Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, 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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(1\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 8 x^{19} + 152 x^{17} - 274 x^{16} - 1061 x^{15} + 3125 x^{14} + 2977 x^{13} - 15474 x^{12} + \cdots + 31 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 889) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.75954\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.75954 | −1.95129 | −0.975644 | − | 0.219359i | \(-0.929603\pi\) | ||||
−0.975644 | + | 0.219359i | \(0.929603\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.61505 | 2.80753 | ||||||||
\(5\) | −0.308409 | −0.137925 | −0.0689623 | − | 0.997619i | \(-0.521969\pi\) | ||||
−0.0689623 | + | 0.997619i | \(0.521969\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −9.97588 | −3.52701 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.851066 | 0.269131 | ||||||||
\(11\) | −1.97479 | −0.595421 | −0.297710 | − | 0.954656i | \(-0.596223\pi\) | ||||
−0.297710 | + | 0.954656i | \(0.596223\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.50333 | −0.416948 | −0.208474 | − | 0.978028i | \(-0.566850\pi\) | ||||
−0.208474 | + | 0.978028i | \(0.566850\pi\) | |||||||
\(14\) | −2.75954 | −0.737518 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.2987 | 4.07468 | ||||||||
\(17\) | 1.53428 | 0.372119 | 0.186059 | − | 0.982539i | \(-0.440428\pi\) | ||||
0.186059 | + | 0.982539i | \(0.440428\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.38101 | 1.00507 | 0.502536 | − | 0.864556i | \(-0.332400\pi\) | ||||
0.502536 | + | 0.864556i | \(0.332400\pi\) | |||||||
\(20\) | −1.73173 | −0.387227 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.44950 | 1.16184 | ||||||||
\(23\) | 5.56049 | 1.15944 | 0.579721 | − | 0.814815i | \(-0.303161\pi\) | ||||
0.579721 | + | 0.814815i | \(0.303161\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.90488 | −0.980977 | ||||||||
\(26\) | 4.14849 | 0.813585 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.61505 | 1.06115 | ||||||||
\(29\) | −6.08293 | −1.12957 | −0.564786 | − | 0.825237i | \(-0.691041\pi\) | ||||
−0.564786 | + | 0.825237i | \(0.691041\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.88474 | 0.877324 | 0.438662 | − | 0.898652i | \(-0.355452\pi\) | ||||
0.438662 | + | 0.898652i | \(0.355452\pi\) | |||||||
\(32\) | −25.0252 | −4.42387 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.23392 | −0.726111 | ||||||||
\(35\) | −0.308409 | −0.0521306 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.19832 | 0.690200 | 0.345100 | − | 0.938566i | \(-0.387845\pi\) | ||||
0.345100 | + | 0.938566i | \(0.387845\pi\) | |||||||
\(38\) | −12.0896 | −1.96119 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.07665 | 0.486461 | ||||||||
\(41\) | −9.66235 | −1.50901 | −0.754503 | − | 0.656297i | \(-0.772122\pi\) | ||||
−0.754503 | + | 0.656297i | \(0.772122\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.29439 | −0.807387 | −0.403693 | − | 0.914894i | \(-0.632274\pi\) | ||||
−0.403693 | + | 0.914894i | \(0.632274\pi\) | |||||||
\(44\) | −11.0885 | −1.67166 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −15.3444 | −2.26241 | ||||||||
\(47\) | 1.73288 | 0.252766 | 0.126383 | − | 0.991982i | \(-0.459663\pi\) | ||||
0.126383 | + | 0.991982i | \(0.459663\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 13.5352 | 1.91417 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −8.44126 | −1.17059 | ||||||||
\(53\) | 11.5579 | 1.58760 | 0.793799 | − | 0.608180i | \(-0.208100\pi\) | ||||
0.793799 | + | 0.608180i | \(0.208100\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.609042 | 0.0821232 | ||||||||
\(56\) | −9.97588 | −1.33308 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 16.7861 | 2.20412 | ||||||||
\(59\) | −4.40906 | −0.574011 | −0.287006 | − | 0.957929i | \(-0.592660\pi\) | ||||
−0.287006 | + | 0.957929i | \(0.592660\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.1347 | −1.80976 | −0.904880 | − | 0.425666i | \(-0.860040\pi\) | ||||
−0.904880 | + | 0.425666i | \(0.860040\pi\) | |||||||
\(62\) | −13.4796 | −1.71191 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 36.4605 | 4.55757 | ||||||||
\(65\) | 0.463639 | 0.0575073 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.4930 | −1.40409 | −0.702047 | − | 0.712131i | \(-0.747730\pi\) | ||||
−0.702047 | + | 0.712131i | \(0.747730\pi\) | |||||||
\(68\) | 8.61509 | 1.04473 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.851066 | 0.101722 | ||||||||
\(71\) | 6.35836 | 0.754599 | 0.377299 | − | 0.926091i | \(-0.376853\pi\) | ||||
0.377299 | + | 0.926091i | \(0.376853\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.8604 | −1.50520 | −0.752599 | − | 0.658479i | \(-0.771200\pi\) | ||||
−0.752599 | + | 0.658479i | \(0.771200\pi\) | |||||||
\(74\) | −11.5854 | −1.34678 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 24.5996 | 2.82177 | ||||||||
\(77\) | −1.97479 | −0.225048 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.329262 | 0.0370448 | 0.0185224 | − | 0.999828i | \(-0.494104\pi\) | ||||
0.0185224 | + | 0.999828i | \(0.494104\pi\) | |||||||
\(80\) | −5.02667 | −0.561999 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 26.6636 | 2.94451 | ||||||||
\(83\) | 6.82127 | 0.748732 | 0.374366 | − | 0.927281i | \(-0.377860\pi\) | ||||
0.374366 | + | 0.927281i | \(0.377860\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.473187 | −0.0513243 | ||||||||
\(86\) | 14.6101 | 1.57544 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 19.7002 | 2.10005 | ||||||||
\(89\) | 9.25437 | 0.980962 | 0.490481 | − | 0.871452i | \(-0.336821\pi\) | ||||
0.490481 | + | 0.871452i | \(0.336821\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.50333 | −0.157591 | ||||||||
\(92\) | 31.2225 | 3.25517 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.78194 | −0.493219 | ||||||||
\(95\) | −1.35114 | −0.138624 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.74074 | 0.481349 | 0.240674 | − | 0.970606i | \(-0.422631\pi\) | ||||
0.240674 | + | 0.970606i | \(0.422631\pi\) | |||||||
\(98\) | −2.75954 | −0.278756 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −27.5412 | −2.75412 | ||||||||
\(101\) | 15.1594 | 1.50842 | 0.754210 | − | 0.656633i | \(-0.228020\pi\) | ||||
0.754210 | + | 0.656633i | \(0.228020\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.27078 | 0.814944 | 0.407472 | − | 0.913218i | \(-0.366410\pi\) | ||||
0.407472 | + | 0.913218i | \(0.366410\pi\) | |||||||
\(104\) | 14.9970 | 1.47058 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −31.8944 | −3.09786 | ||||||||
\(107\) | −2.93782 | −0.284010 | −0.142005 | − | 0.989866i | \(-0.545355\pi\) | ||||
