Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.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: | \(48.1098672178\) |
Analytic rank: | \(1\) |
Dimension: | \(46\) |
Twist minimal: | no (minimal twist has level 1205) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.760721 | −0.537911 | −0.268956 | − | 0.963153i | \(-0.586678\pi\) | ||||
−0.268956 | + | 0.963153i | \(0.586678\pi\) | |||||||
\(3\) | 1.12938 | 0.652049 | 0.326025 | − | 0.945361i | \(-0.394291\pi\) | ||||
0.326025 | + | 0.945361i | \(0.394291\pi\) | |||||||
\(4\) | −1.42130 | −0.710652 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.859145 | −0.350745 | ||||||||
\(7\) | 2.53853 | 0.959473 | 0.479737 | − | 0.877413i | \(-0.340732\pi\) | ||||
0.479737 | + | 0.877413i | \(0.340732\pi\) | |||||||
\(8\) | 2.60266 | 0.920179 | ||||||||
\(9\) | −1.72450 | −0.574832 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.06253 | −0.621877 | −0.310939 | − | 0.950430i | \(-0.600643\pi\) | ||||
−0.310939 | + | 0.950430i | \(0.600643\pi\) | |||||||
\(12\) | −1.60519 | −0.463380 | ||||||||
\(13\) | −4.79651 | −1.33031 | −0.665156 | − | 0.746705i | \(-0.731635\pi\) | ||||
−0.665156 | + | 0.746705i | \(0.731635\pi\) | |||||||
\(14\) | −1.93111 | −0.516111 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.862709 | 0.215677 | ||||||||
\(17\) | −1.95237 | −0.473518 | −0.236759 | − | 0.971568i | \(-0.576085\pi\) | ||||
−0.236759 | + | 0.971568i | \(0.576085\pi\) | |||||||
\(18\) | 1.31186 | 0.309209 | ||||||||
\(19\) | −1.03825 | −0.238190 | −0.119095 | − | 0.992883i | \(-0.537999\pi\) | ||||
−0.119095 | + | 0.992883i | \(0.537999\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.86697 | 0.625623 | ||||||||
\(22\) | 1.56901 | 0.334515 | ||||||||
\(23\) | 2.68585 | 0.560039 | 0.280019 | − | 0.959994i | \(-0.409659\pi\) | ||||
0.280019 | + | 0.959994i | \(0.409659\pi\) | |||||||
\(24\) | 2.93940 | 0.600002 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.64880 | 0.715589 | ||||||||
\(27\) | −5.33576 | −1.02687 | ||||||||
\(28\) | −3.60802 | −0.681851 | ||||||||
\(29\) | 5.84308 | 1.08503 | 0.542516 | − | 0.840046i | \(-0.317472\pi\) | ||||
0.542516 | + | 0.840046i | \(0.317472\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.76074 | 1.39387 | 0.696935 | − | 0.717134i | \(-0.254547\pi\) | ||||
0.696935 | + | 0.717134i | \(0.254547\pi\) | |||||||
\(32\) | −5.86160 | −1.03619 | ||||||||
\(33\) | −2.32939 | −0.405494 | ||||||||
\(34\) | 1.48521 | 0.254711 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.45103 | 0.408505 | ||||||||
\(37\) | 9.08041 | 1.49281 | 0.746405 | − | 0.665492i | \(-0.231778\pi\) | ||||
0.746405 | + | 0.665492i | \(0.231778\pi\) | |||||||
\(38\) | 0.789817 | 0.128125 | ||||||||
\(39\) | −5.41709 | −0.867428 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.18849 | 1.43500 | 0.717501 | − | 0.696558i | \(-0.245286\pi\) | ||||
0.717501 | + | 0.696558i | \(0.245286\pi\) | |||||||
\(42\) | −2.18096 | −0.336530 | ||||||||
\(43\) | 3.23632 | 0.493534 | 0.246767 | − | 0.969075i | \(-0.420632\pi\) | ||||
0.246767 | + | 0.969075i | \(0.420632\pi\) | |||||||
\(44\) | 2.93148 | 0.441938 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.04318 | −0.301251 | ||||||||
\(47\) | −4.22721 | −0.616603 | −0.308301 | − | 0.951289i | \(-0.599761\pi\) | ||||
−0.308301 | + | 0.951289i | \(0.599761\pi\) | |||||||
\(48\) | 0.974328 | 0.140632 | ||||||||
\(49\) | −0.555881 | −0.0794116 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.20497 | −0.308757 | ||||||||
\(52\) | 6.81729 | 0.945388 | ||||||||
\(53\) | −6.32114 | −0.868276 | −0.434138 | − | 0.900846i | \(-0.642947\pi\) | ||||
−0.434138 | + | 0.900846i | \(0.642947\pi\) | |||||||
\(54\) | 4.05903 | 0.552364 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 6.60692 | 0.882887 | ||||||||
\(57\) | −1.17258 | −0.155312 | ||||||||
\(58\) | −4.44495 | −0.583651 | ||||||||
\(59\) | 2.97769 | 0.387662 | 0.193831 | − | 0.981035i | \(-0.437909\pi\) | ||||
0.193831 | + | 0.981035i | \(0.437909\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.0977 | −1.42091 | −0.710456 | − | 0.703741i | \(-0.751511\pi\) | ||||
−0.710456 | + | 0.703741i | \(0.751511\pi\) | |||||||
\(62\) | −5.90376 | −0.749778 | ||||||||
\(63\) | −4.37768 | −0.551536 | ||||||||
\(64\) | 2.73362 | 0.341703 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.77202 | 0.218120 | ||||||||
\(67\) | −1.40319 | −0.171427 | −0.0857134 | − | 0.996320i | \(-0.527317\pi\) | ||||
−0.0857134 | + | 0.996320i | \(0.527317\pi\) | |||||||
\(68\) | 2.77490 | 0.336506 | ||||||||
\(69\) | 3.03335 | 0.365173 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.51732 | −0.773464 | −0.386732 | − | 0.922192i | \(-0.626396\pi\) | ||||
−0.386732 | + | 0.922192i | \(0.626396\pi\) | |||||||
\(72\) | −4.48827 | −0.528948 | ||||||||
\(73\) | 1.89995 | 0.222373 | 0.111186 | − | 0.993800i | \(-0.464535\pi\) | ||||
0.111186 | + | 0.993800i | \(0.464535\pi\) | |||||||
\(74\) | −6.90766 | −0.802999 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.47566 | 0.169270 | ||||||||
\(77\) | −5.23580 | −0.596674 | ||||||||
\(78\) | 4.12089 | 0.466599 | ||||||||
\(79\) | −13.9020 | −1.56410 | −0.782050 | − | 0.623215i | \(-0.785826\pi\) | ||||
−0.782050 | + | 0.623215i | \(0.785826\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.852626 | −0.0947362 | ||||||||
\(82\) | −6.98988 | −0.771904 | ||||||||
\(83\) | −6.49943 | −0.713405 | −0.356703 | − | 0.934218i | \(-0.616099\pi\) | ||||
−0.356703 | + | 0.934218i | \(0.616099\pi\) | |||||||
\(84\) | −4.07483 | −0.444600 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.46194 | −0.265477 | ||||||||
\(87\) | 6.59906 | 0.707494 | ||||||||
\(88\) | −5.36807 | −0.572238 | ||||||||
\(89\) | −0.236437 | −0.0250623 | −0.0125311 | − | 0.999921i | \(-0.503989\pi\) | ||||
−0.0125311 | + | 0.999921i | \(0.503989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.1761 | −1.27640 | ||||||||
\(92\) | −3.81741 | −0.397992 | ||||||||
\(93\) | 8.76484 | 0.908871 | ||||||||
\(94\) | 3.21573 | 0.331677 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −6.61998 | −0.675649 | ||||||||
\(97\) | −13.5524 | −1.37604 | −0.688020 | − | 0.725691i | \(-0.741520\pi\) | ||||
−0.688020 | + | 0.725691i | \(0.741520\pi\) | |||||||
\(98\) | 0.422870 | 0.0427164 | ||||||||
\(99\) | 3.55683 | 0.357475 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.0004 | −1.19409 | −0.597044 | − | 0.802209i | \(-0.703658\pi\) | ||||
−0.597044 | + | 0.802209i | \(0.703658\pi\) | |||||||
\(102\) | 1.67737 | 0.166084 | ||||||||
\(103\) | 13.6216 | 1.34218 | 0.671088 | − | 0.741377i | \(-0.265827\pi\) | ||||
0.671088 | + | 0.741377i | \(0.265827\pi\) | |||||||
\(104\) | −12.4837 | −1.22412 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.80863 | 0.467055 | ||||||||
\(107\) | −13.8286 | −1.33686 | −0.668432 | − | 0.743773i | \(-0.733034\pi\) | ||||
−0.668432 | + | 0.743773i | \(0.733034\pi\) | |||||||
