Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [619,2,Mod(1,619)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(619, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("619.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 619 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 619.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: | \(4.94273988512\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 619.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.938541 | −0.663649 | −0.331824 | − | 0.943341i | \(-0.607664\pi\) | ||||
−0.331824 | + | 0.943341i | \(0.607664\pi\) | |||||||
\(3\) | 2.04590 | 1.18120 | 0.590600 | − | 0.806964i | \(-0.298891\pi\) | ||||
0.590600 | + | 0.806964i | \(0.298891\pi\) | |||||||
\(4\) | −1.11914 | −0.559571 | ||||||||
\(5\) | 3.68832 | 1.64947 | 0.824734 | − | 0.565521i | \(-0.191325\pi\) | ||||
0.824734 | + | 0.565521i | \(0.191325\pi\) | |||||||
\(6\) | −1.92016 | −0.783902 | ||||||||
\(7\) | −2.71706 | −1.02695 | −0.513475 | − | 0.858104i | \(-0.671642\pi\) | ||||
−0.513475 | + | 0.858104i | \(0.671642\pi\) | |||||||
\(8\) | 2.92744 | 1.03501 | ||||||||
\(9\) | 1.18571 | 0.395235 | ||||||||
\(10\) | −3.46164 | −1.09467 | ||||||||
\(11\) | −2.41470 | −0.728060 | −0.364030 | − | 0.931387i | \(-0.618599\pi\) | ||||
−0.364030 | + | 0.931387i | \(0.618599\pi\) | |||||||
\(12\) | −2.28965 | −0.660965 | ||||||||
\(13\) | 5.06418 | 1.40455 | 0.702275 | − | 0.711905i | \(-0.252168\pi\) | ||||
0.702275 | + | 0.711905i | \(0.252168\pi\) | |||||||
\(14\) | 2.55007 | 0.681534 | ||||||||
\(15\) | 7.54594 | 1.94835 | ||||||||
\(16\) | −0.509241 | −0.127310 | ||||||||
\(17\) | 2.79712 | 0.678401 | 0.339201 | − | 0.940714i | \(-0.389843\pi\) | ||||
0.339201 | + | 0.940714i | \(0.389843\pi\) | |||||||
\(18\) | −1.11283 | −0.262297 | ||||||||
\(19\) | 4.67066 | 1.07152 | 0.535762 | − | 0.844369i | \(-0.320024\pi\) | ||||
0.535762 | + | 0.844369i | \(0.320024\pi\) | |||||||
\(20\) | −4.12775 | −0.922994 | ||||||||
\(21\) | −5.55882 | −1.21303 | ||||||||
\(22\) | 2.26630 | 0.483176 | ||||||||
\(23\) | 2.15658 | 0.449678 | 0.224839 | − | 0.974396i | \(-0.427814\pi\) | ||||
0.224839 | + | 0.974396i | \(0.427814\pi\) | |||||||
\(24\) | 5.98925 | 1.22255 | ||||||||
\(25\) | 8.60372 | 1.72074 | ||||||||
\(26\) | −4.75294 | −0.932128 | ||||||||
\(27\) | −3.71186 | −0.714349 | ||||||||
\(28\) | 3.04077 | 0.574651 | ||||||||
\(29\) | 0.405665 | 0.0753302 | 0.0376651 | − | 0.999290i | \(-0.488008\pi\) | ||||
0.0376651 | + | 0.999290i | \(0.488008\pi\) | |||||||
\(30\) | −7.08217 | −1.29302 | ||||||||
\(31\) | −2.87253 | −0.515922 | −0.257961 | − | 0.966155i | \(-0.583051\pi\) | ||||
−0.257961 | + | 0.966155i | \(0.583051\pi\) | |||||||
\(32\) | −5.37694 | −0.950518 | ||||||||
\(33\) | −4.94024 | −0.859985 | ||||||||
\(34\) | −2.62521 | −0.450220 | ||||||||
\(35\) | −10.0214 | −1.69392 | ||||||||
\(36\) | −1.32697 | −0.221162 | ||||||||
\(37\) | 4.37362 | 0.719019 | 0.359509 | − | 0.933141i | \(-0.382944\pi\) | ||||
0.359509 | + | 0.933141i | \(0.382944\pi\) | |||||||
\(38\) | −4.38361 | −0.711115 | ||||||||
\(39\) | 10.3608 | 1.65906 | ||||||||
\(40\) | 10.7973 | 1.70721 | ||||||||
\(41\) | −2.91057 | −0.454555 | −0.227278 | − | 0.973830i | \(-0.572982\pi\) | ||||
−0.227278 | + | 0.973830i | \(0.572982\pi\) | |||||||
\(42\) | 5.21718 | 0.805029 | ||||||||
\(43\) | 4.39958 | 0.670930 | 0.335465 | − | 0.942053i | \(-0.391107\pi\) | ||||
0.335465 | + | 0.942053i | \(0.391107\pi\) | |||||||
\(44\) | 2.70239 | 0.407401 | ||||||||
\(45\) | 4.37326 | 0.651928 | ||||||||
\(46\) | −2.02404 | −0.298428 | ||||||||
\(47\) | −4.68612 | −0.683540 | −0.341770 | − | 0.939784i | \(-0.611026\pi\) | ||||
−0.341770 | + | 0.939784i | \(0.611026\pi\) | |||||||
\(48\) | −1.04186 | −0.150379 | ||||||||
\(49\) | 0.382395 | 0.0546278 | ||||||||
\(50\) | −8.07494 | −1.14197 | ||||||||
\(51\) | 5.72263 | 0.801328 | ||||||||
\(52\) | −5.66753 | −0.785945 | ||||||||
\(53\) | 5.90078 | 0.810534 | 0.405267 | − | 0.914198i | \(-0.367178\pi\) | ||||
0.405267 | + | 0.914198i | \(0.367178\pi\) | |||||||
\(54\) | 3.48374 | 0.474076 | ||||||||
\(55\) | −8.90619 | −1.20091 | ||||||||
\(56\) | −7.95402 | −1.06290 | ||||||||
\(57\) | 9.55571 | 1.26568 | ||||||||
\(58\) | −0.380734 | −0.0499928 | ||||||||
\(59\) | 2.92099 | 0.380280 | 0.190140 | − | 0.981757i | \(-0.439106\pi\) | ||||
0.190140 | + | 0.981757i | \(0.439106\pi\) | |||||||
\(60\) | −8.44497 | −1.09024 | ||||||||
\(61\) | −8.81228 | −1.12830 | −0.564148 | − | 0.825673i | \(-0.690795\pi\) | ||||
−0.564148 | + | 0.825673i | \(0.690795\pi\) | |||||||
\(62\) | 2.69599 | 0.342391 | ||||||||
\(63\) | −3.22163 | −0.405887 | ||||||||
\(64\) | 6.06496 | 0.758120 | ||||||||
\(65\) | 18.6783 | 2.31676 | ||||||||
\(66\) | 4.63661 | 0.570728 | ||||||||
\(67\) | 6.63389 | 0.810459 | 0.405230 | − | 0.914215i | \(-0.367192\pi\) | ||||
0.405230 | + | 0.914215i | \(0.367192\pi\) | |||||||
\(68\) | −3.13037 | −0.379613 | ||||||||
\(69\) | 4.41214 | 0.531160 | ||||||||
\(70\) | 9.40547 | 1.12417 | ||||||||
\(71\) | 1.75461 | 0.208234 | 0.104117 | − | 0.994565i | \(-0.466798\pi\) | ||||
0.104117 | + | 0.994565i | \(0.466798\pi\) | |||||||
\(72\) | 3.47108 | 0.409071 | ||||||||
\(73\) | 11.6980 | 1.36914 | 0.684571 | − | 0.728946i | \(-0.259990\pi\) | ||||
0.684571 | + | 0.728946i | \(0.259990\pi\) | |||||||
\(74\) | −4.10482 | −0.477176 | ||||||||
\(75\) | 17.6023 | 2.03254 | ||||||||
\(76\) | −5.22713 | −0.599593 | ||||||||
\(77\) | 6.56088 | 0.747681 | ||||||||
\(78\) | −9.72404 | −1.10103 | ||||||||
\(79\) | −17.0954 | −1.92338 | −0.961690 | − | 0.274141i | \(-0.911607\pi\) | ||||
−0.961690 | + | 0.274141i | \(0.911607\pi\) | |||||||
\(80\) | −1.87824 | −0.209994 | ||||||||
\(81\) | −11.1512 | −1.23902 | ||||||||
\(82\) | 2.73169 | 0.301665 | ||||||||
\(83\) | −9.17823 | −1.00744 | −0.503721 | − | 0.863867i | \(-0.668036\pi\) | ||||
−0.503721 | + | 0.863867i | \(0.668036\pi\) | |||||||
\(84\) | 6.22111 | 0.678779 | ||||||||
\(85\) | 10.3167 | 1.11900 | ||||||||
\(86\) | −4.12919 | −0.445262 | ||||||||
\(87\) | 0.829951 | 0.0889801 | ||||||||
\(88\) | −7.06889 | −0.753547 | ||||||||
\(89\) | −10.6864 | −1.13276 | −0.566378 | − | 0.824146i | \(-0.691656\pi\) | ||||
−0.566378 | + | 0.824146i | \(0.691656\pi\) | |||||||
\(90\) | −4.10449 | −0.432651 | ||||||||
\(91\) | −13.7597 | −1.44240 | ||||||||
\(92\) | −2.41352 | −0.251627 | ||||||||
\(93\) | −5.87692 | −0.609408 | ||||||||
\(94\) | 4.39811 | 0.453630 | ||||||||
\(95\) | 17.2269 | 1.76744 | ||||||||
\(96\) | −11.0007 | −1.12275 | ||||||||
\(97\) | −6.48573 | −0.658526 | −0.329263 | − | 0.944238i | \(-0.606800\pi\) | ||||
−0.329263 | + | 0.944238i | \(0.606800\pi\) | |||||||
\(98\) | −0.358893 | −0.0362537 | ||||||||
\(99\) | −2.86312 | −0.287755 | ||||||||
\(100\) | −9.62877 | −0.962877 | ||||||||
\(101\) | 13.6998 | 1.36318 | 0.681590 | − | 0.731734i | \(-0.261289\pi\) | ||||
0.681590 | + | 0.731734i | \(0.261289\pi\) | |||||||
\(102\) | −5.37092 | −0.531800 | ||||||||
\(103\) | −19.4892 | −1.92032 | −0.960162 | − | 0.279444i | \(-0.909850\pi\) | ||||
−0.960162 | + | 0.279444i | \(0.909850\pi\) | |||||||
\(104\) | 14.8251 | 1.45372 | ||||||||
