Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6001,2,Mod(1,6001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6001 = 17 \cdot 353 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6001.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: | \(47.9182262530\) |
Analytic rank: | \(1\) |
Dimension: | \(114\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 6001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.61975 | −1.85244 | −0.926221 | − | 0.376980i | \(-0.876963\pi\) | ||||
−0.926221 | + | 0.376980i | \(0.876963\pi\) | |||||||
\(3\) | −2.31872 | −1.33871 | −0.669357 | − | 0.742941i | \(-0.733430\pi\) | ||||
−0.669357 | + | 0.742941i | \(0.733430\pi\) | |||||||
\(4\) | 4.86309 | 2.43154 | ||||||||
\(5\) | 0.216177 | 0.0966771 | 0.0483385 | − | 0.998831i | \(-0.484607\pi\) | ||||
0.0483385 | + | 0.998831i | \(0.484607\pi\) | |||||||
\(6\) | 6.07447 | 2.47989 | ||||||||
\(7\) | 3.38406 | 1.27905 | 0.639527 | − | 0.768768i | \(-0.279130\pi\) | ||||
0.639527 | + | 0.768768i | \(0.279130\pi\) | |||||||
\(8\) | −7.50057 | −2.65185 | ||||||||
\(9\) | 2.37647 | 0.792155 | ||||||||
\(10\) | −0.566328 | −0.179089 | ||||||||
\(11\) | 0.605807 | 0.182658 | 0.0913288 | − | 0.995821i | \(-0.470889\pi\) | ||||
0.0913288 | + | 0.995821i | \(0.470889\pi\) | |||||||
\(12\) | −11.2761 | −3.25514 | ||||||||
\(13\) | −3.04846 | −0.845491 | −0.422746 | − | 0.906248i | \(-0.638934\pi\) | ||||
−0.422746 | + | 0.906248i | \(0.638934\pi\) | |||||||
\(14\) | −8.86539 | −2.36938 | ||||||||
\(15\) | −0.501253 | −0.129423 | ||||||||
\(16\) | 9.92345 | 2.48086 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −6.22574 | −1.46742 | ||||||||
\(19\) | 4.98478 | 1.14359 | 0.571793 | − | 0.820398i | \(-0.306248\pi\) | ||||
0.571793 | + | 0.820398i | \(0.306248\pi\) | |||||||
\(20\) | 1.05129 | 0.235075 | ||||||||
\(21\) | −7.84669 | −1.71229 | ||||||||
\(22\) | −1.58706 | −0.338363 | ||||||||
\(23\) | 1.60592 | 0.334858 | 0.167429 | − | 0.985884i | \(-0.446453\pi\) | ||||
0.167429 | + | 0.985884i | \(0.446453\pi\) | |||||||
\(24\) | 17.3917 | 3.55007 | ||||||||
\(25\) | −4.95327 | −0.990654 | ||||||||
\(26\) | 7.98621 | 1.56622 | ||||||||
\(27\) | 1.44580 | 0.278245 | ||||||||
\(28\) | 16.4570 | 3.11008 | ||||||||
\(29\) | −10.5141 | −1.95242 | −0.976211 | − | 0.216824i | \(-0.930430\pi\) | ||||
−0.976211 | + | 0.216824i | \(0.930430\pi\) | |||||||
\(30\) | 1.31316 | 0.239749 | ||||||||
\(31\) | 5.87827 | 1.05577 | 0.527884 | − | 0.849317i | \(-0.322986\pi\) | ||||
0.527884 | + | 0.849317i | \(0.322986\pi\) | |||||||
\(32\) | −10.9958 | −1.94380 | ||||||||
\(33\) | −1.40470 | −0.244526 | ||||||||
\(34\) | −2.61975 | −0.449283 | ||||||||
\(35\) | 0.731555 | 0.123655 | ||||||||
\(36\) | 11.5570 | 1.92616 | ||||||||
\(37\) | −3.75203 | −0.616830 | −0.308415 | − | 0.951252i | \(-0.599799\pi\) | ||||
−0.308415 | + | 0.951252i | \(0.599799\pi\) | |||||||
\(38\) | −13.0589 | −2.11843 | ||||||||
\(39\) | 7.06853 | 1.13187 | ||||||||
\(40\) | −1.62145 | −0.256373 | ||||||||
\(41\) | −0.864890 | −0.135073 | −0.0675366 | − | 0.997717i | \(-0.521514\pi\) | ||||
−0.0675366 | + | 0.997717i | \(0.521514\pi\) | |||||||
\(42\) | 20.5564 | 3.17192 | ||||||||
\(43\) | 6.40616 | 0.976930 | 0.488465 | − | 0.872583i | \(-0.337557\pi\) | ||||
0.488465 | + | 0.872583i | \(0.337557\pi\) | |||||||
\(44\) | 2.94609 | 0.444140 | ||||||||
\(45\) | 0.513736 | 0.0765832 | ||||||||
\(46\) | −4.20712 | −0.620305 | ||||||||
\(47\) | 0.621685 | 0.0906821 | 0.0453411 | − | 0.998972i | \(-0.485563\pi\) | ||||
0.0453411 | + | 0.998972i | \(0.485563\pi\) | |||||||
\(48\) | −23.0097 | −3.32117 | ||||||||
\(49\) | 4.45187 | 0.635982 | ||||||||
\(50\) | 12.9763 | 1.83513 | ||||||||
\(51\) | −2.31872 | −0.324686 | ||||||||
\(52\) | −14.8249 | −2.05585 | ||||||||
\(53\) | 9.64958 | 1.32547 | 0.662736 | − | 0.748853i | \(-0.269395\pi\) | ||||
0.662736 | + | 0.748853i | \(0.269395\pi\) | |||||||
\(54\) | −3.78764 | −0.515432 | ||||||||
\(55\) | 0.130961 | 0.0176588 | ||||||||
\(56\) | −25.3824 | −3.39187 | ||||||||
\(57\) | −11.5583 | −1.53094 | ||||||||
\(58\) | 27.5443 | 3.61675 | ||||||||
\(59\) | −5.81342 | −0.756843 | −0.378422 | − | 0.925633i | \(-0.623533\pi\) | ||||
−0.378422 | + | 0.925633i | \(0.623533\pi\) | |||||||
\(60\) | −2.43764 | −0.314698 | ||||||||
\(61\) | −6.34225 | −0.812042 | −0.406021 | − | 0.913864i | \(-0.633084\pi\) | ||||
−0.406021 | + | 0.913864i | \(0.633084\pi\) | |||||||
\(62\) | −15.3996 | −1.95575 | ||||||||
\(63\) | 8.04211 | 1.01321 | ||||||||
\(64\) | 8.95936 | 1.11992 | ||||||||
\(65\) | −0.659006 | −0.0817396 | ||||||||
\(66\) | 3.67995 | 0.452971 | ||||||||
\(67\) | 8.53186 | 1.04233 | 0.521166 | − | 0.853455i | \(-0.325497\pi\) | ||||
0.521166 | + | 0.853455i | \(0.325497\pi\) | |||||||
\(68\) | 4.86309 | 0.589736 | ||||||||
\(69\) | −3.72369 | −0.448279 | ||||||||
\(70\) | −1.91649 | −0.229064 | ||||||||
\(71\) | −12.8904 | −1.52981 | −0.764904 | − | 0.644144i | \(-0.777214\pi\) | ||||
−0.764904 | + | 0.644144i | \(0.777214\pi\) | |||||||
\(72\) | −17.8249 | −2.10068 | ||||||||
\(73\) | 16.5475 | 1.93673 | 0.968367 | − | 0.249530i | \(-0.0802762\pi\) | ||||
0.968367 | + | 0.249530i | \(0.0802762\pi\) | |||||||
\(74\) | 9.82938 | 1.14264 | ||||||||
\(75\) | 11.4852 | 1.32620 | ||||||||
\(76\) | 24.2414 | 2.78068 | ||||||||
\(77\) | 2.05009 | 0.233629 | ||||||||
\(78\) | −18.5178 | −2.09673 | ||||||||
\(79\) | 0.298557 | 0.0335902 | 0.0167951 | − | 0.999859i | \(-0.494654\pi\) | ||||
0.0167951 | + | 0.999859i | \(0.494654\pi\) | |||||||
\(80\) | 2.14522 | 0.239843 | ||||||||
\(81\) | −10.4818 | −1.16465 | ||||||||
\(82\) | 2.26579 | 0.250215 | ||||||||
\(83\) | 3.17470 | 0.348468 | 0.174234 | − | 0.984704i | \(-0.444255\pi\) | ||||
0.174234 | + | 0.984704i | \(0.444255\pi\) | |||||||
\(84\) | −38.1592 | −4.16351 | ||||||||
\(85\) | 0.216177 | 0.0234476 | ||||||||
\(86\) | −16.7825 | −1.80971 | ||||||||
\(87\) | 24.3793 | 2.61373 | ||||||||
\(88\) | −4.54390 | −0.484381 | ||||||||
\(89\) | −6.23133 | −0.660520 | −0.330260 | − | 0.943890i | \(-0.607136\pi\) | ||||
−0.330260 | + | 0.943890i | \(0.607136\pi\) | |||||||
\(90\) | −1.34586 | −0.141866 | ||||||||
\(91\) | −10.3162 | −1.08143 | ||||||||
\(92\) | 7.80974 | 0.814222 | ||||||||
\(93\) | −13.6301 | −1.41337 | ||||||||
\(94\) | −1.62866 | −0.167983 | ||||||||
\(95\) | 1.07759 | 0.110559 | ||||||||
\(96\) | 25.4962 | 2.60220 | ||||||||
\(97\) | −18.2172 | −1.84967 | −0.924837 | − | 0.380363i | \(-0.875799\pi\) | ||||
−0.924837 | + | 0.380363i | \(0.875799\pi\) | |||||||
\(98\) | −11.6628 | −1.17812 | ||||||||
\(99\) | 1.43968 | 0.144693 | ||||||||
\(100\) | −24.0882 | −2.40882 | ||||||||
\(101\) | −14.5345 | −1.44624 | −0.723119 | − | 0.690724i | \(-0.757292\pi\) | ||||
−0.723119 | + | 0.690724i | \(0.757292\pi\) | |||||||
\(102\) | 6.07447 | 0.601462 | ||||||||
\(103\) | −4.71810 | −0.464888 | −0.232444 | − | 0.972610i | \(-0.574672\pi\) | ||||
−0.232444 | + | 0.972610i | \(0.574672\pi\) | |||||||
\(104\) | 22.8652 | 2.24212 | ||||||||
\(105\) | −1.69627 | −0.165539 | ||||||||
\(106\) | −25.2795 | −2.45536 | ||||||||
\(107\) | −15.4790 | −1.49642 | −0.748208 | − | 0.663465i | \(-0.769085\pi\) | ||||
