Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2738,2,Mod(1,2738)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2738, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2738.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2738 = 2 \cdot 37^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2738.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: | \(21.8630400734\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 8 x^{17} - 8 x^{16} + 209 x^{15} - 253 x^{14} - 1996 x^{13} + 4196 x^{12} + 8667 x^{11} - 24522 x^{10} - 18284 x^{9} + 68697 x^{8} + 20865 x^{7} - 97011 x^{6} + \cdots + 113 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.39715\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2738.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.75172 | −1.01135 | −0.505677 | − | 0.862723i | \(-0.668757\pi\) | ||||
−0.505677 | + | 0.862723i | \(0.668757\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.09131 | −0.935260 | −0.467630 | − | 0.883924i | \(-0.654892\pi\) | ||||
−0.467630 | + | 0.883924i | \(0.654892\pi\) | |||||||
\(6\) | −1.75172 | −0.715136 | ||||||||
\(7\) | 1.21116 | 0.457776 | 0.228888 | − | 0.973453i | \(-0.426491\pi\) | ||||
0.228888 | + | 0.973453i | \(0.426491\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.0685155 | 0.0228385 | ||||||||
\(10\) | −2.09131 | −0.661329 | ||||||||
\(11\) | 5.93957 | 1.79085 | 0.895423 | − | 0.445215i | \(-0.146873\pi\) | ||||
0.895423 | + | 0.445215i | \(0.146873\pi\) | |||||||
\(12\) | −1.75172 | −0.505677 | ||||||||
\(13\) | 1.68357 | 0.466939 | 0.233470 | − | 0.972364i | \(-0.424992\pi\) | ||||
0.233470 | + | 0.972364i | \(0.424992\pi\) | |||||||
\(14\) | 1.21116 | 0.323697 | ||||||||
\(15\) | 3.66338 | 0.945880 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.38331 | −1.30564 | −0.652822 | − | 0.757511i | \(-0.726415\pi\) | ||||
−0.652822 | + | 0.757511i | \(0.726415\pi\) | |||||||
\(18\) | 0.0685155 | 0.0161492 | ||||||||
\(19\) | −0.495716 | −0.113725 | −0.0568625 | − | 0.998382i | \(-0.518110\pi\) | ||||
−0.0568625 | + | 0.998382i | \(0.518110\pi\) | |||||||
\(20\) | −2.09131 | −0.467630 | ||||||||
\(21\) | −2.12161 | −0.462974 | ||||||||
\(22\) | 5.93957 | 1.26632 | ||||||||
\(23\) | −2.33910 | −0.487736 | −0.243868 | − | 0.969808i | \(-0.578416\pi\) | ||||
−0.243868 | + | 0.969808i | \(0.578416\pi\) | |||||||
\(24\) | −1.75172 | −0.357568 | ||||||||
\(25\) | −0.626440 | −0.125288 | ||||||||
\(26\) | 1.68357 | 0.330176 | ||||||||
\(27\) | 5.13513 | 0.988257 | ||||||||
\(28\) | 1.21116 | 0.228888 | ||||||||
\(29\) | −8.30651 | −1.54248 | −0.771240 | − | 0.636544i | \(-0.780363\pi\) | ||||
−0.771240 | + | 0.636544i | \(0.780363\pi\) | |||||||
\(30\) | 3.66338 | 0.668838 | ||||||||
\(31\) | 9.20267 | 1.65285 | 0.826425 | − | 0.563047i | \(-0.190371\pi\) | ||||
0.826425 | + | 0.563047i | \(0.190371\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −10.4044 | −1.81118 | ||||||||
\(34\) | −5.38331 | −0.923230 | ||||||||
\(35\) | −2.53291 | −0.428140 | ||||||||
\(36\) | 0.0685155 | 0.0114192 | ||||||||
\(37\) | 0 | 0 | ||||||||
\(38\) | −0.495716 | −0.0804157 | ||||||||
\(39\) | −2.94915 | −0.472241 | ||||||||
\(40\) | −2.09131 | −0.330664 | ||||||||
\(41\) | 10.4036 | 1.62477 | 0.812383 | − | 0.583124i | \(-0.198170\pi\) | ||||
0.812383 | + | 0.583124i | \(0.198170\pi\) | |||||||
\(42\) | −2.12161 | −0.327372 | ||||||||
\(43\) | 1.93690 | 0.295375 | 0.147687 | − | 0.989034i | \(-0.452817\pi\) | ||||
0.147687 | + | 0.989034i | \(0.452817\pi\) | |||||||
\(44\) | 5.93957 | 0.895423 | ||||||||
\(45\) | −0.143287 | −0.0213599 | ||||||||
\(46\) | −2.33910 | −0.344881 | ||||||||
\(47\) | 8.87715 | 1.29487 | 0.647433 | − | 0.762122i | \(-0.275843\pi\) | ||||
0.647433 | + | 0.762122i | \(0.275843\pi\) | |||||||
\(48\) | −1.75172 | −0.252839 | ||||||||
\(49\) | −5.53309 | −0.790441 | ||||||||
\(50\) | −0.626440 | −0.0885920 | ||||||||
\(51\) | 9.43004 | 1.32047 | ||||||||
\(52\) | 1.68357 | 0.233470 | ||||||||
\(53\) | −6.58882 | −0.905044 | −0.452522 | − | 0.891753i | \(-0.649476\pi\) | ||||
−0.452522 | + | 0.891753i | \(0.649476\pi\) | |||||||
\(54\) | 5.13513 | 0.698803 | ||||||||
\(55\) | −12.4215 | −1.67491 | ||||||||
\(56\) | 1.21116 | 0.161848 | ||||||||
\(57\) | 0.868354 | 0.115016 | ||||||||
\(58\) | −8.30651 | −1.09070 | ||||||||
\(59\) | 1.02706 | 0.133712 | 0.0668560 | − | 0.997763i | \(-0.478703\pi\) | ||||
0.0668560 | + | 0.997763i | \(0.478703\pi\) | |||||||
\(60\) | 3.66338 | 0.472940 | ||||||||
\(61\) | −1.46885 | −0.188067 | −0.0940337 | − | 0.995569i | \(-0.529976\pi\) | ||||
−0.0940337 | + | 0.995569i | \(0.529976\pi\) | |||||||
\(62\) | 9.20267 | 1.16874 | ||||||||
\(63\) | 0.0829833 | 0.0104549 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.52087 | −0.436710 | ||||||||
\(66\) | −10.4044 | −1.28070 | ||||||||
\(67\) | 12.2895 | 1.50140 | 0.750702 | − | 0.660642i | \(-0.229716\pi\) | ||||
0.750702 | + | 0.660642i | \(0.229716\pi\) | |||||||
\(68\) | −5.38331 | −0.652822 | ||||||||
\(69\) | 4.09744 | 0.493274 | ||||||||
\(70\) | −2.53291 | −0.302741 | ||||||||
\(71\) | −13.0711 | −1.55125 | −0.775627 | − | 0.631191i | \(-0.782566\pi\) | ||||
−0.775627 | + | 0.631191i | \(0.782566\pi\) | |||||||
\(72\) | 0.0685155 | 0.00807462 | ||||||||
\(73\) | 8.54942 | 1.00063 | 0.500317 | − | 0.865842i | \(-0.333217\pi\) | ||||
0.500317 | + | 0.865842i | \(0.333217\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.09735 | 0.126711 | ||||||||
\(76\) | −0.495716 | −0.0568625 | ||||||||
\(77\) | 7.19378 | 0.819807 | ||||||||
\(78\) | −2.94915 | −0.333925 | ||||||||
\(79\) | 6.28496 | 0.707113 | 0.353556 | − | 0.935413i | \(-0.384972\pi\) | ||||
0.353556 | + | 0.935413i | \(0.384972\pi\) | |||||||
\(80\) | −2.09131 | −0.233815 | ||||||||
\(81\) | −9.20085 | −1.02232 | ||||||||
\(82\) | 10.4036 | 1.14888 | ||||||||
\(83\) | 3.91197 | 0.429394 | 0.214697 | − | 0.976681i | \(-0.431124\pi\) | ||||
0.214697 | + | 0.976681i | \(0.431124\pi\) | |||||||
\(84\) | −2.12161 | −0.231487 | ||||||||
\(85\) | 11.2581 | 1.22112 | ||||||||
\(86\) | 1.93690 | 0.208861 | ||||||||
\(87\) | 14.5507 | 1.55999 | ||||||||
\(88\) | 5.93957 | 0.633160 | ||||||||
\(89\) | 18.0337 | 1.91157 | 0.955784 | − | 0.294070i | \(-0.0950098\pi\) | ||||
0.955784 | + | 0.294070i | \(0.0950098\pi\) | |||||||
\(90\) | −0.143287 | −0.0151038 | ||||||||
\(91\) | 2.03908 | 0.213754 | ||||||||
\(92\) | −2.33910 | −0.243868 | ||||||||
\(93\) | −16.1205 | −1.67162 | ||||||||
\(94\) | 8.87715 | 0.915609 | ||||||||
\(95\) | 1.03669 | 0.106363 | ||||||||
\(96\) | −1.75172 | −0.178784 | ||||||||
\(97\) | 8.12116 | 0.824579 | 0.412290 | − | 0.911053i | \(-0.364729\pi\) | ||||
0.412290 | + | 0.911053i | \(0.364729\pi\) | |||||||
\(98\) | −5.53309 | −0.558926 | ||||||||
\(99\) | 0.406952 | 0.0409002 | ||||||||
\(100\) | −0.626440 | −0.0626440 | ||||||||
\(101\) | −9.39363 | −0.934701 | −0.467351 | − | 0.884072i | \(-0.654791\pi\) | ||||
−0.467351 | + | 0.884072i | \(0.654791\pi\) | |||||||
\(102\) | 9.43004 | 0.933713 | ||||||||
\(103\) | −0.279274 | −0.0275177 | −0.0137588 | − | 0.999905i | \(-0.504380\pi\) | ||||
−0.0137588 | + | 0.999905i | \(0.504380\pi\) | |||||||
\(104\) | 1.68357 | 0.165088 | ||||||||
