Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8016,2,Mod(1,8016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8016 = 2^{4} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8016.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: | \(64.0080822603\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 8x^{6} + 15x^{5} + 19x^{4} - 31x^{3} - 13x^{2} + 14x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 501) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(2.22210\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8016.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.56175 | 0.698437 | 0.349218 | − | 0.937041i | \(-0.386447\pi\) | ||||
0.349218 | + | 0.937041i | \(0.386447\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.60397 | −1.74014 | −0.870068 | − | 0.492932i | \(-0.835925\pi\) | ||||
−0.870068 | + | 0.492932i | \(0.835925\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.677161 | 0.204172 | 0.102086 | − | 0.994776i | \(-0.467448\pi\) | ||||
0.102086 | + | 0.994776i | \(0.467448\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.42101 | 0.671467 | 0.335734 | − | 0.941957i | \(-0.391016\pi\) | ||||
0.335734 | + | 0.941957i | \(0.391016\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.56175 | 0.403243 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.541579 | −0.131352 | −0.0656761 | − | 0.997841i | \(-0.520920\pi\) | ||||
−0.0656761 | + | 0.997841i | \(0.520920\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.86493 | −0.657260 | −0.328630 | − | 0.944459i | \(-0.606587\pi\) | ||||
−0.328630 | + | 0.944459i | \(0.606587\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.60397 | −1.00467 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.52905 | 1.15289 | 0.576443 | − | 0.817137i | \(-0.304440\pi\) | ||||
0.576443 | + | 0.817137i | \(0.304440\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.56093 | −0.512186 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.48876 | 0.833543 | 0.416771 | − | 0.909011i | \(-0.363162\pi\) | ||||
0.416771 | + | 0.909011i | \(0.363162\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.27589 | −1.12718 | −0.563591 | − | 0.826054i | \(-0.690581\pi\) | ||||
−0.563591 | + | 0.826054i | \(0.690581\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.677161 | 0.117879 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.19026 | −1.21538 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.48690 | −0.737642 | −0.368821 | − | 0.929500i | \(-0.620239\pi\) | ||||
−0.368821 | + | 0.929500i | \(0.620239\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.42101 | 0.387672 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.64946 | −0.413776 | −0.206888 | − | 0.978365i | \(-0.566334\pi\) | ||||
−0.206888 | + | 0.978365i | \(0.566334\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.5513 | −1.60906 | −0.804532 | − | 0.593909i | \(-0.797584\pi\) | ||||
−0.804532 | + | 0.593909i | \(0.797584\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.56175 | 0.232812 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.130851 | 0.0190866 | 0.00954328 | − | 0.999954i | \(-0.496962\pi\) | ||||
0.00954328 | + | 0.999954i | \(0.496962\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.1965 | 2.02807 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.541579 | −0.0758362 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.86586 | −0.256296 | −0.128148 | − | 0.991755i | \(-0.540903\pi\) | ||||
−0.128148 | + | 0.991755i | \(0.540903\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.05756 | 0.142601 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.86493 | −0.379469 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.40860 | 0.183384 | 0.0916920 | − | 0.995787i | \(-0.470772\pi\) | ||||
0.0916920 | + | 0.995787i | \(0.470772\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.55445 | −0.583138 | −0.291569 | − | 0.956550i | \(-0.594177\pi\) | ||||
−0.291569 | + | 0.956550i | \(0.594177\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.60397 | −0.580045 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.78102 | 0.468977 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.39601 | 0.292719 | 0.146359 | − | 0.989231i | \(-0.453244\pi\) | ||||
0.146359 | + | 0.989231i | \(0.453244\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.52905 | 0.665619 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.71089 | −1.15247 | −0.576235 | − | 0.817284i | \(-0.695479\pi\) | ||||
−0.576235 | + | 0.817284i | \(0.695479\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.237876 | 0.0278413 | 0.0139207 | − | 0.999903i | \(-0.495569\pi\) | ||||
0.0139207 | + | 0.999903i | \(0.495569\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.56093 | −0.295711 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.11763 | −0.355286 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.7562 | −1.32267 | −0.661337 | − | 0.750089i | \(-0.730011\pi\) | ||||
−0.661337 | + | 0.750089i | \(0.730011\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.539478 | 0.0592154 | 0.0296077 | − | 0.999562i | \(-0.490574\pi\) | ||||
0.0296077 | + | 0.999562i | \(0.490574\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.845813 | −0.0917412 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.48876 | 0.481246 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.24695 | 0.556175 | 0.278088 | − | 0.960556i | \(-0.410299\pi\) | ||||
0.278088 | + | 0.960556i | \(0.410299\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.1462 | −1.16844 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.27589 | −0.650779 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.47431 | −0.459054 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −18.9230 | −1.92134 | −0.960671 | − | 0.277690i | \(-0.910431\pi\) | ||||
−0.960671 | + | 0.277690i | \(0.910431\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.677161 | 0.0680572 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 19.2071 | 1.91118 | 0.955591 | − | 0.294697i | \(-0.0952187\pi\) | ||||
0.955591 | + | 0.294697i | \(0.0952187\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.1285 | 1.39212 | 0.696060 | − | 0.717983i | \(-0.254935\pi\) | ||||
0.696060 | + | 0.717983i | \(0.254935\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.19026 | −0.701697 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.40350 | 0.232355 | 0.116178 | − | 0.993228i | \(-0.462936\pi\) | ||||
