Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6042,2,Mod(1,6042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6042, 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("6042.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6042.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: | \(48.2456129013\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 4x^{8} - 16x^{7} + 76x^{6} + 30x^{5} - 366x^{4} + 300x^{3} + 101x^{2} - 106x + 16 \) |
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 | 1.8 | ||
Root | \(0.394407\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6042.1 |
$q$-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 | ||||||||
\(5\) | 1.69036 | 0.755951 | 0.377975 | − | 0.925816i | \(-0.376620\pi\) | ||||
0.377975 | + | 0.925816i | \(0.376620\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −0.605593 | −0.228893 | −0.114446 | − | 0.993429i | \(-0.536509\pi\) | ||||
−0.114446 | + | 0.993429i | \(0.536509\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.69036 | 0.534538 | ||||||||
\(11\) | 5.02636 | 1.51550 | 0.757752 | − | 0.652543i | \(-0.226298\pi\) | ||||
0.757752 | + | 0.652543i | \(0.226298\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −2.72240 | −0.755058 | −0.377529 | − | 0.925998i | \(-0.623226\pi\) | ||||
−0.377529 | + | 0.925998i | \(0.623226\pi\) | |||||||
\(14\) | −0.605593 | −0.161852 | ||||||||
\(15\) | −1.69036 | −0.436448 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.51617 | −1.33787 | −0.668934 | − | 0.743322i | \(-0.733249\pi\) | ||||
−0.668934 | + | 0.743322i | \(0.733249\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 1.69036 | 0.377975 | ||||||||
\(21\) | 0.605593 | 0.132151 | ||||||||
\(22\) | 5.02636 | 1.07162 | ||||||||
\(23\) | −7.58679 | −1.58196 | −0.790978 | − | 0.611845i | \(-0.790428\pi\) | ||||
−0.790978 | + | 0.611845i | \(0.790428\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −2.14269 | −0.428538 | ||||||||
\(26\) | −2.72240 | −0.533907 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.605593 | −0.114446 | ||||||||
\(29\) | 3.16748 | 0.588186 | 0.294093 | − | 0.955777i | \(-0.404983\pi\) | ||||
0.294093 | + | 0.955777i | \(0.404983\pi\) | |||||||
\(30\) | −1.69036 | −0.308616 | ||||||||
\(31\) | −9.54506 | −1.71434 | −0.857172 | − | 0.515031i | \(-0.827781\pi\) | ||||
−0.857172 | + | 0.515031i | \(0.827781\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −5.02636 | −0.874977 | ||||||||
\(34\) | −5.51617 | −0.946016 | ||||||||
\(35\) | −1.02367 | −0.173032 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −9.34723 | −1.53667 | −0.768337 | − | 0.640045i | \(-0.778916\pi\) | ||||
−0.768337 | + | 0.640045i | \(0.778916\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 2.72240 | 0.435933 | ||||||||
\(40\) | 1.69036 | 0.267269 | ||||||||
\(41\) | 0.396182 | 0.0618732 | 0.0309366 | − | 0.999521i | \(-0.490151\pi\) | ||||
0.0309366 | + | 0.999521i | \(0.490151\pi\) | |||||||
\(42\) | 0.605593 | 0.0934450 | ||||||||
\(43\) | −3.81919 | −0.582421 | −0.291211 | − | 0.956659i | \(-0.594058\pi\) | ||||
−0.291211 | + | 0.956659i | \(0.594058\pi\) | |||||||
\(44\) | 5.02636 | 0.757752 | ||||||||
\(45\) | 1.69036 | 0.251984 | ||||||||
\(46\) | −7.58679 | −1.11861 | ||||||||
\(47\) | 4.86584 | 0.709756 | 0.354878 | − | 0.934913i | \(-0.384522\pi\) | ||||
0.354878 | + | 0.934913i | \(0.384522\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −6.63326 | −0.947608 | ||||||||
\(50\) | −2.14269 | −0.303022 | ||||||||
\(51\) | 5.51617 | 0.772419 | ||||||||
\(52\) | −2.72240 | −0.377529 | ||||||||
\(53\) | 1.00000 | 0.137361 | ||||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 8.49634 | 1.14565 | ||||||||
\(56\) | −0.605593 | −0.0809258 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | 3.16748 | 0.415910 | ||||||||
\(59\) | −1.33806 | −0.174201 | −0.0871004 | − | 0.996200i | \(-0.527760\pi\) | ||||
−0.0871004 | + | 0.996200i | \(0.527760\pi\) | |||||||
\(60\) | −1.69036 | −0.218224 | ||||||||
\(61\) | 9.23020 | 1.18181 | 0.590903 | − | 0.806743i | \(-0.298772\pi\) | ||||
0.590903 | + | 0.806743i | \(0.298772\pi\) | |||||||
\(62\) | −9.54506 | −1.21222 | ||||||||
\(63\) | −0.605593 | −0.0762975 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.60183 | −0.570787 | ||||||||
\(66\) | −5.02636 | −0.618702 | ||||||||
\(67\) | −10.6347 | −1.29923 | −0.649616 | − | 0.760262i | \(-0.725070\pi\) | ||||
−0.649616 | + | 0.760262i | \(0.725070\pi\) | |||||||
\(68\) | −5.51617 | −0.668934 | ||||||||
\(69\) | 7.58679 | 0.913342 | ||||||||
\(70\) | −1.02367 | −0.122352 | ||||||||
\(71\) | −6.43229 | −0.763373 | −0.381686 | − | 0.924292i | \(-0.624657\pi\) | ||||
−0.381686 | + | 0.924292i | \(0.624657\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −11.5216 | −1.34850 | −0.674250 | − | 0.738504i | \(-0.735533\pi\) | ||||
−0.674250 | + | 0.738504i | \(0.735533\pi\) | |||||||
\(74\) | −9.34723 | −1.08659 | ||||||||
\(75\) | 2.14269 | 0.247417 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −3.04393 | −0.346888 | ||||||||
\(78\) | 2.72240 | 0.308251 | ||||||||
\(79\) | −1.45010 | −0.163149 | −0.0815746 | − | 0.996667i | \(-0.525995\pi\) | ||||
−0.0815746 | + | 0.996667i | \(0.525995\pi\) | |||||||
\(80\) | 1.69036 | 0.188988 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.396182 | 0.0437510 | ||||||||
\(83\) | −11.7496 | −1.28969 | −0.644844 | − | 0.764314i | \(-0.723078\pi\) | ||||
−0.644844 | + | 0.764314i | \(0.723078\pi\) | |||||||
\(84\) | 0.605593 | 0.0660756 | ||||||||
\(85\) | −9.32430 | −1.01136 | ||||||||
\(86\) | −3.81919 | −0.411834 | ||||||||
\(87\) | −3.16748 | −0.339589 | ||||||||
\(88\) | 5.02636 | 0.535812 | ||||||||
\(89\) | 11.5259 | 1.22174 | 0.610872 | − | 0.791729i | \(-0.290819\pi\) | ||||
0.610872 | + | 0.791729i | \(0.290819\pi\) | |||||||
\(90\) | 1.69036 | 0.178179 | ||||||||
\(91\) | 1.64867 | 0.172827 | ||||||||
\(92\) | −7.58679 | −0.790978 | ||||||||
\(93\) | 9.54506 | 0.989777 | ||||||||
\(94\) | 4.86584 | 0.501873 | ||||||||
\(95\) | −1.69036 | −0.173427 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −6.47681 | −0.657621 | −0.328810 | − | 0.944396i | \(-0.606648\pi\) | ||||
−0.328810 | + | 0.944396i | \(0.606648\pi\) | |||||||
\(98\) | −6.63326 | −0.670060 | ||||||||
\(99\) | 5.02636 | 0.505168 | ||||||||
\(100\) | −2.14269 | −0.214269 | ||||||||
\(101\) | 3.24349 | 0.322740 | 0.161370 | − | 0.986894i | \(-0.448409\pi\) | ||||
0.161370 | + | 0.986894i | \(0.448409\pi\) | |||||||
\(102\) | 5.51617 | 0.546182 | ||||||||
\(103\) | 20.1540 | 1.98583 | 0.992915 | − | 0.118824i | \(-0.0379124\pi\) | ||||
0.992915 | + | 0.118824i | \(0.0379124\pi\) | |||||||
\(104\) | −2.72240 | −0.266953 | ||||||||
\(105\) | 1.02367 | 0.0998998 | ||||||||
\(106\) | 1.00000 | 0.0971286 | ||||||||
\(107\) | 2.85147 | 0.275662 | 0.137831 | − | 0.990456i | \(-0.455987\pi\) | ||||
0.137831 | + | 0.990456i | \(0.455987\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 4.79123 | 0.458916 | 0.229458 | − | 0.973319i | \(-0.426305\pi\) | ||||
0.229458 | + | 0.973319i | \(0.426305\pi\) | |||||||
\(110\) | 8.49634 | 0.810094 | ||||||||
