Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6013,2,Mod(1,6013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6013, 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("6013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6013 = 7 \cdot 859 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6013.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: | \(48.0140467354\) |
Analytic rank: | \(0\) |
Dimension: | \(109\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 6013.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.09226 | −1.47945 | −0.739725 | − | 0.672910i | \(-0.765044\pi\) | ||||
−0.739725 | + | 0.672910i | \(0.765044\pi\) | |||||||
\(3\) | 2.05769 | 1.18801 | 0.594005 | − | 0.804462i | \(-0.297546\pi\) | ||||
0.594005 | + | 0.804462i | \(0.297546\pi\) | |||||||
\(4\) | 2.37754 | 1.18877 | ||||||||
\(5\) | −3.21058 | −1.43582 | −0.717908 | − | 0.696138i | \(-0.754900\pi\) | ||||
−0.717908 | + | 0.696138i | \(0.754900\pi\) | |||||||
\(6\) | −4.30522 | −1.75760 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −0.789909 | −0.279275 | ||||||||
\(9\) | 1.23410 | 0.411366 | ||||||||
\(10\) | 6.71736 | 2.12422 | ||||||||
\(11\) | −1.05106 | −0.316906 | −0.158453 | − | 0.987367i | \(-0.550651\pi\) | ||||
−0.158453 | + | 0.987367i | \(0.550651\pi\) | |||||||
\(12\) | 4.89224 | 1.41227 | ||||||||
\(13\) | −6.03586 | −1.67405 | −0.837024 | − | 0.547167i | \(-0.815706\pi\) | ||||
−0.837024 | + | 0.547167i | \(0.815706\pi\) | |||||||
\(14\) | −2.09226 | −0.559179 | ||||||||
\(15\) | −6.60639 | −1.70576 | ||||||||
\(16\) | −3.10239 | −0.775597 | ||||||||
\(17\) | −0.303396 | −0.0735842 | −0.0367921 | − | 0.999323i | \(-0.511714\pi\) | ||||
−0.0367921 | + | 0.999323i | \(0.511714\pi\) | |||||||
\(18\) | −2.58205 | −0.608595 | ||||||||
\(19\) | −7.88878 | −1.80981 | −0.904905 | − | 0.425613i | \(-0.860059\pi\) | ||||
−0.904905 | + | 0.425613i | \(0.860059\pi\) | |||||||
\(20\) | −7.63328 | −1.70685 | ||||||||
\(21\) | 2.05769 | 0.449025 | ||||||||
\(22\) | 2.19908 | 0.468846 | ||||||||
\(23\) | −5.99646 | −1.25035 | −0.625175 | − | 0.780485i | \(-0.714972\pi\) | ||||
−0.625175 | + | 0.780485i | \(0.714972\pi\) | |||||||
\(24\) | −1.62539 | −0.331781 | ||||||||
\(25\) | 5.30784 | 1.06157 | ||||||||
\(26\) | 12.6286 | 2.47667 | ||||||||
\(27\) | −3.63368 | −0.699303 | ||||||||
\(28\) | 2.37754 | 0.449313 | ||||||||
\(29\) | −5.87597 | −1.09114 | −0.545570 | − | 0.838065i | \(-0.683687\pi\) | ||||
−0.545570 | + | 0.838065i | \(0.683687\pi\) | |||||||
\(30\) | 13.8223 | 2.52359 | ||||||||
\(31\) | −3.70314 | −0.665104 | −0.332552 | − | 0.943085i | \(-0.607910\pi\) | ||||
−0.332552 | + | 0.943085i | \(0.607910\pi\) | |||||||
\(32\) | 8.07081 | 1.42673 | ||||||||
\(33\) | −2.16275 | −0.376487 | ||||||||
\(34\) | 0.634781 | 0.108864 | ||||||||
\(35\) | −3.21058 | −0.542687 | ||||||||
\(36\) | 2.93412 | 0.489019 | ||||||||
\(37\) | 0.931951 | 0.153212 | 0.0766059 | − | 0.997061i | \(-0.475592\pi\) | ||||
0.0766059 | + | 0.997061i | \(0.475592\pi\) | |||||||
\(38\) | 16.5054 | 2.67752 | ||||||||
\(39\) | −12.4199 | −1.98878 | ||||||||
\(40\) | 2.53607 | 0.400987 | ||||||||
\(41\) | −2.50984 | −0.391971 | −0.195985 | − | 0.980607i | \(-0.562791\pi\) | ||||
−0.195985 | + | 0.980607i | \(0.562791\pi\) | |||||||
\(42\) | −4.30522 | −0.664310 | ||||||||
\(43\) | 3.08098 | 0.469845 | 0.234923 | − | 0.972014i | \(-0.424516\pi\) | ||||
0.234923 | + | 0.972014i | \(0.424516\pi\) | |||||||
\(44\) | −2.49893 | −0.376728 | ||||||||
\(45\) | −3.96217 | −0.590646 | ||||||||
\(46\) | 12.5461 | 1.84983 | ||||||||
\(47\) | −1.55414 | −0.226694 | −0.113347 | − | 0.993555i | \(-0.536157\pi\) | ||||
−0.113347 | + | 0.993555i | \(0.536157\pi\) | |||||||
\(48\) | −6.38376 | −0.921416 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −11.1054 | −1.57053 | ||||||||
\(51\) | −0.624295 | −0.0874187 | ||||||||
\(52\) | −14.3505 | −1.99006 | ||||||||
\(53\) | 0.950773 | 0.130599 | 0.0652994 | − | 0.997866i | \(-0.479200\pi\) | ||||
0.0652994 | + | 0.997866i | \(0.479200\pi\) | |||||||
\(54\) | 7.60260 | 1.03458 | ||||||||
\(55\) | 3.37451 | 0.455018 | ||||||||
\(56\) | −0.789909 | −0.105556 | ||||||||
\(57\) | −16.2327 | −2.15007 | ||||||||
\(58\) | 12.2940 | 1.61429 | ||||||||
\(59\) | 8.70133 | 1.13282 | 0.566408 | − | 0.824125i | \(-0.308332\pi\) | ||||
0.566408 | + | 0.824125i | \(0.308332\pi\) | |||||||
\(60\) | −15.7070 | −2.02776 | ||||||||
\(61\) | −1.10085 | −0.140949 | −0.0704745 | − | 0.997514i | \(-0.522451\pi\) | ||||
−0.0704745 | + | 0.997514i | \(0.522451\pi\) | |||||||
\(62\) | 7.74793 | 0.983988 | ||||||||
\(63\) | 1.23410 | 0.155482 | ||||||||
\(64\) | −10.6814 | −1.33518 | ||||||||
\(65\) | 19.3786 | 2.40362 | ||||||||
\(66\) | 4.52503 | 0.556993 | ||||||||
\(67\) | −6.34168 | −0.774760 | −0.387380 | − | 0.921920i | \(-0.626620\pi\) | ||||
−0.387380 | + | 0.921920i | \(0.626620\pi\) | |||||||
\(68\) | −0.721335 | −0.0874747 | ||||||||
\(69\) | −12.3389 | −1.48543 | ||||||||
\(70\) | 6.71736 | 0.802878 | ||||||||
\(71\) | 0.621219 | 0.0737251 | 0.0368625 | − | 0.999320i | \(-0.488264\pi\) | ||||
0.0368625 | + | 0.999320i | \(0.488264\pi\) | |||||||
\(72\) | −0.974825 | −0.114884 | ||||||||
\(73\) | −2.68798 | −0.314605 | −0.157302 | − | 0.987550i | \(-0.550280\pi\) | ||||
−0.157302 | + | 0.987550i | \(0.550280\pi\) | |||||||
\(74\) | −1.94988 | −0.226669 | ||||||||
\(75\) | 10.9219 | 1.26115 | ||||||||
\(76\) | −18.7559 | −2.15145 | ||||||||
\(77\) | −1.05106 | −0.119779 | ||||||||
\(78\) | 25.9857 | 2.94230 | ||||||||
\(79\) | 13.4934 | 1.51813 | 0.759063 | − | 0.651017i | \(-0.225657\pi\) | ||||
0.759063 | + | 0.651017i | \(0.225657\pi\) | |||||||
\(80\) | 9.96047 | 1.11361 | ||||||||
\(81\) | −11.1793 | −1.24214 | ||||||||
\(82\) | 5.25123 | 0.579901 | ||||||||
\(83\) | 16.1640 | 1.77423 | 0.887115 | − | 0.461549i | \(-0.152706\pi\) | ||||
0.887115 | + | 0.461549i | \(0.152706\pi\) | |||||||
\(84\) | 4.89224 | 0.533788 | ||||||||
\(85\) | 0.974076 | 0.105653 | ||||||||
\(86\) | −6.44620 | −0.695112 | ||||||||
\(87\) | −12.0909 | −1.29628 | ||||||||
\(88\) | 0.830239 | 0.0885038 | ||||||||
\(89\) | 10.0831 | 1.06881 | 0.534403 | − | 0.845230i | \(-0.320536\pi\) | ||||
0.534403 | + | 0.845230i | \(0.320536\pi\) | |||||||
\(90\) | 8.28988 | 0.873830 | ||||||||
\(91\) | −6.03586 | −0.632730 | ||||||||
\(92\) | −14.2568 | −1.48638 | ||||||||
\(93\) | −7.61993 | −0.790150 | ||||||||
\(94\) | 3.25165 | 0.335382 | ||||||||
\(95\) | 25.3276 | 2.59856 | ||||||||
\(96\) | 16.6072 | 1.69497 | ||||||||
\(97\) | 11.8556 | 1.20375 | 0.601875 | − | 0.798590i | \(-0.294421\pi\) | ||||
0.601875 | + | 0.798590i | \(0.294421\pi\) | |||||||
\(98\) | −2.09226 | −0.211350 | ||||||||
\(99\) | −1.29711 | −0.130364 | ||||||||
\(100\) | 12.6196 | 1.26196 | ||||||||
\(101\) | 15.1082 | 1.50332 | 0.751659 | − | 0.659552i | \(-0.229254\pi\) | ||||
0.751659 | + | 0.659552i | \(0.229254\pi\) | |||||||
\(102\) | 1.30618 | 0.129332 | ||||||||
\(103\) | −12.9375 | −1.27477 | −0.637383 | − | 0.770547i | \(-0.719983\pi\) | ||||
−0.637383 | + | 0.770547i | \(0.719983\pi\) | |||||||
\(104\) | 4.76778 | 0.467519 | ||||||||
\(105\) | −6.60639 | −0.644718 | ||||||||
