Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1815,2,Mod(1,1815)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1815, 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("1815.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1815 = 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1815.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: | \(14.4928479669\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.437199552.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 13x^{4} + 49x^{2} - 48 \) |
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 | 1.1 | ||
Root | \(-2.63162\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1815.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.63162 | −1.86084 | −0.930418 | − | 0.366500i | \(-0.880556\pi\) | ||||
−0.930418 | + | 0.366500i | \(0.880556\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 4.92542 | 2.46271 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 2.63162 | 1.07435 | ||||||||
\(7\) | 4.16741 | 1.57513 | 0.787567 | − | 0.616229i | \(-0.211341\pi\) | ||||
0.787567 | + | 0.616229i | \(0.211341\pi\) | |||||||
\(8\) | −7.69860 | −2.72187 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.63162 | −0.832191 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −4.92542 | −1.42185 | ||||||||
\(13\) | −5.26324 | −1.45976 | −0.729880 | − | 0.683575i | \(-0.760424\pi\) | ||||
−0.729880 | + | 0.683575i | \(0.760424\pi\) | |||||||
\(14\) | −10.9670 | −2.93107 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 10.4089 | 2.60224 | ||||||||
\(17\) | −4.23450 | −1.02702 | −0.513508 | − | 0.858085i | \(-0.671655\pi\) | ||||
−0.513508 | + | 0.858085i | \(0.671655\pi\) | |||||||
\(18\) | −2.63162 | −0.620279 | ||||||||
\(19\) | 2.50245 | 0.574101 | 0.287051 | − | 0.957915i | \(-0.407325\pi\) | ||||
0.287051 | + | 0.957915i | \(0.407325\pi\) | |||||||
\(20\) | 4.92542 | 1.10136 | ||||||||
\(21\) | −4.16741 | −0.909404 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.48352 | 1.14339 | 0.571697 | − | 0.820465i | \(-0.306285\pi\) | ||||
0.571697 | + | 0.820465i | \(0.306285\pi\) | |||||||
\(24\) | 7.69860 | 1.57147 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 13.8508 | 2.71637 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 20.5263 | 3.87910 | ||||||||
\(29\) | −5.26324 | −0.977359 | −0.488680 | − | 0.872463i | \(-0.662521\pi\) | ||||
−0.488680 | + | 0.872463i | \(0.662521\pi\) | |||||||
\(30\) | 2.63162 | 0.480466 | ||||||||
\(31\) | 10.1162 | 1.81692 | 0.908461 | − | 0.417969i | \(-0.137258\pi\) | ||||
0.908461 | + | 0.417969i | \(0.137258\pi\) | |||||||
\(32\) | −11.9952 | −2.12047 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 11.1436 | 1.91111 | ||||||||
\(35\) | 4.16741 | 0.704421 | ||||||||
\(36\) | 4.92542 | 0.820904 | ||||||||
\(37\) | −4.48352 | −0.737087 | −0.368543 | − | 0.929611i | \(-0.620143\pi\) | ||||
−0.368543 | + | 0.929611i | \(0.620143\pi\) | |||||||
\(38\) | −6.58549 | −1.06831 | ||||||||
\(39\) | 5.26324 | 0.842793 | ||||||||
\(40\) | −7.69860 | −1.21726 | ||||||||
\(41\) | 3.46410 | 0.541002 | 0.270501 | − | 0.962720i | \(-0.412811\pi\) | ||||
0.270501 | + | 0.962720i | \(0.412811\pi\) | |||||||
\(42\) | 10.9670 | 1.69225 | ||||||||
\(43\) | 6.66986 | 1.01714 | 0.508572 | − | 0.861019i | \(-0.330174\pi\) | ||||
0.508572 | + | 0.861019i | \(0.330174\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | −14.4305 | −2.12767 | ||||||||
\(47\) | 4.21817 | 0.615283 | 0.307642 | − | 0.951502i | \(-0.400460\pi\) | ||||
0.307642 | + | 0.951502i | \(0.400460\pi\) | |||||||
\(48\) | −10.4089 | −1.50240 | ||||||||
\(49\) | 10.3673 | 1.48105 | ||||||||
\(50\) | −2.63162 | −0.372167 | ||||||||
\(51\) | 4.23450 | 0.592949 | ||||||||
\(52\) | −25.9237 | −3.59497 | ||||||||
\(53\) | −3.63268 | −0.498986 | −0.249493 | − | 0.968377i | \(-0.580264\pi\) | ||||
−0.249493 | + | 0.968377i | \(0.580264\pi\) | |||||||
\(54\) | 2.63162 | 0.358118 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −32.0832 | −4.28730 | ||||||||
\(57\) | −2.50245 | −0.331457 | ||||||||
\(58\) | 13.8508 | 1.81871 | ||||||||
\(59\) | −6.58549 | −0.857358 | −0.428679 | − | 0.903457i | \(-0.641021\pi\) | ||||
−0.428679 | + | 0.903457i | \(0.641021\pi\) | |||||||
\(60\) | −4.92542 | −0.635869 | ||||||||
\(61\) | 12.2585 | 1.56954 | 0.784772 | − | 0.619785i | \(-0.212780\pi\) | ||||
0.784772 | + | 0.619785i | \(0.212780\pi\) | |||||||
\(62\) | −26.6220 | −3.38100 | ||||||||
\(63\) | 4.16741 | 0.525045 | ||||||||
\(64\) | 10.7489 | 1.34361 | ||||||||
\(65\) | −5.26324 | −0.652825 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.48352 | −0.547749 | −0.273875 | − | 0.961765i | \(-0.588305\pi\) | ||||
−0.273875 | + | 0.961765i | \(0.588305\pi\) | |||||||
\(68\) | −20.8567 | −2.52925 | ||||||||
\(69\) | −5.48352 | −0.660138 | ||||||||
\(70\) | −10.9670 | −1.31081 | ||||||||
\(71\) | 1.26535 | 0.150170 | 0.0750849 | − | 0.997177i | \(-0.476077\pi\) | ||||
0.0750849 | + | 0.997177i | \(0.476077\pi\) | |||||||
\(72\) | −7.69860 | −0.907289 | ||||||||
\(73\) | −4.55993 | −0.533699 | −0.266850 | − | 0.963738i | \(-0.585983\pi\) | ||||
−0.266850 | + | 0.963738i | \(0.585983\pi\) | |||||||
\(74\) | 11.7989 | 1.37160 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 12.3256 | 1.41385 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −13.8508 | −1.56830 | ||||||||
\(79\) | 6.86112 | 0.771936 | 0.385968 | − | 0.922512i | \(-0.373868\pi\) | ||||
0.385968 | + | 0.922512i | \(0.373868\pi\) | |||||||
\(80\) | 10.4089 | 1.16376 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −9.11620 | −1.00672 | ||||||||
\(83\) | 4.87072 | 0.534631 | 0.267316 | − | 0.963609i | \(-0.413863\pi\) | ||||
0.267316 | + | 0.963609i | \(0.413863\pi\) | |||||||
\(84\) | −20.5263 | −2.23960 | ||||||||
\(85\) | −4.23450 | −0.459296 | ||||||||
\(86\) | −17.5525 | −1.89274 | ||||||||
\(87\) | 5.26324 | 0.564279 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.1162 | 1.60231 | 0.801157 | − | 0.598454i | \(-0.204218\pi\) | ||||
0.801157 | + | 0.598454i | \(0.204218\pi\) | |||||||
\(90\) | −2.63162 | −0.277397 | ||||||||
\(91\) | −21.9341 | −2.29932 | ||||||||
\(92\) | 27.0087 | 2.81585 | ||||||||
\(93\) | −10.1162 | −1.04900 | ||||||||
\(94\) | −11.1006 | −1.14494 | ||||||||
\(95\) | 2.50245 | 0.256746 | ||||||||
\(96\) | 11.9952 | 1.22425 | ||||||||
\(97\) | −16.1852 | −1.64336 | −0.821680 | − | 0.569949i | \(-0.806963\pi\) | ||||
−0.821680 | + | 0.569949i | \(0.806963\pi\) | |||||||
\(98\) | −27.2829 | −2.75598 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.92542 | 0.492542 | ||||||||
\(101\) | 3.59828 | 0.358042 | 0.179021 | − | 0.983845i | \(-0.442707\pi\) | ||||
0.179021 | + | 0.983845i | \(0.442707\pi\) | |||||||
\(102\) | −11.1436 | −1.10338 | ||||||||
\(103\) | 1.36732 | 0.134726 | 0.0673632 | − | 0.997729i | \(-0.478541\pi\) | ||||
0.0673632 | + | 0.997729i | \(0.478541\pi\) | |||||||
\(104\) | 40.5196 | 3.97327 | ||||||||
\(105\) | −4.16741 | −0.406698 | ||||||||
\(106\) | 9.55982 | 0.928532 | ||||||||
\(107\) | 12.9618 | 1.25307 | 0.626534 | − | 0.779394i | \(-0.284473\pi\) | ||||
