Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4006,2,Mod(1,4006)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4006, 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("4006.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4006 = 2 \cdot 2003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4006.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: | \(31.9880710497\) |
Analytic rank: | \(1\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 4006.1 |
$q$-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 | ||||||||
\(3\) | −2.30611 | −1.33144 | −0.665718 | − | 0.746204i | \(-0.731874\pi\) | ||||
−0.665718 | + | 0.746204i | \(0.731874\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.88128 | 1.73576 | 0.867880 | − | 0.496774i | \(-0.165482\pi\) | ||||
0.867880 | + | 0.496774i | \(0.165482\pi\) | |||||||
\(6\) | 2.30611 | 0.941467 | ||||||||
\(7\) | 0.245423 | 0.0927612 | 0.0463806 | − | 0.998924i | \(-0.485231\pi\) | ||||
0.0463806 | + | 0.998924i | \(0.485231\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.31816 | 0.772720 | ||||||||
\(10\) | −3.88128 | −1.22737 | ||||||||
\(11\) | −2.29954 | −0.693338 | −0.346669 | − | 0.937988i | \(-0.612687\pi\) | ||||
−0.346669 | + | 0.937988i | \(0.612687\pi\) | |||||||
\(12\) | −2.30611 | −0.665718 | ||||||||
\(13\) | −5.34839 | −1.48338 | −0.741689 | − | 0.670744i | \(-0.765975\pi\) | ||||
−0.741689 | + | 0.670744i | \(0.765975\pi\) | |||||||
\(14\) | −0.245423 | −0.0655921 | ||||||||
\(15\) | −8.95067 | −2.31105 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.60721 | −0.632341 | −0.316170 | − | 0.948702i | \(-0.602397\pi\) | ||||
−0.316170 | + | 0.948702i | \(0.602397\pi\) | |||||||
\(18\) | −2.31816 | −0.546395 | ||||||||
\(19\) | 8.55592 | 1.96286 | 0.981431 | − | 0.191816i | \(-0.0614377\pi\) | ||||
0.981431 | + | 0.191816i | \(0.0614377\pi\) | |||||||
\(20\) | 3.88128 | 0.867880 | ||||||||
\(21\) | −0.565974 | −0.123506 | ||||||||
\(22\) | 2.29954 | 0.490264 | ||||||||
\(23\) | 2.94694 | 0.614480 | 0.307240 | − | 0.951632i | \(-0.400595\pi\) | ||||
0.307240 | + | 0.951632i | \(0.400595\pi\) | |||||||
\(24\) | 2.30611 | 0.470733 | ||||||||
\(25\) | 10.0643 | 2.01286 | ||||||||
\(26\) | 5.34839 | 1.04891 | ||||||||
\(27\) | 1.57240 | 0.302609 | ||||||||
\(28\) | 0.245423 | 0.0463806 | ||||||||
\(29\) | −7.74114 | −1.43749 | −0.718747 | − | 0.695272i | \(-0.755284\pi\) | ||||
−0.718747 | + | 0.695272i | \(0.755284\pi\) | |||||||
\(30\) | 8.95067 | 1.63416 | ||||||||
\(31\) | −5.79274 | −1.04041 | −0.520204 | − | 0.854042i | \(-0.674144\pi\) | ||||
−0.520204 | + | 0.854042i | \(0.674144\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 5.30300 | 0.923135 | ||||||||
\(34\) | 2.60721 | 0.447132 | ||||||||
\(35\) | 0.952555 | 0.161011 | ||||||||
\(36\) | 2.31816 | 0.386360 | ||||||||
\(37\) | 9.58016 | 1.57497 | 0.787484 | − | 0.616335i | \(-0.211383\pi\) | ||||
0.787484 | + | 0.616335i | \(0.211383\pi\) | |||||||
\(38\) | −8.55592 | −1.38795 | ||||||||
\(39\) | 12.3340 | 1.97502 | ||||||||
\(40\) | −3.88128 | −0.613684 | ||||||||
\(41\) | −6.77464 | −1.05802 | −0.529010 | − | 0.848615i | \(-0.677437\pi\) | ||||
−0.529010 | + | 0.848615i | \(0.677437\pi\) | |||||||
\(42\) | 0.565974 | 0.0873316 | ||||||||
\(43\) | 3.09940 | 0.472654 | 0.236327 | − | 0.971674i | \(-0.424056\pi\) | ||||
0.236327 | + | 0.971674i | \(0.424056\pi\) | |||||||
\(44\) | −2.29954 | −0.346669 | ||||||||
\(45\) | 8.99742 | 1.34126 | ||||||||
\(46\) | −2.94694 | −0.434503 | ||||||||
\(47\) | −7.31928 | −1.06763 | −0.533814 | − | 0.845602i | \(-0.679242\pi\) | ||||
−0.533814 | + | 0.845602i | \(0.679242\pi\) | |||||||
\(48\) | −2.30611 | −0.332859 | ||||||||
\(49\) | −6.93977 | −0.991395 | ||||||||
\(50\) | −10.0643 | −1.42331 | ||||||||
\(51\) | 6.01252 | 0.841921 | ||||||||
\(52\) | −5.34839 | −0.741689 | ||||||||
\(53\) | 5.03416 | 0.691495 | 0.345748 | − | 0.938328i | \(-0.387625\pi\) | ||||
0.345748 | + | 0.938328i | \(0.387625\pi\) | |||||||
\(54\) | −1.57240 | −0.213977 | ||||||||
\(55\) | −8.92516 | −1.20347 | ||||||||
\(56\) | −0.245423 | −0.0327960 | ||||||||
\(57\) | −19.7309 | −2.61342 | ||||||||
\(58\) | 7.74114 | 1.01646 | ||||||||
\(59\) | −8.17961 | −1.06489 | −0.532447 | − | 0.846463i | \(-0.678727\pi\) | ||||
−0.532447 | + | 0.846463i | \(0.678727\pi\) | |||||||
\(60\) | −8.95067 | −1.15553 | ||||||||
\(61\) | −8.95515 | −1.14659 | −0.573295 | − | 0.819349i | \(-0.694335\pi\) | ||||
−0.573295 | + | 0.819349i | \(0.694335\pi\) | |||||||
\(62\) | 5.79274 | 0.735679 | ||||||||
\(63\) | 0.568930 | 0.0716784 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −20.7586 | −2.57479 | ||||||||
\(66\) | −5.30300 | −0.652755 | ||||||||
\(67\) | −3.26763 | −0.399204 | −0.199602 | − | 0.979877i | \(-0.563965\pi\) | ||||
−0.199602 | + | 0.979877i | \(0.563965\pi\) | |||||||
\(68\) | −2.60721 | −0.316170 | ||||||||
\(69\) | −6.79598 | −0.818140 | ||||||||
\(70\) | −0.952555 | −0.113852 | ||||||||
\(71\) | 12.8152 | 1.52088 | 0.760440 | − | 0.649408i | \(-0.224983\pi\) | ||||
0.760440 | + | 0.649408i | \(0.224983\pi\) | |||||||
\(72\) | −2.31816 | −0.273198 | ||||||||
\(73\) | 7.56389 | 0.885287 | 0.442643 | − | 0.896698i | \(-0.354041\pi\) | ||||
0.442643 | + | 0.896698i | \(0.354041\pi\) | |||||||
\(74\) | −9.58016 | −1.11367 | ||||||||
\(75\) | −23.2094 | −2.68000 | ||||||||
\(76\) | 8.55592 | 0.981431 | ||||||||
\(77\) | −0.564361 | −0.0643149 | ||||||||
\(78\) | −12.3340 | −1.39655 | ||||||||
\(79\) | 13.8552 | 1.55883 | 0.779417 | − | 0.626506i | \(-0.215515\pi\) | ||||
0.779417 | + | 0.626506i | \(0.215515\pi\) | |||||||
\(80\) | 3.88128 | 0.433940 | ||||||||
\(81\) | −10.5806 | −1.17562 | ||||||||
\(82\) | 6.77464 | 0.748134 | ||||||||
\(83\) | −7.26049 | −0.796942 | −0.398471 | − | 0.917181i | \(-0.630459\pi\) | ||||
−0.398471 | + | 0.917181i | \(0.630459\pi\) | |||||||
\(84\) | −0.565974 | −0.0617528 | ||||||||
\(85\) | −10.1193 | −1.09759 | ||||||||
\(86\) | −3.09940 | −0.334217 | ||||||||
\(87\) | 17.8519 | 1.91393 | ||||||||
\(88\) | 2.29954 | 0.245132 | ||||||||
\(89\) | −12.3995 | −1.31434 | −0.657172 | − | 0.753741i | \(-0.728247\pi\) | ||||
−0.657172 | + | 0.753741i | \(0.728247\pi\) | |||||||
\(90\) | −8.99742 | −0.948411 | ||||||||
\(91\) | −1.31262 | −0.137600 | ||||||||
\(92\) | 2.94694 | 0.307240 | ||||||||
\(93\) | 13.3587 | 1.38523 | ||||||||
\(94\) | 7.31928 | 0.754926 | ||||||||
\(95\) | 33.2079 | 3.40706 | ||||||||
\(96\) | 2.30611 | 0.235367 | ||||||||
\(97\) | −7.83860 | −0.795889 | −0.397944 | − | 0.917409i | \(-0.630276\pi\) | ||||
−0.397944 | + | 0.917409i | \(0.630276\pi\) | |||||||
\(98\) | 6.93977 | 0.701022 | ||||||||
\(99\) | −5.33070 | −0.535756 | ||||||||
\(100\) | 10.0643 | 1.00643 | ||||||||
\(101\) | −2.14814 | −0.213748 | −0.106874 | − | 0.994273i | \(-0.534084\pi\) | ||||
−0.106874 | + | 0.994273i | \(0.534084\pi\) | |||||||
\(102\) | −6.01252 | −0.595328 | ||||||||
\(103\) | −9.24718 | −0.911152 | −0.455576 | − | 0.890197i | \(-0.650567\pi\) | ||||
−0.455576 | + | 0.890197i | \(0.650567\pi\) | |||||||
\(104\) | 5.34839 | 0.524453 | ||||||||
\(105\) | −2.19670 | −0.214376 | ||||||||
\(106\) | −5.03416 | −0.488961 | ||||||||
