Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1098672178\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 2 x^{14} - 16 x^{13} + 31 x^{12} + 99 x^{11} - 184 x^{10} - 296 x^{9} + 519 x^{8} + 437 x^{7} - 699 x^{6} - 297 x^{5} + 394 x^{4} + 89 x^{3} - 57 x^{2} - 17 x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1205) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(-1.39546\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.39546 | 0.986739 | 0.493369 | − | 0.869820i | \(-0.335765\pi\) | ||||
0.493369 | + | 0.869820i | \(0.335765\pi\) | |||||||
\(3\) | −2.59963 | −1.50090 | −0.750449 | − | 0.660928i | \(-0.770163\pi\) | ||||
−0.750449 | + | 0.660928i | \(0.770163\pi\) | |||||||
\(4\) | −0.0526942 | −0.0263471 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.62768 | −1.48099 | ||||||||
\(7\) | 1.49578 | 0.565353 | 0.282676 | − | 0.959215i | \(-0.408778\pi\) | ||||
0.282676 | + | 0.959215i | \(0.408778\pi\) | |||||||
\(8\) | −2.86445 | −1.01274 | ||||||||
\(9\) | 3.75808 | 1.25269 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.55651 | −0.469305 | −0.234653 | − | 0.972079i | \(-0.575395\pi\) | ||||
−0.234653 | + | 0.972079i | \(0.575395\pi\) | |||||||
\(12\) | 0.136985 | 0.0395443 | ||||||||
\(13\) | −0.546921 | −0.151688 | −0.0758442 | − | 0.997120i | \(-0.524165\pi\) | ||||
−0.0758442 | + | 0.997120i | \(0.524165\pi\) | |||||||
\(14\) | 2.08730 | 0.557856 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.89183 | −0.972959 | ||||||||
\(17\) | 6.16738 | 1.49581 | 0.747905 | − | 0.663806i | \(-0.231060\pi\) | ||||
0.747905 | + | 0.663806i | \(0.231060\pi\) | |||||||
\(18\) | 5.24425 | 1.23608 | ||||||||
\(19\) | −4.52461 | −1.03802 | −0.519009 | − | 0.854769i | \(-0.673699\pi\) | ||||
−0.519009 | + | 0.854769i | \(0.673699\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.88849 | −0.848537 | ||||||||
\(22\) | −2.17205 | −0.463082 | ||||||||
\(23\) | 0.734249 | 0.153101 | 0.0765507 | − | 0.997066i | \(-0.475609\pi\) | ||||
0.0765507 | + | 0.997066i | \(0.475609\pi\) | |||||||
\(24\) | 7.44652 | 1.52001 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.763205 | −0.149677 | ||||||||
\(27\) | −1.97074 | −0.379268 | ||||||||
\(28\) | −0.0788191 | −0.0148954 | ||||||||
\(29\) | 3.56695 | 0.662366 | 0.331183 | − | 0.943567i | \(-0.392552\pi\) | ||||
0.331183 | + | 0.943567i | \(0.392552\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.59944 | −0.826085 | −0.413042 | − | 0.910712i | \(-0.635534\pi\) | ||||
−0.413042 | + | 0.910712i | \(0.635534\pi\) | |||||||
\(32\) | 0.298005 | 0.0526804 | ||||||||
\(33\) | 4.04635 | 0.704379 | ||||||||
\(34\) | 8.60633 | 1.47597 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.198029 | −0.0330049 | ||||||||
\(37\) | −2.22842 | −0.366350 | −0.183175 | − | 0.983080i | \(-0.558638\pi\) | ||||
−0.183175 | + | 0.983080i | \(0.558638\pi\) | |||||||
\(38\) | −6.31391 | −1.02425 | ||||||||
\(39\) | 1.42179 | 0.227669 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.66717 | 0.572715 | 0.286358 | − | 0.958123i | \(-0.407555\pi\) | ||||
0.286358 | + | 0.958123i | \(0.407555\pi\) | |||||||
\(42\) | −5.42622 | −0.837284 | ||||||||
\(43\) | 1.59094 | 0.242616 | 0.121308 | − | 0.992615i | \(-0.461291\pi\) | ||||
0.121308 | + | 0.992615i | \(0.461291\pi\) | |||||||
\(44\) | 0.0820190 | 0.0123648 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.02461 | 0.151071 | ||||||||
\(47\) | 1.47299 | 0.214858 | 0.107429 | − | 0.994213i | \(-0.465738\pi\) | ||||
0.107429 | + | 0.994213i | \(0.465738\pi\) | |||||||
\(48\) | 10.1173 | 1.46031 | ||||||||
\(49\) | −4.76263 | −0.680376 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −16.0329 | −2.24506 | ||||||||
\(52\) | 0.0288195 | 0.00399655 | ||||||||
\(53\) | 9.96172 | 1.36835 | 0.684174 | − | 0.729319i | \(-0.260163\pi\) | ||||
0.684174 | + | 0.729319i | \(0.260163\pi\) | |||||||
\(54\) | −2.75008 | −0.374239 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.28460 | −0.572553 | ||||||||
\(57\) | 11.7623 | 1.55796 | ||||||||
\(58\) | 4.97753 | 0.653582 | ||||||||
\(59\) | 7.91122 | 1.02995 | 0.514977 | − | 0.857204i | \(-0.327801\pi\) | ||||
0.514977 | + | 0.857204i | \(0.327801\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.49744 | −0.703875 | −0.351937 | − | 0.936024i | \(-0.614477\pi\) | ||||
−0.351937 | + | 0.936024i | \(0.614477\pi\) | |||||||
\(62\) | −6.41834 | −0.815130 | ||||||||
\(63\) | 5.62128 | 0.708214 | ||||||||
\(64\) | 8.19952 | 1.02494 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.64652 | 0.695038 | ||||||||
\(67\) | 9.98877 | 1.22032 | 0.610161 | − | 0.792277i | \(-0.291105\pi\) | ||||
0.610161 | + | 0.792277i | \(0.291105\pi\) | |||||||
\(68\) | −0.324985 | −0.0394103 | ||||||||
\(69\) | −1.90878 | −0.229790 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.33755 | −1.10816 | −0.554082 | − | 0.832462i | \(-0.686931\pi\) | ||||
−0.554082 | + | 0.832462i | \(0.686931\pi\) | |||||||
\(72\) | −10.7648 | −1.26865 | ||||||||
\(73\) | −12.9880 | −1.52013 | −0.760067 | − | 0.649845i | \(-0.774834\pi\) | ||||
−0.760067 | + | 0.649845i | \(0.774834\pi\) | |||||||
\(74\) | −3.10967 | −0.361492 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.238421 | 0.0273487 | ||||||||
\(77\) | −2.32820 | −0.265323 | ||||||||
\(78\) | 1.98405 | 0.224650 | ||||||||
\(79\) | −12.9488 | −1.45685 | −0.728425 | − | 0.685126i | \(-0.759747\pi\) | ||||
−0.728425 | + | 0.685126i | \(0.759747\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.15106 | −0.683451 | ||||||||
\(82\) | 5.11738 | 0.565120 | ||||||||
\(83\) | 9.19093 | 1.00884 | 0.504418 | − | 0.863460i | \(-0.331707\pi\) | ||||
0.504418 | + | 0.863460i | \(0.331707\pi\) | |||||||
\(84\) | 0.204901 | 0.0223565 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.22009 | 0.239398 | ||||||||
\(87\) | −9.27276 | −0.994144 | ||||||||
\(88\) | 4.45855 | 0.475283 | ||||||||
\(89\) | 7.28523 | 0.772233 | 0.386116 | − | 0.922450i | \(-0.373816\pi\) | ||||
0.386116 | + | 0.922450i | \(0.373816\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.818075 | −0.0857575 | ||||||||
\(92\) | −0.0386907 | −0.00403378 | ||||||||
\(93\) | 11.9569 | 1.23987 | ||||||||
\(94\) | 2.05550 | 0.212009 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.774703 | −0.0790678 | ||||||||
\(97\) | 6.07774 | 0.617101 | 0.308551 | − | 0.951208i | \(-0.400156\pi\) | ||||
0.308551 | + | 0.951208i | \(0.400156\pi\) | |||||||
\(98\) | −6.64606 | −0.671353 | ||||||||
\(99\) | −5.84949 | −0.587896 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.7307 | 1.06774 | 0.533870 | − | 0.845566i | \(-0.320737\pi\) | ||||
0.533870 | + | 0.845566i | \(0.320737\pi\) | |||||||
\(102\) | −22.3733 | −2.21529 | ||||||||
\(103\) | −6.81952 | −0.671947 | −0.335974 | − | 0.941871i | \(-0.609065\pi\) | ||||
−0.335974 | + | 0.941871i | \(0.609065\pi\) | |||||||
\(104\) | 1.56663 | 0.153620 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13.9012 | 1.35020 | ||||||||
