Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2667,2,Mod(1,2667)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2667, 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("2667.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2667 = 3 \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2667.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: | \(21.2961022191\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 4 x^{12} - 10 x^{11} + 53 x^{10} + 19 x^{9} - 242 x^{8} + 61 x^{7} + 467 x^{6} - 211 x^{5} + \cdots - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(2.29288\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2667.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.29288 | 1.62131 | 0.810654 | − | 0.585526i | \(-0.199112\pi\) | ||||
0.810654 | + | 0.585526i | \(0.199112\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.25728 | 1.62864 | ||||||||
\(5\) | −0.132682 | −0.0593372 | −0.0296686 | − | 0.999560i | \(-0.509445\pi\) | ||||
−0.0296686 | + | 0.999560i | \(0.509445\pi\) | |||||||
\(6\) | −2.29288 | −0.936062 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.88278 | 1.01922 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.304223 | −0.0962039 | ||||||||
\(11\) | −1.38028 | −0.416170 | −0.208085 | − | 0.978111i | \(-0.566723\pi\) | ||||
−0.208085 | + | 0.978111i | \(0.566723\pi\) | |||||||
\(12\) | −3.25728 | −0.940295 | ||||||||
\(13\) | 3.00012 | 0.832083 | 0.416042 | − | 0.909346i | \(-0.363417\pi\) | ||||
0.416042 | + | 0.909346i | \(0.363417\pi\) | |||||||
\(14\) | 2.29288 | 0.612797 | ||||||||
\(15\) | 0.132682 | 0.0342584 | ||||||||
\(16\) | 0.0952967 | 0.0238242 | ||||||||
\(17\) | 4.60865 | 1.11776 | 0.558880 | − | 0.829248i | \(-0.311231\pi\) | ||||
0.558880 | + | 0.829248i | \(0.311231\pi\) | |||||||
\(18\) | 2.29288 | 0.540436 | ||||||||
\(19\) | −1.78380 | −0.409232 | −0.204616 | − | 0.978842i | \(-0.565595\pi\) | ||||
−0.204616 | + | 0.978842i | \(0.565595\pi\) | |||||||
\(20\) | −0.432182 | −0.0966388 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −3.16481 | −0.674739 | ||||||||
\(23\) | 6.02678 | 1.25667 | 0.628336 | − | 0.777942i | \(-0.283736\pi\) | ||||
0.628336 | + | 0.777942i | \(0.283736\pi\) | |||||||
\(24\) | −2.88278 | −0.588445 | ||||||||
\(25\) | −4.98240 | −0.996479 | ||||||||
\(26\) | 6.87890 | 1.34906 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 3.25728 | 0.615567 | ||||||||
\(29\) | 2.00225 | 0.371808 | 0.185904 | − | 0.982568i | \(-0.440479\pi\) | ||||
0.185904 | + | 0.982568i | \(0.440479\pi\) | |||||||
\(30\) | 0.304223 | 0.0555433 | ||||||||
\(31\) | 9.54114 | 1.71364 | 0.856820 | − | 0.515616i | \(-0.172437\pi\) | ||||
0.856820 | + | 0.515616i | \(0.172437\pi\) | |||||||
\(32\) | −5.54705 | −0.980590 | ||||||||
\(33\) | 1.38028 | 0.240276 | ||||||||
\(34\) | 10.5670 | 1.81223 | ||||||||
\(35\) | −0.132682 | −0.0224274 | ||||||||
\(36\) | 3.25728 | 0.542879 | ||||||||
\(37\) | 2.84160 | 0.467156 | 0.233578 | − | 0.972338i | \(-0.424957\pi\) | ||||
0.233578 | + | 0.972338i | \(0.424957\pi\) | |||||||
\(38\) | −4.09003 | −0.663491 | ||||||||
\(39\) | −3.00012 | −0.480404 | ||||||||
\(40\) | −0.382493 | −0.0604774 | ||||||||
\(41\) | 2.18268 | 0.340878 | 0.170439 | − | 0.985368i | \(-0.445481\pi\) | ||||
0.170439 | + | 0.985368i | \(0.445481\pi\) | |||||||
\(42\) | −2.29288 | −0.353798 | ||||||||
\(43\) | 9.51578 | 1.45114 | 0.725571 | − | 0.688147i | \(-0.241576\pi\) | ||||
0.725571 | + | 0.688147i | \(0.241576\pi\) | |||||||
\(44\) | −4.49595 | −0.677790 | ||||||||
\(45\) | −0.132682 | −0.0197791 | ||||||||
\(46\) | 13.8187 | 2.03745 | ||||||||
\(47\) | 2.52668 | 0.368554 | 0.184277 | − | 0.982874i | \(-0.441006\pi\) | ||||
0.184277 | + | 0.982874i | \(0.441006\pi\) | |||||||
\(48\) | −0.0952967 | −0.0137549 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −11.4240 | −1.61560 | ||||||||
\(51\) | −4.60865 | −0.645340 | ||||||||
\(52\) | 9.77222 | 1.35516 | ||||||||
\(53\) | −8.38962 | −1.15240 | −0.576202 | − | 0.817308i | \(-0.695466\pi\) | ||||
−0.576202 | + | 0.817308i | \(0.695466\pi\) | |||||||
\(54\) | −2.29288 | −0.312021 | ||||||||
\(55\) | 0.183138 | 0.0246944 | ||||||||
\(56\) | 2.88278 | 0.385227 | ||||||||
\(57\) | 1.78380 | 0.236270 | ||||||||
\(58\) | 4.59090 | 0.602815 | ||||||||
\(59\) | 7.78977 | 1.01414 | 0.507071 | − | 0.861904i | \(-0.330728\pi\) | ||||
0.507071 | + | 0.861904i | \(0.330728\pi\) | |||||||
\(60\) | 0.432182 | 0.0557945 | ||||||||
\(61\) | 3.77711 | 0.483609 | 0.241804 | − | 0.970325i | \(-0.422261\pi\) | ||||
0.241804 | + | 0.970325i | \(0.422261\pi\) | |||||||
\(62\) | 21.8766 | 2.77834 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −12.9093 | −1.61366 | ||||||||
\(65\) | −0.398062 | −0.0493735 | ||||||||
\(66\) | 3.16481 | 0.389561 | ||||||||
\(67\) | −10.1772 | −1.24334 | −0.621670 | − | 0.783280i | \(-0.713545\pi\) | ||||
−0.621670 | + | 0.783280i | \(0.713545\pi\) | |||||||
\(68\) | 15.0116 | 1.82043 | ||||||||
\(69\) | −6.02678 | −0.725540 | ||||||||
\(70\) | −0.304223 | −0.0363616 | ||||||||
\(71\) | −2.19559 | −0.260569 | −0.130284 | − | 0.991477i | \(-0.541589\pi\) | ||||
−0.130284 | + | 0.991477i | \(0.541589\pi\) | |||||||
\(72\) | 2.88278 | 0.339739 | ||||||||
\(73\) | 1.19059 | 0.139348 | 0.0696738 | − | 0.997570i | \(-0.477804\pi\) | ||||
0.0696738 | + | 0.997570i | \(0.477804\pi\) | |||||||
\(74\) | 6.51543 | 0.757403 | ||||||||
\(75\) | 4.98240 | 0.575317 | ||||||||
\(76\) | −5.81033 | −0.666491 | ||||||||
\(77\) | −1.38028 | −0.157297 | ||||||||
\(78\) | −6.87890 | −0.778882 | ||||||||
\(79\) | −10.3605 | −1.16565 | −0.582826 | − | 0.812597i | \(-0.698053\pi\) | ||||
−0.582826 | + | 0.812597i | \(0.698053\pi\) | |||||||
\(80\) | −0.0126442 | −0.00141366 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 5.00462 | 0.552668 | ||||||||
\(83\) | 1.81059 | 0.198738 | 0.0993688 | − | 0.995051i | \(-0.468318\pi\) | ||||
0.0993688 | + | 0.995051i | \(0.468318\pi\) | |||||||
\(84\) | −3.25728 | −0.355398 | ||||||||
\(85\) | −0.611485 | −0.0663248 | ||||||||
\(86\) | 21.8185 | 2.35275 | ||||||||
\(87\) | −2.00225 | −0.214663 | ||||||||
\(88\) | −3.97904 | −0.424167 | ||||||||
\(89\) | −7.25065 | −0.768567 | −0.384284 | − | 0.923215i | \(-0.625552\pi\) | ||||
−0.384284 | + | 0.923215i | \(0.625552\pi\) | |||||||
\(90\) | −0.304223 | −0.0320680 | ||||||||
\(91\) | 3.00012 | 0.314498 | ||||||||
\(92\) | 19.6309 | 2.04666 | ||||||||
\(93\) | −9.54114 | −0.989370 | ||||||||
\(94\) | 5.79337 | 0.597540 | ||||||||
\(95\) | 0.236678 | 0.0242827 | ||||||||
\(96\) | 5.54705 | 0.566144 | ||||||||
\(97\) | 2.14183 | 0.217469 | 0.108735 | − | 0.994071i | \(-0.465320\pi\) | ||||
0.108735 | + | 0.994071i | \(0.465320\pi\) | |||||||
\(98\) | 2.29288 | 0.231615 | ||||||||
\(99\) | −1.38028 | −0.138723 | ||||||||
\(100\) | −16.2290 | −1.62290 | ||||||||
\(101\) | 16.2730 | 1.61922 | 0.809610 | − | 0.586969i | \(-0.199679\pi\) | ||||
0.809610 | + | 0.586969i | \(0.199679\pi\) | |||||||
\(102\) | −10.5670 | −1.04629 | ||||||||
\(103\) | −12.7663 | −1.25790 | −0.628952 | − | 0.777444i | \(-0.716516\pi\) | ||||
−0.628952 | + | 0.777444i | \(0.716516\pi\) | |||||||
\(104\) | 8.64868 | 0.848073 | ||||||||
\(105\) | 0.132682 | 0.0129484 | ||||||||