−0.748208 | + | 0.663465i | \(0.769085\pi\) | |||||||
\(108\) | 7.03106 | 0.676564 | ||||||||
\(109\) | −17.9470 | −1.71902 | −0.859508 | − | 0.511123i | \(-0.829230\pi\) | ||||
−0.859508 | + | 0.511123i | \(0.829230\pi\) | |||||||
\(110\) | −0.343085 | −0.0327119 | ||||||||
\(111\) | 8.69991 | 0.825759 | ||||||||
\(112\) | 33.5816 | 3.17316 | ||||||||
\(113\) | −6.04866 | −0.569010 | −0.284505 | − | 0.958675i | \(-0.591829\pi\) | ||||
−0.284505 | + | 0.958675i | \(0.591829\pi\) | |||||||
\(114\) | 30.2799 | 2.83597 | ||||||||
\(115\) | 0.347163 | 0.0323731 | ||||||||
\(116\) | −51.1310 | −4.74740 | ||||||||
\(117\) | −7.24457 | −0.669760 | ||||||||
\(118\) | 15.2297 | 1.40201 | ||||||||
\(119\) | 3.38406 | 0.310216 | ||||||||
\(120\) | 3.75968 | 0.343211 | ||||||||
\(121\) | −10.6330 | −0.966636 | ||||||||
\(122\) | 16.6151 | 1.50426 | ||||||||
\(123\) | 2.00544 | 0.180824 | ||||||||
\(124\) | 28.5865 | 2.56715 | ||||||||
\(125\) | −2.15166 | −0.192451 | ||||||||
\(126\) | −21.0683 | −1.87691 | ||||||||
\(127\) | −15.5307 | −1.37812 | −0.689062 | − | 0.724702i | \(-0.741977\pi\) | ||||
−0.689062 | + | 0.724702i | \(0.741977\pi\) | |||||||
\(128\) | −1.47967 | −0.130786 | ||||||||
\(129\) | −14.8541 | −1.30783 | ||||||||
\(130\) | 1.72643 | 0.151418 | ||||||||
\(131\) | 2.50539 | 0.218897 | 0.109449 | − | 0.993992i | \(-0.465091\pi\) | ||||
0.109449 | + | 0.993992i | \(0.465091\pi\) | |||||||
\(132\) | −6.83116 | −0.594576 | ||||||||
\(133\) | 16.8688 | 1.46271 | ||||||||
\(134\) | −22.3513 | −1.93086 | ||||||||
\(135\) | 0.312548 | 0.0268999 | ||||||||
\(136\) | −7.50057 | −0.643169 | ||||||||
\(137\) | 13.0927 | 1.11859 | 0.559294 | − | 0.828969i | \(-0.311072\pi\) | ||||
0.559294 | + | 0.828969i | \(0.311072\pi\) | |||||||
\(138\) | 9.75513 | 0.830411 | ||||||||
\(139\) | 15.5926 | 1.32254 | 0.661272 | − | 0.750146i | \(-0.270017\pi\) | ||||
0.661272 | + | 0.750146i | \(0.270017\pi\) | |||||||
\(140\) | 3.55761 | 0.300673 | ||||||||
\(141\) | −1.44151 | −0.121397 | ||||||||
\(142\) | 33.7696 | 2.83388 | ||||||||
\(143\) | −1.84678 | −0.154435 | ||||||||
\(144\) | 23.5827 | 1.96523 | ||||||||
\(145\) | −2.27290 | −0.188754 | ||||||||
\(146\) | −43.3502 | −3.58769 | ||||||||
\(147\) | −10.3226 | −0.851398 | ||||||||
\(148\) | −18.2465 | −1.49985 | ||||||||
\(149\) | −16.3563 | −1.33996 | −0.669979 | − | 0.742380i | \(-0.733697\pi\) | ||||
−0.669979 | + | 0.742380i | \(0.733697\pi\) | |||||||
\(150\) | −30.0885 | −2.45671 | ||||||||
\(151\) | 8.22364 | 0.669230 | 0.334615 | − | 0.942355i | \(-0.391394\pi\) | ||||
0.334615 | + | 0.942355i | \(0.391394\pi\) | |||||||
\(152\) | −37.3887 | −3.03263 | ||||||||
\(153\) | 2.37647 | 0.192126 | ||||||||
\(154\) | −5.37071 | −0.432784 | ||||||||
\(155\) | 1.27074 | 0.102069 | ||||||||
\(156\) | 34.3749 | 2.75219 | ||||||||
\(157\) | 8.76181 | 0.699269 | 0.349634 | − | 0.936886i | \(-0.386306\pi\) | ||||
0.349634 | + | 0.936886i | \(0.386306\pi\) | |||||||
\(158\) | −0.782144 | −0.0622240 | ||||||||
\(159\) | −22.3747 | −1.77443 | ||||||||
\(160\) | −2.37704 | −0.187921 | ||||||||
\(161\) | 5.43454 | 0.428302 | ||||||||
\(162\) | 27.4597 | 2.15744 | ||||||||
\(163\) | 21.0887 | 1.65179 | 0.825896 | − | 0.563823i | \(-0.190670\pi\) | ||||
0.825896 | + | 0.563823i | \(0.190670\pi\) | |||||||
\(164\) | −4.20604 | −0.328436 | ||||||||
\(165\) | −0.303662 | −0.0236401 | ||||||||
\(166\) | −8.31691 | −0.645517 | ||||||||
\(167\) | 2.81554 | 0.217873 | 0.108937 | − | 0.994049i | \(-0.465255\pi\) | ||||
0.108937 | + | 0.994049i | \(0.465255\pi\) | |||||||
\(168\) | 58.8547 | 4.54074 | ||||||||
\(169\) | −3.70688 | −0.285144 | ||||||||
\(170\) | −0.566328 | −0.0434354 | ||||||||
\(171\) | 11.8462 | 0.905898 | ||||||||
\(172\) | 31.1537 | 2.37545 | ||||||||
\(173\) | 21.6542 | 1.64634 | 0.823170 | − | 0.567795i | \(-0.192203\pi\) | ||||
0.823170 | + | 0.567795i | \(0.192203\pi\) | |||||||
\(174\) | −63.8676 | −4.84179 | ||||||||
\(175\) | −16.7622 | −1.26710 | ||||||||
\(176\) | 6.01169 | 0.453148 | ||||||||
\(177\) | 13.4797 | 1.01320 | ||||||||
\(178\) | 16.3245 | 1.22358 | ||||||||
\(179\) | 21.6382 | 1.61732 | 0.808659 | − | 0.588277i | \(-0.200194\pi\) | ||||
0.808659 | + | 0.588277i | \(0.200194\pi\) | |||||||
\(180\) | 2.49834 | 0.186216 | ||||||||
\(181\) | 13.4427 | 0.999187 | 0.499594 | − | 0.866260i | \(-0.333483\pi\) | ||||
0.499594 | + | 0.866260i | \(0.333483\pi\) | |||||||
\(182\) | 27.0258 | 2.00329 | ||||||||
\(183\) | 14.7059 | 1.08709 | ||||||||
\(184\) | −12.0453 | −0.887994 | ||||||||
\(185\) | −0.811101 | −0.0596333 | ||||||||
\(186\) | 35.7073 | 2.61819 | ||||||||
\(187\) | 0.605807 | 0.0443010 | ||||||||
\(188\) | 3.02331 | 0.220498 | ||||||||
\(189\) | 4.89268 | 0.355890 | ||||||||
\(190\) | −2.82302 | −0.204804 | ||||||||
\(191\) | −17.6388 | −1.27630 | −0.638148 | − | 0.769914i | \(-0.720299\pi\) | ||||
−0.638148 | + | 0.769914i | \(0.720299\pi\) | |||||||
\(192\) | −20.7743 | −1.49925 | ||||||||
\(193\) | −13.6671 | −0.983779 | −0.491890 | − | 0.870658i | \(-0.663694\pi\) | ||||
−0.491890 | + | 0.870658i | \(0.663694\pi\) | |||||||
\(194\) | 47.7244 | 3.42642 | ||||||||
\(195\) | 1.52805 | 0.109426 | ||||||||
\(196\) | 21.6498 | 1.54642 | ||||||||
\(197\) | −22.5607 | −1.60738 | −0.803691 | − | 0.595046i | \(-0.797134\pi\) | ||||
−0.803691 | + | 0.595046i | \(0.797134\pi\) | |||||||
\(198\) | −3.77160 | −0.268036 | ||||||||
\(199\) | −18.0931 | −1.28259 | −0.641294 | − | 0.767295i | \(-0.721602\pi\) | ||||
−0.641294 | + | 0.767295i | \(0.721602\pi\) | |||||||
\(200\) | 37.1524 | 2.62707 | ||||||||
\(201\) | −19.7830 | −1.39538 | ||||||||
\(202\) | 38.0768 | 2.67907 | ||||||||
\(203\) | −35.5804 | −2.49725 | ||||||||
\(204\) | −11.2761 | −0.789488 | ||||||||
\(205\) | −0.186969 | −0.0130585 | ||||||||
\(206\) | 12.3602 | 0.861179 | ||||||||
\(207\) | 3.81642 | 0.265260 | ||||||||
\(208\) | −30.2513 | −2.09755 | ||||||||
\(209\) | 3.01981 | 0.208885 | ||||||||
\(210\) | 4.44380 | 0.306652 | ||||||||
\(211\) | 20.1155 | 1.38481 | 0.692403 | − | 0.721511i | \(-0.256552\pi\) | ||||
0.692403 | + | 0.721511i | \(0.256552\pi\) | |||||||
\(212\) | 46.9268 | 3.22294 | ||||||||
\(213\) | 29.8892 | 2.04798 | ||||||||
\(214\) | 40.5512 | 2.77202 | ||||||||
\(215\) | 1.38486 | 0.0944468 | ||||||||
\(216\) | −10.8443 | −0.737864 | ||||||||
\(217\) | 19.8924 | 1.35038 | ||||||||
\(218\) | 47.0168 | 3.18438 | ||||||||
\(219\) | −38.3689 | −2.59273 | ||||||||
\(220\) | 0.636876 | 0.0429382 | ||||||||
\(221\) | −3.04846 | −0.205062 | ||||||||
\(222\) | −22.7916 | −1.52967 | ||||||||
\(223\) | −6.23690 | −0.417653 | −0.208827 | − | 0.977953i | \(-0.566964\pi\) | ||||
−0.208827 | + | 0.977953i | \(0.566964\pi\) | |||||||
\(224\) | −37.2105 | −2.48623 | ||||||||
\(225\) | −11.7713 | −0.784751 | ||||||||
\(226\) | 15.8460 | 1.05406 | ||||||||
\(227\) | 13.0031 | 0.863049 | 0.431524 | − | 0.902101i | \(-0.357976\pi\) | ||||
0.431524 | + | 0.902101i | \(0.357976\pi\) | |||||||
\(228\) | −56.2091 | −3.72254 | ||||||||
\(229\) | 13.9959 | 0.924878 | 0.462439 | − | 0.886651i | \(-0.346974\pi\) | ||||
0.462439 | + | 0.886651i | \(0.346974\pi\) | |||||||
