Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7225,2,Mod(1,7225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7225.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7225 = 5^{2} \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7225.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: | \(57.6919154604\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 21 x^{13} - 2 x^{12} + 171 x^{11} + 30 x^{10} - 678 x^{9} - 153 x^{8} + 1350 x^{7} + 301 x^{6} + \cdots + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.50743\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.50743 | −1.77302 | −0.886511 | − | 0.462707i | \(-0.846878\pi\) | ||||
−0.886511 | + | 0.462707i | \(0.846878\pi\) | |||||||
\(3\) | 0.598298 | 0.345427 | 0.172714 | − | 0.984972i | \(-0.444746\pi\) | ||||
0.172714 | + | 0.984972i | \(0.444746\pi\) | |||||||
\(4\) | 4.28722 | 2.14361 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.50019 | −0.612451 | ||||||||
\(7\) | −3.52603 | −1.33271 | −0.666357 | − | 0.745633i | \(-0.732147\pi\) | ||||
−0.666357 | + | 0.745633i | \(0.732147\pi\) | |||||||
\(8\) | −5.73504 | −2.02764 | ||||||||
\(9\) | −2.64204 | −0.880680 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.05962 | 0.922509 | 0.461254 | − | 0.887268i | \(-0.347400\pi\) | ||||
0.461254 | + | 0.887268i | \(0.347400\pi\) | |||||||
\(12\) | 2.56503 | 0.740461 | ||||||||
\(13\) | −5.62679 | −1.56059 | −0.780296 | − | 0.625411i | \(-0.784931\pi\) | ||||
−0.780296 | + | 0.625411i | \(0.784931\pi\) | |||||||
\(14\) | 8.84128 | 2.36293 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 5.80580 | 1.45145 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 6.62474 | 1.56147 | ||||||||
\(19\) | −4.57297 | −1.04911 | −0.524556 | − | 0.851376i | \(-0.675769\pi\) | ||||
−0.524556 | + | 0.851376i | \(0.675769\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.10961 | −0.460356 | ||||||||
\(22\) | −7.67178 | −1.63563 | ||||||||
\(23\) | −0.455839 | −0.0950490 | −0.0475245 | − | 0.998870i | \(-0.515133\pi\) | ||||
−0.0475245 | + | 0.998870i | \(0.515133\pi\) | |||||||
\(24\) | −3.43126 | −0.700404 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 14.1088 | 2.76696 | ||||||||
\(27\) | −3.37562 | −0.649638 | ||||||||
\(28\) | −15.1168 | −2.85682 | ||||||||
\(29\) | 9.46268 | 1.75718 | 0.878588 | − | 0.477581i | \(-0.158486\pi\) | ||||
0.878588 | + | 0.477581i | \(0.158486\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.24066 | 0.761646 | 0.380823 | − | 0.924648i | \(-0.375641\pi\) | ||||
0.380823 | + | 0.924648i | \(0.375641\pi\) | |||||||
\(32\) | −3.08756 | −0.545809 | ||||||||
\(33\) | 1.83056 | 0.318660 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −11.3270 | −1.88783 | ||||||||
\(37\) | 9.85143 | 1.61957 | 0.809783 | − | 0.586730i | \(-0.199585\pi\) | ||||
0.809783 | + | 0.586730i | \(0.199585\pi\) | |||||||
\(38\) | 11.4664 | 1.86010 | ||||||||
\(39\) | −3.36650 | −0.539071 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.505315 | −0.0789169 | −0.0394584 | − | 0.999221i | \(-0.512563\pi\) | ||||
−0.0394584 | + | 0.999221i | \(0.512563\pi\) | |||||||
\(42\) | 5.28972 | 0.816221 | ||||||||
\(43\) | −9.70924 | −1.48065 | −0.740323 | − | 0.672252i | \(-0.765327\pi\) | ||||
−0.740323 | + | 0.672252i | \(0.765327\pi\) | |||||||
\(44\) | 13.1172 | 1.97750 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.14299 | 0.168524 | ||||||||
\(47\) | 4.72552 | 0.689288 | 0.344644 | − | 0.938734i | \(-0.388000\pi\) | ||||
0.344644 | + | 0.938734i | \(0.388000\pi\) | |||||||
\(48\) | 3.47360 | 0.501370 | ||||||||
\(49\) | 5.43287 | 0.776125 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −24.1233 | −3.34530 | ||||||||
\(53\) | 12.0203 | 1.65112 | 0.825559 | − | 0.564316i | \(-0.190860\pi\) | ||||
0.825559 | + | 0.564316i | \(0.190860\pi\) | |||||||
\(54\) | 8.46414 | 1.15182 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 20.2219 | 2.70227 | ||||||||
\(57\) | −2.73600 | −0.362392 | ||||||||
\(58\) | −23.7270 | −3.11551 | ||||||||
\(59\) | −10.8652 | −1.41453 | −0.707267 | − | 0.706946i | \(-0.750072\pi\) | ||||
−0.707267 | + | 0.706946i | \(0.750072\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.8337 | 1.77122 | 0.885612 | − | 0.464425i | \(-0.153739\pi\) | ||||
0.885612 | + | 0.464425i | \(0.153739\pi\) | |||||||
\(62\) | −10.6332 | −1.35041 | ||||||||
\(63\) | 9.31591 | 1.17369 | ||||||||
\(64\) | −3.86974 | −0.483718 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.59001 | −0.564991 | ||||||||
\(67\) | 3.04488 | 0.371991 | 0.185996 | − | 0.982551i | \(-0.440449\pi\) | ||||
0.185996 | + | 0.982551i | \(0.440449\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.272728 | −0.0328325 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.20889 | 0.499503 | 0.249752 | − | 0.968310i | \(-0.419651\pi\) | ||||
0.249752 | + | 0.968310i | \(0.419651\pi\) | |||||||
\(72\) | 15.1522 | 1.78571 | ||||||||
\(73\) | 8.48279 | 0.992836 | 0.496418 | − | 0.868084i | \(-0.334648\pi\) | ||||
0.496418 | + | 0.868084i | \(0.334648\pi\) | |||||||
\(74\) | −24.7018 | −2.87153 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −19.6053 | −2.24888 | ||||||||
\(77\) | −10.7883 | −1.22944 | ||||||||
\(78\) | 8.44126 | 0.955785 | ||||||||
\(79\) | 3.66719 | 0.412591 | 0.206296 | − | 0.978490i | \(-0.433859\pi\) | ||||
0.206296 | + | 0.978490i | \(0.433859\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.90649 | 0.656277 | ||||||||
\(82\) | 1.26704 | 0.139921 | ||||||||
\(83\) | 2.54818 | 0.279699 | 0.139849 | − | 0.990173i | \(-0.455338\pi\) | ||||
0.139849 | + | 0.990173i | \(0.455338\pi\) | |||||||
\(84\) | −9.04438 | −0.986822 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 24.3453 | 2.62522 | ||||||||
\(87\) | 5.66150 | 0.606976 | ||||||||
\(88\) | −17.5470 | −1.87052 | ||||||||
\(89\) | 4.72824 | 0.501192 | 0.250596 | − | 0.968092i | \(-0.419373\pi\) | ||||
0.250596 | + | 0.968092i | \(0.419373\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 19.8402 | 2.07982 | ||||||||
\(92\) | −1.95428 | −0.203748 | ||||||||
\(93\) | 2.53718 | 0.263093 | ||||||||
\(94\) | −11.8489 | −1.22212 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.84728 | −0.188537 | ||||||||
\(97\) | −3.05976 | −0.310672 | −0.155336 | − | 0.987862i | \(-0.549646\pi\) | ||||
−0.155336 | + | 0.987862i | \(0.549646\pi\) | |||||||
\(98\) | −13.6226 | −1.37609 | ||||||||
\(99\) | −8.08363 | −0.812435 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.0465 | 1.29817 | 0.649086 | − | 0.760715i | \(-0.275151\pi\) | ||||
0.649086 | + | 0.760715i | \(0.275151\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.23728 | −0.811643 | −0.405822 | − | 0.913952i | \(-0.633015\pi\) | ||||
−0.405822 | + | 0.913952i | \(0.633015\pi\) | |||||||