\(106\) | −1.98926 | −0.193214 | ||||||||
\(107\) | 18.0641 | 1.74632 | 0.873161 | − | 0.487431i | \(-0.162066\pi\) | ||||
0.873161 | + | 0.487431i | \(0.162066\pi\) | |||||||
\(108\) | −8.63922 | −0.831310 | ||||||||
\(109\) | 16.9133 | 1.62000 | 0.810001 | − | 0.586428i | \(-0.199466\pi\) | ||||
0.810001 | + | 0.586428i | \(0.199466\pi\) | |||||||
\(110\) | −7.06033 | −0.673176 | ||||||||
\(111\) | 1.91767 | 0.182017 | ||||||||
\(112\) | −3.10239 | −0.293148 | ||||||||
\(113\) | 3.86760 | 0.363833 | 0.181916 | − | 0.983314i | \(-0.441770\pi\) | ||||
0.181916 | + | 0.983314i | \(0.441770\pi\) | |||||||
\(114\) | 33.9630 | 3.18092 | ||||||||
\(115\) | 19.2521 | 1.79527 | ||||||||
\(116\) | −13.9704 | −1.29711 | ||||||||
\(117\) | −7.44885 | −0.688646 | ||||||||
\(118\) | −18.2054 | −1.67594 | ||||||||
\(119\) | −0.303396 | −0.0278122 | ||||||||
\(120\) | 5.21844 | 0.476377 | ||||||||
\(121\) | −9.89528 | −0.899571 | ||||||||
\(122\) | 2.30325 | 0.208527 | ||||||||
\(123\) | −5.16448 | −0.465665 | ||||||||
\(124\) | −8.80437 | −0.790656 | ||||||||
\(125\) | −0.988335 | −0.0883994 | ||||||||
\(126\) | −2.58205 | −0.230027 | ||||||||
\(127\) | −20.9173 | −1.85611 | −0.928056 | − | 0.372442i | \(-0.878521\pi\) | ||||
−0.928056 | + | 0.372442i | \(0.878521\pi\) | |||||||
\(128\) | 6.20668 | 0.548598 | ||||||||
\(129\) | 6.33971 | 0.558180 | ||||||||
\(130\) | −40.5451 | −3.55604 | ||||||||
\(131\) | 7.96847 | 0.696209 | 0.348104 | − | 0.937456i | \(-0.386826\pi\) | ||||
0.348104 | + | 0.937456i | \(0.386826\pi\) | |||||||
\(132\) | −5.14203 | −0.447556 | ||||||||
\(133\) | −7.88878 | −0.684044 | ||||||||
\(134\) | 13.2684 | 1.14622 | ||||||||
\(135\) | 11.6662 | 1.00407 | ||||||||
\(136\) | 0.239655 | 0.0205502 | ||||||||
\(137\) | −21.3156 | −1.82111 | −0.910556 | − | 0.413385i | \(-0.864346\pi\) | ||||
−0.910556 | + | 0.413385i | \(0.864346\pi\) | |||||||
\(138\) | 25.8161 | 2.19761 | ||||||||
\(139\) | −23.1319 | −1.96202 | −0.981010 | − | 0.193955i | \(-0.937868\pi\) | ||||
−0.981010 | + | 0.193955i | \(0.937868\pi\) | |||||||
\(140\) | −7.63328 | −0.645130 | ||||||||
\(141\) | −3.19793 | −0.269315 | ||||||||
\(142\) | −1.29975 | −0.109073 | ||||||||
\(143\) | 6.34404 | 0.530515 | ||||||||
\(144\) | −3.82865 | −0.319054 | ||||||||
\(145\) | 18.8653 | 1.56668 | ||||||||
\(146\) | 5.62395 | 0.465442 | ||||||||
\(147\) | 2.05769 | 0.169716 | ||||||||
\(148\) | 2.21575 | 0.182133 | ||||||||
\(149\) | −14.8882 | −1.21969 | −0.609844 | − | 0.792521i | \(-0.708768\pi\) | ||||
−0.609844 | + | 0.792521i | \(0.708768\pi\) | |||||||
\(150\) | −22.8514 | −1.86581 | ||||||||
\(151\) | −15.0300 | −1.22312 | −0.611562 | − | 0.791197i | \(-0.709459\pi\) | ||||
−0.611562 | + | 0.791197i | \(0.709459\pi\) | |||||||
\(152\) | 6.23142 | 0.505435 | ||||||||
\(153\) | −0.374420 | −0.0302700 | ||||||||
\(154\) | 2.19908 | 0.177207 | ||||||||
\(155\) | 11.8892 | 0.954967 | ||||||||
\(156\) | −29.5289 | −2.36421 | ||||||||
\(157\) | 0.373102 | 0.0297768 | 0.0148884 | − | 0.999889i | \(-0.495261\pi\) | ||||
0.0148884 | + | 0.999889i | \(0.495261\pi\) | |||||||
\(158\) | −28.2317 | −2.24599 | ||||||||
\(159\) | 1.95640 | 0.155152 | ||||||||
\(160\) | −25.9120 | −2.04852 | ||||||||
\(161\) | −5.99646 | −0.472588 | ||||||||
\(162\) | 23.3900 | 1.83769 | ||||||||
\(163\) | 12.0449 | 0.943426 | 0.471713 | − | 0.881752i | \(-0.343636\pi\) | ||||
0.471713 | + | 0.881752i | \(0.343636\pi\) | |||||||
\(164\) | −5.96724 | −0.465963 | ||||||||
\(165\) | 6.94369 | 0.540566 | ||||||||
\(166\) | −33.8192 | −2.62488 | ||||||||
\(167\) | −0.413096 | −0.0319663 | −0.0159832 | − | 0.999872i | \(-0.505088\pi\) | ||||
−0.0159832 | + | 0.999872i | \(0.505088\pi\) | |||||||
\(168\) | −1.62539 | −0.125401 | ||||||||
\(169\) | 23.4316 | 1.80243 | ||||||||
\(170\) | −2.03802 | −0.156309 | ||||||||
\(171\) | −9.73553 | −0.744495 | ||||||||
\(172\) | 7.32515 | 0.558538 | ||||||||
\(173\) | 16.6210 | 1.26367 | 0.631834 | − | 0.775104i | \(-0.282303\pi\) | ||||
0.631834 | + | 0.775104i | \(0.282303\pi\) | |||||||
\(174\) | 25.2974 | 1.91779 | ||||||||
\(175\) | 5.30784 | 0.401235 | ||||||||
\(176\) | 3.26079 | 0.245791 | ||||||||
\(177\) | 17.9047 | 1.34580 | ||||||||
\(178\) | −21.0964 | −1.58125 | ||||||||
\(179\) | −7.34138 | −0.548721 | −0.274360 | − | 0.961627i | \(-0.588466\pi\) | ||||
−0.274360 | + | 0.961627i | \(0.588466\pi\) | |||||||
\(180\) | −9.42022 | −0.702142 | ||||||||
\(181\) | −6.93257 | −0.515294 | −0.257647 | − | 0.966239i | \(-0.582947\pi\) | ||||
−0.257647 | + | 0.966239i | \(0.582947\pi\) | |||||||
\(182\) | 12.6286 | 0.936092 | ||||||||
\(183\) | −2.26520 | −0.167449 | ||||||||
\(184\) | 4.73666 | 0.349191 | ||||||||
\(185\) | −2.99210 | −0.219984 | ||||||||
\(186\) | 15.9429 | 1.16899 | ||||||||
\(187\) | 0.318886 | 0.0233193 | ||||||||
\(188\) | −3.69502 | −0.269487 | ||||||||
\(189\) | −3.63368 | −0.264312 | ||||||||
\(190\) | −52.9918 | −3.84443 | ||||||||
\(191\) | 12.2337 | 0.885196 | 0.442598 | − | 0.896720i | \(-0.354057\pi\) | ||||
0.442598 | + | 0.896720i | \(0.354057\pi\) | |||||||
\(192\) | −21.9791 | −1.58620 | ||||||||
\(193\) | 7.51507 | 0.540947 | 0.270473 | − | 0.962727i | \(-0.412820\pi\) | ||||
0.270473 | + | 0.962727i | \(0.412820\pi\) | |||||||
\(194\) | −24.8049 | −1.78089 | ||||||||
\(195\) | 39.8753 | 2.85553 | ||||||||
\(196\) | 2.37754 | 0.169824 | ||||||||
\(197\) | −20.8935 | −1.48860 | −0.744300 | − | 0.667846i | \(-0.767217\pi\) | ||||
−0.744300 | + | 0.667846i | \(0.767217\pi\) | |||||||
\(198\) | 2.71388 | 0.192867 | ||||||||
\(199\) | 22.3430 | 1.58386 | 0.791928 | − | 0.610615i | \(-0.209078\pi\) | ||||
0.791928 | + | 0.610615i | \(0.209078\pi\) | |||||||
\(200\) | −4.19271 | −0.296469 | ||||||||
\(201\) | −13.0492 | −0.920422 | ||||||||
\(202\) | −31.6102 | −2.22408 | ||||||||
\(203\) | −5.87597 | −0.412412 | ||||||||
\(204\) | −1.48428 | −0.103921 | ||||||||
\(205\) | 8.05804 | 0.562798 | ||||||||
\(206\) | 27.0685 | 1.88595 | ||||||||
\(207\) | −7.40022 | −0.514351 | ||||||||
\(208\) | 18.7256 | 1.29839 | ||||||||
\(209\) | 8.29156 | 0.573539 | ||||||||
\(210\) | 13.8223 | 0.953827 | ||||||||
\(211\) | −2.30648 | −0.158784 | −0.0793922 | − | 0.996843i | \(-0.525298\pi\) | ||||
−0.0793922 | + | 0.996843i | \(0.525298\pi\) | |||||||
\(212\) | 2.26050 | 0.155252 | ||||||||
\(213\) | 1.27828 | 0.0875861 | ||||||||
\(214\) | −37.7947 | −2.58360 | ||||||||
\(215\) | −9.89174 | −0.674611 | ||||||||
\(216\) | 2.87028 | 0.195298 | ||||||||
\(217\) | −3.70314 | −0.251386 | ||||||||
\(218\) | −35.3870 | −2.39671 | ||||||||
\(219\) | −5.53104 | −0.373753 | ||||||||
\(220\) | 8.02302 | 0.540912 | ||||||||
\(221\) | 1.83125 | 0.123183 | ||||||||
\(222\) | −4.01225 | −0.269285 | ||||||||
\(223\) | −2.23474 | −0.149649 | −0.0748246 | − | 0.997197i | \(-0.523840\pi\) | ||||
−0.0748246 | + | 0.997197i | \(0.523840\pi\) | |||||||
\(224\) | 8.07081 | 0.539253 | ||||||||
\(225\) | 6.55039 | 0.436693 | ||||||||
\(226\) | −8.09200 | −0.538272 | ||||||||
\(227\) | 18.7056 | 1.24153 | 0.620767 | − | 0.783995i | \(-0.286821\pi\) | ||||
0.620767 | + | 0.783995i | \(0.286821\pi\) | |||||||
\(228\) | −38.5939 | −2.55594 | ||||||||