\(107\) | −11.0128 | −1.06465 | −0.532324 | − | 0.846540i | \(-0.678681\pi\) | ||||
−0.532324 | + | 0.846540i | \(0.678681\pi\) | |||||||
\(108\) | 0.103846 | 0.00999262 | ||||||||
\(109\) | 0.696884 | 0.0667494 | 0.0333747 | − | 0.999443i | \(-0.489375\pi\) | ||||
0.0333747 | + | 0.999443i | \(0.489375\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.79307 | 0.549854 | ||||||||
\(112\) | −5.82134 | −0.550065 | ||||||||
\(113\) | −0.767182 | −0.0721704 | −0.0360852 | − | 0.999349i | \(-0.511489\pi\) | ||||
−0.0360852 | + | 0.999349i | \(0.511489\pi\) | |||||||
\(114\) | 16.4138 | 1.53730 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.187958 | −0.0174514 | ||||||||
\(117\) | −2.05537 | −0.190019 | ||||||||
\(118\) | 11.0398 | 1.01630 | ||||||||
\(119\) | 9.22507 | 0.845661 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.57728 | −0.779752 | ||||||||
\(122\) | −7.67145 | −0.694540 | ||||||||
\(123\) | −9.53328 | −0.859587 | ||||||||
\(124\) | 0.242364 | 0.0217649 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 7.84426 | 0.698823 | ||||||||
\(127\) | −0.285703 | −0.0253520 | −0.0126760 | − | 0.999920i | \(-0.504035\pi\) | ||||
−0.0126760 | + | 0.999920i | \(0.504035\pi\) | |||||||
\(128\) | 10.8461 | 0.958668 | ||||||||
\(129\) | −4.13585 | −0.364142 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.06655 | −0.792149 | −0.396074 | − | 0.918218i | \(-0.629628\pi\) | ||||
−0.396074 | + | 0.918218i | \(0.629628\pi\) | |||||||
\(132\) | −0.213219 | −0.0185584 | ||||||||
\(133\) | −6.76784 | −0.586846 | ||||||||
\(134\) | 13.9389 | 1.20414 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −17.6662 | −1.51486 | ||||||||
\(137\) | 7.33267 | 0.626473 | 0.313236 | − | 0.949675i | \(-0.398587\pi\) | ||||
0.313236 | + | 0.949675i | \(0.398587\pi\) | |||||||
\(138\) | −2.66362 | −0.226742 | ||||||||
\(139\) | −16.4589 | −1.39602 | −0.698011 | − | 0.716087i | \(-0.745932\pi\) | ||||
−0.698011 | + | 0.716087i | \(0.745932\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.82924 | −0.322480 | ||||||||
\(142\) | −13.0302 | −1.09347 | ||||||||
\(143\) | 0.851287 | 0.0711882 | ||||||||
\(144\) | −14.6258 | −1.21882 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −18.1243 | −1.49997 | ||||||||
\(147\) | 12.3811 | 1.02117 | ||||||||
\(148\) | 0.117425 | 0.00965226 | ||||||||
\(149\) | 4.41947 | 0.362057 | 0.181029 | − | 0.983478i | \(-0.442057\pi\) | ||||
0.181029 | + | 0.983478i | \(0.442057\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.74677 | 0.142150 | 0.0710751 | − | 0.997471i | \(-0.477357\pi\) | ||||
0.0710751 | + | 0.997471i | \(0.477357\pi\) | |||||||
\(152\) | 12.9605 | 1.05124 | ||||||||
\(153\) | 23.1775 | 1.87379 | ||||||||
\(154\) | −3.24891 | −0.261805 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.0749202 | −0.00599841 | ||||||||
\(157\) | −4.91853 | −0.392541 | −0.196271 | − | 0.980550i | \(-0.562883\pi\) | ||||
−0.196271 | + | 0.980550i | \(0.562883\pi\) | |||||||
\(158\) | −18.0695 | −1.43753 | ||||||||
\(159\) | −25.8968 | −2.05375 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.09828 | 0.0865564 | ||||||||
\(162\) | −8.58355 | −0.674388 | ||||||||
\(163\) | 3.88912 | 0.304619 | 0.152310 | − | 0.988333i | \(-0.451329\pi\) | ||||
0.152310 | + | 0.988333i | \(0.451329\pi\) | |||||||
\(164\) | −0.193238 | −0.0150894 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.8256 | 0.995457 | ||||||||
\(167\) | −12.6867 | −0.981728 | −0.490864 | − | 0.871236i | \(-0.663319\pi\) | ||||
−0.490864 | + | 0.871236i | \(0.663319\pi\) | |||||||
\(168\) | 11.1384 | 0.859344 | ||||||||
\(169\) | −12.7009 | −0.976991 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −17.0039 | −1.30032 | ||||||||
\(172\) | −0.0838332 | −0.00639222 | ||||||||
\(173\) | −4.59895 | −0.349652 | −0.174826 | − | 0.984599i | \(-0.555936\pi\) | ||||
−0.174826 | + | 0.984599i | \(0.555936\pi\) | |||||||
\(174\) | −12.9398 | −0.980960 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.05768 | 0.456615 | ||||||||
\(177\) | −20.5663 | −1.54586 | ||||||||
\(178\) | 10.1662 | 0.761992 | ||||||||
\(179\) | −5.43732 | −0.406405 | −0.203202 | − | 0.979137i | \(-0.565135\pi\) | ||||
−0.203202 | + | 0.979137i | \(0.565135\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.4739 | 1.15017 | 0.575084 | − | 0.818095i | \(-0.304969\pi\) | ||||
0.575084 | + | 0.818095i | \(0.304969\pi\) | |||||||
\(182\) | −1.14159 | −0.0846203 | ||||||||
\(183\) | 14.2913 | 1.05644 | ||||||||
\(184\) | −2.10322 | −0.155051 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 16.6853 | 1.22343 | ||||||||
\(187\) | −9.59959 | −0.701992 | ||||||||
\(188\) | −0.0776183 | −0.00566089 | ||||||||
\(189\) | −2.94779 | −0.214421 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.05889 | 0.510764 | 0.255382 | − | 0.966840i | \(-0.417799\pi\) | ||||
0.255382 | + | 0.966840i | \(0.417799\pi\) | |||||||
\(192\) | −21.3157 | −1.53833 | ||||||||
\(193\) | −0.916001 | −0.0659352 | −0.0329676 | − | 0.999456i | \(-0.510496\pi\) | ||||
−0.0329676 | + | 0.999456i | \(0.510496\pi\) | |||||||
\(194\) | 8.48124 | 0.608917 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.250963 | 0.0179259 | ||||||||
\(197\) | −9.83214 | −0.700511 | −0.350255 | − | 0.936654i | \(-0.613905\pi\) | ||||
−0.350255 | + | 0.936654i | \(0.613905\pi\) | |||||||
\(198\) | −8.16273 | −0.580100 | ||||||||
\(199\) | −21.1464 | −1.49903 | −0.749514 | − | 0.661989i | \(-0.769713\pi\) | ||||
−0.749514 | + | 0.661989i | \(0.769713\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −25.9671 | −1.83158 | ||||||||
\(202\) | 14.9742 | 1.05358 | ||||||||
\(203\) | 5.33539 | 0.374471 | ||||||||
\(204\) | 0.844842 | 0.0591508 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −9.51636 | −0.663036 | ||||||||
\(207\) | 2.75937 | 0.191789 | ||||||||
\(208\) | 2.12852 | 0.147587 | ||||||||
\(209\) | 7.04260 | 0.487147 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.81286 | −0.606703 | −0.303351 | − | 0.952879i | \(-0.598106\pi\) | ||||
−0.303351 | + | 0.952879i | \(0.598106\pi\) | |||||||
\(212\) | −0.524925 | −0.0360520 | ||||||||
\(213\) | 24.2742 | 1.66324 | ||||||||
\(214\) | −15.3679 | −1.05053 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 5.64508 | 0.384099 | ||||||||
\(217\) | −6.87977 | −0.467029 | ||||||||
\(218\) | 0.972474 | 0.0658642 | ||||||||
\(219\) | 33.7641 | 2.28157 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.37307 | −0.226897 | ||||||||
\(222\) | 8.08400 | 0.542562 | ||||||||
\(223\) | −27.1229 | −1.81629 | −0.908143 | − | 0.418660i | \(-0.862500\pi\) | ||||
−0.908143 | + | 0.418660i | \(0.862500\pi\) | |||||||
\(224\) | 0.445751 | 0.0297830 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.07057 | −0.0712133 | ||||||||
\(227\) | −25.6938 | −1.70536 | −0.852680 | − | 0.522434i | \(-0.825024\pi\) | ||||
−0.852680 | + | 0.522434i | \(0.825024\pi\) | |||||||
\(228\) | −0.619806 | −0.0410477 | ||||||||
