Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2009,2,Mod(1,2009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2009, 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("2009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2009 = 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2009.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: | \(16.0419457661\) |
Analytic rank: | \(0\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{17} - 3 x^{16} - 25 x^{15} + 77 x^{14} + 247 x^{13} - 790 x^{12} - 1231 x^{11} + 4173 x^{10} + \cdots - 464 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 287) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.48154\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2009.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.48154 | −1.75471 | −0.877356 | − | 0.479841i | \(-0.840694\pi\) | ||||
−0.877356 | + | 0.479841i | \(0.840694\pi\) | |||||||
\(3\) | 1.40932 | 0.813671 | 0.406836 | − | 0.913501i | \(-0.366632\pi\) | ||||
0.406836 | + | 0.913501i | \(0.366632\pi\) | |||||||
\(4\) | 4.15802 | 2.07901 | ||||||||
\(5\) | −1.01447 | −0.453687 | −0.226843 | − | 0.973931i | \(-0.572841\pi\) | ||||
−0.226843 | + | 0.973931i | \(0.572841\pi\) | |||||||
\(6\) | −3.49728 | −1.42776 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −5.35521 | −1.89335 | ||||||||
\(9\) | −1.01382 | −0.337939 | ||||||||
\(10\) | 2.51746 | 0.796089 | ||||||||
\(11\) | −5.25436 | −1.58425 | −0.792124 | − | 0.610360i | \(-0.791025\pi\) | ||||
−0.792124 | + | 0.610360i | \(0.791025\pi\) | |||||||
\(12\) | 5.85999 | 1.69163 | ||||||||
\(13\) | 3.75990 | 1.04281 | 0.521405 | − | 0.853309i | \(-0.325408\pi\) | ||||
0.521405 | + | 0.853309i | \(0.325408\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.42972 | −0.369152 | ||||||||
\(16\) | 4.97311 | 1.24328 | ||||||||
\(17\) | 7.45725 | 1.80865 | 0.904324 | − | 0.426847i | \(-0.140376\pi\) | ||||
0.904324 | + | 0.426847i | \(0.140376\pi\) | |||||||
\(18\) | 2.51582 | 0.592985 | ||||||||
\(19\) | 4.15386 | 0.952960 | 0.476480 | − | 0.879185i | \(-0.341912\pi\) | ||||
0.476480 | + | 0.879185i | \(0.341912\pi\) | |||||||
\(20\) | −4.21821 | −0.943220 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 13.0389 | 2.77990 | ||||||||
\(23\) | −8.16729 | −1.70300 | −0.851499 | − | 0.524357i | \(-0.824306\pi\) | ||||
−0.851499 | + | 0.524357i | \(0.824306\pi\) | |||||||
\(24\) | −7.54721 | −1.54057 | ||||||||
\(25\) | −3.97084 | −0.794168 | ||||||||
\(26\) | −9.33034 | −1.82983 | ||||||||
\(27\) | −5.65675 | −1.08864 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.264385 | 0.0490951 | 0.0245475 | − | 0.999699i | \(-0.492185\pi\) | ||||
0.0245475 | + | 0.999699i | \(0.492185\pi\) | |||||||
\(30\) | 3.54790 | 0.647755 | ||||||||
\(31\) | 0.457773 | 0.0822184 | 0.0411092 | − | 0.999155i | \(-0.486911\pi\) | ||||
0.0411092 | + | 0.999155i | \(0.486911\pi\) | |||||||
\(32\) | −1.63052 | −0.288238 | ||||||||
\(33\) | −7.40507 | −1.28906 | ||||||||
\(34\) | −18.5054 | −3.17365 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.21547 | −0.702579 | ||||||||
\(37\) | 3.90164 | 0.641426 | 0.320713 | − | 0.947176i | \(-0.396078\pi\) | ||||
0.320713 | + | 0.947176i | \(0.396078\pi\) | |||||||
\(38\) | −10.3079 | −1.67217 | ||||||||
\(39\) | 5.29891 | 0.848504 | ||||||||
\(40\) | 5.43273 | 0.858990 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.82356 | 1.34558 | 0.672790 | − | 0.739833i | \(-0.265096\pi\) | ||||
0.672790 | + | 0.739833i | \(0.265096\pi\) | |||||||
\(44\) | −21.8477 | −3.29367 | ||||||||
\(45\) | 1.02849 | 0.153318 | ||||||||
\(46\) | 20.2674 | 2.98827 | ||||||||
\(47\) | 6.34286 | 0.925201 | 0.462601 | − | 0.886567i | \(-0.346916\pi\) | ||||
0.462601 | + | 0.886567i | \(0.346916\pi\) | |||||||
\(48\) | 7.00870 | 1.01162 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 9.85379 | 1.39354 | ||||||||
\(51\) | 10.5096 | 1.47164 | ||||||||
\(52\) | 15.6338 | 2.16801 | ||||||||
\(53\) | −0.762475 | −0.104734 | −0.0523670 | − | 0.998628i | \(-0.516677\pi\) | ||||
−0.0523670 | + | 0.998628i | \(0.516677\pi\) | |||||||
\(54\) | 14.0374 | 1.91025 | ||||||||
\(55\) | 5.33041 | 0.718753 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.85412 | 0.775397 | ||||||||
\(58\) | −0.656081 | −0.0861477 | ||||||||
\(59\) | −7.76331 | −1.01070 | −0.505348 | − | 0.862915i | \(-0.668636\pi\) | ||||
−0.505348 | + | 0.862915i | \(0.668636\pi\) | |||||||
\(60\) | −5.94481 | −0.767471 | ||||||||
\(61\) | −4.34168 | −0.555895 | −0.277947 | − | 0.960596i | \(-0.589654\pi\) | ||||
−0.277947 | + | 0.960596i | \(0.589654\pi\) | |||||||
\(62\) | −1.13598 | −0.144270 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.90001 | −0.737502 | ||||||||
\(65\) | −3.81433 | −0.473109 | ||||||||
\(66\) | 18.3760 | 2.26192 | ||||||||
\(67\) | 1.34131 | 0.163867 | 0.0819336 | − | 0.996638i | \(-0.473890\pi\) | ||||
0.0819336 | + | 0.996638i | \(0.473890\pi\) | |||||||
\(68\) | 31.0074 | 3.76020 | ||||||||
\(69\) | −11.5103 | −1.38568 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.8510 | 1.76249 | 0.881246 | − | 0.472658i | \(-0.156705\pi\) | ||||
0.881246 | + | 0.472658i | \(0.156705\pi\) | |||||||
\(72\) | 5.42920 | 0.639838 | ||||||||
\(73\) | 8.36734 | 0.979323 | 0.489661 | − | 0.871913i | \(-0.337120\pi\) | ||||
0.489661 | + | 0.871913i | \(0.337120\pi\) | |||||||
\(74\) | −9.68206 | −1.12552 | ||||||||
\(75\) | −5.59619 | −0.646192 | ||||||||
\(76\) | 17.2718 | 1.98122 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −13.1494 | −1.48888 | ||||||||
\(79\) | 9.72739 | 1.09442 | 0.547208 | − | 0.836996i | \(-0.315691\pi\) | ||||
0.547208 | + | 0.836996i | \(0.315691\pi\) | |||||||
\(80\) | −5.04509 | −0.564058 | ||||||||
\(81\) | −4.93073 | −0.547859 | ||||||||
\(82\) | −2.48154 | −0.274040 | ||||||||
\(83\) | 9.69101 | 1.06373 | 0.531864 | − | 0.846830i | \(-0.321492\pi\) | ||||
0.531864 | + | 0.846830i | \(0.321492\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.56519 | −0.820560 | ||||||||
\(86\) | −21.8960 | −2.36111 | ||||||||
\(87\) | 0.372603 | 0.0399473 | ||||||||
\(88\) | 28.1382 | 2.99954 | ||||||||
\(89\) | 3.01789 | 0.319896 | 0.159948 | − | 0.987125i | \(-0.448867\pi\) | ||||
0.159948 | + | 0.987125i | \(0.448867\pi\) | |||||||
\(90\) | −2.55224 | −0.269030 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −33.9598 | −3.54055 | ||||||||
\(93\) | 0.645149 | 0.0668988 | ||||||||
\(94\) | −15.7400 | −1.62346 | ||||||||
\(95\) | −4.21398 | −0.432346 | ||||||||
\(96\) | −2.29793 | −0.234531 | ||||||||
\(97\) | −0.317155 | −0.0322022 | −0.0161011 | − | 0.999870i | \(-0.505125\pi\) | ||||
−0.0161011 | + | 0.999870i | \(0.505125\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.32695 | 0.535379 | ||||||||
\(100\) | −16.5108 | −1.65108 | ||||||||
\(101\) | −6.20307 | −0.617228 | −0.308614 | − | 0.951187i | \(-0.599865\pi\) | ||||
−0.308614 | + | 0.951187i | \(0.599865\pi\) | |||||||
\(102\) | −26.0801 | −2.58231 | ||||||||
\(103\) | 10.4187 | 1.02659 | 0.513295 | − | 0.858212i | \(-0.328425\pi\) | ||||
