Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,2,Mod(1,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("74.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.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: | \(0.590892974957\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 74.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.61803 | −0.934172 | −0.467086 | − | 0.884212i | \(-0.654696\pi\) | ||||
−0.467086 | + | 0.884212i | \(0.654696\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.85410 | 1.72361 | 0.861803 | − | 0.507242i | \(-0.169335\pi\) | ||||
0.861803 | + | 0.507242i | \(0.169335\pi\) | |||||||
\(6\) | −1.61803 | −0.660560 | ||||||||
\(7\) | −3.23607 | −1.22312 | −0.611559 | − | 0.791199i | \(-0.709457\pi\) | ||||
−0.611559 | + | 0.791199i | \(0.709457\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.381966 | −0.127322 | ||||||||
\(10\) | 3.85410 | 1.21877 | ||||||||
\(11\) | −1.38197 | −0.416678 | −0.208339 | − | 0.978057i | \(-0.566806\pi\) | ||||
−0.208339 | + | 0.978057i | \(0.566806\pi\) | |||||||
\(12\) | −1.61803 | −0.467086 | ||||||||
\(13\) | −2.85410 | −0.791585 | −0.395793 | − | 0.918340i | \(-0.629530\pi\) | ||||
−0.395793 | + | 0.918340i | \(0.629530\pi\) | |||||||
\(14\) | −3.23607 | −0.864876 | ||||||||
\(15\) | −6.23607 | −1.61015 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.47214 | −1.08465 | −0.542326 | − | 0.840168i | \(-0.682456\pi\) | ||||
−0.542326 | + | 0.840168i | \(0.682456\pi\) | |||||||
\(18\) | −0.381966 | −0.0900303 | ||||||||
\(19\) | 4.47214 | 1.02598 | 0.512989 | − | 0.858395i | \(-0.328538\pi\) | ||||
0.512989 | + | 0.858395i | \(0.328538\pi\) | |||||||
\(20\) | 3.85410 | 0.861803 | ||||||||
\(21\) | 5.23607 | 1.14260 | ||||||||
\(22\) | −1.38197 | −0.294636 | ||||||||
\(23\) | 2.85410 | 0.595121 | 0.297561 | − | 0.954703i | \(-0.403827\pi\) | ||||
0.297561 | + | 0.954703i | \(0.403827\pi\) | |||||||
\(24\) | −1.61803 | −0.330280 | ||||||||
\(25\) | 9.85410 | 1.97082 | ||||||||
\(26\) | −2.85410 | −0.559735 | ||||||||
\(27\) | 5.47214 | 1.05311 | ||||||||
\(28\) | −3.23607 | −0.611559 | ||||||||
\(29\) | −9.32624 | −1.73184 | −0.865919 | − | 0.500183i | \(-0.833266\pi\) | ||||
−0.865919 | + | 0.500183i | \(0.833266\pi\) | |||||||
\(30\) | −6.23607 | −1.13855 | ||||||||
\(31\) | 7.38197 | 1.32584 | 0.662920 | − | 0.748690i | \(-0.269317\pi\) | ||||
0.662920 | + | 0.748690i | \(0.269317\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 2.23607 | 0.389249 | ||||||||
\(34\) | −4.47214 | −0.766965 | ||||||||
\(35\) | −12.4721 | −2.10818 | ||||||||
\(36\) | −0.381966 | −0.0636610 | ||||||||
\(37\) | −1.00000 | −0.164399 | ||||||||
\(38\) | 4.47214 | 0.725476 | ||||||||
\(39\) | 4.61803 | 0.739477 | ||||||||
\(40\) | 3.85410 | 0.609387 | ||||||||
\(41\) | 9.61803 | 1.50208 | 0.751042 | − | 0.660254i | \(-0.229551\pi\) | ||||
0.751042 | + | 0.660254i | \(0.229551\pi\) | |||||||
\(42\) | 5.23607 | 0.807943 | ||||||||
\(43\) | −5.23607 | −0.798493 | −0.399246 | − | 0.916844i | \(-0.630728\pi\) | ||||
−0.399246 | + | 0.916844i | \(0.630728\pi\) | |||||||
\(44\) | −1.38197 | −0.208339 | ||||||||
\(45\) | −1.47214 | −0.219453 | ||||||||
\(46\) | 2.85410 | 0.420814 | ||||||||
\(47\) | −1.23607 | −0.180299 | −0.0901495 | − | 0.995928i | \(-0.528734\pi\) | ||||
−0.0901495 | + | 0.995928i | \(0.528734\pi\) | |||||||
\(48\) | −1.61803 | −0.233543 | ||||||||
\(49\) | 3.47214 | 0.496019 | ||||||||
\(50\) | 9.85410 | 1.39358 | ||||||||
\(51\) | 7.23607 | 1.01325 | ||||||||
\(52\) | −2.85410 | −0.395793 | ||||||||
\(53\) | 0.472136 | 0.0648529 | 0.0324264 | − | 0.999474i | \(-0.489677\pi\) | ||||
0.0324264 | + | 0.999474i | \(0.489677\pi\) | |||||||
\(54\) | 5.47214 | 0.744663 | ||||||||
\(55\) | −5.32624 | −0.718190 | ||||||||
\(56\) | −3.23607 | −0.432438 | ||||||||
\(57\) | −7.23607 | −0.958441 | ||||||||
\(58\) | −9.32624 | −1.22460 | ||||||||
\(59\) | −4.76393 | −0.620211 | −0.310106 | − | 0.950702i | \(-0.600364\pi\) | ||||
−0.310106 | + | 0.950702i | \(0.600364\pi\) | |||||||
\(60\) | −6.23607 | −0.805073 | ||||||||
\(61\) | 10.6180 | 1.35950 | 0.679750 | − | 0.733444i | \(-0.262088\pi\) | ||||
0.679750 | + | 0.733444i | \(0.262088\pi\) | |||||||
\(62\) | 7.38197 | 0.937511 | ||||||||
\(63\) | 1.23607 | 0.155730 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −11.0000 | −1.36438 | ||||||||
\(66\) | 2.23607 | 0.275241 | ||||||||
\(67\) | 1.09017 | 0.133185 | 0.0665927 | − | 0.997780i | \(-0.478787\pi\) | ||||
0.0665927 | + | 0.997780i | \(0.478787\pi\) | |||||||
\(68\) | −4.47214 | −0.542326 | ||||||||
\(69\) | −4.61803 | −0.555946 | ||||||||
\(70\) | −12.4721 | −1.49071 | ||||||||
\(71\) | 2.94427 | 0.349421 | 0.174710 | − | 0.984620i | \(-0.444101\pi\) | ||||
0.174710 | + | 0.984620i | \(0.444101\pi\) | |||||||
\(72\) | −0.381966 | −0.0450151 | ||||||||
\(73\) | 7.09017 | 0.829842 | 0.414921 | − | 0.909858i | \(-0.363809\pi\) | ||||
0.414921 | + | 0.909858i | \(0.363809\pi\) | |||||||
\(74\) | −1.00000 | −0.116248 | ||||||||
\(75\) | −15.9443 | −1.84109 | ||||||||
\(76\) | 4.47214 | 0.512989 | ||||||||
\(77\) | 4.47214 | 0.509647 | ||||||||
\(78\) | 4.61803 | 0.522889 | ||||||||
\(79\) | −8.56231 | −0.963335 | −0.481667 | − | 0.876354i | \(-0.659969\pi\) | ||||
−0.481667 | + | 0.876354i | \(0.659969\pi\) | |||||||
\(80\) | 3.85410 | 0.430902 | ||||||||
\(81\) | −7.70820 | −0.856467 | ||||||||
\(82\) | 9.61803 | 1.06213 | ||||||||
\(83\) | −14.4721 | −1.58852 | −0.794262 | − | 0.607576i | \(-0.792142\pi\) | ||||
−0.794262 | + | 0.607576i | \(0.792142\pi\) | |||||||
\(84\) | 5.23607 | 0.571302 | ||||||||
\(85\) | −17.2361 | −1.86951 | ||||||||
\(86\) | −5.23607 | −0.564620 | ||||||||
\(87\) | 15.0902 | 1.61784 | ||||||||
\(88\) | −1.38197 | −0.147318 | ||||||||
\(89\) | −1.52786 | −0.161953 | −0.0809766 | − | 0.996716i | \(-0.525804\pi\) | ||||
−0.0809766 | + | 0.996716i | \(0.525804\pi\) | |||||||
\(90\) | −1.47214 | −0.155177 | ||||||||
\(91\) | 9.23607 | 0.968203 | ||||||||
\(92\) | 2.85410 | 0.297561 | ||||||||
\(93\) | −11.9443 | −1.23856 | ||||||||
\(94\) | −1.23607 | −0.127491 | ||||||||
\(95\) | 17.2361 | 1.76838 | ||||||||
\(96\) | −1.61803 | −0.165140 | ||||||||
\(97\) | −0.472136 | −0.0479381 | −0.0239691 | − | 0.999713i | \(-0.507630\pi\) | ||||
−0.0239691 | + | 0.999713i | \(0.507630\pi\) | |||||||
\(98\) | 3.47214 | 0.350739 | ||||||||
\(99\) | 0.527864 | 0.0530523 | ||||||||
\(100\) | 9.85410 | 0.985410 | ||||||||
\(101\) | 3.52786 | 0.351036 | 0.175518 | − | 0.984476i | \(-0.443840\pi\) | ||||
0.175518 | + | 0.984476i | \(0.443840\pi\) | |||||||
\(102\) | 7.23607 | 0.716477 | ||||||||
\(103\) | 17.2705 | 1.70171 | 0.850857 | − | 0.525397i | \(-0.176083\pi\) | ||||
0.850857 | + | 0.525397i | \(0.176083\pi\) | |||||||
\(104\) | −2.85410 | −0.279868 | ||||||||
\(105\) | 20.1803 | 1.96940 | ||||||||
\(106\) | 0.472136 | 0.0458579 | ||||||||
\(107\) | −7.32624 | −0.708254 | −0.354127 | − | 0.935197i | \(-0.615222\pi\) | ||||
−0.354127 | + | 0.935197i | \(0.615222\pi\) | |||||||
