Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3174,2,Mod(1,3174)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3174, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3174.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3174 = 2 \cdot 3 \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3174.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: | \(25.3445176016\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\Q(\zeta_{22})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 4x^{3} + 3x^{2} + 3x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 138) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.91899\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3174.1 |
$q$-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 | ||||||||
\(5\) | 3.82306 | 1.70972 | 0.854862 | − | 0.518856i | \(-0.173642\pi\) | ||||
0.854862 | + | 0.518856i | \(0.173642\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 2.89389 | 1.09379 | 0.546895 | − | 0.837201i | \(-0.315810\pi\) | ||||
0.546895 | + | 0.837201i | \(0.315810\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.82306 | 1.20896 | ||||||||
\(11\) | −1.58065 | −0.476583 | −0.238291 | − | 0.971194i | \(-0.576587\pi\) | ||||
−0.238291 | + | 0.971194i | \(0.576587\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 4.70981 | 1.30627 | 0.653133 | − | 0.757243i | \(-0.273454\pi\) | ||||
0.653133 | + | 0.757243i | \(0.273454\pi\) | |||||||
\(14\) | 2.89389 | 0.773426 | ||||||||
\(15\) | −3.82306 | −0.987109 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.73780 | −1.14909 | −0.574543 | − | 0.818475i | \(-0.694820\pi\) | ||||
−0.574543 | + | 0.818475i | \(0.694820\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 2.14832 | 0.492859 | 0.246430 | − | 0.969161i | \(-0.420743\pi\) | ||||
0.246430 | + | 0.969161i | \(0.420743\pi\) | |||||||
\(20\) | 3.82306 | 0.854862 | ||||||||
\(21\) | −2.89389 | −0.631499 | ||||||||
\(22\) | −1.58065 | −0.336995 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 9.61578 | 1.92316 | ||||||||
\(26\) | 4.70981 | 0.923670 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.89389 | 0.546895 | ||||||||
\(29\) | −0.588417 | −0.109266 | −0.0546332 | − | 0.998506i | \(-0.517399\pi\) | ||||
−0.0546332 | + | 0.998506i | \(0.517399\pi\) | |||||||
\(30\) | −3.82306 | −0.697992 | ||||||||
\(31\) | 0.170752 | 0.0306680 | 0.0153340 | − | 0.999882i | \(-0.495119\pi\) | ||||
0.0153340 | + | 0.999882i | \(0.495119\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.58065 | 0.275155 | ||||||||
\(34\) | −4.73780 | −0.812526 | ||||||||
\(35\) | 11.0635 | 1.87008 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 4.81881 | 0.792208 | 0.396104 | − | 0.918206i | \(-0.370362\pi\) | ||||
0.396104 | + | 0.918206i | \(0.370362\pi\) | |||||||
\(38\) | 2.14832 | 0.348504 | ||||||||
\(39\) | −4.70981 | −0.754173 | ||||||||
\(40\) | 3.82306 | 0.604479 | ||||||||
\(41\) | −10.3972 | −1.62378 | −0.811889 | − | 0.583812i | \(-0.801560\pi\) | ||||
−0.811889 | + | 0.583812i | \(0.801560\pi\) | |||||||
\(42\) | −2.89389 | −0.446538 | ||||||||
\(43\) | 12.2681 | 1.87087 | 0.935433 | − | 0.353505i | \(-0.115010\pi\) | ||||
0.935433 | + | 0.353505i | \(0.115010\pi\) | |||||||
\(44\) | −1.58065 | −0.238291 | ||||||||
\(45\) | 3.82306 | 0.569908 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.45520 | 0.795723 | 0.397862 | − | 0.917445i | \(-0.369752\pi\) | ||||
0.397862 | + | 0.917445i | \(0.369752\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 1.37462 | 0.196375 | ||||||||
\(50\) | 9.61578 | 1.35988 | ||||||||
\(51\) | 4.73780 | 0.663425 | ||||||||
\(52\) | 4.70981 | 0.653133 | ||||||||
\(53\) | −10.3078 | −1.41588 | −0.707941 | − | 0.706272i | \(-0.750376\pi\) | ||||
−0.707941 | + | 0.706272i | \(0.750376\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −6.04290 | −0.814825 | ||||||||
\(56\) | 2.89389 | 0.386713 | ||||||||
\(57\) | −2.14832 | −0.284552 | ||||||||
\(58\) | −0.588417 | −0.0772630 | ||||||||
\(59\) | −1.90272 | −0.247714 | −0.123857 | − | 0.992300i | \(-0.539526\pi\) | ||||
−0.123857 | + | 0.992300i | \(0.539526\pi\) | |||||||
\(60\) | −3.82306 | −0.493555 | ||||||||
\(61\) | −12.6545 | −1.62024 | −0.810119 | − | 0.586265i | \(-0.800598\pi\) | ||||
−0.810119 | + | 0.586265i | \(0.800598\pi\) | |||||||
\(62\) | 0.170752 | 0.0216856 | ||||||||
\(63\) | 2.89389 | 0.364596 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 18.0059 | 2.23335 | ||||||||
\(66\) | 1.58065 | 0.194564 | ||||||||
\(67\) | 5.87608 | 0.717878 | 0.358939 | − | 0.933361i | \(-0.383139\pi\) | ||||
0.358939 | + | 0.933361i | \(0.383139\pi\) | |||||||
\(68\) | −4.73780 | −0.574543 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 11.0635 | 1.32234 | ||||||||
\(71\) | −11.8216 | −1.40297 | −0.701483 | − | 0.712686i | \(-0.747478\pi\) | ||||
−0.701483 | + | 0.712686i | \(0.747478\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −13.2135 | −1.54653 | −0.773264 | − | 0.634084i | \(-0.781377\pi\) | ||||
−0.773264 | + | 0.634084i | \(0.781377\pi\) | |||||||
\(74\) | 4.81881 | 0.560176 | ||||||||
\(75\) | −9.61578 | −1.11033 | ||||||||
\(76\) | 2.14832 | 0.246430 | ||||||||
\(77\) | −4.57422 | −0.521281 | ||||||||
\(78\) | −4.70981 | −0.533281 | ||||||||
\(79\) | 11.6845 | 1.31461 | 0.657307 | − | 0.753623i | \(-0.271696\pi\) | ||||
0.657307 | + | 0.753623i | \(0.271696\pi\) | |||||||
\(80\) | 3.82306 | 0.427431 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −10.3972 | −1.14818 | ||||||||
\(83\) | −0.113248 | −0.0124306 | −0.00621528 | − | 0.999981i | \(-0.501978\pi\) | ||||
−0.00621528 | + | 0.999981i | \(0.501978\pi\) | |||||||
\(84\) | −2.89389 | −0.315750 | ||||||||
\(85\) | −18.1129 | −1.96462 | ||||||||
\(86\) | 12.2681 | 1.32290 | ||||||||
\(87\) | 0.588417 | 0.0630850 | ||||||||
\(88\) | −1.58065 | −0.168497 | ||||||||
\(89\) | −12.2386 | −1.29729 | −0.648646 | − | 0.761090i | \(-0.724664\pi\) | ||||
−0.648646 | + | 0.761090i | \(0.724664\pi\) | |||||||
\(90\) | 3.82306 | 0.402986 | ||||||||
\(91\) | 13.6297 | 1.42878 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.170752 | −0.0177062 | ||||||||
\(94\) | 5.45520 | 0.562661 | ||||||||
\(95\) | 8.21316 | 0.842653 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 0.873537 | 0.0886943 | 0.0443471 | − | 0.999016i | \(-0.485879\pi\) | ||||
0.0443471 | + | 0.999016i | \(0.485879\pi\) | |||||||
\(98\) | 1.37462 | 0.138858 | ||||||||
\(99\) | −1.58065 | −0.158861 | ||||||||
\(100\) | 9.61578 | 0.961578 | ||||||||
\(101\) | −10.9103 | −1.08561 | −0.542807 | − | 0.839858i | \(-0.682638\pi\) | ||||
−0.542807 | + | 0.839858i | \(0.682638\pi\) | |||||||
\(102\) | 4.73780 | 0.469112 | ||||||||
\(103\) | 3.69279 | 0.363862 | 0.181931 | − | 0.983311i | \(-0.441765\pi\) | ||||
0.181931 | + | 0.983311i | \(0.441765\pi\) | |||||||
\(104\) | 4.70981 | 0.461835 | ||||||||
\(105\) | −11.0635 | −1.07969 | ||||||||
\(106\) | −10.3078 | −1.00118 | ||||||||
\(107\) | 10.7665 | 1.04083 | 0.520416 | − | 0.853913i | \(-0.325777\pi\) | ||||
0.520416 | + | 0.853913i | \(0.325777\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −8.31357 | −0.796296 | −0.398148 | − | 0.917321i | \(-0.630347\pi\) | ||||