−0.142005 | + | 0.989866i | \(0.545355\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.12177 | 0.299012 | 0.149506 | − | 0.988761i | \(-0.452232\pi\) | ||||
0.149506 | + | 0.988761i | \(0.452232\pi\) | |||||||
\(110\) | −1.68067 | −0.160246 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 16.2987 | 1.54008 | ||||||||
\(113\) | −3.67619 | −0.345827 | −0.172913 | − | 0.984937i | \(-0.555318\pi\) | ||||
−0.172913 | + | 0.984937i | \(0.555318\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.71490 | −0.159916 | ||||||||
\(116\) | −34.1560 | −3.17130 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 12.1670 | 1.12006 | ||||||||
\(119\) | 1.53428 | 0.140648 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.10022 | −0.645474 | ||||||||
\(122\) | 39.0052 | 3.53136 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 27.4281 | 2.46311 | ||||||||
\(125\) | 3.05475 | 0.273225 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | −50.5639 | −4.46926 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.27943 | −0.112213 | ||||||||
\(131\) | −13.9223 | −1.21640 | −0.608199 | − | 0.793784i | \(-0.708108\pi\) | ||||
−0.608199 | + | 0.793784i | \(0.708108\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.38101 | 0.379882 | ||||||||
\(134\) | 31.7154 | 2.73979 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −15.3058 | −1.31247 | ||||||||
\(137\) | −4.12414 | −0.352349 | −0.176175 | − | 0.984359i | \(-0.556372\pi\) | ||||
−0.176175 | + | 0.984359i | \(0.556372\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.0250793 | 0.00212720 | 0.00106360 | − | 0.999999i | \(-0.499661\pi\) | ||||
0.00106360 | + | 0.999999i | \(0.499661\pi\) | |||||||
\(140\) | −1.73173 | −0.146358 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −17.5462 | −1.47244 | ||||||||
\(143\) | 2.96875 | 0.248259 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.87603 | 0.155796 | ||||||||
\(146\) | 35.4888 | 2.93707 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 23.5738 | 1.93775 | ||||||||
\(149\) | −17.9241 | −1.46840 | −0.734200 | − | 0.678933i | \(-0.762443\pi\) | ||||
−0.734200 | + | 0.678933i | \(0.762443\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.0202 | 1.54784 | 0.773919 | − | 0.633284i | \(-0.218294\pi\) | ||||
0.773919 | + | 0.633284i | \(0.218294\pi\) | |||||||
\(152\) | −43.7044 | −3.54490 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.44950 | 0.439133 | ||||||||
\(155\) | −1.50650 | −0.121005 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.7828 | −1.41922 | −0.709611 | − | 0.704594i | \(-0.751129\pi\) | ||||
−0.709611 | + | 0.704594i | \(0.751129\pi\) | |||||||
\(158\) | −0.908610 | −0.0722852 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 7.71799 | 0.610161 | ||||||||
\(161\) | 5.56049 | 0.438228 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.2728 | 1.58789 | 0.793945 | − | 0.607989i | \(-0.208024\pi\) | ||||
0.793945 | + | 0.607989i | \(0.208024\pi\) | |||||||
\(164\) | −54.2546 | −4.23657 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −18.8236 | −1.46099 | ||||||||
\(167\) | −20.8220 | −1.61126 | −0.805629 | − | 0.592420i | \(-0.798172\pi\) | ||||
−0.805629 | + | 0.592420i | \(0.798172\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.7400 | −0.826155 | ||||||||
\(170\) | 1.30578 | 0.100149 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −29.7283 | −2.26676 | ||||||||
\(173\) | 9.45710 | 0.719010 | 0.359505 | − | 0.933143i | \(-0.382946\pi\) | ||||
0.359505 | + | 0.933143i | \(0.382946\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.90488 | −0.370774 | ||||||||
\(176\) | −32.1865 | −2.42615 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −25.5378 | −1.91414 | ||||||||
\(179\) | 8.00826 | 0.598565 | 0.299283 | − | 0.954165i | \(-0.403253\pi\) | ||||
0.299283 | + | 0.954165i | \(0.403253\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.31397 | −0.320655 | −0.160327 | − | 0.987064i | \(-0.551255\pi\) | ||||
−0.160327 | + | 0.987064i | \(0.551255\pi\) | |||||||
\(182\) | 4.14849 | 0.307506 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −55.4708 | −4.08936 | ||||||||
\(185\) | −1.29480 | −0.0951955 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.02989 | −0.221567 | ||||||||
\(188\) | 9.73019 | 0.709647 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.72853 | 0.270496 | ||||||||
\(191\) | −1.09157 | −0.0789831 | −0.0394915 | − | 0.999220i | \(-0.512574\pi\) | ||||
−0.0394915 | + | 0.999220i | \(0.512574\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.8329 | −0.923735 | −0.461868 | − | 0.886949i | \(-0.652821\pi\) | ||||
−0.461868 | + | 0.886949i | \(0.652821\pi\) | |||||||
\(194\) | −13.0822 | −0.939251 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.61505 | 0.401075 | ||||||||
\(197\) | 23.7467 | 1.69188 | 0.845942 | − | 0.533274i | \(-0.179039\pi\) | ||||
0.845942 | + | 0.533274i | \(0.179039\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.3672 | 1.16024 | 0.580122 | − | 0.814530i | \(-0.303005\pi\) | ||||
0.580122 | + | 0.814530i | \(0.303005\pi\) | |||||||
\(200\) | 48.9305 | 3.45991 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −41.8331 | −2.94336 | ||||||||
\(203\) | −6.08293 | −0.426938 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.97995 | 0.208129 | ||||||||
\(206\) | −22.8235 | −1.59019 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −24.5023 | −1.69893 | ||||||||
\(209\) | −8.65156 | −0.598441 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.2266 | −1.46130 | −0.730649 | − | 0.682754i | \(-0.760782\pi\) | ||||
−0.730649 | + | 0.682754i | \(0.760782\pi\) | |||||||
\(212\) | 64.8982 | 4.45722 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.10702 | 0.554185 | ||||||||
\(215\) | 1.63284 | 0.111359 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.88474 | 0.331597 | ||||||||
\(218\) | −8.61466 | −0.583458 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.41980 | 0.230563 | ||||||||
\(221\) | −2.30653 | −0.155154 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.7914 | 0.856576 | 0.428288 | − | 0.903642i | \(-0.359117\pi\) | ||||
0.428288 | + | 0.903642i | \(0.359117\pi\) | |||||||
\(224\) | −25.0252 | −1.67207 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.1446 | 0.674808 | ||||||||
\(227\) | −5.96574 | −0.395960 | −0.197980 | − | 0.980206i | \(-0.563438\pi\) | ||||
−0.197980 | + | 0.980206i | \(0.563438\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.1405 | −0.802270 | −0.401135 | − | 0.916019i | \(-0.631384\pi\) | ||||
−0.401135 | + | 0.916019i | \(0.631384\pi\) | |||||||
\(230\) | 4.73234 | 0.312042 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 60.6826 | 3.98401 | ||||||||
