Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2006,2,Mod(1,2006)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2006, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2006.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2006 = 2 \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2006.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: | \(16.0179906455\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} - 13x^{6} + 24x^{5} + 50x^{4} - 50x^{3} - 62x^{2} + 28x + 24 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(1.19822\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2006.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 3.14832 | 1.81768 | 0.908841 | − | 0.417143i | \(-0.136969\pi\) | ||||
0.908841 | + | 0.417143i | \(0.136969\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.589028 | 0.263421 | 0.131711 | − | 0.991288i | \(-0.457953\pi\) | ||||
0.131711 | + | 0.991288i | \(0.457953\pi\) | |||||||
\(6\) | 3.14832 | 1.28529 | ||||||||
\(7\) | −2.62587 | −0.992487 | −0.496244 | − | 0.868183i | \(-0.665288\pi\) | ||||
−0.496244 | + | 0.868183i | \(0.665288\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 6.91190 | 2.30397 | ||||||||
\(10\) | 0.589028 | 0.186267 | ||||||||
\(11\) | 3.58585 | 1.08117 | 0.540587 | − | 0.841288i | \(-0.318202\pi\) | ||||
0.540587 | + | 0.841288i | \(0.318202\pi\) | |||||||
\(12\) | 3.14832 | 0.908841 | ||||||||
\(13\) | −4.90040 | −1.35913 | −0.679563 | − | 0.733617i | \(-0.737831\pi\) | ||||
−0.679563 | + | 0.733617i | \(0.737831\pi\) | |||||||
\(14\) | −2.62587 | −0.701794 | ||||||||
\(15\) | 1.85445 | 0.478816 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 6.91190 | 1.62915 | ||||||||
\(19\) | 8.15303 | 1.87043 | 0.935217 | − | 0.354075i | \(-0.115204\pi\) | ||||
0.935217 | + | 0.354075i | \(0.115204\pi\) | |||||||
\(20\) | 0.589028 | 0.131711 | ||||||||
\(21\) | −8.26708 | −1.80403 | ||||||||
\(22\) | 3.58585 | 0.764506 | ||||||||
\(23\) | −1.78981 | −0.373202 | −0.186601 | − | 0.982436i | \(-0.559747\pi\) | ||||
−0.186601 | + | 0.982436i | \(0.559747\pi\) | |||||||
\(24\) | 3.14832 | 0.642647 | ||||||||
\(25\) | −4.65305 | −0.930609 | ||||||||
\(26\) | −4.90040 | −0.961047 | ||||||||
\(27\) | 12.3159 | 2.37019 | ||||||||
\(28\) | −2.62587 | −0.496244 | ||||||||
\(29\) | 5.42280 | 1.00699 | 0.503494 | − | 0.863999i | \(-0.332048\pi\) | ||||
0.503494 | + | 0.863999i | \(0.332048\pi\) | |||||||
\(30\) | 1.85445 | 0.338574 | ||||||||
\(31\) | 5.43645 | 0.976415 | 0.488207 | − | 0.872728i | \(-0.337651\pi\) | ||||
0.488207 | + | 0.872728i | \(0.337651\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 11.2894 | 1.96523 | ||||||||
\(34\) | −1.00000 | −0.171499 | ||||||||
\(35\) | −1.54671 | −0.261442 | ||||||||
\(36\) | 6.91190 | 1.15198 | ||||||||
\(37\) | −3.32482 | −0.546597 | −0.273298 | − | 0.961929i | \(-0.588115\pi\) | ||||
−0.273298 | + | 0.961929i | \(0.588115\pi\) | |||||||
\(38\) | 8.15303 | 1.32260 | ||||||||
\(39\) | −15.4280 | −2.47046 | ||||||||
\(40\) | 0.589028 | 0.0931335 | ||||||||
\(41\) | 9.74951 | 1.52262 | 0.761309 | − | 0.648389i | \(-0.224557\pi\) | ||||
0.761309 | + | 0.648389i | \(0.224557\pi\) | |||||||
\(42\) | −8.26708 | −1.27564 | ||||||||
\(43\) | −9.25681 | −1.41165 | −0.705825 | − | 0.708386i | \(-0.749424\pi\) | ||||
−0.705825 | + | 0.708386i | \(0.749424\pi\) | |||||||
\(44\) | 3.58585 | 0.540587 | ||||||||
\(45\) | 4.07130 | 0.606914 | ||||||||
\(46\) | −1.78981 | −0.263894 | ||||||||
\(47\) | −9.60374 | −1.40085 | −0.700425 | − | 0.713726i | \(-0.747006\pi\) | ||||
−0.700425 | + | 0.713726i | \(0.747006\pi\) | |||||||
\(48\) | 3.14832 | 0.454420 | ||||||||
\(49\) | −0.104783 | −0.0149690 | ||||||||
\(50\) | −4.65305 | −0.658040 | ||||||||
\(51\) | −3.14832 | −0.440852 | ||||||||
\(52\) | −4.90040 | −0.679563 | ||||||||
\(53\) | 10.9465 | 1.50361 | 0.751807 | − | 0.659383i | \(-0.229183\pi\) | ||||
0.751807 | + | 0.659383i | \(0.229183\pi\) | |||||||
\(54\) | 12.3159 | 1.67598 | ||||||||
\(55\) | 2.11217 | 0.284804 | ||||||||
\(56\) | −2.62587 | −0.350897 | ||||||||
\(57\) | 25.6683 | 3.39985 | ||||||||
\(58\) | 5.42280 | 0.712048 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | 1.85445 | 0.239408 | ||||||||
\(61\) | −3.90881 | −0.500472 | −0.250236 | − | 0.968185i | \(-0.580508\pi\) | ||||
−0.250236 | + | 0.968185i | \(0.580508\pi\) | |||||||
\(62\) | 5.43645 | 0.690429 | ||||||||
\(63\) | −18.1498 | −2.28666 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.88647 | −0.358023 | ||||||||
\(66\) | 11.2894 | 1.38963 | ||||||||
\(67\) | −9.90992 | −1.21069 | −0.605345 | − | 0.795963i | \(-0.706965\pi\) | ||||
−0.605345 | + | 0.795963i | \(0.706965\pi\) | |||||||
\(68\) | −1.00000 | −0.121268 | ||||||||
\(69\) | −5.63490 | −0.678363 | ||||||||
\(70\) | −1.54671 | −0.184868 | ||||||||
\(71\) | −9.05114 | −1.07417 | −0.537086 | − | 0.843527i | \(-0.680475\pi\) | ||||
−0.537086 | + | 0.843527i | \(0.680475\pi\) | |||||||
\(72\) | 6.91190 | 0.814575 | ||||||||
\(73\) | −4.75977 | −0.557089 | −0.278545 | − | 0.960423i | \(-0.589852\pi\) | ||||
−0.278545 | + | 0.960423i | \(0.589852\pi\) | |||||||
\(74\) | −3.32482 | −0.386502 | ||||||||
\(75\) | −14.6493 | −1.69155 | ||||||||
\(76\) | 8.15303 | 0.935217 | ||||||||
\(77\) | −9.41600 | −1.07305 | ||||||||
\(78\) | −15.4280 | −1.74688 | ||||||||
\(79\) | −1.62676 | −0.183025 | −0.0915124 | − | 0.995804i | \(-0.529170\pi\) | ||||
−0.0915124 | + | 0.995804i | \(0.529170\pi\) | |||||||
\(80\) | 0.589028 | 0.0658553 | ||||||||
\(81\) | 18.0386 | 2.00429 | ||||||||
\(82\) | 9.74951 | 1.07665 | ||||||||
\(83\) | 1.59084 | 0.174618 | 0.0873088 | − | 0.996181i | \(-0.472173\pi\) | ||||
0.0873088 | + | 0.996181i | \(0.472173\pi\) | |||||||
\(84\) | −8.26708 | −0.902013 | ||||||||
\(85\) | −0.589028 | −0.0638890 | ||||||||
\(86\) | −9.25681 | −0.998188 | ||||||||
\(87\) | 17.0727 | 1.83038 | ||||||||
\(88\) | 3.58585 | 0.382253 | ||||||||
\(89\) | −11.6838 | −1.23848 | −0.619239 | − | 0.785202i | \(-0.712559\pi\) | ||||
−0.619239 | + | 0.785202i | \(0.712559\pi\) | |||||||
\(90\) | 4.07130 | 0.429153 | ||||||||
\(91\) | 12.8678 | 1.34892 | ||||||||
\(92\) | −1.78981 | −0.186601 | ||||||||
\(93\) | 17.1157 | 1.77481 | ||||||||
\(94\) | −9.60374 | −0.990550 | ||||||||
\(95\) | 4.80236 | 0.492712 | ||||||||
\(96\) | 3.14832 | 0.321324 | ||||||||
\(97\) | 4.19543 | 0.425982 | 0.212991 | − | 0.977054i | \(-0.431680\pi\) | ||||
0.212991 | + | 0.977054i | \(0.431680\pi\) | |||||||
\(98\) | −0.104783 | −0.0105847 | ||||||||
\(99\) | 24.7850 | 2.49099 | ||||||||
\(100\) | −4.65305 | −0.465305 | ||||||||
\(101\) | 6.48405 | 0.645187 | 0.322594 | − | 0.946538i | \(-0.395445\pi\) | ||||
0.322594 | + | 0.946538i | \(0.395445\pi\) | |||||||
\(102\) | −3.14832 | −0.311730 | ||||||||
\(103\) | −12.0123 | −1.18361 | −0.591805 | − | 0.806081i | \(-0.701584\pi\) | ||||
−0.591805 | + | 0.806081i | \(0.701584\pi\) | |||||||
\(104\) | −4.90040 | −0.480524 | ||||||||
\(105\) | −4.86954 | −0.475219 | ||||||||
\(106\) | 10.9465 | 1.06322 | ||||||||
\(107\) | −0.472405 | −0.0456691 | −0.0228346 | − | 0.999739i | \(-0.507269\pi\) | ||||
−0.0228346 | + | 0.999739i | \(0.507269\pi\) | |||||||
