Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [731,2,Mod(1,731)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(731, 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("731.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 731 = 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 731.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: | \(5.83706438776\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.2460365.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 6x^{4} + 6x^{3} + 7x^{2} - 7x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.668929\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 731.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.55253 | 1.09781 | 0.548904 | − | 0.835886i | \(-0.315045\pi\) | ||||
0.548904 | + | 0.835886i | \(0.315045\pi\) | |||||||
\(3\) | 0.467968 | 0.270182 | 0.135091 | − | 0.990833i | \(-0.456867\pi\) | ||||
0.135091 | + | 0.990833i | \(0.456867\pi\) | |||||||
\(4\) | 0.410361 | 0.205180 | ||||||||
\(5\) | −1.37639 | −0.615542 | −0.307771 | − | 0.951460i | \(-0.599583\pi\) | ||||
−0.307771 | + | 0.951460i | \(0.599583\pi\) | |||||||
\(6\) | 0.726536 | 0.296607 | ||||||||
\(7\) | −3.35157 | −1.26678 | −0.633388 | − | 0.773835i | \(-0.718336\pi\) | ||||
−0.633388 | + | 0.773835i | \(0.718336\pi\) | |||||||
\(8\) | −2.46797 | −0.872559 | ||||||||
\(9\) | −2.78101 | −0.927002 | ||||||||
\(10\) | −2.13690 | −0.675746 | ||||||||
\(11\) | 2.05761 | 0.620392 | 0.310196 | − | 0.950673i | \(-0.399605\pi\) | ||||
0.310196 | + | 0.950673i | \(0.399605\pi\) | |||||||
\(12\) | 0.192036 | 0.0554360 | ||||||||
\(13\) | −1.60557 | −0.445306 | −0.222653 | − | 0.974898i | \(-0.571472\pi\) | ||||
−0.222653 | + | 0.974898i | \(0.571472\pi\) | |||||||
\(14\) | −5.20343 | −1.39068 | ||||||||
\(15\) | −0.644108 | −0.166308 | ||||||||
\(16\) | −4.65233 | −1.16308 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −4.31761 | −1.01767 | ||||||||
\(19\) | 4.43647 | 1.01780 | 0.508898 | − | 0.860827i | \(-0.330053\pi\) | ||||
0.508898 | + | 0.860827i | \(0.330053\pi\) | |||||||
\(20\) | −0.564818 | −0.126297 | ||||||||
\(21\) | −1.56843 | −0.342259 | ||||||||
\(22\) | 3.19450 | 0.681071 | ||||||||
\(23\) | −2.95501 | −0.616162 | −0.308081 | − | 0.951360i | \(-0.599687\pi\) | ||||
−0.308081 | + | 0.951360i | \(0.599687\pi\) | |||||||
\(24\) | −1.15493 | −0.235749 | ||||||||
\(25\) | −3.10554 | −0.621108 | ||||||||
\(26\) | −2.49271 | −0.488860 | ||||||||
\(27\) | −2.70533 | −0.520640 | ||||||||
\(28\) | −1.37535 | −0.259918 | ||||||||
\(29\) | −3.13539 | −0.582226 | −0.291113 | − | 0.956689i | \(-0.594026\pi\) | ||||
−0.291113 | + | 0.956689i | \(0.594026\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | −4.72687 | −0.848970 | −0.424485 | − | 0.905435i | \(-0.639545\pi\) | ||||
−0.424485 | + | 0.905435i | \(0.639545\pi\) | |||||||
\(32\) | −2.28696 | −0.404281 | ||||||||
\(33\) | 0.962895 | 0.167618 | ||||||||
\(34\) | −1.55253 | −0.266257 | ||||||||
\(35\) | 4.61308 | 0.779753 | ||||||||
\(36\) | −1.14122 | −0.190203 | ||||||||
\(37\) | 6.73408 | 1.10708 | 0.553538 | − | 0.832824i | \(-0.313277\pi\) | ||||
0.553538 | + | 0.832824i | \(0.313277\pi\) | |||||||
\(38\) | 6.88777 | 1.11734 | ||||||||
\(39\) | −0.751357 | −0.120313 | ||||||||
\(40\) | 3.39690 | 0.537096 | ||||||||
\(41\) | 9.28079 | 1.44942 | 0.724708 | − | 0.689056i | \(-0.241975\pi\) | ||||
0.724708 | + | 0.689056i | \(0.241975\pi\) | |||||||
\(42\) | −2.43504 | −0.375735 | ||||||||
\(43\) | −1.00000 | −0.152499 | ||||||||
\(44\) | 0.844362 | 0.127292 | ||||||||
\(45\) | 3.82776 | 0.570609 | ||||||||
\(46\) | −4.58775 | −0.676427 | ||||||||
\(47\) | −8.52365 | −1.24330 | −0.621651 | − | 0.783295i | \(-0.713538\pi\) | ||||
−0.621651 | + | 0.783295i | \(0.713538\pi\) | |||||||
\(48\) | −2.17714 | −0.314243 | ||||||||
\(49\) | 4.23304 | 0.604720 | ||||||||
\(50\) | −4.82146 | −0.681857 | ||||||||
\(51\) | −0.467968 | −0.0655287 | ||||||||
\(52\) | −0.658865 | −0.0913681 | ||||||||
\(53\) | 9.33387 | 1.28211 | 0.641053 | − | 0.767497i | \(-0.278498\pi\) | ||||
0.641053 | + | 0.767497i | \(0.278498\pi\) | |||||||
\(54\) | −4.20011 | −0.571563 | ||||||||
\(55\) | −2.83208 | −0.381877 | ||||||||
\(56\) | 8.27157 | 1.10534 | ||||||||
\(57\) | 2.07613 | 0.274990 | ||||||||
\(58\) | −4.86779 | −0.639172 | ||||||||
\(59\) | −9.83672 | −1.28063 | −0.640316 | − | 0.768111i | \(-0.721197\pi\) | ||||
−0.640316 | + | 0.768111i | \(0.721197\pi\) | |||||||
\(60\) | −0.264317 | −0.0341232 | ||||||||
\(61\) | 2.75383 | 0.352591 | 0.176296 | − | 0.984337i | \(-0.443589\pi\) | ||||
0.176296 | + | 0.984337i | \(0.443589\pi\) | |||||||
\(62\) | −7.33862 | −0.932006 | ||||||||
\(63\) | 9.32074 | 1.17430 | ||||||||
\(64\) | 5.75407 | 0.719259 | ||||||||
\(65\) | 2.20990 | 0.274104 | ||||||||
\(66\) | 1.49493 | 0.184013 | ||||||||
\(67\) | 8.84901 | 1.08108 | 0.540539 | − | 0.841319i | \(-0.318220\pi\) | ||||
0.540539 | + | 0.841319i | \(0.318220\pi\) | |||||||
\(68\) | −0.410361 | −0.0497636 | ||||||||
\(69\) | −1.38285 | −0.166476 | ||||||||
\(70\) | 7.16197 | 0.856019 | ||||||||
\(71\) | −1.37235 | −0.162868 | −0.0814342 | − | 0.996679i | \(-0.525950\pi\) | ||||
−0.0814342 | + | 0.996679i | \(0.525950\pi\) | |||||||
\(72\) | 6.86343 | 0.808863 | ||||||||
\(73\) | −0.237911 | −0.0278454 | −0.0139227 | − | 0.999903i | \(-0.504432\pi\) | ||||
−0.0139227 | + | 0.999903i | \(0.504432\pi\) | |||||||
\(74\) | 10.4549 | 1.21536 | ||||||||
\(75\) | −1.45329 | −0.167812 | ||||||||
\(76\) | 1.82055 | 0.208832 | ||||||||
\(77\) | −6.89622 | −0.785897 | ||||||||
\(78\) | −1.16651 | −0.132081 | ||||||||
\(79\) | −7.25698 | −0.816474 | −0.408237 | − | 0.912876i | \(-0.633856\pi\) | ||||
−0.408237 | + | 0.912876i | \(0.633856\pi\) | |||||||
\(80\) | 6.40343 | 0.715925 | ||||||||
\(81\) | 7.07701 | 0.786334 | ||||||||
\(82\) | 14.4087 | 1.59118 | ||||||||
\(83\) | −2.15336 | −0.236362 | −0.118181 | − | 0.992992i | \(-0.537706\pi\) | ||||
−0.118181 | + | 0.992992i | \(0.537706\pi\) | |||||||
\(84\) | −0.643622 | −0.0702249 | ||||||||
\(85\) | 1.37639 | 0.149291 | ||||||||
\(86\) | −1.55253 | −0.167414 | ||||||||
\(87\) | −1.46726 | −0.157307 | ||||||||
\(88\) | −5.07811 | −0.541328 | ||||||||
\(89\) | −13.4194 | −1.42246 | −0.711229 | − | 0.702961i | \(-0.751861\pi\) | ||||
−0.711229 | + | 0.702961i | \(0.751861\pi\) | |||||||
\(90\) | 5.94272 | 0.626418 | ||||||||
\(91\) | 5.38120 | 0.564103 | ||||||||
\(92\) | −1.21262 | −0.126424 | ||||||||
\(93\) | −2.21202 | −0.229376 | ||||||||
\(94\) | −13.2332 | −1.36491 | ||||||||
\(95\) | −6.10633 | −0.626496 | ||||||||
\(96\) | −1.07022 | −0.109229 | ||||||||
\(97\) | −12.3738 | −1.25636 | −0.628182 | − | 0.778066i | \(-0.716201\pi\) | ||||
−0.628182 | + | 0.778066i | \(0.716201\pi\) | |||||||
\(98\) | 6.57194 | 0.663866 | ||||||||
\(99\) | −5.72222 | −0.575104 | ||||||||
\(100\) | −1.27439 | −0.127439 | ||||||||
\(101\) | −16.9693 | −1.68850 | −0.844252 | − | 0.535946i | \(-0.819955\pi\) | ||||
−0.844252 | + | 0.535946i | \(0.819955\pi\) | |||||||
\(102\) | −0.726536 | −0.0719378 | ||||||||
\(103\) | 1.00189 | 0.0987190 | 0.0493595 | − | 0.998781i | \(-0.484282\pi\) | ||||
0.0493595 | + | 0.998781i | \(0.484282\pi\) | |||||||
\(104\) | 3.96250 | 0.388555 | ||||||||
