Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(47.9341963334\) |
Analytic rank: | \(1\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.06922 | 0.756051 | 0.378025 | − | 0.925795i | \(-0.376603\pi\) | ||||
0.378025 | + | 0.925795i | \(0.376603\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.856774 | −0.428387 | ||||||||
\(5\) | −0.420836 | −0.188204 | −0.0941019 | − | 0.995563i | \(-0.529998\pi\) | ||||
−0.0941019 | + | 0.995563i | \(0.529998\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.13415 | 0.428670 | 0.214335 | − | 0.976760i | \(-0.431242\pi\) | ||||
0.214335 | + | 0.976760i | \(0.431242\pi\) | |||||||
\(8\) | −3.05451 | −1.07993 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.449966 | −0.142292 | ||||||||
\(11\) | 2.91779 | 0.879748 | 0.439874 | − | 0.898059i | \(-0.355023\pi\) | ||||
0.439874 | + | 0.898059i | \(0.355023\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.70064 | −0.471672 | −0.235836 | − | 0.971793i | \(-0.575783\pi\) | ||||
−0.235836 | + | 0.971793i | \(0.575783\pi\) | |||||||
\(14\) | 1.21266 | 0.324096 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.55239 | −0.388097 | ||||||||
\(17\) | −0.536110 | −0.130026 | −0.0650128 | − | 0.997884i | \(-0.520709\pi\) | ||||
−0.0650128 | + | 0.997884i | \(0.520709\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.585904 | 0.134416 | 0.0672078 | − | 0.997739i | \(-0.478591\pi\) | ||||
0.0672078 | + | 0.997739i | \(0.478591\pi\) | |||||||
\(20\) | 0.360562 | 0.0806240 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.11976 | 0.665134 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.82290 | −0.964579 | ||||||||
\(26\) | −1.81835 | −0.356608 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.971713 | −0.183637 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.49962 | 1.34697 | 0.673486 | − | 0.739200i | \(-0.264796\pi\) | ||||
0.673486 | + | 0.739200i | \(0.264796\pi\) | |||||||
\(32\) | 4.44918 | 0.786512 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.573218 | −0.0983060 | ||||||||
\(35\) | −0.477293 | −0.0806772 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.22414 | −0.201247 | −0.100623 | − | 0.994925i | \(-0.532084\pi\) | ||||
−0.100623 | + | 0.994925i | \(0.532084\pi\) | |||||||
\(38\) | 0.626459 | 0.101625 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.28545 | 0.203247 | ||||||||
\(41\) | −12.2002 | −1.90535 | −0.952676 | − | 0.303987i | \(-0.901682\pi\) | ||||
−0.952676 | + | 0.303987i | \(0.901682\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.78460 | −0.424647 | −0.212324 | − | 0.977199i | \(-0.568103\pi\) | ||||
−0.212324 | + | 0.977199i | \(0.568103\pi\) | |||||||
\(44\) | −2.49989 | −0.376873 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.06922 | −0.157648 | ||||||||
\(47\) | −0.180494 | −0.0263278 | −0.0131639 | − | 0.999913i | \(-0.504190\pi\) | ||||
−0.0131639 | + | 0.999913i | \(0.504190\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.71370 | −0.816242 | ||||||||
\(50\) | −5.15673 | −0.729271 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.45706 | 0.202058 | ||||||||
\(53\) | 11.0675 | 1.52023 | 0.760116 | − | 0.649787i | \(-0.225142\pi\) | ||||
0.760116 | + | 0.649787i | \(0.225142\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.22791 | −0.165572 | ||||||||
\(56\) | −3.46429 | −0.462935 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.06922 | −0.140395 | ||||||||
\(59\) | 5.86452 | 0.763496 | 0.381748 | − | 0.924266i | \(-0.375322\pi\) | ||||
0.381748 | + | 0.924266i | \(0.375322\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.1083 | 1.55031 | 0.775153 | − | 0.631773i | \(-0.217673\pi\) | ||||
0.775153 | + | 0.631773i | \(0.217673\pi\) | |||||||
\(62\) | 8.01872 | 1.01838 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.86192 | 0.982740 | ||||||||
\(65\) | 0.715690 | 0.0887705 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.3374 | −1.75159 | −0.875794 | − | 0.482686i | \(-0.839661\pi\) | ||||
−0.875794 | + | 0.482686i | \(0.839661\pi\) | |||||||
\(68\) | 0.459325 | 0.0557013 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.510330 | −0.0609961 | ||||||||
\(71\) | −13.2457 | −1.57198 | −0.785988 | − | 0.618242i | \(-0.787845\pi\) | ||||
−0.785988 | + | 0.618242i | \(0.787845\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.56789 | −0.534632 | −0.267316 | − | 0.963609i | \(-0.586137\pi\) | ||||
−0.267316 | + | 0.963609i | \(0.586137\pi\) | |||||||
\(74\) | −1.30887 | −0.152153 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.501988 | −0.0575819 | ||||||||
\(77\) | 3.30923 | 0.377121 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.89701 | −0.775974 | −0.387987 | − | 0.921665i | \(-0.626829\pi\) | ||||
−0.387987 | + | 0.921665i | \(0.626829\pi\) | |||||||
\(80\) | 0.653302 | 0.0730414 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −13.0447 | −1.44054 | ||||||||
\(83\) | 8.57178 | 0.940875 | 0.470438 | − | 0.882433i | \(-0.344096\pi\) | ||||
0.470438 | + | 0.882433i | \(0.344096\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.225614 | 0.0244713 | ||||||||
\(86\) | −2.97734 | −0.321055 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −8.91244 | −0.950069 | ||||||||
\(89\) | −2.75169 | −0.291678 | −0.145839 | − | 0.989308i | \(-0.546588\pi\) | ||||
−0.145839 | + | 0.989308i | \(0.546588\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.92878 | −0.202192 | ||||||||
\(92\) | 0.856774 | 0.0893249 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.192988 | −0.0199052 | ||||||||
\(95\) | −0.246570 | −0.0252975 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.28509 | −0.739689 | −0.369844 | − | 0.929094i | \(-0.620589\pi\) | ||||
−0.369844 | + | 0.929094i | \(0.620589\pi\) | |||||||
\(98\) | −6.10918 | −0.617121 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.13213 | 0.413213 | ||||||||
\(101\) | 7.18183 | 0.714618 | 0.357309 | − | 0.933986i | \(-0.383694\pi\) | ||||
0.357309 | + | 0.933986i | \(0.383694\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.02471 | 0.298034 | 0.149017 | − | 0.988835i | \(-0.452389\pi\) | ||||
0.149017 | + | 0.988835i | \(0.452389\pi\) | |||||||
\(104\) | 5.19462 | 0.509374 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.8335 | 1.14937 | ||||||||
\(107\) | −9.61926 | −0.929929 | −0.464965 | − | 0.885329i | \(-0.653933\pi\) | ||||
−0.464965 | + | 0.885329i | \(0.653933\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0908 | 0.966521 | 0.483261 | − | 0.875477i | \(-0.339452\pi\) | ||||
0.483261 | + | 0.875477i | \(0.339452\pi\) | |||||||
\(110\) | −1.31291 | −0.125181 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.76065 | −0.166366 | ||||||||