\(229\) | −4.34230 | −0.286947 | −0.143474 | − | 0.989654i | \(-0.545827\pi\) | ||||
−0.143474 | + | 0.989654i | \(0.545827\pi\) | |||||||
\(230\) | −40.2804 | −2.65601 | ||||||||
\(231\) | −2.16275 | −0.142299 | ||||||||
\(232\) | 4.64148 | 0.304728 | ||||||||
\(233\) | −5.59457 | −0.366512 | −0.183256 | − | 0.983065i | \(-0.558664\pi\) | ||||
−0.183256 | + | 0.983065i | \(0.558664\pi\) | |||||||
\(234\) | 15.5849 | 1.01882 | ||||||||
\(235\) | 4.98968 | 0.325491 | ||||||||
\(236\) | 20.6878 | 1.34666 | ||||||||
\(237\) | 27.7653 | 1.80355 | ||||||||
\(238\) | 0.634781 | 0.0411468 | ||||||||
\(239\) | 6.59741 | 0.426751 | 0.213375 | − | 0.976970i | \(-0.431554\pi\) | ||||
0.213375 | + | 0.976970i | \(0.431554\pi\) | |||||||
\(240\) | 20.4956 | 1.32298 | ||||||||
\(241\) | −5.67322 | −0.365444 | −0.182722 | − | 0.983165i | \(-0.558491\pi\) | ||||
−0.182722 | + | 0.983165i | \(0.558491\pi\) | |||||||
\(242\) | 20.7035 | 1.33087 | ||||||||
\(243\) | −12.1025 | −0.776376 | ||||||||
\(244\) | −2.61730 | −0.167556 | ||||||||
\(245\) | −3.21058 | −0.205117 | ||||||||
\(246\) | 10.8054 | 0.688928 | ||||||||
\(247\) | 47.6156 | 3.02971 | ||||||||
\(248\) | 2.92515 | 0.185747 | ||||||||
\(249\) | 33.2605 | 2.10780 | ||||||||
\(250\) | 2.06785 | 0.130782 | ||||||||
\(251\) | −6.54340 | −0.413016 | −0.206508 | − | 0.978445i | \(-0.566210\pi\) | ||||
−0.206508 | + | 0.978445i | \(0.566210\pi\) | |||||||
\(252\) | 2.93412 | 0.184832 | ||||||||
\(253\) | 6.30263 | 0.396243 | ||||||||
\(254\) | 43.7644 | 2.74602 | ||||||||
\(255\) | 2.00435 | 0.125517 | ||||||||
\(256\) | 8.37689 | 0.523556 | ||||||||
\(257\) | 5.99910 | 0.374213 | 0.187107 | − | 0.982340i | \(-0.440089\pi\) | ||||
0.187107 | + | 0.982340i | \(0.440089\pi\) | |||||||
\(258\) | −13.2643 | −0.825800 | ||||||||
\(259\) | 0.931951 | 0.0579086 | ||||||||
\(260\) | 46.0735 | 2.85735 | ||||||||
\(261\) | −7.25152 | −0.448858 | ||||||||
\(262\) | −16.6721 | −1.03001 | ||||||||
\(263\) | −31.3468 | −1.93293 | −0.966463 | − | 0.256804i | \(-0.917330\pi\) | ||||
−0.966463 | + | 0.256804i | \(0.917330\pi\) | |||||||
\(264\) | 1.70838 | 0.105143 | ||||||||
\(265\) | −3.05253 | −0.187516 | ||||||||
\(266\) | 16.5054 | 1.01201 | ||||||||
\(267\) | 20.7479 | 1.26975 | ||||||||
\(268\) | −15.0776 | −0.921011 | ||||||||
\(269\) | −0.857537 | −0.0522850 | −0.0261425 | − | 0.999658i | \(-0.508322\pi\) | ||||
−0.0261425 | + | 0.999658i | \(0.508322\pi\) | |||||||
\(270\) | −24.4088 | −1.48547 | ||||||||
\(271\) | 14.0768 | 0.855102 | 0.427551 | − | 0.903991i | \(-0.359376\pi\) | ||||
0.427551 | + | 0.903991i | \(0.359376\pi\) | |||||||
\(272\) | 0.941250 | 0.0570717 | ||||||||
\(273\) | −12.4199 | −0.751689 | ||||||||
\(274\) | 44.5977 | 2.69424 | ||||||||
\(275\) | −5.57884 | −0.336417 | ||||||||
\(276\) | −29.3362 | −1.76583 | ||||||||
\(277\) | −20.6830 | −1.24272 | −0.621362 | − | 0.783524i | \(-0.713420\pi\) | ||||
−0.621362 | + | 0.783524i | \(0.713420\pi\) | |||||||
\(278\) | 48.3978 | 2.90271 | ||||||||
\(279\) | −4.57004 | −0.273601 | ||||||||
\(280\) | 2.53607 | 0.151559 | ||||||||
\(281\) | −17.6810 | −1.05476 | −0.527379 | − | 0.849630i | \(-0.676825\pi\) | ||||
−0.527379 | + | 0.849630i | \(0.676825\pi\) | |||||||
\(282\) | 6.69090 | 0.398437 | ||||||||
\(283\) | 26.8893 | 1.59841 | 0.799203 | − | 0.601062i | \(-0.205255\pi\) | ||||
0.799203 | + | 0.601062i | \(0.205255\pi\) | |||||||
\(284\) | 1.47697 | 0.0876421 | ||||||||
\(285\) | 52.1164 | 3.08711 | ||||||||
\(286\) | −13.2734 | −0.784870 | ||||||||
\(287\) | −2.50984 | −0.148151 | ||||||||
\(288\) | 9.96017 | 0.586908 | ||||||||
\(289\) | −16.9080 | −0.994585 | ||||||||
\(290\) | −39.4710 | −2.31782 | ||||||||
\(291\) | 24.3951 | 1.43007 | ||||||||
\(292\) | −6.39079 | −0.373993 | ||||||||
\(293\) | −28.7899 | −1.68193 | −0.840963 | − | 0.541093i | \(-0.818011\pi\) | ||||
−0.840963 | + | 0.541093i | \(0.818011\pi\) | |||||||
\(294\) | −4.30522 | −0.251086 | ||||||||
\(295\) | −27.9363 | −1.62652 | ||||||||
\(296\) | −0.736156 | −0.0427882 | ||||||||
\(297\) | 3.81921 | 0.221613 | ||||||||
\(298\) | 31.1499 | 1.80447 | ||||||||
\(299\) | 36.1938 | 2.09314 | ||||||||
\(300\) | 25.9672 | 1.49922 | ||||||||
\(301\) | 3.08098 | 0.177585 | ||||||||
\(302\) | 31.4466 | 1.80955 | ||||||||
\(303\) | 31.0880 | 1.78596 | ||||||||
\(304\) | 24.4741 | 1.40368 | ||||||||
\(305\) | 3.53436 | 0.202377 | ||||||||
\(306\) | 0.783382 | 0.0447830 | ||||||||
\(307\) | −1.61826 | −0.0923587 | −0.0461794 | − | 0.998933i | \(-0.514705\pi\) | ||||
−0.0461794 | + | 0.998933i | \(0.514705\pi\) | |||||||
\(308\) | −2.49893 | −0.142390 | ||||||||
\(309\) | −26.6213 | −1.51443 | ||||||||
\(310\) | −24.8754 | −1.41283 | ||||||||
\(311\) | 15.3868 | 0.872505 | 0.436252 | − | 0.899824i | \(-0.356306\pi\) | ||||
0.436252 | + | 0.899824i | \(0.356306\pi\) | |||||||
\(312\) | 9.81062 | 0.555417 | ||||||||
\(313\) | −32.4562 | −1.83453 | −0.917266 | − | 0.398275i | \(-0.869609\pi\) | ||||
−0.917266 | + | 0.398275i | \(0.869609\pi\) | |||||||
\(314\) | −0.780625 | −0.0440532 | ||||||||
\(315\) | −3.96217 | −0.223243 | ||||||||
\(316\) | 32.0811 | 1.80470 | ||||||||
\(317\) | 4.54123 | 0.255061 | 0.127530 | − | 0.991835i | \(-0.459295\pi\) | ||||
0.127530 | + | 0.991835i | \(0.459295\pi\) | |||||||
\(318\) | −4.09329 | −0.229540 | ||||||||
\(319\) | 6.17598 | 0.345789 | ||||||||
\(320\) | 34.2936 | 1.91707 | ||||||||
\(321\) | 37.1704 | 2.07465 | ||||||||
\(322\) | 12.5461 | 0.699169 | ||||||||
\(323\) | 2.39342 | 0.133174 | ||||||||
\(324\) | −26.5792 | −1.47662 | ||||||||
\(325\) | −32.0374 | −1.77711 | ||||||||
\(326\) | −25.2009 | −1.39575 | ||||||||
\(327\) | 34.8024 | 1.92458 | ||||||||
\(328\) | 1.98254 | 0.109468 | ||||||||
\(329\) | −1.55414 | −0.0856823 | ||||||||
\(330\) | −14.5280 | −0.799740 | ||||||||
\(331\) | 8.81519 | 0.484527 | 0.242263 | − | 0.970211i | \(-0.422110\pi\) | ||||
0.242263 | + | 0.970211i | \(0.422110\pi\) | |||||||
\(332\) | 38.4305 | 2.10915 | ||||||||
\(333\) | 1.15012 | 0.0630261 | ||||||||
\(334\) | 0.864302 | 0.0472925 | ||||||||
\(335\) | 20.3605 | 1.11241 | ||||||||
\(336\) | −6.38376 | −0.348262 | ||||||||
\(337\) | −11.0261 | −0.600628 | −0.300314 | − | 0.953840i | \(-0.597091\pi\) | ||||
−0.300314 | + | 0.953840i | \(0.597091\pi\) | |||||||
\(338\) | −49.0250 | −2.66661 | ||||||||
\(339\) | 7.95832 | 0.432237 | ||||||||
\(340\) | 2.31590 | 0.125598 | ||||||||
\(341\) | 3.89222 | 0.210775 | ||||||||
\(342\) | 20.3692 | 1.10144 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −2.43369 | −0.131216 | ||||||||
\(345\) | 39.6150 | 2.13280 | ||||||||
\(346\) | −34.7753 | −1.86953 | ||||||||
\(347\) | 13.6991 | 0.735408 | 0.367704 | − | 0.929943i | \(-0.380144\pi\) | ||||
0.367704 | + | 0.929943i | \(0.380144\pi\) | |||||||
\(348\) | −28.7467 | −1.54098 | ||||||||
\(349\) | −16.5436 | −0.885561 | −0.442780 | − | 0.896630i | \(-0.646008\pi\) | ||||
−0.442780 | + | 0.896630i | \(0.646008\pi\) | |||||||
\(350\) | −11.1054 | −0.593606 | ||||||||
\(351\) | 21.9324 | 1.17067 | ||||||||
\(352\) | −8.48288 | −0.452139 | ||||||||
\(353\) | 21.8507 | 1.16299 | 0.581497 | − | 0.813548i | \(-0.302467\pi\) | ||||
0.581497 | + | 0.813548i | \(0.302467\pi\) | |||||||
