Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8026,2,Mod(1,8026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8026, 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("8026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8026 = 2 \cdot 4013 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8026.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: | \(64.0879326623\) |
Analytic rank: | \(1\) |
Dimension: | \(71\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 8026.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −3.18837 | −1.84081 | −0.920404 | − | 0.390969i | \(-0.872140\pi\) | ||||
−0.920404 | + | 0.390969i | \(0.872140\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.76077 | 0.787438 | 0.393719 | − | 0.919231i | \(-0.371188\pi\) | ||||
0.393719 | + | 0.919231i | \(0.371188\pi\) | |||||||
\(6\) | −3.18837 | −1.30165 | ||||||||
\(7\) | −1.56118 | −0.590071 | −0.295036 | − | 0.955486i | \(-0.595332\pi\) | ||||
−0.295036 | + | 0.955486i | \(0.595332\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 7.16572 | 2.38857 | ||||||||
\(10\) | 1.76077 | 0.556803 | ||||||||
\(11\) | −1.60222 | −0.483089 | −0.241544 | − | 0.970390i | \(-0.577654\pi\) | ||||
−0.241544 | + | 0.970390i | \(0.577654\pi\) | |||||||
\(12\) | −3.18837 | −0.920404 | ||||||||
\(13\) | −5.05138 | −1.40100 | −0.700500 | − | 0.713652i | \(-0.747040\pi\) | ||||
−0.700500 | + | 0.713652i | \(0.747040\pi\) | |||||||
\(14\) | −1.56118 | −0.417243 | ||||||||
\(15\) | −5.61398 | −1.44952 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.05056 | −0.497335 | −0.248667 | − | 0.968589i | \(-0.579993\pi\) | ||||
−0.248667 | + | 0.968589i | \(0.579993\pi\) | |||||||
\(18\) | 7.16572 | 1.68898 | ||||||||
\(19\) | 4.32464 | 0.992141 | 0.496070 | − | 0.868282i | \(-0.334776\pi\) | ||||
0.496070 | + | 0.868282i | \(0.334776\pi\) | |||||||
\(20\) | 1.76077 | 0.393719 | ||||||||
\(21\) | 4.97763 | 1.08621 | ||||||||
\(22\) | −1.60222 | −0.341595 | ||||||||
\(23\) | 7.66530 | 1.59832 | 0.799162 | − | 0.601115i | \(-0.205277\pi\) | ||||
0.799162 | + | 0.601115i | \(0.205277\pi\) | |||||||
\(24\) | −3.18837 | −0.650824 | ||||||||
\(25\) | −1.89971 | −0.379941 | ||||||||
\(26\) | −5.05138 | −0.990657 | ||||||||
\(27\) | −13.2819 | −2.55610 | ||||||||
\(28\) | −1.56118 | −0.295036 | ||||||||
\(29\) | −0.340949 | −0.0633127 | −0.0316564 | − | 0.999499i | \(-0.510078\pi\) | ||||
−0.0316564 | + | 0.999499i | \(0.510078\pi\) | |||||||
\(30\) | −5.61398 | −1.02497 | ||||||||
\(31\) | −2.72687 | −0.489760 | −0.244880 | − | 0.969553i | \(-0.578749\pi\) | ||||
−0.244880 | + | 0.969553i | \(0.578749\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 5.10849 | 0.889274 | ||||||||
\(34\) | −2.05056 | −0.351669 | ||||||||
\(35\) | −2.74887 | −0.464645 | ||||||||
\(36\) | 7.16572 | 1.19429 | ||||||||
\(37\) | −0.830414 | −0.136519 | −0.0682596 | − | 0.997668i | \(-0.521745\pi\) | ||||
−0.0682596 | + | 0.997668i | \(0.521745\pi\) | |||||||
\(38\) | 4.32464 | 0.701549 | ||||||||
\(39\) | 16.1057 | 2.57897 | ||||||||
\(40\) | 1.76077 | 0.278401 | ||||||||
\(41\) | 6.18698 | 0.966244 | 0.483122 | − | 0.875553i | \(-0.339503\pi\) | ||||
0.483122 | + | 0.875553i | \(0.339503\pi\) | |||||||
\(42\) | 4.97763 | 0.768065 | ||||||||
\(43\) | 0.936856 | 0.142869 | 0.0714346 | − | 0.997445i | \(-0.477242\pi\) | ||||
0.0714346 | + | 0.997445i | \(0.477242\pi\) | |||||||
\(44\) | −1.60222 | −0.241544 | ||||||||
\(45\) | 12.6172 | 1.88085 | ||||||||
\(46\) | 7.66530 | 1.13019 | ||||||||
\(47\) | 7.09986 | 1.03562 | 0.517810 | − | 0.855495i | \(-0.326747\pi\) | ||||
0.517810 | + | 0.855495i | \(0.326747\pi\) | |||||||
\(48\) | −3.18837 | −0.460202 | ||||||||
\(49\) | −4.56271 | −0.651816 | ||||||||
\(50\) | −1.89971 | −0.268659 | ||||||||
\(51\) | 6.53796 | 0.915498 | ||||||||
\(52\) | −5.05138 | −0.700500 | ||||||||
\(53\) | 7.47223 | 1.02639 | 0.513195 | − | 0.858272i | \(-0.328462\pi\) | ||||
0.513195 | + | 0.858272i | \(0.328462\pi\) | |||||||
\(54\) | −13.2819 | −1.80743 | ||||||||
\(55\) | −2.82114 | −0.380402 | ||||||||
\(56\) | −1.56118 | −0.208622 | ||||||||
\(57\) | −13.7886 | −1.82634 | ||||||||
\(58\) | −0.340949 | −0.0447688 | ||||||||
\(59\) | −8.64683 | −1.12572 | −0.562861 | − | 0.826552i | \(-0.690299\pi\) | ||||
−0.562861 | + | 0.826552i | \(0.690299\pi\) | |||||||
\(60\) | −5.61398 | −0.724761 | ||||||||
\(61\) | −10.0752 | −1.29000 | −0.644999 | − | 0.764184i | \(-0.723142\pi\) | ||||
−0.644999 | + | 0.764184i | \(0.723142\pi\) | |||||||
\(62\) | −2.72687 | −0.346313 | ||||||||
\(63\) | −11.1870 | −1.40943 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −8.89429 | −1.10320 | ||||||||
\(66\) | 5.10849 | 0.628811 | ||||||||
\(67\) | 11.2757 | 1.37755 | 0.688775 | − | 0.724975i | \(-0.258149\pi\) | ||||
0.688775 | + | 0.724975i | \(0.258149\pi\) | |||||||
\(68\) | −2.05056 | −0.248667 | ||||||||
\(69\) | −24.4398 | −2.94221 | ||||||||
\(70\) | −2.74887 | −0.328553 | ||||||||
\(71\) | −3.38843 | −0.402133 | −0.201066 | − | 0.979578i | \(-0.564441\pi\) | ||||
−0.201066 | + | 0.979578i | \(0.564441\pi\) | |||||||
\(72\) | 7.16572 | 0.844488 | ||||||||
\(73\) | −7.23868 | −0.847223 | −0.423611 | − | 0.905844i | \(-0.639238\pi\) | ||||
−0.423611 | + | 0.905844i | \(0.639238\pi\) | |||||||
\(74\) | −0.830414 | −0.0965337 | ||||||||
\(75\) | 6.05697 | 0.699399 | ||||||||
\(76\) | 4.32464 | 0.496070 | ||||||||
\(77\) | 2.50136 | 0.285057 | ||||||||
\(78\) | 16.1057 | 1.82361 | ||||||||
\(79\) | −1.04892 | −0.118012 | −0.0590062 | − | 0.998258i | \(-0.518793\pi\) | ||||
−0.0590062 | + | 0.998258i | \(0.518793\pi\) | |||||||
\(80\) | 1.76077 | 0.196860 | ||||||||
\(81\) | 20.8504 | 2.31671 | ||||||||
\(82\) | 6.18698 | 0.683238 | ||||||||
\(83\) | 1.10682 | 0.121489 | 0.0607447 | − | 0.998153i | \(-0.480652\pi\) | ||||
0.0607447 | + | 0.998153i | \(0.480652\pi\) | |||||||
\(84\) | 4.97763 | 0.543104 | ||||||||
\(85\) | −3.61056 | −0.391620 | ||||||||
\(86\) | 0.936856 | 0.101024 | ||||||||
\(87\) | 1.08707 | 0.116547 | ||||||||
\(88\) | −1.60222 | −0.170798 | ||||||||
\(89\) | −12.5594 | −1.33129 | −0.665645 | − | 0.746268i | \(-0.731844\pi\) | ||||
−0.665645 | + | 0.746268i | \(0.731844\pi\) | |||||||
\(90\) | 12.6172 | 1.32996 | ||||||||
\(91\) | 7.88612 | 0.826690 | ||||||||
\(92\) | 7.66530 | 0.799162 | ||||||||
\(93\) | 8.69427 | 0.901554 | ||||||||
\(94\) | 7.09986 | 0.732294 | ||||||||
\(95\) | 7.61468 | 0.781249 | ||||||||
\(96\) | −3.18837 | −0.325412 | ||||||||
\(97\) | 3.65708 | 0.371320 | 0.185660 | − | 0.982614i | \(-0.440558\pi\) | ||||
0.185660 | + | 0.982614i | \(0.440558\pi\) | |||||||
\(98\) | −4.56271 | −0.460904 | ||||||||
\(99\) | −11.4811 | −1.15389 | ||||||||
\(100\) | −1.89971 | −0.189971 | ||||||||
\(101\) | −9.15937 | −0.911392 | −0.455696 | − | 0.890136i | \(-0.650610\pi\) | ||||
−0.455696 | + | 0.890136i | \(0.650610\pi\) | |||||||
\(102\) | 6.53796 | 0.647355 | ||||||||
\(103\) | −0.368513 | −0.0363106 | −0.0181553 | − | 0.999835i | \(-0.505779\pi\) | ||||
−0.0181553 | + | 0.999835i | \(0.505779\pi\) | |||||||
\(104\) | −5.05138 | −0.495329 | ||||||||
\(105\) | 8.76444 | 0.855321 | ||||||||
\(106\) | 7.47223 | 0.725767 | ||||||||