\(233\) | −27.2091 | −1.78253 | −0.891263 | − | 0.453488i | \(-0.850180\pi\) | ||||
−0.891263 | + | 0.453488i | \(0.850180\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.534434 | −0.0348626 | ||||||||
\(236\) | −24.7571 | −1.61155 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.23392 | −0.274444 | ||||||||
\(239\) | −6.50151 | −0.420548 | −0.210274 | − | 0.977643i | \(-0.567436\pi\) | ||||
−0.210274 | + | 0.977643i | \(0.567436\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.0546 | −1.35624 | −0.678122 | − | 0.734950i | \(-0.737206\pi\) | ||||
−0.678122 | + | 0.734950i | \(0.737206\pi\) | |||||||
\(242\) | 19.5933 | 1.25951 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −79.3670 | −5.08095 | ||||||||
\(245\) | −0.308409 | −0.0197035 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.58609 | −0.419063 | ||||||||
\(248\) | −48.7295 | −3.09433 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −8.42971 | −0.533142 | ||||||||
\(251\) | 20.3697 | 1.28572 | 0.642861 | − | 0.765983i | \(-0.277747\pi\) | ||||
0.642861 | + | 0.765983i | \(0.277747\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.9808 | −0.690356 | ||||||||
\(254\) | 2.75954 | 0.173149 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 66.6120 | 4.16325 | ||||||||
\(257\) | 5.38398 | 0.335843 | 0.167922 | − | 0.985800i | \(-0.446294\pi\) | ||||
0.167922 | + | 0.985800i | \(0.446294\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.19832 | 0.260871 | ||||||||
\(260\) | 2.60336 | 0.161453 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 38.4192 | 2.37354 | ||||||||
\(263\) | 3.53018 | 0.217680 | 0.108840 | − | 0.994059i | \(-0.465286\pi\) | ||||
0.108840 | + | 0.994059i | \(0.465286\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.56455 | −0.218969 | ||||||||
\(266\) | −12.0896 | −0.741259 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −64.5338 | −3.94203 | ||||||||
\(269\) | −17.8009 | −1.08534 | −0.542671 | − | 0.839946i | \(-0.682587\pi\) | ||||
−0.542671 | + | 0.839946i | \(0.682587\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.28732 | 0.199690 | 0.0998451 | − | 0.995003i | \(-0.468165\pi\) | ||||
0.0998451 | + | 0.995003i | \(0.468165\pi\) | |||||||
\(272\) | 25.0069 | 1.51626 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.3807 | 0.687535 | ||||||||
\(275\) | 9.68610 | 0.584094 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 27.1056 | 1.62862 | 0.814308 | − | 0.580434i | \(-0.197117\pi\) | ||||
0.814308 | + | 0.580434i | \(0.197117\pi\) | |||||||
\(278\) | −0.0692074 | −0.00415079 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.07665 | 0.183865 | ||||||||
\(281\) | −20.4693 | −1.22109 | −0.610547 | − | 0.791980i | \(-0.709050\pi\) | ||||
−0.610547 | + | 0.791980i | \(0.709050\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.16403 | 0.128639 | 0.0643193 | − | 0.997929i | \(-0.479512\pi\) | ||||
0.0643193 | + | 0.997929i | \(0.479512\pi\) | |||||||
\(284\) | 35.7026 | 2.11856 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −8.19238 | −0.484426 | ||||||||
\(287\) | −9.66235 | −0.570351 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.6460 | −0.861528 | ||||||||
\(290\) | −5.17698 | −0.304003 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −72.2119 | −4.22588 | ||||||||
\(293\) | 26.9859 | 1.57653 | 0.788265 | − | 0.615336i | \(-0.210980\pi\) | ||||
0.788265 | + | 0.615336i | \(0.210980\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.35979 | 0.0791703 | ||||||||
\(296\) | −41.8820 | −2.43434 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 49.4623 | 2.86527 | ||||||||
\(299\) | −8.35923 | −0.483427 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.29439 | −0.305164 | ||||||||
\(302\) | −52.4869 | −3.02028 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 71.4049 | 4.09535 | ||||||||
\(305\) | 4.35926 | 0.249610 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.23124 | −0.0702707 | −0.0351353 | − | 0.999383i | \(-0.511186\pi\) | ||||
−0.0351353 | + | 0.999383i | \(0.511186\pi\) | |||||||
\(308\) | −11.0885 | −0.631828 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.15723 | 0.236115 | ||||||||
\(311\) | −13.0193 | −0.738256 | −0.369128 | − | 0.929379i | \(-0.620344\pi\) | ||||
−0.369128 | + | 0.929379i | \(0.620344\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.1422 | −1.13851 | −0.569253 | − | 0.822163i | \(-0.692767\pi\) | ||||
−0.569253 | + | 0.822163i | \(0.692767\pi\) | |||||||
\(314\) | 49.0723 | 2.76931 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.84882 | 0.104004 | ||||||||
\(317\) | −5.78161 | −0.324728 | −0.162364 | − | 0.986731i | \(-0.551912\pi\) | ||||
−0.162364 | + | 0.986731i | \(0.551912\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.0125 | 0.672571 | ||||||||
\(320\) | −11.2448 | −0.628601 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −15.3444 | −0.855109 | ||||||||
\(323\) | 6.72172 | 0.374006 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.37364 | 0.409016 | ||||||||
\(326\) | −55.9437 | −3.09843 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 96.3905 | 5.32227 | ||||||||
\(329\) | 1.73288 | 0.0955365 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.6048 | 1.57226 | 0.786130 | − | 0.618061i | \(-0.212082\pi\) | ||||
0.786130 | + | 0.618061i | \(0.212082\pi\) | |||||||
\(332\) | 38.3018 | 2.10208 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 57.4592 | 3.14403 | ||||||||
\(335\) | 3.54454 | 0.193659 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.78711 | 0.260771 | 0.130385 | − | 0.991463i | \(-0.458379\pi\) | ||||
0.130385 | + | 0.991463i | \(0.458379\pi\) | |||||||
\(338\) | 29.6375 | 1.61207 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.65697 | −0.144094 | ||||||||
\(341\) | −9.64631 | −0.522377 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 52.8162 | 2.84766 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −26.0972 | −1.40300 | ||||||||
\(347\) | 0.522899 | 0.0280707 | 0.0140353 | − | 0.999901i | \(-0.495532\pi\) | ||||
0.0140353 | + | 0.999901i | \(0.495532\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.5273 | 0.938216 | 0.469108 | − | 0.883141i | \(-0.344575\pi\) | ||||
0.469108 | + | 0.883141i | \(0.344575\pi\) | |||||||
\(350\) | 13.5352 | 0.723488 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 49.4194 | 2.63406 | ||||||||
\(353\) | −13.8534 | −0.737341 | −0.368671 | − | 0.929560i | \(-0.620187\pi\) | ||||
−0.368671 | + | 0.929560i | \(0.620187\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.96098 | −0.104078 | ||||||||
\(356\) | 51.9638 | 2.75408 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −22.0991 | −1.16797 | ||||||||
\(359\) | −4.94008 | −0.260727 | −0.130364 | − | 0.991466i | \(-0.541614\pi\) | ||||