0.626534 | + | 0.779394i | \(0.284473\pi\) | |||||||
\(108\) | −4.92542 | −0.473949 | ||||||||
\(109\) | 5.96655 | 0.571492 | 0.285746 | − | 0.958305i | \(-0.407759\pi\) | ||||
0.285746 | + | 0.958305i | \(0.407759\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.48352 | 0.425557 | ||||||||
\(112\) | 43.3784 | 4.09887 | ||||||||
\(113\) | −6.06902 | −0.570925 | −0.285462 | − | 0.958390i | \(-0.592147\pi\) | ||||
−0.285462 | + | 0.958390i | \(0.592147\pi\) | |||||||
\(114\) | 6.58549 | 0.616788 | ||||||||
\(115\) | 5.48352 | 0.511341 | ||||||||
\(116\) | −25.9237 | −2.40695 | ||||||||
\(117\) | −5.26324 | −0.486587 | ||||||||
\(118\) | 17.3305 | 1.59540 | ||||||||
\(119\) | −17.6469 | −1.61769 | ||||||||
\(120\) | 7.69860 | 0.702783 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −32.2598 | −2.92066 | ||||||||
\(123\) | −3.46410 | −0.312348 | ||||||||
\(124\) | 49.8266 | 4.47456 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −10.9670 | −0.977022 | ||||||||
\(127\) | 9.82317 | 0.871665 | 0.435833 | − | 0.900028i | \(-0.356454\pi\) | ||||
0.435833 | + | 0.900028i | \(0.356454\pi\) | |||||||
\(128\) | −4.29658 | −0.379768 | ||||||||
\(129\) | −6.66986 | −0.587248 | ||||||||
\(130\) | 13.8508 | 1.21480 | ||||||||
\(131\) | 3.46410 | 0.302660 | 0.151330 | − | 0.988483i | \(-0.451644\pi\) | ||||
0.151330 | + | 0.988483i | \(0.451644\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.4287 | 0.904286 | ||||||||
\(134\) | 11.7989 | 1.01927 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 32.5997 | 2.79540 | ||||||||
\(137\) | 20.5997 | 1.75995 | 0.879976 | − | 0.475017i | \(-0.157558\pi\) | ||||
0.879976 | + | 0.475017i | \(0.157558\pi\) | |||||||
\(138\) | 14.4305 | 1.22841 | ||||||||
\(139\) | −17.6984 | −1.50116 | −0.750579 | − | 0.660781i | \(-0.770225\pi\) | ||||
−0.750579 | + | 0.660781i | \(0.770225\pi\) | |||||||
\(140\) | 20.5263 | 1.73479 | ||||||||
\(141\) | −4.21817 | −0.355234 | ||||||||
\(142\) | −3.32993 | −0.279441 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 10.4089 | 0.867412 | ||||||||
\(145\) | −5.26324 | −0.437088 | ||||||||
\(146\) | 12.0000 | 0.993127 | ||||||||
\(147\) | −10.3673 | −0.855082 | ||||||||
\(148\) | −22.0832 | −1.81523 | ||||||||
\(149\) | −20.5263 | −1.68158 | −0.840789 | − | 0.541363i | \(-0.817908\pi\) | ||||
−0.840789 | + | 0.541363i | \(0.817908\pi\) | |||||||
\(150\) | 2.63162 | 0.214871 | ||||||||
\(151\) | −3.84198 | −0.312656 | −0.156328 | − | 0.987705i | \(-0.549966\pi\) | ||||
−0.156328 | + | 0.987705i | \(0.549966\pi\) | |||||||
\(152\) | −19.2654 | −1.56263 | ||||||||
\(153\) | −4.23450 | −0.342339 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.1162 | 0.812553 | ||||||||
\(156\) | 25.9237 | 2.07556 | ||||||||
\(157\) | −0.781830 | −0.0623969 | −0.0311984 | − | 0.999513i | \(-0.509932\pi\) | ||||
−0.0311984 | + | 0.999513i | \(0.509932\pi\) | |||||||
\(158\) | −18.0558 | −1.43645 | ||||||||
\(159\) | 3.63268 | 0.288090 | ||||||||
\(160\) | −11.9952 | −0.948303 | ||||||||
\(161\) | 22.8521 | 1.80100 | ||||||||
\(162\) | −2.63162 | −0.206760 | ||||||||
\(163\) | −7.74887 | −0.606939 | −0.303469 | − | 0.952841i | \(-0.598145\pi\) | ||||
−0.303469 | + | 0.952841i | \(0.598145\pi\) | |||||||
\(164\) | 17.0622 | 1.33233 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −12.8179 | −0.994861 | ||||||||
\(167\) | 14.8851 | 1.15185 | 0.575924 | − | 0.817504i | \(-0.304643\pi\) | ||||
0.575924 | + | 0.817504i | \(0.304643\pi\) | |||||||
\(168\) | 32.0832 | 2.47528 | ||||||||
\(169\) | 14.7017 | 1.13090 | ||||||||
\(170\) | 11.1436 | 0.854675 | ||||||||
\(171\) | 2.50245 | 0.191367 | ||||||||
\(172\) | 32.8519 | 2.50493 | ||||||||
\(173\) | 2.19166 | 0.166628 | 0.0833142 | − | 0.996523i | \(-0.473449\pi\) | ||||
0.0833142 | + | 0.996523i | \(0.473449\pi\) | |||||||
\(174\) | −13.8508 | −1.05003 | ||||||||
\(175\) | 4.16741 | 0.315027 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.58549 | 0.494996 | ||||||||
\(178\) | −39.7801 | −2.98164 | ||||||||
\(179\) | −13.8508 | −1.03526 | −0.517630 | − | 0.855604i | \(-0.673186\pi\) | ||||
−0.517630 | + | 0.855604i | \(0.673186\pi\) | |||||||
\(180\) | 4.92542 | 0.367119 | ||||||||
\(181\) | 7.36732 | 0.547609 | 0.273804 | − | 0.961785i | \(-0.411718\pi\) | ||||
0.273804 | + | 0.961785i | \(0.411718\pi\) | |||||||
\(182\) | 57.7222 | 4.27865 | ||||||||
\(183\) | −12.2585 | −0.906177 | ||||||||
\(184\) | −42.2154 | −3.11216 | ||||||||
\(185\) | −4.48352 | −0.329635 | ||||||||
\(186\) | 26.6220 | 1.95202 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 20.7763 | 1.51527 | ||||||||
\(189\) | −4.16741 | −0.303135 | ||||||||
\(190\) | −6.58549 | −0.477762 | ||||||||
\(191\) | 0.679859 | 0.0491929 | 0.0245965 | − | 0.999697i | \(-0.492170\pi\) | ||||
0.0245965 | + | 0.999697i | \(0.492170\pi\) | |||||||
\(192\) | −10.7489 | −0.775733 | ||||||||
\(193\) | 4.95245 | 0.356485 | 0.178242 | − | 0.983987i | \(-0.442959\pi\) | ||||
0.178242 | + | 0.983987i | \(0.442959\pi\) | |||||||
\(194\) | 42.5933 | 3.05802 | ||||||||
\(195\) | 5.26324 | 0.376908 | ||||||||
\(196\) | 51.0635 | 3.64739 | ||||||||
\(197\) | 3.59828 | 0.256367 | 0.128183 | − | 0.991750i | \(-0.459085\pi\) | ||||
0.128183 | + | 0.991750i | \(0.459085\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.88380 | 0.275315 | 0.137658 | − | 0.990480i | \(-0.456043\pi\) | ||||
0.137658 | + | 0.990480i | \(0.456043\pi\) | |||||||
\(200\) | −7.69860 | −0.544373 | ||||||||
\(201\) | 4.48352 | 0.316243 | ||||||||
\(202\) | −9.46929 | −0.666257 | ||||||||
\(203\) | −21.9341 | −1.53947 | ||||||||
\(204\) | 20.8567 | 1.46026 | ||||||||
\(205\) | 3.46410 | 0.241943 | ||||||||
\(206\) | −3.59828 | −0.250704 | ||||||||
\(207\) | 5.48352 | 0.381131 | ||||||||
\(208\) | −54.7848 | −3.79864 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 10.9670 | 0.756798 | ||||||||
\(211\) | 24.4500 | 1.68321 | 0.841603 | − | 0.540097i | \(-0.181612\pi\) | ||||
0.841603 | + | 0.540097i | \(0.181612\pi\) | |||||||
\(212\) | −17.8925 | −1.22886 | ||||||||
\(213\) | −1.26535 | −0.0867005 | ||||||||
\(214\) | −34.1106 | −2.33176 | ||||||||
\(215\) | 6.66986 | 0.454881 | ||||||||
\(216\) | 7.69860 | 0.523823 | ||||||||
\(217\) | 42.1584 | 2.86190 | ||||||||
\(218\) | −15.7017 | −1.06345 | ||||||||
\(219\) | 4.55993 | 0.308131 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.2872 | 1.49920 | ||||||||
\(222\) | −11.7989 | −0.791892 | ||||||||
\(223\) | 1.59972 | 0.107125 | 0.0535626 | − | 0.998564i | \(-0.482942\pi\) | ||||
0.0535626 | + | 0.998564i | \(0.482942\pi\) | |||||||
\(224\) | −49.9889 | −3.34002 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 15.9713 | 1.06240 | ||||||||
\(227\) | 18.6176 | 1.23569 | 0.617847 | − | 0.786299i | \(-0.288005\pi\) | ||||
0.617847 | + | 0.786299i | \(0.288005\pi\) | |||||||
\(228\) | −12.3256 | −0.816284 | ||||||||
\(229\) | 23.3344 | 1.54198 | 0.770989 | − | 0.636848i | \(-0.219762\pi\) | ||||
0.770989 | + | 0.636848i | \(0.219762\pi\) | |||||||
\(230\) | −14.4305 | −0.951522 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 40.5196 | 2.66024 | ||||||||
