Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9075,2,Mod(1,9075)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9075, 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("9075.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9075 = 3 \cdot 5^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9075.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: | \(72.4642398343\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} - 10 x^{10} + 52 x^{9} + 18 x^{8} - 220 x^{7} + 61 x^{6} + 330 x^{5} - 145 x^{4} - 148 x^{3} + 71 x^{2} + 10 x - 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(0.488299\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9075.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.488299 | −0.345279 | −0.172640 | − | 0.984985i | \(-0.555230\pi\) | ||||
−0.172640 | + | 0.984985i | \(0.555230\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.76156 | −0.880782 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.488299 | −0.199347 | ||||||||
\(7\) | −5.10895 | −1.93100 | −0.965500 | − | 0.260403i | \(-0.916145\pi\) | ||||
−0.965500 | + | 0.260403i | \(0.916145\pi\) | |||||||
\(8\) | 1.83677 | 0.649395 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.76156 | −0.508520 | ||||||||
\(13\) | −1.81774 | −0.504150 | −0.252075 | − | 0.967708i | \(-0.581113\pi\) | ||||
−0.252075 | + | 0.967708i | \(0.581113\pi\) | |||||||
\(14\) | 2.49469 | 0.666735 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.62624 | 0.656559 | ||||||||
\(17\) | −0.639966 | −0.155214 | −0.0776072 | − | 0.996984i | \(-0.524728\pi\) | ||||
−0.0776072 | + | 0.996984i | \(0.524728\pi\) | |||||||
\(18\) | −0.488299 | −0.115093 | ||||||||
\(19\) | −4.39788 | −1.00894 | −0.504471 | − | 0.863429i | \(-0.668312\pi\) | ||||
−0.504471 | + | 0.863429i | \(0.668312\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.10895 | −1.11486 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.37977 | 0.913246 | 0.456623 | − | 0.889660i | \(-0.349059\pi\) | ||||
0.456623 | + | 0.889660i | \(0.349059\pi\) | |||||||
\(24\) | 1.83677 | 0.374929 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.887599 | 0.174073 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 8.99974 | 1.70079 | ||||||||
\(29\) | 7.56018 | 1.40389 | 0.701945 | − | 0.712231i | \(-0.252315\pi\) | ||||
0.701945 | + | 0.712231i | \(0.252315\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.20501 | 0.396032 | 0.198016 | − | 0.980199i | \(-0.436550\pi\) | ||||
0.198016 | + | 0.980199i | \(0.436550\pi\) | |||||||
\(32\) | −4.95592 | −0.876092 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.312494 | 0.0535924 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.76156 | −0.293594 | ||||||||
\(37\) | 5.97194 | 0.981780 | 0.490890 | − | 0.871221i | \(-0.336672\pi\) | ||||
0.490890 | + | 0.871221i | \(0.336672\pi\) | |||||||
\(38\) | 2.14748 | 0.348367 | ||||||||
\(39\) | −1.81774 | −0.291071 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.23182 | −0.348551 | −0.174276 | − | 0.984697i | \(-0.555758\pi\) | ||||
−0.174276 | + | 0.984697i | \(0.555758\pi\) | |||||||
\(42\) | 2.49469 | 0.384939 | ||||||||
\(43\) | −3.38068 | −0.515549 | −0.257775 | − | 0.966205i | \(-0.582989\pi\) | ||||
−0.257775 | + | 0.966205i | \(0.582989\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.13864 | −0.315325 | ||||||||
\(47\) | −1.51581 | −0.221103 | −0.110552 | − | 0.993870i | \(-0.535262\pi\) | ||||
−0.110552 | + | 0.993870i | \(0.535262\pi\) | |||||||
\(48\) | 2.62624 | 0.379065 | ||||||||
\(49\) | 19.1013 | 2.72876 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.639966 | −0.0896131 | ||||||||
\(52\) | 3.20206 | 0.444046 | ||||||||
\(53\) | −9.17695 | −1.26055 | −0.630275 | − | 0.776372i | \(-0.717058\pi\) | ||||
−0.630275 | + | 0.776372i | \(0.717058\pi\) | |||||||
\(54\) | −0.488299 | −0.0664491 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −9.38395 | −1.25398 | ||||||||
\(57\) | −4.39788 | −0.582513 | ||||||||
\(58\) | −3.69163 | −0.484734 | ||||||||
\(59\) | 5.37174 | 0.699341 | 0.349671 | − | 0.936873i | \(-0.386294\pi\) | ||||
0.349671 | + | 0.936873i | \(0.386294\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.26768 | 0.930531 | 0.465266 | − | 0.885171i | \(-0.345959\pi\) | ||||
0.465266 | + | 0.885171i | \(0.345959\pi\) | |||||||
\(62\) | −1.07670 | −0.136742 | ||||||||
\(63\) | −5.10895 | −0.643667 | ||||||||
\(64\) | −2.83250 | −0.354063 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.25598 | −0.886459 | −0.443230 | − | 0.896408i | \(-0.646167\pi\) | ||||
−0.443230 | + | 0.896408i | \(0.646167\pi\) | |||||||
\(68\) | 1.12734 | 0.136710 | ||||||||
\(69\) | 4.37977 | 0.527263 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.50864 | 0.653756 | 0.326878 | − | 0.945067i | \(-0.394003\pi\) | ||||
0.326878 | + | 0.945067i | \(0.394003\pi\) | |||||||
\(72\) | 1.83677 | 0.216465 | ||||||||
\(73\) | 7.14322 | 0.836051 | 0.418026 | − | 0.908435i | \(-0.362722\pi\) | ||||
0.418026 | + | 0.908435i | \(0.362722\pi\) | |||||||
\(74\) | −2.91609 | −0.338988 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.74714 | 0.888658 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.887599 | 0.100501 | ||||||||
\(79\) | 1.90516 | 0.214347 | 0.107174 | − | 0.994240i | \(-0.465820\pi\) | ||||
0.107174 | + | 0.994240i | \(0.465820\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.08979 | 0.120348 | ||||||||
\(83\) | −0.161902 | −0.0177710 | −0.00888551 | − | 0.999961i | \(-0.502828\pi\) | ||||
−0.00888551 | + | 0.999961i | \(0.502828\pi\) | |||||||
\(84\) | 8.99974 | 0.981952 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.65078 | 0.178009 | ||||||||
\(87\) | 7.56018 | 0.810536 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.19539 | −0.126711 | −0.0633554 | − | 0.997991i | \(-0.520180\pi\) | ||||
−0.0633554 | + | 0.997991i | \(0.520180\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.28673 | 0.973514 | ||||||||
\(92\) | −7.71525 | −0.804371 | ||||||||
\(93\) | 2.20501 | 0.228649 | ||||||||
\(94\) | 0.740167 | 0.0763424 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.95592 | −0.505812 | ||||||||
\(97\) | 14.2823 | 1.45015 | 0.725073 | − | 0.688672i | \(-0.241806\pi\) | ||||
0.725073 | + | 0.688672i | \(0.241806\pi\) | |||||||
\(98\) | −9.32716 | −0.942185 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.29089 | −0.426960 | −0.213480 | − | 0.976947i | \(-0.568480\pi\) | ||||
−0.213480 | + | 0.976947i | \(0.568480\pi\) | |||||||
\(102\) | 0.312494 | 0.0309416 | ||||||||
\(103\) | 9.49802 | 0.935868 | 0.467934 | − | 0.883763i | \(-0.344998\pi\) | ||||
0.467934 | + | 0.883763i | \(0.344998\pi\) | |||||||
\(104\) | −3.33876 | −0.327393 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.48109 | 0.435242 | ||||||||
\(107\) | 8.27470 | 0.799945 | 0.399973 | − | 0.916527i | \(-0.369020\pi\) | ||||
0.399973 | + | 0.916527i | \(0.369020\pi\) | |||||||
\(108\) | −1.76156 | −0.169507 | ||||||||