−0.398148 | + | 0.917321i | \(0.630347\pi\) | |||||||
\(110\) | −6.04290 | −0.576168 | ||||||||
\(111\) | −4.81881 | −0.457382 | ||||||||
\(112\) | 2.89389 | 0.273447 | ||||||||
\(113\) | 7.51278 | 0.706743 | 0.353372 | − | 0.935483i | \(-0.385035\pi\) | ||||
0.353372 | + | 0.935483i | \(0.385035\pi\) | |||||||
\(114\) | −2.14832 | −0.201209 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.588417 | −0.0546332 | ||||||||
\(117\) | 4.70981 | 0.435422 | ||||||||
\(118\) | −1.90272 | −0.175160 | ||||||||
\(119\) | −13.7107 | −1.25686 | ||||||||
\(120\) | −3.82306 | −0.348996 | ||||||||
\(121\) | −8.50156 | −0.772869 | ||||||||
\(122\) | −12.6545 | −1.14568 | ||||||||
\(123\) | 10.3972 | 0.937488 | ||||||||
\(124\) | 0.170752 | 0.0153340 | ||||||||
\(125\) | 17.6464 | 1.57834 | ||||||||
\(126\) | 2.89389 | 0.257809 | ||||||||
\(127\) | −7.58758 | −0.673289 | −0.336645 | − | 0.941632i | \(-0.609292\pi\) | ||||
−0.336645 | + | 0.941632i | \(0.609292\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −12.2681 | −1.08014 | ||||||||
\(130\) | 18.0059 | 1.57922 | ||||||||
\(131\) | 17.8085 | 1.55594 | 0.777970 | − | 0.628302i | \(-0.216250\pi\) | ||||
0.777970 | + | 0.628302i | \(0.216250\pi\) | |||||||
\(132\) | 1.58065 | 0.137578 | ||||||||
\(133\) | 6.21702 | 0.539084 | ||||||||
\(134\) | 5.87608 | 0.507616 | ||||||||
\(135\) | −3.82306 | −0.329036 | ||||||||
\(136\) | −4.73780 | −0.406263 | ||||||||
\(137\) | −0.762968 | −0.0651847 | −0.0325924 | − | 0.999469i | \(-0.510376\pi\) | ||||
−0.0325924 | + | 0.999469i | \(0.510376\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.22612 | 0.782549 | 0.391275 | − | 0.920274i | \(-0.372034\pi\) | ||||
0.391275 | + | 0.920274i | \(0.372034\pi\) | |||||||
\(140\) | 11.0635 | 0.935039 | ||||||||
\(141\) | −5.45520 | −0.459411 | ||||||||
\(142\) | −11.8216 | −0.992047 | ||||||||
\(143\) | −7.44454 | −0.622544 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −2.24955 | −0.186815 | ||||||||
\(146\) | −13.2135 | −1.09356 | ||||||||
\(147\) | −1.37462 | −0.113377 | ||||||||
\(148\) | 4.81881 | 0.396104 | ||||||||
\(149\) | 18.4911 | 1.51485 | 0.757424 | − | 0.652923i | \(-0.226458\pi\) | ||||
0.757424 | + | 0.652923i | \(0.226458\pi\) | |||||||
\(150\) | −9.61578 | −0.785125 | ||||||||
\(151\) | −0.991887 | −0.0807186 | −0.0403593 | − | 0.999185i | \(-0.512850\pi\) | ||||
−0.0403593 | + | 0.999185i | \(0.512850\pi\) | |||||||
\(152\) | 2.14832 | 0.174252 | ||||||||
\(153\) | −4.73780 | −0.383028 | ||||||||
\(154\) | −4.57422 | −0.368601 | ||||||||
\(155\) | 0.652796 | 0.0524339 | ||||||||
\(156\) | −4.70981 | −0.377087 | ||||||||
\(157\) | 8.10972 | 0.647226 | 0.323613 | − | 0.946189i | \(-0.395102\pi\) | ||||
0.323613 | + | 0.946189i | \(0.395102\pi\) | |||||||
\(158\) | 11.6845 | 0.929572 | ||||||||
\(159\) | 10.3078 | 0.817460 | ||||||||
\(160\) | 3.82306 | 0.302239 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −23.0759 | −1.80745 | −0.903724 | − | 0.428116i | \(-0.859177\pi\) | ||||
−0.903724 | + | 0.428116i | \(0.859177\pi\) | |||||||
\(164\) | −10.3972 | −0.811889 | ||||||||
\(165\) | 6.04290 | 0.470439 | ||||||||
\(166\) | −0.113248 | −0.00878973 | ||||||||
\(167\) | −5.28482 | −0.408952 | −0.204476 | − | 0.978872i | \(-0.565549\pi\) | ||||
−0.204476 | + | 0.978872i | \(0.565549\pi\) | |||||||
\(168\) | −2.89389 | −0.223269 | ||||||||
\(169\) | 9.18232 | 0.706332 | ||||||||
\(170\) | −18.1129 | −1.38919 | ||||||||
\(171\) | 2.14832 | 0.164286 | ||||||||
\(172\) | 12.2681 | 0.935433 | ||||||||
\(173\) | 14.3906 | 1.09410 | 0.547049 | − | 0.837101i | \(-0.315751\pi\) | ||||
0.547049 | + | 0.837101i | \(0.315751\pi\) | |||||||
\(174\) | 0.588417 | 0.0446078 | ||||||||
\(175\) | 27.8270 | 2.10353 | ||||||||
\(176\) | −1.58065 | −0.119146 | ||||||||
\(177\) | 1.90272 | 0.143018 | ||||||||
\(178\) | −12.2386 | −0.917324 | ||||||||
\(179\) | 11.2001 | 0.837132 | 0.418566 | − | 0.908186i | \(-0.362533\pi\) | ||||
0.418566 | + | 0.908186i | \(0.362533\pi\) | |||||||
\(180\) | 3.82306 | 0.284954 | ||||||||
\(181\) | 8.79467 | 0.653703 | 0.326852 | − | 0.945076i | \(-0.394012\pi\) | ||||
0.326852 | + | 0.945076i | \(0.394012\pi\) | |||||||
\(182\) | 13.6297 | 1.01030 | ||||||||
\(183\) | 12.6545 | 0.935445 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 18.4226 | 1.35446 | ||||||||
\(186\) | −0.170752 | −0.0125202 | ||||||||
\(187\) | 7.48878 | 0.547634 | ||||||||
\(188\) | 5.45520 | 0.397862 | ||||||||
\(189\) | −2.89389 | −0.210500 | ||||||||
\(190\) | 8.21316 | 0.595846 | ||||||||
\(191\) | −6.33200 | −0.458168 | −0.229084 | − | 0.973407i | \(-0.573573\pi\) | ||||
−0.229084 | + | 0.973407i | \(0.573573\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −3.07385 | −0.221261 | −0.110630 | − | 0.993862i | \(-0.535287\pi\) | ||||
−0.110630 | + | 0.993862i | \(0.535287\pi\) | |||||||
\(194\) | 0.873537 | 0.0627163 | ||||||||
\(195\) | −18.0059 | −1.28943 | ||||||||
\(196\) | 1.37462 | 0.0981874 | ||||||||
\(197\) | −0.963415 | −0.0686405 | −0.0343202 | − | 0.999411i | \(-0.510927\pi\) | ||||
−0.0343202 | + | 0.999411i | \(0.510927\pi\) | |||||||
\(198\) | −1.58065 | −0.112332 | ||||||||
\(199\) | 3.27328 | 0.232037 | 0.116018 | − | 0.993247i | \(-0.462987\pi\) | ||||
0.116018 | + | 0.993247i | \(0.462987\pi\) | |||||||
\(200\) | 9.61578 | 0.679938 | ||||||||
\(201\) | −5.87608 | −0.414467 | ||||||||
\(202\) | −10.9103 | −0.767645 | ||||||||
\(203\) | −1.70282 | −0.119514 | ||||||||
\(204\) | 4.73780 | 0.331712 | ||||||||
\(205\) | −39.7493 | −2.77621 | ||||||||
\(206\) | 3.69279 | 0.257289 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.70981 | 0.326567 | ||||||||
\(209\) | −3.39574 | −0.234888 | ||||||||
\(210\) | −11.0635 | −0.763456 | ||||||||
\(211\) | −24.4174 | −1.68097 | −0.840483 | − | 0.541838i | \(-0.817728\pi\) | ||||
−0.840483 | + | 0.541838i | \(0.817728\pi\) | |||||||
\(212\) | −10.3078 | −0.707941 | ||||||||
\(213\) | 11.8216 | 0.810003 | ||||||||
\(214\) | 10.7665 | 0.735979 | ||||||||
\(215\) | 46.9016 | 3.19866 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0.494139 | 0.0335444 | ||||||||
\(218\) | −8.31357 | −0.563066 | ||||||||
\(219\) | 13.2135 | 0.892888 | ||||||||
\(220\) | −6.04290 | −0.407412 | ||||||||
\(221\) | −22.3141 | −1.50101 | ||||||||
\(222\) | −4.81881 | −0.323418 | ||||||||
\(223\) | 15.1991 | 1.01781 | 0.508904 | − | 0.860823i | \(-0.330051\pi\) | ||||
0.508904 | + | 0.860823i | \(0.330051\pi\) | |||||||
\(224\) | 2.89389 | 0.193356 | ||||||||
\(225\) | 9.61578 | 0.641052 | ||||||||
\(226\) | 7.51278 | 0.499743 | ||||||||
\(227\) | 12.9325 | 0.858358 | 0.429179 | − | 0.903220i | \(-0.358803\pi\) | ||||
0.429179 | + | 0.903220i | \(0.358803\pi\) | |||||||
\(228\) | −2.14832 | −0.142276 | ||||||||
\(229\) | −0.948502 | −0.0626788 | −0.0313394 | − | 0.999509i | \(-0.509977\pi\) | ||||
−0.0313394 | + | 0.999509i | \(0.509977\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.57422 | 0.300962 | ||||||||
\(232\) | −0.588417 | −0.0386315 | ||||||||
\(233\) | 13.9482 | 0.913778 | 0.456889 | − | 0.889524i | \(-0.348964\pi\) | ||||
0.456889 | + | 0.889524i | \(0.348964\pi\) | |||||||
\(234\) | 4.70981 | 0.307890 | ||||||||
