Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4030,2,Mod(1,4030)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4030, 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("4030.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4030.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1797120146\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.3081125.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 8x^{4} + 6x^{3} + 16x^{2} - 10x - 5 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.13283\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4030.1 |
$q$-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 | ||||||||
\(3\) | −1.44295 | −0.833085 | −0.416543 | − | 0.909116i | \(-0.636758\pi\) | ||||
−0.416543 | + | 0.909116i | \(0.636758\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.44295 | 0.589080 | ||||||||
\(7\) | −1.84953 | −0.699056 | −0.349528 | − | 0.936926i | \(-0.613658\pi\) | ||||
−0.349528 | + | 0.936926i | \(0.613658\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.917908 | −0.305969 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 2.03486 | 0.613534 | 0.306767 | − | 0.951785i | \(-0.400753\pi\) | ||||
0.306767 | + | 0.951785i | \(0.400753\pi\) | |||||||
\(12\) | −1.44295 | −0.416543 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 1.84953 | 0.494307 | ||||||||
\(15\) | 1.44295 | 0.372567 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.02676 | 0.976633 | 0.488317 | − | 0.872667i | \(-0.337611\pi\) | ||||
0.488317 | + | 0.872667i | \(0.337611\pi\) | |||||||
\(18\) | 0.917908 | 0.216353 | ||||||||
\(19\) | −3.37914 | −0.775228 | −0.387614 | − | 0.921822i | \(-0.626701\pi\) | ||||
−0.387614 | + | 0.921822i | \(0.626701\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 2.66877 | 0.582373 | ||||||||
\(22\) | −2.03486 | −0.433834 | ||||||||
\(23\) | −4.58382 | −0.955792 | −0.477896 | − | 0.878417i | \(-0.658600\pi\) | ||||
−0.477896 | + | 0.878417i | \(0.658600\pi\) | |||||||
\(24\) | 1.44295 | 0.294540 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | 5.65333 | 1.08798 | ||||||||
\(28\) | −1.84953 | −0.349528 | ||||||||
\(29\) | −5.94991 | −1.10487 | −0.552435 | − | 0.833556i | \(-0.686301\pi\) | ||||
−0.552435 | + | 0.833556i | \(0.686301\pi\) | |||||||
\(30\) | −1.44295 | −0.263445 | ||||||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −2.93619 | −0.511126 | ||||||||
\(34\) | −4.02676 | −0.690584 | ||||||||
\(35\) | 1.84953 | 0.312627 | ||||||||
\(36\) | −0.917908 | −0.152985 | ||||||||
\(37\) | 5.74352 | 0.944229 | 0.472114 | − | 0.881537i | \(-0.343491\pi\) | ||||
0.472114 | + | 0.881537i | \(0.343491\pi\) | |||||||
\(38\) | 3.37914 | 0.548169 | ||||||||
\(39\) | −1.44295 | −0.231056 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −3.43297 | −0.536140 | −0.268070 | − | 0.963399i | \(-0.586386\pi\) | ||||
−0.268070 | + | 0.963399i | \(0.586386\pi\) | |||||||
\(42\) | −2.66877 | −0.411800 | ||||||||
\(43\) | 3.71713 | 0.566858 | 0.283429 | − | 0.958993i | \(-0.408528\pi\) | ||||
0.283429 | + | 0.958993i | \(0.408528\pi\) | |||||||
\(44\) | 2.03486 | 0.306767 | ||||||||
\(45\) | 0.917908 | 0.136834 | ||||||||
\(46\) | 4.58382 | 0.675847 | ||||||||
\(47\) | 10.4630 | 1.52618 | 0.763090 | − | 0.646292i | \(-0.223681\pi\) | ||||
0.763090 | + | 0.646292i | \(0.223681\pi\) | |||||||
\(48\) | −1.44295 | −0.208271 | ||||||||
\(49\) | −3.57924 | −0.511320 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −5.81040 | −0.813618 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | 5.37307 | 0.738047 | 0.369024 | − | 0.929420i | \(-0.379692\pi\) | ||||
0.369024 | + | 0.929420i | \(0.379692\pi\) | |||||||
\(54\) | −5.65333 | −0.769321 | ||||||||
\(55\) | −2.03486 | −0.274381 | ||||||||
\(56\) | 1.84953 | 0.247154 | ||||||||
\(57\) | 4.87591 | 0.645831 | ||||||||
\(58\) | 5.94991 | 0.781261 | ||||||||
\(59\) | −4.54161 | −0.591268 | −0.295634 | − | 0.955301i | \(-0.595531\pi\) | ||||
−0.295634 | + | 0.955301i | \(0.595531\pi\) | |||||||
\(60\) | 1.44295 | 0.186283 | ||||||||
\(61\) | 1.05465 | 0.135034 | 0.0675170 | − | 0.997718i | \(-0.478492\pi\) | ||||
0.0675170 | + | 0.997718i | \(0.478492\pi\) | |||||||
\(62\) | −1.00000 | −0.127000 | ||||||||
\(63\) | 1.69770 | 0.213890 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 2.93619 | 0.361421 | ||||||||
\(67\) | 7.49609 | 0.915794 | 0.457897 | − | 0.889005i | \(-0.348603\pi\) | ||||
0.457897 | + | 0.889005i | \(0.348603\pi\) | |||||||
\(68\) | 4.02676 | 0.488317 | ||||||||
\(69\) | 6.61420 | 0.796256 | ||||||||
\(70\) | −1.84953 | −0.221061 | ||||||||
\(71\) | 4.90554 | 0.582180 | 0.291090 | − | 0.956696i | \(-0.405982\pi\) | ||||
0.291090 | + | 0.956696i | \(0.405982\pi\) | |||||||
\(72\) | 0.917908 | 0.108176 | ||||||||
\(73\) | −9.06629 | −1.06113 | −0.530564 | − | 0.847645i | \(-0.678020\pi\) | ||||
−0.530564 | + | 0.847645i | \(0.678020\pi\) | |||||||
\(74\) | −5.74352 | −0.667671 | ||||||||
\(75\) | −1.44295 | −0.166617 | ||||||||
\(76\) | −3.37914 | −0.387614 | ||||||||
\(77\) | −3.76353 | −0.428895 | ||||||||
\(78\) | 1.44295 | 0.163381 | ||||||||
\(79\) | 11.0383 | 1.24191 | 0.620953 | − | 0.783848i | \(-0.286746\pi\) | ||||
0.620953 | + | 0.783848i | \(0.286746\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −5.40372 | −0.600413 | ||||||||
\(82\) | 3.43297 | 0.379108 | ||||||||
\(83\) | −3.39594 | −0.372753 | −0.186377 | − | 0.982478i | \(-0.559674\pi\) | ||||
−0.186377 | + | 0.982478i | \(0.559674\pi\) | |||||||
\(84\) | 2.66877 | 0.291187 | ||||||||
\(85\) | −4.02676 | −0.436764 | ||||||||
\(86\) | −3.71713 | −0.400829 | ||||||||
\(87\) | 8.58539 | 0.920451 | ||||||||
\(88\) | −2.03486 | −0.216917 | ||||||||
\(89\) | 9.80514 | 1.03934 | 0.519672 | − | 0.854366i | \(-0.326054\pi\) | ||||
0.519672 | + | 0.854366i | \(0.326054\pi\) | |||||||
\(90\) | −0.917908 | −0.0967560 | ||||||||
\(91\) | −1.84953 | −0.193883 | ||||||||
\(92\) | −4.58382 | −0.477896 | ||||||||
\(93\) | −1.44295 | −0.149626 | ||||||||
\(94\) | −10.4630 | −1.07917 | ||||||||
\(95\) | 3.37914 | 0.346692 | ||||||||
\(96\) | 1.44295 | 0.147270 | ||||||||
\(97\) | 6.54755 | 0.664803 | 0.332401 | − | 0.943138i | \(-0.392141\pi\) | ||||
0.332401 | + | 0.943138i | \(0.392141\pi\) | |||||||
\(98\) | 3.57924 | 0.361558 | ||||||||
\(99\) | −1.86782 | −0.187722 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −8.77067 | −0.872715 | −0.436357 | − | 0.899773i | \(-0.643732\pi\) | ||||
−0.436357 | + | 0.899773i | \(0.643732\pi\) | |||||||
\(102\) | 5.81040 | 0.575315 | ||||||||
\(103\) | 8.52722 | 0.840212 | 0.420106 | − | 0.907475i | \(-0.361993\pi\) | ||||
0.420106 | + | 0.907475i | \(0.361993\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | −2.66877 | −0.260445 | ||||||||
\(106\) | −5.37307 | −0.521878 | ||||||||
\(107\) | 7.04378 | 0.680948 | 0.340474 | − | 0.940254i | \(-0.389412\pi\) | ||||
0.340474 | + | 0.940254i | \(0.389412\pi\) | |||||||
\(108\) | 5.65333 | 0.543992 | ||||||||
\(109\) | −16.2833 | −1.55965 | −0.779827 | − | 0.625995i | \(-0.784693\pi\) | ||||
−0.779827 | + | 0.625995i | \(0.784693\pi\) | |||||||
\(110\) | 2.03486 | 0.194016 | ||||||||