\(229\) | −20.0651 | −1.32594 | −0.662968 | − | 0.748648i | \(-0.730703\pi\) | ||||
−0.662968 | + | 0.748648i | \(0.730703\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.05247 | 0.398223 | ||||||||
\(232\) | −10.2174 | −0.670802 | ||||||||
\(233\) | 2.23570 | 0.146466 | 0.0732328 | − | 0.997315i | \(-0.476668\pi\) | ||||
0.0732328 | + | 0.997315i | \(0.476668\pi\) | |||||||
\(234\) | −2.86819 | −0.187499 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.416876 | −0.0271363 | ||||||||
\(237\) | 33.6620 | 2.18658 | ||||||||
\(238\) | 12.8732 | 0.834446 | ||||||||
\(239\) | 7.02691 | 0.454533 | 0.227267 | − | 0.973833i | \(-0.427021\pi\) | ||||
0.227267 | + | 0.973833i | \(0.427021\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | −0.0644157 | ||||||||
\(242\) | −11.9692 | −0.769412 | ||||||||
\(243\) | 21.9027 | 1.40506 | ||||||||
\(244\) | 0.289683 | 0.0185451 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −13.3033 | −0.848188 | ||||||||
\(247\) | 2.47460 | 0.157455 | ||||||||
\(248\) | 13.1749 | 0.836606 | ||||||||
\(249\) | −23.8930 | −1.51416 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.8840 | 1.38130 | 0.690652 | − | 0.723188i | \(-0.257324\pi\) | ||||
0.690652 | + | 0.723188i | \(0.257324\pi\) | |||||||
\(252\) | −0.296209 | −0.0186594 | ||||||||
\(253\) | −1.14287 | −0.0718513 | ||||||||
\(254\) | −0.398686 | −0.0250158 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.26378 | −0.0789859 | ||||||||
\(257\) | −7.72517 | −0.481883 | −0.240941 | − | 0.970540i | \(-0.577456\pi\) | ||||
−0.240941 | + | 0.970540i | \(0.577456\pi\) | |||||||
\(258\) | −5.77141 | −0.359312 | ||||||||
\(259\) | −3.33324 | −0.207117 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.4049 | 0.829742 | ||||||||
\(262\) | −12.6520 | −0.781643 | ||||||||
\(263\) | −28.0301 | −1.72841 | −0.864206 | − | 0.503138i | \(-0.832179\pi\) | ||||
−0.864206 | + | 0.503138i | \(0.832179\pi\) | |||||||
\(264\) | −11.5906 | −0.713351 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −9.44424 | −0.579064 | ||||||||
\(267\) | −18.9389 | −1.15904 | ||||||||
\(268\) | −0.526350 | −0.0321520 | ||||||||
\(269\) | 0.617409 | 0.0376441 | 0.0188221 | − | 0.999823i | \(-0.494008\pi\) | ||||
0.0188221 | + | 0.999823i | \(0.494008\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.8799 | −1.02538 | −0.512690 | − | 0.858574i | \(-0.671351\pi\) | ||||
−0.512690 | + | 0.858574i | \(0.671351\pi\) | |||||||
\(272\) | −24.0024 | −1.45536 | ||||||||
\(273\) | 2.12669 | 0.128713 | ||||||||
\(274\) | 10.2324 | 0.618165 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.100581 | 0.00605429 | ||||||||
\(277\) | −4.37569 | −0.262910 | −0.131455 | − | 0.991322i | \(-0.541965\pi\) | ||||
−0.131455 | + | 0.991322i | \(0.541965\pi\) | |||||||
\(278\) | −22.9677 | −1.37751 | ||||||||
\(279\) | −17.2851 | −1.03483 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.0475 | −1.19594 | −0.597968 | − | 0.801520i | \(-0.704025\pi\) | ||||
−0.597968 | + | 0.801520i | \(0.704025\pi\) | |||||||
\(282\) | −5.34355 | −0.318204 | ||||||||
\(283\) | −11.4403 | −0.680052 | −0.340026 | − | 0.940416i | \(-0.610436\pi\) | ||||
−0.340026 | + | 0.940416i | \(0.610436\pi\) | |||||||
\(284\) | 0.492035 | 0.0291969 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.18794 | 0.0702442 | ||||||||
\(287\) | 5.48529 | 0.323786 | ||||||||
\(288\) | 1.11993 | 0.0659924 | ||||||||
\(289\) | 21.0366 | 1.23745 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −15.7999 | −0.926206 | ||||||||
\(292\) | 0.684394 | 0.0400511 | ||||||||
\(293\) | −27.4146 | −1.60158 | −0.800789 | − | 0.598947i | \(-0.795586\pi\) | ||||
−0.800789 | + | 0.598947i | \(0.795586\pi\) | |||||||
\(294\) | 17.2773 | 1.00763 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6.38320 | 0.371016 | ||||||||
\(297\) | 3.06747 | 0.177993 | ||||||||
\(298\) | 6.16720 | 0.357256 | ||||||||
\(299\) | −0.401576 | −0.0232237 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.37970 | 0.137164 | ||||||||
\(302\) | 2.43755 | 0.140265 | ||||||||
\(303\) | −27.8958 | −1.60257 | ||||||||
\(304\) | 17.6090 | 1.00995 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 32.3433 | 1.84894 | ||||||||
\(307\) | −1.74676 | −0.0996929 | −0.0498465 | − | 0.998757i | \(-0.515873\pi\) | ||||
−0.0498465 | + | 0.998757i | \(0.515873\pi\) | |||||||
\(308\) | 0.122683 | 0.00699050 | ||||||||
\(309\) | 17.7282 | 1.00852 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.28578 | 0.186320 | 0.0931598 | − | 0.995651i | \(-0.470303\pi\) | ||||
0.0931598 | + | 0.995651i | \(0.470303\pi\) | |||||||
\(312\) | −4.07265 | −0.230569 | ||||||||
\(313\) | 24.9618 | 1.41092 | 0.705461 | − | 0.708749i | \(-0.250740\pi\) | ||||
0.705461 | + | 0.708749i | \(0.250740\pi\) | |||||||
\(314\) | −6.86361 | −0.387336 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.682325 | 0.0383838 | ||||||||
\(317\) | −13.9705 | −0.784660 | −0.392330 | − | 0.919825i | \(-0.628331\pi\) | ||||
−0.392330 | + | 0.919825i | \(0.628331\pi\) | |||||||
\(318\) | −36.1379 | −2.02651 | ||||||||
\(319\) | −5.55199 | −0.310852 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 28.6293 | 1.59793 | ||||||||
\(322\) | 1.53260 | 0.0854085 | ||||||||
\(323\) | −27.9050 | −1.55268 | ||||||||
\(324\) | 0.324125 | 0.0180070 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.42710 | 0.300579 | ||||||||
\(327\) | −1.81164 | −0.100184 | ||||||||
\(328\) | −10.5044 | −0.580009 | ||||||||
\(329\) | 2.20328 | 0.121471 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.7315 | −0.919644 | −0.459822 | − | 0.888011i | \(-0.652087\pi\) | ||||
−0.459822 | + | 0.888011i | \(0.652087\pi\) | |||||||
\(332\) | −0.484309 | −0.0265799 | ||||||||
\(333\) | −8.37459 | −0.458925 | ||||||||
\(334\) | −17.7038 | −0.968708 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 15.1333 | 0.825592 | ||||||||
\(337\) | −27.9838 | −1.52437 | −0.762187 | − | 0.647357i | \(-0.775874\pi\) | ||||
−0.762187 | + | 0.647357i | \(0.775874\pi\) | |||||||
\(338\) | −17.7236 | −0.964034 | ||||||||
\(339\) | 1.99439 | 0.108320 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.15908 | 0.387686 | ||||||||
\(342\) | −23.7282 | −1.28307 | ||||||||
\(343\) | −17.5943 | −0.950006 | ||||||||
\(344\) | −4.55716 | −0.245706 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.41765 | −0.345015 | ||||||||
\(347\) | 8.11985 | 0.435897 | 0.217948 | − | 0.975960i | \(-0.430064\pi\) | ||||
0.217948 | + | 0.975960i | \(0.430064\pi\) | |||||||
\(348\) | 0.488621 | 0.0261928 | ||||||||
\(349\) | 11.8282 | 0.633148 | 0.316574 | − | 0.948568i | \(-0.397467\pi\) | ||||
0.316574 | + | 0.948568i | \(0.397467\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.07784 | 0.0575306 | ||||||||
\(352\) | −0.463848 | −0.0247232 | ||||||||
\(353\) | −6.31287 | −0.336000 | −0.168000 | − | 0.985787i | \(-0.553731\pi\) | ||||
−0.168000 | + | 0.985787i | \(0.553731\pi\) | |||||||
\(354\) | −28.6994 | −1.52536 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.383889 | −0.0203461 | ||||||||
