Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4026,2,Mod(1,4026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4026, 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("4026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4026.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: | \(32.1477718538\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} - 22x^{6} + 42x^{5} + 182x^{4} - 111x^{3} - 538x^{2} - 256x - 32 \) |
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 | 1.5 | ||
Root | \(-2.68569\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4026.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.94066 | 0.867888 | 0.433944 | − | 0.900940i | \(-0.357122\pi\) | ||||
0.433944 | + | 0.900940i | \(0.357122\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 4.68569 | 1.77103 | 0.885513 | − | 0.464615i | \(-0.153807\pi\) | ||||
0.885513 | + | 0.464615i | \(0.153807\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.94066 | 0.613689 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 3.54296 | 0.982640 | 0.491320 | − | 0.870979i | \(-0.336515\pi\) | ||||
0.491320 | + | 0.870979i | \(0.336515\pi\) | |||||||
\(14\) | 4.68569 | 1.25230 | ||||||||
\(15\) | 1.94066 | 0.501075 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.52111 | −1.09653 | −0.548265 | − | 0.836305i | \(-0.684711\pi\) | ||||
−0.548265 | + | 0.836305i | \(0.684711\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −6.57912 | −1.50935 | −0.754677 | − | 0.656096i | \(-0.772207\pi\) | ||||
−0.754677 | + | 0.656096i | \(0.772207\pi\) | |||||||
\(20\) | 1.94066 | 0.433944 | ||||||||
\(21\) | 4.68569 | 1.02250 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 2.30849 | 0.481354 | 0.240677 | − | 0.970605i | \(-0.422630\pi\) | ||||
0.240677 | + | 0.970605i | \(0.422630\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −1.23385 | −0.246771 | ||||||||
\(26\) | 3.54296 | 0.694831 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 4.68569 | 0.885513 | ||||||||
\(29\) | 8.87158 | 1.64741 | 0.823706 | − | 0.567018i | \(-0.191903\pi\) | ||||
0.823706 | + | 0.567018i | \(0.191903\pi\) | |||||||
\(30\) | 1.94066 | 0.354314 | ||||||||
\(31\) | −2.24915 | −0.403959 | −0.201980 | − | 0.979390i | \(-0.564737\pi\) | ||||
−0.201980 | + | 0.979390i | \(0.564737\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | −4.52111 | −0.775364 | ||||||||
\(35\) | 9.09332 | 1.53705 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 10.2387 | 1.68324 | 0.841619 | − | 0.540071i | \(-0.181603\pi\) | ||||
0.841619 | + | 0.540071i | \(0.181603\pi\) | |||||||
\(38\) | −6.57912 | −1.06727 | ||||||||
\(39\) | 3.54296 | 0.567327 | ||||||||
\(40\) | 1.94066 | 0.306845 | ||||||||
\(41\) | 3.95278 | 0.617320 | 0.308660 | − | 0.951172i | \(-0.400120\pi\) | ||||
0.308660 | + | 0.951172i | \(0.400120\pi\) | |||||||
\(42\) | 4.68569 | 0.723018 | ||||||||
\(43\) | −12.8057 | −1.95286 | −0.976429 | − | 0.215840i | \(-0.930751\pi\) | ||||
−0.976429 | + | 0.215840i | \(0.930751\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 1.94066 | 0.289296 | ||||||||
\(46\) | 2.30849 | 0.340369 | ||||||||
\(47\) | −9.63852 | −1.40592 | −0.702961 | − | 0.711228i | \(-0.748139\pi\) | ||||
−0.702961 | + | 0.711228i | \(0.748139\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 14.9557 | 2.13653 | ||||||||
\(50\) | −1.23385 | −0.174493 | ||||||||
\(51\) | −4.52111 | −0.633082 | ||||||||
\(52\) | 3.54296 | 0.491320 | ||||||||
\(53\) | 1.32122 | 0.181484 | 0.0907419 | − | 0.995874i | \(-0.471076\pi\) | ||||
0.0907419 | + | 0.995874i | \(0.471076\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −1.94066 | −0.261678 | ||||||||
\(56\) | 4.68569 | 0.626152 | ||||||||
\(57\) | −6.57912 | −0.871426 | ||||||||
\(58\) | 8.87158 | 1.16490 | ||||||||
\(59\) | −2.76033 | −0.359365 | −0.179682 | − | 0.983725i | \(-0.557507\pi\) | ||||
−0.179682 | + | 0.983725i | \(0.557507\pi\) | |||||||
\(60\) | 1.94066 | 0.250538 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | −2.24915 | −0.285642 | ||||||||
\(63\) | 4.68569 | 0.590342 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 6.87566 | 0.852821 | ||||||||
\(66\) | −1.00000 | −0.123091 | ||||||||
\(67\) | −7.05220 | −0.861564 | −0.430782 | − | 0.902456i | \(-0.641762\pi\) | ||||
−0.430782 | + | 0.902456i | \(0.641762\pi\) | |||||||
\(68\) | −4.52111 | −0.548265 | ||||||||
\(69\) | 2.30849 | 0.277910 | ||||||||
\(70\) | 9.09332 | 1.08686 | ||||||||
\(71\) | −4.17995 | −0.496069 | −0.248034 | − | 0.968751i | \(-0.579785\pi\) | ||||
−0.248034 | + | 0.968751i | \(0.579785\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 14.6272 | 1.71198 | 0.855989 | − | 0.516993i | \(-0.172949\pi\) | ||||
0.855989 | + | 0.516993i | \(0.172949\pi\) | |||||||
\(74\) | 10.2387 | 1.19023 | ||||||||
\(75\) | −1.23385 | −0.142473 | ||||||||
\(76\) | −6.57912 | −0.754677 | ||||||||
\(77\) | −4.68569 | −0.533984 | ||||||||
\(78\) | 3.54296 | 0.401161 | ||||||||
\(79\) | 1.12670 | 0.126763 | 0.0633817 | − | 0.997989i | \(-0.479811\pi\) | ||||
0.0633817 | + | 0.997989i | \(0.479811\pi\) | |||||||
\(80\) | 1.94066 | 0.216972 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.95278 | 0.436511 | ||||||||
\(83\) | 2.01082 | 0.220716 | 0.110358 | − | 0.993892i | \(-0.464800\pi\) | ||||
0.110358 | + | 0.993892i | \(0.464800\pi\) | |||||||
\(84\) | 4.68569 | 0.511251 | ||||||||
\(85\) | −8.77391 | −0.951665 | ||||||||
\(86\) | −12.8057 | −1.38088 | ||||||||
\(87\) | 8.87158 | 0.951133 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −16.3921 | −1.73756 | −0.868779 | − | 0.495201i | \(-0.835094\pi\) | ||||
−0.868779 | + | 0.495201i | \(0.835094\pi\) | |||||||
\(90\) | 1.94066 | 0.204563 | ||||||||
\(91\) | 16.6012 | 1.74028 | ||||||||
\(92\) | 2.30849 | 0.240677 | ||||||||
\(93\) | −2.24915 | −0.233226 | ||||||||
\(94\) | −9.63852 | −0.994137 | ||||||||
\(95\) | −12.7678 | −1.30995 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 3.05621 | 0.310311 | 0.155156 | − | 0.987890i | \(-0.450412\pi\) | ||||
0.155156 | + | 0.987890i | \(0.450412\pi\) | |||||||
\(98\) | 14.9557 | 1.51076 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | −1.23385 | −0.123385 | ||||||||
\(101\) | −18.8931 | −1.87993 | −0.939966 | − | 0.341268i | \(-0.889144\pi\) | ||||
−0.939966 | + | 0.341268i | \(0.889144\pi\) | |||||||
\(102\) | −4.52111 | −0.447656 | ||||||||
\(103\) | 2.51786 | 0.248092 | 0.124046 | − | 0.992276i | \(-0.460413\pi\) | ||||
0.124046 | + | 0.992276i | \(0.460413\pi\) | |||||||
\(104\) | 3.54296 | 0.347416 | ||||||||
\(105\) | 9.09332 | 0.887417 | ||||||||
\(106\) | 1.32122 | 0.128328 | ||||||||
\(107\) | 0.804104 | 0.0777356 | 0.0388678 | − | 0.999244i | \(-0.487625\pi\) | ||||
0.0388678 | + | 0.999244i | \(0.487625\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −12.6101 | −1.20783 | −0.603913 | − | 0.797051i | \(-0.706392\pi\) | ||||
−0.603913 | + | 0.797051i | \(0.706392\pi\) | |||||||
\(110\) | −1.94066 | −0.185034 | ||||||||
\(111\) | 10.2387 | 0.971818 | ||||||||
\(112\) | 4.68569 | 0.442756 | ||||||||
\(113\) | −2.76273 | −0.259896 | −0.129948 | − | 0.991521i | \(-0.541481\pi\) | ||||