\(107\) | 13.5248 | 1.30749 | 0.653746 | − | 0.756714i | \(-0.273196\pi\) | ||||
0.653746 | + | 0.756714i | \(0.273196\pi\) | |||||||
\(108\) | −13.2819 | −1.27805 | ||||||||
\(109\) | −2.12016 | −0.203074 | −0.101537 | − | 0.994832i | \(-0.532376\pi\) | ||||
−0.101537 | + | 0.994832i | \(0.532376\pi\) | |||||||
\(110\) | −2.82114 | −0.268985 | ||||||||
\(111\) | 2.64767 | 0.251306 | ||||||||
\(112\) | −1.56118 | −0.147518 | ||||||||
\(113\) | −13.0833 | −1.23078 | −0.615389 | − | 0.788224i | \(-0.711001\pi\) | ||||
−0.615389 | + | 0.788224i | \(0.711001\pi\) | |||||||
\(114\) | −13.7886 | −1.29142 | ||||||||
\(115\) | 13.4968 | 1.25858 | ||||||||
\(116\) | −0.340949 | −0.0316564 | ||||||||
\(117\) | −36.1968 | −3.34639 | ||||||||
\(118\) | −8.64683 | −0.796006 | ||||||||
\(119\) | 3.20130 | 0.293463 | ||||||||
\(120\) | −5.61398 | −0.512483 | ||||||||
\(121\) | −8.43288 | −0.766625 | ||||||||
\(122\) | −10.0752 | −0.912166 | ||||||||
\(123\) | −19.7264 | −1.77867 | ||||||||
\(124\) | −2.72687 | −0.244880 | ||||||||
\(125\) | −12.1488 | −1.08662 | ||||||||
\(126\) | −11.1870 | −0.996617 | ||||||||
\(127\) | −9.61584 | −0.853268 | −0.426634 | − | 0.904424i | \(-0.640301\pi\) | ||||
−0.426634 | + | 0.904424i | \(0.640301\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −2.98705 | −0.262995 | ||||||||
\(130\) | −8.89429 | −0.780081 | ||||||||
\(131\) | 10.6120 | 0.927174 | 0.463587 | − | 0.886051i | \(-0.346562\pi\) | ||||
0.463587 | + | 0.886051i | \(0.346562\pi\) | |||||||
\(132\) | 5.10849 | 0.444637 | ||||||||
\(133\) | −6.75155 | −0.585434 | ||||||||
\(134\) | 11.2757 | 0.974075 | ||||||||
\(135\) | −23.3863 | −2.01277 | ||||||||
\(136\) | −2.05056 | −0.175834 | ||||||||
\(137\) | 18.4358 | 1.57508 | 0.787538 | − | 0.616265i | \(-0.211355\pi\) | ||||
0.787538 | + | 0.616265i | \(0.211355\pi\) | |||||||
\(138\) | −24.4398 | −2.08046 | ||||||||
\(139\) | 12.3160 | 1.04463 | 0.522317 | − | 0.852751i | \(-0.325068\pi\) | ||||
0.522317 | + | 0.852751i | \(0.325068\pi\) | |||||||
\(140\) | −2.74887 | −0.232322 | ||||||||
\(141\) | −22.6370 | −1.90638 | ||||||||
\(142\) | −3.38843 | −0.284351 | ||||||||
\(143\) | 8.09344 | 0.676808 | ||||||||
\(144\) | 7.16572 | 0.597143 | ||||||||
\(145\) | −0.600332 | −0.0498548 | ||||||||
\(146\) | −7.23868 | −0.599077 | ||||||||
\(147\) | 14.5476 | 1.19987 | ||||||||
\(148\) | −0.830414 | −0.0682596 | ||||||||
\(149\) | 8.96690 | 0.734597 | 0.367298 | − | 0.930103i | \(-0.380283\pi\) | ||||
0.367298 | + | 0.930103i | \(0.380283\pi\) | |||||||
\(150\) | 6.05697 | 0.494550 | ||||||||
\(151\) | −11.0030 | −0.895412 | −0.447706 | − | 0.894181i | \(-0.647759\pi\) | ||||
−0.447706 | + | 0.894181i | \(0.647759\pi\) | |||||||
\(152\) | 4.32464 | 0.350775 | ||||||||
\(153\) | −14.6938 | −1.18792 | ||||||||
\(154\) | 2.50136 | 0.201566 | ||||||||
\(155\) | −4.80137 | −0.385656 | ||||||||
\(156\) | 16.1057 | 1.28949 | ||||||||
\(157\) | −9.92152 | −0.791824 | −0.395912 | − | 0.918289i | \(-0.629571\pi\) | ||||
−0.395912 | + | 0.918289i | \(0.629571\pi\) | |||||||
\(158\) | −1.04892 | −0.0834474 | ||||||||
\(159\) | −23.8243 | −1.88939 | ||||||||
\(160\) | 1.76077 | 0.139201 | ||||||||
\(161\) | −11.9669 | −0.943125 | ||||||||
\(162\) | 20.8504 | 1.63816 | ||||||||
\(163\) | 0.00712968 | 0.000558439 0 | 0.000279220 | − | 1.00000i | \(-0.499911\pi\) | ||||
0.000279220 | 1.00000i | \(0.499911\pi\) | ||||||||
\(164\) | 6.18698 | 0.483122 | ||||||||
\(165\) | 8.99485 | 0.700248 | ||||||||
\(166\) | 1.10682 | 0.0859060 | ||||||||
\(167\) | 15.8324 | 1.22515 | 0.612573 | − | 0.790414i | \(-0.290135\pi\) | ||||
0.612573 | + | 0.790414i | \(0.290135\pi\) | |||||||
\(168\) | 4.97763 | 0.384032 | ||||||||
\(169\) | 12.5164 | 0.962803 | ||||||||
\(170\) | −3.61056 | −0.276917 | ||||||||
\(171\) | 30.9892 | 2.36980 | ||||||||
\(172\) | 0.936856 | 0.0714346 | ||||||||
\(173\) | 11.3445 | 0.862503 | 0.431251 | − | 0.902232i | \(-0.358072\pi\) | ||||
0.431251 | + | 0.902232i | \(0.358072\pi\) | |||||||
\(174\) | 1.08707 | 0.0824108 | ||||||||
\(175\) | 2.96579 | 0.224192 | ||||||||
\(176\) | −1.60222 | −0.120772 | ||||||||
\(177\) | 27.5693 | 2.07224 | ||||||||
\(178\) | −12.5594 | −0.941364 | ||||||||
\(179\) | 11.5861 | 0.865987 | 0.432993 | − | 0.901397i | \(-0.357457\pi\) | ||||
0.432993 | + | 0.901397i | \(0.357457\pi\) | |||||||
\(180\) | 12.6172 | 0.940427 | ||||||||
\(181\) | −3.68403 | −0.273832 | −0.136916 | − | 0.990583i | \(-0.543719\pi\) | ||||
−0.136916 | + | 0.990583i | \(0.543719\pi\) | |||||||
\(182\) | 7.88612 | 0.584558 | ||||||||
\(183\) | 32.1235 | 2.37464 | ||||||||
\(184\) | 7.66530 | 0.565093 | ||||||||
\(185\) | −1.46216 | −0.107500 | ||||||||
\(186\) | 8.69427 | 0.637495 | ||||||||
\(187\) | 3.28546 | 0.240257 | ||||||||
\(188\) | 7.09986 | 0.517810 | ||||||||
\(189\) | 20.7354 | 1.50828 | ||||||||
\(190\) | 7.61468 | 0.552427 | ||||||||
\(191\) | −2.77288 | −0.200639 | −0.100319 | − | 0.994955i | \(-0.531986\pi\) | ||||
−0.100319 | + | 0.994955i | \(0.531986\pi\) | |||||||
\(192\) | −3.18837 | −0.230101 | ||||||||
\(193\) | −4.13574 | −0.297697 | −0.148849 | − | 0.988860i | \(-0.547557\pi\) | ||||
−0.148849 | + | 0.988860i | \(0.547557\pi\) | |||||||
\(194\) | 3.65708 | 0.262563 | ||||||||
\(195\) | 28.3583 | 2.03078 | ||||||||
\(196\) | −4.56271 | −0.325908 | ||||||||
\(197\) | −4.84442 | −0.345150 | −0.172575 | − | 0.984996i | \(-0.555209\pi\) | ||||
−0.172575 | + | 0.984996i | \(0.555209\pi\) | |||||||
\(198\) | −11.4811 | −0.815926 | ||||||||
\(199\) | −12.3355 | −0.874442 | −0.437221 | − | 0.899354i | \(-0.644037\pi\) | ||||
−0.437221 | + | 0.899354i | \(0.644037\pi\) | |||||||
\(200\) | −1.89971 | −0.134330 | ||||||||
\(201\) | −35.9512 | −2.53581 | ||||||||
\(202\) | −9.15937 | −0.644451 | ||||||||
\(203\) | 0.532284 | 0.0373590 | ||||||||
\(204\) | 6.53796 | 0.457749 | ||||||||
\(205\) | 10.8938 | 0.760857 | ||||||||
\(206\) | −0.368513 | −0.0256755 | ||||||||
\(207\) | 54.9274 | 3.81772 | ||||||||
\(208\) | −5.05138 | −0.350250 | ||||||||
\(209\) | −6.92904 | −0.479292 | ||||||||
\(210\) | 8.76444 | 0.604803 | ||||||||
\(211\) | −13.4414 | −0.925344 | −0.462672 | − | 0.886530i | \(-0.653109\pi\) | ||||
−0.462672 | + | 0.886530i | \(0.653109\pi\) | |||||||
\(212\) | 7.47223 | 0.513195 | ||||||||
\(213\) | 10.8036 | 0.740250 | ||||||||
\(214\) | 13.5248 | 0.924537 | ||||||||
\(215\) | 1.64958 | 0.112501 | ||||||||
\(216\) | −13.2819 | −0.903717 | ||||||||
\(217\) | 4.25714 | 0.288993 | ||||||||
\(218\) | −2.12016 | −0.143595 | ||||||||
\(219\) | 23.0796 | 1.55957 | ||||||||
\(220\) | −2.82114 | −0.190201 | ||||||||
\(221\) | 10.3582 | 0.696767 | ||||||||
\(222\) | 2.64767 | 0.177700 | ||||||||
\(223\) | −17.7707 | −1.19001 | −0.595007 | − | 0.803720i | \(-0.702851\pi\) | ||||
−0.595007 | + | 0.803720i | \(0.702851\pi\) | |||||||
\(224\) | −1.56118 | −0.104311 | ||||||||
\(225\) | −13.6128 | −0.907518 | ||||||||
\(226\) | −13.0833 | −0.870291 | ||||||||
\(227\) | 13.7933 | 0.915491 | 0.457745 | − | 0.889083i | \(-0.348657\pi\) | ||||
0.457745 | + | 0.889083i | \(0.348657\pi\) | |||||||
\(228\) | −13.7886 | −0.913170 | ||||||||
\(229\) | −13.2868 | −0.878018 | −0.439009 | − | 0.898483i | \(-0.644670\pi\) | ||||
