Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6038,2,Mod(1,6038)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6038, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6038.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6038 = 2 \cdot 3019 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6038.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: | \(48.2136727404\) |
Analytic rank: | \(0\) |
Dimension: | \(70\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 6038.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.93737 | −1.69589 | −0.847946 | − | 0.530082i | \(-0.822161\pi\) | ||||
−0.847946 | + | 0.530082i | \(0.822161\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.45627 | −1.54569 | −0.772845 | − | 0.634594i | \(-0.781167\pi\) | ||||
−0.772845 | + | 0.634594i | \(0.781167\pi\) | |||||||
\(6\) | −2.93737 | −1.19918 | ||||||||
\(7\) | 2.34218 | 0.885262 | 0.442631 | − | 0.896704i | \(-0.354045\pi\) | ||||
0.442631 | + | 0.896704i | \(0.354045\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 5.62815 | 1.87605 | ||||||||
\(10\) | −3.45627 | −1.09297 | ||||||||
\(11\) | −0.656795 | −0.198031 | −0.0990156 | − | 0.995086i | \(-0.531569\pi\) | ||||
−0.0990156 | + | 0.995086i | \(0.531569\pi\) | |||||||
\(12\) | −2.93737 | −0.847946 | ||||||||
\(13\) | 2.18567 | 0.606197 | 0.303098 | − | 0.952959i | \(-0.401979\pi\) | ||||
0.303098 | + | 0.952959i | \(0.401979\pi\) | |||||||
\(14\) | 2.34218 | 0.625975 | ||||||||
\(15\) | 10.1524 | 2.62133 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.83197 | 1.41446 | 0.707231 | − | 0.706983i | \(-0.249944\pi\) | ||||
0.707231 | + | 0.706983i | \(0.249944\pi\) | |||||||
\(18\) | 5.62815 | 1.32657 | ||||||||
\(19\) | 1.72800 | 0.396430 | 0.198215 | − | 0.980159i | \(-0.436486\pi\) | ||||
0.198215 | + | 0.980159i | \(0.436486\pi\) | |||||||
\(20\) | −3.45627 | −0.772845 | ||||||||
\(21\) | −6.87986 | −1.50131 | ||||||||
\(22\) | −0.656795 | −0.140029 | ||||||||
\(23\) | −2.54416 | −0.530494 | −0.265247 | − | 0.964181i | \(-0.585453\pi\) | ||||
−0.265247 | + | 0.964181i | \(0.585453\pi\) | |||||||
\(24\) | −2.93737 | −0.599589 | ||||||||
\(25\) | 6.94580 | 1.38916 | ||||||||
\(26\) | 2.18567 | 0.428646 | ||||||||
\(27\) | −7.71987 | −1.48569 | ||||||||
\(28\) | 2.34218 | 0.442631 | ||||||||
\(29\) | −0.470989 | −0.0874604 | −0.0437302 | − | 0.999043i | \(-0.513924\pi\) | ||||
−0.0437302 | + | 0.999043i | \(0.513924\pi\) | |||||||
\(30\) | 10.1524 | 1.85356 | ||||||||
\(31\) | 7.36041 | 1.32197 | 0.660984 | − | 0.750400i | \(-0.270139\pi\) | ||||
0.660984 | + | 0.750400i | \(0.270139\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.92925 | 0.335840 | ||||||||
\(34\) | 5.83197 | 1.00018 | ||||||||
\(35\) | −8.09521 | −1.36834 | ||||||||
\(36\) | 5.62815 | 0.938026 | ||||||||
\(37\) | −4.86352 | −0.799558 | −0.399779 | − | 0.916612i | \(-0.630913\pi\) | ||||
−0.399779 | + | 0.916612i | \(0.630913\pi\) | |||||||
\(38\) | 1.72800 | 0.280318 | ||||||||
\(39\) | −6.42013 | −1.02804 | ||||||||
\(40\) | −3.45627 | −0.546484 | ||||||||
\(41\) | 8.72477 | 1.36258 | 0.681290 | − | 0.732013i | \(-0.261419\pi\) | ||||
0.681290 | + | 0.732013i | \(0.261419\pi\) | |||||||
\(42\) | −6.87986 | −1.06159 | ||||||||
\(43\) | 2.91867 | 0.445093 | 0.222546 | − | 0.974922i | \(-0.428563\pi\) | ||||
0.222546 | + | 0.974922i | \(0.428563\pi\) | |||||||
\(44\) | −0.656795 | −0.0990156 | ||||||||
\(45\) | −19.4524 | −2.89980 | ||||||||
\(46\) | −2.54416 | −0.375116 | ||||||||
\(47\) | −6.33452 | −0.923984 | −0.461992 | − | 0.886884i | \(-0.652865\pi\) | ||||
−0.461992 | + | 0.886884i | \(0.652865\pi\) | |||||||
\(48\) | −2.93737 | −0.423973 | ||||||||
\(49\) | −1.51418 | −0.216312 | ||||||||
\(50\) | 6.94580 | 0.982285 | ||||||||
\(51\) | −17.1307 | −2.39877 | ||||||||
\(52\) | 2.18567 | 0.303098 | ||||||||
\(53\) | −12.0542 | −1.65578 | −0.827888 | − | 0.560894i | \(-0.810457\pi\) | ||||
−0.827888 | + | 0.560894i | \(0.810457\pi\) | |||||||
\(54\) | −7.71987 | −1.05054 | ||||||||
\(55\) | 2.27006 | 0.306095 | ||||||||
\(56\) | 2.34218 | 0.312987 | ||||||||
\(57\) | −5.07577 | −0.672303 | ||||||||
\(58\) | −0.470989 | −0.0618439 | ||||||||
\(59\) | −8.19890 | −1.06741 | −0.533703 | − | 0.845672i | \(-0.679200\pi\) | ||||
−0.533703 | + | 0.845672i | \(0.679200\pi\) | |||||||
\(60\) | 10.1524 | 1.31066 | ||||||||
\(61\) | −14.6553 | −1.87642 | −0.938208 | − | 0.346073i | \(-0.887515\pi\) | ||||
−0.938208 | + | 0.346073i | \(0.887515\pi\) | |||||||
\(62\) | 7.36041 | 0.934773 | ||||||||
\(63\) | 13.1822 | 1.66080 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −7.55427 | −0.936992 | ||||||||
\(66\) | 1.92925 | 0.237474 | ||||||||
\(67\) | 10.6610 | 1.30245 | 0.651225 | − | 0.758885i | \(-0.274255\pi\) | ||||
0.651225 | + | 0.758885i | \(0.274255\pi\) | |||||||
\(68\) | 5.83197 | 0.707231 | ||||||||
\(69\) | 7.47314 | 0.899660 | ||||||||
\(70\) | −8.09521 | −0.967563 | ||||||||
\(71\) | −2.15041 | −0.255207 | −0.127603 | − | 0.991825i | \(-0.540728\pi\) | ||||
−0.127603 | + | 0.991825i | \(0.540728\pi\) | |||||||
\(72\) | 5.62815 | 0.663284 | ||||||||
\(73\) | 6.44525 | 0.754359 | 0.377179 | − | 0.926140i | \(-0.376894\pi\) | ||||
0.377179 | + | 0.926140i | \(0.376894\pi\) | |||||||
\(74\) | −4.86352 | −0.565373 | ||||||||
\(75\) | −20.4024 | −2.35587 | ||||||||
\(76\) | 1.72800 | 0.198215 | ||||||||
\(77\) | −1.53833 | −0.175309 | ||||||||
\(78\) | −6.42013 | −0.726937 | ||||||||
\(79\) | 10.8656 | 1.22248 | 0.611240 | − | 0.791445i | \(-0.290671\pi\) | ||||
0.611240 | + | 0.791445i | \(0.290671\pi\) | |||||||
\(80\) | −3.45627 | −0.386423 | ||||||||
\(81\) | 5.79166 | 0.643518 | ||||||||
\(82\) | 8.72477 | 0.963490 | ||||||||
\(83\) | −2.43535 | −0.267314 | −0.133657 | − | 0.991028i | \(-0.542672\pi\) | ||||
−0.133657 | + | 0.991028i | \(0.542672\pi\) | |||||||
\(84\) | −6.87986 | −0.750654 | ||||||||
\(85\) | −20.1569 | −2.18632 | ||||||||
\(86\) | 2.91867 | 0.314728 | ||||||||
\(87\) | 1.38347 | 0.148323 | ||||||||
\(88\) | −0.656795 | −0.0700146 | ||||||||
\(89\) | −10.8482 | −1.14990 | −0.574952 | − | 0.818187i | \(-0.694979\pi\) | ||||
−0.574952 | + | 0.818187i | \(0.694979\pi\) | |||||||
\(90\) | −19.4524 | −2.05047 | ||||||||
\(91\) | 5.11924 | 0.536643 | ||||||||
\(92\) | −2.54416 | −0.265247 | ||||||||
\(93\) | −21.6203 | −2.24192 | ||||||||
\(94\) | −6.33452 | −0.653355 | ||||||||
\(95\) | −5.97243 | −0.612758 | ||||||||
\(96\) | −2.93737 | −0.299794 | ||||||||
\(97\) | 8.27674 | 0.840375 | 0.420188 | − | 0.907437i | \(-0.361964\pi\) | ||||
0.420188 | + | 0.907437i | \(0.361964\pi\) | |||||||
\(98\) | −1.51418 | −0.152955 | ||||||||
\(99\) | −3.69654 | −0.371517 | ||||||||
\(100\) | 6.94580 | 0.694580 | ||||||||
\(101\) | 18.4330 | 1.83415 | 0.917075 | − | 0.398715i | \(-0.130544\pi\) | ||||
0.917075 | + | 0.398715i | \(0.130544\pi\) | |||||||
\(102\) | −17.1307 | −1.69619 | ||||||||
\(103\) | 8.72607 | 0.859805 | 0.429902 | − | 0.902875i | \(-0.358548\pi\) | ||||
0.429902 | + | 0.902875i | \(0.358548\pi\) | |||||||
\(104\) | 2.18567 | 0.214323 | ||||||||
\(105\) | 23.7787 | 2.32056 | ||||||||
\(106\) | −12.0542 | −1.17081 | ||||||||