\(106\) | −19.2364 | −1.86840 | ||||||||
\(107\) | 1.40448 | 0.135776 | 0.0678880 | − | 0.997693i | \(-0.478374\pi\) | ||||
0.0678880 | + | 0.997693i | \(0.478374\pi\) | |||||||
\(108\) | −3.25728 | −0.313432 | ||||||||
\(109\) | 11.1108 | 1.06422 | 0.532111 | − | 0.846674i | \(-0.321399\pi\) | ||||
0.532111 | + | 0.846674i | \(0.321399\pi\) | |||||||
\(110\) | 0.419913 | 0.0400371 | ||||||||
\(111\) | −2.84160 | −0.269712 | ||||||||
\(112\) | 0.0952967 | 0.00900469 | ||||||||
\(113\) | 17.6560 | 1.66094 | 0.830469 | − | 0.557065i | \(-0.188073\pi\) | ||||
0.830469 | + | 0.557065i | \(0.188073\pi\) | |||||||
\(114\) | 4.09003 | 0.383067 | ||||||||
\(115\) | −0.799646 | −0.0745674 | ||||||||
\(116\) | 6.52187 | 0.605540 | ||||||||
\(117\) | 3.00012 | 0.277361 | ||||||||
\(118\) | 17.8610 | 1.64424 | ||||||||
\(119\) | 4.60865 | 0.422474 | ||||||||
\(120\) | 0.382493 | 0.0349167 | ||||||||
\(121\) | −9.09483 | −0.826803 | ||||||||
\(122\) | 8.66043 | 0.784079 | ||||||||
\(123\) | −2.18268 | −0.196806 | ||||||||
\(124\) | 31.0781 | 2.79090 | ||||||||
\(125\) | 1.32448 | 0.118466 | ||||||||
\(126\) | 2.29288 | 0.204266 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | −18.5053 | −1.63565 | ||||||||
\(129\) | −9.51578 | −0.837817 | ||||||||
\(130\) | −0.912706 | −0.0800497 | ||||||||
\(131\) | 5.73840 | 0.501367 | 0.250683 | − | 0.968069i | \(-0.419345\pi\) | ||||
0.250683 | + | 0.968069i | \(0.419345\pi\) | |||||||
\(132\) | 4.49595 | 0.391322 | ||||||||
\(133\) | −1.78380 | −0.154675 | ||||||||
\(134\) | −23.3350 | −2.01584 | ||||||||
\(135\) | 0.132682 | 0.0114195 | ||||||||
\(136\) | 13.2857 | 1.13924 | ||||||||
\(137\) | −9.98542 | −0.853112 | −0.426556 | − | 0.904461i | \(-0.640273\pi\) | ||||
−0.426556 | + | 0.904461i | \(0.640273\pi\) | |||||||
\(138\) | −13.8187 | −1.17632 | ||||||||
\(139\) | 7.44343 | 0.631344 | 0.315672 | − | 0.948868i | \(-0.397770\pi\) | ||||
0.315672 | + | 0.948868i | \(0.397770\pi\) | |||||||
\(140\) | −0.432182 | −0.0365261 | ||||||||
\(141\) | −2.52668 | −0.212785 | ||||||||
\(142\) | −5.03422 | −0.422462 | ||||||||
\(143\) | −4.14100 | −0.346288 | ||||||||
\(144\) | 0.0952967 | 0.00794139 | ||||||||
\(145\) | −0.265662 | −0.0220620 | ||||||||
\(146\) | 2.72987 | 0.225925 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 9.25587 | 0.760828 | ||||||||
\(149\) | 8.64989 | 0.708626 | 0.354313 | − | 0.935127i | \(-0.384715\pi\) | ||||
0.354313 | + | 0.935127i | \(0.384715\pi\) | |||||||
\(150\) | 11.4240 | 0.932767 | ||||||||
\(151\) | 0.112505 | 0.00915555 | 0.00457778 | − | 0.999990i | \(-0.498543\pi\) | ||||
0.00457778 | + | 0.999990i | \(0.498543\pi\) | |||||||
\(152\) | −5.14230 | −0.417096 | ||||||||
\(153\) | 4.60865 | 0.372587 | ||||||||
\(154\) | −3.16481 | −0.255027 | ||||||||
\(155\) | −1.26594 | −0.101683 | ||||||||
\(156\) | −9.77222 | −0.782404 | ||||||||
\(157\) | 10.2079 | 0.814679 | 0.407340 | − | 0.913277i | \(-0.366457\pi\) | ||||
0.407340 | + | 0.913277i | \(0.366457\pi\) | |||||||
\(158\) | −23.7554 | −1.88988 | ||||||||
\(159\) | 8.38962 | 0.665340 | ||||||||
\(160\) | 0.735994 | 0.0581854 | ||||||||
\(161\) | 6.02678 | 0.474977 | ||||||||
\(162\) | 2.29288 | 0.180145 | ||||||||
\(163\) | −12.2432 | −0.958964 | −0.479482 | − | 0.877552i | \(-0.659175\pi\) | ||||
−0.479482 | + | 0.877552i | \(0.659175\pi\) | |||||||
\(164\) | 7.10961 | 0.555167 | ||||||||
\(165\) | −0.183138 | −0.0142573 | ||||||||
\(166\) | 4.15145 | 0.322215 | ||||||||
\(167\) | −21.7101 | −1.67998 | −0.839990 | − | 0.542602i | \(-0.817439\pi\) | ||||
−0.839990 | + | 0.542602i | \(0.817439\pi\) | |||||||
\(168\) | −2.88278 | −0.222411 | ||||||||
\(169\) | −3.99928 | −0.307637 | ||||||||
\(170\) | −1.40206 | −0.107533 | ||||||||
\(171\) | −1.78380 | −0.136411 | ||||||||
\(172\) | 30.9955 | 2.36339 | ||||||||
\(173\) | −2.24784 | −0.170900 | −0.0854501 | − | 0.996342i | \(-0.527233\pi\) | ||||
−0.0854501 | + | 0.996342i | \(0.527233\pi\) | |||||||
\(174\) | −4.59090 | −0.348035 | ||||||||
\(175\) | −4.98240 | −0.376634 | ||||||||
\(176\) | −0.131536 | −0.00991490 | ||||||||
\(177\) | −7.78977 | −0.585515 | ||||||||
\(178\) | −16.6248 | −1.24608 | ||||||||
\(179\) | −2.39212 | −0.178796 | −0.0893979 | − | 0.995996i | \(-0.528494\pi\) | ||||
−0.0893979 | + | 0.995996i | \(0.528494\pi\) | |||||||
\(180\) | −0.432182 | −0.0322129 | ||||||||
\(181\) | −20.6405 | −1.53420 | −0.767098 | − | 0.641530i | \(-0.778300\pi\) | ||||
−0.767098 | + | 0.641530i | \(0.778300\pi\) | |||||||
\(182\) | 6.87890 | 0.509898 | ||||||||
\(183\) | −3.77711 | −0.279212 | ||||||||
\(184\) | 17.3739 | 1.28082 | ||||||||
\(185\) | −0.377029 | −0.0277197 | ||||||||
\(186\) | −21.8766 | −1.60407 | ||||||||
\(187\) | −6.36122 | −0.465178 | ||||||||
\(188\) | 8.23010 | 0.600242 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0.542674 | 0.0393697 | ||||||||
\(191\) | −16.1222 | −1.16656 | −0.583279 | − | 0.812272i | \(-0.698231\pi\) | ||||
−0.583279 | + | 0.812272i | \(0.698231\pi\) | |||||||
\(192\) | 12.9093 | 0.931648 | ||||||||
\(193\) | 8.63114 | 0.621283 | 0.310642 | − | 0.950527i | \(-0.399456\pi\) | ||||
0.310642 | + | 0.950527i | \(0.399456\pi\) | |||||||
\(194\) | 4.91094 | 0.352585 | ||||||||
\(195\) | 0.398062 | 0.0285058 | ||||||||
\(196\) | 3.25728 | 0.232663 | ||||||||
\(197\) | 0.747074 | 0.0532268 | 0.0266134 | − | 0.999646i | \(-0.491528\pi\) | ||||
0.0266134 | + | 0.999646i | \(0.491528\pi\) | |||||||
\(198\) | −3.16481 | −0.224913 | ||||||||
\(199\) | −1.78469 | −0.126513 | −0.0632565 | − | 0.997997i | \(-0.520149\pi\) | ||||
−0.0632565 | + | 0.997997i | \(0.520149\pi\) | |||||||
\(200\) | −14.3631 | −1.01563 | ||||||||
\(201\) | 10.1772 | 0.717842 | ||||||||
\(202\) | 37.3118 | 2.62525 | ||||||||
\(203\) | 2.00225 | 0.140530 | ||||||||
\(204\) | −15.0116 | −1.05102 | ||||||||
\(205\) | −0.289603 | −0.0202268 | ||||||||
\(206\) | −29.2716 | −2.03945 | ||||||||
\(207\) | 6.02678 | 0.418890 | ||||||||
\(208\) | 0.285902 | 0.0198237 | ||||||||
\(209\) | 2.46214 | 0.170310 | ||||||||
\(210\) | 0.304223 | 0.0209934 | ||||||||
\(211\) | −13.0567 | −0.898862 | −0.449431 | − | 0.893315i | \(-0.648373\pi\) | ||||
−0.449431 | + | 0.893315i | \(0.648373\pi\) | |||||||
\(212\) | −27.3273 | −1.87685 | ||||||||
\(213\) | 2.19559 | 0.150440 | ||||||||
\(214\) | 3.22029 | 0.220135 | ||||||||
\(215\) | −1.26257 | −0.0861067 | ||||||||
\(216\) | −2.88278 | −0.196148 | ||||||||
\(217\) | 9.54114 | 0.647695 | ||||||||
\(218\) | 25.4757 | 1.72543 | ||||||||
\(219\) | −1.19059 | −0.0804524 | ||||||||
\(220\) | 0.596532 | 0.0402182 | ||||||||
\(221\) | 13.8265 | 0.930070 | ||||||||
\(222\) | −6.51543 | −0.437287 | ||||||||
\(223\) | −9.47976 | −0.634812 | −0.317406 | − | 0.948290i | \(-0.602812\pi\) | ||||
−0.317406 | + | 0.948290i | \(0.602812\pi\) | |||||||
\(224\) | −5.54705 | −0.370628 | ||||||||
\(225\) | −4.98240 | −0.332160 | ||||||||
\(226\) | 40.4830 | 2.69289 | ||||||||
\(227\) | 3.99593 | 0.265219 | 0.132610 | − | 0.991168i | \(-0.457664\pi\) | ||||
0.132610 | + | 0.991168i | \(0.457664\pi\) | |||||||
\(228\) | 5.81033 | 0.384799 | ||||||||
\(229\) | 5.69325 | 0.376220 | 0.188110 | − | 0.982148i | \(-0.439764\pi\) | ||||
0.188110 | + | 0.982148i | \(0.439764\pi\) | |||||||
