Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6031,2,Mod(1,6031)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6031, 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("6031.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6031 = 37 \cdot 163 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6031.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: | \(48.1577774590\) |
Analytic rank: | \(0\) |
Dimension: | \(133\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 6031.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.45235 | −1.73407 | −0.867037 | − | 0.498245i | \(-0.833978\pi\) | ||||
−0.867037 | + | 0.498245i | \(0.833978\pi\) | |||||||
\(3\) | −2.50002 | −1.44339 | −0.721693 | − | 0.692214i | \(-0.756636\pi\) | ||||
−0.721693 | + | 0.692214i | \(0.756636\pi\) | |||||||
\(4\) | 4.01402 | 2.00701 | ||||||||
\(5\) | −3.16357 | −1.41479 | −0.707395 | − | 0.706819i | \(-0.750130\pi\) | ||||
−0.707395 | + | 0.706819i | \(0.750130\pi\) | |||||||
\(6\) | 6.13092 | 2.50294 | ||||||||
\(7\) | −0.556288 | −0.210257 | −0.105129 | − | 0.994459i | \(-0.533525\pi\) | ||||
−0.105129 | + | 0.994459i | \(0.533525\pi\) | |||||||
\(8\) | −4.93908 | −1.74623 | ||||||||
\(9\) | 3.25009 | 1.08336 | ||||||||
\(10\) | 7.75817 | 2.45335 | ||||||||
\(11\) | 0.948061 | 0.285851 | 0.142926 | − | 0.989733i | \(-0.454349\pi\) | ||||
0.142926 | + | 0.989733i | \(0.454349\pi\) | |||||||
\(12\) | −10.0351 | −2.89689 | ||||||||
\(13\) | −4.46540 | −1.23848 | −0.619240 | − | 0.785202i | \(-0.712559\pi\) | ||||
−0.619240 | + | 0.785202i | \(0.712559\pi\) | |||||||
\(14\) | 1.36421 | 0.364601 | ||||||||
\(15\) | 7.90897 | 2.04209 | ||||||||
\(16\) | 4.08431 | 1.02108 | ||||||||
\(17\) | 0.621048 | 0.150626 | 0.0753132 | − | 0.997160i | \(-0.476004\pi\) | ||||
0.0753132 | + | 0.997160i | \(0.476004\pi\) | |||||||
\(18\) | −7.97035 | −1.87863 | ||||||||
\(19\) | 3.59352 | 0.824411 | 0.412205 | − | 0.911091i | \(-0.364759\pi\) | ||||
0.412205 | + | 0.911091i | \(0.364759\pi\) | |||||||
\(20\) | −12.6986 | −2.83950 | ||||||||
\(21\) | 1.39073 | 0.303482 | ||||||||
\(22\) | −2.32498 | −0.495687 | ||||||||
\(23\) | 4.39121 | 0.915631 | 0.457815 | − | 0.889047i | \(-0.348632\pi\) | ||||
0.457815 | + | 0.889047i | \(0.348632\pi\) | |||||||
\(24\) | 12.3478 | 2.52048 | ||||||||
\(25\) | 5.00815 | 1.00163 | ||||||||
\(26\) | 10.9507 | 2.14762 | ||||||||
\(27\) | −0.625218 | −0.120323 | ||||||||
\(28\) | −2.23295 | −0.421988 | ||||||||
\(29\) | 0.608404 | 0.112978 | 0.0564889 | − | 0.998403i | \(-0.482009\pi\) | ||||
0.0564889 | + | 0.998403i | \(0.482009\pi\) | |||||||
\(30\) | −19.3956 | −3.54113 | ||||||||
\(31\) | 5.87987 | 1.05606 | 0.528028 | − | 0.849227i | \(-0.322932\pi\) | ||||
0.528028 | + | 0.849227i | \(0.322932\pi\) | |||||||
\(32\) | −0.138001 | −0.0243954 | ||||||||
\(33\) | −2.37017 | −0.412594 | ||||||||
\(34\) | −1.52303 | −0.261197 | ||||||||
\(35\) | 1.75985 | 0.297469 | ||||||||
\(36\) | 13.0459 | 2.17432 | ||||||||
\(37\) | −1.00000 | −0.164399 | ||||||||
\(38\) | −8.81257 | −1.42959 | ||||||||
\(39\) | 11.1636 | 1.78760 | ||||||||
\(40\) | 15.6251 | 2.47055 | ||||||||
\(41\) | 4.96366 | 0.775194 | 0.387597 | − | 0.921829i | \(-0.373305\pi\) | ||||
0.387597 | + | 0.921829i | \(0.373305\pi\) | |||||||
\(42\) | −3.41055 | −0.526260 | ||||||||
\(43\) | −12.0167 | −1.83253 | −0.916265 | − | 0.400573i | \(-0.868811\pi\) | ||||
−0.916265 | + | 0.400573i | \(0.868811\pi\) | |||||||
\(44\) | 3.80554 | 0.573706 | ||||||||
\(45\) | −10.2819 | −1.53273 | ||||||||
\(46\) | −10.7688 | −1.58777 | ||||||||
\(47\) | 9.02763 | 1.31682 | 0.658408 | − | 0.752662i | \(-0.271230\pi\) | ||||
0.658408 | + | 0.752662i | \(0.271230\pi\) | |||||||
\(48\) | −10.2108 | −1.47381 | ||||||||
\(49\) | −6.69054 | −0.955792 | ||||||||
\(50\) | −12.2817 | −1.73690 | ||||||||
\(51\) | −1.55263 | −0.217412 | ||||||||
\(52\) | −17.9242 | −2.48564 | ||||||||
\(53\) | 0.333636 | 0.0458284 | 0.0229142 | − | 0.999737i | \(-0.492706\pi\) | ||||
0.0229142 | + | 0.999737i | \(0.492706\pi\) | |||||||
\(54\) | 1.53325 | 0.208649 | ||||||||
\(55\) | −2.99925 | −0.404419 | ||||||||
\(56\) | 2.74755 | 0.367157 | ||||||||
\(57\) | −8.98387 | −1.18994 | ||||||||
\(58\) | −1.49202 | −0.195912 | ||||||||
\(59\) | 4.14371 | 0.539465 | 0.269733 | − | 0.962935i | \(-0.413065\pi\) | ||||
0.269733 | + | 0.962935i | \(0.413065\pi\) | |||||||
\(60\) | 31.7467 | 4.09849 | ||||||||
\(61\) | 3.73513 | 0.478234 | 0.239117 | − | 0.970991i | \(-0.423142\pi\) | ||||
0.239117 | + | 0.970991i | \(0.423142\pi\) | |||||||
\(62\) | −14.4195 | −1.83128 | ||||||||
\(63\) | −1.80798 | −0.227784 | ||||||||
\(64\) | −7.83020 | −0.978774 | ||||||||
\(65\) | 14.1266 | 1.75219 | ||||||||
\(66\) | 5.81248 | 0.715467 | ||||||||
\(67\) | −0.200881 | −0.0245416 | −0.0122708 | − | 0.999925i | \(-0.503906\pi\) | ||||
−0.0122708 | + | 0.999925i | \(0.503906\pi\) | |||||||
\(68\) | 2.49290 | 0.302308 | ||||||||
\(69\) | −10.9781 | −1.32161 | ||||||||
\(70\) | −4.31577 | −0.515834 | ||||||||
\(71\) | 16.0585 | 1.90580 | 0.952898 | − | 0.303292i | \(-0.0980857\pi\) | ||||
0.952898 | + | 0.303292i | \(0.0980857\pi\) | |||||||
\(72\) | −16.0524 | −1.89180 | ||||||||
\(73\) | 6.90138 | 0.807746 | 0.403873 | − | 0.914815i | \(-0.367664\pi\) | ||||
0.403873 | + | 0.914815i | \(0.367664\pi\) | |||||||
\(74\) | 2.45235 | 0.285080 | ||||||||
\(75\) | −12.5205 | −1.44574 | ||||||||
\(76\) | 14.4245 | 1.65460 | ||||||||
\(77\) | −0.527395 | −0.0601022 | ||||||||
\(78\) | −27.3770 | −3.09984 | ||||||||
\(79\) | 16.1956 | 1.82215 | 0.911075 | − | 0.412241i | \(-0.135254\pi\) | ||||
0.911075 | + | 0.412241i | \(0.135254\pi\) | |||||||
\(80\) | −12.9210 | −1.44461 | ||||||||
\(81\) | −8.18720 | −0.909689 | ||||||||
\(82\) | −12.1726 | −1.34424 | ||||||||
\(83\) | −4.01716 | −0.440941 | −0.220470 | − | 0.975394i | \(-0.570759\pi\) | ||||
−0.220470 | + | 0.975394i | \(0.570759\pi\) | |||||||
\(84\) | 5.58241 | 0.609091 | ||||||||
\(85\) | −1.96473 | −0.213105 | ||||||||
\(86\) | 29.4692 | 3.17774 | ||||||||
\(87\) | −1.52102 | −0.163071 | ||||||||
\(88\) | −4.68255 | −0.499162 | ||||||||
\(89\) | −9.80757 | −1.03960 | −0.519800 | − | 0.854288i | \(-0.673994\pi\) | ||||
−0.519800 | + | 0.854288i | \(0.673994\pi\) | |||||||
\(90\) | 25.2147 | 2.65786 | ||||||||
\(91\) | 2.48405 | 0.260399 | ||||||||
\(92\) | 17.6264 | 1.83768 | ||||||||
\(93\) | −14.6998 | −1.52429 | ||||||||
\(94\) | −22.1389 | −2.28345 | ||||||||
\(95\) | −11.3683 | −1.16637 | ||||||||
\(96\) | 0.345005 | 0.0352119 | ||||||||
\(97\) | −9.24184 | −0.938367 | −0.469184 | − | 0.883101i | \(-0.655452\pi\) | ||||
−0.469184 | + | 0.883101i | \(0.655452\pi\) | |||||||
\(98\) | 16.4076 | 1.65741 | ||||||||
\(99\) | 3.08128 | 0.309680 | ||||||||
\(100\) | 20.1028 | 2.01028 | ||||||||
\(101\) | 9.01552 | 0.897078 | 0.448539 | − | 0.893763i | \(-0.351944\pi\) | ||||
0.448539 | + | 0.893763i | \(0.351944\pi\) | |||||||
\(102\) | 3.80759 | 0.377008 | ||||||||
\(103\) | 8.88180 | 0.875150 | 0.437575 | − | 0.899182i | \(-0.355838\pi\) | ||||
0.437575 | + | 0.899182i | \(0.355838\pi\) | |||||||
\(104\) | 22.0550 | 2.16267 | ||||||||
\(105\) | −4.39966 | −0.429363 | ||||||||