\(107\) | 16.7483 | 1.61912 | 0.809558 | − | 0.587040i | \(-0.199707\pi\) | ||||
0.809558 | + | 0.587040i | \(0.199707\pi\) | |||||||
\(108\) | 1.57240 | 0.151305 | ||||||||
\(109\) | −13.1018 | −1.25492 | −0.627461 | − | 0.778648i | \(-0.715906\pi\) | ||||
−0.627461 | + | 0.778648i | \(0.715906\pi\) | |||||||
\(110\) | 8.92516 | 0.850981 | ||||||||
\(111\) | −22.0929 | −2.09697 | ||||||||
\(112\) | 0.245423 | 0.0231903 | ||||||||
\(113\) | 0.805981 | 0.0758204 | 0.0379102 | − | 0.999281i | \(-0.487930\pi\) | ||||
0.0379102 | + | 0.999281i | \(0.487930\pi\) | |||||||
\(114\) | 19.7309 | 1.84797 | ||||||||
\(115\) | 11.4379 | 1.06659 | ||||||||
\(116\) | −7.74114 | −0.718747 | ||||||||
\(117\) | −12.3984 | −1.14623 | ||||||||
\(118\) | 8.17961 | 0.752994 | ||||||||
\(119\) | −0.639869 | −0.0586567 | ||||||||
\(120\) | 8.95067 | 0.817080 | ||||||||
\(121\) | −5.71211 | −0.519282 | ||||||||
\(122\) | 8.95515 | 0.810761 | ||||||||
\(123\) | 15.6231 | 1.40869 | ||||||||
\(124\) | −5.79274 | −0.520204 | ||||||||
\(125\) | 19.6560 | 1.75809 | ||||||||
\(126\) | −0.568930 | −0.0506843 | ||||||||
\(127\) | −12.8644 | −1.14154 | −0.570768 | − | 0.821112i | \(-0.693354\pi\) | ||||
−0.570768 | + | 0.821112i | \(0.693354\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −7.14756 | −0.629308 | ||||||||
\(130\) | 20.7586 | 1.82065 | ||||||||
\(131\) | 1.17305 | 0.102489 | 0.0512447 | − | 0.998686i | \(-0.483681\pi\) | ||||
0.0512447 | + | 0.998686i | \(0.483681\pi\) | |||||||
\(132\) | 5.30300 | 0.461567 | ||||||||
\(133\) | 2.09982 | 0.182077 | ||||||||
\(134\) | 3.26763 | 0.282280 | ||||||||
\(135\) | 6.10293 | 0.525257 | ||||||||
\(136\) | 2.60721 | 0.223566 | ||||||||
\(137\) | 3.53163 | 0.301728 | 0.150864 | − | 0.988555i | \(-0.451794\pi\) | ||||
0.150864 | + | 0.988555i | \(0.451794\pi\) | |||||||
\(138\) | 6.79598 | 0.578512 | ||||||||
\(139\) | −1.28089 | −0.108644 | −0.0543218 | − | 0.998523i | \(-0.517300\pi\) | ||||
−0.0543218 | + | 0.998523i | \(0.517300\pi\) | |||||||
\(140\) | 0.952555 | 0.0805056 | ||||||||
\(141\) | 16.8791 | 1.42148 | ||||||||
\(142\) | −12.8152 | −1.07542 | ||||||||
\(143\) | 12.2989 | 1.02848 | ||||||||
\(144\) | 2.31816 | 0.193180 | ||||||||
\(145\) | −30.0455 | −2.49514 | ||||||||
\(146\) | −7.56389 | −0.625992 | ||||||||
\(147\) | 16.0039 | 1.31998 | ||||||||
\(148\) | 9.58016 | 0.787484 | ||||||||
\(149\) | 11.0768 | 0.907446 | 0.453723 | − | 0.891143i | \(-0.350096\pi\) | ||||
0.453723 | + | 0.891143i | \(0.350096\pi\) | |||||||
\(150\) | 23.2094 | 1.89504 | ||||||||
\(151\) | −3.83532 | −0.312114 | −0.156057 | − | 0.987748i | \(-0.549878\pi\) | ||||
−0.156057 | + | 0.987748i | \(0.549878\pi\) | |||||||
\(152\) | −8.55592 | −0.693976 | ||||||||
\(153\) | −6.04392 | −0.488622 | ||||||||
\(154\) | 0.564361 | 0.0454775 | ||||||||
\(155\) | −22.4832 | −1.80590 | ||||||||
\(156\) | 12.3340 | 0.987510 | ||||||||
\(157\) | 3.37953 | 0.269716 | 0.134858 | − | 0.990865i | \(-0.456942\pi\) | ||||
0.134858 | + | 0.990865i | \(0.456942\pi\) | |||||||
\(158\) | −13.8552 | −1.10226 | ||||||||
\(159\) | −11.6094 | −0.920681 | ||||||||
\(160\) | −3.88128 | −0.306842 | ||||||||
\(161\) | 0.723247 | 0.0569999 | ||||||||
\(162\) | 10.5806 | 0.831292 | ||||||||
\(163\) | 21.8575 | 1.71201 | 0.856004 | − | 0.516969i | \(-0.172940\pi\) | ||||
0.856004 | + | 0.516969i | \(0.172940\pi\) | |||||||
\(164\) | −6.77464 | −0.529010 | ||||||||
\(165\) | 20.5824 | 1.60234 | ||||||||
\(166\) | 7.26049 | 0.563523 | ||||||||
\(167\) | −0.223008 | −0.0172569 | −0.00862843 | − | 0.999963i | \(-0.502747\pi\) | ||||
−0.00862843 | + | 0.999963i | \(0.502747\pi\) | |||||||
\(168\) | 0.565974 | 0.0436658 | ||||||||
\(169\) | 15.6053 | 1.20041 | ||||||||
\(170\) | 10.1193 | 0.776114 | ||||||||
\(171\) | 19.8340 | 1.51674 | ||||||||
\(172\) | 3.09940 | 0.236327 | ||||||||
\(173\) | 3.38213 | 0.257139 | 0.128569 | − | 0.991701i | \(-0.458961\pi\) | ||||
0.128569 | + | 0.991701i | \(0.458961\pi\) | |||||||
\(174\) | −17.8519 | −1.35335 | ||||||||
\(175\) | 2.47002 | 0.186716 | ||||||||
\(176\) | −2.29954 | −0.173334 | ||||||||
\(177\) | 18.8631 | 1.41784 | ||||||||
\(178\) | 12.3995 | 0.929381 | ||||||||
\(179\) | −17.8962 | −1.33762 | −0.668811 | − | 0.743433i | \(-0.733196\pi\) | ||||
−0.668811 | + | 0.743433i | \(0.733196\pi\) | |||||||
\(180\) | 8.99742 | 0.670628 | ||||||||
\(181\) | −20.8892 | −1.55268 | −0.776340 | − | 0.630314i | \(-0.782926\pi\) | ||||
−0.776340 | + | 0.630314i | \(0.782926\pi\) | |||||||
\(182\) | 1.31262 | 0.0972978 | ||||||||
\(183\) | 20.6516 | 1.52661 | ||||||||
\(184\) | −2.94694 | −0.217251 | ||||||||
\(185\) | 37.1832 | 2.73377 | ||||||||
\(186\) | −13.3587 | −0.979509 | ||||||||
\(187\) | 5.99538 | 0.438426 | ||||||||
\(188\) | −7.31928 | −0.533814 | ||||||||
\(189\) | 0.385904 | 0.0280704 | ||||||||
\(190\) | −33.2079 | −2.40915 | ||||||||
\(191\) | −19.5612 | −1.41540 | −0.707699 | − | 0.706514i | \(-0.750267\pi\) | ||||
−0.707699 | + | 0.706514i | \(0.750267\pi\) | |||||||
\(192\) | −2.30611 | −0.166429 | ||||||||
\(193\) | −5.83600 | −0.420085 | −0.210042 | − | 0.977692i | \(-0.567360\pi\) | ||||
−0.210042 | + | 0.977692i | \(0.567360\pi\) | |||||||
\(194\) | 7.83860 | 0.562778 | ||||||||
\(195\) | 47.8717 | 3.42816 | ||||||||
\(196\) | −6.93977 | −0.495698 | ||||||||
\(197\) | 5.29845 | 0.377499 | 0.188749 | − | 0.982025i | \(-0.439557\pi\) | ||||
0.188749 | + | 0.982025i | \(0.439557\pi\) | |||||||
\(198\) | 5.33070 | 0.378837 | ||||||||
\(199\) | 8.35379 | 0.592185 | 0.296092 | − | 0.955159i | \(-0.404316\pi\) | ||||
0.296092 | + | 0.955159i | \(0.404316\pi\) | |||||||
\(200\) | −10.0643 | −0.711654 | ||||||||
\(201\) | 7.53552 | 0.531515 | ||||||||
\(202\) | 2.14814 | 0.151143 | ||||||||
\(203\) | −1.89985 | −0.133344 | ||||||||
\(204\) | 6.01252 | 0.420960 | ||||||||
\(205\) | −26.2943 | −1.83647 | ||||||||
\(206\) | 9.24718 | 0.644282 | ||||||||
\(207\) | 6.83148 | 0.474820 | ||||||||
\(208\) | −5.34839 | −0.370844 | ||||||||
\(209\) | −19.6747 | −1.36093 | ||||||||
\(210\) | 2.19670 | 0.151587 | ||||||||
\(211\) | 9.73855 | 0.670430 | 0.335215 | − | 0.942142i | \(-0.391191\pi\) | ||||
0.335215 | + | 0.942142i | \(0.391191\pi\) | |||||||
\(212\) | 5.03416 | 0.345748 | ||||||||
\(213\) | −29.5532 | −2.02495 | ||||||||
\(214\) | −16.7483 | −1.14489 | ||||||||
\(215\) | 12.0296 | 0.820414 | ||||||||
\(216\) | −1.57240 | −0.106988 | ||||||||
\(217\) | −1.42167 | −0.0965094 | ||||||||
\(218\) | 13.1018 | 0.887364 | ||||||||
\(219\) | −17.4432 | −1.17870 | ||||||||
\(220\) | −8.92516 | −0.601734 | ||||||||
\(221\) | 13.9444 | 0.938000 | ||||||||
\(222\) | 22.0929 | 1.48278 | ||||||||
\(223\) | −18.3042 | −1.22574 | −0.612871 | − | 0.790183i | \(-0.709985\pi\) | ||||
−0.612871 | + | 0.790183i | \(0.709985\pi\) | |||||||
\(224\) | −0.245423 | −0.0163980 | ||||||||
\(225\) | 23.3307 | 1.55538 | ||||||||
\(226\) | −0.805981 | −0.0536131 | ||||||||
\(227\) | −5.33077 | −0.353816 | −0.176908 | − | 0.984227i | \(-0.556609\pi\) | ||||
−0.176908 | + | 0.984227i | \(0.556609\pi\) | |||||||
\(228\) | −19.7309 | −1.30671 | ||||||||
\(229\) | −17.6356 | −1.16540 | −0.582698 | − | 0.812689i | \(-0.698003\pi\) | ||||
