Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4010,2,Mod(1,4010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4010, 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("4010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4010 = 2 \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4010.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: | \(32.0200112105\) |
Analytic rank: | \(0\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{17} - 3 x^{16} - 24 x^{15} + 70 x^{14} + 228 x^{13} - 638 x^{12} - 1075 x^{11} + 2854 x^{10} + 2544 x^{9} - 6415 x^{8} - 2573 x^{7} + 6456 x^{6} + 485 x^{5} - 1839 x^{4} + \cdots - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-0.548857\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4010.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.548857 | −0.316883 | −0.158441 | − | 0.987368i | \(-0.550647\pi\) | ||||
−0.158441 | + | 0.987368i | \(0.550647\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0.548857 | 0.224070 | ||||||||
\(7\) | −1.86676 | −0.705570 | −0.352785 | − | 0.935704i | \(-0.614765\pi\) | ||||
−0.352785 | + | 0.935704i | \(0.614765\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.69876 | −0.899585 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0.761515 | 0.229606 | 0.114803 | − | 0.993388i | \(-0.463376\pi\) | ||||
0.114803 | + | 0.993388i | \(0.463376\pi\) | |||||||
\(12\) | −0.548857 | −0.158441 | ||||||||
\(13\) | −4.22069 | −1.17061 | −0.585304 | − | 0.810814i | \(-0.699025\pi\) | ||||
−0.585304 | + | 0.810814i | \(0.699025\pi\) | |||||||
\(14\) | 1.86676 | 0.498913 | ||||||||
\(15\) | 0.548857 | 0.141714 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.77958 | 0.431613 | 0.215806 | − | 0.976436i | \(-0.430762\pi\) | ||||
0.215806 | + | 0.976436i | \(0.430762\pi\) | |||||||
\(18\) | 2.69876 | 0.636103 | ||||||||
\(19\) | −7.51631 | −1.72436 | −0.862179 | − | 0.506603i | \(-0.830901\pi\) | ||||
−0.862179 | + | 0.506603i | \(0.830901\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 1.02458 | 0.223583 | ||||||||
\(22\) | −0.761515 | −0.162356 | ||||||||
\(23\) | 2.16755 | 0.451965 | 0.225982 | − | 0.974131i | \(-0.427441\pi\) | ||||
0.225982 | + | 0.974131i | \(0.427441\pi\) | |||||||
\(24\) | 0.548857 | 0.112035 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 4.22069 | 0.827745 | ||||||||
\(27\) | 3.12780 | 0.601945 | ||||||||
\(28\) | −1.86676 | −0.352785 | ||||||||
\(29\) | −1.35794 | −0.252163 | −0.126081 | − | 0.992020i | \(-0.540240\pi\) | ||||
−0.126081 | + | 0.992020i | \(0.540240\pi\) | |||||||
\(30\) | −0.548857 | −0.100207 | ||||||||
\(31\) | 2.74334 | 0.492719 | 0.246359 | − | 0.969179i | \(-0.420766\pi\) | ||||
0.246359 | + | 0.969179i | \(0.420766\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.417963 | −0.0727580 | ||||||||
\(34\) | −1.77958 | −0.305196 | ||||||||
\(35\) | 1.86676 | 0.315540 | ||||||||
\(36\) | −2.69876 | −0.449793 | ||||||||
\(37\) | −8.22343 | −1.35192 | −0.675962 | − | 0.736937i | \(-0.736271\pi\) | ||||
−0.675962 | + | 0.736937i | \(0.736271\pi\) | |||||||
\(38\) | 7.51631 | 1.21931 | ||||||||
\(39\) | 2.31655 | 0.370945 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −11.9509 | −1.86642 | −0.933209 | − | 0.359333i | \(-0.883004\pi\) | ||||
−0.933209 | + | 0.359333i | \(0.883004\pi\) | |||||||
\(42\) | −1.02458 | −0.158097 | ||||||||
\(43\) | −11.2893 | −1.72161 | −0.860803 | − | 0.508938i | \(-0.830038\pi\) | ||||
−0.860803 | + | 0.508938i | \(0.830038\pi\) | |||||||
\(44\) | 0.761515 | 0.114803 | ||||||||
\(45\) | 2.69876 | 0.402307 | ||||||||
\(46\) | −2.16755 | −0.319587 | ||||||||
\(47\) | 3.51558 | 0.512799 | 0.256400 | − | 0.966571i | \(-0.417464\pi\) | ||||
0.256400 | + | 0.966571i | \(0.417464\pi\) | |||||||
\(48\) | −0.548857 | −0.0792206 | ||||||||
\(49\) | −3.51520 | −0.502171 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −0.976737 | −0.136770 | ||||||||
\(52\) | −4.22069 | −0.585304 | ||||||||
\(53\) | 11.0125 | 1.51269 | 0.756344 | − | 0.654174i | \(-0.226983\pi\) | ||||
0.756344 | + | 0.654174i | \(0.226983\pi\) | |||||||
\(54\) | −3.12780 | −0.425640 | ||||||||
\(55\) | −0.761515 | −0.102683 | ||||||||
\(56\) | 1.86676 | 0.249457 | ||||||||
\(57\) | 4.12537 | 0.546419 | ||||||||
\(58\) | 1.35794 | 0.178306 | ||||||||
\(59\) | −12.1732 | −1.58482 | −0.792409 | − | 0.609991i | \(-0.791173\pi\) | ||||
−0.792409 | + | 0.609991i | \(0.791173\pi\) | |||||||
\(60\) | 0.548857 | 0.0708571 | ||||||||
\(61\) | 6.48721 | 0.830601 | 0.415301 | − | 0.909684i | \(-0.363676\pi\) | ||||
0.415301 | + | 0.909684i | \(0.363676\pi\) | |||||||
\(62\) | −2.74334 | −0.348405 | ||||||||
\(63\) | 5.03794 | 0.634720 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.22069 | 0.523512 | ||||||||
\(66\) | 0.417963 | 0.0514477 | ||||||||
\(67\) | 7.99847 | 0.977168 | 0.488584 | − | 0.872517i | \(-0.337514\pi\) | ||||
0.488584 | + | 0.872517i | \(0.337514\pi\) | |||||||
\(68\) | 1.77958 | 0.215806 | ||||||||
\(69\) | −1.18967 | −0.143220 | ||||||||
\(70\) | −1.86676 | −0.223121 | ||||||||
\(71\) | −4.51275 | −0.535564 | −0.267782 | − | 0.963479i | \(-0.586291\pi\) | ||||
−0.267782 | + | 0.963479i | \(0.586291\pi\) | |||||||
\(72\) | 2.69876 | 0.318051 | ||||||||
\(73\) | 16.3206 | 1.91018 | 0.955091 | − | 0.296313i | \(-0.0957570\pi\) | ||||
0.955091 | + | 0.296313i | \(0.0957570\pi\) | |||||||
\(74\) | 8.22343 | 0.955954 | ||||||||
\(75\) | −0.548857 | −0.0633765 | ||||||||
\(76\) | −7.51631 | −0.862179 | ||||||||
\(77\) | −1.42157 | −0.162003 | ||||||||
\(78\) | −2.31655 | −0.262298 | ||||||||
\(79\) | −13.9449 | −1.56893 | −0.784465 | − | 0.620174i | \(-0.787062\pi\) | ||||
−0.784465 | + | 0.620174i | \(0.787062\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 6.37956 | 0.708840 | ||||||||
\(82\) | 11.9509 | 1.31976 | ||||||||
\(83\) | −0.0586654 | −0.00643936 | −0.00321968 | − | 0.999995i | \(-0.501025\pi\) | ||||
−0.00321968 | + | 0.999995i | \(0.501025\pi\) | |||||||
\(84\) | 1.02458 | 0.111791 | ||||||||
\(85\) | −1.77958 | −0.193023 | ||||||||
\(86\) | 11.2893 | 1.21736 | ||||||||
\(87\) | 0.745313 | 0.0799059 | ||||||||
\(88\) | −0.761515 | −0.0811778 | ||||||||
\(89\) | −0.122663 | −0.0130022 | −0.00650111 | − | 0.999979i | \(-0.502069\pi\) | ||||
−0.00650111 | + | 0.999979i | \(0.502069\pi\) | |||||||
\(90\) | −2.69876 | −0.284474 | ||||||||
\(91\) | 7.87902 | 0.825945 | ||||||||
\(92\) | 2.16755 | 0.225982 | ||||||||
\(93\) | −1.50570 | −0.156134 | ||||||||
\(94\) | −3.51558 | −0.362604 | ||||||||
\(95\) | 7.51631 | 0.771157 | ||||||||
\(96\) | 0.548857 | 0.0560174 | ||||||||
\(97\) | −2.83378 | −0.287727 | −0.143863 | − | 0.989598i | \(-0.545953\pi\) | ||||
−0.143863 | + | 0.989598i | \(0.545953\pi\) | |||||||
\(98\) | 3.51520 | 0.355089 | ||||||||
\(99\) | −2.05514 | −0.206550 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 0.212072 | 0.0211020 | 0.0105510 | − | 0.999944i | \(-0.496641\pi\) | ||||
0.0105510 | + | 0.999944i | \(0.496641\pi\) | |||||||
\(102\) | 0.976737 | 0.0967113 | ||||||||
\(103\) | 1.08106 | 0.106520 | 0.0532600 | − | 0.998581i | \(-0.483039\pi\) | ||||
0.0532600 | + | 0.998581i | \(0.483039\pi\) | |||||||
\(104\) | 4.22069 | 0.413872 | ||||||||
\(105\) | −1.02458 | −0.0999892 | ||||||||