\(357\) | −23.9818 | −1.26925 | ||||||||
\(358\) | −7.58756 | −0.401015 | ||||||||
\(359\) | 11.1472 | 0.588325 | 0.294163 | − | 0.955755i | \(-0.404959\pi\) | ||||
0.294163 | + | 0.955755i | \(0.404959\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.47212 | 0.0774801 | ||||||||
\(362\) | 21.5932 | 1.13491 | ||||||||
\(363\) | 22.2978 | 1.17033 | ||||||||
\(364\) | 0.0431078 | 0.00225946 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 19.9429 | 1.04243 | ||||||||
\(367\) | 32.7868 | 1.71145 | 0.855727 | − | 0.517427i | \(-0.173110\pi\) | ||||
0.855727 | + | 0.517427i | \(0.173110\pi\) | |||||||
\(368\) | −2.85758 | −0.148961 | ||||||||
\(369\) | 13.7815 | 0.717437 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14.9006 | 0.773600 | ||||||||
\(372\) | −0.630057 | −0.0326669 | ||||||||
\(373\) | 16.5445 | 0.856640 | 0.428320 | − | 0.903627i | \(-0.359106\pi\) | ||||
0.428320 | + | 0.903627i | \(0.359106\pi\) | |||||||
\(374\) | −13.3958 | −0.692682 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.21932 | −0.217595 | ||||||||
\(377\) | −1.95084 | −0.100473 | ||||||||
\(378\) | −4.11353 | −0.211577 | ||||||||
\(379\) | 5.75770 | 0.295753 | 0.147877 | − | 0.989006i | \(-0.452756\pi\) | ||||
0.147877 | + | 0.989006i | \(0.452756\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.742721 | 0.0380508 | ||||||||
\(382\) | 9.85040 | 0.503990 | ||||||||
\(383\) | −6.47172 | −0.330689 | −0.165345 | − | 0.986236i | \(-0.552874\pi\) | ||||
−0.165345 | + | 0.986236i | \(0.552874\pi\) | |||||||
\(384\) | −28.1958 | −1.43886 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.27824 | −0.0650608 | ||||||||
\(387\) | 5.97888 | 0.303923 | ||||||||
\(388\) | −0.320262 | −0.0162588 | ||||||||
\(389\) | −12.2278 | −0.619975 | −0.309987 | − | 0.950741i | \(-0.600325\pi\) | ||||
−0.309987 | + | 0.950741i | \(0.600325\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.52839 | 0.229011 | ||||||||
\(392\) | 13.6423 | 0.689041 | ||||||||
\(393\) | 23.5697 | 1.18893 | ||||||||
\(394\) | −13.7203 | −0.691221 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.308234 | 0.0154894 | ||||||||
\(397\) | 1.09657 | 0.0550355 | 0.0275177 | − | 0.999621i | \(-0.491240\pi\) | ||||
0.0275177 | + | 0.999621i | \(0.491240\pi\) | |||||||
\(398\) | −29.5089 | −1.47915 | ||||||||
\(399\) | 17.5939 | 0.880796 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.55809 | 0.327495 | 0.163748 | − | 0.986502i | \(-0.447642\pi\) | ||||
0.163748 | + | 0.986502i | \(0.447642\pi\) | |||||||
\(402\) | −36.2360 | −1.80729 | ||||||||
\(403\) | 2.51553 | 0.125308 | ||||||||
\(404\) | −0.565444 | −0.0281319 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.44531 | 0.369505 | ||||||||
\(407\) | 3.46856 | 0.171930 | ||||||||
\(408\) | 45.9255 | 2.27365 | ||||||||
\(409\) | 20.0458 | 0.991202 | 0.495601 | − | 0.868550i | \(-0.334948\pi\) | ||||
0.495601 | + | 0.868550i | \(0.334948\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −19.0622 | −0.940271 | ||||||||
\(412\) | 0.359349 | 0.0177039 | ||||||||
\(413\) | 11.8335 | 0.582287 | ||||||||
\(414\) | 3.85058 | 0.189246 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.162985 | −0.00799100 | ||||||||
\(417\) | 42.7870 | 2.09529 | ||||||||
\(418\) | 9.82767 | 0.480687 | ||||||||
\(419\) | 4.90086 | 0.239423 | 0.119711 | − | 0.992809i | \(-0.461803\pi\) | ||||
0.119711 | + | 0.992809i | \(0.461803\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.63934 | −0.177371 | −0.0886853 | − | 0.996060i | \(-0.528267\pi\) | ||||
−0.0886853 | + | 0.996060i | \(0.528267\pi\) | |||||||
\(422\) | −12.2980 | −0.598657 | ||||||||
\(423\) | 5.53564 | 0.269152 | ||||||||
\(424\) | −28.5349 | −1.38578 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 33.8736 | 1.64118 | ||||||||
\(427\) | −8.22298 | −0.397938 | ||||||||
\(428\) | 0.580311 | 0.0280504 | ||||||||
\(429\) | −2.21303 | −0.106846 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.9532 | 1.05745 | 0.528725 | − | 0.848793i | \(-0.322670\pi\) | ||||
0.528725 | + | 0.848793i | \(0.322670\pi\) | |||||||
\(432\) | 7.66978 | 0.369013 | ||||||||
\(433\) | 11.2852 | 0.542331 | 0.271166 | − | 0.962533i | \(-0.412591\pi\) | ||||
0.271166 | + | 0.962533i | \(0.412591\pi\) | |||||||
\(434\) | −9.60044 | −0.460836 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.0367218 | −0.00175865 | ||||||||
\(437\) | −3.32219 | −0.158922 | ||||||||
\(438\) | 47.1164 | 2.25131 | ||||||||
\(439\) | −17.7827 | −0.848720 | −0.424360 | − | 0.905493i | \(-0.639501\pi\) | ||||
−0.424360 | + | 0.905493i | \(0.639501\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −17.8984 | −0.852303 | ||||||||
\(442\) | −4.70698 | −0.223888 | ||||||||
\(443\) | −1.37491 | −0.0653239 | −0.0326620 | − | 0.999466i | \(-0.510398\pi\) | ||||
−0.0326620 | + | 0.999466i | \(0.510398\pi\) | |||||||
\(444\) | −0.305261 | −0.0144871 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −37.8489 | −1.79220 | ||||||||
\(447\) | −11.4890 | −0.543411 | ||||||||
\(448\) | 12.2647 | 0.579453 | ||||||||
\(449\) | −7.98926 | −0.377036 | −0.188518 | − | 0.982070i | \(-0.560368\pi\) | ||||
−0.188518 | + | 0.982070i | \(0.560368\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.70798 | −0.268778 | ||||||||
\(452\) | 0.0404260 | 0.00190148 | ||||||||
\(453\) | −4.54096 | −0.213353 | ||||||||
\(454\) | −35.8547 | −1.68274 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −33.6926 | −1.57780 | ||||||||
\(457\) | 5.73846 | 0.268434 | 0.134217 | − | 0.990952i | \(-0.457148\pi\) | ||||
0.134217 | + | 0.990952i | \(0.457148\pi\) | |||||||
\(458\) | −28.0000 | −1.30835 | ||||||||
\(459\) | −12.1543 | −0.567313 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.2346 | −0.476671 | −0.238336 | − | 0.971183i | \(-0.576602\pi\) | ||||
−0.238336 | + | 0.971183i | \(0.576602\pi\) | |||||||
\(462\) | 8.44597 | 0.392942 | ||||||||
\(463\) | −36.0973 | −1.67759 | −0.838793 | − | 0.544451i | \(-0.816738\pi\) | ||||
−0.838793 | + | 0.544451i | \(0.816738\pi\) | |||||||
\(464\) | −13.8820 | −0.644455 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.11983 | 0.144523 | ||||||||
\(467\) | 17.6441 | 0.816471 | 0.408235 | − | 0.912877i | \(-0.366144\pi\) | ||||
0.408235 | + | 0.912877i | \(0.366144\pi\) | |||||||
\(468\) | 0.108306 | 0.00500646 | ||||||||
\(469\) | 14.9410 | 0.689913 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.7864 | 0.589165 | ||||||||
\(472\) | −22.6613 | −1.04307 | ||||||||
\(473\) | −2.47631 | −0.113861 | ||||||||
\(474\) | 46.9740 | 2.15759 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.486108 | −0.0222807 | ||||||||
\(477\) | 37.4370 | 1.71412 | ||||||||
\(478\) | 9.80577 | 0.448505 | ||||||||
\(479\) | −28.6326 | −1.30826 | −0.654129 | − | 0.756383i | \(-0.726965\pi\) | ||||
−0.654129 | + | 0.756383i | \(0.726965\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.21877 | 0.0555711 | ||||||||
\(482\) | −1.39546 | −0.0635614 | ||||||||
