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 | 1.7 | ||
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 | ||||||||
\(3\) | −2.23215 | −1.28873 | −0.644365 | − | 0.764718i | \(-0.722878\pi\) | ||||
−0.644365 | + | 0.764718i | \(0.722878\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.75227 | −1.23085 | −0.615427 | − | 0.788194i | \(-0.711016\pi\) | ||||
−0.615427 | + | 0.788194i | \(0.711016\pi\) | |||||||
\(6\) | 2.23215 | 0.911270 | ||||||||
\(7\) | −2.11016 | −0.797566 | −0.398783 | − | 0.917045i | \(-0.630567\pi\) | ||||
−0.398783 | + | 0.917045i | \(0.630567\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.98248 | 0.660826 | ||||||||
\(10\) | 2.75227 | 0.870345 | ||||||||
\(11\) | −1.85331 | −0.558795 | −0.279398 | − | 0.960175i | \(-0.590135\pi\) | ||||
−0.279398 | + | 0.960175i | \(0.590135\pi\) | |||||||
\(12\) | −2.23215 | −0.644365 | ||||||||
\(13\) | −5.20404 | −1.44334 | −0.721671 | − | 0.692236i | \(-0.756626\pi\) | ||||
−0.721671 | + | 0.692236i | \(0.756626\pi\) | |||||||
\(14\) | 2.11016 | 0.563965 | ||||||||
\(15\) | 6.14348 | 1.58624 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.15695 | 0.765674 | 0.382837 | − | 0.923816i | \(-0.374947\pi\) | ||||
0.382837 | + | 0.923816i | \(0.374947\pi\) | |||||||
\(18\) | −1.98248 | −0.467274 | ||||||||
\(19\) | −7.18933 | −1.64935 | −0.824673 | − | 0.565610i | \(-0.808641\pi\) | ||||
−0.824673 | + | 0.565610i | \(0.808641\pi\) | |||||||
\(20\) | −2.75227 | −0.615427 | ||||||||
\(21\) | 4.71019 | 1.02785 | ||||||||
\(22\) | 1.85331 | 0.395128 | ||||||||
\(23\) | 5.98802 | 1.24859 | 0.624294 | − | 0.781190i | \(-0.285387\pi\) | ||||
0.624294 | + | 0.781190i | \(0.285387\pi\) | |||||||
\(24\) | 2.23215 | 0.455635 | ||||||||
\(25\) | 2.57501 | 0.515002 | ||||||||
\(26\) | 5.20404 | 1.02060 | ||||||||
\(27\) | 2.27126 | 0.437104 | ||||||||
\(28\) | −2.11016 | −0.398783 | ||||||||
\(29\) | 0.982740 | 0.182490 | 0.0912451 | − | 0.995828i | \(-0.470915\pi\) | ||||
0.0912451 | + | 0.995828i | \(0.470915\pi\) | |||||||
\(30\) | −6.14348 | −1.12164 | ||||||||
\(31\) | 8.19185 | 1.47130 | 0.735650 | − | 0.677362i | \(-0.236877\pi\) | ||||
0.735650 | + | 0.677362i | \(0.236877\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 4.13687 | 0.720137 | ||||||||
\(34\) | −3.15695 | −0.541413 | ||||||||
\(35\) | 5.80774 | 0.981688 | ||||||||
\(36\) | 1.98248 | 0.330413 | ||||||||
\(37\) | 4.83696 | 0.795192 | 0.397596 | − | 0.917561i | \(-0.369845\pi\) | ||||
0.397596 | + | 0.917561i | \(0.369845\pi\) | |||||||
\(38\) | 7.18933 | 1.16626 | ||||||||
\(39\) | 11.6162 | 1.86008 | ||||||||
\(40\) | 2.75227 | 0.435173 | ||||||||
\(41\) | 1.04417 | 0.163072 | 0.0815362 | − | 0.996670i | \(-0.474017\pi\) | ||||
0.0815362 | + | 0.996670i | \(0.474017\pi\) | |||||||
\(42\) | −4.71019 | −0.726798 | ||||||||
\(43\) | −0.753058 | −0.114840 | −0.0574201 | − | 0.998350i | \(-0.518287\pi\) | ||||
−0.0574201 | + | 0.998350i | \(0.518287\pi\) | |||||||
\(44\) | −1.85331 | −0.279398 | ||||||||
\(45\) | −5.45632 | −0.813380 | ||||||||
\(46\) | −5.98802 | −0.882885 | ||||||||
\(47\) | −3.72764 | −0.543733 | −0.271866 | − | 0.962335i | \(-0.587641\pi\) | ||||
−0.271866 | + | 0.962335i | \(0.587641\pi\) | |||||||
\(48\) | −2.23215 | −0.322183 | ||||||||
\(49\) | −2.54722 | −0.363888 | ||||||||
\(50\) | −2.57501 | −0.364162 | ||||||||
\(51\) | −7.04678 | −0.986747 | ||||||||
\(52\) | −5.20404 | −0.721671 | ||||||||
\(53\) | −5.58254 | −0.766821 | −0.383410 | − | 0.923578i | \(-0.625250\pi\) | ||||
−0.383410 | + | 0.923578i | \(0.625250\pi\) | |||||||
\(54\) | −2.27126 | −0.309079 | ||||||||
\(55\) | 5.10083 | 0.687796 | ||||||||
\(56\) | 2.11016 | 0.281982 | ||||||||
\(57\) | 16.0476 | 2.12556 | ||||||||
\(58\) | −0.982740 | −0.129040 | ||||||||
\(59\) | −8.16846 | −1.06344 | −0.531722 | − | 0.846919i | \(-0.678455\pi\) | ||||
−0.531722 | + | 0.846919i | \(0.678455\pi\) | |||||||
\(60\) | 6.14348 | 0.793120 | ||||||||
\(61\) | 14.4526 | 1.85047 | 0.925235 | − | 0.379395i | \(-0.123868\pi\) | ||||
0.925235 | + | 0.379395i | \(0.123868\pi\) | |||||||
\(62\) | −8.19185 | −1.04037 | ||||||||
\(63\) | −4.18335 | −0.527052 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 14.3230 | 1.77654 | ||||||||
\(66\) | −4.13687 | −0.509213 | ||||||||
\(67\) | 11.4721 | 1.40154 | 0.700771 | − | 0.713386i | \(-0.252839\pi\) | ||||
0.700771 | + | 0.713386i | \(0.252839\pi\) | |||||||
\(68\) | 3.15695 | 0.382837 | ||||||||
\(69\) | −13.3661 | −1.60909 | ||||||||
\(70\) | −5.80774 | −0.694158 | ||||||||
\(71\) | −0.0465372 | −0.00552295 | −0.00276147 | − | 0.999996i | \(-0.500879\pi\) | ||||
−0.00276147 | + | 0.999996i | \(0.500879\pi\) | |||||||
\(72\) | −1.98248 | −0.233637 | ||||||||
\(73\) | −3.43957 | −0.402571 | −0.201285 | − | 0.979533i | \(-0.564512\pi\) | ||||
−0.201285 | + | 0.979533i | \(0.564512\pi\) | |||||||
\(74\) | −4.83696 | −0.562285 | ||||||||
\(75\) | −5.74780 | −0.663699 | ||||||||
\(76\) | −7.18933 | −0.824673 | ||||||||
\(77\) | 3.91079 | 0.445676 | ||||||||
\(78\) | −11.6162 | −1.31527 | ||||||||
\(79\) | 0.984521 | 0.110767 | 0.0553837 | − | 0.998465i | \(-0.482362\pi\) | ||||
0.0553837 | + | 0.998465i | \(0.482362\pi\) | |||||||
\(80\) | −2.75227 | −0.307714 | ||||||||
\(81\) | −11.0172 | −1.22414 | ||||||||
\(82\) | −1.04417 | −0.115310 | ||||||||
\(83\) | −1.05397 | −0.115688 | −0.0578441 | − | 0.998326i | \(-0.518423\pi\) | ||||
−0.0578441 | + | 0.998326i | \(0.518423\pi\) | |||||||
\(84\) | 4.71019 | 0.513924 | ||||||||
\(85\) | −8.68880 | −0.942433 | ||||||||
\(86\) | 0.753058 | 0.0812043 | ||||||||
\(87\) | −2.19362 | −0.235181 | ||||||||
\(88\) | 1.85331 | 0.197564 | ||||||||
\(89\) | −4.09263 | −0.433817 | −0.216909 | − | 0.976192i | \(-0.569597\pi\) | ||||
−0.216909 | + | 0.976192i | \(0.569597\pi\) | |||||||
\(90\) | 5.45632 | 0.575147 | ||||||||
\(91\) | 10.9814 | 1.15116 | ||||||||
\(92\) | 5.98802 | 0.624294 | ||||||||
\(93\) | −18.2854 | −1.89611 | ||||||||
\(94\) | 3.72764 | 0.384477 | ||||||||
\(95\) | 19.7870 | 2.03010 | ||||||||
\(96\) | 2.23215 | 0.227817 | ||||||||
\(97\) | 11.5509 | 1.17281 | 0.586406 | − | 0.810017i | \(-0.300542\pi\) | ||||
0.586406 | + | 0.810017i | \(0.300542\pi\) | |||||||
\(98\) | 2.54722 | 0.257308 | ||||||||
\(99\) | −3.67416 | −0.369266 | ||||||||
\(100\) | 2.57501 | 0.257501 | ||||||||
\(101\) | −0.816156 | −0.0812106 | −0.0406053 | − | 0.999175i | \(-0.512929\pi\) | ||||
−0.0406053 | + | 0.999175i | \(0.512929\pi\) | |||||||
\(102\) | 7.04678 | 0.697735 | ||||||||
\(103\) | 11.6081 | 1.14378 | 0.571891 | − | 0.820330i | \(-0.306210\pi\) | ||||
0.571891 | + | 0.820330i | \(0.306210\pi\) | |||||||
\(104\) | 5.20404 | 0.510298 | ||||||||
\(105\) | −12.9637 | −1.26513 | ||||||||
\(106\) | 5.58254 | 0.542224 | ||||||||
\(107\) | 18.4241 | 1.78113 | 0.890565 | − | 0.454856i | \(-0.150309\pi\) | ||||
0.890565 | + | 0.454856i | \(0.150309\pi\) | |||||||
\(108\) | 2.27126 | 0.218552 | ||||||||
\(109\) | −7.36454 | −0.705395 | −0.352697 | − | 0.935737i | \(-0.614735\pi\) | ||||
−0.352697 | + | 0.935737i | \(0.614735\pi\) | |||||||
\(110\) | −5.10083 | −0.486345 | ||||||||
\(111\) | −10.7968 | −1.02479 | ||||||||
