Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1075,2,Mod(1,1075)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1075, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1075.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1075 = 5^{2} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1075.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: | \(8.58391821729\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.32503921.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} - 5x^{4} + 13x^{3} + 9x^{2} - 11x - 7 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 215) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.840555\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1075.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.84056 | −1.30147 | −0.650735 | − | 0.759305i | \(-0.725539\pi\) | ||||
−0.650735 | + | 0.759305i | \(0.725539\pi\) | |||||||
\(3\) | −0.291442 | −0.168264 | −0.0841320 | − | 0.996455i | \(-0.526812\pi\) | ||||
−0.0841320 | + | 0.996455i | \(0.526812\pi\) | |||||||
\(4\) | 1.38764 | 0.693822 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.536415 | 0.218991 | ||||||||
\(7\) | −5.13977 | −1.94265 | −0.971326 | − | 0.237752i | \(-0.923589\pi\) | ||||
−0.971326 | + | 0.237752i | \(0.923589\pi\) | |||||||
\(8\) | 1.12707 | 0.398481 | ||||||||
\(9\) | −2.91506 | −0.971687 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.03950 | 1.51947 | 0.759733 | − | 0.650236i | \(-0.225330\pi\) | ||||
0.759733 | + | 0.650236i | \(0.225330\pi\) | |||||||
\(12\) | −0.404418 | −0.116745 | ||||||||
\(13\) | 1.68111 | 0.466256 | 0.233128 | − | 0.972446i | \(-0.425104\pi\) | ||||
0.233128 | + | 0.972446i | \(0.425104\pi\) | |||||||
\(14\) | 9.46004 | 2.52830 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.84973 | −1.21243 | ||||||||
\(17\) | 7.47071 | 1.81191 | 0.905957 | − | 0.423370i | \(-0.139153\pi\) | ||||
0.905957 | + | 0.423370i | \(0.139153\pi\) | |||||||
\(18\) | 5.36533 | 1.26462 | ||||||||
\(19\) | −0.608281 | −0.139549 | −0.0697746 | − | 0.997563i | \(-0.522228\pi\) | ||||
−0.0697746 | + | 0.997563i | \(0.522228\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.49795 | 0.326878 | ||||||||
\(22\) | −9.27547 | −1.97754 | ||||||||
\(23\) | 1.48871 | 0.310417 | 0.155208 | − | 0.987882i | \(-0.450395\pi\) | ||||
0.155208 | + | 0.987882i | \(0.450395\pi\) | |||||||
\(24\) | −0.328477 | −0.0670501 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.09418 | −0.606818 | ||||||||
\(27\) | 1.72390 | 0.331764 | ||||||||
\(28\) | −7.13218 | −1.34785 | ||||||||
\(29\) | −5.51410 | −1.02394 | −0.511972 | − | 0.859002i | \(-0.671085\pi\) | ||||
−0.511972 | + | 0.859002i | \(0.671085\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.88966 | 0.339394 | 0.169697 | − | 0.985496i | \(-0.445721\pi\) | ||||
0.169697 | + | 0.985496i | \(0.445721\pi\) | |||||||
\(32\) | 6.67205 | 1.17946 | ||||||||
\(33\) | −1.46872 | −0.255671 | ||||||||
\(34\) | −13.7503 | −2.35815 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.04507 | −0.674178 | ||||||||
\(37\) | −5.08289 | −0.835622 | −0.417811 | − | 0.908534i | \(-0.637203\pi\) | ||||
−0.417811 | + | 0.908534i | \(0.637203\pi\) | |||||||
\(38\) | 1.11957 | 0.181619 | ||||||||
\(39\) | −0.489946 | −0.0784542 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.85633 | −1.07078 | −0.535389 | − | 0.844605i | \(-0.679835\pi\) | ||||
−0.535389 | + | 0.844605i | \(0.679835\pi\) | |||||||
\(42\) | −2.75705 | −0.425422 | ||||||||
\(43\) | −1.00000 | −0.152499 | ||||||||
\(44\) | 6.99303 | 1.05424 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.74005 | −0.403998 | ||||||||
\(47\) | −8.54354 | −1.24620 | −0.623102 | − | 0.782141i | \(-0.714128\pi\) | ||||
−0.623102 | + | 0.782141i | \(0.714128\pi\) | |||||||
\(48\) | 1.41342 | 0.204009 | ||||||||
\(49\) | 19.4173 | 2.77390 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.17728 | −0.304880 | ||||||||
\(52\) | 2.33278 | 0.323499 | ||||||||
\(53\) | −9.18537 | −1.26171 | −0.630854 | − | 0.775902i | \(-0.717295\pi\) | ||||
−0.630854 | + | 0.775902i | \(0.717295\pi\) | |||||||
\(54\) | −3.17293 | −0.431781 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −5.79291 | −0.774110 | ||||||||
\(57\) | 0.177279 | 0.0234811 | ||||||||
\(58\) | 10.1490 | 1.33263 | ||||||||
\(59\) | 7.44326 | 0.969030 | 0.484515 | − | 0.874783i | \(-0.338996\pi\) | ||||
0.484515 | + | 0.874783i | \(0.338996\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.51814 | −1.09064 | −0.545318 | − | 0.838229i | \(-0.683591\pi\) | ||||
−0.545318 | + | 0.838229i | \(0.683591\pi\) | |||||||
\(62\) | −3.47803 | −0.441711 | ||||||||
\(63\) | 14.9828 | 1.88765 | ||||||||
\(64\) | −2.58081 | −0.322602 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.70326 | 0.332748 | ||||||||
\(67\) | 4.71055 | 0.575485 | 0.287743 | − | 0.957708i | \(-0.407095\pi\) | ||||
0.287743 | + | 0.957708i | \(0.407095\pi\) | |||||||
\(68\) | 10.3667 | 1.25715 | ||||||||
\(69\) | −0.433871 | −0.0522320 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.25011 | 0.385717 | 0.192858 | − | 0.981227i | \(-0.438224\pi\) | ||||
0.192858 | + | 0.981227i | \(0.438224\pi\) | |||||||
\(72\) | −3.28549 | −0.387199 | ||||||||
\(73\) | −6.48385 | −0.758877 | −0.379438 | − | 0.925217i | \(-0.623883\pi\) | ||||
−0.379438 | + | 0.925217i | \(0.623883\pi\) | |||||||
\(74\) | 9.35534 | 1.08754 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.844077 | −0.0968223 | ||||||||
\(77\) | −25.9019 | −2.95179 | ||||||||
\(78\) | 0.901773 | 0.102106 | ||||||||
\(79\) | −3.22785 | −0.363162 | −0.181581 | − | 0.983376i | \(-0.558121\pi\) | ||||
−0.181581 | + | 0.983376i | \(0.558121\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.24277 | 0.915863 | ||||||||
\(82\) | 12.6195 | 1.39359 | ||||||||
\(83\) | 6.51534 | 0.715152 | 0.357576 | − | 0.933884i | \(-0.383603\pi\) | ||||
0.357576 | + | 0.933884i | \(0.383603\pi\) | |||||||
\(84\) | 2.07862 | 0.226796 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.84056 | 0.198472 | ||||||||
\(87\) | 1.60704 | 0.172293 | ||||||||
\(88\) | 5.67989 | 0.605478 | ||||||||
\(89\) | −11.5677 | −1.22617 | −0.613087 | − | 0.790016i | \(-0.710072\pi\) | ||||
−0.613087 | + | 0.790016i | \(0.710072\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.64053 | −0.905773 | ||||||||
\(92\) | 2.06579 | 0.215374 | ||||||||
\(93\) | −0.550728 | −0.0571078 | ||||||||
\(94\) | 15.7249 | 1.62190 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.94452 | −0.198461 | ||||||||
\(97\) | −1.06878 | −0.108518 | −0.0542591 | − | 0.998527i | \(-0.517280\pi\) | ||||
−0.0542591 | + | 0.998527i | \(0.517280\pi\) | |||||||
\(98\) | −35.7386 | −3.61014 | ||||||||
\(99\) | −14.6904 | −1.47644 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.7267 | −1.56487 | −0.782433 | − | 0.622735i | \(-0.786022\pi\) | ||||
−0.782433 | + | 0.622735i | \(0.786022\pi\) | |||||||
\(102\) | 4.00740 | 0.396792 | ||||||||
\(103\) | −16.4707 | −1.62290 | −0.811451 | − | 0.584421i | \(-0.801322\pi\) | ||||
−0.811451 | + | 0.584421i | \(0.801322\pi\) | |||||||
