Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1502,2,Mod(1,1502)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1502, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1502.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1502 = 2 \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1502.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: | \(11.9935303836\) |
Analytic rank: | \(0\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 6 x^{18} - 23 x^{17} + 190 x^{16} + 128 x^{15} - 2394 x^{14} + 749 x^{13} + 15539 x^{12} - 11338 x^{11} - 56744 x^{10} + 50183 x^{9} + 120237 x^{8} - 102992 x^{7} + \cdots + 4222 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Root | \(2.91512\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1502.1 |
$q$-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 | ||||||||
\(3\) | 2.91512 | 1.68305 | 0.841524 | − | 0.540220i | \(-0.181659\pi\) | ||||
0.841524 | + | 0.540220i | \(0.181659\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.49286 | −0.667629 | −0.333814 | − | 0.942639i | \(-0.608336\pi\) | ||||
−0.333814 | + | 0.942639i | \(0.608336\pi\) | |||||||
\(6\) | −2.91512 | −1.19009 | ||||||||
\(7\) | 3.25503 | 1.23028 | 0.615142 | − | 0.788416i | \(-0.289098\pi\) | ||||
0.615142 | + | 0.788416i | \(0.289098\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 5.49794 | 1.83265 | ||||||||
\(10\) | 1.49286 | 0.472085 | ||||||||
\(11\) | 0.928887 | 0.280070 | 0.140035 | − | 0.990147i | \(-0.455279\pi\) | ||||
0.140035 | + | 0.990147i | \(0.455279\pi\) | |||||||
\(12\) | 2.91512 | 0.841524 | ||||||||
\(13\) | 4.49624 | 1.24703 | 0.623516 | − | 0.781810i | \(-0.285704\pi\) | ||||
0.623516 | + | 0.781810i | \(0.285704\pi\) | |||||||
\(14\) | −3.25503 | −0.869943 | ||||||||
\(15\) | −4.35188 | −1.12365 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.77875 | −0.673947 | −0.336973 | − | 0.941514i | \(-0.609403\pi\) | ||||
−0.336973 | + | 0.941514i | \(0.609403\pi\) | |||||||
\(18\) | −5.49794 | −1.29588 | ||||||||
\(19\) | 7.13629 | 1.63718 | 0.818589 | − | 0.574380i | \(-0.194757\pi\) | ||||
0.818589 | + | 0.574380i | \(0.194757\pi\) | |||||||
\(20\) | −1.49286 | −0.333814 | ||||||||
\(21\) | 9.48881 | 2.07063 | ||||||||
\(22\) | −0.928887 | −0.198039 | ||||||||
\(23\) | −4.26032 | −0.888337 | −0.444169 | − | 0.895943i | \(-0.646501\pi\) | ||||
−0.444169 | + | 0.895943i | \(0.646501\pi\) | |||||||
\(24\) | −2.91512 | −0.595047 | ||||||||
\(25\) | −2.77136 | −0.554272 | ||||||||
\(26\) | −4.49624 | −0.881785 | ||||||||
\(27\) | 7.28181 | 1.40139 | ||||||||
\(28\) | 3.25503 | 0.615142 | ||||||||
\(29\) | 5.01897 | 0.931999 | 0.465999 | − | 0.884785i | \(-0.345695\pi\) | ||||
0.465999 | + | 0.884785i | \(0.345695\pi\) | |||||||
\(30\) | 4.35188 | 0.794541 | ||||||||
\(31\) | −8.01202 | −1.43900 | −0.719501 | − | 0.694492i | \(-0.755629\pi\) | ||||
−0.719501 | + | 0.694492i | \(0.755629\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 2.70782 | 0.471371 | ||||||||
\(34\) | 2.77875 | 0.476552 | ||||||||
\(35\) | −4.85931 | −0.821374 | ||||||||
\(36\) | 5.49794 | 0.916324 | ||||||||
\(37\) | −5.12886 | −0.843180 | −0.421590 | − | 0.906787i | \(-0.638528\pi\) | ||||
−0.421590 | + | 0.906787i | \(0.638528\pi\) | |||||||
\(38\) | −7.13629 | −1.15766 | ||||||||
\(39\) | 13.1071 | 2.09881 | ||||||||
\(40\) | 1.49286 | 0.236042 | ||||||||
\(41\) | −5.10790 | −0.797720 | −0.398860 | − | 0.917012i | \(-0.630594\pi\) | ||||
−0.398860 | + | 0.917012i | \(0.630594\pi\) | |||||||
\(42\) | −9.48881 | −1.46415 | ||||||||
\(43\) | 4.93752 | 0.752965 | 0.376483 | − | 0.926424i | \(-0.377133\pi\) | ||||
0.376483 | + | 0.926424i | \(0.377133\pi\) | |||||||
\(44\) | 0.928887 | 0.140035 | ||||||||
\(45\) | −8.20768 | −1.22353 | ||||||||
\(46\) | 4.26032 | 0.628149 | ||||||||
\(47\) | −3.97539 | −0.579871 | −0.289935 | − | 0.957046i | \(-0.593634\pi\) | ||||
−0.289935 | + | 0.957046i | \(0.593634\pi\) | |||||||
\(48\) | 2.91512 | 0.420762 | ||||||||
\(49\) | 3.59521 | 0.513601 | ||||||||
\(50\) | 2.77136 | 0.391929 | ||||||||
\(51\) | −8.10041 | −1.13428 | ||||||||
\(52\) | 4.49624 | 0.623516 | ||||||||
\(53\) | 4.97697 | 0.683640 | 0.341820 | − | 0.939766i | \(-0.388957\pi\) | ||||
0.341820 | + | 0.939766i | \(0.388957\pi\) | |||||||
\(54\) | −7.28181 | −0.990929 | ||||||||
\(55\) | −1.38670 | −0.186983 | ||||||||
\(56\) | −3.25503 | −0.434971 | ||||||||
\(57\) | 20.8032 | 2.75545 | ||||||||
\(58\) | −5.01897 | −0.659023 | ||||||||
\(59\) | −3.30780 | −0.430639 | −0.215320 | − | 0.976544i | \(-0.569079\pi\) | ||||
−0.215320 | + | 0.976544i | \(0.569079\pi\) | |||||||
\(60\) | −4.35188 | −0.561826 | ||||||||
\(61\) | 2.18885 | 0.280253 | 0.140127 | − | 0.990134i | \(-0.455249\pi\) | ||||
0.140127 | + | 0.990134i | \(0.455249\pi\) | |||||||
\(62\) | 8.01202 | 1.01753 | ||||||||
\(63\) | 17.8960 | 2.25468 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −6.71227 | −0.832555 | ||||||||
\(66\) | −2.70782 | −0.333310 | ||||||||
\(67\) | 6.27089 | 0.766111 | 0.383055 | − | 0.923725i | \(-0.374872\pi\) | ||||
0.383055 | + | 0.923725i | \(0.374872\pi\) | |||||||
\(68\) | −2.77875 | −0.336973 | ||||||||
\(69\) | −12.4193 | −1.49511 | ||||||||
\(70\) | 4.85931 | 0.580799 | ||||||||
\(71\) | 0.214802 | 0.0254923 | 0.0127461 | − | 0.999919i | \(-0.495943\pi\) | ||||
0.0127461 | + | 0.999919i | \(0.495943\pi\) | |||||||
\(72\) | −5.49794 | −0.647939 | ||||||||
\(73\) | 15.0530 | 1.76182 | 0.880912 | − | 0.473280i | \(-0.156930\pi\) | ||||
0.880912 | + | 0.473280i | \(0.156930\pi\) | |||||||
\(74\) | 5.12886 | 0.596218 | ||||||||
\(75\) | −8.07885 | −0.932865 | ||||||||
\(76\) | 7.13629 | 0.818589 | ||||||||
\(77\) | 3.02355 | 0.344566 | ||||||||
\(78\) | −13.1071 | −1.48409 | ||||||||
\(79\) | 5.14629 | 0.579003 | 0.289502 | − | 0.957178i | \(-0.406510\pi\) | ||||
0.289502 | + | 0.957178i | \(0.406510\pi\) | |||||||
\(80\) | −1.49286 | −0.166907 | ||||||||
\(81\) | 4.73355 | 0.525950 | ||||||||
\(82\) | 5.10790 | 0.564074 | ||||||||
\(83\) | 12.4793 | 1.36978 | 0.684889 | − | 0.728647i | \(-0.259850\pi\) | ||||
0.684889 | + | 0.728647i | \(0.259850\pi\) | |||||||
\(84\) | 9.48881 | 1.03531 | ||||||||
\(85\) | 4.14830 | 0.449946 | ||||||||
\(86\) | −4.93752 | −0.532427 | ||||||||
\(87\) | 14.6309 | 1.56860 | ||||||||
\(88\) | −0.928887 | −0.0990197 | ||||||||
\(89\) | −3.90016 | −0.413416 | −0.206708 | − | 0.978403i | \(-0.566275\pi\) | ||||
−0.206708 | + | 0.978403i | \(0.566275\pi\) | |||||||
\(90\) | 8.20768 | 0.865166 | ||||||||
\(91\) | 14.6354 | 1.53421 | ||||||||
\(92\) | −4.26032 | −0.444169 | ||||||||
\(93\) | −23.3560 | −2.42191 | ||||||||
\(94\) | 3.97539 | 0.410031 | ||||||||
\(95\) | −10.6535 | −1.09303 | ||||||||
\(96\) | −2.91512 | −0.297524 | ||||||||
\(97\) | −7.22768 | −0.733860 | −0.366930 | − | 0.930249i | \(-0.619591\pi\) | ||||
−0.366930 | + | 0.930249i | \(0.619591\pi\) | |||||||
\(98\) | −3.59521 | −0.363171 | ||||||||
\(99\) | 5.10697 | 0.513270 | ||||||||
\(100\) | −2.77136 | −0.277136 | ||||||||
\(101\) | −3.30748 | −0.329107 | −0.164553 | − | 0.986368i | \(-0.552618\pi\) | ||||
−0.164553 | + | 0.986368i | \(0.552618\pi\) | |||||||
\(102\) | 8.10041 | 0.802060 | ||||||||