\(112\) | −2.11016 | −0.199392 | ||||||||
\(113\) | 12.5555 | 1.18112 | 0.590560 | − | 0.806994i | \(-0.298907\pi\) | ||||
0.590560 | + | 0.806994i | \(0.298907\pi\) | |||||||
\(114\) | −16.0476 | −1.50300 | ||||||||
\(115\) | −16.4807 | −1.53683 | ||||||||
\(116\) | 0.982740 | 0.0912451 | ||||||||
\(117\) | −10.3169 | −0.953798 | ||||||||
\(118\) | 8.16846 | 0.751968 | ||||||||
\(119\) | −6.66168 | −0.610676 | ||||||||
\(120\) | −6.14348 | −0.560820 | ||||||||
\(121\) | −7.56522 | −0.687748 | ||||||||
\(122\) | −14.4526 | −1.30848 | ||||||||
\(123\) | −2.33075 | −0.210156 | ||||||||
\(124\) | 8.19185 | 0.735650 | ||||||||
\(125\) | 6.67423 | 0.596962 | ||||||||
\(126\) | 4.18335 | 0.372682 | ||||||||
\(127\) | 11.0872 | 0.983828 | 0.491914 | − | 0.870644i | \(-0.336297\pi\) | ||||
0.491914 | + | 0.870644i | \(0.336297\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 1.68094 | 0.147998 | ||||||||
\(130\) | −14.3230 | −1.25621 | ||||||||
\(131\) | 7.46737 | 0.652427 | 0.326214 | − | 0.945296i | \(-0.394227\pi\) | ||||
0.326214 | + | 0.945296i | \(0.394227\pi\) | |||||||
\(132\) | 4.13687 | 0.360068 | ||||||||
\(133\) | 15.1707 | 1.31546 | ||||||||
\(134\) | −11.4721 | −0.991040 | ||||||||
\(135\) | −6.25113 | −0.538011 | ||||||||
\(136\) | −3.15695 | −0.270707 | ||||||||
\(137\) | 2.46456 | 0.210562 | 0.105281 | − | 0.994443i | \(-0.466426\pi\) | ||||
0.105281 | + | 0.994443i | \(0.466426\pi\) | |||||||
\(138\) | 13.3661 | 1.13780 | ||||||||
\(139\) | −14.9720 | −1.26991 | −0.634955 | − | 0.772549i | \(-0.718981\pi\) | ||||
−0.634955 | + | 0.772549i | \(0.718981\pi\) | |||||||
\(140\) | 5.80774 | 0.490844 | ||||||||
\(141\) | 8.32065 | 0.700725 | ||||||||
\(142\) | 0.0465372 | 0.00390531 | ||||||||
\(143\) | 9.64473 | 0.806533 | ||||||||
\(144\) | 1.98248 | 0.165206 | ||||||||
\(145\) | −2.70477 | −0.224619 | ||||||||
\(146\) | 3.43957 | 0.284661 | ||||||||
\(147\) | 5.68576 | 0.468954 | ||||||||
\(148\) | 4.83696 | 0.397596 | ||||||||
\(149\) | −12.9068 | −1.05736 | −0.528682 | − | 0.848820i | \(-0.677314\pi\) | ||||
−0.528682 | + | 0.848820i | \(0.677314\pi\) | |||||||
\(150\) | 5.74780 | 0.469306 | ||||||||
\(151\) | 8.45894 | 0.688379 | 0.344190 | − | 0.938900i | \(-0.388154\pi\) | ||||
0.344190 | + | 0.938900i | \(0.388154\pi\) | |||||||
\(152\) | 7.18933 | 0.583132 | ||||||||
\(153\) | 6.25859 | 0.505977 | ||||||||
\(154\) | −3.91079 | −0.315141 | ||||||||
\(155\) | −22.5462 | −1.81096 | ||||||||
\(156\) | 11.6162 | 0.930039 | ||||||||
\(157\) | −9.38080 | −0.748670 | −0.374335 | − | 0.927294i | \(-0.622129\pi\) | ||||
−0.374335 | + | 0.927294i | \(0.622129\pi\) | |||||||
\(158\) | −0.984521 | −0.0783243 | ||||||||
\(159\) | 12.4610 | 0.988225 | ||||||||
\(160\) | 2.75227 | 0.217586 | ||||||||
\(161\) | −12.6357 | −0.995832 | ||||||||
\(162\) | 11.0172 | 0.865594 | ||||||||
\(163\) | −12.2248 | −0.957520 | −0.478760 | − | 0.877946i | \(-0.658914\pi\) | ||||
−0.478760 | + | 0.877946i | \(0.658914\pi\) | |||||||
\(164\) | 1.04417 | 0.0815362 | ||||||||
\(165\) | −11.3858 | −0.886383 | ||||||||
\(166\) | 1.05397 | 0.0818039 | ||||||||
\(167\) | −11.2733 | −0.872358 | −0.436179 | − | 0.899860i | \(-0.643668\pi\) | ||||
−0.436179 | + | 0.899860i | \(0.643668\pi\) | |||||||
\(168\) | −4.71019 | −0.363399 | ||||||||
\(169\) | 14.0821 | 1.08324 | ||||||||
\(170\) | 8.68880 | 0.666401 | ||||||||
\(171\) | −14.2527 | −1.08993 | ||||||||
\(172\) | −0.753058 | −0.0574201 | ||||||||
\(173\) | −2.55843 | −0.194514 | −0.0972569 | − | 0.995259i | \(-0.531007\pi\) | ||||
−0.0972569 | + | 0.995259i | \(0.531007\pi\) | |||||||
\(174\) | 2.19362 | 0.166298 | ||||||||
\(175\) | −5.43369 | −0.410748 | ||||||||
\(176\) | −1.85331 | −0.139699 | ||||||||
\(177\) | 18.2332 | 1.37049 | ||||||||
\(178\) | 4.09263 | 0.306755 | ||||||||
\(179\) | 0.299051 | 0.0223521 | 0.0111760 | − | 0.999938i | \(-0.496442\pi\) | ||||
0.0111760 | + | 0.999938i | \(0.496442\pi\) | |||||||
\(180\) | −5.45632 | −0.406690 | ||||||||
\(181\) | 10.4338 | 0.775538 | 0.387769 | − | 0.921757i | \(-0.373246\pi\) | ||||
0.387769 | + | 0.921757i | \(0.373246\pi\) | |||||||
\(182\) | −10.9814 | −0.813994 | ||||||||
\(183\) | −32.2604 | −2.38476 | ||||||||
\(184\) | −5.98802 | −0.441442 | ||||||||
\(185\) | −13.3126 | −0.978765 | ||||||||
\(186\) | 18.2854 | 1.34075 | ||||||||
\(187\) | −5.85083 | −0.427855 | ||||||||
\(188\) | −3.72764 | −0.271866 | ||||||||
\(189\) | −4.79272 | −0.348619 | ||||||||
\(190\) | −19.7870 | −1.43550 | ||||||||
\(191\) | −13.5586 | −0.981066 | −0.490533 | − | 0.871423i | \(-0.663198\pi\) | ||||
−0.490533 | + | 0.871423i | \(0.663198\pi\) | |||||||
\(192\) | −2.23215 | −0.161091 | ||||||||
\(193\) | 9.87008 | 0.710464 | 0.355232 | − | 0.934778i | \(-0.384402\pi\) | ||||
0.355232 | + | 0.934778i | \(0.384402\pi\) | |||||||
\(194\) | −11.5509 | −0.829304 | ||||||||
\(195\) | −31.9709 | −2.28949 | ||||||||
\(196\) | −2.54722 | −0.181944 | ||||||||
\(197\) | −13.9126 | −0.991229 | −0.495614 | − | 0.868543i | \(-0.665057\pi\) | ||||
−0.495614 | + | 0.868543i | \(0.665057\pi\) | |||||||
\(198\) | 3.67416 | 0.261111 | ||||||||
\(199\) | 3.99828 | 0.283431 | 0.141715 | − | 0.989907i | \(-0.454738\pi\) | ||||
0.141715 | + | 0.989907i | \(0.454738\pi\) | |||||||
\(200\) | −2.57501 | −0.182081 | ||||||||
\(201\) | −25.6074 | −1.80621 | ||||||||
\(202\) | 0.816156 | 0.0574246 | ||||||||
\(203\) | −2.07374 | −0.145548 | ||||||||
\(204\) | −7.04678 | −0.493373 | ||||||||
\(205\) | −2.87385 | −0.200718 | ||||||||
\(206\) | −11.6081 | −0.808776 | ||||||||
\(207\) | 11.8711 | 0.825099 | ||||||||
\(208\) | −5.20404 | −0.360836 | ||||||||
\(209\) | 13.3241 | 0.921647 | ||||||||
\(210\) | 12.9637 | 0.894583 | ||||||||
\(211\) | 2.75626 | 0.189749 | 0.0948743 | − | 0.995489i | \(-0.469755\pi\) | ||||
0.0948743 | + | 0.995489i | \(0.469755\pi\) | |||||||
\(212\) | −5.58254 | −0.383410 | ||||||||
\(213\) | 0.103878 | 0.00711759 | ||||||||
\(214\) | −18.4241 | −1.25945 | ||||||||
\(215\) | 2.07262 | 0.141352 | ||||||||
\(216\) | −2.27126 | −0.154540 | ||||||||
\(217\) | −17.2861 | −1.17346 | ||||||||
\(218\) | 7.36454 | 0.498789 | ||||||||
\(219\) | 7.67762 | 0.518805 | ||||||||
\(220\) | 5.10083 | 0.343898 | ||||||||
\(221\) | −16.4289 | −1.10513 | ||||||||
\(222\) | 10.7968 | 0.724634 | ||||||||
\(223\) | 1.88498 | 0.126228 | 0.0631139 | − | 0.998006i | \(-0.479897\pi\) | ||||
0.0631139 | + | 0.998006i | \(0.479897\pi\) | |||||||
\(224\) | 2.11016 | 0.140991 | ||||||||
\(225\) | 5.10490 | 0.340327 | ||||||||
\(226\) | −12.5555 | −0.835178 | ||||||||
\(227\) | −1.41936 | −0.0942060 | −0.0471030 | − | 0.998890i | \(-0.514999\pi\) | ||||
−0.0471030 | + | 0.998890i | \(0.514999\pi\) | |||||||
\(228\) | 16.0476 | 1.06278 | ||||||||
\(229\) | −13.1725 | −0.870462 | −0.435231 | − | 0.900319i | \(-0.643333\pi\) | ||||
−0.435231 | + | 0.900319i | \(0.643333\pi\) | |||||||
\(230\) | 16.4807 | 1.08670 | ||||||||
\(231\) | −8.72947 | −0.574357 | ||||||||
\(232\) | −0.982740 | −0.0645201 | ||||||||
\(233\) | −3.47205 | −0.227461 | −0.113731 | − | 0.993512i | \(-0.536280\pi\) | ||||
−0.113731 | + | 0.993512i | \(0.536280\pi\) | |||||||