\(105\) | 2.15878 | 0.210675 | ||||||||
\(106\) | 14.4911 | 1.40750 | ||||||||
\(107\) | 17.2371 | 1.66637 | 0.833185 | − | 0.552994i | \(-0.186515\pi\) | ||||
0.833185 | + | 0.552994i | \(0.186515\pi\) | |||||||
\(108\) | −1.11016 | −0.106825 | ||||||||
\(109\) | −9.48121 | −0.908135 | −0.454068 | − | 0.890967i | \(-0.650028\pi\) | ||||
−0.454068 | + | 0.890967i | \(0.650028\pi\) | |||||||
\(110\) | −4.39690 | −0.419228 | ||||||||
\(111\) | 3.15134 | 0.299112 | ||||||||
\(112\) | 15.5926 | 1.47336 | ||||||||
\(113\) | −5.69643 | −0.535875 | −0.267937 | − | 0.963436i | \(-0.586342\pi\) | ||||
−0.267937 | + | 0.963436i | \(0.586342\pi\) | |||||||
\(114\) | 3.22326 | 0.301886 | ||||||||
\(115\) | 4.06725 | 0.379273 | ||||||||
\(116\) | −1.28664 | −0.119462 | ||||||||
\(117\) | 4.46511 | 0.412799 | ||||||||
\(118\) | −15.2718 | −1.40589 | ||||||||
\(119\) | 3.35157 | 0.307238 | ||||||||
\(120\) | 1.58964 | 0.145114 | ||||||||
\(121\) | −6.76625 | −0.615114 | ||||||||
\(122\) | 4.27541 | 0.387077 | ||||||||
\(123\) | 4.34312 | 0.391606 | ||||||||
\(124\) | −1.93972 | −0.174192 | ||||||||
\(125\) | 11.1564 | 0.997860 | ||||||||
\(126\) | 14.4708 | 1.28916 | ||||||||
\(127\) | −9.03729 | −0.801930 | −0.400965 | − | 0.916093i | \(-0.631325\pi\) | ||||
−0.400965 | + | 0.916093i | \(0.631325\pi\) | |||||||
\(128\) | 13.5073 | 1.19389 | ||||||||
\(129\) | −0.467968 | −0.0412023 | ||||||||
\(130\) | 3.43095 | 0.300914 | ||||||||
\(131\) | 13.2079 | 1.15398 | 0.576990 | − | 0.816751i | \(-0.304227\pi\) | ||||
0.576990 | + | 0.816751i | \(0.304227\pi\) | |||||||
\(132\) | 0.395134 | 0.0343920 | ||||||||
\(133\) | −14.8691 | −1.28932 | ||||||||
\(134\) | 13.7384 | 1.18682 | ||||||||
\(135\) | 3.72359 | 0.320476 | ||||||||
\(136\) | 2.46797 | 0.211627 | ||||||||
\(137\) | 0.498421 | 0.0425830 | 0.0212915 | − | 0.999773i | \(-0.493222\pi\) | ||||
0.0212915 | + | 0.999773i | \(0.493222\pi\) | |||||||
\(138\) | −2.14692 | −0.182758 | ||||||||
\(139\) | 13.0119 | 1.10366 | 0.551829 | − | 0.833957i | \(-0.313930\pi\) | ||||
0.551829 | + | 0.833957i | \(0.313930\pi\) | |||||||
\(140\) | 1.89303 | 0.159990 | ||||||||
\(141\) | −3.98880 | −0.335917 | ||||||||
\(142\) | −2.13062 | −0.178798 | ||||||||
\(143\) | −3.30364 | −0.276264 | ||||||||
\(144\) | 12.9381 | 1.07818 | ||||||||
\(145\) | 4.31552 | 0.358385 | ||||||||
\(146\) | −0.369365 | −0.0305689 | ||||||||
\(147\) | 1.98093 | 0.163384 | ||||||||
\(148\) | 2.76341 | 0.227151 | ||||||||
\(149\) | −18.6715 | −1.52963 | −0.764813 | − | 0.644253i | \(-0.777168\pi\) | ||||
−0.764813 | + | 0.644253i | \(0.777168\pi\) | |||||||
\(150\) | −2.25629 | −0.184225 | ||||||||
\(151\) | −14.9169 | −1.21392 | −0.606960 | − | 0.794733i | \(-0.707611\pi\) | ||||
−0.606960 | + | 0.794733i | \(0.707611\pi\) | |||||||
\(152\) | −10.9491 | −0.888086 | ||||||||
\(153\) | 2.78101 | 0.224831 | ||||||||
\(154\) | −10.7066 | −0.862764 | ||||||||
\(155\) | 6.50603 | 0.522577 | ||||||||
\(156\) | −0.308328 | −0.0246860 | ||||||||
\(157\) | 19.2406 | 1.53556 | 0.767782 | − | 0.640711i | \(-0.221360\pi\) | ||||
0.767782 | + | 0.640711i | \(0.221360\pi\) | |||||||
\(158\) | −11.2667 | −0.896331 | ||||||||
\(159\) | 4.36795 | 0.346401 | ||||||||
\(160\) | 3.14775 | 0.248852 | ||||||||
\(161\) | 9.90393 | 0.780539 | ||||||||
\(162\) | 10.9873 | 0.863244 | ||||||||
\(163\) | 6.92729 | 0.542587 | 0.271294 | − | 0.962497i | \(-0.412549\pi\) | ||||
0.271294 | + | 0.962497i | \(0.412549\pi\) | |||||||
\(164\) | 3.80848 | 0.297392 | ||||||||
\(165\) | −1.32532 | −0.103176 | ||||||||
\(166\) | −3.34316 | −0.259480 | ||||||||
\(167\) | 11.3060 | 0.874881 | 0.437441 | − | 0.899247i | \(-0.355885\pi\) | ||||
0.437441 | + | 0.899247i | \(0.355885\pi\) | |||||||
\(168\) | 3.87083 | 0.298641 | ||||||||
\(169\) | −10.4221 | −0.801703 | ||||||||
\(170\) | 2.13690 | 0.163893 | ||||||||
\(171\) | −12.3378 | −0.943499 | ||||||||
\(172\) | −0.410361 | −0.0312897 | ||||||||
\(173\) | 18.8950 | 1.43656 | 0.718281 | − | 0.695754i | \(-0.244929\pi\) | ||||
0.718281 | + | 0.695754i | \(0.244929\pi\) | |||||||
\(174\) | −2.27797 | −0.172693 | ||||||||
\(175\) | 10.4084 | 0.786805 | ||||||||
\(176\) | −9.57266 | −0.721566 | ||||||||
\(177\) | −4.60327 | −0.346003 | ||||||||
\(178\) | −20.8341 | −1.56158 | ||||||||
\(179\) | −16.1432 | −1.20660 | −0.603300 | − | 0.797515i | \(-0.706148\pi\) | ||||
−0.603300 | + | 0.797515i | \(0.706148\pi\) | |||||||
\(180\) | 1.57076 | 0.117078 | ||||||||
\(181\) | −17.6672 | −1.31319 | −0.656596 | − | 0.754242i | \(-0.728004\pi\) | ||||
−0.656596 | + | 0.754242i | \(0.728004\pi\) | |||||||
\(182\) | 8.35449 | 0.619276 | ||||||||
\(183\) | 1.28870 | 0.0952637 | ||||||||
\(184\) | 7.29287 | 0.537637 | ||||||||
\(185\) | −9.26875 | −0.681452 | ||||||||
\(186\) | −3.43424 | −0.251811 | ||||||||
\(187\) | −2.05761 | −0.150467 | ||||||||
\(188\) | −3.49777 | −0.255101 | ||||||||
\(189\) | 9.06710 | 0.659534 | ||||||||
\(190\) | −9.48028 | −0.687772 | ||||||||
\(191\) | −5.21087 | −0.377045 | −0.188523 | − | 0.982069i | \(-0.560370\pi\) | ||||
−0.188523 | + | 0.982069i | \(0.560370\pi\) | |||||||
\(192\) | 2.69272 | 0.194331 | ||||||||
\(193\) | −10.0275 | −0.721797 | −0.360898 | − | 0.932605i | \(-0.617530\pi\) | ||||
−0.360898 | + | 0.932605i | \(0.617530\pi\) | |||||||
\(194\) | −19.2107 | −1.37925 | ||||||||
\(195\) | 1.03416 | 0.0740580 | ||||||||
\(196\) | 1.73707 | 0.124077 | ||||||||
\(197\) | −8.23341 | −0.586606 | −0.293303 | − | 0.956020i | \(-0.594754\pi\) | ||||
−0.293303 | + | 0.956020i | \(0.594754\pi\) | |||||||
\(198\) | −8.88394 | −0.631354 | ||||||||
\(199\) | −0.596092 | −0.0422559 | −0.0211279 | − | 0.999777i | \(-0.506726\pi\) | ||||
−0.0211279 | + | 0.999777i | \(0.506726\pi\) | |||||||
\(200\) | 7.66438 | 0.541953 | ||||||||
\(201\) | 4.14105 | 0.292087 | ||||||||
\(202\) | −26.3454 | −1.85365 | ||||||||
\(203\) | 10.5085 | 0.737550 | ||||||||
\(204\) | −0.192036 | −0.0134452 | ||||||||
\(205\) | −12.7740 | −0.892176 | ||||||||
\(206\) | 1.55547 | 0.108374 | ||||||||
\(207\) | 8.21790 | 0.571183 | ||||||||
\(208\) | 7.46965 | 0.517927 | ||||||||
\(209\) | 9.12851 | 0.631432 | ||||||||
\(210\) | 3.35157 | 0.231280 | ||||||||
\(211\) | −2.11726 | −0.145758 | −0.0728790 | − | 0.997341i | \(-0.523219\pi\) | ||||
−0.0728790 | + | 0.997341i | \(0.523219\pi\) | |||||||
\(212\) | 3.83026 | 0.263063 | ||||||||
\(213\) | −0.642217 | −0.0440040 | ||||||||
\(214\) | 26.7611 | 1.82935 | ||||||||
\(215\) | 1.37639 | 0.0938693 | ||||||||
\(216\) | 6.67666 | 0.454289 | ||||||||
\(217\) | 15.8424 | 1.07545 | ||||||||
\(218\) | −14.7199 | −0.996958 | ||||||||
\(219\) | −0.111335 | −0.00752332 | ||||||||
\(220\) | −1.16217 | −0.0783538 | ||||||||
\(221\) | 1.60557 | 0.108003 | ||||||||
\(222\) | 4.89256 | 0.328367 | ||||||||
\(223\) | −21.3509 | −1.42976 | −0.714881 | − | 0.699247i | \(-0.753519\pi\) | ||||
−0.714881 | + | 0.699247i | \(0.753519\pi\) | |||||||
\(224\) | 7.66490 | 0.512133 | ||||||||
\(225\) | 8.63653 | 0.575768 | ||||||||
\(226\) | −8.84389 | −0.588287 | ||||||||
\(227\) | 17.2277 | 1.14344 | 0.571720 | − | 0.820449i | \(-0.306276\pi\) | ||||
0.571720 | + | 0.820449i | \(0.306276\pi\) | |||||||
\(228\) | 0.851961 | 0.0564225 | ||||||||