\(105\) | 4.43694 | 0.433001 | ||||||||
\(106\) | −6.58882 | −0.639963 | ||||||||
\(107\) | 11.1237 | 1.07537 | 0.537685 | − | 0.843146i | \(-0.319299\pi\) | ||||
0.537685 | + | 0.843146i | \(0.319299\pi\) | |||||||
\(108\) | 5.13513 | 0.494128 | ||||||||
\(109\) | 4.40630 | 0.422047 | 0.211024 | − | 0.977481i | \(-0.432320\pi\) | ||||
0.211024 | + | 0.977481i | \(0.432320\pi\) | |||||||
\(110\) | −12.4215 | −1.18434 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.21116 | 0.114444 | ||||||||
\(113\) | 13.3652 | 1.25729 | 0.628646 | − | 0.777691i | \(-0.283609\pi\) | ||||
0.628646 | + | 0.777691i | \(0.283609\pi\) | |||||||
\(114\) | 0.868354 | 0.0813288 | ||||||||
\(115\) | 4.89177 | 0.456160 | ||||||||
\(116\) | −8.30651 | −0.771240 | ||||||||
\(117\) | 0.115351 | 0.0106642 | ||||||||
\(118\) | 1.02706 | 0.0945486 | ||||||||
\(119\) | −6.52006 | −0.597692 | ||||||||
\(120\) | 3.66338 | 0.334419 | ||||||||
\(121\) | 24.2785 | 2.20713 | ||||||||
\(122\) | −1.46885 | −0.132984 | ||||||||
\(123\) | −18.2241 | −1.64321 | ||||||||
\(124\) | 9.20267 | 0.826425 | ||||||||
\(125\) | 11.7666 | 1.05244 | ||||||||
\(126\) | 0.0829833 | 0.00739274 | ||||||||
\(127\) | 19.0384 | 1.68938 | 0.844692 | − | 0.535253i | \(-0.179784\pi\) | ||||
0.844692 | + | 0.535253i | \(0.179784\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −3.39290 | −0.298728 | ||||||||
\(130\) | −3.52087 | −0.308801 | ||||||||
\(131\) | 2.32597 | 0.203221 | 0.101610 | − | 0.994824i | \(-0.467600\pi\) | ||||
0.101610 | + | 0.994824i | \(0.467600\pi\) | |||||||
\(132\) | −10.4044 | −0.905591 | ||||||||
\(133\) | −0.600392 | −0.0520606 | ||||||||
\(134\) | 12.2895 | 1.06165 | ||||||||
\(135\) | −10.7391 | −0.924278 | ||||||||
\(136\) | −5.38331 | −0.461615 | ||||||||
\(137\) | −9.64452 | −0.823987 | −0.411993 | − | 0.911187i | \(-0.635167\pi\) | ||||
−0.411993 | + | 0.911187i | \(0.635167\pi\) | |||||||
\(138\) | 4.09744 | 0.348797 | ||||||||
\(139\) | 6.05196 | 0.513321 | 0.256660 | − | 0.966502i | \(-0.417378\pi\) | ||||
0.256660 | + | 0.966502i | \(0.417378\pi\) | |||||||
\(140\) | −2.53291 | −0.214070 | ||||||||
\(141\) | −15.5503 | −1.30957 | ||||||||
\(142\) | −13.0711 | −1.09690 | ||||||||
\(143\) | 9.99970 | 0.836217 | ||||||||
\(144\) | 0.0685155 | 0.00570962 | ||||||||
\(145\) | 17.3715 | 1.44262 | ||||||||
\(146\) | 8.54942 | 0.707555 | ||||||||
\(147\) | 9.69241 | 0.799416 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.10585 | 0.664057 | 0.332029 | − | 0.943269i | \(-0.392267\pi\) | ||||
0.332029 | + | 0.943269i | \(0.392267\pi\) | |||||||
\(150\) | 1.09735 | 0.0895979 | ||||||||
\(151\) | 4.99063 | 0.406131 | 0.203066 | − | 0.979165i | \(-0.434910\pi\) | ||||
0.203066 | + | 0.979165i | \(0.434910\pi\) | |||||||
\(152\) | −0.495716 | −0.0402079 | ||||||||
\(153\) | −0.368840 | −0.0298189 | ||||||||
\(154\) | 7.19378 | 0.579691 | ||||||||
\(155\) | −19.2456 | −1.54584 | ||||||||
\(156\) | −2.94915 | −0.236121 | ||||||||
\(157\) | 4.80321 | 0.383338 | 0.191669 | − | 0.981460i | \(-0.438610\pi\) | ||||
0.191669 | + | 0.981460i | \(0.438610\pi\) | |||||||
\(158\) | 6.28496 | 0.500004 | ||||||||
\(159\) | 11.5418 | 0.915321 | ||||||||
\(160\) | −2.09131 | −0.165332 | ||||||||
\(161\) | −2.83303 | −0.223274 | ||||||||
\(162\) | −9.20085 | −0.722887 | ||||||||
\(163\) | 5.92541 | 0.464114 | 0.232057 | − | 0.972702i | \(-0.425454\pi\) | ||||
0.232057 | + | 0.972702i | \(0.425454\pi\) | |||||||
\(164\) | 10.4036 | 0.812383 | ||||||||
\(165\) | 21.7589 | 1.69393 | ||||||||
\(166\) | 3.91197 | 0.303627 | ||||||||
\(167\) | −0.571625 | −0.0442337 | −0.0221168 | − | 0.999755i | \(-0.507041\pi\) | ||||
−0.0221168 | + | 0.999755i | \(0.507041\pi\) | |||||||
\(168\) | −2.12161 | −0.163686 | ||||||||
\(169\) | −10.1656 | −0.781968 | ||||||||
\(170\) | 11.2581 | 0.863460 | ||||||||
\(171\) | −0.0339642 | −0.00259731 | ||||||||
\(172\) | 1.93690 | 0.147687 | ||||||||
\(173\) | 16.1829 | 1.23036 | 0.615180 | − | 0.788386i | \(-0.289083\pi\) | ||||
0.615180 | + | 0.788386i | \(0.289083\pi\) | |||||||
\(174\) | 14.5507 | 1.10308 | ||||||||
\(175\) | −0.758720 | −0.0573538 | ||||||||
\(176\) | 5.93957 | 0.447712 | ||||||||
\(177\) | −1.79912 | −0.135230 | ||||||||
\(178\) | 18.0337 | 1.35168 | ||||||||
\(179\) | −6.59689 | −0.493075 | −0.246538 | − | 0.969133i | \(-0.579293\pi\) | ||||
−0.246538 | + | 0.969133i | \(0.579293\pi\) | |||||||
\(180\) | −0.143287 | −0.0106800 | ||||||||
\(181\) | 1.47280 | 0.109472 | 0.0547360 | − | 0.998501i | \(-0.482568\pi\) | ||||
0.0547360 | + | 0.998501i | \(0.482568\pi\) | |||||||
\(182\) | 2.03908 | 0.151147 | ||||||||
\(183\) | 2.57302 | 0.190203 | ||||||||
\(184\) | −2.33910 | −0.172441 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −16.1205 | −1.18201 | ||||||||
\(187\) | −31.9745 | −2.33821 | ||||||||
\(188\) | 8.87715 | 0.647433 | ||||||||
\(189\) | 6.21948 | 0.452400 | ||||||||
\(190\) | 1.03669 | 0.0752097 | ||||||||
\(191\) | −23.8560 | −1.72616 | −0.863080 | − | 0.505067i | \(-0.831468\pi\) | ||||
−0.863080 | + | 0.505067i | \(0.831468\pi\) | |||||||
\(192\) | −1.75172 | −0.126419 | ||||||||
\(193\) | −16.8415 | −1.21228 | −0.606138 | − | 0.795360i | \(-0.707282\pi\) | ||||
−0.606138 | + | 0.795360i | \(0.707282\pi\) | |||||||
\(194\) | 8.12116 | 0.583066 | ||||||||
\(195\) | 6.16757 | 0.441669 | ||||||||
\(196\) | −5.53309 | −0.395221 | ||||||||
\(197\) | 18.0955 | 1.28925 | 0.644625 | − | 0.764499i | \(-0.277014\pi\) | ||||
0.644625 | + | 0.764499i | \(0.277014\pi\) | |||||||
\(198\) | 0.406952 | 0.0289208 | ||||||||
\(199\) | −15.9676 | −1.13191 | −0.565956 | − | 0.824435i | \(-0.691493\pi\) | ||||
−0.565956 | + | 0.824435i | \(0.691493\pi\) | |||||||
\(200\) | −0.626440 | −0.0442960 | ||||||||
\(201\) | −21.5278 | −1.51845 | ||||||||
\(202\) | −9.39363 | −0.660934 | ||||||||
\(203\) | −10.0605 | −0.706111 | ||||||||
\(204\) | 9.43004 | 0.660235 | ||||||||
\(205\) | −21.7571 | −1.51958 | ||||||||
\(206\) | −0.279274 | −0.0194579 | ||||||||
\(207\) | −0.160264 | −0.0111391 | ||||||||
\(208\) | 1.68357 | 0.116735 | ||||||||
\(209\) | −2.94434 | −0.203664 | ||||||||
\(210\) | 4.43694 | 0.306178 | ||||||||
\(211\) | −7.31223 | −0.503395 | −0.251697 | − | 0.967806i | \(-0.580989\pi\) | ||||
−0.251697 | + | 0.967806i | \(0.580989\pi\) | |||||||
\(212\) | −6.58882 | −0.452522 | ||||||||
\(213\) | 22.8969 | 1.56887 | ||||||||
\(214\) | 11.1237 | 0.760402 | ||||||||
\(215\) | −4.05065 | −0.276252 | ||||||||
\(216\) | 5.13513 | 0.349402 | ||||||||
\(217\) | 11.1459 | 0.756635 | ||||||||
\(218\) | 4.40630 | 0.298432 | ||||||||
\(219\) | −14.9762 | −1.01200 | ||||||||
\(220\) | −12.4215 | −0.837454 | ||||||||
\(221\) | −9.06320 | −0.609657 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.9777 | 1.06995 | 0.534973 | − | 0.844869i | \(-0.320322\pi\) | ||||
0.534973 | + | 0.844869i | \(0.320322\pi\) | |||||||
\(224\) | 1.21116 | 0.0809241 | ||||||||
\(225\) | −0.0429208 | −0.00286139 | ||||||||
\(226\) | 13.3652 | 0.889040 | ||||||||
\(227\) | 3.46336 | 0.229871 | 0.114936 | − | 0.993373i | \(-0.463334\pi\) | ||||
0.114936 | + | 0.993373i | \(0.463334\pi\) | |||||||
\(228\) | 0.868354 | 0.0575082 | ||||||||
\(229\) | −15.1822 | −1.00327 | −0.501635 | − | 0.865079i | \(-0.667268\pi\) | ||||