\(113\) | −6.82687 | −0.642218 | −0.321109 | − | 0.947042i | \(-0.604056\pi\) | ||||
−0.321109 | + | 0.947042i | \(0.604056\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.420836 | 0.0392432 | ||||||||
\(116\) | 0.856774 | 0.0795495 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.27045 | 0.577242 | ||||||||
\(119\) | −0.608031 | −0.0557381 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.48647 | −0.226043 | ||||||||
\(122\) | 12.9464 | 1.17211 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.42548 | −0.577025 | ||||||||
\(125\) | 4.13383 | 0.369741 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.53291 | −0.490967 | −0.245483 | − | 0.969401i | \(-0.578947\pi\) | ||||
−0.245483 | + | 0.969401i | \(0.578947\pi\) | |||||||
\(128\) | −0.492261 | −0.0435101 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.765229 | 0.0671150 | ||||||||
\(131\) | −13.4974 | −1.17927 | −0.589637 | − | 0.807668i | \(-0.700729\pi\) | ||||
−0.589637 | + | 0.807668i | \(0.700729\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.664505 | 0.0576199 | ||||||||
\(134\) | −15.3298 | −1.32429 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.63755 | 0.140419 | ||||||||
\(137\) | −5.83987 | −0.498934 | −0.249467 | − | 0.968383i | \(-0.580255\pi\) | ||||
−0.249467 | + | 0.968383i | \(0.580255\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −22.3348 | −1.89442 | −0.947208 | − | 0.320619i | \(-0.896109\pi\) | ||||
−0.947208 | + | 0.320619i | \(0.896109\pi\) | |||||||
\(140\) | 0.408932 | 0.0345611 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −14.1625 | −1.18849 | ||||||||
\(143\) | −4.96211 | −0.414953 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.420836 | 0.0349486 | ||||||||
\(146\) | −4.88407 | −0.404209 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.04881 | 0.0862116 | ||||||||
\(149\) | 0.856186 | 0.0701415 | 0.0350707 | − | 0.999385i | \(-0.488834\pi\) | ||||
0.0350707 | + | 0.999385i | \(0.488834\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.82116 | −0.473720 | −0.236860 | − | 0.971544i | \(-0.576118\pi\) | ||||
−0.236860 | + | 0.971544i | \(0.576118\pi\) | |||||||
\(152\) | −1.78965 | −0.145160 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.53828 | 0.285123 | ||||||||
\(155\) | −3.15611 | −0.253505 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.59058 | −0.126942 | −0.0634709 | − | 0.997984i | \(-0.520217\pi\) | ||||
−0.0634709 | + | 0.997984i | \(0.520217\pi\) | |||||||
\(158\) | −7.37440 | −0.586676 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.87238 | −0.148024 | ||||||||
\(161\) | −1.13415 | −0.0893838 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.80469 | −0.767963 | −0.383981 | − | 0.923341i | \(-0.625447\pi\) | ||||
−0.383981 | + | 0.923341i | \(0.625447\pi\) | |||||||
\(164\) | 10.4528 | 0.816228 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.16510 | 0.711349 | ||||||||
\(167\) | −16.2385 | −1.25658 | −0.628288 | − | 0.777981i | \(-0.716244\pi\) | ||||
−0.628288 | + | 0.777981i | \(0.716244\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.1078 | −0.777525 | ||||||||
\(170\) | 0.241231 | 0.0185016 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.38577 | 0.181913 | ||||||||
\(173\) | 14.2547 | 1.08376 | 0.541881 | − | 0.840455i | \(-0.317712\pi\) | ||||
0.541881 | + | 0.840455i | \(0.317712\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.46991 | −0.413486 | ||||||||
\(176\) | −4.52955 | −0.341428 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.94215 | −0.220524 | ||||||||
\(179\) | −0.143629 | −0.0107353 | −0.00536766 | − | 0.999986i | \(-0.501709\pi\) | ||||
−0.00536766 | + | 0.999986i | \(0.501709\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.6508 | −0.865997 | −0.432998 | − | 0.901395i | \(-0.642544\pi\) | ||||
−0.432998 | + | 0.901395i | \(0.642544\pi\) | |||||||
\(182\) | −2.06229 | −0.152867 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.05451 | 0.225182 | ||||||||
\(185\) | 0.515161 | 0.0378754 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.56426 | −0.114390 | ||||||||
\(188\) | 0.154643 | 0.0112785 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.263637 | −0.0191262 | ||||||||
\(191\) | −26.1784 | −1.89420 | −0.947100 | − | 0.320939i | \(-0.896002\pi\) | ||||
−0.947100 | + | 0.320939i | \(0.896002\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.02480 | 0.505656 | 0.252828 | − | 0.967511i | \(-0.418639\pi\) | ||||
0.252828 | + | 0.967511i | \(0.418639\pi\) | |||||||
\(194\) | −7.78934 | −0.559242 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.89535 | 0.349668 | ||||||||
\(197\) | −3.74205 | −0.266610 | −0.133305 | − | 0.991075i | \(-0.542559\pi\) | ||||
−0.133305 | + | 0.991075i | \(0.542559\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.8087 | 0.978875 | 0.489437 | − | 0.872038i | \(-0.337202\pi\) | ||||
0.489437 | + | 0.872038i | \(0.337202\pi\) | |||||||
\(200\) | 14.7316 | 1.04168 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7.67893 | 0.540288 | ||||||||
\(203\) | −1.13415 | −0.0796020 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.13429 | 0.358594 | ||||||||
\(206\) | 3.23407 | 0.225329 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.64005 | 0.183055 | ||||||||
\(209\) | 1.70955 | 0.118252 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.17516 | 0.356273 | 0.178136 | − | 0.984006i | \(-0.442993\pi\) | ||||
0.178136 | + | 0.984006i | \(0.442993\pi\) | |||||||
\(212\) | −9.48231 | −0.651248 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −10.2851 | −0.703074 | ||||||||
\(215\) | 1.17186 | 0.0799202 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.50572 | 0.577406 | ||||||||
\(218\) | 10.7892 | 0.730739 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.05205 | 0.0709289 | ||||||||
\(221\) | 0.911728 | 0.0613295 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.8518 | −0.860617 | −0.430308 | − | 0.902682i | \(-0.641595\pi\) | ||||
−0.430308 | + | 0.902682i | \(0.641595\pi\) | |||||||
\(224\) | 5.04606 | 0.337154 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.29941 | −0.485550 | ||||||||
\(227\) | 12.5847 | 0.835278 | 0.417639 | − | 0.908613i | \(-0.362858\pi\) | ||||
0.417639 | + | 0.908613i | \(0.362858\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.4879 | 1.28779 | 0.643897 | − | 0.765112i | \(-0.277316\pi\) | ||||
0.643897 | + | 0.765112i | \(0.277316\pi\) | |||||||
\(230\) | 0.449966 | 0.0296699 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.05451 | 0.200539 | ||||||||
\(233\) | 11.0040 | 0.720893 | 0.360446 | − | 0.932780i | \(-0.382624\pi\) | ||||
0.360446 | + | 0.932780i | \(0.382624\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.0759586 | 0.00495499 | ||||||||
