Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4730,2,Mod(1,4730)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4730, 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("4730.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4730.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: | \(37.7692401561\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - x^{10} - 22 x^{9} + 21 x^{8} + 165 x^{7} - 130 x^{6} - 535 x^{5} + 323 x^{4} + 710 x^{3} + \cdots + 128 \) |
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 | 1.4 | ||
Root | \(1.48284\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4730.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.48284 | −0.856115 | −0.428058 | − | 0.903751i | \(-0.640802\pi\) | ||||
−0.428058 | + | 0.903751i | \(0.640802\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.48284 | 0.605365 | ||||||||
\(7\) | 4.82678 | 1.82435 | 0.912175 | − | 0.409801i | \(-0.134402\pi\) | ||||
0.912175 | + | 0.409801i | \(0.134402\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.801199 | −0.267066 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −1.48284 | −0.428058 | ||||||||
\(13\) | 3.11595 | 0.864209 | 0.432105 | − | 0.901823i | \(-0.357771\pi\) | ||||
0.432105 | + | 0.901823i | \(0.357771\pi\) | |||||||
\(14\) | −4.82678 | −1.29001 | ||||||||
\(15\) | 1.48284 | 0.382866 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.03311 | 1.70578 | 0.852890 | − | 0.522091i | \(-0.174848\pi\) | ||||
0.852890 | + | 0.522091i | \(0.174848\pi\) | |||||||
\(18\) | 0.801199 | 0.188844 | ||||||||
\(19\) | 6.23135 | 1.42957 | 0.714785 | − | 0.699345i | \(-0.246525\pi\) | ||||
0.714785 | + | 0.699345i | \(0.246525\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −7.15731 | −1.56185 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 1.11595 | 0.232692 | 0.116346 | − | 0.993209i | \(-0.462882\pi\) | ||||
0.116346 | + | 0.993209i | \(0.462882\pi\) | |||||||
\(24\) | 1.48284 | 0.302682 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −3.11595 | −0.611088 | ||||||||
\(27\) | 5.63655 | 1.08476 | ||||||||
\(28\) | 4.82678 | 0.912175 | ||||||||
\(29\) | 3.16385 | 0.587512 | 0.293756 | − | 0.955880i | \(-0.405095\pi\) | ||||
0.293756 | + | 0.955880i | \(0.405095\pi\) | |||||||
\(30\) | −1.48284 | −0.270727 | ||||||||
\(31\) | −4.13157 | −0.742052 | −0.371026 | − | 0.928623i | \(-0.620994\pi\) | ||||
−0.371026 | + | 0.928623i | \(0.620994\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.48284 | 0.258129 | ||||||||
\(34\) | −7.03311 | −1.20617 | ||||||||
\(35\) | −4.82678 | −0.815874 | ||||||||
\(36\) | −0.801199 | −0.133533 | ||||||||
\(37\) | 3.75260 | 0.616924 | 0.308462 | − | 0.951237i | \(-0.400186\pi\) | ||||
0.308462 | + | 0.951237i | \(0.400186\pi\) | |||||||
\(38\) | −6.23135 | −1.01086 | ||||||||
\(39\) | −4.62044 | −0.739863 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −5.76616 | −0.900524 | −0.450262 | − | 0.892897i | \(-0.648669\pi\) | ||||
−0.450262 | + | 0.892897i | \(0.648669\pi\) | |||||||
\(42\) | 7.15731 | 1.10440 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 0.801199 | 0.119436 | ||||||||
\(46\) | −1.11595 | −0.164538 | ||||||||
\(47\) | 10.3447 | 1.50893 | 0.754464 | − | 0.656342i | \(-0.227897\pi\) | ||||
0.754464 | + | 0.656342i | \(0.227897\pi\) | |||||||
\(48\) | −1.48284 | −0.214029 | ||||||||
\(49\) | 16.2978 | 2.32825 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −10.4289 | −1.46034 | ||||||||
\(52\) | 3.11595 | 0.432105 | ||||||||
\(53\) | −10.1774 | −1.39797 | −0.698987 | − | 0.715134i | \(-0.746366\pi\) | ||||
−0.698987 | + | 0.715134i | \(0.746366\pi\) | |||||||
\(54\) | −5.63655 | −0.767038 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | −4.82678 | −0.645005 | ||||||||
\(57\) | −9.24006 | −1.22388 | ||||||||
\(58\) | −3.16385 | −0.415434 | ||||||||
\(59\) | 9.27380 | 1.20735 | 0.603673 | − | 0.797232i | \(-0.293703\pi\) | ||||
0.603673 | + | 0.797232i | \(0.293703\pi\) | |||||||
\(60\) | 1.48284 | 0.191433 | ||||||||
\(61\) | 11.2530 | 1.44080 | 0.720400 | − | 0.693559i | \(-0.243958\pi\) | ||||
0.720400 | + | 0.693559i | \(0.243958\pi\) | |||||||
\(62\) | 4.13157 | 0.524710 | ||||||||
\(63\) | −3.86721 | −0.487223 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.11595 | −0.386486 | ||||||||
\(66\) | −1.48284 | −0.182524 | ||||||||
\(67\) | −11.3564 | −1.38740 | −0.693701 | − | 0.720263i | \(-0.744021\pi\) | ||||
−0.693701 | + | 0.720263i | \(0.744021\pi\) | |||||||
\(68\) | 7.03311 | 0.852890 | ||||||||
\(69\) | −1.65477 | −0.199211 | ||||||||
\(70\) | 4.82678 | 0.576910 | ||||||||
\(71\) | 1.75115 | 0.207823 | 0.103912 | − | 0.994587i | \(-0.466864\pi\) | ||||
0.103912 | + | 0.994587i | \(0.466864\pi\) | |||||||
\(72\) | 0.801199 | 0.0944222 | ||||||||
\(73\) | 6.29746 | 0.737062 | 0.368531 | − | 0.929615i | \(-0.379861\pi\) | ||||
0.368531 | + | 0.929615i | \(0.379861\pi\) | |||||||
\(74\) | −3.75260 | −0.436231 | ||||||||
\(75\) | −1.48284 | −0.171223 | ||||||||
\(76\) | 6.23135 | 0.714785 | ||||||||
\(77\) | −4.82678 | −0.550062 | ||||||||
\(78\) | 4.62044 | 0.523162 | ||||||||
\(79\) | −9.80398 | −1.10303 | −0.551517 | − | 0.834164i | \(-0.685951\pi\) | ||||
−0.551517 | + | 0.834164i | \(0.685951\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −5.95448 | −0.661609 | ||||||||
\(82\) | 5.76616 | 0.636766 | ||||||||
\(83\) | −7.75457 | −0.851174 | −0.425587 | − | 0.904917i | \(-0.639932\pi\) | ||||
−0.425587 | + | 0.904917i | \(0.639932\pi\) | |||||||
\(84\) | −7.15731 | −0.780927 | ||||||||
\(85\) | −7.03311 | −0.762848 | ||||||||
\(86\) | −1.00000 | −0.107833 | ||||||||
\(87\) | −4.69147 | −0.502978 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | −11.1654 | −1.18353 | −0.591764 | − | 0.806111i | \(-0.701568\pi\) | ||||
−0.591764 | + | 0.806111i | \(0.701568\pi\) | |||||||
\(90\) | −0.801199 | −0.0844538 | ||||||||
\(91\) | 15.0400 | 1.57662 | ||||||||
\(92\) | 1.11595 | 0.116346 | ||||||||
\(93\) | 6.12644 | 0.635282 | ||||||||
\(94\) | −10.3447 | −1.06697 | ||||||||
\(95\) | −6.23135 | −0.639323 | ||||||||
\(96\) | 1.48284 | 0.151341 | ||||||||
\(97\) | −0.459065 | −0.0466110 | −0.0233055 | − | 0.999728i | \(-0.507419\pi\) | ||||
−0.0233055 | + | 0.999728i | \(0.507419\pi\) | |||||||
\(98\) | −16.2978 | −1.64632 | ||||||||
\(99\) | 0.801199 | 0.0805236 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −5.99326 | −0.596351 | −0.298176 | − | 0.954511i | \(-0.596378\pi\) | ||||
−0.298176 | + | 0.954511i | \(0.596378\pi\) | |||||||
\(102\) | 10.4289 | 1.03262 | ||||||||
\(103\) | 12.0077 | 1.18315 | 0.591575 | − | 0.806250i | \(-0.298506\pi\) | ||||
0.591575 | + | 0.806250i | \(0.298506\pi\) | |||||||
\(104\) | −3.11595 | −0.305544 | ||||||||
\(105\) | 7.15731 | 0.698482 | ||||||||
\(106\) | 10.1774 | 0.988517 | ||||||||
\(107\) | 2.10185 | 0.203193 | 0.101597 | − | 0.994826i | \(-0.467605\pi\) | ||||
0.101597 | + | 0.994826i | \(0.467605\pi\) | |||||||
\(108\) | 5.63655 | 0.542378 | ||||||||
\(109\) | 7.83137 | 0.750109 | 0.375055 | − | 0.927003i | \(-0.377624\pi\) | ||||
0.375055 | + | 0.927003i | \(0.377624\pi\) | |||||||
\(110\) | −1.00000 | −0.0953463 | ||||||||