−0.582698 | + | 0.812689i | \(0.698003\pi\) | |||||||
\(230\) | −11.4379 | −0.754192 | ||||||||
\(231\) | 1.30148 | 0.0856311 | ||||||||
\(232\) | 7.74114 | 0.508231 | ||||||||
\(233\) | 20.1558 | 1.32045 | 0.660226 | − | 0.751067i | \(-0.270461\pi\) | ||||
0.660226 | + | 0.751067i | \(0.270461\pi\) | |||||||
\(234\) | 12.3984 | 0.810510 | ||||||||
\(235\) | −28.4082 | −1.85314 | ||||||||
\(236\) | −8.17961 | −0.532447 | ||||||||
\(237\) | −31.9517 | −2.07549 | ||||||||
\(238\) | 0.639869 | 0.0414766 | ||||||||
\(239\) | −20.4747 | −1.32440 | −0.662198 | − | 0.749329i | \(-0.730376\pi\) | ||||
−0.662198 | + | 0.749329i | \(0.730376\pi\) | |||||||
\(240\) | −8.95067 | −0.577763 | ||||||||
\(241\) | 12.6703 | 0.816167 | 0.408084 | − | 0.912945i | \(-0.366197\pi\) | ||||
0.408084 | + | 0.912945i | \(0.366197\pi\) | |||||||
\(242\) | 5.71211 | 0.367188 | ||||||||
\(243\) | 19.6829 | 1.26266 | ||||||||
\(244\) | −8.95515 | −0.573295 | ||||||||
\(245\) | −26.9352 | −1.72082 | ||||||||
\(246\) | −15.6231 | −0.996092 | ||||||||
\(247\) | −45.7604 | −2.91166 | ||||||||
\(248\) | 5.79274 | 0.367839 | ||||||||
\(249\) | 16.7435 | 1.06108 | ||||||||
\(250\) | −19.6560 | −1.24315 | ||||||||
\(251\) | −13.6399 | −0.860941 | −0.430471 | − | 0.902605i | \(-0.641652\pi\) | ||||
−0.430471 | + | 0.902605i | \(0.641652\pi\) | |||||||
\(252\) | 0.568930 | 0.0358392 | ||||||||
\(253\) | −6.77661 | −0.426042 | ||||||||
\(254\) | 12.8644 | 0.807187 | ||||||||
\(255\) | 23.3362 | 1.46137 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −24.0699 | −1.50144 | −0.750720 | − | 0.660621i | \(-0.770293\pi\) | ||||
−0.750720 | + | 0.660621i | \(0.770293\pi\) | |||||||
\(258\) | 7.14756 | 0.444988 | ||||||||
\(259\) | 2.35119 | 0.146096 | ||||||||
\(260\) | −20.7586 | −1.28739 | ||||||||
\(261\) | −17.9452 | −1.11078 | ||||||||
\(262\) | −1.17305 | −0.0724710 | ||||||||
\(263\) | 27.3360 | 1.68561 | 0.842804 | − | 0.538221i | \(-0.180903\pi\) | ||||
0.842804 | + | 0.538221i | \(0.180903\pi\) | |||||||
\(264\) | −5.30300 | −0.326377 | ||||||||
\(265\) | 19.5390 | 1.20027 | ||||||||
\(266\) | −2.09982 | −0.128748 | ||||||||
\(267\) | 28.5946 | 1.74996 | ||||||||
\(268\) | −3.26763 | −0.199602 | ||||||||
\(269\) | −32.5010 | −1.98162 | −0.990809 | − | 0.135265i | \(-0.956812\pi\) | ||||
−0.990809 | + | 0.135265i | \(0.956812\pi\) | |||||||
\(270\) | −6.10293 | −0.371413 | ||||||||
\(271\) | −3.73702 | −0.227008 | −0.113504 | − | 0.993538i | \(-0.536207\pi\) | ||||
−0.113504 | + | 0.993538i | \(0.536207\pi\) | |||||||
\(272\) | −2.60721 | −0.158085 | ||||||||
\(273\) | 3.02705 | 0.183205 | ||||||||
\(274\) | −3.53163 | −0.213354 | ||||||||
\(275\) | −23.1433 | −1.39559 | ||||||||
\(276\) | −6.79598 | −0.409070 | ||||||||
\(277\) | 10.3068 | 0.619275 | 0.309638 | − | 0.950855i | \(-0.399792\pi\) | ||||
0.309638 | + | 0.950855i | \(0.399792\pi\) | |||||||
\(278\) | 1.28089 | 0.0768226 | ||||||||
\(279\) | −13.4285 | −0.803943 | ||||||||
\(280\) | −0.952555 | −0.0569261 | ||||||||
\(281\) | −14.2098 | −0.847687 | −0.423843 | − | 0.905736i | \(-0.639319\pi\) | ||||
−0.423843 | + | 0.905736i | \(0.639319\pi\) | |||||||
\(282\) | −16.8791 | −1.00514 | ||||||||
\(283\) | 21.5215 | 1.27932 | 0.639660 | − | 0.768658i | \(-0.279075\pi\) | ||||
0.639660 | + | 0.768658i | \(0.279075\pi\) | |||||||
\(284\) | 12.8152 | 0.760440 | ||||||||
\(285\) | −76.5811 | −4.53628 | ||||||||
\(286\) | −12.2989 | −0.727246 | ||||||||
\(287\) | −1.66265 | −0.0981433 | ||||||||
\(288\) | −2.31816 | −0.136599 | ||||||||
\(289\) | −10.2025 | −0.600145 | ||||||||
\(290\) | 30.0455 | 1.76433 | ||||||||
\(291\) | 18.0767 | 1.05967 | ||||||||
\(292\) | 7.56389 | 0.442643 | ||||||||
\(293\) | −4.58164 | −0.267662 | −0.133831 | − | 0.991004i | \(-0.542728\pi\) | ||||
−0.133831 | + | 0.991004i | \(0.542728\pi\) | |||||||
\(294\) | −16.0039 | −0.933366 | ||||||||
\(295\) | −31.7473 | −1.84840 | ||||||||
\(296\) | −9.58016 | −0.556835 | ||||||||
\(297\) | −3.61581 | −0.209810 | ||||||||
\(298\) | −11.0768 | −0.641661 | ||||||||
\(299\) | −15.7614 | −0.911505 | ||||||||
\(300\) | −23.2094 | −1.34000 | ||||||||
\(301\) | 0.760664 | 0.0438440 | ||||||||
\(302\) | 3.83532 | 0.220698 | ||||||||
\(303\) | 4.95385 | 0.284591 | ||||||||
\(304\) | 8.55592 | 0.490715 | ||||||||
\(305\) | −34.7574 | −1.99020 | ||||||||
\(306\) | 6.04392 | 0.345508 | ||||||||
\(307\) | −29.3783 | −1.67671 | −0.838355 | − | 0.545125i | \(-0.816482\pi\) | ||||
−0.838355 | + | 0.545125i | \(0.816482\pi\) | |||||||
\(308\) | −0.564361 | −0.0321574 | ||||||||
\(309\) | 21.3251 | 1.21314 | ||||||||
\(310\) | 22.4832 | 1.27696 | ||||||||
\(311\) | 7.10079 | 0.402649 | 0.201324 | − | 0.979525i | \(-0.435475\pi\) | ||||
0.201324 | + | 0.979525i | \(0.435475\pi\) | |||||||
\(312\) | −12.3340 | −0.698275 | ||||||||
\(313\) | 1.74949 | 0.0988872 | 0.0494436 | − | 0.998777i | \(-0.484255\pi\) | ||||
0.0494436 | + | 0.998777i | \(0.484255\pi\) | |||||||
\(314\) | −3.37953 | −0.190718 | ||||||||
\(315\) | 2.20817 | 0.124417 | ||||||||
\(316\) | 13.8552 | 0.779417 | ||||||||
\(317\) | −24.5895 | −1.38108 | −0.690542 | − | 0.723292i | \(-0.742628\pi\) | ||||
−0.690542 | + | 0.723292i | \(0.742628\pi\) | |||||||
\(318\) | 11.6094 | 0.651020 | ||||||||
\(319\) | 17.8011 | 0.996669 | ||||||||
\(320\) | 3.88128 | 0.216970 | ||||||||
\(321\) | −38.6234 | −2.15575 | ||||||||
\(322\) | −0.723247 | −0.0403050 | ||||||||
\(323\) | −22.3070 | −1.24120 | ||||||||
\(324\) | −10.5806 | −0.587812 | ||||||||
\(325\) | −53.8279 | −2.98583 | ||||||||
\(326\) | −21.8575 | −1.21057 | ||||||||
\(327\) | 30.2142 | 1.67085 | ||||||||
\(328\) | 6.77464 | 0.374067 | ||||||||
\(329\) | −1.79632 | −0.0990344 | ||||||||
\(330\) | −20.5824 | −1.13303 | ||||||||
\(331\) | −1.60774 | −0.0883692 | −0.0441846 | − | 0.999023i | \(-0.514069\pi\) | ||||
−0.0441846 | + | 0.999023i | \(0.514069\pi\) | |||||||
\(332\) | −7.26049 | −0.398471 | ||||||||
\(333\) | 22.2083 | 1.21701 | ||||||||
\(334\) | 0.223008 | 0.0122024 | ||||||||
\(335\) | −12.6826 | −0.692923 | ||||||||
\(336\) | −0.565974 | −0.0308764 | ||||||||
\(337\) | 20.8938 | 1.13816 | 0.569080 | − | 0.822282i | \(-0.307299\pi\) | ||||
0.569080 | + | 0.822282i | \(0.307299\pi\) | |||||||
\(338\) | −15.6053 | −0.848816 | ||||||||
\(339\) | −1.85868 | −0.100950 | ||||||||
\(340\) | −10.1193 | −0.548796 | ||||||||
\(341\) | 13.3207 | 0.721354 | ||||||||
\(342\) | −19.8340 | −1.07250 | ||||||||
\(343\) | −3.42114 | −0.184724 | ||||||||
\(344\) | −3.09940 | −0.167108 | ||||||||
\(345\) | −26.3771 | −1.42009 | ||||||||
\(346\) | −3.38213 | −0.181825 | ||||||||
\(347\) | −3.34010 | −0.179306 | −0.0896529 | − | 0.995973i | \(-0.528576\pi\) | ||||
−0.0896529 | + | 0.995973i | \(0.528576\pi\) | |||||||
\(348\) | 17.8519 | 0.956965 | ||||||||
\(349\) | 1.62440 | 0.0869522 | 0.0434761 | − | 0.999054i | \(-0.486157\pi\) | ||||
0.0434761 | + | 0.999054i | \(0.486157\pi\) | |||||||
\(350\) | −2.47002 | −0.132028 | ||||||||
\(351\) | −8.40983 | −0.448883 | ||||||||
\(352\) | 2.29954 | 0.122566 | ||||||||
\(353\) | −33.8642 | −1.80241 | −0.901206 | − | 0.433391i | \(-0.857317\pi\) | ||||
−0.901206 | + | 0.433391i | \(0.857317\pi\) | |||||||