\(235\) | 20.8556 | 1.36047 | ||||||||
\(236\) | −1.90272 | −0.123857 | ||||||||
\(237\) | −11.6845 | −0.758992 | ||||||||
\(238\) | −13.7107 | −0.888732 | ||||||||
\(239\) | −2.44329 | −0.158043 | −0.0790217 | − | 0.996873i | \(-0.525180\pi\) | ||||
−0.0790217 | + | 0.996873i | \(0.525180\pi\) | |||||||
\(240\) | −3.82306 | −0.246777 | ||||||||
\(241\) | 10.8636 | 0.699784 | 0.349892 | − | 0.936790i | \(-0.386218\pi\) | ||||
0.349892 | + | 0.936790i | \(0.386218\pi\) | |||||||
\(242\) | −8.50156 | −0.546501 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −12.6545 | −0.810119 | ||||||||
\(245\) | 5.25527 | 0.335747 | ||||||||
\(246\) | 10.3972 | 0.662904 | ||||||||
\(247\) | 10.1182 | 0.643805 | ||||||||
\(248\) | 0.170752 | 0.0108428 | ||||||||
\(249\) | 0.113248 | 0.00717678 | ||||||||
\(250\) | 17.6464 | 1.11606 | ||||||||
\(251\) | −14.3211 | −0.903940 | −0.451970 | − | 0.892033i | \(-0.649279\pi\) | ||||
−0.451970 | + | 0.892033i | \(0.649279\pi\) | |||||||
\(252\) | 2.89389 | 0.182298 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −7.58758 | −0.476087 | ||||||||
\(255\) | 18.1129 | 1.13427 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.24430 | −0.264752 | −0.132376 | − | 0.991200i | \(-0.542261\pi\) | ||||
−0.132376 | + | 0.991200i | \(0.542261\pi\) | |||||||
\(258\) | −12.2681 | −0.763777 | ||||||||
\(259\) | 13.9451 | 0.866509 | ||||||||
\(260\) | 18.0059 | 1.11668 | ||||||||
\(261\) | −0.588417 | −0.0364221 | ||||||||
\(262\) | 17.8085 | 1.10022 | ||||||||
\(263\) | −7.10375 | −0.438036 | −0.219018 | − | 0.975721i | \(-0.570285\pi\) | ||||
−0.219018 | + | 0.975721i | \(0.570285\pi\) | |||||||
\(264\) | 1.58065 | 0.0972820 | ||||||||
\(265\) | −39.4072 | −2.42077 | ||||||||
\(266\) | 6.21702 | 0.381190 | ||||||||
\(267\) | 12.2386 | 0.748992 | ||||||||
\(268\) | 5.87608 | 0.358939 | ||||||||
\(269\) | −7.73235 | −0.471450 | −0.235725 | − | 0.971820i | \(-0.575746\pi\) | ||||
−0.235725 | + | 0.971820i | \(0.575746\pi\) | |||||||
\(270\) | −3.82306 | −0.232664 | ||||||||
\(271\) | −5.08058 | −0.308623 | −0.154312 | − | 0.988022i | \(-0.549316\pi\) | ||||
−0.154312 | + | 0.988022i | \(0.549316\pi\) | |||||||
\(272\) | −4.73780 | −0.287271 | ||||||||
\(273\) | −13.6297 | −0.824907 | ||||||||
\(274\) | −0.762968 | −0.0460926 | ||||||||
\(275\) | −15.1991 | −0.916543 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.3909 | −0.924751 | −0.462376 | − | 0.886684i | \(-0.653003\pi\) | ||||
−0.462376 | + | 0.886684i | \(0.653003\pi\) | |||||||
\(278\) | 9.22612 | 0.553346 | ||||||||
\(279\) | 0.170752 | 0.0102227 | ||||||||
\(280\) | 11.0635 | 0.661172 | ||||||||
\(281\) | −3.29958 | −0.196836 | −0.0984181 | − | 0.995145i | \(-0.531378\pi\) | ||||
−0.0984181 | + | 0.995145i | \(0.531378\pi\) | |||||||
\(282\) | −5.45520 | −0.324853 | ||||||||
\(283\) | −25.8826 | −1.53856 | −0.769280 | − | 0.638911i | \(-0.779385\pi\) | ||||
−0.769280 | + | 0.638911i | \(0.779385\pi\) | |||||||
\(284\) | −11.8216 | −0.701483 | ||||||||
\(285\) | −8.21316 | −0.486506 | ||||||||
\(286\) | −7.44454 | −0.440205 | ||||||||
\(287\) | −30.0885 | −1.77607 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 5.44675 | 0.320397 | ||||||||
\(290\) | −2.24955 | −0.132098 | ||||||||
\(291\) | −0.873537 | −0.0512077 | ||||||||
\(292\) | −13.2135 | −0.773264 | ||||||||
\(293\) | 6.52568 | 0.381234 | 0.190617 | − | 0.981664i | \(-0.438951\pi\) | ||||
0.190617 | + | 0.981664i | \(0.438951\pi\) | |||||||
\(294\) | −1.37462 | −0.0801697 | ||||||||
\(295\) | −7.27423 | −0.423522 | ||||||||
\(296\) | 4.81881 | 0.280088 | ||||||||
\(297\) | 1.58065 | 0.0917184 | ||||||||
\(298\) | 18.4911 | 1.07116 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −9.61578 | −0.555167 | ||||||||
\(301\) | 35.5025 | 2.04633 | ||||||||
\(302\) | −0.991887 | −0.0570767 | ||||||||
\(303\) | 10.9103 | 0.626779 | ||||||||
\(304\) | 2.14832 | 0.123215 | ||||||||
\(305\) | −48.3788 | −2.77016 | ||||||||
\(306\) | −4.73780 | −0.270842 | ||||||||
\(307\) | 4.61726 | 0.263521 | 0.131761 | − | 0.991282i | \(-0.457937\pi\) | ||||
0.131761 | + | 0.991282i | \(0.457937\pi\) | |||||||
\(308\) | −4.57422 | −0.260641 | ||||||||
\(309\) | −3.69279 | −0.210076 | ||||||||
\(310\) | 0.652796 | 0.0370763 | ||||||||
\(311\) | −10.7400 | −0.609011 | −0.304506 | − | 0.952511i | \(-0.598491\pi\) | ||||
−0.304506 | + | 0.952511i | \(0.598491\pi\) | |||||||
\(312\) | −4.70981 | −0.266641 | ||||||||
\(313\) | 26.6899 | 1.50860 | 0.754301 | − | 0.656529i | \(-0.227976\pi\) | ||||
0.754301 | + | 0.656529i | \(0.227976\pi\) | |||||||
\(314\) | 8.10972 | 0.457658 | ||||||||
\(315\) | 11.0635 | 0.623359 | ||||||||
\(316\) | 11.6845 | 0.657307 | ||||||||
\(317\) | 19.1814 | 1.07733 | 0.538667 | − | 0.842518i | \(-0.318928\pi\) | ||||
0.538667 | + | 0.842518i | \(0.318928\pi\) | |||||||
\(318\) | 10.3078 | 0.578031 | ||||||||
\(319\) | 0.930080 | 0.0520745 | ||||||||
\(320\) | 3.82306 | 0.213715 | ||||||||
\(321\) | −10.7665 | −0.600925 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.1783 | −0.566337 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 45.2885 | 2.51215 | ||||||||
\(326\) | −23.0759 | −1.27806 | ||||||||
\(327\) | 8.31357 | 0.459742 | ||||||||
\(328\) | −10.3972 | −0.574092 | ||||||||
\(329\) | 15.7868 | 0.870353 | ||||||||
\(330\) | 6.04290 | 0.332651 | ||||||||
\(331\) | 8.74066 | 0.480430 | 0.240215 | − | 0.970720i | \(-0.422782\pi\) | ||||
0.240215 | + | 0.970720i | \(0.422782\pi\) | |||||||
\(332\) | −0.113248 | −0.00621528 | ||||||||
\(333\) | 4.81881 | 0.264069 | ||||||||
\(334\) | −5.28482 | −0.289173 | ||||||||
\(335\) | 22.4646 | 1.22737 | ||||||||
\(336\) | −2.89389 | −0.157875 | ||||||||
\(337\) | −3.25394 | −0.177253 | −0.0886267 | − | 0.996065i | \(-0.528248\pi\) | ||||
−0.0886267 | + | 0.996065i | \(0.528248\pi\) | |||||||
\(338\) | 9.18232 | 0.499452 | ||||||||
\(339\) | −7.51278 | −0.408038 | ||||||||
\(340\) | −18.1129 | −0.982309 | ||||||||
\(341\) | −0.269899 | −0.0146159 | ||||||||
\(342\) | 2.14832 | 0.116168 | ||||||||
\(343\) | −16.2792 | −0.878997 | ||||||||
\(344\) | 12.2681 | 0.661451 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.3906 | 0.773644 | ||||||||
\(347\) | −5.21179 | −0.279783 | −0.139892 | − | 0.990167i | \(-0.544675\pi\) | ||||
−0.139892 | + | 0.990167i | \(0.544675\pi\) | |||||||
\(348\) | 0.588417 | 0.0315425 | ||||||||
\(349\) | 15.4731 | 0.828256 | 0.414128 | − | 0.910219i | \(-0.364087\pi\) | ||||
0.414128 | + | 0.910219i | \(0.364087\pi\) | |||||||
\(350\) | 27.8270 | 1.48742 | ||||||||
\(351\) | −4.70981 | −0.251391 | ||||||||
\(352\) | −1.58065 | −0.0842487 | ||||||||
\(353\) | −1.61663 | −0.0860448 | −0.0430224 | − | 0.999074i | \(-0.513699\pi\) | ||||
−0.0430224 | + | 0.999074i | \(0.513699\pi\) | |||||||
\(354\) | 1.90272 | 0.101129 | ||||||||
\(355\) | −45.1947 | −2.39868 | ||||||||
\(356\) | −12.2386 | −0.648646 | ||||||||
\(357\) | 13.7107 | 0.725647 | ||||||||
\(358\) | 11.2001 | 0.591942 | ||||||||
\(359\) | 13.5579 | 0.715561 | 0.357780 | − | 0.933806i | \(-0.383534\pi\) | ||||
0.357780 | + | 0.933806i | \(0.383534\pi\) | |||||||
\(360\) | 3.82306 | 0.201493 | ||||||||
\(361\) | −14.3847 | −0.757090 | ||||||||
