Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6422,2,Mod(1,6422)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6422, 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("6422.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6422 = 2 \cdot 13^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6422.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: | \(51.2799281781\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 4 x^{13} - 22 x^{12} + 98 x^{11} + 164 x^{10} - 912 x^{9} - 374 x^{8} + 3996 x^{7} - 817 x^{6} - 8194 x^{5} + 4418 x^{4} + 6430 x^{3} - 4327 x^{2} - 922 x + 358 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 494) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(1.50159\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6422.1 |
$q$-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 | ||||||||
\(3\) | 1.50159 | 0.866945 | 0.433473 | − | 0.901167i | \(-0.357288\pi\) | ||||
0.433473 | + | 0.901167i | \(0.357288\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.98870 | −1.33659 | −0.668293 | − | 0.743898i | \(-0.732975\pi\) | ||||
−0.668293 | + | 0.743898i | \(0.732975\pi\) | |||||||
\(6\) | −1.50159 | −0.613023 | ||||||||
\(7\) | −3.73146 | −1.41036 | −0.705180 | − | 0.709029i | \(-0.749134\pi\) | ||||
−0.705180 | + | 0.709029i | \(0.749134\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.745218 | −0.248406 | ||||||||
\(10\) | 2.98870 | 0.945109 | ||||||||
\(11\) | −3.81437 | −1.15007 | −0.575037 | − | 0.818127i | \(-0.695012\pi\) | ||||
−0.575037 | + | 0.818127i | \(0.695012\pi\) | |||||||
\(12\) | 1.50159 | 0.433473 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 3.73146 | 0.997274 | ||||||||
\(15\) | −4.48781 | −1.15875 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.89129 | −0.701242 | −0.350621 | − | 0.936517i | \(-0.614029\pi\) | ||||
−0.350621 | + | 0.936517i | \(0.614029\pi\) | |||||||
\(18\) | 0.745218 | 0.175650 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −2.98870 | −0.668293 | ||||||||
\(21\) | −5.60313 | −1.22270 | ||||||||
\(22\) | 3.81437 | 0.813225 | ||||||||
\(23\) | −1.66948 | −0.348112 | −0.174056 | − | 0.984736i | \(-0.555687\pi\) | ||||
−0.174056 | + | 0.984736i | \(0.555687\pi\) | |||||||
\(24\) | −1.50159 | −0.306511 | ||||||||
\(25\) | 3.93232 | 0.786464 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.62379 | −1.08230 | ||||||||
\(28\) | −3.73146 | −0.705180 | ||||||||
\(29\) | −8.51244 | −1.58072 | −0.790360 | − | 0.612643i | \(-0.790106\pi\) | ||||
−0.790360 | + | 0.612643i | \(0.790106\pi\) | |||||||
\(30\) | 4.48781 | 0.819358 | ||||||||
\(31\) | −1.71712 | −0.308404 | −0.154202 | − | 0.988039i | \(-0.549281\pi\) | ||||
−0.154202 | + | 0.988039i | \(0.549281\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −5.72763 | −0.997052 | ||||||||
\(34\) | 2.89129 | 0.495853 | ||||||||
\(35\) | 11.1522 | 1.88507 | ||||||||
\(36\) | −0.745218 | −0.124203 | ||||||||
\(37\) | −5.22055 | −0.858254 | −0.429127 | − | 0.903244i | \(-0.641179\pi\) | ||||
−0.429127 | + | 0.903244i | \(0.641179\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.98870 | 0.472555 | ||||||||
\(41\) | −10.6438 | −1.66229 | −0.831145 | − | 0.556056i | \(-0.812314\pi\) | ||||
−0.831145 | + | 0.556056i | \(0.812314\pi\) | |||||||
\(42\) | 5.60313 | 0.864582 | ||||||||
\(43\) | 5.42719 | 0.827639 | 0.413820 | − | 0.910359i | \(-0.364194\pi\) | ||||
0.413820 | + | 0.910359i | \(0.364194\pi\) | |||||||
\(44\) | −3.81437 | −0.575037 | ||||||||
\(45\) | 2.22723 | 0.332016 | ||||||||
\(46\) | 1.66948 | 0.246152 | ||||||||
\(47\) | 6.13466 | 0.894831 | 0.447416 | − | 0.894326i | \(-0.352344\pi\) | ||||
0.447416 | + | 0.894326i | \(0.352344\pi\) | |||||||
\(48\) | 1.50159 | 0.216736 | ||||||||
\(49\) | 6.92379 | 0.989113 | ||||||||
\(50\) | −3.93232 | −0.556114 | ||||||||
\(51\) | −4.34155 | −0.607938 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −13.2870 | −1.82511 | −0.912553 | − | 0.408959i | \(-0.865892\pi\) | ||||
−0.912553 | + | 0.408959i | \(0.865892\pi\) | |||||||
\(54\) | 5.62379 | 0.765301 | ||||||||
\(55\) | 11.4000 | 1.53717 | ||||||||
\(56\) | 3.73146 | 0.498637 | ||||||||
\(57\) | −1.50159 | −0.198891 | ||||||||
\(58\) | 8.51244 | 1.11774 | ||||||||
\(59\) | −5.52632 | −0.719465 | −0.359732 | − | 0.933055i | \(-0.617132\pi\) | ||||
−0.359732 | + | 0.933055i | \(0.617132\pi\) | |||||||
\(60\) | −4.48781 | −0.579374 | ||||||||
\(61\) | −5.99153 | −0.767137 | −0.383568 | − | 0.923512i | \(-0.625305\pi\) | ||||
−0.383568 | + | 0.923512i | \(0.625305\pi\) | |||||||
\(62\) | 1.71712 | 0.218075 | ||||||||
\(63\) | 2.78075 | 0.350342 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.72763 | 0.705022 | ||||||||
\(67\) | 7.35059 | 0.898018 | 0.449009 | − | 0.893527i | \(-0.351777\pi\) | ||||
0.449009 | + | 0.893527i | \(0.351777\pi\) | |||||||
\(68\) | −2.89129 | −0.350621 | ||||||||
\(69\) | −2.50689 | −0.301794 | ||||||||
\(70\) | −11.1522 | −1.33294 | ||||||||
\(71\) | 9.75998 | 1.15830 | 0.579148 | − | 0.815222i | \(-0.303385\pi\) | ||||
0.579148 | + | 0.815222i | \(0.303385\pi\) | |||||||
\(72\) | 0.745218 | 0.0878248 | ||||||||
\(73\) | 0.118233 | 0.0138382 | 0.00691908 | − | 0.999976i | \(-0.497798\pi\) | ||||
0.00691908 | + | 0.999976i | \(0.497798\pi\) | |||||||
\(74\) | 5.22055 | 0.606877 | ||||||||
\(75\) | 5.90474 | 0.681821 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 14.2332 | 1.62202 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.04474 | 0.342560 | 0.171280 | − | 0.985222i | \(-0.445210\pi\) | ||||
0.171280 | + | 0.985222i | \(0.445210\pi\) | |||||||
\(80\) | −2.98870 | −0.334147 | ||||||||
\(81\) | −6.20900 | −0.689888 | ||||||||
\(82\) | 10.6438 | 1.17542 | ||||||||
\(83\) | 1.22342 | 0.134288 | 0.0671439 | − | 0.997743i | \(-0.478611\pi\) | ||||
0.0671439 | + | 0.997743i | \(0.478611\pi\) | |||||||
\(84\) | −5.60313 | −0.611352 | ||||||||
\(85\) | 8.64121 | 0.937271 | ||||||||
\(86\) | −5.42719 | −0.585229 | ||||||||
\(87\) | −12.7822 | −1.37040 | ||||||||
\(88\) | 3.81437 | 0.406613 | ||||||||
\(89\) | −14.8184 | −1.57074 | −0.785372 | − | 0.619023i | \(-0.787529\pi\) | ||||
−0.785372 | + | 0.619023i | \(0.787529\pi\) | |||||||
\(90\) | −2.22723 | −0.234771 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.66948 | −0.174056 | ||||||||
\(93\) | −2.57842 | −0.267370 | ||||||||
\(94\) | −6.13466 | −0.632741 | ||||||||
\(95\) | 2.98870 | 0.306634 | ||||||||
\(96\) | −1.50159 | −0.153256 | ||||||||
\(97\) | −14.8790 | −1.51073 | −0.755366 | − | 0.655303i | \(-0.772541\pi\) | ||||
−0.755366 | + | 0.655303i | \(0.772541\pi\) | |||||||
\(98\) | −6.92379 | −0.699408 | ||||||||
\(99\) | 2.84253 | 0.285685 | ||||||||
\(100\) | 3.93232 | 0.393232 | ||||||||
\(101\) | 14.4250 | 1.43534 | 0.717669 | − | 0.696384i | \(-0.245209\pi\) | ||||
0.717669 | + | 0.696384i | \(0.245209\pi\) | |||||||
\(102\) | 4.34155 | 0.429877 | ||||||||
\(103\) | 9.25772 | 0.912190 | 0.456095 | − | 0.889931i | \(-0.349248\pi\) | ||||
0.456095 | + | 0.889931i | \(0.349248\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 16.7461 | 1.63425 | ||||||||
\(106\) | 13.2870 | 1.29054 | ||||||||