\(104\) | 1.89474 | 0.185794 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 16.9062 | 1.64207 | ||||||||
\(107\) | −2.13751 | −0.206641 | −0.103320 | − | 0.994648i | \(-0.532947\pi\) | ||||
−0.103320 | + | 0.994648i | \(0.532947\pi\) | |||||||
\(108\) | 2.39216 | 0.230185 | ||||||||
\(109\) | −1.91506 | −0.183430 | −0.0917148 | − | 0.995785i | \(-0.529235\pi\) | ||||
−0.0917148 | + | 0.995785i | \(0.529235\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.48137 | 0.140605 | ||||||||
\(112\) | 24.9265 | 2.35534 | ||||||||
\(113\) | −10.3309 | −0.971853 | −0.485926 | − | 0.874000i | \(-0.661518\pi\) | ||||
−0.485926 | + | 0.874000i | \(0.661518\pi\) | |||||||
\(114\) | −0.326291 | −0.0305599 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −7.65161 | −0.710434 | ||||||||
\(117\) | −4.90054 | −0.453055 | ||||||||
\(118\) | −13.6997 | −1.26116 | ||||||||
\(119\) | −38.3978 | −3.51992 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.3965 | 1.30877 | ||||||||
\(122\) | 15.6781 | 1.41943 | ||||||||
\(123\) | 1.99822 | 0.180174 | ||||||||
\(124\) | 2.62218 | 0.235479 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −27.5766 | −2.45672 | ||||||||
\(127\) | −12.1166 | −1.07517 | −0.537587 | − | 0.843208i | \(-0.680664\pi\) | ||||
−0.537587 | + | 0.843208i | \(0.680664\pi\) | |||||||
\(128\) | −8.59397 | −0.759607 | ||||||||
\(129\) | 0.291442 | 0.0256600 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.00984495 | −0.000860157 0 | −0.000430079 | − | 1.00000i | \(-0.500137\pi\) | ||||
−0.000430079 | 1.00000i | \(0.500137\pi\) | ||||||||
\(132\) | −2.03806 | −0.177390 | ||||||||
\(133\) | 3.12643 | 0.271095 | ||||||||
\(134\) | −8.67003 | −0.748976 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.42005 | 0.722013 | ||||||||
\(137\) | −7.64961 | −0.653551 | −0.326775 | − | 0.945102i | \(-0.605962\pi\) | ||||
−0.326775 | + | 0.945102i | \(0.605962\pi\) | |||||||
\(138\) | 0.798564 | 0.0679783 | ||||||||
\(139\) | 10.8055 | 0.916509 | 0.458255 | − | 0.888821i | \(-0.348475\pi\) | ||||
0.458255 | + | 0.888821i | \(0.348475\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.48995 | 0.209691 | ||||||||
\(142\) | −5.98200 | −0.501999 | ||||||||
\(143\) | 8.47195 | 0.708460 | ||||||||
\(144\) | 14.1373 | 1.17811 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 11.9339 | 0.987655 | ||||||||
\(147\) | −5.65901 | −0.466747 | ||||||||
\(148\) | −7.05324 | −0.579773 | ||||||||
\(149\) | −3.39172 | −0.277860 | −0.138930 | − | 0.990302i | \(-0.544366\pi\) | ||||
−0.138930 | + | 0.990302i | \(0.544366\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.387678 | 0.0315488 | 0.0157744 | − | 0.999876i | \(-0.494979\pi\) | ||||
0.0157744 | + | 0.999876i | \(0.494979\pi\) | |||||||
\(152\) | −0.685578 | −0.0556077 | ||||||||
\(153\) | −21.7776 | −1.76061 | ||||||||
\(154\) | 47.6738 | 3.84167 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.679871 | −0.0544332 | ||||||||
\(157\) | 20.2046 | 1.61250 | 0.806252 | − | 0.591573i | \(-0.201493\pi\) | ||||
0.806252 | + | 0.591573i | \(0.201493\pi\) | |||||||
\(158\) | 5.94104 | 0.472644 | ||||||||
\(159\) | 2.67700 | 0.212300 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.65161 | −0.603032 | ||||||||
\(162\) | −15.1713 | −1.19197 | ||||||||
\(163\) | −10.9097 | −0.854510 | −0.427255 | − | 0.904131i | \(-0.640519\pi\) | ||||
−0.427255 | + | 0.904131i | \(0.640519\pi\) | |||||||
\(164\) | −9.51415 | −0.742930 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −11.9918 | −0.930748 | ||||||||
\(167\) | −1.54073 | −0.119225 | −0.0596127 | − | 0.998222i | \(-0.518987\pi\) | ||||
−0.0596127 | + | 0.998222i | \(0.518987\pi\) | |||||||
\(168\) | 1.68830 | 0.130255 | ||||||||
\(169\) | −10.1739 | −0.782605 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.77318 | 0.135598 | ||||||||
\(172\) | −1.38764 | −0.105807 | ||||||||
\(173\) | 6.99994 | 0.532196 | 0.266098 | − | 0.963946i | \(-0.414266\pi\) | ||||
0.266098 | + | 0.963946i | \(0.414266\pi\) | |||||||
\(174\) | −2.95785 | −0.224234 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −24.4402 | −1.84225 | ||||||||
\(177\) | −2.16928 | −0.163053 | ||||||||
\(178\) | 21.2910 | 1.59583 | ||||||||
\(179\) | −11.8268 | −0.883974 | −0.441987 | − | 0.897021i | \(-0.645726\pi\) | ||||
−0.441987 | + | 0.897021i | \(0.645726\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.74546 | −0.129739 | −0.0648694 | − | 0.997894i | \(-0.520663\pi\) | ||||
−0.0648694 | + | 0.997894i | \(0.520663\pi\) | |||||||
\(182\) | 15.9034 | 1.17884 | ||||||||
\(183\) | 2.48254 | 0.183515 | ||||||||
\(184\) | 1.67788 | 0.123695 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.01364 | 0.0743240 | ||||||||
\(187\) | 37.6486 | 2.75314 | ||||||||
\(188\) | −11.8554 | −0.864644 | ||||||||
\(189\) | −8.86044 | −0.644502 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.9963 | 1.59159 | 0.795797 | − | 0.605564i | \(-0.207052\pi\) | ||||
0.795797 | + | 0.605564i | \(0.207052\pi\) | |||||||
\(192\) | 0.752158 | 0.0542823 | ||||||||
\(193\) | −15.1264 | −1.08882 | −0.544412 | − | 0.838818i | \(-0.683247\pi\) | ||||
−0.544412 | + | 0.838818i | \(0.683247\pi\) | |||||||
\(194\) | 1.96715 | 0.141233 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 26.9443 | 1.92459 | ||||||||
\(197\) | 14.5354 | 1.03560 | 0.517802 | − | 0.855501i | \(-0.326750\pi\) | ||||
0.517802 | + | 0.855501i | \(0.326750\pi\) | |||||||
\(198\) | 27.0386 | 1.92155 | ||||||||
\(199\) | −7.46791 | −0.529386 | −0.264693 | − | 0.964333i | \(-0.585271\pi\) | ||||
−0.264693 | + | 0.964333i | \(0.585271\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.37285 | −0.0968335 | ||||||||
\(202\) | 28.9459 | 2.03662 | ||||||||
\(203\) | 28.3412 | 1.98917 | ||||||||
\(204\) | −3.02129 | −0.211532 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 30.3151 | 2.11216 | ||||||||
\(207\) | −4.33967 | −0.301628 | ||||||||
\(208\) | −8.15294 | −0.565304 | ||||||||
\(209\) | −3.06543 | −0.212040 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.81738 | −0.607014 | −0.303507 | − | 0.952829i | \(-0.598157\pi\) | ||||
−0.303507 | + | 0.952829i | \(0.598157\pi\) | |||||||
\(212\) | −12.7460 | −0.875401 | ||||||||
\(213\) | −0.947218 | −0.0649023 | ||||||||
\(214\) | 3.93421 | 0.268937 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.94296 | 0.132202 | ||||||||
\(217\) | −9.71245 | −0.659324 | ||||||||
\(218\) | 3.52478 | 0.238728 | ||||||||
\(219\) | 1.88966 | 0.127692 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.5591 | 0.844816 | ||||||||
\(222\) | −2.72654 | −0.182993 | ||||||||
\(223\) | 3.76333 | 0.252011 | 0.126006 | − | 0.992030i | \(-0.459784\pi\) | ||||
0.126006 | + | 0.992030i | \(0.459784\pi\) | |||||||
\(224\) | −34.2928 | −2.29129 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 19.0147 | 1.26484 | ||||||||
\(227\) | 21.9658 | 1.45792 | 0.728960 | − | 0.684556i | \(-0.240004\pi\) | ||||
0.728960 | + | 0.684556i | \(0.240004\pi\) | |||||||
\(228\) | 0.245999 | 0.0162917 | ||||||||