\(230\) | −0.909480 | −0.0599693 | ||||||||
\(231\) | −4.75358 | −0.312763 | ||||||||
\(232\) | 78.8619 | 5.17754 | ||||||||
\(233\) | −17.3041 | −1.13363 | −0.566815 | − | 0.823845i | \(-0.691825\pi\) | ||||
−0.566815 | + | 0.823845i | \(0.691825\pi\) | |||||||
\(234\) | 18.9790 | 1.24069 | ||||||||
\(235\) | 0.134394 | 0.00876688 | ||||||||
\(236\) | −28.2712 | −1.84030 | ||||||||
\(237\) | −0.692270 | −0.0449677 | ||||||||
\(238\) | −8.86539 | −0.574658 | ||||||||
\(239\) | 29.9641 | 1.93822 | 0.969109 | − | 0.246634i | \(-0.0793247\pi\) | ||||
0.969109 | + | 0.246634i | \(0.0793247\pi\) | |||||||
\(240\) | −4.97416 | −0.321081 | ||||||||
\(241\) | 27.1082 | 1.74619 | 0.873097 | − | 0.487546i | \(-0.162108\pi\) | ||||
0.873097 | + | 0.487546i | \(0.162108\pi\) | |||||||
\(242\) | 27.8558 | 1.79064 | ||||||||
\(243\) | 19.9670 | 1.28088 | ||||||||
\(244\) | −30.8429 | −1.97452 | ||||||||
\(245\) | 0.962390 | 0.0614848 | ||||||||
\(246\) | −5.25375 | −0.334967 | ||||||||
\(247\) | −15.1959 | −0.966893 | ||||||||
\(248\) | −44.0904 | −2.79974 | ||||||||
\(249\) | −7.36123 | −0.466499 | ||||||||
\(250\) | 5.63682 | 0.356504 | ||||||||
\(251\) | 3.10278 | 0.195846 | 0.0979228 | − | 0.995194i | \(-0.468780\pi\) | ||||
0.0979228 | + | 0.995194i | \(0.468780\pi\) | |||||||
\(252\) | 39.1095 | 2.46366 | ||||||||
\(253\) | 0.972879 | 0.0611644 | ||||||||
\(254\) | 40.6865 | 2.55290 | ||||||||
\(255\) | −0.501253 | −0.0313897 | ||||||||
\(256\) | −14.0424 | −0.877647 | ||||||||
\(257\) | −3.18613 | −0.198745 | −0.0993726 | − | 0.995050i | \(-0.531684\pi\) | ||||
−0.0993726 | + | 0.995050i | \(0.531684\pi\) | |||||||
\(258\) | 38.9140 | 2.42268 | ||||||||
\(259\) | −12.6971 | −0.788960 | ||||||||
\(260\) | −3.20480 | −0.198754 | ||||||||
\(261\) | −24.9864 | −1.54662 | ||||||||
\(262\) | −6.56351 | −0.405495 | ||||||||
\(263\) | −0.0320315 | −0.00197515 | −0.000987573 | − | 1.00000i | \(-0.500314\pi\) | ||||
−0.000987573 | 1.00000i | \(0.500314\pi\) | ||||||||
\(264\) | 10.5360 | 0.648448 | ||||||||
\(265\) | 2.08601 | 0.128143 | ||||||||
\(266\) | −44.1920 | −2.70959 | ||||||||
\(267\) | 14.4487 | 0.884247 | ||||||||
\(268\) | 41.4912 | 2.53448 | ||||||||
\(269\) | −12.0236 | −0.733094 | −0.366547 | − | 0.930399i | \(-0.619460\pi\) | ||||
−0.366547 | + | 0.930399i | \(0.619460\pi\) | |||||||
\(270\) | −0.818799 | −0.0498305 | ||||||||
\(271\) | −7.27379 | −0.441851 | −0.220926 | − | 0.975291i | \(-0.570908\pi\) | ||||
−0.220926 | + | 0.975291i | \(0.570908\pi\) | |||||||
\(272\) | 9.92345 | 0.601698 | ||||||||
\(273\) | 23.9204 | 1.44773 | ||||||||
\(274\) | −34.2997 | −2.07212 | ||||||||
\(275\) | −3.00072 | −0.180950 | ||||||||
\(276\) | −18.1086 | −1.09001 | ||||||||
\(277\) | 15.7552 | 0.946640 | 0.473320 | − | 0.880891i | \(-0.343055\pi\) | ||||
0.473320 | + | 0.880891i | \(0.343055\pi\) | |||||||
\(278\) | −40.8486 | −2.44994 | ||||||||
\(279\) | 13.9695 | 0.836332 | ||||||||
\(280\) | −5.48708 | −0.327916 | ||||||||
\(281\) | −16.0943 | −0.960108 | −0.480054 | − | 0.877239i | \(-0.659383\pi\) | ||||
−0.480054 | + | 0.877239i | \(0.659383\pi\) | |||||||
\(282\) | 3.77641 | 0.224882 | ||||||||
\(283\) | −13.7318 | −0.816272 | −0.408136 | − | 0.912921i | \(-0.633821\pi\) | ||||
−0.408136 | + | 0.912921i | \(0.633821\pi\) | |||||||
\(284\) | −62.6871 | −3.71980 | ||||||||
\(285\) | −2.49864 | −0.148006 | ||||||||
\(286\) | 4.83810 | 0.286083 | ||||||||
\(287\) | −2.92684 | −0.172766 | ||||||||
\(288\) | −26.1312 | −1.53979 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 5.95444 | 0.349657 | ||||||||
\(291\) | 42.2405 | 2.47618 | ||||||||
\(292\) | 80.4718 | 4.70925 | ||||||||
\(293\) | 15.4912 | 0.905005 | 0.452502 | − | 0.891763i | \(-0.350531\pi\) | ||||
0.452502 | + | 0.891763i | \(0.350531\pi\) | |||||||
\(294\) | 27.0427 | 1.57717 | ||||||||
\(295\) | −1.25673 | −0.0731694 | ||||||||
\(296\) | 28.1424 | 1.63574 | ||||||||
\(297\) | 0.875876 | 0.0508235 | ||||||||
\(298\) | 42.8493 | 2.48219 | ||||||||
\(299\) | −4.89560 | −0.283120 | ||||||||
\(300\) | 55.8538 | 3.22472 | ||||||||
\(301\) | 21.6788 | 1.24955 | ||||||||
\(302\) | −21.5439 | −1.23971 | ||||||||
\(303\) | 33.7015 | 1.93610 | ||||||||
\(304\) | 49.4662 | 2.83708 | ||||||||
\(305\) | −1.37105 | −0.0785059 | ||||||||
\(306\) | −6.22574 | −0.355902 | ||||||||
\(307\) | 10.4733 | 0.597743 | 0.298872 | − | 0.954293i | \(-0.403390\pi\) | ||||
0.298872 | + | 0.954293i | \(0.403390\pi\) | |||||||
\(308\) | 9.96975 | 0.568079 | ||||||||
\(309\) | 10.9400 | 0.622352 | ||||||||
\(310\) | −3.32903 | −0.189076 | ||||||||
\(311\) | −8.12547 | −0.460753 | −0.230377 | − | 0.973102i | \(-0.573996\pi\) | ||||
−0.230377 | + | 0.973102i | \(0.573996\pi\) | |||||||
\(312\) | −53.0181 | −3.00156 | ||||||||
\(313\) | −9.96182 | −0.563075 | −0.281538 | − | 0.959550i | \(-0.590844\pi\) | ||||
−0.281538 | + | 0.959550i | \(0.590844\pi\) | |||||||
\(314\) | −22.9537 | −1.29535 | ||||||||
\(315\) | 1.73851 | 0.0979542 | ||||||||
\(316\) | 1.45191 | 0.0816762 | ||||||||
\(317\) | 15.0746 | 0.846671 | 0.423336 | − | 0.905973i | \(-0.360859\pi\) | ||||
0.423336 | + | 0.905973i | \(0.360859\pi\) | |||||||
\(318\) | 58.6161 | 3.28703 | ||||||||
\(319\) | −6.36952 | −0.356625 | ||||||||
\(320\) | 1.93680 | 0.108271 | ||||||||
\(321\) | 35.8916 | 2.00327 | ||||||||
\(322\) | −14.2371 | −0.793405 | ||||||||
\(323\) | 4.98478 | 0.277361 | ||||||||
\(324\) | −50.9740 | −2.83189 | ||||||||
\(325\) | 15.0999 | 0.837589 | ||||||||
\(326\) | −55.2470 | −3.05985 | ||||||||
\(327\) | 41.6142 | 2.30127 | ||||||||
\(328\) | 6.48717 | 0.358194 | ||||||||
\(329\) | 2.10382 | 0.115987 | ||||||||
\(330\) | 0.795519 | 0.0437919 | ||||||||
\(331\) | 33.4525 | 1.83872 | 0.919359 | − | 0.393420i | \(-0.128708\pi\) | ||||
0.919359 | + | 0.393420i | \(0.128708\pi\) | |||||||
\(332\) | 15.4388 | 0.847316 | ||||||||
\(333\) | −8.91657 | −0.488625 | ||||||||
\(334\) | −7.37601 | −0.403597 | ||||||||
\(335\) | 1.84439 | 0.100770 | ||||||||
\(336\) | −77.8663 | −4.24795 | ||||||||
\(337\) | −20.3557 | −1.10885 | −0.554423 | − | 0.832235i | \(-0.687061\pi\) | ||||
−0.554423 | + | 0.832235i | \(0.687061\pi\) | |||||||
\(338\) | 9.71109 | 0.528213 | ||||||||
\(339\) | 14.0252 | 0.761742 | ||||||||
\(340\) | 1.05129 | 0.0570140 | ||||||||
\(341\) | 3.56109 | 0.192844 | ||||||||
\(342\) | −31.0340 | −1.67812 | ||||||||
\(343\) | −8.62302 | −0.465600 | ||||||||
\(344\) | −48.0499 | −2.59068 | ||||||||
\(345\) | −0.804973 | −0.0433383 | ||||||||
\(346\) | −56.7286 | −3.04975 | ||||||||
\(347\) | −7.32242 | −0.393088 | −0.196544 | − | 0.980495i | \(-0.562972\pi\) | ||||
−0.196544 | + | 0.980495i | \(0.562972\pi\) | |||||||
\(348\) | 118.559 | 6.35541 | ||||||||
\(349\) | 16.7811 | 0.898271 | 0.449136 | − | 0.893464i | \(-0.351732\pi\) | ||||
0.449136 | + | 0.893464i | \(0.351732\pi\) | |||||||
\(350\) | 43.9127 | 2.34723 | ||||||||
\(351\) | −4.40747 | −0.235254 | ||||||||
\(352\) | −6.66133 | −0.355050 | ||||||||
\(353\) | 1.00000 | 0.0532246 | ||||||||
\(354\) | −35.3135 | −1.87689 | ||||||||
\(355\) | −2.78660 | −0.147897 | ||||||||
\(356\) | −30.3035 | −1.60608 | ||||||||
\(357\) | −7.84669 | −0.415291 | ||||||||