\(111\) | 9.34723 | 0.887199 | ||||||||
\(112\) | −0.605593 | −0.0572232 | ||||||||
\(113\) | 7.20098 | 0.677411 | 0.338706 | − | 0.940892i | \(-0.390011\pi\) | ||||
0.338706 | + | 0.940892i | \(0.390011\pi\) | |||||||
\(114\) | 1.00000 | 0.0936586 | ||||||||
\(115\) | −12.8244 | −1.19588 | ||||||||
\(116\) | 3.16748 | 0.294093 | ||||||||
\(117\) | −2.72240 | −0.251686 | ||||||||
\(118\) | −1.33806 | −0.123179 | ||||||||
\(119\) | 3.34056 | 0.306228 | ||||||||
\(120\) | −1.69036 | −0.154308 | ||||||||
\(121\) | 14.2643 | 1.29675 | ||||||||
\(122\) | 9.23020 | 0.835663 | ||||||||
\(123\) | −0.396182 | −0.0357225 | ||||||||
\(124\) | −9.54506 | −0.857172 | ||||||||
\(125\) | −12.0737 | −1.07990 | ||||||||
\(126\) | −0.605593 | −0.0539505 | ||||||||
\(127\) | 15.9360 | 1.41409 | 0.707046 | − | 0.707167i | \(-0.250027\pi\) | ||||
0.707046 | + | 0.707167i | \(0.250027\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 3.81919 | 0.336261 | ||||||||
\(130\) | −4.60183 | −0.403607 | ||||||||
\(131\) | 14.5372 | 1.27012 | 0.635059 | − | 0.772464i | \(-0.280976\pi\) | ||||
0.635059 | + | 0.772464i | \(0.280976\pi\) | |||||||
\(132\) | −5.02636 | −0.437488 | ||||||||
\(133\) | 0.605593 | 0.0525116 | ||||||||
\(134\) | −10.6347 | −0.918696 | ||||||||
\(135\) | −1.69036 | −0.145483 | ||||||||
\(136\) | −5.51617 | −0.473008 | ||||||||
\(137\) | −15.6691 | −1.33871 | −0.669353 | − | 0.742945i | \(-0.733428\pi\) | ||||
−0.669353 | + | 0.742945i | \(0.733428\pi\) | |||||||
\(138\) | 7.58679 | 0.645831 | ||||||||
\(139\) | −0.653234 | −0.0554066 | −0.0277033 | − | 0.999616i | \(-0.508819\pi\) | ||||
−0.0277033 | + | 0.999616i | \(0.508819\pi\) | |||||||
\(140\) | −1.02367 | −0.0865158 | ||||||||
\(141\) | −4.86584 | −0.409778 | ||||||||
\(142\) | −6.43229 | −0.539786 | ||||||||
\(143\) | −13.6838 | −1.14429 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 5.35417 | 0.444639 | ||||||||
\(146\) | −11.5216 | −0.953533 | ||||||||
\(147\) | 6.63326 | 0.547102 | ||||||||
\(148\) | −9.34723 | −0.768337 | ||||||||
\(149\) | 22.9327 | 1.87872 | 0.939360 | − | 0.342933i | \(-0.111421\pi\) | ||||
0.939360 | + | 0.342933i | \(0.111421\pi\) | |||||||
\(150\) | 2.14269 | 0.174950 | ||||||||
\(151\) | 19.3661 | 1.57599 | 0.787996 | − | 0.615680i | \(-0.211119\pi\) | ||||
0.787996 | + | 0.615680i | \(0.211119\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | −5.51617 | −0.445956 | ||||||||
\(154\) | −3.04393 | −0.245287 | ||||||||
\(155\) | −16.1346 | −1.29596 | ||||||||
\(156\) | 2.72240 | 0.217967 | ||||||||
\(157\) | 0.0490296 | 0.00391299 | 0.00195649 | − | 0.999998i | \(-0.499377\pi\) | ||||
0.00195649 | + | 0.999998i | \(0.499377\pi\) | |||||||
\(158\) | −1.45010 | −0.115364 | ||||||||
\(159\) | −1.00000 | −0.0793052 | ||||||||
\(160\) | 1.69036 | 0.133635 | ||||||||
\(161\) | 4.59451 | 0.362098 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −18.0273 | −1.41201 | −0.706005 | − | 0.708207i | \(-0.749504\pi\) | ||||
−0.706005 | + | 0.708207i | \(0.749504\pi\) | |||||||
\(164\) | 0.396182 | 0.0309366 | ||||||||
\(165\) | −8.49634 | −0.661439 | ||||||||
\(166\) | −11.7496 | −0.911947 | ||||||||
\(167\) | 23.0036 | 1.78007 | 0.890035 | − | 0.455892i | \(-0.150680\pi\) | ||||
0.890035 | + | 0.455892i | \(0.150680\pi\) | |||||||
\(168\) | 0.605593 | 0.0467225 | ||||||||
\(169\) | −5.58853 | −0.429887 | ||||||||
\(170\) | −9.32430 | −0.715142 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | −3.81919 | −0.291211 | ||||||||
\(173\) | −16.3622 | −1.24400 | −0.621998 | − | 0.783018i | \(-0.713679\pi\) | ||||
−0.621998 | + | 0.783018i | \(0.713679\pi\) | |||||||
\(174\) | −3.16748 | −0.240126 | ||||||||
\(175\) | 1.29760 | 0.0980892 | ||||||||
\(176\) | 5.02636 | 0.378876 | ||||||||
\(177\) | 1.33806 | 0.100575 | ||||||||
\(178\) | 11.5259 | 0.863904 | ||||||||
\(179\) | 1.18880 | 0.0888552 | 0.0444276 | − | 0.999013i | \(-0.485854\pi\) | ||||
0.0444276 | + | 0.999013i | \(0.485854\pi\) | |||||||
\(180\) | 1.69036 | 0.125992 | ||||||||
\(181\) | −10.2668 | −0.763127 | −0.381564 | − | 0.924343i | \(-0.624614\pi\) | ||||
−0.381564 | + | 0.924343i | \(0.624614\pi\) | |||||||
\(182\) | 1.64867 | 0.122207 | ||||||||
\(183\) | −9.23020 | −0.682316 | ||||||||
\(184\) | −7.58679 | −0.559306 | ||||||||
\(185\) | −15.8002 | −1.16165 | ||||||||
\(186\) | 9.54506 | 0.699878 | ||||||||
\(187\) | −27.7263 | −2.02754 | ||||||||
\(188\) | 4.86584 | 0.354878 | ||||||||
\(189\) | 0.605593 | 0.0440504 | ||||||||
\(190\) | −1.69036 | −0.122631 | ||||||||
\(191\) | 3.04006 | 0.219971 | 0.109985 | − | 0.993933i | \(-0.464920\pi\) | ||||
0.109985 | + | 0.993933i | \(0.464920\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −5.67822 | −0.408728 | −0.204364 | − | 0.978895i | \(-0.565513\pi\) | ||||
−0.204364 | + | 0.978895i | \(0.565513\pi\) | |||||||
\(194\) | −6.47681 | −0.465008 | ||||||||
\(195\) | 4.60183 | 0.329544 | ||||||||
\(196\) | −6.63326 | −0.473804 | ||||||||
\(197\) | −7.73625 | −0.551185 | −0.275593 | − | 0.961275i | \(-0.588874\pi\) | ||||
−0.275593 | + | 0.961275i | \(0.588874\pi\) | |||||||
\(198\) | 5.02636 | 0.357208 | ||||||||
\(199\) | −26.6283 | −1.88763 | −0.943815 | − | 0.330473i | \(-0.892792\pi\) | ||||
−0.943815 | + | 0.330473i | \(0.892792\pi\) | |||||||
\(200\) | −2.14269 | −0.151511 | ||||||||
\(201\) | 10.6347 | 0.750112 | ||||||||
\(202\) | 3.24349 | 0.228211 | ||||||||
\(203\) | −1.91820 | −0.134631 | ||||||||
\(204\) | 5.51617 | 0.386209 | ||||||||
\(205\) | 0.669689 | 0.0467731 | ||||||||
\(206\) | 20.1540 | 1.40419 | ||||||||
\(207\) | −7.58679 | −0.527319 | ||||||||
\(208\) | −2.72240 | −0.188765 | ||||||||
\(209\) | −5.02636 | −0.347680 | ||||||||
\(210\) | 1.02367 | 0.0706399 | ||||||||
\(211\) | −25.9291 | −1.78503 | −0.892517 | − | 0.451013i | \(-0.851063\pi\) | ||||
−0.892517 | + | 0.451013i | \(0.851063\pi\) | |||||||
\(212\) | 1.00000 | 0.0686803 | ||||||||
\(213\) | 6.43229 | 0.440733 | ||||||||
\(214\) | 2.85147 | 0.194922 | ||||||||
\(215\) | −6.45580 | −0.440282 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 5.78042 | 0.392401 | ||||||||
\(218\) | 4.79123 | 0.324503 | ||||||||
\(219\) | 11.5216 | 0.778556 | ||||||||
\(220\) | 8.49634 | 0.572823 | ||||||||
\(221\) | 15.0172 | 1.01017 | ||||||||
\(222\) | 9.34723 | 0.627345 | ||||||||
\(223\) | 25.3006 | 1.69425 | 0.847126 | − | 0.531392i | \(-0.178331\pi\) | ||||
0.847126 | + | 0.531392i | \(0.178331\pi\) | |||||||
\(224\) | −0.605593 | −0.0404629 | ||||||||
\(225\) | −2.14269 | −0.142846 | ||||||||
\(226\) | 7.20098 | 0.479002 | ||||||||
\(227\) | −8.58401 | −0.569741 | −0.284870 | − | 0.958566i | \(-0.591951\pi\) | ||||
−0.284870 | + | 0.958566i | \(0.591951\pi\) | |||||||
\(228\) | 1.00000 | 0.0662266 | ||||||||
\(229\) | −23.8247 | −1.57438 | −0.787190 | − | 0.616711i | \(-0.788465\pi\) | ||||
−0.787190 | + | 0.616711i | \(0.788465\pi\) | |||||||
\(230\) | −12.8244 | −0.845615 | ||||||||
\(231\) | 3.04393 | 0.200276 | ||||||||
\(232\) | 3.16748 | 0.207955 | ||||||||
\(233\) | 20.2870 | 1.32904 | 0.664521 | − | 0.747269i | \(-0.268636\pi\) | ||||
0.664521 | + | 0.747269i | \(0.268636\pi\) | |||||||
\(234\) | −2.72240 | −0.177969 | ||||||||
