||||||
\(629\) | −7.06859 | −0.281843 | ||||||||
\(630\) | −3.66230 | −0.145910 | ||||||||
\(631\) | 28.3347 | 1.12799 | 0.563993 | − | 0.825780i | \(-0.309264\pi\) | ||||
0.563993 | + | 0.825780i | \(0.309264\pi\) | |||||||
\(632\) | 4.63855 | 0.184511 | ||||||||
\(633\) | 6.22307 | 0.247345 | ||||||||
\(634\) | −0.961763 | −0.0381965 | ||||||||
\(635\) | −22.2184 | −0.881710 | ||||||||
\(636\) | 2.19905 | 0.0871979 | ||||||||
\(637\) | 4.48732 | 0.177794 | ||||||||
\(638\) | 29.4571 | 1.16622 | ||||||||
\(639\) | −21.0409 | −0.832365 | ||||||||
\(640\) | 1.29038 | 0.0510067 | ||||||||
\(641\) | 10.1810 | 0.402127 | 0.201063 | − | 0.979578i | \(-0.435560\pi\) | ||||
0.201063 | + | 0.979578i | \(0.435560\pi\) | |||||||
\(642\) | −3.23195 | −0.127555 | ||||||||
\(643\) | −26.1316 | −1.03053 | −0.515264 | − | 0.857031i | \(-0.672306\pi\) | ||||
−0.515264 | + | 0.857031i | \(0.672306\pi\) | |||||||
\(644\) | 1.57271 | 0.0619736 | ||||||||
\(645\) | −5.29130 | −0.208345 | ||||||||
\(646\) | 21.6809 | 0.853025 | ||||||||
\(647\) | −9.77741 | −0.384390 | −0.192195 | − | 0.981357i | \(-0.561561\pi\) | ||||
−0.192195 | + | 0.981357i | \(0.561561\pi\) | |||||||
\(648\) | 7.56962 | 0.297363 | ||||||||
\(649\) | 37.9596 | 1.49004 | ||||||||
\(650\) | −14.9649 | −0.586970 | ||||||||
\(651\) | 1.97735 | 0.0774984 | ||||||||
\(652\) | −10.3606 | −0.405752 | ||||||||
\(653\) | 4.35039 | 0.170244 | 0.0851219 | − | 0.996371i | \(-0.472872\pi\) | ||||
0.0851219 | + | 0.996371i | \(0.472872\pi\) | |||||||
\(654\) | −0.0679703 | −0.00265785 | ||||||||
\(655\) | −18.3656 | −0.717604 | ||||||||
\(656\) | −12.7678 | −0.498500 | ||||||||
\(657\) | −47.9050 | −1.86895 | ||||||||
\(658\) | −10.9210 | −0.425744 | ||||||||
\(659\) | 30.0844 | 1.17192 | 0.585961 | − | 0.810339i | \(-0.300717\pi\) | ||||
0.585961 | + | 0.810339i | \(0.300717\pi\) | |||||||
\(660\) | −2.21633 | −0.0862704 | ||||||||
\(661\) | 4.34251 | 0.168904 | 0.0844521 | − | 0.996428i | \(-0.473086\pi\) | ||||
0.0844521 | + | 0.996428i | \(0.473086\pi\) | |||||||
\(662\) | 17.1265 | 0.665642 | ||||||||
\(663\) | −9.55218 | −0.370976 | ||||||||
\(664\) | 13.3622 | 0.518555 | ||||||||
\(665\) | −5.28718 | −0.205028 | ||||||||
\(666\) | −3.79139 | −0.146913 | ||||||||
\(667\) | −10.8509 | −0.420150 | ||||||||
\(668\) | 6.98350 | 0.270200 | ||||||||
\(669\) | 4.91848 | 0.190159 | ||||||||
\(670\) | 7.85482 | 0.303458 | ||||||||
\(671\) | −15.1046 | −0.583107 | ||||||||
\(672\) | 0.402295 | 0.0155189 | ||||||||
\(673\) | 35.1476 | 1.35484 | 0.677421 | − | 0.735596i | \(-0.263098\pi\) | ||||
