Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0000972201\) |
Analytic rank: | \(0\) |
Dimension: | \(62\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.57 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.42755 | 1.71654 | 0.858270 | − | 0.513199i | \(-0.171540\pi\) | ||||
0.858270 | + | 0.513199i | \(0.171540\pi\) | |||||||
\(3\) | 1.02702 | 0.592953 | 0.296476 | − | 0.955040i | \(-0.404188\pi\) | ||||
0.296476 | + | 0.955040i | \(0.404188\pi\) | |||||||
\(4\) | 3.89301 | 1.94651 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 2.49316 | 1.01783 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 4.59539 | 1.62472 | ||||||||
\(9\) | −1.94522 | −0.648407 | ||||||||
\(10\) | −2.42755 | −0.767660 | ||||||||
\(11\) | 0.740098 | 0.223148 | 0.111574 | − | 0.993756i | \(-0.464411\pi\) | ||||
0.111574 | + | 0.993756i | \(0.464411\pi\) | |||||||
\(12\) | 3.99822 | 1.15419 | ||||||||
\(13\) | −0.862758 | −0.239286 | −0.119643 | − | 0.992817i | \(-0.538175\pi\) | ||||
−0.119643 | + | 0.992817i | \(0.538175\pi\) | |||||||
\(14\) | −2.42755 | −0.648791 | ||||||||
\(15\) | −1.02702 | −0.265177 | ||||||||
\(16\) | 3.36953 | 0.842383 | ||||||||
\(17\) | 2.25071 | 0.545878 | 0.272939 | − | 0.962031i | \(-0.412004\pi\) | ||||
0.272939 | + | 0.962031i | \(0.412004\pi\) | |||||||
\(18\) | −4.72213 | −1.11302 | ||||||||
\(19\) | 4.76201 | 1.09248 | 0.546240 | − | 0.837629i | \(-0.316059\pi\) | ||||
0.546240 | + | 0.837629i | \(0.316059\pi\) | |||||||
\(20\) | −3.89301 | −0.870505 | ||||||||
\(21\) | −1.02702 | −0.224115 | ||||||||
\(22\) | 1.79663 | 0.383042 | ||||||||
\(23\) | −0.0894125 | −0.0186438 | −0.00932190 | − | 0.999957i | \(-0.502967\pi\) | ||||
−0.00932190 | + | 0.999957i | \(0.502967\pi\) | |||||||
\(24\) | 4.71958 | 0.963380 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −2.09439 | −0.410744 | ||||||||
\(27\) | −5.07886 | −0.977428 | ||||||||
\(28\) | −3.89301 | −0.735711 | ||||||||
\(29\) | 10.3886 | 1.92912 | 0.964562 | − | 0.263857i | \(-0.0849948\pi\) | ||||
0.964562 | + | 0.263857i | \(0.0849948\pi\) | |||||||
\(30\) | −2.49316 | −0.455186 | ||||||||
\(31\) | 7.27024 | 1.30577 | 0.652887 | − | 0.757455i | \(-0.273558\pi\) | ||||
0.652887 | + | 0.757455i | \(0.273558\pi\) | |||||||
\(32\) | −1.01107 | −0.178733 | ||||||||
\(33\) | 0.760098 | 0.132316 | ||||||||
\(34\) | 5.46373 | 0.937022 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | −7.57277 | −1.26213 | ||||||||
\(37\) | 1.86231 | 0.306161 | 0.153081 | − | 0.988214i | \(-0.451081\pi\) | ||||
0.153081 | + | 0.988214i | \(0.451081\pi\) | |||||||
\(38\) | 11.5600 | 1.87529 | ||||||||
\(39\) | −0.886074 | −0.141885 | ||||||||
\(40\) | −4.59539 | −0.726596 | ||||||||
\(41\) | 1.00466 | 0.156902 | 0.0784510 | − | 0.996918i | \(-0.475003\pi\) | ||||
0.0784510 | + | 0.996918i | \(0.475003\pi\) | |||||||
\(42\) | −2.49316 | −0.384702 | ||||||||
\(43\) | 5.65130 | 0.861815 | 0.430908 | − | 0.902396i | \(-0.358193\pi\) | ||||
0.430908 | + | 0.902396i | \(0.358193\pi\) | |||||||
\(44\) | 2.88121 | 0.434359 | ||||||||
\(45\) | 1.94522 | 0.289976 | ||||||||
\(46\) | −0.217054 | −0.0320028 | ||||||||
\(47\) | 0.888047 | 0.129535 | 0.0647675 | − | 0.997900i | \(-0.479369\pi\) | ||||
0.0647675 | + | 0.997900i | \(0.479369\pi\) | |||||||
\(48\) | 3.46059 | 0.499494 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 2.42755 | 0.343308 | ||||||||
\(51\) | 2.31154 | 0.323680 | ||||||||
\(52\) | −3.35873 | −0.465772 | ||||||||
\(53\) | 13.1121 | 1.80109 | 0.900545 | − | 0.434764i | \(-0.143168\pi\) | ||||
0.900545 | + | 0.434764i | \(0.143168\pi\) | |||||||
\(54\) | −12.3292 | −1.67779 | ||||||||
\(55\) | −0.740098 | −0.0997948 | ||||||||
\(56\) | −4.59539 | −0.614085 | ||||||||
\(57\) | 4.89070 | 0.647789 | ||||||||
\(58\) | 25.2190 | 3.31142 | ||||||||
\(59\) | 9.57154 | 1.24611 | 0.623054 | − | 0.782178i | \(-0.285892\pi\) | ||||
0.623054 | + | 0.782178i | \(0.285892\pi\) | |||||||
\(60\) | −3.99822 | −0.516168 | ||||||||
\(61\) | 6.37429 | 0.816145 | 0.408072 | − | 0.912950i | \(-0.366201\pi\) | ||||
0.408072 | + | 0.912950i | \(0.366201\pi\) | |||||||
\(62\) | 17.6489 | 2.24141 | ||||||||
\(63\) | 1.94522 | 0.245075 | ||||||||
\(64\) | −9.19348 | −1.14919 | ||||||||
\(65\) | 0.862758 | 0.107012 | ||||||||
\(66\) | 1.84518 | 0.227126 | ||||||||
\(67\) | −14.4564 | −1.76613 | −0.883066 | − | 0.469248i | \(-0.844525\pi\) | ||||
−0.883066 | + | 0.469248i | \(0.844525\pi\) | |||||||
\(68\) | 8.76206 | 1.06256 | ||||||||
\(69\) | −0.0918288 | −0.0110549 | ||||||||
\(70\) | 2.42755 | 0.290148 | ||||||||
\(71\) | −9.82493 | −1.16601 | −0.583003 | − | 0.812470i | \(-0.698122\pi\) | ||||
−0.583003 | + | 0.812470i | \(0.698122\pi\) | |||||||
\(72\) | −8.93906 | −1.05348 | ||||||||
\(73\) | −14.0816 | −1.64813 | −0.824066 | − | 0.566494i | \(-0.808300\pi\) | ||||
−0.824066 | + | 0.566494i | \(0.808300\pi\) | |||||||
\(74\) | 4.52085 | 0.525538 | ||||||||
\(75\) | 1.02702 | 0.118591 | ||||||||
\(76\) | 18.5386 | 2.12652 | ||||||||
\(77\) | −0.740098 | −0.0843420 | ||||||||
\(78\) | −2.15099 | −0.243552 | ||||||||
\(79\) | 8.20700 | 0.923360 | 0.461680 | − | 0.887047i | \(-0.347247\pi\) | ||||
0.461680 | + | 0.887047i | \(0.347247\pi\) | |||||||
\(80\) | −3.36953 | −0.376725 | ||||||||
\(81\) | 0.619547 | 0.0688386 | ||||||||
\(82\) | 2.43887 | 0.269328 | ||||||||
\(83\) | 5.30835 | 0.582667 | 0.291334 | − | 0.956621i | \(-0.405901\pi\) | ||||
0.291334 | + | 0.956621i | \(0.405901\pi\) | |||||||
\(84\) | −3.99822 | −0.436242 | ||||||||
\(85\) | −2.25071 | −0.244124 | ||||||||
\(86\) | 13.7188 | 1.47934 | ||||||||
\(87\) | 10.6694 | 1.14388 | ||||||||
\(88\) | 3.40104 | 0.362552 | ||||||||
\(89\) | −11.9860 | −1.27052 | −0.635258 | − | 0.772300i | \(-0.719106\pi\) | ||||
−0.635258 | + | 0.772300i | \(0.719106\pi\) | |||||||
\(90\) | 4.72213 | 0.497756 | ||||||||
\(91\) | 0.862758 | 0.0904416 | ||||||||
\(92\) | −0.348084 | −0.0362903 | ||||||||
\(93\) | 7.46672 | 0.774262 | ||||||||
\(94\) | 2.15578 | 0.222352 | ||||||||
\(95\) | −4.76201 | −0.488572 | ||||||||
\(96\) | −1.03839 | −0.105980 | ||||||||
\(97\) | 16.9852 | 1.72459 | 0.862295 | − | 0.506406i | \(-0.169026\pi\) | ||||
0.862295 | + | 0.506406i | \(0.169026\pi\) | |||||||
\(98\) | 2.42755 | 0.245220 | ||||||||
\(99\) | −1.43965 | −0.144691 | ||||||||
\(100\) | 3.89301 | 0.389301 | ||||||||
\(101\) | 8.16261 | 0.812210 | 0.406105 | − | 0.913826i | \(-0.366887\pi\) | ||||
0.406105 | + | 0.913826i | \(0.366887\pi\) | |||||||
\(102\) | 5.61138 | 0.555610 | ||||||||
\(103\) | −8.40818 | −0.828483 | −0.414241 | − | 0.910167i | \(-0.635953\pi\) | ||||
−0.414241 | + | 0.910167i | \(0.635953\pi\) | |||||||
\(104\) | −3.96471 | −0.388772 | ||||||||
\(105\) | 1.02702 | 0.100227 | ||||||||
\(106\) | 31.8304 | 3.09164 | ||||||||
\(107\) | 11.4992 | 1.11167 | 0.555834 | − | 0.831294i | \(-0.312399\pi\) | ||||
0.555834 | + | 0.831294i | \(0.312399\pi\) | |||||||
\(108\) | −19.7721 | −1.90257 | ||||||||
\(109\) | −1.37478 | −0.131680 | −0.0658399 | − | 0.997830i | \(-0.520973\pi\) | ||||
−0.0658399 | + | 0.997830i | \(0.520973\pi\) | |||||||
\(110\) | −1.79663 | −0.171302 | ||||||||