\(106\) | −11.0125 | −1.06963 | ||||||||
\(107\) | 11.8016 | 1.14091 | 0.570453 | − | 0.821330i | \(-0.306768\pi\) | ||||
0.570453 | + | 0.821330i | \(0.306768\pi\) | |||||||
\(108\) | 3.12780 | 0.300973 | ||||||||
\(109\) | 18.0977 | 1.73345 | 0.866723 | − | 0.498790i | \(-0.166222\pi\) | ||||
0.866723 | + | 0.498790i | \(0.166222\pi\) | |||||||
\(110\) | 0.761515 | 0.0726077 | ||||||||
\(111\) | 4.51348 | 0.428401 | ||||||||
\(112\) | −1.86676 | −0.176392 | ||||||||
\(113\) | −6.50418 | −0.611862 | −0.305931 | − | 0.952054i | \(-0.598968\pi\) | ||||
−0.305931 | + | 0.952054i | \(0.598968\pi\) | |||||||
\(114\) | −4.12537 | −0.386377 | ||||||||
\(115\) | −2.16755 | −0.202125 | ||||||||
\(116\) | −1.35794 | −0.126081 | ||||||||
\(117\) | 11.3906 | 1.05306 | ||||||||
\(118\) | 12.1732 | 1.12063 | ||||||||
\(119\) | −3.32206 | −0.304533 | ||||||||
\(120\) | −0.548857 | −0.0501035 | ||||||||
\(121\) | −10.4201 | −0.947281 | ||||||||
\(122\) | −6.48721 | −0.587324 | ||||||||
\(123\) | 6.55934 | 0.591435 | ||||||||
\(124\) | 2.74334 | 0.246359 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −5.03794 | −0.448815 | ||||||||
\(127\) | −21.3259 | −1.89237 | −0.946183 | − | 0.323633i | \(-0.895096\pi\) | ||||
−0.946183 | + | 0.323633i | \(0.895096\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 6.19622 | 0.545547 | ||||||||
\(130\) | −4.22069 | −0.370179 | ||||||||
\(131\) | 11.9874 | 1.04735 | 0.523674 | − | 0.851919i | \(-0.324561\pi\) | ||||
0.523674 | + | 0.851919i | \(0.324561\pi\) | |||||||
\(132\) | −0.417963 | −0.0363790 | ||||||||
\(133\) | 14.0312 | 1.21666 | ||||||||
\(134\) | −7.99847 | −0.690962 | ||||||||
\(135\) | −3.12780 | −0.269198 | ||||||||
\(136\) | −1.77958 | −0.152598 | ||||||||
\(137\) | −8.61417 | −0.735959 | −0.367979 | − | 0.929834i | \(-0.619950\pi\) | ||||
−0.367979 | + | 0.929834i | \(0.619950\pi\) | |||||||
\(138\) | 1.18967 | 0.101272 | ||||||||
\(139\) | 0.313769 | 0.0266135 | 0.0133068 | − | 0.999911i | \(-0.495764\pi\) | ||||
0.0133068 | + | 0.999911i | \(0.495764\pi\) | |||||||
\(140\) | 1.86676 | 0.157770 | ||||||||
\(141\) | −1.92955 | −0.162497 | ||||||||
\(142\) | 4.51275 | 0.378701 | ||||||||
\(143\) | −3.21412 | −0.268778 | ||||||||
\(144\) | −2.69876 | −0.224896 | ||||||||
\(145\) | 1.35794 | 0.112771 | ||||||||
\(146\) | −16.3206 | −1.35070 | ||||||||
\(147\) | 1.92934 | 0.159129 | ||||||||
\(148\) | −8.22343 | −0.675962 | ||||||||
\(149\) | −17.3878 | −1.42447 | −0.712234 | − | 0.701942i | \(-0.752316\pi\) | ||||
−0.712234 | + | 0.701942i | \(0.752316\pi\) | |||||||
\(150\) | 0.548857 | 0.0448140 | ||||||||
\(151\) | 11.6514 | 0.948176 | 0.474088 | − | 0.880478i | \(-0.342778\pi\) | ||||
0.474088 | + | 0.880478i | \(0.342778\pi\) | |||||||
\(152\) | 7.51631 | 0.609653 | ||||||||
\(153\) | −4.80266 | −0.388272 | ||||||||
\(154\) | 1.42157 | 0.114553 | ||||||||
\(155\) | −2.74334 | −0.220351 | ||||||||
\(156\) | 2.31655 | 0.185473 | ||||||||
\(157\) | 15.9952 | 1.27656 | 0.638279 | − | 0.769805i | \(-0.279647\pi\) | ||||
0.638279 | + | 0.769805i | \(0.279647\pi\) | |||||||
\(158\) | 13.9449 | 1.10940 | ||||||||
\(159\) | −6.04431 | −0.479345 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −4.04629 | −0.318893 | ||||||||
\(162\) | −6.37956 | −0.501225 | ||||||||
\(163\) | 7.07887 | 0.554460 | 0.277230 | − | 0.960804i | \(-0.410584\pi\) | ||||
0.277230 | + | 0.960804i | \(0.410584\pi\) | |||||||
\(164\) | −11.9509 | −0.933209 | ||||||||
\(165\) | 0.417963 | 0.0325384 | ||||||||
\(166\) | 0.0586654 | 0.00455332 | ||||||||
\(167\) | 12.2111 | 0.944924 | 0.472462 | − | 0.881351i | \(-0.343365\pi\) | ||||
0.472462 | + | 0.881351i | \(0.343365\pi\) | |||||||
\(168\) | −1.02458 | −0.0790484 | ||||||||
\(169\) | 4.81419 | 0.370322 | ||||||||
\(170\) | 1.77958 | 0.136488 | ||||||||
\(171\) | 20.2847 | 1.55121 | ||||||||
\(172\) | −11.2893 | −0.860803 | ||||||||
\(173\) | −17.3158 | −1.31650 | −0.658248 | − | 0.752801i | \(-0.728702\pi\) | ||||
−0.658248 | + | 0.752801i | \(0.728702\pi\) | |||||||
\(174\) | −0.745313 | −0.0565020 | ||||||||
\(175\) | −1.86676 | −0.141114 | ||||||||
\(176\) | 0.761515 | 0.0574014 | ||||||||
\(177\) | 6.68135 | 0.502201 | ||||||||
\(178\) | 0.122663 | 0.00919395 | ||||||||
\(179\) | 10.8140 | 0.808274 | 0.404137 | − | 0.914698i | \(-0.367572\pi\) | ||||
0.404137 | + | 0.914698i | \(0.367572\pi\) | |||||||
\(180\) | 2.69876 | 0.201153 | ||||||||
\(181\) | 14.7439 | 1.09591 | 0.547954 | − | 0.836508i | \(-0.315407\pi\) | ||||
0.547954 | + | 0.836508i | \(0.315407\pi\) | |||||||
\(182\) | −7.87902 | −0.584032 | ||||||||
\(183\) | −3.56055 | −0.263203 | ||||||||
\(184\) | −2.16755 | −0.159794 | ||||||||
\(185\) | 8.22343 | 0.604598 | ||||||||
\(186\) | 1.50570 | 0.110403 | ||||||||
\(187\) | 1.35518 | 0.0991006 | ||||||||
\(188\) | 3.51558 | 0.256400 | ||||||||
\(189\) | −5.83886 | −0.424715 | ||||||||
\(190\) | −7.51631 | −0.545290 | ||||||||
\(191\) | −6.89586 | −0.498967 | −0.249483 | − | 0.968379i | \(-0.580261\pi\) | ||||
−0.249483 | + | 0.968379i | \(0.580261\pi\) | |||||||
\(192\) | −0.548857 | −0.0396103 | ||||||||
\(193\) | 11.5661 | 0.832543 | 0.416272 | − | 0.909240i | \(-0.363337\pi\) | ||||
0.416272 | + | 0.909240i | \(0.363337\pi\) | |||||||
\(194\) | 2.83378 | 0.203454 | ||||||||
\(195\) | −2.31655 | −0.165892 | ||||||||
\(196\) | −3.51520 | −0.251086 | ||||||||
\(197\) | 25.0540 | 1.78502 | 0.892511 | − | 0.451026i | \(-0.148942\pi\) | ||||
0.892511 | + | 0.451026i | \(0.148942\pi\) | |||||||
\(198\) | 2.05514 | 0.146053 | ||||||||
\(199\) | 10.1371 | 0.718599 | 0.359299 | − | 0.933222i | \(-0.383016\pi\) | ||||
0.359299 | + | 0.933222i | \(0.383016\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −4.39001 | −0.309647 | ||||||||
\(202\) | −0.212072 | −0.0149214 | ||||||||
\(203\) | 2.53495 | 0.177918 | ||||||||
\(204\) | −0.976737 | −0.0683852 | ||||||||
\(205\) | 11.9509 | 0.834688 | ||||||||
\(206\) | −1.08106 | −0.0753210 | ||||||||
\(207\) | −5.84968 | −0.406581 | ||||||||
\(208\) | −4.22069 | −0.292652 | ||||||||
\(209\) | −5.72378 | −0.395922 | ||||||||
\(210\) | 1.02458 | 0.0707031 | ||||||||
\(211\) | 10.9855 | 0.756274 | 0.378137 | − | 0.925750i | \(-0.376565\pi\) | ||||
0.378137 | + | 0.925750i | \(0.376565\pi\) | |||||||
\(212\) | 11.0125 | 0.756344 | ||||||||
\(213\) | 2.47685 | 0.169711 | ||||||||
\(214\) | −11.8016 | −0.806743 | ||||||||
\(215\) | 11.2893 | 0.769926 | ||||||||
\(216\) | −3.12780 | −0.212820 | ||||||||
\(217\) | −5.12117 | −0.347648 | ||||||||
\(218\) | −18.0977 | −1.22573 | ||||||||
\(219\) | −8.95767 | −0.605303 | ||||||||
\(220\) | −0.761515 | −0.0513414 | ||||||||
\(221\) | −7.51107 | −0.505249 | ||||||||
\(222\) | −4.51348 | −0.302925 | ||||||||
\(223\) | 10.1950 | 0.682711 | 0.341355 | − | 0.939934i | \(-0.389114\pi\) | ||||
0.341355 | + | 0.939934i | \(0.389114\pi\) | |||||||
\(224\) | 1.86676 | 0.124728 | ||||||||
\(225\) | −2.69876 | −0.179917 | ||||||||
\(226\) | 6.50418 | 0.432652 | ||||||||
\(227\) | 19.1164 | 1.26880 | 0.634398 | − | 0.773006i | \(-0.281248\pi\) | ||||
0.634398 | + | 0.773006i | \(0.281248\pi\) | |||||||
\(228\) | 4.12537 | 0.273210 | ||||||||
\(229\) | 12.7450 | 0.842211 | 0.421105 | − | 0.907012i | \(-0.361642\pi\) | ||||