\(229\) | −0.830329 | −0.0548697 | −0.0274348 | − | 0.999624i | \(-0.508734\pi\) | ||||
−0.0274348 | + | 0.999624i | \(0.508734\pi\) | |||||||
\(230\) | 6.31455 | 0.416369 | ||||||||
\(231\) | −3.22721 | −0.212335 | ||||||||
\(232\) | 7.73803 | 0.508027 | ||||||||
\(233\) | −17.7159 | −1.16061 | −0.580303 | − | 0.814401i | \(-0.697066\pi\) | ||||
−0.580303 | + | 0.814401i | \(0.697066\pi\) | |||||||
\(234\) | 6.93223 | 0.453174 | ||||||||
\(235\) | 11.7319 | 0.765304 | ||||||||
\(236\) | −4.03661 | −0.262761 | ||||||||
\(237\) | −3.39604 | −0.220596 | ||||||||
\(238\) | 5.20343 | 0.337288 | ||||||||
\(239\) | −20.7223 | −1.34041 | −0.670207 | − | 0.742174i | \(-0.733795\pi\) | ||||
−0.670207 | + | 0.742174i | \(0.733795\pi\) | |||||||
\(240\) | 2.99660 | 0.193430 | ||||||||
\(241\) | 8.01971 | 0.516595 | 0.258297 | − | 0.966065i | \(-0.416839\pi\) | ||||
0.258297 | + | 0.966065i | \(0.416839\pi\) | |||||||
\(242\) | −10.5048 | −0.675276 | ||||||||
\(243\) | 11.4278 | 0.733093 | ||||||||
\(244\) | 1.13006 | 0.0723449 | ||||||||
\(245\) | −5.82633 | −0.372230 | ||||||||
\(246\) | 6.74283 | 0.429907 | ||||||||
\(247\) | −7.12308 | −0.453231 | ||||||||
\(248\) | 11.6658 | 0.740776 | ||||||||
\(249\) | −1.00770 | −0.0638606 | ||||||||
\(250\) | 17.3207 | 1.09546 | ||||||||
\(251\) | 12.0601 | 0.761228 | 0.380614 | − | 0.924734i | \(-0.375713\pi\) | ||||
0.380614 | + | 0.924734i | \(0.375713\pi\) | |||||||
\(252\) | 3.82487 | 0.240944 | ||||||||
\(253\) | −6.08025 | −0.382262 | ||||||||
\(254\) | −14.0307 | −0.880365 | ||||||||
\(255\) | 0.644108 | 0.0403356 | ||||||||
\(256\) | 9.46240 | 0.591400 | ||||||||
\(257\) | −0.113536 | −0.00708217 | −0.00354108 | − | 0.999994i | \(-0.501127\pi\) | ||||
−0.00354108 | + | 0.999994i | \(0.501127\pi\) | |||||||
\(258\) | −0.726536 | −0.0452322 | ||||||||
\(259\) | −22.5698 | −1.40242 | ||||||||
\(260\) | 0.906857 | 0.0562409 | ||||||||
\(261\) | 8.71952 | 0.539725 | ||||||||
\(262\) | 20.5057 | 1.26685 | ||||||||
\(263\) | −1.04330 | −0.0643325 | −0.0321663 | − | 0.999483i | \(-0.510241\pi\) | ||||
−0.0321663 | + | 0.999483i | \(0.510241\pi\) | |||||||
\(264\) | −2.37639 | −0.146257 | ||||||||
\(265\) | −12.8471 | −0.789190 | ||||||||
\(266\) | −23.0849 | −1.41542 | ||||||||
\(267\) | −6.27987 | −0.384322 | ||||||||
\(268\) | 3.63129 | 0.221816 | ||||||||
\(269\) | −3.25815 | −0.198653 | −0.0993265 | − | 0.995055i | \(-0.531669\pi\) | ||||
−0.0993265 | + | 0.995055i | \(0.531669\pi\) | |||||||
\(270\) | 5.78101 | 0.351821 | ||||||||
\(271\) | 2.16125 | 0.131286 | 0.0656432 | − | 0.997843i | \(-0.479090\pi\) | ||||
0.0656432 | + | 0.997843i | \(0.479090\pi\) | |||||||
\(272\) | 4.65233 | 0.282089 | ||||||||
\(273\) | 2.51823 | 0.152410 | ||||||||
\(274\) | 0.773816 | 0.0467479 | ||||||||
\(275\) | −6.38998 | −0.385330 | ||||||||
\(276\) | −0.567468 | −0.0341575 | ||||||||
\(277\) | −2.06077 | −0.123820 | −0.0619098 | − | 0.998082i | \(-0.519719\pi\) | ||||
−0.0619098 | + | 0.998082i | \(0.519719\pi\) | |||||||
\(278\) | 20.2015 | 1.21160 | ||||||||
\(279\) | 13.1454 | 0.786997 | ||||||||
\(280\) | −11.3849 | −0.680380 | ||||||||
\(281\) | 19.6254 | 1.17075 | 0.585375 | − | 0.810763i | \(-0.300947\pi\) | ||||
0.585375 | + | 0.810763i | \(0.300947\pi\) | |||||||
\(282\) | −6.19274 | −0.368772 | ||||||||
\(283\) | 29.8412 | 1.77388 | 0.886939 | − | 0.461888i | \(-0.152828\pi\) | ||||
0.886939 | + | 0.461888i | \(0.152828\pi\) | |||||||
\(284\) | −0.563160 | −0.0334174 | ||||||||
\(285\) | −2.85757 | −0.169268 | ||||||||
\(286\) | −5.12901 | −0.303285 | ||||||||
\(287\) | −31.1053 | −1.83608 | ||||||||
\(288\) | 6.36004 | 0.374769 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 6.70000 | 0.393437 | ||||||||
\(291\) | −5.79052 | −0.339447 | ||||||||
\(292\) | −0.0976295 | −0.00571334 | ||||||||
\(293\) | 9.76035 | 0.570206 | 0.285103 | − | 0.958497i | \(-0.407972\pi\) | ||||
0.285103 | + | 0.958497i | \(0.407972\pi\) | |||||||
\(294\) | 3.07546 | 0.179364 | ||||||||
\(295\) | 13.5392 | 0.788283 | ||||||||
\(296\) | −16.6195 | −0.965989 | ||||||||
\(297\) | −5.56650 | −0.323001 | ||||||||
\(298\) | −28.9881 | −1.67923 | ||||||||
\(299\) | 4.74448 | 0.274381 | ||||||||
\(300\) | −0.596375 | −0.0344317 | ||||||||
\(301\) | 3.35157 | 0.193181 | ||||||||
\(302\) | −23.1590 | −1.33265 | ||||||||
\(303\) | −7.94108 | −0.456203 | ||||||||
\(304\) | −20.6399 | −1.18378 | ||||||||
\(305\) | −3.79035 | −0.217035 | ||||||||
\(306\) | 4.31761 | 0.246821 | ||||||||
\(307\) | 5.45230 | 0.311179 | 0.155590 | − | 0.987822i | \(-0.450272\pi\) | ||||
0.155590 | + | 0.987822i | \(0.450272\pi\) | |||||||
\(308\) | −2.82994 | −0.161251 | ||||||||
\(309\) | 0.468852 | 0.0266721 | ||||||||
\(310\) | 10.1008 | 0.573689 | ||||||||
\(311\) | 6.91146 | 0.391913 | 0.195956 | − | 0.980613i | \(-0.437219\pi\) | ||||
0.195956 | + | 0.980613i | \(0.437219\pi\) | |||||||
\(312\) | 1.85433 | 0.104981 | ||||||||
\(313\) | −30.2823 | −1.71166 | −0.855830 | − | 0.517258i | \(-0.826953\pi\) | ||||
−0.855830 | + | 0.517258i | \(0.826953\pi\) | |||||||
\(314\) | 29.8716 | 1.68575 | ||||||||
\(315\) | −12.8290 | −0.722833 | ||||||||
\(316\) | −2.97798 | −0.167525 | ||||||||
\(317\) | −1.05835 | −0.0594431 | −0.0297215 | − | 0.999558i | \(-0.509462\pi\) | ||||
−0.0297215 | + | 0.999558i | \(0.509462\pi\) | |||||||
\(318\) | 6.78140 | 0.380282 | ||||||||
\(319\) | −6.45139 | −0.361209 | ||||||||
\(320\) | −7.91987 | −0.442734 | ||||||||
\(321\) | 8.06640 | 0.450223 | ||||||||
\(322\) | 15.3762 | 0.856881 | ||||||||
\(323\) | −4.43647 | −0.246852 | ||||||||
\(324\) | 2.90413 | 0.161340 | ||||||||
\(325\) | 4.98617 | 0.276583 | ||||||||
\(326\) | 10.7549 | 0.595656 | ||||||||
\(327\) | −4.43691 | −0.245361 | ||||||||
\(328\) | −22.9047 | −1.26470 | ||||||||
\(329\) | 28.5676 | 1.57498 | ||||||||
\(330\) | −2.05761 | −0.113268 | ||||||||
\(331\) | 6.60561 | 0.363077 | 0.181539 | − | 0.983384i | \(-0.441892\pi\) | ||||
0.181539 | + | 0.983384i | \(0.441892\pi\) | |||||||
\(332\) | −0.883654 | −0.0484968 | ||||||||
\(333\) | −18.7275 | −1.02626 | ||||||||
\(334\) | 17.5529 | 0.960451 | ||||||||
\(335\) | −12.1797 | −0.665449 | ||||||||
\(336\) | 7.29684 | 0.398076 | ||||||||
\(337\) | −7.79916 | −0.424847 | −0.212424 | − | 0.977178i | \(-0.568136\pi\) | ||||
−0.212424 | + | 0.977178i | \(0.568136\pi\) | |||||||
\(338\) | −16.1807 | −0.880115 | ||||||||
\(339\) | −2.66575 | −0.144783 | ||||||||
\(340\) | 0.564818 | 0.0306316 | ||||||||
\(341\) | −9.72604 | −0.526694 | ||||||||
\(342\) | −19.1549 | −1.03578 | ||||||||
\(343\) | 9.27367 | 0.500731 | ||||||||
\(344\) | 2.46797 | 0.133064 | ||||||||
\(345\) | 1.90335 | 0.102473 | ||||||||
\(346\) | 29.3351 | 1.57707 | ||||||||
\(347\) | −9.84344 | −0.528424 | −0.264212 | − | 0.964465i | \(-0.585112\pi\) | ||||
−0.264212 | + | 0.964465i | \(0.585112\pi\) | |||||||
\(348\) | −0.602106 | −0.0322763 | ||||||||
\(349\) | −30.2937 | −1.62158 | −0.810791 | − | 0.585335i | \(-0.800963\pi\) | ||||
−0.810791 | + | 0.585335i | \(0.800963\pi\) | |||||||
\(350\) | 16.1595 | 0.863760 | ||||||||
\(351\) | 4.34360 | 0.231844 | ||||||||
\(352\) | −4.70566 | −0.250812 | ||||||||
\(353\) | −3.33858 | −0.177695 | −0.0888473 | − | 0.996045i | \(-0.528318\pi\) | ||||
−0.0888473 | + | 0.996045i | \(0.528318\pi\) | |||||||