−0.129948 | + | 0.991521i | \(0.541481\pi\) | |||||||
\(114\) | −6.57912 | −0.616191 | ||||||||
\(115\) | 4.47999 | 0.417762 | ||||||||
\(116\) | 8.87158 | 0.823706 | ||||||||
\(117\) | 3.54296 | 0.327547 | ||||||||
\(118\) | −2.76033 | −0.254109 | ||||||||
\(119\) | −21.1845 | −1.94198 | ||||||||
\(120\) | 1.94066 | 0.177157 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 1.00000 | 0.0905357 | ||||||||
\(123\) | 3.95278 | 0.356410 | ||||||||
\(124\) | −2.24915 | −0.201980 | ||||||||
\(125\) | −12.0978 | −1.08206 | ||||||||
\(126\) | 4.68569 | 0.417435 | ||||||||
\(127\) | −7.83021 | −0.694819 | −0.347409 | − | 0.937714i | \(-0.612939\pi\) | ||||
−0.347409 | + | 0.937714i | \(0.612939\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −12.8057 | −1.12748 | ||||||||
\(130\) | 6.87566 | 0.603035 | ||||||||
\(131\) | 0.294983 | 0.0257728 | 0.0128864 | − | 0.999917i | \(-0.495898\pi\) | ||||
0.0128864 | + | 0.999917i | \(0.495898\pi\) | |||||||
\(132\) | −1.00000 | −0.0870388 | ||||||||
\(133\) | −30.8277 | −2.67310 | ||||||||
\(134\) | −7.05220 | −0.609217 | ||||||||
\(135\) | 1.94066 | 0.167025 | ||||||||
\(136\) | −4.52111 | −0.387682 | ||||||||
\(137\) | −6.63420 | −0.566798 | −0.283399 | − | 0.959002i | \(-0.591462\pi\) | ||||
−0.283399 | + | 0.959002i | \(0.591462\pi\) | |||||||
\(138\) | 2.30849 | 0.196512 | ||||||||
\(139\) | 21.7689 | 1.84642 | 0.923209 | − | 0.384298i | \(-0.125557\pi\) | ||||
0.923209 | + | 0.384298i | \(0.125557\pi\) | |||||||
\(140\) | 9.09332 | 0.768526 | ||||||||
\(141\) | −9.63852 | −0.811710 | ||||||||
\(142\) | −4.17995 | −0.350774 | ||||||||
\(143\) | −3.54296 | −0.296277 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 17.2167 | 1.42977 | ||||||||
\(146\) | 14.6272 | 1.21055 | ||||||||
\(147\) | 14.9557 | 1.23353 | ||||||||
\(148\) | 10.2387 | 0.841619 | ||||||||
\(149\) | −15.9373 | −1.30563 | −0.652816 | − | 0.757516i | \(-0.726413\pi\) | ||||
−0.652816 | + | 0.757516i | \(0.726413\pi\) | |||||||
\(150\) | −1.23385 | −0.100744 | ||||||||
\(151\) | −0.395019 | −0.0321462 | −0.0160731 | − | 0.999871i | \(-0.505116\pi\) | ||||
−0.0160731 | + | 0.999871i | \(0.505116\pi\) | |||||||
\(152\) | −6.57912 | −0.533637 | ||||||||
\(153\) | −4.52111 | −0.365510 | ||||||||
\(154\) | −4.68569 | −0.377584 | ||||||||
\(155\) | −4.36483 | −0.350591 | ||||||||
\(156\) | 3.54296 | 0.283664 | ||||||||
\(157\) | 16.6154 | 1.32605 | 0.663026 | − | 0.748596i | \(-0.269272\pi\) | ||||
0.663026 | + | 0.748596i | \(0.269272\pi\) | |||||||
\(158\) | 1.12670 | 0.0896352 | ||||||||
\(159\) | 1.32122 | 0.104780 | ||||||||
\(160\) | 1.94066 | 0.153422 | ||||||||
\(161\) | 10.8169 | 0.852491 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −11.5483 | −0.904532 | −0.452266 | − | 0.891883i | \(-0.649384\pi\) | ||||
−0.452266 | + | 0.891883i | \(0.649384\pi\) | |||||||
\(164\) | 3.95278 | 0.308660 | ||||||||
\(165\) | −1.94066 | −0.151080 | ||||||||
\(166\) | 2.01082 | 0.156070 | ||||||||
\(167\) | 13.1731 | 1.01937 | 0.509684 | − | 0.860362i | \(-0.329762\pi\) | ||||
0.509684 | + | 0.860362i | \(0.329762\pi\) | |||||||
\(168\) | 4.68569 | 0.361509 | ||||||||
\(169\) | −0.447449 | −0.0344191 | ||||||||
\(170\) | −8.77391 | −0.672929 | ||||||||
\(171\) | −6.57912 | −0.503118 | ||||||||
\(172\) | −12.8057 | −0.976429 | ||||||||
\(173\) | −18.9212 | −1.43855 | −0.719274 | − | 0.694726i | \(-0.755526\pi\) | ||||
−0.719274 | + | 0.694726i | \(0.755526\pi\) | |||||||
\(174\) | 8.87158 | 0.672553 | ||||||||
\(175\) | −5.78146 | −0.437038 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | −2.76033 | −0.207479 | ||||||||
\(178\) | −16.3921 | −1.22864 | ||||||||
\(179\) | 16.4768 | 1.23154 | 0.615768 | − | 0.787928i | \(-0.288846\pi\) | ||||
0.615768 | + | 0.787928i | \(0.288846\pi\) | |||||||
\(180\) | 1.94066 | 0.144648 | ||||||||
\(181\) | 11.2607 | 0.836998 | 0.418499 | − | 0.908217i | \(-0.362556\pi\) | ||||
0.418499 | + | 0.908217i | \(0.362556\pi\) | |||||||
\(182\) | 16.6012 | 1.23056 | ||||||||
\(183\) | 1.00000 | 0.0739221 | ||||||||
\(184\) | 2.30849 | 0.170184 | ||||||||
\(185\) | 19.8699 | 1.46086 | ||||||||
\(186\) | −2.24915 | −0.164916 | ||||||||
\(187\) | 4.52111 | 0.330616 | ||||||||
\(188\) | −9.63852 | −0.702961 | ||||||||
\(189\) | 4.68569 | 0.340834 | ||||||||
\(190\) | −12.7678 | −0.926275 | ||||||||
\(191\) | 18.5307 | 1.34083 | 0.670417 | − | 0.741985i | \(-0.266115\pi\) | ||||
0.670417 | + | 0.741985i | \(0.266115\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 1.37903 | 0.0992650 | 0.0496325 | − | 0.998768i | \(-0.484195\pi\) | ||||
0.0496325 | + | 0.998768i | \(0.484195\pi\) | |||||||
\(194\) | 3.05621 | 0.219423 | ||||||||
\(195\) | 6.87566 | 0.492376 | ||||||||
\(196\) | 14.9557 | 1.06827 | ||||||||
\(197\) | 0.395172 | 0.0281549 | 0.0140774 | − | 0.999901i | \(-0.495519\pi\) | ||||
0.0140774 | + | 0.999901i | \(0.495519\pi\) | |||||||
\(198\) | −1.00000 | −0.0710669 | ||||||||
\(199\) | 4.97157 | 0.352426 | 0.176213 | − | 0.984352i | \(-0.443615\pi\) | ||||
0.176213 | + | 0.984352i | \(0.443615\pi\) | |||||||
\(200\) | −1.23385 | −0.0872467 | ||||||||
\(201\) | −7.05220 | −0.497424 | ||||||||
\(202\) | −18.8931 | −1.32931 | ||||||||
\(203\) | 41.5695 | 2.91761 | ||||||||
\(204\) | −4.52111 | −0.316541 | ||||||||
\(205\) | 7.67098 | 0.535764 | ||||||||
\(206\) | 2.51786 | 0.175428 | ||||||||
\(207\) | 2.30849 | 0.160451 | ||||||||
\(208\) | 3.54296 | 0.245660 | ||||||||
\(209\) | 6.57912 | 0.455087 | ||||||||
\(210\) | 9.09332 | 0.627498 | ||||||||
\(211\) | 7.02591 | 0.483684 | 0.241842 | − | 0.970316i | \(-0.422248\pi\) | ||||
0.241842 | + | 0.970316i | \(0.422248\pi\) | |||||||
\(212\) | 1.32122 | 0.0907419 | ||||||||
\(213\) | −4.17995 | −0.286406 | ||||||||
\(214\) | 0.804104 | 0.0549674 | ||||||||
\(215\) | −24.8515 | −1.69486 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −10.5388 | −0.715422 | ||||||||
\(218\) | −12.6101 | −0.854061 | ||||||||
\(219\) | 14.6272 | 0.988411 | ||||||||
\(220\) | −1.94066 | −0.130839 | ||||||||
\(221\) | −16.0181 | −1.07749 | ||||||||
\(222\) | 10.2387 | 0.687179 | ||||||||
\(223\) | −21.0936 | −1.41253 | −0.706265 | − | 0.707948i | \(-0.749621\pi\) | ||||
−0.706265 | + | 0.707948i | \(0.749621\pi\) | |||||||
\(224\) | 4.68569 | 0.313076 | ||||||||
\(225\) | −1.23385 | −0.0822570 | ||||||||
\(226\) | −2.76273 | −0.183774 | ||||||||
\(227\) | 4.60697 | 0.305776 | 0.152888 | − | 0.988244i | \(-0.451143\pi\) | ||||
0.152888 | + | 0.988244i | \(0.451143\pi\) | |||||||
\(228\) | −6.57912 | −0.435713 | ||||||||
\(229\) | 7.72279 | 0.510337 | 0.255168 | − | 0.966897i | \(-0.417869\pi\) | ||||
0.255168 | + | 0.966897i | \(0.417869\pi\) | |||||||
\(230\) | 4.47999 | 0.295402 | ||||||||
\(231\) | −4.68569 | −0.308296 | ||||||||
\(232\) | 8.87158 | 0.582448 | ||||||||
\(233\) | 17.7056 | 1.15993 | 0.579965 | − | 0.814641i | \(-0.303066\pi\) | ||||
0.579965 | + | 0.814641i | \(0.303066\pi\) | |||||||
\(234\) | 3.54296 | 0.231610 | ||||||||
\(235\) | −18.7051 | −1.22018 | ||||||||
\(236\) | −2.76033 | −0.179682 | ||||||||
