Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(1\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.28 | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.23843 | 1.58281 | 0.791406 | − | 0.611291i | \(-0.209349\pi\) | ||||
0.791406 | + | 0.611291i | \(0.209349\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.01059 | 1.50529 | ||||||||
\(5\) | 0.715002 | 0.319759 | 0.159879 | − | 0.987137i | \(-0.448889\pi\) | ||||
0.159879 | + | 0.987137i | \(0.448889\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.26213 | 0.799784 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.60049 | 0.506118 | ||||||||
\(11\) | 3.48743 | 1.05150 | 0.525750 | − | 0.850639i | \(-0.323785\pi\) | ||||
0.525750 | + | 0.850639i | \(0.323785\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.88025 | −1.07619 | −0.538093 | − | 0.842885i | \(-0.680855\pi\) | ||||
−0.538093 | + | 0.842885i | \(0.680855\pi\) | |||||||
\(14\) | −2.23843 | −0.598247 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.957541 | −0.239385 | ||||||||
\(17\) | −2.02085 | −0.490127 | −0.245064 | − | 0.969507i | \(-0.578809\pi\) | ||||
−0.245064 | + | 0.969507i | \(0.578809\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.32595 | 0.304194 | 0.152097 | − | 0.988366i | \(-0.451397\pi\) | ||||
0.152097 | + | 0.988366i | \(0.451397\pi\) | |||||||
\(20\) | 2.15258 | 0.481331 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 7.80638 | 1.66433 | ||||||||
\(23\) | −4.77444 | −0.995540 | −0.497770 | − | 0.867309i | \(-0.665848\pi\) | ||||
−0.497770 | + | 0.867309i | \(0.665848\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.48877 | −0.897754 | ||||||||
\(26\) | −8.68568 | −1.70340 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.01059 | −0.568947 | ||||||||
\(29\) | −8.26004 | −1.53385 | −0.766925 | − | 0.641737i | \(-0.778214\pi\) | ||||
−0.766925 | + | 0.641737i | \(0.778214\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.73204 | −0.849900 | −0.424950 | − | 0.905217i | \(-0.639708\pi\) | ||||
−0.424950 | + | 0.905217i | \(0.639708\pi\) | |||||||
\(32\) | −6.66766 | −1.17869 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.52353 | −0.775779 | ||||||||
\(35\) | −0.715002 | −0.120857 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.4983 | −1.72591 | −0.862954 | − | 0.505283i | \(-0.831388\pi\) | ||||
−0.862954 | + | 0.505283i | \(0.831388\pi\) | |||||||
\(38\) | 2.96805 | 0.481482 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.61743 | 0.255738 | ||||||||
\(41\) | 0.827289 | 0.129201 | 0.0646004 | − | 0.997911i | \(-0.479423\pi\) | ||||
0.0646004 | + | 0.997911i | \(0.479423\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.69972 | 0.411703 | 0.205851 | − | 0.978583i | \(-0.434004\pi\) | ||||
0.205851 | + | 0.978583i | \(0.434004\pi\) | |||||||
\(44\) | 10.4992 | 1.58281 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −10.6873 | −1.57575 | ||||||||
\(47\) | −9.44282 | −1.37738 | −0.688688 | − | 0.725058i | \(-0.741813\pi\) | ||||
−0.688688 | + | 0.725058i | \(0.741813\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −10.0478 | −1.42098 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −11.6818 | −1.61998 | ||||||||
\(53\) | 7.12745 | 0.979030 | 0.489515 | − | 0.871995i | \(-0.337174\pi\) | ||||
0.489515 | + | 0.871995i | \(0.337174\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.49352 | 0.336226 | ||||||||
\(56\) | −2.26213 | −0.302290 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −18.4895 | −2.42780 | ||||||||
\(59\) | −6.64479 | −0.865078 | −0.432539 | − | 0.901615i | \(-0.642382\pi\) | ||||
−0.432539 | + | 0.901615i | \(0.642382\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.79645 | 1.25431 | 0.627153 | − | 0.778896i | \(-0.284220\pi\) | ||||
0.627153 | + | 0.778896i | \(0.284220\pi\) | |||||||
\(62\) | −10.5924 | −1.34523 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −13.0100 | −1.62625 | ||||||||
\(65\) | −2.77439 | −0.344120 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.4839 | 1.28081 | 0.640407 | − | 0.768036i | \(-0.278766\pi\) | ||||
0.640407 | + | 0.768036i | \(0.278766\pi\) | |||||||
\(68\) | −6.08393 | −0.737785 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.60049 | −0.191295 | ||||||||
\(71\) | 8.80029 | 1.04440 | 0.522201 | − | 0.852823i | \(-0.325111\pi\) | ||||
0.522201 | + | 0.852823i | \(0.325111\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.52998 | 0.764276 | 0.382138 | − | 0.924105i | \(-0.375188\pi\) | ||||
0.382138 | + | 0.924105i | \(0.375188\pi\) | |||||||
\(74\) | −23.4997 | −2.73179 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.99189 | 0.457901 | ||||||||
\(77\) | −3.48743 | −0.397429 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.16978 | −0.131611 | −0.0658053 | − | 0.997832i | \(-0.520962\pi\) | ||||
−0.0658053 | + | 0.997832i | \(0.520962\pi\) | |||||||
\(80\) | −0.684644 | −0.0765455 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.85183 | 0.204501 | ||||||||
\(83\) | −4.68620 | −0.514377 | −0.257189 | − | 0.966361i | \(-0.582796\pi\) | ||||
−0.257189 | + | 0.966361i | \(0.582796\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.44491 | −0.156722 | ||||||||
\(86\) | 6.04313 | 0.651648 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 7.88902 | 0.840973 | ||||||||
\(89\) | −3.95955 | −0.419712 | −0.209856 | − | 0.977732i | \(-0.567299\pi\) | ||||
−0.209856 | + | 0.977732i | \(0.567299\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.88025 | 0.406760 | ||||||||
\(92\) | −14.3739 | −1.49858 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −21.1371 | −2.18013 | ||||||||
\(95\) | 0.948058 | 0.0972687 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.83283 | 0.693768 | 0.346884 | − | 0.937908i | \(-0.387240\pi\) | ||||
0.346884 | + | 0.937908i | \(0.387240\pi\) | |||||||
\(98\) | 2.23843 | 0.226116 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −13.5138 | −1.35138 | ||||||||
\(101\) | −14.4018 | −1.43303 | −0.716517 | − | 0.697569i | \(-0.754265\pi\) | ||||
−0.716517 | + | 0.697569i | \(0.754265\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.78657 | 0.471635 | 0.235817 | − | 0.971797i | \(-0.424223\pi\) | ||||
0.235817 | + | 0.971797i | \(0.424223\pi\) | |||||||
\(104\) | −8.77763 | −0.860717 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 15.9543 | 1.54962 | ||||||||
\(107\) | 8.11171 | 0.784189 | 0.392094 | − | 0.919925i | \(-0.371751\pi\) | ||||
0.392094 | + | 0.919925i | \(0.371751\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.982270 | 0.0940844 | 0.0470422 | − | 0.998893i | \(-0.485020\pi\) | ||||
0.0470422 | + | 0.998893i | \(0.485020\pi\) | |||||||