0.677421 | + | 0.735596i | \(0.263098\pi\) | |||||||
\(674\) | −11.3371 | −0.436688 | ||||||||
\(675\) | 7.83259 | 0.301477 | ||||||||
\(676\) | 7.13604 | 0.274463 | ||||||||
\(677\) | 44.3919 | 1.70612 | 0.853061 | − | 0.521812i | \(-0.174744\pi\) | ||||
0.853061 | + | 0.521812i | \(0.174744\pi\) | |||||||
\(678\) | 6.86688 | 0.263721 | ||||||||
\(679\) | −11.1611 | −0.428322 | ||||||||
\(680\) | −6.82793 | −0.261839 | ||||||||
\(681\) | 5.26870 | 0.201897 | ||||||||
\(682\) | −20.9851 | −0.803561 | ||||||||
\(683\) | −22.0053 | −0.842011 | −0.421006 | − | 0.907058i | \(-0.638323\pi\) | ||||
−0.421006 | + | 0.907058i | \(0.638323\pi\) | |||||||
\(684\) | 11.6290 | 0.444647 | ||||||||
\(685\) | −13.4273 | −0.513031 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 7.77731 | 0.296723 | ||||||||
\(688\) | −10.1930 | −0.388603 | ||||||||
\(689\) | 24.5289 | 0.934475 | ||||||||
\(690\) | 0.816416 | 0.0310804 | ||||||||
\(691\) | 45.8748 | 1.74516 | 0.872580 | − | 0.488471i | \(-0.162445\pi\) | ||||
0.872580 | + | 0.488471i | \(0.162445\pi\) | |||||||
\(692\) | 8.61652 | 0.327551 | ||||||||
\(693\) | 12.1174 | 0.460301 | ||||||||
\(694\) | −18.6999 | −0.709837 | ||||||||
\(695\) | 1.08282 | 0.0410738 | ||||||||
\(696\) | −2.77563 | −0.105210 | ||||||||
\(697\) | 67.5599 | 2.55901 | ||||||||
\(698\) | 23.4872 | 0.889002 | ||||||||
\(699\) | −7.08592 | −0.268014 | ||||||||
\(700\) | −3.33492 | −0.126048 | ||||||||
\(701\) | −3.27195 | −0.123580 | −0.0617900 | − | 0.998089i | \(-0.519681\pi\) | ||||
−0.0617900 | + | 0.998089i | \(0.519681\pi\) | |||||||
\(702\) | −10.5392 | −0.397776 | ||||||||
\(703\) | −5.47354 | −0.206439 | ||||||||
\(704\) | −4.26945 | −0.160911 | ||||||||
\(705\) | −5.66923 | −0.213515 | ||||||||
\(706\) | 19.2863 | 0.725848 | ||||||||
\(707\) | −14.1440 | −0.531942 | ||||||||
\(708\) | −3.57679 | −0.134424 | ||||||||
\(709\) | −35.3918 | −1.32917 | −0.664584 | − | 0.747214i | \(-0.731391\pi\) | ||||
−0.664584 | + | 0.747214i | \(0.731391\pi\) | |||||||
\(710\) | 9.56633 | 0.359018 | ||||||||
\(711\) | −13.1649 | −0.493724 | ||||||||
\(712\) | −13.1678 | −0.493483 | ||||||||
\(713\) | 7.73017 | 0.289497 | ||||||||
\(714\) | −2.12871 | −0.0796648 | ||||||||
\(715\) | −24.7216 | −0.924536 | ||||||||
\(716\) | 6.07710 | 0.227112 | ||||||||
\(717\) | 5.41739 | 0.202316 | ||||||||
\(718\) | 8.66200 | 0.323263 | ||||||||
\(719\) | −36.9034 | −1.37626 | −0.688132 | − | 0.725586i | \(-0.741569\pi\) | ||||
−0.688132 | + | 0.725586i | \(0.741569\pi\) | |||||||
\(720\) | −3.66230 | −0.136486 | ||||||||