\(237\) | 1.12670 | 0.0731869 | ||||||||
\(238\) | −21.1845 | −1.37319 | ||||||||
\(239\) | −19.8454 | −1.28369 | −0.641845 | − | 0.766834i | \(-0.721831\pi\) | ||||
−0.641845 | + | 0.766834i | \(0.721831\pi\) | |||||||
\(240\) | 1.94066 | 0.125269 | ||||||||
\(241\) | 24.1295 | 1.55431 | 0.777157 | − | 0.629306i | \(-0.216661\pi\) | ||||
0.777157 | + | 0.629306i | \(0.216661\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 1.00000 | 0.0640184 | ||||||||
\(245\) | 29.0239 | 1.85427 | ||||||||
\(246\) | 3.95278 | 0.252020 | ||||||||
\(247\) | −23.3096 | −1.48315 | ||||||||
\(248\) | −2.24915 | −0.142821 | ||||||||
\(249\) | 2.01082 | 0.127431 | ||||||||
\(250\) | −12.0978 | −0.765130 | ||||||||
\(251\) | 7.32052 | 0.462067 | 0.231034 | − | 0.972946i | \(-0.425789\pi\) | ||||
0.231034 | + | 0.972946i | \(0.425789\pi\) | |||||||
\(252\) | 4.68569 | 0.295171 | ||||||||
\(253\) | −2.30849 | −0.145134 | ||||||||
\(254\) | −7.83021 | −0.491311 | ||||||||
\(255\) | −8.77391 | −0.549444 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −20.8803 | −1.30248 | −0.651238 | − | 0.758873i | \(-0.725750\pi\) | ||||
−0.651238 | + | 0.758873i | \(0.725750\pi\) | |||||||
\(258\) | −12.8057 | −0.797251 | ||||||||
\(259\) | 47.9756 | 2.98106 | ||||||||
\(260\) | 6.87566 | 0.426410 | ||||||||
\(261\) | 8.87158 | 0.549137 | ||||||||
\(262\) | 0.294983 | 0.0182241 | ||||||||
\(263\) | −6.51652 | −0.401826 | −0.200913 | − | 0.979609i | \(-0.564391\pi\) | ||||
−0.200913 | + | 0.979609i | \(0.564391\pi\) | |||||||
\(264\) | −1.00000 | −0.0615457 | ||||||||
\(265\) | 2.56404 | 0.157508 | ||||||||
\(266\) | −30.8277 | −1.89017 | ||||||||
\(267\) | −16.3921 | −1.00318 | ||||||||
\(268\) | −7.05220 | −0.430782 | ||||||||
\(269\) | 17.3097 | 1.05539 | 0.527695 | − | 0.849434i | \(-0.323056\pi\) | ||||
0.527695 | + | 0.849434i | \(0.323056\pi\) | |||||||
\(270\) | 1.94066 | 0.118105 | ||||||||
\(271\) | 3.52912 | 0.214379 | 0.107189 | − | 0.994239i | \(-0.465815\pi\) | ||||
0.107189 | + | 0.994239i | \(0.465815\pi\) | |||||||
\(272\) | −4.52111 | −0.274132 | ||||||||
\(273\) | 16.6012 | 1.00475 | ||||||||
\(274\) | −6.63420 | −0.400787 | ||||||||
\(275\) | 1.23385 | 0.0744042 | ||||||||
\(276\) | 2.30849 | 0.138955 | ||||||||
\(277\) | 10.9000 | 0.654920 | 0.327460 | − | 0.944865i | \(-0.393807\pi\) | ||||
0.327460 | + | 0.944865i | \(0.393807\pi\) | |||||||
\(278\) | 21.7689 | 1.30561 | ||||||||
\(279\) | −2.24915 | −0.134653 | ||||||||
\(280\) | 9.09332 | 0.543430 | ||||||||
\(281\) | 10.8840 | 0.649282 | 0.324641 | − | 0.945837i | \(-0.394757\pi\) | ||||
0.324641 | + | 0.945837i | \(0.394757\pi\) | |||||||
\(282\) | −9.63852 | −0.573966 | ||||||||
\(283\) | −12.7121 | −0.755658 | −0.377829 | − | 0.925875i | \(-0.623329\pi\) | ||||
−0.377829 | + | 0.925875i | \(0.623329\pi\) | |||||||
\(284\) | −4.17995 | −0.248034 | ||||||||
\(285\) | −12.7678 | −0.756300 | ||||||||
\(286\) | −3.54296 | −0.209499 | ||||||||
\(287\) | 18.5215 | 1.09329 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 3.44042 | 0.202377 | ||||||||
\(290\) | 17.2167 | 1.01100 | ||||||||
\(291\) | 3.05621 | 0.179158 | ||||||||
\(292\) | 14.6272 | 0.855989 | ||||||||
\(293\) | 11.2244 | 0.655737 | 0.327869 | − | 0.944723i | \(-0.393670\pi\) | ||||
0.327869 | + | 0.944723i | \(0.393670\pi\) | |||||||
\(294\) | 14.9557 | 0.872235 | ||||||||
\(295\) | −5.35686 | −0.311888 | ||||||||
\(296\) | 10.2387 | 0.595115 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | −15.9373 | −0.923221 | ||||||||
\(299\) | 8.17890 | 0.472998 | ||||||||
\(300\) | −1.23385 | −0.0712366 | ||||||||
\(301\) | −60.0038 | −3.45856 | ||||||||
\(302\) | −0.395019 | −0.0227308 | ||||||||
\(303\) | −18.8931 | −1.08538 | ||||||||
\(304\) | −6.57912 | −0.377339 | ||||||||
\(305\) | 1.94066 | 0.111122 | ||||||||
\(306\) | −4.52111 | −0.258455 | ||||||||
\(307\) | 1.14250 | 0.0652058 | 0.0326029 | − | 0.999468i | \(-0.489620\pi\) | ||||
0.0326029 | + | 0.999468i | \(0.489620\pi\) | |||||||
\(308\) | −4.68569 | −0.266992 | ||||||||
\(309\) | 2.51786 | 0.143236 | ||||||||
\(310\) | −4.36483 | −0.247906 | ||||||||
\(311\) | −27.3801 | −1.55258 | −0.776292 | − | 0.630373i | \(-0.782902\pi\) | ||||
−0.776292 | + | 0.630373i | \(0.782902\pi\) | |||||||
\(312\) | 3.54296 | 0.200580 | ||||||||
\(313\) | 3.89382 | 0.220092 | 0.110046 | − | 0.993927i | \(-0.464900\pi\) | ||||
0.110046 | + | 0.993927i | \(0.464900\pi\) | |||||||
\(314\) | 16.6154 | 0.937660 | ||||||||
\(315\) | 9.09332 | 0.512350 | ||||||||
\(316\) | 1.12670 | 0.0633817 | ||||||||
\(317\) | −19.0542 | −1.07019 | −0.535094 | − | 0.844793i | \(-0.679724\pi\) | ||||
−0.535094 | + | 0.844793i | \(0.679724\pi\) | |||||||
\(318\) | 1.32122 | 0.0740905 | ||||||||
\(319\) | −8.87158 | −0.496713 | ||||||||
\(320\) | 1.94066 | 0.108486 | ||||||||
\(321\) | 0.804104 | 0.0448807 | ||||||||
\(322\) | 10.8169 | 0.602802 | ||||||||
\(323\) | 29.7449 | 1.65505 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −4.37150 | −0.242487 | ||||||||
\(326\) | −11.5483 | −0.639601 | ||||||||
\(327\) | −12.6101 | −0.697338 | ||||||||
\(328\) | 3.95278 | 0.218255 | ||||||||
\(329\) | −45.1631 | −2.48992 | ||||||||
\(330\) | −1.94066 | −0.106830 | ||||||||
\(331\) | −16.5174 | −0.907878 | −0.453939 | − | 0.891033i | \(-0.649982\pi\) | ||||
−0.453939 | + | 0.891033i | \(0.649982\pi\) | |||||||
\(332\) | 2.01082 | 0.110358 | ||||||||
\(333\) | 10.2387 | 0.561079 | ||||||||
\(334\) | 13.1731 | 0.720802 | ||||||||
\(335\) | −13.6859 | −0.747740 | ||||||||
\(336\) | 4.68569 | 0.255625 | ||||||||
\(337\) | −23.4235 | −1.27596 | −0.637981 | − | 0.770052i | \(-0.720230\pi\) | ||||
−0.637981 | + | 0.770052i | \(0.720230\pi\) | |||||||
\(338\) | −0.447449 | −0.0243380 | ||||||||
\(339\) | −2.76273 | −0.150051 | ||||||||
\(340\) | −8.77391 | −0.475832 | ||||||||
\(341\) | 2.24915 | 0.121798 | ||||||||
\(342\) | −6.57912 | −0.355758 | ||||||||
\(343\) | 37.2780 | 2.01282 | ||||||||
\(344\) | −12.8057 | −0.690439 | ||||||||
\(345\) | 4.47999 | 0.241195 | ||||||||
\(346\) | −18.9212 | −1.01721 | ||||||||
\(347\) | −17.5562 | −0.942466 | −0.471233 | − | 0.882009i | \(-0.656191\pi\) | ||||
−0.471233 | + | 0.882009i | \(0.656191\pi\) | |||||||
\(348\) | 8.87158 | 0.475567 | ||||||||
\(349\) | 22.5290 | 1.20595 | 0.602976 | − | 0.797759i | \(-0.293982\pi\) | ||||
0.602976 | + | 0.797759i | \(0.293982\pi\) | |||||||
\(350\) | −5.78146 | −0.309032 | ||||||||
\(351\) | 3.54296 | 0.189109 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | 8.20436 | 0.436674 | 0.218337 | − | 0.975873i | \(-0.429937\pi\) | ||||
0.218337 | + | 0.975873i | \(0.429937\pi\) | |||||||
\(354\) | −2.76033 | −0.146710 | ||||||||
\(355\) | −8.11185 | −0.430532 | ||||||||
\(356\) | −16.3921 | −0.868779 | ||||||||
\(357\) | −21.1845 | −1.12120 | ||||||||
\(358\) | 16.4768 | 0.870827 | ||||||||
\(359\) | −11.9885 | −0.632729 | −0.316365 | − | 0.948638i | \(-0.602462\pi\) | ||||
−0.316365 | + | 0.948638i | \(0.602462\pi\) | |||||||
\(360\) | 1.94066 | 0.102282 | ||||||||
\(361\) | 24.2849 | 1.27815 | ||||||||