−0.130364 | + | 0.991466i | \(0.541614\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.193250 | 0.0101711 | ||||||||
\(362\) | 11.9046 | 0.625690 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −8.44126 | −0.442442 | ||||||||
\(365\) | 3.96626 | 0.207604 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.4313 | 0.857708 | 0.428854 | − | 0.903374i | \(-0.358918\pi\) | ||||
0.428854 | + | 0.903374i | \(0.358918\pi\) | |||||||
\(368\) | 90.6289 | 4.72436 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.57305 | 0.185754 | ||||||||
\(371\) | 11.5579 | 0.600056 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.5850 | 0.962297 | 0.481148 | − | 0.876639i | \(-0.340220\pi\) | ||||
0.481148 | + | 0.876639i | \(0.340220\pi\) | |||||||
\(374\) | 8.36109 | 0.432342 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −17.2870 | −0.891507 | ||||||||
\(377\) | 9.14463 | 0.470973 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.2500 | −0.526505 | −0.263253 | − | 0.964727i | \(-0.584795\pi\) | ||||
−0.263253 | + | 0.964727i | \(0.584795\pi\) | |||||||
\(380\) | −7.58674 | −0.389191 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.01222 | 0.154119 | ||||||||
\(383\) | −25.5087 | −1.30344 | −0.651718 | − | 0.758462i | \(-0.725951\pi\) | ||||
−0.651718 | + | 0.758462i | \(0.725951\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.609042 | 0.0310396 | ||||||||
\(386\) | 35.4130 | 1.80247 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 26.6195 | 1.35140 | ||||||||
\(389\) | 1.62422 | 0.0823511 | 0.0411756 | − | 0.999152i | \(-0.486890\pi\) | ||||
0.0411756 | + | 0.999152i | \(0.486890\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.53138 | 0.431450 | ||||||||
\(392\) | −9.97588 | −0.503858 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −65.5300 | −3.30136 | ||||||||
\(395\) | −0.101547 | −0.00510939 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.7976 | 1.04380 | 0.521902 | − | 0.853006i | \(-0.325223\pi\) | ||||
0.521902 | + | 0.853006i | \(0.325223\pi\) | |||||||
\(398\) | −45.1660 | −2.26397 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −79.9433 | −3.99717 | ||||||||
\(401\) | −34.6555 | −1.73061 | −0.865306 | − | 0.501245i | \(-0.832876\pi\) | ||||
−0.865306 | + | 0.501245i | \(0.832876\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.34335 | −0.365798 | ||||||||
\(404\) | 85.1211 | 4.23493 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 16.7861 | 0.833080 | ||||||||
\(407\) | −8.29079 | −0.410959 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −28.7690 | −1.42253 | −0.711267 | − | 0.702922i | \(-0.751878\pi\) | ||||
−0.711267 | + | 0.702922i | \(0.751878\pi\) | |||||||
\(410\) | −8.22330 | −0.406120 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 46.4409 | 2.28798 | ||||||||
\(413\) | −4.40906 | −0.216956 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.10374 | −0.103269 | ||||||||
\(416\) | 37.6210 | 1.84452 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 23.8743 | 1.16773 | ||||||||
\(419\) | 5.64930 | 0.275986 | 0.137993 | − | 0.990433i | \(-0.455935\pi\) | ||||
0.137993 | + | 0.990433i | \(0.455935\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.1531 | −0.933464 | −0.466732 | − | 0.884399i | \(-0.654569\pi\) | ||||
−0.466732 | + | 0.884399i | \(0.654569\pi\) | |||||||
\(422\) | 58.5755 | 2.85141 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −115.300 | −5.59947 | ||||||||
\(425\) | −7.52549 | −0.365040 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.1347 | −0.684025 | ||||||||
\(428\) | −16.4960 | −0.797364 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.50587 | −0.217293 | ||||||||
\(431\) | 39.3607 | 1.89594 | 0.947970 | − | 0.318359i | \(-0.103132\pi\) | ||||
0.947970 | + | 0.318359i | \(0.103132\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.1173 | 1.35123 | 0.675615 | − | 0.737254i | \(-0.263878\pi\) | ||||
0.675615 | + | 0.737254i | \(0.263878\pi\) | |||||||
\(434\) | −13.4796 | −0.647042 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 17.5289 | 0.839483 | ||||||||
\(437\) | 24.3606 | 1.16532 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −28.7294 | −1.37118 | −0.685590 | − | 0.727988i | \(-0.740456\pi\) | ||||
−0.685590 | + | 0.727988i | \(0.740456\pi\) | |||||||
\(440\) | −6.07573 | −0.289649 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.36496 | 0.302750 | ||||||||
\(443\) | −7.89956 | −0.375319 | −0.187660 | − | 0.982234i | \(-0.560090\pi\) | ||||
−0.187660 | + | 0.982234i | \(0.560090\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.85413 | −0.135299 | ||||||||
\(446\) | −35.2984 | −1.67143 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 36.4605 | 1.72260 | ||||||||
\(449\) | −29.4416 | −1.38943 | −0.694717 | − | 0.719283i | \(-0.744471\pi\) | ||||
−0.694717 | + | 0.719283i | \(0.744471\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.0811 | 0.898493 | ||||||||
\(452\) | −20.6420 | −0.970918 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 16.4627 | 0.772632 | ||||||||
\(455\) | 0.463639 | 0.0217357 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.4590 | 1.14414 | 0.572072 | − | 0.820203i | \(-0.306140\pi\) | ||||
0.572072 | + | 0.820203i | \(0.306140\pi\) | |||||||
\(458\) | 33.5023 | 1.56546 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −9.62928 | −0.448968 | ||||||||
\(461\) | −11.5852 | −0.539578 | −0.269789 | − | 0.962920i | \(-0.586954\pi\) | ||||
−0.269789 | + | 0.962920i | \(0.586954\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.17913 | 0.240694 | 0.120347 | − | 0.992732i | \(-0.461599\pi\) | ||||
0.120347 | + | 0.992732i | \(0.461599\pi\) | |||||||
\(464\) | −99.1440 | −4.60265 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 75.0845 | 3.47822 | ||||||||
\(467\) | 11.3176 | 0.523716 | 0.261858 | − | 0.965106i | \(-0.415665\pi\) | ||||
0.261858 | + | 0.965106i | \(0.415665\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.4930 | −0.530697 | ||||||||
\(470\) | 1.47479 | 0.0680271 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 43.9843 | 2.02454 | ||||||||
\(473\) | 10.4553 | 0.480735 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −21.4883 | −0.985953 | ||||||||
\(476\) | 8.61509 | 0.394872 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 17.9412 | 0.820610 | ||||||||
\(479\) | −38.1976 | −1.74529 | −0.872646 | − | 0.488354i | \(-0.837598\pi\) | ||||
−0.872646 | + | 0.488354i | \(0.837598\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.31145 | −0.287777 | ||||||||
\(482\) | 58.1009 | 2.64642 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −39.8681 | −1.81219 | ||||||||