−0.501635 | + | 0.865079i | \(0.667268\pi\) | |||||||
\(230\) | 4.89177 | 0.322554 | ||||||||
\(231\) | −12.6015 | −0.829116 | ||||||||
\(232\) | −8.30651 | −0.545349 | ||||||||
\(233\) | −5.71207 | −0.374210 | −0.187105 | − | 0.982340i | \(-0.559910\pi\) | ||||
−0.187105 | + | 0.982340i | \(0.559910\pi\) | |||||||
\(234\) | 0.115351 | 0.00754072 | ||||||||
\(235\) | −18.5648 | −1.21104 | ||||||||
\(236\) | 1.02706 | 0.0668560 | ||||||||
\(237\) | −11.0095 | −0.715142 | ||||||||
\(238\) | −6.52006 | −0.422632 | ||||||||
\(239\) | −7.10847 | −0.459809 | −0.229904 | − | 0.973213i | \(-0.573841\pi\) | ||||
−0.229904 | + | 0.973213i | \(0.573841\pi\) | |||||||
\(240\) | 3.66338 | 0.236470 | ||||||||
\(241\) | −10.1248 | −0.652193 | −0.326096 | − | 0.945337i | \(-0.605733\pi\) | ||||
−0.326096 | + | 0.945337i | \(0.605733\pi\) | |||||||
\(242\) | 24.2785 | 1.56068 | ||||||||
\(243\) | 0.711895 | 0.0456681 | ||||||||
\(244\) | −1.46885 | −0.0940337 | ||||||||
\(245\) | 11.5714 | 0.739268 | ||||||||
\(246\) | −18.2241 | −1.16193 | ||||||||
\(247\) | −0.834575 | −0.0531027 | ||||||||
\(248\) | 9.20267 | 0.584370 | ||||||||
\(249\) | −6.85266 | −0.434270 | ||||||||
\(250\) | 11.7666 | 0.744186 | ||||||||
\(251\) | 13.7490 | 0.867832 | 0.433916 | − | 0.900953i | \(-0.357131\pi\) | ||||
0.433916 | + | 0.900953i | \(0.357131\pi\) | |||||||
\(252\) | 0.0829833 | 0.00522746 | ||||||||
\(253\) | −13.8932 | −0.873460 | ||||||||
\(254\) | 19.0384 | 1.19457 | ||||||||
\(255\) | −19.7211 | −1.23498 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −7.08203 | −0.441765 | −0.220883 | − | 0.975300i | \(-0.570894\pi\) | ||||
−0.220883 | + | 0.975300i | \(0.570894\pi\) | |||||||
\(258\) | −3.39290 | −0.211233 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −3.52087 | −0.218355 | ||||||||
\(261\) | −0.569124 | −0.0352279 | ||||||||
\(262\) | 2.32597 | 0.143699 | ||||||||
\(263\) | 4.60769 | 0.284122 | 0.142061 | − | 0.989858i | \(-0.454627\pi\) | ||||
0.142061 | + | 0.989858i | \(0.454627\pi\) | |||||||
\(264\) | −10.4044 | −0.640349 | ||||||||
\(265\) | 13.7792 | 0.846452 | ||||||||
\(266\) | −0.600392 | −0.0368124 | ||||||||
\(267\) | −31.5899 | −1.93327 | ||||||||
\(268\) | 12.2895 | 0.750702 | ||||||||
\(269\) | −5.21884 | −0.318198 | −0.159099 | − | 0.987263i | \(-0.550859\pi\) | ||||
−0.159099 | + | 0.987263i | \(0.550859\pi\) | |||||||
\(270\) | −10.7391 | −0.653563 | ||||||||
\(271\) | 11.2863 | 0.685596 | 0.342798 | − | 0.939409i | \(-0.388625\pi\) | ||||
0.342798 | + | 0.939409i | \(0.388625\pi\) | |||||||
\(272\) | −5.38331 | −0.326411 | ||||||||
\(273\) | −3.57189 | −0.216181 | ||||||||
\(274\) | −9.64452 | −0.582647 | ||||||||
\(275\) | −3.72078 | −0.224372 | ||||||||
\(276\) | 4.09744 | 0.246637 | ||||||||
\(277\) | 0.522535 | 0.0313961 | 0.0156981 | − | 0.999877i | \(-0.495003\pi\) | ||||
0.0156981 | + | 0.999877i | \(0.495003\pi\) | |||||||
\(278\) | 6.05196 | 0.362973 | ||||||||
\(279\) | 0.630525 | 0.0377486 | ||||||||
\(280\) | −2.53291 | −0.151370 | ||||||||
\(281\) | −14.8186 | −0.884005 | −0.442003 | − | 0.897014i | \(-0.645732\pi\) | ||||
−0.442003 | + | 0.897014i | \(0.645732\pi\) | |||||||
\(282\) | −15.5503 | −0.926005 | ||||||||
\(283\) | 3.99925 | 0.237731 | 0.118865 | − | 0.992910i | \(-0.462074\pi\) | ||||
0.118865 | + | 0.992910i | \(0.462074\pi\) | |||||||
\(284\) | −13.0711 | −0.775627 | ||||||||
\(285\) | −1.81599 | −0.107570 | ||||||||
\(286\) | 9.99970 | 0.591295 | ||||||||
\(287\) | 12.6004 | 0.743779 | ||||||||
\(288\) | 0.0685155 | 0.00403731 | ||||||||
\(289\) | 11.9800 | 0.704706 | ||||||||
\(290\) | 17.3715 | 1.02009 | ||||||||
\(291\) | −14.2260 | −0.833942 | ||||||||
\(292\) | 8.54942 | 0.500317 | ||||||||
\(293\) | −10.1604 | −0.593579 | −0.296789 | − | 0.954943i | \(-0.595916\pi\) | ||||
−0.296789 | + | 0.954943i | \(0.595916\pi\) | |||||||
\(294\) | 9.69241 | 0.565273 | ||||||||
\(295\) | −2.14790 | −0.125056 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 30.5005 | 1.76982 | ||||||||
\(298\) | 8.10585 | 0.469559 | ||||||||
\(299\) | −3.93805 | −0.227743 | ||||||||
\(300\) | 1.09735 | 0.0633553 | ||||||||
\(301\) | 2.34590 | 0.135215 | ||||||||
\(302\) | 4.99063 | 0.287178 | ||||||||
\(303\) | 16.4550 | 0.945314 | ||||||||
\(304\) | −0.495716 | −0.0284313 | ||||||||
\(305\) | 3.07182 | 0.175892 | ||||||||
\(306\) | −0.368840 | −0.0210852 | ||||||||
\(307\) | 22.4774 | 1.28285 | 0.641425 | − | 0.767186i | \(-0.278344\pi\) | ||||
0.641425 | + | 0.767186i | \(0.278344\pi\) | |||||||
\(308\) | 7.19378 | 0.409903 | ||||||||
\(309\) | 0.489209 | 0.0278301 | ||||||||
\(310\) | −19.2456 | −1.09308 | ||||||||
\(311\) | −4.40563 | −0.249820 | −0.124910 | − | 0.992168i | \(-0.539864\pi\) | ||||
−0.124910 | + | 0.992168i | \(0.539864\pi\) | |||||||
\(312\) | −2.94915 | −0.166963 | ||||||||
\(313\) | −0.741008 | −0.0418842 | −0.0209421 | − | 0.999781i | \(-0.506667\pi\) | ||||
−0.0209421 | + | 0.999781i | \(0.506667\pi\) | |||||||
\(314\) | 4.80321 | 0.271061 | ||||||||
\(315\) | −0.173543 | −0.00977806 | ||||||||
\(316\) | 6.28496 | 0.353556 | ||||||||
\(317\) | 25.2386 | 1.41754 | 0.708772 | − | 0.705438i | \(-0.249250\pi\) | ||||
0.708772 | + | 0.705438i | \(0.249250\pi\) | |||||||
\(318\) | 11.5418 | 0.647229 | ||||||||
\(319\) | −49.3371 | −2.76235 | ||||||||
\(320\) | −2.09131 | −0.116908 | ||||||||
\(321\) | −19.4856 | −1.08758 | ||||||||
\(322\) | −2.83303 | −0.157878 | ||||||||
\(323\) | 2.66859 | 0.148484 | ||||||||
\(324\) | −9.20085 | −0.511158 | ||||||||
\(325\) | −1.05466 | −0.0585019 | ||||||||
\(326\) | 5.92541 | 0.328178 | ||||||||
\(327\) | −7.71859 | −0.426839 | ||||||||
\(328\) | 10.4036 | 0.574442 | ||||||||
\(329\) | 10.7517 | 0.592759 | ||||||||
\(330\) | 21.7589 | 1.19779 | ||||||||
\(331\) | 4.58769 | 0.252162 | 0.126081 | − | 0.992020i | \(-0.459760\pi\) | ||||
0.126081 | + | 0.992020i | \(0.459760\pi\) | |||||||
\(332\) | 3.91197 | 0.214697 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.571625 | −0.0312779 | ||||||||
\(335\) | −25.7011 | −1.40420 | ||||||||
\(336\) | −2.12161 | −0.115743 | ||||||||
\(337\) | −25.8343 | −1.40729 | −0.703643 | − | 0.710554i | \(-0.748445\pi\) | ||||
−0.703643 | + | 0.710554i | \(0.748445\pi\) | |||||||
\(338\) | −10.1656 | −0.552935 | ||||||||
\(339\) | −23.4121 | −1.27157 | ||||||||
\(340\) | 11.2581 | 0.610559 | ||||||||
\(341\) | 54.6599 | 2.96000 | ||||||||
\(342\) | −0.0339642 | −0.00183657 | ||||||||
\(343\) | −15.1796 | −0.819621 | ||||||||
\(344\) | 1.93690 | 0.104431 | ||||||||
\(345\) | −8.56900 | −0.461340 | ||||||||
\(346\) | 16.1829 | 0.869996 | ||||||||
\(347\) | −4.89892 | −0.262988 | −0.131494 | − | 0.991317i | \(-0.541977\pi\) | ||||
−0.131494 | + | 0.991317i | \(0.541977\pi\) | |||||||
\(348\) | 14.5507 | 0.779997 | ||||||||
\(349\) | 29.0275 | 1.55381 | 0.776904 | − | 0.629619i | \(-0.216789\pi\) | ||||
0.776904 | + | 0.629619i | \(0.216789\pi\) | |||||||
\(350\) | −0.758720 | −0.0405553 | ||||||||
\(351\) | 8.64538 | 0.461456 | ||||||||
\(352\) | 5.93957 | 0.316580 | ||||||||
\(353\) | −26.9530 | −1.43456 | −0.717282 | − | 0.696783i | \(-0.754614\pi\) | ||||
−0.717282 | + | 0.696783i | \(0.754614\pi\) | |||||||