\(235\) | 8.22501 | 0.536540 | ||||||||
\(236\) | −1.33806 | −0.0871004 | ||||||||
\(237\) | 1.45010 | 0.0941942 | ||||||||
\(238\) | 3.34056 | 0.216536 | ||||||||
\(239\) | 7.70613 | 0.498468 | 0.249234 | − | 0.968443i | \(-0.419821\pi\) | ||||
0.249234 | + | 0.968443i | \(0.419821\pi\) | |||||||
\(240\) | −1.69036 | −0.109112 | ||||||||
\(241\) | 11.7300 | 0.755596 | 0.377798 | − | 0.925888i | \(-0.376681\pi\) | ||||
0.377798 | + | 0.925888i | \(0.376681\pi\) | |||||||
\(242\) | 14.2643 | 0.916942 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 9.23020 | 0.590903 | ||||||||
\(245\) | −11.2126 | −0.716345 | ||||||||
\(246\) | −0.396182 | −0.0252596 | ||||||||
\(247\) | 2.72240 | 0.173222 | ||||||||
\(248\) | −9.54506 | −0.606112 | ||||||||
\(249\) | 11.7496 | 0.744602 | ||||||||
\(250\) | −12.0737 | −0.763608 | ||||||||
\(251\) | 15.0680 | 0.951082 | 0.475541 | − | 0.879693i | \(-0.342252\pi\) | ||||
0.475541 | + | 0.879693i | \(0.342252\pi\) | |||||||
\(252\) | −0.605593 | −0.0381488 | ||||||||
\(253\) | −38.1339 | −2.39746 | ||||||||
\(254\) | 15.9360 | 0.999914 | ||||||||
\(255\) | 9.32430 | 0.583911 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 11.0652 | 0.690231 | 0.345116 | − | 0.938560i | \(-0.387840\pi\) | ||||
0.345116 | + | 0.938560i | \(0.387840\pi\) | |||||||
\(258\) | 3.81919 | 0.237773 | ||||||||
\(259\) | 5.66061 | 0.351733 | ||||||||
\(260\) | −4.60183 | −0.285393 | ||||||||
\(261\) | 3.16748 | 0.196062 | ||||||||
\(262\) | 14.5372 | 0.898109 | ||||||||
\(263\) | −7.24748 | −0.446899 | −0.223449 | − | 0.974716i | \(-0.571732\pi\) | ||||
−0.223449 | + | 0.974716i | \(0.571732\pi\) | |||||||
\(264\) | −5.02636 | −0.309351 | ||||||||
\(265\) | 1.69036 | 0.103838 | ||||||||
\(266\) | 0.605593 | 0.0371313 | ||||||||
\(267\) | −11.5259 | −0.705374 | ||||||||
\(268\) | −10.6347 | −0.649616 | ||||||||
\(269\) | −13.0141 | −0.793486 | −0.396743 | − | 0.917930i | \(-0.629860\pi\) | ||||
−0.396743 | + | 0.917930i | \(0.629860\pi\) | |||||||
\(270\) | −1.69036 | −0.102872 | ||||||||
\(271\) | −11.8664 | −0.720831 | −0.360416 | − | 0.932792i | \(-0.617365\pi\) | ||||
−0.360416 | + | 0.932792i | \(0.617365\pi\) | |||||||
\(272\) | −5.51617 | −0.334467 | ||||||||
\(273\) | −1.64867 | −0.0997819 | ||||||||
\(274\) | −15.6691 | −0.946608 | ||||||||
\(275\) | −10.7699 | −0.649451 | ||||||||
\(276\) | 7.58679 | 0.456671 | ||||||||
\(277\) | −23.5480 | −1.41486 | −0.707431 | − | 0.706783i | \(-0.750146\pi\) | ||||
−0.707431 | + | 0.706783i | \(0.750146\pi\) | |||||||
\(278\) | −0.653234 | −0.0391784 | ||||||||
\(279\) | −9.54506 | −0.571448 | ||||||||
\(280\) | −1.02367 | −0.0611759 | ||||||||
\(281\) | −16.1100 | −0.961041 | −0.480521 | − | 0.876983i | \(-0.659552\pi\) | ||||
−0.480521 | + | 0.876983i | \(0.659552\pi\) | |||||||
\(282\) | −4.86584 | −0.289757 | ||||||||
\(283\) | −8.17754 | −0.486104 | −0.243052 | − | 0.970013i | \(-0.578149\pi\) | ||||
−0.243052 | + | 0.970013i | \(0.578149\pi\) | |||||||
\(284\) | −6.43229 | −0.381686 | ||||||||
\(285\) | 1.69036 | 0.100128 | ||||||||
\(286\) | −13.6838 | −0.809138 | ||||||||
\(287\) | −0.239925 | −0.0141623 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 13.4282 | 0.789892 | ||||||||
\(290\) | 5.35417 | 0.314408 | ||||||||
\(291\) | 6.47681 | 0.379677 | ||||||||
\(292\) | −11.5216 | −0.674250 | ||||||||
\(293\) | 16.7634 | 0.979328 | 0.489664 | − | 0.871911i | \(-0.337119\pi\) | ||||
0.489664 | + | 0.871911i | \(0.337119\pi\) | |||||||
\(294\) | 6.63326 | 0.386859 | ||||||||
\(295\) | −2.26180 | −0.131687 | ||||||||
\(296\) | −9.34723 | −0.543296 | ||||||||
\(297\) | −5.02636 | −0.291659 | ||||||||
\(298\) | 22.9327 | 1.32846 | ||||||||
\(299\) | 20.6543 | 1.19447 | ||||||||
\(300\) | 2.14269 | 0.123708 | ||||||||
\(301\) | 2.31288 | 0.133312 | ||||||||
\(302\) | 19.3661 | 1.11439 | ||||||||
\(303\) | −3.24349 | −0.186334 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 15.6023 | 0.893388 | ||||||||
\(306\) | −5.51617 | −0.315339 | ||||||||
\(307\) | 0.494661 | 0.0282318 | 0.0141159 | − | 0.999900i | \(-0.495507\pi\) | ||||
0.0141159 | + | 0.999900i | \(0.495507\pi\) | |||||||
\(308\) | −3.04393 | −0.173444 | ||||||||
\(309\) | −20.1540 | −1.14652 | ||||||||
\(310\) | −16.1346 | −0.916382 | ||||||||
\(311\) | 0.669217 | 0.0379478 | 0.0189739 | − | 0.999820i | \(-0.493960\pi\) | ||||
0.0189739 | + | 0.999820i | \(0.493960\pi\) | |||||||
\(312\) | 2.72240 | 0.154126 | ||||||||
\(313\) | −21.8402 | −1.23448 | −0.617240 | − | 0.786775i | \(-0.711749\pi\) | ||||
−0.617240 | + | 0.786775i | \(0.711749\pi\) | |||||||
\(314\) | 0.0490296 | 0.00276690 | ||||||||
\(315\) | −1.02367 | −0.0576772 | ||||||||
\(316\) | −1.45010 | −0.0815746 | ||||||||
\(317\) | −12.3228 | −0.692116 | −0.346058 | − | 0.938213i | \(-0.612480\pi\) | ||||
−0.346058 | + | 0.938213i | \(0.612480\pi\) | |||||||
\(318\) | −1.00000 | −0.0560772 | ||||||||
\(319\) | 15.9209 | 0.891397 | ||||||||
\(320\) | 1.69036 | 0.0944939 | ||||||||
\(321\) | −2.85147 | −0.159153 | ||||||||
\(322\) | 4.59451 | 0.256042 | ||||||||
\(323\) | 5.51617 | 0.306928 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 5.83326 | 0.323571 | ||||||||
\(326\) | −18.0273 | −0.998442 | ||||||||
\(327\) | −4.79123 | −0.264955 | ||||||||
\(328\) | 0.396182 | 0.0218755 | ||||||||
\(329\) | −2.94672 | −0.162458 | ||||||||
\(330\) | −8.49634 | −0.467708 | ||||||||
\(331\) | 15.9874 | 0.878745 | 0.439373 | − | 0.898305i | \(-0.355201\pi\) | ||||
0.439373 | + | 0.898305i | \(0.355201\pi\) | |||||||
\(332\) | −11.7496 | −0.644844 | ||||||||
\(333\) | −9.34723 | −0.512225 | ||||||||
\(334\) | 23.0036 | 1.25870 | ||||||||
\(335\) | −17.9764 | −0.982156 | ||||||||
\(336\) | 0.605593 | 0.0330378 | ||||||||
\(337\) | 32.6872 | 1.78058 | 0.890292 | − | 0.455391i | \(-0.150501\pi\) | ||||
0.890292 | + | 0.455391i | \(0.150501\pi\) | |||||||
\(338\) | −5.58853 | −0.303976 | ||||||||
\(339\) | −7.20098 | −0.391104 | ||||||||
\(340\) | −9.32430 | −0.505681 | ||||||||
\(341\) | −47.9769 | −2.59809 | ||||||||
\(342\) | −1.00000 | −0.0540738 | ||||||||
\(343\) | 8.25620 | 0.445793 | ||||||||
\(344\) | −3.81919 | −0.205917 | ||||||||
\(345\) | 12.8244 | 0.690442 | ||||||||
\(346\) | −16.3622 | −0.879639 | ||||||||
\(347\) | 24.6711 | 1.32441 | 0.662206 | − | 0.749321i | \(-0.269620\pi\) | ||||
0.662206 | + | 0.749321i | \(0.269620\pi\) | |||||||
\(348\) | −3.16748 | −0.169795 | ||||||||
\(349\) | −15.1792 | −0.812522 | −0.406261 | − | 0.913757i | \(-0.633168\pi\) | ||||
−0.406261 | + | 0.913757i | \(0.633168\pi\) | |||||||
\(350\) | 1.29760 | 0.0693596 | ||||||||
\(351\) | 2.72240 | 0.145311 | ||||||||
\(352\) | 5.02636 | 0.267906 | ||||||||
\(353\) | −31.2775 | −1.66473 | −0.832367 | − | 0.554224i | \(-0.813015\pi\) | ||||
−0.832367 | + | 0.554224i | \(0.813015\pi\) | |||||||
\(354\) | 1.33806 | 0.0711172 | ||||||||
\(355\) | −10.8729 | −0.577072 | ||||||||
\(356\) | 11.5259 | 0.610872 | ||||||||
\(357\) | −3.34056 | −0.176801 | ||||||||
\(358\) | 1.18880 | 0.0628301 | ||||||||
\(359\) | 24.6442 | 1.30067 | 0.650335 | − | 0.759648i | \(-0.274629\pi\) | ||||