\(485\) | −1.46208 | −0.0663899 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.7287 | −0.712735 | −0.356368 | − | 0.934346i | \(-0.615985\pi\) | ||||
−0.356368 | + | 0.934346i | \(0.615985\pi\) | |||||||
\(488\) | 141.006 | 6.38304 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.851066 | 0.0384472 | ||||||||
\(491\) | 26.9989 | 1.21844 | 0.609222 | − | 0.792999i | \(-0.291482\pi\) | ||||
0.609222 | + | 0.792999i | \(0.291482\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.33295 | −0.420335 | ||||||||
\(494\) | 18.1746 | 0.817712 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 79.6150 | 3.57482 | ||||||||
\(497\) | 6.35836 | 0.285212 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −42.2261 | −1.89030 | −0.945149 | − | 0.326639i | \(-0.894084\pi\) | ||||
−0.945149 | + | 0.326639i | \(0.894084\pi\) | |||||||
\(500\) | 17.1526 | 0.767088 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −56.2109 | −2.50881 | ||||||||
\(503\) | −14.1095 | −0.629113 | −0.314557 | − | 0.949239i | \(-0.601856\pi\) | ||||
−0.314557 | + | 0.949239i | \(0.601856\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.67530 | −0.208048 | ||||||||
\(506\) | 30.3019 | 1.34708 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.61505 | −0.249128 | ||||||||
\(509\) | −18.0732 | −0.801079 | −0.400539 | − | 0.916280i | \(-0.631177\pi\) | ||||
−0.400539 | + | 0.916280i | \(0.631177\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.8604 | −0.568911 | ||||||||
\(512\) | −82.6905 | −3.65444 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −14.8573 | −0.655327 | ||||||||
\(515\) | −2.55078 | −0.112401 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.42206 | −0.150502 | ||||||||
\(518\) | −11.5854 | −0.509035 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.62521 | −0.202829 | ||||||||
\(521\) | −7.36327 | −0.322591 | −0.161295 | − | 0.986906i | \(-0.551567\pi\) | ||||
−0.161295 | + | 0.986906i | \(0.551567\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.668564 | −0.0292343 | −0.0146171 | − | 0.999893i | \(-0.504653\pi\) | ||||
−0.0146171 | + | 0.999893i | \(0.504653\pi\) | |||||||
\(524\) | −78.1746 | −3.41507 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.74168 | −0.424757 | ||||||||
\(527\) | 7.49458 | 0.326469 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.91906 | 0.344307 | ||||||||
\(530\) | 9.83653 | 0.427271 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 24.5996 | 1.06653 | ||||||||
\(533\) | 14.5257 | 0.629177 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.906049 | 0.0391719 | ||||||||
\(536\) | 114.653 | 4.95225 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 49.1223 | 2.11781 | ||||||||
\(539\) | −1.97479 | −0.0850601 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −36.7082 | −1.57821 | −0.789104 | − | 0.614260i | \(-0.789455\pi\) | ||||
−0.789104 | + | 0.614260i | \(0.789455\pi\) | |||||||
\(542\) | −9.07147 | −0.389653 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −38.3958 | −1.64621 | ||||||||
\(545\) | −0.962782 | −0.0412411 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.3575 | 1.12697 | 0.563483 | − | 0.826128i | \(-0.309461\pi\) | ||||
0.563483 | + | 0.826128i | \(0.309461\pi\) | |||||||
\(548\) | −23.1573 | −0.989230 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −26.7292 | −1.13974 | ||||||||
\(551\) | −26.6494 | −1.13530 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.329262 | 0.0140016 | ||||||||
\(554\) | −74.7988 | −3.17790 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.140822 | 0.00597218 | ||||||||
\(557\) | 22.1623 | 0.939047 | 0.469524 | − | 0.882920i | \(-0.344426\pi\) | ||||
0.469524 | + | 0.882920i | \(0.344426\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.95920 | 0.336638 | ||||||||
\(560\) | −5.02667 | −0.212416 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 56.4858 | 2.38271 | ||||||||
\(563\) | 16.1850 | 0.682118 | 0.341059 | − | 0.940042i | \(-0.389214\pi\) | ||||
0.341059 | + | 0.940042i | \(0.389214\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.13377 | 0.0476980 | ||||||||
\(566\) | −5.97174 | −0.251011 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −63.4303 | −2.66148 | ||||||||
\(569\) | 14.6693 | 0.614969 | 0.307485 | − | 0.951553i | \(-0.400513\pi\) | ||||
0.307485 | + | 0.951553i | \(0.400513\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 43.0790 | 1.80280 | 0.901399 | − | 0.432989i | \(-0.142541\pi\) | ||||
0.901399 | + | 0.432989i | \(0.142541\pi\) | |||||||
\(572\) | 16.6697 | 0.696995 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 26.6636 | 1.11292 | ||||||||
\(575\) | −27.2736 | −1.13739 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.86799 | 0.369179 | 0.184590 | − | 0.982816i | \(-0.440904\pi\) | ||||
0.184590 | + | 0.982816i | \(0.440904\pi\) | |||||||
\(578\) | 40.4161 | 1.68109 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 10.5340 | 0.437401 | ||||||||
\(581\) | 6.82127 | 0.282994 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22.8244 | −0.945289 | ||||||||
\(584\) | 128.294 | 5.30884 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −74.4685 | −3.07627 | ||||||||
\(587\) | −16.7226 | −0.690214 | −0.345107 | − | 0.938563i | \(-0.612157\pi\) | ||||
−0.345107 | + | 0.938563i | \(0.612157\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21.4001 | 0.881775 | ||||||||
\(590\) | −3.75240 | −0.154484 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 68.4273 | 2.81234 | ||||||||
\(593\) | −36.7541 | −1.50931 | −0.754655 | − | 0.656122i | \(-0.772196\pi\) | ||||
−0.754655 | + | 0.656122i | \(0.772196\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.473187 | −0.0193988 | ||||||||
\(596\) | −100.645 | −4.12258 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 23.0676 | 0.943305 | ||||||||
\(599\) | 39.3871 | 1.60931 | 0.804656 | − | 0.593742i | \(-0.202350\pi\) | ||||
0.804656 | + | 0.593742i | \(0.202350\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.93379 | −0.282835 | −0.141418 | − | 0.989950i | \(-0.545166\pi\) | ||||
−0.141418 | + | 0.989950i | \(0.545166\pi\) | |||||||
\(602\) | 14.6101 | 0.595462 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 106.799 | 4.34560 | ||||||||
\(605\) | 2.18977 | 0.0890268 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.1875 | −0.616441 | −0.308221 | − | 0.951315i | \(-0.599734\pi\) | ||||
−0.308221 | + | 0.951315i | \(0.599734\pi\) | |||||||
\(608\) | −109.636 | −4.44631 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.0295 | −0.487062 | ||||||||
\(611\) | −2.60508 | −0.105390 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −35.2659 | −1.42438 | −0.712188 | − | 0.701989i | \(-0.752296\pi\) | ||||
−0.712188 | + | 0.701989i | \(0.752296\pi\) | |||||||