\(106\) | −0.818192 | −0.0794699 | ||||||||
\(107\) | −5.71407 | −0.552400 | −0.276200 | − | 0.961100i | \(-0.589075\pi\) | ||||
−0.276200 | + | 0.961100i | \(0.589075\pi\) | |||||||
\(108\) | −2.50964 | −0.241490 | ||||||||
\(109\) | 3.89873 | 0.373430 | 0.186715 | − | 0.982414i | \(-0.440216\pi\) | ||||
0.186715 | + | 0.982414i | \(0.440216\pi\) | |||||||
\(110\) | 7.35522 | 0.701293 | ||||||||
\(111\) | 2.50002 | 0.237291 | ||||||||
\(112\) | −2.27205 | −0.214689 | ||||||||
\(113\) | 14.6331 | 1.37657 | 0.688284 | − | 0.725442i | \(-0.258364\pi\) | ||||
0.688284 | + | 0.725442i | \(0.258364\pi\) | |||||||
\(114\) | 22.0316 | 2.06345 | ||||||||
\(115\) | −13.8919 | −1.29542 | ||||||||
\(116\) | 2.44215 | 0.226748 | ||||||||
\(117\) | −14.5129 | −1.34172 | ||||||||
\(118\) | −10.1618 | −0.935472 | ||||||||
\(119\) | −0.345481 | −0.0316702 | ||||||||
\(120\) | −39.0630 | −3.56595 | ||||||||
\(121\) | −10.1012 | −0.918289 | ||||||||
\(122\) | −9.15984 | −0.829293 | ||||||||
\(123\) | −12.4092 | −1.11890 | ||||||||
\(124\) | 23.6019 | 2.11951 | ||||||||
\(125\) | −0.0257707 | −0.00230500 | ||||||||
\(126\) | 4.43381 | 0.394995 | ||||||||
\(127\) | −15.6325 | −1.38716 | −0.693578 | − | 0.720381i | \(-0.743967\pi\) | ||||
−0.693578 | + | 0.720381i | \(0.743967\pi\) | |||||||
\(128\) | 19.4784 | 1.72166 | ||||||||
\(129\) | 30.0420 | 2.64505 | ||||||||
\(130\) | −34.6434 | −3.03842 | ||||||||
\(131\) | −0.388080 | −0.0339067 | −0.0169534 | − | 0.999856i | \(-0.505397\pi\) | ||||
−0.0169534 | + | 0.999856i | \(0.505397\pi\) | |||||||
\(132\) | −9.51391 | −0.828079 | ||||||||
\(133\) | −1.99903 | −0.173338 | ||||||||
\(134\) | 0.492632 | 0.0425569 | ||||||||
\(135\) | 1.97792 | 0.170232 | ||||||||
\(136\) | −3.06741 | −0.263028 | ||||||||
\(137\) | 8.69332 | 0.742721 | 0.371360 | − | 0.928489i | \(-0.378891\pi\) | ||||
0.371360 | + | 0.928489i | \(0.378891\pi\) | |||||||
\(138\) | 26.9221 | 2.29176 | ||||||||
\(139\) | 16.1711 | 1.37161 | 0.685807 | − | 0.727784i | \(-0.259450\pi\) | ||||
0.685807 | + | 0.727784i | \(0.259450\pi\) | |||||||
\(140\) | 7.06408 | 0.597024 | ||||||||
\(141\) | −22.5692 | −1.90067 | ||||||||
\(142\) | −39.3811 | −3.30479 | ||||||||
\(143\) | −4.23348 | −0.354021 | ||||||||
\(144\) | 13.2744 | 1.10620 | ||||||||
\(145\) | −1.92473 | −0.159840 | ||||||||
\(146\) | −16.9246 | −1.40069 | ||||||||
\(147\) | 16.7265 | 1.37958 | ||||||||
\(148\) | −4.01402 | −0.329950 | ||||||||
\(149\) | −11.2259 | −0.919661 | −0.459830 | − | 0.888007i | \(-0.652090\pi\) | ||||
−0.459830 | + | 0.888007i | \(0.652090\pi\) | |||||||
\(150\) | 30.7045 | 2.50701 | ||||||||
\(151\) | −19.9777 | −1.62576 | −0.812881 | − | 0.582429i | \(-0.802102\pi\) | ||||
−0.812881 | + | 0.582429i | \(0.802102\pi\) | |||||||
\(152\) | −17.7487 | −1.43961 | ||||||||
\(153\) | 2.01846 | 0.163183 | ||||||||
\(154\) | 1.29336 | 0.104222 | ||||||||
\(155\) | −18.6013 | −1.49410 | ||||||||
\(156\) | 44.8108 | 3.58774 | ||||||||
\(157\) | −22.4663 | −1.79301 | −0.896504 | − | 0.443035i | \(-0.853902\pi\) | ||||
−0.896504 | + | 0.443035i | \(0.853902\pi\) | |||||||
\(158\) | −39.7173 | −3.15974 | ||||||||
\(159\) | −0.834096 | −0.0661481 | ||||||||
\(160\) | 0.436576 | 0.0345143 | ||||||||
\(161\) | −2.44278 | −0.192518 | ||||||||
\(162\) | 20.0779 | 1.57747 | ||||||||
\(163\) | 1.00000 | 0.0783260 | ||||||||
\(164\) | 19.9242 | 1.55582 | ||||||||
\(165\) | 7.49819 | 0.583733 | ||||||||
\(166\) | 9.85149 | 0.764624 | ||||||||
\(167\) | −1.68205 | −0.130161 | −0.0650805 | − | 0.997880i | \(-0.520730\pi\) | ||||
−0.0650805 | + | 0.997880i | \(0.520730\pi\) | |||||||
\(168\) | −6.86892 | −0.529949 | ||||||||
\(169\) | 6.93983 | 0.533833 | ||||||||
\(170\) | 4.81820 | 0.369539 | ||||||||
\(171\) | 11.6793 | 0.893135 | ||||||||
\(172\) | −48.2353 | −3.67790 | ||||||||
\(173\) | −16.9837 | −1.29124 | −0.645622 | − | 0.763658i | \(-0.723402\pi\) | ||||
−0.645622 | + | 0.763658i | \(0.723402\pi\) | |||||||
\(174\) | 3.73008 | 0.282776 | ||||||||
\(175\) | −2.78597 | −0.210600 | ||||||||
\(176\) | 3.87218 | 0.291876 | ||||||||
\(177\) | −10.3593 | −0.778656 | ||||||||
\(178\) | 24.0516 | 1.80274 | ||||||||
\(179\) | 8.47960 | 0.633795 | 0.316898 | − | 0.948460i | \(-0.397359\pi\) | ||||
0.316898 | + | 0.948460i | \(0.397359\pi\) | |||||||
\(180\) | −41.2716 | −3.07620 | ||||||||
\(181\) | −24.1537 | −1.79533 | −0.897664 | − | 0.440680i | \(-0.854737\pi\) | ||||
−0.897664 | + | 0.440680i | \(0.854737\pi\) | |||||||
\(182\) | −6.09176 | −0.451551 | ||||||||
\(183\) | −9.33789 | −0.690276 | ||||||||
\(184\) | −21.6885 | −1.59890 | ||||||||
\(185\) | 3.16357 | 0.232590 | ||||||||
\(186\) | 36.0490 | 2.64324 | ||||||||
\(187\) | 0.588792 | 0.0430567 | ||||||||
\(188\) | 36.2371 | 2.64286 | ||||||||
\(189\) | 0.347801 | 0.0252988 | ||||||||
\(190\) | 27.8792 | 2.02257 | ||||||||
\(191\) | 15.9993 | 1.15767 | 0.578833 | − | 0.815446i | \(-0.303508\pi\) | ||||
0.578833 | + | 0.815446i | \(0.303508\pi\) | |||||||
\(192\) | 19.5756 | 1.41275 | ||||||||
\(193\) | 21.4051 | 1.54077 | 0.770385 | − | 0.637579i | \(-0.220064\pi\) | ||||
0.770385 | + | 0.637579i | \(0.220064\pi\) | |||||||
\(194\) | 22.6642 | 1.62720 | ||||||||
\(195\) | −35.3167 | −2.52908 | ||||||||
\(196\) | −26.8560 | −1.91828 | ||||||||
\(197\) | −16.7343 | −1.19227 | −0.596134 | − | 0.802885i | \(-0.703297\pi\) | ||||
−0.596134 | + | 0.802885i | \(0.703297\pi\) | |||||||
\(198\) | −7.55638 | −0.537008 | ||||||||
\(199\) | −20.1377 | −1.42752 | −0.713761 | − | 0.700389i | \(-0.753010\pi\) | ||||
−0.713761 | + | 0.700389i | \(0.753010\pi\) | |||||||
\(200\) | −24.7356 | −1.74907 | ||||||||
\(201\) | 0.502207 | 0.0354230 | ||||||||
\(202\) | −22.1092 | −1.55560 | ||||||||
\(203\) | −0.338448 | −0.0237544 | ||||||||
\(204\) | −6.23229 | −0.436348 | ||||||||
\(205\) | −15.7029 | −1.09674 | ||||||||
\(206\) | −21.7813 | −1.51757 | ||||||||
\(207\) | 14.2718 | 0.991959 | ||||||||
\(208\) | −18.2381 | −1.26458 | ||||||||
\(209\) | 3.40688 | 0.235659 | ||||||||
\(210\) | 10.7895 | 0.744547 | ||||||||
\(211\) | 4.08421 | 0.281169 | 0.140584 | − | 0.990069i | \(-0.455102\pi\) | ||||
0.140584 | + | 0.990069i | \(0.455102\pi\) | |||||||
\(212\) | 1.33922 | 0.0919781 | ||||||||
\(213\) | −40.1466 | −2.75080 | ||||||||
\(214\) | 14.0129 | 0.957902 | ||||||||
\(215\) | 38.0156 | 2.59264 | ||||||||
\(216\) | 3.08800 | 0.210112 | ||||||||
\(217\) | −3.27090 | −0.222043 | ||||||||
\(218\) | −9.56104 | −0.647555 | ||||||||
\(219\) | −17.2536 | −1.16589 | ||||||||
\(220\) | −12.0391 | −0.811674 | ||||||||
\(221\) | −2.77323 | −0.186548 | ||||||||
\(222\) | −6.13092 | −0.411480 | ||||||||
\(223\) | 11.4014 | 0.763491 | 0.381745 | − | 0.924267i | \(-0.375323\pi\) | ||||
0.381745 | + | 0.924267i | \(0.375323\pi\) | |||||||
\(224\) | 0.0767683 | 0.00512930 | ||||||||
\(225\) | 16.2769 | 1.08513 | ||||||||
\(226\) | −35.8855 | −2.38707 | ||||||||
\(227\) | −15.9466 | −1.05841 | −0.529206 | − | 0.848493i | \(-0.677510\pi\) | ||||
−0.529206 | + | 0.848493i | \(0.677510\pi\) | |||||||
\(228\) | −36.0614 | −2.38823 | ||||||||
\(229\) | −10.8155 | −0.714706 | −0.357353 | − | 0.933969i | \(-0.616321\pi\) | ||||