\(236\) | −5.02457 | −0.327072 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.650117 | −0.0421408 | ||||||||
\(239\) | −9.61008 | −0.621625 | −0.310812 | − | 0.950471i | \(-0.600601\pi\) | ||||
−0.310812 | + | 0.950471i | \(0.600601\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.96508 | −0.384244 | −0.192122 | − | 0.981371i | \(-0.561537\pi\) | ||||
−0.192122 | + | 0.981371i | \(0.561537\pi\) | |||||||
\(242\) | −2.65858 | −0.170900 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −10.3741 | −0.664131 | ||||||||
\(245\) | 2.40453 | 0.153620 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.996411 | −0.0634001 | ||||||||
\(248\) | −22.9077 | −1.45464 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.41997 | 0.279543 | ||||||||
\(251\) | 9.33642 | 0.589310 | 0.294655 | − | 0.955604i | \(-0.404795\pi\) | ||||
0.294655 | + | 0.955604i | \(0.404795\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.91779 | −0.183440 | ||||||||
\(254\) | −5.91589 | −0.371196 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −16.2502 | −1.01564 | ||||||||
\(257\) | −27.9492 | −1.74342 | −0.871711 | − | 0.490021i | \(-0.836989\pi\) | ||||
−0.871711 | + | 0.490021i | \(0.836989\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.38836 | −0.0862685 | ||||||||
\(260\) | −0.613185 | −0.0380281 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −14.4317 | −0.891591 | ||||||||
\(263\) | 27.8535 | 1.71752 | 0.858760 | − | 0.512379i | \(-0.171236\pi\) | ||||
0.858760 | + | 0.512379i | \(0.171236\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.65759 | −0.286113 | ||||||||
\(266\) | 0.710501 | 0.0435636 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 12.2839 | 0.750357 | ||||||||
\(269\) | −8.33222 | −0.508025 | −0.254012 | − | 0.967201i | \(-0.581750\pi\) | ||||
−0.254012 | + | 0.967201i | \(0.581750\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.0222 | −1.51999 | −0.759995 | − | 0.649929i | \(-0.774799\pi\) | ||||
−0.759995 | + | 0.649929i | \(0.774799\pi\) | |||||||
\(272\) | 0.832251 | 0.0504626 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.24409 | −0.377219 | ||||||||
\(275\) | −14.0722 | −0.848587 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.5910 | −1.05694 | −0.528469 | − | 0.848952i | \(-0.677234\pi\) | ||||
−0.528469 | + | 0.848952i | \(0.677234\pi\) | |||||||
\(278\) | −23.8808 | −1.43228 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.45790 | 0.0871260 | ||||||||
\(281\) | −2.63805 | −0.157373 | −0.0786864 | − | 0.996899i | \(-0.525073\pi\) | ||||
−0.0786864 | + | 0.996899i | \(0.525073\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.9340 | −1.00662 | −0.503312 | − | 0.864105i | \(-0.667885\pi\) | ||||
−0.503312 | + | 0.864105i | \(0.667885\pi\) | |||||||
\(284\) | 11.3486 | 0.673414 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.30558 | −0.313725 | ||||||||
\(287\) | −13.8369 | −0.816767 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.7126 | −0.983093 | ||||||||
\(290\) | 0.449966 | 0.0264229 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.91365 | 0.229029 | ||||||||
\(293\) | −4.73836 | −0.276818 | −0.138409 | − | 0.990375i | \(-0.544199\pi\) | ||||
−0.138409 | + | 0.990375i | \(0.544199\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.46800 | −0.143693 | ||||||||
\(296\) | 3.73914 | 0.217333 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.915449 | 0.0530305 | ||||||||
\(299\) | 1.70064 | 0.0983504 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.15816 | −0.182034 | ||||||||
\(302\) | −6.22409 | −0.358156 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.909552 | −0.0521664 | ||||||||
\(305\) | −5.09561 | −0.291774 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −34.0679 | −1.94436 | −0.972178 | − | 0.234243i | \(-0.924739\pi\) | ||||
−0.972178 | + | 0.234243i | \(0.924739\pi\) | |||||||
\(308\) | −2.83526 | −0.161554 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.37457 | −0.191663 | ||||||||
\(311\) | 3.97157 | 0.225207 | 0.112604 | − | 0.993640i | \(-0.464081\pi\) | ||||
0.112604 | + | 0.993640i | \(0.464081\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.4087 | 1.21009 | 0.605045 | − | 0.796192i | \(-0.293155\pi\) | ||||
0.605045 | + | 0.796192i | \(0.293155\pi\) | |||||||
\(314\) | −1.70067 | −0.0959744 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.90918 | 0.332417 | ||||||||
\(317\) | 28.2785 | 1.58828 | 0.794140 | − | 0.607735i | \(-0.207922\pi\) | ||||
0.794140 | + | 0.607735i | \(0.207922\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.91779 | −0.163365 | ||||||||
\(320\) | −3.30858 | −0.184955 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.21266 | −0.0675787 | ||||||||
\(323\) | −0.314109 | −0.0174775 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.20200 | 0.454965 | ||||||||
\(326\) | −10.4833 | −0.580619 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 37.2657 | 2.05765 | ||||||||
\(329\) | −0.204708 | −0.0112859 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.6922 | −0.972450 | −0.486225 | − | 0.873834i | \(-0.661627\pi\) | ||||
−0.486225 | + | 0.873834i | \(0.661627\pi\) | |||||||
\(332\) | −7.34408 | −0.403059 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −17.3625 | −0.950035 | ||||||||
\(335\) | 6.03368 | 0.329655 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.4660 | −1.06038 | −0.530191 | − | 0.847878i | \(-0.677880\pi\) | ||||
−0.530191 | + | 0.847878i | \(0.677880\pi\) | |||||||
\(338\) | −10.8075 | −0.587849 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.193301 | −0.0104832 | ||||||||
\(341\) | 21.8823 | 1.18500 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.4193 | −0.778568 | ||||||||
\(344\) | 8.50559 | 0.458591 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 15.2413 | 0.819379 | ||||||||
\(347\) | 7.18999 | 0.385979 | 0.192989 | − | 0.981201i | \(-0.438182\pi\) | ||||
0.192989 | + | 0.981201i | \(0.438182\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.0083 | 1.01749 | 0.508746 | − | 0.860917i | \(-0.330109\pi\) | ||||
0.508746 | + | 0.860917i | \(0.330109\pi\) | |||||||
\(350\) | −5.84852 | −0.312616 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 12.9818 | 0.691932 | ||||||||
\(353\) | 3.18574 | 0.169560 | 0.0847799 | − | 0.996400i | \(-0.472981\pi\) | ||||
0.0847799 | + | 0.996400i | \(0.472981\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.57427 | 0.295852 | ||||||||
\(356\) | 2.35758 | 0.124951 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.153571 | −0.00811645 | ||||||||
\(359\) | −10.3826 | −0.547973 | −0.273986 | − | 0.961734i | \(-0.588342\pi\) | ||||
