Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6023,2,Mod(1,6023)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6023, 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("6023.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6023 = 19 \cdot 317 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6023.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: | \(48.0938971374\) |
Analytic rank: | \(1\) |
Dimension: | \(99\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 6023.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.79086 | −1.97344 | −0.986719 | − | 0.162439i | \(-0.948064\pi\) | ||||
−0.986719 | + | 0.162439i | \(0.948064\pi\) | |||||||
\(3\) | −1.66708 | −0.962488 | −0.481244 | − | 0.876587i | \(-0.659815\pi\) | ||||
−0.481244 | + | 0.876587i | \(0.659815\pi\) | |||||||
\(4\) | 5.78891 | 2.89445 | ||||||||
\(5\) | 1.47477 | 0.659535 | 0.329768 | − | 0.944062i | \(-0.393030\pi\) | ||||
0.329768 | + | 0.944062i | \(0.393030\pi\) | |||||||
\(6\) | 4.65258 | 1.89941 | ||||||||
\(7\) | −1.60538 | −0.606778 | −0.303389 | − | 0.952867i | \(-0.598118\pi\) | ||||
−0.303389 | + | 0.952867i | \(0.598118\pi\) | |||||||
\(8\) | −10.5743 | −3.73859 | ||||||||
\(9\) | −0.220852 | −0.0736173 | ||||||||
\(10\) | −4.11587 | −1.30155 | ||||||||
\(11\) | 1.76231 | 0.531356 | 0.265678 | − | 0.964062i | \(-0.414404\pi\) | ||||
0.265678 | + | 0.964062i | \(0.414404\pi\) | |||||||
\(12\) | −9.65056 | −2.78588 | ||||||||
\(13\) | 3.00110 | 0.832354 | 0.416177 | − | 0.909284i | \(-0.363370\pi\) | ||||
0.416177 | + | 0.909284i | \(0.363370\pi\) | |||||||
\(14\) | 4.48040 | 1.19744 | ||||||||
\(15\) | −2.45855 | −0.634795 | ||||||||
\(16\) | 17.9336 | 4.48341 | ||||||||
\(17\) | −0.637489 | −0.154614 | −0.0773069 | − | 0.997007i | \(-0.524632\pi\) | ||||
−0.0773069 | + | 0.997007i | \(0.524632\pi\) | |||||||
\(18\) | 0.616367 | 0.145279 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 8.53728 | 1.90899 | ||||||||
\(21\) | 2.67630 | 0.584016 | ||||||||
\(22\) | −4.91836 | −1.04860 | ||||||||
\(23\) | −6.91710 | −1.44231 | −0.721157 | − | 0.692771i | \(-0.756390\pi\) | ||||
−0.721157 | + | 0.692771i | \(0.756390\pi\) | |||||||
\(24\) | 17.6282 | 3.59834 | ||||||||
\(25\) | −2.82507 | −0.565013 | ||||||||
\(26\) | −8.37564 | −1.64260 | ||||||||
\(27\) | 5.36941 | 1.03334 | ||||||||
\(28\) | −9.29341 | −1.75629 | ||||||||
\(29\) | 7.56995 | 1.40570 | 0.702852 | − | 0.711336i | \(-0.251910\pi\) | ||||
0.702852 | + | 0.711336i | \(0.251910\pi\) | |||||||
\(30\) | 6.86147 | 1.25273 | ||||||||
\(31\) | 4.71855 | 0.847477 | 0.423738 | − | 0.905785i | \(-0.360718\pi\) | ||||
0.423738 | + | 0.905785i | \(0.360718\pi\) | |||||||
\(32\) | −28.9017 | −5.10914 | ||||||||
\(33\) | −2.93791 | −0.511424 | ||||||||
\(34\) | 1.77914 | 0.305121 | ||||||||
\(35\) | −2.36756 | −0.400191 | ||||||||
\(36\) | −1.27849 | −0.213082 | ||||||||
\(37\) | −7.76535 | −1.27662 | −0.638308 | − | 0.769781i | \(-0.720365\pi\) | ||||
−0.638308 | + | 0.769781i | \(0.720365\pi\) | |||||||
\(38\) | 2.79086 | 0.452738 | ||||||||
\(39\) | −5.00306 | −0.801131 | ||||||||
\(40\) | −15.5946 | −2.46573 | ||||||||
\(41\) | 2.91992 | 0.456015 | 0.228008 | − | 0.973659i | \(-0.426779\pi\) | ||||
0.228008 | + | 0.973659i | \(0.426779\pi\) | |||||||
\(42\) | −7.46918 | −1.15252 | ||||||||
\(43\) | −11.8373 | −1.80517 | −0.902585 | − | 0.430511i | \(-0.858333\pi\) | ||||
−0.902585 | + | 0.430511i | \(0.858333\pi\) | |||||||
\(44\) | 10.2018 | 1.53799 | ||||||||
\(45\) | −0.325705 | −0.0485532 | ||||||||
\(46\) | 19.3047 | 2.84632 | ||||||||
\(47\) | 10.5942 | 1.54532 | 0.772659 | − | 0.634821i | \(-0.218926\pi\) | ||||
0.772659 | + | 0.634821i | \(0.218926\pi\) | |||||||
\(48\) | −29.8968 | −4.31523 | ||||||||
\(49\) | −4.42275 | −0.631821 | ||||||||
\(50\) | 7.88437 | 1.11502 | ||||||||
\(51\) | 1.06274 | 0.148814 | ||||||||
\(52\) | 17.3731 | 2.40921 | ||||||||
\(53\) | 8.67812 | 1.19203 | 0.596016 | − | 0.802973i | \(-0.296750\pi\) | ||||
0.596016 | + | 0.802973i | \(0.296750\pi\) | |||||||
\(54\) | −14.9853 | −2.03924 | ||||||||
\(55\) | 2.59899 | 0.350448 | ||||||||
\(56\) | 16.9758 | 2.26849 | ||||||||
\(57\) | 1.66708 | 0.220810 | ||||||||
\(58\) | −21.1267 | −2.77407 | ||||||||
\(59\) | −9.03653 | −1.17646 | −0.588228 | − | 0.808695i | \(-0.700174\pi\) | ||||
−0.588228 | + | 0.808695i | \(0.700174\pi\) | |||||||
\(60\) | −14.2323 | −1.83738 | ||||||||
\(61\) | −0.869732 | −0.111358 | −0.0556789 | − | 0.998449i | \(-0.517732\pi\) | ||||
−0.0556789 | + | 0.998449i | \(0.517732\pi\) | |||||||
\(62\) | −13.1688 | −1.67244 | ||||||||
\(63\) | 0.354552 | 0.0446693 | ||||||||
\(64\) | 44.7932 | 5.59916 | ||||||||
\(65\) | 4.42591 | 0.548967 | ||||||||
\(66\) | 8.19929 | 1.00926 | ||||||||
\(67\) | 5.37380 | 0.656515 | 0.328257 | − | 0.944588i | \(-0.393539\pi\) | ||||
0.328257 | + | 0.944588i | \(0.393539\pi\) | |||||||
\(68\) | −3.69037 | −0.447523 | ||||||||
\(69\) | 11.5313 | 1.38821 | ||||||||
\(70\) | 6.60754 | 0.789752 | ||||||||
\(71\) | 11.9269 | 1.41546 | 0.707732 | − | 0.706481i | \(-0.249719\pi\) | ||||
0.707732 | + | 0.706481i | \(0.249719\pi\) | |||||||
\(72\) | 2.33536 | 0.275224 | ||||||||
\(73\) | −8.83344 | −1.03388 | −0.516938 | − | 0.856023i | \(-0.672928\pi\) | ||||
−0.516938 | + | 0.856023i | \(0.672928\pi\) | |||||||
\(74\) | 21.6720 | 2.51932 | ||||||||
\(75\) | 4.70960 | 0.543818 | ||||||||
\(76\) | −5.78891 | −0.664033 | ||||||||
\(77\) | −2.82918 | −0.322415 | ||||||||
\(78\) | 13.9628 | 1.58098 | ||||||||
\(79\) | 8.24783 | 0.927954 | 0.463977 | − | 0.885847i | \(-0.346422\pi\) | ||||
0.463977 | + | 0.885847i | \(0.346422\pi\) | |||||||
\(80\) | 26.4479 | 2.95697 | ||||||||
\(81\) | −8.28867 | −0.920963 | ||||||||
\(82\) | −8.14910 | −0.899918 | ||||||||
\(83\) | 13.0316 | 1.43041 | 0.715204 | − | 0.698916i | \(-0.246334\pi\) | ||||
0.715204 | + | 0.698916i | \(0.246334\pi\) | |||||||
\(84\) | 15.4928 | 1.69041 | ||||||||
\(85\) | −0.940147 | −0.101973 | ||||||||
\(86\) | 33.0362 | 3.56239 | ||||||||
\(87\) | −12.6197 | −1.35297 | ||||||||
\(88\) | −18.6352 | −1.98652 | ||||||||
\(89\) | −4.35438 | −0.461563 | −0.230782 | − | 0.973006i | \(-0.574128\pi\) | ||||
−0.230782 | + | 0.973006i | \(0.574128\pi\) | |||||||
\(90\) | 0.908997 | 0.0958167 | ||||||||
\(91\) | −4.81791 | −0.505054 | ||||||||
\(92\) | −40.0424 | −4.17471 | ||||||||
\(93\) | −7.86619 | −0.815686 | ||||||||
\(94\) | −29.5669 | −3.04959 | ||||||||
\(95\) | −1.47477 | −0.151308 | ||||||||
\(96\) | 48.1813 | 4.91748 | ||||||||
\(97\) | −7.99494 | −0.811763 | −0.405882 | − | 0.913926i | \(-0.633036\pi\) | ||||
−0.405882 | + | 0.913926i | \(0.633036\pi\) | |||||||
\(98\) | 12.3433 | 1.24686 | ||||||||
\(99\) | −0.389209 | −0.0391170 | ||||||||
\(100\) | −16.3540 | −1.63540 | ||||||||
\(101\) | −11.1419 | −1.10866 | −0.554331 | − | 0.832296i | \(-0.687026\pi\) | ||||
−0.554331 | + | 0.832296i | \(0.687026\pi\) | |||||||
\(102\) | −2.96597 | −0.293675 | ||||||||
\(103\) | −3.87795 | −0.382105 | −0.191053 | − | 0.981580i | \(-0.561190\pi\) | ||||
−0.191053 | + | 0.981580i | \(0.561190\pi\) | |||||||
\(104\) | −31.7345 | −3.11183 | ||||||||
\(105\) | 3.94691 | 0.385179 | ||||||||