0.650335 | + | 0.759648i | \(0.274629\pi\) | |||||||
\(360\) | 1.69036 | 0.0890897 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −10.2668 | −0.539612 | ||||||||
\(363\) | −14.2643 | −0.748680 | ||||||||
\(364\) | 1.64867 | 0.0864136 | ||||||||
\(365\) | −19.4756 | −1.01940 | ||||||||
\(366\) | −9.23020 | −0.482470 | ||||||||
\(367\) | −12.5851 | −0.656938 | −0.328469 | − | 0.944515i | \(-0.606533\pi\) | ||||
−0.328469 | + | 0.944515i | \(0.606533\pi\) | |||||||
\(368\) | −7.58679 | −0.395489 | ||||||||
\(369\) | 0.396182 | 0.0206244 | ||||||||
\(370\) | −15.8002 | −0.821411 | ||||||||
\(371\) | −0.605593 | −0.0314408 | ||||||||
\(372\) | 9.54506 | 0.494888 | ||||||||
\(373\) | 30.5532 | 1.58198 | 0.790992 | − | 0.611827i | \(-0.209565\pi\) | ||||
0.790992 | + | 0.611827i | \(0.209565\pi\) | |||||||
\(374\) | −27.7263 | −1.43369 | ||||||||
\(375\) | 12.0737 | 0.623483 | ||||||||
\(376\) | 4.86584 | 0.250937 | ||||||||
\(377\) | −8.62314 | −0.444114 | ||||||||
\(378\) | 0.605593 | 0.0311483 | ||||||||
\(379\) | 5.55156 | 0.285164 | 0.142582 | − | 0.989783i | \(-0.454459\pi\) | ||||
0.142582 | + | 0.989783i | \(0.454459\pi\) | |||||||
\(380\) | −1.69036 | −0.0867135 | ||||||||
\(381\) | −15.9360 | −0.816427 | ||||||||
\(382\) | 3.04006 | 0.155543 | ||||||||
\(383\) | 6.04178 | 0.308721 | 0.154360 | − | 0.988015i | \(-0.450668\pi\) | ||||
0.154360 | + | 0.988015i | \(0.450668\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −5.14533 | −0.262230 | ||||||||
\(386\) | −5.67822 | −0.289014 | ||||||||
\(387\) | −3.81919 | −0.194140 | ||||||||
\(388\) | −6.47681 | −0.328810 | ||||||||
\(389\) | −7.97723 | −0.404462 | −0.202231 | − | 0.979338i | \(-0.564819\pi\) | ||||
−0.202231 | + | 0.979338i | \(0.564819\pi\) | |||||||
\(390\) | 4.60183 | 0.233023 | ||||||||
\(391\) | 41.8501 | 2.11645 | ||||||||
\(392\) | −6.63326 | −0.335030 | ||||||||
\(393\) | −14.5372 | −0.733303 | ||||||||
\(394\) | −7.73625 | −0.389747 | ||||||||
\(395\) | −2.45119 | −0.123333 | ||||||||
\(396\) | 5.02636 | 0.252584 | ||||||||
\(397\) | 30.2267 | 1.51703 | 0.758517 | − | 0.651653i | \(-0.225924\pi\) | ||||
0.758517 | + | 0.651653i | \(0.225924\pi\) | |||||||
\(398\) | −26.6283 | −1.33476 | ||||||||
\(399\) | −0.605593 | −0.0303176 | ||||||||
\(400\) | −2.14269 | −0.107135 | ||||||||
\(401\) | 5.15637 | 0.257497 | 0.128748 | − | 0.991677i | \(-0.458904\pi\) | ||||
0.128748 | + | 0.991677i | \(0.458904\pi\) | |||||||
\(402\) | 10.6347 | 0.530409 | ||||||||
\(403\) | 25.9855 | 1.29443 | ||||||||
\(404\) | 3.24349 | 0.161370 | ||||||||
\(405\) | 1.69036 | 0.0839945 | ||||||||
\(406\) | −1.91820 | −0.0951987 | ||||||||
\(407\) | −46.9825 | −2.32884 | ||||||||
\(408\) | 5.51617 | 0.273091 | ||||||||
\(409\) | −9.56914 | −0.473164 | −0.236582 | − | 0.971612i | \(-0.576027\pi\) | ||||
−0.236582 | + | 0.971612i | \(0.576027\pi\) | |||||||
\(410\) | 0.669689 | 0.0330736 | ||||||||
\(411\) | 15.6691 | 0.772902 | ||||||||
\(412\) | 20.1540 | 0.992915 | ||||||||
\(413\) | 0.810321 | 0.0398733 | ||||||||
\(414\) | −7.58679 | −0.372871 | ||||||||
\(415\) | −19.8611 | −0.974941 | ||||||||
\(416\) | −2.72240 | −0.133477 | ||||||||
\(417\) | 0.653234 | 0.0319890 | ||||||||
\(418\) | −5.02636 | −0.245847 | ||||||||
\(419\) | −23.2252 | −1.13463 | −0.567313 | − | 0.823502i | \(-0.692017\pi\) | ||||
−0.567313 | + | 0.823502i | \(0.692017\pi\) | |||||||
\(420\) | 1.02367 | 0.0499499 | ||||||||
\(421\) | 5.67045 | 0.276361 | 0.138180 | − | 0.990407i | \(-0.455875\pi\) | ||||
0.138180 | + | 0.990407i | \(0.455875\pi\) | |||||||
\(422\) | −25.9291 | −1.26221 | ||||||||
\(423\) | 4.86584 | 0.236585 | ||||||||
\(424\) | 1.00000 | 0.0485643 | ||||||||
\(425\) | 11.8195 | 0.573328 | ||||||||
\(426\) | 6.43229 | 0.311646 | ||||||||
\(427\) | −5.58975 | −0.270507 | ||||||||
\(428\) | 2.85147 | 0.137831 | ||||||||
\(429\) | 13.6838 | 0.660658 | ||||||||
\(430\) | −6.45580 | −0.311326 | ||||||||
\(431\) | −15.2246 | −0.733342 | −0.366671 | − | 0.930351i | \(-0.619503\pi\) | ||||
−0.366671 | + | 0.930351i | \(0.619503\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 6.37413 | 0.306321 | 0.153161 | − | 0.988201i | \(-0.451055\pi\) | ||||
0.153161 | + | 0.988201i | \(0.451055\pi\) | |||||||
\(434\) | 5.78042 | 0.277469 | ||||||||
\(435\) | −5.35417 | −0.256713 | ||||||||
\(436\) | 4.79123 | 0.229458 | ||||||||
\(437\) | 7.58679 | 0.362926 | ||||||||
\(438\) | 11.5216 | 0.550522 | ||||||||
\(439\) | −5.06870 | −0.241916 | −0.120958 | − | 0.992658i | \(-0.538597\pi\) | ||||
−0.120958 | + | 0.992658i | \(0.538597\pi\) | |||||||
\(440\) | 8.49634 | 0.405047 | ||||||||
\(441\) | −6.63326 | −0.315869 | ||||||||
\(442\) | 15.0172 | 0.714297 | ||||||||
\(443\) | −22.9923 | −1.09240 | −0.546199 | − | 0.837656i | \(-0.683926\pi\) | ||||
−0.546199 | + | 0.837656i | \(0.683926\pi\) | |||||||
\(444\) | 9.34723 | 0.443600 | ||||||||
\(445\) | 19.4829 | 0.923579 | ||||||||
\(446\) | 25.3006 | 1.19802 | ||||||||
\(447\) | −22.9327 | −1.08468 | ||||||||
\(448\) | −0.605593 | −0.0286116 | ||||||||
\(449\) | 6.29872 | 0.297255 | 0.148627 | − | 0.988893i | \(-0.452514\pi\) | ||||
0.148627 | + | 0.988893i | \(0.452514\pi\) | |||||||
\(450\) | −2.14269 | −0.101007 | ||||||||
\(451\) | 1.99135 | 0.0937692 | ||||||||
\(452\) | 7.20098 | 0.338706 | ||||||||
\(453\) | −19.3661 | −0.909899 | ||||||||
\(454\) | −8.58401 | −0.402868 | ||||||||
\(455\) | 2.78684 | 0.130649 | ||||||||
\(456\) | 1.00000 | 0.0468293 | ||||||||
\(457\) | 3.56508 | 0.166767 | 0.0833836 | − | 0.996518i | \(-0.473427\pi\) | ||||
0.0833836 | + | 0.996518i | \(0.473427\pi\) | |||||||
\(458\) | −23.8247 | −1.11325 | ||||||||
\(459\) | 5.51617 | 0.257473 | ||||||||
\(460\) | −12.8244 | −0.597940 | ||||||||
\(461\) | −19.6891 | −0.917013 | −0.458507 | − | 0.888691i | \(-0.651615\pi\) | ||||
−0.458507 | + | 0.888691i | \(0.651615\pi\) | |||||||
\(462\) | 3.04393 | 0.141616 | ||||||||
\(463\) | −19.2726 | −0.895673 | −0.447836 | − | 0.894116i | \(-0.647805\pi\) | ||||
−0.447836 | + | 0.894116i | \(0.647805\pi\) | |||||||
\(464\) | 3.16748 | 0.147046 | ||||||||
\(465\) | 16.1346 | 0.748223 | ||||||||
\(466\) | 20.2870 | 0.939775 | ||||||||
\(467\) | −9.21783 | −0.426550 | −0.213275 | − | 0.976992i | \(-0.568413\pi\) | ||||
−0.213275 | + | 0.976992i | \(0.568413\pi\) | |||||||
\(468\) | −2.72240 | −0.125843 | ||||||||
\(469\) | 6.44028 | 0.297385 | ||||||||
\(470\) | 8.22501 | 0.379391 | ||||||||
\(471\) | −0.0490296 | −0.00225917 | ||||||||
\(472\) | −1.33806 | −0.0615893 | ||||||||
\(473\) | −19.1966 | −0.882662 | ||||||||
\(474\) | 1.45010 | 0.0666054 | ||||||||
\(475\) | 2.14269 | 0.0983134 | ||||||||
\(476\) | 3.34056 | 0.153114 | ||||||||
\(477\) | 1.00000 | 0.0457869 | ||||||||
\(478\) | 7.70613 | 0.352470 | ||||||||
\(479\) | 26.8437 | 1.22652 | 0.613261 | − | 0.789880i | \(-0.289857\pi\) | ||||
0.613261 | + | 0.789880i | \(0.289857\pi\) | |||||||
\(480\) | −1.69036 | −0.0771539 | ||||||||
\(481\) | 25.4469 | 1.16028 | ||||||||
\(482\) | 11.7300 | 0.534287 | ||||||||
\(483\) | −4.59451 | −0.209057 | ||||||||
\(484\) | 14.2643 | 0.648376 | ||||||||
