Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1287,2,Mod(298,1287)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1287, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1287.298");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1287 = 3^{2} \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1287.b (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(10.2767467401\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} + 23x^{12} + 201x^{10} + 835x^{8} + 1695x^{6} + 1565x^{4} + 511x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 429) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 298.3 | ||
Root | \(-2.15754i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1287.298 |
Dual form | 1287.2.b.c.298.12 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1287\mathbb{Z}\right)^\times\).
\(n\) | \(496\) | \(937\) | \(1145\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.15754i | − | 1.52561i | −0.646628 | − | 0.762806i | \(-0.723821\pi\) | ||
0.646628 | − | 0.762806i | \(-0.276179\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.65498 | −1.32749 | ||||||||
\(5\) | 0.710210i | 0.317616i | 0.987310 | + | 0.158808i | \(0.0507650\pi\) | ||||
−0.987310 | + | 0.158808i | \(0.949235\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.30964i | 0.872963i | 0.899713 | + | 0.436482i | \(0.143776\pi\) | ||||
−0.899713 | + | 0.436482i | \(0.856224\pi\) | |||||||
\(8\) | 1.41315i | 0.499622i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.53231 | 0.484558 | ||||||||
\(11\) | − | 1.00000i | − | 0.301511i | ||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.40848 | + | 3.31906i | −0.390642 | + | 0.920543i | ||||
\(14\) | 4.98315 | 1.33180 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.26104 | −0.565261 | ||||||||
\(17\) | −6.68027 | −1.62020 | −0.810102 | − | 0.586289i | \(-0.800588\pi\) | ||||
−0.810102 | + | 0.586289i | \(0.800588\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.242517i | 0.0556372i | 0.999613 | + | 0.0278186i | \(0.00885607\pi\) | ||||
−0.999613 | + | 0.0278186i | \(0.991144\pi\) | |||||||
\(20\) | − | 1.88559i | − | 0.421631i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.15754 | −0.459989 | ||||||||
\(23\) | 9.53531 | 1.98825 | 0.994125 | − | 0.108242i | \(-0.0345220\pi\) | ||||
0.994125 | + | 0.108242i | \(0.0345220\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.49560 | 0.899120 | ||||||||
\(26\) | 7.16101 | + | 3.03885i | 1.40439 | + | 0.595968i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 6.13206i | − | 1.15885i | ||||||
\(29\) | 2.95273 | 0.548308 | 0.274154 | − | 0.961686i | \(-0.411602\pi\) | ||||
0.274154 | + | 0.961686i | \(0.411602\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.02017i | 0.722044i | 0.932557 | + | 0.361022i | \(0.117572\pi\) | ||||
−0.932557 | + | 0.361022i | \(0.882428\pi\) | |||||||
\(32\) | 7.70458i | 1.36199i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 14.4130i | 2.47180i | ||||||||
\(35\) | −1.64033 | −0.277267 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.42304i | 0.562744i | 0.959599 | + | 0.281372i | \(0.0907895\pi\) | ||||
−0.959599 | + | 0.281372i | \(0.909211\pi\) | |||||||
\(38\) | 0.523240 | 0.0848807 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00363 | −0.158688 | ||||||||
\(41\) | 9.46022i | 1.47744i | 0.674013 | + | 0.738719i | \(0.264569\pi\) | ||||
−0.674013 | + | 0.738719i | \(0.735431\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.8791 | 1.81155 | 0.905776 | − | 0.423757i | \(-0.139289\pi\) | ||||
0.905776 | + | 0.423757i | \(0.139289\pi\) | |||||||
\(44\) | 2.65498i | 0.400253i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 20.5728i | − | 3.03330i | ||||||
\(47\) | 12.9178i | 1.88426i | 0.335249 | + | 0.942130i | \(0.391180\pi\) | ||||
−0.335249 | + | 0.942130i | \(0.608820\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.66555 | 0.237935 | ||||||||
\(50\) | − | 9.69944i | − | 1.37171i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.73948 | − | 8.81205i | 0.518573 | − | 1.22201i | ||||
\(53\) | −6.78954 | −0.932615 | −0.466307 | − | 0.884623i | \(-0.654416\pi\) | ||||
−0.466307 | + | 0.884623i | \(0.654416\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.710210 | 0.0957647 | ||||||||
\(56\) | −3.26386 | −0.436152 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 6.37063i | − | 0.836504i | ||||||
\(59\) | − | 7.81320i | − | 1.01719i | −0.861005 | − | 0.508596i | \(-0.830165\pi\) | ||
0.861005 | − | 0.508596i | \(-0.169835\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.910585 | 0.116588 | 0.0582942 | − | 0.998299i | \(-0.481434\pi\) | ||||
0.0582942 | + | 0.998299i | \(0.481434\pi\) | |||||||
\(62\) | 8.67368 | 1.10156 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 12.1009 | 1.51261 | ||||||||
\(65\) | −2.35723 | − | 1.00032i | −0.292379 | − | 0.124074i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 9.32216i | − | 1.13888i | −0.822032 | − | 0.569442i | \(-0.807159\pi\) | ||
0.822032 | − | 0.569442i | \(-0.192841\pi\) | |||||||
\(68\) | 17.7360 | 2.15080 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.53908i | 0.423001i | ||||||||
\(71\) | 12.9704i | 1.53930i | 0.638466 | + | 0.769650i | \(0.279569\pi\) | ||||
−0.638466 | + | 0.769650i | \(0.720431\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.51665i | 0.996798i | 0.866948 | + | 0.498399i | \(0.166079\pi\) | ||||
−0.866948 | + | 0.498399i | \(0.833921\pi\) | |||||||
\(74\) | 7.38534 | 0.858529 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 0.643877i | − | 0.0738578i | ||||||
\(77\) | 2.30964 | 0.263208 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.82360 | 0.205172 | 0.102586 | − | 0.994724i | \(-0.467288\pi\) | ||||
0.102586 | + | 0.994724i | \(0.467288\pi\) | |||||||
\(80\) | − | 1.60581i | − | 0.179536i | ||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 20.4108 | 2.25400 | ||||||||
\(83\) | 4.64671i | 0.510042i | 0.966935 | + | 0.255021i | \(0.0820824\pi\) | ||||
−0.966935 | + | 0.255021i | \(0.917918\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 4.74440i | − | 0.514602i | ||||||
\(86\) | − | 25.6297i | − | 2.76372i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.41315 | 0.150642 | ||||||||
\(89\) | − | 14.7714i | − | 1.56576i | −0.622171 | − | 0.782881i | \(-0.713749\pi\) | ||
0.622171 | − | 0.782881i | \(-0.286251\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.66585 | − | 3.25308i | −0.803600 | − | 0.341016i | ||||
\(92\) | −25.3161 | −2.63938 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 27.8707 | 2.87465 | ||||||||
\(95\) | −0.172238 | −0.0176712 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.86542i | − | 0.189405i | −0.995506 | − | 0.0947025i | \(-0.969810\pi\) | ||
0.995506 | − | 0.0947025i | \(-0.0301900\pi\) | |||||||
\(98\) | − | 3.59349i | − | 0.362997i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −11.9357 | −1.19357 | ||||||||
\(101\) | −2.45086 | −0.243870 | −0.121935 | − | 0.992538i | \(-0.538910\pi\) | ||||
−0.121935 | + | 0.992538i | \(0.538910\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.2811 | −1.01302 | −0.506512 | − | 0.862233i | \(-0.669066\pi\) | ||||