0.513295 | + | 0.858212i | \(0.328425\pi\) | |||||||
\(104\) | −20.1351 | −1.97441 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.89211 | 0.183778 | ||||||||
\(107\) | 5.81878 | 0.562522 | 0.281261 | − | 0.959631i | \(-0.409247\pi\) | ||||
0.281261 | + | 0.959631i | \(0.409247\pi\) | |||||||
\(108\) | −23.5209 | −2.26330 | ||||||||
\(109\) | −4.04343 | −0.387291 | −0.193645 | − | 0.981072i | \(-0.562031\pi\) | ||||
−0.193645 | + | 0.981072i | \(0.562031\pi\) | |||||||
\(110\) | −13.2276 | −1.26120 | ||||||||
\(111\) | 5.49866 | 0.521910 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.11145 | −0.763061 | −0.381531 | − | 0.924356i | \(-0.624603\pi\) | ||||
−0.381531 | + | 0.924356i | \(0.624603\pi\) | |||||||
\(114\) | −14.5272 | −1.36060 | ||||||||
\(115\) | 8.28551 | 0.772628 | ||||||||
\(116\) | 1.09932 | 0.102069 | ||||||||
\(117\) | −3.81185 | −0.352406 | ||||||||
\(118\) | 19.2649 | 1.77348 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 7.65645 | 0.698935 | ||||||||
\(121\) | 16.6083 | 1.50984 | ||||||||
\(122\) | 10.7740 | 0.975434 | ||||||||
\(123\) | 1.40932 | 0.127074 | ||||||||
\(124\) | 1.90343 | 0.170933 | ||||||||
\(125\) | 9.10069 | 0.813991 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.25266 | −0.111156 | −0.0555780 | − | 0.998454i | \(-0.517700\pi\) | ||||
−0.0555780 | + | 0.998454i | \(0.517700\pi\) | |||||||
\(128\) | 17.9021 | 1.58234 | ||||||||
\(129\) | 12.4352 | 1.09486 | ||||||||
\(130\) | 9.46539 | 0.830170 | ||||||||
\(131\) | 10.3433 | 0.903696 | 0.451848 | − | 0.892095i | \(-0.350765\pi\) | ||||
0.451848 | + | 0.892095i | \(0.350765\pi\) | |||||||
\(132\) | −30.7905 | −2.67996 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −3.32851 | −0.287540 | ||||||||
\(135\) | 5.73863 | 0.493903 | ||||||||
\(136\) | −39.9351 | −3.42441 | ||||||||
\(137\) | −10.7983 | −0.922557 | −0.461279 | − | 0.887255i | \(-0.652609\pi\) | ||||
−0.461279 | + | 0.887255i | \(0.652609\pi\) | |||||||
\(138\) | 28.5633 | 2.43147 | ||||||||
\(139\) | −10.7249 | −0.909672 | −0.454836 | − | 0.890575i | \(-0.650302\pi\) | ||||
−0.454836 | + | 0.890575i | \(0.650302\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.93912 | 0.752810 | ||||||||
\(142\) | −36.8533 | −3.09266 | ||||||||
\(143\) | −19.7559 | −1.65207 | ||||||||
\(144\) | −5.04182 | −0.420151 | ||||||||
\(145\) | −0.268212 | −0.0222738 | ||||||||
\(146\) | −20.7638 | −1.71843 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 16.2231 | 1.33353 | ||||||||
\(149\) | −4.58155 | −0.375335 | −0.187668 | − | 0.982233i | \(-0.560093\pi\) | ||||
−0.187668 | + | 0.982233i | \(0.560093\pi\) | |||||||
\(150\) | 13.8871 | 1.13388 | ||||||||
\(151\) | 15.0593 | 1.22551 | 0.612756 | − | 0.790272i | \(-0.290061\pi\) | ||||
0.612756 | + | 0.790272i | \(0.290061\pi\) | |||||||
\(152\) | −22.2448 | −1.80429 | ||||||||
\(153\) | −7.56028 | −0.611212 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.464399 | −0.0373014 | ||||||||
\(156\) | 22.0330 | 1.76405 | ||||||||
\(157\) | −10.9728 | −0.875721 | −0.437861 | − | 0.899043i | \(-0.644264\pi\) | ||||
−0.437861 | + | 0.899043i | \(0.644264\pi\) | |||||||
\(158\) | −24.1389 | −1.92039 | ||||||||
\(159\) | −1.07457 | −0.0852190 | ||||||||
\(160\) | 1.65412 | 0.130770 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 12.2358 | 0.961333 | ||||||||
\(163\) | 14.2612 | 1.11703 | 0.558513 | − | 0.829496i | \(-0.311372\pi\) | ||||
0.558513 | + | 0.829496i | \(0.311372\pi\) | |||||||
\(164\) | 4.15802 | 0.324687 | ||||||||
\(165\) | 7.51226 | 0.584828 | ||||||||
\(166\) | −24.0486 | −1.86653 | ||||||||
\(167\) | 16.3462 | 1.26490 | 0.632452 | − | 0.774599i | \(-0.282048\pi\) | ||||
0.632452 | + | 0.774599i | \(0.282048\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.13688 | 0.0874521 | ||||||||
\(170\) | 18.7733 | 1.43985 | ||||||||
\(171\) | −4.21125 | −0.322042 | ||||||||
\(172\) | 36.6886 | 2.79748 | ||||||||
\(173\) | 0.848058 | 0.0644766 | 0.0322383 | − | 0.999480i | \(-0.489736\pi\) | ||||
0.0322383 | + | 0.999480i | \(0.489736\pi\) | |||||||
\(174\) | −0.924628 | −0.0700959 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −26.1305 | −1.96966 | ||||||||
\(177\) | −10.9410 | −0.822375 | ||||||||
\(178\) | −7.48900 | −0.561325 | ||||||||
\(179\) | 15.3327 | 1.14602 | 0.573010 | − | 0.819549i | \(-0.305776\pi\) | ||||
0.573010 | + | 0.819549i | \(0.305776\pi\) | |||||||
\(180\) | 4.27649 | 0.318751 | ||||||||
\(181\) | 7.53427 | 0.560018 | 0.280009 | − | 0.959997i | \(-0.409663\pi\) | ||||
0.280009 | + | 0.959997i | \(0.409663\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.11881 | −0.452315 | ||||||||
\(184\) | 43.7376 | 3.22438 | ||||||||
\(185\) | −3.95812 | −0.291007 | ||||||||
\(186\) | −1.60096 | −0.117388 | ||||||||
\(187\) | −39.1830 | −2.86535 | ||||||||
\(188\) | 26.3738 | 1.92350 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 10.4572 | 0.758642 | ||||||||
\(191\) | 18.6681 | 1.35077 | 0.675387 | − | 0.737463i | \(-0.263977\pi\) | ||||
0.675387 | + | 0.737463i | \(0.263977\pi\) | |||||||
\(192\) | −8.31501 | −0.600084 | ||||||||
\(193\) | 10.3641 | 0.746026 | 0.373013 | − | 0.927826i | \(-0.378325\pi\) | ||||
0.373013 | + | 0.927826i | \(0.378325\pi\) | |||||||
\(194\) | 0.787032 | 0.0565056 | ||||||||
\(195\) | −5.37561 | −0.384955 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.76991 | −0.553583 | −0.276792 | − | 0.960930i | \(-0.589271\pi\) | ||||
−0.276792 | + | 0.960930i | \(0.589271\pi\) | |||||||
\(198\) | −13.2190 | −0.939435 | ||||||||
\(199\) | 14.9397 | 1.05905 | 0.529525 | − | 0.848294i | \(-0.322370\pi\) | ||||
0.529525 | + | 0.848294i | \(0.322370\pi\) | |||||||
\(200\) | 21.2647 | 1.50364 | ||||||||
\(201\) | 1.89034 | 0.133334 | ||||||||
\(202\) | 15.3931 | 1.08306 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 43.6994 | 3.05957 | ||||||||
\(205\) | −1.01447 | −0.0708540 | ||||||||
\(206\) | −25.8545 | −1.80137 | ||||||||
\(207\) | 8.28013 | 0.575509 | ||||||||
\(208\) | 18.6984 | 1.29650 | ||||||||
\(209\) | −21.8258 | −1.50973 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.3885 | −0.990548 | −0.495274 | − | 0.868737i | \(-0.664932\pi\) | ||||
−0.495274 | + | 0.868737i | \(0.664932\pi\) | |||||||
\(212\) | −3.17039 | −0.217743 | ||||||||
\(213\) | 20.9298 | 1.43409 | ||||||||
\(214\) | −14.4395 | −0.987064 | ||||||||
\(215\) | −8.95128 | −0.610472 | ||||||||
\(216\) | 30.2931 | 2.06118 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 10.0339 | 0.679583 | ||||||||
\(219\) | 11.7923 | 0.796847 | ||||||||
\(220\) | 22.1640 | 1.49429 | ||||||||
\(221\) | 28.0385 | 1.88608 | ||||||||
\(222\) | −13.6451 | −0.915801 | ||||||||
\(223\) | −13.0474 | −0.873718 | −0.436859 | − | 0.899530i | \(-0.643909\pi\) | ||||
−0.436859 | + | 0.899530i | \(0.643909\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.02570 | 0.268380 | ||||||||
\(226\) | 20.1289 | 1.33895 | ||||||||
\(227\) | 29.3223 | 1.94619 | 0.973094 | − | 0.230408i | \(-0.0740060\pi\) | ||||
0.973094 | + | 0.230408i | \(0.0740060\pi\) | |||||||
\(228\) | 24.3415 | 1.61206 | ||||||||