\(614\) | 3.39766 | 0.137118 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 19.7002 | 0.793745 | ||||||||
\(617\) | −3.48007 | −0.140102 | −0.0700512 | − | 0.997543i | \(-0.522316\pi\) | ||||
−0.0700512 | + | 0.997543i | \(0.522316\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −47.5147 | −1.90978 | −0.954888 | − | 0.296965i | \(-0.904026\pi\) | ||||
−0.954888 | + | 0.296965i | \(0.904026\pi\) | |||||||
\(620\) | −8.45905 | −0.339724 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 35.9272 | 1.44055 | ||||||||
\(623\) | 9.25437 | 0.370769 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.5823 | 0.943292 | ||||||||
\(626\) | 55.5832 | 2.22155 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −99.8514 | −3.98450 | ||||||||
\(629\) | 6.44142 | 0.256836 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.36804 | 0.173889 | 0.0869446 | − | 0.996213i | \(-0.472290\pi\) | ||||
0.0869446 | + | 0.996213i | \(0.472290\pi\) | |||||||
\(632\) | −3.28468 | −0.130657 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 15.9546 | 0.633637 | ||||||||
\(635\) | 0.308409 | 0.0122388 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.50333 | −0.0595640 | ||||||||
\(638\) | −33.1489 | −1.31238 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 15.5944 | 0.616421 | ||||||||
\(641\) | 16.2774 | 0.642918 | 0.321459 | − | 0.946924i | \(-0.395827\pi\) | ||||
0.321459 | + | 0.946924i | \(0.395827\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −37.7904 | −1.49031 | −0.745155 | − | 0.666891i | \(-0.767624\pi\) | ||||
−0.745155 | + | 0.666891i | \(0.767624\pi\) | |||||||
\(644\) | 31.2225 | 1.23034 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −18.5488 | −0.729794 | ||||||||
\(647\) | 21.8216 | 0.857894 | 0.428947 | − | 0.903330i | \(-0.358885\pi\) | ||||
0.428947 | + | 0.903330i | \(0.358885\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.70696 | 0.341778 | ||||||||
\(650\) | −20.3478 | −0.798108 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 113.833 | 4.45805 | ||||||||
\(653\) | −30.9287 | −1.21033 | −0.605167 | − | 0.796099i | \(-0.706894\pi\) | ||||
−0.605167 | + | 0.796099i | \(0.706894\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.29376 | 0.167771 | ||||||||
\(656\) | −157.484 | −6.14872 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.78194 | −0.186419 | ||||||||
\(659\) | −15.3388 | −0.597513 | −0.298757 | − | 0.954329i | \(-0.596572\pi\) | ||||
−0.298757 | + | 0.954329i | \(0.596572\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 48.9904 | 1.90550 | 0.952752 | − | 0.303749i | \(-0.0982385\pi\) | ||||
0.952752 | + | 0.303749i | \(0.0982385\pi\) | |||||||
\(662\) | −78.9359 | −3.06793 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −68.0482 | −2.64078 | ||||||||
\(665\) | −1.35114 | −0.0523950 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −33.8241 | −1.30967 | ||||||||
\(668\) | −116.917 | −4.52365 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −9.78130 | −0.377885 | ||||||||
\(671\) | 27.9130 | 1.07757 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.8519 | 1.15070 | 0.575352 | − | 0.817906i | \(-0.304865\pi\) | ||||
0.575352 | + | 0.817906i | \(0.304865\pi\) | |||||||
\(674\) | −13.2102 | −0.508839 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −60.3057 | −2.31945 | ||||||||
\(677\) | 47.9132 | 1.84146 | 0.920728 | − | 0.390206i | \(-0.127596\pi\) | ||||
0.920728 | + | 0.390206i | \(0.127596\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.74074 | 0.181933 | ||||||||
\(680\) | 4.72046 | 0.181021 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 26.6194 | 1.01931 | ||||||||
\(683\) | 41.6076 | 1.59207 | 0.796034 | − | 0.605251i | \(-0.206927\pi\) | ||||
0.796034 | + | 0.605251i | \(0.206927\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.27192 | 0.0485976 | ||||||||
\(686\) | −2.75954 | −0.105360 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −86.2918 | −3.28984 | ||||||||
\(689\) | −17.3753 | −0.661945 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.91082 | −0.338984 | −0.169492 | − | 0.985532i | \(-0.554213\pi\) | ||||
−0.169492 | + | 0.985532i | \(0.554213\pi\) | |||||||
\(692\) | 53.1021 | 2.01864 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.44296 | −0.0547740 | ||||||||
\(695\) | −0.00773469 | −0.000293394 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.8248 | −0.561529 | ||||||||
\(698\) | −48.3673 | −1.83073 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −27.5412 | −1.04096 | ||||||||
\(701\) | −13.9575 | −0.527167 | −0.263583 | − | 0.964637i | \(-0.584904\pi\) | ||||
−0.263583 | + | 0.964637i | \(0.584904\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.3929 | 0.693701 | ||||||||
\(704\) | −72.0018 | −2.71367 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 38.2289 | 1.43877 | ||||||||
\(707\) | 15.1594 | 0.570129 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.2898 | 0.574221 | 0.287111 | − | 0.957897i | \(-0.407305\pi\) | ||||
0.287111 | + | 0.957897i | \(0.407305\pi\) | |||||||
\(710\) | 5.41139 | 0.203086 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −92.3205 | −3.45986 | ||||||||
\(713\) | 27.1615 | 1.01721 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.915588 | −0.0342411 | ||||||||
\(716\) | 44.9668 | 1.68049 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 13.6323 | 0.508754 | ||||||||
\(719\) | −23.0445 | −0.859416 | −0.429708 | − | 0.902968i | \(-0.641383\pi\) | ||||
−0.429708 | + | 0.902968i | \(0.641383\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.27078 | 0.308020 | ||||||||
\(722\) | −0.533282 | −0.0198467 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −24.2232 | −0.900247 | ||||||||
\(725\) | 29.8361 | 1.10808 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.2173 | 1.15778 | 0.578892 | − | 0.815404i | \(-0.303485\pi\) | ||||
0.578892 | + | 0.815404i | \(0.303485\pi\) | |||||||
\(728\) | 14.9970 | 0.555826 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −10.9451 | −0.405095 | ||||||||
\(731\) | −8.12310 | −0.300444 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.4495 | −1.01387 | −0.506935 | − | 0.861984i | \(-0.669222\pi\) | ||||
−0.506935 | + | 0.861984i | \(0.669222\pi\) | |||||||
\(734\) | −45.3429 | −1.67364 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −139.152 | −5.12922 | ||||||||
\(737\) | 22.6962 | 0.836026 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29.2357 | 1.07545 | 0.537727 | − | 0.843119i | \(-0.319283\pi\) | ||||
0.537727 | + | 0.843119i | \(0.319283\pi\) | |||||||
\(740\) | −7.27037 | −0.267264 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −31.8944 | −1.17088 | ||||||||
\(743\) | 12.2500 | 0.449410 | 0.224705 | − | 0.974427i | \(-0.427858\pi\) | ||||