\(111\) | −5.56449 | −0.528158 | ||||||||
\(112\) | 4.82678 | 0.456088 | ||||||||
\(113\) | −2.25538 | −0.212169 | −0.106084 | − | 0.994357i | \(-0.533831\pi\) | ||||
−0.106084 | + | 0.994357i | \(0.533831\pi\) | |||||||
\(114\) | 9.24006 | 0.865411 | ||||||||
\(115\) | −1.11595 | −0.104063 | ||||||||
\(116\) | 3.16385 | 0.293756 | ||||||||
\(117\) | −2.49650 | −0.230801 | ||||||||
\(118\) | −9.27380 | −0.853723 | ||||||||
\(119\) | 33.9472 | 3.11194 | ||||||||
\(120\) | −1.48284 | −0.135364 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −11.2530 | −1.01880 | ||||||||
\(123\) | 8.55027 | 0.770952 | ||||||||
\(124\) | −4.13157 | −0.371026 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 3.86721 | 0.344518 | ||||||||
\(127\) | −20.9378 | −1.85793 | −0.928963 | − | 0.370173i | \(-0.879298\pi\) | ||||
−0.928963 | + | 0.370173i | \(0.879298\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −1.48284 | −0.130556 | ||||||||
\(130\) | 3.11595 | 0.273287 | ||||||||
\(131\) | 1.76078 | 0.153840 | 0.0769200 | − | 0.997037i | \(-0.475491\pi\) | ||||
0.0769200 | + | 0.997037i | \(0.475491\pi\) | |||||||
\(132\) | 1.48284 | 0.129064 | ||||||||
\(133\) | 30.0773 | 2.60803 | ||||||||
\(134\) | 11.3564 | 0.981041 | ||||||||
\(135\) | −5.63655 | −0.485117 | ||||||||
\(136\) | −7.03311 | −0.603084 | ||||||||
\(137\) | 9.43115 | 0.805758 | 0.402879 | − | 0.915253i | \(-0.368010\pi\) | ||||
0.402879 | + | 0.915253i | \(0.368010\pi\) | |||||||
\(138\) | 1.65477 | 0.140863 | ||||||||
\(139\) | 16.0028 | 1.35734 | 0.678670 | − | 0.734444i | \(-0.262557\pi\) | ||||
0.678670 | + | 0.734444i | \(0.262557\pi\) | |||||||
\(140\) | −4.82678 | −0.407937 | ||||||||
\(141\) | −15.3395 | −1.29182 | ||||||||
\(142\) | −1.75115 | −0.146953 | ||||||||
\(143\) | −3.11595 | −0.260569 | ||||||||
\(144\) | −0.801199 | −0.0667666 | ||||||||
\(145\) | −3.16385 | −0.262744 | ||||||||
\(146\) | −6.29746 | −0.521182 | ||||||||
\(147\) | −24.1669 | −1.99325 | ||||||||
\(148\) | 3.75260 | 0.308462 | ||||||||
\(149\) | 4.39902 | 0.360382 | 0.180191 | − | 0.983632i | \(-0.442328\pi\) | ||||
0.180191 | + | 0.983632i | \(0.442328\pi\) | |||||||
\(150\) | 1.48284 | 0.121073 | ||||||||
\(151\) | −18.2702 | −1.48680 | −0.743402 | − | 0.668845i | \(-0.766789\pi\) | ||||
−0.743402 | + | 0.668845i | \(0.766789\pi\) | |||||||
\(152\) | −6.23135 | −0.505429 | ||||||||
\(153\) | −5.63492 | −0.455556 | ||||||||
\(154\) | 4.82678 | 0.388953 | ||||||||
\(155\) | 4.13157 | 0.331856 | ||||||||
\(156\) | −4.62044 | −0.369931 | ||||||||
\(157\) | −8.48633 | −0.677283 | −0.338641 | − | 0.940916i | \(-0.609967\pi\) | ||||
−0.338641 | + | 0.940916i | \(0.609967\pi\) | |||||||
\(158\) | 9.80398 | 0.779963 | ||||||||
\(159\) | 15.0914 | 1.19683 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 5.38644 | 0.424511 | ||||||||
\(162\) | 5.95448 | 0.467828 | ||||||||
\(163\) | −5.34228 | −0.418440 | −0.209220 | − | 0.977869i | \(-0.567092\pi\) | ||||
−0.209220 | + | 0.977869i | \(0.567092\pi\) | |||||||
\(164\) | −5.76616 | −0.450262 | ||||||||
\(165\) | −1.48284 | −0.115439 | ||||||||
\(166\) | 7.75457 | 0.601871 | ||||||||
\(167\) | −24.0863 | −1.86385 | −0.931925 | − | 0.362651i | \(-0.881872\pi\) | ||||
−0.931925 | + | 0.362651i | \(0.881872\pi\) | |||||||
\(168\) | 7.15731 | 0.552199 | ||||||||
\(169\) | −3.29085 | −0.253142 | ||||||||
\(170\) | 7.03311 | 0.539415 | ||||||||
\(171\) | −4.99255 | −0.381790 | ||||||||
\(172\) | 1.00000 | 0.0762493 | ||||||||
\(173\) | −21.9002 | −1.66504 | −0.832522 | − | 0.553992i | \(-0.813104\pi\) | ||||
−0.832522 | + | 0.553992i | \(0.813104\pi\) | |||||||
\(174\) | 4.69147 | 0.355659 | ||||||||
\(175\) | 4.82678 | 0.364870 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | −13.7515 | −1.03363 | ||||||||
\(178\) | 11.1654 | 0.836880 | ||||||||
\(179\) | 6.07104 | 0.453770 | 0.226885 | − | 0.973921i | \(-0.427146\pi\) | ||||
0.226885 | + | 0.973921i | \(0.427146\pi\) | |||||||
\(180\) | 0.801199 | 0.0597179 | ||||||||
\(181\) | 10.3540 | 0.769606 | 0.384803 | − | 0.922999i | \(-0.374269\pi\) | ||||
0.384803 | + | 0.922999i | \(0.374269\pi\) | |||||||
\(182\) | −15.0400 | −1.11484 | ||||||||
\(183\) | −16.6864 | −1.23349 | ||||||||
\(184\) | −1.11595 | −0.0822690 | ||||||||
\(185\) | −3.75260 | −0.275897 | ||||||||
\(186\) | −6.12644 | −0.449212 | ||||||||
\(187\) | −7.03311 | −0.514312 | ||||||||
\(188\) | 10.3447 | 0.754464 | ||||||||
\(189\) | 27.2064 | 1.97897 | ||||||||
\(190\) | 6.23135 | 0.452069 | ||||||||
\(191\) | −15.9490 | −1.15403 | −0.577015 | − | 0.816733i | \(-0.695783\pi\) | ||||
−0.577015 | + | 0.816733i | \(0.695783\pi\) | |||||||
\(192\) | −1.48284 | −0.107014 | ||||||||
\(193\) | −2.80456 | −0.201877 | −0.100938 | − | 0.994893i | \(-0.532185\pi\) | ||||
−0.100938 | + | 0.994893i | \(0.532185\pi\) | |||||||
\(194\) | 0.459065 | 0.0329590 | ||||||||
\(195\) | 4.62044 | 0.330877 | ||||||||
\(196\) | 16.2978 | 1.16413 | ||||||||
\(197\) | 15.2867 | 1.08914 | 0.544568 | − | 0.838717i | \(-0.316694\pi\) | ||||
0.544568 | + | 0.838717i | \(0.316694\pi\) | |||||||
\(198\) | −0.801199 | −0.0569388 | ||||||||
\(199\) | −10.4346 | −0.739686 | −0.369843 | − | 0.929094i | \(-0.620589\pi\) | ||||
−0.369843 | + | 0.929094i | \(0.620589\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 16.8396 | 1.18778 | ||||||||
\(202\) | 5.99326 | 0.421684 | ||||||||
\(203\) | 15.2712 | 1.07183 | ||||||||
\(204\) | −10.4289 | −0.730172 | ||||||||
\(205\) | 5.76616 | 0.402726 | ||||||||
\(206\) | −12.0077 | −0.836614 | ||||||||
\(207\) | −0.894099 | −0.0621442 | ||||||||
\(208\) | 3.11595 | 0.216052 | ||||||||
\(209\) | −6.23135 | −0.431031 | ||||||||
\(210\) | −7.15731 | −0.493902 | ||||||||
\(211\) | 18.4743 | 1.27183 | 0.635913 | − | 0.771761i | \(-0.280624\pi\) | ||||
0.635913 | + | 0.771761i | \(0.280624\pi\) | |||||||
\(212\) | −10.1774 | −0.698987 | ||||||||
\(213\) | −2.59666 | −0.177921 | ||||||||
\(214\) | −2.10185 | −0.143679 | ||||||||
\(215\) | −1.00000 | −0.0681994 | ||||||||
\(216\) | −5.63655 | −0.383519 | ||||||||
\(217\) | −19.9422 | −1.35376 | ||||||||
\(218\) | −7.83137 | −0.530407 | ||||||||
\(219\) | −9.33810 | −0.631010 | ||||||||
\(220\) | 1.00000 | 0.0674200 | ||||||||
\(221\) | 21.9148 | 1.47415 | ||||||||
\(222\) | 5.56449 | 0.373464 | ||||||||
\(223\) | 5.99924 | 0.401739 | 0.200870 | − | 0.979618i | \(-0.435623\pi\) | ||||
0.200870 | + | 0.979618i | \(0.435623\pi\) | |||||||
\(224\) | −4.82678 | −0.322503 | ||||||||
\(225\) | −0.801199 | −0.0534133 | ||||||||
\(226\) | 2.25538 | 0.150026 | ||||||||
\(227\) | −9.51703 | −0.631668 | −0.315834 | − | 0.948815i | \(-0.602284\pi\) | ||||
−0.315834 | + | 0.948815i | \(0.602284\pi\) | |||||||
\(228\) | −9.24006 | −0.611938 | ||||||||
\(229\) | 21.3780 | 1.41270 | 0.706349 | − | 0.707863i | \(-0.250341\pi\) | ||||
0.706349 | + | 0.707863i | \(0.250341\pi\) | |||||||
\(230\) | 1.11595 | 0.0735836 | ||||||||
\(231\) | 7.15731 | 0.470917 | ||||||||
\(232\) | −3.16385 | −0.207717 | ||||||||
\(233\) | −26.2946 | −1.72262 | −0.861308 | − | 0.508083i | \(-0.830354\pi\) | ||||
−0.861308 | + | 0.508083i | \(0.830354\pi\) | |||||||