\(233\) | 9.75608 | 0.639142 | 0.319571 | − | 0.947562i | \(-0.396461\pi\) | ||||
0.319571 | + | 0.947562i | \(0.396461\pi\) | |||||||
\(234\) | 13.8508 | 0.905458 | ||||||||
\(235\) | 4.21817 | 0.275163 | ||||||||
\(236\) | −32.4363 | −2.11143 | ||||||||
\(237\) | −6.86112 | −0.445677 | ||||||||
\(238\) | 46.4399 | 3.01025 | ||||||||
\(239\) | −8.59317 | −0.555846 | −0.277923 | − | 0.960603i | \(-0.589646\pi\) | ||||
−0.277923 | + | 0.960603i | \(0.589646\pi\) | |||||||
\(240\) | −10.4089 | −0.671895 | ||||||||
\(241\) | −8.97105 | −0.577876 | −0.288938 | − | 0.957348i | \(-0.593302\pi\) | ||||
−0.288938 | + | 0.957348i | \(0.593302\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 60.3784 | 3.86533 | ||||||||
\(245\) | 10.3673 | 0.662344 | ||||||||
\(246\) | 9.11620 | 0.581228 | ||||||||
\(247\) | −13.1710 | −0.838050 | ||||||||
\(248\) | −77.8806 | −4.94542 | ||||||||
\(249\) | −4.87072 | −0.308670 | ||||||||
\(250\) | −2.63162 | −0.166438 | ||||||||
\(251\) | 5.32014 | 0.335804 | 0.167902 | − | 0.985804i | \(-0.446301\pi\) | ||||
0.167902 | + | 0.985804i | \(0.446301\pi\) | |||||||
\(252\) | 20.5263 | 1.29303 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −25.8508 | −1.62203 | ||||||||
\(255\) | 4.23450 | 0.265175 | ||||||||
\(256\) | −10.1908 | −0.636923 | ||||||||
\(257\) | 27.7707 | 1.73229 | 0.866145 | − | 0.499794i | \(-0.166591\pi\) | ||||
0.866145 | + | 0.499794i | \(0.166591\pi\) | |||||||
\(258\) | 17.5525 | 1.09277 | ||||||||
\(259\) | −18.6847 | −1.16101 | ||||||||
\(260\) | −25.9237 | −1.60772 | ||||||||
\(261\) | −5.26324 | −0.325786 | ||||||||
\(262\) | −9.11620 | −0.563201 | ||||||||
\(263\) | 5.89946 | 0.363776 | 0.181888 | − | 0.983319i | \(-0.441779\pi\) | ||||
0.181888 | + | 0.983319i | \(0.441779\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.63268 | −0.223154 | ||||||||
\(266\) | −27.4445 | −1.68273 | ||||||||
\(267\) | −15.1162 | −0.925096 | ||||||||
\(268\) | −22.0832 | −1.34895 | ||||||||
\(269\) | −6.23240 | −0.379996 | −0.189998 | − | 0.981784i | \(-0.560848\pi\) | ||||
−0.189998 | + | 0.981784i | \(0.560848\pi\) | |||||||
\(270\) | 2.63162 | 0.160155 | ||||||||
\(271\) | −29.7657 | −1.80814 | −0.904068 | − | 0.427389i | \(-0.859433\pi\) | ||||
−0.904068 | + | 0.427389i | \(0.859433\pi\) | |||||||
\(272\) | −44.0767 | −2.67254 | ||||||||
\(273\) | 21.9341 | 1.32751 | ||||||||
\(274\) | −54.2106 | −3.27498 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −27.0087 | −1.62573 | ||||||||
\(277\) | 9.29648 | 0.558571 | 0.279286 | − | 0.960208i | \(-0.409902\pi\) | ||||
0.279286 | + | 0.960208i | \(0.409902\pi\) | |||||||
\(278\) | 46.5754 | 2.79341 | ||||||||
\(279\) | 10.1162 | 0.605641 | ||||||||
\(280\) | −32.0832 | −1.91734 | ||||||||
\(281\) | 11.5406 | 0.688453 | 0.344227 | − | 0.938887i | \(-0.388141\pi\) | ||||
0.344227 | + | 0.938887i | \(0.388141\pi\) | |||||||
\(282\) | 11.1006 | 0.661032 | ||||||||
\(283\) | −7.50735 | −0.446265 | −0.223133 | − | 0.974788i | \(-0.571628\pi\) | ||||
−0.223133 | + | 0.974788i | \(0.571628\pi\) | |||||||
\(284\) | 6.23240 | 0.369825 | ||||||||
\(285\) | −2.50245 | −0.148232 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.4363 | 0.852150 | ||||||||
\(288\) | −11.9952 | −0.706823 | ||||||||
\(289\) | 0.930985 | 0.0547638 | ||||||||
\(290\) | 13.8508 | 0.813350 | ||||||||
\(291\) | 16.1852 | 0.948794 | ||||||||
\(292\) | −22.4596 | −1.31435 | ||||||||
\(293\) | −18.0909 | −1.05688 | −0.528441 | − | 0.848970i | \(-0.677223\pi\) | ||||
−0.528441 | + | 0.848970i | \(0.677223\pi\) | |||||||
\(294\) | 27.2829 | 1.59117 | ||||||||
\(295\) | −6.58549 | −0.383422 | ||||||||
\(296\) | 34.5168 | 2.00625 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 54.0173 | 3.12914 | ||||||||
\(299\) | −28.8611 | −1.66908 | ||||||||
\(300\) | −4.92542 | −0.284369 | ||||||||
\(301\) | 27.7961 | 1.60214 | ||||||||
\(302\) | 10.1106 | 0.581802 | ||||||||
\(303\) | −3.59828 | −0.206716 | ||||||||
\(304\) | 26.0478 | 1.49395 | ||||||||
\(305\) | 12.2585 | 0.701921 | ||||||||
\(306\) | 11.1436 | 0.637037 | ||||||||
\(307\) | 3.90907 | 0.223102 | 0.111551 | − | 0.993759i | \(-0.464418\pi\) | ||||
0.111551 | + | 0.993759i | \(0.464418\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.36732 | −0.0777843 | ||||||||
\(310\) | −26.6220 | −1.51203 | ||||||||
\(311\) | 22.5196 | 1.27697 | 0.638484 | − | 0.769635i | \(-0.279562\pi\) | ||||
0.638484 | + | 0.769635i | \(0.279562\pi\) | |||||||
\(312\) | −40.5196 | −2.29397 | ||||||||
\(313\) | 19.2542 | 1.08831 | 0.544157 | − | 0.838984i | \(-0.316850\pi\) | ||||
0.544157 | + | 0.838984i | \(0.316850\pi\) | |||||||
\(314\) | 2.05748 | 0.116110 | ||||||||
\(315\) | 4.16741 | 0.234807 | ||||||||
\(316\) | 33.7939 | 1.90106 | ||||||||
\(317\) | −8.36732 | −0.469956 | −0.234978 | − | 0.972001i | \(-0.575502\pi\) | ||||
−0.234978 | + | 0.972001i | \(0.575502\pi\) | |||||||
\(318\) | −9.55982 | −0.536088 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 10.7489 | 0.600880 | ||||||||
\(321\) | −12.9618 | −0.723459 | ||||||||
\(322\) | −60.1380 | −3.35136 | ||||||||
\(323\) | −10.5966 | −0.589612 | ||||||||
\(324\) | 4.92542 | 0.273635 | ||||||||
\(325\) | −5.26324 | −0.291952 | ||||||||
\(326\) | 20.3921 | 1.12941 | ||||||||
\(327\) | −5.96655 | −0.329951 | ||||||||
\(328\) | −26.6687 | −1.47253 | ||||||||
\(329\) | 17.5789 | 0.969153 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.5525 | −0.689950 | −0.344975 | − | 0.938612i | \(-0.612113\pi\) | ||||
−0.344975 | + | 0.938612i | \(0.612113\pi\) | |||||||
\(332\) | 23.9904 | 1.31664 | ||||||||
\(333\) | −4.48352 | −0.245696 | ||||||||
\(334\) | −39.1720 | −2.14340 | ||||||||
\(335\) | −4.48352 | −0.244961 | ||||||||
\(336\) | −43.3784 | −2.36648 | ||||||||
\(337\) | 21.3638 | 1.16376 | 0.581879 | − | 0.813275i | \(-0.302318\pi\) | ||||
0.581879 | + | 0.813275i | \(0.302318\pi\) | |||||||
\(338\) | −38.6893 | −2.10442 | ||||||||
\(339\) | 6.06902 | 0.329624 | ||||||||
\(340\) | −20.8567 | −1.13111 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −6.58549 | −0.356103 | ||||||||
\(343\) | 14.0330 | 0.757712 | ||||||||
\(344\) | −51.3486 | −2.76853 | ||||||||
\(345\) | −5.48352 | −0.295223 | ||||||||
\(346\) | −5.76760 | −0.310068 | ||||||||
\(347\) | 8.22529 | 0.441557 | 0.220778 | − | 0.975324i | \(-0.429140\pi\) | ||||
0.220778 | + | 0.975324i | \(0.429140\pi\) | |||||||
\(348\) | 25.9237 | 1.38966 | ||||||||
\(349\) | −6.11536 | −0.327348 | −0.163674 | − | 0.986515i | \(-0.552334\pi\) | ||||
−0.163674 | + | 0.986515i | \(0.552334\pi\) | |||||||
\(350\) | −10.9670 | −0.586213 | ||||||||
\(351\) | 5.26324 | 0.280931 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −23.0361 | −1.22609 | −0.613043 | − | 0.790050i | \(-0.710055\pi\) | ||||
−0.613043 | + | 0.790050i | \(0.710055\pi\) | |||||||
\(354\) | −17.3305 | −0.921106 | ||||||||
\(355\) | 1.26535 | 0.0671579 | ||||||||
\(356\) | 74.4537 | 3.94604 | ||||||||
\(357\) | 17.6469 | 0.933973 | ||||||||
\(358\) | 36.4502 | 1.92645 | ||||||||
\(359\) | 15.2630 | 0.805552 | 0.402776 | − | 0.915299i | \(-0.368045\pi\) | ||||