\(103\) | 0.832862 | 0.0820643 | 0.0410322 | − | 0.999158i | \(-0.486935\pi\) | ||||
0.0410322 | + | 0.999158i | \(0.486935\pi\) | |||||||
\(104\) | −4.49624 | −0.440893 | ||||||||
\(105\) | −14.1655 | −1.38241 | ||||||||
\(106\) | −4.97697 | −0.483406 | ||||||||
\(107\) | 13.8805 | 1.34188 | 0.670941 | − | 0.741511i | \(-0.265890\pi\) | ||||
0.670941 | + | 0.741511i | \(0.265890\pi\) | |||||||
\(108\) | 7.28181 | 0.700693 | ||||||||
\(109\) | 4.18477 | 0.400828 | 0.200414 | − | 0.979711i | \(-0.435771\pi\) | ||||
0.200414 | + | 0.979711i | \(0.435771\pi\) | |||||||
\(110\) | 1.38670 | 0.132217 | ||||||||
\(111\) | −14.9513 | −1.41911 | ||||||||
\(112\) | 3.25503 | 0.307571 | ||||||||
\(113\) | −16.7698 | −1.57757 | −0.788783 | − | 0.614672i | \(-0.789288\pi\) | ||||
−0.788783 | + | 0.614672i | \(0.789288\pi\) | |||||||
\(114\) | −20.8032 | −1.94840 | ||||||||
\(115\) | 6.36007 | 0.593080 | ||||||||
\(116\) | 5.01897 | 0.465999 | ||||||||
\(117\) | 24.7201 | 2.28537 | ||||||||
\(118\) | 3.30780 | 0.304508 | ||||||||
\(119\) | −9.04492 | −0.829147 | ||||||||
\(120\) | 4.35188 | 0.397271 | ||||||||
\(121\) | −10.1372 | −0.921561 | ||||||||
\(122\) | −2.18885 | −0.198169 | ||||||||
\(123\) | −14.8902 | −1.34260 | ||||||||
\(124\) | −8.01202 | −0.719501 | ||||||||
\(125\) | 11.6016 | 1.03768 | ||||||||
\(126\) | −17.8960 | −1.59430 | ||||||||
\(127\) | −20.1589 | −1.78882 | −0.894408 | − | 0.447253i | \(-0.852402\pi\) | ||||
−0.894408 | + | 0.447253i | \(0.852402\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 14.3935 | 1.26728 | ||||||||
\(130\) | 6.71227 | 0.588705 | ||||||||
\(131\) | 5.52709 | 0.482904 | 0.241452 | − | 0.970413i | \(-0.422376\pi\) | ||||
0.241452 | + | 0.970413i | \(0.422376\pi\) | |||||||
\(132\) | 2.70782 | 0.235685 | ||||||||
\(133\) | 23.2288 | 2.01420 | ||||||||
\(134\) | −6.27089 | −0.541722 | ||||||||
\(135\) | −10.8708 | −0.935606 | ||||||||
\(136\) | 2.77875 | 0.238276 | ||||||||
\(137\) | −4.83457 | −0.413045 | −0.206522 | − | 0.978442i | \(-0.566215\pi\) | ||||
−0.206522 | + | 0.978442i | \(0.566215\pi\) | |||||||
\(138\) | 12.4193 | 1.05720 | ||||||||
\(139\) | −9.72387 | −0.824768 | −0.412384 | − | 0.911010i | \(-0.635304\pi\) | ||||
−0.412384 | + | 0.911010i | \(0.635304\pi\) | |||||||
\(140\) | −4.85931 | −0.410687 | ||||||||
\(141\) | −11.5888 | −0.975950 | ||||||||
\(142\) | −0.214802 | −0.0180258 | ||||||||
\(143\) | 4.17650 | 0.349256 | ||||||||
\(144\) | 5.49794 | 0.458162 | ||||||||
\(145\) | −7.49264 | −0.622229 | ||||||||
\(146\) | −15.0530 | −1.24580 | ||||||||
\(147\) | 10.4805 | 0.864415 | ||||||||
\(148\) | −5.12886 | −0.421590 | ||||||||
\(149\) | −0.478897 | −0.0392328 | −0.0196164 | − | 0.999808i | \(-0.506244\pi\) | ||||
−0.0196164 | + | 0.999808i | \(0.506244\pi\) | |||||||
\(150\) | 8.07885 | 0.659635 | ||||||||
\(151\) | −19.0949 | −1.55392 | −0.776959 | − | 0.629551i | \(-0.783239\pi\) | ||||
−0.776959 | + | 0.629551i | \(0.783239\pi\) | |||||||
\(152\) | −7.13629 | −0.578830 | ||||||||
\(153\) | −15.2774 | −1.23511 | ||||||||
\(154\) | −3.02355 | −0.243645 | ||||||||
\(155\) | 11.9609 | 0.960719 | ||||||||
\(156\) | 13.1071 | 1.04941 | ||||||||
\(157\) | −23.4859 | −1.87438 | −0.937189 | − | 0.348821i | \(-0.886582\pi\) | ||||
−0.937189 | + | 0.348821i | \(0.886582\pi\) | |||||||
\(158\) | −5.14629 | −0.409417 | ||||||||
\(159\) | 14.5085 | 1.15060 | ||||||||
\(160\) | 1.49286 | 0.118021 | ||||||||
\(161\) | −13.8674 | −1.09291 | ||||||||
\(162\) | −4.73355 | −0.371903 | ||||||||
\(163\) | 8.95881 | 0.701708 | 0.350854 | − | 0.936430i | \(-0.385891\pi\) | ||||
0.350854 | + | 0.936430i | \(0.385891\pi\) | |||||||
\(164\) | −5.10790 | −0.398860 | ||||||||
\(165\) | −4.04241 | −0.314701 | ||||||||
\(166\) | −12.4793 | −0.968580 | ||||||||
\(167\) | 4.96670 | 0.384335 | 0.192167 | − | 0.981362i | \(-0.438448\pi\) | ||||
0.192167 | + | 0.981362i | \(0.438448\pi\) | |||||||
\(168\) | −9.48881 | −0.732077 | ||||||||
\(169\) | 7.21617 | 0.555090 | ||||||||
\(170\) | −4.14830 | −0.318160 | ||||||||
\(171\) | 39.2349 | 3.00037 | ||||||||
\(172\) | 4.93752 | 0.376483 | ||||||||
\(173\) | −3.09836 | −0.235564 | −0.117782 | − | 0.993039i | \(-0.537578\pi\) | ||||
−0.117782 | + | 0.993039i | \(0.537578\pi\) | |||||||
\(174\) | −14.6309 | −1.10917 | ||||||||
\(175\) | −9.02085 | −0.681912 | ||||||||
\(176\) | 0.928887 | 0.0700175 | ||||||||
\(177\) | −9.64266 | −0.724787 | ||||||||
\(178\) | 3.90016 | 0.292329 | ||||||||
\(179\) | 4.95495 | 0.370350 | 0.185175 | − | 0.982706i | \(-0.440715\pi\) | ||||
0.185175 | + | 0.982706i | \(0.440715\pi\) | |||||||
\(180\) | −8.20768 | −0.611764 | ||||||||
\(181\) | 0.0380714 | 0.00282982 | 0.00141491 | − | 0.999999i | \(-0.499550\pi\) | ||||
0.00141491 | + | 0.999999i | \(0.499550\pi\) | |||||||
\(182\) | −14.6354 | −1.08485 | ||||||||
\(183\) | 6.38076 | 0.471679 | ||||||||
\(184\) | 4.26032 | 0.314075 | ||||||||
\(185\) | 7.65669 | 0.562931 | ||||||||
\(186\) | 23.3560 | 1.71255 | ||||||||
\(187\) | −2.58115 | −0.188752 | ||||||||
\(188\) | −3.97539 | −0.289935 | ||||||||
\(189\) | 23.7025 | 1.72410 | ||||||||
\(190\) | 10.6535 | 0.772887 | ||||||||
\(191\) | 26.7411 | 1.93492 | 0.967459 | − | 0.253028i | \(-0.0814265\pi\) | ||||
0.967459 | + | 0.253028i | \(0.0814265\pi\) | |||||||
\(192\) | 2.91512 | 0.210381 | ||||||||
\(193\) | 3.83897 | 0.276335 | 0.138168 | − | 0.990409i | \(-0.455879\pi\) | ||||
0.138168 | + | 0.990409i | \(0.455879\pi\) | |||||||
\(194\) | 7.22768 | 0.518917 | ||||||||
\(195\) | −19.5671 | −1.40123 | ||||||||
\(196\) | 3.59521 | 0.256801 | ||||||||
\(197\) | −27.7419 | −1.97653 | −0.988263 | − | 0.152762i | \(-0.951183\pi\) | ||||
−0.988263 | + | 0.152762i | \(0.951183\pi\) | |||||||
\(198\) | −5.10697 | −0.362936 | ||||||||
\(199\) | 15.2322 | 1.07978 | 0.539891 | − | 0.841735i | \(-0.318466\pi\) | ||||
0.539891 | + | 0.841735i | \(0.318466\pi\) | |||||||
\(200\) | 2.77136 | 0.195965 | ||||||||
\(201\) | 18.2804 | 1.28940 | ||||||||
\(202\) | 3.30748 | 0.232713 | ||||||||
\(203\) | 16.3369 | 1.14662 | ||||||||
\(204\) | −8.10041 | −0.567142 | ||||||||
\(205\) | 7.62540 | 0.532581 | ||||||||
\(206\) | −0.832862 | −0.0580282 | ||||||||
\(207\) | −23.4230 | −1.62801 | ||||||||
\(208\) | 4.49624 | 0.311758 | ||||||||
\(209\) | 6.62881 | 0.458524 | ||||||||
\(210\) | 14.1655 | 0.977512 | ||||||||
\(211\) | 8.31911 | 0.572711 | 0.286356 | − | 0.958123i | \(-0.407556\pi\) | ||||
0.286356 | + | 0.958123i | \(0.407556\pi\) | |||||||
\(212\) | 4.97697 | 0.341820 | ||||||||
\(213\) | 0.626173 | 0.0429047 | ||||||||
\(214\) | −13.8805 | −0.948854 | ||||||||
\(215\) | −7.37105 | −0.502701 | ||||||||
\(216\) | −7.28181 | −0.495465 | ||||||||
\(217\) | −26.0793 | −1.77038 | ||||||||
\(218\) | −4.18477 | −0.283429 | ||||||||
\(219\) | 43.8814 | 2.96523 | ||||||||
\(220\) | −1.38670 | −0.0934914 | ||||||||
\(221\) | −12.4939 | −0.840434 | ||||||||
\(222\) | 14.9513 | 1.00346 | ||||||||
\(223\) | 4.08943 | 0.273848 | 0.136924 | − | 0.990582i | \(-0.456278\pi\) | ||||
0.136924 | + | 0.990582i | \(0.456278\pi\) | |||||||
\(224\) | −3.25503 | −0.217486 | ||||||||
\(225\) | −15.2368 | −1.01578 | ||||||||
\(226\) | 16.7698 | 1.11551 | ||||||||