\(721\) | 8.10218 | 0.301741 | ||||||||
\(722\) | −2.21144 | −0.0823013 | ||||||||
\(723\) | −10.1896 | −0.378956 | ||||||||
\(724\) | 24.2041 | 0.899537 | ||||||||
\(725\) | 23.0093 | 0.854544 | ||||||||
\(726\) | 2.90787 | 0.107921 | ||||||||
\(727\) | 47.9409 | 1.77803 | 0.889014 | − | 0.457880i | \(-0.151391\pi\) | ||||
0.889014 | + | 0.457880i | \(0.151391\pi\) | |||||||
\(728\) | 4.48732 | 0.166311 | ||||||||
\(729\) | −18.6492 | −0.690712 | ||||||||
\(730\) | 21.7802 | 0.806121 | ||||||||
\(731\) | 53.9351 | 1.99486 | ||||||||
\(732\) | 1.42325 | 0.0526049 | ||||||||
\(733\) | −7.47973 | −0.276270 | −0.138135 | − | 0.990413i | \(-0.544111\pi\) | ||||
−0.138135 | + | 0.990413i | \(0.544111\pi\) | |||||||
\(734\) | −0.608611 | −0.0224642 | ||||||||
\(735\) | 0.519113 | 0.0191478 | ||||||||
\(736\) | 1.57271 | 0.0579710 | ||||||||
\(737\) | −25.9891 | −0.957320 | ||||||||
\(738\) | 36.2372 | 1.33391 | ||||||||
\(739\) | −21.5957 | −0.794410 | −0.397205 | − | 0.917730i | \(-0.630020\pi\) | ||||
−0.397205 | + | 0.917730i | \(0.630020\pi\) | |||||||
\(740\) | 1.72377 | 0.0633671 | ||||||||
\(741\) | −7.39670 | −0.271725 | ||||||||
\(742\) | 5.46626 | 0.200673 | ||||||||
\(743\) | −29.2867 | −1.07443 | −0.537213 | − | 0.843447i | \(-0.680523\pi\) | ||||
−0.537213 | + | 0.843447i | \(0.680523\pi\) | |||||||
\(744\) | 1.97735 | 0.0724931 | ||||||||
\(745\) | 9.17807 | 0.336258 | ||||||||
\(746\) | −28.4115 | −1.04022 | ||||||||
\(747\) | −37.9241 | −1.38757 | ||||||||
\(748\) | 22.5914 | 0.826024 | ||||||||
\(749\) | −8.03379 | −0.293548 | ||||||||
\(750\) | −4.32677 | −0.157991 | ||||||||
\(751\) | −15.1490 | −0.552795 | −0.276397 | − | 0.961043i | \(-0.589141\pi\) | ||||
−0.276397 | + | 0.961043i | \(0.589141\pi\) | |||||||
\(752\) | −10.9210 | −0.398247 | ||||||||
\(753\) | −0.638227 | −0.0232583 | ||||||||
\(754\) | −30.9603 | −1.12751 | ||||||||
\(755\) | 5.33764 | 0.194257 | ||||||||
\(756\) | −2.34866 | −0.0854200 | ||||||||
\(757\) | 8.37899 | 0.304539 | 0.152270 | − | 0.988339i | \(-0.451342\pi\) | ||||
0.152270 | + | 0.988339i | \(0.451342\pi\) | |||||||
\(758\) | 13.6763 | 0.496745 | ||||||||
\(759\) | −2.70126 | −0.0980495 | ||||||||
\(760\) | −5.28718 | −0.191786 | ||||||||
\(761\) | 25.4673 | 0.923190 | 0.461595 | − | 0.887091i | \(-0.347277\pi\) | ||||
0.461595 | + | 0.887091i | \(0.347277\pi\) | |||||||
\(762\) | −6.92691 | −0.250935 | ||||||||
\(763\) | −0.168957 | −0.00611664 | ||||||||
\(764\) | −18.9466 | −0.685464 | ||||||||
\(765\) | 19.3787 | 0.700640 | ||||||||
\(766\) | −17.9619 | −0.648990 | ||||||||