\(229\) | −14.2515 | −0.941765 | −0.470883 | − | 0.882196i | \(-0.656064\pi\) | ||||
−0.470883 | + | 0.882196i | \(0.656064\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.54889 | 0.496681 | ||||||||
\(232\) | −6.21481 | −0.408022 | ||||||||
\(233\) | 16.5427 | 1.08375 | 0.541875 | − | 0.840459i | \(-0.317715\pi\) | ||||
0.541875 | + | 0.840459i | \(0.317715\pi\) | |||||||
\(234\) | 9.01972 | 0.589637 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 10.3286 | 0.672335 | ||||||||
\(237\) | 0.940731 | 0.0611071 | ||||||||
\(238\) | 70.6732 | 4.58106 | ||||||||
\(239\) | −9.08775 | −0.587838 | −0.293919 | − | 0.955830i | \(-0.594960\pi\) | ||||
−0.293919 | + | 0.955830i | \(0.594960\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.24141 | −0.208797 | −0.104399 | − | 0.994536i | \(-0.533292\pi\) | ||||
−0.104399 | + | 0.994536i | \(0.533292\pi\) | |||||||
\(242\) | −26.4976 | −1.70333 | ||||||||
\(243\) | −7.57398 | −0.485871 | ||||||||
\(244\) | −11.8202 | −0.756708 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.67784 | −0.234490 | ||||||||
\(247\) | −1.02259 | −0.0650657 | ||||||||
\(248\) | 2.12979 | 0.135242 | ||||||||
\(249\) | −1.89884 | −0.120334 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.88255 | 0.560661 | 0.280331 | − | 0.959903i | \(-0.409556\pi\) | ||||
0.280331 | + | 0.959903i | \(0.409556\pi\) | |||||||
\(252\) | 20.7907 | 1.30969 | ||||||||
\(253\) | 7.50233 | 0.471667 | ||||||||
\(254\) | 22.3013 | 1.39931 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.9793 | 1.31121 | ||||||||
\(257\) | −20.4758 | −1.27724 | −0.638622 | − | 0.769520i | \(-0.720495\pi\) | ||||
−0.638622 | + | 0.769520i | \(0.720495\pi\) | |||||||
\(258\) | −0.536415 | −0.0333957 | ||||||||
\(259\) | 26.1249 | 1.62332 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 16.0740 | 0.994953 | ||||||||
\(262\) | 0.0181202 | 0.00111947 | ||||||||
\(263\) | −14.6293 | −0.902083 | −0.451041 | − | 0.892503i | \(-0.648947\pi\) | ||||
−0.451041 | + | 0.892503i | \(0.648947\pi\) | |||||||
\(264\) | −1.65536 | −0.101880 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −5.75436 | −0.352822 | ||||||||
\(267\) | 3.37131 | 0.206321 | ||||||||
\(268\) | 6.53657 | 0.399284 | ||||||||
\(269\) | −12.5266 | −0.763762 | −0.381881 | − | 0.924211i | \(-0.624724\pi\) | ||||
−0.381881 | + | 0.924211i | \(0.624724\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.66641 | 0.161973 | 0.0809863 | − | 0.996715i | \(-0.474193\pi\) | ||||
0.0809863 | + | 0.996715i | \(0.474193\pi\) | |||||||
\(272\) | −36.2309 | −2.19682 | ||||||||
\(273\) | 2.51821 | 0.152409 | ||||||||
\(274\) | 14.0795 | 0.850576 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.602059 | −0.0362397 | ||||||||
\(277\) | 4.83731 | 0.290646 | 0.145323 | − | 0.989384i | \(-0.453578\pi\) | ||||
0.145323 | + | 0.989384i | \(0.453578\pi\) | |||||||
\(278\) | −19.8881 | −1.19281 | ||||||||
\(279\) | −5.50849 | −0.329785 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −27.6927 | −1.65201 | −0.826004 | − | 0.563664i | \(-0.809391\pi\) | ||||
−0.826004 | + | 0.563664i | \(0.809391\pi\) | |||||||
\(282\) | −4.58288 | −0.272907 | ||||||||
\(283\) | 4.82203 | 0.286640 | 0.143320 | − | 0.989676i | \(-0.454222\pi\) | ||||
0.143320 | + | 0.989676i | \(0.454222\pi\) | |||||||
\(284\) | 4.50999 | 0.267619 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −15.5931 | −0.922039 | ||||||||
\(287\) | 35.2400 | 2.08015 | ||||||||
\(288\) | −19.4494 | −1.14607 | ||||||||
\(289\) | 38.8115 | 2.28303 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.311488 | 0.0182597 | ||||||||
\(292\) | −8.99727 | −0.526525 | ||||||||
\(293\) | 28.1922 | 1.64700 | 0.823502 | − | 0.567314i | \(-0.192017\pi\) | ||||
0.823502 | + | 0.567314i | \(0.192017\pi\) | |||||||
\(294\) | 10.4157 | 0.607457 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −5.72880 | −0.332979 | ||||||||
\(297\) | 8.68757 | 0.504104 | ||||||||
\(298\) | 6.24265 | 0.361627 | ||||||||
\(299\) | 2.50268 | 0.144734 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.13977 | 0.296252 | ||||||||
\(302\) | −0.713543 | −0.0410598 | ||||||||
\(303\) | 4.58342 | 0.263311 | ||||||||
\(304\) | 2.95000 | 0.169194 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 40.0828 | 2.29138 | ||||||||
\(307\) | −5.79727 | −0.330868 | −0.165434 | − | 0.986221i | \(-0.552902\pi\) | ||||
−0.165434 | + | 0.986221i | \(0.552902\pi\) | |||||||
\(308\) | −35.9426 | −2.04802 | ||||||||
\(309\) | 4.80024 | 0.273076 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.0774 | −0.854959 | −0.427479 | − | 0.904025i | \(-0.640598\pi\) | ||||
−0.427479 | + | 0.904025i | \(0.640598\pi\) | |||||||
\(312\) | −0.552206 | −0.0312625 | ||||||||
\(313\) | 0.780361 | 0.0441086 | 0.0220543 | − | 0.999757i | \(-0.492979\pi\) | ||||
0.0220543 | + | 0.999757i | \(0.492979\pi\) | |||||||
\(314\) | −37.1877 | −2.09862 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.47911 | −0.251970 | ||||||||
\(317\) | −21.4989 | −1.20750 | −0.603750 | − | 0.797174i | \(-0.706327\pi\) | ||||
−0.603750 | + | 0.797174i | \(0.706327\pi\) | |||||||
\(318\) | −4.92717 | −0.276302 | ||||||||
\(319\) | −27.7883 | −1.55585 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.622960 | 0.0347702 | ||||||||
\(322\) | 14.0832 | 0.784827 | ||||||||
\(323\) | −4.54429 | −0.252851 | ||||||||
\(324\) | 11.4380 | 0.635446 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 20.0798 | 1.11212 | ||||||||
\(327\) | 0.558129 | 0.0308646 | ||||||||
\(328\) | −7.72760 | −0.426685 | ||||||||
\(329\) | 43.9119 | 2.42094 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.6324 | 0.969163 | 0.484581 | − | 0.874746i | \(-0.338972\pi\) | ||||
0.484581 | + | 0.874746i | \(0.338972\pi\) | |||||||
\(332\) | 9.04098 | 0.496188 | ||||||||
\(333\) | 14.8169 | 0.811963 | ||||||||
\(334\) | 2.83580 | 0.155168 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −7.26463 | −0.396318 | ||||||||
\(337\) | −26.9345 | −1.46722 | −0.733608 | − | 0.679573i | \(-0.762165\pi\) | ||||
−0.733608 | + | 0.679573i | \(0.762165\pi\) | |||||||
\(338\) | 18.7256 | 1.01854 | ||||||||
\(339\) | 3.01087 | 0.163528 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.52296 | 0.515697 | ||||||||
\(342\) | −3.26363 | −0.176477 | ||||||||
\(343\) | −63.8219 | −3.44606 | ||||||||
\(344\) | −1.12707 | −0.0607678 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.8838 | −0.692636 | ||||||||
\(347\) | −11.4381 | −0.614028 | −0.307014 | − | 0.951705i | \(-0.599330\pi\) | ||||
−0.307014 | + | 0.951705i | \(0.599330\pi\) | |||||||
\(348\) | 2.23000 | 0.119541 | ||||||||
\(349\) | 9.05483 | 0.484694 | 0.242347 | − | 0.970190i | \(-0.422083\pi\) | ||||
0.242347 | + | 0.970190i | \(0.422083\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.89806 | 0.154687 | ||||||||
\(352\) | 33.6238 | 1.79215 | ||||||||
\(353\) | −9.57877 | −0.509827 | −0.254913 | − | 0.966964i | \(-0.582047\pi\) | ||||
−0.254913 | + | 0.966964i | \(0.582047\pi\) | |||||||
\(354\) | 3.99268 | 0.212208 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −16.0518 | −0.850746 | ||||||||
