Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(47.9341963334\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.395940 | 0.279972 | 0.139986 | − | 0.990153i | \(-0.455294\pi\) | ||||
0.139986 | + | 0.990153i | \(0.455294\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.84323 | −0.921616 | ||||||||
\(5\) | −0.579308 | −0.259074 | −0.129537 | − | 0.991575i | \(-0.541349\pi\) | ||||
−0.129537 | + | 0.991575i | \(0.541349\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.59556 | −0.981031 | −0.490515 | − | 0.871433i | \(-0.663191\pi\) | ||||
−0.490515 | + | 0.871433i | \(0.663191\pi\) | |||||||
\(8\) | −1.52169 | −0.537999 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.229371 | −0.0725336 | ||||||||
\(11\) | 1.87640 | 0.565756 | 0.282878 | − | 0.959156i | \(-0.408711\pi\) | ||||
0.282878 | + | 0.959156i | \(0.408711\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.20966 | −1.72225 | −0.861124 | − | 0.508394i | \(-0.830239\pi\) | ||||
−0.861124 | + | 0.508394i | \(0.830239\pi\) | |||||||
\(14\) | −1.02769 | −0.274661 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.08396 | 0.770991 | ||||||||
\(17\) | 4.01505 | 0.973794 | 0.486897 | − | 0.873459i | \(-0.338129\pi\) | ||||
0.486897 | + | 0.873459i | \(0.338129\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.79036 | −0.640152 | −0.320076 | − | 0.947392i | \(-0.603708\pi\) | ||||
−0.320076 | + | 0.947392i | \(0.603708\pi\) | |||||||
\(20\) | 1.06780 | 0.238767 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.742943 | 0.158396 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.66440 | −0.932880 | ||||||||
\(26\) | −2.45865 | −0.482182 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.78422 | 0.904133 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.08724 | −0.554485 | −0.277242 | − | 0.960800i | \(-0.589420\pi\) | ||||
−0.277242 | + | 0.960800i | \(0.589420\pi\) | |||||||
\(32\) | 4.26445 | 0.753855 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.58972 | 0.272635 | ||||||||
\(35\) | 1.50363 | 0.254160 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.22901 | −0.530846 | −0.265423 | − | 0.964132i | \(-0.585512\pi\) | ||||
−0.265423 | + | 0.964132i | \(0.585512\pi\) | |||||||
\(38\) | −1.10481 | −0.179225 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.881527 | 0.139382 | ||||||||
\(41\) | −8.40860 | −1.31320 | −0.656602 | − | 0.754238i | \(-0.728007\pi\) | ||||
−0.656602 | + | 0.754238i | \(0.728007\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.56696 | −1.00145 | −0.500726 | − | 0.865606i | \(-0.666934\pi\) | ||||
−0.500726 | + | 0.865606i | \(0.666934\pi\) | |||||||
\(44\) | −3.45864 | −0.521410 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.395940 | 0.0583782 | ||||||||
\(47\) | −0.0783194 | −0.0114241 | −0.00571203 | − | 0.999984i | \(-0.501818\pi\) | ||||
−0.00571203 | + | 0.999984i | \(0.501818\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.263051 | −0.0375788 | ||||||||
\(50\) | −1.84683 | −0.261181 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 11.4458 | 1.58725 | ||||||||
\(53\) | 9.39482 | 1.29048 | 0.645239 | − | 0.763981i | \(-0.276758\pi\) | ||||
0.645239 | + | 0.763981i | \(0.276758\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.08701 | −0.146573 | ||||||||
\(56\) | 3.94964 | 0.527793 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.395940 | −0.0519895 | ||||||||
\(59\) | −7.94475 | −1.03432 | −0.517159 | − | 0.855889i | \(-0.673011\pi\) | ||||
−0.517159 | + | 0.855889i | \(0.673011\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.00728 | −1.15326 | −0.576632 | − | 0.817004i | \(-0.695633\pi\) | ||||
−0.576632 | + | 0.817004i | \(0.695633\pi\) | |||||||
\(62\) | −1.22236 | −0.155240 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.47946 | −0.559933 | ||||||||
\(65\) | 3.59730 | 0.446190 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.596834 | 0.0729149 | 0.0364574 | − | 0.999335i | \(-0.488393\pi\) | ||||
0.0364574 | + | 0.999335i | \(0.488393\pi\) | |||||||
\(68\) | −7.40067 | −0.897463 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.595348 | 0.0711577 | ||||||||
\(71\) | 4.73876 | 0.562387 | 0.281194 | − | 0.959651i | \(-0.409270\pi\) | ||||
0.281194 | + | 0.959651i | \(0.409270\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.703822 | 0.0823762 | 0.0411881 | − | 0.999151i | \(-0.486886\pi\) | ||||
0.0411881 | + | 0.999151i | \(0.486886\pi\) | |||||||
\(74\) | −1.27850 | −0.148622 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.14327 | 0.589974 | ||||||||
\(77\) | −4.87032 | −0.555024 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.70957 | 0.304851 | 0.152425 | − | 0.988315i | \(-0.451292\pi\) | ||||
0.152425 | + | 0.988315i | \(0.451292\pi\) | |||||||
\(80\) | −1.78656 | −0.199744 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.32931 | −0.367660 | ||||||||
\(83\) | −9.68330 | −1.06288 | −0.531440 | − | 0.847096i | \(-0.678349\pi\) | ||||
−0.531440 | + | 0.847096i | \(0.678349\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.32595 | −0.252285 | ||||||||
\(86\) | −2.60012 | −0.280379 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.85530 | −0.304376 | ||||||||
\(89\) | 9.96833 | 1.05664 | 0.528321 | − | 0.849045i | \(-0.322822\pi\) | ||||
0.528321 | + | 0.849045i | \(0.322822\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.1176 | 1.68958 | ||||||||
\(92\) | −1.84323 | −0.192170 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.0310098 | −0.00319842 | ||||||||
\(95\) | 1.61648 | 0.165847 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.0713 | 1.22566 | 0.612829 | − | 0.790215i | \(-0.290031\pi\) | ||||
0.612829 | + | 0.790215i | \(0.290031\pi\) | |||||||
\(98\) | −0.104153 | −0.0105210 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 8.59757 | 0.859757 | ||||||||
\(101\) | −1.15152 | −0.114581 | −0.0572903 | − | 0.998358i | \(-0.518246\pi\) | ||||
−0.0572903 | + | 0.998358i | \(0.518246\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.06395 | 0.794565 | 0.397282 | − | 0.917696i | \(-0.369953\pi\) | ||||
0.397282 | + | 0.917696i | \(0.369953\pi\) | |||||||
\(104\) | 9.44917 | 0.926568 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.71979 | 0.361298 | ||||||||
\(107\) | 6.95139 | 0.672016 | 0.336008 | − | 0.941859i | \(-0.390923\pi\) | ||||
0.336008 | + | 0.941859i | \(0.390923\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.35459 | 0.800225 | 0.400112 | − | 0.916466i | \(-0.368971\pi\) | ||||
0.400112 | + | 0.916466i | \(0.368971\pi\) | |||||||
\(110\) | −0.430393 | −0.0410363 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −8.00462 | −0.756366 | ||||||||
