Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.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: | \(64.1518129839\) |
Analytic rank: | \(1\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 6 x^{13} - 29 x^{12} + 207 x^{11} + 269 x^{10} - 2601 x^{9} - 847 x^{8} + 14851 x^{7} + 678 x^{6} - 39390 x^{5} - 3280 x^{4} + 42456 x^{3} + 10816 x^{2} + \cdots - 2048 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-0.480706\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.480706 | 0.214978 | 0.107489 | − | 0.994206i | \(-0.465719\pi\) | ||||
0.107489 | + | 0.994206i | \(0.465719\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0.765483 | 0.289326 | 0.144663 | − | 0.989481i | \(-0.453790\pi\) | ||||
0.144663 | + | 0.989481i | \(0.453790\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.480706 | −0.152013 | ||||||||
\(11\) | −1.12221 | −0.338359 | −0.169180 | − | 0.985585i | \(-0.554112\pi\) | ||||
−0.169180 | + | 0.985585i | \(0.554112\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −0.765483 | −0.204584 | ||||||||
\(15\) | 0.480706 | 0.124118 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.131422 | 0.0318746 | 0.0159373 | − | 0.999873i | \(-0.494927\pi\) | ||||
0.0159373 | + | 0.999873i | \(0.494927\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 7.23270 | 1.65929 | 0.829647 | − | 0.558288i | \(-0.188542\pi\) | ||||
0.829647 | + | 0.558288i | \(0.188542\pi\) | |||||||
\(20\) | 0.480706 | 0.107489 | ||||||||
\(21\) | 0.765483 | 0.167042 | ||||||||
\(22\) | 1.12221 | 0.239256 | ||||||||
\(23\) | −6.47882 | −1.35093 | −0.675464 | − | 0.737393i | \(-0.736057\pi\) | ||||
−0.675464 | + | 0.737393i | \(0.736057\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −4.76892 | −0.953784 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.765483 | 0.144663 | ||||||||
\(29\) | −5.92565 | −1.10036 | −0.550182 | − | 0.835044i | \(-0.685442\pi\) | ||||
−0.550182 | + | 0.835044i | \(0.685442\pi\) | |||||||
\(30\) | −0.480706 | −0.0877645 | ||||||||
\(31\) | 0.823617 | 0.147926 | 0.0739630 | − | 0.997261i | \(-0.476435\pi\) | ||||
0.0739630 | + | 0.997261i | \(0.476435\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.12221 | −0.195352 | ||||||||
\(34\) | −0.131422 | −0.0225387 | ||||||||
\(35\) | 0.367973 | 0.0621987 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −5.74456 | −0.944400 | −0.472200 | − | 0.881491i | \(-0.656540\pi\) | ||||
−0.472200 | + | 0.881491i | \(0.656540\pi\) | |||||||
\(38\) | −7.23270 | −1.17330 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | −0.480706 | −0.0760063 | ||||||||
\(41\) | 9.71768 | 1.51765 | 0.758823 | − | 0.651297i | \(-0.225775\pi\) | ||||
0.758823 | + | 0.651297i | \(0.225775\pi\) | |||||||
\(42\) | −0.765483 | −0.118117 | ||||||||
\(43\) | −1.79479 | −0.273703 | −0.136851 | − | 0.990592i | \(-0.543698\pi\) | ||||
−0.136851 | + | 0.990592i | \(0.543698\pi\) | |||||||
\(44\) | −1.12221 | −0.169180 | ||||||||
\(45\) | 0.480706 | 0.0716594 | ||||||||
\(46\) | 6.47882 | 0.955250 | ||||||||
\(47\) | −1.21402 | −0.177083 | −0.0885414 | − | 0.996073i | \(-0.528221\pi\) | ||||
−0.0885414 | + | 0.996073i | \(0.528221\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −6.41404 | −0.916291 | ||||||||
\(50\) | 4.76892 | 0.674427 | ||||||||
\(51\) | 0.131422 | 0.0184028 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | −6.16740 | −0.847158 | −0.423579 | − | 0.905859i | \(-0.639226\pi\) | ||||
−0.423579 | + | 0.905859i | \(0.639226\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −0.539454 | −0.0727399 | ||||||||
\(56\) | −0.765483 | −0.102292 | ||||||||
\(57\) | 7.23270 | 0.957994 | ||||||||
\(58\) | 5.92565 | 0.778076 | ||||||||
\(59\) | −7.84426 | −1.02124 | −0.510618 | − | 0.859808i | \(-0.670583\pi\) | ||||
−0.510618 | + | 0.859808i | \(0.670583\pi\) | |||||||
\(60\) | 0.480706 | 0.0620589 | ||||||||
\(61\) | 8.36385 | 1.07088 | 0.535441 | − | 0.844573i | \(-0.320145\pi\) | ||||
0.535441 | + | 0.844573i | \(0.320145\pi\) | |||||||
\(62\) | −0.823617 | −0.104599 | ||||||||
\(63\) | 0.765483 | 0.0964418 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.480706 | −0.0596243 | ||||||||
\(66\) | 1.12221 | 0.138135 | ||||||||
\(67\) | −12.4809 | −1.52478 | −0.762392 | − | 0.647115i | \(-0.775975\pi\) | ||||
−0.762392 | + | 0.647115i | \(0.775975\pi\) | |||||||
\(68\) | 0.131422 | 0.0159373 | ||||||||
\(69\) | −6.47882 | −0.779959 | ||||||||
\(70\) | −0.367973 | −0.0439811 | ||||||||
\(71\) | −16.6763 | −1.97911 | −0.989557 | − | 0.144140i | \(-0.953958\pi\) | ||||
−0.989557 | + | 0.144140i | \(0.953958\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −2.44935 | −0.286675 | −0.143337 | − | 0.989674i | \(-0.545783\pi\) | ||||
−0.143337 | + | 0.989674i | \(0.545783\pi\) | |||||||
\(74\) | 5.74456 | 0.667792 | ||||||||
\(75\) | −4.76892 | −0.550668 | ||||||||
\(76\) | 7.23270 | 0.829647 | ||||||||
\(77\) | −0.859034 | −0.0978960 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | 7.55695 | 0.850223 | 0.425111 | − | 0.905141i | \(-0.360235\pi\) | ||||
0.425111 | + | 0.905141i | \(0.360235\pi\) | |||||||
\(80\) | 0.480706 | 0.0537446 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −9.71768 | −1.07314 | ||||||||
\(83\) | 14.6910 | 1.61255 | 0.806273 | − | 0.591544i | \(-0.201481\pi\) | ||||
0.806273 | + | 0.591544i | \(0.201481\pi\) | |||||||
\(84\) | 0.765483 | 0.0835211 | ||||||||
\(85\) | 0.0631755 | 0.00685234 | ||||||||
\(86\) | 1.79479 | 0.193537 | ||||||||
\(87\) | −5.92565 | −0.635296 | ||||||||
\(88\) | 1.12221 | 0.119628 | ||||||||
\(89\) | −16.8623 | −1.78740 | −0.893702 | − | 0.448661i | \(-0.851901\pi\) | ||||
−0.893702 | + | 0.448661i | \(0.851901\pi\) | |||||||
\(90\) | −0.480706 | −0.0506709 | ||||||||
\(91\) | −0.765483 | −0.0802445 | ||||||||
\(92\) | −6.47882 | −0.675464 | ||||||||
\(93\) | 0.823617 | 0.0854051 | ||||||||
\(94\) | 1.21402 | 0.125216 | ||||||||
\(95\) | 3.47680 | 0.356712 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 13.3568 | 1.35618 | 0.678089 | − | 0.734980i | \(-0.262809\pi\) | ||||
0.678089 | + | 0.734980i | \(0.262809\pi\) | |||||||
\(98\) | 6.41404 | 0.647915 | ||||||||
\(99\) | −1.12221 | −0.112786 | ||||||||
\(100\) | −4.76892 | −0.476892 | ||||||||
\(101\) | −17.0194 | −1.69350 | −0.846748 | − | 0.531994i | \(-0.821443\pi\) | ||||
−0.846748 | + | 0.531994i | \(0.821443\pi\) | |||||||
\(102\) | −0.131422 | −0.0130127 | ||||||||
\(103\) | 1.00000 | 0.0985329 | ||||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | 0.367973 | 0.0359104 | ||||||||
\(106\) | 6.16740 | 0.599031 | ||||||||
\(107\) | −4.57541 | −0.442321 | −0.221161 | − | 0.975237i | \(-0.570985\pi\) | ||||
−0.221161 | + | 0.975237i | \(0.570985\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 4.28510 | 0.410438 | 0.205219 | − | 0.978716i | \(-0.434209\pi\) | ||||
0.205219 | + | 0.978716i | \(0.434209\pi\) | |||||||
\(110\) | 0.539454 | 0.0514349 | ||||||||
\(111\) | −5.74456 | −0.545249 | ||||||||
\(112\) | 0.765483 | 0.0723314 | ||||||||
\(113\) | 18.0957 | 1.70230 | 0.851151 | − | 0.524921i | \(-0.175905\pi\) | ||||
0.851151 | + | 0.524921i | \(0.175905\pi\) | |||||||