\(362\) | 11.2607 | 0.591847 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 16.6012 | 0.870140 | ||||||||
\(365\) | 28.3863 | 1.48581 | ||||||||
\(366\) | 1.00000 | 0.0522708 | ||||||||
\(367\) | 15.0644 | 0.786355 | 0.393178 | − | 0.919463i | \(-0.371376\pi\) | ||||
0.393178 | + | 0.919463i | \(0.371376\pi\) | |||||||
\(368\) | 2.30849 | 0.120339 | ||||||||
\(369\) | 3.95278 | 0.205773 | ||||||||
\(370\) | 19.8699 | 1.03299 | ||||||||
\(371\) | 6.19084 | 0.321413 | ||||||||
\(372\) | −2.24915 | −0.116613 | ||||||||
\(373\) | 17.8052 | 0.921917 | 0.460958 | − | 0.887422i | \(-0.347506\pi\) | ||||
0.460958 | + | 0.887422i | \(0.347506\pi\) | |||||||
\(374\) | 4.52111 | 0.233781 | ||||||||
\(375\) | −12.0978 | −0.624726 | ||||||||
\(376\) | −9.63852 | −0.497069 | ||||||||
\(377\) | 31.4316 | 1.61881 | ||||||||
\(378\) | 4.68569 | 0.241006 | ||||||||
\(379\) | 0.435287 | 0.0223592 | 0.0111796 | − | 0.999938i | \(-0.496441\pi\) | ||||
0.0111796 | + | 0.999938i | \(0.496441\pi\) | |||||||
\(380\) | −12.7678 | −0.654975 | ||||||||
\(381\) | −7.83021 | −0.401154 | ||||||||
\(382\) | 18.5307 | 0.948112 | ||||||||
\(383\) | −11.9463 | −0.610428 | −0.305214 | − | 0.952284i | \(-0.598728\pi\) | ||||
−0.305214 | + | 0.952284i | \(0.598728\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −9.09332 | −0.463438 | ||||||||
\(386\) | 1.37903 | 0.0701909 | ||||||||
\(387\) | −12.8057 | −0.650953 | ||||||||
\(388\) | 3.05621 | 0.155156 | ||||||||
\(389\) | 23.6560 | 1.19940 | 0.599702 | − | 0.800223i | \(-0.295286\pi\) | ||||
0.599702 | + | 0.800223i | \(0.295286\pi\) | |||||||
\(390\) | 6.87566 | 0.348163 | ||||||||
\(391\) | −10.4370 | −0.527819 | ||||||||
\(392\) | 14.9557 | 0.755378 | ||||||||
\(393\) | 0.294983 | 0.0148799 | ||||||||
\(394\) | 0.395172 | 0.0199085 | ||||||||
\(395\) | 2.18653 | 0.110016 | ||||||||
\(396\) | −1.00000 | −0.0502519 | ||||||||
\(397\) | 9.23778 | 0.463631 | 0.231815 | − | 0.972760i | \(-0.425533\pi\) | ||||
0.231815 | + | 0.972760i | \(0.425533\pi\) | |||||||
\(398\) | 4.97157 | 0.249203 | ||||||||
\(399\) | −30.8277 | −1.54332 | ||||||||
\(400\) | −1.23385 | −0.0616927 | ||||||||
\(401\) | −18.6248 | −0.930077 | −0.465039 | − | 0.885290i | \(-0.653960\pi\) | ||||
−0.465039 | + | 0.885290i | \(0.653960\pi\) | |||||||
\(402\) | −7.05220 | −0.351732 | ||||||||
\(403\) | −7.96865 | −0.396947 | ||||||||
\(404\) | −18.8931 | −0.939966 | ||||||||
\(405\) | 1.94066 | 0.0964320 | ||||||||
\(406\) | 41.5695 | 2.06306 | ||||||||
\(407\) | −10.2387 | −0.507516 | ||||||||
\(408\) | −4.52111 | −0.223828 | ||||||||
\(409\) | 22.9387 | 1.13425 | 0.567124 | − | 0.823633i | \(-0.308056\pi\) | ||||
0.567124 | + | 0.823633i | \(0.308056\pi\) | |||||||
\(410\) | 7.67098 | 0.378843 | ||||||||
\(411\) | −6.63420 | −0.327241 | ||||||||
\(412\) | 2.51786 | 0.124046 | ||||||||
\(413\) | −12.9341 | −0.636444 | ||||||||
\(414\) | 2.30849 | 0.113456 | ||||||||
\(415\) | 3.90231 | 0.191557 | ||||||||
\(416\) | 3.54296 | 0.173708 | ||||||||
\(417\) | 21.7689 | 1.06603 | ||||||||
\(418\) | 6.57912 | 0.321795 | ||||||||
\(419\) | −19.8711 | −0.970767 | −0.485384 | − | 0.874301i | \(-0.661320\pi\) | ||||
−0.485384 | + | 0.874301i | \(0.661320\pi\) | |||||||
\(420\) | 9.09332 | 0.443708 | ||||||||
\(421\) | −32.9028 | −1.60358 | −0.801792 | − | 0.597603i | \(-0.796120\pi\) | ||||
−0.801792 | + | 0.597603i | \(0.796120\pi\) | |||||||
\(422\) | 7.02591 | 0.342016 | ||||||||
\(423\) | −9.63852 | −0.468641 | ||||||||
\(424\) | 1.32122 | 0.0641642 | ||||||||
\(425\) | 5.57839 | 0.270592 | ||||||||
\(426\) | −4.17995 | −0.202519 | ||||||||
\(427\) | 4.68569 | 0.226757 | ||||||||
\(428\) | 0.804104 | 0.0388678 | ||||||||
\(429\) | −3.54296 | −0.171056 | ||||||||
\(430\) | −24.8515 | −1.19845 | ||||||||
\(431\) | −28.0055 | −1.34898 | −0.674490 | − | 0.738284i | \(-0.735636\pi\) | ||||
−0.674490 | + | 0.738284i | \(0.735636\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 19.7345 | 0.948382 | 0.474191 | − | 0.880422i | \(-0.342741\pi\) | ||||
0.474191 | + | 0.880422i | \(0.342741\pi\) | |||||||
\(434\) | −10.5388 | −0.505880 | ||||||||
\(435\) | 17.2167 | 0.825477 | ||||||||
\(436\) | −12.6101 | −0.603913 | ||||||||
\(437\) | −15.1879 | −0.726534 | ||||||||
\(438\) | 14.6272 | 0.698912 | ||||||||
\(439\) | 34.1613 | 1.63043 | 0.815215 | − | 0.579159i | \(-0.196619\pi\) | ||||
0.815215 | + | 0.579159i | \(0.196619\pi\) | |||||||
\(440\) | −1.94066 | −0.0925171 | ||||||||
\(441\) | 14.9557 | 0.712177 | ||||||||
\(442\) | −16.0181 | −0.761903 | ||||||||
\(443\) | 2.73228 | 0.129814 | 0.0649072 | − | 0.997891i | \(-0.479325\pi\) | ||||
0.0649072 | + | 0.997891i | \(0.479325\pi\) | |||||||
\(444\) | 10.2387 | 0.485909 | ||||||||
\(445\) | −31.8114 | −1.50800 | ||||||||
\(446\) | −21.0936 | −0.998809 | ||||||||
\(447\) | −15.9373 | −0.753807 | ||||||||
\(448\) | 4.68569 | 0.221378 | ||||||||
\(449\) | −4.69807 | −0.221716 | −0.110858 | − | 0.993836i | \(-0.535360\pi\) | ||||
−0.110858 | + | 0.993836i | \(0.535360\pi\) | |||||||
\(450\) | −1.23385 | −0.0581645 | ||||||||
\(451\) | −3.95278 | −0.186129 | ||||||||
\(452\) | −2.76273 | −0.129948 | ||||||||
\(453\) | −0.395019 | −0.0185596 | ||||||||
\(454\) | 4.60697 | 0.216216 | ||||||||
\(455\) | 32.2172 | 1.51037 | ||||||||
\(456\) | −6.57912 | −0.308096 | ||||||||
\(457\) | −15.4353 | −0.722032 | −0.361016 | − | 0.932560i | \(-0.617570\pi\) | ||||
−0.361016 | + | 0.932560i | \(0.617570\pi\) | |||||||
\(458\) | 7.72279 | 0.360862 | ||||||||
\(459\) | −4.52111 | −0.211027 | ||||||||
\(460\) | 4.47999 | 0.208881 | ||||||||
\(461\) | 32.2504 | 1.50205 | 0.751025 | − | 0.660274i | \(-0.229560\pi\) | ||||
0.751025 | + | 0.660274i | \(0.229560\pi\) | |||||||
\(462\) | −4.68569 | −0.217998 | ||||||||
\(463\) | 15.1119 | 0.702311 | 0.351155 | − | 0.936317i | \(-0.385789\pi\) | ||||
0.351155 | + | 0.936317i | \(0.385789\pi\) | |||||||
\(464\) | 8.87158 | 0.411853 | ||||||||
\(465\) | −4.36483 | −0.202414 | ||||||||
\(466\) | 17.7056 | 0.820194 | ||||||||
\(467\) | 22.3900 | 1.03608 | 0.518042 | − | 0.855355i | \(-0.326661\pi\) | ||||
0.518042 | + | 0.855355i | \(0.326661\pi\) | |||||||
\(468\) | 3.54296 | 0.163773 | ||||||||
\(469\) | −33.0445 | −1.52585 | ||||||||
\(470\) | −18.7051 | −0.862800 | ||||||||
\(471\) | 16.6154 | 0.765596 | ||||||||
\(472\) | −2.76033 | −0.127055 | ||||||||
\(473\) | 12.8057 | 0.588809 | ||||||||
\(474\) | 1.12670 | 0.0517509 | ||||||||
\(475\) | 8.11768 | 0.372465 | ||||||||
\(476\) | −21.1845 | −0.970991 | ||||||||
\(477\) | 1.32122 | 0.0604946 | ||||||||
\(478\) | −19.8454 | −0.907706 | ||||||||
\(479\) | −17.9121 | −0.818427 | −0.409213 | − | 0.912439i | \(-0.634197\pi\) | ||||
−0.409213 | + | 0.912439i | \(0.634197\pi\) | |||||||
\(480\) | 1.94066 | 0.0885784 | ||||||||
\(481\) | 36.2754 | 1.65402 | ||||||||
\(482\) | 24.1295 | 1.09907 | ||||||||
\(483\) | 10.8169 | 0.492186 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 5.93105 | 0.269315 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 22.6522 | 1.02647 | 0.513235 | − | 0.858248i | \(-0.328447\pi\) | ||||
0.513235 | + | 0.858248i | \(0.328447\pi\) | |||||||