\(354\) | −7.14674 | −0.379845 | ||||||||
\(355\) | 1.88890 | 0.100252 | ||||||||
\(356\) | −5.50681 | −0.291861 | ||||||||
\(357\) | 1.56843 | 0.0830101 | ||||||||
\(358\) | −25.0629 | −1.32461 | ||||||||
\(359\) | 32.9629 | 1.73972 | 0.869858 | − | 0.493301i | \(-0.164210\pi\) | ||||
0.869858 | + | 0.493301i | \(0.164210\pi\) | |||||||
\(360\) | −9.44679 | −0.497889 | ||||||||
\(361\) | 0.682261 | 0.0359085 | ||||||||
\(362\) | −27.4289 | −1.44163 | ||||||||
\(363\) | −3.16639 | −0.166192 | ||||||||
\(364\) | 2.20823 | 0.115743 | ||||||||
\(365\) | 0.327460 | 0.0171400 | ||||||||
\(366\) | 2.00075 | 0.104581 | ||||||||
\(367\) | 19.8773 | 1.03759 | 0.518793 | − | 0.854900i | \(-0.326382\pi\) | ||||
0.518793 | + | 0.854900i | \(0.326382\pi\) | |||||||
\(368\) | 13.7477 | 0.716646 | ||||||||
\(369\) | −25.8099 | −1.34361 | ||||||||
\(370\) | −14.3900 | −0.748103 | ||||||||
\(371\) | −31.2831 | −1.62414 | ||||||||
\(372\) | −0.907728 | −0.0470635 | ||||||||
\(373\) | 31.8286 | 1.64802 | 0.824011 | − | 0.566574i | \(-0.191732\pi\) | ||||
0.824011 | + | 0.566574i | \(0.191732\pi\) | |||||||
\(374\) | −3.19450 | −0.165184 | ||||||||
\(375\) | 5.22085 | 0.269603 | ||||||||
\(376\) | 21.0361 | 1.08485 | ||||||||
\(377\) | 5.03409 | 0.259269 | ||||||||
\(378\) | 14.0770 | 0.724042 | ||||||||
\(379\) | −18.3892 | −0.944590 | −0.472295 | − | 0.881440i | \(-0.656574\pi\) | ||||
−0.472295 | + | 0.881440i | \(0.656574\pi\) | |||||||
\(380\) | −2.50580 | −0.128545 | ||||||||
\(381\) | −4.22917 | −0.216667 | ||||||||
\(382\) | −8.09005 | −0.413923 | ||||||||
\(383\) | 31.4493 | 1.60699 | 0.803493 | − | 0.595314i | \(-0.202972\pi\) | ||||
0.803493 | + | 0.595314i | \(0.202972\pi\) | |||||||
\(384\) | 6.32099 | 0.322567 | ||||||||
\(385\) | 9.49191 | 0.483753 | ||||||||
\(386\) | −15.5681 | −0.792394 | ||||||||
\(387\) | 2.78101 | 0.141366 | ||||||||
\(388\) | −5.07771 | −0.257782 | ||||||||
\(389\) | −36.1960 | −1.83521 | −0.917604 | − | 0.397496i | \(-0.869879\pi\) | ||||
−0.917604 | + | 0.397496i | \(0.869879\pi\) | |||||||
\(390\) | 1.60557 | 0.0813014 | ||||||||
\(391\) | 2.95501 | 0.149441 | ||||||||
\(392\) | −10.4470 | −0.527654 | ||||||||
\(393\) | 6.18088 | 0.311784 | ||||||||
\(394\) | −12.7826 | −0.643980 | ||||||||
\(395\) | 9.98846 | 0.502574 | ||||||||
\(396\) | −2.34817 | −0.118000 | ||||||||
\(397\) | −16.0708 | −0.806569 | −0.403284 | − | 0.915075i | \(-0.632131\pi\) | ||||
−0.403284 | + | 0.915075i | \(0.632131\pi\) | |||||||
\(398\) | −0.925454 | −0.0463888 | ||||||||
\(399\) | −6.95829 | −0.348350 | ||||||||
\(400\) | 14.4480 | 0.722399 | ||||||||
\(401\) | 18.3382 | 0.915766 | 0.457883 | − | 0.889013i | \(-0.348608\pi\) | ||||
0.457883 | + | 0.889013i | \(0.348608\pi\) | |||||||
\(402\) | 6.42913 | 0.320656 | ||||||||
\(403\) | 7.58933 | 0.378052 | ||||||||
\(404\) | −6.96352 | −0.346448 | ||||||||
\(405\) | −9.74075 | −0.484022 | ||||||||
\(406\) | 16.3148 | 0.809688 | ||||||||
\(407\) | 13.8561 | 0.686821 | ||||||||
\(408\) | 1.15493 | 0.0571776 | ||||||||
\(409\) | −21.6593 | −1.07098 | −0.535491 | − | 0.844541i | \(-0.679874\pi\) | ||||
−0.535491 | + | 0.844541i | \(0.679874\pi\) | |||||||
\(410\) | −19.8321 | −0.979438 | ||||||||
\(411\) | 0.233245 | 0.0115051 | ||||||||
\(412\) | 0.411136 | 0.0202552 | ||||||||
\(413\) | 32.9685 | 1.62227 | ||||||||
\(414\) | 12.7586 | 0.627049 | ||||||||
\(415\) | 2.96387 | 0.145491 | ||||||||
\(416\) | 3.67188 | 0.180029 | ||||||||
\(417\) | 6.08918 | 0.298188 | ||||||||
\(418\) | 14.1723 | 0.693191 | ||||||||
\(419\) | −0.799500 | −0.0390581 | −0.0195291 | − | 0.999809i | \(-0.506217\pi\) | ||||
−0.0195291 | + | 0.999809i | \(0.506217\pi\) | |||||||
\(420\) | 0.885877 | 0.0432264 | ||||||||
\(421\) | −21.4459 | −1.04521 | −0.522604 | − | 0.852576i | \(-0.675039\pi\) | ||||
−0.522604 | + | 0.852576i | \(0.675039\pi\) | |||||||
\(422\) | −3.28711 | −0.160014 | ||||||||
\(423\) | 23.7043 | 1.15254 | ||||||||
\(424\) | −23.0357 | −1.11871 | ||||||||
\(425\) | 3.10554 | 0.150641 | ||||||||
\(426\) | −0.997064 | −0.0483079 | ||||||||
\(427\) | −9.22965 | −0.446654 | ||||||||
\(428\) | 7.07342 | 0.341907 | ||||||||
\(429\) | −1.54600 | −0.0746415 | ||||||||
\(430\) | 2.13690 | 0.103050 | ||||||||
\(431\) | −12.5374 | −0.603905 | −0.301953 | − | 0.953323i | \(-0.597638\pi\) | ||||
−0.301953 | + | 0.953323i | \(0.597638\pi\) | |||||||
\(432\) | 12.5861 | 0.605547 | ||||||||
\(433\) | 0.316199 | 0.0151956 | 0.00759778 | − | 0.999971i | \(-0.497582\pi\) | ||||
0.00759778 | + | 0.999971i | \(0.497582\pi\) | |||||||
\(434\) | 24.5959 | 1.18064 | ||||||||
\(435\) | 2.01953 | 0.0968290 | ||||||||
\(436\) | −3.89072 | −0.186332 | ||||||||
\(437\) | −13.1098 | −0.627127 | ||||||||
\(438\) | −0.172851 | −0.00825915 | ||||||||
\(439\) | −39.0690 | −1.86466 | −0.932331 | − | 0.361607i | \(-0.882228\pi\) | ||||
−0.932331 | + | 0.361607i | \(0.882228\pi\) | |||||||
\(440\) | 6.98948 | 0.333210 | ||||||||
\(441\) | −11.7721 | −0.560577 | ||||||||
\(442\) | 2.49271 | 0.118566 | ||||||||
\(443\) | 2.92193 | 0.138825 | 0.0694125 | − | 0.997588i | \(-0.477888\pi\) | ||||
0.0694125 | + | 0.997588i | \(0.477888\pi\) | |||||||
\(444\) | 1.29319 | 0.0613719 | ||||||||
\(445\) | 18.4704 | 0.875582 | ||||||||
\(446\) | −33.1480 | −1.56960 | ||||||||
\(447\) | −8.73765 | −0.413277 | ||||||||
\(448\) | −19.2852 | −0.911140 | ||||||||
\(449\) | 3.14960 | 0.148639 | 0.0743195 | − | 0.997234i | \(-0.476322\pi\) | ||||
0.0743195 | + | 0.997234i | \(0.476322\pi\) | |||||||
\(450\) | 13.4085 | 0.632083 | ||||||||
\(451\) | 19.0962 | 0.899206 | ||||||||
\(452\) | −2.33759 | −0.109951 | ||||||||
\(453\) | −6.98063 | −0.327979 | ||||||||
\(454\) | 26.7465 | 1.25528 | ||||||||
\(455\) | −7.40664 | −0.347229 | ||||||||
\(456\) | −5.12381 | −0.239945 | ||||||||
\(457\) | −31.7688 | −1.48608 | −0.743040 | − | 0.669247i | \(-0.766617\pi\) | ||||
−0.743040 | + | 0.669247i | \(0.766617\pi\) | |||||||
\(458\) | −1.28911 | −0.0602363 | ||||||||
\(459\) | 2.70533 | 0.126274 | ||||||||
\(460\) | 1.66904 | 0.0778195 | ||||||||
\(461\) | 27.5045 | 1.28101 | 0.640505 | − | 0.767954i | \(-0.278725\pi\) | ||||
0.640505 | + | 0.767954i | \(0.278725\pi\) | |||||||
\(462\) | −5.01035 | −0.233103 | ||||||||
\(463\) | −6.28353 | −0.292020 | −0.146010 | − | 0.989283i | \(-0.546643\pi\) | ||||
−0.146010 | + | 0.989283i | \(0.546643\pi\) | |||||||
\(464\) | 14.5868 | 0.677177 | ||||||||
\(465\) | 3.04462 | 0.141191 | ||||||||
\(466\) | −27.5045 | −1.27412 | ||||||||
\(467\) | −15.1305 | −0.700158 | −0.350079 | − | 0.936720i | \(-0.613845\pi\) | ||||
−0.350079 | + | 0.936720i | \(0.613845\pi\) | |||||||
\(468\) | 1.83231 | 0.0846984 | ||||||||
\(469\) | −29.6581 | −1.36948 | ||||||||
\(470\) | 18.2142 | 0.840156 | ||||||||
\(471\) | 9.00397 | 0.414881 | ||||||||
\(472\) | 24.2767 | 1.11743 | ||||||||
\(473\) | −2.05761 | −0.0946089 | ||||||||
\(474\) | −5.27246 | −0.242172 | ||||||||
\(475\) | −13.7776 | −0.632161 | ||||||||
\(476\) | 1.37535 | 0.0630393 | ||||||||
\(477\) | −25.9575 | −1.18851 | ||||||||
\(478\) | −32.1721 | −1.47152 | ||||||||
\(479\) | 18.3840 | 0.839984 | 0.419992 | − | 0.907528i | \(-0.362033\pi\) | ||||
0.419992 | + | 0.907528i | \(0.362033\pi\) | |||||||