\(105\) | −20.5027 | −2.00086 | ||||||||
\(106\) | −5.53812 | −0.537910 | ||||||||
\(107\) | 4.56732 | 0.441540 | 0.220770 | − | 0.975326i | \(-0.429143\pi\) | ||||
0.220770 | + | 0.975326i | \(0.429143\pi\) | |||||||
\(108\) | 4.15410 | 0.399729 | ||||||||
\(109\) | 7.39066 | 0.707897 | 0.353949 | − | 0.935265i | \(-0.384839\pi\) | ||||
0.353949 | + | 0.935265i | \(0.384839\pi\) | |||||||
\(110\) | 8.35883 | 0.796983 | ||||||||
\(111\) | 8.94799 | 0.849305 | ||||||||
\(112\) | 1.38364 | 0.130741 | ||||||||
\(113\) | 18.9441 | 1.78211 | 0.891056 | − | 0.453894i | \(-0.149965\pi\) | ||||
0.891056 | + | 0.453894i | \(0.149965\pi\) | |||||||
\(114\) | −8.96842 | −0.839970 | ||||||||
\(115\) | 7.95416 | 0.741729 | ||||||||
\(116\) | −0.453997 | −0.0421526 | ||||||||
\(117\) | 6.00463 | 0.555128 | ||||||||
\(118\) | −2.74147 | −0.252373 | ||||||||
\(119\) | −7.59993 | −0.696685 | ||||||||
\(120\) | 22.0903 | 2.01656 | ||||||||
\(121\) | −5.16922 | −0.469929 | ||||||||
\(122\) | 8.27068 | 0.748793 | ||||||||
\(123\) | −5.95474 | −0.536921 | ||||||||
\(124\) | 3.21477 | 0.288695 | ||||||||
\(125\) | 13.2917 | 1.18884 | ||||||||
\(126\) | 3.02363 | 0.269366 | ||||||||
\(127\) | 3.05033 | 0.270673 | 0.135337 | − | 0.990800i | \(-0.456788\pi\) | ||||
0.135337 | + | 0.990800i | \(0.456788\pi\) | |||||||
\(128\) | 5.06167 | 0.447393 | ||||||||
\(129\) | 9.00110 | 0.792503 | ||||||||
\(130\) | −17.5304 | −1.53752 | ||||||||
\(131\) | −12.7959 | −1.11798 | −0.558990 | − | 0.829174i | \(-0.688811\pi\) | ||||
−0.558990 | + | 0.829174i | \(0.688811\pi\) | |||||||
\(132\) | 5.52882 | 0.481222 | ||||||||
\(133\) | −12.6905 | −1.10040 | ||||||||
\(134\) | −6.22618 | −0.537860 | ||||||||
\(135\) | −13.6906 | −1.17829 | ||||||||
\(136\) | 8.18840 | 0.702150 | ||||||||
\(137\) | −17.3319 | −1.48076 | −0.740380 | − | 0.672188i | \(-0.765354\pi\) | ||||
−0.740380 | + | 0.672188i | \(0.765354\pi\) | |||||||
\(138\) | −4.14098 | −0.352503 | ||||||||
\(139\) | −12.8884 | −1.09318 | −0.546590 | − | 0.837401i | \(-0.684074\pi\) | ||||
−0.546590 | + | 0.837401i | \(0.684074\pi\) | |||||||
\(140\) | 11.2153 | 0.947869 | ||||||||
\(141\) | −9.58732 | −0.807398 | ||||||||
\(142\) | −1.64677 | −0.138194 | ||||||||
\(143\) | −12.2285 | −1.02260 | ||||||||
\(144\) | −0.603809 | −0.0503174 | ||||||||
\(145\) | 1.49622 | 0.124255 | ||||||||
\(146\) | −10.9790 | −0.908629 | ||||||||
\(147\) | 0.782341 | 0.0645264 | ||||||||
\(148\) | −4.89470 | −0.402342 | ||||||||
\(149\) | −18.6003 | −1.52380 | −0.761898 | − | 0.647697i | \(-0.775732\pi\) | ||||
−0.761898 | + | 0.647697i | \(0.775732\pi\) | |||||||
\(150\) | −16.5205 | −1.34889 | ||||||||
\(151\) | 13.3926 | 1.08987 | 0.544936 | − | 0.838478i | \(-0.316554\pi\) | ||||
0.544936 | + | 0.838478i | \(0.316554\pi\) | |||||||
\(152\) | 13.6731 | 1.10903 | ||||||||
\(153\) | 3.31656 | 0.268128 | ||||||||
\(154\) | −6.15765 | −0.496198 | ||||||||
\(155\) | −10.5948 | −0.850997 | ||||||||
\(156\) | −11.5952 | −0.928359 | ||||||||
\(157\) | −5.06098 | −0.403910 | −0.201955 | − | 0.979395i | \(-0.564730\pi\) | ||||
−0.201955 | + | 0.979395i | \(0.564730\pi\) | |||||||
\(158\) | 16.0447 | 1.27645 | ||||||||
\(159\) | 12.0724 | 0.957404 | ||||||||
\(160\) | −19.8319 | −1.56785 | ||||||||
\(161\) | −5.85955 | −0.461797 | ||||||||
\(162\) | 10.4659 | 0.822277 | ||||||||
\(163\) | −10.1216 | −0.792782 | −0.396391 | − | 0.918082i | \(-0.629738\pi\) | ||||
−0.396391 | + | 0.918082i | \(0.629738\pi\) | |||||||
\(164\) | 3.25734 | 0.254356 | ||||||||
\(165\) | −18.2212 | −1.41852 | ||||||||
\(166\) | 8.61414 | 0.668587 | ||||||||
\(167\) | 11.3630 | 0.879299 | 0.439649 | − | 0.898169i | \(-0.355103\pi\) | ||||
0.439649 | + | 0.898169i | \(0.355103\pi\) | |||||||
\(168\) | −16.2731 | −1.25550 | ||||||||
\(169\) | 12.6459 | 0.972763 | ||||||||
\(170\) | −9.68262 | −0.742623 | ||||||||
\(171\) | 5.53803 | 0.423504 | ||||||||
\(172\) | −4.92375 | −0.375433 | ||||||||
\(173\) | −18.1125 | −1.37707 | −0.688533 | − | 0.725205i | \(-0.741745\pi\) | ||||
−0.688533 | + | 0.725205i | \(0.741745\pi\) | |||||||
\(174\) | −0.778943 | −0.0590515 | ||||||||
\(175\) | −23.3768 | −1.76712 | ||||||||
\(176\) | 1.22966 | 0.0926894 | ||||||||
\(177\) | 5.97605 | 0.449188 | ||||||||
\(178\) | 10.0296 | 0.751751 | ||||||||
\(179\) | 9.43259 | 0.705025 | 0.352513 | − | 0.935807i | \(-0.385327\pi\) | ||||
0.352513 | + | 0.935807i | \(0.385327\pi\) | |||||||
\(180\) | −4.89430 | −0.364800 | ||||||||
\(181\) | −24.5527 | −1.82499 | −0.912495 | − | 0.409089i | \(-0.865847\pi\) | ||||
−0.912495 | + | 0.409089i | \(0.865847\pi\) | |||||||
\(182\) | 12.9140 | 0.957250 | ||||||||
\(183\) | −18.0290 | −1.33275 | ||||||||
\(184\) | 6.31326 | 0.465420 | ||||||||
\(185\) | 16.1313 | 1.18600 | ||||||||
\(186\) | 5.51573 | 0.404433 | ||||||||
\(187\) | −6.75421 | −0.493916 | ||||||||
\(188\) | 5.24443 | 0.382489 | ||||||||
\(189\) | 10.0853 | 0.733601 | ||||||||
\(190\) | −16.1682 | −1.17296 | ||||||||
\(191\) | −17.5270 | −1.26821 | −0.634106 | − | 0.773246i | \(-0.718632\pi\) | ||||
−0.634106 | + | 0.773246i | \(0.718632\pi\) | |||||||
\(192\) | 12.4083 | 0.895492 | ||||||||
\(193\) | −22.6101 | −1.62751 | −0.813756 | − | 0.581206i | \(-0.802581\pi\) | ||||
−0.813756 | + | 0.581206i | \(0.802581\pi\) | |||||||
\(194\) | 6.08712 | 0.437030 | ||||||||
\(195\) | 38.2140 | 2.73656 | ||||||||
\(196\) | −0.427954 | −0.0305681 | ||||||||
\(197\) | 17.7717 | 1.26618 | 0.633091 | − | 0.774078i | \(-0.281786\pi\) | ||||
0.633091 | + | 0.774078i | \(0.281786\pi\) | |||||||
\(198\) | 2.68716 | 0.190968 | ||||||||
\(199\) | −10.2870 | −0.729228 | −0.364614 | − | 0.931159i | \(-0.618799\pi\) | ||||
−0.364614 | + | 0.931159i | \(0.618799\pi\) | |||||||
\(200\) | 25.1869 | 1.78098 | ||||||||
\(201\) | 13.5723 | 0.957315 | ||||||||
\(202\) | −12.8578 | −0.904672 | ||||||||
\(203\) | −1.10222 | −0.0773604 | ||||||||
\(204\) | −6.40443 | −0.448400 | ||||||||
\(205\) | −10.7351 | −0.749774 | ||||||||
\(206\) | 18.2914 | 1.27442 | ||||||||
\(207\) | 2.55707 | 0.177729 | ||||||||
\(208\) | −2.57889 | −0.178814 | ||||||||
\(209\) | −11.2783 | −0.780133 | ||||||||
\(210\) | 19.2427 | 1.32787 | ||||||||
\(211\) | 15.1797 | 1.04502 | 0.522508 | − | 0.852634i | \(-0.324996\pi\) | ||||
0.522508 | + | 0.852634i | \(0.324996\pi\) | |||||||
\(212\) | −6.60381 | −0.453551 | ||||||||
\(213\) | 3.58976 | 0.245966 | ||||||||
\(214\) | −4.28662 | −0.293027 | ||||||||
\(215\) | 16.2271 | 1.10668 | ||||||||
\(216\) | −10.8663 | −0.739356 | ||||||||
\(217\) | 7.80484 | 0.529827 | ||||||||
\(218\) | −6.93644 | −0.469795 | ||||||||
\(219\) | 23.9328 | 1.61723 | ||||||||
\(220\) | 9.96729 | 0.671994 | ||||||||
\(221\) | 14.1651 | 0.952849 | ||||||||
\(222\) | −8.39805 | −0.563640 | ||||||||
\(223\) | −18.6218 | −1.24701 | −0.623505 | − | 0.781820i | \(-0.714292\pi\) | ||||
−0.623505 | + | 0.781820i | \(0.714292\pi\) | |||||||
\(224\) | 14.6094 | 0.976135 | ||||||||
\(225\) | 10.2015 | 0.680098 | ||||||||
\(226\) | −17.7798 | −1.18270 | ||||||||
\(227\) | −24.7238 | −1.64098 | −0.820488 | − | 0.571664i | \(-0.806298\pi\) | ||||
−0.820488 | + | 0.571664i | \(0.806298\pi\) | |||||||
\(228\) | −10.6942 | −0.708240 | ||||||||
