Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 14 x^{14} + 68 x^{13} + 64 x^{12} - 456 x^{11} - 54 x^{10} + 1532 x^{9} - 400 x^{8} + \cdots - 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(-0.404293\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.404293 | 0.285878 | 0.142939 | − | 0.989731i | \(-0.454345\pi\) | ||||
0.142939 | + | 0.989731i | \(0.454345\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.83655 | −0.918274 | ||||||||
\(5\) | −3.62653 | −1.62183 | −0.810917 | − | 0.585162i | \(-0.801031\pi\) | ||||
−0.810917 | + | 0.585162i | \(0.801031\pi\) | |||||||
\(6\) | 0.404293 | 0.165052 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.55109 | −0.548393 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.46618 | −0.463647 | ||||||||
\(11\) | −5.64899 | −1.70323 | −0.851617 | − | 0.524165i | \(-0.824377\pi\) | ||||
−0.851617 | + | 0.524165i | \(0.824377\pi\) | |||||||
\(12\) | −1.83655 | −0.530166 | ||||||||
\(13\) | 4.03783 | 1.11989 | 0.559946 | − | 0.828529i | \(-0.310822\pi\) | ||||
0.559946 | + | 0.828529i | \(0.310822\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.62653 | −0.936366 | ||||||||
\(16\) | 3.04600 | 0.761500 | ||||||||
\(17\) | 2.00918 | 0.487297 | 0.243649 | − | 0.969864i | \(-0.421656\pi\) | ||||
0.243649 | + | 0.969864i | \(0.421656\pi\) | |||||||
\(18\) | 0.404293 | 0.0952928 | ||||||||
\(19\) | −1.50889 | −0.346163 | −0.173081 | − | 0.984908i | \(-0.555372\pi\) | ||||
−0.173081 | + | 0.984908i | \(0.555372\pi\) | |||||||
\(20\) | 6.66029 | 1.48929 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.28385 | −0.486917 | ||||||||
\(23\) | 7.05059 | 1.47015 | 0.735075 | − | 0.677986i | \(-0.237147\pi\) | ||||
0.735075 | + | 0.677986i | \(0.237147\pi\) | |||||||
\(24\) | −1.55109 | −0.316615 | ||||||||
\(25\) | 8.15172 | 1.63034 | ||||||||
\(26\) | 1.63246 | 0.320153 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.14414 | 0.955242 | 0.477621 | − | 0.878566i | \(-0.341499\pi\) | ||||
0.477621 | + | 0.878566i | \(0.341499\pi\) | |||||||
\(30\) | −1.46618 | −0.267687 | ||||||||
\(31\) | −3.25825 | −0.585199 | −0.292600 | − | 0.956235i | \(-0.594520\pi\) | ||||
−0.292600 | + | 0.956235i | \(0.594520\pi\) | |||||||
\(32\) | 4.33365 | 0.766089 | ||||||||
\(33\) | −5.64899 | −0.983362 | ||||||||
\(34\) | 0.812296 | 0.139308 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.83655 | −0.306091 | ||||||||
\(37\) | 0.612983 | 0.100774 | 0.0503869 | − | 0.998730i | \(-0.483955\pi\) | ||||
0.0503869 | + | 0.998730i | \(0.483955\pi\) | |||||||
\(38\) | −0.610033 | −0.0989604 | ||||||||
\(39\) | 4.03783 | 0.646570 | ||||||||
\(40\) | 5.62507 | 0.889402 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.57300 | 0.239881 | 0.119940 | − | 0.992781i | \(-0.461730\pi\) | ||||
0.119940 | + | 0.992781i | \(0.461730\pi\) | |||||||
\(44\) | 10.3746 | 1.56403 | ||||||||
\(45\) | −3.62653 | −0.540611 | ||||||||
\(46\) | 2.85050 | 0.420284 | ||||||||
\(47\) | 0.256386 | 0.0373977 | 0.0186989 | − | 0.999825i | \(-0.494048\pi\) | ||||
0.0186989 | + | 0.999825i | \(0.494048\pi\) | |||||||
\(48\) | 3.04600 | 0.439652 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.29568 | 0.466080 | ||||||||
\(51\) | 2.00918 | 0.281341 | ||||||||
\(52\) | −7.41566 | −1.02837 | ||||||||
\(53\) | −7.87725 | −1.08202 | −0.541012 | − | 0.841015i | \(-0.681959\pi\) | ||||
−0.541012 | + | 0.841015i | \(0.681959\pi\) | |||||||
\(54\) | 0.404293 | 0.0550173 | ||||||||
\(55\) | 20.4862 | 2.76236 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.50889 | −0.199857 | ||||||||
\(58\) | 2.07974 | 0.273083 | ||||||||
\(59\) | −4.32499 | −0.563066 | −0.281533 | − | 0.959552i | \(-0.590843\pi\) | ||||
−0.281533 | + | 0.959552i | \(0.590843\pi\) | |||||||
\(60\) | 6.66029 | 0.859840 | ||||||||
\(61\) | 2.81546 | 0.360483 | 0.180242 | − | 0.983622i | \(-0.442312\pi\) | ||||
0.180242 | + | 0.983622i | \(0.442312\pi\) | |||||||
\(62\) | −1.31729 | −0.167296 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.33993 | −0.542492 | ||||||||
\(65\) | −14.6433 | −1.81628 | ||||||||
\(66\) | −2.28385 | −0.281122 | ||||||||
\(67\) | −13.3202 | −1.62732 | −0.813659 | − | 0.581342i | \(-0.802528\pi\) | ||||
−0.813659 | + | 0.581342i | \(0.802528\pi\) | |||||||
\(68\) | −3.68995 | −0.447472 | ||||||||
\(69\) | 7.05059 | 0.848791 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.92409 | 0.347026 | 0.173513 | − | 0.984832i | \(-0.444488\pi\) | ||||
0.173513 | + | 0.984832i | \(0.444488\pi\) | |||||||
\(72\) | −1.55109 | −0.182798 | ||||||||
\(73\) | 5.90098 | 0.690657 | 0.345329 | − | 0.938482i | \(-0.387767\pi\) | ||||
0.345329 | + | 0.938482i | \(0.387767\pi\) | |||||||
\(74\) | 0.247825 | 0.0288090 | ||||||||
\(75\) | 8.15172 | 0.941280 | ||||||||
\(76\) | 2.77114 | 0.317872 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.63246 | 0.184840 | ||||||||
\(79\) | −1.04645 | −0.117735 | −0.0588674 | − | 0.998266i | \(-0.518749\pi\) | ||||
−0.0588674 | + | 0.998266i | \(0.518749\pi\) | |||||||
\(80\) | −11.0464 | −1.23503 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.404293 | 0.0446467 | ||||||||
\(83\) | −10.3790 | −1.13925 | −0.569623 | − | 0.821906i | \(-0.692911\pi\) | ||||
−0.569623 | + | 0.821906i | \(0.692911\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.28634 | −0.790315 | ||||||||
\(86\) | 0.635955 | 0.0685767 | ||||||||
\(87\) | 5.14414 | 0.551509 | ||||||||
\(88\) | 8.76208 | 0.934041 | ||||||||
\(89\) | 9.74008 | 1.03245 | 0.516223 | − | 0.856454i | \(-0.327338\pi\) | ||||
0.516223 | + | 0.856454i | \(0.327338\pi\) | |||||||
\(90\) | −1.46618 | −0.154549 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −12.9487 | −1.35000 | ||||||||
\(93\) | −3.25825 | −0.337865 | ||||||||
\(94\) | 0.103655 | 0.0106912 | ||||||||
\(95\) | 5.47203 | 0.561418 | ||||||||
\(96\) | 4.33365 | 0.442302 | ||||||||
\(97\) | −8.22998 | −0.835628 | −0.417814 | − | 0.908533i | \(-0.637204\pi\) | ||||
−0.417814 | + | 0.908533i | \(0.637204\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.64899 | −0.567744 | ||||||||
\(100\) | −14.9710 | −1.49710 | ||||||||
\(101\) | 13.1011 | 1.30361 | 0.651806 | − | 0.758386i | \(-0.274012\pi\) | ||||
0.651806 | + | 0.758386i | \(0.274012\pi\) | |||||||
\(102\) | 0.812296 | 0.0804293 | ||||||||
\(103\) | 12.0801 | 1.19029 | 0.595143 | − | 0.803620i | \(-0.297095\pi\) | ||||
0.595143 | + | 0.803620i | \(0.297095\pi\) | |||||||
\(104\) | −6.26303 | −0.614140 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.18472 | −0.309327 | ||||||||
\(107\) | −10.0504 | −0.971613 | −0.485806 | − | 0.874066i | \(-0.661474\pi\) | ||||
−0.485806 | + | 0.874066i | \(0.661474\pi\) | |||||||
\(108\) | −1.83655 | −0.176722 | ||||||||
\(109\) | −11.8153 | −1.13170 | −0.565849 | − | 0.824509i | \(-0.691451\pi\) | ||||
−0.565849 | + | 0.824509i | \(0.691451\pi\) | |||||||
\(110\) | 8.28243 | 0.789699 | ||||||||
\(111\) | 0.612983 | 0.0581818 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.5214 | −1.74235 | −0.871173 | − | 0.490976i | \(-0.836640\pi\) | ||||