\(108\) | 7.58373 | 0.729745 | ||||||||
\(109\) | 13.7652 | 1.31846 | 0.659232 | − | 0.751940i | \(-0.270882\pi\) | ||||
0.659232 | + | 0.751940i | \(0.270882\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.2553 | 0.973386 | ||||||||
\(112\) | 2.19001 | 0.206936 | ||||||||
\(113\) | 6.68313 | 0.628696 | 0.314348 | − | 0.949308i | \(-0.398214\pi\) | ||||
0.314348 | + | 0.949308i | \(0.398214\pi\) | |||||||
\(114\) | 0.892005 | 0.0835439 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −8.30478 | −0.771080 | ||||||||
\(117\) | 8.27155 | 0.764705 | ||||||||
\(118\) | −2.26519 | −0.208528 | ||||||||
\(119\) | −4.95613 | −0.454328 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.74596 | −0.613269 | ||||||||
\(122\) | 8.44224 | 0.764325 | ||||||||
\(123\) | 10.3773 | 0.935692 | ||||||||
\(124\) | −11.0304 | −0.990556 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.33019 | 0.296677 | ||||||||
\(127\) | 4.63183 | 0.411008 | 0.205504 | − | 0.978656i | \(-0.434117\pi\) | ||||
0.205504 | + | 0.978656i | \(0.434117\pi\) | |||||||
\(128\) | 9.64367 | 0.852388 | ||||||||
\(129\) | 3.65504 | 0.321808 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.6049 | −0.926558 | −0.463279 | − | 0.886212i | \(-0.653327\pi\) | ||||
−0.463279 | + | 0.886212i | \(0.653327\pi\) | |||||||
\(132\) | 3.31077 | 0.288165 | ||||||||
\(133\) | −2.63562 | −0.228537 | ||||||||
\(134\) | 1.06744 | 0.0922124 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.08134 | −0.435721 | ||||||||
\(137\) | −18.3739 | −1.56979 | −0.784895 | − | 0.619629i | \(-0.787283\pi\) | ||||
−0.784895 | + | 0.619629i | \(0.787283\pi\) | |||||||
\(138\) | −2.30754 | −0.196431 | ||||||||
\(139\) | −5.98608 | −0.507733 | −0.253866 | − | 0.967239i | \(-0.581702\pi\) | ||||
−0.253866 | + | 0.967239i | \(0.581702\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.77414 | −0.402055 | ||||||||
\(142\) | 4.95787 | 0.416055 | ||||||||
\(143\) | 9.89295 | 0.827290 | ||||||||
\(144\) | −1.48774 | −0.123978 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.44534 | −0.119617 | ||||||||
\(147\) | −0.627802 | −0.0517802 | ||||||||
\(148\) | −12.9060 | −1.06087 | ||||||||
\(149\) | −6.99343 | −0.572924 | −0.286462 | − | 0.958092i | \(-0.592479\pi\) | ||||
−0.286462 | + | 0.958092i | \(0.592479\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −23.3270 | −1.89833 | −0.949164 | − | 0.314783i | \(-0.898068\pi\) | ||||
−0.949164 | + | 0.314783i | \(0.898068\pi\) | |||||||
\(152\) | −2.70220 | −0.219178 | ||||||||
\(153\) | 3.36685 | 0.272193 | ||||||||
\(154\) | 3.98298 | 0.320958 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 7.69932 | 0.616439 | ||||||||
\(157\) | −6.99961 | −0.558630 | −0.279315 | − | 0.960200i | \(-0.590107\pi\) | ||||
−0.279315 | + | 0.960200i | \(0.590107\pi\) | |||||||
\(158\) | 10.5756 | 0.841347 | ||||||||
\(159\) | −7.13899 | −0.566158 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.81811 | 0.537342 | ||||||||
\(162\) | 0.648610 | 0.0509596 | ||||||||
\(163\) | −7.32590 | −0.573809 | −0.286904 | − | 0.957959i | \(-0.592626\pi\) | ||||
−0.286904 | + | 0.957959i | \(0.592626\pi\) | |||||||
\(164\) | −13.0596 | −1.01979 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.94426 | 0.383749 | ||||||||
\(167\) | 10.8149 | 0.836882 | 0.418441 | − | 0.908244i | \(-0.362577\pi\) | ||||
0.418441 | + | 0.908244i | \(0.362577\pi\) | |||||||
\(168\) | 7.46174 | 0.575685 | ||||||||
\(169\) | 10.0065 | 0.769728 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.79045 | 0.136919 | ||||||||
\(172\) | −4.59979 | −0.350731 | ||||||||
\(173\) | 8.58809 | 0.652941 | 0.326470 | − | 0.945207i | \(-0.394141\pi\) | ||||
0.326470 | + | 0.945207i | \(0.394141\pi\) | |||||||
\(174\) | −5.02005 | −0.380569 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.77936 | −0.134125 | ||||||||
\(177\) | 3.36295 | 0.252775 | ||||||||
\(178\) | 0.179863 | 0.0134813 | ||||||||
\(179\) | 7.06513 | 0.528073 | 0.264036 | − | 0.964513i | \(-0.414946\pi\) | ||||
0.264036 | + | 0.964513i | \(0.414946\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.5251 | −1.67427 | −0.837137 | − | 0.546993i | \(-0.815773\pi\) | ||||
−0.837137 | + | 0.546993i | \(0.815773\pi\) | |||||||
\(182\) | 9.26259 | 0.686589 | ||||||||
\(183\) | −12.5335 | −0.926505 | ||||||||
\(184\) | 6.99035 | 0.515336 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −6.66760 | −0.488892 | ||||||||
\(187\) | 4.02682 | 0.294470 | ||||||||
\(188\) | 6.00815 | 0.438190 | ||||||||
\(189\) | −13.5450 | −0.985252 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.0033 | 1.15796 | 0.578981 | − | 0.815341i | \(-0.303451\pi\) | ||||
0.578981 | + | 0.815341i | \(0.303451\pi\) | |||||||
\(192\) | 3.08731 | 0.222807 | ||||||||
\(193\) | −15.9736 | −1.14981 | −0.574903 | − | 0.818221i | \(-0.694960\pi\) | ||||
−0.574903 | + | 0.818221i | \(0.694960\pi\) | |||||||
\(194\) | 10.3096 | 0.740188 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.790075 | 0.0564339 | ||||||||
\(197\) | 24.2137 | 1.72516 | 0.862579 | − | 0.505922i | \(-0.168848\pi\) | ||||
0.862579 | + | 0.505922i | \(0.168848\pi\) | |||||||
\(198\) | −2.70576 | −0.192290 | ||||||||
\(199\) | −12.3227 | −0.873535 | −0.436768 | − | 0.899574i | \(-0.643877\pi\) | ||||
−0.436768 | + | 0.899574i | \(0.643877\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.58474 | −0.111779 | ||||||||
\(202\) | 9.12899 | 0.642313 | ||||||||
\(203\) | 14.8328 | 1.04106 | ||||||||
\(204\) | 3.13393 | 0.219419 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −10.3622 | −0.721972 | ||||||||
\(207\) | −4.63174 | −0.321928 | ||||||||
\(208\) | −4.13799 | −0.286918 | ||||||||
\(209\) | 2.14142 | 0.148125 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.5630 | 1.82867 | 0.914335 | − | 0.404959i | \(-0.132714\pi\) | ||||
0.914335 | + | 0.404959i | \(0.132714\pi\) | |||||||
\(212\) | 8.98426 | 0.617042 | ||||||||
\(213\) | −7.36055 | −0.504336 | ||||||||
\(214\) | 10.5197 | 0.719114 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −13.8872 | −0.944902 | ||||||||
\(217\) | 19.7008 | 1.33738 | ||||||||
\(218\) | −10.4715 | −0.709216 | ||||||||
\(219\) | 2.14577 | 0.144998 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.36453 | 0.629927 | ||||||||
\(222\) | −7.80139 | −0.523595 | ||||||||
\(223\) | −8.33195 | −0.557949 | −0.278974 | − | 0.960299i | \(-0.589994\pi\) | ||||
−0.278974 | + | 0.960299i | \(0.589994\pi\) | |||||||
\(224\) | −14.8798 | −0.994200 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.08400 | −0.338183 | ||||||||
\(227\) | 4.33870 | 0.287970 | 0.143985 | − | 0.989580i | \(-0.454008\pi\) | ||||
0.143985 | + | 0.989580i | \(0.454008\pi\) | |||||||
\(228\) | 1.66659 | 0.110373 | ||||||||
\(229\) | 29.3533 | 1.93972 | 0.969859 | − | 0.243665i | \(-0.0783499\pi\) | ||||
0.969859 | + | 0.243665i | \(0.0783499\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.91321 | −0.389061 | ||||||||
\(232\) | 15.2075 | 0.998423 | ||||||||