\(485\) | −10.9481 | −0.497129 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −13.0977 | −0.593515 | −0.296757 | − | 0.954953i | \(-0.595905\pi\) | ||||
−0.296757 | + | 0.954953i | \(0.595905\pi\) | |||||||
\(488\) | 9.23020 | 0.417832 | ||||||||
\(489\) | 18.0273 | 0.815224 | ||||||||
\(490\) | −11.2126 | −0.506533 | ||||||||
\(491\) | 33.6171 | 1.51712 | 0.758560 | − | 0.651603i | \(-0.225903\pi\) | ||||
0.758560 | + | 0.651603i | \(0.225903\pi\) | |||||||
\(492\) | −0.396182 | −0.0178613 | ||||||||
\(493\) | −17.4723 | −0.786915 | ||||||||
\(494\) | 2.72240 | 0.122487 | ||||||||
\(495\) | 8.49634 | 0.381882 | ||||||||
\(496\) | −9.54506 | −0.428586 | ||||||||
\(497\) | 3.89535 | 0.174730 | ||||||||
\(498\) | 11.7496 | 0.526513 | ||||||||
\(499\) | 9.85886 | 0.441343 | 0.220672 | − | 0.975348i | \(-0.429175\pi\) | ||||
0.220672 | + | 0.975348i | \(0.429175\pi\) | |||||||
\(500\) | −12.0737 | −0.539952 | ||||||||
\(501\) | −23.0036 | −1.02772 | ||||||||
\(502\) | 15.0680 | 0.672517 | ||||||||
\(503\) | −38.9447 | −1.73646 | −0.868230 | − | 0.496162i | \(-0.834742\pi\) | ||||
−0.868230 | + | 0.496162i | \(0.834742\pi\) | |||||||
\(504\) | −0.605593 | −0.0269753 | ||||||||
\(505\) | 5.48266 | 0.243975 | ||||||||
\(506\) | −38.1339 | −1.69526 | ||||||||
\(507\) | 5.58853 | 0.248195 | ||||||||
\(508\) | 15.9360 | 0.707046 | ||||||||
\(509\) | −42.3073 | −1.87524 | −0.937620 | − | 0.347663i | \(-0.886975\pi\) | ||||
−0.937620 | + | 0.347663i | \(0.886975\pi\) | |||||||
\(510\) | 9.32430 | 0.412887 | ||||||||
\(511\) | 6.97739 | 0.308662 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | 11.0652 | 0.488067 | ||||||||
\(515\) | 34.0674 | 1.50119 | ||||||||
\(516\) | 3.81919 | 0.168131 | ||||||||
\(517\) | 24.4575 | 1.07564 | ||||||||
\(518\) | 5.66061 | 0.248713 | ||||||||
\(519\) | 16.3622 | 0.718222 | ||||||||
\(520\) | −4.60183 | −0.201804 | ||||||||
\(521\) | −17.9456 | −0.786209 | −0.393105 | − | 0.919494i | \(-0.628599\pi\) | ||||
−0.393105 | + | 0.919494i | \(0.628599\pi\) | |||||||
\(522\) | 3.16748 | 0.138637 | ||||||||
\(523\) | −25.5247 | −1.11612 | −0.558059 | − | 0.829801i | \(-0.688454\pi\) | ||||
−0.558059 | + | 0.829801i | \(0.688454\pi\) | |||||||
\(524\) | 14.5372 | 0.635059 | ||||||||
\(525\) | −1.29760 | −0.0566318 | ||||||||
\(526\) | −7.24748 | −0.316005 | ||||||||
\(527\) | 52.6522 | 2.29357 | ||||||||
\(528\) | −5.02636 | −0.218744 | ||||||||
\(529\) | 34.5594 | 1.50258 | ||||||||
\(530\) | 1.69036 | 0.0734244 | ||||||||
\(531\) | −1.33806 | −0.0580669 | ||||||||
\(532\) | 0.605593 | 0.0262558 | ||||||||
\(533\) | −1.07857 | −0.0467179 | ||||||||
\(534\) | −11.5259 | −0.498775 | ||||||||
\(535\) | 4.82000 | 0.208387 | ||||||||
\(536\) | −10.6347 | −0.459348 | ||||||||
\(537\) | −1.18880 | −0.0513006 | ||||||||
\(538\) | −13.0141 | −0.561079 | ||||||||
\(539\) | −33.3411 | −1.43610 | ||||||||
\(540\) | −1.69036 | −0.0727414 | ||||||||
\(541\) | −34.6426 | −1.48940 | −0.744702 | − | 0.667397i | \(-0.767408\pi\) | ||||
−0.744702 | + | 0.667397i | \(0.767408\pi\) | |||||||
\(542\) | −11.8664 | −0.509705 | ||||||||
\(543\) | 10.2668 | 0.440592 | ||||||||
\(544\) | −5.51617 | −0.236504 | ||||||||
\(545\) | 8.09889 | 0.346918 | ||||||||
\(546\) | −1.64867 | −0.0705564 | ||||||||
\(547\) | 6.22085 | 0.265984 | 0.132992 | − | 0.991117i | \(-0.457541\pi\) | ||||
0.132992 | + | 0.991117i | \(0.457541\pi\) | |||||||
\(548\) | −15.6691 | −0.669353 | ||||||||
\(549\) | 9.23020 | 0.393935 | ||||||||
\(550\) | −10.7699 | −0.459231 | ||||||||
\(551\) | −3.16748 | −0.134939 | ||||||||
\(552\) | 7.58679 | 0.322915 | ||||||||
\(553\) | 0.878171 | 0.0373436 | ||||||||
\(554\) | −23.5480 | −1.00046 | ||||||||
\(555\) | 15.8002 | 0.670679 | ||||||||
\(556\) | −0.653234 | −0.0277033 | ||||||||
\(557\) | 10.0944 | 0.427712 | 0.213856 | − | 0.976865i | \(-0.431398\pi\) | ||||
0.213856 | + | 0.976865i | \(0.431398\pi\) | |||||||
\(558\) | −9.54506 | −0.404075 | ||||||||
\(559\) | 10.3974 | 0.439762 | ||||||||
\(560\) | −1.02367 | −0.0432579 | ||||||||
\(561\) | 27.7263 | 1.17060 | ||||||||
\(562\) | −16.1100 | −0.679559 | ||||||||
\(563\) | 18.9732 | 0.799625 | 0.399813 | − | 0.916597i | \(-0.369075\pi\) | ||||
0.399813 | + | 0.916597i | \(0.369075\pi\) | |||||||
\(564\) | −4.86584 | −0.204889 | ||||||||
\(565\) | 12.1722 | 0.512090 | ||||||||
\(566\) | −8.17754 | −0.343728 | ||||||||
\(567\) | −0.605593 | −0.0254325 | ||||||||
\(568\) | −6.43229 | −0.269893 | ||||||||
\(569\) | 3.30430 | 0.138523 | 0.0692617 | − | 0.997599i | \(-0.477936\pi\) | ||||
0.0692617 | + | 0.997599i | \(0.477936\pi\) | |||||||
\(570\) | 1.69036 | 0.0708013 | ||||||||
\(571\) | 20.3094 | 0.849922 | 0.424961 | − | 0.905212i | \(-0.360288\pi\) | ||||
0.424961 | + | 0.905212i | \(0.360288\pi\) | |||||||
\(572\) | −13.6838 | −0.572147 | ||||||||
\(573\) | −3.04006 | −0.127000 | ||||||||
\(574\) | −0.239925 | −0.0100143 | ||||||||
\(575\) | 16.2562 | 0.677928 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 31.1092 | 1.29509 | 0.647547 | − | 0.762026i | \(-0.275795\pi\) | ||||
0.647547 | + | 0.762026i | \(0.275795\pi\) | |||||||
\(578\) | 13.4282 | 0.558538 | ||||||||
\(579\) | 5.67822 | 0.235979 | ||||||||
\(580\) | 5.35417 | 0.222320 | ||||||||
\(581\) | 7.11549 | 0.295200 | ||||||||
\(582\) | 6.47681 | 0.268473 | ||||||||
\(583\) | 5.02636 | 0.208170 | ||||||||
\(584\) | −11.5216 | −0.476766 | ||||||||
\(585\) | −4.60183 | −0.190262 | ||||||||
\(586\) | 16.7634 | 0.692490 | ||||||||
\(587\) | 20.2031 | 0.833870 | 0.416935 | − | 0.908936i | \(-0.363104\pi\) | ||||
0.416935 | + | 0.908936i | \(0.363104\pi\) | |||||||
\(588\) | 6.63326 | 0.273551 | ||||||||
\(589\) | 9.54506 | 0.393297 | ||||||||
\(590\) | −2.26180 | −0.0931170 | ||||||||
\(591\) | 7.73625 | 0.318227 | ||||||||
\(592\) | −9.34723 | −0.384169 | ||||||||
\(593\) | −36.3982 | −1.49469 | −0.747347 | − | 0.664434i | \(-0.768673\pi\) | ||||
−0.747347 | + | 0.664434i | \(0.768673\pi\) | |||||||
\(594\) | −5.02636 | −0.206234 | ||||||||
\(595\) | 5.64673 | 0.231493 | ||||||||
\(596\) | 22.9327 | 0.939360 | ||||||||
\(597\) | 26.6283 | 1.08982 | ||||||||
\(598\) | 20.6543 | 0.844617 | ||||||||
\(599\) | 17.7160 | 0.723855 | 0.361927 | − | 0.932206i | \(-0.382119\pi\) | ||||
0.361927 | + | 0.932206i | \(0.382119\pi\) | |||||||
\(600\) | 2.14269 | 0.0874750 | ||||||||
\(601\) | −46.5989 | −1.90081 | −0.950405 | − | 0.311015i | \(-0.899331\pi\) | ||||
−0.950405 | + | 0.311015i | \(0.899331\pi\) | |||||||
\(602\) | 2.31288 | 0.0942658 | ||||||||
\(603\) | −10.6347 | −0.433077 | ||||||||
\(604\) | 19.3661 | 0.787996 | ||||||||
\(605\) | 24.1117 | 0.980281 | ||||||||
\(606\) | −3.24349 | −0.131758 | ||||||||
\(607\) | −36.0480 | −1.46314 | −0.731572 | − | 0.681765i | \(-0.761213\pi\) | ||||
−0.731572 | + | 0.681765i | \(0.761213\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 1.91820 | 0.0777294 | ||||||||
\(610\) | 15.6023 | 0.631720 | ||||||||
\(611\) | −13.2468 | −0.535907 | ||||||||
\(612\) | −5.51617 | −0.222978 | ||||||||
\(613\) | 5.92023 | 0.239116 | 0.119558 | − | 0.992827i | \(-0.461852\pi\) | ||||
0.119558 | + | 0.992827i | \(0.461852\pi\) | |||||||
\(614\) | 0.494661 | 0.0199629 | ||||||||