\(113\) | 3.30753 | 0.311146 | 0.155573 | − | 0.987824i | \(-0.450278\pi\) | ||||
0.155573 | + | 0.987824i | \(0.450278\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.579308 | −0.0540207 | ||||||||
\(116\) | 1.84323 | 0.171140 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.14565 | −0.289580 | ||||||||
\(119\) | −10.4213 | −0.955321 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.47912 | −0.679920 | ||||||||
\(122\) | −3.56635 | −0.322882 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.69050 | 0.511022 | ||||||||
\(125\) | 5.59866 | 0.500760 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.82193 | 0.161670 | 0.0808350 | − | 0.996727i | \(-0.474241\pi\) | ||||
0.0808350 | + | 0.996727i | \(0.474241\pi\) | |||||||
\(128\) | −10.3025 | −0.910620 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.42432 | 0.124921 | ||||||||
\(131\) | 19.4572 | 1.69999 | 0.849993 | − | 0.526794i | \(-0.176606\pi\) | ||||
0.849993 | + | 0.526794i | \(0.176606\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.24255 | 0.628008 | ||||||||
\(134\) | 0.236311 | 0.0204141 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.10967 | −0.523900 | ||||||||
\(137\) | −15.9089 | −1.35919 | −0.679593 | − | 0.733589i | \(-0.737844\pi\) | ||||
−0.679593 | + | 0.733589i | \(0.737844\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.26742 | −0.616414 | −0.308207 | − | 0.951319i | \(-0.599729\pi\) | ||||
−0.308207 | + | 0.951319i | \(0.599729\pi\) | |||||||
\(140\) | −2.77154 | −0.234238 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.87627 | 0.157453 | ||||||||
\(143\) | −11.6518 | −0.974373 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.579308 | 0.0481089 | ||||||||
\(146\) | 0.278672 | 0.0230630 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.95181 | 0.489236 | ||||||||
\(149\) | 19.9493 | 1.63431 | 0.817155 | − | 0.576418i | \(-0.195550\pi\) | ||||
0.817155 | + | 0.576418i | \(0.195550\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.9350 | −0.971257 | −0.485629 | − | 0.874165i | \(-0.661409\pi\) | ||||
−0.485629 | + | 0.874165i | \(0.661409\pi\) | |||||||
\(152\) | 4.24606 | 0.344401 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.92836 | −0.155391 | ||||||||
\(155\) | 1.78846 | 0.143653 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.42143 | 0.672103 | 0.336051 | − | 0.941844i | \(-0.390908\pi\) | ||||
0.336051 | + | 0.941844i | \(0.390908\pi\) | |||||||
\(158\) | 1.07283 | 0.0853497 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.47043 | −0.195304 | ||||||||
\(161\) | −2.59556 | −0.204559 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 23.6060 | 1.84896 | 0.924482 | − | 0.381225i | \(-0.124498\pi\) | ||||
0.924482 | + | 0.381225i | \(0.124498\pi\) | |||||||
\(164\) | 15.4990 | 1.21027 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.83401 | −0.297577 | ||||||||
\(167\) | 18.5080 | 1.43219 | 0.716095 | − | 0.698002i | \(-0.245928\pi\) | ||||
0.716095 | + | 0.698002i | \(0.245928\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 25.5598 | 1.96614 | ||||||||
\(170\) | −0.920938 | −0.0706327 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 12.1044 | 0.922954 | ||||||||
\(173\) | 9.70767 | 0.738060 | 0.369030 | − | 0.929417i | \(-0.379690\pi\) | ||||
0.369030 | + | 0.929417i | \(0.379690\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.1068 | 0.915184 | ||||||||
\(176\) | 5.78676 | 0.436193 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.94687 | 0.295830 | ||||||||
\(179\) | 1.12703 | 0.0842380 | 0.0421190 | − | 0.999113i | \(-0.486589\pi\) | ||||
0.0421190 | + | 0.999113i | \(0.486589\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.6177 | 1.60683 | 0.803414 | − | 0.595420i | \(-0.203014\pi\) | ||||
0.803414 | + | 0.595420i | \(0.203014\pi\) | |||||||
\(182\) | 6.38159 | 0.473035 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.52169 | −0.112180 | ||||||||
\(185\) | 1.87059 | 0.137529 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.53385 | 0.550930 | ||||||||
\(188\) | 0.144361 | 0.0105286 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.640028 | 0.0464325 | ||||||||
\(191\) | −2.62732 | −0.190106 | −0.0950529 | − | 0.995472i | \(-0.530302\pi\) | ||||
−0.0950529 | + | 0.995472i | \(0.530302\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.5354 | −1.55015 | −0.775076 | − | 0.631868i | \(-0.782288\pi\) | ||||
−0.775076 | + | 0.631868i | \(0.782288\pi\) | |||||||
\(194\) | 4.77953 | 0.343150 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.484865 | 0.0346332 | ||||||||
\(197\) | −19.5960 | −1.39616 | −0.698080 | − | 0.716019i | \(-0.745962\pi\) | ||||
−0.698080 | + | 0.716019i | \(0.745962\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.6926 | 1.32508 | 0.662541 | − | 0.749026i | \(-0.269478\pi\) | ||||
0.662541 | + | 0.749026i | \(0.269478\pi\) | |||||||
\(200\) | 7.09778 | 0.501889 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.455933 | −0.0320794 | ||||||||
\(203\) | 2.59556 | 0.182173 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.87117 | 0.340217 | ||||||||
\(206\) | 3.19284 | 0.222456 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −19.1504 | −1.32784 | ||||||||
\(209\) | −5.23583 | −0.362170 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.2932 | −0.777456 | −0.388728 | − | 0.921353i | \(-0.627085\pi\) | ||||
−0.388728 | + | 0.921353i | \(0.627085\pi\) | |||||||
\(212\) | −17.3168 | −1.18932 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.75233 | 0.188146 | ||||||||
\(215\) | 3.80429 | 0.259451 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.01312 | 0.543966 | ||||||||
\(218\) | 3.30792 | 0.224041 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.00362 | 0.135084 | ||||||||
\(221\) | −24.9321 | −1.67711 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.83799 | −0.190046 | −0.0950228 | − | 0.995475i | \(-0.530292\pi\) | ||||
−0.0950228 | + | 0.995475i | \(0.530292\pi\) | |||||||
\(224\) | −11.0686 | −0.739555 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.30958 | 0.0871121 | ||||||||
\(227\) | 4.57810 | 0.303859 | 0.151930 | − | 0.988391i | \(-0.451451\pi\) | ||||
0.151930 | + | 0.988391i | \(0.451451\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.97141 | −0.262438 | −0.131219 | − | 0.991353i | \(-0.541889\pi\) | ||||
−0.131219 | + | 0.991353i | \(0.541889\pi\) | |||||||
\(230\) | −0.229371 | −0.0151243 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.52169 | 0.0999039 | ||||||||
\(233\) | −15.7838 | −1.03403 | −0.517017 | − | 0.855975i | \(-0.672958\pi\) | ||||
−0.517017 | + | 0.855975i | \(0.672958\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.0453711 | 0.00295968 | ||||||||