\(107\) | −11.6631 | −1.12752 | −0.563759 | − | 0.825939i | \(-0.690645\pi\) | ||||
−0.563759 | + | 0.825939i | \(0.690645\pi\) | |||||||
\(108\) | −5.62379 | −0.541150 | ||||||||
\(109\) | −6.07064 | −0.581462 | −0.290731 | − | 0.956805i | \(-0.593898\pi\) | ||||
−0.290731 | + | 0.956805i | \(0.593898\pi\) | |||||||
\(110\) | −11.4000 | −1.08695 | ||||||||
\(111\) | −7.83915 | −0.744059 | ||||||||
\(112\) | −3.73146 | −0.352590 | ||||||||
\(113\) | −5.29092 | −0.497728 | −0.248864 | − | 0.968538i | \(-0.580057\pi\) | ||||
−0.248864 | + | 0.968538i | \(0.580057\pi\) | |||||||
\(114\) | 1.50159 | 0.140637 | ||||||||
\(115\) | 4.98959 | 0.465281 | ||||||||
\(116\) | −8.51244 | −0.790360 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.52632 | 0.508739 | ||||||||
\(119\) | 10.7887 | 0.989003 | ||||||||
\(120\) | 4.48781 | 0.409679 | ||||||||
\(121\) | 3.54939 | 0.322671 | ||||||||
\(122\) | 5.99153 | 0.542448 | ||||||||
\(123\) | −15.9827 | −1.44111 | ||||||||
\(124\) | −1.71712 | −0.154202 | ||||||||
\(125\) | 3.19098 | 0.285410 | ||||||||
\(126\) | −2.78075 | −0.247729 | ||||||||
\(127\) | −11.2686 | −0.999927 | −0.499963 | − | 0.866046i | \(-0.666653\pi\) | ||||
−0.499963 | + | 0.866046i | \(0.666653\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 8.14944 | 0.717518 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.7617 | −1.11499 | −0.557495 | − | 0.830180i | \(-0.688238\pi\) | ||||
−0.557495 | + | 0.830180i | \(0.688238\pi\) | |||||||
\(132\) | −5.72763 | −0.498526 | ||||||||
\(133\) | 3.73146 | 0.323559 | ||||||||
\(134\) | −7.35059 | −0.634994 | ||||||||
\(135\) | 16.8078 | 1.44659 | ||||||||
\(136\) | 2.89129 | 0.247926 | ||||||||
\(137\) | 8.10390 | 0.692363 | 0.346182 | − | 0.938168i | \(-0.387478\pi\) | ||||
0.346182 | + | 0.938168i | \(0.387478\pi\) | |||||||
\(138\) | 2.50689 | 0.213400 | ||||||||
\(139\) | 9.90009 | 0.839714 | 0.419857 | − | 0.907590i | \(-0.362080\pi\) | ||||
0.419857 | + | 0.907590i | \(0.362080\pi\) | |||||||
\(140\) | 11.1522 | 0.942534 | ||||||||
\(141\) | 9.21176 | 0.775770 | ||||||||
\(142\) | −9.75998 | −0.819039 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.745218 | −0.0621015 | ||||||||
\(145\) | 25.4411 | 2.11277 | ||||||||
\(146\) | −0.118233 | −0.00978506 | ||||||||
\(147\) | 10.3967 | 0.857506 | ||||||||
\(148\) | −5.22055 | −0.429127 | ||||||||
\(149\) | 23.1692 | 1.89809 | 0.949045 | − | 0.315139i | \(-0.102051\pi\) | ||||
0.949045 | + | 0.315139i | \(0.102051\pi\) | |||||||
\(150\) | −5.90474 | −0.482120 | ||||||||
\(151\) | 20.1390 | 1.63889 | 0.819446 | − | 0.573157i | \(-0.194282\pi\) | ||||
0.819446 | + | 0.573157i | \(0.194282\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 2.15464 | 0.174193 | ||||||||
\(154\) | −14.2332 | −1.14694 | ||||||||
\(155\) | 5.13196 | 0.412209 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.0900 | −1.04470 | −0.522349 | − | 0.852732i | \(-0.674944\pi\) | ||||
−0.522349 | + | 0.852732i | \(0.674944\pi\) | |||||||
\(158\) | −3.04474 | −0.242226 | ||||||||
\(159\) | −19.9516 | −1.58227 | ||||||||
\(160\) | 2.98870 | 0.236277 | ||||||||
\(161\) | 6.22961 | 0.490962 | ||||||||
\(162\) | 6.20900 | 0.487825 | ||||||||
\(163\) | −5.90255 | −0.462323 | −0.231162 | − | 0.972915i | \(-0.574253\pi\) | ||||
−0.231162 | + | 0.972915i | \(0.574253\pi\) | |||||||
\(164\) | −10.6438 | −0.831145 | ||||||||
\(165\) | 17.1181 | 1.33265 | ||||||||
\(166\) | −1.22342 | −0.0949559 | ||||||||
\(167\) | −16.6567 | −1.28894 | −0.644468 | − | 0.764631i | \(-0.722921\pi\) | ||||
−0.644468 | + | 0.764631i | \(0.722921\pi\) | |||||||
\(168\) | 5.60313 | 0.432291 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −8.64121 | −0.662750 | ||||||||
\(171\) | 0.745218 | 0.0569882 | ||||||||
\(172\) | 5.42719 | 0.413820 | ||||||||
\(173\) | −9.47289 | −0.720211 | −0.360105 | − | 0.932912i | \(-0.617259\pi\) | ||||
−0.360105 | + | 0.932912i | \(0.617259\pi\) | |||||||
\(174\) | 12.7822 | 0.969017 | ||||||||
\(175\) | −14.6733 | −1.10920 | ||||||||
\(176\) | −3.81437 | −0.287519 | ||||||||
\(177\) | −8.29828 | −0.623737 | ||||||||
\(178\) | 14.8184 | 1.11068 | ||||||||
\(179\) | −5.00441 | −0.374047 | −0.187024 | − | 0.982355i | \(-0.559884\pi\) | ||||
−0.187024 | + | 0.982355i | \(0.559884\pi\) | |||||||
\(180\) | 2.22723 | 0.166008 | ||||||||
\(181\) | −1.97399 | −0.146726 | −0.0733629 | − | 0.997305i | \(-0.523373\pi\) | ||||
−0.0733629 | + | 0.997305i | \(0.523373\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.99684 | −0.665065 | ||||||||
\(184\) | 1.66948 | 0.123076 | ||||||||
\(185\) | 15.6027 | 1.14713 | ||||||||
\(186\) | 2.57842 | 0.189059 | ||||||||
\(187\) | 11.0285 | 0.806480 | ||||||||
\(188\) | 6.13466 | 0.447416 | ||||||||
\(189\) | 20.9850 | 1.52643 | ||||||||
\(190\) | −2.98870 | −0.216823 | ||||||||
\(191\) | −20.8136 | −1.50602 | −0.753010 | − | 0.658009i | \(-0.771399\pi\) | ||||
−0.753010 | + | 0.658009i | \(0.771399\pi\) | |||||||
\(192\) | 1.50159 | 0.108368 | ||||||||
\(193\) | −21.3064 | −1.53367 | −0.766833 | − | 0.641847i | \(-0.778169\pi\) | ||||
−0.766833 | + | 0.641847i | \(0.778169\pi\) | |||||||
\(194\) | 14.8790 | 1.06825 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.92379 | 0.494556 | ||||||||
\(197\) | 8.62246 | 0.614325 | 0.307162 | − | 0.951657i | \(-0.400621\pi\) | ||||
0.307162 | + | 0.951657i | \(0.400621\pi\) | |||||||
\(198\) | −2.84253 | −0.202010 | ||||||||
\(199\) | 4.00411 | 0.283844 | 0.141922 | − | 0.989878i | \(-0.454672\pi\) | ||||
0.141922 | + | 0.989878i | \(0.454672\pi\) | |||||||
\(200\) | −3.93232 | −0.278057 | ||||||||
\(201\) | 11.0376 | 0.778532 | ||||||||
\(202\) | −14.4250 | −1.01494 | ||||||||
\(203\) | 31.7638 | 2.22938 | ||||||||
\(204\) | −4.34155 | −0.303969 | ||||||||
\(205\) | 31.8112 | 2.22179 | ||||||||
\(206\) | −9.25772 | −0.645016 | ||||||||
\(207\) | 1.24413 | 0.0864730 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.81437 | 0.263845 | ||||||||
\(210\) | −16.7461 | −1.15559 | ||||||||
\(211\) | 8.29916 | 0.571338 | 0.285669 | − | 0.958328i | \(-0.407784\pi\) | ||||
0.285669 | + | 0.958328i | \(0.407784\pi\) | |||||||
\(212\) | −13.2870 | −0.912553 | ||||||||
\(213\) | 14.6555 | 1.00418 | ||||||||
\(214\) | 11.6631 | 0.797276 | ||||||||
\(215\) | −16.2202 | −1.10621 | ||||||||
\(216\) | 5.62379 | 0.382651 | ||||||||
\(217\) | 6.40737 | 0.434961 | ||||||||
\(218\) | 6.07064 | 0.411155 | ||||||||
\(219\) | 0.177538 | 0.0119969 | ||||||||
\(220\) | 11.4000 | 0.768587 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 7.83915 | 0.526129 | ||||||||
\(223\) | −8.81599 | −0.590362 | −0.295181 | − | 0.955441i | \(-0.595380\pi\) | ||||
−0.295181 | + | 0.955441i | \(0.595380\pi\) | |||||||
\(224\) | 3.73146 | 0.249319 | ||||||||
\(225\) | −2.93043 | −0.195362 | ||||||||
\(226\) | 5.29092 | 0.351947 | ||||||||
\(227\) | 4.18895 | 0.278030 | 0.139015 | − | 0.990290i | \(-0.455606\pi\) | ||||
0.139015 | + | 0.990290i | \(0.455606\pi\) | |||||||
\(228\) | −1.50159 | −0.0994454 | ||||||||
\(229\) | 24.2635 | 1.60338 | 0.801689 | − | 0.597741i | \(-0.203935\pi\) | ||||
0.801689 | + | 0.597741i | \(0.203935\pi\) | |||||||