\(111\) | 1.91263 | 0.181539 | ||||||||
\(112\) | −3.36953 | −0.318391 | ||||||||
\(113\) | 8.92213 | 0.839323 | 0.419662 | − | 0.907681i | \(-0.362149\pi\) | ||||
0.419662 | + | 0.907681i | \(0.362149\pi\) | |||||||
\(114\) | 11.8724 | 1.11196 | ||||||||
\(115\) | 0.0894125 | 0.00833776 | ||||||||
\(116\) | 40.4432 | 3.75505 | ||||||||
\(117\) | 1.67826 | 0.155155 | ||||||||
\(118\) | 23.2354 | 2.13899 | ||||||||
\(119\) | −2.25071 | −0.206323 | ||||||||
\(120\) | −4.71958 | −0.430837 | ||||||||
\(121\) | −10.4523 | −0.950205 | ||||||||
\(122\) | 15.4739 | 1.40094 | ||||||||
\(123\) | 1.03181 | 0.0930354 | ||||||||
\(124\) | 28.3032 | 2.54170 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 4.72213 | 0.420681 | ||||||||
\(127\) | 0.785135 | 0.0696695 | 0.0348347 | − | 0.999393i | \(-0.488910\pi\) | ||||
0.0348347 | + | 0.999393i | \(0.488910\pi\) | |||||||
\(128\) | −20.2955 | −1.79389 | ||||||||
\(129\) | 5.80402 | 0.511016 | ||||||||
\(130\) | 2.09439 | 0.183690 | ||||||||
\(131\) | −4.24712 | −0.371072 | −0.185536 | − | 0.982637i | \(-0.559402\pi\) | ||||
−0.185536 | + | 0.982637i | \(0.559402\pi\) | |||||||
\(132\) | 2.95907 | 0.257554 | ||||||||
\(133\) | −4.76201 | −0.412919 | ||||||||
\(134\) | −35.0937 | −3.03164 | ||||||||
\(135\) | 5.07886 | 0.437119 | ||||||||
\(136\) | 10.3429 | 0.886898 | ||||||||
\(137\) | 21.6224 | 1.84733 | 0.923664 | − | 0.383204i | \(-0.125179\pi\) | ||||
0.923664 | + | 0.383204i | \(0.125179\pi\) | |||||||
\(138\) | −0.222919 | −0.0189762 | ||||||||
\(139\) | −5.79999 | −0.491949 | −0.245974 | − | 0.969276i | \(-0.579108\pi\) | ||||
−0.245974 | + | 0.969276i | \(0.579108\pi\) | |||||||
\(140\) | 3.89301 | 0.329020 | ||||||||
\(141\) | 0.912046 | 0.0768081 | ||||||||
\(142\) | −23.8506 | −2.00149 | ||||||||
\(143\) | −0.638525 | −0.0533962 | ||||||||
\(144\) | −6.55449 | −0.546207 | ||||||||
\(145\) | −10.3886 | −0.862730 | ||||||||
\(146\) | −34.1840 | −2.82908 | ||||||||
\(147\) | 1.02702 | 0.0847075 | ||||||||
\(148\) | 7.24999 | 0.595945 | ||||||||
\(149\) | −6.37255 | −0.522060 | −0.261030 | − | 0.965331i | \(-0.584062\pi\) | ||||
−0.261030 | + | 0.965331i | \(0.584062\pi\) | |||||||
\(150\) | 2.49316 | 0.203565 | ||||||||
\(151\) | −22.6558 | −1.84370 | −0.921852 | − | 0.387541i | \(-0.873325\pi\) | ||||
−0.921852 | + | 0.387541i | \(0.873325\pi\) | |||||||
\(152\) | 21.8833 | 1.77497 | ||||||||
\(153\) | −4.37814 | −0.353951 | ||||||||
\(154\) | −1.79663 | −0.144776 | ||||||||
\(155\) | −7.27024 | −0.583960 | ||||||||
\(156\) | −3.44950 | −0.276181 | ||||||||
\(157\) | 0.332918 | 0.0265697 | 0.0132849 | − | 0.999912i | \(-0.495771\pi\) | ||||
0.0132849 | + | 0.999912i | \(0.495771\pi\) | |||||||
\(158\) | 19.9229 | 1.58498 | ||||||||
\(159\) | 13.4665 | 1.06796 | ||||||||
\(160\) | 1.01107 | 0.0799318 | ||||||||
\(161\) | 0.0894125 | 0.00704669 | ||||||||
\(162\) | 1.50398 | 0.118164 | ||||||||
\(163\) | 10.2993 | 0.806700 | 0.403350 | − | 0.915046i | \(-0.367846\pi\) | ||||
0.403350 | + | 0.915046i | \(0.367846\pi\) | |||||||
\(164\) | 3.91117 | 0.305411 | ||||||||
\(165\) | −0.760098 | −0.0591736 | ||||||||
\(166\) | 12.8863 | 1.00017 | ||||||||
\(167\) | 11.7609 | 0.910085 | 0.455042 | − | 0.890470i | \(-0.349624\pi\) | ||||
0.455042 | + | 0.890470i | \(0.349624\pi\) | |||||||
\(168\) | −4.71958 | −0.364124 | ||||||||
\(169\) | −12.2556 | −0.942742 | ||||||||
\(170\) | −5.46373 | −0.419049 | ||||||||
\(171\) | −9.26316 | −0.708372 | ||||||||
\(172\) | 22.0006 | 1.67753 | ||||||||
\(173\) | 1.63055 | 0.123969 | 0.0619843 | − | 0.998077i | \(-0.480257\pi\) | ||||
0.0619843 | + | 0.998077i | \(0.480257\pi\) | |||||||
\(174\) | 25.9005 | 1.96351 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 2.49378 | 0.187976 | ||||||||
\(177\) | 9.83021 | 0.738884 | ||||||||
\(178\) | −29.0967 | −2.18089 | ||||||||
\(179\) | −17.9204 | −1.33943 | −0.669717 | − | 0.742616i | \(-0.733585\pi\) | ||||
−0.669717 | + | 0.742616i | \(0.733585\pi\) | |||||||
\(180\) | 7.57277 | 0.564441 | ||||||||
\(181\) | 8.17518 | 0.607656 | 0.303828 | − | 0.952727i | \(-0.401735\pi\) | ||||
0.303828 | + | 0.952727i | \(0.401735\pi\) | |||||||
\(182\) | 2.09439 | 0.155247 | ||||||||
\(183\) | 6.54656 | 0.483935 | ||||||||
\(184\) | −0.410886 | −0.0302909 | ||||||||
\(185\) | −1.86231 | −0.136919 | ||||||||
\(186\) | 18.1259 | 1.32905 | ||||||||
\(187\) | 1.66575 | 0.121812 | ||||||||
\(188\) | 3.45718 | 0.252141 | ||||||||
\(189\) | 5.07886 | 0.369433 | ||||||||
\(190\) | −11.5600 | −0.838653 | ||||||||
\(191\) | −8.00026 | −0.578878 | −0.289439 | − | 0.957196i | \(-0.593469\pi\) | ||||
−0.289439 | + | 0.957196i | \(0.593469\pi\) | |||||||
\(192\) | −9.44193 | −0.681413 | ||||||||
\(193\) | −16.3017 | −1.17343 | −0.586713 | − | 0.809795i | \(-0.699578\pi\) | ||||
−0.586713 | + | 0.809795i | \(0.699578\pi\) | |||||||
\(194\) | 41.2326 | 2.96033 | ||||||||
\(195\) | 0.886074 | 0.0634531 | ||||||||
\(196\) | 3.89301 | 0.278072 | ||||||||
\(197\) | −6.85481 | −0.488385 | −0.244193 | − | 0.969727i | \(-0.578523\pi\) | ||||
−0.244193 | + | 0.969727i | \(0.578523\pi\) | |||||||
\(198\) | −3.49484 | −0.248367 | ||||||||
\(199\) | 1.90350 | 0.134935 | 0.0674677 | − | 0.997721i | \(-0.478508\pi\) | ||||
0.0674677 | + | 0.997721i | \(0.478508\pi\) | |||||||
\(200\) | 4.59539 | 0.324943 | ||||||||
\(201\) | −14.8471 | −1.04723 | ||||||||
\(202\) | 19.8152 | 1.39419 | ||||||||
\(203\) | −10.3886 | −0.729140 | ||||||||
\(204\) | 8.99885 | 0.630046 | ||||||||
\(205\) | −1.00466 | −0.0701687 | ||||||||
\(206\) | −20.4113 | −1.42212 | ||||||||
\(207\) | 0.173927 | 0.0120888 | ||||||||
\(208\) | −2.90709 | −0.201571 | ||||||||
\(209\) | 3.52435 | 0.243785 | ||||||||
\(210\) | 2.49316 | 0.172044 | ||||||||
\(211\) | −10.3078 | −0.709619 | −0.354810 | − | 0.934939i | \(-0.615454\pi\) | ||||
−0.354810 | + | 0.934939i | \(0.615454\pi\) | |||||||
\(212\) | 51.0457 | 3.50583 | ||||||||
\(213\) | −10.0904 | −0.691386 | ||||||||
\(214\) | 27.9149 | 1.90822 | ||||||||
\(215\) | −5.65130 | −0.385416 | ||||||||
\(216\) | −23.3394 | −1.58804 | ||||||||
\(217\) | −7.27024 | −0.493536 | ||||||||
\(218\) | −3.33734 | −0.226033 | ||||||||
\(219\) | −14.4622 | −0.977265 | ||||||||
\(220\) | −2.88121 | −0.194251 | ||||||||
\(221\) | −1.94182 | −0.130621 | ||||||||
\(222\) | 4.64302 | 0.311619 | ||||||||
\(223\) | 15.4523 | 1.03476 | 0.517381 | − | 0.855755i | \(-0.326907\pi\) | ||||
0.517381 | + | 0.855755i | \(0.326907\pi\) | |||||||
\(224\) | 1.01107 | 0.0675547 | ||||||||
\(225\) | −1.94522 | −0.129681 | ||||||||
\(226\) | 21.6589 | 1.44073 | ||||||||
\(227\) | −6.62030 | −0.439405 | −0.219702 | − | 0.975567i | \(-0.570509\pi\) | ||||
−0.219702 | + | 0.975567i | \(0.570509\pi\) | |||||||
\(228\) | 19.0396 | 1.26093 | ||||||||
\(229\) | 1.00000 | 0.0660819 | ||||||||
\(230\) | 0.217054 | 0.0143121 | ||||||||
\(231\) | −0.760098 | −0.0500108 | ||||||||
\(232\) | 47.7399 | 3.13428 | ||||||||
\(233\) | −5.37938 | −0.352415 | −0.176208 | − | 0.984353i | \(-0.556383\pi\) | ||||
−0.176208 | + | 0.984353i | \(0.556383\pi\) | |||||||
\(234\) | 4.07405 | 0.266329 | ||||||||
\(235\) | −0.888047 | −0.0579298 | ||||||||