\(229\) | 4.39930 | 0.290714 | 0.145357 | − | 0.989379i | \(-0.453567\pi\) | ||||
0.145357 | + | 0.989379i | \(0.453567\pi\) | |||||||
\(230\) | −7.46530 | −0.492247 | ||||||||
\(231\) | 13.4229 | 0.883162 | ||||||||
\(232\) | 1.18756 | 0.0779673 | ||||||||
\(233\) | 23.3827 | 1.53185 | 0.765926 | − | 0.642929i | \(-0.222281\pi\) | ||||
0.765926 | + | 0.642929i | \(0.222281\pi\) | |||||||
\(234\) | −5.63559 | −0.368410 | ||||||||
\(235\) | −17.2839 | −1.12748 | ||||||||
\(236\) | −3.26900 | −0.212794 | ||||||||
\(237\) | −34.9754 | −2.27190 | ||||||||
\(238\) | 7.13285 | 0.462354 | ||||||||
\(239\) | 19.1315 | 1.23752 | 0.618758 | − | 0.785582i | \(-0.287636\pi\) | ||||
0.618758 | + | 0.785582i | \(0.287636\pi\) | |||||||
\(240\) | −3.84270 | −0.248045 | ||||||||
\(241\) | 10.0131 | 0.644998 | 0.322499 | − | 0.946570i | \(-0.395477\pi\) | ||||
0.322499 | + | 0.946570i | \(0.395477\pi\) | |||||||
\(242\) | 4.85152 | 0.311868 | ||||||||
\(243\) | −11.6787 | −0.749188 | ||||||||
\(244\) | 9.86219 | 0.631362 | ||||||||
\(245\) | 1.41040 | 0.0901068 | ||||||||
\(246\) | 5.58877 | 0.356327 | ||||||||
\(247\) | 23.6531 | 1.50501 | ||||||||
\(248\) | −8.40918 | −0.533983 | ||||||||
\(249\) | −18.7777 | −1.18999 | ||||||||
\(250\) | −12.4748 | −0.788974 | ||||||||
\(251\) | 1.41992 | 0.0896248 | 0.0448124 | − | 0.998995i | \(-0.485731\pi\) | ||||
0.0448124 | + | 0.998995i | \(0.485731\pi\) | |||||||
\(252\) | 3.60546 | 0.227122 | ||||||||
\(253\) | −5.20749 | −0.327392 | ||||||||
\(254\) | −2.86286 | −0.179632 | ||||||||
\(255\) | 21.1069 | 1.32176 | ||||||||
\(256\) | −16.8805 | −1.05503 | ||||||||
\(257\) | 24.5756 | 1.53298 | 0.766492 | − | 0.642254i | \(-0.222000\pi\) | ||||
0.766492 | + | 0.642254i | \(0.222000\pi\) | |||||||
\(258\) | −8.44790 | −0.525943 | ||||||||
\(259\) | −11.8834 | −0.738397 | ||||||||
\(260\) | −20.9037 | −1.29639 | ||||||||
\(261\) | 0.481000 | 0.0297731 | ||||||||
\(262\) | 12.0094 | 0.741946 | ||||||||
\(263\) | 28.8924 | 1.78158 | 0.890789 | − | 0.454416i | \(-0.150152\pi\) | ||||
0.890789 | + | 0.454416i | \(0.150152\pi\) | |||||||
\(264\) | −14.4622 | −0.890090 | ||||||||
\(265\) | 21.7640 | 1.33695 | ||||||||
\(266\) | 11.9105 | 0.730280 | ||||||||
\(267\) | −21.8633 | −1.33801 | ||||||||
\(268\) | −7.42426 | −0.453509 | ||||||||
\(269\) | −17.2295 | −1.05050 | −0.525250 | − | 0.850948i | \(-0.676028\pi\) | ||||
−0.525250 | + | 0.850948i | \(0.676028\pi\) | |||||||
\(270\) | 12.8491 | 0.781974 | ||||||||
\(271\) | 19.4823 | 1.18347 | 0.591734 | − | 0.806133i | \(-0.298444\pi\) | ||||
0.591734 | + | 0.806133i | \(0.298444\pi\) | |||||||
\(272\) | −1.42441 | −0.0863673 | ||||||||
\(273\) | −28.1509 | −1.70377 | ||||||||
\(274\) | 16.2667 | 0.982704 | ||||||||
\(275\) | −20.7754 | −1.25280 | ||||||||
\(276\) | −4.93781 | −0.297221 | ||||||||
\(277\) | 11.3433 | 0.681554 | 0.340777 | − | 0.940144i | \(-0.389310\pi\) | ||||
0.340777 | + | 0.940144i | \(0.389310\pi\) | |||||||
\(278\) | 12.0963 | 0.725487 | ||||||||
\(279\) | −3.40598 | −0.203911 | ||||||||
\(280\) | −29.3370 | −1.75322 | ||||||||
\(281\) | −19.3347 | −1.15341 | −0.576705 | − | 0.816952i | \(-0.695662\pi\) | ||||
−0.576705 | + | 0.816952i | \(0.695662\pi\) | |||||||
\(282\) | 8.99809 | 0.535829 | ||||||||
\(283\) | 10.2100 | 0.606923 | 0.303462 | − | 0.952844i | \(-0.401858\pi\) | ||||
0.303462 | + | 0.952844i | \(0.401858\pi\) | |||||||
\(284\) | −1.96366 | −0.116522 | ||||||||
\(285\) | 35.2445 | 2.08771 | ||||||||
\(286\) | 11.4769 | 0.678645 | ||||||||
\(287\) | 7.90819 | 0.466806 | ||||||||
\(288\) | −6.37547 | −0.375678 | ||||||||
\(289\) | −9.17612 | −0.539772 | ||||||||
\(290\) | −1.40427 | −0.0824615 | ||||||||
\(291\) | −13.2692 | −0.777852 | ||||||||
\(292\) | −13.0917 | −0.766132 | ||||||||
\(293\) | 12.0608 | 0.704600 | 0.352300 | − | 0.935887i | \(-0.385400\pi\) | ||||
0.352300 | + | 0.935887i | \(0.385400\pi\) | |||||||
\(294\) | −0.734259 | −0.0428229 | ||||||||
\(295\) | 10.7736 | 0.627260 | ||||||||
\(296\) | 12.8035 | 0.744189 | ||||||||
\(297\) | 8.96304 | 0.520088 | ||||||||
\(298\) | 17.4571 | 1.01126 | ||||||||
\(299\) | 10.9213 | 0.631595 | ||||||||
\(300\) | −19.6995 | −1.13735 | ||||||||
\(301\) | −11.9539 | −0.689012 | ||||||||
\(302\) | −12.5695 | −0.723292 | ||||||||
\(303\) | 28.0284 | 1.61019 | ||||||||
\(304\) | −2.37849 | −0.136416 | ||||||||
\(305\) | −32.5025 | −1.86109 | ||||||||
\(306\) | −3.11273 | −0.177943 | ||||||||
\(307\) | −0.550676 | −0.0314288 | −0.0157144 | − | 0.999877i | \(-0.505002\pi\) | ||||
−0.0157144 | + | 0.999877i | \(0.505002\pi\) | |||||||
\(308\) | −7.34255 | −0.418381 | ||||||||
\(309\) | −39.8729 | −2.26829 | ||||||||
\(310\) | 9.94368 | 0.564763 | ||||||||
\(311\) | 19.9296 | 1.13010 | 0.565051 | − | 0.825056i | \(-0.308857\pi\) | ||||
0.565051 | + | 0.825056i | \(0.308857\pi\) | |||||||
\(312\) | 30.3306 | 1.71713 | ||||||||
\(313\) | −21.7539 | −1.22961 | −0.614803 | − | 0.788681i | \(-0.710764\pi\) | ||||
−0.614803 | + | 0.788681i | \(0.710764\pi\) | |||||||
\(314\) | 4.74994 | 0.268055 | ||||||||
\(315\) | −11.8824 | −0.669498 | ||||||||
\(316\) | 19.1321 | 1.07627 | ||||||||
\(317\) | −16.7111 | −0.938588 | −0.469294 | − | 0.883042i | \(-0.655492\pi\) | ||||
−0.469294 | + | 0.883042i | \(0.655492\pi\) | |||||||
\(318\) | −11.3304 | −0.635380 | ||||||||
\(319\) | −0.979561 | −0.0548449 | ||||||||
\(320\) | 22.3695 | 1.25049 | ||||||||
\(321\) | 9.34428 | 0.521547 | ||||||||
\(322\) | 5.49942 | 0.306471 | ||||||||
\(323\) | 13.0644 | 0.726923 | ||||||||
\(324\) | 12.4798 | 0.693322 | ||||||||
\(325\) | 43.5708 | 2.41687 | ||||||||
\(326\) | 9.49950 | 0.526129 | ||||||||
\(327\) | 15.1206 | 0.836169 | ||||||||
\(328\) | −8.52054 | −0.470468 | ||||||||
\(329\) | 12.7324 | 0.701962 | ||||||||
\(330\) | 17.1013 | 0.941397 | ||||||||
\(331\) | −8.57405 | −0.471273 | −0.235636 | − | 0.971841i | \(-0.575717\pi\) | ||||
−0.235636 | + | 0.971841i | \(0.575717\pi\) | |||||||
\(332\) | 10.2717 | 0.563734 | ||||||||
\(333\) | 5.18583 | 0.284181 | ||||||||
\(334\) | −10.6647 | −0.583545 | ||||||||
\(335\) | 24.4679 | 1.33683 | ||||||||
\(336\) | 2.83078 | 0.154432 | ||||||||
\(337\) | 6.53912 | 0.356209 | 0.178104 | − | 0.984012i | \(-0.443004\pi\) | ||||
0.178104 | + | 0.984012i | \(0.443004\pi\) | |||||||
\(338\) | −11.8687 | −0.645572 | ||||||||
\(339\) | 38.7577 | 2.10503 | ||||||||
\(340\) | −11.5458 | −0.626160 | ||||||||
\(341\) | 6.93631 | 0.375622 | ||||||||
\(342\) | −5.19767 | −0.281058 | ||||||||
\(343\) | 17.9804 | 0.970851 | ||||||||
\(344\) | 12.8795 | 0.694417 | ||||||||
\(345\) | 16.2734 | 0.876131 | ||||||||
\(346\) | 16.9993 | 0.913888 | ||||||||
\(347\) | −13.6009 | −0.730136 | −0.365068 | − | 0.930981i | \(-0.618954\pi\) | ||||
−0.365068 | + | 0.930981i | \(0.618954\pi\) | |||||||
\(348\) | −0.928832 | −0.0497906 | ||||||||
\(349\) | −8.81304 | −0.471751 | −0.235876 | − | 0.971783i | \(-0.575796\pi\) | ||||
−0.235876 | + | 0.971783i | \(0.575796\pi\) | |||||||
\(350\) | 21.9401 | 1.17275 | ||||||||
\(351\) | −18.7975 | −1.00334 | ||||||||
\(352\) | 12.9837 | 0.692034 | ||||||||
\(353\) | −10.1022 | −0.537688 | −0.268844 | − | 0.963184i | \(-0.586642\pi\) | ||||
−0.268844 | + | 0.963184i | \(0.586642\pi\) | |||||||