\(107\) | 8.38135 | 0.810256 | 0.405128 | − | 0.914260i | \(-0.367227\pi\) | ||||
0.405128 | + | 0.914260i | \(0.367227\pi\) | |||||||
\(108\) | −7.71987 | −0.742845 | ||||||||
\(109\) | 15.2202 | 1.45783 | 0.728915 | − | 0.684604i | \(-0.240025\pi\) | ||||
0.728915 | + | 0.684604i | \(0.240025\pi\) | |||||||
\(110\) | 2.27006 | 0.216442 | ||||||||
\(111\) | 14.2860 | 1.35596 | ||||||||
\(112\) | 2.34218 | 0.221315 | ||||||||
\(113\) | 14.5126 | 1.36523 | 0.682614 | − | 0.730779i | \(-0.260843\pi\) | ||||
0.682614 | + | 0.730779i | \(0.260843\pi\) | |||||||
\(114\) | −5.07577 | −0.475390 | ||||||||
\(115\) | 8.79330 | 0.819979 | ||||||||
\(116\) | −0.470989 | −0.0437302 | ||||||||
\(117\) | 12.3013 | 1.13726 | ||||||||
\(118\) | −8.19890 | −0.754770 | ||||||||
\(119\) | 13.6595 | 1.25217 | ||||||||
\(120\) | 10.1524 | 0.926779 | ||||||||
\(121\) | −10.5686 | −0.960784 | ||||||||
\(122\) | −14.6553 | −1.32683 | ||||||||
\(123\) | −25.6279 | −2.31079 | ||||||||
\(124\) | 7.36041 | 0.660984 | ||||||||
\(125\) | −6.72521 | −0.601521 | ||||||||
\(126\) | 13.1822 | 1.17436 | ||||||||
\(127\) | −11.5680 | −1.02650 | −0.513249 | − | 0.858240i | \(-0.671558\pi\) | ||||
−0.513249 | + | 0.858240i | \(0.671558\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −8.57321 | −0.754829 | ||||||||
\(130\) | −7.55427 | −0.662554 | ||||||||
\(131\) | −6.72344 | −0.587430 | −0.293715 | − | 0.955893i | \(-0.594892\pi\) | ||||
−0.293715 | + | 0.955893i | \(0.594892\pi\) | |||||||
\(132\) | 1.92925 | 0.167920 | ||||||||
\(133\) | 4.04729 | 0.350944 | ||||||||
\(134\) | 10.6610 | 0.920972 | ||||||||
\(135\) | 26.6819 | 2.29642 | ||||||||
\(136\) | 5.83197 | 0.500088 | ||||||||
\(137\) | −4.65670 | −0.397849 | −0.198924 | − | 0.980015i | \(-0.563745\pi\) | ||||
−0.198924 | + | 0.980015i | \(0.563745\pi\) | |||||||
\(138\) | 7.47314 | 0.636156 | ||||||||
\(139\) | 5.37841 | 0.456191 | 0.228096 | − | 0.973639i | \(-0.426750\pi\) | ||||
0.228096 | + | 0.973639i | \(0.426750\pi\) | |||||||
\(140\) | −8.09521 | −0.684171 | ||||||||
\(141\) | 18.6068 | 1.56698 | ||||||||
\(142\) | −2.15041 | −0.180458 | ||||||||
\(143\) | −1.43554 | −0.120046 | ||||||||
\(144\) | 5.62815 | 0.469013 | ||||||||
\(145\) | 1.62786 | 0.135187 | ||||||||
\(146\) | 6.44525 | 0.533412 | ||||||||
\(147\) | 4.44771 | 0.366841 | ||||||||
\(148\) | −4.86352 | −0.399779 | ||||||||
\(149\) | −17.8551 | −1.46275 | −0.731374 | − | 0.681976i | \(-0.761121\pi\) | ||||
−0.731374 | + | 0.681976i | \(0.761121\pi\) | |||||||
\(150\) | −20.4024 | −1.66585 | ||||||||
\(151\) | 14.8705 | 1.21014 | 0.605071 | − | 0.796171i | \(-0.293145\pi\) | ||||
0.605071 | + | 0.796171i | \(0.293145\pi\) | |||||||
\(152\) | 1.72800 | 0.140159 | ||||||||
\(153\) | 32.8233 | 2.65360 | ||||||||
\(154\) | −1.53833 | −0.123962 | ||||||||
\(155\) | −25.4396 | −2.04335 | ||||||||
\(156\) | −6.42013 | −0.514022 | ||||||||
\(157\) | 7.61667 | 0.607877 | 0.303938 | − | 0.952692i | \(-0.401698\pi\) | ||||
0.303938 | + | 0.952692i | \(0.401698\pi\) | |||||||
\(158\) | 10.8656 | 0.864424 | ||||||||
\(159\) | 35.4077 | 2.80802 | ||||||||
\(160\) | −3.45627 | −0.273242 | ||||||||
\(161\) | −5.95888 | −0.469626 | ||||||||
\(162\) | 5.79166 | 0.455036 | ||||||||
\(163\) | −3.99369 | −0.312810 | −0.156405 | − | 0.987693i | \(-0.549990\pi\) | ||||
−0.156405 | + | 0.987693i | \(0.549990\pi\) | |||||||
\(164\) | 8.72477 | 0.681290 | ||||||||
\(165\) | −6.66801 | −0.519104 | ||||||||
\(166\) | −2.43535 | −0.189020 | ||||||||
\(167\) | −20.5551 | −1.59060 | −0.795299 | − | 0.606218i | \(-0.792686\pi\) | ||||
−0.795299 | + | 0.606218i | \(0.792686\pi\) | |||||||
\(168\) | −6.87986 | −0.530793 | ||||||||
\(169\) | −8.22284 | −0.632526 | ||||||||
\(170\) | −20.1569 | −1.54596 | ||||||||
\(171\) | 9.72544 | 0.743723 | ||||||||
\(172\) | 2.91867 | 0.222546 | ||||||||
\(173\) | 19.2480 | 1.46340 | 0.731699 | − | 0.681628i | \(-0.238728\pi\) | ||||
0.731699 | + | 0.681628i | \(0.238728\pi\) | |||||||
\(174\) | 1.38347 | 0.104881 | ||||||||
\(175\) | 16.2683 | 1.22977 | ||||||||
\(176\) | −0.656795 | −0.0495078 | ||||||||
\(177\) | 24.0832 | 1.81021 | ||||||||
\(178\) | −10.8482 | −0.813105 | ||||||||
\(179\) | 11.9834 | 0.895680 | 0.447840 | − | 0.894114i | \(-0.352193\pi\) | ||||
0.447840 | + | 0.894114i | \(0.352193\pi\) | |||||||
\(180\) | −19.4524 | −1.44990 | ||||||||
\(181\) | −22.1192 | −1.64410 | −0.822052 | − | 0.569412i | \(-0.807171\pi\) | ||||
−0.822052 | + | 0.569412i | \(0.807171\pi\) | |||||||
\(182\) | 5.11924 | 0.379464 | ||||||||
\(183\) | 43.0480 | 3.18220 | ||||||||
\(184\) | −2.54416 | −0.187558 | ||||||||
\(185\) | 16.8096 | 1.23587 | ||||||||
\(186\) | −21.6203 | −1.58527 | ||||||||
\(187\) | −3.83041 | −0.280107 | ||||||||
\(188\) | −6.33452 | −0.461992 | ||||||||
\(189\) | −18.0813 | −1.31522 | ||||||||
\(190\) | −5.97243 | −0.433286 | ||||||||
\(191\) | −13.9667 | −1.01060 | −0.505299 | − | 0.862945i | \(-0.668618\pi\) | ||||
−0.505299 | + | 0.862945i | \(0.668618\pi\) | |||||||
\(192\) | −2.93737 | −0.211987 | ||||||||
\(193\) | −6.62364 | −0.476780 | −0.238390 | − | 0.971169i | \(-0.576620\pi\) | ||||
−0.238390 | + | 0.971169i | \(0.576620\pi\) | |||||||
\(194\) | 8.27674 | 0.594235 | ||||||||
\(195\) | 22.1897 | 1.58904 | ||||||||
\(196\) | −1.51418 | −0.108156 | ||||||||
\(197\) | −9.12796 | −0.650340 | −0.325170 | − | 0.945655i | \(-0.605422\pi\) | ||||
−0.325170 | + | 0.945655i | \(0.605422\pi\) | |||||||
\(198\) | −3.69654 | −0.262702 | ||||||||
\(199\) | 2.28989 | 0.162326 | 0.0811629 | − | 0.996701i | \(-0.474137\pi\) | ||||
0.0811629 | + | 0.996701i | \(0.474137\pi\) | |||||||
\(200\) | 6.94580 | 0.491142 | ||||||||
\(201\) | −31.3154 | −2.20882 | ||||||||
\(202\) | 18.4330 | 1.29694 | ||||||||
\(203\) | −1.10314 | −0.0774254 | ||||||||
\(204\) | −17.1307 | −1.19939 | ||||||||
\(205\) | −30.1552 | −2.10613 | ||||||||
\(206\) | 8.72607 | 0.607974 | ||||||||
\(207\) | −14.3189 | −0.995234 | ||||||||
\(208\) | 2.18567 | 0.151549 | ||||||||
\(209\) | −1.13494 | −0.0785055 | ||||||||
\(210\) | 23.7787 | 1.64088 | ||||||||
\(211\) | 9.98014 | 0.687061 | 0.343531 | − | 0.939141i | \(-0.388377\pi\) | ||||
0.343531 | + | 0.939141i | \(0.388377\pi\) | |||||||
\(212\) | −12.0542 | −0.827888 | ||||||||
\(213\) | 6.31656 | 0.432803 | ||||||||
\(214\) | 8.38135 | 0.572938 | ||||||||
\(215\) | −10.0877 | −0.687976 | ||||||||
\(216\) | −7.71987 | −0.525270 | ||||||||
\(217\) | 17.2394 | 1.17029 | ||||||||
\(218\) | 15.2202 | 1.03084 | ||||||||
\(219\) | −18.9321 | −1.27931 | ||||||||
\(220\) | 2.27006 | 0.153047 | ||||||||
\(221\) | 12.7468 | 0.857442 | ||||||||
\(222\) | 14.2860 | 0.958811 | ||||||||
\(223\) | 12.7627 | 0.854656 | 0.427328 | − | 0.904097i | \(-0.359455\pi\) | ||||
0.427328 | + | 0.904097i | \(0.359455\pi\) | |||||||
\(224\) | 2.34218 | 0.156494 | ||||||||
\(225\) | 39.0920 | 2.60614 | ||||||||
\(226\) | 14.5126 | 0.965362 | ||||||||
\(227\) | 2.90519 | 0.192824 | 0.0964121 | − | 0.995342i | \(-0.469263\pi\) | ||||
0.0964121 | + | 0.995342i | \(0.469263\pi\) | |||||||
\(228\) | −5.07577 | −0.336151 | ||||||||
\(229\) | 2.08724 | 0.137929 | 0.0689643 | − | 0.997619i | \(-0.478031\pi\) | ||||
0.0689643 | + | 0.997619i | \(0.478031\pi\) | |||||||