\(615\) | −0.669689 | −0.0270045 | ||||||||
\(616\) | −3.04393 | −0.122643 | ||||||||
\(617\) | −1.51772 | −0.0611013 | −0.0305506 | − | 0.999533i | \(-0.509726\pi\) | ||||
−0.0305506 | + | 0.999533i | \(0.509726\pi\) | |||||||
\(618\) | −20.1540 | −0.810712 | ||||||||
\(619\) | 37.9119 | 1.52381 | 0.761904 | − | 0.647690i | \(-0.224265\pi\) | ||||
0.761904 | + | 0.647690i | \(0.224265\pi\) | |||||||
\(620\) | −16.1346 | −0.647980 | ||||||||
\(621\) | 7.58679 | 0.304447 | ||||||||
\(622\) | 0.669217 | 0.0268332 | ||||||||
\(623\) | −6.98001 | −0.279648 | ||||||||
\(624\) | 2.72240 | 0.108983 | ||||||||
\(625\) | −9.69542 | −0.387817 | ||||||||
\(626\) | −21.8402 | −0.872909 | ||||||||
\(627\) | 5.02636 | 0.200733 | ||||||||
\(628\) | 0.0490296 | 0.00195649 | ||||||||
\(629\) | 51.5609 | 2.05587 | ||||||||
\(630\) | −1.02367 | −0.0407839 | ||||||||
\(631\) | 40.5797 | 1.61545 | 0.807726 | − | 0.589559i | \(-0.200698\pi\) | ||||
0.807726 | + | 0.589559i | \(0.200698\pi\) | |||||||
\(632\) | −1.45010 | −0.0576819 | ||||||||
\(633\) | 25.9291 | 1.03059 | ||||||||
\(634\) | −12.3228 | −0.489400 | ||||||||
\(635\) | 26.9376 | 1.06898 | ||||||||
\(636\) | −1.00000 | −0.0396526 | ||||||||
\(637\) | 18.0584 | 0.715499 | ||||||||
\(638\) | 15.9209 | 0.630313 | ||||||||
\(639\) | −6.43229 | −0.254458 | ||||||||
\(640\) | 1.69036 | 0.0668173 | ||||||||
\(641\) | 2.95517 | 0.116722 | 0.0583610 | − | 0.998296i | \(-0.481413\pi\) | ||||
0.0583610 | + | 0.998296i | \(0.481413\pi\) | |||||||
\(642\) | −2.85147 | −0.112538 | ||||||||
\(643\) | 8.38579 | 0.330703 | 0.165352 | − | 0.986235i | \(-0.447124\pi\) | ||||
0.165352 | + | 0.986235i | \(0.447124\pi\) | |||||||
\(644\) | 4.59451 | 0.181049 | ||||||||
\(645\) | 6.45580 | 0.254197 | ||||||||
\(646\) | 5.51617 | 0.217031 | ||||||||
\(647\) | −39.1819 | −1.54040 | −0.770200 | − | 0.637803i | \(-0.779843\pi\) | ||||
−0.770200 | + | 0.637803i | \(0.779843\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −6.72558 | −0.264002 | ||||||||
\(650\) | 5.83326 | 0.228799 | ||||||||
\(651\) | −5.78042 | −0.226553 | ||||||||
\(652\) | −18.0273 | −0.706005 | ||||||||
\(653\) | 8.24952 | 0.322829 | 0.161414 | − | 0.986887i | \(-0.448394\pi\) | ||||
0.161414 | + | 0.986887i | \(0.448394\pi\) | |||||||
\(654\) | −4.79123 | −0.187352 | ||||||||
\(655\) | 24.5730 | 0.960147 | ||||||||
\(656\) | 0.396182 | 0.0154683 | ||||||||
\(657\) | −11.5216 | −0.449500 | ||||||||
\(658\) | −2.94672 | −0.114875 | ||||||||
\(659\) | −30.7268 | −1.19695 | −0.598473 | − | 0.801143i | \(-0.704226\pi\) | ||||
−0.598473 | + | 0.801143i | \(0.704226\pi\) | |||||||
\(660\) | −8.49634 | −0.330720 | ||||||||
\(661\) | −30.8161 | −1.19861 | −0.599303 | − | 0.800522i | \(-0.704556\pi\) | ||||
−0.599303 | + | 0.800522i | \(0.704556\pi\) | |||||||
\(662\) | 15.9874 | 0.621367 | ||||||||
\(663\) | −15.0172 | −0.583221 | ||||||||
\(664\) | −11.7496 | −0.455974 | ||||||||
\(665\) | 1.02367 | 0.0396962 | ||||||||
\(666\) | −9.34723 | −0.362198 | ||||||||
\(667\) | −24.0310 | −0.930483 | ||||||||
\(668\) | 23.0036 | 0.890035 | ||||||||
\(669\) | −25.3006 | −0.978177 | ||||||||
\(670\) | −17.9764 | −0.694489 | ||||||||
\(671\) | 46.3943 | 1.79103 | ||||||||
\(672\) | 0.605593 | 0.0233613 | ||||||||
\(673\) | 40.7427 | 1.57051 | 0.785257 | − | 0.619170i | \(-0.212531\pi\) | ||||
0.785257 | + | 0.619170i | \(0.212531\pi\) | |||||||
\(674\) | 32.6872 | 1.25906 | ||||||||
\(675\) | 2.14269 | 0.0824722 | ||||||||
\(676\) | −5.58853 | −0.214944 | ||||||||
\(677\) | −20.6647 | −0.794208 | −0.397104 | − | 0.917774i | \(-0.629985\pi\) | ||||
−0.397104 | + | 0.917774i | \(0.629985\pi\) | |||||||
\(678\) | −7.20098 | −0.276552 | ||||||||
\(679\) | 3.92231 | 0.150525 | ||||||||
\(680\) | −9.32430 | −0.357571 | ||||||||
\(681\) | 8.58401 | 0.328940 | ||||||||
\(682\) | −47.9769 | −1.83713 | ||||||||
\(683\) | 27.0666 | 1.03567 | 0.517837 | − | 0.855479i | \(-0.326737\pi\) | ||||
0.517837 | + | 0.855479i | \(0.326737\pi\) | |||||||
\(684\) | −1.00000 | −0.0382360 | ||||||||
\(685\) | −26.4865 | −1.01200 | ||||||||
\(686\) | 8.25620 | 0.315223 | ||||||||
\(687\) | 23.8247 | 0.908969 | ||||||||
\(688\) | −3.81919 | −0.145605 | ||||||||
\(689\) | −2.72240 | −0.103715 | ||||||||
\(690\) | 12.8244 | 0.488216 | ||||||||
\(691\) | 34.8261 | 1.32485 | 0.662423 | − | 0.749130i | \(-0.269528\pi\) | ||||
0.662423 | + | 0.749130i | \(0.269528\pi\) | |||||||
\(692\) | −16.3622 | −0.621998 | ||||||||
\(693\) | −3.04393 | −0.115629 | ||||||||
\(694\) | 24.6711 | 0.936501 | ||||||||
\(695\) | −1.10420 | −0.0418847 | ||||||||
\(696\) | −3.16748 | −0.120063 | ||||||||
\(697\) | −2.18541 | −0.0827783 | ||||||||
\(698\) | −15.1792 | −0.574540 | ||||||||
\(699\) | −20.2870 | −0.767323 | ||||||||
\(700\) | 1.29760 | 0.0490446 | ||||||||
\(701\) | 41.5066 | 1.56768 | 0.783842 | − | 0.620960i | \(-0.213257\pi\) | ||||
0.783842 | + | 0.620960i | \(0.213257\pi\) | |||||||
\(702\) | 2.72240 | 0.102750 | ||||||||
\(703\) | 9.34723 | 0.352537 | ||||||||
\(704\) | 5.02636 | 0.189438 | ||||||||
\(705\) | −8.22501 | −0.309772 | ||||||||
\(706\) | −31.2775 | −1.17715 | ||||||||
\(707\) | −1.96424 | −0.0738727 | ||||||||
\(708\) | 1.33806 | 0.0502874 | ||||||||
\(709\) | −8.49344 | −0.318978 | −0.159489 | − | 0.987200i | \(-0.550985\pi\) | ||||
−0.159489 | + | 0.987200i | \(0.550985\pi\) | |||||||
\(710\) | −10.8729 | −0.408052 | ||||||||
\(711\) | −1.45010 | −0.0543830 | ||||||||
\(712\) | 11.5259 | 0.431952 | ||||||||
\(713\) | 72.4164 | 2.71202 | ||||||||
\(714\) | −3.34056 | −0.125017 | ||||||||
\(715\) | −23.1304 | −0.865030 | ||||||||
\(716\) | 1.18880 | 0.0444276 | ||||||||
\(717\) | −7.70613 | −0.287791 | ||||||||
\(718\) | 24.6442 | 0.919712 | ||||||||
\(719\) | −15.2099 | −0.567235 | −0.283617 | − | 0.958938i | \(-0.591535\pi\) | ||||
−0.283617 | + | 0.958938i | \(0.591535\pi\) | |||||||
\(720\) | 1.69036 | 0.0629959 | ||||||||
\(721\) | −12.2051 | −0.454542 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | −11.7300 | −0.436244 | ||||||||
\(724\) | −10.2668 | −0.381564 | ||||||||
\(725\) | −6.78692 | −0.252060 | ||||||||
\(726\) | −14.2643 | −0.529397 | ||||||||
\(727\) | −8.57395 | −0.317990 | −0.158995 | − | 0.987279i | \(-0.550825\pi\) | ||||
−0.158995 | + | 0.987279i | \(0.550825\pi\) | |||||||
\(728\) | 1.64867 | 0.0611037 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −19.4756 | −0.720824 | ||||||||
\(731\) | 21.0673 | 0.779203 | ||||||||
\(732\) | −9.23020 | −0.341158 | ||||||||
\(733\) | −35.1291 | −1.29752 | −0.648762 | − | 0.760991i | \(-0.724713\pi\) | ||||
−0.648762 | + | 0.760991i | \(0.724713\pi\) | |||||||
\(734\) | −12.5851 | −0.464525 | ||||||||
\(735\) | 11.2126 | 0.413582 | ||||||||
\(736\) | −7.58679 | −0.279653 | ||||||||
\(737\) | −53.4537 | −1.96899 | ||||||||
\(738\) | 0.396182 | 0.0145837 | ||||||||
\(739\) | 35.2246 | 1.29576 | 0.647879 | − | 0.761743i | \(-0.275656\pi\) | ||||
0.647879 | + | 0.761743i | \(0.275656\pi\) | |||||||
\(740\) | −15.8002 | −0.580825 | ||||||||
\(741\) | −2.72240 | −0.100010 | ||||||||
\(742\) | −0.605593 | −0.0222320 | ||||||||