−0.439009 | + | 0.898483i | \(0.644670\pi\) | |||||||
\(230\) | 13.4968 | 0.889952 | ||||||||
\(231\) | −7.97528 | −0.524735 | ||||||||
\(232\) | −0.340949 | −0.0223844 | ||||||||
\(233\) | −15.3937 | −1.00847 | −0.504236 | − | 0.863566i | \(-0.668226\pi\) | ||||
−0.504236 | + | 0.863566i | \(0.668226\pi\) | |||||||
\(234\) | −36.1968 | −2.36626 | ||||||||
\(235\) | 12.5012 | 0.815487 | ||||||||
\(236\) | −8.64683 | −0.562861 | ||||||||
\(237\) | 3.34434 | 0.217238 | ||||||||
\(238\) | 3.20130 | 0.207510 | ||||||||
\(239\) | −1.03722 | −0.0670921 | −0.0335460 | − | 0.999437i | \(-0.510680\pi\) | ||||
−0.0335460 | + | 0.999437i | \(0.510680\pi\) | |||||||
\(240\) | −5.61398 | −0.362381 | ||||||||
\(241\) | −16.3323 | −1.05206 | −0.526029 | − | 0.850467i | \(-0.676320\pi\) | ||||
−0.526029 | + | 0.850467i | \(0.676320\pi\) | |||||||
\(242\) | −8.43288 | −0.542086 | ||||||||
\(243\) | −26.6332 | −1.70852 | ||||||||
\(244\) | −10.0752 | −0.644999 | ||||||||
\(245\) | −8.03386 | −0.513265 | ||||||||
\(246\) | −19.7264 | −1.25771 | ||||||||
\(247\) | −21.8454 | −1.38999 | ||||||||
\(248\) | −2.72687 | −0.173156 | ||||||||
\(249\) | −3.52896 | −0.223639 | ||||||||
\(250\) | −12.1488 | −0.768355 | ||||||||
\(251\) | −19.2479 | −1.21492 | −0.607459 | − | 0.794351i | \(-0.707811\pi\) | ||||
−0.607459 | + | 0.794351i | \(0.707811\pi\) | |||||||
\(252\) | −11.1870 | −0.704714 | ||||||||
\(253\) | −12.2815 | −0.772133 | ||||||||
\(254\) | −9.61584 | −0.603351 | ||||||||
\(255\) | 11.5118 | 0.720898 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −11.2496 | −0.701733 | −0.350866 | − | 0.936426i | \(-0.614113\pi\) | ||||
−0.350866 | + | 0.936426i | \(0.614113\pi\) | |||||||
\(258\) | −2.98705 | −0.185965 | ||||||||
\(259\) | 1.29643 | 0.0805561 | ||||||||
\(260\) | −8.89429 | −0.551601 | ||||||||
\(261\) | −2.44315 | −0.151227 | ||||||||
\(262\) | 10.6120 | 0.655611 | ||||||||
\(263\) | 10.3469 | 0.638014 | 0.319007 | − | 0.947752i | \(-0.396651\pi\) | ||||
0.319007 | + | 0.947752i | \(0.396651\pi\) | |||||||
\(264\) | 5.10849 | 0.314406 | ||||||||
\(265\) | 13.1568 | 0.808219 | ||||||||
\(266\) | −6.75155 | −0.413964 | ||||||||
\(267\) | 40.0440 | 2.45065 | ||||||||
\(268\) | 11.2757 | 0.688775 | ||||||||
\(269\) | 26.3732 | 1.60801 | 0.804003 | − | 0.594626i | \(-0.202700\pi\) | ||||
0.804003 | + | 0.594626i | \(0.202700\pi\) | |||||||
\(270\) | −23.3863 | −1.42324 | ||||||||
\(271\) | −18.2888 | −1.11097 | −0.555484 | − | 0.831527i | \(-0.687467\pi\) | ||||
−0.555484 | + | 0.831527i | \(0.687467\pi\) | |||||||
\(272\) | −2.05056 | −0.124334 | ||||||||
\(273\) | −25.1439 | −1.52178 | ||||||||
\(274\) | 18.4358 | 1.11375 | ||||||||
\(275\) | 3.04376 | 0.183545 | ||||||||
\(276\) | −24.4398 | −1.47110 | ||||||||
\(277\) | −1.93375 | −0.116188 | −0.0580939 | − | 0.998311i | \(-0.518502\pi\) | ||||
−0.0580939 | + | 0.998311i | \(0.518502\pi\) | |||||||
\(278\) | 12.3160 | 0.738668 | ||||||||
\(279\) | −19.5400 | −1.16983 | ||||||||
\(280\) | −2.74887 | −0.164277 | ||||||||
\(281\) | −24.7920 | −1.47897 | −0.739484 | − | 0.673174i | \(-0.764930\pi\) | ||||
−0.739484 | + | 0.673174i | \(0.764930\pi\) | |||||||
\(282\) | −22.6370 | −1.34801 | ||||||||
\(283\) | −26.8377 | −1.59534 | −0.797669 | − | 0.603096i | \(-0.793934\pi\) | ||||
−0.797669 | + | 0.603096i | \(0.793934\pi\) | |||||||
\(284\) | −3.38843 | −0.201066 | ||||||||
\(285\) | −24.2784 | −1.43813 | ||||||||
\(286\) | 8.09344 | 0.478575 | ||||||||
\(287\) | −9.65900 | −0.570153 | ||||||||
\(288\) | 7.16572 | 0.422244 | ||||||||
\(289\) | −12.7952 | −0.752658 | ||||||||
\(290\) | −0.600332 | −0.0352527 | ||||||||
\(291\) | −11.6601 | −0.683529 | ||||||||
\(292\) | −7.23868 | −0.423611 | ||||||||
\(293\) | 19.2353 | 1.12374 | 0.561868 | − | 0.827227i | \(-0.310083\pi\) | ||||
0.561868 | + | 0.827227i | \(0.310083\pi\) | |||||||
\(294\) | 14.5476 | 0.848435 | ||||||||
\(295\) | −15.2250 | −0.886436 | ||||||||
\(296\) | −0.830414 | −0.0482668 | ||||||||
\(297\) | 21.2805 | 1.23482 | ||||||||
\(298\) | 8.96690 | 0.519438 | ||||||||
\(299\) | −38.7203 | −2.23925 | ||||||||
\(300\) | 6.05697 | 0.349699 | ||||||||
\(301\) | −1.46260 | −0.0843030 | ||||||||
\(302\) | −11.0030 | −0.633152 | ||||||||
\(303\) | 29.2035 | 1.67770 | ||||||||
\(304\) | 4.32464 | 0.248035 | ||||||||
\(305\) | −17.7401 | −1.01579 | ||||||||
\(306\) | −14.6938 | −0.839987 | ||||||||
\(307\) | −24.6003 | −1.40402 | −0.702008 | − | 0.712169i | \(-0.747713\pi\) | ||||
−0.702008 | + | 0.712169i | \(0.747713\pi\) | |||||||
\(308\) | 2.50136 | 0.142528 | ||||||||
\(309\) | 1.17496 | 0.0668409 | ||||||||
\(310\) | −4.80137 | −0.272700 | ||||||||
\(311\) | −32.0503 | −1.81741 | −0.908704 | − | 0.417441i | \(-0.862927\pi\) | ||||
−0.908704 | + | 0.417441i | \(0.862927\pi\) | |||||||
\(312\) | 16.1057 | 0.911805 | ||||||||
\(313\) | −3.16599 | −0.178952 | −0.0894762 | − | 0.995989i | \(-0.528519\pi\) | ||||
−0.0894762 | + | 0.995989i | \(0.528519\pi\) | |||||||
\(314\) | −9.92152 | −0.559904 | ||||||||
\(315\) | −19.6977 | −1.10984 | ||||||||
\(316\) | −1.04892 | −0.0590062 | ||||||||
\(317\) | −8.51115 | −0.478034 | −0.239017 | − | 0.971015i | \(-0.576825\pi\) | ||||
−0.239017 | + | 0.971015i | \(0.576825\pi\) | |||||||
\(318\) | −23.8243 | −1.33600 | ||||||||
\(319\) | 0.546277 | 0.0305857 | ||||||||
\(320\) | 1.76077 | 0.0984298 | ||||||||
\(321\) | −43.1221 | −2.40684 | ||||||||
\(322\) | −11.9669 | −0.666890 | ||||||||
\(323\) | −8.86796 | −0.493426 | ||||||||
\(324\) | 20.8504 | 1.15836 | ||||||||
\(325\) | 9.59614 | 0.532298 | ||||||||
\(326\) | 0.00712968 | 0.000394876 0 | ||||||||
\(327\) | 6.75985 | 0.373821 | ||||||||
\(328\) | 6.18698 | 0.341619 | ||||||||
\(329\) | −11.0842 | −0.611090 | ||||||||
\(330\) | 8.99485 | 0.495150 | ||||||||
\(331\) | 27.2826 | 1.49959 | 0.749794 | − | 0.661671i | \(-0.230152\pi\) | ||||
0.749794 | + | 0.661671i | \(0.230152\pi\) | |||||||
\(332\) | 1.10682 | 0.0607447 | ||||||||
\(333\) | −5.95052 | −0.326086 | ||||||||
\(334\) | 15.8324 | 0.866309 | ||||||||
\(335\) | 19.8539 | 1.08474 | ||||||||
\(336\) | 4.97763 | 0.271552 | ||||||||
\(337\) | 3.19555 | 0.174073 | 0.0870363 | − | 0.996205i | \(-0.472260\pi\) | ||||
0.0870363 | + | 0.996205i | \(0.472260\pi\) | |||||||
\(338\) | 12.5164 | 0.680805 | ||||||||
\(339\) | 41.7146 | 2.26563 | ||||||||
\(340\) | −3.61056 | −0.195810 | ||||||||
\(341\) | 4.36905 | 0.236598 | ||||||||
\(342\) | 30.9892 | 1.67570 | ||||||||
\(343\) | 18.0515 | 0.974689 | ||||||||
\(344\) | 0.936856 | 0.0505119 | ||||||||
\(345\) | −43.0328 | −2.31681 | ||||||||
\(346\) | 11.3445 | 0.609881 | ||||||||
\(347\) | −2.86923 | −0.154028 | −0.0770142 | − | 0.997030i | \(-0.524539\pi\) | ||||
−0.0770142 | + | 0.997030i | \(0.524539\pi\) | |||||||
\(348\) | 1.08707 | 0.0582733 | ||||||||
\(349\) | −11.0513 | −0.591565 | −0.295782 | − | 0.955255i | \(-0.595580\pi\) | ||||
−0.295782 | + | 0.955255i | \(0.595580\pi\) | |||||||
\(350\) | 2.96579 | 0.158528 | ||||||||
\(351\) | 67.0918 | 3.58110 | ||||||||
\(352\) | −1.60222 | −0.0853988 | ||||||||
\(353\) | −6.36400 | −0.338722 | −0.169361 | − | 0.985554i | \(-0.554170\pi\) | ||||
−0.169361 | + | 0.985554i | \(0.554170\pi\) | |||||||
\(354\) | 27.5693 | 1.46529 | ||||||||