\(358\) | −56.6868 | −2.99599 | ||||||||
\(359\) | −30.3103 | −1.59972 | −0.799859 | − | 0.600189i | \(-0.795092\pi\) | ||||
−0.799859 | + | 0.600189i | \(0.795092\pi\) | |||||||
\(360\) | −3.85332 | −0.203088 | ||||||||
\(361\) | 5.84803 | 0.307791 | ||||||||
\(362\) | −35.2165 | −1.85094 | ||||||||
\(363\) | 24.6550 | 1.29405 | ||||||||
\(364\) | −50.1685 | −2.62954 | ||||||||
\(365\) | 3.57717 | 0.187238 | ||||||||
\(366\) | −38.5258 | −2.01378 | ||||||||
\(367\) | −32.4415 | −1.69343 | −0.846717 | − | 0.532043i | \(-0.821424\pi\) | ||||
−0.846717 | + | 0.532043i | \(0.821424\pi\) | |||||||
\(368\) | 15.9363 | 0.830737 | ||||||||
\(369\) | −2.05538 | −0.106999 | ||||||||
\(370\) | 2.12488 | 0.110467 | ||||||||
\(371\) | 32.6548 | 1.69535 | ||||||||
\(372\) | −66.2842 | −3.43667 | ||||||||
\(373\) | −33.0668 | −1.71214 | −0.856068 | − | 0.516864i | \(-0.827099\pi\) | ||||
−0.856068 | + | 0.516864i | \(0.827099\pi\) | |||||||
\(374\) | −1.58706 | −0.0820650 | ||||||||
\(375\) | 4.98910 | 0.257636 | ||||||||
\(376\) | −4.66300 | −0.240476 | ||||||||
\(377\) | 32.0519 | 1.65076 | ||||||||
\(378\) | −12.8176 | −0.659266 | ||||||||
\(379\) | −18.7297 | −0.962082 | −0.481041 | − | 0.876698i | \(-0.659741\pi\) | ||||
−0.481041 | + | 0.876698i | \(0.659741\pi\) | |||||||
\(380\) | 5.24043 | 0.268828 | ||||||||
\(381\) | 36.0113 | 1.84491 | ||||||||
\(382\) | 46.2091 | 2.36426 | ||||||||
\(383\) | −31.5763 | −1.61347 | −0.806737 | − | 0.590911i | \(-0.798769\pi\) | ||||
−0.806737 | + | 0.590911i | \(0.798769\pi\) | |||||||
\(384\) | 3.43094 | 0.175085 | ||||||||
\(385\) | 0.443181 | 0.0225866 | ||||||||
\(386\) | 35.8044 | 1.82239 | ||||||||
\(387\) | 15.2240 | 0.773880 | ||||||||
\(388\) | −88.5917 | −4.49756 | ||||||||
\(389\) | 2.38448 | 0.120898 | 0.0604489 | − | 0.998171i | \(-0.480747\pi\) | ||||
0.0604489 | + | 0.998171i | \(0.480747\pi\) | |||||||
\(390\) | −4.00311 | −0.202705 | ||||||||
\(391\) | 1.60592 | 0.0812150 | ||||||||
\(392\) | −33.3916 | −1.68653 | ||||||||
\(393\) | −5.80931 | −0.293041 | ||||||||
\(394\) | 59.1034 | 2.97758 | ||||||||
\(395\) | 0.0645409 | 0.00324741 | ||||||||
\(396\) | 7.00128 | 0.351828 | ||||||||
\(397\) | 24.2645 | 1.21780 | 0.608900 | − | 0.793247i | \(-0.291611\pi\) | ||||
0.608900 | + | 0.793247i | \(0.291611\pi\) | |||||||
\(398\) | 47.3995 | 2.37592 | ||||||||
\(399\) | −39.1140 | −1.95815 | ||||||||
\(400\) | −49.1535 | −2.45768 | ||||||||
\(401\) | 20.7258 | 1.03500 | 0.517498 | − | 0.855684i | \(-0.326863\pi\) | ||||
0.517498 | + | 0.855684i | \(0.326863\pi\) | |||||||
\(402\) | 51.8265 | 2.58487 | ||||||||
\(403\) | −17.9197 | −0.892642 | ||||||||
\(404\) | −70.6826 | −3.51659 | ||||||||
\(405\) | −2.26592 | −0.112595 | ||||||||
\(406\) | 93.2117 | 4.62602 | ||||||||
\(407\) | −2.27301 | −0.112669 | ||||||||
\(408\) | 17.3917 | 0.861019 | ||||||||
\(409\) | −14.0876 | −0.696585 | −0.348292 | − | 0.937386i | \(-0.613238\pi\) | ||||
−0.348292 | + | 0.937386i | \(0.613238\pi\) | |||||||
\(410\) | 0.489812 | 0.0241901 | ||||||||
\(411\) | −30.3584 | −1.49747 | ||||||||
\(412\) | −22.9445 | −1.13040 | ||||||||
\(413\) | −19.6730 | −0.968044 | ||||||||
\(414\) | −9.99807 | −0.491378 | ||||||||
\(415\) | 0.686295 | 0.0336889 | ||||||||
\(416\) | 33.5203 | 1.64347 | ||||||||
\(417\) | −36.1548 | −1.77051 | ||||||||
\(418\) | −7.91115 | −0.386947 | ||||||||
\(419\) | 10.5781 | 0.516773 | 0.258386 | − | 0.966042i | \(-0.416809\pi\) | ||||
0.258386 | + | 0.966042i | \(0.416809\pi\) | |||||||
\(420\) | −8.24911 | −0.402516 | ||||||||
\(421\) | −21.1281 | −1.02972 | −0.514860 | − | 0.857274i | \(-0.672156\pi\) | ||||
−0.514860 | + | 0.857274i | \(0.672156\pi\) | |||||||
\(422\) | −52.6975 | −2.56528 | ||||||||
\(423\) | 1.47741 | 0.0718343 | ||||||||
\(424\) | −72.3774 | −3.51496 | ||||||||
\(425\) | −4.95327 | −0.240269 | ||||||||
\(426\) | −78.3023 | −3.79376 | ||||||||
\(427\) | −21.4626 | −1.03865 | ||||||||
\(428\) | −75.2759 | −3.63860 | ||||||||
\(429\) | 4.28216 | 0.206745 | ||||||||
\(430\) | −3.62799 | −0.174957 | ||||||||
\(431\) | −29.5237 | −1.42211 | −0.711054 | − | 0.703138i | \(-0.751782\pi\) | ||||
−0.711054 | + | 0.703138i | \(0.751782\pi\) | |||||||
\(432\) | 14.3473 | 0.690287 | ||||||||
\(433\) | −23.1646 | −1.11322 | −0.556609 | − | 0.830774i | \(-0.687898\pi\) | ||||
−0.556609 | + | 0.830774i | \(0.687898\pi\) | |||||||
\(434\) | −52.1131 | −2.50151 | ||||||||
\(435\) | 5.27023 | 0.252688 | ||||||||
\(436\) | −87.2781 | −4.17986 | ||||||||
\(437\) | 8.00517 | 0.382939 | ||||||||
\(438\) | 100.517 | 4.80289 | ||||||||
\(439\) | 31.8923 | 1.52214 | 0.761068 | − | 0.648672i | \(-0.224675\pi\) | ||||
0.761068 | + | 0.648672i | \(0.224675\pi\) | |||||||
\(440\) | −0.982284 | −0.0468285 | ||||||||
\(441\) | 10.5797 | 0.503796 | ||||||||
\(442\) | 7.98621 | 0.379865 | ||||||||
\(443\) | −30.0347 | −1.42699 | −0.713497 | − | 0.700658i | \(-0.752890\pi\) | ||||
−0.713497 | + | 0.700658i | \(0.752890\pi\) | |||||||
\(444\) | 42.3084 | 2.00787 | ||||||||
\(445\) | −1.34707 | −0.0638571 | ||||||||
\(446\) | 16.3391 | 0.773679 | ||||||||
\(447\) | 37.9256 | 1.79382 | ||||||||
\(448\) | 30.3190 | 1.43244 | ||||||||
\(449\) | −32.2392 | −1.52146 | −0.760732 | − | 0.649066i | \(-0.775160\pi\) | ||||
−0.760732 | + | 0.649066i | \(0.775160\pi\) | |||||||
\(450\) | 30.8378 | 1.45371 | ||||||||
\(451\) | −0.523956 | −0.0246721 | ||||||||
\(452\) | −29.4152 | −1.38357 | ||||||||
\(453\) | −19.0683 | −0.895908 | ||||||||
\(454\) | −34.0650 | −1.59875 | ||||||||
\(455\) | −2.23012 | −0.104549 | ||||||||
\(456\) | 86.6940 | 4.05982 | ||||||||
\(457\) | 40.0897 | 1.87532 | 0.937658 | − | 0.347560i | \(-0.112990\pi\) | ||||
0.937658 | + | 0.347560i | \(0.112990\pi\) | |||||||
\(458\) | −36.6659 | −1.71328 | ||||||||
\(459\) | 1.44580 | 0.0674843 | ||||||||
\(460\) | 1.68828 | 0.0787166 | ||||||||
\(461\) | −37.9134 | −1.76580 | −0.882901 | − | 0.469559i | \(-0.844413\pi\) | ||||
−0.882901 | + | 0.469559i | \(0.844413\pi\) | |||||||
\(462\) | 12.4532 | 0.579375 | ||||||||
\(463\) | −4.18769 | −0.194618 | −0.0973092 | − | 0.995254i | \(-0.531024\pi\) | ||||
−0.0973092 | + | 0.995254i | \(0.531024\pi\) | |||||||
\(464\) | −104.336 | −4.84369 | ||||||||
\(465\) | −2.94650 | −0.136641 | ||||||||
\(466\) | 45.3324 | 2.09998 | ||||||||
\(467\) | 10.6805 | 0.494236 | 0.247118 | − | 0.968985i | \(-0.420517\pi\) | ||||
0.247118 | + | 0.968985i | \(0.420517\pi\) | |||||||
\(468\) | −35.2310 | −1.62855 | ||||||||
\(469\) | 28.8723 | 1.33320 | ||||||||
\(470\) | −0.352078 | −0.0162401 | ||||||||
\(471\) | −20.3162 | −0.936121 | ||||||||
\(472\) | 43.6040 | 2.00704 | ||||||||
\(473\) | 3.88089 | 0.178444 | ||||||||
\(474\) | 1.81357 | 0.0833002 | ||||||||
\(475\) | −24.6909 | −1.13290 | ||||||||
\(476\) | 16.4570 | 0.754305 | ||||||||
\(477\) | 22.9319 | 1.04998 | ||||||||
\(478\) | −78.4985 | −3.59044 | ||||||||
\(479\) | 21.8653 | 0.999051 | 0.499525 | − | 0.866299i | \(-0.333508\pi\) | ||||
0.499525 | + | 0.866299i | \(0.333508\pi\) | |||||||
\(480\) | 5.51168 | 0.251573 | ||||||||
\(481\) | 11.4379 | 0.521525 | ||||||||
\(482\) | −71.0168 | −3.23473 | ||||||||
