Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6042,2,Mod(1,6042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6042, 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("6042.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6042.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: | \(48.2456129013\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5 x^{11} - 27 x^{10} + 134 x^{9} + 294 x^{8} - 1313 x^{7} - 1685 x^{6} + 5910 x^{5} + 5237 x^{4} - 12206 x^{3} - 7876 x^{2} + 9264 x + 4048 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.22349\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6042.1 |
$q$-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 | ||||||||
\(5\) | −4.22349 | −1.88880 | −0.944401 | − | 0.328795i | \(-0.893358\pi\) | ||||
−0.944401 | + | 0.328795i | \(0.893358\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 3.89357 | 1.47163 | 0.735816 | − | 0.677181i | \(-0.236799\pi\) | ||||
0.735816 | + | 0.677181i | \(0.236799\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 4.22349 | 1.33559 | ||||||||
\(11\) | 1.39763 | 0.421402 | 0.210701 | − | 0.977551i | \(-0.432425\pi\) | ||||
0.210701 | + | 0.977551i | \(0.432425\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 6.39181 | 1.77277 | 0.886384 | − | 0.462950i | \(-0.153209\pi\) | ||||
0.886384 | + | 0.462950i | \(0.153209\pi\) | |||||||
\(14\) | −3.89357 | −1.04060 | ||||||||
\(15\) | −4.22349 | −1.09050 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.62509 | 1.60682 | 0.803410 | − | 0.595426i | \(-0.203017\pi\) | ||||
0.803410 | + | 0.595426i | \(0.203017\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −4.22349 | −0.944401 | ||||||||
\(21\) | 3.89357 | 0.849647 | ||||||||
\(22\) | −1.39763 | −0.297976 | ||||||||
\(23\) | 4.91438 | 1.02472 | 0.512359 | − | 0.858771i | \(-0.328772\pi\) | ||||
0.512359 | + | 0.858771i | \(0.328772\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 12.8379 | 2.56758 | ||||||||
\(26\) | −6.39181 | −1.25354 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 3.89357 | 0.735816 | ||||||||
\(29\) | 5.17021 | 0.960084 | 0.480042 | − | 0.877246i | \(-0.340621\pi\) | ||||
0.480042 | + | 0.877246i | \(0.340621\pi\) | |||||||
\(30\) | 4.22349 | 0.771101 | ||||||||
\(31\) | 9.08792 | 1.63224 | 0.816119 | − | 0.577884i | \(-0.196121\pi\) | ||||
0.816119 | + | 0.577884i | \(0.196121\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.39763 | 0.243297 | ||||||||
\(34\) | −6.62509 | −1.13619 | ||||||||
\(35\) | −16.4445 | −2.77962 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 3.19935 | 0.525970 | 0.262985 | − | 0.964800i | \(-0.415293\pi\) | ||||
0.262985 | + | 0.964800i | \(0.415293\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 6.39181 | 1.02351 | ||||||||
\(40\) | 4.22349 | 0.667793 | ||||||||
\(41\) | −8.33052 | −1.30101 | −0.650504 | − | 0.759503i | \(-0.725442\pi\) | ||||
−0.650504 | + | 0.759503i | \(0.725442\pi\) | |||||||
\(42\) | −3.89357 | −0.600791 | ||||||||
\(43\) | −2.91438 | −0.444439 | −0.222219 | − | 0.974997i | \(-0.571330\pi\) | ||||
−0.222219 | + | 0.974997i | \(0.571330\pi\) | |||||||
\(44\) | 1.39763 | 0.210701 | ||||||||
\(45\) | −4.22349 | −0.629601 | ||||||||
\(46\) | −4.91438 | −0.724586 | ||||||||
\(47\) | −3.31449 | −0.483468 | −0.241734 | − | 0.970343i | \(-0.577716\pi\) | ||||
−0.241734 | + | 0.970343i | \(0.577716\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 8.15991 | 1.16570 | ||||||||
\(50\) | −12.8379 | −1.81555 | ||||||||
\(51\) | 6.62509 | 0.927698 | ||||||||
\(52\) | 6.39181 | 0.886384 | ||||||||
\(53\) | 1.00000 | 0.137361 | ||||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −5.90289 | −0.795945 | ||||||||
\(56\) | −3.89357 | −0.520301 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | −5.17021 | −0.678882 | ||||||||
\(59\) | 1.28144 | 0.166830 | 0.0834149 | − | 0.996515i | \(-0.473417\pi\) | ||||
0.0834149 | + | 0.996515i | \(0.473417\pi\) | |||||||
\(60\) | −4.22349 | −0.545250 | ||||||||
\(61\) | −14.2334 | −1.82240 | −0.911199 | − | 0.411967i | \(-0.864842\pi\) | ||||
−0.911199 | + | 0.411967i | \(0.864842\pi\) | |||||||
\(62\) | −9.08792 | −1.15417 | ||||||||
\(63\) | 3.89357 | 0.490544 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −26.9957 | −3.34841 | ||||||||
\(66\) | −1.39763 | −0.172037 | ||||||||
\(67\) | 1.72928 | 0.211265 | 0.105633 | − | 0.994405i | \(-0.466313\pi\) | ||||
0.105633 | + | 0.994405i | \(0.466313\pi\) | |||||||
\(68\) | 6.62509 | 0.803410 | ||||||||
\(69\) | 4.91438 | 0.591622 | ||||||||
\(70\) | 16.4445 | 1.96549 | ||||||||
\(71\) | −14.6340 | −1.73673 | −0.868367 | − | 0.495923i | \(-0.834830\pi\) | ||||
−0.868367 | + | 0.495923i | \(0.834830\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −8.59442 | −1.00590 | −0.502951 | − | 0.864315i | \(-0.667752\pi\) | ||||
−0.502951 | + | 0.864315i | \(0.667752\pi\) | |||||||
\(74\) | −3.19935 | −0.371917 | ||||||||
\(75\) | 12.8379 | 1.48239 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 5.44178 | 0.620149 | ||||||||
\(78\) | −6.39181 | −0.723730 | ||||||||
\(79\) | 0.401082 | 0.0451253 | 0.0225626 | − | 0.999745i | \(-0.492817\pi\) | ||||
0.0225626 | + | 0.999745i | \(0.492817\pi\) | |||||||
\(80\) | −4.22349 | −0.472201 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 8.33052 | 0.919952 | ||||||||
\(83\) | 17.6808 | 1.94072 | 0.970360 | − | 0.241663i | \(-0.0776927\pi\) | ||||
0.970360 | + | 0.241663i | \(0.0776927\pi\) | |||||||
\(84\) | 3.89357 | 0.424824 | ||||||||
\(85\) | −27.9810 | −3.03497 | ||||||||
\(86\) | 2.91438 | 0.314266 | ||||||||
\(87\) | 5.17021 | 0.554305 | ||||||||
\(88\) | −1.39763 | −0.148988 | ||||||||
\(89\) | −3.45446 | −0.366172 | −0.183086 | − | 0.983097i | \(-0.558609\pi\) | ||||
−0.183086 | + | 0.983097i | \(0.558609\pi\) | |||||||
\(90\) | 4.22349 | 0.445195 | ||||||||
\(91\) | 24.8870 | 2.60886 | ||||||||
\(92\) | 4.91438 | 0.512359 | ||||||||
\(93\) | 9.08792 | 0.942373 | ||||||||
\(94\) | 3.31449 | 0.341863 | ||||||||
\(95\) | −4.22349 | −0.433321 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −12.2819 | −1.24703 | −0.623517 | − | 0.781809i | \(-0.714297\pi\) | ||||
−0.623517 | + | 0.781809i | \(0.714297\pi\) | |||||||
\(98\) | −8.15991 | −0.824275 | ||||||||
\(99\) | 1.39763 | 0.140467 | ||||||||
\(100\) | 12.8379 | 1.28379 | ||||||||
\(101\) | 16.3423 | 1.62611 | 0.813057 | − | 0.582183i | \(-0.197801\pi\) | ||||
0.813057 | + | 0.582183i | \(0.197801\pi\) | |||||||
\(102\) | −6.62509 | −0.655982 | ||||||||
\(103\) | −12.1122 | −1.19345 | −0.596724 | − | 0.802446i | \(-0.703531\pi\) | ||||
−0.596724 | + | 0.802446i | \(0.703531\pi\) | |||||||
\(104\) | −6.39181 | −0.626768 | ||||||||
\(105\) | −16.4445 | −1.60482 | ||||||||
\(106\) | −1.00000 | −0.0971286 | ||||||||
\(107\) | −7.11873 | −0.688194 | −0.344097 | − | 0.938934i | \(-0.611815\pi\) | ||||
−0.344097 | + | 0.938934i | \(0.611815\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 15.5533 | 1.48973 | 0.744867 | − | 0.667213i | \(-0.232513\pi\) | ||||
0.744867 | + | 0.667213i | \(0.232513\pi\) | |||||||
\(110\) | 5.90289 | 0.562818 | ||||||||