\(227\) | 11.9712 | 0.794558 | 0.397279 | − | 0.917698i | \(-0.369955\pi\) | ||||
0.397279 | + | 0.917698i | \(0.369955\pi\) | |||||||
\(228\) | 20.8032 | 1.37772 | ||||||||
\(229\) | 26.2492 | 1.73460 | 0.867299 | − | 0.497788i | \(-0.165854\pi\) | ||||
0.867299 | + | 0.497788i | \(0.165854\pi\) | |||||||
\(230\) | −6.36007 | −0.419371 | ||||||||
\(231\) | 8.81403 | 0.579920 | ||||||||
\(232\) | −5.01897 | −0.329511 | ||||||||
\(233\) | 0.168495 | 0.0110384 | 0.00551922 | − | 0.999985i | \(-0.498243\pi\) | ||||
0.00551922 | + | 0.999985i | \(0.498243\pi\) | |||||||
\(234\) | −24.7201 | −1.61600 | ||||||||
\(235\) | 5.93472 | 0.387139 | ||||||||
\(236\) | −3.30780 | −0.215320 | ||||||||
\(237\) | 15.0021 | 0.974490 | ||||||||
\(238\) | 9.04492 | 0.586295 | ||||||||
\(239\) | −5.00385 | −0.323672 | −0.161836 | − | 0.986818i | \(-0.551742\pi\) | ||||
−0.161836 | + | 0.986818i | \(0.551742\pi\) | |||||||
\(240\) | −4.35188 | −0.280913 | ||||||||
\(241\) | −26.3551 | −1.69768 | −0.848841 | − | 0.528648i | \(-0.822699\pi\) | ||||
−0.848841 | + | 0.528648i | \(0.822699\pi\) | |||||||
\(242\) | 10.1372 | 0.651642 | ||||||||
\(243\) | −8.04655 | −0.516186 | ||||||||
\(244\) | 2.18885 | 0.140127 | ||||||||
\(245\) | −5.36715 | −0.342895 | ||||||||
\(246\) | 14.8902 | 0.949362 | ||||||||
\(247\) | 32.0865 | 2.04161 | ||||||||
\(248\) | 8.01202 | 0.508764 | ||||||||
\(249\) | 36.3786 | 2.30540 | ||||||||
\(250\) | −11.6016 | −0.733748 | ||||||||
\(251\) | 14.6780 | 0.926465 | 0.463233 | − | 0.886237i | \(-0.346689\pi\) | ||||
0.463233 | + | 0.886237i | \(0.346689\pi\) | |||||||
\(252\) | 17.8960 | 1.12734 | ||||||||
\(253\) | −3.95735 | −0.248797 | ||||||||
\(254\) | 20.1589 | 1.26488 | ||||||||
\(255\) | 12.0928 | 0.757281 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 9.00926 | 0.561983 | 0.280991 | − | 0.959710i | \(-0.409337\pi\) | ||||
0.280991 | + | 0.959710i | \(0.409337\pi\) | |||||||
\(258\) | −14.3935 | −0.896099 | ||||||||
\(259\) | −16.6946 | −1.03735 | ||||||||
\(260\) | −6.71227 | −0.416277 | ||||||||
\(261\) | 27.5940 | 1.70803 | ||||||||
\(262\) | −5.52709 | −0.341464 | ||||||||
\(263\) | −29.0832 | −1.79335 | −0.896674 | − | 0.442691i | \(-0.854024\pi\) | ||||
−0.896674 | + | 0.442691i | \(0.854024\pi\) | |||||||
\(264\) | −2.70782 | −0.166655 | ||||||||
\(265\) | −7.42994 | −0.456418 | ||||||||
\(266\) | −23.2288 | −1.42425 | ||||||||
\(267\) | −11.3694 | −0.695798 | ||||||||
\(268\) | 6.27089 | 0.383055 | ||||||||
\(269\) | −11.7279 | −0.715063 | −0.357532 | − | 0.933901i | \(-0.616382\pi\) | ||||
−0.357532 | + | 0.933901i | \(0.616382\pi\) | |||||||
\(270\) | 10.8708 | 0.661573 | ||||||||
\(271\) | −24.2213 | −1.47134 | −0.735671 | − | 0.677339i | \(-0.763133\pi\) | ||||
−0.735671 | + | 0.677339i | \(0.763133\pi\) | |||||||
\(272\) | −2.77875 | −0.168487 | ||||||||
\(273\) | 42.6640 | 2.58214 | ||||||||
\(274\) | 4.83457 | 0.292067 | ||||||||
\(275\) | −2.57428 | −0.155235 | ||||||||
\(276\) | −12.4193 | −0.747557 | ||||||||
\(277\) | −6.71572 | −0.403509 | −0.201754 | − | 0.979436i | \(-0.564664\pi\) | ||||
−0.201754 | + | 0.979436i | \(0.564664\pi\) | |||||||
\(278\) | 9.72387 | 0.583199 | ||||||||
\(279\) | −44.0496 | −2.63718 | ||||||||
\(280\) | 4.85931 | 0.290400 | ||||||||
\(281\) | 15.6567 | 0.934003 | 0.467001 | − | 0.884257i | \(-0.345334\pi\) | ||||
0.467001 | + | 0.884257i | \(0.345334\pi\) | |||||||
\(282\) | 11.5888 | 0.690101 | ||||||||
\(283\) | −23.0211 | −1.36846 | −0.684232 | − | 0.729264i | \(-0.739862\pi\) | ||||
−0.684232 | + | 0.729264i | \(0.739862\pi\) | |||||||
\(284\) | 0.214802 | 0.0127461 | ||||||||
\(285\) | −31.0563 | −1.83962 | ||||||||
\(286\) | −4.17650 | −0.246961 | ||||||||
\(287\) | −16.6264 | −0.981423 | ||||||||
\(288\) | −5.49794 | −0.323969 | ||||||||
\(289\) | −9.27853 | −0.545796 | ||||||||
\(290\) | 7.49264 | 0.439983 | ||||||||
\(291\) | −21.0696 | −1.23512 | ||||||||
\(292\) | 15.0530 | 0.880912 | ||||||||
\(293\) | −11.3369 | −0.662306 | −0.331153 | − | 0.943577i | \(-0.607438\pi\) | ||||
−0.331153 | + | 0.943577i | \(0.607438\pi\) | |||||||
\(294\) | −10.4805 | −0.611234 | ||||||||
\(295\) | 4.93810 | 0.287507 | ||||||||
\(296\) | 5.12886 | 0.298109 | ||||||||
\(297\) | 6.76398 | 0.392486 | ||||||||
\(298\) | 0.478897 | 0.0277418 | ||||||||
\(299\) | −19.1554 | −1.10779 | ||||||||
\(300\) | −8.07885 | −0.466433 | ||||||||
\(301\) | 16.0718 | 0.926362 | ||||||||
\(302\) | 19.0949 | 1.09879 | ||||||||
\(303\) | −9.64171 | −0.553902 | ||||||||
\(304\) | 7.13629 | 0.409295 | ||||||||
\(305\) | −3.26765 | −0.187105 | ||||||||
\(306\) | 15.2774 | 0.873353 | ||||||||
\(307\) | 17.3822 | 0.992052 | 0.496026 | − | 0.868308i | \(-0.334792\pi\) | ||||
0.496026 | + | 0.868308i | \(0.334792\pi\) | |||||||
\(308\) | 3.02355 | 0.172283 | ||||||||
\(309\) | 2.42789 | 0.138118 | ||||||||
\(310\) | −11.9609 | −0.679331 | ||||||||
\(311\) | −22.4588 | −1.27352 | −0.636761 | − | 0.771061i | \(-0.719726\pi\) | ||||
−0.636761 | + | 0.771061i | \(0.719726\pi\) | |||||||
\(312\) | −13.1071 | −0.742043 | ||||||||
\(313\) | −23.6953 | −1.33934 | −0.669669 | − | 0.742660i | \(-0.733564\pi\) | ||||
−0.669669 | + | 0.742660i | \(0.733564\pi\) | |||||||
\(314\) | 23.4859 | 1.32539 | ||||||||
\(315\) | −26.7162 | −1.50529 | ||||||||
\(316\) | 5.14629 | 0.289502 | ||||||||
\(317\) | −7.48626 | −0.420470 | −0.210235 | − | 0.977651i | \(-0.567423\pi\) | ||||
−0.210235 | + | 0.977651i | \(0.567423\pi\) | |||||||
\(318\) | −14.5085 | −0.813595 | ||||||||
\(319\) | 4.66205 | 0.261025 | ||||||||
\(320\) | −1.49286 | −0.0834536 | ||||||||
\(321\) | 40.4635 | 2.25845 | ||||||||
\(322\) | 13.8674 | 0.772803 | ||||||||
\(323\) | −19.8300 | −1.10337 | ||||||||
\(324\) | 4.73355 | 0.262975 | ||||||||
\(325\) | −12.4607 | −0.691195 | ||||||||
\(326\) | −8.95881 | −0.496183 | ||||||||
\(327\) | 12.1991 | 0.674613 | ||||||||
\(328\) | 5.10790 | 0.282037 | ||||||||
\(329\) | −12.9400 | −0.713406 | ||||||||
\(330\) | 4.04241 | 0.222527 | ||||||||
\(331\) | 3.52357 | 0.193673 | 0.0968364 | − | 0.995300i | \(-0.469128\pi\) | ||||
0.0968364 | + | 0.995300i | \(0.469128\pi\) | |||||||
\(332\) | 12.4793 | 0.684889 | ||||||||
\(333\) | −28.1982 | −1.54525 | ||||||||
\(334\) | −4.96670 | −0.271766 | ||||||||
\(335\) | −9.36158 | −0.511478 | ||||||||
\(336\) | 9.48881 | 0.517657 | ||||||||
\(337\) | −7.72046 | −0.420560 | −0.210280 | − | 0.977641i | \(-0.567438\pi\) | ||||
−0.210280 | + | 0.977641i | \(0.567438\pi\) | |||||||
\(338\) | −7.21617 | −0.392508 | ||||||||
\(339\) | −48.8859 | −2.65512 | ||||||||
\(340\) | 4.14830 | 0.224973 | ||||||||
\(341\) | −7.44226 | −0.403021 | ||||||||
\(342\) | −39.2349 | −2.12158 | ||||||||
\(343\) | −11.0827 | −0.598409 | ||||||||
\(344\) | −4.93752 | −0.266213 | ||||||||
\(345\) | 18.5404 | 0.998181 | ||||||||
\(346\) | 3.09836 | 0.166569 | ||||||||
\(347\) | 6.82229 | 0.366240 | 0.183120 | − | 0.983091i | \(-0.441380\pi\) | ||||
0.183120 | + | 0.983091i | \(0.441380\pi\) | |||||||
\(348\) | 14.6309 | 0.784299 | ||||||||
\(349\) | −23.4882 | −1.25729 | −0.628647 | − | 0.777691i | \(-0.716391\pi\) | ||||
−0.628647 | + | 0.777691i | \(0.716391\pi\) | |||||||
\(350\) | 9.02085 | 0.482185 | ||||||||
\(351\) | 32.7408 | 1.74757 | ||||||||