\(483\) | −12.6012 | −0.573374 | ||||||||
\(484\) | −51.7092 | −2.35042 | ||||||||
\(485\) | −3.93813 | −0.178821 | ||||||||
\(486\) | −52.3085 | −2.37276 | ||||||||
\(487\) | 27.2950 | 1.23685 | 0.618427 | − | 0.785842i | \(-0.287770\pi\) | ||||
0.618427 | + | 0.785842i | \(0.287770\pi\) | |||||||
\(488\) | 47.5705 | 2.15342 | ||||||||
\(489\) | −48.8987 | −2.21128 | ||||||||
\(490\) | −2.52122 | −0.113897 | ||||||||
\(491\) | 1.76167 | 0.0795031 | 0.0397516 | − | 0.999210i | \(-0.487343\pi\) | ||||
0.0397516 | + | 0.999210i | \(0.487343\pi\) | |||||||
\(492\) | 9.75262 | 0.439682 | ||||||||
\(493\) | −10.5141 | −0.473532 | ||||||||
\(494\) | 39.8095 | 1.79111 | ||||||||
\(495\) | 0.311225 | 0.0139885 | ||||||||
\(496\) | 58.3327 | 2.61921 | ||||||||
\(497\) | −43.6219 | −1.95671 | ||||||||
\(498\) | 19.2846 | 0.864163 | ||||||||
\(499\) | 24.6671 | 1.10425 | 0.552126 | − | 0.833761i | \(-0.313817\pi\) | ||||
0.552126 | + | 0.833761i | \(0.313817\pi\) | |||||||
\(500\) | −10.4637 | −0.467952 | ||||||||
\(501\) | −6.52845 | −0.291670 | ||||||||
\(502\) | −8.12850 | −0.362793 | ||||||||
\(503\) | 20.7548 | 0.925409 | 0.462704 | − | 0.886513i | \(-0.346879\pi\) | ||||
0.462704 | + | 0.886513i | \(0.346879\pi\) | |||||||
\(504\) | −60.3204 | −2.68688 | ||||||||
\(505\) | −3.14202 | −0.139818 | ||||||||
\(506\) | −2.54870 | −0.113303 | ||||||||
\(507\) | 8.59521 | 0.381727 | ||||||||
\(508\) | −75.5270 | −3.35097 | ||||||||
\(509\) | −34.9462 | −1.54896 | −0.774481 | − | 0.632597i | \(-0.781989\pi\) | ||||
−0.774481 | + | 0.632597i | \(0.781989\pi\) | |||||||
\(510\) | 1.31316 | 0.0581476 | ||||||||
\(511\) | 55.9976 | 2.47719 | ||||||||
\(512\) | 39.7468 | 1.75658 | ||||||||
\(513\) | 7.20701 | 0.318197 | ||||||||
\(514\) | 8.34686 | 0.368164 | ||||||||
\(515\) | −1.01994 | −0.0449440 | ||||||||
\(516\) | −72.2368 | −3.18005 | ||||||||
\(517\) | 0.376621 | 0.0165638 | ||||||||
\(518\) | 33.2632 | 1.46150 | ||||||||
\(519\) | −50.2101 | −2.20398 | ||||||||
\(520\) | 4.94292 | 0.216762 | ||||||||
\(521\) | 14.1237 | 0.618771 | 0.309385 | − | 0.950937i | \(-0.399877\pi\) | ||||
0.309385 | + | 0.950937i | \(0.399877\pi\) | |||||||
\(522\) | 65.4582 | 2.86503 | ||||||||
\(523\) | −2.80695 | −0.122739 | −0.0613697 | − | 0.998115i | \(-0.519547\pi\) | ||||
−0.0613697 | + | 0.998115i | \(0.519547\pi\) | |||||||
\(524\) | 12.1840 | 0.532259 | ||||||||
\(525\) | 38.8668 | 1.69628 | ||||||||
\(526\) | 0.0839145 | 0.00365885 | ||||||||
\(527\) | 5.87827 | 0.256061 | ||||||||
\(528\) | −13.9394 | −0.606636 | ||||||||
\(529\) | −20.4210 | −0.887870 | ||||||||
\(530\) | −5.46483 | −0.237377 | ||||||||
\(531\) | −13.8154 | −0.599537 | ||||||||
\(532\) | 82.0345 | 3.55665 | ||||||||
\(533\) | 2.63658 | 0.114203 | ||||||||
\(534\) | −37.8520 | −1.63802 | ||||||||
\(535\) | −3.34620 | −0.144669 | ||||||||
\(536\) | −63.9938 | −2.76411 | ||||||||
\(537\) | −50.1730 | −2.16513 | ||||||||
\(538\) | 31.4989 | 1.35802 | ||||||||
\(539\) | 2.69697 | 0.116167 | ||||||||
\(540\) | 1.51995 | 0.0654083 | ||||||||
\(541\) | −21.7805 | −0.936418 | −0.468209 | − | 0.883618i | \(-0.655100\pi\) | ||||
−0.468209 | + | 0.883618i | \(0.655100\pi\) | |||||||
\(542\) | 19.0555 | 0.818504 | ||||||||
\(543\) | −31.1698 | −1.33763 | ||||||||
\(544\) | −10.9958 | −0.471441 | ||||||||
\(545\) | −3.87973 | −0.166189 | ||||||||
\(546\) | −62.6653 | −2.68183 | ||||||||
\(547\) | 17.0651 | 0.729651 | 0.364825 | − | 0.931076i | \(-0.381129\pi\) | ||||
0.364825 | + | 0.931076i | \(0.381129\pi\) | |||||||
\(548\) | 63.6712 | 2.71990 | ||||||||
\(549\) | −15.0721 | −0.643264 | ||||||||
\(550\) | 7.86114 | 0.335200 | ||||||||
\(551\) | −52.4105 | −2.23276 | ||||||||
\(552\) | 27.9298 | 1.18877 | ||||||||
\(553\) | 1.01033 | 0.0429638 | ||||||||
\(554\) | −41.2748 | −1.75360 | ||||||||
\(555\) | 1.88072 | 0.0798320 | ||||||||
\(556\) | 75.8280 | 3.21582 | ||||||||
\(557\) | 40.2072 | 1.70363 | 0.851816 | − | 0.523840i | \(-0.175501\pi\) | ||||
0.851816 | + | 0.523840i | \(0.175501\pi\) | |||||||
\(558\) | −36.5966 | −1.54926 | ||||||||
\(559\) | −19.5289 | −0.825986 | ||||||||
\(560\) | 7.25955 | 0.306772 | ||||||||
\(561\) | −1.40470 | −0.0593063 | ||||||||
\(562\) | 42.1632 | 1.77855 | ||||||||
\(563\) | −6.67822 | −0.281453 | −0.140727 | − | 0.990048i | \(-0.544944\pi\) | ||||
−0.140727 | + | 0.990048i | \(0.544944\pi\) | |||||||
\(564\) | −7.01021 | −0.295183 | ||||||||
\(565\) | −1.30758 | −0.0550103 | ||||||||
\(566\) | 35.9739 | 1.51210 | ||||||||
\(567\) | −35.4711 | −1.48965 | ||||||||
\(568\) | 96.6853 | 4.05683 | ||||||||
\(569\) | −0.960867 | −0.0402816 | −0.0201408 | − | 0.999797i | \(-0.506411\pi\) | ||||
−0.0201408 | + | 0.999797i | \(0.506411\pi\) | |||||||
\(570\) | 6.54580 | 0.274173 | ||||||||
\(571\) | 10.5338 | 0.440827 | 0.220414 | − | 0.975407i | \(-0.429259\pi\) | ||||
0.220414 | + | 0.975407i | \(0.429259\pi\) | |||||||
\(572\) | −8.98105 | −0.375517 | ||||||||
\(573\) | 40.8993 | 1.70859 | ||||||||
\(574\) | 7.66759 | 0.320039 | ||||||||
\(575\) | −7.95457 | −0.331728 | ||||||||
\(576\) | 21.2916 | 0.887151 | ||||||||
\(577\) | 27.7951 | 1.15712 | 0.578562 | − | 0.815638i | \(-0.303614\pi\) | ||||
0.578562 | + | 0.815638i | \(0.303614\pi\) | |||||||
\(578\) | −2.61975 | −0.108967 | ||||||||
\(579\) | 31.6902 | 1.31700 | ||||||||
\(580\) | −11.0533 | −0.458965 | ||||||||
\(581\) | 10.7434 | 0.445710 | ||||||||
\(582\) | −110.660 | −4.58699 | ||||||||
\(583\) | 5.84578 | 0.242107 | ||||||||
\(584\) | −124.115 | −5.13593 | ||||||||
\(585\) | −1.56611 | −0.0647505 | ||||||||
\(586\) | −40.5830 | −1.67647 | ||||||||
\(587\) | 16.9858 | 0.701081 | 0.350540 | − | 0.936548i | \(-0.385998\pi\) | ||||
0.350540 | + | 0.936548i | \(0.385998\pi\) | |||||||
\(588\) | −50.1999 | −2.07021 | ||||||||
\(589\) | 29.3019 | 1.20736 | ||||||||
\(590\) | 3.29231 | 0.135542 | ||||||||
\(591\) | 52.3120 | 2.15183 | ||||||||
\(592\) | −37.2331 | −1.53027 | ||||||||
\(593\) | −5.88610 | −0.241713 | −0.120857 | − | 0.992670i | \(-0.538564\pi\) | ||||
−0.120857 | + | 0.992670i | \(0.538564\pi\) | |||||||
\(594\) | −2.29458 | −0.0941476 | ||||||||
\(595\) | 0.731555 | 0.0299908 | ||||||||
\(596\) | −79.5419 | −3.25816 | ||||||||
\(597\) | 41.9529 | 1.71702 | ||||||||
\(598\) | 12.8252 | 0.524463 | ||||||||
\(599\) | 39.5784 | 1.61713 | 0.808565 | − | 0.588407i | \(-0.200245\pi\) | ||||
0.808565 | + | 0.588407i | \(0.200245\pi\) | |||||||
\(600\) | −86.1459 | −3.51689 | ||||||||
\(601\) | −10.2614 | −0.418573 | −0.209286 | − | 0.977854i | \(-0.567114\pi\) | ||||
−0.209286 | + | 0.977854i | \(0.567114\pi\) | |||||||
\(602\) | −56.7931 | −2.31472 | ||||||||
\(603\) | 20.2757 | 0.825689 | ||||||||
\(604\) | 39.9923 | 1.62726 | ||||||||
\(605\) | −2.29860 | −0.0934516 | ||||||||
\(606\) | −88.2894 | −3.58651 | ||||||||
\(607\) | −33.6135 | −1.36433 | −0.682164 | − | 0.731199i | \(-0.738961\pi\) | ||||
−0.682164 | + | 0.731199i | \(0.738961\pi\) | |||||||
\(608\) | −54.8117 | −2.22291 | ||||||||
\(609\) | 82.5010 | 3.34311 | ||||||||
\(610\) | 3.59180 | 0.145428 | ||||||||
\(611\) | −1.89518 | −0.0766709 | ||||||||
\(612\) | 11.5570 | 0.467163 | ||||||||