\(354\) | −37.4612 | −1.99104 | ||||||||
\(355\) | −1.99447 | −0.105856 | ||||||||
\(356\) | 23.9730 | 1.27057 | ||||||||
\(357\) | −0.624295 | −0.0330412 | ||||||||
\(358\) | 15.3601 | 0.811805 | ||||||||
\(359\) | 23.4410 | 1.23717 | 0.618584 | − | 0.785719i | \(-0.287707\pi\) | ||||
0.618584 | + | 0.785719i | \(0.287707\pi\) | |||||||
\(360\) | 3.12975 | 0.164953 | ||||||||
\(361\) | 43.2329 | 2.27542 | ||||||||
\(362\) | 14.5047 | 0.762351 | ||||||||
\(363\) | −20.3614 | −1.06870 | ||||||||
\(364\) | −14.3505 | −0.752171 | ||||||||
\(365\) | 8.62999 | 0.451715 | ||||||||
\(366\) | 4.73939 | 0.247732 | ||||||||
\(367\) | −16.5785 | −0.865391 | −0.432695 | − | 0.901540i | \(-0.642437\pi\) | ||||
−0.432695 | + | 0.901540i | \(0.642437\pi\) | |||||||
\(368\) | 18.6033 | 0.969766 | ||||||||
\(369\) | −3.09739 | −0.161243 | ||||||||
\(370\) | 6.26025 | 0.325455 | ||||||||
\(371\) | 0.950773 | 0.0493617 | ||||||||
\(372\) | −18.1167 | −0.939306 | ||||||||
\(373\) | −19.3598 | −1.00241 | −0.501207 | − | 0.865327i | \(-0.667111\pi\) | ||||
−0.501207 | + | 0.865327i | \(0.667111\pi\) | |||||||
\(374\) | −0.667192 | −0.0344997 | ||||||||
\(375\) | −2.03369 | −0.105019 | ||||||||
\(376\) | 1.22762 | 0.0633099 | ||||||||
\(377\) | 35.4666 | 1.82662 | ||||||||
\(378\) | 7.60260 | 0.391035 | ||||||||
\(379\) | −27.8640 | −1.43128 | −0.715638 | − | 0.698471i | \(-0.753864\pi\) | ||||
−0.715638 | + | 0.698471i | \(0.753864\pi\) | |||||||
\(380\) | 60.2173 | 3.08908 | ||||||||
\(381\) | −43.0414 | −2.20508 | ||||||||
\(382\) | −25.5960 | −1.30960 | ||||||||
\(383\) | −18.0382 | −0.921707 | −0.460853 | − | 0.887476i | \(-0.652457\pi\) | ||||
−0.460853 | + | 0.887476i | \(0.652457\pi\) | |||||||
\(384\) | 12.7714 | 0.651740 | ||||||||
\(385\) | 3.37451 | 0.171981 | ||||||||
\(386\) | −15.7235 | −0.800303 | ||||||||
\(387\) | 3.80223 | 0.193278 | ||||||||
\(388\) | 28.1871 | 1.43098 | ||||||||
\(389\) | −2.27990 | −0.115596 | −0.0577978 | − | 0.998328i | \(-0.518408\pi\) | ||||
−0.0577978 | + | 0.998328i | \(0.518408\pi\) | |||||||
\(390\) | −83.4293 | −4.22461 | ||||||||
\(391\) | 1.81930 | 0.0920060 | ||||||||
\(392\) | −0.789909 | −0.0398964 | ||||||||
\(393\) | 16.3967 | 0.827102 | ||||||||
\(394\) | 43.7145 | 2.20231 | ||||||||
\(395\) | −43.3217 | −2.17975 | ||||||||
\(396\) | −3.08392 | −0.154973 | ||||||||
\(397\) | 10.6924 | 0.536637 | 0.268319 | − | 0.963330i | \(-0.413532\pi\) | ||||
0.268319 | + | 0.963330i | \(0.413532\pi\) | |||||||
\(398\) | −46.7474 | −2.34323 | ||||||||
\(399\) | −16.2327 | −0.812651 | ||||||||
\(400\) | −16.4670 | −0.823348 | ||||||||
\(401\) | −18.5628 | −0.926984 | −0.463492 | − | 0.886101i | \(-0.653404\pi\) | ||||
−0.463492 | + | 0.886101i | \(0.653404\pi\) | |||||||
\(402\) | 27.3023 | 1.36172 | ||||||||
\(403\) | 22.3517 | 1.11342 | ||||||||
\(404\) | 35.9203 | 1.78710 | ||||||||
\(405\) | 35.8920 | 1.78349 | ||||||||
\(406\) | 12.2940 | 0.610143 | ||||||||
\(407\) | −0.979534 | −0.0485537 | ||||||||
\(408\) | 0.493136 | 0.0244139 | ||||||||
\(409\) | 4.60656 | 0.227780 | 0.113890 | − | 0.993493i | \(-0.463669\pi\) | ||||
0.113890 | + | 0.993493i | \(0.463669\pi\) | |||||||
\(410\) | −16.8595 | −0.832631 | ||||||||
\(411\) | −43.8609 | −2.16350 | ||||||||
\(412\) | −30.7593 | −1.51540 | ||||||||
\(413\) | 8.70133 | 0.428165 | ||||||||
\(414\) | 15.4832 | 0.760956 | ||||||||
\(415\) | −51.8959 | −2.54747 | ||||||||
\(416\) | −48.7143 | −2.38841 | ||||||||
\(417\) | −47.5983 | −2.33090 | ||||||||
\(418\) | −17.3481 | −0.848522 | ||||||||
\(419\) | 34.0273 | 1.66234 | 0.831172 | − | 0.556016i | \(-0.187671\pi\) | ||||
0.831172 | + | 0.556016i | \(0.187671\pi\) | |||||||
\(420\) | −15.7070 | −0.766421 | ||||||||
\(421\) | 30.7029 | 1.49637 | 0.748185 | − | 0.663490i | \(-0.230926\pi\) | ||||
0.748185 | + | 0.663490i | \(0.230926\pi\) | |||||||
\(422\) | 4.82574 | 0.234913 | ||||||||
\(423\) | −1.91796 | −0.0932542 | ||||||||
\(424\) | −0.751024 | −0.0364729 | ||||||||
\(425\) | −1.61037 | −0.0781146 | ||||||||
\(426\) | −2.67448 | −0.129579 | ||||||||
\(427\) | −1.10085 | −0.0532737 | ||||||||
\(428\) | 42.9481 | 2.07598 | ||||||||
\(429\) | 13.0541 | 0.630257 | ||||||||
\(430\) | 20.6961 | 0.998053 | ||||||||
\(431\) | −3.80752 | −0.183402 | −0.0917008 | − | 0.995787i | \(-0.529230\pi\) | ||||
−0.0917008 | + | 0.995787i | \(0.529230\pi\) | |||||||
\(432\) | 11.2731 | 0.542377 | ||||||||
\(433\) | −14.1584 | −0.680407 | −0.340203 | − | 0.940352i | \(-0.610496\pi\) | ||||
−0.340203 | + | 0.940352i | \(0.610496\pi\) | |||||||
\(434\) | 7.74793 | 0.371913 | ||||||||
\(435\) | 38.8190 | 1.86123 | ||||||||
\(436\) | 40.2121 | 1.92581 | ||||||||
\(437\) | 47.3048 | 2.26290 | ||||||||
\(438\) | 11.5724 | 0.552949 | ||||||||
\(439\) | −23.6054 | −1.12662 | −0.563312 | − | 0.826244i | \(-0.690473\pi\) | ||||
−0.563312 | + | 0.826244i | \(0.690473\pi\) | |||||||
\(440\) | −2.66555 | −0.127075 | ||||||||
\(441\) | 1.23410 | 0.0587666 | ||||||||
\(442\) | −3.83145 | −0.182244 | ||||||||
\(443\) | 3.43824 | 0.163356 | 0.0816778 | − | 0.996659i | \(-0.473972\pi\) | ||||
0.0816778 | + | 0.996659i | \(0.473972\pi\) | |||||||
\(444\) | 4.55933 | 0.216376 | ||||||||
\(445\) | −32.3726 | −1.53461 | ||||||||
\(446\) | 4.67565 | 0.221398 | ||||||||
\(447\) | −30.6353 | −1.44900 | ||||||||
\(448\) | −10.6814 | −0.504650 | ||||||||
\(449\) | −18.8171 | −0.888036 | −0.444018 | − | 0.896018i | \(-0.646447\pi\) | ||||
−0.444018 | + | 0.896018i | \(0.646447\pi\) | |||||||
\(450\) | −13.7051 | −0.646065 | ||||||||
\(451\) | 2.63798 | 0.124218 | ||||||||
\(452\) | 9.19536 | 0.432513 | ||||||||
\(453\) | −30.9271 | −1.45308 | ||||||||
\(454\) | −39.1369 | −1.83678 | ||||||||
\(455\) | 19.3786 | 0.908484 | ||||||||
\(456\) | 12.8223 | 0.600461 | ||||||||
\(457\) | 18.9213 | 0.885100 | 0.442550 | − | 0.896744i | \(-0.354074\pi\) | ||||
0.442550 | + | 0.896744i | \(0.354074\pi\) | |||||||
\(458\) | 9.08521 | 0.424524 | ||||||||
\(459\) | 1.10244 | 0.0514576 | ||||||||
\(460\) | 45.7727 | 2.13416 | ||||||||
\(461\) | 0.871546 | 0.0405920 | 0.0202960 | − | 0.999794i | \(-0.493539\pi\) | ||||
0.0202960 | + | 0.999794i | \(0.493539\pi\) | |||||||
\(462\) | 4.52503 | 0.210524 | ||||||||
\(463\) | −3.55195 | −0.165073 | −0.0825365 | − | 0.996588i | \(-0.526302\pi\) | ||||
−0.0825365 | + | 0.996588i | \(0.526302\pi\) | |||||||
\(464\) | 18.2295 | 0.846285 | ||||||||
\(465\) | 24.4644 | 1.13451 | ||||||||
\(466\) | 11.7053 | 0.542236 | ||||||||
\(467\) | −0.750411 | −0.0347249 | −0.0173624 | − | 0.999849i | \(-0.505527\pi\) | ||||
−0.0173624 | + | 0.999849i | \(0.505527\pi\) | |||||||
\(468\) | −17.7099 | −0.818641 | ||||||||
\(469\) | −6.34168 | −0.292832 | ||||||||
\(470\) | −10.4397 | −0.481547 | ||||||||
\(471\) | 0.767729 | 0.0353751 | ||||||||
\(472\) | −6.87326 | −0.316367 | ||||||||
\(473\) | −3.23829 | −0.148897 | ||||||||
\(474\) | −58.0921 | −2.66826 | ||||||||
\(475\) | −41.8724 | −1.92124 | ||||||||
\(476\) | −0.721335 | −0.0330623 | ||||||||
\(477\) | 1.17335 | 0.0537239 | ||||||||
\(478\) | −13.8035 | −0.631356 | ||||||||
\(479\) | −10.5208 | −0.480707 | −0.240354 | − | 0.970685i | \(-0.577263\pi\) | ||||