\(354\) | −1.79912 | −0.0956222 | ||||||||
\(355\) | 27.3357 | 1.45083 | ||||||||
\(356\) | 18.0337 | 0.955784 | ||||||||
\(357\) | 11.4213 | 0.604479 | ||||||||
\(358\) | −6.59689 | −0.348657 | ||||||||
\(359\) | −2.33163 | −0.123058 | −0.0615292 | − | 0.998105i | \(-0.519598\pi\) | ||||
−0.0615292 | + | 0.998105i | \(0.519598\pi\) | |||||||
\(360\) | −0.143287 | −0.00755188 | ||||||||
\(361\) | −18.7543 | −0.987067 | ||||||||
\(362\) | 1.47280 | 0.0774084 | ||||||||
\(363\) | −42.5290 | −2.23219 | ||||||||
\(364\) | 2.03908 | 0.106877 | ||||||||
\(365\) | −17.8795 | −0.935854 | ||||||||
\(366\) | 2.57302 | 0.134494 | ||||||||
\(367\) | 1.11791 | 0.0583544 | 0.0291772 | − | 0.999574i | \(-0.490711\pi\) | ||||
0.0291772 | + | 0.999574i | \(0.490711\pi\) | |||||||
\(368\) | −2.33910 | −0.121934 | ||||||||
\(369\) | 0.712806 | 0.0371072 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.98013 | −0.414307 | ||||||||
\(372\) | −16.1205 | −0.835808 | ||||||||
\(373\) | −7.12913 | −0.369132 | −0.184566 | − | 0.982820i | \(-0.559088\pi\) | ||||
−0.184566 | + | 0.982820i | \(0.559088\pi\) | |||||||
\(374\) | −31.9745 | −1.65336 | ||||||||
\(375\) | −20.6118 | −1.06439 | ||||||||
\(376\) | 8.87715 | 0.457804 | ||||||||
\(377\) | −13.9846 | −0.720245 | ||||||||
\(378\) | 6.21948 | 0.319895 | ||||||||
\(379\) | 4.72138 | 0.242521 | 0.121260 | − | 0.992621i | \(-0.461306\pi\) | ||||
0.121260 | + | 0.992621i | \(0.461306\pi\) | |||||||
\(380\) | 1.03669 | 0.0531813 | ||||||||
\(381\) | −33.3499 | −1.70857 | ||||||||
\(382\) | −23.8560 | −1.22058 | ||||||||
\(383\) | −17.4079 | −0.889505 | −0.444752 | − | 0.895654i | \(-0.646708\pi\) | ||||
−0.444752 | + | 0.895654i | \(0.646708\pi\) | |||||||
\(384\) | −1.75172 | −0.0893920 | ||||||||
\(385\) | −15.0444 | −0.766733 | ||||||||
\(386\) | −16.8415 | −0.857208 | ||||||||
\(387\) | 0.132708 | 0.00674591 | ||||||||
\(388\) | 8.12116 | 0.412290 | ||||||||
\(389\) | −35.7110 | −1.81062 | −0.905309 | − | 0.424754i | \(-0.860361\pi\) | ||||
−0.905309 | + | 0.424754i | \(0.860361\pi\) | |||||||
\(390\) | 6.16757 | 0.312307 | ||||||||
\(391\) | 12.5921 | 0.636809 | ||||||||
\(392\) | −5.53309 | −0.279463 | ||||||||
\(393\) | −4.07444 | −0.205528 | ||||||||
\(394\) | 18.0955 | 0.911637 | ||||||||
\(395\) | −13.1438 | −0.661335 | ||||||||
\(396\) | 0.406952 | 0.0204501 | ||||||||
\(397\) | −11.6241 | −0.583396 | −0.291698 | − | 0.956510i | \(-0.594220\pi\) | ||||
−0.291698 | + | 0.956510i | \(0.594220\pi\) | |||||||
\(398\) | −15.9676 | −0.800383 | ||||||||
\(399\) | 1.05172 | 0.0526517 | ||||||||
\(400\) | −0.626440 | −0.0313220 | ||||||||
\(401\) | 29.4827 | 1.47229 | 0.736147 | − | 0.676822i | \(-0.236643\pi\) | ||||
0.736147 | + | 0.676822i | \(0.236643\pi\) | |||||||
\(402\) | −21.5278 | −1.07371 | ||||||||
\(403\) | 15.4934 | 0.771781 | ||||||||
\(404\) | −9.39363 | −0.467351 | ||||||||
\(405\) | 19.2418 | 0.956133 | ||||||||
\(406\) | −10.0605 | −0.499296 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 9.43004 | 0.466856 | ||||||||
\(409\) | 32.8533 | 1.62449 | 0.812245 | − | 0.583317i | \(-0.198245\pi\) | ||||
0.812245 | + | 0.583317i | \(0.198245\pi\) | |||||||
\(410\) | −21.7571 | −1.07450 | ||||||||
\(411\) | 16.8945 | 0.833343 | ||||||||
\(412\) | −0.279274 | −0.0137588 | ||||||||
\(413\) | 1.24394 | 0.0612101 | ||||||||
\(414\) | −0.160264 | −0.00787657 | ||||||||
\(415\) | −8.18112 | −0.401595 | ||||||||
\(416\) | 1.68357 | 0.0825440 | ||||||||
\(417\) | −10.6013 | −0.519149 | ||||||||
\(418\) | −2.94434 | −0.144012 | ||||||||
\(419\) | 19.2145 | 0.938692 | 0.469346 | − | 0.883014i | \(-0.344490\pi\) | ||||
0.469346 | + | 0.883014i | \(0.344490\pi\) | |||||||
\(420\) | 4.43694 | 0.216501 | ||||||||
\(421\) | 36.4583 | 1.77687 | 0.888435 | − | 0.459002i | \(-0.151793\pi\) | ||||
0.888435 | + | 0.459002i | \(0.151793\pi\) | |||||||
\(422\) | −7.31223 | −0.355954 | ||||||||
\(423\) | 0.608222 | 0.0295728 | ||||||||
\(424\) | −6.58882 | −0.319981 | ||||||||
\(425\) | 3.37232 | 0.163581 | ||||||||
\(426\) | 22.8969 | 1.10936 | ||||||||
\(427\) | −1.77902 | −0.0860928 | ||||||||
\(428\) | 11.1237 | 0.537685 | ||||||||
\(429\) | −17.5167 | −0.845712 | ||||||||
\(430\) | −4.05065 | −0.195340 | ||||||||
\(431\) | −9.26831 | −0.446439 | −0.223219 | − | 0.974768i | \(-0.571657\pi\) | ||||
−0.223219 | + | 0.974768i | \(0.571657\pi\) | |||||||
\(432\) | 5.13513 | 0.247064 | ||||||||
\(433\) | −24.0022 | −1.15347 | −0.576735 | − | 0.816931i | \(-0.695674\pi\) | ||||
−0.576735 | + | 0.816931i | \(0.695674\pi\) | |||||||
\(434\) | 11.1459 | 0.535022 | ||||||||
\(435\) | −30.4299 | −1.45900 | ||||||||
\(436\) | 4.40630 | 0.211024 | ||||||||
\(437\) | 1.15953 | 0.0554678 | ||||||||
\(438\) | −14.9762 | −0.715590 | ||||||||
\(439\) | −6.86675 | −0.327732 | −0.163866 | − | 0.986483i | \(-0.552396\pi\) | ||||
−0.163866 | + | 0.986483i | \(0.552396\pi\) | |||||||
\(440\) | −12.4215 | −0.592169 | ||||||||
\(441\) | −0.379102 | −0.0180525 | ||||||||
\(442\) | −9.06320 | −0.431092 | ||||||||
\(443\) | 0.332029 | 0.0157752 | 0.00788759 | − | 0.999969i | \(-0.497489\pi\) | ||||
0.00788759 | + | 0.999969i | \(0.497489\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −37.7140 | −1.78781 | ||||||||
\(446\) | 15.9777 | 0.756566 | ||||||||
\(447\) | −14.1992 | −0.671597 | ||||||||
\(448\) | 1.21116 | 0.0572220 | ||||||||
\(449\) | 9.94564 | 0.469364 | 0.234682 | − | 0.972072i | \(-0.424595\pi\) | ||||
0.234682 | + | 0.972072i | \(0.424595\pi\) | |||||||
\(450\) | −0.0429208 | −0.00202331 | ||||||||
\(451\) | 61.7928 | 2.90971 | ||||||||
\(452\) | 13.3652 | 0.628646 | ||||||||
\(453\) | −8.74217 | −0.410743 | ||||||||
\(454\) | 3.46336 | 0.162544 | ||||||||
\(455\) | −4.26434 | −0.199915 | ||||||||
\(456\) | 0.868354 | 0.0406644 | ||||||||
\(457\) | 28.3766 | 1.32740 | 0.663701 | − | 0.747998i | \(-0.268985\pi\) | ||||
0.663701 | + | 0.747998i | \(0.268985\pi\) | |||||||
\(458\) | −15.1822 | −0.709420 | ||||||||
\(459\) | −27.6440 | −1.29031 | ||||||||
\(460\) | 4.89177 | 0.228080 | ||||||||
\(461\) | 4.57081 | 0.212884 | 0.106442 | − | 0.994319i | \(-0.466054\pi\) | ||||
0.106442 | + | 0.994319i | \(0.466054\pi\) | |||||||
\(462\) | −12.6015 | −0.586273 | ||||||||
\(463\) | 13.6661 | 0.635116 | 0.317558 | − | 0.948239i | \(-0.397137\pi\) | ||||
0.317558 | + | 0.948239i | \(0.397137\pi\) | |||||||
\(464\) | −8.30651 | −0.385620 | ||||||||
\(465\) | 33.7129 | 1.56340 | ||||||||
\(466\) | −5.71207 | −0.264607 | ||||||||
\(467\) | 5.16486 | 0.239001 | 0.119501 | − | 0.992834i | \(-0.461871\pi\) | ||||
0.119501 | + | 0.992834i | \(0.461871\pi\) | |||||||
\(468\) | 0.115351 | 0.00533210 | ||||||||
\(469\) | 14.8846 | 0.687306 | ||||||||
\(470\) | −18.5648 | −0.856332 | ||||||||
\(471\) | −8.41386 | −0.387690 | ||||||||
\(472\) | 1.02706 | 0.0472743 | ||||||||
\(473\) | 11.5044 | 0.528971 | ||||||||
\(474\) | −11.0095 | −0.505682 | ||||||||
\(475\) | 0.310536 | 0.0142484 | ||||||||
\(476\) | −6.52006 | −0.298846 | ||||||||
\(477\) | −0.451436 | −0.0206698 | ||||||||
\(478\) | −7.10847 | −0.325134 | ||||||||
\(479\) | −33.7622 | −1.54264 | −0.771318 | − | 0.636450i | \(-0.780402\pi\) | ||||
−0.771318 | + | 0.636450i | \(0.780402\pi\) | |||||||