\(354\) | −5.60877 | −0.298103 | ||||||||
\(355\) | 6.47157 | 0.343475 | ||||||||
\(356\) | 11.9596 | 0.633857 | ||||||||
\(357\) | −15.5487 | −0.822924 | ||||||||
\(358\) | −8.85287 | −0.467889 | ||||||||
\(359\) | 21.5410 | 1.13689 | 0.568445 | − | 0.822721i | \(-0.307545\pi\) | ||||
0.568445 | + | 0.822721i | \(0.307545\pi\) | |||||||
\(360\) | 12.8025 | 0.674750 | ||||||||
\(361\) | 2.81510 | 0.148163 | ||||||||
\(362\) | 23.0437 | 1.21115 | ||||||||
\(363\) | −10.5757 | −0.555081 | ||||||||
\(364\) | 15.3990 | 0.807127 | ||||||||
\(365\) | 43.1458 | 2.25836 | ||||||||
\(366\) | 16.9210 | 0.884474 | ||||||||
\(367\) | 7.76452 | 0.405305 | 0.202652 | − | 0.979251i | \(-0.435044\pi\) | ||||
0.202652 | + | 0.979251i | \(0.435044\pi\) | |||||||
\(368\) | −1.09822 | −0.0572486 | ||||||||
\(369\) | −3.45108 | −0.179656 | ||||||||
\(370\) | −15.1399 | −0.787086 | ||||||||
\(371\) | −16.0328 | −0.832379 | ||||||||
\(372\) | 6.57710 | 0.341007 | ||||||||
\(373\) | 29.4708 | 1.52594 | 0.762970 | − | 0.646434i | \(-0.223740\pi\) | ||||
0.762970 | + | 0.646434i | \(0.223740\pi\) | |||||||
\(374\) | 6.33910 | 0.327787 | ||||||||
\(375\) | 27.1934 | 1.40426 | ||||||||
\(376\) | −13.7183 | −0.707469 | ||||||||
\(377\) | 2.05436 | 0.105805 | ||||||||
\(378\) | −9.46551 | −0.486853 | ||||||||
\(379\) | 8.31615 | 0.427172 | 0.213586 | − | 0.976924i | \(-0.431486\pi\) | ||||
0.213586 | + | 0.976924i | \(0.431486\pi\) | |||||||
\(380\) | −19.2793 | −0.989009 | ||||||||
\(381\) | 6.24068 | 0.319720 | ||||||||
\(382\) | 16.4498 | 0.841647 | ||||||||
\(383\) | 5.60989 | 0.286652 | 0.143326 | − | 0.989676i | \(-0.454220\pi\) | ||||
0.143326 | + | 0.989676i | \(0.454220\pi\) | |||||||
\(384\) | 10.3557 | 0.528460 | ||||||||
\(385\) | 24.1986 | 1.23328 | ||||||||
\(386\) | 21.2205 | 1.08010 | ||||||||
\(387\) | 5.21661 | 0.265175 | ||||||||
\(388\) | 7.25845 | 0.368492 | ||||||||
\(389\) | −0.563342 | −0.0285626 | −0.0142813 | − | 0.999898i | \(-0.504546\pi\) | ||||
−0.0142813 | + | 0.999898i | \(0.504546\pi\) | |||||||
\(390\) | −35.8654 | −1.81611 | ||||||||
\(391\) | 6.03221 | 0.305062 | ||||||||
\(392\) | 1.11944 | 0.0565402 | ||||||||
\(393\) | −26.1791 | −1.32056 | ||||||||
\(394\) | −16.6795 | −0.840299 | ||||||||
\(395\) | −63.0532 | −3.17255 | ||||||||
\(396\) | 3.20424 | 0.161019 | ||||||||
\(397\) | −7.43322 | −0.373063 | −0.186531 | − | 0.982449i | \(-0.559725\pi\) | ||||
−0.186531 | + | 0.982449i | \(0.559725\pi\) | |||||||
\(398\) | 9.65480 | 0.483951 | ||||||||
\(399\) | −25.9634 | −1.29980 | ||||||||
\(400\) | −4.38136 | −0.219068 | ||||||||
\(401\) | 15.9423 | 0.796119 | 0.398059 | − | 0.917360i | \(-0.369684\pi\) | ||||
0.398059 | + | 0.917360i | \(0.369684\pi\) | |||||||
\(402\) | −12.7381 | −0.635321 | ||||||||
\(403\) | −14.5470 | −0.724639 | ||||||||
\(404\) | −15.3320 | −0.762795 | ||||||||
\(405\) | −41.1293 | −2.04373 | ||||||||
\(406\) | 1.03447 | 0.0513401 | ||||||||
\(407\) | −10.5610 | −0.523488 | ||||||||
\(408\) | 16.7527 | 0.829380 | ||||||||
\(409\) | −28.5003 | −1.40925 | −0.704624 | − | 0.709581i | \(-0.748884\pi\) | ||||
−0.704624 | + | 0.709581i | \(0.748884\pi\) | |||||||
\(410\) | 10.0754 | 0.497587 | ||||||||
\(411\) | −35.4592 | −1.74908 | ||||||||
\(412\) | 21.8111 | 1.07456 | ||||||||
\(413\) | −7.93649 | −0.390529 | ||||||||
\(414\) | −2.39991 | −0.117949 | ||||||||
\(415\) | −33.8522 | −1.66174 | ||||||||
\(416\) | −27.2298 | −1.33505 | ||||||||
\(417\) | −26.3684 | −1.29126 | ||||||||
\(418\) | 10.5851 | 0.517734 | ||||||||
\(419\) | 4.52331 | 0.220978 | 0.110489 | − | 0.993877i | \(-0.464758\pi\) | ||||
0.110489 | + | 0.993877i | \(0.464758\pi\) | |||||||
\(420\) | 22.9455 | 1.11962 | ||||||||
\(421\) | 16.3341 | 0.796074 | 0.398037 | − | 0.917369i | \(-0.369692\pi\) | ||||
0.398037 | + | 0.917369i | \(0.369692\pi\) | |||||||
\(422\) | −14.2468 | −0.693523 | ||||||||
\(423\) | −5.55635 | −0.270159 | ||||||||
\(424\) | 17.2742 | 0.838909 | ||||||||
\(425\) | 24.0656 | 1.16735 | ||||||||
\(426\) | −3.36913 | −0.163235 | ||||||||
\(427\) | 23.9435 | 1.15871 | ||||||||
\(428\) | −5.11148 | −0.247073 | ||||||||
\(429\) | −25.0182 | −1.20789 | ||||||||
\(430\) | −15.2298 | −0.734445 | ||||||||
\(431\) | −3.98556 | −0.191978 | −0.0959889 | − | 0.995382i | \(-0.530601\pi\) | ||||
−0.0959889 | + | 0.995382i | \(0.530601\pi\) | |||||||
\(432\) | 1.89023 | 0.0909438 | ||||||||
\(433\) | 26.3837 | 1.26792 | 0.633959 | − | 0.773366i | \(-0.281429\pi\) | ||||
0.633959 | + | 0.773366i | \(0.281429\pi\) | |||||||
\(434\) | −7.32516 | −0.351619 | ||||||||
\(435\) | 3.06113 | 0.146770 | ||||||||
\(436\) | −8.27120 | −0.396118 | ||||||||
\(437\) | 10.0727 | 0.481840 | ||||||||
\(438\) | −22.4620 | −1.07327 | ||||||||
\(439\) | 32.3911 | 1.54595 | 0.772973 | − | 0.634439i | \(-0.218769\pi\) | ||||
0.772973 | + | 0.634439i | \(0.218769\pi\) | |||||||
\(440\) | −26.0724 | −1.24295 | ||||||||
\(441\) | 0.453408 | 0.0215908 | ||||||||
\(442\) | −13.2945 | −0.632357 | ||||||||
\(443\) | −2.29328 | −0.108957 | −0.0544785 | − | 0.998515i | \(-0.517350\pi\) | ||||
−0.0544785 | + | 0.998515i | \(0.517350\pi\) | |||||||
\(444\) | −10.0141 | −0.475246 | ||||||||
\(445\) | −39.4149 | −1.86844 | ||||||||
\(446\) | 17.4773 | 0.827576 | ||||||||
\(447\) | −38.0543 | −1.79991 | ||||||||
\(448\) | −16.4788 | −0.778552 | ||||||||
\(449\) | 19.5422 | 0.922254 | 0.461127 | − | 0.887334i | \(-0.347445\pi\) | ||||
0.461127 | + | 0.887334i | \(0.347445\pi\) | |||||||
\(450\) | −9.57450 | −0.451346 | ||||||||
\(451\) | 7.02817 | 0.330943 | ||||||||
\(452\) | −21.2011 | −0.997217 | ||||||||
\(453\) | 27.3998 | 1.28736 | ||||||||
\(454\) | 23.2043 | 1.08903 | ||||||||
\(455\) | −50.7501 | −2.37920 | ||||||||
\(456\) | 27.9738 | 1.30999 | ||||||||
\(457\) | −4.68139 | −0.218986 | −0.109493 | − | 0.993988i | \(-0.534923\pi\) | ||||
−0.109493 | + | 0.993988i | \(0.534923\pi\) | |||||||
\(458\) | −4.12892 | −0.192932 | ||||||||
\(459\) | −10.3825 | −0.484615 | ||||||||
\(460\) | −8.90183 | −0.415050 | ||||||||
\(461\) | 8.93426 | 0.416110 | 0.208055 | − | 0.978117i | \(-0.433287\pi\) | ||||
0.208055 | + | 0.978117i | \(0.433287\pi\) | |||||||
\(462\) | −12.5979 | −0.586109 | ||||||||
\(463\) | −30.6401 | −1.42397 | −0.711983 | − | 0.702197i | \(-0.752203\pi\) | ||||
−0.711983 | + | 0.702197i | \(0.752203\pi\) | |||||||
\(464\) | −0.206581 | −0.00959030 | ||||||||
\(465\) | −21.6760 | −1.00520 | ||||||||
\(466\) | −21.9456 | −1.01661 | ||||||||
\(467\) | −26.9036 | −1.24495 | −0.622475 | − | 0.782640i | \(-0.713873\pi\) | ||||
−0.622475 | + | 0.782640i | \(0.713873\pi\) | |||||||
\(468\) | −6.72002 | −0.310633 | ||||||||
\(469\) | −18.0247 | −0.832301 | ||||||||
\(470\) | 16.2216 | 0.748249 | ||||||||
\(471\) | −10.3543 | −0.477099 | ||||||||
\(472\) | 8.55103 | 0.393593 | ||||||||
\(473\) | −10.6237 | −0.488477 | ||||||||
\(474\) | 32.8258 | 1.50774 | ||||||||
\(475\) | 40.1851 | 1.84382 | ||||||||
\(476\) | 8.50540 | 0.389844 | ||||||||
\(477\) | 6.99659 | 0.320352 | ||||||||
\(478\) | −17.9557 | −0.821276 | ||||||||
\(479\) | 33.0101 | 1.50827 | 0.754135 | − | 0.656719i | \(-0.228056\pi\) | ||||
0.754135 | + | 0.656719i | \(0.228056\pi\) | |||||||