\(111\) | 3.19935 | 0.303669 | ||||||||
\(112\) | 3.89357 | 0.367908 | ||||||||
\(113\) | 13.3002 | 1.25118 | 0.625588 | − | 0.780154i | \(-0.284859\pi\) | ||||
0.625588 | + | 0.780154i | \(0.284859\pi\) | |||||||
\(114\) | −1.00000 | −0.0936586 | ||||||||
\(115\) | −20.7558 | −1.93549 | ||||||||
\(116\) | 5.17021 | 0.480042 | ||||||||
\(117\) | 6.39181 | 0.590923 | ||||||||
\(118\) | −1.28144 | −0.117966 | ||||||||
\(119\) | 25.7953 | 2.36465 | ||||||||
\(120\) | 4.22349 | 0.385550 | ||||||||
\(121\) | −9.04662 | −0.822420 | ||||||||
\(122\) | 14.2334 | 1.28863 | ||||||||
\(123\) | −8.33052 | −0.751138 | ||||||||
\(124\) | 9.08792 | 0.816119 | ||||||||
\(125\) | −33.1032 | −2.96084 | ||||||||
\(126\) | −3.89357 | −0.346867 | ||||||||
\(127\) | −0.284449 | −0.0252408 | −0.0126204 | − | 0.999920i | \(-0.504017\pi\) | ||||
−0.0126204 | + | 0.999920i | \(0.504017\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −2.91438 | −0.256597 | ||||||||
\(130\) | 26.9957 | 2.36768 | ||||||||
\(131\) | 5.09021 | 0.444734 | 0.222367 | − | 0.974963i | \(-0.428622\pi\) | ||||
0.222367 | + | 0.974963i | \(0.428622\pi\) | |||||||
\(132\) | 1.39763 | 0.121648 | ||||||||
\(133\) | 3.89357 | 0.337616 | ||||||||
\(134\) | −1.72928 | −0.149387 | ||||||||
\(135\) | −4.22349 | −0.363500 | ||||||||
\(136\) | −6.62509 | −0.568097 | ||||||||
\(137\) | −22.5889 | −1.92990 | −0.964948 | − | 0.262441i | \(-0.915473\pi\) | ||||
−0.964948 | + | 0.262441i | \(0.915473\pi\) | |||||||
\(138\) | −4.91438 | −0.418340 | ||||||||
\(139\) | 20.7843 | 1.76290 | 0.881452 | − | 0.472273i | \(-0.156566\pi\) | ||||
0.881452 | + | 0.472273i | \(0.156566\pi\) | |||||||
\(140\) | −16.4445 | −1.38981 | ||||||||
\(141\) | −3.31449 | −0.279130 | ||||||||
\(142\) | 14.6340 | 1.22806 | ||||||||
\(143\) | 8.93340 | 0.747048 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −21.8363 | −1.81341 | ||||||||
\(146\) | 8.59442 | 0.711280 | ||||||||
\(147\) | 8.15991 | 0.673018 | ||||||||
\(148\) | 3.19935 | 0.262985 | ||||||||
\(149\) | −12.9791 | −1.06329 | −0.531644 | − | 0.846968i | \(-0.678426\pi\) | ||||
−0.531644 | + | 0.846968i | \(0.678426\pi\) | |||||||
\(150\) | −12.8379 | −1.04821 | ||||||||
\(151\) | 14.2437 | 1.15913 | 0.579567 | − | 0.814924i | \(-0.303222\pi\) | ||||
0.579567 | + | 0.814924i | \(0.303222\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 6.62509 | 0.535607 | ||||||||
\(154\) | −5.44178 | −0.438511 | ||||||||
\(155\) | −38.3827 | −3.08298 | ||||||||
\(156\) | 6.39181 | 0.511754 | ||||||||
\(157\) | 14.8382 | 1.18422 | 0.592109 | − | 0.805858i | \(-0.298296\pi\) | ||||
0.592109 | + | 0.805858i | \(0.298296\pi\) | |||||||
\(158\) | −0.401082 | −0.0319084 | ||||||||
\(159\) | 1.00000 | 0.0793052 | ||||||||
\(160\) | 4.22349 | 0.333896 | ||||||||
\(161\) | 19.1345 | 1.50801 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −15.5059 | −1.21452 | −0.607258 | − | 0.794505i | \(-0.707731\pi\) | ||||
−0.607258 | + | 0.794505i | \(0.707731\pi\) | |||||||
\(164\) | −8.33052 | −0.650504 | ||||||||
\(165\) | −5.90289 | −0.459539 | ||||||||
\(166\) | −17.6808 | −1.37230 | ||||||||
\(167\) | 7.97057 | 0.616781 | 0.308391 | − | 0.951260i | \(-0.400210\pi\) | ||||
0.308391 | + | 0.951260i | \(0.400210\pi\) | |||||||
\(168\) | −3.89357 | −0.300396 | ||||||||
\(169\) | 27.8552 | 2.14271 | ||||||||
\(170\) | 27.9810 | 2.14605 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | −2.91438 | −0.222219 | ||||||||
\(173\) | −21.5813 | −1.64080 | −0.820398 | − | 0.571793i | \(-0.806248\pi\) | ||||
−0.820398 | + | 0.571793i | \(0.806248\pi\) | |||||||
\(174\) | −5.17021 | −0.391953 | ||||||||
\(175\) | 49.9852 | 3.77853 | ||||||||
\(176\) | 1.39763 | 0.105351 | ||||||||
\(177\) | 1.28144 | 0.0963192 | ||||||||
\(178\) | 3.45446 | 0.258923 | ||||||||
\(179\) | −8.43180 | −0.630222 | −0.315111 | − | 0.949055i | \(-0.602042\pi\) | ||||
−0.315111 | + | 0.949055i | \(0.602042\pi\) | |||||||
\(180\) | −4.22349 | −0.314800 | ||||||||
\(181\) | 8.13253 | 0.604486 | 0.302243 | − | 0.953231i | \(-0.402265\pi\) | ||||
0.302243 | + | 0.953231i | \(0.402265\pi\) | |||||||
\(182\) | −24.8870 | −1.84475 | ||||||||
\(183\) | −14.2334 | −1.05216 | ||||||||
\(184\) | −4.91438 | −0.362293 | ||||||||
\(185\) | −13.5124 | −0.993454 | ||||||||
\(186\) | −9.08792 | −0.666359 | ||||||||
\(187\) | 9.25944 | 0.677117 | ||||||||
\(188\) | −3.31449 | −0.241734 | ||||||||
\(189\) | 3.89357 | 0.283216 | ||||||||
\(190\) | 4.22349 | 0.306404 | ||||||||
\(191\) | −13.8455 | −1.00183 | −0.500914 | − | 0.865497i | \(-0.667003\pi\) | ||||
−0.500914 | + | 0.865497i | \(0.667003\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 0.356400 | 0.0256542 | 0.0128271 | − | 0.999918i | \(-0.495917\pi\) | ||||
0.0128271 | + | 0.999918i | \(0.495917\pi\) | |||||||
\(194\) | 12.2819 | 0.881787 | ||||||||
\(195\) | −26.9957 | −1.93321 | ||||||||
\(196\) | 8.15991 | 0.582851 | ||||||||
\(197\) | −3.72524 | −0.265413 | −0.132706 | − | 0.991155i | \(-0.542367\pi\) | ||||
−0.132706 | + | 0.991155i | \(0.542367\pi\) | |||||||
\(198\) | −1.39763 | −0.0993254 | ||||||||
\(199\) | −7.09049 | −0.502632 | −0.251316 | − | 0.967905i | \(-0.580863\pi\) | ||||
−0.251316 | + | 0.967905i | \(0.580863\pi\) | |||||||
\(200\) | −12.8379 | −0.907775 | ||||||||
\(201\) | 1.72928 | 0.121974 | ||||||||
\(202\) | −16.3423 | −1.14984 | ||||||||
\(203\) | 20.1306 | 1.41289 | ||||||||
\(204\) | 6.62509 | 0.463849 | ||||||||
\(205\) | 35.1839 | 2.45735 | ||||||||
\(206\) | 12.1122 | 0.843895 | ||||||||
\(207\) | 4.91438 | 0.341573 | ||||||||
\(208\) | 6.39181 | 0.443192 | ||||||||
\(209\) | 1.39763 | 0.0966763 | ||||||||
\(210\) | 16.4445 | 1.13478 | ||||||||
\(211\) | −6.34960 | −0.437124 | −0.218562 | − | 0.975823i | \(-0.570137\pi\) | ||||
−0.218562 | + | 0.975823i | \(0.570137\pi\) | |||||||
\(212\) | 1.00000 | 0.0686803 | ||||||||
\(213\) | −14.6340 | −1.00270 | ||||||||
\(214\) | 7.11873 | 0.486626 | ||||||||
\(215\) | 12.3089 | 0.839457 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 35.3845 | 2.40205 | ||||||||
\(218\) | −15.5533 | −1.05340 | ||||||||
\(219\) | −8.59442 | −0.580757 | ||||||||
\(220\) | −5.90289 | −0.397973 | ||||||||
\(221\) | 42.3463 | 2.84852 | ||||||||
\(222\) | −3.19935 | −0.214726 | ||||||||
\(223\) | −15.3317 | −1.02669 | −0.513343 | − | 0.858183i | \(-0.671593\pi\) | ||||
−0.513343 | + | 0.858183i | \(0.671593\pi\) | |||||||
\(224\) | −3.89357 | −0.260150 | ||||||||
\(225\) | 12.8379 | 0.855859 | ||||||||
\(226\) | −13.3002 | −0.884715 | ||||||||
\(227\) | 10.2980 | 0.683503 | 0.341751 | − | 0.939790i | \(-0.388980\pi\) | ||||
0.341751 | + | 0.939790i | \(0.388980\pi\) | |||||||
\(228\) | 1.00000 | 0.0662266 | ||||||||
\(229\) | −21.0001 | −1.38772 | −0.693862 | − | 0.720108i | \(-0.744092\pi\) | ||||
−0.693862 | + | 0.720108i | \(0.744092\pi\) | |||||||
\(230\) | 20.7558 | 1.36860 | ||||||||
\(231\) | 5.44178 | 0.358043 | ||||||||
\(232\) | −5.17021 | −0.339441 | ||||||||
\(233\) | 10.4476 | 0.684442 | 0.342221 | − | 0.939620i | \(-0.388821\pi\) | ||||
0.342221 | + | 0.939620i | \(0.388821\pi\) | |||||||
\(234\) | −6.39181 | −0.417846 | ||||||||