−0.357353 | + | 0.933969i | \(0.616321\pi\) | |||||||
\(230\) | 34.0677 | 2.24636 | ||||||||
\(231\) | 1.31850 | 0.0867507 | ||||||||
\(232\) | −3.00496 | −0.197285 | ||||||||
\(233\) | −17.1471 | −1.12335 | −0.561673 | − | 0.827359i | \(-0.689842\pi\) | ||||
−0.561673 | + | 0.827359i | \(0.689842\pi\) | |||||||
\(234\) | 35.5908 | 2.32664 | ||||||||
\(235\) | −28.5595 | −1.86302 | ||||||||
\(236\) | 16.6329 | 1.08271 | ||||||||
\(237\) | −40.4893 | −2.63006 | ||||||||
\(238\) | 0.847241 | 0.0549185 | ||||||||
\(239\) | 20.1793 | 1.30529 | 0.652645 | − | 0.757663i | \(-0.273659\pi\) | ||||
0.652645 | + | 0.757663i | \(0.273659\pi\) | |||||||
\(240\) | 32.3027 | 2.08513 | ||||||||
\(241\) | 6.87226 | 0.442681 | 0.221340 | − | 0.975197i | \(-0.428957\pi\) | ||||
0.221340 | + | 0.975197i | \(0.428957\pi\) | |||||||
\(242\) | 24.7716 | 1.59238 | ||||||||
\(243\) | 22.3438 | 1.43336 | ||||||||
\(244\) | 14.9929 | 0.959821 | ||||||||
\(245\) | 21.1660 | 1.35224 | ||||||||
\(246\) | 30.4318 | 1.94026 | ||||||||
\(247\) | −16.0465 | −1.02102 | ||||||||
\(248\) | −29.0411 | −1.84411 | ||||||||
\(249\) | 10.0430 | 0.636448 | ||||||||
\(250\) | 0.0631987 | 0.00399704 | ||||||||
\(251\) | −25.8974 | −1.63463 | −0.817315 | − | 0.576191i | \(-0.804538\pi\) | ||||
−0.817315 | + | 0.576191i | \(0.804538\pi\) | |||||||
\(252\) | −7.25728 | −0.457165 | ||||||||
\(253\) | 4.16314 | 0.261734 | ||||||||
\(254\) | 38.3363 | 2.40543 | ||||||||
\(255\) | 4.91185 | 0.307592 | ||||||||
\(256\) | −32.1074 | −2.00671 | ||||||||
\(257\) | 13.1215 | 0.818494 | 0.409247 | − | 0.912424i | \(-0.365791\pi\) | ||||
0.409247 | + | 0.912424i | \(0.365791\pi\) | |||||||
\(258\) | −73.6734 | −4.58670 | ||||||||
\(259\) | 0.556288 | 0.0345660 | ||||||||
\(260\) | 56.7044 | 3.51666 | ||||||||
\(261\) | 1.97737 | 0.122396 | ||||||||
\(262\) | 0.951708 | 0.0587967 | ||||||||
\(263\) | −11.0032 | −0.678487 | −0.339243 | − | 0.940699i | \(-0.610171\pi\) | ||||
−0.339243 | + | 0.940699i | \(0.610171\pi\) | |||||||
\(264\) | 11.7065 | 0.720483 | ||||||||
\(265\) | −1.05548 | −0.0648376 | ||||||||
\(266\) | 4.90233 | 0.300581 | ||||||||
\(267\) | 24.5191 | 1.50054 | ||||||||
\(268\) | −0.806342 | −0.0492552 | ||||||||
\(269\) | 16.8350 | 1.02645 | 0.513223 | − | 0.858255i | \(-0.328451\pi\) | ||||
0.513223 | + | 0.858255i | \(0.328451\pi\) | |||||||
\(270\) | −4.85054 | −0.295195 | ||||||||
\(271\) | 18.5243 | 1.12527 | 0.562635 | − | 0.826705i | \(-0.309788\pi\) | ||||
0.562635 | + | 0.826705i | \(0.309788\pi\) | |||||||
\(272\) | 2.53655 | 0.153801 | ||||||||
\(273\) | −6.21017 | −0.375856 | ||||||||
\(274\) | −21.3191 | −1.28793 | ||||||||
\(275\) | 4.74803 | 0.286317 | ||||||||
\(276\) | −44.0663 | −2.65248 | ||||||||
\(277\) | 0.405043 | 0.0243367 | 0.0121683 | − | 0.999926i | \(-0.496127\pi\) | ||||
0.0121683 | + | 0.999926i | \(0.496127\pi\) | |||||||
\(278\) | −39.6572 | −2.37848 | ||||||||
\(279\) | 19.1101 | 1.14409 | ||||||||
\(280\) | −8.69205 | −0.519449 | ||||||||
\(281\) | −22.2049 | −1.32464 | −0.662318 | − | 0.749223i | \(-0.730427\pi\) | ||||
−0.662318 | + | 0.749223i | \(0.730427\pi\) | |||||||
\(282\) | 55.3476 | 3.29590 | ||||||||
\(283\) | 10.8694 | 0.646117 | 0.323059 | − | 0.946379i | \(-0.395289\pi\) | ||||
0.323059 | + | 0.946379i | \(0.395289\pi\) | |||||||
\(284\) | 64.4592 | 3.82495 | ||||||||
\(285\) | 28.4210 | 1.68352 | ||||||||
\(286\) | 10.3820 | 0.613898 | ||||||||
\(287\) | −2.76122 | −0.162990 | ||||||||
\(288\) | −0.448515 | −0.0264290 | ||||||||
\(289\) | −16.6143 | −0.977312 | ||||||||
\(290\) | 4.72010 | 0.277174 | ||||||||
\(291\) | 23.1048 | 1.35443 | ||||||||
\(292\) | 27.7023 | 1.62115 | ||||||||
\(293\) | 2.25054 | 0.131478 | 0.0657390 | − | 0.997837i | \(-0.479060\pi\) | ||||
0.0657390 | + | 0.997837i | \(0.479060\pi\) | |||||||
\(294\) | −41.0192 | −2.39229 | ||||||||
\(295\) | −13.1089 | −0.763230 | ||||||||
\(296\) | 4.93908 | 0.287078 | ||||||||
\(297\) | −0.592745 | −0.0343945 | ||||||||
\(298\) | 27.5298 | 1.59476 | ||||||||
\(299\) | −19.6085 | −1.13399 | ||||||||
\(300\) | −50.2573 | −2.90161 | ||||||||
\(301\) | 6.68474 | 0.385302 | ||||||||
\(302\) | 48.9923 | 2.81919 | ||||||||
\(303\) | −22.5390 | −1.29483 | ||||||||
\(304\) | 14.6771 | 0.841787 | ||||||||
\(305\) | −11.8163 | −0.676601 | ||||||||
\(306\) | −4.94997 | −0.282971 | ||||||||
\(307\) | 19.8687 | 1.13397 | 0.566985 | − | 0.823728i | \(-0.308110\pi\) | ||||
0.566985 | + | 0.823728i | \(0.308110\pi\) | |||||||
\(308\) | −2.11697 | −0.120626 | ||||||||
\(309\) | −22.2047 | −1.26318 | ||||||||
\(310\) | 45.6170 | 2.59087 | ||||||||
\(311\) | −1.52261 | −0.0863395 | −0.0431697 | − | 0.999068i | \(-0.513746\pi\) | ||||
−0.0431697 | + | 0.999068i | \(0.513746\pi\) | |||||||
\(312\) | −55.1378 | −3.12157 | ||||||||
\(313\) | 15.8357 | 0.895085 | 0.447543 | − | 0.894263i | \(-0.352299\pi\) | ||||
0.447543 | + | 0.894263i | \(0.352299\pi\) | |||||||
\(314\) | 55.0953 | 3.10921 | ||||||||
\(315\) | 5.71967 | 0.322267 | ||||||||
\(316\) | 65.0095 | 3.65707 | ||||||||
\(317\) | −3.55705 | −0.199784 | −0.0998920 | − | 0.994998i | \(-0.531850\pi\) | ||||
−0.0998920 | + | 0.994998i | \(0.531850\pi\) | |||||||
\(318\) | 2.04549 | 0.114706 | ||||||||
\(319\) | 0.576805 | 0.0322949 | ||||||||
\(320\) | 24.7713 | 1.38476 | ||||||||
\(321\) | 14.2853 | 0.797326 | ||||||||
\(322\) | 5.99054 | 0.333840 | ||||||||
\(323\) | 2.23175 | 0.124178 | ||||||||
\(324\) | −32.8636 | −1.82575 | ||||||||
\(325\) | −22.3634 | −1.24050 | ||||||||
\(326\) | −2.45235 | −0.135823 | ||||||||
\(327\) | −9.74688 | −0.539004 | ||||||||
\(328\) | −24.5159 | −1.35367 | ||||||||
\(329\) | −5.02196 | −0.276870 | ||||||||
\(330\) | −18.3882 | −1.01224 | ||||||||
\(331\) | −26.8565 | −1.47617 | −0.738083 | − | 0.674710i | \(-0.764269\pi\) | ||||
−0.738083 | + | 0.674710i | \(0.764269\pi\) | |||||||
\(332\) | −16.1250 | −0.884972 | ||||||||
\(333\) | −3.25009 | −0.178104 | ||||||||
\(334\) | 4.12498 | 0.225709 | ||||||||
\(335\) | 0.635502 | 0.0347212 | ||||||||
\(336\) | 5.68017 | 0.309879 | ||||||||
\(337\) | −31.2241 | −1.70089 | −0.850444 | − | 0.526066i | \(-0.823667\pi\) | ||||
−0.850444 | + | 0.526066i | \(0.823667\pi\) | |||||||
\(338\) | −17.0189 | −0.925706 | ||||||||
\(339\) | −36.5830 | −1.98692 | ||||||||
\(340\) | −7.88645 | −0.427703 | ||||||||
\(341\) | 5.57447 | 0.301875 | ||||||||
\(342\) | −28.6416 | −1.54876 | ||||||||
\(343\) | 7.61588 | 0.411219 | ||||||||
\(344\) | 59.3514 | 3.20001 | ||||||||
\(345\) | 34.7299 | 1.86980 | ||||||||
\(346\) | 41.6499 | 2.23911 | ||||||||
\(347\) | 5.31829 | 0.285501 | 0.142750 | − | 0.989759i | \(-0.454405\pi\) | ||||
0.142750 | + | 0.989759i | \(0.454405\pi\) | |||||||
\(348\) | −6.10541 | −0.327284 | ||||||||
\(349\) | 0.0607852 | 0.00325376 | 0.00162688 | − | 0.999999i | \(-0.499482\pi\) | ||||
0.00162688 | + | 0.999999i | \(0.499482\pi\) | |||||||
\(350\) | 6.83217 | 0.365195 | ||||||||
\(351\) | 2.79185 | 0.149018 | ||||||||
\(352\) | −0.130834 | −0.00697345 | ||||||||
\(353\) | −15.3660 | −0.817847 | −0.408924 | − | 0.912569i | \(-0.634096\pi\) | ||||
−0.408924 | + | 0.912569i | \(0.634096\pi\) | |||||||
\(354\) | 25.4047 | 1.35025 | ||||||||