\(230\) | −4.98959 | −0.329004 | ||||||||
\(231\) | 21.3724 | 1.40620 | ||||||||
\(232\) | 8.51244 | 0.558869 | ||||||||
\(233\) | 17.9212 | 1.17405 | 0.587027 | − | 0.809567i | \(-0.300298\pi\) | ||||
0.587027 | + | 0.809567i | \(0.300298\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18.3346 | −1.19602 | ||||||||
\(236\) | −5.52632 | −0.359732 | ||||||||
\(237\) | 4.57196 | 0.296981 | ||||||||
\(238\) | −10.7887 | −0.699331 | ||||||||
\(239\) | 22.3178 | 1.44362 | 0.721808 | − | 0.692093i | \(-0.243311\pi\) | ||||
0.721808 | + | 0.692093i | \(0.243311\pi\) | |||||||
\(240\) | −4.48781 | −0.289687 | ||||||||
\(241\) | −22.3962 | −1.44267 | −0.721334 | − | 0.692588i | \(-0.756471\pi\) | ||||
−0.721334 | + | 0.692588i | \(0.756471\pi\) | |||||||
\(242\) | −3.54939 | −0.228163 | ||||||||
\(243\) | 7.54799 | 0.484204 | ||||||||
\(244\) | −5.99153 | −0.383568 | ||||||||
\(245\) | −20.6931 | −1.32203 | ||||||||
\(246\) | 15.9827 | 1.01902 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1.71712 | 0.109037 | ||||||||
\(249\) | 1.83708 | 0.116420 | ||||||||
\(250\) | −3.19098 | −0.201815 | ||||||||
\(251\) | 3.68665 | 0.232699 | 0.116350 | − | 0.993208i | \(-0.462881\pi\) | ||||
0.116350 | + | 0.993208i | \(0.462881\pi\) | |||||||
\(252\) | 2.78075 | 0.175171 | ||||||||
\(253\) | 6.36802 | 0.400354 | ||||||||
\(254\) | 11.2686 | 0.707055 | ||||||||
\(255\) | 12.9756 | 0.812562 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 12.7082 | 0.792718 | 0.396359 | − | 0.918096i | \(-0.370274\pi\) | ||||
0.396359 | + | 0.918096i | \(0.370274\pi\) | |||||||
\(258\) | −8.14944 | −0.507362 | ||||||||
\(259\) | 19.4803 | 1.21045 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.34362 | 0.392660 | ||||||||
\(262\) | 12.7617 | 0.788418 | ||||||||
\(263\) | 3.24916 | 0.200352 | 0.100176 | − | 0.994970i | \(-0.468059\pi\) | ||||
0.100176 | + | 0.994970i | \(0.468059\pi\) | |||||||
\(264\) | 5.72763 | 0.352511 | ||||||||
\(265\) | 39.7107 | 2.43941 | ||||||||
\(266\) | −3.73146 | −0.228790 | ||||||||
\(267\) | −22.2512 | −1.36175 | ||||||||
\(268\) | 7.35059 | 0.449009 | ||||||||
\(269\) | 10.9402 | 0.667037 | 0.333519 | − | 0.942744i | \(-0.391764\pi\) | ||||
0.333519 | + | 0.942744i | \(0.391764\pi\) | |||||||
\(270\) | −16.8078 | −1.02289 | ||||||||
\(271\) | 0.968555 | 0.0588355 | 0.0294178 | − | 0.999567i | \(-0.490635\pi\) | ||||
0.0294178 | + | 0.999567i | \(0.490635\pi\) | |||||||
\(272\) | −2.89129 | −0.175310 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.10390 | −0.489575 | ||||||||
\(275\) | −14.9993 | −0.904492 | ||||||||
\(276\) | −2.50689 | −0.150897 | ||||||||
\(277\) | 8.02640 | 0.482260 | 0.241130 | − | 0.970493i | \(-0.422482\pi\) | ||||
0.241130 | + | 0.970493i | \(0.422482\pi\) | |||||||
\(278\) | −9.90009 | −0.593768 | ||||||||
\(279\) | 1.27963 | 0.0766094 | ||||||||
\(280\) | −11.1522 | −0.666472 | ||||||||
\(281\) | 4.41792 | 0.263551 | 0.131775 | − | 0.991280i | \(-0.457932\pi\) | ||||
0.131775 | + | 0.991280i | \(0.457932\pi\) | |||||||
\(282\) | −9.21176 | −0.548552 | ||||||||
\(283\) | −15.7900 | −0.938621 | −0.469310 | − | 0.883033i | \(-0.655497\pi\) | ||||
−0.469310 | + | 0.883033i | \(0.655497\pi\) | |||||||
\(284\) | 9.75998 | 0.579148 | ||||||||
\(285\) | 4.48781 | 0.265835 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 39.7171 | 2.34442 | ||||||||
\(288\) | 0.745218 | 0.0439124 | ||||||||
\(289\) | −8.64042 | −0.508260 | ||||||||
\(290\) | −25.4411 | −1.49395 | ||||||||
\(291\) | −22.3422 | −1.30972 | ||||||||
\(292\) | 0.118233 | 0.00691908 | ||||||||
\(293\) | −34.0058 | −1.98664 | −0.993320 | − | 0.115389i | \(-0.963188\pi\) | ||||
−0.993320 | + | 0.115389i | \(0.963188\pi\) | |||||||
\(294\) | −10.3967 | −0.606349 | ||||||||
\(295\) | 16.5165 | 0.961627 | ||||||||
\(296\) | 5.22055 | 0.303438 | ||||||||
\(297\) | 21.4512 | 1.24473 | ||||||||
\(298\) | −23.1692 | −1.34215 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 5.90474 | 0.340911 | ||||||||
\(301\) | −20.2513 | −1.16727 | ||||||||
\(302\) | −20.1390 | −1.15887 | ||||||||
\(303\) | 21.6604 | 1.24436 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 17.9069 | 1.02534 | ||||||||
\(306\) | −2.15464 | −0.123173 | ||||||||
\(307\) | 29.2156 | 1.66743 | 0.833713 | − | 0.552199i | \(-0.186211\pi\) | ||||
0.833713 | + | 0.552199i | \(0.186211\pi\) | |||||||
\(308\) | 14.2332 | 0.811009 | ||||||||
\(309\) | 13.9013 | 0.790819 | ||||||||
\(310\) | −5.13196 | −0.291476 | ||||||||
\(311\) | −13.1516 | −0.745761 | −0.372881 | − | 0.927879i | \(-0.621630\pi\) | ||||
−0.372881 | + | 0.927879i | \(0.621630\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.1828 | 1.25385 | 0.626924 | − | 0.779080i | \(-0.284314\pi\) | ||||
0.626924 | + | 0.779080i | \(0.284314\pi\) | |||||||
\(314\) | 13.0900 | 0.738712 | ||||||||
\(315\) | −8.31082 | −0.468262 | ||||||||
\(316\) | 3.04474 | 0.171280 | ||||||||
\(317\) | 25.2932 | 1.42061 | 0.710303 | − | 0.703896i | \(-0.248558\pi\) | ||||
0.710303 | + | 0.703896i | \(0.248558\pi\) | |||||||
\(318\) | 19.9516 | 1.11883 | ||||||||
\(319\) | 32.4695 | 1.81795 | ||||||||
\(320\) | −2.98870 | −0.167073 | ||||||||
\(321\) | −17.5133 | −0.977496 | ||||||||
\(322\) | −6.22961 | −0.347163 | ||||||||
\(323\) | 2.89129 | 0.160876 | ||||||||
\(324\) | −6.20900 | −0.344944 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.90255 | 0.326912 | ||||||||
\(327\) | −9.11563 | −0.504095 | ||||||||
\(328\) | 10.6438 | 0.587708 | ||||||||
\(329\) | −22.8912 | −1.26203 | ||||||||
\(330\) | −17.1181 | −0.942323 | ||||||||
\(331\) | −27.6235 | −1.51832 | −0.759162 | − | 0.650901i | \(-0.774391\pi\) | ||||
−0.759162 | + | 0.650901i | \(0.774391\pi\) | |||||||
\(332\) | 1.22342 | 0.0671439 | ||||||||
\(333\) | 3.89045 | 0.213195 | ||||||||
\(334\) | 16.6567 | 0.911416 | ||||||||
\(335\) | −21.9687 | −1.20028 | ||||||||
\(336\) | −5.60313 | −0.305676 | ||||||||
\(337\) | −21.3984 | −1.16565 | −0.582824 | − | 0.812599i | \(-0.698052\pi\) | ||||
−0.582824 | + | 0.812599i | \(0.698052\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.94481 | −0.431503 | ||||||||
\(340\) | 8.64121 | 0.468635 | ||||||||
\(341\) | 6.54973 | 0.354688 | ||||||||
\(342\) | −0.745218 | −0.0402968 | ||||||||
\(343\) | 0.284381 | 0.0153551 | ||||||||
\(344\) | −5.42719 | −0.292615 | ||||||||
\(345\) | 7.49233 | 0.403373 | ||||||||
\(346\) | 9.47289 | 0.509266 | ||||||||
\(347\) | −8.49897 | −0.456249 | −0.228124 | − | 0.973632i | \(-0.573259\pi\) | ||||
−0.228124 | + | 0.973632i | \(0.573259\pi\) | |||||||
\(348\) | −12.7822 | −0.685199 | ||||||||
\(349\) | 21.6315 | 1.15791 | 0.578953 | − | 0.815361i | \(-0.303462\pi\) | ||||
0.578953 | + | 0.815361i | \(0.303462\pi\) | |||||||
\(350\) | 14.6733 | 0.784320 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.81437 | 0.203306 | ||||||||
\(353\) | −28.9686 | −1.54184 | −0.770922 | − | 0.636930i | \(-0.780204\pi\) | ||||
−0.770922 | + | 0.636930i | \(0.780204\pi\) | |||||||
\(354\) | 8.29828 | 0.441048 | ||||||||
\(355\) | −29.1696 | −1.54816 | ||||||||
\(356\) | −14.8184 | −0.785372 | ||||||||
\(357\) | 16.2003 | 0.857411 | ||||||||