\(104\) | 32.2699 | 3.16432 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −30.1401 | −2.92747 | ||||||||
\(107\) | −6.96309 | −0.673148 | −0.336574 | − | 0.941657i | \(-0.609268\pi\) | ||||
−0.336574 | + | 0.941657i | \(0.609268\pi\) | |||||||
\(108\) | −14.4720 | −1.39257 | ||||||||
\(109\) | −10.8324 | −1.03756 | −0.518779 | − | 0.854909i | \(-0.673613\pi\) | ||||
−0.518779 | + | 0.854909i | \(0.673613\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.89409 | 0.559442 | ||||||||
\(112\) | −20.4714 | −1.93437 | ||||||||
\(113\) | −7.61490 | −0.716349 | −0.358175 | − | 0.933655i | \(-0.616601\pi\) | ||||
−0.358175 | + | 0.933655i | \(0.616601\pi\) | |||||||
\(114\) | 6.86033 | 0.642529 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 40.5686 | 3.76670 | ||||||||
\(117\) | 14.8662 | 1.37438 | ||||||||
\(118\) | 27.2439 | 2.50800 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.63875 | −0.148977 | ||||||||
\(122\) | −34.6871 | −3.14042 | ||||||||
\(123\) | −0.302329 | −0.0272600 | ||||||||
\(124\) | 18.1806 | 1.63267 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −23.3590 | −2.08099 | ||||||||
\(127\) | 7.44264 | 0.660427 | 0.330214 | − | 0.943906i | \(-0.392879\pi\) | ||||
0.330214 | + | 0.943906i | \(0.392879\pi\) | |||||||
\(128\) | 15.8782 | 1.40345 | ||||||||
\(129\) | −5.80902 | −0.511455 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.70296 | 0.148789 | 0.0743943 | − | 0.997229i | \(-0.476298\pi\) | ||||
0.0743943 | + | 0.997229i | \(0.476298\pi\) | |||||||
\(132\) | 7.84801 | 0.683082 | ||||||||
\(133\) | 16.1244 | 1.39817 | ||||||||
\(134\) | −7.63483 | −0.659549 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.390352 | 0.0333500 | 0.0166750 | − | 0.999861i | \(-0.494692\pi\) | ||||
0.0166750 | + | 0.999861i | \(0.494692\pi\) | |||||||
\(138\) | 0.683846 | 0.0582128 | ||||||||
\(139\) | −18.6534 | −1.58216 | −0.791079 | − | 0.611714i | \(-0.790480\pi\) | ||||
−0.791079 | + | 0.611714i | \(0.790480\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.82727 | 0.238099 | ||||||||
\(142\) | −10.5535 | −0.885630 | ||||||||
\(143\) | −17.2158 | −1.43966 | ||||||||
\(144\) | −15.3392 | −1.27826 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −21.2700 | −1.76032 | ||||||||
\(147\) | 3.25048 | 0.268095 | ||||||||
\(148\) | 42.2352 | 3.47172 | ||||||||
\(149\) | −4.90578 | −0.401897 | −0.200948 | − | 0.979602i | \(-0.564402\pi\) | ||||
−0.200948 | + | 0.979602i | \(0.564402\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.12643 | 0.498562 | 0.249281 | − | 0.968431i | \(-0.419806\pi\) | ||||
0.249281 | + | 0.968431i | \(0.419806\pi\) | |||||||
\(152\) | 26.2262 | 2.12722 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 27.0509 | 2.17982 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −14.4329 | −1.15556 | ||||||||
\(157\) | −4.45503 | −0.355550 | −0.177775 | − | 0.984071i | \(-0.556890\pi\) | ||||
−0.177775 | + | 0.984071i | \(0.556890\pi\) | |||||||
\(158\) | −9.19523 | −0.731533 | ||||||||
\(159\) | 7.19173 | 0.570341 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.60730 | 0.126673 | ||||||||
\(162\) | −14.8101 | −1.16359 | ||||||||
\(163\) | 7.75241 | 0.607215 | 0.303608 | − | 0.952797i | \(-0.401809\pi\) | ||||
0.303608 | + | 0.952797i | \(0.401809\pi\) | |||||||
\(164\) | −2.16639 | −0.169167 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.38939 | −0.495913 | ||||||||
\(167\) | −24.7876 | −1.91812 | −0.959062 | − | 0.283197i | \(-0.908605\pi\) | ||||
−0.959062 | + | 0.283197i | \(0.908605\pi\) | |||||||
\(168\) | 12.0987 | 0.933437 | ||||||||
\(169\) | 18.6608 | 1.43545 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.0820 | 0.923932 | ||||||||
\(172\) | −41.6256 | −3.17392 | ||||||||
\(173\) | 0.830544 | 0.0631451 | 0.0315726 | − | 0.999501i | \(-0.489948\pi\) | ||||
0.0315726 | + | 0.999501i | \(0.489948\pi\) | |||||||
\(174\) | −14.1958 | −1.07618 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 17.7635 | 1.33898 | ||||||||
\(177\) | −6.50065 | −0.488619 | ||||||||
\(178\) | −11.8557 | −0.888626 | ||||||||
\(179\) | 11.7896 | 0.881195 | 0.440597 | − | 0.897705i | \(-0.354767\pi\) | ||||
0.440597 | + | 0.897705i | \(0.354767\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.23289 | −0.0916397 | −0.0458199 | − | 0.998950i | \(-0.514590\pi\) | ||||
−0.0458199 | + | 0.998950i | \(0.514590\pi\) | |||||||
\(182\) | −49.7480 | −3.68757 | ||||||||
\(183\) | 8.27668 | 0.611830 | ||||||||
\(184\) | 2.61426 | 0.192726 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −6.36181 | −0.466470 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 20.2593 | 1.47756 | ||||||||
\(189\) | 11.9025 | 0.865782 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.0772 | −0.946235 | −0.473118 | − | 0.880999i | \(-0.656871\pi\) | ||||
−0.473118 | + | 0.880999i | \(0.656871\pi\) | |||||||
\(192\) | −2.31526 | −0.167089 | ||||||||
\(193\) | 0.307240 | 0.0221156 | 0.0110578 | − | 0.999939i | \(-0.496480\pi\) | ||||
0.0110578 | + | 0.999939i | \(0.496480\pi\) | |||||||
\(194\) | 7.67215 | 0.550828 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 23.2919 | 1.66371 | ||||||||
\(197\) | −14.1967 | −1.01147 | −0.505736 | − | 0.862688i | \(-0.668779\pi\) | ||||
−0.505736 | + | 0.862688i | \(0.668779\pi\) | |||||||
\(198\) | 20.2691 | 1.44047 | ||||||||
\(199\) | −15.7904 | −1.11935 | −0.559675 | − | 0.828712i | \(-0.689074\pi\) | ||||
−0.559675 | + | 0.828712i | \(0.689074\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.82174 | 0.128496 | ||||||||
\(202\) | −32.7131 | −2.30169 | ||||||||
\(203\) | −33.3657 | −2.34181 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 20.6544 | 1.43906 | ||||||||
\(207\) | 1.20435 | 0.0837078 | ||||||||
\(208\) | −32.6680 | −2.26512 | ||||||||
\(209\) | −13.9915 | −0.967815 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.85984 | −0.472251 | −0.236126 | − | 0.971723i | \(-0.575878\pi\) | ||||
−0.236126 | + | 0.971723i | \(0.575878\pi\) | |||||||
\(212\) | 51.5337 | 3.53935 | ||||||||
\(213\) | 2.51817 | 0.172542 | ||||||||
\(214\) | 17.4595 | 1.19351 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 19.3593 | 1.31724 | ||||||||
\(217\) | −14.9527 | −1.01506 | ||||||||
\(218\) | 27.1616 | 1.83961 | ||||||||
\(219\) | 5.07524 | 0.342953 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −14.7790 | −0.991904 | ||||||||
\(223\) | −13.4206 | −0.898711 | −0.449356 | − | 0.893353i | \(-0.648346\pi\) | ||||
−0.449356 | + | 0.893353i | \(0.648346\pi\) | |||||||
\(224\) | 10.8868 | 0.727407 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 19.0938 | 1.27010 | ||||||||
\(227\) | 3.47659 | 0.230750 | 0.115375 | − | 0.993322i | \(-0.463193\pi\) | ||||
0.115375 | + | 0.993322i | \(0.463193\pi\) | |||||||
\(228\) | −11.7298 | −0.776826 | ||||||||
\(229\) | −19.1819 | −1.26758 | −0.633789 | − | 0.773506i | \(-0.718501\pi\) | ||||