\(355\) | −50.8022 | −2.69630 | ||||||||
\(356\) | −39.3678 | −2.08649 | ||||||||
\(357\) | 0.863710 | 0.0457124 | ||||||||
\(358\) | −20.7950 | −1.09905 | ||||||||
\(359\) | 13.6250 | 0.719102 | 0.359551 | − | 0.933125i | \(-0.382930\pi\) | ||||
0.359551 | + | 0.933125i | \(0.382930\pi\) | |||||||
\(360\) | 50.7829 | 2.67649 | ||||||||
\(361\) | −6.08660 | −0.320347 | ||||||||
\(362\) | 59.2332 | 3.11323 | ||||||||
\(363\) | 25.2531 | 1.32545 | ||||||||
\(364\) | 9.97102 | 0.522624 | ||||||||
\(365\) | −21.8330 | −1.14279 | ||||||||
\(366\) | 22.8998 | 1.19699 | ||||||||
\(367\) | 2.44722 | 0.127744 | 0.0638718 | − | 0.997958i | \(-0.479655\pi\) | ||||
0.0638718 | + | 0.997958i | \(0.479655\pi\) | |||||||
\(368\) | 17.9351 | 0.934930 | ||||||||
\(369\) | 16.1323 | 0.839815 | ||||||||
\(370\) | −7.75817 | −0.403328 | ||||||||
\(371\) | −0.185598 | −0.00963575 | ||||||||
\(372\) | −59.0051 | −3.05927 | ||||||||
\(373\) | 31.6569 | 1.63913 | 0.819567 | − | 0.572984i | \(-0.194214\pi\) | ||||
0.819567 | + | 0.572984i | \(0.194214\pi\) | |||||||
\(374\) | −1.44392 | −0.0746635 | ||||||||
\(375\) | 0.0644272 | 0.00332700 | ||||||||
\(376\) | −44.5882 | −2.29946 | ||||||||
\(377\) | −2.71677 | −0.139921 | ||||||||
\(378\) | −0.852930 | −0.0438700 | ||||||||
\(379\) | −23.8632 | −1.22577 | −0.612884 | − | 0.790173i | \(-0.709991\pi\) | ||||
−0.612884 | + | 0.790173i | \(0.709991\pi\) | |||||||
\(380\) | −45.6327 | −2.34091 | ||||||||
\(381\) | 39.0814 | 2.00220 | ||||||||
\(382\) | −39.2358 | −2.00748 | ||||||||
\(383\) | −32.3630 | −1.65367 | −0.826836 | − | 0.562443i | \(-0.809861\pi\) | ||||
−0.826836 | + | 0.562443i | \(0.809861\pi\) | |||||||
\(384\) | −48.6963 | −2.48502 | ||||||||
\(385\) | 1.66845 | 0.0850320 | ||||||||
\(386\) | −52.4927 | −2.67181 | ||||||||
\(387\) | −39.0553 | −1.98529 | ||||||||
\(388\) | −37.0969 | −1.88331 | ||||||||
\(389\) | −2.28838 | −0.116026 | −0.0580128 | − | 0.998316i | \(-0.518476\pi\) | ||||
−0.0580128 | + | 0.998316i | \(0.518476\pi\) | |||||||
\(390\) | 86.6090 | 4.38562 | ||||||||
\(391\) | 2.72715 | 0.137918 | ||||||||
\(392\) | 33.0451 | 1.66903 | ||||||||
\(393\) | 0.970207 | 0.0489405 | ||||||||
\(394\) | 41.0383 | 2.06748 | ||||||||
\(395\) | −51.2359 | −2.57796 | ||||||||
\(396\) | 12.3683 | 0.621531 | ||||||||
\(397\) | 7.70007 | 0.386455 | 0.193228 | − | 0.981154i | \(-0.438104\pi\) | ||||
0.193228 | + | 0.981154i | \(0.438104\pi\) | |||||||
\(398\) | 49.3846 | 2.47543 | ||||||||
\(399\) | 4.99761 | 0.250194 | ||||||||
\(400\) | 20.4548 | 1.02274 | ||||||||
\(401\) | −1.60522 | −0.0801608 | −0.0400804 | − | 0.999196i | \(-0.512761\pi\) | ||||
−0.0400804 | + | 0.999196i | \(0.512761\pi\) | |||||||
\(402\) | −1.23159 | −0.0614260 | ||||||||
\(403\) | −26.2560 | −1.30790 | ||||||||
\(404\) | 36.1885 | 1.80044 | ||||||||
\(405\) | 25.9007 | 1.28702 | ||||||||
\(406\) | 0.829993 | 0.0411918 | ||||||||
\(407\) | −0.948061 | −0.0469937 | ||||||||
\(408\) | 7.66857 | 0.379651 | ||||||||
\(409\) | −9.08886 | −0.449415 | −0.224708 | − | 0.974426i | \(-0.572143\pi\) | ||||
−0.224708 | + | 0.974426i | \(0.572143\pi\) | |||||||
\(410\) | 38.5089 | 1.90182 | ||||||||
\(411\) | −21.7335 | −1.07203 | ||||||||
\(412\) | 35.6517 | 1.75643 | ||||||||
\(413\) | −2.30510 | −0.113426 | ||||||||
\(414\) | −34.9995 | −1.72013 | ||||||||
\(415\) | 12.7086 | 0.623838 | ||||||||
\(416\) | 0.616231 | 0.0302132 | ||||||||
\(417\) | −40.4280 | −1.97977 | ||||||||
\(418\) | −8.35486 | −0.408650 | ||||||||
\(419\) | 23.8976 | 1.16747 | 0.583737 | − | 0.811943i | \(-0.301590\pi\) | ||||
0.583737 | + | 0.811943i | \(0.301590\pi\) | |||||||
\(420\) | −17.6603 | −0.861736 | ||||||||
\(421\) | 32.9620 | 1.60647 | 0.803235 | − | 0.595662i | \(-0.203110\pi\) | ||||
0.803235 | + | 0.595662i | \(0.203110\pi\) | |||||||
\(422\) | −10.0159 | −0.487567 | ||||||||
\(423\) | 29.3406 | 1.42659 | ||||||||
\(424\) | −1.64785 | −0.0800269 | ||||||||
\(425\) | 3.11030 | 0.150872 | ||||||||
\(426\) | 98.4534 | 4.77008 | ||||||||
\(427\) | −2.07781 | −0.100552 | ||||||||
\(428\) | −22.9364 | −1.10867 | ||||||||
\(429\) | 10.5838 | 0.510989 | ||||||||
\(430\) | −93.2276 | −4.49583 | ||||||||
\(431\) | −13.9182 | −0.670417 | −0.335209 | − | 0.942144i | \(-0.608807\pi\) | ||||
−0.335209 | + | 0.942144i | \(0.608807\pi\) | |||||||
\(432\) | −2.55358 | −0.122859 | ||||||||
\(433\) | 10.3590 | 0.497822 | 0.248911 | − | 0.968526i | \(-0.419927\pi\) | ||||
0.248911 | + | 0.968526i | \(0.419927\pi\) | |||||||
\(434\) | 8.02138 | 0.385039 | ||||||||
\(435\) | 4.81185 | 0.230711 | ||||||||
\(436\) | 15.6496 | 0.749478 | ||||||||
\(437\) | 15.7799 | 0.754855 | ||||||||
\(438\) | 42.3118 | 2.02174 | ||||||||
\(439\) | 38.2486 | 1.82551 | 0.912753 | − | 0.408512i | \(-0.133952\pi\) | ||||
0.912753 | + | 0.408512i | \(0.133952\pi\) | |||||||
\(440\) | 14.8136 | 0.706208 | ||||||||
\(441\) | −21.7448 | −1.03547 | ||||||||
\(442\) | 6.80093 | 0.323487 | ||||||||
\(443\) | 28.6492 | 1.36117 | 0.680583 | − | 0.732671i | \(-0.261727\pi\) | ||||
0.680583 | + | 0.732671i | \(0.261727\pi\) | |||||||
\(444\) | 10.0351 | 0.476246 | ||||||||
\(445\) | 31.0269 | 1.47081 | ||||||||
\(446\) | −27.9601 | −1.32395 | ||||||||
\(447\) | 28.0649 | 1.32742 | ||||||||
\(448\) | 4.35584 | 0.205794 | ||||||||
\(449\) | 11.2527 | 0.531049 | 0.265525 | − | 0.964104i | \(-0.414455\pi\) | ||||
0.265525 | + | 0.964104i | \(0.414455\pi\) | |||||||
\(450\) | −39.9167 | −1.88169 | ||||||||
\(451\) | 4.70586 | 0.221590 | ||||||||
\(452\) | 58.7376 | 2.76278 | ||||||||
\(453\) | 49.9446 | 2.34660 | ||||||||
\(454\) | 39.1066 | 1.83536 | ||||||||
\(455\) | −7.85845 | −0.368410 | ||||||||
\(456\) | 44.3720 | 2.07791 | ||||||||
\(457\) | −15.3755 | −0.719235 | −0.359618 | − | 0.933100i | \(-0.617093\pi\) | ||||
−0.359618 | + | 0.933100i | \(0.617093\pi\) | |||||||
\(458\) | 26.5233 | 1.23935 | ||||||||
\(459\) | −0.388290 | −0.0181238 | ||||||||
\(460\) | −55.7623 | −2.59993 | ||||||||
\(461\) | 34.3222 | 1.59854 | 0.799272 | − | 0.600970i | \(-0.205219\pi\) | ||||
0.799272 | + | 0.600970i | \(0.205219\pi\) | |||||||
\(462\) | −3.23341 | −0.150432 | ||||||||
\(463\) | −18.2991 | −0.850433 | −0.425217 | − | 0.905092i | \(-0.639802\pi\) | ||||
−0.425217 | + | 0.905092i | \(0.639802\pi\) | |||||||
\(464\) | 2.48491 | 0.115359 | ||||||||
\(465\) | 46.5037 | 2.15656 | ||||||||
\(466\) | 42.0508 | 1.94797 | ||||||||
\(467\) | 15.5999 | 0.721878 | 0.360939 | − | 0.932589i | \(-0.382456\pi\) | ||||
0.360939 | + | 0.932589i | \(0.382456\pi\) | |||||||
\(468\) | −58.2552 | −2.69285 | ||||||||
\(469\) | 0.111748 | 0.00516004 | ||||||||
\(470\) | 70.0379 | 3.23061 | ||||||||
\(471\) | 56.1662 | 2.58800 | ||||||||
\(472\) | −20.4661 | −0.942029 | ||||||||
\(473\) | −11.3926 | −0.523831 | ||||||||
\(474\) | 99.2940 | 4.56072 | ||||||||
\(475\) | 17.9969 | 0.825754 | ||||||||
\(476\) | −1.38677 | −0.0635625 | ||||||||
\(477\) | 1.08435 | 0.0496488 | ||||||||
\(478\) | −49.4867 | −2.26347 | ||||||||
\(479\) | 7.69371 | 0.351534 | 0.175767 | − | 0.984432i | \(-0.443759\pi\) | ||||
0.175767 | + | 0.984432i | \(0.443759\pi\) | |||||||
\(480\) | −1.09145 | −0.0498175 | ||||||||
\(481\) | 4.46540 | 0.203605 | ||||||||