\(355\) | −5.96623 | −0.316655 | ||||||||
\(356\) | −12.5594 | −0.665645 | ||||||||
\(357\) | −10.2069 | −0.540209 | ||||||||
\(358\) | 11.5861 | 0.612345 | ||||||||
\(359\) | −10.9510 | −0.577974 | −0.288987 | − | 0.957333i | \(-0.593318\pi\) | ||||
−0.288987 | + | 0.957333i | \(0.593318\pi\) | |||||||
\(360\) | 12.6172 | 0.664982 | ||||||||
\(361\) | −0.297477 | −0.0156567 | ||||||||
\(362\) | −3.68403 | −0.193629 | ||||||||
\(363\) | 26.8872 | 1.41121 | ||||||||
\(364\) | 7.88612 | 0.413345 | ||||||||
\(365\) | −12.7456 | −0.667136 | ||||||||
\(366\) | 32.1235 | 1.67912 | ||||||||
\(367\) | −2.58644 | −0.135011 | −0.0675055 | − | 0.997719i | \(-0.521504\pi\) | ||||
−0.0675055 | + | 0.997719i | \(0.521504\pi\) | |||||||
\(368\) | 7.66530 | 0.399581 | ||||||||
\(369\) | 44.3342 | 2.30794 | ||||||||
\(370\) | −1.46216 | −0.0760143 | ||||||||
\(371\) | −11.6655 | −0.605643 | ||||||||
\(372\) | 8.69427 | 0.450777 | ||||||||
\(373\) | −35.1217 | −1.81853 | −0.909266 | − | 0.416216i | \(-0.863356\pi\) | ||||
−0.909266 | + | 0.416216i | \(0.863356\pi\) | |||||||
\(374\) | 3.28546 | 0.169887 | ||||||||
\(375\) | 38.7348 | 2.00026 | ||||||||
\(376\) | 7.09986 | 0.366147 | ||||||||
\(377\) | 1.72226 | 0.0887012 | ||||||||
\(378\) | 20.7354 | 1.06651 | ||||||||
\(379\) | 6.14724 | 0.315762 | 0.157881 | − | 0.987458i | \(-0.449534\pi\) | ||||
0.157881 | + | 0.987458i | \(0.449534\pi\) | |||||||
\(380\) | 7.61468 | 0.390625 | ||||||||
\(381\) | 30.6589 | 1.57070 | ||||||||
\(382\) | −2.77288 | −0.141873 | ||||||||
\(383\) | −22.1836 | −1.13353 | −0.566764 | − | 0.823880i | \(-0.691805\pi\) | ||||
−0.566764 | + | 0.823880i | \(0.691805\pi\) | |||||||
\(384\) | −3.18837 | −0.162706 | ||||||||
\(385\) | 4.40431 | 0.224465 | ||||||||
\(386\) | −4.13574 | −0.210504 | ||||||||
\(387\) | 6.71325 | 0.341254 | ||||||||
\(388\) | 3.65708 | 0.185660 | ||||||||
\(389\) | 8.36423 | 0.424083 | 0.212042 | − | 0.977261i | \(-0.431989\pi\) | ||||
0.212042 | + | 0.977261i | \(0.431989\pi\) | |||||||
\(390\) | 28.3583 | 1.43598 | ||||||||
\(391\) | −15.7182 | −0.794903 | ||||||||
\(392\) | −4.56271 | −0.230452 | ||||||||
\(393\) | −33.8350 | −1.70675 | ||||||||
\(394\) | −4.84442 | −0.244058 | ||||||||
\(395\) | −1.84690 | −0.0929275 | ||||||||
\(396\) | −11.4811 | −0.576947 | ||||||||
\(397\) | 10.4305 | 0.523494 | 0.261747 | − | 0.965137i | \(-0.415701\pi\) | ||||
0.261747 | + | 0.965137i | \(0.415701\pi\) | |||||||
\(398\) | −12.3355 | −0.618324 | ||||||||
\(399\) | 21.5265 | 1.07767 | ||||||||
\(400\) | −1.89971 | −0.0949853 | ||||||||
\(401\) | −10.7377 | −0.536213 | −0.268107 | − | 0.963389i | \(-0.586398\pi\) | ||||
−0.268107 | + | 0.963389i | \(0.586398\pi\) | |||||||
\(402\) | −35.9512 | −1.79309 | ||||||||
\(403\) | 13.7745 | 0.686154 | ||||||||
\(404\) | −9.15937 | −0.455696 | ||||||||
\(405\) | 36.7127 | 1.82427 | ||||||||
\(406\) | 0.532284 | 0.0264168 | ||||||||
\(407\) | 1.33051 | 0.0659509 | ||||||||
\(408\) | 6.53796 | 0.323677 | ||||||||
\(409\) | −16.4325 | −0.812534 | −0.406267 | − | 0.913754i | \(-0.633170\pi\) | ||||
−0.406267 | + | 0.913754i | \(0.633170\pi\) | |||||||
\(410\) | 10.8938 | 0.538007 | ||||||||
\(411\) | −58.7802 | −2.89941 | ||||||||
\(412\) | −0.368513 | −0.0181553 | ||||||||
\(413\) | 13.4993 | 0.664256 | ||||||||
\(414\) | 54.9274 | 2.69953 | ||||||||
\(415\) | 1.94885 | 0.0956653 | ||||||||
\(416\) | −5.05138 | −0.247664 | ||||||||
\(417\) | −39.2682 | −1.92297 | ||||||||
\(418\) | −6.92904 | −0.338911 | ||||||||
\(419\) | 0.515672 | 0.0251922 | 0.0125961 | − | 0.999921i | \(-0.495990\pi\) | ||||
0.0125961 | + | 0.999921i | \(0.495990\pi\) | |||||||
\(420\) | 8.76444 | 0.427661 | ||||||||
\(421\) | 18.2572 | 0.889802 | 0.444901 | − | 0.895580i | \(-0.353239\pi\) | ||||
0.444901 | + | 0.895580i | \(0.353239\pi\) | |||||||
\(422\) | −13.4414 | −0.654317 | ||||||||
\(423\) | 50.8756 | 2.47366 | ||||||||
\(424\) | 7.47223 | 0.362884 | ||||||||
\(425\) | 3.89547 | 0.188958 | ||||||||
\(426\) | 10.8036 | 0.523435 | ||||||||
\(427\) | 15.7292 | 0.761190 | ||||||||
\(428\) | 13.5248 | 0.653746 | ||||||||
\(429\) | −25.8049 | −1.24587 | ||||||||
\(430\) | 1.64958 | 0.0795500 | ||||||||
\(431\) | −17.1360 | −0.825412 | −0.412706 | − | 0.910864i | \(-0.635416\pi\) | ||||
−0.412706 | + | 0.910864i | \(0.635416\pi\) | |||||||
\(432\) | −13.2819 | −0.639024 | ||||||||
\(433\) | 30.8145 | 1.48085 | 0.740426 | − | 0.672138i | \(-0.234624\pi\) | ||||
0.740426 | + | 0.672138i | \(0.234624\pi\) | |||||||
\(434\) | 4.25714 | 0.204349 | ||||||||
\(435\) | 1.91408 | 0.0917732 | ||||||||
\(436\) | −2.12016 | −0.101537 | ||||||||
\(437\) | 33.1497 | 1.58576 | ||||||||
\(438\) | 23.0796 | 1.10279 | ||||||||
\(439\) | −22.0206 | −1.05099 | −0.525494 | − | 0.850797i | \(-0.676119\pi\) | ||||
−0.525494 | + | 0.850797i | \(0.676119\pi\) | |||||||
\(440\) | −2.82114 | −0.134493 | ||||||||
\(441\) | −32.6951 | −1.55691 | ||||||||
\(442\) | 10.3582 | 0.492688 | ||||||||
\(443\) | −0.701050 | −0.0333079 | −0.0166540 | − | 0.999861i | \(-0.505301\pi\) | ||||
−0.0166540 | + | 0.999861i | \(0.505301\pi\) | |||||||
\(444\) | 2.64767 | 0.125653 | ||||||||
\(445\) | −22.1141 | −1.04831 | ||||||||
\(446\) | −17.7707 | −0.841467 | ||||||||
\(447\) | −28.5898 | −1.35225 | ||||||||
\(448\) | −1.56118 | −0.0737589 | ||||||||
\(449\) | −22.0338 | −1.03984 | −0.519919 | − | 0.854216i | \(-0.674038\pi\) | ||||
−0.519919 | + | 0.854216i | \(0.674038\pi\) | |||||||
\(450\) | −13.6128 | −0.641712 | ||||||||
\(451\) | −9.91293 | −0.466781 | ||||||||
\(452\) | −13.0833 | −0.615389 | ||||||||
\(453\) | 35.0817 | 1.64828 | ||||||||
\(454\) | 13.7933 | 0.647350 | ||||||||
\(455\) | 13.8856 | 0.650967 | ||||||||
\(456\) | −13.7886 | −0.645709 | ||||||||
\(457\) | −4.53353 | −0.212070 | −0.106035 | − | 0.994362i | \(-0.533815\pi\) | ||||
−0.106035 | + | 0.994362i | \(0.533815\pi\) | |||||||
\(458\) | −13.2868 | −0.620853 | ||||||||
\(459\) | 27.2353 | 1.27124 | ||||||||
\(460\) | 13.4968 | 0.629291 | ||||||||
\(461\) | 25.5224 | 1.18870 | 0.594349 | − | 0.804207i | \(-0.297410\pi\) | ||||
0.594349 | + | 0.804207i | \(0.297410\pi\) | |||||||
\(462\) | −7.97528 | −0.371043 | ||||||||
\(463\) | 16.1435 | 0.750250 | 0.375125 | − | 0.926974i | \(-0.377600\pi\) | ||||
0.375125 | + | 0.926974i | \(0.377600\pi\) | |||||||
\(464\) | −0.340949 | −0.0158282 | ||||||||
\(465\) | 15.3086 | 0.709918 | ||||||||
\(466\) | −15.3937 | −0.713098 | ||||||||
\(467\) | −33.1085 | −1.53208 | −0.766040 | − | 0.642793i | \(-0.777776\pi\) | ||||
−0.766040 | + | 0.642793i | \(0.777776\pi\) | |||||||
\(468\) | −36.1968 | −1.67320 | ||||||||
\(469\) | −17.6035 | −0.812853 | ||||||||
\(470\) | 12.5012 | 0.576636 | ||||||||
\(471\) | 31.6335 | 1.45760 | ||||||||
\(472\) | −8.64683 | −0.398003 | ||||||||
\(473\) | −1.50105 | −0.0690185 | ||||||||
\(474\) | 3.34434 | 0.153611 | ||||||||
\(475\) | −8.21555 | −0.376955 | ||||||||
\(476\) | 3.20130 | 0.146731 | ||||||||
\(477\) | 53.5439 | 2.45161 | ||||||||
\(478\) | −1.03722 | −0.0474413 | ||||||||
\(479\) | 36.8589 | 1.68412 | 0.842062 | − | 0.539380i | \(-0.181341\pi\) | ||||
0.842062 | + | 0.539380i | \(0.181341\pi\) | |||||||
\(480\) | −5.61398 | −0.256242 | ||||||||