\(480\) | 3.66338 | 0.167210 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −10.1248 | −0.461170 | ||||||||
\(483\) | 4.96266 | 0.225809 | ||||||||
\(484\) | 24.2785 | 1.10357 | ||||||||
\(485\) | −16.9838 | −0.771196 | ||||||||
\(486\) | 0.711895 | 0.0322922 | ||||||||
\(487\) | 32.6970 | 1.48164 | 0.740821 | − | 0.671703i | \(-0.234437\pi\) | ||||
0.740821 | + | 0.671703i | \(0.234437\pi\) | |||||||
\(488\) | −1.46885 | −0.0664919 | ||||||||
\(489\) | −10.3796 | −0.469384 | ||||||||
\(490\) | 11.5714 | 0.522742 | ||||||||
\(491\) | −24.2572 | −1.09471 | −0.547356 | − | 0.836900i | \(-0.684366\pi\) | ||||
−0.547356 | + | 0.836900i | \(0.684366\pi\) | |||||||
\(492\) | −18.2241 | −0.821607 | ||||||||
\(493\) | 44.7165 | 2.01393 | ||||||||
\(494\) | −0.834575 | −0.0375493 | ||||||||
\(495\) | −0.851061 | −0.0382524 | ||||||||
\(496\) | 9.20267 | 0.413212 | ||||||||
\(497\) | −15.8312 | −0.710127 | ||||||||
\(498\) | −6.85266 | −0.307075 | ||||||||
\(499\) | −18.6640 | −0.835514 | −0.417757 | − | 0.908559i | \(-0.637184\pi\) | ||||
−0.417757 | + | 0.908559i | \(0.637184\pi\) | |||||||
\(500\) | 11.7666 | 0.526219 | ||||||||
\(501\) | 1.00133 | 0.0447359 | ||||||||
\(502\) | 13.7490 | 0.613650 | ||||||||
\(503\) | −8.58318 | −0.382705 | −0.191353 | − | 0.981521i | \(-0.561287\pi\) | ||||
−0.191353 | + | 0.981521i | \(0.561287\pi\) | |||||||
\(504\) | 0.0829833 | 0.00369637 | ||||||||
\(505\) | 19.6450 | 0.874189 | ||||||||
\(506\) | −13.8932 | −0.617630 | ||||||||
\(507\) | 17.8072 | 0.790847 | ||||||||
\(508\) | 19.0384 | 0.844692 | ||||||||
\(509\) | −24.8965 | −1.10352 | −0.551759 | − | 0.834004i | \(-0.686043\pi\) | ||||
−0.551759 | + | 0.834004i | \(0.686043\pi\) | |||||||
\(510\) | −19.7211 | −0.873265 | ||||||||
\(511\) | 10.3547 | 0.458066 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −2.54557 | −0.112390 | ||||||||
\(514\) | −7.08203 | −0.312375 | ||||||||
\(515\) | 0.584047 | 0.0257362 | ||||||||
\(516\) | −3.39290 | −0.149364 | ||||||||
\(517\) | 52.7265 | 2.31891 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −28.3478 | −1.24433 | ||||||||
\(520\) | −3.52087 | −0.154400 | ||||||||
\(521\) | −14.2132 | −0.622691 | −0.311345 | − | 0.950297i | \(-0.600780\pi\) | ||||
−0.311345 | + | 0.950297i | \(0.600780\pi\) | |||||||
\(522\) | −0.569124 | −0.0249099 | ||||||||
\(523\) | 33.4160 | 1.46118 | 0.730591 | − | 0.682816i | \(-0.239245\pi\) | ||||
0.730591 | + | 0.682816i | \(0.239245\pi\) | |||||||
\(524\) | 2.32597 | 0.101610 | ||||||||
\(525\) | 1.32906 | 0.0580051 | ||||||||
\(526\) | 4.60769 | 0.200905 | ||||||||
\(527\) | −49.5408 | −2.15803 | ||||||||
\(528\) | −10.4044 | −0.452795 | ||||||||
\(529\) | −17.5286 | −0.762114 | ||||||||
\(530\) | 13.7792 | 0.598532 | ||||||||
\(531\) | 0.0703696 | 0.00305378 | ||||||||
\(532\) | −0.600392 | −0.0260303 | ||||||||
\(533\) | 17.5152 | 0.758667 | ||||||||
\(534\) | −31.5899 | −1.36703 | ||||||||
\(535\) | −23.2631 | −1.00575 | ||||||||
\(536\) | 12.2895 | 0.530826 | ||||||||
\(537\) | 11.5559 | 0.498674 | ||||||||
\(538\) | −5.21884 | −0.225000 | ||||||||
\(539\) | −32.8641 | −1.41556 | ||||||||
\(540\) | −10.7391 | −0.462139 | ||||||||
\(541\) | −26.5225 | −1.14029 | −0.570146 | − | 0.821544i | \(-0.693113\pi\) | ||||
−0.570146 | + | 0.821544i | \(0.693113\pi\) | |||||||
\(542\) | 11.2863 | 0.484790 | ||||||||
\(543\) | −2.57992 | −0.110715 | ||||||||
\(544\) | −5.38331 | −0.230807 | ||||||||
\(545\) | −9.21492 | −0.394724 | ||||||||
\(546\) | −3.57189 | −0.152863 | ||||||||
\(547\) | 7.21041 | 0.308295 | 0.154147 | − | 0.988048i | \(-0.450737\pi\) | ||||
0.154147 | + | 0.988048i | \(0.450737\pi\) | |||||||
\(548\) | −9.64452 | −0.411993 | ||||||||
\(549\) | −0.100639 | −0.00429518 | ||||||||
\(550\) | −3.72078 | −0.158655 | ||||||||
\(551\) | 4.11767 | 0.175419 | ||||||||
\(552\) | 4.09744 | 0.174399 | ||||||||
\(553\) | 7.61210 | 0.323699 | ||||||||
\(554\) | 0.522535 | 0.0222004 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.05196 | 0.256660 | ||||||||
\(557\) | 12.5459 | 0.531585 | 0.265793 | − | 0.964030i | \(-0.414366\pi\) | ||||
0.265793 | + | 0.964030i | \(0.414366\pi\) | |||||||
\(558\) | 0.630525 | 0.0266923 | ||||||||
\(559\) | 3.26092 | 0.137922 | ||||||||
\(560\) | −2.53291 | −0.107035 | ||||||||
\(561\) | 56.0103 | 2.36476 | ||||||||
\(562\) | −14.8186 | −0.625086 | ||||||||
\(563\) | 19.9469 | 0.840660 | 0.420330 | − | 0.907371i | \(-0.361914\pi\) | ||||
0.420330 | + | 0.907371i | \(0.361914\pi\) | |||||||
\(564\) | −15.5503 | −0.654784 | ||||||||
\(565\) | −27.9507 | −1.17590 | ||||||||
\(566\) | 3.99925 | 0.168101 | ||||||||
\(567\) | −11.1437 | −0.467992 | ||||||||
\(568\) | −13.0711 | −0.548451 | ||||||||
\(569\) | −2.55565 | −0.107138 | −0.0535692 | − | 0.998564i | \(-0.517060\pi\) | ||||
−0.0535692 | + | 0.998564i | \(0.517060\pi\) | |||||||
\(570\) | −1.81599 | −0.0760636 | ||||||||
\(571\) | −11.1405 | −0.466216 | −0.233108 | − | 0.972451i | \(-0.574889\pi\) | ||||
−0.233108 | + | 0.972451i | \(0.574889\pi\) | |||||||
\(572\) | 9.99970 | 0.418109 | ||||||||
\(573\) | 41.7890 | 1.74576 | ||||||||
\(574\) | 12.6004 | 0.525931 | ||||||||
\(575\) | 1.46531 | 0.0611074 | ||||||||
\(576\) | 0.0685155 | 0.00285481 | ||||||||
\(577\) | −16.6278 | −0.692226 | −0.346113 | − | 0.938193i | \(-0.612499\pi\) | ||||
−0.346113 | + | 0.938193i | \(0.612499\pi\) | |||||||
\(578\) | 11.9800 | 0.498302 | ||||||||
\(579\) | 29.5015 | 1.22604 | ||||||||
\(580\) | 17.3715 | 0.721310 | ||||||||
\(581\) | 4.73802 | 0.196566 | ||||||||
\(582\) | −14.2260 | −0.589686 | ||||||||
\(583\) | −39.1347 | −1.62080 | ||||||||
\(584\) | 8.54942 | 0.353778 | ||||||||
\(585\) | −0.241234 | −0.00997380 | ||||||||
\(586\) | −10.1604 | −0.419724 | ||||||||
\(587\) | −26.0244 | −1.07414 | −0.537070 | − | 0.843538i | \(-0.680469\pi\) | ||||
−0.537070 | + | 0.843538i | \(0.680469\pi\) | |||||||
\(588\) | 9.69241 | 0.399708 | ||||||||
\(589\) | −4.56191 | −0.187970 | ||||||||
\(590\) | −2.14790 | −0.0884276 | ||||||||
\(591\) | −31.6982 | −1.30389 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −17.1659 | −0.704917 | −0.352459 | − | 0.935827i | \(-0.614654\pi\) | ||||
−0.352459 | + | 0.935827i | \(0.614654\pi\) | |||||||
\(594\) | 30.5005 | 1.25145 | ||||||||
\(595\) | 13.6354 | 0.558998 | ||||||||
\(596\) | 8.10585 | 0.332029 | ||||||||
\(597\) | 27.9707 | 1.14477 | ||||||||
\(598\) | −3.93805 | −0.161039 | ||||||||
\(599\) | −18.8295 | −0.769351 | −0.384675 | − | 0.923052i | \(-0.625687\pi\) | ||||
−0.384675 | + | 0.923052i | \(0.625687\pi\) | |||||||
\(600\) | 1.09735 | 0.0447990 | ||||||||
\(601\) | 28.5102 | 1.16295 | 0.581477 | − | 0.813563i | \(-0.302475\pi\) | ||||
0.581477 | + | 0.813563i | \(0.302475\pi\) | |||||||
\(602\) | 2.34590 | 0.0956117 | ||||||||
\(603\) | 0.842022 | 0.0342898 | ||||||||
\(604\) | 4.99063 | 0.203066 | ||||||||
\(605\) | −50.7737 | −2.06424 | ||||||||
\(606\) | 16.4550 | 0.668438 | ||||||||
\(607\) | −35.6551 | −1.44720 | −0.723598 | − | 0.690222i | \(-0.757513\pi\) | ||||
−0.723598 | + | 0.690222i | \(0.757513\pi\) | |||||||
\(608\) | −0.495716 | −0.0201039 | ||||||||
\(609\) | 17.6232 | 0.714128 | ||||||||
\(610\) | 3.07182 | 0.124374 | ||||||||
\(611\) | 14.9453 | 0.604624 | ||||||||