−0.633789 | + | 0.773506i | \(0.718501\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.45461 | −0.424682 | ||||||||
\(232\) | −54.2689 | −3.56293 | ||||||||
\(233\) | −15.1991 | −0.995728 | −0.497864 | − | 0.867255i | \(-0.665882\pi\) | ||||
−0.497864 | + | 0.867255i | \(0.665882\pi\) | |||||||
\(234\) | −37.2760 | −2.43681 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −46.5817 | −3.03221 | ||||||||
\(237\) | 2.19407 | 0.142520 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.18197 | −0.464563 | −0.232281 | − | 0.972649i | \(-0.574619\pi\) | ||||
−0.232281 | + | 0.972649i | \(0.574619\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.0247 | −0.903411 | −0.451705 | − | 0.892167i | \(-0.649184\pi\) | ||||
−0.451705 | + | 0.892167i | \(0.649184\pi\) | |||||||
\(242\) | 4.10906 | 0.264140 | ||||||||
\(243\) | 13.6607 | 0.876334 | ||||||||
\(244\) | 59.3081 | 3.79681 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.758068 | 0.0483327 | ||||||||
\(247\) | 25.7312 | 1.63723 | ||||||||
\(248\) | −24.3204 | −1.54435 | ||||||||
\(249\) | 1.52457 | 0.0966157 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.3367 | −1.47300 | −0.736499 | − | 0.676439i | \(-0.763522\pi\) | ||||
−0.736499 | + | 0.676439i | \(0.763522\pi\) | |||||||
\(252\) | 39.9393 | 2.51594 | ||||||||
\(253\) | −1.39469 | −0.0876836 | ||||||||
\(254\) | −18.6619 | −1.17095 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −32.0741 | −2.00463 | ||||||||
\(257\) | 3.23211 | 0.201613 | 0.100807 | − | 0.994906i | \(-0.467858\pi\) | ||||
0.100807 | + | 0.994906i | \(0.467858\pi\) | |||||||
\(258\) | 14.5657 | 0.906822 | ||||||||
\(259\) | −34.7364 | −2.15842 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −25.0008 | −1.54751 | ||||||||
\(262\) | −4.27007 | −0.263806 | ||||||||
\(263\) | −21.0607 | −1.29866 | −0.649331 | − | 0.760506i | \(-0.724951\pi\) | ||||
−0.649331 | + | 0.760506i | \(0.724951\pi\) | |||||||
\(264\) | −10.4983 | −0.646129 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −40.4309 | −2.47898 | ||||||||
\(267\) | 2.82890 | 0.173126 | ||||||||
\(268\) | 13.0541 | 0.797403 | ||||||||
\(269\) | −25.8825 | −1.57809 | −0.789043 | − | 0.614338i | \(-0.789423\pi\) | ||||
−0.789043 | + | 0.614338i | \(0.789423\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.2896 | 0.807283 | 0.403642 | − | 0.914917i | \(-0.367744\pi\) | ||||
0.403642 | + | 0.914917i | \(0.367744\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.8704 | 0.718427 | ||||||||
\(274\) | −0.978782 | −0.0591304 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.16924 | −0.0703801 | ||||||||
\(277\) | −10.2506 | −0.615898 | −0.307949 | − | 0.951403i | \(-0.599643\pi\) | ||||
−0.307949 | + | 0.951403i | \(0.599643\pi\) | |||||||
\(278\) | 46.7721 | 2.80520 | ||||||||
\(279\) | −11.2040 | −0.670766 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.95640 | −0.593949 | −0.296975 | − | 0.954885i | \(-0.595978\pi\) | ||||
−0.296975 | + | 0.954885i | \(0.595978\pi\) | |||||||
\(282\) | −7.08918 | −0.422155 | ||||||||
\(283\) | −14.6111 | −0.868538 | −0.434269 | − | 0.900783i | \(-0.642993\pi\) | ||||
−0.434269 | + | 0.900783i | \(0.642993\pi\) | |||||||
\(284\) | 18.0444 | 1.07074 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 43.1675 | 2.55255 | ||||||||
\(287\) | 1.78175 | 0.105174 | ||||||||
\(288\) | 8.15746 | 0.480683 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.83065 | −0.107315 | ||||||||
\(292\) | 36.3676 | 2.12825 | ||||||||
\(293\) | −21.2483 | −1.24134 | −0.620669 | − | 0.784073i | \(-0.713139\pi\) | ||||
−0.620669 | + | 0.784073i | \(0.713139\pi\) | |||||||
\(294\) | −8.15035 | −0.475338 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −56.4984 | −3.28390 | ||||||||
\(297\) | −10.3281 | −0.599297 | ||||||||
\(298\) | 12.3009 | 0.712572 | ||||||||
\(299\) | 2.56491 | 0.148333 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 34.2351 | 1.97328 | ||||||||
\(302\) | −15.3616 | −0.883961 | ||||||||
\(303\) | 7.80567 | 0.448424 | ||||||||
\(304\) | −26.5498 | −1.52273 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.59078 | 0.319082 | 0.159541 | − | 0.987191i | \(-0.448999\pi\) | ||||
0.159541 | + | 0.987191i | \(0.448999\pi\) | |||||||
\(308\) | −46.2518 | −2.63544 | ||||||||
\(309\) | −4.92835 | −0.280364 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.38479 | 0.475458 | 0.237729 | − | 0.971332i | \(-0.423597\pi\) | ||||
0.237729 | + | 0.971332i | \(0.423597\pi\) | |||||||
\(312\) | 19.3070 | 1.09304 | ||||||||
\(313\) | 34.6879 | 1.96068 | 0.980339 | − | 0.197322i | \(-0.0632245\pi\) | ||||
0.980339 | + | 0.197322i | \(0.0632245\pi\) | |||||||
\(314\) | 11.1707 | 0.630398 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15.7220 | 0.884434 | ||||||||
\(317\) | 11.6878 | 0.656451 | 0.328226 | − | 0.944599i | \(-0.393549\pi\) | ||||
0.328226 | + | 0.944599i | \(0.393549\pi\) | |||||||
\(318\) | −18.0328 | −1.01123 | ||||||||
\(319\) | 28.9522 | 1.62101 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.16600 | −0.232524 | ||||||||
\(322\) | −4.03020 | −0.224594 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 25.3224 | 1.40680 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −19.4386 | −1.07661 | ||||||||
\(327\) | −6.48101 | −0.358401 | ||||||||
\(328\) | 2.89800 | 0.160015 | ||||||||
\(329\) | −16.6623 | −0.918623 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.5772 | −0.581375 | −0.290688 | − | 0.956818i | \(-0.593884\pi\) | ||||
−0.290688 | + | 0.956818i | \(0.593884\pi\) | |||||||
\(332\) | 10.9246 | 0.599565 | ||||||||
\(333\) | −26.0279 | −1.42632 | ||||||||
\(334\) | 62.1533 | 3.40088 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −12.2480 | −0.668183 | ||||||||
\(337\) | −5.20193 | −0.283367 | −0.141684 | − | 0.989912i | \(-0.545252\pi\) | ||||
−0.141684 | + | 0.989912i | \(0.545252\pi\) | |||||||
\(338\) | −46.7907 | −2.54508 | ||||||||
\(339\) | −4.55598 | −0.247447 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.9748 | 0.702625 | ||||||||
\(342\) | −30.2947 | −1.63815 | ||||||||
\(343\) | 5.52573 | 0.298361 | ||||||||
\(344\) | 55.6829 | 3.00222 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.08253 | −0.111958 | ||||||||
\(347\) | 18.3551 | 0.985352 | 0.492676 | − | 0.870213i | \(-0.336019\pi\) | ||||
0.492676 | + | 0.870213i | \(0.336019\pi\) | |||||||
\(348\) | 24.2721 | 1.30112 | ||||||||
\(349\) | 12.3788 | 0.662625 | 0.331312 | − | 0.943521i | \(-0.392509\pi\) | ||||
0.331312 | + | 0.943521i | \(0.392509\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.9939 | 1.01382 | ||||||||
\(352\) | −9.44675 | −0.503514 | ||||||||
\(353\) | 14.1068 | 0.750828 | 0.375414 | − | 0.926857i | \(-0.377501\pi\) | ||||
0.375414 | + | 0.926857i | \(0.377501\pi\) | |||||||