\(767\) | −39.8966 | −1.44058 | ||||||||
\(768\) | 0.402295 | 0.0145166 | ||||||||
\(769\) | −1.98243 | −0.0714884 | −0.0357442 | − | 0.999361i | \(-0.511380\pi\) | ||||
−0.0357442 | + | 0.999361i | \(0.511380\pi\) | |||||||
\(770\) | −5.50921 | −0.198538 | ||||||||
\(771\) | 5.13389 | 0.184893 | ||||||||
\(772\) | 7.10269 | 0.255631 | ||||||||
\(773\) | −26.3293 | −0.947000 | −0.473500 | − | 0.880794i | \(-0.657010\pi\) | ||||
−0.473500 | + | 0.880794i | \(0.657010\pi\) | |||||||
\(774\) | 28.9293 | 1.03984 | ||||||||
\(775\) | −16.3917 | −0.588808 | ||||||||
\(776\) | −11.1611 | −0.400659 | ||||||||
\(777\) | 0.537410 | 0.0192795 | ||||||||
\(778\) | −5.82184 | −0.208723 | ||||||||
\(779\) | 52.3148 | 1.87437 | ||||||||
\(780\) | 2.32943 | 0.0834068 | ||||||||
\(781\) | −31.6519 | −1.13259 | ||||||||
\(782\) | −8.32187 | −0.297590 | ||||||||
\(783\) | 16.2046 | 0.579105 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −26.8872 | −0.959645 | ||||||||
\(786\) | −5.72574 | −0.204231 | ||||||||
\(787\) | 25.6165 | 0.913131 | 0.456566 | − | 0.889690i | \(-0.349079\pi\) | ||||
0.456566 | + | 0.889690i | \(0.349079\pi\) | |||||||
\(788\) | 18.6519 | 0.664447 | ||||||||
\(789\) | −2.39040 | −0.0851004 | ||||||||
\(790\) | 5.98549 | 0.212954 | ||||||||
\(791\) | 17.0693 | 0.606914 | ||||||||
\(792\) | 12.1174 | 0.430572 | ||||||||
\(793\) | 15.8754 | 0.563752 | ||||||||
\(794\) | −33.0817 | −1.17403 | ||||||||
\(795\) | 2.83761 | 0.100640 | ||||||||
\(796\) | 18.6356 | 0.660520 | ||||||||
\(797\) | 23.1954 | 0.821623 | 0.410812 | − | 0.911720i | \(-0.365245\pi\) | ||||
0.410812 | + | 0.911720i | \(0.365245\pi\) | |||||||
\(798\) | −1.64836 | −0.0583512 | ||||||||
\(799\) | 57.7874 | 2.04437 | ||||||||
\(800\) | −3.33492 | −0.117907 | ||||||||
\(801\) | 37.3722 | 1.32048 | ||||||||
\(802\) | −32.8107 | −1.15859 | ||||||||
\(803\) | −72.0636 | −2.54307 | ||||||||
\(804\) | 2.44885 | 0.0863645 | ||||||||
\(805\) | 2.02940 | 0.0715269 | ||||||||
\(806\) | 22.0560 | 0.776888 | ||||||||
\(807\) | −9.18909 | −0.323471 | ||||||||
\(808\) | −14.1440 | −0.497586 | ||||||||
\(809\) | 34.2529 | 1.20427 | 0.602134 | − | 0.798395i | \(-0.294317\pi\) | ||||
0.602134 | + | 0.798395i | \(0.294317\pi\) | |||||||
\(810\) | 9.76769 | 0.343202 | ||||||||
\(811\) | −13.4307 | −0.471614 | −0.235807 | − | 0.971800i | \(-0.575773\pi\) | ||||
−0.235807 | + | 0.971800i | \(0.575773\pi\) | |||||||
\(812\) | −6.89951 | −0.242125 | ||||||||
\(813\) | 1.72431 | 0.0604743 | ||||||||
\(814\) | −5.70340 | −0.199904 | ||||||||
\(815\) | −13.3691 | −0.468299 | ||||||||