0.224705 | + | 0.974427i | \(0.427858\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.52796 | 0.202529 | ||||||||
\(746\) | −51.2861 | −1.87772 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −17.0130 | −0.622056 | ||||||||
\(749\) | −2.93782 | −0.107346 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.29748 | −0.302779 | −0.151390 | − | 0.988474i | \(-0.548375\pi\) | ||||
−0.151390 | + | 0.988474i | \(0.548375\pi\) | |||||||
\(752\) | 28.2437 | 1.02994 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −25.2350 | −0.919003 | ||||||||
\(755\) | −5.86598 | −0.213485 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.0388 | −0.510250 | −0.255125 | − | 0.966908i | \(-0.582117\pi\) | ||||
−0.255125 | + | 0.966908i | \(0.582117\pi\) | |||||||
\(758\) | 28.2852 | 1.02736 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 13.4788 | 0.488929 | ||||||||
\(761\) | −39.3218 | −1.42542 | −0.712708 | − | 0.701461i | \(-0.752531\pi\) | ||||
−0.712708 | + | 0.701461i | \(0.752531\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.12177 | 0.113016 | ||||||||
\(764\) | −6.12921 | −0.221747 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 70.3923 | 2.54338 | ||||||||
\(767\) | 6.62826 | 0.239333 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.0656 | −0.471156 | −0.235578 | − | 0.971855i | \(-0.575698\pi\) | ||||
−0.235578 | + | 0.971855i | \(0.575698\pi\) | |||||||
\(770\) | −1.68067 | −0.0605673 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −72.0577 | −2.59341 | ||||||||
\(773\) | 10.3852 | 0.373529 | 0.186764 | − | 0.982405i | \(-0.440200\pi\) | ||||
0.186764 | + | 0.982405i | \(0.440200\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −23.9591 | −0.860635 | ||||||||
\(776\) | −47.2930 | −1.69772 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.48209 | −0.160691 | ||||||||
\(779\) | −42.3309 | −1.51666 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.5564 | −0.449304 | ||||||||
\(782\) | −23.5427 | −0.841884 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 16.2987 | 0.582097 | ||||||||
\(785\) | 5.48437 | 0.195746 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −51.2006 | −1.82510 | −0.912552 | − | 0.408960i | \(-0.865892\pi\) | ||||
−0.912552 | + | 0.408960i | \(0.865892\pi\) | |||||||
\(788\) | 133.339 | 4.75001 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.280223 | 0.00996990 | ||||||||
\(791\) | −3.67619 | −0.130710 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.2490 | 0.754576 | ||||||||
\(794\) | −57.3919 | −2.03676 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 91.9029 | 3.25741 | ||||||||
\(797\) | 9.61879 | 0.340715 | 0.170358 | − | 0.985382i | \(-0.445508\pi\) | ||||
0.170358 | + | 0.985382i | \(0.445508\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.65872 | 0.0940589 | ||||||||
\(800\) | 122.746 | 4.33972 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 95.6331 | 3.37692 | ||||||||
\(803\) | 25.3966 | 0.896226 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.71490 | −0.0604424 | ||||||||
\(806\) | 20.2643 | 0.713778 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −151.229 | −5.32021 | ||||||||
\(809\) | −35.1085 | −1.23435 | −0.617174 | − | 0.786827i | \(-0.711723\pi\) | ||||
−0.617174 | + | 0.786827i | \(0.711723\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37.9552 | −1.33279 | −0.666394 | − | 0.745599i | \(-0.732163\pi\) | ||||
−0.666394 | + | 0.745599i | \(0.732163\pi\) | |||||||
\(812\) | −34.1560 | −1.19864 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 22.8788 | 0.801900 | ||||||||
\(815\) | −6.25232 | −0.219009 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −23.1948 | −0.811482 | ||||||||
\(818\) | 79.3891 | 2.77578 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 16.7326 | 0.584328 | ||||||||
\(821\) | −27.6250 | −0.964119 | −0.482060 | − | 0.876138i | \(-0.660111\pi\) | ||||
−0.482060 | + | 0.876138i | \(0.660111\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27.4533 | −0.956963 | −0.478481 | − | 0.878098i | \(-0.658813\pi\) | ||||
−0.478481 | + | 0.878098i | \(0.658813\pi\) | |||||||
\(824\) | −82.5083 | −2.87431 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.1670 | 0.423343 | ||||||||
\(827\) | −41.0840 | −1.42863 | −0.714315 | − | 0.699824i | \(-0.753262\pi\) | ||||
−0.714315 | + | 0.699824i | \(0.753262\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.58985 | 0.194144 | 0.0970718 | − | 0.995277i | \(-0.469052\pi\) | ||||
0.0970718 | + | 0.995277i | \(0.469052\pi\) | |||||||
\(830\) | 5.80535 | 0.201507 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −54.8121 | −1.90027 | ||||||||
\(833\) | 1.53428 | 0.0531598 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.42170 | 0.222232 | ||||||||
\(836\) | −48.5790 | −1.68014 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −15.5895 | −0.538529 | ||||||||
\(839\) | −22.6479 | −0.781893 | −0.390947 | − | 0.920413i | \(-0.627852\pi\) | ||||
−0.390947 | + | 0.920413i | \(0.627852\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.00207 | 0.275933 | ||||||||
\(842\) | 52.8537 | 1.82146 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −119.188 | −4.10263 | ||||||||
\(845\) | 3.31231 | 0.113947 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.10022 | −0.243966 | ||||||||
\(848\) | 188.379 | 6.46896 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 20.7669 | 0.712298 | ||||||||
\(851\) | 23.3447 | 0.800247 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.4312 | 0.699551 | 0.349776 | − | 0.936833i | \(-0.386258\pi\) | ||||
0.349776 | + | 0.936833i | \(0.386258\pi\) | |||||||
\(854\) | 39.0052 | 1.33473 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 29.3073 | 1.00170 | ||||||||
\(857\) | −24.8797 | −0.849876 | −0.424938 | − | 0.905223i | \(-0.639704\pi\) | ||||
−0.424938 | + | 0.905223i | \(0.639704\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.79392 | −0.0612078 | −0.0306039 | − | 0.999532i | \(-0.509743\pi\) | ||||
−0.0306039 | + | 0.999532i | \(0.509743\pi\) | |||||||
\(860\) | 9.16846 | 0.312642 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −108.617 | −3.69953 | ||||||||
\(863\) | −50.4753 | −1.71820 | −0.859100 | − | 0.511807i | \(-0.828976\pi\) | ||||
−0.859100 | + | 0.511807i | \(0.828976\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.91665 | −0.0991692 | ||||||||
\(866\) | −77.5907 | −2.63664 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 27.4281 | 0.930969 | ||||||||
\(869\) | −0.650222 | −0.0220573 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.2777 | 0.585434 | ||||||||
\(872\) | −31.1424 | −1.05462 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −67.2239 | −2.27388 | ||||||||