\(111\) | −8.28759 | −0.786623 | ||||||||
\(112\) | −1.84953 | −0.174764 | ||||||||
\(113\) | −1.74246 | −0.163917 | −0.0819584 | − | 0.996636i | \(-0.526117\pi\) | ||||
−0.0819584 | + | 0.996636i | \(0.526117\pi\) | |||||||
\(114\) | −4.87591 | −0.456671 | ||||||||
\(115\) | 4.58382 | 0.427443 | ||||||||
\(116\) | −5.94991 | −0.552435 | ||||||||
\(117\) | −0.917908 | −0.0848606 | ||||||||
\(118\) | 4.54161 | 0.418089 | ||||||||
\(119\) | −7.44761 | −0.682721 | ||||||||
\(120\) | −1.44295 | −0.131722 | ||||||||
\(121\) | −6.85934 | −0.623576 | ||||||||
\(122\) | −1.05465 | −0.0954834 | ||||||||
\(123\) | 4.95359 | 0.446650 | ||||||||
\(124\) | 1.00000 | 0.0898027 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −1.69770 | −0.151243 | ||||||||
\(127\) | −10.2278 | −0.907574 | −0.453787 | − | 0.891110i | \(-0.649927\pi\) | ||||
−0.453787 | + | 0.891110i | \(0.649927\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −5.36362 | −0.472241 | ||||||||
\(130\) | 1.00000 | 0.0877058 | ||||||||
\(131\) | −11.6099 | −1.01436 | −0.507179 | − | 0.861841i | \(-0.669312\pi\) | ||||
−0.507179 | + | 0.861841i | \(0.669312\pi\) | |||||||
\(132\) | −2.93619 | −0.255563 | ||||||||
\(133\) | 6.24982 | 0.541928 | ||||||||
\(134\) | −7.49609 | −0.647564 | ||||||||
\(135\) | −5.65333 | −0.486561 | ||||||||
\(136\) | −4.02676 | −0.345292 | ||||||||
\(137\) | 0.710019 | 0.0606611 | 0.0303305 | − | 0.999540i | \(-0.490344\pi\) | ||||
0.0303305 | + | 0.999540i | \(0.490344\pi\) | |||||||
\(138\) | −6.61420 | −0.563038 | ||||||||
\(139\) | 10.5855 | 0.897849 | 0.448924 | − | 0.893570i | \(-0.351807\pi\) | ||||
0.448924 | + | 0.893570i | \(0.351807\pi\) | |||||||
\(140\) | 1.84953 | 0.156314 | ||||||||
\(141\) | −15.0975 | −1.27144 | ||||||||
\(142\) | −4.90554 | −0.411664 | ||||||||
\(143\) | 2.03486 | 0.170164 | ||||||||
\(144\) | −0.917908 | −0.0764923 | ||||||||
\(145\) | 5.94991 | 0.494113 | ||||||||
\(146\) | 9.06629 | 0.750331 | ||||||||
\(147\) | 5.16465 | 0.425973 | ||||||||
\(148\) | 5.74352 | 0.472114 | ||||||||
\(149\) | −3.46476 | −0.283844 | −0.141922 | − | 0.989878i | \(-0.545328\pi\) | ||||
−0.141922 | + | 0.989878i | \(0.545328\pi\) | |||||||
\(150\) | 1.44295 | 0.117816 | ||||||||
\(151\) | −8.55602 | −0.696279 | −0.348140 | − | 0.937443i | \(-0.613186\pi\) | ||||
−0.348140 | + | 0.937443i | \(0.613186\pi\) | |||||||
\(152\) | 3.37914 | 0.274084 | ||||||||
\(153\) | −3.69620 | −0.298820 | ||||||||
\(154\) | 3.76353 | 0.303274 | ||||||||
\(155\) | −1.00000 | −0.0803219 | ||||||||
\(156\) | −1.44295 | −0.115528 | ||||||||
\(157\) | −2.04229 | −0.162992 | −0.0814962 | − | 0.996674i | \(-0.525970\pi\) | ||||
−0.0814962 | + | 0.996674i | \(0.525970\pi\) | |||||||
\(158\) | −11.0383 | −0.878161 | ||||||||
\(159\) | −7.75304 | −0.614856 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 8.47790 | 0.668152 | ||||||||
\(162\) | 5.40372 | 0.424556 | ||||||||
\(163\) | 0.325069 | 0.0254614 | 0.0127307 | − | 0.999919i | \(-0.495948\pi\) | ||||
0.0127307 | + | 0.999919i | \(0.495948\pi\) | |||||||
\(164\) | −3.43297 | −0.268070 | ||||||||
\(165\) | 2.93619 | 0.228582 | ||||||||
\(166\) | 3.39594 | 0.263576 | ||||||||
\(167\) | −10.3504 | −0.800940 | −0.400470 | − | 0.916310i | \(-0.631153\pi\) | ||||
−0.400470 | + | 0.916310i | \(0.631153\pi\) | |||||||
\(168\) | −2.66877 | −0.205900 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 4.02676 | 0.308839 | ||||||||
\(171\) | 3.10174 | 0.237196 | ||||||||
\(172\) | 3.71713 | 0.283429 | ||||||||
\(173\) | −16.0351 | −1.21913 | −0.609563 | − | 0.792738i | \(-0.708655\pi\) | ||||
−0.609563 | + | 0.792738i | \(0.708655\pi\) | |||||||
\(174\) | −8.58539 | −0.650857 | ||||||||
\(175\) | −1.84953 | −0.139811 | ||||||||
\(176\) | 2.03486 | 0.153383 | ||||||||
\(177\) | 6.55330 | 0.492576 | ||||||||
\(178\) | −9.80514 | −0.734927 | ||||||||
\(179\) | −1.57100 | −0.117422 | −0.0587111 | − | 0.998275i | \(-0.518699\pi\) | ||||
−0.0587111 | + | 0.998275i | \(0.518699\pi\) | |||||||
\(180\) | 0.917908 | 0.0684168 | ||||||||
\(181\) | 0.634377 | 0.0471529 | 0.0235764 | − | 0.999722i | \(-0.492495\pi\) | ||||
0.0235764 | + | 0.999722i | \(0.492495\pi\) | |||||||
\(182\) | 1.84953 | 0.137096 | ||||||||
\(183\) | −1.52180 | −0.112495 | ||||||||
\(184\) | 4.58382 | 0.337923 | ||||||||
\(185\) | −5.74352 | −0.422272 | ||||||||
\(186\) | 1.44295 | 0.105802 | ||||||||
\(187\) | 8.19390 | 0.599197 | ||||||||
\(188\) | 10.4630 | 0.763090 | ||||||||
\(189\) | −10.4560 | −0.760562 | ||||||||
\(190\) | −3.37914 | −0.245149 | ||||||||
\(191\) | −17.6588 | −1.27774 | −0.638872 | − | 0.769313i | \(-0.720599\pi\) | ||||
−0.638872 | + | 0.769313i | \(0.720599\pi\) | |||||||
\(192\) | −1.44295 | −0.104136 | ||||||||
\(193\) | 6.30028 | 0.453504 | 0.226752 | − | 0.973952i | \(-0.427189\pi\) | ||||
0.226752 | + | 0.973952i | \(0.427189\pi\) | |||||||
\(194\) | −6.54755 | −0.470086 | ||||||||
\(195\) | 1.44295 | 0.103331 | ||||||||
\(196\) | −3.57924 | −0.255660 | ||||||||
\(197\) | 17.0669 | 1.21596 | 0.607982 | − | 0.793951i | \(-0.291979\pi\) | ||||
0.607982 | + | 0.793951i | \(0.291979\pi\) | |||||||
\(198\) | 1.86782 | 0.132740 | ||||||||
\(199\) | −9.09507 | −0.644732 | −0.322366 | − | 0.946615i | \(-0.604478\pi\) | ||||
−0.322366 | + | 0.946615i | \(0.604478\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −10.8165 | −0.762934 | ||||||||
\(202\) | 8.77067 | 0.617102 | ||||||||
\(203\) | 11.0045 | 0.772366 | ||||||||
\(204\) | −5.81040 | −0.406809 | ||||||||
\(205\) | 3.43297 | 0.239769 | ||||||||
\(206\) | −8.52722 | −0.594119 | ||||||||
\(207\) | 4.20752 | 0.292443 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | −6.87608 | −0.475628 | ||||||||
\(210\) | 2.66877 | 0.184163 | ||||||||
\(211\) | −6.77778 | −0.466601 | −0.233301 | − | 0.972405i | \(-0.574953\pi\) | ||||
−0.233301 | + | 0.972405i | \(0.574953\pi\) | |||||||
\(212\) | 5.37307 | 0.369024 | ||||||||
\(213\) | −7.07842 | −0.485006 | ||||||||
\(214\) | −7.04378 | −0.481503 | ||||||||
\(215\) | −3.71713 | −0.253506 | ||||||||
\(216\) | −5.65333 | −0.384660 | ||||||||
\(217\) | −1.84953 | −0.125554 | ||||||||
\(218\) | 16.2833 | 1.10284 | ||||||||
\(219\) | 13.0822 | 0.884011 | ||||||||
\(220\) | −2.03486 | −0.137190 | ||||||||
\(221\) | 4.02676 | 0.270869 | ||||||||
\(222\) | 8.28759 | 0.556226 | ||||||||
\(223\) | −9.58886 | −0.642117 | −0.321059 | − | 0.947059i | \(-0.604039\pi\) | ||||
−0.321059 | + | 0.947059i | \(0.604039\pi\) | |||||||
\(224\) | 1.84953 | 0.123577 | ||||||||
\(225\) | −0.917908 | −0.0611939 | ||||||||
\(226\) | 1.74246 | 0.115907 | ||||||||
\(227\) | −8.92629 | −0.592459 | −0.296229 | − | 0.955117i | \(-0.595729\pi\) | ||||
−0.296229 | + | 0.955117i | \(0.595729\pi\) | |||||||
\(228\) | 4.87591 | 0.322915 | ||||||||
\(229\) | 15.4671 | 1.02210 | 0.511048 | − | 0.859552i | \(-0.329257\pi\) | ||||
0.511048 | + | 0.859552i | \(0.329257\pi\) | |||||||
\(230\) | −4.58382 | −0.302248 | ||||||||
\(231\) | 5.43058 | 0.357306 | ||||||||
\(232\) | 5.94991 | 0.390631 | ||||||||
\(233\) | −3.49932 | −0.229248 | −0.114624 | − | 0.993409i | \(-0.536566\pi\) | ||||
−0.114624 | + | 0.993409i | \(0.536566\pi\) | |||||||