\(816\) | −2.12871 | −0.0745196 | ||||||||
\(817\) | 41.7645 | 1.46115 | ||||||||
\(818\) | 24.4040 | 0.853264 | ||||||||
\(819\) | −12.7357 | −0.445022 | ||||||||
\(820\) | −16.4754 | −0.575345 | ||||||||
\(821\) | 49.7187 | 1.73520 | 0.867598 | − | 0.497267i | \(-0.165663\pi\) | ||||
0.867598 | + | 0.497267i | \(0.165663\pi\) | |||||||
\(822\) | −4.18616 | −0.146009 | ||||||||
\(823\) | 8.01807 | 0.279492 | 0.139746 | − | 0.990187i | \(-0.455371\pi\) | ||||
0.139746 | + | 0.990187i | \(0.455371\pi\) | |||||||
\(824\) | 8.10218 | 0.282253 | ||||||||
\(825\) | 5.72798 | 0.199423 | ||||||||
\(826\) | −8.89097 | −0.309356 | ||||||||
\(827\) | −46.1060 | −1.60326 | −0.801631 | − | 0.597819i | \(-0.796034\pi\) | ||||
−0.801631 | + | 0.597819i | \(0.796034\pi\) | |||||||
\(828\) | −4.46361 | −0.155121 | ||||||||
\(829\) | 20.0871 | 0.697655 | 0.348828 | − | 0.937187i | \(-0.386580\pi\) | ||||
0.348828 | + | 0.937187i | \(0.386580\pi\) | |||||||
\(830\) | 17.2424 | 0.598491 | ||||||||
\(831\) | −10.7948 | −0.374468 | ||||||||
\(832\) | 4.48732 | 0.155570 | ||||||||
\(833\) | −5.29141 | −0.183336 | ||||||||
\(834\) | 0.337585 | 0.0116896 | ||||||||
\(835\) | 9.01137 | 0.311851 | ||||||||
\(836\) | 17.4936 | 0.605028 | ||||||||
\(837\) | −11.5441 | −0.399022 | ||||||||
\(838\) | −32.2470 | −1.11395 | ||||||||
\(839\) | 8.72624 | 0.301263 | 0.150632 | − | 0.988590i | \(-0.451869\pi\) | ||||
0.150632 | + | 0.988590i | \(0.451869\pi\) | |||||||
\(840\) | 0.519113 | 0.0179111 | ||||||||
\(841\) | 18.6032 | 0.641489 | ||||||||
\(842\) | −19.6786 | −0.678169 | ||||||||
\(843\) | 2.05819 | 0.0708877 | ||||||||
\(844\) | 15.4689 | 0.532463 | ||||||||
\(845\) | 9.20821 | 0.316772 | ||||||||
\(846\) | 30.9955 | 1.06565 | ||||||||
\(847\) | 7.22821 | 0.248364 | ||||||||
\(848\) | 5.46626 | 0.187712 | ||||||||
\(849\) | −10.5298 | −0.361381 | ||||||||
\(850\) | 17.6464 | 0.605267 | ||||||||
\(851\) | 2.10093 | 0.0720190 | ||||||||
\(852\) | 2.98244 | 0.102177 | ||||||||
\(853\) | 16.1417 | 0.552683 | 0.276341 | − | 0.961060i | \(-0.410878\pi\) | ||||
0.276341 | + | 0.961060i | \(0.410878\pi\) | |||||||
\(854\) | 3.53783 | 0.121062 | ||||||||
\(855\) | 15.0059 | 0.513190 | ||||||||
\(856\) | −8.03379 | −0.274589 | ||||||||
\(857\) | −17.8085 | −0.608327 | −0.304163 | − | 0.952620i | \(-0.598377\pi\) | ||||
−0.304163 | + | 0.952620i | \(0.598377\pi\) | |||||||
\(858\) | −7.70732 | −0.263124 | ||||||||
\(859\) | −0.288568 | −0.00984582 | −0.00492291 | − | 0.999988i | \(-0.501567\pi\) | ||||
−0.00492291 | + | 0.999988i | \(0.501567\pi\) | |||||||