−0.871173 | + | 0.490976i | \(0.836640\pi\) | |||||||
\(114\) | −0.610033 | −0.0571348 | ||||||||
\(115\) | −25.5692 | −2.38434 | ||||||||
\(116\) | −9.44745 | −0.877174 | ||||||||
\(117\) | 4.03783 | 0.373297 | ||||||||
\(118\) | −1.74856 | −0.160968 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 5.62507 | 0.513496 | ||||||||
\(121\) | 20.9110 | 1.90100 | ||||||||
\(122\) | 1.13827 | 0.103054 | ||||||||
\(123\) | 1.00000 | 0.0901670 | ||||||||
\(124\) | 5.98393 | 0.537373 | ||||||||
\(125\) | −11.4298 | −1.02231 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.16826 | 0.724816 | 0.362408 | − | 0.932020i | \(-0.381955\pi\) | ||||
0.362408 | + | 0.932020i | \(0.381955\pi\) | |||||||
\(128\) | −10.4219 | −0.921176 | ||||||||
\(129\) | 1.57300 | 0.138495 | ||||||||
\(130\) | −5.92018 | −0.519234 | ||||||||
\(131\) | −13.2261 | −1.15557 | −0.577786 | − | 0.816188i | \(-0.696083\pi\) | ||||
−0.577786 | + | 0.816188i | \(0.696083\pi\) | |||||||
\(132\) | 10.3746 | 0.902996 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −5.38525 | −0.465215 | ||||||||
\(135\) | −3.62653 | −0.312122 | ||||||||
\(136\) | −3.11641 | −0.267230 | ||||||||
\(137\) | −17.1227 | −1.46289 | −0.731447 | − | 0.681898i | \(-0.761155\pi\) | ||||
−0.731447 | + | 0.681898i | \(0.761155\pi\) | |||||||
\(138\) | 2.85050 | 0.242651 | ||||||||
\(139\) | 18.7120 | 1.58713 | 0.793565 | − | 0.608485i | \(-0.208223\pi\) | ||||
0.793565 | + | 0.608485i | \(0.208223\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.256386 | 0.0215916 | ||||||||
\(142\) | 1.18219 | 0.0992071 | ||||||||
\(143\) | −22.8096 | −1.90744 | ||||||||
\(144\) | 3.04600 | 0.253833 | ||||||||
\(145\) | −18.6554 | −1.54924 | ||||||||
\(146\) | 2.38572 | 0.197444 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.12577 | −0.0925379 | ||||||||
\(149\) | −14.4114 | −1.18063 | −0.590313 | − | 0.807175i | \(-0.700996\pi\) | ||||
−0.590313 | + | 0.807175i | \(0.700996\pi\) | |||||||
\(150\) | 3.29568 | 0.269091 | ||||||||
\(151\) | −7.70354 | −0.626905 | −0.313452 | − | 0.949604i | \(-0.601486\pi\) | ||||
−0.313452 | + | 0.949604i | \(0.601486\pi\) | |||||||
\(152\) | 2.34042 | 0.189833 | ||||||||
\(153\) | 2.00918 | 0.162432 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.8161 | 0.949096 | ||||||||
\(156\) | −7.41566 | −0.593728 | ||||||||
\(157\) | 0.429607 | 0.0342864 | 0.0171432 | − | 0.999853i | \(-0.494543\pi\) | ||||
0.0171432 | + | 0.999853i | \(0.494543\pi\) | |||||||
\(158\) | −0.423072 | −0.0336578 | ||||||||
\(159\) | −7.87725 | −0.624707 | ||||||||
\(160\) | −15.7161 | −1.24247 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.404293 | 0.0317643 | ||||||||
\(163\) | 20.8708 | 1.63472 | 0.817362 | − | 0.576125i | \(-0.195436\pi\) | ||||
0.817362 | + | 0.576125i | \(0.195436\pi\) | |||||||
\(164\) | −1.83655 | −0.143410 | ||||||||
\(165\) | 20.4862 | 1.59485 | ||||||||
\(166\) | −4.19617 | −0.325686 | ||||||||
\(167\) | −15.9352 | −1.23310 | −0.616552 | − | 0.787314i | \(-0.711471\pi\) | ||||
−0.616552 | + | 0.787314i | \(0.711471\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.30404 | 0.254157 | ||||||||
\(170\) | −2.94582 | −0.225934 | ||||||||
\(171\) | −1.50889 | −0.115388 | ||||||||
\(172\) | −2.88890 | −0.220276 | ||||||||
\(173\) | −5.12594 | −0.389718 | −0.194859 | − | 0.980831i | \(-0.562425\pi\) | ||||
−0.194859 | + | 0.980831i | \(0.562425\pi\) | |||||||
\(174\) | 2.07974 | 0.157665 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −17.2068 | −1.29701 | ||||||||
\(177\) | −4.32499 | −0.325086 | ||||||||
\(178\) | 3.93785 | 0.295154 | ||||||||
\(179\) | −5.22886 | −0.390823 | −0.195412 | − | 0.980721i | \(-0.562604\pi\) | ||||
−0.195412 | + | 0.980721i | \(0.562604\pi\) | |||||||
\(180\) | 6.66029 | 0.496429 | ||||||||
\(181\) | 1.60946 | 0.119630 | 0.0598150 | − | 0.998209i | \(-0.480949\pi\) | ||||
0.0598150 | + | 0.998209i | \(0.480949\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.81546 | 0.208125 | ||||||||
\(184\) | −10.9361 | −0.806219 | ||||||||
\(185\) | −2.22300 | −0.163438 | ||||||||
\(186\) | −1.31729 | −0.0965883 | ||||||||
\(187\) | −11.3498 | −0.829981 | ||||||||
\(188\) | −0.470865 | −0.0343413 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.21230 | 0.160497 | ||||||||
\(191\) | −25.0344 | −1.81142 | −0.905712 | − | 0.423893i | \(-0.860663\pi\) | ||||
−0.905712 | + | 0.423893i | \(0.860663\pi\) | |||||||
\(192\) | −4.33993 | −0.313208 | ||||||||
\(193\) | −2.83996 | −0.204425 | −0.102212 | − | 0.994763i | \(-0.532592\pi\) | ||||
−0.102212 | + | 0.994763i | \(0.532592\pi\) | |||||||
\(194\) | −3.32732 | −0.238888 | ||||||||
\(195\) | −14.6433 | −1.04863 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −26.8159 | −1.91056 | −0.955278 | − | 0.295709i | \(-0.904444\pi\) | ||||
−0.955278 | + | 0.295709i | \(0.904444\pi\) | |||||||
\(198\) | −2.28385 | −0.162306 | ||||||||
\(199\) | −7.39204 | −0.524008 | −0.262004 | − | 0.965067i | \(-0.584383\pi\) | ||||
−0.262004 | + | 0.965067i | \(0.584383\pi\) | |||||||
\(200\) | −12.6440 | −0.894069 | ||||||||
\(201\) | −13.3202 | −0.939533 | ||||||||
\(202\) | 5.29670 | 0.372674 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −3.68995 | −0.258348 | ||||||||
\(205\) | −3.62653 | −0.253288 | ||||||||
\(206\) | 4.88389 | 0.340277 | ||||||||
\(207\) | 7.05059 | 0.490050 | ||||||||
\(208\) | 12.2992 | 0.852797 | ||||||||
\(209\) | 8.52369 | 0.589596 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.3498 | 1.53862 | 0.769311 | − | 0.638875i | \(-0.220600\pi\) | ||||
0.769311 | + | 0.638875i | \(0.220600\pi\) | |||||||
\(212\) | 14.4669 | 0.993594 | ||||||||
\(213\) | 2.92409 | 0.200355 | ||||||||
\(214\) | −4.06332 | −0.277763 | ||||||||
\(215\) | −5.70455 | −0.389047 | ||||||||
\(216\) | −1.55109 | −0.105538 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −4.77683 | −0.323528 | ||||||||
\(219\) | 5.90098 | 0.398751 | ||||||||
\(220\) | −37.6239 | −2.53660 | ||||||||
\(221\) | 8.11271 | 0.545720 | ||||||||
\(222\) | 0.247825 | 0.0166329 | ||||||||
\(223\) | 28.5254 | 1.91020 | 0.955102 | − | 0.296276i | \(-0.0957449\pi\) | ||||
0.955102 | + | 0.296276i | \(0.0957449\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.15172 | 0.543448 | ||||||||
\(226\) | −7.48807 | −0.498099 | ||||||||
\(227\) | 23.9051 | 1.58664 | 0.793319 | − | 0.608807i | \(-0.208351\pi\) | ||||
0.793319 | + | 0.608807i | \(0.208351\pi\) | |||||||
\(228\) | 2.77114 | 0.183524 | ||||||||
\(229\) | −5.21232 | −0.344440 | −0.172220 | − | 0.985059i | \(-0.555094\pi\) | ||||
−0.172220 | + | 0.985059i | \(0.555094\pi\) | |||||||
\(230\) | −10.3374 | −0.681630 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.97902 | −0.523848 | ||||||||
\(233\) | −22.9871 | −1.50594 | −0.752969 | − | 0.658056i | \(-0.771379\pi\) | ||||
−0.752969 | + | 0.658056i | \(0.771379\pi\) | |||||||
\(234\) | 1.63246 | 0.106718 | ||||||||