−0.240354 | + | 0.970685i | \(0.577263\pi\) | |||||||
\(480\) | −53.3189 | −2.43366 | ||||||||
\(481\) | −5.62513 | −0.256484 | ||||||||
\(482\) | 11.8698 | 0.540656 | ||||||||
\(483\) | −12.3389 | −0.561438 | ||||||||
\(484\) | −23.5264 | −1.06938 | ||||||||
\(485\) | −38.0633 | −1.72836 | ||||||||
\(486\) | 25.3215 | 1.14861 | ||||||||
\(487\) | −36.4341 | −1.65098 | −0.825492 | − | 0.564413i | \(-0.809103\pi\) | ||||
−0.825492 | + | 0.564413i | \(0.809103\pi\) | |||||||
\(488\) | 0.869568 | 0.0393635 | ||||||||
\(489\) | 24.7846 | 1.12080 | ||||||||
\(490\) | 6.71736 | 0.303460 | ||||||||
\(491\) | −11.4294 | −0.515801 | −0.257901 | − | 0.966171i | \(-0.583031\pi\) | ||||
−0.257901 | + | 0.966171i | \(0.583031\pi\) | |||||||
\(492\) | −12.2787 | −0.553568 | ||||||||
\(493\) | 1.78274 | 0.0802907 | ||||||||
\(494\) | −99.6241 | −4.48230 | ||||||||
\(495\) | 4.16447 | 0.187179 | ||||||||
\(496\) | 11.4886 | 0.515853 | ||||||||
\(497\) | 0.621219 | 0.0278655 | ||||||||
\(498\) | −69.5896 | −3.11838 | ||||||||
\(499\) | −36.1046 | −1.61626 | −0.808131 | − | 0.589003i | \(-0.799521\pi\) | ||||
−0.808131 | + | 0.589003i | \(0.799521\pi\) | |||||||
\(500\) | −2.34981 | −0.105087 | ||||||||
\(501\) | −0.850024 | −0.0379763 | ||||||||
\(502\) | 13.6905 | 0.611036 | ||||||||
\(503\) | 11.3325 | 0.505289 | 0.252645 | − | 0.967559i | \(-0.418700\pi\) | ||||
0.252645 | + | 0.967559i | \(0.418700\pi\) | |||||||
\(504\) | −0.974825 | −0.0434221 | ||||||||
\(505\) | −48.5060 | −2.15849 | ||||||||
\(506\) | −13.1867 | −0.586221 | ||||||||
\(507\) | 48.2151 | 2.14131 | ||||||||
\(508\) | −49.7317 | −2.20649 | ||||||||
\(509\) | 32.2522 | 1.42955 | 0.714777 | − | 0.699353i | \(-0.246528\pi\) | ||||
0.714777 | + | 0.699353i | \(0.246528\pi\) | |||||||
\(510\) | −4.19361 | −0.185696 | ||||||||
\(511\) | −2.68798 | −0.118909 | ||||||||
\(512\) | −29.9400 | −1.32317 | ||||||||
\(513\) | 28.6653 | 1.26561 | ||||||||
\(514\) | −12.5517 | −0.553630 | ||||||||
\(515\) | 41.5368 | 1.83033 | ||||||||
\(516\) | 15.0729 | 0.663548 | ||||||||
\(517\) | 1.63349 | 0.0718406 | ||||||||
\(518\) | −1.94988 | −0.0856728 | ||||||||
\(519\) | 34.2008 | 1.50125 | ||||||||
\(520\) | −15.3073 | −0.671272 | ||||||||
\(521\) | 28.4147 | 1.24487 | 0.622436 | − | 0.782671i | \(-0.286143\pi\) | ||||
0.622436 | + | 0.782671i | \(0.286143\pi\) | |||||||
\(522\) | 15.1721 | 0.664063 | ||||||||
\(523\) | 12.2047 | 0.533672 | 0.266836 | − | 0.963742i | \(-0.414022\pi\) | ||||
0.266836 | + | 0.963742i | \(0.414022\pi\) | |||||||
\(524\) | 18.9454 | 0.827632 | ||||||||
\(525\) | 10.9219 | 0.476671 | ||||||||
\(526\) | 65.5856 | 2.85967 | ||||||||
\(527\) | 1.12352 | 0.0489412 | ||||||||
\(528\) | 6.70969 | 0.292002 | ||||||||
\(529\) | 12.9576 | 0.563373 | ||||||||
\(530\) | 6.38669 | 0.277420 | ||||||||
\(531\) | 10.7383 | 0.466002 | ||||||||
\(532\) | −18.7559 | −0.813171 | ||||||||
\(533\) | 15.1490 | 0.656178 | ||||||||
\(534\) | −43.4100 | −1.87853 | ||||||||
\(535\) | −57.9963 | −2.50740 | ||||||||
\(536\) | 5.00935 | 0.216371 | ||||||||
\(537\) | −15.1063 | −0.651885 | ||||||||
\(538\) | 1.79419 | 0.0773530 | ||||||||
\(539\) | −1.05106 | −0.0452722 | ||||||||
\(540\) | 27.7369 | 1.19361 | ||||||||
\(541\) | −21.1480 | −0.909225 | −0.454612 | − | 0.890689i | \(-0.650222\pi\) | ||||
−0.454612 | + | 0.890689i | \(0.650222\pi\) | |||||||
\(542\) | −29.4522 | −1.26508 | ||||||||
\(543\) | −14.2651 | −0.612174 | ||||||||
\(544\) | −2.44865 | −0.104985 | ||||||||
\(545\) | −54.3016 | −2.32603 | ||||||||
\(546\) | 25.9857 | 1.11209 | ||||||||
\(547\) | −22.0675 | −0.943540 | −0.471770 | − | 0.881722i | \(-0.656385\pi\) | ||||
−0.471770 | + | 0.881722i | \(0.656385\pi\) | |||||||
\(548\) | −50.6786 | −2.16488 | ||||||||
\(549\) | −1.35855 | −0.0579816 | ||||||||
\(550\) | 11.6724 | 0.497711 | ||||||||
\(551\) | 46.3543 | 1.97476 | ||||||||
\(552\) | 9.74659 | 0.414842 | ||||||||
\(553\) | 13.4934 | 0.573798 | ||||||||
\(554\) | 43.2742 | 1.83855 | ||||||||
\(555\) | −6.15683 | −0.261343 | ||||||||
\(556\) | −54.9970 | −2.33239 | ||||||||
\(557\) | 8.63053 | 0.365687 | 0.182844 | − | 0.983142i | \(-0.441470\pi\) | ||||
0.182844 | + | 0.983142i | \(0.441470\pi\) | |||||||
\(558\) | 9.56170 | 0.404779 | ||||||||
\(559\) | −18.5964 | −0.786543 | ||||||||
\(560\) | 9.96047 | 0.420906 | ||||||||
\(561\) | 0.656170 | 0.0277035 | ||||||||
\(562\) | 36.9932 | 1.56046 | ||||||||
\(563\) | −35.5158 | −1.49681 | −0.748406 | − | 0.663241i | \(-0.769180\pi\) | ||||
−0.748406 | + | 0.663241i | \(0.769180\pi\) | |||||||
\(564\) | −7.60321 | −0.320153 | ||||||||
\(565\) | −12.4172 | −0.522397 | ||||||||
\(566\) | −56.2594 | −2.36476 | ||||||||
\(567\) | −11.1793 | −0.469486 | ||||||||
\(568\) | −0.490706 | −0.0205896 | ||||||||
\(569\) | 12.4619 | 0.522429 | 0.261214 | − | 0.965281i | \(-0.415877\pi\) | ||||
0.261214 | + | 0.965281i | \(0.415877\pi\) | |||||||
\(570\) | −109.041 | −4.56722 | ||||||||
\(571\) | −31.1268 | −1.30262 | −0.651309 | − | 0.758813i | \(-0.725780\pi\) | ||||
−0.651309 | + | 0.758813i | \(0.725780\pi\) | |||||||
\(572\) | 15.0832 | 0.630660 | ||||||||
\(573\) | 25.1731 | 1.05162 | ||||||||
\(574\) | 5.25123 | 0.219182 | ||||||||
\(575\) | −31.8282 | −1.32733 | ||||||||
\(576\) | −13.1819 | −0.549247 | ||||||||
\(577\) | 20.2224 | 0.841868 | 0.420934 | − | 0.907091i | \(-0.361702\pi\) | ||||
0.420934 | + | 0.907091i | \(0.361702\pi\) | |||||||
\(578\) | 35.3758 | 1.47144 | ||||||||
\(579\) | 15.4637 | 0.642650 | ||||||||
\(580\) | 44.8530 | 1.86242 | ||||||||
\(581\) | 16.1640 | 0.670596 | ||||||||
\(582\) | −51.0408 | −2.11571 | ||||||||
\(583\) | −0.999317 | −0.0413875 | ||||||||
\(584\) | 2.12326 | 0.0878612 | ||||||||
\(585\) | 23.9151 | 0.988769 | ||||||||
\(586\) | 60.2359 | 2.48832 | ||||||||
\(587\) | 26.1542 | 1.07950 | 0.539749 | − | 0.841826i | \(-0.318519\pi\) | ||||
0.539749 | + | 0.841826i | \(0.318519\pi\) | |||||||
\(588\) | 4.89224 | 0.201753 | ||||||||
\(589\) | 29.2133 | 1.20371 | ||||||||
\(590\) | 58.4500 | 2.40635 | ||||||||
\(591\) | −42.9924 | −1.76847 | ||||||||
\(592\) | −2.89127 | −0.118831 | ||||||||
\(593\) | 24.5242 | 1.00709 | 0.503543 | − | 0.863970i | \(-0.332029\pi\) | ||||
0.503543 | + | 0.863970i | \(0.332029\pi\) | |||||||
\(594\) | −7.99077 | −0.327865 | ||||||||
\(595\) | 0.974076 | 0.0399332 | ||||||||
\(596\) | −35.3973 | −1.44993 | ||||||||
\(597\) | 45.9751 | 1.88164 | ||||||||
\(598\) | −75.7268 | −3.09670 | ||||||||
\(599\) | −37.9591 | −1.55096 | −0.775482 | − | 0.631369i | \(-0.782493\pi\) | ||||
−0.775482 | + | 0.631369i | \(0.782493\pi\) | |||||||
\(600\) | −8.62730 | −0.352208 | ||||||||
\(601\) | 42.4948 | 1.73340 | 0.866699 | − | 0.498831i | \(-0.166237\pi\) | ||||
0.866699 | + | 0.498831i | \(0.166237\pi\) | |||||||
\(602\) | −6.44620 | −0.262728 | ||||||||
\(603\) | −7.82626 | −0.318710 | ||||||||
\(604\) | −35.7344 | −1.45401 | ||||||||
\(605\) | 31.7696 | 1.29162 | ||||||||
\(606\) | −65.0440 | −2.64223 | ||||||||
\(607\) | −23.3747 | −0.948749 | −0.474375 | − | 0.880323i | \(-0.657326\pi\) | ||||
−0.474375 | + | 0.880323i | \(0.657326\pi\) | |||||||
\(608\) | −63.6688 | −2.58211 | ||||||||
\(609\) | −12.0909 | −0.489950 | ||||||||