\(229\) | 7.51012 | 0.496283 | 0.248141 | − | 0.968724i | \(-0.420180\pi\) | ||||
0.248141 | + | 0.968724i | \(0.420180\pi\) | |||||||
\(230\) | −20.5608 | −1.35574 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.41584 | −0.0929543 | ||||||||
\(233\) | −16.4892 | −1.08025 | −0.540123 | − | 0.841586i | \(-0.681622\pi\) | ||||
−0.540123 | + | 0.841586i | \(0.681622\pi\) | |||||||
\(234\) | 9.45925 | 0.618371 | ||||||||
\(235\) | −6.43467 | −0.419752 | ||||||||
\(236\) | −32.2800 | −2.10125 | ||||||||
\(237\) | 13.7090 | 0.890496 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.692747 | 0.0448101 | 0.0224050 | − | 0.999749i | \(-0.492868\pi\) | ||||
0.0224050 | + | 0.999749i | \(0.492868\pi\) | |||||||
\(240\) | −7.11015 | −0.458958 | ||||||||
\(241\) | 8.43104 | 0.543091 | 0.271546 | − | 0.962426i | \(-0.412465\pi\) | ||||
0.271546 | + | 0.962426i | \(0.412465\pi\) | |||||||
\(242\) | −41.2140 | −2.64934 | ||||||||
\(243\) | 10.0213 | 0.642866 | ||||||||
\(244\) | −18.0528 | −1.15571 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.49728 | −0.222978 | ||||||||
\(247\) | 15.6181 | 0.993756 | ||||||||
\(248\) | −2.45147 | −0.155669 | ||||||||
\(249\) | 13.6577 | 0.865524 | ||||||||
\(250\) | −22.5837 | −1.42832 | ||||||||
\(251\) | 9.32963 | 0.588881 | 0.294440 | − | 0.955670i | \(-0.404867\pi\) | ||||
0.294440 | + | 0.955670i | \(0.404867\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 42.9138 | 2.69797 | ||||||||
\(254\) | 3.10853 | 0.195047 | ||||||||
\(255\) | −10.6618 | −0.667666 | ||||||||
\(256\) | −32.6248 | −2.03905 | ||||||||
\(257\) | 4.73517 | 0.295372 | 0.147686 | − | 0.989034i | \(-0.452818\pi\) | ||||
0.147686 | + | 0.989034i | \(0.452818\pi\) | |||||||
\(258\) | −30.8585 | −1.92116 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −15.8601 | −0.983599 | ||||||||
\(261\) | −0.268038 | −0.0165911 | ||||||||
\(262\) | −25.6672 | −1.58573 | ||||||||
\(263\) | −26.1310 | −1.61130 | −0.805652 | − | 0.592389i | \(-0.798185\pi\) | ||||
−0.805652 | + | 0.592389i | \(0.798185\pi\) | |||||||
\(264\) | 39.6557 | 2.44064 | ||||||||
\(265\) | 0.773511 | 0.0475164 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.25317 | 0.260290 | ||||||||
\(268\) | 5.57720 | 0.340682 | ||||||||
\(269\) | −6.63873 | −0.404770 | −0.202385 | − | 0.979306i | \(-0.564869\pi\) | ||||
−0.202385 | + | 0.979306i | \(0.564869\pi\) | |||||||
\(270\) | −14.2406 | −0.866657 | ||||||||
\(271\) | −14.9285 | −0.906844 | −0.453422 | − | 0.891296i | \(-0.649797\pi\) | ||||
−0.453422 | + | 0.891296i | \(0.649797\pi\) | |||||||
\(272\) | 37.0857 | 2.24865 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 26.7963 | 1.61882 | ||||||||
\(275\) | 20.8642 | 1.25816 | ||||||||
\(276\) | −47.8602 | −2.88084 | ||||||||
\(277\) | 15.2060 | 0.913638 | 0.456819 | − | 0.889560i | \(-0.348989\pi\) | ||||
0.456819 | + | 0.889560i | \(0.348989\pi\) | |||||||
\(278\) | 26.6142 | 1.59621 | ||||||||
\(279\) | −0.464098 | −0.0277848 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.69712 | −0.518827 | −0.259413 | − | 0.965766i | \(-0.583529\pi\) | ||||
−0.259413 | + | 0.965766i | \(0.583529\pi\) | |||||||
\(282\) | −22.1828 | −1.32096 | ||||||||
\(283\) | 20.3047 | 1.20699 | 0.603495 | − | 0.797367i | \(-0.293774\pi\) | ||||
0.603495 | + | 0.797367i | \(0.293774\pi\) | |||||||
\(284\) | 61.7509 | 3.66424 | ||||||||
\(285\) | −5.93885 | −0.351787 | ||||||||
\(286\) | 49.0249 | 2.89890 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.65305 | 0.0974069 | ||||||||
\(289\) | 38.6105 | 2.27121 | ||||||||
\(290\) | 0.665578 | 0.0390841 | ||||||||
\(291\) | −0.446973 | −0.0262020 | ||||||||
\(292\) | 34.7916 | 2.03602 | ||||||||
\(293\) | 15.7908 | 0.922507 | 0.461254 | − | 0.887268i | \(-0.347400\pi\) | ||||
0.461254 | + | 0.887268i | \(0.347400\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.87568 | 0.458540 | ||||||||
\(296\) | −20.8941 | −1.21445 | ||||||||
\(297\) | 29.7226 | 1.72468 | ||||||||
\(298\) | 11.3693 | 0.658605 | ||||||||
\(299\) | −30.7082 | −1.77590 | ||||||||
\(300\) | −23.2691 | −1.34344 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −37.3703 | −2.15042 | ||||||||
\(303\) | −8.74211 | −0.502221 | ||||||||
\(304\) | 20.6576 | 1.18479 | ||||||||
\(305\) | 4.40452 | 0.252202 | ||||||||
\(306\) | 18.7611 | 1.07250 | ||||||||
\(307\) | 12.2219 | 0.697540 | 0.348770 | − | 0.937208i | \(-0.386599\pi\) | ||||
0.348770 | + | 0.937208i | \(0.386599\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.6833 | 0.835306 | ||||||||
\(310\) | 1.15242 | 0.0654532 | ||||||||
\(311\) | 11.0350 | 0.625735 | 0.312868 | − | 0.949797i | \(-0.398710\pi\) | ||||
0.312868 | + | 0.949797i | \(0.398710\pi\) | |||||||
\(312\) | −28.3768 | −1.60652 | ||||||||
\(313\) | −2.40000 | −0.135656 | −0.0678280 | − | 0.997697i | \(-0.521607\pi\) | ||||
−0.0678280 | + | 0.997697i | \(0.521607\pi\) | |||||||
\(314\) | 27.2293 | 1.53664 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 40.4467 | 2.27531 | ||||||||
\(317\) | −20.7361 | −1.16466 | −0.582328 | − | 0.812954i | \(-0.697858\pi\) | ||||
−0.582328 | + | 0.812954i | \(0.697858\pi\) | |||||||
\(318\) | 2.66659 | 0.149535 | ||||||||
\(319\) | −1.38917 | −0.0777788 | ||||||||
\(320\) | 5.98541 | 0.334595 | ||||||||
\(321\) | 8.20052 | 0.457708 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 30.9763 | 1.72357 | ||||||||
\(324\) | −20.5021 | −1.13900 | ||||||||
\(325\) | −14.9300 | −0.828166 | ||||||||
\(326\) | −35.3898 | −1.96006 | ||||||||
\(327\) | −5.69849 | −0.315127 | ||||||||
\(328\) | −5.35521 | −0.295692 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −18.6419 | −1.02621 | ||||||||
\(331\) | 8.40745 | 0.462115 | 0.231058 | − | 0.972940i | \(-0.425781\pi\) | ||||
0.231058 | + | 0.972940i | \(0.425781\pi\) | |||||||
\(332\) | 40.2955 | 2.21150 | ||||||||
\(333\) | −3.95555 | −0.216763 | ||||||||
\(334\) | −40.5636 | −2.21954 | ||||||||
\(335\) | −1.36073 | −0.0743444 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.08624 | −0.222592 | −0.111296 | − | 0.993787i | \(-0.535500\pi\) | ||||
−0.111296 | + | 0.993787i | \(0.535500\pi\) | |||||||
\(338\) | −2.82120 | −0.153453 | ||||||||
\(339\) | −11.4316 | −0.620881 | ||||||||
\(340\) | −31.4562 | −1.70595 | ||||||||
\(341\) | −2.40530 | −0.130254 | ||||||||
\(342\) | 10.4504 | 0.565091 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −47.2520 | −2.54766 | ||||||||
\(345\) | 11.6769 | 0.628665 | ||||||||
\(346\) | −2.10449 | −0.113138 | ||||||||
\(347\) | 19.9001 | 1.06830 | 0.534148 | − | 0.845391i | \(-0.320633\pi\) | ||||
0.534148 | + | 0.845391i | \(0.320633\pi\) | |||||||
\(348\) | 1.54929 | 0.0830508 | ||||||||
\(349\) | 25.1660 | 1.34711 | 0.673553 | − | 0.739139i | \(-0.264767\pi\) | ||||
0.673553 | + | 0.739139i | \(0.264767\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −21.2688 | −1.13525 | ||||||||
\(352\) | 8.56735 | 0.456641 | ||||||||
\(353\) | −13.6046 | −0.724097 | −0.362049 | − | 0.932159i | \(-0.617923\pi\) | ||||
−0.362049 | + | 0.932159i | \(0.617923\pi\) | |||||||