\(108\) | 12.3159 | 1.18510 | ||||||||
\(109\) | 0.620390 | 0.0594226 | 0.0297113 | − | 0.999559i | \(-0.490541\pi\) | ||||
0.0297113 | + | 0.999559i | \(0.490541\pi\) | |||||||
\(110\) | 2.11217 | 0.201387 | ||||||||
\(111\) | −10.4676 | −0.993539 | ||||||||
\(112\) | −2.62587 | −0.248122 | ||||||||
\(113\) | −1.76952 | −0.166462 | −0.0832311 | − | 0.996530i | \(-0.526524\pi\) | ||||
−0.0832311 | + | 0.996530i | \(0.526524\pi\) | |||||||
\(114\) | 25.6683 | 2.40406 | ||||||||
\(115\) | −1.05425 | −0.0983094 | ||||||||
\(116\) | 5.42280 | 0.503494 | ||||||||
\(117\) | −33.8710 | −3.13138 | ||||||||
\(118\) | −1.00000 | −0.0920575 | ||||||||
\(119\) | 2.62587 | 0.240714 | ||||||||
\(120\) | 1.85445 | 0.169287 | ||||||||
\(121\) | 1.85833 | 0.168939 | ||||||||
\(122\) | −3.90881 | −0.353887 | ||||||||
\(123\) | 30.6946 | 2.76764 | ||||||||
\(124\) | 5.43645 | 0.488207 | ||||||||
\(125\) | −5.68591 | −0.508564 | ||||||||
\(126\) | −18.1498 | −1.61691 | ||||||||
\(127\) | 0.878973 | 0.0779963 | 0.0389981 | − | 0.999239i | \(-0.487583\pi\) | ||||
0.0389981 | + | 0.999239i | \(0.487583\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −29.1434 | −2.56593 | ||||||||
\(130\) | −2.88647 | −0.253160 | ||||||||
\(131\) | 4.95512 | 0.432931 | 0.216465 | − | 0.976290i | \(-0.430547\pi\) | ||||
0.216465 | + | 0.976290i | \(0.430547\pi\) | |||||||
\(132\) | 11.2894 | 0.982616 | ||||||||
\(133\) | −21.4088 | −1.85638 | ||||||||
\(134\) | −9.90992 | −0.856087 | ||||||||
\(135\) | 7.25440 | 0.624359 | ||||||||
\(136\) | −1.00000 | −0.0857493 | ||||||||
\(137\) | 12.0158 | 1.02658 | 0.513291 | − | 0.858214i | \(-0.328426\pi\) | ||||
0.513291 | + | 0.858214i | \(0.328426\pi\) | |||||||
\(138\) | −5.63490 | −0.479675 | ||||||||
\(139\) | −11.7361 | −0.995439 | −0.497720 | − | 0.867338i | \(-0.665829\pi\) | ||||
−0.497720 | + | 0.867338i | \(0.665829\pi\) | |||||||
\(140\) | −1.54671 | −0.130721 | ||||||||
\(141\) | −30.2356 | −2.54630 | ||||||||
\(142\) | −9.05114 | −0.759555 | ||||||||
\(143\) | −17.5721 | −1.46945 | ||||||||
\(144\) | 6.91190 | 0.575991 | ||||||||
\(145\) | 3.19418 | 0.265262 | ||||||||
\(146\) | −4.75977 | −0.393922 | ||||||||
\(147\) | −0.329890 | −0.0272089 | ||||||||
\(148\) | −3.32482 | −0.273298 | ||||||||
\(149\) | 1.59813 | 0.130924 | 0.0654621 | − | 0.997855i | \(-0.479148\pi\) | ||||
0.0654621 | + | 0.997855i | \(0.479148\pi\) | |||||||
\(150\) | −14.6493 | −1.19611 | ||||||||
\(151\) | −0.621394 | −0.0505683 | −0.0252842 | − | 0.999680i | \(-0.508049\pi\) | ||||
−0.0252842 | + | 0.999680i | \(0.508049\pi\) | |||||||
\(152\) | 8.15303 | 0.661298 | ||||||||
\(153\) | −6.91190 | −0.558794 | ||||||||
\(154\) | −9.41600 | −0.758763 | ||||||||
\(155\) | 3.20222 | 0.257208 | ||||||||
\(156\) | −15.4280 | −1.23523 | ||||||||
\(157\) | −0.0424167 | −0.00338522 | −0.00169261 | − | 0.999999i | \(-0.500539\pi\) | ||||
−0.00169261 | + | 0.999999i | \(0.500539\pi\) | |||||||
\(158\) | −1.62676 | −0.129418 | ||||||||
\(159\) | 34.4630 | 2.73309 | ||||||||
\(160\) | 0.589028 | 0.0465667 | ||||||||
\(161\) | 4.69983 | 0.370398 | ||||||||
\(162\) | 18.0386 | 1.41725 | ||||||||
\(163\) | 7.66429 | 0.600313 | 0.300157 | − | 0.953890i | \(-0.402961\pi\) | ||||
0.300157 | + | 0.953890i | \(0.402961\pi\) | |||||||
\(164\) | 9.74951 | 0.761309 | ||||||||
\(165\) | 6.64977 | 0.517684 | ||||||||
\(166\) | 1.59084 | 0.123473 | ||||||||
\(167\) | −11.4214 | −0.883814 | −0.441907 | − | 0.897061i | \(-0.645698\pi\) | ||||
−0.441907 | + | 0.897061i | \(0.645698\pi\) | |||||||
\(168\) | −8.26708 | −0.637819 | ||||||||
\(169\) | 11.0139 | 0.847224 | ||||||||
\(170\) | −0.589028 | −0.0451764 | ||||||||
\(171\) | 56.3529 | 4.30942 | ||||||||
\(172\) | −9.25681 | −0.705825 | ||||||||
\(173\) | −9.80512 | −0.745469 | −0.372735 | − | 0.927938i | \(-0.621580\pi\) | ||||
−0.372735 | + | 0.927938i | \(0.621580\pi\) | |||||||
\(174\) | 17.0727 | 1.29428 | ||||||||
\(175\) | 12.2183 | 0.923618 | ||||||||
\(176\) | 3.58585 | 0.270294 | ||||||||
\(177\) | −3.14832 | −0.236642 | ||||||||
\(178\) | −11.6838 | −0.875737 | ||||||||
\(179\) | −8.42530 | −0.629736 | −0.314868 | − | 0.949135i | \(-0.601960\pi\) | ||||
−0.314868 | + | 0.949135i | \(0.601960\pi\) | |||||||
\(180\) | 4.07130 | 0.303457 | ||||||||
\(181\) | −8.07166 | −0.599962 | −0.299981 | − | 0.953945i | \(-0.596980\pi\) | ||||
−0.299981 | + | 0.953945i | \(0.596980\pi\) | |||||||
\(182\) | 12.8678 | 0.953827 | ||||||||
\(183\) | −12.3062 | −0.909699 | ||||||||
\(184\) | −1.78981 | −0.131947 | ||||||||
\(185\) | −1.95841 | −0.143985 | ||||||||
\(186\) | 17.1157 | 1.25498 | ||||||||
\(187\) | −3.58585 | −0.262223 | ||||||||
\(188\) | −9.60374 | −0.700425 | ||||||||
\(189\) | −32.3400 | −2.35239 | ||||||||
\(190\) | 4.80236 | 0.348400 | ||||||||
\(191\) | 14.7346 | 1.06616 | 0.533080 | − | 0.846065i | \(-0.321035\pi\) | ||||
0.533080 | + | 0.846065i | \(0.321035\pi\) | |||||||
\(192\) | 3.14832 | 0.227210 | ||||||||
\(193\) | −25.2110 | −1.81473 | −0.907363 | − | 0.420349i | \(-0.861908\pi\) | ||||
−0.907363 | + | 0.420349i | \(0.861908\pi\) | |||||||
\(194\) | 4.19543 | 0.301215 | ||||||||
\(195\) | −9.08753 | −0.650771 | ||||||||
\(196\) | −0.104783 | −0.00748451 | ||||||||
\(197\) | 6.41372 | 0.456958 | 0.228479 | − | 0.973549i | \(-0.426625\pi\) | ||||
0.228479 | + | 0.973549i | \(0.426625\pi\) | |||||||
\(198\) | 24.7850 | 1.76140 | ||||||||
\(199\) | −26.2951 | −1.86401 | −0.932005 | − | 0.362445i | \(-0.881942\pi\) | ||||
−0.932005 | + | 0.362445i | \(0.881942\pi\) | |||||||
\(200\) | −4.65305 | −0.329020 | ||||||||
\(201\) | −31.1996 | −2.20065 | ||||||||
\(202\) | 6.48405 | 0.456216 | ||||||||
\(203\) | −14.2396 | −0.999423 | ||||||||
\(204\) | −3.14832 | −0.220426 | ||||||||
\(205\) | 5.74274 | 0.401090 | ||||||||
\(206\) | −12.0123 | −0.836938 | ||||||||
\(207\) | −12.3710 | −0.859845 | ||||||||
\(208\) | −4.90040 | −0.339782 | ||||||||
\(209\) | 29.2356 | 2.02227 | ||||||||
\(210\) | −4.86954 | −0.336030 | ||||||||
\(211\) | 21.9976 | 1.51438 | 0.757190 | − | 0.653195i | \(-0.226572\pi\) | ||||
0.757190 | + | 0.653195i | \(0.226572\pi\) | |||||||
\(212\) | 10.9465 | 0.751807 | ||||||||
\(213\) | −28.4958 | −1.95250 | ||||||||
\(214\) | −0.472405 | −0.0322929 | ||||||||
\(215\) | −5.45252 | −0.371859 | ||||||||
\(216\) | 12.3159 | 0.837990 | ||||||||
\(217\) | −14.2754 | −0.969079 | ||||||||
\(218\) | 0.620390 | 0.0420181 | ||||||||
\(219\) | −14.9853 | −1.01261 | ||||||||
\(220\) | 2.11217 | 0.142402 | ||||||||
\(221\) | 4.90040 | 0.329637 | ||||||||
\(222\) | −10.4676 | −0.702538 | ||||||||
\(223\) | −9.32882 | −0.624704 | −0.312352 | − | 0.949966i | \(-0.601117\pi\) | ||||
−0.312352 | + | 0.949966i | \(0.601117\pi\) | |||||||
\(224\) | −2.62587 | −0.175449 | ||||||||
\(225\) | −32.1614 | −2.14409 | ||||||||
\(226\) | −1.76952 | −0.117707 | ||||||||
\(227\) | 26.8160 | 1.77984 | 0.889922 | − | 0.456114i | \(-0.150759\pi\) | ||||
0.889922 | + | 0.456114i | \(0.150759\pi\) | |||||||
\(228\) | 25.6683 | 1.69993 | ||||||||
\(229\) | −23.0821 | −1.52531 | −0.762653 | − | 0.646808i | \(-0.776103\pi\) | ||||
−0.762653 | + | 0.646808i | \(0.776103\pi\) | |||||||
\(230\) | −1.05425 | −0.0695152 | ||||||||