\(108\) | 5.47214 | 0.526557 | ||||||||
\(109\) | 2.94427 | 0.282010 | 0.141005 | − | 0.990009i | \(-0.454967\pi\) | ||||
0.141005 | + | 0.990009i | \(0.454967\pi\) | |||||||
\(110\) | −5.32624 | −0.507837 | ||||||||
\(111\) | 1.61803 | 0.153577 | ||||||||
\(112\) | −3.23607 | −0.305780 | ||||||||
\(113\) | −6.94427 | −0.653262 | −0.326631 | − | 0.945152i | \(-0.605913\pi\) | ||||
−0.326631 | + | 0.945152i | \(0.605913\pi\) | |||||||
\(114\) | −7.23607 | −0.677720 | ||||||||
\(115\) | 11.0000 | 1.02576 | ||||||||
\(116\) | −9.32624 | −0.865919 | ||||||||
\(117\) | 1.09017 | 0.100786 | ||||||||
\(118\) | −4.76393 | −0.438555 | ||||||||
\(119\) | 14.4721 | 1.32666 | ||||||||
\(120\) | −6.23607 | −0.569273 | ||||||||
\(121\) | −9.09017 | −0.826379 | ||||||||
\(122\) | 10.6180 | 0.961312 | ||||||||
\(123\) | −15.5623 | −1.40321 | ||||||||
\(124\) | 7.38197 | 0.662920 | ||||||||
\(125\) | 18.7082 | 1.67331 | ||||||||
\(126\) | 1.23607 | 0.110118 | ||||||||
\(127\) | −8.47214 | −0.751780 | −0.375890 | − | 0.926664i | \(-0.622663\pi\) | ||||
−0.375890 | + | 0.926664i | \(0.622663\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 8.47214 | 0.745930 | ||||||||
\(130\) | −11.0000 | −0.964764 | ||||||||
\(131\) | −22.6525 | −1.97916 | −0.989578 | − | 0.143998i | \(-0.954004\pi\) | ||||
−0.989578 | + | 0.143998i | \(0.954004\pi\) | |||||||
\(132\) | 2.23607 | 0.194625 | ||||||||
\(133\) | −14.4721 | −1.25489 | ||||||||
\(134\) | 1.09017 | 0.0941763 | ||||||||
\(135\) | 21.0902 | 1.81515 | ||||||||
\(136\) | −4.47214 | −0.383482 | ||||||||
\(137\) | 3.67376 | 0.313871 | 0.156935 | − | 0.987609i | \(-0.449839\pi\) | ||||
0.156935 | + | 0.987609i | \(0.449839\pi\) | |||||||
\(138\) | −4.61803 | −0.393113 | ||||||||
\(139\) | 4.85410 | 0.411720 | 0.205860 | − | 0.978581i | \(-0.434001\pi\) | ||||
0.205860 | + | 0.978581i | \(0.434001\pi\) | |||||||
\(140\) | −12.4721 | −1.05409 | ||||||||
\(141\) | 2.00000 | 0.168430 | ||||||||
\(142\) | 2.94427 | 0.247078 | ||||||||
\(143\) | 3.94427 | 0.329837 | ||||||||
\(144\) | −0.381966 | −0.0318305 | ||||||||
\(145\) | −35.9443 | −2.98501 | ||||||||
\(146\) | 7.09017 | 0.586787 | ||||||||
\(147\) | −5.61803 | −0.463368 | ||||||||
\(148\) | −1.00000 | −0.0821995 | ||||||||
\(149\) | 16.1803 | 1.32555 | 0.662773 | − | 0.748821i | \(-0.269380\pi\) | ||||
0.662773 | + | 0.748821i | \(0.269380\pi\) | |||||||
\(150\) | −15.9443 | −1.30184 | ||||||||
\(151\) | 4.29180 | 0.349261 | 0.174631 | − | 0.984634i | \(-0.444127\pi\) | ||||
0.174631 | + | 0.984634i | \(0.444127\pi\) | |||||||
\(152\) | 4.47214 | 0.362738 | ||||||||
\(153\) | 1.70820 | 0.138100 | ||||||||
\(154\) | 4.47214 | 0.360375 | ||||||||
\(155\) | 28.4508 | 2.28523 | ||||||||
\(156\) | 4.61803 | 0.369739 | ||||||||
\(157\) | −16.4721 | −1.31462 | −0.657310 | − | 0.753620i | \(-0.728306\pi\) | ||||
−0.657310 | + | 0.753620i | \(0.728306\pi\) | |||||||
\(158\) | −8.56231 | −0.681180 | ||||||||
\(159\) | −0.763932 | −0.0605838 | ||||||||
\(160\) | 3.85410 | 0.304694 | ||||||||
\(161\) | −9.23607 | −0.727904 | ||||||||
\(162\) | −7.70820 | −0.605614 | ||||||||
\(163\) | −3.52786 | −0.276324 | −0.138162 | − | 0.990410i | \(-0.544119\pi\) | ||||
−0.138162 | + | 0.990410i | \(0.544119\pi\) | |||||||
\(164\) | 9.61803 | 0.751042 | ||||||||
\(165\) | 8.61803 | 0.670913 | ||||||||
\(166\) | −14.4721 | −1.12326 | ||||||||
\(167\) | 13.8541 | 1.07206 | 0.536031 | − | 0.844198i | \(-0.319923\pi\) | ||||
0.536031 | + | 0.844198i | \(0.319923\pi\) | |||||||
\(168\) | 5.23607 | 0.403971 | ||||||||
\(169\) | −4.85410 | −0.373392 | ||||||||
\(170\) | −17.2361 | −1.32195 | ||||||||
\(171\) | −1.70820 | −0.130630 | ||||||||
\(172\) | −5.23607 | −0.399246 | ||||||||
\(173\) | −0.472136 | −0.0358958 | −0.0179479 | − | 0.999839i | \(-0.505713\pi\) | ||||
−0.0179479 | + | 0.999839i | \(0.505713\pi\) | |||||||
\(174\) | 15.0902 | 1.14398 | ||||||||
\(175\) | −31.8885 | −2.41055 | ||||||||
\(176\) | −1.38197 | −0.104170 | ||||||||
\(177\) | 7.70820 | 0.579384 | ||||||||
\(178\) | −1.52786 | −0.114518 | ||||||||
\(179\) | −12.6525 | −0.945690 | −0.472845 | − | 0.881146i | \(-0.656773\pi\) | ||||
−0.472845 | + | 0.881146i | \(0.656773\pi\) | |||||||
\(180\) | −1.47214 | −0.109727 | ||||||||
\(181\) | 14.4721 | 1.07571 | 0.537853 | − | 0.843039i | \(-0.319236\pi\) | ||||
0.537853 | + | 0.843039i | \(0.319236\pi\) | |||||||
\(182\) | 9.23607 | 0.684623 | ||||||||
\(183\) | −17.1803 | −1.27001 | ||||||||
\(184\) | 2.85410 | 0.210407 | ||||||||
\(185\) | −3.85410 | −0.283359 | ||||||||
\(186\) | −11.9443 | −0.875797 | ||||||||
\(187\) | 6.18034 | 0.451951 | ||||||||
\(188\) | −1.23607 | −0.0901495 | ||||||||
\(189\) | −17.7082 | −1.28808 | ||||||||
\(190\) | 17.2361 | 1.25044 | ||||||||
\(191\) | −7.09017 | −0.513027 | −0.256513 | − | 0.966541i | \(-0.582574\pi\) | ||||
−0.256513 | + | 0.966541i | \(0.582574\pi\) | |||||||
\(192\) | −1.61803 | −0.116772 | ||||||||
\(193\) | 4.00000 | 0.287926 | 0.143963 | − | 0.989583i | \(-0.454015\pi\) | ||||
0.143963 | + | 0.989583i | \(0.454015\pi\) | |||||||
\(194\) | −0.472136 | −0.0338974 | ||||||||
\(195\) | 17.7984 | 1.27457 | ||||||||
\(196\) | 3.47214 | 0.248010 | ||||||||
\(197\) | −7.52786 | −0.536338 | −0.268169 | − | 0.963372i | \(-0.586419\pi\) | ||||
−0.268169 | + | 0.963372i | \(0.586419\pi\) | |||||||
\(198\) | 0.527864 | 0.0375137 | ||||||||
\(199\) | 3.05573 | 0.216615 | 0.108307 | − | 0.994117i | \(-0.465457\pi\) | ||||
0.108307 | + | 0.994117i | \(0.465457\pi\) | |||||||
\(200\) | 9.85410 | 0.696790 | ||||||||
\(201\) | −1.76393 | −0.124418 | ||||||||
\(202\) | 3.52786 | 0.248220 | ||||||||
\(203\) | 30.1803 | 2.11824 | ||||||||
\(204\) | 7.23607 | 0.506626 | ||||||||
\(205\) | 37.0689 | 2.58900 | ||||||||
\(206\) | 17.2705 | 1.20329 | ||||||||
\(207\) | −1.09017 | −0.0757720 | ||||||||
\(208\) | −2.85410 | −0.197896 | ||||||||
\(209\) | −6.18034 | −0.427503 | ||||||||
\(210\) | 20.1803 | 1.39258 | ||||||||
\(211\) | 11.2705 | 0.775894 | 0.387947 | − | 0.921682i | \(-0.373184\pi\) | ||||
0.387947 | + | 0.921682i | \(0.373184\pi\) | |||||||
\(212\) | 0.472136 | 0.0324264 | ||||||||
\(213\) | −4.76393 | −0.326419 | ||||||||
\(214\) | −7.32624 | −0.500811 | ||||||||
\(215\) | −20.1803 | −1.37629 | ||||||||
\(216\) | 5.47214 | 0.372332 | ||||||||
\(217\) | −23.8885 | −1.62166 | ||||||||
\(218\) | 2.94427 | 0.199411 | ||||||||
\(219\) | −11.4721 | −0.775215 | ||||||||
\(220\) | −5.32624 | −0.359095 | ||||||||
\(221\) | 12.7639 | 0.858595 | ||||||||
\(222\) | 1.61803 | 0.108595 | ||||||||
\(223\) | 14.1803 | 0.949586 | 0.474793 | − | 0.880098i | \(-0.342523\pi\) | ||||
0.474793 | + | 0.880098i | \(0.342523\pi\) | |||||||
\(224\) | −3.23607 | −0.216219 | ||||||||
\(225\) | −3.76393 | −0.250929 | ||||||||
\(226\) | −6.94427 | −0.461926 | ||||||||
\(227\) | −4.29180 | −0.284857 | −0.142428 | − | 0.989805i | \(-0.545491\pi\) | ||||
−0.142428 | + | 0.989805i | \(0.545491\pi\) | |||||||
\(228\) | −7.23607 | −0.479220 | ||||||||
\(229\) | −23.1246 | −1.52812 | −0.764059 | − | 0.645147i | \(-0.776796\pi\) | ||||
