Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1003,2,Mod(1,1003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1003, 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("1003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1003 = 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1003.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: | \(8.00899532273\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 5 x^{17} - 16 x^{16} + 112 x^{15} + 52 x^{14} - 984 x^{13} + 431 x^{12} + 4304 x^{11} + \cdots + 28 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.46111\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1003.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.46111 | −1.74027 | −0.870133 | − | 0.492817i | \(-0.835967\pi\) | ||||
−0.870133 | + | 0.492817i | \(0.835967\pi\) | |||||||
\(3\) | 2.84715 | 1.64380 | 0.821901 | − | 0.569630i | \(-0.192913\pi\) | ||||
0.821901 | + | 0.569630i | \(0.192913\pi\) | |||||||
\(4\) | 4.05705 | 2.02853 | ||||||||
\(5\) | −0.414665 | −0.185444 | −0.0927220 | − | 0.995692i | \(-0.529557\pi\) | ||||
−0.0927220 | + | 0.995692i | \(0.529557\pi\) | |||||||
\(6\) | −7.00714 | −2.86065 | ||||||||
\(7\) | −0.439244 | −0.166019 | −0.0830093 | − | 0.996549i | \(-0.526453\pi\) | ||||
−0.0830093 | + | 0.996549i | \(0.526453\pi\) | |||||||
\(8\) | −5.06262 | −1.78991 | ||||||||
\(9\) | 5.10626 | 1.70209 | ||||||||
\(10\) | 1.02054 | 0.322722 | ||||||||
\(11\) | 4.90924 | 1.48019 | 0.740096 | − | 0.672501i | \(-0.234780\pi\) | ||||
0.740096 | + | 0.672501i | \(0.234780\pi\) | |||||||
\(12\) | 11.5510 | 3.33450 | ||||||||
\(13\) | −0.372782 | −0.103391 | −0.0516955 | − | 0.998663i | \(-0.516463\pi\) | ||||
−0.0516955 | + | 0.998663i | \(0.516463\pi\) | |||||||
\(14\) | 1.08103 | 0.288917 | ||||||||
\(15\) | −1.18061 | −0.304833 | ||||||||
\(16\) | 4.34556 | 1.08639 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −12.5671 | −2.96209 | ||||||||
\(19\) | −1.13847 | −0.261183 | −0.130592 | − | 0.991436i | \(-0.541688\pi\) | ||||
−0.130592 | + | 0.991436i | \(0.541688\pi\) | |||||||
\(20\) | −1.68232 | −0.376178 | ||||||||
\(21\) | −1.25059 | −0.272902 | ||||||||
\(22\) | −12.0822 | −2.57593 | ||||||||
\(23\) | 2.97744 | 0.620840 | 0.310420 | − | 0.950600i | \(-0.399530\pi\) | ||||
0.310420 | + | 0.950600i | \(0.399530\pi\) | |||||||
\(24\) | −14.4140 | −2.94225 | ||||||||
\(25\) | −4.82805 | −0.965611 | ||||||||
\(26\) | 0.917456 | 0.179928 | ||||||||
\(27\) | 5.99685 | 1.15409 | ||||||||
\(28\) | −1.78204 | −0.336773 | ||||||||
\(29\) | 5.04031 | 0.935962 | 0.467981 | − | 0.883739i | \(-0.344982\pi\) | ||||
0.467981 | + | 0.883739i | \(0.344982\pi\) | |||||||
\(30\) | 2.90562 | 0.530491 | ||||||||
\(31\) | 0.227163 | 0.0407997 | 0.0203998 | − | 0.999792i | \(-0.493506\pi\) | ||||
0.0203998 | + | 0.999792i | \(0.493506\pi\) | |||||||
\(32\) | −0.569638 | −0.100699 | ||||||||
\(33\) | 13.9774 | 2.43315 | ||||||||
\(34\) | −2.46111 | −0.422076 | ||||||||
\(35\) | 0.182139 | 0.0307872 | ||||||||
\(36\) | 20.7164 | 3.45273 | ||||||||
\(37\) | 11.6156 | 1.90960 | 0.954798 | − | 0.297255i | \(-0.0960713\pi\) | ||||
0.954798 | + | 0.297255i | \(0.0960713\pi\) | |||||||
\(38\) | 2.80190 | 0.454528 | ||||||||
\(39\) | −1.06137 | −0.169955 | ||||||||
\(40\) | 2.09929 | 0.331927 | ||||||||
\(41\) | −3.23522 | −0.505257 | −0.252628 | − | 0.967563i | \(-0.581295\pi\) | ||||
−0.252628 | + | 0.967563i | \(0.581295\pi\) | |||||||
\(42\) | 3.07785 | 0.474922 | ||||||||
\(43\) | −4.66150 | −0.710872 | −0.355436 | − | 0.934701i | \(-0.615668\pi\) | ||||
−0.355436 | + | 0.934701i | \(0.615668\pi\) | |||||||
\(44\) | 19.9171 | 3.00261 | ||||||||
\(45\) | −2.11739 | −0.315642 | ||||||||
\(46\) | −7.32780 | −1.08043 | ||||||||
\(47\) | 7.42089 | 1.08245 | 0.541224 | − | 0.840879i | \(-0.317961\pi\) | ||||
0.541224 | + | 0.840879i | \(0.317961\pi\) | |||||||
\(48\) | 12.3725 | 1.78581 | ||||||||
\(49\) | −6.80706 | −0.972438 | ||||||||
\(50\) | 11.8824 | 1.68042 | ||||||||
\(51\) | 2.84715 | 0.398681 | ||||||||
\(52\) | −1.51239 | −0.209731 | ||||||||
\(53\) | 1.45997 | 0.200543 | 0.100271 | − | 0.994960i | \(-0.468029\pi\) | ||||
0.100271 | + | 0.994960i | \(0.468029\pi\) | |||||||
\(54\) | −14.7589 | −2.00843 | ||||||||
\(55\) | −2.03569 | −0.274493 | ||||||||
\(56\) | 2.22373 | 0.297158 | ||||||||
\(57\) | −3.24140 | −0.429334 | ||||||||
\(58\) | −12.4047 | −1.62882 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | −4.78981 | −0.618362 | ||||||||
\(61\) | −5.65168 | −0.723623 | −0.361811 | − | 0.932251i | \(-0.617842\pi\) | ||||
−0.361811 | + | 0.932251i | \(0.617842\pi\) | |||||||
\(62\) | −0.559073 | −0.0710023 | ||||||||
\(63\) | −2.24290 | −0.282578 | ||||||||
\(64\) | −7.28917 | −0.911147 | ||||||||
\(65\) | 0.154580 | 0.0191732 | ||||||||
\(66\) | −34.3998 | −4.23432 | ||||||||
\(67\) | 6.82127 | 0.833351 | 0.416676 | − | 0.909055i | \(-0.363195\pi\) | ||||
0.416676 | + | 0.909055i | \(0.363195\pi\) | |||||||
\(68\) | 4.05705 | 0.491990 | ||||||||
\(69\) | 8.47722 | 1.02054 | ||||||||
\(70\) | −0.448264 | −0.0535778 | ||||||||
\(71\) | 6.93924 | 0.823537 | 0.411768 | − | 0.911289i | \(-0.364911\pi\) | ||||
0.411768 | + | 0.911289i | \(0.364911\pi\) | |||||||
\(72\) | −25.8511 | −3.04658 | ||||||||
\(73\) | −1.80317 | −0.211045 | −0.105523 | − | 0.994417i | \(-0.533652\pi\) | ||||
−0.105523 | + | 0.994417i | \(0.533652\pi\) | |||||||
\(74\) | −28.5873 | −3.32320 | ||||||||
\(75\) | −13.7462 | −1.58727 | ||||||||
\(76\) | −4.61883 | −0.529817 | ||||||||
\(77\) | −2.15636 | −0.245740 | ||||||||
\(78\) | 2.61213 | 0.295766 | ||||||||
\(79\) | −6.29048 | −0.707734 | −0.353867 | − | 0.935296i | \(-0.615134\pi\) | ||||
−0.353867 | + | 0.935296i | \(0.615134\pi\) | |||||||
\(80\) | −1.80195 | −0.201464 | ||||||||
\(81\) | 1.75514 | 0.195015 | ||||||||
\(82\) | 7.96223 | 0.879281 | ||||||||
\(83\) | 2.38111 | 0.261361 | 0.130680 | − | 0.991425i | \(-0.458284\pi\) | ||||
0.130680 | + | 0.991425i | \(0.458284\pi\) | |||||||
\(84\) | −5.07372 | −0.553588 | ||||||||
\(85\) | −0.414665 | −0.0449768 | ||||||||
\(86\) | 11.4725 | 1.23711 | ||||||||
\(87\) | 14.3505 | 1.53854 | ||||||||
\(88\) | −24.8536 | −2.64941 | ||||||||
\(89\) | 2.94587 | 0.312262 | 0.156131 | − | 0.987736i | \(-0.450098\pi\) | ||||
0.156131 | + | 0.987736i | \(0.450098\pi\) | |||||||
\(90\) | 5.21112 | 0.549301 | ||||||||
\(91\) | 0.163742 | 0.0171648 | ||||||||
\(92\) | 12.0796 | 1.25939 | ||||||||
\(93\) | 0.646767 | 0.0670666 | ||||||||
\(94\) | −18.2636 | −1.88375 | ||||||||
\(95\) | 0.472084 | 0.0484348 | ||||||||
\(96\) | −1.62184 | −0.165529 | ||||||||
\(97\) | 7.33401 | 0.744656 | 0.372328 | − | 0.928101i | \(-0.378560\pi\) | ||||
0.372328 | + | 0.928101i | \(0.378560\pi\) | |||||||
\(98\) | 16.7529 | 1.69230 | ||||||||
\(99\) | 25.0679 | 2.51942 | ||||||||
\(100\) | −19.5877 | −1.95877 | ||||||||
\(101\) | 3.18475 | 0.316895 | 0.158447 | − | 0.987367i | \(-0.449351\pi\) | ||||
0.158447 | + | 0.987367i | \(0.449351\pi\) | |||||||
\(102\) | −7.00714 | −0.693810 | ||||||||
\(103\) | 12.5911 | 1.24064 | 0.620321 | − | 0.784348i | \(-0.287002\pi\) | ||||
0.620321 | + | 0.784348i | \(0.287002\pi\) | |||||||
\(104\) | 1.88725 | 0.185060 | ||||||||