\(106\) | −24.2194 | −2.35240 | ||||||||
\(107\) | 6.81402 | 0.658736 | 0.329368 | − | 0.944202i | \(-0.393164\pi\) | ||||
0.329368 | + | 0.944202i | \(0.393164\pi\) | |||||||
\(108\) | 31.0830 | 2.99096 | ||||||||
\(109\) | 12.3137 | 1.17944 | 0.589718 | − | 0.807609i | \(-0.299239\pi\) | ||||
0.589718 | + | 0.807609i | \(0.299239\pi\) | |||||||
\(110\) | −7.25343 | −0.691587 | ||||||||
\(111\) | 12.9454 | 1.22873 | ||||||||
\(112\) | −28.7903 | −2.72043 | ||||||||
\(113\) | −15.4757 | −1.45583 | −0.727914 | − | 0.685669i | \(-0.759510\pi\) | ||||
−0.727914 | + | 0.685669i | \(0.759510\pi\) | |||||||
\(114\) | −4.65258 | −0.435754 | ||||||||
\(115\) | −10.2011 | −0.951258 | ||||||||
\(116\) | 43.8217 | 4.06874 | ||||||||
\(117\) | −0.662797 | −0.0612756 | ||||||||
\(118\) | 25.2197 | 2.32166 | ||||||||
\(119\) | 1.02341 | 0.0938162 | ||||||||
\(120\) | 25.9975 | 2.37323 | ||||||||
\(121\) | −7.89427 | −0.717661 | ||||||||
\(122\) | 2.42730 | 0.219758 | ||||||||
\(123\) | −4.86774 | −0.438909 | ||||||||
\(124\) | 27.3153 | 2.45298 | ||||||||
\(125\) | −11.5401 | −1.03218 | ||||||||
\(126\) | −0.989504 | −0.0881521 | ||||||||
\(127\) | −5.13538 | −0.455691 | −0.227846 | − | 0.973697i | \(-0.573168\pi\) | ||||
−0.227846 | + | 0.973697i | \(0.573168\pi\) | |||||||
\(128\) | −67.2084 | −5.94044 | ||||||||
\(129\) | 19.7337 | 1.73745 | ||||||||
\(130\) | −12.3521 | −1.08335 | ||||||||
\(131\) | 13.8666 | 1.21153 | 0.605765 | − | 0.795644i | \(-0.292867\pi\) | ||||
0.605765 | + | 0.795644i | \(0.292867\pi\) | |||||||
\(132\) | −17.0073 | −1.48029 | ||||||||
\(133\) | 1.60538 | 0.139204 | ||||||||
\(134\) | −14.9975 | −1.29559 | ||||||||
\(135\) | 7.91862 | 0.681527 | ||||||||
\(136\) | 6.74101 | 0.578037 | ||||||||
\(137\) | −2.61873 | −0.223733 | −0.111866 | − | 0.993723i | \(-0.535683\pi\) | ||||
−0.111866 | + | 0.993723i | \(0.535683\pi\) | |||||||
\(138\) | −32.1824 | −2.73955 | ||||||||
\(139\) | −13.9434 | −1.18267 | −0.591333 | − | 0.806427i | \(-0.701398\pi\) | ||||
−0.591333 | + | 0.806427i | \(0.701398\pi\) | |||||||
\(140\) | −13.7056 | −1.15833 | ||||||||
\(141\) | −17.6613 | −1.48735 | ||||||||
\(142\) | −33.2863 | −2.79333 | ||||||||
\(143\) | 5.28886 | 0.442276 | ||||||||
\(144\) | −3.96068 | −0.330056 | ||||||||
\(145\) | 11.1639 | 0.927111 | ||||||||
\(146\) | 24.6529 | 2.04029 | ||||||||
\(147\) | 7.37306 | 0.608120 | ||||||||
\(148\) | −44.9529 | −3.69511 | ||||||||
\(149\) | −16.2748 | −1.33329 | −0.666643 | − | 0.745377i | \(-0.732270\pi\) | ||||
−0.666643 | + | 0.745377i | \(0.732270\pi\) | |||||||
\(150\) | −13.1439 | −1.07319 | ||||||||
\(151\) | −12.6627 | −1.03047 | −0.515237 | − | 0.857048i | \(-0.672296\pi\) | ||||
−0.515237 | + | 0.857048i | \(0.672296\pi\) | |||||||
\(152\) | 10.5743 | 0.857690 | ||||||||
\(153\) | 0.140791 | 0.0113822 | ||||||||
\(154\) | 7.89585 | 0.636266 | ||||||||
\(155\) | 6.95876 | 0.558941 | ||||||||
\(156\) | −28.9623 | −2.31884 | ||||||||
\(157\) | 17.1966 | 1.37244 | 0.686218 | − | 0.727396i | \(-0.259270\pi\) | ||||
0.686218 | + | 0.727396i | \(0.259270\pi\) | |||||||
\(158\) | −23.0186 | −1.83126 | ||||||||
\(159\) | −14.4671 | −1.14732 | ||||||||
\(160\) | −42.6232 | −3.36966 | ||||||||
\(161\) | 11.1046 | 0.875164 | ||||||||
\(162\) | 23.1325 | 1.81746 | ||||||||
\(163\) | 10.6954 | 0.837729 | 0.418865 | − | 0.908049i | \(-0.362428\pi\) | ||||
0.418865 | + | 0.908049i | \(0.362428\pi\) | |||||||
\(164\) | 16.9032 | 1.31992 | ||||||||
\(165\) | −4.33272 | −0.337302 | ||||||||
\(166\) | −36.3695 | −2.82282 | ||||||||
\(167\) | 0.00574492 | 0.000444555 0 | 0.000222278 | − | 1.00000i | \(-0.499929\pi\) | ||||
0.000222278 | 1.00000i | \(0.499929\pi\) | ||||||||
\(168\) | −28.3000 | −2.18339 | ||||||||
\(169\) | −3.99342 | −0.307186 | ||||||||
\(170\) | 2.62382 | 0.201238 | ||||||||
\(171\) | 0.220852 | 0.0168890 | ||||||||
\(172\) | −68.5250 | −5.22498 | ||||||||
\(173\) | 3.55506 | 0.270286 | 0.135143 | − | 0.990826i | \(-0.456851\pi\) | ||||
0.135143 | + | 0.990826i | \(0.456851\pi\) | |||||||
\(174\) | 35.2198 | 2.67001 | ||||||||
\(175\) | 4.53531 | 0.342837 | ||||||||
\(176\) | 31.6046 | 2.38229 | ||||||||
\(177\) | 15.0646 | 1.13232 | ||||||||
\(178\) | 12.1525 | 0.910866 | ||||||||
\(179\) | −4.25306 | −0.317889 | −0.158944 | − | 0.987288i | \(-0.550809\pi\) | ||||
−0.158944 | + | 0.987288i | \(0.550809\pi\) | |||||||
\(180\) | −1.88547 | −0.140535 | ||||||||
\(181\) | −25.8527 | −1.92162 | −0.960808 | − | 0.277216i | \(-0.910588\pi\) | ||||
−0.960808 | + | 0.277216i | \(0.910588\pi\) | |||||||
\(182\) | 13.4461 | 0.996692 | ||||||||
\(183\) | 1.44991 | 0.107181 | ||||||||
\(184\) | 73.1436 | 5.39222 | ||||||||
\(185\) | −11.4521 | −0.841973 | ||||||||
\(186\) | 21.9534 | 1.60970 | ||||||||
\(187\) | −1.12345 | −0.0821550 | ||||||||
\(188\) | 61.3287 | 4.47285 | ||||||||
\(189\) | −8.61996 | −0.627010 | ||||||||
\(190\) | 4.11587 | 0.298596 | ||||||||
\(191\) | 22.8318 | 1.65205 | 0.826025 | − | 0.563633i | \(-0.190597\pi\) | ||||
0.826025 | + | 0.563633i | \(0.190597\pi\) | |||||||
\(192\) | −74.6738 | −5.38912 | ||||||||
\(193\) | 9.98216 | 0.718532 | 0.359266 | − | 0.933235i | \(-0.383027\pi\) | ||||
0.359266 | + | 0.933235i | \(0.383027\pi\) | |||||||
\(194\) | 22.3128 | 1.60196 | ||||||||
\(195\) | −7.37834 | −0.528374 | ||||||||
\(196\) | −25.6029 | −1.82878 | ||||||||
\(197\) | −12.1823 | −0.867951 | −0.433976 | − | 0.900925i | \(-0.642890\pi\) | ||||
−0.433976 | + | 0.900925i | \(0.642890\pi\) | |||||||
\(198\) | 1.08623 | 0.0771949 | ||||||||
\(199\) | 19.7516 | 1.40015 | 0.700077 | − | 0.714068i | \(-0.253149\pi\) | ||||
0.700077 | + | 0.714068i | \(0.253149\pi\) | |||||||
\(200\) | 29.8731 | 2.11235 | ||||||||
\(201\) | −8.95855 | −0.631887 | ||||||||
\(202\) | 31.0955 | 2.18787 | ||||||||
\(203\) | −12.1527 | −0.852949 | ||||||||
\(204\) | 6.15213 | 0.430735 | ||||||||
\(205\) | 4.30620 | 0.300758 | ||||||||
\(206\) | 10.8228 | 0.754061 | ||||||||
\(207\) | 1.52765 | 0.106179 | ||||||||
\(208\) | 53.8206 | 3.73178 | ||||||||
\(209\) | −1.76231 | −0.121901 | ||||||||
\(210\) | −11.0153 | −0.760127 | ||||||||
\(211\) | 21.0500 | 1.44914 | 0.724571 | − | 0.689200i | \(-0.242038\pi\) | ||||
0.724571 | + | 0.689200i | \(0.242038\pi\) | |||||||
\(212\) | 50.2368 | 3.45028 | ||||||||
\(213\) | −19.8831 | −1.36237 | ||||||||
\(214\) | −19.0170 | −1.29997 | ||||||||
\(215\) | −17.4572 | −1.19057 | ||||||||
\(216\) | −56.7778 | −3.86324 | ||||||||
\(217\) | −7.57508 | −0.514230 | ||||||||
\(218\) | −34.3657 | −2.32754 | ||||||||
\(219\) | 14.7260 | 0.995093 | ||||||||
\(220\) | 15.0453 | 1.01436 | ||||||||
\(221\) | −1.91317 | −0.128693 | ||||||||
\(222\) | −36.1289 | −2.42482 | ||||||||
\(223\) | −8.20113 | −0.549188 | −0.274594 | − | 0.961560i | \(-0.588543\pi\) | ||||
−0.274594 | + | 0.961560i | \(0.588543\pi\) | |||||||
\(224\) | 46.3982 | 3.10011 | ||||||||
\(225\) | 0.623921 | 0.0415947 | ||||||||
\(226\) | 43.1904 | 2.87298 | ||||||||
\(227\) | −12.8116 | −0.850336 | −0.425168 | − | 0.905114i | \(-0.639785\pi\) | ||||
−0.425168 | + | 0.905114i | \(0.639785\pi\) | |||||||
\(228\) | 9.65056 | 0.639124 | ||||||||