0.116178 | + | 0.993228i | \(0.462936\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.48595 | −0.429676 | −0.214838 | − | 0.976650i | \(-0.568922\pi\) | ||||
−0.214838 | + | 0.976650i | \(0.568922\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.48690 | −0.425878 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.2896 | 0.967961 | 0.483980 | − | 0.875079i | \(-0.339191\pi\) | ||||
0.483980 | + | 0.875079i | \(0.339191\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.63500 | 0.805218 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.42101 | 0.223822 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.49341 | 0.228571 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.5415 | −0.958314 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.64946 | −0.238894 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.8083 | −1.05617 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.3566 | −1.27394 | −0.636970 | − | 0.770889i | \(-0.719812\pi\) | ||||
−0.636970 | + | 0.770889i | \(0.719812\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.5513 | −0.928994 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.1829 | 0.889682 | 0.444841 | − | 0.895610i | \(-0.353260\pi\) | ||||
0.444841 | + | 0.895610i | \(0.353260\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.1900 | 1.14372 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.56175 | 0.134414 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.65142 | −0.739141 | −0.369570 | − | 0.929203i | \(-0.620495\pi\) | ||||
−0.369570 | + | 0.929203i | \(0.620495\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.8616 | 1.51500 | 0.757499 | − | 0.652836i | \(-0.226421\pi\) | ||||
0.757499 | + | 0.652836i | \(0.226421\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.130851 | 0.0110196 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.63941 | 0.137095 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.01034 | 0.582177 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 14.1965 | 1.17091 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.3329 | 1.01035 | 0.505173 | − | 0.863018i | \(-0.331429\pi\) | ||||
0.505173 | + | 0.863018i | \(0.331429\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.5880 | −1.51267 | −0.756336 | − | 0.654184i | \(-0.773012\pi\) | ||||
−0.756336 | + | 0.654184i | \(0.773012\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.541579 | −0.0437841 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.80138 | −0.787266 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.5265 | −0.919916 | −0.459958 | − | 0.887941i | \(-0.652136\pi\) | ||||
−0.459958 | + | 0.887941i | \(0.652136\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.86586 | −0.147972 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −25.4555 | −2.00618 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.881223 | −0.0690227 | −0.0345114 | − | 0.999404i | \(-0.510987\pi\) | ||||
−0.0345114 | + | 0.999404i | \(0.510987\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.05756 | 0.0823308 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.13872 | −0.549132 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.86493 | −0.219087 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.5335 | 1.48510 | 0.742551 | − | 0.669790i | \(-0.233616\pi\) | ||||
0.742551 | + | 0.669790i | \(0.233616\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.7904 | 0.891273 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.40860 | 0.105877 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.0890 | −1.57627 | −0.788134 | − | 0.615504i | \(-0.788952\pi\) | ||||
−0.788134 | + | 0.615504i | \(0.788952\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.3226 | 1.06459 | 0.532295 | − | 0.846559i | \(-0.321330\pi\) | ||||
0.532295 | + | 0.846559i | \(0.321330\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.55445 | −0.336675 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.00743 | −0.515197 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.366736 | −0.0268184 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.60397 | −0.334889 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.93785 | −0.140218 | −0.0701091 | − | 0.997539i | \(-0.522335\pi\) | ||||
−0.0701091 | + | 0.997539i | \(0.522335\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.1251 | −1.52062 | −0.760310 | − | 0.649561i | \(-0.774953\pi\) | ||||
−0.760310 | + | 0.649561i | \(0.774953\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.78102 | 0.270764 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.902280 | 0.0642848 | 0.0321424 | − | 0.999483i | \(-0.489767\pi\) | ||||
0.0321424 | + | 0.999483i | \(0.489767\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.0097 | −0.709568 | −0.354784 | − | 0.934948i | \(-0.615446\pi\) | ||||
−0.354784 | + | 0.934948i | \(0.615446\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.39601 | 0.169001 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −20.6661 | −1.45048 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.13780 | −0.288996 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.52905 | 0.384295 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.94002 | −0.134194 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.8910 | −1.64473 | −0.822364 | − | 0.568962i | \(-0.807345\pi\) | ||||
−0.822364 | + | 0.568962i | \(0.807345\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.71089 | −0.665379 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −16.4786 | −1.12383 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 28.8940 | 1.96145 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.237876 | 0.0160742 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.31117 | −0.0881987 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.6415 | 0.913504 | 0.456752 | − | 0.889594i | \(-0.349013\pi\) | ||||
0.456752 | + | 0.889594i | \(0.349013\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.56093 | −0.170729 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.28044 | −0.549592 | −0.274796 | − | 0.961503i | \(-0.588610\pi\) | ||||
−0.274796 | + | 0.961503i | \(0.588610\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.9527 | −1.12026 | −0.560132 | − | 0.828404i | \(-0.689249\pi\) | ||||
−0.560132 | + | 0.828404i | \(0.689249\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.11763 | −0.205125 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.9174 | −0.977269 | −0.488635 | − | 0.872489i | \(-0.662505\pi\) | ||||