\(234\) | 0.917908 | 0.0600055 | ||||||||
\(235\) | −10.4630 | −0.682529 | ||||||||
\(236\) | −4.54161 | −0.295634 | ||||||||
\(237\) | −15.9277 | −1.03461 | ||||||||
\(238\) | 7.44761 | 0.482757 | ||||||||
\(239\) | 28.4119 | 1.83781 | 0.918907 | − | 0.394474i | \(-0.129073\pi\) | ||||
0.918907 | + | 0.394474i | \(0.129073\pi\) | |||||||
\(240\) | 1.44295 | 0.0931417 | ||||||||
\(241\) | −9.81549 | −0.632271 | −0.316136 | − | 0.948714i | \(-0.602385\pi\) | ||||
−0.316136 | + | 0.948714i | \(0.602385\pi\) | |||||||
\(242\) | 6.85934 | 0.440935 | ||||||||
\(243\) | −9.16271 | −0.587788 | ||||||||
\(244\) | 1.05465 | 0.0675170 | ||||||||
\(245\) | 3.57924 | 0.228669 | ||||||||
\(246\) | −4.95359 | −0.315829 | ||||||||
\(247\) | −3.37914 | −0.215010 | ||||||||
\(248\) | −1.00000 | −0.0635001 | ||||||||
\(249\) | 4.90016 | 0.310535 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 22.5522 | 1.42348 | 0.711741 | − | 0.702442i | \(-0.247907\pi\) | ||||
0.711741 | + | 0.702442i | \(0.247907\pi\) | |||||||
\(252\) | 1.69770 | 0.106945 | ||||||||
\(253\) | −9.32743 | −0.586410 | ||||||||
\(254\) | 10.2278 | 0.641752 | ||||||||
\(255\) | 5.81040 | 0.363861 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −19.3964 | −1.20991 | −0.604957 | − | 0.796258i | \(-0.706810\pi\) | ||||
−0.604957 | + | 0.796258i | \(0.706810\pi\) | |||||||
\(258\) | 5.36362 | 0.333925 | ||||||||
\(259\) | −10.6228 | −0.660069 | ||||||||
\(260\) | −1.00000 | −0.0620174 | ||||||||
\(261\) | 5.46147 | 0.338056 | ||||||||
\(262\) | 11.6099 | 0.717259 | ||||||||
\(263\) | −19.4265 | −1.19789 | −0.598944 | − | 0.800791i | \(-0.704413\pi\) | ||||
−0.598944 | + | 0.800791i | \(0.704413\pi\) | |||||||
\(264\) | 2.93619 | 0.180710 | ||||||||
\(265\) | −5.37307 | −0.330065 | ||||||||
\(266\) | −6.24982 | −0.383201 | ||||||||
\(267\) | −14.1483 | −0.865861 | ||||||||
\(268\) | 7.49609 | 0.457897 | ||||||||
\(269\) | −17.4915 | −1.06647 | −0.533237 | − | 0.845966i | \(-0.679024\pi\) | ||||
−0.533237 | + | 0.845966i | \(0.679024\pi\) | |||||||
\(270\) | 5.65333 | 0.344051 | ||||||||
\(271\) | 23.9044 | 1.45209 | 0.726045 | − | 0.687647i | \(-0.241356\pi\) | ||||
0.726045 | + | 0.687647i | \(0.241356\pi\) | |||||||
\(272\) | 4.02676 | 0.244158 | ||||||||
\(273\) | 2.66877 | 0.161521 | ||||||||
\(274\) | −0.710019 | −0.0428938 | ||||||||
\(275\) | 2.03486 | 0.122707 | ||||||||
\(276\) | 6.61420 | 0.398128 | ||||||||
\(277\) | −9.54560 | −0.573539 | −0.286770 | − | 0.958000i | \(-0.592581\pi\) | ||||
−0.286770 | + | 0.958000i | \(0.592581\pi\) | |||||||
\(278\) | −10.5855 | −0.634875 | ||||||||
\(279\) | −0.917908 | −0.0549537 | ||||||||
\(280\) | −1.84953 | −0.110530 | ||||||||
\(281\) | −19.3263 | −1.15291 | −0.576455 | − | 0.817129i | \(-0.695564\pi\) | ||||
−0.576455 | + | 0.817129i | \(0.695564\pi\) | |||||||
\(282\) | 15.0975 | 0.899043 | ||||||||
\(283\) | −10.1976 | −0.606187 | −0.303093 | − | 0.952961i | \(-0.598019\pi\) | ||||
−0.303093 | + | 0.952961i | \(0.598019\pi\) | |||||||
\(284\) | 4.90554 | 0.291090 | ||||||||
\(285\) | −4.87591 | −0.288824 | ||||||||
\(286\) | −2.03486 | −0.120324 | ||||||||
\(287\) | 6.34938 | 0.374792 | ||||||||
\(288\) | 0.917908 | 0.0540882 | ||||||||
\(289\) | −0.785193 | −0.0461878 | ||||||||
\(290\) | −5.94991 | −0.349391 | ||||||||
\(291\) | −9.44775 | −0.553837 | ||||||||
\(292\) | −9.06629 | −0.530564 | ||||||||
\(293\) | −25.4078 | −1.48434 | −0.742170 | − | 0.670212i | \(-0.766203\pi\) | ||||
−0.742170 | + | 0.670212i | \(0.766203\pi\) | |||||||
\(294\) | −5.16465 | −0.301209 | ||||||||
\(295\) | 4.54161 | 0.264423 | ||||||||
\(296\) | −5.74352 | −0.333835 | ||||||||
\(297\) | 11.5037 | 0.667515 | ||||||||
\(298\) | 3.46476 | 0.200708 | ||||||||
\(299\) | −4.58382 | −0.265089 | ||||||||
\(300\) | −1.44295 | −0.0833085 | ||||||||
\(301\) | −6.87495 | −0.396265 | ||||||||
\(302\) | 8.55602 | 0.492344 | ||||||||
\(303\) | 12.6556 | 0.727046 | ||||||||
\(304\) | −3.37914 | −0.193807 | ||||||||
\(305\) | −1.05465 | −0.0603890 | ||||||||
\(306\) | 3.69620 | 0.211297 | ||||||||
\(307\) | −31.0455 | −1.77186 | −0.885929 | − | 0.463821i | \(-0.846478\pi\) | ||||
−0.885929 | + | 0.463821i | \(0.846478\pi\) | |||||||
\(308\) | −3.76353 | −0.214447 | ||||||||
\(309\) | −12.3043 | −0.699968 | ||||||||
\(310\) | 1.00000 | 0.0567962 | ||||||||
\(311\) | −11.0997 | −0.629408 | −0.314704 | − | 0.949190i | \(-0.601905\pi\) | ||||
−0.314704 | + | 0.949190i | \(0.601905\pi\) | |||||||
\(312\) | 1.44295 | 0.0816907 | ||||||||
\(313\) | 28.4814 | 1.60986 | 0.804932 | − | 0.593367i | \(-0.202202\pi\) | ||||
0.804932 | + | 0.593367i | \(0.202202\pi\) | |||||||
\(314\) | 2.04229 | 0.115253 | ||||||||
\(315\) | −1.69770 | −0.0956544 | ||||||||
\(316\) | 11.0383 | 0.620953 | ||||||||
\(317\) | 13.5242 | 0.759597 | 0.379798 | − | 0.925069i | \(-0.375993\pi\) | ||||
0.379798 | + | 0.925069i | \(0.375993\pi\) | |||||||
\(318\) | 7.75304 | 0.434769 | ||||||||
\(319\) | −12.1072 | −0.677875 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −10.1638 | −0.567288 | ||||||||
\(322\) | −8.47790 | −0.472455 | ||||||||
\(323\) | −13.6070 | −0.757113 | ||||||||
\(324\) | −5.40372 | −0.300207 | ||||||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | −0.325069 | −0.0180039 | ||||||||
\(327\) | 23.4959 | 1.29932 | ||||||||
\(328\) | 3.43297 | 0.189554 | ||||||||
\(329\) | −19.3516 | −1.06689 | ||||||||
\(330\) | −2.93619 | −0.161632 | ||||||||
\(331\) | 21.5750 | 1.18587 | 0.592936 | − | 0.805250i | \(-0.297969\pi\) | ||||
0.592936 | + | 0.805250i | \(0.297969\pi\) | |||||||
\(332\) | −3.39594 | −0.186377 | ||||||||
\(333\) | −5.27202 | −0.288905 | ||||||||
\(334\) | 10.3504 | 0.566350 | ||||||||
\(335\) | −7.49609 | −0.409555 | ||||||||
\(336\) | 2.66877 | 0.145593 | ||||||||
\(337\) | −10.5216 | −0.573148 | −0.286574 | − | 0.958058i | \(-0.592516\pi\) | ||||
−0.286574 | + | 0.958058i | \(0.592516\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | 2.51427 | 0.136557 | ||||||||
\(340\) | −4.02676 | −0.218382 | ||||||||
\(341\) | 2.03486 | 0.110194 | ||||||||
\(342\) | −3.10174 | −0.167723 | ||||||||
\(343\) | 19.5666 | 1.05650 | ||||||||
\(344\) | −3.71713 | −0.200414 | ||||||||
\(345\) | −6.61420 | −0.356096 | ||||||||
\(346\) | 16.0351 | 0.862052 | ||||||||
\(347\) | −31.3970 | −1.68548 | −0.842741 | − | 0.538320i | \(-0.819059\pi\) | ||||
−0.842741 | + | 0.538320i | \(0.819059\pi\) | |||||||
\(348\) | 8.58539 | 0.460225 | ||||||||
\(349\) | −12.0383 | −0.644394 | −0.322197 | − | 0.946673i | \(-0.604421\pi\) | ||||
−0.322197 | + | 0.946673i | \(0.604421\pi\) | |||||||
\(350\) | 1.84953 | 0.0988615 | ||||||||
\(351\) | 5.65333 | 0.301752 | ||||||||
\(352\) | −2.03486 | −0.108458 | ||||||||
\(353\) | −13.7981 | −0.734397 | −0.367199 | − | 0.930143i | \(-0.619683\pi\) | ||||
−0.367199 | + | 0.930143i | \(0.619683\pi\) | |||||||
\(354\) | −6.55330 | −0.348304 | ||||||||
\(355\) | −4.90554 | −0.260359 | ||||||||
\(356\) | 9.80514 | 0.519672 | ||||||||
\(357\) | 10.7465 | 0.568765 | ||||||||
\(358\) | 1.57100 | 0.0830300 | ||||||||
\(359\) | −21.0996 | −1.11359 | −0.556796 | − | 0.830649i | \(-0.687969\pi\) | ||||