\(613\) | 1.09646 | 0.0442858 | 0.0221429 | − | 0.999755i | \(-0.492951\pi\) | ||||
0.0221429 | + | 0.999755i | \(0.492951\pi\) | |||||||
\(614\) | −27.4374 | −1.10728 | ||||||||
\(615\) | 0.433529 | 0.0174816 | ||||||||
\(616\) | −15.3768 | −0.619550 | ||||||||
\(617\) | 21.2959 | 0.857341 | 0.428670 | − | 0.903461i | \(-0.358982\pi\) | ||||
0.428670 | + | 0.903461i | \(0.358982\pi\) | |||||||
\(618\) | −28.6599 | −1.15287 | ||||||||
\(619\) | −1.95401 | −0.0785383 | −0.0392691 | − | 0.999229i | \(-0.512503\pi\) | ||||
−0.0392691 | + | 0.999229i | \(0.512503\pi\) | |||||||
\(620\) | 6.17973 | 0.248184 | ||||||||
\(621\) | 2.32185 | 0.0931725 | ||||||||
\(622\) | 21.2867 | 0.853519 | ||||||||
\(623\) | −21.0872 | −0.844841 | ||||||||
\(624\) | 70.1442 | 2.80802 | ||||||||
\(625\) | 24.3012 | 0.972048 | ||||||||
\(626\) | 26.0975 | 1.04306 | ||||||||
\(627\) | −7.00210 | −0.279637 | ||||||||
\(628\) | 42.6095 | 1.70030 | ||||||||
\(629\) | −3.75203 | −0.149603 | ||||||||
\(630\) | −4.55447 | −0.181455 | ||||||||
\(631\) | −3.11124 | −0.123857 | −0.0619283 | − | 0.998081i | \(-0.519725\pi\) | ||||
−0.0619283 | + | 0.998081i | \(0.519725\pi\) | |||||||
\(632\) | −2.23935 | −0.0890764 | ||||||||
\(633\) | −46.6422 | −1.85386 | ||||||||
\(634\) | −39.4916 | −1.56841 | ||||||||
\(635\) | −3.35737 | −0.133233 | ||||||||
\(636\) | −108.810 | −4.31460 | ||||||||
\(637\) | −13.5714 | −0.537717 | ||||||||
\(638\) | 16.6865 | 0.660627 | ||||||||
\(639\) | −30.6336 | −1.21185 | ||||||||
\(640\) | −0.319870 | −0.0126440 | ||||||||
\(641\) | −2.50666 | −0.0990071 | −0.0495036 | − | 0.998774i | \(-0.515764\pi\) | ||||
−0.0495036 | + | 0.998774i | \(0.515764\pi\) | |||||||
\(642\) | −94.0269 | −3.71095 | ||||||||
\(643\) | 31.7764 | 1.25314 | 0.626570 | − | 0.779365i | \(-0.284458\pi\) | ||||
0.626570 | + | 0.779365i | \(0.284458\pi\) | |||||||
\(644\) | 26.4287 | 1.04143 | ||||||||
\(645\) | −3.21111 | −0.126437 | ||||||||
\(646\) | −13.0589 | −0.513795 | ||||||||
\(647\) | −28.3128 | −1.11309 | −0.556546 | − | 0.830816i | \(-0.687874\pi\) | ||||
−0.556546 | + | 0.830816i | \(0.687874\pi\) | |||||||
\(648\) | 78.6196 | 3.08847 | ||||||||
\(649\) | −3.52181 | −0.138243 | ||||||||
\(650\) | −39.5578 | −1.55159 | ||||||||
\(651\) | −46.1249 | −1.80778 | ||||||||
\(652\) | 102.556 | 4.01640 | ||||||||
\(653\) | −27.6210 | −1.08089 | −0.540447 | − | 0.841378i | \(-0.681745\pi\) | ||||
−0.540447 | + | 0.841378i | \(0.681745\pi\) | |||||||
\(654\) | −109.019 | −4.26297 | ||||||||
\(655\) | 0.541607 | 0.0211624 | ||||||||
\(656\) | −8.58269 | −0.335098 | ||||||||
\(657\) | 39.3245 | 1.53419 | ||||||||
\(658\) | −5.51148 | −0.214860 | ||||||||
\(659\) | 2.81302 | 0.109580 | 0.0547899 | − | 0.998498i | \(-0.482551\pi\) | ||||
0.0547899 | + | 0.998498i | \(0.482551\pi\) | |||||||
\(660\) | −1.47674 | −0.0574819 | ||||||||
\(661\) | −3.28095 | −0.127614 | −0.0638070 | − | 0.997962i | \(-0.520324\pi\) | ||||
−0.0638070 | + | 0.997962i | \(0.520324\pi\) | |||||||
\(662\) | −87.6373 | −3.40612 | ||||||||
\(663\) | 7.06853 | 0.274519 | ||||||||
\(664\) | −23.8120 | −0.924086 | ||||||||
\(665\) | 3.64664 | 0.141411 | ||||||||
\(666\) | 23.3592 | 0.905150 | ||||||||
\(667\) | −16.8848 | −0.653784 | ||||||||
\(668\) | 13.6922 | 0.529768 | ||||||||
\(669\) | 14.4616 | 0.559118 | ||||||||
\(670\) | −4.83183 | −0.186670 | ||||||||
\(671\) | −3.84218 | −0.148326 | ||||||||
\(672\) | 86.2807 | 3.32835 | ||||||||
\(673\) | −11.7832 | −0.454208 | −0.227104 | − | 0.973871i | \(-0.572926\pi\) | ||||
−0.227104 | + | 0.973871i | \(0.572926\pi\) | |||||||
\(674\) | 53.3269 | 2.05407 | ||||||||
\(675\) | −7.16144 | −0.275644 | ||||||||
\(676\) | −18.0269 | −0.693341 | ||||||||
\(677\) | −42.7536 | −1.64315 | −0.821577 | − | 0.570097i | \(-0.806906\pi\) | ||||
−0.821577 | + | 0.570097i | \(0.806906\pi\) | |||||||
\(678\) | −36.7424 | −1.41108 | ||||||||
\(679\) | −61.6480 | −2.36583 | ||||||||
\(680\) | −1.62145 | −0.0621797 | ||||||||
\(681\) | −30.1506 | −1.15538 | ||||||||
\(682\) | −9.32917 | −0.357232 | ||||||||
\(683\) | 13.4457 | 0.514486 | 0.257243 | − | 0.966347i | \(-0.417186\pi\) | ||||
0.257243 | + | 0.966347i | \(0.417186\pi\) | |||||||
\(684\) | 57.6089 | 2.20273 | ||||||||
\(685\) | 2.83034 | 0.108142 | ||||||||
\(686\) | 22.5902 | 0.862496 | ||||||||
\(687\) | −32.4527 | −1.23815 | ||||||||
\(688\) | 63.5712 | 2.42363 | ||||||||
\(689\) | −29.4164 | −1.12067 | ||||||||
\(690\) | 2.10883 | 0.0802817 | ||||||||
\(691\) | −36.2653 | −1.37960 | −0.689798 | − | 0.724002i | \(-0.742301\pi\) | ||||
−0.689798 | + | 0.724002i | \(0.742301\pi\) | |||||||
\(692\) | 105.306 | 4.00315 | ||||||||
\(693\) | 4.87196 | 0.185070 | ||||||||
\(694\) | 19.1829 | 0.728173 | ||||||||
\(695\) | 3.37075 | 0.127860 | ||||||||
\(696\) | −182.859 | −6.93124 | ||||||||
\(697\) | −0.864890 | −0.0327600 | ||||||||
\(698\) | −43.9623 | −1.66400 | ||||||||
\(699\) | 40.1234 | 1.51761 | ||||||||
\(700\) | −81.5159 | −3.08101 | ||||||||
\(701\) | 2.98235 | 0.112642 | 0.0563210 | − | 0.998413i | \(-0.482063\pi\) | ||||
0.0563210 | + | 0.998413i | \(0.482063\pi\) | |||||||
\(702\) | 11.5465 | 0.435794 | ||||||||
\(703\) | −18.7031 | −0.705399 | ||||||||
\(704\) | 5.42764 | 0.204562 | ||||||||
\(705\) | −0.311622 | −0.0117363 | ||||||||
\(706\) | −2.61975 | −0.0985956 | ||||||||
\(707\) | −49.1857 | −1.84982 | ||||||||
\(708\) | 65.5530 | 2.46363 | ||||||||
\(709\) | 27.2729 | 1.02426 | 0.512128 | − | 0.858909i | \(-0.328857\pi\) | ||||
0.512128 | + | 0.858909i | \(0.328857\pi\) | |||||||
\(710\) | 7.30019 | 0.273971 | ||||||||
\(711\) | 0.709510 | 0.0266087 | ||||||||
\(712\) | 46.7386 | 1.75160 | ||||||||
\(713\) | 9.44004 | 0.353532 | ||||||||
\(714\) | 20.5564 | 0.769303 | ||||||||
\(715\) | −0.399230 | −0.0149304 | ||||||||
\(716\) | 105.229 | 3.93258 | ||||||||
\(717\) | −69.4784 | −2.59472 | ||||||||
\(718\) | 79.4054 | 2.96338 | ||||||||
\(719\) | 8.97679 | 0.334778 | 0.167389 | − | 0.985891i | \(-0.446466\pi\) | ||||
0.167389 | + | 0.985891i | \(0.446466\pi\) | |||||||
\(720\) | 5.09803 | 0.189993 | ||||||||
\(721\) | −15.9663 | −0.594618 | ||||||||
\(722\) | −15.3204 | −0.570165 | ||||||||
\(723\) | −62.8564 | −2.33766 | ||||||||
\(724\) | 65.3730 | 2.42957 | ||||||||
\(725\) | 52.0792 | 1.93417 | ||||||||
\(726\) | −64.5898 | −2.39715 | ||||||||
\(727\) | −45.6766 | −1.69405 | −0.847025 | − | 0.531553i | \(-0.821609\pi\) | ||||
−0.847025 | + | 0.531553i | \(0.821609\pi\) | |||||||
\(728\) | 77.3773 | 2.86779 | ||||||||
\(729\) | −14.8524 | −0.550090 | ||||||||
\(730\) | −9.37130 | −0.346847 | ||||||||
\(731\) | 6.40616 | 0.236940 | ||||||||
\(732\) | 71.5162 | 2.64331 | ||||||||
\(733\) | −6.77664 | −0.250301 | −0.125150 | − | 0.992138i | \(-0.539941\pi\) | ||||
−0.125150 | + | 0.992138i | \(0.539941\pi\) | |||||||
\(734\) | 84.9887 | 3.13699 | ||||||||
\(735\) | −2.23151 | −0.0823106 | ||||||||
\(736\) | −17.6584 | −0.650898 | ||||||||
\(737\) | 5.16866 | 0.190390 | ||||||||
\(738\) | 5.38458 | 0.198209 | ||||||||
\(739\) | −26.2113 | −0.964197 | −0.482099 | − | 0.876117i | \(-0.660125\pi\) | ||||
−0.482099 | + | 0.876117i | \(0.660125\pi\) | |||||||
\(740\) | −3.94446 | −0.145001 | ||||||||