\(612\) | −0.368840 | −0.0149095 | ||||||||
\(613\) | −21.3524 | −0.862416 | −0.431208 | − | 0.902253i | \(-0.641912\pi\) | ||||
−0.431208 | + | 0.902253i | \(0.641912\pi\) | |||||||
\(614\) | 22.4774 | 0.907112 | ||||||||
\(615\) | 38.1122 | 1.53683 | ||||||||
\(616\) | 7.19378 | 0.289845 | ||||||||
\(617\) | 4.49896 | 0.181121 | 0.0905606 | − | 0.995891i | \(-0.471134\pi\) | ||||
0.0905606 | + | 0.995891i | \(0.471134\pi\) | |||||||
\(618\) | 0.489209 | 0.0196789 | ||||||||
\(619\) | 28.2607 | 1.13589 | 0.567946 | − | 0.823066i | \(-0.307738\pi\) | ||||
0.567946 | + | 0.823066i | \(0.307738\pi\) | |||||||
\(620\) | −19.2456 | −0.772922 | ||||||||
\(621\) | −12.0116 | −0.482008 | ||||||||
\(622\) | −4.40563 | −0.176650 | ||||||||
\(623\) | 21.8417 | 0.875070 | ||||||||
\(624\) | −2.94915 | −0.118060 | ||||||||
\(625\) | −21.4754 | −0.859015 | ||||||||
\(626\) | −0.741008 | −0.0296166 | ||||||||
\(627\) | 5.15765 | 0.205977 | ||||||||
\(628\) | 4.80321 | 0.191669 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −0.173543 | −0.00691414 | ||||||||
\(631\) | −0.688404 | −0.0274049 | −0.0137025 | − | 0.999906i | \(-0.504362\pi\) | ||||
−0.0137025 | + | 0.999906i | \(0.504362\pi\) | |||||||
\(632\) | 6.28496 | 0.250002 | ||||||||
\(633\) | 12.8090 | 0.509111 | ||||||||
\(634\) | 25.2386 | 1.00235 | ||||||||
\(635\) | −39.8151 | −1.58001 | ||||||||
\(636\) | 11.5418 | 0.457660 | ||||||||
\(637\) | −9.31536 | −0.369088 | ||||||||
\(638\) | −49.3371 | −1.95327 | ||||||||
\(639\) | −0.895572 | −0.0354283 | ||||||||
\(640\) | −2.09131 | −0.0826661 | ||||||||
\(641\) | −23.6488 | −0.934073 | −0.467036 | − | 0.884238i | \(-0.654678\pi\) | ||||
−0.467036 | + | 0.884238i | \(0.654678\pi\) | |||||||
\(642\) | −19.4856 | −0.769036 | ||||||||
\(643\) | −43.3182 | −1.70830 | −0.854151 | − | 0.520026i | \(-0.825922\pi\) | ||||
−0.854151 | + | 0.520026i | \(0.825922\pi\) | |||||||
\(644\) | −2.83303 | −0.111637 | ||||||||
\(645\) | 7.09560 | 0.279389 | ||||||||
\(646\) | 2.66859 | 0.104994 | ||||||||
\(647\) | 34.6124 | 1.36075 | 0.680376 | − | 0.732863i | \(-0.261816\pi\) | ||||
0.680376 | + | 0.732863i | \(0.261816\pi\) | |||||||
\(648\) | −9.20085 | −0.361444 | ||||||||
\(649\) | 6.10030 | 0.239458 | ||||||||
\(650\) | −1.05466 | −0.0413671 | ||||||||
\(651\) | −19.5245 | −0.765226 | ||||||||
\(652\) | 5.92541 | 0.232057 | ||||||||
\(653\) | 29.5930 | 1.15806 | 0.579032 | − | 0.815305i | \(-0.303431\pi\) | ||||
0.579032 | + | 0.815305i | \(0.303431\pi\) | |||||||
\(654\) | −7.71859 | −0.301821 | ||||||||
\(655\) | −4.86431 | −0.190064 | ||||||||
\(656\) | 10.4036 | 0.406192 | ||||||||
\(657\) | 0.585768 | 0.0228530 | ||||||||
\(658\) | 10.7517 | 0.419144 | ||||||||
\(659\) | −44.4752 | −1.73251 | −0.866253 | − | 0.499606i | \(-0.833478\pi\) | ||||
−0.866253 | + | 0.499606i | \(0.833478\pi\) | |||||||
\(660\) | 21.7589 | 0.846963 | ||||||||
\(661\) | 1.68358 | 0.0654838 | 0.0327419 | − | 0.999464i | \(-0.489576\pi\) | ||||
0.0327419 | + | 0.999464i | \(0.489576\pi\) | |||||||
\(662\) | 4.58769 | 0.178306 | ||||||||
\(663\) | 15.8762 | 0.616579 | ||||||||
\(664\) | 3.91197 | 0.151814 | ||||||||
\(665\) | 1.25560 | 0.0486902 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19.4298 | 0.752323 | ||||||||
\(668\) | −0.571625 | −0.0221168 | ||||||||
\(669\) | −27.9884 | −1.08209 | ||||||||
\(670\) | −25.7011 | −0.992921 | ||||||||
\(671\) | −8.72436 | −0.336800 | ||||||||
\(672\) | −2.12161 | −0.0818430 | ||||||||
\(673\) | 26.6133 | 1.02587 | 0.512933 | − | 0.858429i | \(-0.328559\pi\) | ||||
0.512933 | + | 0.858429i | \(0.328559\pi\) | |||||||
\(674\) | −25.8343 | −0.995102 | ||||||||
\(675\) | −3.21685 | −0.123817 | ||||||||
\(676\) | −10.1656 | −0.390984 | ||||||||
\(677\) | 6.85446 | 0.263438 | 0.131719 | − | 0.991287i | \(-0.457950\pi\) | ||||
0.131719 | + | 0.991287i | \(0.457950\pi\) | |||||||
\(678\) | −23.4121 | −0.899135 | ||||||||
\(679\) | 9.83604 | 0.377473 | ||||||||
\(680\) | 11.2581 | 0.431730 | ||||||||
\(681\) | −6.06683 | −0.232482 | ||||||||
\(682\) | 54.6599 | 2.09304 | ||||||||
\(683\) | −41.2133 | −1.57698 | −0.788491 | − | 0.615046i | \(-0.789137\pi\) | ||||
−0.788491 | + | 0.615046i | \(0.789137\pi\) | |||||||
\(684\) | −0.0339642 | −0.00129865 | ||||||||
\(685\) | 20.1696 | 0.770642 | ||||||||
\(686\) | −15.1796 | −0.579560 | ||||||||
\(687\) | 26.5950 | 1.01466 | ||||||||
\(688\) | 1.93690 | 0.0738436 | ||||||||
\(689\) | −11.0928 | −0.422601 | ||||||||
\(690\) | −8.56900 | −0.326216 | ||||||||
\(691\) | −4.89261 | −0.186123 | −0.0930617 | − | 0.995660i | \(-0.529665\pi\) | ||||
−0.0930617 | + | 0.995660i | \(0.529665\pi\) | |||||||
\(692\) | 16.1829 | 0.615180 | ||||||||
\(693\) | 0.492885 | 0.0187231 | ||||||||
\(694\) | −4.89892 | −0.185961 | ||||||||
\(695\) | −12.6565 | −0.480089 | ||||||||
\(696\) | 14.5507 | 0.551541 | ||||||||
\(697\) | −56.0057 | −2.12137 | ||||||||
\(698\) | 29.0275 | 1.09871 | ||||||||
\(699\) | 10.0059 | 0.378459 | ||||||||
\(700\) | −0.758720 | −0.0286769 | ||||||||
\(701\) | 17.3040 | 0.653562 | 0.326781 | − | 0.945100i | \(-0.394036\pi\) | ||||
0.326781 | + | 0.945100i | \(0.394036\pi\) | |||||||
\(702\) | 8.64538 | 0.326299 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 5.93957 | 0.223856 | ||||||||
\(705\) | 32.5204 | 1.22479 | ||||||||
\(706\) | −26.9530 | −1.01439 | ||||||||
\(707\) | −11.3772 | −0.427884 | ||||||||
\(708\) | −1.79912 | −0.0676151 | ||||||||
\(709\) | −5.07624 | −0.190642 | −0.0953212 | − | 0.995447i | \(-0.530388\pi\) | ||||
−0.0953212 | + | 0.995447i | \(0.530388\pi\) | |||||||
\(710\) | 27.3357 | 1.02589 | ||||||||
\(711\) | 0.430617 | 0.0161494 | ||||||||
\(712\) | 18.0337 | 0.675841 | ||||||||
\(713\) | −21.5260 | −0.806154 | ||||||||
\(714\) | 11.4213 | 0.427431 | ||||||||
\(715\) | −20.9124 | −0.782081 | ||||||||
\(716\) | −6.59689 | −0.246538 | ||||||||
\(717\) | 12.4520 | 0.465030 | ||||||||
\(718\) | −2.33163 | −0.0870155 | ||||||||
\(719\) | 24.7862 | 0.924371 | 0.462185 | − | 0.886783i | \(-0.347066\pi\) | ||||
0.462185 | + | 0.886783i | \(0.347066\pi\) | |||||||
\(720\) | −0.143287 | −0.00533998 | ||||||||
\(721\) | −0.338246 | −0.0125969 | ||||||||
\(722\) | −18.7543 | −0.697961 | ||||||||
\(723\) | 17.7357 | 0.659598 | ||||||||
\(724\) | 1.47280 | 0.0547360 | ||||||||
\(725\) | 5.20353 | 0.193254 | ||||||||
\(726\) | −42.5290 | −1.57840 | ||||||||
\(727\) | 3.10240 | 0.115062 | 0.0575308 | − | 0.998344i | \(-0.481677\pi\) | ||||
0.0575308 | + | 0.998344i | \(0.481677\pi\) | |||||||
\(728\) | 2.03908 | 0.0755733 | ||||||||
\(729\) | 26.3555 | 0.976130 | ||||||||
\(730\) | −17.8795 | −0.661749 | ||||||||
\(731\) | −10.4269 | −0.385654 | ||||||||
\(732\) | 2.57302 | 0.0951015 | ||||||||
\(733\) | 17.7619 | 0.656050 | 0.328025 | − | 0.944669i | \(-0.393617\pi\) | ||||
0.328025 | + | 0.944669i | \(0.393617\pi\) | |||||||
\(734\) | 1.11791 | 0.0412628 | ||||||||
\(735\) | −20.2698 | −0.747663 | ||||||||
\(736\) | −2.33910 | −0.0862203 | ||||||||
\(737\) | 72.9944 | 2.68878 | ||||||||
\(738\) | 0.712806 | 0.0262387 | ||||||||
\(739\) | −20.8171 | −0.765771 | −0.382886 | − | 0.923796i | \(-0.625070\pi\) | ||||
−0.382886 | + | 0.923796i | \(0.625070\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.46194 | 0.0537057 | ||||||||