−0.273986 | + | 0.961734i | \(0.588342\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.6567 | −0.981932 | ||||||||
\(362\) | −12.4572 | −0.654737 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.65253 | 0.0866163 | ||||||||
\(365\) | 1.92234 | 0.100620 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.15378 | 0.112426 | 0.0562132 | − | 0.998419i | \(-0.482097\pi\) | ||||
0.0562132 | + | 0.998419i | \(0.482097\pi\) | |||||||
\(368\) | 1.55239 | 0.0809239 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.550820 | 0.0286357 | ||||||||
\(371\) | 12.5522 | 0.651678 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.6902 | 0.553517 | 0.276758 | − | 0.960940i | \(-0.410740\pi\) | ||||
0.276758 | + | 0.960940i | \(0.410740\pi\) | |||||||
\(374\) | −1.67253 | −0.0864846 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.551323 | 0.0284323 | ||||||||
\(377\) | 1.70064 | 0.0875873 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.12577 | 0.468759 | 0.234380 | − | 0.972145i | \(-0.424694\pi\) | ||||
0.234380 | + | 0.972145i | \(0.424694\pi\) | |||||||
\(380\) | 0.211255 | 0.0108371 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −27.9904 | −1.43211 | ||||||||
\(383\) | 11.0898 | 0.566663 | 0.283332 | − | 0.959022i | \(-0.408560\pi\) | ||||
0.283332 | + | 0.959022i | \(0.408560\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.39264 | −0.0709757 | ||||||||
\(386\) | 7.51104 | 0.382302 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.24168 | 0.316873 | ||||||||
\(389\) | 7.52137 | 0.381349 | 0.190674 | − | 0.981653i | \(-0.438933\pi\) | ||||
0.190674 | + | 0.981653i | \(0.438933\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.536110 | 0.0271122 | ||||||||
\(392\) | 17.4526 | 0.881487 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.00106 | −0.201571 | ||||||||
\(395\) | 2.90251 | 0.146041 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.78635 | 0.390786 | 0.195393 | − | 0.980725i | \(-0.437402\pi\) | ||||
0.195393 | + | 0.980725i | \(0.437402\pi\) | |||||||
\(398\) | 14.7645 | 0.740079 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.48702 | 0.374351 | ||||||||
\(401\) | 29.2302 | 1.45968 | 0.729842 | − | 0.683616i | \(-0.239594\pi\) | ||||
0.729842 | + | 0.683616i | \(0.239594\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.7541 | −0.635329 | ||||||||
\(404\) | −6.15320 | −0.306133 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.21266 | −0.0601831 | ||||||||
\(407\) | −3.57178 | −0.177047 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.3398 | −0.659611 | −0.329806 | − | 0.944049i | \(-0.606983\pi\) | ||||
−0.329806 | + | 0.944049i | \(0.606983\pi\) | |||||||
\(410\) | 5.48967 | 0.271116 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.59149 | −0.127674 | ||||||||
\(413\) | 6.65127 | 0.327288 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.60732 | −0.177076 | ||||||||
\(416\) | −7.56645 | −0.370976 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.82788 | 0.0894045 | ||||||||
\(419\) | 28.6408 | 1.39919 | 0.699597 | − | 0.714537i | \(-0.253363\pi\) | ||||
0.699597 | + | 0.714537i | \(0.253363\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −35.9225 | −1.75075 | −0.875377 | − | 0.483441i | \(-0.839387\pi\) | ||||
−0.875377 | + | 0.483441i | \(0.839387\pi\) | |||||||
\(422\) | 5.53337 | 0.269360 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −33.8057 | −1.64175 | ||||||||
\(425\) | 2.58560 | 0.125420 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.7327 | 0.664570 | ||||||||
\(428\) | 8.24154 | 0.398370 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.25297 | 0.0604238 | ||||||||
\(431\) | 27.2374 | 1.31198 | 0.655989 | − | 0.754770i | \(-0.272252\pi\) | ||||
0.655989 | + | 0.754770i | \(0.272252\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.7658 | −1.14211 | −0.571057 | − | 0.820910i | \(-0.693466\pi\) | ||||
−0.571057 | + | 0.820910i | \(0.693466\pi\) | |||||||
\(434\) | 9.09446 | 0.436548 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.64552 | −0.414045 | ||||||||
\(437\) | −0.585904 | −0.0280276 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.4214 | 1.30875 | 0.654377 | − | 0.756169i | \(-0.272931\pi\) | ||||
0.654377 | + | 0.756169i | \(0.272931\pi\) | |||||||
\(440\) | 3.75068 | 0.178807 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.974836 | 0.0463682 | ||||||||
\(443\) | 24.9966 | 1.18763 | 0.593813 | − | 0.804603i | \(-0.297622\pi\) | ||||
0.593813 | + | 0.804603i | \(0.297622\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.15801 | 0.0548950 | ||||||||
\(446\) | −13.7413 | −0.650670 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.91663 | 0.421271 | ||||||||
\(449\) | 19.5495 | 0.922598 | 0.461299 | − | 0.887245i | \(-0.347384\pi\) | ||||
0.461299 | + | 0.887245i | \(0.347384\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −35.5977 | −1.67623 | ||||||||
\(452\) | 5.84909 | 0.275118 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 13.4558 | 0.631512 | ||||||||
\(455\) | 0.811703 | 0.0380532 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.7789 | −0.550995 | −0.275498 | − | 0.961302i | \(-0.588843\pi\) | ||||
−0.275498 | + | 0.961302i | \(0.588843\pi\) | |||||||
\(458\) | 20.8368 | 0.973638 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.360562 | −0.0168113 | ||||||||
\(461\) | −2.35402 | −0.109638 | −0.0548189 | − | 0.998496i | \(-0.517458\pi\) | ||||
−0.0548189 | + | 0.998496i | \(0.517458\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 33.5600 | 1.55967 | 0.779833 | − | 0.625988i | \(-0.215304\pi\) | ||||
0.779833 | + | 0.625988i | \(0.215304\pi\) | |||||||
\(464\) | 1.55239 | 0.0720679 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.7656 | 0.545032 | ||||||||
\(467\) | −17.2653 | −0.798945 | −0.399472 | − | 0.916745i | \(-0.630807\pi\) | ||||
−0.399472 | + | 0.916745i | \(0.630807\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.2608 | −0.750852 | ||||||||
\(470\) | 0.0812163 | 0.00374623 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −17.9133 | −0.824525 | ||||||||
\(473\) | −8.12489 | −0.373583 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.82576 | −0.129655 | ||||||||
\(476\) | 0.520945 | 0.0238775 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −10.2753 | −0.469980 | ||||||||
\(479\) | 31.1558 | 1.42354 | 0.711771 | − | 0.702411i | \(-0.247893\pi\) | ||||
0.711771 | + | 0.702411i | \(0.247893\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.08181 | 0.0949226 | ||||||||
\(482\) | −6.37796 | −0.290508 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.13035 | 0.0968339 | ||||||||