\(354\) | −18.8631 | −1.00256 | ||||||||
\(355\) | 49.7392 | 2.63988 | ||||||||
\(356\) | −12.3995 | −0.657172 | ||||||||
\(357\) | 1.47561 | 0.0780976 | ||||||||
\(358\) | 17.8962 | 0.945842 | ||||||||
\(359\) | −12.7402 | −0.672400 | −0.336200 | − | 0.941791i | \(-0.609142\pi\) | ||||
−0.336200 | + | 0.941791i | \(0.609142\pi\) | |||||||
\(360\) | −8.99742 | −0.474206 | ||||||||
\(361\) | 54.2037 | 2.85283 | ||||||||
\(362\) | 20.8892 | 1.09791 | ||||||||
\(363\) | 13.1728 | 0.691391 | ||||||||
\(364\) | −1.31262 | −0.0687999 | ||||||||
\(365\) | 29.3576 | 1.53664 | ||||||||
\(366\) | −20.6516 | −1.07948 | ||||||||
\(367\) | 27.2995 | 1.42502 | 0.712511 | − | 0.701661i | \(-0.247558\pi\) | ||||
0.712511 | + | 0.701661i | \(0.247558\pi\) | |||||||
\(368\) | 2.94694 | 0.153620 | ||||||||
\(369\) | −15.7047 | −0.817553 | ||||||||
\(370\) | −37.1832 | −1.93306 | ||||||||
\(371\) | 1.23550 | 0.0641440 | ||||||||
\(372\) | 13.3587 | 0.692617 | ||||||||
\(373\) | −12.3032 | −0.637036 | −0.318518 | − | 0.947917i | \(-0.603185\pi\) | ||||
−0.318518 | + | 0.947917i | \(0.603185\pi\) | |||||||
\(374\) | −5.99538 | −0.310014 | ||||||||
\(375\) | −45.3290 | −2.34078 | ||||||||
\(376\) | 7.31928 | 0.377463 | ||||||||
\(377\) | 41.4026 | 2.13234 | ||||||||
\(378\) | −0.385904 | −0.0198488 | ||||||||
\(379\) | 28.5227 | 1.46511 | 0.732555 | − | 0.680708i | \(-0.238328\pi\) | ||||
0.732555 | + | 0.680708i | \(0.238328\pi\) | |||||||
\(380\) | 33.2079 | 1.70353 | ||||||||
\(381\) | 29.6669 | 1.51988 | ||||||||
\(382\) | 19.5612 | 1.00084 | ||||||||
\(383\) | 16.0293 | 0.819057 | 0.409528 | − | 0.912297i | \(-0.365693\pi\) | ||||
0.409528 | + | 0.912297i | \(0.365693\pi\) | |||||||
\(384\) | 2.30611 | 0.117683 | ||||||||
\(385\) | −2.19044 | −0.111635 | ||||||||
\(386\) | 5.83600 | 0.297045 | ||||||||
\(387\) | 7.18490 | 0.365229 | ||||||||
\(388\) | −7.83860 | −0.397944 | ||||||||
\(389\) | −24.6747 | −1.25106 | −0.625529 | − | 0.780201i | \(-0.715117\pi\) | ||||
−0.625529 | + | 0.780201i | \(0.715117\pi\) | |||||||
\(390\) | −47.8717 | −2.42408 | ||||||||
\(391\) | −7.68329 | −0.388560 | ||||||||
\(392\) | 6.93977 | 0.350511 | ||||||||
\(393\) | −2.70518 | −0.136458 | ||||||||
\(394\) | −5.29845 | −0.266932 | ||||||||
\(395\) | 53.7759 | 2.70576 | ||||||||
\(396\) | −5.33070 | −0.267878 | ||||||||
\(397\) | −16.4833 | −0.827275 | −0.413638 | − | 0.910442i | \(-0.635742\pi\) | ||||
−0.413638 | + | 0.910442i | \(0.635742\pi\) | |||||||
\(398\) | −8.35379 | −0.418738 | ||||||||
\(399\) | −4.84242 | −0.242424 | ||||||||
\(400\) | 10.0643 | 0.503216 | ||||||||
\(401\) | 6.14759 | 0.306996 | 0.153498 | − | 0.988149i | \(-0.450946\pi\) | ||||
0.153498 | + | 0.988149i | \(0.450946\pi\) | |||||||
\(402\) | −7.53552 | −0.375838 | ||||||||
\(403\) | 30.9819 | 1.54332 | ||||||||
\(404\) | −2.14814 | −0.106874 | ||||||||
\(405\) | −41.0663 | −2.04060 | ||||||||
\(406\) | 1.89985 | 0.0942882 | ||||||||
\(407\) | −22.0300 | −1.09199 | ||||||||
\(408\) | −6.01252 | −0.297664 | ||||||||
\(409\) | 5.18329 | 0.256297 | 0.128149 | − | 0.991755i | \(-0.459097\pi\) | ||||
0.128149 | + | 0.991755i | \(0.459097\pi\) | |||||||
\(410\) | 26.2943 | 1.29858 | ||||||||
\(411\) | −8.14435 | −0.401731 | ||||||||
\(412\) | −9.24718 | −0.455576 | ||||||||
\(413\) | −2.00746 | −0.0987809 | ||||||||
\(414\) | −6.83148 | −0.335749 | ||||||||
\(415\) | −28.1800 | −1.38330 | ||||||||
\(416\) | 5.34839 | 0.262226 | ||||||||
\(417\) | 2.95387 | 0.144652 | ||||||||
\(418\) | 19.6747 | 0.962320 | ||||||||
\(419\) | −24.2792 | −1.18611 | −0.593057 | − | 0.805160i | \(-0.702079\pi\) | ||||
−0.593057 | + | 0.805160i | \(0.702079\pi\) | |||||||
\(420\) | −2.19670 | −0.107188 | ||||||||
\(421\) | −39.2970 | −1.91522 | −0.957609 | − | 0.288071i | \(-0.906986\pi\) | ||||
−0.957609 | + | 0.288071i | \(0.906986\pi\) | |||||||
\(422\) | −9.73855 | −0.474065 | ||||||||
\(423\) | −16.9673 | −0.824976 | ||||||||
\(424\) | −5.03416 | −0.244481 | ||||||||
\(425\) | −26.2398 | −1.27281 | ||||||||
\(426\) | 29.5532 | 1.43186 | ||||||||
\(427\) | −2.19780 | −0.106359 | ||||||||
\(428\) | 16.7483 | 0.809558 | ||||||||
\(429\) | −28.3625 | −1.36936 | ||||||||
\(430\) | −12.0296 | −0.580120 | ||||||||
\(431\) | 6.91347 | 0.333010 | 0.166505 | − | 0.986041i | \(-0.446752\pi\) | ||||
0.166505 | + | 0.986041i | \(0.446752\pi\) | |||||||
\(432\) | 1.57240 | 0.0756523 | ||||||||
\(433\) | 13.6592 | 0.656420 | 0.328210 | − | 0.944605i | \(-0.393555\pi\) | ||||
0.328210 | + | 0.944605i | \(0.393555\pi\) | |||||||
\(434\) | 1.42167 | 0.0682425 | ||||||||
\(435\) | 69.2883 | 3.32212 | ||||||||
\(436\) | −13.1018 | −0.627461 | ||||||||
\(437\) | 25.2138 | 1.20614 | ||||||||
\(438\) | 17.4432 | 0.833468 | ||||||||
\(439\) | 25.1355 | 1.19965 | 0.599825 | − | 0.800131i | \(-0.295237\pi\) | ||||
0.599825 | + | 0.800131i | \(0.295237\pi\) | |||||||
\(440\) | 8.92516 | 0.425490 | ||||||||
\(441\) | −16.0875 | −0.766071 | ||||||||
\(442\) | −13.9444 | −0.663266 | ||||||||
\(443\) | 10.0652 | 0.478212 | 0.239106 | − | 0.970993i | \(-0.423146\pi\) | ||||
0.239106 | + | 0.970993i | \(0.423146\pi\) | |||||||
\(444\) | −22.0929 | −1.04848 | ||||||||
\(445\) | −48.1259 | −2.28139 | ||||||||
\(446\) | 18.3042 | 0.866730 | ||||||||
\(447\) | −25.5443 | −1.20820 | ||||||||
\(448\) | 0.245423 | 0.0115952 | ||||||||
\(449\) | 6.76853 | 0.319426 | 0.159713 | − | 0.987163i | \(-0.448943\pi\) | ||||
0.159713 | + | 0.987163i | \(0.448943\pi\) | |||||||
\(450\) | −23.3307 | −1.09982 | ||||||||
\(451\) | 15.5786 | 0.733566 | ||||||||
\(452\) | 0.805981 | 0.0379102 | ||||||||
\(453\) | 8.84469 | 0.415560 | ||||||||
\(454\) | 5.33077 | 0.250185 | ||||||||
\(455\) | −5.09464 | −0.238840 | ||||||||
\(456\) | 19.7309 | 0.923985 | ||||||||
\(457\) | −32.9685 | −1.54220 | −0.771100 | − | 0.636714i | \(-0.780293\pi\) | ||||
−0.771100 | + | 0.636714i | \(0.780293\pi\) | |||||||
\(458\) | 17.6356 | 0.824059 | ||||||||
\(459\) | −4.09958 | −0.191352 | ||||||||
\(460\) | 11.4379 | 0.533295 | ||||||||
\(461\) | 13.2362 | 0.616472 | 0.308236 | − | 0.951310i | \(-0.400261\pi\) | ||||
0.308236 | + | 0.951310i | \(0.400261\pi\) | |||||||
\(462\) | −1.30148 | −0.0605503 | ||||||||
\(463\) | −33.6467 | −1.56369 | −0.781846 | − | 0.623471i | \(-0.785722\pi\) | ||||
−0.781846 | + | 0.623471i | \(0.785722\pi\) | |||||||
\(464\) | −7.74114 | −0.359373 | ||||||||
\(465\) | 51.8489 | 2.40443 | ||||||||
\(466\) | −20.1558 | −0.933700 | ||||||||
\(467\) | −26.2198 | −1.21331 | −0.606654 | − | 0.794966i | \(-0.707489\pi\) | ||||
−0.606654 | + | 0.794966i | \(0.707489\pi\) | |||||||
\(468\) | −12.3984 | −0.573117 | ||||||||
\(469\) | −0.801952 | −0.0370307 | ||||||||
\(470\) | 28.4082 | 1.31037 | ||||||||
\(471\) | −7.79359 | −0.359110 | ||||||||
\(472\) | 8.17961 | 0.376497 | ||||||||
\(473\) | −7.12720 | −0.327709 | ||||||||
\(474\) | 31.9517 | 1.46759 | ||||||||
\(475\) | 86.1094 | 3.95097 | ||||||||
\(476\) | −0.639869 | −0.0293284 | ||||||||
\(477\) | 11.6700 | 0.534332 | ||||||||
\(478\) | 20.4747 | 0.936489 | ||||||||
\(479\) | 17.1251 | 0.782467 | 0.391234 | − | 0.920291i | \(-0.372048\pi\) | ||||
0.391234 | + | 0.920291i | \(0.372048\pi\) | |||||||
\(480\) | 8.95067 | 0.408540 | ||||||||