\(362\) | 8.79467 | 0.462238 | ||||||||
\(363\) | 8.50156 | 0.446216 | ||||||||
\(364\) | 13.6297 | 0.714390 | ||||||||
\(365\) | −50.5161 | −2.64414 | ||||||||
\(366\) | 12.6545 | 0.661460 | ||||||||
\(367\) | 16.2735 | 0.849467 | 0.424734 | − | 0.905318i | \(-0.360368\pi\) | ||||
0.424734 | + | 0.905318i | \(0.360368\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.3972 | −0.541259 | ||||||||
\(370\) | 18.4226 | 0.957746 | ||||||||
\(371\) | −29.8296 | −1.54868 | ||||||||
\(372\) | −0.170752 | −0.00885310 | ||||||||
\(373\) | 6.97489 | 0.361146 | 0.180573 | − | 0.983562i | \(-0.442205\pi\) | ||||
0.180573 | + | 0.983562i | \(0.442205\pi\) | |||||||
\(374\) | 7.48878 | 0.387236 | ||||||||
\(375\) | −17.6464 | −0.911255 | ||||||||
\(376\) | 5.45520 | 0.281331 | ||||||||
\(377\) | −2.77133 | −0.142731 | ||||||||
\(378\) | −2.89389 | −0.148846 | ||||||||
\(379\) | 16.5116 | 0.848143 | 0.424072 | − | 0.905629i | \(-0.360600\pi\) | ||||
0.424072 | + | 0.905629i | \(0.360600\pi\) | |||||||
\(380\) | 8.21316 | 0.421326 | ||||||||
\(381\) | 7.58758 | 0.388724 | ||||||||
\(382\) | −6.33200 | −0.323973 | ||||||||
\(383\) | −22.3879 | −1.14397 | −0.571984 | − | 0.820265i | \(-0.693826\pi\) | ||||
−0.571984 | + | 0.820265i | \(0.693826\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −17.4875 | −0.891247 | ||||||||
\(386\) | −3.07385 | −0.156455 | ||||||||
\(387\) | 12.2681 | 0.623622 | ||||||||
\(388\) | 0.873537 | 0.0443471 | ||||||||
\(389\) | −7.54227 | −0.382408 | −0.191204 | − | 0.981550i | \(-0.561239\pi\) | ||||
−0.191204 | + | 0.981550i | \(0.561239\pi\) | |||||||
\(390\) | −18.0059 | −0.911763 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 1.37462 | 0.0694290 | ||||||||
\(393\) | −17.8085 | −0.898322 | ||||||||
\(394\) | −0.963415 | −0.0485361 | ||||||||
\(395\) | 44.6707 | 2.24763 | ||||||||
\(396\) | −1.58065 | −0.0794305 | ||||||||
\(397\) | 28.7582 | 1.44333 | 0.721665 | − | 0.692242i | \(-0.243377\pi\) | ||||
0.721665 | + | 0.692242i | \(0.243377\pi\) | |||||||
\(398\) | 3.27328 | 0.164075 | ||||||||
\(399\) | −6.21702 | −0.311240 | ||||||||
\(400\) | 9.61578 | 0.480789 | ||||||||
\(401\) | 6.81566 | 0.340358 | 0.170179 | − | 0.985413i | \(-0.445565\pi\) | ||||
0.170179 | + | 0.985413i | \(0.445565\pi\) | |||||||
\(402\) | −5.87608 | −0.293072 | ||||||||
\(403\) | 0.804211 | 0.0400606 | ||||||||
\(404\) | −10.9103 | −0.542807 | ||||||||
\(405\) | 3.82306 | 0.189969 | ||||||||
\(406\) | −1.70282 | −0.0845094 | ||||||||
\(407\) | −7.61684 | −0.377553 | ||||||||
\(408\) | 4.73780 | 0.234556 | ||||||||
\(409\) | −27.7947 | −1.37436 | −0.687179 | − | 0.726488i | \(-0.741151\pi\) | ||||
−0.687179 | + | 0.726488i | \(0.741151\pi\) | |||||||
\(410\) | −39.7493 | −1.96308 | ||||||||
\(411\) | 0.762968 | 0.0376344 | ||||||||
\(412\) | 3.69279 | 0.181931 | ||||||||
\(413\) | −5.50628 | −0.270947 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.432953 | −0.0212528 | ||||||||
\(416\) | 4.70981 | 0.230917 | ||||||||
\(417\) | −9.22612 | −0.451805 | ||||||||
\(418\) | −3.39574 | −0.166091 | ||||||||
\(419\) | −15.1417 | −0.739718 | −0.369859 | − | 0.929088i | \(-0.620594\pi\) | ||||
−0.369859 | + | 0.929088i | \(0.620594\pi\) | |||||||
\(420\) | −11.0635 | −0.539845 | ||||||||
\(421\) | 38.1445 | 1.85905 | 0.929524 | − | 0.368762i | \(-0.120218\pi\) | ||||
0.929524 | + | 0.368762i | \(0.120218\pi\) | |||||||
\(422\) | −24.4174 | −1.18862 | ||||||||
\(423\) | 5.45520 | 0.265241 | ||||||||
\(424\) | −10.3078 | −0.500590 | ||||||||
\(425\) | −45.5576 | −2.20987 | ||||||||
\(426\) | 11.8216 | 0.572759 | ||||||||
\(427\) | −36.6207 | −1.77220 | ||||||||
\(428\) | 10.7665 | 0.520416 | ||||||||
\(429\) | 7.44454 | 0.359426 | ||||||||
\(430\) | 46.9016 | 2.26180 | ||||||||
\(431\) | 10.2138 | 0.491981 | 0.245991 | − | 0.969272i | \(-0.420887\pi\) | ||||
0.245991 | + | 0.969272i | \(0.420887\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −9.82271 | −0.472049 | −0.236025 | − | 0.971747i | \(-0.575845\pi\) | ||||
−0.236025 | + | 0.971747i | \(0.575845\pi\) | |||||||
\(434\) | 0.494139 | 0.0237194 | ||||||||
\(435\) | 2.24955 | 0.107858 | ||||||||
\(436\) | −8.31357 | −0.398148 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 13.2135 | 0.631367 | ||||||||
\(439\) | −7.79601 | −0.372083 | −0.186042 | − | 0.982542i | \(-0.559566\pi\) | ||||
−0.186042 | + | 0.982542i | \(0.559566\pi\) | |||||||
\(440\) | −6.04290 | −0.288084 | ||||||||
\(441\) | 1.37462 | 0.0654583 | ||||||||
\(442\) | −22.3141 | −1.06138 | ||||||||
\(443\) | −28.2208 | −1.34081 | −0.670406 | − | 0.741994i | \(-0.733880\pi\) | ||||
−0.670406 | + | 0.741994i | \(0.733880\pi\) | |||||||
\(444\) | −4.81881 | −0.228691 | ||||||||
\(445\) | −46.7890 | −2.21801 | ||||||||
\(446\) | 15.1991 | 0.719699 | ||||||||
\(447\) | −18.4911 | −0.874598 | ||||||||
\(448\) | 2.89389 | 0.136724 | ||||||||
\(449\) | −12.7574 | −0.602061 | −0.301030 | − | 0.953615i | \(-0.597331\pi\) | ||||
−0.301030 | + | 0.953615i | \(0.597331\pi\) | |||||||
\(450\) | 9.61578 | 0.453292 | ||||||||
\(451\) | 16.4344 | 0.773864 | ||||||||
\(452\) | 7.51278 | 0.353372 | ||||||||
\(453\) | 0.991887 | 0.0466029 | ||||||||
\(454\) | 12.9325 | 0.606950 | ||||||||
\(455\) | 52.1071 | 2.44282 | ||||||||
\(456\) | −2.14832 | −0.100604 | ||||||||
\(457\) | 9.37038 | 0.438328 | 0.219164 | − | 0.975688i | \(-0.429667\pi\) | ||||
0.219164 | + | 0.975688i | \(0.429667\pi\) | |||||||
\(458\) | −0.948502 | −0.0443206 | ||||||||
\(459\) | 4.73780 | 0.221142 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.6569 | −0.542916 | −0.271458 | − | 0.962450i | \(-0.587506\pi\) | ||||
−0.271458 | + | 0.962450i | \(0.587506\pi\) | |||||||
\(462\) | 4.57422 | 0.212812 | ||||||||
\(463\) | 13.6279 | 0.633341 | 0.316670 | − | 0.948536i | \(-0.397435\pi\) | ||||
0.316670 | + | 0.948536i | \(0.397435\pi\) | |||||||
\(464\) | −0.588417 | −0.0273166 | ||||||||
\(465\) | −0.652796 | −0.0302727 | ||||||||
\(466\) | 13.9482 | 0.646139 | ||||||||
\(467\) | 6.57700 | 0.304347 | 0.152174 | − | 0.988354i | \(-0.451373\pi\) | ||||
0.152174 | + | 0.988354i | \(0.451373\pi\) | |||||||
\(468\) | 4.70981 | 0.217711 | ||||||||
\(469\) | 17.0048 | 0.785207 | ||||||||
\(470\) | 20.8556 | 0.961995 | ||||||||
\(471\) | −8.10972 | −0.373676 | ||||||||
\(472\) | −1.90272 | −0.0875800 | ||||||||
\(473\) | −19.3915 | −0.891622 | ||||||||
\(474\) | −11.6845 | −0.536689 | ||||||||
\(475\) | 20.6578 | 0.947845 | ||||||||
\(476\) | −13.7107 | −0.628428 | ||||||||
\(477\) | −10.3078 | −0.471961 | ||||||||
\(478\) | −2.44329 | −0.111754 | ||||||||
\(479\) | 9.24047 | 0.422208 | 0.211104 | − | 0.977464i | \(-0.432294\pi\) | ||||
0.211104 | + | 0.977464i | \(0.432294\pi\) | |||||||
\(480\) | −3.82306 | −0.174498 | ||||||||
\(481\) | 22.6957 | 1.03483 | ||||||||
\(482\) | 10.8636 | 0.494822 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.50156 | −0.386434 | ||||||||
\(485\) | 3.33958 | 0.151643 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −38.0246 | −1.72306 | −0.861529 | − | 0.507708i | \(-0.830493\pi\) | ||||
−0.861529 | + | 0.507708i | \(0.830493\pi\) | |||||||
\(488\) | −12.6545 | −0.572841 | ||||||||
\(489\) | 23.0759 | 1.04353 | ||||||||