\(352\) | −0.928887 | −0.0495098 | ||||||||
\(353\) | 20.6971 | 1.10160 | 0.550798 | − | 0.834639i | \(-0.314323\pi\) | ||||
0.550798 | + | 0.834639i | \(0.314323\pi\) | |||||||
\(354\) | 9.64266 | 0.512501 | ||||||||
\(355\) | −0.320670 | −0.0170194 | ||||||||
\(356\) | −3.90016 | −0.206708 | ||||||||
\(357\) | −26.3671 | −1.39549 | ||||||||
\(358\) | −4.95495 | −0.261877 | ||||||||
\(359\) | 20.9481 | 1.10560 | 0.552799 | − | 0.833315i | \(-0.313560\pi\) | ||||
0.552799 | + | 0.833315i | \(0.313560\pi\) | |||||||
\(360\) | 8.20768 | 0.432583 | ||||||||
\(361\) | 31.9267 | 1.68035 | ||||||||
\(362\) | −0.0380714 | −0.00200099 | ||||||||
\(363\) | −29.5511 | −1.55103 | ||||||||
\(364\) | 14.6354 | 0.767103 | ||||||||
\(365\) | −22.4721 | −1.17624 | ||||||||
\(366\) | −6.38076 | −0.333528 | ||||||||
\(367\) | 12.8420 | 0.670348 | 0.335174 | − | 0.942156i | \(-0.391205\pi\) | ||||
0.335174 | + | 0.942156i | \(0.391205\pi\) | |||||||
\(368\) | −4.26032 | −0.222084 | ||||||||
\(369\) | −28.0830 | −1.46194 | ||||||||
\(370\) | −7.65669 | −0.398053 | ||||||||
\(371\) | 16.2002 | 0.841071 | ||||||||
\(372\) | −23.3560 | −1.21095 | ||||||||
\(373\) | 13.3270 | 0.690048 | 0.345024 | − | 0.938594i | \(-0.387871\pi\) | ||||
0.345024 | + | 0.938594i | \(0.387871\pi\) | |||||||
\(374\) | 2.58115 | 0.133468 | ||||||||
\(375\) | 33.8200 | 1.74646 | ||||||||
\(376\) | 3.97539 | 0.205015 | ||||||||
\(377\) | 22.5665 | 1.16223 | ||||||||
\(378\) | −23.7025 | −1.21913 | ||||||||
\(379\) | 6.33684 | 0.325502 | 0.162751 | − | 0.986667i | \(-0.447963\pi\) | ||||
0.162751 | + | 0.986667i | \(0.447963\pi\) | |||||||
\(380\) | −10.6535 | −0.546514 | ||||||||
\(381\) | −58.7658 | −3.01066 | ||||||||
\(382\) | −26.7411 | −1.36819 | ||||||||
\(383\) | −24.1211 | −1.23253 | −0.616266 | − | 0.787538i | \(-0.711356\pi\) | ||||
−0.616266 | + | 0.787538i | \(0.711356\pi\) | |||||||
\(384\) | −2.91512 | −0.148762 | ||||||||
\(385\) | −4.51375 | −0.230042 | ||||||||
\(386\) | −3.83897 | −0.195398 | ||||||||
\(387\) | 27.1462 | 1.37992 | ||||||||
\(388\) | −7.22768 | −0.366930 | ||||||||
\(389\) | −22.4082 | −1.13614 | −0.568069 | − | 0.822981i | \(-0.692309\pi\) | ||||
−0.568069 | + | 0.822981i | \(0.692309\pi\) | |||||||
\(390\) | 19.5671 | 0.990819 | ||||||||
\(391\) | 11.8384 | 0.598692 | ||||||||
\(392\) | −3.59521 | −0.181585 | ||||||||
\(393\) | 16.1121 | 0.812750 | ||||||||
\(394\) | 27.7419 | 1.39761 | ||||||||
\(395\) | −7.68271 | −0.386559 | ||||||||
\(396\) | 5.10697 | 0.256635 | ||||||||
\(397\) | 7.85601 | 0.394282 | 0.197141 | − | 0.980375i | \(-0.436834\pi\) | ||||
0.197141 | + | 0.980375i | \(0.436834\pi\) | |||||||
\(398\) | −15.2322 | −0.763521 | ||||||||
\(399\) | 67.7149 | 3.38999 | ||||||||
\(400\) | −2.77136 | −0.138568 | ||||||||
\(401\) | 16.1596 | 0.806971 | 0.403486 | − | 0.914986i | \(-0.367799\pi\) | ||||
0.403486 | + | 0.914986i | \(0.367799\pi\) | |||||||
\(402\) | −18.2804 | −0.911744 | ||||||||
\(403\) | −36.0240 | −1.79448 | ||||||||
\(404\) | −3.30748 | −0.164553 | ||||||||
\(405\) | −7.06655 | −0.351140 | ||||||||
\(406\) | −16.3369 | −0.810786 | ||||||||
\(407\) | −4.76413 | −0.236149 | ||||||||
\(408\) | 8.10041 | 0.401030 | ||||||||
\(409\) | 21.9292 | 1.08433 | 0.542165 | − | 0.840272i | \(-0.317605\pi\) | ||||
0.542165 | + | 0.840272i | \(0.317605\pi\) | |||||||
\(410\) | −7.62540 | −0.376592 | ||||||||
\(411\) | −14.0934 | −0.695174 | ||||||||
\(412\) | 0.832862 | 0.0410322 | ||||||||
\(413\) | −10.7670 | −0.529809 | ||||||||
\(414\) | 23.4230 | 1.15118 | ||||||||
\(415\) | −18.6299 | −0.914504 | ||||||||
\(416\) | −4.49624 | −0.220446 | ||||||||
\(417\) | −28.3463 | −1.38812 | ||||||||
\(418\) | −6.62881 | −0.324226 | ||||||||
\(419\) | −15.8461 | −0.774135 | −0.387067 | − | 0.922051i | \(-0.626512\pi\) | ||||
−0.387067 | + | 0.922051i | \(0.626512\pi\) | |||||||
\(420\) | −14.1655 | −0.691205 | ||||||||
\(421\) | −14.2514 | −0.694570 | −0.347285 | − | 0.937760i | \(-0.612896\pi\) | ||||
−0.347285 | + | 0.937760i | \(0.612896\pi\) | |||||||
\(422\) | −8.31911 | −0.404968 | ||||||||
\(423\) | −21.8565 | −1.06270 | ||||||||
\(424\) | −4.97697 | −0.241703 | ||||||||
\(425\) | 7.70092 | 0.373550 | ||||||||
\(426\) | −0.626173 | −0.0303382 | ||||||||
\(427\) | 7.12476 | 0.344791 | ||||||||
\(428\) | 13.8805 | 0.670941 | ||||||||
\(429\) | 12.1750 | 0.587815 | ||||||||
\(430\) | 7.37105 | 0.355464 | ||||||||
\(431\) | −26.6546 | −1.28391 | −0.641953 | − | 0.766744i | \(-0.721876\pi\) | ||||
−0.641953 | + | 0.766744i | \(0.721876\pi\) | |||||||
\(432\) | 7.28181 | 0.350346 | ||||||||
\(433\) | −11.0415 | −0.530622 | −0.265311 | − | 0.964163i | \(-0.585475\pi\) | ||||
−0.265311 | + | 0.964163i | \(0.585475\pi\) | |||||||
\(434\) | 26.0793 | 1.25185 | ||||||||
\(435\) | −21.8420 | −1.04724 | ||||||||
\(436\) | 4.18477 | 0.200414 | ||||||||
\(437\) | −30.4029 | −1.45437 | ||||||||
\(438\) | −43.8814 | −2.09674 | ||||||||
\(439\) | −8.58467 | −0.409724 | −0.204862 | − | 0.978791i | \(-0.565675\pi\) | ||||
−0.204862 | + | 0.978791i | \(0.565675\pi\) | |||||||
\(440\) | 1.38670 | 0.0661084 | ||||||||
\(441\) | 19.7662 | 0.941250 | ||||||||
\(442\) | 12.4939 | 0.594276 | ||||||||
\(443\) | −27.8370 | −1.32258 | −0.661288 | − | 0.750132i | \(-0.729990\pi\) | ||||
−0.661288 | + | 0.750132i | \(0.729990\pi\) | |||||||
\(444\) | −14.9513 | −0.709556 | ||||||||
\(445\) | 5.82240 | 0.276008 | ||||||||
\(446\) | −4.08943 | −0.193640 | ||||||||
\(447\) | −1.39604 | −0.0660306 | ||||||||
\(448\) | 3.25503 | 0.153786 | ||||||||
\(449\) | 18.9956 | 0.896457 | 0.448228 | − | 0.893919i | \(-0.352055\pi\) | ||||
0.448228 | + | 0.893919i | \(0.352055\pi\) | |||||||
\(450\) | 15.2368 | 0.718268 | ||||||||
\(451\) | −4.74466 | −0.223417 | ||||||||
\(452\) | −16.7698 | −0.788783 | ||||||||
\(453\) | −55.6639 | −2.61532 | ||||||||
\(454\) | −11.9712 | −0.561837 | ||||||||
\(455\) | −21.8486 | −1.02428 | ||||||||
\(456\) | −20.8032 | −0.974198 | ||||||||
\(457\) | 20.7789 | 0.971994 | 0.485997 | − | 0.873960i | \(-0.338457\pi\) | ||||
0.485997 | + | 0.873960i | \(0.338457\pi\) | |||||||
\(458\) | −26.2492 | −1.22655 | ||||||||
\(459\) | −20.2344 | −0.944460 | ||||||||
\(460\) | 6.36007 | 0.296540 | ||||||||
\(461\) | −0.601112 | −0.0279966 | −0.0139983 | − | 0.999902i | \(-0.504456\pi\) | ||||
−0.0139983 | + | 0.999902i | \(0.504456\pi\) | |||||||
\(462\) | −8.81403 | −0.410066 | ||||||||
\(463\) | 6.18736 | 0.287551 | 0.143775 | − | 0.989610i | \(-0.454076\pi\) | ||||
0.143775 | + | 0.989610i | \(0.454076\pi\) | |||||||
\(464\) | 5.01897 | 0.233000 | ||||||||
\(465\) | 34.8674 | 1.61693 | ||||||||
\(466\) | −0.168495 | −0.00780536 | ||||||||
\(467\) | −18.7722 | −0.868673 | −0.434337 | − | 0.900751i | \(-0.643017\pi\) | ||||
−0.434337 | + | 0.900751i | \(0.643017\pi\) | |||||||
\(468\) | 24.7201 | 1.14269 | ||||||||
\(469\) | 20.4119 | 0.942535 | ||||||||
\(470\) | −5.93472 | −0.273748 | ||||||||
\(471\) | −68.4643 | −3.15467 | ||||||||
\(472\) | 3.30780 | 0.152254 | ||||||||
\(473\) | 4.58640 | 0.210883 | ||||||||
\(474\) | −15.0021 | −0.689068 | ||||||||
\(475\) | −19.7772 | −0.907441 | ||||||||
\(476\) | −9.04492 | −0.414573 | ||||||||
\(477\) | 27.3631 | 1.25287 | ||||||||