\(105\) | 0.518578 | 0.0506080 | ||||||||
\(106\) | −3.59315 | −0.348998 | ||||||||
\(107\) | −9.10169 | −0.879894 | −0.439947 | − | 0.898024i | \(-0.645003\pi\) | ||||
−0.439947 | + | 0.898024i | \(0.645003\pi\) | |||||||
\(108\) | 24.3295 | 2.34111 | ||||||||
\(109\) | −14.8467 | −1.42206 | −0.711030 | − | 0.703162i | \(-0.751771\pi\) | ||||
−0.711030 | + | 0.703162i | \(0.751771\pi\) | |||||||
\(110\) | 5.01006 | 0.477690 | ||||||||
\(111\) | 33.0714 | 3.13900 | ||||||||
\(112\) | −1.90876 | −0.180361 | ||||||||
\(113\) | −8.66928 | −0.815538 | −0.407769 | − | 0.913085i | \(-0.633693\pi\) | ||||
−0.407769 | + | 0.913085i | \(0.633693\pi\) | |||||||
\(114\) | 7.97743 | 0.747154 | ||||||||
\(115\) | −1.23464 | −0.115131 | ||||||||
\(116\) | 20.4488 | 1.89862 | ||||||||
\(117\) | −1.90352 | −0.175981 | ||||||||
\(118\) | 2.46111 | 0.226563 | ||||||||
\(119\) | −0.439244 | −0.0402654 | ||||||||
\(120\) | 5.97700 | 0.545623 | ||||||||
\(121\) | 13.1007 | 1.19097 | ||||||||
\(122\) | 13.9094 | 1.25930 | ||||||||
\(123\) | −9.21116 | −0.830542 | ||||||||
\(124\) | 0.921612 | 0.0827632 | ||||||||
\(125\) | 4.07535 | 0.364511 | ||||||||
\(126\) | 5.52001 | 0.491761 | ||||||||
\(127\) | 12.1211 | 1.07558 | 0.537788 | − | 0.843080i | \(-0.319260\pi\) | ||||
0.537788 | + | 0.843080i | \(0.319260\pi\) | |||||||
\(128\) | 19.0787 | 1.68634 | ||||||||
\(129\) | −13.2720 | −1.16853 | ||||||||
\(130\) | −0.380437 | −0.0333665 | ||||||||
\(131\) | −18.5888 | −1.62411 | −0.812056 | − | 0.583580i | \(-0.801651\pi\) | ||||
−0.812056 | + | 0.583580i | \(0.801651\pi\) | |||||||
\(132\) | 56.7068 | 4.93570 | ||||||||
\(133\) | 0.500067 | 0.0433613 | ||||||||
\(134\) | −16.7879 | −1.45025 | ||||||||
\(135\) | −2.48668 | −0.214020 | ||||||||
\(136\) | −5.06262 | −0.434116 | ||||||||
\(137\) | 10.4264 | 0.890784 | 0.445392 | − | 0.895336i | \(-0.353064\pi\) | ||||
0.445392 | + | 0.895336i | \(0.353064\pi\) | |||||||
\(138\) | −20.8634 | −1.77601 | ||||||||
\(139\) | 2.49442 | 0.211574 | 0.105787 | − | 0.994389i | \(-0.466264\pi\) | ||||
0.105787 | + | 0.994389i | \(0.466264\pi\) | |||||||
\(140\) | 0.738948 | 0.0624525 | ||||||||
\(141\) | 21.1284 | 1.77933 | ||||||||
\(142\) | −17.0782 | −1.43317 | ||||||||
\(143\) | −1.83008 | −0.153039 | ||||||||
\(144\) | 22.1896 | 1.84913 | ||||||||
\(145\) | −2.09004 | −0.173568 | ||||||||
\(146\) | 4.43780 | 0.367275 | ||||||||
\(147\) | −19.3807 | −1.59850 | ||||||||
\(148\) | 47.1251 | 3.87366 | ||||||||
\(149\) | 20.3450 | 1.66672 | 0.833362 | − | 0.552728i | \(-0.186413\pi\) | ||||
0.833362 | + | 0.552728i | \(0.186413\pi\) | |||||||
\(150\) | 33.8309 | 2.76228 | ||||||||
\(151\) | −4.16391 | −0.338854 | −0.169427 | − | 0.985543i | \(-0.554192\pi\) | ||||
−0.169427 | + | 0.985543i | \(0.554192\pi\) | |||||||
\(152\) | 5.76365 | 0.467494 | ||||||||
\(153\) | 5.10626 | 0.412817 | ||||||||
\(154\) | 5.30702 | 0.427652 | ||||||||
\(155\) | −0.0941966 | −0.00756605 | ||||||||
\(156\) | −4.30601 | −0.344757 | ||||||||
\(157\) | −10.8608 | −0.866787 | −0.433393 | − | 0.901205i | \(-0.642684\pi\) | ||||
−0.433393 | + | 0.901205i | \(0.642684\pi\) | |||||||
\(158\) | 15.4816 | 1.23165 | ||||||||
\(159\) | 4.15676 | 0.329653 | ||||||||
\(160\) | 0.236209 | 0.0186740 | ||||||||
\(161\) | −1.30782 | −0.103071 | ||||||||
\(162\) | −4.31958 | −0.339378 | ||||||||
\(163\) | 1.38529 | 0.108504 | 0.0542520 | − | 0.998527i | \(-0.482723\pi\) | ||||
0.0542520 | + | 0.998527i | \(0.482723\pi\) | |||||||
\(164\) | −13.1255 | −1.02493 | ||||||||
\(165\) | −5.79592 | −0.451212 | ||||||||
\(166\) | −5.86017 | −0.454837 | ||||||||
\(167\) | 9.55539 | 0.739419 | 0.369709 | − | 0.929147i | \(-0.379457\pi\) | ||||
0.369709 | + | 0.929147i | \(0.379457\pi\) | |||||||
\(168\) | 6.33128 | 0.488469 | ||||||||
\(169\) | −12.8610 | −0.989310 | ||||||||
\(170\) | 1.02054 | 0.0782715 | ||||||||
\(171\) | −5.81333 | −0.444557 | ||||||||
\(172\) | −18.9119 | −1.44202 | ||||||||
\(173\) | 19.9782 | 1.51891 | 0.759456 | − | 0.650558i | \(-0.225465\pi\) | ||||
0.759456 | + | 0.650558i | \(0.225465\pi\) | |||||||
\(174\) | −35.3182 | −2.67746 | ||||||||
\(175\) | 2.12069 | 0.160309 | ||||||||
\(176\) | 21.3334 | 1.60807 | ||||||||
\(177\) | −2.84715 | −0.214005 | ||||||||
\(178\) | −7.25010 | −0.543418 | ||||||||
\(179\) | −5.32071 | −0.397689 | −0.198844 | − | 0.980031i | \(-0.563719\pi\) | ||||
−0.198844 | + | 0.980031i | \(0.563719\pi\) | |||||||
\(180\) | −8.59036 | −0.640288 | ||||||||
\(181\) | 9.90999 | 0.736604 | 0.368302 | − | 0.929706i | \(-0.379939\pi\) | ||||
0.368302 | + | 0.929706i | \(0.379939\pi\) | |||||||
\(182\) | −0.402987 | −0.0298714 | ||||||||
\(183\) | −16.0912 | −1.18949 | ||||||||
\(184\) | −15.0737 | −1.11125 | ||||||||
\(185\) | −4.81659 | −0.354123 | ||||||||
\(186\) | −1.59176 | −0.116714 | ||||||||
\(187\) | 4.90924 | 0.358999 | ||||||||
\(188\) | 30.1069 | 2.19577 | ||||||||
\(189\) | −2.63408 | −0.191601 | ||||||||
\(190\) | −1.16185 | −0.0842895 | ||||||||
\(191\) | 13.7274 | 0.993276 | 0.496638 | − | 0.867958i | \(-0.334568\pi\) | ||||
0.496638 | + | 0.867958i | \(0.334568\pi\) | |||||||
\(192\) | −20.7534 | −1.49775 | ||||||||
\(193\) | −13.6741 | −0.984282 | −0.492141 | − | 0.870515i | \(-0.663786\pi\) | ||||
−0.492141 | + | 0.870515i | \(0.663786\pi\) | |||||||
\(194\) | −18.0498 | −1.29590 | ||||||||
\(195\) | 0.440111 | 0.0315170 | ||||||||
\(196\) | −27.6166 | −1.97261 | ||||||||
\(197\) | −24.1485 | −1.72051 | −0.860256 | − | 0.509862i | \(-0.829696\pi\) | ||||
−0.860256 | + | 0.509862i | \(0.829696\pi\) | |||||||
\(198\) | −61.6948 | −4.38446 | ||||||||
\(199\) | −22.8277 | −1.61822 | −0.809108 | − | 0.587660i | \(-0.800049\pi\) | ||||
−0.809108 | + | 0.587660i | \(0.800049\pi\) | |||||||
\(200\) | 24.4426 | 1.72835 | ||||||||
\(201\) | 19.4212 | 1.36986 | ||||||||
\(202\) | −7.83802 | −0.551481 | ||||||||
\(203\) | −2.21393 | −0.155387 | ||||||||
\(204\) | 11.5510 | 0.808734 | ||||||||
\(205\) | 1.34153 | 0.0936968 | ||||||||
\(206\) | −30.9881 | −2.15905 | ||||||||
\(207\) | 15.2036 | 1.05672 | ||||||||
\(208\) | −1.61994 | −0.112323 | ||||||||
\(209\) | −5.58903 | −0.386601 | ||||||||
\(210\) | −1.27628 | −0.0880714 | ||||||||
\(211\) | 20.4674 | 1.40903 | 0.704517 | − | 0.709687i | \(-0.251163\pi\) | ||||
0.704517 | + | 0.709687i | \(0.251163\pi\) | |||||||
\(212\) | 5.92319 | 0.406806 | ||||||||
\(213\) | 19.7571 | 1.35373 | ||||||||
\(214\) | 22.4002 | 1.53125 | ||||||||
\(215\) | 1.93296 | 0.131827 | ||||||||
\(216\) | −30.3598 | −2.06572 | ||||||||
\(217\) | −0.0997800 | −0.00677351 | ||||||||
\(218\) | 36.5394 | 2.47476 | ||||||||
\(219\) | −5.13390 | −0.346917 | ||||||||
\(220\) | −8.25891 | −0.556816 | ||||||||
\(221\) | −0.372782 | −0.0250760 | ||||||||
\(222\) | −81.3923 | −5.46269 | ||||||||
\(223\) | 12.7463 | 0.853555 | 0.426778 | − | 0.904357i | \(-0.359649\pi\) | ||||
0.426778 | + | 0.904357i | \(0.359649\pi\) | |||||||
\(224\) | 0.250210 | 0.0167179 | ||||||||
\(225\) | −24.6533 | −1.64355 | ||||||||
\(226\) | 21.3360 | 1.41925 | ||||||||
\(227\) | −16.0792 | −1.06721 | −0.533606 | − | 0.845733i | \(-0.679163\pi\) | ||||
−0.533606 | + | 0.845733i | \(0.679163\pi\) | |||||||
\(228\) | −13.1505 | −0.870914 | ||||||||