0.402776 | + | 0.915299i | \(0.368045\pi\) | |||||||
\(360\) | −7.69860 | −0.405752 | ||||||||
\(361\) | −12.7378 | −0.670408 | ||||||||
\(362\) | −19.3880 | −1.01901 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −108.035 | −5.66255 | ||||||||
\(365\) | −4.55993 | −0.238678 | ||||||||
\(366\) | 32.2598 | 1.68625 | ||||||||
\(367\) | −32.3816 | −1.69030 | −0.845152 | − | 0.534527i | \(-0.820490\pi\) | ||||
−0.845152 | + | 0.534527i | \(0.820490\pi\) | |||||||
\(368\) | 57.0777 | 2.97538 | ||||||||
\(369\) | 3.46410 | 0.180334 | ||||||||
\(370\) | 11.7989 | 0.613397 | ||||||||
\(371\) | −15.1389 | −0.785970 | ||||||||
\(372\) | −49.8266 | −2.58339 | ||||||||
\(373\) | 8.15821 | 0.422416 | 0.211208 | − | 0.977441i | \(-0.432260\pi\) | ||||
0.211208 | + | 0.977441i | \(0.432260\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | −32.4740 | −1.67472 | ||||||||
\(377\) | 27.7017 | 1.42671 | ||||||||
\(378\) | 10.9670 | 0.564084 | ||||||||
\(379\) | 7.48352 | 0.384403 | 0.192201 | − | 0.981356i | \(-0.438437\pi\) | ||||
0.192201 | + | 0.981356i | \(0.438437\pi\) | |||||||
\(380\) | 12.3256 | 0.632291 | ||||||||
\(381\) | −9.82317 | −0.503256 | ||||||||
\(382\) | −1.78913 | −0.0915399 | ||||||||
\(383\) | −18.1380 | −0.926810 | −0.463405 | − | 0.886147i | \(-0.653372\pi\) | ||||
−0.463405 | + | 0.886147i | \(0.653372\pi\) | |||||||
\(384\) | 4.29658 | 0.219259 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −13.0330 | −0.663360 | ||||||||
\(387\) | 6.66986 | 0.339048 | ||||||||
\(388\) | −79.7190 | −4.04712 | ||||||||
\(389\) | 17.7849 | 0.901732 | 0.450866 | − | 0.892592i | \(-0.351115\pi\) | ||||
0.450866 | + | 0.892592i | \(0.351115\pi\) | |||||||
\(390\) | −13.8508 | −0.701365 | ||||||||
\(391\) | −23.2200 | −1.17428 | ||||||||
\(392\) | −79.8139 | −4.03121 | ||||||||
\(393\) | −3.46410 | −0.174741 | ||||||||
\(394\) | −9.46929 | −0.477056 | ||||||||
\(395\) | 6.86112 | 0.345220 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.33437 | −0.418290 | −0.209145 | − | 0.977885i | \(-0.567068\pi\) | ||||
−0.209145 | + | 0.977885i | \(0.567068\pi\) | |||||||
\(398\) | −10.2207 | −0.512317 | ||||||||
\(399\) | −10.4287 | −0.522090 | ||||||||
\(400\) | 10.4089 | 0.520447 | ||||||||
\(401\) | −13.2654 | −0.662440 | −0.331220 | − | 0.943554i | \(-0.607460\pi\) | ||||
−0.331220 | + | 0.943554i | \(0.607460\pi\) | |||||||
\(402\) | −11.7989 | −0.588477 | ||||||||
\(403\) | −53.2440 | −2.65227 | ||||||||
\(404\) | 17.7230 | 0.881754 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 57.7222 | 2.86470 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −32.5997 | −1.61393 | ||||||||
\(409\) | −16.8609 | −0.833718 | −0.416859 | − | 0.908971i | \(-0.636869\pi\) | ||||
−0.416859 | + | 0.908971i | \(0.636869\pi\) | |||||||
\(410\) | −9.11620 | −0.450217 | ||||||||
\(411\) | −20.5997 | −1.01611 | ||||||||
\(412\) | 6.73465 | 0.331792 | ||||||||
\(413\) | −27.4445 | −1.35045 | ||||||||
\(414\) | −14.4305 | −0.709223 | ||||||||
\(415\) | 4.87072 | 0.239094 | ||||||||
\(416\) | 63.1335 | 3.09538 | ||||||||
\(417\) | 17.6984 | 0.866694 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.79606 | 0.478569 | 0.239284 | − | 0.970950i | \(-0.423087\pi\) | ||||
0.239284 | + | 0.970950i | \(0.423087\pi\) | |||||||
\(420\) | −20.5263 | −1.00158 | ||||||||
\(421\) | −17.8651 | −0.870690 | −0.435345 | − | 0.900264i | \(-0.643374\pi\) | ||||
−0.435345 | + | 0.900264i | \(0.643374\pi\) | |||||||
\(422\) | −64.3430 | −3.13217 | ||||||||
\(423\) | 4.21817 | 0.205094 | ||||||||
\(424\) | 27.9665 | 1.35817 | ||||||||
\(425\) | −4.23450 | −0.205403 | ||||||||
\(426\) | 3.32993 | 0.161335 | ||||||||
\(427\) | 51.0863 | 2.47224 | ||||||||
\(428\) | 63.8425 | 3.08595 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −17.5525 | −0.846459 | ||||||||
\(431\) | 37.1959 | 1.79166 | 0.895832 | − | 0.444393i | \(-0.146580\pi\) | ||||
0.895832 | + | 0.444393i | \(0.146580\pi\) | |||||||
\(432\) | −10.4089 | −0.500801 | ||||||||
\(433\) | −10.1852 | −0.489470 | −0.244735 | − | 0.969590i | \(-0.578701\pi\) | ||||
−0.244735 | + | 0.969590i | \(0.578701\pi\) | |||||||
\(434\) | −110.945 | −5.32552 | ||||||||
\(435\) | 5.26324 | 0.252353 | ||||||||
\(436\) | 29.3878 | 1.40742 | ||||||||
\(437\) | 13.7222 | 0.656423 | ||||||||
\(438\) | −12.0000 | −0.573382 | ||||||||
\(439\) | −19.7134 | −0.940870 | −0.470435 | − | 0.882435i | \(-0.655903\pi\) | ||||
−0.470435 | + | 0.882435i | \(0.655903\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10.3673 | 0.493682 | ||||||||
\(442\) | −58.6514 | −2.78976 | ||||||||
\(443\) | −26.4363 | −1.25603 | −0.628014 | − | 0.778202i | \(-0.716132\pi\) | ||||
−0.628014 | + | 0.778202i | \(0.716132\pi\) | |||||||
\(444\) | 22.0832 | 1.04802 | ||||||||
\(445\) | 15.1162 | 0.716577 | ||||||||
\(446\) | −4.20986 | −0.199342 | ||||||||
\(447\) | 20.5263 | 0.970859 | ||||||||
\(448\) | 44.7950 | 2.11636 | ||||||||
\(449\) | −21.7017 | −1.02417 | −0.512083 | − | 0.858936i | \(-0.671126\pi\) | ||||
−0.512083 | + | 0.858936i | \(0.671126\pi\) | |||||||
\(450\) | −2.63162 | −0.124056 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −29.8925 | −1.40602 | ||||||||
\(453\) | 3.84198 | 0.180512 | ||||||||
\(454\) | −48.9944 | −2.29942 | ||||||||
\(455\) | −21.9341 | −1.02829 | ||||||||
\(456\) | 19.2654 | 0.902183 | ||||||||
\(457\) | 11.7989 | 0.551930 | 0.275965 | − | 0.961168i | \(-0.411003\pi\) | ||||
0.275965 | + | 0.961168i | \(0.411003\pi\) | |||||||
\(458\) | −61.4072 | −2.86937 | ||||||||
\(459\) | 4.23450 | 0.197650 | ||||||||
\(460\) | 27.0087 | 1.25929 | ||||||||
\(461\) | 31.0527 | 1.44627 | 0.723135 | − | 0.690706i | \(-0.242700\pi\) | ||||
0.723135 | + | 0.690706i | \(0.242700\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 38.3704 | 1.78323 | 0.891613 | − | 0.452799i | \(-0.149575\pi\) | ||||
0.891613 | + | 0.452799i | \(0.149575\pi\) | |||||||
\(464\) | −54.7848 | −2.54332 | ||||||||
\(465\) | −10.1162 | −0.469127 | ||||||||
\(466\) | −25.6743 | −1.18934 | ||||||||
\(467\) | 14.9528 | 0.691934 | 0.345967 | − | 0.938247i | \(-0.387551\pi\) | ||||
0.345967 | + | 0.938247i | \(0.387551\pi\) | |||||||
\(468\) | −25.9237 | −1.19832 | ||||||||
\(469\) | −18.6847 | −0.862779 | ||||||||
\(470\) | −11.1006 | −0.512033 | ||||||||
\(471\) | 0.781830 | 0.0360248 | ||||||||
\(472\) | 50.6991 | 2.33361 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 18.0558 | 0.829333 | ||||||||
\(475\) | 2.50245 | 0.114820 | ||||||||
\(476\) | −86.9185 | −3.98390 | ||||||||
\(477\) | −3.63268 | −0.166329 | ||||||||
\(478\) | 22.6139 | 1.03434 | ||||||||
\(479\) | 12.1914 | 0.557041 | 0.278521 | − | 0.960430i | \(-0.410156\pi\) | ||||
0.278521 | + | 0.960430i | \(0.410156\pi\) | |||||||
\(480\) | 11.9952 | 0.547503 | ||||||||
\(481\) | 23.5979 | 1.07597 | ||||||||
\(482\) | 23.6084 | 1.07533 | ||||||||
\(483\) | −22.8521 | −1.03981 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16.1852 | −0.734933 | ||||||||
\(486\) | 2.63162 | 0.119373 | ||||||||
\(487\) | 14.2872 | 0.647414 | 0.323707 | − | 0.946157i | \(-0.395071\pi\) | ||||