−0.506512 | + | 0.862233i | \(0.669066\pi\) | |||||||
\(104\) | −4.69032 | − | 1.99039i | −0.459924 | − | 0.195173i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 14.6487i | 1.42281i | ||||||||
\(107\) | −19.6690 | −1.90148 | −0.950739 | − | 0.309993i | \(-0.899673\pi\) | ||||
−0.950739 | + | 0.309993i | \(0.899673\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 1.27506i | − | 0.122128i | −0.998134 | − | 0.0610642i | \(-0.980551\pi\) | ||
0.998134 | − | 0.0610642i | \(-0.0194494\pi\) | |||||||
\(110\) | − | 1.53231i | − | 0.146100i | ||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 5.22220i | − | 0.493452i | ||||||
\(113\) | 0.638739 | 0.0600875 | 0.0300438 | − | 0.999549i | \(-0.490435\pi\) | ||||
0.0300438 | + | 0.999549i | \(0.490435\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.77207i | 0.631499i | ||||||||
\(116\) | −7.83943 | −0.727873 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −16.8573 | −1.55184 | ||||||||
\(119\) | − | 15.4290i | − | 1.41438i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | − | 1.96462i | − | 0.177869i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 10.6735i | − | 0.958506i | ||||||
\(125\) | 6.74387i | 0.603190i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.3681 | −0.920021 | −0.460010 | − | 0.887914i | \(-0.652154\pi\) | ||||
−0.460010 | + | 0.887914i | \(0.652154\pi\) | |||||||
\(128\) | − | 10.6989i | − | 0.945660i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.15822 | + | 5.08582i | −0.189289 | + | 0.446056i | ||||
\(131\) | 5.68692 | 0.496868 | 0.248434 | − | 0.968649i | \(-0.420084\pi\) | ||||
0.248434 | + | 0.968649i | \(0.420084\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.560127 | −0.0485692 | ||||||||
\(134\) | −20.1129 | −1.73749 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 9.44019i | − | 0.809490i | ||||||
\(137\) | − | 4.86363i | − | 0.415528i | −0.978179 | − | 0.207764i | \(-0.933381\pi\) | ||
0.978179 | − | 0.207764i | \(-0.0666186\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.41515 | −0.374488 | −0.187244 | − | 0.982313i | \(-0.559956\pi\) | ||||
−0.187244 | + | 0.982313i | \(0.559956\pi\) | |||||||
\(140\) | 4.35505 | 0.368069 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 27.9841 | 2.34837 | ||||||||
\(143\) | 3.31906 | + | 1.40848i | 0.277554 | + | 0.117783i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.09706i | 0.174151i | ||||||||
\(146\) | 18.3750 | 1.52073 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 9.08810i | − | 0.747037i | ||||||
\(149\) | 9.50356i | 0.778562i | 0.921119 | + | 0.389281i | \(0.127276\pi\) | ||||
−0.921119 | + | 0.389281i | \(0.872724\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.2126i | 1.23798i | 0.785398 | + | 0.618991i | \(0.212458\pi\) | ||||
−0.785398 | + | 0.618991i | \(0.787542\pi\) | |||||||
\(152\) | −0.342711 | −0.0277976 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 4.98315i | − | 0.401554i | ||||||
\(155\) | −2.85516 | −0.229332 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.1949 | 1.61173 | 0.805866 | − | 0.592098i | \(-0.201700\pi\) | ||||
0.805866 | + | 0.592098i | \(0.201700\pi\) | |||||||
\(158\) | − | 3.93450i | − | 0.313012i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.47187 | −0.432589 | ||||||||
\(161\) | 22.0232i | 1.73567i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 16.4974i | − | 1.29217i | −0.763264 | − | 0.646087i | \(-0.776404\pi\) | ||
0.763264 | − | 0.646087i | \(-0.223596\pi\) | |||||||
\(164\) | − | 25.1167i | − | 1.96129i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 10.0255 | 0.778126 | ||||||||
\(167\) | 5.50507i | 0.425995i | 0.977053 | + | 0.212998i | \(0.0683226\pi\) | ||||
−0.977053 | + | 0.212998i | \(0.931677\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.03237 | − | 9.34967i | −0.694798 | − | 0.719205i | ||||
\(170\) | −10.2362 | −0.785082 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −31.5389 | −2.40482 | ||||||||
\(173\) | −12.7126 | −0.966524 | −0.483262 | − | 0.875476i | \(-0.660548\pi\) | ||||
−0.483262 | + | 0.875476i | \(0.660548\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.3832i | 0.784899i | ||||||||
\(176\) | 2.26104i | 0.170432i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −31.8698 | −2.38875 | ||||||||
\(179\) | 24.4279 | 1.82583 | 0.912913 | − | 0.408154i | \(-0.133828\pi\) | ||||
0.912913 | + | 0.408154i | \(0.133828\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.931324 | −0.0692248 | −0.0346124 | − | 0.999401i | \(-0.511020\pi\) | ||||
−0.0346124 | + | 0.999401i | \(0.511020\pi\) | |||||||
\(182\) | −7.01866 | + | 16.5394i | −0.520258 | + | 1.22598i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 13.4748i | 0.993374i | ||||||||
\(185\) | −2.43108 | −0.178736 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.68027i | 0.488510i | ||||||||
\(188\) | − | 34.2966i | − | 2.50134i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.371610i | 0.0269594i | ||||||||
\(191\) | −4.68209 | −0.338784 | −0.169392 | − | 0.985549i | \(-0.554180\pi\) | ||||
−0.169392 | + | 0.985549i | \(0.554180\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 10.2671i | − | 0.739039i | −0.929223 | − | 0.369520i | \(-0.879522\pi\) | ||
0.929223 | − | 0.369520i | \(-0.120478\pi\) | |||||||
\(194\) | −4.02473 | −0.288959 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.42200 | −0.315857 | ||||||||
\(197\) | 11.5842i | 0.825341i | 0.910880 | + | 0.412671i | \(0.135404\pi\) | ||||
−0.910880 | + | 0.412671i | \(0.864596\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.2330 | −1.22162 | −0.610808 | − | 0.791779i | \(-0.709155\pi\) | ||||
−0.610808 | + | 0.791779i | \(0.709155\pi\) | |||||||
\(200\) | 6.35294i | 0.449221i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.28783i | 0.372050i | ||||||||
\(203\) | 6.81975i | 0.478652i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.71875 | −0.469258 | ||||||||
\(206\) | 22.1818i | 1.54548i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.18463 | − | 7.50454i | 0.220814 | − | 0.520346i | ||||
\(209\) | 0.242517 | 0.0167752 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.6905 | −0.735967 | −0.367983 | − | 0.929832i | \(-0.619952\pi\) | ||||
−0.367983 | + | 0.929832i | \(0.619952\pi\) | |||||||
\(212\) | 18.0261 | 1.23804 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 42.4367i | 2.90092i | ||||||||
\(215\) | 8.43668i | 0.575377i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.28516 | −0.630318 | ||||||||
\(218\) | −2.75099 | −0.186320 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.88559 | −0.127127 | ||||||||
\(221\) | 9.40902 | − | 22.1722i | 0.632919 | − | 1.49147i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.33992i | 0.357587i | 0.983887 | + | 0.178794i | \(0.0572194\pi\) | ||||
−0.983887 | + | 0.178794i | \(0.942781\pi\) | |||||||
\(224\) | −17.7948 | −1.18897 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 1.37811i | − | 0.0916702i | ||||||
\(227\) | − | 7.82431i | − | 0.519318i | −0.965700 | − | 0.259659i | \(-0.916390\pi\) | ||