−0.488635 | + | 0.872489i | \(0.662505\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.204357 | 0.0133308 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −11.7562 | −0.763647 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.2260 | 1.04958 | 0.524788 | − | 0.851233i | \(-0.324145\pi\) | ||||
0.524788 | + | 0.851233i | \(0.324145\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.95693 | −0.190473 | −0.0952363 | − | 0.995455i | \(-0.530361\pi\) | ||||
−0.0952363 | + | 0.995455i | \(0.530361\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 22.1714 | 1.41648 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.93602 | −0.441328 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.539478 | 0.0341880 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −26.2547 | −1.65718 | −0.828591 | − | 0.559854i | \(-0.810857\pi\) | ||||
−0.828591 | + | 0.559854i | \(0.810857\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.74405 | 0.235387 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.845813 | −0.0529668 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −25.8500 | −1.61248 | −0.806240 | − | 0.591588i | \(-0.798501\pi\) | ||||
−0.806240 | + | 0.591588i | \(0.798501\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.6576 | 1.28360 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.48876 | 0.277848 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.05966 | 0.558642 | 0.279321 | − | 0.960198i | \(-0.409891\pi\) | ||||
0.279321 | + | 0.960198i | \(0.409891\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.91401 | −0.179007 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.24695 | 0.321108 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −22.5095 | −1.37243 | −0.686213 | − | 0.727401i | \(-0.740728\pi\) | ||||
−0.686213 | + | 0.727401i | \(0.740728\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.12378 | −0.554230 | −0.277115 | − | 0.960837i | \(-0.589378\pi\) | ||||
−0.277115 | + | 0.960837i | \(0.589378\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −11.1462 | −0.674601 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.73416 | −0.104574 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.2854 | −0.858328 | −0.429164 | − | 0.903227i | \(-0.641192\pi\) | ||||
−0.429164 | + | 0.903227i | \(0.641192\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.27589 | −0.375727 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −23.0548 | −1.37533 | −0.687666 | − | 0.726028i | \(-0.741364\pi\) | ||||
−0.687666 | + | 0.726028i | \(0.741364\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.7777 | 1.65121 | 0.825607 | − | 0.564246i | \(-0.190833\pi\) | ||||
0.825607 | + | 0.564246i | \(0.190833\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.47431 | −0.265035 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.1980 | 0.720026 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.7067 | −0.982747 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −18.9230 | −1.10929 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 25.0738 | 1.46483 | 0.732414 | − | 0.680860i | \(-0.238394\pi\) | ||||
0.732414 | + | 0.680860i | \(0.238394\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.19988 | 0.128082 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.677161 | 0.0392929 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 13.3859 | 0.774125 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 48.5780 | 2.79999 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 19.2071 | 1.10342 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.11293 | −0.407285 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.1106 | −0.634115 | −0.317058 | − | 0.948406i | \(-0.602695\pi\) | ||||
−0.317058 | + | 0.948406i | \(0.602695\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.1285 | 0.803741 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.770347 | −0.0436824 | −0.0218412 | − | 0.999761i | \(-0.506953\pi\) | ||||
−0.0218412 | + | 0.999761i | \(0.506953\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.71480 | −0.153450 | −0.0767248 | − | 0.997052i | \(-0.524446\pi\) | ||||
−0.0767248 | + | 0.997052i | \(0.524446\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7.19026 | −0.405125 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −20.2749 | −1.13875 | −0.569375 | − | 0.822078i | \(-0.692815\pi\) | ||||
−0.569375 | + | 0.822078i | \(0.692815\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.03962 | 0.170186 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.40350 | 0.134150 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.55159 | 0.0863325 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.20003 | −0.343916 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.48595 | −0.248074 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.602433 | −0.0332132 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.5475 | −0.634706 | −0.317353 | − | 0.948308i | \(-0.602794\pi\) | ||||
−0.317353 | + | 0.948308i | \(0.602794\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.48690 | −0.245881 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.74197 | 0.204446 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −28.5512 | −1.55528 | −0.777640 | − | 0.628709i | \(-0.783584\pi\) | ||||
−0.777640 | + | 0.628709i | \(0.783584\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.2896 | 0.558852 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.24978 | −0.230139 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −33.1325 | −1.78898 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.63500 | 0.464893 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 30.1278 | 1.61735 | 0.808673 | − | 0.588258i | \(-0.200186\pi\) | ||||
0.808673 | + | 0.588258i | \(0.200186\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.21506 | −0.172098 | −0.0860491 | − | 0.996291i | \(-0.527424\pi\) | ||||
−0.0860491 | + | 0.996291i | \(0.527424\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.42101 | 0.129224 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.71593 | 0.144555 | 0.0722773 | − | 0.997385i | \(-0.476973\pi\) | ||||
0.0722773 | + | 0.997385i | \(0.476973\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.1660 | −0.804928 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.49341 | 0.131965 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 34.4845 | 1.82002 | 0.910010 | − | 0.414587i | \(-0.136074\pi\) | ||||