\(236\) | 14.6440 | 0.953244 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.12622 | −0.267463 | ||||||||
\(239\) | 9.82510 | 0.635533 | 0.317766 | − | 0.948169i | \(-0.397067\pi\) | ||||
0.317766 | + | 0.948169i | \(0.397067\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.2125 | −0.722262 | −0.361131 | − | 0.932515i | \(-0.617609\pi\) | ||||
−0.361131 | + | 0.932515i | \(0.617609\pi\) | |||||||
\(242\) | −2.96128 | −0.190359 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 16.6025 | 1.06287 | ||||||||
\(245\) | 0.152388 | 0.00973570 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 17.3272 | 1.10250 | ||||||||
\(248\) | 4.69782 | 0.298312 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.21674 | 0.140199 | ||||||||
\(251\) | 12.8806 | 0.813016 | 0.406508 | − | 0.913647i | \(-0.366746\pi\) | ||||
0.406508 | + | 0.913647i | \(0.366746\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.87640 | 0.117968 | ||||||||
\(254\) | 0.721375 | 0.0452631 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.87975 | 0.304984 | ||||||||
\(257\) | 29.2876 | 1.82691 | 0.913456 | − | 0.406937i | \(-0.133403\pi\) | ||||
0.913456 | + | 0.406937i | \(0.133403\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.38110 | 0.520776 | ||||||||
\(260\) | −6.63066 | −0.411216 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7.70390 | 0.475949 | ||||||||
\(263\) | −22.3171 | −1.37613 | −0.688066 | − | 0.725648i | \(-0.741540\pi\) | ||||
−0.688066 | + | 0.725648i | \(0.741540\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.44249 | −0.334330 | ||||||||
\(266\) | 2.86762 | 0.175825 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.10010 | −0.0671995 | ||||||||
\(269\) | −0.821814 | −0.0501069 | −0.0250534 | − | 0.999686i | \(-0.507976\pi\) | ||||
−0.0250534 | + | 0.999686i | \(0.507976\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.477020 | −0.0289769 | −0.0144884 | − | 0.999895i | \(-0.504612\pi\) | ||||
−0.0144884 | + | 0.999895i | \(0.504612\pi\) | |||||||
\(272\) | 12.3823 | 0.750786 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.29896 | −0.380534 | ||||||||
\(275\) | −8.75229 | −0.527783 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.0380 | 1.56447 | 0.782235 | − | 0.622983i | \(-0.214080\pi\) | ||||
0.782235 | + | 0.622983i | \(0.214080\pi\) | |||||||
\(278\) | −2.87746 | −0.172579 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.28806 | −0.136738 | ||||||||
\(281\) | 23.0168 | 1.37307 | 0.686534 | − | 0.727098i | \(-0.259131\pi\) | ||||
0.686534 | + | 0.727098i | \(0.259131\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.75884 | −0.104552 | −0.0522761 | − | 0.998633i | \(-0.516648\pi\) | ||||
−0.0522761 | + | 0.998633i | \(0.516648\pi\) | |||||||
\(284\) | −8.73463 | −0.518305 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.61342 | −0.272797 | ||||||||
\(287\) | 21.8251 | 1.28829 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.879340 | −0.0517259 | ||||||||
\(290\) | 0.229371 | 0.0134691 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.29731 | −0.0759192 | ||||||||
\(293\) | −23.1523 | −1.35257 | −0.676285 | − | 0.736640i | \(-0.736411\pi\) | ||||
−0.676285 | + | 0.736640i | \(0.736411\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.60246 | 0.267965 | ||||||||
\(296\) | 4.91355 | 0.285594 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.89873 | 0.457561 | ||||||||
\(299\) | −6.20966 | −0.359114 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.0450 | 0.982455 | ||||||||
\(302\) | −4.72555 | −0.271925 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8.60536 | −0.493551 | ||||||||
\(305\) | 5.21799 | 0.298781 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.9150 | −1.25076 | −0.625379 | − | 0.780321i | \(-0.715056\pi\) | ||||
−0.625379 | + | 0.780321i | \(0.715056\pi\) | |||||||
\(308\) | 8.97713 | 0.511519 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.708124 | 0.0402187 | ||||||||
\(311\) | 16.2132 | 0.919364 | 0.459682 | − | 0.888084i | \(-0.347963\pi\) | ||||
0.459682 | + | 0.888084i | \(0.347963\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.2318 | 0.691380 | 0.345690 | − | 0.938349i | \(-0.387645\pi\) | ||||
0.345690 | + | 0.938349i | \(0.387645\pi\) | |||||||
\(314\) | 3.33438 | 0.188170 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.99437 | −0.280955 | ||||||||
\(317\) | −33.9140 | −1.90480 | −0.952401 | − | 0.304848i | \(-0.901394\pi\) | ||||
−0.952401 | + | 0.304848i | \(0.901394\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.87640 | −0.105058 | ||||||||
\(320\) | 2.59499 | 0.145064 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.02769 | −0.0572708 | ||||||||
\(323\) | −11.2034 | −0.623376 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 28.9643 | 1.60665 | ||||||||
\(326\) | 9.34657 | 0.517659 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 12.7953 | 0.706502 | ||||||||
\(329\) | 0.203283 | 0.0112074 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.36860 | 0.459980 | 0.229990 | − | 0.973193i | \(-0.426131\pi\) | ||||
0.229990 | + | 0.973193i | \(0.426131\pi\) | |||||||
\(332\) | 17.8486 | 0.979567 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7.32806 | 0.400973 | ||||||||
\(335\) | −0.345751 | −0.0188904 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.51180 | −0.0823532 | −0.0411766 | − | 0.999152i | \(-0.513111\pi\) | ||||
−0.0411766 | + | 0.999152i | \(0.513111\pi\) | |||||||
\(338\) | 10.1202 | 0.550465 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.28727 | 0.232510 | ||||||||
\(341\) | −5.79290 | −0.313703 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.8517 | 1.01790 | ||||||||
\(344\) | 9.99288 | 0.538780 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.84366 | 0.206636 | ||||||||
\(347\) | −32.8768 | −1.76492 | −0.882459 | − | 0.470390i | \(-0.844113\pi\) | ||||
−0.882459 | + | 0.470390i | \(0.844113\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.4424 | 0.612500 | 0.306250 | − | 0.951951i | \(-0.400926\pi\) | ||||
0.306250 | + | 0.951951i | \(0.400926\pi\) | |||||||
\(350\) | 4.79355 | 0.256226 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8.00181 | 0.426498 | ||||||||
\(353\) | −19.9449 | −1.06156 | −0.530779 | − | 0.847510i | \(-0.678101\pi\) | ||||
−0.530779 | + | 0.847510i | \(0.678101\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.74520 | −0.145700 | ||||||||
\(356\) | −18.3739 | −0.973817 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.446236 | 0.0235843 | ||||||||
\(359\) | 32.3232 | 1.70595 | 0.852977 | − | 0.521949i | \(-0.174795\pi\) | ||||
0.852977 | + | 0.521949i | \(0.174795\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.2139 | −0.590206 | ||||||||