\(482\) | −16.8532 | −0.767641 | ||||||||
\(483\) | 6.10698 | 0.277877 | ||||||||
\(484\) | −40.5463 | −1.84301 | ||||||||
\(485\) | 29.2372 | 1.32759 | ||||||||
\(486\) | −54.7948 | −2.48554 | ||||||||
\(487\) | −36.8071 | −1.66789 | −0.833944 | − | 0.551850i | \(-0.813922\pi\) | ||||
−0.833944 | + | 0.551850i | \(0.813922\pi\) | |||||||
\(488\) | −18.4481 | −0.835106 | ||||||||
\(489\) | −2.50002 | −0.113055 | ||||||||
\(490\) | −51.9064 | −2.34489 | ||||||||
\(491\) | 16.3533 | 0.738015 | 0.369008 | − | 0.929426i | \(-0.379698\pi\) | ||||
0.369008 | + | 0.929426i | \(0.379698\pi\) | |||||||
\(492\) | −49.8109 | −2.24565 | ||||||||
\(493\) | 0.377848 | 0.0170174 | ||||||||
\(494\) | 39.3517 | 1.77052 | ||||||||
\(495\) | −9.74783 | −0.438132 | ||||||||
\(496\) | 24.0152 | 1.07831 | ||||||||
\(497\) | −8.93316 | −0.400707 | ||||||||
\(498\) | −24.6289 | −1.10365 | ||||||||
\(499\) | 22.2652 | 0.996726 | 0.498363 | − | 0.866968i | \(-0.333935\pi\) | ||||
0.498363 | + | 0.866968i | \(0.333935\pi\) | |||||||
\(500\) | −0.103444 | −0.00462616 | ||||||||
\(501\) | 4.20516 | 0.187873 | ||||||||
\(502\) | 63.5095 | 2.83457 | ||||||||
\(503\) | 3.53657 | 0.157688 | 0.0788440 | − | 0.996887i | \(-0.474877\pi\) | ||||
0.0788440 | + | 0.996887i | \(0.474877\pi\) | |||||||
\(504\) | 8.92977 | 0.397764 | ||||||||
\(505\) | −28.5212 | −1.26918 | ||||||||
\(506\) | −10.2095 | −0.453866 | ||||||||
\(507\) | −17.3497 | −0.770527 | ||||||||
\(508\) | −62.7490 | −2.78404 | ||||||||
\(509\) | −9.99790 | −0.443149 | −0.221574 | − | 0.975143i | \(-0.571120\pi\) | ||||
−0.221574 | + | 0.975143i | \(0.571120\pi\) | |||||||
\(510\) | −12.0456 | −0.533387 | ||||||||
\(511\) | −3.83915 | −0.169834 | ||||||||
\(512\) | 39.7818 | 1.75813 | ||||||||
\(513\) | −2.24673 | −0.0991957 | ||||||||
\(514\) | −32.1784 | −1.41933 | ||||||||
\(515\) | −28.0982 | −1.23815 | ||||||||
\(516\) | 120.589 | 5.30863 | ||||||||
\(517\) | 8.55875 | 0.376413 | ||||||||
\(518\) | −1.36421 | −0.0599400 | ||||||||
\(519\) | 42.4594 | 1.86376 | ||||||||
\(520\) | −69.7724 | −3.05972 | ||||||||
\(521\) | 30.4533 | 1.33418 | 0.667092 | − | 0.744975i | \(-0.267539\pi\) | ||||
0.667092 | + | 0.744975i | \(0.267539\pi\) | |||||||
\(522\) | −4.84919 | −0.212243 | ||||||||
\(523\) | −18.8954 | −0.826238 | −0.413119 | − | 0.910677i | \(-0.635561\pi\) | ||||
−0.413119 | + | 0.910677i | \(0.635561\pi\) | |||||||
\(524\) | −1.55776 | −0.0680511 | ||||||||
\(525\) | 6.96497 | 0.303976 | ||||||||
\(526\) | 26.9837 | 1.17655 | ||||||||
\(527\) | 3.65168 | 0.159070 | ||||||||
\(528\) | −9.68051 | −0.421290 | ||||||||
\(529\) | −3.71728 | −0.161621 | ||||||||
\(530\) | 2.58840 | 0.112433 | ||||||||
\(531\) | 13.4674 | 0.584436 | ||||||||
\(532\) | −8.02415 | −0.347891 | ||||||||
\(533\) | −22.1648 | −0.960062 | ||||||||
\(534\) | −60.1294 | −2.60205 | ||||||||
\(535\) | 18.0768 | 0.781530 | ||||||||
\(536\) | 0.992169 | 0.0428552 | ||||||||
\(537\) | −21.1992 | −0.914811 | ||||||||
\(538\) | −41.2852 | −1.77993 | ||||||||
\(539\) | −6.34305 | −0.273214 | ||||||||
\(540\) | 7.93940 | 0.341657 | ||||||||
\(541\) | 28.7619 | 1.23657 | 0.618285 | − | 0.785954i | \(-0.287828\pi\) | ||||
0.618285 | + | 0.785954i | \(0.287828\pi\) | |||||||
\(542\) | −45.4280 | −1.95130 | ||||||||
\(543\) | 60.3846 | 2.59135 | ||||||||
\(544\) | −0.0857053 | −0.00367459 | ||||||||
\(545\) | −12.3339 | −0.528325 | ||||||||
\(546\) | 15.2295 | 0.651762 | ||||||||
\(547\) | 23.8934 | 1.02161 | 0.510803 | − | 0.859698i | \(-0.329348\pi\) | ||||
0.510803 | + | 0.859698i | \(0.329348\pi\) | |||||||
\(548\) | 34.8952 | 1.49065 | ||||||||
\(549\) | 12.1395 | 0.518101 | ||||||||
\(550\) | −11.6438 | −0.496495 | ||||||||
\(551\) | 2.18631 | 0.0931401 | ||||||||
\(552\) | 54.2217 | 2.30783 | ||||||||
\(553\) | −9.00942 | −0.383120 | ||||||||
\(554\) | −0.993306 | −0.0422015 | ||||||||
\(555\) | −7.90897 | −0.335717 | ||||||||
\(556\) | 64.9110 | 2.75284 | ||||||||
\(557\) | −8.50151 | −0.360221 | −0.180110 | − | 0.983646i | \(-0.557645\pi\) | ||||
−0.180110 | + | 0.983646i | \(0.557645\pi\) | |||||||
\(558\) | −46.8646 | −1.98394 | ||||||||
\(559\) | 53.6594 | 2.26955 | ||||||||
\(560\) | 7.18779 | 0.303739 | ||||||||
\(561\) | −1.47199 | −0.0621474 | ||||||||
\(562\) | 54.4543 | 2.29701 | ||||||||
\(563\) | 11.0886 | 0.467327 | 0.233664 | − | 0.972318i | \(-0.424929\pi\) | ||||
0.233664 | + | 0.972318i | \(0.424929\pi\) | |||||||
\(564\) | −90.5933 | −3.81467 | ||||||||
\(565\) | −46.2928 | −1.94755 | ||||||||
\(566\) | −26.6555 | −1.12041 | ||||||||
\(567\) | 4.55444 | 0.191268 | ||||||||
\(568\) | −79.3143 | −3.32795 | ||||||||
\(569\) | −27.9618 | −1.17222 | −0.586110 | − | 0.810232i | \(-0.699341\pi\) | ||||
−0.586110 | + | 0.810232i | \(0.699341\pi\) | |||||||
\(570\) | −69.6984 | −2.91934 | ||||||||
\(571\) | −4.92636 | −0.206162 | −0.103081 | − | 0.994673i | \(-0.532870\pi\) | ||||
−0.103081 | + | 0.994673i | \(0.532870\pi\) | |||||||
\(572\) | −16.9933 | −0.710524 | ||||||||
\(573\) | −39.9985 | −1.67096 | ||||||||
\(574\) | 6.77149 | 0.282636 | ||||||||
\(575\) | 21.9918 | 0.917122 | ||||||||
\(576\) | −25.4488 | −1.06037 | ||||||||
\(577\) | 33.3049 | 1.38650 | 0.693250 | − | 0.720697i | \(-0.256178\pi\) | ||||
0.693250 | + | 0.720697i | \(0.256178\pi\) | |||||||
\(578\) | 40.7441 | 1.69473 | ||||||||
\(579\) | −53.5130 | −2.22392 | ||||||||
\(580\) | −7.72589 | −0.320800 | ||||||||
\(581\) | 2.23470 | 0.0927109 | ||||||||
\(582\) | −56.6610 | −2.34867 | ||||||||
\(583\) | 0.316307 | 0.0131001 | ||||||||
\(584\) | −34.0865 | −1.41051 | ||||||||
\(585\) | 45.9126 | 1.89825 | ||||||||
\(586\) | −5.51912 | −0.227993 | ||||||||
\(587\) | 20.7393 | 0.856005 | 0.428002 | − | 0.903778i | \(-0.359218\pi\) | ||||
0.428002 | + | 0.903778i | \(0.359218\pi\) | |||||||
\(588\) | 67.1404 | 2.76882 | ||||||||
\(589\) | 21.1294 | 0.870623 | ||||||||
\(590\) | 32.1476 | 1.32350 | ||||||||
\(591\) | 41.8360 | 1.72090 | ||||||||
\(592\) | −4.08431 | −0.167864 | ||||||||
\(593\) | 12.3311 | 0.506376 | 0.253188 | − | 0.967417i | \(-0.418521\pi\) | ||||
0.253188 | + | 0.967417i | \(0.418521\pi\) | |||||||
\(594\) | 1.45362 | 0.0596426 | ||||||||
\(595\) | 1.09295 | 0.0448067 | ||||||||
\(596\) | −45.0609 | −1.84577 | ||||||||
\(597\) | 50.3445 | 2.06046 | ||||||||
\(598\) | 48.0870 | 1.96642 | ||||||||
\(599\) | −28.1193 | −1.14892 | −0.574461 | − | 0.818532i | \(-0.694788\pi\) | ||||
−0.574461 | + | 0.818532i | \(0.694788\pi\) | |||||||
\(600\) | 61.8395 | 2.52459 | ||||||||
\(601\) | 39.3077 | 1.60339 | 0.801696 | − | 0.597732i | \(-0.203931\pi\) | ||||
0.801696 | + | 0.597732i | \(0.203931\pi\) | |||||||
\(602\) | −16.3933 | −0.668142 | ||||||||
\(603\) | −0.652882 | −0.0265874 | ||||||||
\(604\) | −80.1909 | −3.26292 | ||||||||
\(605\) | 31.9557 | 1.29919 | ||||||||
\(606\) | 55.2734 | 2.24533 | ||||||||
\(607\) | −33.8307 | −1.37315 | −0.686574 | − | 0.727060i | \(-0.740886\pi\) | ||||
−0.686574 | + | 0.727060i | \(0.740886\pi\) | |||||||
\(608\) | −0.495910 | −0.0201118 | ||||||||
\(609\) | 0.846125 | 0.0342867 | ||||||||
\(610\) | 28.9778 | 1.17328 | ||||||||
\(611\) | −40.3120 | −1.63085 | ||||||||
\(612\) | 8.10214 | 0.327509 | ||||||||