\(875\) | 3.05475 | 0.103270 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −48.1817 | −1.62698 | −0.813491 | − | 0.581578i | \(-0.802435\pi\) | ||||
−0.813491 | + | 0.581578i | \(0.802435\pi\) | |||||||
\(878\) | 79.2799 | 2.67557 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 9.92660 | 0.334626 | ||||||||
\(881\) | −49.2632 | −1.65972 | −0.829859 | − | 0.557972i | \(-0.811579\pi\) | ||||
−0.829859 | + | 0.557972i | \(0.811579\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.95775 | −0.200494 | −0.100247 | − | 0.994963i | \(-0.531963\pi\) | ||||
−0.100247 | + | 0.994963i | \(0.531963\pi\) | |||||||
\(884\) | −12.9513 | −0.435599 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 21.7991 | 0.732356 | ||||||||
\(887\) | −0.858528 | −0.0288265 | −0.0144133 | − | 0.999896i | \(-0.504588\pi\) | ||||
−0.0144133 | + | 0.999896i | \(0.504588\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.00000 | −0.0335389 | ||||||||
\(890\) | 7.87608 | 0.264007 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 71.8245 | 2.40486 | ||||||||
\(893\) | 7.59174 | 0.254048 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.46982 | −0.0825569 | ||||||||
\(896\) | −50.5639 | −1.68922 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 81.2452 | 2.71119 | ||||||||
\(899\) | −29.7135 | −0.991001 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.7331 | 0.590775 | ||||||||
\(902\) | −52.6550 | −1.75322 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 36.6732 | 1.21973 | ||||||||
\(905\) | 1.33047 | 0.0442262 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.52255 | −0.0505555 | −0.0252777 | − | 0.999680i | \(-0.508047\pi\) | ||||
−0.0252777 | + | 0.999680i | \(0.508047\pi\) | |||||||
\(908\) | −33.4979 | −1.11167 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.27943 | −0.0424127 | ||||||||
\(911\) | −35.4227 | −1.17361 | −0.586803 | − | 0.809729i | \(-0.699614\pi\) | ||||
−0.586803 | + | 0.809729i | \(0.699614\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.4706 | −0.445810 | ||||||||
\(914\) | −67.4956 | −2.23256 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −68.1698 | −2.25239 | ||||||||
\(917\) | −13.9223 | −0.459755 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.78057 | 0.190683 | 0.0953416 | − | 0.995445i | \(-0.469606\pi\) | ||||
0.0953416 | + | 0.995445i | \(0.469606\pi\) | |||||||
\(920\) | 17.1077 | 0.564024 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 31.9699 | 1.05287 | ||||||||
\(923\) | −9.55870 | −0.314628 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.5923 | −0.677070 | ||||||||
\(926\) | −14.2920 | −0.469664 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 152.227 | 4.99708 | ||||||||
\(929\) | −4.86127 | −0.159493 | −0.0797465 | − | 0.996815i | \(-0.525411\pi\) | ||||
−0.0797465 | + | 0.996815i | \(0.525411\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.38101 | 0.143582 | ||||||||
\(932\) | −152.780 | −5.00449 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −31.2314 | −1.02192 | ||||||||
\(935\) | 0.934443 | 0.0305596 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 46.8532 | 1.53063 | 0.765313 | − | 0.643658i | \(-0.222584\pi\) | ||||
0.765313 | + | 0.643658i | \(0.222584\pi\) | |||||||
\(938\) | 31.7154 | 1.03554 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.00088 | −0.0978778 | ||||||||
\(941\) | 15.2517 | 0.497190 | 0.248595 | − | 0.968608i | \(-0.420031\pi\) | ||||
0.248595 | + | 0.968608i | \(0.420031\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −53.7274 | −1.74961 | ||||||||
\(944\) | −71.8621 | −2.33891 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −28.8518 | −0.938052 | ||||||||
\(947\) | −42.7983 | −1.39076 | −0.695379 | − | 0.718643i | \(-0.744764\pi\) | ||||
−0.695379 | + | 0.718643i | \(0.744764\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.3334 | 0.627589 | ||||||||
\(950\) | 59.2979 | 1.92388 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −15.3058 | −0.496065 | ||||||||
\(953\) | −0.841810 | −0.0272689 | −0.0136344 | − | 0.999907i | \(-0.504340\pi\) | ||||
−0.0136344 | + | 0.999907i | \(0.504340\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.336649 | 0.0108937 | ||||||||
\(956\) | −36.5063 | −1.18070 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 105.408 | 3.40557 | ||||||||
\(959\) | −4.12414 | −0.133175 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.13936 | −0.230302 | ||||||||
\(962\) | 17.4167 | 0.561536 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −118.222 | −3.80769 | ||||||||
\(965\) | 3.95779 | 0.127406 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −49.3967 | −1.58849 | −0.794245 | − | 0.607598i | \(-0.792133\pi\) | ||||
−0.794245 | + | 0.607598i | \(0.792133\pi\) | |||||||
\(968\) | 70.8309 | 2.27659 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.03468 | 0.129546 | ||||||||
\(971\) | −33.6708 | −1.08055 | −0.540273 | − | 0.841490i | \(-0.681679\pi\) | ||||
−0.540273 | + | 0.841490i | \(0.681679\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.0250793 | 0.000804007 0 | ||||||||
\(974\) | 43.4040 | 1.39075 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −230.377 | −7.37420 | ||||||||
\(977\) | −41.2147 | −1.31857 | −0.659287 | − | 0.751891i | \(-0.729142\pi\) | ||||
−0.659287 | + | 0.751891i | \(0.729142\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18.2754 | −0.584085 | ||||||||
\(980\) | −1.73173 | −0.0553181 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −74.5046 | −2.37754 | ||||||||
\(983\) | −45.2976 | −1.44477 | −0.722385 | − | 0.691491i | \(-0.756954\pi\) | ||||
−0.722385 | + | 0.691491i | \(0.756954\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.32370 | −0.233353 | ||||||||
\(986\) | 25.7546 | 0.820195 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −36.9812 | −1.17653 | ||||||||
\(989\) | −29.4394 | −0.936119 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.6569 | −0.433826 | −0.216913 | − | 0.976191i | \(-0.569599\pi\) | ||||
−0.216913 | + | 0.976191i | \(0.569599\pi\) | |||||||
\(992\) | −122.241 | −3.88117 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −17.5462 | −0.556530 | ||||||||
\(995\) | −5.04780 | −0.160026 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −41.0717 | −1.30075 | −0.650376 | − | 0.759612i | \(-0.725389\pi\) | ||||
−0.650376 | + | 0.759612i | \(0.725389\pi\) | |||||||
\(998\) | 116.524 | 3.68852 | ||||||||
\(999\) | 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 | 8001.2.a.w.1.1 | 20 | ||
3.2 | odd | 2 | 889.2.a.d.1.20 | ✓ | 20 | ||
21.20 | even | 2 | 6223.2.a.l.1.20 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
889.2.a.d.1.20 | ✓ | 20 | 3.2 | odd | 2 | ||
6223.2.a.l.1.20 | 20 | 21.20 | even | 2 | |||
8001.2.a.w.1.1 | 20 | 1.1 | even | 1 | trivial |