\(234\) | 10.3169 | 0.674437 | ||||||||
\(235\) | 10.2595 | 0.669256 | ||||||||
\(236\) | −8.16846 | −0.531722 | ||||||||
\(237\) | −2.19760 | −0.142749 | ||||||||
\(238\) | 6.66168 | 0.431813 | ||||||||
\(239\) | 4.50429 | 0.291358 | 0.145679 | − | 0.989332i | \(-0.453463\pi\) | ||||
0.145679 | + | 0.989332i | \(0.453463\pi\) | |||||||
\(240\) | 6.14348 | 0.396560 | ||||||||
\(241\) | −4.21948 | −0.271801 | −0.135900 | − | 0.990723i | \(-0.543393\pi\) | ||||
−0.135900 | + | 0.990723i | \(0.543393\pi\) | |||||||
\(242\) | 7.56522 | 0.486311 | ||||||||
\(243\) | 17.7783 | 1.14048 | ||||||||
\(244\) | 14.4526 | 0.925235 | ||||||||
\(245\) | 7.01064 | 0.447893 | ||||||||
\(246\) | 2.33075 | 0.148603 | ||||||||
\(247\) | 37.4136 | 2.38057 | ||||||||
\(248\) | −8.19185 | −0.520183 | ||||||||
\(249\) | 2.35261 | 0.149091 | ||||||||
\(250\) | −6.67423 | −0.422116 | ||||||||
\(251\) | −3.31411 | −0.209185 | −0.104593 | − | 0.994515i | \(-0.533354\pi\) | ||||
−0.104593 | + | 0.994515i | \(0.533354\pi\) | |||||||
\(252\) | −4.18335 | −0.263526 | ||||||||
\(253\) | −11.0977 | −0.697705 | ||||||||
\(254\) | −11.0872 | −0.695672 | ||||||||
\(255\) | 19.3947 | 1.21454 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.48515 | −0.279776 | −0.139888 | − | 0.990167i | \(-0.544674\pi\) | ||||
−0.139888 | + | 0.990167i | \(0.544674\pi\) | |||||||
\(258\) | −1.68094 | −0.104650 | ||||||||
\(259\) | −10.2068 | −0.634218 | ||||||||
\(260\) | 14.3230 | 0.888272 | ||||||||
\(261\) | 1.94826 | 0.120594 | ||||||||
\(262\) | −7.46737 | −0.461336 | ||||||||
\(263\) | 15.9494 | 0.983484 | 0.491742 | − | 0.870741i | \(-0.336360\pi\) | ||||
0.491742 | + | 0.870741i | \(0.336360\pi\) | |||||||
\(264\) | −4.13687 | −0.254607 | ||||||||
\(265\) | 15.3647 | 0.943844 | ||||||||
\(266\) | −15.1707 | −0.930172 | ||||||||
\(267\) | 9.13534 | 0.559074 | ||||||||
\(268\) | 11.4721 | 0.700771 | ||||||||
\(269\) | −19.0622 | −1.16224 | −0.581121 | − | 0.813817i | \(-0.697386\pi\) | ||||
−0.581121 | + | 0.813817i | \(0.697386\pi\) | |||||||
\(270\) | 6.25113 | 0.380431 | ||||||||
\(271\) | 21.9042 | 1.33059 | 0.665294 | − | 0.746582i | \(-0.268306\pi\) | ||||
0.665294 | + | 0.746582i | \(0.268306\pi\) | |||||||
\(272\) | 3.15695 | 0.191418 | ||||||||
\(273\) | −24.5120 | −1.48354 | ||||||||
\(274\) | −2.46456 | −0.148890 | ||||||||
\(275\) | −4.77231 | −0.287781 | ||||||||
\(276\) | −13.3661 | −0.804547 | ||||||||
\(277\) | 22.5490 | 1.35484 | 0.677419 | − | 0.735597i | \(-0.263098\pi\) | ||||
0.677419 | + | 0.735597i | \(0.263098\pi\) | |||||||
\(278\) | 14.9720 | 0.897962 | ||||||||
\(279\) | 16.2402 | 0.972273 | ||||||||
\(280\) | −5.80774 | −0.347079 | ||||||||
\(281\) | −2.43550 | −0.145290 | −0.0726448 | − | 0.997358i | \(-0.523144\pi\) | ||||
−0.0726448 | + | 0.997358i | \(0.523144\pi\) | |||||||
\(282\) | −8.32065 | −0.495487 | ||||||||
\(283\) | 6.63059 | 0.394148 | 0.197074 | − | 0.980389i | \(-0.436856\pi\) | ||||
0.197074 | + | 0.980389i | \(0.436856\pi\) | |||||||
\(284\) | −0.0465372 | −0.00276147 | ||||||||
\(285\) | −44.1675 | −2.61626 | ||||||||
\(286\) | −9.64473 | −0.570305 | ||||||||
\(287\) | −2.20337 | −0.130061 | ||||||||
\(288\) | −1.98248 | −0.116819 | ||||||||
\(289\) | −7.03364 | −0.413744 | ||||||||
\(290\) | 2.70477 | 0.158830 | ||||||||
\(291\) | −25.7832 | −1.51144 | ||||||||
\(292\) | −3.43957 | −0.201285 | ||||||||
\(293\) | −22.5352 | −1.31652 | −0.658259 | − | 0.752791i | \(-0.728707\pi\) | ||||
−0.658259 | + | 0.752791i | \(0.728707\pi\) | |||||||
\(294\) | −5.68576 | −0.331600 | ||||||||
\(295\) | 22.4818 | 1.30894 | ||||||||
\(296\) | −4.83696 | −0.281143 | ||||||||
\(297\) | −4.20936 | −0.244252 | ||||||||
\(298\) | 12.9068 | 0.747669 | ||||||||
\(299\) | −31.1619 | −1.80214 | ||||||||
\(300\) | −5.74780 | −0.331849 | ||||||||
\(301\) | 1.58907 | 0.0915927 | ||||||||
\(302\) | −8.45894 | −0.486757 | ||||||||
\(303\) | 1.82178 | 0.104659 | ||||||||
\(304\) | −7.18933 | −0.412336 | ||||||||
\(305\) | −39.7776 | −2.27766 | ||||||||
\(306\) | −6.25859 | −0.357780 | ||||||||
\(307\) | −19.3513 | −1.10444 | −0.552219 | − | 0.833699i | \(-0.686219\pi\) | ||||
−0.552219 | + | 0.833699i | \(0.686219\pi\) | |||||||
\(308\) | 3.91079 | 0.222838 | ||||||||
\(309\) | −25.9110 | −1.47403 | ||||||||
\(310\) | 22.5462 | 1.28054 | ||||||||
\(311\) | −30.3012 | −1.71822 | −0.859112 | − | 0.511787i | \(-0.828984\pi\) | ||||
−0.859112 | + | 0.511787i | \(0.828984\pi\) | |||||||
\(312\) | −11.6162 | −0.657637 | ||||||||
\(313\) | −3.85715 | −0.218019 | −0.109010 | − | 0.994041i | \(-0.534768\pi\) | ||||
−0.109010 | + | 0.994041i | \(0.534768\pi\) | |||||||
\(314\) | 9.38080 | 0.529389 | ||||||||
\(315\) | 11.5137 | 0.648725 | ||||||||
\(316\) | 0.984521 | 0.0553837 | ||||||||
\(317\) | −8.84967 | −0.497047 | −0.248523 | − | 0.968626i | \(-0.579945\pi\) | ||||
−0.248523 | + | 0.968626i | \(0.579945\pi\) | |||||||
\(318\) | −12.4610 | −0.698781 | ||||||||
\(319\) | −1.82133 | −0.101975 | ||||||||
\(320\) | −2.75227 | −0.153857 | ||||||||
\(321\) | −41.1254 | −2.29540 | ||||||||
\(322\) | 12.6357 | 0.704159 | ||||||||
\(323\) | −22.6964 | −1.26286 | ||||||||
\(324\) | −11.0172 | −0.612068 | ||||||||
\(325\) | −13.4005 | −0.743324 | ||||||||
\(326\) | 12.2248 | 0.677069 | ||||||||
\(327\) | 16.4387 | 0.909063 | ||||||||
\(328\) | −1.04417 | −0.0576548 | ||||||||
\(329\) | 7.86593 | 0.433663 | ||||||||
\(330\) | 11.3858 | 0.626768 | ||||||||
\(331\) | −3.49270 | −0.191976 | −0.0959881 | − | 0.995382i | \(-0.530601\pi\) | ||||
−0.0959881 | + | 0.995382i | \(0.530601\pi\) | |||||||
\(332\) | −1.05397 | −0.0578441 | ||||||||
\(333\) | 9.58917 | 0.525483 | ||||||||
\(334\) | 11.2733 | 0.616850 | ||||||||
\(335\) | −31.5744 | −1.72509 | ||||||||
\(336\) | 4.71019 | 0.256962 | ||||||||
\(337\) | −5.32473 | −0.290057 | −0.145028 | − | 0.989428i | \(-0.546327\pi\) | ||||
−0.145028 | + | 0.989428i | \(0.546327\pi\) | |||||||
\(338\) | −14.0821 | −0.765964 | ||||||||
\(339\) | −28.0257 | −1.52215 | ||||||||
\(340\) | −8.68880 | −0.471216 | ||||||||
\(341\) | −15.1821 | −0.822155 | ||||||||
\(342\) | 14.2527 | 0.770697 | ||||||||
\(343\) | 20.1462 | 1.08779 | ||||||||
\(344\) | 0.753058 | 0.0406022 | ||||||||
\(345\) | 36.7873 | 1.98056 | ||||||||
\(346\) | 2.55843 | 0.137542 | ||||||||
\(347\) | 19.5881 | 1.05154 | 0.525771 | − | 0.850626i | \(-0.323777\pi\) | ||||
0.525771 | + | 0.850626i | \(0.323777\pi\) | |||||||
\(348\) | −2.19362 | −0.117590 | ||||||||
\(349\) | −6.21124 | −0.332480 | −0.166240 | − | 0.986085i | \(-0.553163\pi\) | ||||
−0.166240 | + | 0.986085i | \(0.553163\pi\) | |||||||
\(350\) | 5.43369 | 0.290443 | ||||||||
\(351\) | −11.8197 | −0.630891 | ||||||||
\(352\) | 1.85331 | 0.0987820 | ||||||||
\(353\) | −34.8009 | −1.85226 | −0.926132 | − | 0.377200i | \(-0.876887\pi\) | ||||
−0.926132 | + | 0.377200i | \(0.876887\pi\) | |||||||
\(354\) | −18.2332 | −0.969084 | ||||||||
\(355\) | 0.128083 | 0.00679794 | ||||||||
\(356\) | −4.09263 | −0.216909 | ||||||||
\(357\) | 14.8699 | 0.786996 | ||||||||
\(358\) | −0.299051 | −0.0158053 | ||||||||
\(359\) | −3.75205 | −0.198025 | −0.0990127 | − | 0.995086i | \(-0.531568\pi\) | ||||