0.421105 | + | 0.907012i | \(0.361642\pi\) | |||||||
\(230\) | 2.16755 | 0.142924 | ||||||||
\(231\) | 0.780237 | 0.0513358 | ||||||||
\(232\) | 1.35794 | 0.0891529 | ||||||||
\(233\) | −19.0509 | −1.24807 | −0.624033 | − | 0.781398i | \(-0.714507\pi\) | ||||
−0.624033 | + | 0.781398i | \(0.714507\pi\) | |||||||
\(234\) | −11.3906 | −0.744627 | ||||||||
\(235\) | −3.51558 | −0.229331 | ||||||||
\(236\) | −12.1732 | −0.792409 | ||||||||
\(237\) | 7.65378 | 0.497166 | ||||||||
\(238\) | 3.32206 | 0.215337 | ||||||||
\(239\) | 14.2195 | 0.919783 | 0.459892 | − | 0.887975i | \(-0.347888\pi\) | ||||
0.459892 | + | 0.887975i | \(0.347888\pi\) | |||||||
\(240\) | 0.548857 | 0.0354285 | ||||||||
\(241\) | −25.0784 | −1.61544 | −0.807721 | − | 0.589564i | \(-0.799299\pi\) | ||||
−0.807721 | + | 0.589564i | \(0.799299\pi\) | |||||||
\(242\) | 10.4201 | 0.669829 | ||||||||
\(243\) | −12.8849 | −0.826564 | ||||||||
\(244\) | 6.48721 | 0.415301 | ||||||||
\(245\) | 3.51520 | 0.224578 | ||||||||
\(246\) | −6.55934 | −0.418208 | ||||||||
\(247\) | 31.7240 | 2.01855 | ||||||||
\(248\) | −2.74334 | −0.174202 | ||||||||
\(249\) | 0.0321989 | 0.00204052 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −16.2113 | −1.02325 | −0.511623 | − | 0.859210i | \(-0.670955\pi\) | ||||
−0.511623 | + | 0.859210i | \(0.670955\pi\) | |||||||
\(252\) | 5.03794 | 0.317360 | ||||||||
\(253\) | 1.65062 | 0.103774 | ||||||||
\(254\) | 21.3259 | 1.33810 | ||||||||
\(255\) | 0.976737 | 0.0611656 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.87073 | −0.303828 | −0.151914 | − | 0.988394i | \(-0.548544\pi\) | ||||
−0.151914 | + | 0.988394i | \(0.548544\pi\) | |||||||
\(258\) | −6.19622 | −0.385760 | ||||||||
\(259\) | 15.3512 | 0.953876 | ||||||||
\(260\) | 4.22069 | 0.261756 | ||||||||
\(261\) | 3.66474 | 0.226842 | ||||||||
\(262\) | −11.9874 | −0.740587 | ||||||||
\(263\) | −0.362645 | −0.0223617 | −0.0111808 | − | 0.999937i | \(-0.503559\pi\) | ||||
−0.0111808 | + | 0.999937i | \(0.503559\pi\) | |||||||
\(264\) | 0.417963 | 0.0257238 | ||||||||
\(265\) | −11.0125 | −0.676495 | ||||||||
\(266\) | −14.0312 | −0.860305 | ||||||||
\(267\) | 0.0673242 | 0.00412017 | ||||||||
\(268\) | 7.99847 | 0.488584 | ||||||||
\(269\) | −20.9121 | −1.27503 | −0.637517 | − | 0.770436i | \(-0.720039\pi\) | ||||
−0.637517 | + | 0.770436i | \(0.720039\pi\) | |||||||
\(270\) | 3.12780 | 0.190352 | ||||||||
\(271\) | −9.56595 | −0.581090 | −0.290545 | − | 0.956861i | \(-0.593837\pi\) | ||||
−0.290545 | + | 0.956861i | \(0.593837\pi\) | |||||||
\(272\) | 1.77958 | 0.107903 | ||||||||
\(273\) | −4.32445 | −0.261728 | ||||||||
\(274\) | 8.61417 | 0.520401 | ||||||||
\(275\) | 0.761515 | 0.0459211 | ||||||||
\(276\) | −1.18967 | −0.0716098 | ||||||||
\(277\) | −5.26163 | −0.316141 | −0.158070 | − | 0.987428i | \(-0.550527\pi\) | ||||
−0.158070 | + | 0.987428i | \(0.550527\pi\) | |||||||
\(278\) | −0.313769 | −0.0188186 | ||||||||
\(279\) | −7.40361 | −0.443243 | ||||||||
\(280\) | −1.86676 | −0.111560 | ||||||||
\(281\) | −15.0816 | −0.899691 | −0.449845 | − | 0.893106i | \(-0.648521\pi\) | ||||
−0.449845 | + | 0.893106i | \(0.648521\pi\) | |||||||
\(282\) | 1.92955 | 0.114903 | ||||||||
\(283\) | 21.4410 | 1.27453 | 0.637267 | − | 0.770643i | \(-0.280065\pi\) | ||||
0.637267 | + | 0.770643i | \(0.280065\pi\) | |||||||
\(284\) | −4.51275 | −0.267782 | ||||||||
\(285\) | −4.12537 | −0.244366 | ||||||||
\(286\) | 3.21412 | 0.190055 | ||||||||
\(287\) | 22.3095 | 1.31689 | ||||||||
\(288\) | 2.69876 | 0.159026 | ||||||||
\(289\) | −13.8331 | −0.813711 | ||||||||
\(290\) | −1.35794 | −0.0797408 | ||||||||
\(291\) | 1.55534 | 0.0911756 | ||||||||
\(292\) | 16.3206 | 0.955091 | ||||||||
\(293\) | −2.88070 | −0.168292 | −0.0841461 | − | 0.996453i | \(-0.526816\pi\) | ||||
−0.0841461 | + | 0.996453i | \(0.526816\pi\) | |||||||
\(294\) | −1.92934 | −0.112521 | ||||||||
\(295\) | 12.1732 | 0.708752 | ||||||||
\(296\) | 8.22343 | 0.477977 | ||||||||
\(297\) | 2.38187 | 0.138210 | ||||||||
\(298\) | 17.3878 | 1.00725 | ||||||||
\(299\) | −9.14853 | −0.529073 | ||||||||
\(300\) | −0.548857 | −0.0316883 | ||||||||
\(301\) | 21.0745 | 1.21471 | ||||||||
\(302\) | −11.6514 | −0.670462 | ||||||||
\(303\) | −0.116397 | −0.00668685 | ||||||||
\(304\) | −7.51631 | −0.431090 | ||||||||
\(305\) | −6.48721 | −0.371456 | ||||||||
\(306\) | 4.80266 | 0.274550 | ||||||||
\(307\) | −17.1239 | −0.977313 | −0.488657 | − | 0.872476i | \(-0.662513\pi\) | ||||
−0.488657 | + | 0.872476i | \(0.662513\pi\) | |||||||
\(308\) | −1.42157 | −0.0810014 | ||||||||
\(309\) | −0.593347 | −0.0337543 | ||||||||
\(310\) | 2.74334 | 0.155811 | ||||||||
\(311\) | −16.7400 | −0.949238 | −0.474619 | − | 0.880191i | \(-0.657414\pi\) | ||||
−0.474619 | + | 0.880191i | \(0.657414\pi\) | |||||||
\(312\) | −2.31655 | −0.131149 | ||||||||
\(313\) | −12.5325 | −0.708378 | −0.354189 | − | 0.935174i | \(-0.615243\pi\) | ||||
−0.354189 | + | 0.935174i | \(0.615243\pi\) | |||||||
\(314\) | −15.9952 | −0.902663 | ||||||||
\(315\) | −5.03794 | −0.283856 | ||||||||
\(316\) | −13.9449 | −0.784465 | ||||||||
\(317\) | 33.5037 | 1.88176 | 0.940879 | − | 0.338744i | \(-0.110002\pi\) | ||||
0.940879 | + | 0.338744i | \(0.110002\pi\) | |||||||
\(318\) | 6.04431 | 0.338948 | ||||||||
\(319\) | −1.03409 | −0.0578979 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −6.47740 | −0.361533 | ||||||||
\(322\) | 4.04629 | 0.225491 | ||||||||
\(323\) | −13.3759 | −0.744255 | ||||||||
\(324\) | 6.37956 | 0.354420 | ||||||||
\(325\) | −4.22069 | −0.234122 | ||||||||
\(326\) | −7.07887 | −0.392062 | ||||||||
\(327\) | −9.93304 | −0.549298 | ||||||||
\(328\) | 11.9509 | 0.659879 | ||||||||
\(329\) | −6.56274 | −0.361816 | ||||||||
\(330\) | −0.417963 | −0.0230081 | ||||||||
\(331\) | 34.0309 | 1.87051 | 0.935255 | − | 0.353976i | \(-0.115170\pi\) | ||||
0.935255 | + | 0.353976i | \(0.115170\pi\) | |||||||
\(332\) | −0.0586654 | −0.00321968 | ||||||||
\(333\) | 22.1930 | 1.21617 | ||||||||
\(334\) | −12.2111 | −0.668162 | ||||||||
\(335\) | −7.99847 | −0.437003 | ||||||||
\(336\) | 1.02458 | 0.0558957 | ||||||||
\(337\) | 17.9001 | 0.975083 | 0.487541 | − | 0.873100i | \(-0.337894\pi\) | ||||
0.487541 | + | 0.873100i | \(0.337894\pi\) | |||||||
\(338\) | −4.81419 | −0.261858 | ||||||||
\(339\) | 3.56986 | 0.193888 | ||||||||
\(340\) | −1.77958 | −0.0965115 | ||||||||
\(341\) | 2.08910 | 0.113131 | ||||||||
\(342\) | −20.2847 | −1.09687 | ||||||||
\(343\) | 19.6294 | 1.05989 | ||||||||
\(344\) | 11.2893 | 0.608680 | ||||||||
\(345\) | 1.18967 | 0.0640498 | ||||||||
\(346\) | 17.3158 | 0.930903 | ||||||||
\(347\) | −12.1406 | −0.651740 | −0.325870 | − | 0.945415i | \(-0.605657\pi\) | ||||
−0.325870 | + | 0.945415i | \(0.605657\pi\) | |||||||
\(348\) | 0.745313 | 0.0399530 | ||||||||
\(349\) | −22.3750 | −1.19771 | −0.598854 | − | 0.800858i | \(-0.704377\pi\) | ||||
−0.598854 | + | 0.800858i | \(0.704377\pi\) | |||||||
\(350\) | 1.86676 | 0.0997826 | ||||||||
\(351\) | −13.2015 | −0.704642 | ||||||||
\(352\) | −0.761515 | −0.0405889 | ||||||||
\(353\) | 19.9913 | 1.06403 | 0.532014 | − | 0.846735i | \(-0.321435\pi\) | ||||
0.532014 | + | 0.846735i | \(0.321435\pi\) | |||||||