\(480\) | −40.5740 | −1.85194 | ||||||||
\(481\) | 22.1488 | 1.00990 | ||||||||
\(482\) | −9.39766 | −0.428052 | ||||||||
\(483\) | −11.9880 | −0.545475 | ||||||||
\(484\) | 5.78509 | 0.262959 | ||||||||
\(485\) | −23.9215 | −1.08622 | ||||||||
\(486\) | 10.9609 | 0.497197 | ||||||||
\(487\) | −22.0103 | −0.997383 | −0.498691 | − | 0.866780i | \(-0.666186\pi\) | ||||
−0.498691 | + | 0.866780i | \(0.666186\pi\) | |||||||
\(488\) | −25.7974 | −1.16779 | ||||||||
\(489\) | −20.7077 | −0.936435 | ||||||||
\(490\) | −1.32371 | −0.0597993 | ||||||||
\(491\) | −23.2875 | −1.05095 | −0.525474 | − | 0.850809i | \(-0.676112\pi\) | ||||
−0.525474 | + | 0.850809i | \(0.676112\pi\) | |||||||
\(492\) | 6.66420 | 0.300445 | ||||||||
\(493\) | 1.13469 | 0.0511041 | ||||||||
\(494\) | −22.1994 | −0.998797 | ||||||||
\(495\) | −10.5601 | −0.474642 | ||||||||
\(496\) | 1.46281 | 0.0656822 | ||||||||
\(497\) | −4.76737 | −0.213846 | ||||||||
\(498\) | 17.6237 | 0.789735 | ||||||||
\(499\) | 20.0711 | 0.898507 | 0.449254 | − | 0.893404i | \(-0.351690\pi\) | ||||
0.449254 | + | 0.893404i | \(0.351690\pi\) | |||||||
\(500\) | −14.8753 | −0.665242 | ||||||||
\(501\) | 23.2476 | 1.03863 | ||||||||
\(502\) | −1.33266 | −0.0594794 | ||||||||
\(503\) | 10.8823 | 0.485218 | 0.242609 | − | 0.970124i | \(-0.421997\pi\) | ||||
0.242609 | + | 0.970124i | \(0.421997\pi\) | |||||||
\(504\) | −9.43113 | −0.420096 | ||||||||
\(505\) | 50.5292 | 2.24852 | ||||||||
\(506\) | 4.88745 | 0.217273 | ||||||||
\(507\) | 25.8723 | 1.14903 | ||||||||
\(508\) | −3.41375 | −0.151461 | ||||||||
\(509\) | 3.58455 | 0.158883 | 0.0794413 | − | 0.996840i | \(-0.474686\pi\) | ||||
0.0794413 | + | 0.996840i | \(0.474686\pi\) | |||||||
\(510\) | −19.8097 | −0.877187 | ||||||||
\(511\) | −31.7840 | −1.40604 | ||||||||
\(512\) | 5.71970 | 0.252777 | ||||||||
\(513\) | −17.3369 | −0.765441 | ||||||||
\(514\) | −23.0652 | −1.01736 | ||||||||
\(515\) | −71.8823 | −3.16751 | ||||||||
\(516\) | −10.0735 | −0.443461 | ||||||||
\(517\) | 11.3156 | 0.497658 | ||||||||
\(518\) | 11.1530 | 0.490036 | ||||||||
\(519\) | −37.0563 | −1.62659 | ||||||||
\(520\) | 54.6797 | 2.39786 | ||||||||
\(521\) | 5.42122 | 0.237508 | 0.118754 | − | 0.992924i | \(-0.462110\pi\) | ||||
0.118754 | + | 0.992924i | \(0.462110\pi\) | |||||||
\(522\) | −0.451438 | −0.0197589 | ||||||||
\(523\) | −42.6840 | −1.86644 | −0.933220 | − | 0.359306i | \(-0.883013\pi\) | ||||
−0.933220 | + | 0.359306i | \(0.883013\pi\) | |||||||
\(524\) | 14.3204 | 0.625589 | ||||||||
\(525\) | −47.8266 | −2.08732 | ||||||||
\(526\) | −27.1167 | −1.18234 | ||||||||
\(527\) | −8.03482 | −0.350002 | ||||||||
\(528\) | 2.51577 | 0.109485 | ||||||||
\(529\) | −18.3492 | −0.797790 | ||||||||
\(530\) | −20.4264 | −0.887265 | ||||||||
\(531\) | 3.46343 | 0.150300 | ||||||||
\(532\) | 14.2024 | 0.615753 | ||||||||
\(533\) | −14.7397 | −0.638446 | ||||||||
\(534\) | 20.5196 | 0.887969 | ||||||||
\(535\) | 16.8458 | 0.728305 | ||||||||
\(536\) | 19.4203 | 0.838831 | ||||||||
\(537\) | 19.2981 | 0.832776 | ||||||||
\(538\) | 16.1706 | 0.697163 | ||||||||
\(539\) | −0.923369 | −0.0397723 | ||||||||
\(540\) | 15.3217 | 0.659339 | ||||||||
\(541\) | −12.2836 | −0.528113 | −0.264057 | − | 0.964507i | \(-0.585061\pi\) | ||||
−0.264057 | + | 0.964507i | \(0.585061\pi\) | |||||||
\(542\) | −18.2850 | −0.785407 | ||||||||
\(543\) | −50.2324 | −2.15568 | ||||||||
\(544\) | −15.0399 | −0.644832 | ||||||||
\(545\) | 27.2591 | 1.16765 | ||||||||
\(546\) | 26.4208 | 1.13070 | ||||||||
\(547\) | −19.4082 | −0.829836 | −0.414918 | − | 0.909859i | \(-0.636190\pi\) | ||||
−0.414918 | + | 0.909859i | \(0.636190\pi\) | |||||||
\(548\) | 19.3968 | 0.828590 | ||||||||
\(549\) | −10.4488 | −0.445943 | ||||||||
\(550\) | 19.4986 | 0.831422 | ||||||||
\(551\) | 1.89473 | 0.0807181 | ||||||||
\(552\) | 12.9163 | 0.549754 | ||||||||
\(553\) | 46.4491 | 1.97522 | ||||||||
\(554\) | −10.6462 | −0.452312 | ||||||||
\(555\) | 33.0031 | 1.40090 | ||||||||
\(556\) | 14.4239 | 0.611711 | ||||||||
\(557\) | −12.9922 | −0.550498 | −0.275249 | − | 0.961373i | \(-0.588760\pi\) | ||||
−0.275249 | + | 0.961373i | \(0.588760\pi\) | |||||||
\(558\) | 3.19665 | 0.135325 | ||||||||
\(559\) | 22.2803 | 0.942355 | ||||||||
\(560\) | 5.10329 | 0.215653 | ||||||||
\(561\) | −13.8184 | −0.583415 | ||||||||
\(562\) | 18.1464 | 0.765459 | ||||||||
\(563\) | −32.6802 | −1.37731 | −0.688653 | − | 0.725091i | \(-0.741798\pi\) | ||||
−0.688653 | + | 0.725091i | \(0.741798\pi\) | |||||||
\(564\) | 10.7296 | 0.451796 | ||||||||
\(565\) | 69.8720 | 2.93954 | ||||||||
\(566\) | −9.58253 | −0.402784 | ||||||||
\(567\) | 30.2985 | 1.27242 | ||||||||
\(568\) | 5.13652 | 0.215524 | ||||||||
\(569\) | 28.2125 | 1.18273 | 0.591365 | − | 0.806404i | \(-0.298589\pi\) | ||||
0.591365 | + | 0.806404i | \(0.298589\pi\) | |||||||
\(570\) | −33.0784 | −1.38550 | ||||||||
\(571\) | 6.12528 | 0.256335 | 0.128168 | − | 0.991753i | \(-0.459090\pi\) | ||||
0.128168 | + | 0.991753i | \(0.459090\pi\) | |||||||
\(572\) | 13.6854 | 0.572215 | ||||||||
\(573\) | −35.8586 | −1.49801 | ||||||||
\(574\) | −7.42216 | −0.309795 | ||||||||
\(575\) | 18.5546 | 0.773780 | ||||||||
\(576\) | 7.19125 | 0.299636 | ||||||||
\(577\) | 6.27920 | 0.261406 | 0.130703 | − | 0.991422i | \(-0.458277\pi\) | ||||
0.130703 | + | 0.991422i | \(0.458277\pi\) | |||||||
\(578\) | 8.61217 | 0.358219 | ||||||||
\(579\) | −46.2580 | −1.92242 | ||||||||
\(580\) | −1.67449 | −0.0695293 | ||||||||
\(581\) | 24.9378 | 1.03459 | ||||||||
\(582\) | 12.4536 | 0.516220 | ||||||||
\(583\) | −14.2486 | −0.590117 | ||||||||
\(584\) | 34.2451 | 1.41707 | ||||||||
\(585\) | 22.1470 | 0.915665 | ||||||||
\(586\) | −11.3196 | −0.467606 | ||||||||
\(587\) | 11.0713 | 0.456961 | 0.228481 | − | 0.973548i | \(-0.426624\pi\) | ||||
0.228481 | + | 0.973548i | \(0.426624\pi\) | |||||||
\(588\) | −0.875551 | −0.0361071 | ||||||||
\(589\) | −13.4166 | −0.552823 | ||||||||
\(590\) | −10.1114 | −0.416280 | ||||||||
\(591\) | 36.3591 | 1.49561 | ||||||||
\(592\) | −2.22722 | −0.0915384 | ||||||||
\(593\) | 5.98380 | 0.245725 | 0.122863 | − | 0.992424i | \(-0.460793\pi\) | ||||
0.122863 | + | 0.992424i | \(0.460793\pi\) | |||||||
\(594\) | −8.41218 | −0.345156 | ||||||||
\(595\) | −28.0310 | −1.14916 | ||||||||
\(596\) | 20.8164 | 0.852671 | ||||||||
\(597\) | −21.0462 | −0.861365 | ||||||||
\(598\) | −10.2501 | −0.419157 | ||||||||
\(599\) | −17.4424 | −0.712679 | −0.356339 | − | 0.934357i | \(-0.615975\pi\) | ||||
−0.356339 | + | 0.934357i | \(0.615975\pi\) | |||||||
\(600\) | 51.5298 | 2.10370 | ||||||||
\(601\) | 44.5375 | 1.81672 | 0.908362 | − | 0.418185i | \(-0.137334\pi\) | ||||
0.908362 | + | 0.418185i | \(0.137334\pi\) | |||||||
\(602\) | 11.2192 | 0.457262 | ||||||||
\(603\) | 7.86584 | 0.320322 | ||||||||
\(604\) | −14.9882 | −0.609860 | ||||||||
\(605\) | −19.0657 | −0.775133 | ||||||||
\(606\) | −26.3058 | −1.06860 | ||||||||
\(607\) | 16.9812 | 0.689244 | 0.344622 | − | 0.938742i | \(-0.388007\pi\) | ||||
0.344622 | + | 0.938742i | \(0.388007\pi\) | |||||||
\(608\) | −25.1139 | −1.01850 | ||||||||
\(609\) | −2.25502 | −0.0913781 | ||||||||
\(610\) | 30.5049 | 1.23511 | ||||||||
\(611\) | −23.7313 | −0.960067 | ||||||||