\(229\) | −19.9771 | −1.32013 | −0.660063 | − | 0.751210i | \(-0.729471\pi\) | ||||
−0.660063 | + | 0.751210i | \(0.729471\pi\) | |||||||
\(230\) | 28.4699 | 1.87725 | ||||||||
\(231\) | 4.71646 | 0.310320 | ||||||||
\(232\) | −80.0470 | −5.25534 | ||||||||
\(233\) | 11.6928 | 0.766021 | 0.383010 | − | 0.923744i | \(-0.374887\pi\) | ||||
0.383010 | + | 0.923744i | \(0.374887\pi\) | |||||||
\(234\) | 1.84978 | 0.120924 | ||||||||
\(235\) | 15.6239 | 1.01919 | ||||||||
\(236\) | −52.3116 | −3.40520 | ||||||||
\(237\) | −13.7498 | −0.893144 | ||||||||
\(238\) | −2.85621 | −0.185140 | ||||||||
\(239\) | −7.63505 | −0.493870 | −0.246935 | − | 0.969032i | \(-0.579423\pi\) | ||||
−0.246935 | + | 0.969032i | \(0.579423\pi\) | |||||||
\(240\) | −44.0907 | −2.84604 | ||||||||
\(241\) | 17.7372 | 1.14256 | 0.571278 | − | 0.820757i | \(-0.306448\pi\) | ||||
0.571278 | + | 0.820757i | \(0.306448\pi\) | |||||||
\(242\) | 22.0318 | 1.41626 | ||||||||
\(243\) | −2.29038 | −0.146928 | ||||||||
\(244\) | −5.03480 | −0.322320 | ||||||||
\(245\) | −6.52252 | −0.416708 | ||||||||
\(246\) | 13.5852 | 0.866160 | ||||||||
\(247\) | −3.00110 | −0.190955 | ||||||||
\(248\) | −49.8954 | −3.16836 | ||||||||
\(249\) | −21.7247 | −1.37675 | ||||||||
\(250\) | 32.2069 | 2.03695 | ||||||||
\(251\) | 14.1950 | 0.895982 | 0.447991 | − | 0.894038i | \(-0.352140\pi\) | ||||
0.447991 | + | 0.894038i | \(0.352140\pi\) | |||||||
\(252\) | 2.05247 | 0.129293 | ||||||||
\(253\) | −12.1901 | −0.766383 | ||||||||
\(254\) | 14.3321 | 0.899277 | ||||||||
\(255\) | 1.56730 | 0.0981480 | ||||||||
\(256\) | 97.9829 | 6.12393 | ||||||||
\(257\) | 18.8713 | 1.17716 | 0.588580 | − | 0.808439i | \(-0.299687\pi\) | ||||
0.588580 | + | 0.808439i | \(0.299687\pi\) | |||||||
\(258\) | −55.0740 | −3.42876 | ||||||||
\(259\) | 12.4664 | 0.774622 | ||||||||
\(260\) | 25.6212 | 1.58896 | ||||||||
\(261\) | −1.67184 | −0.103484 | ||||||||
\(262\) | −38.6997 | −2.39088 | ||||||||
\(263\) | −8.04943 | −0.496349 | −0.248175 | − | 0.968715i | \(-0.579831\pi\) | ||||
−0.248175 | + | 0.968715i | \(0.579831\pi\) | |||||||
\(264\) | 31.0663 | 1.91200 | ||||||||
\(265\) | 12.7982 | 0.786187 | ||||||||
\(266\) | −4.48040 | −0.274711 | ||||||||
\(267\) | 7.25909 | 0.444249 | ||||||||
\(268\) | 31.1084 | 1.90025 | ||||||||
\(269\) | 26.1179 | 1.59243 | 0.796217 | − | 0.605011i | \(-0.206831\pi\) | ||||
0.796217 | + | 0.605011i | \(0.206831\pi\) | |||||||
\(270\) | −22.0998 | −1.34495 | ||||||||
\(271\) | −13.6713 | −0.830471 | −0.415235 | − | 0.909714i | \(-0.636301\pi\) | ||||
−0.415235 | + | 0.909714i | \(0.636301\pi\) | |||||||
\(272\) | −11.4325 | −0.693197 | ||||||||
\(273\) | 8.03182 | 0.486108 | ||||||||
\(274\) | 7.30850 | 0.441523 | ||||||||
\(275\) | −4.97864 | −0.300223 | ||||||||
\(276\) | 66.7539 | 4.01811 | ||||||||
\(277\) | −11.4839 | −0.689998 | −0.344999 | − | 0.938603i | \(-0.612121\pi\) | ||||
−0.344999 | + | 0.938603i | \(0.612121\pi\) | |||||||
\(278\) | 38.9142 | 2.33392 | ||||||||
\(279\) | −1.04210 | −0.0623889 | ||||||||
\(280\) | 25.0354 | 1.49615 | ||||||||
\(281\) | −0.834965 | −0.0498099 | −0.0249049 | − | 0.999690i | \(-0.507928\pi\) | ||||
−0.0249049 | + | 0.999690i | \(0.507928\pi\) | |||||||
\(282\) | 49.2902 | 2.93519 | ||||||||
\(283\) | 28.2891 | 1.68161 | 0.840807 | − | 0.541336i | \(-0.182081\pi\) | ||||
0.840807 | + | 0.541336i | \(0.182081\pi\) | |||||||
\(284\) | 69.0438 | 4.09699 | ||||||||
\(285\) | 2.45855 | 0.145632 | ||||||||
\(286\) | −14.7605 | −0.872805 | ||||||||
\(287\) | −4.68759 | −0.276700 | ||||||||
\(288\) | 6.38298 | 0.376121 | ||||||||
\(289\) | −16.5936 | −0.976095 | ||||||||
\(290\) | −31.1569 | −1.82960 | ||||||||
\(291\) | 13.3282 | 0.781312 | ||||||||
\(292\) | −51.1360 | −2.99251 | ||||||||
\(293\) | 3.94594 | 0.230524 | 0.115262 | − | 0.993335i | \(-0.463229\pi\) | ||||
0.115262 | + | 0.993335i | \(0.463229\pi\) | |||||||
\(294\) | −20.5772 | −1.20009 | ||||||||
\(295\) | −13.3268 | −0.775915 | ||||||||
\(296\) | 82.1133 | 4.77274 | ||||||||
\(297\) | 9.46256 | 0.549073 | ||||||||
\(298\) | 45.4208 | 2.63116 | ||||||||
\(299\) | −20.7589 | −1.20052 | ||||||||
\(300\) | 27.2635 | 1.57406 | ||||||||
\(301\) | 19.0034 | 1.09534 | ||||||||
\(302\) | 35.3398 | 2.03357 | ||||||||
\(303\) | 18.5744 | 1.06707 | ||||||||
\(304\) | −17.9336 | −1.02856 | ||||||||
\(305\) | −1.28265 | −0.0734444 | ||||||||
\(306\) | −0.392927 | −0.0224622 | ||||||||
\(307\) | −7.77529 | −0.443759 | −0.221880 | − | 0.975074i | \(-0.571219\pi\) | ||||
−0.221880 | + | 0.975074i | \(0.571219\pi\) | |||||||
\(308\) | −16.3779 | −0.933215 | ||||||||
\(309\) | 6.46484 | 0.367772 | ||||||||
\(310\) | −19.4209 | −1.10303 | ||||||||
\(311\) | 13.1183 | 0.743872 | 0.371936 | − | 0.928258i | \(-0.378694\pi\) | ||||
0.371936 | + | 0.928258i | \(0.378694\pi\) | |||||||
\(312\) | 52.9039 | 2.99510 | ||||||||
\(313\) | −16.6411 | −0.940613 | −0.470306 | − | 0.882503i | \(-0.655857\pi\) | ||||
−0.470306 | + | 0.882503i | \(0.655857\pi\) | |||||||
\(314\) | −47.9933 | −2.70842 | ||||||||
\(315\) | 0.522881 | 0.0294610 | ||||||||
\(316\) | 47.7459 | 2.68592 | ||||||||
\(317\) | −1.00000 | −0.0561656 | ||||||||
\(318\) | 40.3757 | 2.26416 | ||||||||
\(319\) | 13.3406 | 0.746929 | ||||||||
\(320\) | 66.0596 | 3.69284 | ||||||||
\(321\) | −11.3595 | −0.634026 | ||||||||
\(322\) | −30.9914 | −1.72708 | ||||||||
\(323\) | 0.637489 | 0.0354708 | ||||||||
\(324\) | −47.9823 | −2.66569 | ||||||||
\(325\) | −8.47829 | −0.470291 | ||||||||
\(326\) | −29.8494 | −1.65321 | ||||||||
\(327\) | −20.5278 | −1.13519 | ||||||||
\(328\) | −30.8762 | −1.70485 | ||||||||
\(329\) | −17.0077 | −0.937664 | ||||||||
\(330\) | 12.0920 | 0.665644 | ||||||||
\(331\) | −14.3389 | −0.788135 | −0.394067 | − | 0.919082i | \(-0.628932\pi\) | ||||
−0.394067 | + | 0.919082i | \(0.628932\pi\) | |||||||
\(332\) | 75.4389 | 4.14025 | ||||||||
\(333\) | 1.71499 | 0.0939810 | ||||||||
\(334\) | −0.0160333 | −0.000877302 0 | ||||||||
\(335\) | 7.92510 | 0.432995 | ||||||||
\(336\) | 47.9957 | 2.61838 | ||||||||
\(337\) | 4.76806 | 0.259733 | 0.129866 | − | 0.991532i | \(-0.458545\pi\) | ||||
0.129866 | + | 0.991532i | \(0.458545\pi\) | |||||||
\(338\) | 11.1451 | 0.606213 | ||||||||
\(339\) | 25.7991 | 1.40122 | ||||||||
\(340\) | −5.44243 | −0.295157 | ||||||||
\(341\) | 8.31554 | 0.450312 | ||||||||
\(342\) | −0.616367 | −0.0333293 | ||||||||
\(343\) | 18.3379 | 0.990152 | ||||||||
\(344\) | 125.171 | 6.74878 | ||||||||
\(345\) | 17.0060 | 0.915574 | ||||||||
\(346\) | −9.92167 | −0.533392 | ||||||||
\(347\) | 32.1588 | 1.72638 | 0.863189 | − | 0.504882i | \(-0.168464\pi\) | ||||
0.863189 | + | 0.504882i | \(0.168464\pi\) | |||||||
\(348\) | −73.0542 | −3.91612 | ||||||||
\(349\) | 8.42544 | 0.451003 | 0.225502 | − | 0.974243i | \(-0.427598\pi\) | ||||
0.225502 | + | 0.974243i | \(0.427598\pi\) | |||||||
\(350\) | −12.6574 | −0.676568 | ||||||||
\(351\) | 16.1141 | 0.860108 | ||||||||
\(352\) | −50.9336 | −2.71477 | ||||||||
\(353\) | −29.6599 | −1.57864 | −0.789320 | − | 0.613982i | \(-0.789567\pi\) | ||||
−0.789320 | + | 0.613982i | \(0.789567\pi\) | |||||||
\(354\) | −42.0432 | −2.23457 | ||||||||
\(355\) | 17.5894 | 0.933548 | ||||||||