0.910010 | + | 0.414587i | \(0.136074\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.7922 | −0.568010 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.5415 | −0.553283 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.371504 | 0.0194454 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.74370 | −0.299819 | −0.149909 | − | 0.988700i | \(-0.547898\pi\) | ||||
−0.149909 | + | 0.988700i | \(0.547898\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.64946 | −0.137925 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.59036 | 0.445990 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.4774 | 1.11206 | 0.556030 | − | 0.831162i | \(-0.312324\pi\) | ||||
0.556030 | + | 0.831162i | \(0.312324\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.8083 | −0.609778 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.8673 | 0.559696 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.430617 | −0.0221193 | −0.0110597 | − | 0.999939i | \(-0.503520\pi\) | ||||
−0.0110597 | + | 0.999939i | \(0.503520\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.3566 | −0.735509 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.88548 | 0.147441 | 0.0737207 | − | 0.997279i | \(-0.476513\pi\) | ||||
0.0737207 | + | 0.997279i | \(0.476513\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.86896 | −0.248145 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.5513 | −0.536355 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.70045 | −0.390428 | −0.195214 | − | 0.980761i | \(-0.562540\pi\) | ||||
−0.195214 | + | 0.980761i | \(0.562540\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.99442 | −0.151434 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.1829 | 0.513658 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −18.3603 | −0.923805 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.91661 | −0.0961921 | −0.0480961 | − | 0.998843i | \(-0.515315\pi\) | ||||
−0.0480961 | + | 0.998843i | \(0.515315\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 13.1900 | 0.660328 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −38.3129 | −1.91325 | −0.956627 | − | 0.291316i | \(-0.905907\pi\) | ||||
−0.956627 | + | 0.291316i | \(0.905907\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.1940 | −0.756866 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.56175 | 0.0776041 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.03836 | −0.150606 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.7420 | −0.728946 | −0.364473 | − | 0.931214i | \(-0.618751\pi\) | ||||
−0.364473 | + | 0.931214i | \(0.618751\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.65142 | −0.426743 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.48514 | −0.319113 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.842532 | 0.0413582 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17.8616 | 0.874685 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −25.7668 | −1.25879 | −0.629396 | − | 0.777085i | \(-0.716698\pi\) | ||||
−0.629396 | + | 0.777085i | \(0.716698\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.26556 | 0.207891 | 0.103945 | − | 0.994583i | \(-0.466853\pi\) | ||||
0.103945 | + | 0.994583i | \(0.466853\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.130851 | 0.00636219 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.38695 | 0.0672767 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 20.9685 | 1.01474 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.63941 | 0.0791516 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.3243 | 0.834482 | 0.417241 | − | 0.908796i | \(-0.362997\pi\) | ||||
0.417241 | + | 0.908796i | \(0.362997\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.5917 | 1.18180 | 0.590901 | − | 0.806744i | \(-0.298772\pi\) | ||||
0.590901 | + | 0.806744i | \(0.298772\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.01034 | 0.336120 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15.8403 | −0.757745 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.8929 | 1.14035 | 0.570173 | − | 0.821525i | \(-0.306876\pi\) | ||||
0.570173 | + | 0.821525i | \(0.306876\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.1965 | 0.676024 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.36955 | −0.397649 | −0.198825 | − | 0.980035i | \(-0.563712\pi\) | ||||
−0.198825 | + | 0.980035i | \(0.563712\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.19443 | 0.388453 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.3329 | 0.583324 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.5398 | 0.922142 | 0.461071 | − | 0.887363i | \(-0.347465\pi\) | ||||
0.461071 | + | 0.887363i | \(0.347465\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.79411 | −0.0844814 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −18.5880 | −0.873341 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −17.4077 | −0.816084 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −29.7136 | −1.38994 | −0.694972 | − | 0.719037i | \(-0.744583\pi\) | ||||
−0.694972 | + | 0.719037i | \(0.744583\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.541579 | −0.0252787 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.3628 | −0.529216 | −0.264608 | − | 0.964356i | \(-0.585243\pi\) | ||||
−0.264608 | + | 0.964356i | \(0.585243\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −32.2498 | −1.49878 | −0.749388 | − | 0.662131i | \(-0.769652\pi\) | ||||
−0.749388 | + | 0.662131i | \(0.769652\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.80138 | −0.454528 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.07502 | 0.142295 | 0.0711475 | − | 0.997466i | \(-0.477334\pi\) | ||||
0.0711475 | + | 0.997466i | \(0.477334\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.0311 | −0.509370 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.5265 | −0.531114 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.14496 | −0.328525 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.33688 | 0.336639 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.86586 | −0.0854320 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 27.9296 | 1.27614 | 0.638069 | − | 0.769980i | \(-0.279734\pi\) | ||||
0.638069 | + | 0.769980i | \(0.279734\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.8628 | −0.495303 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −25.4555 | −1.15827 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −29.5531 | −1.34194 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.7804 | 0.533823 | 0.266912 | − | 0.963721i | \(-0.413997\pi\) | ||||