\(109\) | −12.4980 | −1.19709 | −0.598546 | − | 0.801089i | \(-0.704255\pi\) | ||||
−0.598546 | + | 0.801089i | \(0.704255\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.97194 | 0.566831 | ||||||||
\(112\) | −13.4173 | −1.26782 | ||||||||
\(113\) | −16.2096 | −1.52487 | −0.762435 | − | 0.647065i | \(-0.775996\pi\) | ||||
−0.762435 | + | 0.647065i | \(0.775996\pi\) | |||||||
\(114\) | 2.14748 | 0.201130 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −13.3177 | −1.23652 | ||||||||
\(117\) | −1.81774 | −0.168050 | ||||||||
\(118\) | −2.62302 | −0.241468 | ||||||||
\(119\) | 3.26955 | 0.299719 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −3.54880 | −0.321293 | ||||||||
\(123\) | −2.23182 | −0.201236 | ||||||||
\(124\) | −3.88427 | −0.348817 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.49469 | 0.222245 | ||||||||
\(127\) | 9.88086 | 0.876785 | 0.438392 | − | 0.898784i | \(-0.355548\pi\) | ||||
0.438392 | + | 0.898784i | \(0.355548\pi\) | |||||||
\(128\) | 11.2950 | 0.998342 | ||||||||
\(129\) | −3.38068 | −0.297653 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.7829 | −1.11685 | −0.558425 | − | 0.829555i | \(-0.688594\pi\) | ||||
−0.558425 | + | 0.829555i | \(0.688594\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 22.4685 | 1.94827 | ||||||||
\(134\) | 3.54309 | 0.306076 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.17547 | −0.100796 | ||||||||
\(137\) | −19.0589 | −1.62831 | −0.814157 | − | 0.580645i | \(-0.802800\pi\) | ||||
−0.814157 | + | 0.580645i | \(0.802800\pi\) | |||||||
\(138\) | −2.13864 | −0.182053 | ||||||||
\(139\) | −11.7146 | −0.993622 | −0.496811 | − | 0.867859i | \(-0.665496\pi\) | ||||
−0.496811 | + | 0.867859i | \(0.665496\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.51581 | −0.127654 | ||||||||
\(142\) | −2.68986 | −0.225728 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.62624 | 0.218853 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.48803 | −0.288671 | ||||||||
\(147\) | 19.1013 | 1.57545 | ||||||||
\(148\) | −10.5199 | −0.864735 | ||||||||
\(149\) | 7.45724 | 0.610921 | 0.305461 | − | 0.952205i | \(-0.401190\pi\) | ||||
0.305461 | + | 0.952205i | \(0.401190\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.95905 | −0.403562 | −0.201781 | − | 0.979431i | \(-0.564673\pi\) | ||||
−0.201781 | + | 0.979431i | \(0.564673\pi\) | |||||||
\(152\) | −8.07787 | −0.655202 | ||||||||
\(153\) | −0.639966 | −0.0517382 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.20206 | 0.256370 | ||||||||
\(157\) | −20.5916 | −1.64339 | −0.821693 | − | 0.569930i | \(-0.806970\pi\) | ||||
−0.821693 | + | 0.569930i | \(0.806970\pi\) | |||||||
\(158\) | −0.930287 | −0.0740096 | ||||||||
\(159\) | −9.17695 | −0.727779 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −22.3760 | −1.76348 | ||||||||
\(162\) | −0.488299 | −0.0383644 | ||||||||
\(163\) | 7.22774 | 0.566120 | 0.283060 | − | 0.959102i | \(-0.408650\pi\) | ||||
0.283060 | + | 0.959102i | \(0.408650\pi\) | |||||||
\(164\) | 3.93149 | 0.306998 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.0790564 | 0.00613597 | ||||||||
\(167\) | 18.3130 | 1.41710 | 0.708550 | − | 0.705660i | \(-0.249349\pi\) | ||||
0.708550 | + | 0.705660i | \(0.249349\pi\) | |||||||
\(168\) | −9.38395 | −0.723987 | ||||||||
\(169\) | −9.69583 | −0.745833 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.39788 | −0.336314 | ||||||||
\(172\) | 5.95529 | 0.454087 | ||||||||
\(173\) | −12.0157 | −0.913536 | −0.456768 | − | 0.889586i | \(-0.650993\pi\) | ||||
−0.456768 | + | 0.889586i | \(0.650993\pi\) | |||||||
\(174\) | −3.69163 | −0.279862 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.37174 | 0.403765 | ||||||||
\(178\) | 0.583706 | 0.0437506 | ||||||||
\(179\) | −6.71004 | −0.501532 | −0.250766 | − | 0.968048i | \(-0.580682\pi\) | ||||
−0.250766 | + | 0.968048i | \(0.580682\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.3348 | −0.842508 | −0.421254 | − | 0.906943i | \(-0.638410\pi\) | ||||
−0.421254 | + | 0.906943i | \(0.638410\pi\) | |||||||
\(182\) | −4.53470 | −0.336134 | ||||||||
\(183\) | 7.26768 | 0.537242 | ||||||||
\(184\) | 8.04463 | 0.593058 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.07670 | −0.0789478 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 2.67019 | 0.194744 | ||||||||
\(189\) | −5.10895 | −0.371621 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.0864 | 0.802186 | 0.401093 | − | 0.916037i | \(-0.368630\pi\) | ||||
0.401093 | + | 0.916037i | \(0.368630\pi\) | |||||||
\(192\) | −2.83250 | −0.204418 | ||||||||
\(193\) | −1.19205 | −0.0858056 | −0.0429028 | − | 0.999079i | \(-0.513661\pi\) | ||||
−0.0429028 | + | 0.999079i | \(0.513661\pi\) | |||||||
\(194\) | −6.97402 | −0.500705 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −33.6482 | −2.40344 | ||||||||
\(197\) | −18.3551 | −1.30775 | −0.653873 | − | 0.756604i | \(-0.726857\pi\) | ||||
−0.653873 | + | 0.756604i | \(0.726857\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.1761 | 1.57202 | 0.786011 | − | 0.618213i | \(-0.212143\pi\) | ||||
0.786011 | + | 0.618213i | \(0.212143\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.25598 | −0.511798 | ||||||||
\(202\) | 2.09524 | 0.147420 | ||||||||
\(203\) | −38.6246 | −2.71091 | ||||||||
\(204\) | 1.12734 | 0.0789296 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.63787 | −0.323136 | ||||||||
\(207\) | 4.37977 | 0.304415 | ||||||||
\(208\) | −4.77381 | −0.331004 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.30729 | 0.571897 | 0.285949 | − | 0.958245i | \(-0.407691\pi\) | ||||
0.285949 | + | 0.958245i | \(0.407691\pi\) | |||||||
\(212\) | 16.1658 | 1.11027 | ||||||||
\(213\) | 5.50864 | 0.377446 | ||||||||
\(214\) | −4.04052 | −0.276205 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.83677 | 0.124976 | ||||||||
\(217\) | −11.2653 | −0.764737 | ||||||||
\(218\) | 6.10276 | 0.413331 | ||||||||
\(219\) | 7.14322 | 0.482694 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.16329 | 0.0782514 | ||||||||
\(222\) | −2.91609 | −0.195715 | ||||||||
\(223\) | 16.5497 | 1.10825 | 0.554124 | − | 0.832434i | \(-0.313053\pi\) | ||||
0.554124 | + | 0.832434i | \(0.313053\pi\) | |||||||
\(224\) | 25.3195 | 1.69173 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.91513 | 0.526506 | ||||||||
\(227\) | −8.48300 | −0.563036 | −0.281518 | − | 0.959556i | \(-0.590838\pi\) | ||||
−0.281518 | + | 0.959556i | \(0.590838\pi\) | |||||||
\(228\) | 7.74714 | 0.513067 | ||||||||
\(229\) | −3.39892 | −0.224607 | −0.112303 | − | 0.993674i | \(-0.535823\pi\) | ||||
−0.112303 | + | 0.993674i | \(0.535823\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 13.8863 | 0.911680 | ||||||||
\(233\) | −15.7123 | −1.02935 | −0.514675 | − | 0.857386i | \(-0.672087\pi\) | ||||
−0.514675 | + | 0.857386i | \(0.672087\pi\) | |||||||
\(234\) | 0.887599 | 0.0580242 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −9.46267 | −0.615967 | ||||||||