\(110\) | 5.58158 | 0.532183 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.957541 | 0.0904791 | ||||||||
\(113\) | 5.77508 | 0.543273 | 0.271637 | − | 0.962400i | \(-0.412435\pi\) | ||||
0.271637 | + | 0.962400i | \(0.412435\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.41374 | −0.318333 | ||||||||
\(116\) | −24.8676 | −2.30889 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −14.8739 | −1.36926 | ||||||||
\(119\) | 2.02085 | 0.185251 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.16215 | 0.105650 | ||||||||
\(122\) | 21.9287 | 1.98533 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −14.2462 | −1.27935 | ||||||||
\(125\) | −6.78450 | −0.606824 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | −15.7868 | −1.39537 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.21028 | −0.544678 | ||||||||
\(131\) | −1.06804 | −0.0933152 | −0.0466576 | − | 0.998911i | \(-0.514857\pi\) | ||||
−0.0466576 | + | 0.998911i | \(0.514857\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.32595 | −0.114975 | ||||||||
\(134\) | 23.4675 | 2.02729 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.57142 | −0.391996 | ||||||||
\(137\) | 12.8058 | 1.09408 | 0.547038 | − | 0.837108i | \(-0.315755\pi\) | ||||
0.547038 | + | 0.837108i | \(0.315755\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.13929 | −0.351090 | −0.175545 | − | 0.984471i | \(-0.556169\pi\) | ||||
−0.175545 | + | 0.984471i | \(0.556169\pi\) | |||||||
\(140\) | −2.15258 | −0.181926 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 19.6989 | 1.65309 | ||||||||
\(143\) | −13.5321 | −1.13161 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.90595 | −0.490462 | ||||||||
\(146\) | 14.6169 | 1.20971 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −31.6060 | −2.59800 | ||||||||
\(149\) | 13.5650 | 1.11129 | 0.555646 | − | 0.831419i | \(-0.312471\pi\) | ||||
0.555646 | + | 0.831419i | \(0.312471\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.40613 | 0.277187 | 0.138594 | − | 0.990349i | \(-0.455742\pi\) | ||||
0.138594 | + | 0.990349i | \(0.455742\pi\) | |||||||
\(152\) | 2.99948 | 0.243290 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −7.80638 | −0.629056 | ||||||||
\(155\) | −3.38342 | −0.271763 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.5876 | −1.64307 | −0.821536 | − | 0.570157i | \(-0.806882\pi\) | ||||
−0.821536 | + | 0.570157i | \(0.806882\pi\) | |||||||
\(158\) | −2.61848 | −0.208315 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.76739 | −0.376895 | ||||||||
\(161\) | 4.77444 | 0.376279 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.3948 | 1.12749 | 0.563744 | − | 0.825950i | \(-0.309360\pi\) | ||||
0.563744 | + | 0.825950i | \(0.309360\pi\) | |||||||
\(164\) | 2.49063 | 0.194485 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −10.4898 | −0.814163 | ||||||||
\(167\) | 14.7266 | 1.13958 | 0.569788 | − | 0.821792i | \(-0.307025\pi\) | ||||
0.569788 | + | 0.821792i | \(0.307025\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.05631 | 0.158178 | ||||||||
\(170\) | −3.23433 | −0.248062 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.12773 | 0.619733 | ||||||||
\(173\) | −12.1096 | −0.920678 | −0.460339 | − | 0.887743i | \(-0.652272\pi\) | ||||
−0.460339 | + | 0.887743i | \(0.652272\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.48877 | 0.339319 | ||||||||
\(176\) | −3.33935 | −0.251713 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −8.86320 | −0.664325 | ||||||||
\(179\) | 10.2816 | 0.768484 | 0.384242 | − | 0.923232i | \(-0.374463\pi\) | ||||
0.384242 | + | 0.923232i | \(0.374463\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.97609 | −0.518529 | −0.259264 | − | 0.965806i | \(-0.583480\pi\) | ||||
−0.259264 | + | 0.965806i | \(0.583480\pi\) | |||||||
\(182\) | 8.68568 | 0.643825 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −10.8004 | −0.796217 | ||||||||
\(185\) | −7.50630 | −0.551874 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.04755 | −0.515368 | ||||||||
\(188\) | −28.4284 | −2.07336 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.12217 | 0.153958 | ||||||||
\(191\) | −16.8925 | −1.22230 | −0.611150 | − | 0.791515i | \(-0.709293\pi\) | ||||
−0.611150 | + | 0.791515i | \(0.709293\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.01576 | 0.361043 | 0.180521 | − | 0.983571i | \(-0.442222\pi\) | ||||
0.180521 | + | 0.983571i | \(0.442222\pi\) | |||||||
\(194\) | 15.2948 | 1.09810 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.01059 | 0.215042 | ||||||||
\(197\) | 8.79497 | 0.626616 | 0.313308 | − | 0.949652i | \(-0.398563\pi\) | ||||
0.313308 | + | 0.949652i | \(0.398563\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.9618 | −1.55683 | −0.778417 | − | 0.627747i | \(-0.783977\pi\) | ||||
−0.778417 | + | 0.627747i | \(0.783977\pi\) | |||||||
\(200\) | −10.1542 | −0.718010 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −32.2375 | −2.26822 | ||||||||
\(203\) | 8.26004 | 0.579741 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.591514 | 0.0413131 | ||||||||
\(206\) | 10.7144 | 0.746509 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.71549 | 0.257623 | ||||||||
\(209\) | 4.62416 | 0.319860 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.3601 | 0.713221 | 0.356610 | − | 0.934253i | \(-0.383932\pi\) | ||||
0.356610 | + | 0.934253i | \(0.383932\pi\) | |||||||
\(212\) | 21.4578 | 1.47373 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 18.1575 | 1.24122 | ||||||||
\(215\) | 1.93030 | 0.131646 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.73204 | 0.321232 | ||||||||
\(218\) | 2.19875 | 0.148918 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 7.50696 | 0.506119 | ||||||||
\(221\) | 7.84138 | 0.527468 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.35678 | −0.425681 | −0.212841 | − | 0.977087i | \(-0.568272\pi\) | ||||
−0.212841 | + | 0.977087i | \(0.568272\pi\) | |||||||
\(224\) | 6.66766 | 0.445501 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 12.9271 | 0.859900 | ||||||||
\(227\) | −7.68768 | −0.510249 | −0.255124 | − | 0.966908i | \(-0.582116\pi\) | ||||
−0.255124 | + | 0.966908i | \(0.582116\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.5663 | −0.698244 | −0.349122 | − | 0.937077i | \(-0.613520\pi\) | ||||
−0.349122 | + | 0.937077i | \(0.613520\pi\) | |||||||
\(230\) | −7.64142 | −0.503861 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −18.6853 | −1.22675 | ||||||||
\(233\) | −25.1211 | −1.64574 | −0.822869 | − | 0.568231i | \(-0.807628\pi\) | ||||
−0.822869 | + | 0.568231i | \(0.807628\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.75164 | −0.440428 | ||||||||