\(229\) | −24.7993 | −1.63879 | −0.819393 | − | 0.573232i | \(-0.805689\pi\) | ||||
−0.819393 | + | 0.573232i | \(0.805689\pi\) | |||||||
\(230\) | 3.03859 | 0.200358 | ||||||||
\(231\) | −6.13947 | −0.403947 | ||||||||
\(232\) | −25.5172 | −1.67529 | ||||||||
\(233\) | −19.0819 | −1.25010 | −0.625050 | − | 0.780585i | \(-0.714921\pi\) | ||||
−0.625050 | + | 0.780585i | \(0.714921\pi\) | |||||||
\(234\) | 4.68477 | 0.306253 | ||||||||
\(235\) | −3.07718 | −0.200733 | ||||||||
\(236\) | −4.05705 | −0.264091 | ||||||||
\(237\) | −17.9099 | −1.16338 | ||||||||
\(238\) | 1.08103 | 0.0700726 | ||||||||
\(239\) | −14.7630 | −0.954939 | −0.477469 | − | 0.878648i | \(-0.658446\pi\) | ||||
−0.477469 | + | 0.878648i | \(0.658446\pi\) | |||||||
\(240\) | −5.13043 | −0.331168 | ||||||||
\(241\) | 10.4380 | 0.672372 | 0.336186 | − | 0.941796i | \(-0.390863\pi\) | ||||
0.336186 | + | 0.941796i | \(0.390863\pi\) | |||||||
\(242\) | −32.2422 | −2.07261 | ||||||||
\(243\) | −12.9934 | −0.833528 | ||||||||
\(244\) | −22.9291 | −1.46789 | ||||||||
\(245\) | 2.82265 | 0.180333 | ||||||||
\(246\) | 22.6697 | 1.44536 | ||||||||
\(247\) | 0.424401 | 0.0270040 | ||||||||
\(248\) | −1.15004 | −0.0730276 | ||||||||
\(249\) | 6.77938 | 0.429626 | ||||||||
\(250\) | −10.0299 | −0.634345 | ||||||||
\(251\) | 3.54105 | 0.223509 | 0.111754 | − | 0.993736i | \(-0.464353\pi\) | ||||
0.111754 | + | 0.993736i | \(0.464353\pi\) | |||||||
\(252\) | −9.09954 | −0.573217 | ||||||||
\(253\) | 14.6170 | 0.918962 | ||||||||
\(254\) | −29.8314 | −1.87179 | ||||||||
\(255\) | −1.18061 | −0.0739329 | ||||||||
\(256\) | −32.3764 | −2.02353 | ||||||||
\(257\) | −21.7241 | −1.35511 | −0.677557 | − | 0.735470i | \(-0.736961\pi\) | ||||
−0.677557 | + | 0.735470i | \(0.736961\pi\) | |||||||
\(258\) | 32.6638 | 2.03356 | ||||||||
\(259\) | −5.10209 | −0.317029 | ||||||||
\(260\) | 0.627137 | 0.0388934 | ||||||||
\(261\) | 25.7371 | 1.59309 | ||||||||
\(262\) | 45.7490 | 2.82639 | ||||||||
\(263\) | −7.47385 | −0.460857 | −0.230429 | − | 0.973089i | \(-0.574013\pi\) | ||||
−0.230429 | + | 0.973089i | \(0.574013\pi\) | |||||||
\(264\) | −70.7621 | −4.35510 | ||||||||
\(265\) | −0.605400 | −0.0371894 | ||||||||
\(266\) | −1.23072 | −0.0754601 | ||||||||
\(267\) | 8.38734 | 0.513297 | ||||||||
\(268\) | 27.6742 | 1.69047 | ||||||||
\(269\) | −4.12462 | −0.251482 | −0.125741 | − | 0.992063i | \(-0.540131\pi\) | ||||
−0.125741 | + | 0.992063i | \(0.540131\pi\) | |||||||
\(270\) | 6.12000 | 0.372451 | ||||||||
\(271\) | 6.50464 | 0.395129 | 0.197564 | − | 0.980290i | \(-0.436697\pi\) | ||||
0.197564 | + | 0.980290i | \(0.436697\pi\) | |||||||
\(272\) | 4.34556 | 0.263488 | ||||||||
\(273\) | 0.466198 | 0.0282156 | ||||||||
\(274\) | −25.6604 | −1.55020 | ||||||||
\(275\) | −23.7021 | −1.42929 | ||||||||
\(276\) | 34.3925 | 2.07019 | ||||||||
\(277\) | −4.16095 | −0.250007 | −0.125004 | − | 0.992156i | \(-0.539894\pi\) | ||||
−0.125004 | + | 0.992156i | \(0.539894\pi\) | |||||||
\(278\) | −6.13903 | −0.368195 | ||||||||
\(279\) | 1.15995 | 0.0694446 | ||||||||
\(280\) | −0.922102 | −0.0551061 | ||||||||
\(281\) | 4.14049 | 0.247001 | 0.123501 | − | 0.992345i | \(-0.460588\pi\) | ||||
0.123501 | + | 0.992345i | \(0.460588\pi\) | |||||||
\(282\) | −51.9992 | −3.09651 | ||||||||
\(283\) | 24.4500 | 1.45340 | 0.726701 | − | 0.686954i | \(-0.241053\pi\) | ||||
0.726701 | + | 0.686954i | \(0.241053\pi\) | |||||||
\(284\) | 28.1529 | 1.67056 | ||||||||
\(285\) | 1.34409 | 0.0796173 | ||||||||
\(286\) | 4.50402 | 0.266328 | ||||||||
\(287\) | 1.42105 | 0.0838820 | ||||||||
\(288\) | −2.90872 | −0.171398 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 5.14382 | 0.302055 | ||||||||
\(291\) | 20.8810 | 1.22407 | ||||||||
\(292\) | −7.31556 | −0.428111 | ||||||||
\(293\) | −14.0484 | −0.820715 | −0.410357 | − | 0.911925i | \(-0.634596\pi\) | ||||
−0.410357 | + | 0.911925i | \(0.634596\pi\) | |||||||
\(294\) | 47.6981 | 2.78181 | ||||||||
\(295\) | 0.414665 | 0.0241427 | ||||||||
\(296\) | −58.8055 | −3.41800 | ||||||||
\(297\) | 29.4400 | 1.70828 | ||||||||
\(298\) | −50.0711 | −2.90054 | ||||||||
\(299\) | −1.10994 | −0.0641892 | ||||||||
\(300\) | −55.7690 | −3.21982 | ||||||||
\(301\) | 2.04754 | 0.118018 | ||||||||
\(302\) | 10.2478 | 0.589696 | ||||||||
\(303\) | 9.06747 | 0.520913 | ||||||||
\(304\) | −4.94729 | −0.283746 | ||||||||
\(305\) | 2.34355 | 0.134191 | ||||||||
\(306\) | −12.5671 | −0.718411 | ||||||||
\(307\) | −11.3082 | −0.645394 | −0.322697 | − | 0.946502i | \(-0.604590\pi\) | ||||
−0.322697 | + | 0.946502i | \(0.604590\pi\) | |||||||
\(308\) | −8.74845 | −0.498489 | ||||||||
\(309\) | 35.8489 | 2.03937 | ||||||||
\(310\) | 0.231828 | 0.0131669 | ||||||||
\(311\) | −7.58019 | −0.429833 | −0.214917 | − | 0.976632i | \(-0.568948\pi\) | ||||
−0.214917 | + | 0.976632i | \(0.568948\pi\) | |||||||
\(312\) | 5.37329 | 0.304203 | ||||||||
\(313\) | −6.83988 | −0.386613 | −0.193306 | − | 0.981138i | \(-0.561921\pi\) | ||||
−0.193306 | + | 0.981138i | \(0.561921\pi\) | |||||||
\(314\) | 26.7296 | 1.50844 | ||||||||
\(315\) | 0.930051 | 0.0524024 | ||||||||
\(316\) | −25.5208 | −1.43566 | ||||||||
\(317\) | 3.05818 | 0.171764 | 0.0858822 | − | 0.996305i | \(-0.472629\pi\) | ||||
0.0858822 | + | 0.996305i | \(0.472629\pi\) | |||||||
\(318\) | −10.2302 | −0.573683 | ||||||||
\(319\) | 24.7441 | 1.38540 | ||||||||
\(320\) | 3.02257 | 0.168967 | ||||||||
\(321\) | −25.9139 | −1.44637 | ||||||||
\(322\) | 3.21869 | 0.179371 | ||||||||
\(323\) | −1.13847 | −0.0633462 | ||||||||
\(324\) | 7.12067 | 0.395593 | ||||||||
\(325\) | 1.79981 | 0.0998355 | ||||||||
\(326\) | −3.40934 | −0.188826 | ||||||||
\(327\) | −42.2709 | −2.33759 | ||||||||
\(328\) | 16.3787 | 0.904363 | ||||||||
\(329\) | −3.25958 | −0.179706 | ||||||||
\(330\) | 14.2644 | 0.785229 | ||||||||
\(331\) | −17.7239 | −0.974196 | −0.487098 | − | 0.873347i | \(-0.661945\pi\) | ||||
−0.487098 | + | 0.873347i | \(0.661945\pi\) | |||||||
\(332\) | 9.66029 | 0.530177 | ||||||||
\(333\) | 59.3124 | 3.25030 | ||||||||
\(334\) | −23.5169 | −1.28678 | ||||||||
\(335\) | −2.82855 | −0.154540 | ||||||||
\(336\) | −5.43453 | −0.296478 | ||||||||
\(337\) | −31.2111 | −1.70018 | −0.850088 | − | 0.526641i | \(-0.823451\pi\) | ||||
−0.850088 | + | 0.526641i | \(0.823451\pi\) | |||||||
\(338\) | 31.6524 | 1.72166 | ||||||||
\(339\) | −24.6828 | −1.34058 | ||||||||
\(340\) | −1.68232 | −0.0912365 | ||||||||
\(341\) | 1.11520 | 0.0603914 | ||||||||
\(342\) | 14.3072 | 0.773647 | ||||||||
\(343\) | 6.06467 | 0.327461 | ||||||||
\(344\) | 23.5994 | 1.27240 | ||||||||
\(345\) | −3.51521 | −0.189253 | ||||||||
\(346\) | −49.1684 | −2.64331 | ||||||||
\(347\) | −20.2060 | −1.08472 | −0.542358 | − | 0.840147i | \(-0.682468\pi\) | ||||
−0.542358 | + | 0.840147i | \(0.682468\pi\) | |||||||
\(348\) | 58.2208 | 3.12096 | ||||||||
\(349\) | −3.10908 | −0.166425 | −0.0832126 | − | 0.996532i | \(-0.526518\pi\) | ||||
−0.0832126 | + | 0.996532i | \(0.526518\pi\) | |||||||
\(350\) | −5.21925 | −0.278981 | ||||||||
\(351\) | −2.23552 | −0.119323 | ||||||||
\(352\) | −2.79649 | −0.149053 | ||||||||
\(353\) | 16.3570 | 0.870594 | 0.435297 | − | 0.900287i | \(-0.356643\pi\) | ||||
0.435297 | + | 0.900287i | \(0.356643\pi\) | |||||||