0.965700 | − | 0.259659i | \(-0.0836101\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 10.6805i | − | 0.705784i | −0.935664 | − | 0.352892i | \(-0.885198\pi\) | ||
0.935664 | − | 0.352892i | \(-0.114802\pi\) | |||||||
\(230\) | 14.6110 | 0.963422 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.17263i | 0.273947i | ||||||||
\(233\) | 15.4509 | 1.01222 | 0.506112 | − | 0.862468i | \(-0.331082\pi\) | ||||
0.506112 | + | 0.862468i | \(0.331082\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.17437 | −0.598470 | ||||||||
\(236\) | 20.7439i | 1.35031i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −33.2888 | −2.15779 | ||||||||
\(239\) | − | 16.9365i | − | 1.09553i | −0.836632 | − | 0.547765i | \(-0.815479\pi\) | ||
0.836632 | − | 0.547765i | \(-0.184521\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 0.0799646i | − | 0.00515098i | −0.999997 | − | 0.00257549i | \(-0.999180\pi\) | ||
0.999997 | − | 0.00257549i | \(-0.000819804\pi\) | |||||||
\(242\) | 2.15754i | 0.138692i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.41758 | −0.154770 | ||||||||
\(245\) | 1.18289i | 0.0755720i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.804929 | − | 0.341580i | −0.0512164 | − | 0.0217342i | ||||
\(248\) | −5.68108 | −0.360749 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 14.5502 | 0.920234 | ||||||||
\(251\) | −7.57174 | −0.477924 | −0.238962 | − | 0.971029i | \(-0.576807\pi\) | ||||
−0.238962 | + | 0.971029i | \(0.576807\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 9.53531i | − | 0.599480i | ||||||
\(254\) | 22.3696i | 1.40359i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.11835 | 0.0698970 | ||||||||
\(257\) | 23.0242 | 1.43621 | 0.718105 | − | 0.695935i | \(-0.245010\pi\) | ||||
0.718105 | + | 0.695935i | \(0.245010\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.90600 | −0.491255 | ||||||||
\(260\) | 6.25840 | + | 2.65582i | 0.388130 | + | 0.164707i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 12.2698i | − | 0.758028i | ||||||
\(263\) | 5.95047 | 0.366922 | 0.183461 | − | 0.983027i | \(-0.441270\pi\) | ||||
0.183461 | + | 0.983027i | \(0.441270\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 4.82200i | − | 0.296213i | ||||||
\(266\) | 1.20850i | 0.0740977i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 24.7502i | 1.51186i | ||||||||
\(269\) | 1.17571 | 0.0716841 | 0.0358420 | − | 0.999357i | \(-0.488589\pi\) | ||||
0.0358420 | + | 0.999357i | \(0.488589\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 7.12706i | − | 0.432938i | −0.976290 | − | 0.216469i | \(-0.930546\pi\) | ||
0.976290 | − | 0.216469i | \(-0.0694540\pi\) | |||||||
\(272\) | 15.1044 | 0.915837 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.4935 | −0.633934 | ||||||||
\(275\) | − | 4.49560i | − | 0.271095i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.9736 | 0.719426 | 0.359713 | − | 0.933063i | \(-0.382875\pi\) | ||||
0.359713 | + | 0.933063i | \(0.382875\pi\) | |||||||
\(278\) | 9.52586i | 0.571323i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | − | 2.31803i | − | 0.138529i | ||||||
\(281\) | − | 18.7901i | − | 1.12092i | −0.828181 | − | 0.560461i | \(-0.810624\pi\) | ||
0.828181 | − | 0.560461i | \(-0.189376\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.5237 | −0.625568 | −0.312784 | − | 0.949824i | \(-0.601262\pi\) | ||||
−0.312784 | + | 0.949824i | \(0.601262\pi\) | |||||||
\(284\) | − | 34.4361i | − | 2.04341i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.03885 | − | 7.16101i | 0.179691 | − | 0.423440i | ||||
\(287\) | −21.8497 | −1.28975 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 27.6260 | 1.62506 | ||||||||
\(290\) | 4.52448 | 0.265687 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 22.6115i | − | 1.32324i | ||||||
\(293\) | 14.0111i | 0.818540i | 0.912413 | + | 0.409270i | \(0.134217\pi\) | ||||
−0.912413 | + | 0.409270i | \(0.865783\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.54901 | 0.323076 | ||||||||
\(296\) | −4.83725 | −0.281159 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 20.5043 | 1.18778 | ||||||||
\(299\) | −13.4303 | + | 31.6483i | −0.776693 | + | 1.83027i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 27.4366i | 1.58142i | ||||||||
\(302\) | 32.8217 | 1.88868 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 0.548341i | − | 0.0314495i | ||||||
\(305\) | 0.646706i | 0.0370303i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.52126i | 0.143896i | 0.997408 | + | 0.0719481i | \(0.0229216\pi\) | ||||
−0.997408 | + | 0.0719481i | \(0.977078\pi\) | |||||||
\(308\) | −6.13206 | −0.349406 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.16013i | 0.349872i | ||||||||
\(311\) | −22.9380 | −1.30069 | −0.650347 | − | 0.759638i | \(-0.725376\pi\) | ||||
−0.650347 | + | 0.759638i | \(0.725376\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.6566 | −1.22410 | −0.612051 | − | 0.790818i | \(-0.709655\pi\) | ||||
−0.612051 | + | 0.790818i | \(0.709655\pi\) | |||||||
\(314\) | − | 43.5714i | − | 2.45888i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.84163 | −0.272363 | ||||||||
\(317\) | 26.6050i | 1.49429i | 0.664664 | + | 0.747143i | \(0.268575\pi\) | ||||
−0.664664 | + | 0.747143i | \(0.731425\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 2.95273i | − | 0.165321i | ||||||
\(320\) | 8.59415i | 0.480428i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 47.5159 | 2.64796 | ||||||||
\(323\) | − | 1.62008i | − | 0.0901435i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.33196 | + | 14.9212i | −0.351234 | + | 0.827679i | ||||
\(326\) | −35.5937 | −1.97135 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −13.3687 | −0.738161 | ||||||||
\(329\) | −29.8356 | −1.64489 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.7670i | 1.36132i | 0.732600 | + | 0.680659i | \(0.238307\pi\) | ||||
−0.732600 | + | 0.680659i | \(0.761693\pi\) | |||||||
\(332\) | − | 12.3369i | − | 0.677076i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 11.8774 | 0.649903 | ||||||||
\(335\) | 6.62069 | 0.361727 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.2890 | 1.54100 | 0.770499 | − | 0.637441i | \(-0.220007\pi\) | ||||
0.770499 | + | 0.637441i | \(0.220007\pi\) | |||||||
\(338\) | −20.1723 | + | 19.4877i | −1.09723 | + | 1.05999i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 12.5963i | 0.683129i | ||||||||
\(341\) | 4.02017 | 0.217704 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0143i | 1.08067i | ||||||||
\(344\) | 16.7869i | 0.905091i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 27.4280i | 1.47454i | ||||||||
\(347\) | 18.0814 | 0.970661 | 0.485331 | − | 0.874331i | \(-0.338699\pi\) | ||||
0.485331 | + | 0.874331i | \(0.338699\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.0326i | 1.12585i | 0.826508 | + | 0.562924i | \(0.190324\pi\) | ||||
−0.826508 | + | 0.562924i | \(0.809676\pi\) | |||||||
\(350\) | 22.4022 | 1.19745 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7.70458 | 0.410655 | ||||||||
\(353\) | 2.20127i | 0.117162i | 0.998283 | + | 0.0585810i | \(0.0186576\pi\) | ||||
−0.998283 | + | 0.0585810i | \(0.981342\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.21169 | −0.488906 | ||||||||