\(236\) | −20.0047 | −1.30220 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.52353 | 0.293217 | ||||||||
\(239\) | 10.8412 | 0.701257 | 0.350629 | − | 0.936515i | \(-0.385968\pi\) | ||||
0.350629 | + | 0.936515i | \(0.385968\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.8749 | −1.15142 | −0.575712 | − | 0.817652i | \(-0.695275\pi\) | ||||
−0.575712 | + | 0.817652i | \(0.695275\pi\) | |||||||
\(242\) | 2.60141 | 0.167225 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 29.4931 | 1.88810 | ||||||||
\(245\) | 0.715002 | 0.0456798 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.14502 | −0.327369 | ||||||||
\(248\) | −10.7045 | −0.679737 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −15.1866 | −0.960488 | ||||||||
\(251\) | −4.79178 | −0.302455 | −0.151227 | − | 0.988499i | \(-0.548323\pi\) | ||||
−0.151227 | + | 0.988499i | \(0.548323\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16.6505 | −1.04681 | ||||||||
\(254\) | −2.23843 | −0.140452 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.31760 | −0.582350 | ||||||||
\(257\) | −6.08661 | −0.379672 | −0.189836 | − | 0.981816i | \(-0.560796\pi\) | ||||
−0.189836 | + | 0.981816i | \(0.560796\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.4983 | 0.652332 | ||||||||
\(260\) | −8.35253 | −0.518002 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.39074 | −0.147700 | ||||||||
\(263\) | −25.1166 | −1.54876 | −0.774378 | − | 0.632723i | \(-0.781937\pi\) | ||||
−0.774378 | + | 0.632723i | \(0.781937\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.09614 | 0.313053 | ||||||||
\(266\) | −2.96805 | −0.181983 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 31.5627 | 1.92800 | ||||||||
\(269\) | −12.2844 | −0.748995 | −0.374498 | − | 0.927228i | \(-0.622185\pi\) | ||||
−0.374498 | + | 0.927228i | \(0.622185\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.354378 | −0.0215269 | −0.0107635 | − | 0.999942i | \(-0.503426\pi\) | ||||
−0.0107635 | + | 0.999942i | \(0.503426\pi\) | |||||||
\(272\) | 1.93504 | 0.117329 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 28.6650 | 1.73172 | ||||||||
\(275\) | −15.6543 | −0.943988 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.8044 | −1.12984 | −0.564922 | − | 0.825144i | \(-0.691094\pi\) | ||||
−0.564922 | + | 0.825144i | \(0.691094\pi\) | |||||||
\(278\) | −9.26552 | −0.555709 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.61743 | −0.0966599 | ||||||||
\(281\) | −22.7302 | −1.35597 | −0.677985 | − | 0.735076i | \(-0.737146\pi\) | ||||
−0.677985 | + | 0.735076i | \(0.737146\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.78820 | −0.581848 | −0.290924 | − | 0.956746i | \(-0.593963\pi\) | ||||
−0.290924 | + | 0.956746i | \(0.593963\pi\) | |||||||
\(284\) | 26.4940 | 1.57213 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −30.2907 | −1.79112 | ||||||||
\(287\) | −0.827289 | −0.0488333 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.9162 | −0.759775 | ||||||||
\(290\) | −13.2201 | −0.776309 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 19.6591 | 1.15046 | ||||||||
\(293\) | 6.16187 | 0.359981 | 0.179990 | − | 0.983668i | \(-0.442393\pi\) | ||||
0.179990 | + | 0.983668i | \(0.442393\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.75104 | −0.276616 | ||||||||
\(296\) | −23.7485 | −1.38035 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 30.3645 | 1.75897 | ||||||||
\(299\) | 18.5260 | 1.07139 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.69972 | −0.155609 | ||||||||
\(302\) | 7.62440 | 0.438735 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.26965 | −0.0728195 | ||||||||
\(305\) | 7.00449 | 0.401076 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.7893 | −0.786999 | −0.393500 | − | 0.919325i | \(-0.628736\pi\) | ||||
−0.393500 | + | 0.919325i | \(0.628736\pi\) | |||||||
\(308\) | −10.4992 | −0.598248 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.57357 | −0.430150 | ||||||||
\(311\) | 7.99152 | 0.453158 | 0.226579 | − | 0.973993i | \(-0.427246\pi\) | ||||
0.226579 | + | 0.973993i | \(0.427246\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.19550 | 0.463237 | 0.231618 | − | 0.972807i | \(-0.425598\pi\) | ||||
0.231618 | + | 0.972807i | \(0.425598\pi\) | |||||||
\(314\) | −46.0840 | −2.60067 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.52173 | −0.198113 | ||||||||
\(317\) | −9.71596 | −0.545703 | −0.272851 | − | 0.962056i | \(-0.587967\pi\) | ||||
−0.272851 | + | 0.962056i | \(0.587967\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −28.8063 | −1.61284 | ||||||||
\(320\) | −9.30220 | −0.520009 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 10.6873 | 0.595578 | ||||||||
\(323\) | −2.67954 | −0.149094 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 17.4175 | 0.966151 | ||||||||
\(326\) | 32.2218 | 1.78460 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.87144 | 0.103333 | ||||||||
\(329\) | 9.44282 | 0.520599 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.7460 | 1.47009 | 0.735047 | − | 0.678017i | \(-0.237160\pi\) | ||||
0.735047 | + | 0.678017i | \(0.237160\pi\) | |||||||
\(332\) | −14.1082 | −0.774289 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 32.9644 | 1.80373 | ||||||||
\(335\) | 7.49602 | 0.409551 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.80788 | 0.425322 | 0.212661 | − | 0.977126i | \(-0.431787\pi\) | ||||
0.212661 | + | 0.977126i | \(0.431787\pi\) | |||||||
\(338\) | 4.60292 | 0.250366 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.35003 | −0.235913 | ||||||||
\(341\) | −16.5027 | −0.893669 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 6.10711 | 0.329273 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −27.1066 | −1.45726 | ||||||||
\(347\) | 16.8929 | 0.906859 | 0.453429 | − | 0.891292i | \(-0.350200\pi\) | ||||
0.453429 | + | 0.891292i | \(0.350200\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.8133 | −0.792937 | −0.396468 | − | 0.918048i | \(-0.629764\pi\) | ||||
−0.396468 | + | 0.918048i | \(0.629764\pi\) | |||||||
\(350\) | 10.0478 | 0.537078 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −23.2530 | −1.23939 | ||||||||
\(353\) | 32.0204 | 1.70427 | 0.852137 | − | 0.523319i | \(-0.175306\pi\) | ||||
0.852137 | + | 0.523319i | \(0.175306\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.29223 | 0.333957 | ||||||||
\(356\) | −11.9206 | −0.631790 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 23.0147 | 1.21637 | ||||||||
\(359\) | 7.14129 | 0.376903 | 0.188451 | − | 0.982083i | \(-0.439653\pi\) | ||||
0.188451 | + | 0.982083i | \(0.439653\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.2419 | −0.907466 | ||||||||