\(612\) | −3.71170 | −0.150037 | ||||||||
\(613\) | 39.8340 | 1.60888 | 0.804439 | − | 0.594035i | \(-0.202466\pi\) | ||||
0.804439 | + | 0.594035i | \(0.202466\pi\) | |||||||
\(614\) | 0.516832 | 0.0208577 | ||||||||
\(615\) | −21.9630 | −0.885634 | ||||||||
\(616\) | 19.2066 | 0.773855 | ||||||||
\(617\) | 8.08667 | 0.325557 | 0.162779 | − | 0.986663i | \(-0.447954\pi\) | ||||
0.162779 | + | 0.986663i | \(0.447954\pi\) | |||||||
\(618\) | 37.4223 | 1.50535 | ||||||||
\(619\) | 1.00000 | 0.0401934 | ||||||||
\(620\) | 11.8571 | 0.476193 | ||||||||
\(621\) | −8.00493 | −0.321227 | ||||||||
\(622\) | −18.7047 | −0.749990 | ||||||||
\(623\) | 29.0355 | 1.16328 | ||||||||
\(624\) | −5.27614 | −0.211215 | ||||||||
\(625\) | 6.00537 | 0.240215 | ||||||||
\(626\) | 20.4170 | 0.816026 | ||||||||
\(627\) | −23.0742 | −0.921494 | ||||||||
\(628\) | 5.66395 | 0.226016 | ||||||||
\(629\) | 12.2335 | 0.487783 | ||||||||
\(630\) | 11.1521 | 0.444311 | ||||||||
\(631\) | 13.6691 | 0.544158 | 0.272079 | − | 0.962275i | \(-0.412289\pi\) | ||||
0.272079 | + | 0.962275i | \(0.412289\pi\) | |||||||
\(632\) | −50.0457 | −1.99071 | ||||||||
\(633\) | 31.0562 | 1.23437 | ||||||||
\(634\) | 15.6840 | 0.622893 | ||||||||
\(635\) | 11.2506 | 0.446467 | ||||||||
\(636\) | −13.5107 | −0.535735 | ||||||||
\(637\) | 1.93652 | 0.0767276 | ||||||||
\(638\) | 0.919358 | 0.0363977 | ||||||||
\(639\) | 2.08045 | 0.0823014 | ||||||||
\(640\) | 18.6691 | 0.737959 | ||||||||
\(641\) | 26.9643 | 1.06503 | 0.532513 | − | 0.846422i | \(-0.321248\pi\) | ||||
0.532513 | + | 0.846422i | \(0.321248\pi\) | |||||||
\(642\) | −8.76999 | −0.346124 | ||||||||
\(643\) | −36.6704 | −1.44614 | −0.723069 | − | 0.690775i | \(-0.757269\pi\) | ||||
−0.723069 | + | 0.690775i | \(0.757269\pi\) | |||||||
\(644\) | 6.55766 | 0.258408 | ||||||||
\(645\) | 33.1990 | 1.30721 | ||||||||
\(646\) | −12.2615 | −0.482421 | ||||||||
\(647\) | −10.7513 | −0.422676 | −0.211338 | − | 0.977413i | \(-0.567782\pi\) | ||||
−0.211338 | + | 0.977413i | \(0.567782\pi\) | |||||||
\(648\) | −32.6445 | −1.28240 | ||||||||
\(649\) | −7.05332 | −0.276867 | ||||||||
\(650\) | −40.8929 | −1.60395 | ||||||||
\(651\) | 15.9679 | 0.625832 | ||||||||
\(652\) | 11.3275 | 0.443618 | ||||||||
\(653\) | −29.5031 | −1.15455 | −0.577273 | − | 0.816552i | \(-0.695883\pi\) | ||||
−0.577273 | + | 0.816552i | \(0.695883\pi\) | |||||||
\(654\) | −14.1913 | −0.554922 | ||||||||
\(655\) | −47.1953 | −1.84407 | ||||||||
\(656\) | 1.48218 | 0.0578695 | ||||||||
\(657\) | 13.8703 | 0.541133 | ||||||||
\(658\) | −11.9499 | −0.465856 | ||||||||
\(659\) | 33.1605 | 1.29175 | 0.645874 | − | 0.763444i | \(-0.276493\pi\) | ||||
0.645874 | + | 0.763444i | \(0.276493\pi\) | |||||||
\(660\) | 20.3921 | 0.793760 | ||||||||
\(661\) | −9.47927 | −0.368701 | −0.184350 | − | 0.982861i | \(-0.559018\pi\) | ||||
−0.184350 | + | 0.982861i | \(0.559018\pi\) | |||||||
\(662\) | 8.04710 | 0.312759 | ||||||||
\(663\) | 28.9804 | 1.12551 | ||||||||
\(664\) | −26.8687 | −1.04271 | ||||||||
\(665\) | −46.8065 | −1.81508 | ||||||||
\(666\) | −4.86711 | −0.188597 | ||||||||
\(667\) | 0.874850 | 0.0338743 | ||||||||
\(668\) | −12.7169 | −0.492030 | ||||||||
\(669\) | −38.0984 | −1.47297 | ||||||||
\(670\) | −22.9642 | −0.887183 | ||||||||
\(671\) | 21.2790 | 0.821467 | ||||||||
\(672\) | 29.8895 | 1.15301 | ||||||||
\(673\) | −35.0763 | −1.35209 | −0.676046 | − | 0.736859i | \(-0.736308\pi\) | ||||
−0.676046 | + | 0.736859i | \(0.736308\pi\) | |||||||
\(674\) | −6.13723 | −0.236397 | ||||||||
\(675\) | −31.9358 | −1.22921 | ||||||||
\(676\) | −14.1526 | −0.544329 | ||||||||
\(677\) | 45.3854 | 1.74430 | 0.872152 | − | 0.489235i | \(-0.162724\pi\) | ||||
0.872152 | + | 0.489235i | \(0.162724\pi\) | |||||||
\(678\) | −36.3757 | −1.39700 | ||||||||
\(679\) | 17.6221 | 0.676274 | ||||||||
\(680\) | 30.2015 | 1.15817 | ||||||||
\(681\) | −50.5824 | −1.93832 | ||||||||
\(682\) | −6.51001 | −0.249281 | ||||||||
\(683\) | 38.5031 | 1.47328 | 0.736640 | − | 0.676285i | \(-0.236411\pi\) | ||||
0.736640 | + | 0.676285i | \(0.236411\pi\) | |||||||
\(684\) | −6.19784 | −0.236980 | ||||||||
\(685\) | −63.9255 | −2.44247 | ||||||||
\(686\) | −16.8753 | −0.644304 | ||||||||
\(687\) | 9.00052 | 0.343391 | ||||||||
\(688\) | −2.24045 | −0.0854162 | ||||||||
\(689\) | 29.8826 | 1.13844 | ||||||||
\(690\) | −15.2733 | −0.581443 | ||||||||
\(691\) | 45.9369 | 1.74752 | 0.873761 | − | 0.486356i | \(-0.161674\pi\) | ||||
0.873761 | + | 0.486356i | \(0.161674\pi\) | |||||||
\(692\) | 20.2704 | 0.770566 | ||||||||
\(693\) | 7.77927 | 0.295510 | ||||||||
\(694\) | 12.7650 | 0.484554 | ||||||||
\(695\) | −47.5365 | −1.80316 | ||||||||
\(696\) | 2.42963 | 0.0920950 | ||||||||
\(697\) | −8.14122 | −0.308371 | ||||||||
\(698\) | 8.27140 | 0.313077 | ||||||||
\(699\) | 47.8387 | 1.80942 | ||||||||
\(700\) | 26.1619 | 0.988828 | ||||||||
\(701\) | 45.3751 | 1.71380 | 0.856898 | − | 0.515486i | \(-0.172389\pi\) | ||||
0.856898 | + | 0.515486i | \(0.172389\pi\) | |||||||
\(702\) | 17.6423 | 0.665864 | ||||||||
\(703\) | 20.4277 | 0.770446 | ||||||||
\(704\) | −14.6451 | −0.551956 | ||||||||
\(705\) | −35.3611 | −1.33178 | ||||||||
\(706\) | 9.48137 | 0.356836 | ||||||||
\(707\) | −37.2231 | −1.39992 | ||||||||
\(708\) | −6.68805 | −0.251352 | ||||||||
\(709\) | 46.4351 | 1.74391 | 0.871954 | − | 0.489589i | \(-0.162853\pi\) | ||||
0.871954 | + | 0.489589i | \(0.162853\pi\) | |||||||
\(710\) | −6.07383 | −0.227947 | ||||||||
\(711\) | −20.2701 | −0.760187 | ||||||||
\(712\) | −31.2838 | −1.17241 | ||||||||
\(713\) | −6.19485 | −0.231999 | ||||||||
\(714\) | 14.5931 | 0.546133 | ||||||||
\(715\) | −45.1026 | −1.68674 | ||||||||
\(716\) | −10.5564 | −0.394511 | ||||||||
\(717\) | 39.1412 | 1.46176 | ||||||||
\(718\) | −20.2171 | −0.754495 | ||||||||
\(719\) | 27.1580 | 1.01282 | 0.506410 | − | 0.862293i | \(-0.330972\pi\) | ||||
0.506410 | + | 0.862293i | \(0.330972\pi\) | |||||||
\(720\) | −2.22704 | −0.0829970 | ||||||||
\(721\) | 52.9532 | 1.97208 | ||||||||
\(722\) | −2.64208 | −0.0983281 | ||||||||
\(723\) | 20.4857 | 0.761872 | ||||||||
\(724\) | 27.4780 | 1.02121 | ||||||||
\(725\) | 3.49023 | 0.129624 | ||||||||
\(726\) | 9.92573 | 0.368378 | ||||||||
\(727\) | −5.60126 | −0.207739 | −0.103870 | − | 0.994591i | \(-0.533122\pi\) | ||||
−0.103870 | + | 0.994591i | \(0.533122\pi\) | |||||||
\(728\) | −40.2806 | −1.49290 | ||||||||
\(729\) | 9.56024 | 0.354083 | ||||||||
\(730\) | −40.4941 | −1.49875 | ||||||||
\(731\) | 12.3062 | 0.455160 | ||||||||
\(732\) | 20.1770 | 0.745765 | ||||||||
\(733\) | 11.3772 | 0.420225 | 0.210113 | − | 0.977677i | \(-0.432617\pi\) | ||||
0.210113 | + | 0.977677i | \(0.432617\pi\) | |||||||
\(734\) | −7.28732 | −0.268980 | ||||||||
\(735\) | 2.88553 | 0.106434 | ||||||||
\(736\) | −11.5958 | −0.427427 | ||||||||
\(737\) | −16.0189 | −0.590063 | ||||||||
\(738\) | 3.23898 | 0.119229 | ||||||||
\(739\) | 17.4817 | 0.643076 | 0.321538 | − | 0.946897i | \(-0.395800\pi\) | ||||
0.321538 | + | 0.946897i | \(0.395800\pi\) | |||||||
\(740\) | −18.0532 | −0.663650 | ||||||||
\(741\) | 48.3918 | 1.77772 | ||||||||
\(742\) | 15.0474 | 0.552407 | ||||||||