−0.556796 | + | 0.830649i | \(0.687969\pi\) | |||||||
\(360\) | −0.917908 | −0.0483780 | ||||||||
\(361\) | −7.58141 | −0.399022 | ||||||||
\(362\) | −0.634377 | −0.0333421 | ||||||||
\(363\) | 9.89765 | 0.519492 | ||||||||
\(364\) | −1.84953 | −0.0969417 | ||||||||
\(365\) | 9.06629 | 0.474551 | ||||||||
\(366\) | 1.52180 | 0.0795458 | ||||||||
\(367\) | 26.5184 | 1.38425 | 0.692124 | − | 0.721778i | \(-0.256675\pi\) | ||||
0.692124 | + | 0.721778i | \(0.256675\pi\) | |||||||
\(368\) | −4.58382 | −0.238948 | ||||||||
\(369\) | 3.15115 | 0.164042 | ||||||||
\(370\) | 5.74352 | 0.298591 | ||||||||
\(371\) | −9.93764 | −0.515937 | ||||||||
\(372\) | −1.44295 | −0.0748132 | ||||||||
\(373\) | −4.72751 | −0.244781 | −0.122391 | − | 0.992482i | \(-0.539056\pi\) | ||||
−0.122391 | + | 0.992482i | \(0.539056\pi\) | |||||||
\(374\) | −8.19390 | −0.423697 | ||||||||
\(375\) | 1.44295 | 0.0745134 | ||||||||
\(376\) | −10.4630 | −0.539586 | ||||||||
\(377\) | −5.94991 | −0.306436 | ||||||||
\(378\) | 10.4560 | 0.537798 | ||||||||
\(379\) | −21.7669 | −1.11809 | −0.559046 | − | 0.829137i | \(-0.688833\pi\) | ||||
−0.559046 | + | 0.829137i | \(0.688833\pi\) | |||||||
\(380\) | 3.37914 | 0.173346 | ||||||||
\(381\) | 14.7582 | 0.756086 | ||||||||
\(382\) | 17.6588 | 0.903502 | ||||||||
\(383\) | 11.2822 | 0.576491 | 0.288246 | − | 0.957557i | \(-0.406928\pi\) | ||||
0.288246 | + | 0.957557i | \(0.406928\pi\) | |||||||
\(384\) | 1.44295 | 0.0736350 | ||||||||
\(385\) | 3.76353 | 0.191807 | ||||||||
\(386\) | −6.30028 | −0.320676 | ||||||||
\(387\) | −3.41199 | −0.173441 | ||||||||
\(388\) | 6.54755 | 0.332401 | ||||||||
\(389\) | −14.1684 | −0.718367 | −0.359183 | − | 0.933267i | \(-0.616945\pi\) | ||||
−0.359183 | + | 0.933267i | \(0.616945\pi\) | |||||||
\(390\) | −1.44295 | −0.0730664 | ||||||||
\(391\) | −18.4579 | −0.933458 | ||||||||
\(392\) | 3.57924 | 0.180779 | ||||||||
\(393\) | 16.7524 | 0.845046 | ||||||||
\(394\) | −17.0669 | −0.859817 | ||||||||
\(395\) | −11.0383 | −0.555398 | ||||||||
\(396\) | −1.86782 | −0.0938612 | ||||||||
\(397\) | 12.1144 | 0.608006 | 0.304003 | − | 0.952671i | \(-0.401677\pi\) | ||||
0.304003 | + | 0.952671i | \(0.401677\pi\) | |||||||
\(398\) | 9.09507 | 0.455895 | ||||||||
\(399\) | −9.01815 | −0.451472 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −31.4824 | −1.57216 | −0.786079 | − | 0.618126i | \(-0.787892\pi\) | ||||
−0.786079 | + | 0.618126i | \(0.787892\pi\) | |||||||
\(402\) | 10.8165 | 0.539476 | ||||||||
\(403\) | 1.00000 | 0.0498135 | ||||||||
\(404\) | −8.77067 | −0.436357 | ||||||||
\(405\) | 5.40372 | 0.268513 | ||||||||
\(406\) | −11.0045 | −0.546145 | ||||||||
\(407\) | 11.6873 | 0.579316 | ||||||||
\(408\) | 5.81040 | 0.287658 | ||||||||
\(409\) | −27.9065 | −1.37989 | −0.689944 | − | 0.723863i | \(-0.742365\pi\) | ||||
−0.689944 | + | 0.723863i | \(0.742365\pi\) | |||||||
\(410\) | −3.43297 | −0.169542 | ||||||||
\(411\) | −1.02452 | −0.0505358 | ||||||||
\(412\) | 8.52722 | 0.420106 | ||||||||
\(413\) | 8.39984 | 0.413329 | ||||||||
\(414\) | −4.20752 | −0.206788 | ||||||||
\(415\) | 3.39594 | 0.166700 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | −15.2743 | −0.747984 | ||||||||
\(418\) | 6.87608 | 0.336320 | ||||||||
\(419\) | 6.49496 | 0.317300 | 0.158650 | − | 0.987335i | \(-0.449286\pi\) | ||||
0.158650 | + | 0.987335i | \(0.449286\pi\) | |||||||
\(420\) | −2.66877 | −0.130223 | ||||||||
\(421\) | −15.8856 | −0.774218 | −0.387109 | − | 0.922034i | \(-0.626526\pi\) | ||||
−0.387109 | + | 0.922034i | \(0.626526\pi\) | |||||||
\(422\) | 6.77778 | 0.329937 | ||||||||
\(423\) | −9.60404 | −0.466964 | ||||||||
\(424\) | −5.37307 | −0.260939 | ||||||||
\(425\) | 4.02676 | 0.195327 | ||||||||
\(426\) | 7.07842 | 0.342951 | ||||||||
\(427\) | −1.95060 | −0.0943963 | ||||||||
\(428\) | 7.04378 | 0.340474 | ||||||||
\(429\) | −2.93619 | −0.141761 | ||||||||
\(430\) | 3.71713 | 0.179256 | ||||||||
\(431\) | −24.8265 | −1.19585 | −0.597924 | − | 0.801553i | \(-0.704008\pi\) | ||||
−0.597924 | + | 0.801553i | \(0.704008\pi\) | |||||||
\(432\) | 5.65333 | 0.271996 | ||||||||
\(433\) | 16.9214 | 0.813190 | 0.406595 | − | 0.913609i | \(-0.366716\pi\) | ||||
0.406595 | + | 0.913609i | \(0.366716\pi\) | |||||||
\(434\) | 1.84953 | 0.0887802 | ||||||||
\(435\) | −8.58539 | −0.411638 | ||||||||
\(436\) | −16.2833 | −0.779827 | ||||||||
\(437\) | 15.4894 | 0.740956 | ||||||||
\(438\) | −13.0822 | −0.625090 | ||||||||
\(439\) | 12.9144 | 0.616373 | 0.308186 | − | 0.951326i | \(-0.400278\pi\) | ||||
0.308186 | + | 0.951326i | \(0.400278\pi\) | |||||||
\(440\) | 2.03486 | 0.0970082 | ||||||||
\(441\) | 3.28542 | 0.156448 | ||||||||
\(442\) | −4.02676 | −0.191534 | ||||||||
\(443\) | −37.8803 | −1.79975 | −0.899874 | − | 0.436149i | \(-0.856342\pi\) | ||||
−0.899874 | + | 0.436149i | \(0.856342\pi\) | |||||||
\(444\) | −8.28759 | −0.393311 | ||||||||
\(445\) | −9.80514 | −0.464808 | ||||||||
\(446\) | 9.58886 | 0.454046 | ||||||||
\(447\) | 4.99946 | 0.236466 | ||||||||
\(448\) | −1.84953 | −0.0873820 | ||||||||
\(449\) | −5.72002 | −0.269944 | −0.134972 | − | 0.990849i | \(-0.543095\pi\) | ||||
−0.134972 | + | 0.990849i | \(0.543095\pi\) | |||||||
\(450\) | 0.917908 | 0.0432706 | ||||||||
\(451\) | −6.98562 | −0.328940 | ||||||||
\(452\) | −1.74246 | −0.0819584 | ||||||||
\(453\) | 12.3459 | 0.580060 | ||||||||
\(454\) | 8.92629 | 0.418932 | ||||||||
\(455\) | 1.84953 | 0.0867073 | ||||||||
\(456\) | −4.87591 | −0.228336 | ||||||||
\(457\) | −28.4558 | −1.33111 | −0.665554 | − | 0.746350i | \(-0.731805\pi\) | ||||
−0.665554 | + | 0.746350i | \(0.731805\pi\) | |||||||
\(458\) | −15.4671 | −0.722731 | ||||||||
\(459\) | 22.7646 | 1.06256 | ||||||||
\(460\) | 4.58382 | 0.213722 | ||||||||
\(461\) | −1.88939 | −0.0879975 | −0.0439987 | − | 0.999032i | \(-0.514010\pi\) | ||||
−0.0439987 | + | 0.999032i | \(0.514010\pi\) | |||||||
\(462\) | −5.43058 | −0.252653 | ||||||||
\(463\) | 11.4219 | 0.530821 | 0.265411 | − | 0.964135i | \(-0.414492\pi\) | ||||
0.265411 | + | 0.964135i | \(0.414492\pi\) | |||||||
\(464\) | −5.94991 | −0.276218 | ||||||||
\(465\) | 1.44295 | 0.0669150 | ||||||||
\(466\) | 3.49932 | 0.162103 | ||||||||
\(467\) | −26.9535 | −1.24726 | −0.623630 | − | 0.781719i | \(-0.714343\pi\) | ||||
−0.623630 | + | 0.781719i | \(0.714343\pi\) | |||||||
\(468\) | −0.917908 | −0.0424303 | ||||||||
\(469\) | −13.8642 | −0.640191 | ||||||||
\(470\) | 10.4630 | 0.482621 | ||||||||
\(471\) | 2.94691 | 0.135787 | ||||||||
\(472\) | 4.54161 | 0.209045 | ||||||||
\(473\) | 7.56385 | 0.347786 | ||||||||
\(474\) | 15.9277 | 0.731583 | ||||||||
\(475\) | −3.37914 | −0.155046 | ||||||||
\(476\) | −7.44761 | −0.341361 | ||||||||
\(477\) | −4.93198 | −0.225820 | ||||||||
\(478\) | −28.4119 | −1.29953 | ||||||||
\(479\) | −29.2802 | −1.33785 | −0.668924 | − | 0.743331i | \(-0.733245\pi\) | ||||
−0.668924 | + | 0.743331i | \(0.733245\pi\) | |||||||
\(480\) | −1.44295 | −0.0658612 | ||||||||
\(481\) | 5.74352 | 0.261882 | ||||||||
\(482\) | 9.81549 | 0.447083 | ||||||||
\(483\) | −12.2331 | −0.556628 | ||||||||
\(484\) | −6.85934 | −0.311788 | ||||||||
\(485\) | −6.54755 | −0.297309 | ||||||||