\(478\) | 5.00385 | 0.228871 | ||||||||
\(479\) | −22.8394 | −1.04356 | −0.521780 | − | 0.853080i | \(-0.674732\pi\) | ||||
−0.521780 | + | 0.853080i | \(0.674732\pi\) | |||||||
\(480\) | 4.35188 | 0.198635 | ||||||||
\(481\) | −23.0606 | −1.05147 | ||||||||
\(482\) | 26.3551 | 1.20044 | ||||||||
\(483\) | −40.4253 | −1.83942 | ||||||||
\(484\) | −10.1372 | −0.460780 | ||||||||
\(485\) | 10.7899 | 0.489946 | ||||||||
\(486\) | 8.04655 | 0.364999 | ||||||||
\(487\) | 35.9728 | 1.63008 | 0.815042 | − | 0.579402i | \(-0.196714\pi\) | ||||
0.815042 | + | 0.579402i | \(0.196714\pi\) | |||||||
\(488\) | −2.18885 | −0.0990845 | ||||||||
\(489\) | 26.1160 | 1.18101 | ||||||||
\(490\) | 5.36715 | 0.242463 | ||||||||
\(491\) | −21.8992 | −0.988299 | −0.494149 | − | 0.869377i | \(-0.664520\pi\) | ||||
−0.494149 | + | 0.869377i | \(0.664520\pi\) | |||||||
\(492\) | −14.8902 | −0.671301 | ||||||||
\(493\) | −13.9465 | −0.628118 | ||||||||
\(494\) | −32.0865 | −1.44364 | ||||||||
\(495\) | −7.62401 | −0.342674 | ||||||||
\(496\) | −8.01202 | −0.359750 | ||||||||
\(497\) | 0.699185 | 0.0313627 | ||||||||
\(498\) | −36.3786 | −1.63017 | ||||||||
\(499\) | −2.85591 | −0.127848 | −0.0639240 | − | 0.997955i | \(-0.520362\pi\) | ||||
−0.0639240 | + | 0.997955i | \(0.520362\pi\) | |||||||
\(500\) | 11.6016 | 0.518838 | ||||||||
\(501\) | 14.4785 | 0.646854 | ||||||||
\(502\) | −14.6780 | −0.655110 | ||||||||
\(503\) | 25.3371 | 1.12972 | 0.564862 | − | 0.825185i | \(-0.308929\pi\) | ||||
0.564862 | + | 0.825185i | \(0.308929\pi\) | |||||||
\(504\) | −17.8960 | −0.797149 | ||||||||
\(505\) | 4.93762 | 0.219721 | ||||||||
\(506\) | 3.95735 | 0.175926 | ||||||||
\(507\) | 21.0360 | 0.934242 | ||||||||
\(508\) | −20.1589 | −0.894408 | ||||||||
\(509\) | −8.66996 | −0.384289 | −0.192145 | − | 0.981367i | \(-0.561544\pi\) | ||||
−0.192145 | + | 0.981367i | \(0.561544\pi\) | |||||||
\(510\) | −12.0928 | −0.535479 | ||||||||
\(511\) | 48.9980 | 2.16755 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 51.9652 | 2.29432 | ||||||||
\(514\) | −9.00926 | −0.397382 | ||||||||
\(515\) | −1.24335 | −0.0547885 | ||||||||
\(516\) | 14.3935 | 0.633638 | ||||||||
\(517\) | −3.69269 | −0.162404 | ||||||||
\(518\) | 16.6946 | 0.733518 | ||||||||
\(519\) | −9.03211 | −0.396465 | ||||||||
\(520\) | 6.71227 | 0.294353 | ||||||||
\(521\) | 25.4825 | 1.11641 | 0.558204 | − | 0.829704i | \(-0.311491\pi\) | ||||
0.558204 | + | 0.829704i | \(0.311491\pi\) | |||||||
\(522\) | −27.5940 | −1.20776 | ||||||||
\(523\) | 25.8411 | 1.12995 | 0.564975 | − | 0.825108i | \(-0.308886\pi\) | ||||
0.564975 | + | 0.825108i | \(0.308886\pi\) | |||||||
\(524\) | 5.52709 | 0.241452 | ||||||||
\(525\) | −26.2969 | −1.14769 | ||||||||
\(526\) | 29.0832 | 1.26809 | ||||||||
\(527\) | 22.2634 | 0.969810 | ||||||||
\(528\) | 2.70782 | 0.117843 | ||||||||
\(529\) | −4.84971 | −0.210857 | ||||||||
\(530\) | 7.42994 | 0.322736 | ||||||||
\(531\) | −18.1861 | −0.789210 | ||||||||
\(532\) | 23.2288 | 1.00710 | ||||||||
\(533\) | −22.9664 | −0.994783 | ||||||||
\(534\) | 11.3694 | 0.492004 | ||||||||
\(535\) | −20.7217 | −0.895879 | ||||||||
\(536\) | −6.27089 | −0.270861 | ||||||||
\(537\) | 14.4443 | 0.623317 | ||||||||
\(538\) | 11.7279 | 0.505626 | ||||||||
\(539\) | 3.33954 | 0.143844 | ||||||||
\(540\) | −10.8708 | −0.467803 | ||||||||
\(541\) | 15.8467 | 0.681304 | 0.340652 | − | 0.940190i | \(-0.389352\pi\) | ||||
0.340652 | + | 0.940190i | \(0.389352\pi\) | |||||||
\(542\) | 24.2213 | 1.04040 | ||||||||
\(543\) | 0.110983 | 0.00476273 | ||||||||
\(544\) | 2.77875 | 0.119138 | ||||||||
\(545\) | −6.24729 | −0.267605 | ||||||||
\(546\) | −42.6640 | −1.82585 | ||||||||
\(547\) | 35.8623 | 1.53336 | 0.766681 | − | 0.642028i | \(-0.221907\pi\) | ||||
0.766681 | + | 0.642028i | \(0.221907\pi\) | |||||||
\(548\) | −4.83457 | −0.206522 | ||||||||
\(549\) | 12.0342 | 0.513605 | ||||||||
\(550\) | 2.57428 | 0.109768 | ||||||||
\(551\) | 35.8168 | 1.52585 | ||||||||
\(552\) | 12.4193 | 0.528602 | ||||||||
\(553\) | 16.7513 | 0.712339 | ||||||||
\(554\) | 6.71572 | 0.285324 | ||||||||
\(555\) | 22.3202 | 0.947440 | ||||||||
\(556\) | −9.72387 | −0.412384 | ||||||||
\(557\) | 14.4638 | 0.612852 | 0.306426 | − | 0.951895i | \(-0.400867\pi\) | ||||
0.306426 | + | 0.951895i | \(0.400867\pi\) | |||||||
\(558\) | 44.0496 | 1.86477 | ||||||||
\(559\) | 22.2003 | 0.938972 | ||||||||
\(560\) | −4.85931 | −0.205343 | ||||||||
\(561\) | −7.52436 | −0.317679 | ||||||||
\(562\) | −15.6567 | −0.660440 | ||||||||
\(563\) | −12.4977 | −0.526717 | −0.263358 | − | 0.964698i | \(-0.584830\pi\) | ||||
−0.263358 | + | 0.964698i | \(0.584830\pi\) | |||||||
\(564\) | −11.5888 | −0.487975 | ||||||||
\(565\) | 25.0350 | 1.05323 | ||||||||
\(566\) | 23.0211 | 0.967650 | ||||||||
\(567\) | 15.4079 | 0.647069 | ||||||||
\(568\) | −0.214802 | −0.00901288 | ||||||||
\(569\) | −8.90081 | −0.373141 | −0.186571 | − | 0.982442i | \(-0.559737\pi\) | ||||
−0.186571 | + | 0.982442i | \(0.559737\pi\) | |||||||
\(570\) | 31.0563 | 1.30081 | ||||||||
\(571\) | −4.72569 | −0.197764 | −0.0988819 | − | 0.995099i | \(-0.531527\pi\) | ||||
−0.0988819 | + | 0.995099i | \(0.531527\pi\) | |||||||
\(572\) | 4.17650 | 0.174628 | ||||||||
\(573\) | 77.9536 | 3.25656 | ||||||||
\(574\) | 16.6264 | 0.693971 | ||||||||
\(575\) | 11.8069 | 0.492380 | ||||||||
\(576\) | 5.49794 | 0.229081 | ||||||||
\(577\) | 4.78401 | 0.199161 | 0.0995805 | − | 0.995030i | \(-0.468250\pi\) | ||||
0.0995805 | + | 0.995030i | \(0.468250\pi\) | |||||||
\(578\) | 9.27853 | 0.385936 | ||||||||
\(579\) | 11.1911 | 0.465085 | ||||||||
\(580\) | −7.49264 | −0.311115 | ||||||||
\(581\) | 40.6204 | 1.68522 | ||||||||
\(582\) | 21.0696 | 0.873362 | ||||||||
\(583\) | 4.62304 | 0.191467 | ||||||||
\(584\) | −15.0530 | −0.622899 | ||||||||
\(585\) | −36.9037 | −1.52578 | ||||||||
\(586\) | 11.3369 | 0.468321 | ||||||||
\(587\) | 38.9819 | 1.60896 | 0.804479 | − | 0.593982i | \(-0.202445\pi\) | ||||
0.804479 | + | 0.593982i | \(0.202445\pi\) | |||||||
\(588\) | 10.4805 | 0.432207 | ||||||||
\(589\) | −57.1761 | −2.35590 | ||||||||
\(590\) | −4.93810 | −0.203298 | ||||||||
\(591\) | −80.8710 | −3.32659 | ||||||||
\(592\) | −5.12886 | −0.210795 | ||||||||
\(593\) | −16.9640 | −0.696629 | −0.348314 | − | 0.937378i | \(-0.613246\pi\) | ||||
−0.348314 | + | 0.937378i | \(0.613246\pi\) | |||||||
\(594\) | −6.76398 | −0.277529 | ||||||||
\(595\) | 13.5028 | 0.553562 | ||||||||
\(596\) | −0.478897 | −0.0196164 | ||||||||
\(597\) | 44.4037 | 1.81732 | ||||||||
\(598\) | 19.1554 | 0.783323 | ||||||||
\(599\) | −44.8188 | −1.83125 | −0.915624 | − | 0.402036i | \(-0.868303\pi\) | ||||
−0.915624 | + | 0.402036i | \(0.868303\pi\) | |||||||
\(600\) | 8.07885 | 0.329818 | ||||||||
\(601\) | 24.3965 | 0.995156 | 0.497578 | − | 0.867419i | \(-0.334223\pi\) | ||||
0.497578 | + | 0.867419i | \(0.334223\pi\) | |||||||
\(602\) | −16.0718 | −0.655037 | ||||||||
\(603\) | 34.4770 | 1.40401 | ||||||||
\(604\) | −19.0949 | −0.776959 | ||||||||
\(605\) | 15.1334 | 0.615261 | ||||||||
\(606\) | 9.64171 | 0.391668 | ||||||||
\(607\) | −45.3298 | −1.83988 | −0.919940 | − | 0.392059i | \(-0.871763\pi\) | ||||
−0.919940 | + | 0.392059i | \(0.871763\pi\) | |||||||