\(234\) | 2.49650 | 0.163201 | ||||||||
\(235\) | −10.3447 | −0.674813 | ||||||||
\(236\) | 9.27380 | 0.603673 | ||||||||
\(237\) | 14.5377 | 0.944325 | ||||||||
\(238\) | −33.9472 | −2.20047 | ||||||||
\(239\) | −10.0042 | −0.647115 | −0.323558 | − | 0.946209i | \(-0.604879\pi\) | ||||
−0.323558 | + | 0.946209i | \(0.604879\pi\) | |||||||
\(240\) | 1.48284 | 0.0957166 | ||||||||
\(241\) | 9.71227 | 0.625622 | 0.312811 | − | 0.949815i | \(-0.398729\pi\) | ||||
0.312811 | + | 0.949815i | \(0.398729\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | −8.08014 | −0.518341 | ||||||||
\(244\) | 11.2530 | 0.720400 | ||||||||
\(245\) | −16.2978 | −1.04123 | ||||||||
\(246\) | −8.55027 | −0.545145 | ||||||||
\(247\) | 19.4166 | 1.23545 | ||||||||
\(248\) | 4.13157 | 0.262355 | ||||||||
\(249\) | 11.4987 | 0.728704 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 25.5642 | 1.61360 | 0.806798 | − | 0.590828i | \(-0.201199\pi\) | ||||
0.806798 | + | 0.590828i | \(0.201199\pi\) | |||||||
\(252\) | −3.86721 | −0.243611 | ||||||||
\(253\) | −1.11595 | −0.0701592 | ||||||||
\(254\) | 20.9378 | 1.31375 | ||||||||
\(255\) | 10.4289 | 0.653086 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 4.82868 | 0.301205 | 0.150603 | − | 0.988594i | \(-0.451879\pi\) | ||||
0.150603 | + | 0.988594i | \(0.451879\pi\) | |||||||
\(258\) | 1.48284 | 0.0923173 | ||||||||
\(259\) | 18.1130 | 1.12548 | ||||||||
\(260\) | −3.11595 | −0.193243 | ||||||||
\(261\) | −2.53488 | −0.156905 | ||||||||
\(262\) | −1.76078 | −0.108781 | ||||||||
\(263\) | −10.2445 | −0.631701 | −0.315850 | − | 0.948809i | \(-0.602290\pi\) | ||||
−0.315850 | + | 0.948809i | \(0.602290\pi\) | |||||||
\(264\) | −1.48284 | −0.0912622 | ||||||||
\(265\) | 10.1774 | 0.625193 | ||||||||
\(266\) | −30.0773 | −1.84416 | ||||||||
\(267\) | 16.5564 | 1.01324 | ||||||||
\(268\) | −11.3564 | −0.693701 | ||||||||
\(269\) | −13.6765 | −0.833870 | −0.416935 | − | 0.908936i | \(-0.636896\pi\) | ||||
−0.416935 | + | 0.908936i | \(0.636896\pi\) | |||||||
\(270\) | 5.63655 | 0.343030 | ||||||||
\(271\) | −11.1336 | −0.676318 | −0.338159 | − | 0.941089i | \(-0.609804\pi\) | ||||
−0.338159 | + | 0.941089i | \(0.609804\pi\) | |||||||
\(272\) | 7.03311 | 0.426445 | ||||||||
\(273\) | −22.3018 | −1.34977 | ||||||||
\(274\) | −9.43115 | −0.569757 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | −1.65477 | −0.0996055 | ||||||||
\(277\) | 20.9792 | 1.26052 | 0.630258 | − | 0.776386i | \(-0.282949\pi\) | ||||
0.630258 | + | 0.776386i | \(0.282949\pi\) | |||||||
\(278\) | −16.0028 | −0.959784 | ||||||||
\(279\) | 3.31021 | 0.198177 | ||||||||
\(280\) | 4.82678 | 0.288455 | ||||||||
\(281\) | −4.12104 | −0.245841 | −0.122920 | − | 0.992417i | \(-0.539226\pi\) | ||||
−0.122920 | + | 0.992417i | \(0.539226\pi\) | |||||||
\(282\) | 15.3395 | 0.913452 | ||||||||
\(283\) | 28.9926 | 1.72343 | 0.861716 | − | 0.507391i | \(-0.169390\pi\) | ||||
0.861716 | + | 0.507391i | \(0.169390\pi\) | |||||||
\(284\) | 1.75115 | 0.103912 | ||||||||
\(285\) | 9.24006 | 0.547334 | ||||||||
\(286\) | 3.11595 | 0.184250 | ||||||||
\(287\) | −27.8320 | −1.64287 | ||||||||
\(288\) | 0.801199 | 0.0472111 | ||||||||
\(289\) | 32.4646 | 1.90968 | ||||||||
\(290\) | 3.16385 | 0.185788 | ||||||||
\(291\) | 0.680718 | 0.0399044 | ||||||||
\(292\) | 6.29746 | 0.368531 | ||||||||
\(293\) | −9.42775 | −0.550775 | −0.275388 | − | 0.961333i | \(-0.588806\pi\) | ||||
−0.275388 | + | 0.961333i | \(0.588806\pi\) | |||||||
\(294\) | 24.1669 | 1.40944 | ||||||||
\(295\) | −9.27380 | −0.539942 | ||||||||
\(296\) | −3.75260 | −0.218115 | ||||||||
\(297\) | −5.63655 | −0.327066 | ||||||||
\(298\) | −4.39902 | −0.254828 | ||||||||
\(299\) | 3.47725 | 0.201094 | ||||||||
\(300\) | −1.48284 | −0.0856115 | ||||||||
\(301\) | 4.82678 | 0.278211 | ||||||||
\(302\) | 18.2702 | 1.05133 | ||||||||
\(303\) | 8.88701 | 0.510545 | ||||||||
\(304\) | 6.23135 | 0.357392 | ||||||||
\(305\) | −11.2530 | −0.644345 | ||||||||
\(306\) | 5.63492 | 0.322127 | ||||||||
\(307\) | 20.6914 | 1.18092 | 0.590460 | − | 0.807067i | \(-0.298946\pi\) | ||||
0.590460 | + | 0.807067i | \(0.298946\pi\) | |||||||
\(308\) | −4.82678 | −0.275031 | ||||||||
\(309\) | −17.8054 | −1.01291 | ||||||||
\(310\) | −4.13157 | −0.234657 | ||||||||
\(311\) | 32.6114 | 1.84922 | 0.924612 | − | 0.380911i | \(-0.124389\pi\) | ||||
0.924612 | + | 0.380911i | \(0.124389\pi\) | |||||||
\(312\) | 4.62044 | 0.261581 | ||||||||
\(313\) | 30.0632 | 1.69927 | 0.849636 | − | 0.527370i | \(-0.176822\pi\) | ||||
0.849636 | + | 0.527370i | \(0.176822\pi\) | |||||||
\(314\) | 8.48633 | 0.478911 | ||||||||
\(315\) | 3.86721 | 0.217893 | ||||||||
\(316\) | −9.80398 | −0.551517 | ||||||||
\(317\) | −5.56557 | −0.312593 | −0.156297 | − | 0.987710i | \(-0.549956\pi\) | ||||
−0.156297 | + | 0.987710i | \(0.549956\pi\) | |||||||
\(318\) | −15.0914 | −0.846285 | ||||||||
\(319\) | −3.16385 | −0.177142 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −3.11669 | −0.173957 | ||||||||
\(322\) | −5.38644 | −0.300175 | ||||||||
\(323\) | 43.8257 | 2.43853 | ||||||||
\(324\) | −5.95448 | −0.330805 | ||||||||
\(325\) | 3.11595 | 0.172842 | ||||||||
\(326\) | 5.34228 | 0.295882 | ||||||||
\(327\) | −11.6126 | −0.642180 | ||||||||
\(328\) | 5.76616 | 0.318383 | ||||||||
\(329\) | 49.9315 | 2.75281 | ||||||||
\(330\) | 1.48284 | 0.0816274 | ||||||||
\(331\) | −6.80814 | −0.374209 | −0.187105 | − | 0.982340i | \(-0.559910\pi\) | ||||
−0.187105 | + | 0.982340i | \(0.559910\pi\) | |||||||
\(332\) | −7.75457 | −0.425587 | ||||||||
\(333\) | −3.00658 | −0.164760 | ||||||||
\(334\) | 24.0863 | 1.31794 | ||||||||
\(335\) | 11.3564 | 0.620465 | ||||||||
\(336\) | −7.15731 | −0.390464 | ||||||||
\(337\) | −17.6757 | −0.962854 | −0.481427 | − | 0.876486i | \(-0.659881\pi\) | ||||
−0.481427 | + | 0.876486i | \(0.659881\pi\) | |||||||
\(338\) | 3.29085 | 0.178999 | ||||||||
\(339\) | 3.34436 | 0.181641 | ||||||||
\(340\) | −7.03311 | −0.381424 | ||||||||
\(341\) | 4.13157 | 0.223737 | ||||||||
\(342\) | 4.99255 | 0.269966 | ||||||||
\(343\) | 44.8783 | 2.42320 | ||||||||
\(344\) | −1.00000 | −0.0539164 | ||||||||
\(345\) | 1.65477 | 0.0890899 | ||||||||
\(346\) | 21.9002 | 1.17736 | ||||||||
\(347\) | −1.50630 | −0.0808623 | −0.0404311 | − | 0.999182i | \(-0.512873\pi\) | ||||
−0.0404311 | + | 0.999182i | \(0.512873\pi\) | |||||||
\(348\) | −4.69147 | −0.251489 | ||||||||
\(349\) | 6.73446 | 0.360487 | 0.180244 | − | 0.983622i | \(-0.442311\pi\) | ||||
0.180244 | + | 0.983622i | \(0.442311\pi\) | |||||||
\(350\) | −4.82678 | −0.258002 | ||||||||
\(351\) | 17.5632 | 0.937455 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | 2.06180 | 0.109739 | 0.0548693 | − | 0.998494i | \(-0.482526\pi\) | ||||
0.0548693 | + | 0.998494i | \(0.482526\pi\) | |||||||
\(354\) | 13.7515 | 0.730885 | ||||||||
\(355\) | −1.75115 | −0.0929413 | ||||||||
\(356\) | −11.1654 | −0.591764 | ||||||||
\(357\) | −50.3382 | −2.66418 | ||||||||
\(358\) | −6.07104 | −0.320864 | ||||||||
\(359\) | 14.9385 | 0.788422 | 0.394211 | − | 0.919020i | \(-0.371018\pi\) | ||||
0.394211 | + | 0.919020i | \(0.371018\pi\) | |||||||