−0.0990127 | + | 0.995086i | \(0.531568\pi\) | |||||||
\(360\) | 5.45632 | 0.287573 | ||||||||
\(361\) | 32.6865 | 1.72034 | ||||||||
\(362\) | −10.4338 | −0.548388 | ||||||||
\(363\) | 16.8867 | 0.886321 | ||||||||
\(364\) | 10.9814 | 0.575580 | ||||||||
\(365\) | 9.46663 | 0.495506 | ||||||||
\(366\) | 32.2604 | 1.68628 | ||||||||
\(367\) | 9.86089 | 0.514734 | 0.257367 | − | 0.966314i | \(-0.417145\pi\) | ||||
0.257367 | + | 0.966314i | \(0.417145\pi\) | |||||||
\(368\) | 5.98802 | 0.312147 | ||||||||
\(369\) | 2.07005 | 0.107762 | ||||||||
\(370\) | 13.3126 | 0.692091 | ||||||||
\(371\) | 11.7801 | 0.611590 | ||||||||
\(372\) | −18.2854 | −0.948054 | ||||||||
\(373\) | 30.1102 | 1.55905 | 0.779523 | − | 0.626374i | \(-0.215462\pi\) | ||||
0.779523 | + | 0.626374i | \(0.215462\pi\) | |||||||
\(374\) | 5.85083 | 0.302539 | ||||||||
\(375\) | −14.8979 | −0.769322 | ||||||||
\(376\) | 3.72764 | 0.192239 | ||||||||
\(377\) | −5.11422 | −0.263396 | ||||||||
\(378\) | 4.79272 | 0.246511 | ||||||||
\(379\) | 26.1492 | 1.34319 | 0.671597 | − | 0.740917i | \(-0.265609\pi\) | ||||
0.671597 | + | 0.740917i | \(0.265609\pi\) | |||||||
\(380\) | 19.7870 | 1.01505 | ||||||||
\(381\) | −24.7482 | −1.26789 | ||||||||
\(382\) | 13.5586 | 0.693719 | ||||||||
\(383\) | −2.23479 | −0.114192 | −0.0570962 | − | 0.998369i | \(-0.518184\pi\) | ||||
−0.0570962 | + | 0.998369i | \(0.518184\pi\) | |||||||
\(384\) | 2.23215 | 0.113909 | ||||||||
\(385\) | −10.7636 | −0.548563 | ||||||||
\(386\) | −9.87008 | −0.502374 | ||||||||
\(387\) | −1.49292 | −0.0758894 | ||||||||
\(388\) | 11.5509 | 0.586406 | ||||||||
\(389\) | −19.4143 | −0.984346 | −0.492173 | − | 0.870497i | \(-0.663797\pi\) | ||||
−0.492173 | + | 0.870497i | \(0.663797\pi\) | |||||||
\(390\) | 31.9709 | 1.61891 | ||||||||
\(391\) | 18.9039 | 0.956011 | ||||||||
\(392\) | 2.54722 | 0.128654 | ||||||||
\(393\) | −16.6683 | −0.840803 | ||||||||
\(394\) | 13.9126 | 0.700904 | ||||||||
\(395\) | −2.70967 | −0.136338 | ||||||||
\(396\) | −3.67416 | −0.184633 | ||||||||
\(397\) | −7.46893 | −0.374855 | −0.187427 | − | 0.982278i | \(-0.560015\pi\) | ||||
−0.187427 | + | 0.982278i | \(0.560015\pi\) | |||||||
\(398\) | −3.99828 | −0.200416 | ||||||||
\(399\) | −33.8631 | −1.69528 | ||||||||
\(400\) | 2.57501 | 0.128751 | ||||||||
\(401\) | 24.0473 | 1.20086 | 0.600432 | − | 0.799676i | \(-0.294995\pi\) | ||||
0.600432 | + | 0.799676i | \(0.294995\pi\) | |||||||
\(402\) | 25.6074 | 1.27718 | ||||||||
\(403\) | −42.6307 | −2.12359 | ||||||||
\(404\) | −0.816156 | −0.0406053 | ||||||||
\(405\) | 30.3224 | 1.50673 | ||||||||
\(406\) | 2.07374 | 0.102918 | ||||||||
\(407\) | −8.96441 | −0.444349 | ||||||||
\(408\) | 7.04678 | 0.348868 | ||||||||
\(409\) | −31.3735 | −1.55132 | −0.775660 | − | 0.631151i | \(-0.782583\pi\) | ||||
−0.775660 | + | 0.631151i | \(0.782583\pi\) | |||||||
\(410\) | 2.87385 | 0.141929 | ||||||||
\(411\) | −5.50126 | −0.271357 | ||||||||
\(412\) | 11.6081 | 0.571891 | ||||||||
\(413\) | 17.2368 | 0.848166 | ||||||||
\(414\) | −11.8711 | −0.583433 | ||||||||
\(415\) | 2.90081 | 0.142395 | ||||||||
\(416\) | 5.20404 | 0.255149 | ||||||||
\(417\) | 33.4198 | 1.63657 | ||||||||
\(418\) | −13.3241 | −0.651703 | ||||||||
\(419\) | −0.844969 | −0.0412794 | −0.0206397 | − | 0.999787i | \(-0.506570\pi\) | ||||
−0.0206397 | + | 0.999787i | \(0.506570\pi\) | |||||||
\(420\) | −12.9637 | −0.632565 | ||||||||
\(421\) | −0.0109361 | −0.000532995 0 | −0.000266497 | − | 1.00000i | \(-0.500085\pi\) | ||||
−0.000266497 | 1.00000i | \(0.500085\pi\) | ||||||||
\(422\) | −2.75626 | −0.134172 | ||||||||
\(423\) | −7.38997 | −0.359313 | ||||||||
\(424\) | 5.58254 | 0.271112 | ||||||||
\(425\) | 8.12919 | 0.394324 | ||||||||
\(426\) | −0.103878 | −0.00503290 | ||||||||
\(427\) | −30.4974 | −1.47587 | ||||||||
\(428\) | 18.4241 | 0.890565 | ||||||||
\(429\) | −21.5285 | −1.03940 | ||||||||
\(430\) | −2.07262 | −0.0999507 | ||||||||
\(431\) | 11.7557 | 0.566250 | 0.283125 | − | 0.959083i | \(-0.408629\pi\) | ||||
0.283125 | + | 0.959083i | \(0.408629\pi\) | |||||||
\(432\) | 2.27126 | 0.109276 | ||||||||
\(433\) | 30.5511 | 1.46819 | 0.734095 | − | 0.679046i | \(-0.237607\pi\) | ||||
0.734095 | + | 0.679046i | \(0.237607\pi\) | |||||||
\(434\) | 17.2861 | 0.829761 | ||||||||
\(435\) | 6.03744 | 0.289473 | ||||||||
\(436\) | −7.36454 | −0.352697 | ||||||||
\(437\) | −43.0498 | −2.05935 | ||||||||
\(438\) | −7.67762 | −0.366851 | ||||||||
\(439\) | 13.4317 | 0.641062 | 0.320531 | − | 0.947238i | \(-0.396139\pi\) | ||||
0.320531 | + | 0.947238i | \(0.396139\pi\) | |||||||
\(440\) | −5.10083 | −0.243173 | ||||||||
\(441\) | −5.04980 | −0.240467 | ||||||||
\(442\) | 16.4289 | 0.781444 | ||||||||
\(443\) | −21.7955 | −1.03553 | −0.517767 | − | 0.855521i | \(-0.673237\pi\) | ||||
−0.517767 | + | 0.855521i | \(0.673237\pi\) | |||||||
\(444\) | −10.7968 | −0.512394 | ||||||||
\(445\) | 11.2640 | 0.533966 | ||||||||
\(446\) | −1.88498 | −0.0892566 | ||||||||
\(447\) | 28.8098 | 1.36266 | ||||||||
\(448\) | −2.11016 | −0.0996958 | ||||||||
\(449\) | 8.83987 | 0.417179 | 0.208590 | − | 0.978003i | \(-0.433113\pi\) | ||||
0.208590 | + | 0.978003i | \(0.433113\pi\) | |||||||
\(450\) | −5.10490 | −0.240647 | ||||||||
\(451\) | −1.93518 | −0.0911241 | ||||||||
\(452\) | 12.5555 | 0.590560 | ||||||||
\(453\) | −18.8816 | −0.887135 | ||||||||
\(454\) | 1.41936 | 0.0666137 | ||||||||
\(455\) | −30.2238 | −1.41691 | ||||||||
\(456\) | −16.0476 | −0.751500 | ||||||||
\(457\) | −7.96665 | −0.372664 | −0.186332 | − | 0.982487i | \(-0.559660\pi\) | ||||
−0.186332 | + | 0.982487i | \(0.559660\pi\) | |||||||
\(458\) | 13.1725 | 0.615509 | ||||||||
\(459\) | 7.17026 | 0.334679 | ||||||||
\(460\) | −16.4807 | −0.768415 | ||||||||
\(461\) | −4.27698 | −0.199199 | −0.0995993 | − | 0.995028i | \(-0.531756\pi\) | ||||
−0.0995993 | + | 0.995028i | \(0.531756\pi\) | |||||||
\(462\) | 8.72947 | 0.406132 | ||||||||
\(463\) | 2.49886 | 0.116132 | 0.0580660 | − | 0.998313i | \(-0.481507\pi\) | ||||
0.0580660 | + | 0.998313i | \(0.481507\pi\) | |||||||
\(464\) | 0.982740 | 0.0456226 | ||||||||
\(465\) | 50.3264 | 2.33383 | ||||||||
\(466\) | 3.47205 | 0.160840 | ||||||||
\(467\) | 39.3888 | 1.82270 | 0.911349 | − | 0.411634i | \(-0.135042\pi\) | ||||
0.911349 | + | 0.411634i | \(0.135042\pi\) | |||||||
\(468\) | −10.3169 | −0.476899 | ||||||||
\(469\) | −24.2080 | −1.11782 | ||||||||
\(470\) | −10.2595 | −0.473235 | ||||||||
\(471\) | 20.9393 | 0.964833 | ||||||||
\(472\) | 8.16846 | 0.375984 | ||||||||
\(473\) | 1.39565 | 0.0641722 | ||||||||
\(474\) | 2.19760 | 0.100939 | ||||||||
\(475\) | −18.5126 | −0.849417 | ||||||||
\(476\) | −6.66168 | −0.305338 | ||||||||
\(477\) | −11.0673 | −0.506735 | ||||||||
\(478\) | −4.50429 | −0.206022 | ||||||||
\(479\) | −7.14596 | −0.326507 | −0.163254 | − | 0.986584i | \(-0.552199\pi\) | ||||
−0.163254 | + | 0.986584i | \(0.552199\pi\) | |||||||
\(480\) | −6.14348 | −0.280410 | ||||||||
\(481\) | −25.1718 | −1.14773 | ||||||||
\(482\) | 4.21948 | 0.192192 | ||||||||
\(483\) | 28.2047 | 1.28336 | ||||||||
\(484\) | −7.56522 | −0.343874 | ||||||||