\(231\) | −29.6445 | −1.95047 | ||||||||
\(232\) | 5.42280 | 0.356024 | ||||||||
\(233\) | 9.38591 | 0.614891 | 0.307446 | − | 0.951566i | \(-0.400526\pi\) | ||||
0.307446 | + | 0.951566i | \(0.400526\pi\) | |||||||
\(234\) | −33.8710 | −2.21422 | ||||||||
\(235\) | −5.65687 | −0.369014 | ||||||||
\(236\) | −1.00000 | −0.0650945 | ||||||||
\(237\) | −5.12155 | −0.332681 | ||||||||
\(238\) | 2.62587 | 0.170210 | ||||||||
\(239\) | −10.0692 | −0.651321 | −0.325660 | − | 0.945487i | \(-0.605587\pi\) | ||||
−0.325660 | + | 0.945487i | \(0.605587\pi\) | |||||||
\(240\) | 1.85445 | 0.119704 | ||||||||
\(241\) | 2.13124 | 0.137285 | 0.0686425 | − | 0.997641i | \(-0.478133\pi\) | ||||
0.0686425 | + | 0.997641i | \(0.478133\pi\) | |||||||
\(242\) | 1.85833 | 0.119458 | ||||||||
\(243\) | 19.8436 | 1.27297 | ||||||||
\(244\) | −3.90881 | −0.250236 | ||||||||
\(245\) | −0.0617202 | −0.00394316 | ||||||||
\(246\) | 30.6946 | 1.95701 | ||||||||
\(247\) | −39.9531 | −2.54216 | ||||||||
\(248\) | 5.43645 | 0.345215 | ||||||||
\(249\) | 5.00847 | 0.317399 | ||||||||
\(250\) | −5.68591 | −0.359609 | ||||||||
\(251\) | −1.55051 | −0.0978673 | −0.0489337 | − | 0.998802i | \(-0.515582\pi\) | ||||
−0.0489337 | + | 0.998802i | \(0.515582\pi\) | |||||||
\(252\) | −18.1498 | −1.14333 | ||||||||
\(253\) | −6.41801 | −0.403497 | ||||||||
\(254\) | 0.878973 | 0.0551517 | ||||||||
\(255\) | −1.85445 | −0.116130 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 29.3848 | 1.83297 | 0.916485 | − | 0.400068i | \(-0.131014\pi\) | ||||
0.916485 | + | 0.400068i | \(0.131014\pi\) | |||||||
\(258\) | −29.1434 | −1.81439 | ||||||||
\(259\) | 8.73056 | 0.542490 | ||||||||
\(260\) | −2.88647 | −0.179011 | ||||||||
\(261\) | 37.4818 | 2.32007 | ||||||||
\(262\) | 4.95512 | 0.306128 | ||||||||
\(263\) | 10.0650 | 0.620637 | 0.310319 | − | 0.950633i | \(-0.399564\pi\) | ||||
0.310319 | + | 0.950633i | \(0.399564\pi\) | |||||||
\(264\) | 11.2894 | 0.694814 | ||||||||
\(265\) | 6.44778 | 0.396084 | ||||||||
\(266\) | −21.4088 | −1.31266 | ||||||||
\(267\) | −36.7843 | −2.25116 | ||||||||
\(268\) | −9.90992 | −0.605345 | ||||||||
\(269\) | 6.73694 | 0.410759 | 0.205379 | − | 0.978682i | \(-0.434157\pi\) | ||||
0.205379 | + | 0.978682i | \(0.434157\pi\) | |||||||
\(270\) | 7.25440 | 0.441489 | ||||||||
\(271\) | 19.6009 | 1.19067 | 0.595334 | − | 0.803479i | \(-0.297020\pi\) | ||||
0.595334 | + | 0.803479i | \(0.297020\pi\) | |||||||
\(272\) | −1.00000 | −0.0606339 | ||||||||
\(273\) | 40.5120 | 2.45190 | ||||||||
\(274\) | 12.0158 | 0.725904 | ||||||||
\(275\) | −16.6851 | −1.00615 | ||||||||
\(276\) | −5.63490 | −0.339181 | ||||||||
\(277\) | 22.6929 | 1.36349 | 0.681743 | − | 0.731592i | \(-0.261222\pi\) | ||||
0.681743 | + | 0.731592i | \(0.261222\pi\) | |||||||
\(278\) | −11.7361 | −0.703882 | ||||||||
\(279\) | 37.5762 | 2.24963 | ||||||||
\(280\) | −1.54671 | −0.0924338 | ||||||||
\(281\) | 2.38415 | 0.142226 | 0.0711132 | − | 0.997468i | \(-0.477345\pi\) | ||||
0.0711132 | + | 0.997468i | \(0.477345\pi\) | |||||||
\(282\) | −30.2356 | −1.80050 | ||||||||
\(283\) | 29.5839 | 1.75858 | 0.879290 | − | 0.476287i | \(-0.158018\pi\) | ||||
0.879290 | + | 0.476287i | \(0.158018\pi\) | |||||||
\(284\) | −9.05114 | −0.537086 | ||||||||
\(285\) | 15.1194 | 0.895594 | ||||||||
\(286\) | −17.5721 | −1.03906 | ||||||||
\(287\) | −25.6010 | −1.51118 | ||||||||
\(288\) | 6.91190 | 0.407287 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 3.19418 | 0.187569 | ||||||||
\(291\) | 13.2086 | 0.774299 | ||||||||
\(292\) | −4.75977 | −0.278545 | ||||||||
\(293\) | −8.70231 | −0.508394 | −0.254197 | − | 0.967152i | \(-0.581811\pi\) | ||||
−0.254197 | + | 0.967152i | \(0.581811\pi\) | |||||||
\(294\) | −0.329890 | −0.0192396 | ||||||||
\(295\) | −0.589028 | −0.0342945 | ||||||||
\(296\) | −3.32482 | −0.193251 | ||||||||
\(297\) | 44.1629 | 2.56259 | ||||||||
\(298\) | 1.59813 | 0.0925774 | ||||||||
\(299\) | 8.77081 | 0.507229 | ||||||||
\(300\) | −14.6493 | −0.845775 | ||||||||
\(301\) | 24.3072 | 1.40105 | ||||||||
\(302\) | −0.621394 | −0.0357572 | ||||||||
\(303\) | 20.4138 | 1.17274 | ||||||||
\(304\) | 8.15303 | 0.467609 | ||||||||
\(305\) | −2.30240 | −0.131835 | ||||||||
\(306\) | −6.91190 | −0.395127 | ||||||||
\(307\) | 26.3123 | 1.50172 | 0.750860 | − | 0.660461i | \(-0.229639\pi\) | ||||
0.750860 | + | 0.660461i | \(0.229639\pi\) | |||||||
\(308\) | −9.41600 | −0.536526 | ||||||||
\(309\) | −37.8186 | −2.15142 | ||||||||
\(310\) | 3.20222 | 0.181874 | ||||||||
\(311\) | −1.11665 | −0.0633196 | −0.0316598 | − | 0.999499i | \(-0.510079\pi\) | ||||
−0.0316598 | + | 0.999499i | \(0.510079\pi\) | |||||||
\(312\) | −15.4280 | −0.873439 | ||||||||
\(313\) | 2.15112 | 0.121588 | 0.0607942 | − | 0.998150i | \(-0.480637\pi\) | ||||
0.0607942 | + | 0.998150i | \(0.480637\pi\) | |||||||
\(314\) | −0.0424167 | −0.00239371 | ||||||||
\(315\) | −10.6907 | −0.602354 | ||||||||
\(316\) | −1.62676 | −0.0915124 | ||||||||
\(317\) | −2.80446 | −0.157514 | −0.0787572 | − | 0.996894i | \(-0.525095\pi\) | ||||
−0.0787572 | + | 0.996894i | \(0.525095\pi\) | |||||||
\(318\) | 34.4630 | 1.93259 | ||||||||
\(319\) | 19.4453 | 1.08873 | ||||||||
\(320\) | 0.589028 | 0.0329277 | ||||||||
\(321\) | −1.48728 | −0.0830119 | ||||||||
\(322\) | 4.69983 | 0.261911 | ||||||||
\(323\) | −8.15303 | −0.453647 | ||||||||
\(324\) | 18.0386 | 1.00215 | ||||||||
\(325\) | 22.8018 | 1.26482 | ||||||||
\(326\) | 7.66429 | 0.424486 | ||||||||
\(327\) | 1.95319 | 0.108011 | ||||||||
\(328\) | 9.74951 | 0.538327 | ||||||||
\(329\) | 25.2182 | 1.39033 | ||||||||
\(330\) | 6.64977 | 0.366058 | ||||||||
\(331\) | 9.32074 | 0.512314 | 0.256157 | − | 0.966635i | \(-0.417544\pi\) | ||||
0.256157 | + | 0.966635i | \(0.417544\pi\) | |||||||
\(332\) | 1.59084 | 0.0873088 | ||||||||
\(333\) | −22.9808 | −1.25934 | ||||||||
\(334\) | −11.4214 | −0.624951 | ||||||||
\(335\) | −5.83722 | −0.318921 | ||||||||
\(336\) | −8.26708 | −0.451006 | ||||||||
\(337\) | −36.1661 | −1.97009 | −0.985047 | − | 0.172287i | \(-0.944884\pi\) | ||||
−0.985047 | + | 0.172287i | \(0.944884\pi\) | |||||||
\(338\) | 11.0139 | 0.599078 | ||||||||
\(339\) | −5.57100 | −0.302575 | ||||||||
\(340\) | −0.589028 | −0.0319445 | ||||||||
\(341\) | 19.4943 | 1.05568 | ||||||||
\(342\) | 56.3529 | 3.04722 | ||||||||
\(343\) | 18.6563 | 1.00734 | ||||||||
\(344\) | −9.25681 | −0.499094 | ||||||||
\(345\) | −3.31911 | −0.178695 | ||||||||
\(346\) | −9.80512 | −0.527126 | ||||||||
\(347\) | −33.3397 | −1.78977 | −0.894886 | − | 0.446296i | \(-0.852743\pi\) | ||||
−0.894886 | + | 0.446296i | \(0.852743\pi\) | |||||||
\(348\) | 17.0727 | 0.915192 | ||||||||
\(349\) | 30.2492 | 1.61920 | 0.809600 | − | 0.586982i | \(-0.199684\pi\) | ||||
0.809600 | + | 0.586982i | \(0.199684\pi\) | |||||||
\(350\) | 12.2183 | 0.653096 | ||||||||
\(351\) | −60.3528 | −3.22139 | ||||||||
\(352\) | 3.58585 | 0.191127 | ||||||||
\(353\) | −8.70630 | −0.463389 | −0.231695 | − | 0.972789i | \(-0.574427\pi\) | ||||
−0.231695 | + | 0.972789i | \(0.574427\pi\) | |||||||
\(354\) | −3.14832 | −0.167331 | ||||||||
\(355\) | −5.33137 | −0.282960 | ||||||||
\(356\) | −11.6838 | −0.619239 | ||||||||