\(235\) | 13.9987 | 0.913175 | ||||||||
\(236\) | 1.28144 | 0.0834149 | ||||||||
\(237\) | 0.401082 | 0.0260531 | ||||||||
\(238\) | −25.7953 | −1.67206 | ||||||||
\(239\) | −22.3004 | −1.44249 | −0.721246 | − | 0.692679i | \(-0.756430\pi\) | ||||
−0.721246 | + | 0.692679i | \(0.756430\pi\) | |||||||
\(240\) | −4.22349 | −0.272625 | ||||||||
\(241\) | −3.10563 | −0.200051 | −0.100026 | − | 0.994985i | \(-0.531893\pi\) | ||||
−0.100026 | + | 0.994985i | \(0.531893\pi\) | |||||||
\(242\) | 9.04662 | 0.581539 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −14.2334 | −0.911199 | ||||||||
\(245\) | −34.4633 | −2.20178 | ||||||||
\(246\) | 8.33052 | 0.531135 | ||||||||
\(247\) | 6.39181 | 0.406701 | ||||||||
\(248\) | −9.08792 | −0.577083 | ||||||||
\(249\) | 17.6808 | 1.12048 | ||||||||
\(250\) | 33.1032 | 2.09363 | ||||||||
\(251\) | 3.24901 | 0.205076 | 0.102538 | − | 0.994729i | \(-0.467304\pi\) | ||||
0.102538 | + | 0.994729i | \(0.467304\pi\) | |||||||
\(252\) | 3.89357 | 0.245272 | ||||||||
\(253\) | 6.86850 | 0.431819 | ||||||||
\(254\) | 0.284449 | 0.0178479 | ||||||||
\(255\) | −27.9810 | −1.75224 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −2.35501 | −0.146902 | −0.0734508 | − | 0.997299i | \(-0.523401\pi\) | ||||
−0.0734508 | + | 0.997299i | \(0.523401\pi\) | |||||||
\(258\) | 2.91438 | 0.181441 | ||||||||
\(259\) | 12.4569 | 0.774035 | ||||||||
\(260\) | −26.9957 | −1.67421 | ||||||||
\(261\) | 5.17021 | 0.320028 | ||||||||
\(262\) | −5.09021 | −0.314474 | ||||||||
\(263\) | −2.60931 | −0.160897 | −0.0804485 | − | 0.996759i | \(-0.525635\pi\) | ||||
−0.0804485 | + | 0.996759i | \(0.525635\pi\) | |||||||
\(264\) | −1.39763 | −0.0860183 | ||||||||
\(265\) | −4.22349 | −0.259447 | ||||||||
\(266\) | −3.89357 | −0.238730 | ||||||||
\(267\) | −3.45446 | −0.211409 | ||||||||
\(268\) | 1.72928 | 0.105633 | ||||||||
\(269\) | 22.2422 | 1.35613 | 0.678065 | − | 0.735002i | \(-0.262819\pi\) | ||||
0.678065 | + | 0.735002i | \(0.262819\pi\) | |||||||
\(270\) | 4.22349 | 0.257034 | ||||||||
\(271\) | −3.51603 | −0.213584 | −0.106792 | − | 0.994281i | \(-0.534058\pi\) | ||||
−0.106792 | + | 0.994281i | \(0.534058\pi\) | |||||||
\(272\) | 6.62509 | 0.401705 | ||||||||
\(273\) | 24.8870 | 1.50623 | ||||||||
\(274\) | 22.5889 | 1.36464 | ||||||||
\(275\) | 17.9426 | 1.08198 | ||||||||
\(276\) | 4.91438 | 0.295811 | ||||||||
\(277\) | 0.273929 | 0.0164588 | 0.00822939 | − | 0.999966i | \(-0.497380\pi\) | ||||
0.00822939 | + | 0.999966i | \(0.497380\pi\) | |||||||
\(278\) | −20.7843 | −1.24656 | ||||||||
\(279\) | 9.08792 | 0.544079 | ||||||||
\(280\) | 16.4445 | 0.982745 | ||||||||
\(281\) | 8.62051 | 0.514257 | 0.257128 | − | 0.966377i | \(-0.417224\pi\) | ||||
0.257128 | + | 0.966377i | \(0.417224\pi\) | |||||||
\(282\) | 3.31449 | 0.197375 | ||||||||
\(283\) | −6.97293 | −0.414498 | −0.207249 | − | 0.978288i | \(-0.566451\pi\) | ||||
−0.207249 | + | 0.978288i | \(0.566451\pi\) | |||||||
\(284\) | −14.6340 | −0.868367 | ||||||||
\(285\) | −4.22349 | −0.250178 | ||||||||
\(286\) | −8.93340 | −0.528243 | ||||||||
\(287\) | −32.4355 | −1.91461 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 26.8918 | 1.58187 | ||||||||
\(290\) | 21.8363 | 1.28227 | ||||||||
\(291\) | −12.2819 | −0.719976 | ||||||||
\(292\) | −8.59442 | −0.502951 | ||||||||
\(293\) | 14.1738 | 0.828044 | 0.414022 | − | 0.910267i | \(-0.364124\pi\) | ||||
0.414022 | + | 0.910267i | \(0.364124\pi\) | |||||||
\(294\) | −8.15991 | −0.475896 | ||||||||
\(295\) | −5.41217 | −0.315109 | ||||||||
\(296\) | −3.19935 | −0.185959 | ||||||||
\(297\) | 1.39763 | 0.0810989 | ||||||||
\(298\) | 12.9791 | 0.751859 | ||||||||
\(299\) | 31.4118 | 1.81659 | ||||||||
\(300\) | 12.8379 | 0.741195 | ||||||||
\(301\) | −11.3473 | −0.654050 | ||||||||
\(302\) | −14.2437 | −0.819632 | ||||||||
\(303\) | 16.3423 | 0.938838 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 60.1146 | 3.44215 | ||||||||
\(306\) | −6.62509 | −0.378731 | ||||||||
\(307\) | −24.9195 | −1.42223 | −0.711116 | − | 0.703075i | \(-0.751810\pi\) | ||||
−0.711116 | + | 0.703075i | \(0.751810\pi\) | |||||||
\(308\) | 5.44178 | 0.310074 | ||||||||
\(309\) | −12.1122 | −0.689038 | ||||||||
\(310\) | 38.3827 | 2.17999 | ||||||||
\(311\) | −1.66374 | −0.0943418 | −0.0471709 | − | 0.998887i | \(-0.515021\pi\) | ||||
−0.0471709 | + | 0.998887i | \(0.515021\pi\) | |||||||
\(312\) | −6.39181 | −0.361865 | ||||||||
\(313\) | −23.7002 | −1.33962 | −0.669808 | − | 0.742535i | \(-0.733623\pi\) | ||||
−0.669808 | + | 0.742535i | \(0.733623\pi\) | |||||||
\(314\) | −14.8382 | −0.837368 | ||||||||
\(315\) | −16.4445 | −0.926541 | ||||||||
\(316\) | 0.401082 | 0.0225626 | ||||||||
\(317\) | −12.5172 | −0.703036 | −0.351518 | − | 0.936181i | \(-0.614334\pi\) | ||||
−0.351518 | + | 0.936181i | \(0.614334\pi\) | |||||||
\(318\) | −1.00000 | −0.0560772 | ||||||||
\(319\) | 7.22605 | 0.404581 | ||||||||
\(320\) | −4.22349 | −0.236100 | ||||||||
\(321\) | −7.11873 | −0.397329 | ||||||||
\(322\) | −19.1345 | −1.06632 | ||||||||
\(323\) | 6.62509 | 0.368630 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 82.0573 | 4.55172 | ||||||||
\(326\) | 15.5059 | 0.858792 | ||||||||
\(327\) | 15.5533 | 0.860098 | ||||||||
\(328\) | 8.33052 | 0.459976 | ||||||||
\(329\) | −12.9052 | −0.711487 | ||||||||
\(330\) | 5.90289 | 0.324943 | ||||||||
\(331\) | 12.0207 | 0.660719 | 0.330359 | − | 0.943855i | \(-0.392830\pi\) | ||||
0.330359 | + | 0.943855i | \(0.392830\pi\) | |||||||
\(332\) | 17.6808 | 0.970360 | ||||||||
\(333\) | 3.19935 | 0.175323 | ||||||||
\(334\) | −7.97057 | −0.436130 | ||||||||
\(335\) | −7.30360 | −0.399038 | ||||||||
\(336\) | 3.89357 | 0.212412 | ||||||||
\(337\) | −27.6560 | −1.50652 | −0.753258 | − | 0.657725i | \(-0.771519\pi\) | ||||
−0.753258 | + | 0.657725i | \(0.771519\pi\) | |||||||
\(338\) | −27.8552 | −1.51512 | ||||||||
\(339\) | 13.3002 | 0.722367 | ||||||||
\(340\) | −27.9810 | −1.51748 | ||||||||
\(341\) | 12.7016 | 0.687829 | ||||||||
\(342\) | −1.00000 | −0.0540738 | ||||||||
\(343\) | 4.51620 | 0.243852 | ||||||||
\(344\) | 2.91438 | 0.157133 | ||||||||
\(345\) | −20.7558 | −1.11746 | ||||||||
\(346\) | 21.5813 | 1.16022 | ||||||||
\(347\) | 19.4805 | 1.04577 | 0.522883 | − | 0.852404i | \(-0.324856\pi\) | ||||
0.522883 | + | 0.852404i | \(0.324856\pi\) | |||||||
\(348\) | 5.17021 | 0.277152 | ||||||||
\(349\) | 0.935636 | 0.0500834 | 0.0250417 | − | 0.999686i | \(-0.492028\pi\) | ||||
0.0250417 | + | 0.999686i | \(0.492028\pi\) | |||||||
\(350\) | −49.9852 | −2.67182 | ||||||||
\(351\) | 6.39181 | 0.341169 | ||||||||
\(352\) | −1.39763 | −0.0744941 | ||||||||
\(353\) | 27.2562 | 1.45070 | 0.725349 | − | 0.688381i | \(-0.241678\pi\) | ||||
0.725349 | + | 0.688381i | \(0.241678\pi\) | |||||||
\(354\) | −1.28144 | −0.0681080 | ||||||||
\(355\) | 61.8065 | 3.28035 | ||||||||
\(356\) | −3.45446 | −0.183086 | ||||||||
\(357\) | 25.7953 | 1.36523 | ||||||||
\(358\) | 8.43180 | 0.445634 | ||||||||
\(359\) | −14.3368 | −0.756665 | −0.378332 | − | 0.925670i | \(-0.623502\pi\) | ||||
−0.378332 | + | 0.925670i | \(0.623502\pi\) | |||||||