\(354\) | 16.2999 | 0.866332 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 20.2710 | 1.07436 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −29.5616 | −1.56238 | ||||||||
\(359\) | −26.9401 | −1.42185 | −0.710923 | − | 0.703270i | \(-0.751722\pi\) | ||||
−0.710923 | + | 0.703270i | \(0.751722\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.91207 | 0.100635 | ||||||||
\(362\) | 3.09138 | 0.162479 | ||||||||
\(363\) | −0.980461 | −0.0514609 | ||||||||
\(364\) | 85.0594 | 4.45832 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −20.7532 | −1.08479 | ||||||||
\(367\) | 10.0103 | 0.522533 | 0.261266 | − | 0.965267i | \(-0.415860\pi\) | ||||
0.261266 | + | 0.965267i | \(0.415860\pi\) | |||||||
\(368\) | −2.64651 | −0.137959 | ||||||||
\(369\) | 1.33506 | 0.0695005 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −42.3840 | −2.20047 | ||||||||
\(372\) | 10.8774 | 0.563969 | ||||||||
\(373\) | 2.35960 | 0.122175 | 0.0610876 | − | 0.998132i | \(-0.480543\pi\) | ||||
0.0610876 | + | 0.998132i | \(0.480543\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −27.1011 | −1.39763 | ||||||||
\(377\) | −53.2445 | −2.74223 | ||||||||
\(378\) | −29.8448 | −1.53505 | ||||||||
\(379\) | 22.2045 | 1.14057 | 0.570283 | − | 0.821448i | \(-0.306833\pi\) | ||||
0.570283 | + | 0.821448i | \(0.306833\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.45291 | 0.228130 | ||||||||
\(382\) | 32.7903 | 1.67770 | ||||||||
\(383\) | 14.0370 | 0.717259 | 0.358630 | − | 0.933480i | \(-0.383244\pi\) | ||||
0.358630 | + | 0.933480i | \(0.383244\pi\) | |||||||
\(384\) | 9.49992 | 0.484791 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.770383 | −0.0392115 | ||||||||
\(387\) | 25.6522 | 1.30397 | ||||||||
\(388\) | −13.1179 | −0.665959 | ||||||||
\(389\) | 25.3269 | 1.28412 | 0.642061 | − | 0.766653i | \(-0.278079\pi\) | ||||
0.642061 | + | 0.766653i | \(0.278079\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −31.1578 | −1.57370 | ||||||||
\(393\) | 1.01888 | 0.0513957 | ||||||||
\(394\) | 35.5972 | 1.79336 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −34.6563 | −1.74154 | ||||||||
\(397\) | −12.5106 | −0.627889 | −0.313945 | − | 0.949441i | \(-0.601651\pi\) | ||||
−0.313945 | + | 0.949441i | \(0.601651\pi\) | |||||||
\(398\) | 39.5933 | 1.98463 | ||||||||
\(399\) | 9.64721 | 0.482964 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.15876 | 0.457367 | 0.228683 | − | 0.973501i | \(-0.426558\pi\) | ||||
0.228683 | + | 0.973501i | \(0.426558\pi\) | |||||||
\(402\) | −4.56790 | −0.227826 | ||||||||
\(403\) | −23.8613 | −1.18862 | ||||||||
\(404\) | 55.9331 | 2.78277 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 83.6622 | 4.15208 | ||||||||
\(407\) | 30.1416 | 1.49406 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 30.1228 | 1.48948 | 0.744739 | − | 0.667356i | \(-0.232574\pi\) | ||||
0.744739 | + | 0.667356i | \(0.232574\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.233547 | 0.0115200 | ||||||||
\(412\) | −35.3150 | −1.73985 | ||||||||
\(413\) | 38.3112 | 1.88517 | ||||||||
\(414\) | −3.01981 | −0.148416 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 17.3731 | 0.851785 | ||||||||
\(417\) | −11.1603 | −0.546521 | ||||||||
\(418\) | 35.0828 | 1.71596 | ||||||||
\(419\) | 37.9818 | 1.85553 | 0.927765 | − | 0.373165i | \(-0.121727\pi\) | ||||
0.927765 | + | 0.373165i | \(0.121727\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.0464 | 0.928263 | 0.464131 | − | 0.885766i | \(-0.346367\pi\) | ||||
0.464131 | + | 0.885766i | \(0.346367\pi\) | |||||||
\(422\) | 17.2006 | 0.837312 | ||||||||
\(423\) | −12.4850 | −0.607042 | ||||||||
\(424\) | −68.9370 | −3.34788 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −6.31414 | −0.305921 | ||||||||
\(427\) | −48.7780 | −2.36054 | ||||||||
\(428\) | −29.8523 | −1.44297 | ||||||||
\(429\) | −10.3002 | −0.497298 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.1877 | −0.779732 | −0.389866 | − | 0.920872i | \(-0.627479\pi\) | ||||
−0.389866 | + | 0.920872i | \(0.627479\pi\) | |||||||
\(432\) | −19.5982 | −0.942917 | ||||||||
\(433\) | 3.06400 | 0.147246 | 0.0736232 | − | 0.997286i | \(-0.476544\pi\) | ||||
0.0736232 | + | 0.997286i | \(0.476544\pi\) | |||||||
\(434\) | 37.4929 | 1.79972 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −46.4409 | −2.22412 | ||||||||
\(437\) | 2.08454 | 0.0997170 | ||||||||
\(438\) | −12.7258 | −0.608063 | ||||||||
\(439\) | −5.66931 | −0.270581 | −0.135291 | − | 0.990806i | \(-0.543197\pi\) | ||||
−0.135291 | + | 0.990806i | \(0.543197\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −14.3539 | −0.683518 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.21373 | −0.152689 | −0.0763444 | − | 0.997082i | \(-0.524325\pi\) | ||||
−0.0763444 | + | 0.997082i | \(0.524325\pi\) | |||||||
\(444\) | 25.2693 | 1.19923 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 33.6513 | 1.59344 | ||||||||
\(447\) | −2.93512 | −0.138826 | ||||||||
\(448\) | 13.6448 | 0.644658 | ||||||||
\(449\) | −13.4157 | −0.633127 | −0.316564 | − | 0.948571i | \(-0.602529\pi\) | ||||
−0.316564 | + | 0.948571i | \(0.602529\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.54607 | −0.0728015 | ||||||||
\(452\) | −32.6467 | −1.53557 | ||||||||
\(453\) | 3.66543 | 0.172217 | ||||||||
\(454\) | −8.71732 | −0.409124 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 15.6911 | 0.734802 | ||||||||
\(457\) | 20.3295 | 0.950974 | 0.475487 | − | 0.879723i | \(-0.342272\pi\) | ||||
0.475487 | + | 0.879723i | \(0.342272\pi\) | |||||||
\(458\) | 48.0974 | 2.24744 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.770520 | −0.0358867 | −0.0179434 | − | 0.999839i | \(-0.505712\pi\) | ||||
−0.0179434 | + | 0.999839i | \(0.505712\pi\) | |||||||
\(462\) | 16.1845 | 0.752971 | ||||||||
\(463\) | 33.1892 | 1.54243 | 0.771216 | − | 0.636573i | \(-0.219649\pi\) | ||||
0.771216 | + | 0.636573i | \(0.219649\pi\) | |||||||
\(464\) | 54.9384 | 2.55045 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 38.1108 | 1.76545 | ||||||||
\(467\) | −27.5913 | −1.27677 | −0.638385 | − | 0.769717i | \(-0.720397\pi\) | ||||
−0.638385 | + | 0.769717i | \(0.720397\pi\) | |||||||
\(468\) | 63.7347 | 2.94614 | ||||||||
\(469\) | −10.7363 | −0.495758 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.66543 | −0.122817 | ||||||||
\(472\) | 62.3126 | 2.86817 | ||||||||
\(473\) | −29.7065 | −1.36591 | ||||||||
\(474\) | −5.50149 | −0.252692 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −31.7581 | −1.45411 | ||||||||
\(478\) | 18.0083 | 0.823681 | ||||||||
\(479\) | 26.3785 | 1.20526 | 0.602632 | − | 0.798019i | \(-0.294119\pi\) | ||||
0.602632 | + | 0.798019i | \(0.294119\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −55.4320 | −2.52748 | ||||||||
\(482\) | 35.1660 | 1.60177 | ||||||||
\(483\) | 0.961645 | 0.0437564 | ||||||||