\(354\) | 7.00714 | 0.372425 | ||||||||
\(355\) | −2.87746 | −0.152720 | ||||||||
\(356\) | 11.9515 | 0.633431 | ||||||||
\(357\) | −1.25059 | −0.0661884 | ||||||||
\(358\) | 13.0948 | 0.692084 | ||||||||
\(359\) | 13.5636 | 0.715858 | 0.357929 | − | 0.933749i | \(-0.383483\pi\) | ||||
0.357929 | + | 0.933749i | \(0.383483\pi\) | |||||||
\(360\) | 10.7195 | 0.564970 | ||||||||
\(361\) | −17.7039 | −0.931783 | ||||||||
\(362\) | −24.3895 | −1.28189 | ||||||||
\(363\) | 37.2996 | 1.95772 | ||||||||
\(364\) | 0.664310 | 0.0348193 | ||||||||
\(365\) | 0.747713 | 0.0391371 | ||||||||
\(366\) | 39.6021 | 2.07003 | ||||||||
\(367\) | 29.1210 | 1.52010 | 0.760051 | − | 0.649864i | \(-0.225174\pi\) | ||||
0.760051 | + | 0.649864i | \(0.225174\pi\) | |||||||
\(368\) | 12.9386 | 0.674473 | ||||||||
\(369\) | −16.5199 | −0.859991 | ||||||||
\(370\) | 11.8542 | 0.616268 | ||||||||
\(371\) | −0.641285 | −0.0332938 | ||||||||
\(372\) | 2.62397 | 0.136046 | ||||||||
\(373\) | −1.86573 | −0.0966037 | −0.0483019 | − | 0.998833i | \(-0.515381\pi\) | ||||
−0.0483019 | + | 0.998833i | \(0.515381\pi\) | |||||||
\(374\) | −12.0822 | −0.624755 | ||||||||
\(375\) | 11.6031 | 0.599184 | ||||||||
\(376\) | −37.5691 | −1.93748 | ||||||||
\(377\) | −1.87894 | −0.0967701 | ||||||||
\(378\) | 6.48275 | 0.333437 | ||||||||
\(379\) | −14.8753 | −0.764095 | −0.382047 | − | 0.924143i | \(-0.624781\pi\) | ||||
−0.382047 | + | 0.924143i | \(0.624781\pi\) | |||||||
\(380\) | 1.91527 | 0.0982513 | ||||||||
\(381\) | 34.5107 | 1.76803 | ||||||||
\(382\) | −33.7845 | −1.72857 | ||||||||
\(383\) | −14.7282 | −0.752574 | −0.376287 | − | 0.926503i | \(-0.622799\pi\) | ||||
−0.376287 | + | 0.926503i | \(0.622799\pi\) | |||||||
\(384\) | 54.3200 | 2.77200 | ||||||||
\(385\) | 0.894166 | 0.0455709 | ||||||||
\(386\) | 33.6534 | 1.71291 | ||||||||
\(387\) | −23.8028 | −1.20997 | ||||||||
\(388\) | 29.7545 | 1.51055 | ||||||||
\(389\) | −19.4758 | −0.987460 | −0.493730 | − | 0.869615i | \(-0.664367\pi\) | ||||
−0.493730 | + | 0.869615i | \(0.664367\pi\) | |||||||
\(390\) | −1.08316 | −0.0548480 | ||||||||
\(391\) | 2.97744 | 0.150576 | ||||||||
\(392\) | 34.4616 | 1.74057 | ||||||||
\(393\) | −52.9251 | −2.66972 | ||||||||
\(394\) | 59.4322 | 2.99415 | ||||||||
\(395\) | 2.60844 | 0.131245 | ||||||||
\(396\) | 101.702 | 5.11070 | ||||||||
\(397\) | −9.08387 | −0.455907 | −0.227953 | − | 0.973672i | \(-0.573203\pi\) | ||||
−0.227953 | + | 0.973672i | \(0.573203\pi\) | |||||||
\(398\) | 56.1815 | 2.81613 | ||||||||
\(399\) | 1.42376 | 0.0712774 | ||||||||
\(400\) | −20.9806 | −1.04903 | ||||||||
\(401\) | 15.9954 | 0.798770 | 0.399385 | − | 0.916783i | \(-0.369224\pi\) | ||||
0.399385 | + | 0.916783i | \(0.369224\pi\) | |||||||
\(402\) | −47.7976 | −2.38393 | ||||||||
\(403\) | −0.0846822 | −0.00421832 | ||||||||
\(404\) | 12.9207 | 0.642829 | ||||||||
\(405\) | −0.727794 | −0.0361644 | ||||||||
\(406\) | 5.44871 | 0.270415 | ||||||||
\(407\) | 57.0239 | 2.82657 | ||||||||
\(408\) | −14.4140 | −0.713602 | ||||||||
\(409\) | −8.87172 | −0.438678 | −0.219339 | − | 0.975649i | \(-0.570390\pi\) | ||||
−0.219339 | + | 0.975649i | \(0.570390\pi\) | |||||||
\(410\) | −3.30166 | −0.163057 | ||||||||
\(411\) | 29.6854 | 1.46427 | ||||||||
\(412\) | 51.0829 | 2.51667 | ||||||||
\(413\) | 0.439244 | 0.0216138 | ||||||||
\(414\) | −37.4177 | −1.83898 | ||||||||
\(415\) | −0.987364 | −0.0484678 | ||||||||
\(416\) | 0.212351 | 0.0104113 | ||||||||
\(417\) | 7.10198 | 0.347786 | ||||||||
\(418\) | 13.7552 | 0.672789 | ||||||||
\(419\) | 1.99544 | 0.0974836 | 0.0487418 | − | 0.998811i | \(-0.484479\pi\) | ||||
0.0487418 | + | 0.998811i | \(0.484479\pi\) | |||||||
\(420\) | 2.10390 | 0.102660 | ||||||||
\(421\) | −38.7803 | −1.89004 | −0.945018 | − | 0.327019i | \(-0.893956\pi\) | ||||
−0.945018 | + | 0.327019i | \(0.893956\pi\) | |||||||
\(422\) | −50.3725 | −2.45210 | ||||||||
\(423\) | 37.8930 | 1.84242 | ||||||||
\(424\) | −7.39129 | −0.358953 | ||||||||
\(425\) | −4.82805 | −0.234195 | ||||||||
\(426\) | −48.6243 | −2.35585 | ||||||||
\(427\) | 2.48246 | 0.120135 | ||||||||
\(428\) | −36.9260 | −1.78489 | ||||||||
\(429\) | −5.21050 | −0.251565 | ||||||||
\(430\) | −4.75723 | −0.229414 | ||||||||
\(431\) | −27.9986 | −1.34865 | −0.674324 | − | 0.738436i | \(-0.735565\pi\) | ||||
−0.674324 | + | 0.738436i | \(0.735565\pi\) | |||||||
\(432\) | 26.0596 | 1.25380 | ||||||||
\(433\) | 38.0831 | 1.83016 | 0.915080 | − | 0.403273i | \(-0.132128\pi\) | ||||
0.915080 | + | 0.403273i | \(0.132128\pi\) | |||||||
\(434\) | 0.245569 | 0.0117877 | ||||||||
\(435\) | −5.95066 | −0.285312 | ||||||||
\(436\) | −60.2340 | −2.88468 | ||||||||
\(437\) | −3.38973 | −0.162153 | ||||||||
\(438\) | 12.6351 | 0.603728 | ||||||||
\(439\) | −27.4585 | −1.31052 | −0.655261 | − | 0.755403i | \(-0.727441\pi\) | ||||
−0.655261 | + | 0.755403i | \(0.727441\pi\) | |||||||
\(440\) | 10.3059 | 0.491317 | ||||||||
\(441\) | −34.7587 | −1.65517 | ||||||||
\(442\) | 0.917456 | 0.0436389 | ||||||||
\(443\) | −7.33361 | −0.348430 | −0.174215 | − | 0.984708i | \(-0.555739\pi\) | ||||
−0.174215 | + | 0.984708i | \(0.555739\pi\) | |||||||
\(444\) | 134.172 | 6.36754 | ||||||||
\(445\) | −1.22155 | −0.0579070 | ||||||||
\(446\) | −31.3700 | −1.48541 | ||||||||
\(447\) | 57.9251 | 2.73976 | ||||||||
\(448\) | 3.20173 | 0.151267 | ||||||||
\(449\) | −22.8690 | −1.07925 | −0.539627 | − | 0.841904i | \(-0.681435\pi\) | ||||
−0.539627 | + | 0.841904i | \(0.681435\pi\) | |||||||
\(450\) | 60.6744 | 2.86022 | ||||||||
\(451\) | −15.8825 | −0.747877 | ||||||||
\(452\) | −35.1717 | −1.65434 | ||||||||
\(453\) | −11.8553 | −0.557010 | ||||||||
\(454\) | 39.5725 | 1.85723 | ||||||||
\(455\) | −0.0678982 | −0.00318312 | ||||||||
\(456\) | 16.4100 | 0.768467 | ||||||||
\(457\) | −39.0640 | −1.82734 | −0.913668 | − | 0.406461i | \(-0.866763\pi\) | ||||
−0.913668 | + | 0.406461i | \(0.866763\pi\) | |||||||
\(458\) | 61.0338 | 2.85192 | ||||||||
\(459\) | 5.99685 | 0.279909 | ||||||||
\(460\) | −5.00900 | −0.233546 | ||||||||
\(461\) | −2.74592 | −0.127890 | −0.0639451 | − | 0.997953i | \(-0.520368\pi\) | ||||
−0.0639451 | + | 0.997953i | \(0.520368\pi\) | |||||||
\(462\) | 15.1099 | 0.702976 | ||||||||
\(463\) | −3.84225 | −0.178565 | −0.0892823 | − | 0.996006i | \(-0.528457\pi\) | ||||
−0.0892823 | + | 0.996006i | \(0.528457\pi\) | |||||||
\(464\) | 21.9029 | 1.01682 | ||||||||
\(465\) | −0.268192 | −0.0124371 | ||||||||
\(466\) | 46.9627 | 2.17551 | ||||||||
\(467\) | −2.87405 | −0.132995 | −0.0664976 | − | 0.997787i | \(-0.521182\pi\) | ||||
−0.0664976 | + | 0.997787i | \(0.521182\pi\) | |||||||
\(468\) | −7.72268 | −0.356981 | ||||||||
\(469\) | −2.99620 | −0.138352 | ||||||||
\(470\) | 7.57328 | 0.349329 | ||||||||
\(471\) | −30.9223 | −1.42483 | ||||||||
\(472\) | 5.06262 | 0.233026 | ||||||||
\(473\) | −22.8844 | −1.05223 | ||||||||
\(474\) | 44.0783 | 2.02458 | ||||||||
\(475\) | 5.49660 | 0.252201 | ||||||||
\(476\) | −1.78204 | −0.0816795 | ||||||||
\(477\) | 7.45501 | 0.341341 | ||||||||
\(478\) | 36.3333 | 1.66185 | ||||||||
\(479\) | 19.9229 | 0.910299 | 0.455150 | − | 0.890415i | \(-0.349586\pi\) | ||||
0.455150 | + | 0.890415i | \(0.349586\pi\) | |||||||