\(362\) | −15.6155 | −0.820733 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 11.6818 | 0.612294 | ||||||||
\(365\) | 4.66895 | 0.244384 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.0108 | 0.992356 | 0.496178 | − | 0.868221i | \(-0.334736\pi\) | ||||
0.496178 | + | 0.868221i | \(0.334736\pi\) | |||||||
\(368\) | 4.57172 | 0.238317 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −16.8024 | −0.873513 | ||||||||
\(371\) | −7.12745 | −0.370039 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 32.6219 | 1.68910 | 0.844550 | − | 0.535476i | \(-0.179868\pi\) | ||||
0.844550 | + | 0.535476i | \(0.179868\pi\) | |||||||
\(374\) | −15.7755 | −0.815731 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −21.3609 | −1.10160 | ||||||||
\(377\) | 32.0510 | 1.65071 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.55764 | 0.490943 | 0.245471 | − | 0.969404i | \(-0.421057\pi\) | ||||
0.245471 | + | 0.969404i | \(0.421057\pi\) | |||||||
\(380\) | 2.85421 | 0.146418 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −37.8128 | −1.93467 | ||||||||
\(383\) | 19.9990 | 1.02190 | 0.510950 | − | 0.859610i | \(-0.329294\pi\) | ||||
0.510950 | + | 0.859610i | \(0.329294\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.49352 | −0.127082 | ||||||||
\(386\) | 11.2275 | 0.571462 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 20.5708 | 1.04432 | ||||||||
\(389\) | 4.07409 | 0.206565 | 0.103282 | − | 0.994652i | \(-0.467066\pi\) | ||||
0.103282 | + | 0.994652i | \(0.467066\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.64841 | 0.487941 | ||||||||
\(392\) | 2.26213 | 0.114255 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 19.6870 | 0.991814 | ||||||||
\(395\) | −0.836396 | −0.0420837 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.7833 | 1.09327 | 0.546636 | − | 0.837370i | \(-0.315908\pi\) | ||||
0.546636 | + | 0.837370i | \(0.315908\pi\) | |||||||
\(398\) | −49.1602 | −2.46418 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.29818 | 0.214909 | ||||||||
\(401\) | −17.3330 | −0.865568 | −0.432784 | − | 0.901498i | \(-0.642469\pi\) | ||||
−0.432784 | + | 0.901498i | \(0.642469\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.3615 | 0.914651 | ||||||||
\(404\) | −43.3579 | −2.15714 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 18.4895 | 0.917621 | ||||||||
\(407\) | −36.6120 | −1.81479 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.4744 | −0.616821 | −0.308410 | − | 0.951253i | \(-0.599797\pi\) | ||||
−0.308410 | + | 0.951253i | \(0.599797\pi\) | |||||||
\(410\) | 1.32406 | 0.0653909 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 14.4104 | 0.709948 | ||||||||
\(413\) | 6.64479 | 0.326969 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.35065 | −0.164477 | ||||||||
\(416\) | 25.8721 | 1.26849 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 10.3509 | 0.506278 | ||||||||
\(419\) | 10.7981 | 0.527524 | 0.263762 | − | 0.964588i | \(-0.415037\pi\) | ||||
0.263762 | + | 0.964588i | \(0.415037\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.59997 | −0.370400 | −0.185200 | − | 0.982701i | \(-0.559293\pi\) | ||||
−0.185200 | + | 0.982701i | \(0.559293\pi\) | |||||||
\(422\) | 23.1905 | 1.12889 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 16.1232 | 0.783013 | ||||||||
\(425\) | 9.07111 | 0.440014 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.79645 | −0.474083 | ||||||||
\(428\) | 24.4210 | 1.18043 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.32086 | 0.208370 | ||||||||
\(431\) | 34.8208 | 1.67726 | 0.838630 | − | 0.544701i | \(-0.183357\pi\) | ||||
0.838630 | + | 0.544701i | \(0.183357\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −33.9006 | −1.62916 | −0.814578 | − | 0.580054i | \(-0.803032\pi\) | ||||
−0.814578 | + | 0.580054i | \(0.803032\pi\) | |||||||
\(434\) | 10.5924 | 0.508450 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.95721 | 0.141625 | ||||||||
\(437\) | −6.33067 | −0.302837 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.04032 | 0.288289 | 0.144144 | − | 0.989557i | \(-0.453957\pi\) | ||||
0.144144 | + | 0.989557i | \(0.453957\pi\) | |||||||
\(440\) | 5.64067 | 0.268908 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 17.5524 | 0.834883 | ||||||||
\(443\) | 32.0832 | 1.52432 | 0.762159 | − | 0.647390i | \(-0.224140\pi\) | ||||
0.762159 | + | 0.647390i | \(0.224140\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.83109 | −0.134207 | ||||||||
\(446\) | −14.2292 | −0.673774 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 13.0100 | 0.614666 | ||||||||
\(449\) | 7.01644 | 0.331126 | 0.165563 | − | 0.986199i | \(-0.447056\pi\) | ||||
0.165563 | + | 0.986199i | \(0.447056\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.88511 | 0.135855 | ||||||||
\(452\) | 17.3864 | 0.817786 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −17.2084 | −0.807628 | ||||||||
\(455\) | 2.77439 | 0.130065 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.8482 | 0.788126 | 0.394063 | − | 0.919083i | \(-0.371069\pi\) | ||||
0.394063 | + | 0.919083i | \(0.371069\pi\) | |||||||
\(458\) | −23.6521 | −1.10519 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −10.2774 | −0.479184 | ||||||||
\(461\) | 17.7603 | 0.827181 | 0.413591 | − | 0.910463i | \(-0.364274\pi\) | ||||
0.413591 | + | 0.910463i | \(0.364274\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.1828 | 0.473236 | 0.236618 | − | 0.971603i | \(-0.423961\pi\) | ||||
0.236618 | + | 0.971603i | \(0.423961\pi\) | |||||||
\(464\) | 7.90932 | 0.367181 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −56.2319 | −2.60489 | ||||||||
\(467\) | 1.65415 | 0.0765449 | 0.0382724 | − | 0.999267i | \(-0.487815\pi\) | ||||
0.0382724 | + | 0.999267i | \(0.487815\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.4839 | −0.484102 | ||||||||
\(470\) | −15.1131 | −0.697115 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −15.0314 | −0.691876 | ||||||||
\(473\) | 9.41506 | 0.432905 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.95189 | −0.273091 | ||||||||
\(476\) | 6.08393 | 0.278857 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 24.2672 | 1.10996 | ||||||||
\(479\) | 12.7961 | 0.584670 | 0.292335 | − | 0.956316i | \(-0.405568\pi\) | ||||
0.292335 | + | 0.956316i | \(0.405568\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 40.7359 | 1.85740 | ||||||||
\(482\) | −40.0118 | −1.82249 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.49877 | 0.159035 | ||||||||
\(485\) | 4.88549 | 0.221839 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.81280 | 0.263403 | 0.131702 | − | 0.991289i | \(-0.457956\pi\) | ||||