\(481\) | −51.2384 | −2.33627 | ||||||||
\(482\) | −12.6703 | −0.577117 | ||||||||
\(483\) | −1.66789 | −0.0758917 | ||||||||
\(484\) | −5.71211 | −0.259641 | ||||||||
\(485\) | −30.4238 | −1.38147 | ||||||||
\(486\) | −19.6829 | −0.892834 | ||||||||
\(487\) | −41.8693 | −1.89728 | −0.948640 | − | 0.316358i | \(-0.897540\pi\) | ||||
−0.948640 | + | 0.316358i | \(0.897540\pi\) | |||||||
\(488\) | 8.95515 | 0.405381 | ||||||||
\(489\) | −50.4058 | −2.27943 | ||||||||
\(490\) | 26.9352 | 1.21681 | ||||||||
\(491\) | 9.28697 | 0.419115 | 0.209558 | − | 0.977796i | \(-0.432798\pi\) | ||||
0.209558 | + | 0.977796i | \(0.432798\pi\) | |||||||
\(492\) | 15.6231 | 0.704343 | ||||||||
\(493\) | 20.1828 | 0.908986 | ||||||||
\(494\) | 45.7604 | 2.05886 | ||||||||
\(495\) | −20.6899 | −0.929944 | ||||||||
\(496\) | −5.79274 | −0.260102 | ||||||||
\(497\) | 3.14514 | 0.141079 | ||||||||
\(498\) | −16.7435 | −0.750295 | ||||||||
\(499\) | 15.5818 | 0.697539 | 0.348769 | − | 0.937209i | \(-0.386600\pi\) | ||||
0.348769 | + | 0.937209i | \(0.386600\pi\) | |||||||
\(500\) | 19.6560 | 0.879043 | ||||||||
\(501\) | 0.514281 | 0.0229764 | ||||||||
\(502\) | 13.6399 | 0.608778 | ||||||||
\(503\) | −17.0783 | −0.761485 | −0.380742 | − | 0.924681i | \(-0.624332\pi\) | ||||
−0.380742 | + | 0.924681i | \(0.624332\pi\) | |||||||
\(504\) | −0.568930 | −0.0253421 | ||||||||
\(505\) | −8.33752 | −0.371015 | ||||||||
\(506\) | 6.77661 | 0.301257 | ||||||||
\(507\) | −35.9876 | −1.59826 | ||||||||
\(508\) | −12.8644 | −0.570768 | ||||||||
\(509\) | −30.8133 | −1.36577 | −0.682887 | − | 0.730524i | \(-0.739276\pi\) | ||||
−0.682887 | + | 0.730524i | \(0.739276\pi\) | |||||||
\(510\) | −23.3362 | −1.03335 | ||||||||
\(511\) | 1.85635 | 0.0821203 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 13.4533 | 0.593980 | ||||||||
\(514\) | 24.0699 | 1.06168 | ||||||||
\(515\) | −35.8909 | −1.58154 | ||||||||
\(516\) | −7.14756 | −0.314654 | ||||||||
\(517\) | 16.8310 | 0.740227 | ||||||||
\(518\) | −2.35119 | −0.103305 | ||||||||
\(519\) | −7.79959 | −0.342364 | ||||||||
\(520\) | 20.7586 | 0.910324 | ||||||||
\(521\) | 25.6533 | 1.12389 | 0.561945 | − | 0.827175i | \(-0.310053\pi\) | ||||
0.561945 | + | 0.827175i | \(0.310053\pi\) | |||||||
\(522\) | 17.9452 | 0.785440 | ||||||||
\(523\) | −10.6299 | −0.464812 | −0.232406 | − | 0.972619i | \(-0.574660\pi\) | ||||
−0.232406 | + | 0.972619i | \(0.574660\pi\) | |||||||
\(524\) | 1.17305 | 0.0512447 | ||||||||
\(525\) | −5.69614 | −0.248600 | ||||||||
\(526\) | −27.3360 | −1.19190 | ||||||||
\(527\) | 15.1029 | 0.657892 | ||||||||
\(528\) | 5.30300 | 0.230784 | ||||||||
\(529\) | −14.3155 | −0.622415 | ||||||||
\(530\) | −19.5390 | −0.848719 | ||||||||
\(531\) | −18.9616 | −0.822864 | ||||||||
\(532\) | 2.09982 | 0.0910387 | ||||||||
\(533\) | 36.2334 | 1.56944 | ||||||||
\(534\) | −28.5946 | −1.23741 | ||||||||
\(535\) | 65.0046 | 2.81040 | ||||||||
\(536\) | 3.26763 | 0.141140 | ||||||||
\(537\) | 41.2706 | 1.78096 | ||||||||
\(538\) | 32.5010 | 1.40122 | ||||||||
\(539\) | 15.9583 | 0.687372 | ||||||||
\(540\) | 6.10293 | 0.262628 | ||||||||
\(541\) | 29.3934 | 1.26372 | 0.631860 | − | 0.775082i | \(-0.282292\pi\) | ||||
0.631860 | + | 0.775082i | \(0.282292\pi\) | |||||||
\(542\) | 3.73702 | 0.160519 | ||||||||
\(543\) | 48.1728 | 2.06729 | ||||||||
\(544\) | 2.60721 | 0.111783 | ||||||||
\(545\) | −50.8516 | −2.17824 | ||||||||
\(546\) | −3.02705 | −0.129546 | ||||||||
\(547\) | −42.8685 | −1.83292 | −0.916462 | − | 0.400121i | \(-0.868968\pi\) | ||||
−0.916462 | + | 0.400121i | \(0.868968\pi\) | |||||||
\(548\) | 3.53163 | 0.150864 | ||||||||
\(549\) | −20.7595 | −0.885992 | ||||||||
\(550\) | 23.1433 | 0.986834 | ||||||||
\(551\) | −66.2325 | −2.82160 | ||||||||
\(552\) | 6.79598 | 0.289256 | ||||||||
\(553\) | 3.40039 | 0.144599 | ||||||||
\(554\) | −10.3068 | −0.437894 | ||||||||
\(555\) | −85.7488 | −3.63983 | ||||||||
\(556\) | −1.28089 | −0.0543218 | ||||||||
\(557\) | 8.46717 | 0.358765 | 0.179383 | − | 0.983779i | \(-0.442590\pi\) | ||||
0.179383 | + | 0.983779i | \(0.442590\pi\) | |||||||
\(558\) | 13.4285 | 0.568473 | ||||||||
\(559\) | −16.5768 | −0.701124 | ||||||||
\(560\) | 0.952555 | 0.0402528 | ||||||||
\(561\) | −13.8260 | −0.583736 | ||||||||
\(562\) | 14.2098 | 0.599405 | ||||||||
\(563\) | −34.7945 | −1.46641 | −0.733206 | − | 0.680006i | \(-0.761977\pi\) | ||||
−0.733206 | + | 0.680006i | \(0.761977\pi\) | |||||||
\(564\) | 16.8791 | 0.710738 | ||||||||
\(565\) | 3.12824 | 0.131606 | ||||||||
\(566\) | −21.5215 | −0.904616 | ||||||||
\(567\) | −2.59673 | −0.109052 | ||||||||
\(568\) | −12.8152 | −0.537712 | ||||||||
\(569\) | −32.1547 | −1.34799 | −0.673997 | − | 0.738734i | \(-0.735424\pi\) | ||||
−0.673997 | + | 0.738734i | \(0.735424\pi\) | |||||||
\(570\) | 76.5811 | 3.20763 | ||||||||
\(571\) | 10.2750 | 0.429997 | 0.214998 | − | 0.976614i | \(-0.431025\pi\) | ||||
0.214998 | + | 0.976614i | \(0.431025\pi\) | |||||||
\(572\) | 12.2989 | 0.514241 | ||||||||
\(573\) | 45.1103 | 1.88451 | ||||||||
\(574\) | 1.66265 | 0.0693978 | ||||||||
\(575\) | 29.6589 | 1.23686 | ||||||||
\(576\) | 2.31816 | 0.0965899 | ||||||||
\(577\) | 8.88109 | 0.369725 | 0.184862 | − | 0.982764i | \(-0.440816\pi\) | ||||
0.184862 | + | 0.982764i | \(0.440816\pi\) | |||||||
\(578\) | 10.2025 | 0.424367 | ||||||||
\(579\) | 13.4585 | 0.559316 | ||||||||
\(580\) | −30.0455 | −1.24757 | ||||||||
\(581\) | −1.78189 | −0.0739253 | ||||||||
\(582\) | −18.0767 | −0.749303 | ||||||||
\(583\) | −11.5763 | −0.479440 | ||||||||
\(584\) | −7.56389 | −0.312996 | ||||||||
\(585\) | −48.1217 | −1.98959 | ||||||||
\(586\) | 4.58164 | 0.189266 | ||||||||
\(587\) | −4.48726 | −0.185209 | −0.0926044 | − | 0.995703i | \(-0.529519\pi\) | ||||
−0.0926044 | + | 0.995703i | \(0.529519\pi\) | |||||||
\(588\) | 16.0039 | 0.659989 | ||||||||
\(589\) | −49.5622 | −2.04218 | ||||||||
\(590\) | 31.7473 | 1.30702 | ||||||||
\(591\) | −12.2188 | −0.502615 | ||||||||
\(592\) | 9.58016 | 0.393742 | ||||||||
\(593\) | −21.6360 | −0.888486 | −0.444243 | − | 0.895906i | \(-0.646527\pi\) | ||||
−0.444243 | + | 0.895906i | \(0.646527\pi\) | |||||||
\(594\) | 3.61581 | 0.148358 | ||||||||
\(595\) | −2.48351 | −0.101814 | ||||||||
\(596\) | 11.0768 | 0.453723 | ||||||||
\(597\) | −19.2648 | −0.788456 | ||||||||
\(598\) | 15.7614 | 0.644531 | ||||||||
\(599\) | 24.4527 | 0.999110 | 0.499555 | − | 0.866282i | \(-0.333497\pi\) | ||||
0.499555 | + | 0.866282i | \(0.333497\pi\) | |||||||
\(600\) | 23.2094 | 0.947522 | ||||||||
\(601\) | 0.0653259 | 0.00266470 | 0.00133235 | − | 0.999999i | \(-0.499576\pi\) | ||||
0.00133235 | + | 0.999999i | \(0.499576\pi\) | |||||||
\(602\) | −0.760664 | −0.0310024 | ||||||||
\(603\) | −7.57488 | −0.308473 | ||||||||
\(604\) | −3.83532 | −0.156057 | ||||||||
\(605\) | −22.1703 | −0.901350 | ||||||||
\(606\) | −4.95385 | −0.201236 | ||||||||
\(607\) | 34.2157 | 1.38877 | 0.694386 | − | 0.719602i | \(-0.255676\pi\) | ||||
0.694386 | + | 0.719602i | \(0.255676\pi\) | |||||||
\(608\) | −8.55592 | −0.346988 | ||||||||
\(609\) | 4.38128 | 0.177538 | ||||||||
\(610\) | 34.7574 | 1.40729 | ||||||||
\(611\) | 39.1464 | 1.58369 | ||||||||