\(480\) | 0.672522 | 0.0306963 | ||||||||
\(481\) | −4.33009 | −0.197435 | ||||||||
\(482\) | −25.6891 | −1.17011 | ||||||||
\(483\) | −3.72357 | −0.169428 | ||||||||
\(484\) | 53.1501 | 2.41591 | ||||||||
\(485\) | −3.04116 | −0.138092 | ||||||||
\(486\) | 31.9782 | 1.45056 | ||||||||
\(487\) | −11.4691 | −0.519715 | −0.259858 | − | 0.965647i | \(-0.583676\pi\) | ||||
−0.259858 | + | 0.965647i | \(0.583676\pi\) | |||||||
\(488\) | 28.6123 | 1.29522 | ||||||||
\(489\) | 3.94412 | 0.178359 | ||||||||
\(490\) | −6.94685 | −0.313827 | ||||||||
\(491\) | −10.2995 | −0.464810 | −0.232405 | − | 0.972619i | \(-0.574659\pi\) | ||||
−0.232405 | + | 0.972619i | \(0.574659\pi\) | |||||||
\(492\) | −37.3701 | −1.68478 | ||||||||
\(493\) | 5.04031 | 0.227004 | ||||||||
\(494\) | −1.04450 | −0.0469941 | ||||||||
\(495\) | −10.3948 | −0.467211 | ||||||||
\(496\) | 0.987150 | 0.0443243 | ||||||||
\(497\) | −3.04802 | −0.136722 | ||||||||
\(498\) | −16.6848 | −0.747663 | ||||||||
\(499\) | 28.6714 | 1.28351 | 0.641754 | − | 0.766911i | \(-0.278207\pi\) | ||||
0.641754 | + | 0.766911i | \(0.278207\pi\) | |||||||
\(500\) | 16.5339 | 0.739419 | ||||||||
\(501\) | 27.2056 | 1.21546 | ||||||||
\(502\) | −8.71490 | −0.388965 | ||||||||
\(503\) | −27.2884 | −1.21673 | −0.608365 | − | 0.793658i | \(-0.708174\pi\) | ||||
−0.608365 | + | 0.793658i | \(0.708174\pi\) | |||||||
\(504\) | 11.3549 | 0.505789 | ||||||||
\(505\) | −1.32061 | −0.0587663 | ||||||||
\(506\) | −35.9740 | −1.59924 | ||||||||
\(507\) | −36.6173 | −1.62623 | ||||||||
\(508\) | 49.1760 | 2.18183 | ||||||||
\(509\) | −24.8152 | −1.09992 | −0.549958 | − | 0.835192i | \(-0.685356\pi\) | ||||
−0.549958 | + | 0.835192i | \(0.685356\pi\) | |||||||
\(510\) | 2.90562 | 0.128663 | ||||||||
\(511\) | 0.792033 | 0.0350375 | ||||||||
\(512\) | 41.5244 | 1.83514 | ||||||||
\(513\) | −6.82724 | −0.301430 | ||||||||
\(514\) | 53.4654 | 2.35826 | ||||||||
\(515\) | −5.22111 | −0.230070 | ||||||||
\(516\) | −53.8451 | −2.37040 | ||||||||
\(517\) | 36.4309 | 1.60223 | ||||||||
\(518\) | 12.5568 | 0.551714 | ||||||||
\(519\) | 56.8809 | 2.49679 | ||||||||
\(520\) | −0.782578 | −0.0343183 | ||||||||
\(521\) | 22.0076 | 0.964168 | 0.482084 | − | 0.876125i | \(-0.339880\pi\) | ||||
0.482084 | + | 0.876125i | \(0.339880\pi\) | |||||||
\(522\) | −63.3419 | −2.77240 | ||||||||
\(523\) | −33.0076 | −1.44332 | −0.721661 | − | 0.692247i | \(-0.756621\pi\) | ||||
−0.721661 | + | 0.692247i | \(0.756621\pi\) | |||||||
\(524\) | −75.4157 | −3.29455 | ||||||||
\(525\) | 6.03793 | 0.263517 | ||||||||
\(526\) | 18.3939 | 0.802014 | ||||||||
\(527\) | 0.227163 | 0.00989538 | ||||||||
\(528\) | 60.7394 | 2.64334 | ||||||||
\(529\) | −14.1348 | −0.614558 | ||||||||
\(530\) | 1.48996 | 0.0647195 | ||||||||
\(531\) | −5.10626 | −0.221593 | ||||||||
\(532\) | 2.02880 | 0.0879594 | ||||||||
\(533\) | 1.20603 | 0.0522390 | ||||||||
\(534\) | −20.6421 | −0.893273 | ||||||||
\(535\) | 3.77416 | 0.163171 | ||||||||
\(536\) | −34.5335 | −1.49162 | ||||||||
\(537\) | −15.1489 | −0.653722 | ||||||||
\(538\) | 10.1511 | 0.437646 | ||||||||
\(539\) | −33.4175 | −1.43940 | ||||||||
\(540\) | −10.0886 | −0.434144 | ||||||||
\(541\) | −32.4326 | −1.39439 | −0.697194 | − | 0.716882i | \(-0.745568\pi\) | ||||
−0.697194 | + | 0.716882i | \(0.745568\pi\) | |||||||
\(542\) | −16.0086 | −0.687629 | ||||||||
\(543\) | 28.2152 | 1.21083 | ||||||||
\(544\) | −0.569638 | −0.0244230 | ||||||||
\(545\) | 6.15643 | 0.263712 | ||||||||
\(546\) | −1.14736 | −0.0491027 | ||||||||
\(547\) | −29.1411 | −1.24598 | −0.622992 | − | 0.782228i | \(-0.714083\pi\) | ||||
−0.622992 | + | 0.782228i | \(0.714083\pi\) | |||||||
\(548\) | 42.3003 | 1.80698 | ||||||||
\(549\) | −28.8589 | −1.23167 | ||||||||
\(550\) | 58.3334 | 2.48734 | ||||||||
\(551\) | −5.73825 | −0.244457 | ||||||||
\(552\) | −42.9170 | −1.82667 | ||||||||
\(553\) | 2.76306 | 0.117497 | ||||||||
\(554\) | 10.2405 | 0.435079 | ||||||||
\(555\) | −13.7136 | −0.582108 | ||||||||
\(556\) | 10.1200 | 0.429183 | ||||||||
\(557\) | 23.6670 | 1.00280 | 0.501402 | − | 0.865214i | \(-0.332818\pi\) | ||||
0.501402 | + | 0.865214i | \(0.332818\pi\) | |||||||
\(558\) | −2.85477 | −0.120852 | ||||||||
\(559\) | 1.73772 | 0.0734978 | ||||||||
\(560\) | 0.791496 | 0.0334468 | ||||||||
\(561\) | 13.9774 | 0.590124 | ||||||||
\(562\) | −10.1902 | −0.429848 | ||||||||
\(563\) | 17.8097 | 0.750590 | 0.375295 | − | 0.926905i | \(-0.377541\pi\) | ||||
0.375295 | + | 0.926905i | \(0.377541\pi\) | |||||||
\(564\) | 85.7189 | 3.60942 | ||||||||
\(565\) | 3.59485 | 0.151237 | ||||||||
\(566\) | −60.1741 | −2.52930 | ||||||||
\(567\) | −0.770933 | −0.0323761 | ||||||||
\(568\) | −35.1308 | −1.47405 | ||||||||
\(569\) | −2.79767 | −0.117284 | −0.0586421 | − | 0.998279i | \(-0.518677\pi\) | ||||
−0.0586421 | + | 0.998279i | \(0.518677\pi\) | |||||||
\(570\) | −3.30796 | −0.138555 | ||||||||
\(571\) | −32.8002 | −1.37264 | −0.686322 | − | 0.727298i | \(-0.740776\pi\) | ||||
−0.686322 | + | 0.727298i | \(0.740776\pi\) | |||||||
\(572\) | −7.42471 | −0.310443 | ||||||||
\(573\) | 39.0838 | 1.63275 | ||||||||
\(574\) | −3.49736 | −0.145977 | ||||||||
\(575\) | −14.3752 | −0.599489 | ||||||||
\(576\) | −37.2204 | −1.55085 | ||||||||
\(577\) | 36.2977 | 1.51109 | 0.755547 | − | 0.655094i | \(-0.227371\pi\) | ||||
0.755547 | + | 0.655094i | \(0.227371\pi\) | |||||||
\(578\) | −2.46111 | −0.102369 | ||||||||
\(579\) | −38.9322 | −1.61797 | ||||||||
\(580\) | −8.47940 | −0.352088 | ||||||||
\(581\) | −1.04589 | −0.0433908 | ||||||||
\(582\) | −51.3905 | −2.13020 | ||||||||
\(583\) | 7.16737 | 0.296842 | ||||||||
\(584\) | 9.12878 | 0.377752 | ||||||||
\(585\) | 0.789324 | 0.0326345 | ||||||||
\(586\) | 34.5745 | 1.42826 | ||||||||
\(587\) | 44.5900 | 1.84043 | 0.920213 | − | 0.391419i | \(-0.128016\pi\) | ||||
0.920213 | + | 0.391419i | \(0.128016\pi\) | |||||||
\(588\) | −78.6286 | −3.24259 | ||||||||
\(589\) | −0.258618 | −0.0106562 | ||||||||
\(590\) | −1.02054 | −0.0420148 | ||||||||
\(591\) | −68.7545 | −2.82818 | ||||||||
\(592\) | 50.4763 | 2.07456 | ||||||||
\(593\) | 26.4638 | 1.08674 | 0.543368 | − | 0.839494i | \(-0.317149\pi\) | ||||
0.543368 | + | 0.839494i | \(0.317149\pi\) | |||||||
\(594\) | −72.4550 | −2.97286 | ||||||||
\(595\) | 0.182139 | 0.00746698 | ||||||||
\(596\) | 82.5405 | 3.38099 | ||||||||
\(597\) | −64.9940 | −2.66003 | ||||||||
\(598\) | 2.73167 | 0.111706 | ||||||||
\(599\) | −22.8572 | −0.933920 | −0.466960 | − | 0.884279i | \(-0.654651\pi\) | ||||
−0.466960 | + | 0.884279i | \(0.654651\pi\) | |||||||
\(600\) | 69.5918 | 2.84107 | ||||||||
\(601\) | 35.2866 | 1.43937 | 0.719686 | − | 0.694300i | \(-0.244286\pi\) | ||||
0.719686 | + | 0.694300i | \(0.244286\pi\) | |||||||
\(602\) | −5.03921 | −0.205383 | ||||||||
\(603\) | 34.8312 | 1.41844 | ||||||||
\(604\) | −16.8932 | −0.687374 | ||||||||
\(605\) | −5.43240 | −0.220858 | ||||||||
\(606\) | −22.3160 | −0.906527 | ||||||||
\(607\) | −22.0108 | −0.893391 | −0.446696 | − | 0.894686i | \(-0.647399\pi\) | ||||
−0.446696 | + | 0.894686i | \(0.647399\pi\) | |||||||
\(608\) | 0.648516 | 0.0263008 | ||||||||
\(609\) | −6.30338 | −0.255426 | ||||||||
\(610\) | −5.76774 | −0.233529 | ||||||||