\(237\) | 1.90516 | 0.123753 | ||||||||
\(238\) | −1.59652 | −0.103487 | ||||||||
\(239\) | 30.6972 | 1.98564 | 0.992819 | − | 0.119624i | \(-0.0381689\pi\) | ||||
0.992819 | + | 0.119624i | \(0.0381689\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.59097 | 0.360146 | 0.180073 | − | 0.983653i | \(-0.442367\pi\) | ||||
0.180073 | + | 0.983653i | \(0.442367\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −12.8025 | −0.819595 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.08979 | 0.0694827 | ||||||||
\(247\) | 7.99419 | 0.508658 | ||||||||
\(248\) | 4.05009 | 0.257181 | ||||||||
\(249\) | −0.161902 | −0.0102601 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.7237 | 1.18183 | 0.590915 | − | 0.806734i | \(-0.298767\pi\) | ||||
0.590915 | + | 0.806734i | \(0.298767\pi\) | |||||||
\(252\) | 8.99974 | 0.566930 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −4.82481 | −0.302736 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.149694 | 0.00935585 | ||||||||
\(257\) | −4.98215 | −0.310778 | −0.155389 | − | 0.987853i | \(-0.549663\pi\) | ||||
−0.155389 | + | 0.987853i | \(0.549663\pi\) | |||||||
\(258\) | 1.65078 | 0.102773 | ||||||||
\(259\) | −30.5103 | −1.89582 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.56018 | 0.467963 | ||||||||
\(262\) | 6.24190 | 0.385626 | ||||||||
\(263\) | −20.0788 | −1.23811 | −0.619055 | − | 0.785347i | \(-0.712484\pi\) | ||||
−0.619055 | + | 0.785347i | \(0.712484\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −10.9713 | −0.672696 | ||||||||
\(267\) | −1.19539 | −0.0731565 | ||||||||
\(268\) | 12.7819 | 0.780778 | ||||||||
\(269\) | −9.53027 | −0.581071 | −0.290535 | − | 0.956864i | \(-0.593833\pi\) | ||||
−0.290535 | + | 0.956864i | \(0.593833\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.18095 | −0.0717375 | −0.0358688 | − | 0.999357i | \(-0.511420\pi\) | ||||
−0.0358688 | + | 0.999357i | \(0.511420\pi\) | |||||||
\(272\) | −1.68070 | −0.101908 | ||||||||
\(273\) | 9.28673 | 0.562058 | ||||||||
\(274\) | 9.30645 | 0.562223 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −7.71525 | −0.464404 | ||||||||
\(277\) | −8.22177 | −0.493998 | −0.246999 | − | 0.969016i | \(-0.579444\pi\) | ||||
−0.246999 | + | 0.969016i | \(0.579444\pi\) | |||||||
\(278\) | 5.72024 | 0.343077 | ||||||||
\(279\) | 2.20501 | 0.132011 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.4453 | 0.623116 | 0.311558 | − | 0.950227i | \(-0.399149\pi\) | ||||
0.311558 | + | 0.950227i | \(0.399149\pi\) | |||||||
\(282\) | 0.740167 | 0.0440763 | ||||||||
\(283\) | −24.8463 | −1.47696 | −0.738480 | − | 0.674275i | \(-0.764456\pi\) | ||||
−0.738480 | + | 0.674275i | \(0.764456\pi\) | |||||||
\(284\) | −9.70383 | −0.575816 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.4022 | 0.673052 | ||||||||
\(288\) | −4.95592 | −0.292031 | ||||||||
\(289\) | −16.5904 | −0.975908 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.2823 | 0.837242 | ||||||||
\(292\) | −12.5832 | −0.736379 | ||||||||
\(293\) | −24.8264 | −1.45037 | −0.725186 | − | 0.688553i | \(-0.758246\pi\) | ||||
−0.725186 | + | 0.688553i | \(0.758246\pi\) | |||||||
\(294\) | −9.32716 | −0.543971 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 10.9691 | 0.637563 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.64136 | −0.210939 | ||||||||
\(299\) | −7.96128 | −0.460413 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.2717 | 0.995526 | ||||||||
\(302\) | 2.42150 | 0.139342 | ||||||||
\(303\) | −4.29089 | −0.246505 | ||||||||
\(304\) | −11.5499 | −0.662430 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.312494 | 0.0178641 | ||||||||
\(307\) | −12.4687 | −0.711624 | −0.355812 | − | 0.934557i | \(-0.615796\pi\) | ||||
−0.355812 | + | 0.934557i | \(0.615796\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.49802 | 0.540324 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.15914 | −0.179138 | −0.0895692 | − | 0.995981i | \(-0.528549\pi\) | ||||
−0.0895692 | + | 0.995981i | \(0.528549\pi\) | |||||||
\(312\) | −3.33876 | −0.189020 | ||||||||
\(313\) | −14.2948 | −0.807988 | −0.403994 | − | 0.914762i | \(-0.632378\pi\) | ||||
−0.403994 | + | 0.914762i | \(0.632378\pi\) | |||||||
\(314\) | 10.0548 | 0.567427 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.35606 | −0.188793 | ||||||||
\(317\) | −26.8771 | −1.50957 | −0.754784 | − | 0.655974i | \(-0.772258\pi\) | ||||
−0.754784 | + | 0.655974i | \(0.772258\pi\) | |||||||
\(318\) | 4.48109 | 0.251287 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.27470 | 0.461849 | ||||||||
\(322\) | 10.9262 | 0.608893 | ||||||||
\(323\) | 2.81449 | 0.156602 | ||||||||
\(324\) | −1.76156 | −0.0978647 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.52930 | −0.195470 | ||||||||
\(327\) | −12.4980 | −0.691141 | ||||||||
\(328\) | −4.09933 | −0.226347 | ||||||||
\(329\) | 7.74418 | 0.426950 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.7763 | 1.08700 | 0.543502 | − | 0.839408i | \(-0.317098\pi\) | ||||
0.543502 | + | 0.839408i | \(0.317098\pi\) | |||||||
\(332\) | 0.285200 | 0.0156524 | ||||||||
\(333\) | 5.97194 | 0.327260 | ||||||||
\(334\) | −8.94221 | −0.489296 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −13.4173 | −0.731974 | ||||||||
\(337\) | 14.2580 | 0.776685 | 0.388343 | − | 0.921515i | \(-0.373048\pi\) | ||||
0.388343 | + | 0.921515i | \(0.373048\pi\) | |||||||
\(338\) | 4.73446 | 0.257521 | ||||||||
\(339\) | −16.2096 | −0.880384 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 2.14748 | 0.116122 | ||||||||
\(343\) | −61.8251 | −3.33824 | ||||||||
\(344\) | −6.20953 | −0.334795 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.86725 | 0.315425 | ||||||||
\(347\) | 15.7954 | 0.847940 | 0.423970 | − | 0.905676i | \(-0.360636\pi\) | ||||
0.423970 | + | 0.905676i | \(0.360636\pi\) | |||||||
\(348\) | −13.3177 | −0.713906 | ||||||||
\(349\) | 1.71442 | 0.0917705 | 0.0458853 | − | 0.998947i | \(-0.485389\pi\) | ||||
0.0458853 | + | 0.998947i | \(0.485389\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.81774 | −0.0970237 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.9610 | 0.743072 | 0.371536 | − | 0.928419i | \(-0.378831\pi\) | ||||
0.371536 | + | 0.928419i | \(0.378831\pi\) | |||||||
\(354\) | −2.62302 | −0.139412 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.10575 | 0.111605 | ||||||||
\(357\) | 3.26955 | 0.173043 | ||||||||
\(358\) | 3.27650 | 0.173169 | ||||||||
\(359\) | −34.3062 | −1.81061 | −0.905306 | − | 0.424759i | \(-0.860359\pi\) | ||||
−0.905306 | + | 0.424759i | \(0.860359\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.341312 | 0.0179638 | ||||||||
\(362\) | 5.53476 | 0.290901 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −16.3592 | −0.857453 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.54880 | −0.185499 | ||||||||
\(367\) | 3.61245 | 0.188569 | 0.0942843 | − | 0.995545i | \(-0.469944\pi\) | ||||