\(357\) | 8.26708 | 0.437540 | ||||||||
\(358\) | −8.42530 | −0.445291 | ||||||||
\(359\) | 20.6559 | 1.09017 | 0.545087 | − | 0.838379i | \(-0.316497\pi\) | ||||
0.545087 | + | 0.838379i | \(0.316497\pi\) | |||||||
\(360\) | 4.07130 | 0.214576 | ||||||||
\(361\) | 47.4720 | 2.49852 | ||||||||
\(362\) | −8.07166 | −0.424237 | ||||||||
\(363\) | 5.85061 | 0.307078 | ||||||||
\(364\) | 12.8678 | 0.674458 | ||||||||
\(365\) | −2.80364 | −0.146749 | ||||||||
\(366\) | −12.3062 | −0.643254 | ||||||||
\(367\) | −32.7200 | −1.70797 | −0.853985 | − | 0.520298i | \(-0.825821\pi\) | ||||
−0.853985 | + | 0.520298i | \(0.825821\pi\) | |||||||
\(368\) | −1.78981 | −0.0933005 | ||||||||
\(369\) | 67.3876 | 3.50806 | ||||||||
\(370\) | −1.95841 | −0.101813 | ||||||||
\(371\) | −28.7441 | −1.49232 | ||||||||
\(372\) | 17.1157 | 0.887405 | ||||||||
\(373\) | 5.93052 | 0.307070 | 0.153535 | − | 0.988143i | \(-0.450934\pi\) | ||||
0.153535 | + | 0.988143i | \(0.450934\pi\) | |||||||
\(374\) | −3.58585 | −0.185420 | ||||||||
\(375\) | −17.9011 | −0.924407 | ||||||||
\(376\) | −9.60374 | −0.495275 | ||||||||
\(377\) | −26.5739 | −1.36862 | ||||||||
\(378\) | −32.3400 | −1.66339 | ||||||||
\(379\) | 34.6780 | 1.78129 | 0.890645 | − | 0.454699i | \(-0.150253\pi\) | ||||
0.890645 | + | 0.454699i | \(0.150253\pi\) | |||||||
\(380\) | 4.80236 | 0.246356 | ||||||||
\(381\) | 2.76729 | 0.141772 | ||||||||
\(382\) | 14.7346 | 0.753889 | ||||||||
\(383\) | 32.2031 | 1.64550 | 0.822751 | − | 0.568402i | \(-0.192438\pi\) | ||||
0.822751 | + | 0.568402i | \(0.192438\pi\) | |||||||
\(384\) | 3.14832 | 0.160662 | ||||||||
\(385\) | −5.54628 | −0.282665 | ||||||||
\(386\) | −25.2110 | −1.28320 | ||||||||
\(387\) | −63.9821 | −3.25239 | ||||||||
\(388\) | 4.19543 | 0.212991 | ||||||||
\(389\) | 4.87596 | 0.247221 | 0.123611 | − | 0.992331i | \(-0.460553\pi\) | ||||
0.123611 | + | 0.992331i | \(0.460553\pi\) | |||||||
\(390\) | −9.08753 | −0.460165 | ||||||||
\(391\) | 1.78981 | 0.0905148 | ||||||||
\(392\) | −0.104783 | −0.00529234 | ||||||||
\(393\) | 15.6003 | 0.786930 | ||||||||
\(394\) | 6.41372 | 0.323118 | ||||||||
\(395\) | −0.958207 | −0.0482126 | ||||||||
\(396\) | 24.7850 | 1.24549 | ||||||||
\(397\) | 8.60978 | 0.432112 | 0.216056 | − | 0.976381i | \(-0.430681\pi\) | ||||
0.216056 | + | 0.976381i | \(0.430681\pi\) | |||||||
\(398\) | −26.2951 | −1.31805 | ||||||||
\(399\) | −67.4018 | −3.37431 | ||||||||
\(400\) | −4.65305 | −0.232652 | ||||||||
\(401\) | 18.7279 | 0.935228 | 0.467614 | − | 0.883933i | \(-0.345114\pi\) | ||||
0.467614 | + | 0.883933i | \(0.345114\pi\) | |||||||
\(402\) | −31.1996 | −1.55609 | ||||||||
\(403\) | −26.6408 | −1.32707 | ||||||||
\(404\) | 6.48405 | 0.322594 | ||||||||
\(405\) | 10.6252 | 0.527973 | ||||||||
\(406\) | −14.2396 | −0.706699 | ||||||||
\(407\) | −11.9223 | −0.590967 | ||||||||
\(408\) | −3.14832 | −0.155865 | ||||||||
\(409\) | −12.9012 | −0.637921 | −0.318961 | − | 0.947768i | \(-0.603334\pi\) | ||||
−0.318961 | + | 0.947768i | \(0.603334\pi\) | |||||||
\(410\) | 5.74274 | 0.283614 | ||||||||
\(411\) | 37.8297 | 1.86600 | ||||||||
\(412\) | −12.0123 | −0.591805 | ||||||||
\(413\) | 2.62587 | 0.129211 | ||||||||
\(414\) | −12.3710 | −0.608002 | ||||||||
\(415\) | 0.937050 | 0.0459980 | ||||||||
\(416\) | −4.90040 | −0.240262 | ||||||||
\(417\) | −36.9488 | −1.80939 | ||||||||
\(418\) | 29.2356 | 1.42996 | ||||||||
\(419\) | 13.2122 | 0.645458 | 0.322729 | − | 0.946491i | \(-0.395400\pi\) | ||||
0.322729 | + | 0.946491i | \(0.395400\pi\) | |||||||
\(420\) | −4.86954 | −0.237609 | ||||||||
\(421\) | 7.23797 | 0.352757 | 0.176379 | − | 0.984322i | \(-0.443562\pi\) | ||||
0.176379 | + | 0.984322i | \(0.443562\pi\) | |||||||
\(422\) | 21.9976 | 1.07083 | ||||||||
\(423\) | −66.3800 | −3.22751 | ||||||||
\(424\) | 10.9465 | 0.531608 | ||||||||
\(425\) | 4.65305 | 0.225706 | ||||||||
\(426\) | −28.4958 | −1.38063 | ||||||||
\(427\) | 10.2641 | 0.496712 | ||||||||
\(428\) | −0.472405 | −0.0228346 | ||||||||
\(429\) | −55.3225 | −2.67100 | ||||||||
\(430\) | −5.45252 | −0.262944 | ||||||||
\(431\) | −30.9120 | −1.48898 | −0.744490 | − | 0.667633i | \(-0.767307\pi\) | ||||
−0.744490 | + | 0.667633i | \(0.767307\pi\) | |||||||
\(432\) | 12.3159 | 0.592548 | ||||||||
\(433\) | −29.4556 | −1.41554 | −0.707772 | − | 0.706441i | \(-0.750300\pi\) | ||||
−0.707772 | + | 0.706441i | \(0.750300\pi\) | |||||||
\(434\) | −14.2754 | −0.685242 | ||||||||
\(435\) | 10.0563 | 0.482162 | ||||||||
\(436\) | 0.620390 | 0.0297113 | ||||||||
\(437\) | −14.5924 | −0.698050 | ||||||||
\(438\) | −14.9853 | −0.716024 | ||||||||
\(439\) | 5.57890 | 0.266266 | 0.133133 | − | 0.991098i | \(-0.457496\pi\) | ||||
0.133133 | + | 0.991098i | \(0.457496\pi\) | |||||||
\(440\) | 2.11217 | 0.100694 | ||||||||
\(441\) | −0.724250 | −0.0344881 | ||||||||
\(442\) | 4.90040 | 0.233088 | ||||||||
\(443\) | 15.9821 | 0.759333 | 0.379667 | − | 0.925123i | \(-0.376039\pi\) | ||||
0.379667 | + | 0.925123i | \(0.376039\pi\) | |||||||
\(444\) | −10.4676 | −0.496769 | ||||||||
\(445\) | −6.88208 | −0.326242 | ||||||||
\(446\) | −9.32882 | −0.441733 | ||||||||
\(447\) | 5.03143 | 0.237979 | ||||||||
\(448\) | −2.62587 | −0.124061 | ||||||||
\(449\) | −13.9942 | −0.660429 | −0.330215 | − | 0.943906i | \(-0.607121\pi\) | ||||
−0.330215 | + | 0.943906i | \(0.607121\pi\) | |||||||
\(450\) | −32.1614 | −1.51610 | ||||||||
\(451\) | 34.9603 | 1.64622 | ||||||||
\(452\) | −1.76952 | −0.0832311 | ||||||||
\(453\) | −1.95635 | −0.0919171 | ||||||||
\(454\) | 26.8160 | 1.25854 | ||||||||
\(455\) | 7.57951 | 0.355333 | ||||||||
\(456\) | 25.6683 | 1.20203 | ||||||||
\(457\) | −21.1888 | −0.991169 | −0.495585 | − | 0.868560i | \(-0.665046\pi\) | ||||
−0.495585 | + | 0.868560i | \(0.665046\pi\) | |||||||
\(458\) | −23.0821 | −1.07855 | ||||||||
\(459\) | −12.3159 | −0.574856 | ||||||||
\(460\) | −1.05425 | −0.0491547 | ||||||||
\(461\) | −20.9031 | −0.973552 | −0.486776 | − | 0.873527i | \(-0.661827\pi\) | ||||
−0.486776 | + | 0.873527i | \(0.661827\pi\) | |||||||
\(462\) | −29.6445 | −1.37919 | ||||||||
\(463\) | 40.6488 | 1.88911 | 0.944554 | − | 0.328356i | \(-0.106495\pi\) | ||||
0.944554 | + | 0.328356i | \(0.106495\pi\) | |||||||
\(464\) | 5.42280 | 0.251747 | ||||||||
\(465\) | 10.0816 | 0.467523 | ||||||||
\(466\) | 9.38591 | 0.434794 | ||||||||
\(467\) | −16.6371 | −0.769871 | −0.384936 | − | 0.922943i | \(-0.625776\pi\) | ||||
−0.384936 | + | 0.922943i | \(0.625776\pi\) | |||||||
\(468\) | −33.8710 | −1.56569 | ||||||||
\(469\) | 26.0222 | 1.20159 | ||||||||
\(470\) | −5.65687 | −0.260932 | ||||||||
\(471\) | −0.133541 | −0.00615325 | ||||||||
\(472\) | −1.00000 | −0.0460287 | ||||||||
\(473\) | −33.1936 | −1.52624 | ||||||||
\(474\) | −5.12155 | −0.235241 | ||||||||
\(475\) | −37.9364 | −1.74064 | ||||||||
\(476\) | 2.62587 | 0.120357 | ||||||||
\(477\) | 75.6609 | 3.46427 | ||||||||
\(478\) | −10.0692 | −0.460553 | ||||||||
\(479\) | 30.6239 | 1.39924 | 0.699620 | − | 0.714515i | \(-0.253352\pi\) | ||||
0.699620 | + | 0.714515i | \(0.253352\pi\) | |||||||
\(480\) | 1.85445 | 0.0846435 | ||||||||
\(481\) | 16.2929 | 0.742894 | ||||||||
\(482\) | 2.13124 | 0.0970752 | ||||||||