\(486\) | 9.16271 | 0.415629 | ||||||||
\(487\) | 10.9477 | 0.496088 | 0.248044 | − | 0.968749i | \(-0.420212\pi\) | ||||
0.248044 | + | 0.968749i | \(0.420212\pi\) | |||||||
\(488\) | −1.05465 | −0.0477417 | ||||||||
\(489\) | −0.469057 | −0.0212115 | ||||||||
\(490\) | −3.57924 | −0.161694 | ||||||||
\(491\) | −5.83895 | −0.263508 | −0.131754 | − | 0.991282i | \(-0.542061\pi\) | ||||
−0.131754 | + | 0.991282i | \(0.542061\pi\) | |||||||
\(492\) | 4.95359 | 0.223325 | ||||||||
\(493\) | −23.9589 | −1.07905 | ||||||||
\(494\) | 3.37914 | 0.152035 | ||||||||
\(495\) | 1.86782 | 0.0839520 | ||||||||
\(496\) | 1.00000 | 0.0449013 | ||||||||
\(497\) | −9.07293 | −0.406977 | ||||||||
\(498\) | −4.90016 | −0.219581 | ||||||||
\(499\) | 33.0226 | 1.47830 | 0.739148 | − | 0.673543i | \(-0.235228\pi\) | ||||
0.739148 | + | 0.673543i | \(0.235228\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 14.9351 | 0.667251 | ||||||||
\(502\) | −22.5522 | −1.00655 | ||||||||
\(503\) | −3.48253 | −0.155278 | −0.0776391 | − | 0.996982i | \(-0.524738\pi\) | ||||
−0.0776391 | + | 0.996982i | \(0.524738\pi\) | |||||||
\(504\) | −1.69770 | −0.0756214 | ||||||||
\(505\) | 8.77067 | 0.390290 | ||||||||
\(506\) | 9.32743 | 0.414655 | ||||||||
\(507\) | −1.44295 | −0.0640835 | ||||||||
\(508\) | −10.2278 | −0.453787 | ||||||||
\(509\) | 4.00085 | 0.177334 | 0.0886672 | − | 0.996061i | \(-0.471739\pi\) | ||||
0.0886672 | + | 0.996061i | \(0.471739\pi\) | |||||||
\(510\) | −5.81040 | −0.257289 | ||||||||
\(511\) | 16.7684 | 0.741789 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −19.1034 | −0.843435 | ||||||||
\(514\) | 19.3964 | 0.855538 | ||||||||
\(515\) | −8.52722 | −0.375754 | ||||||||
\(516\) | −5.36362 | −0.236120 | ||||||||
\(517\) | 21.2907 | 0.936363 | ||||||||
\(518\) | 10.6228 | 0.466739 | ||||||||
\(519\) | 23.1378 | 1.01564 | ||||||||
\(520\) | 1.00000 | 0.0438529 | ||||||||
\(521\) | −4.08024 | −0.178759 | −0.0893793 | − | 0.995998i | \(-0.528488\pi\) | ||||
−0.0893793 | + | 0.995998i | \(0.528488\pi\) | |||||||
\(522\) | −5.46147 | −0.239042 | ||||||||
\(523\) | −8.81282 | −0.385358 | −0.192679 | − | 0.981262i | \(-0.561718\pi\) | ||||
−0.192679 | + | 0.981262i | \(0.561718\pi\) | |||||||
\(524\) | −11.6099 | −0.507179 | ||||||||
\(525\) | 2.66877 | 0.116475 | ||||||||
\(526\) | 19.4265 | 0.847034 | ||||||||
\(527\) | 4.02676 | 0.175408 | ||||||||
\(528\) | −2.93619 | −0.127781 | ||||||||
\(529\) | −1.98863 | −0.0864623 | ||||||||
\(530\) | 5.37307 | 0.233391 | ||||||||
\(531\) | 4.16878 | 0.180910 | ||||||||
\(532\) | 6.24982 | 0.270964 | ||||||||
\(533\) | −3.43297 | −0.148698 | ||||||||
\(534\) | 14.1483 | 0.612256 | ||||||||
\(535\) | −7.04378 | −0.304529 | ||||||||
\(536\) | −7.49609 | −0.323782 | ||||||||
\(537\) | 2.26687 | 0.0978226 | ||||||||
\(538\) | 17.4915 | 0.754111 | ||||||||
\(539\) | −7.28326 | −0.313712 | ||||||||
\(540\) | −5.65333 | −0.243281 | ||||||||
\(541\) | 43.6811 | 1.87800 | 0.938998 | − | 0.343922i | \(-0.111756\pi\) | ||||
0.938998 | + | 0.343922i | \(0.111756\pi\) | |||||||
\(542\) | −23.9044 | −1.02678 | ||||||||
\(543\) | −0.915371 | −0.0392823 | ||||||||
\(544\) | −4.02676 | −0.172646 | ||||||||
\(545\) | 16.2833 | 0.697499 | ||||||||
\(546\) | −2.66877 | −0.114213 | ||||||||
\(547\) | 28.4757 | 1.21753 | 0.608766 | − | 0.793350i | \(-0.291665\pi\) | ||||
0.608766 | + | 0.793350i | \(0.291665\pi\) | |||||||
\(548\) | 0.710019 | 0.0303305 | ||||||||
\(549\) | −0.968070 | −0.0413162 | ||||||||
\(550\) | −2.03486 | −0.0867668 | ||||||||
\(551\) | 20.1056 | 0.856526 | ||||||||
\(552\) | −6.61420 | −0.281519 | ||||||||
\(553\) | −20.4157 | −0.868163 | ||||||||
\(554\) | 9.54560 | 0.405554 | ||||||||
\(555\) | 8.28759 | 0.351788 | ||||||||
\(556\) | 10.5855 | 0.448924 | ||||||||
\(557\) | 16.2543 | 0.688715 | 0.344357 | − | 0.938839i | \(-0.388097\pi\) | ||||
0.344357 | + | 0.938839i | \(0.388097\pi\) | |||||||
\(558\) | 0.917908 | 0.0388581 | ||||||||
\(559\) | 3.71713 | 0.157218 | ||||||||
\(560\) | 1.84953 | 0.0781569 | ||||||||
\(561\) | −11.8234 | −0.499182 | ||||||||
\(562\) | 19.3263 | 0.815230 | ||||||||
\(563\) | −28.6742 | −1.20847 | −0.604236 | − | 0.796805i | \(-0.706522\pi\) | ||||
−0.604236 | + | 0.796805i | \(0.706522\pi\) | |||||||
\(564\) | −15.0975 | −0.635719 | ||||||||
\(565\) | 1.74246 | 0.0733058 | ||||||||
\(566\) | 10.1976 | 0.428639 | ||||||||
\(567\) | 9.99434 | 0.419723 | ||||||||
\(568\) | −4.90554 | −0.205832 | ||||||||
\(569\) | −18.2284 | −0.764174 | −0.382087 | − | 0.924126i | \(-0.624795\pi\) | ||||
−0.382087 | + | 0.924126i | \(0.624795\pi\) | |||||||
\(570\) | 4.87591 | 0.204230 | ||||||||
\(571\) | −8.54529 | −0.357609 | −0.178805 | − | 0.983885i | \(-0.557223\pi\) | ||||
−0.178805 | + | 0.983885i | \(0.557223\pi\) | |||||||
\(572\) | 2.03486 | 0.0850818 | ||||||||
\(573\) | 25.4807 | 1.06447 | ||||||||
\(574\) | −6.34938 | −0.265018 | ||||||||
\(575\) | −4.58382 | −0.191158 | ||||||||
\(576\) | −0.917908 | −0.0382462 | ||||||||
\(577\) | −3.39145 | −0.141188 | −0.0705939 | − | 0.997505i | \(-0.522489\pi\) | ||||
−0.0705939 | + | 0.997505i | \(0.522489\pi\) | |||||||
\(578\) | 0.785193 | 0.0326597 | ||||||||
\(579\) | −9.09097 | −0.377808 | ||||||||
\(580\) | 5.94991 | 0.247056 | ||||||||
\(581\) | 6.28089 | 0.260575 | ||||||||
\(582\) | 9.44775 | 0.391622 | ||||||||
\(583\) | 10.9334 | 0.452817 | ||||||||
\(584\) | 9.06629 | 0.375166 | ||||||||
\(585\) | 0.917908 | 0.0379508 | ||||||||
\(586\) | 25.4078 | 1.04959 | ||||||||
\(587\) | 12.6807 | 0.523389 | 0.261694 | − | 0.965151i | \(-0.415719\pi\) | ||||
0.261694 | + | 0.965151i | \(0.415719\pi\) | |||||||
\(588\) | 5.16465 | 0.212987 | ||||||||
\(589\) | −3.37914 | −0.139235 | ||||||||
\(590\) | −4.54161 | −0.186975 | ||||||||
\(591\) | −24.6266 | −1.01300 | ||||||||
\(592\) | 5.74352 | 0.236057 | ||||||||
\(593\) | −3.53097 | −0.145000 | −0.0724998 | − | 0.997368i | \(-0.523098\pi\) | ||||
−0.0724998 | + | 0.997368i | \(0.523098\pi\) | |||||||
\(594\) | −11.5037 | −0.472004 | ||||||||
\(595\) | 7.44761 | 0.305322 | ||||||||
\(596\) | −3.46476 | −0.141922 | ||||||||
\(597\) | 13.1237 | 0.537117 | ||||||||
\(598\) | 4.58382 | 0.187446 | ||||||||
\(599\) | 7.12763 | 0.291227 | 0.145614 | − | 0.989342i | \(-0.453484\pi\) | ||||
0.145614 | + | 0.989342i | \(0.453484\pi\) | |||||||
\(600\) | 1.44295 | 0.0589080 | ||||||||
\(601\) | −2.28025 | −0.0930132 | −0.0465066 | − | 0.998918i | \(-0.514809\pi\) | ||||
−0.0465066 | + | 0.998918i | \(0.514809\pi\) | |||||||
\(602\) | 6.87495 | 0.280202 | ||||||||
\(603\) | −6.88072 | −0.280205 | ||||||||
\(604\) | −8.55602 | −0.348140 | ||||||||
\(605\) | 6.85934 | 0.278872 | ||||||||
\(606\) | −12.6556 | −0.514099 | ||||||||
\(607\) | 26.3775 | 1.07063 | 0.535315 | − | 0.844652i | \(-0.320193\pi\) | ||||
0.535315 | + | 0.844652i | \(0.320193\pi\) | |||||||
\(608\) | 3.37914 | 0.137042 | ||||||||
\(609\) | −15.8789 | −0.643447 | ||||||||
\(610\) | 1.05465 | 0.0427015 | ||||||||
\(611\) | 10.4630 | 0.423286 | ||||||||
\(612\) | −3.69620 | −0.149410 | ||||||||
\(613\) | 12.0990 | 0.488674 | 0.244337 | − | 0.969690i | \(-0.421430\pi\) | ||||