\(114\) | −7.23270 | −0.677404 | ||||||||
\(115\) | −3.11441 | −0.290420 | ||||||||
\(116\) | −5.92565 | −0.550182 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 7.84426 | 0.722123 | ||||||||
\(119\) | 0.100602 | 0.00922213 | ||||||||
\(120\) | −0.480706 | −0.0438823 | ||||||||
\(121\) | −9.74064 | −0.885513 | ||||||||
\(122\) | −8.36385 | −0.757228 | ||||||||
\(123\) | 9.71768 | 0.876214 | ||||||||
\(124\) | 0.823617 | 0.0739630 | ||||||||
\(125\) | −4.69598 | −0.420021 | ||||||||
\(126\) | −0.765483 | −0.0681947 | ||||||||
\(127\) | 1.93648 | 0.171834 | 0.0859172 | − | 0.996302i | \(-0.472618\pi\) | ||||
0.0859172 | + | 0.996302i | \(0.472618\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −1.79479 | −0.158022 | ||||||||
\(130\) | 0.480706 | 0.0421607 | ||||||||
\(131\) | 17.0455 | 1.48928 | 0.744638 | − | 0.667468i | \(-0.232622\pi\) | ||||
0.744638 | + | 0.667468i | \(0.232622\pi\) | |||||||
\(132\) | −1.12221 | −0.0976760 | ||||||||
\(133\) | 5.53651 | 0.480076 | ||||||||
\(134\) | 12.4809 | 1.07819 | ||||||||
\(135\) | 0.480706 | 0.0413726 | ||||||||
\(136\) | −0.131422 | −0.0112694 | ||||||||
\(137\) | −13.6581 | −1.16689 | −0.583447 | − | 0.812151i | \(-0.698296\pi\) | ||||
−0.583447 | + | 0.812151i | \(0.698296\pi\) | |||||||
\(138\) | 6.47882 | 0.551514 | ||||||||
\(139\) | −16.1582 | −1.37052 | −0.685259 | − | 0.728300i | \(-0.740311\pi\) | ||||
−0.685259 | + | 0.728300i | \(0.740311\pi\) | |||||||
\(140\) | 0.367973 | 0.0310994 | ||||||||
\(141\) | −1.21402 | −0.102239 | ||||||||
\(142\) | 16.6763 | 1.39945 | ||||||||
\(143\) | 1.12221 | 0.0938440 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −2.84849 | −0.236555 | ||||||||
\(146\) | 2.44935 | 0.202710 | ||||||||
\(147\) | −6.41404 | −0.529021 | ||||||||
\(148\) | −5.74456 | −0.472200 | ||||||||
\(149\) | −6.45756 | −0.529024 | −0.264512 | − | 0.964382i | \(-0.585211\pi\) | ||||
−0.264512 | + | 0.964382i | \(0.585211\pi\) | |||||||
\(150\) | 4.76892 | 0.389381 | ||||||||
\(151\) | 6.56350 | 0.534130 | 0.267065 | − | 0.963679i | \(-0.413946\pi\) | ||||
0.267065 | + | 0.963679i | \(0.413946\pi\) | |||||||
\(152\) | −7.23270 | −0.586649 | ||||||||
\(153\) | 0.131422 | 0.0106249 | ||||||||
\(154\) | 0.859034 | 0.0692230 | ||||||||
\(155\) | 0.395918 | 0.0318009 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | −4.46960 | −0.356713 | −0.178357 | − | 0.983966i | \(-0.557078\pi\) | ||||
−0.178357 | + | 0.983966i | \(0.557078\pi\) | |||||||
\(158\) | −7.55695 | −0.601198 | ||||||||
\(159\) | −6.16740 | −0.489107 | ||||||||
\(160\) | −0.480706 | −0.0380032 | ||||||||
\(161\) | −4.95943 | −0.390858 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 11.9349 | 0.934817 | 0.467408 | − | 0.884041i | \(-0.345188\pi\) | ||||
0.467408 | + | 0.884041i | \(0.345188\pi\) | |||||||
\(164\) | 9.71768 | 0.758823 | ||||||||
\(165\) | −0.539454 | −0.0419964 | ||||||||
\(166\) | −14.6910 | −1.14024 | ||||||||
\(167\) | 11.7525 | 0.909437 | 0.454719 | − | 0.890635i | \(-0.349740\pi\) | ||||
0.454719 | + | 0.890635i | \(0.349740\pi\) | |||||||
\(168\) | −0.765483 | −0.0590583 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −0.0631755 | −0.00484534 | ||||||||
\(171\) | 7.23270 | 0.553098 | ||||||||
\(172\) | −1.79479 | −0.136851 | ||||||||
\(173\) | −6.62095 | −0.503381 | −0.251691 | − | 0.967808i | \(-0.580987\pi\) | ||||
−0.251691 | + | 0.967808i | \(0.580987\pi\) | |||||||
\(174\) | 5.92565 | 0.449222 | ||||||||
\(175\) | −3.65053 | −0.275954 | ||||||||
\(176\) | −1.12221 | −0.0845899 | ||||||||
\(177\) | −7.84426 | −0.589611 | ||||||||
\(178\) | 16.8623 | 1.26389 | ||||||||
\(179\) | −2.90096 | −0.216828 | −0.108414 | − | 0.994106i | \(-0.534577\pi\) | ||||
−0.108414 | + | 0.994106i | \(0.534577\pi\) | |||||||
\(180\) | 0.480706 | 0.0358297 | ||||||||
\(181\) | 7.61769 | 0.566218 | 0.283109 | − | 0.959088i | \(-0.408634\pi\) | ||||
0.283109 | + | 0.959088i | \(0.408634\pi\) | |||||||
\(182\) | 0.765483 | 0.0567414 | ||||||||
\(183\) | 8.36385 | 0.618274 | ||||||||
\(184\) | 6.47882 | 0.477625 | ||||||||
\(185\) | −2.76145 | −0.203025 | ||||||||
\(186\) | −0.823617 | −0.0603905 | ||||||||
\(187\) | −0.147484 | −0.0107851 | ||||||||
\(188\) | −1.21402 | −0.0885414 | ||||||||
\(189\) | 0.765483 | 0.0556807 | ||||||||
\(190\) | −3.47680 | −0.252234 | ||||||||
\(191\) | −21.2603 | −1.53834 | −0.769169 | − | 0.639045i | \(-0.779330\pi\) | ||||
−0.769169 | + | 0.639045i | \(0.779330\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 2.66290 | 0.191680 | 0.0958400 | − | 0.995397i | \(-0.469446\pi\) | ||||
0.0958400 | + | 0.995397i | \(0.469446\pi\) | |||||||
\(194\) | −13.3568 | −0.958962 | ||||||||
\(195\) | −0.480706 | −0.0344241 | ||||||||
\(196\) | −6.41404 | −0.458145 | ||||||||
\(197\) | 1.87363 | 0.133491 | 0.0667453 | − | 0.997770i | \(-0.478738\pi\) | ||||
0.0667453 | + | 0.997770i | \(0.478738\pi\) | |||||||
\(198\) | 1.12221 | 0.0797521 | ||||||||
\(199\) | 3.88713 | 0.275551 | 0.137776 | − | 0.990463i | \(-0.456005\pi\) | ||||
0.137776 | + | 0.990463i | \(0.456005\pi\) | |||||||
\(200\) | 4.76892 | 0.337214 | ||||||||
\(201\) | −12.4809 | −0.880335 | ||||||||
\(202\) | 17.0194 | 1.19748 | ||||||||
\(203\) | −4.53598 | −0.318364 | ||||||||
\(204\) | 0.131422 | 0.00920140 | ||||||||
\(205\) | 4.67135 | 0.326261 | ||||||||
\(206\) | −1.00000 | −0.0696733 | ||||||||
\(207\) | −6.47882 | −0.450309 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | −8.11661 | −0.561438 | ||||||||
\(210\) | −0.367973 | −0.0253925 | ||||||||
\(211\) | −12.2619 | −0.844143 | −0.422072 | − | 0.906562i | \(-0.638697\pi\) | ||||
−0.422072 | + | 0.906562i | \(0.638697\pi\) | |||||||
\(212\) | −6.16740 | −0.423579 | ||||||||
\(213\) | −16.6763 | −1.14264 | ||||||||
\(214\) | 4.57541 | 0.312768 | ||||||||
\(215\) | −0.862766 | −0.0588402 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0.630465 | 0.0427987 | ||||||||
\(218\) | −4.28510 | −0.290224 | ||||||||
\(219\) | −2.44935 | −0.165512 | ||||||||
\(220\) | −0.539454 | −0.0363700 | ||||||||
\(221\) | −0.131422 | −0.00884042 | ||||||||
\(222\) | 5.74456 | 0.385550 | ||||||||
\(223\) | −18.6606 | −1.24960 | −0.624802 | − | 0.780783i | \(-0.714820\pi\) | ||||
−0.624802 | + | 0.780783i | \(0.714820\pi\) | |||||||
\(224\) | −0.765483 | −0.0511460 | ||||||||
\(225\) | −4.76892 | −0.317928 | ||||||||
\(226\) | −18.0957 | −1.20371 | ||||||||
\(227\) | −4.40861 | −0.292610 | −0.146305 | − | 0.989240i | \(-0.546738\pi\) | ||||
−0.146305 | + | 0.989240i | \(0.546738\pi\) | |||||||
\(228\) | 7.23270 | 0.478997 | ||||||||
\(229\) | −5.24559 | −0.346639 | −0.173319 | − | 0.984866i | \(-0.555449\pi\) | ||||
−0.173319 | + | 0.984866i | \(0.555449\pi\) | |||||||
\(230\) | 3.11441 | 0.205358 | ||||||||
\(231\) | −0.859034 | −0.0565203 | ||||||||
\(232\) | 5.92565 | 0.389038 | ||||||||
\(233\) | 7.38317 | 0.483687 | 0.241844 | − | 0.970315i | \(-0.422248\pi\) | ||||
0.241844 | + | 0.970315i | \(0.422248\pi\) | |||||||
\(234\) | 1.00000 | 0.0653720 | ||||||||
\(235\) | −0.583586 | −0.0380689 | ||||||||
\(236\) | −7.84426 | −0.510618 | ||||||||
\(237\) | 7.55695 | 0.490876 | ||||||||