0.323707 | + | 0.946157i | \(0.395071\pi\) | |||||||
\(488\) | −94.3735 | −4.27209 | ||||||||
\(489\) | 7.74887 | 0.350416 | ||||||||
\(490\) | −27.2829 | −1.23251 | ||||||||
\(491\) | −26.0579 | −1.17597 | −0.587987 | − | 0.808870i | \(-0.700079\pi\) | ||||
−0.587987 | + | 0.808870i | \(0.700079\pi\) | |||||||
\(492\) | −17.0622 | −0.769222 | ||||||||
\(493\) | 22.2872 | 1.00376 | ||||||||
\(494\) | 34.6610 | 1.55947 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 105.299 | 4.72806 | ||||||||
\(497\) | 5.27325 | 0.236537 | ||||||||
\(498\) | 12.8179 | 0.574383 | ||||||||
\(499\) | 28.8651 | 1.29218 | 0.646089 | − | 0.763262i | \(-0.276403\pi\) | ||||
0.646089 | + | 0.763262i | \(0.276403\pi\) | |||||||
\(500\) | 4.92542 | 0.220272 | ||||||||
\(501\) | −14.8851 | −0.665019 | ||||||||
\(502\) | −14.0006 | −0.624877 | ||||||||
\(503\) | 39.3729 | 1.75555 | 0.877776 | − | 0.479071i | \(-0.159026\pi\) | ||||
0.877776 | + | 0.479071i | \(0.159026\pi\) | |||||||
\(504\) | −32.0832 | −1.42910 | ||||||||
\(505\) | 3.59828 | 0.160121 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −14.7017 | −0.652925 | ||||||||
\(508\) | 48.3833 | 2.14666 | ||||||||
\(509\) | 20.0832 | 0.890174 | 0.445087 | − | 0.895487i | \(-0.353173\pi\) | ||||
0.445087 | + | 0.895487i | \(0.353173\pi\) | |||||||
\(510\) | −11.1436 | −0.493447 | ||||||||
\(511\) | −19.0031 | −0.840648 | ||||||||
\(512\) | 35.4114 | 1.56498 | ||||||||
\(513\) | −2.50245 | −0.110486 | ||||||||
\(514\) | −73.0819 | −3.22351 | ||||||||
\(515\) | 1.36732 | 0.0602515 | ||||||||
\(516\) | −32.8519 | −1.44622 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 49.1710 | 2.16045 | ||||||||
\(519\) | −2.19166 | −0.0962030 | ||||||||
\(520\) | 40.5196 | 1.77690 | ||||||||
\(521\) | −34.7520 | −1.52251 | −0.761256 | − | 0.648452i | \(-0.775417\pi\) | ||||
−0.761256 | + | 0.648452i | \(0.775417\pi\) | |||||||
\(522\) | 13.8508 | 0.606235 | ||||||||
\(523\) | 14.6939 | 0.642519 | 0.321260 | − | 0.946991i | \(-0.395894\pi\) | ||||
0.321260 | + | 0.946991i | \(0.395894\pi\) | |||||||
\(524\) | 17.0622 | 0.745364 | ||||||||
\(525\) | −4.16741 | −0.181881 | ||||||||
\(526\) | −15.5251 | −0.676928 | ||||||||
\(527\) | −42.8370 | −1.86601 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.06902 | 0.307348 | ||||||||
\(530\) | 9.55982 | 0.415252 | ||||||||
\(531\) | −6.58549 | −0.285786 | ||||||||
\(532\) | 51.3659 | 2.22700 | ||||||||
\(533\) | −18.2324 | −0.789733 | ||||||||
\(534\) | 39.7801 | 1.72145 | ||||||||
\(535\) | 12.9618 | 0.560389 | ||||||||
\(536\) | 34.5168 | 1.49090 | ||||||||
\(537\) | 13.8508 | 0.597708 | ||||||||
\(538\) | 16.4013 | 0.707110 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −4.92542 | −0.211956 | ||||||||
\(541\) | −3.32993 | −0.143165 | −0.0715824 | − | 0.997435i | \(-0.522805\pi\) | ||||
−0.0715824 | + | 0.997435i | \(0.522805\pi\) | |||||||
\(542\) | 78.3319 | 3.36464 | ||||||||
\(543\) | −7.36732 | −0.316162 | ||||||||
\(544\) | 50.7936 | 2.17776 | ||||||||
\(545\) | 5.96655 | 0.255579 | ||||||||
\(546\) | −57.7222 | −2.47028 | ||||||||
\(547\) | −27.4545 | −1.17387 | −0.586934 | − | 0.809635i | \(-0.699665\pi\) | ||||
−0.586934 | + | 0.809635i | \(0.699665\pi\) | |||||||
\(548\) | 101.462 | 4.33426 | ||||||||
\(549\) | 12.2585 | 0.523181 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.1710 | −0.561103 | ||||||||
\(552\) | 42.2154 | 1.79681 | ||||||||
\(553\) | 28.5931 | 1.21590 | ||||||||
\(554\) | −24.4648 | −1.03941 | ||||||||
\(555\) | 4.48352 | 0.190315 | ||||||||
\(556\) | −87.1720 | −3.69692 | ||||||||
\(557\) | 26.8283 | 1.13675 | 0.568375 | − | 0.822770i | \(-0.307572\pi\) | ||||
0.568375 | + | 0.822770i | \(0.307572\pi\) | |||||||
\(558\) | −26.6220 | −1.12700 | ||||||||
\(559\) | −35.1051 | −1.48479 | ||||||||
\(560\) | 43.3784 | 1.83307 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −30.3704 | −1.28110 | ||||||||
\(563\) | 36.9668 | 1.55797 | 0.778983 | − | 0.627045i | \(-0.215736\pi\) | ||||
0.778983 | + | 0.627045i | \(0.215736\pi\) | |||||||
\(564\) | −20.7763 | −0.874839 | ||||||||
\(565\) | −6.06902 | −0.255325 | ||||||||
\(566\) | 19.7565 | 0.830427 | ||||||||
\(567\) | 4.16741 | 0.175015 | ||||||||
\(568\) | −9.74145 | −0.408742 | ||||||||
\(569\) | −32.4594 | −1.36077 | −0.680384 | − | 0.732856i | \(-0.738187\pi\) | ||||
−0.680384 | + | 0.732856i | \(0.738187\pi\) | |||||||
\(570\) | 6.58549 | 0.275836 | ||||||||
\(571\) | −18.0092 | −0.753661 | −0.376830 | − | 0.926282i | \(-0.622986\pi\) | ||||
−0.376830 | + | 0.926282i | \(0.622986\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.679859 | −0.0284015 | ||||||||
\(574\) | −37.9910 | −1.58571 | ||||||||
\(575\) | 5.48352 | 0.228679 | ||||||||
\(576\) | 10.7489 | 0.447870 | ||||||||
\(577\) | 39.5997 | 1.64856 | 0.824279 | − | 0.566184i | \(-0.191581\pi\) | ||||
0.824279 | + | 0.566184i | \(0.191581\pi\) | |||||||
\(578\) | −2.45000 | −0.101906 | ||||||||
\(579\) | −4.95245 | −0.205817 | ||||||||
\(580\) | −25.9237 | −1.07642 | ||||||||
\(581\) | 20.2983 | 0.842116 | ||||||||
\(582\) | −42.5933 | −1.76555 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 35.1051 | 1.45266 | ||||||||
\(585\) | −5.26324 | −0.217608 | ||||||||
\(586\) | 47.6084 | 1.96668 | ||||||||
\(587\) | −24.9813 | −1.03109 | −0.515544 | − | 0.856863i | \(-0.672410\pi\) | ||||
−0.515544 | + | 0.856863i | \(0.672410\pi\) | |||||||
\(588\) | −51.0635 | −2.10582 | ||||||||
\(589\) | 25.3153 | 1.04310 | ||||||||
\(590\) | 17.3305 | 0.713486 | ||||||||
\(591\) | −3.59828 | −0.148013 | ||||||||
\(592\) | −46.6687 | −1.91807 | ||||||||
\(593\) | 1.92331 | 0.0789807 | 0.0394904 | − | 0.999220i | \(-0.487427\pi\) | ||||
0.0394904 | + | 0.999220i | \(0.487427\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17.6469 | −0.723453 | ||||||||
\(596\) | −101.101 | −4.14124 | ||||||||
\(597\) | −3.88380 | −0.158953 | ||||||||
\(598\) | 75.9514 | 3.10588 | ||||||||
\(599\) | 19.9889 | 0.816723 | 0.408362 | − | 0.912820i | \(-0.366100\pi\) | ||||
0.408362 | + | 0.912820i | \(0.366100\pi\) | |||||||
\(600\) | 7.69860 | 0.314294 | ||||||||
\(601\) | 0.176619 | 0.00720444 | 0.00360222 | − | 0.999994i | \(-0.498853\pi\) | ||||
0.00360222 | + | 0.999994i | \(0.498853\pi\) | |||||||
\(602\) | −73.1487 | −2.98132 | ||||||||
\(603\) | −4.48352 | −0.182583 | ||||||||
\(604\) | −18.9234 | −0.769982 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 9.46929 | 0.384664 | ||||||||
\(607\) | −11.8089 | −0.479310 | −0.239655 | − | 0.970858i | \(-0.577034\pi\) | ||||
−0.239655 | + | 0.970858i | \(0.577034\pi\) | |||||||
\(608\) | −30.0173 | −1.21736 | ||||||||
\(609\) | 21.9341 | 0.888814 | ||||||||
\(610\) | −32.2598 | −1.30616 | ||||||||
\(611\) | −22.2012 | −0.898166 | ||||||||
\(612\) | −20.8567 | −0.843082 | ||||||||
\(613\) | 13.4114 | 0.541683 | 0.270841 | − | 0.962624i | \(-0.412698\pi\) | ||||
0.270841 | + | 0.962624i | \(0.412698\pi\) | |||||||
\(614\) | −10.2872 | −0.415157 | ||||||||
\(615\) | −3.46410 | −0.139686 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27.9341 | −1.12458 | −0.562292 | − | 0.826939i | \(-0.690080\pi\) | ||||