\(356\) | 39.2177i | 2.07853i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 52.7041i | − | 2.78550i | ||||||
\(359\) | 7.76540i | 0.409842i | 0.978778 | + | 0.204921i | \(0.0656938\pi\) | ||||
−0.978778 | + | 0.204921i | \(0.934306\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.9412 | 0.996905 | ||||||||
\(362\) | 2.00937i | 0.105610i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 20.3527 | + | 8.63687i | 1.06677 | + | 0.452695i | ||||
\(365\) | −6.04861 | −0.316599 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.9604 | −0.624326 | −0.312163 | − | 0.950028i | \(-0.601054\pi\) | ||||
−0.312163 | + | 0.950028i | \(0.601054\pi\) | |||||||
\(368\) | −21.5597 | −1.12388 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5.24514i | 0.272682i | ||||||||
\(371\) | − | 15.6814i | − | 0.814138i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.1243 | 0.731330 | 0.365665 | − | 0.930747i | \(-0.380842\pi\) | ||||
0.365665 | + | 0.930747i | \(0.380842\pi\) | |||||||
\(374\) | 14.4130 | 0.745276 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −18.2548 | −0.941418 | ||||||||
\(377\) | −4.15885 | + | 9.80029i | −0.214192 | + | 0.504741i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.34432i | 0.171786i | 0.996304 | + | 0.0858931i | \(0.0273744\pi\) | ||||
−0.996304 | + | 0.0858931i | \(0.972626\pi\) | |||||||
\(380\) | 0.457288 | 0.0234584 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 10.1018i | 0.516853i | ||||||||
\(383\) | − | 5.63621i | − | 0.287997i | −0.989578 | − | 0.143998i | \(-0.954004\pi\) | ||
0.989578 | − | 0.143998i | \(-0.0459960\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.64033i | 0.0835991i | ||||||||
\(386\) | −22.1516 | −1.12749 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.95266i | 0.251433i | ||||||||
\(389\) | 14.3490 | 0.727523 | 0.363761 | − | 0.931492i | \(-0.381492\pi\) | ||||
0.363761 | + | 0.931492i | \(0.381492\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −63.6984 | −3.22137 | ||||||||
\(392\) | 2.35366i | 0.118878i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 24.9934 | 1.25915 | ||||||||
\(395\) | 1.29514i | 0.0651657i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 14.8769i | − | 0.746648i | −0.927701 | − | 0.373324i | \(-0.878218\pi\) | ||
0.927701 | − | 0.373324i | \(-0.121782\pi\) | |||||||
\(398\) | 37.1809i | 1.86371i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −10.1647 | −0.508237 | ||||||||
\(401\) | − | 19.6380i | − | 0.980675i | −0.871533 | − | 0.490337i | \(-0.836874\pi\) | ||
0.871533 | − | 0.490337i | \(-0.163126\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.3432 | − | 5.66233i | −0.664672 | − | 0.282061i | ||||
\(404\) | 6.50698 | 0.323734 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 14.7139 | 0.730237 | ||||||||
\(407\) | 3.42304 | 0.169674 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 23.1731i | − | 1.14584i | −0.819613 | − | 0.572918i | \(-0.805811\pi\) | ||
0.819613 | − | 0.572918i | \(-0.194189\pi\) | |||||||
\(410\) | 14.4960i | 0.715905i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 27.2961 | 1.34478 | ||||||||
\(413\) | 18.0457 | 0.887971 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.30014 | −0.161997 | ||||||||
\(416\) | −25.5720 | − | 10.8517i | −1.25377 | − | 0.532050i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 0.523240i | − | 0.0255925i | ||||||
\(419\) | 3.70294 | 0.180900 | 0.0904502 | − | 0.995901i | \(-0.471169\pi\) | ||||
0.0904502 | + | 0.995901i | \(0.471169\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 23.7239i | − | 1.15623i | −0.815955 | − | 0.578116i | \(-0.803788\pi\) | ||
0.815955 | − | 0.578116i | \(-0.196212\pi\) | |||||||
\(422\) | 23.0653i | 1.12280i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 9.59460i | − | 0.465955i | ||||||
\(425\) | −30.0318 | −1.45676 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.10313i | 0.101777i | ||||||||
\(428\) | 52.2209 | 2.52419 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 18.2025 | 0.877802 | ||||||||
\(431\) | − | 31.0695i | − | 1.49656i | −0.663381 | − | 0.748282i | \(-0.730879\pi\) | ||
0.663381 | − | 0.748282i | \(-0.269121\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.0541 | −1.10791 | −0.553954 | − | 0.832547i | \(-0.686882\pi\) | ||||
−0.553954 | + | 0.832547i | \(0.686882\pi\) | |||||||
\(434\) | 20.0331i | 0.961620i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.38525i | 0.162124i | ||||||||
\(437\) | 2.31247i | 0.110621i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.39273 | −0.114199 | −0.0570994 | − | 0.998368i | \(-0.518185\pi\) | ||||
−0.0570994 | + | 0.998368i | \(0.518185\pi\) | |||||||
\(440\) | 1.00363i | 0.0478462i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −47.8375 | − | 20.3003i | −2.27540 | − | 0.965589i | ||||
\(443\) | 17.1624 | 0.815411 | 0.407705 | − | 0.913113i | \(-0.366329\pi\) | ||||
0.407705 | + | 0.913113i | \(0.366329\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.4908 | 0.497311 | ||||||||
\(446\) | 11.5211 | 0.545539 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 27.9487i | 1.32045i | ||||||||
\(449\) | − | 29.0646i | − | 1.37164i | −0.727769 | − | 0.685822i | \(-0.759443\pi\) | ||
0.727769 | − | 0.685822i | \(-0.240557\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.46022 | 0.445465 | ||||||||
\(452\) | −1.69584 | −0.0797656 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −16.8813 | −0.792277 | ||||||||
\(455\) | 2.31037 | − | 5.44437i | 0.108312 | − | 0.255236i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.9111i | 1.49274i | 0.665532 | + | 0.746369i | \(0.268205\pi\) | ||||
−0.665532 | + | 0.746369i | \(0.731795\pi\) | |||||||
\(458\) | −23.0435 | −1.07675 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 17.9797i | − | 0.838308i | ||||||
\(461\) | − | 0.706685i | − | 0.0329136i | −0.999865 | − | 0.0164568i | \(-0.994761\pi\) | ||
0.999865 | − | 0.0164568i | \(-0.00523860\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.7813i | 1.19816i | 0.800690 | + | 0.599079i | \(0.204467\pi\) | ||||
−0.800690 | + | 0.599079i | \(0.795533\pi\) | |||||||
\(464\) | −6.67624 | −0.309937 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 33.3360i | − | 1.54426i | ||||||
\(467\) | 37.3541 | 1.72854 | 0.864270 | − | 0.503028i | \(-0.167781\pi\) | ||||
0.864270 | + | 0.503028i | \(0.167781\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 21.5309 | 0.994203 | ||||||||
\(470\) | 19.7941i | 0.913033i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 11.0412 | 0.508212 | ||||||||
\(473\) | − | 11.8791i | − | 0.546203i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.09026i | 0.0500245i | ||||||||
\(476\) | 40.9638i | 1.87757i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −36.5411 | −1.67135 | ||||||||
\(479\) | − | 1.74064i | − | 0.0795318i | −0.999209 | − | 0.0397659i | \(-0.987339\pi\) | ||
0.999209 | − | 0.0397659i | \(-0.0126612\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.3613 | − | 4.82128i | −0.518030 | − | 0.219831i | ||||
\(482\) | −0.172527 | −0.00785839 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.65498 | 0.120681 | ||||||||