\(484\) | −7.02568 | −0.319349 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −34.2533 | −1.55376 | ||||||||
\(487\) | 37.7174 | 1.70914 | 0.854569 | − | 0.519338i | \(-0.173821\pi\) | ||||
0.854569 | + | 0.519338i | \(0.173821\pi\) | |||||||
\(488\) | −79.3369 | −3.59141 | ||||||||
\(489\) | 4.63825 | 0.209749 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.4059 | −0.469613 | −0.234806 | − | 0.972042i | \(-0.575446\pi\) | ||||
−0.234806 | + | 0.972042i | \(0.575446\pi\) | |||||||
\(492\) | −1.29615 | −0.0584349 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −64.5191 | −2.90285 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 24.6204 | 1.10549 | ||||||||
\(497\) | −14.8407 | −0.665695 | ||||||||
\(498\) | −3.82276 | −0.171302 | ||||||||
\(499\) | −26.5160 | −1.18702 | −0.593509 | − | 0.804827i | \(-0.702258\pi\) | ||||
−0.593509 | + | 0.804827i | \(0.702258\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.8304 | −0.662572 | ||||||||
\(502\) | 58.5151 | 2.61166 | ||||||||
\(503\) | −25.4913 | −1.13660 | −0.568301 | − | 0.822821i | \(-0.692399\pi\) | ||||
−0.568301 | + | 0.822821i | \(0.692399\pi\) | |||||||
\(504\) | −53.4271 | −2.37983 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.49710 | 0.155465 | ||||||||
\(507\) | 11.1647 | 0.495842 | ||||||||
\(508\) | 31.9082 | 1.41570 | ||||||||
\(509\) | 19.9285 | 0.883315 | 0.441657 | − | 0.897184i | \(-0.354391\pi\) | ||||
0.441657 | + | 0.897184i | \(0.354391\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −29.9106 | −1.32317 | ||||||||
\(512\) | 48.6673 | 2.15081 | ||||||||
\(513\) | 15.4366 | 0.681543 | ||||||||
\(514\) | −8.10429 | −0.357465 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −24.9045 | −1.09636 | ||||||||
\(517\) | 14.4583 | 0.635874 | ||||||||
\(518\) | 87.0993 | 3.82692 | ||||||||
\(519\) | 0.496913 | 0.0218121 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.1306 | −0.575262 | −0.287631 | − | 0.957741i | \(-0.592868\pi\) | ||||
−0.287631 | + | 0.957741i | \(0.592868\pi\) | |||||||
\(522\) | 62.6877 | 2.74377 | ||||||||
\(523\) | 6.15211 | 0.269013 | 0.134506 | − | 0.990913i | \(-0.457055\pi\) | ||||
0.134506 | + | 0.990913i | \(0.457055\pi\) | |||||||
\(524\) | 7.30098 | 0.318945 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 52.8084 | 2.30256 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 10.6279 | 0.462519 | ||||||||
\(529\) | −22.7922 | −0.990966 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 28.7064 | 1.24575 | ||||||||
\(532\) | 69.1289 | 2.99712 | ||||||||
\(533\) | 2.84330 | 0.123157 | ||||||||
\(534\) | −7.09326 | −0.306956 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −17.4625 | −0.754266 | ||||||||
\(537\) | 7.05368 | 0.304389 | ||||||||
\(538\) | 64.8987 | 2.79798 | ||||||||
\(539\) | 16.6225 | 0.715982 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.7146 | 0.804605 | 0.402302 | − | 0.915507i | \(-0.368210\pi\) | ||||
0.402302 | + | 0.915507i | \(0.368210\pi\) | |||||||
\(542\) | −33.3227 | −1.43133 | ||||||||
\(543\) | −0.737633 | −0.0316549 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −29.7641 | −1.27379 | ||||||||
\(547\) | 10.4089 | 0.445052 | 0.222526 | − | 0.974927i | \(-0.428570\pi\) | ||||
0.222526 | + | 0.974927i | \(0.428570\pi\) | |||||||
\(548\) | 1.67353 | 0.0714895 | ||||||||
\(549\) | −36.5492 | −1.55988 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −43.2726 | −1.84347 | ||||||||
\(552\) | 1.56410 | 0.0665727 | ||||||||
\(553\) | −12.9306 | −0.549866 | ||||||||
\(554\) | 25.7027 | 1.09200 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −79.9711 | −3.39153 | ||||||||
\(557\) | −33.2151 | −1.40737 | −0.703685 | − | 0.710512i | \(-0.748464\pi\) | ||||
−0.703685 | + | 0.710512i | \(0.748464\pi\) | |||||||
\(558\) | 28.0933 | 1.18928 | ||||||||
\(559\) | 54.6319 | 2.31068 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 24.9650 | 1.05309 | ||||||||
\(563\) | 21.7736 | 0.917649 | 0.458824 | − | 0.888527i | \(-0.348271\pi\) | ||||
0.458824 | + | 0.888527i | \(0.348271\pi\) | |||||||
\(564\) | 12.1211 | 0.510391 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 36.6363 | 1.53994 | ||||||||
\(567\) | −20.8265 | −0.874629 | ||||||||
\(568\) | −24.1382 | −1.01281 | ||||||||
\(569\) | 9.98336 | 0.418524 | 0.209262 | − | 0.977860i | \(-0.432894\pi\) | ||||
0.209262 | + | 0.977860i | \(0.432894\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.57244 | −0.400594 | −0.200297 | − | 0.979735i | \(-0.564191\pi\) | ||||
−0.200297 | + | 0.979735i | \(0.564191\pi\) | |||||||
\(572\) | −73.8080 | −3.08607 | ||||||||
\(573\) | −7.82408 | −0.326856 | ||||||||
\(574\) | −4.46763 | −0.186475 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 10.2240 | 0.426001 | ||||||||
\(577\) | −11.3210 | −0.471301 | −0.235650 | − | 0.971838i | \(-0.575722\pi\) | ||||
−0.235650 | + | 0.971838i | \(0.575722\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.183821 | 0.00763933 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.98495 | −0.372759 | ||||||||
\(582\) | 4.59023 | 0.190271 | ||||||||
\(583\) | 36.7775 | 1.52317 | ||||||||
\(584\) | −48.6492 | −2.01312 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 53.2786 | 2.20092 | ||||||||
\(587\) | 3.34528 | 0.138074 | 0.0690372 | − | 0.997614i | \(-0.478007\pi\) | ||||
0.0690372 | + | 0.997614i | \(0.478007\pi\) | |||||||
\(588\) | 13.9355 | 0.574690 | ||||||||
\(589\) | −19.3924 | −0.799051 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.49384 | −0.349390 | ||||||||
\(592\) | 57.1954 | 2.35072 | ||||||||
\(593\) | −38.7935 | −1.59306 | −0.796529 | − | 0.604601i | \(-0.793333\pi\) | ||||
−0.796529 | + | 0.604601i | \(0.793333\pi\) | |||||||
\(594\) | 25.8970 | 1.06257 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −21.0321 | −0.861510 | ||||||||
\(597\) | −9.44735 | −0.386654 | ||||||||
\(598\) | −6.43134 | −0.262997 | ||||||||
\(599\) | −43.4267 | −1.77437 | −0.887184 | − | 0.461416i | \(-0.847342\pi\) | ||||
−0.887184 | + | 0.461416i | \(0.847342\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.4771 | 0.590533 | 0.295266 | − | 0.955415i | \(-0.404592\pi\) | ||||
0.295266 | + | 0.955415i | \(0.404592\pi\) | |||||||
\(602\) | −85.8421 | −3.49866 | ||||||||
\(603\) | −8.04469 | −0.327605 | ||||||||
\(604\) | 26.2653 | 1.06872 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −19.5722 | −0.795066 | ||||||||
\(607\) | 10.8496 | 0.440371 | 0.220185 | − | 0.975458i | \(-0.429334\pi\) | ||||
0.220185 | + | 0.975458i | \(0.429334\pi\) | |||||||
\(608\) | 14.1193 | 0.572615 | ||||||||
\(609\) | −19.9626 | −0.808926 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −26.5895 | −1.07570 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.5871 | 0.427608 | 0.213804 | − | 0.976877i | \(-0.431415\pi\) | ||||
0.213804 | + | 0.976877i | \(0.431415\pi\) | |||||||