\(235\) | −0.929791 | −0.0606529 | ||||||||
\(236\) | 7.94305 | 0.517049 | ||||||||
\(237\) | −1.04645 | −0.0679742 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 30.5972 | 1.97917 | 0.989584 | − | 0.143959i | \(-0.0459832\pi\) | ||||
0.989584 | + | 0.143959i | \(0.0459832\pi\) | |||||||
\(240\) | −11.0464 | −0.713043 | ||||||||
\(241\) | −14.3324 | −0.923232 | −0.461616 | − | 0.887080i | \(-0.652730\pi\) | ||||
−0.461616 | + | 0.887080i | \(0.652730\pi\) | |||||||
\(242\) | 8.45419 | 0.543456 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −5.17073 | −0.331022 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.404293 | 0.0257768 | ||||||||
\(247\) | −6.09263 | −0.387665 | ||||||||
\(248\) | 5.05384 | 0.320919 | ||||||||
\(249\) | −10.3790 | −0.657744 | ||||||||
\(250\) | −4.62099 | −0.292257 | ||||||||
\(251\) | −13.7477 | −0.867746 | −0.433873 | − | 0.900974i | \(-0.642853\pi\) | ||||
−0.433873 | + | 0.900974i | \(0.642853\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −39.8287 | −2.50401 | ||||||||
\(254\) | 3.30237 | 0.207209 | ||||||||
\(255\) | −7.28634 | −0.456289 | ||||||||
\(256\) | 4.46636 | 0.279148 | ||||||||
\(257\) | 12.4136 | 0.774340 | 0.387170 | − | 0.922008i | \(-0.373453\pi\) | ||||
0.387170 | + | 0.922008i | \(0.373453\pi\) | |||||||
\(258\) | 0.635955 | 0.0395928 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 26.8931 | 1.66784 | ||||||||
\(261\) | 5.14414 | 0.318414 | ||||||||
\(262\) | −5.34723 | −0.330353 | ||||||||
\(263\) | 21.1795 | 1.30599 | 0.652993 | − | 0.757364i | \(-0.273513\pi\) | ||||
0.652993 | + | 0.757364i | \(0.273513\pi\) | |||||||
\(264\) | 8.76208 | 0.539269 | ||||||||
\(265\) | 28.5671 | 1.75486 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.74008 | 0.596083 | ||||||||
\(268\) | 24.4631 | 1.49432 | ||||||||
\(269\) | 5.56435 | 0.339264 | 0.169632 | − | 0.985507i | \(-0.445742\pi\) | ||||
0.169632 | + | 0.985507i | \(0.445742\pi\) | |||||||
\(270\) | −1.46618 | −0.0892289 | ||||||||
\(271\) | 11.2067 | 0.680762 | 0.340381 | − | 0.940288i | \(-0.389444\pi\) | ||||
0.340381 | + | 0.940288i | \(0.389444\pi\) | |||||||
\(272\) | 6.11996 | 0.371077 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.92260 | −0.418210 | ||||||||
\(275\) | −46.0489 | −2.77686 | ||||||||
\(276\) | −12.9487 | −0.779422 | ||||||||
\(277\) | 9.16881 | 0.550900 | 0.275450 | − | 0.961315i | \(-0.411173\pi\) | ||||
0.275450 | + | 0.961315i | \(0.411173\pi\) | |||||||
\(278\) | 7.56513 | 0.453726 | ||||||||
\(279\) | −3.25825 | −0.195066 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.2196 | 1.26585 | 0.632927 | − | 0.774212i | \(-0.281853\pi\) | ||||
0.632927 | + | 0.774212i | \(0.281853\pi\) | |||||||
\(282\) | 0.103655 | 0.00617256 | ||||||||
\(283\) | 4.61530 | 0.274351 | 0.137176 | − | 0.990547i | \(-0.456198\pi\) | ||||
0.137176 | + | 0.990547i | \(0.456198\pi\) | |||||||
\(284\) | −5.37023 | −0.318665 | ||||||||
\(285\) | 5.47203 | 0.324135 | ||||||||
\(286\) | −9.22177 | −0.545295 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 4.33365 | 0.255363 | ||||||||
\(289\) | −12.9632 | −0.762541 | ||||||||
\(290\) | −7.54223 | −0.442895 | ||||||||
\(291\) | −8.22998 | −0.482450 | ||||||||
\(292\) | −10.8374 | −0.634212 | ||||||||
\(293\) | −4.86448 | −0.284186 | −0.142093 | − | 0.989853i | \(-0.545383\pi\) | ||||
−0.142093 | + | 0.989853i | \(0.545383\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.6847 | 0.913199 | ||||||||
\(296\) | −0.950791 | −0.0552636 | ||||||||
\(297\) | −5.64899 | −0.327787 | ||||||||
\(298\) | −5.82642 | −0.337515 | ||||||||
\(299\) | 28.4691 | 1.64641 | ||||||||
\(300\) | −14.9710 | −0.864352 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3.11449 | −0.179219 | ||||||||
\(303\) | 13.1011 | 0.752641 | ||||||||
\(304\) | −4.59607 | −0.263603 | ||||||||
\(305\) | −10.2104 | −0.584644 | ||||||||
\(306\) | 0.812296 | 0.0464359 | ||||||||
\(307\) | −5.00629 | −0.285724 | −0.142862 | − | 0.989743i | \(-0.545631\pi\) | ||||
−0.142862 | + | 0.989743i | \(0.545631\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.0801 | 0.687212 | ||||||||
\(310\) | 4.77719 | 0.271326 | ||||||||
\(311\) | −13.3816 | −0.758804 | −0.379402 | − | 0.925232i | \(-0.623870\pi\) | ||||
−0.379402 | + | 0.925232i | \(0.623870\pi\) | |||||||
\(312\) | −6.26303 | −0.354574 | ||||||||
\(313\) | −14.0907 | −0.796451 | −0.398225 | − | 0.917288i | \(-0.630374\pi\) | ||||
−0.398225 | + | 0.917288i | \(0.630374\pi\) | |||||||
\(314\) | 0.173687 | 0.00980173 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.92185 | 0.108113 | ||||||||
\(317\) | −0.790011 | −0.0443714 | −0.0221857 | − | 0.999754i | \(-0.507063\pi\) | ||||
−0.0221857 | + | 0.999754i | \(0.507063\pi\) | |||||||
\(318\) | −3.18472 | −0.178590 | ||||||||
\(319\) | −29.0592 | −1.62700 | ||||||||
\(320\) | 15.7389 | 0.879831 | ||||||||
\(321\) | −10.0504 | −0.560961 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.03162 | −0.168684 | ||||||||
\(324\) | −1.83655 | −0.102030 | ||||||||
\(325\) | 32.9152 | 1.82581 | ||||||||
\(326\) | 8.43790 | 0.467332 | ||||||||
\(327\) | −11.8153 | −0.653386 | ||||||||
\(328\) | −1.55109 | −0.0856446 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 8.28243 | 0.455933 | ||||||||
\(331\) | 4.79253 | 0.263421 | 0.131711 | − | 0.991288i | \(-0.457953\pi\) | ||||
0.131711 | + | 0.991288i | \(0.457953\pi\) | |||||||
\(332\) | 19.0616 | 1.04614 | ||||||||
\(333\) | 0.612983 | 0.0335913 | ||||||||
\(334\) | −6.44250 | −0.352518 | ||||||||
\(335\) | 48.3060 | 2.63924 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.66846 | −0.254307 | −0.127153 | − | 0.991883i | \(-0.540584\pi\) | ||||
−0.127153 | + | 0.991883i | \(0.540584\pi\) | |||||||
\(338\) | 1.33580 | 0.0726580 | ||||||||
\(339\) | −18.5214 | −1.00594 | ||||||||
\(340\) | 13.3817 | 0.725725 | ||||||||
\(341\) | 18.4058 | 0.996731 | ||||||||
\(342\) | −0.610033 | −0.0329868 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2.43987 | −0.131549 | ||||||||
\(345\) | −25.5692 | −1.37660 | ||||||||
\(346\) | −2.07238 | −0.111412 | ||||||||
\(347\) | −24.1667 | −1.29734 | −0.648668 | − | 0.761072i | \(-0.724673\pi\) | ||||
−0.648668 | + | 0.761072i | \(0.724673\pi\) | |||||||
\(348\) | −9.44745 | −0.506437 | ||||||||
\(349\) | −23.7131 | −1.26933 | −0.634665 | − | 0.772787i | \(-0.718862\pi\) | ||||
−0.634665 | + | 0.772787i | \(0.718862\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.03783 | 0.215523 | ||||||||
\(352\) | −24.4808 | −1.30483 | ||||||||
\(353\) | −8.89299 | −0.473326 | −0.236663 | − | 0.971592i | \(-0.576054\pi\) | ||||
−0.236663 | + | 0.971592i | \(0.576054\pi\) | |||||||
\(354\) | −1.74856 | −0.0929351 | ||||||||
\(355\) | −10.6043 | −0.562818 | ||||||||
\(356\) | −17.8881 | −0.948068 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.11399 | −0.111728 | ||||||||
\(359\) | −21.1936 | −1.11856 | −0.559278 | − | 0.828980i | \(-0.688922\pi\) | ||||
−0.559278 | + | 0.828980i | \(0.688922\pi\) | |||||||