\(236\) | 37.2622 | 2.42556 | ||||||||
\(237\) | 8.42879 | 0.547509 | ||||||||
\(238\) | −5.46373 | −0.354161 | ||||||||
\(239\) | −19.9990 | −1.29363 | −0.646815 | − | 0.762647i | \(-0.723899\pi\) | ||||
−0.646815 | + | 0.762647i | \(0.723899\pi\) | |||||||
\(240\) | −3.46059 | −0.223380 | ||||||||
\(241\) | −7.25801 | −0.467530 | −0.233765 | − | 0.972293i | \(-0.575105\pi\) | ||||
−0.233765 | + | 0.972293i | \(0.575105\pi\) | |||||||
\(242\) | −25.3734 | −1.63106 | ||||||||
\(243\) | 15.8729 | 1.01825 | ||||||||
\(244\) | 24.8152 | 1.58863 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 2.50478 | 0.159699 | ||||||||
\(247\) | −4.10846 | −0.261415 | ||||||||
\(248\) | 33.4096 | 2.12151 | ||||||||
\(249\) | 5.45181 | 0.345494 | ||||||||
\(250\) | −2.42755 | −0.153532 | ||||||||
\(251\) | 12.3043 | 0.776644 | 0.388322 | − | 0.921524i | \(-0.373055\pi\) | ||||
0.388322 | + | 0.921524i | \(0.373055\pi\) | |||||||
\(252\) | 7.57277 | 0.477040 | ||||||||
\(253\) | −0.0661740 | −0.00416032 | ||||||||
\(254\) | 1.90596 | 0.119590 | ||||||||
\(255\) | −2.31154 | −0.144754 | ||||||||
\(256\) | −30.8815 | −1.93010 | ||||||||
\(257\) | −6.09684 | −0.380310 | −0.190155 | − | 0.981754i | \(-0.560899\pi\) | ||||
−0.190155 | + | 0.981754i | \(0.560899\pi\) | |||||||
\(258\) | 14.0896 | 0.877179 | ||||||||
\(259\) | −1.86231 | −0.115718 | ||||||||
\(260\) | 3.35873 | 0.208300 | ||||||||
\(261\) | −20.2082 | −1.25086 | ||||||||
\(262\) | −10.3101 | −0.636960 | ||||||||
\(263\) | −9.85239 | −0.607525 | −0.303762 | − | 0.952748i | \(-0.598243\pi\) | ||||
−0.303762 | + | 0.952748i | \(0.598243\pi\) | |||||||
\(264\) | 3.49295 | 0.214976 | ||||||||
\(265\) | −13.1121 | −0.805472 | ||||||||
\(266\) | −11.5600 | −0.708791 | ||||||||
\(267\) | −12.3099 | −0.753356 | ||||||||
\(268\) | −56.2790 | −3.43779 | ||||||||
\(269\) | −2.05818 | −0.125489 | −0.0627446 | − | 0.998030i | \(-0.519985\pi\) | ||||
−0.0627446 | + | 0.998030i | \(0.519985\pi\) | |||||||
\(270\) | 12.3292 | 0.750332 | ||||||||
\(271\) | −3.42212 | −0.207879 | −0.103939 | − | 0.994584i | \(-0.533145\pi\) | ||||
−0.103939 | + | 0.994584i | \(0.533145\pi\) | |||||||
\(272\) | 7.58386 | 0.459839 | ||||||||
\(273\) | 0.886074 | 0.0536276 | ||||||||
\(274\) | 52.4896 | 3.17101 | ||||||||
\(275\) | 0.740098 | 0.0446296 | ||||||||
\(276\) | −0.357491 | −0.0215184 | ||||||||
\(277\) | 32.3702 | 1.94494 | 0.972469 | − | 0.233034i | \(-0.0748653\pi\) | ||||
0.972469 | + | 0.233034i | \(0.0748653\pi\) | |||||||
\(278\) | −14.0798 | −0.844449 | ||||||||
\(279\) | −14.1422 | −0.846673 | ||||||||
\(280\) | 4.59539 | 0.274627 | ||||||||
\(281\) | 1.93110 | 0.115200 | 0.0576000 | − | 0.998340i | \(-0.481655\pi\) | ||||
0.0576000 | + | 0.998340i | \(0.481655\pi\) | |||||||
\(282\) | 2.21404 | 0.131844 | ||||||||
\(283\) | 19.5305 | 1.16097 | 0.580483 | − | 0.814273i | \(-0.302864\pi\) | ||||
0.580483 | + | 0.814273i | \(0.302864\pi\) | |||||||
\(284\) | −38.2486 | −2.26964 | ||||||||
\(285\) | −4.89070 | −0.289700 | ||||||||
\(286\) | −1.55005 | −0.0916566 | ||||||||
\(287\) | −1.00466 | −0.0593034 | ||||||||
\(288\) | 1.96675 | 0.115892 | ||||||||
\(289\) | −11.9343 | −0.702017 | ||||||||
\(290\) | −25.2190 | −1.48091 | ||||||||
\(291\) | 17.4443 | 1.02260 | ||||||||
\(292\) | −54.8201 | −3.20810 | ||||||||
\(293\) | −25.2603 | −1.47572 | −0.737862 | − | 0.674952i | \(-0.764164\pi\) | ||||
−0.737862 | + | 0.674952i | \(0.764164\pi\) | |||||||
\(294\) | 2.49316 | 0.145404 | ||||||||
\(295\) | −9.57154 | −0.557277 | ||||||||
\(296\) | 8.55803 | 0.497425 | ||||||||
\(297\) | −3.75885 | −0.218111 | ||||||||
\(298\) | −15.4697 | −0.896136 | ||||||||
\(299\) | 0.0771414 | 0.00446120 | ||||||||
\(300\) | 3.99822 | 0.230837 | ||||||||
\(301\) | −5.65130 | −0.325736 | ||||||||
\(302\) | −54.9982 | −3.16479 | ||||||||
\(303\) | 8.38320 | 0.481602 | ||||||||
\(304\) | 16.0458 | 0.920287 | ||||||||
\(305\) | −6.37429 | −0.364991 | ||||||||
\(306\) | −10.6282 | −0.607572 | ||||||||
\(307\) | 11.1238 | 0.634867 | 0.317434 | − | 0.948280i | \(-0.397179\pi\) | ||||
0.317434 | + | 0.948280i | \(0.397179\pi\) | |||||||
\(308\) | −2.88121 | −0.164172 | ||||||||
\(309\) | −8.63541 | −0.491251 | ||||||||
\(310\) | −17.6489 | −1.00239 | ||||||||
\(311\) | 27.6045 | 1.56531 | 0.782654 | − | 0.622457i | \(-0.213866\pi\) | ||||
0.782654 | + | 0.622457i | \(0.213866\pi\) | |||||||
\(312\) | −4.07186 | −0.230524 | ||||||||
\(313\) | −18.7243 | −1.05836 | −0.529181 | − | 0.848509i | \(-0.677501\pi\) | ||||
−0.529181 | + | 0.848509i | \(0.677501\pi\) | |||||||
\(314\) | 0.808175 | 0.0456080 | ||||||||
\(315\) | −1.94522 | −0.109601 | ||||||||
\(316\) | 31.9500 | 1.79733 | ||||||||
\(317\) | −1.46196 | −0.0821117 | −0.0410558 | − | 0.999157i | \(-0.513072\pi\) | ||||
−0.0410558 | + | 0.999157i | \(0.513072\pi\) | |||||||
\(318\) | 32.6906 | 1.83320 | ||||||||
\(319\) | 7.68861 | 0.430480 | ||||||||
\(320\) | 9.19348 | 0.513931 | ||||||||
\(321\) | 11.8099 | 0.659166 | ||||||||
\(322\) | 0.217054 | 0.0120959 | ||||||||
\(323\) | 10.7179 | 0.596361 | ||||||||
\(324\) | 2.41191 | 0.133995 | ||||||||
\(325\) | −0.862758 | −0.0478572 | ||||||||
\(326\) | 25.0020 | 1.38473 | ||||||||
\(327\) | −1.41193 | −0.0780799 | ||||||||
\(328\) | 4.61682 | 0.254921 | ||||||||
\(329\) | −0.888047 | −0.0489596 | ||||||||
\(330\) | −1.84518 | −0.101574 | ||||||||
\(331\) | 10.0826 | 0.554190 | 0.277095 | − | 0.960843i | \(-0.410628\pi\) | ||||
0.277095 | + | 0.960843i | \(0.410628\pi\) | |||||||
\(332\) | 20.6655 | 1.13417 | ||||||||
\(333\) | −3.62260 | −0.198517 | ||||||||
\(334\) | 28.5502 | 1.56220 | ||||||||
\(335\) | 14.4564 | 0.789838 | ||||||||
\(336\) | −3.46059 | −0.188791 | ||||||||
\(337\) | −16.4132 | −0.894086 | −0.447043 | − | 0.894512i | \(-0.647523\pi\) | ||||
−0.447043 | + | 0.894512i | \(0.647523\pi\) | |||||||
\(338\) | −29.7512 | −1.61825 | ||||||||
\(339\) | 9.16324 | 0.497679 | ||||||||
\(340\) | −8.76206 | −0.475190 | ||||||||
\(341\) | 5.38069 | 0.291381 | ||||||||
\(342\) | −22.4868 | −1.21595 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 25.9700 | 1.40021 | ||||||||
\(345\) | 0.0918288 | 0.00494390 | ||||||||
\(346\) | 3.95825 | 0.212797 | ||||||||
\(347\) | −31.8614 | −1.71041 | −0.855204 | − | 0.518291i | \(-0.826568\pi\) | ||||
−0.855204 | + | 0.518291i | \(0.826568\pi\) | |||||||
\(348\) | 41.5361 | 2.22657 | ||||||||
\(349\) | 14.7371 | 0.788858 | 0.394429 | − | 0.918926i | \(-0.370942\pi\) | ||||
0.394429 | + | 0.918926i | \(0.370942\pi\) | |||||||
\(350\) | −2.42755 | −0.129758 | ||||||||
\(351\) | 4.38183 | 0.233885 | ||||||||
\(352\) | −0.748287 | −0.0398839 | ||||||||
\(353\) | 32.6134 | 1.73584 | 0.867919 | − | 0.496706i | \(-0.165457\pi\) | ||||
0.867919 | + | 0.496706i | \(0.165457\pi\) | |||||||
\(354\) | 23.8634 | 1.26832 | ||||||||
\(355\) | 9.82493 | 0.521453 | ||||||||
\(356\) | −46.6618 | −2.47307 | ||||||||
\(357\) | −2.31154 | −0.122340 | ||||||||
\(358\) | −43.5027 | −2.29919 | ||||||||
\(359\) | −33.7478 | −1.78114 | −0.890569 | − | 0.454848i | \(-0.849694\pi\) | ||||
−0.890569 | + | 0.454848i | \(0.849694\pi\) | |||||||
\(360\) | 8.93906 | 0.471130 | ||||||||