\(481\) | 4.19474 | 0.191264 | ||||||||
\(482\) | −16.3323 | −0.743917 | ||||||||
\(483\) | 38.1550 | 1.73611 | ||||||||
\(484\) | −8.43288 | −0.383313 | ||||||||
\(485\) | 6.43926 | 0.292392 | ||||||||
\(486\) | −26.6332 | −1.20811 | ||||||||
\(487\) | −42.8576 | −1.94206 | −0.971032 | − | 0.238948i | \(-0.923197\pi\) | ||||
−0.971032 | + | 0.238948i | \(0.923197\pi\) | |||||||
\(488\) | −10.0752 | −0.456083 | ||||||||
\(489\) | −0.0227321 | −0.00102798 | ||||||||
\(490\) | −8.03386 | −0.362933 | ||||||||
\(491\) | −19.4186 | −0.876348 | −0.438174 | − | 0.898890i | \(-0.644375\pi\) | ||||
−0.438174 | + | 0.898890i | \(0.644375\pi\) | |||||||
\(492\) | −19.7264 | −0.889335 | ||||||||
\(493\) | 0.699139 | 0.0314876 | ||||||||
\(494\) | −21.8454 | −0.982871 | ||||||||
\(495\) | −20.2155 | −0.908619 | ||||||||
\(496\) | −2.72687 | −0.122440 | ||||||||
\(497\) | 5.28996 | 0.237287 | ||||||||
\(498\) | −3.52896 | −0.158136 | ||||||||
\(499\) | −12.3810 | −0.554252 | −0.277126 | − | 0.960834i | \(-0.589382\pi\) | ||||
−0.277126 | + | 0.960834i | \(0.589382\pi\) | |||||||
\(500\) | −12.1488 | −0.543309 | ||||||||
\(501\) | −50.4795 | −2.25526 | ||||||||
\(502\) | −19.2479 | −0.859077 | ||||||||
\(503\) | −9.87872 | −0.440470 | −0.220235 | − | 0.975447i | \(-0.570682\pi\) | ||||
−0.220235 | + | 0.975447i | \(0.570682\pi\) | |||||||
\(504\) | −11.1870 | −0.498308 | ||||||||
\(505\) | −16.1275 | −0.717665 | ||||||||
\(506\) | −12.2815 | −0.545980 | ||||||||
\(507\) | −39.9071 | −1.77234 | ||||||||
\(508\) | −9.61584 | −0.426634 | ||||||||
\(509\) | −30.3055 | −1.34327 | −0.671634 | − | 0.740883i | \(-0.734407\pi\) | ||||
−0.671634 | + | 0.740883i | \(0.734407\pi\) | |||||||
\(510\) | 11.5118 | 0.509752 | ||||||||
\(511\) | 11.3009 | 0.499922 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −57.4393 | −2.53601 | ||||||||
\(514\) | −11.2496 | −0.496200 | ||||||||
\(515\) | −0.648864 | −0.0285924 | ||||||||
\(516\) | −2.98705 | −0.131497 | ||||||||
\(517\) | −11.3756 | −0.500297 | ||||||||
\(518\) | 1.29643 | 0.0569617 | ||||||||
\(519\) | −36.1703 | −1.58770 | ||||||||
\(520\) | −8.89429 | −0.390041 | ||||||||
\(521\) | −0.828053 | −0.0362777 | −0.0181388 | − | 0.999835i | \(-0.505774\pi\) | ||||
−0.0181388 | + | 0.999835i | \(0.505774\pi\) | |||||||
\(522\) | −2.44315 | −0.106934 | ||||||||
\(523\) | 21.1567 | 0.925116 | 0.462558 | − | 0.886589i | \(-0.346932\pi\) | ||||
0.462558 | + | 0.886589i | \(0.346932\pi\) | |||||||
\(524\) | 10.6120 | 0.463587 | ||||||||
\(525\) | −9.45603 | −0.412695 | ||||||||
\(526\) | 10.3469 | 0.451144 | ||||||||
\(527\) | 5.59162 | 0.243575 | ||||||||
\(528\) | 5.10849 | 0.222318 | ||||||||
\(529\) | 35.7568 | 1.55464 | ||||||||
\(530\) | 13.1568 | 0.571497 | ||||||||
\(531\) | −61.9608 | −2.68887 | ||||||||
\(532\) | −6.75155 | −0.292717 | ||||||||
\(533\) | −31.2528 | −1.35371 | ||||||||
\(534\) | 40.0440 | 1.73287 | ||||||||
\(535\) | 23.8140 | 1.02957 | ||||||||
\(536\) | 11.2757 | 0.487038 | ||||||||
\(537\) | −36.9408 | −1.59412 | ||||||||
\(538\) | 26.3732 | 1.13703 | ||||||||
\(539\) | 7.31049 | 0.314885 | ||||||||
\(540\) | −23.3863 | −1.00638 | ||||||||
\(541\) | 8.10695 | 0.348545 | 0.174272 | − | 0.984697i | \(-0.444243\pi\) | ||||
0.174272 | + | 0.984697i | \(0.444243\pi\) | |||||||
\(542\) | −18.2888 | −0.785573 | ||||||||
\(543\) | 11.7461 | 0.504072 | ||||||||
\(544\) | −2.05056 | −0.0879172 | ||||||||
\(545\) | −3.73310 | −0.159908 | ||||||||
\(546\) | −25.1439 | −1.07606 | ||||||||
\(547\) | −2.53565 | −0.108417 | −0.0542084 | − | 0.998530i | \(-0.517264\pi\) | ||||
−0.0542084 | + | 0.998530i | \(0.517264\pi\) | |||||||
\(548\) | 18.4358 | 0.787538 | ||||||||
\(549\) | −72.1961 | −3.08125 | ||||||||
\(550\) | 3.04376 | 0.129786 | ||||||||
\(551\) | −1.47448 | −0.0628151 | ||||||||
\(552\) | −24.4398 | −1.04023 | ||||||||
\(553\) | 1.63755 | 0.0696357 | ||||||||
\(554\) | −1.93375 | −0.0821572 | ||||||||
\(555\) | 4.66192 | 0.197888 | ||||||||
\(556\) | 12.3160 | 0.522317 | ||||||||
\(557\) | 9.34584 | 0.395996 | 0.197998 | − | 0.980202i | \(-0.436556\pi\) | ||||
0.197998 | + | 0.980202i | \(0.436556\pi\) | |||||||
\(558\) | −19.5400 | −0.827193 | ||||||||
\(559\) | −4.73242 | −0.200160 | ||||||||
\(560\) | −2.74887 | −0.116161 | ||||||||
\(561\) | −10.4753 | −0.442267 | ||||||||
\(562\) | −24.7920 | −1.04579 | ||||||||
\(563\) | 16.8886 | 0.711771 | 0.355886 | − | 0.934529i | \(-0.384179\pi\) | ||||
0.355886 | + | 0.934529i | \(0.384179\pi\) | |||||||
\(564\) | −22.6370 | −0.953189 | ||||||||
\(565\) | −23.0367 | −0.969161 | ||||||||
\(566\) | −26.8377 | −1.12807 | ||||||||
\(567\) | −32.5513 | −1.36702 | ||||||||
\(568\) | −3.38843 | −0.142175 | ||||||||
\(569\) | −27.0105 | −1.13234 | −0.566169 | − | 0.824289i | \(-0.691575\pi\) | ||||
−0.566169 | + | 0.824289i | \(0.691575\pi\) | |||||||
\(570\) | −24.2784 | −1.01691 | ||||||||
\(571\) | −30.3919 | −1.27186 | −0.635931 | − | 0.771746i | \(-0.719384\pi\) | ||||
−0.635931 | + | 0.771746i | \(0.719384\pi\) | |||||||
\(572\) | 8.09344 | 0.338404 | ||||||||
\(573\) | 8.84098 | 0.369337 | ||||||||
\(574\) | −9.65900 | −0.403159 | ||||||||
\(575\) | −14.5618 | −0.607270 | ||||||||
\(576\) | 7.16572 | 0.298572 | ||||||||
\(577\) | 27.6921 | 1.15284 | 0.576419 | − | 0.817155i | \(-0.304450\pi\) | ||||
0.576419 | + | 0.817155i | \(0.304450\pi\) | |||||||
\(578\) | −12.7952 | −0.532210 | ||||||||
\(579\) | 13.1863 | 0.548003 | ||||||||
\(580\) | −0.600332 | −0.0249274 | ||||||||
\(581\) | −1.72795 | −0.0716874 | ||||||||
\(582\) | −11.6601 | −0.483328 | ||||||||
\(583\) | −11.9722 | −0.495838 | ||||||||
\(584\) | −7.23868 | −0.299539 | ||||||||
\(585\) | −63.7340 | −2.63508 | ||||||||
\(586\) | 19.2353 | 0.794601 | ||||||||
\(587\) | −3.17361 | −0.130989 | −0.0654945 | − | 0.997853i | \(-0.520862\pi\) | ||||
−0.0654945 | + | 0.997853i | \(0.520862\pi\) | |||||||
\(588\) | 14.5476 | 0.599934 | ||||||||
\(589\) | −11.7927 | −0.485911 | ||||||||
\(590\) | −15.2250 | −0.626805 | ||||||||
\(591\) | 15.4458 | 0.635356 | ||||||||
\(592\) | −0.830414 | −0.0341298 | ||||||||
\(593\) | 19.3394 | 0.794175 | 0.397087 | − | 0.917781i | \(-0.370021\pi\) | ||||
0.397087 | + | 0.917781i | \(0.370021\pi\) | |||||||
\(594\) | 21.2805 | 0.873151 | ||||||||
\(595\) | 5.63674 | 0.231084 | ||||||||
\(596\) | 8.96690 | 0.367298 | ||||||||
\(597\) | 39.3302 | 1.60968 | ||||||||
\(598\) | −38.7203 | −1.58339 | ||||||||
\(599\) | 15.7256 | 0.642530 | 0.321265 | − | 0.946989i | \(-0.395892\pi\) | ||||
0.321265 | + | 0.946989i | \(0.395892\pi\) | |||||||
\(600\) | 6.05697 | 0.247275 | ||||||||
\(601\) | 19.8293 | 0.808853 | 0.404427 | − | 0.914570i | \(-0.367471\pi\) | ||||
0.404427 | + | 0.914570i | \(0.367471\pi\) | |||||||
\(602\) | −1.46260 | −0.0596112 | ||||||||
\(603\) | 80.7988 | 3.29038 | ||||||||
\(604\) | −11.0030 | −0.447706 | ||||||||
\(605\) | −14.8483 | −0.603670 | ||||||||
\(606\) | 29.2035 | 1.18631 | ||||||||
\(607\) | 5.94844 | 0.241440 | 0.120720 | − | 0.992687i | \(-0.461480\pi\) | ||||
0.120720 | + | 0.992687i | \(0.461480\pi\) | |||||||
\(608\) | 4.32464 | 0.175387 | ||||||||
\(609\) | −1.69712 | −0.0687708 | ||||||||
\(610\) | −17.7401 | −0.718274 | ||||||||