\(485\) | 3.06583 | 0.139212 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.4246 | 0.608326 | 0.304163 | − | 0.952620i | \(-0.401623\pi\) | ||||
0.304163 | + | 0.952620i | \(0.401623\pi\) | |||||||
\(488\) | −36.9849 | −1.67423 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.57097 | 0.116144 | ||||||||
\(491\) | 4.34995 | 0.196310 | 0.0981552 | − | 0.995171i | \(-0.468706\pi\) | ||||
0.0981552 | + | 0.995171i | \(0.468706\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.536110 | 0.0241452 | ||||||||
\(494\) | −1.06538 | −0.0479337 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −11.6423 | −0.522756 | ||||||||
\(497\) | −15.0227 | −0.673858 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −34.3267 | −1.53668 | −0.768338 | − | 0.640044i | \(-0.778916\pi\) | ||||
−0.768338 | + | 0.640044i | \(0.778916\pi\) | |||||||
\(500\) | −3.54176 | −0.158392 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9.98266 | 0.445548 | ||||||||
\(503\) | −35.4539 | −1.58081 | −0.790406 | − | 0.612584i | \(-0.790130\pi\) | ||||
−0.790406 | + | 0.612584i | \(0.790130\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.02237 | −0.134494 | ||||||||
\(506\) | −3.11976 | −0.138690 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.74046 | 0.210324 | ||||||||
\(509\) | 11.3342 | 0.502378 | 0.251189 | − | 0.967938i | \(-0.419178\pi\) | ||||
0.251189 | + | 0.967938i | \(0.419178\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.18069 | −0.229180 | ||||||||
\(512\) | −16.3905 | −0.724363 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −29.8837 | −1.31812 | ||||||||
\(515\) | −1.27291 | −0.0560910 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.526646 | −0.0231619 | ||||||||
\(518\) | −1.48446 | −0.0652234 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.18609 | −0.0958662 | ||||||||
\(521\) | −13.6651 | −0.598679 | −0.299339 | − | 0.954147i | \(-0.596766\pi\) | ||||
−0.299339 | + | 0.954147i | \(0.596766\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.43578 | 0.193963 | 0.0969816 | − | 0.995286i | \(-0.469081\pi\) | ||||
0.0969816 | + | 0.995286i | \(0.469081\pi\) | |||||||
\(524\) | 11.5642 | 0.505186 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 29.7814 | 1.29853 | ||||||||
\(527\) | −4.02062 | −0.175141 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −4.97997 | −0.216316 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.569331 | −0.0246836 | ||||||||
\(533\) | 20.7481 | 0.898702 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.04814 | 0.175016 | ||||||||
\(536\) | 43.7936 | 1.89160 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8.90896 | −0.384092 | ||||||||
\(539\) | −16.6714 | −0.718088 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −43.6790 | −1.87791 | −0.938954 | − | 0.344044i | \(-0.888203\pi\) | ||||
−0.938954 | + | 0.344044i | \(0.888203\pi\) | |||||||
\(542\) | −26.7542 | −1.14919 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.38525 | −0.102267 | ||||||||
\(545\) | −4.24657 | −0.181903 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.1181 | −0.945702 | −0.472851 | − | 0.881142i | \(-0.656775\pi\) | ||||
−0.472851 | + | 0.881142i | \(0.656775\pi\) | |||||||
\(548\) | 5.00345 | 0.213737 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −15.0463 | −0.641575 | ||||||||
\(551\) | −0.585904 | −0.0249604 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.82226 | −0.332637 | ||||||||
\(554\) | −18.8086 | −0.799099 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 19.1359 | 0.811544 | ||||||||
\(557\) | −4.37611 | −0.185422 | −0.0927108 | − | 0.995693i | \(-0.529553\pi\) | ||||
−0.0927108 | + | 0.995693i | \(0.529553\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.73560 | 0.200294 | ||||||||
\(560\) | 0.740945 | 0.0313106 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.82065 | −0.118982 | ||||||||
\(563\) | 11.8239 | 0.498318 | 0.249159 | − | 0.968463i | \(-0.419846\pi\) | ||||
0.249159 | + | 0.968463i | \(0.419846\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.87300 | 0.120868 | ||||||||
\(566\) | −18.1062 | −0.761058 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 40.4592 | 1.69763 | ||||||||
\(569\) | 38.5706 | 1.61696 | 0.808482 | − | 0.588521i | \(-0.200290\pi\) | ||||
0.808482 | + | 0.588521i | \(0.200290\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.5913 | 0.987264 | 0.493632 | − | 0.869671i | \(-0.335669\pi\) | ||||
0.493632 | + | 0.869671i | \(0.335669\pi\) | |||||||
\(572\) | 4.25141 | 0.177760 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −14.7947 | −0.617517 | ||||||||
\(575\) | 4.82290 | 0.201129 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.28918 | 0.0536692 | 0.0268346 | − | 0.999640i | \(-0.491457\pi\) | ||||
0.0268346 | + | 0.999640i | \(0.491457\pi\) | |||||||
\(578\) | −17.8694 | −0.743269 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.360562 | −0.0149715 | ||||||||
\(581\) | 9.72172 | 0.403325 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 32.2926 | 1.33742 | ||||||||
\(584\) | 13.9527 | 0.577366 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.06634 | −0.209288 | ||||||||
\(587\) | −7.18244 | −0.296451 | −0.148226 | − | 0.988954i | \(-0.547356\pi\) | ||||
−0.148226 | + | 0.988954i | \(0.547356\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.39406 | 0.181054 | ||||||||
\(590\) | −2.63883 | −0.108639 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.90034 | 0.0781034 | ||||||||
\(593\) | 29.1976 | 1.19900 | 0.599502 | − | 0.800373i | \(-0.295365\pi\) | ||||
0.599502 | + | 0.800373i | \(0.295365\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.255881 | 0.0104901 | ||||||||
\(596\) | −0.733558 | −0.0300477 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.81835 | 0.0743579 | ||||||||
\(599\) | −4.66540 | −0.190623 | −0.0953115 | − | 0.995448i | \(-0.530385\pi\) | ||||
−0.0953115 | + | 0.995448i | \(0.530385\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.9769 | 1.05962 | 0.529810 | − | 0.848117i | \(-0.322263\pi\) | ||||
0.529810 | + | 0.848117i | \(0.322263\pi\) | |||||||
\(602\) | −3.37676 | −0.137627 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.98742 | 0.202935 | ||||||||
\(605\) | 1.04640 | 0.0425422 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.6632 | −0.595162 | −0.297581 | − | 0.954697i | \(-0.596180\pi\) | ||||
−0.297581 | + | 0.954697i | \(0.596180\pi\) | |||||||
\(608\) | 2.60680 | 0.105720 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.44831 | −0.220596 | ||||||||
\(611\) | 0.306956 | 0.0124181 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.1212 | −0.610741 | −0.305371 | − | 0.952234i | \(-0.598780\pi\) | ||||
−0.305371 | + | 0.952234i | \(0.598780\pi\) | |||||||