−0.764059 | + | 0.645147i | \(0.776796\pi\) | |||||||
\(230\) | 11.0000 | 0.725319 | ||||||||
\(231\) | −7.23607 | −0.476098 | ||||||||
\(232\) | −9.32624 | −0.612298 | ||||||||
\(233\) | −6.56231 | −0.429911 | −0.214955 | − | 0.976624i | \(-0.568961\pi\) | ||||
−0.214955 | + | 0.976624i | \(0.568961\pi\) | |||||||
\(234\) | 1.09017 | 0.0712666 | ||||||||
\(235\) | −4.76393 | −0.310765 | ||||||||
\(236\) | −4.76393 | −0.310106 | ||||||||
\(237\) | 13.8541 | 0.899921 | ||||||||
\(238\) | 14.4721 | 0.938089 | ||||||||
\(239\) | 9.85410 | 0.637409 | 0.318704 | − | 0.947854i | \(-0.396752\pi\) | ||||
0.318704 | + | 0.947854i | \(0.396752\pi\) | |||||||
\(240\) | −6.23607 | −0.402536 | ||||||||
\(241\) | −1.52786 | −0.0984184 | −0.0492092 | − | 0.998788i | \(-0.515670\pi\) | ||||
−0.0492092 | + | 0.998788i | \(0.515670\pi\) | |||||||
\(242\) | −9.09017 | −0.584338 | ||||||||
\(243\) | −3.94427 | −0.253025 | ||||||||
\(244\) | 10.6180 | 0.679750 | ||||||||
\(245\) | 13.3820 | 0.854942 | ||||||||
\(246\) | −15.5623 | −0.992216 | ||||||||
\(247\) | −12.7639 | −0.812150 | ||||||||
\(248\) | 7.38197 | 0.468755 | ||||||||
\(249\) | 23.4164 | 1.48395 | ||||||||
\(250\) | 18.7082 | 1.18321 | ||||||||
\(251\) | −20.9443 | −1.32199 | −0.660995 | − | 0.750390i | \(-0.729866\pi\) | ||||
−0.660995 | + | 0.750390i | \(0.729866\pi\) | |||||||
\(252\) | 1.23607 | 0.0778650 | ||||||||
\(253\) | −3.94427 | −0.247974 | ||||||||
\(254\) | −8.47214 | −0.531589 | ||||||||
\(255\) | 27.8885 | 1.74645 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −1.05573 | −0.0658545 | −0.0329273 | − | 0.999458i | \(-0.510483\pi\) | ||||
−0.0329273 | + | 0.999458i | \(0.510483\pi\) | |||||||
\(258\) | 8.47214 | 0.527452 | ||||||||
\(259\) | 3.23607 | 0.201079 | ||||||||
\(260\) | −11.0000 | −0.682191 | ||||||||
\(261\) | 3.56231 | 0.220501 | ||||||||
\(262\) | −22.6525 | −1.39947 | ||||||||
\(263\) | −13.2361 | −0.816171 | −0.408085 | − | 0.912944i | \(-0.633803\pi\) | ||||
−0.408085 | + | 0.912944i | \(0.633803\pi\) | |||||||
\(264\) | 2.23607 | 0.137620 | ||||||||
\(265\) | 1.81966 | 0.111781 | ||||||||
\(266\) | −14.4721 | −0.887344 | ||||||||
\(267\) | 2.47214 | 0.151292 | ||||||||
\(268\) | 1.09017 | 0.0665927 | ||||||||
\(269\) | 4.00000 | 0.243884 | 0.121942 | − | 0.992537i | \(-0.461088\pi\) | ||||
0.121942 | + | 0.992537i | \(0.461088\pi\) | |||||||
\(270\) | 21.0902 | 1.28351 | ||||||||
\(271\) | 12.9443 | 0.786309 | 0.393154 | − | 0.919473i | \(-0.371384\pi\) | ||||
0.393154 | + | 0.919473i | \(0.371384\pi\) | |||||||
\(272\) | −4.47214 | −0.271163 | ||||||||
\(273\) | −14.9443 | −0.904468 | ||||||||
\(274\) | 3.67376 | 0.221940 | ||||||||
\(275\) | −13.6180 | −0.821198 | ||||||||
\(276\) | −4.61803 | −0.277973 | ||||||||
\(277\) | 16.7984 | 1.00932 | 0.504658 | − | 0.863319i | \(-0.331619\pi\) | ||||
0.504658 | + | 0.863319i | \(0.331619\pi\) | |||||||
\(278\) | 4.85410 | 0.291130 | ||||||||
\(279\) | −2.81966 | −0.168809 | ||||||||
\(280\) | −12.4721 | −0.745353 | ||||||||
\(281\) | 29.8885 | 1.78300 | 0.891501 | − | 0.453020i | \(-0.149653\pi\) | ||||
0.891501 | + | 0.453020i | \(0.149653\pi\) | |||||||
\(282\) | 2.00000 | 0.119098 | ||||||||
\(283\) | 6.76393 | 0.402074 | 0.201037 | − | 0.979584i | \(-0.435569\pi\) | ||||
0.201037 | + | 0.979584i | \(0.435569\pi\) | |||||||
\(284\) | 2.94427 | 0.174710 | ||||||||
\(285\) | −27.8885 | −1.65197 | ||||||||
\(286\) | 3.94427 | 0.233230 | ||||||||
\(287\) | −31.1246 | −1.83723 | ||||||||
\(288\) | −0.381966 | −0.0225076 | ||||||||
\(289\) | 3.00000 | 0.176471 | ||||||||
\(290\) | −35.9443 | −2.11072 | ||||||||
\(291\) | 0.763932 | 0.0447825 | ||||||||
\(292\) | 7.09017 | 0.414921 | ||||||||
\(293\) | −12.6525 | −0.739166 | −0.369583 | − | 0.929198i | \(-0.620499\pi\) | ||||
−0.369583 | + | 0.929198i | \(0.620499\pi\) | |||||||
\(294\) | −5.61803 | −0.327650 | ||||||||
\(295\) | −18.3607 | −1.06900 | ||||||||
\(296\) | −1.00000 | −0.0581238 | ||||||||
\(297\) | −7.56231 | −0.438809 | ||||||||
\(298\) | 16.1803 | 0.937302 | ||||||||
\(299\) | −8.14590 | −0.471089 | ||||||||
\(300\) | −15.9443 | −0.920543 | ||||||||
\(301\) | 16.9443 | 0.976652 | ||||||||
\(302\) | 4.29180 | 0.246965 | ||||||||
\(303\) | −5.70820 | −0.327928 | ||||||||
\(304\) | 4.47214 | 0.256495 | ||||||||
\(305\) | 40.9230 | 2.34324 | ||||||||
\(306\) | 1.70820 | 0.0976515 | ||||||||
\(307\) | −12.8541 | −0.733622 | −0.366811 | − | 0.930295i | \(-0.619550\pi\) | ||||
−0.366811 | + | 0.930295i | \(0.619550\pi\) | |||||||
\(308\) | 4.47214 | 0.254824 | ||||||||
\(309\) | −27.9443 | −1.58969 | ||||||||
\(310\) | 28.4508 | 1.61590 | ||||||||
\(311\) | −27.0344 | −1.53298 | −0.766491 | − | 0.642255i | \(-0.777999\pi\) | ||||
−0.766491 | + | 0.642255i | \(0.777999\pi\) | |||||||
\(312\) | 4.61803 | 0.261445 | ||||||||
\(313\) | 28.1803 | 1.59285 | 0.796423 | − | 0.604739i | \(-0.206723\pi\) | ||||
0.796423 | + | 0.604739i | \(0.206723\pi\) | |||||||
\(314\) | −16.4721 | −0.929576 | ||||||||
\(315\) | 4.76393 | 0.268417 | ||||||||
\(316\) | −8.56231 | −0.481667 | ||||||||
\(317\) | 20.9443 | 1.17635 | 0.588174 | − | 0.808735i | \(-0.299847\pi\) | ||||
0.588174 | + | 0.808735i | \(0.299847\pi\) | |||||||
\(318\) | −0.763932 | −0.0428392 | ||||||||
\(319\) | 12.8885 | 0.721620 | ||||||||
\(320\) | 3.85410 | 0.215451 | ||||||||
\(321\) | 11.8541 | 0.661631 | ||||||||
\(322\) | −9.23607 | −0.514706 | ||||||||
\(323\) | −20.0000 | −1.11283 | ||||||||
\(324\) | −7.70820 | −0.428234 | ||||||||
\(325\) | −28.1246 | −1.56007 | ||||||||
\(326\) | −3.52786 | −0.195390 | ||||||||
\(327\) | −4.76393 | −0.263446 | ||||||||
\(328\) | 9.61803 | 0.531067 | ||||||||
\(329\) | 4.00000 | 0.220527 | ||||||||
\(330\) | 8.61803 | 0.474407 | ||||||||
\(331\) | 28.0000 | 1.53902 | 0.769510 | − | 0.638635i | \(-0.220501\pi\) | ||||
0.769510 | + | 0.638635i | \(0.220501\pi\) | |||||||
\(332\) | −14.4721 | −0.794262 | ||||||||
\(333\) | 0.381966 | 0.0209316 | ||||||||
\(334\) | 13.8541 | 0.758063 | ||||||||
\(335\) | 4.20163 | 0.229559 | ||||||||
\(336\) | 5.23607 | 0.285651 | ||||||||
\(337\) | 12.0344 | 0.655558 | 0.327779 | − | 0.944754i | \(-0.393700\pi\) | ||||
0.327779 | + | 0.944754i | \(0.393700\pi\) | |||||||
\(338\) | −4.85410 | −0.264028 | ||||||||
\(339\) | 11.2361 | 0.610259 | ||||||||
\(340\) | −17.2361 | −0.934757 | ||||||||
\(341\) | −10.2016 | −0.552449 | ||||||||
\(342\) | −1.70820 | −0.0923691 | ||||||||
\(343\) | 11.4164 | 0.616428 | ||||||||
\(344\) | −5.23607 | −0.282310 | ||||||||
\(345\) | −17.7984 | −0.958232 | ||||||||
\(346\) | −0.472136 | −0.0253822 | ||||||||
\(347\) | 17.2361 | 0.925281 | 0.462640 | − | 0.886546i | \(-0.346902\pi\) | ||||
0.462640 | + | 0.886546i | \(0.346902\pi\) | |||||||
\(348\) | 15.0902 | 0.808918 | ||||||||
\(349\) | −10.1803 | −0.544941 | −0.272471 | − | 0.962164i | \(-0.587841\pi\) | ||||
−0.272471 | + | 0.962164i | \(0.587841\pi\) | |||||||
\(350\) | −31.8885 | −1.70451 | ||||||||
\(351\) | −15.6180 | −0.833629 | ||||||||
\(352\) | −1.38197 | −0.0736590 | ||||||||