0.0942843 | + | 0.995545i | \(0.469944\pi\) | |||||||
\(368\) | 11.5023 | 0.599600 | ||||||||
\(369\) | −2.23182 | −0.116184 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 46.8845 | 2.43412 | ||||||||
\(372\) | −3.88427 | −0.201390 | ||||||||
\(373\) | −18.7064 | −0.968579 | −0.484290 | − | 0.874908i | \(-0.660922\pi\) | ||||
−0.484290 | + | 0.874908i | \(0.660922\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.78418 | −0.143583 | ||||||||
\(377\) | −13.7424 | −0.707771 | ||||||||
\(378\) | 2.49469 | 0.128313 | ||||||||
\(379\) | −9.37468 | −0.481545 | −0.240772 | − | 0.970582i | \(-0.577401\pi\) | ||||
−0.240772 | + | 0.970582i | \(0.577401\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.88086 | 0.506212 | ||||||||
\(382\) | −5.41349 | −0.276978 | ||||||||
\(383\) | −19.2155 | −0.981865 | −0.490932 | − | 0.871198i | \(-0.663344\pi\) | ||||
−0.490932 | + | 0.871198i | \(0.663344\pi\) | |||||||
\(384\) | 11.2950 | 0.576393 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.582076 | 0.0296269 | ||||||||
\(387\) | −3.38068 | −0.171850 | ||||||||
\(388\) | −25.1591 | −1.27726 | ||||||||
\(389\) | −9.29700 | −0.471376 | −0.235688 | − | 0.971829i | \(-0.575734\pi\) | ||||
−0.235688 | + | 0.971829i | \(0.575734\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.80290 | −0.141749 | ||||||||
\(392\) | 35.0847 | 1.77205 | ||||||||
\(393\) | −12.7829 | −0.644814 | ||||||||
\(394\) | 8.96277 | 0.451538 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.8693 | 0.696078 | 0.348039 | − | 0.937480i | \(-0.386848\pi\) | ||||
0.348039 | + | 0.937480i | \(0.386848\pi\) | |||||||
\(398\) | −10.8286 | −0.542787 | ||||||||
\(399\) | 22.4685 | 1.12483 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.6336 | 0.531015 | 0.265507 | − | 0.964109i | \(-0.414461\pi\) | ||||
0.265507 | + | 0.964109i | \(0.414461\pi\) | |||||||
\(402\) | 3.54309 | 0.176713 | ||||||||
\(403\) | −4.00813 | −0.199659 | ||||||||
\(404\) | 7.55868 | 0.376058 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 18.8603 | 0.936022 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −1.17547 | −0.0581943 | ||||||||
\(409\) | 3.71320 | 0.183606 | 0.0918030 | − | 0.995777i | \(-0.470737\pi\) | ||||
0.0918030 | + | 0.995777i | \(0.470737\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −19.0589 | −0.940107 | ||||||||
\(412\) | −16.7314 | −0.824296 | ||||||||
\(413\) | −27.4439 | −1.35043 | ||||||||
\(414\) | −2.13864 | −0.105108 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 9.00857 | 0.441682 | ||||||||
\(417\) | −11.7146 | −0.573668 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.8996 | −0.776745 | −0.388372 | − | 0.921503i | \(-0.626963\pi\) | ||||
−0.388372 | + | 0.921503i | \(0.626963\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.36664 | 0.212817 | 0.106408 | − | 0.994323i | \(-0.466065\pi\) | ||||
0.106408 | + | 0.994323i | \(0.466065\pi\) | |||||||
\(422\) | −4.05644 | −0.197464 | ||||||||
\(423\) | −1.51581 | −0.0737011 | ||||||||
\(424\) | −16.8559 | −0.818596 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2.68986 | −0.130324 | ||||||||
\(427\) | −37.1302 | −1.79686 | ||||||||
\(428\) | −14.5764 | −0.704577 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.1005 | 0.968209 | 0.484105 | − | 0.875010i | \(-0.339145\pi\) | ||||
0.484105 | + | 0.875010i | \(0.339145\pi\) | |||||||
\(432\) | 2.62624 | 0.126355 | ||||||||
\(433\) | −30.7232 | −1.47646 | −0.738230 | − | 0.674549i | \(-0.764338\pi\) | ||||
−0.738230 | + | 0.674549i | \(0.764338\pi\) | |||||||
\(434\) | 5.50082 | 0.264048 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 22.0160 | 1.05438 | ||||||||
\(437\) | −19.2617 | −0.921412 | ||||||||
\(438\) | −3.48803 | −0.166664 | ||||||||
\(439\) | −20.6104 | −0.983679 | −0.491840 | − | 0.870686i | \(-0.663675\pi\) | ||||
−0.491840 | + | 0.870686i | \(0.663675\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.1013 | 0.909587 | ||||||||
\(442\) | −0.568033 | −0.0270186 | ||||||||
\(443\) | 13.7997 | 0.655644 | 0.327822 | − | 0.944740i | \(-0.393685\pi\) | ||||
0.327822 | + | 0.944740i | \(0.393685\pi\) | |||||||
\(444\) | −10.5199 | −0.499255 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −8.08118 | −0.382655 | ||||||||
\(447\) | 7.45724 | 0.352716 | ||||||||
\(448\) | 14.4711 | 0.683696 | ||||||||
\(449\) | 27.2508 | 1.28605 | 0.643023 | − | 0.765847i | \(-0.277680\pi\) | ||||
0.643023 | + | 0.765847i | \(0.277680\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 28.5542 | 1.34308 | ||||||||
\(453\) | −4.95905 | −0.232997 | ||||||||
\(454\) | 4.14224 | 0.194405 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8.07787 | −0.378281 | ||||||||
\(457\) | 4.62255 | 0.216234 | 0.108117 | − | 0.994138i | \(-0.465518\pi\) | ||||
0.108117 | + | 0.994138i | \(0.465518\pi\) | |||||||
\(458\) | 1.65969 | 0.0775521 | ||||||||
\(459\) | −0.639966 | −0.0298710 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.3940 | −1.18272 | −0.591359 | − | 0.806409i | \(-0.701408\pi\) | ||||
−0.591359 | + | 0.806409i | \(0.701408\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.8949 | −0.599275 | −0.299638 | − | 0.954053i | \(-0.596866\pi\) | ||||
−0.299638 | + | 0.954053i | \(0.596866\pi\) | |||||||
\(464\) | 19.8548 | 0.921737 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.67231 | 0.355413 | ||||||||
\(467\) | −3.81025 | −0.176317 | −0.0881587 | − | 0.996106i | \(-0.528098\pi\) | ||||
−0.0881587 | + | 0.996106i | \(0.528098\pi\) | |||||||
\(468\) | 3.20206 | 0.148015 | ||||||||
\(469\) | 37.0704 | 1.71175 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20.5916 | −0.948809 | ||||||||
\(472\) | 9.86664 | 0.454149 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −0.930287 | −0.0427295 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −5.75952 | −0.263987 | ||||||||
\(477\) | −9.17695 | −0.420184 | ||||||||
\(478\) | −14.9894 | −0.685600 | ||||||||
\(479\) | 12.2918 | 0.561625 | 0.280812 | − | 0.959763i | \(-0.409396\pi\) | ||||
0.280812 | + | 0.959763i | \(0.409396\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.8554 | −0.494964 | ||||||||
\(482\) | −2.73006 | −0.124351 | ||||||||
\(483\) | −22.3760 | −1.01814 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.488299 | −0.0221497 | ||||||||
\(487\) | −13.4389 | −0.608975 | −0.304488 | − | 0.952516i | \(-0.598485\pi\) | ||||
−0.304488 | + | 0.952516i | \(0.598485\pi\) | |||||||
\(488\) | 13.3490 | 0.604283 | ||||||||
\(489\) | 7.22774 | 0.326850 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.08182 | −0.274469 | −0.137234 | − | 0.990539i | \(-0.543821\pi\) | ||||
−0.137234 | + | 0.990539i | \(0.543821\pi\) | |||||||
\(492\) | 3.93149 | 0.177245 | ||||||||
\(493\) | −4.83826 | −0.217904 | ||||||||
\(494\) | −3.90355 | −0.175629 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.79088 | 0.260018 | ||||||||
\(497\) | −28.1434 | −1.26240 | ||||||||