\(485\) | −31.7911 | −1.44356 | ||||||||
\(486\) | −17.7783 | −0.806438 | ||||||||
\(487\) | −23.0636 | −1.04511 | −0.522555 | − | 0.852605i | \(-0.675021\pi\) | ||||
−0.522555 | + | 0.852605i | \(0.675021\pi\) | |||||||
\(488\) | −14.4526 | −0.654240 | ||||||||
\(489\) | 27.2875 | 1.23399 | ||||||||
\(490\) | −7.01064 | −0.316708 | ||||||||
\(491\) | −25.1874 | −1.13669 | −0.568346 | − | 0.822790i | \(-0.692417\pi\) | ||||
−0.568346 | + | 0.822790i | \(0.692417\pi\) | |||||||
\(492\) | −2.33075 | −0.105078 | ||||||||
\(493\) | 3.10247 | 0.139728 | ||||||||
\(494\) | −37.4136 | −1.68332 | ||||||||
\(495\) | 10.1123 | 0.454513 | ||||||||
\(496\) | 8.19185 | 0.367825 | ||||||||
\(497\) | 0.0982010 | 0.00440492 | ||||||||
\(498\) | −2.35261 | −0.105423 | ||||||||
\(499\) | 26.4449 | 1.18384 | 0.591918 | − | 0.805998i | \(-0.298371\pi\) | ||||
0.591918 | + | 0.805998i | \(0.298371\pi\) | |||||||
\(500\) | 6.67423 | 0.298481 | ||||||||
\(501\) | 25.1638 | 1.12423 | ||||||||
\(502\) | 3.31411 | 0.147916 | ||||||||
\(503\) | −12.8377 | −0.572403 | −0.286202 | − | 0.958169i | \(-0.592393\pi\) | ||||
−0.286202 | + | 0.958169i | \(0.592393\pi\) | |||||||
\(504\) | 4.18335 | 0.186341 | ||||||||
\(505\) | 2.24629 | 0.0999584 | ||||||||
\(506\) | 11.0977 | 0.493352 | ||||||||
\(507\) | −31.4332 | −1.39600 | ||||||||
\(508\) | 11.0872 | 0.491914 | ||||||||
\(509\) | 4.34117 | 0.192419 | 0.0962095 | − | 0.995361i | \(-0.469328\pi\) | ||||
0.0962095 | + | 0.995361i | \(0.469328\pi\) | |||||||
\(510\) | −19.3947 | −0.858811 | ||||||||
\(511\) | 7.25805 | 0.321077 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −16.3288 | −0.720936 | ||||||||
\(514\) | 4.48515 | 0.197831 | ||||||||
\(515\) | −31.9487 | −1.40783 | ||||||||
\(516\) | 1.68094 | 0.0739990 | ||||||||
\(517\) | 6.90850 | 0.303835 | ||||||||
\(518\) | 10.2068 | 0.448460 | ||||||||
\(519\) | 5.71079 | 0.250676 | ||||||||
\(520\) | −14.3230 | −0.628103 | ||||||||
\(521\) | −22.7965 | −0.998735 | −0.499367 | − | 0.866390i | \(-0.666434\pi\) | ||||
−0.499367 | + | 0.866390i | \(0.666434\pi\) | |||||||
\(522\) | −1.94826 | −0.0852731 | ||||||||
\(523\) | 8.37167 | 0.366068 | 0.183034 | − | 0.983107i | \(-0.441408\pi\) | ||||
0.183034 | + | 0.983107i | \(0.441408\pi\) | |||||||
\(524\) | 7.46737 | 0.326214 | ||||||||
\(525\) | 12.1288 | 0.529344 | ||||||||
\(526\) | −15.9494 | −0.695428 | ||||||||
\(527\) | 25.8613 | 1.12654 | ||||||||
\(528\) | 4.13687 | 0.180034 | ||||||||
\(529\) | 12.8563 | 0.558972 | ||||||||
\(530\) | −15.3647 | −0.667399 | ||||||||
\(531\) | −16.1938 | −0.702751 | ||||||||
\(532\) | 15.1707 | 0.657731 | ||||||||
\(533\) | −5.43392 | −0.235369 | ||||||||
\(534\) | −9.13534 | −0.395325 | ||||||||
\(535\) | −50.7083 | −2.19231 | ||||||||
\(536\) | −11.4721 | −0.495520 | ||||||||
\(537\) | −0.667525 | −0.0288058 | ||||||||
\(538\) | 19.0622 | 0.821829 | ||||||||
\(539\) | 4.72079 | 0.203339 | ||||||||
\(540\) | −6.25113 | −0.269006 | ||||||||
\(541\) | 42.1599 | 1.81259 | 0.906297 | − | 0.422641i | \(-0.138897\pi\) | ||||
0.906297 | + | 0.422641i | \(0.138897\pi\) | |||||||
\(542\) | −21.9042 | −0.940867 | ||||||||
\(543\) | −23.2898 | −0.999459 | ||||||||
\(544\) | −3.15695 | −0.135353 | ||||||||
\(545\) | 20.2692 | 0.868238 | ||||||||
\(546\) | 24.5120 | 1.04902 | ||||||||
\(547\) | −20.2458 | −0.865647 | −0.432824 | − | 0.901479i | \(-0.642483\pi\) | ||||
−0.432824 | + | 0.901479i | \(0.642483\pi\) | |||||||
\(548\) | 2.46456 | 0.105281 | ||||||||
\(549\) | 28.6520 | 1.22284 | ||||||||
\(550\) | 4.77231 | 0.203492 | ||||||||
\(551\) | −7.06525 | −0.300990 | ||||||||
\(552\) | 13.3661 | 0.568900 | ||||||||
\(553\) | −2.07750 | −0.0883443 | ||||||||
\(554\) | −22.5490 | −0.958015 | ||||||||
\(555\) | 29.7158 | 1.26136 | ||||||||
\(556\) | −14.9720 | −0.634955 | ||||||||
\(557\) | −29.0344 | −1.23023 | −0.615113 | − | 0.788439i | \(-0.710890\pi\) | ||||
−0.615113 | + | 0.788439i | \(0.710890\pi\) | |||||||
\(558\) | −16.2402 | −0.687501 | ||||||||
\(559\) | 3.91895 | 0.165754 | ||||||||
\(560\) | 5.80774 | 0.245422 | ||||||||
\(561\) | 13.0599 | 0.551390 | ||||||||
\(562\) | 2.43550 | 0.102735 | ||||||||
\(563\) | 5.37912 | 0.226703 | 0.113352 | − | 0.993555i | \(-0.463841\pi\) | ||||
0.113352 | + | 0.993555i | \(0.463841\pi\) | |||||||
\(564\) | 8.32065 | 0.350362 | ||||||||
\(565\) | −34.5561 | −1.45379 | ||||||||
\(566\) | −6.63059 | −0.278705 | ||||||||
\(567\) | 23.2481 | 0.976329 | ||||||||
\(568\) | 0.0465372 | 0.00195266 | ||||||||
\(569\) | −0.890630 | −0.0373371 | −0.0186686 | − | 0.999826i | \(-0.505943\pi\) | ||||
−0.0186686 | + | 0.999826i | \(0.505943\pi\) | |||||||
\(570\) | 44.1675 | 1.84997 | ||||||||
\(571\) | 25.3434 | 1.06059 | 0.530294 | − | 0.847814i | \(-0.322081\pi\) | ||||
0.530294 | + | 0.847814i | \(0.322081\pi\) | |||||||
\(572\) | 9.64473 | 0.403266 | ||||||||
\(573\) | 30.2648 | 1.26433 | ||||||||
\(574\) | 2.20337 | 0.0919670 | ||||||||
\(575\) | 15.4192 | 0.643026 | ||||||||
\(576\) | 1.98248 | 0.0826032 | ||||||||
\(577\) | −28.0868 | −1.16927 | −0.584635 | − | 0.811297i | \(-0.698762\pi\) | ||||
−0.584635 | + | 0.811297i | \(0.698762\pi\) | |||||||
\(578\) | 7.03364 | 0.292561 | ||||||||
\(579\) | −22.0315 | −0.915596 | ||||||||
\(580\) | −2.70477 | −0.112309 | ||||||||
\(581\) | 2.22405 | 0.0922690 | ||||||||
\(582\) | 25.7832 | 1.06875 | ||||||||
\(583\) | 10.3462 | 0.428496 | ||||||||
\(584\) | 3.43957 | 0.142330 | ||||||||
\(585\) | 28.3949 | 1.17399 | ||||||||
\(586\) | 22.5352 | 0.930919 | ||||||||
\(587\) | −11.0790 | −0.457281 | −0.228640 | − | 0.973511i | \(-0.573428\pi\) | ||||
−0.228640 | + | 0.973511i | \(0.573428\pi\) | |||||||
\(588\) | 5.68576 | 0.234477 | ||||||||
\(589\) | −58.8939 | −2.42668 | ||||||||
\(590\) | −22.4818 | −0.925563 | ||||||||
\(591\) | 31.0549 | 1.27743 | ||||||||
\(592\) | 4.83696 | 0.198798 | ||||||||
\(593\) | 29.3332 | 1.20457 | 0.602284 | − | 0.798282i | \(-0.294257\pi\) | ||||
0.602284 | + | 0.798282i | \(0.294257\pi\) | |||||||
\(594\) | 4.20936 | 0.172712 | ||||||||
\(595\) | 18.3348 | 0.751653 | ||||||||
\(596\) | −12.9068 | −0.528682 | ||||||||
\(597\) | −8.92475 | −0.365266 | ||||||||
\(598\) | 31.1619 | 1.27430 | ||||||||
\(599\) | −10.5150 | −0.429631 | −0.214816 | − | 0.976655i | \(-0.568915\pi\) | ||||
−0.214816 | + | 0.976655i | \(0.568915\pi\) | |||||||
\(600\) | 5.74780 | 0.234653 | ||||||||
\(601\) | −7.21670 | −0.294375 | −0.147188 | − | 0.989109i | \(-0.547022\pi\) | ||||
−0.147188 | + | 0.989109i | \(0.547022\pi\) | |||||||
\(602\) | −1.58907 | −0.0647658 | ||||||||
\(603\) | 22.7432 | 0.926175 | ||||||||
\(604\) | 8.45894 | 0.344190 | ||||||||
\(605\) | 20.8216 | 0.846517 | ||||||||
\(606\) | −1.82178 | −0.0740048 | ||||||||
\(607\) | −14.5597 | −0.590962 | −0.295481 | − | 0.955349i | \(-0.595480\pi\) | ||||
−0.295481 | + | 0.955349i | \(0.595480\pi\) | |||||||
\(608\) | 7.18933 | 0.291566 | ||||||||
\(609\) | 4.62889 | 0.187572 | ||||||||
\(610\) | 39.7776 | 1.61055 | ||||||||
\(611\) | 19.3988 | 0.784792 | ||||||||
\(612\) | 6.25859 | 0.252989 | ||||||||
\(613\) | 34.4849 | 1.39283 | 0.696416 | − | 0.717639i | \(-0.254777\pi\) | ||||