\(354\) | −6.68135 | −0.355110 | ||||||||
\(355\) | 4.51275 | 0.239512 | ||||||||
\(356\) | −0.122663 | −0.00650111 | ||||||||
\(357\) | 1.82333 | 0.0965011 | ||||||||
\(358\) | −10.8140 | −0.571536 | ||||||||
\(359\) | −18.1630 | −0.958608 | −0.479304 | − | 0.877649i | \(-0.659111\pi\) | ||||
−0.479304 | + | 0.877649i | \(0.659111\pi\) | |||||||
\(360\) | −2.69876 | −0.142237 | ||||||||
\(361\) | 37.4949 | 1.97341 | ||||||||
\(362\) | −14.7439 | −0.774924 | ||||||||
\(363\) | 5.71914 | 0.300177 | ||||||||
\(364\) | 7.87902 | 0.412973 | ||||||||
\(365\) | −16.3206 | −0.854259 | ||||||||
\(366\) | 3.56055 | 0.186113 | ||||||||
\(367\) | 19.8279 | 1.03501 | 0.517504 | − | 0.855681i | \(-0.326861\pi\) | ||||
0.517504 | + | 0.855681i | \(0.326861\pi\) | |||||||
\(368\) | 2.16755 | 0.112991 | ||||||||
\(369\) | 32.2526 | 1.67900 | ||||||||
\(370\) | −8.22343 | −0.427516 | ||||||||
\(371\) | −20.5578 | −1.06731 | ||||||||
\(372\) | −1.50570 | −0.0780670 | ||||||||
\(373\) | −4.64418 | −0.240467 | −0.120233 | − | 0.992746i | \(-0.538364\pi\) | ||||
−0.120233 | + | 0.992746i | \(0.538364\pi\) | |||||||
\(374\) | −1.35518 | −0.0700747 | ||||||||
\(375\) | 0.548857 | 0.0283428 | ||||||||
\(376\) | −3.51558 | −0.181302 | ||||||||
\(377\) | 5.73143 | 0.295183 | ||||||||
\(378\) | 5.83886 | 0.300319 | ||||||||
\(379\) | 33.5715 | 1.72445 | 0.862225 | − | 0.506525i | \(-0.169070\pi\) | ||||
0.862225 | + | 0.506525i | \(0.169070\pi\) | |||||||
\(380\) | 7.51631 | 0.385578 | ||||||||
\(381\) | 11.7048 | 0.599658 | ||||||||
\(382\) | 6.89586 | 0.352823 | ||||||||
\(383\) | 12.1617 | 0.621435 | 0.310717 | − | 0.950502i | \(-0.399431\pi\) | ||||
0.310717 | + | 0.950502i | \(0.399431\pi\) | |||||||
\(384\) | 0.548857 | 0.0280087 | ||||||||
\(385\) | 1.42157 | 0.0724498 | ||||||||
\(386\) | −11.5661 | −0.588697 | ||||||||
\(387\) | 30.4672 | 1.54873 | ||||||||
\(388\) | −2.83378 | −0.143863 | ||||||||
\(389\) | −22.6068 | −1.14621 | −0.573106 | − | 0.819481i | \(-0.694262\pi\) | ||||
−0.573106 | + | 0.819481i | \(0.694262\pi\) | |||||||
\(390\) | 2.31655 | 0.117303 | ||||||||
\(391\) | 3.85733 | 0.195074 | ||||||||
\(392\) | 3.51520 | 0.177544 | ||||||||
\(393\) | −6.57939 | −0.331886 | ||||||||
\(394\) | −25.0540 | −1.26220 | ||||||||
\(395\) | 13.9449 | 0.701646 | ||||||||
\(396\) | −2.05514 | −0.103275 | ||||||||
\(397\) | −8.63801 | −0.433529 | −0.216765 | − | 0.976224i | \(-0.569550\pi\) | ||||
−0.216765 | + | 0.976224i | \(0.569550\pi\) | |||||||
\(398\) | −10.1371 | −0.508126 | ||||||||
\(399\) | −7.70109 | −0.385537 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 1.00000 | 0.0499376 | ||||||||
\(402\) | 4.39001 | 0.218954 | ||||||||
\(403\) | −11.5788 | −0.576780 | ||||||||
\(404\) | 0.212072 | 0.0105510 | ||||||||
\(405\) | −6.37956 | −0.317003 | ||||||||
\(406\) | −2.53495 | −0.125807 | ||||||||
\(407\) | −6.26227 | −0.310409 | ||||||||
\(408\) | 0.976737 | 0.0483557 | ||||||||
\(409\) | 24.3843 | 1.20573 | 0.602864 | − | 0.797844i | \(-0.294026\pi\) | ||||
0.602864 | + | 0.797844i | \(0.294026\pi\) | |||||||
\(410\) | −11.9509 | −0.590213 | ||||||||
\(411\) | 4.72795 | 0.233212 | ||||||||
\(412\) | 1.08106 | 0.0532600 | ||||||||
\(413\) | 22.7245 | 1.11820 | ||||||||
\(414\) | 5.84968 | 0.287496 | ||||||||
\(415\) | 0.0586654 | 0.00287977 | ||||||||
\(416\) | 4.22069 | 0.206936 | ||||||||
\(417\) | −0.172214 | −0.00843336 | ||||||||
\(418\) | 5.72378 | 0.279959 | ||||||||
\(419\) | −6.20803 | −0.303282 | −0.151641 | − | 0.988436i | \(-0.548456\pi\) | ||||
−0.151641 | + | 0.988436i | \(0.548456\pi\) | |||||||
\(420\) | −1.02458 | −0.0499946 | ||||||||
\(421\) | 36.0429 | 1.75662 | 0.878311 | − | 0.478090i | \(-0.158671\pi\) | ||||
0.878311 | + | 0.478090i | \(0.158671\pi\) | |||||||
\(422\) | −10.9855 | −0.534766 | ||||||||
\(423\) | −9.48768 | −0.461307 | ||||||||
\(424\) | −11.0125 | −0.534816 | ||||||||
\(425\) | 1.77958 | 0.0863225 | ||||||||
\(426\) | −2.47685 | −0.120004 | ||||||||
\(427\) | −12.1101 | −0.586047 | ||||||||
\(428\) | 11.8016 | 0.570453 | ||||||||
\(429\) | 1.76409 | 0.0851711 | ||||||||
\(430\) | −11.2893 | −0.544420 | ||||||||
\(431\) | 26.0536 | 1.25496 | 0.627480 | − | 0.778633i | \(-0.284086\pi\) | ||||
0.627480 | + | 0.778633i | \(0.284086\pi\) | |||||||
\(432\) | 3.12780 | 0.150486 | ||||||||
\(433\) | −0.698973 | −0.0335905 | −0.0167952 | − | 0.999859i | \(-0.505346\pi\) | ||||
−0.0167952 | + | 0.999859i | \(0.505346\pi\) | |||||||
\(434\) | 5.12117 | 0.245824 | ||||||||
\(435\) | −0.745313 | −0.0357350 | ||||||||
\(436\) | 18.0977 | 0.866723 | ||||||||
\(437\) | −16.2919 | −0.779349 | ||||||||
\(438\) | 8.95767 | 0.428014 | ||||||||
\(439\) | −12.6681 | −0.604614 | −0.302307 | − | 0.953211i | \(-0.597757\pi\) | ||||
−0.302307 | + | 0.953211i | \(0.597757\pi\) | |||||||
\(440\) | 0.761515 | 0.0363038 | ||||||||
\(441\) | 9.48666 | 0.451746 | ||||||||
\(442\) | 7.51107 | 0.357265 | ||||||||
\(443\) | 25.6499 | 1.21866 | 0.609331 | − | 0.792916i | \(-0.291438\pi\) | ||||
0.609331 | + | 0.792916i | \(0.291438\pi\) | |||||||
\(444\) | 4.51348 | 0.214200 | ||||||||
\(445\) | 0.122663 | 0.00581477 | ||||||||
\(446\) | −10.1950 | −0.482749 | ||||||||
\(447\) | 9.54343 | 0.451389 | ||||||||
\(448\) | −1.86676 | −0.0881962 | ||||||||
\(449\) | 34.0187 | 1.60544 | 0.802721 | − | 0.596354i | \(-0.203385\pi\) | ||||
0.802721 | + | 0.596354i | \(0.203385\pi\) | |||||||
\(450\) | 2.69876 | 0.127221 | ||||||||
\(451\) | −9.10080 | −0.428540 | ||||||||
\(452\) | −6.50418 | −0.305931 | ||||||||
\(453\) | −6.39494 | −0.300460 | ||||||||
\(454\) | −19.1164 | −0.897175 | ||||||||
\(455\) | −7.87902 | −0.369374 | ||||||||
\(456\) | −4.12537 | −0.193188 | ||||||||
\(457\) | 15.8036 | 0.739260 | 0.369630 | − | 0.929179i | \(-0.379484\pi\) | ||||
0.369630 | + | 0.929179i | \(0.379484\pi\) | |||||||
\(458\) | −12.7450 | −0.595533 | ||||||||
\(459\) | 5.56618 | 0.259807 | ||||||||
\(460\) | −2.16755 | −0.101062 | ||||||||
\(461\) | 19.6388 | 0.914671 | 0.457336 | − | 0.889294i | \(-0.348804\pi\) | ||||
0.457336 | + | 0.889294i | \(0.348804\pi\) | |||||||
\(462\) | −0.780237 | −0.0362999 | ||||||||
\(463\) | 6.91455 | 0.321346 | 0.160673 | − | 0.987008i | \(-0.448634\pi\) | ||||
0.160673 | + | 0.987008i | \(0.448634\pi\) | |||||||
\(464\) | −1.35794 | −0.0630406 | ||||||||
\(465\) | 1.50570 | 0.0698252 | ||||||||
\(466\) | 19.0509 | 0.882516 | ||||||||
\(467\) | 4.65442 | 0.215381 | 0.107691 | − | 0.994184i | \(-0.465654\pi\) | ||||
0.107691 | + | 0.994184i | \(0.465654\pi\) | |||||||
\(468\) | 11.3906 | 0.526531 | ||||||||
\(469\) | −14.9312 | −0.689460 | ||||||||
\(470\) | 3.51558 | 0.162161 | ||||||||
\(471\) | −8.77909 | −0.404519 | ||||||||
\(472\) | 12.1732 | 0.560317 | ||||||||
\(473\) | −8.59700 | −0.395290 | ||||||||
\(474\) | −7.65378 | −0.351550 | ||||||||
\(475\) | −7.51631 | −0.344872 | ||||||||
\(476\) | −3.32206 | −0.152266 | ||||||||
\(477\) | −29.7202 | −1.36079 | ||||||||
\(478\) | −14.2195 | −0.650385 | ||||||||
\(479\) | −19.0202 | −0.869054 | −0.434527 | − | 0.900659i | \(-0.643084\pi\) | ||||
−0.434527 | + | 0.900659i | \(0.643084\pi\) | |||||||
\(480\) | −0.548857 | −0.0250518 | ||||||||
\(481\) | 34.7085 | 1.58257 | ||||||||
\(482\) | 25.0784 | 1.14229 | ||||||||