\(356\) | −25.2071 | −1.33597 | ||||||||
\(357\) | −1.70611 | −0.0902970 | ||||||||
\(358\) | 11.8697 | 0.627333 | ||||||||
\(359\) | 17.1516 | 0.905229 | 0.452614 | − | 0.891706i | \(-0.350491\pi\) | ||||
0.452614 | + | 0.891706i | \(0.350491\pi\) | |||||||
\(360\) | 3.44410 | 0.181520 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 72.1513 | 3.79219 | ||||||||
\(363\) | 13.1604 | 0.690740 | ||||||||
\(364\) | −27.8904 | −1.46185 | ||||||||
\(365\) | −13.0273 | −0.681878 | ||||||||
\(366\) | −4.04650 | −0.211514 | ||||||||
\(367\) | 8.06530 | 0.421005 | 0.210503 | − | 0.977593i | \(-0.432490\pi\) | ||||
0.210503 | + | 0.977593i | \(0.432490\pi\) | |||||||
\(368\) | −124.049 | −6.46649 | ||||||||
\(369\) | −0.644870 | −0.0335706 | ||||||||
\(370\) | 31.9612 | 1.66158 | ||||||||
\(371\) | −13.9317 | −0.723298 | ||||||||
\(372\) | −45.5367 | −2.36097 | ||||||||
\(373\) | 3.27675 | 0.169663 | 0.0848317 | − | 0.996395i | \(-0.472965\pi\) | ||||
0.0848317 | + | 0.996395i | \(0.472965\pi\) | |||||||
\(374\) | 3.13540 | 0.162128 | ||||||||
\(375\) | 19.2383 | 0.993462 | ||||||||
\(376\) | −112.026 | −5.77730 | ||||||||
\(377\) | 22.7181 | 1.17004 | ||||||||
\(378\) | 24.0571 | 1.23736 | ||||||||
\(379\) | 10.5128 | 0.540009 | 0.270004 | − | 0.962859i | \(-0.412975\pi\) | ||||
0.270004 | + | 0.962859i | \(0.412975\pi\) | |||||||
\(380\) | −8.53728 | −0.437953 | ||||||||
\(381\) | 8.56107 | 0.438597 | ||||||||
\(382\) | −63.7204 | −3.26022 | ||||||||
\(383\) | −18.9950 | −0.970600 | −0.485300 | − | 0.874348i | \(-0.661290\pi\) | ||||
−0.485300 | + | 0.874348i | \(0.661290\pi\) | |||||||
\(384\) | 112.042 | 5.71760 | ||||||||
\(385\) | −4.17238 | −0.212644 | ||||||||
\(386\) | −27.8588 | −1.41798 | ||||||||
\(387\) | 2.61429 | 0.132892 | ||||||||
\(388\) | −46.2820 | −2.34961 | ||||||||
\(389\) | −9.47760 | −0.480534 | −0.240267 | − | 0.970707i | \(-0.577235\pi\) | ||||
−0.240267 | + | 0.970707i | \(0.577235\pi\) | |||||||
\(390\) | 20.5919 | 1.04271 | ||||||||
\(391\) | 4.40958 | 0.223002 | ||||||||
\(392\) | 46.7675 | 2.36212 | ||||||||
\(393\) | −23.1167 | −1.16608 | ||||||||
\(394\) | 33.9990 | 1.71285 | ||||||||
\(395\) | 12.1636 | 0.612018 | ||||||||
\(396\) | −2.25310 | −0.113222 | ||||||||
\(397\) | −34.5485 | −1.73394 | −0.866971 | − | 0.498359i | \(-0.833936\pi\) | ||||
−0.866971 | + | 0.498359i | \(0.833936\pi\) | |||||||
\(398\) | −55.1240 | −2.76311 | ||||||||
\(399\) | −2.67630 | −0.133982 | ||||||||
\(400\) | −50.6637 | −2.53318 | ||||||||
\(401\) | 25.8235 | 1.28956 | 0.644782 | − | 0.764367i | \(-0.276948\pi\) | ||||
0.644782 | + | 0.764367i | \(0.276948\pi\) | |||||||
\(402\) | 25.0021 | 1.24699 | ||||||||
\(403\) | 14.1608 | 0.705401 | ||||||||
\(404\) | −64.4995 | −3.20897 | ||||||||
\(405\) | −12.2238 | −0.607408 | ||||||||
\(406\) | 33.9164 | 1.68324 | ||||||||
\(407\) | −13.6849 | −0.678338 | ||||||||
\(408\) | −11.2378 | −0.556354 | ||||||||
\(409\) | 35.7879 | 1.76960 | 0.884798 | − | 0.465974i | \(-0.154296\pi\) | ||||
0.884798 | + | 0.465974i | \(0.154296\pi\) | |||||||
\(410\) | −12.0180 | −0.593528 | ||||||||
\(411\) | 4.36562 | 0.215340 | ||||||||
\(412\) | −22.4491 | −1.10599 | ||||||||
\(413\) | 14.5071 | 0.713847 | ||||||||
\(414\) | −4.26347 | −0.209538 | ||||||||
\(415\) | 19.2186 | 0.943404 | ||||||||
\(416\) | −86.7366 | −4.25261 | ||||||||
\(417\) | 23.2448 | 1.13830 | ||||||||
\(418\) | 4.91836 | 0.240565 | ||||||||
\(419\) | −37.6689 | −1.84025 | −0.920124 | − | 0.391627i | \(-0.871912\pi\) | ||||
−0.920124 | + | 0.391627i | \(0.871912\pi\) | |||||||
\(420\) | 22.8483 | 1.11488 | ||||||||
\(421\) | −4.57550 | −0.222996 | −0.111498 | − | 0.993765i | \(-0.535565\pi\) | ||||
−0.111498 | + | 0.993765i | \(0.535565\pi\) | |||||||
\(422\) | −58.7476 | −2.85979 | ||||||||
\(423\) | −2.33974 | −0.113762 | ||||||||
\(424\) | −91.7652 | −4.45651 | ||||||||
\(425\) | 1.80095 | 0.0873589 | ||||||||
\(426\) | 55.4909 | 2.68854 | ||||||||
\(427\) | 1.39625 | 0.0675694 | ||||||||
\(428\) | 39.4457 | 1.90668 | ||||||||
\(429\) | −8.81694 | −0.425686 | ||||||||
\(430\) | 48.7207 | 2.34952 | ||||||||
\(431\) | −26.3981 | −1.27155 | −0.635775 | − | 0.771874i | \(-0.719319\pi\) | ||||
−0.635775 | + | 0.771874i | \(0.719319\pi\) | |||||||
\(432\) | 96.2930 | 4.63290 | ||||||||
\(433\) | −20.7339 | −0.996410 | −0.498205 | − | 0.867059i | \(-0.666007\pi\) | ||||
−0.498205 | + | 0.867059i | \(0.666007\pi\) | |||||||
\(434\) | 21.1410 | 1.01480 | ||||||||
\(435\) | −18.6111 | −0.892333 | ||||||||
\(436\) | 71.2827 | 3.41382 | ||||||||
\(437\) | 6.91710 | 0.330890 | ||||||||
\(438\) | −41.0983 | −1.96375 | ||||||||
\(439\) | −7.01026 | −0.334581 | −0.167291 | − | 0.985908i | \(-0.553502\pi\) | ||||
−0.167291 | + | 0.985908i | \(0.553502\pi\) | |||||||
\(440\) | −27.4826 | −1.31018 | ||||||||
\(441\) | 0.976772 | 0.0465129 | ||||||||
\(442\) | 5.33938 | 0.253968 | ||||||||
\(443\) | −8.86017 | −0.420959 | −0.210480 | − | 0.977598i | \(-0.567503\pi\) | ||||
−0.210480 | + | 0.977598i | \(0.567503\pi\) | |||||||
\(444\) | 74.9400 | 3.55649 | ||||||||
\(445\) | −6.42169 | −0.304417 | ||||||||
\(446\) | 22.8882 | 1.08379 | ||||||||
\(447\) | 27.1314 | 1.28327 | ||||||||
\(448\) | −71.9103 | −3.39744 | ||||||||
\(449\) | 18.0063 | 0.849769 | 0.424885 | − | 0.905248i | \(-0.360315\pi\) | ||||
0.424885 | + | 0.905248i | \(0.360315\pi\) | |||||||
\(450\) | −1.74128 | −0.0820846 | ||||||||
\(451\) | 5.14581 | 0.242307 | ||||||||
\(452\) | −89.5871 | −4.21382 | ||||||||
\(453\) | 21.1097 | 0.991818 | ||||||||
\(454\) | 35.7554 | 1.67809 | ||||||||
\(455\) | −7.10528 | −0.333101 | ||||||||
\(456\) | −17.6282 | −0.825516 | ||||||||
\(457\) | 25.4252 | 1.18934 | 0.594671 | − | 0.803969i | \(-0.297282\pi\) | ||||
0.594671 | + | 0.803969i | \(0.297282\pi\) | |||||||
\(458\) | 55.7534 | 2.60519 | ||||||||
\(459\) | −3.42294 | −0.159769 | ||||||||
\(460\) | −59.0532 | −2.75337 | ||||||||
\(461\) | −31.7667 | −1.47952 | −0.739762 | − | 0.672869i | \(-0.765062\pi\) | ||||
−0.739762 | + | 0.672869i | \(0.765062\pi\) | |||||||
\(462\) | −13.1630 | −0.612398 | ||||||||
\(463\) | −33.6176 | −1.56234 | −0.781172 | − | 0.624316i | \(-0.785378\pi\) | ||||
−0.781172 | + | 0.624316i | \(0.785378\pi\) | |||||||
\(464\) | 135.757 | 6.30234 | ||||||||
\(465\) | −11.6008 | −0.537974 | ||||||||
\(466\) | −32.6330 | −1.51169 | ||||||||
\(467\) | 16.8467 | 0.779574 | 0.389787 | − | 0.920905i | \(-0.372549\pi\) | ||||
0.389787 | + | 0.920905i | \(0.372549\pi\) | |||||||
\(468\) | −3.83687 | −0.177360 | ||||||||
\(469\) | −8.62701 | −0.398358 | ||||||||
\(470\) | −43.6042 | −2.01131 | ||||||||
\(471\) | −28.6680 | −1.32095 | ||||||||
\(472\) | 95.5551 | 4.39828 | ||||||||
\(473\) | −20.8610 | −0.959188 | ||||||||
\(474\) | 38.3737 | 1.76256 | ||||||||
\(475\) | 2.82507 | 0.129623 | ||||||||
\(476\) | 5.92445 | 0.271547 | ||||||||
\(477\) | −1.91658 | −0.0877541 | ||||||||
\(478\) | 21.3084 | 0.974622 | ||||||||
\(479\) | 21.6908 | 0.991079 | 0.495539 | − | 0.868585i | \(-0.334970\pi\) | ||||
0.495539 | + | 0.868585i | \(0.334970\pi\) | |||||||
\(480\) | 71.0561 | 3.24325 | ||||||||
\(481\) | −23.3046 | −1.06260 | ||||||||