\(614\) | −14.0185 | −0.565740 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 61.8713 | 2.49287 | ||||||||
\(617\) | 14.1871 | 0.571152 | 0.285576 | − | 0.958356i | \(-0.407815\pi\) | ||||
0.285576 | + | 0.958356i | \(0.407815\pi\) | |||||||
\(618\) | 12.3575 | 0.497091 | ||||||||
\(619\) | 40.6923 | 1.63556 | 0.817780 | − | 0.575531i | \(-0.195205\pi\) | ||||
0.817780 | + | 0.575531i | \(0.195205\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.53874 | 0.0617475 | ||||||||
\(622\) | −21.0243 | −0.842997 | ||||||||
\(623\) | −16.6719 | −0.667946 | ||||||||
\(624\) | −19.5452 | −0.782434 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −86.9776 | −3.47633 | ||||||||
\(627\) | −8.37110 | −0.334310 | ||||||||
\(628\) | −19.0997 | −0.762160 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.3897 | −1.60789 | −0.803944 | − | 0.594705i | \(-0.797269\pi\) | ||||
−0.803944 | + | 0.594705i | \(0.797269\pi\) | |||||||
\(632\) | −21.0315 | −0.836588 | ||||||||
\(633\) | −4.10423 | −0.163128 | ||||||||
\(634\) | −29.3063 | −1.16390 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 30.8325 | 1.22259 | ||||||||
\(637\) | −30.5697 | −1.21121 | ||||||||
\(638\) | −72.5956 | −2.87409 | ||||||||
\(639\) | −11.1201 | −0.439902 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.1261 | −0.913426 | −0.456713 | − | 0.889614i | \(-0.650973\pi\) | ||||
−0.456713 | + | 0.889614i | \(0.650973\pi\) | |||||||
\(642\) | 10.4460 | 0.412270 | ||||||||
\(643\) | 3.81570 | 0.150477 | 0.0752383 | − | 0.997166i | \(-0.476028\pi\) | ||||
0.0752383 | + | 0.997166i | \(0.476028\pi\) | |||||||
\(644\) | 6.89085 | 0.271538 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 43.6126 | 1.71459 | 0.857294 | − | 0.514827i | \(-0.172144\pi\) | ||||
0.857294 | + | 0.514827i | \(0.172144\pi\) | |||||||
\(648\) | −33.8740 | −1.33070 | ||||||||
\(649\) | −33.2435 | −1.30492 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.94617 | −0.350628 | ||||||||
\(652\) | 33.2362 | 1.30163 | ||||||||
\(653\) | 24.7307 | 0.967785 | 0.483893 | − | 0.875127i | \(-0.339223\pi\) | ||||
0.483893 | + | 0.875127i | \(0.339223\pi\) | |||||||
\(654\) | 16.2507 | 0.635453 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.93375 | −0.114544 | ||||||||
\(657\) | −22.4119 | −0.874371 | ||||||||
\(658\) | 41.7796 | 1.62874 | ||||||||
\(659\) | −18.2763 | −0.711942 | −0.355971 | − | 0.934497i | \(-0.615850\pi\) | ||||
−0.355971 | + | 0.934497i | \(0.615850\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.7823 | −0.963921 | −0.481960 | − | 0.876193i | \(-0.660075\pi\) | ||||
−0.481960 | + | 0.876193i | \(0.660075\pi\) | |||||||
\(662\) | 26.5216 | 1.03079 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −14.6139 | −0.567130 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 65.2632 | 2.52890 | ||||||||
\(667\) | −4.31346 | −0.167018 | ||||||||
\(668\) | −106.270 | −4.11171 | ||||||||
\(669\) | −8.02953 | −0.310440 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 42.3258 | 1.63397 | ||||||||
\(672\) | 6.51357 | 0.251266 | ||||||||
\(673\) | 10.5928 | 0.408323 | 0.204162 | − | 0.978937i | \(-0.434553\pi\) | ||||
0.204162 | + | 0.978937i | \(0.434553\pi\) | |||||||
\(674\) | 13.0435 | 0.502416 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 80.0029 | 3.07703 | ||||||||
\(677\) | −8.56246 | −0.329082 | −0.164541 | − | 0.986370i | \(-0.552614\pi\) | ||||
−0.164541 | + | 0.986370i | \(0.552614\pi\) | |||||||
\(678\) | 11.4238 | 0.438728 | ||||||||
\(679\) | 10.7888 | 0.414037 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.08004 | 0.0797072 | ||||||||
\(682\) | −32.5334 | −1.24577 | ||||||||
\(683\) | 42.3447 | 1.62028 | 0.810138 | − | 0.586239i | \(-0.199392\pi\) | ||||
0.810138 | + | 0.586239i | \(0.199392\pi\) | |||||||
\(684\) | 51.7980 | 1.98055 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −13.8554 | −0.529001 | ||||||||
\(687\) | −11.4765 | −0.437856 | ||||||||
\(688\) | −56.3699 | −2.14908 | ||||||||
\(689\) | −67.6358 | −2.57672 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 43.4629 | 1.65341 | 0.826703 | − | 0.562638i | \(-0.190214\pi\) | ||||
0.826703 | + | 0.562638i | \(0.190214\pi\) | |||||||
\(692\) | 3.56072 | 0.135358 | ||||||||
\(693\) | 28.5031 | 1.08274 | ||||||||
\(694\) | −46.0241 | −1.74705 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −32.4689 | −1.23073 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −31.0391 | −1.17485 | ||||||||
\(699\) | −9.09361 | −0.343952 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.3541 | −0.693224 | −0.346612 | − | 0.938009i | \(-0.612668\pi\) | ||||
−0.346612 | + | 0.938009i | \(0.612668\pi\) | |||||||
\(702\) | −47.6260 | −1.79753 | ||||||||
\(703\) | −45.0503 | −1.69911 | ||||||||
\(704\) | −11.8399 | −0.446234 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −35.3718 | −1.33124 | ||||||||
\(707\) | −46.0022 | −1.73009 | ||||||||
\(708\) | −27.8697 | −1.04741 | ||||||||
\(709\) | −33.0240 | −1.24024 | −0.620121 | − | 0.784506i | \(-0.712917\pi\) | ||||
−0.620121 | + | 0.784506i | \(0.712917\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.68886 | −0.363361 | ||||||||
\(712\) | −27.1167 | −1.01624 | ||||||||
\(713\) | −1.93306 | −0.0723937 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 50.5445 | 1.88894 | ||||||||
\(717\) | −4.29696 | −0.160473 | ||||||||
\(718\) | 67.5505 | 2.52096 | ||||||||
\(719\) | −26.1373 | −0.974758 | −0.487379 | − | 0.873191i | \(-0.662047\pi\) | ||||
−0.487379 | + | 0.873191i | \(0.662047\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 29.0449 | 1.08169 | ||||||||
\(722\) | −4.79438 | −0.178428 | ||||||||
\(723\) | −8.39095 | −0.312063 | ||||||||
\(724\) | −5.28565 | −0.196440 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.45844 | 0.0912413 | ||||||||
\(727\) | 17.3108 | 0.642024 | 0.321012 | − | 0.947075i | \(-0.395977\pi\) | ||||
0.321012 | + | 0.947075i | \(0.395977\pi\) | |||||||
\(728\) | −113.785 | −4.21714 | ||||||||
\(729\) | −9.54631 | −0.353567 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 35.4839 | 1.31152 | ||||||||
\(733\) | −7.71364 | −0.284910 | −0.142455 | − | 0.989801i | \(-0.545500\pi\) | ||||
−0.142455 | + | 0.989801i | \(0.545500\pi\) | |||||||
\(734\) | −25.1001 | −0.926462 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.40743 | 0.0518786 | ||||||||
\(737\) | 9.31616 | 0.343165 | ||||||||
\(738\) | −3.34758 | −0.123226 | ||||||||
\(739\) | −3.73009 | −0.137213 | −0.0686067 | − | 0.997644i | \(-0.521855\pi\) | ||||
−0.0686067 | + | 0.997644i | \(0.521855\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.3949 | 0.565546 | ||||||||
\(742\) | 106.275 | 3.90148 | ||||||||
\(743\) | 4.74617 | 0.174120 | 0.0870601 | − | 0.996203i | \(-0.472253\pi\) | ||||
0.0870601 | + | 0.996203i | \(0.472253\pi\) | |||||||