−0.562292 | + | 0.826939i | \(0.690080\pi\) | |||||||
\(618\) | 3.59828 | 0.144744 | ||||||||
\(619\) | 38.2324 | 1.53669 | 0.768345 | − | 0.640036i | \(-0.221081\pi\) | ||||
0.768345 | + | 0.640036i | \(0.221081\pi\) | |||||||
\(620\) | 49.8266 | 2.00108 | ||||||||
\(621\) | −5.48352 | −0.220046 | ||||||||
\(622\) | −59.2630 | −2.37623 | ||||||||
\(623\) | 62.9954 | 2.52386 | ||||||||
\(624\) | 54.7848 | 2.19315 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −50.6698 | −2.02517 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.85085 | −0.153665 | ||||||||
\(629\) | 18.9855 | 0.757000 | ||||||||
\(630\) | −10.9670 | −0.436938 | ||||||||
\(631\) | 0.952817 | 0.0379310 | 0.0189655 | − | 0.999820i | \(-0.493963\pi\) | ||||
0.0189655 | + | 0.999820i | \(0.493963\pi\) | |||||||
\(632\) | −52.8210 | −2.10111 | ||||||||
\(633\) | −24.4500 | −0.971799 | ||||||||
\(634\) | 22.0196 | 0.874511 | ||||||||
\(635\) | 9.82317 | 0.389821 | ||||||||
\(636\) | 17.8925 | 0.709482 | ||||||||
\(637\) | −54.5657 | −2.16197 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.26535 | 0.0500566 | ||||||||
\(640\) | −4.29658 | −0.169837 | ||||||||
\(641\) | 4.47592 | 0.176788 | 0.0883941 | − | 0.996086i | \(-0.471827\pi\) | ||||
0.0883941 | + | 0.996086i | \(0.471827\pi\) | |||||||
\(642\) | 34.1106 | 1.34624 | ||||||||
\(643\) | 21.8980 | 0.863574 | 0.431787 | − | 0.901976i | \(-0.357883\pi\) | ||||
0.431787 | + | 0.901976i | \(0.357883\pi\) | |||||||
\(644\) | 112.556 | 4.43534 | ||||||||
\(645\) | −6.66986 | −0.262626 | ||||||||
\(646\) | 27.8863 | 1.09717 | ||||||||
\(647\) | 21.2796 | 0.836587 | 0.418293 | − | 0.908312i | \(-0.362628\pi\) | ||||
0.418293 | + | 0.908312i | \(0.362628\pi\) | |||||||
\(648\) | −7.69860 | −0.302430 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 13.8508 | 0.543275 | ||||||||
\(651\) | −42.1584 | −1.65232 | ||||||||
\(652\) | −38.1665 | −1.49471 | ||||||||
\(653\) | 20.5307 | 0.803429 | 0.401714 | − | 0.915765i | \(-0.368414\pi\) | ||||
0.401714 | + | 0.915765i | \(0.368414\pi\) | |||||||
\(654\) | 15.7017 | 0.613985 | ||||||||
\(655\) | 3.46410 | 0.135354 | ||||||||
\(656\) | 36.0576 | 1.40781 | ||||||||
\(657\) | −4.55993 | −0.177900 | ||||||||
\(658\) | −46.2609 | −1.80344 | ||||||||
\(659\) | −18.9855 | −0.739569 | −0.369784 | − | 0.929118i | \(-0.620568\pi\) | ||||
−0.369784 | + | 0.929118i | \(0.620568\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.86507 | −0.111438 | −0.0557192 | − | 0.998446i | \(-0.517745\pi\) | ||||
−0.0557192 | + | 0.998446i | \(0.517745\pi\) | |||||||
\(662\) | 33.0335 | 1.28388 | ||||||||
\(663\) | −22.2872 | −0.865563 | ||||||||
\(664\) | −37.4977 | −1.45519 | ||||||||
\(665\) | 10.4287 | 0.404409 | ||||||||
\(666\) | 11.7989 | 0.457199 | ||||||||
\(667\) | −28.8611 | −1.11751 | ||||||||
\(668\) | 73.3156 | 2.83667 | ||||||||
\(669\) | −1.59972 | −0.0618488 | ||||||||
\(670\) | 11.7989 | 0.455832 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 49.9889 | 1.92836 | ||||||||
\(673\) | −49.6033 | −1.91207 | −0.956033 | − | 0.293261i | \(-0.905260\pi\) | ||||
−0.956033 | + | 0.293261i | \(0.905260\pi\) | |||||||
\(674\) | −56.2213 | −2.16556 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 72.4120 | 2.78508 | ||||||||
\(677\) | −34.3927 | −1.32182 | −0.660909 | − | 0.750466i | \(-0.729829\pi\) | ||||
−0.660909 | + | 0.750466i | \(0.729829\pi\) | |||||||
\(678\) | −15.9713 | −0.613376 | ||||||||
\(679\) | −67.4505 | −2.58851 | ||||||||
\(680\) | 32.5997 | 1.25014 | ||||||||
\(681\) | −18.6176 | −0.713428 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.20394 | 0.313915 | 0.156958 | − | 0.987605i | \(-0.449831\pi\) | ||||
0.156958 | + | 0.987605i | \(0.449831\pi\) | |||||||
\(684\) | 12.3256 | 0.471282 | ||||||||
\(685\) | 20.5997 | 0.787075 | ||||||||
\(686\) | −36.9296 | −1.40998 | ||||||||
\(687\) | −23.3344 | −0.890262 | ||||||||
\(688\) | 69.4262 | 2.64685 | ||||||||
\(689\) | 19.1196 | 0.728401 | ||||||||
\(690\) | 14.4305 | 0.549361 | ||||||||
\(691\) | −21.0832 | −0.802044 | −0.401022 | − | 0.916068i | \(-0.631345\pi\) | ||||
−0.401022 | + | 0.916068i | \(0.631345\pi\) | |||||||
\(692\) | 10.7948 | 0.410358 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −21.6458 | −0.821665 | ||||||||
\(695\) | −17.6984 | −0.671338 | ||||||||
\(696\) | −40.5196 | −1.53589 | ||||||||
\(697\) | −14.6687 | −0.555618 | ||||||||
\(698\) | 16.0933 | 0.609141 | ||||||||
\(699\) | −9.75608 | −0.369009 | ||||||||
\(700\) | 20.5263 | 0.775820 | ||||||||
\(701\) | 22.0671 | 0.833461 | 0.416731 | − | 0.909030i | \(-0.363176\pi\) | ||||
0.416731 | + | 0.909030i | \(0.363176\pi\) | |||||||
\(702\) | −13.8508 | −0.522766 | ||||||||
\(703\) | −11.2198 | −0.423162 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.21817 | −0.158865 | ||||||||
\(706\) | 60.6222 | 2.28154 | ||||||||
\(707\) | 14.9955 | 0.563964 | ||||||||
\(708\) | 32.4363 | 1.21903 | ||||||||
\(709\) | −39.7992 | −1.49469 | −0.747344 | − | 0.664437i | \(-0.768671\pi\) | ||||
−0.747344 | + | 0.664437i | \(0.768671\pi\) | |||||||
\(710\) | −3.32993 | −0.124970 | ||||||||
\(711\) | 6.86112 | 0.257312 | ||||||||
\(712\) | −116.374 | −4.36128 | ||||||||
\(713\) | 55.4724 | 2.07746 | ||||||||
\(714\) | −46.4399 | −1.73797 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −68.2213 | −2.54955 | ||||||||
\(717\) | 8.59317 | 0.320918 | ||||||||
\(718\) | −40.1665 | −1.49900 | ||||||||
\(719\) | 12.1380 | 0.452672 | 0.226336 | − | 0.974049i | \(-0.427325\pi\) | ||||
0.226336 | + | 0.974049i | \(0.427325\pi\) | |||||||
\(720\) | 10.4089 | 0.387918 | ||||||||
\(721\) | 5.69820 | 0.212212 | ||||||||
\(722\) | 33.5209 | 1.24752 | ||||||||
\(723\) | 8.97105 | 0.333637 | ||||||||
\(724\) | 36.2872 | 1.34860 | ||||||||
\(725\) | −5.26324 | −0.195472 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.9670 | 1.44521 | 0.722604 | − | 0.691262i | \(-0.242945\pi\) | ||||
0.722604 | + | 0.691262i | \(0.242945\pi\) | |||||||
\(728\) | 168.862 | 6.25843 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 12.0000 | 0.444140 | ||||||||
\(731\) | −28.2435 | −1.04462 | ||||||||
\(732\) | −60.3784 | −2.23165 | ||||||||
\(733\) | 5.65576 | 0.208900 | 0.104450 | − | 0.994530i | \(-0.466692\pi\) | ||||
0.104450 | + | 0.994530i | \(0.466692\pi\) | |||||||
\(734\) | 85.2159 | 3.14538 | ||||||||
\(735\) | −10.3673 | −0.382404 | ||||||||
\(736\) | −65.7759 | −2.42453 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −9.11620 | −0.335572 | ||||||||
\(739\) | −28.8040 | −1.05957 | −0.529786 | − | 0.848131i | \(-0.677728\pi\) | ||||
−0.529786 | + | 0.848131i | \(0.677728\pi\) | |||||||
\(740\) | −22.0832 | −0.811796 | ||||||||
\(741\) | 13.1710 | 0.483848 | ||||||||
\(742\) | 39.8397 | 1.46256 | ||||||||
\(743\) | −43.2688 | −1.58738 | −0.793690 | − | 0.608323i | \(-0.791843\pi\) | ||||
−0.793690 | + | 0.608323i | \(0.791843\pi\) | |||||||
\(744\) | 77.8806 | 2.85524 | ||||||||
\(745\) | −20.5263 | −0.752024 | ||||||||
\(746\) | −21.4693 | −0.786047 | ||||||||