\(233\) | −13.0291 | −0.853563 | −0.426781 | − | 0.904355i | \(-0.640353\pi\) | ||||
−0.426781 | + | 0.904355i | \(0.640353\pi\) | |||||||
\(234\) | −6.29235 | −0.411344 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.23220 | −0.275492 | ||||||||
\(237\) | −15.7007 | −1.01987 | ||||||||
\(238\) | 3.77024 | 0.244388 | ||||||||
\(239\) | 7.27224 | 0.470402 | 0.235201 | − | 0.971947i | \(-0.424425\pi\) | ||||
0.235201 | + | 0.971947i | \(0.424425\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | 0.0644157 | ||||||||
\(242\) | 5.13179 | 0.329884 | ||||||||
\(243\) | 15.0443 | 0.965095 | ||||||||
\(244\) | 15.7732 | 1.00977 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.89425 | −0.503319 | ||||||||
\(247\) | 4.97996 | 0.316867 | ||||||||
\(248\) | 20.1985 | 1.28261 | ||||||||
\(249\) | −7.34034 | −0.465175 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.8592 | −1.75846 | −0.879229 | − | 0.476400i | \(-0.841941\pi\) | ||||
−0.879229 | + | 0.476400i | \(0.841941\pi\) | |||||||
\(252\) | 6.22201 | 0.391950 | ||||||||
\(253\) | −5.53966 | −0.348275 | ||||||||
\(254\) | −3.52353 | −0.221086 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −12.8034 | −0.800212 | ||||||||
\(257\) | −15.9448 | −0.994607 | −0.497303 | − | 0.867577i | \(-0.665676\pi\) | ||||
−0.497303 | + | 0.867577i | \(0.665676\pi\) | |||||||
\(258\) | −2.78047 | −0.173104 | ||||||||
\(259\) | 23.0509 | 1.43231 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.0764 | −0.623711 | ||||||||
\(262\) | 8.06741 | 0.498406 | ||||||||
\(263\) | 0.603786 | 0.0372310 | 0.0186155 | − | 0.999827i | \(-0.494074\pi\) | ||||
0.0186155 | + | 0.999827i | \(0.494074\pi\) | |||||||
\(264\) | −6.06260 | −0.373127 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.00497 | 0.122933 | ||||||||
\(267\) | −0.267028 | −0.0163418 | ||||||||
\(268\) | 1.99436 | 0.121825 | ||||||||
\(269\) | −23.5550 | −1.43618 | −0.718088 | − | 0.695952i | \(-0.754982\pi\) | ||||
−0.718088 | + | 0.695952i | \(0.754982\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.80993 | −0.595911 | −0.297955 | − | 0.954580i | \(-0.596305\pi\) | ||||
−0.297955 | + | 0.954580i | \(0.596305\pi\) | |||||||
\(272\) | −1.68432 | −0.102127 | ||||||||
\(273\) | −13.7514 | −0.832274 | ||||||||
\(274\) | 13.9774 | 0.844407 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.31131 | −0.259511 | ||||||||
\(277\) | 7.76495 | 0.466551 | 0.233275 | − | 0.972411i | \(-0.425056\pi\) | ||||
0.233275 | + | 0.972411i | \(0.425056\pi\) | |||||||
\(278\) | 4.55374 | 0.273115 | ||||||||
\(279\) | −13.3834 | −0.801241 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.7632 | −1.23863 | −0.619314 | − | 0.785143i | \(-0.712589\pi\) | ||||
−0.619314 | + | 0.785143i | \(0.712589\pi\) | |||||||
\(282\) | 3.63179 | 0.216270 | ||||||||
\(283\) | 8.45091 | 0.502355 | 0.251177 | − | 0.967941i | \(-0.419182\pi\) | ||||
0.251177 | + | 0.967941i | \(0.419182\pi\) | |||||||
\(284\) | 9.26309 | 0.549663 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.52578 | −0.445009 | ||||||||
\(287\) | 23.3252 | 1.37685 | ||||||||
\(288\) | 10.1083 | 0.595637 | ||||||||
\(289\) | −13.1883 | −0.775781 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −15.3059 | −0.897246 | ||||||||
\(292\) | −2.70041 | −0.158030 | ||||||||
\(293\) | −13.4756 | −0.787253 | −0.393626 | − | 0.919271i | \(-0.628780\pi\) | ||||
−0.393626 | + | 0.919271i | \(0.628780\pi\) | |||||||
\(294\) | 0.477582 | 0.0278532 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 23.6332 | 1.37365 | ||||||||
\(297\) | 11.0052 | 0.638586 | ||||||||
\(298\) | 5.32005 | 0.308182 | ||||||||
\(299\) | −12.8827 | −0.745026 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.21548 | 0.473533 | ||||||||
\(302\) | 17.7454 | 1.02113 | ||||||||
\(303\) | −13.5531 | −0.778604 | ||||||||
\(304\) | −0.895705 | −0.0513722 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.56123 | −0.146416 | ||||||||
\(307\) | 9.67527 | 0.552197 | 0.276099 | − | 0.961129i | \(-0.410958\pi\) | ||||
0.276099 | + | 0.961129i | \(0.410958\pi\) | |||||||
\(308\) | 7.44165 | 0.424028 | ||||||||
\(309\) | 15.3840 | 0.875165 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −34.8734 | −1.97749 | −0.988746 | − | 0.149607i | \(-0.952199\pi\) | ||||
−0.988746 | + | 0.149607i | \(0.952199\pi\) | |||||||
\(312\) | −14.0988 | −0.798189 | ||||||||
\(313\) | 27.2238 | 1.53878 | 0.769391 | − | 0.638779i | \(-0.220560\pi\) | ||||
0.769391 | + | 0.638779i | \(0.220560\pi\) | |||||||
\(314\) | 5.32475 | 0.300493 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 19.7590 | 1.11153 | ||||||||
\(317\) | 2.90326 | 0.163063 | 0.0815316 | − | 0.996671i | \(-0.474019\pi\) | ||||
0.0815316 | + | 0.996671i | \(0.474019\pi\) | |||||||
\(318\) | 5.43078 | 0.304543 | ||||||||
\(319\) | −12.0515 | −0.674756 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.6178 | −0.871701 | ||||||||
\(322\) | −5.18668 | −0.289042 | ||||||||
\(323\) | 2.02704 | 0.112787 | ||||||||
\(324\) | 1.21184 | 0.0673244 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.57297 | 0.308658 | ||||||||
\(327\) | 15.5461 | 0.859703 | ||||||||
\(328\) | 23.9145 | 1.32046 | ||||||||
\(329\) | −10.7309 | −0.591614 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.82961 | 0.265459 | 0.132730 | − | 0.991152i | \(-0.457626\pi\) | ||||
0.132730 | + | 0.991152i | \(0.457626\pi\) | |||||||
\(332\) | 9.23766 | 0.506983 | ||||||||
\(333\) | −15.6591 | −0.858115 | ||||||||
\(334\) | −8.22712 | −0.450168 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.47336 | 0.134933 | ||||||||
\(337\) | −22.1454 | −1.20634 | −0.603168 | − | 0.797614i | \(-0.706095\pi\) | ||||
−0.603168 | + | 0.797614i | \(0.706095\pi\) | |||||||
\(338\) | −7.61213 | −0.414045 | ||||||||
\(339\) | 7.54781 | 0.409941 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16.0068 | −0.866816 | ||||||||
\(342\) | −1.36204 | −0.0736505 | ||||||||
\(343\) | −19.1808 | −1.03567 | ||||||||
\(344\) | 8.42303 | 0.454139 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.53315 | −0.351224 | ||||||||
\(347\) | −20.1874 | −1.08372 | −0.541859 | − | 0.840470i | \(-0.682279\pi\) | ||||
−0.541859 | + | 0.840470i | \(0.682279\pi\) | |||||||
\(348\) | −9.37927 | −0.502782 | ||||||||
\(349\) | 4.22280 | 0.226041 | 0.113021 | − | 0.993593i | \(-0.463947\pi\) | ||||
0.113021 | + | 0.993593i | \(0.463947\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 25.5930 | 1.36605 | ||||||||
\(352\) | 12.0897 | 0.644385 | ||||||||
\(353\) | −20.2277 | −1.07661 | −0.538305 | − | 0.842750i | \(-0.680935\pi\) | ||||
−0.538305 | + | 0.842750i | \(0.680935\pi\) | |||||||
\(354\) | −2.55826 | −0.135970 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.336048 | 0.0178105 | ||||||||
\(357\) | −5.59737 | −0.296244 | ||||||||
\(358\) | −5.37460 | −0.284056 | ||||||||
\(359\) | −23.0788 | −1.21805 | −0.609027 | − | 0.793149i | \(-0.708440\pi\) | ||||