\(498\) | 0.0790564 | 0.00354260 | ||||||||
\(499\) | 18.7942 | 0.841344 | 0.420672 | − | 0.907213i | \(-0.361794\pi\) | ||||
0.420672 | + | 0.907213i | \(0.361794\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.3130 | 0.818164 | ||||||||
\(502\) | −9.14276 | −0.408061 | ||||||||
\(503\) | −6.06605 | −0.270472 | −0.135236 | − | 0.990813i | \(-0.543179\pi\) | ||||
−0.135236 | + | 0.990813i | \(0.543179\pi\) | |||||||
\(504\) | −9.38395 | −0.417994 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.69583 | −0.430607 | ||||||||
\(508\) | −17.4058 | −0.772256 | ||||||||
\(509\) | −19.7444 | −0.875154 | −0.437577 | − | 0.899181i | \(-0.644163\pi\) | ||||
−0.437577 | + | 0.899181i | \(0.644163\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −36.4943 | −1.61441 | ||||||||
\(512\) | −22.6630 | −1.00157 | ||||||||
\(513\) | −4.39788 | −0.194171 | ||||||||
\(514\) | 2.43278 | 0.107305 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 5.95529 | 0.262167 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 14.8981 | 0.654587 | ||||||||
\(519\) | −12.0157 | −0.527430 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −42.1434 | −1.84634 | −0.923168 | − | 0.384396i | \(-0.874410\pi\) | ||||
−0.923168 | + | 0.384396i | \(0.874410\pi\) | |||||||
\(522\) | −3.69163 | −0.161578 | ||||||||
\(523\) | 6.37047 | 0.278561 | 0.139281 | − | 0.990253i | \(-0.455521\pi\) | ||||
0.139281 | + | 0.990253i | \(0.455521\pi\) | |||||||
\(524\) | 22.5180 | 0.983702 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.80445 | 0.427494 | ||||||||
\(527\) | −1.41113 | −0.0614698 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.81758 | −0.165982 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.37174 | 0.233114 | ||||||||
\(532\) | −39.5797 | −1.71600 | ||||||||
\(533\) | 4.05686 | 0.175722 | ||||||||
\(534\) | 0.583706 | 0.0252594 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −13.3276 | −0.575663 | ||||||||
\(537\) | −6.71004 | −0.289560 | ||||||||
\(538\) | 4.65362 | 0.200632 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.3075 | −0.529140 | −0.264570 | − | 0.964367i | \(-0.585230\pi\) | ||||
−0.264570 | + | 0.964367i | \(0.585230\pi\) | |||||||
\(542\) | 0.576656 | 0.0247695 | ||||||||
\(543\) | −11.3348 | −0.486422 | ||||||||
\(544\) | 3.17162 | 0.135982 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4.53470 | −0.194067 | ||||||||
\(547\) | −5.48939 | −0.234709 | −0.117355 | − | 0.993090i | \(-0.537441\pi\) | ||||
−0.117355 | + | 0.993090i | \(0.537441\pi\) | |||||||
\(548\) | 33.5735 | 1.43419 | ||||||||
\(549\) | 7.26768 | 0.310177 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −33.2487 | −1.41644 | ||||||||
\(552\) | 8.04463 | 0.342402 | ||||||||
\(553\) | −9.73335 | −0.413904 | ||||||||
\(554\) | 4.01468 | 0.170567 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 20.6361 | 0.875165 | ||||||||
\(557\) | −25.4636 | −1.07893 | −0.539464 | − | 0.842009i | \(-0.681373\pi\) | ||||
−0.539464 | + | 0.842009i | \(0.681373\pi\) | |||||||
\(558\) | −1.07670 | −0.0455805 | ||||||||
\(559\) | 6.14520 | 0.259914 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.10044 | −0.215149 | ||||||||
\(563\) | −38.3527 | −1.61638 | −0.808188 | − | 0.588925i | \(-0.799551\pi\) | ||||
−0.808188 | + | 0.588925i | \(0.799551\pi\) | |||||||
\(564\) | 2.67019 | 0.112435 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 12.1324 | 0.509964 | ||||||||
\(567\) | −5.10895 | −0.214556 | ||||||||
\(568\) | 10.1181 | 0.424546 | ||||||||
\(569\) | 9.15245 | 0.383691 | 0.191845 | − | 0.981425i | \(-0.438553\pi\) | ||||
0.191845 | + | 0.981425i | \(0.438553\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.3508 | −0.767957 | −0.383978 | − | 0.923342i | \(-0.625446\pi\) | ||||
−0.383978 | + | 0.923342i | \(0.625446\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.0864 | 0.463142 | ||||||||
\(574\) | −5.56769 | −0.232391 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.83250 | −0.118021 | ||||||||
\(577\) | 19.9317 | 0.829770 | 0.414885 | − | 0.909874i | \(-0.363822\pi\) | ||||
0.414885 | + | 0.909874i | \(0.363822\pi\) | |||||||
\(578\) | 8.10109 | 0.336961 | ||||||||
\(579\) | −1.19205 | −0.0495399 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.827147 | 0.0343158 | ||||||||
\(582\) | −6.97402 | −0.289082 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 13.1204 | 0.542928 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.1227 | 0.500784 | ||||||||
\(587\) | 39.5465 | 1.63226 | 0.816129 | − | 0.577870i | \(-0.196116\pi\) | ||||
0.816129 | + | 0.577870i | \(0.196116\pi\) | |||||||
\(588\) | −33.6482 | −1.38763 | ||||||||
\(589\) | −9.69736 | −0.399573 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.3551 | −0.755028 | ||||||||
\(592\) | 15.6837 | 0.644597 | ||||||||
\(593\) | 12.3314 | 0.506391 | 0.253195 | − | 0.967415i | \(-0.418518\pi\) | ||||
0.253195 | + | 0.967415i | \(0.418518\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −13.1364 | −0.538088 | ||||||||
\(597\) | 22.1761 | 0.907607 | ||||||||
\(598\) | 3.88748 | 0.158971 | ||||||||
\(599\) | 34.7495 | 1.41983 | 0.709913 | − | 0.704289i | \(-0.248734\pi\) | ||||
0.709913 | + | 0.704289i | \(0.248734\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 38.6097 | 1.57492 | 0.787462 | − | 0.616364i | \(-0.211395\pi\) | ||||
0.787462 | + | 0.616364i | \(0.211395\pi\) | |||||||
\(602\) | −8.43376 | −0.343735 | ||||||||
\(603\) | −7.25598 | −0.295486 | ||||||||
\(604\) | 8.73569 | 0.355450 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.09524 | 0.0851132 | ||||||||
\(607\) | −6.26341 | −0.254224 | −0.127112 | − | 0.991888i | \(-0.540571\pi\) | ||||
−0.127112 | + | 0.991888i | \(0.540571\pi\) | |||||||
\(608\) | 21.7955 | 0.883926 | ||||||||
\(609\) | −38.6246 | −1.56515 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.75534 | 0.111469 | ||||||||
\(612\) | 1.12734 | 0.0455700 | ||||||||
\(613\) | −18.9911 | −0.767042 | −0.383521 | − | 0.923532i | \(-0.625289\pi\) | ||||
−0.383521 | + | 0.923532i | \(0.625289\pi\) | |||||||
\(614\) | 6.08844 | 0.245709 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.58574 | 0.305390 | 0.152695 | − | 0.988273i | \(-0.451205\pi\) | ||||
0.152695 | + | 0.988273i | \(0.451205\pi\) | |||||||
\(618\) | −4.63787 | −0.186563 | ||||||||
\(619\) | 27.9795 | 1.12459 | 0.562296 | − | 0.826936i | \(-0.309918\pi\) | ||||
0.562296 | + | 0.826936i | \(0.309918\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.37977 | 0.175754 | ||||||||
\(622\) | 1.54260 | 0.0618528 | ||||||||
\(623\) | 6.10717 | 0.244679 | ||||||||
\(624\) | −4.77381 | −0.191105 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 6.98012 | 0.278982 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 36.2734 | 1.44746 | ||||||||
\(629\) | −3.82183 | −0.152387 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.4321 | −1.01244 | −0.506218 | − | 0.862406i | \(-0.668957\pi\) | ||||