\(611\) | −2.76637 | −0.111915 | ||||||||
\(612\) | 20.7164 | 0.837410 | ||||||||
\(613\) | 40.0601 | 1.61801 | 0.809006 | − | 0.587800i | \(-0.200006\pi\) | ||||
0.809006 | + | 0.587800i | \(0.200006\pi\) | |||||||
\(614\) | 27.8308 | 1.12316 | ||||||||
\(615\) | 3.81955 | 0.154019 | ||||||||
\(616\) | 10.9168 | 0.439851 | ||||||||
\(617\) | 20.3672 | 0.819952 | 0.409976 | − | 0.912096i | \(-0.365537\pi\) | ||||
0.409976 | + | 0.912096i | \(0.365537\pi\) | |||||||
\(618\) | −88.2279 | −3.54905 | ||||||||
\(619\) | −9.06177 | −0.364223 | −0.182112 | − | 0.983278i | \(-0.558293\pi\) | ||||
−0.182112 | + | 0.983278i | \(0.558293\pi\) | |||||||
\(620\) | −0.382160 | −0.0153479 | ||||||||
\(621\) | 17.8553 | 0.716507 | ||||||||
\(622\) | 18.6557 | 0.748024 | ||||||||
\(623\) | −1.29396 | −0.0518413 | ||||||||
\(624\) | −4.61222 | −0.184637 | ||||||||
\(625\) | 22.4504 | 0.898014 | ||||||||
\(626\) | 16.8337 | 0.672809 | ||||||||
\(627\) | −15.9128 | −0.635496 | ||||||||
\(628\) | −44.0628 | −1.75830 | ||||||||
\(629\) | 11.6156 | 0.463145 | ||||||||
\(630\) | −2.28896 | −0.0911942 | ||||||||
\(631\) | 9.51913 | 0.378951 | 0.189475 | − | 0.981885i | \(-0.439321\pi\) | ||||
0.189475 | + | 0.981885i | \(0.439321\pi\) | |||||||
\(632\) | 31.8463 | 1.26678 | ||||||||
\(633\) | 58.2738 | 2.31618 | ||||||||
\(634\) | −7.52651 | −0.298916 | ||||||||
\(635\) | −5.02621 | −0.199459 | ||||||||
\(636\) | 16.8642 | 0.668709 | ||||||||
\(637\) | 2.53755 | 0.100541 | ||||||||
\(638\) | −60.8979 | −2.41097 | ||||||||
\(639\) | 35.4336 | 1.40173 | ||||||||
\(640\) | −7.91128 | −0.312721 | ||||||||
\(641\) | 8.38478 | 0.331179 | 0.165589 | − | 0.986195i | \(-0.447047\pi\) | ||||
0.165589 | + | 0.986195i | \(0.447047\pi\) | |||||||
\(642\) | 63.7769 | 2.51707 | ||||||||
\(643\) | −4.07693 | −0.160779 | −0.0803893 | − | 0.996764i | \(-0.525616\pi\) | ||||
−0.0803893 | + | 0.996764i | \(0.525616\pi\) | |||||||
\(644\) | −5.30591 | −0.209082 | ||||||||
\(645\) | 5.50343 | 0.216697 | ||||||||
\(646\) | 2.80190 | 0.110239 | ||||||||
\(647\) | 16.8543 | 0.662610 | 0.331305 | − | 0.943524i | \(-0.392511\pi\) | ||||
0.331305 | + | 0.943524i | \(0.392511\pi\) | |||||||
\(648\) | −8.88559 | −0.349059 | ||||||||
\(649\) | −4.90924 | −0.192705 | ||||||||
\(650\) | −4.42953 | −0.173740 | ||||||||
\(651\) | −0.284089 | −0.0111343 | ||||||||
\(652\) | 5.62018 | 0.220103 | ||||||||
\(653\) | 4.93861 | 0.193263 | 0.0966314 | − | 0.995320i | \(-0.469193\pi\) | ||||
0.0966314 | + | 0.995320i | \(0.469193\pi\) | |||||||
\(654\) | 104.033 | 4.06802 | ||||||||
\(655\) | 7.70813 | 0.301182 | ||||||||
\(656\) | −14.0588 | −0.548905 | ||||||||
\(657\) | −9.20747 | −0.359218 | ||||||||
\(658\) | 8.02218 | 0.312737 | ||||||||
\(659\) | 12.4396 | 0.484579 | 0.242289 | − | 0.970204i | \(-0.422102\pi\) | ||||
0.242289 | + | 0.970204i | \(0.422102\pi\) | |||||||
\(660\) | −23.5144 | −0.915295 | ||||||||
\(661\) | 31.7053 | 1.23319 | 0.616597 | − | 0.787279i | \(-0.288511\pi\) | ||||
0.616597 | + | 0.787279i | \(0.288511\pi\) | |||||||
\(662\) | 43.6205 | 1.69536 | ||||||||
\(663\) | −1.06137 | −0.0412200 | ||||||||
\(664\) | −12.0547 | −0.467812 | ||||||||
\(665\) | −0.207360 | −0.00804108 | ||||||||
\(666\) | −145.974 | −5.65639 | ||||||||
\(667\) | 15.0072 | 0.581082 | ||||||||
\(668\) | 38.7667 | 1.49993 | ||||||||
\(669\) | 36.2906 | 1.40308 | ||||||||
\(670\) | 6.96135 | 0.268941 | ||||||||
\(671\) | −27.7455 | −1.07110 | ||||||||
\(672\) | 0.712385 | 0.0274809 | ||||||||
\(673\) | 40.5291 | 1.56228 | 0.781140 | − | 0.624356i | \(-0.214638\pi\) | ||||
0.781140 | + | 0.624356i | \(0.214638\pi\) | |||||||
\(674\) | 76.8138 | 2.95876 | ||||||||
\(675\) | −28.9531 | −1.11441 | ||||||||
\(676\) | −52.1779 | −2.00684 | ||||||||
\(677\) | −20.5147 | −0.788443 | −0.394222 | − | 0.919015i | \(-0.628986\pi\) | ||||
−0.394222 | + | 0.919015i | \(0.628986\pi\) | |||||||
\(678\) | 60.7469 | 2.33297 | ||||||||
\(679\) | −3.22142 | −0.123627 | ||||||||
\(680\) | 2.09929 | 0.0805042 | ||||||||
\(681\) | −45.7798 | −1.75428 | ||||||||
\(682\) | −2.74462 | −0.105097 | ||||||||
\(683\) | −47.4022 | −1.81380 | −0.906898 | − | 0.421350i | \(-0.861556\pi\) | ||||
−0.906898 | + | 0.421350i | \(0.861556\pi\) | |||||||
\(684\) | −23.5850 | −0.901794 | ||||||||
\(685\) | −4.32345 | −0.165191 | ||||||||
\(686\) | −14.9258 | −0.569870 | ||||||||
\(687\) | −70.6074 | −2.69384 | ||||||||
\(688\) | −20.2568 | −0.772284 | ||||||||
\(689\) | −0.544251 | −0.0207343 | ||||||||
\(690\) | 8.65131 | 0.329350 | ||||||||
\(691\) | 23.4876 | 0.893512 | 0.446756 | − | 0.894656i | \(-0.352579\pi\) | ||||
0.446756 | + | 0.894656i | \(0.352579\pi\) | |||||||
\(692\) | 81.0525 | 3.08115 | ||||||||
\(693\) | −11.0109 | −0.418270 | ||||||||
\(694\) | 49.7292 | 1.88769 | ||||||||
\(695\) | −1.03435 | −0.0392351 | ||||||||
\(696\) | −72.6512 | −2.75384 | ||||||||
\(697\) | −3.23522 | −0.122543 | ||||||||
\(698\) | 7.65178 | 0.289624 | ||||||||
\(699\) | −54.3291 | −2.05492 | ||||||||
\(700\) | 8.60376 | 0.325192 | ||||||||
\(701\) | 10.7253 | 0.405091 | 0.202545 | − | 0.979273i | \(-0.435079\pi\) | ||||
0.202545 | + | 0.979273i | \(0.435079\pi\) | |||||||
\(702\) | 5.50184 | 0.207654 | ||||||||
\(703\) | −13.2240 | −0.498754 | ||||||||
\(704\) | −35.7843 | −1.34867 | ||||||||
\(705\) | −8.76120 | −0.329966 | ||||||||
\(706\) | −40.2563 | −1.51506 | ||||||||
\(707\) | −1.39888 | −0.0526105 | ||||||||
\(708\) | −11.5510 | −0.434114 | ||||||||
\(709\) | 38.3033 | 1.43851 | 0.719256 | − | 0.694745i | \(-0.244483\pi\) | ||||
0.719256 | + | 0.694745i | \(0.244483\pi\) | |||||||
\(710\) | 7.08175 | 0.265773 | ||||||||
\(711\) | −32.1209 | −1.20463 | ||||||||
\(712\) | −14.9138 | −0.558919 | ||||||||
\(713\) | 0.676365 | 0.0253301 | ||||||||
\(714\) | 3.07785 | 0.115185 | ||||||||
\(715\) | 0.758869 | 0.0283801 | ||||||||
\(716\) | −21.5864 | −0.806721 | ||||||||
\(717\) | −42.0325 | −1.56973 | ||||||||
\(718\) | −33.3814 | −1.24578 | ||||||||
\(719\) | 45.2033 | 1.68580 | 0.842899 | − | 0.538072i | \(-0.180847\pi\) | ||||
0.842899 | + | 0.538072i | \(0.180847\pi\) | |||||||
\(720\) | −9.20124 | −0.342910 | ||||||||
\(721\) | −5.53058 | −0.205970 | ||||||||
\(722\) | 43.5712 | 1.62155 | ||||||||
\(723\) | 29.7186 | 1.10525 | ||||||||
\(724\) | 40.2053 | 1.49422 | ||||||||
\(725\) | −24.3349 | −0.903775 | ||||||||
\(726\) | −91.7983 | −3.40696 | ||||||||
\(727\) | 47.5534 | 1.76366 | 0.881829 | − | 0.471569i | \(-0.156312\pi\) | ||||
0.881829 | + | 0.471569i | \(0.156312\pi\) | |||||||
\(728\) | −0.828965 | −0.0307235 | ||||||||
\(729\) | −42.2596 | −1.56517 | ||||||||
\(730\) | −1.84020 | −0.0681089 | ||||||||
\(731\) | −4.66150 | −0.172412 | ||||||||
\(732\) | −65.2827 | −2.41292 | ||||||||
\(733\) | −12.6151 | −0.465951 | −0.232975 | − | 0.972483i | \(-0.574846\pi\) | ||||
−0.232975 | + | 0.972483i | \(0.574846\pi\) | |||||||
\(734\) | −71.6698 | −2.64538 | ||||||||
\(735\) | 8.03652 | 0.296431 | ||||||||
\(736\) | −1.69606 | −0.0625177 | ||||||||
\(737\) | 33.4873 | 1.23352 | ||||||||
\(738\) | 40.6572 | 1.49661 | ||||||||
\(739\) | −3.44790 | −0.126833 | −0.0634165 | − | 0.997987i | \(-0.520200\pi\) | ||||
−0.0634165 | + | 0.997987i | \(0.520200\pi\) | |||||||
\(740\) | −19.5412 | −0.718347 | ||||||||