\(483\) | 2.22083 | 0.101051 | ||||||||
\(484\) | −10.4201 | −0.473641 | ||||||||
\(485\) | 2.83378 | 0.128675 | ||||||||
\(486\) | 12.8849 | 0.584469 | ||||||||
\(487\) | 2.44044 | 0.110587 | 0.0552934 | − | 0.998470i | \(-0.482391\pi\) | ||||
0.0552934 | + | 0.998470i | \(0.482391\pi\) | |||||||
\(488\) | −6.48721 | −0.293662 | ||||||||
\(489\) | −3.88529 | −0.175699 | ||||||||
\(490\) | −3.51520 | −0.158800 | ||||||||
\(491\) | 19.6388 | 0.886287 | 0.443144 | − | 0.896451i | \(-0.353863\pi\) | ||||
0.443144 | + | 0.896451i | \(0.353863\pi\) | |||||||
\(492\) | 6.55934 | 0.295718 | ||||||||
\(493\) | −2.41656 | −0.108837 | ||||||||
\(494\) | −31.7240 | −1.42733 | ||||||||
\(495\) | 2.05514 | 0.0923719 | ||||||||
\(496\) | 2.74334 | 0.123180 | ||||||||
\(497\) | 8.42422 | 0.377878 | ||||||||
\(498\) | −0.0321989 | −0.00144287 | ||||||||
\(499\) | 43.4800 | 1.94643 | 0.973216 | − | 0.229893i | \(-0.0738376\pi\) | ||||
0.973216 | + | 0.229893i | \(0.0738376\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −6.70215 | −0.299430 | ||||||||
\(502\) | 16.2113 | 0.723544 | ||||||||
\(503\) | −23.3736 | −1.04218 | −0.521089 | − | 0.853502i | \(-0.674474\pi\) | ||||
−0.521089 | + | 0.853502i | \(0.674474\pi\) | |||||||
\(504\) | −5.03794 | −0.224408 | ||||||||
\(505\) | −0.212072 | −0.00943709 | ||||||||
\(506\) | −1.65062 | −0.0733790 | ||||||||
\(507\) | −2.64230 | −0.117349 | ||||||||
\(508\) | −21.3259 | −0.946183 | ||||||||
\(509\) | −26.8089 | −1.18828 | −0.594142 | − | 0.804360i | \(-0.702508\pi\) | ||||
−0.594142 | + | 0.804360i | \(0.702508\pi\) | |||||||
\(510\) | −0.976737 | −0.0432506 | ||||||||
\(511\) | −30.4667 | −1.34777 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −23.5095 | −1.03797 | ||||||||
\(514\) | 4.87073 | 0.214839 | ||||||||
\(515\) | −1.08106 | −0.0476372 | ||||||||
\(516\) | 6.19622 | 0.272774 | ||||||||
\(517\) | 2.67717 | 0.117742 | ||||||||
\(518\) | −15.3512 | −0.674492 | ||||||||
\(519\) | 9.50389 | 0.417174 | ||||||||
\(520\) | −4.22069 | −0.185089 | ||||||||
\(521\) | 1.15191 | 0.0504660 | 0.0252330 | − | 0.999682i | \(-0.491967\pi\) | ||||
0.0252330 | + | 0.999682i | \(0.491967\pi\) | |||||||
\(522\) | −3.66474 | −0.160401 | ||||||||
\(523\) | 13.9791 | 0.611265 | 0.305632 | − | 0.952150i | \(-0.401132\pi\) | ||||
0.305632 | + | 0.952150i | \(0.401132\pi\) | |||||||
\(524\) | 11.9874 | 0.523674 | ||||||||
\(525\) | 1.02458 | 0.0447165 | ||||||||
\(526\) | 0.362645 | 0.0158121 | ||||||||
\(527\) | 4.88201 | 0.212664 | ||||||||
\(528\) | −0.417963 | −0.0181895 | ||||||||
\(529\) | −18.3017 | −0.795728 | ||||||||
\(530\) | 11.0125 | 0.478354 | ||||||||
\(531\) | 32.8525 | 1.42568 | ||||||||
\(532\) | 14.0312 | 0.608328 | ||||||||
\(533\) | 50.4410 | 2.18484 | ||||||||
\(534\) | −0.0673242 | −0.00291340 | ||||||||
\(535\) | −11.8016 | −0.510229 | ||||||||
\(536\) | −7.99847 | −0.345481 | ||||||||
\(537\) | −5.93532 | −0.256128 | ||||||||
\(538\) | 20.9121 | 0.901586 | ||||||||
\(539\) | −2.67688 | −0.115301 | ||||||||
\(540\) | −3.12780 | −0.134599 | ||||||||
\(541\) | −15.9678 | −0.686510 | −0.343255 | − | 0.939242i | \(-0.611530\pi\) | ||||
−0.343255 | + | 0.939242i | \(0.611530\pi\) | |||||||
\(542\) | 9.56595 | 0.410893 | ||||||||
\(543\) | −8.09231 | −0.347274 | ||||||||
\(544\) | −1.77958 | −0.0762990 | ||||||||
\(545\) | −18.0977 | −0.775220 | ||||||||
\(546\) | 4.32445 | 0.185069 | ||||||||
\(547\) | −20.7081 | −0.885413 | −0.442706 | − | 0.896667i | \(-0.645982\pi\) | ||||
−0.442706 | + | 0.896667i | \(0.645982\pi\) | |||||||
\(548\) | −8.61417 | −0.367979 | ||||||||
\(549\) | −17.5074 | −0.747197 | ||||||||
\(550\) | −0.761515 | −0.0324711 | ||||||||
\(551\) | 10.2067 | 0.434819 | ||||||||
\(552\) | 1.18967 | 0.0506358 | ||||||||
\(553\) | 26.0319 | 1.10699 | ||||||||
\(554\) | 5.26163 | 0.223545 | ||||||||
\(555\) | −4.51348 | −0.191587 | ||||||||
\(556\) | 0.313769 | 0.0133068 | ||||||||
\(557\) | −31.3637 | −1.32892 | −0.664461 | − | 0.747323i | \(-0.731339\pi\) | ||||
−0.664461 | + | 0.747323i | \(0.731339\pi\) | |||||||
\(558\) | 7.40361 | 0.313420 | ||||||||
\(559\) | 47.6487 | 2.01533 | ||||||||
\(560\) | 1.86676 | 0.0788851 | ||||||||
\(561\) | −0.743800 | −0.0314033 | ||||||||
\(562\) | 15.0816 | 0.636178 | ||||||||
\(563\) | −28.1159 | −1.18494 | −0.592471 | − | 0.805592i | \(-0.701848\pi\) | ||||
−0.592471 | + | 0.805592i | \(0.701848\pi\) | |||||||
\(564\) | −1.92955 | −0.0812486 | ||||||||
\(565\) | 6.50418 | 0.273633 | ||||||||
\(566\) | −21.4410 | −0.901231 | ||||||||
\(567\) | −11.9091 | −0.500136 | ||||||||
\(568\) | 4.51275 | 0.189351 | ||||||||
\(569\) | 23.5546 | 0.987460 | 0.493730 | − | 0.869615i | \(-0.335633\pi\) | ||||
0.493730 | + | 0.869615i | \(0.335633\pi\) | |||||||
\(570\) | 4.12537 | 0.172793 | ||||||||
\(571\) | −25.2957 | −1.05859 | −0.529296 | − | 0.848437i | \(-0.677544\pi\) | ||||
−0.529296 | + | 0.848437i | \(0.677544\pi\) | |||||||
\(572\) | −3.21412 | −0.134389 | ||||||||
\(573\) | 3.78484 | 0.158114 | ||||||||
\(574\) | −22.3095 | −0.931181 | ||||||||
\(575\) | 2.16755 | 0.0903929 | ||||||||
\(576\) | −2.69876 | −0.112448 | ||||||||
\(577\) | −40.5453 | −1.68792 | −0.843961 | − | 0.536404i | \(-0.819782\pi\) | ||||
−0.843961 | + | 0.536404i | \(0.819782\pi\) | |||||||
\(578\) | 13.8331 | 0.575380 | ||||||||
\(579\) | −6.34811 | −0.263818 | ||||||||
\(580\) | 1.35794 | 0.0563853 | ||||||||
\(581\) | 0.109514 | 0.00454342 | ||||||||
\(582\) | −1.55534 | −0.0644709 | ||||||||
\(583\) | 8.38622 | 0.347322 | ||||||||
\(584\) | −16.3206 | −0.675351 | ||||||||
\(585\) | −11.3906 | −0.470944 | ||||||||
\(586\) | 2.88070 | 0.119001 | ||||||||
\(587\) | 8.72727 | 0.360213 | 0.180106 | − | 0.983647i | \(-0.442356\pi\) | ||||
0.180106 | + | 0.983647i | \(0.442356\pi\) | |||||||
\(588\) | 1.92934 | 0.0795646 | ||||||||
\(589\) | −20.6198 | −0.849624 | ||||||||
\(590\) | −12.1732 | −0.501163 | ||||||||
\(591\) | −13.7510 | −0.565642 | ||||||||
\(592\) | −8.22343 | −0.337981 | ||||||||
\(593\) | 44.2149 | 1.81569 | 0.907844 | − | 0.419308i | \(-0.137727\pi\) | ||||
0.907844 | + | 0.419308i | \(0.137727\pi\) | |||||||
\(594\) | −2.38187 | −0.0977292 | ||||||||
\(595\) | 3.32206 | 0.136191 | ||||||||
\(596\) | −17.3878 | −0.712234 | ||||||||
\(597\) | −5.56381 | −0.227711 | ||||||||
\(598\) | 9.14853 | 0.374111 | ||||||||
\(599\) | −26.3992 | −1.07864 | −0.539322 | − | 0.842100i | \(-0.681319\pi\) | ||||
−0.539322 | + | 0.842100i | \(0.681319\pi\) | |||||||
\(600\) | 0.548857 | 0.0224070 | ||||||||
\(601\) | 13.0659 | 0.532970 | 0.266485 | − | 0.963839i | \(-0.414138\pi\) | ||||
0.266485 | + | 0.963839i | \(0.414138\pi\) | |||||||
\(602\) | −21.0745 | −0.858932 | ||||||||
\(603\) | −21.5859 | −0.879046 | ||||||||
\(604\) | 11.6514 | 0.474088 | ||||||||
\(605\) | 10.4201 | 0.423637 | ||||||||
\(606\) | 0.116397 | 0.00472832 | ||||||||
\(607\) | −0.0516183 | −0.00209512 | −0.00104756 | − | 0.999999i | \(-0.500333\pi\) | ||||
−0.00104756 | + | 0.999999i | \(0.500333\pi\) | |||||||
\(608\) | 7.51631 | 0.304826 | ||||||||
\(609\) | −1.39132 | −0.0563792 | ||||||||
\(610\) | 6.48721 | 0.262659 | ||||||||
\(611\) | −14.8381 | −0.600287 | ||||||||
\(612\) | −4.80266 | −0.194136 | ||||||||