−0.609027 | + | 0.793149i | \(0.708440\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.9220 | −0.943265 | ||||||||
\(362\) | 17.1353 | 0.900611 | ||||||||
\(363\) | −7.61876 | −0.399881 | ||||||||
\(364\) | 17.3059 | 0.907074 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 9.53452 | 0.498377 | ||||||||
\(367\) | 15.5656 | 0.812516 | 0.406258 | − | 0.913758i | \(-0.366833\pi\) | ||||
0.406258 | + | 0.913758i | \(0.366833\pi\) | |||||||
\(368\) | 2.31711 | 0.120788 | ||||||||
\(369\) | −15.8455 | −0.824885 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −16.0464 | −0.833087 | ||||||||
\(372\) | −12.4575 | −0.645891 | ||||||||
\(373\) | −22.9059 | −1.18602 | −0.593011 | − | 0.805194i | \(-0.702061\pi\) | ||||
−0.593011 | + | 0.805194i | \(0.702061\pi\) | |||||||
\(374\) | −3.06329 | −0.158399 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −11.0020 | −0.567385 | ||||||||
\(377\) | −28.0263 | −1.44343 | ||||||||
\(378\) | 10.3040 | 0.529978 | ||||||||
\(379\) | −9.63127 | −0.494725 | −0.247363 | − | 0.968923i | \(-0.579564\pi\) | ||||
−0.247363 | + | 0.968923i | \(0.579564\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.23110 | 0.267997 | ||||||||
\(382\) | −12.1741 | −0.622880 | ||||||||
\(383\) | −1.19113 | −0.0608640 | −0.0304320 | − | 0.999537i | \(-0.509688\pi\) | ||||
−0.0304320 | + | 0.999537i | \(0.509688\pi\) | |||||||
\(384\) | 10.8914 | 0.555799 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.1515 | 0.618494 | ||||||||
\(387\) | −5.58102 | −0.283699 | ||||||||
\(388\) | 19.2621 | 0.977885 | ||||||||
\(389\) | −12.0151 | −0.609188 | −0.304594 | − | 0.952482i | \(-0.598521\pi\) | ||||
−0.304594 | + | 0.952482i | \(0.598521\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.24376 | −0.265189 | ||||||||
\(392\) | −1.44677 | −0.0730728 | ||||||||
\(393\) | −11.9770 | −0.604161 | ||||||||
\(394\) | −18.4199 | −0.927982 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −5.05533 | −0.254040 | ||||||||
\(397\) | 1.30174 | 0.0653324 | 0.0326662 | − | 0.999466i | \(-0.489600\pi\) | ||||
0.0326662 | + | 0.999466i | \(0.489600\pi\) | |||||||
\(398\) | 9.37416 | 0.469884 | ||||||||
\(399\) | −2.97662 | −0.149017 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.7958 | 0.888680 | 0.444340 | − | 0.895858i | \(-0.353438\pi\) | ||||
0.444340 | + | 0.895858i | \(0.353438\pi\) | |||||||
\(402\) | 1.20554 | 0.0601270 | ||||||||
\(403\) | −37.2244 | −1.85428 | ||||||||
\(404\) | 17.0563 | 0.848580 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −11.2836 | −0.559997 | ||||||||
\(407\) | −18.7286 | −0.928345 | ||||||||
\(408\) | −5.73877 | −0.284112 | ||||||||
\(409\) | 1.21607 | 0.0601305 | 0.0300653 | − | 0.999548i | \(-0.490428\pi\) | ||||
0.0300653 | + | 0.999548i | \(0.490428\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −20.7512 | −1.02358 | ||||||||
\(412\) | −19.3604 | −0.953820 | ||||||||
\(413\) | 7.55894 | 0.371951 | ||||||||
\(414\) | 3.52346 | 0.173169 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 28.1152 | 1.37846 | ||||||||
\(417\) | −6.76057 | −0.331067 | ||||||||
\(418\) | −1.62902 | −0.0796781 | ||||||||
\(419\) | −23.5246 | −1.14925 | −0.574626 | − | 0.818416i | \(-0.694853\pi\) | ||||
−0.574626 | + | 0.818416i | \(0.694853\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.1129 | 1.17519 | 0.587596 | − | 0.809154i | \(-0.300074\pi\) | ||||
0.587596 | + | 0.809154i | \(0.300074\pi\) | |||||||
\(422\) | −20.2070 | −0.983662 | ||||||||
\(423\) | 7.28982 | 0.354443 | ||||||||
\(424\) | −16.4518 | −0.798969 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 5.59933 | 0.271288 | ||||||||
\(427\) | −28.1718 | −1.36333 | ||||||||
\(428\) | 19.6547 | 0.950045 | ||||||||
\(429\) | 11.1729 | 0.539434 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.23057 | 0.444621 | 0.222310 | − | 0.974976i | \(-0.428640\pi\) | ||||
0.222310 | + | 0.974976i | \(0.428640\pi\) | |||||||
\(432\) | −4.60321 | −0.221472 | ||||||||
\(433\) | −40.5437 | −1.94841 | −0.974203 | − | 0.225673i | \(-0.927542\pi\) | ||||
−0.974203 | + | 0.225673i | \(0.927542\pi\) | |||||||
\(434\) | −14.9869 | −0.719392 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −19.5645 | −0.936968 | ||||||||
\(437\) | −2.78858 | −0.133396 | ||||||||
\(438\) | −1.63234 | −0.0779960 | ||||||||
\(439\) | 19.5448 | 0.932823 | 0.466411 | − | 0.884568i | \(-0.345547\pi\) | ||||
0.466411 | + | 0.884568i | \(0.345547\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.958614 | 0.0456483 | ||||||||
\(442\) | −7.12380 | −0.338845 | ||||||||
\(443\) | 38.3533 | 1.82222 | 0.911109 | − | 0.412165i | \(-0.135227\pi\) | ||||
0.911109 | + | 0.412165i | \(0.135227\pi\) | |||||||
\(444\) | −14.5758 | −0.691738 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 6.33829 | 0.300127 | ||||||||
\(447\) | −7.89825 | −0.373574 | ||||||||
\(448\) | 6.93938 | 0.327855 | ||||||||
\(449\) | −7.15454 | −0.337643 | −0.168822 | − | 0.985647i | \(-0.553996\pi\) | ||||
−0.168822 | + | 0.985647i | \(0.553996\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.9516 | −0.892395 | ||||||||
\(452\) | −9.49876 | −0.446784 | ||||||||
\(453\) | −26.3451 | −1.23780 | ||||||||
\(454\) | −3.30054 | −0.154902 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.05182 | −0.142915 | ||||||||
\(457\) | −13.2079 | −0.617838 | −0.308919 | − | 0.951088i | \(-0.599967\pi\) | ||||
−0.308919 | + | 0.951088i | \(0.599967\pi\) | |||||||
\(458\) | −22.3297 | −1.04340 | ||||||||
\(459\) | 10.4174 | 0.486241 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 25.6149 | 1.19300 | 0.596502 | − | 0.802612i | \(-0.296557\pi\) | ||||
0.596502 | + | 0.802612i | \(0.296557\pi\) | |||||||
\(462\) | 4.49831 | 0.209280 | ||||||||
\(463\) | 36.7408 | 1.70749 | 0.853745 | − | 0.520691i | \(-0.174326\pi\) | ||||
0.853745 | + | 0.520691i | \(0.174326\pi\) | |||||||
\(464\) | 5.04087 | 0.234017 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.91149 | 0.459141 | ||||||||
\(467\) | −11.5404 | −0.534028 | −0.267014 | − | 0.963693i | \(-0.586037\pi\) | ||||
−0.267014 | + | 0.963693i | \(0.586037\pi\) | |||||||
\(468\) | −11.7564 | −0.543439 | ||||||||
\(469\) | −3.56203 | −0.164479 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.90524 | −0.364254 | ||||||||
\(472\) | 7.74990 | 0.356718 | ||||||||
\(473\) | −6.67502 | −0.306918 | ||||||||
\(474\) | 11.9439 | 0.548600 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 7.04417 | 0.322869 | ||||||||
\(477\) | 10.9008 | 0.499113 | ||||||||
\(478\) | −5.53215 | −0.253035 | ||||||||
\(479\) | 29.9925 | 1.37039 | 0.685197 | − | 0.728358i | \(-0.259716\pi\) | ||||
0.685197 | + | 0.728358i | \(0.259716\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −43.5542 | −1.98590 | ||||||||
\(482\) | −0.760721 | −0.0346499 | ||||||||
\(483\) | 7.70025 | 0.350373 | ||||||||
\(484\) | 9.58805 | 0.435820 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −11.4446 | −0.519135 | ||||||||