\(612\) | −6.04392 | −0.244311 | ||||||||
\(613\) | −20.4991 | −0.827952 | −0.413976 | − | 0.910288i | \(-0.635860\pi\) | ||||
−0.413976 | + | 0.910288i | \(0.635860\pi\) | |||||||
\(614\) | 29.3783 | 1.18561 | ||||||||
\(615\) | 60.6375 | 2.44514 | ||||||||
\(616\) | 0.564361 | 0.0227387 | ||||||||
\(617\) | −4.26274 | −0.171612 | −0.0858058 | − | 0.996312i | \(-0.527346\pi\) | ||||
−0.0858058 | + | 0.996312i | \(0.527346\pi\) | |||||||
\(618\) | −21.3251 | −0.857819 | ||||||||
\(619\) | −8.01079 | −0.321981 | −0.160990 | − | 0.986956i | \(-0.551469\pi\) | ||||
−0.160990 | + | 0.986956i | \(0.551469\pi\) | |||||||
\(620\) | −22.4832 | −0.902948 | ||||||||
\(621\) | 4.63378 | 0.185947 | ||||||||
\(622\) | −7.10079 | −0.284716 | ||||||||
\(623\) | −3.04312 | −0.121920 | ||||||||
\(624\) | 12.3340 | 0.493755 | ||||||||
\(625\) | 25.9688 | 1.03875 | ||||||||
\(626\) | −1.74949 | −0.0699238 | ||||||||
\(627\) | 45.3721 | 1.81199 | ||||||||
\(628\) | 3.37953 | 0.134858 | ||||||||
\(629\) | −24.9775 | −0.995916 | ||||||||
\(630\) | −2.20817 | −0.0879758 | ||||||||
\(631\) | 15.8989 | 0.632923 | 0.316462 | − | 0.948605i | \(-0.397505\pi\) | ||||
0.316462 | + | 0.948605i | \(0.397505\pi\) | |||||||
\(632\) | −13.8552 | −0.551131 | ||||||||
\(633\) | −22.4582 | −0.892634 | ||||||||
\(634\) | 24.5895 | 0.976575 | ||||||||
\(635\) | −49.9305 | −1.98143 | ||||||||
\(636\) | −11.6094 | −0.460341 | ||||||||
\(637\) | 37.1166 | 1.47061 | ||||||||
\(638\) | −17.8011 | −0.704751 | ||||||||
\(639\) | 29.7076 | 1.17521 | ||||||||
\(640\) | −3.88128 | −0.153421 | ||||||||
\(641\) | 3.74559 | 0.147942 | 0.0739710 | − | 0.997260i | \(-0.476433\pi\) | ||||
0.0739710 | + | 0.997260i | \(0.476433\pi\) | |||||||
\(642\) | 38.6234 | 1.52434 | ||||||||
\(643\) | 18.7864 | 0.740862 | 0.370431 | − | 0.928860i | \(-0.379210\pi\) | ||||
0.370431 | + | 0.928860i | \(0.379210\pi\) | |||||||
\(644\) | 0.723247 | 0.0284999 | ||||||||
\(645\) | −27.7417 | −1.09233 | ||||||||
\(646\) | 22.3070 | 0.877659 | ||||||||
\(647\) | −11.8241 | −0.464853 | −0.232426 | − | 0.972614i | \(-0.574666\pi\) | ||||
−0.232426 | + | 0.972614i | \(0.574666\pi\) | |||||||
\(648\) | 10.5806 | 0.415646 | ||||||||
\(649\) | 18.8093 | 0.738332 | ||||||||
\(650\) | 53.8279 | 2.11130 | ||||||||
\(651\) | 3.27854 | 0.128496 | ||||||||
\(652\) | 21.8575 | 0.856004 | ||||||||
\(653\) | −18.5143 | −0.724522 | −0.362261 | − | 0.932077i | \(-0.617995\pi\) | ||||
−0.362261 | + | 0.932077i | \(0.617995\pi\) | |||||||
\(654\) | −30.2142 | −1.18147 | ||||||||
\(655\) | 4.55292 | 0.177897 | ||||||||
\(656\) | −6.77464 | −0.264505 | ||||||||
\(657\) | 17.5343 | 0.684078 | ||||||||
\(658\) | 1.79632 | 0.0700279 | ||||||||
\(659\) | 46.8917 | 1.82664 | 0.913321 | − | 0.407239i | \(-0.133509\pi\) | ||||
0.913321 | + | 0.407239i | \(0.133509\pi\) | |||||||
\(660\) | 20.5824 | 0.801170 | ||||||||
\(661\) | 8.68656 | 0.337868 | 0.168934 | − | 0.985627i | \(-0.445968\pi\) | ||||
0.168934 | + | 0.985627i | \(0.445968\pi\) | |||||||
\(662\) | 1.60774 | 0.0624864 | ||||||||
\(663\) | −32.1573 | −1.24889 | ||||||||
\(664\) | 7.26049 | 0.281762 | ||||||||
\(665\) | 8.14998 | 0.316043 | ||||||||
\(666\) | −22.2083 | −0.860555 | ||||||||
\(667\) | −22.8127 | −0.883310 | ||||||||
\(668\) | −0.223008 | −0.00862843 | ||||||||
\(669\) | 42.2116 | 1.63200 | ||||||||
\(670\) | 12.6826 | 0.489970 | ||||||||
\(671\) | 20.5927 | 0.794974 | ||||||||
\(672\) | 0.565974 | 0.0218329 | ||||||||
\(673\) | −12.5334 | −0.483128 | −0.241564 | − | 0.970385i | \(-0.577660\pi\) | ||||
−0.241564 | + | 0.970385i | \(0.577660\pi\) | |||||||
\(674\) | −20.8938 | −0.804801 | ||||||||
\(675\) | 15.8252 | 0.609111 | ||||||||
\(676\) | 15.6053 | 0.600204 | ||||||||
\(677\) | 9.80719 | 0.376921 | 0.188460 | − | 0.982081i | \(-0.439650\pi\) | ||||
0.188460 | + | 0.982081i | \(0.439650\pi\) | |||||||
\(678\) | 1.85868 | 0.0713823 | ||||||||
\(679\) | −1.92377 | −0.0738276 | ||||||||
\(680\) | 10.1193 | 0.388057 | ||||||||
\(681\) | 12.2934 | 0.471083 | ||||||||
\(682\) | −13.3207 | −0.510074 | ||||||||
\(683\) | 12.9680 | 0.496205 | 0.248103 | − | 0.968734i | \(-0.420193\pi\) | ||||
0.248103 | + | 0.968734i | \(0.420193\pi\) | |||||||
\(684\) | 19.8340 | 0.758371 | ||||||||
\(685\) | 13.7072 | 0.523727 | ||||||||
\(686\) | 3.42114 | 0.130620 | ||||||||
\(687\) | 40.6698 | 1.55165 | ||||||||
\(688\) | 3.09940 | 0.118163 | ||||||||
\(689\) | −26.9247 | −1.02575 | ||||||||
\(690\) | 26.3771 | 1.00416 | ||||||||
\(691\) | −38.8397 | −1.47753 | −0.738765 | − | 0.673963i | \(-0.764591\pi\) | ||||
−0.738765 | + | 0.673963i | \(0.764591\pi\) | |||||||
\(692\) | 3.38213 | 0.128569 | ||||||||
\(693\) | −1.30828 | −0.0496974 | ||||||||
\(694\) | 3.34010 | 0.126788 | ||||||||
\(695\) | −4.97148 | −0.188579 | ||||||||
\(696\) | −17.8519 | −0.676676 | ||||||||
\(697\) | 17.6629 | 0.669030 | ||||||||
\(698\) | −1.62440 | −0.0614845 | ||||||||
\(699\) | −46.4816 | −1.75809 | ||||||||
\(700\) | 2.47002 | 0.0933578 | ||||||||
\(701\) | −28.6510 | −1.08213 | −0.541067 | − | 0.840980i | \(-0.681979\pi\) | ||||
−0.541067 | + | 0.840980i | \(0.681979\pi\) | |||||||
\(702\) | 8.40983 | 0.317409 | ||||||||
\(703\) | 81.9670 | 3.09144 | ||||||||
\(704\) | −2.29954 | −0.0866672 | ||||||||
\(705\) | 65.5125 | 2.46734 | ||||||||
\(706\) | 33.8642 | 1.27450 | ||||||||
\(707\) | −0.527203 | −0.0198275 | ||||||||
\(708\) | 18.8631 | 0.708919 | ||||||||
\(709\) | 34.3459 | 1.28989 | 0.644943 | − | 0.764230i | \(-0.276881\pi\) | ||||
0.644943 | + | 0.764230i | \(0.276881\pi\) | |||||||
\(710\) | −49.7392 | −1.86668 | ||||||||
\(711\) | 32.1186 | 1.20454 | ||||||||
\(712\) | 12.3995 | 0.464691 | ||||||||
\(713\) | −17.0709 | −0.639309 | ||||||||
\(714\) | −1.47561 | −0.0552233 | ||||||||
\(715\) | 47.7353 | 1.78520 | ||||||||
\(716\) | −17.8962 | −0.668811 | ||||||||
\(717\) | 47.2169 | 1.76335 | ||||||||
\(718\) | 12.7402 | 0.475458 | ||||||||
\(719\) | −22.7182 | −0.847247 | −0.423624 | − | 0.905838i | \(-0.639242\pi\) | ||||
−0.423624 | + | 0.905838i | \(0.639242\pi\) | |||||||
\(720\) | 8.99742 | 0.335314 | ||||||||
\(721\) | −2.26947 | −0.0845196 | ||||||||
\(722\) | −54.2037 | −2.01725 | ||||||||
\(723\) | −29.2192 | −1.08667 | ||||||||
\(724\) | −20.8892 | −0.776340 | ||||||||
\(725\) | −77.9092 | −2.89348 | ||||||||
\(726\) | −13.1728 | −0.488887 | ||||||||
\(727\) | 46.4425 | 1.72246 | 0.861229 | − | 0.508217i | \(-0.169695\pi\) | ||||
0.861229 | + | 0.508217i | \(0.169695\pi\) | |||||||
\(728\) | 1.31262 | 0.0486489 | ||||||||
\(729\) | −13.6491 | −0.505523 | ||||||||
\(730\) | −29.3576 | −1.08657 | ||||||||
\(731\) | −8.08078 | −0.298878 | ||||||||
\(732\) | 20.6516 | 0.763305 | ||||||||
\(733\) | 19.4013 | 0.716604 | 0.358302 | − | 0.933606i | \(-0.383356\pi\) | ||||
0.358302 | + | 0.933606i | \(0.383356\pi\) | |||||||
\(734\) | −27.2995 | −1.00764 | ||||||||
\(735\) | 62.1155 | 2.29117 | ||||||||
\(736\) | −2.94694 | −0.108626 | ||||||||
\(737\) | 7.51405 | 0.276783 | ||||||||
\(738\) | 15.7047 | 0.578098 | ||||||||
\(739\) | −22.5901 | −0.830989 | −0.415495 | − | 0.909596i | \(-0.636391\pi\) | ||||
−0.415495 | + | 0.909596i | \(0.636391\pi\) | |||||||