\(360\) | −0.801199 | −0.0422269 | ||||||||
\(361\) | 19.8297 | 1.04367 | ||||||||
\(362\) | −10.3540 | −0.544194 | ||||||||
\(363\) | −1.48284 | −0.0778287 | ||||||||
\(364\) | 15.0400 | 0.788310 | ||||||||
\(365\) | −6.29746 | −0.329624 | ||||||||
\(366\) | 16.6864 | 0.872210 | ||||||||
\(367\) | 14.7313 | 0.768966 | 0.384483 | − | 0.923132i | \(-0.374380\pi\) | ||||
0.384483 | + | 0.923132i | \(0.374380\pi\) | |||||||
\(368\) | 1.11595 | 0.0581729 | ||||||||
\(369\) | 4.61985 | 0.240500 | ||||||||
\(370\) | 3.75260 | 0.195088 | ||||||||
\(371\) | −49.1241 | −2.55039 | ||||||||
\(372\) | 6.12644 | 0.317641 | ||||||||
\(373\) | −13.7561 | −0.712263 | −0.356131 | − | 0.934436i | \(-0.615904\pi\) | ||||
−0.356131 | + | 0.934436i | \(0.615904\pi\) | |||||||
\(374\) | 7.03311 | 0.363673 | ||||||||
\(375\) | 1.48284 | 0.0765733 | ||||||||
\(376\) | −10.3447 | −0.533486 | ||||||||
\(377\) | 9.85841 | 0.507734 | ||||||||
\(378\) | −27.2064 | −1.39935 | ||||||||
\(379\) | −19.6061 | −1.00710 | −0.503550 | − | 0.863966i | \(-0.667973\pi\) | ||||
−0.503550 | + | 0.863966i | \(0.667973\pi\) | |||||||
\(380\) | −6.23135 | −0.319661 | ||||||||
\(381\) | 31.0472 | 1.59060 | ||||||||
\(382\) | 15.9490 | 0.816023 | ||||||||
\(383\) | 32.1235 | 1.64143 | 0.820716 | − | 0.571336i | \(-0.193575\pi\) | ||||
0.820716 | + | 0.571336i | \(0.193575\pi\) | |||||||
\(384\) | 1.48284 | 0.0756706 | ||||||||
\(385\) | 4.82678 | 0.245995 | ||||||||
\(386\) | 2.80456 | 0.142749 | ||||||||
\(387\) | −0.801199 | −0.0407273 | ||||||||
\(388\) | −0.459065 | −0.0233055 | ||||||||
\(389\) | −23.0968 | −1.17105 | −0.585527 | − | 0.810653i | \(-0.699112\pi\) | ||||
−0.585527 | + | 0.810653i | \(0.699112\pi\) | |||||||
\(390\) | −4.62044 | −0.233965 | ||||||||
\(391\) | 7.84860 | 0.396921 | ||||||||
\(392\) | −16.2978 | −0.823162 | ||||||||
\(393\) | −2.61095 | −0.131705 | ||||||||
\(394\) | −15.2867 | −0.770135 | ||||||||
\(395\) | 9.80398 | 0.493292 | ||||||||
\(396\) | 0.801199 | 0.0402618 | ||||||||
\(397\) | 36.8054 | 1.84721 | 0.923604 | − | 0.383348i | \(-0.125229\pi\) | ||||
0.923604 | + | 0.383348i | \(0.125229\pi\) | |||||||
\(398\) | 10.4346 | 0.523037 | ||||||||
\(399\) | −44.5997 | −2.23278 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −6.49490 | −0.324340 | −0.162170 | − | 0.986763i | \(-0.551849\pi\) | ||||
−0.162170 | + | 0.986763i | \(0.551849\pi\) | |||||||
\(402\) | −16.8396 | −0.839884 | ||||||||
\(403\) | −12.8738 | −0.641288 | ||||||||
\(404\) | −5.99326 | −0.298176 | ||||||||
\(405\) | 5.95448 | 0.295881 | ||||||||
\(406\) | −15.2712 | −0.757897 | ||||||||
\(407\) | −3.75260 | −0.186010 | ||||||||
\(408\) | 10.4289 | 0.516310 | ||||||||
\(409\) | 18.1660 | 0.898249 | 0.449125 | − | 0.893469i | \(-0.351736\pi\) | ||||
0.449125 | + | 0.893469i | \(0.351736\pi\) | |||||||
\(410\) | −5.76616 | −0.284771 | ||||||||
\(411\) | −13.9848 | −0.689821 | ||||||||
\(412\) | 12.0077 | 0.591575 | ||||||||
\(413\) | 44.7626 | 2.20262 | ||||||||
\(414\) | 0.894099 | 0.0439426 | ||||||||
\(415\) | 7.75457 | 0.380657 | ||||||||
\(416\) | −3.11595 | −0.152772 | ||||||||
\(417\) | −23.7295 | −1.16204 | ||||||||
\(418\) | 6.23135 | 0.304785 | ||||||||
\(419\) | −8.59949 | −0.420113 | −0.210056 | − | 0.977689i | \(-0.567365\pi\) | ||||
−0.210056 | + | 0.977689i | \(0.567365\pi\) | |||||||
\(420\) | 7.15731 | 0.349241 | ||||||||
\(421\) | −30.7705 | −1.49966 | −0.749831 | − | 0.661630i | \(-0.769865\pi\) | ||||
−0.749831 | + | 0.661630i | \(0.769865\pi\) | |||||||
\(422\) | −18.4743 | −0.899317 | ||||||||
\(423\) | −8.28816 | −0.402984 | ||||||||
\(424\) | 10.1774 | 0.494259 | ||||||||
\(425\) | 7.03311 | 0.341156 | ||||||||
\(426\) | 2.59666 | 0.125809 | ||||||||
\(427\) | 54.3157 | 2.62852 | ||||||||
\(428\) | 2.10185 | 0.101597 | ||||||||
\(429\) | 4.62044 | 0.223077 | ||||||||
\(430\) | 1.00000 | 0.0482243 | ||||||||
\(431\) | 29.0510 | 1.39934 | 0.699669 | − | 0.714467i | \(-0.253331\pi\) | ||||
0.699669 | + | 0.714467i | \(0.253331\pi\) | |||||||
\(432\) | 5.63655 | 0.271189 | ||||||||
\(433\) | −10.6572 | −0.512152 | −0.256076 | − | 0.966657i | \(-0.582430\pi\) | ||||
−0.256076 | + | 0.966657i | \(0.582430\pi\) | |||||||
\(434\) | 19.9422 | 0.957255 | ||||||||
\(435\) | 4.69147 | 0.224939 | ||||||||
\(436\) | 7.83137 | 0.375055 | ||||||||
\(437\) | 6.95388 | 0.332649 | ||||||||
\(438\) | 9.33810 | 0.446192 | ||||||||
\(439\) | 8.49937 | 0.405653 | 0.202826 | − | 0.979215i | \(-0.434987\pi\) | ||||
0.202826 | + | 0.979215i | \(0.434987\pi\) | |||||||
\(440\) | −1.00000 | −0.0476731 | ||||||||
\(441\) | −13.0578 | −0.621798 | ||||||||
\(442\) | −21.9148 | −1.04238 | ||||||||
\(443\) | 12.7886 | 0.607604 | 0.303802 | − | 0.952735i | \(-0.401744\pi\) | ||||
0.303802 | + | 0.952735i | \(0.401744\pi\) | |||||||
\(444\) | −5.56449 | −0.264079 | ||||||||
\(445\) | 11.1654 | 0.529290 | ||||||||
\(446\) | −5.99924 | −0.284072 | ||||||||
\(447\) | −6.52302 | −0.308528 | ||||||||
\(448\) | 4.82678 | 0.228044 | ||||||||
\(449\) | −10.0081 | −0.472312 | −0.236156 | − | 0.971715i | \(-0.575888\pi\) | ||||
−0.236156 | + | 0.971715i | \(0.575888\pi\) | |||||||
\(450\) | 0.801199 | 0.0377689 | ||||||||
\(451\) | 5.76616 | 0.271518 | ||||||||
\(452\) | −2.25538 | −0.106084 | ||||||||
\(453\) | 27.0916 | 1.27288 | ||||||||
\(454\) | 9.51703 | 0.446656 | ||||||||
\(455\) | −15.0400 | −0.705086 | ||||||||
\(456\) | 9.24006 | 0.432706 | ||||||||
\(457\) | −23.1307 | −1.08201 | −0.541004 | − | 0.841020i | \(-0.681956\pi\) | ||||
−0.541004 | + | 0.841020i | \(0.681956\pi\) | |||||||
\(458\) | −21.3780 | −0.998929 | ||||||||
\(459\) | 39.6425 | 1.85035 | ||||||||
\(460\) | −1.11595 | −0.0520315 | ||||||||
\(461\) | −7.38407 | −0.343910 | −0.171955 | − | 0.985105i | \(-0.555008\pi\) | ||||
−0.171955 | + | 0.985105i | \(0.555008\pi\) | |||||||
\(462\) | −7.15731 | −0.332988 | ||||||||
\(463\) | −26.1690 | −1.21618 | −0.608088 | − | 0.793870i | \(-0.708063\pi\) | ||||
−0.608088 | + | 0.793870i | \(0.708063\pi\) | |||||||
\(464\) | 3.16385 | 0.146878 | ||||||||
\(465\) | −6.12644 | −0.284107 | ||||||||
\(466\) | 26.2946 | 1.21807 | ||||||||
\(467\) | −2.76399 | −0.127902 | −0.0639512 | − | 0.997953i | \(-0.520370\pi\) | ||||
−0.0639512 | + | 0.997953i | \(0.520370\pi\) | |||||||
\(468\) | −2.49650 | −0.115401 | ||||||||
\(469\) | −54.8147 | −2.53111 | ||||||||
\(470\) | 10.3447 | 0.477165 | ||||||||
\(471\) | 12.5838 | 0.579832 | ||||||||
\(472\) | −9.27380 | −0.426861 | ||||||||
\(473\) | −1.00000 | −0.0459800 | ||||||||
\(474\) | −14.5377 | −0.667738 | ||||||||
\(475\) | 6.23135 | 0.285914 | ||||||||
\(476\) | 33.9472 | 1.55597 | ||||||||
\(477\) | 8.15413 | 0.373352 | ||||||||
\(478\) | 10.0042 | 0.457579 | ||||||||
\(479\) | 36.2872 | 1.65800 | 0.829001 | − | 0.559247i | \(-0.188910\pi\) | ||||
0.829001 | + | 0.559247i | \(0.188910\pi\) | |||||||
\(480\) | −1.48284 | −0.0676819 | ||||||||
\(481\) | 11.6929 | 0.533151 | ||||||||
\(482\) | −9.71227 | −0.442382 | ||||||||
\(483\) | −7.98721 | −0.363431 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 0.459065 | 0.0208451 | ||||||||
\(486\) | 8.08014 | 0.366523 | ||||||||