\(487\) | 8.15043 | 0.369331 | 0.184666 | − | 0.982801i | \(-0.440880\pi\) | ||||
0.184666 | + | 0.982801i | \(0.440880\pi\) | |||||||
\(488\) | −28.8835 | −1.30749 | ||||||||
\(489\) | −8.27374 | −0.374152 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.89709 | −0.356391 | −0.178195 | − | 0.983995i | \(-0.557026\pi\) | ||||
−0.178195 | + | 0.983995i | \(0.557026\pi\) | |||||||
\(492\) | −14.7493 | −0.664951 | ||||||||
\(493\) | −11.4078 | −0.513782 | ||||||||
\(494\) | −3.78836 | −0.170446 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.69526 | 0.300626 | ||||||||
\(497\) | −16.5444 | −0.742118 | ||||||||
\(498\) | 5.58396 | 0.250223 | ||||||||
\(499\) | −22.4351 | −1.00433 | −0.502166 | − | 0.864771i | \(-0.667463\pi\) | ||||
−0.502166 | + | 0.864771i | \(0.667463\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.2142 | 0.545688 | ||||||||
\(502\) | 21.1931 | 0.945894 | ||||||||
\(503\) | 7.14129 | 0.318415 | 0.159207 | − | 0.987245i | \(-0.449106\pi\) | ||||
0.159207 | + | 0.987245i | \(0.449106\pi\) | |||||||
\(504\) | −11.3936 | −0.507511 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.21414 | 0.187341 | ||||||||
\(507\) | 11.3011 | 0.501900 | ||||||||
\(508\) | −6.58323 | −0.292084 | ||||||||
\(509\) | −12.5554 | −0.556506 | −0.278253 | − | 0.960508i | \(-0.589755\pi\) | ||||
−0.278253 | + | 0.960508i | \(0.589755\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.82308 | 0.213361 | ||||||||
\(512\) | −9.54752 | −0.421945 | ||||||||
\(513\) | 5.53984 | 0.244590 | ||||||||
\(514\) | 12.1295 | 0.535010 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.19492 | −0.228694 | ||||||||
\(517\) | 8.71877 | 0.383451 | ||||||||
\(518\) | −17.5353 | −0.770456 | ||||||||
\(519\) | 9.69924 | 0.425749 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.94447 | 0.216621 | 0.108310 | − | 0.994117i | \(-0.465456\pi\) | ||||
0.108310 | + | 0.994117i | \(0.465456\pi\) | |||||||
\(522\) | 7.66530 | 0.335501 | ||||||||
\(523\) | −1.07988 | −0.0472200 | −0.0236100 | − | 0.999721i | \(-0.507516\pi\) | ||||
−0.0236100 | + | 0.999721i | \(0.507516\pi\) | |||||||
\(524\) | 15.0728 | 0.658460 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.459313 | −0.0200270 | ||||||||
\(527\) | −15.1518 | −0.660023 | ||||||||
\(528\) | −2.00958 | −0.0874559 | ||||||||
\(529\) | −15.7862 | −0.686357 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.13501 | −0.222840 | ||||||||
\(532\) | 3.74601 | 0.162410 | ||||||||
\(533\) | −44.0727 | −1.90900 | ||||||||
\(534\) | 0.203134 | 0.00879045 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.65202 | −0.157743 | ||||||||
\(537\) | 7.97923 | 0.344329 | ||||||||
\(538\) | 17.9188 | 0.772535 | ||||||||
\(539\) | 1.14652 | 0.0493842 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.7184 | −0.675785 | −0.337892 | − | 0.941185i | \(-0.609714\pi\) | ||||
−0.337892 | + | 0.941185i | \(0.609714\pi\) | |||||||
\(542\) | 7.46262 | 0.320547 | ||||||||
\(543\) | −25.4394 | −1.09171 | ||||||||
\(544\) | 11.4440 | 0.490657 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 10.4610 | 0.447689 | ||||||||
\(547\) | 18.6002 | 0.795286 | 0.397643 | − | 0.917540i | \(-0.369828\pi\) | ||||
0.397643 | + | 0.917540i | \(0.369828\pi\) | |||||||
\(548\) | 26.1149 | 1.11557 | ||||||||
\(549\) | 19.1379 | 0.816786 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.06656 | −0.258444 | ||||||||
\(552\) | 7.89478 | 0.336024 | ||||||||
\(553\) | −35.2907 | −1.50071 | ||||||||
\(554\) | −5.90697 | −0.250963 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.50803 | 0.360821 | ||||||||
\(557\) | 1.59319 | 0.0675055 | 0.0337528 | − | 0.999430i | \(-0.489254\pi\) | ||||
0.0337528 | + | 0.999430i | \(0.489254\pi\) | |||||||
\(558\) | 10.1810 | 0.430996 | ||||||||
\(559\) | −15.5230 | −0.656554 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.54782 | 0.192009 | ||||||||
\(562\) | 15.7950 | 0.666272 | ||||||||
\(563\) | 30.0999 | 1.26856 | 0.634280 | − | 0.773103i | \(-0.281297\pi\) | ||||
0.634280 | + | 0.773103i | \(0.281297\pi\) | |||||||
\(564\) | 6.78550 | 0.285721 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −6.42879 | −0.270222 | ||||||||
\(567\) | −2.16441 | −0.0908968 | ||||||||
\(568\) | −16.9624 | −0.711725 | ||||||||
\(569\) | −1.17755 | −0.0493656 | −0.0246828 | − | 0.999695i | \(-0.507858\pi\) | ||||
−0.0246828 | + | 0.999695i | \(0.507858\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.39221 | −0.393052 | −0.196526 | − | 0.980499i | \(-0.562966\pi\) | ||||
−0.196526 | + | 0.980499i | \(0.562966\pi\) | |||||||
\(572\) | −14.0609 | −0.587915 | ||||||||
\(573\) | 18.0739 | 0.755048 | ||||||||
\(574\) | −17.7440 | −0.740621 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.71413 | −0.196422 | ||||||||
\(577\) | 38.4047 | 1.59881 | 0.799405 | − | 0.600792i | \(-0.205148\pi\) | ||||
0.799405 | + | 0.600792i | \(0.205148\pi\) | |||||||
\(578\) | 10.0326 | 0.417301 | ||||||||
\(579\) | −18.0403 | −0.749730 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.4990 | −0.684493 | ||||||||
\(582\) | 11.6435 | 0.482639 | ||||||||
\(583\) | 13.0376 | 0.539961 | ||||||||
\(584\) | 4.94493 | 0.204623 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.2512 | 0.423472 | ||||||||
\(587\) | 32.9101 | 1.35834 | 0.679172 | − | 0.733979i | \(-0.262339\pi\) | ||||
0.679172 | + | 0.733979i | \(0.262339\pi\) | |||||||
\(588\) | 0.892297 | 0.0367977 | ||||||||
\(589\) | −8.05757 | −0.332006 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 27.3466 | 1.12489 | ||||||||
\(592\) | 7.83375 | 0.321965 | ||||||||
\(593\) | 25.5785 | 1.05038 | 0.525191 | − | 0.850984i | \(-0.323994\pi\) | ||||
0.525191 | + | 0.850984i | \(0.323994\pi\) | |||||||
\(594\) | −8.37188 | −0.343502 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.93978 | 0.407149 | ||||||||
\(597\) | −13.9171 | −0.569588 | ||||||||
\(598\) | 9.80015 | 0.400758 | ||||||||
\(599\) | −0.739459 | −0.0302135 | −0.0151067 | − | 0.999886i | \(-0.504809\pi\) | ||||
−0.0151067 | + | 0.999886i | \(0.504809\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.2755 | −0.500730 | −0.250365 | − | 0.968152i | \(-0.580551\pi\) | ||||
−0.250365 | + | 0.968152i | \(0.580551\pi\) | |||||||
\(602\) | −6.24969 | −0.254718 | ||||||||
\(603\) | 2.41979 | 0.0985417 | ||||||||
\(604\) | 33.1548 | 1.34905 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 10.3101 | 0.418820 | ||||||||
\(607\) | −13.7567 | −0.558368 | −0.279184 | − | 0.960238i | \(-0.590064\pi\) | ||||
−0.279184 | + | 0.960238i | \(0.590064\pi\) | |||||||
\(608\) | 6.08579 | 0.246811 | ||||||||
\(609\) | 16.7519 | 0.678821 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.2759 | 0.820273 | ||||||||
\(612\) | −4.78531 | −0.193435 | ||||||||
\(613\) | 32.1681 | 1.29926 | 0.649629 | − | 0.760251i | \(-0.274924\pi\) | ||||
0.649629 | + | 0.760251i | \(0.274924\pi\) | |||||||
\(614\) | −7.36019 | −0.297033 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −13.6270 | −0.549047 | ||||||||