\(482\) | −49.5022 | −2.25476 | ||||||||
\(483\) | −18.5122 | −0.842335 | ||||||||
\(484\) | −45.6992 | −2.07724 | ||||||||
\(485\) | −11.7907 | −0.535387 | ||||||||
\(486\) | 6.39212 | 0.289952 | ||||||||
\(487\) | −35.9859 | −1.63068 | −0.815338 | − | 0.578986i | \(-0.803449\pi\) | ||||
−0.815338 | + | 0.578986i | \(0.803449\pi\) | |||||||
\(488\) | 9.19682 | 0.416321 | ||||||||
\(489\) | −17.8301 | −0.806304 | ||||||||
\(490\) | 18.2034 | 0.822348 | ||||||||
\(491\) | −24.6591 | −1.11285 | −0.556426 | − | 0.830897i | \(-0.687828\pi\) | ||||
−0.556426 | + | 0.830897i | \(0.687828\pi\) | |||||||
\(492\) | −28.1789 | −1.27040 | ||||||||
\(493\) | −4.82576 | −0.217341 | ||||||||
\(494\) | 8.37564 | 0.376838 | ||||||||
\(495\) | −0.573992 | −0.0257990 | ||||||||
\(496\) | 84.6208 | 3.79958 | ||||||||
\(497\) | −19.1472 | −0.858871 | ||||||||
\(498\) | 60.6307 | 2.71693 | ||||||||
\(499\) | −22.2571 | −0.996363 | −0.498181 | − | 0.867073i | \(-0.665999\pi\) | ||||
−0.498181 | + | 0.867073i | \(0.665999\pi\) | |||||||
\(500\) | −66.8048 | −2.98760 | ||||||||
\(501\) | −0.00957723 | −0.000427879 0 | ||||||||
\(502\) | −39.6163 | −1.76816 | ||||||||
\(503\) | −4.03338 | −0.179840 | −0.0899199 | − | 0.995949i | \(-0.528661\pi\) | ||||
−0.0899199 | + | 0.995949i | \(0.528661\pi\) | |||||||
\(504\) | −3.74914 | −0.167000 | ||||||||
\(505\) | −16.4317 | −0.731201 | ||||||||
\(506\) | 34.0208 | 1.51241 | ||||||||
\(507\) | 6.65735 | 0.295663 | ||||||||
\(508\) | −29.7282 | −1.31898 | ||||||||
\(509\) | −38.4965 | −1.70633 | −0.853163 | − | 0.521644i | \(-0.825319\pi\) | ||||
−0.853163 | + | 0.521644i | \(0.825319\pi\) | |||||||
\(510\) | −4.37411 | −0.193689 | ||||||||
\(511\) | 14.1811 | 0.627333 | ||||||||
\(512\) | −139.040 | −6.14475 | ||||||||
\(513\) | −5.36941 | −0.237065 | ||||||||
\(514\) | −52.6672 | −2.32305 | ||||||||
\(515\) | −5.71906 | −0.252012 | ||||||||
\(516\) | 114.237 | 5.02898 | ||||||||
\(517\) | 18.6702 | 0.821114 | ||||||||
\(518\) | −34.7919 | −1.52867 | ||||||||
\(519\) | −5.92656 | −0.260147 | ||||||||
\(520\) | −46.8010 | −2.05236 | ||||||||
\(521\) | 44.2293 | 1.93772 | 0.968860 | − | 0.247608i | \(-0.0796444\pi\) | ||||
0.968860 | + | 0.247608i | \(0.0796444\pi\) | |||||||
\(522\) | 4.66586 | 0.204219 | ||||||||
\(523\) | −26.5160 | −1.15947 | −0.579733 | − | 0.814807i | \(-0.696843\pi\) | ||||
−0.579733 | + | 0.814807i | \(0.696843\pi\) | |||||||
\(524\) | 80.2724 | 3.50671 | ||||||||
\(525\) | −7.56072 | −0.329977 | ||||||||
\(526\) | 22.4648 | 0.979514 | ||||||||
\(527\) | −3.00803 | −0.131032 | ||||||||
\(528\) | −52.6873 | −2.29292 | ||||||||
\(529\) | 24.8463 | 1.08027 | ||||||||
\(530\) | −35.7180 | −1.55149 | ||||||||
\(531\) | 1.99573 | 0.0866075 | ||||||||
\(532\) | 9.29341 | 0.402920 | ||||||||
\(533\) | 8.76297 | 0.379566 | ||||||||
\(534\) | −20.2591 | −0.876698 | ||||||||
\(535\) | 10.0491 | 0.434460 | ||||||||
\(536\) | −56.8243 | −2.45444 | ||||||||
\(537\) | 7.09018 | 0.305964 | ||||||||
\(538\) | −72.8913 | −3.14257 | ||||||||
\(539\) | −7.79425 | −0.335722 | ||||||||
\(540\) | 45.8402 | 1.97265 | ||||||||
\(541\) | −33.1555 | −1.42547 | −0.712734 | − | 0.701435i | \(-0.752543\pi\) | ||||
−0.712734 | + | 0.701435i | \(0.752543\pi\) | |||||||
\(542\) | 38.1546 | 1.63888 | ||||||||
\(543\) | 43.0984 | 1.84953 | ||||||||
\(544\) | 18.4245 | 0.789944 | ||||||||
\(545\) | 18.1598 | 0.777879 | ||||||||
\(546\) | −22.4157 | −0.959304 | ||||||||
\(547\) | 13.5577 | 0.579687 | 0.289843 | − | 0.957074i | \(-0.406397\pi\) | ||||
0.289843 | + | 0.957074i | \(0.406397\pi\) | |||||||
\(548\) | −15.1596 | −0.647585 | ||||||||
\(549\) | 0.192082 | 0.00819786 | ||||||||
\(550\) | 13.8947 | 0.592472 | ||||||||
\(551\) | −7.56995 | −0.322491 | ||||||||
\(552\) | −121.936 | −5.18994 | ||||||||
\(553\) | −13.2409 | −0.563061 | ||||||||
\(554\) | 32.0499 | 1.36167 | ||||||||
\(555\) | 19.0915 | 0.810389 | ||||||||
\(556\) | −80.7172 | −3.42317 | ||||||||
\(557\) | −19.2303 | −0.814814 | −0.407407 | − | 0.913247i | \(-0.633567\pi\) | ||||
−0.407407 | + | 0.913247i | \(0.633567\pi\) | |||||||
\(558\) | 2.90836 | 0.123121 | ||||||||
\(559\) | −35.5249 | −1.50254 | ||||||||
\(560\) | −42.4590 | −1.79422 | ||||||||
\(561\) | 1.87288 | 0.0790732 | ||||||||
\(562\) | 2.33027 | 0.0982966 | ||||||||
\(563\) | −29.7936 | −1.25565 | −0.627825 | − | 0.778354i | \(-0.716055\pi\) | ||||
−0.627825 | + | 0.778354i | \(0.716055\pi\) | |||||||
\(564\) | −102.240 | −4.30507 | ||||||||
\(565\) | −22.8230 | −0.960169 | ||||||||
\(566\) | −78.9510 | −3.31856 | ||||||||
\(567\) | 13.3065 | 0.558820 | ||||||||
\(568\) | −126.119 | −5.29183 | ||||||||
\(569\) | −0.302431 | −0.0126786 | −0.00633928 | − | 0.999980i | \(-0.502018\pi\) | ||||
−0.00633928 | + | 0.999980i | \(0.502018\pi\) | |||||||
\(570\) | −6.86147 | −0.287395 | ||||||||
\(571\) | 8.20964 | 0.343563 | 0.171781 | − | 0.985135i | \(-0.445048\pi\) | ||||
0.171781 | + | 0.985135i | \(0.445048\pi\) | |||||||
\(572\) | 30.6167 | 1.28015 | ||||||||
\(573\) | −38.0624 | −1.59008 | ||||||||
\(574\) | 13.0824 | 0.546050 | ||||||||
\(575\) | 19.5413 | 0.814927 | ||||||||
\(576\) | −9.89267 | −0.412195 | ||||||||
\(577\) | 32.4061 | 1.34908 | 0.674542 | − | 0.738236i | \(-0.264341\pi\) | ||||
0.674542 | + | 0.738236i | \(0.264341\pi\) | |||||||
\(578\) | 46.3105 | 1.92626 | ||||||||
\(579\) | −16.6410 | −0.691578 | ||||||||
\(580\) | 64.6268 | 2.68348 | ||||||||
\(581\) | −20.9207 | −0.867939 | ||||||||
\(582\) | −37.1971 | −1.54187 | ||||||||
\(583\) | 15.2935 | 0.633393 | ||||||||
\(584\) | 93.4076 | 3.86523 | ||||||||
\(585\) | −0.977471 | −0.0404135 | ||||||||
\(586\) | −11.0126 | −0.454925 | ||||||||
\(587\) | 34.9183 | 1.44123 | 0.720617 | − | 0.693333i | \(-0.243859\pi\) | ||||
0.720617 | + | 0.693333i | \(0.243859\pi\) | |||||||
\(588\) | 42.6820 | 1.76018 | ||||||||
\(589\) | −4.71855 | −0.194425 | ||||||||
\(590\) | 37.1932 | 1.53122 | ||||||||
\(591\) | 20.3088 | 0.835392 | ||||||||
\(592\) | −139.261 | −5.72359 | ||||||||
\(593\) | 33.1001 | 1.35926 | 0.679630 | − | 0.733555i | \(-0.262140\pi\) | ||||
0.679630 | + | 0.733555i | \(0.262140\pi\) | |||||||
\(594\) | −26.4087 | −1.08356 | ||||||||
\(595\) | 1.50930 | 0.0618751 | ||||||||
\(596\) | −94.2135 | −3.85914 | ||||||||
\(597\) | −32.9274 | −1.34763 | ||||||||
\(598\) | 57.9351 | 2.36914 | ||||||||
\(599\) | −48.0981 | −1.96523 | −0.982617 | − | 0.185642i | \(-0.940563\pi\) | ||||
−0.982617 | + | 0.185642i | \(0.940563\pi\) | |||||||
\(600\) | −49.8008 | −2.03311 | ||||||||
\(601\) | −28.7990 | −1.17473 | −0.587367 | − | 0.809320i | \(-0.699836\pi\) | ||||
−0.587367 | + | 0.809320i | \(0.699836\pi\) | |||||||
\(602\) | −53.0358 | −2.16158 | ||||||||
\(603\) | −1.18681 | −0.0483308 | ||||||||
\(604\) | −73.3030 | −2.98266 | ||||||||
\(605\) | −11.6422 | −0.473323 | ||||||||
\(606\) | −51.8387 | −2.10580 | ||||||||
\(607\) | −30.0228 | −1.21859 | −0.609294 | − | 0.792945i | \(-0.708547\pi\) | ||||
−0.609294 | + | 0.792945i | \(0.708547\pi\) | |||||||
\(608\) | 28.9017 | 1.17212 | ||||||||
\(609\) | 20.2594 | 0.820953 | ||||||||
\(610\) | 3.57970 | 0.144938 | ||||||||
\(611\) | 31.7941 | 1.28625 | ||||||||