\(360\) | 4.22349 | 0.222598 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −8.13253 | −0.427436 | ||||||||
\(363\) | −9.04662 | −0.474825 | ||||||||
\(364\) | 24.8870 | 1.30443 | ||||||||
\(365\) | 36.2985 | 1.89995 | ||||||||
\(366\) | 14.2334 | 0.743991 | ||||||||
\(367\) | 5.07573 | 0.264951 | 0.132476 | − | 0.991186i | \(-0.457707\pi\) | ||||
0.132476 | + | 0.991186i | \(0.457707\pi\) | |||||||
\(368\) | 4.91438 | 0.256180 | ||||||||
\(369\) | −8.33052 | −0.433670 | ||||||||
\(370\) | 13.5124 | 0.702478 | ||||||||
\(371\) | 3.89357 | 0.202144 | ||||||||
\(372\) | 9.08792 | 0.471187 | ||||||||
\(373\) | 5.06710 | 0.262365 | 0.131182 | − | 0.991358i | \(-0.458123\pi\) | ||||
0.131182 | + | 0.991358i | \(0.458123\pi\) | |||||||
\(374\) | −9.25944 | −0.478794 | ||||||||
\(375\) | −33.1032 | −1.70944 | ||||||||
\(376\) | 3.31449 | 0.170932 | ||||||||
\(377\) | 33.0470 | 1.70201 | ||||||||
\(378\) | −3.89357 | −0.200264 | ||||||||
\(379\) | 21.3462 | 1.09648 | 0.548241 | − | 0.836321i | \(-0.315298\pi\) | ||||
0.548241 | + | 0.836321i | \(0.315298\pi\) | |||||||
\(380\) | −4.22349 | −0.216661 | ||||||||
\(381\) | −0.284449 | −0.0145728 | ||||||||
\(382\) | 13.8455 | 0.708399 | ||||||||
\(383\) | −2.17408 | −0.111090 | −0.0555452 | − | 0.998456i | \(-0.517690\pi\) | ||||
−0.0555452 | + | 0.998456i | \(0.517690\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −22.9833 | −1.17134 | ||||||||
\(386\) | −0.356400 | −0.0181403 | ||||||||
\(387\) | −2.91438 | −0.148146 | ||||||||
\(388\) | −12.2819 | −0.623517 | ||||||||
\(389\) | 24.0139 | 1.21755 | 0.608777 | − | 0.793341i | \(-0.291660\pi\) | ||||
0.608777 | + | 0.793341i | \(0.291660\pi\) | |||||||
\(390\) | 26.9957 | 1.36698 | ||||||||
\(391\) | 32.5582 | 1.64654 | ||||||||
\(392\) | −8.15991 | −0.412138 | ||||||||
\(393\) | 5.09021 | 0.256767 | ||||||||
\(394\) | 3.72524 | 0.187675 | ||||||||
\(395\) | −1.69397 | −0.0852328 | ||||||||
\(396\) | 1.39763 | 0.0702337 | ||||||||
\(397\) | −12.3957 | −0.622120 | −0.311060 | − | 0.950390i | \(-0.600684\pi\) | ||||
−0.311060 | + | 0.950390i | \(0.600684\pi\) | |||||||
\(398\) | 7.09049 | 0.355414 | ||||||||
\(399\) | 3.89357 | 0.194922 | ||||||||
\(400\) | 12.8379 | 0.641894 | ||||||||
\(401\) | −2.39611 | −0.119656 | −0.0598281 | − | 0.998209i | \(-0.519055\pi\) | ||||
−0.0598281 | + | 0.998209i | \(0.519055\pi\) | |||||||
\(402\) | −1.72928 | −0.0862487 | ||||||||
\(403\) | 58.0882 | 2.89358 | ||||||||
\(404\) | 16.3423 | 0.813057 | ||||||||
\(405\) | −4.22349 | −0.209867 | ||||||||
\(406\) | −20.1306 | −0.999064 | ||||||||
\(407\) | 4.47152 | 0.221645 | ||||||||
\(408\) | −6.62509 | −0.327991 | ||||||||
\(409\) | −12.5246 | −0.619302 | −0.309651 | − | 0.950850i | \(-0.600212\pi\) | ||||
−0.309651 | + | 0.950850i | \(0.600212\pi\) | |||||||
\(410\) | −35.1839 | −1.73761 | ||||||||
\(411\) | −22.5889 | −1.11423 | ||||||||
\(412\) | −12.1122 | −0.596724 | ||||||||
\(413\) | 4.98940 | 0.245512 | ||||||||
\(414\) | −4.91438 | −0.241529 | ||||||||
\(415\) | −74.6747 | −3.66564 | ||||||||
\(416\) | −6.39181 | −0.313384 | ||||||||
\(417\) | 20.7843 | 1.01781 | ||||||||
\(418\) | −1.39763 | −0.0683604 | ||||||||
\(419\) | −28.2150 | −1.37839 | −0.689196 | − | 0.724575i | \(-0.742036\pi\) | ||||
−0.689196 | + | 0.724575i | \(0.742036\pi\) | |||||||
\(420\) | −16.4445 | −0.802408 | ||||||||
\(421\) | 16.4246 | 0.800486 | 0.400243 | − | 0.916409i | \(-0.368926\pi\) | ||||
0.400243 | + | 0.916409i | \(0.368926\pi\) | |||||||
\(422\) | 6.34960 | 0.309094 | ||||||||
\(423\) | −3.31449 | −0.161156 | ||||||||
\(424\) | −1.00000 | −0.0485643 | ||||||||
\(425\) | 85.0521 | 4.12563 | ||||||||
\(426\) | 14.6340 | 0.709018 | ||||||||
\(427\) | −55.4187 | −2.68190 | ||||||||
\(428\) | −7.11873 | −0.344097 | ||||||||
\(429\) | 8.93340 | 0.431309 | ||||||||
\(430\) | −12.3089 | −0.593586 | ||||||||
\(431\) | −2.01343 | −0.0969833 | −0.0484917 | − | 0.998824i | \(-0.515441\pi\) | ||||
−0.0484917 | + | 0.998824i | \(0.515441\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −17.3549 | −0.834025 | −0.417013 | − | 0.908901i | \(-0.636923\pi\) | ||||
−0.417013 | + | 0.908901i | \(0.636923\pi\) | |||||||
\(434\) | −35.3845 | −1.69851 | ||||||||
\(435\) | −21.8363 | −1.04697 | ||||||||
\(436\) | 15.5533 | 0.744867 | ||||||||
\(437\) | 4.91438 | 0.235087 | ||||||||
\(438\) | 8.59442 | 0.410657 | ||||||||
\(439\) | −24.5865 | −1.17345 | −0.586724 | − | 0.809787i | \(-0.699583\pi\) | ||||
−0.586724 | + | 0.809787i | \(0.699583\pi\) | |||||||
\(440\) | 5.90289 | 0.281409 | ||||||||
\(441\) | 8.15991 | 0.388567 | ||||||||
\(442\) | −42.3463 | −2.01421 | ||||||||
\(443\) | −14.1705 | −0.673263 | −0.336631 | − | 0.941637i | \(-0.609288\pi\) | ||||
−0.336631 | + | 0.941637i | \(0.609288\pi\) | |||||||
\(444\) | 3.19935 | 0.151835 | ||||||||
\(445\) | 14.5899 | 0.691626 | ||||||||
\(446\) | 15.3317 | 0.725977 | ||||||||
\(447\) | −12.9791 | −0.613890 | ||||||||
\(448\) | 3.89357 | 0.183954 | ||||||||
\(449\) | 40.1610 | 1.89532 | 0.947658 | − | 0.319287i | \(-0.103444\pi\) | ||||
0.947658 | + | 0.319287i | \(0.103444\pi\) | |||||||
\(450\) | −12.8379 | −0.605183 | ||||||||
\(451\) | −11.6430 | −0.548248 | ||||||||
\(452\) | 13.3002 | 0.625588 | ||||||||
\(453\) | 14.2437 | 0.669227 | ||||||||
\(454\) | −10.2980 | −0.483309 | ||||||||
\(455\) | −105.110 | −4.92763 | ||||||||
\(456\) | −1.00000 | −0.0468293 | ||||||||
\(457\) | −14.6789 | −0.686651 | −0.343326 | − | 0.939216i | \(-0.611553\pi\) | ||||
−0.343326 | + | 0.939216i | \(0.611553\pi\) | |||||||
\(458\) | 21.0001 | 0.981269 | ||||||||
\(459\) | 6.62509 | 0.309233 | ||||||||
\(460\) | −20.7558 | −0.967746 | ||||||||
\(461\) | −37.4126 | −1.74248 | −0.871240 | − | 0.490857i | \(-0.836684\pi\) | ||||
−0.871240 | + | 0.490857i | \(0.836684\pi\) | |||||||
\(462\) | −5.44178 | −0.253175 | ||||||||
\(463\) | −39.7374 | −1.84675 | −0.923377 | − | 0.383895i | \(-0.874582\pi\) | ||||
−0.923377 | + | 0.383895i | \(0.874582\pi\) | |||||||
\(464\) | 5.17021 | 0.240021 | ||||||||
\(465\) | −38.3827 | −1.77996 | ||||||||
\(466\) | −10.4476 | −0.483973 | ||||||||
\(467\) | 1.57966 | 0.0730979 | 0.0365490 | − | 0.999332i | \(-0.488364\pi\) | ||||
0.0365490 | + | 0.999332i | \(0.488364\pi\) | |||||||
\(468\) | 6.39181 | 0.295461 | ||||||||
\(469\) | 6.73308 | 0.310905 | ||||||||
\(470\) | −13.9987 | −0.645712 | ||||||||
\(471\) | 14.8382 | 0.683708 | ||||||||
\(472\) | −1.28144 | −0.0589832 | ||||||||
\(473\) | −4.07323 | −0.187287 | ||||||||
\(474\) | −0.401082 | −0.0184223 | ||||||||
\(475\) | 12.8379 | 0.589042 | ||||||||
\(476\) | 25.7953 | 1.18232 | ||||||||
\(477\) | 1.00000 | 0.0457869 | ||||||||
\(478\) | 22.3004 | 1.02000 | ||||||||
\(479\) | −39.8886 | −1.82256 | −0.911278 | − | 0.411792i | \(-0.864903\pi\) | ||||
−0.911278 | + | 0.411792i | \(0.864903\pi\) | |||||||
\(480\) | 4.22349 | 0.192775 | ||||||||
\(481\) | 20.4496 | 0.932424 | ||||||||
\(482\) | 3.10563 | 0.141458 | ||||||||
\(483\) | 19.1345 | 0.870650 | ||||||||
\(484\) | −9.04662 | −0.411210 | ||||||||