\(614\) | −36.4260 | −1.47003 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10.1081 | −0.407266 | ||||||||
\(617\) | −8.37624 | −0.337215 | −0.168607 | − | 0.985683i | \(-0.553927\pi\) | ||||
−0.168607 | + | 0.985683i | \(0.553927\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.4794 | 0.983912 | 0.491956 | − | 0.870620i | \(-0.336282\pi\) | ||||
0.491956 | + | 0.870620i | \(0.336282\pi\) | |||||||
\(620\) | 2.70408 | 0.108598 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.24648 | 0.170268 | ||||||||
\(623\) | −3.12084 | −0.125034 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.3748 | 0.894993 | ||||||||
\(626\) | 22.8905 | 0.914889 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.36276 | 0.0543802 | ||||||||
\(629\) | 0.656272 | 0.0261673 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.8813 | −0.791463 | −0.395731 | − | 0.918366i | \(-0.629509\pi\) | ||||
−0.395731 | + | 0.918366i | \(0.629509\pi\) | |||||||
\(632\) | 21.0670 | 0.838000 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 30.2359 | 1.20082 | ||||||||
\(635\) | 2.32845 | 0.0924018 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.71693 | 0.384999 | ||||||||
\(638\) | −3.11976 | −0.123512 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.207161 | 0.00818876 | ||||||||
\(641\) | 30.4724 | 1.20359 | 0.601793 | − | 0.798652i | \(-0.294453\pi\) | ||||
0.601793 | + | 0.798652i | \(0.294453\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.0989 | 0.634879 | 0.317440 | − | 0.948278i | \(-0.397177\pi\) | ||||
0.317440 | + | 0.948278i | \(0.397177\pi\) | |||||||
\(644\) | 0.971713 | 0.0382909 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.335851 | −0.0132139 | ||||||||
\(647\) | −26.4180 | −1.03860 | −0.519299 | − | 0.854593i | \(-0.673807\pi\) | ||||
−0.519299 | + | 0.854593i | \(0.673807\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.1115 | 0.671684 | ||||||||
\(650\) | 8.76972 | 0.343977 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.40041 | 0.328985 | ||||||||
\(653\) | 29.0738 | 1.13775 | 0.568873 | − | 0.822425i | \(-0.307379\pi\) | ||||
0.568873 | + | 0.822425i | \(0.307379\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.68020 | 0.221944 | ||||||||
\(656\) | 18.9395 | 0.739462 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.218878 | −0.00853275 | ||||||||
\(659\) | 22.7601 | 0.886607 | 0.443303 | − | 0.896372i | \(-0.353806\pi\) | ||||
0.443303 | + | 0.896372i | \(0.353806\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.5742 | 1.38368 | 0.691838 | − | 0.722053i | \(-0.256801\pi\) | ||||
0.691838 | + | 0.722053i | \(0.256801\pi\) | |||||||
\(662\) | −18.9168 | −0.735222 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −26.1826 | −1.01608 | ||||||||
\(665\) | −0.279648 | −0.0108443 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 13.9128 | 0.538301 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.45132 | 0.249236 | ||||||||
\(671\) | 35.3295 | 1.36388 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −45.9525 | −1.77134 | −0.885669 | − | 0.464318i | \(-0.846300\pi\) | ||||
−0.885669 | + | 0.464318i | \(0.846300\pi\) | |||||||
\(674\) | −20.8134 | −0.801703 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8.66013 | 0.333082 | ||||||||
\(677\) | −48.5051 | −1.86420 | −0.932102 | − | 0.362196i | \(-0.882027\pi\) | ||||
−0.932102 | + | 0.362196i | \(0.882027\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.26241 | −0.317082 | ||||||||
\(680\) | −0.689142 | −0.0264274 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 23.3970 | 0.895917 | ||||||||
\(683\) | 1.90270 | 0.0728048 | 0.0364024 | − | 0.999337i | \(-0.488410\pi\) | ||||
0.0364024 | + | 0.999337i | \(0.488410\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.45763 | 0.0939012 | ||||||||
\(686\) | −15.4173 | −0.588637 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.32278 | 0.164805 | ||||||||
\(689\) | −18.8217 | −0.717051 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.71656 | 0.179426 | 0.0897132 | − | 0.995968i | \(-0.471405\pi\) | ||||
0.0897132 | + | 0.995968i | \(0.471405\pi\) | |||||||
\(692\) | −12.2130 | −0.464270 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.68766 | 0.291820 | ||||||||
\(695\) | 9.39931 | 0.356536 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.54065 | 0.247745 | ||||||||
\(698\) | 20.3240 | 0.769276 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.68647 | 0.177132 | ||||||||
\(701\) | 21.6293 | 0.816926 | 0.408463 | − | 0.912775i | \(-0.366065\pi\) | ||||
0.408463 | + | 0.912775i | \(0.366065\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.717227 | −0.0270507 | ||||||||
\(704\) | 22.9395 | 0.864564 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.40625 | 0.128196 | ||||||||
\(707\) | 8.14529 | 0.306335 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.74667 | −0.366044 | −0.183022 | − | 0.983109i | \(-0.558588\pi\) | ||||
−0.183022 | + | 0.983109i | \(0.558588\pi\) | |||||||
\(710\) | 5.96011 | 0.223679 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8.40507 | 0.314993 | ||||||||
\(713\) | −7.49962 | −0.280863 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.08824 | 0.0780957 | ||||||||
\(716\) | 0.123058 | 0.00459888 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −11.1013 | −0.414295 | ||||||||
\(719\) | −24.3097 | −0.906599 | −0.453300 | − | 0.891358i | \(-0.649753\pi\) | ||||
−0.453300 | + | 0.891358i | \(0.649753\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.43049 | 0.127758 | ||||||||
\(722\) | −19.9481 | −0.742391 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9.98210 | 0.370982 | ||||||||
\(725\) | 4.82290 | 0.179118 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.84325 | 0.0683625 | 0.0341812 | − | 0.999416i | \(-0.489118\pi\) | ||||
0.0341812 | + | 0.999416i | \(0.489118\pi\) | |||||||
\(728\) | 5.89150 | 0.218353 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.05540 | 0.0760736 | ||||||||
\(731\) | 1.49285 | 0.0552151 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.7848 | −0.619961 | −0.309981 | − | 0.950743i | \(-0.600323\pi\) | ||||
−0.309981 | + | 0.950743i | \(0.600323\pi\) | |||||||
\(734\) | 2.30286 | 0.0850001 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.44918 | −0.163999 | ||||||||
\(737\) | −41.8335 | −1.54096 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 43.0787 | 1.58467 | 0.792337 | − | 0.610083i | \(-0.208864\pi\) | ||||
0.792337 | + | 0.610083i | \(0.208864\pi\) | |||||||
\(740\) | −0.441377 | −0.0162253 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 13.4210 | 0.492701 | ||||||||
\(743\) | −0.629086 | −0.0230789 | −0.0115395 | − | 0.999933i | \(-0.503673\pi\) | ||||