\(612\) | 0.815024 | 0.0329454 | ||||||||
\(613\) | −39.5554 | −1.59763 | −0.798814 | − | 0.601579i | \(-0.794539\pi\) | ||||
−0.798814 | + | 0.601579i | \(0.794539\pi\) | |||||||
\(614\) | 21.6998 | 0.875731 | ||||||||
\(615\) | −7.17878 | −0.289476 | ||||||||
\(616\) | 29.9166 | 1.20538 | ||||||||
\(617\) | 8.56120 | 0.344661 | 0.172331 | − | 0.985039i | \(-0.444870\pi\) | ||||
0.172331 | + | 0.985039i | \(0.444870\pi\) | |||||||
\(618\) | −18.0425 | −0.725774 | ||||||||
\(619\) | −11.0026 | −0.442231 | −0.221116 | − | 0.975248i | \(-0.570970\pi\) | ||||
−0.221116 | + | 0.975248i | \(0.570970\pi\) | |||||||
\(620\) | 40.2836 | 1.61783 | ||||||||
\(621\) | −37.1407 | −1.49041 | ||||||||
\(622\) | −36.6114 | −1.46799 | ||||||||
\(623\) | 6.99045 | 0.280066 | ||||||||
\(624\) | −89.7230 | −3.59180 | ||||||||
\(625\) | −2.89368 | −0.115747 | ||||||||
\(626\) | 46.4431 | 1.85624 | ||||||||
\(627\) | 2.93791 | 0.117329 | ||||||||
\(628\) | 99.5494 | 3.97245 | ||||||||
\(629\) | 4.95033 | 0.197383 | ||||||||
\(630\) | −1.45929 | −0.0581394 | ||||||||
\(631\) | 11.3136 | 0.450387 | 0.225194 | − | 0.974314i | \(-0.427698\pi\) | ||||
0.225194 | + | 0.974314i | \(0.427698\pi\) | |||||||
\(632\) | −87.2152 | −3.46923 | ||||||||
\(633\) | −35.0920 | −1.39478 | ||||||||
\(634\) | 2.79086 | 0.110839 | ||||||||
\(635\) | −7.57348 | −0.300544 | ||||||||
\(636\) | −83.7487 | −3.32085 | ||||||||
\(637\) | −13.2731 | −0.525899 | ||||||||
\(638\) | −37.2317 | −1.47402 | ||||||||
\(639\) | −2.63408 | −0.104203 | ||||||||
\(640\) | −99.1167 | −3.91793 | ||||||||
\(641\) | −3.43862 | −0.135817 | −0.0679087 | − | 0.997692i | \(-0.521633\pi\) | ||||
−0.0679087 | + | 0.997692i | \(0.521633\pi\) | |||||||
\(642\) | 31.7028 | 1.25121 | ||||||||
\(643\) | −3.44233 | −0.135752 | −0.0678762 | − | 0.997694i | \(-0.521622\pi\) | ||||
−0.0678762 | + | 0.997694i | \(0.521622\pi\) | |||||||
\(644\) | 64.2834 | 2.53312 | ||||||||
\(645\) | 29.1026 | 1.14591 | ||||||||
\(646\) | −1.77914 | −0.0699995 | ||||||||
\(647\) | −14.6929 | −0.577639 | −0.288820 | − | 0.957384i | \(-0.593263\pi\) | ||||
−0.288820 | + | 0.957384i | \(0.593263\pi\) | |||||||
\(648\) | 87.6470 | 3.44310 | ||||||||
\(649\) | −15.9252 | −0.625117 | ||||||||
\(650\) | 23.6617 | 0.928090 | ||||||||
\(651\) | 12.6282 | 0.494940 | ||||||||
\(652\) | 61.9148 | 2.42477 | ||||||||
\(653\) | 15.6734 | 0.613346 | 0.306673 | − | 0.951815i | \(-0.400784\pi\) | ||||
0.306673 | + | 0.951815i | \(0.400784\pi\) | |||||||
\(654\) | 57.2904 | 2.24023 | ||||||||
\(655\) | 20.4500 | 0.799046 | ||||||||
\(656\) | 52.3648 | 2.04450 | ||||||||
\(657\) | 1.95088 | 0.0761111 | ||||||||
\(658\) | 47.4661 | 1.85042 | ||||||||
\(659\) | −33.1709 | −1.29215 | −0.646077 | − | 0.763272i | \(-0.723591\pi\) | ||||
−0.646077 | + | 0.763272i | \(0.723591\pi\) | |||||||
\(660\) | −25.0817 | −0.976305 | ||||||||
\(661\) | −6.98589 | −0.271719 | −0.135860 | − | 0.990728i | \(-0.543380\pi\) | ||||
−0.135860 | + | 0.990728i | \(0.543380\pi\) | |||||||
\(662\) | 40.0177 | 1.55533 | ||||||||
\(663\) | 3.18940 | 0.123866 | ||||||||
\(664\) | −137.801 | −5.34770 | ||||||||
\(665\) | 2.36756 | 0.0918102 | ||||||||
\(666\) | −4.78631 | −0.185466 | ||||||||
\(667\) | −52.3621 | −2.02747 | ||||||||
\(668\) | 0.0332568 | 0.00128674 | ||||||||
\(669\) | 13.6719 | 0.528587 | ||||||||
\(670\) | −22.1179 | −0.854487 | ||||||||
\(671\) | −1.53274 | −0.0591707 | ||||||||
\(672\) | −77.3494 | −2.98382 | ||||||||
\(673\) | 27.2023 | 1.04857 | 0.524285 | − | 0.851543i | \(-0.324333\pi\) | ||||
0.524285 | + | 0.851543i | \(0.324333\pi\) | |||||||
\(674\) | −13.3070 | −0.512566 | ||||||||
\(675\) | −15.1689 | −0.583853 | ||||||||
\(676\) | −23.1176 | −0.889137 | ||||||||
\(677\) | 5.00982 | 0.192543 | 0.0962716 | − | 0.995355i | \(-0.469308\pi\) | ||||
0.0962716 | + | 0.995355i | \(0.469308\pi\) | |||||||
\(678\) | −72.0018 | −2.76521 | ||||||||
\(679\) | 12.8349 | 0.492560 | ||||||||
\(680\) | 9.94141 | 0.381236 | ||||||||
\(681\) | 21.3580 | 0.818438 | ||||||||
\(682\) | −23.2075 | −0.888662 | ||||||||
\(683\) | −0.454863 | −0.0174048 | −0.00870242 | − | 0.999962i | \(-0.502770\pi\) | ||||
−0.00870242 | + | 0.999962i | \(0.502770\pi\) | |||||||
\(684\) | 1.27849 | 0.0488843 | ||||||||
\(685\) | −3.86201 | −0.147560 | ||||||||
\(686\) | −51.1785 | −1.95400 | ||||||||
\(687\) | 33.3034 | 1.27061 | ||||||||
\(688\) | −212.286 | −8.09332 | ||||||||
\(689\) | 26.0439 | 0.992193 | ||||||||
\(690\) | −47.4615 | −1.80683 | ||||||||
\(691\) | 16.3220 | 0.620916 | 0.310458 | − | 0.950587i | \(-0.399518\pi\) | ||||
0.310458 | + | 0.950587i | \(0.399518\pi\) | |||||||
\(692\) | 20.5799 | 0.782330 | ||||||||
\(693\) | 0.624829 | 0.0237353 | ||||||||
\(694\) | −89.7509 | −3.40690 | ||||||||
\(695\) | −20.5633 | −0.780010 | ||||||||
\(696\) | 133.445 | 5.05820 | ||||||||
\(697\) | −1.86142 | −0.0705063 | ||||||||
\(698\) | −23.5142 | −0.890027 | ||||||||
\(699\) | −19.4928 | −0.737286 | ||||||||
\(700\) | 26.2545 | 0.992327 | ||||||||
\(701\) | 4.38283 | 0.165537 | 0.0827687 | − | 0.996569i | \(-0.473624\pi\) | ||||
0.0827687 | + | 0.996569i | \(0.473624\pi\) | |||||||
\(702\) | −44.9723 | −1.69737 | ||||||||
\(703\) | 7.76535 | 0.292876 | ||||||||
\(704\) | 78.9395 | 2.97515 | ||||||||
\(705\) | −26.0463 | −0.980960 | ||||||||
\(706\) | 82.7768 | 3.11535 | ||||||||
\(707\) | 17.8870 | 0.672711 | ||||||||
\(708\) | 87.2076 | 3.27746 | ||||||||
\(709\) | −26.2711 | −0.986632 | −0.493316 | − | 0.869850i | \(-0.664215\pi\) | ||||
−0.493316 | + | 0.869850i | \(0.664215\pi\) | |||||||
\(710\) | −49.0896 | −1.84230 | ||||||||
\(711\) | −1.82155 | −0.0683134 | ||||||||
\(712\) | 46.0446 | 1.72559 | ||||||||
\(713\) | −32.6387 | −1.22233 | ||||||||
\(714\) | 4.76152 | 0.178195 | ||||||||
\(715\) | 7.79983 | 0.291697 | ||||||||
\(716\) | −24.6206 | −0.920114 | ||||||||
\(717\) | 12.7282 | 0.475344 | ||||||||
\(718\) | −47.8678 | −1.78641 | ||||||||
\(719\) | −39.4160 | −1.46997 | −0.734985 | − | 0.678083i | \(-0.762811\pi\) | ||||
−0.734985 | + | 0.678083i | \(0.762811\pi\) | |||||||
\(720\) | −5.84107 | −0.217684 | ||||||||
\(721\) | 6.22559 | 0.231853 | ||||||||
\(722\) | −2.79086 | −0.103865 | ||||||||
\(723\) | −29.5693 | −1.09970 | ||||||||
\(724\) | −149.659 | −5.56203 | ||||||||
\(725\) | −21.3856 | −0.794241 | ||||||||
\(726\) | −36.7287 | −1.36313 | ||||||||
\(727\) | −9.70602 | −0.359976 | −0.179988 | − | 0.983669i | \(-0.557606\pi\) | ||||
−0.179988 | + | 0.983669i | \(0.557606\pi\) | |||||||
\(728\) | 50.9461 | 1.88819 | ||||||||
\(729\) | 28.6842 | 1.06238 | ||||||||
\(730\) | 36.3573 | 1.34564 | ||||||||
\(731\) | 7.54615 | 0.279104 | ||||||||
\(732\) | 8.39340 | 0.310229 | ||||||||
\(733\) | −25.1275 | −0.928106 | −0.464053 | − | 0.885808i | \(-0.653605\pi\) | ||||
−0.464053 | + | 0.885808i | \(0.653605\pi\) | |||||||
\(734\) | −22.5091 | −0.830827 | ||||||||
\(735\) | 10.8735 | 0.401077 | ||||||||
\(736\) | 199.916 | 7.36899 | ||||||||
\(737\) | 9.47030 | 0.348843 | ||||||||
\(738\) | 1.79974 | 0.0662495 | ||||||||
\(739\) | −4.66784 | −0.171709 | −0.0858546 | − | 0.996308i | \(-0.527362\pi\) | ||||
−0.0858546 | + | 0.996308i | \(0.527362\pi\) | |||||||