\(490\) | 5.25527 | 0.237409 | ||||||||
\(491\) | −4.28664 | −0.193453 | −0.0967267 | − | 0.995311i | \(-0.530837\pi\) | ||||
−0.0967267 | + | 0.995311i | \(0.530837\pi\) | |||||||
\(492\) | 10.3972 | 0.468744 | ||||||||
\(493\) | 2.78780 | 0.125556 | ||||||||
\(494\) | 10.1182 | 0.455239 | ||||||||
\(495\) | −6.04290 | −0.271608 | ||||||||
\(496\) | 0.170752 | 0.00766701 | ||||||||
\(497\) | −34.2105 | −1.53455 | ||||||||
\(498\) | 0.113248 | 0.00507475 | ||||||||
\(499\) | −30.2794 | −1.35549 | −0.677746 | − | 0.735297i | \(-0.737043\pi\) | ||||
−0.677746 | + | 0.735297i | \(0.737043\pi\) | |||||||
\(500\) | 17.6464 | 0.789170 | ||||||||
\(501\) | 5.28482 | 0.236109 | ||||||||
\(502\) | −14.3211 | −0.639182 | ||||||||
\(503\) | 11.6641 | 0.520077 | 0.260038 | − | 0.965598i | \(-0.416265\pi\) | ||||
0.260038 | + | 0.965598i | \(0.416265\pi\) | |||||||
\(504\) | 2.89389 | 0.128904 | ||||||||
\(505\) | −41.7107 | −1.85610 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.18232 | −0.407801 | ||||||||
\(508\) | −7.58758 | −0.336645 | ||||||||
\(509\) | −15.3035 | −0.678317 | −0.339159 | − | 0.940729i | \(-0.610142\pi\) | ||||
−0.339159 | + | 0.940729i | \(0.610142\pi\) | |||||||
\(510\) | 18.1129 | 0.802052 | ||||||||
\(511\) | −38.2386 | −1.69158 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −2.14832 | −0.0948508 | ||||||||
\(514\) | −4.24430 | −0.187208 | ||||||||
\(515\) | 14.1178 | 0.622103 | ||||||||
\(516\) | −12.2681 | −0.540072 | ||||||||
\(517\) | −8.62274 | −0.379228 | ||||||||
\(518\) | 13.9451 | 0.612714 | ||||||||
\(519\) | −14.3906 | −0.631678 | ||||||||
\(520\) | 18.0059 | 0.789610 | ||||||||
\(521\) | 1.93070 | 0.0845857 | 0.0422928 | − | 0.999105i | \(-0.486534\pi\) | ||||
0.0422928 | + | 0.999105i | \(0.486534\pi\) | |||||||
\(522\) | −0.588417 | −0.0257543 | ||||||||
\(523\) | −18.2743 | −0.799081 | −0.399540 | − | 0.916716i | \(-0.630830\pi\) | ||||
−0.399540 | + | 0.916716i | \(0.630830\pi\) | |||||||
\(524\) | 17.8085 | 0.777970 | ||||||||
\(525\) | −27.8270 | −1.21447 | ||||||||
\(526\) | −7.10375 | −0.309738 | ||||||||
\(527\) | −0.808991 | −0.0352402 | ||||||||
\(528\) | 1.58065 | 0.0687888 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | −39.4072 | −1.71174 | ||||||||
\(531\) | −1.90272 | −0.0825712 | ||||||||
\(532\) | 6.21702 | 0.269542 | ||||||||
\(533\) | −48.9691 | −2.12109 | ||||||||
\(534\) | 12.2386 | 0.529617 | ||||||||
\(535\) | 41.1608 | 1.77954 | ||||||||
\(536\) | 5.87608 | 0.253808 | ||||||||
\(537\) | −11.2001 | −0.483319 | ||||||||
\(538\) | −7.73235 | −0.333365 | ||||||||
\(539\) | −2.17279 | −0.0935888 | ||||||||
\(540\) | −3.82306 | −0.164518 | ||||||||
\(541\) | 44.4499 | 1.91105 | 0.955525 | − | 0.294910i | \(-0.0952898\pi\) | ||||
0.955525 | + | 0.294910i | \(0.0952898\pi\) | |||||||
\(542\) | −5.08058 | −0.218230 | ||||||||
\(543\) | −8.79467 | −0.377416 | ||||||||
\(544\) | −4.73780 | −0.203131 | ||||||||
\(545\) | −31.7833 | −1.36145 | ||||||||
\(546\) | −13.6297 | −0.583297 | ||||||||
\(547\) | 19.1076 | 0.816981 | 0.408490 | − | 0.912763i | \(-0.366055\pi\) | ||||
0.408490 | + | 0.912763i | \(0.366055\pi\) | |||||||
\(548\) | −0.762968 | −0.0325924 | ||||||||
\(549\) | −12.6545 | −0.540079 | ||||||||
\(550\) | −15.1991 | −0.648093 | ||||||||
\(551\) | −1.26411 | −0.0538529 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 33.8138 | 1.43791 | ||||||||
\(554\) | −15.3909 | −0.653898 | ||||||||
\(555\) | −18.4226 | −0.781996 | ||||||||
\(556\) | 9.22612 | 0.391275 | ||||||||
\(557\) | −44.0806 | −1.86776 | −0.933878 | − | 0.357591i | \(-0.883598\pi\) | ||||
−0.933878 | + | 0.357591i | \(0.883598\pi\) | |||||||
\(558\) | 0.170752 | 0.00722852 | ||||||||
\(559\) | 57.7804 | 2.44385 | ||||||||
\(560\) | 11.0635 | 0.467519 | ||||||||
\(561\) | −7.48878 | −0.316177 | ||||||||
\(562\) | −3.29958 | −0.139184 | ||||||||
\(563\) | 39.4399 | 1.66219 | 0.831096 | − | 0.556129i | \(-0.187714\pi\) | ||||
0.831096 | + | 0.556129i | \(0.187714\pi\) | |||||||
\(564\) | −5.45520 | −0.229705 | ||||||||
\(565\) | 28.7218 | 1.20834 | ||||||||
\(566\) | −25.8826 | −1.08793 | ||||||||
\(567\) | 2.89389 | 0.121532 | ||||||||
\(568\) | −11.8216 | −0.496024 | ||||||||
\(569\) | −38.3267 | −1.60674 | −0.803370 | − | 0.595480i | \(-0.796962\pi\) | ||||
−0.803370 | + | 0.595480i | \(0.796962\pi\) | |||||||
\(570\) | −8.21316 | −0.344012 | ||||||||
\(571\) | −16.9708 | −0.710204 | −0.355102 | − | 0.934828i | \(-0.615554\pi\) | ||||
−0.355102 | + | 0.934828i | \(0.615554\pi\) | |||||||
\(572\) | −7.44454 | −0.311272 | ||||||||
\(573\) | 6.33200 | 0.264523 | ||||||||
\(574\) | −30.0885 | −1.25587 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −29.1794 | −1.21475 | −0.607377 | − | 0.794414i | \(-0.707778\pi\) | ||||
−0.607377 | + | 0.794414i | \(0.707778\pi\) | |||||||
\(578\) | 5.44675 | 0.226555 | ||||||||
\(579\) | 3.07385 | 0.127745 | ||||||||
\(580\) | −2.24955 | −0.0934077 | ||||||||
\(581\) | −0.327727 | −0.0135964 | ||||||||
\(582\) | −0.873537 | −0.0362093 | ||||||||
\(583\) | 16.2929 | 0.674785 | ||||||||
\(584\) | −13.2135 | −0.546780 | ||||||||
\(585\) | 18.0059 | 0.744452 | ||||||||
\(586\) | 6.52568 | 0.269573 | ||||||||
\(587\) | −15.1816 | −0.626613 | −0.313306 | − | 0.949652i | \(-0.601437\pi\) | ||||
−0.313306 | + | 0.949652i | \(0.601437\pi\) | |||||||
\(588\) | −1.37462 | −0.0566885 | ||||||||
\(589\) | 0.366831 | 0.0151150 | ||||||||
\(590\) | −7.27423 | −0.299475 | ||||||||
\(591\) | 0.963415 | 0.0396296 | ||||||||
\(592\) | 4.81881 | 0.198052 | ||||||||
\(593\) | −31.2609 | −1.28373 | −0.641865 | − | 0.766817i | \(-0.721839\pi\) | ||||
−0.641865 | + | 0.766817i | \(0.721839\pi\) | |||||||
\(594\) | 1.58065 | 0.0648547 | ||||||||
\(595\) | −52.4168 | −2.14888 | ||||||||
\(596\) | 18.4911 | 0.757424 | ||||||||
\(597\) | −3.27328 | −0.133967 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.8576 | −1.26081 | −0.630405 | − | 0.776267i | \(-0.717111\pi\) | ||||
−0.630405 | + | 0.776267i | \(0.717111\pi\) | |||||||
\(600\) | −9.61578 | −0.392562 | ||||||||
\(601\) | 6.62774 | 0.270351 | 0.135176 | − | 0.990822i | \(-0.456840\pi\) | ||||
0.135176 | + | 0.990822i | \(0.456840\pi\) | |||||||
\(602\) | 35.5025 | 1.44698 | ||||||||
\(603\) | 5.87608 | 0.239293 | ||||||||
\(604\) | −0.991887 | −0.0403593 | ||||||||
\(605\) | −32.5020 | −1.32139 | ||||||||
\(606\) | 10.9103 | 0.443200 | ||||||||
\(607\) | −23.5777 | −0.956991 | −0.478495 | − | 0.878090i | \(-0.658818\pi\) | ||||
−0.478495 | + | 0.878090i | \(0.658818\pi\) | |||||||
\(608\) | 2.14832 | 0.0871260 | ||||||||
\(609\) | 1.70282 | 0.0690017 | ||||||||
\(610\) | −48.3788 | −1.95880 | ||||||||
\(611\) | 25.6930 | 1.03943 | ||||||||
\(612\) | −4.73780 | −0.191514 | ||||||||
\(613\) | −32.5703 | −1.31550 | −0.657750 | − | 0.753236i | \(-0.728492\pi\) | ||||
−0.657750 | + | 0.753236i | \(0.728492\pi\) | |||||||
\(614\) | 4.61726 | 0.186338 | ||||||||
\(615\) | 39.7493 | 1.60285 | ||||||||
\(616\) | −4.57422 | −0.184301 | ||||||||
\(617\) | −6.00021 | −0.241559 | −0.120780 | − | 0.992679i | \(-0.538539\pi\) | ||||
−0.120780 | + | 0.992679i | \(0.538539\pi\) | |||||||
\(618\) | −3.69279 | −0.148546 | ||||||||