\(610\) | −7.39478 | −0.299406 | ||||||||
\(611\) | 9.38055 | 0.379496 | ||||||||
\(612\) | −0.890198 | −0.0359841 | ||||||||
\(613\) | 36.4687 | 1.47296 | 0.736478 | − | 0.676461i | \(-0.236487\pi\) | ||||
0.736478 | + | 0.676461i | \(0.236487\pi\) | |||||||
\(614\) | 3.38581 | 0.136640 | ||||||||
\(615\) | 16.5810 | 0.668609 | ||||||||
\(616\) | 0.830239 | 0.0334513 | ||||||||
\(617\) | 3.98057 | 0.160252 | 0.0801258 | − | 0.996785i | \(-0.474468\pi\) | ||||
0.0801258 | + | 0.996785i | \(0.474468\pi\) | |||||||
\(618\) | 55.6986 | 2.24053 | ||||||||
\(619\) | −20.5223 | −0.824863 | −0.412431 | − | 0.910989i | \(-0.635320\pi\) | ||||
−0.412431 | + | 0.910989i | \(0.635320\pi\) | |||||||
\(620\) | 28.2672 | 1.13524 | ||||||||
\(621\) | 21.7892 | 0.874372 | ||||||||
\(622\) | −32.1931 | −1.29083 | ||||||||
\(623\) | 10.0831 | 0.403971 | ||||||||
\(624\) | 38.5315 | 1.54249 | ||||||||
\(625\) | −23.3661 | −0.934642 | ||||||||
\(626\) | 67.9067 | 2.71410 | ||||||||
\(627\) | 17.0615 | 0.681370 | ||||||||
\(628\) | 0.887064 | 0.0353977 | ||||||||
\(629\) | −0.282750 | −0.0112740 | ||||||||
\(630\) | 8.28988 | 0.330277 | ||||||||
\(631\) | 12.8376 | 0.511057 | 0.255528 | − | 0.966802i | \(-0.417751\pi\) | ||||
0.255528 | + | 0.966802i | \(0.417751\pi\) | |||||||
\(632\) | −10.6586 | −0.423975 | ||||||||
\(633\) | −4.74602 | −0.188637 | ||||||||
\(634\) | −9.50141 | −0.377349 | ||||||||
\(635\) | 67.1567 | 2.66503 | ||||||||
\(636\) | 4.65141 | 0.184441 | ||||||||
\(637\) | −6.03586 | −0.239150 | ||||||||
\(638\) | −12.9217 | −0.511577 | ||||||||
\(639\) | 0.766645 | 0.0303280 | ||||||||
\(640\) | −19.9271 | −0.787686 | ||||||||
\(641\) | −10.9318 | −0.431778 | −0.215889 | − | 0.976418i | \(-0.569265\pi\) | ||||
−0.215889 | + | 0.976418i | \(0.569265\pi\) | |||||||
\(642\) | −77.7700 | −3.06934 | ||||||||
\(643\) | 50.0723 | 1.97466 | 0.987330 | − | 0.158683i | \(-0.0507249\pi\) | ||||
0.987330 | + | 0.158683i | \(0.0507249\pi\) | |||||||
\(644\) | −14.2568 | −0.561798 | ||||||||
\(645\) | −20.3542 | −0.801444 | ||||||||
\(646\) | −5.00765 | −0.197023 | ||||||||
\(647\) | −15.4963 | −0.609222 | −0.304611 | − | 0.952477i | \(-0.598526\pi\) | ||||
−0.304611 | + | 0.952477i | \(0.598526\pi\) | |||||||
\(648\) | 8.83062 | 0.346900 | ||||||||
\(649\) | −9.14560 | −0.358996 | ||||||||
\(650\) | 67.0304 | 2.62915 | ||||||||
\(651\) | −7.61993 | −0.298649 | ||||||||
\(652\) | 28.6371 | 1.12152 | ||||||||
\(653\) | −40.2282 | −1.57425 | −0.787126 | − | 0.616792i | \(-0.788432\pi\) | ||||
−0.787126 | + | 0.616792i | \(0.788432\pi\) | |||||||
\(654\) | −72.8156 | −2.84732 | ||||||||
\(655\) | −25.5834 | −0.999627 | ||||||||
\(656\) | 7.78649 | 0.304011 | ||||||||
\(657\) | −3.31724 | −0.129418 | ||||||||
\(658\) | 3.25165 | 0.126763 | ||||||||
\(659\) | −2.38576 | −0.0929360 | −0.0464680 | − | 0.998920i | \(-0.514797\pi\) | ||||
−0.0464680 | + | 0.998920i | \(0.514797\pi\) | |||||||
\(660\) | 16.5089 | 0.642608 | ||||||||
\(661\) | 2.24446 | 0.0872993 | 0.0436497 | − | 0.999047i | \(-0.486101\pi\) | ||||
0.0436497 | + | 0.999047i | \(0.486101\pi\) | |||||||
\(662\) | −18.4436 | −0.716833 | ||||||||
\(663\) | 3.76816 | 0.146343 | ||||||||
\(664\) | −12.7681 | −0.495498 | ||||||||
\(665\) | 25.3276 | 0.982162 | ||||||||
\(666\) | −2.40634 | −0.0932439 | ||||||||
\(667\) | 35.2350 | 1.36431 | ||||||||
\(668\) | −0.982151 | −0.0380006 | ||||||||
\(669\) | −4.59840 | −0.177785 | ||||||||
\(670\) | −42.5994 | −1.64576 | ||||||||
\(671\) | 1.15705 | 0.0446675 | ||||||||
\(672\) | 16.6072 | 0.640638 | ||||||||
\(673\) | −0.310404 | −0.0119652 | −0.00598260 | − | 0.999982i | \(-0.501904\pi\) | ||||
−0.00598260 | + | 0.999982i | \(0.501904\pi\) | |||||||
\(674\) | 23.0693 | 0.888598 | ||||||||
\(675\) | −19.2870 | −0.742357 | ||||||||
\(676\) | 55.7096 | 2.14268 | ||||||||
\(677\) | −8.32076 | −0.319793 | −0.159896 | − | 0.987134i | \(-0.551116\pi\) | ||||
−0.159896 | + | 0.987134i | \(0.551116\pi\) | |||||||
\(678\) | −16.6509 | −0.639472 | ||||||||
\(679\) | 11.8556 | 0.454975 | ||||||||
\(680\) | −0.769431 | −0.0295063 | ||||||||
\(681\) | 38.4903 | 1.47495 | ||||||||
\(682\) | −8.14352 | −0.311831 | ||||||||
\(683\) | −1.41649 | −0.0542005 | −0.0271003 | − | 0.999633i | \(-0.508627\pi\) | ||||
−0.0271003 | + | 0.999633i | \(0.508627\pi\) | |||||||
\(684\) | −23.1466 | −0.885033 | ||||||||
\(685\) | 68.4354 | 2.61478 | ||||||||
\(686\) | −2.09226 | −0.0798827 | ||||||||
\(687\) | −8.93512 | −0.340896 | ||||||||
\(688\) | −9.55839 | −0.364410 | ||||||||
\(689\) | −5.73873 | −0.218628 | ||||||||
\(690\) | −82.8847 | −3.15537 | ||||||||
\(691\) | 14.6754 | 0.558279 | 0.279139 | − | 0.960251i | \(-0.409951\pi\) | ||||
0.279139 | + | 0.960251i | \(0.409951\pi\) | |||||||
\(692\) | 39.5170 | 1.50221 | ||||||||
\(693\) | −1.29711 | −0.0492730 | ||||||||
\(694\) | −28.6621 | −1.08800 | ||||||||
\(695\) | 74.2668 | 2.81710 | ||||||||
\(696\) | 9.55074 | 0.362020 | ||||||||
\(697\) | 0.761474 | 0.0288429 | ||||||||
\(698\) | 34.6135 | 1.31014 | ||||||||
\(699\) | −11.5119 | −0.435420 | ||||||||
\(700\) | 12.6196 | 0.476976 | ||||||||
\(701\) | 38.0423 | 1.43684 | 0.718418 | − | 0.695612i | \(-0.244867\pi\) | ||||
0.718418 | + | 0.695612i | \(0.244867\pi\) | |||||||
\(702\) | −45.8882 | −1.73194 | ||||||||
\(703\) | −7.35196 | −0.277284 | ||||||||
\(704\) | 11.2268 | 0.423126 | ||||||||
\(705\) | 10.2672 | 0.386686 | ||||||||
\(706\) | −45.7173 | −1.72059 | ||||||||
\(707\) | 15.1082 | 0.568201 | ||||||||
\(708\) | 42.5690 | 1.59984 | ||||||||
\(709\) | −24.6679 | −0.926424 | −0.463212 | − | 0.886248i | \(-0.653303\pi\) | ||||
−0.463212 | + | 0.886248i | \(0.653303\pi\) | |||||||
\(710\) | 4.17295 | 0.156608 | ||||||||
\(711\) | 16.6522 | 0.624506 | ||||||||
\(712\) | −7.96473 | −0.298491 | ||||||||
\(713\) | 22.2058 | 0.831613 | ||||||||
\(714\) | 1.30618 | 0.0488827 | ||||||||
\(715\) | −20.3681 | −0.761722 | ||||||||
\(716\) | −17.4544 | −0.652303 | ||||||||
\(717\) | 13.5754 | 0.506984 | ||||||||
\(718\) | −49.0446 | −1.83033 | ||||||||
\(719\) | −19.3021 | −0.719847 | −0.359923 | − | 0.932982i | \(-0.617197\pi\) | ||||
−0.359923 | + | 0.932982i | \(0.617197\pi\) | |||||||
\(720\) | 12.2922 | 0.458103 | ||||||||
\(721\) | −12.9375 | −0.481816 | ||||||||
\(722\) | −90.4543 | −3.36636 | ||||||||
\(723\) | −11.6737 | −0.434151 | ||||||||
\(724\) | −16.4825 | −0.612566 | ||||||||
\(725\) | −31.1887 | −1.15832 | ||||||||
\(726\) | 42.6014 | 1.58108 | ||||||||
\(727\) | 22.6204 | 0.838946 | 0.419473 | − | 0.907768i | \(-0.362215\pi\) | ||||
0.419473 | + | 0.907768i | \(0.362215\pi\) | |||||||
\(728\) | 4.76778 | 0.176706 | ||||||||
\(729\) | 8.63466 | 0.319802 | ||||||||
\(730\) | −18.0562 | −0.668289 | ||||||||
\(731\) | −0.934756 | −0.0345732 | ||||||||
\(732\) | −5.38561 | −0.199058 | ||||||||
\(733\) | 13.1730 | 0.486557 | 0.243279 | − | 0.969956i | \(-0.421777\pi\) | ||||
0.243279 | + | 0.969956i | \(0.421777\pi\) | |||||||
\(734\) | 34.6865 | 1.28030 | ||||||||
\(735\) | −6.60639 | −0.243680 | ||||||||
\(736\) | −48.3963 | −1.78391 | ||||||||
\(737\) | 6.66547 | 0.245526 | ||||||||
\(738\) | 6.48053 | 0.238552 | ||||||||
\(739\) | −11.2292 | −0.413071 | −0.206536 | − | 0.978439i | \(-0.566219\pi\) | ||||