\(741\) | 35.2351 | 1.29439 | ||||||||
\(742\) | −85.5473 | −3.14054 | ||||||||
\(743\) | −49.0933 | −1.80106 | −0.900529 | − | 0.434796i | \(-0.856820\pi\) | ||||
−0.900529 | + | 0.434796i | \(0.856820\pi\) | |||||||
\(744\) | 102.233 | 3.74805 | ||||||||
\(745\) | −3.53584 | −0.129543 | ||||||||
\(746\) | 86.6268 | 3.17163 | ||||||||
\(747\) | 7.54456 | 0.276041 | ||||||||
\(748\) | 2.94609 | 0.107720 | ||||||||
\(749\) | −52.3820 | −1.91400 | ||||||||
\(750\) | −13.0702 | −0.477256 | ||||||||
\(751\) | −47.5002 | −1.73331 | −0.866654 | − | 0.498910i | \(-0.833734\pi\) | ||||
−0.866654 | + | 0.498910i | \(0.833734\pi\) | |||||||
\(752\) | 6.16926 | 0.224970 | ||||||||
\(753\) | −7.19447 | −0.262181 | ||||||||
\(754\) | −83.9679 | −3.05793 | ||||||||
\(755\) | 1.77776 | 0.0646992 | ||||||||
\(756\) | 23.7935 | 0.865363 | ||||||||
\(757\) | 11.3486 | 0.412471 | 0.206235 | − | 0.978502i | \(-0.433879\pi\) | ||||
0.206235 | + | 0.978502i | \(0.433879\pi\) | |||||||
\(758\) | 49.0672 | 1.78220 | ||||||||
\(759\) | −2.25583 | −0.0818816 | ||||||||
\(760\) | −8.08256 | −0.293185 | ||||||||
\(761\) | 17.2748 | 0.626213 | 0.313106 | − | 0.949718i | \(-0.398630\pi\) | ||||
0.313106 | + | 0.949718i | \(0.398630\pi\) | |||||||
\(762\) | −94.3405 | −3.41760 | ||||||||
\(763\) | −60.7339 | −2.19871 | ||||||||
\(764\) | −85.7788 | −3.10337 | ||||||||
\(765\) | 0.513736 | 0.0185742 | ||||||||
\(766\) | 82.7220 | 2.98887 | ||||||||
\(767\) | 17.7220 | 0.639905 | ||||||||
\(768\) | 32.5603 | 1.17492 | ||||||||
\(769\) | 26.1758 | 0.943924 | 0.471962 | − | 0.881619i | \(-0.343546\pi\) | ||||
0.471962 | + | 0.881619i | \(0.343546\pi\) | |||||||
\(770\) | −1.16102 | −0.0418403 | ||||||||
\(771\) | 7.38774 | 0.266063 | ||||||||
\(772\) | −66.4643 | −2.39210 | ||||||||
\(773\) | 4.03438 | 0.145107 | 0.0725533 | − | 0.997365i | \(-0.476885\pi\) | ||||
0.0725533 | + | 0.997365i | \(0.476885\pi\) | |||||||
\(774\) | −39.8831 | −1.43357 | ||||||||
\(775\) | −29.1166 | −1.04590 | ||||||||
\(776\) | 136.639 | 4.90507 | ||||||||
\(777\) | 29.4410 | 1.05619 | ||||||||
\(778\) | −6.24674 | −0.223956 | ||||||||
\(779\) | −4.31129 | −0.154468 | ||||||||
\(780\) | 7.43105 | 0.266074 | ||||||||
\(781\) | −7.80908 | −0.279431 | ||||||||
\(782\) | −4.20712 | −0.150446 | ||||||||
\(783\) | −15.2013 | −0.543251 | ||||||||
\(784\) | 44.1779 | 1.57778 | ||||||||
\(785\) | 1.89410 | 0.0676032 | ||||||||
\(786\) | 15.2189 | 0.542842 | ||||||||
\(787\) | −39.5086 | −1.40833 | −0.704165 | − | 0.710036i | \(-0.748679\pi\) | ||||
−0.704165 | + | 0.710036i | \(0.748679\pi\) | |||||||
\(788\) | −109.715 | −3.90842 | ||||||||
\(789\) | 0.0742721 | 0.00264416 | ||||||||
\(790\) | −0.169081 | −0.00601564 | ||||||||
\(791\) | −20.4690 | −0.727795 | ||||||||
\(792\) | −10.7984 | −0.383705 | ||||||||
\(793\) | 19.3341 | 0.686575 | ||||||||
\(794\) | −63.5669 | −2.25590 | ||||||||
\(795\) | −4.83688 | −0.171546 | ||||||||
\(796\) | −87.9885 | −3.11867 | ||||||||
\(797\) | −23.1479 | −0.819940 | −0.409970 | − | 0.912099i | \(-0.634461\pi\) | ||||
−0.409970 | + | 0.912099i | \(0.634461\pi\) | |||||||
\(798\) | 102.469 | 3.62736 | ||||||||
\(799\) | 0.621685 | 0.0219936 | ||||||||
\(800\) | 54.4652 | 1.92563 | ||||||||
\(801\) | −14.8085 | −0.523234 | ||||||||
\(802\) | −54.2964 | −1.91727 | ||||||||
\(803\) | 10.0246 | 0.353759 | ||||||||
\(804\) | −96.2064 | −3.39294 | ||||||||
\(805\) | 1.17482 | 0.0414070 | ||||||||
\(806\) | 46.9451 | 1.65357 | ||||||||
\(807\) | 27.8795 | 0.981404 | ||||||||
\(808\) | 109.017 | 3.83521 | ||||||||
\(809\) | −12.0620 | −0.424077 | −0.212038 | − | 0.977261i | \(-0.568010\pi\) | ||||
−0.212038 | + | 0.977261i | \(0.568010\pi\) | |||||||
\(810\) | 5.93614 | 0.208575 | ||||||||
\(811\) | −16.9298 | −0.594484 | −0.297242 | − | 0.954802i | \(-0.596067\pi\) | ||||
−0.297242 | + | 0.954802i | \(0.596067\pi\) | |||||||
\(812\) | −173.031 | −6.07218 | ||||||||
\(813\) | 16.8659 | 0.591512 | ||||||||
\(814\) | 5.95471 | 0.208712 | ||||||||
\(815\) | 4.55887 | 0.159690 | ||||||||
\(816\) | −23.0097 | −0.805501 | ||||||||
\(817\) | 31.9333 | 1.11720 | ||||||||
\(818\) | 36.9059 | 1.29038 | ||||||||
\(819\) | −24.5161 | −0.856660 | ||||||||
\(820\) | −0.909246 | −0.0317523 | ||||||||
\(821\) | 32.5308 | 1.13533 | 0.567666 | − | 0.823259i | \(-0.307847\pi\) | ||||
0.567666 | + | 0.823259i | \(0.307847\pi\) | |||||||
\(822\) | 79.5315 | 2.77398 | ||||||||
\(823\) | −36.8163 | −1.28334 | −0.641668 | − | 0.766983i | \(-0.721757\pi\) | ||||
−0.641668 | + | 0.766983i | \(0.721757\pi\) | |||||||
\(824\) | 35.3885 | 1.23282 | ||||||||
\(825\) | 6.95784 | 0.242241 | ||||||||
\(826\) | 51.5383 | 1.79325 | ||||||||
\(827\) | 27.8455 | 0.968283 | 0.484142 | − | 0.874990i | \(-0.339132\pi\) | ||||
0.484142 | + | 0.874990i | \(0.339132\pi\) | |||||||
\(828\) | 18.5596 | 0.644990 | ||||||||
\(829\) | −34.8659 | −1.21094 | −0.605471 | − | 0.795868i | \(-0.707015\pi\) | ||||
−0.605471 | + | 0.795868i | \(0.707015\pi\) | |||||||
\(830\) | −1.79792 | −0.0624067 | ||||||||
\(831\) | −36.5320 | −1.26728 | ||||||||
\(832\) | −27.3123 | −0.946883 | ||||||||
\(833\) | 4.45187 | 0.154248 | ||||||||
\(834\) | 94.7165 | 3.27976 | ||||||||
\(835\) | 0.608654 | 0.0210633 | ||||||||
\(836\) | 14.6856 | 0.507913 | ||||||||
\(837\) | 8.49881 | 0.293762 | ||||||||
\(838\) | −27.7119 | −0.957292 | ||||||||
\(839\) | −9.84127 | −0.339759 | −0.169879 | − | 0.985465i | \(-0.554338\pi\) | ||||
−0.169879 | + | 0.985465i | \(0.554338\pi\) | |||||||
\(840\) | 12.7230 | 0.438985 | ||||||||
\(841\) | 81.5465 | 2.81195 | ||||||||
\(842\) | 55.3503 | 1.90750 | ||||||||
\(843\) | 37.3183 | 1.28531 | ||||||||
\(844\) | 97.8234 | 3.36722 | ||||||||
\(845\) | −0.801339 | −0.0275669 | ||||||||
\(846\) | −3.87045 | −0.133069 | ||||||||
\(847\) | −35.9827 | −1.23638 | ||||||||
\(848\) | 95.7571 | 3.28831 | ||||||||
\(849\) | 31.8403 | 1.09275 | ||||||||
\(850\) | 12.9763 | 0.445084 | ||||||||
\(851\) | −6.02547 | −0.206551 | ||||||||
\(852\) | 145.354 | 4.97974 | ||||||||
\(853\) | −15.8307 | −0.542033 | −0.271016 | − | 0.962575i | \(-0.587360\pi\) | ||||
−0.271016 | + | 0.962575i | \(0.587360\pi\) | |||||||
\(854\) | 56.2266 | 1.92403 | ||||||||
\(855\) | 2.56086 | 0.0875796 | ||||||||
\(856\) | 116.102 | 3.96827 | ||||||||
\(857\) | 3.53704 | 0.120823 | 0.0604114 | − | 0.998174i | \(-0.480759\pi\) | ||||
0.0604114 | + | 0.998174i | \(0.480759\pi\) | |||||||
\(858\) | −11.2182 | −0.382983 | ||||||||
\(859\) | −0.251805 | −0.00859147 | −0.00429573 | − | 0.999991i | \(-0.501367\pi\) | ||||
−0.00429573 | + | 0.999991i | \(0.501367\pi\) | |||||||
\(860\) | 6.73470 | 0.229651 | ||||||||
\(861\) | 6.78653 | 0.231284 | ||||||||
\(862\) | 77.3447 | 2.63437 | ||||||||
\(863\) | −27.1322 | −0.923591 | −0.461796 | − | 0.886986i | \(-0.652795\pi\) | ||||
−0.461796 | + | 0.886986i | \(0.652795\pi\) | |||||||
\(864\) | −15.8978 | −0.540853 | ||||||||
\(865\) | 4.68113 | 0.159163 | ||||||||
\(866\) | 60.6854 | 2.06217 | ||||||||
\(867\) | −2.31872 | −0.0787479 | ||||||||
\(868\) | 96.7385 | 3.28352 | ||||||||
\(869\) | 0.180868 | 0.00613551 | ||||||||
\(870\) | −13.8067 | −0.468090 | ||||||||
\(871\) | −26.0090 | −0.881283 | ||||||||