\(480\) | 1.47305 | 0.0672351 | ||||||||
\(481\) | −10.8121 | −0.492988 | ||||||||
\(482\) | 12.4509 | 0.567121 | ||||||||
\(483\) | 4.63472 | 0.210887 | ||||||||
\(484\) | −2.77661 | −0.126209 | ||||||||
\(485\) | 17.0312 | 0.773345 | ||||||||
\(486\) | 17.7420 | 0.804795 | ||||||||
\(487\) | −25.0292 | −1.13418 | −0.567091 | − | 0.823655i | \(-0.691931\pi\) | ||||
−0.567091 | + | 0.823655i | \(0.691931\pi\) | |||||||
\(488\) | −6.79635 | −0.307657 | ||||||||
\(489\) | 3.24175 | 0.146597 | ||||||||
\(490\) | −9.04557 | −0.408637 | ||||||||
\(491\) | 8.38193 | 0.378271 | 0.189136 | − | 0.981951i | \(-0.439431\pi\) | ||||
0.189136 | + | 0.981951i | \(0.439431\pi\) | |||||||
\(492\) | 1.78225 | 0.0803498 | ||||||||
\(493\) | 3.13539 | 0.141211 | ||||||||
\(494\) | −11.0588 | −0.497560 | ||||||||
\(495\) | 7.87602 | 0.354001 | ||||||||
\(496\) | 21.9909 | 0.987422 | ||||||||
\(497\) | 4.59954 | 0.206318 | ||||||||
\(498\) | −1.56449 | −0.0701066 | ||||||||
\(499\) | 12.4436 | 0.557050 | 0.278525 | − | 0.960429i | \(-0.410154\pi\) | ||||
0.278525 | + | 0.960429i | \(0.410154\pi\) | |||||||
\(500\) | 4.57816 | 0.204741 | ||||||||
\(501\) | 5.29083 | 0.236377 | ||||||||
\(502\) | 18.7238 | 0.835682 | ||||||||
\(503\) | −16.3260 | −0.727942 | −0.363971 | − | 0.931410i | \(-0.618579\pi\) | ||||
−0.363971 | + | 0.931410i | \(0.618579\pi\) | |||||||
\(504\) | −23.0033 | −1.02465 | ||||||||
\(505\) | 23.3564 | 1.03935 | ||||||||
\(506\) | −9.43979 | −0.419650 | ||||||||
\(507\) | −4.87723 | −0.216605 | ||||||||
\(508\) | −3.70855 | −0.164540 | ||||||||
\(509\) | 18.4749 | 0.818887 | 0.409443 | − | 0.912336i | \(-0.365723\pi\) | ||||
0.409443 | + | 0.912336i | \(0.365723\pi\) | |||||||
\(510\) | 1.00000 | 0.0442807 | ||||||||
\(511\) | 0.797377 | 0.0352739 | ||||||||
\(512\) | −12.3239 | −0.544645 | ||||||||
\(513\) | −12.0021 | −0.529906 | ||||||||
\(514\) | −0.176268 | −0.00777485 | ||||||||
\(515\) | −1.37899 | −0.0607657 | ||||||||
\(516\) | −0.192036 | −0.00845391 | ||||||||
\(517\) | −17.5383 | −0.771334 | ||||||||
\(518\) | −35.0403 | −1.53958 | ||||||||
\(519\) | 8.84226 | 0.388132 | ||||||||
\(520\) | −5.45396 | −0.239172 | ||||||||
\(521\) | 16.3339 | 0.715600 | 0.357800 | − | 0.933798i | \(-0.383527\pi\) | ||||
0.357800 | + | 0.933798i | \(0.383527\pi\) | |||||||
\(522\) | 13.5374 | 0.592514 | ||||||||
\(523\) | −10.8949 | −0.476399 | −0.238200 | − | 0.971216i | \(-0.576557\pi\) | ||||
−0.238200 | + | 0.971216i | \(0.576557\pi\) | |||||||
\(524\) | 5.42001 | 0.236774 | ||||||||
\(525\) | 4.87082 | 0.212580 | ||||||||
\(526\) | −1.61976 | −0.0706247 | ||||||||
\(527\) | 4.72687 | 0.205906 | ||||||||
\(528\) | −4.47970 | −0.194954 | ||||||||
\(529\) | −14.2679 | −0.620345 | ||||||||
\(530\) | −19.9455 | −0.866378 | ||||||||
\(531\) | 27.3560 | 1.18715 | ||||||||
\(532\) | −6.10172 | −0.264543 | ||||||||
\(533\) | −14.9010 | −0.645434 | ||||||||
\(534\) | −9.74971 | −0.421911 | ||||||||
\(535\) | −23.7250 | −1.02572 | ||||||||
\(536\) | −21.8391 | −0.943304 | ||||||||
\(537\) | −7.55450 | −0.326001 | ||||||||
\(538\) | −5.05839 | −0.218083 | ||||||||
\(539\) | 8.70993 | 0.375163 | ||||||||
\(540\) | 1.52802 | 0.0657554 | ||||||||
\(541\) | 14.6315 | 0.629055 | 0.314528 | − | 0.949248i | \(-0.398154\pi\) | ||||
0.314528 | + | 0.949248i | \(0.398154\pi\) | |||||||
\(542\) | 3.35541 | 0.144127 | ||||||||
\(543\) | −8.26769 | −0.354800 | ||||||||
\(544\) | 2.28696 | 0.0980524 | ||||||||
\(545\) | 13.0499 | 0.558995 | ||||||||
\(546\) | 3.90963 | 0.167317 | ||||||||
\(547\) | 38.8321 | 1.66034 | 0.830170 | − | 0.557510i | \(-0.188243\pi\) | ||||
0.830170 | + | 0.557510i | \(0.188243\pi\) | |||||||
\(548\) | 0.204533 | 0.00873720 | ||||||||
\(549\) | −7.65841 | −0.326853 | ||||||||
\(550\) | −9.92066 | −0.423019 | ||||||||
\(551\) | −13.9100 | −0.592588 | ||||||||
\(552\) | 3.41283 | 0.145260 | ||||||||
\(553\) | 24.3223 | 1.03429 | ||||||||
\(554\) | −3.19941 | −0.135930 | ||||||||
\(555\) | −4.33748 | −0.184116 | ||||||||
\(556\) | 5.33960 | 0.226449 | ||||||||
\(557\) | −15.0377 | −0.637167 | −0.318583 | − | 0.947895i | \(-0.603207\pi\) | ||||
−0.318583 | + | 0.947895i | \(0.603207\pi\) | |||||||
\(558\) | 20.4087 | 0.863971 | ||||||||
\(559\) | 1.60557 | 0.0679085 | ||||||||
\(560\) | −21.4616 | −0.906917 | ||||||||
\(561\) | −0.962895 | −0.0406534 | ||||||||
\(562\) | 30.4690 | 1.28526 | ||||||||
\(563\) | 25.9281 | 1.09274 | 0.546370 | − | 0.837544i | \(-0.316009\pi\) | ||||
0.546370 | + | 0.837544i | \(0.316009\pi\) | |||||||
\(564\) | −1.63685 | −0.0689236 | ||||||||
\(565\) | 7.84052 | 0.329853 | ||||||||
\(566\) | 46.3295 | 1.94737 | ||||||||
\(567\) | −23.7191 | −0.996109 | ||||||||
\(568\) | 3.38692 | 0.142112 | ||||||||
\(569\) | 33.5425 | 1.40617 | 0.703086 | − | 0.711104i | \(-0.251805\pi\) | ||||
0.703086 | + | 0.711104i | \(0.251805\pi\) | |||||||
\(570\) | −4.43647 | −0.185823 | ||||||||
\(571\) | −1.78040 | −0.0745073 | −0.0372536 | − | 0.999306i | \(-0.511861\pi\) | ||||
−0.0372536 | + | 0.999306i | \(0.511861\pi\) | |||||||
\(572\) | −1.35568 | −0.0566840 | ||||||||
\(573\) | −2.43852 | −0.101871 | ||||||||
\(574\) | −48.2920 | −2.01567 | ||||||||
\(575\) | 9.17690 | 0.382703 | ||||||||
\(576\) | −16.0021 | −0.666755 | ||||||||
\(577\) | −5.31057 | −0.221082 | −0.110541 | − | 0.993872i | \(-0.535258\pi\) | ||||
−0.110541 | + | 0.993872i | \(0.535258\pi\) | |||||||
\(578\) | 1.55253 | 0.0645769 | ||||||||
\(579\) | −4.69256 | −0.195016 | ||||||||
\(580\) | 1.77092 | 0.0735336 | ||||||||
\(581\) | 7.21714 | 0.299417 | ||||||||
\(582\) | −8.98998 | −0.372647 | ||||||||
\(583\) | 19.2054 | 0.795408 | ||||||||
\(584\) | 0.587158 | 0.0242968 | ||||||||
\(585\) | −6.14575 | −0.254095 | ||||||||
\(586\) | 15.1533 | 0.625976 | ||||||||
\(587\) | −13.6765 | −0.564488 | −0.282244 | − | 0.959343i | \(-0.591079\pi\) | ||||
−0.282244 | + | 0.959343i | \(0.591079\pi\) | |||||||
\(588\) | 0.812896 | 0.0335232 | ||||||||
\(589\) | −20.9706 | −0.864079 | ||||||||
\(590\) | 21.0201 | 0.865383 | ||||||||
\(591\) | −3.85297 | −0.158490 | ||||||||
\(592\) | −31.3292 | −1.28762 | ||||||||
\(593\) | −23.1903 | −0.952312 | −0.476156 | − | 0.879361i | \(-0.657970\pi\) | ||||
−0.476156 | + | 0.879361i | \(0.657970\pi\) | |||||||
\(594\) | −8.64218 | −0.354593 | ||||||||
\(595\) | −4.61308 | −0.189118 | ||||||||
\(596\) | −7.66204 | −0.313849 | ||||||||
\(597\) | −0.278952 | −0.0114168 | ||||||||
\(598\) | 7.36597 | 0.301217 | ||||||||
\(599\) | 3.62388 | 0.148068 | 0.0740339 | − | 0.997256i | \(-0.476413\pi\) | ||||
0.0740339 | + | 0.997256i | \(0.476413\pi\) | |||||||
\(600\) | 3.58668 | 0.146426 | ||||||||
\(601\) | 10.7756 | 0.439548 | 0.219774 | − | 0.975551i | \(-0.429468\pi\) | ||||
0.219774 | + | 0.975551i | \(0.429468\pi\) | |||||||
\(602\) | 5.20343 | 0.212076 | ||||||||
\(603\) | −24.6091 | −1.00216 | ||||||||
\(604\) | −6.12131 | −0.249073 | ||||||||
\(605\) | 9.31303 | 0.378628 | ||||||||
\(606\) | −12.3288 | −0.500823 | ||||||||
\(607\) | 11.1257 | 0.451578 | 0.225789 | − | 0.974176i | \(-0.427504\pi\) | ||||
0.225789 | + | 0.974176i | \(0.427504\pi\) | |||||||
\(608\) | −10.1460 | −0.411475 | ||||||||
\(609\) | 4.91763 | 0.199272 | ||||||||
\(610\) | −5.88464 | −0.238262 | ||||||||