\(230\) | 8.79330 | 0.579813 | ||||||||
\(231\) | 4.51866 | 0.297306 | ||||||||
\(232\) | −0.470989 | −0.0309219 | ||||||||
\(233\) | 4.84432 | 0.317362 | 0.158681 | − | 0.987330i | \(-0.449276\pi\) | ||||
0.158681 | + | 0.987330i | \(0.449276\pi\) | |||||||
\(234\) | 12.3013 | 0.804161 | ||||||||
\(235\) | 21.8938 | 1.42819 | ||||||||
\(236\) | −8.19890 | −0.533703 | ||||||||
\(237\) | −31.9164 | −2.07319 | ||||||||
\(238\) | 13.6595 | 0.885417 | ||||||||
\(239\) | −17.4412 | −1.12818 | −0.564090 | − | 0.825713i | \(-0.690773\pi\) | ||||
−0.564090 | + | 0.825713i | \(0.690773\pi\) | |||||||
\(240\) | 10.1524 | 0.655331 | ||||||||
\(241\) | 24.0619 | 1.54996 | 0.774981 | − | 0.631984i | \(-0.217759\pi\) | ||||
0.774981 | + | 0.631984i | \(0.217759\pi\) | |||||||
\(242\) | −10.5686 | −0.679377 | ||||||||
\(243\) | 6.14735 | 0.394352 | ||||||||
\(244\) | −14.6553 | −0.938208 | ||||||||
\(245\) | 5.23342 | 0.334351 | ||||||||
\(246\) | −25.6279 | −1.63398 | ||||||||
\(247\) | 3.77684 | 0.240315 | ||||||||
\(248\) | 7.36041 | 0.467386 | ||||||||
\(249\) | 7.15353 | 0.453337 | ||||||||
\(250\) | −6.72521 | −0.425340 | ||||||||
\(251\) | 23.6182 | 1.49077 | 0.745385 | − | 0.666634i | \(-0.232266\pi\) | ||||
0.745385 | + | 0.666634i | \(0.232266\pi\) | |||||||
\(252\) | 13.1822 | 0.830398 | ||||||||
\(253\) | 1.67099 | 0.105054 | ||||||||
\(254\) | −11.5680 | −0.725843 | ||||||||
\(255\) | 59.2082 | 3.70776 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 17.5055 | 1.09197 | 0.545983 | − | 0.837796i | \(-0.316156\pi\) | ||||
0.545983 | + | 0.837796i | \(0.316156\pi\) | |||||||
\(258\) | −8.57321 | −0.533745 | ||||||||
\(259\) | −11.3913 | −0.707818 | ||||||||
\(260\) | −7.55427 | −0.468496 | ||||||||
\(261\) | −2.65080 | −0.164080 | ||||||||
\(262\) | −6.72344 | −0.415376 | ||||||||
\(263\) | −8.91082 | −0.549465 | −0.274732 | − | 0.961521i | \(-0.588589\pi\) | ||||
−0.274732 | + | 0.961521i | \(0.588589\pi\) | |||||||
\(264\) | 1.92925 | 0.118737 | ||||||||
\(265\) | 41.6627 | 2.55932 | ||||||||
\(266\) | 4.04729 | 0.248155 | ||||||||
\(267\) | 31.8651 | 1.95011 | ||||||||
\(268\) | 10.6610 | 0.651225 | ||||||||
\(269\) | 28.9927 | 1.76772 | 0.883858 | − | 0.467755i | \(-0.154937\pi\) | ||||
0.883858 | + | 0.467755i | \(0.154937\pi\) | |||||||
\(270\) | 26.6819 | 1.62381 | ||||||||
\(271\) | 9.15317 | 0.556016 | 0.278008 | − | 0.960579i | \(-0.410326\pi\) | ||||
0.278008 | + | 0.960579i | \(0.410326\pi\) | |||||||
\(272\) | 5.83197 | 0.353615 | ||||||||
\(273\) | −15.0371 | −0.910088 | ||||||||
\(274\) | −4.65670 | −0.281322 | ||||||||
\(275\) | −4.56197 | −0.275097 | ||||||||
\(276\) | 7.47314 | 0.449830 | ||||||||
\(277\) | −19.9289 | −1.19741 | −0.598705 | − | 0.800970i | \(-0.704318\pi\) | ||||
−0.598705 | + | 0.800970i | \(0.704318\pi\) | |||||||
\(278\) | 5.37841 | 0.322576 | ||||||||
\(279\) | 41.4255 | 2.48008 | ||||||||
\(280\) | −8.09521 | −0.483782 | ||||||||
\(281\) | 25.8846 | 1.54414 | 0.772072 | − | 0.635535i | \(-0.219221\pi\) | ||||
0.772072 | + | 0.635535i | \(0.219221\pi\) | |||||||
\(282\) | 18.6068 | 1.10802 | ||||||||
\(283\) | 32.2342 | 1.91613 | 0.958063 | − | 0.286559i | \(-0.0925113\pi\) | ||||
0.958063 | + | 0.286559i | \(0.0925113\pi\) | |||||||
\(284\) | −2.15041 | −0.127603 | ||||||||
\(285\) | 17.5432 | 1.03917 | ||||||||
\(286\) | −1.43554 | −0.0848852 | ||||||||
\(287\) | 20.4350 | 1.20624 | ||||||||
\(288\) | 5.62815 | 0.331642 | ||||||||
\(289\) | 17.0119 | 1.00070 | ||||||||
\(290\) | 1.62786 | 0.0955915 | ||||||||
\(291\) | −24.3119 | −1.42519 | ||||||||
\(292\) | 6.44525 | 0.377179 | ||||||||
\(293\) | 4.39700 | 0.256875 | 0.128438 | − | 0.991718i | \(-0.459004\pi\) | ||||
0.128438 | + | 0.991718i | \(0.459004\pi\) | |||||||
\(294\) | 4.44771 | 0.259396 | ||||||||
\(295\) | 28.3376 | 1.64988 | ||||||||
\(296\) | −4.86352 | −0.282686 | ||||||||
\(297\) | 5.07037 | 0.294213 | ||||||||
\(298\) | −17.8551 | −1.03432 | ||||||||
\(299\) | −5.56070 | −0.321583 | ||||||||
\(300\) | −20.4024 | −1.17793 | ||||||||
\(301\) | 6.83605 | 0.394024 | ||||||||
\(302\) | 14.8705 | 0.855700 | ||||||||
\(303\) | −54.1445 | −3.11052 | ||||||||
\(304\) | 1.72800 | 0.0991075 | ||||||||
\(305\) | 50.6526 | 2.90036 | ||||||||
\(306\) | 32.8233 | 1.87638 | ||||||||
\(307\) | −14.0069 | −0.799416 | −0.399708 | − | 0.916642i | \(-0.630889\pi\) | ||||
−0.399708 | + | 0.916642i | \(0.630889\pi\) | |||||||
\(308\) | −1.53833 | −0.0876547 | ||||||||
\(309\) | −25.6317 | −1.45814 | ||||||||
\(310\) | −25.4396 | −1.44487 | ||||||||
\(311\) | 31.7035 | 1.79774 | 0.898871 | − | 0.438213i | \(-0.144388\pi\) | ||||
0.898871 | + | 0.438213i | \(0.144388\pi\) | |||||||
\(312\) | −6.42013 | −0.363468 | ||||||||
\(313\) | 3.81305 | 0.215526 | 0.107763 | − | 0.994177i | \(-0.465631\pi\) | ||||
0.107763 | + | 0.994177i | \(0.465631\pi\) | |||||||
\(314\) | 7.61667 | 0.429834 | ||||||||
\(315\) | −45.5611 | −2.56708 | ||||||||
\(316\) | 10.8656 | 0.611240 | ||||||||
\(317\) | −2.62533 | −0.147453 | −0.0737265 | − | 0.997278i | \(-0.523489\pi\) | ||||
−0.0737265 | + | 0.997278i | \(0.523489\pi\) | |||||||
\(318\) | 35.4077 | 1.98557 | ||||||||
\(319\) | 0.309343 | 0.0173199 | ||||||||
\(320\) | −3.45627 | −0.193211 | ||||||||
\(321\) | −24.6192 | −1.37411 | ||||||||
\(322\) | −5.95888 | −0.332076 | ||||||||
\(323\) | 10.0776 | 0.560735 | ||||||||
\(324\) | 5.79166 | 0.321759 | ||||||||
\(325\) | 15.1812 | 0.842104 | ||||||||
\(326\) | −3.99369 | −0.221190 | ||||||||
\(327\) | −44.7074 | −2.47232 | ||||||||
\(328\) | 8.72477 | 0.481745 | ||||||||
\(329\) | −14.8366 | −0.817968 | ||||||||
\(330\) | −6.66801 | −0.367062 | ||||||||
\(331\) | 23.9944 | 1.31885 | 0.659425 | − | 0.751770i | \(-0.270800\pi\) | ||||
0.659425 | + | 0.751770i | \(0.270800\pi\) | |||||||
\(332\) | −2.43535 | −0.133657 | ||||||||
\(333\) | −27.3726 | −1.50001 | ||||||||
\(334\) | −20.5551 | −1.12472 | ||||||||
\(335\) | −36.8473 | −2.01319 | ||||||||
\(336\) | −6.87986 | −0.375327 | ||||||||
\(337\) | −15.7215 | −0.856405 | −0.428203 | − | 0.903683i | \(-0.640853\pi\) | ||||
−0.428203 | + | 0.903683i | \(0.640853\pi\) | |||||||
\(338\) | −8.22284 | −0.447263 | ||||||||
\(339\) | −42.6288 | −2.31528 | ||||||||
\(340\) | −20.1569 | −1.09316 | ||||||||
\(341\) | −4.83428 | −0.261791 | ||||||||
\(342\) | 9.72544 | 0.525892 | ||||||||
\(343\) | −19.9418 | −1.07675 | ||||||||
\(344\) | 2.91867 | 0.157364 | ||||||||
\(345\) | −25.8292 | −1.39060 | ||||||||
\(346\) | 19.2480 | 1.03478 | ||||||||
\(347\) | 11.6722 | 0.626596 | 0.313298 | − | 0.949655i | \(-0.398566\pi\) | ||||
0.313298 | + | 0.949655i | \(0.398566\pi\) | |||||||
\(348\) | 1.38347 | 0.0741617 | ||||||||
\(349\) | 3.37470 | 0.180643 | 0.0903217 | − | 0.995913i | \(-0.471210\pi\) | ||||
0.0903217 | + | 0.995913i | \(0.471210\pi\) | |||||||
\(350\) | 16.2683 | 0.869579 | ||||||||
\(351\) | −16.8731 | −0.900620 | ||||||||
\(352\) | −0.656795 | −0.0350073 | ||||||||
\(353\) | −9.97235 | −0.530775 | −0.265387 | − | 0.964142i | \(-0.585500\pi\) | ||||
−0.265387 | + | 0.964142i | \(0.585500\pi\) | |||||||
\(354\) | 24.0832 | 1.28001 | ||||||||
\(355\) | 7.43240 | 0.394471 | ||||||||