\(611\) | −35.8641 | −1.45091 | ||||||||
\(612\) | −14.6938 | −0.593961 | ||||||||
\(613\) | −23.7062 | −0.957483 | −0.478742 | − | 0.877956i | \(-0.658907\pi\) | ||||
−0.478742 | + | 0.877956i | \(0.658907\pi\) | |||||||
\(614\) | −24.6003 | −0.992789 | ||||||||
\(615\) | −34.7335 | −1.40059 | ||||||||
\(616\) | 2.50136 | 0.100783 | ||||||||
\(617\) | 30.2774 | 1.21892 | 0.609461 | − | 0.792816i | \(-0.291386\pi\) | ||||
0.609461 | + | 0.792816i | \(0.291386\pi\) | |||||||
\(618\) | 1.17496 | 0.0472636 | ||||||||
\(619\) | −22.9972 | −0.924334 | −0.462167 | − | 0.886793i | \(-0.652928\pi\) | ||||
−0.462167 | + | 0.886793i | \(0.652928\pi\) | |||||||
\(620\) | −4.80137 | −0.192828 | ||||||||
\(621\) | −101.810 | −4.08547 | ||||||||
\(622\) | −32.0503 | −1.28510 | ||||||||
\(623\) | 19.6075 | 0.785556 | ||||||||
\(624\) | 16.1057 | 0.644743 | ||||||||
\(625\) | −11.8926 | −0.475703 | ||||||||
\(626\) | −3.16599 | −0.126538 | ||||||||
\(627\) | 22.0924 | 0.882285 | ||||||||
\(628\) | −9.92152 | −0.395912 | ||||||||
\(629\) | 1.70282 | 0.0678958 | ||||||||
\(630\) | −19.6977 | −0.784774 | ||||||||
\(631\) | −21.1793 | −0.843133 | −0.421566 | − | 0.906797i | \(-0.638520\pi\) | ||||
−0.421566 | + | 0.906797i | \(0.638520\pi\) | |||||||
\(632\) | −1.04892 | −0.0417237 | ||||||||
\(633\) | 42.8562 | 1.70338 | ||||||||
\(634\) | −8.51115 | −0.338021 | ||||||||
\(635\) | −16.9312 | −0.671895 | ||||||||
\(636\) | −23.8243 | −0.944694 | ||||||||
\(637\) | 23.0480 | 0.913195 | ||||||||
\(638\) | 0.546277 | 0.0216273 | ||||||||
\(639\) | −24.2806 | −0.960524 | ||||||||
\(640\) | 1.76077 | 0.0696003 | ||||||||
\(641\) | −9.74469 | −0.384892 | −0.192446 | − | 0.981308i | \(-0.561642\pi\) | ||||
−0.192446 | + | 0.981308i | \(0.561642\pi\) | |||||||
\(642\) | −43.1221 | −1.70189 | ||||||||
\(643\) | −26.8569 | −1.05913 | −0.529566 | − | 0.848269i | \(-0.677645\pi\) | ||||
−0.529566 | + | 0.848269i | \(0.677645\pi\) | |||||||
\(644\) | −11.9669 | −0.471563 | ||||||||
\(645\) | −5.25949 | −0.207092 | ||||||||
\(646\) | −8.86796 | −0.348905 | ||||||||
\(647\) | −21.9696 | −0.863713 | −0.431857 | − | 0.901942i | \(-0.642141\pi\) | ||||
−0.431857 | + | 0.901942i | \(0.642141\pi\) | |||||||
\(648\) | 20.8504 | 0.819081 | ||||||||
\(649\) | 13.8542 | 0.543824 | ||||||||
\(650\) | 9.59614 | 0.376392 | ||||||||
\(651\) | −13.5733 | −0.531981 | ||||||||
\(652\) | 0.00712968 | 0.000279220 0 | ||||||||
\(653\) | −7.03756 | −0.275401 | −0.137700 | − | 0.990474i | \(-0.543971\pi\) | ||||
−0.137700 | + | 0.990474i | \(0.543971\pi\) | |||||||
\(654\) | 6.75985 | 0.264331 | ||||||||
\(655\) | 18.6852 | 0.730092 | ||||||||
\(656\) | 6.18698 | 0.241561 | ||||||||
\(657\) | −51.8703 | −2.02365 | ||||||||
\(658\) | −11.0842 | −0.432106 | ||||||||
\(659\) | −11.4398 | −0.445631 | −0.222816 | − | 0.974861i | \(-0.571525\pi\) | ||||
−0.222816 | + | 0.974861i | \(0.571525\pi\) | |||||||
\(660\) | 8.99485 | 0.350124 | ||||||||
\(661\) | 47.0485 | 1.82998 | 0.914988 | − | 0.403481i | \(-0.132200\pi\) | ||||
0.914988 | + | 0.403481i | \(0.132200\pi\) | |||||||
\(662\) | 27.2826 | 1.06037 | ||||||||
\(663\) | −33.0257 | −1.28261 | ||||||||
\(664\) | 1.10682 | 0.0429530 | ||||||||
\(665\) | −11.8879 | −0.460993 | ||||||||
\(666\) | −5.95052 | −0.230578 | ||||||||
\(667\) | −2.61348 | −0.101194 | ||||||||
\(668\) | 15.8324 | 0.612573 | ||||||||
\(669\) | 56.6596 | 2.19059 | ||||||||
\(670\) | 19.8539 | 0.767024 | ||||||||
\(671\) | 16.1427 | 0.623183 | ||||||||
\(672\) | 4.97763 | 0.192016 | ||||||||
\(673\) | 2.47436 | 0.0953794 | 0.0476897 | − | 0.998862i | \(-0.484814\pi\) | ||||
0.0476897 | + | 0.998862i | \(0.484814\pi\) | |||||||
\(674\) | 3.19555 | 0.123088 | ||||||||
\(675\) | 25.2317 | 0.971167 | ||||||||
\(676\) | 12.5164 | 0.481402 | ||||||||
\(677\) | −40.4942 | −1.55632 | −0.778160 | − | 0.628066i | \(-0.783847\pi\) | ||||
−0.778160 | + | 0.628066i | \(0.783847\pi\) | |||||||
\(678\) | 41.7146 | 1.60204 | ||||||||
\(679\) | −5.70937 | −0.219105 | ||||||||
\(680\) | −3.61056 | −0.138459 | ||||||||
\(681\) | −43.9780 | −1.68524 | ||||||||
\(682\) | 4.36905 | 0.167300 | ||||||||
\(683\) | 38.5565 | 1.47532 | 0.737662 | − | 0.675170i | \(-0.235930\pi\) | ||||
0.737662 | + | 0.675170i | \(0.235930\pi\) | |||||||
\(684\) | 30.9892 | 1.18490 | ||||||||
\(685\) | 32.4611 | 1.24028 | ||||||||
\(686\) | 18.0515 | 0.689209 | ||||||||
\(687\) | 42.3633 | 1.61626 | ||||||||
\(688\) | 0.936856 | 0.0357173 | ||||||||
\(689\) | −37.7451 | −1.43797 | ||||||||
\(690\) | −43.0328 | −1.63823 | ||||||||
\(691\) | −39.1794 | −1.49045 | −0.745227 | − | 0.666811i | \(-0.767659\pi\) | ||||
−0.745227 | + | 0.666811i | \(0.767659\pi\) | |||||||
\(692\) | 11.3445 | 0.431251 | ||||||||
\(693\) | 17.9241 | 0.680879 | ||||||||
\(694\) | −2.86923 | −0.108915 | ||||||||
\(695\) | 21.6857 | 0.822584 | ||||||||
\(696\) | 1.08707 | 0.0412054 | ||||||||
\(697\) | −12.6868 | −0.480547 | ||||||||
\(698\) | −11.0513 | −0.418300 | ||||||||
\(699\) | 49.0807 | 1.85640 | ||||||||
\(700\) | 2.96579 | 0.112096 | ||||||||
\(701\) | −22.3199 | −0.843012 | −0.421506 | − | 0.906826i | \(-0.638498\pi\) | ||||
−0.421506 | + | 0.906826i | \(0.638498\pi\) | |||||||
\(702\) | 67.0918 | 2.53222 | ||||||||
\(703\) | −3.59124 | −0.135446 | ||||||||
\(704\) | −1.60222 | −0.0603861 | ||||||||
\(705\) | −39.8584 | −1.50115 | ||||||||
\(706\) | −6.36400 | −0.239512 | ||||||||
\(707\) | 14.2994 | 0.537786 | ||||||||
\(708\) | 27.5693 | 1.03612 | ||||||||
\(709\) | −39.3745 | −1.47874 | −0.739370 | − | 0.673300i | \(-0.764876\pi\) | ||||
−0.739370 | + | 0.673300i | \(0.764876\pi\) | |||||||
\(710\) | −5.96623 | −0.223909 | ||||||||
\(711\) | −7.51625 | −0.281881 | ||||||||
\(712\) | −12.5594 | −0.470682 | ||||||||
\(713\) | −20.9023 | −0.782796 | ||||||||
\(714\) | −10.2069 | −0.381985 | ||||||||
\(715\) | 14.2507 | 0.532944 | ||||||||
\(716\) | 11.5861 | 0.432993 | ||||||||
\(717\) | 3.30704 | 0.123504 | ||||||||
\(718\) | −10.9510 | −0.408689 | ||||||||
\(719\) | 36.1666 | 1.34879 | 0.674393 | − | 0.738372i | \(-0.264405\pi\) | ||||
0.674393 | + | 0.738372i | \(0.264405\pi\) | |||||||
\(720\) | 12.6172 | 0.470213 | ||||||||
\(721\) | 0.575315 | 0.0214259 | ||||||||
\(722\) | −0.297477 | −0.0110709 | ||||||||
\(723\) | 52.0736 | 1.93664 | ||||||||
\(724\) | −3.68403 | −0.136916 | ||||||||
\(725\) | 0.647704 | 0.0240551 | ||||||||
\(726\) | 26.8872 | 0.997876 | ||||||||
\(727\) | 1.01733 | 0.0377308 | 0.0188654 | − | 0.999822i | \(-0.493995\pi\) | ||||
0.0188654 | + | 0.999822i | \(0.493995\pi\) | |||||||
\(728\) | 7.88612 | 0.292279 | ||||||||
\(729\) | 22.3655 | 0.828351 | ||||||||
\(730\) | −12.7456 | −0.471736 | ||||||||
\(731\) | −1.92108 | −0.0710539 | ||||||||
\(732\) | 32.1235 | 1.18732 | ||||||||
\(733\) | −33.6959 | −1.24459 | −0.622294 | − | 0.782784i | \(-0.713799\pi\) | ||||
−0.622294 | + | 0.782784i | \(0.713799\pi\) | |||||||
\(734\) | −2.58644 | −0.0954673 | ||||||||
\(735\) | 25.6150 | 0.944822 | ||||||||
\(736\) | 7.66530 | 0.282547 | ||||||||
\(737\) | −18.0663 | −0.665479 | ||||||||
\(738\) | 44.3342 | 1.63196 | ||||||||
\(739\) | 22.0748 | 0.812036 | 0.406018 | − | 0.913865i | \(-0.366917\pi\) | ||||
0.406018 | + | 0.913865i | \(0.366917\pi\) | |||||||