0.244337 | + | 0.969690i | \(0.421430\pi\) | |||||||
\(614\) | 31.0455 | 1.25289 | ||||||||
\(615\) | −4.95359 | −0.199748 | ||||||||
\(616\) | 3.76353 | 0.151637 | ||||||||
\(617\) | −2.81564 | −0.113353 | −0.0566767 | − | 0.998393i | \(-0.518050\pi\) | ||||
−0.0566767 | + | 0.998393i | \(0.518050\pi\) | |||||||
\(618\) | 12.3043 | 0.494952 | ||||||||
\(619\) | −3.30714 | −0.132925 | −0.0664627 | − | 0.997789i | \(-0.521171\pi\) | ||||
−0.0664627 | + | 0.997789i | \(0.521171\pi\) | |||||||
\(620\) | −1.00000 | −0.0401610 | ||||||||
\(621\) | −25.9138 | −1.03989 | ||||||||
\(622\) | 11.0997 | 0.445058 | ||||||||
\(623\) | −18.1349 | −0.726559 | ||||||||
\(624\) | −1.44295 | −0.0577641 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −28.4814 | −1.13835 | ||||||||
\(627\) | 9.92181 | 0.396239 | ||||||||
\(628\) | −2.04229 | −0.0814962 | ||||||||
\(629\) | 23.1278 | 0.922165 | ||||||||
\(630\) | 1.69770 | 0.0676379 | ||||||||
\(631\) | 31.1347 | 1.23945 | 0.619727 | − | 0.784818i | \(-0.287243\pi\) | ||||
0.619727 | + | 0.784818i | \(0.287243\pi\) | |||||||
\(632\) | −11.0383 | −0.439080 | ||||||||
\(633\) | 9.77997 | 0.388719 | ||||||||
\(634\) | −13.5242 | −0.537116 | ||||||||
\(635\) | 10.2278 | 0.405879 | ||||||||
\(636\) | −7.75304 | −0.307428 | ||||||||
\(637\) | −3.57924 | −0.141815 | ||||||||
\(638\) | 12.1072 | 0.479330 | ||||||||
\(639\) | −4.50283 | −0.178129 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −18.3670 | −0.725452 | −0.362726 | − | 0.931896i | \(-0.618154\pi\) | ||||
−0.362726 | + | 0.931896i | \(0.618154\pi\) | |||||||
\(642\) | 10.1638 | 0.401133 | ||||||||
\(643\) | 32.8550 | 1.29568 | 0.647838 | − | 0.761778i | \(-0.275674\pi\) | ||||
0.647838 | + | 0.761778i | \(0.275674\pi\) | |||||||
\(644\) | 8.47790 | 0.334076 | ||||||||
\(645\) | 5.36362 | 0.211192 | ||||||||
\(646\) | 13.6070 | 0.535360 | ||||||||
\(647\) | −24.4053 | −0.959470 | −0.479735 | − | 0.877413i | \(-0.659267\pi\) | ||||
−0.479735 | + | 0.877413i | \(0.659267\pi\) | |||||||
\(648\) | 5.40372 | 0.212278 | ||||||||
\(649\) | −9.24155 | −0.362763 | ||||||||
\(650\) | −1.00000 | −0.0392232 | ||||||||
\(651\) | 2.66877 | 0.104597 | ||||||||
\(652\) | 0.325069 | 0.0127307 | ||||||||
\(653\) | −29.1601 | −1.14112 | −0.570562 | − | 0.821254i | \(-0.693275\pi\) | ||||
−0.570562 | + | 0.821254i | \(0.693275\pi\) | |||||||
\(654\) | −23.4959 | −0.918761 | ||||||||
\(655\) | 11.6099 | 0.453634 | ||||||||
\(656\) | −3.43297 | −0.134035 | ||||||||
\(657\) | 8.32202 | 0.324673 | ||||||||
\(658\) | 19.3516 | 0.754402 | ||||||||
\(659\) | 17.9074 | 0.697575 | 0.348788 | − | 0.937202i | \(-0.386593\pi\) | ||||
0.348788 | + | 0.937202i | \(0.386593\pi\) | |||||||
\(660\) | 2.93619 | 0.114291 | ||||||||
\(661\) | −19.2398 | −0.748340 | −0.374170 | − | 0.927360i | \(-0.622072\pi\) | ||||
−0.374170 | + | 0.927360i | \(0.622072\pi\) | |||||||
\(662\) | −21.5750 | −0.838538 | ||||||||
\(663\) | −5.81040 | −0.225657 | ||||||||
\(664\) | 3.39594 | 0.131788 | ||||||||
\(665\) | −6.24982 | −0.242357 | ||||||||
\(666\) | 5.27202 | 0.204287 | ||||||||
\(667\) | 27.2733 | 1.05603 | ||||||||
\(668\) | −10.3504 | −0.400470 | ||||||||
\(669\) | 13.8362 | 0.534938 | ||||||||
\(670\) | 7.49609 | 0.289599 | ||||||||
\(671\) | 2.14606 | 0.0828479 | ||||||||
\(672\) | −2.66877 | −0.102950 | ||||||||
\(673\) | 3.54166 | 0.136521 | 0.0682605 | − | 0.997668i | \(-0.478255\pi\) | ||||
0.0682605 | + | 0.997668i | \(0.478255\pi\) | |||||||
\(674\) | 10.5216 | 0.405277 | ||||||||
\(675\) | 5.65333 | 0.217597 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 19.9209 | 0.765623 | 0.382812 | − | 0.923826i | \(-0.374956\pi\) | ||||
0.382812 | + | 0.923826i | \(0.374956\pi\) | |||||||
\(678\) | −2.51427 | −0.0965601 | ||||||||
\(679\) | −12.1099 | −0.464734 | ||||||||
\(680\) | 4.02676 | 0.154419 | ||||||||
\(681\) | 12.8802 | 0.493569 | ||||||||
\(682\) | −2.03486 | −0.0779189 | ||||||||
\(683\) | 11.5006 | 0.440059 | 0.220029 | − | 0.975493i | \(-0.429385\pi\) | ||||
0.220029 | + | 0.975493i | \(0.429385\pi\) | |||||||
\(684\) | 3.10174 | 0.118598 | ||||||||
\(685\) | −0.710019 | −0.0271285 | ||||||||
\(686\) | −19.5666 | −0.747057 | ||||||||
\(687\) | −22.3182 | −0.851493 | ||||||||
\(688\) | 3.71713 | 0.141714 | ||||||||
\(689\) | 5.37307 | 0.204697 | ||||||||
\(690\) | 6.61420 | 0.251798 | ||||||||
\(691\) | 23.5873 | 0.897302 | 0.448651 | − | 0.893707i | \(-0.351905\pi\) | ||||
0.448651 | + | 0.893707i | \(0.351905\pi\) | |||||||
\(692\) | −16.0351 | −0.609563 | ||||||||
\(693\) | 3.45458 | 0.131229 | ||||||||
\(694\) | 31.3970 | 1.19182 | ||||||||
\(695\) | −10.5855 | −0.401530 | ||||||||
\(696\) | −8.58539 | −0.325428 | ||||||||
\(697\) | −13.8237 | −0.523612 | ||||||||
\(698\) | 12.0383 | 0.455655 | ||||||||
\(699\) | 5.04933 | 0.190983 | ||||||||
\(700\) | −1.84953 | −0.0699056 | ||||||||
\(701\) | 19.3998 | 0.732720 | 0.366360 | − | 0.930473i | \(-0.380604\pi\) | ||||
0.366360 | + | 0.930473i | \(0.380604\pi\) | |||||||
\(702\) | −5.65333 | −0.213371 | ||||||||
\(703\) | −19.4082 | −0.731992 | ||||||||
\(704\) | 2.03486 | 0.0766917 | ||||||||
\(705\) | 15.0975 | 0.568605 | ||||||||
\(706\) | 13.7981 | 0.519297 | ||||||||
\(707\) | 16.2216 | 0.610077 | ||||||||
\(708\) | 6.55330 | 0.246288 | ||||||||
\(709\) | 9.25576 | 0.347607 | 0.173804 | − | 0.984780i | \(-0.444394\pi\) | ||||
0.173804 | + | 0.984780i | \(0.444394\pi\) | |||||||
\(710\) | 4.90554 | 0.184102 | ||||||||
\(711\) | −10.1322 | −0.379985 | ||||||||
\(712\) | −9.80514 | −0.367463 | ||||||||
\(713\) | −4.58382 | −0.171665 | ||||||||
\(714\) | −10.7465 | −0.402178 | ||||||||
\(715\) | −2.03486 | −0.0760995 | ||||||||
\(716\) | −1.57100 | −0.0587111 | ||||||||
\(717\) | −40.9969 | −1.53106 | ||||||||
\(718\) | 21.0996 | 0.787428 | ||||||||
\(719\) | 4.53546 | 0.169144 | 0.0845721 | − | 0.996417i | \(-0.473048\pi\) | ||||
0.0845721 | + | 0.996417i | \(0.473048\pi\) | |||||||
\(720\) | 0.917908 | 0.0342084 | ||||||||
\(721\) | −15.7713 | −0.587355 | ||||||||
\(722\) | 7.58141 | 0.282151 | ||||||||
\(723\) | 14.1632 | 0.526736 | ||||||||
\(724\) | 0.634377 | 0.0235764 | ||||||||
\(725\) | −5.94991 | −0.220974 | ||||||||
\(726\) | −9.89765 | −0.367336 | ||||||||
\(727\) | 5.90250 | 0.218912 | 0.109456 | − | 0.993992i | \(-0.465089\pi\) | ||||
0.109456 | + | 0.993992i | \(0.465089\pi\) | |||||||
\(728\) | 1.84953 | 0.0685481 | ||||||||
\(729\) | 29.4325 | 1.09009 | ||||||||
\(730\) | −9.06629 | −0.335558 | ||||||||
\(731\) | 14.9680 | 0.553612 | ||||||||
\(732\) | −1.52180 | −0.0562474 | ||||||||
\(733\) | −0.947728 | −0.0350051 | −0.0175026 | − | 0.999847i | \(-0.505572\pi\) | ||||
−0.0175026 | + | 0.999847i | \(0.505572\pi\) | |||||||
\(734\) | −26.5184 | −0.978812 | ||||||||
\(735\) | −5.16465 | −0.190501 | ||||||||
\(736\) | 4.58382 | 0.168962 | ||||||||
\(737\) | 15.2535 | 0.561870 | ||||||||
\(738\) | −3.15115 | −0.115995 | ||||||||
\(739\) | 49.2084 | 1.81016 | 0.905081 | − | 0.425240i | \(-0.139810\pi\) | ||||
0.905081 | + | 0.425240i | \(0.139810\pi\) | |||||||
\(740\) | −5.74352 | −0.211136 | ||||||||
\(741\) | 4.87591 | 0.179121 | ||||||||