\(362\) | 8.55931 | 0.449867 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −29.7084 | −1.55714 | ||||||||
\(365\) | −0.407730 | −0.0213416 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.91262 | 0.152038 | 0.0760188 | − | 0.997106i | \(-0.475779\pi\) | ||||
0.0760188 | + | 0.997106i | \(0.475779\pi\) | |||||||
\(368\) | 3.08396 | 0.160763 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.740642 | 0.0385042 | ||||||||
\(371\) | −24.3848 | −1.26600 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.6742 | 0.708023 | 0.354011 | − | 0.935241i | \(-0.384817\pi\) | ||||
0.354011 | + | 0.935241i | \(0.384817\pi\) | |||||||
\(374\) | 2.98296 | 0.154245 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.119178 | 0.00614613 | ||||||||
\(377\) | 6.20966 | 0.319814 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.5159 | 1.05383 | 0.526916 | − | 0.849917i | \(-0.323348\pi\) | ||||
0.526916 | + | 0.849917i | \(0.323348\pi\) | |||||||
\(380\) | −2.97954 | −0.152847 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.04026 | −0.0532243 | ||||||||
\(383\) | −34.4819 | −1.76194 | −0.880971 | − | 0.473170i | \(-0.843109\pi\) | ||||
−0.880971 | + | 0.473170i | \(0.843109\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.82141 | 0.143793 | ||||||||
\(386\) | −8.52673 | −0.433999 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −22.2503 | −1.12959 | ||||||||
\(389\) | −21.1458 | −1.07214 | −0.536068 | − | 0.844175i | \(-0.680091\pi\) | ||||
−0.536068 | + | 0.844175i | \(0.680091\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.01505 | 0.203050 | ||||||||
\(392\) | 0.400283 | 0.0202173 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7.75887 | −0.390886 | ||||||||
\(395\) | −1.56968 | −0.0789790 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 36.7136 | 1.84260 | 0.921301 | − | 0.388851i | \(-0.127128\pi\) | ||||
0.921301 | + | 0.388851i | \(0.127128\pi\) | |||||||
\(398\) | 7.40114 | 0.370986 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −14.3848 | −0.719242 | ||||||||
\(401\) | 24.2930 | 1.21314 | 0.606568 | − | 0.795031i | \(-0.292546\pi\) | ||||
0.606568 | + | 0.795031i | \(0.292546\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.1707 | 0.954960 | ||||||||
\(404\) | 2.12252 | 0.105599 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.02769 | 0.0510033 | ||||||||
\(407\) | −6.05892 | −0.300330 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.5923 | −0.968776 | −0.484388 | − | 0.874853i | \(-0.660958\pi\) | ||||
−0.484388 | + | 0.874853i | \(0.660958\pi\) | |||||||
\(410\) | 1.92869 | 0.0952513 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −14.8637 | −0.732283 | ||||||||
\(413\) | 20.6211 | 1.01470 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.60961 | 0.275365 | ||||||||
\(416\) | −26.4807 | −1.29833 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.07308 | −0.101397 | ||||||||
\(419\) | 26.2797 | 1.28385 | 0.641923 | − | 0.766769i | \(-0.278137\pi\) | ||||
0.641923 | + | 0.766769i | \(0.278137\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.32333 | 0.454391 | 0.227196 | − | 0.973849i | \(-0.427044\pi\) | ||||
0.227196 | + | 0.973849i | \(0.427044\pi\) | |||||||
\(422\) | −4.47143 | −0.217666 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −14.2960 | −0.694275 | ||||||||
\(425\) | −18.7278 | −0.908433 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 23.3790 | 1.13139 | ||||||||
\(428\) | −12.8130 | −0.619340 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.50627 | 0.0726389 | ||||||||
\(431\) | −16.4763 | −0.793636 | −0.396818 | − | 0.917897i | \(-0.629886\pi\) | ||||
−0.396818 | + | 0.917897i | \(0.629886\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.86255 | 0.185622 | 0.0928111 | − | 0.995684i | \(-0.470415\pi\) | ||||
0.0928111 | + | 0.995684i | \(0.470415\pi\) | |||||||
\(434\) | 3.17272 | 0.152295 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −15.3994 | −0.737499 | ||||||||
\(437\) | −2.79036 | −0.133481 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.55822 | −0.408462 | −0.204231 | − | 0.978923i | \(-0.565469\pi\) | ||||
−0.204231 | + | 0.978923i | \(0.565469\pi\) | |||||||
\(440\) | 1.65410 | 0.0788561 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9.87163 | −0.469545 | ||||||||
\(443\) | −6.08169 | −0.288950 | −0.144475 | − | 0.989508i | \(-0.546149\pi\) | ||||
−0.144475 | + | 0.989508i | \(0.546149\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.77473 | −0.273749 | ||||||||
\(446\) | −1.12367 | −0.0532075 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 11.6267 | 0.549311 | ||||||||
\(449\) | −14.6440 | −0.691092 | −0.345546 | − | 0.938402i | \(-0.612306\pi\) | ||||
−0.345546 | + | 0.938402i | \(0.612306\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.7779 | −0.742953 | ||||||||
\(452\) | −6.09653 | −0.286757 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.81266 | 0.0850721 | ||||||||
\(455\) | −9.33703 | −0.437727 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.8053 | 1.16034 | 0.580171 | − | 0.814495i | \(-0.302986\pi\) | ||||
0.580171 | + | 0.814495i | \(0.302986\pi\) | |||||||
\(458\) | −1.57244 | −0.0734753 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.06780 | 0.0497864 | ||||||||
\(461\) | 32.1947 | 1.49946 | 0.749728 | − | 0.661747i | \(-0.230185\pi\) | ||||
0.749728 | + | 0.661747i | \(0.230185\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.6435 | −0.773488 | −0.386744 | − | 0.922187i | \(-0.626400\pi\) | ||||
−0.386744 | + | 0.922187i | \(0.626400\pi\) | |||||||
\(464\) | −3.08396 | −0.143169 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.24946 | −0.289501 | ||||||||
\(467\) | 28.4988 | 1.31877 | 0.659383 | − | 0.751807i | \(-0.270818\pi\) | ||||
0.659383 | + | 0.751807i | \(0.270818\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.54912 | −0.0715318 | ||||||||
\(470\) | 0.0179642 | 0.000828628 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 12.0895 | 0.556462 | ||||||||
\(473\) | −12.3223 | −0.566578 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.0153 | 0.597185 | ||||||||
\(476\) | 19.2089 | 0.880439 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.89015 | 0.177931 | ||||||||
\(479\) | −32.6240 | −1.49063 | −0.745314 | − | 0.666714i | \(-0.767700\pi\) | ||||
−0.745314 | + | 0.666714i | \(0.767700\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.0510 | 0.914249 | ||||||||
\(482\) | −4.43949 | −0.202213 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 13.7857 | 0.626625 | ||||||||
\(485\) | −6.99302 | −0.317537 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.93284 | 0.404786 | 0.202393 | − | 0.979304i | \(-0.435128\pi\) | ||||