0.696416 | + | 0.717639i | \(0.254777\pi\) | |||||||
\(614\) | 19.3513 | 0.780956 | ||||||||
\(615\) | 6.41485 | 0.258672 | ||||||||
\(616\) | −3.91079 | −0.157570 | ||||||||
\(617\) | −24.7820 | −0.997686 | −0.498843 | − | 0.866692i | \(-0.666242\pi\) | ||||
−0.498843 | + | 0.866692i | \(0.666242\pi\) | |||||||
\(618\) | 25.9110 | 1.04229 | ||||||||
\(619\) | −20.9678 | −0.842768 | −0.421384 | − | 0.906882i | \(-0.638456\pi\) | ||||
−0.421384 | + | 0.906882i | \(0.638456\pi\) | |||||||
\(620\) | −22.5462 | −0.905478 | ||||||||
\(621\) | 13.6003 | 0.545763 | ||||||||
\(622\) | 30.3012 | 1.21497 | ||||||||
\(623\) | 8.63610 | 0.345998 | ||||||||
\(624\) | 11.6162 | 0.465020 | ||||||||
\(625\) | −31.2444 | −1.24977 | ||||||||
\(626\) | 3.85715 | 0.154163 | ||||||||
\(627\) | −29.7413 | −1.18775 | ||||||||
\(628\) | −9.38080 | −0.374335 | ||||||||
\(629\) | 15.2701 | 0.608857 | ||||||||
\(630\) | −11.5137 | −0.458718 | ||||||||
\(631\) | 42.6444 | 1.69765 | 0.848823 | − | 0.528677i | \(-0.177312\pi\) | ||||
0.848823 | + | 0.528677i | \(0.177312\pi\) | |||||||
\(632\) | −0.984521 | −0.0391622 | ||||||||
\(633\) | −6.15237 | −0.244535 | ||||||||
\(634\) | 8.84967 | 0.351465 | ||||||||
\(635\) | −30.5150 | −1.21095 | ||||||||
\(636\) | 12.4610 | 0.494112 | ||||||||
\(637\) | 13.2558 | 0.525215 | ||||||||
\(638\) | 1.82133 | 0.0721070 | ||||||||
\(639\) | −0.0922589 | −0.00364971 | ||||||||
\(640\) | 2.75227 | 0.108793 | ||||||||
\(641\) | −27.7579 | −1.09637 | −0.548186 | − | 0.836357i | \(-0.684681\pi\) | ||||
−0.548186 | + | 0.836357i | \(0.684681\pi\) | |||||||
\(642\) | 41.1254 | 1.62309 | ||||||||
\(643\) | 10.5592 | 0.416415 | 0.208208 | − | 0.978085i | \(-0.433237\pi\) | ||||
0.208208 | + | 0.978085i | \(0.433237\pi\) | |||||||
\(644\) | −12.6357 | −0.497916 | ||||||||
\(645\) | −4.62639 | −0.182164 | ||||||||
\(646\) | 22.6964 | 0.892977 | ||||||||
\(647\) | 22.1479 | 0.870726 | 0.435363 | − | 0.900255i | \(-0.356620\pi\) | ||||
0.435363 | + | 0.900255i | \(0.356620\pi\) | |||||||
\(648\) | 11.0172 | 0.432797 | ||||||||
\(649\) | 15.1387 | 0.594247 | ||||||||
\(650\) | 13.4005 | 0.525610 | ||||||||
\(651\) | 38.5852 | 1.51227 | ||||||||
\(652\) | −12.2248 | −0.478760 | ||||||||
\(653\) | 12.1877 | 0.476943 | 0.238472 | − | 0.971149i | \(-0.423354\pi\) | ||||
0.238472 | + | 0.971149i | \(0.423354\pi\) | |||||||
\(654\) | −16.4387 | −0.642805 | ||||||||
\(655\) | −20.5523 | −0.803043 | ||||||||
\(656\) | 1.04417 | 0.0407681 | ||||||||
\(657\) | −6.81887 | −0.266029 | ||||||||
\(658\) | −7.86593 | −0.306646 | ||||||||
\(659\) | 11.0872 | 0.431898 | 0.215949 | − | 0.976405i | \(-0.430716\pi\) | ||||
0.215949 | + | 0.976405i | \(0.430716\pi\) | |||||||
\(660\) | −11.3858 | −0.443192 | ||||||||
\(661\) | −46.6454 | −1.81429 | −0.907147 | − | 0.420814i | \(-0.861745\pi\) | ||||
−0.907147 | + | 0.420814i | \(0.861745\pi\) | |||||||
\(662\) | 3.49270 | 0.135748 | ||||||||
\(663\) | 36.6718 | 1.42421 | ||||||||
\(664\) | 1.05397 | 0.0409019 | ||||||||
\(665\) | −41.7538 | −1.61914 | ||||||||
\(666\) | −9.58917 | −0.371573 | ||||||||
\(667\) | 5.88467 | 0.227855 | ||||||||
\(668\) | −11.2733 | −0.436179 | ||||||||
\(669\) | −4.20756 | −0.162674 | ||||||||
\(670\) | 31.5744 | 1.21983 | ||||||||
\(671\) | −26.7853 | −1.03403 | ||||||||
\(672\) | −4.71019 | −0.181700 | ||||||||
\(673\) | 40.8156 | 1.57333 | 0.786664 | − | 0.617382i | \(-0.211807\pi\) | ||||
0.786664 | + | 0.617382i | \(0.211807\pi\) | |||||||
\(674\) | 5.32473 | 0.205101 | ||||||||
\(675\) | 5.84852 | 0.225110 | ||||||||
\(676\) | 14.0821 | 0.541618 | ||||||||
\(677\) | 8.61164 | 0.330972 | 0.165486 | − | 0.986212i | \(-0.447081\pi\) | ||||
0.165486 | + | 0.986212i | \(0.447081\pi\) | |||||||
\(678\) | 28.0257 | 1.07632 | ||||||||
\(679\) | −24.3742 | −0.935396 | ||||||||
\(680\) | 8.68880 | 0.333200 | ||||||||
\(681\) | 3.16821 | 0.121406 | ||||||||
\(682\) | 15.1821 | 0.581352 | ||||||||
\(683\) | 6.70095 | 0.256405 | 0.128202 | − | 0.991748i | \(-0.459079\pi\) | ||||
0.128202 | + | 0.991748i | \(0.459079\pi\) | |||||||
\(684\) | −14.2527 | −0.544965 | ||||||||
\(685\) | −6.78315 | −0.259171 | ||||||||
\(686\) | −20.1462 | −0.769184 | ||||||||
\(687\) | 29.4029 | 1.12179 | ||||||||
\(688\) | −0.753058 | −0.0287101 | ||||||||
\(689\) | 29.0518 | 1.10678 | ||||||||
\(690\) | −36.7873 | −1.40047 | ||||||||
\(691\) | 17.3752 | 0.660984 | 0.330492 | − | 0.943809i | \(-0.392785\pi\) | ||||
0.330492 | + | 0.943809i | \(0.392785\pi\) | |||||||
\(692\) | −2.55843 | −0.0972569 | ||||||||
\(693\) | 7.75306 | 0.294514 | ||||||||
\(694\) | −19.5881 | −0.743553 | ||||||||
\(695\) | 41.2071 | 1.56307 | ||||||||
\(696\) | 2.19362 | 0.0831490 | ||||||||
\(697\) | 3.29640 | 0.124860 | ||||||||
\(698\) | 6.21124 | 0.235099 | ||||||||
\(699\) | 7.75012 | 0.293137 | ||||||||
\(700\) | −5.43369 | −0.205374 | ||||||||
\(701\) | 19.8369 | 0.749230 | 0.374615 | − | 0.927181i | \(-0.377775\pi\) | ||||
0.374615 | + | 0.927181i | \(0.377775\pi\) | |||||||
\(702\) | 11.8197 | 0.446107 | ||||||||
\(703\) | −34.7745 | −1.31155 | ||||||||
\(704\) | −1.85331 | −0.0698494 | ||||||||
\(705\) | −22.9007 | −0.862490 | ||||||||
\(706\) | 34.8009 | 1.30975 | ||||||||
\(707\) | 1.72222 | 0.0647708 | ||||||||
\(708\) | 18.2332 | 0.685246 | ||||||||
\(709\) | −24.5811 | −0.923161 | −0.461581 | − | 0.887098i | \(-0.652717\pi\) | ||||
−0.461581 | + | 0.887098i | \(0.652717\pi\) | |||||||
\(710\) | −0.128083 | −0.00480687 | ||||||||
\(711\) | 1.95179 | 0.0731979 | ||||||||
\(712\) | 4.09263 | 0.153378 | ||||||||
\(713\) | 49.0529 | 1.83705 | ||||||||
\(714\) | −14.8699 | −0.556490 | ||||||||
\(715\) | −26.5449 | −0.992724 | ||||||||
\(716\) | 0.299051 | 0.0111760 | ||||||||
\(717\) | −10.0542 | −0.375483 | ||||||||
\(718\) | 3.75205 | 0.140025 | ||||||||
\(719\) | −21.0684 | −0.785718 | −0.392859 | − | 0.919599i | \(-0.628514\pi\) | ||||
−0.392859 | + | 0.919599i | \(0.628514\pi\) | |||||||
\(720\) | −5.45632 | −0.203345 | ||||||||
\(721\) | −24.4950 | −0.912242 | ||||||||
\(722\) | −32.6865 | −1.21647 | ||||||||
\(723\) | 9.41850 | 0.350278 | ||||||||
\(724\) | 10.4338 | 0.387769 | ||||||||
\(725\) | 2.53057 | 0.0939829 | ||||||||
\(726\) | −16.8867 | −0.626724 | ||||||||
\(727\) | −21.9040 | −0.812373 | −0.406186 | − | 0.913790i | \(-0.633142\pi\) | ||||
−0.406186 | + | 0.913790i | \(0.633142\pi\) | |||||||
\(728\) | −10.9814 | −0.406997 | ||||||||
\(729\) | −6.63204 | −0.245631 | ||||||||
\(730\) | −9.46663 | −0.350376 | ||||||||
\(731\) | −2.37737 | −0.0879301 | ||||||||
\(732\) | −32.2604 | −1.19238 | ||||||||
\(733\) | −16.9824 | −0.627259 | −0.313629 | − | 0.949545i | \(-0.601545\pi\) | ||||
−0.313629 | + | 0.949545i | \(0.601545\pi\) | |||||||
\(734\) | −9.86089 | −0.363972 | ||||||||
\(735\) | −15.6488 | −0.577213 | ||||||||
\(736\) | −5.98802 | −0.220721 | ||||||||
\(737\) | −21.2614 | −0.783175 | ||||||||
\(738\) | −2.07005 | −0.0761995 | ||||||||
\(739\) | 43.7947 | 1.61101 | 0.805507 | − | 0.592586i | \(-0.201893\pi\) | ||||
0.805507 | + | 0.592586i | \(0.201893\pi\) | |||||||
\(740\) | −13.3126 | −0.489382 | ||||||||
\(741\) | −83.5126 | −3.06791 | ||||||||