\(238\) | −0.100602 | −0.00652103 | ||||||||
\(239\) | 11.7084 | 0.757351 | 0.378676 | − | 0.925529i | \(-0.376380\pi\) | ||||
0.378676 | + | 0.925529i | \(0.376380\pi\) | |||||||
\(240\) | 0.480706 | 0.0310294 | ||||||||
\(241\) | −24.2815 | −1.56411 | −0.782054 | − | 0.623211i | \(-0.785828\pi\) | ||||
−0.782054 | + | 0.623211i | \(0.785828\pi\) | |||||||
\(242\) | 9.74064 | 0.626152 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 8.36385 | 0.535441 | ||||||||
\(245\) | −3.08327 | −0.196983 | ||||||||
\(246\) | −9.71768 | −0.619577 | ||||||||
\(247\) | −7.23270 | −0.460205 | ||||||||
\(248\) | −0.823617 | −0.0522997 | ||||||||
\(249\) | 14.6910 | 0.931003 | ||||||||
\(250\) | 4.69598 | 0.297000 | ||||||||
\(251\) | 20.9442 | 1.32198 | 0.660992 | − | 0.750393i | \(-0.270136\pi\) | ||||
0.660992 | + | 0.750393i | \(0.270136\pi\) | |||||||
\(252\) | 0.765483 | 0.0482209 | ||||||||
\(253\) | 7.27061 | 0.457099 | ||||||||
\(254\) | −1.93648 | −0.121505 | ||||||||
\(255\) | 0.0631755 | 0.00395620 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −18.5827 | −1.15916 | −0.579578 | − | 0.814917i | \(-0.696783\pi\) | ||||
−0.579578 | + | 0.814917i | \(0.696783\pi\) | |||||||
\(258\) | 1.79479 | 0.111739 | ||||||||
\(259\) | −4.39737 | −0.273239 | ||||||||
\(260\) | −0.480706 | −0.0298121 | ||||||||
\(261\) | −5.92565 | −0.366788 | ||||||||
\(262\) | −17.0455 | −1.05308 | ||||||||
\(263\) | 0.246017 | 0.0151700 | 0.00758502 | − | 0.999971i | \(-0.497586\pi\) | ||||
0.00758502 | + | 0.999971i | \(0.497586\pi\) | |||||||
\(264\) | 1.12221 | 0.0690673 | ||||||||
\(265\) | −2.96471 | −0.182121 | ||||||||
\(266\) | −5.53651 | −0.339465 | ||||||||
\(267\) | −16.8623 | −1.03196 | ||||||||
\(268\) | −12.4809 | −0.762392 | ||||||||
\(269\) | −21.0144 | −1.28127 | −0.640635 | − | 0.767845i | \(-0.721329\pi\) | ||||
−0.640635 | + | 0.767845i | \(0.721329\pi\) | |||||||
\(270\) | −0.480706 | −0.0292548 | ||||||||
\(271\) | −30.8832 | −1.87602 | −0.938011 | − | 0.346605i | \(-0.887334\pi\) | ||||
−0.938011 | + | 0.346605i | \(0.887334\pi\) | |||||||
\(272\) | 0.131422 | 0.00796865 | ||||||||
\(273\) | −0.765483 | −0.0463292 | ||||||||
\(274\) | 13.6581 | 0.825119 | ||||||||
\(275\) | 5.35174 | 0.322722 | ||||||||
\(276\) | −6.47882 | −0.389979 | ||||||||
\(277\) | 12.7814 | 0.767960 | 0.383980 | − | 0.923341i | \(-0.374553\pi\) | ||||
0.383980 | + | 0.923341i | \(0.374553\pi\) | |||||||
\(278\) | 16.1582 | 0.969102 | ||||||||
\(279\) | 0.823617 | 0.0493086 | ||||||||
\(280\) | −0.367973 | −0.0219906 | ||||||||
\(281\) | 11.4614 | 0.683732 | 0.341866 | − | 0.939749i | \(-0.388941\pi\) | ||||
0.341866 | + | 0.939749i | \(0.388941\pi\) | |||||||
\(282\) | 1.21402 | 0.0722937 | ||||||||
\(283\) | 23.9695 | 1.42484 | 0.712418 | − | 0.701755i | \(-0.247600\pi\) | ||||
0.712418 | + | 0.701755i | \(0.247600\pi\) | |||||||
\(284\) | −16.6763 | −0.989557 | ||||||||
\(285\) | 3.47680 | 0.205948 | ||||||||
\(286\) | −1.12221 | −0.0663578 | ||||||||
\(287\) | 7.43872 | 0.439094 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −16.9827 | −0.998984 | ||||||||
\(290\) | 2.84849 | 0.167269 | ||||||||
\(291\) | 13.3568 | 0.782989 | ||||||||
\(292\) | −2.44935 | −0.143337 | ||||||||
\(293\) | −27.6256 | −1.61390 | −0.806951 | − | 0.590618i | \(-0.798884\pi\) | ||||
−0.806951 | + | 0.590618i | \(0.798884\pi\) | |||||||
\(294\) | 6.41404 | 0.374074 | ||||||||
\(295\) | −3.77078 | −0.219543 | ||||||||
\(296\) | 5.74456 | 0.333896 | ||||||||
\(297\) | −1.12221 | −0.0651173 | ||||||||
\(298\) | 6.45756 | 0.374077 | ||||||||
\(299\) | 6.47882 | 0.374680 | ||||||||
\(300\) | −4.76892 | −0.275334 | ||||||||
\(301\) | −1.37388 | −0.0791892 | ||||||||
\(302\) | −6.56350 | −0.377687 | ||||||||
\(303\) | −17.0194 | −0.977740 | ||||||||
\(304\) | 7.23270 | 0.414824 | ||||||||
\(305\) | 4.02056 | 0.230216 | ||||||||
\(306\) | −0.131422 | −0.00751291 | ||||||||
\(307\) | 31.0759 | 1.77360 | 0.886799 | − | 0.462155i | \(-0.152924\pi\) | ||||
0.886799 | + | 0.462155i | \(0.152924\pi\) | |||||||
\(308\) | −0.859034 | −0.0489480 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | −0.395918 | −0.0224866 | ||||||||
\(311\) | −12.4535 | −0.706171 | −0.353085 | − | 0.935591i | \(-0.614867\pi\) | ||||
−0.353085 | + | 0.935591i | \(0.614867\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | 8.68625 | 0.490976 | 0.245488 | − | 0.969400i | \(-0.421052\pi\) | ||||
0.245488 | + | 0.969400i | \(0.421052\pi\) | |||||||
\(314\) | 4.46960 | 0.252234 | ||||||||
\(315\) | 0.367973 | 0.0207329 | ||||||||
\(316\) | 7.55695 | 0.425111 | ||||||||
\(317\) | 6.18684 | 0.347488 | 0.173744 | − | 0.984791i | \(-0.444414\pi\) | ||||
0.173744 | + | 0.984791i | \(0.444414\pi\) | |||||||
\(318\) | 6.16740 | 0.345851 | ||||||||
\(319\) | 6.64983 | 0.372319 | ||||||||
\(320\) | 0.480706 | 0.0268723 | ||||||||
\(321\) | −4.57541 | −0.255374 | ||||||||
\(322\) | 4.95943 | 0.276378 | ||||||||
\(323\) | 0.950537 | 0.0528893 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 4.76892 | 0.264532 | ||||||||
\(326\) | −11.9349 | −0.661015 | ||||||||
\(327\) | 4.28510 | 0.236967 | ||||||||
\(328\) | −9.71768 | −0.536569 | ||||||||
\(329\) | −0.929311 | −0.0512346 | ||||||||
\(330\) | 0.539454 | 0.0296960 | ||||||||
\(331\) | −29.0460 | −1.59651 | −0.798256 | − | 0.602318i | \(-0.794244\pi\) | ||||
−0.798256 | + | 0.602318i | \(0.794244\pi\) | |||||||
\(332\) | 14.6910 | 0.806273 | ||||||||
\(333\) | −5.74456 | −0.314800 | ||||||||
\(334\) | −11.7525 | −0.643069 | ||||||||
\(335\) | −5.99964 | −0.327796 | ||||||||
\(336\) | 0.765483 | 0.0417605 | ||||||||
\(337\) | −0.492714 | −0.0268398 | −0.0134199 | − | 0.999910i | \(-0.504272\pi\) | ||||
−0.0134199 | + | 0.999910i | \(0.504272\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | 18.0957 | 0.982824 | ||||||||
\(340\) | 0.0631755 | 0.00342617 | ||||||||
\(341\) | −0.924272 | −0.0500521 | ||||||||
\(342\) | −7.23270 | −0.391099 | ||||||||
\(343\) | −10.2682 | −0.554432 | ||||||||
\(344\) | 1.79479 | 0.0967685 | ||||||||
\(345\) | −3.11441 | −0.167674 | ||||||||
\(346\) | 6.62095 | 0.355944 | ||||||||
\(347\) | 20.9494 | 1.12462 | 0.562311 | − | 0.826926i | \(-0.309912\pi\) | ||||
0.562311 | + | 0.826926i | \(0.309912\pi\) | |||||||
\(348\) | −5.92565 | −0.317648 | ||||||||
\(349\) | −29.6109 | −1.58503 | −0.792517 | − | 0.609850i | \(-0.791230\pi\) | ||||
−0.792517 | + | 0.609850i | \(0.791230\pi\) | |||||||
\(350\) | 3.65053 | 0.195129 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 1.12221 | 0.0598141 | ||||||||
\(353\) | 12.6044 | 0.670865 | 0.335433 | − | 0.942064i | \(-0.391117\pi\) | ||||
0.335433 | + | 0.942064i | \(0.391117\pi\) | |||||||
\(354\) | 7.84426 | 0.416918 | ||||||||
\(355\) | −8.01641 | −0.425467 | ||||||||
\(356\) | −16.8623 | −0.893702 | ||||||||
\(357\) | 0.100602 | 0.00532440 | ||||||||
\(358\) | 2.90096 | 0.153320 | ||||||||
\(359\) | 27.7883 | 1.46661 | 0.733306 | − | 0.679899i | \(-0.237976\pi\) | ||||
0.733306 | + | 0.679899i | \(0.237976\pi\) | |||||||
\(360\) | −0.480706 | −0.0253354 | ||||||||
\(361\) | 33.3119 | 1.75326 | ||||||||
\(362\) | −7.61769 | −0.400377 | ||||||||