\(353\) | 16.2918 | 0.867125 | 0.433562 | − | 0.901124i | \(-0.357256\pi\) | ||||
0.433562 | + | 0.901124i | \(0.357256\pi\) | |||||||
\(354\) | 7.70820 | 0.409686 | ||||||||
\(355\) | 11.3475 | 0.602264 | ||||||||
\(356\) | −1.52786 | −0.0809766 | ||||||||
\(357\) | −23.4164 | −1.23933 | ||||||||
\(358\) | −12.6525 | −0.668704 | ||||||||
\(359\) | −4.47214 | −0.236030 | −0.118015 | − | 0.993012i | \(-0.537653\pi\) | ||||
−0.118015 | + | 0.993012i | \(0.537653\pi\) | |||||||
\(360\) | −1.47214 | −0.0775884 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 14.4721 | 0.760639 | ||||||||
\(363\) | 14.7082 | 0.771980 | ||||||||
\(364\) | 9.23607 | 0.484102 | ||||||||
\(365\) | 27.3262 | 1.43032 | ||||||||
\(366\) | −17.1803 | −0.898031 | ||||||||
\(367\) | 13.1246 | 0.685099 | 0.342550 | − | 0.939500i | \(-0.388710\pi\) | ||||
0.342550 | + | 0.939500i | \(0.388710\pi\) | |||||||
\(368\) | 2.85410 | 0.148780 | ||||||||
\(369\) | −3.67376 | −0.191248 | ||||||||
\(370\) | −3.85410 | −0.200365 | ||||||||
\(371\) | −1.52786 | −0.0793227 | ||||||||
\(372\) | −11.9443 | −0.619282 | ||||||||
\(373\) | 27.7082 | 1.43468 | 0.717338 | − | 0.696725i | \(-0.245360\pi\) | ||||
0.717338 | + | 0.696725i | \(0.245360\pi\) | |||||||
\(374\) | 6.18034 | 0.319578 | ||||||||
\(375\) | −30.2705 | −1.56316 | ||||||||
\(376\) | −1.23607 | −0.0637453 | ||||||||
\(377\) | 26.6180 | 1.37090 | ||||||||
\(378\) | −17.7082 | −0.910812 | ||||||||
\(379\) | 28.0902 | 1.44290 | 0.721448 | − | 0.692469i | \(-0.243477\pi\) | ||||
0.721448 | + | 0.692469i | \(0.243477\pi\) | |||||||
\(380\) | 17.2361 | 0.884192 | ||||||||
\(381\) | 13.7082 | 0.702293 | ||||||||
\(382\) | −7.09017 | −0.362765 | ||||||||
\(383\) | 17.8885 | 0.914062 | 0.457031 | − | 0.889451i | \(-0.348913\pi\) | ||||
0.457031 | + | 0.889451i | \(0.348913\pi\) | |||||||
\(384\) | −1.61803 | −0.0825700 | ||||||||
\(385\) | 17.2361 | 0.878431 | ||||||||
\(386\) | 4.00000 | 0.203595 | ||||||||
\(387\) | 2.00000 | 0.101666 | ||||||||
\(388\) | −0.472136 | −0.0239691 | ||||||||
\(389\) | −6.85410 | −0.347517 | −0.173758 | − | 0.984788i | \(-0.555591\pi\) | ||||
−0.173758 | + | 0.984788i | \(0.555591\pi\) | |||||||
\(390\) | 17.7984 | 0.901256 | ||||||||
\(391\) | −12.7639 | −0.645500 | ||||||||
\(392\) | 3.47214 | 0.175369 | ||||||||
\(393\) | 36.6525 | 1.84887 | ||||||||
\(394\) | −7.52786 | −0.379248 | ||||||||
\(395\) | −33.0000 | −1.66041 | ||||||||
\(396\) | 0.527864 | 0.0265262 | ||||||||
\(397\) | 20.6525 | 1.03652 | 0.518259 | − | 0.855224i | \(-0.326580\pi\) | ||||
0.518259 | + | 0.855224i | \(0.326580\pi\) | |||||||
\(398\) | 3.05573 | 0.153170 | ||||||||
\(399\) | 23.4164 | 1.17229 | ||||||||
\(400\) | 9.85410 | 0.492705 | ||||||||
\(401\) | −4.76393 | −0.237899 | −0.118950 | − | 0.992900i | \(-0.537953\pi\) | ||||
−0.118950 | + | 0.992900i | \(0.537953\pi\) | |||||||
\(402\) | −1.76393 | −0.0879769 | ||||||||
\(403\) | −21.0689 | −1.04952 | ||||||||
\(404\) | 3.52786 | 0.175518 | ||||||||
\(405\) | −29.7082 | −1.47621 | ||||||||
\(406\) | 30.1803 | 1.49783 | ||||||||
\(407\) | 1.38197 | 0.0685015 | ||||||||
\(408\) | 7.23607 | 0.358239 | ||||||||
\(409\) | −26.1803 | −1.29453 | −0.647267 | − | 0.762263i | \(-0.724088\pi\) | ||||
−0.647267 | + | 0.762263i | \(0.724088\pi\) | |||||||
\(410\) | 37.0689 | 1.83070 | ||||||||
\(411\) | −5.94427 | −0.293209 | ||||||||
\(412\) | 17.2705 | 0.850857 | ||||||||
\(413\) | 15.4164 | 0.758592 | ||||||||
\(414\) | −1.09017 | −0.0535789 | ||||||||
\(415\) | −55.7771 | −2.73799 | ||||||||
\(416\) | −2.85410 | −0.139934 | ||||||||
\(417\) | −7.85410 | −0.384617 | ||||||||
\(418\) | −6.18034 | −0.302290 | ||||||||
\(419\) | −10.5623 | −0.516002 | −0.258001 | − | 0.966145i | \(-0.583064\pi\) | ||||
−0.258001 | + | 0.966145i | \(0.583064\pi\) | |||||||
\(420\) | 20.1803 | 0.984700 | ||||||||
\(421\) | −31.0344 | −1.51253 | −0.756263 | − | 0.654268i | \(-0.772977\pi\) | ||||
−0.756263 | + | 0.654268i | \(0.772977\pi\) | |||||||
\(422\) | 11.2705 | 0.548640 | ||||||||
\(423\) | 0.472136 | 0.0229560 | ||||||||
\(424\) | 0.472136 | 0.0229289 | ||||||||
\(425\) | −44.0689 | −2.13765 | ||||||||
\(426\) | −4.76393 | −0.230813 | ||||||||
\(427\) | −34.3607 | −1.66283 | ||||||||
\(428\) | −7.32624 | −0.354127 | ||||||||
\(429\) | −6.38197 | −0.308124 | ||||||||
\(430\) | −20.1803 | −0.973182 | ||||||||
\(431\) | 12.3607 | 0.595393 | 0.297696 | − | 0.954661i | \(-0.403782\pi\) | ||||
0.297696 | + | 0.954661i | \(0.403782\pi\) | |||||||
\(432\) | 5.47214 | 0.263278 | ||||||||
\(433\) | −20.6738 | −0.993518 | −0.496759 | − | 0.867889i | \(-0.665477\pi\) | ||||
−0.496759 | + | 0.867889i | \(0.665477\pi\) | |||||||
\(434\) | −23.8885 | −1.14669 | ||||||||
\(435\) | 58.1591 | 2.78851 | ||||||||
\(436\) | 2.94427 | 0.141005 | ||||||||
\(437\) | 12.7639 | 0.610582 | ||||||||
\(438\) | −11.4721 | −0.548160 | ||||||||
\(439\) | 7.79837 | 0.372196 | 0.186098 | − | 0.982531i | \(-0.440416\pi\) | ||||
0.186098 | + | 0.982531i | \(0.440416\pi\) | |||||||
\(440\) | −5.32624 | −0.253918 | ||||||||
\(441\) | −1.32624 | −0.0631542 | ||||||||
\(442\) | 12.7639 | 0.607118 | ||||||||
\(443\) | 15.2705 | 0.725524 | 0.362762 | − | 0.931882i | \(-0.381834\pi\) | ||||
0.362762 | + | 0.931882i | \(0.381834\pi\) | |||||||
\(444\) | 1.61803 | 0.0767885 | ||||||||
\(445\) | −5.88854 | −0.279144 | ||||||||
\(446\) | 14.1803 | 0.671459 | ||||||||
\(447\) | −26.1803 | −1.23829 | ||||||||
\(448\) | −3.23607 | −0.152890 | ||||||||
\(449\) | −28.4721 | −1.34368 | −0.671842 | − | 0.740695i | \(-0.734496\pi\) | ||||
−0.671842 | + | 0.740695i | \(0.734496\pi\) | |||||||
\(450\) | −3.76393 | −0.177433 | ||||||||
\(451\) | −13.2918 | −0.625886 | ||||||||
\(452\) | −6.94427 | −0.326631 | ||||||||
\(453\) | −6.94427 | −0.326270 | ||||||||
\(454\) | −4.29180 | −0.201424 | ||||||||
\(455\) | 35.5967 | 1.66880 | ||||||||
\(456\) | −7.23607 | −0.338860 | ||||||||
\(457\) | −24.7639 | −1.15841 | −0.579204 | − | 0.815183i | \(-0.696637\pi\) | ||||
−0.579204 | + | 0.815183i | \(0.696637\pi\) | |||||||
\(458\) | −23.1246 | −1.08054 | ||||||||
\(459\) | −24.4721 | −1.14226 | ||||||||
\(460\) | 11.0000 | 0.512878 | ||||||||
\(461\) | −38.9443 | −1.81382 | −0.906908 | − | 0.421329i | \(-0.861564\pi\) | ||||
−0.906908 | + | 0.421329i | \(0.861564\pi\) | |||||||
\(462\) | −7.23607 | −0.336652 | ||||||||
\(463\) | −4.56231 | −0.212028 | −0.106014 | − | 0.994365i | \(-0.533809\pi\) | ||||
−0.106014 | + | 0.994365i | \(0.533809\pi\) | |||||||
\(464\) | −9.32624 | −0.432960 | ||||||||
\(465\) | −46.0344 | −2.13480 | ||||||||
\(466\) | −6.56231 | −0.303993 | ||||||||
\(467\) | −24.3607 | −1.12728 | −0.563639 | − | 0.826021i | \(-0.690599\pi\) | ||||
−0.563639 | + | 0.826021i | \(0.690599\pi\) | |||||||
\(468\) | 1.09017 | 0.0503931 | ||||||||
\(469\) | −3.52786 | −0.162902 | ||||||||
\(470\) | −4.76393 | −0.219744 | ||||||||
\(471\) | 26.6525 | 1.22808 | ||||||||
\(472\) | −4.76393 | −0.219278 | ||||||||
\(473\) | 7.23607 | 0.332715 | ||||||||
\(474\) | 13.8541 | 0.636340 | ||||||||