\(744\) | −14.5508 | −0.533459 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −5.91653 | −0.216619 | ||||||||
\(747\) | −6.73239 | −0.246325 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 24.5521 | 0.897113 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.6567 | −1.15517 | −0.577584 | − | 0.816331i | \(-0.696004\pi\) | ||||
−0.577584 | + | 0.816331i | \(0.696004\pi\) | |||||||
\(752\) | 27.4354 | 1.00047 | ||||||||
\(753\) | −13.9623 | −0.508814 | ||||||||
\(754\) | 133.507 | 4.86204 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 51.0287 | 1.85590 | ||||||||
\(757\) | −4.00212 | −0.145459 | −0.0727297 | − | 0.997352i | \(-0.523171\pi\) | ||||
−0.0727297 | + | 0.997352i | \(0.523171\pi\) | |||||||
\(758\) | −55.6762 | −2.02225 | ||||||||
\(759\) | −0.834442 | −0.0302883 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.0522 | −0.835641 | −0.417820 | − | 0.908530i | \(-0.637206\pi\) | ||||
−0.417820 | + | 0.908530i | \(0.637206\pi\) | |||||||
\(762\) | −11.1654 | −0.404479 | ||||||||
\(763\) | 38.1954 | 1.38277 | ||||||||
\(764\) | −56.0649 | −2.02836 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −35.1969 | −1.27172 | ||||||||
\(767\) | 61.1365 | 2.20751 | ||||||||
\(768\) | −19.1899 | −0.692455 | ||||||||
\(769\) | −29.1001 | −1.04938 | −0.524688 | − | 0.851295i | \(-0.675818\pi\) | ||||
−0.524688 | + | 0.851295i | \(0.675818\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.93376 | 0.0696427 | ||||||||
\(772\) | 1.31720 | 0.0474072 | ||||||||
\(773\) | −2.49408 | −0.0897059 | −0.0448529 | − | 0.998994i | \(-0.514282\pi\) | ||||
−0.0448529 | + | 0.998994i | \(0.514282\pi\) | |||||||
\(774\) | −64.3212 | −2.31198 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 17.5479 | 0.629932 | ||||||||
\(777\) | −20.7827 | −0.745576 | ||||||||
\(778\) | −63.5054 | −2.27678 | ||||||||
\(779\) | 2.31079 | 0.0827926 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.8776 | 0.460796 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −31.9424 | −1.14153 | ||||||||
\(784\) | 31.5422 | 1.12651 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −2.55477 | −0.0911257 | ||||||||
\(787\) | −44.4841 | −1.58569 | −0.792844 | − | 0.609425i | \(-0.791400\pi\) | ||||
−0.792844 | + | 0.609425i | \(0.791400\pi\) | |||||||
\(788\) | −60.8643 | −2.16820 | ||||||||
\(789\) | −12.6006 | −0.448593 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 26.8503 | 0.954688 | ||||||||
\(792\) | 46.3600 | 1.64733 | ||||||||
\(793\) | −77.8394 | −2.76416 | ||||||||
\(794\) | 31.3695 | 1.11326 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −67.6968 | −2.39945 | ||||||||
\(797\) | 43.4377 | 1.53864 | 0.769322 | − | 0.638861i | \(-0.220594\pi\) | ||||
0.769322 | + | 0.638861i | \(0.220594\pi\) | |||||||
\(798\) | −24.1897 | −0.856307 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.4922 | −0.441390 | ||||||||
\(802\) | −22.9650 | −0.810921 | ||||||||
\(803\) | 25.9541 | 0.915900 | ||||||||
\(804\) | 7.81021 | 0.275445 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 59.8307 | 2.10745 | ||||||||
\(807\) | −15.4855 | −0.545114 | ||||||||
\(808\) | −74.8221 | −2.63223 | ||||||||
\(809\) | −18.4878 | −0.649995 | −0.324998 | − | 0.945715i | \(-0.605363\pi\) | ||||
−0.324998 | + | 0.945715i | \(0.605363\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.5730 | −0.827758 | −0.413879 | − | 0.910332i | \(-0.635826\pi\) | ||||
−0.413879 | + | 0.910332i | \(0.635826\pi\) | |||||||
\(812\) | −143.046 | −5.01993 | ||||||||
\(813\) | 7.95111 | 0.278858 | ||||||||
\(814\) | −75.5780 | −2.64901 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 44.4001 | 1.55336 | ||||||||
\(818\) | −75.5310 | −2.64088 | ||||||||
\(819\) | −52.4187 | −1.83166 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −52.8639 | −1.84496 | −0.922481 | − | 0.386042i | \(-0.873842\pi\) | ||||
−0.922481 | + | 0.386042i | \(0.873842\pi\) | |||||||
\(822\) | −0.585603 | −0.0204253 | ||||||||
\(823\) | −43.2073 | −1.50611 | −0.753057 | − | 0.657956i | \(-0.771421\pi\) | ||||
−0.753057 | + | 0.657956i | \(0.771421\pi\) | |||||||
\(824\) | 47.2412 | 1.64572 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −96.0626 | −3.34245 | ||||||||
\(827\) | −41.5689 | −1.44549 | −0.722745 | − | 0.691114i | \(-0.757120\pi\) | ||||
−0.722745 | + | 0.691114i | \(0.757120\pi\) | |||||||
\(828\) | 5.16329 | 0.179437 | ||||||||
\(829\) | −38.5545 | −1.33905 | −0.669526 | − | 0.742789i | \(-0.733503\pi\) | ||||
−0.669526 | + | 0.742789i | \(0.733503\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.13291 | −0.212748 | ||||||||
\(832\) | 21.7742 | 0.754886 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 27.9836 | 0.968994 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −59.9848 | −2.07462 | ||||||||
\(837\) | −14.3149 | −0.494794 | ||||||||
\(838\) | −95.2367 | −3.28990 | ||||||||
\(839\) | −40.9756 | −1.41463 | −0.707317 | − | 0.706896i | \(-0.750095\pi\) | ||||
−0.707317 | + | 0.706896i | \(0.750095\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 60.5423 | 2.08766 | ||||||||
\(842\) | −47.7575 | −1.64583 | ||||||||
\(843\) | −5.95689 | −0.205166 | ||||||||
\(844\) | −29.4096 | −1.01232 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 31.3053 | 1.07630 | ||||||||
\(847\) | 5.77828 | 0.198544 | ||||||||
\(848\) | 69.7875 | 2.39651 | ||||||||
\(849\) | −8.74177 | −0.300017 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.49067 | −0.153938 | ||||||||
\(852\) | 10.7959 | 0.369863 | ||||||||
\(853\) | −22.9121 | −0.784494 | −0.392247 | − | 0.919860i | \(-0.628302\pi\) | ||||
−0.392247 | + | 0.919860i | \(0.628302\pi\) | |||||||
\(854\) | 122.308 | 4.18528 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 39.9336 | 1.36490 | ||||||||
\(857\) | −19.4301 | −0.663719 | −0.331860 | − | 0.943329i | \(-0.607676\pi\) | ||||
−0.331860 | + | 0.943329i | \(0.607676\pi\) | |||||||
\(858\) | 25.8270 | 0.881720 | ||||||||
\(859\) | 18.3698 | 0.626768 | 0.313384 | − | 0.949626i | \(-0.398537\pi\) | ||||
0.313384 | + | 0.949626i | \(0.398537\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.06602 | 0.0363298 | ||||||||
\(862\) | 40.5895 | 1.38248 | ||||||||
\(863\) | 23.1327 | 0.787447 | 0.393724 | − | 0.919229i | \(-0.371187\pi\) | ||||
0.393724 | + | 0.919229i | \(0.371187\pi\) | |||||||
\(864\) | 10.4224 | 0.354578 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −7.68277 | −0.261071 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −64.1055 | −2.17588 | ||||||||
\(869\) | 11.2202 | 0.380619 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.1329 | −0.580526 | ||||||||
\(872\) | 62.1244 | 2.10380 | ||||||||
\(873\) | 8.08401 | 0.273602 | ||||||||
\(874\) | −5.22684 | −0.176801 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 21.7586 | 0.735156 | ||||||||