\(608\) | −7.13629 | −0.289415 | ||||||||
\(609\) | 47.6240 | 1.92982 | ||||||||
\(610\) | 3.26765 | 0.132303 | ||||||||
\(611\) | −17.8743 | −0.723118 | ||||||||
\(612\) | −15.2774 | −0.617554 | ||||||||
\(613\) | −4.79941 | −0.193847 | −0.0969233 | − | 0.995292i | \(-0.530900\pi\) | ||||
−0.0969233 | + | 0.995292i | \(0.530900\pi\) | |||||||
\(614\) | −17.3822 | −0.701487 | ||||||||
\(615\) | 22.2290 | 0.896359 | ||||||||
\(616\) | −3.02355 | −0.121822 | ||||||||
\(617\) | 2.06921 | 0.0833033 | 0.0416516 | − | 0.999132i | \(-0.486738\pi\) | ||||
0.0416516 | + | 0.999132i | \(0.486738\pi\) | |||||||
\(618\) | −2.42789 | −0.0976642 | ||||||||
\(619\) | −41.1248 | −1.65295 | −0.826473 | − | 0.562976i | \(-0.809656\pi\) | ||||
−0.826473 | + | 0.562976i | \(0.809656\pi\) | |||||||
\(620\) | 11.9609 | 0.480359 | ||||||||
\(621\) | −31.0228 | −1.24490 | ||||||||
\(622\) | 22.4588 | 0.900516 | ||||||||
\(623\) | −12.6951 | −0.508619 | ||||||||
\(624\) | 13.1071 | 0.524704 | ||||||||
\(625\) | −3.46279 | −0.138511 | ||||||||
\(626\) | 23.6953 | 0.947055 | ||||||||
\(627\) | 19.3238 | 0.771718 | ||||||||
\(628\) | −23.4859 | −0.937189 | ||||||||
\(629\) | 14.2518 | 0.568258 | ||||||||
\(630\) | 26.7162 | 1.06440 | ||||||||
\(631\) | −29.4760 | −1.17342 | −0.586710 | − | 0.809797i | \(-0.699577\pi\) | ||||
−0.586710 | + | 0.809797i | \(0.699577\pi\) | |||||||
\(632\) | −5.14629 | −0.204709 | ||||||||
\(633\) | 24.2512 | 0.963900 | ||||||||
\(634\) | 7.48626 | 0.297317 | ||||||||
\(635\) | 30.0945 | 1.19426 | ||||||||
\(636\) | 14.5085 | 0.575299 | ||||||||
\(637\) | 16.1649 | 0.640477 | ||||||||
\(638\) | −4.66205 | −0.184572 | ||||||||
\(639\) | 1.18097 | 0.0467183 | ||||||||
\(640\) | 1.49286 | 0.0590106 | ||||||||
\(641\) | −27.1851 | −1.07375 | −0.536873 | − | 0.843663i | \(-0.680395\pi\) | ||||
−0.536873 | + | 0.843663i | \(0.680395\pi\) | |||||||
\(642\) | −40.4635 | −1.59697 | ||||||||
\(643\) | −31.4818 | −1.24152 | −0.620761 | − | 0.784000i | \(-0.713176\pi\) | ||||
−0.620761 | + | 0.784000i | \(0.713176\pi\) | |||||||
\(644\) | −13.8674 | −0.546454 | ||||||||
\(645\) | −21.4875 | −0.846070 | ||||||||
\(646\) | 19.8300 | 0.780201 | ||||||||
\(647\) | −7.84978 | −0.308607 | −0.154303 | − | 0.988024i | \(-0.549313\pi\) | ||||
−0.154303 | + | 0.988024i | \(0.549313\pi\) | |||||||
\(648\) | −4.73355 | −0.185952 | ||||||||
\(649\) | −3.07258 | −0.120609 | ||||||||
\(650\) | 12.4607 | 0.488748 | ||||||||
\(651\) | −76.0245 | −2.97964 | ||||||||
\(652\) | 8.95881 | 0.350854 | ||||||||
\(653\) | 23.3571 | 0.914032 | 0.457016 | − | 0.889458i | \(-0.348918\pi\) | ||||
0.457016 | + | 0.889458i | \(0.348918\pi\) | |||||||
\(654\) | −12.1991 | −0.477024 | ||||||||
\(655\) | −8.25118 | −0.322400 | ||||||||
\(656\) | −5.10790 | −0.199430 | ||||||||
\(657\) | 82.7607 | 3.22880 | ||||||||
\(658\) | 12.9400 | 0.504454 | ||||||||
\(659\) | 10.7555 | 0.418976 | 0.209488 | − | 0.977811i | \(-0.432820\pi\) | ||||
0.209488 | + | 0.977811i | \(0.432820\pi\) | |||||||
\(660\) | −4.04241 | −0.157350 | ||||||||
\(661\) | 50.1851 | 1.95197 | 0.975987 | − | 0.217830i | \(-0.0698977\pi\) | ||||
0.975987 | + | 0.217830i | \(0.0698977\pi\) | |||||||
\(662\) | −3.52357 | −0.136947 | ||||||||
\(663\) | −36.4214 | −1.41449 | ||||||||
\(664\) | −12.4793 | −0.484290 | ||||||||
\(665\) | −34.6775 | −1.34474 | ||||||||
\(666\) | 28.1982 | 1.09266 | ||||||||
\(667\) | −21.3824 | −0.827929 | ||||||||
\(668\) | 4.96670 | 0.192167 | ||||||||
\(669\) | 11.9212 | 0.460900 | ||||||||
\(670\) | 9.36158 | 0.361669 | ||||||||
\(671\) | 2.03319 | 0.0784905 | ||||||||
\(672\) | −9.48881 | −0.366039 | ||||||||
\(673\) | 12.9753 | 0.500161 | 0.250081 | − | 0.968225i | \(-0.419543\pi\) | ||||
0.250081 | + | 0.968225i | \(0.419543\pi\) | |||||||
\(674\) | 7.72046 | 0.297381 | ||||||||
\(675\) | −20.1805 | −0.776748 | ||||||||
\(676\) | 7.21617 | 0.277545 | ||||||||
\(677\) | 49.2178 | 1.89159 | 0.945796 | − | 0.324760i | \(-0.105284\pi\) | ||||
0.945796 | + | 0.324760i | \(0.105284\pi\) | |||||||
\(678\) | 48.8859 | 1.87745 | ||||||||
\(679\) | −23.5263 | −0.902857 | ||||||||
\(680\) | −4.14830 | −0.159080 | ||||||||
\(681\) | 34.8976 | 1.33728 | ||||||||
\(682\) | 7.44226 | 0.284979 | ||||||||
\(683\) | 23.7176 | 0.907527 | 0.453764 | − | 0.891122i | \(-0.350081\pi\) | ||||
0.453764 | + | 0.891122i | \(0.350081\pi\) | |||||||
\(684\) | 39.2349 | 1.50019 | ||||||||
\(685\) | 7.21735 | 0.275761 | ||||||||
\(686\) | 11.0827 | 0.423139 | ||||||||
\(687\) | 76.5197 | 2.91941 | ||||||||
\(688\) | 4.93752 | 0.188241 | ||||||||
\(689\) | 22.3777 | 0.852521 | ||||||||
\(690\) | −18.5404 | −0.705821 | ||||||||
\(691\) | −9.28834 | −0.353345 | −0.176672 | − | 0.984270i | \(-0.556533\pi\) | ||||
−0.176672 | + | 0.984270i | \(0.556533\pi\) | |||||||
\(692\) | −3.09836 | −0.117782 | ||||||||
\(693\) | 16.6233 | 0.631468 | ||||||||
\(694\) | −6.82229 | −0.258971 | ||||||||
\(695\) | 14.5164 | 0.550639 | ||||||||
\(696\) | −14.6309 | −0.554583 | ||||||||
\(697\) | 14.1936 | 0.537621 | ||||||||
\(698\) | 23.4882 | 0.889041 | ||||||||
\(699\) | 0.491182 | 0.0185782 | ||||||||
\(700\) | −9.02085 | −0.340956 | ||||||||
\(701\) | −27.3674 | −1.03365 | −0.516826 | − | 0.856090i | \(-0.672887\pi\) | ||||
−0.516826 | + | 0.856090i | \(0.672887\pi\) | |||||||
\(702\) | −32.7408 | −1.23572 | ||||||||
\(703\) | −36.6011 | −1.38044 | ||||||||
\(704\) | 0.928887 | 0.0350087 | ||||||||
\(705\) | 17.3004 | 0.651572 | ||||||||
\(706\) | −20.6971 | −0.778946 | ||||||||
\(707\) | −10.7659 | −0.404895 | ||||||||
\(708\) | −9.64266 | −0.362393 | ||||||||
\(709\) | −24.0369 | −0.902723 | −0.451362 | − | 0.892341i | \(-0.649062\pi\) | ||||
−0.451362 | + | 0.892341i | \(0.649062\pi\) | |||||||
\(710\) | 0.320670 | 0.0120345 | ||||||||
\(711\) | 28.2940 | 1.06111 | ||||||||
\(712\) | 3.90016 | 0.146165 | ||||||||
\(713\) | 34.1337 | 1.27832 | ||||||||
\(714\) | 26.3671 | 0.986763 | ||||||||
\(715\) | −6.23494 | −0.233174 | ||||||||
\(716\) | 4.95495 | 0.185175 | ||||||||
\(717\) | −14.5868 | −0.544755 | ||||||||
\(718\) | −20.9481 | −0.781776 | ||||||||
\(719\) | −21.6220 | −0.806364 | −0.403182 | − | 0.915120i | \(-0.632096\pi\) | ||||
−0.403182 | + | 0.915120i | \(0.632096\pi\) | |||||||
\(720\) | −8.20768 | −0.305882 | ||||||||
\(721\) | 2.71099 | 0.100962 | ||||||||
\(722\) | −31.9267 | −1.18819 | ||||||||
\(723\) | −76.8284 | −2.85728 | ||||||||
\(724\) | 0.0380714 | 0.00141491 | ||||||||
\(725\) | −13.9094 | −0.516581 | ||||||||
\(726\) | 29.5511 | 1.09674 | ||||||||
\(727\) | −3.66114 | −0.135784 | −0.0678920 | − | 0.997693i | \(-0.521627\pi\) | ||||
−0.0678920 | + | 0.997693i | \(0.521627\pi\) | |||||||
\(728\) | −14.6354 | −0.542423 | ||||||||
\(729\) | −37.6573 | −1.39472 | ||||||||
\(730\) | 22.4721 | 0.831731 | ||||||||
\(731\) | −13.7202 | −0.507459 | ||||||||
\(732\) | 6.38076 | 0.235840 | ||||||||
\(733\) | −36.2282 | −1.33812 | −0.669060 | − | 0.743209i | \(-0.733303\pi\) | ||||
−0.669060 | + | 0.743209i | \(0.733303\pi\) | |||||||
\(734\) | −12.8420 | −0.474007 | ||||||||
\(735\) | −15.6459 | −0.577108 | ||||||||
\(736\) | 4.26032 | 0.157037 | ||||||||
\(737\) | 5.82495 | 0.214565 | ||||||||