\(357\) | 11.1907 | 0.592276 | ||||||||
\(358\) | 21.7678 | 1.15047 | ||||||||
\(359\) | 1.30335 | 0.0687879 | 0.0343940 | − | 0.999408i | \(-0.489050\pi\) | ||||
0.0343940 | + | 0.999408i | \(0.489050\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.6300 | −0.980526 | ||||||||
\(362\) | 3.21261 | 0.168851 | ||||||||
\(363\) | −4.19575 | −0.220220 | ||||||||
\(364\) | −11.9900 | −0.628446 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −4.56926 | −0.238839 | ||||||||
\(367\) | 17.4149 | 0.909053 | 0.454526 | − | 0.890733i | \(-0.349809\pi\) | ||||
0.454526 | + | 0.890733i | \(0.349809\pi\) | |||||||
\(368\) | −7.21983 | −0.376359 | ||||||||
\(369\) | 19.9866 | 1.04046 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 47.2107 | 2.45106 | ||||||||
\(372\) | −0.764214 | −0.0396226 | ||||||||
\(373\) | −13.5500 | −0.701591 | −0.350796 | − | 0.936452i | \(-0.614089\pi\) | ||||
−0.350796 | + | 0.936452i | \(0.614089\pi\) | |||||||
\(374\) | −69.2944 | −3.58313 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.62921 | −0.496589 | ||||||||
\(377\) | −9.26982 | −0.477420 | ||||||||
\(378\) | 16.3081 | 0.838800 | ||||||||
\(379\) | 8.25854 | 0.424213 | 0.212106 | − | 0.977247i | \(-0.431968\pi\) | ||||
0.212106 | + | 0.977247i | \(0.431968\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.53128 | 0.180913 | ||||||||
\(382\) | −40.4853 | −2.07141 | ||||||||
\(383\) | 17.7331 | 0.906118 | 0.453059 | − | 0.891481i | \(-0.350333\pi\) | ||||
0.453059 | + | 0.891481i | \(0.350333\pi\) | |||||||
\(384\) | 2.50464 | 0.127815 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 27.8410 | 1.41707 | ||||||||
\(387\) | 2.91506 | 0.148181 | ||||||||
\(388\) | −1.48309 | −0.0752923 | ||||||||
\(389\) | −25.0836 | −1.27179 | −0.635894 | − | 0.771776i | \(-0.719368\pi\) | ||||
−0.635894 | + | 0.771776i | \(0.719368\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.1217 | 0.562448 | ||||||||
\(392\) | 21.8847 | 1.10535 | ||||||||
\(393\) | 0.00286923 | 0.000144734 0 | ||||||||
\(394\) | −26.7532 | −1.34781 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −20.3851 | −1.02439 | ||||||||
\(397\) | 1.18706 | 0.0595770 | 0.0297885 | − | 0.999556i | \(-0.490517\pi\) | ||||
0.0297885 | + | 0.999556i | \(0.490517\pi\) | |||||||
\(398\) | 13.7451 | 0.688980 | ||||||||
\(399\) | −0.911171 | −0.0456156 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 34.8646 | 1.74105 | 0.870527 | − | 0.492121i | \(-0.163778\pi\) | ||||
0.870527 | + | 0.492121i | \(0.163778\pi\) | |||||||
\(402\) | 2.52681 | 0.126026 | ||||||||
\(403\) | 3.17674 | 0.158244 | ||||||||
\(404\) | −21.8231 | −1.08574 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −52.1636 | −2.58884 | ||||||||
\(407\) | −25.6152 | −1.26970 | ||||||||
\(408\) | −2.45396 | −0.121489 | ||||||||
\(409\) | 27.2193 | 1.34591 | 0.672954 | − | 0.739684i | \(-0.265025\pi\) | ||||
0.672954 | + | 0.739684i | \(0.265025\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.22942 | 0.109969 | ||||||||
\(412\) | −22.8554 | −1.12600 | ||||||||
\(413\) | −38.2567 | −1.88249 | ||||||||
\(414\) | 7.98740 | 0.392560 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 11.2165 | 0.549932 | ||||||||
\(417\) | −3.14917 | −0.154216 | ||||||||
\(418\) | 5.64209 | 0.275964 | ||||||||
\(419\) | 1.70123 | 0.0831104 | 0.0415552 | − | 0.999136i | \(-0.486769\pi\) | ||||
0.0415552 | + | 0.999136i | \(0.486769\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.3991 | −0.604293 | −0.302147 | − | 0.953261i | \(-0.597703\pi\) | ||||
−0.302147 | + | 0.953261i | \(0.597703\pi\) | |||||||
\(422\) | 16.2289 | 0.790009 | ||||||||
\(423\) | 24.9049 | 1.21092 | ||||||||
\(424\) | −10.3526 | −0.502767 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.74341 | 0.0844683 | ||||||||
\(427\) | 43.7813 | 2.11873 | ||||||||
\(428\) | −2.96610 | −0.143372 | ||||||||
\(429\) | −2.46908 | −0.119208 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.2271 | −0.733465 | −0.366733 | − | 0.930326i | \(-0.619524\pi\) | ||||
−0.366733 | + | 0.930326i | \(0.619524\pi\) | |||||||
\(432\) | −8.36044 | −0.402242 | ||||||||
\(433\) | −5.77913 | −0.277727 | −0.138864 | − | 0.990312i | \(-0.544345\pi\) | ||||
−0.138864 | + | 0.990312i | \(0.544345\pi\) | |||||||
\(434\) | 17.8763 | 0.858090 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.65742 | −0.127268 | ||||||||
\(437\) | −0.905551 | −0.0433184 | ||||||||
\(438\) | −3.47803 | −0.166187 | ||||||||
\(439\) | 7.89384 | 0.376753 | 0.188376 | − | 0.982097i | \(-0.439678\pi\) | ||||
0.188376 | + | 0.982097i | \(0.439678\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −56.6025 | −2.69536 | ||||||||
\(442\) | −23.1157 | −1.09950 | ||||||||
\(443\) | −28.7110 | −1.36410 | −0.682050 | − | 0.731306i | \(-0.738911\pi\) | ||||
−0.682050 | + | 0.731306i | \(0.738911\pi\) | |||||||
\(444\) | 2.05561 | 0.0975549 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −6.92662 | −0.327985 | ||||||||
\(447\) | 0.988489 | 0.0467539 | ||||||||
\(448\) | 13.2648 | 0.626703 | ||||||||
\(449\) | −9.97648 | −0.470819 | −0.235410 | − | 0.971896i | \(-0.575643\pi\) | ||||
−0.235410 | + | 0.971896i | \(0.575643\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −34.5525 | −1.62701 | ||||||||
\(452\) | −14.3357 | −0.674293 | ||||||||
\(453\) | −0.112986 | −0.00530853 | ||||||||
\(454\) | −40.4292 | −1.89744 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.199806 | 0.00935678 | ||||||||
\(457\) | 12.5755 | 0.588255 | 0.294128 | − | 0.955766i | \(-0.404971\pi\) | ||||
0.294128 | + | 0.955766i | \(0.404971\pi\) | |||||||
\(458\) | 26.2307 | 1.22568 | ||||||||
\(459\) | 12.8787 | 0.601128 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.2571 | 1.12977 | 0.564883 | − | 0.825171i | \(-0.308921\pi\) | ||||
0.564883 | + | 0.825171i | \(0.308921\pi\) | |||||||
\(462\) | −13.8942 | −0.646414 | ||||||||
\(463\) | 26.4560 | 1.22951 | 0.614757 | − | 0.788716i | \(-0.289254\pi\) | ||||
0.614757 | + | 0.788716i | \(0.289254\pi\) | |||||||
\(464\) | 26.7419 | 1.24146 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −30.4478 | −1.41047 | ||||||||
\(467\) | −4.66803 | −0.216011 | −0.108005 | − | 0.994150i | \(-0.534446\pi\) | ||||
−0.108005 | + | 0.994150i | \(0.534446\pi\) | |||||||
\(468\) | −6.80021 | −0.314340 | ||||||||
\(469\) | −24.2112 | −1.11797 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.88847 | −0.271326 | ||||||||
\(472\) | 8.38912 | 0.386140 | ||||||||
\(473\) | −5.03950 | −0.231716 | ||||||||
\(474\) | −1.73147 | −0.0795289 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −53.2824 | −2.44220 | ||||||||
\(477\) | 26.7759 | 1.22599 | ||||||||
\(478\) | 16.7265 | 0.765052 | ||||||||
\(479\) | −20.2163 | −0.923707 | −0.461853 | − | 0.886956i | \(-0.652815\pi\) | ||||
−0.461853 | + | 0.886956i | \(0.652815\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.54490 | −0.389614 | ||||||||
\(482\) | 5.96599 | 0.271743 | ||||||||
\(483\) | 2.23000 | 0.101469 | ||||||||
\(484\) | 19.9772 | 0.908057 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 13.9403 | 0.632346 | ||||||||