\(363\) | −9.74064 | −0.511251 | ||||||||
\(364\) | −0.765483 | −0.0401222 | ||||||||
\(365\) | −1.17742 | −0.0616288 | ||||||||
\(366\) | −8.36385 | −0.437186 | ||||||||
\(367\) | 2.77067 | 0.144628 | 0.0723140 | − | 0.997382i | \(-0.476962\pi\) | ||||
0.0723140 | + | 0.997382i | \(0.476962\pi\) | |||||||
\(368\) | −6.47882 | −0.337732 | ||||||||
\(369\) | 9.71768 | 0.505882 | ||||||||
\(370\) | 2.76145 | 0.143561 | ||||||||
\(371\) | −4.72104 | −0.245104 | ||||||||
\(372\) | 0.823617 | 0.0427025 | ||||||||
\(373\) | 25.4710 | 1.31884 | 0.659419 | − | 0.751776i | \(-0.270802\pi\) | ||||
0.659419 | + | 0.751776i | \(0.270802\pi\) | |||||||
\(374\) | 0.147484 | 0.00762619 | ||||||||
\(375\) | −4.69598 | −0.242499 | ||||||||
\(376\) | 1.21402 | 0.0626082 | ||||||||
\(377\) | 5.92565 | 0.305186 | ||||||||
\(378\) | −0.765483 | −0.0393722 | ||||||||
\(379\) | −7.25237 | −0.372529 | −0.186265 | − | 0.982500i | \(-0.559638\pi\) | ||||
−0.186265 | + | 0.982500i | \(0.559638\pi\) | |||||||
\(380\) | 3.47680 | 0.178356 | ||||||||
\(381\) | 1.93648 | 0.0992087 | ||||||||
\(382\) | 21.2603 | 1.08777 | ||||||||
\(383\) | −20.9833 | −1.07219 | −0.536097 | − | 0.844156i | \(-0.680102\pi\) | ||||
−0.536097 | + | 0.844156i | \(0.680102\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −0.412943 | −0.0210455 | ||||||||
\(386\) | −2.66290 | −0.135538 | ||||||||
\(387\) | −1.79479 | −0.0912343 | ||||||||
\(388\) | 13.3568 | 0.678089 | ||||||||
\(389\) | 1.84882 | 0.0937390 | 0.0468695 | − | 0.998901i | \(-0.485076\pi\) | ||||
0.0468695 | + | 0.998901i | \(0.485076\pi\) | |||||||
\(390\) | 0.480706 | 0.0243415 | ||||||||
\(391\) | −0.851462 | −0.0430603 | ||||||||
\(392\) | 6.41404 | 0.323958 | ||||||||
\(393\) | 17.0455 | 0.859834 | ||||||||
\(394\) | −1.87363 | −0.0943921 | ||||||||
\(395\) | 3.63267 | 0.182779 | ||||||||
\(396\) | −1.12221 | −0.0563932 | ||||||||
\(397\) | 38.9381 | 1.95425 | 0.977123 | − | 0.212675i | \(-0.0682177\pi\) | ||||
0.977123 | + | 0.212675i | \(0.0682177\pi\) | |||||||
\(398\) | −3.88713 | −0.194844 | ||||||||
\(399\) | 5.53651 | 0.277172 | ||||||||
\(400\) | −4.76892 | −0.238446 | ||||||||
\(401\) | −18.6730 | −0.932487 | −0.466243 | − | 0.884657i | \(-0.654393\pi\) | ||||
−0.466243 | + | 0.884657i | \(0.654393\pi\) | |||||||
\(402\) | 12.4809 | 0.622491 | ||||||||
\(403\) | −0.823617 | −0.0410273 | ||||||||
\(404\) | −17.0194 | −0.846748 | ||||||||
\(405\) | 0.480706 | 0.0238865 | ||||||||
\(406\) | 4.53598 | 0.225117 | ||||||||
\(407\) | 6.44661 | 0.319547 | ||||||||
\(408\) | −0.131422 | −0.00650637 | ||||||||
\(409\) | 26.4718 | 1.30895 | 0.654474 | − | 0.756084i | \(-0.272890\pi\) | ||||
0.654474 | + | 0.756084i | \(0.272890\pi\) | |||||||
\(410\) | −4.67135 | −0.230701 | ||||||||
\(411\) | −13.6581 | −0.673707 | ||||||||
\(412\) | 1.00000 | 0.0492665 | ||||||||
\(413\) | −6.00465 | −0.295470 | ||||||||
\(414\) | 6.47882 | 0.318417 | ||||||||
\(415\) | 7.06205 | 0.346662 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | −16.1582 | −0.791269 | ||||||||
\(418\) | 8.11661 | 0.396997 | ||||||||
\(419\) | 14.5263 | 0.709654 | 0.354827 | − | 0.934932i | \(-0.384540\pi\) | ||||
0.354827 | + | 0.934932i | \(0.384540\pi\) | |||||||
\(420\) | 0.367973 | 0.0179552 | ||||||||
\(421\) | −13.3600 | −0.651129 | −0.325564 | − | 0.945520i | \(-0.605554\pi\) | ||||
−0.325564 | + | 0.945520i | \(0.605554\pi\) | |||||||
\(422\) | 12.2619 | 0.596899 | ||||||||
\(423\) | −1.21402 | −0.0590276 | ||||||||
\(424\) | 6.16740 | 0.299516 | ||||||||
\(425\) | −0.626743 | −0.0304015 | ||||||||
\(426\) | 16.6763 | 0.807970 | ||||||||
\(427\) | 6.40239 | 0.309833 | ||||||||
\(428\) | −4.57541 | −0.221161 | ||||||||
\(429\) | 1.12221 | 0.0541809 | ||||||||
\(430\) | 0.862766 | 0.0416063 | ||||||||
\(431\) | −40.1593 | −1.93441 | −0.967203 | − | 0.254006i | \(-0.918252\pi\) | ||||
−0.967203 | + | 0.254006i | \(0.918252\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 15.9722 | 0.767577 | 0.383789 | − | 0.923421i | \(-0.374619\pi\) | ||||
0.383789 | + | 0.923421i | \(0.374619\pi\) | |||||||
\(434\) | −0.630465 | −0.0302633 | ||||||||
\(435\) | −2.84849 | −0.136575 | ||||||||
\(436\) | 4.28510 | 0.205219 | ||||||||
\(437\) | −46.8593 | −2.24159 | ||||||||
\(438\) | 2.44935 | 0.117034 | ||||||||
\(439\) | −9.11229 | −0.434906 | −0.217453 | − | 0.976071i | \(-0.569775\pi\) | ||||
−0.217453 | + | 0.976071i | \(0.569775\pi\) | |||||||
\(440\) | 0.539454 | 0.0257175 | ||||||||
\(441\) | −6.41404 | −0.305430 | ||||||||
\(442\) | 0.131422 | 0.00625112 | ||||||||
\(443\) | 7.39207 | 0.351208 | 0.175604 | − | 0.984461i | \(-0.443812\pi\) | ||||
0.175604 | + | 0.984461i | \(0.443812\pi\) | |||||||
\(444\) | −5.74456 | −0.272625 | ||||||||
\(445\) | −8.10583 | −0.384253 | ||||||||
\(446\) | 18.6606 | 0.883604 | ||||||||
\(447\) | −6.45756 | −0.305432 | ||||||||
\(448\) | 0.765483 | 0.0361657 | ||||||||
\(449\) | 29.3660 | 1.38587 | 0.692933 | − | 0.721002i | \(-0.256318\pi\) | ||||
0.692933 | + | 0.721002i | \(0.256318\pi\) | |||||||
\(450\) | 4.76892 | 0.224809 | ||||||||
\(451\) | −10.9053 | −0.513510 | ||||||||
\(452\) | 18.0957 | 0.851151 | ||||||||
\(453\) | 6.56350 | 0.308380 | ||||||||
\(454\) | 4.40861 | 0.206906 | ||||||||
\(455\) | −0.367973 | −0.0172508 | ||||||||
\(456\) | −7.23270 | −0.338702 | ||||||||
\(457\) | 24.8708 | 1.16341 | 0.581703 | − | 0.813401i | \(-0.302387\pi\) | ||||
0.581703 | + | 0.813401i | \(0.302387\pi\) | |||||||
\(458\) | 5.24559 | 0.245110 | ||||||||
\(459\) | 0.131422 | 0.00613427 | ||||||||
\(460\) | −3.11441 | −0.145210 | ||||||||
\(461\) | −26.9015 | −1.25293 | −0.626464 | − | 0.779451i | \(-0.715498\pi\) | ||||
−0.626464 | + | 0.779451i | \(0.715498\pi\) | |||||||
\(462\) | 0.859034 | 0.0399659 | ||||||||
\(463\) | −19.5006 | −0.906268 | −0.453134 | − | 0.891442i | \(-0.649694\pi\) | ||||
−0.453134 | + | 0.891442i | \(0.649694\pi\) | |||||||
\(464\) | −5.92565 | −0.275091 | ||||||||
\(465\) | 0.395918 | 0.0183602 | ||||||||
\(466\) | −7.38317 | −0.342019 | ||||||||
\(467\) | −15.4476 | −0.714828 | −0.357414 | − | 0.933946i | \(-0.616342\pi\) | ||||
−0.357414 | + | 0.933946i | \(0.616342\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | −9.55392 | −0.441159 | ||||||||
\(470\) | 0.583586 | 0.0269188 | ||||||||
\(471\) | −4.46960 | −0.205948 | ||||||||
\(472\) | 7.84426 | 0.361061 | ||||||||
\(473\) | 2.01413 | 0.0926099 | ||||||||
\(474\) | −7.55695 | −0.347102 | ||||||||
\(475\) | −34.4922 | −1.58261 | ||||||||
\(476\) | 0.100602 | 0.00461107 | ||||||||
\(477\) | −6.16740 | −0.282386 | ||||||||
\(478\) | −11.7084 | −0.535528 | ||||||||
\(479\) | −27.7327 | −1.26714 | −0.633569 | − | 0.773686i | \(-0.718411\pi\) | ||||
−0.633569 | + | 0.773686i | \(0.718411\pi\) | |||||||
\(480\) | −0.480706 | −0.0219411 | ||||||||
\(481\) | 5.74456 | 0.261929 | ||||||||
\(482\) | 24.2815 | 1.10599 | ||||||||
\(483\) | −4.95943 | −0.225662 | ||||||||
\(484\) | −9.74064 | −0.442756 | ||||||||
\(485\) | 6.42069 | 0.291549 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 33.1502 | 1.50218 | 0.751090 | − | 0.660200i | \(-0.229529\pi\) | ||||
0.751090 | + | 0.660200i | \(0.229529\pi\) | |||||||