−0.206536 | + | 0.978439i | \(0.566219\pi\) | |||||||
\(740\) | −7.11384 | −0.261510 | ||||||||
\(741\) | 97.9783 | 3.59932 | ||||||||
\(742\) | −1.98926 | −0.0730281 | ||||||||
\(743\) | 37.3398 | 1.36987 | 0.684933 | − | 0.728606i | \(-0.259832\pi\) | ||||
0.684933 | + | 0.728606i | \(0.259832\pi\) | |||||||
\(744\) | 6.01905 | 0.220669 | ||||||||
\(745\) | 47.7998 | 1.75125 | ||||||||
\(746\) | 40.5058 | 1.48302 | ||||||||
\(747\) | 19.9480 | 0.729858 | ||||||||
\(748\) | 0.758164 | 0.0277212 | ||||||||
\(749\) | 18.0641 | 0.660048 | ||||||||
\(750\) | 4.25500 | 0.155371 | ||||||||
\(751\) | −16.2709 | −0.593733 | −0.296866 | − | 0.954919i | \(-0.595942\pi\) | ||||
−0.296866 | + | 0.954919i | \(0.595942\pi\) | |||||||
\(752\) | 4.82153 | 0.175823 | ||||||||
\(753\) | −13.4643 | −0.490666 | ||||||||
\(754\) | −74.2051 | −2.70239 | ||||||||
\(755\) | 48.2550 | 1.75618 | ||||||||
\(756\) | −8.63922 | −0.314206 | ||||||||
\(757\) | −0.162248 | −0.00589701 | −0.00294851 | − | 0.999996i | \(-0.500939\pi\) | ||||
−0.00294851 | + | 0.999996i | \(0.500939\pi\) | |||||||
\(758\) | 58.2986 | 2.11750 | ||||||||
\(759\) | 12.9689 | 0.470740 | ||||||||
\(760\) | −20.0065 | −0.725711 | ||||||||
\(761\) | −14.6180 | −0.529903 | −0.264952 | − | 0.964262i | \(-0.585356\pi\) | ||||
−0.264952 | + | 0.964262i | \(0.585356\pi\) | |||||||
\(762\) | 90.0536 | 3.26230 | ||||||||
\(763\) | 16.9133 | 0.612303 | ||||||||
\(764\) | 29.0860 | 1.05229 | ||||||||
\(765\) | 1.20211 | 0.0434622 | ||||||||
\(766\) | 37.7405 | 1.36362 | ||||||||
\(767\) | −52.5200 | −1.89639 | ||||||||
\(768\) | 17.2371 | 0.621989 | ||||||||
\(769\) | 52.0790 | 1.87802 | 0.939008 | − | 0.343896i | \(-0.111747\pi\) | ||||
0.939008 | + | 0.343896i | \(0.111747\pi\) | |||||||
\(770\) | −7.06033 | −0.254437 | ||||||||
\(771\) | 12.3443 | 0.444569 | ||||||||
\(772\) | 17.8674 | 0.643061 | ||||||||
\(773\) | 48.0473 | 1.72814 | 0.864070 | − | 0.503371i | \(-0.167907\pi\) | ||||
0.864070 | + | 0.503371i | \(0.167907\pi\) | |||||||
\(774\) | −7.95525 | −0.285945 | ||||||||
\(775\) | −19.6557 | −0.706053 | ||||||||
\(776\) | −9.36481 | −0.336177 | ||||||||
\(777\) | 1.91767 | 0.0687960 | ||||||||
\(778\) | 4.77014 | 0.171018 | ||||||||
\(779\) | 19.7996 | 0.709393 | ||||||||
\(780\) | 94.8050 | 3.39456 | ||||||||
\(781\) | −0.652936 | −0.0233639 | ||||||||
\(782\) | −3.80644 | −0.136118 | ||||||||
\(783\) | 21.3514 | 0.763037 | ||||||||
\(784\) | −3.10239 | −0.110800 | ||||||||
\(785\) | −1.19787 | −0.0427540 | ||||||||
\(786\) | −34.3060 | −1.22366 | ||||||||
\(787\) | 51.2322 | 1.82623 | 0.913116 | − | 0.407701i | \(-0.133669\pi\) | ||||
0.913116 | + | 0.407701i | \(0.133669\pi\) | |||||||
\(788\) | −49.6751 | −1.76960 | ||||||||
\(789\) | −64.5021 | −2.29633 | ||||||||
\(790\) | 90.6401 | 3.22483 | ||||||||
\(791\) | 3.86760 | 0.137516 | ||||||||
\(792\) | 1.02460 | 0.0364075 | ||||||||
\(793\) | 6.64456 | 0.235955 | ||||||||
\(794\) | −22.3713 | −0.793928 | ||||||||
\(795\) | −6.28118 | −0.222770 | ||||||||
\(796\) | 53.1214 | 1.88284 | ||||||||
\(797\) | 33.2854 | 1.17903 | 0.589515 | − | 0.807758i | \(-0.299319\pi\) | ||||
0.589515 | + | 0.807758i | \(0.299319\pi\) | |||||||
\(798\) | 33.9630 | 1.20228 | ||||||||
\(799\) | 0.471518 | 0.0166811 | ||||||||
\(800\) | 42.8385 | 1.51457 | ||||||||
\(801\) | 12.4435 | 0.439671 | ||||||||
\(802\) | 38.8382 | 1.37143 | ||||||||
\(803\) | 2.82523 | 0.0997000 | ||||||||
\(804\) | −31.0251 | −1.09417 | ||||||||
\(805\) | 19.2521 | 0.678549 | ||||||||
\(806\) | −46.7654 | −1.64724 | ||||||||
\(807\) | −1.76455 | −0.0621150 | ||||||||
\(808\) | −11.9341 | −0.419839 | ||||||||
\(809\) | 4.08686 | 0.143686 | 0.0718431 | − | 0.997416i | \(-0.477112\pi\) | ||||
0.0718431 | + | 0.997416i | \(0.477112\pi\) | |||||||
\(810\) | −75.0954 | −2.63858 | ||||||||
\(811\) | −20.7905 | −0.730053 | −0.365027 | − | 0.930997i | \(-0.618940\pi\) | ||||
−0.365027 | + | 0.930997i | \(0.618940\pi\) | |||||||
\(812\) | −13.9704 | −0.490263 | ||||||||
\(813\) | 28.9656 | 1.01587 | ||||||||
\(814\) | 2.04944 | 0.0718327 | ||||||||
\(815\) | −38.6710 | −1.35459 | ||||||||
\(816\) | 1.93680 | 0.0678017 | ||||||||
\(817\) | −24.3052 | −0.850331 | ||||||||
\(818\) | −9.63811 | −0.336988 | ||||||||
\(819\) | −7.44885 | −0.260284 | ||||||||
\(820\) | 19.1583 | 0.669037 | ||||||||
\(821\) | 9.67690 | 0.337726 | 0.168863 | − | 0.985640i | \(-0.445990\pi\) | ||||
0.168863 | + | 0.985640i | \(0.445990\pi\) | |||||||
\(822\) | 91.7683 | 3.20079 | ||||||||
\(823\) | 24.1830 | 0.842966 | 0.421483 | − | 0.906836i | \(-0.361510\pi\) | ||||
0.421483 | + | 0.906836i | \(0.361510\pi\) | |||||||
\(824\) | 10.2194 | 0.356010 | ||||||||
\(825\) | −11.4795 | −0.399666 | ||||||||
\(826\) | −18.2054 | −0.633448 | ||||||||
\(827\) | −22.6651 | −0.788143 | −0.394071 | − | 0.919080i | \(-0.628934\pi\) | ||||
−0.394071 | + | 0.919080i | \(0.628934\pi\) | |||||||
\(828\) | −17.5943 | −0.611445 | ||||||||
\(829\) | −28.7050 | −0.996967 | −0.498484 | − | 0.866899i | \(-0.666110\pi\) | ||||
−0.498484 | + | 0.866899i | \(0.666110\pi\) | |||||||
\(830\) | 108.579 | 3.76885 | ||||||||
\(831\) | −42.5593 | −1.47637 | ||||||||
\(832\) | 64.4716 | 2.23515 | ||||||||
\(833\) | −0.303396 | −0.0105120 | ||||||||
\(834\) | 99.5879 | 3.44845 | ||||||||
\(835\) | 1.32628 | 0.0458977 | ||||||||
\(836\) | 19.7135 | 0.681806 | ||||||||
\(837\) | 13.4561 | 0.465109 | ||||||||
\(838\) | −71.1939 | −2.45935 | ||||||||
\(839\) | −26.8058 | −0.925438 | −0.462719 | − | 0.886505i | \(-0.653126\pi\) | ||||
−0.462719 | + | 0.886505i | \(0.653126\pi\) | |||||||
\(840\) | 5.21844 | 0.180053 | ||||||||
\(841\) | 5.52704 | 0.190587 | ||||||||
\(842\) | −64.2384 | −2.21380 | ||||||||
\(843\) | −36.3820 | −1.25306 | ||||||||
\(844\) | −5.48374 | −0.188758 | ||||||||
\(845\) | −75.2292 | −2.58796 | ||||||||
\(846\) | 4.01286 | 0.137965 | ||||||||
\(847\) | −9.89528 | −0.340006 | ||||||||
\(848\) | −2.94966 | −0.101292 | ||||||||
\(849\) | 55.3300 | 1.89892 | ||||||||
\(850\) | 3.36932 | 0.115567 | ||||||||
\(851\) | −5.58841 | −0.191568 | ||||||||
\(852\) | 3.03915 | 0.104120 | ||||||||
\(853\) | 4.97057 | 0.170189 | 0.0850946 | − | 0.996373i | \(-0.472881\pi\) | ||||
0.0850946 | + | 0.996373i | \(0.472881\pi\) | |||||||
\(854\) | 2.30325 | 0.0788157 | ||||||||
\(855\) | 31.2567 | 1.06896 | ||||||||
\(856\) | −14.2690 | −0.487704 | ||||||||
\(857\) | 7.34376 | 0.250858 | 0.125429 | − | 0.992103i | \(-0.459969\pi\) | ||||
0.125429 | + | 0.992103i | \(0.459969\pi\) | |||||||
\(858\) | −27.3125 | −0.932433 | ||||||||
\(859\) | −1.00000 | −0.0341196 | ||||||||
\(860\) | −23.5180 | −0.801957 | ||||||||
\(861\) | −5.16448 | −0.176005 | ||||||||
\(862\) | 7.96631 | 0.271333 | ||||||||
\(863\) | 29.9151 | 1.01832 | 0.509161 | − | 0.860671i | \(-0.329956\pi\) | ||||
0.509161 | + | 0.860671i | \(0.329956\pi\) | |||||||
\(864\) | −29.3268 | −0.997716 | ||||||||
\(865\) | −53.3629 | −1.81439 | ||||||||
\(866\) | 29.6229 | 1.00663 | ||||||||
\(867\) | −34.7914 | −1.18158 | ||||||||
\(868\) | −8.80437 | −0.298840 | ||||||||
\(869\) | −14.1823 | −0.481103 | ||||||||
\(870\) | −81.2192 | −2.75359 | ||||||||