\(613\) | −12.9780 | −0.524175 | −0.262088 | − | 0.965044i | \(-0.584411\pi\) | ||||
−0.262088 | + | 0.965044i | \(0.584411\pi\) | |||||||
\(614\) | −48.7251 | −1.96639 | ||||||||
\(615\) | 39.2574 | 1.58301 | ||||||||
\(616\) | 2.60485 | 0.104952 | ||||||||
\(617\) | −11.3411 | −0.456576 | −0.228288 | − | 0.973594i | \(-0.573313\pi\) | ||||
−0.228288 | + | 0.973594i | \(0.573313\pi\) | |||||||
\(618\) | 54.4536 | 2.19044 | ||||||||
\(619\) | −9.98612 | −0.401376 | −0.200688 | − | 0.979655i | \(-0.564318\pi\) | ||||
−0.200688 | + | 0.979655i | \(0.564318\pi\) | |||||||
\(620\) | −74.6661 | −2.99866 | ||||||||
\(621\) | −2.74546 | −0.110172 | ||||||||
\(622\) | 3.73398 | 0.149719 | ||||||||
\(623\) | 5.45583 | 0.218583 | ||||||||
\(624\) | 45.5956 | 1.82528 | ||||||||
\(625\) | −24.9592 | −0.998368 | ||||||||
\(626\) | −38.8346 | −1.55214 | ||||||||
\(627\) | −8.51726 | −0.340146 | ||||||||
\(628\) | −90.1803 | −3.59859 | ||||||||
\(629\) | −0.621048 | −0.0247628 | ||||||||
\(630\) | −14.0266 | −0.558834 | ||||||||
\(631\) | −29.8938 | −1.19005 | −0.595026 | − | 0.803707i | \(-0.702858\pi\) | ||||
−0.595026 | + | 0.803707i | \(0.702858\pi\) | |||||||
\(632\) | −79.9914 | −3.18189 | ||||||||
\(633\) | −10.2106 | −0.405835 | ||||||||
\(634\) | 8.72314 | 0.346440 | ||||||||
\(635\) | 49.4543 | 1.96253 | ||||||||
\(636\) | −3.34808 | −0.132760 | ||||||||
\(637\) | 29.8760 | 1.18373 | ||||||||
\(638\) | −1.41453 | −0.0560016 | ||||||||
\(639\) | 52.1916 | 2.06467 | ||||||||
\(640\) | −61.6211 | −2.43579 | ||||||||
\(641\) | 28.0591 | 1.10827 | 0.554134 | − | 0.832428i | \(-0.313050\pi\) | ||||
0.554134 | + | 0.832428i | \(0.313050\pi\) | |||||||
\(642\) | −35.0325 | −1.38262 | ||||||||
\(643\) | −15.7198 | −0.619929 | −0.309965 | − | 0.950748i | \(-0.600317\pi\) | ||||
−0.309965 | + | 0.950748i | \(0.600317\pi\) | |||||||
\(644\) | −9.80535 | −0.386385 | ||||||||
\(645\) | −95.0397 | −3.74218 | ||||||||
\(646\) | −5.47303 | −0.215334 | ||||||||
\(647\) | −31.6461 | −1.24414 | −0.622068 | − | 0.782963i | \(-0.713707\pi\) | ||||
−0.622068 | + | 0.782963i | \(0.713707\pi\) | |||||||
\(648\) | 40.4372 | 1.58852 | ||||||||
\(649\) | 3.92849 | 0.154207 | ||||||||
\(650\) | 54.8429 | 2.15111 | ||||||||
\(651\) | 8.17730 | 0.320494 | ||||||||
\(652\) | 4.01402 | 0.157201 | ||||||||
\(653\) | 26.5789 | 1.04011 | 0.520055 | − | 0.854133i | \(-0.325911\pi\) | ||||
0.520055 | + | 0.854133i | \(0.325911\pi\) | |||||||
\(654\) | 23.9028 | 0.934672 | ||||||||
\(655\) | 1.22772 | 0.0479709 | ||||||||
\(656\) | 20.2731 | 0.791533 | ||||||||
\(657\) | 22.4301 | 0.875081 | ||||||||
\(658\) | 12.3156 | 0.480112 | ||||||||
\(659\) | −7.49464 | −0.291950 | −0.145975 | − | 0.989288i | \(-0.546632\pi\) | ||||
−0.145975 | + | 0.989288i | \(0.546632\pi\) | |||||||
\(660\) | 30.0979 | 1.17156 | ||||||||
\(661\) | 28.2757 | 1.09980 | 0.549898 | − | 0.835232i | \(-0.314667\pi\) | ||||
0.549898 | + | 0.835232i | \(0.314667\pi\) | |||||||
\(662\) | 65.8615 | 2.55978 | ||||||||
\(663\) | 6.93312 | 0.269260 | ||||||||
\(664\) | 19.8411 | 0.769983 | ||||||||
\(665\) | 6.32407 | 0.245237 | ||||||||
\(666\) | 7.97035 | 0.308845 | ||||||||
\(667\) | 2.67163 | 0.103446 | ||||||||
\(668\) | −6.75179 | −0.261234 | ||||||||
\(669\) | −28.5036 | −1.10201 | ||||||||
\(670\) | −1.55847 | −0.0602090 | ||||||||
\(671\) | 3.54113 | 0.136704 | ||||||||
\(672\) | −0.191922 | −0.00740356 | ||||||||
\(673\) | 25.4612 | 0.981458 | 0.490729 | − | 0.871312i | \(-0.336731\pi\) | ||||
0.490729 | + | 0.871312i | \(0.336731\pi\) | |||||||
\(674\) | 76.5725 | 2.94946 | ||||||||
\(675\) | −3.13118 | −0.120519 | ||||||||
\(676\) | 27.8566 | 1.07141 | ||||||||
\(677\) | 40.8394 | 1.56959 | 0.784793 | − | 0.619758i | \(-0.212769\pi\) | ||||
0.784793 | + | 0.619758i | \(0.212769\pi\) | |||||||
\(678\) | 89.7144 | 3.44546 | ||||||||
\(679\) | 5.14112 | 0.197298 | ||||||||
\(680\) | 9.70394 | 0.372129 | ||||||||
\(681\) | 39.8667 | 1.52770 | ||||||||
\(682\) | −13.6706 | −0.523473 | ||||||||
\(683\) | −5.75268 | −0.220120 | −0.110060 | − | 0.993925i | \(-0.535104\pi\) | ||||
−0.110060 | + | 0.993925i | \(0.535104\pi\) | |||||||
\(684\) | 46.8807 | 1.79253 | ||||||||
\(685\) | −27.5019 | −1.05079 | ||||||||
\(686\) | −18.6768 | −0.713084 | ||||||||
\(687\) | 27.0388 | 1.03160 | ||||||||
\(688\) | −49.0799 | −1.87116 | ||||||||
\(689\) | −1.48982 | −0.0567576 | ||||||||
\(690\) | −85.1699 | −3.24236 | ||||||||
\(691\) | 24.5318 | 0.933234 | 0.466617 | − | 0.884459i | \(-0.345473\pi\) | ||||
0.466617 | + | 0.884459i | \(0.345473\pi\) | |||||||
\(692\) | −68.1727 | −2.59154 | ||||||||
\(693\) | −1.71408 | −0.0651125 | ||||||||
\(694\) | −13.0423 | −0.495079 | ||||||||
\(695\) | −51.1583 | −1.94054 | ||||||||
\(696\) | 7.51244 | 0.284758 | ||||||||
\(697\) | 3.08267 | 0.116765 | ||||||||
\(698\) | −0.149067 | −0.00564225 | ||||||||
\(699\) | 42.8682 | 1.62142 | ||||||||
\(700\) | −11.1829 | −0.422675 | ||||||||
\(701\) | −5.38410 | −0.203355 | −0.101677 | − | 0.994817i | \(-0.532421\pi\) | ||||
−0.101677 | + | 0.994817i | \(0.532421\pi\) | |||||||
\(702\) | −6.84659 | −0.258408 | ||||||||
\(703\) | −3.59352 | −0.135532 | ||||||||
\(704\) | −7.42351 | −0.279784 | ||||||||
\(705\) | 71.3992 | 2.68905 | ||||||||
\(706\) | 37.6827 | 1.41821 | ||||||||
\(707\) | −5.01523 | −0.188617 | ||||||||
\(708\) | −41.5826 | −1.56277 | ||||||||
\(709\) | 8.49291 | 0.318958 | 0.159479 | − | 0.987201i | \(-0.449019\pi\) | ||||
0.159479 | + | 0.987201i | \(0.449019\pi\) | |||||||
\(710\) | 124.585 | 4.67558 | ||||||||
\(711\) | 52.6371 | 1.97405 | ||||||||
\(712\) | 48.4403 | 1.81538 | ||||||||
\(713\) | 25.8197 | 0.966956 | ||||||||
\(714\) | −2.11812 | −0.0792686 | ||||||||
\(715\) | 13.3929 | 0.500865 | ||||||||
\(716\) | 34.0373 | 1.27203 | ||||||||
\(717\) | −50.4486 | −1.88404 | ||||||||
\(718\) | −33.4134 | −1.24698 | ||||||||
\(719\) | −10.0594 | −0.375151 | −0.187576 | − | 0.982250i | \(-0.560063\pi\) | ||||
−0.187576 | + | 0.982250i | \(0.560063\pi\) | |||||||
\(720\) | −41.9943 | −1.56504 | ||||||||
\(721\) | −4.94084 | −0.184006 | ||||||||
\(722\) | 14.9265 | 0.555506 | ||||||||
\(723\) | −17.1808 | −0.638959 | ||||||||
\(724\) | −96.9533 | −3.60324 | ||||||||
\(725\) | 3.04698 | 0.113162 | ||||||||
\(726\) | −61.9295 | −2.29842 | ||||||||
\(727\) | 37.2385 | 1.38110 | 0.690550 | − | 0.723285i | \(-0.257369\pi\) | ||||
0.690550 | + | 0.723285i | \(0.257369\pi\) | |||||||
\(728\) | −12.2689 | −0.454716 | ||||||||
\(729\) | −31.2983 | −1.15920 | ||||||||
\(730\) | 53.5421 | 1.98168 | ||||||||
\(731\) | −7.46295 | −0.276027 | ||||||||
\(732\) | −37.4824 | −1.38539 | ||||||||
\(733\) | −2.68782 | −0.0992771 | −0.0496385 | − | 0.998767i | \(-0.515807\pi\) | ||||
−0.0496385 | + | 0.998767i | \(0.515807\pi\) | |||||||
\(734\) | −6.00143 | −0.221517 | ||||||||
\(735\) | −52.9153 | −1.95181 | ||||||||
\(736\) | −0.605992 | −0.0223372 | ||||||||
\(737\) | −0.190448 | −0.00701524 | ||||||||
\(738\) | −39.5621 | −1.45630 | ||||||||
\(739\) | 30.0418 | 1.10511 | 0.552553 | − | 0.833478i | \(-0.313654\pi\) | ||||
0.552553 | + | 0.833478i | \(0.313654\pi\) | |||||||
\(740\) | 12.6986 | 0.466810 | ||||||||