0.202393 | + | 0.979304i | \(0.435128\pi\) | |||||||
\(488\) | 13.7063 | 0.620455 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.0603365 | 0.00272572 | ||||||||
\(491\) | 5.36028 | 0.241906 | 0.120953 | − | 0.992658i | \(-0.461405\pi\) | ||||
0.120953 | + | 0.992658i | \(0.461405\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.01505 | −0.180829 | ||||||||
\(494\) | 6.86052 | 0.308669 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −9.52093 | −0.427503 | ||||||||
\(497\) | −12.2997 | −0.551719 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.44297 | −0.243661 | −0.121830 | − | 0.992551i | \(-0.538876\pi\) | ||||
−0.121830 | + | 0.992551i | \(0.538876\pi\) | |||||||
\(500\) | −10.3196 | −0.461508 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.09995 | 0.227622 | ||||||||
\(503\) | 13.8756 | 0.618683 | 0.309341 | − | 0.950951i | \(-0.399891\pi\) | ||||
0.309341 | + | 0.950951i | \(0.399891\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.667085 | 0.0296849 | ||||||||
\(506\) | 0.742943 | 0.0330279 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.35823 | −0.148998 | ||||||||
\(509\) | 6.70153 | 0.297040 | 0.148520 | − | 0.988909i | \(-0.452549\pi\) | ||||
0.148520 | + | 0.988909i | \(0.452549\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.82682 | −0.0808136 | ||||||||
\(512\) | 22.5371 | 0.996007 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 11.5962 | 0.511485 | ||||||||
\(515\) | −4.67151 | −0.205851 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.146959 | −0.00646324 | ||||||||
\(518\) | 3.31842 | 0.145803 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.47398 | −0.240050 | ||||||||
\(521\) | 2.66765 | 0.116872 | 0.0584359 | − | 0.998291i | \(-0.481389\pi\) | ||||
0.0584359 | + | 0.998291i | \(0.481389\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.2171 | −0.752852 | −0.376426 | − | 0.926447i | \(-0.622847\pi\) | ||||
−0.376426 | + | 0.926447i | \(0.622847\pi\) | |||||||
\(524\) | −35.8642 | −1.56673 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.83624 | −0.385279 | ||||||||
\(527\) | −12.3954 | −0.539953 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −2.15490 | −0.0936030 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −13.3497 | −0.578782 | ||||||||
\(533\) | 52.2145 | 2.26166 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.02699 | −0.174102 | ||||||||
\(536\) | −0.908197 | −0.0392281 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.325389 | −0.0140285 | ||||||||
\(539\) | −0.493590 | −0.0212604 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.3783 | −0.747152 | −0.373576 | − | 0.927600i | \(-0.621868\pi\) | ||||
−0.373576 | + | 0.927600i | \(0.621868\pi\) | |||||||
\(542\) | −0.188871 | −0.00811272 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 17.1220 | 0.734099 | ||||||||
\(545\) | −4.83988 | −0.207318 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −38.8067 | −1.65925 | −0.829627 | − | 0.558318i | \(-0.811447\pi\) | ||||
−0.829627 | + | 0.558318i | \(0.811447\pi\) | |||||||
\(548\) | 29.3237 | 1.25265 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.46539 | −0.147765 | ||||||||
\(551\) | 2.79036 | 0.118873 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.03287 | −0.299068 | ||||||||
\(554\) | 10.3095 | 0.438008 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13.3955 | 0.568097 | ||||||||
\(557\) | −45.7836 | −1.93991 | −0.969956 | − | 0.243279i | \(-0.921777\pi\) | ||||
−0.969956 | + | 0.243279i | \(0.921777\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 40.7786 | 1.72475 | ||||||||
\(560\) | 4.63714 | 0.195955 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.11329 | 0.384421 | ||||||||
\(563\) | 5.07837 | 0.214028 | 0.107014 | − | 0.994258i | \(-0.465871\pi\) | ||||
0.107014 | + | 0.994258i | \(0.465871\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.91608 | −0.0806099 | ||||||||
\(566\) | −0.696395 | −0.0292717 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.21092 | −0.302564 | ||||||||
\(569\) | −8.39350 | −0.351874 | −0.175937 | − | 0.984401i | \(-0.556295\pi\) | ||||
−0.175937 | + | 0.984401i | \(0.556295\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.836227 | 0.0349950 | 0.0174975 | − | 0.999847i | \(-0.494430\pi\) | ||||
0.0174975 | + | 0.999847i | \(0.494430\pi\) | |||||||
\(572\) | 21.4770 | 0.897998 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 8.64142 | 0.360686 | ||||||||
\(575\) | −4.66440 | −0.194519 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.30822 | 0.179353 | 0.0896767 | − | 0.995971i | \(-0.471417\pi\) | ||||
0.0896767 | + | 0.995971i | \(0.471417\pi\) | |||||||
\(578\) | −0.348166 | −0.0144818 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.06780 | −0.0443379 | ||||||||
\(581\) | 25.1336 | 1.04272 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.6285 | 0.730096 | ||||||||
\(584\) | −1.07100 | −0.0443183 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.16692 | −0.378682 | ||||||||
\(587\) | 45.2320 | 1.86692 | 0.933462 | − | 0.358676i | \(-0.116772\pi\) | ||||
0.933462 | + | 0.358676i | \(0.116772\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.61450 | 0.354954 | ||||||||
\(590\) | 1.82230 | 0.0750228 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −9.95815 | −0.409277 | ||||||||
\(593\) | −28.7912 | −1.18231 | −0.591156 | − | 0.806557i | \(-0.701328\pi\) | ||||
−0.591156 | + | 0.806557i | \(0.701328\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.03716 | 0.247499 | ||||||||
\(596\) | −36.7712 | −1.50621 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.45865 | −0.100542 | ||||||||
\(599\) | −9.30640 | −0.380249 | −0.190125 | − | 0.981760i | \(-0.560889\pi\) | ||||
−0.190125 | + | 0.981760i | \(0.560889\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.2220 | −0.865662 | −0.432831 | − | 0.901475i | \(-0.642485\pi\) | ||||
−0.432831 | + | 0.901475i | \(0.642485\pi\) | |||||||
\(602\) | 6.74879 | 0.275060 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 21.9990 | 0.895126 | ||||||||
\(605\) | 4.33271 | 0.176150 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.64480 | 0.107349 | 0.0536745 | − | 0.998558i | \(-0.482907\pi\) | ||||
0.0536745 | + | 0.998558i | \(0.482907\pi\) | |||||||
\(608\) | −11.8993 | −0.482581 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.06601 | 0.0836504 | ||||||||
\(611\) | 0.486337 | 0.0196751 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.97028 | 0.362306 | 0.181153 | − | 0.983455i | \(-0.442017\pi\) | ||||
0.181153 | + | 0.983455i | \(0.442017\pi\) | |||||||