\(358\) | 5.00441 | 0.264491 | ||||||||
\(359\) | −7.42119 | −0.391675 | −0.195838 | − | 0.980636i | \(-0.562743\pi\) | ||||
−0.195838 | + | 0.980636i | \(0.562743\pi\) | |||||||
\(360\) | −2.22723 | −0.117385 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 1.97399 | 0.103751 | ||||||||
\(363\) | 5.32973 | 0.279738 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.353364 | −0.0184959 | ||||||||
\(366\) | 8.99684 | 0.470272 | ||||||||
\(367\) | 13.6135 | 0.710619 | 0.355310 | − | 0.934749i | \(-0.384375\pi\) | ||||
0.355310 | + | 0.934749i | \(0.384375\pi\) | |||||||
\(368\) | −1.66948 | −0.0870279 | ||||||||
\(369\) | 7.93198 | 0.412923 | ||||||||
\(370\) | −15.6027 | −0.811144 | ||||||||
\(371\) | 49.5798 | 2.57405 | ||||||||
\(372\) | −2.57842 | −0.133685 | ||||||||
\(373\) | −2.73685 | −0.141709 | −0.0708544 | − | 0.997487i | \(-0.522573\pi\) | ||||
−0.0708544 | + | 0.997487i | \(0.522573\pi\) | |||||||
\(374\) | −11.0285 | −0.570268 | ||||||||
\(375\) | 4.79155 | 0.247434 | ||||||||
\(376\) | −6.13466 | −0.316371 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −20.9850 | −1.07935 | ||||||||
\(379\) | 1.62208 | 0.0833208 | 0.0416604 | − | 0.999132i | \(-0.486735\pi\) | ||||
0.0416604 | + | 0.999132i | \(0.486735\pi\) | |||||||
\(380\) | 2.98870 | 0.153317 | ||||||||
\(381\) | −16.9209 | −0.866882 | ||||||||
\(382\) | 20.8136 | 1.06492 | ||||||||
\(383\) | −31.9773 | −1.63396 | −0.816981 | − | 0.576664i | \(-0.804354\pi\) | ||||
−0.816981 | + | 0.576664i | \(0.804354\pi\) | |||||||
\(384\) | −1.50159 | −0.0766279 | ||||||||
\(385\) | −42.5386 | −2.16797 | ||||||||
\(386\) | 21.3064 | 1.08447 | ||||||||
\(387\) | −4.04444 | −0.205591 | ||||||||
\(388\) | −14.8790 | −0.755366 | ||||||||
\(389\) | −4.42183 | −0.224195 | −0.112098 | − | 0.993697i | \(-0.535757\pi\) | ||||
−0.112098 | + | 0.993697i | \(0.535757\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.82697 | 0.244110 | ||||||||
\(392\) | −6.92379 | −0.349704 | ||||||||
\(393\) | −19.1628 | −0.966636 | ||||||||
\(394\) | −8.62246 | −0.434393 | ||||||||
\(395\) | −9.09981 | −0.457861 | ||||||||
\(396\) | 2.84253 | 0.142843 | ||||||||
\(397\) | −0.227725 | −0.0114292 | −0.00571459 | − | 0.999984i | \(-0.501819\pi\) | ||||
−0.00571459 | + | 0.999984i | \(0.501819\pi\) | |||||||
\(398\) | −4.00411 | −0.200708 | ||||||||
\(399\) | 5.60313 | 0.280508 | ||||||||
\(400\) | 3.93232 | 0.196616 | ||||||||
\(401\) | −6.80150 | −0.339651 | −0.169825 | − | 0.985474i | \(-0.554320\pi\) | ||||
−0.169825 | + | 0.985474i | \(0.554320\pi\) | |||||||
\(402\) | −11.0376 | −0.550505 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 14.4250 | 0.717669 | ||||||||
\(405\) | 18.5568 | 0.922096 | ||||||||
\(406\) | −31.7638 | −1.57641 | ||||||||
\(407\) | 19.9131 | 0.987056 | ||||||||
\(408\) | 4.34155 | 0.214939 | ||||||||
\(409\) | −16.0814 | −0.795175 | −0.397588 | − | 0.917564i | \(-0.630153\pi\) | ||||
−0.397588 | + | 0.917564i | \(0.630153\pi\) | |||||||
\(410\) | −31.8112 | −1.57105 | ||||||||
\(411\) | 12.1688 | 0.600241 | ||||||||
\(412\) | 9.25772 | 0.456095 | ||||||||
\(413\) | 20.6212 | 1.01470 | ||||||||
\(414\) | −1.24413 | −0.0611456 | ||||||||
\(415\) | −3.65644 | −0.179487 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.8659 | 0.727986 | ||||||||
\(418\) | −3.81437 | −0.186567 | ||||||||
\(419\) | −21.3995 | −1.04544 | −0.522718 | − | 0.852506i | \(-0.675082\pi\) | ||||
−0.522718 | + | 0.852506i | \(0.675082\pi\) | |||||||
\(420\) | 16.7461 | 0.817125 | ||||||||
\(421\) | −26.3895 | −1.28615 | −0.643074 | − | 0.765804i | \(-0.722341\pi\) | ||||
−0.643074 | + | 0.765804i | \(0.722341\pi\) | |||||||
\(422\) | −8.29916 | −0.403997 | ||||||||
\(423\) | −4.57165 | −0.222281 | ||||||||
\(424\) | 13.2870 | 0.645272 | ||||||||
\(425\) | −11.3695 | −0.551501 | ||||||||
\(426\) | −14.6555 | −0.710062 | ||||||||
\(427\) | 22.3571 | 1.08194 | ||||||||
\(428\) | −11.6631 | −0.563759 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 16.2202 | 0.782210 | ||||||||
\(431\) | −22.5479 | −1.08609 | −0.543047 | − | 0.839702i | \(-0.682729\pi\) | ||||
−0.543047 | + | 0.839702i | \(0.682729\pi\) | |||||||
\(432\) | −5.62379 | −0.270575 | ||||||||
\(433\) | 11.5129 | 0.553273 | 0.276636 | − | 0.960975i | \(-0.410780\pi\) | ||||
0.276636 | + | 0.960975i | \(0.410780\pi\) | |||||||
\(434\) | −6.40737 | −0.307564 | ||||||||
\(435\) | 38.2022 | 1.83165 | ||||||||
\(436\) | −6.07064 | −0.290731 | ||||||||
\(437\) | 1.66948 | 0.0798623 | ||||||||
\(438\) | −0.177538 | −0.00848311 | ||||||||
\(439\) | −11.6448 | −0.555778 | −0.277889 | − | 0.960613i | \(-0.589635\pi\) | ||||
−0.277889 | + | 0.960613i | \(0.589635\pi\) | |||||||
\(440\) | −11.4000 | −0.543473 | ||||||||
\(441\) | −5.15973 | −0.245701 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.0168 | 1.23609 | 0.618047 | − | 0.786141i | \(-0.287924\pi\) | ||||
0.618047 | + | 0.786141i | \(0.287924\pi\) | |||||||
\(444\) | −7.83915 | −0.372029 | ||||||||
\(445\) | 44.2877 | 2.09944 | ||||||||
\(446\) | 8.81599 | 0.417449 | ||||||||
\(447\) | 34.7906 | 1.64554 | ||||||||
\(448\) | −3.73146 | −0.176295 | ||||||||
\(449\) | −11.7314 | −0.553640 | −0.276820 | − | 0.960922i | \(-0.589281\pi\) | ||||
−0.276820 | + | 0.960922i | \(0.589281\pi\) | |||||||
\(450\) | 2.93043 | 0.138142 | ||||||||
\(451\) | 40.5995 | 1.91176 | ||||||||
\(452\) | −5.29092 | −0.248864 | ||||||||
\(453\) | 30.2406 | 1.42083 | ||||||||
\(454\) | −4.18895 | −0.196597 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.50159 | 0.0703185 | ||||||||
\(457\) | 36.7678 | 1.71993 | 0.859963 | − | 0.510356i | \(-0.170486\pi\) | ||||
0.859963 | + | 0.510356i | \(0.170486\pi\) | |||||||
\(458\) | −24.2635 | −1.13376 | ||||||||
\(459\) | 16.2600 | 0.758954 | ||||||||
\(460\) | 4.98959 | 0.232641 | ||||||||
\(461\) | 12.0022 | 0.558996 | 0.279498 | − | 0.960146i | \(-0.409832\pi\) | ||||
0.279498 | + | 0.960146i | \(0.409832\pi\) | |||||||
\(462\) | −21.3724 | −0.994334 | ||||||||
\(463\) | −15.5101 | −0.720815 | −0.360407 | − | 0.932795i | \(-0.617362\pi\) | ||||
−0.360407 | + | 0.932795i | \(0.617362\pi\) | |||||||
\(464\) | −8.51244 | −0.395180 | ||||||||
\(465\) | 7.70612 | 0.357363 | ||||||||
\(466\) | −17.9212 | −0.830182 | ||||||||
\(467\) | −25.8302 | −1.19528 | −0.597639 | − | 0.801765i | \(-0.703894\pi\) | ||||
−0.597639 | + | 0.801765i | \(0.703894\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −27.4284 | −1.26653 | ||||||||
\(470\) | 18.3346 | 0.845714 | ||||||||
\(471\) | −19.6559 | −0.905695 | ||||||||
\(472\) | 5.52632 | 0.254369 | ||||||||
\(473\) | −20.7013 | −0.951847 | ||||||||
\(474\) | −4.57196 | −0.209997 | ||||||||
\(475\) | −3.93232 | −0.180427 | ||||||||
\(476\) | 10.7887 | 0.494501 | ||||||||
\(477\) | 9.90169 | 0.453367 | ||||||||
\(478\) | −22.3178 | −1.02079 | ||||||||
\(479\) | −10.0622 | −0.459753 | −0.229876 | − | 0.973220i | \(-0.573832\pi\) | ||||
−0.229876 | + | 0.973220i | \(0.573832\pi\) | |||||||
\(480\) | 4.48781 | 0.204840 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 22.3962 | 1.02012 | ||||||||
\(483\) | 9.35434 | 0.425637 | ||||||||