\(740\) | 37.1832 | 1.36688 | ||||||||
\(741\) | 105.529 | 3.87669 | ||||||||
\(742\) | −1.23550 | −0.0453566 | ||||||||
\(743\) | −17.9253 | −0.657614 | −0.328807 | − | 0.944397i | \(-0.606647\pi\) | ||||
−0.328807 | + | 0.944397i | \(0.606647\pi\) | |||||||
\(744\) | −13.3587 | −0.489754 | ||||||||
\(745\) | 42.9921 | 1.57511 | ||||||||
\(746\) | 12.3032 | 0.450453 | ||||||||
\(747\) | −16.8310 | −0.615813 | ||||||||
\(748\) | 5.99538 | 0.219213 | ||||||||
\(749\) | 4.11041 | 0.150191 | ||||||||
\(750\) | 45.3290 | 1.65518 | ||||||||
\(751\) | −7.23733 | −0.264094 | −0.132047 | − | 0.991243i | \(-0.542155\pi\) | ||||
−0.132047 | + | 0.991243i | \(0.542155\pi\) | |||||||
\(752\) | −7.31928 | −0.266907 | ||||||||
\(753\) | 31.4551 | 1.14629 | ||||||||
\(754\) | −41.4026 | −1.50780 | ||||||||
\(755\) | −14.8860 | −0.541755 | ||||||||
\(756\) | 0.385904 | 0.0140352 | ||||||||
\(757\) | 14.5203 | 0.527749 | 0.263874 | − | 0.964557i | \(-0.415000\pi\) | ||||
0.263874 | + | 0.964557i | \(0.415000\pi\) | |||||||
\(758\) | −28.5227 | −1.03599 | ||||||||
\(759\) | 15.6276 | 0.567247 | ||||||||
\(760\) | −33.2079 | −1.20458 | ||||||||
\(761\) | 41.1224 | 1.49069 | 0.745343 | − | 0.666681i | \(-0.232286\pi\) | ||||
0.745343 | + | 0.666681i | \(0.232286\pi\) | |||||||
\(762\) | −29.6669 | −1.07472 | ||||||||
\(763\) | −3.21548 | −0.116408 | ||||||||
\(764\) | −19.5612 | −0.707699 | ||||||||
\(765\) | −23.4581 | −0.848131 | ||||||||
\(766\) | −16.0293 | −0.579160 | ||||||||
\(767\) | 43.7477 | 1.57964 | ||||||||
\(768\) | −2.30611 | −0.0832147 | ||||||||
\(769\) | −18.2255 | −0.657227 | −0.328614 | − | 0.944464i | \(-0.606581\pi\) | ||||
−0.328614 | + | 0.944464i | \(0.606581\pi\) | |||||||
\(770\) | 2.19044 | 0.0789380 | ||||||||
\(771\) | 55.5079 | 1.99907 | ||||||||
\(772\) | −5.83600 | −0.210042 | ||||||||
\(773\) | 9.89491 | 0.355895 | 0.177948 | − | 0.984040i | \(-0.443054\pi\) | ||||
0.177948 | + | 0.984040i | \(0.443054\pi\) | |||||||
\(774\) | −7.18490 | −0.258256 | ||||||||
\(775\) | −58.3000 | −2.09420 | ||||||||
\(776\) | 7.83860 | 0.281389 | ||||||||
\(777\) | −5.42212 | −0.194517 | ||||||||
\(778\) | 24.6747 | 0.884632 | ||||||||
\(779\) | −57.9632 | −2.07675 | ||||||||
\(780\) | 47.8717 | 1.71408 | ||||||||
\(781\) | −29.4690 | −1.05448 | ||||||||
\(782\) | 7.68329 | 0.274754 | ||||||||
\(783\) | −12.1722 | −0.434999 | ||||||||
\(784\) | −6.93977 | −0.247849 | ||||||||
\(785\) | 13.1169 | 0.468163 | ||||||||
\(786\) | 2.70518 | 0.0964905 | ||||||||
\(787\) | −26.8624 | −0.957540 | −0.478770 | − | 0.877940i | \(-0.658917\pi\) | ||||
−0.478770 | + | 0.877940i | \(0.658917\pi\) | |||||||
\(788\) | 5.29845 | 0.188749 | ||||||||
\(789\) | −63.0398 | −2.24428 | ||||||||
\(790\) | −53.7759 | −1.91326 | ||||||||
\(791\) | 0.197807 | 0.00703319 | ||||||||
\(792\) | 5.33070 | 0.189418 | ||||||||
\(793\) | 47.8957 | 1.70082 | ||||||||
\(794\) | 16.4833 | 0.584972 | ||||||||
\(795\) | −45.0591 | −1.59808 | ||||||||
\(796\) | 8.35379 | 0.296092 | ||||||||
\(797\) | −34.4149 | −1.21904 | −0.609518 | − | 0.792772i | \(-0.708637\pi\) | ||||
−0.609518 | + | 0.792772i | \(0.708637\pi\) | |||||||
\(798\) | 4.84242 | 0.171420 | ||||||||
\(799\) | 19.0829 | 0.675104 | ||||||||
\(800\) | −10.0643 | −0.355827 | ||||||||
\(801\) | −28.7440 | −1.01562 | ||||||||
\(802\) | −6.14759 | −0.217079 | ||||||||
\(803\) | −17.3935 | −0.613803 | ||||||||
\(804\) | 7.53552 | 0.265757 | ||||||||
\(805\) | 2.80712 | 0.0989381 | ||||||||
\(806\) | −30.9819 | −1.09129 | ||||||||
\(807\) | 74.9509 | 2.63840 | ||||||||
\(808\) | 2.14814 | 0.0755713 | ||||||||
\(809\) | 14.2937 | 0.502541 | 0.251270 | − | 0.967917i | \(-0.419152\pi\) | ||||
0.251270 | + | 0.967917i | \(0.419152\pi\) | |||||||
\(810\) | 41.0663 | 1.44292 | ||||||||
\(811\) | 36.8290 | 1.29324 | 0.646620 | − | 0.762812i | \(-0.276182\pi\) | ||||
0.646620 | + | 0.762812i | \(0.276182\pi\) | |||||||
\(812\) | −1.89985 | −0.0666718 | ||||||||
\(813\) | 8.61800 | 0.302246 | ||||||||
\(814\) | 22.0300 | 0.772150 | ||||||||
\(815\) | 84.8349 | 2.97164 | ||||||||
\(816\) | 6.01252 | 0.210480 | ||||||||
\(817\) | 26.5182 | 0.927754 | ||||||||
\(818\) | −5.18329 | −0.181230 | ||||||||
\(819\) | −3.04286 | −0.106326 | ||||||||
\(820\) | −26.2943 | −0.918235 | ||||||||
\(821\) | 24.3840 | 0.851008 | 0.425504 | − | 0.904957i | \(-0.360097\pi\) | ||||
0.425504 | + | 0.904957i | \(0.360097\pi\) | |||||||
\(822\) | 8.14435 | 0.284067 | ||||||||
\(823\) | −56.9478 | −1.98507 | −0.992537 | − | 0.121943i | \(-0.961087\pi\) | ||||
−0.992537 | + | 0.121943i | \(0.961087\pi\) | |||||||
\(824\) | 9.24718 | 0.322141 | ||||||||
\(825\) | 53.3711 | 1.85814 | ||||||||
\(826\) | 2.00746 | 0.0698486 | ||||||||
\(827\) | −23.0295 | −0.800814 | −0.400407 | − | 0.916337i | \(-0.631131\pi\) | ||||
−0.400407 | + | 0.916337i | \(0.631131\pi\) | |||||||
\(828\) | 6.83148 | 0.237410 | ||||||||
\(829\) | 11.1243 | 0.386364 | 0.193182 | − | 0.981163i | \(-0.438119\pi\) | ||||
0.193182 | + | 0.981163i | \(0.438119\pi\) | |||||||
\(830\) | 28.1800 | 0.978141 | ||||||||
\(831\) | −23.7686 | −0.824525 | ||||||||
\(832\) | −5.34839 | −0.185422 | ||||||||
\(833\) | 18.0934 | 0.626900 | ||||||||
\(834\) | −2.95387 | −0.102284 | ||||||||
\(835\) | −0.865555 | −0.0299538 | ||||||||
\(836\) | −19.6747 | −0.680463 | ||||||||
\(837\) | −9.10852 | −0.314837 | ||||||||
\(838\) | 24.2792 | 0.838710 | ||||||||
\(839\) | −27.2044 | −0.939199 | −0.469599 | − | 0.882880i | \(-0.655602\pi\) | ||||
−0.469599 | + | 0.882880i | \(0.655602\pi\) | |||||||
\(840\) | 2.19670 | 0.0757934 | ||||||||
\(841\) | 30.9252 | 1.06639 | ||||||||
\(842\) | 39.2970 | 1.35426 | ||||||||
\(843\) | 32.7695 | 1.12864 | ||||||||
\(844\) | 9.73855 | 0.335215 | ||||||||
\(845\) | 60.5685 | 2.08362 | ||||||||
\(846\) | 16.9673 | 0.583346 | ||||||||
\(847\) | −1.40188 | −0.0481693 | ||||||||
\(848\) | 5.03416 | 0.172874 | ||||||||
\(849\) | −49.6310 | −1.70333 | ||||||||
\(850\) | 26.2398 | 0.900016 | ||||||||
\(851\) | 28.2322 | 0.967786 | ||||||||
\(852\) | −29.5532 | −1.01248 | ||||||||
\(853\) | −2.33799 | −0.0800514 | −0.0400257 | − | 0.999199i | \(-0.512744\pi\) | ||||
−0.0400257 | + | 0.999199i | \(0.512744\pi\) | |||||||
\(854\) | 2.19780 | 0.0752072 | ||||||||
\(855\) | 76.9811 | 2.63270 | ||||||||
\(856\) | −16.7483 | −0.572444 | ||||||||
\(857\) | 24.7769 | 0.846363 | 0.423181 | − | 0.906045i | \(-0.360913\pi\) | ||||
0.423181 | + | 0.906045i | \(0.360913\pi\) | |||||||
\(858\) | 28.3625 | 0.968281 | ||||||||
\(859\) | −1.10000 | −0.0375315 | −0.0187657 | − | 0.999824i | \(-0.505974\pi\) | ||||
−0.0187657 | + | 0.999824i | \(0.505974\pi\) | |||||||
\(860\) | 12.0296 | 0.410207 | ||||||||
\(861\) | 3.83427 | 0.130671 | ||||||||
\(862\) | −6.91347 | −0.235474 | ||||||||
\(863\) | −20.1234 | −0.685007 | −0.342504 | − | 0.939517i | \(-0.611275\pi\) | ||||
−0.342504 | + | 0.939517i | \(0.611275\pi\) | |||||||
\(864\) | −1.57240 | −0.0534942 | ||||||||
\(865\) | 13.1270 | 0.446332 | ||||||||
\(866\) | −13.6592 | −0.464159 | ||||||||
\(867\) | 23.5281 | 0.799054 | ||||||||
\(868\) | −1.42167 | −0.0482547 | ||||||||
\(869\) | −31.8607 | −1.08080 | ||||||||
\(870\) | −69.2883 | −2.34909 | ||||||||