\(485\) | 1.32484 | 0.0601580 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 5.69783i | − | 0.258193i | −0.991632 | − | 0.129097i | \(-0.958792\pi\) | ||
0.991632 | − | 0.129097i | \(-0.0412078\pi\) | |||||||
\(488\) | 1.28679i | 0.0582502i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.55213 | 0.115293 | ||||||||
\(491\) | −27.7388 | −1.25183 | −0.625917 | − | 0.779890i | \(-0.715275\pi\) | ||||
−0.625917 | + | 0.779890i | \(0.715275\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.7250 | −0.888370 | ||||||||
\(494\) | −0.736972 | + | 1.73667i | −0.0331580 | + | 0.0781363i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 9.08977i | − | 0.408143i | ||||||
\(497\) | −29.9569 | −1.34375 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 8.27073i | − | 0.370249i | −0.982715 | − | 0.185124i | \(-0.940731\pi\) | ||
0.982715 | − | 0.185124i | \(-0.0592688\pi\) | |||||||
\(500\) | − | 17.9048i | − | 0.800729i | ||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 16.3363i | 0.729126i | ||||||||
\(503\) | 12.7099 | 0.566706 | 0.283353 | − | 0.959016i | \(-0.408553\pi\) | ||||
0.283353 | + | 0.959016i | \(0.408553\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 1.74062i | − | 0.0774568i | ||||||
\(506\) | −20.5728 | −0.914573 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 27.5271 | 1.22132 | ||||||||
\(509\) | 5.55978i | 0.246433i | 0.992380 | + | 0.123216i | \(0.0393210\pi\) | ||||
−0.992380 | + | 0.123216i | \(0.960679\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19.6704 | −0.870168 | ||||||||
\(512\) | − | 23.8107i | − | 1.05230i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 49.6756i | − | 2.19110i | ||||||
\(515\) | − | 7.30172i | − | 0.321752i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.9178 | 0.568126 | ||||||||
\(518\) | 17.0575i | 0.749464i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.41359 | − | 3.33111i | 0.0619901 | − | 0.146079i | ||||
\(521\) | 4.41425 | 0.193392 | 0.0966958 | − | 0.995314i | \(-0.469173\pi\) | ||||
0.0966958 | + | 0.995314i | \(0.469173\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.5162 | 0.678474 | 0.339237 | − | 0.940701i | \(-0.389831\pi\) | ||||
0.339237 | + | 0.940701i | \(0.389831\pi\) | |||||||
\(524\) | −15.0986 | −0.659587 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 12.8384i | − | 0.559780i | ||||||
\(527\) | − | 26.8558i | − | 1.16986i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 67.9221 | 2.95314 | ||||||||
\(530\) | −10.4037 | −0.451906 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.48713 | 0.0644751 | ||||||||
\(533\) | −31.3991 | − | 13.3245i | −1.36005 | − | 0.577150i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 13.9691i | − | 0.603939i | ||||||
\(536\) | 13.1736 | 0.569011 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 2.53663i | − | 0.109362i | ||||||
\(539\) | − | 1.66555i | − | 0.0717402i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 27.9827i | − | 1.20307i | −0.798846 | − | 0.601536i | \(-0.794556\pi\) | ||
0.798846 | − | 0.601536i | \(-0.205444\pi\) | |||||||
\(542\) | −15.3769 | −0.660495 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 51.4687i | − | 2.20670i | ||||||
\(545\) | 0.905559 | 0.0387899 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.1470 | −1.03245 | −0.516226 | − | 0.856453i | \(-0.672663\pi\) | ||||
−0.516226 | + | 0.856453i | \(0.672663\pi\) | |||||||
\(548\) | 12.9128i | 0.551609i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −9.69944 | −0.413586 | ||||||||
\(551\) | 0.716086i | 0.0305063i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.21188i | 0.179107i | ||||||||
\(554\) | − | 25.8336i | − | 1.09756i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 11.7221 | 0.497129 | ||||||||
\(557\) | − | 19.1326i | − | 0.810675i | −0.914167 | − | 0.405337i | \(-0.867154\pi\) | ||
0.914167 | − | 0.405337i | \(-0.132846\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.7315 | + | 39.4276i | −0.707668 | + | 1.66761i | ||||
\(560\) | 3.70886 | 0.156728 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −40.5404 | −1.71009 | ||||||||
\(563\) | −3.91199 | −0.164871 | −0.0824353 | − | 0.996596i | \(-0.526270\pi\) | ||||
−0.0824353 | + | 0.996596i | \(0.526270\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.453639i | 0.0190847i | ||||||||
\(566\) | 22.7053i | 0.954373i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −18.3290 | −0.769069 | ||||||||
\(569\) | −15.8002 | −0.662377 | −0.331189 | − | 0.943565i | \(-0.607450\pi\) | ||||
−0.331189 | + | 0.943565i | \(0.607450\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.2458 | −0.847262 | −0.423631 | − | 0.905835i | \(-0.639245\pi\) | ||||
−0.423631 | + | 0.905835i | \(0.639245\pi\) | |||||||
\(572\) | −8.81205 | − | 3.73948i | −0.368450 | − | 0.156356i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 47.1417i | 1.96766i | ||||||||
\(575\) | 42.8669 | 1.78768 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.07073i | 0.294358i | 0.989110 | + | 0.147179i | \(0.0470194\pi\) | ||||
−0.989110 | + | 0.147179i | \(0.952981\pi\) | |||||||
\(578\) | − | 59.6042i | − | 2.47921i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 5.56764i | − | 0.231184i | ||||||
\(581\) | −10.7322 | −0.445248 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.78954i | 0.281194i | ||||||||
\(584\) | −12.0353 | −0.498023 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 30.2296 | 1.24877 | ||||||||
\(587\) | 27.1767i | 1.12170i | 0.827917 | + | 0.560851i | \(0.189526\pi\) | ||||
−0.827917 | + | 0.560851i | \(0.810474\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.974959 | −0.0401725 | ||||||||
\(590\) | − | 11.9722i | − | 0.492889i | ||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 7.73963i | − | 0.318097i | ||||||
\(593\) | − | 20.0431i | − | 0.823070i | −0.911394 | − | 0.411535i | \(-0.864993\pi\) | ||
0.911394 | − | 0.411535i | \(-0.135007\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.9579 | 0.449228 | ||||||||
\(596\) | − | 25.2318i | − | 1.03353i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 68.2825 | + | 28.9764i | 2.79228 | + | 1.18493i | ||||
\(599\) | 24.5855 | 1.00454 | 0.502268 | − | 0.864712i | \(-0.332499\pi\) | ||||
0.502268 | + | 0.864712i | \(0.332499\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.1098 | −1.39137 | −0.695683 | − | 0.718349i | \(-0.744898\pi\) | ||||
−0.695683 | + | 0.718349i | \(0.744898\pi\) | |||||||
\(602\) | 59.1955 | 2.41263 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 40.3891i | − | 1.64341i | ||||||
\(605\) | − | 0.710210i | − | 0.0288741i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.9453 | 0.850143 | 0.425071 | − | 0.905160i | \(-0.360249\pi\) | ||||
0.425071 | + | 0.905160i | \(0.360249\pi\) | |||||||
\(608\) | −1.86849 | −0.0757773 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.39530 | 0.0564938 | ||||||||
\(611\) | −42.8751 | − | 18.1945i | −1.73454 | − | 0.736071i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.2792i | 0.899848i | 0.893067 | + | 0.449924i | \(0.148549\pi\) | ||||
−0.893067 | + | 0.449924i | \(0.851451\pi\) | |||||||