\(611\) | 13.6853 | 0.553650 | ||||||||
\(612\) | 1.14122 | 0.0461309 | ||||||||
\(613\) | −33.5257 | −1.35409 | −0.677046 | − | 0.735941i | \(-0.736740\pi\) | ||||
−0.677046 | + | 0.735941i | \(0.736740\pi\) | |||||||
\(614\) | 8.46488 | 0.341615 | ||||||||
\(615\) | −5.97784 | −0.241050 | ||||||||
\(616\) | 17.0197 | 0.685741 | ||||||||
\(617\) | 40.9696 | 1.64937 | 0.824686 | − | 0.565591i | \(-0.191352\pi\) | ||||
0.824686 | + | 0.565591i | \(0.191352\pi\) | |||||||
\(618\) | 0.727909 | 0.0292808 | ||||||||
\(619\) | −18.3291 | −0.736709 | −0.368355 | − | 0.929685i | \(-0.620079\pi\) | ||||
−0.368355 | + | 0.929685i | \(0.620079\pi\) | |||||||
\(620\) | 2.66982 | 0.107223 | ||||||||
\(621\) | 7.99426 | 0.320799 | ||||||||
\(622\) | 10.7303 | 0.430245 | ||||||||
\(623\) | 44.9762 | 1.80193 | ||||||||
\(624\) | 3.49556 | 0.139934 | ||||||||
\(625\) | 0.172088 | 0.00688353 | ||||||||
\(626\) | −47.0144 | −1.87907 | ||||||||
\(627\) | 4.27185 | 0.170601 | ||||||||
\(628\) | 7.89558 | 0.315068 | ||||||||
\(629\) | −6.73408 | −0.268506 | ||||||||
\(630\) | −19.9175 | −0.793531 | ||||||||
\(631\) | 4.31547 | 0.171796 | 0.0858981 | − | 0.996304i | \(-0.472624\pi\) | ||||
0.0858981 | + | 0.996304i | \(0.472624\pi\) | |||||||
\(632\) | 17.9100 | 0.712422 | ||||||||
\(633\) | −0.990809 | −0.0393811 | ||||||||
\(634\) | −1.64313 | −0.0652570 | ||||||||
\(635\) | 12.4389 | 0.493622 | ||||||||
\(636\) | 1.79244 | 0.0710748 | ||||||||
\(637\) | −6.79646 | −0.269285 | ||||||||
\(638\) | −10.0160 | −0.396537 | ||||||||
\(639\) | 3.81652 | 0.150979 | ||||||||
\(640\) | −18.5914 | −0.734888 | ||||||||
\(641\) | 39.4483 | 1.55811 | 0.779057 | − | 0.626953i | \(-0.215698\pi\) | ||||
0.779057 | + | 0.626953i | \(0.215698\pi\) | |||||||
\(642\) | 12.5234 | 0.494258 | ||||||||
\(643\) | 44.4275 | 1.75205 | 0.876024 | − | 0.482267i | \(-0.160186\pi\) | ||||
0.876024 | + | 0.482267i | \(0.160186\pi\) | |||||||
\(644\) | 4.06418 | 0.160151 | ||||||||
\(645\) | 0.644108 | 0.0253617 | ||||||||
\(646\) | −6.88777 | −0.270996 | ||||||||
\(647\) | −14.5542 | −0.572183 | −0.286091 | − | 0.958202i | \(-0.592356\pi\) | ||||
−0.286091 | + | 0.958202i | \(0.592356\pi\) | |||||||
\(648\) | −17.4658 | −0.686123 | ||||||||
\(649\) | −20.2401 | −0.794494 | ||||||||
\(650\) | 7.74120 | 0.303635 | ||||||||
\(651\) | 7.41376 | 0.290568 | ||||||||
\(652\) | 2.84269 | 0.111328 | ||||||||
\(653\) | −5.75768 | −0.225315 | −0.112658 | − | 0.993634i | \(-0.535936\pi\) | ||||
−0.112658 | + | 0.993634i | \(0.535936\pi\) | |||||||
\(654\) | −6.88845 | −0.269360 | ||||||||
\(655\) | −18.1793 | −0.710323 | ||||||||
\(656\) | −43.1773 | −1.68579 | ||||||||
\(657\) | 0.661633 | 0.0258128 | ||||||||
\(658\) | 44.3522 | 1.72903 | ||||||||
\(659\) | 34.6474 | 1.34967 | 0.674835 | − | 0.737969i | \(-0.264215\pi\) | ||||
0.674835 | + | 0.737969i | \(0.264215\pi\) | |||||||
\(660\) | −0.543860 | −0.0211697 | ||||||||
\(661\) | −2.04505 | −0.0795432 | −0.0397716 | − | 0.999209i | \(-0.512663\pi\) | ||||
−0.0397716 | + | 0.999209i | \(0.512663\pi\) | |||||||
\(662\) | 10.2554 | 0.398589 | ||||||||
\(663\) | 0.751357 | 0.0291803 | ||||||||
\(664\) | 5.31442 | 0.206240 | ||||||||
\(665\) | 20.4658 | 0.793630 | ||||||||
\(666\) | −29.0751 | −1.12664 | ||||||||
\(667\) | 9.26509 | 0.358746 | ||||||||
\(668\) | 4.63952 | 0.179509 | ||||||||
\(669\) | −9.99154 | −0.386295 | ||||||||
\(670\) | −18.9094 | −0.730535 | ||||||||
\(671\) | 5.66629 | 0.218745 | ||||||||
\(672\) | 3.58693 | 0.138369 | ||||||||
\(673\) | −37.3113 | −1.43825 | −0.719123 | − | 0.694883i | \(-0.755456\pi\) | ||||
−0.719123 | + | 0.694883i | \(0.755456\pi\) | |||||||
\(674\) | −12.1085 | −0.466400 | ||||||||
\(675\) | 8.40150 | 0.323374 | ||||||||
\(676\) | −4.27684 | −0.164494 | ||||||||
\(677\) | 0.572224 | 0.0219924 | 0.0109962 | − | 0.999940i | \(-0.496500\pi\) | ||||
0.0109962 | + | 0.999940i | \(0.496500\pi\) | |||||||
\(678\) | −4.13866 | −0.158944 | ||||||||
\(679\) | 41.4715 | 1.59153 | ||||||||
\(680\) | −3.39690 | −0.130265 | ||||||||
\(681\) | 8.06199 | 0.308936 | ||||||||
\(682\) | −15.1000 | −0.578209 | ||||||||
\(683\) | −40.0033 | −1.53069 | −0.765343 | − | 0.643623i | \(-0.777430\pi\) | ||||
−0.765343 | + | 0.643623i | \(0.777430\pi\) | |||||||
\(684\) | −5.06297 | −0.193588 | ||||||||
\(685\) | −0.686024 | −0.0262116 | ||||||||
\(686\) | 14.3977 | 0.549706 | ||||||||
\(687\) | −0.388568 | −0.0148248 | ||||||||
\(688\) | 4.65233 | 0.177368 | ||||||||
\(689\) | −14.9862 | −0.570929 | ||||||||
\(690\) | 2.95501 | 0.112495 | ||||||||
\(691\) | 19.8850 | 0.756461 | 0.378231 | − | 0.925711i | \(-0.376533\pi\) | ||||
0.378231 | + | 0.925711i | \(0.376533\pi\) | |||||||
\(692\) | 7.75378 | 0.294754 | ||||||||
\(693\) | 19.1784 | 0.728528 | ||||||||
\(694\) | −15.2823 | −0.580107 | ||||||||
\(695\) | −17.9096 | −0.679348 | ||||||||
\(696\) | 3.62115 | 0.137259 | ||||||||
\(697\) | −9.28079 | −0.351535 | ||||||||
\(698\) | −47.0319 | −1.78019 | ||||||||
\(699\) | −8.29046 | −0.313574 | ||||||||
\(700\) | 4.27122 | 0.161437 | ||||||||
\(701\) | 19.6778 | 0.743222 | 0.371611 | − | 0.928389i | \(-0.378806\pi\) | ||||
0.371611 | + | 0.928389i | \(0.378806\pi\) | |||||||
\(702\) | 6.74359 | 0.254520 | ||||||||
\(703\) | 29.8756 | 1.12678 | ||||||||
\(704\) | 11.8396 | 0.446223 | ||||||||
\(705\) | 5.49015 | 0.206771 | ||||||||
\(706\) | −5.18325 | −0.195074 | ||||||||
\(707\) | 56.8737 | 2.13896 | ||||||||
\(708\) | −1.88900 | −0.0709931 | ||||||||
\(709\) | 19.6415 | 0.737653 | 0.368827 | − | 0.929498i | \(-0.379760\pi\) | ||||
0.368827 | + | 0.929498i | \(0.379760\pi\) | |||||||
\(710\) | 2.93258 | 0.110058 | ||||||||
\(711\) | 20.1817 | 0.756873 | ||||||||
\(712\) | 33.1187 | 1.24118 | ||||||||
\(713\) | 13.9679 | 0.523103 | ||||||||
\(714\) | 2.43504 | 0.0911291 | ||||||||
\(715\) | 4.54711 | 0.170052 | ||||||||
\(716\) | −6.62454 | −0.247571 | ||||||||
\(717\) | −9.69738 | −0.362155 | ||||||||
\(718\) | 51.1761 | 1.90987 | ||||||||
\(719\) | 37.4428 | 1.39638 | 0.698191 | − | 0.715912i | \(-0.253989\pi\) | ||||
0.698191 | + | 0.715912i | \(0.253989\pi\) | |||||||
\(720\) | −17.8080 | −0.663664 | ||||||||
\(721\) | −3.35790 | −0.125055 | ||||||||
\(722\) | 1.05923 | 0.0394206 | ||||||||
\(723\) | 3.75297 | 0.139574 | ||||||||
\(724\) | −7.24993 | −0.269442 | ||||||||
\(725\) | 9.73707 | 0.361626 | ||||||||
\(726\) | −4.91593 | −0.182447 | ||||||||
\(727\) | 37.6367 | 1.39587 | 0.697933 | − | 0.716163i | \(-0.254103\pi\) | ||||
0.697933 | + | 0.716163i | \(0.254103\pi\) | |||||||
\(728\) | −13.2806 | −0.492213 | ||||||||
\(729\) | −15.8832 | −0.588266 | ||||||||
\(730\) | 0.508392 | 0.0188164 | ||||||||
\(731\) | 1.00000 | 0.0369863 | ||||||||
\(732\) | 0.528833 | 0.0195462 | ||||||||
\(733\) | 2.42520 | 0.0895766 | 0.0447883 | − | 0.998996i | \(-0.485739\pi\) | ||||
0.0447883 | + | 0.998996i | \(0.485739\pi\) | |||||||
\(734\) | 30.8602 | 1.13907 | ||||||||
\(735\) | −2.72654 | −0.100570 | ||||||||
\(736\) | 6.75798 | 0.249102 | ||||||||
\(737\) | 18.2078 | 0.670692 | ||||||||
\(738\) | −40.0708 | −1.47503 | ||||||||
\(739\) | −9.87099 | −0.363110 | −0.181555 | − | 0.983381i | \(-0.558113\pi\) | ||||
−0.181555 | + | 0.983381i | \(0.558113\pi\) | |||||||
\(740\) | −3.80353 | −0.139821 | ||||||||