−0.0115395 | + | 0.999933i | \(0.503673\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.360314 | −0.0132009 | ||||||||
\(746\) | 11.4301 | 0.418487 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.34022 | 0.0490031 | ||||||||
\(749\) | −10.9097 | −0.398633 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32.3302 | 1.17975 | 0.589873 | − | 0.807496i | \(-0.299178\pi\) | ||||
0.589873 | + | 0.807496i | \(0.299178\pi\) | |||||||
\(752\) | 0.280198 | 0.0102178 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.81835 | 0.0662205 | ||||||||
\(755\) | 2.44976 | 0.0891558 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.8728 | 1.52189 | 0.760946 | − | 0.648815i | \(-0.224735\pi\) | ||||
0.760946 | + | 0.648815i | \(0.224735\pi\) | |||||||
\(758\) | 9.75744 | 0.354406 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.753151 | 0.0273196 | ||||||||
\(761\) | −22.7021 | −0.822950 | −0.411475 | − | 0.911421i | \(-0.634986\pi\) | ||||
−0.411475 | + | 0.911421i | \(0.634986\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.4445 | 0.414318 | ||||||||
\(764\) | 22.4289 | 0.811451 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 11.8574 | 0.428426 | ||||||||
\(767\) | −9.97343 | −0.360120 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −39.9953 | −1.44227 | −0.721134 | − | 0.692795i | \(-0.756379\pi\) | ||||
−0.721134 | + | 0.692795i | \(0.756379\pi\) | |||||||
\(770\) | −1.48904 | −0.0536612 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6.01867 | −0.216617 | ||||||||
\(773\) | −6.67792 | −0.240188 | −0.120094 | − | 0.992763i | \(-0.538320\pi\) | ||||
−0.120094 | + | 0.992763i | \(0.538320\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −36.1699 | −1.29926 | ||||||||
\(776\) | 22.2524 | 0.798815 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.04198 | 0.288319 | ||||||||
\(779\) | −7.14815 | −0.256109 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −38.6482 | −1.38294 | ||||||||
\(782\) | 0.573218 | 0.0204982 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 8.86988 | 0.316782 | ||||||||
\(785\) | 0.669372 | 0.0238909 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.5400 | 0.946048 | 0.473024 | − | 0.881050i | \(-0.343162\pi\) | ||||
0.473024 | + | 0.881050i | \(0.343162\pi\) | |||||||
\(788\) | 3.20609 | 0.114212 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.10342 | 0.110415 | ||||||||
\(791\) | −7.74272 | −0.275299 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.5918 | −0.731237 | ||||||||
\(794\) | 8.32530 | 0.295454 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.8310 | −0.419337 | ||||||||
\(797\) | −31.8075 | −1.12668 | −0.563340 | − | 0.826225i | \(-0.690484\pi\) | ||||
−0.563340 | + | 0.826225i | \(0.690484\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.0967648 | 0.00342329 | ||||||||
\(800\) | −21.4580 | −0.758653 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 31.2534 | 1.10360 | ||||||||
\(803\) | −13.3282 | −0.470341 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.477293 | 0.0168224 | ||||||||
\(806\) | −13.6369 | −0.480341 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −21.9370 | −0.771740 | ||||||||
\(809\) | 17.4024 | 0.611836 | 0.305918 | − | 0.952058i | \(-0.401037\pi\) | ||||
0.305918 | + | 0.952058i | \(0.401037\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 48.5297 | 1.70411 | 0.852055 | − | 0.523452i | \(-0.175356\pi\) | ||||
0.852055 | + | 0.523452i | \(0.175356\pi\) | |||||||
\(812\) | 0.971713 | 0.0341005 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.81901 | −0.133856 | ||||||||
\(815\) | 4.12617 | 0.144533 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.63151 | −0.0570793 | ||||||||
\(818\) | −14.2632 | −0.498700 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.39893 | −0.153617 | ||||||||
\(821\) | 21.8969 | 0.764207 | 0.382103 | − | 0.924120i | \(-0.375200\pi\) | ||||
0.382103 | + | 0.924120i | \(0.375200\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.2048 | −0.425433 | −0.212717 | − | 0.977114i | \(-0.568231\pi\) | ||||
−0.212717 | + | 0.977114i | \(0.568231\pi\) | |||||||
\(824\) | −9.23902 | −0.321856 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.11165 | 0.247446 | ||||||||
\(827\) | 36.2068 | 1.25903 | 0.629516 | − | 0.776987i | \(-0.283253\pi\) | ||||
0.629516 | + | 0.776987i | \(0.283253\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.38205 | −0.0827320 | −0.0413660 | − | 0.999144i | \(-0.513171\pi\) | ||||
−0.0413660 | + | 0.999144i | \(0.513171\pi\) | |||||||
\(830\) | −3.85701 | −0.133879 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −13.3703 | −0.463531 | ||||||||
\(833\) | 3.06317 | 0.106132 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.83377 | 0.236492 | ||||||||
\(836\) | −1.46470 | −0.0506576 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 30.6232 | 1.05786 | ||||||||
\(839\) | 52.3933 | 1.80882 | 0.904408 | − | 0.426668i | \(-0.140313\pi\) | ||||
0.904408 | + | 0.426668i | \(0.140313\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −38.4089 | −1.32366 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.43394 | −0.152623 | ||||||||
\(845\) | 4.25374 | 0.146333 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.82004 | −0.0968978 | ||||||||
\(848\) | −17.1810 | −0.589998 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.76457 | 0.0948240 | ||||||||
\(851\) | 1.22414 | 0.0419629 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.3989 | −0.424529 | −0.212265 | − | 0.977212i | \(-0.568084\pi\) | ||||
−0.212265 | + | 0.977212i | \(0.568084\pi\) | |||||||
\(854\) | 14.6832 | 0.502448 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 29.3822 | 1.00426 | ||||||||
\(857\) | 11.3105 | 0.386359 | 0.193179 | − | 0.981163i | \(-0.438120\pi\) | ||||
0.193179 | + | 0.981163i | \(0.438120\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −27.2778 | −0.930706 | −0.465353 | − | 0.885125i | \(-0.654073\pi\) | ||||
−0.465353 | + | 0.885125i | \(0.654073\pi\) | |||||||
\(860\) | −1.00402 | −0.0342368 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 29.1227 | 0.991923 | ||||||||
\(863\) | −26.0532 | −0.886863 | −0.443431 | − | 0.896308i | \(-0.646239\pi\) | ||||
−0.443431 | + | 0.896308i | \(0.646239\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.99888 | −0.203968 | ||||||||
\(866\) | −25.4109 | −0.863496 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.28748 | −0.247353 | ||||||||
\(869\) | −20.1240 | −0.682662 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.3827 | 0.826175 | ||||||||
\(872\) | −30.8224 | −1.04378 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.626459 | −0.0211903 | ||||||||