\(488\) | −8.36385 | −0.378614 | ||||||||
\(489\) | 11.9349 | 0.539717 | ||||||||
\(490\) | 3.08327 | 0.139288 | ||||||||
\(491\) | 6.41368 | 0.289445 | 0.144723 | − | 0.989472i | \(-0.453771\pi\) | ||||
0.144723 | + | 0.989472i | \(0.453771\pi\) | |||||||
\(492\) | 9.71768 | 0.438107 | ||||||||
\(493\) | −0.778762 | −0.0350737 | ||||||||
\(494\) | 7.23270 | 0.325414 | ||||||||
\(495\) | −0.539454 | −0.0242466 | ||||||||
\(496\) | 0.823617 | 0.0369815 | ||||||||
\(497\) | −12.7654 | −0.572608 | ||||||||
\(498\) | −14.6910 | −0.658319 | ||||||||
\(499\) | −24.8825 | −1.11389 | −0.556947 | − | 0.830548i | \(-0.688027\pi\) | ||||
−0.556947 | + | 0.830548i | \(0.688027\pi\) | |||||||
\(500\) | −4.69598 | −0.210011 | ||||||||
\(501\) | 11.7525 | 0.525064 | ||||||||
\(502\) | −20.9442 | −0.934783 | ||||||||
\(503\) | 5.87473 | 0.261941 | 0.130971 | − | 0.991386i | \(-0.458191\pi\) | ||||
0.130971 | + | 0.991386i | \(0.458191\pi\) | |||||||
\(504\) | −0.765483 | −0.0340973 | ||||||||
\(505\) | −8.18134 | −0.364065 | ||||||||
\(506\) | −7.27061 | −0.323218 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 1.93648 | 0.0859172 | ||||||||
\(509\) | −11.1462 | −0.494046 | −0.247023 | − | 0.969010i | \(-0.579452\pi\) | ||||
−0.247023 | + | 0.969010i | \(0.579452\pi\) | |||||||
\(510\) | −0.0631755 | −0.00279746 | ||||||||
\(511\) | −1.87494 | −0.0829423 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 7.23270 | 0.319331 | ||||||||
\(514\) | 18.5827 | 0.819647 | ||||||||
\(515\) | 0.480706 | 0.0211824 | ||||||||
\(516\) | −1.79479 | −0.0790112 | ||||||||
\(517\) | 1.36238 | 0.0599176 | ||||||||
\(518\) | 4.39737 | 0.193209 | ||||||||
\(519\) | −6.62095 | −0.290627 | ||||||||
\(520\) | 0.480706 | 0.0210804 | ||||||||
\(521\) | 31.9050 | 1.39778 | 0.698891 | − | 0.715228i | \(-0.253677\pi\) | ||||
0.698891 | + | 0.715228i | \(0.253677\pi\) | |||||||
\(522\) | 5.92565 | 0.259359 | ||||||||
\(523\) | −4.89722 | −0.214140 | −0.107070 | − | 0.994251i | \(-0.534147\pi\) | ||||
−0.107070 | + | 0.994251i | \(0.534147\pi\) | |||||||
\(524\) | 17.0455 | 0.744638 | ||||||||
\(525\) | −3.65053 | −0.159322 | ||||||||
\(526\) | −0.246017 | −0.0107268 | ||||||||
\(527\) | 0.108242 | 0.00471508 | ||||||||
\(528\) | −1.12221 | −0.0488380 | ||||||||
\(529\) | 18.9751 | 0.825006 | ||||||||
\(530\) | 2.96471 | 0.128779 | ||||||||
\(531\) | −7.84426 | −0.340412 | ||||||||
\(532\) | 5.53651 | 0.240038 | ||||||||
\(533\) | −9.71768 | −0.420919 | ||||||||
\(534\) | 16.8623 | 0.729704 | ||||||||
\(535\) | −2.19943 | −0.0950895 | ||||||||
\(536\) | 12.4809 | 0.539093 | ||||||||
\(537\) | −2.90096 | −0.125185 | ||||||||
\(538\) | 21.0144 | 0.905995 | ||||||||
\(539\) | 7.19790 | 0.310036 | ||||||||
\(540\) | 0.480706 | 0.0206863 | ||||||||
\(541\) | 36.2873 | 1.56011 | 0.780057 | − | 0.625708i | \(-0.215190\pi\) | ||||
0.780057 | + | 0.625708i | \(0.215190\pi\) | |||||||
\(542\) | 30.8832 | 1.32655 | ||||||||
\(543\) | 7.61769 | 0.326906 | ||||||||
\(544\) | −0.131422 | −0.00563468 | ||||||||
\(545\) | 2.05987 | 0.0882353 | ||||||||
\(546\) | 0.765483 | 0.0327597 | ||||||||
\(547\) | 27.5912 | 1.17971 | 0.589856 | − | 0.807508i | \(-0.299184\pi\) | ||||
0.589856 | + | 0.807508i | \(0.299184\pi\) | |||||||
\(548\) | −13.6581 | −0.583447 | ||||||||
\(549\) | 8.36385 | 0.356961 | ||||||||
\(550\) | −5.35174 | −0.228199 | ||||||||
\(551\) | −42.8584 | −1.82583 | ||||||||
\(552\) | 6.47882 | 0.275757 | ||||||||
\(553\) | 5.78472 | 0.245991 | ||||||||
\(554\) | −12.7814 | −0.543030 | ||||||||
\(555\) | −2.76145 | −0.117217 | ||||||||
\(556\) | −16.1582 | −0.685259 | ||||||||
\(557\) | −33.3217 | −1.41189 | −0.705943 | − | 0.708269i | \(-0.749476\pi\) | ||||
−0.705943 | + | 0.708269i | \(0.749476\pi\) | |||||||
\(558\) | −0.823617 | −0.0348665 | ||||||||
\(559\) | 1.79479 | 0.0759115 | ||||||||
\(560\) | 0.367973 | 0.0155497 | ||||||||
\(561\) | −0.147484 | −0.00622676 | ||||||||
\(562\) | −11.4614 | −0.483471 | ||||||||
\(563\) | −30.0026 | −1.26446 | −0.632230 | − | 0.774781i | \(-0.717860\pi\) | ||||
−0.632230 | + | 0.774781i | \(0.717860\pi\) | |||||||
\(564\) | −1.21402 | −0.0511194 | ||||||||
\(565\) | 8.69872 | 0.365958 | ||||||||
\(566\) | −23.9695 | −1.00751 | ||||||||
\(567\) | 0.765483 | 0.0321473 | ||||||||
\(568\) | 16.6763 | 0.699723 | ||||||||
\(569\) | 15.9275 | 0.667713 | 0.333857 | − | 0.942624i | \(-0.391650\pi\) | ||||
0.333857 | + | 0.942624i | \(0.391650\pi\) | |||||||
\(570\) | −3.47680 | −0.145627 | ||||||||
\(571\) | −22.7744 | −0.953079 | −0.476539 | − | 0.879153i | \(-0.658109\pi\) | ||||
−0.476539 | + | 0.879153i | \(0.658109\pi\) | |||||||
\(572\) | 1.12221 | 0.0469220 | ||||||||
\(573\) | −21.2603 | −0.888160 | ||||||||
\(574\) | −7.43872 | −0.310486 | ||||||||
\(575\) | 30.8970 | 1.28849 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −29.6358 | −1.23376 | −0.616878 | − | 0.787059i | \(-0.711603\pi\) | ||||
−0.616878 | + | 0.787059i | \(0.711603\pi\) | |||||||
\(578\) | 16.9827 | 0.706388 | ||||||||
\(579\) | 2.66290 | 0.110667 | ||||||||
\(580\) | −2.84849 | −0.118277 | ||||||||
\(581\) | 11.2457 | 0.466551 | ||||||||
\(582\) | −13.3568 | −0.553657 | ||||||||
\(583\) | 6.92113 | 0.286644 | ||||||||
\(584\) | 2.44935 | 0.101355 | ||||||||
\(585\) | −0.480706 | −0.0198748 | ||||||||
\(586\) | 27.6256 | 1.14120 | ||||||||
\(587\) | −18.3847 | −0.758816 | −0.379408 | − | 0.925229i | \(-0.623872\pi\) | ||||
−0.379408 | + | 0.925229i | \(0.623872\pi\) | |||||||
\(588\) | −6.41404 | −0.264510 | ||||||||
\(589\) | 5.95697 | 0.245453 | ||||||||
\(590\) | 3.77078 | 0.155241 | ||||||||
\(591\) | 1.87363 | 0.0770709 | ||||||||
\(592\) | −5.74456 | −0.236100 | ||||||||
\(593\) | −42.2315 | −1.73424 | −0.867121 | − | 0.498098i | \(-0.834032\pi\) | ||||
−0.867121 | + | 0.498098i | \(0.834032\pi\) | |||||||
\(594\) | 1.12221 | 0.0460449 | ||||||||
\(595\) | 0.0483598 | 0.00198256 | ||||||||
\(596\) | −6.45756 | −0.264512 | ||||||||
\(597\) | 3.88713 | 0.159090 | ||||||||
\(598\) | −6.47882 | −0.264939 | ||||||||
\(599\) | −30.6689 | −1.25310 | −0.626549 | − | 0.779382i | \(-0.715533\pi\) | ||||
−0.626549 | + | 0.779382i | \(0.715533\pi\) | |||||||
\(600\) | 4.76892 | 0.194690 | ||||||||
\(601\) | 4.48766 | 0.183055 | 0.0915276 | − | 0.995803i | \(-0.470825\pi\) | ||||
0.0915276 | + | 0.995803i | \(0.470825\pi\) | |||||||
\(602\) | 1.37388 | 0.0559952 | ||||||||
\(603\) | −12.4809 | −0.508261 | ||||||||
\(604\) | 6.56350 | 0.267065 | ||||||||
\(605\) | −4.68239 | −0.190366 | ||||||||
\(606\) | 17.0194 | 0.691367 | ||||||||
\(607\) | 31.0647 | 1.26088 | 0.630439 | − | 0.776239i | \(-0.282875\pi\) | ||||
0.630439 | + | 0.776239i | \(0.282875\pi\) | |||||||
\(608\) | −7.23270 | −0.293325 | ||||||||
\(609\) | −4.53598 | −0.183807 | ||||||||
\(610\) | −4.02056 | −0.162788 | ||||||||
\(611\) | 1.21402 | 0.0491139 | ||||||||
\(612\) | 0.131422 | 0.00531243 | ||||||||
\(613\) | 26.9085 | 1.08682 | 0.543412 | − | 0.839466i | \(-0.317132\pi\) | ||||
0.543412 | + | 0.839466i | \(0.317132\pi\) | |||||||
\(614\) | −31.0759 | −1.25412 | ||||||||
\(615\) | 4.67135 | 0.188367 | ||||||||