\(742\) | −7.98013 | −0.292960 | ||||||||
\(743\) | 47.5877 | 1.74583 | 0.872913 | − | 0.487877i | \(-0.162228\pi\) | ||||
0.872913 | + | 0.487877i | \(0.162228\pi\) | |||||||
\(744\) | −16.1205 | −0.591006 | ||||||||
\(745\) | −16.9518 | −0.621066 | ||||||||
\(746\) | −7.12913 | −0.261016 | ||||||||
\(747\) | 0.268030 | 0.00980671 | ||||||||
\(748\) | −31.9745 | −1.16910 | ||||||||
\(749\) | 13.4726 | 0.492279 | ||||||||
\(750\) | −20.6118 | −0.752636 | ||||||||
\(751\) | 31.6665 | 1.15553 | 0.577764 | − | 0.816204i | \(-0.303925\pi\) | ||||
0.577764 | + | 0.816204i | \(0.303925\pi\) | |||||||
\(752\) | 8.87715 | 0.323717 | ||||||||
\(753\) | −24.0844 | −0.877686 | ||||||||
\(754\) | −13.9846 | −0.509290 | ||||||||
\(755\) | −10.4369 | −0.379839 | ||||||||
\(756\) | 6.21948 | 0.226200 | ||||||||
\(757\) | −33.1698 | −1.20558 | −0.602789 | − | 0.797900i | \(-0.705944\pi\) | ||||
−0.602789 | + | 0.797900i | \(0.705944\pi\) | |||||||
\(758\) | 4.72138 | 0.171488 | ||||||||
\(759\) | 24.3370 | 0.883378 | ||||||||
\(760\) | 1.03669 | 0.0376048 | ||||||||
\(761\) | −5.42177 | −0.196539 | −0.0982696 | − | 0.995160i | \(-0.531331\pi\) | ||||
−0.0982696 | + | 0.995160i | \(0.531331\pi\) | |||||||
\(762\) | −33.3499 | −1.20814 | ||||||||
\(763\) | 5.33674 | 0.193203 | ||||||||
\(764\) | −23.8560 | −0.863080 | ||||||||
\(765\) | 0.771357 | 0.0278885 | ||||||||
\(766\) | −17.4079 | −0.628975 | ||||||||
\(767\) | 1.72913 | 0.0624354 | ||||||||
\(768\) | −1.75172 | −0.0632097 | ||||||||
\(769\) | 38.1392 | 1.37533 | 0.687666 | − | 0.726027i | \(-0.258635\pi\) | ||||
0.687666 | + | 0.726027i | \(0.258635\pi\) | |||||||
\(770\) | −15.0444 | −0.542162 | ||||||||
\(771\) | 12.4057 | 0.446781 | ||||||||
\(772\) | −16.8415 | −0.606138 | ||||||||
\(773\) | −16.5982 | −0.596995 | −0.298497 | − | 0.954410i | \(-0.596485\pi\) | ||||
−0.298497 | + | 0.954410i | \(0.596485\pi\) | |||||||
\(774\) | 0.132708 | 0.00477008 | ||||||||
\(775\) | −5.76492 | −0.207082 | ||||||||
\(776\) | 8.12116 | 0.291533 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −35.7110 | −1.28030 | ||||||||
\(779\) | −5.15722 | −0.184777 | ||||||||
\(780\) | 6.16757 | 0.220834 | ||||||||
\(781\) | −77.6367 | −2.77806 | ||||||||
\(782\) | 12.5921 | 0.450292 | ||||||||
\(783\) | −42.6550 | −1.52437 | ||||||||
\(784\) | −5.53309 | −0.197610 | ||||||||
\(785\) | −10.0450 | −0.358521 | ||||||||
\(786\) | −4.07444 | −0.145330 | ||||||||
\(787\) | 36.6308 | 1.30575 | 0.652873 | − | 0.757467i | \(-0.273564\pi\) | ||||
0.652873 | + | 0.757467i | \(0.273564\pi\) | |||||||
\(788\) | 18.0955 | 0.644625 | ||||||||
\(789\) | −8.07137 | −0.287348 | ||||||||
\(790\) | −13.1438 | −0.467634 | ||||||||
\(791\) | 16.1874 | 0.575558 | ||||||||
\(792\) | 0.406952 | 0.0144604 | ||||||||
\(793\) | −2.47292 | −0.0878161 | ||||||||
\(794\) | −11.6241 | −0.412523 | ||||||||
\(795\) | −24.1373 | −0.856063 | ||||||||
\(796\) | −15.9676 | −0.565956 | ||||||||
\(797\) | 25.4663 | 0.902063 | 0.451031 | − | 0.892508i | \(-0.351056\pi\) | ||||
0.451031 | + | 0.892508i | \(0.351056\pi\) | |||||||
\(798\) | 1.05172 | 0.0372304 | ||||||||
\(799\) | −47.7885 | −1.69063 | ||||||||
\(800\) | −0.626440 | −0.0221480 | ||||||||
\(801\) | 1.23559 | 0.0436573 | ||||||||
\(802\) | 29.4827 | 1.04107 | ||||||||
\(803\) | 50.7799 | 1.79198 | ||||||||
\(804\) | −21.5278 | −0.759226 | ||||||||
\(805\) | 5.92473 | 0.208819 | ||||||||
\(806\) | 15.4934 | 0.545731 | ||||||||
\(807\) | 9.14194 | 0.321811 | ||||||||
\(808\) | −9.39363 | −0.330467 | ||||||||
\(809\) | 25.7424 | 0.905055 | 0.452528 | − | 0.891750i | \(-0.350522\pi\) | ||||
0.452528 | + | 0.891750i | \(0.350522\pi\) | |||||||
\(810\) | 19.2418 | 0.676088 | ||||||||
\(811\) | −24.9867 | −0.877403 | −0.438702 | − | 0.898633i | \(-0.644561\pi\) | ||||
−0.438702 | + | 0.898633i | \(0.644561\pi\) | |||||||
\(812\) | −10.0605 | −0.353055 | ||||||||
\(813\) | −19.7705 | −0.693381 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.3918 | −0.434067 | ||||||||
\(816\) | 9.43004 | 0.330117 | ||||||||
\(817\) | −0.960152 | −0.0335915 | ||||||||
\(818\) | 32.8533 | 1.14869 | ||||||||
\(819\) | 0.139709 | 0.00488181 | ||||||||
\(820\) | −21.7571 | −0.759790 | ||||||||
\(821\) | −27.6049 | −0.963417 | −0.481708 | − | 0.876332i | \(-0.659984\pi\) | ||||
−0.481708 | + | 0.876332i | \(0.659984\pi\) | |||||||
\(822\) | 16.8945 | 0.589262 | ||||||||
\(823\) | −47.0065 | −1.63855 | −0.819273 | − | 0.573404i | \(-0.805622\pi\) | ||||
−0.819273 | + | 0.573404i | \(0.805622\pi\) | |||||||
\(824\) | −0.279274 | −0.00972897 | ||||||||
\(825\) | 6.51776 | 0.226919 | ||||||||
\(826\) | 1.24394 | 0.0432821 | ||||||||
\(827\) | −20.9656 | −0.729044 | −0.364522 | − | 0.931195i | \(-0.618768\pi\) | ||||
−0.364522 | + | 0.931195i | \(0.618768\pi\) | |||||||
\(828\) | −0.160264 | −0.00556957 | ||||||||
\(829\) | 47.6008 | 1.65324 | 0.826622 | − | 0.562758i | \(-0.190260\pi\) | ||||
0.826622 | + | 0.562758i | \(0.190260\pi\) | |||||||
\(830\) | −8.18112 | −0.283971 | ||||||||
\(831\) | −0.915335 | −0.0317526 | ||||||||
\(832\) | 1.68357 | 0.0583674 | ||||||||
\(833\) | 29.7863 | 1.03203 | ||||||||
\(834\) | −10.6013 | −0.367094 | ||||||||
\(835\) | 1.19544 | 0.0413700 | ||||||||
\(836\) | −2.94434 | −0.101832 | ||||||||
\(837\) | 47.2570 | 1.63344 | ||||||||
\(838\) | 19.2145 | 0.663755 | ||||||||
\(839\) | −18.2819 | −0.631162 | −0.315581 | − | 0.948899i | \(-0.602199\pi\) | ||||
−0.315581 | + | 0.948899i | \(0.602199\pi\) | |||||||
\(840\) | 4.43694 | 0.153089 | ||||||||
\(841\) | 39.9981 | 1.37925 | ||||||||
\(842\) | 36.4583 | 1.25644 | ||||||||
\(843\) | 25.9580 | 0.894043 | ||||||||
\(844\) | −7.31223 | −0.251697 | ||||||||
\(845\) | 21.2593 | 0.731343 | ||||||||
\(846\) | 0.608222 | 0.0209111 | ||||||||
\(847\) | 29.4051 | 1.01037 | ||||||||
\(848\) | −6.58882 | −0.226261 | ||||||||
\(849\) | −7.00556 | −0.240430 | ||||||||
\(850\) | 3.37232 | 0.115670 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 22.8969 | 0.784434 | ||||||||
\(853\) | −18.3882 | −0.629601 | −0.314801 | − | 0.949158i | \(-0.601938\pi\) | ||||
−0.314801 | + | 0.949158i | \(0.601938\pi\) | |||||||
\(854\) | −1.77902 | −0.0608768 | ||||||||
\(855\) | 0.0710295 | 0.00242916 | ||||||||
\(856\) | 11.1237 | 0.380201 | ||||||||
\(857\) | −5.01983 | −0.171474 | −0.0857371 | − | 0.996318i | \(-0.527324\pi\) | ||||
−0.0857371 | + | 0.996318i | \(0.527324\pi\) | |||||||
\(858\) | −17.5167 | −0.598009 | ||||||||
\(859\) | 7.42957 | 0.253494 | 0.126747 | − | 0.991935i | \(-0.459546\pi\) | ||||
0.126747 | + | 0.991935i | \(0.459546\pi\) | |||||||
\(860\) | −4.05065 | −0.138126 | ||||||||
\(861\) | −22.0724 | −0.752224 | ||||||||
\(862\) | −9.26831 | −0.315680 | ||||||||
\(863\) | −12.2648 | −0.417498 | −0.208749 | − | 0.977969i | \(-0.566939\pi\) | ||||
−0.208749 | + | 0.977969i | \(0.566939\pi\) | |||||||
\(864\) | 5.13513 | 0.174701 | ||||||||
\(865\) | −33.8433 | −1.15071 | ||||||||
\(866\) | −24.0022 | −0.815627 | ||||||||
\(867\) | −20.9856 | −0.712708 | ||||||||
\(868\) | 11.1459 | 0.378317 | ||||||||
\(869\) | 37.3299 | 1.26633 | ||||||||
\(870\) | −30.4299 | −1.03167 | ||||||||
\(871\) | 20.6903 | 0.701064 | ||||||||