\(356\) | −10.8482 | −0.574952 | ||||||||
\(357\) | −40.1232 | −2.12354 | ||||||||
\(358\) | 11.9834 | 0.633341 | ||||||||
\(359\) | 4.48256 | 0.236580 | 0.118290 | − | 0.992979i | \(-0.462259\pi\) | ||||
0.118290 | + | 0.992979i | \(0.462259\pi\) | |||||||
\(360\) | −19.4524 | −1.02523 | ||||||||
\(361\) | −16.0140 | −0.842843 | ||||||||
\(362\) | −22.1192 | −1.16256 | ||||||||
\(363\) | 31.0440 | 1.62939 | ||||||||
\(364\) | 5.11924 | 0.268321 | ||||||||
\(365\) | −22.2765 | −1.16601 | ||||||||
\(366\) | 43.0480 | 2.25015 | ||||||||
\(367\) | −12.7562 | −0.665870 | −0.332935 | − | 0.942950i | \(-0.608039\pi\) | ||||
−0.332935 | + | 0.942950i | \(0.608039\pi\) | |||||||
\(368\) | −2.54416 | −0.132623 | ||||||||
\(369\) | 49.1044 | 2.55627 | ||||||||
\(370\) | 16.8096 | 0.873891 | ||||||||
\(371\) | −28.2332 | −1.46579 | ||||||||
\(372\) | −21.6203 | −1.12096 | ||||||||
\(373\) | 8.66272 | 0.448539 | 0.224269 | − | 0.974527i | \(-0.428000\pi\) | ||||
0.224269 | + | 0.974527i | \(0.428000\pi\) | |||||||
\(374\) | −3.83041 | −0.198066 | ||||||||
\(375\) | 19.7545 | 1.02012 | ||||||||
\(376\) | −6.33452 | −0.326678 | ||||||||
\(377\) | −1.02943 | −0.0530182 | ||||||||
\(378\) | −18.0813 | −0.930004 | ||||||||
\(379\) | −5.69401 | −0.292482 | −0.146241 | − | 0.989249i | \(-0.546717\pi\) | ||||
−0.146241 | + | 0.989249i | \(0.546717\pi\) | |||||||
\(380\) | −5.97243 | −0.306379 | ||||||||
\(381\) | 33.9796 | 1.74083 | ||||||||
\(382\) | −13.9667 | −0.714600 | ||||||||
\(383\) | 32.1072 | 1.64060 | 0.820300 | − | 0.571934i | \(-0.193807\pi\) | ||||
0.820300 | + | 0.571934i | \(0.193807\pi\) | |||||||
\(384\) | −2.93737 | −0.149897 | ||||||||
\(385\) | 5.31690 | 0.270974 | ||||||||
\(386\) | −6.62364 | −0.337135 | ||||||||
\(387\) | 16.4267 | 0.835017 | ||||||||
\(388\) | 8.27674 | 0.420188 | ||||||||
\(389\) | −28.0029 | −1.41980 | −0.709902 | − | 0.704301i | \(-0.751261\pi\) | ||||
−0.709902 | + | 0.704301i | \(0.751261\pi\) | |||||||
\(390\) | 22.1897 | 1.12362 | ||||||||
\(391\) | −14.8375 | −0.750363 | ||||||||
\(392\) | −1.51418 | −0.0764777 | ||||||||
\(393\) | 19.7493 | 0.996218 | ||||||||
\(394\) | −9.12796 | −0.459860 | ||||||||
\(395\) | −37.5546 | −1.88958 | ||||||||
\(396\) | −3.69654 | −0.185758 | ||||||||
\(397\) | 11.5059 | 0.577462 | 0.288731 | − | 0.957410i | \(-0.406767\pi\) | ||||
0.288731 | + | 0.957410i | \(0.406767\pi\) | |||||||
\(398\) | 2.28989 | 0.114782 | ||||||||
\(399\) | −11.8884 | −0.595164 | ||||||||
\(400\) | 6.94580 | 0.347290 | ||||||||
\(401\) | −4.18547 | −0.209013 | −0.104506 | − | 0.994524i | \(-0.533326\pi\) | ||||
−0.104506 | + | 0.994524i | \(0.533326\pi\) | |||||||
\(402\) | −31.3154 | −1.56187 | ||||||||
\(403\) | 16.0874 | 0.801373 | ||||||||
\(404\) | 18.4330 | 0.917075 | ||||||||
\(405\) | −20.0175 | −0.994679 | ||||||||
\(406\) | −1.10314 | −0.0547480 | ||||||||
\(407\) | 3.19434 | 0.158337 | ||||||||
\(408\) | −17.1307 | −0.848095 | ||||||||
\(409\) | 34.4497 | 1.70343 | 0.851713 | − | 0.524008i | \(-0.175564\pi\) | ||||
0.851713 | + | 0.524008i | \(0.175564\pi\) | |||||||
\(410\) | −30.1552 | −1.48926 | ||||||||
\(411\) | 13.6785 | 0.674709 | ||||||||
\(412\) | 8.72607 | 0.429902 | ||||||||
\(413\) | −19.2033 | −0.944934 | ||||||||
\(414\) | −14.3189 | −0.703736 | ||||||||
\(415\) | 8.41723 | 0.413186 | ||||||||
\(416\) | 2.18567 | 0.107161 | ||||||||
\(417\) | −15.7984 | −0.773651 | ||||||||
\(418\) | −1.13494 | −0.0555118 | ||||||||
\(419\) | −18.3632 | −0.897101 | −0.448551 | − | 0.893757i | \(-0.648060\pi\) | ||||
−0.448551 | + | 0.893757i | \(0.648060\pi\) | |||||||
\(420\) | 23.7787 | 1.16028 | ||||||||
\(421\) | 2.40129 | 0.117032 | 0.0585158 | − | 0.998286i | \(-0.481363\pi\) | ||||
0.0585158 | + | 0.998286i | \(0.481363\pi\) | |||||||
\(422\) | 9.98014 | 0.485826 | ||||||||
\(423\) | −35.6516 | −1.73344 | ||||||||
\(424\) | −12.0542 | −0.585405 | ||||||||
\(425\) | 40.5077 | 1.96491 | ||||||||
\(426\) | 6.31656 | 0.306038 | ||||||||
\(427\) | −34.3253 | −1.66112 | ||||||||
\(428\) | 8.38135 | 0.405128 | ||||||||
\(429\) | 4.21671 | 0.203585 | ||||||||
\(430\) | −10.0877 | −0.486472 | ||||||||
\(431\) | 23.4929 | 1.13162 | 0.565808 | − | 0.824537i | \(-0.308564\pi\) | ||||
0.565808 | + | 0.824537i | \(0.308564\pi\) | |||||||
\(432\) | −7.71987 | −0.371422 | ||||||||
\(433\) | 18.9816 | 0.912197 | 0.456099 | − | 0.889929i | \(-0.349246\pi\) | ||||
0.456099 | + | 0.889929i | \(0.349246\pi\) | |||||||
\(434\) | 17.2394 | 0.827519 | ||||||||
\(435\) | −4.78164 | −0.229262 | ||||||||
\(436\) | 15.2202 | 0.728915 | ||||||||
\(437\) | −4.39630 | −0.210304 | ||||||||
\(438\) | −18.9321 | −0.904610 | ||||||||
\(439\) | −5.98493 | −0.285645 | −0.142823 | − | 0.989748i | \(-0.545618\pi\) | ||||
−0.142823 | + | 0.989748i | \(0.545618\pi\) | |||||||
\(440\) | 2.27006 | 0.108221 | ||||||||
\(441\) | −8.52205 | −0.405812 | ||||||||
\(442\) | 12.7468 | 0.606303 | ||||||||
\(443\) | 19.9090 | 0.945906 | 0.472953 | − | 0.881088i | \(-0.343188\pi\) | ||||
0.472953 | + | 0.881088i | \(0.343188\pi\) | |||||||
\(444\) | 14.2860 | 0.677982 | ||||||||
\(445\) | 37.4942 | 1.77740 | ||||||||
\(446\) | 12.7627 | 0.604333 | ||||||||
\(447\) | 52.4471 | 2.48066 | ||||||||
\(448\) | 2.34218 | 0.110658 | ||||||||
\(449\) | 6.38575 | 0.301362 | 0.150681 | − | 0.988582i | \(-0.451853\pi\) | ||||
0.150681 | + | 0.988582i | \(0.451853\pi\) | |||||||
\(450\) | 39.0920 | 1.84282 | ||||||||
\(451\) | −5.73039 | −0.269833 | ||||||||
\(452\) | 14.5126 | 0.682614 | ||||||||
\(453\) | −43.6801 | −2.05227 | ||||||||
\(454\) | 2.90519 | 0.136347 | ||||||||
\(455\) | −17.6935 | −0.829484 | ||||||||
\(456\) | −5.07577 | −0.237695 | ||||||||
\(457\) | −24.4654 | −1.14444 | −0.572221 | − | 0.820099i | \(-0.693918\pi\) | ||||
−0.572221 | + | 0.820099i | \(0.693918\pi\) | |||||||
\(458\) | 2.08724 | 0.0975303 | ||||||||
\(459\) | −45.0221 | −2.10145 | ||||||||
\(460\) | 8.79330 | 0.409990 | ||||||||
\(461\) | −0.238585 | −0.0111120 | −0.00555602 | − | 0.999985i | \(-0.501769\pi\) | ||||
−0.00555602 | + | 0.999985i | \(0.501769\pi\) | |||||||
\(462\) | 4.51866 | 0.210227 | ||||||||
\(463\) | −1.83537 | −0.0852969 | −0.0426485 | − | 0.999090i | \(-0.513580\pi\) | ||||
−0.0426485 | + | 0.999090i | \(0.513580\pi\) | |||||||
\(464\) | −0.470989 | −0.0218651 | ||||||||
\(465\) | 74.7254 | 3.46531 | ||||||||
\(466\) | 4.84432 | 0.224409 | ||||||||
\(467\) | −0.102036 | −0.00472164 | −0.00236082 | − | 0.999997i | \(-0.500751\pi\) | ||||
−0.00236082 | + | 0.999997i | \(0.500751\pi\) | |||||||
\(468\) | 12.3013 | 0.568628 | ||||||||
\(469\) | 24.9700 | 1.15301 | ||||||||
\(470\) | 21.8938 | 1.00989 | ||||||||
\(471\) | −22.3730 | −1.03089 | ||||||||
\(472\) | −8.19890 | −0.377385 | ||||||||
\(473\) | −1.91697 | −0.0881422 | ||||||||
\(474\) | −31.9164 | −1.46597 | ||||||||
\(475\) | 12.0023 | 0.550705 | ||||||||
\(476\) | 13.6595 | 0.626084 | ||||||||
\(477\) | −67.8430 | −3.10632 | ||||||||
\(478\) | −17.4412 | −0.797744 | ||||||||
\(479\) | −18.6033 | −0.850008 | −0.425004 | − | 0.905192i | \(-0.639727\pi\) | ||||
−0.425004 | + | 0.905192i | \(0.639727\pi\) | |||||||
\(480\) | 10.1524 | 0.463389 | ||||||||
\(481\) | −10.6301 | −0.484689 | ||||||||