\(354\) | 27.1505 | 1.44303 | ||||||||
\(355\) | −15.0660 | −0.799619 | ||||||||
\(356\) | 12.5485 | 0.665067 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −38.0486 | −2.01093 | ||||||||
\(359\) | 4.26958 | 0.225340 | 0.112670 | − | 0.993632i | \(-0.464060\pi\) | ||||
0.112670 | + | 0.993632i | \(0.464060\pi\) | |||||||
\(360\) | −5.50779 | −0.290286 | ||||||||
\(361\) | −1.74547 | −0.0918667 | ||||||||
\(362\) | −18.6966 | −0.982670 | ||||||||
\(363\) | 23.4064 | 1.22852 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.48845 | −0.444306 | ||||||||
\(366\) | 15.1841 | 0.793683 | ||||||||
\(367\) | −31.2622 | −1.63187 | −0.815937 | − | 0.578141i | \(-0.803778\pi\) | ||||
−0.815937 | + | 0.578141i | \(0.803778\pi\) | |||||||
\(368\) | −40.6168 | −2.11730 | ||||||||
\(369\) | −1.01382 | −0.0527772 | ||||||||
\(370\) | 9.82221 | 0.510632 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.68254 | 0.139083 | ||||||||
\(373\) | −20.2661 | −1.04934 | −0.524671 | − | 0.851305i | \(-0.675812\pi\) | ||||
−0.524671 | + | 0.851305i | \(0.675812\pi\) | |||||||
\(374\) | 97.2341 | 5.02786 | ||||||||
\(375\) | 12.8258 | 0.662321 | ||||||||
\(376\) | −33.9674 | −1.75173 | ||||||||
\(377\) | 0.994062 | 0.0511968 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.19409 | −0.215436 | −0.107718 | − | 0.994181i | \(-0.534354\pi\) | ||||
−0.107718 | + | 0.994181i | \(0.534354\pi\) | |||||||
\(380\) | −17.5218 | −0.898851 | ||||||||
\(381\) | −1.76540 | −0.0904444 | ||||||||
\(382\) | −46.3255 | −2.37022 | ||||||||
\(383\) | 1.84647 | 0.0943504 | 0.0471752 | − | 0.998887i | \(-0.484978\pi\) | ||||
0.0471752 | + | 0.998887i | \(0.484978\pi\) | |||||||
\(384\) | 25.2299 | 1.28751 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −25.7190 | −1.30906 | ||||||||
\(387\) | −8.94547 | −0.454724 | ||||||||
\(388\) | −1.31874 | −0.0669488 | ||||||||
\(389\) | −14.7145 | −0.746053 | −0.373026 | − | 0.927821i | \(-0.621680\pi\) | ||||
−0.373026 | + | 0.927821i | \(0.621680\pi\) | |||||||
\(390\) | 13.3398 | 0.675485 | ||||||||
\(391\) | −60.9055 | −3.08012 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14.5770 | 0.735312 | ||||||||
\(394\) | 19.2813 | 0.971379 | ||||||||
\(395\) | −9.86819 | −0.496523 | ||||||||
\(396\) | 22.1496 | 1.11306 | ||||||||
\(397\) | 13.0761 | 0.656271 | 0.328135 | − | 0.944631i | \(-0.393580\pi\) | ||||
0.328135 | + | 0.944631i | \(0.393580\pi\) | |||||||
\(398\) | −37.0735 | −1.85833 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −19.7474 | −0.987371 | ||||||||
\(401\) | 33.3330 | 1.66457 | 0.832285 | − | 0.554349i | \(-0.187033\pi\) | ||||
0.832285 | + | 0.554349i | \(0.187033\pi\) | |||||||
\(402\) | −4.69094 | −0.233963 | ||||||||
\(403\) | 1.72118 | 0.0857382 | ||||||||
\(404\) | −25.7925 | −1.28322 | ||||||||
\(405\) | 5.00210 | 0.248556 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −20.5006 | −1.01618 | ||||||||
\(408\) | −56.2814 | −2.78634 | ||||||||
\(409\) | 16.3431 | 0.808114 | 0.404057 | − | 0.914734i | \(-0.367600\pi\) | ||||
0.404057 | + | 0.914734i | \(0.367600\pi\) | |||||||
\(410\) | 2.51746 | 0.124328 | ||||||||
\(411\) | −15.2182 | −0.750658 | ||||||||
\(412\) | 43.3214 | 2.13429 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −20.5474 | −1.00985 | ||||||||
\(415\) | −9.83129 | −0.482599 | ||||||||
\(416\) | −6.13061 | −0.300578 | ||||||||
\(417\) | −15.1148 | −0.740174 | ||||||||
\(418\) | 54.1616 | 2.64913 | ||||||||
\(419\) | −14.5565 | −0.711131 | −0.355566 | − | 0.934651i | \(-0.615712\pi\) | ||||
−0.355566 | + | 0.934651i | \(0.615712\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.0444 | −0.781957 | −0.390979 | − | 0.920400i | \(-0.627863\pi\) | ||||
−0.390979 | + | 0.920400i | \(0.627863\pi\) | |||||||
\(422\) | 35.7057 | 1.73813 | ||||||||
\(423\) | −6.43050 | −0.312661 | ||||||||
\(424\) | 4.08321 | 0.198298 | ||||||||
\(425\) | −29.6115 | −1.43637 | ||||||||
\(426\) | −51.9382 | −2.51641 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 24.1946 | 1.16949 | ||||||||
\(429\) | −27.8424 | −1.34424 | ||||||||
\(430\) | 22.2129 | 1.07120 | ||||||||
\(431\) | 33.5871 | 1.61783 | 0.808917 | − | 0.587923i | \(-0.200054\pi\) | ||||
0.808917 | + | 0.587923i | \(0.200054\pi\) | |||||||
\(432\) | −28.1316 | −1.35348 | ||||||||
\(433\) | −23.7405 | −1.14090 | −0.570449 | − | 0.821333i | \(-0.693231\pi\) | ||||
−0.570449 | + | 0.821333i | \(0.693231\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.377997 | −0.0181235 | ||||||||
\(436\) | −16.8127 | −0.805182 | ||||||||
\(437\) | −33.9258 | −1.62289 | ||||||||
\(438\) | −29.2629 | −1.39824 | ||||||||
\(439\) | 32.1612 | 1.53497 | 0.767486 | − | 0.641066i | \(-0.221507\pi\) | ||||
0.767486 | + | 0.641066i | \(0.221507\pi\) | |||||||
\(440\) | −28.5455 | −1.36085 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −69.5786 | −3.30952 | ||||||||
\(443\) | 5.93198 | 0.281837 | 0.140918 | − | 0.990021i | \(-0.454995\pi\) | ||||
0.140918 | + | 0.990021i | \(0.454995\pi\) | |||||||
\(444\) | 22.8636 | 1.08506 | ||||||||
\(445\) | −3.06157 | −0.145133 | ||||||||
\(446\) | 32.3776 | 1.53312 | ||||||||
\(447\) | −6.45687 | −0.305399 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.1624 | 0.809945 | 0.404972 | − | 0.914329i | \(-0.367281\pi\) | ||||
0.404972 | + | 0.914329i | \(0.367281\pi\) | |||||||
\(450\) | −9.98993 | −0.470930 | ||||||||
\(451\) | −5.25436 | −0.247418 | ||||||||
\(452\) | −33.7276 | −1.58641 | ||||||||
\(453\) | 21.2234 | 0.997163 | ||||||||
\(454\) | −72.7643 | −3.41500 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −31.3500 | −1.46810 | ||||||||
\(457\) | −41.0148 | −1.91859 | −0.959297 | − | 0.282401i | \(-0.908869\pi\) | ||||
−0.959297 | + | 0.282401i | \(0.908869\pi\) | |||||||
\(458\) | −18.6366 | −0.870833 | ||||||||
\(459\) | −42.1838 | −1.96897 | ||||||||
\(460\) | 34.4513 | 1.60630 | ||||||||
\(461\) | 40.1685 | 1.87083 | 0.935416 | − | 0.353550i | \(-0.115026\pi\) | ||||
0.935416 | + | 0.353550i | \(0.115026\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.8876 | −1.20310 | −0.601549 | − | 0.798836i | \(-0.705449\pi\) | ||||
−0.601549 | + | 0.798836i | \(0.705449\pi\) | |||||||
\(464\) | 1.31482 | 0.0610388 | ||||||||
\(465\) | −0.654487 | −0.0303511 | ||||||||
\(466\) | 40.9187 | 1.89552 | ||||||||
\(467\) | −22.2641 | −1.03026 | −0.515129 | − | 0.857113i | \(-0.672256\pi\) | ||||
−0.515129 | + | 0.857113i | \(0.672256\pi\) | |||||||
\(468\) | −15.8498 | −0.732656 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 15.9679 | 0.736543 | ||||||||
\(471\) | −15.4641 | −0.712549 | ||||||||
\(472\) | 41.5742 | 1.91361 | ||||||||
\(473\) | −46.3621 | −2.13173 | ||||||||
\(474\) | −34.0194 | −1.56256 | ||||||||
\(475\) | −16.4943 | −0.756811 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.773010 | 0.0353937 | ||||||||
\(478\) | −1.71908 | −0.0786288 | ||||||||
\(479\) | −29.7682 | −1.36015 | −0.680073 | − | 0.733145i | \(-0.738052\pi\) | ||||
−0.680073 | + | 0.733145i | \(0.738052\pi\) | |||||||
\(480\) | 2.33119 | 0.106404 | ||||||||