\(361\) | 3.67674 | 0.193513 | ||||||||
\(362\) | 19.8457 | 1.04307 | ||||||||
\(363\) | −10.7347 | −0.563427 | ||||||||
\(364\) | 3.35873 | 0.176045 | ||||||||
\(365\) | 14.0816 | 0.737067 | ||||||||
\(366\) | 15.8921 | 0.830694 | ||||||||
\(367\) | 27.9198 | 1.45740 | 0.728701 | − | 0.684831i | \(-0.240124\pi\) | ||||
0.728701 | + | 0.684831i | \(0.240124\pi\) | |||||||
\(368\) | −0.301278 | −0.0157052 | ||||||||
\(369\) | −1.95429 | −0.101736 | ||||||||
\(370\) | −4.52085 | −0.235028 | ||||||||
\(371\) | −13.1121 | −0.680748 | ||||||||
\(372\) | 29.0680 | 1.50711 | ||||||||
\(373\) | −0.956503 | −0.0495258 | −0.0247629 | − | 0.999693i | \(-0.507883\pi\) | ||||
−0.0247629 | + | 0.999693i | \(0.507883\pi\) | |||||||
\(374\) | 4.04369 | 0.209094 | ||||||||
\(375\) | −1.02702 | −0.0530353 | ||||||||
\(376\) | 4.08093 | 0.210458 | ||||||||
\(377\) | −8.96289 | −0.461612 | ||||||||
\(378\) | 12.3292 | 0.634146 | ||||||||
\(379\) | 25.1473 | 1.29173 | 0.645864 | − | 0.763452i | \(-0.276497\pi\) | ||||
0.645864 | + | 0.763452i | \(0.276497\pi\) | |||||||
\(380\) | −18.5386 | −0.951009 | ||||||||
\(381\) | 0.806353 | 0.0413107 | ||||||||
\(382\) | −19.4211 | −0.993667 | ||||||||
\(383\) | −27.6762 | −1.41419 | −0.707095 | − | 0.707118i | \(-0.749995\pi\) | ||||
−0.707095 | + | 0.707118i | \(0.749995\pi\) | |||||||
\(384\) | −20.8440 | −1.06369 | ||||||||
\(385\) | 0.740098 | 0.0377189 | ||||||||
\(386\) | −39.5734 | −2.01423 | ||||||||
\(387\) | −10.9930 | −0.558807 | ||||||||
\(388\) | 66.1238 | 3.35693 | ||||||||
\(389\) | 7.36030 | 0.373182 | 0.186591 | − | 0.982438i | \(-0.440256\pi\) | ||||
0.186591 | + | 0.982438i | \(0.440256\pi\) | |||||||
\(390\) | 2.15099 | 0.108920 | ||||||||
\(391\) | −0.201242 | −0.0101772 | ||||||||
\(392\) | 4.59539 | 0.232102 | ||||||||
\(393\) | −4.36189 | −0.220028 | ||||||||
\(394\) | −16.6404 | −0.838333 | ||||||||
\(395\) | −8.20700 | −0.412939 | ||||||||
\(396\) | −5.60459 | −0.281641 | ||||||||
\(397\) | −27.2854 | −1.36941 | −0.684707 | − | 0.728819i | \(-0.740070\pi\) | ||||
−0.684707 | + | 0.728819i | \(0.740070\pi\) | |||||||
\(398\) | 4.62084 | 0.231622 | ||||||||
\(399\) | −4.89070 | −0.244841 | ||||||||
\(400\) | 3.36953 | 0.168477 | ||||||||
\(401\) | 17.8903 | 0.893401 | 0.446700 | − | 0.894684i | \(-0.352599\pi\) | ||||
0.446700 | + | 0.894684i | \(0.352599\pi\) | |||||||
\(402\) | −36.0421 | −1.79762 | ||||||||
\(403\) | −6.27246 | −0.312454 | ||||||||
\(404\) | 31.7772 | 1.58097 | ||||||||
\(405\) | −0.619547 | −0.0307855 | ||||||||
\(406\) | −25.2190 | −1.25160 | ||||||||
\(407\) | 1.37829 | 0.0683192 | ||||||||
\(408\) | 10.6224 | 0.525889 | ||||||||
\(409\) | 9.77211 | 0.483200 | 0.241600 | − | 0.970376i | \(-0.422328\pi\) | ||||
0.241600 | + | 0.970376i | \(0.422328\pi\) | |||||||
\(410\) | −2.43887 | −0.120447 | ||||||||
\(411\) | 22.2067 | 1.09538 | ||||||||
\(412\) | −32.7332 | −1.61265 | ||||||||
\(413\) | −9.57154 | −0.470985 | ||||||||
\(414\) | 0.422217 | 0.0207508 | ||||||||
\(415\) | −5.30835 | −0.260577 | ||||||||
\(416\) | 0.872305 | 0.0427683 | ||||||||
\(417\) | −5.95673 | −0.291702 | ||||||||
\(418\) | 8.55555 | 0.418466 | ||||||||
\(419\) | −5.52138 | −0.269737 | −0.134868 | − | 0.990864i | \(-0.543061\pi\) | ||||
−0.134868 | + | 0.990864i | \(0.543061\pi\) | |||||||
\(420\) | 3.99822 | 0.195093 | ||||||||
\(421\) | 2.37531 | 0.115766 | 0.0578828 | − | 0.998323i | \(-0.481565\pi\) | ||||
0.0578828 | + | 0.998323i | \(0.481565\pi\) | |||||||
\(422\) | −25.0228 | −1.21809 | ||||||||
\(423\) | −1.72745 | −0.0839914 | ||||||||
\(424\) | 60.2554 | 2.92626 | ||||||||
\(425\) | 2.25071 | 0.109176 | ||||||||
\(426\) | −24.4951 | −1.18679 | ||||||||
\(427\) | −6.37429 | −0.308474 | ||||||||
\(428\) | 44.7664 | 2.16387 | ||||||||
\(429\) | −0.655781 | −0.0316614 | ||||||||
\(430\) | −13.7188 | −0.661581 | ||||||||
\(431\) | −15.0116 | −0.723085 | −0.361542 | − | 0.932356i | \(-0.617750\pi\) | ||||
−0.361542 | + | 0.932356i | \(0.617750\pi\) | |||||||
\(432\) | −17.1134 | −0.823369 | ||||||||
\(433\) | −5.97353 | −0.287069 | −0.143535 | − | 0.989645i | \(-0.545847\pi\) | ||||
−0.143535 | + | 0.989645i | \(0.545847\pi\) | |||||||
\(434\) | −17.6489 | −0.847174 | ||||||||
\(435\) | −10.6694 | −0.511558 | ||||||||
\(436\) | −5.35203 | −0.256316 | ||||||||
\(437\) | −0.425783 | −0.0203680 | ||||||||
\(438\) | −35.1078 | −1.67751 | ||||||||
\(439\) | −35.1370 | −1.67700 | −0.838498 | − | 0.544905i | \(-0.816566\pi\) | ||||
−0.838498 | + | 0.544905i | \(0.816566\pi\) | |||||||
\(440\) | −3.40104 | −0.162138 | ||||||||
\(441\) | −1.94522 | −0.0926296 | ||||||||
\(442\) | −4.71388 | −0.224216 | ||||||||
\(443\) | −14.8550 | −0.705783 | −0.352892 | − | 0.935664i | \(-0.614802\pi\) | ||||
−0.352892 | + | 0.935664i | \(0.614802\pi\) | |||||||
\(444\) | 7.44591 | 0.353367 | ||||||||
\(445\) | 11.9860 | 0.568192 | ||||||||
\(446\) | 37.5112 | 1.77621 | ||||||||
\(447\) | −6.54477 | −0.309557 | ||||||||
\(448\) | 9.19348 | 0.434351 | ||||||||
\(449\) | 13.3464 | 0.629855 | 0.314927 | − | 0.949116i | \(-0.398020\pi\) | ||||
0.314927 | + | 0.949116i | \(0.398020\pi\) | |||||||
\(450\) | −4.72213 | −0.222603 | ||||||||
\(451\) | 0.743548 | 0.0350123 | ||||||||
\(452\) | 34.7340 | 1.63375 | ||||||||
\(453\) | −23.2681 | −1.09323 | ||||||||
\(454\) | −16.0711 | −0.754256 | ||||||||
\(455\) | −0.862758 | −0.0404467 | ||||||||
\(456\) | 22.4747 | 1.05247 | ||||||||
\(457\) | 15.9288 | 0.745118 | 0.372559 | − | 0.928009i | \(-0.378480\pi\) | ||||
0.372559 | + | 0.928009i | \(0.378480\pi\) | |||||||
\(458\) | 2.42755 | 0.113432 | ||||||||
\(459\) | −11.4311 | −0.533557 | ||||||||
\(460\) | 0.348084 | 0.0162295 | ||||||||
\(461\) | 28.4199 | 1.32365 | 0.661824 | − | 0.749659i | \(-0.269783\pi\) | ||||
0.661824 | + | 0.749659i | \(0.269783\pi\) | |||||||
\(462\) | −1.84518 | −0.0858455 | ||||||||
\(463\) | 9.35157 | 0.434605 | 0.217302 | − | 0.976104i | \(-0.430274\pi\) | ||||
0.217302 | + | 0.976104i | \(0.430274\pi\) | |||||||
\(464\) | 35.0049 | 1.62506 | ||||||||
\(465\) | −7.46672 | −0.346261 | ||||||||
\(466\) | −13.0587 | −0.604934 | ||||||||
\(467\) | −3.27005 | −0.151320 | −0.0756598 | − | 0.997134i | \(-0.524106\pi\) | ||||
−0.0756598 | + | 0.997134i | \(0.524106\pi\) | |||||||
\(468\) | 6.53347 | 0.302010 | ||||||||
\(469\) | 14.4564 | 0.667535 | ||||||||
\(470\) | −2.15578 | −0.0994388 | ||||||||
\(471\) | 0.341915 | 0.0157546 | ||||||||
\(472\) | 43.9850 | 2.02457 | ||||||||
\(473\) | 4.18252 | 0.192312 | ||||||||
\(474\) | 20.4613 | 0.939820 | ||||||||
\(475\) | 4.76201 | 0.218496 | ||||||||
\(476\) | −8.76206 | −0.401609 | ||||||||
\(477\) | −25.5060 | −1.16784 | ||||||||
\(478\) | −48.5487 | −2.22057 | ||||||||
\(479\) | 18.5245 | 0.846408 | 0.423204 | − | 0.906034i | \(-0.360905\pi\) | ||||
0.423204 | + | 0.906034i | \(0.360905\pi\) | |||||||
\(480\) | 1.03839 | 0.0473958 | ||||||||
\(481\) | −1.60672 | −0.0732601 | ||||||||
\(482\) | −17.6192 | −0.802533 | ||||||||
\(483\) | 0.0918288 | 0.00417836 | ||||||||
\(484\) | −40.6908 | −1.84958 | ||||||||
\(485\) | −16.9852 | −0.771260 | ||||||||
\(486\) | 38.5323 | 1.74786 | ||||||||