\(475\) | 44.0689 | 2.02202 | ||||||||
\(476\) | 14.4721 | 0.663329 | ||||||||
\(477\) | −0.180340 | −0.00825720 | ||||||||
\(478\) | 9.85410 | 0.450716 | ||||||||
\(479\) | 36.5623 | 1.67057 | 0.835287 | − | 0.549814i | \(-0.185301\pi\) | ||||
0.835287 | + | 0.549814i | \(0.185301\pi\) | |||||||
\(480\) | −6.23607 | −0.284636 | ||||||||
\(481\) | 2.85410 | 0.130136 | ||||||||
\(482\) | −1.52786 | −0.0695923 | ||||||||
\(483\) | 14.9443 | 0.679988 | ||||||||
\(484\) | −9.09017 | −0.413190 | ||||||||
\(485\) | −1.81966 | −0.0826265 | ||||||||
\(486\) | −3.94427 | −0.178916 | ||||||||
\(487\) | 37.3050 | 1.69045 | 0.845224 | − | 0.534412i | \(-0.179467\pi\) | ||||
0.845224 | + | 0.534412i | \(0.179467\pi\) | |||||||
\(488\) | 10.6180 | 0.480656 | ||||||||
\(489\) | 5.70820 | 0.258134 | ||||||||
\(490\) | 13.3820 | 0.604536 | ||||||||
\(491\) | −28.4508 | −1.28397 | −0.641984 | − | 0.766718i | \(-0.721889\pi\) | ||||
−0.641984 | + | 0.766718i | \(0.721889\pi\) | |||||||
\(492\) | −15.5623 | −0.701603 | ||||||||
\(493\) | 41.7082 | 1.87844 | ||||||||
\(494\) | −12.7639 | −0.574276 | ||||||||
\(495\) | 2.03444 | 0.0914414 | ||||||||
\(496\) | 7.38197 | 0.331460 | ||||||||
\(497\) | −9.52786 | −0.427383 | ||||||||
\(498\) | 23.4164 | 1.04931 | ||||||||
\(499\) | 10.2918 | 0.460724 | 0.230362 | − | 0.973105i | \(-0.426009\pi\) | ||||
0.230362 | + | 0.973105i | \(0.426009\pi\) | |||||||
\(500\) | 18.7082 | 0.836656 | ||||||||
\(501\) | −22.4164 | −1.00149 | ||||||||
\(502\) | −20.9443 | −0.934789 | ||||||||
\(503\) | 19.0902 | 0.851189 | 0.425594 | − | 0.904914i | \(-0.360065\pi\) | ||||
0.425594 | + | 0.904914i | \(0.360065\pi\) | |||||||
\(504\) | 1.23607 | 0.0550588 | ||||||||
\(505\) | 13.5967 | 0.605047 | ||||||||
\(506\) | −3.94427 | −0.175344 | ||||||||
\(507\) | 7.85410 | 0.348813 | ||||||||
\(508\) | −8.47214 | −0.375890 | ||||||||
\(509\) | −17.7082 | −0.784902 | −0.392451 | − | 0.919773i | \(-0.628373\pi\) | ||||
−0.392451 | + | 0.919773i | \(0.628373\pi\) | |||||||
\(510\) | 27.8885 | 1.23493 | ||||||||
\(511\) | −22.9443 | −1.01499 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 24.4721 | 1.08047 | ||||||||
\(514\) | −1.05573 | −0.0465662 | ||||||||
\(515\) | 66.5623 | 2.93309 | ||||||||
\(516\) | 8.47214 | 0.372965 | ||||||||
\(517\) | 1.70820 | 0.0751267 | ||||||||
\(518\) | 3.23607 | 0.142185 | ||||||||
\(519\) | 0.763932 | 0.0335329 | ||||||||
\(520\) | −11.0000 | −0.482382 | ||||||||
\(521\) | −1.41641 | −0.0620540 | −0.0310270 | − | 0.999519i | \(-0.509878\pi\) | ||||
−0.0310270 | + | 0.999519i | \(0.509878\pi\) | |||||||
\(522\) | 3.56231 | 0.155918 | ||||||||
\(523\) | 11.8197 | 0.516838 | 0.258419 | − | 0.966033i | \(-0.416799\pi\) | ||||
0.258419 | + | 0.966033i | \(0.416799\pi\) | |||||||
\(524\) | −22.6525 | −0.989578 | ||||||||
\(525\) | 51.5967 | 2.25187 | ||||||||
\(526\) | −13.2361 | −0.577120 | ||||||||
\(527\) | −33.0132 | −1.43808 | ||||||||
\(528\) | 2.23607 | 0.0973124 | ||||||||
\(529\) | −14.8541 | −0.645831 | ||||||||
\(530\) | 1.81966 | 0.0790410 | ||||||||
\(531\) | 1.81966 | 0.0789665 | ||||||||
\(532\) | −14.4721 | −0.627447 | ||||||||
\(533\) | −27.4508 | −1.18903 | ||||||||
\(534\) | 2.47214 | 0.106980 | ||||||||
\(535\) | −28.2361 | −1.22075 | ||||||||
\(536\) | 1.09017 | 0.0470882 | ||||||||
\(537\) | 20.4721 | 0.883438 | ||||||||
\(538\) | 4.00000 | 0.172452 | ||||||||
\(539\) | −4.79837 | −0.206681 | ||||||||
\(540\) | 21.0902 | 0.907576 | ||||||||
\(541\) | −10.3262 | −0.443960 | −0.221980 | − | 0.975051i | \(-0.571252\pi\) | ||||
−0.221980 | + | 0.975051i | \(0.571252\pi\) | |||||||
\(542\) | 12.9443 | 0.556004 | ||||||||
\(543\) | −23.4164 | −1.00489 | ||||||||
\(544\) | −4.47214 | −0.191741 | ||||||||
\(545\) | 11.3475 | 0.486075 | ||||||||
\(546\) | −14.9443 | −0.639556 | ||||||||
\(547\) | −16.0689 | −0.687056 | −0.343528 | − | 0.939142i | \(-0.611622\pi\) | ||||
−0.343528 | + | 0.939142i | \(0.611622\pi\) | |||||||
\(548\) | 3.67376 | 0.156935 | ||||||||
\(549\) | −4.05573 | −0.173094 | ||||||||
\(550\) | −13.6180 | −0.580675 | ||||||||
\(551\) | −41.7082 | −1.77683 | ||||||||
\(552\) | −4.61803 | −0.196557 | ||||||||
\(553\) | 27.7082 | 1.17827 | ||||||||
\(554\) | 16.7984 | 0.713695 | ||||||||
\(555\) | 6.23607 | 0.264706 | ||||||||
\(556\) | 4.85410 | 0.205860 | ||||||||
\(557\) | 19.5623 | 0.828882 | 0.414441 | − | 0.910076i | \(-0.363977\pi\) | ||||
0.414441 | + | 0.910076i | \(0.363977\pi\) | |||||||
\(558\) | −2.81966 | −0.119366 | ||||||||
\(559\) | 14.9443 | 0.632075 | ||||||||
\(560\) | −12.4721 | −0.527044 | ||||||||
\(561\) | −10.0000 | −0.422200 | ||||||||
\(562\) | 29.8885 | 1.26077 | ||||||||
\(563\) | 7.88854 | 0.332462 | 0.166231 | − | 0.986087i | \(-0.446840\pi\) | ||||
0.166231 | + | 0.986087i | \(0.446840\pi\) | |||||||
\(564\) | 2.00000 | 0.0842152 | ||||||||
\(565\) | −26.7639 | −1.12597 | ||||||||
\(566\) | 6.76393 | 0.284309 | ||||||||
\(567\) | 24.9443 | 1.04756 | ||||||||
\(568\) | 2.94427 | 0.123539 | ||||||||
\(569\) | 13.8885 | 0.582238 | 0.291119 | − | 0.956687i | \(-0.405972\pi\) | ||||
0.291119 | + | 0.956687i | \(0.405972\pi\) | |||||||
\(570\) | −27.8885 | −1.16812 | ||||||||
\(571\) | −10.5623 | −0.442019 | −0.221009 | − | 0.975272i | \(-0.570935\pi\) | ||||
−0.221009 | + | 0.975272i | \(0.570935\pi\) | |||||||
\(572\) | 3.94427 | 0.164918 | ||||||||
\(573\) | 11.4721 | 0.479255 | ||||||||
\(574\) | −31.1246 | −1.29912 | ||||||||
\(575\) | 28.1246 | 1.17288 | ||||||||
\(576\) | −0.381966 | −0.0159153 | ||||||||
\(577\) | 10.6525 | 0.443468 | 0.221734 | − | 0.975107i | \(-0.428828\pi\) | ||||
0.221734 | + | 0.975107i | \(0.428828\pi\) | |||||||
\(578\) | 3.00000 | 0.124784 | ||||||||
\(579\) | −6.47214 | −0.268973 | ||||||||
\(580\) | −35.9443 | −1.49250 | ||||||||
\(581\) | 46.8328 | 1.94295 | ||||||||
\(582\) | 0.763932 | 0.0316660 | ||||||||
\(583\) | −0.652476 | −0.0270228 | ||||||||
\(584\) | 7.09017 | 0.293393 | ||||||||
\(585\) | 4.20163 | 0.173716 | ||||||||
\(586\) | −12.6525 | −0.522669 | ||||||||
\(587\) | −13.0557 | −0.538868 | −0.269434 | − | 0.963019i | \(-0.586837\pi\) | ||||
−0.269434 | + | 0.963019i | \(0.586837\pi\) | |||||||
\(588\) | −5.61803 | −0.231684 | ||||||||
\(589\) | 33.0132 | 1.36028 | ||||||||
\(590\) | −18.3607 | −0.755897 | ||||||||
\(591\) | 12.1803 | 0.501032 | ||||||||
\(592\) | −1.00000 | −0.0410997 | ||||||||
\(593\) | 17.5623 | 0.721197 | 0.360599 | − | 0.932721i | \(-0.382572\pi\) | ||||
0.360599 | + | 0.932721i | \(0.382572\pi\) | |||||||
\(594\) | −7.56231 | −0.310285 | ||||||||
\(595\) | 55.7771 | 2.28664 | ||||||||
\(596\) | 16.1803 | 0.662773 | ||||||||
\(597\) | −4.94427 | −0.202356 | ||||||||
\(598\) | −8.14590 | −0.333111 | ||||||||
\(599\) | −6.36068 | −0.259890 | −0.129945 | − | 0.991521i | \(-0.541480\pi\) | ||||
−0.129945 | + | 0.991521i | \(0.541480\pi\) | |||||||
\(600\) | −15.9443 | −0.650922 | ||||||||
\(601\) | −24.6869 | −1.00700 | −0.503500 | − | 0.863995i | \(-0.667955\pi\) | ||||
−0.503500 | + | 0.863995i | \(0.667955\pi\) | |||||||