\(877\) | 52.7767 | 1.78214 | 0.891071 | − | 0.453864i | \(-0.149955\pi\) | ||||
0.891071 | + | 0.453864i | \(0.149955\pi\) | |||||||
\(878\) | 14.2154 | 0.479747 | ||||||||
\(879\) | −12.7128 | −0.428792 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.90383 | −0.232596 | −0.116298 | − | 0.993214i | \(-0.537103\pi\) | ||||
−0.116298 | + | 0.993214i | \(0.537103\pi\) | |||||||
\(882\) | 35.9914 | 1.21189 | ||||||||
\(883\) | 3.78214 | 0.127279 | 0.0636395 | − | 0.997973i | \(-0.479729\pi\) | ||||
0.0636395 | + | 0.997973i | \(0.479729\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.05820 | 0.270721 | ||||||||
\(887\) | −18.1504 | −0.609431 | −0.304716 | − | 0.952443i | \(-0.598561\pi\) | ||||
−0.304716 | + | 0.952443i | \(0.598561\pi\) | |||||||
\(888\) | −33.8029 | −1.13435 | ||||||||
\(889\) | −26.2430 | −0.880160 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 18.0716 | 0.605421 | ||||||||
\(892\) | −57.5371 | −1.92649 | ||||||||
\(893\) | −21.6097 | −0.723140 | ||||||||
\(894\) | 7.35960 | 0.246142 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −55.9871 | −1.87040 | ||||||||
\(897\) | 1.53458 | 0.0512382 | ||||||||
\(898\) | 33.6390 | 1.12255 | ||||||||
\(899\) | 40.1280 | 1.33834 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 3.87666 | 0.129079 | ||||||||
\(903\) | 20.4828 | 0.681623 | ||||||||
\(904\) | 43.6718 | 1.45250 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −9.19081 | −0.305344 | ||||||||
\(907\) | −18.2255 | −0.605167 | −0.302584 | − | 0.953123i | \(-0.597849\pi\) | ||||
−0.302584 | + | 0.953123i | \(0.597849\pi\) | |||||||
\(908\) | 14.9049 | 0.494637 | ||||||||
\(909\) | −34.4693 | −1.14327 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.9725 | 0.893638 | 0.446819 | − | 0.894624i | \(-0.352557\pi\) | ||||
0.446819 | + | 0.894624i | \(0.352557\pi\) | |||||||
\(912\) | −15.8847 | −0.525994 | ||||||||
\(913\) | 7.79645 | 0.258025 | ||||||||
\(914\) | −50.9749 | −1.68610 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −82.2371 | −2.71719 | ||||||||
\(917\) | −6.00470 | −0.198293 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.07053 | −0.0353134 | −0.0176567 | − | 0.999844i | \(-0.505621\pi\) | ||||
−0.0176567 | + | 0.999844i | \(0.505621\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.34495 | 0.110220 | ||||||||
\(922\) | 1.93203 | 0.0636280 | ||||||||
\(923\) | −23.6825 | −0.779520 | ||||||||
\(924\) | −27.6723 | −0.910352 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −83.2196 | −2.73477 | ||||||||
\(927\) | 21.7632 | 0.714798 | ||||||||
\(928\) | −29.2166 | −0.959082 | ||||||||
\(929\) | −10.3780 | −0.340492 | −0.170246 | − | 0.985402i | \(-0.554456\pi\) | ||||
−0.170246 | + | 0.985402i | \(0.554456\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24.8444 | −0.814242 | ||||||||
\(932\) | −65.1620 | −2.13445 | ||||||||
\(933\) | 5.01660 | 0.164236 | ||||||||
\(934\) | 69.1832 | 2.26374 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −85.2584 | −2.78676 | ||||||||
\(937\) | 7.66960 | 0.250555 | 0.125277 | − | 0.992122i | \(-0.460018\pi\) | ||||
0.125277 | + | 0.992122i | \(0.460018\pi\) | |||||||
\(938\) | 26.9206 | 0.878989 | ||||||||
\(939\) | 20.7537 | 0.677272 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 46.9716 | 1.53123 | 0.765615 | − | 0.643300i | \(-0.222435\pi\) | ||||
0.765615 | + | 0.643300i | \(0.222435\pi\) | |||||||
\(942\) | 6.68339 | 0.217757 | ||||||||
\(943\) | 0.230342 | 0.00750097 | ||||||||
\(944\) | −63.0814 | −2.05313 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 74.4872 | 2.42179 | ||||||||
\(947\) | −15.6994 | −0.510163 | −0.255081 | − | 0.966920i | \(-0.582102\pi\) | ||||
−0.255081 | + | 0.966920i | \(0.582102\pi\) | |||||||
\(948\) | 9.40646 | 0.305508 | ||||||||
\(949\) | −47.7309 | −1.54941 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.99278 | 0.226756 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17.7725 | −0.575708 | −0.287854 | − | 0.957674i | \(-0.592942\pi\) | ||||
−0.287854 | + | 0.957674i | \(0.592942\pi\) | |||||||
\(954\) | 79.6314 | 2.57816 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −30.7907 | −0.995841 | ||||||||
\(957\) | 17.3220 | 0.559941 | ||||||||
\(958\) | −66.1423 | −2.13696 | ||||||||
\(959\) | −1.37639 | −0.0444461 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.0168 | −0.419896 | ||||||||
\(962\) | 138.992 | 4.48128 | ||||||||
\(963\) | 18.3968 | 0.592828 | ||||||||
\(964\) | −60.1270 | −1.93656 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.41126 | −0.0775810 | ||||||||
\(967\) | 11.9909 | 0.385600 | 0.192800 | − | 0.981238i | \(-0.438243\pi\) | ||||
0.192800 | + | 0.981238i | \(0.438243\pi\) | |||||||
\(968\) | 9.39831 | 0.302073 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.5354 | 0.626920 | 0.313460 | − | 0.949601i | \(-0.398512\pi\) | ||||
0.313460 | + | 0.949601i | \(0.398512\pi\) | |||||||
\(972\) | 58.5664 | 1.87852 | ||||||||
\(973\) | 65.7723 | 2.10856 | ||||||||
\(974\) | −94.5738 | −3.03034 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 80.3157 | 2.57084 | ||||||||
\(977\) | 37.0958 | 1.18680 | 0.593400 | − | 0.804907i | \(-0.297785\pi\) | ||||
0.593400 | + | 0.804907i | \(0.297785\pi\) | |||||||
\(978\) | −11.6301 | −0.371889 | ||||||||
\(979\) | 14.4666 | 0.462354 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 28.6197 | 0.913756 | ||||||||
\(982\) | 26.0921 | 0.832634 | ||||||||
\(983\) | 2.44368 | 0.0779412 | 0.0389706 | − | 0.999240i | \(-0.487592\pi\) | ||||
0.0389706 | + | 0.999240i | \(0.487592\pi\) | |||||||
\(984\) | 1.73387 | 0.0552737 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −9.96902 | −0.317318 | ||||||||
\(988\) | 110.315 | 3.50959 | ||||||||
\(989\) | 4.42585 | 0.140734 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 41.1240 | 1.30635 | 0.653174 | − | 0.757208i | \(-0.273437\pi\) | ||||
0.653174 | + | 0.757208i | \(0.273437\pi\) | |||||||
\(992\) | −13.0933 | −0.415713 | ||||||||
\(993\) | −6.32831 | −0.200823 | ||||||||
\(994\) | 37.2120 | 1.18029 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 6.53616 | 0.207106 | ||||||||
\(997\) | −22.7241 | −0.719679 | −0.359839 | − | 0.933014i | \(-0.617168\pi\) | ||||
−0.359839 | + | 0.933014i | \(0.617168\pi\) | |||||||
\(998\) | 66.4870 | 2.10461 | ||||||||
\(999\) | −33.2547 | −1.05213 |
(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 | 7225.2.a.bt.1.1 | ✓ | 15 | |
5.4 | even | 2 | 7225.2.a.bv.1.15 | yes | 15 | ||
17.16 | even | 2 | 7225.2.a.bw.1.1 | yes | 15 | ||
85.84 | even | 2 | 7225.2.a.bu.1.15 | yes | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7225.2.a.bt.1.1 | ✓ | 15 | 1.1 | even | 1 | trivial | |
7225.2.a.bu.1.15 | yes | 15 | 85.84 | even | 2 | ||
7225.2.a.bv.1.15 | yes | 15 | 5.4 | even | 2 | ||
7225.2.a.bw.1.1 | yes | 15 | 17.16 | even | 2 |