\(614\) | 5.43973 | 0.219530 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.26386i | 0.131505i | ||||||||
\(617\) | 27.4366i | 1.10456i | 0.833660 | + | 0.552279i | \(0.186242\pi\) | ||||
−0.833660 | + | 0.552279i | \(0.813758\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 47.9288i | − | 1.92642i | −0.268747 | − | 0.963211i | \(-0.586610\pi\) | ||
0.268747 | − | 0.963211i | \(-0.413390\pi\) | |||||||
\(620\) | 7.58040 | 0.304436 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 49.4896i | 1.98435i | ||||||||
\(623\) | 34.1166 | 1.36685 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.6884 | 0.707538 | ||||||||
\(626\) | 46.7250i | 1.86751i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −53.6171 | −2.13956 | ||||||||
\(629\) | − | 22.8668i | − | 0.911760i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.8277i | 0.948567i | 0.880372 | + | 0.474284i | \(0.157293\pi\) | ||||
−0.880372 | + | 0.474284i | \(0.842707\pi\) | |||||||
\(632\) | 2.57702i | 0.102508i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 57.4013 | 2.27970 | ||||||||
\(635\) | − | 7.36353i | − | 0.292213i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.34589 | + | 5.52806i | −0.0929475 | + | 0.219030i | ||||
\(638\) | −6.37063 | −0.252216 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 7.59848 | 0.300356 | ||||||||
\(641\) | −8.30355 | −0.327970 | −0.163985 | − | 0.986463i | \(-0.552435\pi\) | ||||
−0.163985 | + | 0.986463i | \(0.552435\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 29.9185i | − | 1.17987i | −0.807451 | − | 0.589934i | \(-0.799154\pi\) | ||
0.807451 | − | 0.589934i | \(-0.200846\pi\) | |||||||
\(644\) | − | 58.4710i | − | 2.30408i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.49538 | −0.137524 | ||||||||
\(647\) | 5.87308 | 0.230895 | 0.115447 | − | 0.993314i | \(-0.463170\pi\) | ||||
0.115447 | + | 0.993314i | \(0.463170\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.81320 | −0.306695 | ||||||||
\(650\) | 32.1931 | + | 13.6615i | 1.26272 | + | 0.535847i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 43.8002i | 1.71535i | ||||||||
\(653\) | 5.43262 | 0.212595 | 0.106297 | − | 0.994334i | \(-0.466100\pi\) | ||||
0.106297 | + | 0.994334i | \(0.466100\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.03891i | 0.157813i | ||||||||
\(656\) | − | 21.3900i | − | 0.835138i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 64.3715i | 2.50946i | ||||||||
\(659\) | −26.5954 | −1.03601 | −0.518004 | − | 0.855378i | \(-0.673325\pi\) | ||||
−0.518004 | + | 0.855378i | \(0.673325\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 27.7763i | − | 1.08037i | −0.841545 | − | 0.540187i | \(-0.818354\pi\) | ||
0.841545 | − | 0.540187i | \(-0.181646\pi\) | |||||||
\(662\) | 53.4359 | 2.07684 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.56647 | −0.254828 | ||||||||
\(665\) | − | 0.397808i | − | 0.0154263i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 28.1552 | 1.09017 | ||||||||
\(668\) | − | 14.6158i | − | 0.565504i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − | 14.2844i | − | 0.551855i | ||||||
\(671\) | − | 0.910585i | − | 0.0351527i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.00054 | −0.115663 | −0.0578313 | − | 0.998326i | \(-0.518419\pi\) | ||||
−0.0578313 | + | 0.998326i | \(0.518419\pi\) | |||||||
\(674\) | − | 61.0346i | − | 2.35096i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 23.9808 | + | 24.8232i | 0.922337 | + | 0.954737i | ||||
\(677\) | 25.1724 | 0.967452 | 0.483726 | − | 0.875219i | \(-0.339283\pi\) | ||||
0.483726 | + | 0.875219i | \(0.339283\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.30846 | 0.165344 | ||||||||
\(680\) | 6.70452 | 0.257107 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 8.67368i | − | 0.332132i | ||||||
\(683\) | − | 39.1652i | − | 1.49861i | −0.662223 | − | 0.749307i | \(-0.730387\pi\) | ||
0.662223 | − | 0.749307i | \(-0.269613\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.45420 | 0.131978 | ||||||||
\(686\) | 43.1817 | 1.64869 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −26.8592 | −1.02400 | ||||||||
\(689\) | 9.56293 | − | 22.5349i | 0.364318 | − | 0.858512i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 33.3472i | − | 1.26859i | −0.773092 | − | 0.634294i | \(-0.781291\pi\) | ||
0.773092 | − | 0.634294i | \(-0.218709\pi\) | |||||||
\(692\) | 33.7518 | 1.28305 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 39.0114i | − | 1.48085i | ||||||
\(695\) | − | 3.13568i | − | 0.118943i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 63.1969i | − | 2.39375i | ||||||
\(698\) | 45.3787 | 1.71761 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | − | 27.5673i | − | 1.04195i | ||||||
\(701\) | 8.45704 | 0.319418 | 0.159709 | − | 0.987164i | \(-0.448944\pi\) | ||||
0.159709 | + | 0.987164i | \(0.448944\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.830144 | −0.0313095 | ||||||||
\(704\) | − | 12.1009i | − | 0.456068i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.74934 | 0.178744 | ||||||||
\(707\) | − | 5.66061i | − | 0.212889i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 7.03783i | − | 0.264311i | −0.991229 | − | 0.132156i | \(-0.957810\pi\) | ||
0.991229 | − | 0.132156i | \(-0.0421899\pi\) | |||||||
\(710\) | 19.8746i | 0.745880i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 20.8741 | 0.782290 | ||||||||
\(713\) | 38.3336i | 1.43560i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.00032 | + | 2.35723i | −0.0374097 | + | 0.0881555i | ||||
\(716\) | −64.8555 | −2.42377 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 16.7542 | 0.625260 | ||||||||
\(719\) | −5.52947 | −0.206215 | −0.103107 | − | 0.994670i | \(-0.532879\pi\) | ||||
−0.103107 | + | 0.994670i | \(0.532879\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 23.7456i | − | 0.884333i | ||||||
\(722\) | − | 40.8664i | − | 1.52089i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.47265 | 0.0918952 | ||||||||
\(725\) | 13.2743 | 0.492995 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.7533 | 1.43728 | 0.718640 | − | 0.695383i | \(-0.244765\pi\) | ||||
0.718640 | + | 0.695383i | \(0.244765\pi\) | |||||||
\(728\) | 4.59708 | − | 10.8330i | 0.170379 | − | 0.401496i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 13.0501i | 0.483006i | ||||||||
\(731\) | −79.3558 | −2.93508 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 9.60595i | − | 0.354804i | −0.984138 | − | 0.177402i | \(-0.943231\pi\) | ||
0.984138 | − | 0.177402i | \(-0.0567693\pi\) | |||||||
\(734\) | 25.8050i | 0.952480i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 73.4655i | 2.70798i | ||||||||
\(737\) | −9.32216 | −0.343386 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.6659i | 0.796995i | 0.917169 | + | 0.398497i | \(0.130468\pi\) | ||||
−0.917169 | + | 0.398497i | \(0.869532\pi\) | |||||||
\(740\) | 6.45446 | 0.237271 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −33.8333 | −1.24206 | ||||||||
\(743\) | 12.3149i | 0.451790i | 0.974152 | + | 0.225895i | \(0.0725305\pi\) | ||||
−0.974152 | + | 0.225895i | \(0.927469\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.74952 | −0.247283 | ||||||||