\(738\) | 28.0830 | 1.03375 | ||||||||
\(739\) | 46.2968 | 1.70306 | 0.851528 | − | 0.524310i | \(-0.175677\pi\) | ||||
0.851528 | + | 0.524310i | \(0.175677\pi\) | |||||||
\(740\) | 7.65669 | 0.281466 | ||||||||
\(741\) | 93.5361 | 3.43613 | ||||||||
\(742\) | −16.2002 | −0.594727 | ||||||||
\(743\) | 46.5840 | 1.70900 | 0.854500 | − | 0.519451i | \(-0.173864\pi\) | ||||
0.854500 | + | 0.519451i | \(0.173864\pi\) | |||||||
\(744\) | 23.3560 | 0.856273 | ||||||||
\(745\) | 0.714928 | 0.0261929 | ||||||||
\(746\) | −13.3270 | −0.487937 | ||||||||
\(747\) | 68.6104 | 2.51032 | ||||||||
\(748\) | −2.58115 | −0.0943761 | ||||||||
\(749\) | 45.1815 | 1.65090 | ||||||||
\(750\) | −33.8200 | −1.23493 | ||||||||
\(751\) | 1.00000 | 0.0364905 | ||||||||
\(752\) | −3.97539 | −0.144968 | ||||||||
\(753\) | 42.7881 | 1.55928 | ||||||||
\(754\) | −22.5665 | −0.821823 | ||||||||
\(755\) | 28.5060 | 1.03744 | ||||||||
\(756\) | 23.7025 | 0.862052 | ||||||||
\(757\) | −24.8281 | −0.902392 | −0.451196 | − | 0.892425i | \(-0.649002\pi\) | ||||
−0.451196 | + | 0.892425i | \(0.649002\pi\) | |||||||
\(758\) | −6.33684 | −0.230164 | ||||||||
\(759\) | −11.5362 | −0.418736 | ||||||||
\(760\) | 10.6535 | 0.386444 | ||||||||
\(761\) | 16.0722 | 0.582618 | 0.291309 | − | 0.956629i | \(-0.405909\pi\) | ||||
0.291309 | + | 0.956629i | \(0.405909\pi\) | |||||||
\(762\) | 58.7658 | 2.12886 | ||||||||
\(763\) | 13.6215 | 0.493133 | ||||||||
\(764\) | 26.7411 | 0.967459 | ||||||||
\(765\) | 22.8071 | 0.824593 | ||||||||
\(766\) | 24.1211 | 0.871532 | ||||||||
\(767\) | −14.8727 | −0.537021 | ||||||||
\(768\) | 2.91512 | 0.105190 | ||||||||
\(769\) | 14.3686 | 0.518147 | 0.259073 | − | 0.965858i | \(-0.416583\pi\) | ||||
0.259073 | + | 0.965858i | \(0.416583\pi\) | |||||||
\(770\) | 4.51375 | 0.162664 | ||||||||
\(771\) | 26.2631 | 0.945843 | ||||||||
\(772\) | 3.83897 | 0.138168 | ||||||||
\(773\) | 7.91260 | 0.284597 | 0.142298 | − | 0.989824i | \(-0.454551\pi\) | ||||
0.142298 | + | 0.989824i | \(0.454551\pi\) | |||||||
\(774\) | −27.1462 | −0.975751 | ||||||||
\(775\) | 22.2042 | 0.797597 | ||||||||
\(776\) | 7.22768 | 0.259459 | ||||||||
\(777\) | −48.6668 | −1.74591 | ||||||||
\(778\) | 22.4082 | 0.803371 | ||||||||
\(779\) | −36.4515 | −1.30601 | ||||||||
\(780\) | −19.5671 | −0.700615 | ||||||||
\(781\) | 0.199526 | 0.00713962 | ||||||||
\(782\) | −11.8384 | −0.423339 | ||||||||
\(783\) | 36.5472 | 1.30609 | ||||||||
\(784\) | 3.59521 | 0.128400 | ||||||||
\(785\) | 35.0612 | 1.25139 | ||||||||
\(786\) | −16.1121 | −0.574701 | ||||||||
\(787\) | 33.6860 | 1.20078 | 0.600388 | − | 0.799709i | \(-0.295013\pi\) | ||||
0.600388 | + | 0.799709i | \(0.295013\pi\) | |||||||
\(788\) | −27.7419 | −0.988263 | ||||||||
\(789\) | −84.7812 | −3.01829 | ||||||||
\(790\) | 7.68271 | 0.273339 | ||||||||
\(791\) | −54.5860 | −1.94085 | ||||||||
\(792\) | −5.10697 | −0.181468 | ||||||||
\(793\) | 9.84158 | 0.349485 | ||||||||
\(794\) | −7.85601 | −0.278799 | ||||||||
\(795\) | −21.6592 | −0.768172 | ||||||||
\(796\) | 15.2322 | 0.539891 | ||||||||
\(797\) | 43.7146 | 1.54845 | 0.774225 | − | 0.632910i | \(-0.218140\pi\) | ||||
0.774225 | + | 0.632910i | \(0.218140\pi\) | |||||||
\(798\) | −67.7149 | −2.39708 | ||||||||
\(799\) | 11.0466 | 0.390802 | ||||||||
\(800\) | 2.77136 | 0.0979823 | ||||||||
\(801\) | −21.4428 | −0.757646 | ||||||||
\(802\) | −16.1596 | −0.570615 | ||||||||
\(803\) | 13.9826 | 0.493434 | ||||||||
\(804\) | 18.2804 | 0.644700 | ||||||||
\(805\) | 20.7022 | 0.729657 | ||||||||
\(806\) | 36.0240 | 1.26889 | ||||||||
\(807\) | −34.1883 | −1.20348 | ||||||||
\(808\) | 3.30748 | 0.116357 | ||||||||
\(809\) | 36.9956 | 1.30070 | 0.650348 | − | 0.759637i | \(-0.274623\pi\) | ||||
0.650348 | + | 0.759637i | \(0.274623\pi\) | |||||||
\(810\) | 7.06655 | 0.248293 | ||||||||
\(811\) | 40.4822 | 1.42152 | 0.710761 | − | 0.703434i | \(-0.248351\pi\) | ||||
0.710761 | + | 0.703434i | \(0.248351\pi\) | |||||||
\(812\) | 16.3369 | 0.573312 | ||||||||
\(813\) | −70.6082 | −2.47634 | ||||||||
\(814\) | 4.76413 | 0.166983 | ||||||||
\(815\) | −13.3743 | −0.468481 | ||||||||
\(816\) | −8.10041 | −0.283571 | ||||||||
\(817\) | 35.2356 | 1.23274 | ||||||||
\(818\) | −21.9292 | −0.766738 | ||||||||
\(819\) | 80.4645 | 2.81166 | ||||||||
\(820\) | 7.62540 | 0.266291 | ||||||||
\(821\) | 52.1358 | 1.81955 | 0.909776 | − | 0.415100i | \(-0.136253\pi\) | ||||
0.909776 | + | 0.415100i | \(0.136253\pi\) | |||||||
\(822\) | 14.0934 | 0.491562 | ||||||||
\(823\) | −10.9477 | −0.381611 | −0.190806 | − | 0.981628i | \(-0.561110\pi\) | ||||
−0.190806 | + | 0.981628i | \(0.561110\pi\) | |||||||
\(824\) | −0.832862 | −0.0290141 | ||||||||
\(825\) | −7.50434 | −0.261267 | ||||||||
\(826\) | 10.7670 | 0.374632 | ||||||||
\(827\) | −42.5251 | −1.47874 | −0.739371 | − | 0.673298i | \(-0.764877\pi\) | ||||
−0.739371 | + | 0.673298i | \(0.764877\pi\) | |||||||
\(828\) | −23.4230 | −0.814005 | ||||||||
\(829\) | −53.8318 | −1.86965 | −0.934827 | − | 0.355103i | \(-0.884446\pi\) | ||||
−0.934827 | + | 0.355103i | \(0.884446\pi\) | |||||||
\(830\) | 18.6299 | 0.646652 | ||||||||
\(831\) | −19.5772 | −0.679124 | ||||||||
\(832\) | 4.49624 | 0.155879 | ||||||||
\(833\) | −9.99020 | −0.346140 | ||||||||
\(834\) | 28.3463 | 0.981552 | ||||||||
\(835\) | −7.41461 | −0.256593 | ||||||||
\(836\) | 6.62881 | 0.229262 | ||||||||
\(837\) | −58.3420 | −2.01660 | ||||||||
\(838\) | 15.8461 | 0.547396 | ||||||||
\(839\) | −42.1427 | −1.45493 | −0.727463 | − | 0.686147i | \(-0.759301\pi\) | ||||
−0.727463 | + | 0.686147i | \(0.759301\pi\) | |||||||
\(840\) | 14.1655 | 0.488756 | ||||||||
\(841\) | −3.80996 | −0.131378 | ||||||||
\(842\) | 14.2514 | 0.491135 | ||||||||
\(843\) | 45.6413 | 1.57197 | ||||||||
\(844\) | 8.31911 | 0.286356 | ||||||||
\(845\) | −10.7728 | −0.370594 | ||||||||
\(846\) | 21.8565 | 0.751442 | ||||||||
\(847\) | −32.9968 | −1.13378 | ||||||||
\(848\) | 4.97697 | 0.170910 | ||||||||
\(849\) | −67.1094 | −2.30319 | ||||||||
\(850\) | −7.70092 | −0.264139 | ||||||||
\(851\) | 21.8506 | 0.749028 | ||||||||
\(852\) | 0.626173 | 0.0214523 | ||||||||
\(853\) | 29.8307 | 1.02138 | 0.510692 | − | 0.859764i | \(-0.329389\pi\) | ||||
0.510692 | + | 0.859764i | \(0.329389\pi\) | |||||||
\(854\) | −7.12476 | −0.243804 | ||||||||
\(855\) | −58.5724 | −2.00313 | ||||||||
\(856\) | −13.8805 | −0.474427 | ||||||||
\(857\) | −4.55580 | −0.155623 | −0.0778116 | − | 0.996968i | \(-0.524793\pi\) | ||||
−0.0778116 | + | 0.996968i | \(0.524793\pi\) | |||||||
\(858\) | −12.1750 | −0.415648 | ||||||||
\(859\) | 33.6547 | 1.14828 | 0.574141 | − | 0.818756i | \(-0.305336\pi\) | ||||
0.574141 | + | 0.818756i | \(0.305336\pi\) | |||||||
\(860\) | −7.37105 | −0.251351 | ||||||||
\(861\) | −48.4679 | −1.65178 | ||||||||
\(862\) | 26.6546 | 0.907859 | ||||||||
\(863\) | 28.1850 | 0.959429 | 0.479714 | − | 0.877425i | \(-0.340740\pi\) | ||||
0.479714 | + | 0.877425i | \(0.340740\pi\) | |||||||
\(864\) | −7.28181 | −0.247732 | ||||||||
\(865\) | 4.62543 | 0.157269 | ||||||||
\(866\) | 11.0415 | 0.375207 | ||||||||
\(867\) | −27.0480 | −0.918600 | ||||||||
\(868\) | −26.0793 | −0.885191 | ||||||||
\(869\) | 4.78032 | 0.162161 | ||||||||