\(619\) | −12.8869 | −0.517968 | −0.258984 | − | 0.965882i | \(-0.583388\pi\) | ||||
−0.258984 | + | 0.965882i | \(0.583388\pi\) | |||||||
\(620\) | 0.652796 | 0.0262169 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −10.7400 | −0.430636 | ||||||||
\(623\) | −35.4173 | −1.41896 | ||||||||
\(624\) | −4.70981 | −0.188543 | ||||||||
\(625\) | 19.3843 | 0.775371 | ||||||||
\(626\) | 26.6899 | 1.06674 | ||||||||
\(627\) | 3.39574 | 0.135613 | ||||||||
\(628\) | 8.10972 | 0.323613 | ||||||||
\(629\) | −22.8306 | −0.910315 | ||||||||
\(630\) | 11.0635 | 0.440781 | ||||||||
\(631\) | 21.4418 | 0.853585 | 0.426792 | − | 0.904350i | \(-0.359644\pi\) | ||||
0.426792 | + | 0.904350i | \(0.359644\pi\) | |||||||
\(632\) | 11.6845 | 0.464786 | ||||||||
\(633\) | 24.4174 | 0.970506 | ||||||||
\(634\) | 19.1814 | 0.761791 | ||||||||
\(635\) | −29.0078 | −1.15114 | ||||||||
\(636\) | 10.3078 | 0.408730 | ||||||||
\(637\) | 6.47422 | 0.256518 | ||||||||
\(638\) | 0.930080 | 0.0368222 | ||||||||
\(639\) | −11.8216 | −0.467655 | ||||||||
\(640\) | 3.82306 | 0.151120 | ||||||||
\(641\) | 30.7587 | 1.21489 | 0.607447 | − | 0.794360i | \(-0.292194\pi\) | ||||
0.607447 | + | 0.794360i | \(0.292194\pi\) | |||||||
\(642\) | −10.7665 | −0.424918 | ||||||||
\(643\) | 28.7980 | 1.13568 | 0.567842 | − | 0.823138i | \(-0.307778\pi\) | ||||
0.567842 | + | 0.823138i | \(0.307778\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −46.9016 | −1.84675 | ||||||||
\(646\) | −10.1783 | −0.400461 | ||||||||
\(647\) | −20.8594 | −0.820069 | −0.410035 | − | 0.912070i | \(-0.634483\pi\) | ||||
−0.410035 | + | 0.912070i | \(0.634483\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 3.00753 | 0.118056 | ||||||||
\(650\) | 45.2885 | 1.77636 | ||||||||
\(651\) | −0.494139 | −0.0193668 | ||||||||
\(652\) | −23.0759 | −0.903724 | ||||||||
\(653\) | 26.5838 | 1.04031 | 0.520153 | − | 0.854073i | \(-0.325875\pi\) | ||||
0.520153 | + | 0.854073i | \(0.325875\pi\) | |||||||
\(654\) | 8.31357 | 0.325086 | ||||||||
\(655\) | 68.0831 | 2.66023 | ||||||||
\(656\) | −10.3972 | −0.405944 | ||||||||
\(657\) | −13.2135 | −0.515509 | ||||||||
\(658\) | 15.7868 | 0.615433 | ||||||||
\(659\) | −27.4167 | −1.06800 | −0.534002 | − | 0.845483i | \(-0.679313\pi\) | ||||
−0.534002 | + | 0.845483i | \(0.679313\pi\) | |||||||
\(660\) | 6.04290 | 0.235220 | ||||||||
\(661\) | 8.13934 | 0.316583 | 0.158292 | − | 0.987392i | \(-0.449401\pi\) | ||||
0.158292 | + | 0.987392i | \(0.449401\pi\) | |||||||
\(662\) | 8.74066 | 0.339715 | ||||||||
\(663\) | 22.3141 | 0.866609 | ||||||||
\(664\) | −0.113248 | −0.00439486 | ||||||||
\(665\) | 23.7680 | 0.921685 | ||||||||
\(666\) | 4.81881 | 0.186725 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −5.28482 | −0.204476 | ||||||||
\(669\) | −15.1991 | −0.587632 | ||||||||
\(670\) | 22.4646 | 0.867884 | ||||||||
\(671\) | 20.0022 | 0.772178 | ||||||||
\(672\) | −2.89389 | −0.111634 | ||||||||
\(673\) | 31.0127 | 1.19545 | 0.597726 | − | 0.801700i | \(-0.296071\pi\) | ||||
0.597726 | + | 0.801700i | \(0.296071\pi\) | |||||||
\(674\) | −3.25394 | −0.125337 | ||||||||
\(675\) | −9.61578 | −0.370111 | ||||||||
\(676\) | 9.18232 | 0.353166 | ||||||||
\(677\) | −20.4045 | −0.784208 | −0.392104 | − | 0.919921i | \(-0.628253\pi\) | ||||
−0.392104 | + | 0.919921i | \(0.628253\pi\) | |||||||
\(678\) | −7.51278 | −0.288527 | ||||||||
\(679\) | 2.52792 | 0.0970128 | ||||||||
\(680\) | −18.1129 | −0.694597 | ||||||||
\(681\) | −12.9325 | −0.495573 | ||||||||
\(682\) | −0.269899 | −0.0103350 | ||||||||
\(683\) | 20.7857 | 0.795342 | 0.397671 | − | 0.917528i | \(-0.369819\pi\) | ||||
0.397671 | + | 0.917528i | \(0.369819\pi\) | |||||||
\(684\) | 2.14832 | 0.0821432 | ||||||||
\(685\) | −2.91687 | −0.111448 | ||||||||
\(686\) | −16.2792 | −0.621544 | ||||||||
\(687\) | 0.948502 | 0.0361876 | ||||||||
\(688\) | 12.2681 | 0.467716 | ||||||||
\(689\) | −48.5477 | −1.84952 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.6695 | −0.520012 | −0.260006 | − | 0.965607i | \(-0.583725\pi\) | ||||
−0.260006 | + | 0.965607i | \(0.583725\pi\) | |||||||
\(692\) | 14.3906 | 0.547049 | ||||||||
\(693\) | −4.57422 | −0.173760 | ||||||||
\(694\) | −5.21179 | −0.197837 | ||||||||
\(695\) | 35.2720 | 1.33794 | ||||||||
\(696\) | 0.588417 | 0.0223039 | ||||||||
\(697\) | 49.2601 | 1.86586 | ||||||||
\(698\) | 15.4731 | 0.585665 | ||||||||
\(699\) | −13.9482 | −0.527570 | ||||||||
\(700\) | 27.8270 | 1.05176 | ||||||||
\(701\) | −2.20983 | −0.0834641 | −0.0417320 | − | 0.999129i | \(-0.513288\pi\) | ||||
−0.0417320 | + | 0.999129i | \(0.513288\pi\) | |||||||
\(702\) | −4.70981 | −0.177760 | ||||||||
\(703\) | 10.3524 | 0.390447 | ||||||||
\(704\) | −1.58065 | −0.0595728 | ||||||||
\(705\) | −20.8556 | −0.785466 | ||||||||
\(706\) | −1.61663 | −0.0608428 | ||||||||
\(707\) | −31.5732 | −1.18743 | ||||||||
\(708\) | 1.90272 | 0.0715088 | ||||||||
\(709\) | −18.7677 | −0.704837 | −0.352418 | − | 0.935843i | \(-0.614641\pi\) | ||||
−0.352418 | + | 0.935843i | \(0.614641\pi\) | |||||||
\(710\) | −45.1947 | −1.69613 | ||||||||
\(711\) | 11.6845 | 0.438204 | ||||||||
\(712\) | −12.2386 | −0.458662 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 13.7107 | 0.513110 | ||||||||
\(715\) | −28.4609 | −1.06438 | ||||||||
\(716\) | 11.2001 | 0.418566 | ||||||||
\(717\) | 2.44329 | 0.0912465 | ||||||||
\(718\) | 13.5579 | 0.505978 | ||||||||
\(719\) | 20.6700 | 0.770862 | 0.385431 | − | 0.922737i | \(-0.374053\pi\) | ||||
0.385431 | + | 0.922737i | \(0.374053\pi\) | |||||||
\(720\) | 3.82306 | 0.142477 | ||||||||
\(721\) | 10.6865 | 0.397988 | ||||||||
\(722\) | −14.3847 | −0.535343 | ||||||||
\(723\) | −10.8636 | −0.404021 | ||||||||
\(724\) | 8.79467 | 0.326852 | ||||||||
\(725\) | −5.65809 | −0.210136 | ||||||||
\(726\) | 8.50156 | 0.315522 | ||||||||
\(727\) | −31.5454 | −1.16996 | −0.584978 | − | 0.811049i | \(-0.698897\pi\) | ||||
−0.584978 | + | 0.811049i | \(0.698897\pi\) | |||||||
\(728\) | 13.6297 | 0.505150 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −50.5161 | −1.86969 | ||||||||
\(731\) | −58.1237 | −2.14978 | ||||||||
\(732\) | 12.6545 | 0.467723 | ||||||||
\(733\) | −24.4270 | −0.902232 | −0.451116 | − | 0.892465i | \(-0.648974\pi\) | ||||
−0.451116 | + | 0.892465i | \(0.648974\pi\) | |||||||
\(734\) | 16.2735 | 0.600664 | ||||||||
\(735\) | −5.25527 | −0.193843 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.28801 | −0.342128 | ||||||||
\(738\) | −10.3972 | −0.382728 | ||||||||
\(739\) | −42.1528 | −1.55062 | −0.775308 | − | 0.631583i | \(-0.782405\pi\) | ||||
−0.775308 | + | 0.631583i | \(0.782405\pi\) | |||||||
\(740\) | 18.4226 | 0.677229 | ||||||||
\(741\) | −10.1182 | −0.371701 | ||||||||
\(742\) | −29.8296 | −1.09508 | ||||||||
\(743\) | 2.98913 | 0.109661 | 0.0548303 | − | 0.998496i | \(-0.482538\pi\) | ||||
0.0548303 | + | 0.998496i | \(0.482538\pi\) | |||||||
\(744\) | −0.170752 | −0.00626009 | ||||||||
\(745\) | 70.6925 | 2.58997 | ||||||||
\(746\) | 6.97489 | 0.255369 | ||||||||
\(747\) | −0.113248 | −0.00414352 | ||||||||
\(748\) | 7.48878 | 0.273817 | ||||||||
\(749\) | 31.1570 | 1.13845 | ||||||||
\(750\) | −17.6464 | −0.644355 | ||||||||