\(746\) | − | 30.4738i | − | 1.11572i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 17.7360i | − | 0.648492i | ||||||
\(749\) | − | 45.4285i | − | 1.65992i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.50813 | −0.0915231 | −0.0457616 | − | 0.998952i | \(-0.514571\pi\) | ||||
−0.0457616 | + | 0.998952i | \(0.514571\pi\) | |||||||
\(752\) | − | 29.2078i | − | 1.06510i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 21.1445 | + | 8.97290i | 0.770038 | + | 0.326774i | ||||
\(755\) | −10.8041 | −0.393202 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.89889 | 0.105362 | 0.0526809 | − | 0.998611i | \(-0.483223\pi\) | ||||
0.0526809 | + | 0.998611i | \(0.483223\pi\) | |||||||
\(758\) | 7.21551 | 0.262079 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | − | 0.243397i | − | 0.00882894i | ||||||
\(761\) | 33.6764i | 1.22077i | 0.792105 | + | 0.610384i | \(0.208985\pi\) | ||||
−0.792105 | + | 0.610384i | \(0.791015\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.94493 | 0.106614 | ||||||||
\(764\) | 12.4309 | 0.449733 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −12.1604 | −0.439371 | ||||||||
\(767\) | 25.9325 | + | 11.0047i | 0.936369 | + | 0.397358i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 25.1224i | − | 0.905935i | −0.891527 | − | 0.452968i | \(-0.850365\pi\) | ||
0.891527 | − | 0.452968i | \(-0.149635\pi\) | |||||||
\(770\) | 3.53908 | 0.127540 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 27.2588i | 0.981067i | ||||||||
\(773\) | 31.6336i | 1.13778i | 0.822413 | + | 0.568891i | \(0.192627\pi\) | ||||
−0.822413 | + | 0.568891i | \(0.807373\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18.0731i | 0.649204i | ||||||||
\(776\) | 2.63611 | 0.0946310 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 30.9585i | − | 1.10992i | ||||||
\(779\) | −2.29426 | −0.0822005 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.9704 | 0.464117 | ||||||||
\(782\) | 137.432i | 4.91456i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.76587 | −0.134495 | ||||||||
\(785\) | 14.3426i | 0.511911i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.2041i | 0.827137i | 0.910473 | + | 0.413569i | \(0.135718\pi\) | ||||
−0.910473 | + | 0.413569i | \(0.864282\pi\) | |||||||
\(788\) | − | 30.7559i | − | 1.09563i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.79432 | 0.0994175 | ||||||||
\(791\) | 1.47526i | 0.0524542i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.28254 | + | 3.02229i | −0.0455443 | + | 0.107325i | ||||
\(794\) | −32.0974 | −1.13909 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 45.7533 | 1.62168 | ||||||||
\(797\) | 16.5706 | 0.586960 | 0.293480 | − | 0.955965i | \(-0.405187\pi\) | ||||
0.293480 | + | 0.955965i | \(0.405187\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 86.2946i | − | 3.05288i | ||||||
\(800\) | 34.6367i | 1.22459i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −42.3698 | −1.49613 | ||||||||
\(803\) | 8.51665 | 0.300546 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −15.6411 | −0.551275 | ||||||||
\(806\) | −12.2167 | + | 28.7885i | −0.430315 | + | 1.01403i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 3.46342i | − | 0.121843i | ||||||
\(809\) | −8.97637 | −0.315592 | −0.157796 | − | 0.987472i | \(-0.550439\pi\) | ||||
−0.157796 | + | 0.987472i | \(0.550439\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 2.09499i | − | 0.0735651i | −0.999323 | − | 0.0367826i | \(-0.988289\pi\) | ||
0.999323 | − | 0.0367826i | \(-0.0117109\pi\) | |||||||
\(812\) | − | 18.1063i | − | 0.635406i | ||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 7.38534i | − | 0.258856i | ||||||
\(815\) | 11.7166 | 0.410414 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.88089i | 0.100790i | ||||||||
\(818\) | −49.9969 | −1.74810 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 17.8381 | 0.622935 | ||||||||
\(821\) | − | 32.8066i | − | 1.14496i | −0.819919 | − | 0.572480i | \(-0.805982\pi\) | ||
0.819919 | − | 0.572480i | \(-0.194018\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.37447 | 0.222200 | 0.111100 | − | 0.993809i | \(-0.464563\pi\) | ||||
0.111100 | + | 0.993809i | \(0.464563\pi\) | |||||||
\(824\) | − | 14.5287i | − | 0.506130i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | − | 38.9343i | − | 1.35470i | ||||||
\(827\) | 14.7476i | 0.512825i | 0.966567 | + | 0.256413i | \(0.0825406\pi\) | ||||
−0.966567 | + | 0.256413i | \(0.917459\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.4837 | 0.885085 | 0.442542 | − | 0.896748i | \(-0.354077\pi\) | ||||
0.442542 | + | 0.896748i | \(0.354077\pi\) | |||||||
\(830\) | 7.12018i | 0.247145i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −17.0438 | + | 40.1635i | −0.590888 | + | 1.39242i | ||||
\(833\) | −11.1263 | −0.385504 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.90976 | −0.135303 | ||||||||
\(836\) | −0.643877 | −0.0222690 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 7.98924i | − | 0.275984i | ||||||
\(839\) | 41.7953i | 1.44293i | 0.692449 | + | 0.721467i | \(0.256532\pi\) | ||||
−0.692449 | + | 0.721467i | \(0.743468\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.2814 | −0.699359 | ||||||||
\(842\) | −51.1852 | −1.76396 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 28.3831 | 0.976988 | ||||||||
\(845\) | 6.64023 | − | 6.41488i | 0.228431 | − | 0.220679i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 2.30964i | − | 0.0793603i | ||||||
\(848\) | 15.3514 | 0.527170 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 64.7949i | 2.22245i | ||||||||
\(851\) | 32.6397i | 1.11888i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 25.2825i | − | 0.865655i | −0.901477 | − | 0.432827i | \(-0.857516\pi\) | ||
0.901477 | − | 0.432827i | \(-0.142484\pi\) | |||||||
\(854\) | 4.53758 | 0.155273 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 27.7952i | − | 0.950021i | ||||||
\(857\) | −26.8626 | −0.917609 | −0.458804 | − | 0.888537i | \(-0.651722\pi\) | ||||
−0.458804 | + | 0.888537i | \(0.651722\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.11713 | 0.208714 | 0.104357 | − | 0.994540i | \(-0.466722\pi\) | ||||
0.104357 | + | 0.994540i | \(0.466722\pi\) | |||||||
\(860\) | − | 22.3992i | − | 0.763807i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −67.0336 | −2.28318 | ||||||||
\(863\) | 32.1517i | 1.09446i | 0.836984 | + | 0.547228i | \(0.184317\pi\) | ||||
−0.836984 | + | 0.547228i | \(0.815683\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 9.02865i | − | 0.306983i | ||||||
\(866\) | 49.7401i | 1.69024i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 24.6519 | 0.836740 | ||||||||
\(869\) | − | 1.82360i | − | 0.0618616i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.9409 | + | 13.1301i | 1.04839 | + | 0.444896i | ||||
\(872\) | 1.80184 | 0.0610180 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.98925 | 0.168764 | ||||||||
\(875\) | −15.5759 | −0.526563 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.9062i | 0.604648i | 0.953205 | + | 0.302324i | \(0.0977625\pi\) | ||||
−0.953205 | + | 0.302324i | \(0.902237\pi\) | |||||||