\(484\) | 3.54939 | 0.161336 | ||||||||
\(485\) | 44.4688 | 2.01922 | ||||||||
\(486\) | −7.54799 | −0.342384 | ||||||||
\(487\) | 5.76723 | 0.261338 | 0.130669 | − | 0.991426i | \(-0.458287\pi\) | ||||
0.130669 | + | 0.991426i | \(0.458287\pi\) | |||||||
\(488\) | 5.99153 | 0.271224 | ||||||||
\(489\) | −8.86323 | −0.400809 | ||||||||
\(490\) | 20.6931 | 0.934820 | ||||||||
\(491\) | 19.4673 | 0.878546 | 0.439273 | − | 0.898354i | \(-0.355236\pi\) | ||||
0.439273 | + | 0.898354i | \(0.355236\pi\) | |||||||
\(492\) | −15.9827 | −0.720557 | ||||||||
\(493\) | 24.6120 | 1.10847 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.49548 | −0.381843 | ||||||||
\(496\) | −1.71712 | −0.0771010 | ||||||||
\(497\) | −36.4190 | −1.63361 | ||||||||
\(498\) | −1.83708 | −0.0823215 | ||||||||
\(499\) | −4.74563 | −0.212444 | −0.106222 | − | 0.994342i | \(-0.533875\pi\) | ||||
−0.106222 | + | 0.994342i | \(0.533875\pi\) | |||||||
\(500\) | 3.19098 | 0.142705 | ||||||||
\(501\) | −25.0116 | −1.11744 | ||||||||
\(502\) | −3.68665 | −0.164543 | ||||||||
\(503\) | −30.4469 | −1.35756 | −0.678779 | − | 0.734342i | \(-0.737491\pi\) | ||||
−0.678779 | + | 0.734342i | \(0.737491\pi\) | |||||||
\(504\) | −2.78075 | −0.123864 | ||||||||
\(505\) | −43.1119 | −1.91845 | ||||||||
\(506\) | −6.36802 | −0.283093 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −11.2686 | −0.499963 | ||||||||
\(509\) | 6.35941 | 0.281876 | 0.140938 | − | 0.990018i | \(-0.454988\pi\) | ||||
0.140938 | + | 0.990018i | \(0.454988\pi\) | |||||||
\(510\) | −12.9756 | −0.574568 | ||||||||
\(511\) | −0.441183 | −0.0195168 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 5.62379 | 0.248297 | ||||||||
\(514\) | −12.7082 | −0.560536 | ||||||||
\(515\) | −27.6685 | −1.21922 | ||||||||
\(516\) | 8.14944 | 0.358759 | ||||||||
\(517\) | −23.3998 | −1.02912 | ||||||||
\(518\) | −19.4803 | −0.855914 | ||||||||
\(519\) | −14.2244 | −0.624383 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.30076 | 0.363663 | 0.181832 | − | 0.983330i | \(-0.441797\pi\) | ||||
0.181832 | + | 0.983330i | \(0.441797\pi\) | |||||||
\(522\) | −6.34362 | −0.277653 | ||||||||
\(523\) | 0.111917 | 0.00489377 | 0.00244688 | − | 0.999997i | \(-0.499221\pi\) | ||||
0.00244688 | + | 0.999997i | \(0.499221\pi\) | |||||||
\(524\) | −12.7617 | −0.557495 | ||||||||
\(525\) | −22.0333 | −0.961613 | ||||||||
\(526\) | −3.24916 | −0.141670 | ||||||||
\(527\) | 4.96470 | 0.216266 | ||||||||
\(528\) | −5.72763 | −0.249263 | ||||||||
\(529\) | −20.2128 | −0.878818 | ||||||||
\(530\) | −39.7107 | −1.72492 | ||||||||
\(531\) | 4.11831 | 0.178719 | ||||||||
\(532\) | 3.73146 | 0.161779 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 22.2512 | 0.962903 | ||||||||
\(535\) | 34.8576 | 1.50703 | ||||||||
\(536\) | −7.35059 | −0.317497 | ||||||||
\(537\) | −7.51459 | −0.324278 | ||||||||
\(538\) | −10.9402 | −0.471667 | ||||||||
\(539\) | −26.4099 | −1.13755 | ||||||||
\(540\) | 16.8078 | 0.723294 | ||||||||
\(541\) | −36.1474 | −1.55410 | −0.777049 | − | 0.629440i | \(-0.783284\pi\) | ||||
−0.777049 | + | 0.629440i | \(0.783284\pi\) | |||||||
\(542\) | −0.968555 | −0.0416030 | ||||||||
\(543\) | −2.96414 | −0.127203 | ||||||||
\(544\) | 2.89129 | 0.123963 | ||||||||
\(545\) | 18.1433 | 0.777174 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.56274 | −0.237846 | −0.118923 | − | 0.992904i | \(-0.537944\pi\) | ||||
−0.118923 | + | 0.992904i | \(0.537944\pi\) | |||||||
\(548\) | 8.10390 | 0.346182 | ||||||||
\(549\) | 4.46500 | 0.190561 | ||||||||
\(550\) | 14.9993 | 0.639572 | ||||||||
\(551\) | 8.51244 | 0.362642 | ||||||||
\(552\) | 2.50689 | 0.106700 | ||||||||
\(553\) | −11.3613 | −0.483132 | ||||||||
\(554\) | −8.02640 | −0.341009 | ||||||||
\(555\) | 23.4288 | 0.994499 | ||||||||
\(556\) | 9.90009 | 0.419857 | ||||||||
\(557\) | −12.7166 | −0.538820 | −0.269410 | − | 0.963026i | \(-0.586829\pi\) | ||||
−0.269410 | + | 0.963026i | \(0.586829\pi\) | |||||||
\(558\) | −1.27963 | −0.0541711 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 11.1522 | 0.471267 | ||||||||
\(561\) | 16.5603 | 0.699174 | ||||||||
\(562\) | −4.41792 | −0.186359 | ||||||||
\(563\) | −32.2272 | −1.35821 | −0.679106 | − | 0.734040i | \(-0.737633\pi\) | ||||
−0.679106 | + | 0.734040i | \(0.737633\pi\) | |||||||
\(564\) | 9.21176 | 0.387885 | ||||||||
\(565\) | 15.8130 | 0.665256 | ||||||||
\(566\) | 15.7900 | 0.663705 | ||||||||
\(567\) | 23.1686 | 0.972990 | ||||||||
\(568\) | −9.75998 | −0.409520 | ||||||||
\(569\) | −3.69103 | −0.154736 | −0.0773680 | − | 0.997003i | \(-0.524652\pi\) | ||||
−0.0773680 | + | 0.997003i | \(0.524652\pi\) | |||||||
\(570\) | −4.48781 | −0.187974 | ||||||||
\(571\) | −21.2298 | −0.888440 | −0.444220 | − | 0.895918i | \(-0.646519\pi\) | ||||
−0.444220 | + | 0.895918i | \(0.646519\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −31.2536 | −1.30564 | ||||||||
\(574\) | −39.7171 | −1.65776 | ||||||||
\(575\) | −6.56495 | −0.273777 | ||||||||
\(576\) | −0.745218 | −0.0310507 | ||||||||
\(577\) | −16.7181 | −0.695983 | −0.347992 | − | 0.937498i | \(-0.613136\pi\) | ||||
−0.347992 | + | 0.937498i | \(0.613136\pi\) | |||||||
\(578\) | 8.64042 | 0.359394 | ||||||||
\(579\) | −31.9935 | −1.32960 | ||||||||
\(580\) | 25.4411 | 1.05638 | ||||||||
\(581\) | −4.56514 | −0.189394 | ||||||||
\(582\) | 22.3422 | 0.926113 | ||||||||
\(583\) | 50.6814 | 2.09901 | ||||||||
\(584\) | −0.118233 | −0.00489253 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 34.0058 | 1.40477 | ||||||||
\(587\) | −25.7669 | −1.06351 | −0.531757 | − | 0.846897i | \(-0.678468\pi\) | ||||
−0.531757 | + | 0.846897i | \(0.678468\pi\) | |||||||
\(588\) | 10.3967 | 0.428753 | ||||||||
\(589\) | 1.71712 | 0.0707528 | ||||||||
\(590\) | −16.5165 | −0.679973 | ||||||||
\(591\) | 12.9474 | 0.532586 | ||||||||
\(592\) | −5.22055 | −0.214563 | ||||||||
\(593\) | 22.0804 | 0.906734 | 0.453367 | − | 0.891324i | \(-0.350223\pi\) | ||||
0.453367 | + | 0.891324i | \(0.350223\pi\) | |||||||
\(594\) | −21.4512 | −0.880154 | ||||||||
\(595\) | −32.2443 | −1.32189 | ||||||||
\(596\) | 23.1692 | 0.949045 | ||||||||
\(597\) | 6.01254 | 0.246077 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.2400 | −0.990421 | −0.495211 | − | 0.868773i | \(-0.664909\pi\) | ||||
−0.495211 | + | 0.868773i | \(0.664909\pi\) | |||||||
\(600\) | −5.90474 | −0.241060 | ||||||||
\(601\) | −25.0975 | −1.02375 | −0.511875 | − | 0.859060i | \(-0.671049\pi\) | ||||
−0.511875 | + | 0.859060i | \(0.671049\pi\) | |||||||
\(602\) | 20.2513 | 0.825383 | ||||||||
\(603\) | −5.47779 | −0.223073 | ||||||||
\(604\) | 20.1390 | 0.819446 | ||||||||
\(605\) | −10.6080 | −0.431278 | ||||||||
\(606\) | −21.6604 | −0.879895 | ||||||||
\(607\) | 39.1982 | 1.59101 | 0.795503 | − | 0.605950i | \(-0.207207\pi\) | ||||
0.795503 | + | 0.605950i | \(0.207207\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 47.6963 | 1.93275 | ||||||||
\(610\) | −17.9069 | −0.725028 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 2.15464 | 0.0870963 | ||||||||
\(613\) | 31.8846 | 1.28781 | 0.643904 | − | 0.765106i | \(-0.277314\pi\) | ||||