\(487\) | 23.6802 | 1.07305 | 0.536527 | − | 0.843883i | \(-0.319736\pi\) | ||||
0.536527 | + | 0.843883i | \(0.319736\pi\) | |||||||
\(488\) | −9.60059 | −0.434598 | ||||||||
\(489\) | 3.17953 | 0.143783 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.723299 | 0.0326420 | 0.0163210 | − | 0.999867i | \(-0.494805\pi\) | ||||
0.0163210 | + | 0.999867i | \(0.494805\pi\) | |||||||
\(492\) | 2.77282 | 0.125008 | ||||||||
\(493\) | −41.1943 | −1.85530 | ||||||||
\(494\) | 1.88213 | 0.0846810 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −9.16437 | −0.411492 | ||||||||
\(497\) | −16.7048 | −0.749314 | ||||||||
\(498\) | 3.49493 | 0.156611 | ||||||||
\(499\) | −0.367937 | −0.0164711 | −0.00823556 | − | 0.999966i | \(-0.502621\pi\) | ||||
−0.00823556 | + | 0.999966i | \(0.502621\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.449034 | 0.0200614 | ||||||||
\(502\) | −16.3488 | −0.729683 | ||||||||
\(503\) | 9.38700 | 0.418546 | 0.209273 | − | 0.977857i | \(-0.432890\pi\) | ||||
0.209273 | + | 0.977857i | \(0.432890\pi\) | |||||||
\(504\) | 16.8867 | 0.752193 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −13.8085 | −0.613861 | ||||||||
\(507\) | 2.96509 | 0.131684 | ||||||||
\(508\) | −16.8135 | −0.745979 | ||||||||
\(509\) | −13.6908 | −0.606836 | −0.303418 | − | 0.952858i | \(-0.598128\pi\) | ||||
−0.303418 | + | 0.952858i | \(0.598128\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 33.3255 | 1.47423 | ||||||||
\(512\) | −21.4256 | −0.946888 | ||||||||
\(513\) | −1.04861 | −0.0462974 | ||||||||
\(514\) | 37.6868 | 1.66229 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.404418 | 0.0178035 | ||||||||
\(517\) | −43.0551 | −1.89356 | ||||||||
\(518\) | −48.0843 | −2.11270 | ||||||||
\(519\) | −2.04008 | −0.0895494 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.85102 | −0.343960 | −0.171980 | − | 0.985100i | \(-0.555016\pi\) | ||||
−0.171980 | + | 0.985100i | \(0.555016\pi\) | |||||||
\(522\) | −29.5850 | −1.29490 | ||||||||
\(523\) | 6.26463 | 0.273933 | 0.136967 | − | 0.990576i | \(-0.456265\pi\) | ||||
0.136967 | + | 0.990576i | \(0.456265\pi\) | |||||||
\(524\) | −0.0136613 | −0.000596796 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 26.9261 | 1.17403 | ||||||||
\(527\) | 14.1171 | 0.614952 | ||||||||
\(528\) | 7.12290 | 0.309984 | ||||||||
\(529\) | −20.7838 | −0.903641 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −21.6976 | −0.941594 | ||||||||
\(532\) | 4.33837 | 0.188092 | ||||||||
\(533\) | −11.5263 | −0.499257 | ||||||||
\(534\) | −6.20509 | −0.268520 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.30914 | 0.229320 | ||||||||
\(537\) | 3.44682 | 0.148741 | ||||||||
\(538\) | 23.0560 | 0.994013 | ||||||||
\(539\) | 97.8533 | 4.21484 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −37.2677 | −1.60226 | −0.801131 | − | 0.598488i | \(-0.795768\pi\) | ||||
−0.801131 | + | 0.598488i | \(0.795768\pi\) | |||||||
\(542\) | −4.90767 | −0.210802 | ||||||||
\(543\) | 0.508699 | 0.0218304 | ||||||||
\(544\) | 49.8450 | 2.13709 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4.63491 | −0.198356 | ||||||||
\(547\) | 41.7401 | 1.78468 | 0.892339 | − | 0.451366i | \(-0.149063\pi\) | ||||
0.892339 | + | 0.451366i | \(0.149063\pi\) | |||||||
\(548\) | −10.6149 | −0.453448 | ||||||||
\(549\) | 24.8309 | 1.05976 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.35412 | 0.142890 | ||||||||
\(552\) | −0.489006 | −0.0208135 | ||||||||
\(553\) | 16.5904 | 0.705497 | ||||||||
\(554\) | −8.90334 | −0.378267 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 14.9942 | 0.635894 | ||||||||
\(557\) | 13.6095 | 0.576652 | 0.288326 | − | 0.957532i | \(-0.406901\pi\) | ||||
0.288326 | + | 0.957532i | \(0.406901\pi\) | |||||||
\(558\) | 10.1387 | 0.429205 | ||||||||
\(559\) | −1.68111 | −0.0711034 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.9724 | −0.463255 | ||||||||
\(562\) | 50.9700 | 2.15004 | ||||||||
\(563\) | −41.4317 | −1.74614 | −0.873068 | − | 0.487598i | \(-0.837873\pi\) | ||||
−0.873068 | + | 0.487598i | \(0.837873\pi\) | |||||||
\(564\) | 3.45516 | 0.145488 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −8.87522 | −0.373053 | ||||||||
\(567\) | −42.3660 | −1.77920 | ||||||||
\(568\) | 3.66312 | 0.153701 | ||||||||
\(569\) | 1.50042 | 0.0629007 | 0.0314504 | − | 0.999505i | \(-0.489987\pi\) | ||||
0.0314504 | + | 0.999505i | \(0.489987\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 42.5501 | 1.78066 | 0.890332 | − | 0.455311i | \(-0.150472\pi\) | ||||
0.890332 | + | 0.455311i | \(0.150472\pi\) | |||||||
\(572\) | 11.7561 | 0.491545 | ||||||||
\(573\) | −6.41063 | −0.267808 | ||||||||
\(574\) | −64.8611 | −2.70725 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 7.52323 | 0.313468 | ||||||||
\(577\) | −14.1072 | −0.587290 | −0.293645 | − | 0.955915i | \(-0.594868\pi\) | ||||
−0.293645 | + | 0.955915i | \(0.594868\pi\) | |||||||
\(578\) | −71.4348 | −2.97129 | ||||||||
\(579\) | 4.40847 | 0.183210 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −33.4874 | −1.38929 | ||||||||
\(582\) | −0.573310 | −0.0237645 | ||||||||
\(583\) | −46.2896 | −1.91712 | ||||||||
\(584\) | −7.30778 | −0.302398 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −51.8892 | −2.14352 | ||||||||
\(587\) | −41.2458 | −1.70240 | −0.851198 | − | 0.524845i | \(-0.824123\pi\) | ||||
−0.851198 | + | 0.524845i | \(0.824123\pi\) | |||||||
\(588\) | −7.85269 | −0.323839 | ||||||||
\(589\) | −1.14945 | −0.0473621 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.23622 | −0.174255 | ||||||||
\(592\) | 24.6506 | 1.01314 | ||||||||
\(593\) | −6.83172 | −0.280545 | −0.140273 | − | 0.990113i | \(-0.544798\pi\) | ||||
−0.140273 | + | 0.990113i | \(0.544798\pi\) | |||||||
\(594\) | −15.9900 | −0.656076 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.70650 | −0.192786 | ||||||||
\(597\) | 2.17646 | 0.0890767 | ||||||||
\(598\) | −4.60632 | −0.188367 | ||||||||
\(599\) | −0.441871 | −0.0180543 | −0.00902717 | − | 0.999959i | \(-0.502873\pi\) | ||||
−0.00902717 | + | 0.999959i | \(0.502873\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.3310 | −0.910899 | −0.455450 | − | 0.890262i | \(-0.650521\pi\) | ||||
−0.455450 | + | 0.890262i | \(0.650521\pi\) | |||||||
\(602\) | −9.46004 | −0.385562 | ||||||||
\(603\) | −13.7315 | −0.559192 | ||||||||
\(604\) | 0.537959 | 0.0218893 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −8.43604 | −0.342691 | ||||||||
\(607\) | −21.6504 | −0.878763 | −0.439381 | − | 0.898301i | \(-0.644802\pi\) | ||||
−0.439381 | + | 0.898301i | \(0.644802\pi\) | |||||||
\(608\) | −4.05848 | −0.164593 | ||||||||
\(609\) | −8.25983 | −0.334705 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14.3626 | −0.581050 | ||||||||
\(612\) | −30.2195 | −1.22155 | ||||||||
\(613\) | 25.4719 | 1.02880 | 0.514399 | − | 0.857551i | \(-0.328015\pi\) | ||||
0.514399 | + | 0.857551i | \(0.328015\pi\) | |||||||
\(614\) | 10.6702 | 0.430614 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −29.1933 | −1.17623 | ||||||||