0.266912 | + | 0.963721i | \(0.413997\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.881223 | −0.0398503 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 35.8557 | 1.61814 | 0.809072 | − | 0.587710i | \(-0.199970\pi\) | ||||
0.809072 | + | 0.587710i | \(0.199970\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.43102 | −0.109488 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.05756 | 0.0475337 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 44.7086 | 2.00545 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.2035 | 0.859666 | 0.429833 | − | 0.902908i | \(-0.358572\pi\) | ||||
0.429833 | + | 0.902908i | \(0.358572\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −30.8353 | −1.37488 | −0.687440 | − | 0.726241i | \(-0.741265\pi\) | ||||
−0.687440 | + | 0.726241i | \(0.741265\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 29.9968 | 1.33484 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.13872 | −0.317041 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.93321 | 0.174336 | 0.0871682 | − | 0.996194i | \(-0.472218\pi\) | ||||
0.0871682 | + | 0.996194i | \(0.472218\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.09517 | −0.0484477 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.86493 | −0.126490 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 22.0652 | 0.972309 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.0886071 | 0.00389694 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19.5335 | 0.857424 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.97954 | −0.349590 | −0.174795 | − | 0.984605i | \(-0.555926\pi\) | ||||
−0.174795 | + | 0.984605i | \(0.555926\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.7612 | −1.08273 | −0.541365 | − | 0.840788i | \(-0.682092\pi\) | ||||
−0.541365 | + | 0.840788i | \(0.682092\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 11.7904 | 0.514577 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.39889 | 0.148058 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.57036 | 0.329146 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.40860 | 0.0611280 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.41436 | −0.277837 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.75368 | 0.162286 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −21.0890 | −0.910058 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.61332 | 0.414075 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.1179 | 1.46685 | 0.733423 | − | 0.679773i | \(-0.237922\pi\) | ||||
0.733423 | + | 0.679773i | \(0.237922\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 14.3226 | 0.614641 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.00594 | −0.300102 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.75529 | 0.160565 | 0.0802823 | − | 0.996772i | \(-0.474418\pi\) | ||||
0.0802823 | + | 0.996772i | \(0.474418\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.55445 | −0.194379 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.8600 | −0.547854 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 54.1251 | 2.30163 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.00743 | −0.297449 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 29.3144 | 1.24209 | 0.621045 | − | 0.783775i | \(-0.286708\pi\) | ||||
0.621045 | + | 0.783775i | \(0.286708\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −25.5449 | −1.08043 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.366736 | −0.0154836 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.8655 | 0.500070 | 0.250035 | − | 0.968237i | \(-0.419558\pi\) | ||||
0.250035 | + | 0.968237i | \(0.419558\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.0698 | 0.676060 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.60397 | −0.193348 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.9575 | −0.794739 | −0.397370 | − | 0.917659i | \(-0.630077\pi\) | ||||
−0.397370 | + | 0.917659i | \(0.630077\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.8768 | 0.706270 | 0.353135 | − | 0.935572i | \(-0.385116\pi\) | ||||
0.353135 | + | 0.935572i | \(0.385116\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.93785 | −0.0809550 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −14.1595 | −0.590492 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.2738 | 0.968901 | 0.484451 | − | 0.874819i | \(-0.339019\pi\) | ||||
0.484451 | + | 0.874819i | \(0.339019\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −21.1251 | −0.877930 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.48374 | −0.103043 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.26349 | −0.0523284 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.78102 | 0.156326 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.9457 | −0.616873 | −0.308437 | − | 0.951245i | \(-0.599806\pi\) | ||||
−0.308437 | + | 0.951245i | \(0.599806\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.9800 | 0.740851 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.902280 | 0.0371149 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.4973 | 0.841724 | 0.420862 | − | 0.907125i | \(-0.361728\pi\) | ||||
0.420862 | + | 0.907125i | \(0.361728\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.89409 | 0.159642 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10.0097 | −0.409669 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.8824 | −0.526361 | −0.263180 | − | 0.964747i | \(-0.584771\pi\) | ||||
−0.263180 | + | 0.964747i | \(0.584771\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.2054 | 0.742613 | 0.371307 | − | 0.928510i | \(-0.378910\pi\) | ||||
0.371307 | + | 0.928510i | \(0.378910\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.39601 | 0.0975729 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −16.4631 | −0.669322 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.2271 | 0.861583 | 0.430791 | − | 0.902452i | \(-0.358234\pi\) | ||||
0.430791 | + | 0.902452i | \(0.358234\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −20.6661 | −0.837433 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.316791 | 0.0128160 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.85113 | −0.195935 | −0.0979676 | − | 0.995190i | \(-0.531234\pi\) | ||||
−0.0979676 | + | 0.995190i | \(0.531234\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.13780 | −0.166852 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −33.5898 | −1.35228 | −0.676138 | − | 0.736775i | \(-0.736348\pi\) | ||||