\(743\) | 17.4349 | 0.639625 | 0.319813 | − | 0.947481i | \(-0.396380\pi\) | ||||
0.319813 | + | 0.947481i | \(0.396380\pi\) | |||||||
\(744\) | 9.54506 | 0.349939 | ||||||||
\(745\) | 38.7645 | 1.42022 | ||||||||
\(746\) | 30.5532 | 1.11863 | ||||||||
\(747\) | −11.7496 | −0.429896 | ||||||||
\(748\) | −27.7263 | −1.01377 | ||||||||
\(749\) | −1.72683 | −0.0630969 | ||||||||
\(750\) | 12.0737 | 0.440869 | ||||||||
\(751\) | −15.6510 | −0.571112 | −0.285556 | − | 0.958362i | \(-0.592178\pi\) | ||||
−0.285556 | + | 0.958362i | \(0.592178\pi\) | |||||||
\(752\) | 4.86584 | 0.177439 | ||||||||
\(753\) | −15.0680 | −0.549108 | ||||||||
\(754\) | −8.62314 | −0.314036 | ||||||||
\(755\) | 32.7357 | 1.19137 | ||||||||
\(756\) | 0.605593 | 0.0220252 | ||||||||
\(757\) | 22.8933 | 0.832072 | 0.416036 | − | 0.909348i | \(-0.363419\pi\) | ||||
0.416036 | + | 0.909348i | \(0.363419\pi\) | |||||||
\(758\) | 5.55156 | 0.201642 | ||||||||
\(759\) | 38.1339 | 1.38417 | ||||||||
\(760\) | −1.69036 | −0.0613157 | ||||||||
\(761\) | −21.4767 | −0.778528 | −0.389264 | − | 0.921126i | \(-0.627271\pi\) | ||||
−0.389264 | + | 0.921126i | \(0.627271\pi\) | |||||||
\(762\) | −15.9360 | −0.577301 | ||||||||
\(763\) | −2.90153 | −0.105043 | ||||||||
\(764\) | 3.04006 | 0.109985 | ||||||||
\(765\) | −9.32430 | −0.337121 | ||||||||
\(766\) | 6.04178 | 0.218299 | ||||||||
\(767\) | 3.64274 | 0.131532 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −19.3350 | −0.697236 | −0.348618 | − | 0.937265i | \(-0.613349\pi\) | ||||
−0.348618 | + | 0.937265i | \(0.613349\pi\) | |||||||
\(770\) | −5.14533 | −0.185425 | ||||||||
\(771\) | −11.0652 | −0.398505 | ||||||||
\(772\) | −5.67822 | −0.204364 | ||||||||
\(773\) | −53.2953 | −1.91690 | −0.958449 | − | 0.285263i | \(-0.907919\pi\) | ||||
−0.958449 | + | 0.285263i | \(0.907919\pi\) | |||||||
\(774\) | −3.81919 | −0.137278 | ||||||||
\(775\) | 20.4521 | 0.734662 | ||||||||
\(776\) | −6.47681 | −0.232504 | ||||||||
\(777\) | −5.66061 | −0.203073 | ||||||||
\(778\) | −7.97723 | −0.285998 | ||||||||
\(779\) | −0.396182 | −0.0141947 | ||||||||
\(780\) | 4.60183 | 0.164772 | ||||||||
\(781\) | −32.3310 | −1.15689 | ||||||||
\(782\) | 41.8501 | 1.49655 | ||||||||
\(783\) | −3.16748 | −0.113196 | ||||||||
\(784\) | −6.63326 | −0.236902 | ||||||||
\(785\) | 0.0828776 | 0.00295803 | ||||||||
\(786\) | −14.5372 | −0.518523 | ||||||||
\(787\) | 7.91503 | 0.282140 | 0.141070 | − | 0.990000i | \(-0.454946\pi\) | ||||
0.141070 | + | 0.990000i | \(0.454946\pi\) | |||||||
\(788\) | −7.73625 | −0.275593 | ||||||||
\(789\) | 7.24748 | 0.258017 | ||||||||
\(790\) | −2.45119 | −0.0872094 | ||||||||
\(791\) | −4.36086 | −0.155054 | ||||||||
\(792\) | 5.02636 | 0.178604 | ||||||||
\(793\) | −25.1283 | −0.892332 | ||||||||
\(794\) | 30.2267 | 1.07270 | ||||||||
\(795\) | −1.69036 | −0.0599508 | ||||||||
\(796\) | −26.6283 | −0.943815 | ||||||||
\(797\) | −39.3451 | −1.39368 | −0.696838 | − | 0.717229i | \(-0.745410\pi\) | ||||
−0.696838 | + | 0.717229i | \(0.745410\pi\) | |||||||
\(798\) | −0.605593 | −0.0214378 | ||||||||
\(799\) | −26.8408 | −0.949560 | ||||||||
\(800\) | −2.14269 | −0.0757556 | ||||||||
\(801\) | 11.5259 | 0.407248 | ||||||||
\(802\) | 5.15637 | 0.182078 | ||||||||
\(803\) | −57.9116 | −2.04366 | ||||||||
\(804\) | 10.6347 | 0.375056 | ||||||||
\(805\) | 7.76636 | 0.273728 | ||||||||
\(806\) | 25.9855 | 0.915300 | ||||||||
\(807\) | 13.0141 | 0.458119 | ||||||||
\(808\) | 3.24349 | 0.114106 | ||||||||
\(809\) | −31.7853 | −1.11751 | −0.558756 | − | 0.829332i | \(-0.688721\pi\) | ||||
−0.558756 | + | 0.829332i | \(0.688721\pi\) | |||||||
\(810\) | 1.69036 | 0.0593931 | ||||||||
\(811\) | 40.2364 | 1.41289 | 0.706446 | − | 0.707767i | \(-0.250297\pi\) | ||||
0.706446 | + | 0.707767i | \(0.250297\pi\) | |||||||
\(812\) | −1.91820 | −0.0673157 | ||||||||
\(813\) | 11.8664 | 0.416172 | ||||||||
\(814\) | −46.9825 | −1.64674 | ||||||||
\(815\) | −30.4726 | −1.06741 | ||||||||
\(816\) | 5.51617 | 0.193105 | ||||||||
\(817\) | 3.81919 | 0.133617 | ||||||||
\(818\) | −9.56914 | −0.334577 | ||||||||
\(819\) | 1.64867 | 0.0576091 | ||||||||
\(820\) | 0.669689 | 0.0233866 | ||||||||
\(821\) | −33.7454 | −1.17772 | −0.588862 | − | 0.808234i | \(-0.700424\pi\) | ||||
−0.588862 | + | 0.808234i | \(0.700424\pi\) | |||||||
\(822\) | 15.6691 | 0.546524 | ||||||||
\(823\) | 39.5858 | 1.37987 | 0.689936 | − | 0.723870i | \(-0.257638\pi\) | ||||
0.689936 | + | 0.723870i | \(0.257638\pi\) | |||||||
\(824\) | 20.1540 | 0.702097 | ||||||||
\(825\) | 10.7699 | 0.374961 | ||||||||
\(826\) | 0.810321 | 0.0281947 | ||||||||
\(827\) | 5.55246 | 0.193078 | 0.0965390 | − | 0.995329i | \(-0.469223\pi\) | ||||
0.0965390 | + | 0.995329i | \(0.469223\pi\) | |||||||
\(828\) | −7.58679 | −0.263659 | ||||||||
\(829\) | 3.98995 | 0.138577 | 0.0692884 | − | 0.997597i | \(-0.477927\pi\) | ||||
0.0692884 | + | 0.997597i | \(0.477927\pi\) | |||||||
\(830\) | −19.8611 | −0.689388 | ||||||||
\(831\) | 23.5480 | 0.816871 | ||||||||
\(832\) | −2.72240 | −0.0943823 | ||||||||
\(833\) | 36.5902 | 1.26778 | ||||||||
\(834\) | 0.653234 | 0.0226197 | ||||||||
\(835\) | 38.8843 | 1.34565 | ||||||||
\(836\) | −5.02636 | −0.173840 | ||||||||
\(837\) | 9.54506 | 0.329926 | ||||||||
\(838\) | −23.2252 | −0.802302 | ||||||||
\(839\) | 9.30463 | 0.321231 | 0.160616 | − | 0.987017i | \(-0.448652\pi\) | ||||
0.160616 | + | 0.987017i | \(0.448652\pi\) | |||||||
\(840\) | 1.02367 | 0.0353199 | ||||||||
\(841\) | −18.9671 | −0.654038 | ||||||||
\(842\) | 5.67045 | 0.195416 | ||||||||
\(843\) | 16.1100 | 0.554857 | ||||||||
\(844\) | −25.9291 | −0.892517 | ||||||||
\(845\) | −9.44662 | −0.324974 | ||||||||
\(846\) | 4.86584 | 0.167291 | ||||||||
\(847\) | −8.63834 | −0.296817 | ||||||||
\(848\) | 1.00000 | 0.0343401 | ||||||||
\(849\) | 8.17754 | 0.280652 | ||||||||
\(850\) | 11.8195 | 0.405404 | ||||||||
\(851\) | 70.9155 | 2.43095 | ||||||||
\(852\) | 6.43229 | 0.220367 | ||||||||
\(853\) | −21.6029 | −0.739668 | −0.369834 | − | 0.929098i | \(-0.620586\pi\) | ||||
−0.369834 | + | 0.929098i | \(0.620586\pi\) | |||||||
\(854\) | −5.58975 | −0.191277 | ||||||||
\(855\) | −1.69036 | −0.0578090 | ||||||||
\(856\) | 2.85147 | 0.0974611 | ||||||||
\(857\) | −38.0281 | −1.29901 | −0.649507 | − | 0.760356i | \(-0.725025\pi\) | ||||
−0.649507 | + | 0.760356i | \(0.725025\pi\) | |||||||
\(858\) | 13.6838 | 0.467156 | ||||||||
\(859\) | 3.42251 | 0.116774 | 0.0583872 | − | 0.998294i | \(-0.481404\pi\) | ||||
0.0583872 | + | 0.998294i | \(0.481404\pi\) | |||||||
\(860\) | −6.45580 | −0.220141 | ||||||||
\(861\) | 0.239925 | 0.00817663 | ||||||||
\(862\) | −15.2246 | −0.518551 | ||||||||
\(863\) | 16.8323 | 0.572978 | 0.286489 | − | 0.958083i | \(-0.407512\pi\) | ||||
0.286489 | + | 0.958083i | \(0.407512\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −27.6580 | −0.940401 | ||||||||
\(866\) | 6.37413 | 0.216602 | ||||||||
\(867\) | −13.4282 | −0.456044 | ||||||||
\(868\) | 5.78042 | 0.196200 | ||||||||
\(869\) | −7.28873 | −0.247253 | ||||||||
\(870\) | −5.35417 | −0.181523 | ||||||||
\(871\) | 28.9518 | 0.980996 | ||||||||
\(872\) | 4.79123 | 0.162251 | ||||||||