\(617\) | −33.9269 | −1.36585 | −0.682923 | − | 0.730490i | \(-0.739292\pi\) | ||||
−0.682923 | + | 0.730490i | \(0.739292\pi\) | |||||||
\(618\) | −8.83510 | −0.355400 | ||||||||
\(619\) | −36.1265 | −1.45205 | −0.726024 | − | 0.687670i | \(-0.758634\pi\) | ||||
−0.726024 | + | 0.687670i | \(0.758634\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.56638 | 0.102985 | ||||||||
\(622\) | 27.7507 | 1.11270 | ||||||||
\(623\) | 59.4553 | 2.38203 | ||||||||
\(624\) | 2.37611 | 0.0951204 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.43630 | −0.0574060 | ||||||||
\(627\) | 0.893394 | 0.0356787 | ||||||||
\(628\) | 28.0368 | 1.11879 | ||||||||
\(629\) | −37.9728 | −1.51407 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.67874 | −0.305686 | −0.152843 | − | 0.988251i | \(-0.548843\pi\) | ||||
−0.152843 | + | 0.988251i | \(0.548843\pi\) | |||||||
\(632\) | −3.63803 | −0.144713 | ||||||||
\(633\) | 2.56975 | 0.102139 | ||||||||
\(634\) | 39.5699 | 1.57152 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.71473 | 0.147298 | ||||||||
\(637\) | 32.6426 | 1.29335 | ||||||||
\(638\) | 51.1459 | 2.02489 | ||||||||
\(639\) | −9.47427 | −0.374796 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.35930 | 0.369670 | 0.184835 | − | 0.982770i | \(-0.440825\pi\) | ||||
0.184835 | + | 0.982770i | \(0.440825\pi\) | |||||||
\(642\) | −1.14659 | −0.0452524 | ||||||||
\(643\) | −5.80473 | −0.228916 | −0.114458 | − | 0.993428i | \(-0.536513\pi\) | ||||
−0.114458 | + | 0.993428i | \(0.536513\pi\) | |||||||
\(644\) | −10.6177 | −0.418397 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8.36402 | 0.329078 | ||||||||
\(647\) | 26.8056 | 1.05384 | 0.526919 | − | 0.849915i | \(-0.323347\pi\) | ||||
0.526919 | + | 0.849915i | \(0.323347\pi\) | |||||||
\(648\) | 9.29022 | 0.364954 | ||||||||
\(649\) | 37.5103 | 1.47241 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.83061 | 0.110941 | ||||||||
\(652\) | −15.1387 | −0.592878 | ||||||||
\(653\) | 7.24374 | 0.283469 | 0.141735 | − | 0.989905i | \(-0.454732\pi\) | ||||
0.141735 | + | 0.989905i | \(0.454732\pi\) | |||||||
\(654\) | −1.02727 | −0.0401694 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 33.2514 | 1.29825 | ||||||||
\(657\) | 18.9008 | 0.737391 | ||||||||
\(658\) | −80.8222 | −3.15078 | ||||||||
\(659\) | 30.2151 | 1.17701 | 0.588507 | − | 0.808492i | \(-0.299716\pi\) | ||||
0.588507 | + | 0.808492i | \(0.299716\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.97273 | −0.0767304 | −0.0383652 | − | 0.999264i | \(-0.512215\pi\) | ||||
−0.0383652 | + | 0.999264i | \(0.512215\pi\) | |||||||
\(662\) | −32.4534 | −1.26134 | ||||||||
\(663\) | −3.66025 | −0.142152 | ||||||||
\(664\) | 7.34328 | 0.284975 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −27.2714 | −1.05674 | ||||||||
\(667\) | −8.20888 | −0.317849 | ||||||||
\(668\) | −2.13799 | −0.0827212 | ||||||||
\(669\) | −1.09679 | −0.0424044 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −42.9272 | −1.65718 | ||||||||
\(672\) | 9.99437 | 0.385541 | ||||||||
\(673\) | 51.0499 | 1.96783 | 0.983915 | − | 0.178638i | \(-0.0571691\pi\) | ||||
0.983915 | + | 0.178638i | \(0.0571691\pi\) | |||||||
\(674\) | 49.5744 | 1.90954 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −14.1177 | −0.542989 | ||||||||
\(677\) | −18.6165 | −0.715490 | −0.357745 | − | 0.933819i | \(-0.616454\pi\) | ||||
−0.357745 | + | 0.933819i | \(0.616454\pi\) | |||||||
\(678\) | −5.54167 | −0.212827 | ||||||||
\(679\) | 5.49329 | 0.210813 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.40175 | −0.245316 | ||||||||
\(682\) | −17.5275 | −0.671164 | ||||||||
\(683\) | −5.53670 | −0.211856 | −0.105928 | − | 0.994374i | \(-0.533781\pi\) | ||||
−0.105928 | + | 0.994374i | \(0.533781\pi\) | |||||||
\(684\) | 2.46054 | 0.0940810 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 117.468 | 4.48494 | ||||||||
\(687\) | 4.15348 | 0.158465 | ||||||||
\(688\) | 4.84973 | 0.184894 | ||||||||
\(689\) | −15.4416 | −0.588279 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.0622 | −0.687120 | −0.343560 | − | 0.939131i | \(-0.611633\pi\) | ||||
−0.343560 | + | 0.939131i | \(0.611633\pi\) | |||||||
\(692\) | 9.71343 | 0.369249 | ||||||||
\(693\) | 75.5055 | 2.86822 | ||||||||
\(694\) | 21.0524 | 0.799139 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.81126 | 0.0686555 | ||||||||
\(697\) | −51.2217 | −1.94016 | ||||||||
\(698\) | −16.6659 | −0.630815 | ||||||||
\(699\) | −4.82124 | −0.182356 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.7231 | −0.971547 | −0.485774 | − | 0.874085i | \(-0.661462\pi\) | ||||
−0.485774 | + | 0.874085i | \(0.661462\pi\) | |||||||
\(702\) | −5.33404 | −0.201320 | ||||||||
\(703\) | 3.09182 | 0.116610 | ||||||||
\(704\) | −13.0060 | −0.490182 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 17.6303 | 0.663524 | ||||||||
\(707\) | 80.8317 | 3.03999 | ||||||||
\(708\) | −3.01019 | −0.113130 | ||||||||
\(709\) | 22.8874 | 0.859556 | 0.429778 | − | 0.902935i | \(-0.358592\pi\) | ||||
0.429778 | + | 0.902935i | \(0.358592\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.40938 | 0.352879 | ||||||||
\(712\) | −13.0377 | −0.488607 | ||||||||
\(713\) | 2.81316 | 0.105354 | ||||||||
\(714\) | −20.5971 | −0.770828 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −16.4113 | −0.613321 | ||||||||
\(717\) | 2.64855 | 0.0989119 | ||||||||
\(718\) | −2.39888 | −0.0895254 | ||||||||
\(719\) | 33.5392 | 1.25080 | 0.625400 | − | 0.780304i | \(-0.284936\pi\) | ||||
0.625400 | + | 0.780304i | \(0.284936\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 84.6554 | 3.15273 | ||||||||
\(722\) | 34.2895 | 1.27612 | ||||||||
\(723\) | 0.944682 | 0.0351331 | ||||||||
\(724\) | −2.42207 | −0.0900157 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 7.72251 | 0.286609 | ||||||||
\(727\) | −47.3713 | −1.75690 | −0.878452 | − | 0.477831i | \(-0.841423\pi\) | ||||
−0.878452 | + | 0.477831i | \(0.841423\pi\) | |||||||
\(728\) | −9.73852 | −0.360934 | ||||||||
\(729\) | −22.5209 | −0.834109 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.47071 | −0.276314 | ||||||||
\(732\) | 3.44489 | 0.127327 | ||||||||
\(733\) | 28.8063 | 1.06399 | 0.531993 | − | 0.846749i | \(-0.321443\pi\) | ||||
0.531993 | + | 0.846749i | \(0.321443\pi\) | |||||||
\(734\) | −32.0532 | −1.18310 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.93272 | 0.366125 | ||||||||
\(737\) | 23.7388 | 0.874430 | ||||||||
\(738\) | −36.7865 | −1.35413 | ||||||||
\(739\) | −44.3061 | −1.62982 | −0.814912 | − | 0.579584i | \(-0.803215\pi\) | ||||
−0.814912 | + | 0.579584i | \(0.803215\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.298025 | 0.0109482 | ||||||||
\(742\) | −86.8939 | −3.18998 | ||||||||
\(743\) | 8.81533 | 0.323403 | 0.161702 | − | 0.986840i | \(-0.448302\pi\) | ||||
0.161702 | + | 0.986840i | \(0.448302\pi\) | |||||||
\(744\) | −0.620711 | −0.0227564 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 24.9395 | 0.913099 | ||||||||
\(747\) | −18.9926 | −0.694904 | ||||||||