\(751\) | 39.2254 | 1.43135 | 0.715677 | − | 0.698431i | \(-0.246118\pi\) | ||||
0.715677 | + | 0.698431i | \(0.246118\pi\) | |||||||
\(752\) | 5.45520 | 0.198931 | ||||||||
\(753\) | 14.3211 | 0.521890 | ||||||||
\(754\) | −2.77133 | −0.100926 | ||||||||
\(755\) | −3.79204 | −0.138007 | ||||||||
\(756\) | −2.89389 | −0.105250 | ||||||||
\(757\) | −47.4506 | −1.72462 | −0.862311 | − | 0.506379i | \(-0.830984\pi\) | ||||
−0.862311 | + | 0.506379i | \(0.830984\pi\) | |||||||
\(758\) | 16.5116 | 0.599728 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 8.21316 | 0.297923 | ||||||||
\(761\) | −30.7455 | −1.11452 | −0.557261 | − | 0.830337i | \(-0.688148\pi\) | ||||
−0.557261 | + | 0.830337i | \(0.688148\pi\) | |||||||
\(762\) | 7.58758 | 0.274869 | ||||||||
\(763\) | −24.0586 | −0.870980 | ||||||||
\(764\) | −6.33200 | −0.229084 | ||||||||
\(765\) | −18.1129 | −0.654873 | ||||||||
\(766\) | −22.3879 | −0.808907 | ||||||||
\(767\) | −8.96147 | −0.323580 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −32.4747 | −1.17107 | −0.585533 | − | 0.810648i | \(-0.699115\pi\) | ||||
−0.585533 | + | 0.810648i | \(0.699115\pi\) | |||||||
\(770\) | −17.4875 | −0.630206 | ||||||||
\(771\) | 4.24430 | 0.152855 | ||||||||
\(772\) | −3.07385 | −0.110630 | ||||||||
\(773\) | 12.4335 | 0.447202 | 0.223601 | − | 0.974681i | \(-0.428219\pi\) | ||||
0.223601 | + | 0.974681i | \(0.428219\pi\) | |||||||
\(774\) | 12.2681 | 0.440967 | ||||||||
\(775\) | 1.64192 | 0.0589794 | ||||||||
\(776\) | 0.873537 | 0.0313582 | ||||||||
\(777\) | −13.9451 | −0.500279 | ||||||||
\(778\) | −7.54227 | −0.270403 | ||||||||
\(779\) | −22.3366 | −0.800293 | ||||||||
\(780\) | −18.0059 | −0.644714 | ||||||||
\(781\) | 18.6858 | 0.668629 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.588417 | 0.0210283 | ||||||||
\(784\) | 1.37462 | 0.0490937 | ||||||||
\(785\) | 31.0039 | 1.10658 | ||||||||
\(786\) | −17.8085 | −0.635210 | ||||||||
\(787\) | −4.10539 | −0.146341 | −0.0731707 | − | 0.997319i | \(-0.523312\pi\) | ||||
−0.0731707 | + | 0.997319i | \(0.523312\pi\) | |||||||
\(788\) | −0.963415 | −0.0343202 | ||||||||
\(789\) | 7.10375 | 0.252900 | ||||||||
\(790\) | 44.6707 | 1.58931 | ||||||||
\(791\) | 21.7412 | 0.773028 | ||||||||
\(792\) | −1.58065 | −0.0561658 | ||||||||
\(793\) | −59.6001 | −2.11646 | ||||||||
\(794\) | 28.7582 | 1.02059 | ||||||||
\(795\) | 39.4072 | 1.39763 | ||||||||
\(796\) | 3.27328 | 0.116018 | ||||||||
\(797\) | −38.6182 | −1.36793 | −0.683963 | − | 0.729517i | \(-0.739745\pi\) | ||||
−0.683963 | + | 0.729517i | \(0.739745\pi\) | |||||||
\(798\) | −6.21702 | −0.220080 | ||||||||
\(799\) | −25.8457 | −0.914354 | ||||||||
\(800\) | 9.61578 | 0.339969 | ||||||||
\(801\) | −12.2386 | −0.432431 | ||||||||
\(802\) | 6.81566 | 0.240669 | ||||||||
\(803\) | 20.8859 | 0.737048 | ||||||||
\(804\) | −5.87608 | −0.207233 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.804211 | 0.0283271 | ||||||||
\(807\) | 7.73235 | 0.272191 | ||||||||
\(808\) | −10.9103 | −0.383822 | ||||||||
\(809\) | 36.8332 | 1.29499 | 0.647494 | − | 0.762071i | \(-0.275817\pi\) | ||||
0.647494 | + | 0.762071i | \(0.275817\pi\) | |||||||
\(810\) | 3.82306 | 0.134329 | ||||||||
\(811\) | −44.7013 | −1.56968 | −0.784838 | − | 0.619701i | \(-0.787254\pi\) | ||||
−0.784838 | + | 0.619701i | \(0.787254\pi\) | |||||||
\(812\) | −1.70282 | −0.0597572 | ||||||||
\(813\) | 5.08058 | 0.178184 | ||||||||
\(814\) | −7.61684 | −0.266970 | ||||||||
\(815\) | −88.2207 | −3.09024 | ||||||||
\(816\) | 4.73780 | 0.165856 | ||||||||
\(817\) | 26.3558 | 0.922073 | ||||||||
\(818\) | −27.7947 | −0.971818 | ||||||||
\(819\) | 13.6297 | 0.476260 | ||||||||
\(820\) | −39.7493 | −1.38811 | ||||||||
\(821\) | 37.2008 | 1.29832 | 0.649159 | − | 0.760653i | \(-0.275121\pi\) | ||||
0.649159 | + | 0.760653i | \(0.275121\pi\) | |||||||
\(822\) | 0.762968 | 0.0266116 | ||||||||
\(823\) | 41.0413 | 1.43061 | 0.715304 | − | 0.698813i | \(-0.246288\pi\) | ||||
0.715304 | + | 0.698813i | \(0.246288\pi\) | |||||||
\(824\) | 3.69279 | 0.128645 | ||||||||
\(825\) | 15.1991 | 0.529166 | ||||||||
\(826\) | −5.50628 | −0.191588 | ||||||||
\(827\) | 6.42848 | 0.223540 | 0.111770 | − | 0.993734i | \(-0.464348\pi\) | ||||
0.111770 | + | 0.993734i | \(0.464348\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.8721 | 0.551262 | 0.275631 | − | 0.961264i | \(-0.411113\pi\) | ||||
0.275631 | + | 0.961264i | \(0.411113\pi\) | |||||||
\(830\) | −0.432953 | −0.0150280 | ||||||||
\(831\) | 15.3909 | 0.533905 | ||||||||
\(832\) | 4.70981 | 0.163283 | ||||||||
\(833\) | −6.51269 | −0.225651 | ||||||||
\(834\) | −9.22612 | −0.319474 | ||||||||
\(835\) | −20.2042 | −0.699195 | ||||||||
\(836\) | −3.39574 | −0.117444 | ||||||||
\(837\) | −0.170752 | −0.00590207 | ||||||||
\(838\) | −15.1417 | −0.523060 | ||||||||
\(839\) | 10.4265 | 0.359963 | 0.179981 | − | 0.983670i | \(-0.442396\pi\) | ||||
0.179981 | + | 0.983670i | \(0.442396\pi\) | |||||||
\(840\) | −11.0635 | −0.381728 | ||||||||
\(841\) | −28.6538 | −0.988061 | ||||||||
\(842\) | 38.1445 | 1.31455 | ||||||||
\(843\) | 3.29958 | 0.113643 | ||||||||
\(844\) | −24.4174 | −0.840483 | ||||||||
\(845\) | 35.1045 | 1.20763 | ||||||||
\(846\) | 5.45520 | 0.187554 | ||||||||
\(847\) | −24.6026 | −0.845356 | ||||||||
\(848\) | −10.3078 | −0.353971 | ||||||||
\(849\) | 25.8826 | 0.888289 | ||||||||
\(850\) | −45.5576 | −1.56261 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 11.8216 | 0.405001 | ||||||||
\(853\) | 26.2935 | 0.900271 | 0.450135 | − | 0.892960i | \(-0.351376\pi\) | ||||
0.450135 | + | 0.892960i | \(0.351376\pi\) | |||||||
\(854\) | −36.6207 | −1.25313 | ||||||||
\(855\) | 8.21316 | 0.280884 | ||||||||
\(856\) | 10.7665 | 0.367990 | ||||||||
\(857\) | 32.4336 | 1.10791 | 0.553955 | − | 0.832547i | \(-0.313118\pi\) | ||||
0.553955 | + | 0.832547i | \(0.313118\pi\) | |||||||
\(858\) | 7.44454 | 0.254153 | ||||||||
\(859\) | −55.1643 | −1.88218 | −0.941091 | − | 0.338154i | \(-0.890198\pi\) | ||||
−0.941091 | + | 0.338154i | \(0.890198\pi\) | |||||||
\(860\) | 46.9016 | 1.59933 | ||||||||
\(861\) | 30.0885 | 1.02541 | ||||||||
\(862\) | 10.2138 | 0.347883 | ||||||||
\(863\) | 18.2143 | 0.620023 | 0.310012 | − | 0.950733i | \(-0.399667\pi\) | ||||
0.310012 | + | 0.950733i | \(0.399667\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 55.0161 | 1.87060 | ||||||||
\(866\) | −9.82271 | −0.333789 | ||||||||
\(867\) | −5.44675 | −0.184981 | ||||||||
\(868\) | 0.494139 | 0.0167722 | ||||||||
\(869\) | −18.4691 | −0.626522 | ||||||||
\(870\) | 2.24955 | 0.0762670 | ||||||||
\(871\) | 27.6752 | 0.937740 | ||||||||
\(872\) | −8.31357 | −0.281533 | ||||||||
\(873\) | 0.873537 | 0.0295648 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 51.0668 | 1.72637 | ||||||||
\(876\) | 13.2135 | 0.446444 | ||||||||
\(877\) | −28.7970 | −0.972407 | −0.486203 | − | 0.873846i | \(-0.661619\pi\) | ||||
−0.486203 | + | 0.873846i | \(0.661619\pi\) | |||||||
\(878\) | −7.79601 | −0.263103 | ||||||||
\(879\) | −6.52568 | −0.220106 | ||||||||
\(880\) | −6.04290 | −0.203706 | ||||||||
\(881\) | −21.0631 | −0.709633 | −0.354816 | − | 0.934936i | \(-0.615457\pi\) | ||||