\(482\) | 24.0619 | 1.09599 | ||||||||
\(483\) | 17.5035 | 0.796435 | ||||||||
\(484\) | −10.5686 | −0.480392 | ||||||||
\(485\) | −28.6066 | −1.29896 | ||||||||
\(486\) | 6.14735 | 0.278849 | ||||||||
\(487\) | 3.46285 | 0.156917 | 0.0784584 | − | 0.996917i | \(-0.475000\pi\) | ||||
0.0784584 | + | 0.996917i | \(0.475000\pi\) | |||||||
\(488\) | −14.6553 | −0.663413 | ||||||||
\(489\) | 11.7309 | 0.530491 | ||||||||
\(490\) | 5.23342 | 0.236422 | ||||||||
\(491\) | −15.0131 | −0.677532 | −0.338766 | − | 0.940871i | \(-0.610010\pi\) | ||||
−0.338766 | + | 0.940871i | \(0.610010\pi\) | |||||||
\(492\) | −25.6279 | −1.15540 | ||||||||
\(493\) | −2.74679 | −0.123709 | ||||||||
\(494\) | 3.77684 | 0.169928 | ||||||||
\(495\) | 12.7763 | 0.574250 | ||||||||
\(496\) | 7.36041 | 0.330492 | ||||||||
\(497\) | −5.03665 | −0.225925 | ||||||||
\(498\) | 7.15353 | 0.320557 | ||||||||
\(499\) | −3.92722 | −0.175806 | −0.0879032 | − | 0.996129i | \(-0.528017\pi\) | ||||
−0.0879032 | + | 0.996129i | \(0.528017\pi\) | |||||||
\(500\) | −6.72521 | −0.300761 | ||||||||
\(501\) | 60.3778 | 2.69748 | ||||||||
\(502\) | 23.6182 | 1.05413 | ||||||||
\(503\) | 43.1056 | 1.92198 | 0.960991 | − | 0.276579i | \(-0.0892007\pi\) | ||||
0.960991 | + | 0.276579i | \(0.0892007\pi\) | |||||||
\(504\) | 13.1822 | 0.587180 | ||||||||
\(505\) | −63.7093 | −2.83503 | ||||||||
\(506\) | 1.67099 | 0.0742846 | ||||||||
\(507\) | 24.1535 | 1.07270 | ||||||||
\(508\) | −11.5680 | −0.513249 | ||||||||
\(509\) | −28.5067 | −1.26354 | −0.631769 | − | 0.775157i | \(-0.717671\pi\) | ||||
−0.631769 | + | 0.775157i | \(0.717671\pi\) | |||||||
\(510\) | 59.2082 | 2.62179 | ||||||||
\(511\) | 15.0959 | 0.667805 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −13.3399 | −0.588972 | ||||||||
\(514\) | 17.5055 | 0.772136 | ||||||||
\(515\) | −30.1596 | −1.32899 | ||||||||
\(516\) | −8.57321 | −0.377415 | ||||||||
\(517\) | 4.16048 | 0.182978 | ||||||||
\(518\) | −11.3913 | −0.500503 | ||||||||
\(519\) | −56.5385 | −2.48177 | ||||||||
\(520\) | −7.55427 | −0.331277 | ||||||||
\(521\) | 20.0442 | 0.878153 | 0.439077 | − | 0.898450i | \(-0.355306\pi\) | ||||
0.439077 | + | 0.898450i | \(0.355306\pi\) | |||||||
\(522\) | −2.65080 | −0.116022 | ||||||||
\(523\) | 15.6380 | 0.683800 | 0.341900 | − | 0.939736i | \(-0.388930\pi\) | ||||
0.341900 | + | 0.939736i | \(0.388930\pi\) | |||||||
\(524\) | −6.72344 | −0.293715 | ||||||||
\(525\) | −47.7861 | −2.08556 | ||||||||
\(526\) | −8.91082 | −0.388530 | ||||||||
\(527\) | 42.9257 | 1.86987 | ||||||||
\(528\) | 1.92925 | 0.0839599 | ||||||||
\(529\) | −16.5273 | −0.718576 | ||||||||
\(530\) | 41.6627 | 1.80971 | ||||||||
\(531\) | −46.1447 | −2.00251 | ||||||||
\(532\) | 4.04729 | 0.175472 | ||||||||
\(533\) | 19.0695 | 0.825992 | ||||||||
\(534\) | 31.8651 | 1.37894 | ||||||||
\(535\) | −28.9682 | −1.25241 | ||||||||
\(536\) | 10.6610 | 0.460486 | ||||||||
\(537\) | −35.1996 | −1.51898 | ||||||||
\(538\) | 28.9927 | 1.24996 | ||||||||
\(539\) | 0.994507 | 0.0428364 | ||||||||
\(540\) | 26.6819 | 1.14821 | ||||||||
\(541\) | 18.2496 | 0.784610 | 0.392305 | − | 0.919835i | \(-0.371678\pi\) | ||||
0.392305 | + | 0.919835i | \(0.371678\pi\) | |||||||
\(542\) | 9.15317 | 0.393162 | ||||||||
\(543\) | 64.9722 | 2.78823 | ||||||||
\(544\) | 5.83197 | 0.250044 | ||||||||
\(545\) | −52.6051 | −2.25335 | ||||||||
\(546\) | −15.0371 | −0.643530 | ||||||||
\(547\) | 34.0979 | 1.45792 | 0.728961 | − | 0.684556i | \(-0.240004\pi\) | ||||
0.728961 | + | 0.684556i | \(0.240004\pi\) | |||||||
\(548\) | −4.65670 | −0.198924 | ||||||||
\(549\) | −82.4821 | −3.52025 | ||||||||
\(550\) | −4.56197 | −0.194523 | ||||||||
\(551\) | −0.813868 | −0.0346719 | ||||||||
\(552\) | 7.47314 | 0.318078 | ||||||||
\(553\) | 25.4493 | 1.08221 | ||||||||
\(554\) | −19.9289 | −0.846697 | ||||||||
\(555\) | −49.3762 | −2.09590 | ||||||||
\(556\) | 5.37841 | 0.228096 | ||||||||
\(557\) | −24.3055 | −1.02986 | −0.514929 | − | 0.857233i | \(-0.672182\pi\) | ||||
−0.514929 | + | 0.857233i | \(0.672182\pi\) | |||||||
\(558\) | 41.4255 | 1.75368 | ||||||||
\(559\) | 6.37925 | 0.269814 | ||||||||
\(560\) | −8.09521 | −0.342085 | ||||||||
\(561\) | 11.2513 | 0.475032 | ||||||||
\(562\) | 25.8846 | 1.09187 | ||||||||
\(563\) | 20.9132 | 0.881386 | 0.440693 | − | 0.897658i | \(-0.354733\pi\) | ||||
0.440693 | + | 0.897658i | \(0.354733\pi\) | |||||||
\(564\) | 18.6068 | 0.783489 | ||||||||
\(565\) | −50.1594 | −2.11022 | ||||||||
\(566\) | 32.2342 | 1.35491 | ||||||||
\(567\) | 13.5651 | 0.569682 | ||||||||
\(568\) | −2.15041 | −0.0902292 | ||||||||
\(569\) | 18.3885 | 0.770885 | 0.385442 | − | 0.922732i | \(-0.374049\pi\) | ||||
0.385442 | + | 0.922732i | \(0.374049\pi\) | |||||||
\(570\) | 17.5432 | 0.734806 | ||||||||
\(571\) | −4.13329 | −0.172973 | −0.0864863 | − | 0.996253i | \(-0.527564\pi\) | ||||
−0.0864863 | + | 0.996253i | \(0.527564\pi\) | |||||||
\(572\) | −1.43554 | −0.0600229 | ||||||||
\(573\) | 41.0255 | 1.71386 | ||||||||
\(574\) | 20.4350 | 0.852941 | ||||||||
\(575\) | −17.6712 | −0.736941 | ||||||||
\(576\) | 5.62815 | 0.234506 | ||||||||
\(577\) | 0.0386552 | 0.00160924 | 0.000804618 | − | 1.00000i | \(-0.499744\pi\) | ||||
0.000804618 | 1.00000i | \(0.499744\pi\) | ||||||||
\(578\) | 17.0119 | 0.707603 | ||||||||
\(579\) | 19.4561 | 0.808568 | ||||||||
\(580\) | 1.62786 | 0.0675934 | ||||||||
\(581\) | −5.70404 | −0.236643 | ||||||||
\(582\) | −24.3119 | −1.00776 | ||||||||
\(583\) | 7.91715 | 0.327895 | ||||||||
\(584\) | 6.44525 | 0.266706 | ||||||||
\(585\) | −42.5166 | −1.75785 | ||||||||
\(586\) | 4.39700 | 0.181638 | ||||||||
\(587\) | 39.1374 | 1.61537 | 0.807687 | − | 0.589612i | \(-0.200719\pi\) | ||||
0.807687 | + | 0.589612i | \(0.200719\pi\) | |||||||
\(588\) | 4.44771 | 0.183421 | ||||||||
\(589\) | 12.7188 | 0.524068 | ||||||||
\(590\) | 28.3376 | 1.16664 | ||||||||
\(591\) | 26.8122 | 1.10291 | ||||||||
\(592\) | −4.86352 | −0.199889 | ||||||||
\(593\) | 18.4599 | 0.758057 | 0.379028 | − | 0.925385i | \(-0.376258\pi\) | ||||
0.379028 | + | 0.925385i | \(0.376258\pi\) | |||||||
\(594\) | 5.07037 | 0.208040 | ||||||||
\(595\) | −47.2111 | −1.93547 | ||||||||
\(596\) | −17.8551 | −0.731374 | ||||||||
\(597\) | −6.72625 | −0.275287 | ||||||||
\(598\) | −5.56070 | −0.227394 | ||||||||
\(599\) | −29.2823 | −1.19644 | −0.598221 | − | 0.801331i | \(-0.704125\pi\) | ||||
−0.598221 | + | 0.801331i | \(0.704125\pi\) | |||||||
\(600\) | −20.4024 | −0.832925 | ||||||||
\(601\) | 7.08242 | 0.288898 | 0.144449 | − | 0.989512i | \(-0.453859\pi\) | ||||
0.144449 | + | 0.989512i | \(0.453859\pi\) | |||||||
\(602\) | 6.83605 | 0.278617 | ||||||||
\(603\) | 60.0018 | 2.44346 | ||||||||
\(604\) | 14.8705 | 0.605071 | ||||||||
\(605\) | 36.5280 | 1.48507 | ||||||||
\(606\) | −54.1445 | −2.19947 | ||||||||
\(607\) | −18.9946 | −0.770967 | −0.385484 | − | 0.922715i | \(-0.625965\pi\) | ||||
−0.385484 | + | 0.922715i | \(0.625965\pi\) | |||||||
\(608\) | 1.72800 | 0.0700796 | ||||||||
\(609\) | 3.24034 | 0.131305 | ||||||||
\(610\) | 50.6526 | 2.05086 | ||||||||
\(611\) | −13.8452 | −0.560116 | ||||||||
\(612\) | 32.8233 | 1.32680 | ||||||||