0.131702 | + | 0.991289i | \(0.457956\pi\) | |||||||
\(488\) | 22.1609 | 1.00317 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.60049 | 0.0723026 | ||||||||
\(491\) | −5.28049 | −0.238305 | −0.119153 | − | 0.992876i | \(-0.538018\pi\) | ||||
−0.119153 | + | 0.992876i | \(0.538018\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.6923 | 0.751782 | ||||||||
\(494\) | −11.5168 | −0.518164 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.53113 | 0.203454 | ||||||||
\(497\) | −8.80029 | −0.394747 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.0549 | −0.897778 | −0.448889 | − | 0.893587i | \(-0.648180\pi\) | ||||
−0.448889 | + | 0.893587i | \(0.648180\pi\) | |||||||
\(500\) | −20.4253 | −0.913448 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −10.7261 | −0.478729 | ||||||||
\(503\) | −14.1949 | −0.632920 | −0.316460 | − | 0.948606i | \(-0.602494\pi\) | ||||
−0.316460 | + | 0.948606i | \(0.602494\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.2973 | −0.458225 | ||||||||
\(506\) | −37.2711 | −1.65690 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.01059 | −0.133573 | ||||||||
\(509\) | −34.0499 | −1.50923 | −0.754617 | − | 0.656166i | \(-0.772177\pi\) | ||||
−0.754617 | + | 0.656166i | \(0.772177\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.52998 | −0.288869 | ||||||||
\(512\) | 10.7167 | 0.473617 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −13.6245 | −0.600950 | ||||||||
\(515\) | 3.42241 | 0.150809 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −32.9311 | −1.44831 | ||||||||
\(518\) | 23.4997 | 1.03252 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.27603 | −0.275222 | ||||||||
\(521\) | −4.82296 | −0.211298 | −0.105649 | − | 0.994403i | \(-0.533692\pi\) | ||||
−0.105649 | + | 0.994403i | \(0.533692\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.29591 | −0.100393 | −0.0501965 | − | 0.998739i | \(-0.515985\pi\) | ||||
−0.0501965 | + | 0.998739i | \(0.515985\pi\) | |||||||
\(524\) | −3.21543 | −0.140467 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −56.2219 | −2.45139 | ||||||||
\(527\) | 9.56273 | 0.416559 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.204717 | −0.00890074 | ||||||||
\(530\) | 11.4074 | 0.495505 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.99189 | −0.173070 | ||||||||
\(533\) | −3.21009 | −0.139044 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.79989 | 0.250751 | ||||||||
\(536\) | 23.7160 | 1.02437 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −27.4979 | −1.18552 | ||||||||
\(539\) | 3.48743 | 0.150214 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.1848 | −0.566857 | −0.283429 | − | 0.958993i | \(-0.591472\pi\) | ||||
−0.283429 | + | 0.958993i | \(0.591472\pi\) | |||||||
\(542\) | −0.793252 | −0.0340731 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 13.4743 | 0.577706 | ||||||||
\(545\) | 0.702325 | 0.0300843 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.144810 | −0.00619164 | −0.00309582 | − | 0.999995i | \(-0.500985\pi\) | ||||
−0.00309582 | + | 0.999995i | \(0.500985\pi\) | |||||||
\(548\) | 38.5531 | 1.64691 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −35.0410 | −1.49416 | ||||||||
\(551\) | −10.9524 | −0.466588 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.16978 | 0.0497441 | ||||||||
\(554\) | −42.0923 | −1.78833 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −12.4617 | −0.528493 | ||||||||
\(557\) | 6.35824 | 0.269407 | 0.134704 | − | 0.990886i | \(-0.456992\pi\) | ||||
0.134704 | + | 0.990886i | \(0.456992\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.4756 | −0.443069 | ||||||||
\(560\) | 0.684644 | 0.0289315 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −50.8800 | −2.14624 | ||||||||
\(563\) | 27.7532 | 1.16966 | 0.584829 | − | 0.811157i | \(-0.301162\pi\) | ||||
0.584829 | + | 0.811157i | \(0.301162\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.12919 | 0.173716 | ||||||||
\(566\) | −21.9102 | −0.920956 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 19.9074 | 0.835296 | ||||||||
\(569\) | −6.89351 | −0.288991 | −0.144495 | − | 0.989505i | \(-0.546156\pi\) | ||||
−0.144495 | + | 0.989505i | \(0.546156\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.4924 | 0.648337 | 0.324168 | − | 0.945999i | \(-0.394916\pi\) | ||||
0.324168 | + | 0.945999i | \(0.394916\pi\) | |||||||
\(572\) | −40.7395 | −1.70340 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.85183 | −0.0772940 | ||||||||
\(575\) | 21.4314 | 0.893750 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.1702 | 1.08948 | 0.544741 | − | 0.838605i | \(-0.316628\pi\) | ||||
0.544741 | + | 0.838605i | \(0.316628\pi\) | |||||||
\(578\) | −28.9120 | −1.20258 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −17.7804 | −0.738289 | ||||||||
\(581\) | 4.68620 | 0.194416 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 24.8565 | 1.02945 | ||||||||
\(584\) | 14.7717 | 0.611256 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13.7929 | 0.569781 | ||||||||
\(587\) | −34.8064 | −1.43662 | −0.718308 | − | 0.695725i | \(-0.755083\pi\) | ||||
−0.718308 | + | 0.695725i | \(0.755083\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.27446 | −0.258534 | ||||||||
\(590\) | −10.6349 | −0.437831 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10.0525 | 0.413157 | ||||||||
\(593\) | 24.0643 | 0.988203 | 0.494101 | − | 0.869404i | \(-0.335497\pi\) | ||||
0.494101 | + | 0.869404i | \(0.335497\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.44491 | 0.0592355 | ||||||||
\(596\) | 40.8387 | 1.67282 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 41.4692 | 1.69580 | ||||||||
\(599\) | 0.508407 | 0.0207729 | 0.0103865 | − | 0.999946i | \(-0.496694\pi\) | ||||
0.0103865 | + | 0.999946i | \(0.496694\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.1016 | 0.942333 | 0.471166 | − | 0.882044i | \(-0.343833\pi\) | ||||
0.471166 | + | 0.882044i | \(0.343833\pi\) | |||||||
\(602\) | −6.04313 | −0.246300 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10.2545 | 0.417248 | ||||||||
\(605\) | 0.830943 | 0.0337826 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −35.7095 | −1.44940 | −0.724701 | − | 0.689063i | \(-0.758022\pi\) | ||||
−0.724701 | + | 0.689063i | \(0.758022\pi\) | |||||||
\(608\) | −8.84098 | −0.358549 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 15.6791 | 0.634827 | ||||||||
\(611\) | 36.6405 | 1.48231 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.75584 | −0.394035 | −0.197017 | − | 0.980400i | \(-0.563126\pi\) | ||||
−0.197017 | + | 0.980400i | \(0.563126\pi\) | |||||||
\(614\) | −30.8665 | −1.24567 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.88902 | −0.317858 | ||||||||