\(487\) | −9.59755 | −0.434907 | −0.217453 | − | 0.976071i | \(-0.569775\pi\) | ||||
−0.217453 | + | 0.976071i | \(0.569775\pi\) | |||||||
\(488\) | 29.2924 | 1.32600 | ||||||||
\(489\) | 10.5776 | 0.478335 | ||||||||
\(490\) | −2.42755 | −0.109666 | ||||||||
\(491\) | −20.5181 | −0.925968 | −0.462984 | − | 0.886367i | \(-0.653221\pi\) | ||||
−0.462984 | + | 0.886367i | \(0.653221\pi\) | |||||||
\(492\) | 4.01686 | 0.181094 | ||||||||
\(493\) | 23.3819 | 1.05307 | ||||||||
\(494\) | −9.97352 | −0.448730 | ||||||||
\(495\) | 1.43965 | 0.0647076 | ||||||||
\(496\) | 24.4973 | 1.09996 | ||||||||
\(497\) | 9.82493 | 0.440709 | ||||||||
\(498\) | 13.2346 | 0.593055 | ||||||||
\(499\) | 10.6166 | 0.475264 | 0.237632 | − | 0.971355i | \(-0.423629\pi\) | ||||
0.237632 | + | 0.971355i | \(0.423629\pi\) | |||||||
\(500\) | −3.89301 | −0.174101 | ||||||||
\(501\) | 12.0787 | 0.539637 | ||||||||
\(502\) | 29.8695 | 1.33314 | ||||||||
\(503\) | −19.1511 | −0.853906 | −0.426953 | − | 0.904274i | \(-0.640413\pi\) | ||||
−0.426953 | + | 0.904274i | \(0.640413\pi\) | |||||||
\(504\) | 8.93906 | 0.398177 | ||||||||
\(505\) | −8.16261 | −0.363231 | ||||||||
\(506\) | −0.160641 | −0.00714136 | ||||||||
\(507\) | −12.5868 | −0.559002 | ||||||||
\(508\) | 3.05654 | 0.135612 | ||||||||
\(509\) | −7.65209 | −0.339173 | −0.169586 | − | 0.985515i | \(-0.554243\pi\) | ||||
−0.169586 | + | 0.985515i | \(0.554243\pi\) | |||||||
\(510\) | −5.61138 | −0.248476 | ||||||||
\(511\) | 14.0816 | 0.622935 | ||||||||
\(512\) | −34.3755 | −1.51920 | ||||||||
\(513\) | −24.1856 | −1.06782 | ||||||||
\(514\) | −14.8004 | −0.652818 | ||||||||
\(515\) | 8.40818 | 0.370509 | ||||||||
\(516\) | 22.5952 | 0.994696 | ||||||||
\(517\) | 0.657242 | 0.0289055 | ||||||||
\(518\) | −4.52085 | −0.198635 | ||||||||
\(519\) | 1.67462 | 0.0735076 | ||||||||
\(520\) | 3.96471 | 0.173864 | ||||||||
\(521\) | −26.2816 | −1.15142 | −0.575708 | − | 0.817655i | \(-0.695274\pi\) | ||||
−0.575708 | + | 0.817655i | \(0.695274\pi\) | |||||||
\(522\) | −49.0565 | −2.14715 | ||||||||
\(523\) | 12.2118 | 0.533986 | 0.266993 | − | 0.963698i | \(-0.413970\pi\) | ||||
0.266993 | + | 0.963698i | \(0.413970\pi\) | |||||||
\(524\) | −16.5341 | −0.722295 | ||||||||
\(525\) | −1.02702 | −0.0448230 | ||||||||
\(526\) | −23.9172 | −1.04284 | ||||||||
\(527\) | 16.3632 | 0.712794 | ||||||||
\(528\) | 2.56118 | 0.111461 | ||||||||
\(529\) | −22.9920 | −0.999652 | ||||||||
\(530\) | −31.8304 | −1.38262 | ||||||||
\(531\) | −18.6188 | −0.807986 | ||||||||
\(532\) | −18.5386 | −0.803749 | ||||||||
\(533\) | −0.866781 | −0.0375445 | ||||||||
\(534\) | −29.8830 | −1.29317 | ||||||||
\(535\) | −11.4992 | −0.497153 | ||||||||
\(536\) | −66.4329 | −2.86947 | ||||||||
\(537\) | −18.4047 | −0.794221 | ||||||||
\(538\) | −4.99633 | −0.215407 | ||||||||
\(539\) | 0.740098 | 0.0318783 | ||||||||
\(540\) | 19.7721 | 0.850855 | ||||||||
\(541\) | 23.8332 | 1.02467 | 0.512334 | − | 0.858786i | \(-0.328781\pi\) | ||||
0.512334 | + | 0.858786i | \(0.328781\pi\) | |||||||
\(542\) | −8.30737 | −0.356832 | ||||||||
\(543\) | 8.39611 | 0.360312 | ||||||||
\(544\) | −2.27562 | −0.0975664 | ||||||||
\(545\) | 1.37478 | 0.0588890 | ||||||||
\(546\) | 2.15099 | 0.0920539 | ||||||||
\(547\) | 31.5100 | 1.34727 | 0.673636 | − | 0.739063i | \(-0.264732\pi\) | ||||
0.673636 | + | 0.739063i | \(0.264732\pi\) | |||||||
\(548\) | 84.1764 | 3.59584 | ||||||||
\(549\) | −12.3994 | −0.529194 | ||||||||
\(550\) | 1.79663 | 0.0766084 | ||||||||
\(551\) | 49.4708 | 2.10753 | ||||||||
\(552\) | −0.421990 | −0.0179611 | ||||||||
\(553\) | −8.20700 | −0.348997 | ||||||||
\(554\) | 78.5804 | 3.33856 | ||||||||
\(555\) | −1.91263 | −0.0811868 | ||||||||
\(556\) | −22.5794 | −0.957582 | ||||||||
\(557\) | 15.8148 | 0.670096 | 0.335048 | − | 0.942201i | \(-0.391248\pi\) | ||||
0.335048 | + | 0.942201i | \(0.391248\pi\) | |||||||
\(558\) | −34.3310 | −1.45335 | ||||||||
\(559\) | −4.87571 | −0.206220 | ||||||||
\(560\) | 3.36953 | 0.142389 | ||||||||
\(561\) | 1.71076 | 0.0722285 | ||||||||
\(562\) | 4.68785 | 0.197745 | ||||||||
\(563\) | 31.3699 | 1.32208 | 0.661041 | − | 0.750350i | \(-0.270115\pi\) | ||||
0.661041 | + | 0.750350i | \(0.270115\pi\) | |||||||
\(564\) | 3.55061 | 0.149508 | ||||||||
\(565\) | −8.92213 | −0.375357 | ||||||||
\(566\) | 47.4112 | 1.99284 | ||||||||
\(567\) | −0.619547 | −0.0260185 | ||||||||
\(568\) | −45.1494 | −1.89443 | ||||||||
\(569\) | −43.9884 | −1.84409 | −0.922044 | − | 0.387085i | \(-0.873482\pi\) | ||||
−0.922044 | + | 0.387085i | \(0.873482\pi\) | |||||||
\(570\) | −11.8724 | −0.497282 | ||||||||
\(571\) | −31.3586 | −1.31231 | −0.656157 | − | 0.754624i | \(-0.727819\pi\) | ||||
−0.656157 | + | 0.754624i | \(0.727819\pi\) | |||||||
\(572\) | −2.48579 | −0.103936 | ||||||||
\(573\) | −8.21646 | −0.343248 | ||||||||
\(574\) | −2.43887 | −0.101797 | ||||||||
\(575\) | −0.0894125 | −0.00372876 | ||||||||
\(576\) | 17.8834 | 0.745140 | ||||||||
\(577\) | −8.86781 | −0.369172 | −0.184586 | − | 0.982816i | \(-0.559094\pi\) | ||||
−0.184586 | + | 0.982816i | \(0.559094\pi\) | |||||||
\(578\) | −28.9711 | −1.20504 | ||||||||
\(579\) | −16.7423 | −0.695786 | ||||||||
\(580\) | −40.4432 | −1.67931 | ||||||||
\(581\) | −5.30835 | −0.220228 | ||||||||
\(582\) | 42.3469 | 1.75533 | ||||||||
\(583\) | 9.70426 | 0.401909 | ||||||||
\(584\) | −64.7107 | −2.67775 | ||||||||
\(585\) | −1.67826 | −0.0693873 | ||||||||
\(586\) | −61.3208 | −2.53314 | ||||||||
\(587\) | 36.7954 | 1.51871 | 0.759354 | − | 0.650678i | \(-0.225515\pi\) | ||||
0.759354 | + | 0.650678i | \(0.225515\pi\) | |||||||
\(588\) | 3.99822 | 0.164884 | ||||||||
\(589\) | 34.6210 | 1.42653 | ||||||||
\(590\) | −23.2354 | −0.956588 | ||||||||
\(591\) | −7.04006 | −0.289589 | ||||||||
\(592\) | 6.27510 | 0.257905 | ||||||||
\(593\) | −10.1339 | −0.416151 | −0.208075 | − | 0.978113i | \(-0.566720\pi\) | ||||
−0.208075 | + | 0.978113i | \(0.566720\pi\) | |||||||
\(594\) | −9.12482 | −0.374396 | ||||||||
\(595\) | 2.25071 | 0.0922703 | ||||||||
\(596\) | −24.8084 | −1.01619 | ||||||||
\(597\) | 1.95494 | 0.0800103 | ||||||||
\(598\) | 0.187265 | 0.00765783 | ||||||||
\(599\) | −40.0591 | −1.63677 | −0.818385 | − | 0.574670i | \(-0.805130\pi\) | ||||
−0.818385 | + | 0.574670i | \(0.805130\pi\) | |||||||
\(600\) | 4.71958 | 0.192676 | ||||||||
\(601\) | −20.7435 | −0.846145 | −0.423073 | − | 0.906096i | \(-0.639048\pi\) | ||||
−0.423073 | + | 0.906096i | \(0.639048\pi\) | |||||||
\(602\) | −13.7188 | −0.559138 | ||||||||
\(603\) | 28.1209 | 1.14517 | ||||||||
\(604\) | −88.1995 | −3.58878 | ||||||||
\(605\) | 10.4523 | 0.424945 | ||||||||
\(606\) | 20.3507 | 0.826689 | ||||||||
\(607\) | −26.5072 | −1.07589 | −0.537947 | − | 0.842978i | \(-0.680800\pi\) | ||||
−0.537947 | + | 0.842978i | \(0.680800\pi\) | |||||||
\(608\) | −4.81471 | −0.195262 | ||||||||
\(609\) | −10.6694 | −0.432346 | ||||||||
\(610\) | −15.4739 | −0.626522 | ||||||||
\(611\) | −0.766170 | −0.0309959 | ||||||||
\(612\) | −17.0442 | −0.688969 | ||||||||
\(613\) | 9.87842 | 0.398986 | 0.199493 | − | 0.979899i | \(-0.436071\pi\) | ||||
0.199493 | + | 0.979899i | \(0.436071\pi\) | |||||||