\(230\) | −1.83349 | −0.120897 | ||||||||
\(231\) | 1.38028 | 0.0908157 | ||||||||
\(232\) | 5.77203 | 0.378952 | ||||||||
\(233\) | −11.1279 | −0.729014 | −0.364507 | − | 0.931201i | \(-0.618762\pi\) | ||||
−0.364507 | + | 0.931201i | \(0.618762\pi\) | |||||||
\(234\) | 6.87890 | 0.449688 | ||||||||
\(235\) | −0.335245 | −0.0218690 | ||||||||
\(236\) | 25.3734 | 1.65167 | ||||||||
\(237\) | 10.3605 | 0.672990 | ||||||||
\(238\) | 10.5670 | 0.684960 | ||||||||
\(239\) | −8.65428 | −0.559799 | −0.279900 | − | 0.960029i | \(-0.590301\pi\) | ||||
−0.279900 | + | 0.960029i | \(0.590301\pi\) | |||||||
\(240\) | 0.0126442 | 0.000816177 0 | ||||||||
\(241\) | −26.5941 | −1.71308 | −0.856538 | − | 0.516083i | \(-0.827390\pi\) | ||||
−0.856538 | + | 0.516083i | \(0.827390\pi\) | |||||||
\(242\) | −20.8533 | −1.34050 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 12.3031 | 0.787624 | ||||||||
\(245\) | −0.132682 | −0.00847674 | ||||||||
\(246\) | −5.00462 | −0.319083 | ||||||||
\(247\) | −5.35162 | −0.340515 | ||||||||
\(248\) | 27.5050 | 1.74657 | ||||||||
\(249\) | −1.81059 | −0.114741 | ||||||||
\(250\) | 3.03688 | 0.192069 | ||||||||
\(251\) | −6.80462 | −0.429504 | −0.214752 | − | 0.976669i | \(-0.568894\pi\) | ||||
−0.214752 | + | 0.976669i | \(0.568894\pi\) | |||||||
\(252\) | 3.25728 | 0.205189 | ||||||||
\(253\) | −8.31864 | −0.522989 | ||||||||
\(254\) | −2.29288 | −0.143868 | ||||||||
\(255\) | 0.611485 | 0.0382926 | ||||||||
\(256\) | −16.6117 | −1.03823 | ||||||||
\(257\) | 25.0375 | 1.56180 | 0.780898 | − | 0.624658i | \(-0.214762\pi\) | ||||
0.780898 | + | 0.624658i | \(0.214762\pi\) | |||||||
\(258\) | −21.8185 | −1.35836 | ||||||||
\(259\) | 2.84160 | 0.176568 | ||||||||
\(260\) | −1.29660 | −0.0804116 | ||||||||
\(261\) | 2.00225 | 0.123936 | ||||||||
\(262\) | 13.1574 | 0.812870 | ||||||||
\(263\) | −18.7441 | −1.15581 | −0.577905 | − | 0.816104i | \(-0.696130\pi\) | ||||
−0.577905 | + | 0.816104i | \(0.696130\pi\) | |||||||
\(264\) | 3.97904 | 0.244893 | ||||||||
\(265\) | 1.11315 | 0.0683804 | ||||||||
\(266\) | −4.09003 | −0.250776 | ||||||||
\(267\) | 7.25065 | 0.443732 | ||||||||
\(268\) | −33.1499 | −2.02495 | ||||||||
\(269\) | 11.3046 | 0.689253 | 0.344627 | − | 0.938740i | \(-0.388005\pi\) | ||||
0.344627 | + | 0.938740i | \(0.388005\pi\) | |||||||
\(270\) | 0.304223 | 0.0185144 | ||||||||
\(271\) | −19.6892 | −1.19604 | −0.598018 | − | 0.801483i | \(-0.704045\pi\) | ||||
−0.598018 | + | 0.801483i | \(0.704045\pi\) | |||||||
\(272\) | 0.439189 | 0.0266297 | ||||||||
\(273\) | −3.00012 | −0.181576 | ||||||||
\(274\) | −22.8953 | −1.38316 | ||||||||
\(275\) | 6.87710 | 0.414704 | ||||||||
\(276\) | −19.6309 | −1.18164 | ||||||||
\(277\) | −19.1796 | −1.15239 | −0.576196 | − | 0.817311i | \(-0.695464\pi\) | ||||
−0.576196 | + | 0.817311i | \(0.695464\pi\) | |||||||
\(278\) | 17.0669 | 1.02360 | ||||||||
\(279\) | 9.54114 | 0.571213 | ||||||||
\(280\) | −0.382493 | −0.0228583 | ||||||||
\(281\) | −5.36195 | −0.319867 | −0.159934 | − | 0.987128i | \(-0.551128\pi\) | ||||
−0.159934 | + | 0.987128i | \(0.551128\pi\) | |||||||
\(282\) | −5.79337 | −0.344990 | ||||||||
\(283\) | −25.2685 | −1.50206 | −0.751028 | − | 0.660271i | \(-0.770442\pi\) | ||||
−0.751028 | + | 0.660271i | \(0.770442\pi\) | |||||||
\(284\) | −7.15165 | −0.424372 | ||||||||
\(285\) | −0.236678 | −0.0140196 | ||||||||
\(286\) | −9.49480 | −0.561439 | ||||||||
\(287\) | 2.18268 | 0.128840 | ||||||||
\(288\) | −5.54705 | −0.326863 | ||||||||
\(289\) | 4.23962 | 0.249389 | ||||||||
\(290\) | −0.609130 | −0.0357694 | ||||||||
\(291\) | −2.14183 | −0.125556 | ||||||||
\(292\) | 3.87807 | 0.226947 | ||||||||
\(293\) | 18.0751 | 1.05596 | 0.527980 | − | 0.849257i | \(-0.322950\pi\) | ||||
0.527980 | + | 0.849257i | \(0.322950\pi\) | |||||||
\(294\) | −2.29288 | −0.133723 | ||||||||
\(295\) | −1.03356 | −0.0601763 | ||||||||
\(296\) | 8.19169 | 0.476132 | ||||||||
\(297\) | 1.38028 | 0.0800919 | ||||||||
\(298\) | 19.8331 | 1.14890 | ||||||||
\(299\) | 18.0811 | 1.04566 | ||||||||
\(300\) | 16.2290 | 0.936984 | ||||||||
\(301\) | 9.51578 | 0.548480 | ||||||||
\(302\) | 0.257961 | 0.0148440 | ||||||||
\(303\) | −16.2730 | −0.934857 | ||||||||
\(304\) | −0.169990 | −0.00974962 | ||||||||
\(305\) | −0.501154 | −0.0286960 | ||||||||
\(306\) | 10.5670 | 0.604078 | ||||||||
\(307\) | 19.0494 | 1.08721 | 0.543604 | − | 0.839342i | \(-0.317059\pi\) | ||||
0.543604 | + | 0.839342i | \(0.317059\pi\) | |||||||
\(308\) | −4.49595 | −0.256181 | ||||||||
\(309\) | 12.7663 | 0.726251 | ||||||||
\(310\) | −2.90264 | −0.164859 | ||||||||
\(311\) | 4.75698 | 0.269744 | 0.134872 | − | 0.990863i | \(-0.456938\pi\) | ||||
0.134872 | + | 0.990863i | \(0.456938\pi\) | |||||||
\(312\) | −8.64868 | −0.489635 | ||||||||
\(313\) | 1.35571 | 0.0766292 | 0.0383146 | − | 0.999266i | \(-0.487801\pi\) | ||||
0.0383146 | + | 0.999266i | \(0.487801\pi\) | |||||||
\(314\) | 23.4054 | 1.32085 | ||||||||
\(315\) | −0.132682 | −0.00747579 | ||||||||
\(316\) | −33.7472 | −1.89843 | ||||||||
\(317\) | −13.3742 | −0.751173 | −0.375586 | − | 0.926787i | \(-0.622559\pi\) | ||||
−0.375586 | + | 0.926787i | \(0.622559\pi\) | |||||||
\(318\) | 19.2364 | 1.07872 | ||||||||
\(319\) | −2.76366 | −0.154735 | ||||||||
\(320\) | 1.71283 | 0.0957502 | ||||||||
\(321\) | −1.40448 | −0.0783903 | ||||||||
\(322\) | 13.8187 | 0.770084 | ||||||||
\(323\) | −8.22091 | −0.457424 | ||||||||
\(324\) | 3.25728 | 0.180960 | ||||||||
\(325\) | −14.9478 | −0.829154 | ||||||||
\(326\) | −28.0722 | −1.55477 | ||||||||
\(327\) | −11.1108 | −0.614429 | ||||||||
\(328\) | 6.29219 | 0.347428 | ||||||||
\(329\) | 2.52668 | 0.139300 | ||||||||
\(330\) | −0.419913 | −0.0231155 | ||||||||
\(331\) | −11.6504 | −0.640367 | −0.320183 | − | 0.947356i | \(-0.603744\pi\) | ||||
−0.320183 | + | 0.947356i | \(0.603744\pi\) | |||||||
\(332\) | 5.89758 | 0.323672 | ||||||||
\(333\) | 2.84160 | 0.155719 | ||||||||
\(334\) | −49.7786 | −2.72376 | ||||||||
\(335\) | 1.35033 | 0.0737763 | ||||||||
\(336\) | −0.0952967 | −0.00519886 | ||||||||
\(337\) | 16.5945 | 0.903962 | 0.451981 | − | 0.892028i | \(-0.350718\pi\) | ||||
0.451981 | + | 0.892028i | \(0.350718\pi\) | |||||||
\(338\) | −9.16985 | −0.498774 | ||||||||
\(339\) | −17.6560 | −0.958943 | ||||||||
\(340\) | −1.99177 | −0.108019 | ||||||||
\(341\) | −13.1694 | −0.713165 | ||||||||
\(342\) | −4.09003 | −0.221164 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 27.4319 | 1.47903 | ||||||||
\(345\) | 0.799646 | 0.0430515 | ||||||||
\(346\) | −5.15402 | −0.277082 | ||||||||
\(347\) | 1.74448 | 0.0936485 | 0.0468242 | − | 0.998903i | \(-0.485090\pi\) | ||||
0.0468242 | + | 0.998903i | \(0.485090\pi\) | |||||||
\(348\) | −6.52187 | −0.349609 | ||||||||
\(349\) | 32.0356 | 1.71483 | 0.857413 | − | 0.514629i | \(-0.172070\pi\) | ||||
0.857413 | + | 0.514629i | \(0.172070\pi\) | |||||||
\(350\) | −11.4240 | −0.610639 | ||||||||
\(351\) | −3.00012 | −0.160135 | ||||||||
\(352\) | 7.65648 | 0.408092 | ||||||||
\(353\) | −15.9793 | −0.850494 | −0.425247 | − | 0.905077i | \(-0.639813\pi\) | ||||
−0.425247 | + | 0.905077i | \(0.639813\pi\) | |||||||
\(354\) | −17.8610 | −0.949300 | ||||||||
\(355\) | 0.291316 | 0.0154614 | ||||||||