\(872\) | 4.40630 | 0.149216 | ||||||||
\(873\) | 0.556425 | 0.0188321 | ||||||||
\(874\) | 1.15953 | 0.0392216 | ||||||||
\(875\) | 14.2513 | 0.481781 | ||||||||
\(876\) | −14.9762 | −0.505998 | ||||||||
\(877\) | 32.9639 | 1.11311 | 0.556557 | − | 0.830810i | \(-0.312122\pi\) | ||||
0.556557 | + | 0.830810i | \(0.312122\pi\) | |||||||
\(878\) | −6.86675 | −0.231742 | ||||||||
\(879\) | 17.7982 | 0.600319 | ||||||||
\(880\) | −12.4215 | −0.418727 | ||||||||
\(881\) | 9.29779 | 0.313250 | 0.156625 | − | 0.987658i | \(-0.449939\pi\) | ||||
0.156625 | + | 0.987658i | \(0.449939\pi\) | |||||||
\(882\) | −0.379102 | −0.0127650 | ||||||||
\(883\) | 20.6007 | 0.693268 | 0.346634 | − | 0.938000i | \(-0.387325\pi\) | ||||
0.346634 | + | 0.938000i | \(0.387325\pi\) | |||||||
\(884\) | −9.06320 | −0.304828 | ||||||||
\(885\) | 3.76251 | 0.126475 | ||||||||
\(886\) | 0.332029 | 0.0111547 | ||||||||
\(887\) | −29.9457 | −1.00548 | −0.502740 | − | 0.864438i | \(-0.667675\pi\) | ||||
−0.502740 | + | 0.864438i | \(0.667675\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23.0586 | 0.773359 | ||||||||
\(890\) | −37.7140 | −1.26418 | ||||||||
\(891\) | −54.6491 | −1.83081 | ||||||||
\(892\) | 15.9777 | 0.534973 | ||||||||
\(893\) | −4.40055 | −0.147259 | ||||||||
\(894\) | −14.1992 | −0.474891 | ||||||||
\(895\) | 13.7961 | 0.461154 | ||||||||
\(896\) | 1.21116 | 0.0404621 | ||||||||
\(897\) | 6.89835 | 0.230329 | ||||||||
\(898\) | 9.94564 | 0.331890 | ||||||||
\(899\) | −76.4421 | −2.54949 | ||||||||
\(900\) | −0.0429208 | −0.00143069 | ||||||||
\(901\) | 35.4696 | 1.18167 | ||||||||
\(902\) | 61.7928 | 2.05747 | ||||||||
\(903\) | −4.10935 | −0.136751 | ||||||||
\(904\) | 13.3652 | 0.444520 | ||||||||
\(905\) | −3.08007 | −0.102385 | ||||||||
\(906\) | −8.74217 | −0.290439 | ||||||||
\(907\) | 51.2156 | 1.70059 | 0.850294 | − | 0.526308i | \(-0.176424\pi\) | ||||
0.850294 | + | 0.526308i | \(0.176424\pi\) | |||||||
\(908\) | 3.46336 | 0.114936 | ||||||||
\(909\) | −0.643609 | −0.0213472 | ||||||||
\(910\) | −4.26434 | −0.141362 | ||||||||
\(911\) | −26.5131 | −0.878417 | −0.439208 | − | 0.898385i | \(-0.644741\pi\) | ||||
−0.439208 | + | 0.898385i | \(0.644741\pi\) | |||||||
\(912\) | 0.868354 | 0.0287541 | ||||||||
\(913\) | 23.2354 | 0.768979 | ||||||||
\(914\) | 28.3766 | 0.938614 | ||||||||
\(915\) | −5.38097 | −0.177889 | ||||||||
\(916\) | −15.1822 | −0.501635 | ||||||||
\(917\) | 2.81712 | 0.0930296 | ||||||||
\(918\) | −27.6440 | −0.912388 | ||||||||
\(919\) | −27.6594 | −0.912400 | −0.456200 | − | 0.889877i | \(-0.650790\pi\) | ||||
−0.456200 | + | 0.889877i | \(0.650790\pi\) | |||||||
\(920\) | 4.89177 | 0.161277 | ||||||||
\(921\) | −39.3740 | −1.29742 | ||||||||
\(922\) | 4.57081 | 0.150532 | ||||||||
\(923\) | −22.0062 | −0.724342 | ||||||||
\(924\) | −12.6015 | −0.414558 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 13.6661 | 0.449095 | ||||||||
\(927\) | −0.0191346 | −0.000628462 0 | ||||||||
\(928\) | −8.30651 | −0.272675 | ||||||||
\(929\) | 9.35560 | 0.306947 | 0.153474 | − | 0.988153i | \(-0.450954\pi\) | ||||
0.153474 | + | 0.988153i | \(0.450954\pi\) | |||||||
\(930\) | 33.7129 | 1.10549 | ||||||||
\(931\) | 2.74284 | 0.0898929 | ||||||||
\(932\) | −5.71207 | −0.187105 | ||||||||
\(933\) | 7.71742 | 0.252657 | ||||||||
\(934\) | 5.16486 | 0.168999 | ||||||||
\(935\) | 66.8685 | 2.18683 | ||||||||
\(936\) | 0.115351 | 0.00377036 | ||||||||
\(937\) | −19.8079 | −0.647097 | −0.323549 | − | 0.946212i | \(-0.604876\pi\) | ||||
−0.323549 | + | 0.946212i | \(0.604876\pi\) | |||||||
\(938\) | 14.8846 | 0.485999 | ||||||||
\(939\) | 1.29804 | 0.0423598 | ||||||||
\(940\) | −18.5648 | −0.605518 | ||||||||
\(941\) | −4.37434 | −0.142599 | −0.0712997 | − | 0.997455i | \(-0.522715\pi\) | ||||
−0.0712997 | + | 0.997455i | \(0.522715\pi\) | |||||||
\(942\) | −8.41386 | −0.274139 | ||||||||
\(943\) | −24.3350 | −0.792457 | ||||||||
\(944\) | 1.02706 | 0.0334280 | ||||||||
\(945\) | −13.0068 | −0.423112 | ||||||||
\(946\) | 11.5044 | 0.374039 | ||||||||
\(947\) | 23.8564 | 0.775230 | 0.387615 | − | 0.921821i | \(-0.373299\pi\) | ||||
0.387615 | + | 0.921821i | \(0.373299\pi\) | |||||||
\(948\) | −11.0095 | −0.357571 | ||||||||
\(949\) | 14.3936 | 0.467236 | ||||||||
\(950\) | 0.310536 | 0.0100751 | ||||||||
\(951\) | −44.2110 | −1.43364 | ||||||||
\(952\) | −6.52006 | −0.211316 | ||||||||
\(953\) | 56.3661 | 1.82588 | 0.912938 | − | 0.408098i | \(-0.133808\pi\) | ||||
0.912938 | + | 0.408098i | \(0.133808\pi\) | |||||||
\(954\) | −0.451436 | −0.0146158 | ||||||||
\(955\) | 49.8902 | 1.61441 | ||||||||
\(956\) | −7.10847 | −0.229904 | ||||||||
\(957\) | 86.4247 | 2.79371 | ||||||||
\(958\) | −33.7622 | −1.09081 | ||||||||
\(959\) | −11.6811 | −0.377201 | ||||||||
\(960\) | 3.66338 | 0.118235 | ||||||||
\(961\) | 53.6892 | 1.73191 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.762147 | 0.0245598 | ||||||||
\(964\) | −10.1248 | −0.326096 | ||||||||
\(965\) | 35.2207 | 1.13379 | ||||||||
\(966\) | 4.96266 | 0.159671 | ||||||||
\(967\) | 46.6038 | 1.49868 | 0.749338 | − | 0.662188i | \(-0.230372\pi\) | ||||
0.749338 | + | 0.662188i | \(0.230372\pi\) | |||||||
\(968\) | 24.2785 | 0.780339 | ||||||||
\(969\) | −4.67462 | −0.150170 | ||||||||
\(970\) | −16.9838 | −0.545318 | ||||||||
\(971\) | 33.1861 | 1.06499 | 0.532496 | − | 0.846432i | \(-0.321254\pi\) | ||||
0.532496 | + | 0.846432i | \(0.321254\pi\) | |||||||
\(972\) | 0.711895 | 0.0228341 | ||||||||
\(973\) | 7.32990 | 0.234986 | ||||||||
\(974\) | 32.6970 | 1.04768 | ||||||||
\(975\) | 1.84746 | 0.0591662 | ||||||||
\(976\) | −1.46885 | −0.0470169 | ||||||||
\(977\) | −20.7016 | −0.662304 | −0.331152 | − | 0.943577i | \(-0.607437\pi\) | ||||
−0.331152 | + | 0.943577i | \(0.607437\pi\) | |||||||
\(978\) | −10.3796 | −0.331904 | ||||||||
\(979\) | 107.112 | 3.42333 | ||||||||
\(980\) | 11.5714 | 0.369634 | ||||||||
\(981\) | 0.301900 | 0.00963891 | ||||||||
\(982\) | −24.2572 | −0.774079 | ||||||||
\(983\) | −16.2367 | −0.517871 | −0.258935 | − | 0.965895i | \(-0.583372\pi\) | ||||
−0.258935 | + | 0.965895i | \(0.583372\pi\) | |||||||
\(984\) | −18.2241 | −0.580964 | ||||||||
\(985\) | −37.8432 | −1.20578 | ||||||||
\(986\) | 44.7165 | 1.42406 | ||||||||
\(987\) | −18.8339 | −0.599489 | ||||||||
\(988\) | −0.834575 | −0.0265514 | ||||||||
\(989\) | −4.53060 | −0.144065 | ||||||||
\(990\) | −0.851061 | −0.0270485 | ||||||||
\(991\) | 2.25933 | 0.0717699 | 0.0358849 | − | 0.999356i | \(-0.488575\pi\) | ||||
0.0358849 | + | 0.999356i | \(0.488575\pi\) | |||||||
\(992\) | 9.20267 | 0.292185 | ||||||||
\(993\) | −8.03634 | −0.255026 | ||||||||
\(994\) | −15.8312 | −0.502136 | ||||||||
\(995\) | 33.3931 | 1.05863 | ||||||||
\(996\) | −6.85266 | −0.217135 | ||||||||
\(997\) | −40.1141 | −1.27043 | −0.635213 | − | 0.772337i | \(-0.719088\pi\) | ||||
−0.635213 | + | 0.772337i | \(0.719088\pi\) | |||||||
\(998\) | −18.6640 | −0.590798 | ||||||||
\(999\) | 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 | 2738.2.a.x.1.4 | yes | 18 | |
37.36 | even | 2 | 2738.2.a.w.1.4 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2738.2.a.w.1.4 | ✓ | 18 | 37.36 | even | 2 | ||
2738.2.a.x.1.4 | yes | 18 | 1.1 | even | 1 | trivial |