\(360\) | 5.62507 | 0.296467 | ||||||||
\(361\) | −16.7233 | −0.880171 | ||||||||
\(362\) | 0.650692 | 0.0341996 | ||||||||
\(363\) | 20.9110 | 1.09754 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −21.4001 | −1.12013 | ||||||||
\(366\) | 1.13827 | 0.0594984 | ||||||||
\(367\) | 21.4776 | 1.12112 | 0.560560 | − | 0.828114i | \(-0.310586\pi\) | ||||
0.560560 | + | 0.828114i | \(0.310586\pi\) | |||||||
\(368\) | 21.4761 | 1.11952 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | −0.898743 | −0.0467234 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 5.98393 | 0.310253 | ||||||||
\(373\) | −37.7164 | −1.95288 | −0.976442 | − | 0.215781i | \(-0.930770\pi\) | ||||
−0.976442 | + | 0.215781i | \(0.930770\pi\) | |||||||
\(374\) | −4.58865 | −0.237273 | ||||||||
\(375\) | −11.4298 | −0.590233 | ||||||||
\(376\) | −0.397677 | −0.0205086 | ||||||||
\(377\) | 20.7711 | 1.06977 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.8102 | −0.812115 | −0.406057 | − | 0.913848i | \(-0.633097\pi\) | ||||
−0.406057 | + | 0.913848i | \(0.633097\pi\) | |||||||
\(380\) | −10.0496 | −0.515536 | ||||||||
\(381\) | 8.16826 | 0.418472 | ||||||||
\(382\) | −10.1212 | −0.517847 | ||||||||
\(383\) | 17.8178 | 0.910449 | 0.455225 | − | 0.890377i | \(-0.349559\pi\) | ||||
0.455225 | + | 0.890377i | \(0.349559\pi\) | |||||||
\(384\) | −10.4219 | −0.531841 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.14818 | −0.0584406 | ||||||||
\(387\) | 1.57300 | 0.0799603 | ||||||||
\(388\) | 15.1147 | 0.767335 | ||||||||
\(389\) | −35.3148 | −1.79053 | −0.895265 | − | 0.445534i | \(-0.853014\pi\) | ||||
−0.895265 | + | 0.445534i | \(0.853014\pi\) | |||||||
\(390\) | −5.92018 | −0.299780 | ||||||||
\(391\) | 14.1659 | 0.716400 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.2261 | −0.667170 | ||||||||
\(394\) | −10.8415 | −0.546186 | ||||||||
\(395\) | 3.79498 | 0.190946 | ||||||||
\(396\) | 10.3746 | 0.521345 | ||||||||
\(397\) | −5.29392 | −0.265694 | −0.132847 | − | 0.991137i | \(-0.542412\pi\) | ||||
−0.132847 | + | 0.991137i | \(0.542412\pi\) | |||||||
\(398\) | −2.98855 | −0.149802 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 24.8301 | 1.24151 | ||||||||
\(401\) | −29.3969 | −1.46801 | −0.734005 | − | 0.679144i | \(-0.762351\pi\) | ||||
−0.734005 | + | 0.679144i | \(0.762351\pi\) | |||||||
\(402\) | −5.38525 | −0.268592 | ||||||||
\(403\) | −13.1563 | −0.655360 | ||||||||
\(404\) | −24.0609 | −1.19707 | ||||||||
\(405\) | −3.62653 | −0.180204 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.46273 | −0.171641 | ||||||||
\(408\) | −3.11641 | −0.154285 | ||||||||
\(409\) | −21.6968 | −1.07284 | −0.536419 | − | 0.843952i | \(-0.680223\pi\) | ||||
−0.536419 | + | 0.843952i | \(0.680223\pi\) | |||||||
\(410\) | −1.46618 | −0.0724095 | ||||||||
\(411\) | −17.1227 | −0.844602 | ||||||||
\(412\) | −22.1856 | −1.09301 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 2.85050 | 0.140095 | ||||||||
\(415\) | 37.6398 | 1.84767 | ||||||||
\(416\) | 17.4985 | 0.857937 | ||||||||
\(417\) | 18.7120 | 0.916330 | ||||||||
\(418\) | 3.44607 | 0.168553 | ||||||||
\(419\) | 1.07735 | 0.0526321 | 0.0263161 | − | 0.999654i | \(-0.491622\pi\) | ||||
0.0263161 | + | 0.999654i | \(0.491622\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.8444 | −0.918418 | −0.459209 | − | 0.888328i | \(-0.651867\pi\) | ||||
−0.459209 | + | 0.888328i | \(0.651867\pi\) | |||||||
\(422\) | 9.03586 | 0.439859 | ||||||||
\(423\) | 0.256386 | 0.0124659 | ||||||||
\(424\) | 12.2183 | 0.593374 | ||||||||
\(425\) | 16.3783 | 0.794462 | ||||||||
\(426\) | 1.18219 | 0.0572773 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 18.4581 | 0.892206 | ||||||||
\(429\) | −22.8096 | −1.10126 | ||||||||
\(430\) | −2.30631 | −0.111220 | ||||||||
\(431\) | 21.2760 | 1.02483 | 0.512414 | − | 0.858739i | \(-0.328751\pi\) | ||||
0.512414 | + | 0.858739i | \(0.328751\pi\) | |||||||
\(432\) | 3.04600 | 0.146551 | ||||||||
\(433\) | 36.1242 | 1.73602 | 0.868010 | − | 0.496546i | \(-0.165399\pi\) | ||||
0.868010 | + | 0.496546i | \(0.165399\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −18.6554 | −0.894457 | ||||||||
\(436\) | 21.6993 | 1.03921 | ||||||||
\(437\) | −10.6385 | −0.508911 | ||||||||
\(438\) | 2.38572 | 0.113994 | ||||||||
\(439\) | 24.0930 | 1.14989 | 0.574947 | − | 0.818191i | \(-0.305023\pi\) | ||||
0.574947 | + | 0.818191i | \(0.305023\pi\) | |||||||
\(440\) | −31.7759 | −1.51486 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.27991 | 0.156010 | ||||||||
\(443\) | 18.9748 | 0.901519 | 0.450759 | − | 0.892645i | \(-0.351153\pi\) | ||||
0.450759 | + | 0.892645i | \(0.351153\pi\) | |||||||
\(444\) | −1.12577 | −0.0534268 | ||||||||
\(445\) | −35.3227 | −1.67446 | ||||||||
\(446\) | 11.5326 | 0.546086 | ||||||||
\(447\) | −14.4114 | −0.681635 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.3690 | 0.678115 | 0.339058 | − | 0.940766i | \(-0.389892\pi\) | ||||
0.339058 | + | 0.940766i | \(0.389892\pi\) | |||||||
\(450\) | 3.29568 | 0.155360 | ||||||||
\(451\) | −5.64899 | −0.266000 | ||||||||
\(452\) | 34.0154 | 1.59995 | ||||||||
\(453\) | −7.70354 | −0.361944 | ||||||||
\(454\) | 9.66466 | 0.453585 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.34042 | 0.109600 | ||||||||
\(457\) | 8.51958 | 0.398529 | 0.199265 | − | 0.979946i | \(-0.436145\pi\) | ||||
0.199265 | + | 0.979946i | \(0.436145\pi\) | |||||||
\(458\) | −2.10730 | −0.0984679 | ||||||||
\(459\) | 2.00918 | 0.0937804 | ||||||||
\(460\) | 46.9590 | 2.18947 | ||||||||
\(461\) | −32.8708 | −1.53095 | −0.765473 | − | 0.643468i | \(-0.777495\pi\) | ||||
−0.765473 | + | 0.643468i | \(0.777495\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.4709 | 1.50905 | 0.754526 | − | 0.656270i | \(-0.227867\pi\) | ||||
0.754526 | + | 0.656270i | \(0.227867\pi\) | |||||||
\(464\) | 15.6690 | 0.727417 | ||||||||
\(465\) | 11.8161 | 0.547961 | ||||||||
\(466\) | −9.29354 | −0.430515 | ||||||||
\(467\) | −28.5450 | −1.32091 | −0.660453 | − | 0.750867i | \(-0.729636\pi\) | ||||
−0.660453 | + | 0.750867i | \(0.729636\pi\) | |||||||
\(468\) | −7.41566 | −0.342789 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.375908 | −0.0173393 | ||||||||
\(471\) | 0.429607 | 0.0197952 | ||||||||
\(472\) | 6.70845 | 0.308781 | ||||||||
\(473\) | −8.88588 | −0.408573 | ||||||||
\(474\) | −0.423072 | −0.0194323 | ||||||||
\(475\) | −12.3000 | −0.564364 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.87725 | −0.360675 | ||||||||
\(478\) | 12.3702 | 0.565801 | ||||||||
\(479\) | −22.9726 | −1.04964 | −0.524822 | − | 0.851212i | \(-0.675868\pi\) | ||||
−0.524822 | + | 0.851212i | \(0.675868\pi\) | |||||||
\(480\) | −15.7161 | −0.717340 | ||||||||
\(481\) | 2.47512 | 0.112856 | ||||||||
\(482\) | −5.79450 | −0.263932 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −38.4041 | −1.74564 | ||||||||
\(485\) | 29.8463 | 1.35525 | ||||||||
\(486\) | 0.404293 | 0.0183391 | ||||||||