\(748\) | 52.2429 | 1.91019 | ||||||||
\(749\) | 10.9863 | 0.401431 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.39589 | 0.160408 | 0.0802041 | − | 0.996778i | \(-0.474443\pi\) | ||||
0.0802041 | + | 0.996778i | \(0.474443\pi\) | |||||||
\(752\) | 41.4339 | 1.51094 | ||||||||
\(753\) | −2.58875 | −0.0943392 | ||||||||
\(754\) | 17.0616 | 0.621347 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −12.2951 | −0.447170 | ||||||||
\(757\) | −3.60759 | −0.131120 | −0.0655600 | − | 0.997849i | \(-0.520883\pi\) | ||||
−0.0655600 | + | 0.997849i | \(0.520883\pi\) | |||||||
\(758\) | −15.2003 | −0.552100 | ||||||||
\(759\) | −2.18649 | −0.0793647 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.6606 | 0.422696 | 0.211348 | − | 0.977411i | \(-0.432215\pi\) | ||||
0.211348 | + | 0.977411i | \(0.432215\pi\) | |||||||
\(762\) | −6.49952 | −0.235453 | ||||||||
\(763\) | 9.84298 | 0.356340 | ||||||||
\(764\) | 30.5230 | 1.10428 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −32.6387 | −1.17928 | ||||||||
\(767\) | 12.5130 | 0.451816 | ||||||||
\(768\) | −6.11425 | −0.220629 | ||||||||
\(769\) | −1.46086 | −0.0526800 | −0.0263400 | − | 0.999653i | \(-0.508385\pi\) | ||||
−0.0263400 | + | 0.999653i | \(0.508385\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.96750 | 0.214914 | ||||||||
\(772\) | −20.9901 | −0.755450 | ||||||||
\(773\) | −11.5351 | −0.414887 | −0.207444 | − | 0.978247i | \(-0.566514\pi\) | ||||
−0.207444 | + | 0.978247i | \(0.566514\pi\) | |||||||
\(774\) | −5.36533 | −0.192853 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.20460 | −0.0432425 | ||||||||
\(777\) | −7.61389 | −0.273147 | ||||||||
\(778\) | 46.1677 | 1.65519 | ||||||||
\(779\) | 4.17057 | 0.149426 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.3789 | 0.586083 | ||||||||
\(782\) | −20.4701 | −0.732009 | ||||||||
\(783\) | −9.50575 | −0.339708 | ||||||||
\(784\) | −94.1686 | −3.36316 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.00528098 | −0.000188366 0 | ||||||||
\(787\) | 1.47008 | 0.0524028 | 0.0262014 | − | 0.999657i | \(-0.491659\pi\) | ||||
0.0262014 | + | 0.999657i | \(0.491659\pi\) | |||||||
\(788\) | 20.1700 | 0.718525 | ||||||||
\(789\) | 4.26360 | 0.151788 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 53.0987 | 1.88797 | ||||||||
\(792\) | −16.5572 | −0.588335 | ||||||||
\(793\) | −14.3199 | −0.508516 | ||||||||
\(794\) | −2.18486 | −0.0775377 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.3628 | −0.367300 | ||||||||
\(797\) | 43.1788 | 1.52947 | 0.764735 | − | 0.644345i | \(-0.222870\pi\) | ||||
0.764735 | + | 0.644345i | \(0.222870\pi\) | |||||||
\(798\) | 1.67706 | 0.0593673 | ||||||||
\(799\) | −63.8263 | −2.25801 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 33.7206 | 1.19146 | ||||||||
\(802\) | −64.1702 | −2.26593 | ||||||||
\(803\) | −32.6753 | −1.15309 | ||||||||
\(804\) | −1.90503 | −0.0671852 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.84696 | −0.205950 | ||||||||
\(807\) | 3.65079 | 0.128514 | ||||||||
\(808\) | −17.7252 | −0.623569 | ||||||||
\(809\) | −21.8926 | −0.769704 | −0.384852 | − | 0.922978i | \(-0.625748\pi\) | ||||
−0.384852 | + | 0.922978i | \(0.625748\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41.6105 | 1.46114 | 0.730572 | − | 0.682836i | \(-0.239254\pi\) | ||||
0.730572 | + | 0.682836i | \(0.239254\pi\) | |||||||
\(812\) | 39.3276 | 1.38013 | ||||||||
\(813\) | −0.777102 | −0.0272542 | ||||||||
\(814\) | 47.1462 | 1.65247 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 10.5592 | 0.369647 | ||||||||
\(817\) | 0.608281 | 0.0212810 | ||||||||
\(818\) | −50.0987 | −1.75166 | ||||||||
\(819\) | 25.1877 | 0.880128 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.9071 | −0.520262 | −0.260131 | − | 0.965573i | \(-0.583766\pi\) | ||||
−0.260131 | + | 0.965573i | \(0.583766\pi\) | |||||||
\(822\) | −4.10337 | −0.143121 | ||||||||
\(823\) | 26.2455 | 0.914860 | 0.457430 | − | 0.889246i | \(-0.348770\pi\) | ||||
0.457430 | + | 0.889246i | \(0.348770\pi\) | |||||||
\(824\) | −18.5637 | −0.646696 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 70.4136 | 2.45000 | ||||||||
\(827\) | 6.14518 | 0.213689 | 0.106844 | − | 0.994276i | \(-0.465925\pi\) | ||||
0.106844 | + | 0.994276i | \(0.465925\pi\) | |||||||
\(828\) | −6.02192 | −0.209276 | ||||||||
\(829\) | 23.4428 | 0.814200 | 0.407100 | − | 0.913384i | \(-0.366540\pi\) | ||||
0.407100 | + | 0.913384i | \(0.366540\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.40979 | −0.0489052 | ||||||||
\(832\) | −4.33864 | −0.150415 | ||||||||
\(833\) | 145.061 | 5.02606 | ||||||||
\(834\) | 5.79622 | 0.200707 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4.25372 | −0.147118 | ||||||||
\(837\) | 3.25759 | 0.112599 | ||||||||
\(838\) | −3.13120 | −0.108166 | ||||||||
\(839\) | 37.5665 | 1.29694 | 0.648470 | − | 0.761240i | \(-0.275409\pi\) | ||||
0.648470 | + | 0.761240i | \(0.275409\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.40533 | 0.0484598 | ||||||||
\(842\) | 22.8212 | 0.786469 | ||||||||
\(843\) | 8.07082 | 0.277974 | ||||||||
\(844\) | −12.2354 | −0.421159 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −45.8389 | −1.57598 | ||||||||
\(847\) | −73.9948 | −2.54249 | ||||||||
\(848\) | 44.5466 | 1.52974 | ||||||||
\(849\) | −1.40534 | −0.0482312 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.56693 | −0.259391 | ||||||||
\(852\) | −1.31440 | −0.0450307 | ||||||||
\(853\) | −22.1842 | −0.759571 | −0.379786 | − | 0.925075i | \(-0.624002\pi\) | ||||
−0.379786 | + | 0.925075i | \(0.624002\pi\) | |||||||
\(854\) | −80.5820 | −2.75746 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.40913 | −0.0823425 | ||||||||
\(857\) | 24.9840 | 0.853437 | 0.426718 | − | 0.904385i | \(-0.359670\pi\) | ||||
0.426718 | + | 0.904385i | \(0.359670\pi\) | |||||||
\(858\) | 4.54448 | 0.155146 | ||||||||
\(859\) | −18.7825 | −0.640850 | −0.320425 | − | 0.947274i | \(-0.603826\pi\) | ||||
−0.320425 | + | 0.947274i | \(0.603826\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.2704 | −0.350015 | ||||||||
\(862\) | 28.0264 | 0.954583 | ||||||||
\(863\) | −35.7173 | −1.21583 | −0.607916 | − | 0.794001i | \(-0.707994\pi\) | ||||
−0.607916 | + | 0.794001i | \(0.707994\pi\) | |||||||
\(864\) | 11.5019 | 0.391304 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 10.6368 | 0.361454 | ||||||||
\(867\) | −11.3113 | −0.384152 | ||||||||
\(868\) | −13.4774 | −0.457454 | ||||||||
\(869\) | −16.2667 | −0.551811 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.91895 | 0.268324 | ||||||||
\(872\) | −2.15842 | −0.0730932 | ||||||||
\(873\) | 3.11556 | 0.105446 | ||||||||
\(874\) | 1.66672 | 0.0563776 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.62218 | 0.0885953 | ||||||||
\(877\) | 42.4124 | 1.43216 | 0.716082 | − | 0.698016i | \(-0.245934\pi\) | ||||
0.716082 | + | 0.698016i | \(0.245934\pi\) | |||||||
\(878\) | −14.5291 | −0.490332 | ||||||||
\(879\) | −8.21638 | −0.277132 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.5019 | −0.892873 | −0.446437 | − | 0.894815i | \(-0.647307\pi\) | ||||