\(614\) | −8.67705 | −0.350177 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.41112 | 0.298602 | ||||||||
\(617\) | 11.9943 | 0.482874 | 0.241437 | − | 0.970416i | \(-0.422381\pi\) | ||||
0.241437 | + | 0.970416i | \(0.422381\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 45.9586 | 1.84723 | 0.923616 | − | 0.383318i | \(-0.125219\pi\) | ||||
0.923616 | + | 0.383318i | \(0.125219\pi\) | |||||||
\(620\) | −3.29655 | −0.132393 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.41944 | 0.257396 | ||||||||
\(623\) | −25.8734 | −1.03660 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.0787 | 0.803146 | ||||||||
\(626\) | 4.84305 | 0.193567 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −15.5226 | −0.619421 | ||||||||
\(629\) | −12.9646 | −0.516934 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.6300 | −1.21936 | −0.609680 | − | 0.792648i | \(-0.708702\pi\) | ||||
−0.609680 | + | 0.792648i | \(0.708702\pi\) | |||||||
\(632\) | −4.12313 | −0.164009 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −13.4279 | −0.533291 | ||||||||
\(635\) | −1.05546 | −0.0418845 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.63346 | 0.0647200 | ||||||||
\(638\) | −0.742943 | −0.0294134 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 5.96831 | 0.235918 | ||||||||
\(641\) | 3.35392 | 0.132472 | 0.0662360 | − | 0.997804i | \(-0.478901\pi\) | ||||
0.0662360 | + | 0.997804i | \(0.478901\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 35.8942 | 1.41553 | 0.707764 | − | 0.706449i | \(-0.249704\pi\) | ||||
0.707764 | + | 0.706449i | \(0.249704\pi\) | |||||||
\(644\) | 4.78422 | 0.188525 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.43589 | −0.174528 | ||||||||
\(647\) | 16.8868 | 0.663887 | 0.331943 | − | 0.943299i | \(-0.392296\pi\) | ||||
0.331943 | + | 0.943299i | \(0.392296\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.9075 | −0.585172 | ||||||||
\(650\) | 11.4681 | 0.449818 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −43.5113 | −1.70403 | ||||||||
\(653\) | 31.5936 | 1.23635 | 0.618177 | − | 0.786039i | \(-0.287872\pi\) | ||||
0.618177 | + | 0.786039i | \(0.287872\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.2717 | −0.440423 | ||||||||
\(656\) | −25.9318 | −1.01247 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.0804879 | 0.00313775 | ||||||||
\(659\) | 4.95273 | 0.192931 | 0.0964656 | − | 0.995336i | \(-0.469246\pi\) | ||||
0.0964656 | + | 0.995336i | \(0.469246\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.25253 | −0.0876131 | −0.0438066 | − | 0.999040i | \(-0.513949\pi\) | ||||
−0.0438066 | + | 0.999040i | \(0.513949\pi\) | |||||||
\(662\) | 3.31347 | 0.128782 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14.7350 | 0.571828 | ||||||||
\(665\) | −4.19566 | −0.162701 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | −34.1145 | −1.31993 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −0.136897 | −0.00528878 | ||||||||
\(671\) | −16.9013 | −0.652467 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 40.7757 | 1.57179 | 0.785893 | − | 0.618363i | \(-0.212204\pi\) | ||||
0.785893 | + | 0.618363i | \(0.212204\pi\) | |||||||
\(674\) | −0.598584 | −0.0230566 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −47.1127 | −1.81203 | ||||||||
\(677\) | 40.2860 | 1.54832 | 0.774158 | − | 0.632992i | \(-0.218173\pi\) | ||||
0.774158 | + | 0.632992i | \(0.218173\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −31.3319 | −1.20241 | ||||||||
\(680\) | 3.53938 | 0.135729 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.29364 | −0.0878281 | ||||||||
\(683\) | −26.0249 | −0.995816 | −0.497908 | − | 0.867230i | \(-0.665898\pi\) | ||||
−0.497908 | + | 0.867230i | \(0.665898\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.21613 | 0.352130 | ||||||||
\(686\) | 7.46415 | 0.284983 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −20.2523 | −0.772111 | ||||||||
\(689\) | −58.3386 | −2.22252 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.9608 | −1.02564 | −0.512819 | − | 0.858497i | \(-0.671399\pi\) | ||||
−0.512819 | + | 0.858497i | \(0.671399\pi\) | |||||||
\(692\) | −17.8935 | −0.680208 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −13.0172 | −0.494128 | ||||||||
\(695\) | 4.21007 | 0.159697 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −33.7610 | −1.27879 | ||||||||
\(698\) | 4.53053 | 0.171483 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −22.3155 | −0.843448 | ||||||||
\(701\) | 15.6620 | 0.591546 | 0.295773 | − | 0.955258i | \(-0.404423\pi\) | ||||
0.295773 | + | 0.955258i | \(0.404423\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.01009 | 0.339822 | ||||||||
\(704\) | −8.40527 | −0.316786 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.89698 | −0.297207 | ||||||||
\(707\) | 2.98884 | 0.112407 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26.5765 | −0.998101 | −0.499050 | − | 0.866573i | \(-0.666318\pi\) | ||||
−0.499050 | + | 0.866573i | \(0.666318\pi\) | |||||||
\(710\) | −1.08694 | −0.0407919 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −15.1687 | −0.568472 | ||||||||
\(713\) | −3.08724 | −0.115618 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.74998 | 0.252435 | ||||||||
\(716\) | −2.07737 | −0.0776351 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 12.7981 | 0.477619 | ||||||||
\(719\) | −31.8619 | −1.18825 | −0.594124 | − | 0.804373i | \(-0.702501\pi\) | ||||
−0.594124 | + | 0.804373i | \(0.702501\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.9305 | −0.779492 | ||||||||
\(722\) | −4.44004 | −0.165241 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −39.8464 | −1.48088 | ||||||||
\(725\) | 4.66440 | 0.173232 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.67239 | 0.136201 | 0.0681007 | − | 0.997678i | \(-0.478306\pi\) | ||||
0.0681007 | + | 0.997678i | \(0.478306\pi\) | |||||||
\(728\) | −24.5259 | −0.908991 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.161437 | −0.00597504 | ||||||||
\(731\) | −26.3667 | −0.975208 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34.8917 | −1.28875 | −0.644377 | − | 0.764708i | \(-0.722883\pi\) | ||||
−0.644377 | + | 0.764708i | \(0.722883\pi\) | |||||||
\(734\) | 1.15322 | 0.0425663 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.26445 | 0.157190 | ||||||||
\(737\) | 1.11990 | 0.0412521 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36.6332 | 1.34757 | 0.673787 | − | 0.738925i | \(-0.264666\pi\) | ||||
0.673787 | + | 0.738925i | \(0.264666\pi\) | |||||||
\(740\) | −3.44793 | −0.126748 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.65494 | −0.354444 | ||||||||
\(743\) | −30.0312 | −1.10174 | −0.550869 | − | 0.834592i | \(-0.685703\pi\) | ||||