\(356\) | −23.6174 | −1.25172 | ||||||||
\(357\) | −4.60865 | −0.243915 | ||||||||
\(358\) | −5.48484 | −0.289883 | ||||||||
\(359\) | −22.8017 | −1.20343 | −0.601713 | − | 0.798712i | \(-0.705515\pi\) | ||||
−0.601713 | + | 0.798712i | \(0.705515\pi\) | |||||||
\(360\) | −0.382493 | −0.0201591 | ||||||||
\(361\) | −15.8181 | −0.832529 | ||||||||
\(362\) | −47.3261 | −2.48740 | ||||||||
\(363\) | 9.09483 | 0.477355 | ||||||||
\(364\) | 9.77222 | 0.512203 | ||||||||
\(365\) | −0.157969 | −0.00826850 | ||||||||
\(366\) | −8.66043 | −0.452688 | ||||||||
\(367\) | −2.46175 | −0.128502 | −0.0642511 | − | 0.997934i | \(-0.520466\pi\) | ||||
−0.0642511 | + | 0.997934i | \(0.520466\pi\) | |||||||
\(368\) | 0.574333 | 0.0299392 | ||||||||
\(369\) | 2.18268 | 0.113626 | ||||||||
\(370\) | −0.864480 | −0.0449422 | ||||||||
\(371\) | −8.38962 | −0.435567 | ||||||||
\(372\) | −31.0781 | −1.61133 | ||||||||
\(373\) | −25.6753 | −1.32942 | −0.664708 | − | 0.747103i | \(-0.731444\pi\) | ||||
−0.664708 | + | 0.747103i | \(0.731444\pi\) | |||||||
\(374\) | −14.5855 | −0.754197 | ||||||||
\(375\) | −1.32448 | −0.0683961 | ||||||||
\(376\) | 7.28386 | 0.375637 | ||||||||
\(377\) | 6.00698 | 0.309375 | ||||||||
\(378\) | −2.29288 | −0.117933 | ||||||||
\(379\) | 28.6117 | 1.46968 | 0.734842 | − | 0.678239i | \(-0.237256\pi\) | ||||
0.734842 | + | 0.678239i | \(0.237256\pi\) | |||||||
\(380\) | 0.770927 | 0.0395477 | ||||||||
\(381\) | 1.00000 | 0.0512316 | ||||||||
\(382\) | −36.9661 | −1.89135 | ||||||||
\(383\) | −28.5878 | −1.46077 | −0.730385 | − | 0.683036i | \(-0.760659\pi\) | ||||
−0.730385 | + | 0.683036i | \(0.760659\pi\) | |||||||
\(384\) | 18.5053 | 0.944344 | ||||||||
\(385\) | 0.183138 | 0.00933359 | ||||||||
\(386\) | 19.7901 | 1.00729 | ||||||||
\(387\) | 9.51578 | 0.483714 | ||||||||
\(388\) | 6.97652 | 0.354179 | ||||||||
\(389\) | 17.3188 | 0.878096 | 0.439048 | − | 0.898464i | \(-0.355316\pi\) | ||||
0.439048 | + | 0.898464i | \(0.355316\pi\) | |||||||
\(390\) | 0.912706 | 0.0462167 | ||||||||
\(391\) | 27.7753 | 1.40466 | ||||||||
\(392\) | 2.88278 | 0.145602 | ||||||||
\(393\) | −5.73840 | −0.289464 | ||||||||
\(394\) | 1.71295 | 0.0862970 | ||||||||
\(395\) | 1.37466 | 0.0691666 | ||||||||
\(396\) | −4.49595 | −0.225930 | ||||||||
\(397\) | −15.8409 | −0.795031 | −0.397515 | − | 0.917595i | \(-0.630127\pi\) | ||||
−0.397515 | + | 0.917595i | \(0.630127\pi\) | |||||||
\(398\) | −4.09206 | −0.205116 | ||||||||
\(399\) | 1.78380 | 0.0893017 | ||||||||
\(400\) | −0.474806 | −0.0237403 | ||||||||
\(401\) | 25.1098 | 1.25392 | 0.626962 | − | 0.779050i | \(-0.284298\pi\) | ||||
0.626962 | + | 0.779050i | \(0.284298\pi\) | |||||||
\(402\) | 23.3350 | 1.16384 | ||||||||
\(403\) | 28.6246 | 1.42589 | ||||||||
\(404\) | 53.0055 | 2.63712 | ||||||||
\(405\) | −0.132682 | −0.00659302 | ||||||||
\(406\) | 4.59090 | 0.227843 | ||||||||
\(407\) | −3.92220 | −0.194416 | ||||||||
\(408\) | −13.2857 | −0.657740 | ||||||||
\(409\) | 8.42996 | 0.416835 | 0.208417 | − | 0.978040i | \(-0.433169\pi\) | ||||
0.208417 | + | 0.978040i | \(0.433169\pi\) | |||||||
\(410\) | −0.664024 | −0.0327938 | ||||||||
\(411\) | 9.98542 | 0.492544 | ||||||||
\(412\) | −41.5835 | −2.04867 | ||||||||
\(413\) | 7.78977 | 0.383310 | ||||||||
\(414\) | 13.8187 | 0.679150 | ||||||||
\(415\) | −0.240232 | −0.0117925 | ||||||||
\(416\) | −16.6418 | −0.815932 | ||||||||
\(417\) | −7.44343 | −0.364506 | ||||||||
\(418\) | 5.64539 | 0.276125 | ||||||||
\(419\) | −17.2527 | −0.842851 | −0.421425 | − | 0.906863i | \(-0.638470\pi\) | ||||
−0.421425 | + | 0.906863i | \(0.638470\pi\) | |||||||
\(420\) | 0.432182 | 0.0210883 | ||||||||
\(421\) | 27.9955 | 1.36442 | 0.682209 | − | 0.731157i | \(-0.261019\pi\) | ||||
0.682209 | + | 0.731157i | \(0.261019\pi\) | |||||||
\(422\) | −29.9375 | −1.45733 | ||||||||
\(423\) | 2.52668 | 0.122851 | ||||||||
\(424\) | −24.1854 | −1.17455 | ||||||||
\(425\) | −22.9621 | −1.11383 | ||||||||
\(426\) | 5.03422 | 0.243909 | ||||||||
\(427\) | 3.77711 | 0.182787 | ||||||||
\(428\) | 4.57477 | 0.221130 | ||||||||
\(429\) | 4.14100 | 0.199929 | ||||||||
\(430\) | −2.89492 | −0.139605 | ||||||||
\(431\) | −12.7499 | −0.614142 | −0.307071 | − | 0.951687i | \(-0.599349\pi\) | ||||
−0.307071 | + | 0.951687i | \(0.599349\pi\) | |||||||
\(432\) | −0.0952967 | −0.00458496 | ||||||||
\(433\) | 5.67855 | 0.272894 | 0.136447 | − | 0.990647i | \(-0.456432\pi\) | ||||
0.136447 | + | 0.990647i | \(0.456432\pi\) | |||||||
\(434\) | 21.8766 | 1.05011 | ||||||||
\(435\) | 0.265662 | 0.0127375 | ||||||||
\(436\) | 36.1910 | 1.73323 | ||||||||
\(437\) | −10.7506 | −0.514270 | ||||||||
\(438\) | −2.72987 | −0.130438 | ||||||||
\(439\) | −37.3733 | −1.78373 | −0.891865 | − | 0.452302i | \(-0.850603\pi\) | ||||
−0.891865 | + | 0.452302i | \(0.850603\pi\) | |||||||
\(440\) | 0.527947 | 0.0251689 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 31.7024 | 1.50793 | ||||||||
\(443\) | 22.9515 | 1.09046 | 0.545230 | − | 0.838287i | \(-0.316442\pi\) | ||||
0.545230 | + | 0.838287i | \(0.316442\pi\) | |||||||
\(444\) | −9.25587 | −0.439264 | ||||||||
\(445\) | 0.962031 | 0.0456046 | ||||||||
\(446\) | −21.7359 | −1.02922 | ||||||||
\(447\) | −8.64989 | −0.409126 | ||||||||
\(448\) | −12.9093 | −0.609907 | ||||||||
\(449\) | 30.4308 | 1.43612 | 0.718059 | − | 0.695982i | \(-0.245031\pi\) | ||||
0.718059 | + | 0.695982i | \(0.245031\pi\) | |||||||
\(450\) | −11.4240 | −0.538533 | ||||||||
\(451\) | −3.01271 | −0.141863 | ||||||||
\(452\) | 57.5105 | 2.70507 | ||||||||
\(453\) | −0.112505 | −0.00528596 | ||||||||
\(454\) | 9.16216 | 0.430002 | ||||||||
\(455\) | −0.398062 | −0.0186614 | ||||||||
\(456\) | 5.14230 | 0.240810 | ||||||||
\(457\) | −32.1203 | −1.50252 | −0.751261 | − | 0.660005i | \(-0.770554\pi\) | ||||
−0.751261 | + | 0.660005i | \(0.770554\pi\) | |||||||
\(458\) | 13.0539 | 0.609969 | ||||||||
\(459\) | −4.60865 | −0.215113 | ||||||||
\(460\) | −2.60467 | −0.121443 | ||||||||
\(461\) | 11.1704 | 0.520259 | 0.260129 | − | 0.965574i | \(-0.416235\pi\) | ||||
0.260129 | + | 0.965574i | \(0.416235\pi\) | |||||||
\(462\) | 3.16481 | 0.147240 | ||||||||
\(463\) | 25.3971 | 1.18030 | 0.590152 | − | 0.807292i | \(-0.299068\pi\) | ||||
0.590152 | + | 0.807292i | \(0.299068\pi\) | |||||||
\(464\) | 0.190807 | 0.00885802 | ||||||||
\(465\) | 1.26594 | 0.0587065 | ||||||||
\(466\) | −25.5149 | −1.18196 | ||||||||
\(467\) | 37.9241 | 1.75492 | 0.877459 | − | 0.479652i | \(-0.159237\pi\) | ||||
0.877459 | + | 0.479652i | \(0.159237\pi\) | |||||||
\(468\) | 9.77222 | 0.451721 | ||||||||
\(469\) | −10.1772 | −0.469938 | ||||||||
\(470\) | −0.768676 | −0.0354564 | ||||||||
\(471\) | −10.2079 | −0.470355 | ||||||||
\(472\) | 22.4562 | 1.03363 | ||||||||
\(473\) | −13.1344 | −0.603921 | ||||||||
\(474\) | 23.7554 | 1.09112 | ||||||||
\(475\) | 8.88760 | 0.407791 | ||||||||
\(476\) | 15.0116 | 0.688057 | ||||||||
\(477\) | −8.38962 | −0.384134 | ||||||||
\(478\) | −19.8432 | −0.907606 | ||||||||
\(479\) | −9.94380 | −0.454344 | −0.227172 | − | 0.973855i | \(-0.572948\pi\) | ||||
−0.227172 | + | 0.973855i | \(0.572948\pi\) | |||||||
\(480\) | −0.735994 | −0.0335934 | ||||||||
\(481\) | 8.52513 | 0.388713 | ||||||||
\(482\) | −60.9770 | −2.77742 | ||||||||