\(614\) | 27.0036 | 1.08977 | ||||||||
\(615\) | −1.03181 | −0.0416067 | ||||||||
\(616\) | −3.40104 | −0.137032 | ||||||||
\(617\) | 12.0395 | 0.484692 | 0.242346 | − | 0.970190i | \(-0.422083\pi\) | ||||
0.242346 | + | 0.970190i | \(0.422083\pi\) | |||||||
\(618\) | −20.9629 | −0.843252 | ||||||||
\(619\) | −13.2428 | −0.532275 | −0.266137 | − | 0.963935i | \(-0.585747\pi\) | ||||
−0.266137 | + | 0.963935i | \(0.585747\pi\) | |||||||
\(620\) | −28.3032 | −1.13668 | ||||||||
\(621\) | 0.454114 | 0.0182230 | ||||||||
\(622\) | 67.0114 | 2.68691 | ||||||||
\(623\) | 11.9860 | 0.480210 | ||||||||
\(624\) | −2.98566 | −0.119522 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −45.4543 | −1.81672 | ||||||||
\(627\) | 3.61960 | 0.144553 | ||||||||
\(628\) | 1.29605 | 0.0517182 | ||||||||
\(629\) | 4.19152 | 0.167127 | ||||||||
\(630\) | −4.72213 | −0.188134 | ||||||||
\(631\) | −1.71942 | −0.0684492 | −0.0342246 | − | 0.999414i | \(-0.510896\pi\) | ||||
−0.0342246 | + | 0.999414i | \(0.510896\pi\) | |||||||
\(632\) | 37.7144 | 1.50020 | ||||||||
\(633\) | −10.5864 | −0.420771 | ||||||||
\(634\) | −3.54898 | −0.140948 | ||||||||
\(635\) | −0.785135 | −0.0311571 | ||||||||
\(636\) | 52.4252 | 2.07879 | ||||||||
\(637\) | −0.862758 | −0.0341837 | ||||||||
\(638\) | 18.6645 | 0.738935 | ||||||||
\(639\) | 19.1117 | 0.756046 | ||||||||
\(640\) | 20.2955 | 0.802252 | ||||||||
\(641\) | −12.9327 | −0.510811 | −0.255405 | − | 0.966834i | \(-0.582209\pi\) | ||||
−0.255405 | + | 0.966834i | \(0.582209\pi\) | |||||||
\(642\) | 28.6692 | 1.13148 | ||||||||
\(643\) | 22.2330 | 0.876782 | 0.438391 | − | 0.898784i | \(-0.355549\pi\) | ||||
0.438391 | + | 0.898784i | \(0.355549\pi\) | |||||||
\(644\) | 0.348084 | 0.0137164 | ||||||||
\(645\) | −5.80402 | −0.228533 | ||||||||
\(646\) | 26.0183 | 1.02368 | ||||||||
\(647\) | 4.19045 | 0.164744 | 0.0823718 | − | 0.996602i | \(-0.473751\pi\) | ||||
0.0823718 | + | 0.996602i | \(0.473751\pi\) | |||||||
\(648\) | 2.84706 | 0.111843 | ||||||||
\(649\) | 7.08388 | 0.278067 | ||||||||
\(650\) | −2.09439 | −0.0821488 | ||||||||
\(651\) | −7.46672 | −0.292644 | ||||||||
\(652\) | 40.0952 | 1.57025 | ||||||||
\(653\) | −22.2995 | −0.872646 | −0.436323 | − | 0.899790i | \(-0.643720\pi\) | ||||
−0.436323 | + | 0.899790i | \(0.643720\pi\) | |||||||
\(654\) | −3.42753 | −0.134027 | ||||||||
\(655\) | 4.24712 | 0.165949 | ||||||||
\(656\) | 3.38524 | 0.132172 | ||||||||
\(657\) | 27.3919 | 1.06866 | ||||||||
\(658\) | −2.15578 | −0.0840411 | ||||||||
\(659\) | 23.4989 | 0.915389 | 0.457694 | − | 0.889110i | \(-0.348675\pi\) | ||||
0.457694 | + | 0.889110i | \(0.348675\pi\) | |||||||
\(660\) | −2.95907 | −0.115182 | ||||||||
\(661\) | 28.0632 | 1.09153 | 0.545767 | − | 0.837937i | \(-0.316239\pi\) | ||||
0.545767 | + | 0.837937i | \(0.316239\pi\) | |||||||
\(662\) | 24.4760 | 0.951288 | ||||||||
\(663\) | −1.99430 | −0.0774522 | ||||||||
\(664\) | 24.3940 | 0.946670 | ||||||||
\(665\) | 4.76201 | 0.184663 | ||||||||
\(666\) | −8.79405 | −0.340762 | ||||||||
\(667\) | −0.928875 | −0.0359662 | ||||||||
\(668\) | 45.7853 | 1.77149 | ||||||||
\(669\) | 15.8699 | 0.613565 | ||||||||
\(670\) | 35.0937 | 1.35579 | ||||||||
\(671\) | 4.71760 | 0.182121 | ||||||||
\(672\) | 1.03839 | 0.0400567 | ||||||||
\(673\) | −32.3781 | −1.24809 | −0.624043 | − | 0.781390i | \(-0.714511\pi\) | ||||
−0.624043 | + | 0.781390i | \(0.714511\pi\) | |||||||
\(674\) | −39.8440 | −1.53473 | ||||||||
\(675\) | −5.07886 | −0.195486 | ||||||||
\(676\) | −47.7114 | −1.83505 | ||||||||
\(677\) | 41.4384 | 1.59261 | 0.796303 | − | 0.604898i | \(-0.206786\pi\) | ||||
0.796303 | + | 0.604898i | \(0.206786\pi\) | |||||||
\(678\) | 22.2443 | 0.854286 | ||||||||
\(679\) | −16.9852 | −0.651834 | ||||||||
\(680\) | −10.3429 | −0.396633 | ||||||||
\(681\) | −6.79921 | −0.260546 | ||||||||
\(682\) | 13.0619 | 0.500166 | ||||||||
\(683\) | −9.20148 | −0.352085 | −0.176042 | − | 0.984383i | \(-0.556330\pi\) | ||||
−0.176042 | + | 0.984383i | \(0.556330\pi\) | |||||||
\(684\) | −36.0616 | −1.37885 | ||||||||
\(685\) | −21.6224 | −0.826150 | ||||||||
\(686\) | −2.42755 | −0.0926844 | ||||||||
\(687\) | 1.02702 | 0.0391834 | ||||||||
\(688\) | 19.0422 | 0.725979 | ||||||||
\(689\) | −11.3126 | −0.430976 | ||||||||
\(690\) | 0.222919 | 0.00848639 | ||||||||
\(691\) | 45.6389 | 1.73619 | 0.868093 | − | 0.496402i | \(-0.165346\pi\) | ||||
0.868093 | + | 0.496402i | \(0.165346\pi\) | |||||||
\(692\) | 6.34777 | 0.241306 | ||||||||
\(693\) | 1.43965 | 0.0546879 | ||||||||
\(694\) | −77.3452 | −2.93598 | ||||||||
\(695\) | 5.79999 | 0.220006 | ||||||||
\(696\) | 49.0301 | 1.85848 | ||||||||
\(697\) | 2.26121 | 0.0856494 | ||||||||
\(698\) | 35.7751 | 1.35411 | ||||||||
\(699\) | −5.52476 | −0.208966 | ||||||||
\(700\) | −3.89301 | −0.147142 | ||||||||
\(701\) | −38.9258 | −1.47021 | −0.735104 | − | 0.677954i | \(-0.762867\pi\) | ||||
−0.735104 | + | 0.677954i | \(0.762867\pi\) | |||||||
\(702\) | 10.6371 | 0.401473 | ||||||||
\(703\) | 8.86832 | 0.334475 | ||||||||
\(704\) | −6.80408 | −0.256438 | ||||||||
\(705\) | −0.912046 | −0.0343496 | ||||||||
\(706\) | 79.1709 | 2.97963 | ||||||||
\(707\) | −8.16261 | −0.306987 | ||||||||
\(708\) | 38.2691 | 1.43824 | ||||||||
\(709\) | −41.2626 | −1.54965 | −0.774825 | − | 0.632176i | \(-0.782162\pi\) | ||||
−0.774825 | + | 0.632176i | \(0.782162\pi\) | |||||||
\(710\) | 23.8506 | 0.895095 | ||||||||
\(711\) | −15.9644 | −0.598713 | ||||||||
\(712\) | −55.0805 | −2.06423 | ||||||||
\(713\) | −0.650051 | −0.0243446 | ||||||||
\(714\) | −5.61138 | −0.210001 | ||||||||
\(715\) | 0.638525 | 0.0238795 | ||||||||
\(716\) | −69.7644 | −2.60722 | ||||||||
\(717\) | −20.5395 | −0.767061 | ||||||||
\(718\) | −81.9245 | −3.05739 | ||||||||
\(719\) | 12.8627 | 0.479699 | 0.239849 | − | 0.970810i | \(-0.422902\pi\) | ||||
0.239849 | + | 0.970810i | \(0.422902\pi\) | |||||||
\(720\) | 6.55449 | 0.244271 | ||||||||
\(721\) | 8.40818 | 0.313137 | ||||||||
\(722\) | 8.92549 | 0.332172 | ||||||||
\(723\) | −7.45416 | −0.277223 | ||||||||
\(724\) | 31.8261 | 1.18281 | ||||||||
\(725\) | 10.3886 | 0.385825 | ||||||||
\(726\) | −26.0591 | −0.967144 | ||||||||
\(727\) | 7.79574 | 0.289128 | 0.144564 | − | 0.989495i | \(-0.453822\pi\) | ||||
0.144564 | + | 0.989495i | \(0.453822\pi\) | |||||||
\(728\) | 3.96471 | 0.146942 | ||||||||
\(729\) | 14.4432 | 0.534933 | ||||||||
\(730\) | 34.1840 | 1.26520 | ||||||||
\(731\) | 12.7195 | 0.470446 | ||||||||
\(732\) | 25.4858 | 0.941984 | ||||||||
\(733\) | −9.51550 | −0.351463 | −0.175732 | − | 0.984438i | \(-0.556229\pi\) | ||||
−0.175732 | + | 0.984438i | \(0.556229\pi\) | |||||||
\(734\) | 67.7769 | 2.50169 | ||||||||
\(735\) | −1.02702 | −0.0378824 | ||||||||
\(736\) | 0.0904019 | 0.00333226 | ||||||||
\(737\) | −10.6992 | −0.394109 | ||||||||
\(738\) | −4.74414 | −0.174634 | ||||||||
\(739\) | 18.8977 | 0.695165 | 0.347582 | − | 0.937649i | \(-0.387003\pi\) | ||||
0.347582 | + | 0.937649i | \(0.387003\pi\) | |||||||
\(740\) | −7.24999 | −0.266515 | ||||||||
\(741\) | −4.21949 | −0.155007 | ||||||||
\(742\) | −31.8304 | −1.16853 | ||||||||