\(483\) | −2.85512 | −0.129912 | ||||||||
\(484\) | 0.451973 | 0.0205442 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 30.5643 | 1.38643 | ||||||||
\(487\) | −15.0219 | −0.680709 | −0.340355 | − | 0.940297i | \(-0.610547\pi\) | ||||
−0.340355 | + | 0.940297i | \(0.610547\pi\) | |||||||
\(488\) | 15.7471 | 0.712839 | ||||||||
\(489\) | −10.1103 | −0.457202 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.0898 | −0.771252 | −0.385626 | − | 0.922655i | \(-0.626015\pi\) | ||||
−0.385626 | + | 0.922655i | \(0.626015\pi\) | |||||||
\(492\) | 0.502349 | 0.0226476 | ||||||||
\(493\) | 21.9988 | 0.990774 | ||||||||
\(494\) | 3.45321 | 0.155367 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 17.9003 | 0.803746 | ||||||||
\(497\) | −13.9670 | −0.626504 | ||||||||
\(498\) | −33.3417 | −1.49408 | ||||||||
\(499\) | 18.3197 | 0.820101 | 0.410050 | − | 0.912063i | \(-0.365511\pi\) | ||||
0.410050 | + | 0.912063i | \(0.365511\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 32.9808 | 1.47347 | ||||||||
\(502\) | 30.5382 | 1.36298 | ||||||||
\(503\) | −37.8954 | −1.68967 | −0.844836 | − | 0.535025i | \(-0.820302\pi\) | ||||
−0.844836 | + | 0.535025i | \(0.820302\pi\) | |||||||
\(504\) | −16.1019 | −0.717234 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.59482 | −0.0708985 | ||||||||
\(507\) | 33.0176 | 1.46636 | ||||||||
\(508\) | 0.0150549 | 0.000667952 0 | ||||||||
\(509\) | 18.1079 | 0.802618 | 0.401309 | − | 0.915943i | \(-0.368555\pi\) | ||||
0.401309 | + | 0.915943i | \(0.368555\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19.4273 | −0.859412 | ||||||||
\(512\) | −23.4557 | −1.03661 | ||||||||
\(513\) | 8.91682 | 0.393687 | ||||||||
\(514\) | −10.7802 | −0.475492 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.217935 | 0.00959407 | ||||||||
\(517\) | −2.29273 | −0.100834 | ||||||||
\(518\) | −4.65139 | −0.204370 | ||||||||
\(519\) | 11.9556 | 0.524792 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.0795 | −1.27400 | −0.636998 | − | 0.770866i | \(-0.719824\pi\) | ||||
−0.636998 | + | 0.770866i | \(0.719824\pi\) | |||||||
\(522\) | 18.7060 | 0.818739 | ||||||||
\(523\) | 11.1298 | 0.486670 | 0.243335 | − | 0.969942i | \(-0.421759\pi\) | ||||
0.243335 | + | 0.969942i | \(0.421759\pi\) | |||||||
\(524\) | 0.477755 | 0.0208708 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −39.1149 | −1.70549 | ||||||||
\(527\) | −28.3665 | −1.23567 | ||||||||
\(528\) | −15.7477 | −0.685332 | ||||||||
\(529\) | −22.4609 | −0.976560 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 29.7310 | 1.29022 | ||||||||
\(532\) | 0.356626 | 0.0154617 | ||||||||
\(533\) | −2.00565 | −0.0868743 | ||||||||
\(534\) | −26.4285 | −1.14367 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −28.6123 | −1.23586 | ||||||||
\(537\) | 14.1350 | 0.609972 | ||||||||
\(538\) | 0.861569 | 0.0371449 | ||||||||
\(539\) | 7.41308 | 0.319304 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 36.6182 | 1.57434 | 0.787170 | − | 0.616736i | \(-0.211545\pi\) | ||||
0.787170 | + | 0.616736i | \(0.211545\pi\) | |||||||
\(542\) | −23.5552 | −1.01178 | ||||||||
\(543\) | −40.2265 | −1.72628 | ||||||||
\(544\) | 1.83791 | 0.0787998 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.96771 | 0.127006 | ||||||||
\(547\) | 30.0556 | 1.28508 | 0.642542 | − | 0.766251i | \(-0.277880\pi\) | ||||
0.642542 | + | 0.766251i | \(0.277880\pi\) | |||||||
\(548\) | −0.386389 | −0.0165057 | ||||||||
\(549\) | −20.6598 | −0.881740 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16.1391 | −0.687548 | ||||||||
\(552\) | 5.46759 | 0.232716 | ||||||||
\(553\) | −19.3685 | −0.823634 | ||||||||
\(554\) | −6.10609 | −0.259423 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.867287 | 0.0367812 | ||||||||
\(557\) | −1.04047 | −0.0440862 | −0.0220431 | − | 0.999757i | \(-0.507017\pi\) | ||||
−0.0220431 | + | 0.999757i | \(0.507017\pi\) | |||||||
\(558\) | −24.1206 | −1.02111 | ||||||||
\(559\) | −0.870117 | −0.0368020 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 24.9554 | 1.05362 | ||||||||
\(562\) | −27.9755 | −1.18008 | ||||||||
\(563\) | 37.5268 | 1.58157 | 0.790784 | − | 0.612096i | \(-0.209673\pi\) | ||||
0.790784 | + | 0.612096i | \(0.209673\pi\) | |||||||
\(564\) | 0.201779 | 0.00849642 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −15.9644 | −0.671034 | ||||||||
\(567\) | −9.20065 | −0.386391 | ||||||||
\(568\) | 26.7470 | 1.12228 | ||||||||
\(569\) | −29.4439 | −1.23435 | −0.617176 | − | 0.786825i | \(-0.711723\pi\) | ||||
−0.617176 | + | 0.786825i | \(0.711723\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.6027 | 0.987742 | 0.493871 | − | 0.869535i | \(-0.335581\pi\) | ||||
0.493871 | + | 0.869535i | \(0.335581\pi\) | |||||||
\(572\) | −0.0448579 | −0.00187560 | ||||||||
\(573\) | −18.3505 | −0.766604 | ||||||||
\(574\) | 7.65449 | 0.319492 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 30.8145 | 1.28394 | ||||||||
\(577\) | 42.3104 | 1.76141 | 0.880703 | − | 0.473669i | \(-0.157071\pi\) | ||||
0.880703 | + | 0.473669i | \(0.157071\pi\) | |||||||
\(578\) | 29.3557 | 1.22104 | ||||||||
\(579\) | 2.38126 | 0.0989620 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.7476 | 0.570348 | ||||||||
\(582\) | −22.0481 | −0.913923 | ||||||||
\(583\) | −15.5055 | −0.642173 | ||||||||
\(584\) | 37.2036 | 1.53949 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −38.2559 | −1.58034 | ||||||||
\(587\) | 31.7942 | 1.31229 | 0.656144 | − | 0.754636i | \(-0.272186\pi\) | ||||
0.656144 | + | 0.754636i | \(0.272186\pi\) | |||||||
\(588\) | −0.652411 | −0.0269050 | ||||||||
\(589\) | 20.8107 | 0.857490 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 25.5599 | 1.05140 | ||||||||
\(592\) | 8.67265 | 0.356444 | ||||||||
\(593\) | 21.5382 | 0.884468 | 0.442234 | − | 0.896900i | \(-0.354186\pi\) | ||||
0.442234 | + | 0.896900i | \(0.354186\pi\) | |||||||
\(594\) | 4.28053 | 0.175632 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.232881 | −0.00953916 | ||||||||
\(597\) | 54.9728 | 2.24989 | ||||||||
\(598\) | −0.560382 | −0.0229157 | ||||||||
\(599\) | 12.1627 | 0.496953 | 0.248477 | − | 0.968638i | \(-0.420070\pi\) | ||||
0.248477 | + | 0.968638i | \(0.420070\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.8351 | 1.13542 | 0.567708 | − | 0.823230i | \(-0.307830\pi\) | ||||
0.567708 | + | 0.823230i | \(0.307830\pi\) | |||||||
\(602\) | 3.32077 | 0.135345 | ||||||||
\(603\) | 37.5386 | 1.52869 | ||||||||
\(604\) | −0.0920447 | −0.00374525 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −38.9274 | −1.58132 | ||||||||
\(607\) | 16.6194 | 0.674562 | 0.337281 | − | 0.941404i | \(-0.390493\pi\) | ||||
0.337281 | + | 0.941404i | \(0.390493\pi\) | |||||||
\(608\) | −1.34836 | −0.0546831 | ||||||||
\(609\) | −13.8700 | −0.562042 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.805611 | −0.0325915 | ||||||||
\(612\) | −1.22132 | −0.0493690 | ||||||||