\(617\) | −29.1316 | −1.17279 | −0.586397 | − | 0.810024i | \(-0.699454\pi\) | ||||
−0.586397 | + | 0.810024i | \(0.699454\pi\) | |||||||
\(618\) | −11.7029 | −0.470761 | ||||||||
\(619\) | 4.25398 | 0.170982 | 0.0854909 | − | 0.996339i | \(-0.472754\pi\) | ||||
0.0854909 | + | 0.996339i | \(0.472754\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −14.3311 | −0.575086 | ||||||||
\(622\) | 26.5290 | 1.06371 | ||||||||
\(623\) | −0.600201 | −0.0240466 | ||||||||
\(624\) | −4.67337 | −0.187084 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −20.7097 | −0.827728 | ||||||||
\(627\) | 2.41848 | 0.0965848 | ||||||||
\(628\) | 9.94857 | 0.396991 | ||||||||
\(629\) | −17.7283 | −0.706873 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.94679 | 0.356166 | 0.178083 | − | 0.984015i | \(-0.443010\pi\) | ||||
0.178083 | + | 0.984015i | \(0.443010\pi\) | |||||||
\(632\) | −36.1822 | −1.43925 | ||||||||
\(633\) | 29.9997 | 1.19238 | ||||||||
\(634\) | −2.20857 | −0.0877135 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 10.1467 | 0.402341 | ||||||||
\(637\) | 2.66629 | 0.105642 | ||||||||
\(638\) | 9.16786 | 0.362959 | ||||||||
\(639\) | 11.2391 | 0.444612 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.6413 | 0.459803 | 0.229902 | − | 0.973214i | \(-0.426160\pi\) | ||||
0.229902 | + | 0.973214i | \(0.426160\pi\) | |||||||
\(642\) | 11.8808 | 0.468898 | ||||||||
\(643\) | 31.5371 | 1.24370 | 0.621851 | − | 0.783136i | \(-0.286381\pi\) | ||||
0.621851 | + | 0.783136i | \(0.286381\pi\) | |||||||
\(644\) | −9.69060 | −0.381863 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.54201 | −0.0606696 | ||||||||
\(647\) | −7.63153 | −0.300027 | −0.150013 | − | 0.988684i | \(-0.547932\pi\) | ||||
−0.150013 | + | 0.988684i | \(0.547932\pi\) | |||||||
\(648\) | −2.21909 | −0.0871742 | ||||||||
\(649\) | −6.14158 | −0.241078 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 22.2498 | 0.872038 | ||||||||
\(652\) | 10.4123 | 0.407778 | ||||||||
\(653\) | −25.3578 | −0.992328 | −0.496164 | − | 0.868229i | \(-0.665259\pi\) | ||||
−0.496164 | + | 0.868229i | \(0.665259\pi\) | |||||||
\(654\) | −11.8263 | −0.462444 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 7.92699 | 0.309497 | ||||||||
\(657\) | −3.27646 | −0.127827 | ||||||||
\(658\) | 8.16322 | 0.318236 | ||||||||
\(659\) | −39.0160 | −1.51985 | −0.759924 | − | 0.650011i | \(-0.774764\pi\) | ||||
−0.759924 | + | 0.650011i | \(0.774764\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 48.6676 | 1.89295 | 0.946474 | − | 0.322779i | \(-0.104617\pi\) | ||||
0.946474 | + | 0.322779i | \(0.104617\pi\) | |||||||
\(662\) | −3.67399 | −0.142794 | ||||||||
\(663\) | 10.5761 | 0.410743 | ||||||||
\(664\) | −16.9158 | −0.656460 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 11.9122 | 0.461590 | ||||||||
\(667\) | 15.6936 | 0.607660 | ||||||||
\(668\) | −15.3713 | −0.594732 | ||||||||
\(669\) | −9.40995 | −0.363810 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 22.8893 | 0.883633 | ||||||||
\(672\) | −16.8050 | −0.648267 | ||||||||
\(673\) | −20.8488 | −0.803664 | −0.401832 | − | 0.915713i | \(-0.631626\pi\) | ||||
−0.401832 | + | 0.915713i | \(0.631626\pi\) | |||||||
\(674\) | 16.8465 | 0.648902 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −14.2222 | −0.547008 | ||||||||
\(677\) | 30.6907 | 1.17954 | 0.589769 | − | 0.807572i | \(-0.299219\pi\) | ||||
0.589769 | + | 0.807572i | \(0.299219\pi\) | |||||||
\(678\) | −5.74178 | −0.220512 | ||||||||
\(679\) | −34.4032 | −1.32027 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.90005 | 0.187770 | ||||||||
\(682\) | 12.1767 | 0.466270 | ||||||||
\(683\) | 22.3276 | 0.854344 | 0.427172 | − | 0.904170i | \(-0.359510\pi\) | ||||
0.427172 | + | 0.904170i | \(0.359510\pi\) | |||||||
\(684\) | −2.54478 | −0.0973020 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 14.5912 | 0.557096 | ||||||||
\(687\) | 33.1511 | 1.26479 | ||||||||
\(688\) | 2.79200 | 0.106444 | ||||||||
\(689\) | 30.3194 | 1.15508 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.0489 | −1.02899 | −0.514495 | − | 0.857493i | \(-0.672021\pi\) | ||||
−0.514495 | + | 0.857493i | \(0.672021\pi\) | |||||||
\(692\) | −12.2063 | −0.464013 | ||||||||
\(693\) | 9.02911 | 0.342987 | ||||||||
\(694\) | 15.3570 | 0.582944 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 17.1751 | 0.651021 | ||||||||
\(697\) | −17.9393 | −0.679499 | ||||||||
\(698\) | −3.21238 | −0.121590 | ||||||||
\(699\) | −14.7148 | −0.556565 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −39.0100 | −1.47339 | −0.736693 | − | 0.676227i | \(-0.763614\pi\) | ||||
−0.736693 | + | 0.676227i | \(0.763614\pi\) | |||||||
\(702\) | −19.4691 | −0.734816 | ||||||||
\(703\) | −9.42771 | −0.355573 | ||||||||
\(704\) | −5.63819 | −0.212497 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15.3876 | 0.579121 | ||||||||
\(707\) | −30.4634 | −1.14570 | ||||||||
\(708\) | −4.77977 | −0.179635 | ||||||||
\(709\) | −12.6642 | −0.475612 | −0.237806 | − | 0.971313i | \(-0.576428\pi\) | ||||
−0.237806 | + | 0.971313i | \(0.576428\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 23.9740 | 0.899095 | ||||||||
\(712\) | −0.615364 | −0.0230618 | ||||||||
\(713\) | 20.8442 | 0.780621 | ||||||||
\(714\) | 4.25804 | 0.159353 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −10.0417 | −0.375276 | ||||||||
\(717\) | 8.21314 | 0.306725 | ||||||||
\(718\) | 17.5566 | 0.655205 | ||||||||
\(719\) | 18.1316 | 0.676193 | 0.338096 | − | 0.941111i | \(-0.390217\pi\) | ||||
0.338096 | + | 0.941111i | \(0.390217\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 34.5788 | 1.28778 | ||||||||
\(722\) | 13.6337 | 0.507393 | ||||||||
\(723\) | 1.12938 | 0.0420022 | ||||||||
\(724\) | 32.0149 | 1.18983 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 5.79576 | 0.215101 | ||||||||
\(727\) | 21.4455 | 0.795368 | 0.397684 | − | 0.917522i | \(-0.369814\pi\) | ||||
0.397684 | + | 0.917522i | \(0.369814\pi\) | |||||||
\(728\) | −31.6901 | −1.17451 | ||||||||
\(729\) | 19.5487 | 0.724026 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.31848 | −0.233697 | ||||||||
\(732\) | 17.8139 | 0.658422 | ||||||||
\(733\) | −0.379985 | −0.0140350 | −0.00701752 | − | 0.999975i | \(-0.502234\pi\) | ||||
−0.00701752 | + | 0.999975i | \(0.502234\pi\) | |||||||
\(734\) | −11.8411 | −0.437061 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −15.7434 | −0.580309 | ||||||||
\(737\) | 2.89412 | 0.106606 | ||||||||
\(738\) | 12.0540 | 0.443715 | ||||||||
\(739\) | 42.6584 | 1.56921 | 0.784607 | − | 0.619993i | \(-0.212865\pi\) | ||||
0.784607 | + | 0.619993i | \(0.212865\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.62428 | 0.206613 | ||||||||
\(742\) | 12.2068 | 0.448127 | ||||||||
\(743\) | 17.0856 | 0.626810 | 0.313405 | − | 0.949620i | \(-0.398530\pi\) | ||||
0.313405 | + | 0.949620i | \(0.398530\pi\) | |||||||