0.643904 | + | 0.765106i | \(0.277314\pi\) | |||||||
\(614\) | −29.2156 | −1.17905 | ||||||||
\(615\) | 47.7675 | 1.92617 | ||||||||
\(616\) | −14.2332 | −0.573470 | ||||||||
\(617\) | −29.2084 | −1.17589 | −0.587944 | − | 0.808902i | \(-0.700062\pi\) | ||||
−0.587944 | + | 0.808902i | \(0.700062\pi\) | |||||||
\(618\) | −13.9013 | −0.559193 | ||||||||
\(619\) | −34.6290 | −1.39186 | −0.695929 | − | 0.718111i | \(-0.745007\pi\) | ||||
−0.695929 | + | 0.718111i | \(0.745007\pi\) | |||||||
\(620\) | 5.13196 | 0.206104 | ||||||||
\(621\) | 9.38884 | 0.376761 | ||||||||
\(622\) | 13.1516 | 0.527333 | ||||||||
\(623\) | 55.2942 | 2.21531 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.1985 | −1.16794 | ||||||||
\(626\) | −22.1828 | −0.886605 | ||||||||
\(627\) | 5.72763 | 0.228739 | ||||||||
\(628\) | −13.0900 | −0.522349 | ||||||||
\(629\) | 15.0942 | 0.601843 | ||||||||
\(630\) | 8.31082 | 0.331111 | ||||||||
\(631\) | 16.9719 | 0.675640 | 0.337820 | − | 0.941211i | \(-0.390311\pi\) | ||||
0.337820 | + | 0.941211i | \(0.390311\pi\) | |||||||
\(632\) | −3.04474 | −0.121113 | ||||||||
\(633\) | 12.4620 | 0.495318 | ||||||||
\(634\) | −25.2932 | −1.00452 | ||||||||
\(635\) | 33.6785 | 1.33649 | ||||||||
\(636\) | −19.9516 | −0.791133 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −32.4695 | −1.28548 | ||||||||
\(639\) | −7.27331 | −0.287728 | ||||||||
\(640\) | 2.98870 | 0.118139 | ||||||||
\(641\) | −22.2794 | −0.879982 | −0.439991 | − | 0.898002i | \(-0.645018\pi\) | ||||
−0.439991 | + | 0.898002i | \(0.645018\pi\) | |||||||
\(642\) | 17.5133 | 0.691194 | ||||||||
\(643\) | 42.5539 | 1.67816 | 0.839080 | − | 0.544007i | \(-0.183094\pi\) | ||||
0.839080 | + | 0.544007i | \(0.183094\pi\) | |||||||
\(644\) | 6.22961 | 0.245481 | ||||||||
\(645\) | −24.3562 | −0.959025 | ||||||||
\(646\) | −2.89129 | −0.113756 | ||||||||
\(647\) | 37.1643 | 1.46108 | 0.730539 | − | 0.682871i | \(-0.239269\pi\) | ||||
0.730539 | + | 0.682871i | \(0.239269\pi\) | |||||||
\(648\) | 6.20900 | 0.243912 | ||||||||
\(649\) | 21.0794 | 0.827438 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.62126 | 0.377087 | ||||||||
\(652\) | −5.90255 | −0.231162 | ||||||||
\(653\) | −42.4412 | −1.66085 | −0.830427 | − | 0.557127i | \(-0.811904\pi\) | ||||
−0.830427 | + | 0.557127i | \(0.811904\pi\) | |||||||
\(654\) | 9.11563 | 0.356449 | ||||||||
\(655\) | 38.1407 | 1.49028 | ||||||||
\(656\) | −10.6438 | −0.415572 | ||||||||
\(657\) | −0.0881096 | −0.00343748 | ||||||||
\(658\) | 22.8912 | 0.892392 | ||||||||
\(659\) | −32.8747 | −1.28062 | −0.640308 | − | 0.768118i | \(-0.721193\pi\) | ||||
−0.640308 | + | 0.768118i | \(0.721193\pi\) | |||||||
\(660\) | 17.1181 | 0.666323 | ||||||||
\(661\) | −15.2765 | −0.594189 | −0.297094 | − | 0.954848i | \(-0.596018\pi\) | ||||
−0.297094 | + | 0.954848i | \(0.596018\pi\) | |||||||
\(662\) | 27.6235 | 1.07362 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.22342 | −0.0474779 | ||||||||
\(665\) | −11.1522 | −0.432464 | ||||||||
\(666\) | −3.89045 | −0.150752 | ||||||||
\(667\) | 14.2114 | 0.550267 | ||||||||
\(668\) | −16.6567 | −0.644468 | ||||||||
\(669\) | −13.2380 | −0.511812 | ||||||||
\(670\) | 21.9687 | 0.848725 | ||||||||
\(671\) | 22.8539 | 0.882264 | ||||||||
\(672\) | 5.60313 | 0.216146 | ||||||||
\(673\) | 6.81905 | 0.262855 | 0.131428 | − | 0.991326i | \(-0.458044\pi\) | ||||
0.131428 | + | 0.991326i | \(0.458044\pi\) | |||||||
\(674\) | 21.3984 | 0.824237 | ||||||||
\(675\) | −22.1146 | −0.851190 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.0962 | 0.810793 | 0.405396 | − | 0.914141i | \(-0.367134\pi\) | ||||
0.405396 | + | 0.914141i | \(0.367134\pi\) | |||||||
\(678\) | 7.94481 | 0.305119 | ||||||||
\(679\) | 55.5203 | 2.13067 | ||||||||
\(680\) | −8.64121 | −0.331375 | ||||||||
\(681\) | 6.29010 | 0.241037 | ||||||||
\(682\) | −6.54973 | −0.250802 | ||||||||
\(683\) | −43.7151 | −1.67271 | −0.836355 | − | 0.548188i | \(-0.815318\pi\) | ||||
−0.836355 | + | 0.548188i | \(0.815318\pi\) | |||||||
\(684\) | 0.745218 | 0.0284941 | ||||||||
\(685\) | −24.2201 | −0.925403 | ||||||||
\(686\) | −0.284381 | −0.0108577 | ||||||||
\(687\) | 36.4339 | 1.39004 | ||||||||
\(688\) | 5.42719 | 0.206910 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −7.49233 | −0.285228 | ||||||||
\(691\) | −43.6813 | −1.66172 | −0.830858 | − | 0.556485i | \(-0.812150\pi\) | ||||
−0.830858 | + | 0.556485i | \(0.812150\pi\) | |||||||
\(692\) | −9.47289 | −0.360105 | ||||||||
\(693\) | −10.6068 | −0.402919 | ||||||||
\(694\) | 8.49897 | 0.322617 | ||||||||
\(695\) | −29.5884 | −1.12235 | ||||||||
\(696\) | 12.7822 | 0.484509 | ||||||||
\(697\) | 30.7745 | 1.16567 | ||||||||
\(698\) | −21.6315 | −0.818763 | ||||||||
\(699\) | 26.9103 | 1.01784 | ||||||||
\(700\) | −14.6733 | −0.554598 | ||||||||
\(701\) | 12.9613 | 0.489540 | 0.244770 | − | 0.969581i | \(-0.421288\pi\) | ||||
0.244770 | + | 0.969581i | \(0.421288\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.22055 | 0.196897 | ||||||||
\(704\) | −3.81437 | −0.143759 | ||||||||
\(705\) | −27.5312 | −1.03688 | ||||||||
\(706\) | 28.9686 | 1.09025 | ||||||||
\(707\) | −53.8262 | −2.02434 | ||||||||
\(708\) | −8.29828 | −0.311868 | ||||||||
\(709\) | 3.19138 | 0.119855 | 0.0599275 | − | 0.998203i | \(-0.480913\pi\) | ||||
0.0599275 | + | 0.998203i | \(0.480913\pi\) | |||||||
\(710\) | 29.1696 | 1.09472 | ||||||||
\(711\) | −2.26899 | −0.0850939 | ||||||||
\(712\) | 14.8184 | 0.555342 | ||||||||
\(713\) | 2.86671 | 0.107359 | ||||||||
\(714\) | −16.2003 | −0.606281 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.00441 | −0.187024 | ||||||||
\(717\) | 33.5122 | 1.25154 | ||||||||
\(718\) | 7.42119 | 0.276956 | ||||||||
\(719\) | 52.2035 | 1.94686 | 0.973431 | − | 0.228980i | \(-0.0735391\pi\) | ||||
0.973431 | + | 0.228980i | \(0.0735391\pi\) | |||||||
\(720\) | 2.22723 | 0.0830040 | ||||||||
\(721\) | −34.5448 | −1.28652 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | −33.6300 | −1.25071 | ||||||||
\(724\) | −1.97399 | −0.0733629 | ||||||||
\(725\) | −33.4736 | −1.24318 | ||||||||
\(726\) | −5.32973 | −0.197805 | ||||||||
\(727\) | −44.7559 | −1.65990 | −0.829952 | − | 0.557835i | \(-0.811632\pi\) | ||||
−0.829952 | + | 0.557835i | \(0.811632\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.9610 | 1.10967 | ||||||||
\(730\) | 0.353364 | 0.0130786 | ||||||||
\(731\) | −15.6916 | −0.580375 | ||||||||
\(732\) | −8.99684 | −0.332533 | ||||||||
\(733\) | 12.8805 | 0.475753 | 0.237877 | − | 0.971295i | \(-0.423549\pi\) | ||||
0.237877 | + | 0.971295i | \(0.423549\pi\) | |||||||
\(734\) | −13.6135 | −0.502484 | ||||||||
\(735\) | −31.0726 | −1.14613 | ||||||||
\(736\) | 1.66948 | 0.0615380 | ||||||||
\(737\) | −28.0378 | −1.03279 | ||||||||
\(738\) | −7.93198 | −0.291980 | ||||||||
\(739\) | −31.0761 | −1.14315 | −0.571577 | − | 0.820549i | \(-0.693668\pi\) | ||||
−0.571577 | + | 0.820549i | \(0.693668\pi\) | |||||||
\(740\) | 15.6027 | 0.573565 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −49.5798 | −1.82013 | ||||||||
\(743\) | −33.6944 | −1.23613 | −0.618064 | − | 0.786128i | \(-0.712083\pi\) | ||||