−0.676138 | + | 0.736775i | \(0.736348\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.864216 | 0.0347358 | 0.0173679 | − | 0.999849i | \(-0.494471\pi\) | ||||
0.0173679 | + | 0.999849i | \(0.494471\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.52905 | 0.221873 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −24.1568 | −0.967820 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.63700 | −0.225480 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.94002 | −0.0774769 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.43001 | 0.0968910 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.6907 | 0.704254 | 0.352127 | − | 0.935952i | \(-0.385458\pi\) | ||||
0.352127 | + | 0.935952i | \(0.385458\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −23.8910 | −0.949584 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −22.4214 | −0.889767 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 34.3699 | 1.36178 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.71089 | −0.384157 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 34.8330 | 1.37582 | 0.687910 | − | 0.725796i | \(-0.258528\pi\) | ||||
0.687910 | + | 0.725796i | \(0.258528\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.7079 | 1.28987 | 0.644937 | − | 0.764236i | \(-0.276884\pi\) | ||||
0.644937 | + | 0.764236i | \(0.276884\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −16.4786 | −0.648844 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 45.0734 | 1.77202 | 0.886008 | − | 0.463669i | \(-0.153467\pi\) | ||||
0.886008 | + | 0.463669i | \(0.153467\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.953849 | 0.0374418 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 28.8940 | 1.13244 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 37.5770 | 1.47050 | 0.735252 | − | 0.677794i | \(-0.237064\pi\) | ||||
0.735252 | + | 0.677794i | \(0.237064\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15.9031 | 0.621387 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.237876 | 0.00928044 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32.1271 | 1.25149 | 0.625747 | − | 0.780026i | \(-0.284794\pi\) | ||||
0.625747 | + | 0.780026i | \(0.284794\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.2467 | 0.748610 | 0.374305 | − | 0.927306i | \(-0.377881\pi\) | ||||
0.374305 | + | 0.927306i | \(0.377881\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.31117 | −0.0509215 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 20.5996 | 0.798817 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 24.8186 | 0.960980 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13.6415 | 0.527412 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.08410 | −0.119060 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 37.4707 | 1.44439 | 0.722195 | − | 0.691690i | \(-0.243133\pi\) | ||||
0.722195 | + | 0.691690i | \(0.243133\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.56093 | −0.0985702 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 45.5562 | 1.75087 | 0.875433 | − | 0.483339i | \(-0.160576\pi\) | ||||
0.875433 | + | 0.483339i | \(0.160576\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 87.1209 | 3.34339 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.28044 | −0.317307 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.30725 | −0.317868 | −0.158934 | − | 0.987289i | \(-0.550806\pi\) | ||||
−0.158934 | + | 0.987289i | \(0.550806\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.5114 | −0.516243 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.9527 | −0.646784 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.51727 | −0.172094 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −51.1454 | −1.94566 | −0.972831 | − | 0.231516i | \(-0.925631\pi\) | ||||
−0.972831 | + | 0.231516i | \(0.925631\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.11763 | −0.118429 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 27.8954 | 1.05813 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.43489 | 0.0543504 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −14.9174 | −0.564227 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.8929 | 1.28012 | 0.640059 | − | 0.768325i | \(-0.278910\pi\) | ||||
0.640059 | + | 0.768325i | \(0.278910\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.8547 | 0.484823 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.204357 | 0.00769652 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −88.4290 | −3.32571 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.85245 | 0.294905 | 0.147452 | − | 0.989069i | \(-0.452893\pi\) | ||||
0.147452 | + | 0.989069i | \(0.452893\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.7562 | −0.440892 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −34.6997 | −1.29951 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.56036 | 0.0957519 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.2260 | 0.605973 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32.9194 | 1.22768 | 0.613842 | − | 0.789429i | \(-0.289623\pi\) | ||||
0.613842 | + | 0.789429i | \(0.289623\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −65.0471 | −2.42248 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.95693 | −0.109969 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −11.4954 | −0.426929 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.2103 | −0.527029 | −0.263515 | − | 0.964655i | \(-0.584882\pi\) | ||||
−0.263515 | + | 0.964655i | \(0.584882\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.71439 | 0.211354 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32.0616 | −1.18422 | −0.592112 | − | 0.805856i | \(-0.701706\pi\) | ||||
−0.592112 | + | 0.805856i | \(0.701706\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 22.1714 | 0.817805 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.62248 | 0.0597649 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.29038 | −0.157824 | −0.0789121 | − | 0.996882i | \(-0.525145\pi\) | ||||
−0.0789121 | + | 0.996882i | \(0.525145\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.93602 | −0.254801 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −43.8196 | −1.60758 | −0.803792 | − | 0.594910i | \(-0.797187\pi\) | ||||