\(488\) | 1.00000 | 0.0452679 | ||||||||
\(489\) | −11.5483 | −0.522232 | ||||||||
\(490\) | 29.0239 | 1.31117 | ||||||||
\(491\) | −25.4936 | −1.15051 | −0.575254 | − | 0.817975i | \(-0.695097\pi\) | ||||
−0.575254 | + | 0.817975i | \(0.695097\pi\) | |||||||
\(492\) | 3.95278 | 0.178205 | ||||||||
\(493\) | −40.1094 | −1.80644 | ||||||||
\(494\) | −23.3096 | −1.04875 | ||||||||
\(495\) | −1.94066 | −0.0872260 | ||||||||
\(496\) | −2.24915 | −0.100990 | ||||||||
\(497\) | −19.5860 | −0.878551 | ||||||||
\(498\) | 2.01082 | 0.0901071 | ||||||||
\(499\) | −2.80077 | −0.125380 | −0.0626899 | − | 0.998033i | \(-0.519968\pi\) | ||||
−0.0626899 | + | 0.998033i | \(0.519968\pi\) | |||||||
\(500\) | −12.0978 | −0.541029 | ||||||||
\(501\) | 13.1731 | 0.588532 | ||||||||
\(502\) | 7.32052 | 0.326731 | ||||||||
\(503\) | 31.8978 | 1.42225 | 0.711127 | − | 0.703064i | \(-0.248185\pi\) | ||||
0.711127 | + | 0.703064i | \(0.248185\pi\) | |||||||
\(504\) | 4.68569 | 0.208717 | ||||||||
\(505\) | −36.6650 | −1.63157 | ||||||||
\(506\) | −2.30849 | −0.102625 | ||||||||
\(507\) | −0.447449 | −0.0198719 | ||||||||
\(508\) | −7.83021 | −0.347409 | ||||||||
\(509\) | −41.3679 | −1.83360 | −0.916799 | − | 0.399349i | \(-0.869236\pi\) | ||||
−0.916799 | + | 0.399349i | \(0.869236\pi\) | |||||||
\(510\) | −8.77391 | −0.388515 | ||||||||
\(511\) | 68.5383 | 3.03196 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −6.57912 | −0.290475 | ||||||||
\(514\) | −20.8803 | −0.920990 | ||||||||
\(515\) | 4.88630 | 0.215316 | ||||||||
\(516\) | −12.8057 | −0.563741 | ||||||||
\(517\) | 9.63852 | 0.423902 | ||||||||
\(518\) | 47.9756 | 2.10793 | ||||||||
\(519\) | −18.9212 | −0.830547 | ||||||||
\(520\) | 6.87566 | 0.301518 | ||||||||
\(521\) | −3.79183 | −0.166123 | −0.0830615 | − | 0.996544i | \(-0.526470\pi\) | ||||
−0.0830615 | + | 0.996544i | \(0.526470\pi\) | |||||||
\(522\) | 8.87158 | 0.388299 | ||||||||
\(523\) | −6.15004 | −0.268922 | −0.134461 | − | 0.990919i | \(-0.542930\pi\) | ||||
−0.134461 | + | 0.990919i | \(0.542930\pi\) | |||||||
\(524\) | 0.294983 | 0.0128864 | ||||||||
\(525\) | −5.78146 | −0.252324 | ||||||||
\(526\) | −6.51652 | −0.284134 | ||||||||
\(527\) | 10.1687 | 0.442953 | ||||||||
\(528\) | −1.00000 | −0.0435194 | ||||||||
\(529\) | −17.6709 | −0.768298 | ||||||||
\(530\) | 2.56404 | 0.111375 | ||||||||
\(531\) | −2.76033 | −0.119788 | ||||||||
\(532\) | −30.8277 | −1.33655 | ||||||||
\(533\) | 14.0045 | 0.606603 | ||||||||
\(534\) | −16.3921 | −0.709355 | ||||||||
\(535\) | 1.56049 | 0.0674658 | ||||||||
\(536\) | −7.05220 | −0.304609 | ||||||||
\(537\) | 16.4768 | 0.711027 | ||||||||
\(538\) | 17.3097 | 0.746274 | ||||||||
\(539\) | −14.9557 | −0.644188 | ||||||||
\(540\) | 1.94066 | 0.0835125 | ||||||||
\(541\) | −36.5498 | −1.57140 | −0.785700 | − | 0.618608i | \(-0.787697\pi\) | ||||
−0.785700 | + | 0.618608i | \(0.787697\pi\) | |||||||
\(542\) | 3.52912 | 0.151589 | ||||||||
\(543\) | 11.2607 | 0.483241 | ||||||||
\(544\) | −4.52111 | −0.193841 | ||||||||
\(545\) | −24.4718 | −1.04826 | ||||||||
\(546\) | 16.6012 | 0.710466 | ||||||||
\(547\) | 13.9550 | 0.596671 | 0.298335 | − | 0.954461i | \(-0.403569\pi\) | ||||
0.298335 | + | 0.954461i | \(0.403569\pi\) | |||||||
\(548\) | −6.63420 | −0.283399 | ||||||||
\(549\) | 1.00000 | 0.0426790 | ||||||||
\(550\) | 1.23385 | 0.0526117 | ||||||||
\(551\) | −58.3672 | −2.48653 | ||||||||
\(552\) | 2.30849 | 0.0982561 | ||||||||
\(553\) | 5.27936 | 0.224501 | ||||||||
\(554\) | 10.9000 | 0.463099 | ||||||||
\(555\) | 19.8699 | 0.843429 | ||||||||
\(556\) | 21.7689 | 0.923209 | ||||||||
\(557\) | 15.2605 | 0.646608 | 0.323304 | − | 0.946295i | \(-0.395206\pi\) | ||||
0.323304 | + | 0.946295i | \(0.395206\pi\) | |||||||
\(558\) | −2.24915 | −0.0952141 | ||||||||
\(559\) | −45.3702 | −1.91896 | ||||||||
\(560\) | 9.09332 | 0.384263 | ||||||||
\(561\) | 4.52111 | 0.190881 | ||||||||
\(562\) | 10.8840 | 0.459112 | ||||||||
\(563\) | 13.0591 | 0.550375 | 0.275188 | − | 0.961391i | \(-0.411260\pi\) | ||||
0.275188 | + | 0.961391i | \(0.411260\pi\) | |||||||
\(564\) | −9.63852 | −0.405855 | ||||||||
\(565\) | −5.36152 | −0.225561 | ||||||||
\(566\) | −12.7121 | −0.534331 | ||||||||
\(567\) | 4.68569 | 0.196781 | ||||||||
\(568\) | −4.17995 | −0.175387 | ||||||||
\(569\) | −0.493809 | −0.0207015 | −0.0103508 | − | 0.999946i | \(-0.503295\pi\) | ||||
−0.0103508 | + | 0.999946i | \(0.503295\pi\) | |||||||
\(570\) | −12.7678 | −0.534785 | ||||||||
\(571\) | −43.3189 | −1.81284 | −0.906420 | − | 0.422377i | \(-0.861196\pi\) | ||||
−0.906420 | + | 0.422377i | \(0.861196\pi\) | |||||||
\(572\) | −3.54296 | −0.148139 | ||||||||
\(573\) | 18.5307 | 0.774130 | ||||||||
\(574\) | 18.5215 | 0.773072 | ||||||||
\(575\) | −2.84835 | −0.118784 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −26.5623 | −1.10580 | −0.552902 | − | 0.833246i | \(-0.686480\pi\) | ||||
−0.552902 | + | 0.833246i | \(0.686480\pi\) | |||||||
\(578\) | 3.44042 | 0.143102 | ||||||||
\(579\) | 1.37903 | 0.0573107 | ||||||||
\(580\) | 17.2167 | 0.714884 | ||||||||
\(581\) | 9.42210 | 0.390894 | ||||||||
\(582\) | 3.05621 | 0.126684 | ||||||||
\(583\) | −1.32122 | −0.0547194 | ||||||||
\(584\) | 14.6272 | 0.605276 | ||||||||
\(585\) | 6.87566 | 0.284274 | ||||||||
\(586\) | 11.2244 | 0.463676 | ||||||||
\(587\) | −14.0625 | −0.580422 | −0.290211 | − | 0.956963i | \(-0.593726\pi\) | ||||
−0.290211 | + | 0.956963i | \(0.593726\pi\) | |||||||
\(588\) | 14.9557 | 0.616763 | ||||||||
\(589\) | 14.7974 | 0.609718 | ||||||||
\(590\) | −5.35686 | −0.220538 | ||||||||
\(591\) | 0.395172 | 0.0162552 | ||||||||
\(592\) | 10.2387 | 0.420810 | ||||||||
\(593\) | 9.91252 | 0.407058 | 0.203529 | − | 0.979069i | \(-0.434759\pi\) | ||||
0.203529 | + | 0.979069i | \(0.434759\pi\) | |||||||
\(594\) | −1.00000 | −0.0410305 | ||||||||
\(595\) | −41.1119 | −1.68542 | ||||||||
\(596\) | −15.9373 | −0.652816 | ||||||||
\(597\) | 4.97157 | 0.203473 | ||||||||
\(598\) | 8.17890 | 0.334460 | ||||||||
\(599\) | −25.7820 | −1.05342 | −0.526712 | − | 0.850044i | \(-0.676576\pi\) | ||||
−0.526712 | + | 0.850044i | \(0.676576\pi\) | |||||||
\(600\) | −1.23385 | −0.0503719 | ||||||||
\(601\) | −21.7545 | −0.887384 | −0.443692 | − | 0.896179i | \(-0.646332\pi\) | ||||
−0.443692 | + | 0.896179i | \(0.646332\pi\) | |||||||
\(602\) | −60.0038 | −2.44557 | ||||||||
\(603\) | −7.05220 | −0.287188 | ||||||||
\(604\) | −0.395019 | −0.0160731 | ||||||||
\(605\) | 1.94066 | 0.0788989 | ||||||||
\(606\) | −18.8931 | −0.767479 | ||||||||
\(607\) | −35.2839 | −1.43213 | −0.716065 | − | 0.698034i | \(-0.754058\pi\) | ||||
−0.716065 | + | 0.698034i | \(0.754058\pi\) | |||||||
\(608\) | −6.57912 | −0.266819 | ||||||||
\(609\) | 41.5695 | 1.68448 | ||||||||
\(610\) | 1.94066 | 0.0785749 | ||||||||
\(611\) | −34.1489 | −1.38152 | ||||||||
\(612\) | −4.52111 | −0.182755 | ||||||||
\(613\) | −11.1593 | −0.450718 | −0.225359 | − | 0.974276i | \(-0.572356\pi\) | ||||
−0.225359 | + | 0.974276i | \(0.572356\pi\) | |||||||
\(614\) | 1.14250 | 0.0461075 | ||||||||