\(741\) | −3.33337 | −0.122455 | ||||||||
\(742\) | −48.5681 | −1.78299 | ||||||||
\(743\) | 25.0556 | 0.919202 | 0.459601 | − | 0.888125i | \(-0.347992\pi\) | ||||
0.459601 | + | 0.888125i | \(0.347992\pi\) | |||||||
\(744\) | 5.45920 | 0.200144 | ||||||||
\(745\) | 25.6993 | 0.941548 | ||||||||
\(746\) | 49.4149 | 1.80921 | ||||||||
\(747\) | 5.98850 | 0.219108 | ||||||||
\(748\) | −0.844362 | −0.0308729 | ||||||||
\(749\) | −57.7713 | −2.11092 | ||||||||
\(750\) | 8.10554 | 0.295973 | ||||||||
\(751\) | −17.8673 | −0.651987 | −0.325993 | − | 0.945372i | \(-0.605699\pi\) | ||||
−0.325993 | + | 0.945372i | \(0.605699\pi\) | |||||||
\(752\) | 39.6548 | 1.44606 | ||||||||
\(753\) | 5.64375 | 0.205670 | ||||||||
\(754\) | 7.81560 | 0.284627 | ||||||||
\(755\) | 20.5315 | 0.747218 | ||||||||
\(756\) | 3.72078 | 0.135324 | ||||||||
\(757\) | −29.2824 | −1.06429 | −0.532144 | − | 0.846654i | \(-0.678614\pi\) | ||||
−0.532144 | + | 0.846654i | \(0.678614\pi\) | |||||||
\(758\) | −28.5499 | −1.03698 | ||||||||
\(759\) | −2.84536 | −0.103280 | ||||||||
\(760\) | 15.0702 | 0.546654 | ||||||||
\(761\) | 29.8059 | 1.08046 | 0.540231 | − | 0.841517i | \(-0.318337\pi\) | ||||
0.540231 | + | 0.841517i | \(0.318337\pi\) | |||||||
\(762\) | −6.56592 | −0.237858 | ||||||||
\(763\) | 31.7770 | 1.15040 | ||||||||
\(764\) | −2.13834 | −0.0773623 | ||||||||
\(765\) | −3.82776 | −0.138393 | ||||||||
\(766\) | 48.8262 | 1.76416 | ||||||||
\(767\) | 15.7936 | 0.570273 | ||||||||
\(768\) | 4.42810 | 0.159785 | ||||||||
\(769\) | −6.62324 | −0.238840 | −0.119420 | − | 0.992844i | \(-0.538104\pi\) | ||||
−0.119420 | + | 0.992844i | \(0.538104\pi\) | |||||||
\(770\) | 14.7365 | 0.531067 | ||||||||
\(771\) | −0.0531311 | −0.00191347 | ||||||||
\(772\) | −4.11490 | −0.148099 | ||||||||
\(773\) | 42.7240 | 1.53667 | 0.768337 | − | 0.640045i | \(-0.221084\pi\) | ||||
0.768337 | + | 0.640045i | \(0.221084\pi\) | |||||||
\(774\) | 4.31761 | 0.155193 | ||||||||
\(775\) | 14.6795 | 0.527302 | ||||||||
\(776\) | 30.5380 | 1.09625 | ||||||||
\(777\) | −10.5619 | −0.378907 | ||||||||
\(778\) | −56.1954 | −2.01470 | ||||||||
\(779\) | 41.1740 | 1.47521 | ||||||||
\(780\) | 0.424380 | 0.0151952 | ||||||||
\(781\) | −2.82376 | −0.101042 | ||||||||
\(782\) | 4.58775 | 0.164058 | ||||||||
\(783\) | 8.48224 | 0.303131 | ||||||||
\(784\) | −19.6935 | −0.703339 | ||||||||
\(785\) | −26.4826 | −0.945204 | ||||||||
\(786\) | 9.59602 | 0.342279 | ||||||||
\(787\) | −54.3543 | −1.93752 | −0.968760 | − | 0.247999i | \(-0.920227\pi\) | ||||
−0.968760 | + | 0.247999i | \(0.920227\pi\) | |||||||
\(788\) | −3.37867 | −0.120360 | ||||||||
\(789\) | −0.488231 | −0.0173815 | ||||||||
\(790\) | 15.5074 | 0.551730 | ||||||||
\(791\) | 19.0920 | 0.678833 | ||||||||
\(792\) | 14.1223 | 0.501812 | ||||||||
\(793\) | −4.42147 | −0.157011 | ||||||||
\(794\) | −24.9504 | −0.885457 | ||||||||
\(795\) | −6.01202 | −0.213225 | ||||||||
\(796\) | −0.244613 | −0.00867008 | ||||||||
\(797\) | 39.0251 | 1.38234 | 0.691171 | − | 0.722692i | \(-0.257095\pi\) | ||||
0.691171 | + | 0.722692i | \(0.257095\pi\) | |||||||
\(798\) | −10.8030 | −0.382421 | ||||||||
\(799\) | 8.52365 | 0.301545 | ||||||||
\(800\) | 7.10224 | 0.251102 | ||||||||
\(801\) | 37.3195 | 1.31862 | ||||||||
\(802\) | 28.4707 | 1.00533 | ||||||||
\(803\) | −0.489528 | −0.0172751 | ||||||||
\(804\) | 1.69933 | 0.0599307 | ||||||||
\(805\) | −13.6317 | −0.480454 | ||||||||
\(806\) | 11.7827 | 0.415028 | ||||||||
\(807\) | −1.52471 | −0.0536724 | ||||||||
\(808\) | 41.8796 | 1.47332 | ||||||||
\(809\) | 1.18490 | 0.0416590 | 0.0208295 | − | 0.999783i | \(-0.493369\pi\) | ||||
0.0208295 | + | 0.999783i | \(0.493369\pi\) | |||||||
\(810\) | −15.1228 | −0.531363 | ||||||||
\(811\) | 10.4542 | 0.367098 | 0.183549 | − | 0.983011i | \(-0.441241\pi\) | ||||
0.183549 | + | 0.983011i | \(0.441241\pi\) | |||||||
\(812\) | 4.31227 | 0.151331 | ||||||||
\(813\) | 1.01139 | 0.0354712 | ||||||||
\(814\) | 21.5121 | 0.753997 | ||||||||
\(815\) | −9.53468 | −0.333985 | ||||||||
\(816\) | 2.17714 | 0.0762152 | ||||||||
\(817\) | −4.43647 | −0.155212 | ||||||||
\(818\) | −33.6268 | −1.17573 | ||||||||
\(819\) | −14.9651 | −0.522924 | ||||||||
\(820\) | −5.24196 | −0.183057 | ||||||||
\(821\) | 13.1726 | 0.459727 | 0.229863 | − | 0.973223i | \(-0.426172\pi\) | ||||
0.229863 | + | 0.973223i | \(0.426172\pi\) | |||||||
\(822\) | 0.362121 | 0.0126304 | ||||||||
\(823\) | −31.6599 | −1.10360 | −0.551798 | − | 0.833978i | \(-0.686058\pi\) | ||||
−0.551798 | + | 0.833978i | \(0.686058\pi\) | |||||||
\(824\) | −2.47263 | −0.0861381 | ||||||||
\(825\) | −2.99031 | −0.104109 | ||||||||
\(826\) | 51.1847 | 1.78094 | ||||||||
\(827\) | 3.05427 | 0.106208 | 0.0531038 | − | 0.998589i | \(-0.483089\pi\) | ||||
0.0531038 | + | 0.998589i | \(0.483089\pi\) | |||||||
\(828\) | 3.37230 | 0.117196 | ||||||||
\(829\) | −1.45481 | −0.0505276 | −0.0252638 | − | 0.999681i | \(-0.508043\pi\) | ||||
−0.0252638 | + | 0.999681i | \(0.508043\pi\) | |||||||
\(830\) | 4.60151 | 0.159721 | ||||||||
\(831\) | −0.964374 | −0.0334538 | ||||||||
\(832\) | −9.23859 | −0.320290 | ||||||||
\(833\) | −4.23304 | −0.146666 | ||||||||
\(834\) | 9.45365 | 0.327353 | ||||||||
\(835\) | −15.5614 | −0.538526 | ||||||||
\(836\) | 3.74598 | 0.129558 | ||||||||
\(837\) | 12.7877 | 0.442008 | ||||||||
\(838\) | −1.24125 | −0.0428783 | ||||||||
\(839\) | −6.85018 | −0.236494 | −0.118247 | − | 0.992984i | \(-0.537728\pi\) | ||||
−0.118247 | + | 0.992984i | \(0.537728\pi\) | |||||||
\(840\) | −5.32779 | −0.183826 | ||||||||
\(841\) | −19.1694 | −0.661012 | ||||||||
\(842\) | −33.2954 | −1.14744 | ||||||||
\(843\) | 9.18404 | 0.316315 | ||||||||
\(844\) | −0.868840 | −0.0299067 | ||||||||
\(845\) | 14.3450 | 0.493482 | ||||||||
\(846\) | 36.8017 | 1.26527 | ||||||||
\(847\) | 22.6776 | 0.779211 | ||||||||
\(848\) | −43.4242 | −1.49119 | ||||||||
\(849\) | 13.9647 | 0.479269 | ||||||||
\(850\) | 4.82146 | 0.165375 | ||||||||
\(851\) | −19.8993 | −0.682138 | ||||||||
\(852\) | −0.263541 | −0.00902877 | ||||||||
\(853\) | −17.5620 | −0.601310 | −0.300655 | − | 0.953733i | \(-0.597205\pi\) | ||||
−0.300655 | + | 0.953733i | \(0.597205\pi\) | |||||||
\(854\) | −14.3293 | −0.490340 | ||||||||
\(855\) | 16.9817 | 0.580763 | ||||||||
\(856\) | −42.5406 | −1.45401 | ||||||||
\(857\) | −6.67420 | −0.227986 | −0.113993 | − | 0.993482i | \(-0.536364\pi\) | ||||
−0.113993 | + | 0.993482i | \(0.536364\pi\) | |||||||
\(858\) | −2.40021 | −0.0819420 | ||||||||
\(859\) | −19.3448 | −0.660036 | −0.330018 | − | 0.943975i | \(-0.607055\pi\) | ||||
−0.330018 | + | 0.943975i | \(0.607055\pi\) | |||||||
\(860\) | 0.564818 | 0.0192601 | ||||||||
\(861\) | −14.5563 | −0.496076 | ||||||||
\(862\) | −19.4647 | −0.662971 | ||||||||
\(863\) | −30.8248 | −1.04929 | −0.524645 | − | 0.851321i | \(-0.675802\pi\) | ||||
−0.524645 | + | 0.851321i | \(0.675802\pi\) | |||||||
\(864\) | 6.18696 | 0.210485 | ||||||||
\(865\) | −26.0070 | −0.884264 | ||||||||
\(866\) | 0.490910 | 0.0166818 | ||||||||
\(867\) | 0.467968 | 0.0158930 | ||||||||
\(868\) | 6.50112 | 0.220662 | ||||||||
\(869\) | −14.9320 | −0.506534 | ||||||||
\(870\) | 3.13539 | 0.106300 | ||||||||
\(871\) | −14.2077 | −0.481411 | ||||||||