\(617\) | −4.62163 | −0.186060 | −0.0930299 | − | 0.995663i | \(-0.529655\pi\) | ||||
−0.0930299 | + | 0.995663i | \(0.529655\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −46.6480 | −1.87494 | −0.937471 | − | 0.348062i | \(-0.886840\pi\) | ||||
−0.937471 | + | 0.348062i | \(0.886840\pi\) | |||||||
\(620\) | −10.1861 | −0.409083 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 17.8885 | 0.717263 | ||||||||
\(623\) | 3.95955 | 0.158636 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.5929 | 0.703717 | ||||||||
\(626\) | 18.3451 | 0.733217 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −61.9808 | −2.47330 | ||||||||
\(629\) | 21.2154 | 0.845914 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.7101 | −1.62064 | −0.810322 | − | 0.585984i | \(-0.800708\pi\) | ||||
−0.810322 | + | 0.585984i | \(0.800708\pi\) | |||||||
\(632\) | −2.64620 | −0.105260 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −21.7485 | −0.863745 | ||||||||
\(635\) | −0.715002 | −0.0283740 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.88025 | −0.153741 | ||||||||
\(638\) | −64.4810 | −2.55283 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −11.2876 | −0.446181 | ||||||||
\(641\) | −16.0725 | −0.634826 | −0.317413 | − | 0.948287i | \(-0.602814\pi\) | ||||
−0.317413 | + | 0.948287i | \(0.602814\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.75968 | 0.266576 | 0.133288 | − | 0.991077i | \(-0.457446\pi\) | ||||
0.133288 | + | 0.991077i | \(0.457446\pi\) | |||||||
\(644\) | 14.3739 | 0.566410 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.99798 | −0.235987 | ||||||||
\(647\) | −26.3074 | −1.03425 | −0.517125 | − | 0.855910i | \(-0.672998\pi\) | ||||
−0.517125 | + | 0.855910i | \(0.672998\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −23.1732 | −0.909628 | ||||||||
\(650\) | 38.9880 | 1.52924 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 43.3368 | 1.69720 | ||||||||
\(653\) | −15.4078 | −0.602954 | −0.301477 | − | 0.953473i | \(-0.597480\pi\) | ||||
−0.301477 | + | 0.953473i | \(0.597480\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.763652 | −0.0298384 | ||||||||
\(656\) | −0.792163 | −0.0309288 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 21.1371 | 0.824011 | ||||||||
\(659\) | 11.1639 | 0.434885 | 0.217442 | − | 0.976073i | \(-0.430229\pi\) | ||||
0.217442 | + | 0.976073i | \(0.430229\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.7973 | 0.653338 | 0.326669 | − | 0.945139i | \(-0.394074\pi\) | ||||
0.326669 | + | 0.945139i | \(0.394074\pi\) | |||||||
\(662\) | 59.8692 | 2.32688 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10.6008 | −0.411391 | ||||||||
\(665\) | −0.948058 | −0.0367641 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 39.4371 | 1.52701 | ||||||||
\(668\) | 44.3356 | 1.71539 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 16.7794 | 0.648243 | ||||||||
\(671\) | 34.1644 | 1.31890 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 36.1418 | 1.39317 | 0.696583 | − | 0.717476i | \(-0.254703\pi\) | ||||
0.696583 | + | 0.717476i | \(0.254703\pi\) | |||||||
\(674\) | 17.4774 | 0.673205 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.19071 | 0.238104 | ||||||||
\(677\) | −36.2462 | −1.39306 | −0.696528 | − | 0.717530i | \(-0.745273\pi\) | ||||
−0.696528 | + | 0.717530i | \(0.745273\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.83283 | −0.262220 | ||||||||
\(680\) | −3.26858 | −0.125344 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −36.9401 | −1.41451 | ||||||||
\(683\) | 21.5032 | 0.822796 | 0.411398 | − | 0.911456i | \(-0.365041\pi\) | ||||
0.411398 | + | 0.911456i | \(0.365041\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.15620 | 0.349840 | ||||||||
\(686\) | −2.23843 | −0.0854638 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.58509 | −0.0985555 | ||||||||
\(689\) | −27.6562 | −1.05362 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.8476 | −0.640913 | −0.320456 | − | 0.947263i | \(-0.603836\pi\) | ||||
−0.320456 | + | 0.947263i | \(0.603836\pi\) | |||||||
\(692\) | −36.4571 | −1.38589 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 37.8137 | 1.43539 | ||||||||
\(695\) | −2.95960 | −0.112264 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.67182 | −0.0633248 | ||||||||
\(698\) | −33.1585 | −1.25507 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 13.5138 | 0.510775 | ||||||||
\(701\) | −8.39278 | −0.316991 | −0.158495 | − | 0.987360i | \(-0.550664\pi\) | ||||
−0.158495 | + | 0.987360i | \(0.550664\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.9202 | −0.525011 | ||||||||
\(704\) | −45.3715 | −1.71000 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 71.6756 | 2.69755 | ||||||||
\(707\) | 14.4018 | 0.541636 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.8508 | −0.858181 | −0.429091 | − | 0.903261i | \(-0.641166\pi\) | ||||
−0.429091 | + | 0.903261i | \(0.641166\pi\) | |||||||
\(710\) | 14.0847 | 0.528591 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8.95703 | −0.335679 | ||||||||
\(713\) | 22.5929 | 0.846109 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.67547 | −0.361842 | ||||||||
\(716\) | 30.9537 | 1.15679 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 15.9853 | 0.596566 | ||||||||
\(719\) | 29.0142 | 1.08205 | 0.541023 | − | 0.841008i | \(-0.318037\pi\) | ||||
0.541023 | + | 0.841008i | \(0.318037\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.78657 | −0.178261 | ||||||||
\(722\) | −38.5948 | −1.43635 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −21.0021 | −0.780538 | ||||||||
\(725\) | 37.0774 | 1.37702 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.71536 | 0.0636190 | 0.0318095 | − | 0.999494i | \(-0.489873\pi\) | ||||
0.0318095 | + | 0.999494i | \(0.489873\pi\) | |||||||
\(728\) | 8.77763 | 0.325321 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 10.4511 | 0.386814 | ||||||||
\(731\) | −5.45571 | −0.201787 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 32.0548 | 1.18397 | 0.591986 | − | 0.805948i | \(-0.298344\pi\) | ||||
0.591986 | + | 0.805948i | \(0.298344\pi\) | |||||||
\(734\) | 42.5544 | 1.57071 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 31.8343 | 1.17343 | ||||||||
\(737\) | 36.5619 | 1.34677 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.0497 | 0.553613 | 0.276807 | − | 0.960926i | \(-0.410724\pi\) | ||||
0.276807 | + | 0.960926i | \(0.410724\pi\) | |||||||
\(740\) | −22.5984 | −0.830732 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −15.9543 | −0.585701 | ||||||||
\(743\) | −1.95125 | −0.0715845 | −0.0357922 | − | 0.999359i | \(-0.511395\pi\) | ||||