\(613\) | 37.9319 | 1.53205 | 0.766027 | − | 0.642809i | \(-0.222231\pi\) | ||||
0.766027 | + | 0.642809i | \(0.222231\pi\) | |||||||
\(614\) | −2.43753 | −0.0983708 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.66902 | 0.268702 | ||||||||
\(617\) | 5.11850 | 0.206063 | 0.103032 | − | 0.994678i | \(-0.467146\pi\) | ||||
0.103032 | + | 0.994678i | \(0.467146\pi\) | |||||||
\(618\) | 24.7390 | 0.995150 | ||||||||
\(619\) | −29.4556 | −1.18392 | −0.591960 | − | 0.805967i | \(-0.701646\pi\) | ||||
−0.591960 | + | 0.805967i | \(0.701646\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.44701 | −0.0580665 | ||||||||
\(622\) | 4.58517 | 0.183849 | ||||||||
\(623\) | 10.8971 | 0.436584 | ||||||||
\(624\) | −5.53338 | −0.221512 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 34.8331 | 1.39221 | ||||||||
\(627\) | −18.3082 | −0.731158 | ||||||||
\(628\) | 0.259178 | 0.0103423 | ||||||||
\(629\) | −13.7435 | −0.547990 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.6744 | 1.45998 | 0.729992 | − | 0.683456i | \(-0.239524\pi\) | ||||
0.729992 | + | 0.683456i | \(0.239524\pi\) | |||||||
\(632\) | 37.0911 | 1.47540 | ||||||||
\(633\) | 22.9102 | 0.910599 | ||||||||
\(634\) | −19.4952 | −0.774254 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.36461 | 0.0541104 | ||||||||
\(637\) | 2.60478 | 0.103205 | ||||||||
\(638\) | −7.74758 | −0.306730 | ||||||||
\(639\) | −35.0913 | −1.38819 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −48.5952 | −1.91940 | −0.959698 | − | 0.281035i | \(-0.909322\pi\) | ||||
−0.959698 | + | 0.281035i | \(0.909322\pi\) | |||||||
\(642\) | 39.9510 | 1.57674 | ||||||||
\(643\) | −2.40148 | −0.0947050 | −0.0473525 | − | 0.998878i | \(-0.515078\pi\) | ||||
−0.0473525 | + | 0.998878i | \(0.515078\pi\) | |||||||
\(644\) | −0.0578728 | −0.00228051 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −38.9403 | −1.53209 | ||||||||
\(647\) | −10.6830 | −0.419993 | −0.209997 | − | 0.977702i | \(-0.567345\pi\) | ||||
−0.209997 | + | 0.977702i | \(0.567345\pi\) | |||||||
\(648\) | 17.6194 | 0.692156 | ||||||||
\(649\) | −12.3139 | −0.483363 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 17.8849 | 0.700963 | ||||||||
\(652\) | −0.204934 | −0.00802583 | ||||||||
\(653\) | −39.8844 | −1.56080 | −0.780399 | − | 0.625282i | \(-0.784984\pi\) | ||||
−0.780399 | + | 0.625282i | \(0.784984\pi\) | |||||||
\(654\) | −2.52807 | −0.0988555 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −14.2720 | −0.557228 | ||||||||
\(657\) | −48.8101 | −1.90426 | ||||||||
\(658\) | 3.07459 | 0.119860 | ||||||||
\(659\) | 12.5725 | 0.489753 | 0.244877 | − | 0.969554i | \(-0.421253\pi\) | ||||
0.244877 | + | 0.969554i | \(0.421253\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.9933 | −0.583174 | −0.291587 | − | 0.956544i | \(-0.594183\pi\) | ||||
−0.291587 | + | 0.956544i | \(0.594183\pi\) | |||||||
\(662\) | −23.3481 | −0.907448 | ||||||||
\(663\) | 8.76873 | 0.340549 | ||||||||
\(664\) | −26.3270 | −1.02168 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −11.6864 | −0.452839 | ||||||||
\(667\) | 2.61903 | 0.101409 | ||||||||
\(668\) | 0.668516 | 0.0258657 | ||||||||
\(669\) | 70.5096 | 2.72606 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.55682 | 0.330332 | ||||||||
\(672\) | −1.15879 | −0.0447012 | ||||||||
\(673\) | −26.5273 | −1.02255 | −0.511277 | − | 0.859416i | \(-0.670827\pi\) | ||||
−0.511277 | + | 0.859416i | \(0.670827\pi\) | |||||||
\(674\) | −39.0502 | −1.50416 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.669263 | 0.0257409 | ||||||||
\(677\) | 41.7855 | 1.60595 | 0.802973 | − | 0.596015i | \(-0.203250\pi\) | ||||
0.802973 | + | 0.596015i | \(0.203250\pi\) | |||||||
\(678\) | 2.78309 | 0.106884 | ||||||||
\(679\) | 9.09098 | 0.348880 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 66.7945 | 2.55957 | ||||||||
\(682\) | 9.99021 | 0.382545 | ||||||||
\(683\) | −9.83634 | −0.376377 | −0.188188 | − | 0.982133i | \(-0.560262\pi\) | ||||
−0.188188 | + | 0.982133i | \(0.560262\pi\) | |||||||
\(684\) | 0.896005 | 0.0342596 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −24.5522 | −0.937407 | ||||||||
\(687\) | 52.1617 | 1.99009 | ||||||||
\(688\) | −6.19167 | −0.236055 | ||||||||
\(689\) | −5.44827 | −0.207563 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −34.1488 | −1.29908 | −0.649541 | − | 0.760327i | \(-0.725039\pi\) | ||||
−0.649541 | + | 0.760327i | \(0.725039\pi\) | |||||||
\(692\) | 0.242338 | 0.00921231 | ||||||||
\(693\) | −8.74958 | −0.332369 | ||||||||
\(694\) | 11.3309 | 0.430116 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 26.5614 | 1.00681 | ||||||||
\(697\) | 22.6168 | 0.856673 | ||||||||
\(698\) | 16.5057 | 0.624752 | ||||||||
\(699\) | −5.81200 | −0.219830 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.15872 | 0.119303 | 0.0596517 | − | 0.998219i | \(-0.481001\pi\) | ||||
0.0596517 | + | 0.998219i | \(0.481001\pi\) | |||||||
\(702\) | 1.50408 | 0.0567677 | ||||||||
\(703\) | 10.0827 | 0.380278 | ||||||||
\(704\) | −12.7626 | −0.481010 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.80935 | −0.331544 | ||||||||
\(707\) | 16.0507 | 0.603650 | ||||||||
\(708\) | 1.08372 | 0.0407288 | ||||||||
\(709\) | 2.50229 | 0.0939753 | 0.0469876 | − | 0.998895i | \(-0.485038\pi\) | ||||
0.0469876 | + | 0.998895i | \(0.485038\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −48.6625 | −1.82499 | ||||||||
\(712\) | −20.8682 | −0.782068 | ||||||||
\(713\) | −3.37714 | −0.126475 | ||||||||
\(714\) | −33.4656 | −1.25242 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.286515 | 0.0107076 | ||||||||
\(717\) | −18.2674 | −0.682208 | ||||||||
\(718\) | 15.5554 | 0.580523 | ||||||||
\(719\) | −31.0417 | −1.15766 | −0.578830 | − | 0.815448i | \(-0.696490\pi\) | ||||
−0.578830 | + | 0.815448i | \(0.696490\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.2005 | −0.379887 | ||||||||
\(722\) | 2.05429 | 0.0764526 | ||||||||
\(723\) | 2.59963 | 0.0966813 | ||||||||
\(724\) | −0.815386 | −0.0303036 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 31.1156 | 1.15481 | ||||||||
\(727\) | 11.0652 | 0.410386 | 0.205193 | − | 0.978722i | \(-0.434218\pi\) | ||||
0.205193 | + | 0.978722i | \(0.434218\pi\) | |||||||
\(728\) | 2.34333 | 0.0868498 | ||||||||
\(729\) | −38.4858 | −1.42540 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.81192 | 0.362907 | ||||||||
\(732\) | −0.753069 | −0.0278342 | ||||||||
\(733\) | −6.43274 | −0.237599 | −0.118799 | − | 0.992918i | \(-0.537905\pi\) | ||||
−0.118799 | + | 0.992918i | \(0.537905\pi\) | |||||||
\(734\) | 45.7526 | 1.68876 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.218810 | 0.00806544 | ||||||||
\(737\) | −15.5476 | −0.572704 | ||||||||
\(738\) | 19.2315 | 0.707923 | ||||||||
\(739\) | −13.6029 | −0.500392 | −0.250196 | − | 0.968195i | \(-0.580495\pi\) | ||||
−0.250196 | + | 0.968195i | \(0.580495\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.43306 | −0.236324 | ||||||||