\(741\) | 40.1166 | 1.47372 | ||||||||
\(742\) | 0.455150 | 0.0167091 | ||||||||
\(743\) | 10.0355 | 0.368168 | 0.184084 | − | 0.982910i | \(-0.441068\pi\) | ||||
0.184084 | + | 0.982910i | \(0.441068\pi\) | |||||||
\(744\) | 72.6033 | 2.66177 | ||||||||
\(745\) | 35.5138 | 1.30113 | ||||||||
\(746\) | −77.6339 | −2.84238 | ||||||||
\(747\) | −13.0561 | −0.477698 | ||||||||
\(748\) | 2.36342 | 0.0864152 | ||||||||
\(749\) | 3.17867 | 0.116146 | ||||||||
\(750\) | −0.157998 | −0.00576927 | ||||||||
\(751\) | 0.980624 | 0.0357835 | 0.0178917 | − | 0.999840i | \(-0.494305\pi\) | ||||
0.0178917 | + | 0.999840i | \(0.494305\pi\) | |||||||
\(752\) | 36.8716 | 1.34457 | ||||||||
\(753\) | 64.7440 | 2.35940 | ||||||||
\(754\) | 6.66247 | 0.242633 | ||||||||
\(755\) | 63.2008 | 2.30011 | ||||||||
\(756\) | 1.39608 | 0.0507749 | ||||||||
\(757\) | 29.1983 | 1.06123 | 0.530616 | − | 0.847612i | \(-0.321961\pi\) | ||||
0.530616 | + | 0.847612i | \(0.321961\pi\) | |||||||
\(758\) | 58.5208 | 2.12557 | ||||||||
\(759\) | −10.4079 | −0.377783 | ||||||||
\(760\) | 56.1491 | 2.03674 | ||||||||
\(761\) | −4.70124 | −0.170420 | −0.0852099 | − | 0.996363i | \(-0.527156\pi\) | ||||
−0.0852099 | + | 0.996363i | \(0.527156\pi\) | |||||||
\(762\) | −95.8413 | −3.47196 | ||||||||
\(763\) | −2.16881 | −0.0785163 | ||||||||
\(764\) | 64.2214 | 2.32345 | ||||||||
\(765\) | −6.38553 | −0.230869 | ||||||||
\(766\) | 79.3654 | 2.86759 | ||||||||
\(767\) | −18.5033 | −0.668117 | ||||||||
\(768\) | 80.2691 | 2.89646 | ||||||||
\(769\) | 44.3979 | 1.60103 | 0.800515 | − | 0.599312i | \(-0.204559\pi\) | ||||
0.800515 | + | 0.599312i | \(0.204559\pi\) | |||||||
\(770\) | −4.09162 | −0.147452 | ||||||||
\(771\) | −32.8039 | −1.18140 | ||||||||
\(772\) | 85.9203 | 3.09234 | ||||||||
\(773\) | −23.3478 | −0.839761 | −0.419881 | − | 0.907579i | \(-0.637928\pi\) | ||||
−0.419881 | + | 0.907579i | \(0.637928\pi\) | |||||||
\(774\) | 95.7773 | 3.44264 | ||||||||
\(775\) | 29.4472 | 1.05778 | ||||||||
\(776\) | 45.6462 | 1.63860 | ||||||||
\(777\) | −1.39073 | −0.0498921 | ||||||||
\(778\) | 5.61192 | 0.201197 | ||||||||
\(779\) | 17.8370 | 0.639078 | ||||||||
\(780\) | −141.762 | −5.07590 | ||||||||
\(781\) | 15.2245 | 0.544774 | ||||||||
\(782\) | −6.68793 | −0.239160 | ||||||||
\(783\) | −0.380385 | −0.0135939 | ||||||||
\(784\) | −27.3263 | −0.975938 | ||||||||
\(785\) | 71.0737 | 2.53673 | ||||||||
\(786\) | −2.37929 | −0.0848663 | ||||||||
\(787\) | −32.3704 | −1.15388 | −0.576940 | − | 0.816787i | \(-0.695753\pi\) | ||||
−0.576940 | + | 0.816787i | \(0.695753\pi\) | |||||||
\(788\) | −67.1717 | −2.39289 | ||||||||
\(789\) | 27.5082 | 0.979318 | ||||||||
\(790\) | 125.648 | 4.47037 | ||||||||
\(791\) | −8.14022 | −0.289433 | ||||||||
\(792\) | −15.2187 | −0.540773 | ||||||||
\(793\) | −16.6789 | −0.592284 | ||||||||
\(794\) | −18.8833 | −0.670142 | ||||||||
\(795\) | 2.63872 | 0.0935856 | ||||||||
\(796\) | −80.8330 | −2.86505 | ||||||||
\(797\) | −16.5771 | −0.587192 | −0.293596 | − | 0.955930i | \(-0.594852\pi\) | ||||
−0.293596 | + | 0.955930i | \(0.594852\pi\) | |||||||
\(798\) | −12.2559 | −0.433854 | ||||||||
\(799\) | 5.60659 | 0.198347 | ||||||||
\(800\) | −0.691130 | −0.0244351 | ||||||||
\(801\) | −31.8754 | −1.12626 | ||||||||
\(802\) | 3.93656 | 0.139005 | ||||||||
\(803\) | 6.54293 | 0.230895 | ||||||||
\(804\) | 2.01587 | 0.0710942 | ||||||||
\(805\) | 7.72788 | 0.272372 | ||||||||
\(806\) | 64.3888 | 2.26800 | ||||||||
\(807\) | −42.0877 | −1.48156 | ||||||||
\(808\) | −44.5284 | −1.56650 | ||||||||
\(809\) | 16.5622 | 0.582296 | 0.291148 | − | 0.956678i | \(-0.405963\pi\) | ||||
0.291148 | + | 0.956678i | \(0.405963\pi\) | |||||||
\(810\) | −63.5177 | −2.23178 | ||||||||
\(811\) | −28.6788 | −1.00705 | −0.503525 | − | 0.863981i | \(-0.667964\pi\) | ||||
−0.503525 | + | 0.863981i | \(0.667964\pi\) | |||||||
\(812\) | −1.35854 | −0.0476753 | ||||||||
\(813\) | −46.3110 | −1.62420 | ||||||||
\(814\) | 2.32498 | 0.0814904 | ||||||||
\(815\) | −3.16357 | −0.110815 | ||||||||
\(816\) | −6.34143 | −0.221994 | ||||||||
\(817\) | −43.1823 | −1.51076 | ||||||||
\(818\) | 22.2891 | 0.779319 | ||||||||
\(819\) | 8.07337 | 0.282106 | ||||||||
\(820\) | −63.0316 | −2.20116 | ||||||||
\(821\) | −9.95255 | −0.347346 | −0.173673 | − | 0.984803i | \(-0.555564\pi\) | ||||
−0.173673 | + | 0.984803i | \(0.555564\pi\) | |||||||
\(822\) | 53.2980 | 1.85898 | ||||||||
\(823\) | −4.01530 | −0.139964 | −0.0699822 | − | 0.997548i | \(-0.522294\pi\) | ||||
−0.0699822 | + | 0.997548i | \(0.522294\pi\) | |||||||
\(824\) | −43.8679 | −1.52821 | ||||||||
\(825\) | −11.8702 | −0.413266 | ||||||||
\(826\) | 5.65290 | 0.196690 | ||||||||
\(827\) | 50.7656 | 1.76529 | 0.882646 | − | 0.470039i | \(-0.155760\pi\) | ||||
0.882646 | + | 0.470039i | \(0.155760\pi\) | |||||||
\(828\) | 57.2873 | 1.99087 | ||||||||
\(829\) | −15.7327 | −0.546418 | −0.273209 | − | 0.961955i | \(-0.588085\pi\) | ||||
−0.273209 | + | 0.961955i | \(0.588085\pi\) | |||||||
\(830\) | −31.1658 | −1.08178 | ||||||||
\(831\) | −1.01261 | −0.0351272 | ||||||||
\(832\) | 34.9650 | 1.21219 | ||||||||
\(833\) | −4.15515 | −0.143967 | ||||||||
\(834\) | 99.1436 | 3.43306 | ||||||||
\(835\) | 5.32128 | 0.184150 | ||||||||
\(836\) | 13.6753 | 0.472969 | ||||||||
\(837\) | −3.67620 | −0.127068 | ||||||||
\(838\) | −58.6053 | −2.02449 | ||||||||
\(839\) | 39.7538 | 1.37245 | 0.686227 | − | 0.727387i | \(-0.259266\pi\) | ||||
0.686227 | + | 0.727387i | \(0.259266\pi\) | |||||||
\(840\) | 21.7303 | 0.749766 | ||||||||
\(841\) | −28.6298 | −0.987236 | ||||||||
\(842\) | −80.8344 | −2.78574 | ||||||||
\(843\) | 55.5127 | 1.91196 | ||||||||
\(844\) | 16.3941 | 0.564308 | ||||||||
\(845\) | −21.9546 | −0.755261 | ||||||||
\(846\) | −71.9533 | −2.47381 | ||||||||
\(847\) | 5.61916 | 0.193077 | ||||||||
\(848\) | 1.36267 | 0.0467944 | ||||||||
\(849\) | −27.1736 | −0.932596 | ||||||||
\(850\) | −7.62754 | −0.261623 | ||||||||
\(851\) | −4.39121 | −0.150529 | ||||||||
\(852\) | −161.149 | −5.52088 | ||||||||
\(853\) | 27.1508 | 0.929625 | 0.464813 | − | 0.885409i | \(-0.346122\pi\) | ||||
0.464813 | + | 0.885409i | \(0.346122\pi\) | |||||||
\(854\) | 5.09551 | 0.174365 | ||||||||
\(855\) | −36.9481 | −1.26360 | ||||||||
\(856\) | 28.2222 | 0.964616 | ||||||||
\(857\) | 34.0867 | 1.16438 | 0.582189 | − | 0.813053i | \(-0.302196\pi\) | ||||
0.582189 | + | 0.813053i | \(0.302196\pi\) | |||||||
\(858\) | −25.9551 | −0.886092 | ||||||||
\(859\) | 24.4139 | 0.832992 | 0.416496 | − | 0.909137i | \(-0.363258\pi\) | ||||
0.416496 | + | 0.909137i | \(0.363258\pi\) | |||||||
\(860\) | 152.595 | 5.20346 | ||||||||
\(861\) | 6.90311 | 0.235257 | ||||||||
\(862\) | 34.1323 | 1.16255 | ||||||||
\(863\) | −45.0763 | −1.53441 | −0.767207 | − | 0.641400i | \(-0.778354\pi\) | ||||
−0.767207 | + | 0.641400i | \(0.778354\pi\) | |||||||
\(864\) | 0.0862807 | 0.00293533 | ||||||||
\(865\) | 53.7289 | 1.82684 | ||||||||
\(866\) | −25.4039 | −0.863260 | ||||||||
\(867\) | 41.5360 | 1.41064 | ||||||||
\(868\) | −13.1294 | −0.445642 | ||||||||
\(869\) | 15.3544 | 0.520864 | ||||||||
\(870\) | −11.8003 | −0.400069 | ||||||||
\(871\) | 0.897017 | 0.0303943 | ||||||||