\(483\) | −6.02678 | −0.274228 | ||||||||
\(484\) | −29.6244 | −1.34656 | ||||||||
\(485\) | −0.284182 | −0.0129040 | ||||||||
\(486\) | −2.29288 | −0.104007 | ||||||||
\(487\) | −3.73337 | −0.169175 | −0.0845876 | − | 0.996416i | \(-0.526957\pi\) | ||||
−0.0845876 | + | 0.996416i | \(0.526957\pi\) | |||||||
\(488\) | 10.8886 | 0.492902 | ||||||||
\(489\) | 12.2432 | 0.553658 | ||||||||
\(490\) | −0.304223 | −0.0137434 | ||||||||
\(491\) | 37.0833 | 1.67355 | 0.836773 | − | 0.547550i | \(-0.184439\pi\) | ||||
0.836773 | + | 0.547550i | \(0.184439\pi\) | |||||||
\(492\) | −7.10961 | −0.320526 | ||||||||
\(493\) | 9.22765 | 0.415592 | ||||||||
\(494\) | −12.2706 | −0.552080 | ||||||||
\(495\) | 0.183138 | 0.00823145 | ||||||||
\(496\) | 0.909239 | 0.0408260 | ||||||||
\(497\) | −2.19559 | −0.0984858 | ||||||||
\(498\) | −4.15145 | −0.186031 | ||||||||
\(499\) | 24.7993 | 1.11017 | 0.555084 | − | 0.831795i | \(-0.312686\pi\) | ||||
0.555084 | + | 0.831795i | \(0.312686\pi\) | |||||||
\(500\) | 4.31421 | 0.192937 | ||||||||
\(501\) | 21.7101 | 0.969937 | ||||||||
\(502\) | −15.6021 | −0.696357 | ||||||||
\(503\) | −27.4762 | −1.22510 | −0.612551 | − | 0.790431i | \(-0.709857\pi\) | ||||
−0.612551 | + | 0.790431i | \(0.709857\pi\) | |||||||
\(504\) | 2.88278 | 0.128409 | ||||||||
\(505\) | −2.15913 | −0.0960800 | ||||||||
\(506\) | −19.0736 | −0.847925 | ||||||||
\(507\) | 3.99928 | 0.177614 | ||||||||
\(508\) | −3.25728 | −0.144518 | ||||||||
\(509\) | 2.58766 | 0.114696 | 0.0573481 | − | 0.998354i | \(-0.481736\pi\) | ||||
0.0573481 | + | 0.998354i | \(0.481736\pi\) | |||||||
\(510\) | 1.40206 | 0.0620842 | ||||||||
\(511\) | 1.19059 | 0.0526684 | ||||||||
\(512\) | −1.07805 | −0.0476437 | ||||||||
\(513\) | 1.78380 | 0.0787567 | ||||||||
\(514\) | 57.4079 | 2.53215 | ||||||||
\(515\) | 1.69386 | 0.0746405 | ||||||||
\(516\) | −30.9955 | −1.36450 | ||||||||
\(517\) | −3.48753 | −0.153381 | ||||||||
\(518\) | 6.51543 | 0.286271 | ||||||||
\(519\) | 2.24784 | 0.0986692 | ||||||||
\(520\) | −1.14752 | −0.0503223 | ||||||||
\(521\) | −0.605284 | −0.0265180 | −0.0132590 | − | 0.999912i | \(-0.504221\pi\) | ||||
−0.0132590 | + | 0.999912i | \(0.504221\pi\) | |||||||
\(522\) | 4.59090 | 0.200938 | ||||||||
\(523\) | −17.0952 | −0.747522 | −0.373761 | − | 0.927525i | \(-0.621932\pi\) | ||||
−0.373761 | + | 0.927525i | \(0.621932\pi\) | |||||||
\(524\) | 18.6916 | 0.816545 | ||||||||
\(525\) | 4.98240 | 0.217450 | ||||||||
\(526\) | −42.9779 | −1.87392 | ||||||||
\(527\) | 43.9717 | 1.91544 | ||||||||
\(528\) | 0.131536 | 0.00572437 | ||||||||
\(529\) | 13.3221 | 0.579223 | ||||||||
\(530\) | 2.55232 | 0.110866 | ||||||||
\(531\) | 7.78977 | 0.338047 | ||||||||
\(532\) | −5.81033 | −0.251910 | ||||||||
\(533\) | 6.54831 | 0.283639 | ||||||||
\(534\) | 16.6248 | 0.719427 | ||||||||
\(535\) | −0.186349 | −0.00805656 | ||||||||
\(536\) | −29.3385 | −1.26723 | ||||||||
\(537\) | 2.39212 | 0.103228 | ||||||||
\(538\) | 25.9200 | 1.11749 | ||||||||
\(539\) | −1.38028 | −0.0594528 | ||||||||
\(540\) | 0.432182 | 0.0185982 | ||||||||
\(541\) | 3.19188 | 0.137230 | 0.0686149 | − | 0.997643i | \(-0.478142\pi\) | ||||
0.0686149 | + | 0.997643i | \(0.478142\pi\) | |||||||
\(542\) | −45.1449 | −1.93914 | ||||||||
\(543\) | 20.6405 | 0.885768 | ||||||||
\(544\) | −25.5644 | −1.09606 | ||||||||
\(545\) | −1.47421 | −0.0631480 | ||||||||
\(546\) | −6.87890 | −0.294390 | ||||||||
\(547\) | −44.2108 | −1.89032 | −0.945159 | − | 0.326610i | \(-0.894094\pi\) | ||||
−0.945159 | + | 0.326610i | \(0.894094\pi\) | |||||||
\(548\) | −32.5253 | −1.38941 | ||||||||
\(549\) | 3.77711 | 0.161203 | ||||||||
\(550\) | 15.7683 | 0.672363 | ||||||||
\(551\) | −3.57161 | −0.152156 | ||||||||
\(552\) | −17.3739 | −0.739481 | ||||||||
\(553\) | −10.3605 | −0.440575 | ||||||||
\(554\) | −43.9765 | −1.86838 | ||||||||
\(555\) | 0.377029 | 0.0160040 | ||||||||
\(556\) | 24.2453 | 1.02823 | ||||||||
\(557\) | −35.3458 | −1.49765 | −0.748826 | − | 0.662767i | \(-0.769382\pi\) | ||||
−0.748826 | + | 0.662767i | \(0.769382\pi\) | |||||||
\(558\) | 21.8766 | 0.926112 | ||||||||
\(559\) | 28.5485 | 1.20747 | ||||||||
\(560\) | −0.0126442 | −0.000534313 0 | ||||||||
\(561\) | 6.36122 | 0.268571 | ||||||||
\(562\) | −12.2943 | −0.518603 | ||||||||
\(563\) | −18.2180 | −0.767798 | −0.383899 | − | 0.923375i | \(-0.625419\pi\) | ||||
−0.383899 | + | 0.923375i | \(0.625419\pi\) | |||||||
\(564\) | −8.23010 | −0.346550 | ||||||||
\(565\) | −2.34264 | −0.0985554 | ||||||||
\(566\) | −57.9375 | −2.43529 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −6.32941 | −0.265576 | ||||||||
\(569\) | 30.8334 | 1.29260 | 0.646301 | − | 0.763083i | \(-0.276315\pi\) | ||||
0.646301 | + | 0.763083i | \(0.276315\pi\) | |||||||
\(570\) | −0.542674 | −0.0227301 | ||||||||
\(571\) | −19.1022 | −0.799401 | −0.399701 | − | 0.916646i | \(-0.630886\pi\) | ||||
−0.399701 | + | 0.916646i | \(0.630886\pi\) | |||||||
\(572\) | −13.4884 | −0.563978 | ||||||||
\(573\) | 16.1222 | 0.673513 | ||||||||
\(574\) | 5.00462 | 0.208889 | ||||||||
\(575\) | −30.0278 | −1.25225 | ||||||||
\(576\) | −12.9093 | −0.537887 | ||||||||
\(577\) | 19.0295 | 0.792207 | 0.396103 | − | 0.918206i | \(-0.370362\pi\) | ||||
0.396103 | + | 0.918206i | \(0.370362\pi\) | |||||||
\(578\) | 9.72091 | 0.404337 | ||||||||
\(579\) | −8.63114 | −0.358698 | ||||||||
\(580\) | −0.865335 | −0.0359311 | ||||||||
\(581\) | 1.81059 | 0.0751158 | ||||||||
\(582\) | −4.91094 | −0.203565 | ||||||||
\(583\) | 11.5800 | 0.479595 | ||||||||
\(584\) | 3.43220 | 0.142025 | ||||||||
\(585\) | −0.398062 | −0.0164578 | ||||||||
\(586\) | 41.4440 | 1.71203 | ||||||||
\(587\) | 13.9522 | 0.575868 | 0.287934 | − | 0.957650i | \(-0.407032\pi\) | ||||
0.287934 | + | 0.957650i | \(0.407032\pi\) | |||||||
\(588\) | −3.25728 | −0.134328 | ||||||||
\(589\) | −17.0195 | −0.701276 | ||||||||
\(590\) | −2.36983 | −0.0975644 | ||||||||
\(591\) | −0.747074 | −0.0307305 | ||||||||
\(592\) | 0.270795 | 0.0111296 | ||||||||
\(593\) | −11.3635 | −0.466642 | −0.233321 | − | 0.972400i | \(-0.574959\pi\) | ||||
−0.233321 | + | 0.972400i | \(0.574959\pi\) | |||||||
\(594\) | 3.16481 | 0.129854 | ||||||||
\(595\) | −0.611485 | −0.0250684 | ||||||||
\(596\) | 28.1751 | 1.15410 | ||||||||
\(597\) | 1.78469 | 0.0730423 | ||||||||
\(598\) | 41.4576 | 1.69533 | ||||||||
\(599\) | −7.97960 | −0.326037 | −0.163019 | − | 0.986623i | \(-0.552123\pi\) | ||||
−0.163019 | + | 0.986623i | \(0.552123\pi\) | |||||||
\(600\) | 14.3631 | 0.586373 | ||||||||
\(601\) | −27.4921 | −1.12143 | −0.560713 | − | 0.828010i | \(-0.689473\pi\) | ||||
−0.560713 | + | 0.828010i | \(0.689473\pi\) | |||||||
\(602\) | 21.8185 | 0.889255 | ||||||||
\(603\) | −10.1772 | −0.414446 | ||||||||
\(604\) | 0.366461 | 0.0149111 | ||||||||
\(605\) | 1.20672 | 0.0490602 | ||||||||
\(606\) | −37.3118 | −1.51569 | ||||||||
\(607\) | −1.64188 | −0.0666420 | −0.0333210 | − | 0.999445i | \(-0.510608\pi\) | ||||
−0.0333210 | + | 0.999445i | \(0.510608\pi\) | |||||||
\(608\) | 9.89484 | 0.401289 | ||||||||
\(609\) | −2.00225 | −0.0811351 | ||||||||
\(610\) | −1.14908 | −0.0465250 | ||||||||
\(611\) | 7.58035 | 0.306668 | ||||||||
\(612\) | 15.0116 | 0.606809 | ||||||||