\(872\) | 134.613 | 4.55858 | ||||||||
\(873\) | −43.2925 | −1.46523 | ||||||||
\(874\) | −20.9715 | −0.709373 | ||||||||
\(875\) | −7.28136 | −0.246155 | ||||||||
\(876\) | −186.592 | −6.30434 | ||||||||
\(877\) | 31.9378 | 1.07846 | 0.539231 | − | 0.842158i | \(-0.318715\pi\) | ||||
0.539231 | + | 0.842158i | \(0.318715\pi\) | |||||||
\(878\) | −83.5498 | −2.81967 | ||||||||
\(879\) | −35.9197 | −1.21154 | ||||||||
\(880\) | 1.29959 | 0.0438091 | ||||||||
\(881\) | −2.65980 | −0.0896110 | −0.0448055 | − | 0.998996i | \(-0.514267\pi\) | ||||
−0.0448055 | + | 0.998996i | \(0.514267\pi\) | |||||||
\(882\) | −27.7162 | −0.933254 | ||||||||
\(883\) | −17.9088 | −0.602678 | −0.301339 | − | 0.953517i | \(-0.597434\pi\) | ||||
−0.301339 | + | 0.953517i | \(0.597434\pi\) | |||||||
\(884\) | −14.8249 | −0.498617 | ||||||||
\(885\) | 2.91400 | 0.0979529 | ||||||||
\(886\) | 78.6835 | 2.64342 | ||||||||
\(887\) | 49.1193 | 1.64927 | 0.824633 | − | 0.565668i | \(-0.191382\pi\) | ||||
0.824633 | + | 0.565668i | \(0.191382\pi\) | |||||||
\(888\) | −65.2543 | −2.18979 | ||||||||
\(889\) | −52.5567 | −1.76270 | ||||||||
\(890\) | 3.52898 | 0.118292 | ||||||||
\(891\) | −6.34995 | −0.212731 | ||||||||
\(892\) | −30.3306 | −1.01554 | ||||||||
\(893\) | 3.09896 | 0.103703 | ||||||||
\(894\) | −99.3556 | −3.32295 | ||||||||
\(895\) | 4.67768 | 0.156358 | ||||||||
\(896\) | −5.00730 | −0.167282 | ||||||||
\(897\) | 11.3515 | 0.379016 | ||||||||
\(898\) | 84.4587 | 2.81842 | ||||||||
\(899\) | −61.8047 | −2.06130 | ||||||||
\(900\) | −57.2447 | −1.90816 | ||||||||
\(901\) | 9.64958 | 0.321474 | ||||||||
\(902\) | 1.37263 | 0.0457037 | ||||||||
\(903\) | −50.2672 | −1.67279 | ||||||||
\(904\) | 45.3684 | 1.50893 | ||||||||
\(905\) | 2.90599 | 0.0965985 | ||||||||
\(906\) | 49.9542 | 1.65962 | ||||||||
\(907\) | −12.9245 | −0.429150 | −0.214575 | − | 0.976708i | \(-0.568837\pi\) | ||||
−0.214575 | + | 0.976708i | \(0.568837\pi\) | |||||||
\(908\) | 63.2354 | 2.09854 | ||||||||
\(909\) | −34.5408 | −1.14564 | ||||||||
\(910\) | 5.84235 | 0.193672 | ||||||||
\(911\) | −23.5415 | −0.779966 | −0.389983 | − | 0.920822i | \(-0.627519\pi\) | ||||
−0.389983 | + | 0.920822i | \(0.627519\pi\) | |||||||
\(912\) | −114.698 | −3.79804 | ||||||||
\(913\) | 1.92325 | 0.0636503 | ||||||||
\(914\) | −105.025 | −3.47391 | ||||||||
\(915\) | 3.17907 | 0.105097 | ||||||||
\(916\) | 68.0635 | 2.24888 | ||||||||
\(917\) | 8.47841 | 0.279982 | ||||||||
\(918\) | −3.78764 | −0.125011 | ||||||||
\(919\) | −30.5981 | −1.00934 | −0.504670 | − | 0.863312i | \(-0.668386\pi\) | ||||
−0.504670 | + | 0.863312i | \(0.668386\pi\) | |||||||
\(920\) | −2.60392 | −0.0858487 | ||||||||
\(921\) | −24.2847 | −0.800207 | ||||||||
\(922\) | 99.3236 | 3.27105 | ||||||||
\(923\) | 39.2959 | 1.29344 | ||||||||
\(924\) | −23.1171 | −0.760496 | ||||||||
\(925\) | 18.5848 | 0.611065 | ||||||||
\(926\) | 10.9707 | 0.360519 | ||||||||
\(927\) | −11.2124 | −0.368264 | ||||||||
\(928\) | 115.611 | 3.79512 | ||||||||
\(929\) | 8.54374 | 0.280311 | 0.140155 | − | 0.990130i | \(-0.455240\pi\) | ||||
0.140155 | + | 0.990130i | \(0.455240\pi\) | |||||||
\(930\) | 7.71909 | 0.253119 | ||||||||
\(931\) | 22.1916 | 0.727300 | ||||||||
\(932\) | −84.1514 | −2.75647 | ||||||||
\(933\) | 18.8407 | 0.616817 | ||||||||
\(934\) | −27.9803 | −0.915543 | ||||||||
\(935\) | 0.130961 | 0.00428289 | ||||||||
\(936\) | 54.3384 | 1.77611 | ||||||||
\(937\) | −10.6927 | −0.349315 | −0.174657 | − | 0.984629i | \(-0.555882\pi\) | ||||
−0.174657 | + | 0.984629i | \(0.555882\pi\) | |||||||
\(938\) | −75.6383 | −2.46968 | ||||||||
\(939\) | 23.0987 | 0.753797 | ||||||||
\(940\) | 0.653569 | 0.0213171 | ||||||||
\(941\) | −27.1679 | −0.885648 | −0.442824 | − | 0.896609i | \(-0.646023\pi\) | ||||
−0.442824 | + | 0.896609i | \(0.646023\pi\) | |||||||
\(942\) | 53.2233 | 1.73411 | ||||||||
\(943\) | −1.38895 | −0.0452303 | ||||||||
\(944\) | −57.6892 | −1.87762 | ||||||||
\(945\) | 1.05768 | 0.0344064 | ||||||||
\(946\) | −10.1670 | −0.330557 | ||||||||
\(947\) | 1.95002 | 0.0633671 | 0.0316835 | − | 0.999498i | \(-0.489913\pi\) | ||||
0.0316835 | + | 0.999498i | \(0.489913\pi\) | |||||||
\(948\) | −3.36657 | −0.109341 | ||||||||
\(949\) | −50.4443 | −1.63749 | ||||||||
\(950\) | 64.6841 | 2.09863 | ||||||||
\(951\) | −34.9537 | −1.13345 | ||||||||
\(952\) | −25.3824 | −0.822648 | ||||||||
\(953\) | 55.5344 | 1.79893 | 0.899467 | − | 0.436988i | \(-0.143955\pi\) | ||||
0.899467 | + | 0.436988i | \(0.143955\pi\) | |||||||
\(954\) | −60.0758 | −1.94503 | ||||||||
\(955\) | −3.81308 | −0.123389 | ||||||||
\(956\) | 145.718 | 4.71286 | ||||||||
\(957\) | 14.7691 | 0.477418 | ||||||||
\(958\) | −57.2816 | −1.85068 | ||||||||
\(959\) | 44.3067 | 1.43074 | ||||||||
\(960\) | −4.49091 | −0.144943 | ||||||||
\(961\) | 3.55400 | 0.114645 | ||||||||
\(962\) | −29.9645 | −0.966095 | ||||||||
\(963\) | −36.7854 | −1.18539 | ||||||||
\(964\) | 131.830 | 4.24595 | ||||||||
\(965\) | −2.95451 | −0.0951089 | ||||||||
\(966\) | 33.0119 | 1.06214 | ||||||||
\(967\) | 34.5966 | 1.11255 | 0.556276 | − | 0.830998i | \(-0.312230\pi\) | ||||
0.556276 | + | 0.830998i | \(0.312230\pi\) | |||||||
\(968\) | 79.7536 | 2.56338 | ||||||||
\(969\) | −11.5583 | −0.371306 | ||||||||
\(970\) | 10.3169 | 0.331256 | ||||||||
\(971\) | −12.5948 | −0.404188 | −0.202094 | − | 0.979366i | \(-0.564775\pi\) | ||||
−0.202094 | + | 0.979366i | \(0.564775\pi\) | |||||||
\(972\) | 97.1012 | 3.11452 | ||||||||
\(973\) | 52.7662 | 1.69161 | ||||||||
\(974\) | −71.5060 | −2.29120 | ||||||||
\(975\) | −35.0123 | −1.12129 | ||||||||
\(976\) | −62.9370 | −2.01457 | ||||||||
\(977\) | 22.4304 | 0.717612 | 0.358806 | − | 0.933412i | \(-0.383184\pi\) | ||||
0.358806 | + | 0.933412i | \(0.383184\pi\) | |||||||
\(978\) | 128.102 | 4.09626 | ||||||||
\(979\) | −3.77498 | −0.120649 | ||||||||
\(980\) | 4.68019 | 0.149503 | ||||||||
\(981\) | −42.6505 | −1.36173 | ||||||||
\(982\) | −4.61514 | −0.147275 | ||||||||
\(983\) | 18.6869 | 0.596020 | 0.298010 | − | 0.954563i | \(-0.403677\pi\) | ||||
0.298010 | + | 0.954563i | \(0.403677\pi\) | |||||||
\(984\) | −15.0419 | −0.479519 | ||||||||
\(985\) | −4.87709 | −0.155397 | ||||||||
\(986\) | 27.5443 | 0.877190 | ||||||||
\(987\) | −4.87817 | −0.155274 | ||||||||
\(988\) | −73.8991 | −2.35104 | ||||||||
\(989\) | 10.2878 | 0.327133 | ||||||||
\(990\) | −0.815331 | −0.0259129 | ||||||||
\(991\) | −25.3301 | −0.804639 | −0.402319 | − | 0.915499i | \(-0.631796\pi\) | ||||
−0.402319 | + | 0.915499i | \(0.631796\pi\) | |||||||
\(992\) | −64.6363 | −2.05220 | ||||||||
\(993\) | −77.5671 | −2.46152 | ||||||||
\(994\) | 114.278 | 3.62469 | ||||||||
\(995\) | −3.91131 | −0.123997 | ||||||||
\(996\) | −35.7983 | −1.13431 | ||||||||
\(997\) | 13.6496 | 0.432286 | 0.216143 | − | 0.976362i | \(-0.430652\pi\) | ||||
0.216143 | + | 0.976362i | \(0.430652\pi\) | |||||||
\(998\) | −64.6216 | −2.04556 | ||||||||
\(999\) | −5.42470 | −0.171630 |
(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 | 6001.2.a.b.1.7 | ✓ | 114 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6001.2.a.b.1.7 | ✓ | 114 | 1.1 | even | 1 | trivial |