\(747\) | 4.87072 | 0.178210 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 54.0173 | 1.97375 | ||||||||
\(750\) | 2.63162 | 0.0960932 | ||||||||
\(751\) | 7.58549 | 0.276799 | 0.138399 | − | 0.990377i | \(-0.455804\pi\) | ||||
0.138399 | + | 0.990377i | \(0.455804\pi\) | |||||||
\(752\) | 43.9067 | 1.60111 | ||||||||
\(753\) | −5.32014 | −0.193877 | ||||||||
\(754\) | −72.9003 | −2.65487 | ||||||||
\(755\) | −3.84198 | −0.139824 | ||||||||
\(756\) | −20.5263 | −0.746533 | ||||||||
\(757\) | 42.1741 | 1.53284 | 0.766422 | − | 0.642338i | \(-0.222035\pi\) | ||||
0.766422 | + | 0.642338i | \(0.222035\pi\) | |||||||
\(758\) | −19.6938 | −0.715310 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −19.2654 | −0.698828 | ||||||||
\(761\) | 6.15318 | 0.223052 | 0.111526 | − | 0.993761i | \(-0.464426\pi\) | ||||
0.111526 | + | 0.993761i | \(0.464426\pi\) | |||||||
\(762\) | 25.8508 | 0.936477 | ||||||||
\(763\) | 24.8651 | 0.900176 | ||||||||
\(764\) | 3.34860 | 0.121148 | ||||||||
\(765\) | −4.23450 | −0.153099 | ||||||||
\(766\) | 47.7324 | 1.72464 | ||||||||
\(767\) | 34.6610 | 1.25154 | ||||||||
\(768\) | 10.1908 | 0.367728 | ||||||||
\(769\) | 20.4592 | 0.737777 | 0.368888 | − | 0.929474i | \(-0.379738\pi\) | ||||
0.368888 | + | 0.929474i | \(0.379738\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −27.7707 | −1.00014 | ||||||||
\(772\) | 24.3929 | 0.877919 | ||||||||
\(773\) | 34.2355 | 1.23137 | 0.615683 | − | 0.787994i | \(-0.288880\pi\) | ||||
0.615683 | + | 0.787994i | \(0.288880\pi\) | |||||||
\(774\) | −17.5525 | −0.630913 | ||||||||
\(775\) | 10.1162 | 0.363385 | ||||||||
\(776\) | 124.604 | 4.47301 | ||||||||
\(777\) | 18.6847 | 0.670309 | ||||||||
\(778\) | −46.8032 | −1.67798 | ||||||||
\(779\) | 8.66874 | 0.310590 | ||||||||
\(780\) | 25.9237 | 0.928217 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 61.1061 | 2.18515 | ||||||||
\(783\) | 5.26324 | 0.188093 | ||||||||
\(784\) | 107.913 | 3.85403 | ||||||||
\(785\) | −0.781830 | −0.0279047 | ||||||||
\(786\) | 9.11620 | 0.325164 | ||||||||
\(787\) | −4.73655 | −0.168840 | −0.0844199 | − | 0.996430i | \(-0.526904\pi\) | ||||
−0.0844199 | + | 0.996430i | \(0.526904\pi\) | |||||||
\(788\) | 17.7230 | 0.631357 | ||||||||
\(789\) | −5.89946 | −0.210026 | ||||||||
\(790\) | −18.0558 | −0.642398 | ||||||||
\(791\) | −25.2921 | −0.899283 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −64.5196 | −2.29116 | ||||||||
\(794\) | 21.9329 | 0.778369 | ||||||||
\(795\) | 3.63268 | 0.128838 | ||||||||
\(796\) | 19.1294 | 0.678022 | ||||||||
\(797\) | −20.5307 | −0.727235 | −0.363617 | − | 0.931548i | \(-0.618458\pi\) | ||||
−0.363617 | + | 0.931548i | \(0.618458\pi\) | |||||||
\(798\) | 27.4445 | 0.971523 | ||||||||
\(799\) | −17.8618 | −0.631906 | ||||||||
\(800\) | −11.9952 | −0.424094 | ||||||||
\(801\) | 15.1162 | 0.534105 | ||||||||
\(802\) | 34.9094 | 1.23269 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 22.0832 | 0.778816 | ||||||||
\(805\) | 22.8521 | 0.805431 | ||||||||
\(806\) | 140.118 | 4.93544 | ||||||||
\(807\) | 6.23240 | 0.219391 | ||||||||
\(808\) | −27.7017 | −0.974542 | ||||||||
\(809\) | −48.8707 | −1.71820 | −0.859101 | − | 0.511807i | \(-0.828976\pi\) | ||||
−0.859101 | + | 0.511807i | \(0.828976\pi\) | |||||||
\(810\) | −2.63162 | −0.0924657 | ||||||||
\(811\) | −10.9468 | −0.384394 | −0.192197 | − | 0.981356i | \(-0.561561\pi\) | ||||
−0.192197 | + | 0.981356i | \(0.561561\pi\) | |||||||
\(812\) | −108.035 | −3.79127 | ||||||||
\(813\) | 29.7657 | 1.04393 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.74887 | −0.271431 | ||||||||
\(816\) | 44.0767 | 1.54299 | ||||||||
\(817\) | 16.6910 | 0.583944 | ||||||||
\(818\) | 44.3715 | 1.55141 | ||||||||
\(819\) | −21.9341 | −0.766439 | ||||||||
\(820\) | 17.0622 | 0.595837 | ||||||||
\(821\) | −26.8136 | −0.935802 | −0.467901 | − | 0.883781i | \(-0.654990\pi\) | ||||
−0.467901 | + | 0.883781i | \(0.654990\pi\) | |||||||
\(822\) | 54.2106 | 1.89081 | ||||||||
\(823\) | −20.1020 | −0.700711 | −0.350355 | − | 0.936617i | \(-0.613939\pi\) | ||||
−0.350355 | + | 0.936617i | \(0.613939\pi\) | |||||||
\(824\) | −10.5265 | −0.366707 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 72.2234 | 2.51297 | ||||||||
\(827\) | 23.1104 | 0.803629 | 0.401814 | − | 0.915721i | \(-0.368380\pi\) | ||||
0.401814 | + | 0.915721i | \(0.368380\pi\) | |||||||
\(828\) | 27.0087 | 0.938616 | ||||||||
\(829\) | −41.0721 | −1.42649 | −0.713247 | − | 0.700913i | \(-0.752776\pi\) | ||||
−0.713247 | + | 0.700913i | \(0.752776\pi\) | |||||||
\(830\) | −12.8179 | −0.444915 | ||||||||
\(831\) | −9.29648 | −0.322491 | ||||||||
\(832\) | −56.5739 | −1.96135 | ||||||||
\(833\) | −43.9004 | −1.52106 | ||||||||
\(834\) | −46.5754 | −1.61278 | ||||||||
\(835\) | 14.8851 | 0.515122 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.1162 | −0.349667 | ||||||||
\(838\) | −25.7795 | −0.890538 | ||||||||
\(839\) | −7.40338 | −0.255593 | −0.127797 | − | 0.991800i | \(-0.540790\pi\) | ||||
−0.127797 | + | 0.991800i | \(0.540790\pi\) | |||||||
\(840\) | 32.0832 | 1.10698 | ||||||||
\(841\) | −1.29831 | −0.0447693 | ||||||||
\(842\) | 47.0141 | 1.62021 | ||||||||
\(843\) | −11.5406 | −0.397479 | ||||||||
\(844\) | 120.426 | 4.14525 | ||||||||
\(845\) | 14.7017 | 0.505754 | ||||||||
\(846\) | −11.1006 | −0.381647 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −37.8123 | −1.29848 | ||||||||
\(849\) | 7.50735 | 0.257651 | ||||||||
\(850\) | 11.1436 | 0.382222 | ||||||||
\(851\) | −24.5855 | −0.842780 | ||||||||
\(852\) | −6.23240 | −0.213518 | ||||||||
\(853\) | −26.3686 | −0.902845 | −0.451423 | − | 0.892310i | \(-0.649083\pi\) | ||||
−0.451423 | + | 0.892310i | \(0.649083\pi\) | |||||||
\(854\) | −134.440 | −4.60044 | ||||||||
\(855\) | 2.50245 | 0.0855819 | ||||||||
\(856\) | −99.7880 | −3.41068 | ||||||||
\(857\) | 38.3588 | 1.31031 | 0.655156 | − | 0.755493i | \(-0.272603\pi\) | ||||
0.655156 | + | 0.755493i | \(0.272603\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.53831 | 0.0866060 | 0.0433030 | − | 0.999062i | \(-0.486212\pi\) | ||||
0.0433030 | + | 0.999062i | \(0.486212\pi\) | |||||||
\(860\) | 32.8519 | 1.12024 | ||||||||
\(861\) | −14.4363 | −0.491989 | ||||||||
\(862\) | −97.8855 | −3.33399 | ||||||||
\(863\) | −12.0000 | −0.408485 | −0.204242 | − | 0.978920i | \(-0.565473\pi\) | ||||
−0.204242 | + | 0.978920i | \(0.565473\pi\) | |||||||
\(864\) | 11.9952 | 0.408084 | ||||||||
\(865\) | 2.19166 | 0.0745185 | ||||||||
\(866\) | 26.8036 | 0.910824 | ||||||||
\(867\) | −0.930985 | −0.0316179 | ||||||||
\(868\) | 207.648 | 7.04803 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −13.8508 | −0.469588 | ||||||||
\(871\) | 23.5979 | 0.799583 | ||||||||
\(872\) | −45.9341 | −1.55552 | ||||||||
\(873\) | −16.1852 | −0.547786 | ||||||||
\(874\) | −36.1117 | −1.22150 | ||||||||
\(875\) | 4.16741 | 0.140884 | ||||||||
\(876\) | 22.4596 | 0.758839 | ||||||||
\(877\) | 32.1386 | 1.08524 | 0.542621 | − | 0.839978i | \(-0.317432\pi\) | ||||
0.542621 | + | 0.839978i | \(0.317432\pi\) | |||||||
\(878\) | 51.8782 | 1.75081 | ||||||||