\(613\) | −21.9275 | −0.885642 | −0.442821 | − | 0.896610i | \(-0.646022\pi\) | ||||
−0.442821 | + | 0.896610i | \(0.646022\pi\) | |||||||
\(614\) | 43.6780 | 1.76270 | ||||||||
\(615\) | 0.289603 | 0.0116779 | ||||||||
\(616\) | −3.97904 | −0.160320 | ||||||||
\(617\) | −28.4427 | −1.14506 | −0.572530 | − | 0.819883i | \(-0.694038\pi\) | ||||
−0.572530 | + | 0.819883i | \(0.694038\pi\) | |||||||
\(618\) | 29.2716 | 1.17748 | ||||||||
\(619\) | 28.9635 | 1.16414 | 0.582071 | − | 0.813138i | \(-0.302243\pi\) | ||||
0.582071 | + | 0.813138i | \(0.302243\pi\) | |||||||
\(620\) | −4.12351 | −0.165604 | ||||||||
\(621\) | −6.02678 | −0.241847 | ||||||||
\(622\) | 10.9072 | 0.437338 | ||||||||
\(623\) | −7.25065 | −0.290491 | ||||||||
\(624\) | −0.285902 | −0.0114452 | ||||||||
\(625\) | 24.7362 | 0.989450 | ||||||||
\(626\) | 3.10847 | 0.124240 | ||||||||
\(627\) | −2.46214 | −0.0983285 | ||||||||
\(628\) | 33.2499 | 1.32682 | ||||||||
\(629\) | 13.0959 | 0.522168 | ||||||||
\(630\) | −0.304223 | −0.0121205 | ||||||||
\(631\) | −26.5333 | −1.05627 | −0.528136 | − | 0.849160i | \(-0.677109\pi\) | ||||
−0.528136 | + | 0.849160i | \(0.677109\pi\) | |||||||
\(632\) | −29.8672 | −1.18805 | ||||||||
\(633\) | 13.0567 | 0.518958 | ||||||||
\(634\) | −30.6655 | −1.21788 | ||||||||
\(635\) | 0.132682 | 0.00526533 | ||||||||
\(636\) | 27.3273 | 1.08360 | ||||||||
\(637\) | 3.00012 | 0.118869 | ||||||||
\(638\) | −6.33672 | −0.250873 | ||||||||
\(639\) | −2.19559 | −0.0868563 | ||||||||
\(640\) | 2.45532 | 0.0970550 | ||||||||
\(641\) | 25.6409 | 1.01276 | 0.506378 | − | 0.862312i | \(-0.330984\pi\) | ||||
0.506378 | + | 0.862312i | \(0.330984\pi\) | |||||||
\(642\) | −3.22029 | −0.127095 | ||||||||
\(643\) | −43.4896 | −1.71506 | −0.857532 | − | 0.514431i | \(-0.828003\pi\) | ||||
−0.857532 | + | 0.514431i | \(0.828003\pi\) | |||||||
\(644\) | 19.6309 | 0.773566 | ||||||||
\(645\) | 1.26257 | 0.0497137 | ||||||||
\(646\) | −18.8495 | −0.741624 | ||||||||
\(647\) | 7.81527 | 0.307250 | 0.153625 | − | 0.988129i | \(-0.450905\pi\) | ||||
0.153625 | + | 0.988129i | \(0.450905\pi\) | |||||||
\(648\) | 2.88278 | 0.113246 | ||||||||
\(649\) | −10.7521 | −0.422055 | ||||||||
\(650\) | −34.2734 | −1.34431 | ||||||||
\(651\) | −9.54114 | −0.373947 | ||||||||
\(652\) | −39.8796 | −1.56180 | ||||||||
\(653\) | −20.2875 | −0.793912 | −0.396956 | − | 0.917838i | \(-0.629933\pi\) | ||||
−0.396956 | + | 0.917838i | \(0.629933\pi\) | |||||||
\(654\) | −25.4757 | −0.996179 | ||||||||
\(655\) | −0.761383 | −0.0297497 | ||||||||
\(656\) | 0.208003 | 0.00812114 | ||||||||
\(657\) | 1.19059 | 0.0464492 | ||||||||
\(658\) | 5.79337 | 0.225849 | ||||||||
\(659\) | 44.0567 | 1.71620 | 0.858102 | − | 0.513479i | \(-0.171644\pi\) | ||||
0.858102 | + | 0.513479i | \(0.171644\pi\) | |||||||
\(660\) | −0.596532 | −0.0232200 | ||||||||
\(661\) | −7.35149 | −0.285940 | −0.142970 | − | 0.989727i | \(-0.545665\pi\) | ||||
−0.142970 | + | 0.989727i | \(0.545665\pi\) | |||||||
\(662\) | −26.7130 | −1.03823 | ||||||||
\(663\) | −13.8265 | −0.536976 | ||||||||
\(664\) | 5.21952 | 0.202557 | ||||||||
\(665\) | 0.236678 | 0.00917799 | ||||||||
\(666\) | 6.51543 | 0.252468 | ||||||||
\(667\) | 12.0671 | 0.467240 | ||||||||
\(668\) | −70.7159 | −2.73608 | ||||||||
\(669\) | 9.47976 | 0.366509 | ||||||||
\(670\) | 3.09613 | 0.119614 | ||||||||
\(671\) | −5.21346 | −0.201263 | ||||||||
\(672\) | 5.54705 | 0.213982 | ||||||||
\(673\) | 19.8435 | 0.764912 | 0.382456 | − | 0.923974i | \(-0.375078\pi\) | ||||
0.382456 | + | 0.923974i | \(0.375078\pi\) | |||||||
\(674\) | 38.0492 | 1.46560 | ||||||||
\(675\) | 4.98240 | 0.191772 | ||||||||
\(676\) | −13.0268 | −0.501030 | ||||||||
\(677\) | −13.3359 | −0.512539 | −0.256269 | − | 0.966605i | \(-0.582493\pi\) | ||||
−0.256269 | + | 0.966605i | \(0.582493\pi\) | |||||||
\(678\) | −40.4830 | −1.55474 | ||||||||
\(679\) | 2.14183 | 0.0821957 | ||||||||
\(680\) | −1.76277 | −0.0675993 | ||||||||
\(681\) | −3.99593 | −0.153124 | ||||||||
\(682\) | −30.1959 | −1.15626 | ||||||||
\(683\) | −15.1569 | −0.579962 | −0.289981 | − | 0.957032i | \(-0.593649\pi\) | ||||
−0.289981 | + | 0.957032i | \(0.593649\pi\) | |||||||
\(684\) | −5.81033 | −0.222164 | ||||||||
\(685\) | 1.32489 | 0.0506213 | ||||||||
\(686\) | 2.29288 | 0.0875424 | ||||||||
\(687\) | −5.69325 | −0.217211 | ||||||||
\(688\) | 0.906822 | 0.0345723 | ||||||||
\(689\) | −25.1699 | −0.958895 | ||||||||
\(690\) | 1.83349 | 0.0697997 | ||||||||
\(691\) | −43.0546 | −1.63788 | −0.818938 | − | 0.573882i | \(-0.805437\pi\) | ||||
−0.818938 | + | 0.573882i | \(0.805437\pi\) | |||||||
\(692\) | −7.32184 | −0.278334 | ||||||||
\(693\) | −1.38028 | −0.0524325 | ||||||||
\(694\) | 3.99987 | 0.151833 | ||||||||
\(695\) | −0.987610 | −0.0374622 | ||||||||
\(696\) | −5.77203 | −0.218788 | ||||||||
\(697\) | 10.0592 | 0.381020 | ||||||||
\(698\) | 73.4536 | 2.78026 | ||||||||
\(699\) | 11.1279 | 0.420896 | ||||||||
\(700\) | −16.2290 | −0.613400 | ||||||||
\(701\) | 30.1134 | 1.13737 | 0.568685 | − | 0.822556i | \(-0.307453\pi\) | ||||
0.568685 | + | 0.822556i | \(0.307453\pi\) | |||||||
\(702\) | −6.87890 | −0.259627 | ||||||||
\(703\) | −5.06884 | −0.191175 | ||||||||
\(704\) | 17.8184 | 0.671557 | ||||||||
\(705\) | 0.335245 | 0.0126261 | ||||||||
\(706\) | −36.6386 | −1.37891 | ||||||||
\(707\) | 16.2730 | 0.612007 | ||||||||
\(708\) | −25.3734 | −0.953592 | ||||||||
\(709\) | −23.1425 | −0.869136 | −0.434568 | − | 0.900639i | \(-0.643099\pi\) | ||||
−0.434568 | + | 0.900639i | \(0.643099\pi\) | |||||||
\(710\) | 0.667951 | 0.0250677 | ||||||||
\(711\) | −10.3605 | −0.388551 | ||||||||
\(712\) | −20.9020 | −0.783336 | ||||||||
\(713\) | 57.5024 | 2.15348 | ||||||||
\(714\) | −10.5670 | −0.395462 | ||||||||
\(715\) | 0.549437 | 0.0205478 | ||||||||
\(716\) | −7.79181 | −0.291194 | ||||||||
\(717\) | 8.65428 | 0.323200 | ||||||||
\(718\) | −52.2814 | −1.95112 | ||||||||
\(719\) | 6.88533 | 0.256780 | 0.128390 | − | 0.991724i | \(-0.459019\pi\) | ||||
0.128390 | + | 0.991724i | \(0.459019\pi\) | |||||||
\(720\) | −0.0126442 | −0.000471220 0 | ||||||||
\(721\) | −12.7663 | −0.475443 | ||||||||
\(722\) | −36.2688 | −1.34979 | ||||||||
\(723\) | 26.5941 | 0.989045 | ||||||||
\(724\) | −67.2318 | −2.49865 | ||||||||
\(725\) | −9.97598 | −0.370499 | ||||||||
\(726\) | 20.8533 | 0.773939 | ||||||||
\(727\) | −3.64321 | −0.135119 | −0.0675596 | − | 0.997715i | \(-0.521521\pi\) | ||||
−0.0675596 | + | 0.997715i | \(0.521521\pi\) | |||||||
\(728\) | 8.64868 | 0.320541 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.362204 | −0.0134058 | ||||||||
\(731\) | 43.8548 | 1.62203 | ||||||||
\(732\) | −12.3031 | −0.454735 | ||||||||
\(733\) | 27.4346 | 1.01332 | 0.506660 | − | 0.862146i | \(-0.330880\pi\) | ||||
0.506660 | + | 0.862146i | \(0.330880\pi\) | |||||||
\(734\) | −5.64448 | −0.208342 | ||||||||
\(735\) | 0.132682 | 0.00489405 | ||||||||
\(736\) | −33.4309 | −1.23228 | ||||||||
\(737\) | 14.0473 | 0.517440 | ||||||||
\(738\) | 5.00462 | 0.184223 | ||||||||
\(739\) | −3.92099 | −0.144236 | −0.0721179 | − | 0.997396i | \(-0.522976\pi\) | ||||
−0.0721179 | + | 0.997396i | \(0.522976\pi\) | |||||||
\(740\) | −1.22809 | −0.0451454 | ||||||||
\(741\) | 5.35162 | 0.196597 | ||||||||