\(741\) | 1.20833 | 0.0443892 | ||||||||
\(742\) | 1.57827 | 0.0579401 | ||||||||
\(743\) | −30.2974 | −1.11150 | −0.555751 | − | 0.831349i | \(-0.687569\pi\) | ||||
−0.555751 | + | 0.831349i | \(0.687569\pi\) | |||||||
\(744\) | −3.27434 | −0.120043 | ||||||||
\(745\) | −8.43634 | −0.309084 | ||||||||
\(746\) | 4.59176 | 0.168116 | ||||||||
\(747\) | 12.1586 | 0.444859 | ||||||||
\(748\) | 19.9171 | 0.728239 | ||||||||
\(749\) | 3.99787 | 0.146079 | ||||||||
\(750\) | −28.5566 | −1.04274 | ||||||||
\(751\) | −45.6320 | −1.66513 | −0.832567 | − | 0.553924i | \(-0.813130\pi\) | ||||
−0.832567 | + | 0.553924i | \(0.813130\pi\) | |||||||
\(752\) | 32.2479 | 1.17596 | ||||||||
\(753\) | 10.0819 | 0.367405 | ||||||||
\(754\) | 4.62426 | 0.168406 | ||||||||
\(755\) | 1.72663 | 0.0628385 | ||||||||
\(756\) | −10.6866 | −0.388668 | ||||||||
\(757\) | 39.7419 | 1.44444 | 0.722222 | − | 0.691661i | \(-0.243121\pi\) | ||||
0.722222 | + | 0.691661i | \(0.243121\pi\) | |||||||
\(758\) | 36.6098 | 1.32973 | ||||||||
\(759\) | 41.6168 | 1.51059 | ||||||||
\(760\) | −2.38998 | −0.0866938 | ||||||||
\(761\) | 30.0509 | 1.08934 | 0.544672 | − | 0.838649i | \(-0.316654\pi\) | ||||
0.544672 | + | 0.838649i | \(0.316654\pi\) | |||||||
\(762\) | −84.9344 | −3.07685 | ||||||||
\(763\) | 6.52134 | 0.236088 | ||||||||
\(764\) | 55.6926 | 2.01489 | ||||||||
\(765\) | −2.11739 | −0.0765544 | ||||||||
\(766\) | 36.2476 | 1.30968 | ||||||||
\(767\) | 0.372782 | 0.0134604 | ||||||||
\(768\) | −92.1805 | −3.32628 | ||||||||
\(769\) | −52.0456 | −1.87681 | −0.938406 | − | 0.345536i | \(-0.887697\pi\) | ||||
−0.938406 | + | 0.345536i | \(0.887697\pi\) | |||||||
\(770\) | −2.20064 | −0.0793055 | ||||||||
\(771\) | −61.8519 | −2.22754 | ||||||||
\(772\) | −55.4764 | −1.99664 | ||||||||
\(773\) | 0.659575 | 0.0237233 | 0.0118616 | − | 0.999930i | \(-0.496224\pi\) | ||||
0.0118616 | + | 0.999930i | \(0.496224\pi\) | |||||||
\(774\) | 58.5814 | 2.10566 | ||||||||
\(775\) | −1.09676 | −0.0393966 | ||||||||
\(776\) | −37.1293 | −1.33287 | ||||||||
\(777\) | −14.5264 | −0.521132 | ||||||||
\(778\) | 47.9319 | 1.71844 | ||||||||
\(779\) | 3.68321 | 0.131965 | ||||||||
\(780\) | 1.78555 | 0.0639331 | ||||||||
\(781\) | 34.0664 | 1.21899 | ||||||||
\(782\) | −7.32780 | −0.262042 | ||||||||
\(783\) | 30.2260 | 1.08019 | ||||||||
\(784\) | −29.5805 | −1.05645 | ||||||||
\(785\) | 4.50360 | 0.160740 | ||||||||
\(786\) | 130.254 | 4.64602 | ||||||||
\(787\) | −26.0887 | −0.929963 | −0.464981 | − | 0.885320i | \(-0.653939\pi\) | ||||
−0.464981 | + | 0.885320i | \(0.653939\pi\) | |||||||
\(788\) | −97.9718 | −3.49010 | ||||||||
\(789\) | −21.2792 | −0.757558 | ||||||||
\(790\) | −6.41966 | −0.228401 | ||||||||
\(791\) | 3.80793 | 0.135394 | ||||||||
\(792\) | −126.909 | −4.50952 | ||||||||
\(793\) | 2.10684 | 0.0748161 | ||||||||
\(794\) | 22.3564 | 0.793399 | ||||||||
\(795\) | −1.72367 | −0.0611321 | ||||||||
\(796\) | −92.6133 | −3.28259 | ||||||||
\(797\) | 49.9440 | 1.76911 | 0.884554 | − | 0.466438i | \(-0.154463\pi\) | ||||
0.884554 | + | 0.466438i | \(0.154463\pi\) | |||||||
\(798\) | −3.50404 | −0.124042 | ||||||||
\(799\) | 7.42089 | 0.262532 | ||||||||
\(800\) | 2.75024 | 0.0972357 | ||||||||
\(801\) | 15.0424 | 0.531497 | ||||||||
\(802\) | −39.3663 | −1.39007 | ||||||||
\(803\) | −8.85221 | −0.312388 | ||||||||
\(804\) | 78.7927 | 2.77881 | ||||||||
\(805\) | 0.542309 | 0.0191139 | ||||||||
\(806\) | 0.208412 | 0.00734100 | ||||||||
\(807\) | −11.7434 | −0.413387 | ||||||||
\(808\) | −16.1232 | −0.567213 | ||||||||
\(809\) | −42.5204 | −1.49494 | −0.747468 | − | 0.664297i | \(-0.768731\pi\) | ||||
−0.747468 | + | 0.664297i | \(0.768731\pi\) | |||||||
\(810\) | 1.79118 | 0.0629356 | ||||||||
\(811\) | 54.5386 | 1.91511 | 0.957555 | − | 0.288249i | \(-0.0930731\pi\) | ||||
0.957555 | + | 0.288249i | \(0.0930731\pi\) | |||||||
\(812\) | −8.98201 | −0.315207 | ||||||||
\(813\) | 18.5197 | 0.649514 | ||||||||
\(814\) | −140.342 | −4.91898 | ||||||||
\(815\) | −0.574430 | −0.0201214 | ||||||||
\(816\) | 12.3725 | 0.433122 | ||||||||
\(817\) | 5.30698 | 0.185668 | ||||||||
\(818\) | 21.8343 | 0.763417 | ||||||||
\(819\) | 0.836111 | 0.0292161 | ||||||||
\(820\) | 5.44267 | 0.190066 | ||||||||
\(821\) | 40.5488 | 1.41516 | 0.707582 | − | 0.706631i | \(-0.249786\pi\) | ||||
0.707582 | + | 0.706631i | \(0.249786\pi\) | |||||||
\(822\) | −73.0590 | −2.54823 | ||||||||
\(823\) | −3.02659 | −0.105500 | −0.0527502 | − | 0.998608i | \(-0.516799\pi\) | ||||
−0.0527502 | + | 0.998608i | \(0.516799\pi\) | |||||||
\(824\) | −63.7442 | −2.22063 | ||||||||
\(825\) | −67.4834 | −2.34947 | ||||||||
\(826\) | −1.08103 | −0.0376137 | ||||||||
\(827\) | 7.60079 | 0.264305 | 0.132153 | − | 0.991229i | \(-0.457811\pi\) | ||||
0.132153 | + | 0.991229i | \(0.457811\pi\) | |||||||
\(828\) | 61.6818 | 2.14359 | ||||||||
\(829\) | −39.9171 | −1.38638 | −0.693188 | − | 0.720756i | \(-0.743795\pi\) | ||||
−0.693188 | + | 0.720756i | \(0.743795\pi\) | |||||||
\(830\) | 2.43001 | 0.0843468 | ||||||||
\(831\) | −11.8468 | −0.410962 | ||||||||
\(832\) | 2.71727 | 0.0942044 | ||||||||
\(833\) | −6.80706 | −0.235851 | ||||||||
\(834\) | −17.4787 | −0.605240 | ||||||||
\(835\) | −3.96229 | −0.137121 | ||||||||
\(836\) | −22.6750 | −0.784231 | ||||||||
\(837\) | 1.36226 | 0.0470867 | ||||||||
\(838\) | −4.91099 | −0.169647 | ||||||||
\(839\) | −52.9006 | −1.82633 | −0.913165 | − | 0.407589i | \(-0.866370\pi\) | ||||
−0.913165 | + | 0.407589i | \(0.866370\pi\) | |||||||
\(840\) | −2.62536 | −0.0905836 | ||||||||
\(841\) | −3.59528 | −0.123975 | ||||||||
\(842\) | 95.4425 | 3.28916 | ||||||||
\(843\) | 11.7886 | 0.406021 | ||||||||
\(844\) | 83.0373 | 2.85826 | ||||||||
\(845\) | 5.33302 | 0.183462 | ||||||||
\(846\) | −93.2587 | −3.20630 | ||||||||
\(847\) | −5.75440 | −0.197723 | ||||||||
\(848\) | 6.34440 | 0.217867 | ||||||||
\(849\) | 69.6128 | 2.38911 | ||||||||
\(850\) | 11.8824 | 0.407561 | ||||||||
\(851\) | 34.5848 | 1.18555 | ||||||||
\(852\) | 80.1554 | 2.74608 | ||||||||
\(853\) | 20.0639 | 0.686975 | 0.343487 | − | 0.939157i | \(-0.388392\pi\) | ||||
0.343487 | + | 0.939157i | \(0.388392\pi\) | |||||||
\(854\) | −6.10961 | −0.209067 | ||||||||
\(855\) | 2.41059 | 0.0824403 | ||||||||
\(856\) | 46.0784 | 1.57493 | ||||||||
\(857\) | 42.2226 | 1.44229 | 0.721147 | − | 0.692782i | \(-0.243615\pi\) | ||||
0.721147 | + | 0.692782i | \(0.243615\pi\) | |||||||
\(858\) | 12.8236 | 0.437791 | ||||||||
\(859\) | −32.5422 | −1.11032 | −0.555162 | − | 0.831742i | \(-0.687344\pi\) | ||||
−0.555162 | + | 0.831742i | \(0.687344\pi\) | |||||||
\(860\) | 7.84213 | 0.267414 | ||||||||
\(861\) | 4.04595 | 0.137886 | ||||||||
\(862\) | 68.9077 | 2.34700 | ||||||||
\(863\) | −48.2028 | −1.64084 | −0.820422 | − | 0.571759i | \(-0.806261\pi\) | ||||
−0.820422 | + | 0.571759i | \(0.806261\pi\) | |||||||
\(864\) | −3.41603 | −0.116216 | ||||||||
\(865\) | −8.28426 | −0.281673 | ||||||||
\(866\) | −93.7267 | −3.18496 | ||||||||
\(867\) | 2.84715 | 0.0966943 | ||||||||
\(868\) | −0.404812 | −0.0137402 | ||||||||
\(869\) | −30.8815 | −1.04758 | ||||||||
\(870\) | 14.6452 | 0.496519 | ||||||||
\(871\) | −2.54285 | −0.0861610 | ||||||||