\(602\) | 16.9443 | 0.690597 | ||||||||
\(603\) | −0.416408 | −0.0169574 | ||||||||
\(604\) | 4.29180 | 0.174631 | ||||||||
\(605\) | −35.0344 | −1.42435 | ||||||||
\(606\) | −5.70820 | −0.231880 | ||||||||
\(607\) | 35.0344 | 1.42200 | 0.711002 | − | 0.703190i | \(-0.248242\pi\) | ||||
0.711002 | + | 0.703190i | \(0.248242\pi\) | |||||||
\(608\) | 4.47214 | 0.181369 | ||||||||
\(609\) | −48.8328 | −1.97881 | ||||||||
\(610\) | 40.9230 | 1.65692 | ||||||||
\(611\) | 3.52786 | 0.142722 | ||||||||
\(612\) | 1.70820 | 0.0690501 | ||||||||
\(613\) | −13.8197 | −0.558171 | −0.279085 | − | 0.960266i | \(-0.590031\pi\) | ||||
−0.279085 | + | 0.960266i | \(0.590031\pi\) | |||||||
\(614\) | −12.8541 | −0.518749 | ||||||||
\(615\) | −59.9787 | −2.41858 | ||||||||
\(616\) | 4.47214 | 0.180187 | ||||||||
\(617\) | 0.0901699 | 0.00363011 | 0.00181505 | − | 0.999998i | \(-0.499422\pi\) | ||||
0.00181505 | + | 0.999998i | \(0.499422\pi\) | |||||||
\(618\) | −27.9443 | −1.12408 | ||||||||
\(619\) | −15.2705 | −0.613774 | −0.306887 | − | 0.951746i | \(-0.599287\pi\) | ||||
−0.306887 | + | 0.951746i | \(0.599287\pi\) | |||||||
\(620\) | 28.4508 | 1.14261 | ||||||||
\(621\) | 15.6180 | 0.626730 | ||||||||
\(622\) | −27.0344 | −1.08398 | ||||||||
\(623\) | 4.94427 | 0.198088 | ||||||||
\(624\) | 4.61803 | 0.184869 | ||||||||
\(625\) | 22.8328 | 0.913313 | ||||||||
\(626\) | 28.1803 | 1.12631 | ||||||||
\(627\) | 10.0000 | 0.399362 | ||||||||
\(628\) | −16.4721 | −0.657310 | ||||||||
\(629\) | 4.47214 | 0.178316 | ||||||||
\(630\) | 4.76393 | 0.189800 | ||||||||
\(631\) | −47.3951 | −1.88677 | −0.943385 | − | 0.331700i | \(-0.892378\pi\) | ||||
−0.943385 | + | 0.331700i | \(0.892378\pi\) | |||||||
\(632\) | −8.56231 | −0.340590 | ||||||||
\(633\) | −18.2361 | −0.724819 | ||||||||
\(634\) | 20.9443 | 0.831803 | ||||||||
\(635\) | −32.6525 | −1.29577 | ||||||||
\(636\) | −0.763932 | −0.0302919 | ||||||||
\(637\) | −9.90983 | −0.392642 | ||||||||
\(638\) | 12.8885 | 0.510262 | ||||||||
\(639\) | −1.12461 | −0.0444890 | ||||||||
\(640\) | 3.85410 | 0.152347 | ||||||||
\(641\) | 15.5066 | 0.612473 | 0.306236 | − | 0.951955i | \(-0.400930\pi\) | ||||
0.306236 | + | 0.951955i | \(0.400930\pi\) | |||||||
\(642\) | 11.8541 | 0.467844 | ||||||||
\(643\) | −28.7639 | −1.13434 | −0.567169 | − | 0.823601i | \(-0.691962\pi\) | ||||
−0.567169 | + | 0.823601i | \(0.691962\pi\) | |||||||
\(644\) | −9.23607 | −0.363952 | ||||||||
\(645\) | 32.6525 | 1.28569 | ||||||||
\(646\) | −20.0000 | −0.786889 | ||||||||
\(647\) | 30.0902 | 1.18297 | 0.591483 | − | 0.806317i | \(-0.298543\pi\) | ||||
0.591483 | + | 0.806317i | \(0.298543\pi\) | |||||||
\(648\) | −7.70820 | −0.302807 | ||||||||
\(649\) | 6.58359 | 0.258429 | ||||||||
\(650\) | −28.1246 | −1.10314 | ||||||||
\(651\) | 38.6525 | 1.51491 | ||||||||
\(652\) | −3.52786 | −0.138162 | ||||||||
\(653\) | −38.2705 | −1.49764 | −0.748820 | − | 0.662773i | \(-0.769379\pi\) | ||||
−0.748820 | + | 0.662773i | \(0.769379\pi\) | |||||||
\(654\) | −4.76393 | −0.186284 | ||||||||
\(655\) | −87.3050 | −3.41129 | ||||||||
\(656\) | 9.61803 | 0.375521 | ||||||||
\(657\) | −2.70820 | −0.105657 | ||||||||
\(658\) | 4.00000 | 0.155936 | ||||||||
\(659\) | 40.4508 | 1.57574 | 0.787871 | − | 0.615841i | \(-0.211184\pi\) | ||||
0.787871 | + | 0.615841i | \(0.211184\pi\) | |||||||
\(660\) | 8.61803 | 0.335457 | ||||||||
\(661\) | 17.3262 | 0.673913 | 0.336956 | − | 0.941520i | \(-0.390603\pi\) | ||||
0.336956 | + | 0.941520i | \(0.390603\pi\) | |||||||
\(662\) | 28.0000 | 1.08825 | ||||||||
\(663\) | −20.6525 | −0.802076 | ||||||||
\(664\) | −14.4721 | −0.561628 | ||||||||
\(665\) | −55.7771 | −2.16294 | ||||||||
\(666\) | 0.381966 | 0.0148009 | ||||||||
\(667\) | −26.6180 | −1.03065 | ||||||||
\(668\) | 13.8541 | 0.536031 | ||||||||
\(669\) | −22.9443 | −0.887077 | ||||||||
\(670\) | 4.20163 | 0.162323 | ||||||||
\(671\) | −14.6738 | −0.566474 | ||||||||
\(672\) | 5.23607 | 0.201986 | ||||||||
\(673\) | 11.1459 | 0.429643 | 0.214821 | − | 0.976653i | \(-0.431083\pi\) | ||||
0.214821 | + | 0.976653i | \(0.431083\pi\) | |||||||
\(674\) | 12.0344 | 0.463549 | ||||||||
\(675\) | 53.9230 | 2.07550 | ||||||||
\(676\) | −4.85410 | −0.186696 | ||||||||
\(677\) | 34.6525 | 1.33180 | 0.665901 | − | 0.746040i | \(-0.268047\pi\) | ||||
0.665901 | + | 0.746040i | \(0.268047\pi\) | |||||||
\(678\) | 11.2361 | 0.431519 | ||||||||
\(679\) | 1.52786 | 0.0586340 | ||||||||
\(680\) | −17.2361 | −0.660973 | ||||||||
\(681\) | 6.94427 | 0.266105 | ||||||||
\(682\) | −10.2016 | −0.390640 | ||||||||
\(683\) | −8.58359 | −0.328442 | −0.164221 | − | 0.986424i | \(-0.552511\pi\) | ||||
−0.164221 | + | 0.986424i | \(0.552511\pi\) | |||||||
\(684\) | −1.70820 | −0.0653148 | ||||||||
\(685\) | 14.1591 | 0.540990 | ||||||||
\(686\) | 11.4164 | 0.435880 | ||||||||
\(687\) | 37.4164 | 1.42752 | ||||||||
\(688\) | −5.23607 | −0.199623 | ||||||||
\(689\) | −1.34752 | −0.0513366 | ||||||||
\(690\) | −17.7984 | −0.677573 | ||||||||
\(691\) | 35.7771 | 1.36102 | 0.680512 | − | 0.732737i | \(-0.261757\pi\) | ||||
0.680512 | + | 0.732737i | \(0.261757\pi\) | |||||||
\(692\) | −0.472136 | −0.0179479 | ||||||||
\(693\) | −1.70820 | −0.0648893 | ||||||||
\(694\) | 17.2361 | 0.654272 | ||||||||
\(695\) | 18.7082 | 0.709643 | ||||||||
\(696\) | 15.0902 | 0.571991 | ||||||||
\(697\) | −43.0132 | −1.62924 | ||||||||
\(698\) | −10.1803 | −0.385332 | ||||||||
\(699\) | 10.6180 | 0.401611 | ||||||||
\(700\) | −31.8885 | −1.20527 | ||||||||
\(701\) | −42.9787 | −1.62328 | −0.811642 | − | 0.584155i | \(-0.801426\pi\) | ||||
−0.811642 | + | 0.584155i | \(0.801426\pi\) | |||||||
\(702\) | −15.6180 | −0.589465 | ||||||||
\(703\) | −4.47214 | −0.168670 | ||||||||
\(704\) | −1.38197 | −0.0520848 | ||||||||
\(705\) | 7.70820 | 0.290308 | ||||||||
\(706\) | 16.2918 | 0.613150 | ||||||||
\(707\) | −11.4164 | −0.429358 | ||||||||
\(708\) | 7.70820 | 0.289692 | ||||||||
\(709\) | −8.21478 | −0.308513 | −0.154256 | − | 0.988031i | \(-0.549298\pi\) | ||||
−0.154256 | + | 0.988031i | \(0.549298\pi\) | |||||||
\(710\) | 11.3475 | 0.425865 | ||||||||
\(711\) | 3.27051 | 0.122654 | ||||||||
\(712\) | −1.52786 | −0.0572591 | ||||||||
\(713\) | 21.0689 | 0.789036 | ||||||||
\(714\) | −23.4164 | −0.876337 | ||||||||
\(715\) | 15.2016 | 0.568509 | ||||||||
\(716\) | −12.6525 | −0.472845 | ||||||||
\(717\) | −15.9443 | −0.595450 | ||||||||
\(718\) | −4.47214 | −0.166899 | ||||||||
\(719\) | 27.4164 | 1.02246 | 0.511230 | − | 0.859444i | \(-0.329190\pi\) | ||||
0.511230 | + | 0.859444i | \(0.329190\pi\) | |||||||
\(720\) | −1.47214 | −0.0548633 | ||||||||
\(721\) | −55.8885 | −2.08140 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | 2.47214 | 0.0919397 | ||||||||
\(724\) | 14.4721 | 0.537853 | ||||||||
\(725\) | −91.9017 | −3.41314 | ||||||||
\(726\) | 14.7082 | 0.545873 | ||||||||
\(727\) | −29.8541 | −1.10723 | −0.553614 | − | 0.832774i | \(-0.686752\pi\) | ||||
−0.553614 | + | 0.832774i | \(0.686752\pi\) | |||||||
\(728\) | 9.23607 | 0.342311 | ||||||||
\(729\) | 29.5066 | 1.09284 | ||||||||