\(860\) | −13.1528 | −0.448507 | ||||||||
\(861\) | −5.13644 | −0.175049 | ||||||||
\(862\) | −1.00000 | −0.0340601 | ||||||||
\(863\) | −3.94842 | −0.134406 | −0.0672029 | − | 0.997739i | \(-0.521407\pi\) | ||||
−0.0672029 | + | 0.997739i | \(0.521407\pi\) | |||||||
\(864\) | −2.34866 | −0.0799031 | ||||||||
\(865\) | 11.1186 | 0.378043 | ||||||||
\(866\) | −1.99480 | −0.0677861 | ||||||||
\(867\) | 4.42484 | 0.150275 | ||||||||
\(868\) | 4.91518 | 0.166832 | ||||||||
\(869\) | −19.8040 | −0.671806 | ||||||||
\(870\) | −3.58162 | −0.121428 | ||||||||
\(871\) | 27.3153 | 0.925543 | ||||||||
\(872\) | −0.168957 | −0.00572159 | ||||||||
\(873\) | 31.6769 | 1.07210 | ||||||||
\(874\) | −6.44401 | −0.217972 | ||||||||
\(875\) | −10.7552 | −0.363593 | ||||||||
\(876\) | 6.79029 | 0.229423 | ||||||||
\(877\) | −45.1598 | −1.52494 | −0.762469 | − | 0.647024i | \(-0.776013\pi\) | ||||
−0.762469 | + | 0.647024i | \(0.776013\pi\) | |||||||
\(878\) | −35.9660 | −1.21379 | ||||||||
\(879\) | −5.43297 | −0.183250 | ||||||||
\(880\) | −5.50921 | −0.185716 | ||||||||
\(881\) | −27.4688 | −0.925449 | −0.462724 | − | 0.886502i | \(-0.653128\pi\) | ||||
−0.462724 | + | 0.886502i | \(0.653128\pi\) | |||||||
\(882\) | −2.83816 | −0.0955658 | ||||||||
\(883\) | −31.3245 | −1.05415 | −0.527076 | − | 0.849818i | \(-0.676712\pi\) | ||||
−0.527076 | + | 0.849818i | \(0.676712\pi\) | |||||||
\(884\) | −23.7442 | −0.798605 | ||||||||
\(885\) | −4.61542 | −0.155146 | ||||||||
\(886\) | −34.2598 | −1.15098 | ||||||||
\(887\) | 44.9727 | 1.51004 | 0.755019 | − | 0.655703i | \(-0.227628\pi\) | ||||
0.755019 | + | 0.655703i | \(0.227628\pi\) | |||||||
\(888\) | 0.537410 | 0.0180343 | ||||||||
\(889\) | −17.2185 | −0.577490 | ||||||||
\(890\) | −16.9914 | −0.569554 | ||||||||
\(891\) | −32.3181 | −1.08270 | ||||||||
\(892\) | 12.2261 | 0.409359 | ||||||||
\(893\) | 44.7475 | 1.49742 | ||||||||
\(894\) | 2.86140 | 0.0956994 | ||||||||
\(895\) | 7.84177 | 0.262121 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 2.83910 | 0.0947949 | ||||||||
\(898\) | 3.00677 | 0.100337 | ||||||||
\(899\) | −33.9123 | −1.13104 | ||||||||
\(900\) | 9.46503 | 0.315501 | ||||||||
\(901\) | −28.9242 | −0.963606 | ||||||||
\(902\) | 54.5117 | 1.81504 | ||||||||
\(903\) | −4.10058 | −0.136459 | ||||||||
\(904\) | 17.0693 | 0.567716 | ||||||||
\(905\) | 31.2325 | 1.03820 | ||||||||
\(906\) | 1.66409 | 0.0552856 | ||||||||
\(907\) | −19.6842 | −0.653602 | −0.326801 | − | 0.945093i | \(-0.605971\pi\) | ||||
−0.326801 | + | 0.945093i | \(0.605971\pi\) | |||||||
\(908\) | 13.0966 | 0.434626 | ||||||||