\(481\) | 14.6698 | 0.668885 | ||||||||
\(482\) | −20.9219 | −0.952968 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 69.0575 | 3.13898 | ||||||||
\(485\) | 0.321746 | 0.0146097 | ||||||||
\(486\) | −24.8682 | −1.12804 | ||||||||
\(487\) | 16.7135 | 0.757363 | 0.378682 | − | 0.925527i | \(-0.376378\pi\) | ||||
0.378682 | + | 0.925527i | \(0.376378\pi\) | |||||||
\(488\) | 23.2506 | 1.05250 | ||||||||
\(489\) | 20.0986 | 0.908892 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −27.0953 | −1.22279 | −0.611396 | − | 0.791325i | \(-0.709392\pi\) | ||||
−0.611396 | + | 0.791325i | \(0.709392\pi\) | |||||||
\(492\) | 5.85999 | 0.264189 | ||||||||
\(493\) | 1.97158 | 0.0887957 | ||||||||
\(494\) | −38.7569 | −1.74376 | ||||||||
\(495\) | −5.40406 | −0.242894 | ||||||||
\(496\) | 2.27655 | 0.102220 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −33.8922 | −1.51875 | ||||||||
\(499\) | −28.7606 | −1.28750 | −0.643751 | − | 0.765235i | \(-0.722623\pi\) | ||||
−0.643751 | + | 0.765235i | \(0.722623\pi\) | |||||||
\(500\) | 37.8409 | 1.69230 | ||||||||
\(501\) | 23.0370 | 1.02922 | ||||||||
\(502\) | −23.1518 | −1.03332 | ||||||||
\(503\) | 8.89437 | 0.396580 | 0.198290 | − | 0.980143i | \(-0.436461\pi\) | ||||
0.198290 | + | 0.980143i | \(0.436461\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.29285 | 0.280028 | ||||||||
\(506\) | −106.492 | −4.73416 | ||||||||
\(507\) | 1.60222 | 0.0711573 | ||||||||
\(508\) | −5.20860 | −0.231094 | ||||||||
\(509\) | 30.3963 | 1.34729 | 0.673646 | − | 0.739054i | \(-0.264727\pi\) | ||||
0.673646 | + | 0.739054i | \(0.264727\pi\) | |||||||
\(510\) | 26.4576 | 1.17156 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 45.1553 | 1.99560 | ||||||||
\(513\) | −23.4973 | −1.03743 | ||||||||
\(514\) | −11.7505 | −0.518292 | ||||||||
\(515\) | −10.5696 | −0.465750 | ||||||||
\(516\) | 51.7059 | 2.27623 | ||||||||
\(517\) | −33.3277 | −1.46575 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.19518 | 0.0524628 | ||||||||
\(520\) | 20.4265 | 0.895763 | ||||||||
\(521\) | −4.28263 | −0.187625 | −0.0938127 | − | 0.995590i | \(-0.529905\pi\) | ||||
−0.0938127 | + | 0.995590i | \(0.529905\pi\) | |||||||
\(522\) | 0.665146 | 0.0291126 | ||||||||
\(523\) | 15.2026 | 0.664762 | 0.332381 | − | 0.943145i | \(-0.392148\pi\) | ||||
0.332381 | + | 0.943145i | \(0.392148\pi\) | |||||||
\(524\) | 43.0076 | 1.87879 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 64.8449 | 2.82737 | ||||||||
\(527\) | 3.41372 | 0.148704 | ||||||||
\(528\) | −36.8262 | −1.60266 | ||||||||
\(529\) | 43.7046 | 1.90020 | ||||||||
\(530\) | −1.91950 | −0.0833776 | ||||||||
\(531\) | 7.87057 | 0.341554 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.75990 | 0.162860 | ||||||||
\(534\) | −10.5544 | −0.456734 | ||||||||
\(535\) | −5.90300 | −0.255209 | ||||||||
\(536\) | −7.18301 | −0.310259 | ||||||||
\(537\) | 21.6087 | 0.932483 | ||||||||
\(538\) | 16.4742 | 0.710255 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 23.8614 | 1.02683 | ||||||||
\(541\) | 9.86849 | 0.424279 | 0.212140 | − | 0.977239i | \(-0.431957\pi\) | ||||
0.212140 | + | 0.977239i | \(0.431957\pi\) | |||||||
\(542\) | 37.0457 | 1.59125 | ||||||||
\(543\) | 10.6182 | 0.455671 | ||||||||
\(544\) | −12.1592 | −0.521322 | ||||||||
\(545\) | 4.10196 | 0.175709 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.77390 | −0.0758466 | −0.0379233 | − | 0.999281i | \(-0.512074\pi\) | ||||
−0.0379233 | + | 0.999281i | \(0.512074\pi\) | |||||||
\(548\) | −44.8994 | −1.91801 | ||||||||
\(549\) | 4.40166 | 0.187858 | ||||||||
\(550\) | −51.7753 | −2.20771 | ||||||||
\(551\) | 1.09822 | 0.0467856 | ||||||||
\(552\) | 61.6402 | 2.62358 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −37.7342 | −1.60317 | ||||||||
\(555\) | −5.57825 | −0.236784 | ||||||||
\(556\) | −44.5943 | −1.89122 | ||||||||
\(557\) | −21.9654 | −0.930705 | −0.465352 | − | 0.885126i | \(-0.654072\pi\) | ||||
−0.465352 | + | 0.885126i | \(0.654072\pi\) | |||||||
\(558\) | 1.15168 | 0.0487543 | ||||||||
\(559\) | 33.1757 | 1.40318 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −55.2214 | −2.33145 | ||||||||
\(562\) | 21.5822 | 0.910391 | ||||||||
\(563\) | −43.6484 | −1.83956 | −0.919780 | − | 0.392434i | \(-0.871633\pi\) | ||||
−0.919780 | + | 0.392434i | \(0.871633\pi\) | |||||||
\(564\) | 37.1691 | 1.56510 | ||||||||
\(565\) | 8.22886 | 0.346191 | ||||||||
\(566\) | −50.3869 | −2.11792 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −79.5304 | −3.33702 | ||||||||
\(569\) | 28.9235 | 1.21254 | 0.606269 | − | 0.795260i | \(-0.292665\pi\) | ||||
0.606269 | + | 0.795260i | \(0.292665\pi\) | |||||||
\(570\) | 14.7375 | 0.617285 | ||||||||
\(571\) | −3.28763 | −0.137583 | −0.0687916 | − | 0.997631i | \(-0.521914\pi\) | ||||
−0.0687916 | + | 0.997631i | \(0.521914\pi\) | |||||||
\(572\) | −82.1454 | −3.43467 | ||||||||
\(573\) | 26.3093 | 1.09909 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 32.4310 | 1.35247 | ||||||||
\(576\) | 5.98153 | 0.249230 | ||||||||
\(577\) | −35.7021 | −1.48630 | −0.743149 | − | 0.669126i | \(-0.766669\pi\) | ||||
−0.743149 | + | 0.669126i | \(0.766669\pi\) | |||||||
\(578\) | −95.8134 | −3.98531 | ||||||||
\(579\) | 14.6064 | 0.607020 | ||||||||
\(580\) | −1.11523 | −0.0463075 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.10918 | 0.0459770 | ||||||||
\(583\) | 4.00631 | 0.165925 | ||||||||
\(584\) | −44.8089 | −1.85420 | ||||||||
\(585\) | 3.86703 | 0.159882 | ||||||||
\(586\) | −39.1854 | −1.61873 | ||||||||
\(587\) | −37.3851 | −1.54305 | −0.771524 | − | 0.636200i | \(-0.780505\pi\) | ||||
−0.771524 | + | 0.636200i | \(0.780505\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.90152 | 0.0783509 | ||||||||
\(590\) | −19.5438 | −0.804605 | ||||||||
\(591\) | −10.9503 | −0.450435 | ||||||||
\(592\) | 19.4033 | 0.797470 | ||||||||
\(593\) | −36.2967 | −1.49053 | −0.745263 | − | 0.666770i | \(-0.767676\pi\) | ||||
−0.745263 | + | 0.666770i | \(0.767676\pi\) | |||||||
\(594\) | −73.7577 | −3.02632 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −19.0502 | −0.780326 | ||||||||
\(597\) | 21.0549 | 0.861719 | ||||||||
\(598\) | 76.2036 | 3.11620 | ||||||||
\(599\) | −0.260042 | −0.0106250 | −0.00531252 | − | 0.999986i | \(-0.501691\pi\) | ||||
−0.00531252 | + | 0.999986i | \(0.501691\pi\) | |||||||
\(600\) | 29.9688 | 1.22347 | ||||||||
\(601\) | −18.1572 | −0.740648 | −0.370324 | − | 0.928903i | \(-0.620753\pi\) | ||||
−0.370324 | + | 0.928903i | \(0.620753\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.35984 | −0.0553771 | ||||||||
\(604\) | 62.6171 | 2.54785 | ||||||||
\(605\) | −16.8487 | −0.684995 | ||||||||
\(606\) | 21.6939 | 0.881253 | ||||||||
\(607\) | −4.95145 | −0.200973 | −0.100487 | − | 0.994938i | \(-0.532040\pi\) | ||||
−0.100487 | + | 0.994938i | \(0.532040\pi\) | |||||||
\(608\) | −6.77296 | −0.274680 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −10.9300 | −0.442542 | ||||||||
\(611\) | 23.8485 | 0.964809 | ||||||||
\(612\) | −31.4358 | −1.27072 | ||||||||