\(487\) | 12.2972 | 0.557240 | 0.278620 | − | 0.960401i | \(-0.410123\pi\) | ||||
0.278620 | + | 0.960401i | \(0.410123\pi\) | |||||||
\(488\) | −11.2530 | −0.509400 | ||||||||
\(489\) | 7.92173 | 0.358233 | ||||||||
\(490\) | 16.2978 | 0.736258 | ||||||||
\(491\) | 20.5937 | 0.929383 | 0.464691 | − | 0.885473i | \(-0.346165\pi\) | ||||
0.464691 | + | 0.885473i | \(0.346165\pi\) | |||||||
\(492\) | 8.55027 | 0.385476 | ||||||||
\(493\) | 22.2517 | 1.00217 | ||||||||
\(494\) | −19.4166 | −0.873593 | ||||||||
\(495\) | −0.801199 | −0.0360112 | ||||||||
\(496\) | −4.13157 | −0.185513 | ||||||||
\(497\) | 8.45240 | 0.379142 | ||||||||
\(498\) | −11.4987 | −0.515271 | ||||||||
\(499\) | 10.9689 | 0.491038 | 0.245519 | − | 0.969392i | \(-0.421042\pi\) | ||||
0.245519 | + | 0.969392i | \(0.421042\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 35.7159 | 1.59567 | ||||||||
\(502\) | −25.5642 | −1.14098 | ||||||||
\(503\) | 6.60727 | 0.294603 | 0.147302 | − | 0.989092i | \(-0.452941\pi\) | ||||
0.147302 | + | 0.989092i | \(0.452941\pi\) | |||||||
\(504\) | 3.86721 | 0.172259 | ||||||||
\(505\) | 5.99326 | 0.266696 | ||||||||
\(506\) | 1.11595 | 0.0496101 | ||||||||
\(507\) | 4.87979 | 0.216719 | ||||||||
\(508\) | −20.9378 | −0.928963 | ||||||||
\(509\) | 28.0503 | 1.24331 | 0.621654 | − | 0.783292i | \(-0.286461\pi\) | ||||
0.621654 | + | 0.783292i | \(0.286461\pi\) | |||||||
\(510\) | −10.4289 | −0.461801 | ||||||||
\(511\) | 30.3964 | 1.34466 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 35.1233 | 1.55073 | ||||||||
\(514\) | −4.82868 | −0.212984 | ||||||||
\(515\) | −12.0077 | −0.529121 | ||||||||
\(516\) | −1.48284 | −0.0652782 | ||||||||
\(517\) | −10.3447 | −0.454959 | ||||||||
\(518\) | −18.1130 | −0.795838 | ||||||||
\(519\) | 32.4744 | 1.42547 | ||||||||
\(520\) | 3.11595 | 0.136643 | ||||||||
\(521\) | 37.5182 | 1.64370 | 0.821851 | − | 0.569702i | \(-0.192941\pi\) | ||||
0.821851 | + | 0.569702i | \(0.192941\pi\) | |||||||
\(522\) | 2.53488 | 0.110948 | ||||||||
\(523\) | 6.94141 | 0.303527 | 0.151763 | − | 0.988417i | \(-0.451505\pi\) | ||||
0.151763 | + | 0.988417i | \(0.451505\pi\) | |||||||
\(524\) | 1.76078 | 0.0769200 | ||||||||
\(525\) | −7.15731 | −0.312371 | ||||||||
\(526\) | 10.2445 | 0.446680 | ||||||||
\(527\) | −29.0578 | −1.26578 | ||||||||
\(528\) | 1.48284 | 0.0645321 | ||||||||
\(529\) | −21.7547 | −0.945855 | ||||||||
\(530\) | −10.1774 | −0.442078 | ||||||||
\(531\) | −7.43017 | −0.322442 | ||||||||
\(532\) | 30.0773 | 1.30402 | ||||||||
\(533\) | −17.9671 | −0.778241 | ||||||||
\(534\) | −16.5564 | −0.716466 | ||||||||
\(535\) | −2.10185 | −0.0908708 | ||||||||
\(536\) | 11.3564 | 0.490521 | ||||||||
\(537\) | −9.00235 | −0.388480 | ||||||||
\(538\) | 13.6765 | 0.589635 | ||||||||
\(539\) | −16.2978 | −0.701995 | ||||||||
\(540\) | −5.63655 | −0.242559 | ||||||||
\(541\) | 21.3494 | 0.917884 | 0.458942 | − | 0.888466i | \(-0.348229\pi\) | ||||
0.458942 | + | 0.888466i | \(0.348229\pi\) | |||||||
\(542\) | 11.1336 | 0.478229 | ||||||||
\(543\) | −15.3533 | −0.658872 | ||||||||
\(544\) | −7.03311 | −0.301542 | ||||||||
\(545\) | −7.83137 | −0.335459 | ||||||||
\(546\) | 22.3018 | 0.954431 | ||||||||
\(547\) | −9.21096 | −0.393832 | −0.196916 | − | 0.980420i | \(-0.563093\pi\) | ||||
−0.196916 | + | 0.980420i | \(0.563093\pi\) | |||||||
\(548\) | 9.43115 | 0.402879 | ||||||||
\(549\) | −9.01590 | −0.384789 | ||||||||
\(550\) | 1.00000 | 0.0426401 | ||||||||
\(551\) | 19.7151 | 0.839890 | ||||||||
\(552\) | 1.65477 | 0.0704317 | ||||||||
\(553\) | −47.3216 | −2.01232 | ||||||||
\(554\) | −20.9792 | −0.891319 | ||||||||
\(555\) | 5.56449 | 0.236199 | ||||||||
\(556\) | 16.0028 | 0.678670 | ||||||||
\(557\) | 0.983118 | 0.0416560 | 0.0208280 | − | 0.999783i | \(-0.493370\pi\) | ||||
0.0208280 | + | 0.999783i | \(0.493370\pi\) | |||||||
\(558\) | −3.31021 | −0.140132 | ||||||||
\(559\) | 3.11595 | 0.131791 | ||||||||
\(560\) | −4.82678 | −0.203969 | ||||||||
\(561\) | 10.4289 | 0.440310 | ||||||||
\(562\) | 4.12104 | 0.173836 | ||||||||
\(563\) | −5.42395 | −0.228592 | −0.114296 | − | 0.993447i | \(-0.536461\pi\) | ||||
−0.114296 | + | 0.993447i | \(0.536461\pi\) | |||||||
\(564\) | −15.3395 | −0.645908 | ||||||||
\(565\) | 2.25538 | 0.0948847 | ||||||||
\(566\) | −28.9926 | −1.21865 | ||||||||
\(567\) | −28.7410 | −1.20701 | ||||||||
\(568\) | −1.75115 | −0.0734765 | ||||||||
\(569\) | −34.1852 | −1.43312 | −0.716559 | − | 0.697527i | \(-0.754284\pi\) | ||||
−0.716559 | + | 0.697527i | \(0.754284\pi\) | |||||||
\(570\) | −9.24006 | −0.387024 | ||||||||
\(571\) | 21.9627 | 0.919111 | 0.459556 | − | 0.888149i | \(-0.348009\pi\) | ||||
0.459556 | + | 0.888149i | \(0.348009\pi\) | |||||||
\(572\) | −3.11595 | −0.130284 | ||||||||
\(573\) | 23.6498 | 0.987983 | ||||||||
\(574\) | 27.8320 | 1.16168 | ||||||||
\(575\) | 1.11595 | 0.0465384 | ||||||||
\(576\) | −0.801199 | −0.0333833 | ||||||||
\(577\) | −13.5274 | −0.563153 | −0.281577 | − | 0.959539i | \(-0.590857\pi\) | ||||
−0.281577 | + | 0.959539i | \(0.590857\pi\) | |||||||
\(578\) | −32.4646 | −1.35035 | ||||||||
\(579\) | 4.15871 | 0.172830 | ||||||||
\(580\) | −3.16385 | −0.131372 | ||||||||
\(581\) | −37.4296 | −1.55284 | ||||||||
\(582\) | −0.680718 | −0.0282167 | ||||||||
\(583\) | 10.1774 | 0.421505 | ||||||||
\(584\) | −6.29746 | −0.260591 | ||||||||
\(585\) | 2.49650 | 0.103217 | ||||||||
\(586\) | 9.42775 | 0.389457 | ||||||||
\(587\) | −41.1694 | −1.69924 | −0.849621 | − | 0.527394i | \(-0.823169\pi\) | ||||
−0.849621 | + | 0.527394i | \(0.823169\pi\) | |||||||
\(588\) | −24.1669 | −0.996627 | ||||||||
\(589\) | −25.7452 | −1.06081 | ||||||||
\(590\) | 9.27380 | 0.381796 | ||||||||
\(591\) | −22.6677 | −0.932426 | ||||||||
\(592\) | 3.75260 | 0.154231 | ||||||||
\(593\) | 7.26639 | 0.298395 | 0.149197 | − | 0.988807i | \(-0.452331\pi\) | ||||
0.149197 | + | 0.988807i | \(0.452331\pi\) | |||||||
\(594\) | 5.63655 | 0.231271 | ||||||||
\(595\) | −33.9472 | −1.39170 | ||||||||
\(596\) | 4.39902 | 0.180191 | ||||||||
\(597\) | 15.4727 | 0.633257 | ||||||||
\(598\) | −3.47725 | −0.142195 | ||||||||
\(599\) | −1.35091 | −0.0551967 | −0.0275984 | − | 0.999619i | \(-0.508786\pi\) | ||||
−0.0275984 | + | 0.999619i | \(0.508786\pi\) | |||||||
\(600\) | 1.48284 | 0.0605365 | ||||||||
\(601\) | −9.92951 | −0.405033 | −0.202516 | − | 0.979279i | \(-0.564912\pi\) | ||||
−0.202516 | + | 0.979279i | \(0.564912\pi\) | |||||||
\(602\) | −4.82678 | −0.196725 | ||||||||
\(603\) | 9.09872 | 0.370528 | ||||||||
\(604\) | −18.2702 | −0.743402 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | −8.88701 | −0.361010 | ||||||||
\(607\) | −23.4087 | −0.950131 | −0.475066 | − | 0.879950i | \(-0.657576\pi\) | ||||
−0.475066 | + | 0.879950i | \(0.657576\pi\) | |||||||
\(608\) | −6.23135 | −0.252714 | ||||||||
\(609\) | −22.6447 | −0.917609 | ||||||||
\(610\) | 11.2530 | 0.455621 | ||||||||
\(611\) | 32.2335 | 1.30403 | ||||||||
\(612\) | −5.63492 | −0.227778 | ||||||||
\(613\) | −7.18631 | −0.290252 | −0.145126 | − | 0.989413i | \(-0.546359\pi\) | ||||
−0.145126 | + | 0.989413i | \(0.546359\pi\) | |||||||