\(730\) | 27.3262 | 1.01139 | ||||||||
\(731\) | 23.4164 | 0.866087 | ||||||||
\(732\) | −17.1803 | −0.635004 | ||||||||
\(733\) | 27.5279 | 1.01676 | 0.508382 | − | 0.861131i | \(-0.330244\pi\) | ||||
0.508382 | + | 0.861131i | \(0.330244\pi\) | |||||||
\(734\) | 13.1246 | 0.484438 | ||||||||
\(735\) | −21.6525 | −0.798664 | ||||||||
\(736\) | 2.85410 | 0.105204 | ||||||||
\(737\) | −1.50658 | −0.0554955 | ||||||||
\(738\) | −3.67376 | −0.135233 | ||||||||
\(739\) | −10.9098 | −0.401325 | −0.200662 | − | 0.979660i | \(-0.564309\pi\) | ||||
−0.200662 | + | 0.979660i | \(0.564309\pi\) | |||||||
\(740\) | −3.85410 | −0.141680 | ||||||||
\(741\) | 20.6525 | 0.758688 | ||||||||
\(742\) | −1.52786 | −0.0560897 | ||||||||
\(743\) | −48.0689 | −1.76348 | −0.881738 | − | 0.471739i | \(-0.843626\pi\) | ||||
−0.881738 | + | 0.471739i | \(0.843626\pi\) | |||||||
\(744\) | −11.9443 | −0.437898 | ||||||||
\(745\) | 62.3607 | 2.28472 | ||||||||
\(746\) | 27.7082 | 1.01447 | ||||||||
\(747\) | 5.52786 | 0.202254 | ||||||||
\(748\) | 6.18034 | 0.225976 | ||||||||
\(749\) | 23.7082 | 0.866279 | ||||||||
\(750\) | −30.2705 | −1.10532 | ||||||||
\(751\) | −1.05573 | −0.0385241 | −0.0192620 | − | 0.999814i | \(-0.506132\pi\) | ||||
−0.0192620 | + | 0.999814i | \(0.506132\pi\) | |||||||
\(752\) | −1.23607 | −0.0450748 | ||||||||
\(753\) | 33.8885 | 1.23497 | ||||||||
\(754\) | 26.6180 | 0.969372 | ||||||||
\(755\) | 16.5410 | 0.601989 | ||||||||
\(756\) | −17.7082 | −0.644041 | ||||||||
\(757\) | −4.14590 | −0.150685 | −0.0753426 | − | 0.997158i | \(-0.524005\pi\) | ||||
−0.0753426 | + | 0.997158i | \(0.524005\pi\) | |||||||
\(758\) | 28.0902 | 1.02028 | ||||||||
\(759\) | 6.38197 | 0.231651 | ||||||||
\(760\) | 17.2361 | 0.625218 | ||||||||
\(761\) | −19.1459 | −0.694038 | −0.347019 | − | 0.937858i | \(-0.612806\pi\) | ||||
−0.347019 | + | 0.937858i | \(0.612806\pi\) | |||||||
\(762\) | 13.7082 | 0.496596 | ||||||||
\(763\) | −9.52786 | −0.344932 | ||||||||
\(764\) | −7.09017 | −0.256513 | ||||||||
\(765\) | 6.58359 | 0.238030 | ||||||||
\(766\) | 17.8885 | 0.646339 | ||||||||
\(767\) | 13.5967 | 0.490950 | ||||||||
\(768\) | −1.61803 | −0.0583858 | ||||||||
\(769\) | 23.8885 | 0.861443 | 0.430721 | − | 0.902485i | \(-0.358259\pi\) | ||||
0.430721 | + | 0.902485i | \(0.358259\pi\) | |||||||
\(770\) | 17.2361 | 0.621145 | ||||||||
\(771\) | 1.70820 | 0.0615195 | ||||||||
\(772\) | 4.00000 | 0.143963 | ||||||||
\(773\) | −24.0000 | −0.863220 | −0.431610 | − | 0.902060i | \(-0.642054\pi\) | ||||
−0.431610 | + | 0.902060i | \(0.642054\pi\) | |||||||
\(774\) | 2.00000 | 0.0718885 | ||||||||
\(775\) | 72.7426 | 2.61299 | ||||||||
\(776\) | −0.472136 | −0.0169487 | ||||||||
\(777\) | −5.23607 | −0.187843 | ||||||||
\(778\) | −6.85410 | −0.245731 | ||||||||
\(779\) | 43.0132 | 1.54111 | ||||||||
\(780\) | 17.7984 | 0.637284 | ||||||||
\(781\) | −4.06888 | −0.145596 | ||||||||
\(782\) | −12.7639 | −0.456437 | ||||||||
\(783\) | −51.0344 | −1.82382 | ||||||||
\(784\) | 3.47214 | 0.124005 | ||||||||
\(785\) | −63.4853 | −2.26589 | ||||||||
\(786\) | 36.6525 | 1.30735 | ||||||||
\(787\) | −25.5279 | −0.909970 | −0.454985 | − | 0.890499i | \(-0.650355\pi\) | ||||
−0.454985 | + | 0.890499i | \(0.650355\pi\) | |||||||
\(788\) | −7.52786 | −0.268169 | ||||||||
\(789\) | 21.4164 | 0.762444 | ||||||||
\(790\) | −33.0000 | −1.17409 | ||||||||
\(791\) | 22.4721 | 0.799017 | ||||||||
\(792\) | 0.527864 | 0.0187568 | ||||||||
\(793\) | −30.3050 | −1.07616 | ||||||||
\(794\) | 20.6525 | 0.732929 | ||||||||
\(795\) | −2.94427 | −0.104423 | ||||||||
\(796\) | 3.05573 | 0.108307 | ||||||||
\(797\) | 46.2705 | 1.63899 | 0.819493 | − | 0.573090i | \(-0.194255\pi\) | ||||
0.819493 | + | 0.573090i | \(0.194255\pi\) | |||||||
\(798\) | 23.4164 | 0.828932 | ||||||||
\(799\) | 5.52786 | 0.195562 | ||||||||
\(800\) | 9.85410 | 0.348395 | ||||||||
\(801\) | 0.583592 | 0.0206202 | ||||||||
\(802\) | −4.76393 | −0.168220 | ||||||||
\(803\) | −9.79837 | −0.345777 | ||||||||
\(804\) | −1.76393 | −0.0622091 | ||||||||
\(805\) | −35.5967 | −1.25462 | ||||||||
\(806\) | −21.0689 | −0.742120 | ||||||||
\(807\) | −6.47214 | −0.227830 | ||||||||
\(808\) | 3.52786 | 0.124110 | ||||||||
\(809\) | −13.1246 | −0.461437 | −0.230718 | − | 0.973021i | \(-0.574108\pi\) | ||||
−0.230718 | + | 0.973021i | \(0.574108\pi\) | |||||||
\(810\) | −29.7082 | −1.04384 | ||||||||
\(811\) | −34.1033 | −1.19753 | −0.598765 | − | 0.800925i | \(-0.704342\pi\) | ||||
−0.598765 | + | 0.800925i | \(0.704342\pi\) | |||||||
\(812\) | 30.1803 | 1.05912 | ||||||||
\(813\) | −20.9443 | −0.734548 | ||||||||
\(814\) | 1.38197 | 0.0484379 | ||||||||
\(815\) | −13.5967 | −0.476273 | ||||||||
\(816\) | 7.23607 | 0.253313 | ||||||||
\(817\) | −23.4164 | −0.819236 | ||||||||
\(818\) | −26.1803 | −0.915374 | ||||||||
\(819\) | −3.52786 | −0.123274 | ||||||||
\(820\) | 37.0689 | 1.29450 | ||||||||
\(821\) | −5.41641 | −0.189034 | −0.0945170 | − | 0.995523i | \(-0.530131\pi\) | ||||
−0.0945170 | + | 0.995523i | \(0.530131\pi\) | |||||||
\(822\) | −5.94427 | −0.207330 | ||||||||
\(823\) | 1.88854 | 0.0658305 | 0.0329152 | − | 0.999458i | \(-0.489521\pi\) | ||||
0.0329152 | + | 0.999458i | \(0.489521\pi\) | |||||||
\(824\) | 17.2705 | 0.601647 | ||||||||
\(825\) | 22.0344 | 0.767141 | ||||||||
\(826\) | 15.4164 | 0.536405 | ||||||||
\(827\) | −2.06888 | −0.0719421 | −0.0359711 | − | 0.999353i | \(-0.511452\pi\) | ||||
−0.0359711 | + | 0.999353i | \(0.511452\pi\) | |||||||
\(828\) | −1.09017 | −0.0378860 | ||||||||
\(829\) | 55.7984 | 1.93796 | 0.968979 | − | 0.247144i | \(-0.0794920\pi\) | ||||
0.968979 | + | 0.247144i | \(0.0794920\pi\) | |||||||
\(830\) | −55.7771 | −1.93605 | ||||||||
\(831\) | −27.1803 | −0.942876 | ||||||||
\(832\) | −2.85410 | −0.0989482 | ||||||||
\(833\) | −15.5279 | −0.538009 | ||||||||
\(834\) | −7.85410 | −0.271965 | ||||||||
\(835\) | 53.3951 | 1.84781 | ||||||||
\(836\) | −6.18034 | −0.213752 | ||||||||
\(837\) | 40.3951 | 1.39626 | ||||||||
\(838\) | −10.5623 | −0.364869 | ||||||||
\(839\) | −36.6525 | −1.26538 | −0.632692 | − | 0.774404i | \(-0.718050\pi\) | ||||
−0.632692 | + | 0.774404i | \(0.718050\pi\) | |||||||
\(840\) | 20.1803 | 0.696288 | ||||||||
\(841\) | 57.9787 | 1.99927 | ||||||||
\(842\) | −31.0344 | −1.06952 | ||||||||
\(843\) | −48.3607 | −1.66563 | ||||||||
\(844\) | 11.2705 | 0.387947 | ||||||||
\(845\) | −18.7082 | −0.643582 | ||||||||
\(846\) | 0.472136 | 0.0162324 | ||||||||
\(847\) | 29.4164 | 1.01076 | ||||||||
\(848\) | 0.472136 | 0.0162132 | ||||||||
\(849\) | −10.9443 | −0.375606 | ||||||||
\(850\) | −44.0689 | −1.51155 | ||||||||
\(851\) | −2.85410 | −0.0978374 | ||||||||
\(852\) | −4.76393 | −0.163210 | ||||||||
\(853\) | 29.7426 | 1.01837 | 0.509184 | − | 0.860657i | \(-0.329947\pi\) | ||||
0.509184 | + | 0.860657i | \(0.329947\pi\) | |||||||
\(854\) | −34.3607 | −1.17580 | ||||||||
\(855\) | −6.58359 | −0.225154 | ||||||||
\(856\) | −7.32624 | −0.250406 | ||||||||
\(857\) | −9.05573 | −0.309338 | −0.154669 | − | 0.987966i | \(-0.549431\pi\) | ||||