\(742\) | −19.2364 | −0.706189 | ||||||||
\(743\) | 50.9410 | 1.86885 | 0.934423 | − | 0.356165i | \(-0.115916\pi\) | ||||
0.934423 | + | 0.356165i | \(0.115916\pi\) | |||||||
\(744\) | −27.5050 | −1.00838 | ||||||||
\(745\) | −1.14768 | −0.0420479 | ||||||||
\(746\) | −58.8703 | −2.15539 | ||||||||
\(747\) | 1.81059 | 0.0662459 | ||||||||
\(748\) | −20.7202 | −0.757607 | ||||||||
\(749\) | 1.40448 | 0.0513185 | ||||||||
\(750\) | −3.03688 | −0.110891 | ||||||||
\(751\) | 3.73352 | 0.136238 | 0.0681191 | − | 0.997677i | \(-0.478300\pi\) | ||||
0.0681191 | + | 0.997677i | \(0.478300\pi\) | |||||||
\(752\) | 0.240784 | 0.00878051 | ||||||||
\(753\) | 6.80462 | 0.247974 | ||||||||
\(754\) | 13.7733 | 0.501592 | ||||||||
\(755\) | −0.0149274 | −0.000543265 0 | ||||||||
\(756\) | −3.25728 | −0.118466 | ||||||||
\(757\) | −0.802306 | −0.0291603 | −0.0145802 | − | 0.999894i | \(-0.504641\pi\) | ||||
−0.0145802 | + | 0.999894i | \(0.504641\pi\) | |||||||
\(758\) | 65.6030 | 2.38281 | ||||||||
\(759\) | 8.31864 | 0.301948 | ||||||||
\(760\) | 0.682291 | 0.0247493 | ||||||||
\(761\) | −28.3858 | −1.02899 | −0.514493 | − | 0.857495i | \(-0.672020\pi\) | ||||
−0.514493 | + | 0.857495i | \(0.672020\pi\) | |||||||
\(762\) | 2.29288 | 0.0830621 | ||||||||
\(763\) | 11.1108 | 0.402238 | ||||||||
\(764\) | −52.5143 | −1.89990 | ||||||||
\(765\) | −0.611485 | −0.0221083 | ||||||||
\(766\) | −65.5483 | −2.36836 | ||||||||
\(767\) | 23.3702 | 0.843851 | ||||||||
\(768\) | 16.6117 | 0.599424 | ||||||||
\(769\) | 37.0161 | 1.33483 | 0.667417 | − | 0.744684i | \(-0.267400\pi\) | ||||
0.667417 | + | 0.744684i | \(0.267400\pi\) | |||||||
\(770\) | 0.419913 | 0.0151326 | ||||||||
\(771\) | −25.0375 | −0.901704 | ||||||||
\(772\) | 28.1140 | 1.01185 | ||||||||
\(773\) | 13.8879 | 0.499514 | 0.249757 | − | 0.968309i | \(-0.419649\pi\) | ||||
0.249757 | + | 0.968309i | \(0.419649\pi\) | |||||||
\(774\) | 21.8185 | 0.784249 | ||||||||
\(775\) | −47.5377 | −1.70761 | ||||||||
\(776\) | 6.17441 | 0.221648 | ||||||||
\(777\) | −2.84160 | −0.101942 | ||||||||
\(778\) | 39.7098 | 1.42366 | ||||||||
\(779\) | −3.89347 | −0.139498 | ||||||||
\(780\) | 1.29660 | 0.0464257 | ||||||||
\(781\) | 3.03053 | 0.108441 | ||||||||
\(782\) | 63.6853 | 2.27738 | ||||||||
\(783\) | −2.00225 | −0.0715545 | ||||||||
\(784\) | 0.0952967 | 0.00340345 | ||||||||
\(785\) | −1.35440 | −0.0483408 | ||||||||
\(786\) | −13.1574 | −0.469311 | ||||||||
\(787\) | −4.72348 | −0.168374 | −0.0841869 | − | 0.996450i | \(-0.526829\pi\) | ||||
−0.0841869 | + | 0.996450i | \(0.526829\pi\) | |||||||
\(788\) | 2.43343 | 0.0866872 | ||||||||
\(789\) | 18.7441 | 0.667307 | ||||||||
\(790\) | 3.15192 | 0.112140 | ||||||||
\(791\) | 17.6560 | 0.627775 | ||||||||
\(792\) | −3.97904 | −0.141389 | ||||||||
\(793\) | 11.3318 | 0.402403 | ||||||||
\(794\) | −36.3212 | −1.28899 | ||||||||
\(795\) | −1.11315 | −0.0394794 | ||||||||
\(796\) | −5.81321 | −0.206044 | ||||||||
\(797\) | 7.11438 | 0.252004 | 0.126002 | − | 0.992030i | \(-0.459785\pi\) | ||||
0.126002 | + | 0.992030i | \(0.459785\pi\) | |||||||
\(798\) | 4.09003 | 0.144786 | ||||||||
\(799\) | 11.6446 | 0.411956 | ||||||||
\(800\) | 27.6376 | 0.977137 | ||||||||
\(801\) | −7.25065 | −0.256189 | ||||||||
\(802\) | 57.5736 | 2.03300 | ||||||||
\(803\) | −1.64334 | −0.0579923 | ||||||||
\(804\) | 33.1499 | 1.16911 | ||||||||
\(805\) | −0.799646 | −0.0281838 | ||||||||
\(806\) | 65.6325 | 2.31181 | ||||||||
\(807\) | −11.3046 | −0.397941 | ||||||||
\(808\) | 46.9113 | 1.65033 | ||||||||
\(809\) | −49.9190 | −1.75506 | −0.877529 | − | 0.479523i | \(-0.840810\pi\) | ||||
−0.877529 | + | 0.479523i | \(0.840810\pi\) | |||||||
\(810\) | −0.304223 | −0.0106893 | ||||||||
\(811\) | 24.6467 | 0.865464 | 0.432732 | − | 0.901523i | \(-0.357550\pi\) | ||||
0.432732 | + | 0.901523i | \(0.357550\pi\) | |||||||
\(812\) | 6.52187 | 0.228873 | ||||||||
\(813\) | 19.6892 | 0.690531 | ||||||||
\(814\) | −8.99311 | −0.315208 | ||||||||
\(815\) | 1.62446 | 0.0569022 | ||||||||
\(816\) | −0.439189 | −0.0153747 | ||||||||
\(817\) | −16.9743 | −0.593854 | ||||||||
\(818\) | 19.3288 | 0.675817 | ||||||||
\(819\) | 3.00012 | 0.104833 | ||||||||
\(820\) | −0.943317 | −0.0329421 | ||||||||
\(821\) | 19.0309 | 0.664183 | 0.332092 | − | 0.943247i | \(-0.392246\pi\) | ||||
0.332092 | + | 0.943247i | \(0.392246\pi\) | |||||||
\(822\) | 22.8953 | 0.798566 | ||||||||
\(823\) | 20.8785 | 0.727780 | 0.363890 | − | 0.931442i | \(-0.381448\pi\) | ||||
0.363890 | + | 0.931442i | \(0.381448\pi\) | |||||||
\(824\) | −36.8025 | −1.28208 | ||||||||
\(825\) | −6.87710 | −0.239430 | ||||||||
\(826\) | 17.8610 | 0.621463 | ||||||||
\(827\) | 30.7068 | 1.06778 | 0.533890 | − | 0.845554i | \(-0.320730\pi\) | ||||
0.533890 | + | 0.845554i | \(0.320730\pi\) | |||||||
\(828\) | 19.6309 | 0.682221 | ||||||||
\(829\) | 9.14687 | 0.317684 | 0.158842 | − | 0.987304i | \(-0.449224\pi\) | ||||
0.158842 | + | 0.987304i | \(0.449224\pi\) | |||||||
\(830\) | −0.550822 | −0.0191193 | ||||||||
\(831\) | 19.1796 | 0.665334 | ||||||||
\(832\) | −38.7294 | −1.34270 | ||||||||
\(833\) | 4.60865 | 0.159680 | ||||||||
\(834\) | −17.0669 | −0.590977 | ||||||||
\(835\) | 2.88054 | 0.0996853 | ||||||||
\(836\) | 8.01988 | 0.277373 | ||||||||
\(837\) | −9.54114 | −0.329790 | ||||||||
\(838\) | −39.5583 | −1.36652 | ||||||||
\(839\) | 48.3089 | 1.66781 | 0.833904 | − | 0.551909i | \(-0.186101\pi\) | ||||
0.833904 | + | 0.551909i | \(0.186101\pi\) | |||||||
\(840\) | 0.382493 | 0.0131973 | ||||||||
\(841\) | −24.9910 | −0.861759 | ||||||||
\(842\) | 64.1902 | 2.21214 | ||||||||
\(843\) | 5.36195 | 0.184676 | ||||||||
\(844\) | −42.5294 | −1.46392 | ||||||||
\(845\) | 0.530633 | 0.0182543 | ||||||||
\(846\) | 5.79337 | 0.199180 | ||||||||
\(847\) | −9.09483 | −0.312502 | ||||||||
\(848\) | −0.799503 | −0.0274551 | ||||||||
\(849\) | 25.2685 | 0.867212 | ||||||||
\(850\) | −52.6492 | −1.80585 | ||||||||
\(851\) | 17.1257 | 0.587061 | ||||||||
\(852\) | 7.15165 | 0.245012 | ||||||||
\(853\) | 1.91745 | 0.0656523 | 0.0328261 | − | 0.999461i | \(-0.489549\pi\) | ||||
0.0328261 | + | 0.999461i | \(0.489549\pi\) | |||||||
\(854\) | 8.66043 | 0.296354 | ||||||||
\(855\) | 0.236678 | 0.00809423 | ||||||||
\(856\) | 4.04880 | 0.138385 | ||||||||
\(857\) | 42.3948 | 1.44818 | 0.724090 | − | 0.689705i | \(-0.242260\pi\) | ||||
0.724090 | + | 0.689705i | \(0.242260\pi\) | |||||||
\(858\) | 9.49480 | 0.324147 | ||||||||
\(859\) | −12.3574 | −0.421629 | −0.210815 | − | 0.977526i | \(-0.567612\pi\) | ||||
−0.210815 | + | 0.977526i | \(0.567612\pi\) | |||||||
\(860\) | −4.11255 | −0.140237 | ||||||||
\(861\) | −2.18268 | −0.0743857 | ||||||||
\(862\) | −29.2340 | −0.995714 | ||||||||
\(863\) | −6.84551 | −0.233024 | −0.116512 | − | 0.993189i | \(-0.537171\pi\) | ||||
−0.116512 | + | 0.993189i | \(0.537171\pi\) | |||||||
\(864\) | 5.54705 | 0.188715 | ||||||||
\(865\) | 0.298248 | 0.0101407 | ||||||||
\(866\) | 13.0202 | 0.442445 | ||||||||
\(867\) | −4.23962 | −0.143985 | ||||||||
\(868\) | 31.0781 | 1.05486 | ||||||||
\(869\) | 14.3004 | 0.485109 | ||||||||
\(870\) | 0.609130 | 0.0206514 | ||||||||
\(871\) | −30.5327 | −1.03456 | ||||||||
\(872\) | 32.0300 | 1.08467 | ||||||||