\(616\) | 0.859034 | 0.0346115 | ||||||||
\(617\) | −39.4434 | −1.58793 | −0.793966 | − | 0.607962i | \(-0.791987\pi\) | ||||
−0.793966 | + | 0.607962i | \(0.791987\pi\) | |||||||
\(618\) | −1.00000 | −0.0402259 | ||||||||
\(619\) | −11.9302 | −0.479515 | −0.239758 | − | 0.970833i | \(-0.577068\pi\) | ||||
−0.239758 | + | 0.970833i | \(0.577068\pi\) | |||||||
\(620\) | 0.395918 | 0.0159004 | ||||||||
\(621\) | −6.47882 | −0.259986 | ||||||||
\(622\) | 12.4535 | 0.499338 | ||||||||
\(623\) | −12.9078 | −0.517141 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | 21.5872 | 0.863489 | ||||||||
\(626\) | −8.68625 | −0.347172 | ||||||||
\(627\) | −8.11661 | −0.324146 | ||||||||
\(628\) | −4.46960 | −0.178357 | ||||||||
\(629\) | −0.754963 | −0.0301023 | ||||||||
\(630\) | −0.367973 | −0.0146604 | ||||||||
\(631\) | 22.2362 | 0.885209 | 0.442604 | − | 0.896717i | \(-0.354055\pi\) | ||||
0.442604 | + | 0.896717i | \(0.354055\pi\) | |||||||
\(632\) | −7.55695 | −0.300599 | ||||||||
\(633\) | −12.2619 | −0.487366 | ||||||||
\(634\) | −6.18684 | −0.245711 | ||||||||
\(635\) | 0.930876 | 0.0369407 | ||||||||
\(636\) | −6.16740 | −0.244553 | ||||||||
\(637\) | 6.41404 | 0.254133 | ||||||||
\(638\) | −6.64983 | −0.263269 | ||||||||
\(639\) | −16.6763 | −0.659705 | ||||||||
\(640\) | −0.480706 | −0.0190016 | ||||||||
\(641\) | −41.1262 | −1.62439 | −0.812194 | − | 0.583387i | \(-0.801727\pi\) | ||||
−0.812194 | + | 0.583387i | \(0.801727\pi\) | |||||||
\(642\) | 4.57541 | 0.180577 | ||||||||
\(643\) | 9.83517 | 0.387861 | 0.193931 | − | 0.981015i | \(-0.437876\pi\) | ||||
0.193931 | + | 0.981015i | \(0.437876\pi\) | |||||||
\(644\) | −4.95943 | −0.195429 | ||||||||
\(645\) | −0.862766 | −0.0339714 | ||||||||
\(646\) | −0.950537 | −0.0373984 | ||||||||
\(647\) | 33.4506 | 1.31508 | 0.657540 | − | 0.753419i | \(-0.271597\pi\) | ||||
0.657540 | + | 0.753419i | \(0.271597\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 8.80292 | 0.345545 | ||||||||
\(650\) | −4.76892 | −0.187052 | ||||||||
\(651\) | 0.630465 | 0.0247099 | ||||||||
\(652\) | 11.9349 | 0.467408 | ||||||||
\(653\) | 23.3997 | 0.915701 | 0.457850 | − | 0.889029i | \(-0.348620\pi\) | ||||
0.457850 | + | 0.889029i | \(0.348620\pi\) | |||||||
\(654\) | −4.28510 | −0.167561 | ||||||||
\(655\) | 8.19390 | 0.320162 | ||||||||
\(656\) | 9.71768 | 0.379412 | ||||||||
\(657\) | −2.44935 | −0.0955582 | ||||||||
\(658\) | 0.929311 | 0.0362283 | ||||||||
\(659\) | −19.9669 | −0.777798 | −0.388899 | − | 0.921280i | \(-0.627145\pi\) | ||||
−0.388899 | + | 0.921280i | \(0.627145\pi\) | |||||||
\(660\) | −0.539454 | −0.0209982 | ||||||||
\(661\) | −12.5468 | −0.488015 | −0.244007 | − | 0.969773i | \(-0.578462\pi\) | ||||
−0.244007 | + | 0.969773i | \(0.578462\pi\) | |||||||
\(662\) | 29.0460 | 1.12890 | ||||||||
\(663\) | −0.131422 | −0.00510402 | ||||||||
\(664\) | −14.6910 | −0.570121 | ||||||||
\(665\) | 2.66143 | 0.103206 | ||||||||
\(666\) | 5.74456 | 0.222597 | ||||||||
\(667\) | 38.3912 | 1.48651 | ||||||||
\(668\) | 11.7525 | 0.454719 | ||||||||
\(669\) | −18.6606 | −0.721459 | ||||||||
\(670\) | 5.99964 | 0.231786 | ||||||||
\(671\) | −9.38601 | −0.362343 | ||||||||
\(672\) | −0.765483 | −0.0295292 | ||||||||
\(673\) | 14.3712 | 0.553968 | 0.276984 | − | 0.960874i | \(-0.410665\pi\) | ||||
0.276984 | + | 0.960874i | \(0.410665\pi\) | |||||||
\(674\) | 0.492714 | 0.0189786 | ||||||||
\(675\) | −4.76892 | −0.183556 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −31.6177 | −1.21517 | −0.607584 | − | 0.794255i | \(-0.707861\pi\) | ||||
−0.607584 | + | 0.794255i | \(0.707861\pi\) | |||||||
\(678\) | −18.0957 | −0.694962 | ||||||||
\(679\) | 10.2244 | 0.392377 | ||||||||
\(680\) | −0.0631755 | −0.00242267 | ||||||||
\(681\) | −4.40861 | −0.168938 | ||||||||
\(682\) | 0.924272 | 0.0353922 | ||||||||
\(683\) | −42.9732 | −1.64432 | −0.822162 | − | 0.569254i | \(-0.807232\pi\) | ||||
−0.822162 | + | 0.569254i | \(0.807232\pi\) | |||||||
\(684\) | 7.23270 | 0.276549 | ||||||||
\(685\) | −6.56555 | −0.250857 | ||||||||
\(686\) | 10.2682 | 0.392043 | ||||||||
\(687\) | −5.24559 | −0.200132 | ||||||||
\(688\) | −1.79479 | −0.0684257 | ||||||||
\(689\) | 6.16740 | 0.234959 | ||||||||
\(690\) | 3.11441 | 0.118564 | ||||||||
\(691\) | −37.8566 | −1.44013 | −0.720066 | − | 0.693905i | \(-0.755889\pi\) | ||||
−0.720066 | + | 0.693905i | \(0.755889\pi\) | |||||||
\(692\) | −6.62095 | −0.251691 | ||||||||
\(693\) | −0.859034 | −0.0326320 | ||||||||
\(694\) | −20.9494 | −0.795227 | ||||||||
\(695\) | −7.76733 | −0.294631 | ||||||||
\(696\) | 5.92565 | 0.224611 | ||||||||
\(697\) | 1.27712 | 0.0483743 | ||||||||
\(698\) | 29.6109 | 1.12079 | ||||||||
\(699\) | 7.38317 | 0.279257 | ||||||||
\(700\) | −3.65053 | −0.137977 | ||||||||
\(701\) | 45.8771 | 1.73275 | 0.866377 | − | 0.499391i | \(-0.166443\pi\) | ||||
0.866377 | + | 0.499391i | \(0.166443\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | −41.5487 | −1.56704 | ||||||||
\(704\) | −1.12221 | −0.0422949 | ||||||||
\(705\) | −0.583586 | −0.0219791 | ||||||||
\(706\) | −12.6044 | −0.474374 | ||||||||
\(707\) | −13.0281 | −0.489972 | ||||||||
\(708\) | −7.84426 | −0.294805 | ||||||||
\(709\) | 4.87459 | 0.183069 | 0.0915345 | − | 0.995802i | \(-0.470823\pi\) | ||||
0.0915345 | + | 0.995802i | \(0.470823\pi\) | |||||||
\(710\) | 8.01641 | 0.300850 | ||||||||
\(711\) | 7.55695 | 0.283408 | ||||||||
\(712\) | 16.8623 | 0.631943 | ||||||||
\(713\) | −5.33607 | −0.199837 | ||||||||
\(714\) | −0.100602 | −0.00376492 | ||||||||
\(715\) | 0.539454 | 0.0201744 | ||||||||
\(716\) | −2.90096 | −0.108414 | ||||||||
\(717\) | 11.7084 | 0.437257 | ||||||||
\(718\) | −27.7883 | −1.03705 | ||||||||
\(719\) | −29.5494 | −1.10201 | −0.551003 | − | 0.834503i | \(-0.685755\pi\) | ||||
−0.551003 | + | 0.834503i | \(0.685755\pi\) | |||||||
\(720\) | 0.480706 | 0.0179149 | ||||||||
\(721\) | 0.765483 | 0.0285081 | ||||||||
\(722\) | −33.3119 | −1.23974 | ||||||||
\(723\) | −24.2815 | −0.903038 | ||||||||
\(724\) | 7.61769 | 0.283109 | ||||||||
\(725\) | 28.2589 | 1.04951 | ||||||||
\(726\) | 9.74064 | 0.361509 | ||||||||
\(727\) | 29.9698 | 1.11152 | 0.555759 | − | 0.831344i | \(-0.312428\pi\) | ||||
0.555759 | + | 0.831344i | \(0.312428\pi\) | |||||||
\(728\) | 0.765483 | 0.0283707 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.17742 | 0.0435782 | ||||||||
\(731\) | −0.235875 | −0.00872416 | ||||||||
\(732\) | 8.36385 | 0.309137 | ||||||||
\(733\) | −16.5241 | −0.610331 | −0.305165 | − | 0.952299i | \(-0.598712\pi\) | ||||
−0.305165 | + | 0.952299i | \(0.598712\pi\) | |||||||
\(734\) | −2.77067 | −0.102267 | ||||||||
\(735\) | −3.08327 | −0.113728 | ||||||||
\(736\) | 6.47882 | 0.238813 | ||||||||
\(737\) | 14.0062 | 0.515925 | ||||||||
\(738\) | −9.71768 | −0.357713 | ||||||||
\(739\) | −34.7278 | −1.27748 | −0.638742 | − | 0.769421i | \(-0.720545\pi\) | ||||
−0.638742 | + | 0.769421i | \(0.720545\pi\) | |||||||
\(740\) | −2.76145 | −0.101513 | ||||||||
\(741\) | −7.23270 | −0.265700 | ||||||||
\(742\) | 4.72104 | 0.173315 | ||||||||
\(743\) | −1.58390 | −0.0581077 | −0.0290538 | − | 0.999578i | \(-0.509249\pi\) | ||||