\(872\) | −19.2561 | −0.652094 | ||||||||
\(873\) | −30.0368 | −1.01659 | ||||||||
\(874\) | −38.6979 | −1.30897 | ||||||||
\(875\) | 0.0143359 | 0.000484643 0 | ||||||||
\(876\) | −69.2562 | −2.33995 | ||||||||
\(877\) | −45.2647 | −1.52848 | −0.764240 | − | 0.644932i | \(-0.776886\pi\) | ||||
−0.764240 | + | 0.644932i | \(0.776886\pi\) | |||||||
\(878\) | −93.7989 | −3.16556 | ||||||||
\(879\) | −5.62639 | −0.189774 | ||||||||
\(880\) | −12.2499 | −0.412944 | ||||||||
\(881\) | −41.3400 | −1.39278 | −0.696390 | − | 0.717663i | \(-0.745212\pi\) | ||||
−0.696390 | + | 0.717663i | \(0.745212\pi\) | |||||||
\(882\) | 53.3259 | 1.79558 | ||||||||
\(883\) | 7.22939 | 0.243288 | 0.121644 | − | 0.992574i | \(-0.461183\pi\) | ||||
0.121644 | + | 0.992574i | \(0.461183\pi\) | |||||||
\(884\) | −11.1318 | −0.374403 | ||||||||
\(885\) | 32.7725 | 1.10163 | ||||||||
\(886\) | −70.2579 | −2.36036 | ||||||||
\(887\) | 24.7830 | 0.832132 | 0.416066 | − | 0.909334i | \(-0.363409\pi\) | ||||
0.416066 | + | 0.909334i | \(0.363409\pi\) | |||||||
\(888\) | −12.3478 | −0.414364 | ||||||||
\(889\) | 8.69615 | 0.291659 | ||||||||
\(890\) | −76.0887 | −2.55050 | ||||||||
\(891\) | −7.76197 | −0.260036 | ||||||||
\(892\) | 45.7652 | 1.53233 | ||||||||
\(893\) | 32.4410 | 1.08560 | ||||||||
\(894\) | −68.8250 | −2.30185 | ||||||||
\(895\) | −26.8258 | −0.896687 | ||||||||
\(896\) | −10.8356 | −0.361991 | ||||||||
\(897\) | 49.0216 | 1.63679 | ||||||||
\(898\) | −27.5956 | −0.920878 | ||||||||
\(899\) | 3.57734 | 0.119311 | ||||||||
\(900\) | 65.3358 | 2.17786 | ||||||||
\(901\) | 0.207204 | 0.00690297 | ||||||||
\(902\) | −11.5404 | −0.384254 | ||||||||
\(903\) | −16.7120 | −0.556140 | ||||||||
\(904\) | −72.2741 | −2.40380 | ||||||||
\(905\) | 76.4117 | 2.54001 | ||||||||
\(906\) | −122.482 | −4.06918 | ||||||||
\(907\) | −51.7026 | −1.71676 | −0.858378 | − | 0.513018i | \(-0.828527\pi\) | ||||
−0.858378 | + | 0.513018i | \(0.828527\pi\) | |||||||
\(908\) | −64.0099 | −2.12424 | ||||||||
\(909\) | 29.3012 | 0.971860 | ||||||||
\(910\) | 19.2717 | 0.638850 | ||||||||
\(911\) | 36.5303 | 1.21030 | 0.605152 | − | 0.796110i | \(-0.293112\pi\) | ||||
0.605152 | + | 0.796110i | \(0.293112\pi\) | |||||||
\(912\) | −36.6929 | −1.21502 | ||||||||
\(913\) | −3.80852 | −0.126043 | ||||||||
\(914\) | 37.7061 | 1.24721 | ||||||||
\(915\) | 29.5410 | 0.976596 | ||||||||
\(916\) | −43.4135 | −1.43442 | ||||||||
\(917\) | 0.215884 | 0.00712912 | ||||||||
\(918\) | 0.952224 | 0.0314281 | ||||||||
\(919\) | 23.0844 | 0.761483 | 0.380741 | − | 0.924682i | \(-0.375669\pi\) | ||||
0.380741 | + | 0.924682i | \(0.375669\pi\) | |||||||
\(920\) | 68.6131 | 2.26211 | ||||||||
\(921\) | −49.6722 | −1.63675 | ||||||||
\(922\) | −84.1700 | −2.77199 | ||||||||
\(923\) | −71.7078 | −2.36029 | ||||||||
\(924\) | 5.29247 | 0.174109 | ||||||||
\(925\) | −5.00815 | −0.164667 | ||||||||
\(926\) | 44.8759 | 1.47471 | ||||||||
\(927\) | 28.8666 | 0.948104 | ||||||||
\(928\) | −0.0839605 | −0.00275614 | ||||||||
\(929\) | 18.3149 | 0.600894 | 0.300447 | − | 0.953799i | \(-0.402864\pi\) | ||||
0.300447 | + | 0.953799i | \(0.402864\pi\) | |||||||
\(930\) | −114.043 | −3.73963 | ||||||||
\(931\) | −24.0426 | −0.787965 | ||||||||
\(932\) | −68.8290 | −2.25457 | ||||||||
\(933\) | 3.80656 | 0.124621 | ||||||||
\(934\) | −38.2564 | −1.25179 | ||||||||
\(935\) | −1.86268 | −0.0609162 | ||||||||
\(936\) | 71.6806 | 2.34295 | ||||||||
\(937\) | 36.4602 | 1.19110 | 0.595552 | − | 0.803317i | \(-0.296933\pi\) | ||||
0.595552 | + | 0.803317i | \(0.296933\pi\) | |||||||
\(938\) | −0.274045 | −0.00894788 | ||||||||
\(939\) | −39.5895 | −1.29195 | ||||||||
\(940\) | −114.638 | −3.73909 | ||||||||
\(941\) | −9.64613 | −0.314455 | −0.157227 | − | 0.987562i | \(-0.550256\pi\) | ||||
−0.157227 | + | 0.987562i | \(0.550256\pi\) | |||||||
\(942\) | −137.739 | −4.48779 | ||||||||
\(943\) | 21.7965 | 0.709791 | ||||||||
\(944\) | 16.9242 | 0.550836 | ||||||||
\(945\) | −1.10029 | −0.0357925 | ||||||||
\(946\) | 27.9386 | 0.908361 | ||||||||
\(947\) | 34.6949 | 1.12743 | 0.563717 | − | 0.825968i | \(-0.309371\pi\) | ||||
0.563717 | + | 0.825968i | \(0.309371\pi\) | |||||||
\(948\) | −162.525 | −5.27856 | ||||||||
\(949\) | −30.8175 | −1.00038 | ||||||||
\(950\) | −44.1347 | −1.43192 | ||||||||
\(951\) | 8.89269 | 0.288365 | ||||||||
\(952\) | 1.70636 | 0.0553035 | ||||||||
\(953\) | 46.4095 | 1.50335 | 0.751676 | − | 0.659533i | \(-0.229246\pi\) | ||||
0.751676 | + | 0.659533i | \(0.229246\pi\) | |||||||
\(954\) | −2.65919 | −0.0860946 | ||||||||
\(955\) | −50.6148 | −1.63785 | ||||||||
\(956\) | 81.0001 | 2.61973 | ||||||||
\(957\) | −1.44202 | −0.0466139 | ||||||||
\(958\) | −18.8677 | −0.609586 | ||||||||
\(959\) | −4.83599 | −0.156162 | ||||||||
\(960\) | −61.9288 | −1.99874 | ||||||||
\(961\) | 3.57283 | 0.115253 | ||||||||
\(962\) | −10.9507 | −0.353066 | ||||||||
\(963\) | −18.5712 | −0.598449 | ||||||||
\(964\) | 27.5854 | 0.888465 | ||||||||
\(965\) | −67.7163 | −2.17986 | ||||||||
\(966\) | −14.9765 | −0.481860 | ||||||||
\(967\) | 34.3735 | 1.10538 | 0.552689 | − | 0.833388i | \(-0.313602\pi\) | ||||
0.552689 | + | 0.833388i | \(0.313602\pi\) | |||||||
\(968\) | 49.8905 | 1.60354 | ||||||||
\(969\) | −5.57941 | −0.179237 | ||||||||
\(970\) | −71.6998 | −2.30214 | ||||||||
\(971\) | −48.1365 | −1.54477 | −0.772387 | − | 0.635152i | \(-0.780937\pi\) | ||||
−0.772387 | + | 0.635152i | \(0.780937\pi\) | |||||||
\(972\) | 89.6884 | 2.87676 | ||||||||
\(973\) | −8.99578 | −0.288391 | ||||||||
\(974\) | 90.2638 | 2.89224 | ||||||||
\(975\) | 55.9089 | 1.79052 | ||||||||
\(976\) | 15.2554 | 0.488314 | ||||||||
\(977\) | −41.0575 | −1.31355 | −0.656773 | − | 0.754089i | \(-0.728079\pi\) | ||||
−0.656773 | + | 0.754089i | \(0.728079\pi\) | |||||||
\(978\) | 6.13092 | 0.196045 | ||||||||
\(979\) | −9.29817 | −0.297171 | ||||||||
\(980\) | 84.9606 | 2.71397 | ||||||||
\(981\) | 12.6712 | 0.404560 | ||||||||
\(982\) | −40.1041 | −1.27977 | ||||||||
\(983\) | −0.291337 | −0.00929220 | −0.00464610 | − | 0.999989i | \(-0.501479\pi\) | ||||
−0.00464610 | + | 0.999989i | \(0.501479\pi\) | |||||||
\(984\) | 61.2902 | 1.95386 | ||||||||
\(985\) | 52.9400 | 1.68681 | ||||||||
\(986\) | −0.926616 | −0.0295095 | ||||||||
\(987\) | 12.5550 | 0.399630 | ||||||||
\(988\) | −64.4111 | −2.04919 | ||||||||
\(989\) | −52.7679 | −1.67792 | ||||||||
\(990\) | 23.9051 | 0.759754 | ||||||||
\(991\) | −35.8599 | −1.13913 | −0.569563 | − | 0.821948i | \(-0.692888\pi\) | ||||
−0.569563 | + | 0.821948i | \(0.692888\pi\) | |||||||
\(992\) | −0.811428 | −0.0257629 | ||||||||
\(993\) | 67.1416 | 2.13068 | ||||||||
\(994\) | 21.9072 | 0.694855 | ||||||||
\(995\) | 63.7069 | 2.01964 | ||||||||
\(996\) | 40.3127 | 1.27736 | ||||||||
\(997\) | 28.4075 | 0.899673 | 0.449837 | − | 0.893111i | \(-0.351482\pi\) | ||||
0.449837 | + | 0.893111i | \(0.351482\pi\) | |||||||
\(998\) | −54.6020 | −1.72840 | ||||||||
\(999\) | 0.625218 | 0.0197810 |
(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 | 6031.2.a.d.1.10 | ✓ | 133 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6031.2.a.d.1.10 | ✓ | 133 | 1.1 | even | 1 | trivial |