\(873\) | −6.47681 | −0.219207 | ||||||||
\(874\) | 7.58679 | 0.256627 | ||||||||
\(875\) | 7.31175 | 0.247182 | ||||||||
\(876\) | 11.5216 | 0.389278 | ||||||||
\(877\) | 46.1626 | 1.55880 | 0.779400 | − | 0.626527i | \(-0.215524\pi\) | ||||
0.779400 | + | 0.626527i | \(0.215524\pi\) | |||||||
\(878\) | −5.06870 | −0.171060 | ||||||||
\(879\) | −16.7634 | −0.565415 | ||||||||
\(880\) | 8.49634 | 0.286412 | ||||||||
\(881\) | −11.0089 | −0.370899 | −0.185449 | − | 0.982654i | \(-0.559374\pi\) | ||||
−0.185449 | + | 0.982654i | \(0.559374\pi\) | |||||||
\(882\) | −6.63326 | −0.223353 | ||||||||
\(883\) | 5.16240 | 0.173729 | 0.0868644 | − | 0.996220i | \(-0.472315\pi\) | ||||
0.0868644 | + | 0.996220i | \(0.472315\pi\) | |||||||
\(884\) | 15.0172 | 0.505084 | ||||||||
\(885\) | 2.26180 | 0.0760297 | ||||||||
\(886\) | −22.9923 | −0.772442 | ||||||||
\(887\) | 28.7966 | 0.966896 | 0.483448 | − | 0.875373i | \(-0.339384\pi\) | ||||
0.483448 | + | 0.875373i | \(0.339384\pi\) | |||||||
\(888\) | 9.34723 | 0.313672 | ||||||||
\(889\) | −9.65074 | −0.323675 | ||||||||
\(890\) | 19.4829 | 0.653069 | ||||||||
\(891\) | 5.02636 | 0.168389 | ||||||||
\(892\) | 25.3006 | 0.847126 | ||||||||
\(893\) | −4.86584 | −0.162829 | ||||||||
\(894\) | −22.9327 | −0.766984 | ||||||||
\(895\) | 2.00950 | 0.0671702 | ||||||||
\(896\) | −0.605593 | −0.0202314 | ||||||||
\(897\) | −20.6543 | −0.689627 | ||||||||
\(898\) | 6.29872 | 0.210191 | ||||||||
\(899\) | −30.2338 | −1.00835 | ||||||||
\(900\) | −2.14269 | −0.0714230 | ||||||||
\(901\) | −5.51617 | −0.183770 | ||||||||
\(902\) | 1.99135 | 0.0663048 | ||||||||
\(903\) | −2.31288 | −0.0769677 | ||||||||
\(904\) | 7.20098 | 0.239501 | ||||||||
\(905\) | −17.3546 | −0.576887 | ||||||||
\(906\) | −19.3661 | −0.643396 | ||||||||
\(907\) | 34.1769 | 1.13483 | 0.567413 | − | 0.823433i | \(-0.307944\pi\) | ||||
0.567413 | + | 0.823433i | \(0.307944\pi\) | |||||||
\(908\) | −8.58401 | −0.284870 | ||||||||
\(909\) | 3.24349 | 0.107580 | ||||||||
\(910\) | 2.78684 | 0.0923827 | ||||||||
\(911\) | −23.1219 | −0.766061 | −0.383031 | − | 0.923736i | \(-0.625120\pi\) | ||||
−0.383031 | + | 0.923736i | \(0.625120\pi\) | |||||||
\(912\) | 1.00000 | 0.0331133 | ||||||||
\(913\) | −59.0578 | −1.95453 | ||||||||
\(914\) | 3.56508 | 0.117922 | ||||||||
\(915\) | −15.6023 | −0.515798 | ||||||||
\(916\) | −23.8247 | −0.787190 | ||||||||
\(917\) | −8.80360 | −0.290721 | ||||||||
\(918\) | 5.51617 | 0.182061 | ||||||||
\(919\) | −19.1746 | −0.632512 | −0.316256 | − | 0.948674i | \(-0.602426\pi\) | ||||
−0.316256 | + | 0.948674i | \(0.602426\pi\) | |||||||
\(920\) | −12.8244 | −0.422808 | ||||||||
\(921\) | −0.494661 | −0.0162996 | ||||||||
\(922\) | −19.6891 | −0.648426 | ||||||||
\(923\) | 17.5113 | 0.576391 | ||||||||
\(924\) | 3.04393 | 0.100138 | ||||||||
\(925\) | 20.0282 | 0.658524 | ||||||||
\(926\) | −19.2726 | −0.633336 | ||||||||
\(927\) | 20.1540 | 0.661944 | ||||||||
\(928\) | 3.16748 | 0.103977 | ||||||||
\(929\) | 53.5219 | 1.75600 | 0.877998 | − | 0.478665i | \(-0.158879\pi\) | ||||
0.877998 | + | 0.478665i | \(0.158879\pi\) | |||||||
\(930\) | 16.1346 | 0.529073 | ||||||||
\(931\) | 6.63326 | 0.217396 | ||||||||
\(932\) | 20.2870 | 0.664521 | ||||||||
\(933\) | −0.669217 | −0.0219092 | ||||||||
\(934\) | −9.21783 | −0.301617 | ||||||||
\(935\) | −46.8673 | −1.53272 | ||||||||
\(936\) | −2.72240 | −0.0889845 | ||||||||
\(937\) | 30.7200 | 1.00358 | 0.501789 | − | 0.864990i | \(-0.332675\pi\) | ||||
0.501789 | + | 0.864990i | \(0.332675\pi\) | |||||||
\(938\) | 6.44028 | 0.210283 | ||||||||
\(939\) | 21.8402 | 0.712727 | ||||||||
\(940\) | 8.22501 | 0.268270 | ||||||||
\(941\) | −44.0264 | −1.43522 | −0.717610 | − | 0.696445i | \(-0.754764\pi\) | ||||
−0.717610 | + | 0.696445i | \(0.754764\pi\) | |||||||
\(942\) | −0.0490296 | −0.00159747 | ||||||||
\(943\) | −3.00575 | −0.0978807 | ||||||||
\(944\) | −1.33806 | −0.0435502 | ||||||||
\(945\) | 1.02367 | 0.0332999 | ||||||||
\(946\) | −19.1966 | −0.624136 | ||||||||
\(947\) | −14.3997 | −0.467928 | −0.233964 | − | 0.972245i | \(-0.575170\pi\) | ||||
−0.233964 | + | 0.972245i | \(0.575170\pi\) | |||||||
\(948\) | 1.45010 | 0.0470971 | ||||||||
\(949\) | 31.3664 | 1.01820 | ||||||||
\(950\) | 2.14269 | 0.0695181 | ||||||||
\(951\) | 12.3228 | 0.399593 | ||||||||
\(952\) | 3.34056 | 0.108268 | ||||||||
\(953\) | −9.44941 | −0.306096 | −0.153048 | − | 0.988219i | \(-0.548909\pi\) | ||||
−0.153048 | + | 0.988219i | \(0.548909\pi\) | |||||||
\(954\) | 1.00000 | 0.0323762 | ||||||||
\(955\) | 5.13878 | 0.166287 | ||||||||
\(956\) | 7.70613 | 0.249234 | ||||||||
\(957\) | −15.9209 | −0.514649 | ||||||||
\(958\) | 26.8437 | 0.867282 | ||||||||
\(959\) | 9.48912 | 0.306420 | ||||||||
\(960\) | −1.69036 | −0.0545561 | ||||||||
\(961\) | 60.1082 | 1.93897 | ||||||||
\(962\) | 25.4469 | 0.820441 | ||||||||
\(963\) | 2.85147 | 0.0918872 | ||||||||
\(964\) | 11.7300 | 0.377798 | ||||||||
\(965\) | −9.59823 | −0.308978 | ||||||||
\(966\) | −4.59451 | −0.147826 | ||||||||
\(967\) | −18.6951 | −0.601194 | −0.300597 | − | 0.953751i | \(-0.597186\pi\) | ||||
−0.300597 | + | 0.953751i | \(0.597186\pi\) | |||||||
\(968\) | 14.2643 | 0.458471 | ||||||||
\(969\) | −5.51617 | −0.177205 | ||||||||
\(970\) | −10.9481 | −0.351523 | ||||||||
\(971\) | 34.4053 | 1.10412 | 0.552060 | − | 0.833805i | \(-0.313842\pi\) | ||||
0.552060 | + | 0.833805i | \(0.313842\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0.395594 | 0.0126822 | ||||||||
\(974\) | −13.0977 | −0.419678 | ||||||||
\(975\) | −5.83326 | −0.186814 | ||||||||
\(976\) | 9.23020 | 0.295452 | ||||||||
\(977\) | −5.03680 | −0.161142 | −0.0805708 | − | 0.996749i | \(-0.525674\pi\) | ||||
−0.0805708 | + | 0.996749i | \(0.525674\pi\) | |||||||
\(978\) | 18.0273 | 0.576450 | ||||||||
\(979\) | 57.9334 | 1.85156 | ||||||||
\(980\) | −11.2126 | −0.358173 | ||||||||
\(981\) | 4.79123 | 0.152972 | ||||||||
\(982\) | 33.6171 | 1.07277 | ||||||||
\(983\) | −16.7963 | −0.535718 | −0.267859 | − | 0.963458i | \(-0.586316\pi\) | ||||
−0.267859 | + | 0.963458i | \(0.586316\pi\) | |||||||
\(984\) | −0.396182 | −0.0126298 | ||||||||
\(985\) | −13.0770 | −0.416669 | ||||||||
\(986\) | −17.4723 | −0.556433 | ||||||||
\(987\) | 2.94672 | 0.0937951 | ||||||||
\(988\) | 2.72240 | 0.0866111 | ||||||||
\(989\) | 28.9754 | 0.921365 | ||||||||
\(990\) | 8.49634 | 0.270031 | ||||||||
\(991\) | 55.7358 | 1.77051 | 0.885254 | − | 0.465109i | \(-0.153985\pi\) | ||||
0.885254 | + | 0.465109i | \(0.153985\pi\) | |||||||
\(992\) | −9.54506 | −0.303056 | ||||||||
\(993\) | −15.9874 | −0.507344 | ||||||||
\(994\) | 3.89535 | 0.123553 | ||||||||
\(995\) | −45.0114 | −1.42696 | ||||||||
\(996\) | 11.7496 | 0.372301 | ||||||||
\(997\) | −37.5350 | −1.18874 | −0.594372 | − | 0.804190i | \(-0.702599\pi\) | ||||
−0.594372 | + | 0.804190i | \(0.702599\pi\) | |||||||
\(998\) | 9.85886 | 0.312077 | ||||||||
\(999\) | 9.34723 | 0.295733 |
(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 | 6042.2.a.bb.1.8 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6042.2.a.bb.1.8 | ✓ | 9 | 1.1 | even | 1 | trivial |