−0.803792 | + | 0.594910i | \(0.797187\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 19.2609 | 0.705664 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.539478 | 0.0197385 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.0656 | −0.404330 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.5132 | 0.566086 | 0.283043 | − | 0.959107i | \(-0.408656\pi\) | ||||
0.283043 | + | 0.959107i | \(0.408656\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −26.2547 | −0.956775 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −29.0299 | −1.05651 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.1852 | 0.733644 | 0.366822 | − | 0.930291i | \(-0.380446\pi\) | ||||
0.366822 | + | 0.930291i | \(0.380446\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.74405 | 0.135901 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.09852 | 0.184821 | 0.0924106 | − | 0.995721i | \(-0.470543\pi\) | ||||
0.0924106 | + | 0.995721i | \(0.470543\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20.6532 | 0.747695 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.845813 | −0.0305804 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.41023 | 0.123136 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.3364 | 1.23820 | 0.619101 | − | 0.785311i | \(-0.287497\pi\) | ||||
0.619101 | + | 0.785311i | \(0.287497\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −25.8500 | −0.930966 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −37.6942 | −1.35577 | −0.677883 | − | 0.735169i | \(-0.737103\pi\) | ||||
−0.677883 | + | 0.735169i | \(0.737103\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 16.0721 | 0.577327 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 20.6576 | 0.741086 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.59051 | 0.271958 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.57583 | −0.235302 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.48876 | 0.160415 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −18.0016 | −0.642504 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.9530 | 0.533016 | 0.266508 | − | 0.963833i | \(-0.414130\pi\) | ||||
0.266508 | + | 0.963833i | \(0.414130\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.05966 | 0.322532 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −47.3728 | −1.68438 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.0264 | −0.391558 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.91401 | −0.103349 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.47658 | −0.0877250 | −0.0438625 | − | 0.999038i | \(-0.513966\pi\) | ||||
−0.0438625 | + | 0.999038i | \(0.513966\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.0708661 | −0.00250706 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.24695 | 0.185392 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.161081 | 0.00568441 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −39.7553 | −1.40119 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −22.5095 | −0.792370 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.33836 | −0.152528 | −0.0762642 | − | 0.997088i | \(-0.524299\pi\) | ||||
−0.0762642 | + | 0.997088i | \(0.524299\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.1575 | −0.567368 | −0.283684 | − | 0.958918i | \(-0.591557\pi\) | ||||
−0.283684 | + | 0.958918i | \(0.591557\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.12378 | −0.319985 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.37625 | −0.0482080 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 30.2288 | 1.05757 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −11.1462 | −0.389481 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −46.1374 | −1.61021 | −0.805104 | − | 0.593134i | \(-0.797890\pi\) | ||||
−0.805104 | + | 0.593134i | \(0.797890\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.60911 | −0.300095 | −0.150047 | − | 0.988679i | \(-0.547943\pi\) | ||||
−0.150047 | + | 0.988679i | \(0.547943\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.73416 | −0.0603757 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.69291 | 0.197962 | 0.0989810 | − | 0.995089i | \(-0.468442\pi\) | ||||
0.0989810 | + | 0.995089i | \(0.468442\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −29.2285 | −1.01515 | −0.507573 | − | 0.861609i | \(-0.669457\pi\) | ||||
−0.507573 | + | 0.861609i | \(0.669457\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.2854 | −0.495556 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.68853 | −0.266392 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.56175 | −0.0540467 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.27589 | −0.216926 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −38.4973 | −1.32907 | −0.664537 | − | 0.747255i | \(-0.731371\pi\) | ||||
−0.664537 | + | 0.747255i | \(0.731371\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.85099 | −0.305207 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −23.0548 | −0.794048 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.1489 | −0.383534 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 48.5325 | 1.66760 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 27.7777 | 0.953328 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −24.8083 | −0.850418 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23.7885 | −0.814503 | −0.407252 | − | 0.913316i | \(-0.633513\pi\) | ||||
−0.407252 | + | 0.913316i | \(0.633513\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.47431 | −0.153018 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −41.9478 | −1.43291 | −0.716454 | − | 0.697634i | \(-0.754236\pi\) | ||||
−0.716454 | + | 0.697634i | \(0.754236\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.74487 | −0.264252 | −0.132126 | − | 0.991233i | \(-0.542180\pi\) | ||||
−0.132126 | + | 0.991233i | \(0.542180\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.1980 | 0.415707 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12.3871 | −0.421663 | −0.210831 | − | 0.977522i | \(-0.567617\pi\) | ||||
−0.210831 | + | 0.977522i | \(0.567617\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 30.5064 | 1.03725 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.7067 | −0.567389 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.96083 | −0.270053 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.80075 | 0.196551 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −18.9230 | −0.640447 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 54.3650 | 1.83787 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.3076 | −0.550667 | −0.275334 | − | 0.961349i | \(-0.588788\pi\) | ||||