\(613\) | 6.63738 | 0.268081 | 0.134041 | − | 0.990976i | \(-0.457205\pi\) | ||||
0.134041 | + | 0.990976i | \(0.457205\pi\) | |||||||
\(614\) | −14.0069 | −0.565273 | ||||||||
\(615\) | 88.5770 | 3.57177 | ||||||||
\(616\) | −1.53833 | −0.0619812 | ||||||||
\(617\) | 38.3917 | 1.54559 | 0.772796 | − | 0.634654i | \(-0.218858\pi\) | ||||
0.772796 | + | 0.634654i | \(0.218858\pi\) | |||||||
\(618\) | −25.6317 | −1.03106 | ||||||||
\(619\) | 8.07832 | 0.324695 | 0.162348 | − | 0.986734i | \(-0.448093\pi\) | ||||
0.162348 | + | 0.986734i | \(0.448093\pi\) | |||||||
\(620\) | −25.4396 | −1.02168 | ||||||||
\(621\) | 19.6406 | 0.788149 | ||||||||
\(622\) | 31.7035 | 1.27120 | ||||||||
\(623\) | −25.4084 | −1.01797 | ||||||||
\(624\) | −6.42013 | −0.257011 | ||||||||
\(625\) | −11.4849 | −0.459394 | ||||||||
\(626\) | 3.81305 | 0.152400 | ||||||||
\(627\) | 3.33374 | 0.133137 | ||||||||
\(628\) | 7.61667 | 0.303938 | ||||||||
\(629\) | −28.3639 | −1.13094 | ||||||||
\(630\) | −45.5611 | −1.81520 | ||||||||
\(631\) | 8.63352 | 0.343695 | 0.171848 | − | 0.985124i | \(-0.445026\pi\) | ||||
0.171848 | + | 0.985124i | \(0.445026\pi\) | |||||||
\(632\) | 10.8656 | 0.432212 | ||||||||
\(633\) | −29.3154 | −1.16518 | ||||||||
\(634\) | −2.62533 | −0.104265 | ||||||||
\(635\) | 39.9823 | 1.58665 | ||||||||
\(636\) | 35.4077 | 1.40401 | ||||||||
\(637\) | −3.30950 | −0.131127 | ||||||||
\(638\) | 0.309343 | 0.0122470 | ||||||||
\(639\) | −12.1028 | −0.478781 | ||||||||
\(640\) | −3.45627 | −0.136621 | ||||||||
\(641\) | −15.9103 | −0.628421 | −0.314210 | − | 0.949353i | \(-0.601740\pi\) | ||||
−0.314210 | + | 0.949353i | \(0.601740\pi\) | |||||||
\(642\) | −24.6192 | −0.971641 | ||||||||
\(643\) | −7.85935 | −0.309942 | −0.154971 | − | 0.987919i | \(-0.549528\pi\) | ||||
−0.154971 | + | 0.987919i | \(0.549528\pi\) | |||||||
\(644\) | −5.95888 | −0.234813 | ||||||||
\(645\) | 29.6313 | 1.16673 | ||||||||
\(646\) | 10.0776 | 0.396500 | ||||||||
\(647\) | −25.9792 | −1.02135 | −0.510675 | − | 0.859774i | \(-0.670604\pi\) | ||||
−0.510675 | + | 0.859774i | \(0.670604\pi\) | |||||||
\(648\) | 5.79166 | 0.227518 | ||||||||
\(649\) | 5.38500 | 0.211380 | ||||||||
\(650\) | 15.1812 | 0.595458 | ||||||||
\(651\) | −50.6386 | −1.98468 | ||||||||
\(652\) | −3.99369 | −0.156405 | ||||||||
\(653\) | −12.2098 | −0.477807 | −0.238903 | − | 0.971043i | \(-0.576788\pi\) | ||||
−0.238903 | + | 0.971043i | \(0.576788\pi\) | |||||||
\(654\) | −44.7074 | −1.74820 | ||||||||
\(655\) | 23.2380 | 0.907985 | ||||||||
\(656\) | 8.72477 | 0.340645 | ||||||||
\(657\) | 36.2748 | 1.41522 | ||||||||
\(658\) | −14.8366 | −0.578391 | ||||||||
\(659\) | −21.1041 | −0.822099 | −0.411050 | − | 0.911613i | \(-0.634838\pi\) | ||||
−0.411050 | + | 0.911613i | \(0.634838\pi\) | |||||||
\(660\) | −6.66801 | −0.259552 | ||||||||
\(661\) | −46.6871 | −1.81592 | −0.907959 | − | 0.419059i | \(-0.862360\pi\) | ||||
−0.907959 | + | 0.419059i | \(0.862360\pi\) | |||||||
\(662\) | 23.9944 | 0.932568 | ||||||||
\(663\) | −37.4421 | −1.45413 | ||||||||
\(664\) | −2.43535 | −0.0945099 | ||||||||
\(665\) | −13.9885 | −0.542452 | ||||||||
\(666\) | −27.3726 | −1.06067 | ||||||||
\(667\) | 1.19827 | 0.0463972 | ||||||||
\(668\) | −20.5551 | −0.795299 | ||||||||
\(669\) | −37.4889 | −1.44940 | ||||||||
\(670\) | −36.8473 | −1.42354 | ||||||||
\(671\) | 9.62551 | 0.371589 | ||||||||
\(672\) | −6.87986 | −0.265396 | ||||||||
\(673\) | −44.0678 | −1.69869 | −0.849345 | − | 0.527838i | \(-0.823003\pi\) | ||||
−0.849345 | + | 0.527838i | \(0.823003\pi\) | |||||||
\(674\) | −15.7215 | −0.605570 | ||||||||
\(675\) | −53.6207 | −2.06386 | ||||||||
\(676\) | −8.22284 | −0.316263 | ||||||||
\(677\) | −27.3116 | −1.04967 | −0.524836 | − | 0.851203i | \(-0.675873\pi\) | ||||
−0.524836 | + | 0.851203i | \(0.675873\pi\) | |||||||
\(678\) | −42.6288 | −1.63715 | ||||||||
\(679\) | 19.3856 | 0.743952 | ||||||||
\(680\) | −20.1569 | −0.772981 | ||||||||
\(681\) | −8.53362 | −0.327009 | ||||||||
\(682\) | −4.83428 | −0.185114 | ||||||||
\(683\) | −10.5043 | −0.401937 | −0.200968 | − | 0.979598i | \(-0.564409\pi\) | ||||
−0.200968 | + | 0.979598i | \(0.564409\pi\) | |||||||
\(684\) | 9.72544 | 0.371862 | ||||||||
\(685\) | 16.0948 | 0.614951 | ||||||||
\(686\) | −19.9418 | −0.761380 | ||||||||
\(687\) | −6.13100 | −0.233912 | ||||||||
\(688\) | 2.91867 | 0.111273 | ||||||||
\(689\) | −26.3466 | −1.00373 | ||||||||
\(690\) | −25.8292 | −0.983300 | ||||||||
\(691\) | 9.12533 | 0.347144 | 0.173572 | − | 0.984821i | \(-0.444469\pi\) | ||||
0.173572 | + | 0.984821i | \(0.444469\pi\) | |||||||
\(692\) | 19.2480 | 0.731699 | ||||||||
\(693\) | −8.65798 | −0.328889 | ||||||||
\(694\) | 11.6722 | 0.443070 | ||||||||
\(695\) | −18.5892 | −0.705130 | ||||||||
\(696\) | 1.38347 | 0.0524403 | ||||||||
\(697\) | 50.8827 | 1.92732 | ||||||||
\(698\) | 3.37470 | 0.127734 | ||||||||
\(699\) | −14.2296 | −0.538211 | ||||||||
\(700\) | 16.2683 | 0.614885 | ||||||||
\(701\) | −34.7665 | −1.31311 | −0.656556 | − | 0.754277i | \(-0.727988\pi\) | ||||
−0.656556 | + | 0.754277i | \(0.727988\pi\) | |||||||
\(702\) | −16.8731 | −0.636834 | ||||||||
\(703\) | −8.40416 | −0.316969 | ||||||||
\(704\) | −0.656795 | −0.0247539 | ||||||||
\(705\) | −64.3102 | −2.42206 | ||||||||
\(706\) | −9.97235 | −0.375314 | ||||||||
\(707\) | 43.1734 | 1.62370 | ||||||||
\(708\) | 24.0832 | 0.905103 | ||||||||
\(709\) | 38.6532 | 1.45165 | 0.725825 | − | 0.687879i | \(-0.241458\pi\) | ||||
0.725825 | + | 0.687879i | \(0.241458\pi\) | |||||||
\(710\) | 7.43240 | 0.278933 | ||||||||
\(711\) | 61.1535 | 2.29343 | ||||||||
\(712\) | −10.8482 | −0.406552 | ||||||||
\(713\) | −18.7260 | −0.701296 | ||||||||
\(714\) | −40.1232 | −1.50157 | ||||||||
\(715\) | 4.96161 | 0.185554 | ||||||||
\(716\) | 11.9834 | 0.447840 | ||||||||
\(717\) | 51.2314 | 1.91327 | ||||||||
\(718\) | 4.48256 | 0.167288 | ||||||||
\(719\) | −41.5614 | −1.54998 | −0.774989 | − | 0.631975i | \(-0.782244\pi\) | ||||
−0.774989 | + | 0.631975i | \(0.782244\pi\) | |||||||
\(720\) | −19.4524 | −0.724949 | ||||||||
\(721\) | 20.4380 | 0.761152 | ||||||||
\(722\) | −16.0140 | −0.595980 | ||||||||
\(723\) | −70.6787 | −2.62857 | ||||||||
\(724\) | −22.1192 | −0.822052 | ||||||||
\(725\) | −3.27139 | −0.121497 | ||||||||
\(726\) | 31.0440 | 1.15215 | ||||||||
\(727\) | 21.2684 | 0.788801 | 0.394400 | − | 0.918939i | \(-0.370952\pi\) | ||||
0.394400 | + | 0.918939i | \(0.370952\pi\) | |||||||
\(728\) | 5.11924 | 0.189732 | ||||||||
\(729\) | −35.4320 | −1.31230 | ||||||||
\(730\) | −22.2765 | −0.824491 | ||||||||
\(731\) | 17.0216 | 0.629567 | ||||||||
\(732\) | 43.0480 | 1.59110 | ||||||||
\(733\) | −14.4927 | −0.535299 | −0.267650 | − | 0.963516i | \(-0.586247\pi\) | ||||
−0.267650 | + | 0.963516i | \(0.586247\pi\) | |||||||
\(734\) | −12.7562 | −0.470841 | ||||||||
\(735\) | −15.3725 | −0.567023 | ||||||||
\(736\) | −2.54416 | −0.0937789 | ||||||||
\(737\) | −7.00210 | −0.257926 | ||||||||
\(738\) | 49.1044 | 1.80756 | ||||||||
\(739\) | 8.29924 | 0.305292 | 0.152646 | − | 0.988281i | \(-0.451221\pi\) | ||||
0.152646 | + | 0.988281i | \(0.451221\pi\) | |||||||
\(740\) | 16.8096 | 0.617935 | ||||||||