\(487\) | 10.4709 | 0.474483 | 0.237242 | − | 0.971451i | \(-0.423757\pi\) | ||||
0.237242 | + | 0.971451i | \(0.423757\pi\) | |||||||
\(488\) | −4.36703 | −0.197686 | ||||||||
\(489\) | 20.8708 | 0.943808 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.5729 | −1.10896 | −0.554479 | − | 0.832198i | \(-0.687082\pi\) | ||||
−0.554479 | + | 0.832198i | \(0.687082\pi\) | |||||||
\(492\) | −1.83655 | −0.0827979 | ||||||||
\(493\) | 10.3355 | 0.465487 | ||||||||
\(494\) | −2.46321 | −0.110825 | ||||||||
\(495\) | 20.4862 | 0.920787 | ||||||||
\(496\) | −9.92464 | −0.445629 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −4.19617 | −0.188035 | ||||||||
\(499\) | −24.2119 | −1.08387 | −0.541937 | − | 0.840419i | \(-0.682309\pi\) | ||||
−0.541937 | + | 0.840419i | \(0.682309\pi\) | |||||||
\(500\) | 20.9914 | 0.938763 | ||||||||
\(501\) | −15.9352 | −0.711933 | ||||||||
\(502\) | −5.55809 | −0.248070 | ||||||||
\(503\) | 2.90630 | 0.129586 | 0.0647928 | − | 0.997899i | \(-0.479361\pi\) | ||||
0.0647928 | + | 0.997899i | \(0.479361\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −47.5117 | −2.11424 | ||||||||
\(506\) | −16.1025 | −0.715841 | ||||||||
\(507\) | 3.30404 | 0.146738 | ||||||||
\(508\) | −15.0014 | −0.665579 | ||||||||
\(509\) | −2.21101 | −0.0980015 | −0.0490008 | − | 0.998799i | \(-0.515604\pi\) | ||||
−0.0490008 | + | 0.998799i | \(0.515604\pi\) | |||||||
\(510\) | −2.94582 | −0.130443 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.6495 | 1.00098 | ||||||||
\(513\) | −1.50889 | −0.0666190 | ||||||||
\(514\) | 5.01874 | 0.221367 | ||||||||
\(515\) | −43.8088 | −1.93045 | ||||||||
\(516\) | −2.88890 | −0.127177 | ||||||||
\(517\) | −1.44832 | −0.0636970 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.12594 | −0.225004 | ||||||||
\(520\) | 22.7131 | 0.996034 | ||||||||
\(521\) | 7.75309 | 0.339669 | 0.169835 | − | 0.985473i | \(-0.445677\pi\) | ||||
0.169835 | + | 0.985473i | \(0.445677\pi\) | |||||||
\(522\) | 2.07974 | 0.0910277 | ||||||||
\(523\) | −17.8791 | −0.781798 | −0.390899 | − | 0.920434i | \(-0.627836\pi\) | ||||
−0.390899 | + | 0.920434i | \(0.627836\pi\) | |||||||
\(524\) | 24.2904 | 1.06113 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.56274 | 0.373353 | ||||||||
\(527\) | −6.54641 | −0.285166 | ||||||||
\(528\) | −17.2068 | −0.748830 | ||||||||
\(529\) | 26.7108 | 1.16134 | ||||||||
\(530\) | 11.5495 | 0.501677 | ||||||||
\(531\) | −4.32499 | −0.187689 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.03783 | 0.174898 | ||||||||
\(534\) | 3.93785 | 0.170407 | ||||||||
\(535\) | 36.4482 | 1.57579 | ||||||||
\(536\) | 20.6608 | 0.892410 | ||||||||
\(537\) | −5.22886 | −0.225642 | ||||||||
\(538\) | 2.24963 | 0.0969883 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 6.66029 | 0.286613 | ||||||||
\(541\) | −8.00513 | −0.344167 | −0.172084 | − | 0.985082i | \(-0.555050\pi\) | ||||
−0.172084 | + | 0.985082i | \(0.555050\pi\) | |||||||
\(542\) | 4.53081 | 0.194615 | ||||||||
\(543\) | 1.60946 | 0.0690684 | ||||||||
\(544\) | 8.70708 | 0.373313 | ||||||||
\(545\) | 42.8484 | 1.83543 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.5624 | 0.750915 | 0.375458 | − | 0.926840i | \(-0.377486\pi\) | ||||
0.375458 | + | 0.926840i | \(0.377486\pi\) | |||||||
\(548\) | 31.4467 | 1.34334 | ||||||||
\(549\) | 2.81546 | 0.120161 | ||||||||
\(550\) | −18.6173 | −0.793843 | ||||||||
\(551\) | −7.76193 | −0.330669 | ||||||||
\(552\) | −10.9361 | −0.465471 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 3.70688 | 0.157490 | ||||||||
\(555\) | −2.22300 | −0.0943611 | ||||||||
\(556\) | −34.3655 | −1.45742 | ||||||||
\(557\) | 24.1031 | 1.02128 | 0.510640 | − | 0.859794i | \(-0.329408\pi\) | ||||
0.510640 | + | 0.859794i | \(0.329408\pi\) | |||||||
\(558\) | −1.31729 | −0.0557653 | ||||||||
\(559\) | 6.35152 | 0.268641 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.3498 | −0.479190 | ||||||||
\(562\) | 8.57892 | 0.361880 | ||||||||
\(563\) | 38.9921 | 1.64332 | 0.821662 | − | 0.569976i | \(-0.193047\pi\) | ||||
0.821662 | + | 0.569976i | \(0.193047\pi\) | |||||||
\(564\) | −0.470865 | −0.0198270 | ||||||||
\(565\) | 67.1684 | 2.82580 | ||||||||
\(566\) | 1.86593 | 0.0784311 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.53553 | −0.190306 | ||||||||
\(569\) | 10.9127 | 0.457485 | 0.228743 | − | 0.973487i | \(-0.426539\pi\) | ||||
0.228743 | + | 0.973487i | \(0.426539\pi\) | |||||||
\(570\) | 2.21230 | 0.0926631 | ||||||||
\(571\) | −33.5273 | −1.40307 | −0.701537 | − | 0.712633i | \(-0.747503\pi\) | ||||
−0.701537 | + | 0.712633i | \(0.747503\pi\) | |||||||
\(572\) | 41.8910 | 1.75155 | ||||||||
\(573\) | −25.0344 | −1.04583 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 57.4744 | 2.39685 | ||||||||
\(576\) | −4.33993 | −0.180831 | ||||||||
\(577\) | −34.2097 | −1.42417 | −0.712084 | − | 0.702094i | \(-0.752248\pi\) | ||||
−0.712084 | + | 0.702094i | \(0.752248\pi\) | |||||||
\(578\) | −5.24093 | −0.217994 | ||||||||
\(579\) | −2.83996 | −0.118025 | ||||||||
\(580\) | 34.2615 | 1.42263 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −3.32732 | −0.137922 | ||||||||
\(583\) | 44.4985 | 1.84294 | ||||||||
\(584\) | −9.15294 | −0.378751 | ||||||||
\(585\) | −14.6433 | −0.605426 | ||||||||
\(586\) | −1.96667 | −0.0812426 | ||||||||
\(587\) | 34.0227 | 1.40427 | 0.702134 | − | 0.712045i | \(-0.252231\pi\) | ||||
0.702134 | + | 0.712045i | \(0.252231\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.91634 | 0.202574 | ||||||||
\(590\) | 6.34122 | 0.261064 | ||||||||
\(591\) | −26.8159 | −1.10306 | ||||||||
\(592\) | 1.86715 | 0.0767392 | ||||||||
\(593\) | −35.1165 | −1.44206 | −0.721030 | − | 0.692904i | \(-0.756331\pi\) | ||||
−0.721030 | + | 0.692904i | \(0.756331\pi\) | |||||||
\(594\) | −2.28385 | −0.0937073 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 26.4672 | 1.08414 | ||||||||
\(597\) | −7.39204 | −0.302536 | ||||||||
\(598\) | 11.5098 | 0.470672 | ||||||||
\(599\) | −7.10088 | −0.290134 | −0.145067 | − | 0.989422i | \(-0.546340\pi\) | ||||
−0.145067 | + | 0.989422i | \(0.546340\pi\) | |||||||
\(600\) | −12.6440 | −0.516191 | ||||||||
\(601\) | −1.73551 | −0.0707930 | −0.0353965 | − | 0.999373i | \(-0.511269\pi\) | ||||
−0.0353965 | + | 0.999373i | \(0.511269\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.3202 | −0.542439 | ||||||||
\(604\) | 14.1479 | 0.575670 | ||||||||
\(605\) | −75.8345 | −3.08311 | ||||||||
\(606\) | 5.29670 | 0.215164 | ||||||||
\(607\) | 13.3765 | 0.542934 | 0.271467 | − | 0.962448i | \(-0.412491\pi\) | ||||
0.271467 | + | 0.962448i | \(0.412491\pi\) | |||||||
\(608\) | −6.53900 | −0.265191 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.12798 | −0.167137 | ||||||||
\(611\) | 1.03524 | 0.0418814 | ||||||||
\(612\) | −3.68995 | −0.149157 | ||||||||
\(613\) | −1.90309 | −0.0768652 | −0.0384326 | − | 0.999261i | \(-0.512236\pi\) | ||||
−0.0384326 | + | 0.999261i | \(0.512236\pi\) | |||||||
\(614\) | −2.02401 | −0.0816824 | ||||||||