\(878\) | 5.16241i | 0.174223i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.60581 | −0.0541320 | ||||||||
\(881\) | 40.5751 | 1.36701 | 0.683504 | − | 0.729947i | \(-0.260455\pi\) | ||||
0.683504 | + | 0.729947i | \(0.260455\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.6601 | 0.829879 | 0.414940 | − | 0.909849i | \(-0.363803\pi\) | ||||
0.414940 | + | 0.909849i | \(0.363803\pi\) | |||||||
\(884\) | −24.9808 | + | 58.8669i | −0.840194 | + | 1.97991i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − | 37.0286i | − | 1.24400i | ||||||
\(887\) | −27.2662 | −0.915510 | −0.457755 | − | 0.889078i | \(-0.651346\pi\) | ||||
−0.457755 | + | 0.889078i | \(0.651346\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 23.9466i | − | 0.803144i | ||||||
\(890\) | − | 22.6343i | − | 0.758703i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 14.1774i | − | 0.474693i | ||||||
\(893\) | −3.13279 | −0.104835 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17.3489i | 0.579911i | ||||||||
\(896\) | 24.7107 | 0.825526 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −62.7081 | −2.09260 | ||||||||
\(899\) | 11.8705i | 0.395902i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 45.3560 | 1.51103 | ||||||||
\(902\) | − | 20.4108i | − | 0.679606i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.902631i | 0.0300211i | ||||||||
\(905\) | − | 0.661436i | − | 0.0219869i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.121526 | −0.00403521 | −0.00201760 | − | 0.999998i | \(-0.500642\pi\) | ||||
−0.00201760 | + | 0.999998i | \(0.500642\pi\) | |||||||
\(908\) | 20.7734i | 0.689389i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −11.7464 | − | 4.98472i | −0.389391 | − | 0.165242i | ||||
\(911\) | 40.6736 | 1.34758 | 0.673788 | − | 0.738925i | \(-0.264666\pi\) | ||||
0.673788 | + | 0.738925i | \(0.264666\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.64671 | 0.153784 | ||||||||
\(914\) | 68.8495 | 2.27734 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 28.3564i | 0.936921i | ||||||||
\(917\) | 13.1347i | 0.433748i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.0713 | −0.860012 | −0.430006 | − | 0.902826i | \(-0.641489\pi\) | ||||
−0.430006 | + | 0.902826i | \(0.641489\pi\) | |||||||
\(920\) | −9.56992 | −0.315511 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.52470 | −0.0502134 | ||||||||
\(923\) | −43.0495 | − | 18.2685i | −1.41699 | − | 0.601315i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.3886i | 0.505975i | ||||||||
\(926\) | 55.6242 | 1.82792 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 22.7495i | 0.746790i | ||||||||
\(929\) | − | 26.9849i | − | 0.885346i | −0.896683 | − | 0.442673i | \(-0.854030\pi\) | ||
0.896683 | − | 0.442673i | \(-0.145970\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.403923i | 0.0132381i | ||||||||
\(932\) | −41.0219 | −1.34372 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 80.5929i | − | 2.63708i | ||||||
\(935\) | −4.74440 | −0.155158 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.9915 | 1.04512 | 0.522559 | − | 0.852603i | \(-0.324977\pi\) | ||||
0.522559 | + | 0.852603i | \(0.324977\pi\) | |||||||
\(938\) | − | 46.4537i | − | 1.51677i | ||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 24.3578 | 0.794463 | ||||||||
\(941\) | − | 31.7257i | − | 1.03423i | −0.855916 | − | 0.517115i | \(-0.827006\pi\) | ||
0.855916 | − | 0.517115i | \(-0.172994\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 90.2062i | 2.93752i | ||||||||
\(944\) | 17.6660i | 0.574979i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −25.6297 | −0.833294 | ||||||||
\(947\) | 46.5444i | 1.51249i | 0.654289 | + | 0.756245i | \(0.272968\pi\) | ||||
−0.654289 | + | 0.756245i | \(0.727032\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28.2673 | − | 11.9955i | −0.917595 | − | 0.389391i | ||||
\(950\) | 2.35228 | 0.0763180 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 21.8035 | 0.706655 | ||||||||
\(953\) | 37.1054 | 1.20196 | 0.600981 | − | 0.799263i | \(-0.294777\pi\) | ||||
0.600981 | + | 0.799263i | \(0.294777\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 3.32527i | − | 0.107603i | ||||||
\(956\) | 44.9660i | 1.45430i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.75550 | −0.121335 | ||||||||
\(959\) | 11.2332 | 0.362740 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.8382 | 0.478653 | ||||||||
\(962\) | −10.4021 | + | 24.5124i | −0.335377 | + | 0.790312i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.212305i | 0.00683787i | ||||||||
\(965\) | 7.29177 | 0.234730 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 33.1854i | − | 1.06717i | −0.845746 | − | 0.533586i | \(-0.820844\pi\) | ||
0.845746 | − | 0.533586i | \(-0.179156\pi\) | |||||||
\(968\) | − | 1.41315i | − | 0.0454202i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | − | 2.85840i | − | 0.0917777i | ||||||
\(971\) | −23.0990 | −0.741283 | −0.370642 | − | 0.928776i | \(-0.620862\pi\) | ||||
−0.370642 | + | 0.928776i | \(0.620862\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 10.1974i | − | 0.326914i | ||||||
\(974\) | −12.2933 | −0.393903 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.05887 | −0.0659028 | ||||||||
\(977\) | 32.4063i | 1.03677i | 0.855147 | + | 0.518385i | \(0.173467\pi\) | ||||
−0.855147 | + | 0.518385i | \(0.826533\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.7714 | −0.472095 | ||||||||
\(980\) | − | 3.14055i | − | 0.100321i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 59.8475i | 1.90981i | ||||||||
\(983\) | 1.17252i | 0.0373976i | 0.999825 | + | 0.0186988i | \(0.00595236\pi\) | ||||
−0.999825 | + | 0.0186988i | \(0.994048\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.22723 | −0.262141 | ||||||||
\(986\) | 42.5575i | 1.35531i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.13707 | + | 0.906888i | 0.0679892 | + | 0.0288519i | ||||
\(989\) | 113.271 | 3.60182 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.78159 | −0.151892 | −0.0759462 | − | 0.997112i | \(-0.524198\pi\) | ||||
−0.0759462 | + | 0.997112i | \(0.524198\pi\) | |||||||
\(992\) | −30.9737 | −0.983416 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 64.6333i | 2.05004i | ||||||||
\(995\) | − | 12.2391i | − | 0.388004i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 55.7577 | 1.76586 | 0.882932 | − | 0.469502i | \(-0.155566\pi\) | ||||
0.882932 | + | 0.469502i | \(0.155566\pi\) | |||||||
\(998\) | −17.8444 | −0.564856 | ||||||||
\(999\) | 0 | 0 |
(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 | 1287.2.b.c.298.3 | 14 | ||
3.2 | odd | 2 | 429.2.b.b.298.12 | yes | 14 | ||
13.12 | even | 2 | inner | 1287.2.b.c.298.12 | 14 | ||
39.5 | even | 4 | 5577.2.a.x.1.7 | 7 | |||
39.8 | even | 4 | 5577.2.a.y.1.1 | 7 | |||
39.38 | odd | 2 | 429.2.b.b.298.3 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.b.b.298.3 | ✓ | 14 | 39.38 | odd | 2 | ||
429.2.b.b.298.12 | yes | 14 | 3.2 | odd | 2 | ||
1287.2.b.c.298.3 | 14 | 1.1 | even | 1 | trivial | ||
1287.2.b.c.298.12 | 14 | 13.12 | even | 2 | inner | ||
5577.2.a.x.1.7 | 7 | 39.5 | even | 4 | |||
5577.2.a.y.1.1 | 7 | 39.8 | even | 4 |