\(613\) | −18.0550 | −0.729234 | −0.364617 | − | 0.931158i | \(-0.618800\pi\) | ||||
−0.364617 | + | 0.931158i | \(0.618800\pi\) | |||||||
\(614\) | 17.1239 | 0.691065 | ||||||||
\(615\) | −6.55934 | −0.264498 | ||||||||
\(616\) | 1.42157 | 0.0572766 | ||||||||
\(617\) | 19.9740 | 0.804124 | 0.402062 | − | 0.915612i | \(-0.368294\pi\) | ||||
0.402062 | + | 0.915612i | \(0.368294\pi\) | |||||||
\(618\) | 0.593347 | 0.0238679 | ||||||||
\(619\) | 10.9321 | 0.439397 | 0.219698 | − | 0.975568i | \(-0.429493\pi\) | ||||
0.219698 | + | 0.975568i | \(0.429493\pi\) | |||||||
\(620\) | −2.74334 | −0.110175 | ||||||||
\(621\) | 6.77965 | 0.272058 | ||||||||
\(622\) | 16.7400 | 0.671213 | ||||||||
\(623\) | 0.228982 | 0.00917397 | ||||||||
\(624\) | 2.31655 | 0.0927363 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 12.5325 | 0.500899 | ||||||||
\(627\) | 3.14154 | 0.125461 | ||||||||
\(628\) | 15.9952 | 0.638279 | ||||||||
\(629\) | −14.6343 | −0.583507 | ||||||||
\(630\) | 5.03794 | 0.200716 | ||||||||
\(631\) | −25.8454 | −1.02889 | −0.514445 | − | 0.857523i | \(-0.672002\pi\) | ||||
−0.514445 | + | 0.857523i | \(0.672002\pi\) | |||||||
\(632\) | 13.9449 | 0.554700 | ||||||||
\(633\) | −6.02947 | −0.239650 | ||||||||
\(634\) | −33.5037 | −1.33060 | ||||||||
\(635\) | 21.3259 | 0.846292 | ||||||||
\(636\) | −6.04431 | −0.239672 | ||||||||
\(637\) | 14.8366 | 0.587846 | ||||||||
\(638\) | 1.03409 | 0.0409400 | ||||||||
\(639\) | 12.1788 | 0.481786 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 28.3830 | 1.12106 | 0.560531 | − | 0.828133i | \(-0.310597\pi\) | ||||
0.560531 | + | 0.828133i | \(0.310597\pi\) | |||||||
\(642\) | 6.47740 | 0.255643 | ||||||||
\(643\) | −9.24838 | −0.364720 | −0.182360 | − | 0.983232i | \(-0.558374\pi\) | ||||
−0.182360 | + | 0.983232i | \(0.558374\pi\) | |||||||
\(644\) | −4.04629 | −0.159446 | ||||||||
\(645\) | −6.19622 | −0.243976 | ||||||||
\(646\) | 13.3759 | 0.526268 | ||||||||
\(647\) | 15.2499 | 0.599537 | 0.299769 | − | 0.954012i | \(-0.403091\pi\) | ||||
0.299769 | + | 0.954012i | \(0.403091\pi\) | |||||||
\(648\) | −6.37956 | −0.250613 | ||||||||
\(649\) | −9.27009 | −0.363883 | ||||||||
\(650\) | 4.22069 | 0.165549 | ||||||||
\(651\) | 2.81079 | 0.110163 | ||||||||
\(652\) | 7.07887 | 0.277230 | ||||||||
\(653\) | −44.5302 | −1.74260 | −0.871301 | − | 0.490750i | \(-0.836723\pi\) | ||||
−0.871301 | + | 0.490750i | \(0.836723\pi\) | |||||||
\(654\) | 9.93304 | 0.388413 | ||||||||
\(655\) | −11.9874 | −0.468388 | ||||||||
\(656\) | −11.9509 | −0.466605 | ||||||||
\(657\) | −44.0453 | −1.71837 | ||||||||
\(658\) | 6.56274 | 0.255842 | ||||||||
\(659\) | −0.386052 | −0.0150384 | −0.00751922 | − | 0.999972i | \(-0.502393\pi\) | ||||
−0.00751922 | + | 0.999972i | \(0.502393\pi\) | |||||||
\(660\) | 0.417963 | 0.0162692 | ||||||||
\(661\) | 26.2732 | 1.02191 | 0.510955 | − | 0.859608i | \(-0.329292\pi\) | ||||
0.510955 | + | 0.859608i | \(0.329292\pi\) | |||||||
\(662\) | −34.0309 | −1.32265 | ||||||||
\(663\) | 4.12250 | 0.160105 | ||||||||
\(664\) | 0.0586654 | 0.00227666 | ||||||||
\(665\) | −14.0312 | −0.544105 | ||||||||
\(666\) | −22.1930 | −0.859962 | ||||||||
\(667\) | −2.94339 | −0.113969 | ||||||||
\(668\) | 12.2111 | 0.472462 | ||||||||
\(669\) | −5.59562 | −0.216339 | ||||||||
\(670\) | 7.99847 | 0.309008 | ||||||||
\(671\) | 4.94011 | 0.190711 | ||||||||
\(672\) | −1.02458 | −0.0395242 | ||||||||
\(673\) | 2.29890 | 0.0886161 | 0.0443081 | − | 0.999018i | \(-0.485892\pi\) | ||||
0.0443081 | + | 0.999018i | \(0.485892\pi\) | |||||||
\(674\) | −17.9001 | −0.689488 | ||||||||
\(675\) | 3.12780 | 0.120389 | ||||||||
\(676\) | 4.81419 | 0.185161 | ||||||||
\(677\) | −24.3399 | −0.935457 | −0.467728 | − | 0.883872i | \(-0.654927\pi\) | ||||
−0.467728 | + | 0.883872i | \(0.654927\pi\) | |||||||
\(678\) | −3.56986 | −0.137100 | ||||||||
\(679\) | 5.29000 | 0.203011 | ||||||||
\(680\) | 1.77958 | 0.0682439 | ||||||||
\(681\) | −10.4921 | −0.402060 | ||||||||
\(682\) | −2.08910 | −0.0799957 | ||||||||
\(683\) | 2.65464 | 0.101577 | 0.0507885 | − | 0.998709i | \(-0.483827\pi\) | ||||
0.0507885 | + | 0.998709i | \(0.483827\pi\) | |||||||
\(684\) | 20.2847 | 0.775604 | ||||||||
\(685\) | 8.61417 | 0.329131 | ||||||||
\(686\) | −19.6294 | −0.749453 | ||||||||
\(687\) | −6.99516 | −0.266882 | ||||||||
\(688\) | −11.2893 | −0.430402 | ||||||||
\(689\) | −46.4805 | −1.77077 | ||||||||
\(690\) | −1.18967 | −0.0452900 | ||||||||
\(691\) | 0.454025 | 0.0172719 | 0.00863596 | − | 0.999963i | \(-0.497251\pi\) | ||||
0.00863596 | + | 0.999963i | \(0.497251\pi\) | |||||||
\(692\) | −17.3158 | −0.658248 | ||||||||
\(693\) | 3.83647 | 0.145735 | ||||||||
\(694\) | 12.1406 | 0.460850 | ||||||||
\(695\) | −0.313769 | −0.0119019 | ||||||||
\(696\) | −0.745313 | −0.0282510 | ||||||||
\(697\) | −21.2677 | −0.805570 | ||||||||
\(698\) | 22.3750 | 0.846907 | ||||||||
\(699\) | 10.4562 | 0.395490 | ||||||||
\(700\) | −1.86676 | −0.0705570 | ||||||||
\(701\) | −40.8562 | −1.54312 | −0.771558 | − | 0.636159i | \(-0.780522\pi\) | ||||
−0.771558 | + | 0.636159i | \(0.780522\pi\) | |||||||
\(702\) | 13.2015 | 0.498257 | ||||||||
\(703\) | 61.8098 | 2.33120 | ||||||||
\(704\) | 0.761515 | 0.0287007 | ||||||||
\(705\) | 1.92955 | 0.0726709 | ||||||||
\(706\) | −19.9913 | −0.752382 | ||||||||
\(707\) | −0.395888 | −0.0148889 | ||||||||
\(708\) | 6.68135 | 0.251100 | ||||||||
\(709\) | −19.0442 | −0.715219 | −0.357609 | − | 0.933871i | \(-0.616408\pi\) | ||||
−0.357609 | + | 0.933871i | \(0.616408\pi\) | |||||||
\(710\) | −4.51275 | −0.169360 | ||||||||
\(711\) | 37.6340 | 1.41139 | ||||||||
\(712\) | 0.122663 | 0.00459698 | ||||||||
\(713\) | 5.94632 | 0.222691 | ||||||||
\(714\) | −1.82333 | −0.0682366 | ||||||||
\(715\) | 3.21412 | 0.120201 | ||||||||
\(716\) | 10.8140 | 0.404137 | ||||||||
\(717\) | −7.80447 | −0.291463 | ||||||||
\(718\) | 18.1630 | 0.677838 | ||||||||
\(719\) | −36.0186 | −1.34327 | −0.671633 | − | 0.740884i | \(-0.734407\pi\) | ||||
−0.671633 | + | 0.740884i | \(0.734407\pi\) | |||||||
\(720\) | 2.69876 | 0.100577 | ||||||||
\(721\) | −2.01808 | −0.0751573 | ||||||||
\(722\) | −37.4949 | −1.39541 | ||||||||
\(723\) | 13.7645 | 0.511906 | ||||||||
\(724\) | 14.7439 | 0.547954 | ||||||||
\(725\) | −1.35794 | −0.0504325 | ||||||||
\(726\) | −5.71914 | −0.212257 | ||||||||
\(727\) | 3.08100 | 0.114268 | 0.0571339 | − | 0.998367i | \(-0.481804\pi\) | ||||
0.0571339 | + | 0.998367i | \(0.481804\pi\) | |||||||
\(728\) | −7.87902 | −0.292016 | ||||||||
\(729\) | −12.0667 | −0.446916 | ||||||||
\(730\) | 16.3206 | 0.604053 | ||||||||
\(731\) | −20.0903 | −0.743067 | ||||||||
\(732\) | −3.56055 | −0.131602 | ||||||||
\(733\) | −34.1974 | −1.26311 | −0.631556 | − | 0.775330i | \(-0.717583\pi\) | ||||
−0.631556 | + | 0.775330i | \(0.717583\pi\) | |||||||
\(734\) | −19.8279 | −0.731861 | ||||||||
\(735\) | −1.92934 | −0.0711648 | ||||||||
\(736\) | −2.16755 | −0.0798968 | ||||||||
\(737\) | 6.09096 | 0.224363 | ||||||||
\(738\) | −32.2526 | −1.18723 | ||||||||
\(739\) | 50.3886 | 1.85357 | 0.926787 | − | 0.375587i | \(-0.122559\pi\) | ||||
0.926787 | + | 0.375587i | \(0.122559\pi\) | |||||||
\(740\) | 8.22343 | 0.302299 | ||||||||