\(743\) | 45.6012 | 1.67294 | 0.836472 | − | 0.548010i | \(-0.184614\pi\) | ||||
0.836472 | + | 0.548010i | \(0.184614\pi\) | |||||||
\(744\) | 34.3125 | 1.25796 | ||||||||
\(745\) | 6.37255 | 0.233472 | ||||||||
\(746\) | −2.32196 | −0.0850130 | ||||||||
\(747\) | −10.3259 | −0.377806 | ||||||||
\(748\) | 6.48478 | 0.237107 | ||||||||
\(749\) | −11.4992 | −0.420171 | ||||||||
\(750\) | −2.49316 | −0.0910372 | ||||||||
\(751\) | 13.4090 | 0.489302 | 0.244651 | − | 0.969611i | \(-0.421327\pi\) | ||||
0.244651 | + | 0.969611i | \(0.421327\pi\) | |||||||
\(752\) | 2.99230 | 0.109118 | ||||||||
\(753\) | 12.6369 | 0.460513 | ||||||||
\(754\) | −21.7579 | −0.792376 | ||||||||
\(755\) | 22.6558 | 0.824530 | ||||||||
\(756\) | 19.7721 | 0.719104 | ||||||||
\(757\) | −36.5920 | −1.32996 | −0.664979 | − | 0.746862i | \(-0.731560\pi\) | ||||
−0.664979 | + | 0.746862i | \(0.731560\pi\) | |||||||
\(758\) | 61.0463 | 2.21730 | ||||||||
\(759\) | −0.0679623 | −0.00246687 | ||||||||
\(760\) | −21.8833 | −0.793791 | ||||||||
\(761\) | 51.2608 | 1.85820 | 0.929101 | − | 0.369827i | \(-0.120583\pi\) | ||||
0.929101 | + | 0.369827i | \(0.120583\pi\) | |||||||
\(762\) | 1.95746 | 0.0709115 | ||||||||
\(763\) | 1.37478 | 0.0497703 | ||||||||
\(764\) | −31.1451 | −1.12679 | ||||||||
\(765\) | 4.37814 | 0.158292 | ||||||||
\(766\) | −67.1856 | −2.42751 | ||||||||
\(767\) | −8.25793 | −0.298177 | ||||||||
\(768\) | −31.7161 | −1.14446 | ||||||||
\(769\) | −29.3683 | −1.05905 | −0.529524 | − | 0.848295i | \(-0.677629\pi\) | ||||
−0.529524 | + | 0.848295i | \(0.677629\pi\) | |||||||
\(770\) | 1.79663 | 0.0647459 | ||||||||
\(771\) | −6.26160 | −0.225506 | ||||||||
\(772\) | −63.4629 | −2.28408 | ||||||||
\(773\) | −13.6105 | −0.489537 | −0.244769 | − | 0.969582i | \(-0.578712\pi\) | ||||
−0.244769 | + | 0.969582i | \(0.578712\pi\) | |||||||
\(774\) | −26.6862 | −0.959214 | ||||||||
\(775\) | 7.27024 | 0.261155 | ||||||||
\(776\) | 78.0539 | 2.80197 | ||||||||
\(777\) | −1.91263 | −0.0686154 | ||||||||
\(778\) | 17.8675 | 0.640581 | ||||||||
\(779\) | 4.78421 | 0.171412 | ||||||||
\(780\) | 3.44950 | 0.123512 | ||||||||
\(781\) | −7.27141 | −0.260192 | ||||||||
\(782\) | −0.488526 | −0.0174696 | ||||||||
\(783\) | −52.7625 | −1.88558 | ||||||||
\(784\) | 3.36953 | 0.120340 | ||||||||
\(785\) | −0.332918 | −0.0118823 | ||||||||
\(786\) | −10.5887 | −0.377687 | ||||||||
\(787\) | 6.09675 | 0.217326 | 0.108663 | − | 0.994079i | \(-0.465343\pi\) | ||||
0.108663 | + | 0.994079i | \(0.465343\pi\) | |||||||
\(788\) | −26.6859 | −0.950646 | ||||||||
\(789\) | −10.1186 | −0.360233 | ||||||||
\(790\) | −19.9229 | −0.708826 | ||||||||
\(791\) | −8.92213 | −0.317234 | ||||||||
\(792\) | −6.61577 | −0.235081 | ||||||||
\(793\) | −5.49948 | −0.195292 | ||||||||
\(794\) | −66.2367 | −2.35065 | ||||||||
\(795\) | −13.4665 | −0.477607 | ||||||||
\(796\) | 7.41035 | 0.262653 | ||||||||
\(797\) | 1.10018 | 0.0389702 | 0.0194851 | − | 0.999810i | \(-0.493797\pi\) | ||||
0.0194851 | + | 0.999810i | \(0.493797\pi\) | |||||||
\(798\) | −11.8724 | −0.420280 | ||||||||
\(799\) | 1.99874 | 0.0707104 | ||||||||
\(800\) | −1.01107 | −0.0357466 | ||||||||
\(801\) | 23.3155 | 0.823812 | ||||||||
\(802\) | 43.4297 | 1.53356 | ||||||||
\(803\) | −10.4218 | −0.367777 | ||||||||
\(804\) | −57.7999 | −2.03845 | ||||||||
\(805\) | −0.0894125 | −0.00315138 | ||||||||
\(806\) | −15.2267 | −0.536339 | ||||||||
\(807\) | −2.11380 | −0.0744092 | ||||||||
\(808\) | 37.5104 | 1.31961 | ||||||||
\(809\) | −6.31862 | −0.222151 | −0.111076 | − | 0.993812i | \(-0.535430\pi\) | ||||
−0.111076 | + | 0.993812i | \(0.535430\pi\) | |||||||
\(810\) | −1.50398 | −0.0528446 | ||||||||
\(811\) | −19.3061 | −0.677929 | −0.338964 | − | 0.940799i | \(-0.610077\pi\) | ||||
−0.338964 | + | 0.940799i | \(0.610077\pi\) | |||||||
\(812\) | −40.4432 | −1.41928 | ||||||||
\(813\) | −3.51460 | −0.123262 | ||||||||
\(814\) | 3.34587 | 0.117273 | ||||||||
\(815\) | −10.2993 | −0.360767 | ||||||||
\(816\) | 7.78881 | 0.272663 | ||||||||
\(817\) | 26.9116 | 0.941516 | ||||||||
\(818\) | 23.7223 | 0.829431 | ||||||||
\(819\) | −1.67826 | −0.0586430 | ||||||||
\(820\) | −3.91117 | −0.136584 | ||||||||
\(821\) | −42.5637 | −1.48548 | −0.742741 | − | 0.669579i | \(-0.766475\pi\) | ||||
−0.742741 | + | 0.669579i | \(0.766475\pi\) | |||||||
\(822\) | 53.9081 | 1.88026 | ||||||||
\(823\) | −47.9332 | −1.67084 | −0.835422 | − | 0.549608i | \(-0.814777\pi\) | ||||
−0.835422 | + | 0.549608i | \(0.814777\pi\) | |||||||
\(824\) | −38.6389 | −1.34605 | ||||||||
\(825\) | 0.760098 | 0.0264632 | ||||||||
\(826\) | −23.2354 | −0.808464 | ||||||||
\(827\) | 2.82311 | 0.0981690 | 0.0490845 | − | 0.998795i | \(-0.484370\pi\) | ||||
0.0490845 | + | 0.998795i | \(0.484370\pi\) | |||||||
\(828\) | 0.677101 | 0.0235309 | ||||||||
\(829\) | 54.3745 | 1.88851 | 0.944253 | − | 0.329221i | \(-0.106786\pi\) | ||||
0.944253 | + | 0.329221i | \(0.106786\pi\) | |||||||
\(830\) | −12.8863 | −0.447290 | ||||||||
\(831\) | 33.2450 | 1.15326 | ||||||||
\(832\) | 7.93175 | 0.274984 | ||||||||
\(833\) | 2.25071 | 0.0779826 | ||||||||
\(834\) | −14.4603 | −0.500719 | ||||||||
\(835\) | −11.7609 | −0.407002 | ||||||||
\(836\) | 13.7204 | 0.474528 | ||||||||
\(837\) | −36.9246 | −1.27630 | ||||||||
\(838\) | −13.4034 | −0.463014 | ||||||||
\(839\) | −10.8966 | −0.376193 | −0.188097 | − | 0.982151i | \(-0.560232\pi\) | ||||
−0.188097 | + | 0.982151i | \(0.560232\pi\) | |||||||
\(840\) | 4.71958 | 0.162841 | ||||||||
\(841\) | 78.9240 | 2.72152 | ||||||||
\(842\) | 5.76619 | 0.198716 | ||||||||
\(843\) | 1.98329 | 0.0683081 | ||||||||
\(844\) | −40.1285 | −1.38128 | ||||||||
\(845\) | 12.2556 | 0.421607 | ||||||||
\(846\) | −4.19347 | −0.144175 | ||||||||
\(847\) | 10.4523 | 0.359144 | ||||||||
\(848\) | 44.1818 | 1.51721 | ||||||||
\(849\) | 20.0583 | 0.688397 | ||||||||
\(850\) | 5.46373 | 0.187404 | ||||||||
\(851\) | −0.166513 | −0.00570801 | ||||||||
\(852\) | −39.2823 | −1.34579 | ||||||||
\(853\) | 8.16287 | 0.279491 | 0.139746 | − | 0.990187i | \(-0.455372\pi\) | ||||
0.139746 | + | 0.990187i | \(0.455372\pi\) | |||||||
\(854\) | −15.4739 | −0.529507 | ||||||||
\(855\) | 9.26316 | 0.316793 | ||||||||
\(856\) | 52.8432 | 1.80614 | ||||||||
\(857\) | 1.47516 | 0.0503906 | 0.0251953 | − | 0.999683i | \(-0.491979\pi\) | ||||
0.0251953 | + | 0.999683i | \(0.491979\pi\) | |||||||
\(858\) | −1.59194 | −0.0543481 | ||||||||
\(859\) | 11.2257 | 0.383016 | 0.191508 | − | 0.981491i | \(-0.438662\pi\) | ||||
0.191508 | + | 0.981491i | \(0.438662\pi\) | |||||||
\(860\) | −22.0006 | −0.750214 | ||||||||
\(861\) | −1.03181 | −0.0351641 | ||||||||
\(862\) | −36.4415 | −1.24120 | ||||||||
\(863\) | 5.66106 | 0.192705 | 0.0963524 | − | 0.995347i | \(-0.469282\pi\) | ||||
0.0963524 | + | 0.995347i | \(0.469282\pi\) | |||||||
\(864\) | 5.13506 | 0.174698 | ||||||||
\(865\) | −1.63055 | −0.0554405 | ||||||||
\(866\) | −14.5011 | −0.492766 | ||||||||
\(867\) | −12.2568 | −0.416263 | ||||||||
\(868\) | −28.3032 | −0.960672 | ||||||||
\(869\) | 6.07398 | 0.206046 | ||||||||
\(870\) | −25.9005 | −0.878110 | ||||||||
\(871\) | 12.4724 | 0.422611 | ||||||||
\(872\) | −6.31764 | −0.213942 | ||||||||