\(870\) | 21.8420 | 0.740512 | ||||||||
\(871\) | 28.1954 | 0.955365 | ||||||||
\(872\) | −4.18477 | −0.141714 | ||||||||
\(873\) | −39.7374 | −1.34491 | ||||||||
\(874\) | 30.4029 | 1.02839 | ||||||||
\(875\) | 37.7635 | 1.27664 | ||||||||
\(876\) | 43.8814 | 1.48262 | ||||||||
\(877\) | −46.0368 | −1.55455 | −0.777276 | − | 0.629160i | \(-0.783399\pi\) | ||||
−0.777276 | + | 0.629160i | \(0.783399\pi\) | |||||||
\(878\) | 8.58467 | 0.289719 | ||||||||
\(879\) | −33.0483 | −1.11469 | ||||||||
\(880\) | −1.38670 | −0.0467457 | ||||||||
\(881\) | 5.88384 | 0.198231 | 0.0991157 | − | 0.995076i | \(-0.468399\pi\) | ||||
0.0991157 | + | 0.995076i | \(0.468399\pi\) | |||||||
\(882\) | −19.7662 | −0.665564 | ||||||||
\(883\) | 24.4465 | 0.822691 | 0.411346 | − | 0.911479i | \(-0.365059\pi\) | ||||
0.411346 | + | 0.911479i | \(0.365059\pi\) | |||||||
\(884\) | −12.4939 | −0.420217 | ||||||||
\(885\) | 14.3952 | 0.483888 | ||||||||
\(886\) | 27.8370 | 0.935203 | ||||||||
\(887\) | 50.0875 | 1.68177 | 0.840887 | − | 0.541211i | \(-0.182034\pi\) | ||||
0.840887 | + | 0.541211i | \(0.182034\pi\) | |||||||
\(888\) | 14.9513 | 0.501732 | ||||||||
\(889\) | −65.6179 | −2.20075 | ||||||||
\(890\) | −5.82240 | −0.195167 | ||||||||
\(891\) | 4.39694 | 0.147303 | ||||||||
\(892\) | 4.08943 | 0.136924 | ||||||||
\(893\) | −28.3696 | −0.949352 | ||||||||
\(894\) | 1.39604 | 0.0466907 | ||||||||
\(895\) | −7.39706 | −0.247257 | ||||||||
\(896\) | −3.25503 | −0.108743 | ||||||||
\(897\) | −55.8404 | −1.86446 | ||||||||
\(898\) | −18.9956 | −0.633891 | ||||||||
\(899\) | −40.2121 | −1.34115 | ||||||||
\(900\) | −15.2368 | −0.507892 | ||||||||
\(901\) | −13.8298 | −0.460737 | ||||||||
\(902\) | 4.74466 | 0.157980 | ||||||||
\(903\) | 46.8512 | 1.55911 | ||||||||
\(904\) | 16.7698 | 0.557754 | ||||||||
\(905\) | −0.0568354 | −0.00188927 | ||||||||
\(906\) | 55.6639 | 1.84931 | ||||||||
\(907\) | −55.4951 | −1.84268 | −0.921342 | − | 0.388753i | \(-0.872906\pi\) | ||||
−0.921342 | + | 0.388753i | \(0.872906\pi\) | |||||||
\(908\) | 11.9712 | 0.397279 | ||||||||
\(909\) | −18.1843 | −0.603136 | ||||||||
\(910\) | 21.8486 | 0.724275 | ||||||||
\(911\) | −42.1133 | −1.39528 | −0.697638 | − | 0.716451i | \(-0.745766\pi\) | ||||
−0.697638 | + | 0.716451i | \(0.745766\pi\) | |||||||
\(912\) | 20.8032 | 0.688862 | ||||||||
\(913\) | 11.5918 | 0.383634 | ||||||||
\(914\) | −20.7789 | −0.687303 | ||||||||
\(915\) | −9.52560 | −0.314907 | ||||||||
\(916\) | 26.2492 | 0.867299 | ||||||||
\(917\) | 17.9908 | 0.594109 | ||||||||
\(918\) | 20.2344 | 0.667834 | ||||||||
\(919\) | 48.3699 | 1.59558 | 0.797788 | − | 0.602938i | \(-0.206003\pi\) | ||||
0.797788 | + | 0.602938i | \(0.206003\pi\) | |||||||
\(920\) | −6.36007 | −0.209685 | ||||||||
\(921\) | 50.6711 | 1.66967 | ||||||||
\(922\) | 0.601112 | 0.0197966 | ||||||||
\(923\) | 0.965799 | 0.0317897 | ||||||||
\(924\) | 8.81403 | 0.289960 | ||||||||
\(925\) | 14.2139 | 0.467351 | ||||||||
\(926\) | −6.18736 | −0.203329 | ||||||||
\(927\) | 4.57903 | 0.150395 | ||||||||
\(928\) | −5.01897 | −0.164756 | ||||||||
\(929\) | 51.9047 | 1.70294 | 0.851470 | − | 0.524404i | \(-0.175712\pi\) | ||||
0.851470 | + | 0.524404i | \(0.175712\pi\) | |||||||
\(930\) | −34.8674 | −1.14335 | ||||||||
\(931\) | 25.6565 | 0.840856 | ||||||||
\(932\) | 0.168495 | 0.00551922 | ||||||||
\(933\) | −65.4702 | −2.14340 | ||||||||
\(934\) | 18.7722 | 0.614245 | ||||||||
\(935\) | 3.85330 | 0.126016 | ||||||||
\(936\) | −24.7201 | −0.808001 | ||||||||
\(937\) | −35.1507 | −1.14832 | −0.574161 | − | 0.818743i | \(-0.694672\pi\) | ||||
−0.574161 | + | 0.818743i | \(0.694672\pi\) | |||||||
\(938\) | −20.4119 | −0.666473 | ||||||||
\(939\) | −69.0747 | −2.25417 | ||||||||
\(940\) | 5.93472 | 0.193569 | ||||||||
\(941\) | −45.3754 | −1.47920 | −0.739598 | − | 0.673049i | \(-0.764984\pi\) | ||||
−0.739598 | + | 0.673049i | \(0.764984\pi\) | |||||||
\(942\) | 68.4643 | 2.23069 | ||||||||
\(943\) | 21.7613 | 0.708645 | ||||||||
\(944\) | −3.30780 | −0.107660 | ||||||||
\(945\) | −35.3846 | −1.15106 | ||||||||
\(946\) | −4.58640 | −0.149117 | ||||||||
\(947\) | 28.8082 | 0.936141 | 0.468070 | − | 0.883691i | \(-0.344949\pi\) | ||||
0.468070 | + | 0.883691i | \(0.344949\pi\) | |||||||
\(948\) | 15.0021 | 0.487245 | ||||||||
\(949\) | 67.6820 | 2.19705 | ||||||||
\(950\) | 19.7772 | 0.641658 | ||||||||
\(951\) | −21.8234 | −0.707671 | ||||||||
\(952\) | 9.04492 | 0.293148 | ||||||||
\(953\) | −25.9657 | −0.841111 | −0.420555 | − | 0.907267i | \(-0.638165\pi\) | ||||
−0.420555 | + | 0.907267i | \(0.638165\pi\) | |||||||
\(954\) | −27.3631 | −0.885913 | ||||||||
\(955\) | −39.9208 | −1.29181 | ||||||||
\(956\) | −5.00385 | −0.161836 | ||||||||
\(957\) | 13.5905 | 0.439317 | ||||||||
\(958\) | 22.8394 | 0.737909 | ||||||||
\(959\) | −15.7366 | −0.508163 | ||||||||
\(960\) | −4.35188 | −0.140456 | ||||||||
\(961\) | 33.1924 | 1.07072 | ||||||||
\(962\) | 23.0606 | 0.743503 | ||||||||
\(963\) | 76.3144 | 2.45920 | ||||||||
\(964\) | −26.3551 | −0.848841 | ||||||||
\(965\) | −5.73106 | −0.184489 | ||||||||
\(966\) | 40.4253 | 1.30066 | ||||||||
\(967\) | 14.0626 | 0.452224 | 0.226112 | − | 0.974101i | \(-0.427398\pi\) | ||||
0.226112 | + | 0.974101i | \(0.427398\pi\) | |||||||
\(968\) | 10.1372 | 0.325821 | ||||||||
\(969\) | −57.8069 | −1.85703 | ||||||||
\(970\) | −10.7899 | −0.346444 | ||||||||
\(971\) | 12.6707 | 0.406622 | 0.203311 | − | 0.979114i | \(-0.434830\pi\) | ||||
0.203311 | + | 0.979114i | \(0.434830\pi\) | |||||||
\(972\) | −8.04655 | −0.258093 | ||||||||
\(973\) | −31.6515 | −1.01470 | ||||||||
\(974\) | −35.9728 | −1.15264 | ||||||||
\(975\) | −36.3244 | −1.16331 | ||||||||
\(976\) | 2.18885 | 0.0700633 | ||||||||
\(977\) | 5.59021 | 0.178847 | 0.0894234 | − | 0.995994i | \(-0.471498\pi\) | ||||
0.0894234 | + | 0.995994i | \(0.471498\pi\) | |||||||
\(978\) | −26.1160 | −0.835099 | ||||||||
\(979\) | −3.62280 | −0.115785 | ||||||||
\(980\) | −5.36715 | −0.171447 | ||||||||
\(981\) | 23.0076 | 0.734577 | ||||||||
\(982\) | 21.8992 | 0.698833 | ||||||||
\(983\) | −21.6558 | −0.690714 | −0.345357 | − | 0.938471i | \(-0.612242\pi\) | ||||
−0.345357 | + | 0.938471i | \(0.612242\pi\) | |||||||
\(984\) | 14.8902 | 0.474681 | ||||||||
\(985\) | 41.4148 | 1.31959 | ||||||||
\(986\) | 13.9465 | 0.444146 | ||||||||
\(987\) | −37.7218 | −1.20070 | ||||||||
\(988\) | 32.0865 | 1.02081 | ||||||||
\(989\) | −21.0354 | −0.668887 | ||||||||
\(990\) | 7.62401 | 0.242307 | ||||||||
\(991\) | 36.3543 | 1.15483 | 0.577417 | − | 0.816450i | \(-0.304061\pi\) | ||||
0.577417 | + | 0.816450i | \(0.304061\pi\) | |||||||
\(992\) | 8.01202 | 0.254382 | ||||||||
\(993\) | 10.2716 | 0.325961 | ||||||||
\(994\) | −0.699185 | −0.0221768 | ||||||||
\(995\) | −22.7396 | −0.720893 | ||||||||
\(996\) | 36.3786 | 1.15270 | ||||||||
\(997\) | 43.8215 | 1.38784 | 0.693921 | − | 0.720051i | \(-0.255882\pi\) | ||||
0.693921 | + | 0.720051i | \(0.255882\pi\) | |||||||
\(998\) | 2.85591 | 0.0904022 | ||||||||
\(999\) | −37.3474 | −1.18162 |
(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 | 1502.2.a.h.1.18 | ✓ | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1502.2.a.h.1.18 | ✓ | 19 | 1.1 | even | 1 | trivial |