−0.354816 | + | 0.934936i | \(0.615457\pi\) | |||||||
\(882\) | 1.37462 | 0.0462860 | ||||||||
\(883\) | −14.1593 | −0.476498 | −0.238249 | − | 0.971204i | \(-0.576573\pi\) | ||||
−0.238249 | + | 0.971204i | \(0.576573\pi\) | |||||||
\(884\) | −22.3141 | −0.750506 | ||||||||
\(885\) | 7.27423 | 0.244521 | ||||||||
\(886\) | −28.2208 | −0.948098 | ||||||||
\(887\) | 57.5302 | 1.93167 | 0.965837 | − | 0.259150i | \(-0.0834424\pi\) | ||||
0.965837 | + | 0.259150i | \(0.0834424\pi\) | |||||||
\(888\) | −4.81881 | −0.161709 | ||||||||
\(889\) | −21.9577 | −0.736436 | ||||||||
\(890\) | −46.7890 | −1.56837 | ||||||||
\(891\) | −1.58065 | −0.0529536 | ||||||||
\(892\) | 15.1991 | 0.508904 | ||||||||
\(893\) | 11.7195 | 0.392179 | ||||||||
\(894\) | −18.4911 | −0.618434 | ||||||||
\(895\) | 42.8185 | 1.43127 | ||||||||
\(896\) | 2.89389 | 0.0966782 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −12.7574 | −0.425721 | ||||||||
\(899\) | −0.100474 | −0.00335098 | ||||||||
\(900\) | 9.61578 | 0.320526 | ||||||||
\(901\) | 48.8362 | 1.62697 | ||||||||
\(902\) | 16.4344 | 0.547205 | ||||||||
\(903\) | −35.5025 | −1.18145 | ||||||||
\(904\) | 7.51278 | 0.249871 | ||||||||
\(905\) | 33.6226 | 1.11765 | ||||||||
\(906\) | 0.991887 | 0.0329532 | ||||||||
\(907\) | 45.1699 | 1.49984 | 0.749921 | − | 0.661528i | \(-0.230092\pi\) | ||||
0.749921 | + | 0.661528i | \(0.230092\pi\) | |||||||
\(908\) | 12.9325 | 0.429179 | ||||||||
\(909\) | −10.9103 | −0.361871 | ||||||||
\(910\) | 52.1071 | 1.72733 | ||||||||
\(911\) | 24.4377 | 0.809656 | 0.404828 | − | 0.914393i | \(-0.367331\pi\) | ||||
0.404828 | + | 0.914393i | \(0.367331\pi\) | |||||||
\(912\) | −2.14832 | −0.0711381 | ||||||||
\(913\) | 0.179005 | 0.00592419 | ||||||||
\(914\) | 9.37038 | 0.309945 | ||||||||
\(915\) | 48.3788 | 1.59935 | ||||||||
\(916\) | −0.948502 | −0.0313394 | ||||||||
\(917\) | 51.5360 | 1.70187 | ||||||||
\(918\) | 4.73780 | 0.156371 | ||||||||
\(919\) | −1.40194 | −0.0462457 | −0.0231229 | − | 0.999733i | \(-0.507361\pi\) | ||||
−0.0231229 | + | 0.999733i | \(0.507361\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.61726 | −0.152144 | ||||||||
\(922\) | −11.6569 | −0.383899 | ||||||||
\(923\) | −55.6775 | −1.83265 | ||||||||
\(924\) | 4.57422 | 0.150481 | ||||||||
\(925\) | 46.3366 | 1.52354 | ||||||||
\(926\) | 13.6279 | 0.447840 | ||||||||
\(927\) | 3.69279 | 0.121287 | ||||||||
\(928\) | −0.588417 | −0.0193157 | ||||||||
\(929\) | −8.73879 | −0.286710 | −0.143355 | − | 0.989671i | \(-0.545789\pi\) | ||||
−0.143355 | + | 0.989671i | \(0.545789\pi\) | |||||||
\(930\) | −0.652796 | −0.0214060 | ||||||||
\(931\) | 2.95313 | 0.0967851 | ||||||||
\(932\) | 13.9482 | 0.456889 | ||||||||
\(933\) | 10.7400 | 0.351613 | ||||||||
\(934\) | 6.57700 | 0.215206 | ||||||||
\(935\) | 28.6301 | 0.936303 | ||||||||
\(936\) | 4.70981 | 0.153945 | ||||||||
\(937\) | 7.95252 | 0.259798 | 0.129899 | − | 0.991527i | \(-0.458535\pi\) | ||||
0.129899 | + | 0.991527i | \(0.458535\pi\) | |||||||
\(938\) | 17.0048 | 0.555225 | ||||||||
\(939\) | −26.6899 | −0.870992 | ||||||||
\(940\) | 20.8556 | 0.680233 | ||||||||
\(941\) | 20.7252 | 0.675622 | 0.337811 | − | 0.941214i | \(-0.390314\pi\) | ||||
0.337811 | + | 0.941214i | \(0.390314\pi\) | |||||||
\(942\) | −8.10972 | −0.264229 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −1.90272 | −0.0619284 | ||||||||
\(945\) | −11.0635 | −0.359897 | ||||||||
\(946\) | −19.3915 | −0.630472 | ||||||||
\(947\) | 54.9184 | 1.78461 | 0.892304 | − | 0.451435i | \(-0.149088\pi\) | ||||
0.892304 | + | 0.451435i | \(0.149088\pi\) | |||||||
\(948\) | −11.6845 | −0.379496 | ||||||||
\(949\) | −62.2333 | −2.02018 | ||||||||
\(950\) | 20.6578 | 0.670227 | ||||||||
\(951\) | −19.1814 | −0.622000 | ||||||||
\(952\) | −13.7107 | −0.444366 | ||||||||
\(953\) | 8.68947 | 0.281480 | 0.140740 | − | 0.990047i | \(-0.455052\pi\) | ||||
0.140740 | + | 0.990047i | \(0.455052\pi\) | |||||||
\(954\) | −10.3078 | −0.333727 | ||||||||
\(955\) | −24.2076 | −0.783340 | ||||||||
\(956\) | −2.44329 | −0.0790217 | ||||||||
\(957\) | −0.930080 | −0.0300652 | ||||||||
\(958\) | 9.24047 | 0.298546 | ||||||||
\(959\) | −2.20795 | −0.0712984 | ||||||||
\(960\) | −3.82306 | −0.123389 | ||||||||
\(961\) | −30.9708 | −0.999059 | ||||||||
\(962\) | 22.6957 | 0.731739 | ||||||||
\(963\) | 10.7665 | 0.346944 | ||||||||
\(964\) | 10.8636 | 0.349892 | ||||||||
\(965\) | −11.7515 | −0.378295 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39.3485 | 1.26536 | 0.632681 | − | 0.774412i | \(-0.281954\pi\) | ||||
0.632681 | + | 0.774412i | \(0.281954\pi\) | |||||||
\(968\) | −8.50156 | −0.273250 | ||||||||
\(969\) | 10.1783 | 0.326975 | ||||||||
\(970\) | 3.33958 | 0.107228 | ||||||||
\(971\) | −16.1185 | −0.517268 | −0.258634 | − | 0.965975i | \(-0.583272\pi\) | ||||
−0.258634 | + | 0.965975i | \(0.583272\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 26.6994 | 0.855944 | ||||||||
\(974\) | −38.0246 | −1.21839 | ||||||||
\(975\) | −45.2885 | −1.45039 | ||||||||
\(976\) | −12.6545 | −0.405060 | ||||||||
\(977\) | −35.5575 | −1.13758 | −0.568792 | − | 0.822482i | \(-0.692589\pi\) | ||||
−0.568792 | + | 0.822482i | \(0.692589\pi\) | |||||||
\(978\) | 23.0759 | 0.737887 | ||||||||
\(979\) | 19.3449 | 0.618267 | ||||||||
\(980\) | 5.25527 | 0.167873 | ||||||||
\(981\) | −8.31357 | −0.265432 | ||||||||
\(982\) | −4.28664 | −0.136792 | ||||||||
\(983\) | −54.6156 | −1.74197 | −0.870984 | − | 0.491311i | \(-0.836518\pi\) | ||||
−0.870984 | + | 0.491311i | \(0.836518\pi\) | |||||||
\(984\) | 10.3972 | 0.331452 | ||||||||
\(985\) | −3.68319 | −0.117356 | ||||||||
\(986\) | 2.78780 | 0.0887818 | ||||||||
\(987\) | −15.7868 | −0.502499 | ||||||||
\(988\) | 10.1182 | 0.321903 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −6.04290 | −0.192056 | ||||||||
\(991\) | 26.8734 | 0.853663 | 0.426832 | − | 0.904331i | \(-0.359630\pi\) | ||||
0.426832 | + | 0.904331i | \(0.359630\pi\) | |||||||
\(992\) | 0.170752 | 0.00542139 | ||||||||
\(993\) | −8.74066 | −0.277376 | ||||||||
\(994\) | −34.2105 | −1.08509 | ||||||||
\(995\) | 12.5140 | 0.396719 | ||||||||
\(996\) | 0.113248 | 0.00358839 | ||||||||
\(997\) | −26.9729 | −0.854239 | −0.427119 | − | 0.904195i | \(-0.640472\pi\) | ||||
−0.427119 | + | 0.904195i | \(0.640472\pi\) | |||||||
\(998\) | −30.2794 | −0.958477 | ||||||||
\(999\) | −4.81881 | −0.152461 |
(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 | 3174.2.a.ba.1.5 | 5 | ||
3.2 | odd | 2 | 9522.2.a.bs.1.1 | 5 | |||
23.3 | even | 11 | 138.2.e.b.55.1 | ✓ | 10 | ||
23.8 | even | 11 | 138.2.e.b.133.1 | yes | 10 | ||
23.22 | odd | 2 | 3174.2.a.bb.1.1 | 5 | |||
69.8 | odd | 22 | 414.2.i.e.271.1 | 10 | |||
69.26 | odd | 22 | 414.2.i.e.55.1 | 10 | |||
69.68 | even | 2 | 9522.2.a.br.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
138.2.e.b.55.1 | ✓ | 10 | 23.3 | even | 11 | ||
138.2.e.b.133.1 | yes | 10 | 23.8 | even | 11 | ||
414.2.i.e.55.1 | 10 | 69.26 | odd | 22 | |||
414.2.i.e.271.1 | 10 | 69.8 | odd | 22 | |||
3174.2.a.ba.1.5 | 5 | 1.1 | even | 1 | trivial | ||
3174.2.a.bb.1.1 | 5 | 23.22 | odd | 2 | |||
9522.2.a.br.1.5 | 5 | 69.68 | even | 2 | |||
9522.2.a.bs.1.1 | 5 | 3.2 | odd | 2 |