−0.0290538 | + | 0.999578i | \(0.509249\pi\) | |||||||
\(744\) | −0.823617 | −0.0301953 | ||||||||
\(745\) | −3.10419 | −0.113729 | ||||||||
\(746\) | −25.4710 | −0.932559 | ||||||||
\(747\) | 14.6910 | 0.537515 | ||||||||
\(748\) | −0.147484 | −0.00539253 | ||||||||
\(749\) | −3.50240 | −0.127975 | ||||||||
\(750\) | 4.69598 | 0.171473 | ||||||||
\(751\) | 11.0699 | 0.403945 | 0.201973 | − | 0.979391i | \(-0.435265\pi\) | ||||
0.201973 | + | 0.979391i | \(0.435265\pi\) | |||||||
\(752\) | −1.21402 | −0.0442707 | ||||||||
\(753\) | 20.9442 | 0.763247 | ||||||||
\(754\) | −5.92565 | −0.215799 | ||||||||
\(755\) | 3.15511 | 0.114826 | ||||||||
\(756\) | 0.765483 | 0.0278404 | ||||||||
\(757\) | −51.6099 | −1.87579 | −0.937897 | − | 0.346915i | \(-0.887229\pi\) | ||||
−0.937897 | + | 0.346915i | \(0.887229\pi\) | |||||||
\(758\) | 7.25237 | 0.263418 | ||||||||
\(759\) | 7.27061 | 0.263906 | ||||||||
\(760\) | −3.47680 | −0.126117 | ||||||||
\(761\) | −19.1241 | −0.693246 | −0.346623 | − | 0.938004i | \(-0.612672\pi\) | ||||
−0.346623 | + | 0.938004i | \(0.612672\pi\) | |||||||
\(762\) | −1.93648 | −0.0701511 | ||||||||
\(763\) | 3.28017 | 0.118750 | ||||||||
\(764\) | −21.2603 | −0.769169 | ||||||||
\(765\) | 0.0631755 | 0.00228411 | ||||||||
\(766\) | 20.9833 | 0.758156 | ||||||||
\(767\) | 7.84426 | 0.283240 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 1.19596 | 0.0431276 | 0.0215638 | − | 0.999767i | \(-0.493135\pi\) | ||||
0.0215638 | + | 0.999767i | \(0.493135\pi\) | |||||||
\(770\) | 0.412943 | 0.0148814 | ||||||||
\(771\) | −18.5827 | −0.669239 | ||||||||
\(772\) | 2.66290 | 0.0958400 | ||||||||
\(773\) | 18.2539 | 0.656547 | 0.328274 | − | 0.944583i | \(-0.393533\pi\) | ||||
0.328274 | + | 0.944583i | \(0.393533\pi\) | |||||||
\(774\) | 1.79479 | 0.0645124 | ||||||||
\(775\) | −3.92776 | −0.141089 | ||||||||
\(776\) | −13.3568 | −0.479481 | ||||||||
\(777\) | −4.39737 | −0.157755 | ||||||||
\(778\) | −1.84882 | −0.0662835 | ||||||||
\(779\) | 70.2850 | 2.51822 | ||||||||
\(780\) | −0.480706 | −0.0172120 | ||||||||
\(781\) | 18.7144 | 0.669652 | ||||||||
\(782\) | 0.851462 | 0.0304482 | ||||||||
\(783\) | −5.92565 | −0.211765 | ||||||||
\(784\) | −6.41404 | −0.229073 | ||||||||
\(785\) | −2.14857 | −0.0766856 | ||||||||
\(786\) | −17.0455 | −0.607995 | ||||||||
\(787\) | −7.19066 | −0.256319 | −0.128160 | − | 0.991754i | \(-0.540907\pi\) | ||||
−0.128160 | + | 0.991754i | \(0.540907\pi\) | |||||||
\(788\) | 1.87363 | 0.0667453 | ||||||||
\(789\) | 0.246017 | 0.00875842 | ||||||||
\(790\) | −3.63267 | −0.129245 | ||||||||
\(791\) | 13.8520 | 0.492519 | ||||||||
\(792\) | 1.12221 | 0.0398760 | ||||||||
\(793\) | −8.36385 | −0.297009 | ||||||||
\(794\) | −38.9381 | −1.38186 | ||||||||
\(795\) | −2.96471 | −0.105147 | ||||||||
\(796\) | 3.88713 | 0.137776 | ||||||||
\(797\) | −48.8498 | −1.73035 | −0.865175 | − | 0.501470i | \(-0.832793\pi\) | ||||
−0.865175 | + | 0.501470i | \(0.832793\pi\) | |||||||
\(798\) | −5.53651 | −0.195990 | ||||||||
\(799\) | −0.159549 | −0.00564444 | ||||||||
\(800\) | 4.76892 | 0.168607 | ||||||||
\(801\) | −16.8623 | −0.595801 | ||||||||
\(802\) | 18.6730 | 0.659368 | ||||||||
\(803\) | 2.74869 | 0.0969991 | ||||||||
\(804\) | −12.4809 | −0.440167 | ||||||||
\(805\) | −2.38403 | −0.0840260 | ||||||||
\(806\) | 0.823617 | 0.0290107 | ||||||||
\(807\) | −21.0144 | −0.739742 | ||||||||
\(808\) | 17.0194 | 0.598741 | ||||||||
\(809\) | 44.5321 | 1.56566 | 0.782832 | − | 0.622233i | \(-0.213774\pi\) | ||||
0.782832 | + | 0.622233i | \(0.213774\pi\) | |||||||
\(810\) | −0.480706 | −0.0168903 | ||||||||
\(811\) | 46.2106 | 1.62267 | 0.811337 | − | 0.584579i | \(-0.198740\pi\) | ||||
0.811337 | + | 0.584579i | \(0.198740\pi\) | |||||||
\(812\) | −4.53598 | −0.159182 | ||||||||
\(813\) | −30.8832 | −1.08312 | ||||||||
\(814\) | −6.44661 | −0.225954 | ||||||||
\(815\) | 5.73720 | 0.200965 | ||||||||
\(816\) | 0.131422 | 0.00460070 | ||||||||
\(817\) | −12.9812 | −0.454153 | ||||||||
\(818\) | −26.4718 | −0.925566 | ||||||||
\(819\) | −0.765483 | −0.0267482 | ||||||||
\(820\) | 4.67135 | 0.163131 | ||||||||
\(821\) | 36.7399 | 1.28223 | 0.641115 | − | 0.767445i | \(-0.278472\pi\) | ||||
0.641115 | + | 0.767445i | \(0.278472\pi\) | |||||||
\(822\) | 13.6581 | 0.476383 | ||||||||
\(823\) | −22.6385 | −0.789128 | −0.394564 | − | 0.918869i | \(-0.629104\pi\) | ||||
−0.394564 | + | 0.918869i | \(0.629104\pi\) | |||||||
\(824\) | −1.00000 | −0.0348367 | ||||||||
\(825\) | 5.35174 | 0.186324 | ||||||||
\(826\) | 6.00465 | 0.208928 | ||||||||
\(827\) | −9.97795 | −0.346967 | −0.173484 | − | 0.984837i | \(-0.555502\pi\) | ||||
−0.173484 | + | 0.984837i | \(0.555502\pi\) | |||||||
\(828\) | −6.47882 | −0.225155 | ||||||||
\(829\) | 10.5754 | 0.367298 | 0.183649 | − | 0.982992i | \(-0.441209\pi\) | ||||
0.183649 | + | 0.982992i | \(0.441209\pi\) | |||||||
\(830\) | −7.06205 | −0.245127 | ||||||||
\(831\) | 12.7814 | 0.443382 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | −0.842947 | −0.0292064 | ||||||||
\(834\) | 16.1582 | 0.559511 | ||||||||
\(835\) | 5.64951 | 0.195509 | ||||||||
\(836\) | −8.11661 | −0.280719 | ||||||||
\(837\) | 0.823617 | 0.0284684 | ||||||||
\(838\) | −14.5263 | −0.501801 | ||||||||
\(839\) | 24.4530 | 0.844212 | 0.422106 | − | 0.906547i | \(-0.361291\pi\) | ||||
0.422106 | + | 0.906547i | \(0.361291\pi\) | |||||||
\(840\) | −0.367973 | −0.0126963 | ||||||||
\(841\) | 6.11329 | 0.210803 | ||||||||
\(842\) | 13.3600 | 0.460417 | ||||||||
\(843\) | 11.4614 | 0.394753 | ||||||||
\(844\) | −12.2619 | −0.422072 | ||||||||
\(845\) | 0.480706 | 0.0165368 | ||||||||
\(846\) | 1.21402 | 0.0417388 | ||||||||
\(847\) | −7.45630 | −0.256201 | ||||||||
\(848\) | −6.16740 | −0.211789 | ||||||||
\(849\) | 23.9695 | 0.822630 | ||||||||
\(850\) | 0.626743 | 0.0214971 | ||||||||
\(851\) | 37.2180 | 1.27582 | ||||||||
\(852\) | −16.6763 | −0.571321 | ||||||||
\(853\) | 22.0285 | 0.754243 | 0.377121 | − | 0.926164i | \(-0.376914\pi\) | ||||
0.377121 | + | 0.926164i | \(0.376914\pi\) | |||||||
\(854\) | −6.40239 | −0.219085 | ||||||||
\(855\) | 3.47680 | 0.118904 | ||||||||
\(856\) | 4.57541 | 0.156384 | ||||||||
\(857\) | 12.5241 | 0.427816 | 0.213908 | − | 0.976854i | \(-0.431381\pi\) | ||||
0.213908 | + | 0.976854i | \(0.431381\pi\) | |||||||
\(858\) | −1.12221 | −0.0383117 | ||||||||
\(859\) | −39.6779 | −1.35379 | −0.676897 | − | 0.736078i | \(-0.736676\pi\) | ||||
−0.676897 | + | 0.736078i | \(0.736676\pi\) | |||||||
\(860\) | −0.862766 | −0.0294201 | ||||||||
\(861\) | 7.43872 | 0.253511 | ||||||||
\(862\) | 40.1593 | 1.36783 | ||||||||
\(863\) | −28.9247 | −0.984609 | −0.492305 | − | 0.870423i | \(-0.663845\pi\) | ||||
−0.492305 | + | 0.870423i | \(0.663845\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −3.18273 | −0.108216 | ||||||||
\(866\) | −15.9722 | −0.542759 | ||||||||
\(867\) | −16.9827 | −0.576764 | ||||||||
\(868\) | 0.630465 | 0.0213994 | ||||||||
\(869\) | −8.48049 | −0.287681 | ||||||||
\(870\) | 2.84849 | 0.0965730 | ||||||||
\(871\) | 12.4809 | 0.422899 | ||||||||
\(872\) | −4.28510 | −0.145112 | ||||||||