\(740\) | −66.2950 | −2.43705 | ||||||||
\(741\) | 5.00306 | 0.183792 | ||||||||
\(742\) | 38.8815 | 1.42738 | ||||||||
\(743\) | 4.75426 | 0.174417 | 0.0872085 | − | 0.996190i | \(-0.472205\pi\) | ||||
0.0872085 | + | 0.996190i | \(0.472205\pi\) | |||||||
\(744\) | 83.1796 | 3.04951 | ||||||||
\(745\) | −24.0016 | −0.879350 | ||||||||
\(746\) | −9.14494 | −0.334820 | ||||||||
\(747\) | −2.87806 | −0.105303 | ||||||||
\(748\) | −6.50356 | −0.237794 | ||||||||
\(749\) | −10.9391 | −0.399706 | ||||||||
\(750\) | −53.6915 | −1.96053 | ||||||||
\(751\) | 4.10506 | 0.149796 | 0.0748979 | − | 0.997191i | \(-0.476137\pi\) | ||||
0.0748979 | + | 0.997191i | \(0.476137\pi\) | |||||||
\(752\) | 189.992 | 6.92829 | ||||||||
\(753\) | −23.6642 | −0.862371 | ||||||||
\(754\) | −63.4032 | −2.30901 | ||||||||
\(755\) | −18.6745 | −0.679634 | ||||||||
\(756\) | −49.9001 | −1.81485 | ||||||||
\(757\) | 16.6814 | 0.606296 | 0.303148 | − | 0.952943i | \(-0.401962\pi\) | ||||
0.303148 | + | 0.952943i | \(0.401962\pi\) | |||||||
\(758\) | −29.3399 | −1.06567 | ||||||||
\(759\) | 20.3218 | 0.737634 | ||||||||
\(760\) | 15.5946 | 0.565677 | ||||||||
\(761\) | −40.2784 | −1.46009 | −0.730046 | − | 0.683398i | \(-0.760501\pi\) | ||||
−0.730046 | + | 0.683398i | \(0.760501\pi\) | |||||||
\(762\) | −23.8928 | −0.865544 | ||||||||
\(763\) | −19.7681 | −0.715655 | ||||||||
\(764\) | 132.171 | 4.78178 | ||||||||
\(765\) | 0.207633 | 0.00750699 | ||||||||
\(766\) | 53.0125 | 1.91542 | ||||||||
\(767\) | −27.1195 | −0.979228 | ||||||||
\(768\) | −163.345 | −5.89421 | ||||||||
\(769\) | 12.8078 | 0.461862 | 0.230931 | − | 0.972970i | \(-0.425823\pi\) | ||||
0.230931 | + | 0.972970i | \(0.425823\pi\) | |||||||
\(770\) | 11.6445 | 0.419640 | ||||||||
\(771\) | −31.4600 | −1.13300 | ||||||||
\(772\) | 57.7858 | 2.07976 | ||||||||
\(773\) | −2.57445 | −0.0925966 | −0.0462983 | − | 0.998928i | \(-0.514742\pi\) | ||||
−0.0462983 | + | 0.998928i | \(0.514742\pi\) | |||||||
\(774\) | −7.29612 | −0.262253 | ||||||||
\(775\) | −13.3302 | −0.478836 | ||||||||
\(776\) | 84.5410 | 3.03485 | ||||||||
\(777\) | −20.7824 | −0.745564 | ||||||||
\(778\) | 26.4507 | 0.948303 | ||||||||
\(779\) | −2.91992 | −0.104617 | ||||||||
\(780\) | −42.7125 | −1.52935 | ||||||||
\(781\) | 21.0189 | 0.752115 | ||||||||
\(782\) | −12.3065 | −0.440080 | ||||||||
\(783\) | 40.6461 | 1.45257 | ||||||||
\(784\) | −79.3159 | −2.83271 | ||||||||
\(785\) | 25.3609 | 0.905170 | ||||||||
\(786\) | 64.5154 | 2.30119 | ||||||||
\(787\) | −41.2312 | −1.46973 | −0.734866 | − | 0.678212i | \(-0.762755\pi\) | ||||
−0.734866 | + | 0.678212i | \(0.762755\pi\) | |||||||
\(788\) | −70.5220 | −2.51224 | ||||||||
\(789\) | 13.4190 | 0.477730 | ||||||||
\(790\) | −33.9470 | −1.20778 | ||||||||
\(791\) | 24.8443 | 0.883363 | ||||||||
\(792\) | 4.11562 | 0.146242 | ||||||||
\(793\) | −2.61015 | −0.0926891 | ||||||||
\(794\) | 96.4202 | 3.42182 | ||||||||
\(795\) | −21.3356 | −0.756695 | ||||||||
\(796\) | 114.340 | 4.05268 | ||||||||
\(797\) | −20.5250 | −0.727034 | −0.363517 | − | 0.931588i | \(-0.618424\pi\) | ||||
−0.363517 | + | 0.931588i | \(0.618424\pi\) | |||||||
\(798\) | 7.46918 | 0.264406 | ||||||||
\(799\) | −6.75367 | −0.238928 | ||||||||
\(800\) | 81.6491 | 2.88673 | ||||||||
\(801\) | 0.961673 | 0.0339790 | ||||||||
\(802\) | −72.0698 | −2.54487 | ||||||||
\(803\) | −15.5673 | −0.549356 | ||||||||
\(804\) | −51.8602 | −1.82897 | ||||||||
\(805\) | 16.3767 | 0.577202 | ||||||||
\(806\) | −39.5209 | −1.39206 | ||||||||
\(807\) | −43.5405 | −1.53270 | ||||||||
\(808\) | 117.818 | 4.14483 | ||||||||
\(809\) | −22.1283 | −0.777990 | −0.388995 | − | 0.921240i | \(-0.627178\pi\) | ||||
−0.388995 | + | 0.921240i | \(0.627178\pi\) | |||||||
\(810\) | 34.1151 | 1.19868 | ||||||||
\(811\) | 33.8533 | 1.18875 | 0.594375 | − | 0.804188i | \(-0.297399\pi\) | ||||
0.594375 | + | 0.804188i | \(0.297399\pi\) | |||||||
\(812\) | −70.3506 | −2.46882 | ||||||||
\(813\) | 22.7911 | 0.799318 | ||||||||
\(814\) | 38.1928 | 1.33866 | ||||||||
\(815\) | 15.7732 | 0.552512 | ||||||||
\(816\) | 19.0589 | 0.667194 | ||||||||
\(817\) | 11.8373 | 0.414135 | ||||||||
\(818\) | −99.8790 | −3.49219 | ||||||||
\(819\) | 1.06404 | 0.0371807 | ||||||||
\(820\) | 24.9282 | 0.870531 | ||||||||
\(821\) | 19.7718 | 0.690042 | 0.345021 | − | 0.938595i | \(-0.387872\pi\) | ||||
0.345021 | + | 0.938595i | \(0.387872\pi\) | |||||||
\(822\) | −12.1838 | −0.424960 | ||||||||
\(823\) | 22.2353 | 0.775075 | 0.387537 | − | 0.921854i | \(-0.373326\pi\) | ||||
0.387537 | + | 0.921854i | \(0.373326\pi\) | |||||||
\(824\) | 41.0066 | 1.42853 | ||||||||
\(825\) | 8.29978 | 0.288961 | ||||||||
\(826\) | −40.4873 | −1.40873 | ||||||||
\(827\) | 49.9926 | 1.73841 | 0.869206 | − | 0.494450i | \(-0.164631\pi\) | ||||
0.869206 | + | 0.494450i | \(0.164631\pi\) | |||||||
\(828\) | 8.84345 | 0.307331 | ||||||||
\(829\) | −33.0179 | −1.14676 | −0.573379 | − | 0.819290i | \(-0.694368\pi\) | ||||
−0.573379 | + | 0.819290i | \(0.694368\pi\) | |||||||
\(830\) | −53.6365 | −1.86175 | ||||||||
\(831\) | 19.1445 | 0.664115 | ||||||||
\(832\) | 134.429 | 4.66048 | ||||||||
\(833\) | 2.81945 | 0.0976883 | ||||||||
\(834\) | −64.8730 | −2.24637 | ||||||||
\(835\) | 0.00847241 | 0.000293200 0 | ||||||||
\(836\) | −10.2018 | −0.352838 | ||||||||
\(837\) | 25.3358 | 0.875735 | ||||||||
\(838\) | 105.129 | 3.63161 | ||||||||
\(839\) | 22.3431 | 0.771369 | 0.385684 | − | 0.922631i | \(-0.373965\pi\) | ||||
0.385684 | + | 0.922631i | \(0.373965\pi\) | |||||||
\(840\) | −41.7359 | −1.44003 | ||||||||
\(841\) | 28.3041 | 0.976002 | ||||||||
\(842\) | 12.7696 | 0.440069 | ||||||||
\(843\) | 1.39195 | 0.0479414 | ||||||||
\(844\) | 121.856 | 4.19447 | ||||||||
\(845\) | −5.88937 | −0.202600 | ||||||||
\(846\) | 6.52989 | 0.224502 | ||||||||
\(847\) | 12.6733 | 0.435460 | ||||||||
\(848\) | 155.630 | 5.34437 | ||||||||
\(849\) | −47.1602 | −1.61853 | ||||||||
\(850\) | −5.02620 | −0.172397 | ||||||||
\(851\) | 53.7137 | 1.84128 | ||||||||
\(852\) | −115.101 | −3.94331 | ||||||||
\(853\) | 16.1099 | 0.551592 | 0.275796 | − | 0.961216i | \(-0.411059\pi\) | ||||
0.275796 | + | 0.961216i | \(0.411059\pi\) | |||||||
\(854\) | −3.89675 | −0.133344 | ||||||||
\(855\) | 0.325705 | 0.0111389 | ||||||||
\(856\) | −72.0536 | −2.46274 | ||||||||
\(857\) | −49.2768 | −1.68326 | −0.841631 | − | 0.540053i | \(-0.818404\pi\) | ||||
−0.841631 | + | 0.540053i | \(0.818404\pi\) | |||||||
\(858\) | 24.6068 | 0.840064 | ||||||||
\(859\) | −38.3647 | −1.30899 | −0.654494 | − | 0.756067i | \(-0.727118\pi\) | ||||
−0.654494 | + | 0.756067i | \(0.727118\pi\) | |||||||
\(860\) | −101.058 | −3.44606 | ||||||||
\(861\) | 7.81458 | 0.266320 | ||||||||
\(862\) | 73.6734 | 2.50932 | ||||||||
\(863\) | 4.61485 | 0.157091 | 0.0785456 | − | 0.996911i | \(-0.474972\pi\) | ||||
0.0785456 | + | 0.996911i | \(0.474972\pi\) | |||||||
\(864\) | −155.185 | −5.27950 | ||||||||
\(865\) | 5.24288 | 0.178263 | ||||||||
\(866\) | 57.8656 | 1.96635 | ||||||||
\(867\) | 27.6628 | 0.939479 | ||||||||
\(868\) | −43.8514 | −1.48841 | ||||||||
\(869\) | 14.5352 | 0.493074 | ||||||||
\(870\) | 51.9410 | 1.76096 | ||||||||