\(872\) | 23.3993 | 0.792401 | ||||||||
\(873\) | 34.4115 | 1.16465 | ||||||||
\(874\) | −20.3534 | −0.688464 | ||||||||
\(875\) | −37.3915 | −1.26406 | ||||||||
\(876\) | −0.0456875 | −0.00154364 | ||||||||
\(877\) | −9.29617 | −0.313909 | −0.156955 | − | 0.987606i | \(-0.550168\pi\) | ||||
−0.156955 | + | 0.987606i | \(0.550168\pi\) | |||||||
\(878\) | −60.6559 | −2.04704 | ||||||||
\(879\) | 4.56753 | 0.154059 | ||||||||
\(880\) | 13.1757 | 0.444154 | ||||||||
\(881\) | 10.8604 | 0.365896 | 0.182948 | − | 0.983123i | \(-0.441436\pi\) | ||||
0.182948 | + | 0.983123i | \(0.441436\pi\) | |||||||
\(882\) | −18.2766 | −0.615405 | ||||||||
\(883\) | 5.78586 | 0.194710 | 0.0973549 | − | 0.995250i | \(-0.468962\pi\) | ||||
0.0973549 | + | 0.995250i | \(0.468962\pi\) | |||||||
\(884\) | 0.658865 | 0.0221600 | ||||||||
\(885\) | 6.33592 | 0.212980 | ||||||||
\(886\) | 4.53639 | 0.152403 | ||||||||
\(887\) | 23.4572 | 0.787615 | 0.393807 | − | 0.919193i | \(-0.371158\pi\) | ||||
0.393807 | + | 0.919193i | \(0.371158\pi\) | |||||||
\(888\) | −7.77740 | −0.260992 | ||||||||
\(889\) | 30.2891 | 1.01587 | ||||||||
\(890\) | 28.6760 | 0.961220 | ||||||||
\(891\) | 14.5617 | 0.487836 | ||||||||
\(892\) | −8.76157 | −0.293359 | ||||||||
\(893\) | −37.8149 | −1.26543 | ||||||||
\(894\) | −13.5655 | −0.453698 | ||||||||
\(895\) | 22.2194 | 0.742713 | ||||||||
\(896\) | −45.2707 | −1.51239 | ||||||||
\(897\) | 2.22027 | 0.0741326 | ||||||||
\(898\) | 4.88986 | 0.163177 | ||||||||
\(899\) | 14.8206 | 0.494293 | ||||||||
\(900\) | 3.54409 | 0.118136 | ||||||||
\(901\) | −9.33387 | −0.310956 | ||||||||
\(902\) | 29.6475 | 0.987155 | ||||||||
\(903\) | 1.56843 | 0.0521941 | ||||||||
\(904\) | 14.0586 | 0.467582 | ||||||||
\(905\) | 24.3170 | 0.808325 | ||||||||
\(906\) | −10.8377 | −0.360057 | ||||||||
\(907\) | −24.4247 | −0.811009 | −0.405504 | − | 0.914093i | \(-0.632904\pi\) | ||||
−0.405504 | + | 0.914093i | \(0.632904\pi\) | |||||||
\(908\) | 7.06956 | 0.234611 | ||||||||
\(909\) | 47.1916 | 1.56525 | ||||||||
\(910\) | −11.4991 | −0.381190 | ||||||||
\(911\) | −29.5612 | −0.979406 | −0.489703 | − | 0.871889i | \(-0.662895\pi\) | ||||
−0.489703 | + | 0.871889i | \(0.662895\pi\) | |||||||
\(912\) | −9.65882 | −0.319835 | ||||||||
\(913\) | −4.43077 | −0.146637 | ||||||||
\(914\) | −49.3221 | −1.63143 | ||||||||
\(915\) | −1.77376 | −0.0586388 | ||||||||
\(916\) | −0.340735 | −0.0112582 | ||||||||
\(917\) | −44.2672 | −1.46183 | ||||||||
\(918\) | 4.20011 | 0.138624 | ||||||||
\(919\) | −8.03175 | −0.264943 | −0.132471 | − | 0.991187i | \(-0.542291\pi\) | ||||
−0.132471 | + | 0.991187i | \(0.542291\pi\) | |||||||
\(920\) | −10.0379 | −0.330938 | ||||||||
\(921\) | 2.55150 | 0.0840749 | ||||||||
\(922\) | 42.7016 | 1.40630 | ||||||||
\(923\) | 2.20341 | 0.0725262 | ||||||||
\(924\) | −1.32432 | −0.0435670 | ||||||||
\(925\) | −20.9130 | −0.687614 | ||||||||
\(926\) | −9.75539 | −0.320582 | ||||||||
\(927\) | −2.78626 | −0.0915127 | ||||||||
\(928\) | 7.17049 | 0.235383 | ||||||||
\(929\) | 34.6810 | 1.13785 | 0.568924 | − | 0.822390i | \(-0.307360\pi\) | ||||
0.568924 | + | 0.822390i | \(0.307360\pi\) | |||||||
\(930\) | 4.72687 | 0.155000 | ||||||||
\(931\) | 18.7798 | 0.615481 | ||||||||
\(932\) | −7.26990 | −0.238134 | ||||||||
\(933\) | 3.23434 | 0.105888 | ||||||||
\(934\) | −23.4907 | −0.768638 | ||||||||
\(935\) | 2.83208 | 0.0926188 | ||||||||
\(936\) | −11.0197 | −0.360192 | ||||||||
\(937\) | 35.9363 | 1.17399 | 0.586994 | − | 0.809591i | \(-0.300311\pi\) | ||||
0.586994 | + | 0.809591i | \(0.300311\pi\) | |||||||
\(938\) | −46.0452 | −1.50343 | ||||||||
\(939\) | −14.1712 | −0.462459 | ||||||||
\(940\) | 4.81431 | 0.157025 | ||||||||
\(941\) | −48.1664 | −1.57018 | −0.785090 | − | 0.619382i | \(-0.787383\pi\) | ||||
−0.785090 | + | 0.619382i | \(0.787383\pi\) | |||||||
\(942\) | 13.9790 | 0.455460 | ||||||||
\(943\) | −27.4248 | −0.893075 | ||||||||
\(944\) | 45.7636 | 1.48948 | ||||||||
\(945\) | −12.4799 | −0.405971 | ||||||||
\(946\) | −3.19450 | −0.103862 | ||||||||
\(947\) | 50.0891 | 1.62768 | 0.813839 | − | 0.581091i | \(-0.197374\pi\) | ||||
0.813839 | + | 0.581091i | \(0.197374\pi\) | |||||||
\(948\) | −1.39360 | −0.0452621 | ||||||||
\(949\) | 0.381984 | 0.0123997 | ||||||||
\(950\) | −21.3902 | −0.693991 | ||||||||
\(951\) | −0.495276 | −0.0160604 | ||||||||
\(952\) | −8.27157 | −0.268083 | ||||||||
\(953\) | −47.1986 | −1.52891 | −0.764457 | − | 0.644675i | \(-0.776993\pi\) | ||||
−0.764457 | + | 0.644675i | \(0.776993\pi\) | |||||||
\(954\) | −40.3000 | −1.30476 | ||||||||
\(955\) | 7.17221 | 0.232087 | ||||||||
\(956\) | −8.50363 | −0.275027 | ||||||||
\(957\) | −3.01905 | −0.0975919 | ||||||||
\(958\) | 28.5417 | 0.922141 | ||||||||
\(959\) | −1.67050 | −0.0539431 | ||||||||
\(960\) | −3.70625 | −0.119619 | ||||||||
\(961\) | −8.65672 | −0.279249 | ||||||||
\(962\) | −16.7861 | −0.541206 | ||||||||
\(963\) | −47.9364 | −1.54473 | ||||||||
\(964\) | 3.29097 | 0.105995 | ||||||||
\(965\) | 13.8018 | 0.444296 | ||||||||
\(966\) | 7.19556 | 0.231513 | ||||||||
\(967\) | 50.7117 | 1.63078 | 0.815390 | − | 0.578912i | \(-0.196523\pi\) | ||||
0.815390 | + | 0.578912i | \(0.196523\pi\) | |||||||
\(968\) | 16.6989 | 0.536723 | ||||||||
\(969\) | −2.07613 | −0.0666948 | ||||||||
\(970\) | 26.4414 | 0.848984 | ||||||||
\(971\) | 14.3657 | 0.461017 | 0.230508 | − | 0.973070i | \(-0.425961\pi\) | ||||
0.230508 | + | 0.973070i | \(0.425961\pi\) | |||||||
\(972\) | 4.68952 | 0.150416 | ||||||||
\(973\) | −43.6105 | −1.39809 | ||||||||
\(974\) | −38.8587 | −1.24511 | ||||||||
\(975\) | 2.33337 | 0.0747277 | ||||||||
\(976\) | −12.8117 | −0.410092 | ||||||||
\(977\) | 3.90889 | 0.125056 | 0.0625282 | − | 0.998043i | \(-0.480084\pi\) | ||||
0.0625282 | + | 0.998043i | \(0.480084\pi\) | |||||||
\(978\) | 5.03293 | 0.160935 | ||||||||
\(979\) | −27.6119 | −0.882481 | ||||||||
\(980\) | −2.39090 | −0.0763744 | ||||||||
\(981\) | 26.3673 | 0.841843 | ||||||||
\(982\) | 13.0132 | 0.415269 | ||||||||
\(983\) | 46.8969 | 1.49578 | 0.747889 | − | 0.663824i | \(-0.231067\pi\) | ||||
0.747889 | + | 0.663824i | \(0.231067\pi\) | |||||||
\(984\) | −10.7187 | −0.341699 | ||||||||
\(985\) | 11.3324 | 0.361081 | ||||||||
\(986\) | 4.86779 | 0.155022 | ||||||||
\(987\) | 13.3687 | 0.425532 | ||||||||
\(988\) | −2.92303 | −0.0929941 | ||||||||
\(989\) | 2.95501 | 0.0939638 | ||||||||
\(990\) | 12.2278 | 0.388625 | ||||||||
\(991\) | −31.8168 | −1.01069 | −0.505347 | − | 0.862916i | \(-0.668635\pi\) | ||||
−0.505347 | + | 0.862916i | \(0.668635\pi\) | |||||||
\(992\) | 10.8101 | 0.343222 | ||||||||
\(993\) | 3.09121 | 0.0980967 | ||||||||
\(994\) | 7.14094 | 0.226497 | ||||||||
\(995\) | 0.820458 | 0.0260103 | ||||||||
\(996\) | −0.413522 | −0.0131029 | ||||||||
\(997\) | −19.3075 | −0.611473 | −0.305737 | − | 0.952116i | \(-0.598903\pi\) | ||||
−0.305737 | + | 0.952116i | \(0.598903\pi\) | |||||||
\(998\) | 19.3191 | 0.611534 | ||||||||
\(999\) | −18.2179 | −0.576389 |
(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 | 731.2.a.c.1.5 | ✓ | 6 | |
3.2 | odd | 2 | 6579.2.a.j.1.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
731.2.a.c.1.5 | ✓ | 6 | 1.1 | even | 1 | trivial | |
6579.2.a.j.1.2 | 6 | 3.2 | odd | 2 |