\(743\) | 0.403961 | 0.0148199 | 0.00740994 | − | 0.999973i | \(-0.497641\pi\) | ||||
0.00740994 | + | 0.999973i | \(0.497641\pi\) | |||||||
\(744\) | −17.2043 | −0.630741 | ||||||||
\(745\) | −68.6039 | −2.51345 | ||||||||
\(746\) | −27.6596 | −1.01269 | ||||||||
\(747\) | −10.8827 | −0.398176 | ||||||||
\(748\) | 7.55891 | 0.276381 | ||||||||
\(749\) | −12.4097 | −0.453439 | ||||||||
\(750\) | −25.5221 | −0.931937 | ||||||||
\(751\) | −32.7479 | −1.19499 | −0.597494 | − | 0.801874i | \(-0.703837\pi\) | ||||
−0.597494 | + | 0.801874i | \(0.703837\pi\) | |||||||
\(752\) | 2.38636 | 0.0870216 | ||||||||
\(753\) | 2.90502 | 0.105865 | ||||||||
\(754\) | −1.92810 | −0.0702174 | ||||||||
\(755\) | 49.3961 | 1.79771 | ||||||||
\(756\) | −11.2869 | −0.410501 | ||||||||
\(757\) | −26.3257 | −0.956823 | −0.478411 | − | 0.878136i | \(-0.658787\pi\) | ||||
−0.478411 | + | 0.878136i | \(0.658787\pi\) | |||||||
\(758\) | −7.80505 | −0.283492 | ||||||||
\(759\) | −10.6540 | −0.386716 | ||||||||
\(760\) | 50.4308 | 1.82932 | ||||||||
\(761\) | −22.9125 | −0.830578 | −0.415289 | − | 0.909689i | \(-0.636320\pi\) | ||||
−0.415289 | + | 0.909689i | \(0.636320\pi\) | |||||||
\(762\) | −5.85713 | −0.212181 | ||||||||
\(763\) | −20.0809 | −0.726976 | ||||||||
\(764\) | 19.6152 | 0.709654 | ||||||||
\(765\) | 12.2325 | 0.442268 | ||||||||
\(766\) | −5.26511 | −0.190236 | ||||||||
\(767\) | 14.7924 | 0.534123 | ||||||||
\(768\) | −34.5358 | −1.24620 | ||||||||
\(769\) | 9.94215 | 0.358523 | 0.179262 | − | 0.983801i | \(-0.442629\pi\) | ||||
0.179262 | + | 0.983801i | \(0.442629\pi\) | |||||||
\(770\) | −22.7114 | −0.818462 | ||||||||
\(771\) | 50.2792 | 1.81076 | ||||||||
\(772\) | 25.3039 | 0.910708 | ||||||||
\(773\) | −33.5600 | −1.20707 | −0.603535 | − | 0.797337i | \(-0.706242\pi\) | ||||
−0.603535 | + | 0.797337i | \(0.706242\pi\) | |||||||
\(774\) | −4.89600 | −0.175983 | ||||||||
\(775\) | −24.7145 | −0.887770 | ||||||||
\(776\) | −18.9866 | −0.681579 | ||||||||
\(777\) | −24.3122 | −0.872195 | ||||||||
\(778\) | 0.528719 | 0.0189555 | ||||||||
\(779\) | −13.5943 | −0.487067 | ||||||||
\(780\) | −42.7668 | −1.53130 | ||||||||
\(781\) | −4.23686 | −0.151607 | ||||||||
\(782\) | −5.66148 | −0.202454 | ||||||||
\(783\) | −1.50578 | −0.0538120 | ||||||||
\(784\) | −0.194731 | −0.00695468 | ||||||||
\(785\) | −18.6665 | −0.666237 | ||||||||
\(786\) | 24.5701 | 0.876387 | ||||||||
\(787\) | −22.0758 | −0.786916 | −0.393458 | − | 0.919343i | \(-0.628721\pi\) | ||||
−0.393458 | + | 0.919343i | \(0.628721\pi\) | |||||||
\(788\) | −19.8890 | −0.708518 | ||||||||
\(789\) | 59.1109 | 2.10440 | ||||||||
\(790\) | 59.1780 | 2.10546 | ||||||||
\(791\) | −51.4722 | −1.83014 | ||||||||
\(792\) | −8.38163 | −0.297828 | ||||||||
\(793\) | −44.6270 | −1.58475 | ||||||||
\(794\) | 6.97638 | 0.247582 | ||||||||
\(795\) | 44.5269 | 1.57921 | ||||||||
\(796\) | 11.5126 | 0.408055 | ||||||||
\(797\) | 10.0663 | 0.356567 | 0.178283 | − | 0.983979i | \(-0.442946\pi\) | ||||
0.178283 | + | 0.983979i | \(0.442946\pi\) | |||||||
\(798\) | 24.3677 | 0.862608 | ||||||||
\(799\) | −13.1076 | −0.463714 | ||||||||
\(800\) | −46.2617 | −1.63560 | ||||||||
\(801\) | −12.6709 | −0.447705 | ||||||||
\(802\) | −14.9625 | −0.528343 | ||||||||
\(803\) | −28.2471 | −0.996817 | ||||||||
\(804\) | −15.1893 | −0.535685 | ||||||||
\(805\) | −21.6119 | −0.761719 | ||||||||
\(806\) | 13.6530 | 0.480906 | ||||||||
\(807\) | −35.2498 | −1.24085 | ||||||||
\(808\) | 40.1053 | 1.41090 | ||||||||
\(809\) | 28.9342 | 1.01727 | 0.508635 | − | 0.860982i | \(-0.330150\pi\) | ||||
0.508635 | + | 0.860982i | \(0.330150\pi\) | |||||||
\(810\) | 38.6015 | 1.35632 | ||||||||
\(811\) | −43.6513 | −1.53280 | −0.766402 | − | 0.642362i | \(-0.777955\pi\) | ||||
−0.766402 | + | 0.642362i | \(0.777955\pi\) | |||||||
\(812\) | 1.23354 | 0.0432886 | ||||||||
\(813\) | 39.8589 | 1.39791 | ||||||||
\(814\) | 9.91191 | 0.347412 | ||||||||
\(815\) | −37.3316 | −1.30767 | ||||||||
\(816\) | −2.91419 | −0.102017 | ||||||||
\(817\) | 20.5490 | 0.718917 | ||||||||
\(818\) | 26.7487 | 0.935246 | ||||||||
\(819\) | −16.3149 | −0.570089 | ||||||||
\(820\) | 12.0141 | 0.419552 | ||||||||
\(821\) | 23.3643 | 0.815420 | 0.407710 | − | 0.913112i | \(-0.366328\pi\) | ||||
0.407710 | + | 0.913112i | \(0.366328\pi\) | |||||||
\(822\) | 33.2799 | 1.16077 | ||||||||
\(823\) | −12.8335 | −0.447346 | −0.223673 | − | 0.974664i | \(-0.571805\pi\) | ||||
−0.223673 | + | 0.974664i | \(0.571805\pi\) | |||||||
\(824\) | −57.0534 | −1.98755 | ||||||||
\(825\) | −42.5044 | −1.47981 | ||||||||
\(826\) | 7.44872 | 0.259174 | ||||||||
\(827\) | 39.1758 | 1.36227 | 0.681137 | − | 0.732156i | \(-0.261486\pi\) | ||||
0.681137 | + | 0.732156i | \(0.261486\pi\) | |||||||
\(828\) | −2.86172 | −0.0994517 | ||||||||
\(829\) | −1.61275 | −0.0560133 | −0.0280066 | − | 0.999608i | \(-0.508916\pi\) | ||||
−0.0280066 | + | 0.999608i | \(0.508916\pi\) | |||||||
\(830\) | 31.7717 | 1.10281 | ||||||||
\(831\) | 23.2073 | 0.805052 | ||||||||
\(832\) | 30.7140 | 1.06482 | ||||||||
\(833\) | 1.06960 | 0.0370596 | ||||||||
\(834\) | 24.7478 | 0.856945 | ||||||||
\(835\) | 41.9106 | 1.45037 | ||||||||
\(836\) | 12.6220 | 0.436540 | ||||||||
\(837\) | 10.6625 | 0.368549 | ||||||||
\(838\) | −4.24531 | −0.146652 | ||||||||
\(839\) | 36.9833 | 1.27680 | 0.638402 | − | 0.769703i | \(-0.279596\pi\) | ||||
0.638402 | + | 0.769703i | \(0.279596\pi\) | |||||||
\(840\) | −60.0205 | −2.07091 | ||||||||
\(841\) | −28.8354 | −0.994325 | ||||||||
\(842\) | −15.3302 | −0.528313 | ||||||||
\(843\) | −39.5568 | −1.36241 | ||||||||
\(844\) | −16.9883 | −0.584760 | ||||||||
\(845\) | 46.6422 | 1.60454 | ||||||||
\(846\) | 5.21486 | 0.179291 | ||||||||
\(847\) | 14.0451 | 0.482594 | ||||||||
\(848\) | −3.00492 | −0.103189 | ||||||||
\(849\) | 20.8887 | 0.716898 | ||||||||
\(850\) | −22.5866 | −0.774713 | ||||||||
\(851\) | 9.43206 | 0.323327 | ||||||||
\(852\) | −4.01744 | −0.137635 | ||||||||
\(853\) | 34.2323 | 1.17209 | 0.586046 | − | 0.810278i | \(-0.300684\pi\) | ||||
0.586046 | + | 0.810278i | \(0.300684\pi\) | |||||||
\(854\) | −22.4719 | −0.768973 | ||||||||
\(855\) | 20.4260 | 0.698556 | ||||||||
\(856\) | 13.3706 | 0.456996 | ||||||||
\(857\) | −15.6699 | −0.535275 | −0.267637 | − | 0.963520i | \(-0.586243\pi\) | ||||
−0.267637 | + | 0.963520i | \(0.586243\pi\) | |||||||
\(858\) | 23.4806 | 0.801616 | ||||||||
\(859\) | −52.0826 | −1.77703 | −0.888517 | − | 0.458844i | \(-0.848264\pi\) | ||||
−0.888517 | + | 0.458844i | \(0.848264\pi\) | |||||||
\(860\) | −18.1604 | −0.619264 | ||||||||
\(861\) | 16.1794 | 0.551392 | ||||||||
\(862\) | 3.74061 | 0.127406 | ||||||||
\(863\) | 48.0878 | 1.63693 | 0.818463 | − | 0.574559i | \(-0.194826\pi\) | ||||
0.818463 | + | 0.574559i | \(0.194826\pi\) | |||||||
\(864\) | 19.9585 | 0.679001 | ||||||||
\(865\) | −66.8046 | −2.27143 | ||||||||
\(866\) | −24.7622 | −0.841452 | ||||||||
\(867\) | −18.7734 | −0.637579 | ||||||||
\(868\) | −8.73472 | −0.296476 | ||||||||
\(869\) | 41.2802 | 1.40033 | ||||||||
\(870\) | −2.87299 | −0.0974035 | ||||||||
\(871\) | 33.5952 | 1.13833 | ||||||||
\(872\) | 21.6357 | 0.732678 | ||||||||
\(873\) | −7.69017 | −0.260273 | ||||||||