\(742\) | −11.7801 | −0.432460 | ||||||||
\(743\) | 48.9409 | 1.79547 | 0.897734 | − | 0.440538i | \(-0.145212\pi\) | ||||
0.897734 | + | 0.440538i | \(0.145212\pi\) | |||||||
\(744\) | 18.2854 | 0.670375 | ||||||||
\(745\) | 35.5230 | 1.30146 | ||||||||
\(746\) | −30.1102 | −1.10241 | ||||||||
\(747\) | −2.08947 | −0.0764497 | ||||||||
\(748\) | −5.85083 | −0.213927 | ||||||||
\(749\) | −38.8779 | −1.42057 | ||||||||
\(750\) | 14.8979 | 0.543993 | ||||||||
\(751\) | 22.3322 | 0.814915 | 0.407457 | − | 0.913224i | \(-0.366415\pi\) | ||||
0.407457 | + | 0.913224i | \(0.366415\pi\) | |||||||
\(752\) | −3.72764 | −0.135933 | ||||||||
\(753\) | 7.39759 | 0.269583 | ||||||||
\(754\) | 5.11422 | 0.186249 | ||||||||
\(755\) | −23.2813 | −0.847294 | ||||||||
\(756\) | −4.79272 | −0.174310 | ||||||||
\(757\) | −30.2187 | −1.09832 | −0.549158 | − | 0.835719i | \(-0.685051\pi\) | ||||
−0.549158 | + | 0.835719i | \(0.685051\pi\) | |||||||
\(758\) | −26.1492 | −0.949782 | ||||||||
\(759\) | 24.7716 | 0.899154 | ||||||||
\(760\) | −19.7870 | −0.717750 | ||||||||
\(761\) | 25.8559 | 0.937277 | 0.468638 | − | 0.883390i | \(-0.344745\pi\) | ||||
0.468638 | + | 0.883390i | \(0.344745\pi\) | |||||||
\(762\) | 24.7482 | 0.896533 | ||||||||
\(763\) | 15.5404 | 0.562599 | ||||||||
\(764\) | −13.5586 | −0.490533 | ||||||||
\(765\) | −17.2254 | −0.622784 | ||||||||
\(766\) | 2.23479 | 0.0807462 | ||||||||
\(767\) | 42.5090 | 1.53491 | ||||||||
\(768\) | −2.23215 | −0.0805456 | ||||||||
\(769\) | 6.47879 | 0.233631 | 0.116816 | − | 0.993154i | \(-0.462731\pi\) | ||||
0.116816 | + | 0.993154i | \(0.462731\pi\) | |||||||
\(770\) | 10.7636 | 0.387892 | ||||||||
\(771\) | 10.0115 | 0.360556 | ||||||||
\(772\) | 9.87008 | 0.355232 | ||||||||
\(773\) | −16.2589 | −0.584793 | −0.292397 | − | 0.956297i | \(-0.594453\pi\) | ||||
−0.292397 | + | 0.956297i | \(0.594453\pi\) | |||||||
\(774\) | 1.49292 | 0.0536619 | ||||||||
\(775\) | 21.0941 | 0.757722 | ||||||||
\(776\) | −11.5509 | −0.414652 | ||||||||
\(777\) | 22.7830 | 0.817336 | ||||||||
\(778\) | 19.4143 | 0.696038 | ||||||||
\(779\) | −7.50690 | −0.268963 | ||||||||
\(780\) | −31.9709 | −1.14474 | ||||||||
\(781\) | 0.0862481 | 0.00308620 | ||||||||
\(782\) | −18.9039 | −0.676002 | ||||||||
\(783\) | 2.23206 | 0.0797672 | ||||||||
\(784\) | −2.54722 | −0.0909720 | ||||||||
\(785\) | 25.8185 | 0.921503 | ||||||||
\(786\) | 16.6683 | 0.594538 | ||||||||
\(787\) | 36.1243 | 1.28769 | 0.643847 | − | 0.765154i | \(-0.277337\pi\) | ||||
0.643847 | + | 0.765154i | \(0.277337\pi\) | |||||||
\(788\) | −13.9126 | −0.495614 | ||||||||
\(789\) | −35.6015 | −1.26745 | ||||||||
\(790\) | 2.70967 | 0.0964058 | ||||||||
\(791\) | −26.4941 | −0.942022 | ||||||||
\(792\) | 3.67416 | 0.130555 | ||||||||
\(793\) | −75.2121 | −2.67086 | ||||||||
\(794\) | 7.46893 | 0.265062 | ||||||||
\(795\) | −34.2962 | −1.21636 | ||||||||
\(796\) | 3.99828 | 0.141715 | ||||||||
\(797\) | 35.2385 | 1.24821 | 0.624105 | − | 0.781340i | \(-0.285464\pi\) | ||||
0.624105 | + | 0.781340i | \(0.285464\pi\) | |||||||
\(798\) | 33.8631 | 1.19874 | ||||||||
\(799\) | −11.7680 | −0.416322 | ||||||||
\(800\) | −2.57501 | −0.0910404 | ||||||||
\(801\) | −8.11354 | −0.286678 | ||||||||
\(802\) | −24.0473 | −0.849139 | ||||||||
\(803\) | 6.37460 | 0.224955 | ||||||||
\(804\) | −25.6074 | −0.903105 | ||||||||
\(805\) | 34.7769 | 1.22572 | ||||||||
\(806\) | 42.6307 | 1.50160 | ||||||||
\(807\) | 42.5496 | 1.49782 | ||||||||
\(808\) | 0.816156 | 0.0287123 | ||||||||
\(809\) | 9.45066 | 0.332268 | 0.166134 | − | 0.986103i | \(-0.446872\pi\) | ||||
0.166134 | + | 0.986103i | \(0.446872\pi\) | |||||||
\(810\) | −30.3224 | −1.06542 | ||||||||
\(811\) | 54.2957 | 1.90658 | 0.953290 | − | 0.302057i | \(-0.0976732\pi\) | ||||
0.953290 | + | 0.302057i | \(0.0976732\pi\) | |||||||
\(812\) | −2.07374 | −0.0727741 | ||||||||
\(813\) | −48.8934 | −1.71477 | ||||||||
\(814\) | 8.96441 | 0.314202 | ||||||||
\(815\) | 33.6460 | 1.17857 | ||||||||
\(816\) | −7.04678 | −0.246687 | ||||||||
\(817\) | 5.41398 | 0.189411 | ||||||||
\(818\) | 31.3735 | 1.09695 | ||||||||
\(819\) | 21.7703 | 0.760717 | ||||||||
\(820\) | −2.87385 | −0.100359 | ||||||||
\(821\) | −24.8819 | −0.868385 | −0.434192 | − | 0.900820i | \(-0.642966\pi\) | ||||
−0.434192 | + | 0.900820i | \(0.642966\pi\) | |||||||
\(822\) | 5.50126 | 0.191879 | ||||||||
\(823\) | 31.5703 | 1.10047 | 0.550237 | − | 0.835009i | \(-0.314538\pi\) | ||||
0.550237 | + | 0.835009i | \(0.314538\pi\) | |||||||
\(824\) | −11.6081 | −0.404388 | ||||||||
\(825\) | 10.6525 | 0.370872 | ||||||||
\(826\) | −17.2368 | −0.599744 | ||||||||
\(827\) | 13.1657 | 0.457816 | 0.228908 | − | 0.973448i | \(-0.426484\pi\) | ||||
0.228908 | + | 0.973448i | \(0.426484\pi\) | |||||||
\(828\) | 11.8711 | 0.412550 | ||||||||
\(829\) | −45.8047 | −1.59086 | −0.795431 | − | 0.606044i | \(-0.792756\pi\) | ||||
−0.795431 | + | 0.606044i | \(0.792756\pi\) | |||||||
\(830\) | −2.90081 | −0.100689 | ||||||||
\(831\) | −50.3327 | −1.74602 | ||||||||
\(832\) | −5.20404 | −0.180418 | ||||||||
\(833\) | −8.04144 | −0.278620 | ||||||||
\(834\) | −33.4198 | −1.15723 | ||||||||
\(835\) | 31.0273 | 1.07375 | ||||||||
\(836\) | 13.3241 | 0.460823 | ||||||||
\(837\) | 18.6058 | 0.643111 | ||||||||
\(838\) | 0.844969 | 0.0291890 | ||||||||
\(839\) | −45.8675 | −1.58352 | −0.791762 | − | 0.610830i | \(-0.790836\pi\) | ||||
−0.791762 | + | 0.610830i | \(0.790836\pi\) | |||||||
\(840\) | 12.9637 | 0.447291 | ||||||||
\(841\) | −28.0342 | −0.966697 | ||||||||
\(842\) | 0.0109361 | 0.000376884 0 | ||||||||
\(843\) | 5.43639 | 0.187239 | ||||||||
\(844\) | 2.75626 | 0.0948743 | ||||||||
\(845\) | −38.7577 | −1.33331 | ||||||||
\(846\) | 7.38997 | 0.254072 | ||||||||
\(847\) | 15.9638 | 0.548524 | ||||||||
\(848\) | −5.58254 | −0.191705 | ||||||||
\(849\) | −14.8005 | −0.507950 | ||||||||
\(850\) | −8.12919 | −0.278829 | ||||||||
\(851\) | 28.9638 | 0.992867 | ||||||||
\(852\) | 0.103878 | 0.00355880 | ||||||||
\(853\) | 32.1839 | 1.10196 | 0.550978 | − | 0.834520i | \(-0.314255\pi\) | ||||
0.550978 | + | 0.834520i | \(0.314255\pi\) | |||||||
\(854\) | 30.4974 | 1.04360 | ||||||||
\(855\) | 39.2273 | 1.34155 | ||||||||
\(856\) | −18.4241 | −0.629724 | ||||||||
\(857\) | −14.6138 | −0.499199 | −0.249600 | − | 0.968349i | \(-0.580299\pi\) | ||||
−0.249600 | + | 0.968349i | \(0.580299\pi\) | |||||||
\(858\) | 21.5285 | 0.734969 | ||||||||
\(859\) | −18.1537 | −0.619397 | −0.309699 | − | 0.950835i | \(-0.600228\pi\) | ||||
−0.309699 | + | 0.950835i | \(0.600228\pi\) | |||||||
\(860\) | 2.07262 | 0.0706758 | ||||||||
\(861\) | 4.91825 | 0.167614 | ||||||||
\(862\) | −11.7557 | −0.400399 | ||||||||
\(863\) | −6.79309 | −0.231239 | −0.115620 | − | 0.993294i | \(-0.536885\pi\) | ||||
−0.115620 | + | 0.993294i | \(0.536885\pi\) | |||||||
\(864\) | −2.27126 | −0.0772698 | ||||||||
\(865\) | 7.04150 | 0.239418 | ||||||||
\(866\) | −30.5511 | −1.03817 | ||||||||
\(867\) | 15.7001 | 0.533204 | ||||||||
\(868\) | −17.2861 | −0.586729 | ||||||||
\(869\) | −1.82463 | −0.0618963 | ||||||||
\(870\) | −6.03744 | −0.204689 | ||||||||