\(871\) | 38.2775 | 1.29698 | ||||||||
\(872\) | −13.3600 | −0.452426 | ||||||||
\(873\) | 14.6309 | 0.495182 | ||||||||
\(874\) | −98.9738 | −3.34784 | ||||||||
\(875\) | −0.988335 | −0.0334118 | ||||||||
\(876\) | −13.1503 | −0.444307 | ||||||||
\(877\) | 42.4956 | 1.43498 | 0.717488 | − | 0.696571i | \(-0.245292\pi\) | ||||
0.717488 | + | 0.696571i | \(0.245292\pi\) | |||||||
\(878\) | 49.3886 | 1.66678 | ||||||||
\(879\) | −59.2408 | −1.99814 | ||||||||
\(880\) | −10.4690 | −0.352911 | ||||||||
\(881\) | 43.1741 | 1.45457 | 0.727286 | − | 0.686334i | \(-0.240781\pi\) | ||||
0.727286 | + | 0.686334i | \(0.240781\pi\) | |||||||
\(882\) | −2.58205 | −0.0869421 | ||||||||
\(883\) | −43.4766 | −1.46311 | −0.731553 | − | 0.681785i | \(-0.761204\pi\) | ||||
−0.731553 | + | 0.681785i | \(0.761204\pi\) | |||||||
\(884\) | 4.35388 | 0.146437 | ||||||||
\(885\) | −57.4844 | −1.93232 | ||||||||
\(886\) | −7.19367 | −0.241676 | ||||||||
\(887\) | −57.5739 | −1.93314 | −0.966571 | − | 0.256398i | \(-0.917464\pi\) | ||||
−0.966571 | + | 0.256398i | \(0.917464\pi\) | |||||||
\(888\) | −1.51478 | −0.0508328 | ||||||||
\(889\) | −20.9173 | −0.701544 | ||||||||
\(890\) | 67.7319 | 2.27038 | ||||||||
\(891\) | 11.7501 | 0.393643 | ||||||||
\(892\) | −5.31318 | −0.177898 | ||||||||
\(893\) | 12.2602 | 0.410273 | ||||||||
\(894\) | 64.0970 | 2.14372 | ||||||||
\(895\) | 23.5701 | 0.787862 | ||||||||
\(896\) | 6.20668 | 0.207351 | ||||||||
\(897\) | 74.4758 | 2.48667 | ||||||||
\(898\) | 39.3703 | 1.31380 | ||||||||
\(899\) | 21.7596 | 0.725722 | ||||||||
\(900\) | 15.5738 | 0.519127 | ||||||||
\(901\) | −0.288460 | −0.00961000 | ||||||||
\(902\) | −5.51934 | −0.183774 | ||||||||
\(903\) | 6.33971 | 0.210972 | ||||||||
\(904\) | −3.05505 | −0.101609 | ||||||||
\(905\) | 22.2576 | 0.739867 | ||||||||
\(906\) | 64.7075 | 2.14976 | ||||||||
\(907\) | 14.2605 | 0.473511 | 0.236756 | − | 0.971569i | \(-0.423916\pi\) | ||||
0.236756 | + | 0.971569i | \(0.423916\pi\) | |||||||
\(908\) | 44.4732 | 1.47590 | ||||||||
\(909\) | 18.6450 | 0.618414 | ||||||||
\(910\) | −40.5451 | −1.34406 | ||||||||
\(911\) | 40.6462 | 1.34667 | 0.673335 | − | 0.739338i | \(-0.264861\pi\) | ||||
0.673335 | + | 0.739338i | \(0.264861\pi\) | |||||||
\(912\) | 50.3601 | 1.66759 | ||||||||
\(913\) | −16.9893 | −0.562264 | ||||||||
\(914\) | −39.5882 | −1.30946 | ||||||||
\(915\) | 7.27262 | 0.240425 | ||||||||
\(916\) | −10.3240 | −0.341114 | ||||||||
\(917\) | 7.96847 | 0.263142 | ||||||||
\(918\) | −2.30659 | −0.0761290 | ||||||||
\(919\) | −53.0069 | −1.74854 | −0.874269 | − | 0.485443i | \(-0.838658\pi\) | ||||
−0.874269 | + | 0.485443i | \(0.838658\pi\) | |||||||
\(920\) | −15.2074 | −0.501374 | ||||||||
\(921\) | −3.32987 | −0.109723 | ||||||||
\(922\) | −1.82350 | −0.0600537 | ||||||||
\(923\) | −3.74959 | −0.123419 | ||||||||
\(924\) | −5.14203 | −0.169160 | ||||||||
\(925\) | 4.94664 | 0.162645 | ||||||||
\(926\) | 7.43158 | 0.244217 | ||||||||
\(927\) | −15.9661 | −0.524395 | ||||||||
\(928\) | −47.4238 | −1.55676 | ||||||||
\(929\) | 53.4740 | 1.75442 | 0.877212 | − | 0.480103i | \(-0.159401\pi\) | ||||
0.877212 | + | 0.480103i | \(0.159401\pi\) | |||||||
\(930\) | −51.1858 | −1.67845 | ||||||||
\(931\) | −7.88878 | −0.258544 | ||||||||
\(932\) | −13.3013 | −0.435699 | ||||||||
\(933\) | 31.6613 | 1.03654 | ||||||||
\(934\) | 1.57005 | 0.0513737 | ||||||||
\(935\) | −1.02381 | −0.0334822 | ||||||||
\(936\) | 5.88391 | 0.192322 | ||||||||
\(937\) | −2.90038 | −0.0947513 | −0.0473756 | − | 0.998877i | \(-0.515086\pi\) | ||||
−0.0473756 | + | 0.998877i | \(0.515086\pi\) | |||||||
\(938\) | 13.2684 | 0.433230 | ||||||||
\(939\) | −66.7849 | −2.17944 | ||||||||
\(940\) | 11.8632 | 0.386934 | ||||||||
\(941\) | −0.709175 | −0.0231184 | −0.0115592 | − | 0.999933i | \(-0.503679\pi\) | ||||
−0.0115592 | + | 0.999933i | \(0.503679\pi\) | |||||||
\(942\) | −1.60629 | −0.0523356 | ||||||||
\(943\) | 15.0502 | 0.490100 | ||||||||
\(944\) | −26.9949 | −0.878609 | ||||||||
\(945\) | 11.6662 | 0.379503 | ||||||||
\(946\) | 6.77533 | 0.220285 | ||||||||
\(947\) | 31.4146 | 1.02084 | 0.510419 | − | 0.859926i | \(-0.329490\pi\) | ||||
0.510419 | + | 0.859926i | \(0.329490\pi\) | |||||||
\(948\) | 66.0130 | 2.14400 | ||||||||
\(949\) | 16.2243 | 0.526663 | ||||||||
\(950\) | 87.6078 | 2.84237 | ||||||||
\(951\) | 9.34445 | 0.303014 | ||||||||
\(952\) | 0.239655 | 0.00776726 | ||||||||
\(953\) | 7.77814 | 0.251959 | 0.125979 | − | 0.992033i | \(-0.459793\pi\) | ||||
0.125979 | + | 0.992033i | \(0.459793\pi\) | |||||||
\(954\) | −2.45494 | −0.0794817 | ||||||||
\(955\) | −39.2772 | −1.27098 | ||||||||
\(956\) | 15.6856 | 0.507309 | ||||||||
\(957\) | 12.7083 | 0.410800 | ||||||||
\(958\) | 22.0122 | 0.711182 | ||||||||
\(959\) | −21.3156 | −0.688316 | ||||||||
\(960\) | 70.5657 | 2.27750 | ||||||||
\(961\) | −17.2867 | −0.557636 | ||||||||
\(962\) | 11.7692 | 0.379455 | ||||||||
\(963\) | 22.2929 | 0.718378 | ||||||||
\(964\) | −13.4883 | −0.434429 | ||||||||
\(965\) | −24.1278 | −0.776700 | ||||||||
\(966\) | 25.8161 | 0.830619 | ||||||||
\(967\) | −31.9037 | −1.02595 | −0.512977 | − | 0.858403i | \(-0.671457\pi\) | ||||
−0.512977 | + | 0.858403i | \(0.671457\pi\) | |||||||
\(968\) | 7.81637 | 0.251228 | ||||||||
\(969\) | 4.92493 | 0.158211 | ||||||||
\(970\) | 79.6381 | 2.55703 | ||||||||
\(971\) | −18.3994 | −0.590464 | −0.295232 | − | 0.955426i | \(-0.595397\pi\) | ||||
−0.295232 | + | 0.955426i | \(0.595397\pi\) | |||||||
\(972\) | −28.7742 | −0.922932 | ||||||||
\(973\) | −23.1319 | −0.741574 | ||||||||
\(974\) | 76.2294 | 2.44255 | ||||||||
\(975\) | −65.9231 | −2.11123 | ||||||||
\(976\) | 3.41525 | 0.109319 | ||||||||
\(977\) | −33.6004 | −1.07497 | −0.537485 | − | 0.843273i | \(-0.680626\pi\) | ||||
−0.537485 | + | 0.843273i | \(0.680626\pi\) | |||||||
\(978\) | −51.8558 | −1.65817 | ||||||||
\(979\) | −10.5979 | −0.338711 | ||||||||
\(980\) | −7.63328 | −0.243836 | ||||||||
\(981\) | 20.8727 | 0.666414 | ||||||||
\(982\) | 23.9132 | 0.763102 | ||||||||
\(983\) | 19.3439 | 0.616974 | 0.308487 | − | 0.951229i | \(-0.400177\pi\) | ||||
0.308487 | + | 0.951229i | \(0.400177\pi\) | |||||||
\(984\) | 4.07946 | 0.130049 | ||||||||
\(985\) | 67.0803 | 2.13735 | ||||||||
\(986\) | −3.72996 | −0.118786 | ||||||||
\(987\) | −3.19793 | −0.101791 | ||||||||
\(988\) | 113.208 | 3.60163 | ||||||||
\(989\) | −18.4750 | −0.587470 | ||||||||
\(990\) | −8.71314 | −0.276922 | ||||||||
\(991\) | 58.5652 | 1.86039 | 0.930193 | − | 0.367071i | \(-0.119639\pi\) | ||||
0.930193 | + | 0.367071i | \(0.119639\pi\) | |||||||
\(992\) | −29.8874 | −0.948925 | ||||||||
\(993\) | 18.1390 | 0.575622 | ||||||||
\(994\) | −1.29975 | −0.0412255 | ||||||||
\(995\) | −71.7341 | −2.27413 | ||||||||
\(996\) | 79.0782 | 2.50569 | ||||||||
\(997\) | 29.5582 | 0.936117 | 0.468059 | − | 0.883697i | \(-0.344954\pi\) | ||||
0.468059 | + | 0.883697i | \(0.344954\pi\) | |||||||
\(998\) | 75.5400 | 2.39118 | ||||||||
\(999\) | −3.38641 | −0.107141 |
(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 | 6013.2.a.e.1.15 | ✓ | 109 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6013.2.a.e.1.15 | ✓ | 109 | 1.1 | even | 1 | trivial |