\(909\) | 40.1431 | 1.33146 | ||||||||
\(910\) | 5.79035 | 0.191948 | ||||||||
\(911\) | 35.4480 | 1.17444 | 0.587222 | − | 0.809426i | \(-0.300222\pi\) | ||||
0.587222 | + | 0.809426i | \(0.300222\pi\) | |||||||
\(912\) | −1.64836 | −0.0545825 | ||||||||
\(913\) | −57.0494 | −1.88806 | ||||||||
\(914\) | −19.5362 | −0.646199 | ||||||||
\(915\) | 1.83654 | 0.0607140 | ||||||||
\(916\) | 19.3324 | 0.638760 | ||||||||
\(917\) | −14.2327 | −0.470005 | ||||||||
\(918\) | 12.4277 | 0.410176 | ||||||||
\(919\) | 48.4550 | 1.59838 | 0.799191 | − | 0.601077i | \(-0.205261\pi\) | ||||
0.799191 | + | 0.601077i | \(0.205261\pi\) | |||||||
\(920\) | 2.02940 | 0.0669073 | ||||||||
\(921\) | 7.54637 | 0.248661 | ||||||||
\(922\) | 24.2117 | 0.797368 | ||||||||
\(923\) | 33.2671 | 1.09500 | ||||||||
\(924\) | −1.71758 | −0.0565042 | ||||||||
\(925\) | −4.45499 | −0.146479 | ||||||||
\(926\) | 35.4816 | 1.16600 | ||||||||
\(927\) | −22.9953 | −0.755264 | ||||||||
\(928\) | −6.89951 | −0.226487 | ||||||||
\(929\) | 9.57160 | 0.314034 | 0.157017 | − | 0.987596i | \(-0.449812\pi\) | ||||
0.157017 | + | 0.987596i | \(0.449812\pi\) | |||||||
\(930\) | 2.55153 | 0.0836680 | ||||||||
\(931\) | −4.09738 | −0.134286 | ||||||||
\(932\) | −17.6137 | −0.576958 | ||||||||
\(933\) | −1.51409 | −0.0495692 | ||||||||
\(934\) | 25.0107 | 0.818376 | ||||||||
\(935\) | 29.1515 | 0.953356 | ||||||||
\(936\) | −12.7357 | −0.416280 | ||||||||
\(937\) | −16.1334 | −0.527055 | −0.263527 | − | 0.964652i | \(-0.584886\pi\) | ||||
−0.263527 | + | 0.964652i | \(0.584886\pi\) | |||||||
\(938\) | 6.08722 | 0.198755 | ||||||||
\(939\) | 5.76123 | 0.188011 | ||||||||
\(940\) | −14.0922 | −0.459638 | ||||||||
\(941\) | 52.1665 | 1.70058 | 0.850289 | − | 0.526316i | \(-0.176427\pi\) | ||||
0.850289 | + | 0.526316i | \(0.176427\pi\) | |||||||
\(942\) | −8.38247 | −0.273116 | ||||||||
\(943\) | −20.0802 | −0.653900 | ||||||||
\(944\) | −8.89097 | −0.289376 | ||||||||
\(945\) | −3.03066 | −0.0985875 | ||||||||
\(946\) | 43.5184 | 1.41490 | ||||||||
\(947\) | 16.6449 | 0.540885 | 0.270443 | − | 0.962736i | \(-0.412830\pi\) | ||||
0.270443 | + | 0.962736i | \(0.412830\pi\) | |||||||
\(948\) | 1.86606 | 0.0606069 | ||||||||
\(949\) | 75.7410 | 2.45866 | ||||||||
\(950\) | 13.6644 | 0.443333 | ||||||||
\(951\) | −0.386912 | −0.0125465 | ||||||||
\(952\) | −5.29141 | −0.171496 | ||||||||
\(953\) | 25.1333 | 0.814147 | 0.407073 | − | 0.913395i | \(-0.366549\pi\) | ||||
0.407073 | + | 0.913395i | \(0.366549\pi\) | |||||||
\(954\) | −15.5141 | −0.502288 | ||||||||