\(485\) | 51.8724 | 2.35540 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −8.41305 | −0.381232 | −0.190616 | − | 0.981665i | \(-0.561048\pi\) | ||||
−0.190616 | + | 0.981665i | \(0.561048\pi\) | |||||||
\(488\) | 14.2334 | 0.644315 | ||||||||
\(489\) | −15.5059 | −0.701201 | ||||||||
\(490\) | 34.4633 | 1.55689 | ||||||||
\(491\) | −17.4356 | −0.786858 | −0.393429 | − | 0.919355i | \(-0.628711\pi\) | ||||
−0.393429 | + | 0.919355i | \(0.628711\pi\) | |||||||
\(492\) | −8.33052 | −0.375569 | ||||||||
\(493\) | 34.2531 | 1.54268 | ||||||||
\(494\) | −6.39181 | −0.287581 | ||||||||
\(495\) | −5.90289 | −0.265315 | ||||||||
\(496\) | 9.08792 | 0.408060 | ||||||||
\(497\) | −56.9784 | −2.55583 | ||||||||
\(498\) | −17.6808 | −0.792296 | ||||||||
\(499\) | −13.6058 | −0.609080 | −0.304540 | − | 0.952500i | \(-0.598503\pi\) | ||||
−0.304540 | + | 0.952500i | \(0.598503\pi\) | |||||||
\(500\) | −33.1032 | −1.48042 | ||||||||
\(501\) | 7.97057 | 0.356099 | ||||||||
\(502\) | −3.24901 | −0.145010 | ||||||||
\(503\) | 15.7280 | 0.701276 | 0.350638 | − | 0.936511i | \(-0.385965\pi\) | ||||
0.350638 | + | 0.936511i | \(0.385965\pi\) | |||||||
\(504\) | −3.89357 | −0.173434 | ||||||||
\(505\) | −69.0214 | −3.07141 | ||||||||
\(506\) | −6.86850 | −0.305342 | ||||||||
\(507\) | 27.8552 | 1.23709 | ||||||||
\(508\) | −0.284449 | −0.0126204 | ||||||||
\(509\) | −1.79321 | −0.0794825 | −0.0397413 | − | 0.999210i | \(-0.512653\pi\) | ||||
−0.0397413 | + | 0.999210i | \(0.512653\pi\) | |||||||
\(510\) | 27.9810 | 1.23902 | ||||||||
\(511\) | −33.4630 | −1.48032 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | 2.35501 | 0.103875 | ||||||||
\(515\) | 51.1557 | 2.25419 | ||||||||
\(516\) | −2.91438 | −0.128298 | ||||||||
\(517\) | −4.63243 | −0.203734 | ||||||||
\(518\) | −12.4569 | −0.547325 | ||||||||
\(519\) | −21.5813 | −0.947314 | ||||||||
\(520\) | 26.9957 | 1.18384 | ||||||||
\(521\) | −8.06785 | −0.353459 | −0.176729 | − | 0.984259i | \(-0.556552\pi\) | ||||
−0.176729 | + | 0.984259i | \(0.556552\pi\) | |||||||
\(522\) | −5.17021 | −0.226294 | ||||||||
\(523\) | 26.7063 | 1.16778 | 0.583892 | − | 0.811831i | \(-0.301529\pi\) | ||||
0.583892 | + | 0.811831i | \(0.301529\pi\) | |||||||
\(524\) | 5.09021 | 0.222367 | ||||||||
\(525\) | 49.9852 | 2.18153 | ||||||||
\(526\) | 2.60931 | 0.113771 | ||||||||
\(527\) | 60.2083 | 2.62271 | ||||||||
\(528\) | 1.39763 | 0.0608241 | ||||||||
\(529\) | 1.15112 | 0.0500489 | ||||||||
\(530\) | 4.22349 | 0.183457 | ||||||||
\(531\) | 1.28144 | 0.0556099 | ||||||||
\(532\) | 3.89357 | 0.168808 | ||||||||
\(533\) | −53.2471 | −2.30639 | ||||||||
\(534\) | 3.45446 | 0.149489 | ||||||||
\(535\) | 30.0659 | 1.29986 | ||||||||
\(536\) | −1.72928 | −0.0746935 | ||||||||
\(537\) | −8.43180 | −0.363859 | ||||||||
\(538\) | −22.2422 | −0.958929 | ||||||||
\(539\) | 11.4046 | 0.491229 | ||||||||
\(540\) | −4.22349 | −0.181750 | ||||||||
\(541\) | 21.8595 | 0.939812 | 0.469906 | − | 0.882716i | \(-0.344288\pi\) | ||||
0.469906 | + | 0.882716i | \(0.344288\pi\) | |||||||
\(542\) | 3.51603 | 0.151026 | ||||||||
\(543\) | 8.13253 | 0.349000 | ||||||||
\(544\) | −6.62509 | −0.284048 | ||||||||
\(545\) | −65.6891 | −2.81381 | ||||||||
\(546\) | −24.8870 | −1.06506 | ||||||||
\(547\) | −41.1697 | −1.76029 | −0.880145 | − | 0.474706i | \(-0.842554\pi\) | ||||
−0.880145 | + | 0.474706i | \(0.842554\pi\) | |||||||
\(548\) | −22.5889 | −0.964948 | ||||||||
\(549\) | −14.2334 | −0.607466 | ||||||||
\(550\) | −17.9426 | −0.765077 | ||||||||
\(551\) | 5.17021 | 0.220258 | ||||||||
\(552\) | −4.91438 | −0.209170 | ||||||||
\(553\) | 1.56164 | 0.0664078 | ||||||||
\(554\) | −0.273929 | −0.0116381 | ||||||||
\(555\) | −13.5124 | −0.573571 | ||||||||
\(556\) | 20.7843 | 0.881452 | ||||||||
\(557\) | 1.61913 | 0.0686047 | 0.0343024 | − | 0.999412i | \(-0.489079\pi\) | ||||
0.0343024 | + | 0.999412i | \(0.489079\pi\) | |||||||
\(558\) | −9.08792 | −0.384722 | ||||||||
\(559\) | −18.6282 | −0.787887 | ||||||||
\(560\) | −16.4445 | −0.694906 | ||||||||
\(561\) | 9.25944 | 0.390934 | ||||||||
\(562\) | −8.62051 | −0.363634 | ||||||||
\(563\) | −3.83903 | −0.161796 | −0.0808979 | − | 0.996722i | \(-0.525779\pi\) | ||||
−0.0808979 | + | 0.996722i | \(0.525779\pi\) | |||||||
\(564\) | −3.31449 | −0.139565 | ||||||||
\(565\) | −56.1732 | −2.36322 | ||||||||
\(566\) | 6.97293 | 0.293094 | ||||||||
\(567\) | 3.89357 | 0.163515 | ||||||||
\(568\) | 14.6340 | 0.614028 | ||||||||
\(569\) | 21.2492 | 0.890811 | 0.445405 | − | 0.895329i | \(-0.353060\pi\) | ||||
0.445405 | + | 0.895329i | \(0.353060\pi\) | |||||||
\(570\) | 4.22349 | 0.176903 | ||||||||
\(571\) | 25.3748 | 1.06190 | 0.530951 | − | 0.847403i | \(-0.321835\pi\) | ||||
0.530951 | + | 0.847403i | \(0.321835\pi\) | |||||||
\(572\) | 8.93340 | 0.373524 | ||||||||
\(573\) | −13.8455 | −0.578405 | ||||||||
\(574\) | 32.4355 | 1.35383 | ||||||||
\(575\) | 63.0902 | 2.63104 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −37.7782 | −1.57273 | −0.786363 | − | 0.617765i | \(-0.788038\pi\) | ||||
−0.786363 | + | 0.617765i | \(0.788038\pi\) | |||||||
\(578\) | −26.8918 | −1.11855 | ||||||||
\(579\) | 0.356400 | 0.0148115 | ||||||||
\(580\) | −21.8363 | −0.906704 | ||||||||
\(581\) | 68.8415 | 2.85603 | ||||||||
\(582\) | 12.2819 | 0.509100 | ||||||||
\(583\) | 1.39763 | 0.0578840 | ||||||||
\(584\) | 8.59442 | 0.355640 | ||||||||
\(585\) | −26.9957 | −1.11614 | ||||||||
\(586\) | −14.1738 | −0.585515 | ||||||||
\(587\) | 40.0748 | 1.65406 | 0.827032 | − | 0.562155i | \(-0.190028\pi\) | ||||
0.827032 | + | 0.562155i | \(0.190028\pi\) | |||||||
\(588\) | 8.15991 | 0.336509 | ||||||||
\(589\) | 9.08792 | 0.374461 | ||||||||
\(590\) | 5.41217 | 0.222815 | ||||||||
\(591\) | −3.72524 | −0.153236 | ||||||||
\(592\) | 3.19935 | 0.131493 | ||||||||
\(593\) | 2.24843 | 0.0923318 | 0.0461659 | − | 0.998934i | \(-0.485300\pi\) | ||||
0.0461659 | + | 0.998934i | \(0.485300\pi\) | |||||||
\(594\) | −1.39763 | −0.0573456 | ||||||||
\(595\) | −108.946 | −4.46635 | ||||||||
\(596\) | −12.9791 | −0.531644 | ||||||||
\(597\) | −7.09049 | −0.290195 | ||||||||
\(598\) | −31.4118 | −1.28452 | ||||||||
\(599\) | −39.8670 | −1.62892 | −0.814460 | − | 0.580219i | \(-0.802967\pi\) | ||||
−0.814460 | + | 0.580219i | \(0.802967\pi\) | |||||||
\(600\) | −12.8379 | −0.524104 | ||||||||
\(601\) | 19.9169 | 0.812425 | 0.406213 | − | 0.913779i | \(-0.366849\pi\) | ||||
0.406213 | + | 0.913779i | \(0.366849\pi\) | |||||||
\(602\) | 11.3473 | 0.462483 | ||||||||
\(603\) | 1.72928 | 0.0704217 | ||||||||
\(604\) | 14.2437 | 0.579567 | ||||||||
\(605\) | 38.2083 | 1.55339 | ||||||||
\(606\) | −16.3423 | −0.663859 | ||||||||
\(607\) | 6.34974 | 0.257728 | 0.128864 | − | 0.991662i | \(-0.458867\pi\) | ||||
0.128864 | + | 0.991662i | \(0.458867\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 20.1306 | 0.815733 | ||||||||
\(610\) | −60.1146 | −2.43397 | ||||||||
\(611\) | −21.1856 | −0.857076 | ||||||||
\(612\) | 6.62509 | 0.267803 | ||||||||
\(613\) | −1.12114 | −0.0452823 | −0.0226411 | − | 0.999744i | \(-0.507208\pi\) | ||||
−0.0226411 | + | 0.999744i | \(0.507208\pi\) | |||||||