\(744\) | 22.8119 | 0.836324 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 17.4250 | 0.637975 | ||||||||
\(747\) | 11.2082 | 0.410088 | ||||||||
\(748\) | −5.72333 | −0.209266 | ||||||||
\(749\) | −35.1044 | −1.28269 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −33.7135 | −1.23022 | −0.615111 | − | 0.788441i | \(-0.710889\pi\) | ||||
−0.615111 | + | 0.788441i | \(0.710889\pi\) | |||||||
\(752\) | −3.64685 | −0.132987 | ||||||||
\(753\) | −31.4637 | −1.14660 | ||||||||
\(754\) | 21.3202 | 0.776437 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 19.2515 | 0.700171 | ||||||||
\(757\) | 16.7814 | 0.609932 | 0.304966 | − | 0.952363i | \(-0.401355\pi\) | ||||
0.304966 | + | 0.952363i | \(0.401355\pi\) | |||||||
\(758\) | 7.32671 | 0.266118 | ||||||||
\(759\) | −6.25639 | −0.227093 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29.8307 | −1.08136 | −0.540681 | − | 0.841227i | \(-0.681834\pi\) | ||||
−0.540681 | + | 0.841227i | \(0.681834\pi\) | |||||||
\(762\) | −3.97941 | −0.144159 | ||||||||
\(763\) | 34.9432 | 1.26503 | ||||||||
\(764\) | −22.7456 | −0.822907 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.906120 | 0.0327394 | ||||||||
\(767\) | −14.2825 | −0.515711 | ||||||||
\(768\) | −14.4599 | −0.521778 | ||||||||
\(769\) | 7.89994 | 0.284879 | 0.142440 | − | 0.989803i | \(-0.454505\pi\) | ||||
0.142440 | + | 0.989803i | \(0.454505\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.0077 | −0.648532 | ||||||||
\(772\) | 22.7034 | 0.817112 | ||||||||
\(773\) | −25.4969 | −0.917061 | −0.458530 | − | 0.888679i | \(-0.651624\pi\) | ||||
−0.458530 | + | 0.888679i | \(0.651624\pi\) | |||||||
\(774\) | 4.24560 | 0.152605 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −35.2723 | −1.26620 | ||||||||
\(777\) | 26.0332 | 0.933937 | ||||||||
\(778\) | 9.14012 | 0.327689 | ||||||||
\(779\) | −9.53993 | −0.341803 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.4422 | 0.480999 | ||||||||
\(782\) | 3.98904 | 0.142648 | ||||||||
\(783\) | −31.1773 | −1.11418 | ||||||||
\(784\) | −0.479563 | −0.0171273 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 9.11119 | 0.324985 | ||||||||
\(787\) | −49.0412 | −1.74813 | −0.874065 | − | 0.485809i | \(-0.838525\pi\) | ||||
−0.874065 | + | 0.485809i | \(0.838525\pi\) | |||||||
\(788\) | −34.4151 | −1.22599 | ||||||||
\(789\) | 0.681905 | 0.0242764 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.9653 | 0.603217 | ||||||||
\(792\) | 9.25721 | 0.328941 | ||||||||
\(793\) | 53.2301 | 1.89026 | ||||||||
\(794\) | −0.990260 | −0.0351430 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17.5143 | 0.620779 | ||||||||
\(797\) | −1.15733 | −0.0409948 | −0.0204974 | − | 0.999790i | \(-0.506525\pi\) | ||||
−0.0204974 | + | 0.999790i | \(0.506525\pi\) | |||||||
\(798\) | 2.26438 | 0.0801581 | ||||||||
\(799\) | 8.25307 | 0.291973 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.407734 | 0.0144066 | ||||||||
\(802\) | −13.5377 | −0.478031 | ||||||||
\(803\) | −3.91872 | −0.138289 | ||||||||
\(804\) | 2.25239 | 0.0794357 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 28.3174 | 0.997438 | ||||||||
\(807\) | −26.6026 | −0.936457 | ||||||||
\(808\) | −31.2330 | −1.09877 | ||||||||
\(809\) | −31.6665 | −1.11334 | −0.556668 | − | 0.830735i | \(-0.687920\pi\) | ||||
−0.556668 | + | 0.830735i | \(0.687920\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.0360 | 1.26540 | 0.632698 | − | 0.774398i | \(-0.281947\pi\) | ||||
0.632698 | + | 0.774398i | \(0.281947\pi\) | |||||||
\(812\) | −21.0819 | −0.739830 | ||||||||
\(813\) | −11.0792 | −0.388563 | ||||||||
\(814\) | 14.2473 | 0.499367 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.90224 | −0.0665918 | ||||||||
\(817\) | −3.36010 | −0.117555 | ||||||||
\(818\) | −0.925087 | −0.0323449 | ||||||||
\(819\) | 20.9976 | 0.733714 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.1203 | 1.05121 | 0.525603 | − | 0.850730i | \(-0.323840\pi\) | ||||
0.525603 | + | 0.850730i | \(0.323840\pi\) | |||||||
\(822\) | 15.7859 | 0.550595 | ||||||||
\(823\) | 21.5975 | 0.752843 | 0.376421 | − | 0.926449i | \(-0.377155\pi\) | ||||
0.376421 | + | 0.926449i | \(0.377155\pi\) | |||||||
\(824\) | 35.4524 | 1.23504 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.75025 | −0.200077 | ||||||||
\(827\) | 2.37687 | 0.0826519 | 0.0413259 | − | 0.999146i | \(-0.486842\pi\) | ||||
0.0413259 | + | 0.999146i | \(0.486842\pi\) | |||||||
\(828\) | 6.58311 | 0.228779 | ||||||||
\(829\) | −20.4204 | −0.709230 | −0.354615 | − | 0.935012i | \(-0.615388\pi\) | ||||
−0.354615 | + | 0.935012i | \(0.615388\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.76960 | 0.304214 | ||||||||
\(832\) | −13.1118 | −0.454571 | ||||||||
\(833\) | 1.08528 | 0.0376028 | ||||||||
\(834\) | 5.14291 | 0.178084 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.04361 | −0.105265 | ||||||||
\(837\) | −41.4094 | −1.43132 | ||||||||
\(838\) | 17.8957 | 0.618196 | ||||||||
\(839\) | 2.84185 | 0.0981115 | 0.0490557 | − | 0.998796i | \(-0.484379\pi\) | ||||
0.0490557 | + | 0.998796i | \(0.484379\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.14153 | 0.177294 | ||||||||
\(842\) | −18.3432 | −0.632149 | ||||||||
\(843\) | −23.4496 | −0.807646 | ||||||||
\(844\) | −37.7540 | −1.29955 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −5.54552 | −0.190659 | ||||||||
\(847\) | −17.1248 | −0.588415 | ||||||||
\(848\) | −5.45330 | −0.187267 | ||||||||
\(849\) | 9.54431 | 0.327560 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24.3886 | 0.836032 | ||||||||
\(852\) | 10.4616 | 0.358407 | ||||||||
\(853\) | 13.8008 | 0.472530 | 0.236265 | − | 0.971689i | \(-0.424077\pi\) | ||||
0.236265 | + | 0.971689i | \(0.424077\pi\) | |||||||
\(854\) | 21.4309 | 0.733349 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −35.9912 | −1.23015 | ||||||||
\(857\) | −2.06240 | −0.0704502 | −0.0352251 | − | 0.999379i | \(-0.511215\pi\) | ||||
−0.0352251 | + | 0.999379i | \(0.511215\pi\) | |||||||
\(858\) | −8.49948 | −0.290167 | ||||||||
\(859\) | −22.7067 | −0.774742 | −0.387371 | − | 0.921924i | \(-0.626617\pi\) | ||||
−0.387371 | + | 0.921924i | \(0.626617\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 26.3431 | 0.897771 | ||||||||
\(862\) | −7.02189 | −0.239166 | ||||||||
\(863\) | −25.2543 | −0.859667 | −0.429833 | − | 0.902908i | \(-0.641428\pi\) | ||||
−0.429833 | + | 0.902908i | \(0.641428\pi\) | |||||||
\(864\) | 31.2761 | 1.06403 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 30.8425 | 1.04807 | ||||||||
\(867\) | −14.8946 | −0.505847 | ||||||||
\(868\) | −28.0009 | −0.950411 | ||||||||
\(869\) | 28.6734 | 0.972678 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.73041 | 0.228051 | ||||||||
\(872\) | 35.8260 | 1.21322 | ||||||||
\(873\) | 23.3711 | 0.790992 | ||||||||
\(874\) | 2.12133 | 0.0717551 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.04980 | −0.103043 | ||||||||
\(877\) | −23.5255 | −0.794401 | −0.397200 | − | 0.917732i | \(-0.630018\pi\) | ||||