−0.0357922 | + | 0.999359i | \(0.511395\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.69904 | 0.355345 | ||||||||
\(746\) | 73.0221 | 2.67353 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −21.2173 | −0.775780 | ||||||||
\(749\) | −8.11171 | −0.296395 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.9594 | −0.509385 | −0.254692 | − | 0.967022i | \(-0.581974\pi\) | ||||
−0.254692 | + | 0.967022i | \(0.581974\pi\) | |||||||
\(752\) | 9.04188 | 0.329724 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 71.7440 | 2.61276 | ||||||||
\(755\) | 2.43539 | 0.0886330 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.9434 | −0.870238 | −0.435119 | − | 0.900373i | \(-0.643294\pi\) | ||||
−0.435119 | + | 0.900373i | \(0.643294\pi\) | |||||||
\(758\) | 21.3941 | 0.777070 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.14463 | 0.0777940 | ||||||||
\(761\) | 17.6709 | 0.640569 | 0.320285 | − | 0.947321i | \(-0.396221\pi\) | ||||
0.320285 | + | 0.947321i | \(0.396221\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.982270 | −0.0355606 | ||||||||
\(764\) | −50.8564 | −1.83992 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 44.7664 | 1.61748 | ||||||||
\(767\) | 25.7834 | 0.930985 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.34345 | −0.120568 | −0.0602839 | − | 0.998181i | \(-0.519201\pi\) | ||||
−0.0602839 | + | 0.998181i | \(0.519201\pi\) | |||||||
\(770\) | −5.58158 | −0.201146 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 15.1004 | 0.543475 | ||||||||
\(773\) | 35.6247 | 1.28133 | 0.640665 | − | 0.767821i | \(-0.278659\pi\) | ||||
0.640665 | + | 0.767821i | \(0.278659\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.2411 | 0.763002 | ||||||||
\(776\) | 15.4568 | 0.554865 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.11958 | 0.326953 | ||||||||
\(779\) | 1.09694 | 0.0393021 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 30.6904 | 1.09819 | ||||||||
\(782\) | 21.5973 | 0.772319 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.957541 | −0.0341979 | ||||||||
\(785\) | −14.7202 | −0.525386 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −49.3147 | −1.75788 | −0.878939 | − | 0.476935i | \(-0.841748\pi\) | ||||
−0.878939 | + | 0.476935i | \(0.841748\pi\) | |||||||
\(788\) | 26.4780 | 0.943240 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.87222 | −0.0666105 | ||||||||
\(791\) | −5.77508 | −0.205338 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −38.0126 | −1.34987 | ||||||||
\(794\) | 48.7605 | 1.73045 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −66.1181 | −2.34349 | ||||||||
\(797\) | −18.8764 | −0.668637 | −0.334318 | − | 0.942460i | \(-0.608506\pi\) | ||||
−0.334318 | + | 0.942460i | \(0.608506\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.0825 | 0.675089 | ||||||||
\(800\) | 29.9296 | 1.05817 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −38.7988 | −1.37003 | ||||||||
\(803\) | 22.7728 | 0.803636 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.41374 | 0.120318 | ||||||||
\(806\) | 41.1010 | 1.44772 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −32.5788 | −1.14612 | ||||||||
\(809\) | −27.6464 | −0.971994 | −0.485997 | − | 0.873960i | \(-0.661543\pi\) | ||||
−0.485997 | + | 0.873960i | \(0.661543\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.0155 | −1.40514 | −0.702568 | − | 0.711617i | \(-0.747963\pi\) | ||||
−0.702568 | + | 0.711617i | \(0.747963\pi\) | |||||||
\(812\) | 24.8676 | 0.872680 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −81.9536 | −2.87247 | ||||||||
\(815\) | 10.2923 | 0.360524 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.57969 | 0.125237 | ||||||||
\(818\) | −27.9232 | −0.976311 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.78080 | 0.0621884 | ||||||||
\(821\) | 7.00349 | 0.244423 | 0.122212 | − | 0.992504i | \(-0.461001\pi\) | ||||
0.122212 | + | 0.992504i | \(0.461001\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.48955 | 0.261069 | 0.130535 | − | 0.991444i | \(-0.458331\pi\) | ||||
0.130535 | + | 0.991444i | \(0.458331\pi\) | |||||||
\(824\) | 10.8278 | 0.377206 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 14.8739 | 0.517530 | ||||||||
\(827\) | −5.69107 | −0.197898 | −0.0989490 | − | 0.995093i | \(-0.531548\pi\) | ||||
−0.0989490 | + | 0.995093i | \(0.531548\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −46.9867 | −1.63192 | −0.815958 | − | 0.578111i | \(-0.803790\pi\) | ||||
−0.815958 | + | 0.578111i | \(0.803790\pi\) | |||||||
\(830\) | −7.50020 | −0.260336 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 50.4821 | 1.75015 | ||||||||
\(833\) | −2.02085 | −0.0700182 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.5295 | 0.364389 | ||||||||
\(836\) | 13.9214 | 0.481483 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 24.1709 | 0.834971 | ||||||||
\(839\) | 23.2141 | 0.801441 | 0.400721 | − | 0.916200i | \(-0.368760\pi\) | ||||
0.400721 | + | 0.916200i | \(0.368760\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 39.2282 | 1.35270 | ||||||||
\(842\) | −17.0120 | −0.586273 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 31.1901 | 1.07361 | ||||||||
\(845\) | 1.47027 | 0.0505788 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.16215 | −0.0399321 | ||||||||
\(848\) | −6.82482 | −0.234365 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 20.3051 | 0.696459 | ||||||||
\(851\) | 50.1234 | 1.71821 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.3267 | −1.03837 | −0.519183 | − | 0.854663i | \(-0.673764\pi\) | ||||
−0.519183 | + | 0.854663i | \(0.673764\pi\) | |||||||
\(854\) | −21.9287 | −0.750385 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 18.3498 | 0.627182 | ||||||||
\(857\) | 22.4832 | 0.768011 | 0.384005 | − | 0.923331i | \(-0.374544\pi\) | ||||
0.384005 | + | 0.923331i | \(0.374544\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36.3023 | −1.23862 | −0.619309 | − | 0.785147i | \(-0.712587\pi\) | ||||
−0.619309 | + | 0.785147i | \(0.712587\pi\) | |||||||
\(860\) | 5.81134 | 0.198165 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 77.9441 | 2.65479 | ||||||||
\(863\) | 32.5087 | 1.10661 | 0.553305 | − | 0.832979i | \(-0.313367\pi\) | ||||
0.553305 | + | 0.832979i | \(0.313367\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.65842 | −0.294395 | ||||||||
\(866\) | −75.8841 | −2.57865 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 14.2462 | 0.483549 | ||||||||
\(869\) | −4.07953 | −0.138388 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −40.6802 | −1.37839 | ||||||||
\(872\) | 2.22202 | 0.0752472 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −14.1708 | −0.479334 | ||||||||