\(483\) | 14.7965 | 0.673266 | ||||||||
\(484\) | 1.85833 | 0.0844696 | ||||||||
\(485\) | 2.47123 | 0.112213 | ||||||||
\(486\) | 19.8436 | 0.900124 | ||||||||
\(487\) | −37.4899 | −1.69883 | −0.849416 | − | 0.527724i | \(-0.823045\pi\) | ||||
−0.849416 | + | 0.527724i | \(0.823045\pi\) | |||||||
\(488\) | −3.90881 | −0.176944 | ||||||||
\(489\) | 24.1296 | 1.09118 | ||||||||
\(490\) | −0.0617202 | −0.00278823 | ||||||||
\(491\) | −25.1759 | −1.13617 | −0.568087 | − | 0.822969i | \(-0.692316\pi\) | ||||
−0.568087 | + | 0.822969i | \(0.692316\pi\) | |||||||
\(492\) | 30.6946 | 1.38382 | ||||||||
\(493\) | −5.42280 | −0.244230 | ||||||||
\(494\) | −39.9531 | −1.79758 | ||||||||
\(495\) | 14.5991 | 0.656180 | ||||||||
\(496\) | 5.43645 | 0.244104 | ||||||||
\(497\) | 23.7672 | 1.06610 | ||||||||
\(498\) | 5.00847 | 0.224435 | ||||||||
\(499\) | −13.5773 | −0.607806 | −0.303903 | − | 0.952703i | \(-0.598290\pi\) | ||||
−0.303903 | + | 0.952703i | \(0.598290\pi\) | |||||||
\(500\) | −5.68591 | −0.254282 | ||||||||
\(501\) | −35.9582 | −1.60649 | ||||||||
\(502\) | −1.55051 | −0.0692026 | ||||||||
\(503\) | 6.89724 | 0.307533 | 0.153766 | − | 0.988107i | \(-0.450860\pi\) | ||||
0.153766 | + | 0.988107i | \(0.450860\pi\) | |||||||
\(504\) | −18.1498 | −0.808455 | ||||||||
\(505\) | 3.81929 | 0.169956 | ||||||||
\(506\) | −6.41801 | −0.285315 | ||||||||
\(507\) | 34.6753 | 1.53998 | ||||||||
\(508\) | 0.878973 | 0.0389981 | ||||||||
\(509\) | −11.9721 | −0.530655 | −0.265327 | − | 0.964158i | \(-0.585480\pi\) | ||||
−0.265327 | + | 0.964158i | \(0.585480\pi\) | |||||||
\(510\) | −1.85445 | −0.0821163 | ||||||||
\(511\) | 12.4986 | 0.552904 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 100.412 | 4.43329 | ||||||||
\(514\) | 29.3848 | 1.29611 | ||||||||
\(515\) | −7.07559 | −0.311788 | ||||||||
\(516\) | −29.1434 | −1.28297 | ||||||||
\(517\) | −34.4376 | −1.51456 | ||||||||
\(518\) | 8.73056 | 0.383599 | ||||||||
\(519\) | −30.8696 | −1.35503 | ||||||||
\(520\) | −2.88647 | −0.126580 | ||||||||
\(521\) | −13.8530 | −0.606909 | −0.303455 | − | 0.952846i | \(-0.598140\pi\) | ||||
−0.303455 | + | 0.952846i | \(0.598140\pi\) | |||||||
\(522\) | 37.4818 | 1.64053 | ||||||||
\(523\) | 26.0093 | 1.13731 | 0.568653 | − | 0.822578i | \(-0.307465\pi\) | ||||
0.568653 | + | 0.822578i | \(0.307465\pi\) | |||||||
\(524\) | 4.95512 | 0.216465 | ||||||||
\(525\) | 38.4671 | 1.67884 | ||||||||
\(526\) | 10.0650 | 0.438857 | ||||||||
\(527\) | −5.43645 | −0.236815 | ||||||||
\(528\) | 11.2894 | 0.491308 | ||||||||
\(529\) | −19.7966 | −0.860720 | ||||||||
\(530\) | 6.44778 | 0.280074 | ||||||||
\(531\) | −6.91190 | −0.299951 | ||||||||
\(532\) | −21.4088 | −0.928191 | ||||||||
\(533\) | −47.7765 | −2.06943 | ||||||||
\(534\) | −36.7843 | −1.59181 | ||||||||
\(535\) | −0.278260 | −0.0120302 | ||||||||
\(536\) | −9.90992 | −0.428043 | ||||||||
\(537\) | −26.5255 | −1.14466 | ||||||||
\(538\) | 6.73694 | 0.290450 | ||||||||
\(539\) | −0.375737 | −0.0161841 | ||||||||
\(540\) | 7.25440 | 0.312180 | ||||||||
\(541\) | 46.2395 | 1.98799 | 0.993996 | − | 0.109419i | \(-0.0348990\pi\) | ||||
0.993996 | + | 0.109419i | \(0.0348990\pi\) | |||||||
\(542\) | 19.6009 | 0.841929 | ||||||||
\(543\) | −25.4121 | −1.09054 | ||||||||
\(544\) | −1.00000 | −0.0428746 | ||||||||
\(545\) | 0.365427 | 0.0156532 | ||||||||
\(546\) | 40.5120 | 1.73375 | ||||||||
\(547\) | 0.147916 | 0.00632442 | 0.00316221 | − | 0.999995i | \(-0.498993\pi\) | ||||
0.00316221 | + | 0.999995i | \(0.498993\pi\) | |||||||
\(548\) | 12.0158 | 0.513291 | ||||||||
\(549\) | −27.0173 | −1.15307 | ||||||||
\(550\) | −16.6851 | −0.711456 | ||||||||
\(551\) | 44.2122 | 1.88350 | ||||||||
\(552\) | −5.63490 | −0.239837 | ||||||||
\(553\) | 4.27167 | 0.181650 | ||||||||
\(554\) | 22.6929 | 0.964130 | ||||||||
\(555\) | −6.16570 | −0.261719 | ||||||||
\(556\) | −11.7361 | −0.497720 | ||||||||
\(557\) | −44.2063 | −1.87308 | −0.936541 | − | 0.350558i | \(-0.885992\pi\) | ||||
−0.936541 | + | 0.350558i | \(0.885992\pi\) | |||||||
\(558\) | 37.5762 | 1.59073 | ||||||||
\(559\) | 45.3621 | 1.91861 | ||||||||
\(560\) | −1.54671 | −0.0653606 | ||||||||
\(561\) | −11.2894 | −0.476639 | ||||||||
\(562\) | 2.38415 | 0.100569 | ||||||||
\(563\) | 5.11645 | 0.215633 | 0.107816 | − | 0.994171i | \(-0.465614\pi\) | ||||
0.107816 | + | 0.994171i | \(0.465614\pi\) | |||||||
\(564\) | −30.2356 | −1.27315 | ||||||||
\(565\) | −1.04230 | −0.0438497 | ||||||||
\(566\) | 29.5839 | 1.24350 | ||||||||
\(567\) | −47.3671 | −1.98923 | ||||||||
\(568\) | −9.05114 | −0.379777 | ||||||||
\(569\) | 44.3822 | 1.86060 | 0.930299 | − | 0.366803i | \(-0.119548\pi\) | ||||
0.930299 | + | 0.366803i | \(0.119548\pi\) | |||||||
\(570\) | 15.1194 | 0.633280 | ||||||||
\(571\) | 11.9347 | 0.499452 | 0.249726 | − | 0.968316i | \(-0.419659\pi\) | ||||
0.249726 | + | 0.968316i | \(0.419659\pi\) | |||||||
\(572\) | −17.5721 | −0.734727 | ||||||||
\(573\) | 46.3892 | 1.93794 | ||||||||
\(574\) | −25.6010 | −1.06857 | ||||||||
\(575\) | 8.32809 | 0.347305 | ||||||||
\(576\) | 6.91190 | 0.287996 | ||||||||
\(577\) | −31.9722 | −1.33102 | −0.665510 | − | 0.746389i | \(-0.731786\pi\) | ||||
−0.665510 | + | 0.746389i | \(0.731786\pi\) | |||||||
\(578\) | 1.00000 | 0.0415945 | ||||||||
\(579\) | −79.3721 | −3.29859 | ||||||||
\(580\) | 3.19418 | 0.132631 | ||||||||
\(581\) | −4.17735 | −0.173306 | ||||||||
\(582\) | 13.2086 | 0.547512 | ||||||||
\(583\) | 39.2524 | 1.62567 | ||||||||
\(584\) | −4.75977 | −0.196961 | ||||||||
\(585\) | −19.9510 | −0.824872 | ||||||||
\(586\) | −8.70231 | −0.359489 | ||||||||
\(587\) | −6.58269 | −0.271697 | −0.135848 | − | 0.990730i | \(-0.543376\pi\) | ||||
−0.135848 | + | 0.990730i | \(0.543376\pi\) | |||||||
\(588\) | −0.329890 | −0.0136044 | ||||||||
\(589\) | 44.3235 | 1.82632 | ||||||||
\(590\) | −0.589028 | −0.0242499 | ||||||||
\(591\) | 20.1924 | 0.830605 | ||||||||
\(592\) | −3.32482 | −0.136649 | ||||||||
\(593\) | −5.61928 | −0.230756 | −0.115378 | − | 0.993322i | \(-0.536808\pi\) | ||||
−0.115378 | + | 0.993322i | \(0.536808\pi\) | |||||||
\(594\) | 44.1629 | 1.81203 | ||||||||
\(595\) | 1.54671 | 0.0634091 | ||||||||
\(596\) | 1.59813 | 0.0654621 | ||||||||
\(597\) | −82.7853 | −3.38818 | ||||||||
\(598\) | 8.77081 | 0.358665 | ||||||||
\(599\) | −20.7347 | −0.847196 | −0.423598 | − | 0.905850i | \(-0.639233\pi\) | ||||
−0.423598 | + | 0.905850i | \(0.639233\pi\) | |||||||
\(600\) | −14.6493 | −0.598054 | ||||||||
\(601\) | 27.7369 | 1.13141 | 0.565706 | − | 0.824607i | \(-0.308604\pi\) | ||||
0.565706 | + | 0.824607i | \(0.308604\pi\) | |||||||
\(602\) | 24.3072 | 0.990689 | ||||||||
\(603\) | −68.4964 | −2.78939 | ||||||||
\(604\) | −0.621394 | −0.0252842 | ||||||||
\(605\) | 1.09461 | 0.0445022 | ||||||||
\(606\) | 20.4138 | 0.829256 | ||||||||
\(607\) | 22.2879 | 0.904636 | 0.452318 | − | 0.891857i | \(-0.350597\pi\) | ||||
0.452318 | + | 0.891857i | \(0.350597\pi\) | |||||||
\(608\) | 8.15303 | 0.330649 | ||||||||
\(609\) | −44.8307 | −1.81663 | ||||||||
\(610\) | −2.30240 | −0.0932214 | ||||||||
\(611\) | 47.0622 | 1.90393 | ||||||||
\(612\) | −6.91190 | −0.279397 | ||||||||