\(873\) | −33.0400 | −1.11824 | ||||||||
\(874\) | −1.03361 | −0.0349624 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −56.3015 | −1.90225 | ||||||||
\(877\) | 2.87821 | 0.0971901 | 0.0485951 | − | 0.998819i | \(-0.484526\pi\) | ||||
0.0485951 | + | 0.998819i | \(0.484526\pi\) | |||||||
\(878\) | −85.2968 | −2.87863 | ||||||||
\(879\) | −25.9430 | −0.875034 | ||||||||
\(880\) | −2.49378 | −0.0840654 | ||||||||
\(881\) | −26.6780 | −0.898805 | −0.449403 | − | 0.893329i | \(-0.648363\pi\) | ||||
−0.449403 | + | 0.893329i | \(0.648363\pi\) | |||||||
\(882\) | −4.72213 | −0.159002 | ||||||||
\(883\) | −26.6351 | −0.896341 | −0.448171 | − | 0.893948i | \(-0.647924\pi\) | ||||
−0.448171 | + | 0.893948i | \(0.647924\pi\) | |||||||
\(884\) | −7.55954 | −0.254255 | ||||||||
\(885\) | −9.83021 | −0.330439 | ||||||||
\(886\) | −36.0613 | −1.21150 | ||||||||
\(887\) | −2.75874 | −0.0926293 | −0.0463146 | − | 0.998927i | \(-0.514748\pi\) | ||||
−0.0463146 | + | 0.998927i | \(0.514748\pi\) | |||||||
\(888\) | 8.78931 | 0.294950 | ||||||||
\(889\) | −0.785135 | −0.0263326 | ||||||||
\(890\) | 29.0967 | 0.975324 | ||||||||
\(891\) | 0.458525 | 0.0153612 | ||||||||
\(892\) | 60.1560 | 2.01417 | ||||||||
\(893\) | 4.22889 | 0.141514 | ||||||||
\(894\) | −15.8878 | −0.531366 | ||||||||
\(895\) | 17.9204 | 0.599013 | ||||||||
\(896\) | 20.2955 | 0.678026 | ||||||||
\(897\) | 0.0792261 | 0.00264528 | ||||||||
\(898\) | 32.3990 | 1.08117 | ||||||||
\(899\) | 75.5280 | 2.51900 | ||||||||
\(900\) | −7.57277 | −0.252426 | ||||||||
\(901\) | 29.5117 | 0.983176 | ||||||||
\(902\) | 1.80500 | 0.0601000 | ||||||||
\(903\) | −5.80402 | −0.193146 | ||||||||
\(904\) | 41.0007 | 1.36366 | ||||||||
\(905\) | −8.17518 | −0.271752 | ||||||||
\(906\) | −56.4845 | −1.87657 | ||||||||
\(907\) | 32.6785 | 1.08507 | 0.542536 | − | 0.840032i | \(-0.317464\pi\) | ||||
0.542536 | + | 0.840032i | \(0.317464\pi\) | |||||||
\(908\) | −25.7729 | −0.855305 | ||||||||
\(909\) | −15.8781 | −0.526643 | ||||||||
\(910\) | −2.09439 | −0.0694284 | ||||||||
\(911\) | 5.72577 | 0.189703 | 0.0948516 | − | 0.995491i | \(-0.469762\pi\) | ||||
0.0948516 | + | 0.995491i | \(0.469762\pi\) | |||||||
\(912\) | 16.4794 | 0.545687 | ||||||||
\(913\) | 3.92870 | 0.130021 | ||||||||
\(914\) | 38.6680 | 1.27902 | ||||||||
\(915\) | −6.54656 | −0.216422 | ||||||||
\(916\) | 3.89301 | 0.128629 | ||||||||
\(917\) | 4.24712 | 0.140252 | ||||||||
\(918\) | −27.7495 | −0.915871 | ||||||||
\(919\) | −50.5430 | −1.66726 | −0.833630 | − | 0.552323i | \(-0.813742\pi\) | ||||
−0.833630 | + | 0.552323i | \(0.813742\pi\) | |||||||
\(920\) | 0.410886 | 0.0135465 | ||||||||
\(921\) | 11.4244 | 0.376446 | ||||||||
\(922\) | 68.9909 | 2.27209 | ||||||||
\(923\) | 8.47654 | 0.279009 | ||||||||
\(924\) | −2.95907 | −0.0973464 | ||||||||
\(925\) | 1.86231 | 0.0612323 | ||||||||
\(926\) | 22.7014 | 0.746016 | ||||||||
\(927\) | 16.3558 | 0.537194 | ||||||||
\(928\) | −10.5036 | −0.344798 | ||||||||
\(929\) | −36.4764 | −1.19675 | −0.598377 | − | 0.801215i | \(-0.704187\pi\) | ||||
−0.598377 | + | 0.801215i | \(0.704187\pi\) | |||||||
\(930\) | −18.1259 | −0.594370 | ||||||||
\(931\) | 4.76201 | 0.156069 | ||||||||
\(932\) | −20.9420 | −0.685979 | ||||||||
\(933\) | 28.3505 | 0.928154 | ||||||||
\(934\) | −7.93821 | −0.259746 | ||||||||
\(935\) | −1.66575 | −0.0544758 | ||||||||
\(936\) | 7.71224 | 0.252083 | ||||||||
\(937\) | 26.1983 | 0.855860 | 0.427930 | − | 0.903812i | \(-0.359243\pi\) | ||||
0.427930 | + | 0.903812i | \(0.359243\pi\) | |||||||
\(938\) | 35.0937 | 1.14585 | ||||||||
\(939\) | −19.2303 | −0.627559 | ||||||||
\(940\) | −3.45718 | −0.112761 | ||||||||
\(941\) | 1.11635 | 0.0363918 | 0.0181959 | − | 0.999834i | \(-0.494208\pi\) | ||||
0.0181959 | + | 0.999834i | \(0.494208\pi\) | |||||||
\(942\) | 0.830016 | 0.0270434 | ||||||||
\(943\) | −0.0898294 | −0.00292525 | ||||||||
\(944\) | 32.2516 | 1.04970 | ||||||||
\(945\) | −5.07886 | −0.165215 | ||||||||
\(946\) | 10.1533 | 0.330112 | ||||||||
\(947\) | 46.3600 | 1.50650 | 0.753249 | − | 0.657735i | \(-0.228485\pi\) | ||||
0.753249 | + | 0.657735i | \(0.228485\pi\) | |||||||
\(948\) | 32.8134 | 1.06573 | ||||||||
\(949\) | 12.1491 | 0.394375 | ||||||||
\(950\) | 11.5600 | 0.375057 | ||||||||
\(951\) | −1.50147 | −0.0486884 | ||||||||
\(952\) | −10.3429 | −0.335216 | ||||||||
\(953\) | 48.8790 | 1.58335 | 0.791673 | − | 0.610945i | \(-0.209210\pi\) | ||||
0.791673 | + | 0.610945i | \(0.209210\pi\) | |||||||
\(954\) | −61.9171 | −2.00464 | ||||||||
\(955\) | 8.00026 | 0.258882 | ||||||||
\(956\) | −77.8565 | −2.51806 | ||||||||
\(957\) | 7.89639 | 0.255254 | ||||||||
\(958\) | 44.9693 | 1.45289 | ||||||||
\(959\) | −21.6224 | −0.698224 | ||||||||
\(960\) | 9.44193 | 0.304737 | ||||||||
\(961\) | 21.8564 | 0.705046 | ||||||||
\(962\) | −3.90040 | −0.125754 | ||||||||
\(963\) | −22.3684 | −0.720813 | ||||||||
\(964\) | −28.2556 | −0.910050 | ||||||||
\(965\) | 16.3017 | 0.524772 | ||||||||
\(966\) | 0.222919 | 0.00717231 | ||||||||
\(967\) | 5.25610 | 0.169025 | 0.0845124 | − | 0.996422i | \(-0.473067\pi\) | ||||
0.0845124 | + | 0.996422i | \(0.473067\pi\) | |||||||
\(968\) | −48.0322 | −1.54381 | ||||||||
\(969\) | 11.0076 | 0.353614 | ||||||||
\(970\) | −41.2326 | −1.32390 | ||||||||
\(971\) | −2.41366 | −0.0774581 | −0.0387290 | − | 0.999250i | \(-0.512331\pi\) | ||||
−0.0387290 | + | 0.999250i | \(0.512331\pi\) | |||||||
\(972\) | 61.7933 | 1.98202 | ||||||||
\(973\) | 5.79999 | 0.185939 | ||||||||
\(974\) | −23.2986 | −0.746534 | ||||||||
\(975\) | −0.886074 | −0.0283771 | ||||||||
\(976\) | 21.4784 | 0.687507 | ||||||||
\(977\) | −8.57934 | −0.274477 | −0.137239 | − | 0.990538i | \(-0.543823\pi\) | ||||
−0.137239 | + | 0.990538i | \(0.543823\pi\) | |||||||
\(978\) | 25.6777 | 0.821081 | ||||||||
\(979\) | −8.87083 | −0.283513 | ||||||||
\(980\) | −3.89301 | −0.124358 | ||||||||
\(981\) | 2.67425 | 0.0853821 | ||||||||
\(982\) | −49.8087 | −1.58946 | ||||||||
\(983\) | −31.5729 | −1.00702 | −0.503510 | − | 0.863989i | \(-0.667958\pi\) | ||||
−0.503510 | + | 0.863989i | \(0.667958\pi\) | |||||||
\(984\) | 4.74159 | 0.151156 | ||||||||
\(985\) | 6.85481 | 0.218413 | ||||||||
\(986\) | 56.7608 | 1.80763 | ||||||||
\(987\) | −0.912046 | −0.0290307 | ||||||||
\(988\) | −15.9943 | −0.508847 | ||||||||
\(989\) | −0.505297 | −0.0160675 | ||||||||
\(990\) | 3.49484 | 0.111073 | ||||||||
\(991\) | 10.7656 | 0.341980 | 0.170990 | − | 0.985273i | \(-0.445303\pi\) | ||||
0.170990 | + | 0.985273i | \(0.445303\pi\) | |||||||
\(992\) | −7.35069 | −0.233385 | ||||||||
\(993\) | 10.3551 | 0.328608 | ||||||||
\(994\) | 23.8506 | 0.756494 | ||||||||
\(995\) | −1.90350 | −0.0603450 | ||||||||
\(996\) | 21.2240 | 0.672507 | ||||||||
\(997\) | −14.5568 | −0.461017 | −0.230509 | − | 0.973070i | \(-0.574039\pi\) | ||||
−0.230509 | + | 0.973070i | \(0.574039\pi\) | |||||||
\(998\) | 25.7723 | 0.815809 | ||||||||
\(999\) | −9.45840 | −0.299250 |
(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 | 8015.2.a.l.1.57 | ✓ | 62 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.l.1.57 | ✓ | 62 | 1.1 | even | 1 | trivial |