\(615\) | 7.67098 | 0.309324 | ||||||||
\(616\) | −4.68569 | −0.188792 | ||||||||
\(617\) | 27.2684 | 1.09779 | 0.548893 | − | 0.835893i | \(-0.315050\pi\) | ||||
0.548893 | + | 0.835893i | \(0.315050\pi\) | |||||||
\(618\) | 2.51786 | 0.101283 | ||||||||
\(619\) | 18.3387 | 0.737095 | 0.368548 | − | 0.929609i | \(-0.379855\pi\) | ||||
0.368548 | + | 0.929609i | \(0.379855\pi\) | |||||||
\(620\) | −4.36483 | −0.175296 | ||||||||
\(621\) | 2.30849 | 0.0926367 | ||||||||
\(622\) | −27.3801 | −1.09784 | ||||||||
\(623\) | −76.8082 | −3.07726 | ||||||||
\(624\) | 3.54296 | 0.141832 | ||||||||
\(625\) | −17.3083 | −0.692333 | ||||||||
\(626\) | 3.89382 | 0.155628 | ||||||||
\(627\) | 6.57912 | 0.262745 | ||||||||
\(628\) | 16.6154 | 0.663026 | ||||||||
\(629\) | −46.2904 | −1.84572 | ||||||||
\(630\) | 9.09332 | 0.362286 | ||||||||
\(631\) | 46.4935 | 1.85088 | 0.925439 | − | 0.378897i | \(-0.123696\pi\) | ||||
0.925439 | + | 0.378897i | \(0.123696\pi\) | |||||||
\(632\) | 1.12670 | 0.0448176 | ||||||||
\(633\) | 7.02591 | 0.279255 | ||||||||
\(634\) | −19.0542 | −0.756737 | ||||||||
\(635\) | −15.1957 | −0.603025 | ||||||||
\(636\) | 1.32122 | 0.0523899 | ||||||||
\(637\) | 52.9875 | 2.09944 | ||||||||
\(638\) | −8.87158 | −0.351229 | ||||||||
\(639\) | −4.17995 | −0.165356 | ||||||||
\(640\) | 1.94066 | 0.0767112 | ||||||||
\(641\) | −34.5917 | −1.36629 | −0.683145 | − | 0.730283i | \(-0.739388\pi\) | ||||
−0.683145 | + | 0.730283i | \(0.739388\pi\) | |||||||
\(642\) | 0.804104 | 0.0317354 | ||||||||
\(643\) | 16.0110 | 0.631411 | 0.315706 | − | 0.948857i | \(-0.397759\pi\) | ||||
0.315706 | + | 0.948857i | \(0.397759\pi\) | |||||||
\(644\) | 10.8169 | 0.426245 | ||||||||
\(645\) | −24.8515 | −0.978529 | ||||||||
\(646\) | 29.7449 | 1.17030 | ||||||||
\(647\) | 27.6401 | 1.08664 | 0.543322 | − | 0.839524i | \(-0.317166\pi\) | ||||
0.543322 | + | 0.839524i | \(0.317166\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 2.76033 | 0.108353 | ||||||||
\(650\) | −4.37150 | −0.171464 | ||||||||
\(651\) | −10.5388 | −0.413049 | ||||||||
\(652\) | −11.5483 | −0.452266 | ||||||||
\(653\) | 13.4487 | 0.526288 | 0.263144 | − | 0.964757i | \(-0.415241\pi\) | ||||
0.263144 | + | 0.964757i | \(0.415241\pi\) | |||||||
\(654\) | −12.6101 | −0.493092 | ||||||||
\(655\) | 0.572461 | 0.0223679 | ||||||||
\(656\) | 3.95278 | 0.154330 | ||||||||
\(657\) | 14.6272 | 0.570660 | ||||||||
\(658\) | −45.1631 | −1.76064 | ||||||||
\(659\) | 25.0126 | 0.974351 | 0.487176 | − | 0.873304i | \(-0.338027\pi\) | ||||
0.487176 | + | 0.873304i | \(0.338027\pi\) | |||||||
\(660\) | −1.94066 | −0.0755399 | ||||||||
\(661\) | −5.04968 | −0.196410 | −0.0982048 | − | 0.995166i | \(-0.531310\pi\) | ||||
−0.0982048 | + | 0.995166i | \(0.531310\pi\) | |||||||
\(662\) | −16.5174 | −0.641966 | ||||||||
\(663\) | −16.0181 | −0.622091 | ||||||||
\(664\) | 2.01082 | 0.0780350 | ||||||||
\(665\) | −59.8261 | −2.31995 | ||||||||
\(666\) | 10.2387 | 0.396743 | ||||||||
\(667\) | 20.4800 | 0.792989 | ||||||||
\(668\) | 13.1731 | 0.509684 | ||||||||
\(669\) | −21.0936 | −0.815524 | ||||||||
\(670\) | −13.6859 | −0.528732 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | 4.68569 | 0.180755 | ||||||||
\(673\) | 9.40282 | 0.362452 | 0.181226 | − | 0.983441i | \(-0.441993\pi\) | ||||
0.181226 | + | 0.983441i | \(0.441993\pi\) | |||||||
\(674\) | −23.4235 | −0.902241 | ||||||||
\(675\) | −1.23385 | −0.0474911 | ||||||||
\(676\) | −0.447449 | −0.0172096 | ||||||||
\(677\) | −25.3988 | −0.976157 | −0.488078 | − | 0.872800i | \(-0.662302\pi\) | ||||
−0.488078 | + | 0.872800i | \(0.662302\pi\) | |||||||
\(678\) | −2.76273 | −0.106102 | ||||||||
\(679\) | 14.3205 | 0.549569 | ||||||||
\(680\) | −8.77391 | −0.336464 | ||||||||
\(681\) | 4.60697 | 0.176540 | ||||||||
\(682\) | 2.24915 | 0.0861244 | ||||||||
\(683\) | −12.8173 | −0.490439 | −0.245220 | − | 0.969468i | \(-0.578860\pi\) | ||||
−0.245220 | + | 0.969468i | \(0.578860\pi\) | |||||||
\(684\) | −6.57912 | −0.251559 | ||||||||
\(685\) | −12.8747 | −0.491917 | ||||||||
\(686\) | 37.2780 | 1.42328 | ||||||||
\(687\) | 7.72279 | 0.294643 | ||||||||
\(688\) | −12.8057 | −0.488214 | ||||||||
\(689\) | 4.68104 | 0.178333 | ||||||||
\(690\) | 4.47999 | 0.170550 | ||||||||
\(691\) | −36.6610 | −1.39465 | −0.697326 | − | 0.716754i | \(-0.745627\pi\) | ||||
−0.697326 | + | 0.716754i | \(0.745627\pi\) | |||||||
\(692\) | −18.9212 | −0.719274 | ||||||||
\(693\) | −4.68569 | −0.177995 | ||||||||
\(694\) | −17.5562 | −0.666424 | ||||||||
\(695\) | 42.2460 | 1.60248 | ||||||||
\(696\) | 8.87158 | 0.336276 | ||||||||
\(697\) | −17.8709 | −0.676909 | ||||||||
\(698\) | 22.5290 | 0.852737 | ||||||||
\(699\) | 17.7056 | 0.669686 | ||||||||
\(700\) | −5.78146 | −0.218519 | ||||||||
\(701\) | 30.5068 | 1.15223 | 0.576113 | − | 0.817370i | \(-0.304569\pi\) | ||||
0.576113 | + | 0.817370i | \(0.304569\pi\) | |||||||
\(702\) | 3.54296 | 0.133720 | ||||||||
\(703\) | −67.3619 | −2.54060 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | −18.7051 | −0.704473 | ||||||||
\(706\) | 8.20436 | 0.308775 | ||||||||
\(707\) | −88.5272 | −3.32941 | ||||||||
\(708\) | −2.76033 | −0.103740 | ||||||||
\(709\) | −10.0246 | −0.376482 | −0.188241 | − | 0.982123i | \(-0.560279\pi\) | ||||
−0.188241 | + | 0.982123i | \(0.560279\pi\) | |||||||
\(710\) | −8.11185 | −0.304432 | ||||||||
\(711\) | 1.12670 | 0.0422545 | ||||||||
\(712\) | −16.3921 | −0.614319 | ||||||||
\(713\) | −5.19215 | −0.194448 | ||||||||
\(714\) | −21.1845 | −0.792811 | ||||||||
\(715\) | −6.87566 | −0.257135 | ||||||||
\(716\) | 16.4768 | 0.615768 | ||||||||
\(717\) | −19.8454 | −0.741139 | ||||||||
\(718\) | −11.9885 | −0.447407 | ||||||||
\(719\) | −32.9021 | −1.22704 | −0.613520 | − | 0.789679i | \(-0.710247\pi\) | ||||
−0.613520 | + | 0.789679i | \(0.710247\pi\) | |||||||
\(720\) | 1.94066 | 0.0723240 | ||||||||
\(721\) | 11.7979 | 0.439377 | ||||||||
\(722\) | 24.2849 | 0.903789 | ||||||||
\(723\) | 24.1295 | 0.897384 | ||||||||
\(724\) | 11.2607 | 0.418499 | ||||||||
\(725\) | −10.9462 | −0.406533 | ||||||||
\(726\) | 1.00000 | 0.0371135 | ||||||||
\(727\) | 47.1188 | 1.74754 | 0.873770 | − | 0.486339i | \(-0.161668\pi\) | ||||
0.873770 | + | 0.486339i | \(0.161668\pi\) | |||||||
\(728\) | 16.6012 | 0.615282 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 28.3863 | 1.05062 | ||||||||
\(731\) | 57.8962 | 2.14137 | ||||||||
\(732\) | 1.00000 | 0.0369611 | ||||||||
\(733\) | 40.1029 | 1.48123 | 0.740617 | − | 0.671928i | \(-0.234533\pi\) | ||||
0.740617 | + | 0.671928i | \(0.234533\pi\) | |||||||
\(734\) | 15.0644 | 0.556037 | ||||||||
\(735\) | 29.0239 | 1.07056 | ||||||||
\(736\) | 2.30849 | 0.0850922 | ||||||||
\(737\) | 7.05220 | 0.259771 | ||||||||
\(738\) | 3.95278 | 0.145504 | ||||||||
\(739\) | 9.05667 | 0.333155 | 0.166577 | − | 0.986028i | \(-0.446728\pi\) | ||||
0.166577 | + | 0.986028i | \(0.446728\pi\) | |||||||
\(740\) | 19.8699 | 0.730431 | ||||||||
\(741\) | −23.3096 | −0.856298 | ||||||||
\(742\) | 6.19084 | 0.227273 | ||||||||
\(743\) | −22.4504 | −0.823624 | −0.411812 | − | 0.911269i | \(-0.635104\pi\) | ||||