\(613\) | −14.5885 | −0.589224 | −0.294612 | − | 0.955617i | \(-0.595190\pi\) | ||||
−0.294612 | + | 0.955617i | \(0.595190\pi\) | |||||||
\(614\) | 26.3123 | 1.06188 | ||||||||
\(615\) | 18.0800 | 0.729054 | ||||||||
\(616\) | −9.41600 | −0.379381 | ||||||||
\(617\) | −39.1794 | −1.57731 | −0.788653 | − | 0.614839i | \(-0.789221\pi\) | ||||
−0.788653 | + | 0.614839i | \(0.789221\pi\) | |||||||
\(618\) | −37.8186 | −1.52129 | ||||||||
\(619\) | 0.0685856 | 0.00275669 | 0.00137834 | − | 0.999999i | \(-0.499561\pi\) | ||||
0.00137834 | + | 0.999999i | \(0.499561\pi\) | |||||||
\(620\) | 3.20222 | 0.128604 | ||||||||
\(621\) | −22.0432 | −0.884561 | ||||||||
\(622\) | −1.11665 | −0.0447737 | ||||||||
\(623\) | 30.6802 | 1.22917 | ||||||||
\(624\) | −15.4280 | −0.617615 | ||||||||
\(625\) | 19.9161 | 0.796643 | ||||||||
\(626\) | 2.15112 | 0.0859760 | ||||||||
\(627\) | 92.0428 | 3.67584 | ||||||||
\(628\) | −0.0424167 | −0.00169261 | ||||||||
\(629\) | 3.32482 | 0.132569 | ||||||||
\(630\) | −10.6907 | −0.425929 | ||||||||
\(631\) | −3.07945 | −0.122591 | −0.0612954 | − | 0.998120i | \(-0.519523\pi\) | ||||
−0.0612954 | + | 0.998120i | \(0.519523\pi\) | |||||||
\(632\) | −1.62676 | −0.0647090 | ||||||||
\(633\) | 69.2555 | 2.75266 | ||||||||
\(634\) | −2.80446 | −0.111379 | ||||||||
\(635\) | 0.517740 | 0.0205459 | ||||||||
\(636\) | 34.4630 | 1.36655 | ||||||||
\(637\) | 0.513479 | 0.0203448 | ||||||||
\(638\) | 19.4453 | 0.769848 | ||||||||
\(639\) | −62.5605 | −2.47486 | ||||||||
\(640\) | 0.589028 | 0.0232834 | ||||||||
\(641\) | −41.4532 | −1.63730 | −0.818651 | − | 0.574292i | \(-0.805277\pi\) | ||||
−0.818651 | + | 0.574292i | \(0.805277\pi\) | |||||||
\(642\) | −1.48728 | −0.0586983 | ||||||||
\(643\) | 22.6981 | 0.895128 | 0.447564 | − | 0.894252i | \(-0.352292\pi\) | ||||
0.447564 | + | 0.894252i | \(0.352292\pi\) | |||||||
\(644\) | 4.69983 | 0.185199 | ||||||||
\(645\) | −17.1663 | −0.675921 | ||||||||
\(646\) | −8.15303 | −0.320777 | ||||||||
\(647\) | 41.2330 | 1.62104 | 0.810519 | − | 0.585713i | \(-0.199185\pi\) | ||||
0.810519 | + | 0.585713i | \(0.199185\pi\) | |||||||
\(648\) | 18.0386 | 0.708624 | ||||||||
\(649\) | −3.58585 | −0.140757 | ||||||||
\(650\) | 22.8018 | 0.894360 | ||||||||
\(651\) | −44.9436 | −1.76148 | ||||||||
\(652\) | 7.66429 | 0.300157 | ||||||||
\(653\) | −15.7894 | −0.617888 | −0.308944 | − | 0.951080i | \(-0.599976\pi\) | ||||
−0.308944 | + | 0.951080i | \(0.599976\pi\) | |||||||
\(654\) | 1.95319 | 0.0763756 | ||||||||
\(655\) | 2.91870 | 0.114043 | ||||||||
\(656\) | 9.74951 | 0.380655 | ||||||||
\(657\) | −32.8991 | −1.28351 | ||||||||
\(658\) | 25.2182 | 0.983108 | ||||||||
\(659\) | −46.1195 | −1.79656 | −0.898280 | − | 0.439424i | \(-0.855183\pi\) | ||||
−0.898280 | + | 0.439424i | \(0.855183\pi\) | |||||||
\(660\) | 6.64977 | 0.258842 | ||||||||
\(661\) | 11.9859 | 0.466198 | 0.233099 | − | 0.972453i | \(-0.425113\pi\) | ||||
0.233099 | + | 0.972453i | \(0.425113\pi\) | |||||||
\(662\) | 9.32074 | 0.362261 | ||||||||
\(663\) | 15.4280 | 0.599174 | ||||||||
\(664\) | 1.59084 | 0.0617366 | ||||||||
\(665\) | −12.6104 | −0.489011 | ||||||||
\(666\) | −22.9808 | −0.890488 | ||||||||
\(667\) | −9.70580 | −0.375810 | ||||||||
\(668\) | −11.4214 | −0.441907 | ||||||||
\(669\) | −29.3701 | −1.13551 | ||||||||
\(670\) | −5.83722 | −0.225512 | ||||||||
\(671\) | −14.0164 | −0.541098 | ||||||||
\(672\) | −8.26708 | −0.318910 | ||||||||
\(673\) | 36.7056 | 1.41490 | 0.707448 | − | 0.706765i | \(-0.249846\pi\) | ||||
0.707448 | + | 0.706765i | \(0.249846\pi\) | |||||||
\(674\) | −36.1661 | −1.39307 | ||||||||
\(675\) | −57.3064 | −2.20572 | ||||||||
\(676\) | 11.0139 | 0.423612 | ||||||||
\(677\) | 7.22593 | 0.277715 | 0.138858 | − | 0.990312i | \(-0.455657\pi\) | ||||
0.138858 | + | 0.990312i | \(0.455657\pi\) | |||||||
\(678\) | −5.57100 | −0.213953 | ||||||||
\(679\) | −11.0167 | −0.422781 | ||||||||
\(680\) | −0.589028 | −0.0225882 | ||||||||
\(681\) | 84.4254 | 3.23519 | ||||||||
\(682\) | 19.4943 | 0.746475 | ||||||||
\(683\) | 44.6159 | 1.70718 | 0.853590 | − | 0.520945i | \(-0.174420\pi\) | ||||
0.853590 | + | 0.520945i | \(0.174420\pi\) | |||||||
\(684\) | 56.3529 | 2.15471 | ||||||||
\(685\) | 7.07767 | 0.270424 | ||||||||
\(686\) | 18.6563 | 0.712300 | ||||||||
\(687\) | −72.6696 | −2.77252 | ||||||||
\(688\) | −9.25681 | −0.352913 | ||||||||
\(689\) | −53.6421 | −2.04360 | ||||||||
\(690\) | −3.31911 | −0.126357 | ||||||||
\(691\) | 12.6916 | 0.482813 | 0.241407 | − | 0.970424i | \(-0.422391\pi\) | ||||
0.241407 | + | 0.970424i | \(0.422391\pi\) | |||||||
\(692\) | −9.80512 | −0.372735 | ||||||||
\(693\) | −65.0824 | −2.47228 | ||||||||
\(694\) | −33.3397 | −1.26556 | ||||||||
\(695\) | −6.91286 | −0.262220 | ||||||||
\(696\) | 17.0727 | 0.647138 | ||||||||
\(697\) | −9.74951 | −0.369289 | ||||||||
\(698\) | 30.2492 | 1.14495 | ||||||||
\(699\) | 29.5498 | 1.11768 | ||||||||
\(700\) | 12.2183 | 0.461809 | ||||||||
\(701\) | 19.8428 | 0.749453 | 0.374726 | − | 0.927135i | \(-0.377737\pi\) | ||||
0.374726 | + | 0.927135i | \(0.377737\pi\) | |||||||
\(702\) | −60.3528 | −2.27787 | ||||||||
\(703\) | −27.1074 | −1.02237 | ||||||||
\(704\) | 3.58585 | 0.135147 | ||||||||
\(705\) | −17.8096 | −0.670749 | ||||||||
\(706\) | −8.70630 | −0.327666 | ||||||||
\(707\) | −17.0263 | −0.640340 | ||||||||
\(708\) | −3.14832 | −0.118321 | ||||||||
\(709\) | −34.6184 | −1.30012 | −0.650061 | − | 0.759882i | \(-0.725257\pi\) | ||||
−0.650061 | + | 0.759882i | \(0.725257\pi\) | |||||||
\(710\) | −5.33137 | −0.200083 | ||||||||
\(711\) | −11.2440 | −0.421683 | ||||||||
\(712\) | −11.6838 | −0.437868 | ||||||||
\(713\) | −9.73023 | −0.364400 | ||||||||
\(714\) | 8.26708 | 0.309388 | ||||||||
\(715\) | −10.3505 | −0.387085 | ||||||||
\(716\) | −8.42530 | −0.314868 | ||||||||
\(717\) | −31.7009 | −1.18389 | ||||||||
\(718\) | 20.6559 | 0.770870 | ||||||||
\(719\) | 22.8201 | 0.851046 | 0.425523 | − | 0.904948i | \(-0.360090\pi\) | ||||
0.425523 | + | 0.904948i | \(0.360090\pi\) | |||||||
\(720\) | 4.07130 | 0.151728 | ||||||||
\(721\) | 31.5428 | 1.17472 | ||||||||
\(722\) | 47.4720 | 1.76672 | ||||||||
\(723\) | 6.70981 | 0.249540 | ||||||||
\(724\) | −8.07166 | −0.299981 | ||||||||
\(725\) | −25.2325 | −0.937112 | ||||||||
\(726\) | 5.85061 | 0.217137 | ||||||||
\(727\) | −16.8020 | −0.623150 | −0.311575 | − | 0.950221i | \(-0.600857\pi\) | ||||
−0.311575 | + | 0.950221i | \(0.600857\pi\) | |||||||
\(728\) | 12.8678 | 0.476914 | ||||||||
\(729\) | 8.35812 | 0.309560 | ||||||||
\(730\) | −2.80364 | −0.103767 | ||||||||
\(731\) | 9.25681 | 0.342376 | ||||||||
\(732\) | −12.3062 | −0.454849 | ||||||||
\(733\) | −15.7741 | −0.582629 | −0.291314 | − | 0.956627i | \(-0.594093\pi\) | ||||
−0.291314 | + | 0.956627i | \(0.594093\pi\) | |||||||
\(734\) | −32.7200 | −1.20772 | ||||||||
\(735\) | −0.194315 | −0.00716740 | ||||||||
\(736\) | −1.78981 | −0.0659734 | ||||||||
\(737\) | −35.5355 | −1.30897 | ||||||||
\(738\) | 67.3876 | 2.48057 | ||||||||
\(739\) | 0.450468 | 0.0165707 | 0.00828537 | − | 0.999966i | \(-0.497363\pi\) | ||||
0.00828537 | + | 0.999966i | \(0.497363\pi\) | |||||||
\(740\) | −1.95841 | −0.0719926 | ||||||||