\(874\) | −9.45360 | −0.319773 | ||||||||
\(875\) | −36.1142 | −1.22088 | ||||||||
\(876\) | −26.7842 | −0.904955 | ||||||||
\(877\) | −53.0077 | −1.78994 | −0.894971 | − | 0.446125i | \(-0.852804\pi\) | ||||
−0.894971 | + | 0.446125i | \(0.852804\pi\) | |||||||
\(878\) | −30.4004 | −1.02596 | ||||||||
\(879\) | 24.6752 | 0.832273 | ||||||||
\(880\) | 4.53539 | 0.152888 | ||||||||
\(881\) | 16.0327 | 0.540156 | 0.270078 | − | 0.962838i | \(-0.412950\pi\) | ||||
0.270078 | + | 0.962838i | \(0.412950\pi\) | |||||||
\(882\) | −0.425542 | −0.0143287 | ||||||||
\(883\) | 9.79720 | 0.329702 | 0.164851 | − | 0.986318i | \(-0.447286\pi\) | ||||
0.164851 | + | 0.986318i | \(0.447286\pi\) | |||||||
\(884\) | −15.8528 | −0.533186 | ||||||||
\(885\) | 22.0416 | 0.740920 | ||||||||
\(886\) | 2.15234 | 0.0723092 | ||||||||
\(887\) | 18.9336 | 0.635727 | 0.317863 | − | 0.948137i | \(-0.397035\pi\) | ||||
0.317863 | + | 0.948137i | \(0.397035\pi\) | |||||||
\(888\) | 26.1947 | 0.879037 | ||||||||
\(889\) | −8.28793 | −0.277968 | ||||||||
\(890\) | 36.9924 | 1.23999 | ||||||||
\(891\) | 26.9269 | 0.902084 | ||||||||
\(892\) | 20.8404 | 0.697790 | ||||||||
\(893\) | −21.8873 | −0.732430 | ||||||||
\(894\) | 35.7155 | 1.19451 | ||||||||
\(895\) | 34.7904 | 1.16292 | ||||||||
\(896\) | −13.7528 | −0.459450 | ||||||||
\(897\) | 22.3439 | 0.746041 | ||||||||
\(898\) | −18.3412 | −0.612053 | ||||||||
\(899\) | −1.16529 | −0.0388645 | ||||||||
\(900\) | −11.4169 | −0.380563 | ||||||||
\(901\) | 16.5052 | 0.549867 | ||||||||
\(902\) | −6.59622 | −0.219630 | ||||||||
\(903\) | −24.4565 | −0.813861 | ||||||||
\(904\) | 55.4578 | 1.84450 | ||||||||
\(905\) | −90.5583 | −3.01026 | ||||||||
\(906\) | −25.7159 | −0.854353 | ||||||||
\(907\) | −4.06639 | −0.135022 | −0.0675111 | − | 0.997719i | \(-0.521506\pi\) | ||||
−0.0675111 | + | 0.997719i | \(0.521506\pi\) | |||||||
\(908\) | 27.6694 | 0.918242 | ||||||||
\(909\) | 16.2439 | 0.538777 | ||||||||
\(910\) | 47.6310 | 1.57895 | ||||||||
\(911\) | 9.87329 | 0.327117 | 0.163558 | − | 0.986534i | \(-0.447703\pi\) | ||||
0.163558 | + | 0.986534i | \(0.447703\pi\) | |||||||
\(912\) | −4.86615 | −0.161134 | ||||||||
\(913\) | 22.1627 | 0.733477 | ||||||||
\(914\) | 4.39368 | 0.145330 | ||||||||
\(915\) | −66.4969 | −2.19832 | ||||||||
\(916\) | −4.92344 | −0.162675 | ||||||||
\(917\) | 34.7671 | 1.14811 | ||||||||
\(918\) | 9.74443 | 0.321614 | ||||||||
\(919\) | 5.98000 | 0.197262 | 0.0986311 | − | 0.995124i | \(-0.468554\pi\) | ||||
0.0986311 | + | 0.995124i | \(0.468554\pi\) | |||||||
\(920\) | 23.2853 | 0.767695 | ||||||||
\(921\) | −1.12663 | −0.0371237 | ||||||||
\(922\) | −8.38517 | −0.276151 | ||||||||
\(923\) | 8.88566 | 0.292475 | ||||||||
\(924\) | −15.0221 | −0.494191 | ||||||||
\(925\) | 37.6294 | 1.23725 | ||||||||
\(926\) | 28.7570 | 0.945013 | ||||||||
\(927\) | −23.1084 | −0.758980 | ||||||||
\(928\) | −2.18124 | −0.0716027 | ||||||||
\(929\) | 2.88995 | 0.0948162 | 0.0474081 | − | 0.998876i | \(-0.484904\pi\) | ||||
0.0474081 | + | 0.998876i | \(0.484904\pi\) | |||||||
\(930\) | 20.3438 | 0.667099 | ||||||||
\(931\) | 1.78604 | 0.0585350 | ||||||||
\(932\) | −26.1685 | −0.857179 | ||||||||
\(933\) | 40.7739 | 1.33488 | ||||||||
\(934\) | 25.2501 | 0.826209 | ||||||||
\(935\) | −24.9117 | −0.814699 | ||||||||
\(936\) | 17.5782 | 0.574561 | ||||||||
\(937\) | 6.34674 | 0.207339 | 0.103670 | − | 0.994612i | \(-0.466942\pi\) | ||||
0.103670 | + | 0.994612i | \(0.466942\pi\) | |||||||
\(938\) | 16.9169 | 0.552356 | ||||||||
\(939\) | −44.5064 | −1.45241 | ||||||||
\(940\) | 19.3431 | 0.630903 | ||||||||
\(941\) | 12.1993 | 0.397685 | 0.198843 | − | 0.980031i | \(-0.436282\pi\) | ||||
0.198843 | + | 0.980031i | \(0.436282\pi\) | |||||||
\(942\) | 9.71790 | 0.316626 | ||||||||
\(943\) | −6.27688 | −0.204403 | ||||||||
\(944\) | −1.48749 | −0.0484136 | ||||||||
\(945\) | 37.1980 | 1.21005 | ||||||||
\(946\) | 9.97075 | 0.324177 | ||||||||
\(947\) | −37.1970 | −1.20874 | −0.604370 | − | 0.796704i | \(-0.706575\pi\) | ||||
−0.604370 | + | 0.796704i | \(0.706575\pi\) | |||||||
\(948\) | 39.1424 | 1.27129 | ||||||||
\(949\) | 59.2406 | 1.92303 | ||||||||
\(950\) | −37.7153 | −1.22365 | ||||||||
\(951\) | −34.1892 | −1.10866 | ||||||||
\(952\) | −22.2484 | −0.721073 | ||||||||
\(953\) | −56.1815 | −1.81990 | −0.909948 | − | 0.414722i | \(-0.863879\pi\) | ||||
−0.909948 | + | 0.414722i | \(0.863879\pi\) | |||||||
\(954\) | −6.56658 | −0.212601 | ||||||||
\(955\) | −64.6454 | −2.09187 | ||||||||
\(956\) | −21.4109 | −0.692478 | ||||||||
\(957\) | −2.00408 | −0.0647828 | ||||||||
\(958\) | −30.9813 | −1.00096 | ||||||||
\(959\) | 47.0916 | 1.52067 | ||||||||
\(960\) | 45.7658 | 1.47708 | ||||||||
\(961\) | −22.7485 | −0.733824 | ||||||||
\(962\) | −20.7875 | −0.670217 | ||||||||
\(963\) | 5.41550 | 0.174512 | ||||||||
\(964\) | −11.2060 | −0.360922 | ||||||||
\(965\) | −83.3934 | −2.68453 | ||||||||
\(966\) | 11.2513 | 0.362004 | ||||||||
\(967\) | 32.7394 | 1.05283 | 0.526414 | − | 0.850229i | \(-0.323536\pi\) | ||||
0.526414 | + | 0.850229i | \(0.323536\pi\) | |||||||
\(968\) | −15.1326 | −0.486380 | ||||||||
\(969\) | 26.7285 | 0.858642 | ||||||||
\(970\) | 22.4513 | 0.720867 | ||||||||
\(971\) | −34.8206 | −1.11744 | −0.558722 | − | 0.829355i | \(-0.688708\pi\) | ||||
−0.558722 | + | 0.829355i | \(0.688708\pi\) | |||||||
\(972\) | 13.0701 | 0.419223 | ||||||||
\(973\) | 35.0185 | 1.12264 | ||||||||
\(974\) | 20.6576 | 0.661912 | ||||||||
\(975\) | 89.1414 | 2.85481 | ||||||||
\(976\) | 4.48757 | 0.143644 | ||||||||
\(977\) | 21.5209 | 0.688515 | 0.344258 | − | 0.938875i | \(-0.388131\pi\) | ||||
0.344258 | + | 0.938875i | \(0.388131\pi\) | |||||||
\(978\) | 19.4350 | 0.621464 | ||||||||
\(979\) | 25.8044 | 0.824713 | ||||||||
\(980\) | −1.57843 | −0.0504211 | ||||||||
\(981\) | 8.76315 | 0.279786 | ||||||||
\(982\) | 21.8562 | 0.697461 | ||||||||
\(983\) | 18.7063 | 0.596638 | 0.298319 | − | 0.954466i | \(-0.403574\pi\) | ||||
0.298319 | + | 0.954466i | \(0.403574\pi\) | |||||||
\(984\) | −17.4322 | −0.555717 | ||||||||
\(985\) | 65.5478 | 2.08853 | ||||||||
\(986\) | −1.06496 | −0.0339151 | ||||||||
\(987\) | 26.0493 | 0.829158 | ||||||||
\(988\) | −26.4711 | −0.842159 | ||||||||
\(989\) | 9.48805 | 0.301702 | ||||||||
\(990\) | 9.91111 | 0.314996 | ||||||||
\(991\) | −45.2879 | −1.43862 | −0.719308 | − | 0.694691i | \(-0.755541\pi\) | ||||
−0.719308 | + | 0.694691i | \(0.755541\pi\) | |||||||
\(992\) | 15.4454 | 0.490393 | ||||||||
\(993\) | −17.5416 | −0.556667 | ||||||||
\(994\) | 4.47438 | 0.141919 | ||||||||
\(995\) | −37.9419 | −1.20284 | ||||||||
\(996\) | 21.0149 | 0.665884 | ||||||||
\(997\) | 43.1794 | 1.36751 | 0.683753 | − | 0.729713i | \(-0.260346\pi\) | ||||
0.683753 | + | 0.729713i | \(0.260346\pi\) | |||||||
\(998\) | −18.8376 | −0.596293 | ||||||||
\(999\) | −16.2343 | −0.513630 |
(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 | 619.2.a.b.1.10 | ✓ | 30 | |
3.2 | odd | 2 | 5571.2.a.g.1.21 | 30 | |||
4.3 | odd | 2 | 9904.2.a.n.1.9 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
619.2.a.b.1.10 | ✓ | 30 | 1.1 | even | 1 | trivial | |
5571.2.a.g.1.21 | 30 | 3.2 | odd | 2 | |||
9904.2.a.n.1.9 | 30 | 4.3 | odd | 2 |