−0.411812 | + | 0.911269i | \(0.635104\pi\) | |||||||
\(744\) | −2.24915 | −0.0824579 | ||||||||
\(745\) | −30.9288 | −1.13314 | ||||||||
\(746\) | 17.8052 | 0.651894 | ||||||||
\(747\) | 2.01082 | 0.0735721 | ||||||||
\(748\) | 4.52111 | 0.165308 | ||||||||
\(749\) | 3.76778 | 0.137672 | ||||||||
\(750\) | −12.0978 | −0.441748 | ||||||||
\(751\) | 25.8709 | 0.944041 | 0.472020 | − | 0.881588i | \(-0.343525\pi\) | ||||
0.472020 | + | 0.881588i | \(0.343525\pi\) | |||||||
\(752\) | −9.63852 | −0.351481 | ||||||||
\(753\) | 7.32052 | 0.266775 | ||||||||
\(754\) | 31.4316 | 1.14467 | ||||||||
\(755\) | −0.766597 | −0.0278993 | ||||||||
\(756\) | 4.68569 | 0.170417 | ||||||||
\(757\) | 48.0925 | 1.74795 | 0.873976 | − | 0.485970i | \(-0.161533\pi\) | ||||
0.873976 | + | 0.485970i | \(0.161533\pi\) | |||||||
\(758\) | 0.435287 | 0.0158103 | ||||||||
\(759\) | −2.30849 | −0.0837930 | ||||||||
\(760\) | −12.7678 | −0.463137 | ||||||||
\(761\) | −22.4777 | −0.814817 | −0.407409 | − | 0.913246i | \(-0.633568\pi\) | ||||
−0.407409 | + | 0.913246i | \(0.633568\pi\) | |||||||
\(762\) | −7.83021 | −0.283659 | ||||||||
\(763\) | −59.0869 | −2.13909 | ||||||||
\(764\) | 18.5307 | 0.670417 | ||||||||
\(765\) | −8.77391 | −0.317222 | ||||||||
\(766\) | −11.9463 | −0.431638 | ||||||||
\(767\) | −9.77974 | −0.353126 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 41.2006 | 1.48573 | 0.742866 | − | 0.669440i | \(-0.233466\pi\) | ||||
0.742866 | + | 0.669440i | \(0.233466\pi\) | |||||||
\(770\) | −9.09332 | −0.327700 | ||||||||
\(771\) | −20.8803 | −0.751985 | ||||||||
\(772\) | 1.37903 | 0.0496325 | ||||||||
\(773\) | −17.5906 | −0.632689 | −0.316345 | − | 0.948644i | \(-0.602456\pi\) | ||||
−0.316345 | + | 0.948644i | \(0.602456\pi\) | |||||||
\(774\) | −12.8057 | −0.460293 | ||||||||
\(775\) | 2.77512 | 0.0996854 | ||||||||
\(776\) | 3.05621 | 0.109712 | ||||||||
\(777\) | 47.9756 | 1.72111 | ||||||||
\(778\) | 23.6560 | 0.848107 | ||||||||
\(779\) | −26.0058 | −0.931754 | ||||||||
\(780\) | 6.87566 | 0.246188 | ||||||||
\(781\) | 4.17995 | 0.149570 | ||||||||
\(782\) | −10.4370 | −0.373225 | ||||||||
\(783\) | 8.87158 | 0.317044 | ||||||||
\(784\) | 14.9557 | 0.534133 | ||||||||
\(785\) | 32.2447 | 1.15086 | ||||||||
\(786\) | 0.294983 | 0.0105217 | ||||||||
\(787\) | 3.68134 | 0.131226 | 0.0656128 | − | 0.997845i | \(-0.479100\pi\) | ||||
0.0656128 | + | 0.997845i | \(0.479100\pi\) | |||||||
\(788\) | 0.395172 | 0.0140774 | ||||||||
\(789\) | −6.51652 | −0.231994 | ||||||||
\(790\) | 2.18653 | 0.0777933 | ||||||||
\(791\) | −12.9453 | −0.460283 | ||||||||
\(792\) | −1.00000 | −0.0355335 | ||||||||
\(793\) | 3.54296 | 0.125814 | ||||||||
\(794\) | 9.23778 | 0.327836 | ||||||||
\(795\) | 2.56404 | 0.0909371 | ||||||||
\(796\) | 4.97157 | 0.176213 | ||||||||
\(797\) | 9.81203 | 0.347560 | 0.173780 | − | 0.984785i | \(-0.444402\pi\) | ||||
0.173780 | + | 0.984785i | \(0.444402\pi\) | |||||||
\(798\) | −30.8277 | −1.09129 | ||||||||
\(799\) | 43.5768 | 1.54164 | ||||||||
\(800\) | −1.23385 | −0.0436233 | ||||||||
\(801\) | −16.3921 | −0.579186 | ||||||||
\(802\) | −18.6248 | −0.657664 | ||||||||
\(803\) | −14.6272 | −0.516181 | ||||||||
\(804\) | −7.05220 | −0.248712 | ||||||||
\(805\) | 20.9919 | 0.739866 | ||||||||
\(806\) | −7.96865 | −0.280684 | ||||||||
\(807\) | 17.3097 | 0.609330 | ||||||||
\(808\) | −18.8931 | −0.664656 | ||||||||
\(809\) | −23.3940 | −0.822489 | −0.411245 | − | 0.911525i | \(-0.634906\pi\) | ||||
−0.411245 | + | 0.911525i | \(0.634906\pi\) | |||||||
\(810\) | 1.94066 | 0.0681877 | ||||||||
\(811\) | −2.24057 | −0.0786771 | −0.0393385 | − | 0.999226i | \(-0.512525\pi\) | ||||
−0.0393385 | + | 0.999226i | \(0.512525\pi\) | |||||||
\(812\) | 41.5695 | 1.45880 | ||||||||
\(813\) | 3.52912 | 0.123772 | ||||||||
\(814\) | −10.2387 | −0.358868 | ||||||||
\(815\) | −22.4113 | −0.785032 | ||||||||
\(816\) | −4.52111 | −0.158270 | ||||||||
\(817\) | 84.2506 | 2.94755 | ||||||||
\(818\) | 22.9387 | 0.802034 | ||||||||
\(819\) | 16.6012 | 0.580093 | ||||||||
\(820\) | 7.67098 | 0.267882 | ||||||||
\(821\) | −4.20978 | −0.146922 | −0.0734612 | − | 0.997298i | \(-0.523405\pi\) | ||||
−0.0734612 | + | 0.997298i | \(0.523405\pi\) | |||||||
\(822\) | −6.63420 | −0.231394 | ||||||||
\(823\) | 6.24729 | 0.217767 | 0.108883 | − | 0.994055i | \(-0.465272\pi\) | ||||
0.108883 | + | 0.994055i | \(0.465272\pi\) | |||||||
\(824\) | 2.51786 | 0.0877138 | ||||||||
\(825\) | 1.23385 | 0.0429573 | ||||||||
\(826\) | −12.9341 | −0.450034 | ||||||||
\(827\) | 30.7905 | 1.07069 | 0.535346 | − | 0.844633i | \(-0.320181\pi\) | ||||
0.535346 | + | 0.844633i | \(0.320181\pi\) | |||||||
\(828\) | 2.30849 | 0.0802257 | ||||||||
\(829\) | −35.2703 | −1.22499 | −0.612494 | − | 0.790475i | \(-0.709834\pi\) | ||||
−0.612494 | + | 0.790475i | \(0.709834\pi\) | |||||||
\(830\) | 3.90231 | 0.135451 | ||||||||
\(831\) | 10.9000 | 0.378118 | ||||||||
\(832\) | 3.54296 | 0.122830 | ||||||||
\(833\) | −67.6164 | −2.34277 | ||||||||
\(834\) | 21.7689 | 0.753797 | ||||||||
\(835\) | 25.5645 | 0.884696 | ||||||||
\(836\) | 6.57912 | 0.227544 | ||||||||
\(837\) | −2.24915 | −0.0777420 | ||||||||
\(838\) | −19.8711 | −0.686436 | ||||||||
\(839\) | −32.4869 | −1.12157 | −0.560786 | − | 0.827961i | \(-0.689501\pi\) | ||||
−0.560786 | + | 0.827961i | \(0.689501\pi\) | |||||||
\(840\) | 9.09332 | 0.313749 | ||||||||
\(841\) | 49.7049 | 1.71396 | ||||||||
\(842\) | −32.9028 | −1.13391 | ||||||||
\(843\) | 10.8840 | 0.374863 | ||||||||
\(844\) | 7.02591 | 0.241842 | ||||||||
\(845\) | −0.868344 | −0.0298719 | ||||||||
\(846\) | −9.63852 | −0.331379 | ||||||||
\(847\) | 4.68569 | 0.161002 | ||||||||
\(848\) | 1.32122 | 0.0453710 | ||||||||
\(849\) | −12.7121 | −0.436279 | ||||||||
\(850\) | 5.57839 | 0.191337 | ||||||||
\(851\) | 23.6361 | 0.810234 | ||||||||
\(852\) | −4.17995 | −0.143203 | ||||||||
\(853\) | 13.9865 | 0.478888 | 0.239444 | − | 0.970910i | \(-0.423035\pi\) | ||||
0.239444 | + | 0.970910i | \(0.423035\pi\) | |||||||
\(854\) | 4.68569 | 0.160341 | ||||||||
\(855\) | −12.7678 | −0.436650 | ||||||||
\(856\) | 0.804104 | 0.0274837 | ||||||||
\(857\) | 18.0088 | 0.615170 | 0.307585 | − | 0.951521i | \(-0.400479\pi\) | ||||
0.307585 | + | 0.951521i | \(0.400479\pi\) | |||||||
\(858\) | −3.54296 | −0.120955 | ||||||||
\(859\) | −5.44862 | −0.185905 | −0.0929523 | − | 0.995671i | \(-0.529630\pi\) | ||||
−0.0929523 | + | 0.995671i | \(0.529630\pi\) | |||||||
\(860\) | −24.8515 | −0.847431 | ||||||||
\(861\) | 18.5215 | 0.631211 | ||||||||
\(862\) | −28.0055 | −0.953873 | ||||||||
\(863\) | 42.6014 | 1.45017 | 0.725084 | − | 0.688660i | \(-0.241801\pi\) | ||||
0.725084 | + | 0.688660i | \(0.241801\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −36.7195 | −1.24850 | ||||||||
\(866\) | 19.7345 | 0.670607 | ||||||||
\(867\) | 3.44042 | 0.116843 | ||||||||
\(868\) | −10.5388 | −0.357711 | ||||||||
\(869\) | −1.12670 | −0.0382206 | ||||||||
\(870\) | 17.2167 | 0.583700 | ||||||||
\(871\) | −24.9857 | −0.846607 | ||||||||
\(872\) | −12.6101 | −0.427031 | ||||||||