\(741\) | −17.4119 | −0.639643 | ||||||||
\(742\) | 20.5578 | 0.754700 | ||||||||
\(743\) | −35.6132 | −1.30652 | −0.653260 | − | 0.757134i | \(-0.726599\pi\) | ||||
−0.653260 | + | 0.757134i | \(0.726599\pi\) | |||||||
\(744\) | 1.50570 | 0.0552017 | ||||||||
\(745\) | 17.3878 | 0.637041 | ||||||||
\(746\) | 4.64418 | 0.170036 | ||||||||
\(747\) | 0.158324 | 0.00579276 | ||||||||
\(748\) | 1.35518 | 0.0495503 | ||||||||
\(749\) | −22.0308 | −0.804989 | ||||||||
\(750\) | −0.548857 | −0.0200414 | ||||||||
\(751\) | 29.9318 | 1.09223 | 0.546114 | − | 0.837711i | \(-0.316107\pi\) | ||||
0.546114 | + | 0.837711i | \(0.316107\pi\) | |||||||
\(752\) | 3.51558 | 0.128200 | ||||||||
\(753\) | 8.89766 | 0.324249 | ||||||||
\(754\) | −5.73143 | −0.208726 | ||||||||
\(755\) | −11.6514 | −0.424037 | ||||||||
\(756\) | −5.83886 | −0.212357 | ||||||||
\(757\) | 2.45166 | 0.0891072 | 0.0445536 | − | 0.999007i | \(-0.485813\pi\) | ||||
0.0445536 | + | 0.999007i | \(0.485813\pi\) | |||||||
\(758\) | −33.5715 | −1.21937 | ||||||||
\(759\) | −0.905953 | −0.0328840 | ||||||||
\(760\) | −7.51631 | −0.272645 | ||||||||
\(761\) | −47.2602 | −1.71318 | −0.856590 | − | 0.515997i | \(-0.827422\pi\) | ||||
−0.856590 | + | 0.515997i | \(0.827422\pi\) | |||||||
\(762\) | −11.7048 | −0.424022 | ||||||||
\(763\) | −33.7841 | −1.22307 | ||||||||
\(764\) | −6.89586 | −0.249483 | ||||||||
\(765\) | 4.80266 | 0.173641 | ||||||||
\(766\) | −12.1617 | −0.439421 | ||||||||
\(767\) | 51.3793 | 1.85520 | ||||||||
\(768\) | −0.548857 | −0.0198052 | ||||||||
\(769\) | −36.5371 | −1.31756 | −0.658781 | − | 0.752335i | \(-0.728927\pi\) | ||||
−0.658781 | + | 0.752335i | \(0.728927\pi\) | |||||||
\(770\) | −1.42157 | −0.0512298 | ||||||||
\(771\) | 2.67333 | 0.0962777 | ||||||||
\(772\) | 11.5661 | 0.416272 | ||||||||
\(773\) | −45.1575 | −1.62420 | −0.812101 | − | 0.583517i | \(-0.801676\pi\) | ||||
−0.812101 | + | 0.583517i | \(0.801676\pi\) | |||||||
\(774\) | −30.4672 | −1.09512 | ||||||||
\(775\) | 2.74334 | 0.0985438 | ||||||||
\(776\) | 2.83378 | 0.101727 | ||||||||
\(777\) | −8.42560 | −0.302267 | ||||||||
\(778\) | 22.6068 | 0.810495 | ||||||||
\(779\) | 89.8267 | 3.21838 | ||||||||
\(780\) | −2.31655 | −0.0829459 | ||||||||
\(781\) | −3.43653 | −0.122969 | ||||||||
\(782\) | −3.85733 | −0.137938 | ||||||||
\(783\) | −4.24736 | −0.151788 | ||||||||
\(784\) | −3.51520 | −0.125543 | ||||||||
\(785\) | −15.9952 | −0.570894 | ||||||||
\(786\) | 6.57939 | 0.234679 | ||||||||
\(787\) | 40.5568 | 1.44569 | 0.722847 | − | 0.691008i | \(-0.242833\pi\) | ||||
0.722847 | + | 0.691008i | \(0.242833\pi\) | |||||||
\(788\) | 25.0540 | 0.892511 | ||||||||
\(789\) | 0.199040 | 0.00708602 | ||||||||
\(790\) | −13.9449 | −0.496139 | ||||||||
\(791\) | 12.1418 | 0.431712 | ||||||||
\(792\) | 2.05514 | 0.0730264 | ||||||||
\(793\) | −27.3805 | −0.972309 | ||||||||
\(794\) | 8.63801 | 0.306551 | ||||||||
\(795\) | 6.04431 | 0.214369 | ||||||||
\(796\) | 10.1371 | 0.359299 | ||||||||
\(797\) | 14.8745 | 0.526883 | 0.263441 | − | 0.964675i | \(-0.415142\pi\) | ||||
0.263441 | + | 0.964675i | \(0.415142\pi\) | |||||||
\(798\) | 7.70109 | 0.272616 | ||||||||
\(799\) | 6.25626 | 0.221331 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 0.331036 | 0.0116966 | ||||||||
\(802\) | −1.00000 | −0.0353112 | ||||||||
\(803\) | 12.4284 | 0.438588 | ||||||||
\(804\) | −4.39001 | −0.154824 | ||||||||
\(805\) | 4.04629 | 0.142613 | ||||||||
\(806\) | 11.5788 | 0.407845 | ||||||||
\(807\) | 11.4778 | 0.404036 | ||||||||
\(808\) | −0.212072 | −0.00746068 | ||||||||
\(809\) | −7.79676 | −0.274120 | −0.137060 | − | 0.990563i | \(-0.543765\pi\) | ||||
−0.137060 | + | 0.990563i | \(0.543765\pi\) | |||||||
\(810\) | 6.37956 | 0.224155 | ||||||||
\(811\) | −31.8247 | −1.11752 | −0.558759 | − | 0.829330i | \(-0.688722\pi\) | ||||
−0.558759 | + | 0.829330i | \(0.688722\pi\) | |||||||
\(812\) | 2.53495 | 0.0889591 | ||||||||
\(813\) | 5.25033 | 0.184137 | ||||||||
\(814\) | 6.26227 | 0.219492 | ||||||||
\(815\) | −7.07887 | −0.247962 | ||||||||
\(816\) | −0.976737 | −0.0341926 | ||||||||
\(817\) | 84.8541 | 2.96867 | ||||||||
\(818\) | −24.3843 | −0.852578 | ||||||||
\(819\) | −21.2636 | −0.743009 | ||||||||
\(820\) | 11.9509 | 0.417344 | ||||||||
\(821\) | 23.2473 | 0.811337 | 0.405669 | − | 0.914020i | \(-0.367039\pi\) | ||||
0.405669 | + | 0.914020i | \(0.367039\pi\) | |||||||
\(822\) | −4.72795 | −0.164906 | ||||||||
\(823\) | 32.4608 | 1.13151 | 0.565757 | − | 0.824572i | \(-0.308584\pi\) | ||||
0.565757 | + | 0.824572i | \(0.308584\pi\) | |||||||
\(824\) | −1.08106 | −0.0376605 | ||||||||
\(825\) | −0.417963 | −0.0145516 | ||||||||
\(826\) | −22.7245 | −0.790686 | ||||||||
\(827\) | 42.7624 | 1.48699 | 0.743496 | − | 0.668740i | \(-0.233166\pi\) | ||||
0.743496 | + | 0.668740i | \(0.233166\pi\) | |||||||
\(828\) | −5.84968 | −0.203290 | ||||||||
\(829\) | −16.9781 | −0.589674 | −0.294837 | − | 0.955548i | \(-0.595265\pi\) | ||||
−0.294837 | + | 0.955548i | \(0.595265\pi\) | |||||||
\(830\) | −0.0586654 | −0.00203630 | ||||||||
\(831\) | 2.88788 | 0.100180 | ||||||||
\(832\) | −4.22069 | −0.146326 | ||||||||
\(833\) | −6.25559 | −0.216743 | ||||||||
\(834\) | 0.172214 | 0.00596328 | ||||||||
\(835\) | −12.2111 | −0.422583 | ||||||||
\(836\) | −5.72378 | −0.197961 | ||||||||
\(837\) | 8.58063 | 0.296590 | ||||||||
\(838\) | 6.20803 | 0.214453 | ||||||||
\(839\) | −0.805427 | −0.0278064 | −0.0139032 | − | 0.999903i | \(-0.504426\pi\) | ||||
−0.0139032 | + | 0.999903i | \(0.504426\pi\) | |||||||
\(840\) | 1.02458 | 0.0353515 | ||||||||
\(841\) | −27.1560 | −0.936414 | ||||||||
\(842\) | −36.0429 | −1.24212 | ||||||||
\(843\) | 8.27762 | 0.285096 | ||||||||
\(844\) | 10.9855 | 0.378137 | ||||||||
\(845\) | −4.81419 | −0.165613 | ||||||||
\(846\) | 9.48768 | 0.326193 | ||||||||
\(847\) | 19.4518 | 0.668373 | ||||||||
\(848\) | 11.0125 | 0.378172 | ||||||||
\(849\) | −11.7680 | −0.403877 | ||||||||
\(850\) | −1.77958 | −0.0610392 | ||||||||
\(851\) | −17.8247 | −0.611021 | ||||||||
\(852\) | 2.47685 | 0.0848555 | ||||||||
\(853\) | 19.5314 | 0.668743 | 0.334372 | − | 0.942441i | \(-0.391476\pi\) | ||||
0.334372 | + | 0.942441i | \(0.391476\pi\) | |||||||
\(854\) | 12.1101 | 0.414398 | ||||||||
\(855\) | −20.2847 | −0.693721 | ||||||||
\(856\) | −11.8016 | −0.403371 | ||||||||
\(857\) | −53.5256 | −1.82840 | −0.914199 | − | 0.405265i | \(-0.867179\pi\) | ||||
−0.914199 | + | 0.405265i | \(0.867179\pi\) | |||||||
\(858\) | −1.76409 | −0.0602250 | ||||||||
\(859\) | −16.8448 | −0.574736 | −0.287368 | − | 0.957820i | \(-0.592780\pi\) | ||||
−0.287368 | + | 0.957820i | \(0.592780\pi\) | |||||||
\(860\) | 11.2893 | 0.384963 | ||||||||
\(861\) | −12.2447 | −0.417299 | ||||||||
\(862\) | −26.0536 | −0.887391 | ||||||||
\(863\) | 23.2906 | 0.792823 | 0.396411 | − | 0.918073i | \(-0.370255\pi\) | ||||
0.396411 | + | 0.918073i | \(0.370255\pi\) | |||||||
\(864\) | −3.12780 | −0.106410 | ||||||||
\(865\) | 17.3158 | 0.588755 | ||||||||
\(866\) | 0.698973 | 0.0237521 | ||||||||
\(867\) | 7.59238 | 0.257851 | ||||||||
\(868\) | −5.12117 | −0.173824 | ||||||||
\(869\) | −10.6193 | −0.360235 | ||||||||
\(870\) | 0.745313 | 0.0252685 | ||||||||
\(871\) | −33.7590 | −1.14388 | ||||||||