\(615\) | −3.62653 | −0.146236 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.72463 | −0.391499 | −0.195749 | − | 0.980654i | \(-0.562714\pi\) | ||||
−0.195749 | + | 0.980654i | \(0.562714\pi\) | |||||||
\(618\) | 4.88389 | 0.196459 | ||||||||
\(619\) | −6.45607 | −0.259491 | −0.129746 | − | 0.991547i | \(-0.541416\pi\) | ||||
−0.129746 | + | 0.991547i | \(0.541416\pi\) | |||||||
\(620\) | −21.7009 | −0.871530 | ||||||||
\(621\) | 7.05059 | 0.282930 | ||||||||
\(622\) | −5.41011 | −0.216925 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 12.2992 | 0.492363 | ||||||||
\(625\) | 0.691937 | 0.0276775 | ||||||||
\(626\) | −5.69675 | −0.227688 | ||||||||
\(627\) | 8.52369 | 0.340403 | ||||||||
\(628\) | −0.788993 | −0.0314843 | ||||||||
\(629\) | 1.23159 | 0.0491068 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.1970 | −1.36136 | −0.680681 | − | 0.732580i | \(-0.738316\pi\) | ||||
−0.680681 | + | 0.732580i | \(0.738316\pi\) | |||||||
\(632\) | 1.62314 | 0.0645649 | ||||||||
\(633\) | 22.3498 | 0.888324 | ||||||||
\(634\) | −0.319396 | −0.0126848 | ||||||||
\(635\) | −29.6224 | −1.17553 | ||||||||
\(636\) | 14.4669 | 0.573652 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −11.7484 | −0.465124 | ||||||||
\(639\) | 2.92409 | 0.115675 | ||||||||
\(640\) | 37.7954 | 1.49399 | ||||||||
\(641\) | 4.71311 | 0.186157 | 0.0930784 | − | 0.995659i | \(-0.470329\pi\) | ||||
0.0930784 | + | 0.995659i | \(0.470329\pi\) | |||||||
\(642\) | −4.06332 | −0.160367 | ||||||||
\(643\) | −15.6912 | −0.618800 | −0.309400 | − | 0.950932i | \(-0.600128\pi\) | ||||
−0.309400 | + | 0.950932i | \(0.600128\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.70455 | −0.224616 | ||||||||
\(646\) | −1.22566 | −0.0482231 | ||||||||
\(647\) | −20.5419 | −0.807585 | −0.403793 | − | 0.914851i | \(-0.632308\pi\) | ||||
−0.403793 | + | 0.914851i | \(0.632308\pi\) | |||||||
\(648\) | −1.55109 | −0.0609325 | ||||||||
\(649\) | 24.4318 | 0.959033 | ||||||||
\(650\) | 13.3074 | 0.521959 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −38.3301 | −1.50112 | ||||||||
\(653\) | −16.9600 | −0.663698 | −0.331849 | − | 0.943333i | \(-0.607672\pi\) | ||||
−0.331849 | + | 0.943333i | \(0.607672\pi\) | |||||||
\(654\) | −4.77683 | −0.186789 | ||||||||
\(655\) | 47.9649 | 1.87414 | ||||||||
\(656\) | 3.04600 | 0.118926 | ||||||||
\(657\) | 5.90098 | 0.230219 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.00491 | 0.0391459 | 0.0195729 | − | 0.999808i | \(-0.493769\pi\) | ||||
0.0195729 | + | 0.999808i | \(0.493769\pi\) | |||||||
\(660\) | −37.6239 | −1.46451 | ||||||||
\(661\) | −1.53402 | −0.0596663 | −0.0298332 | − | 0.999555i | \(-0.509498\pi\) | ||||
−0.0298332 | + | 0.999555i | \(0.509498\pi\) | |||||||
\(662\) | 1.93759 | 0.0753065 | ||||||||
\(663\) | 8.11271 | 0.315072 | ||||||||
\(664\) | 16.0988 | 0.624754 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.247825 | 0.00960301 | ||||||||
\(667\) | 36.2692 | 1.40435 | ||||||||
\(668\) | 29.2658 | 1.13233 | ||||||||
\(669\) | 28.5254 | 1.10286 | ||||||||
\(670\) | 19.5298 | 0.754501 | ||||||||
\(671\) | −15.9045 | −0.613987 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.78993 | −0.184638 | −0.0923192 | − | 0.995729i | \(-0.529428\pi\) | ||||
−0.0923192 | + | 0.995729i | \(0.529428\pi\) | |||||||
\(674\) | −1.88742 | −0.0727008 | ||||||||
\(675\) | 8.15172 | 0.313760 | ||||||||
\(676\) | −6.06803 | −0.233386 | ||||||||
\(677\) | 34.0664 | 1.30928 | 0.654638 | − | 0.755942i | \(-0.272821\pi\) | ||||
0.654638 | + | 0.755942i | \(0.272821\pi\) | |||||||
\(678\) | −7.48807 | −0.287578 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 11.3018 | 0.433403 | ||||||||
\(681\) | 23.9051 | 0.916045 | ||||||||
\(682\) | 7.44134 | 0.284944 | ||||||||
\(683\) | −9.63255 | −0.368579 | −0.184290 | − | 0.982872i | \(-0.558998\pi\) | ||||
−0.184290 | + | 0.982872i | \(0.558998\pi\) | |||||||
\(684\) | 2.77114 | 0.105957 | ||||||||
\(685\) | 62.0961 | 2.37257 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.21232 | −0.198862 | ||||||||
\(688\) | 4.79137 | 0.182669 | ||||||||
\(689\) | −31.8070 | −1.21175 | ||||||||
\(690\) | −10.3374 | −0.393539 | ||||||||
\(691\) | 42.1141 | 1.60210 | 0.801049 | − | 0.598599i | \(-0.204276\pi\) | ||||
0.801049 | + | 0.598599i | \(0.204276\pi\) | |||||||
\(692\) | 9.41403 | 0.357868 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.77042 | −0.370880 | ||||||||
\(695\) | −67.8596 | −2.57406 | ||||||||
\(696\) | −7.97902 | −0.302444 | ||||||||
\(697\) | 2.00918 | 0.0761030 | ||||||||
\(698\) | −9.58702 | −0.362874 | ||||||||
\(699\) | −22.9871 | −0.869453 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.5053 | −1.15217 | −0.576084 | − | 0.817391i | \(-0.695420\pi\) | ||||
−0.576084 | + | 0.817391i | \(0.695420\pi\) | |||||||
\(702\) | 1.63246 | 0.0616134 | ||||||||
\(703\) | −0.924922 | −0.0348841 | ||||||||
\(704\) | 24.5162 | 0.923990 | ||||||||
\(705\) | −0.929791 | −0.0350179 | ||||||||
\(706\) | −3.59537 | −0.135314 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 7.94305 | 0.298518 | ||||||||
\(709\) | 46.4610 | 1.74488 | 0.872440 | − | 0.488721i | \(-0.162536\pi\) | ||||
0.872440 | + | 0.488721i | \(0.162536\pi\) | |||||||
\(710\) | −4.28724 | −0.160897 | ||||||||
\(711\) | −1.04645 | −0.0392449 | ||||||||
\(712\) | −15.1077 | −0.566186 | ||||||||
\(713\) | −22.9726 | −0.860330 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 82.7198 | 3.09354 | ||||||||
\(716\) | 9.60305 | 0.358883 | ||||||||
\(717\) | 30.5972 | 1.14267 | ||||||||
\(718\) | −8.56843 | −0.319771 | ||||||||
\(719\) | −42.8582 | −1.59834 | −0.799170 | − | 0.601105i | \(-0.794727\pi\) | ||||
−0.799170 | + | 0.601105i | \(0.794727\pi\) | |||||||
\(720\) | −11.0464 | −0.411675 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −6.76109 | −0.251622 | ||||||||
\(723\) | −14.3324 | −0.533028 | ||||||||
\(724\) | −2.95584 | −0.109853 | ||||||||
\(725\) | 41.9336 | 1.55737 | ||||||||
\(726\) | 8.45419 | 0.313764 | ||||||||
\(727\) | −18.9785 | −0.703874 | −0.351937 | − | 0.936024i | \(-0.614477\pi\) | ||||
−0.351937 | + | 0.936024i | \(0.614477\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −8.65190 | −0.320221 | ||||||||
\(731\) | 3.16045 | 0.116893 | ||||||||
\(732\) | −5.17073 | −0.191116 | ||||||||
\(733\) | −43.0175 | −1.58889 | −0.794445 | − | 0.607337i | \(-0.792238\pi\) | ||||
−0.794445 | + | 0.607337i | \(0.792238\pi\) | |||||||
\(734\) | 8.68323 | 0.320504 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 30.5548 | 1.12627 | ||||||||
\(737\) | 75.2455 | 2.77170 | ||||||||
\(738\) | 0.404293 | 0.0148822 | ||||||||
\(739\) | −16.2946 | −0.599408 | −0.299704 | − | 0.954032i | \(-0.596888\pi\) | ||||
−0.299704 | + | 0.954032i | \(0.596888\pi\) | |||||||
\(740\) | 4.08265 | 0.150081 | ||||||||
\(741\) | −6.09263 | −0.223818 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24.1083 | −0.884449 | −0.442224 | − | 0.896905i | \(-0.645810\pi\) | ||||