−0.506218 | + | 0.862406i | \(0.668957\pi\) | |||||||
\(632\) | 3.49933 | 0.139196 | ||||||||
\(633\) | 8.30729 | 0.330185 | ||||||||
\(634\) | 13.1240 | 0.521223 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 16.1658 | 0.641015 | ||||||||
\(637\) | −34.7212 | −1.37570 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.50864 | 0.217919 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.90150 | −0.351588 | −0.175794 | − | 0.984427i | \(-0.556249\pi\) | ||||
−0.175794 | + | 0.984427i | \(0.556249\pi\) | |||||||
\(642\) | −4.04052 | −0.159467 | ||||||||
\(643\) | −19.4814 | −0.768272 | −0.384136 | − | 0.923276i | \(-0.625501\pi\) | ||||
−0.384136 | + | 0.923276i | \(0.625501\pi\) | |||||||
\(644\) | 39.4168 | 1.55324 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.37431 | −0.0540716 | ||||||||
\(647\) | 32.8093 | 1.28987 | 0.644934 | − | 0.764238i | \(-0.276885\pi\) | ||||
0.644934 | + | 0.764238i | \(0.276885\pi\) | |||||||
\(648\) | 1.83677 | 0.0721550 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.2653 | −0.441521 | ||||||||
\(652\) | −12.7321 | −0.498629 | ||||||||
\(653\) | 14.9010 | 0.583122 | 0.291561 | − | 0.956552i | \(-0.405825\pi\) | ||||
0.291561 | + | 0.956552i | \(0.405825\pi\) | |||||||
\(654\) | 6.10276 | 0.238637 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −5.86128 | −0.228844 | ||||||||
\(657\) | 7.14322 | 0.278684 | ||||||||
\(658\) | −3.78147 | −0.147417 | ||||||||
\(659\) | −25.7059 | −1.00136 | −0.500680 | − | 0.865633i | \(-0.666917\pi\) | ||||
−0.500680 | + | 0.865633i | \(0.666917\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.4887 | −0.485753 | −0.242876 | − | 0.970057i | \(-0.578091\pi\) | ||||
−0.242876 | + | 0.970057i | \(0.578091\pi\) | |||||||
\(662\) | −9.65675 | −0.375320 | ||||||||
\(663\) | 1.16329 | 0.0451784 | ||||||||
\(664\) | −0.297376 | −0.0115404 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.91609 | −0.112996 | ||||||||
\(667\) | 33.1119 | 1.28210 | ||||||||
\(668\) | −32.2595 | −1.24816 | ||||||||
\(669\) | 16.5497 | 0.639847 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 25.3195 | 0.976723 | ||||||||
\(673\) | 40.3440 | 1.55515 | 0.777573 | − | 0.628793i | \(-0.216451\pi\) | ||||
0.777573 | + | 0.628793i | \(0.216451\pi\) | |||||||
\(674\) | −6.96219 | −0.268173 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 17.0798 | 0.656916 | ||||||||
\(677\) | −5.64803 | −0.217071 | −0.108536 | − | 0.994093i | \(-0.534616\pi\) | ||||
−0.108536 | + | 0.994093i | \(0.534616\pi\) | |||||||
\(678\) | 7.91513 | 0.303979 | ||||||||
\(679\) | −72.9674 | −2.80023 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.48300 | −0.325069 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.7349 | 1.02298 | 0.511492 | − | 0.859288i | \(-0.329093\pi\) | ||||
0.511492 | + | 0.859288i | \(0.329093\pi\) | |||||||
\(684\) | 7.74714 | 0.296219 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 30.1891 | 1.15263 | ||||||||
\(687\) | −3.39892 | −0.129677 | ||||||||
\(688\) | −8.87848 | −0.338489 | ||||||||
\(689\) | 16.6813 | 0.635506 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.2696 | 1.49389 | 0.746943 | − | 0.664888i | \(-0.231521\pi\) | ||||
0.746943 | + | 0.664888i | \(0.231521\pi\) | |||||||
\(692\) | 21.1664 | 0.804626 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.71286 | −0.292776 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 13.8863 | 0.526359 | ||||||||
\(697\) | 1.42829 | 0.0541002 | ||||||||
\(698\) | −0.837147 | −0.0316865 | ||||||||
\(699\) | −15.7123 | −0.594295 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.23493 | −0.273259 | −0.136630 | − | 0.990622i | \(-0.543627\pi\) | ||||
−0.136630 | + | 0.990622i | \(0.543627\pi\) | |||||||
\(702\) | 0.887599 | 0.0335003 | ||||||||
\(703\) | −26.2638 | −0.990559 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.81716 | −0.256567 | ||||||||
\(707\) | 21.9219 | 0.824459 | ||||||||
\(708\) | −9.46267 | −0.355629 | ||||||||
\(709\) | −9.96887 | −0.374389 | −0.187194 | − | 0.982323i | \(-0.559939\pi\) | ||||
−0.187194 | + | 0.982323i | \(0.559939\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.90516 | 0.0714490 | ||||||||
\(712\) | −2.19565 | −0.0822854 | ||||||||
\(713\) | 9.65745 | 0.361674 | ||||||||
\(714\) | −1.59652 | −0.0597482 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11.8202 | 0.441740 | ||||||||
\(717\) | 30.6972 | 1.14641 | ||||||||
\(718\) | 16.7517 | 0.625167 | ||||||||
\(719\) | 33.1006 | 1.23445 | 0.617223 | − | 0.786788i | \(-0.288258\pi\) | ||||
0.617223 | + | 0.786788i | \(0.288258\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −48.5249 | −1.80716 | ||||||||
\(722\) | −0.166662 | −0.00620253 | ||||||||
\(723\) | 5.59097 | 0.207930 | ||||||||
\(724\) | 19.9669 | 0.742066 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.7123 | −0.694000 | −0.347000 | − | 0.937865i | \(-0.612800\pi\) | ||||
−0.347000 | + | 0.937865i | \(0.612800\pi\) | |||||||
\(728\) | 17.0576 | 0.632195 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.16352 | 0.0800207 | ||||||||
\(732\) | −12.8025 | −0.473193 | ||||||||
\(733\) | 10.9499 | 0.404442 | 0.202221 | − | 0.979340i | \(-0.435184\pi\) | ||||
0.202221 | + | 0.979340i | \(0.435184\pi\) | |||||||
\(734\) | −1.76396 | −0.0651089 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −21.7058 | −0.800087 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 1.08979 | 0.0401158 | ||||||||
\(739\) | 38.0842 | 1.40095 | 0.700474 | − | 0.713677i | \(-0.252972\pi\) | ||||
0.700474 | + | 0.713677i | \(0.252972\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.99419 | 0.293674 | ||||||||
\(742\) | −22.8937 | −0.840453 | ||||||||
\(743\) | 16.5258 | 0.606275 | 0.303137 | − | 0.952947i | \(-0.401966\pi\) | ||||
0.303137 | + | 0.952947i | \(0.401966\pi\) | |||||||
\(744\) | 4.05009 | 0.148484 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 9.13430 | 0.334430 | ||||||||
\(747\) | −0.161902 | −0.00592367 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −42.2750 | −1.54469 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.9317 | −0.654336 | −0.327168 | − | 0.944966i | \(-0.606094\pi\) | ||||
−0.327168 | + | 0.944966i | \(0.606094\pi\) | |||||||
\(752\) | −3.98087 | −0.145167 | ||||||||
\(753\) | 18.7237 | 0.682329 | ||||||||
\(754\) | 6.71041 | 0.244379 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 8.99974 | 0.327317 | ||||||||
\(757\) | −14.0679 | −0.511307 | −0.255653 | − | 0.966768i | \(-0.582291\pi\) | ||||
−0.255653 | + | 0.966768i | \(0.582291\pi\) | |||||||
\(758\) | 4.57764 | 0.166267 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.1182 | 0.366783 | 0.183392 | − | 0.983040i | \(-0.441292\pi\) | ||||
0.183392 | + | 0.983040i | \(0.441292\pi\) | |||||||
\(762\) | −4.82481 | −0.174785 | ||||||||
\(763\) | 63.8516 | 2.31158 | ||||||||
\(764\) | −19.5295 | −0.706551 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.38289 | 0.339018 | ||||||||