\(740\) | −1.46216 | −0.0537502 | ||||||||
\(741\) | 69.6513 | 2.55870 | ||||||||
\(742\) | −11.6655 | −0.428254 | ||||||||
\(743\) | 40.0012 | 1.46750 | 0.733751 | − | 0.679418i | \(-0.237768\pi\) | ||||
0.733751 | + | 0.679418i | \(0.237768\pi\) | |||||||
\(744\) | 8.69427 | 0.318748 | ||||||||
\(745\) | 15.7886 | 0.578449 | ||||||||
\(746\) | −35.1217 | −1.28590 | ||||||||
\(747\) | 7.93117 | 0.290186 | ||||||||
\(748\) | 3.28546 | 0.120128 | ||||||||
\(749\) | −21.1147 | −0.771514 | ||||||||
\(750\) | 38.7348 | 1.41439 | ||||||||
\(751\) | −8.78921 | −0.320723 | −0.160361 | − | 0.987058i | \(-0.551266\pi\) | ||||
−0.160361 | + | 0.987058i | \(0.551266\pi\) | |||||||
\(752\) | 7.09986 | 0.258905 | ||||||||
\(753\) | 61.3696 | 2.23643 | ||||||||
\(754\) | 1.72226 | 0.0627212 | ||||||||
\(755\) | −19.3737 | −0.705081 | ||||||||
\(756\) | 20.7354 | 0.754140 | ||||||||
\(757\) | −25.1400 | −0.913729 | −0.456864 | − | 0.889536i | \(-0.651028\pi\) | ||||
−0.456864 | + | 0.889536i | \(0.651028\pi\) | |||||||
\(758\) | 6.14724 | 0.223278 | ||||||||
\(759\) | 39.1581 | 1.42135 | ||||||||
\(760\) | 7.61468 | 0.276213 | ||||||||
\(761\) | −35.6544 | −1.29247 | −0.646235 | − | 0.763138i | \(-0.723658\pi\) | ||||
−0.646235 | + | 0.763138i | \(0.723658\pi\) | |||||||
\(762\) | 30.6589 | 1.11065 | ||||||||
\(763\) | 3.30995 | 0.119828 | ||||||||
\(764\) | −2.77288 | −0.100319 | ||||||||
\(765\) | −25.8723 | −0.935414 | ||||||||
\(766\) | −22.1836 | −0.801526 | ||||||||
\(767\) | 43.6784 | 1.57714 | ||||||||
\(768\) | −3.18837 | −0.115050 | ||||||||
\(769\) | 4.25159 | 0.153316 | 0.0766580 | − | 0.997057i | \(-0.475575\pi\) | ||||
0.0766580 | + | 0.997057i | \(0.475575\pi\) | |||||||
\(770\) | 4.40431 | 0.158720 | ||||||||
\(771\) | 35.8680 | 1.29175 | ||||||||
\(772\) | −4.13574 | −0.148849 | ||||||||
\(773\) | −39.0701 | −1.40525 | −0.702626 | − | 0.711559i | \(-0.747989\pi\) | ||||
−0.702626 | + | 0.711559i | \(0.747989\pi\) | |||||||
\(774\) | 6.71325 | 0.241303 | ||||||||
\(775\) | 5.18025 | 0.186080 | ||||||||
\(776\) | 3.65708 | 0.131282 | ||||||||
\(777\) | −4.13349 | −0.148288 | ||||||||
\(778\) | 8.36423 | 0.299872 | ||||||||
\(779\) | 26.7565 | 0.958650 | ||||||||
\(780\) | 28.3583 | 1.01539 | ||||||||
\(781\) | 5.42903 | 0.194266 | ||||||||
\(782\) | −15.7182 | −0.562081 | ||||||||
\(783\) | 4.52845 | 0.161833 | ||||||||
\(784\) | −4.56271 | −0.162954 | ||||||||
\(785\) | −17.4695 | −0.623512 | ||||||||
\(786\) | −33.8350 | −1.20685 | ||||||||
\(787\) | −16.4952 | −0.587991 | −0.293995 | − | 0.955807i | \(-0.594985\pi\) | ||||
−0.293995 | + | 0.955807i | \(0.594985\pi\) | |||||||
\(788\) | −4.84442 | −0.172575 | ||||||||
\(789\) | −32.9896 | −1.17446 | ||||||||
\(790\) | −1.84690 | −0.0657096 | ||||||||
\(791\) | 20.4255 | 0.726247 | ||||||||
\(792\) | −11.4811 | −0.407963 | ||||||||
\(793\) | 50.8937 | 1.80729 | ||||||||
\(794\) | 10.4305 | 0.370166 | ||||||||
\(795\) | −41.9489 | −1.48778 | ||||||||
\(796\) | −12.3355 | −0.437221 | ||||||||
\(797\) | 22.5708 | 0.799499 | 0.399749 | − | 0.916624i | \(-0.369097\pi\) | ||||
0.399749 | + | 0.916624i | \(0.369097\pi\) | |||||||
\(798\) | 21.5265 | 0.762028 | ||||||||
\(799\) | −14.5587 | −0.515050 | ||||||||
\(800\) | −1.89971 | −0.0671648 | ||||||||
\(801\) | −89.9969 | −3.17989 | ||||||||
\(802\) | −10.7377 | −0.379160 | ||||||||
\(803\) | 11.5980 | 0.409284 | ||||||||
\(804\) | −35.9512 | −1.26790 | ||||||||
\(805\) | −21.0709 | −0.742653 | ||||||||
\(806\) | 13.7745 | 0.485184 | ||||||||
\(807\) | −84.0877 | −2.96003 | ||||||||
\(808\) | −9.15937 | −0.322226 | ||||||||
\(809\) | 6.13926 | 0.215845 | 0.107923 | − | 0.994159i | \(-0.465580\pi\) | ||||
0.107923 | + | 0.994159i | \(0.465580\pi\) | |||||||
\(810\) | 36.7127 | 1.28995 | ||||||||
\(811\) | −12.6099 | −0.442793 | −0.221397 | − | 0.975184i | \(-0.571062\pi\) | ||||
−0.221397 | + | 0.975184i | \(0.571062\pi\) | |||||||
\(812\) | 0.532284 | 0.0186795 | ||||||||
\(813\) | 58.3116 | 2.04508 | ||||||||
\(814\) | 1.33051 | 0.0466343 | ||||||||
\(815\) | 0.0125537 | 0.000439736 0 | ||||||||
\(816\) | 6.53796 | 0.228875 | ||||||||
\(817\) | 4.05157 | 0.141746 | ||||||||
\(818\) | −16.4325 | −0.574549 | ||||||||
\(819\) | 56.5098 | 1.97461 | ||||||||
\(820\) | 10.8938 | 0.380429 | ||||||||
\(821\) | −2.43571 | −0.0850067 | −0.0425034 | − | 0.999096i | \(-0.513533\pi\) | ||||
−0.0425034 | + | 0.999096i | \(0.513533\pi\) | |||||||
\(822\) | −58.7802 | −2.05020 | ||||||||
\(823\) | −38.3762 | −1.33771 | −0.668855 | − | 0.743393i | \(-0.733215\pi\) | ||||
−0.668855 | + | 0.743393i | \(0.733215\pi\) | |||||||
\(824\) | −0.368513 | −0.0128377 | ||||||||
\(825\) | −9.70463 | −0.337872 | ||||||||
\(826\) | 13.4993 | 0.469700 | ||||||||
\(827\) | 42.0778 | 1.46319 | 0.731594 | − | 0.681740i | \(-0.238777\pi\) | ||||
0.731594 | + | 0.681740i | \(0.238777\pi\) | |||||||
\(828\) | 54.9274 | 1.90886 | ||||||||
\(829\) | 31.4243 | 1.09141 | 0.545705 | − | 0.837977i | \(-0.316262\pi\) | ||||
0.545705 | + | 0.837977i | \(0.316262\pi\) | |||||||
\(830\) | 1.94885 | 0.0676456 | ||||||||
\(831\) | 6.16552 | 0.213880 | ||||||||
\(832\) | −5.05138 | −0.175125 | ||||||||
\(833\) | 9.35613 | 0.324171 | ||||||||
\(834\) | −39.2682 | −1.35975 | ||||||||
\(835\) | 27.8771 | 0.964727 | ||||||||
\(836\) | −6.92904 | −0.239646 | ||||||||
\(837\) | 36.2179 | 1.25187 | ||||||||
\(838\) | 0.515672 | 0.0178136 | ||||||||
\(839\) | −49.1624 | −1.69728 | −0.848638 | − | 0.528974i | \(-0.822577\pi\) | ||||
−0.848638 | + | 0.528974i | \(0.822577\pi\) | |||||||
\(840\) | 8.76444 | 0.302402 | ||||||||
\(841\) | −28.8838 | −0.995992 | ||||||||
\(842\) | 18.2572 | 0.629185 | ||||||||
\(843\) | 79.0462 | 2.72250 | ||||||||
\(844\) | −13.4414 | −0.462672 | ||||||||
\(845\) | 22.0385 | 0.758148 | ||||||||
\(846\) | 50.8756 | 1.74914 | ||||||||
\(847\) | 13.1653 | 0.452363 | ||||||||
\(848\) | 7.47223 | 0.256598 | ||||||||
\(849\) | 85.5687 | 2.93671 | ||||||||
\(850\) | 3.89547 | 0.133614 | ||||||||
\(851\) | −6.36537 | −0.218202 | ||||||||
\(852\) | 10.8036 | 0.370125 | ||||||||
\(853\) | −7.35791 | −0.251930 | −0.125965 | − | 0.992035i | \(-0.540203\pi\) | ||||
−0.125965 | + | 0.992035i | \(0.540203\pi\) | |||||||
\(854\) | 15.7292 | 0.538243 | ||||||||
\(855\) | 54.5647 | 1.86607 | ||||||||
\(856\) | 13.5248 | 0.462268 | ||||||||
\(857\) | 36.8397 | 1.25842 | 0.629210 | − | 0.777236i | \(-0.283379\pi\) | ||||
0.629210 | + | 0.777236i | \(0.283379\pi\) | |||||||
\(858\) | −25.8049 | −0.880965 | ||||||||
\(859\) | −25.3202 | −0.863915 | −0.431957 | − | 0.901894i | \(-0.642177\pi\) | ||||
−0.431957 | + | 0.901894i | \(0.642177\pi\) | |||||||
\(860\) | 1.64958 | 0.0562503 | ||||||||
\(861\) | 30.7965 | 1.04954 | ||||||||
\(862\) | −17.1360 | −0.583654 | ||||||||
\(863\) | −8.16205 | −0.277839 | −0.138920 | − | 0.990304i | \(-0.544363\pi\) | ||||
−0.138920 | + | 0.990304i | \(0.544363\pi\) | |||||||
\(864\) | −13.2819 | −0.451859 | ||||||||
\(865\) | 19.9749 | 0.679167 | ||||||||
\(866\) | 30.8145 | 1.04712 | ||||||||
\(867\) | 40.7958 | 1.38550 | ||||||||
\(868\) | 4.25714 | 0.144497 | ||||||||
\(869\) | 1.68060 | 0.0570105 | ||||||||
\(870\) | 1.91408 | 0.0648934 | ||||||||