\(871\) | 17.4766 | 0.592170 | ||||||||
\(872\) | 13.1018 | 0.443682 | ||||||||
\(873\) | −18.1711 | −0.614999 | ||||||||
\(874\) | −25.2138 | −0.852869 | ||||||||
\(875\) | 4.82404 | 0.163082 | ||||||||
\(876\) | −17.4432 | −0.589351 | ||||||||
\(877\) | 34.3113 | 1.15861 | 0.579305 | − | 0.815111i | \(-0.303324\pi\) | ||||
0.579305 | + | 0.815111i | \(0.303324\pi\) | |||||||
\(878\) | −25.1355 | −0.848281 | ||||||||
\(879\) | 10.5658 | 0.356375 | ||||||||
\(880\) | −8.92516 | −0.300867 | ||||||||
\(881\) | −30.3058 | −1.02103 | −0.510515 | − | 0.859869i | \(-0.670545\pi\) | ||||
−0.510515 | + | 0.859869i | \(0.670545\pi\) | |||||||
\(882\) | 16.0875 | 0.541694 | ||||||||
\(883\) | −28.2442 | −0.950492 | −0.475246 | − | 0.879853i | \(-0.657641\pi\) | ||||
−0.475246 | + | 0.879853i | \(0.657641\pi\) | |||||||
\(884\) | 13.9444 | 0.469000 | ||||||||
\(885\) | 73.2129 | 2.46103 | ||||||||
\(886\) | −10.0652 | −0.338147 | ||||||||
\(887\) | 24.7531 | 0.831129 | 0.415564 | − | 0.909564i | \(-0.363584\pi\) | ||||
0.415564 | + | 0.909564i | \(0.363584\pi\) | |||||||
\(888\) | 22.0929 | 0.741390 | ||||||||
\(889\) | −3.15723 | −0.105890 | ||||||||
\(890\) | 48.1259 | 1.61318 | ||||||||
\(891\) | 24.3306 | 0.815105 | ||||||||
\(892\) | −18.3042 | −0.612871 | ||||||||
\(893\) | −62.6232 | −2.09560 | ||||||||
\(894\) | 25.5443 | 0.854330 | ||||||||
\(895\) | −69.4600 | −2.32179 | ||||||||
\(896\) | −0.245423 | −0.00819901 | ||||||||
\(897\) | 36.3476 | 1.21361 | ||||||||
\(898\) | −6.76853 | −0.225869 | ||||||||
\(899\) | 44.8424 | 1.49558 | ||||||||
\(900\) | 23.3307 | 0.777689 | ||||||||
\(901\) | −13.1251 | −0.437261 | ||||||||
\(902\) | −15.5786 | −0.518710 | ||||||||
\(903\) | −1.75418 | −0.0583754 | ||||||||
\(904\) | −0.805981 | −0.0268065 | ||||||||
\(905\) | −81.0767 | −2.69508 | ||||||||
\(906\) | −8.84469 | −0.293845 | ||||||||
\(907\) | −37.3213 | −1.23923 | −0.619617 | − | 0.784904i | \(-0.712712\pi\) | ||||
−0.619617 | + | 0.784904i | \(0.712712\pi\) | |||||||
\(908\) | −5.33077 | −0.176908 | ||||||||
\(909\) | −4.97973 | −0.165167 | ||||||||
\(910\) | 5.09464 | 0.168886 | ||||||||
\(911\) | −44.6928 | −1.48074 | −0.740369 | − | 0.672201i | \(-0.765349\pi\) | ||||
−0.740369 | + | 0.672201i | \(0.765349\pi\) | |||||||
\(912\) | −19.7309 | −0.653356 | ||||||||
\(913\) | 16.6958 | 0.552550 | ||||||||
\(914\) | 32.9685 | 1.09050 | ||||||||
\(915\) | 80.1546 | 2.64983 | ||||||||
\(916\) | −17.6356 | −0.582698 | ||||||||
\(917\) | 0.287893 | 0.00950705 | ||||||||
\(918\) | 4.09958 | 0.135306 | ||||||||
\(919\) | 58.7669 | 1.93854 | 0.969271 | − | 0.245996i | \(-0.0791151\pi\) | ||||
0.969271 | + | 0.245996i | \(0.0791151\pi\) | |||||||
\(920\) | −11.4379 | −0.377096 | ||||||||
\(921\) | 67.7497 | 2.23243 | ||||||||
\(922\) | −13.2362 | −0.435912 | ||||||||
\(923\) | −68.5405 | −2.25604 | ||||||||
\(924\) | 1.30148 | 0.0428156 | ||||||||
\(925\) | 96.4177 | 3.17019 | ||||||||
\(926\) | 33.6467 | 1.10570 | ||||||||
\(927\) | −21.4364 | −0.704065 | ||||||||
\(928\) | 7.74114 | 0.254115 | ||||||||
\(929\) | −33.9373 | −1.11345 | −0.556723 | − | 0.830698i | \(-0.687941\pi\) | ||||
−0.556723 | + | 0.830698i | \(0.687941\pi\) | |||||||
\(930\) | −51.8489 | −1.70019 | ||||||||
\(931\) | −59.3761 | −1.94597 | ||||||||
\(932\) | 20.1558 | 0.660226 | ||||||||
\(933\) | −16.3752 | −0.536101 | ||||||||
\(934\) | 26.2198 | 0.857939 | ||||||||
\(935\) | 23.2697 | 0.761002 | ||||||||
\(936\) | 12.3984 | 0.405255 | ||||||||
\(937\) | 16.3375 | 0.533722 | 0.266861 | − | 0.963735i | \(-0.414013\pi\) | ||||
0.266861 | + | 0.963735i | \(0.414013\pi\) | |||||||
\(938\) | 0.801952 | 0.0261846 | ||||||||
\(939\) | −4.03453 | −0.131662 | ||||||||
\(940\) | −28.4082 | −0.926572 | ||||||||
\(941\) | −28.7689 | −0.937839 | −0.468919 | − | 0.883241i | \(-0.655356\pi\) | ||||
−0.468919 | + | 0.883241i | \(0.655356\pi\) | |||||||
\(942\) | 7.79359 | 0.253929 | ||||||||
\(943\) | −19.9645 | −0.650132 | ||||||||
\(944\) | −8.17961 | −0.266224 | ||||||||
\(945\) | 1.49780 | 0.0487235 | ||||||||
\(946\) | 7.12720 | 0.231725 | ||||||||
\(947\) | 20.8200 | 0.676560 | 0.338280 | − | 0.941046i | \(-0.390155\pi\) | ||||
0.338280 | + | 0.941046i | \(0.390155\pi\) | |||||||
\(948\) | −31.9517 | −1.03774 | ||||||||
\(949\) | −40.4547 | −1.31321 | ||||||||
\(950\) | −86.1094 | −2.79376 | ||||||||
\(951\) | 56.7062 | 1.83883 | ||||||||
\(952\) | 0.639869 | 0.0207383 | ||||||||
\(953\) | 44.5829 | 1.44418 | 0.722091 | − | 0.691798i | \(-0.243181\pi\) | ||||
0.722091 | + | 0.691798i | \(0.243181\pi\) | |||||||
\(954\) | −11.6700 | −0.377830 | ||||||||
\(955\) | −75.9224 | −2.45679 | ||||||||
\(956\) | −20.4747 | −0.662198 | ||||||||
\(957\) | −41.0513 | −1.32700 | ||||||||
\(958\) | −17.1251 | −0.553288 | ||||||||
\(959\) | 0.866745 | 0.0279886 | ||||||||
\(960\) | −8.95067 | −0.288881 | ||||||||
\(961\) | 2.55585 | 0.0824468 | ||||||||
\(962\) | 51.2384 | 1.65199 | ||||||||
\(963\) | 38.8251 | 1.25112 | ||||||||
\(964\) | 12.6703 | 0.408084 | ||||||||
\(965\) | −22.6511 | −0.729166 | ||||||||
\(966\) | 1.66789 | 0.0536635 | ||||||||
\(967\) | 20.2883 | 0.652429 | 0.326214 | − | 0.945296i | \(-0.394227\pi\) | ||||
0.326214 | + | 0.945296i | \(0.394227\pi\) | |||||||
\(968\) | 5.71211 | 0.183594 | ||||||||
\(969\) | 51.4426 | 1.65257 | ||||||||
\(970\) | 30.4238 | 0.976848 | ||||||||
\(971\) | −16.8673 | −0.541297 | −0.270648 | − | 0.962678i | \(-0.587238\pi\) | ||||
−0.270648 | + | 0.962678i | \(0.587238\pi\) | |||||||
\(972\) | 19.6829 | 0.631329 | ||||||||
\(973\) | −0.314360 | −0.0100779 | ||||||||
\(974\) | 41.8693 | 1.34158 | ||||||||
\(975\) | 124.133 | 3.97544 | ||||||||
\(976\) | −8.95515 | −0.286647 | ||||||||
\(977\) | −17.5910 | −0.562784 | −0.281392 | − | 0.959593i | \(-0.590796\pi\) | ||||
−0.281392 | + | 0.959593i | \(0.590796\pi\) | |||||||
\(978\) | 50.4058 | 1.61180 | ||||||||
\(979\) | 28.5132 | 0.911285 | ||||||||
\(980\) | −26.9352 | −0.860412 | ||||||||
\(981\) | −30.3720 | −0.969703 | ||||||||
\(982\) | −9.28697 | −0.296359 | ||||||||
\(983\) | −44.0687 | −1.40557 | −0.702786 | − | 0.711401i | \(-0.748061\pi\) | ||||
−0.702786 | + | 0.711401i | \(0.748061\pi\) | |||||||
\(984\) | −15.6231 | −0.498046 | ||||||||
\(985\) | 20.5647 | 0.655247 | ||||||||
\(986\) | −20.1828 | −0.642750 | ||||||||
\(987\) | 4.14252 | 0.131858 | ||||||||
\(988\) | −45.7604 | −1.45583 | ||||||||
\(989\) | 9.13374 | 0.290436 | ||||||||
\(990\) | 20.6899 | 0.657569 | ||||||||
\(991\) | −24.4886 | −0.777907 | −0.388954 | − | 0.921257i | \(-0.627163\pi\) | ||||
−0.388954 | + | 0.921257i | \(0.627163\pi\) | |||||||
\(992\) | 5.79274 | 0.183920 | ||||||||
\(993\) | 3.70762 | 0.117658 | ||||||||
\(994\) | −3.14514 | −0.0997577 | ||||||||
\(995\) | 32.4234 | 1.02789 | ||||||||
\(996\) | 16.7435 | 0.530538 | ||||||||
\(997\) | 16.0599 | 0.508622 | 0.254311 | − | 0.967122i | \(-0.418151\pi\) | ||||
0.254311 | + | 0.967122i | \(0.418151\pi\) | |||||||
\(998\) | −15.5818 | −0.493234 | ||||||||
\(999\) | 15.0639 | 0.476600 |
(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 | 4006.2.a.g.1.6 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4006.2.a.g.1.6 | ✓ | 40 | 1.1 | even | 1 | trivial |