−0.275334 | + | 0.961349i | \(0.588788\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 25.0738 | 0.845719 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −57.6688 | −1.94291 | −0.971455 | − | 0.237224i | \(-0.923763\pi\) | ||||
−0.971455 | + | 0.237224i | \(0.923763\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 46.7514 | 1.57331 | 0.786654 | − | 0.617394i | \(-0.211811\pi\) | ||||
0.786654 | + | 0.617394i | \(0.211811\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.19988 | 0.0739483 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 23.2845 | 0.781817 | 0.390908 | − | 0.920430i | \(-0.372161\pi\) | ||||
0.390908 | + | 0.920430i | \(0.372161\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 66.0972 | 2.21683 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.677161 | 0.0226857 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.374879 | −0.0125448 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −32.9358 | −1.10092 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 13.3859 | 0.446941 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −28.1710 | −0.939555 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.01051 | 0.0336650 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 48.5780 | 1.61658 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 22.3683 | 0.743549 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.2329 | 0.937457 | 0.468729 | − | 0.883342i | \(-0.344712\pi\) | ||||
0.468729 | + | 0.883342i | \(0.344712\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 19.2071 | 0.637061 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.9302 | −0.362134 | −0.181067 | − | 0.983471i | \(-0.557955\pi\) | ||||
−0.181067 | + | 0.983471i | \(0.557955\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.365314 | 0.0120901 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.11293 | −0.235146 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −46.8816 | −1.54817 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.5647 | −0.381483 | −0.190742 | − | 0.981640i | \(-0.561089\pi\) | ||||
−0.190742 | + | 0.981640i | \(0.561089\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.1106 | −0.366107 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −23.5101 | −0.773846 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.4906 | 0.377810 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.1285 | 0.464040 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 47.7565 | 1.56684 | 0.783420 | − | 0.621492i | \(-0.213473\pi\) | ||||
0.783420 | + | 0.621492i | \(0.213473\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −40.6720 | −1.33297 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.770347 | −0.0252200 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.572751 | −0.0187310 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.0882 | 1.04828 | 0.524138 | − | 0.851634i | \(-0.324388\pi\) | ||||
0.524138 | + | 0.851634i | \(0.324388\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.71480 | −0.0885942 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 40.1773 | 1.30974 | 0.654872 | − | 0.755740i | \(-0.272723\pi\) | ||||
0.654872 | + | 0.755740i | \(0.272723\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14.6490 | −0.477037 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.19026 | −0.233899 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.1399 | −0.491980 | −0.245990 | − | 0.969272i | \(-0.579113\pi\) | ||||
−0.245990 | + | 0.969272i | \(0.579113\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.575901 | 0.0186945 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −20.2749 | −0.657457 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −48.8590 | −1.58270 | −0.791350 | − | 0.611364i | \(-0.790621\pi\) | ||||
−0.791350 | + | 0.611364i | \(0.790621\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.02645 | −0.0979336 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.03962 | 0.0982568 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 39.8309 | 1.28621 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.38674 | 0.270540 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.40350 | 0.0774518 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −32.9922 | −1.06206 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.6147 | 0.566452 | 0.283226 | − | 0.959053i | \(-0.408595\pi\) | ||||
0.283226 | + | 0.959053i | \(0.408595\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.55159 | 0.0498441 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.82455 | 0.0585526 | 0.0292763 | − | 0.999571i | \(-0.490680\pi\) | ||||
0.0292763 | + | 0.999571i | \(0.490680\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −82.2341 | −2.63630 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.20003 | −0.198560 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.4709 | 0.430972 | 0.215486 | − | 0.976507i | \(-0.430866\pi\) | ||||
0.215486 | + | 0.976507i | \(0.430866\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.55303 | 0.113555 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.48595 | −0.143225 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.6193 | −0.880920 | −0.440460 | − | 0.897772i | \(-0.645185\pi\) | ||||
−0.440460 | + | 0.897772i | \(0.645185\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.40914 | 0.0448989 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.602433 | −0.0191757 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −58.3389 | −1.85507 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.62752 | 0.146998 | 0.0734990 | − | 0.997295i | \(-0.476583\pi\) | ||||
0.0734990 | + | 0.997295i | \(0.476583\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −11.5475 | −0.366448 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.6327 | −0.495589 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 60.6827 | 1.92184 | 0.960921 | − | 0.276824i | \(-0.0892818\pi\) | ||||
0.960921 | + | 0.276824i | \(0.0892818\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.48690 | −0.141959 |
(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 | 8016.2.a.z.1.7 | 8 | ||
4.3 | odd | 2 | 501.2.a.d.1.3 | ✓ | 8 | ||
12.11 | even | 2 | 1503.2.a.f.1.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
501.2.a.d.1.3 | ✓ | 8 | 4.3 | odd | 2 | ||
1503.2.a.f.1.6 | 8 | 12.11 | even | 2 | |||
8016.2.a.z.1.7 | 8 | 1.1 | even | 1 | trivial |