\(741\) | −11.0940 | −0.407548 | ||||||||
\(742\) | −28.2332 | −1.03647 | ||||||||
\(743\) | 52.9087 | 1.94103 | 0.970516 | − | 0.241036i | \(-0.0774873\pi\) | ||||
0.970516 | + | 0.241036i | \(0.0774873\pi\) | |||||||
\(744\) | −21.6203 | −0.792637 | ||||||||
\(745\) | 61.7121 | 2.26096 | ||||||||
\(746\) | 8.66272 | 0.317165 | ||||||||
\(747\) | −13.7065 | −0.501496 | ||||||||
\(748\) | −3.83041 | −0.140054 | ||||||||
\(749\) | 19.6307 | 0.717289 | ||||||||
\(750\) | 19.7545 | 0.721331 | ||||||||
\(751\) | 33.4170 | 1.21940 | 0.609702 | − | 0.792631i | \(-0.291289\pi\) | ||||
0.609702 | + | 0.792631i | \(0.291289\pi\) | |||||||
\(752\) | −6.33452 | −0.230996 | ||||||||
\(753\) | −69.3756 | −2.52819 | ||||||||
\(754\) | −1.02943 | −0.0374895 | ||||||||
\(755\) | −51.3964 | −1.87051 | ||||||||
\(756\) | −18.0813 | −0.657612 | ||||||||
\(757\) | −41.8525 | −1.52116 | −0.760578 | − | 0.649247i | \(-0.775084\pi\) | ||||
−0.760578 | + | 0.649247i | \(0.775084\pi\) | |||||||
\(758\) | −5.69401 | −0.206816 | ||||||||
\(759\) | −4.90832 | −0.178161 | ||||||||
\(760\) | −5.97243 | −0.216643 | ||||||||
\(761\) | 15.3238 | 0.555488 | 0.277744 | − | 0.960655i | \(-0.410413\pi\) | ||||
0.277744 | + | 0.960655i | \(0.410413\pi\) | |||||||
\(762\) | 33.9796 | 1.23095 | ||||||||
\(763\) | 35.6485 | 1.29056 | ||||||||
\(764\) | −13.9667 | −0.505299 | ||||||||
\(765\) | −113.446 | −4.10165 | ||||||||
\(766\) | 32.1072 | 1.16008 | ||||||||
\(767\) | −17.9201 | −0.647058 | ||||||||
\(768\) | −2.93737 | −0.105993 | ||||||||
\(769\) | −38.5588 | −1.39047 | −0.695234 | − | 0.718784i | \(-0.744699\pi\) | ||||
−0.695234 | + | 0.718784i | \(0.744699\pi\) | |||||||
\(770\) | 5.31690 | 0.191608 | ||||||||
\(771\) | −51.4203 | −1.85186 | ||||||||
\(772\) | −6.62364 | −0.238390 | ||||||||
\(773\) | −17.6953 | −0.636456 | −0.318228 | − | 0.948014i | \(-0.603088\pi\) | ||||
−0.318228 | + | 0.948014i | \(0.603088\pi\) | |||||||
\(774\) | 16.4267 | 0.590446 | ||||||||
\(775\) | 51.1239 | 1.83643 | ||||||||
\(776\) | 8.27674 | 0.297118 | ||||||||
\(777\) | 33.4603 | 1.20038 | ||||||||
\(778\) | −28.0029 | −1.00395 | ||||||||
\(779\) | 15.0764 | 0.540168 | ||||||||
\(780\) | 22.1897 | 0.794519 | ||||||||
\(781\) | 1.41238 | 0.0505389 | ||||||||
\(782\) | −14.8375 | −0.530587 | ||||||||
\(783\) | 3.63597 | 0.129939 | ||||||||
\(784\) | −1.51418 | −0.0540779 | ||||||||
\(785\) | −26.3253 | −0.939589 | ||||||||
\(786\) | 19.7493 | 0.704433 | ||||||||
\(787\) | 29.7056 | 1.05889 | 0.529446 | − | 0.848344i | \(-0.322400\pi\) | ||||
0.529446 | + | 0.848344i | \(0.322400\pi\) | |||||||
\(788\) | −9.12796 | −0.325170 | ||||||||
\(789\) | 26.1744 | 0.931833 | ||||||||
\(790\) | −37.5546 | −1.33613 | ||||||||
\(791\) | 33.9911 | 1.20858 | ||||||||
\(792\) | −3.69654 | −0.131351 | ||||||||
\(793\) | −32.0316 | −1.13748 | ||||||||
\(794\) | 11.5059 | 0.408327 | ||||||||
\(795\) | −122.379 | −4.34033 | ||||||||
\(796\) | 2.28989 | 0.0811629 | ||||||||
\(797\) | 15.3006 | 0.541976 | 0.270988 | − | 0.962583i | \(-0.412650\pi\) | ||||
0.270988 | + | 0.962583i | \(0.412650\pi\) | |||||||
\(798\) | −11.8884 | −0.420844 | ||||||||
\(799\) | −36.9427 | −1.30694 | ||||||||
\(800\) | 6.94580 | 0.245571 | ||||||||
\(801\) | −61.0552 | −2.15728 | ||||||||
\(802\) | −4.18547 | −0.147794 | ||||||||
\(803\) | −4.23321 | −0.149387 | ||||||||
\(804\) | −31.3154 | −1.10441 | ||||||||
\(805\) | 20.5955 | 0.725896 | ||||||||
\(806\) | 16.0874 | 0.566656 | ||||||||
\(807\) | −85.1624 | −2.99786 | ||||||||
\(808\) | 18.4330 | 0.648470 | ||||||||
\(809\) | 4.58106 | 0.161061 | 0.0805307 | − | 0.996752i | \(-0.474338\pi\) | ||||
0.0805307 | + | 0.996752i | \(0.474338\pi\) | |||||||
\(810\) | −20.0175 | −0.703344 | ||||||||
\(811\) | −18.4837 | −0.649049 | −0.324524 | − | 0.945877i | \(-0.605204\pi\) | ||||
−0.324524 | + | 0.945877i | \(0.605204\pi\) | |||||||
\(812\) | −1.10314 | −0.0387127 | ||||||||
\(813\) | −26.8863 | −0.942943 | ||||||||
\(814\) | 3.19434 | 0.111961 | ||||||||
\(815\) | 13.8033 | 0.483507 | ||||||||
\(816\) | −17.1307 | −0.599694 | ||||||||
\(817\) | 5.04345 | 0.176448 | ||||||||
\(818\) | 34.4497 | 1.20450 | ||||||||
\(819\) | 28.8119 | 1.00677 | ||||||||
\(820\) | −30.1552 | −1.05306 | ||||||||
\(821\) | −1.57384 | −0.0549274 | −0.0274637 | − | 0.999623i | \(-0.508743\pi\) | ||||
−0.0274637 | + | 0.999623i | \(0.508743\pi\) | |||||||
\(822\) | 13.6785 | 0.477091 | ||||||||
\(823\) | −11.1197 | −0.387609 | −0.193805 | − | 0.981040i | \(-0.562083\pi\) | ||||
−0.193805 | + | 0.981040i | \(0.562083\pi\) | |||||||
\(824\) | 8.72607 | 0.303987 | ||||||||
\(825\) | 13.4002 | 0.466535 | ||||||||
\(826\) | −19.2033 | −0.668169 | ||||||||
\(827\) | −2.55863 | −0.0889724 | −0.0444862 | − | 0.999010i | \(-0.514165\pi\) | ||||
−0.0444862 | + | 0.999010i | \(0.514165\pi\) | |||||||
\(828\) | −14.3189 | −0.497617 | ||||||||
\(829\) | 1.40191 | 0.0486902 | 0.0243451 | − | 0.999704i | \(-0.492250\pi\) | ||||
0.0243451 | + | 0.999704i | \(0.492250\pi\) | |||||||
\(830\) | 8.41723 | 0.292166 | ||||||||
\(831\) | 58.5385 | 2.03068 | ||||||||
\(832\) | 2.18567 | 0.0757746 | ||||||||
\(833\) | −8.83067 | −0.305964 | ||||||||
\(834\) | −15.7984 | −0.547054 | ||||||||
\(835\) | 71.0438 | 2.45857 | ||||||||
\(836\) | −1.13494 | −0.0392527 | ||||||||
\(837\) | −56.8214 | −1.96403 | ||||||||
\(838\) | −18.3632 | −0.634346 | ||||||||
\(839\) | −35.0322 | −1.20944 | −0.604722 | − | 0.796436i | \(-0.706716\pi\) | ||||
−0.604722 | + | 0.796436i | \(0.706716\pi\) | |||||||
\(840\) | 23.7787 | 0.820442 | ||||||||
\(841\) | −28.7782 | −0.992351 | ||||||||
\(842\) | 2.40129 | 0.0827539 | ||||||||
\(843\) | −76.0326 | −2.61870 | ||||||||
\(844\) | 9.98014 | 0.343531 | ||||||||
\(845\) | 28.4203 | 0.977689 | ||||||||
\(846\) | −35.6516 | −1.22573 | ||||||||
\(847\) | −24.7536 | −0.850545 | ||||||||
\(848\) | −12.0542 | −0.413944 | ||||||||
\(849\) | −94.6839 | −3.24954 | ||||||||
\(850\) | 40.5077 | 1.38940 | ||||||||
\(851\) | 12.3736 | 0.424160 | ||||||||
\(852\) | 6.31656 | 0.216402 | ||||||||
\(853\) | 30.3635 | 1.03963 | 0.519814 | − | 0.854279i | \(-0.326001\pi\) | ||||
0.519814 | + | 0.854279i | \(0.326001\pi\) | |||||||
\(854\) | −34.3253 | −1.17459 | ||||||||
\(855\) | −33.6138 | −1.14957 | ||||||||
\(856\) | 8.38135 | 0.286469 | ||||||||
\(857\) | −55.5795 | −1.89856 | −0.949280 | − | 0.314433i | \(-0.898186\pi\) | ||||
−0.949280 | + | 0.314433i | \(0.898186\pi\) | |||||||
\(858\) | 4.21671 | 0.143956 | ||||||||
\(859\) | 9.56023 | 0.326191 | 0.163095 | − | 0.986610i | \(-0.447852\pi\) | ||||
0.163095 | + | 0.986610i | \(0.447852\pi\) | |||||||
\(860\) | −10.0877 | −0.343988 | ||||||||
\(861\) | −60.0252 | −2.04565 | ||||||||
\(862\) | 23.4929 | 0.800173 | ||||||||
\(863\) | −22.8250 | −0.776973 | −0.388487 | − | 0.921454i | \(-0.627002\pi\) | ||||
−0.388487 | + | 0.921454i | \(0.627002\pi\) | |||||||
\(864\) | −7.71987 | −0.262635 | ||||||||
\(865\) | −66.5263 | −2.26196 | ||||||||
\(866\) | 18.9816 | 0.645021 | ||||||||
\(867\) | −49.9704 | −1.69708 | ||||||||
\(868\) | 17.2394 | 0.585144 | ||||||||
\(869\) | −7.13650 | −0.242089 | ||||||||
\(870\) | −4.78164 | −0.162113 | ||||||||