\(614\) | 24.9195 | 1.00567 | ||||||||
\(615\) | 35.1839 | 1.41875 | ||||||||
\(616\) | −5.44178 | −0.219256 | ||||||||
\(617\) | 22.3742 | 0.900750 | 0.450375 | − | 0.892840i | \(-0.351290\pi\) | ||||
0.450375 | + | 0.892840i | \(0.351290\pi\) | |||||||
\(618\) | 12.1122 | 0.487223 | ||||||||
\(619\) | 11.0226 | 0.443036 | 0.221518 | − | 0.975156i | \(-0.428899\pi\) | ||||
0.221518 | + | 0.975156i | \(0.428899\pi\) | |||||||
\(620\) | −38.3827 | −1.54149 | ||||||||
\(621\) | 4.91438 | 0.197207 | ||||||||
\(622\) | 1.66374 | 0.0667097 | ||||||||
\(623\) | −13.4502 | −0.538870 | ||||||||
\(624\) | 6.39181 | 0.255877 | ||||||||
\(625\) | 75.6218 | 3.02487 | ||||||||
\(626\) | 23.7002 | 0.947251 | ||||||||
\(627\) | 1.39763 | 0.0558161 | ||||||||
\(628\) | 14.8382 | 0.592109 | ||||||||
\(629\) | 21.1960 | 0.845140 | ||||||||
\(630\) | 16.4445 | 0.655163 | ||||||||
\(631\) | 9.27017 | 0.369040 | 0.184520 | − | 0.982829i | \(-0.440927\pi\) | ||||
0.184520 | + | 0.982829i | \(0.440927\pi\) | |||||||
\(632\) | −0.401082 | −0.0159542 | ||||||||
\(633\) | −6.34960 | −0.252374 | ||||||||
\(634\) | 12.5172 | 0.497121 | ||||||||
\(635\) | 1.20137 | 0.0476748 | ||||||||
\(636\) | 1.00000 | 0.0396526 | ||||||||
\(637\) | 52.1566 | 2.06652 | ||||||||
\(638\) | −7.22605 | −0.286082 | ||||||||
\(639\) | −14.6340 | −0.578911 | ||||||||
\(640\) | 4.22349 | 0.166948 | ||||||||
\(641\) | −3.04109 | −0.120116 | −0.0600578 | − | 0.998195i | \(-0.519129\pi\) | ||||
−0.0600578 | + | 0.998195i | \(0.519129\pi\) | |||||||
\(642\) | 7.11873 | 0.280954 | ||||||||
\(643\) | 21.8414 | 0.861340 | 0.430670 | − | 0.902509i | \(-0.358277\pi\) | ||||
0.430670 | + | 0.902509i | \(0.358277\pi\) | |||||||
\(644\) | 19.1345 | 0.754005 | ||||||||
\(645\) | 12.3089 | 0.484661 | ||||||||
\(646\) | −6.62509 | −0.260661 | ||||||||
\(647\) | 0.490380 | 0.0192788 | 0.00963941 | − | 0.999954i | \(-0.496932\pi\) | ||||
0.00963941 | + | 0.999954i | \(0.496932\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 1.79099 | 0.0703024 | ||||||||
\(650\) | −82.0573 | −3.21855 | ||||||||
\(651\) | 35.3845 | 1.38683 | ||||||||
\(652\) | −15.5059 | −0.607258 | ||||||||
\(653\) | −12.8838 | −0.504182 | −0.252091 | − | 0.967704i | \(-0.581118\pi\) | ||||
−0.252091 | + | 0.967704i | \(0.581118\pi\) | |||||||
\(654\) | −15.5533 | −0.608181 | ||||||||
\(655\) | −21.4985 | −0.840014 | ||||||||
\(656\) | −8.33052 | −0.325252 | ||||||||
\(657\) | −8.59442 | −0.335300 | ||||||||
\(658\) | 12.9052 | 0.503097 | ||||||||
\(659\) | −21.2815 | −0.829010 | −0.414505 | − | 0.910047i | \(-0.636045\pi\) | ||||
−0.414505 | + | 0.910047i | \(0.636045\pi\) | |||||||
\(660\) | −5.90289 | −0.229770 | ||||||||
\(661\) | −27.7790 | −1.08048 | −0.540238 | − | 0.841512i | \(-0.681666\pi\) | ||||
−0.540238 | + | 0.841512i | \(0.681666\pi\) | |||||||
\(662\) | −12.0207 | −0.467199 | ||||||||
\(663\) | 42.3463 | 1.64459 | ||||||||
\(664\) | −17.6808 | −0.686148 | ||||||||
\(665\) | −16.4445 | −0.637689 | ||||||||
\(666\) | −3.19935 | −0.123972 | ||||||||
\(667\) | 25.4084 | 0.983816 | ||||||||
\(668\) | 7.97057 | 0.308391 | ||||||||
\(669\) | −15.3317 | −0.592758 | ||||||||
\(670\) | 7.30360 | 0.282163 | ||||||||
\(671\) | −19.8930 | −0.767962 | ||||||||
\(672\) | −3.89357 | −0.150198 | ||||||||
\(673\) | −36.5990 | −1.41079 | −0.705394 | − | 0.708815i | \(-0.749230\pi\) | ||||
−0.705394 | + | 0.708815i | \(0.749230\pi\) | |||||||
\(674\) | 27.6560 | 1.06527 | ||||||||
\(675\) | 12.8379 | 0.494130 | ||||||||
\(676\) | 27.8552 | 1.07135 | ||||||||
\(677\) | −18.3026 | −0.703425 | −0.351712 | − | 0.936108i | \(-0.614401\pi\) | ||||
−0.351712 | + | 0.936108i | \(0.614401\pi\) | |||||||
\(678\) | −13.3002 | −0.510790 | ||||||||
\(679\) | −47.8204 | −1.83518 | ||||||||
\(680\) | 27.9810 | 1.07302 | ||||||||
\(681\) | 10.2980 | 0.394621 | ||||||||
\(682\) | −12.7016 | −0.486368 | ||||||||
\(683\) | 27.7691 | 1.06255 | 0.531277 | − | 0.847198i | \(-0.321712\pi\) | ||||
0.531277 | + | 0.847198i | \(0.321712\pi\) | |||||||
\(684\) | 1.00000 | 0.0382360 | ||||||||
\(685\) | 95.4038 | 3.64519 | ||||||||
\(686\) | −4.51620 | −0.172429 | ||||||||
\(687\) | −21.0001 | −0.801203 | ||||||||
\(688\) | −2.91438 | −0.111110 | ||||||||
\(689\) | 6.39181 | 0.243509 | ||||||||
\(690\) | 20.7558 | 0.790161 | ||||||||
\(691\) | 20.3886 | 0.775619 | 0.387810 | − | 0.921740i | \(-0.373232\pi\) | ||||
0.387810 | + | 0.921740i | \(0.373232\pi\) | |||||||
\(692\) | −21.5813 | −0.820398 | ||||||||
\(693\) | 5.44178 | 0.206716 | ||||||||
\(694\) | −19.4805 | −0.739468 | ||||||||
\(695\) | −87.7825 | −3.32978 | ||||||||
\(696\) | −5.17021 | −0.195976 | ||||||||
\(697\) | −55.1904 | −2.09049 | ||||||||
\(698\) | −0.935636 | −0.0354143 | ||||||||
\(699\) | 10.4476 | 0.395163 | ||||||||
\(700\) | 49.9852 | 1.88926 | ||||||||
\(701\) | −0.0916529 | −0.00346168 | −0.00173084 | − | 0.999999i | \(-0.500551\pi\) | ||||
−0.00173084 | + | 0.999999i | \(0.500551\pi\) | |||||||
\(702\) | −6.39181 | −0.241243 | ||||||||
\(703\) | 3.19935 | 0.120666 | ||||||||
\(704\) | 1.39763 | 0.0526753 | ||||||||
\(705\) | 13.9987 | 0.527222 | ||||||||
\(706\) | −27.2562 | −1.02580 | ||||||||
\(707\) | 63.6298 | 2.39304 | ||||||||
\(708\) | 1.28144 | 0.0481596 | ||||||||
\(709\) | −2.51581 | −0.0944832 | −0.0472416 | − | 0.998883i | \(-0.515043\pi\) | ||||
−0.0472416 | + | 0.998883i | \(0.515043\pi\) | |||||||
\(710\) | −61.8065 | −2.31956 | ||||||||
\(711\) | 0.401082 | 0.0150418 | ||||||||
\(712\) | 3.45446 | 0.129461 | ||||||||
\(713\) | 44.6615 | 1.67259 | ||||||||
\(714\) | −25.7953 | −0.965364 | ||||||||
\(715\) | −37.7301 | −1.41103 | ||||||||
\(716\) | −8.43180 | −0.315111 | ||||||||
\(717\) | −22.3004 | −0.832823 | ||||||||
\(718\) | 14.3368 | 0.535043 | ||||||||
\(719\) | 7.92057 | 0.295388 | 0.147694 | − | 0.989033i | \(-0.452815\pi\) | ||||
0.147694 | + | 0.989033i | \(0.452815\pi\) | |||||||
\(720\) | −4.22349 | −0.157400 | ||||||||
\(721\) | −47.1597 | −1.75632 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | −3.10563 | −0.115500 | ||||||||
\(724\) | 8.13253 | 0.302243 | ||||||||
\(725\) | 66.3745 | 2.46509 | ||||||||
\(726\) | 9.04662 | 0.335752 | ||||||||
\(727\) | 37.1761 | 1.37879 | 0.689393 | − | 0.724388i | \(-0.257878\pi\) | ||||
0.689393 | + | 0.724388i | \(0.257878\pi\) | |||||||
\(728\) | −24.8870 | −0.922373 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −36.2985 | −1.34347 | ||||||||
\(731\) | −19.3080 | −0.714133 | ||||||||
\(732\) | −14.2334 | −0.526081 | ||||||||
\(733\) | −8.20806 | −0.303172 | −0.151586 | − | 0.988444i | \(-0.548438\pi\) | ||||
−0.151586 | + | 0.988444i | \(0.548438\pi\) | |||||||
\(734\) | −5.07573 | −0.187349 | ||||||||
\(735\) | −34.4633 | −1.27120 | ||||||||
\(736\) | −4.91438 | −0.181146 | ||||||||
\(737\) | 2.41690 | 0.0890276 | ||||||||
\(738\) | 8.33052 | 0.306651 | ||||||||
\(739\) | 28.4210 | 1.04548 | 0.522742 | − | 0.852491i | \(-0.324909\pi\) | ||||
0.522742 | + | 0.852491i | \(0.324909\pi\) | |||||||
\(740\) | −13.5124 | −0.496727 | ||||||||
\(741\) | 6.39181 | 0.234809 | ||||||||
\(742\) | −3.89357 | −0.142938 | ||||||||