\(879\) | 18.0909 | 0.610191 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 47.1051 | 1.58701 | 0.793505 | − | 0.608564i | \(-0.208254\pi\) | ||||
0.793505 | + | 0.608564i | \(0.208254\pi\) | |||||||
\(882\) | −27.2829 | −0.918661 | ||||||||
\(883\) | −19.9528 | −0.671466 | −0.335733 | − | 0.941957i | \(-0.608984\pi\) | ||||
−0.335733 | + | 0.941957i | \(0.608984\pi\) | |||||||
\(884\) | 109.774 | 3.69209 | ||||||||
\(885\) | 6.58549 | 0.221369 | ||||||||
\(886\) | 69.5704 | 2.33726 | ||||||||
\(887\) | 48.6316 | 1.63289 | 0.816445 | − | 0.577424i | \(-0.195942\pi\) | ||||
0.816445 | + | 0.577424i | \(0.195942\pi\) | |||||||
\(888\) | −34.5168 | −1.15831 | ||||||||
\(889\) | 40.9372 | 1.37299 | ||||||||
\(890\) | −39.7801 | −1.33343 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7.87930 | 0.263819 | ||||||||
\(893\) | 10.5558 | 0.353235 | ||||||||
\(894\) | −54.0173 | −1.80661 | ||||||||
\(895\) | −13.8508 | −0.462983 | ||||||||
\(896\) | −17.9056 | −0.598185 | ||||||||
\(897\) | 28.8611 | 0.963644 | ||||||||
\(898\) | 57.1106 | 1.90581 | ||||||||
\(899\) | −53.2440 | −1.77579 | ||||||||
\(900\) | 4.92542 | 0.164181 | ||||||||
\(901\) | 15.3826 | 0.512468 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −27.7961 | −0.924995 | ||||||||
\(904\) | 46.7229 | 1.55398 | ||||||||
\(905\) | 7.36732 | 0.244898 | ||||||||
\(906\) | −10.1106 | −0.335903 | ||||||||
\(907\) | 40.0361 | 1.32938 | 0.664688 | − | 0.747121i | \(-0.268565\pi\) | ||||
0.664688 | + | 0.747121i | \(0.268565\pi\) | |||||||
\(908\) | 91.6995 | 3.04316 | ||||||||
\(909\) | 3.59828 | 0.119347 | ||||||||
\(910\) | 57.7222 | 1.91347 | ||||||||
\(911\) | −22.1492 | −0.733834 | −0.366917 | − | 0.930254i | \(-0.619587\pi\) | ||||
−0.366917 | + | 0.930254i | \(0.619587\pi\) | |||||||
\(912\) | −26.0478 | −0.862530 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −31.0503 | −1.02705 | ||||||||
\(915\) | −12.2585 | −0.405255 | ||||||||
\(916\) | 114.932 | 3.79745 | ||||||||
\(917\) | 14.4363 | 0.476730 | ||||||||
\(918\) | −11.1436 | −0.367793 | ||||||||
\(919\) | −24.4453 | −0.806377 | −0.403189 | − | 0.915117i | \(-0.632098\pi\) | ||||
−0.403189 | + | 0.915117i | \(0.632098\pi\) | |||||||
\(920\) | −42.2154 | −1.39180 | ||||||||
\(921\) | −3.90907 | −0.128808 | ||||||||
\(922\) | −81.7190 | −2.69127 | ||||||||
\(923\) | −6.65985 | −0.219212 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.48352 | −0.147417 | ||||||||
\(926\) | −100.976 | −3.31829 | ||||||||
\(927\) | 1.36732 | 0.0449088 | ||||||||
\(928\) | 63.1335 | 2.07246 | ||||||||
\(929\) | −57.2716 | −1.87902 | −0.939509 | − | 0.342523i | \(-0.888719\pi\) | ||||
−0.939509 | + | 0.342523i | \(0.888719\pi\) | |||||||
\(930\) | 26.6220 | 0.872969 | ||||||||
\(931\) | 25.9437 | 0.850270 | ||||||||
\(932\) | 48.0528 | 1.57402 | ||||||||
\(933\) | −22.5196 | −0.737258 | ||||||||
\(934\) | −39.3501 | −1.28758 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 40.5196 | 1.32442 | ||||||||
\(937\) | −51.0099 | −1.66642 | −0.833210 | − | 0.552957i | \(-0.813500\pi\) | ||||
−0.833210 | + | 0.552957i | \(0.813500\pi\) | |||||||
\(938\) | 49.1710 | 1.60549 | ||||||||
\(939\) | −19.2542 | −0.628338 | ||||||||
\(940\) | 20.7763 | 0.677647 | ||||||||
\(941\) | −15.1681 | −0.494467 | −0.247233 | − | 0.968956i | \(-0.579521\pi\) | ||||
−0.247233 | + | 0.968956i | \(0.579521\pi\) | |||||||
\(942\) | −2.05748 | −0.0670363 | ||||||||
\(943\) | 18.9955 | 0.618578 | ||||||||
\(944\) | −68.5480 | −2.23105 | ||||||||
\(945\) | −4.16741 | −0.135566 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −55.9199 | −1.81715 | −0.908576 | − | 0.417720i | \(-0.862829\pi\) | ||||
−0.908576 | + | 0.417720i | \(0.862829\pi\) | |||||||
\(948\) | −33.7939 | −1.09757 | ||||||||
\(949\) | 24.0000 | 0.779073 | ||||||||
\(950\) | −6.58549 | −0.213662 | ||||||||
\(951\) | 8.36732 | 0.271329 | ||||||||
\(952\) | 135.856 | 4.40313 | ||||||||
\(953\) | −32.7177 | −1.05983 | −0.529915 | − | 0.848051i | \(-0.677776\pi\) | ||||
−0.529915 | + | 0.848051i | \(0.677776\pi\) | |||||||
\(954\) | 9.55982 | 0.309511 | ||||||||
\(955\) | 0.679859 | 0.0219997 | ||||||||
\(956\) | −42.3250 | −1.36889 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −32.0832 | −1.03656 | ||||||||
\(959\) | 85.8475 | 2.77216 | ||||||||
\(960\) | −10.7489 | −0.346918 | ||||||||
\(961\) | 71.3375 | 2.30121 | ||||||||
\(962\) | −62.1006 | −2.00220 | ||||||||
\(963\) | 12.9618 | 0.417689 | ||||||||
\(964\) | −44.1862 | −1.42314 | ||||||||
\(965\) | 4.95245 | 0.159425 | ||||||||
\(966\) | 60.1380 | 1.93491 | ||||||||
\(967\) | −53.9473 | −1.73483 | −0.867414 | − | 0.497587i | \(-0.834219\pi\) | ||||
−0.867414 | + | 0.497587i | \(0.834219\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 10.5966 | 0.340412 | ||||||||
\(970\) | 42.5933 | 1.36759 | ||||||||
\(971\) | 4.14915 | 0.133153 | 0.0665763 | − | 0.997781i | \(-0.478792\pi\) | ||||
0.0665763 | + | 0.997781i | \(0.478792\pi\) | |||||||
\(972\) | −4.92542 | −0.157983 | ||||||||
\(973\) | −73.7565 | −2.36452 | ||||||||
\(974\) | −37.5984 | −1.20473 | ||||||||
\(975\) | 5.26324 | 0.168559 | ||||||||
\(976\) | 127.598 | 4.08432 | ||||||||
\(977\) | −13.5668 | −0.434039 | −0.217020 | − | 0.976167i | \(-0.569634\pi\) | ||||
−0.217020 | + | 0.976167i | \(0.569634\pi\) | |||||||
\(978\) | −20.3921 | −0.652067 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 51.0635 | 1.63116 | ||||||||
\(981\) | 5.96655 | 0.190497 | ||||||||
\(982\) | 68.5744 | 2.18830 | ||||||||
\(983\) | 36.7489 | 1.17211 | 0.586054 | − | 0.810272i | \(-0.300681\pi\) | ||||
0.586054 | + | 0.810272i | \(0.300681\pi\) | |||||||
\(984\) | 26.6687 | 0.850168 | ||||||||
\(985\) | 3.59828 | 0.114651 | ||||||||
\(986\) | −58.6514 | −1.86784 | ||||||||
\(987\) | −17.5789 | −0.559541 | ||||||||
\(988\) | −64.8727 | −2.06387 | ||||||||
\(989\) | 36.5743 | 1.16300 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −48.6830 | −1.54647 | −0.773233 | − | 0.634122i | \(-0.781362\pi\) | ||||
−0.773233 | + | 0.634122i | \(0.781362\pi\) | |||||||
\(992\) | −121.346 | −3.85273 | ||||||||
\(993\) | 12.5525 | 0.398343 | ||||||||
\(994\) | −13.8772 | −0.440157 | ||||||||
\(995\) | 3.88380 | 0.123125 | ||||||||
\(996\) | −23.9904 | −0.760164 | ||||||||
\(997\) | −41.7558 | −1.32242 | −0.661210 | − | 0.750200i | \(-0.729957\pi\) | ||||
−0.661210 | + | 0.750200i | \(0.729957\pi\) | |||||||
\(998\) | −75.9619 | −2.40453 | ||||||||
\(999\) | 4.48352 | 0.141852 |
(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 | 1815.2.a.y.1.1 | ✓ | 6 | |
3.2 | odd | 2 | 5445.2.a.bz.1.6 | 6 | |||
5.4 | even | 2 | 9075.2.a.dq.1.6 | 6 | |||
11.10 | odd | 2 | inner | 1815.2.a.y.1.6 | yes | 6 | |
33.32 | even | 2 | 5445.2.a.bz.1.1 | 6 | |||
55.54 | odd | 2 | 9075.2.a.dq.1.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1815.2.a.y.1.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
1815.2.a.y.1.6 | yes | 6 | 11.10 | odd | 2 | inner | |
5445.2.a.bz.1.1 | 6 | 33.32 | even | 2 | |||
5445.2.a.bz.1.6 | 6 | 3.2 | odd | 2 | |||
9075.2.a.dq.1.1 | 6 | 55.54 | odd | 2 | |||
9075.2.a.dq.1.6 | 6 | 5.4 | even | 2 |