\(873\) | 2.14183 | 0.0724898 | ||||||||
\(874\) | −24.6497 | −0.833790 | ||||||||
\(875\) | 1.32448 | 0.0447758 | ||||||||
\(876\) | −3.87807 | −0.131028 | ||||||||
\(877\) | 24.0490 | 0.812077 | 0.406038 | − | 0.913856i | \(-0.366910\pi\) | ||||
0.406038 | + | 0.913856i | \(0.366910\pi\) | |||||||
\(878\) | −85.6923 | −2.89197 | ||||||||
\(879\) | −18.0751 | −0.609658 | ||||||||
\(880\) | 0.0174525 | 0.000588323 0 | ||||||||
\(881\) | −13.2032 | −0.444826 | −0.222413 | − | 0.974953i | \(-0.571393\pi\) | ||||
−0.222413 | + | 0.974953i | \(0.571393\pi\) | |||||||
\(882\) | 2.29288 | 0.0772051 | ||||||||
\(883\) | 13.8993 | 0.467749 | 0.233874 | − | 0.972267i | \(-0.424860\pi\) | ||||
0.233874 | + | 0.972267i | \(0.424860\pi\) | |||||||
\(884\) | 45.0367 | 1.51475 | ||||||||
\(885\) | 1.03356 | 0.0347428 | ||||||||
\(886\) | 52.6250 | 1.76797 | ||||||||
\(887\) | 19.1216 | 0.642041 | 0.321020 | − | 0.947072i | \(-0.395974\pi\) | ||||
0.321020 | + | 0.947072i | \(0.395974\pi\) | |||||||
\(888\) | −8.19169 | −0.274895 | ||||||||
\(889\) | −1.00000 | −0.0335389 | ||||||||
\(890\) | 2.20582 | 0.0739391 | ||||||||
\(891\) | −1.38028 | −0.0462411 | ||||||||
\(892\) | −30.8782 | −1.03388 | ||||||||
\(893\) | −4.50710 | −0.150824 | ||||||||
\(894\) | −19.8331 | −0.663318 | ||||||||
\(895\) | 0.317392 | 0.0106092 | ||||||||
\(896\) | −18.5053 | −0.618218 | ||||||||
\(897\) | −18.0811 | −0.603710 | ||||||||
\(898\) | 69.7741 | 2.32839 | ||||||||
\(899\) | 19.1037 | 0.637145 | ||||||||
\(900\) | −16.2290 | −0.540968 | ||||||||
\(901\) | −38.6648 | −1.28811 | ||||||||
\(902\) | −6.90778 | −0.230004 | ||||||||
\(903\) | −9.51578 | −0.316665 | ||||||||
\(904\) | 50.8983 | 1.69285 | ||||||||
\(905\) | 2.73862 | 0.0910349 | ||||||||
\(906\) | −0.257961 | −0.00857017 | ||||||||
\(907\) | −4.48188 | −0.148818 | −0.0744091 | − | 0.997228i | \(-0.523707\pi\) | ||||
−0.0744091 | + | 0.997228i | \(0.523707\pi\) | |||||||
\(908\) | 13.0158 | 0.431946 | ||||||||
\(909\) | 16.2730 | 0.539740 | ||||||||
\(910\) | −0.912706 | −0.0302559 | ||||||||
\(911\) | 10.0337 | 0.332430 | 0.166215 | − | 0.986090i | \(-0.446845\pi\) | ||||
0.166215 | + | 0.986090i | \(0.446845\pi\) | |||||||
\(912\) | 0.169990 | 0.00562894 | ||||||||
\(913\) | −2.49911 | −0.0827086 | ||||||||
\(914\) | −73.6477 | −2.43605 | ||||||||
\(915\) | 0.501154 | 0.0165676 | ||||||||
\(916\) | 18.5445 | 0.612727 | ||||||||
\(917\) | 5.73840 | 0.189499 | ||||||||
\(918\) | −10.5670 | −0.348765 | ||||||||
\(919\) | 14.4554 | 0.476839 | 0.238419 | − | 0.971162i | \(-0.423371\pi\) | ||||
0.238419 | + | 0.971162i | \(0.423371\pi\) | |||||||
\(920\) | −2.30520 | −0.0760003 | ||||||||
\(921\) | −19.0494 | −0.627700 | ||||||||
\(922\) | 25.6124 | 0.843500 | ||||||||
\(923\) | −6.58704 | −0.216815 | ||||||||
\(924\) | 4.49595 | 0.147906 | ||||||||
\(925\) | −14.1580 | −0.465511 | ||||||||
\(926\) | 58.2324 | 1.91364 | ||||||||
\(927\) | −12.7663 | −0.419301 | ||||||||
\(928\) | −11.1066 | −0.364591 | ||||||||
\(929\) | 53.1010 | 1.74219 | 0.871093 | − | 0.491117i | \(-0.163411\pi\) | ||||
0.871093 | + | 0.491117i | \(0.163411\pi\) | |||||||
\(930\) | 2.90264 | 0.0951812 | ||||||||
\(931\) | −1.78380 | −0.0584617 | ||||||||
\(932\) | −36.2467 | −1.18730 | ||||||||
\(933\) | −4.75698 | −0.155737 | ||||||||
\(934\) | 86.9552 | 2.84526 | ||||||||
\(935\) | 0.844019 | 0.0276024 | ||||||||
\(936\) | 8.64868 | 0.282691 | ||||||||
\(937\) | −0.659156 | −0.0215337 | −0.0107668 | − | 0.999942i | \(-0.503427\pi\) | ||||
−0.0107668 | + | 0.999942i | \(0.503427\pi\) | |||||||
\(938\) | −23.3350 | −0.761914 | ||||||||
\(939\) | −1.35571 | −0.0442419 | ||||||||
\(940\) | −1.09199 | −0.0356167 | ||||||||
\(941\) | −59.8621 | −1.95145 | −0.975724 | − | 0.219006i | \(-0.929719\pi\) | ||||
−0.975724 | + | 0.219006i | \(0.929719\pi\) | |||||||
\(942\) | −23.4054 | −0.762590 | ||||||||
\(943\) | 13.1546 | 0.428372 | ||||||||
\(944\) | 0.742339 | 0.0241611 | ||||||||
\(945\) | 0.132682 | 0.00431615 | ||||||||
\(946\) | −30.1156 | −0.979142 | ||||||||
\(947\) | 40.1186 | 1.30368 | 0.651840 | − | 0.758357i | \(-0.273998\pi\) | ||||
0.651840 | + | 0.758357i | \(0.273998\pi\) | |||||||
\(948\) | 33.7472 | 1.09606 | ||||||||
\(949\) | 3.57190 | 0.115949 | ||||||||
\(950\) | 20.3782 | 0.661155 | ||||||||
\(951\) | 13.3742 | 0.433690 | ||||||||
\(952\) | 13.2857 | 0.430592 | ||||||||
\(953\) | 24.9277 | 0.807487 | 0.403744 | − | 0.914872i | \(-0.367709\pi\) | ||||
0.403744 | + | 0.914872i | \(0.367709\pi\) | |||||||
\(954\) | −19.2364 | −0.622800 | ||||||||
\(955\) | 2.13912 | 0.0692203 | ||||||||
\(956\) | −28.1894 | −0.911710 | ||||||||
\(957\) | 2.76366 | 0.0893364 | ||||||||
\(958\) | −22.7999 | −0.736631 | ||||||||
\(959\) | −9.98542 | −0.322446 | ||||||||
\(960\) | −1.71283 | −0.0552814 | ||||||||
\(961\) | 60.0334 | 1.93656 | ||||||||
\(962\) | 19.5471 | 0.630223 | ||||||||
\(963\) | 1.40448 | 0.0452586 | ||||||||
\(964\) | −86.6244 | −2.78998 | ||||||||
\(965\) | −1.14520 | −0.0368652 | ||||||||
\(966\) | −13.8187 | −0.444608 | ||||||||
\(967\) | 26.4870 | 0.851764 | 0.425882 | − | 0.904779i | \(-0.359964\pi\) | ||||
0.425882 | + | 0.904779i | \(0.359964\pi\) | |||||||
\(968\) | −26.2184 | −0.842690 | ||||||||
\(969\) | 8.22091 | 0.264094 | ||||||||
\(970\) | −0.651594 | −0.0209214 | ||||||||
\(971\) | 5.35158 | 0.171740 | 0.0858702 | − | 0.996306i | \(-0.472633\pi\) | ||||
0.0858702 | + | 0.996306i | \(0.472633\pi\) | |||||||
\(972\) | −3.25728 | −0.104477 | ||||||||
\(973\) | 7.44343 | 0.238625 | ||||||||
\(974\) | −8.56016 | −0.274285 | ||||||||
\(975\) | 14.9478 | 0.478712 | ||||||||
\(976\) | 0.359946 | 0.0115216 | ||||||||
\(977\) | −34.3412 | −1.09867 | −0.549336 | − | 0.835602i | \(-0.685119\pi\) | ||||
−0.549336 | + | 0.835602i | \(0.685119\pi\) | |||||||
\(978\) | 28.0722 | 0.897650 | ||||||||
\(979\) | 10.0079 | 0.319854 | ||||||||
\(980\) | −0.432182 | −0.0138055 | ||||||||
\(981\) | 11.1108 | 0.354741 | ||||||||
\(982\) | 85.0274 | 2.71333 | ||||||||
\(983\) | −29.9723 | −0.955968 | −0.477984 | − | 0.878369i | \(-0.658632\pi\) | ||||
−0.477984 | + | 0.878369i | \(0.658632\pi\) | |||||||
\(984\) | −6.29219 | −0.200588 | ||||||||
\(985\) | −0.0991233 | −0.00315833 | ||||||||
\(986\) | 21.1578 | 0.673803 | ||||||||
\(987\) | −2.52668 | −0.0804252 | ||||||||
\(988\) | −17.4317 | −0.554576 | ||||||||
\(989\) | 57.3495 | 1.82361 | ||||||||
\(990\) | 0.419913 | 0.0133457 | ||||||||
\(991\) | 27.5987 | 0.876703 | 0.438351 | − | 0.898804i | \(-0.355563\pi\) | ||||
0.438351 | + | 0.898804i | \(0.355563\pi\) | |||||||
\(992\) | −52.9252 | −1.68038 | ||||||||
\(993\) | 11.6504 | 0.369716 | ||||||||
\(994\) | −5.03422 | −0.159676 | ||||||||
\(995\) | 0.236796 | 0.00750693 | ||||||||
\(996\) | −5.89758 | −0.186872 | ||||||||
\(997\) | 53.8873 | 1.70663 | 0.853314 | − | 0.521397i | \(-0.174589\pi\) | ||||
0.853314 | + | 0.521397i | \(0.174589\pi\) | |||||||
\(998\) | 56.8616 | 1.79992 | ||||||||
\(999\) | −2.84160 | −0.0899042 |
(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 | 2667.2.a.l.1.12 | ✓ | 13 | |
3.2 | odd | 2 | 8001.2.a.o.1.2 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.l.1.12 | ✓ | 13 | 1.1 | even | 1 | trivial | |
8001.2.a.o.1.2 | 13 | 3.2 | odd | 2 |