\(742\) | 20.7932 | 0.763341 | ||||||||
\(743\) | 21.7856 | 0.799237 | 0.399618 | − | 0.916682i | \(-0.369143\pi\) | ||||
0.399618 | + | 0.916682i | \(0.369143\pi\) | |||||||
\(744\) | −34.2498 | −1.25566 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 23.0871 | 0.845279 | ||||||||
\(747\) | 34.5403 | 1.26376 | ||||||||
\(748\) | 0.505843 | 0.0184954 | ||||||||
\(749\) | −16.4728 | −0.601902 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.2742 | −0.520872 | −0.260436 | − | 0.965491i | \(-0.583866\pi\) | ||||
−0.260436 | + | 0.965491i | \(0.583866\pi\) | |||||||
\(752\) | −5.73265 | −0.209048 | ||||||||
\(753\) | −56.8902 | −2.07319 | ||||||||
\(754\) | −2.72232 | −0.0991409 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.155332 | 0.00564936 | ||||||||
\(757\) | −47.4470 | −1.72449 | −0.862245 | − | 0.506492i | \(-0.830942\pi\) | ||||
−0.862245 | + | 0.506492i | \(0.830942\pi\) | |||||||
\(758\) | 8.03464 | 0.291831 | ||||||||
\(759\) | 2.97103 | 0.107842 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.87598 | 0.104254 | 0.0521270 | − | 0.998640i | \(-0.483400\pi\) | ||||
0.0521270 | + | 0.998640i | \(0.483400\pi\) | |||||||
\(762\) | 1.03644 | 0.0375462 | ||||||||
\(763\) | 1.04239 | 0.0377370 | ||||||||
\(764\) | −0.371963 | −0.0134571 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.03102 | −0.326304 | ||||||||
\(767\) | −4.32681 | −0.156232 | ||||||||
\(768\) | 3.28535 | 0.118550 | ||||||||
\(769\) | 35.9147 | 1.29512 | 0.647559 | − | 0.762015i | \(-0.275790\pi\) | ||||
0.647559 | + | 0.762015i | \(0.275790\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.0826 | 0.723257 | ||||||||
\(772\) | 0.0482679 | 0.00173720 | ||||||||
\(773\) | −21.3574 | −0.768172 | −0.384086 | − | 0.923297i | \(-0.625483\pi\) | ||||
−0.384086 | + | 0.923297i | \(0.625483\pi\) | |||||||
\(774\) | 8.34328 | 0.299893 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −17.4094 | −0.624961 | ||||||||
\(777\) | 8.66518 | 0.310862 | ||||||||
\(778\) | −17.0634 | −0.611753 | ||||||||
\(779\) | −16.5925 | −0.594488 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.5340 | 0.520067 | ||||||||
\(782\) | 6.31919 | 0.225974 | ||||||||
\(783\) | −7.02952 | −0.251215 | ||||||||
\(784\) | 18.5354 | 0.661978 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 32.8905 | 1.17317 | ||||||||
\(787\) | 37.9490 | 1.35274 | 0.676368 | − | 0.736564i | \(-0.263553\pi\) | ||||
0.676368 | + | 0.736564i | \(0.263553\pi\) | |||||||
\(788\) | 0.518097 | 0.0184564 | ||||||||
\(789\) | 72.8680 | 2.59417 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.14754 | −0.0408018 | ||||||||
\(792\) | 16.7556 | 0.595384 | ||||||||
\(793\) | 3.00666 | 0.106770 | ||||||||
\(794\) | 1.53022 | 0.0543056 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.11429 | 0.0394950 | ||||||||
\(797\) | −0.639305 | −0.0226454 | −0.0113227 | − | 0.999936i | \(-0.503604\pi\) | ||||
−0.0113227 | + | 0.999936i | \(0.503604\pi\) | |||||||
\(798\) | 24.5516 | 0.869116 | ||||||||
\(799\) | 9.08452 | 0.321387 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 27.3785 | 0.967372 | ||||||||
\(802\) | 9.15155 | 0.323152 | ||||||||
\(803\) | 20.2160 | 0.713407 | ||||||||
\(804\) | 1.36832 | 0.0482568 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.51032 | 0.123646 | ||||||||
\(807\) | −1.60504 | −0.0565000 | ||||||||
\(808\) | −30.7375 | −1.08134 | ||||||||
\(809\) | 33.4426 | 1.17578 | 0.587890 | − | 0.808941i | \(-0.299959\pi\) | ||||
0.587890 | + | 0.808941i | \(0.299959\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 47.2141 | 1.65791 | 0.828955 | − | 0.559315i | \(-0.188936\pi\) | ||||
0.828955 | + | 0.559315i | \(0.188936\pi\) | |||||||
\(812\) | −0.281144 | −0.00986622 | ||||||||
\(813\) | 43.8815 | 1.53899 | ||||||||
\(814\) | 4.84023 | 0.169650 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 62.3975 | 2.18435 | ||||||||
\(817\) | −7.19838 | −0.251839 | ||||||||
\(818\) | 27.9731 | 0.978058 | ||||||||
\(819\) | −3.07439 | −0.107428 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −43.9114 | −1.53252 | −0.766259 | − | 0.642532i | \(-0.777884\pi\) | ||||
−0.766259 | + | 0.642532i | \(0.777884\pi\) | |||||||
\(822\) | −26.6006 | −0.927802 | ||||||||
\(823\) | 4.44055 | 0.154788 | 0.0773939 | − | 0.997001i | \(-0.475340\pi\) | ||||
0.0773939 | + | 0.997001i | \(0.475340\pi\) | |||||||
\(824\) | 19.5342 | 0.680505 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 16.5131 | 0.574565 | ||||||||
\(827\) | −28.1589 | −0.979180 | −0.489590 | − | 0.871953i | \(-0.662854\pi\) | ||||
−0.489590 | + | 0.871953i | \(0.662854\pi\) | |||||||
\(828\) | −0.145403 | −0.00505309 | ||||||||
\(829\) | 9.65478 | 0.335325 | 0.167662 | − | 0.985844i | \(-0.446378\pi\) | ||||
0.167662 | + | 0.985844i | \(0.446378\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.3752 | 0.394601 | ||||||||
\(832\) | −4.48449 | −0.155472 | ||||||||
\(833\) | −29.3730 | −1.01771 | ||||||||
\(834\) | 59.7075 | 2.06750 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.371104 | −0.0128349 | ||||||||
\(837\) | 9.06429 | 0.313308 | ||||||||
\(838\) | 6.83895 | 0.236248 | ||||||||
\(839\) | −43.0759 | −1.48715 | −0.743573 | − | 0.668655i | \(-0.766870\pi\) | ||||
−0.743573 | + | 0.668655i | \(0.766870\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.2769 | −0.561271 | ||||||||
\(842\) | −5.07855 | −0.175018 | ||||||||
\(843\) | 52.1162 | 1.79498 | ||||||||
\(844\) | 0.464387 | 0.0159849 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 7.72475 | 0.265582 | ||||||||
\(847\) | −12.8297 | −0.440835 | ||||||||
\(848\) | −38.7694 | −1.33135 | ||||||||
\(849\) | 29.7404 | 1.02069 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.63622 | −0.0560887 | ||||||||
\(852\) | −1.27911 | −0.0438216 | ||||||||
\(853\) | −11.0630 | −0.378791 | −0.189395 | − | 0.981901i | \(-0.560653\pi\) | ||||
−0.189395 | + | 0.981901i | \(0.560653\pi\) | |||||||
\(854\) | −11.4748 | −0.392660 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 31.5457 | 1.07821 | ||||||||
\(857\) | 32.8888 | 1.12346 | 0.561730 | − | 0.827320i | \(-0.310136\pi\) | ||||
0.561730 | + | 0.827320i | \(0.310136\pi\) | |||||||
\(858\) | −3.08820 | −0.105429 | ||||||||
\(859\) | −26.4534 | −0.902579 | −0.451289 | − | 0.892378i | \(-0.649036\pi\) | ||||
−0.451289 | + | 0.892378i | \(0.649036\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.2597 | −0.485970 | ||||||||
\(862\) | 30.6349 | 1.04343 | ||||||||
\(863\) | 17.2512 | 0.587238 | 0.293619 | − | 0.955922i | \(-0.405140\pi\) | ||||
0.293619 | + | 0.955922i | \(0.405140\pi\) | |||||||
\(864\) | −0.587290 | −0.0199800 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 15.7480 | 0.535139 | ||||||||
\(867\) | −54.6874 | −1.85728 | ||||||||
\(868\) | 0.362524 | 0.0123049 | ||||||||
\(869\) | 20.1549 | 0.683707 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.46306 | −0.185109 | ||||||||
\(872\) | −1.99619 | −0.0675996 | ||||||||
\(873\) | 22.8407 | 0.773039 | ||||||||