\(871\) | 16.1273 | 0.546453 | ||||||||
\(872\) | −130.209 | −4.40942 | ||||||||
\(873\) | 1.76570 | 0.0597598 | ||||||||
\(874\) | −19.3047 | −0.652990 | ||||||||
\(875\) | 18.5263 | 0.626305 | ||||||||
\(876\) | 85.2476 | 2.88025 | ||||||||
\(877\) | −3.22479 | −0.108894 | −0.0544468 | − | 0.998517i | \(-0.517340\pi\) | ||||
−0.0544468 | + | 0.998517i | \(0.517340\pi\) | |||||||
\(878\) | 19.5647 | 0.660275 | ||||||||
\(879\) | −6.57819 | −0.221877 | ||||||||
\(880\) | 46.6094 | 1.57120 | ||||||||
\(881\) | −0.585620 | −0.0197300 | −0.00986502 | − | 0.999951i | \(-0.503140\pi\) | ||||
−0.00986502 | + | 0.999951i | \(0.503140\pi\) | |||||||
\(882\) | −2.72603 | −0.0917904 | ||||||||
\(883\) | −41.6107 | −1.40031 | −0.700155 | − | 0.713991i | \(-0.746886\pi\) | ||||
−0.700155 | + | 0.713991i | \(0.746886\pi\) | |||||||
\(884\) | −11.0751 | −0.372497 | ||||||||
\(885\) | 22.2168 | 0.746808 | ||||||||
\(886\) | 24.7275 | 0.830737 | ||||||||
\(887\) | 17.3700 | 0.583228 | 0.291614 | − | 0.956536i | \(-0.405808\pi\) | ||||
0.291614 | + | 0.956536i | \(0.405808\pi\) | |||||||
\(888\) | −136.889 | −4.59370 | ||||||||
\(889\) | 8.24424 | 0.276503 | ||||||||
\(890\) | 17.9221 | 0.600749 | ||||||||
\(891\) | −14.6072 | −0.489359 | ||||||||
\(892\) | −47.4756 | −1.58960 | ||||||||
\(893\) | −10.5942 | −0.354520 | ||||||||
\(894\) | −75.7200 | −2.53246 | ||||||||
\(895\) | −6.27227 | −0.209659 | ||||||||
\(896\) | 107.895 | 3.60453 | ||||||||
\(897\) | 34.6067 | 1.15548 | ||||||||
\(898\) | −50.2530 | −1.67697 | ||||||||
\(899\) | 35.7192 | 1.19130 | ||||||||
\(900\) | 3.61182 | 0.120394 | ||||||||
\(901\) | −5.53221 | −0.184305 | ||||||||
\(902\) | −14.3612 | −0.478177 | ||||||||
\(903\) | −31.6801 | −1.05425 | ||||||||
\(904\) | 163.644 | 5.44273 | ||||||||
\(905\) | −38.1267 | −1.26737 | ||||||||
\(906\) | −58.9141 | −1.95729 | ||||||||
\(907\) | −32.5385 | −1.08042 | −0.540211 | − | 0.841530i | \(-0.681656\pi\) | ||||
−0.540211 | + | 0.841530i | \(0.681656\pi\) | |||||||
\(908\) | −74.1652 | −2.46126 | ||||||||
\(909\) | 2.46071 | 0.0816166 | ||||||||
\(910\) | 19.8299 | 0.657354 | ||||||||
\(911\) | −32.8722 | −1.08910 | −0.544552 | − | 0.838727i | \(-0.683300\pi\) | ||||
−0.544552 | + | 0.838727i | \(0.683300\pi\) | |||||||
\(912\) | 29.8968 | 0.989981 | ||||||||
\(913\) | 22.9658 | 0.760056 | ||||||||
\(914\) | −70.9583 | −2.34709 | ||||||||
\(915\) | 2.13828 | 0.0706893 | ||||||||
\(916\) | −115.646 | −3.82104 | ||||||||
\(917\) | −22.2612 | −0.735129 | ||||||||
\(918\) | 9.55295 | 0.315294 | ||||||||
\(919\) | 58.0395 | 1.91455 | 0.957274 | − | 0.289182i | \(-0.0933834\pi\) | ||||
0.957274 | + | 0.289182i | \(0.0933834\pi\) | |||||||
\(920\) | 107.870 | 3.55636 | ||||||||
\(921\) | 12.9620 | 0.427113 | ||||||||
\(922\) | 88.6565 | 2.91975 | ||||||||
\(923\) | 35.7938 | 1.17817 | ||||||||
\(924\) | 27.3032 | 0.898208 | ||||||||
\(925\) | 21.9376 | 0.721305 | ||||||||
\(926\) | 93.8222 | 3.08319 | ||||||||
\(927\) | 0.856451 | 0.0281295 | ||||||||
\(928\) | −218.784 | −7.18193 | ||||||||
\(929\) | −32.0482 | −1.05147 | −0.525734 | − | 0.850649i | \(-0.676209\pi\) | ||||
−0.525734 | + | 0.850649i | \(0.676209\pi\) | |||||||
\(930\) | 32.3762 | 1.06166 | ||||||||
\(931\) | 4.42275 | 0.144950 | ||||||||
\(932\) | 67.6885 | 2.21721 | ||||||||
\(933\) | −21.8693 | −0.715968 | ||||||||
\(934\) | −47.0169 | −1.53844 | ||||||||
\(935\) | −1.65683 | −0.0541841 | ||||||||
\(936\) | 7.00863 | 0.229084 | ||||||||
\(937\) | 4.59366 | 0.150068 | 0.0750342 | − | 0.997181i | \(-0.476093\pi\) | ||||
0.0750342 | + | 0.997181i | \(0.476093\pi\) | |||||||
\(938\) | 24.0768 | 0.786135 | ||||||||
\(939\) | 27.7421 | 0.905328 | ||||||||
\(940\) | 90.4454 | 2.95000 | ||||||||
\(941\) | −7.13058 | −0.232450 | −0.116225 | − | 0.993223i | \(-0.537079\pi\) | ||||
−0.116225 | + | 0.993223i | \(0.537079\pi\) | |||||||
\(942\) | 80.0085 | 2.60682 | ||||||||
\(943\) | −20.1974 | −0.657718 | ||||||||
\(944\) | −162.058 | −5.27453 | ||||||||
\(945\) | −12.7124 | −0.413535 | ||||||||
\(946\) | 58.2201 | 1.89290 | ||||||||
\(947\) | −11.0836 | −0.360169 | −0.180084 | − | 0.983651i | \(-0.557637\pi\) | ||||
−0.180084 | + | 0.983651i | \(0.557637\pi\) | |||||||
\(948\) | −79.5962 | −2.58516 | ||||||||
\(949\) | −26.5100 | −0.860551 | ||||||||
\(950\) | −7.88437 | −0.255803 | ||||||||
\(951\) | 1.66708 | 0.0540587 | ||||||||
\(952\) | −10.8219 | −0.350740 | ||||||||
\(953\) | −17.2942 | −0.560214 | −0.280107 | − | 0.959969i | \(-0.590370\pi\) | ||||
−0.280107 | + | 0.959969i | \(0.590370\pi\) | |||||||
\(954\) | 5.34891 | 0.173177 | ||||||||
\(955\) | 33.6715 | 1.08959 | ||||||||
\(956\) | −44.1986 | −1.42949 | ||||||||
\(957\) | −22.2398 | −0.718910 | ||||||||
\(958\) | −60.5361 | −1.95583 | ||||||||
\(959\) | 4.20406 | 0.135756 | ||||||||
\(960\) | −110.126 | −3.55431 | ||||||||
\(961\) | −8.73528 | −0.281783 | ||||||||
\(962\) | 65.0398 | 2.09697 | ||||||||
\(963\) | −1.50489 | −0.0484944 | ||||||||
\(964\) | 102.679 | 3.30707 | ||||||||
\(965\) | 14.7213 | 0.473897 | ||||||||
\(966\) | 51.6650 | 1.66229 | ||||||||
\(967\) | −30.6001 | −0.984031 | −0.492016 | − | 0.870586i | \(-0.663740\pi\) | ||||
−0.492016 | + | 0.870586i | \(0.663740\pi\) | |||||||
\(968\) | 83.4765 | 2.68304 | ||||||||
\(969\) | −1.06274 | −0.0341403 | ||||||||
\(970\) | 32.9061 | 1.05655 | ||||||||
\(971\) | −54.1496 | −1.73774 | −0.868872 | − | 0.495036i | \(-0.835155\pi\) | ||||
−0.868872 | + | 0.495036i | \(0.835155\pi\) | |||||||
\(972\) | −13.2588 | −0.425275 | ||||||||
\(973\) | 22.3845 | 0.717616 | ||||||||
\(974\) | 100.432 | 3.21803 | ||||||||
\(975\) | 14.1340 | 0.452649 | ||||||||
\(976\) | −15.5975 | −0.499263 | ||||||||
\(977\) | 9.65440 | 0.308872 | 0.154436 | − | 0.988003i | \(-0.450644\pi\) | ||||
0.154436 | + | 0.988003i | \(0.450644\pi\) | |||||||
\(978\) | 49.7613 | 1.59119 | ||||||||
\(979\) | −7.67376 | −0.245255 | ||||||||
\(980\) | −37.7582 | −1.20614 | ||||||||
\(981\) | −2.71950 | −0.0868268 | ||||||||
\(982\) | 68.8202 | 2.19614 | ||||||||
\(983\) | 33.3082 | 1.06237 | 0.531183 | − | 0.847257i | \(-0.321748\pi\) | ||||
0.531183 | + | 0.847257i | \(0.321748\pi\) | |||||||
\(984\) | 51.4730 | 1.64090 | ||||||||
\(985\) | −17.9660 | −0.572444 | ||||||||
\(986\) | 13.4680 | 0.428909 | ||||||||
\(987\) | 28.3531 | 0.902491 | ||||||||
\(988\) | −17.3731 | −0.552711 | ||||||||
\(989\) | 81.8797 | 2.60362 | ||||||||
\(990\) | 1.60193 | 0.0509128 | ||||||||
\(991\) | 25.0874 | 0.796929 | 0.398464 | − | 0.917184i | \(-0.369543\pi\) | ||||
0.398464 | + | 0.917184i | \(0.369543\pi\) | |||||||
\(992\) | −136.374 | −4.32988 | ||||||||
\(993\) | 23.9040 | 0.758570 | ||||||||
\(994\) | 53.4373 | 1.69493 | ||||||||
\(995\) | 29.1290 | 0.923451 | ||||||||
\(996\) | −125.763 | −3.98494 | ||||||||
\(997\) | −26.4911 | −0.838982 | −0.419491 | − | 0.907760i | \(-0.637791\pi\) | ||||
−0.419491 | + | 0.907760i | \(0.637791\pi\) | |||||||
\(998\) | 62.1164 | 1.96626 | ||||||||
\(999\) | −41.6954 | −1.31918 |
(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 | 6023.2.a.b.1.1 | ✓ | 99 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6023.2.a.b.1.1 | ✓ | 99 | 1.1 | even | 1 | trivial |