−0.442224 | + | 0.896905i | \(0.645810\pi\) | |||||||
\(744\) | 5.05384 | 0.185283 | ||||||||
\(745\) | 52.2633 | 1.91478 | ||||||||
\(746\) | −15.2485 | −0.558287 | ||||||||
\(747\) | −10.3790 | −0.379749 | ||||||||
\(748\) | 20.8445 | 0.762149 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −4.62099 | −0.168735 | ||||||||
\(751\) | −39.4430 | −1.43929 | −0.719647 | − | 0.694340i | \(-0.755697\pi\) | ||||
−0.719647 | + | 0.694340i | \(0.755697\pi\) | |||||||
\(752\) | 0.780951 | 0.0284784 | ||||||||
\(753\) | −13.7477 | −0.500994 | ||||||||
\(754\) | 8.39762 | 0.305823 | ||||||||
\(755\) | 27.9371 | 1.01674 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.32835 | −0.120971 | −0.0604855 | − | 0.998169i | \(-0.519265\pi\) | ||||
−0.0604855 | + | 0.998169i | \(0.519265\pi\) | |||||||
\(758\) | −6.39195 | −0.232166 | ||||||||
\(759\) | −39.8287 | −1.44569 | ||||||||
\(760\) | −8.48760 | −0.307878 | ||||||||
\(761\) | −54.7231 | −1.98371 | −0.991856 | − | 0.127364i | \(-0.959348\pi\) | ||||
−0.991856 | + | 0.127364i | \(0.959348\pi\) | |||||||
\(762\) | 3.30237 | 0.119632 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 45.9768 | 1.66338 | ||||||||
\(765\) | −7.28634 | −0.263438 | ||||||||
\(766\) | 7.20363 | 0.260278 | ||||||||
\(767\) | −17.4636 | −0.630573 | ||||||||
\(768\) | 4.46636 | 0.161166 | ||||||||
\(769\) | 23.7003 | 0.854655 | 0.427328 | − | 0.904097i | \(-0.359455\pi\) | ||||
0.427328 | + | 0.904097i | \(0.359455\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.4136 | 0.447065 | ||||||||
\(772\) | 5.21572 | 0.187718 | ||||||||
\(773\) | 32.7011 | 1.17618 | 0.588089 | − | 0.808796i | \(-0.299880\pi\) | ||||
0.588089 | + | 0.808796i | \(0.299880\pi\) | |||||||
\(774\) | 0.635955 | 0.0228589 | ||||||||
\(775\) | −26.5604 | −0.954076 | ||||||||
\(776\) | 12.7654 | 0.458252 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −14.2775 | −0.511874 | ||||||||
\(779\) | −1.50889 | −0.0540615 | ||||||||
\(780\) | 26.8931 | 0.962928 | ||||||||
\(781\) | −16.5181 | −0.591066 | ||||||||
\(782\) | 5.72717 | 0.204803 | ||||||||
\(783\) | 5.14414 | 0.183836 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.55798 | −0.0556068 | ||||||||
\(786\) | −5.34723 | −0.190729 | ||||||||
\(787\) | −18.2860 | −0.651824 | −0.325912 | − | 0.945400i | \(-0.605671\pi\) | ||||
−0.325912 | + | 0.945400i | \(0.605671\pi\) | |||||||
\(788\) | 49.2487 | 1.75441 | ||||||||
\(789\) | 21.1795 | 0.754011 | ||||||||
\(790\) | 1.53428 | 0.0545873 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 8.76208 | 0.311347 | ||||||||
\(793\) | 11.3684 | 0.403702 | ||||||||
\(794\) | −2.14030 | −0.0759563 | ||||||||
\(795\) | 28.5671 | 1.01317 | ||||||||
\(796\) | 13.5758 | 0.481183 | ||||||||
\(797\) | −7.87343 | −0.278891 | −0.139446 | − | 0.990230i | \(-0.544532\pi\) | ||||
−0.139446 | + | 0.990230i | \(0.544532\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.515125 | 0.0182238 | ||||||||
\(800\) | 35.3267 | 1.24899 | ||||||||
\(801\) | 9.74008 | 0.344149 | ||||||||
\(802\) | −11.8849 | −0.419672 | ||||||||
\(803\) | −33.3345 | −1.17635 | ||||||||
\(804\) | 24.4631 | 0.862748 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.31898 | −0.187353 | ||||||||
\(807\) | 5.56435 | 0.195874 | ||||||||
\(808\) | −20.3210 | −0.714892 | ||||||||
\(809\) | 19.0892 | 0.671140 | 0.335570 | − | 0.942015i | \(-0.391071\pi\) | ||||
0.335570 | + | 0.942015i | \(0.391071\pi\) | |||||||
\(810\) | −1.46618 | −0.0515163 | ||||||||
\(811\) | 20.5665 | 0.722186 | 0.361093 | − | 0.932530i | \(-0.382404\pi\) | ||||
0.361093 | + | 0.932530i | \(0.382404\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.2067 | 0.393038 | ||||||||
\(814\) | −1.39996 | −0.0490685 | ||||||||
\(815\) | −75.6884 | −2.65125 | ||||||||
\(816\) | 6.11996 | 0.214241 | ||||||||
\(817\) | −2.37349 | −0.0830378 | ||||||||
\(818\) | −8.77186 | −0.306701 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.66029 | 0.232588 | ||||||||
\(821\) | −2.65350 | −0.0926079 | −0.0463040 | − | 0.998927i | \(-0.514744\pi\) | ||||
−0.0463040 | + | 0.998927i | \(0.514744\pi\) | |||||||
\(822\) | −6.92260 | −0.241453 | ||||||||
\(823\) | 30.8909 | 1.07679 | 0.538394 | − | 0.842693i | \(-0.319031\pi\) | ||||
0.538394 | + | 0.842693i | \(0.319031\pi\) | |||||||
\(824\) | −18.7373 | −0.652744 | ||||||||
\(825\) | −46.0489 | −1.60322 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.774423 | 0.0269293 | 0.0134647 | − | 0.999909i | \(-0.495714\pi\) | ||||
0.0134647 | + | 0.999909i | \(0.495714\pi\) | |||||||
\(828\) | −12.9487 | −0.450000 | ||||||||
\(829\) | −15.5292 | −0.539352 | −0.269676 | − | 0.962951i | \(-0.586917\pi\) | ||||
−0.269676 | + | 0.962951i | \(0.586917\pi\) | |||||||
\(830\) | 15.2175 | 0.528208 | ||||||||
\(831\) | 9.16881 | 0.318062 | ||||||||
\(832\) | −17.5239 | −0.607532 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 7.56513 | 0.261959 | ||||||||
\(835\) | 57.7896 | 1.99989 | ||||||||
\(836\) | −15.6542 | −0.541410 | ||||||||
\(837\) | −3.25825 | −0.112622 | ||||||||
\(838\) | 0.435566 | 0.0150464 | ||||||||
\(839\) | −2.34091 | −0.0808172 | −0.0404086 | − | 0.999183i | \(-0.512866\pi\) | ||||
−0.0404086 | + | 0.999183i | \(0.512866\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.53785 | −0.0875119 | ||||||||
\(842\) | −7.61864 | −0.262556 | ||||||||
\(843\) | 21.2196 | 0.730841 | ||||||||
\(844\) | −41.0464 | −1.41288 | ||||||||
\(845\) | −11.9822 | −0.412201 | ||||||||
\(846\) | 0.103655 | 0.00356373 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −23.9941 | −0.823961 | ||||||||
\(849\) | 4.61530 | 0.158397 | ||||||||
\(850\) | 6.62161 | 0.227119 | ||||||||
\(851\) | 4.32189 | 0.148152 | ||||||||
\(852\) | −5.37023 | −0.183981 | ||||||||
\(853\) | 46.7682 | 1.60131 | 0.800656 | − | 0.599125i | \(-0.204485\pi\) | ||||
0.800656 | + | 0.599125i | \(0.204485\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.47203 | 0.187139 | ||||||||
\(856\) | 15.5891 | 0.532825 | ||||||||
\(857\) | −3.78098 | −0.129156 | −0.0645778 | − | 0.997913i | \(-0.520570\pi\) | ||||
−0.0645778 | + | 0.997913i | \(0.520570\pi\) | |||||||
\(858\) | −9.22177 | −0.314826 | ||||||||
\(859\) | 16.9802 | 0.579357 | 0.289679 | − | 0.957124i | \(-0.406452\pi\) | ||||
0.289679 | + | 0.957124i | \(0.406452\pi\) | |||||||
\(860\) | 10.4767 | 0.357251 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8.60172 | 0.292976 | ||||||||
\(863\) | 42.9271 | 1.46125 | 0.730627 | − | 0.682776i | \(-0.239228\pi\) | ||||
0.730627 | + | 0.682776i | \(0.239228\pi\) | |||||||
\(864\) | 4.33365 | 0.147434 | ||||||||
\(865\) | 18.5894 | 0.632058 | ||||||||
\(866\) | 14.6048 | 0.496291 | ||||||||
\(867\) | −12.9632 | −0.440253 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.91138 | 0.200530 | ||||||||
\(870\) | −7.54223 | −0.255706 | ||||||||
\(871\) | −53.7846 | −1.82242 | ||||||||
\(872\) | 18.3265 | 0.620615 | ||||||||
\(873\) | −8.22998 | −0.278543 | ||||||||