\(875\) | 6.78450 | 0.229358 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.43887 | −0.217425 | −0.108713 | − | 0.994073i | \(-0.534673\pi\) | ||||
−0.108713 | + | 0.994073i | \(0.534673\pi\) | |||||||
\(878\) | 13.5209 | 0.456307 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.38765 | −0.0804876 | ||||||||
\(881\) | 50.9542 | 1.71669 | 0.858346 | − | 0.513072i | \(-0.171493\pi\) | ||||
0.858346 | + | 0.513072i | \(0.171493\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.41232 | −0.0475284 | −0.0237642 | − | 0.999718i | \(-0.507565\pi\) | ||||
−0.0237642 | + | 0.999718i | \(0.507565\pi\) | |||||||
\(884\) | 23.6072 | 0.793994 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 71.8161 | 2.41271 | ||||||||
\(887\) | 9.49697 | 0.318877 | 0.159438 | − | 0.987208i | \(-0.449032\pi\) | ||||
0.159438 | + | 0.987208i | \(0.449032\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | −6.33721 | −0.212424 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −19.1376 | −0.640775 | ||||||||
\(893\) | −12.5207 | −0.418990 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.35138 | 0.245730 | ||||||||
\(896\) | 15.7868 | 0.527399 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 15.7058 | 0.524110 | ||||||||
\(899\) | 39.0869 | 1.30362 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.4035 | −0.479849 | ||||||||
\(902\) | 6.45813 | 0.215032 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13.0640 | 0.434502 | ||||||||
\(905\) | −4.98792 | −0.165804 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −48.9510 | −1.62539 | −0.812695 | − | 0.582689i | \(-0.802000\pi\) | ||||
−0.812695 | + | 0.582689i | \(0.802000\pi\) | |||||||
\(908\) | −23.1444 | −0.768074 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 6.21028 | 0.205869 | ||||||||
\(911\) | 5.99796 | 0.198721 | 0.0993607 | − | 0.995051i | \(-0.468320\pi\) | ||||
0.0993607 | + | 0.995051i | \(0.468320\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16.3428 | −0.540867 | ||||||||
\(914\) | 37.7136 | 1.24746 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −31.8109 | −1.05106 | ||||||||
\(917\) | 1.06804 | 0.0352698 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.999658 | −0.0329757 | −0.0164878 | − | 0.999864i | \(-0.505248\pi\) | ||||
−0.0164878 | + | 0.999864i | \(0.505248\pi\) | |||||||
\(920\) | −7.72232 | −0.254597 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 39.7553 | 1.30927 | ||||||||
\(923\) | −34.1473 | −1.12397 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 47.1244 | 1.54944 | ||||||||
\(926\) | 22.7936 | 0.749044 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 55.0751 | 1.80793 | ||||||||
\(929\) | 55.3468 | 1.81587 | 0.907935 | − | 0.419110i | \(-0.137658\pi\) | ||||
0.907935 | + | 0.419110i | \(0.137658\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.32595 | 0.0434563 | ||||||||
\(932\) | −75.6293 | −2.47732 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.70270 | 0.121156 | ||||||||
\(935\) | −5.03902 | −0.164794 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.27880 | −0.0417766 | −0.0208883 | − | 0.999782i | \(-0.506649\pi\) | ||||
−0.0208883 | + | 0.999782i | \(0.506649\pi\) | |||||||
\(938\) | −23.4675 | −0.766242 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −20.3264 | −0.662974 | ||||||||
\(941\) | 22.7871 | 0.742837 | 0.371419 | − | 0.928466i | \(-0.378872\pi\) | ||||
0.371419 | + | 0.928466i | \(0.378872\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.94984 | −0.128625 | ||||||||
\(944\) | 6.36265 | 0.207087 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 21.0750 | 0.685207 | ||||||||
\(947\) | 8.91484 | 0.289693 | 0.144847 | − | 0.989454i | \(-0.453731\pi\) | ||||
0.144847 | + | 0.989454i | \(0.453731\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −25.3379 | −0.822504 | ||||||||
\(950\) | −13.3229 | −0.432252 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.57142 | 0.148161 | ||||||||
\(953\) | 8.13381 | 0.263480 | 0.131740 | − | 0.991284i | \(-0.457944\pi\) | ||||
0.131740 | + | 0.991284i | \(0.457944\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.0782 | −0.390841 | ||||||||
\(956\) | 32.6383 | 1.05560 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 28.6433 | 0.925423 | ||||||||
\(959\) | −12.8058 | −0.413522 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.60776 | −0.277670 | ||||||||
\(962\) | 91.1847 | 2.93991 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −53.8140 | −1.73323 | ||||||||
\(965\) | 3.58628 | 0.115447 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.9426 | −0.512679 | −0.256339 | − | 0.966587i | \(-0.582516\pi\) | ||||
−0.256339 | + | 0.966587i | \(0.582516\pi\) | |||||||
\(968\) | 2.62895 | 0.0844975 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 10.9358 | 0.351129 | ||||||||
\(971\) | −43.2242 | −1.38713 | −0.693566 | − | 0.720393i | \(-0.743961\pi\) | ||||
−0.693566 | + | 0.720393i | \(0.743961\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.13929 | 0.132699 | ||||||||
\(974\) | 13.0116 | 0.416918 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.38050 | −0.300262 | ||||||||
\(977\) | −11.4772 | −0.367190 | −0.183595 | − | 0.983002i | \(-0.558773\pi\) | ||||
−0.183595 | + | 0.983002i | \(0.558773\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.8087 | −0.441327 | ||||||||
\(980\) | 2.15258 | 0.0687616 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −11.8200 | −0.377192 | ||||||||
\(983\) | −32.2991 | −1.03018 | −0.515090 | − | 0.857136i | \(-0.672242\pi\) | ||||
−0.515090 | + | 0.857136i | \(0.672242\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.28842 | 0.200366 | ||||||||
\(986\) | 37.3645 | 1.18993 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −15.4895 | −0.492787 | ||||||||
\(989\) | −12.8896 | −0.409866 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −46.4069 | −1.47416 | −0.737081 | − | 0.675804i | \(-0.763796\pi\) | ||||
−0.737081 | + | 0.675804i | \(0.763796\pi\) | |||||||
\(992\) | 31.5516 | 1.00177 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −19.6989 | −0.624810 | ||||||||
\(995\) | −15.7028 | −0.497812 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 36.8281 | 1.16636 | 0.583179 | − | 0.812344i | \(-0.301809\pi\) | ||||
0.583179 | + | 0.812344i | \(0.301809\pi\) | |||||||
\(998\) | −44.8915 | −1.42101 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8001.2.a.z.1.28 | yes | 32 | |
3.2 | odd | 2 | inner | 8001.2.a.z.1.5 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8001.2.a.z.1.5 | ✓ | 32 | 3.2 | odd | 2 | inner | |
8001.2.a.z.1.28 | yes | 32 | 1.1 | even | 1 | trivial |