\(873\) | 3.05621 | 0.103437 | ||||||||
\(874\) | −15.1879 | −0.513737 | ||||||||
\(875\) | −56.6864 | −1.91635 | ||||||||
\(876\) | 14.6272 | 0.494206 | ||||||||
\(877\) | 19.5835 | 0.661288 | 0.330644 | − | 0.943755i | \(-0.392734\pi\) | ||||
0.330644 | + | 0.943755i | \(0.392734\pi\) | |||||||
\(878\) | 34.1613 | 1.15289 | ||||||||
\(879\) | 11.2244 | 0.378590 | ||||||||
\(880\) | −1.94066 | −0.0654195 | ||||||||
\(881\) | 34.9248 | 1.17665 | 0.588323 | − | 0.808626i | \(-0.299788\pi\) | ||||
0.588323 | + | 0.808626i | \(0.299788\pi\) | |||||||
\(882\) | 14.9557 | 0.503585 | ||||||||
\(883\) | −0.782444 | −0.0263313 | −0.0131657 | − | 0.999913i | \(-0.504191\pi\) | ||||
−0.0131657 | + | 0.999913i | \(0.504191\pi\) | |||||||
\(884\) | −16.0181 | −0.538747 | ||||||||
\(885\) | −5.35686 | −0.180069 | ||||||||
\(886\) | 2.73228 | 0.0917926 | ||||||||
\(887\) | 31.0312 | 1.04193 | 0.520963 | − | 0.853579i | \(-0.325573\pi\) | ||||
0.520963 | + | 0.853579i | \(0.325573\pi\) | |||||||
\(888\) | 10.2387 | 0.343590 | ||||||||
\(889\) | −36.6900 | −1.23054 | ||||||||
\(890\) | −31.8114 | −1.06632 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | −21.0936 | −0.706265 | ||||||||
\(893\) | 63.4130 | 2.12204 | ||||||||
\(894\) | −15.9373 | −0.533022 | ||||||||
\(895\) | 31.9758 | 1.06883 | ||||||||
\(896\) | 4.68569 | 0.156538 | ||||||||
\(897\) | 8.17890 | 0.273086 | ||||||||
\(898\) | −4.69807 | −0.156777 | ||||||||
\(899\) | −19.9535 | −0.665487 | ||||||||
\(900\) | −1.23385 | −0.0411285 | ||||||||
\(901\) | −5.97339 | −0.199002 | ||||||||
\(902\) | −3.95278 | −0.131613 | ||||||||
\(903\) | −60.0038 | −1.99680 | ||||||||
\(904\) | −2.76273 | −0.0918872 | ||||||||
\(905\) | 21.8531 | 0.726421 | ||||||||
\(906\) | −0.395019 | −0.0131236 | ||||||||
\(907\) | −32.8869 | −1.09199 | −0.545995 | − | 0.837788i | \(-0.683848\pi\) | ||||
−0.545995 | + | 0.837788i | \(0.683848\pi\) | |||||||
\(908\) | 4.60697 | 0.152888 | ||||||||
\(909\) | −18.8931 | −0.626644 | ||||||||
\(910\) | 32.2172 | 1.06799 | ||||||||
\(911\) | 8.50095 | 0.281649 | 0.140825 | − | 0.990035i | \(-0.455025\pi\) | ||||
0.140825 | + | 0.990035i | \(0.455025\pi\) | |||||||
\(912\) | −6.57912 | −0.217857 | ||||||||
\(913\) | −2.01082 | −0.0665485 | ||||||||
\(914\) | −15.4353 | −0.510554 | ||||||||
\(915\) | 1.94066 | 0.0641561 | ||||||||
\(916\) | 7.72279 | 0.255168 | ||||||||
\(917\) | 1.38220 | 0.0456443 | ||||||||
\(918\) | −4.52111 | −0.149219 | ||||||||
\(919\) | 8.11405 | 0.267658 | 0.133829 | − | 0.991004i | \(-0.457273\pi\) | ||||
0.133829 | + | 0.991004i | \(0.457273\pi\) | |||||||
\(920\) | 4.47999 | 0.147701 | ||||||||
\(921\) | 1.14250 | 0.0376466 | ||||||||
\(922\) | 32.2504 | 1.06211 | ||||||||
\(923\) | −14.8094 | −0.487457 | ||||||||
\(924\) | −4.68569 | −0.154148 | ||||||||
\(925\) | −12.6331 | −0.415374 | ||||||||
\(926\) | 15.1119 | 0.496609 | ||||||||
\(927\) | 2.51786 | 0.0826974 | ||||||||
\(928\) | 8.87158 | 0.291224 | ||||||||
\(929\) | 45.4901 | 1.49248 | 0.746241 | − | 0.665676i | \(-0.231857\pi\) | ||||
0.746241 | + | 0.665676i | \(0.231857\pi\) | |||||||
\(930\) | −4.36483 | −0.143128 | ||||||||
\(931\) | −98.3955 | −3.22478 | ||||||||
\(932\) | 17.7056 | 0.579965 | ||||||||
\(933\) | −27.3801 | −0.896385 | ||||||||
\(934\) | 22.3900 | 0.732622 | ||||||||
\(935\) | 8.77391 | 0.286938 | ||||||||
\(936\) | 3.54296 | 0.115805 | ||||||||
\(937\) | 35.1925 | 1.14969 | 0.574844 | − | 0.818263i | \(-0.305063\pi\) | ||||
0.574844 | + | 0.818263i | \(0.305063\pi\) | |||||||
\(938\) | −33.0445 | −1.07894 | ||||||||
\(939\) | 3.89382 | 0.127070 | ||||||||
\(940\) | −18.7051 | −0.610092 | ||||||||
\(941\) | 10.6839 | 0.348285 | 0.174143 | − | 0.984720i | \(-0.444285\pi\) | ||||
0.174143 | + | 0.984720i | \(0.444285\pi\) | |||||||
\(942\) | 16.6154 | 0.541358 | ||||||||
\(943\) | 9.12496 | 0.297150 | ||||||||
\(944\) | −2.76033 | −0.0898412 | ||||||||
\(945\) | 9.09332 | 0.295806 | ||||||||
\(946\) | 12.8057 | 0.416351 | ||||||||
\(947\) | −39.6950 | −1.28991 | −0.644956 | − | 0.764219i | \(-0.723124\pi\) | ||||
−0.644956 | + | 0.764219i | \(0.723124\pi\) | |||||||
\(948\) | 1.12670 | 0.0365934 | ||||||||
\(949\) | 51.8234 | 1.68226 | ||||||||
\(950\) | 8.11768 | 0.263372 | ||||||||
\(951\) | −19.0542 | −0.617873 | ||||||||
\(952\) | −21.1845 | −0.686594 | ||||||||
\(953\) | 34.5087 | 1.11785 | 0.558923 | − | 0.829220i | \(-0.311215\pi\) | ||||
0.558923 | + | 0.829220i | \(0.311215\pi\) | |||||||
\(954\) | 1.32122 | 0.0427762 | ||||||||
\(955\) | 35.9617 | 1.16369 | ||||||||
\(956\) | −19.8454 | −0.641845 | ||||||||
\(957\) | −8.87158 | −0.286777 | ||||||||
\(958\) | −17.9121 | −0.578715 | ||||||||
\(959\) | −31.0858 | −1.00381 | ||||||||
\(960\) | 1.94066 | 0.0626344 | ||||||||
\(961\) | −25.9413 | −0.836817 | ||||||||
\(962\) | 36.2754 | 1.16957 | ||||||||
\(963\) | 0.804104 | 0.0259119 | ||||||||
\(964\) | 24.1295 | 0.777157 | ||||||||
\(965\) | 2.67623 | 0.0861508 | ||||||||
\(966\) | 10.8169 | 0.348028 | ||||||||
\(967\) | −19.8974 | −0.639856 | −0.319928 | − | 0.947442i | \(-0.603659\pi\) | ||||
−0.319928 | + | 0.947442i | \(0.603659\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 29.7449 | 0.955545 | ||||||||
\(970\) | 5.93105 | 0.190435 | ||||||||
\(971\) | −9.96197 | −0.319695 | −0.159847 | − | 0.987142i | \(-0.551100\pi\) | ||||
−0.159847 | + | 0.987142i | \(0.551100\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 102.003 | 3.27005 | ||||||||
\(974\) | 22.6522 | 0.725824 | ||||||||
\(975\) | −4.37150 | −0.140000 | ||||||||
\(976\) | 1.00000 | 0.0320092 | ||||||||
\(977\) | −22.1448 | −0.708474 | −0.354237 | − | 0.935156i | \(-0.615259\pi\) | ||||
−0.354237 | + | 0.935156i | \(0.615259\pi\) | |||||||
\(978\) | −11.5483 | −0.369274 | ||||||||
\(979\) | 16.3921 | 0.523893 | ||||||||
\(980\) | 29.0239 | 0.927134 | ||||||||
\(981\) | −12.6101 | −0.402608 | ||||||||
\(982\) | −25.4936 | −0.813532 | ||||||||
\(983\) | −45.9669 | −1.46612 | −0.733058 | − | 0.680166i | \(-0.761908\pi\) | ||||
−0.733058 | + | 0.680166i | \(0.761908\pi\) | |||||||
\(984\) | 3.95278 | 0.126010 | ||||||||
\(985\) | 0.766893 | 0.0244353 | ||||||||
\(986\) | −40.1094 | −1.27734 | ||||||||
\(987\) | −45.1631 | −1.43756 | ||||||||
\(988\) | −23.3096 | −0.741576 | ||||||||
\(989\) | −29.5620 | −0.940017 | ||||||||
\(990\) | −1.94066 | −0.0616781 | ||||||||
\(991\) | −25.3095 | −0.803984 | −0.401992 | − | 0.915643i | \(-0.631682\pi\) | ||||
−0.401992 | + | 0.915643i | \(0.631682\pi\) | |||||||
\(992\) | −2.24915 | −0.0714106 | ||||||||
\(993\) | −16.5174 | −0.524163 | ||||||||
\(994\) | −19.5860 | −0.621229 | ||||||||
\(995\) | 9.64812 | 0.305866 | ||||||||
\(996\) | 2.01082 | 0.0637154 | ||||||||
\(997\) | −19.1672 | −0.607031 | −0.303516 | − | 0.952826i | \(-0.598160\pi\) | ||||
−0.303516 | + | 0.952826i | \(0.598160\pi\) | |||||||
\(998\) | −2.80077 | −0.0886569 | ||||||||
\(999\) | 10.2387 | 0.323939 |
(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 | 4026.2.a.bb.1.5 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4026.2.a.bb.1.5 | ✓ | 8 | 1.1 | even | 1 | trivial |