\(614\) | −20.6914 | −0.835036 | ||||||||
\(615\) | −8.55027 | −0.344780 | ||||||||
\(616\) | 4.82678 | 0.194476 | ||||||||
\(617\) | −7.29957 | −0.293869 | −0.146935 | − | 0.989146i | \(-0.546941\pi\) | ||||
−0.146935 | + | 0.989146i | \(0.546941\pi\) | |||||||
\(618\) | 17.8054 | 0.716238 | ||||||||
\(619\) | 35.5846 | 1.43027 | 0.715133 | − | 0.698989i | \(-0.246366\pi\) | ||||
0.715133 | + | 0.698989i | \(0.246366\pi\) | |||||||
\(620\) | 4.13157 | 0.165928 | ||||||||
\(621\) | 6.29011 | 0.252414 | ||||||||
\(622\) | −32.6114 | −1.30760 | ||||||||
\(623\) | −53.8928 | −2.15917 | ||||||||
\(624\) | −4.62044 | −0.184966 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −30.0632 | −1.20157 | ||||||||
\(627\) | 9.24006 | 0.369013 | ||||||||
\(628\) | −8.48633 | −0.338641 | ||||||||
\(629\) | 26.3925 | 1.05234 | ||||||||
\(630\) | −3.86721 | −0.154073 | ||||||||
\(631\) | −18.0131 | −0.717090 | −0.358545 | − | 0.933513i | \(-0.616727\pi\) | ||||
−0.358545 | + | 0.933513i | \(0.616727\pi\) | |||||||
\(632\) | 9.80398 | 0.389982 | ||||||||
\(633\) | −27.3944 | −1.08883 | ||||||||
\(634\) | 5.56557 | 0.221037 | ||||||||
\(635\) | 20.9378 | 0.830889 | ||||||||
\(636\) | 15.0914 | 0.598414 | ||||||||
\(637\) | 50.7831 | 2.01210 | ||||||||
\(638\) | 3.16385 | 0.125258 | ||||||||
\(639\) | −1.40302 | −0.0555026 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −9.51890 | −0.375974 | −0.187987 | − | 0.982172i | \(-0.560196\pi\) | ||||
−0.187987 | + | 0.982172i | \(0.560196\pi\) | |||||||
\(642\) | 3.11669 | 0.123006 | ||||||||
\(643\) | −35.6561 | −1.40614 | −0.703069 | − | 0.711122i | \(-0.748187\pi\) | ||||
−0.703069 | + | 0.711122i | \(0.748187\pi\) | |||||||
\(644\) | 5.38644 | 0.212256 | ||||||||
\(645\) | 1.48284 | 0.0583866 | ||||||||
\(646\) | −43.8257 | −1.72430 | ||||||||
\(647\) | 20.4070 | 0.802281 | 0.401141 | − | 0.916017i | \(-0.368614\pi\) | ||||
0.401141 | + | 0.916017i | \(0.368614\pi\) | |||||||
\(648\) | 5.95448 | 0.233914 | ||||||||
\(649\) | −9.27380 | −0.364029 | ||||||||
\(650\) | −3.11595 | −0.122218 | ||||||||
\(651\) | 29.5709 | 1.15898 | ||||||||
\(652\) | −5.34228 | −0.209220 | ||||||||
\(653\) | −35.5748 | −1.39215 | −0.696074 | − | 0.717970i | \(-0.745072\pi\) | ||||
−0.696074 | + | 0.717970i | \(0.745072\pi\) | |||||||
\(654\) | 11.6126 | 0.454090 | ||||||||
\(655\) | −1.76078 | −0.0687993 | ||||||||
\(656\) | −5.76616 | −0.225131 | ||||||||
\(657\) | −5.04552 | −0.196845 | ||||||||
\(658\) | −49.9315 | −1.94653 | ||||||||
\(659\) | 22.8345 | 0.889507 | 0.444754 | − | 0.895653i | \(-0.353291\pi\) | ||||
0.444754 | + | 0.895653i | \(0.353291\pi\) | |||||||
\(660\) | −1.48284 | −0.0577193 | ||||||||
\(661\) | −0.0985728 | −0.00383404 | −0.00191702 | − | 0.999998i | \(-0.500610\pi\) | ||||
−0.00191702 | + | 0.999998i | \(0.500610\pi\) | |||||||
\(662\) | 6.80814 | 0.264606 | ||||||||
\(663\) | −32.4961 | −1.26204 | ||||||||
\(664\) | 7.75457 | 0.300936 | ||||||||
\(665\) | −30.0773 | −1.16635 | ||||||||
\(666\) | 3.00658 | 0.116503 | ||||||||
\(667\) | 3.53070 | 0.136709 | ||||||||
\(668\) | −24.0863 | −0.931925 | ||||||||
\(669\) | −8.89589 | −0.343935 | ||||||||
\(670\) | −11.3564 | −0.438735 | ||||||||
\(671\) | −11.2530 | −0.434417 | ||||||||
\(672\) | 7.15731 | 0.276099 | ||||||||
\(673\) | −1.64560 | −0.0634332 | −0.0317166 | − | 0.999497i | \(-0.510097\pi\) | ||||
−0.0317166 | + | 0.999497i | \(0.510097\pi\) | |||||||
\(674\) | 17.6757 | 0.680841 | ||||||||
\(675\) | 5.63655 | 0.216951 | ||||||||
\(676\) | −3.29085 | −0.126571 | ||||||||
\(677\) | −12.0789 | −0.464231 | −0.232116 | − | 0.972688i | \(-0.574565\pi\) | ||||
−0.232116 | + | 0.972688i | \(0.574565\pi\) | |||||||
\(678\) | −3.34436 | −0.128439 | ||||||||
\(679\) | −2.21581 | −0.0850348 | ||||||||
\(680\) | 7.03311 | 0.269707 | ||||||||
\(681\) | 14.1122 | 0.540780 | ||||||||
\(682\) | −4.13157 | −0.158206 | ||||||||
\(683\) | 21.7046 | 0.830503 | 0.415251 | − | 0.909707i | \(-0.363694\pi\) | ||||
0.415251 | + | 0.909707i | \(0.363694\pi\) | |||||||
\(684\) | −4.99255 | −0.190895 | ||||||||
\(685\) | −9.43115 | −0.360346 | ||||||||
\(686\) | −44.8783 | −1.71346 | ||||||||
\(687\) | −31.7001 | −1.20943 | ||||||||
\(688\) | 1.00000 | 0.0381246 | ||||||||
\(689\) | −31.7123 | −1.20814 | ||||||||
\(690\) | −1.65477 | −0.0629961 | ||||||||
\(691\) | −21.4673 | −0.816656 | −0.408328 | − | 0.912835i | \(-0.633888\pi\) | ||||
−0.408328 | + | 0.912835i | \(0.633888\pi\) | |||||||
\(692\) | −21.9002 | −0.832522 | ||||||||
\(693\) | 3.86721 | 0.146903 | ||||||||
\(694\) | 1.50630 | 0.0571783 | ||||||||
\(695\) | −16.0028 | −0.607021 | ||||||||
\(696\) | 4.69147 | 0.177830 | ||||||||
\(697\) | −40.5541 | −1.53609 | ||||||||
\(698\) | −6.73446 | −0.254903 | ||||||||
\(699\) | 38.9906 | 1.47476 | ||||||||
\(700\) | 4.82678 | 0.182435 | ||||||||
\(701\) | −15.7822 | −0.596085 | −0.298042 | − | 0.954553i | \(-0.596334\pi\) | ||||
−0.298042 | + | 0.954553i | \(0.596334\pi\) | |||||||
\(702\) | −17.5632 | −0.662881 | ||||||||
\(703\) | 23.3838 | 0.881935 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | 15.3395 | 0.577718 | ||||||||
\(706\) | −2.06180 | −0.0775969 | ||||||||
\(707\) | −28.9281 | −1.08795 | ||||||||
\(708\) | −13.7515 | −0.516814 | ||||||||
\(709\) | −49.3521 | −1.85346 | −0.926729 | − | 0.375731i | \(-0.877392\pi\) | ||||
−0.926729 | + | 0.375731i | \(0.877392\pi\) | |||||||
\(710\) | 1.75115 | 0.0657194 | ||||||||
\(711\) | 7.85495 | 0.294583 | ||||||||
\(712\) | 11.1654 | 0.418440 | ||||||||
\(713\) | −4.61063 | −0.172669 | ||||||||
\(714\) | 50.3382 | 1.88386 | ||||||||
\(715\) | 3.11595 | 0.116530 | ||||||||
\(716\) | 6.07104 | 0.226885 | ||||||||
\(717\) | 14.8345 | 0.554005 | ||||||||
\(718\) | −14.9385 | −0.557499 | ||||||||
\(719\) | −39.6827 | −1.47991 | −0.739957 | − | 0.672654i | \(-0.765154\pi\) | ||||
−0.739957 | + | 0.672654i | \(0.765154\pi\) | |||||||
\(720\) | 0.801199 | 0.0298589 | ||||||||
\(721\) | 57.9583 | 2.15848 | ||||||||
\(722\) | −19.8297 | −0.737985 | ||||||||
\(723\) | −14.4017 | −0.535605 | ||||||||
\(724\) | 10.3540 | 0.384803 | ||||||||
\(725\) | 3.16385 | 0.117502 | ||||||||
\(726\) | 1.48284 | 0.0550332 | ||||||||
\(727\) | −25.7743 | −0.955917 | −0.477959 | − | 0.878382i | \(-0.658623\pi\) | ||||
−0.477959 | + | 0.878382i | \(0.658623\pi\) | |||||||
\(728\) | −15.0400 | −0.557419 | ||||||||
\(729\) | 29.8450 | 1.10537 | ||||||||
\(730\) | 6.29746 | 0.233079 | ||||||||
\(731\) | 7.03311 | 0.260129 | ||||||||
\(732\) | −16.6864 | −0.616745 | ||||||||
\(733\) | −8.72247 | −0.322172 | −0.161086 | − | 0.986940i | \(-0.551500\pi\) | ||||
−0.161086 | + | 0.986940i | \(0.551500\pi\) | |||||||
\(734\) | −14.7313 | −0.543741 | ||||||||
\(735\) | 24.1669 | 0.891410 | ||||||||
\(736\) | −1.11595 | −0.0411345 | ||||||||
\(737\) | 11.3564 | 0.418317 | ||||||||
\(738\) | −4.61985 | −0.170059 | ||||||||
\(739\) | 49.5319 | 1.82206 | 0.911030 | − | 0.412341i | \(-0.135289\pi\) | ||||
0.911030 | + | 0.412341i | \(0.135289\pi\) | |||||||
\(740\) | −3.75260 | −0.137948 | ||||||||
\(741\) | −28.7916 | −1.05769 | ||||||||
\(742\) | 49.1241 | 1.80340 | ||||||||