\(741\) | −125.785 | −4.62083 | ||||||||
\(742\) | −28.7441 | −1.05523 | ||||||||
\(743\) | 6.69559 | 0.245637 | 0.122819 | − | 0.992429i | \(-0.460807\pi\) | ||||
0.122819 | + | 0.992429i | \(0.460807\pi\) | |||||||
\(744\) | 17.1157 | 0.627490 | ||||||||
\(745\) | 0.941346 | 0.0344882 | ||||||||
\(746\) | 5.93052 | 0.217132 | ||||||||
\(747\) | 10.9957 | 0.402313 | ||||||||
\(748\) | −3.58585 | −0.131112 | ||||||||
\(749\) | 1.24048 | 0.0453260 | ||||||||
\(750\) | −17.9011 | −0.653654 | ||||||||
\(751\) | −20.3601 | −0.742952 | −0.371476 | − | 0.928443i | \(-0.621148\pi\) | ||||
−0.371476 | + | 0.928443i | \(0.621148\pi\) | |||||||
\(752\) | −9.60374 | −0.350212 | ||||||||
\(753\) | −4.88150 | −0.177892 | ||||||||
\(754\) | −26.5739 | −0.967763 | ||||||||
\(755\) | −0.366019 | −0.0133208 | ||||||||
\(756\) | −32.3400 | −1.17619 | ||||||||
\(757\) | 37.5495 | 1.36476 | 0.682380 | − | 0.730998i | \(-0.260945\pi\) | ||||
0.682380 | + | 0.730998i | \(0.260945\pi\) | |||||||
\(758\) | 34.6780 | 1.25956 | ||||||||
\(759\) | −20.2059 | −0.733429 | ||||||||
\(760\) | 4.80236 | 0.174200 | ||||||||
\(761\) | −45.8112 | −1.66066 | −0.830328 | − | 0.557275i | \(-0.811847\pi\) | ||||
−0.830328 | + | 0.557275i | \(0.811847\pi\) | |||||||
\(762\) | 2.76729 | 0.100248 | ||||||||
\(763\) | −1.62907 | −0.0589762 | ||||||||
\(764\) | 14.7346 | 0.533080 | ||||||||
\(765\) | −4.07130 | −0.147198 | ||||||||
\(766\) | 32.2031 | 1.16355 | ||||||||
\(767\) | 4.90040 | 0.176943 | ||||||||
\(768\) | 3.14832 | 0.113605 | ||||||||
\(769\) | −9.61553 | −0.346745 | −0.173372 | − | 0.984856i | \(-0.555466\pi\) | ||||
−0.173372 | + | 0.984856i | \(0.555466\pi\) | |||||||
\(770\) | −5.54628 | −0.199874 | ||||||||
\(771\) | 92.5125 | 3.33176 | ||||||||
\(772\) | −25.2110 | −0.907363 | ||||||||
\(773\) | 32.2908 | 1.16142 | 0.580709 | − | 0.814111i | \(-0.302775\pi\) | ||||
0.580709 | + | 0.814111i | \(0.302775\pi\) | |||||||
\(774\) | −63.9821 | −2.29979 | ||||||||
\(775\) | −25.2960 | −0.908661 | ||||||||
\(776\) | 4.19543 | 0.150607 | ||||||||
\(777\) | 27.4866 | 0.986075 | ||||||||
\(778\) | 4.87596 | 0.174812 | ||||||||
\(779\) | 79.4881 | 2.84796 | ||||||||
\(780\) | −9.08753 | −0.325386 | ||||||||
\(781\) | −32.4560 | −1.16137 | ||||||||
\(782\) | 1.78981 | 0.0640036 | ||||||||
\(783\) | 66.7865 | 2.38676 | ||||||||
\(784\) | −0.104783 | −0.00374225 | ||||||||
\(785\) | −0.0249846 | −0.000891738 0 | ||||||||
\(786\) | 15.6003 | 0.556443 | ||||||||
\(787\) | 23.2881 | 0.830130 | 0.415065 | − | 0.909792i | \(-0.363759\pi\) | ||||
0.415065 | + | 0.909792i | \(0.363759\pi\) | |||||||
\(788\) | 6.41372 | 0.228479 | ||||||||
\(789\) | 31.6879 | 1.12812 | ||||||||
\(790\) | −0.958207 | −0.0340915 | ||||||||
\(791\) | 4.64653 | 0.165212 | ||||||||
\(792\) | 24.7850 | 0.880698 | ||||||||
\(793\) | 19.1547 | 0.680205 | ||||||||
\(794\) | 8.60978 | 0.305550 | ||||||||
\(795\) | 20.2996 | 0.719954 | ||||||||
\(796\) | −26.2951 | −0.932005 | ||||||||
\(797\) | 54.0863 | 1.91583 | 0.957917 | − | 0.287044i | \(-0.0926727\pi\) | ||||
0.957917 | + | 0.287044i | \(0.0926727\pi\) | |||||||
\(798\) | −67.4018 | −2.38600 | ||||||||
\(799\) | 9.60374 | 0.339756 | ||||||||
\(800\) | −4.65305 | −0.164510 | ||||||||
\(801\) | −80.7571 | −2.85341 | ||||||||
\(802\) | 18.7279 | 0.661306 | ||||||||
\(803\) | −17.0678 | −0.602311 | ||||||||
\(804\) | −31.1996 | −1.10032 | ||||||||
\(805\) | 2.76833 | 0.0975708 | ||||||||
\(806\) | −26.6408 | −0.938381 | ||||||||
\(807\) | 21.2100 | 0.746628 | ||||||||
\(808\) | 6.48405 | 0.228108 | ||||||||
\(809\) | 33.6627 | 1.18352 | 0.591758 | − | 0.806116i | \(-0.298434\pi\) | ||||
0.591758 | + | 0.806116i | \(0.298434\pi\) | |||||||
\(810\) | 10.6252 | 0.373333 | ||||||||
\(811\) | −3.20530 | −0.112553 | −0.0562766 | − | 0.998415i | \(-0.517923\pi\) | ||||
−0.0562766 | + | 0.998415i | \(0.517923\pi\) | |||||||
\(812\) | −14.2396 | −0.499711 | ||||||||
\(813\) | 61.7097 | 2.16425 | ||||||||
\(814\) | −11.9223 | −0.417877 | ||||||||
\(815\) | 4.51448 | 0.158135 | ||||||||
\(816\) | −3.14832 | −0.110213 | ||||||||
\(817\) | −75.4711 | −2.64040 | ||||||||
\(818\) | −12.9012 | −0.451078 | ||||||||
\(819\) | 88.9411 | 3.10785 | ||||||||
\(820\) | 5.74274 | 0.200545 | ||||||||
\(821\) | 10.6513 | 0.371733 | 0.185866 | − | 0.982575i | \(-0.440491\pi\) | ||||
0.185866 | + | 0.982575i | \(0.440491\pi\) | |||||||
\(822\) | 37.8297 | 1.31946 | ||||||||
\(823\) | −23.2965 | −0.812066 | −0.406033 | − | 0.913858i | \(-0.633088\pi\) | ||||
−0.406033 | + | 0.913858i | \(0.633088\pi\) | |||||||
\(824\) | −12.0123 | −0.418469 | ||||||||
\(825\) | −52.5301 | −1.82886 | ||||||||
\(826\) | 2.62587 | 0.0913659 | ||||||||
\(827\) | −38.3685 | −1.33420 | −0.667101 | − | 0.744967i | \(-0.732465\pi\) | ||||
−0.667101 | + | 0.744967i | \(0.732465\pi\) | |||||||
\(828\) | −12.3710 | −0.429922 | ||||||||
\(829\) | 43.1479 | 1.49859 | 0.749294 | − | 0.662237i | \(-0.230393\pi\) | ||||
0.749294 | + | 0.662237i | \(0.230393\pi\) | |||||||
\(830\) | 0.937050 | 0.0325255 | ||||||||
\(831\) | 71.4445 | 2.47838 | ||||||||
\(832\) | −4.90040 | −0.169891 | ||||||||
\(833\) | 0.104783 | 0.00363052 | ||||||||
\(834\) | −36.9488 | −1.27943 | ||||||||
\(835\) | −6.72752 | −0.232815 | ||||||||
\(836\) | 29.2356 | 1.01113 | ||||||||
\(837\) | 66.9547 | 2.31429 | ||||||||
\(838\) | 13.2122 | 0.456408 | ||||||||
\(839\) | −3.05301 | −0.105402 | −0.0527008 | − | 0.998610i | \(-0.516783\pi\) | ||||
−0.0527008 | + | 0.998610i | \(0.516783\pi\) | |||||||
\(840\) | −4.86954 | −0.168015 | ||||||||
\(841\) | 0.406722 | 0.0140249 | ||||||||
\(842\) | 7.23797 | 0.249437 | ||||||||
\(843\) | 7.50605 | 0.258522 | ||||||||
\(844\) | 21.9976 | 0.757190 | ||||||||
\(845\) | 6.48750 | 0.223177 | ||||||||
\(846\) | −66.3800 | −2.28219 | ||||||||
\(847\) | −4.87974 | −0.167670 | ||||||||
\(848\) | 10.9465 | 0.375903 | ||||||||
\(849\) | 93.1394 | 3.19654 | ||||||||
\(850\) | 4.65305 | 0.159598 | ||||||||
\(851\) | 5.95081 | 0.203991 | ||||||||
\(852\) | −28.4958 | −0.976252 | ||||||||
\(853\) | 19.7483 | 0.676167 | 0.338084 | − | 0.941116i | \(-0.390221\pi\) | ||||
0.338084 | + | 0.941116i | \(0.390221\pi\) | |||||||
\(854\) | 10.2641 | 0.351229 | ||||||||
\(855\) | 33.1934 | 1.13519 | ||||||||
\(856\) | −0.472405 | −0.0161465 | ||||||||
\(857\) | −22.1097 | −0.755253 | −0.377626 | − | 0.925958i | \(-0.623260\pi\) | ||||
−0.377626 | + | 0.925958i | \(0.623260\pi\) | |||||||
\(858\) | −55.3225 | −1.88868 | ||||||||
\(859\) | −14.6412 | −0.499551 | −0.249775 | − | 0.968304i | \(-0.580357\pi\) | ||||
−0.249775 | + | 0.968304i | \(0.580357\pi\) | |||||||
\(860\) | −5.45252 | −0.185929 | ||||||||
\(861\) | −80.6001 | −2.74684 | ||||||||
\(862\) | −30.9120 | −1.05287 | ||||||||
\(863\) | −6.48574 | −0.220777 | −0.110389 | − | 0.993889i | \(-0.535210\pi\) | ||||
−0.110389 | + | 0.993889i | \(0.535210\pi\) | |||||||
\(864\) | 12.3159 | 0.418995 | ||||||||
\(865\) | −5.77549 | −0.196372 | ||||||||
\(866\) | −29.4556 | −1.00094 | ||||||||
\(867\) | 3.14832 | 0.106922 | ||||||||
\(868\) | −14.2754 | −0.484540 | ||||||||
\(869\) | −5.83332 | −0.197882 | ||||||||
\(870\) | 10.0563 | 0.340940 | ||||||||
\(871\) | 48.5626 | 1.64548 | ||||||||