−0.550869 | + | 0.834592i | \(0.685703\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.5568 | −0.423408 | ||||||||
\(746\) | 5.41416 | 0.198227 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −13.8866 | −0.507746 | ||||||||
\(749\) | −18.0428 | −0.659268 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −49.0657 | −1.79043 | −0.895217 | − | 0.445630i | \(-0.852980\pi\) | ||||
−0.895217 | + | 0.445630i | \(0.852980\pi\) | |||||||
\(752\) | −0.241534 | −0.00880785 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.45865 | 0.0895389 | ||||||||
\(755\) | 6.91405 | 0.251628 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31.6108 | −1.14891 | −0.574457 | − | 0.818535i | \(-0.694787\pi\) | ||||
−0.574457 | + | 0.818535i | \(0.694787\pi\) | |||||||
\(758\) | 8.12309 | 0.295044 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.45978 | −0.0892254 | ||||||||
\(761\) | −39.4073 | −1.42852 | −0.714258 | − | 0.699883i | \(-0.753235\pi\) | ||||
−0.714258 | + | 0.699883i | \(0.753235\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −21.6849 | −0.785045 | ||||||||
\(764\) | 4.84275 | 0.175205 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −13.6528 | −0.493295 | ||||||||
\(767\) | 49.3342 | 1.78135 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.31376 | 0.0834363 | 0.0417182 | − | 0.999129i | \(-0.486717\pi\) | ||||
0.0417182 | + | 0.999129i | \(0.486717\pi\) | |||||||
\(770\) | 1.11711 | 0.0402579 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 39.6947 | 1.42864 | ||||||||
\(773\) | 9.67989 | 0.348161 | 0.174081 | − | 0.984731i | \(-0.444305\pi\) | ||||
0.174081 | + | 0.984731i | \(0.444305\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.4001 | 0.517268 | ||||||||
\(776\) | −18.3688 | −0.659403 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.37248 | −0.300168 | ||||||||
\(779\) | 23.4630 | 0.840649 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.89181 | 0.318174 | ||||||||
\(782\) | 1.58972 | 0.0568483 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.811241 | −0.0289729 | ||||||||
\(785\) | −4.87860 | −0.174125 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.4981 | 0.801970 | 0.400985 | − | 0.916085i | \(-0.368668\pi\) | ||||
0.400985 | + | 0.916085i | \(0.368668\pi\) | |||||||
\(788\) | 36.1200 | 1.28672 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.621498 | −0.0221119 | ||||||||
\(791\) | −8.58489 | −0.305244 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 55.9321 | 1.98621 | ||||||||
\(794\) | 14.5364 | 0.515877 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −34.4547 | −1.22122 | ||||||||
\(797\) | 31.7414 | 1.12434 | 0.562169 | − | 0.827023i | \(-0.309967\pi\) | ||||
0.562169 | + | 0.827023i | \(0.309967\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.314457 | −0.0111247 | ||||||||
\(800\) | −19.8911 | −0.703256 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.61860 | 0.339644 | ||||||||
\(803\) | 1.32065 | 0.0466049 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.50363 | 0.0529960 | ||||||||
\(806\) | 7.59045 | 0.267362 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.75226 | 0.0616442 | ||||||||
\(809\) | 47.1833 | 1.65888 | 0.829439 | − | 0.558597i | \(-0.188660\pi\) | ||||
0.829439 | + | 0.558597i | \(0.188660\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37.6766 | −1.32300 | −0.661502 | − | 0.749943i | \(-0.730081\pi\) | ||||
−0.661502 | + | 0.749943i | \(0.730081\pi\) | |||||||
\(812\) | −4.78422 | −0.167893 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.39897 | −0.0840839 | ||||||||
\(815\) | −13.6751 | −0.479019 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.3242 | 0.641081 | ||||||||
\(818\) | −7.75737 | −0.271230 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.97869 | −0.313550 | ||||||||
\(821\) | −28.6192 | −0.998817 | −0.499409 | − | 0.866367i | \(-0.666449\pi\) | ||||
−0.499409 | + | 0.866367i | \(0.666449\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.8950 | 0.379775 | 0.189887 | − | 0.981806i | \(-0.439188\pi\) | ||||
0.189887 | + | 0.981806i | \(0.439188\pi\) | |||||||
\(824\) | −12.2708 | −0.427475 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.16473 | 0.284087 | ||||||||
\(827\) | 40.0272 | 1.39188 | 0.695941 | − | 0.718099i | \(-0.254987\pi\) | ||||
0.695941 | + | 0.718099i | \(0.254987\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.3663 | 1.08939 | 0.544697 | − | 0.838633i | \(-0.316644\pi\) | ||||
0.544697 | + | 0.838633i | \(0.316644\pi\) | |||||||
\(830\) | 2.22107 | 0.0770945 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 27.8159 | 0.964343 | ||||||||
\(833\) | −1.05617 | −0.0365940 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.7218 | −0.371044 | ||||||||
\(836\) | 9.65085 | 0.333781 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 10.4052 | 0.359441 | ||||||||
\(839\) | 7.36911 | 0.254410 | 0.127205 | − | 0.991876i | \(-0.459399\pi\) | ||||
0.127205 | + | 0.991876i | \(0.459399\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 3.69148 | 0.127217 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 20.8160 | 0.716516 | ||||||||
\(845\) | −14.8070 | −0.509377 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 19.4125 | 0.667022 | ||||||||
\(848\) | 28.9733 | 0.994946 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −7.41510 | −0.254336 | ||||||||
\(851\) | −3.22901 | −0.110689 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.23153 | 0.0764061 | 0.0382031 | − | 0.999270i | \(-0.487837\pi\) | ||||
0.0382031 | + | 0.999270i | \(0.487837\pi\) | |||||||
\(854\) | 9.25668 | 0.316757 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.5779 | −0.361544 | ||||||||
\(857\) | 3.20003 | 0.109311 | 0.0546555 | − | 0.998505i | \(-0.482594\pi\) | ||||
0.0546555 | + | 0.998505i | \(0.482594\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −55.8487 | −1.90553 | −0.952766 | − | 0.303706i | \(-0.901776\pi\) | ||||
−0.952766 | + | 0.303706i | \(0.901776\pi\) | |||||||
\(860\) | −7.01219 | −0.239114 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.52363 | −0.222196 | ||||||||
\(863\) | 45.5794 | 1.55154 | 0.775770 | − | 0.631015i | \(-0.217362\pi\) | ||||
0.775770 | + | 0.631015i | \(0.217362\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.62373 | −0.191212 | ||||||||
\(866\) | 1.52934 | 0.0519690 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −14.7700 | −0.501328 | ||||||||
\(869\) | 5.08425 | 0.172471 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.70613 | −0.125578 | ||||||||
\(872\) | −12.7131 | −0.430520 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.10481 | −0.0373709 | ||||||||