−0.618064 | + | 0.786128i | \(0.712083\pi\) | |||||||
\(744\) | 2.57842 | 0.0945294 | ||||||||
\(745\) | −69.2456 | −2.53696 | ||||||||
\(746\) | 2.73685 | 0.100203 | ||||||||
\(747\) | −0.911715 | −0.0333579 | ||||||||
\(748\) | 11.0285 | 0.403240 | ||||||||
\(749\) | 43.5205 | 1.59021 | ||||||||
\(750\) | −4.79155 | −0.174963 | ||||||||
\(751\) | 1.70343 | 0.0621589 | 0.0310794 | − | 0.999517i | \(-0.490106\pi\) | ||||
0.0310794 | + | 0.999517i | \(0.490106\pi\) | |||||||
\(752\) | 6.13466 | 0.223708 | ||||||||
\(753\) | 5.53585 | 0.201738 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −60.1895 | −2.19052 | ||||||||
\(756\) | 20.9850 | 0.763216 | ||||||||
\(757\) | 35.2712 | 1.28195 | 0.640976 | − | 0.767561i | \(-0.278530\pi\) | ||||
0.640976 | + | 0.767561i | \(0.278530\pi\) | |||||||
\(758\) | −1.62208 | −0.0589167 | ||||||||
\(759\) | 9.56218 | 0.347085 | ||||||||
\(760\) | −2.98870 | −0.108411 | ||||||||
\(761\) | −6.63116 | −0.240379 | −0.120190 | − | 0.992751i | \(-0.538350\pi\) | ||||
−0.120190 | + | 0.992751i | \(0.538350\pi\) | |||||||
\(762\) | 16.9209 | 0.612978 | ||||||||
\(763\) | 22.6523 | 0.820070 | ||||||||
\(764\) | −20.8136 | −0.753010 | ||||||||
\(765\) | −6.43958 | −0.232824 | ||||||||
\(766\) | 31.9773 | 1.15539 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.50159 | 0.0541841 | ||||||||
\(769\) | 19.7122 | 0.710840 | 0.355420 | − | 0.934707i | \(-0.384338\pi\) | ||||
0.355420 | + | 0.934707i | \(0.384338\pi\) | |||||||
\(770\) | 42.5386 | 1.53298 | ||||||||
\(771\) | 19.0826 | 0.687243 | ||||||||
\(772\) | −21.3064 | −0.766833 | ||||||||
\(773\) | −10.8204 | −0.389184 | −0.194592 | − | 0.980884i | \(-0.562338\pi\) | ||||
−0.194592 | + | 0.980884i | \(0.562338\pi\) | |||||||
\(774\) | 4.04444 | 0.145374 | ||||||||
\(775\) | −6.75227 | −0.242549 | ||||||||
\(776\) | 14.8790 | 0.534124 | ||||||||
\(777\) | 29.2515 | 1.04939 | ||||||||
\(778\) | 4.42183 | 0.158530 | ||||||||
\(779\) | 10.6438 | 0.381355 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −37.2281 | −1.33213 | ||||||||
\(782\) | −4.82697 | −0.172612 | ||||||||
\(783\) | 47.8722 | 1.71081 | ||||||||
\(784\) | 6.92379 | 0.247278 | ||||||||
\(785\) | 39.1221 | 1.39633 | ||||||||
\(786\) | 19.1628 | 0.683515 | ||||||||
\(787\) | 48.0124 | 1.71146 | 0.855729 | − | 0.517424i | \(-0.173109\pi\) | ||||
0.855729 | + | 0.517424i | \(0.173109\pi\) | |||||||
\(788\) | 8.62246 | 0.307162 | ||||||||
\(789\) | 4.87891 | 0.173694 | ||||||||
\(790\) | 9.09981 | 0.323757 | ||||||||
\(791\) | 19.7429 | 0.701975 | ||||||||
\(792\) | −2.84253 | −0.101005 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0.227725 | 0.00808165 | ||||||||
\(795\) | 59.6294 | 2.11484 | ||||||||
\(796\) | 4.00411 | 0.141922 | ||||||||
\(797\) | 22.8603 | 0.809755 | 0.404878 | − | 0.914371i | \(-0.367314\pi\) | ||||
0.404878 | + | 0.914371i | \(0.367314\pi\) | |||||||
\(798\) | −5.60313 | −0.198349 | ||||||||
\(799\) | −17.7371 | −0.627493 | ||||||||
\(800\) | −3.93232 | −0.139028 | ||||||||
\(801\) | 11.0429 | 0.390182 | ||||||||
\(802\) | 6.80150 | 0.240169 | ||||||||
\(803\) | −0.450985 | −0.0159149 | ||||||||
\(804\) | 11.0376 | 0.389266 | ||||||||
\(805\) | −18.6184 | −0.656214 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.4278 | 0.578285 | ||||||||
\(808\) | −14.4250 | −0.507469 | ||||||||
\(809\) | 16.3061 | 0.573294 | 0.286647 | − | 0.958036i | \(-0.407459\pi\) | ||||
0.286647 | + | 0.958036i | \(0.407459\pi\) | |||||||
\(810\) | −18.5568 | −0.652020 | ||||||||
\(811\) | 0.810412 | 0.0284574 | 0.0142287 | − | 0.999899i | \(-0.495471\pi\) | ||||
0.0142287 | + | 0.999899i | \(0.495471\pi\) | |||||||
\(812\) | 31.7638 | 1.11469 | ||||||||
\(813\) | 1.45437 | 0.0510072 | ||||||||
\(814\) | −19.9131 | −0.697954 | ||||||||
\(815\) | 17.6409 | 0.617935 | ||||||||
\(816\) | −4.34155 | −0.151985 | ||||||||
\(817\) | −5.42719 | −0.189873 | ||||||||
\(818\) | 16.0814 | 0.562274 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 31.8112 | 1.11090 | ||||||||
\(821\) | 6.51020 | 0.227208 | 0.113604 | − | 0.993526i | \(-0.463761\pi\) | ||||
0.113604 | + | 0.993526i | \(0.463761\pi\) | |||||||
\(822\) | −12.1688 | −0.424434 | ||||||||
\(823\) | 22.1663 | 0.772670 | 0.386335 | − | 0.922359i | \(-0.373741\pi\) | ||||
0.386335 | + | 0.922359i | \(0.373741\pi\) | |||||||
\(824\) | −9.25772 | −0.322508 | ||||||||
\(825\) | −22.5229 | −0.784145 | ||||||||
\(826\) | −20.6212 | −0.717504 | ||||||||
\(827\) | −8.74542 | −0.304108 | −0.152054 | − | 0.988372i | \(-0.548589\pi\) | ||||
−0.152054 | + | 0.988372i | \(0.548589\pi\) | |||||||
\(828\) | 1.24413 | 0.0432365 | ||||||||
\(829\) | −22.2016 | −0.771092 | −0.385546 | − | 0.922689i | \(-0.625987\pi\) | ||||
−0.385546 | + | 0.922689i | \(0.625987\pi\) | |||||||
\(830\) | 3.65644 | 0.126917 | ||||||||
\(831\) | 12.0524 | 0.418093 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −20.0187 | −0.693607 | ||||||||
\(834\) | −14.8659 | −0.514764 | ||||||||
\(835\) | 49.7819 | 1.72278 | ||||||||
\(836\) | 3.81437 | 0.131923 | ||||||||
\(837\) | 9.65674 | 0.333786 | ||||||||
\(838\) | 21.3995 | 0.739234 | ||||||||
\(839\) | −31.7739 | −1.09696 | −0.548479 | − | 0.836164i | \(-0.684793\pi\) | ||||
−0.548479 | + | 0.836164i | \(0.684793\pi\) | |||||||
\(840\) | −16.7461 | −0.577795 | ||||||||
\(841\) | 43.4616 | 1.49868 | ||||||||
\(842\) | 26.3895 | 0.909444 | ||||||||
\(843\) | 6.63391 | 0.228484 | ||||||||
\(844\) | 8.29916 | 0.285669 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.57165 | 0.157177 | ||||||||
\(847\) | −13.2444 | −0.455083 | ||||||||
\(848\) | −13.2870 | −0.456276 | ||||||||
\(849\) | −23.7102 | −0.813733 | ||||||||
\(850\) | 11.3695 | 0.389970 | ||||||||
\(851\) | 8.71563 | 0.298768 | ||||||||
\(852\) | 14.6555 | 0.502090 | ||||||||
\(853\) | −56.4010 | −1.93113 | −0.965567 | − | 0.260154i | \(-0.916227\pi\) | ||||
−0.965567 | + | 0.260154i | \(0.916227\pi\) | |||||||
\(854\) | −22.3571 | −0.765046 | ||||||||
\(855\) | −2.22723 | −0.0761697 | ||||||||
\(856\) | 11.6631 | 0.398638 | ||||||||
\(857\) | −26.8812 | −0.918244 | −0.459122 | − | 0.888373i | \(-0.651836\pi\) | ||||
−0.459122 | + | 0.888373i | \(0.651836\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.5548 | 0.735440 | 0.367720 | − | 0.929937i | \(-0.380138\pi\) | ||||
0.367720 | + | 0.929937i | \(0.380138\pi\) | |||||||
\(860\) | −16.2202 | −0.553106 | ||||||||
\(861\) | 59.6389 | 2.03249 | ||||||||
\(862\) | 22.5479 | 0.767984 | ||||||||
\(863\) | 28.9587 | 0.985767 | 0.492883 | − | 0.870095i | \(-0.335943\pi\) | ||||
0.492883 | + | 0.870095i | \(0.335943\pi\) | |||||||
\(864\) | 5.62379 | 0.191325 | ||||||||
\(865\) | 28.3116 | 0.962624 | ||||||||
\(866\) | −11.5129 | −0.391223 | ||||||||
\(867\) | −12.9744 | −0.440633 | ||||||||
\(868\) | 6.40737 | 0.217480 | ||||||||
\(869\) | −11.6137 | −0.393969 | ||||||||
\(870\) | −38.2022 | −1.29518 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 6.07064 | 0.205578 | ||||||||
\(873\) | 11.0881 | 0.375275 | ||||||||
\(874\) | −1.66948 | −0.0564711 | ||||||||
\(875\) | −11.9070 | −0.402530 | ||||||||
\(876\) | 0.177538 | 0.00599846 | ||||||||