\(767\) | −9.76442 | −0.352573 | ||||||||
\(768\) | 0.149694 | 0.00540160 | ||||||||
\(769\) | −16.0423 | −0.578499 | −0.289250 | − | 0.957254i | \(-0.593406\pi\) | ||||
−0.289250 | + | 0.957254i | \(0.593406\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.98215 | −0.179428 | ||||||||
\(772\) | 2.09987 | 0.0755760 | ||||||||
\(773\) | −40.4357 | −1.45437 | −0.727185 | − | 0.686442i | \(-0.759172\pi\) | ||||
−0.727185 | + | 0.686442i | \(0.759172\pi\) | |||||||
\(774\) | 1.65078 | 0.0593362 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 26.2332 | 0.941718 | ||||||||
\(777\) | −30.5103 | −1.09455 | ||||||||
\(778\) | 4.53971 | 0.162757 | ||||||||
\(779\) | 9.81525 | 0.351668 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 1.36866 | 0.0489430 | ||||||||
\(783\) | 7.56018 | 0.270179 | ||||||||
\(784\) | 50.1646 | 1.79159 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 6.24190 | 0.222641 | ||||||||
\(787\) | −16.4314 | −0.585716 | −0.292858 | − | 0.956156i | \(-0.594606\pi\) | ||||
−0.292858 | + | 0.956156i | \(0.594606\pi\) | |||||||
\(788\) | 32.3337 | 1.15184 | ||||||||
\(789\) | −20.0788 | −0.714824 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 82.8140 | 2.94453 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.2107 | −0.469127 | ||||||||
\(794\) | −6.77235 | −0.240342 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −39.0646 | −1.38461 | ||||||||
\(797\) | −11.8928 | −0.421266 | −0.210633 | − | 0.977565i | \(-0.567552\pi\) | ||||
−0.210633 | + | 0.977565i | \(0.567552\pi\) | |||||||
\(798\) | −10.9713 | −0.388381 | ||||||||
\(799\) | 0.970064 | 0.0343184 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.19539 | −0.0422370 | ||||||||
\(802\) | −5.19236 | −0.183349 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 12.7819 | 0.450782 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.95717 | 0.0689382 | ||||||||
\(807\) | −9.53027 | −0.335481 | ||||||||
\(808\) | −7.88137 | −0.277266 | ||||||||
\(809\) | 39.7032 | 1.39589 | 0.697944 | − | 0.716152i | \(-0.254098\pi\) | ||||
0.697944 | + | 0.716152i | \(0.254098\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.1509 | 1.02363 | 0.511814 | − | 0.859096i | \(-0.328974\pi\) | ||||
0.511814 | + | 0.859096i | \(0.328974\pi\) | |||||||
\(812\) | 68.0396 | 2.38772 | ||||||||
\(813\) | −1.18095 | −0.0414177 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.68070 | −0.0588363 | ||||||||
\(817\) | 14.8678 | 0.520159 | ||||||||
\(818\) | −1.81315 | −0.0633954 | ||||||||
\(819\) | 9.28673 | 0.324505 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 47.6040 | 1.66139 | 0.830696 | − | 0.556727i | \(-0.187943\pi\) | ||||
0.830696 | + | 0.556727i | \(0.187943\pi\) | |||||||
\(822\) | 9.30645 | 0.324600 | ||||||||
\(823\) | −19.2238 | −0.670099 | −0.335049 | − | 0.942201i | \(-0.608753\pi\) | ||||
−0.335049 | + | 0.942201i | \(0.608753\pi\) | |||||||
\(824\) | 17.4457 | 0.607748 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13.4008 | 0.466275 | ||||||||
\(827\) | −30.6312 | −1.06515 | −0.532576 | − | 0.846382i | \(-0.678776\pi\) | ||||
−0.532576 | + | 0.846382i | \(0.678776\pi\) | |||||||
\(828\) | −7.71525 | −0.268124 | ||||||||
\(829\) | −44.8613 | −1.55810 | −0.779048 | − | 0.626964i | \(-0.784297\pi\) | ||||
−0.779048 | + | 0.626964i | \(0.784297\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.22177 | −0.285210 | ||||||||
\(832\) | 5.14875 | 0.178501 | ||||||||
\(833\) | −12.2242 | −0.423543 | ||||||||
\(834\) | 5.72024 | 0.198076 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.20501 | 0.0762163 | ||||||||
\(838\) | 7.76374 | 0.268194 | ||||||||
\(839\) | 4.34435 | 0.149984 | 0.0749919 | − | 0.997184i | \(-0.476107\pi\) | ||||
0.0749919 | + | 0.997184i | \(0.476107\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.1563 | 0.970908 | ||||||||
\(842\) | −2.13222 | −0.0734813 | ||||||||
\(843\) | 10.4453 | 0.359756 | ||||||||
\(844\) | −14.6338 | −0.503717 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.740167 | 0.0254475 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −24.1008 | −0.827626 | ||||||||
\(849\) | −24.8463 | −0.852724 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 26.1557 | 0.896607 | ||||||||
\(852\) | −9.70383 | −0.332448 | ||||||||
\(853\) | −40.3581 | −1.38183 | −0.690917 | − | 0.722934i | \(-0.742793\pi\) | ||||
−0.690917 | + | 0.722934i | \(0.742793\pi\) | |||||||
\(854\) | 18.1306 | 0.620417 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.1987 | 0.519481 | ||||||||
\(857\) | 36.6122 | 1.25065 | 0.625324 | − | 0.780365i | \(-0.284967\pi\) | ||||
0.625324 | + | 0.780365i | \(0.284967\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.5710 | 0.974831 | 0.487415 | − | 0.873170i | \(-0.337940\pi\) | ||||
0.487415 | + | 0.873170i | \(0.337940\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.4022 | 0.388587 | ||||||||
\(862\) | −9.81507 | −0.334303 | ||||||||
\(863\) | −29.3094 | −0.997704 | −0.498852 | − | 0.866687i | \(-0.666245\pi\) | ||||
−0.498852 | + | 0.866687i | \(0.666245\pi\) | |||||||
\(864\) | −4.95592 | −0.168604 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 15.0021 | 0.509791 | ||||||||
\(867\) | −16.5904 | −0.563441 | ||||||||
\(868\) | 19.8445 | 0.673567 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.1895 | 0.446908 | ||||||||
\(872\) | −22.9559 | −0.777386 | ||||||||
\(873\) | 14.2823 | 0.483382 | ||||||||
\(874\) | 9.40547 | 0.318145 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −12.5832 | −0.425149 | ||||||||
\(877\) | −3.67475 | −0.124087 | −0.0620437 | − | 0.998073i | \(-0.519762\pi\) | ||||
−0.0620437 | + | 0.998073i | \(0.519762\pi\) | |||||||
\(878\) | 10.0640 | 0.339644 | ||||||||
\(879\) | −24.8264 | −0.837373 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.1723 | −0.376403 | −0.188202 | − | 0.982130i | \(-0.560266\pi\) | ||||
−0.188202 | + | 0.982130i | \(0.560266\pi\) | |||||||
\(882\) | −9.32716 | −0.314062 | ||||||||
\(883\) | −42.2570 | −1.42206 | −0.711030 | − | 0.703161i | \(-0.751771\pi\) | ||||
−0.711030 | + | 0.703161i | \(0.751771\pi\) | |||||||
\(884\) | −2.04921 | −0.0689224 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.73838 | −0.226380 | ||||||||
\(887\) | −55.8459 | −1.87512 | −0.937562 | − | 0.347819i | \(-0.886922\pi\) | ||||
−0.937562 | + | 0.347819i | \(0.886922\pi\) | |||||||
\(888\) | 10.9691 | 0.368097 | ||||||||
\(889\) | −50.4808 | −1.69307 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −29.1533 | −0.976125 | ||||||||
\(893\) | 6.66633 | 0.223080 | ||||||||
\(894\) | −3.64136 | −0.121785 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −57.7053 | −1.92780 | ||||||||
\(897\) | −7.96128 | −0.265819 | ||||||||
\(898\) | −13.3066 | −0.444045 | ||||||||
\(899\) | 16.6703 | 0.555985 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.87293 | 0.195656 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 17.2717 | 0.574767 | ||||||||