\(743\) | 33.6058 | 1.23288 | 0.616439 | − | 0.787403i | \(-0.288575\pi\) | ||||
0.616439 | + | 0.787403i | \(0.288575\pi\) | |||||||
\(744\) | −6.12644 | −0.224606 | ||||||||
\(745\) | −4.39902 | −0.161168 | ||||||||
\(746\) | 13.7561 | 0.503646 | ||||||||
\(747\) | 6.21295 | 0.227320 | ||||||||
\(748\) | −7.03311 | −0.257156 | ||||||||
\(749\) | 10.1452 | 0.370696 | ||||||||
\(750\) | −1.48284 | −0.0541455 | ||||||||
\(751\) | −12.0723 | −0.440525 | −0.220263 | − | 0.975441i | \(-0.570691\pi\) | ||||
−0.220263 | + | 0.975441i | \(0.570691\pi\) | |||||||
\(752\) | 10.3447 | 0.377232 | ||||||||
\(753\) | −37.9074 | −1.38142 | ||||||||
\(754\) | −9.85841 | −0.359022 | ||||||||
\(755\) | 18.2702 | 0.664919 | ||||||||
\(756\) | 27.2064 | 0.989486 | ||||||||
\(757\) | 11.3058 | 0.410917 | 0.205459 | − | 0.978666i | \(-0.434131\pi\) | ||||
0.205459 | + | 0.978666i | \(0.434131\pi\) | |||||||
\(758\) | 19.6061 | 0.712127 | ||||||||
\(759\) | 1.65477 | 0.0600644 | ||||||||
\(760\) | 6.23135 | 0.226035 | ||||||||
\(761\) | 11.6839 | 0.423540 | 0.211770 | − | 0.977320i | \(-0.432077\pi\) | ||||
0.211770 | + | 0.977320i | \(0.432077\pi\) | |||||||
\(762\) | −31.0472 | −1.12472 | ||||||||
\(763\) | 37.8003 | 1.36846 | ||||||||
\(764\) | −15.9490 | −0.577015 | ||||||||
\(765\) | 5.63492 | 0.203731 | ||||||||
\(766\) | −32.1235 | −1.16067 | ||||||||
\(767\) | 28.8967 | 1.04340 | ||||||||
\(768\) | −1.48284 | −0.0535072 | ||||||||
\(769\) | −39.7026 | −1.43171 | −0.715856 | − | 0.698248i | \(-0.753963\pi\) | ||||
−0.715856 | + | 0.698248i | \(0.753963\pi\) | |||||||
\(770\) | −4.82678 | −0.173945 | ||||||||
\(771\) | −7.16014 | −0.257866 | ||||||||
\(772\) | −2.80456 | −0.100938 | ||||||||
\(773\) | 31.8511 | 1.14560 | 0.572802 | − | 0.819694i | \(-0.305856\pi\) | ||||
0.572802 | + | 0.819694i | \(0.305856\pi\) | |||||||
\(774\) | 0.801199 | 0.0287985 | ||||||||
\(775\) | −4.13157 | −0.148410 | ||||||||
\(776\) | 0.459065 | 0.0164795 | ||||||||
\(777\) | −26.8585 | −0.963545 | ||||||||
\(778\) | 23.0968 | 0.828060 | ||||||||
\(779\) | −35.9310 | −1.28736 | ||||||||
\(780\) | 4.62044 | 0.165438 | ||||||||
\(781\) | −1.75115 | −0.0626610 | ||||||||
\(782\) | −7.84860 | −0.280665 | ||||||||
\(783\) | 17.8332 | 0.637307 | ||||||||
\(784\) | 16.2978 | 0.582063 | ||||||||
\(785\) | 8.48633 | 0.302890 | ||||||||
\(786\) | 2.61095 | 0.0931294 | ||||||||
\(787\) | 21.4486 | 0.764560 | 0.382280 | − | 0.924047i | \(-0.375139\pi\) | ||||
0.382280 | + | 0.924047i | \(0.375139\pi\) | |||||||
\(788\) | 15.2867 | 0.544568 | ||||||||
\(789\) | 15.1909 | 0.540809 | ||||||||
\(790\) | −9.80398 | −0.348810 | ||||||||
\(791\) | −10.8862 | −0.387070 | ||||||||
\(792\) | −0.801199 | −0.0284694 | ||||||||
\(793\) | 35.0638 | 1.24515 | ||||||||
\(794\) | −36.8054 | −1.30617 | ||||||||
\(795\) | −15.0914 | −0.535237 | ||||||||
\(796\) | −10.4346 | −0.369843 | ||||||||
\(797\) | −24.7674 | −0.877306 | −0.438653 | − | 0.898657i | \(-0.644544\pi\) | ||||
−0.438653 | + | 0.898657i | \(0.644544\pi\) | |||||||
\(798\) | 44.5997 | 1.57881 | ||||||||
\(799\) | 72.7553 | 2.57390 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 8.94569 | 0.316080 | ||||||||
\(802\) | 6.49490 | 0.229343 | ||||||||
\(803\) | −6.29746 | −0.222233 | ||||||||
\(804\) | 16.8396 | 0.593888 | ||||||||
\(805\) | −5.38644 | −0.189847 | ||||||||
\(806\) | 12.8738 | 0.453459 | ||||||||
\(807\) | 20.2800 | 0.713889 | ||||||||
\(808\) | 5.99326 | 0.210842 | ||||||||
\(809\) | −19.4659 | −0.684385 | −0.342192 | − | 0.939630i | \(-0.611169\pi\) | ||||
−0.342192 | + | 0.939630i | \(0.611169\pi\) | |||||||
\(810\) | −5.95448 | −0.209219 | ||||||||
\(811\) | 15.6211 | 0.548532 | 0.274266 | − | 0.961654i | \(-0.411565\pi\) | ||||
0.274266 | + | 0.961654i | \(0.411565\pi\) | |||||||
\(812\) | 15.2712 | 0.535914 | ||||||||
\(813\) | 16.5093 | 0.579006 | ||||||||
\(814\) | 3.75260 | 0.131529 | ||||||||
\(815\) | 5.34228 | 0.187132 | ||||||||
\(816\) | −10.4289 | −0.365086 | ||||||||
\(817\) | 6.23135 | 0.218007 | ||||||||
\(818\) | −18.1660 | −0.635158 | ||||||||
\(819\) | −12.0500 | −0.421062 | ||||||||
\(820\) | 5.76616 | 0.201363 | ||||||||
\(821\) | −37.8925 | −1.32246 | −0.661229 | − | 0.750185i | \(-0.729965\pi\) | ||||
−0.661229 | + | 0.750185i | \(0.729965\pi\) | |||||||
\(822\) | 13.9848 | 0.487777 | ||||||||
\(823\) | −2.27751 | −0.0793890 | −0.0396945 | − | 0.999212i | \(-0.512638\pi\) | ||||
−0.0396945 | + | 0.999212i | \(0.512638\pi\) | |||||||
\(824\) | −12.0077 | −0.418307 | ||||||||
\(825\) | 1.48284 | 0.0516257 | ||||||||
\(826\) | −44.7626 | −1.55749 | ||||||||
\(827\) | −17.0461 | −0.592749 | −0.296375 | − | 0.955072i | \(-0.595778\pi\) | ||||
−0.296375 | + | 0.955072i | \(0.595778\pi\) | |||||||
\(828\) | −0.894099 | −0.0310721 | ||||||||
\(829\) | 49.9099 | 1.73344 | 0.866721 | − | 0.498793i | \(-0.166223\pi\) | ||||
0.866721 | + | 0.498793i | \(0.166223\pi\) | |||||||
\(830\) | −7.75457 | −0.269165 | ||||||||
\(831\) | −31.1086 | −1.07915 | ||||||||
\(832\) | 3.11595 | 0.108026 | ||||||||
\(833\) | 114.624 | 3.97149 | ||||||||
\(834\) | 23.7295 | 0.821686 | ||||||||
\(835\) | 24.0863 | 0.833539 | ||||||||
\(836\) | −6.23135 | −0.215516 | ||||||||
\(837\) | −23.2878 | −0.804945 | ||||||||
\(838\) | 8.59949 | 0.297064 | ||||||||
\(839\) | 18.6811 | 0.644944 | 0.322472 | − | 0.946579i | \(-0.395486\pi\) | ||||
0.322472 | + | 0.946579i | \(0.395486\pi\) | |||||||
\(840\) | −7.15731 | −0.246951 | ||||||||
\(841\) | −18.9900 | −0.654829 | ||||||||
\(842\) | 30.7705 | 1.06042 | ||||||||
\(843\) | 6.11082 | 0.210468 | ||||||||
\(844\) | 18.4743 | 0.635913 | ||||||||
\(845\) | 3.29085 | 0.113209 | ||||||||
\(846\) | 8.28816 | 0.284953 | ||||||||
\(847\) | 4.82678 | 0.165850 | ||||||||
\(848\) | −10.1774 | −0.349494 | ||||||||
\(849\) | −42.9913 | −1.47546 | ||||||||
\(850\) | −7.03311 | −0.241234 | ||||||||
\(851\) | 4.18772 | 0.143553 | ||||||||
\(852\) | −2.59666 | −0.0889603 | ||||||||
\(853\) | −19.1968 | −0.657287 | −0.328644 | − | 0.944454i | \(-0.606591\pi\) | ||||
−0.328644 | + | 0.944454i | \(0.606591\pi\) | |||||||
\(854\) | −54.3157 | −1.85865 | ||||||||
\(855\) | 4.99255 | 0.170742 | ||||||||
\(856\) | −2.10185 | −0.0718397 | ||||||||
\(857\) | −20.8282 | −0.711478 | −0.355739 | − | 0.934585i | \(-0.615771\pi\) | ||||
−0.355739 | + | 0.934585i | \(0.615771\pi\) | |||||||
\(858\) | −4.62044 | −0.157739 | ||||||||
\(859\) | −44.8598 | −1.53060 | −0.765298 | − | 0.643676i | \(-0.777408\pi\) | ||||
−0.765298 | + | 0.643676i | \(0.777408\pi\) | |||||||
\(860\) | −1.00000 | −0.0340997 | ||||||||
\(861\) | 41.2703 | 1.40649 | ||||||||
\(862\) | −29.0510 | −0.989481 | ||||||||
\(863\) | 51.5633 | 1.75524 | 0.877618 | − | 0.479361i | \(-0.159132\pi\) | ||||
0.877618 | + | 0.479361i | \(0.159132\pi\) | |||||||
\(864\) | −5.63655 | −0.191759 | ||||||||
\(865\) | 21.9002 | 0.744630 | ||||||||
\(866\) | 10.6572 | 0.362146 | ||||||||
\(867\) | −48.1397 | −1.63491 | ||||||||
\(868\) | −19.9422 | −0.676881 | ||||||||
\(869\) | 9.80398 | 0.332577 | ||||||||
\(870\) | −4.69147 | −0.159056 | ||||||||
\(871\) | −35.3859 | −1.19901 | ||||||||