\(873\) | 13.3568 | 0.452059 | ||||||||
\(874\) | 46.8593 | 1.58504 | ||||||||
\(875\) | −3.59470 | −0.121523 | ||||||||
\(876\) | −2.44935 | −0.0827558 | ||||||||
\(877\) | −0.160892 | −0.00543295 | −0.00271648 | − | 0.999996i | \(-0.500865\pi\) | ||||
−0.00271648 | + | 0.999996i | \(0.500865\pi\) | |||||||
\(878\) | 9.11229 | 0.307525 | ||||||||
\(879\) | −27.6256 | −0.931787 | ||||||||
\(880\) | −0.539454 | −0.0181850 | ||||||||
\(881\) | 1.77982 | 0.0599636 | 0.0299818 | − | 0.999550i | \(-0.490455\pi\) | ||||
0.0299818 | + | 0.999550i | \(0.490455\pi\) | |||||||
\(882\) | 6.41404 | 0.215972 | ||||||||
\(883\) | 56.4860 | 1.90090 | 0.950452 | − | 0.310871i | \(-0.100621\pi\) | ||||
0.950452 | + | 0.310871i | \(0.100621\pi\) | |||||||
\(884\) | −0.131422 | −0.00442021 | ||||||||
\(885\) | −3.77078 | −0.126753 | ||||||||
\(886\) | −7.39207 | −0.248342 | ||||||||
\(887\) | −37.2982 | −1.25235 | −0.626175 | − | 0.779682i | \(-0.715380\pi\) | ||||
−0.626175 | + | 0.779682i | \(0.715380\pi\) | |||||||
\(888\) | 5.74456 | 0.192775 | ||||||||
\(889\) | 1.48234 | 0.0497161 | ||||||||
\(890\) | 8.10583 | 0.271708 | ||||||||
\(891\) | −1.12221 | −0.0375955 | ||||||||
\(892\) | −18.6606 | −0.624802 | ||||||||
\(893\) | −8.78062 | −0.293832 | ||||||||
\(894\) | 6.45756 | 0.215973 | ||||||||
\(895\) | −1.39451 | −0.0466132 | ||||||||
\(896\) | −0.765483 | −0.0255730 | ||||||||
\(897\) | 6.47882 | 0.216322 | ||||||||
\(898\) | −29.3660 | −0.979955 | ||||||||
\(899\) | −4.88046 | −0.162773 | ||||||||
\(900\) | −4.76892 | −0.158964 | ||||||||
\(901\) | −0.810534 | −0.0270028 | ||||||||
\(902\) | 10.9053 | 0.363106 | ||||||||
\(903\) | −1.37388 | −0.0457199 | ||||||||
\(904\) | −18.0957 | −0.601854 | ||||||||
\(905\) | 3.66187 | 0.121725 | ||||||||
\(906\) | −6.56350 | −0.218058 | ||||||||
\(907\) | 27.4272 | 0.910706 | 0.455353 | − | 0.890311i | \(-0.349513\pi\) | ||||
0.455353 | + | 0.890311i | \(0.349513\pi\) | |||||||
\(908\) | −4.40861 | −0.146305 | ||||||||
\(909\) | −17.0194 | −0.564499 | ||||||||
\(910\) | 0.367973 | 0.0121982 | ||||||||
\(911\) | −14.0108 | −0.464200 | −0.232100 | − | 0.972692i | \(-0.574560\pi\) | ||||
−0.232100 | + | 0.972692i | \(0.574560\pi\) | |||||||
\(912\) | 7.23270 | 0.239498 | ||||||||
\(913\) | −16.4864 | −0.545620 | ||||||||
\(914\) | −24.8708 | −0.822652 | ||||||||
\(915\) | 4.02056 | 0.132915 | ||||||||
\(916\) | −5.24559 | −0.173319 | ||||||||
\(917\) | 13.0481 | 0.430886 | ||||||||
\(918\) | −0.131422 | −0.00433758 | ||||||||
\(919\) | −12.8254 | −0.423071 | −0.211535 | − | 0.977370i | \(-0.567846\pi\) | ||||
−0.211535 | + | 0.977370i | \(0.567846\pi\) | |||||||
\(920\) | 3.11441 | 0.102679 | ||||||||
\(921\) | 31.0759 | 1.02399 | ||||||||
\(922\) | 26.9015 | 0.885953 | ||||||||
\(923\) | 16.6763 | 0.548908 | ||||||||
\(924\) | −0.859034 | −0.0282602 | ||||||||
\(925\) | 27.3954 | 0.900754 | ||||||||
\(926\) | 19.5006 | 0.640828 | ||||||||
\(927\) | 1.00000 | 0.0328443 | ||||||||
\(928\) | 5.92565 | 0.194519 | ||||||||
\(929\) | 58.8254 | 1.93000 | 0.964999 | − | 0.262254i | \(-0.0844659\pi\) | ||||
0.964999 | + | 0.262254i | \(0.0844659\pi\) | |||||||
\(930\) | −0.395918 | −0.0129826 | ||||||||
\(931\) | −46.3908 | −1.52040 | ||||||||
\(932\) | 7.38317 | 0.241844 | ||||||||
\(933\) | −12.4535 | −0.407708 | ||||||||
\(934\) | 15.4476 | 0.505460 | ||||||||
\(935\) | −0.0708963 | −0.00231856 | ||||||||
\(936\) | 1.00000 | 0.0326860 | ||||||||
\(937\) | −35.1385 | −1.14792 | −0.573962 | − | 0.818882i | \(-0.694594\pi\) | ||||
−0.573962 | + | 0.818882i | \(0.694594\pi\) | |||||||
\(938\) | 9.55392 | 0.311947 | ||||||||
\(939\) | 8.68625 | 0.283465 | ||||||||
\(940\) | −0.583586 | −0.0190345 | ||||||||
\(941\) | −33.1669 | −1.08121 | −0.540606 | − | 0.841276i | \(-0.681805\pi\) | ||||
−0.540606 | + | 0.841276i | \(0.681805\pi\) | |||||||
\(942\) | 4.46960 | 0.145628 | ||||||||
\(943\) | −62.9591 | −2.05023 | ||||||||
\(944\) | −7.84426 | −0.255309 | ||||||||
\(945\) | 0.367973 | 0.0119701 | ||||||||
\(946\) | −2.01413 | −0.0654851 | ||||||||
\(947\) | −12.6520 | −0.411134 | −0.205567 | − | 0.978643i | \(-0.565904\pi\) | ||||
−0.205567 | + | 0.978643i | \(0.565904\pi\) | |||||||
\(948\) | 7.55695 | 0.245438 | ||||||||
\(949\) | 2.44935 | 0.0795092 | ||||||||
\(950\) | 34.4922 | 1.11907 | ||||||||
\(951\) | 6.18684 | 0.200622 | ||||||||
\(952\) | −0.100602 | −0.00326052 | ||||||||
\(953\) | 43.0310 | 1.39391 | 0.696956 | − | 0.717114i | \(-0.254537\pi\) | ||||
0.696956 | + | 0.717114i | \(0.254537\pi\) | |||||||
\(954\) | 6.16740 | 0.199677 | ||||||||
\(955\) | −10.2199 | −0.330709 | ||||||||
\(956\) | 11.7084 | 0.378676 | ||||||||
\(957\) | 6.64983 | 0.214958 | ||||||||
\(958\) | 27.7327 | 0.896003 | ||||||||
\(959\) | −10.4551 | −0.337612 | ||||||||
\(960\) | 0.480706 | 0.0155147 | ||||||||
\(961\) | −30.3217 | −0.978118 | ||||||||
\(962\) | −5.74456 | −0.185212 | ||||||||
\(963\) | −4.57541 | −0.147440 | ||||||||
\(964\) | −24.2815 | −0.782054 | ||||||||
\(965\) | 1.28007 | 0.0412070 | ||||||||
\(966\) | 4.95943 | 0.159567 | ||||||||
\(967\) | 44.2881 | 1.42421 | 0.712105 | − | 0.702073i | \(-0.247742\pi\) | ||||
0.712105 | + | 0.702073i | \(0.247742\pi\) | |||||||
\(968\) | 9.74064 | 0.313076 | ||||||||
\(969\) | 0.950537 | 0.0305357 | ||||||||
\(970\) | −6.42069 | −0.206156 | ||||||||
\(971\) | 35.4241 | 1.13681 | 0.568406 | − | 0.822748i | \(-0.307560\pi\) | ||||
0.568406 | + | 0.822748i | \(0.307560\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −12.3688 | −0.396526 | ||||||||
\(974\) | −33.1502 | −1.06220 | ||||||||
\(975\) | 4.76892 | 0.152728 | ||||||||
\(976\) | 8.36385 | 0.267720 | ||||||||
\(977\) | 24.0530 | 0.769524 | 0.384762 | − | 0.923016i | \(-0.374283\pi\) | ||||
0.384762 | + | 0.923016i | \(0.374283\pi\) | |||||||
\(978\) | −11.9349 | −0.381637 | ||||||||
\(979\) | 18.9231 | 0.604785 | ||||||||
\(980\) | −3.08327 | −0.0984913 | ||||||||
\(981\) | 4.28510 | 0.136813 | ||||||||
\(982\) | −6.41368 | −0.204669 | ||||||||
\(983\) | 25.4509 | 0.811758 | 0.405879 | − | 0.913927i | \(-0.366965\pi\) | ||||
0.405879 | + | 0.913927i | \(0.366965\pi\) | |||||||
\(984\) | −9.71768 | −0.309788 | ||||||||
\(985\) | 0.900666 | 0.0286976 | ||||||||
\(986\) | 0.778762 | 0.0248008 | ||||||||
\(987\) | −0.929311 | −0.0295803 | ||||||||
\(988\) | −7.23270 | −0.230103 | ||||||||
\(989\) | 11.6281 | 0.369753 | ||||||||
\(990\) | 0.539454 | 0.0171450 | ||||||||
\(991\) | 18.3877 | 0.584104 | 0.292052 | − | 0.956402i | \(-0.405662\pi\) | ||||
0.292052 | + | 0.956402i | \(0.405662\pi\) | |||||||
\(992\) | −0.823617 | −0.0261499 | ||||||||
\(993\) | −29.0460 | −0.921747 | ||||||||
\(994\) | 12.7654 | 0.404895 | ||||||||
\(995\) | 1.86857 | 0.0592376 | ||||||||
\(996\) | 14.6910 | 0.465502 | ||||||||
\(997\) | −15.3558 | −0.486322 | −0.243161 | − | 0.969986i | \(-0.578184\pi\) | ||||
−0.243161 | + | 0.969986i | \(0.578184\pi\) | |||||||
\(998\) | 24.8825 | 0.787642 | ||||||||
\(999\) | −5.74456 | −0.181750 |
(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 | 8034.2.a.bb.1.9 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.bb.1.9 | ✓ | 14 | 1.1 | even | 1 | trivial |