\(874\) | −4.30109 | −0.145487 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −10.8374 | −0.366163 | ||||||||
\(877\) | −14.8161 | −0.500303 | −0.250152 | − | 0.968207i | \(-0.580480\pi\) | ||||
−0.250152 | + | 0.968207i | \(0.580480\pi\) | |||||||
\(878\) | 9.74061 | 0.328730 | ||||||||
\(879\) | −4.86448 | −0.164075 | ||||||||
\(880\) | 62.4010 | 2.10354 | ||||||||
\(881\) | 48.7594 | 1.64275 | 0.821373 | − | 0.570391i | \(-0.193208\pi\) | ||||
0.821373 | + | 0.570391i | \(0.193208\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27.6259 | −0.929687 | −0.464843 | − | 0.885393i | \(-0.653889\pi\) | ||||
−0.464843 | + | 0.885393i | \(0.653889\pi\) | |||||||
\(884\) | −14.8994 | −0.501120 | ||||||||
\(885\) | 15.6847 | 0.527236 | ||||||||
\(886\) | 7.67137 | 0.257725 | ||||||||
\(887\) | −29.6770 | −0.996457 | −0.498229 | − | 0.867046i | \(-0.666016\pi\) | ||||
−0.498229 | + | 0.867046i | \(0.666016\pi\) | |||||||
\(888\) | −0.950791 | −0.0319065 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −14.2807 | −0.478691 | ||||||||
\(891\) | −5.64899 | −0.189248 | ||||||||
\(892\) | −52.3883 | −1.75409 | ||||||||
\(893\) | −0.386857 | −0.0129457 | ||||||||
\(894\) | −5.82642 | −0.194865 | ||||||||
\(895\) | 18.9626 | 0.633850 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 28.4691 | 0.950554 | ||||||||
\(898\) | 5.80929 | 0.193858 | ||||||||
\(899\) | −16.7609 | −0.559007 | ||||||||
\(900\) | −14.9710 | −0.499034 | ||||||||
\(901\) | −15.8268 | −0.527267 | ||||||||
\(902\) | −2.28385 | −0.0760437 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 28.7283 | 0.955490 | ||||||||
\(905\) | −5.83674 | −0.194020 | ||||||||
\(906\) | −3.11449 | −0.103472 | ||||||||
\(907\) | 35.1406 | 1.16683 | 0.583413 | − | 0.812176i | \(-0.301717\pi\) | ||||
0.583413 | + | 0.812176i | \(0.301717\pi\) | |||||||
\(908\) | −43.9028 | −1.45697 | ||||||||
\(909\) | 13.1011 | 0.434537 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48.9016 | 1.62018 | 0.810091 | − | 0.586305i | \(-0.199418\pi\) | ||||
0.810091 | + | 0.586305i | \(0.199418\pi\) | |||||||
\(912\) | −4.59607 | −0.152191 | ||||||||
\(913\) | 58.6310 | 1.94040 | ||||||||
\(914\) | 3.44441 | 0.113931 | ||||||||
\(915\) | −10.2104 | −0.337544 | ||||||||
\(916\) | 9.57267 | 0.316290 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.812296 | 0.0268098 | ||||||||
\(919\) | 29.0668 | 0.958825 | 0.479412 | − | 0.877590i | \(-0.340850\pi\) | ||||
0.479412 | + | 0.877590i | \(0.340850\pi\) | |||||||
\(920\) | 39.6601 | 1.30755 | ||||||||
\(921\) | −5.00629 | −0.164963 | ||||||||
\(922\) | −13.2894 | −0.437664 | ||||||||
\(923\) | 11.8070 | 0.388631 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.99686 | 0.164296 | ||||||||
\(926\) | 13.1278 | 0.431405 | ||||||||
\(927\) | 12.0801 | 0.396762 | ||||||||
\(928\) | 22.2929 | 0.731801 | ||||||||
\(929\) | 4.60405 | 0.151054 | 0.0755271 | − | 0.997144i | \(-0.475936\pi\) | ||||
0.0755271 | + | 0.997144i | \(0.475936\pi\) | |||||||
\(930\) | 4.77719 | 0.156650 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 42.2170 | 1.38286 | ||||||||
\(933\) | −13.3816 | −0.438095 | ||||||||
\(934\) | −11.5406 | −0.377618 | ||||||||
\(935\) | 41.1605 | 1.34609 | ||||||||
\(936\) | −6.26303 | −0.204713 | ||||||||
\(937\) | −9.16034 | −0.299255 | −0.149628 | − | 0.988742i | \(-0.547807\pi\) | ||||
−0.149628 | + | 0.988742i | \(0.547807\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −14.0907 | −0.459831 | ||||||||
\(940\) | 1.70760 | 0.0556959 | ||||||||
\(941\) | −49.9191 | −1.62732 | −0.813658 | − | 0.581344i | \(-0.802527\pi\) | ||||
−0.813658 | + | 0.581344i | \(0.802527\pi\) | |||||||
\(942\) | 0.173687 | 0.00565903 | ||||||||
\(943\) | 7.05059 | 0.229599 | ||||||||
\(944\) | −13.1739 | −0.428775 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.59250 | −0.116802 | ||||||||
\(947\) | 46.5491 | 1.51264 | 0.756322 | − | 0.654200i | \(-0.226994\pi\) | ||||
0.756322 | + | 0.654200i | \(0.226994\pi\) | |||||||
\(948\) | 1.92185 | 0.0624189 | ||||||||
\(949\) | 23.8271 | 0.773461 | ||||||||
\(950\) | −4.97282 | −0.161339 | ||||||||
\(951\) | −0.790011 | −0.0256179 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.7321 | −0.380041 | −0.190020 | − | 0.981780i | \(-0.560855\pi\) | ||||
−0.190020 | + | 0.981780i | \(0.560855\pi\) | |||||||
\(954\) | −3.18472 | −0.103109 | ||||||||
\(955\) | 90.7880 | 2.93783 | ||||||||
\(956\) | −56.1932 | −1.81742 | ||||||||
\(957\) | −29.0592 | −0.939349 | ||||||||
\(958\) | −9.28765 | −0.300070 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 15.7389 | 0.507971 | ||||||||
\(961\) | −20.3838 | −0.657542 | ||||||||
\(962\) | 1.00067 | 0.0322630 | ||||||||
\(963\) | −10.0504 | −0.323871 | ||||||||
\(964\) | 26.3222 | 0.847780 | ||||||||
\(965\) | 10.2992 | 0.331543 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −57.4991 | −1.84905 | −0.924523 | − | 0.381127i | \(-0.875536\pi\) | ||||
−0.924523 | + | 0.381127i | \(0.875536\pi\) | |||||||
\(968\) | −32.4349 | −1.04250 | ||||||||
\(969\) | −3.03162 | −0.0973898 | ||||||||
\(970\) | 12.0666 | 0.387436 | ||||||||
\(971\) | −48.4020 | −1.55329 | −0.776647 | − | 0.629936i | \(-0.783081\pi\) | ||||
−0.776647 | + | 0.629936i | \(0.783081\pi\) | |||||||
\(972\) | −1.83655 | −0.0589073 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 4.23332 | 0.135644 | ||||||||
\(975\) | 32.9152 | 1.05413 | ||||||||
\(976\) | 8.57590 | 0.274508 | ||||||||
\(977\) | 20.1753 | 0.645464 | 0.322732 | − | 0.946490i | \(-0.395399\pi\) | ||||
0.322732 | + | 0.946490i | \(0.395399\pi\) | |||||||
\(978\) | 8.43790 | 0.269814 | ||||||||
\(979\) | −55.0216 | −1.75850 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.8153 | −0.377233 | ||||||||
\(982\) | −9.93463 | −0.317027 | ||||||||
\(983\) | −32.6666 | −1.04190 | −0.520952 | − | 0.853586i | \(-0.674423\pi\) | ||||
−0.520952 | + | 0.853586i | \(0.674423\pi\) | |||||||
\(984\) | −1.55109 | −0.0494469 | ||||||||
\(985\) | 97.2488 | 3.09860 | ||||||||
\(986\) | 4.17857 | 0.133073 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 11.1894 | 0.355982 | ||||||||
\(989\) | 11.0906 | 0.352661 | ||||||||
\(990\) | 8.28243 | 0.263233 | ||||||||
\(991\) | 35.1121 | 1.11537 | 0.557686 | − | 0.830052i | \(-0.311689\pi\) | ||||
0.557686 | + | 0.830052i | \(0.311689\pi\) | |||||||
\(992\) | −14.1201 | −0.448315 | ||||||||
\(993\) | 4.79253 | 0.152086 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 26.8075 | 0.849854 | ||||||||
\(996\) | 19.0616 | 0.603989 | ||||||||
\(997\) | −12.4124 | −0.393104 | −0.196552 | − | 0.980493i | \(-0.562974\pi\) | ||||
−0.196552 | + | 0.980493i | \(0.562974\pi\) | |||||||
\(998\) | −9.78870 | −0.309856 | ||||||||
\(999\) | 0.612983 | 0.0193939 |
(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 | 6027.2.a.bm.1.10 | yes | 16 | |
7.6 | odd | 2 | 6027.2.a.bl.1.10 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6027.2.a.bl.1.10 | ✓ | 16 | 7.6 | odd | 2 | ||
6027.2.a.bm.1.10 | yes | 16 | 1.1 | even | 1 | trivial |