\(904\) | −29.7733 | −0.990244 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 2.42150 | 0.0804490 | ||||||||
\(907\) | −12.0875 | −0.401358 | −0.200679 | − | 0.979657i | \(-0.564315\pi\) | ||||
−0.200679 | + | 0.979657i | \(0.564315\pi\) | |||||||
\(908\) | 14.9433 | 0.495912 | ||||||||
\(909\) | −4.29089 | −0.142320 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.2306 | −1.33290 | −0.666450 | − | 0.745550i | \(-0.732187\pi\) | ||||
−0.666450 | + | 0.745550i | \(0.732187\pi\) | |||||||
\(912\) | −11.5499 | −0.382454 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −2.25719 | −0.0746611 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.98741 | 0.197830 | ||||||||
\(917\) | 65.3074 | 2.15664 | ||||||||
\(918\) | 0.312494 | 0.0103139 | ||||||||
\(919\) | 3.65013 | 0.120407 | 0.0602033 | − | 0.998186i | \(-0.480825\pi\) | ||||
0.0602033 | + | 0.998186i | \(0.480825\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.4687 | −0.410857 | ||||||||
\(922\) | 12.3999 | 0.408368 | ||||||||
\(923\) | −10.0133 | −0.329591 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 6.29655 | 0.206917 | ||||||||
\(927\) | 9.49802 | 0.311956 | ||||||||
\(928\) | −37.4677 | −1.22994 | ||||||||
\(929\) | 10.0510 | 0.329762 | 0.164881 | − | 0.986313i | \(-0.447276\pi\) | ||||
0.164881 | + | 0.986313i | \(0.447276\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −84.0053 | −2.75316 | ||||||||
\(932\) | 27.6783 | 0.906632 | ||||||||
\(933\) | −3.15914 | −0.103426 | ||||||||
\(934\) | 1.86054 | 0.0608788 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.33876 | −0.109131 | ||||||||
\(937\) | −28.2337 | −0.922355 | −0.461177 | − | 0.887308i | \(-0.652573\pi\) | ||||
−0.461177 | + | 0.887308i | \(0.652573\pi\) | |||||||
\(938\) | −18.1014 | −0.591033 | ||||||||
\(939\) | −14.2948 | −0.466492 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.6668 | 1.06491 | 0.532453 | − | 0.846459i | \(-0.321270\pi\) | ||||
0.532453 | + | 0.846459i | \(0.321270\pi\) | |||||||
\(942\) | 10.0548 | 0.327604 | ||||||||
\(943\) | −9.77485 | −0.318313 | ||||||||
\(944\) | 14.1075 | 0.459159 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −57.1073 | −1.85574 | −0.927869 | − | 0.372906i | \(-0.878361\pi\) | ||||
−0.927869 | + | 0.372906i | \(0.878361\pi\) | |||||||
\(948\) | −3.35606 | −0.109000 | ||||||||
\(949\) | −12.9845 | −0.421495 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −26.8771 | −0.871549 | ||||||||
\(952\) | 6.00540 | 0.194636 | ||||||||
\(953\) | −4.51422 | −0.146230 | −0.0731150 | − | 0.997324i | \(-0.523294\pi\) | ||||
−0.0731150 | + | 0.997324i | \(0.523294\pi\) | |||||||
\(954\) | 4.48109 | 0.145081 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −54.0751 | −1.74891 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6.00205 | −0.193917 | ||||||||
\(959\) | 97.3710 | 3.14427 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.1379 | −0.843159 | ||||||||
\(962\) | 5.30069 | 0.170901 | ||||||||
\(963\) | 8.27470 | 0.266648 | ||||||||
\(964\) | −9.84886 | −0.317210 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 10.9262 | 0.351544 | ||||||||
\(967\) | 1.33608 | 0.0429654 | 0.0214827 | − | 0.999769i | \(-0.493161\pi\) | ||||
0.0214827 | + | 0.999769i | \(0.493161\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.81449 | 0.0904144 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.71644 | 0.0871747 | 0.0435873 | − | 0.999050i | \(-0.486121\pi\) | ||||
0.0435873 | + | 0.999050i | \(0.486121\pi\) | |||||||
\(972\) | −1.76156 | −0.0565022 | ||||||||
\(973\) | 59.8494 | 1.91868 | ||||||||
\(974\) | 6.56221 | 0.210267 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 19.0867 | 0.610949 | ||||||||
\(977\) | −16.6829 | −0.533733 | −0.266866 | − | 0.963734i | \(-0.585988\pi\) | ||||
−0.266866 | + | 0.963734i | \(0.585988\pi\) | |||||||
\(978\) | −3.52930 | −0.112854 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.4980 | −0.399031 | ||||||||
\(982\) | 2.96975 | 0.0947684 | ||||||||
\(983\) | 26.2517 | 0.837298 | 0.418649 | − | 0.908148i | \(-0.362504\pi\) | ||||
0.418649 | + | 0.908148i | \(0.362504\pi\) | |||||||
\(984\) | −4.09933 | −0.130682 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.36251 | 0.0752378 | ||||||||
\(987\) | 7.74418 | 0.246500 | ||||||||
\(988\) | −14.0823 | −0.448017 | ||||||||
\(989\) | −14.8066 | −0.470823 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −50.3117 | −1.59821 | −0.799103 | − | 0.601195i | \(-0.794692\pi\) | ||||
−0.799103 | + | 0.601195i | \(0.794692\pi\) | |||||||
\(992\) | −10.9279 | −0.346960 | ||||||||
\(993\) | 19.7763 | 0.627583 | ||||||||
\(994\) | 13.7424 | 0.435881 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.285200 | 0.00903691 | ||||||||
\(997\) | −45.2449 | −1.43292 | −0.716460 | − | 0.697628i | \(-0.754239\pi\) | ||||
−0.716460 | + | 0.697628i | \(0.754239\pi\) | |||||||
\(998\) | −9.17719 | −0.290499 | ||||||||
\(999\) | 5.97194 | 0.188944 |
(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 | 9075.2.a.dy.1.6 | 12 | ||
5.2 | odd | 4 | 1815.2.c.j.364.10 | 24 | |||
5.3 | odd | 4 | 1815.2.c.j.364.15 | 24 | |||
5.4 | even | 2 | 9075.2.a.dz.1.7 | 12 | |||
11.3 | even | 5 | 825.2.n.p.526.3 | 24 | |||
11.4 | even | 5 | 825.2.n.p.676.3 | 24 | |||
11.10 | odd | 2 | 9075.2.a.ea.1.7 | 12 | |||
55.3 | odd | 20 | 165.2.s.a.64.8 | yes | 48 | ||
55.4 | even | 10 | 825.2.n.o.676.4 | 24 | |||
55.14 | even | 10 | 825.2.n.o.526.4 | 24 | |||
55.32 | even | 4 | 1815.2.c.k.364.15 | 24 | |||
55.37 | odd | 20 | 165.2.s.a.49.8 | yes | 48 | ||
55.43 | even | 4 | 1815.2.c.k.364.10 | 24 | |||
55.47 | odd | 20 | 165.2.s.a.64.5 | yes | 48 | ||
55.48 | odd | 20 | 165.2.s.a.49.5 | ✓ | 48 | ||
55.54 | odd | 2 | 9075.2.a.dx.1.6 | 12 | |||
165.47 | even | 20 | 495.2.ba.c.64.8 | 48 | |||
165.92 | even | 20 | 495.2.ba.c.379.5 | 48 | |||
165.113 | even | 20 | 495.2.ba.c.64.5 | 48 | |||
165.158 | even | 20 | 495.2.ba.c.379.8 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.s.a.49.5 | ✓ | 48 | 55.48 | odd | 20 | ||
165.2.s.a.49.8 | yes | 48 | 55.37 | odd | 20 | ||
165.2.s.a.64.5 | yes | 48 | 55.47 | odd | 20 | ||
165.2.s.a.64.8 | yes | 48 | 55.3 | odd | 20 | ||
495.2.ba.c.64.5 | 48 | 165.113 | even | 20 | |||
495.2.ba.c.64.8 | 48 | 165.47 | even | 20 | |||
495.2.ba.c.379.5 | 48 | 165.92 | even | 20 | |||
495.2.ba.c.379.8 | 48 | 165.158 | even | 20 | |||
825.2.n.o.526.4 | 24 | 55.14 | even | 10 | |||
825.2.n.o.676.4 | 24 | 55.4 | even | 10 | |||
825.2.n.p.526.3 | 24 | 11.3 | even | 5 | |||
825.2.n.p.676.3 | 24 | 11.4 | even | 5 | |||
1815.2.c.j.364.10 | 24 | 5.2 | odd | 4 | |||
1815.2.c.j.364.15 | 24 | 5.3 | odd | 4 | |||
1815.2.c.k.364.10 | 24 | 55.43 | even | 4 | |||
1815.2.c.k.364.15 | 24 | 55.32 | even | 4 | |||
9075.2.a.dx.1.6 | 12 | 55.54 | odd | 2 | |||
9075.2.a.dy.1.6 | 12 | 1.1 | even | 1 | trivial | ||
9075.2.a.dz.1.7 | 12 | 5.4 | even | 2 | |||
9075.2.a.ea.1.7 | 12 | 11.10 | odd | 2 |