\(742\) | 9.93764 | 0.364822 | ||||||||
\(743\) | −13.5439 | −0.496877 | −0.248439 | − | 0.968648i | \(-0.579917\pi\) | ||||
−0.248439 | + | 0.968648i | \(0.579917\pi\) | |||||||
\(744\) | 1.44295 | 0.0529010 | ||||||||
\(745\) | 3.46476 | 0.126939 | ||||||||
\(746\) | 4.72751 | 0.173086 | ||||||||
\(747\) | 3.11716 | 0.114051 | ||||||||
\(748\) | 8.19390 | 0.299599 | ||||||||
\(749\) | −13.0277 | −0.476021 | ||||||||
\(750\) | −1.44295 | −0.0526889 | ||||||||
\(751\) | 28.2562 | 1.03108 | 0.515542 | − | 0.856864i | \(-0.327591\pi\) | ||||
0.515542 | + | 0.856864i | \(0.327591\pi\) | |||||||
\(752\) | 10.4630 | 0.381545 | ||||||||
\(753\) | −32.5416 | −1.18588 | ||||||||
\(754\) | 5.94991 | 0.216683 | ||||||||
\(755\) | 8.55602 | 0.311386 | ||||||||
\(756\) | −10.4560 | −0.380281 | ||||||||
\(757\) | 1.21705 | 0.0442344 | 0.0221172 | − | 0.999755i | \(-0.492959\pi\) | ||||
0.0221172 | + | 0.999755i | \(0.492959\pi\) | |||||||
\(758\) | 21.7669 | 0.790611 | ||||||||
\(759\) | 13.4590 | 0.488530 | ||||||||
\(760\) | −3.37914 | −0.122574 | ||||||||
\(761\) | −38.3444 | −1.38998 | −0.694991 | − | 0.719018i | \(-0.744592\pi\) | ||||
−0.694991 | + | 0.719018i | \(0.744592\pi\) | |||||||
\(762\) | −14.7582 | −0.534634 | ||||||||
\(763\) | 30.1164 | 1.09029 | ||||||||
\(764\) | −17.6588 | −0.638872 | ||||||||
\(765\) | 3.69620 | 0.133636 | ||||||||
\(766\) | −11.2822 | −0.407641 | ||||||||
\(767\) | −4.54161 | −0.163988 | ||||||||
\(768\) | −1.44295 | −0.0520678 | ||||||||
\(769\) | −26.1540 | −0.943138 | −0.471569 | − | 0.881829i | \(-0.656312\pi\) | ||||
−0.471569 | + | 0.881829i | \(0.656312\pi\) | |||||||
\(770\) | −3.76353 | −0.135628 | ||||||||
\(771\) | 27.9879 | 1.00796 | ||||||||
\(772\) | 6.30028 | 0.226752 | ||||||||
\(773\) | 7.96569 | 0.286506 | 0.143253 | − | 0.989686i | \(-0.454244\pi\) | ||||
0.143253 | + | 0.989686i | \(0.454244\pi\) | |||||||
\(774\) | 3.41199 | 0.122641 | ||||||||
\(775\) | 1.00000 | 0.0359211 | ||||||||
\(776\) | −6.54755 | −0.235043 | ||||||||
\(777\) | 15.3281 | 0.549894 | ||||||||
\(778\) | 14.1684 | 0.507962 | ||||||||
\(779\) | 11.6005 | 0.415630 | ||||||||
\(780\) | 1.44295 | 0.0516657 | ||||||||
\(781\) | 9.98209 | 0.357187 | ||||||||
\(782\) | 18.4579 | 0.660054 | ||||||||
\(783\) | −33.6368 | −1.20208 | ||||||||
\(784\) | −3.57924 | −0.127830 | ||||||||
\(785\) | 2.04229 | 0.0728925 | ||||||||
\(786\) | −16.7524 | −0.597538 | ||||||||
\(787\) | 11.7439 | 0.418624 | 0.209312 | − | 0.977849i | \(-0.432878\pi\) | ||||
0.209312 | + | 0.977849i | \(0.432878\pi\) | |||||||
\(788\) | 17.0669 | 0.607982 | ||||||||
\(789\) | 28.0313 | 0.997942 | ||||||||
\(790\) | 11.0383 | 0.392725 | ||||||||
\(791\) | 3.22273 | 0.114587 | ||||||||
\(792\) | 1.86782 | 0.0663699 | ||||||||
\(793\) | 1.05465 | 0.0374517 | ||||||||
\(794\) | −12.1144 | −0.429925 | ||||||||
\(795\) | 7.75304 | 0.274972 | ||||||||
\(796\) | −9.09507 | −0.322366 | ||||||||
\(797\) | 17.3224 | 0.613592 | 0.306796 | − | 0.951775i | \(-0.400743\pi\) | ||||
0.306796 | + | 0.951775i | \(0.400743\pi\) | |||||||
\(798\) | 9.01815 | 0.319239 | ||||||||
\(799\) | 42.1319 | 1.49052 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −9.00022 | −0.318007 | ||||||||
\(802\) | 31.4824 | 1.11168 | ||||||||
\(803\) | −18.4486 | −0.651038 | ||||||||
\(804\) | −10.8165 | −0.381467 | ||||||||
\(805\) | −8.47790 | −0.298807 | ||||||||
\(806\) | −1.00000 | −0.0352235 | ||||||||
\(807\) | 25.2392 | 0.888463 | ||||||||
\(808\) | 8.77067 | 0.308551 | ||||||||
\(809\) | −24.4215 | −0.858613 | −0.429306 | − | 0.903159i | \(-0.641242\pi\) | ||||
−0.429306 | + | 0.903159i | \(0.641242\pi\) | |||||||
\(810\) | −5.40372 | −0.189867 | ||||||||
\(811\) | 43.2200 | 1.51766 | 0.758830 | − | 0.651288i | \(-0.225771\pi\) | ||||
0.758830 | + | 0.651288i | \(0.225771\pi\) | |||||||
\(812\) | 11.0045 | 0.386183 | ||||||||
\(813\) | −34.4928 | −1.20971 | ||||||||
\(814\) | −11.6873 | −0.409638 | ||||||||
\(815\) | −0.325069 | −0.0113867 | ||||||||
\(816\) | −5.81040 | −0.203405 | ||||||||
\(817\) | −12.5607 | −0.439444 | ||||||||
\(818\) | 27.9065 | 0.975728 | ||||||||
\(819\) | 1.69770 | 0.0593223 | ||||||||
\(820\) | 3.43297 | 0.119884 | ||||||||
\(821\) | −10.6087 | −0.370247 | −0.185124 | − | 0.982715i | \(-0.559269\pi\) | ||||
−0.185124 | + | 0.982715i | \(0.559269\pi\) | |||||||
\(822\) | 1.02452 | 0.0357342 | ||||||||
\(823\) | −20.9897 | −0.731654 | −0.365827 | − | 0.930683i | \(-0.619214\pi\) | ||||
−0.365827 | + | 0.930683i | \(0.619214\pi\) | |||||||
\(824\) | −8.52722 | −0.297060 | ||||||||
\(825\) | −2.93619 | −0.102225 | ||||||||
\(826\) | −8.39984 | −0.292268 | ||||||||
\(827\) | 17.0443 | 0.592687 | 0.296343 | − | 0.955081i | \(-0.404233\pi\) | ||||
0.296343 | + | 0.955081i | \(0.404233\pi\) | |||||||
\(828\) | 4.20752 | 0.146221 | ||||||||
\(829\) | −42.1519 | −1.46400 | −0.731999 | − | 0.681306i | \(-0.761412\pi\) | ||||
−0.731999 | + | 0.681306i | \(0.761412\pi\) | |||||||
\(830\) | −3.39594 | −0.117875 | ||||||||
\(831\) | 13.7738 | 0.477807 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | −14.4128 | −0.499372 | ||||||||
\(834\) | 15.2743 | 0.528905 | ||||||||
\(835\) | 10.3504 | 0.358191 | ||||||||
\(836\) | −6.87608 | −0.237814 | ||||||||
\(837\) | 5.65333 | 0.195408 | ||||||||
\(838\) | −6.49496 | −0.224365 | ||||||||
\(839\) | 6.21357 | 0.214516 | 0.107258 | − | 0.994231i | \(-0.465793\pi\) | ||||
0.107258 | + | 0.994231i | \(0.465793\pi\) | |||||||
\(840\) | 2.66877 | 0.0920813 | ||||||||
\(841\) | 6.40140 | 0.220738 | ||||||||
\(842\) | 15.8856 | 0.547455 | ||||||||
\(843\) | 27.8868 | 0.960472 | ||||||||
\(844\) | −6.77778 | −0.233301 | ||||||||
\(845\) | −1.00000 | −0.0344010 | ||||||||
\(846\) | 9.60404 | 0.330194 | ||||||||
\(847\) | 12.6865 | 0.435915 | ||||||||
\(848\) | 5.37307 | 0.184512 | ||||||||
\(849\) | 14.7146 | 0.505005 | ||||||||
\(850\) | −4.02676 | −0.138117 | ||||||||
\(851\) | −26.3272 | −0.902486 | ||||||||
\(852\) | −7.07842 | −0.242503 | ||||||||
\(853\) | 14.9176 | 0.510770 | 0.255385 | − | 0.966839i | \(-0.417798\pi\) | ||||
0.255385 | + | 0.966839i | \(0.417798\pi\) | |||||||
\(854\) | 1.95060 | 0.0667483 | ||||||||
\(855\) | −3.10174 | −0.106077 | ||||||||
\(856\) | −7.04378 | −0.240751 | ||||||||
\(857\) | 42.2741 | 1.44406 | 0.722029 | − | 0.691863i | \(-0.243210\pi\) | ||||
0.722029 | + | 0.691863i | \(0.243210\pi\) | |||||||
\(858\) | 2.93619 | 0.100240 | ||||||||
\(859\) | −22.0777 | −0.753283 | −0.376642 | − | 0.926359i | \(-0.622921\pi\) | ||||
−0.376642 | + | 0.926359i | \(0.622921\pi\) | |||||||
\(860\) | −3.71713 | −0.126753 | ||||||||
\(861\) | −9.16180 | −0.312233 | ||||||||
\(862\) | 24.8265 | 0.845592 | ||||||||
\(863\) | 27.1135 | 0.922953 | 0.461477 | − | 0.887152i | \(-0.347320\pi\) | ||||
0.461477 | + | 0.887152i | \(0.347320\pi\) | |||||||
\(864\) | −5.65333 | −0.192330 | ||||||||
\(865\) | 16.0351 | 0.545210 | ||||||||
\(866\) | −16.9214 | −0.575012 | ||||||||
\(867\) | 1.13299 | 0.0384784 | ||||||||
\(868\) | −1.84953 | −0.0627771 | ||||||||
\(869\) | 22.4614 | 0.761952 | ||||||||
\(870\) | 8.58539 | 0.291072 | ||||||||
\(871\) | 7.49609 | 0.253995 | ||||||||