\(875\) | 4.68840 | 0.158497 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −53.0592 | −1.79168 | −0.895841 | − | 0.444375i | \(-0.853426\pi\) | ||||
−0.895841 | + | 0.444375i | \(0.853426\pi\) | |||||||
\(878\) | 29.3195 | 0.989484 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.90620 | 0.0642580 | ||||||||
\(881\) | −40.1909 | −1.35406 | −0.677032 | − | 0.735953i | \(-0.736734\pi\) | ||||
−0.677032 | + | 0.735953i | \(0.736734\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.1420 | 0.677833 | 0.338916 | − | 0.940816i | \(-0.389940\pi\) | ||||
0.338916 | + | 0.940816i | \(0.389940\pi\) | |||||||
\(884\) | −0.781145 | −0.0262728 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 26.7268 | 0.897906 | ||||||||
\(887\) | 28.3924 | 0.953325 | 0.476662 | − | 0.879086i | \(-0.341846\pi\) | ||||
0.476662 | + | 0.879086i | \(0.341846\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.27517 | −0.210463 | ||||||||
\(890\) | 1.23816 | 0.0415034 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 11.0110 | 0.368677 | ||||||||
\(893\) | −0.105752 | −0.00353887 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.0604443 | 0.00202043 | ||||||||
\(896\) | −0.558299 | −0.0186515 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 20.9027 | 0.697531 | ||||||||
\(899\) | −7.49962 | −0.250126 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.93337 | −0.197669 | ||||||||
\(902\) | −38.0617 | −1.26732 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 20.8528 | 0.693553 | ||||||||
\(905\) | 4.90308 | 0.162984 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.3598 | −0.808854 | −0.404427 | − | 0.914570i | \(-0.632529\pi\) | ||||
−0.404427 | + | 0.914570i | \(0.632529\pi\) | |||||||
\(908\) | −10.7823 | −0.357822 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.867887 | 0.0287702 | ||||||||
\(911\) | 33.0626 | 1.09541 | 0.547707 | − | 0.836670i | \(-0.315501\pi\) | ||||
0.547707 | + | 0.836670i | \(0.315501\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.0107 | 0.827733 | ||||||||
\(914\) | −12.5942 | −0.416580 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16.6967 | −0.551675 | ||||||||
\(917\) | −15.3081 | −0.505519 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 47.7236 | 1.57426 | 0.787128 | − | 0.616789i | \(-0.211567\pi\) | ||||
0.787128 | + | 0.616789i | \(0.211567\pi\) | |||||||
\(920\) | −1.28545 | −0.0423800 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.51696 | −0.0828918 | ||||||||
\(923\) | 22.5261 | 0.741457 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.90389 | 0.194119 | ||||||||
\(926\) | 35.8829 | 1.17919 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.44918 | −0.146052 | ||||||||
\(929\) | 21.6699 | 0.710968 | 0.355484 | − | 0.934682i | \(-0.384316\pi\) | ||||
0.355484 | + | 0.934682i | \(0.384316\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.34768 | −0.109716 | ||||||||
\(932\) | −9.42790 | −0.308821 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −18.4604 | −0.604043 | ||||||||
\(935\) | 0.658297 | 0.0215286 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.3492 | 0.370764 | 0.185382 | − | 0.982667i | \(-0.440648\pi\) | ||||
0.185382 | + | 0.982667i | \(0.440648\pi\) | |||||||
\(938\) | −17.3863 | −0.567683 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.0650794 | −0.00212266 | ||||||||
\(941\) | −12.8107 | −0.417618 | −0.208809 | − | 0.977956i | \(-0.566959\pi\) | ||||
−0.208809 | + | 0.977956i | \(0.566959\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.2002 | 0.397293 | ||||||||
\(944\) | −9.10403 | −0.296311 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.68727 | −0.282448 | ||||||||
\(947\) | 17.0001 | 0.552428 | 0.276214 | − | 0.961096i | \(-0.410920\pi\) | ||||
0.276214 | + | 0.961096i | \(0.410920\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.76834 | 0.252171 | ||||||||
\(950\) | −3.02135 | −0.0980255 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.85724 | 0.0601934 | ||||||||
\(953\) | 36.4300 | 1.18008 | 0.590042 | − | 0.807373i | \(-0.299111\pi\) | ||||
0.590042 | + | 0.807373i | \(0.299111\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11.0168 | 0.356495 | ||||||||
\(956\) | 8.23367 | 0.266296 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 33.3123 | 1.07627 | ||||||||
\(959\) | −6.62331 | −0.213878 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.2443 | 0.814332 | ||||||||
\(962\) | 2.22591 | 0.0717663 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5.11072 | 0.164605 | ||||||||
\(965\) | −2.95629 | −0.0951664 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −23.2204 | −0.746719 | −0.373359 | − | 0.927687i | \(-0.621794\pi\) | ||||
−0.373359 | + | 0.927687i | \(0.621794\pi\) | |||||||
\(968\) | 7.59497 | 0.244111 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.27804 | 0.105252 | ||||||||
\(971\) | −25.4051 | −0.815289 | −0.407644 | − | 0.913141i | \(-0.633650\pi\) | ||||
−0.407644 | + | 0.913141i | \(0.633650\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −25.3311 | −0.812079 | ||||||||
\(974\) | 14.3538 | 0.459926 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −18.7968 | −0.601670 | ||||||||
\(977\) | 35.6930 | 1.14192 | 0.570961 | − | 0.820978i | \(-0.306571\pi\) | ||||
0.570961 | + | 0.820978i | \(0.306571\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.02886 | −0.256604 | ||||||||
\(980\) | −2.06014 | −0.0658088 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.65104 | 0.148421 | ||||||||
\(983\) | −30.1919 | −0.962973 | −0.481486 | − | 0.876454i | \(-0.659903\pi\) | ||||
−0.481486 | + | 0.876454i | \(0.659903\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.57479 | 0.0501770 | ||||||||
\(986\) | 0.573218 | 0.0182550 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.853699 | 0.0271598 | ||||||||
\(989\) | 2.78460 | 0.0885451 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.5980 | −0.590784 | −0.295392 | − | 0.955376i | \(-0.595450\pi\) | ||||
−0.295392 | + | 0.955376i | \(0.595450\pi\) | |||||||
\(992\) | 33.3672 | 1.05941 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −16.0625 | −0.509471 | ||||||||
\(995\) | −5.81122 | −0.184228 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −57.0452 | −1.80664 | −0.903319 | − | 0.428969i | \(-0.858877\pi\) | ||||
−0.903319 | + | 0.428969i | \(0.858877\pi\) | |||||||
\(998\) | −36.7027 | −1.16181 | ||||||||
\(999\) | 0 | 0 |
(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 | 6003.2.a.u.1.14 | yes | 22 | |
3.2 | odd | 2 | 6003.2.a.t.1.9 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6003.2.a.t.1.9 | ✓ | 22 | 3.2 | odd | 2 | ||
6003.2.a.u.1.14 | yes | 22 | 1.1 | even | 1 | trivial |