\(613\) | −6.55127 | −0.264603 | −0.132302 | − | 0.991210i | \(-0.542237\pi\) | ||||
−0.132302 | + | 0.991210i | \(0.542237\pi\) | |||||||
\(614\) | −30.3291 | −1.22398 | ||||||||
\(615\) | −1.42972 | −0.0576519 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.05131 | 0.0423241 | 0.0211620 | − | 0.999776i | \(-0.493263\pi\) | ||||
0.0211620 | + | 0.999776i | \(0.493263\pi\) | |||||||
\(618\) | −36.4373 | −1.46572 | ||||||||
\(619\) | 0.0534770 | 0.00214942 | 0.00107471 | − | 0.999999i | \(-0.499658\pi\) | ||||
0.00107471 | + | 0.999999i | \(0.499658\pi\) | |||||||
\(620\) | −1.93098 | −0.0775501 | ||||||||
\(621\) | 46.2003 | 1.85396 | ||||||||
\(622\) | −27.3837 | −1.09798 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 26.3520 | 1.05493 | ||||||||
\(625\) | 10.6218 | 0.424871 | ||||||||
\(626\) | 5.95569 | 0.238037 | ||||||||
\(627\) | −30.7596 | −1.22842 | ||||||||
\(628\) | −45.6250 | −1.82063 | ||||||||
\(629\) | 29.0955 | 1.16011 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.0619 | 1.47541 | 0.737706 | − | 0.675122i | \(-0.235909\pi\) | ||||
0.737706 | + | 0.675122i | \(0.235909\pi\) | |||||||
\(632\) | −52.0922 | −2.07212 | ||||||||
\(633\) | −20.2781 | −0.805981 | ||||||||
\(634\) | 51.4574 | 2.04363 | ||||||||
\(635\) | 1.27080 | 0.0504300 | ||||||||
\(636\) | −4.46809 | −0.177171 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.44728 | 0.136479 | ||||||||
\(639\) | −15.0562 | −0.595614 | ||||||||
\(640\) | −18.1613 | −0.717887 | ||||||||
\(641\) | −18.9766 | −0.749532 | −0.374766 | − | 0.927119i | \(-0.622277\pi\) | ||||
−0.374766 | + | 0.927119i | \(0.622277\pi\) | |||||||
\(642\) | −20.3499 | −0.803146 | ||||||||
\(643\) | −21.9771 | −0.866693 | −0.433346 | − | 0.901227i | \(-0.642667\pi\) | ||||
−0.433346 | + | 0.901227i | \(0.642667\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −12.6152 | −0.496724 | ||||||||
\(646\) | −76.8689 | −3.02437 | ||||||||
\(647\) | 36.3748 | 1.43004 | 0.715020 | − | 0.699104i | \(-0.246418\pi\) | ||||
0.715020 | + | 0.699104i | \(0.246418\pi\) | |||||||
\(648\) | 26.4051 | 1.03729 | ||||||||
\(649\) | 40.7912 | 1.60119 | ||||||||
\(650\) | 37.0493 | 1.45319 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 59.2985 | 2.32231 | ||||||||
\(653\) | −25.3274 | −0.991138 | −0.495569 | − | 0.868569i | \(-0.665040\pi\) | ||||
−0.495569 | + | 0.868569i | \(0.665040\pi\) | |||||||
\(654\) | 14.1410 | 0.552957 | ||||||||
\(655\) | −10.4930 | −0.409995 | ||||||||
\(656\) | 4.97311 | 0.194167 | ||||||||
\(657\) | −8.48294 | −0.330951 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.76844 | 0.302615 | 0.151308 | − | 0.988487i | \(-0.451652\pi\) | ||||
0.151308 | + | 0.988487i | \(0.451652\pi\) | |||||||
\(660\) | 31.2361 | 1.21586 | ||||||||
\(661\) | −0.350738 | −0.0136421 | −0.00682107 | − | 0.999977i | \(-0.502171\pi\) | ||||
−0.00682107 | + | 0.999977i | \(0.502171\pi\) | |||||||
\(662\) | −20.8634 | −0.810879 | ||||||||
\(663\) | 39.5153 | 1.53465 | ||||||||
\(664\) | −51.8974 | −2.01401 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9.81584 | 0.380356 | ||||||||
\(667\) | −2.15931 | −0.0836088 | ||||||||
\(668\) | 67.9677 | 2.62975 | ||||||||
\(669\) | −18.3879 | −0.710919 | ||||||||
\(670\) | 3.37669 | 0.130453 | ||||||||
\(671\) | 22.8127 | 0.880675 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.3135 | −0.397555 | −0.198778 | − | 0.980045i | \(-0.563697\pi\) | ||||
−0.198778 | + | 0.980045i | \(0.563697\pi\) | |||||||
\(674\) | 10.1402 | 0.390584 | ||||||||
\(675\) | 22.4621 | 0.864565 | ||||||||
\(676\) | 4.72716 | 0.181814 | ||||||||
\(677\) | −2.23553 | −0.0859185 | −0.0429592 | − | 0.999077i | \(-0.513679\pi\) | ||||
−0.0429592 | + | 0.999077i | \(0.513679\pi\) | |||||||
\(678\) | 28.3680 | 1.08947 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 40.5132 | 1.55361 | ||||||||
\(681\) | 41.3245 | 1.58356 | ||||||||
\(682\) | 5.96884 | 0.228559 | ||||||||
\(683\) | 34.4761 | 1.31919 | 0.659595 | − | 0.751621i | \(-0.270728\pi\) | ||||
0.659595 | + | 0.751621i | \(0.270728\pi\) | |||||||
\(684\) | −17.5105 | −0.669530 | ||||||||
\(685\) | 10.9546 | 0.418552 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.5842 | 0.403811 | ||||||||
\(688\) | 43.8805 | 1.67293 | ||||||||
\(689\) | −2.86683 | −0.109218 | ||||||||
\(690\) | −28.9767 | −1.10313 | ||||||||
\(691\) | 9.76177 | 0.371355 | 0.185678 | − | 0.982611i | \(-0.440552\pi\) | ||||
0.185678 | + | 0.982611i | \(0.440552\pi\) | |||||||
\(692\) | 3.52624 | 0.134048 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −49.3829 | −1.87455 | ||||||||
\(695\) | 10.8801 | 0.412706 | ||||||||
\(696\) | −1.99537 | −0.0756343 | ||||||||
\(697\) | 7.45725 | 0.282463 | ||||||||
\(698\) | −62.4504 | −2.36378 | ||||||||
\(699\) | −23.2386 | −0.878966 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.6354 | −0.666081 | −0.333041 | − | 0.942913i | \(-0.608075\pi\) | ||||
−0.333041 | + | 0.942913i | \(0.608075\pi\) | |||||||
\(702\) | 52.7794 | 1.99203 | ||||||||
\(703\) | 16.2069 | 0.611253 | ||||||||
\(704\) | 31.0008 | 1.16839 | ||||||||
\(705\) | −9.06851 | −0.341540 | ||||||||
\(706\) | 33.7602 | 1.27058 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −45.4929 | −1.70973 | ||||||||
\(709\) | 15.4989 | 0.582074 | 0.291037 | − | 0.956712i | \(-0.406000\pi\) | ||||
0.291037 | + | 0.956712i | \(0.406000\pi\) | |||||||
\(710\) | 37.3868 | 1.40310 | ||||||||
\(711\) | −9.86179 | −0.369846 | ||||||||
\(712\) | −16.1614 | −0.605676 | ||||||||
\(713\) | −3.73876 | −0.140018 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20.0418 | 0.749522 | ||||||||
\(716\) | 63.7537 | 2.38259 | ||||||||
\(717\) | 0.976303 | 0.0364607 | ||||||||
\(718\) | −10.5951 | −0.395406 | ||||||||
\(719\) | −21.2526 | −0.792589 | −0.396294 | − | 0.918123i | \(-0.629704\pi\) | ||||
−0.396294 | + | 0.918123i | \(0.629704\pi\) | |||||||
\(720\) | 5.11480 | 0.190617 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 4.33144 | 0.161200 | ||||||||
\(723\) | 11.8820 | 0.441898 | ||||||||
\(724\) | 31.3277 | 1.16428 | ||||||||
\(725\) | −1.04983 | −0.0389897 | ||||||||
\(726\) | −58.0837 | −2.15569 | ||||||||
\(727\) | −19.3154 | −0.716369 | −0.358185 | − | 0.933651i | \(-0.616604\pi\) | ||||
−0.358185 | + | 0.933651i | \(0.616604\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 28.9154 | 1.07094 | ||||||||
\(730\) | 21.0644 | 0.779628 | ||||||||
\(731\) | 65.7995 | 2.43368 | ||||||||
\(732\) | −25.4422 | −0.940369 | ||||||||
\(733\) | −1.50305 | −0.0555165 | −0.0277582 | − | 0.999615i | \(-0.508837\pi\) | ||||
−0.0277582 | + | 0.999615i | \(0.508837\pi\) | |||||||
\(734\) | 77.5783 | 2.86347 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 13.3169 | 0.490869 | ||||||||
\(737\) | −7.04773 | −0.259606 | ||||||||
\(738\) | 2.51582 | 0.0926087 | ||||||||
\(739\) | 43.6440 | 1.60547 | 0.802735 | − | 0.596335i | \(-0.203377\pi\) | ||||
0.802735 | + | 0.596335i | \(0.203377\pi\) | |||||||
\(740\) | −16.4579 | −0.605006 | ||||||||
\(741\) | 22.0109 | 0.808591 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.6077 | 0.535906 | 0.267953 | − | 0.963432i | \(-0.413653\pi\) | ||||