\(872\) | −7.83137 | −0.265204 | ||||||||
\(873\) | 0.367803 | 0.0124482 | ||||||||
\(874\) | −6.95388 | −0.235218 | ||||||||
\(875\) | −4.82678 | −0.163175 | ||||||||
\(876\) | −9.33810 | −0.315505 | ||||||||
\(877\) | −21.6569 | −0.731302 | −0.365651 | − | 0.930752i | \(-0.619154\pi\) | ||||
−0.365651 | + | 0.930752i | \(0.619154\pi\) | |||||||
\(878\) | −8.49937 | −0.286840 | ||||||||
\(879\) | 13.9798 | 0.471527 | ||||||||
\(880\) | 1.00000 | 0.0337100 | ||||||||
\(881\) | 11.2800 | 0.380032 | 0.190016 | − | 0.981781i | \(-0.439146\pi\) | ||||
0.190016 | + | 0.981781i | \(0.439146\pi\) | |||||||
\(882\) | 13.0578 | 0.439678 | ||||||||
\(883\) | −16.4809 | −0.554627 | −0.277314 | − | 0.960779i | \(-0.589444\pi\) | ||||
−0.277314 | + | 0.960779i | \(0.589444\pi\) | |||||||
\(884\) | 21.9148 | 0.737075 | ||||||||
\(885\) | 13.7515 | 0.462252 | ||||||||
\(886\) | −12.7886 | −0.429641 | ||||||||
\(887\) | −18.6243 | −0.625341 | −0.312671 | − | 0.949862i | \(-0.601224\pi\) | ||||
−0.312671 | + | 0.949862i | \(0.601224\pi\) | |||||||
\(888\) | 5.56449 | 0.186732 | ||||||||
\(889\) | −101.062 | −3.38951 | ||||||||
\(890\) | −11.1654 | −0.374264 | ||||||||
\(891\) | 5.95448 | 0.199483 | ||||||||
\(892\) | 5.99924 | 0.200870 | ||||||||
\(893\) | 64.4613 | 2.15712 | ||||||||
\(894\) | 6.52302 | 0.218162 | ||||||||
\(895\) | −6.07104 | −0.202932 | ||||||||
\(896\) | −4.82678 | −0.161251 | ||||||||
\(897\) | −5.15618 | −0.172160 | ||||||||
\(898\) | 10.0081 | 0.333975 | ||||||||
\(899\) | −13.0717 | −0.435965 | ||||||||
\(900\) | −0.801199 | −0.0267066 | ||||||||
\(901\) | −71.5788 | −2.38464 | ||||||||
\(902\) | −5.76616 | −0.191992 | ||||||||
\(903\) | −7.15731 | −0.238181 | ||||||||
\(904\) | 2.25538 | 0.0750129 | ||||||||
\(905\) | −10.3540 | −0.344178 | ||||||||
\(906\) | −27.0916 | −0.900059 | ||||||||
\(907\) | −40.8310 | −1.35577 | −0.677885 | − | 0.735168i | \(-0.737103\pi\) | ||||
−0.677885 | + | 0.735168i | \(0.737103\pi\) | |||||||
\(908\) | −9.51703 | −0.315834 | ||||||||
\(909\) | 4.80179 | 0.159265 | ||||||||
\(910\) | 15.0400 | 0.498571 | ||||||||
\(911\) | 26.0470 | 0.862977 | 0.431488 | − | 0.902118i | \(-0.357989\pi\) | ||||
0.431488 | + | 0.902118i | \(0.357989\pi\) | |||||||
\(912\) | −9.24006 | −0.305969 | ||||||||
\(913\) | 7.75457 | 0.256639 | ||||||||
\(914\) | 23.1307 | 0.765095 | ||||||||
\(915\) | 16.6864 | 0.551634 | ||||||||
\(916\) | 21.3780 | 0.706349 | ||||||||
\(917\) | 8.49889 | 0.280658 | ||||||||
\(918\) | −39.6425 | −1.30840 | ||||||||
\(919\) | −45.7537 | −1.50928 | −0.754638 | − | 0.656141i | \(-0.772188\pi\) | ||||
−0.754638 | + | 0.656141i | \(0.772188\pi\) | |||||||
\(920\) | 1.11595 | 0.0367918 | ||||||||
\(921\) | −30.6819 | −1.01100 | ||||||||
\(922\) | 7.38407 | 0.243181 | ||||||||
\(923\) | 5.45649 | 0.179603 | ||||||||
\(924\) | 7.15731 | 0.235458 | ||||||||
\(925\) | 3.75260 | 0.123385 | ||||||||
\(926\) | 26.1690 | 0.859966 | ||||||||
\(927\) | −9.62053 | −0.315980 | ||||||||
\(928\) | −3.16385 | −0.103859 | ||||||||
\(929\) | 25.7773 | 0.845725 | 0.422862 | − | 0.906194i | \(-0.361025\pi\) | ||||
0.422862 | + | 0.906194i | \(0.361025\pi\) | |||||||
\(930\) | 6.12644 | 0.200894 | ||||||||
\(931\) | 101.557 | 3.32840 | ||||||||
\(932\) | −26.2946 | −0.861308 | ||||||||
\(933\) | −48.3574 | −1.58315 | ||||||||
\(934\) | 2.76399 | 0.0904406 | ||||||||
\(935\) | 7.03311 | 0.230007 | ||||||||
\(936\) | 2.49650 | 0.0816006 | ||||||||
\(937\) | −44.7046 | −1.46044 | −0.730219 | − | 0.683214i | \(-0.760582\pi\) | ||||
−0.730219 | + | 0.683214i | \(0.760582\pi\) | |||||||
\(938\) | 54.8147 | 1.78976 | ||||||||
\(939\) | −44.5788 | −1.45477 | ||||||||
\(940\) | −10.3447 | −0.337406 | ||||||||
\(941\) | 33.2819 | 1.08496 | 0.542480 | − | 0.840069i | \(-0.317485\pi\) | ||||
0.542480 | + | 0.840069i | \(0.317485\pi\) | |||||||
\(942\) | −12.5838 | −0.410003 | ||||||||
\(943\) | −6.43475 | −0.209544 | ||||||||
\(944\) | 9.27380 | 0.301837 | ||||||||
\(945\) | −27.2064 | −0.885024 | ||||||||
\(946\) | 1.00000 | 0.0325128 | ||||||||
\(947\) | 45.2271 | 1.46968 | 0.734841 | − | 0.678239i | \(-0.237257\pi\) | ||||
0.734841 | + | 0.678239i | \(0.237257\pi\) | |||||||
\(948\) | 14.5377 | 0.472162 | ||||||||
\(949\) | 19.6226 | 0.636976 | ||||||||
\(950\) | −6.23135 | −0.202172 | ||||||||
\(951\) | 8.25282 | 0.267616 | ||||||||
\(952\) | −33.9472 | −1.10024 | ||||||||
\(953\) | 26.3035 | 0.852055 | 0.426027 | − | 0.904710i | \(-0.359913\pi\) | ||||
0.426027 | + | 0.904710i | \(0.359913\pi\) | |||||||
\(954\) | −8.15413 | −0.264000 | ||||||||
\(955\) | 15.9490 | 0.516098 | ||||||||
\(956\) | −10.0042 | −0.323558 | ||||||||
\(957\) | 4.69147 | 0.151654 | ||||||||
\(958\) | −36.2872 | −1.17238 | ||||||||
\(959\) | 45.5221 | 1.46998 | ||||||||
\(960\) | 1.48284 | 0.0478583 | ||||||||
\(961\) | −13.9301 | −0.449359 | ||||||||
\(962\) | −11.6929 | −0.376995 | ||||||||
\(963\) | −1.68400 | −0.0542661 | ||||||||
\(964\) | 9.71227 | 0.312811 | ||||||||
\(965\) | 2.80456 | 0.0902821 | ||||||||
\(966\) | 7.98721 | 0.256984 | ||||||||
\(967\) | 33.5040 | 1.07742 | 0.538708 | − | 0.842493i | \(-0.318913\pi\) | ||||
0.538708 | + | 0.842493i | \(0.318913\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | −64.9864 | −2.08766 | ||||||||
\(970\) | −0.459065 | −0.0147397 | ||||||||
\(971\) | −23.1013 | −0.741356 | −0.370678 | − | 0.928761i | \(-0.620875\pi\) | ||||
−0.370678 | + | 0.928761i | \(0.620875\pi\) | |||||||
\(972\) | −8.08014 | −0.259171 | ||||||||
\(973\) | 77.2419 | 2.47626 | ||||||||
\(974\) | −12.2972 | −0.394028 | ||||||||
\(975\) | −4.62044 | −0.147973 | ||||||||
\(976\) | 11.2530 | 0.360200 | ||||||||
\(977\) | 48.8724 | 1.56357 | 0.781783 | − | 0.623551i | \(-0.214310\pi\) | ||||
0.781783 | + | 0.623551i | \(0.214310\pi\) | |||||||
\(978\) | −7.92173 | −0.253309 | ||||||||
\(979\) | 11.1654 | 0.356847 | ||||||||
\(980\) | −16.2978 | −0.520613 | ||||||||
\(981\) | −6.27449 | −0.200329 | ||||||||
\(982\) | −20.5937 | −0.657173 | ||||||||
\(983\) | −33.1114 | −1.05609 | −0.528045 | − | 0.849216i | \(-0.677075\pi\) | ||||
−0.528045 | + | 0.849216i | \(0.677075\pi\) | |||||||
\(984\) | −8.55027 | −0.272573 | ||||||||
\(985\) | −15.2867 | −0.487076 | ||||||||
\(986\) | −22.2517 | −0.708639 | ||||||||
\(987\) | −74.0402 | −2.35672 | ||||||||
\(988\) | 19.4166 | 0.617723 | ||||||||
\(989\) | 1.11595 | 0.0354852 | ||||||||
\(990\) | 0.801199 | 0.0254638 | ||||||||
\(991\) | 45.9388 | 1.45929 | 0.729647 | − | 0.683824i | \(-0.239684\pi\) | ||||
0.729647 | + | 0.683824i | \(0.239684\pi\) | |||||||
\(992\) | 4.13157 | 0.131177 | ||||||||
\(993\) | 10.0954 | 0.320366 | ||||||||
\(994\) | −8.45240 | −0.268094 | ||||||||
\(995\) | 10.4346 | 0.330798 | ||||||||
\(996\) | 11.4987 | 0.364352 | ||||||||
\(997\) | 2.25804 | 0.0715127 | 0.0357564 | − | 0.999361i | \(-0.488616\pi\) | ||||
0.0357564 | + | 0.999361i | \(0.488616\pi\) | |||||||
\(998\) | −10.9689 | −0.347216 | ||||||||
\(999\) | 21.1517 | 0.669211 |
(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 | 4730.2.a.bb.1.4 | ✓ | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4730.2.a.bb.1.4 | ✓ | 11 | 1.1 | even | 1 | trivial |