\(874\) | −4.63598 | −0.156814 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.77917 | −0.0601126 | ||||||||
\(877\) | 5.63475 | 0.190272 | 0.0951360 | − | 0.995464i | \(-0.469671\pi\) | ||||
0.0951360 | + | 0.995464i | \(0.469671\pi\) | |||||||
\(878\) | −24.8150 | −0.837465 | ||||||||
\(879\) | 71.2678 | 2.40380 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −40.2057 | −1.35456 | −0.677282 | − | 0.735723i | \(-0.736842\pi\) | ||||
−0.677282 | + | 0.735723i | \(0.736842\pi\) | |||||||
\(882\) | −24.9764 | −0.841000 | ||||||||
\(883\) | −22.0100 | −0.740697 | −0.370349 | − | 0.928893i | \(-0.620762\pi\) | ||||
−0.370349 | + | 0.928893i | \(0.620762\pi\) | |||||||
\(884\) | 0.177741 | 0.00597808 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.91863 | −0.0644576 | ||||||||
\(887\) | 45.8151 | 1.53832 | 0.769161 | − | 0.639055i | \(-0.220674\pi\) | ||||
0.769161 | + | 0.639055i | \(0.220674\pi\) | |||||||
\(888\) | −16.5940 | −0.556857 | ||||||||
\(889\) | −0.427349 | −0.0143328 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.57419 | 0.320747 | ||||||||
\(892\) | 1.42922 | 0.0478539 | ||||||||
\(893\) | −6.66473 | −0.223027 | ||||||||
\(894\) | −16.0324 | −0.536205 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 16.2234 | 0.541986 | ||||||||
\(897\) | 1.04395 | 0.0348564 | ||||||||
\(898\) | −11.1487 | −0.372036 | ||||||||
\(899\) | −16.4060 | −0.547171 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 61.4378 | 2.04679 | ||||||||
\(902\) | −7.96525 | −0.265214 | ||||||||
\(903\) | −6.18634 | −0.205868 | ||||||||
\(904\) | 2.19755 | 0.0730896 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −6.33672 | −0.210524 | ||||||||
\(907\) | 53.4694 | 1.77542 | 0.887712 | − | 0.460399i | \(-0.152294\pi\) | ||||
0.887712 | + | 0.460399i | \(0.152294\pi\) | |||||||
\(908\) | 1.35392 | 0.0449313 | ||||||||
\(909\) | 40.3267 | 1.33755 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.0764 | −0.532634 | −0.266317 | − | 0.963886i | \(-0.585807\pi\) | ||||
−0.266317 | + | 0.963886i | \(0.585807\pi\) | |||||||
\(912\) | −45.7770 | −1.51583 | ||||||||
\(913\) | −14.3058 | −0.473452 | ||||||||
\(914\) | 8.00778 | 0.264874 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.05731 | 0.0349346 | ||||||||
\(917\) | −13.5616 | −0.447844 | ||||||||
\(918\) | −16.9608 | −0.559790 | ||||||||
\(919\) | −31.6187 | −1.04301 | −0.521503 | − | 0.853250i | \(-0.674628\pi\) | ||||
−0.521503 | + | 0.853250i | \(0.674628\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.54093 | 0.149629 | ||||||||
\(922\) | −14.2819 | −0.470350 | ||||||||
\(923\) | 5.10690 | 0.168096 | ||||||||
\(924\) | −0.318930 | −0.0104920 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −50.3724 | −1.65534 | ||||||||
\(927\) | −25.6283 | −0.841744 | ||||||||
\(928\) | 1.06297 | 0.0348937 | ||||||||
\(929\) | 7.78861 | 0.255536 | 0.127768 | − | 0.991804i | \(-0.459219\pi\) | ||||
0.127768 | + | 0.991804i | \(0.459219\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21.5491 | 0.706242 | ||||||||
\(932\) | −0.117808 | −0.00385894 | ||||||||
\(933\) | −8.54182 | −0.279647 | ||||||||
\(934\) | 24.6216 | 0.805643 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.88751 | 0.192439 | ||||||||
\(937\) | −14.6575 | −0.478838 | −0.239419 | − | 0.970916i | \(-0.576957\pi\) | ||||
−0.239419 | + | 0.970916i | \(0.576957\pi\) | |||||||
\(938\) | 20.8496 | 0.680764 | ||||||||
\(939\) | −64.8914 | −2.11765 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.3781 | −0.794703 | −0.397352 | − | 0.917666i | \(-0.630071\pi\) | ||||
−0.397352 | + | 0.917666i | \(0.630071\pi\) | |||||||
\(942\) | 17.8429 | 0.581351 | ||||||||
\(943\) | 2.69261 | 0.0876835 | ||||||||
\(944\) | −30.7892 | −1.00210 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.45559 | −0.112351 | ||||||||
\(947\) | 18.4596 | 0.599857 | 0.299928 | − | 0.953962i | \(-0.403037\pi\) | ||||
0.299928 | + | 0.953962i | \(0.403037\pi\) | |||||||
\(948\) | −1.77379 | −0.0576101 | ||||||||
\(949\) | 7.10342 | 0.230587 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 36.3181 | 1.17769 | ||||||||
\(952\) | −26.4248 | −0.856431 | ||||||||
\(953\) | −28.1238 | −0.911020 | −0.455510 | − | 0.890231i | \(-0.650543\pi\) | ||||
−0.455510 | + | 0.890231i | \(0.650543\pi\) | |||||||
\(954\) | 52.2418 | 1.69139 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.370277 | −0.0119756 | ||||||||
\(957\) | 14.4331 | 0.466557 | ||||||||
\(958\) | −39.9557 | −1.29091 | ||||||||
\(959\) | 10.9681 | 0.354178 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.84511 | −0.317584 | ||||||||
\(962\) | 1.70074 | 0.0548341 | ||||||||
\(963\) | −41.3871 | −1.33368 | ||||||||
\(964\) | 0.0526942 | 0.00169717 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −3.98420 | −0.128189 | ||||||||
\(967\) | −6.01949 | −0.193574 | −0.0967869 | − | 0.995305i | \(-0.530857\pi\) | ||||
−0.0967869 | + | 0.995305i | \(0.530857\pi\) | |||||||
\(968\) | 24.5692 | 0.789684 | ||||||||
\(969\) | 72.5428 | 2.33041 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.4218 | −0.880008 | −0.440004 | − | 0.897996i | \(-0.645023\pi\) | ||||
−0.440004 | + | 0.897996i | \(0.645023\pi\) | |||||||
\(972\) | −1.15415 | −0.0370192 | ||||||||
\(973\) | −24.6189 | −0.789246 | ||||||||
\(974\) | −20.9625 | −0.671682 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 21.3951 | 0.684841 | ||||||||
\(977\) | −14.9584 | −0.478561 | −0.239280 | − | 0.970951i | \(-0.576911\pi\) | ||||
−0.239280 | + | 0.970951i | \(0.576911\pi\) | |||||||
\(978\) | −14.1085 | −0.451139 | ||||||||
\(979\) | −11.3395 | −0.362413 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.61895 | 0.0836166 | ||||||||
\(982\) | −23.8481 | −0.761024 | ||||||||
\(983\) | −20.0229 | −0.638631 | −0.319316 | − | 0.947648i | \(-0.603453\pi\) | ||||
−0.319316 | + | 0.947648i | \(0.603453\pi\) | |||||||
\(984\) | 27.3076 | 0.870535 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 30.6984 | 0.977635 | ||||||||
\(987\) | −5.72772 | −0.182315 | ||||||||
\(988\) | −0.130397 | −0.00414849 | ||||||||
\(989\) | 1.16814 | 0.0371448 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.9116 | −1.04547 | −0.522736 | − | 0.852495i | \(-0.675089\pi\) | ||||
−0.522736 | + | 0.852495i | \(0.675089\pi\) | |||||||
\(992\) | −1.37066 | −0.0435184 | ||||||||
\(993\) | 43.4956 | 1.38029 | ||||||||
\(994\) | −19.4903 | −0.618195 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.25902 | 0.0398937 | ||||||||
\(997\) | 27.1461 | 0.859726 | 0.429863 | − | 0.902894i | \(-0.358562\pi\) | ||||
0.429863 | + | 0.902894i | \(0.358562\pi\) | |||||||
\(998\) | 25.5643 | 0.809225 | ||||||||
\(999\) | 4.39163 | 0.138945 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6025.2.a.i.1.12 | 15 | ||
5.4 | even | 2 | 1205.2.a.c.1.4 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1205.2.a.c.1.4 | ✓ | 15 | 5.4 | even | 2 | ||
6025.2.a.i.1.12 | 15 | 1.1 | even | 1 | trivial |