0.267953 | + | 0.963432i | \(0.413653\pi\) | |||||||
\(744\) | −3.45491 | −0.126663 | ||||||||
\(745\) | 4.64787 | 0.170285 | ||||||||
\(746\) | 50.2912 | 1.84129 | ||||||||
\(747\) | −9.82491 | −0.359475 | ||||||||
\(748\) | −162.924 | −5.95709 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −31.8277 | −1.16218 | ||||||||
\(751\) | −44.0504 | −1.60742 | −0.803711 | − | 0.595019i | \(-0.797144\pi\) | ||||
−0.803711 | + | 0.595019i | \(0.797144\pi\) | |||||||
\(752\) | 31.5437 | 1.15028 | ||||||||
\(753\) | 13.1484 | 0.479156 | ||||||||
\(754\) | −2.46680 | −0.0898356 | ||||||||
\(755\) | −15.2773 | −0.555998 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.37561 | 0.268071 | 0.134036 | − | 0.990977i | \(-0.457206\pi\) | ||||
0.134036 | + | 0.990977i | \(0.457206\pi\) | |||||||
\(758\) | 10.4078 | 0.378028 | ||||||||
\(759\) | 60.4793 | 2.19526 | ||||||||
\(760\) | 22.5668 | 0.818583 | ||||||||
\(761\) | −49.3445 | −1.78874 | −0.894368 | − | 0.447331i | \(-0.852375\pi\) | ||||
−0.894368 | + | 0.447331i | \(0.852375\pi\) | |||||||
\(762\) | 4.38092 | 0.158704 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 77.6223 | 2.80827 | ||||||||
\(765\) | 7.66971 | 0.277299 | ||||||||
\(766\) | −4.58209 | −0.165558 | ||||||||
\(767\) | −29.1893 | −1.05396 | ||||||||
\(768\) | −45.9788 | −1.65912 | ||||||||
\(769\) | −14.5456 | −0.524526 | −0.262263 | − | 0.964996i | \(-0.584469\pi\) | ||||
−0.262263 | + | 0.964996i | \(0.584469\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.67336 | 0.240335 | ||||||||
\(772\) | 43.0943 | 1.55100 | ||||||||
\(773\) | 39.1871 | 1.40946 | 0.704731 | − | 0.709475i | \(-0.251068\pi\) | ||||
0.704731 | + | 0.709475i | \(0.251068\pi\) | |||||||
\(774\) | 22.1985 | 0.797909 | ||||||||
\(775\) | −1.81774 | −0.0652953 | ||||||||
\(776\) | 1.69843 | 0.0609702 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 36.5145 | 1.30911 | ||||||||
\(779\) | 4.15386 | 0.148827 | ||||||||
\(780\) | −22.3519 | −0.800327 | ||||||||
\(781\) | −78.0326 | −2.79222 | ||||||||
\(782\) | 151.139 | 5.40472 | ||||||||
\(783\) | −1.49556 | −0.0534470 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.1316 | 0.397303 | ||||||||
\(786\) | −36.1733 | −1.29026 | ||||||||
\(787\) | −47.8452 | −1.70550 | −0.852749 | − | 0.522322i | \(-0.825066\pi\) | ||||
−0.852749 | + | 0.522322i | \(0.825066\pi\) | |||||||
\(788\) | −32.3075 | −1.15091 | ||||||||
\(789\) | −36.8269 | −1.31107 | ||||||||
\(790\) | 24.4883 | 0.871254 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −28.5270 | −1.01366 | ||||||||
\(793\) | −16.3243 | −0.579692 | ||||||||
\(794\) | −32.4488 | −1.15157 | ||||||||
\(795\) | 1.09013 | 0.0386628 | ||||||||
\(796\) | 62.1198 | 2.20178 | ||||||||
\(797\) | 26.1138 | 0.924998 | 0.462499 | − | 0.886620i | \(-0.346953\pi\) | ||||
0.462499 | + | 0.886620i | \(0.346953\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 47.3003 | 1.67336 | ||||||||
\(800\) | 6.47455 | 0.228910 | ||||||||
\(801\) | −3.05959 | −0.108105 | ||||||||
\(802\) | −82.7170 | −2.92084 | ||||||||
\(803\) | −43.9650 | −1.55149 | ||||||||
\(804\) | 7.86007 | 0.277203 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.27118 | −0.150446 | ||||||||
\(807\) | −9.35610 | −0.329350 | ||||||||
\(808\) | 33.2187 | 1.16863 | ||||||||
\(809\) | 32.8565 | 1.15517 | 0.577587 | − | 0.816329i | \(-0.303994\pi\) | ||||
0.577587 | + | 0.816329i | \(0.303994\pi\) | |||||||
\(810\) | −12.4129 | −0.436144 | ||||||||
\(811\) | 27.7057 | 0.972879 | 0.486439 | − | 0.873714i | \(-0.338295\pi\) | ||||
0.486439 | + | 0.873714i | \(0.338295\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −21.0391 | −0.737873 | ||||||||
\(814\) | 50.8730 | 1.78310 | ||||||||
\(815\) | −14.4677 | −0.506780 | ||||||||
\(816\) | 52.2656 | 1.82966 | ||||||||
\(817\) | 36.6518 | 1.28228 | ||||||||
\(818\) | −40.5560 | −1.41801 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.21821 | −0.147306 | ||||||||
\(821\) | −37.3553 | −1.30371 | −0.651855 | − | 0.758344i | \(-0.726009\pi\) | ||||
−0.651855 | + | 0.758344i | \(0.726009\pi\) | |||||||
\(822\) | 37.7645 | 1.31719 | ||||||||
\(823\) | 36.8291 | 1.28378 | 0.641891 | − | 0.766796i | \(-0.278150\pi\) | ||||
0.641891 | + | 0.766796i | \(0.278150\pi\) | |||||||
\(824\) | −55.7946 | −1.94370 | ||||||||
\(825\) | 29.4044 | 1.02373 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −15.8549 | −0.551330 | −0.275665 | − | 0.961254i | \(-0.588898\pi\) | ||||
−0.275665 | + | 0.961254i | \(0.588898\pi\) | |||||||
\(828\) | 34.4290 | 1.19649 | ||||||||
\(829\) | −31.4052 | −1.09075 | −0.545374 | − | 0.838193i | \(-0.683612\pi\) | ||||
−0.545374 | + | 0.838193i | \(0.683612\pi\) | |||||||
\(830\) | 24.3967 | 0.846822 | ||||||||
\(831\) | 21.4301 | 0.743401 | ||||||||
\(832\) | −22.1835 | −0.769074 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 37.5079 | 1.29879 | ||||||||
\(835\) | −16.5828 | −0.573871 | ||||||||
\(836\) | −90.7524 | −3.13874 | ||||||||
\(837\) | −2.58951 | −0.0895065 | ||||||||
\(838\) | 36.1225 | 1.24783 | ||||||||
\(839\) | 11.1872 | 0.386224 | 0.193112 | − | 0.981177i | \(-0.438142\pi\) | ||||
0.193112 | + | 0.981177i | \(0.438142\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9301 | −0.997590 | ||||||||
\(842\) | 39.8148 | 1.37211 | ||||||||
\(843\) | −12.2570 | −0.422154 | ||||||||
\(844\) | −59.8279 | −2.05936 | ||||||||
\(845\) | −1.15333 | −0.0396759 | ||||||||
\(846\) | 15.9575 | 0.548631 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.79187 | −0.130213 | ||||||||
\(849\) | 28.6158 | 0.982093 | ||||||||
\(850\) | 73.4821 | 2.52042 | ||||||||
\(851\) | −31.8658 | −1.09235 | ||||||||
\(852\) | 87.0268 | 2.98149 | ||||||||
\(853\) | 11.9114 | 0.407840 | 0.203920 | − | 0.978988i | \(-0.434632\pi\) | ||||
0.203920 | + | 0.978988i | \(0.434632\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.27221 | 0.146106 | ||||||||
\(856\) | −31.1608 | −1.06505 | ||||||||
\(857\) | −23.1449 | −0.790615 | −0.395307 | − | 0.918549i | \(-0.629362\pi\) | ||||
−0.395307 | + | 0.918549i | \(0.629362\pi\) | |||||||
\(858\) | 69.0918 | 2.35876 | ||||||||
\(859\) | −18.2362 | −0.622212 | −0.311106 | − | 0.950375i | \(-0.600699\pi\) | ||||
−0.311106 | + | 0.950375i | \(0.600699\pi\) | |||||||
\(860\) | −37.2196 | −1.26918 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −83.3476 | −2.83883 | ||||||||
\(863\) | 17.0867 | 0.581638 | 0.290819 | − | 0.956778i | \(-0.406072\pi\) | ||||
0.290819 | + | 0.956778i | \(0.406072\pi\) | |||||||
\(864\) | 9.22346 | 0.313789 | ||||||||
\(865\) | −0.860333 | −0.0292522 | ||||||||
\(866\) | 58.9130 | 2.00195 | ||||||||
\(867\) | 54.4146 | 1.84802 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −51.1112 | −1.73383 | ||||||||
\(870\) | 0.938012 | 0.0318016 | ||||||||
\(871\) | 5.04320 | 0.170882 | ||||||||
\(872\) | 21.6534 | 0.733278 | ||||||||
\(873\) | 0.321537 | 0.0108824 | ||||||||
\(874\) | 84.1880 | 2.84770 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 49.0325 | 1.65665 | ||||||||