\(872\) | 75.1634 | 2.54535 | ||||||||
\(873\) | 37.4494 | 1.26747 | ||||||||
\(874\) | 8.34249 | 0.282189 | ||||||||
\(875\) | −1.79007 | −0.0605156 | ||||||||
\(876\) | −20.8285 | −0.703730 | ||||||||
\(877\) | 30.1658 | 1.01863 | 0.509313 | − | 0.860582i | \(-0.329900\pi\) | ||||
0.509313 | + | 0.860582i | \(0.329900\pi\) | |||||||
\(878\) | 67.5783 | 2.28066 | ||||||||
\(879\) | −39.9978 | −1.34909 | ||||||||
\(880\) | −8.84622 | −0.298206 | ||||||||
\(881\) | 44.0873 | 1.48534 | 0.742669 | − | 0.669659i | \(-0.233560\pi\) | ||||
0.742669 | + | 0.669659i | \(0.233560\pi\) | |||||||
\(882\) | 85.5448 | 2.88044 | ||||||||
\(883\) | −8.32945 | −0.280308 | −0.140154 | − | 0.990130i | \(-0.544760\pi\) | ||||
−0.140154 | + | 0.990130i | \(0.544760\pi\) | |||||||
\(884\) | −1.51239 | −0.0508673 | ||||||||
\(885\) | 1.18061 | 0.0396859 | ||||||||
\(886\) | 18.0488 | 0.606362 | ||||||||
\(887\) | 23.7301 | 0.796778 | 0.398389 | − | 0.917216i | \(-0.369569\pi\) | ||||
0.398389 | + | 0.917216i | \(0.369569\pi\) | |||||||
\(888\) | −167.428 | −5.61852 | ||||||||
\(889\) | −5.32413 | −0.178566 | ||||||||
\(890\) | 3.00637 | 0.100774 | ||||||||
\(891\) | 8.61639 | 0.288660 | ||||||||
\(892\) | 51.7124 | 1.73146 | ||||||||
\(893\) | −8.44846 | −0.282717 | ||||||||
\(894\) | −142.560 | −4.76792 | ||||||||
\(895\) | 2.20631 | 0.0737490 | ||||||||
\(896\) | −8.38021 | −0.279963 | ||||||||
\(897\) | −3.16015 | −0.105514 | ||||||||
\(898\) | 56.2831 | 1.87819 | ||||||||
\(899\) | 1.14497 | 0.0381870 | ||||||||
\(900\) | −100.020 | −3.33399 | ||||||||
\(901\) | 1.45997 | 0.0486388 | ||||||||
\(902\) | 39.0885 | 1.30151 | ||||||||
\(903\) | 5.82964 | 0.193998 | ||||||||
\(904\) | 43.8893 | 1.45974 | ||||||||
\(905\) | −4.10933 | −0.136599 | ||||||||
\(906\) | 29.1771 | 0.969345 | ||||||||
\(907\) | 1.34729 | 0.0447359 | 0.0223679 | − | 0.999750i | \(-0.492879\pi\) | ||||
0.0223679 | + | 0.999750i | \(0.492879\pi\) | |||||||
\(908\) | −65.2339 | −2.16486 | ||||||||
\(909\) | 16.2622 | 0.539383 | ||||||||
\(910\) | 0.167105 | 0.00553947 | ||||||||
\(911\) | −38.5728 | −1.27797 | −0.638986 | − | 0.769218i | \(-0.720646\pi\) | ||||
−0.638986 | + | 0.769218i | \(0.720646\pi\) | |||||||
\(912\) | −14.0857 | −0.466423 | ||||||||
\(913\) | 11.6895 | 0.386865 | ||||||||
\(914\) | 96.1407 | 3.18005 | ||||||||
\(915\) | 6.67245 | 0.220584 | ||||||||
\(916\) | −100.612 | −3.32432 | ||||||||
\(917\) | 8.16502 | 0.269633 | ||||||||
\(918\) | −14.7589 | −0.487116 | ||||||||
\(919\) | −1.97678 | −0.0652079 | −0.0326040 | − | 0.999468i | \(-0.510380\pi\) | ||||
−0.0326040 | + | 0.999468i | \(0.510380\pi\) | |||||||
\(920\) | 6.25052 | 0.206074 | ||||||||
\(921\) | −32.1962 | −1.06090 | ||||||||
\(922\) | 6.75800 | 0.222563 | ||||||||
\(923\) | −2.58682 | −0.0851463 | ||||||||
\(924\) | −24.9081 | −0.819418 | ||||||||
\(925\) | −56.0808 | −1.84393 | ||||||||
\(926\) | 9.45620 | 0.310750 | ||||||||
\(927\) | 64.2937 | 2.11168 | ||||||||
\(928\) | −2.87115 | −0.0942501 | ||||||||
\(929\) | 40.7689 | 1.33758 | 0.668791 | − | 0.743450i | \(-0.266812\pi\) | ||||
0.668791 | + | 0.743450i | \(0.266812\pi\) | |||||||
\(930\) | 0.660049 | 0.0216439 | ||||||||
\(931\) | 7.74964 | 0.253984 | ||||||||
\(932\) | −77.4164 | −2.53586 | ||||||||
\(933\) | −21.5819 | −0.706561 | ||||||||
\(934\) | 7.07335 | 0.231447 | ||||||||
\(935\) | −2.03569 | −0.0665743 | ||||||||
\(936\) | 9.63681 | 0.314989 | ||||||||
\(937\) | 8.87970 | 0.290087 | 0.145044 | − | 0.989425i | \(-0.453668\pi\) | ||||
0.145044 | + | 0.989425i | \(0.453668\pi\) | |||||||
\(938\) | 7.37398 | 0.240769 | ||||||||
\(939\) | −19.4742 | −0.635516 | ||||||||
\(940\) | −12.4843 | −0.407193 | ||||||||
\(941\) | −23.8029 | −0.775953 | −0.387976 | − | 0.921669i | \(-0.626826\pi\) | ||||
−0.387976 | + | 0.921669i | \(0.626826\pi\) | |||||||
\(942\) | 76.1032 | 2.47958 | ||||||||
\(943\) | −9.63268 | −0.313683 | ||||||||
\(944\) | −4.34556 | −0.141436 | ||||||||
\(945\) | 1.09226 | 0.0355313 | ||||||||
\(946\) | 56.3211 | 1.83116 | ||||||||
\(947\) | −5.76904 | −0.187469 | −0.0937343 | − | 0.995597i | \(-0.529880\pi\) | ||||
−0.0937343 | + | 0.995597i | \(0.529880\pi\) | |||||||
\(948\) | −72.6615 | −2.35994 | ||||||||
\(949\) | 0.672190 | 0.0218202 | ||||||||
\(950\) | −13.5277 | −0.438897 | ||||||||
\(951\) | 8.70709 | 0.282347 | ||||||||
\(952\) | 2.22373 | 0.0720714 | ||||||||
\(953\) | 14.6045 | 0.473085 | 0.236542 | − | 0.971621i | \(-0.423986\pi\) | ||||
0.236542 | + | 0.971621i | \(0.423986\pi\) | |||||||
\(954\) | −18.3476 | −0.594025 | ||||||||
\(955\) | −5.69226 | −0.184197 | ||||||||
\(956\) | −59.8942 | −1.93712 | ||||||||
\(957\) | 70.4502 | 2.27733 | ||||||||
\(958\) | −49.0323 | −1.58416 | ||||||||
\(959\) | −4.57972 | −0.147887 | ||||||||
\(960\) | 8.60570 | 0.277748 | ||||||||
\(961\) | −30.9484 | −0.998335 | ||||||||
\(962\) | 10.6568 | 0.343590 | ||||||||
\(963\) | −46.4756 | −1.49766 | ||||||||
\(964\) | 42.3476 | 1.36392 | ||||||||
\(965\) | 5.67017 | 0.182529 | ||||||||
\(966\) | 9.16411 | 0.294850 | ||||||||
\(967\) | −12.3588 | −0.397433 | −0.198717 | − | 0.980057i | \(-0.563677\pi\) | ||||
−0.198717 | + | 0.980057i | \(0.563677\pi\) | |||||||
\(968\) | −66.3238 | −2.13173 | ||||||||
\(969\) | −3.24140 | −0.104129 | ||||||||
\(970\) | 7.48462 | 0.240317 | ||||||||
\(971\) | 58.7545 | 1.88552 | 0.942761 | − | 0.333470i | \(-0.108220\pi\) | ||||
0.942761 | + | 0.333470i | \(0.108220\pi\) | |||||||
\(972\) | −52.7149 | −1.69083 | ||||||||
\(973\) | −1.09566 | −0.0351252 | ||||||||
\(974\) | 28.2267 | 0.904442 | ||||||||
\(975\) | 5.12433 | 0.164110 | ||||||||
\(976\) | −24.5597 | −0.786136 | ||||||||
\(977\) | −40.4003 | −1.29252 | −0.646261 | − | 0.763117i | \(-0.723668\pi\) | ||||
−0.646261 | + | 0.763117i | \(0.723668\pi\) | |||||||
\(978\) | −9.70690 | −0.310392 | ||||||||
\(979\) | 14.4620 | 0.462207 | ||||||||
\(980\) | 11.4516 | 0.365809 | ||||||||
\(981\) | −75.8114 | −2.42047 | ||||||||
\(982\) | 25.3482 | 0.808893 | ||||||||
\(983\) | −16.7890 | −0.535487 | −0.267744 | − | 0.963490i | \(-0.586278\pi\) | ||||
−0.267744 | + | 0.963490i | \(0.586278\pi\) | |||||||
\(984\) | 46.6326 | 1.48659 | ||||||||
\(985\) | 10.0136 | 0.319059 | ||||||||
\(986\) | −12.4047 | −0.395048 | ||||||||
\(987\) | −9.28051 | −0.295402 | ||||||||
\(988\) | 1.72182 | 0.0547783 | ||||||||
\(989\) | −13.8793 | −0.441338 | ||||||||
\(990\) | 25.5827 | 0.813071 | ||||||||
\(991\) | 37.9861 | 1.20667 | 0.603334 | − | 0.797489i | \(-0.293839\pi\) | ||||
0.603334 | + | 0.797489i | \(0.293839\pi\) | |||||||
\(992\) | −0.129401 | −0.00410847 | ||||||||
\(993\) | −50.4627 | −1.60139 | ||||||||
\(994\) | 7.50151 | 0.237933 | ||||||||
\(995\) | 9.46587 | 0.300088 | ||||||||
\(996\) | 27.5043 | 0.871507 | ||||||||
\(997\) | 20.7881 | 0.658365 | 0.329183 | − | 0.944266i | \(-0.393227\pi\) | ||||
0.329183 | + | 0.944266i | \(0.393227\pi\) | |||||||
\(998\) | −70.5634 | −2.23364 | ||||||||
\(999\) | 69.6571 | 2.20385 |
(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 | 1003.2.a.i.1.2 | ✓ | 18 | |
3.2 | odd | 2 | 9027.2.a.q.1.17 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1003.2.a.i.1.2 | ✓ | 18 | 1.1 | even | 1 | trivial | |
9027.2.a.q.1.17 | 18 | 3.2 | odd | 2 |