\(875\) | −14.5317 | −0.491261 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 52.0667 | 1.75817 | 0.879084 | − | 0.476667i | \(-0.158155\pi\) | ||||
0.879084 | + | 0.476667i | \(0.158155\pi\) | |||||||
\(878\) | −3.38855 | −0.114358 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.35231 | −0.113006 | ||||||||
\(881\) | 20.6461 | 0.695586 | 0.347793 | − | 0.937571i | \(-0.386931\pi\) | ||||
0.347793 | + | 0.937571i | \(0.386931\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −57.1293 | −1.92255 | −0.961277 | − | 0.275585i | \(-0.911129\pi\) | ||||
−0.961277 | + | 0.275585i | \(0.911129\pi\) | |||||||
\(884\) | 45.9556 | 1.54566 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.40799 | −0.0808979 | ||||||||
\(887\) | 30.4357 | 1.02193 | 0.510966 | − | 0.859601i | \(-0.329288\pi\) | ||||
0.510966 | + | 0.859601i | \(0.329288\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.72893 | −0.158603 | ||||||||
\(890\) | −2.28645 | −0.0766420 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.23107 | 0.175149 | ||||||||
\(893\) | 0.218539 | 0.00731313 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.652896 | −0.0218239 | ||||||||
\(896\) | 26.7408 | 0.893346 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5.79814 | −0.193486 | ||||||||
\(899\) | 3.08724 | 0.102965 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 37.7207 | 1.25666 | ||||||||
\(902\) | −6.24711 | −0.208006 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.03303 | −0.167396 | ||||||||
\(905\) | −12.5233 | −0.416288 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 39.6703 | 1.31723 | 0.658615 | − | 0.752480i | \(-0.271143\pi\) | ||||
0.658615 | + | 0.752480i | \(0.271143\pi\) | |||||||
\(908\) | −8.43850 | −0.280041 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.69691 | −0.122551 | ||||||||
\(911\) | −17.5930 | −0.582882 | −0.291441 | − | 0.956589i | \(-0.594135\pi\) | ||||
−0.291441 | + | 0.956589i | \(0.594135\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.1698 | −0.601331 | ||||||||
\(914\) | 9.82141 | 0.324863 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.32022 | 0.241867 | ||||||||
\(917\) | −50.5025 | −1.66774 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −22.9102 | −0.755737 | −0.377868 | − | 0.925859i | \(-0.623343\pi\) | ||||
−0.377868 | + | 0.925859i | \(0.623343\pi\) | |||||||
\(920\) | 0.881527 | 0.0290631 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 12.7472 | 0.419806 | ||||||||
\(923\) | −29.4261 | −0.968570 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.0614 | 0.495216 | ||||||||
\(926\) | −6.58982 | −0.216555 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.26445 | −0.139987 | ||||||||
\(929\) | 11.8132 | 0.387578 | 0.193789 | − | 0.981043i | \(-0.437922\pi\) | ||||
0.193789 | + | 0.981043i | \(0.437922\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.734008 | 0.0240561 | ||||||||
\(932\) | 29.0933 | 0.952982 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 11.2838 | 0.369218 | ||||||||
\(935\) | −4.36442 | −0.142732 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.9816 | −0.652771 | −0.326386 | − | 0.945237i | \(-0.605831\pi\) | ||||
−0.326386 | + | 0.945237i | \(0.605831\pi\) | |||||||
\(938\) | −0.613359 | −0.0200269 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.0836293 | −0.00272769 | ||||||||
\(941\) | 40.1760 | 1.30970 | 0.654850 | − | 0.755759i | \(-0.272732\pi\) | ||||
0.654850 | + | 0.755759i | \(0.272732\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.40860 | −0.273822 | ||||||||
\(944\) | −24.5013 | −0.797450 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.87888 | −0.158626 | ||||||||
\(947\) | 22.2543 | 0.723168 | 0.361584 | − | 0.932339i | \(-0.382236\pi\) | ||||
0.361584 | + | 0.932339i | \(0.382236\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.37049 | −0.141872 | ||||||||
\(950\) | 5.15330 | 0.167195 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 15.8580 | 0.513962 | ||||||||
\(953\) | −6.40819 | −0.207582 | −0.103791 | − | 0.994599i | \(-0.533097\pi\) | ||||
−0.103791 | + | 0.994599i | \(0.533097\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.52202 | 0.0492516 | ||||||||
\(956\) | −18.1099 | −0.585717 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −12.9171 | −0.417334 | ||||||||
\(959\) | 41.2925 | 1.33340 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.4690 | −0.692547 | ||||||||
\(962\) | 7.93902 | 0.255964 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 20.6673 | 0.665648 | ||||||||
\(965\) | 12.4756 | 0.401605 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −44.7836 | −1.44014 | −0.720072 | − | 0.693899i | \(-0.755891\pi\) | ||||
−0.720072 | + | 0.693899i | \(0.755891\pi\) | |||||||
\(968\) | 11.3809 | 0.365796 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.76882 | −0.0889014 | ||||||||
\(971\) | −38.1900 | −1.22558 | −0.612788 | − | 0.790248i | \(-0.709952\pi\) | ||||
−0.612788 | + | 0.790248i | \(0.709952\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.8630 | 0.604721 | ||||||||
\(974\) | 3.53687 | 0.113329 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −27.7781 | −0.889157 | ||||||||
\(977\) | 1.05944 | 0.0338944 | 0.0169472 | − | 0.999856i | \(-0.494605\pi\) | ||||
0.0169472 | + | 0.999856i | \(0.494605\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.7046 | 0.597802 | ||||||||
\(980\) | −0.280886 | −0.00897257 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.12235 | 0.0677269 | ||||||||
\(983\) | 26.8563 | 0.856584 | 0.428292 | − | 0.903640i | \(-0.359116\pi\) | ||||
0.428292 | + | 0.903640i | \(0.359116\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.3521 | 0.361709 | ||||||||
\(986\) | −1.58972 | −0.0506271 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −31.9380 | −1.01608 | ||||||||
\(989\) | −6.56696 | −0.208817 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.6798 | −0.942810 | −0.471405 | − | 0.881917i | \(-0.656253\pi\) | ||||
−0.471405 | + | 0.881917i | \(0.656253\pi\) | |||||||
\(992\) | −13.1654 | −0.418001 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.86996 | −0.154466 | ||||||||
\(995\) | −10.8288 | −0.343295 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 48.9821 | 1.55128 | 0.775640 | − | 0.631175i | \(-0.217427\pi\) | ||||
0.775640 | + | 0.631175i | \(0.217427\pi\) | |||||||
\(998\) | −2.15509 | −0.0682182 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6003.2.a.v.1.16 | ✓ | 30 | |
3.2 | odd | 2 | 6003.2.a.w.1.15 | yes | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6003.2.a.v.1.16 | ✓ | 30 | 1.1 | even | 1 | trivial | |
6003.2.a.w.1.15 | yes | 30 | 3.2 | odd | 2 |