\(871\) | −56.9580 | −1.92995 | ||||||||
\(872\) | −2.12016 | −0.0717976 | ||||||||
\(873\) | 26.2056 | 0.886926 | ||||||||
\(874\) | 33.1497 | 1.12130 | ||||||||
\(875\) | 18.9664 | 0.641182 | ||||||||
\(876\) | 23.0796 | 0.779787 | ||||||||
\(877\) | 7.84546 | 0.264922 | 0.132461 | − | 0.991188i | \(-0.457712\pi\) | ||||
0.132461 | + | 0.991188i | \(0.457712\pi\) | |||||||
\(878\) | −22.0206 | −0.743160 | ||||||||
\(879\) | −61.3292 | −2.06858 | ||||||||
\(880\) | −2.82114 | −0.0951006 | ||||||||
\(881\) | 6.90796 | 0.232735 | 0.116368 | − | 0.993206i | \(-0.462875\pi\) | ||||
0.116368 | + | 0.993206i | \(0.462875\pi\) | |||||||
\(882\) | −32.6951 | −1.10090 | ||||||||
\(883\) | 33.7164 | 1.13465 | 0.567324 | − | 0.823495i | \(-0.307979\pi\) | ||||
0.567324 | + | 0.823495i | \(0.307979\pi\) | |||||||
\(884\) | 10.3582 | 0.348383 | ||||||||
\(885\) | 48.5431 | 1.63176 | ||||||||
\(886\) | −0.701050 | −0.0235523 | ||||||||
\(887\) | 34.3899 | 1.15470 | 0.577349 | − | 0.816497i | \(-0.304087\pi\) | ||||
0.577349 | + | 0.816497i | \(0.304087\pi\) | |||||||
\(888\) | 2.64767 | 0.0888500 | ||||||||
\(889\) | 15.0121 | 0.503489 | ||||||||
\(890\) | −22.1141 | −0.741266 | ||||||||
\(891\) | −33.4070 | −1.11918 | ||||||||
\(892\) | −17.7707 | −0.595007 | ||||||||
\(893\) | 30.7043 | 1.02748 | ||||||||
\(894\) | −28.5898 | −0.956186 | ||||||||
\(895\) | 20.4004 | 0.681911 | ||||||||
\(896\) | −1.56118 | −0.0521554 | ||||||||
\(897\) | 123.455 | 4.12204 | ||||||||
\(898\) | −22.0338 | −0.735276 | ||||||||
\(899\) | 0.929724 | 0.0310080 | ||||||||
\(900\) | −13.6128 | −0.453759 | ||||||||
\(901\) | −15.3223 | −0.510460 | ||||||||
\(902\) | −9.91293 | −0.330064 | ||||||||
\(903\) | 4.66332 | 0.155186 | ||||||||
\(904\) | −13.0833 | −0.435146 | ||||||||
\(905\) | −6.48672 | −0.215626 | ||||||||
\(906\) | 35.0817 | 1.16551 | ||||||||
\(907\) | 5.39802 | 0.179238 | 0.0896192 | − | 0.995976i | \(-0.471435\pi\) | ||||
0.0896192 | + | 0.995976i | \(0.471435\pi\) | |||||||
\(908\) | 13.7933 | 0.457745 | ||||||||
\(909\) | −65.6335 | −2.17693 | ||||||||
\(910\) | 13.8856 | 0.460303 | ||||||||
\(911\) | 30.2896 | 1.00354 | 0.501770 | − | 0.865001i | \(-0.332682\pi\) | ||||
0.501770 | + | 0.865001i | \(0.332682\pi\) | |||||||
\(912\) | −13.7886 | −0.456585 | ||||||||
\(913\) | −1.77337 | −0.0586901 | ||||||||
\(914\) | −4.53353 | −0.149956 | ||||||||
\(915\) | 56.5619 | 1.86988 | ||||||||
\(916\) | −13.2868 | −0.439009 | ||||||||
\(917\) | −16.5672 | −0.547099 | ||||||||
\(918\) | 27.2353 | 0.898900 | ||||||||
\(919\) | 13.3834 | 0.441477 | 0.220739 | − | 0.975333i | \(-0.429153\pi\) | ||||
0.220739 | + | 0.975333i | \(0.429153\pi\) | |||||||
\(920\) | 13.4968 | 0.444976 | ||||||||
\(921\) | 78.4350 | 2.58452 | ||||||||
\(922\) | 25.5224 | 0.840537 | ||||||||
\(923\) | 17.1163 | 0.563389 | ||||||||
\(924\) | −7.97528 | −0.262367 | ||||||||
\(925\) | 1.57754 | 0.0518693 | ||||||||
\(926\) | 16.1435 | 0.530507 | ||||||||
\(927\) | −2.64066 | −0.0867306 | ||||||||
\(928\) | −0.340949 | −0.0111922 | ||||||||
\(929\) | −5.85105 | −0.191967 | −0.0959834 | − | 0.995383i | \(-0.530600\pi\) | ||||
−0.0959834 | + | 0.995383i | \(0.530600\pi\) | |||||||
\(930\) | 15.3086 | 0.501988 | ||||||||
\(931\) | −19.7321 | −0.646693 | ||||||||
\(932\) | −15.3937 | −0.504236 | ||||||||
\(933\) | 102.188 | 3.34550 | ||||||||
\(934\) | −33.1085 | −1.08334 | ||||||||
\(935\) | 5.78493 | 0.189187 | ||||||||
\(936\) | −36.1968 | −1.18313 | ||||||||
\(937\) | 7.55557 | 0.246830 | 0.123415 | − | 0.992355i | \(-0.460615\pi\) | ||||
0.123415 | + | 0.992355i | \(0.460615\pi\) | |||||||
\(938\) | −17.6035 | −0.574774 | ||||||||
\(939\) | 10.0944 | 0.329417 | ||||||||
\(940\) | 12.5012 | 0.407743 | ||||||||
\(941\) | 19.0297 | 0.620352 | 0.310176 | − | 0.950679i | \(-0.399612\pi\) | ||||
0.310176 | + | 0.950679i | \(0.399612\pi\) | |||||||
\(942\) | 31.6335 | 1.03068 | ||||||||
\(943\) | 47.4250 | 1.54437 | ||||||||
\(944\) | −8.64683 | −0.281430 | ||||||||
\(945\) | 36.5102 | 1.18768 | ||||||||
\(946\) | −1.50105 | −0.0488035 | ||||||||
\(947\) | −1.35220 | −0.0439407 | −0.0219703 | − | 0.999759i | \(-0.506994\pi\) | ||||
−0.0219703 | + | 0.999759i | \(0.506994\pi\) | |||||||
\(948\) | 3.34434 | 0.108619 | ||||||||
\(949\) | 36.5653 | 1.18696 | ||||||||
\(950\) | −8.21555 | −0.266548 | ||||||||
\(951\) | 27.1367 | 0.879969 | ||||||||
\(952\) | 3.20130 | 0.103755 | ||||||||
\(953\) | 39.3768 | 1.27554 | 0.637770 | − | 0.770227i | \(-0.279857\pi\) | ||||
0.637770 | + | 0.770227i | \(0.279857\pi\) | |||||||
\(954\) | 53.5439 | 1.73355 | ||||||||
\(955\) | −4.88239 | −0.157991 | ||||||||
\(956\) | −1.03722 | −0.0335460 | ||||||||
\(957\) | −1.74174 | −0.0563023 | ||||||||
\(958\) | 36.8589 | 1.19086 | ||||||||
\(959\) | −28.7816 | −0.929408 | ||||||||
\(960\) | −5.61398 | −0.181190 | ||||||||
\(961\) | −23.5642 | −0.760135 | ||||||||
\(962\) | 4.19474 | 0.135244 | ||||||||
\(963\) | 96.9150 | 3.12304 | ||||||||
\(964\) | −16.3323 | −0.526029 | ||||||||
\(965\) | −7.28207 | −0.234418 | ||||||||
\(966\) | 38.1550 | 1.22762 | ||||||||
\(967\) | −21.2109 | −0.682097 | −0.341049 | − | 0.940046i | \(-0.610782\pi\) | ||||
−0.341049 | + | 0.940046i | \(0.610782\pi\) | |||||||
\(968\) | −8.43288 | −0.271043 | ||||||||
\(969\) | 28.2743 | 0.908303 | ||||||||
\(970\) | 6.43926 | 0.206752 | ||||||||
\(971\) | −18.4749 | −0.592889 | −0.296444 | − | 0.955050i | \(-0.595801\pi\) | ||||
−0.296444 | + | 0.955050i | \(0.595801\pi\) | |||||||
\(972\) | −26.6332 | −0.854261 | ||||||||
\(973\) | −19.2276 | −0.616408 | ||||||||
\(974\) | −42.8576 | −1.37325 | ||||||||
\(975\) | −30.5961 | −0.979859 | ||||||||
\(976\) | −10.0752 | −0.322499 | ||||||||
\(977\) | 14.4216 | 0.461389 | 0.230694 | − | 0.973026i | \(-0.425900\pi\) | ||||
0.230694 | + | 0.973026i | \(0.425900\pi\) | |||||||
\(978\) | −0.0227321 | −0.000726891 0 | ||||||||
\(979\) | 20.1229 | 0.643131 | ||||||||
\(980\) | −8.03386 | −0.256632 | ||||||||
\(981\) | −15.1925 | −0.485058 | ||||||||
\(982\) | −19.4186 | −0.619672 | ||||||||
\(983\) | −24.7203 | −0.788455 | −0.394227 | − | 0.919013i | \(-0.628988\pi\) | ||||
−0.394227 | + | 0.919013i | \(0.628988\pi\) | |||||||
\(984\) | −19.7264 | −0.628855 | ||||||||
\(985\) | −8.52988 | −0.271785 | ||||||||
\(986\) | 0.699139 | 0.0222651 | ||||||||
\(987\) | 35.3405 | 1.12490 | ||||||||
\(988\) | −21.8454 | −0.694995 | ||||||||
\(989\) | 7.18128 | 0.228351 | ||||||||
\(990\) | −20.2155 | −0.642491 | ||||||||
\(991\) | 37.9665 | 1.20605 | 0.603023 | − | 0.797724i | \(-0.293963\pi\) | ||||
0.603023 | + | 0.797724i | \(0.293963\pi\) | |||||||
\(992\) | −2.72687 | −0.0865782 | ||||||||
\(993\) | −86.9872 | −2.76046 | ||||||||
\(994\) | 5.28996 | 0.167787 | ||||||||
\(995\) | −21.7200 | −0.688569 | ||||||||
\(996\) | −3.52896 | −0.111819 | ||||||||
\(997\) | 1.96182 | 0.0621313 | 0.0310657 | − | 0.999517i | \(-0.490110\pi\) | ||||
0.0310657 | + | 0.999517i | \(0.490110\pi\) | |||||||
\(998\) | −12.3810 | −0.391915 | ||||||||
\(999\) | 11.0295 | 0.348957 |
(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 | 8026.2.a.a.1.2 | ✓ | 71 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8026.2.a.a.1.2 | ✓ | 71 | 1.1 | even | 1 | trivial |