\(872\) | 0.620390 | 0.0210091 | ||||||||
\(873\) | 28.9984 | 0.981447 | ||||||||
\(874\) | −14.5924 | −0.493596 | ||||||||
\(875\) | 14.9305 | 0.504743 | ||||||||
\(876\) | −14.9853 | −0.506305 | ||||||||
\(877\) | −14.4030 | −0.486356 | −0.243178 | − | 0.969982i | \(-0.578190\pi\) | ||||
−0.243178 | + | 0.969982i | \(0.578190\pi\) | |||||||
\(878\) | 5.57890 | 0.188279 | ||||||||
\(879\) | −27.3976 | −0.924099 | ||||||||
\(880\) | 2.11217 | 0.0712011 | ||||||||
\(881\) | −39.5663 | −1.33302 | −0.666512 | − | 0.745495i | \(-0.732213\pi\) | ||||
−0.666512 | + | 0.745495i | \(0.732213\pi\) | |||||||
\(882\) | −0.724250 | −0.0243868 | ||||||||
\(883\) | 3.34992 | 0.112734 | 0.0563670 | − | 0.998410i | \(-0.482048\pi\) | ||||
0.0563670 | + | 0.998410i | \(0.482048\pi\) | |||||||
\(884\) | 4.90040 | 0.164818 | ||||||||
\(885\) | −1.85445 | −0.0623365 | ||||||||
\(886\) | 15.9821 | 0.536930 | ||||||||
\(887\) | −54.5587 | −1.83190 | −0.915951 | − | 0.401290i | \(-0.868562\pi\) | ||||
−0.915951 | + | 0.401290i | \(0.868562\pi\) | |||||||
\(888\) | −10.4676 | −0.351269 | ||||||||
\(889\) | −2.30807 | −0.0774103 | ||||||||
\(890\) | −6.88208 | −0.230688 | ||||||||
\(891\) | 64.6838 | 2.16699 | ||||||||
\(892\) | −9.32882 | −0.312352 | ||||||||
\(893\) | −78.2996 | −2.62020 | ||||||||
\(894\) | 5.03143 | 0.168276 | ||||||||
\(895\) | −4.96274 | −0.165886 | ||||||||
\(896\) | −2.62587 | −0.0877243 | ||||||||
\(897\) | 27.6133 | 0.921980 | ||||||||
\(898\) | −13.9942 | −0.466994 | ||||||||
\(899\) | 29.4807 | 0.983238 | ||||||||
\(900\) | −32.1614 | −1.07205 | ||||||||
\(901\) | −10.9465 | −0.364680 | ||||||||
\(902\) | 34.9603 | 1.16405 | ||||||||
\(903\) | 76.5268 | 2.54665 | ||||||||
\(904\) | −1.76952 | −0.0588533 | ||||||||
\(905\) | −4.75443 | −0.158043 | ||||||||
\(906\) | −1.95635 | −0.0649952 | ||||||||
\(907\) | 0.825674 | 0.0274160 | 0.0137080 | − | 0.999906i | \(-0.495636\pi\) | ||||
0.0137080 | + | 0.999906i | \(0.495636\pi\) | |||||||
\(908\) | 26.8160 | 0.889922 | ||||||||
\(909\) | 44.8171 | 1.48649 | ||||||||
\(910\) | 7.57951 | 0.251258 | ||||||||
\(911\) | −22.3106 | −0.739183 | −0.369591 | − | 0.929194i | \(-0.620502\pi\) | ||||
−0.369591 | + | 0.929194i | \(0.620502\pi\) | |||||||
\(912\) | 25.6683 | 0.849963 | ||||||||
\(913\) | 5.70452 | 0.188792 | ||||||||
\(914\) | −21.1888 | −0.700863 | ||||||||
\(915\) | −7.24868 | −0.239634 | ||||||||
\(916\) | −23.0821 | −0.762653 | ||||||||
\(917\) | −13.0115 | −0.429678 | ||||||||
\(918\) | −12.3159 | −0.406485 | ||||||||
\(919\) | −1.38141 | −0.0455684 | −0.0227842 | − | 0.999740i | \(-0.507253\pi\) | ||||
−0.0227842 | + | 0.999740i | \(0.507253\pi\) | |||||||
\(920\) | −1.05425 | −0.0347576 | ||||||||
\(921\) | 82.8394 | 2.72965 | ||||||||
\(922\) | −20.9031 | −0.688406 | ||||||||
\(923\) | 44.3542 | 1.45994 | ||||||||
\(924\) | −29.6445 | −0.975234 | ||||||||
\(925\) | 15.4705 | 0.508668 | ||||||||
\(926\) | 40.6488 | 1.33580 | ||||||||
\(927\) | −83.0279 | −2.72699 | ||||||||
\(928\) | 5.42280 | 0.178012 | ||||||||
\(929\) | −2.61999 | −0.0859590 | −0.0429795 | − | 0.999076i | \(-0.513685\pi\) | ||||
−0.0429795 | + | 0.999076i | \(0.513685\pi\) | |||||||
\(930\) | 10.0816 | 0.330589 | ||||||||
\(931\) | −0.854300 | −0.0279985 | ||||||||
\(932\) | 9.38591 | 0.307446 | ||||||||
\(933\) | −3.51558 | −0.115095 | ||||||||
\(934\) | −16.6371 | −0.544381 | ||||||||
\(935\) | −2.11217 | −0.0690752 | ||||||||
\(936\) | −33.8710 | −1.10711 | ||||||||
\(937\) | 13.0633 | 0.426759 | 0.213380 | − | 0.976969i | \(-0.431553\pi\) | ||||
0.213380 | + | 0.976969i | \(0.431553\pi\) | |||||||
\(938\) | 26.0222 | 0.849655 | ||||||||
\(939\) | 6.77240 | 0.221009 | ||||||||
\(940\) | −5.65687 | −0.184507 | ||||||||
\(941\) | 33.5340 | 1.09318 | 0.546589 | − | 0.837401i | \(-0.315926\pi\) | ||||
0.546589 | + | 0.837401i | \(0.315926\pi\) | |||||||
\(942\) | −0.133541 | −0.00435100 | ||||||||
\(943\) | −17.4498 | −0.568244 | ||||||||
\(944\) | −1.00000 | −0.0325472 | ||||||||
\(945\) | −19.0491 | −0.619669 | ||||||||
\(946\) | −33.1936 | −1.07922 | ||||||||
\(947\) | 40.5897 | 1.31899 | 0.659494 | − | 0.751710i | \(-0.270770\pi\) | ||||
0.659494 | + | 0.751710i | \(0.270770\pi\) | |||||||
\(948\) | −5.12155 | −0.166340 | ||||||||
\(949\) | 23.3248 | 0.757155 | ||||||||
\(950\) | −37.9364 | −1.23082 | ||||||||
\(951\) | −8.82934 | −0.286311 | ||||||||
\(952\) | 2.62587 | 0.0851051 | ||||||||
\(953\) | 30.2004 | 0.978286 | 0.489143 | − | 0.872204i | \(-0.337310\pi\) | ||||
0.489143 | + | 0.872204i | \(0.337310\pi\) | |||||||
\(954\) | 75.6609 | 2.44961 | ||||||||
\(955\) | 8.67910 | 0.280849 | ||||||||
\(956\) | −10.0692 | −0.325660 | ||||||||
\(957\) | 61.2201 | 1.97896 | ||||||||
\(958\) | 30.6239 | 0.989413 | ||||||||
\(959\) | −31.5521 | −1.01887 | ||||||||
\(960\) | 1.85445 | 0.0598520 | ||||||||
\(961\) | −1.44504 | −0.0466143 | ||||||||
\(962\) | 16.2929 | 0.525305 | ||||||||
\(963\) | −3.26521 | −0.105220 | ||||||||
\(964\) | 2.13124 | 0.0686425 | ||||||||
\(965\) | −14.8500 | −0.478037 | ||||||||
\(966\) | 14.7965 | 0.476071 | ||||||||
\(967\) | 31.7672 | 1.02157 | 0.510783 | − | 0.859710i | \(-0.329356\pi\) | ||||
0.510783 | + | 0.859710i | \(0.329356\pi\) | |||||||
\(968\) | 1.85833 | 0.0597290 | ||||||||
\(969\) | −25.6683 | −0.824585 | ||||||||
\(970\) | 2.47123 | 0.0793463 | ||||||||
\(971\) | 44.8009 | 1.43773 | 0.718865 | − | 0.695150i | \(-0.244662\pi\) | ||||
0.718865 | + | 0.695150i | \(0.244662\pi\) | |||||||
\(972\) | 19.8436 | 0.636484 | ||||||||
\(973\) | 30.8174 | 0.987961 | ||||||||
\(974\) | −37.4899 | −1.20126 | ||||||||
\(975\) | 71.7872 | 2.29903 | ||||||||
\(976\) | −3.90881 | −0.125118 | ||||||||
\(977\) | −28.5384 | −0.913023 | −0.456511 | − | 0.889718i | \(-0.650901\pi\) | ||||
−0.456511 | + | 0.889718i | \(0.650901\pi\) | |||||||
\(978\) | 24.1296 | 0.771580 | ||||||||
\(979\) | −41.8963 | −1.33901 | ||||||||
\(980\) | −0.0617202 | −0.00197158 | ||||||||
\(981\) | 4.28807 | 0.136908 | ||||||||
\(982\) | −25.1759 | −0.803396 | ||||||||
\(983\) | 3.29883 | 0.105216 | 0.0526082 | − | 0.998615i | \(-0.483247\pi\) | ||||
0.0526082 | + | 0.998615i | \(0.483247\pi\) | |||||||
\(984\) | 30.6946 | 0.978507 | ||||||||
\(985\) | 3.77786 | 0.120373 | ||||||||
\(986\) | −5.42280 | −0.172697 | ||||||||
\(987\) | 79.3949 | 2.52717 | ||||||||
\(988\) | −39.9531 | −1.27108 | ||||||||
\(989\) | 16.5680 | 0.526831 | ||||||||
\(990\) | 14.5991 | 0.463989 | ||||||||
\(991\) | −34.7089 | −1.10257 | −0.551283 | − | 0.834319i | \(-0.685861\pi\) | ||||
−0.551283 | + | 0.834319i | \(0.685861\pi\) | |||||||
\(992\) | 5.43645 | 0.172607 | ||||||||
\(993\) | 29.3447 | 0.931224 | ||||||||
\(994\) | 23.7672 | 0.753848 | ||||||||
\(995\) | −15.4885 | −0.491020 | ||||||||
\(996\) | 5.00847 | 0.158700 | ||||||||
\(997\) | 53.7657 | 1.70278 | 0.851389 | − | 0.524535i | \(-0.175761\pi\) | ||||
0.851389 | + | 0.524535i | \(0.175761\pi\) | |||||||
\(998\) | −13.5773 | −0.429783 | ||||||||
\(999\) | −40.9481 | −1.29554 |
(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 | 2006.2.a.t.1.7 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2006.2.a.t.1.7 | ✓ | 8 | 1.1 | even | 1 | trivial |