−0.446437 | + | 0.894815i | \(0.647307\pi\) | |||||||
\(882\) | 104.180 | 3.50793 | ||||||||
\(883\) | 9.84464 | 0.331299 | 0.165649 | − | 0.986185i | \(-0.447028\pi\) | ||||
0.165649 | + | 0.986185i | \(0.447028\pi\) | |||||||
\(884\) | 17.4276 | 0.586152 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 52.8441 | 1.77533 | ||||||||
\(887\) | −48.1046 | −1.61519 | −0.807597 | − | 0.589735i | \(-0.799232\pi\) | ||||
−0.807597 | + | 0.589735i | \(0.799232\pi\) | |||||||
\(888\) | 1.66961 | 0.0560285 | ||||||||
\(889\) | 62.2765 | 2.08869 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 41.5394 | 1.39162 | ||||||||
\(892\) | 5.22216 | 0.174851 | ||||||||
\(893\) | 5.19687 | 0.173907 | ||||||||
\(894\) | −1.81937 | −0.0608488 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 44.1711 | 1.47565 | ||||||||
\(897\) | −0.729386 | −0.0243535 | ||||||||
\(898\) | 18.3623 | 0.612757 | ||||||||
\(899\) | −10.4198 | −0.347520 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −68.6212 | −2.28610 | ||||||||
\(902\) | 63.5957 | 2.11751 | ||||||||
\(903\) | −1.49795 | −0.0498485 | ||||||||
\(904\) | −11.6437 | −0.387265 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.207956 | 0.00690889 | ||||||||
\(907\) | 44.8522 | 1.48929 | 0.744646 | − | 0.667459i | \(-0.232618\pi\) | ||||
0.744646 | + | 0.667459i | \(0.232618\pi\) | |||||||
\(908\) | 30.4807 | 1.01154 | ||||||||
\(909\) | 45.8443 | 1.52056 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −49.9719 | −1.65564 | −0.827822 | − | 0.560991i | \(-0.810420\pi\) | ||||
−0.827822 | + | 0.560991i | \(0.810420\pi\) | |||||||
\(912\) | −0.859753 | −0.0284693 | ||||||||
\(913\) | 32.8340 | 1.08665 | ||||||||
\(914\) | −23.1458 | −0.765596 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −19.7760 | −0.653417 | ||||||||
\(917\) | 0.0506008 | 0.00167099 | ||||||||
\(918\) | −23.7040 | −0.782350 | ||||||||
\(919\) | 12.3429 | 0.407155 | 0.203577 | − | 0.979059i | \(-0.434743\pi\) | ||||
0.203577 | + | 0.979059i | \(0.434743\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.68957 | 0.0556732 | ||||||||
\(922\) | −44.6466 | −1.47036 | ||||||||
\(923\) | 5.46379 | 0.179843 | ||||||||
\(924\) | 10.4752 | 0.344608 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −48.6937 | −1.60018 | ||||||||
\(927\) | 48.0130 | 1.57695 | ||||||||
\(928\) | −36.7904 | −1.20770 | ||||||||
\(929\) | 20.2913 | 0.665735 | 0.332867 | − | 0.942974i | \(-0.391984\pi\) | ||||
0.332867 | + | 0.942974i | \(0.391984\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.8112 | −0.387095 | ||||||||
\(932\) | 22.9554 | 0.751930 | ||||||||
\(933\) | 4.39417 | 0.143859 | ||||||||
\(934\) | 8.59177 | 0.281131 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5.52328 | −0.180534 | ||||||||
\(937\) | 5.50728 | 0.179915 | 0.0899576 | − | 0.995946i | \(-0.471327\pi\) | ||||
0.0899576 | + | 0.995946i | \(0.471327\pi\) | |||||||
\(938\) | 44.5620 | 1.45500 | ||||||||
\(939\) | −0.227430 | −0.00742190 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29.3989 | 0.958378 | 0.479189 | − | 0.877712i | \(-0.340931\pi\) | ||||
0.479189 | + | 0.877712i | \(0.340931\pi\) | |||||||
\(942\) | 10.8381 | 0.353123 | ||||||||
\(943\) | −10.2071 | −0.332388 | ||||||||
\(944\) | −36.0978 | −1.17488 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.27547 | 0.301572 | ||||||||
\(947\) | 10.8670 | 0.353130 | 0.176565 | − | 0.984289i | \(-0.443501\pi\) | ||||
0.176565 | + | 0.984289i | \(0.443501\pi\) | |||||||
\(948\) | 1.30540 | 0.0423974 | ||||||||
\(949\) | −10.9001 | −0.353831 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.26568 | 0.203179 | ||||||||
\(952\) | −43.2772 | −1.40262 | ||||||||
\(953\) | −51.5990 | −1.67146 | −0.835728 | − | 0.549144i | \(-0.814954\pi\) | ||||
−0.835728 | + | 0.549144i | \(0.814954\pi\) | |||||||
\(954\) | −49.2826 | −1.59558 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −12.6106 | −0.407855 | ||||||||
\(957\) | 8.09868 | 0.261793 | ||||||||
\(958\) | 37.2092 | 1.20218 | ||||||||
\(959\) | 39.3173 | 1.26962 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.4292 | −0.884812 | ||||||||
\(962\) | 15.7274 | 0.507070 | ||||||||
\(963\) | 6.23097 | 0.200790 | ||||||||
\(964\) | −4.49792 | −0.144868 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.10444 | −0.132058 | ||||||||
\(967\) | 49.7367 | 1.59942 | 0.799712 | − | 0.600383i | \(-0.204985\pi\) | ||||
0.799712 | + | 0.600383i | \(0.204985\pi\) | |||||||
\(968\) | 16.2260 | 0.521522 | ||||||||
\(969\) | 1.32440 | 0.0425457 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.7725 | 0.762896 | 0.381448 | − | 0.924390i | \(-0.375426\pi\) | ||||
0.381448 | + | 0.924390i | \(0.375426\pi\) | |||||||
\(972\) | −10.5100 | −0.337108 | ||||||||
\(973\) | −55.5377 | −1.78046 | ||||||||
\(974\) | −43.5848 | −1.39655 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 41.3107 | 1.32232 | ||||||||
\(977\) | −40.5334 | −1.29678 | −0.648389 | − | 0.761309i | \(-0.724557\pi\) | ||||
−0.648389 | + | 0.761309i | \(0.724557\pi\) | |||||||
\(978\) | −5.85210 | −0.187130 | ||||||||
\(979\) | −58.2954 | −1.86313 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.58252 | 0.178236 | ||||||||
\(982\) | −1.33127 | −0.0424826 | ||||||||
\(983\) | −60.6697 | −1.93506 | −0.967532 | − | 0.252749i | \(-0.918665\pi\) | ||||
−0.967532 | + | 0.252749i | \(0.918665\pi\) | |||||||
\(984\) | 2.25215 | 0.0717958 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 75.8203 | 2.41461 | ||||||||
\(987\) | −12.7978 | −0.407357 | ||||||||
\(988\) | −1.41899 | −0.0451440 | ||||||||
\(989\) | −1.48871 | −0.0473381 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −35.5820 | −1.13030 | −0.565150 | − | 0.824988i | \(-0.691182\pi\) | ||||
−0.565150 | + | 0.824988i | \(0.691182\pi\) | |||||||
\(992\) | 12.6079 | 0.400302 | ||||||||
\(993\) | −5.13881 | −0.163075 | ||||||||
\(994\) | 30.7461 | 0.975209 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.63492 | −0.0834906 | ||||||||
\(997\) | −0.728331 | −0.0230665 | −0.0115332 | − | 0.999933i | \(-0.503671\pi\) | ||||
−0.0115332 | + | 0.999933i | \(0.503671\pi\) | |||||||
\(998\) | 0.677208 | 0.0214366 | ||||||||
\(999\) | −8.76238 | −0.277229 |
(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 | 1075.2.a.p.1.2 | 6 | ||
3.2 | odd | 2 | 9675.2.a.cl.1.5 | 6 | |||
5.2 | odd | 4 | 1075.2.b.k.474.3 | 12 | |||
5.3 | odd | 4 | 1075.2.b.k.474.10 | 12 | |||
5.4 | even | 2 | 215.2.a.d.1.5 | ✓ | 6 | ||
15.14 | odd | 2 | 1935.2.a.z.1.2 | 6 | |||
20.19 | odd | 2 | 3440.2.a.x.1.4 | 6 | |||
215.214 | odd | 2 | 9245.2.a.n.1.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
215.2.a.d.1.5 | ✓ | 6 | 5.4 | even | 2 | ||
1075.2.a.p.1.2 | 6 | 1.1 | even | 1 | trivial | ||
1075.2.b.k.474.3 | 12 | 5.2 | odd | 4 | |||
1075.2.b.k.474.10 | 12 | 5.3 | odd | 4 | |||
1935.2.a.z.1.2 | 6 | 15.14 | odd | 2 | |||
3440.2.a.x.1.4 | 6 | 20.19 | odd | 2 | |||
9245.2.a.n.1.2 | 6 | 215.214 | odd | 2 | |||
9675.2.a.cl.1.5 | 6 | 3.2 | odd | 2 |