\(743\) | 10.3261 | 0.378828 | 0.189414 | − | 0.981897i | \(-0.439341\pi\) | ||||
0.189414 | + | 0.981897i | \(0.439341\pi\) | |||||||
\(744\) | −9.08792 | −0.333179 | ||||||||
\(745\) | 54.8171 | 2.00834 | ||||||||
\(746\) | −5.06710 | −0.185520 | ||||||||
\(747\) | 17.6808 | 0.646907 | ||||||||
\(748\) | 9.25944 | 0.338559 | ||||||||
\(749\) | −27.7173 | −1.01277 | ||||||||
\(750\) | 33.1032 | 1.20876 | ||||||||
\(751\) | 22.9979 | 0.839207 | 0.419603 | − | 0.907708i | \(-0.362169\pi\) | ||||
0.419603 | + | 0.907708i | \(0.362169\pi\) | |||||||
\(752\) | −3.31449 | −0.120867 | ||||||||
\(753\) | 3.24901 | 0.118401 | ||||||||
\(754\) | −33.0470 | −1.20350 | ||||||||
\(755\) | −60.1581 | −2.18938 | ||||||||
\(756\) | 3.89357 | 0.141608 | ||||||||
\(757\) | 20.4806 | 0.744379 | 0.372189 | − | 0.928157i | \(-0.378607\pi\) | ||||
0.372189 | + | 0.928157i | \(0.378607\pi\) | |||||||
\(758\) | −21.3462 | −0.775330 | ||||||||
\(759\) | 6.86850 | 0.249311 | ||||||||
\(760\) | 4.22349 | 0.153202 | ||||||||
\(761\) | −3.61334 | −0.130983 | −0.0654917 | − | 0.997853i | \(-0.520862\pi\) | ||||
−0.0654917 | + | 0.997853i | \(0.520862\pi\) | |||||||
\(762\) | 0.284449 | 0.0103045 | ||||||||
\(763\) | 60.5578 | 2.19234 | ||||||||
\(764\) | −13.8455 | −0.500914 | ||||||||
\(765\) | −27.9810 | −1.01166 | ||||||||
\(766\) | 2.17408 | 0.0785528 | ||||||||
\(767\) | 8.19075 | 0.295751 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 28.1348 | 1.01457 | 0.507283 | − | 0.861780i | \(-0.330650\pi\) | ||||
0.507283 | + | 0.861780i | \(0.330650\pi\) | |||||||
\(770\) | 22.9833 | 0.828262 | ||||||||
\(771\) | −2.35501 | −0.0848136 | ||||||||
\(772\) | 0.356400 | 0.0128271 | ||||||||
\(773\) | 28.8510 | 1.03770 | 0.518849 | − | 0.854866i | \(-0.326361\pi\) | ||||
0.518849 | + | 0.854866i | \(0.326361\pi\) | |||||||
\(774\) | 2.91438 | 0.104755 | ||||||||
\(775\) | 116.670 | 4.19090 | ||||||||
\(776\) | 12.2819 | 0.440893 | ||||||||
\(777\) | 12.4569 | 0.446889 | ||||||||
\(778\) | −24.0139 | −0.860941 | ||||||||
\(779\) | −8.33052 | −0.298472 | ||||||||
\(780\) | −26.9957 | −0.966603 | ||||||||
\(781\) | −20.4529 | −0.731863 | ||||||||
\(782\) | −32.5582 | −1.16428 | ||||||||
\(783\) | 5.17021 | 0.184768 | ||||||||
\(784\) | 8.15991 | 0.291425 | ||||||||
\(785\) | −62.6690 | −2.23675 | ||||||||
\(786\) | −5.09021 | −0.181562 | ||||||||
\(787\) | −10.8334 | −0.386171 | −0.193085 | − | 0.981182i | \(-0.561849\pi\) | ||||
−0.193085 | + | 0.981182i | \(0.561849\pi\) | |||||||
\(788\) | −3.72524 | −0.132706 | ||||||||
\(789\) | −2.60931 | −0.0928939 | ||||||||
\(790\) | 1.69397 | 0.0602687 | ||||||||
\(791\) | 51.7852 | 1.84127 | ||||||||
\(792\) | −1.39763 | −0.0496627 | ||||||||
\(793\) | −90.9770 | −3.23069 | ||||||||
\(794\) | 12.3957 | 0.439906 | ||||||||
\(795\) | −4.22349 | −0.149792 | ||||||||
\(796\) | −7.09049 | −0.251316 | ||||||||
\(797\) | 35.7948 | 1.26792 | 0.633959 | − | 0.773367i | \(-0.281429\pi\) | ||||
0.633959 | + | 0.773367i | \(0.281429\pi\) | |||||||
\(798\) | −3.89357 | −0.137831 | ||||||||
\(799\) | −21.9588 | −0.776845 | ||||||||
\(800\) | −12.8379 | −0.453888 | ||||||||
\(801\) | −3.45446 | −0.122057 | ||||||||
\(802\) | 2.39611 | 0.0846097 | ||||||||
\(803\) | −12.0118 | −0.423889 | ||||||||
\(804\) | 1.72928 | 0.0609870 | ||||||||
\(805\) | −80.8144 | −2.84833 | ||||||||
\(806\) | −58.0882 | −2.04607 | ||||||||
\(807\) | 22.2422 | 0.782963 | ||||||||
\(808\) | −16.3423 | −0.574918 | ||||||||
\(809\) | −7.72351 | −0.271544 | −0.135772 | − | 0.990740i | \(-0.543352\pi\) | ||||
−0.135772 | + | 0.990740i | \(0.543352\pi\) | |||||||
\(810\) | 4.22349 | 0.148398 | ||||||||
\(811\) | 13.8613 | 0.486736 | 0.243368 | − | 0.969934i | \(-0.421748\pi\) | ||||
0.243368 | + | 0.969934i | \(0.421748\pi\) | |||||||
\(812\) | 20.1306 | 0.706445 | ||||||||
\(813\) | −3.51603 | −0.123313 | ||||||||
\(814\) | −4.47152 | −0.156727 | ||||||||
\(815\) | 65.4890 | 2.29398 | ||||||||
\(816\) | 6.62509 | 0.231925 | ||||||||
\(817\) | −2.91438 | −0.101961 | ||||||||
\(818\) | 12.5246 | 0.437913 | ||||||||
\(819\) | 24.8870 | 0.869621 | ||||||||
\(820\) | 35.1839 | 1.22867 | ||||||||
\(821\) | 4.91887 | 0.171670 | 0.0858349 | − | 0.996309i | \(-0.472644\pi\) | ||||
0.0858349 | + | 0.996309i | \(0.472644\pi\) | |||||||
\(822\) | 22.5889 | 0.787877 | ||||||||
\(823\) | −27.5695 | −0.961014 | −0.480507 | − | 0.876991i | \(-0.659547\pi\) | ||||
−0.480507 | + | 0.876991i | \(0.659547\pi\) | |||||||
\(824\) | 12.1122 | 0.421948 | ||||||||
\(825\) | 17.9426 | 0.624682 | ||||||||
\(826\) | −4.98940 | −0.173603 | ||||||||
\(827\) | −0.146357 | −0.00508935 | −0.00254467 | − | 0.999997i | \(-0.500810\pi\) | ||||
−0.00254467 | + | 0.999997i | \(0.500810\pi\) | |||||||
\(828\) | 4.91438 | 0.170786 | ||||||||
\(829\) | 8.69894 | 0.302127 | 0.151063 | − | 0.988524i | \(-0.451730\pi\) | ||||
0.151063 | + | 0.988524i | \(0.451730\pi\) | |||||||
\(830\) | 74.6747 | 2.59200 | ||||||||
\(831\) | 0.273929 | 0.00950249 | ||||||||
\(832\) | 6.39181 | 0.221596 | ||||||||
\(833\) | 54.0601 | 1.87307 | ||||||||
\(834\) | −20.7843 | −0.719703 | ||||||||
\(835\) | −33.6636 | −1.16498 | ||||||||
\(836\) | 1.39763 | 0.0483381 | ||||||||
\(837\) | 9.08792 | 0.314124 | ||||||||
\(838\) | 28.2150 | 0.974670 | ||||||||
\(839\) | −26.2455 | −0.906097 | −0.453048 | − | 0.891486i | \(-0.649664\pi\) | ||||
−0.453048 | + | 0.891486i | \(0.649664\pi\) | |||||||
\(840\) | 16.4445 | 0.567388 | ||||||||
\(841\) | −2.26894 | −0.0782393 | ||||||||
\(842\) | −16.4246 | −0.566029 | ||||||||
\(843\) | 8.62051 | 0.296906 | ||||||||
\(844\) | −6.34960 | −0.218562 | ||||||||
\(845\) | −117.646 | −4.04715 | ||||||||
\(846\) | 3.31449 | 0.113954 | ||||||||
\(847\) | −35.2237 | −1.21030 | ||||||||
\(848\) | 1.00000 | 0.0343401 | ||||||||
\(849\) | −6.97293 | −0.239310 | ||||||||
\(850\) | −85.0521 | −2.91726 | ||||||||
\(851\) | 15.7228 | 0.538972 | ||||||||
\(852\) | −14.6340 | −0.501352 | ||||||||
\(853\) | 51.1742 | 1.75217 | 0.876086 | − | 0.482156i | \(-0.160146\pi\) | ||||
0.876086 | + | 0.482156i | \(0.160146\pi\) | |||||||
\(854\) | 55.4187 | 1.89639 | ||||||||
\(855\) | −4.22349 | −0.144440 | ||||||||
\(856\) | 7.11873 | 0.243313 | ||||||||
\(857\) | −30.5716 | −1.04430 | −0.522152 | − | 0.852852i | \(-0.674871\pi\) | ||||
−0.522152 | + | 0.852852i | \(0.674871\pi\) | |||||||
\(858\) | −8.93340 | −0.304981 | ||||||||
\(859\) | −19.8443 | −0.677078 | −0.338539 | − | 0.940952i | \(-0.609933\pi\) | ||||
−0.338539 | + | 0.940952i | \(0.609933\pi\) | |||||||
\(860\) | 12.3089 | 0.419729 | ||||||||
\(861\) | −32.4355 | −1.10540 | ||||||||
\(862\) | 2.01343 | 0.0685776 | ||||||||
\(863\) | −7.54342 | −0.256781 | −0.128390 | − | 0.991724i | \(-0.540981\pi\) | ||||
−0.128390 | + | 0.991724i | \(0.540981\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 91.1484 | 3.09914 | ||||||||
\(866\) | 17.3549 | 0.589745 | ||||||||
\(867\) | 26.8918 | 0.913294 | ||||||||
\(868\) | 35.3845 | 1.20103 | ||||||||
\(869\) | 0.560566 | 0.0190159 | ||||||||
\(870\) | 21.8363 | 0.740321 | ||||||||
\(871\) | 11.0532 | 0.374524 | ||||||||
\(872\) | −15.5533 | −0.526700 | ||||||||