\(877\) | −9.29627 | −0.313913 | −0.156956 | − | 0.987606i | \(-0.550168\pi\) | ||||
−0.156956 | + | 0.987606i | \(0.550168\pi\) | |||||||
\(878\) | 11.6448 | 0.392994 | ||||||||
\(879\) | −51.0629 | −1.72231 | ||||||||
\(880\) | 11.4000 | 0.384294 | ||||||||
\(881\) | −16.6824 | −0.562046 | −0.281023 | − | 0.959701i | \(-0.590674\pi\) | ||||
−0.281023 | + | 0.959701i | \(0.590674\pi\) | |||||||
\(882\) | 5.15973 | 0.173737 | ||||||||
\(883\) | 44.8252 | 1.50849 | 0.754245 | − | 0.656594i | \(-0.228003\pi\) | ||||
0.754245 | + | 0.656594i | \(0.228003\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 24.8011 | 0.833678 | ||||||||
\(886\) | −26.0168 | −0.874050 | ||||||||
\(887\) | 51.4991 | 1.72917 | 0.864586 | − | 0.502485i | \(-0.167581\pi\) | ||||
0.864586 | + | 0.502485i | \(0.167581\pi\) | |||||||
\(888\) | 7.83915 | 0.263065 | ||||||||
\(889\) | 42.0483 | 1.41026 | ||||||||
\(890\) | −44.2877 | −1.48453 | ||||||||
\(891\) | 23.6834 | 0.793423 | ||||||||
\(892\) | −8.81599 | −0.295181 | ||||||||
\(893\) | −6.13466 | −0.205288 | ||||||||
\(894\) | −34.7906 | −1.16357 | ||||||||
\(895\) | 14.9567 | 0.499946 | ||||||||
\(896\) | 3.73146 | 0.124659 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 11.7314 | 0.391482 | ||||||||
\(899\) | 14.6169 | 0.487501 | ||||||||
\(900\) | −2.93043 | −0.0976812 | ||||||||
\(901\) | 38.4165 | 1.27984 | ||||||||
\(902\) | −40.5995 | −1.35182 | ||||||||
\(903\) | −30.4093 | −1.01196 | ||||||||
\(904\) | 5.29092 | 0.175973 | ||||||||
\(905\) | 5.89967 | 0.196112 | ||||||||
\(906\) | −30.2406 | −1.00468 | ||||||||
\(907\) | 31.7073 | 1.05282 | 0.526411 | − | 0.850230i | \(-0.323537\pi\) | ||||
0.526411 | + | 0.850230i | \(0.323537\pi\) | |||||||
\(908\) | 4.18895 | 0.139015 | ||||||||
\(909\) | −10.7497 | −0.356546 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46.0327 | −1.52513 | −0.762566 | − | 0.646911i | \(-0.776061\pi\) | ||||
−0.762566 | + | 0.646911i | \(0.776061\pi\) | |||||||
\(912\) | −1.50159 | −0.0497227 | ||||||||
\(913\) | −4.66657 | −0.154441 | ||||||||
\(914\) | −36.7678 | −1.21617 | ||||||||
\(915\) | 26.8888 | 0.888918 | ||||||||
\(916\) | 24.2635 | 0.801689 | ||||||||
\(917\) | 47.6196 | 1.57254 | ||||||||
\(918\) | −16.2600 | −0.536661 | ||||||||
\(919\) | 16.5907 | 0.547278 | 0.273639 | − | 0.961832i | \(-0.411773\pi\) | ||||
0.273639 | + | 0.961832i | \(0.411773\pi\) | |||||||
\(920\) | −4.98959 | −0.164502 | ||||||||
\(921\) | 43.8700 | 1.44557 | ||||||||
\(922\) | −12.0022 | −0.395270 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 21.3724 | 0.703100 | ||||||||
\(925\) | −20.5289 | −0.674985 | ||||||||
\(926\) | 15.5101 | 0.509693 | ||||||||
\(927\) | −6.89902 | −0.226593 | ||||||||
\(928\) | 8.51244 | 0.279434 | ||||||||
\(929\) | 48.8958 | 1.60422 | 0.802110 | − | 0.597176i | \(-0.203711\pi\) | ||||
0.802110 | + | 0.597176i | \(0.203711\pi\) | |||||||
\(930\) | −7.70612 | −0.252693 | ||||||||
\(931\) | −6.92379 | −0.226918 | ||||||||
\(932\) | 17.9212 | 0.587027 | ||||||||
\(933\) | −19.7484 | −0.646534 | ||||||||
\(934\) | 25.8302 | 0.845189 | ||||||||
\(935\) | −32.9607 | −1.07793 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.3908 | 0.764144 | 0.382072 | − | 0.924133i | \(-0.375211\pi\) | ||||
0.382072 | + | 0.924133i | \(0.375211\pi\) | |||||||
\(938\) | 27.4284 | 0.895570 | ||||||||
\(939\) | 33.3096 | 1.08702 | ||||||||
\(940\) | −18.3346 | −0.598010 | ||||||||
\(941\) | −17.0539 | −0.555940 | −0.277970 | − | 0.960590i | \(-0.589662\pi\) | ||||
−0.277970 | + | 0.960590i | \(0.589662\pi\) | |||||||
\(942\) | 19.6559 | 0.640423 | ||||||||
\(943\) | 17.7697 | 0.578662 | ||||||||
\(944\) | −5.52632 | −0.179866 | ||||||||
\(945\) | −62.7177 | −2.04021 | ||||||||
\(946\) | 20.7013 | 0.673057 | ||||||||
\(947\) | 17.9107 | 0.582021 | 0.291010 | − | 0.956720i | \(-0.406009\pi\) | ||||
0.291010 | + | 0.956720i | \(0.406009\pi\) | |||||||
\(948\) | 4.57196 | 0.148490 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 3.93232 | 0.127581 | ||||||||
\(951\) | 37.9800 | 1.23159 | ||||||||
\(952\) | −10.7887 | −0.349665 | ||||||||
\(953\) | 8.02689 | 0.260016 | 0.130008 | − | 0.991513i | \(-0.458500\pi\) | ||||
0.130008 | + | 0.991513i | \(0.458500\pi\) | |||||||
\(954\) | −9.90169 | −0.320579 | ||||||||
\(955\) | 62.2056 | 2.01293 | ||||||||
\(956\) | 22.3178 | 0.721808 | ||||||||
\(957\) | 48.7560 | 1.57606 | ||||||||
\(958\) | 10.0622 | 0.325094 | ||||||||
\(959\) | −30.2394 | −0.976481 | ||||||||
\(960\) | −4.48781 | −0.144843 | ||||||||
\(961\) | −28.0515 | −0.904887 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.69158 | 0.280082 | ||||||||
\(964\) | −22.3962 | −0.721334 | ||||||||
\(965\) | 63.6783 | 2.04988 | ||||||||
\(966\) | −9.35434 | −0.300971 | ||||||||
\(967\) | −31.4562 | −1.01156 | −0.505781 | − | 0.862662i | \(-0.668796\pi\) | ||||
−0.505781 | + | 0.862662i | \(0.668796\pi\) | |||||||
\(968\) | −3.54939 | −0.114082 | ||||||||
\(969\) | 4.34155 | 0.139471 | ||||||||
\(970\) | −44.4688 | −1.42781 | ||||||||
\(971\) | −16.7191 | −0.536542 | −0.268271 | − | 0.963343i | \(-0.586452\pi\) | ||||
−0.268271 | + | 0.963343i | \(0.586452\pi\) | |||||||
\(972\) | 7.54799 | 0.242102 | ||||||||
\(973\) | −36.9418 | −1.18430 | ||||||||
\(974\) | −5.76723 | −0.184794 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.99153 | −0.191784 | ||||||||
\(977\) | 9.07353 | 0.290288 | 0.145144 | − | 0.989411i | \(-0.453635\pi\) | ||||
0.145144 | + | 0.989411i | \(0.453635\pi\) | |||||||
\(978\) | 8.86323 | 0.283415 | ||||||||
\(979\) | 56.5227 | 1.80647 | ||||||||
\(980\) | −20.6931 | −0.661017 | ||||||||
\(981\) | 4.52395 | 0.144439 | ||||||||
\(982\) | −19.4673 | −0.621226 | ||||||||
\(983\) | −48.1584 | −1.53601 | −0.768007 | − | 0.640442i | \(-0.778751\pi\) | ||||
−0.768007 | + | 0.640442i | \(0.778751\pi\) | |||||||
\(984\) | 15.9827 | 0.509511 | ||||||||
\(985\) | −25.7699 | −0.821098 | ||||||||
\(986\) | −24.6120 | −0.783804 | ||||||||
\(987\) | −34.3733 | −1.09411 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.06061 | −0.288111 | ||||||||
\(990\) | 8.49548 | 0.270004 | ||||||||
\(991\) | −43.3084 | −1.37574 | −0.687869 | − | 0.725835i | \(-0.741454\pi\) | ||||
−0.687869 | + | 0.725835i | \(0.741454\pi\) | |||||||
\(992\) | 1.71712 | 0.0545187 | ||||||||
\(993\) | −41.4793 | −1.31630 | ||||||||
\(994\) | 36.4190 | 1.15514 | ||||||||
\(995\) | −11.9671 | −0.379382 | ||||||||
\(996\) | 1.83708 | 0.0582101 | ||||||||
\(997\) | −57.6729 | −1.82652 | −0.913260 | − | 0.407377i | \(-0.866444\pi\) | ||||
−0.913260 | + | 0.407377i | \(0.866444\pi\) | |||||||
\(998\) | 4.74563 | 0.150220 | ||||||||
\(999\) | 29.3593 | 0.928888 |
(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 | 6422.2.a.bm.1.9 | 14 | ||
13.2 | odd | 12 | 494.2.m.b.381.3 | yes | 28 | ||
13.7 | odd | 12 | 494.2.m.b.153.3 | ✓ | 28 | ||
13.12 | even | 2 | 6422.2.a.bn.1.9 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
494.2.m.b.153.3 | ✓ | 28 | 13.7 | odd | 12 | ||
494.2.m.b.381.3 | yes | 28 | 13.2 | odd | 12 | ||
6422.2.a.bm.1.9 | 14 | 1.1 | even | 1 | trivial | ||
6422.2.a.bn.1.9 | 14 | 13.12 | even | 2 |