−0.397200 | + | 0.917732i | \(0.630018\pi\) | |||||||
\(878\) | −14.8681 | −0.501776 | ||||||||
\(879\) | −15.2191 | −0.513327 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.8946 | −0.805029 | −0.402515 | − | 0.915414i | \(-0.631864\pi\) | ||||
−0.402515 | + | 0.915414i | \(0.631864\pi\) | |||||||
\(882\) | −0.729238 | −0.0245547 | ||||||||
\(883\) | −12.9066 | −0.434342 | −0.217171 | − | 0.976134i | \(-0.569683\pi\) | ||||
−0.217171 | + | 0.976134i | \(0.569683\pi\) | |||||||
\(884\) | −13.3098 | −0.447658 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −29.1761 | −0.980192 | ||||||||
\(887\) | 26.6396 | 0.894471 | 0.447235 | − | 0.894416i | \(-0.352409\pi\) | ||||
0.447235 | + | 0.894416i | \(0.352409\pi\) | |||||||
\(888\) | 26.6909 | 0.895689 | ||||||||
\(889\) | 11.7580 | 0.394351 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.75857 | 0.0589143 | ||||||||
\(892\) | 11.8422 | 0.396507 | ||||||||
\(893\) | 4.38889 | 0.146869 | ||||||||
\(894\) | 6.00837 | 0.200950 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 24.4807 | 0.817843 | ||||||||
\(897\) | −14.5495 | −0.485793 | ||||||||
\(898\) | 5.44261 | 0.181622 | ||||||||
\(899\) | 45.3466 | 1.51239 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.3412 | 0.411144 | ||||||||
\(902\) | 14.4169 | 0.480029 | ||||||||
\(903\) | 9.27842 | 0.308766 | ||||||||
\(904\) | 17.3939 | 0.578513 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 20.0413 | 0.665828 | ||||||||
\(907\) | −21.2193 | −0.704574 | −0.352287 | − | 0.935892i | \(-0.614596\pi\) | ||||
−0.352287 | + | 0.935892i | \(0.614596\pi\) | |||||||
\(908\) | −6.16661 | −0.204646 | ||||||||
\(909\) | 20.6947 | 0.686400 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.50032 | −0.215365 | −0.107683 | − | 0.994185i | \(-0.534343\pi\) | ||||
−0.107683 | + | 0.994185i | \(0.534343\pi\) | |||||||
\(912\) | −1.01159 | −0.0334972 | ||||||||
\(913\) | 13.4053 | 0.443650 | ||||||||
\(914\) | 10.0475 | 0.332342 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −41.7199 | −1.37846 | ||||||||
\(917\) | −26.9209 | −0.889008 | ||||||||
\(918\) | −7.92471 | −0.261554 | ||||||||
\(919\) | 19.1428 | 0.631461 | 0.315731 | − | 0.948849i | \(-0.397750\pi\) | ||||
0.315731 | + | 0.948849i | \(0.397750\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.9271 | 0.360060 | ||||||||
\(922\) | −19.4858 | −0.641730 | ||||||||
\(923\) | 31.2604 | 1.02895 | ||||||||
\(924\) | 8.40447 | 0.276487 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −27.9495 | −0.918478 | ||||||||
\(927\) | −23.4904 | −0.771526 | ||||||||
\(928\) | −34.2498 | −1.12430 | ||||||||
\(929\) | −58.3414 | −1.91412 | −0.957059 | − | 0.289892i | \(-0.906381\pi\) | ||||
−0.957059 | + | 0.289892i | \(0.906381\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.577142 | 0.0189151 | ||||||||
\(932\) | 18.5183 | 0.606586 | ||||||||
\(933\) | −39.3854 | −1.28942 | ||||||||
\(934\) | 8.77906 | 0.287260 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 21.5280 | 0.703666 | ||||||||
\(937\) | 15.6711 | 0.511952 | 0.255976 | − | 0.966683i | \(-0.417603\pi\) | ||||
0.255976 | + | 0.966683i | \(0.417603\pi\) | |||||||
\(938\) | 2.70972 | 0.0884753 | ||||||||
\(939\) | 30.7461 | 1.00336 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.8470 | 0.418799 | 0.209399 | − | 0.977830i | \(-0.432849\pi\) | ||||
0.209399 | + | 0.977830i | \(0.432849\pi\) | |||||||
\(942\) | 6.01368 | 0.195936 | ||||||||
\(943\) | 24.6789 | 0.803657 | ||||||||
\(944\) | 2.56888 | 0.0836098 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.07783 | 0.165094 | ||||||||
\(947\) | 22.7709 | 0.739954 | 0.369977 | − | 0.929041i | \(-0.379366\pi\) | ||||
0.369977 | + | 0.929041i | \(0.379366\pi\) | |||||||
\(948\) | 22.3155 | 0.724772 | ||||||||
\(949\) | −9.11314 | −0.295825 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.27889 | 0.106325 | ||||||||
\(952\) | −12.8991 | −0.418063 | ||||||||
\(953\) | −23.0127 | −0.745453 | −0.372727 | − | 0.927941i | \(-0.621577\pi\) | ||||
−0.372727 | + | 0.927941i | \(0.621577\pi\) | |||||||
\(954\) | −8.29246 | −0.268478 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −10.3361 | −0.334292 | ||||||||
\(957\) | −13.6108 | −0.439974 | ||||||||
\(958\) | −22.8160 | −0.737150 | ||||||||
\(959\) | −46.6427 | −1.50617 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.2291 | 0.942873 | ||||||||
\(962\) | 33.1326 | 1.06824 | ||||||||
\(963\) | 23.8474 | 0.768472 | ||||||||
\(964\) | −1.42130 | −0.0457771 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −5.85774 | −0.188470 | ||||||||
\(967\) | −8.23926 | −0.264957 | −0.132478 | − | 0.991186i | \(-0.542294\pi\) | ||||
−0.132478 | + | 0.991186i | \(0.542294\pi\) | |||||||
\(968\) | −17.5574 | −0.564317 | ||||||||
\(969\) | 2.28930 | 0.0735429 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −42.6419 | −1.36845 | −0.684223 | − | 0.729273i | \(-0.739858\pi\) | ||||
−0.684223 | + | 0.729273i | \(0.739858\pi\) | |||||||
\(972\) | −21.3826 | −0.685846 | ||||||||
\(973\) | −15.1958 | −0.487156 | ||||||||
\(974\) | −6.20021 | −0.198667 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.57407 | −0.306458 | ||||||||
\(977\) | 5.17109 | 0.165438 | 0.0827189 | − | 0.996573i | \(-0.473640\pi\) | ||||
0.0827189 | + | 0.996573i | \(0.473640\pi\) | |||||||
\(978\) | 6.29401 | 0.201260 | ||||||||
\(979\) | 0.487659 | 0.0155856 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −23.7380 | −0.757895 | ||||||||
\(982\) | 6.00749 | 0.191707 | ||||||||
\(983\) | 20.8634 | 0.665438 | 0.332719 | − | 0.943026i | \(-0.392034\pi\) | ||||
0.332719 | + | 0.943026i | \(0.392034\pi\) | |||||||
\(984\) | 27.0086 | 0.861003 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 8.67817 | 0.276369 | ||||||||
\(987\) | −12.1193 | −0.385761 | ||||||||
\(988\) | −7.07803 | −0.225182 | ||||||||
\(989\) | 8.69227 | 0.276398 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.2535 | 0.516311 | 0.258155 | − | 0.966103i | \(-0.416885\pi\) | ||||
0.258155 | + | 0.966103i | \(0.416885\pi\) | |||||||
\(992\) | −45.4903 | −1.44432 | ||||||||
\(993\) | 5.45448 | 0.173093 | ||||||||
\(994\) | 12.5857 | 0.399193 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 10.4329 | 0.330578 | ||||||||
\(997\) | 27.4154 | 0.868254 | 0.434127 | − | 0.900852i | \(-0.357057\pi\) | ||||
0.434127 | + | 0.900852i | \(0.357057\pi\) | |||||||
\(998\) | 17.0668 | 0.540241 | ||||||||
\(999\) | −48.4509 | −1.53292 |
(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 | 6025.2.a.p.1.18 | 46 | ||
5.2 | odd | 4 | 1205.2.b.c.724.18 | ✓ | 46 | ||
5.3 | odd | 4 | 1205.2.b.c.724.29 | yes | 46 | ||
5.4 | even | 2 | inner | 6025.2.a.p.1.29 | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1205.2.b.c.724.18 | ✓ | 46 | 5.2 | odd | 4 | ||
1205.2.b.c.724.29 | yes | 46 | 5.3 | odd | 4 | ||
6025.2.a.p.1.18 | 46 | 1.1 | even | 1 | trivial | ||
6025.2.a.p.1.29 | 46 | 5.4 | even | 2 | inner |