\(873\) | −12.2819 | −0.415678 | ||||||||
\(874\) | −4.91438 | −0.166231 | ||||||||
\(875\) | −128.890 | −4.35727 | ||||||||
\(876\) | −8.59442 | −0.290379 | ||||||||
\(877\) | −45.2366 | −1.52753 | −0.763766 | − | 0.645494i | \(-0.776652\pi\) | ||||
−0.763766 | + | 0.645494i | \(0.776652\pi\) | |||||||
\(878\) | 24.5865 | 0.829753 | ||||||||
\(879\) | 14.1738 | 0.478071 | ||||||||
\(880\) | −5.90289 | −0.198986 | ||||||||
\(881\) | 43.7496 | 1.47396 | 0.736981 | − | 0.675914i | \(-0.236251\pi\) | ||||
0.736981 | + | 0.675914i | \(0.236251\pi\) | |||||||
\(882\) | −8.15991 | −0.274758 | ||||||||
\(883\) | −33.1294 | −1.11489 | −0.557446 | − | 0.830213i | \(-0.688219\pi\) | ||||
−0.557446 | + | 0.830213i | \(0.688219\pi\) | |||||||
\(884\) | 42.3463 | 1.42426 | ||||||||
\(885\) | −5.41217 | −0.181928 | ||||||||
\(886\) | 14.1705 | 0.476068 | ||||||||
\(887\) | −24.2227 | −0.813318 | −0.406659 | − | 0.913580i | \(-0.633306\pi\) | ||||
−0.406659 | + | 0.913580i | \(0.633306\pi\) | |||||||
\(888\) | −3.19935 | −0.107363 | ||||||||
\(889\) | −1.10752 | −0.0371451 | ||||||||
\(890\) | −14.5899 | −0.489054 | ||||||||
\(891\) | 1.39763 | 0.0468224 | ||||||||
\(892\) | −15.3317 | −0.513343 | ||||||||
\(893\) | −3.31449 | −0.110915 | ||||||||
\(894\) | 12.9791 | 0.434086 | ||||||||
\(895\) | 35.6116 | 1.19037 | ||||||||
\(896\) | −3.89357 | −0.130075 | ||||||||
\(897\) | 31.4118 | 1.04881 | ||||||||
\(898\) | −40.1610 | −1.34019 | ||||||||
\(899\) | 46.9864 | 1.56709 | ||||||||
\(900\) | 12.8379 | 0.427929 | ||||||||
\(901\) | 6.62509 | 0.220714 | ||||||||
\(902\) | 11.6430 | 0.387670 | ||||||||
\(903\) | −11.3473 | −0.377616 | ||||||||
\(904\) | −13.3002 | −0.442357 | ||||||||
\(905\) | −34.3477 | −1.14176 | ||||||||
\(906\) | −14.2437 | −0.473215 | ||||||||
\(907\) | 10.2660 | 0.340878 | 0.170439 | − | 0.985368i | \(-0.445481\pi\) | ||||
0.170439 | + | 0.985368i | \(0.445481\pi\) | |||||||
\(908\) | 10.2980 | 0.341751 | ||||||||
\(909\) | 16.3423 | 0.542038 | ||||||||
\(910\) | 105.110 | 3.48436 | ||||||||
\(911\) | 8.39506 | 0.278141 | 0.139070 | − | 0.990283i | \(-0.455589\pi\) | ||||
0.139070 | + | 0.990283i | \(0.455589\pi\) | |||||||
\(912\) | 1.00000 | 0.0331133 | ||||||||
\(913\) | 24.7113 | 0.817824 | ||||||||
\(914\) | 14.6789 | 0.485536 | ||||||||
\(915\) | 60.1146 | 1.98733 | ||||||||
\(916\) | −21.0001 | −0.693862 | ||||||||
\(917\) | 19.8191 | 0.654484 | ||||||||
\(918\) | −6.62509 | −0.218661 | ||||||||
\(919\) | 46.9164 | 1.54763 | 0.773815 | − | 0.633412i | \(-0.218346\pi\) | ||||
0.773815 | + | 0.633412i | \(0.218346\pi\) | |||||||
\(920\) | 20.7558 | 0.684300 | ||||||||
\(921\) | −24.9195 | −0.821126 | ||||||||
\(922\) | 37.4126 | 1.23212 | ||||||||
\(923\) | −93.5376 | −3.07883 | ||||||||
\(924\) | 5.44178 | 0.179022 | ||||||||
\(925\) | 41.0729 | 1.35047 | ||||||||
\(926\) | 39.7374 | 1.30585 | ||||||||
\(927\) | −12.1122 | −0.397816 | ||||||||
\(928\) | −5.17021 | −0.169720 | ||||||||
\(929\) | −40.8766 | −1.34112 | −0.670559 | − | 0.741857i | \(-0.733946\pi\) | ||||
−0.670559 | + | 0.741857i | \(0.733946\pi\) | |||||||
\(930\) | 38.3827 | 1.25862 | ||||||||
\(931\) | 8.15991 | 0.267430 | ||||||||
\(932\) | 10.4476 | 0.342221 | ||||||||
\(933\) | −1.66374 | −0.0544682 | ||||||||
\(934\) | −1.57966 | −0.0516880 | ||||||||
\(935\) | −39.1072 | −1.27894 | ||||||||
\(936\) | −6.39181 | −0.208923 | ||||||||
\(937\) | 54.6283 | 1.78463 | 0.892314 | − | 0.451416i | \(-0.149081\pi\) | ||||
0.892314 | + | 0.451416i | \(0.149081\pi\) | |||||||
\(938\) | −6.73308 | −0.219843 | ||||||||
\(939\) | −23.7002 | −0.773427 | ||||||||
\(940\) | 13.9987 | 0.456587 | ||||||||
\(941\) | 40.8345 | 1.33117 | 0.665584 | − | 0.746323i | \(-0.268183\pi\) | ||||
0.665584 | + | 0.746323i | \(0.268183\pi\) | |||||||
\(942\) | −14.8382 | −0.483455 | ||||||||
\(943\) | −40.9393 | −1.33317 | ||||||||
\(944\) | 1.28144 | 0.0417075 | ||||||||
\(945\) | −16.4445 | −0.534939 | ||||||||
\(946\) | 4.07323 | 0.132432 | ||||||||
\(947\) | −11.3667 | −0.369368 | −0.184684 | − | 0.982798i | \(-0.559126\pi\) | ||||
−0.184684 | + | 0.982798i | \(0.559126\pi\) | |||||||
\(948\) | 0.401082 | 0.0130265 | ||||||||
\(949\) | −54.9339 | −1.78323 | ||||||||
\(950\) | −12.8379 | −0.416516 | ||||||||
\(951\) | −12.5172 | −0.405898 | ||||||||
\(952\) | −25.7953 | −0.836029 | ||||||||
\(953\) | 3.25471 | 0.105430 | 0.0527152 | − | 0.998610i | \(-0.483212\pi\) | ||||
0.0527152 | + | 0.998610i | \(0.483212\pi\) | |||||||
\(954\) | −1.00000 | −0.0323762 | ||||||||
\(955\) | 58.4765 | 1.89225 | ||||||||
\(956\) | −22.3004 | −0.721246 | ||||||||
\(957\) | 7.22605 | 0.233585 | ||||||||
\(958\) | 39.8886 | 1.28874 | ||||||||
\(959\) | −87.9514 | −2.84010 | ||||||||
\(960\) | −4.22349 | −0.136313 | ||||||||
\(961\) | 51.5903 | 1.66420 | ||||||||
\(962\) | −20.4496 | −0.659323 | ||||||||
\(963\) | −7.11873 | −0.229398 | ||||||||
\(964\) | −3.10563 | −0.100026 | ||||||||
\(965\) | −1.50525 | −0.0484558 | ||||||||
\(966\) | −19.1345 | −0.615642 | ||||||||
\(967\) | −51.7706 | −1.66483 | −0.832414 | − | 0.554154i | \(-0.813042\pi\) | ||||
−0.832414 | + | 0.554154i | \(0.813042\pi\) | |||||||
\(968\) | 9.04662 | 0.290769 | ||||||||
\(969\) | 6.62509 | 0.212829 | ||||||||
\(970\) | −51.8724 | −1.66552 | ||||||||
\(971\) | 55.3421 | 1.77601 | 0.888006 | − | 0.459832i | \(-0.152090\pi\) | ||||
0.888006 | + | 0.459832i | \(0.152090\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 80.9254 | 2.59435 | ||||||||
\(974\) | 8.41305 | 0.269571 | ||||||||
\(975\) | 82.0573 | 2.62794 | ||||||||
\(976\) | −14.2334 | −0.455599 | ||||||||
\(977\) | 48.8817 | 1.56386 | 0.781932 | − | 0.623364i | \(-0.214234\pi\) | ||||
0.781932 | + | 0.623364i | \(0.214234\pi\) | |||||||
\(978\) | 15.5059 | 0.495824 | ||||||||
\(979\) | −4.82806 | −0.154306 | ||||||||
\(980\) | −34.4633 | −1.10089 | ||||||||
\(981\) | 15.5533 | 0.496578 | ||||||||
\(982\) | 17.4356 | 0.556393 | ||||||||
\(983\) | −23.9367 | −0.763463 | −0.381732 | − | 0.924273i | \(-0.624672\pi\) | ||||
−0.381732 | + | 0.924273i | \(0.624672\pi\) | |||||||
\(984\) | 8.33052 | 0.265567 | ||||||||
\(985\) | 15.7335 | 0.501312 | ||||||||
\(986\) | −34.2531 | −1.09084 | ||||||||
\(987\) | −12.9052 | −0.410777 | ||||||||
\(988\) | 6.39181 | 0.203351 | ||||||||
\(989\) | −14.3224 | −0.455425 | ||||||||
\(990\) | 5.90289 | 0.187606 | ||||||||
\(991\) | −15.9344 | −0.506174 | −0.253087 | − | 0.967444i | \(-0.581446\pi\) | ||||
−0.253087 | + | 0.967444i | \(0.581446\pi\) | |||||||
\(992\) | −9.08792 | −0.288542 | ||||||||
\(993\) | 12.0207 | 0.381466 | ||||||||
\(994\) | 56.9784 | 1.80725 | ||||||||
\(995\) | 29.9466 | 0.949372 | ||||||||
\(996\) | 17.6808 | 0.560238 | ||||||||
\(997\) | −41.1437 | −1.30303 | −0.651517 | − | 0.758634i | \(-0.725867\pi\) | ||||
−0.651517 | + | 0.758634i | \(0.725867\pi\) | |||||||
\(998\) | 13.6058 | 0.430684 | ||||||||
\(999\) | 3.19935 | 0.101223 |
(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 | 6042.2.a.bf.1.1 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6042.2.a.bf.1.1 | ✓ | 12 | 1.1 | even | 1 | trivial |