\(871\) | 23.3015 | 0.789541 | ||||||||
\(872\) | 15.2202 | 0.515421 | ||||||||
\(873\) | 46.5828 | 1.57659 | ||||||||
\(874\) | −4.39630 | −0.148707 | ||||||||
\(875\) | −15.7517 | −0.532504 | ||||||||
\(876\) | −18.9321 | −0.639656 | ||||||||
\(877\) | 42.3655 | 1.43058 | 0.715291 | − | 0.698827i | \(-0.246294\pi\) | ||||
0.715291 | + | 0.698827i | \(0.246294\pi\) | |||||||
\(878\) | −5.98493 | −0.201982 | ||||||||
\(879\) | −12.9156 | −0.435633 | ||||||||
\(880\) | 2.27006 | 0.0765237 | ||||||||
\(881\) | 20.9401 | 0.705490 | 0.352745 | − | 0.935720i | \(-0.385248\pi\) | ||||
0.352745 | + | 0.935720i | \(0.385248\pi\) | |||||||
\(882\) | −8.52205 | −0.286952 | ||||||||
\(883\) | 24.3357 | 0.818961 | 0.409480 | − | 0.912319i | \(-0.365710\pi\) | ||||
0.409480 | + | 0.912319i | \(0.365710\pi\) | |||||||
\(884\) | 12.7468 | 0.428721 | ||||||||
\(885\) | −83.2381 | −2.79802 | ||||||||
\(886\) | 19.9090 | 0.668857 | ||||||||
\(887\) | −6.73701 | −0.226207 | −0.113103 | − | 0.993583i | \(-0.536079\pi\) | ||||
−0.113103 | + | 0.993583i | \(0.536079\pi\) | |||||||
\(888\) | 14.2860 | 0.479406 | ||||||||
\(889\) | −27.0945 | −0.908719 | ||||||||
\(890\) | 37.4942 | 1.25681 | ||||||||
\(891\) | −3.80393 | −0.127437 | ||||||||
\(892\) | 12.7627 | 0.427328 | ||||||||
\(893\) | −10.9460 | −0.366295 | ||||||||
\(894\) | 52.4471 | 1.75409 | ||||||||
\(895\) | −41.4178 | −1.38444 | ||||||||
\(896\) | 2.34218 | 0.0782468 | ||||||||
\(897\) | 16.3338 | 0.545371 | ||||||||
\(898\) | 6.38575 | 0.213095 | ||||||||
\(899\) | −3.46667 | −0.115620 | ||||||||
\(900\) | 39.0920 | 1.30307 | ||||||||
\(901\) | −70.2999 | −2.34203 | ||||||||
\(902\) | −5.73039 | −0.190801 | ||||||||
\(903\) | −20.0800 | −0.668222 | ||||||||
\(904\) | 14.5126 | 0.482681 | ||||||||
\(905\) | 76.4498 | 2.54128 | ||||||||
\(906\) | −43.6801 | −1.45117 | ||||||||
\(907\) | 27.9050 | 0.926571 | 0.463285 | − | 0.886209i | \(-0.346670\pi\) | ||||
0.463285 | + | 0.886209i | \(0.346670\pi\) | |||||||
\(908\) | 2.90519 | 0.0964121 | ||||||||
\(909\) | 103.744 | 3.44096 | ||||||||
\(910\) | −17.6935 | −0.586533 | ||||||||
\(911\) | 12.9143 | 0.427870 | 0.213935 | − | 0.976848i | \(-0.431372\pi\) | ||||
0.213935 | + | 0.976848i | \(0.431372\pi\) | |||||||
\(912\) | −5.07577 | −0.168076 | ||||||||
\(913\) | 1.59953 | 0.0529366 | ||||||||
\(914\) | −24.4654 | −0.809243 | ||||||||
\(915\) | −148.785 | −4.91870 | ||||||||
\(916\) | 2.08724 | 0.0689643 | ||||||||
\(917\) | −15.7475 | −0.520029 | ||||||||
\(918\) | −45.0221 | −1.48595 | ||||||||
\(919\) | 32.5572 | 1.07396 | 0.536981 | − | 0.843594i | \(-0.319565\pi\) | ||||
0.536981 | + | 0.843594i | \(0.319565\pi\) | |||||||
\(920\) | 8.79330 | 0.289906 | ||||||||
\(921\) | 41.1435 | 1.35572 | ||||||||
\(922\) | −0.238585 | −0.00785739 | ||||||||
\(923\) | −4.70009 | −0.154705 | ||||||||
\(924\) | 4.51866 | 0.148653 | ||||||||
\(925\) | −33.7810 | −1.11071 | ||||||||
\(926\) | −1.83537 | −0.0603140 | ||||||||
\(927\) | 49.1116 | 1.61304 | ||||||||
\(928\) | −0.470989 | −0.0154610 | ||||||||
\(929\) | −34.7541 | −1.14024 | −0.570122 | − | 0.821560i | \(-0.693104\pi\) | ||||
−0.570122 | + | 0.821560i | \(0.693104\pi\) | |||||||
\(930\) | 74.7254 | 2.45034 | ||||||||
\(931\) | −2.61650 | −0.0857524 | ||||||||
\(932\) | 4.84432 | 0.158681 | ||||||||
\(933\) | −93.1251 | −3.04878 | ||||||||
\(934\) | −0.102036 | −0.00333871 | ||||||||
\(935\) | 13.2389 | 0.432959 | ||||||||
\(936\) | 12.3013 | 0.402081 | ||||||||
\(937\) | −17.1286 | −0.559566 | −0.279783 | − | 0.960063i | \(-0.590263\pi\) | ||||
−0.279783 | + | 0.960063i | \(0.590263\pi\) | |||||||
\(938\) | 24.9700 | 0.815301 | ||||||||
\(939\) | −11.2003 | −0.365509 | ||||||||
\(940\) | 21.8938 | 0.714097 | ||||||||
\(941\) | 32.4308 | 1.05721 | 0.528607 | − | 0.848866i | \(-0.322714\pi\) | ||||
0.528607 | + | 0.848866i | \(0.322714\pi\) | |||||||
\(942\) | −22.3730 | −0.728952 | ||||||||
\(943\) | −22.1972 | −0.722841 | ||||||||
\(944\) | −8.19890 | −0.266851 | ||||||||
\(945\) | 62.4940 | 2.03293 | ||||||||
\(946\) | −1.91697 | −0.0623260 | ||||||||
\(947\) | 60.2748 | 1.95867 | 0.979333 | − | 0.202253i | \(-0.0648265\pi\) | ||||
0.979333 | + | 0.202253i | \(0.0648265\pi\) | |||||||
\(948\) | −31.9164 | −1.03660 | ||||||||
\(949\) | 14.0872 | 0.457290 | ||||||||
\(950\) | 12.0023 | 0.389407 | ||||||||
\(951\) | 7.71156 | 0.250065 | ||||||||
\(952\) | 13.6595 | 0.442708 | ||||||||
\(953\) | −35.6405 | −1.15451 | −0.577254 | − | 0.816565i | \(-0.695876\pi\) | ||||
−0.577254 | + | 0.816565i | \(0.695876\pi\) | |||||||
\(954\) | −67.8430 | −2.19650 | ||||||||
\(955\) | 48.2728 | 1.56207 | ||||||||
\(956\) | −17.4412 | −0.564090 | ||||||||
\(957\) | −0.908656 | −0.0293727 | ||||||||
\(958\) | −18.6033 | −0.601046 | ||||||||
\(959\) | −10.9068 | −0.352200 | ||||||||
\(960\) | 10.1524 | 0.327666 | ||||||||
\(961\) | 23.1756 | 0.747601 | ||||||||
\(962\) | −10.6301 | −0.342727 | ||||||||
\(963\) | 47.1716 | 1.52008 | ||||||||
\(964\) | 24.0619 | 0.774981 | ||||||||
\(965\) | 22.8931 | 0.736955 | ||||||||
\(966\) | 17.5035 | 0.563165 | ||||||||
\(967\) | 23.1386 | 0.744086 | 0.372043 | − | 0.928215i | \(-0.378657\pi\) | ||||
0.372043 | + | 0.928215i | \(0.378657\pi\) | |||||||
\(968\) | −10.5686 | −0.339688 | ||||||||
\(969\) | −29.6018 | −0.950946 | ||||||||
\(970\) | −28.6066 | −0.918504 | ||||||||
\(971\) | 1.44238 | 0.0462881 | 0.0231440 | − | 0.999732i | \(-0.492632\pi\) | ||||
0.0231440 | + | 0.999732i | \(0.492632\pi\) | |||||||
\(972\) | 6.14735 | 0.197176 | ||||||||
\(973\) | 12.5972 | 0.403848 | ||||||||
\(974\) | 3.46285 | 0.110957 | ||||||||
\(975\) | −44.5930 | −1.42812 | ||||||||
\(976\) | −14.6553 | −0.469104 | ||||||||
\(977\) | −24.0426 | −0.769190 | −0.384595 | − | 0.923085i | \(-0.625659\pi\) | ||||
−0.384595 | + | 0.923085i | \(0.625659\pi\) | |||||||
\(978\) | 11.7309 | 0.375114 | ||||||||
\(979\) | 7.12502 | 0.227717 | ||||||||
\(980\) | 5.23342 | 0.167175 | ||||||||
\(981\) | 85.6616 | 2.73496 | ||||||||
\(982\) | −15.0131 | −0.479088 | ||||||||
\(983\) | −10.3359 | −0.329664 | −0.164832 | − | 0.986322i | \(-0.552708\pi\) | ||||
−0.164832 | + | 0.986322i | \(0.552708\pi\) | |||||||
\(984\) | −25.6279 | −0.816988 | ||||||||
\(985\) | 31.5487 | 1.00523 | ||||||||
\(986\) | −2.74679 | −0.0874758 | ||||||||
\(987\) | 43.5806 | 1.38719 | ||||||||
\(988\) | 3.77684 | 0.120157 | ||||||||
\(989\) | −7.42556 | −0.236119 | ||||||||
\(990\) | 12.7763 | 0.406056 | ||||||||
\(991\) | 45.1795 | 1.43517 | 0.717587 | − | 0.696469i | \(-0.245247\pi\) | ||||
0.717587 | + | 0.696469i | \(0.245247\pi\) | |||||||
\(992\) | 7.36041 | 0.233693 | ||||||||
\(993\) | −70.4804 | −2.23663 | ||||||||
\(994\) | −5.03665 | −0.159753 | ||||||||
\(995\) | −7.91447 | −0.250905 | ||||||||
\(996\) | 7.15353 | 0.226668 | ||||||||
\(997\) | 25.2300 | 0.799041 | 0.399521 | − | 0.916724i | \(-0.369177\pi\) | ||||
0.399521 | + | 0.916724i | \(0.369177\pi\) | |||||||
\(998\) | −3.92722 | −0.124314 | ||||||||
\(999\) | 37.5457 | 1.18789 |
(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 | 6038.2.a.e.1.4 | ✓ | 70 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6038.2.a.e.1.4 | ✓ | 70 | 1.1 | even | 1 | trivial |