\(872\) | −18.0977 | −0.612865 | ||||||||
\(873\) | 7.64768 | 0.258835 | ||||||||
\(874\) | 16.2919 | 0.551083 | ||||||||
\(875\) | 1.86676 | 0.0631081 | ||||||||
\(876\) | −8.95767 | −0.302652 | ||||||||
\(877\) | −32.8314 | −1.10864 | −0.554319 | − | 0.832305i | \(-0.687021\pi\) | ||||
−0.554319 | + | 0.832305i | \(0.687021\pi\) | |||||||
\(878\) | 12.6681 | 0.427527 | ||||||||
\(879\) | 1.58109 | 0.0533288 | ||||||||
\(880\) | −0.761515 | −0.0256707 | ||||||||
\(881\) | −40.6644 | −1.37002 | −0.685010 | − | 0.728534i | \(-0.740202\pi\) | ||||
−0.685010 | + | 0.728534i | \(0.740202\pi\) | |||||||
\(882\) | −9.48666 | −0.319433 | ||||||||
\(883\) | −7.63075 | −0.256795 | −0.128398 | − | 0.991723i | \(-0.540983\pi\) | ||||
−0.128398 | + | 0.991723i | \(0.540983\pi\) | |||||||
\(884\) | −7.51107 | −0.252624 | ||||||||
\(885\) | −6.68135 | −0.224591 | ||||||||
\(886\) | −25.6499 | −0.861725 | ||||||||
\(887\) | −50.0573 | −1.68076 | −0.840380 | − | 0.541998i | \(-0.817668\pi\) | ||||
−0.840380 | + | 0.541998i | \(0.817668\pi\) | |||||||
\(888\) | −4.51348 | −0.151463 | ||||||||
\(889\) | 39.8103 | 1.33520 | ||||||||
\(890\) | −0.122663 | −0.00411166 | ||||||||
\(891\) | 4.85813 | 0.162753 | ||||||||
\(892\) | 10.1950 | 0.341355 | ||||||||
\(893\) | −26.4241 | −0.884250 | ||||||||
\(894\) | −9.54343 | −0.319180 | ||||||||
\(895\) | −10.8140 | −0.361471 | ||||||||
\(896\) | 1.86676 | 0.0623642 | ||||||||
\(897\) | 5.02123 | 0.167654 | ||||||||
\(898\) | −34.0187 | −1.13522 | ||||||||
\(899\) | −3.72529 | −0.124245 | ||||||||
\(900\) | −2.69876 | −0.0899585 | ||||||||
\(901\) | 19.5977 | 0.652895 | ||||||||
\(902\) | 9.10080 | 0.303024 | ||||||||
\(903\) | −11.5669 | −0.384922 | ||||||||
\(904\) | 6.50418 | 0.216326 | ||||||||
\(905\) | −14.7439 | −0.490105 | ||||||||
\(906\) | 6.39494 | 0.212458 | ||||||||
\(907\) | −15.6195 | −0.518637 | −0.259318 | − | 0.965792i | \(-0.583498\pi\) | ||||
−0.259318 | + | 0.965792i | \(0.583498\pi\) | |||||||
\(908\) | 19.1164 | 0.634398 | ||||||||
\(909\) | −0.572331 | −0.0189830 | ||||||||
\(910\) | 7.87902 | 0.261187 | ||||||||
\(911\) | −5.79468 | −0.191986 | −0.0959932 | − | 0.995382i | \(-0.530603\pi\) | ||||
−0.0959932 | + | 0.995382i | \(0.530603\pi\) | |||||||
\(912\) | 4.12537 | 0.136605 | ||||||||
\(913\) | −0.0446746 | −0.00147851 | ||||||||
\(914\) | −15.8036 | −0.522736 | ||||||||
\(915\) | 3.56055 | 0.117708 | ||||||||
\(916\) | 12.7450 | 0.421105 | ||||||||
\(917\) | −22.3777 | −0.738977 | ||||||||
\(918\) | −5.56618 | −0.183711 | ||||||||
\(919\) | −57.0861 | −1.88310 | −0.941549 | − | 0.336877i | \(-0.890629\pi\) | ||||
−0.941549 | + | 0.336877i | \(0.890629\pi\) | |||||||
\(920\) | 2.16755 | 0.0714619 | ||||||||
\(921\) | 9.39857 | 0.309693 | ||||||||
\(922\) | −19.6388 | −0.646770 | ||||||||
\(923\) | 19.0469 | 0.626936 | ||||||||
\(924\) | 0.780237 | 0.0256679 | ||||||||
\(925\) | −8.22343 | −0.270385 | ||||||||
\(926\) | −6.91455 | −0.227226 | ||||||||
\(927\) | −2.91752 | −0.0958239 | ||||||||
\(928\) | 1.35794 | 0.0445765 | ||||||||
\(929\) | −32.7557 | −1.07468 | −0.537340 | − | 0.843366i | \(-0.680571\pi\) | ||||
−0.537340 | + | 0.843366i | \(0.680571\pi\) | |||||||
\(930\) | −1.50570 | −0.0493739 | ||||||||
\(931\) | 26.4213 | 0.865923 | ||||||||
\(932\) | −19.0509 | −0.624033 | ||||||||
\(933\) | 9.18786 | 0.300797 | ||||||||
\(934\) | −4.65442 | −0.152297 | ||||||||
\(935\) | −1.35518 | −0.0443192 | ||||||||
\(936\) | −11.3906 | −0.372314 | ||||||||
\(937\) | 19.3678 | 0.632719 | 0.316360 | − | 0.948639i | \(-0.397539\pi\) | ||||
0.316360 | + | 0.948639i | \(0.397539\pi\) | |||||||
\(938\) | 14.9312 | 0.487522 | ||||||||
\(939\) | 6.87854 | 0.224473 | ||||||||
\(940\) | −3.51558 | −0.114665 | ||||||||
\(941\) | 10.1407 | 0.330576 | 0.165288 | − | 0.986245i | \(-0.447145\pi\) | ||||
0.165288 | + | 0.986245i | \(0.447145\pi\) | |||||||
\(942\) | 8.77909 | 0.286038 | ||||||||
\(943\) | −25.9041 | −0.843555 | ||||||||
\(944\) | −12.1732 | −0.396204 | ||||||||
\(945\) | 5.83886 | 0.189938 | ||||||||
\(946\) | 8.59700 | 0.279513 | ||||||||
\(947\) | −17.8730 | −0.580796 | −0.290398 | − | 0.956906i | \(-0.593788\pi\) | ||||
−0.290398 | + | 0.956906i | \(0.593788\pi\) | |||||||
\(948\) | 7.65378 | 0.248583 | ||||||||
\(949\) | −68.8841 | −2.23607 | ||||||||
\(950\) | 7.51631 | 0.243861 | ||||||||
\(951\) | −18.3887 | −0.596296 | ||||||||
\(952\) | 3.32206 | 0.107669 | ||||||||
\(953\) | −43.4985 | −1.40905 | −0.704527 | − | 0.709677i | \(-0.748841\pi\) | ||||
−0.704527 | + | 0.709677i | \(0.748841\pi\) | |||||||
\(954\) | 29.7202 | 0.962226 | ||||||||
\(955\) | 6.89586 | 0.223145 | ||||||||
\(956\) | 14.2195 | 0.459892 | ||||||||
\(957\) | 0.567567 | 0.0183468 | ||||||||
\(958\) | 19.0202 | 0.614514 | ||||||||
\(959\) | 16.0806 | 0.519270 | ||||||||
\(960\) | 0.548857 | 0.0177143 | ||||||||
\(961\) | −23.4741 | −0.757228 | ||||||||
\(962\) | −34.7085 | −1.11905 | ||||||||
\(963\) | −31.8497 | −1.02634 | ||||||||
\(964\) | −25.0784 | −0.807721 | ||||||||
\(965\) | −11.5661 | −0.372325 | ||||||||
\(966\) | −2.22083 | −0.0714542 | ||||||||
\(967\) | −33.5502 | −1.07890 | −0.539452 | − | 0.842017i | \(-0.681368\pi\) | ||||
−0.539452 | + | 0.842017i | \(0.681368\pi\) | |||||||
\(968\) | 10.4201 | 0.334915 | ||||||||
\(969\) | 7.34145 | 0.235841 | ||||||||
\(970\) | −2.83378 | −0.0909872 | ||||||||
\(971\) | 57.3589 | 1.84073 | 0.920367 | − | 0.391056i | \(-0.127890\pi\) | ||||
0.920367 | + | 0.391056i | \(0.127890\pi\) | |||||||
\(972\) | −12.8849 | −0.413282 | ||||||||
\(973\) | −0.585732 | −0.0187777 | ||||||||
\(974\) | −2.44044 | −0.0781967 | ||||||||
\(975\) | 2.31655 | 0.0741890 | ||||||||
\(976\) | 6.48721 | 0.207650 | ||||||||
\(977\) | 10.5052 | 0.336092 | 0.168046 | − | 0.985779i | \(-0.446254\pi\) | ||||
0.168046 | + | 0.985779i | \(0.446254\pi\) | |||||||
\(978\) | 3.88529 | 0.124238 | ||||||||
\(979\) | −0.0934095 | −0.00298538 | ||||||||
\(980\) | 3.51520 | 0.112289 | ||||||||
\(981\) | −48.8413 | −1.55938 | ||||||||
\(982\) | −19.6388 | −0.626700 | ||||||||
\(983\) | 27.3192 | 0.871347 | 0.435673 | − | 0.900105i | \(-0.356510\pi\) | ||||
0.435673 | + | 0.900105i | \(0.356510\pi\) | |||||||
\(984\) | −6.55934 | −0.209104 | ||||||||
\(985\) | −25.0540 | −0.798286 | ||||||||
\(986\) | 2.41656 | 0.0769590 | ||||||||
\(987\) | 3.60201 | 0.114653 | ||||||||
\(988\) | 31.7240 | 1.00927 | ||||||||
\(989\) | −24.4701 | −0.778105 | ||||||||
\(990\) | −2.05514 | −0.0653168 | ||||||||
\(991\) | 4.32711 | 0.137455 | 0.0687275 | − | 0.997635i | \(-0.478106\pi\) | ||||
0.0687275 | + | 0.997635i | \(0.478106\pi\) | |||||||
\(992\) | −2.74334 | −0.0871012 | ||||||||
\(993\) | −18.6781 | −0.592732 | ||||||||
\(994\) | −8.42422 | −0.267200 | ||||||||
\(995\) | −10.1371 | −0.321367 | ||||||||
\(996\) | 0.0321989 | 0.00102026 | ||||||||
\(997\) | 24.9385 | 0.789811 | 0.394906 | − | 0.918722i | \(-0.370777\pi\) | ||||
0.394906 | + | 0.918722i | \(0.370777\pi\) | |||||||
\(998\) | −43.4800 | −1.37634 | ||||||||
\(999\) | −25.7212 | −0.813784 |
(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 | 4010.2.a.l.1.6 | ✓ | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4010.2.a.l.1.6 | ✓ | 17 | 1.1 | even | 1 | trivial |