\(955\) | −24.4483 | −0.791129 | ||||||||
\(956\) | 13.4662 | 0.435529 | ||||||||
\(957\) | 11.8504 | 0.383070 | ||||||||
\(958\) | 2.45113 | 0.0791923 | ||||||||
\(959\) | −10.4057 | −0.336018 | ||||||||
\(960\) | 0.519113 | 0.0167543 | ||||||||
\(961\) | −6.84105 | −0.220679 | ||||||||
\(962\) | 5.99444 | 0.193269 | ||||||||
\(963\) | 22.8012 | 0.734758 | ||||||||
\(964\) | −25.3288 | −0.815785 | ||||||||
\(965\) | 9.16517 | 0.295037 | ||||||||
\(966\) | 0.632695 | 0.0203566 | ||||||||
\(967\) | −45.4028 | −1.46006 | −0.730028 | − | 0.683418i | \(-0.760493\pi\) | ||||
−0.730028 | + | 0.683418i | \(0.760493\pi\) | |||||||
\(968\) | 7.22821 | 0.232324 | ||||||||
\(969\) | 8.72213 | 0.280195 | ||||||||
\(970\) | −14.4020 | −0.462421 | ||||||||
\(971\) | 40.6123 | 1.30331 | 0.651656 | − | 0.758515i | \(-0.274075\pi\) | ||||
0.651656 | + | 0.758515i | \(0.274075\pi\) | |||||||
\(972\) | 10.0912 | 0.323675 | ||||||||
\(973\) | 0.839150 | 0.0269019 | ||||||||
\(974\) | −32.6827 | −1.04722 | ||||||||
\(975\) | −6.02028 | −0.192803 | ||||||||
\(976\) | 3.53783 | 0.113243 | ||||||||
\(977\) | 51.8364 | 1.65839 | 0.829197 | − | 0.558957i | \(-0.188798\pi\) | ||||
0.829197 | + | 0.558957i | \(0.188798\pi\) | |||||||
\(978\) | −4.16801 | −0.133278 | ||||||||
\(979\) | 56.2192 | 1.79677 | ||||||||
\(980\) | 1.29038 | 0.0412197 | ||||||||
\(981\) | 0.479526 | 0.0153101 | ||||||||
\(982\) | 40.8488 | 1.30354 | ||||||||
\(983\) | −14.8605 | −0.473978 | −0.236989 | − | 0.971512i | \(-0.576160\pi\) | ||||
−0.236989 | + | 0.971512i | \(0.576160\pi\) | |||||||
\(984\) | −5.13644 | −0.163744 | ||||||||
\(985\) | 24.0681 | 0.766872 | ||||||||
\(986\) | 36.5081 | 1.16265 | ||||||||
\(987\) | −4.39345 | −0.139845 | ||||||||
\(988\) | −18.3863 | −0.584945 | ||||||||
\(989\) | −16.0306 | −0.509744 | ||||||||
\(990\) | 15.6360 | 0.496946 | ||||||||
\(991\) | −28.0159 | −0.889954 | −0.444977 | − | 0.895542i | \(-0.646788\pi\) | ||||
−0.444977 | + | 0.895542i | \(0.646788\pi\) | |||||||
\(992\) | 4.91518 | 0.156057 | ||||||||
\(993\) | 6.88992 | 0.218645 | ||||||||
\(994\) | 7.41357 | 0.235144 | ||||||||
\(995\) | 24.0470 | 0.762340 | ||||||||
\(996\) | 5.37555 | 0.170331 | ||||||||
\(997\) | −6.69582 | −0.212059 | −0.106029 | − | 0.994363i | \(-0.533814\pi\) | ||||
−0.106029 | + | 0.994363i | \(0.533814\pi\) | |||||||
\(998\) | 21.8637 | 0.692083 | ||||||||
\(999\) | −3.13749 | −0.0992657 |
(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 | 6034.2.a.m.1.13 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6034.2.a.m.1.13 | ✓ | 21 | 1.1 | even | 1 | trivial |