\(872\) | 16.2833 | 0.551421 | ||||||||
\(873\) | −6.01004 | −0.203409 | ||||||||
\(874\) | −15.4894 | −0.523935 | ||||||||
\(875\) | 1.84953 | 0.0625255 | ||||||||
\(876\) | 13.0822 | 0.442005 | ||||||||
\(877\) | −40.7572 | −1.37627 | −0.688137 | − | 0.725581i | \(-0.741571\pi\) | ||||
−0.688137 | + | 0.725581i | \(0.741571\pi\) | |||||||
\(878\) | −12.9144 | −0.435842 | ||||||||
\(879\) | 36.6621 | 1.23658 | ||||||||
\(880\) | −2.03486 | −0.0685952 | ||||||||
\(881\) | −49.7166 | −1.67500 | −0.837498 | − | 0.546441i | \(-0.815982\pi\) | ||||
−0.837498 | + | 0.546441i | \(0.815982\pi\) | |||||||
\(882\) | −3.28542 | −0.110626 | ||||||||
\(883\) | −26.9476 | −0.906860 | −0.453430 | − | 0.891292i | \(-0.649800\pi\) | ||||
−0.453430 | + | 0.891292i | \(0.649800\pi\) | |||||||
\(884\) | 4.02676 | 0.135435 | ||||||||
\(885\) | −6.55330 | −0.220287 | ||||||||
\(886\) | 37.8803 | 1.27261 | ||||||||
\(887\) | −7.33741 | −0.246366 | −0.123183 | − | 0.992384i | \(-0.539310\pi\) | ||||
−0.123183 | + | 0.992384i | \(0.539310\pi\) | |||||||
\(888\) | 8.28759 | 0.278113 | ||||||||
\(889\) | 18.9167 | 0.634445 | ||||||||
\(890\) | 9.80514 | 0.328669 | ||||||||
\(891\) | −10.9958 | −0.368374 | ||||||||
\(892\) | −9.58886 | −0.321059 | ||||||||
\(893\) | −35.3558 | −1.18314 | ||||||||
\(894\) | −4.99946 | −0.167207 | ||||||||
\(895\) | 1.57100 | 0.0525128 | ||||||||
\(896\) | 1.84953 | 0.0617884 | ||||||||
\(897\) | 6.61420 | 0.220842 | ||||||||
\(898\) | 5.72002 | 0.190880 | ||||||||
\(899\) | −5.94991 | −0.198441 | ||||||||
\(900\) | −0.917908 | −0.0305969 | ||||||||
\(901\) | 21.6361 | 0.720801 | ||||||||
\(902\) | 6.98562 | 0.232596 | ||||||||
\(903\) | 9.92017 | 0.330123 | ||||||||
\(904\) | 1.74246 | 0.0579533 | ||||||||
\(905\) | −0.634377 | −0.0210874 | ||||||||
\(906\) | −12.3459 | −0.410164 | ||||||||
\(907\) | 7.26600 | 0.241263 | 0.120632 | − | 0.992697i | \(-0.461508\pi\) | ||||
0.120632 | + | 0.992697i | \(0.461508\pi\) | |||||||
\(908\) | −8.92629 | −0.296229 | ||||||||
\(909\) | 8.05067 | 0.267024 | ||||||||
\(910\) | −1.84953 | −0.0613113 | ||||||||
\(911\) | 17.9114 | 0.593430 | 0.296715 | − | 0.954966i | \(-0.404109\pi\) | ||||
0.296715 | + | 0.954966i | \(0.404109\pi\) | |||||||
\(912\) | 4.87591 | 0.161458 | ||||||||
\(913\) | −6.91027 | −0.228697 | ||||||||
\(914\) | 28.4558 | 0.941236 | ||||||||
\(915\) | 1.52180 | 0.0503092 | ||||||||
\(916\) | 15.4671 | 0.511048 | ||||||||
\(917\) | 21.4728 | 0.709093 | ||||||||
\(918\) | −22.7646 | −0.751344 | ||||||||
\(919\) | 8.94938 | 0.295213 | 0.147606 | − | 0.989046i | \(-0.452843\pi\) | ||||
0.147606 | + | 0.989046i | \(0.452843\pi\) | |||||||
\(920\) | −4.58382 | −0.151124 | ||||||||
\(921\) | 44.7969 | 1.47611 | ||||||||
\(922\) | 1.88939 | 0.0622236 | ||||||||
\(923\) | 4.90554 | 0.161468 | ||||||||
\(924\) | 5.43058 | 0.178653 | ||||||||
\(925\) | 5.74352 | 0.188846 | ||||||||
\(926\) | −11.4219 | −0.375347 | ||||||||
\(927\) | −7.82720 | −0.257079 | ||||||||
\(928\) | 5.94991 | 0.195315 | ||||||||
\(929\) | −5.22227 | −0.171337 | −0.0856686 | − | 0.996324i | \(-0.527303\pi\) | ||||
−0.0856686 | + | 0.996324i | \(0.527303\pi\) | |||||||
\(930\) | −1.44295 | −0.0473161 | ||||||||
\(931\) | 12.0948 | 0.396390 | ||||||||
\(932\) | −3.49932 | −0.114624 | ||||||||
\(933\) | 16.0163 | 0.524350 | ||||||||
\(934\) | 26.9535 | 0.881946 | ||||||||
\(935\) | −8.19390 | −0.267969 | ||||||||
\(936\) | 0.917908 | 0.0300028 | ||||||||
\(937\) | −2.15383 | −0.0703627 | −0.0351813 | − | 0.999381i | \(-0.511201\pi\) | ||||
−0.0351813 | + | 0.999381i | \(0.511201\pi\) | |||||||
\(938\) | 13.8642 | 0.452684 | ||||||||
\(939\) | −41.0971 | −1.34115 | ||||||||
\(940\) | −10.4630 | −0.341264 | ||||||||
\(941\) | 1.98296 | 0.0646425 | 0.0323213 | − | 0.999478i | \(-0.489710\pi\) | ||||
0.0323213 | + | 0.999478i | \(0.489710\pi\) | |||||||
\(942\) | −2.94691 | −0.0960156 | ||||||||
\(943\) | 15.7361 | 0.512438 | ||||||||
\(944\) | −4.54161 | −0.147817 | ||||||||
\(945\) | 10.4560 | 0.340134 | ||||||||
\(946\) | −7.56385 | −0.245922 | ||||||||
\(947\) | 55.9977 | 1.81968 | 0.909840 | − | 0.414960i | \(-0.136204\pi\) | ||||
0.909840 | + | 0.414960i | \(0.136204\pi\) | |||||||
\(948\) | −15.9277 | −0.517307 | ||||||||
\(949\) | −9.06629 | −0.294304 | ||||||||
\(950\) | 3.37914 | 0.109634 | ||||||||
\(951\) | −19.5147 | −0.632809 | ||||||||
\(952\) | 7.44761 | 0.241378 | ||||||||
\(953\) | −48.7331 | −1.57862 | −0.789310 | − | 0.613994i | \(-0.789562\pi\) | ||||
−0.789310 | + | 0.613994i | \(0.789562\pi\) | |||||||
\(954\) | 4.93198 | 0.159679 | ||||||||
\(955\) | 17.6588 | 0.571425 | ||||||||
\(956\) | 28.4119 | 0.918907 | ||||||||
\(957\) | 17.4701 | 0.564728 | ||||||||
\(958\) | 29.2802 | 0.946001 | ||||||||
\(959\) | −1.31320 | −0.0424055 | ||||||||
\(960\) | 1.44295 | 0.0465709 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | −5.74352 | −0.185179 | ||||||||
\(963\) | −6.46554 | −0.208349 | ||||||||
\(964\) | −9.81549 | −0.316136 | ||||||||
\(965\) | −6.30028 | −0.202813 | ||||||||
\(966\) | 12.2331 | 0.393595 | ||||||||
\(967\) | 11.8907 | 0.382378 | 0.191189 | − | 0.981553i | \(-0.438766\pi\) | ||||
0.191189 | + | 0.981553i | \(0.438766\pi\) | |||||||
\(968\) | 6.85934 | 0.220468 | ||||||||
\(969\) | 19.6341 | 0.630740 | ||||||||
\(970\) | 6.54755 | 0.210229 | ||||||||
\(971\) | 51.5315 | 1.65373 | 0.826863 | − | 0.562404i | \(-0.190123\pi\) | ||||
0.826863 | + | 0.562404i | \(0.190123\pi\) | |||||||
\(972\) | −9.16271 | −0.293894 | ||||||||
\(973\) | −19.5782 | −0.627647 | ||||||||
\(974\) | −10.9477 | −0.350787 | ||||||||
\(975\) | −1.44295 | −0.0462112 | ||||||||
\(976\) | 1.05465 | 0.0337585 | ||||||||
\(977\) | 22.1561 | 0.708835 | 0.354418 | − | 0.935087i | \(-0.384679\pi\) | ||||
0.354418 | + | 0.935087i | \(0.384679\pi\) | |||||||
\(978\) | 0.469057 | 0.0149988 | ||||||||
\(979\) | 19.9521 | 0.637672 | ||||||||
\(980\) | 3.57924 | 0.114335 | ||||||||
\(981\) | 14.9465 | 0.477206 | ||||||||
\(982\) | 5.83895 | 0.186328 | ||||||||
\(983\) | 35.9323 | 1.14606 | 0.573031 | − | 0.819534i | \(-0.305768\pi\) | ||||
0.573031 | + | 0.819534i | \(0.305768\pi\) | |||||||
\(984\) | −4.95359 | −0.157915 | ||||||||
\(985\) | −17.0669 | −0.543796 | ||||||||
\(986\) | 23.9589 | 0.763005 | ||||||||
\(987\) | 27.9233 | 0.888807 | ||||||||
\(988\) | −3.37914 | −0.107505 | ||||||||
\(989\) | −17.0387 | −0.541798 | ||||||||
\(990\) | −1.86782 | −0.0593631 | ||||||||
\(991\) | 20.1323 | 0.639525 | 0.319762 | − | 0.947498i | \(-0.396397\pi\) | ||||
0.319762 | + | 0.947498i | \(0.396397\pi\) | |||||||
\(992\) | −1.00000 | −0.0317500 | ||||||||
\(993\) | −31.1316 | −0.987932 | ||||||||
\(994\) | 9.07293 | 0.287776 | ||||||||
\(995\) | 9.09507 | 0.288333 | ||||||||
\(996\) | 4.90016 | 0.155268 | ||||||||
\(997\) | 41.2043 | 1.30495 | 0.652477 | − | 0.757808i | \(-0.273730\pi\) | ||||
0.652477 | + | 0.757808i | \(0.273730\pi\) | |||||||
\(998\) | −33.0226 | −1.04531 | ||||||||
\(999\) | 32.4700 | 1.02731 |
(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 | 4030.2.a.c.1.2 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4030.2.a.c.1.2 | ✓ | 6 | 1.1 | even | 1 | trivial |