\(871\) | −59.7014 | −2.02290 | ||||||||
\(872\) | 7.36454 | 0.249395 | ||||||||
\(873\) | 22.8993 | 0.775025 | ||||||||
\(874\) | 43.0498 | 1.45618 | ||||||||
\(875\) | −14.0837 | −0.476116 | ||||||||
\(876\) | 7.67762 | 0.259403 | ||||||||
\(877\) | −28.5280 | −0.963322 | −0.481661 | − | 0.876358i | \(-0.659966\pi\) | ||||
−0.481661 | + | 0.876358i | \(0.659966\pi\) | |||||||
\(878\) | −13.4317 | −0.453299 | ||||||||
\(879\) | 50.3018 | 1.69664 | ||||||||
\(880\) | 5.10083 | 0.171949 | ||||||||
\(881\) | 33.6221 | 1.13276 | 0.566379 | − | 0.824145i | \(-0.308344\pi\) | ||||
0.566379 | + | 0.824145i | \(0.308344\pi\) | |||||||
\(882\) | 5.04980 | 0.170036 | ||||||||
\(883\) | 37.7700 | 1.27106 | 0.635531 | − | 0.772075i | \(-0.280781\pi\) | ||||
0.635531 | + | 0.772075i | \(0.280781\pi\) | |||||||
\(884\) | −16.4289 | −0.552565 | ||||||||
\(885\) | −50.1828 | −1.68688 | ||||||||
\(886\) | 21.7955 | 0.732234 | ||||||||
\(887\) | 25.3961 | 0.852717 | 0.426359 | − | 0.904554i | \(-0.359796\pi\) | ||||
0.426359 | + | 0.904554i | \(0.359796\pi\) | |||||||
\(888\) | 10.7968 | 0.362317 | ||||||||
\(889\) | −23.3957 | −0.784668 | ||||||||
\(890\) | −11.2640 | −0.377571 | ||||||||
\(891\) | 20.4184 | 0.684041 | ||||||||
\(892\) | 1.88498 | 0.0631139 | ||||||||
\(893\) | 26.7993 | 0.896803 | ||||||||
\(894\) | −28.8098 | −0.963544 | ||||||||
\(895\) | −0.823069 | −0.0275122 | ||||||||
\(896\) | 2.11016 | 0.0704956 | ||||||||
\(897\) | 69.5579 | 2.32247 | ||||||||
\(898\) | −8.83987 | −0.294990 | ||||||||
\(899\) | 8.05046 | 0.268498 | ||||||||
\(900\) | 5.10490 | 0.170163 | ||||||||
\(901\) | −17.6238 | −0.587134 | ||||||||
\(902\) | 1.93518 | 0.0644344 | ||||||||
\(903\) | −3.54705 | −0.118038 | ||||||||
\(904\) | −12.5555 | −0.417589 | ||||||||
\(905\) | −28.7167 | −0.954574 | ||||||||
\(906\) | 18.8816 | 0.627299 | ||||||||
\(907\) | 2.39378 | 0.0794843 | 0.0397421 | − | 0.999210i | \(-0.487346\pi\) | ||||
0.0397421 | + | 0.999210i | \(0.487346\pi\) | |||||||
\(908\) | −1.41936 | −0.0471030 | ||||||||
\(909\) | −1.61801 | −0.0536661 | ||||||||
\(910\) | 30.2238 | 1.00191 | ||||||||
\(911\) | −46.3233 | −1.53476 | −0.767380 | − | 0.641193i | \(-0.778440\pi\) | ||||
−0.767380 | + | 0.641193i | \(0.778440\pi\) | |||||||
\(912\) | 16.0476 | 0.531390 | ||||||||
\(913\) | 1.95334 | 0.0646460 | ||||||||
\(914\) | 7.96665 | 0.263513 | ||||||||
\(915\) | 88.7894 | 2.93529 | ||||||||
\(916\) | −13.1725 | −0.435231 | ||||||||
\(917\) | −15.7574 | −0.520354 | ||||||||
\(918\) | −7.17026 | −0.236654 | ||||||||
\(919\) | −7.69608 | −0.253870 | −0.126935 | − | 0.991911i | \(-0.540514\pi\) | ||||
−0.126935 | + | 0.991911i | \(0.540514\pi\) | |||||||
\(920\) | 16.4807 | 0.543351 | ||||||||
\(921\) | 43.1950 | 1.42332 | ||||||||
\(922\) | 4.27698 | 0.140855 | ||||||||
\(923\) | 0.242182 | 0.00797150 | ||||||||
\(924\) | −8.72947 | −0.287178 | ||||||||
\(925\) | 12.4552 | 0.409525 | ||||||||
\(926\) | −2.49886 | −0.0821177 | ||||||||
\(927\) | 23.0128 | 0.755841 | ||||||||
\(928\) | −0.982740 | −0.0322600 | ||||||||
\(929\) | 40.2897 | 1.32186 | 0.660931 | − | 0.750447i | \(-0.270162\pi\) | ||||
0.660931 | + | 0.750447i | \(0.270162\pi\) | |||||||
\(930\) | −50.3264 | −1.65027 | ||||||||
\(931\) | 18.3128 | 0.600177 | ||||||||
\(932\) | −3.47205 | −0.113731 | ||||||||
\(933\) | 67.6368 | 2.21433 | ||||||||
\(934\) | −39.3888 | −1.28884 | ||||||||
\(935\) | 16.1031 | 0.526627 | ||||||||
\(936\) | 10.3169 | 0.337218 | ||||||||
\(937\) | 14.2365 | 0.465085 | 0.232543 | − | 0.972586i | \(-0.425295\pi\) | ||||
0.232543 | + | 0.972586i | \(0.425295\pi\) | |||||||
\(938\) | 24.2080 | 0.790420 | ||||||||
\(939\) | 8.60973 | 0.280968 | ||||||||
\(940\) | 10.2595 | 0.334628 | ||||||||
\(941\) | 52.9745 | 1.72692 | 0.863459 | − | 0.504418i | \(-0.168293\pi\) | ||||
0.863459 | + | 0.504418i | \(0.168293\pi\) | |||||||
\(942\) | −20.9393 | −0.682240 | ||||||||
\(943\) | 6.25252 | 0.203610 | ||||||||
\(944\) | −8.16846 | −0.265861 | ||||||||
\(945\) | 13.1909 | 0.429100 | ||||||||
\(946\) | −1.39565 | −0.0453766 | ||||||||
\(947\) | 0.634653 | 0.0206234 | 0.0103117 | − | 0.999947i | \(-0.496718\pi\) | ||||
0.0103117 | + | 0.999947i | \(0.496718\pi\) | |||||||
\(948\) | −2.19760 | −0.0713746 | ||||||||
\(949\) | 17.8997 | 0.581048 | ||||||||
\(950\) | 18.5126 | 0.600628 | ||||||||
\(951\) | 19.7538 | 0.640559 | ||||||||
\(952\) | 6.66168 | 0.215906 | ||||||||
\(953\) | 37.5100 | 1.21507 | 0.607535 | − | 0.794293i | \(-0.292159\pi\) | ||||
0.607535 | + | 0.794293i | \(0.292159\pi\) | |||||||
\(954\) | 11.0673 | 0.358316 | ||||||||
\(955\) | 37.3170 | 1.20755 | ||||||||
\(956\) | 4.50429 | 0.145679 | ||||||||
\(957\) | 4.06547 | 0.131418 | ||||||||
\(958\) | 7.14596 | 0.230876 | ||||||||
\(959\) | −5.20062 | −0.167937 | ||||||||
\(960\) | 6.14348 | 0.198280 | ||||||||
\(961\) | 36.1064 | 1.16472 | ||||||||
\(962\) | 25.1718 | 0.811570 | ||||||||
\(963\) | 36.5255 | 1.17702 | ||||||||
\(964\) | −4.21948 | −0.135900 | ||||||||
\(965\) | −27.1652 | −0.874477 | ||||||||
\(966\) | −28.2047 | −0.907471 | ||||||||
\(967\) | 15.3024 | 0.492091 | 0.246046 | − | 0.969258i | \(-0.420869\pi\) | ||||
0.246046 | + | 0.969258i | \(0.420869\pi\) | |||||||
\(968\) | 7.56522 | 0.243156 | ||||||||
\(969\) | 50.6617 | 1.62749 | ||||||||
\(970\) | 31.7911 | 1.02075 | ||||||||
\(971\) | −29.6941 | −0.952929 | −0.476465 | − | 0.879194i | \(-0.658082\pi\) | ||||
−0.476465 | + | 0.879194i | \(0.658082\pi\) | |||||||
\(972\) | 17.7783 | 0.570238 | ||||||||
\(973\) | 31.5934 | 1.01284 | ||||||||
\(974\) | 23.0636 | 0.739005 | ||||||||
\(975\) | 29.9118 | 0.957945 | ||||||||
\(976\) | 14.4526 | 0.462617 | ||||||||
\(977\) | −48.4235 | −1.54920 | −0.774602 | − | 0.632449i | \(-0.782050\pi\) | ||||
−0.774602 | + | 0.632449i | \(0.782050\pi\) | |||||||
\(978\) | −27.2875 | −0.872559 | ||||||||
\(979\) | 7.58492 | 0.242415 | ||||||||
\(980\) | 7.01064 | 0.223947 | ||||||||
\(981\) | −14.6000 | −0.466143 | ||||||||
\(982\) | 25.1874 | 0.803763 | ||||||||
\(983\) | −52.5449 | −1.67592 | −0.837960 | − | 0.545731i | \(-0.816252\pi\) | ||||
−0.837960 | + | 0.545731i | \(0.816252\pi\) | |||||||
\(984\) | 2.33075 | 0.0743015 | ||||||||
\(985\) | 38.2912 | 1.22006 | ||||||||
\(986\) | −3.10247 | −0.0988026 | ||||||||
\(987\) | −17.5579 | −0.558875 | ||||||||
\(988\) | 37.4136 | 1.19029 | ||||||||
\(989\) | −4.50932 | −0.143388 | ||||||||
\(990\) | −10.1123 | −0.321389 | ||||||||
\(991\) | −32.7726 | −1.04105 | −0.520527 | − | 0.853845i | \(-0.674265\pi\) | ||||
−0.520527 | + | 0.853845i | \(0.674265\pi\) | |||||||
\(992\) | −8.19185 | −0.260091 | ||||||||
\(993\) | 7.79622 | 0.247406 | ||||||||
\(994\) | −0.0982010 | −0.00311475 | ||||||||
\(995\) | −11.0044 | −0.348862 | ||||||||
\(996\) | 2.35261 | 0.0745454 | ||||||||
\(997\) | −38.4466 | −1.21762 | −0.608808 | − | 0.793318i | \(-0.708352\pi\) | ||||
−0.608808 | + | 0.793318i | \(0.708352\pi\) | |||||||
\(998\) | −26.4449 | −0.837099 | ||||||||
\(999\) | 10.9860 | 0.347581 |
(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.1.7 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4006.2.a.g.1.7 | ✓ | 40 | 1.1 | even | 1 | trivial |