\(877\) | −10.1529 | −0.342840 | −0.171420 | − | 0.985198i | \(-0.554836\pi\) | ||||
−0.171420 | + | 0.985198i | \(0.554836\pi\) | |||||||
\(878\) | −79.8093 | −2.69343 | ||||||||
\(879\) | 22.2543 | 0.750618 | ||||||||
\(880\) | 26.5087 | 0.893608 | ||||||||
\(881\) | −21.9643 | −0.739997 | −0.369998 | − | 0.929032i | \(-0.620642\pi\) | ||||
−0.369998 | + | 0.929032i | \(0.620642\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.08924 | 0.0366558 | 0.0183279 | − | 0.999832i | \(-0.494166\pi\) | ||||
0.0183279 | + | 0.999832i | \(0.494166\pi\) | |||||||
\(884\) | 116.585 | 3.92117 | ||||||||
\(885\) | 11.0994 | 0.373101 | ||||||||
\(886\) | −14.7204 | −0.494542 | ||||||||
\(887\) | 3.76904 | 0.126552 | 0.0632760 | − | 0.997996i | \(-0.479845\pi\) | ||||
0.0632760 | + | 0.997996i | \(0.479845\pi\) | |||||||
\(888\) | −29.4465 | −0.988160 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 7.59741 | 0.254666 | ||||||||
\(891\) | 25.9078 | 0.867944 | ||||||||
\(892\) | −54.2513 | −1.81647 | ||||||||
\(893\) | 26.3473 | 0.881680 | ||||||||
\(894\) | 16.0230 | 0.535888 | ||||||||
\(895\) | −15.5546 | −0.519934 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −43.2777 | −1.44500 | ||||||||
\(898\) | −42.5892 | −1.42122 | ||||||||
\(899\) | 0.121028 | 0.00403652 | ||||||||
\(900\) | 16.7390 | 0.557966 | ||||||||
\(901\) | −5.68596 | −0.189427 | ||||||||
\(902\) | 13.0389 | 0.434147 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 43.4385 | 1.44474 | ||||||||
\(905\) | −7.64333 | −0.254073 | ||||||||
\(906\) | −52.6667 | −1.74973 | ||||||||
\(907\) | −30.8489 | −1.02432 | −0.512160 | − | 0.858890i | \(-0.671154\pi\) | ||||
−0.512160 | + | 0.858890i | \(0.671154\pi\) | |||||||
\(908\) | 121.923 | 4.04615 | ||||||||
\(909\) | 6.28877 | 0.208585 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.0614 | 1.12850 | 0.564252 | − | 0.825603i | \(-0.309165\pi\) | ||||
0.564252 | + | 0.825603i | \(0.309165\pi\) | |||||||
\(912\) | 29.1131 | 0.964032 | ||||||||
\(913\) | −50.9200 | −1.68521 | ||||||||
\(914\) | 101.780 | 3.36658 | ||||||||
\(915\) | 6.20738 | 0.205210 | ||||||||
\(916\) | 31.2272 | 1.03178 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 104.681 | 3.45498 | ||||||||
\(919\) | −6.17017 | −0.203535 | −0.101768 | − | 0.994808i | \(-0.532450\pi\) | ||||
−0.101768 | + | 0.994808i | \(0.532450\pi\) | |||||||
\(920\) | −44.3706 | −1.46286 | ||||||||
\(921\) | 17.2246 | 0.567569 | ||||||||
\(922\) | −99.6795 | −3.28277 | ||||||||
\(923\) | 55.8384 | 1.83794 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.4928 | −0.509400 | ||||||||
\(926\) | 64.2409 | 2.11109 | ||||||||
\(927\) | −10.5627 | −0.346924 | ||||||||
\(928\) | −0.431086 | −0.0141511 | ||||||||
\(929\) | 47.4777 | 1.55769 | 0.778846 | − | 0.627215i | \(-0.215805\pi\) | ||||
0.778846 | + | 0.627215i | \(0.215805\pi\) | |||||||
\(930\) | 1.62413 | 0.0532574 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −68.5627 | −2.24584 | ||||||||
\(933\) | 15.5518 | 0.509143 | ||||||||
\(934\) | 55.2491 | 1.80781 | ||||||||
\(935\) | 39.7502 | 1.29997 | ||||||||
\(936\) | 20.4133 | 0.667229 | ||||||||
\(937\) | −30.9791 | −1.01204 | −0.506021 | − | 0.862521i | \(-0.668884\pi\) | ||||
−0.506021 | + | 0.862521i | \(0.668884\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.38237 | −0.110379 | ||||||||
\(940\) | −26.7555 | −0.872669 | ||||||||
\(941\) | −44.7355 | −1.45834 | −0.729168 | − | 0.684335i | \(-0.760093\pi\) | ||||
−0.729168 | + | 0.684335i | \(0.760093\pi\) | |||||||
\(942\) | 38.3748 | 1.25032 | ||||||||
\(943\) | −8.16729 | −0.265964 | ||||||||
\(944\) | −38.6078 | −1.25658 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 115.049 | 3.74058 | ||||||||
\(947\) | 39.8424 | 1.29470 | 0.647352 | − | 0.762192i | \(-0.275877\pi\) | ||||
0.647352 | + | 0.762192i | \(0.275877\pi\) | |||||||
\(948\) | 57.0024 | 1.85135 | ||||||||
\(949\) | 31.4604 | 1.02125 | ||||||||
\(950\) | 40.9312 | 1.32798 | ||||||||
\(951\) | −29.2238 | −0.947647 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.16051 | 0.296738 | 0.148369 | − | 0.988932i | \(-0.452598\pi\) | ||||
0.148369 | + | 0.988932i | \(0.452598\pi\) | |||||||
\(954\) | −1.91825 | −0.0621057 | ||||||||
\(955\) | −18.9383 | −0.612829 | ||||||||
\(956\) | 2.88046 | 0.0931607 | ||||||||
\(957\) | −1.95779 | −0.0632864 | ||||||||
\(958\) | 73.8709 | 2.38666 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 8.43537 | 0.272250 | ||||||||
\(961\) | −30.7904 | −0.993240 | ||||||||
\(962\) | −36.4036 | −1.17370 | ||||||||
\(963\) | −5.89917 | −0.190098 | ||||||||
\(964\) | 35.0565 | 1.12909 | ||||||||
\(965\) | −10.5141 | −0.338462 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.43523 | 0.110469 | 0.0552347 | − | 0.998473i | \(-0.482409\pi\) | ||||
0.0552347 | + | 0.998473i | \(0.482409\pi\) | |||||||
\(968\) | −88.9407 | −2.85866 | ||||||||
\(969\) | 43.6556 | 1.40242 | ||||||||
\(970\) | −0.798424 | −0.0256359 | ||||||||
\(971\) | −45.3254 | −1.45456 | −0.727281 | − | 0.686340i | \(-0.759216\pi\) | ||||
−0.727281 | + | 0.686340i | \(0.759216\pi\) | |||||||
\(972\) | 41.6687 | 1.33653 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −41.4753 | −1.32895 | ||||||||
\(975\) | −21.0411 | −0.673855 | ||||||||
\(976\) | −21.5916 | −0.691131 | ||||||||
\(977\) | 19.8006 | 0.633476 | 0.316738 | − | 0.948513i | \(-0.397412\pi\) | ||||
0.316738 | + | 0.948513i | \(0.397412\pi\) | |||||||
\(978\) | −49.8755 | −1.59484 | ||||||||
\(979\) | −15.8571 | −0.506794 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.09930 | 0.130881 | ||||||||
\(982\) | 67.2379 | 2.14565 | ||||||||
\(983\) | −40.2660 | −1.28429 | −0.642143 | − | 0.766585i | \(-0.721955\pi\) | ||||
−0.642143 | + | 0.766585i | \(0.721955\pi\) | |||||||
\(984\) | −7.54721 | −0.240596 | ||||||||
\(985\) | 7.88238 | 0.251154 | ||||||||
\(986\) | −4.89256 | −0.155811 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 64.9404 | 2.06603 | ||||||||
\(989\) | −72.0646 | −2.29152 | ||||||||
\(990\) | 13.4104 | 0.426210 | ||||||||
\(991\) | −51.9256 | −1.64947 | −0.824736 | − | 0.565518i | \(-0.808676\pi\) | ||||
−0.824736 | + | 0.565518i | \(0.808676\pi\) | |||||||
\(992\) | −0.746409 | −0.0236985 | ||||||||
\(993\) | 11.8488 | 0.376010 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.1560 | −0.480477 | ||||||||
\(996\) | 56.7892 | 1.79943 | ||||||||
\(997\) | 35.1549 | 1.11337 | 0.556684 | − | 0.830725i | \(-0.312074\pi\) | ||||
0.556684 | + | 0.830725i | \(0.312074\pi\) | |||||||
\(998\) | 71.3705 | 2.25919 | ||||||||
\(999\) | −22.0706 | −0.698284 |
(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 | 2009.2.a.s.1.2 | 17 | ||
7.2 | even | 3 | 287.2.e.d.165.16 | ✓ | 34 | ||
7.4 | even | 3 | 287.2.e.d.247.16 | yes | 34 | ||
7.6 | odd | 2 | 2009.2.a.r.1.2 | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
287.2.e.d.165.16 | ✓ | 34 | 7.2 | even | 3 | ||
287.2.e.d.247.16 | yes | 34 | 7.4 | even | 3 | ||
2009.2.a.r.1.2 | 17 | 7.6 | odd | 2 | |||
2009.2.a.s.1.2 | 17 | 1.1 | even | 1 | trivial |