−0.154669 | + | 0.987966i | \(0.549431\pi\) | |||||||
\(858\) | −6.38197 | −0.217877 | ||||||||
\(859\) | 53.4164 | 1.82254 | 0.911272 | − | 0.411805i | \(-0.135101\pi\) | ||||
0.911272 | + | 0.411805i | \(0.135101\pi\) | |||||||
\(860\) | −20.1803 | −0.688144 | ||||||||
\(861\) | 50.3607 | 1.71629 | ||||||||
\(862\) | 12.3607 | 0.421006 | ||||||||
\(863\) | 19.4164 | 0.660942 | 0.330471 | − | 0.943816i | \(-0.392792\pi\) | ||||
0.330471 | + | 0.943816i | \(0.392792\pi\) | |||||||
\(864\) | 5.47214 | 0.186166 | ||||||||
\(865\) | −1.81966 | −0.0618703 | ||||||||
\(866\) | −20.6738 | −0.702523 | ||||||||
\(867\) | −4.85410 | −0.164854 | ||||||||
\(868\) | −23.8885 | −0.810830 | ||||||||
\(869\) | 11.8328 | 0.401401 | ||||||||
\(870\) | 58.1591 | 1.97178 | ||||||||
\(871\) | −3.11146 | −0.105428 | ||||||||
\(872\) | 2.94427 | 0.0997056 | ||||||||
\(873\) | 0.180340 | 0.00610358 | ||||||||
\(874\) | 12.7639 | 0.431746 | ||||||||
\(875\) | −60.5410 | −2.04666 | ||||||||
\(876\) | −11.4721 | −0.387608 | ||||||||
\(877\) | −16.8328 | −0.568404 | −0.284202 | − | 0.958764i | \(-0.591729\pi\) | ||||
−0.284202 | + | 0.958764i | \(0.591729\pi\) | |||||||
\(878\) | 7.79837 | 0.263182 | ||||||||
\(879\) | 20.4721 | 0.690508 | ||||||||
\(880\) | −5.32624 | −0.179547 | ||||||||
\(881\) | 19.7426 | 0.665147 | 0.332573 | − | 0.943077i | \(-0.392083\pi\) | ||||
0.332573 | + | 0.943077i | \(0.392083\pi\) | |||||||
\(882\) | −1.32624 | −0.0446568 | ||||||||
\(883\) | −33.3050 | −1.12080 | −0.560400 | − | 0.828222i | \(-0.689353\pi\) | ||||
−0.560400 | + | 0.828222i | \(0.689353\pi\) | |||||||
\(884\) | 12.7639 | 0.429297 | ||||||||
\(885\) | 29.7082 | 0.998630 | ||||||||
\(886\) | 15.2705 | 0.513023 | ||||||||
\(887\) | 27.8885 | 0.936406 | 0.468203 | − | 0.883621i | \(-0.344902\pi\) | ||||
0.468203 | + | 0.883621i | \(0.344902\pi\) | |||||||
\(888\) | 1.61803 | 0.0542977 | ||||||||
\(889\) | 27.4164 | 0.919517 | ||||||||
\(890\) | −5.88854 | −0.197384 | ||||||||
\(891\) | 10.6525 | 0.356871 | ||||||||
\(892\) | 14.1803 | 0.474793 | ||||||||
\(893\) | −5.52786 | −0.184983 | ||||||||
\(894\) | −26.1803 | −0.875602 | ||||||||
\(895\) | −48.7639 | −1.63000 | ||||||||
\(896\) | −3.23607 | −0.108109 | ||||||||
\(897\) | 13.1803 | 0.440079 | ||||||||
\(898\) | −28.4721 | −0.950127 | ||||||||
\(899\) | −68.8460 | −2.29614 | ||||||||
\(900\) | −3.76393 | −0.125464 | ||||||||
\(901\) | −2.11146 | −0.0703428 | ||||||||
\(902\) | −13.2918 | −0.442568 | ||||||||
\(903\) | −27.4164 | −0.912361 | ||||||||
\(904\) | −6.94427 | −0.230963 | ||||||||
\(905\) | 55.7771 | 1.85409 | ||||||||
\(906\) | −6.94427 | −0.230708 | ||||||||
\(907\) | −55.8885 | −1.85575 | −0.927874 | − | 0.372893i | \(-0.878366\pi\) | ||||
−0.927874 | + | 0.372893i | \(0.878366\pi\) | |||||||
\(908\) | −4.29180 | −0.142428 | ||||||||
\(909\) | −1.34752 | −0.0446946 | ||||||||
\(910\) | 35.5967 | 1.18002 | ||||||||
\(911\) | 13.8885 | 0.460148 | 0.230074 | − | 0.973173i | \(-0.426103\pi\) | ||||
0.230074 | + | 0.973173i | \(0.426103\pi\) | |||||||
\(912\) | −7.23607 | −0.239610 | ||||||||
\(913\) | 20.0000 | 0.661903 | ||||||||
\(914\) | −24.7639 | −0.819118 | ||||||||
\(915\) | −66.2148 | −2.18899 | ||||||||
\(916\) | −23.1246 | −0.764059 | ||||||||
\(917\) | 73.3050 | 2.42074 | ||||||||
\(918\) | −24.4721 | −0.807701 | ||||||||
\(919\) | −5.88854 | −0.194245 | −0.0971226 | − | 0.995272i | \(-0.530964\pi\) | ||||
−0.0971226 | + | 0.995272i | \(0.530964\pi\) | |||||||
\(920\) | 11.0000 | 0.362659 | ||||||||
\(921\) | 20.7984 | 0.685330 | ||||||||
\(922\) | −38.9443 | −1.28256 | ||||||||
\(923\) | −8.40325 | −0.276596 | ||||||||
\(924\) | −7.23607 | −0.238049 | ||||||||
\(925\) | −9.85410 | −0.324001 | ||||||||
\(926\) | −4.56231 | −0.149927 | ||||||||
\(927\) | −6.59675 | −0.216666 | ||||||||
\(928\) | −9.32624 | −0.306149 | ||||||||
\(929\) | −27.4508 | −0.900633 | −0.450317 | − | 0.892869i | \(-0.648689\pi\) | ||||
−0.450317 | + | 0.892869i | \(0.648689\pi\) | |||||||
\(930\) | −46.0344 | −1.50953 | ||||||||
\(931\) | 15.5279 | 0.508905 | ||||||||
\(932\) | −6.56231 | −0.214955 | ||||||||
\(933\) | 43.7426 | 1.43207 | ||||||||
\(934\) | −24.3607 | −0.797106 | ||||||||
\(935\) | 23.8197 | 0.778986 | ||||||||
\(936\) | 1.09017 | 0.0356333 | ||||||||
\(937\) | −48.0476 | −1.56965 | −0.784823 | − | 0.619720i | \(-0.787246\pi\) | ||||
−0.784823 | + | 0.619720i | \(0.787246\pi\) | |||||||
\(938\) | −3.52786 | −0.115189 | ||||||||
\(939\) | −45.5967 | −1.48799 | ||||||||
\(940\) | −4.76393 | −0.155382 | ||||||||
\(941\) | −26.1803 | −0.853455 | −0.426727 | − | 0.904380i | \(-0.640334\pi\) | ||||
−0.426727 | + | 0.904380i | \(0.640334\pi\) | |||||||
\(942\) | 26.6525 | 0.868385 | ||||||||
\(943\) | 27.4508 | 0.893923 | ||||||||
\(944\) | −4.76393 | −0.155053 | ||||||||
\(945\) | −68.2492 | −2.22015 | ||||||||
\(946\) | 7.23607 | 0.235265 | ||||||||
\(947\) | 18.8328 | 0.611984 | 0.305992 | − | 0.952034i | \(-0.401012\pi\) | ||||
0.305992 | + | 0.952034i | \(0.401012\pi\) | |||||||
\(948\) | 13.8541 | 0.449960 | ||||||||
\(949\) | −20.2361 | −0.656891 | ||||||||
\(950\) | 44.0689 | 1.42978 | ||||||||
\(951\) | −33.8885 | −1.09891 | ||||||||
\(952\) | 14.4721 | 0.469045 | ||||||||
\(953\) | 11.4508 | 0.370929 | 0.185465 | − | 0.982651i | \(-0.440621\pi\) | ||||
0.185465 | + | 0.982651i | \(0.440621\pi\) | |||||||
\(954\) | −0.180340 | −0.00583872 | ||||||||
\(955\) | −27.3262 | −0.884256 | ||||||||
\(956\) | 9.85410 | 0.318704 | ||||||||
\(957\) | −20.8541 | −0.674117 | ||||||||
\(958\) | 36.5623 | 1.18127 | ||||||||
\(959\) | −11.8885 | −0.383901 | ||||||||
\(960\) | −6.23607 | −0.201268 | ||||||||
\(961\) | 23.4934 | 0.757852 | ||||||||
\(962\) | 2.85410 | 0.0920199 | ||||||||
\(963\) | 2.79837 | 0.0901763 | ||||||||
\(964\) | −1.52786 | −0.0492092 | ||||||||
\(965\) | 15.4164 | 0.496272 | ||||||||
\(966\) | 14.9443 | 0.480824 | ||||||||
\(967\) | 45.2705 | 1.45580 | 0.727901 | − | 0.685683i | \(-0.240496\pi\) | ||||
0.727901 | + | 0.685683i | \(0.240496\pi\) | |||||||
\(968\) | −9.09017 | −0.292169 | ||||||||
\(969\) | 32.3607 | 1.03957 | ||||||||
\(970\) | −1.81966 | −0.0584258 | ||||||||
\(971\) | 42.3262 | 1.35831 | 0.679157 | − | 0.733993i | \(-0.262346\pi\) | ||||
0.679157 | + | 0.733993i | \(0.262346\pi\) | |||||||
\(972\) | −3.94427 | −0.126513 | ||||||||
\(973\) | −15.7082 | −0.503582 | ||||||||
\(974\) | 37.3050 | 1.19533 | ||||||||
\(975\) | 45.5066 | 1.45738 | ||||||||
\(976\) | 10.6180 | 0.339875 | ||||||||
\(977\) | 43.5279 | 1.39258 | 0.696290 | − | 0.717761i | \(-0.254833\pi\) | ||||
0.696290 | + | 0.717761i | \(0.254833\pi\) | |||||||
\(978\) | 5.70820 | 0.182528 | ||||||||
\(979\) | 2.11146 | 0.0674824 | ||||||||
\(980\) | 13.3820 | 0.427471 | ||||||||
\(981\) | −1.12461 | −0.0359061 | ||||||||
\(982\) | −28.4508 | −0.907903 | ||||||||
\(983\) | −31.7771 | −1.01353 | −0.506766 | − | 0.862084i | \(-0.669159\pi\) | ||||
−0.506766 | + | 0.862084i | \(0.669159\pi\) | |||||||
\(984\) | −15.5623 | −0.496108 | ||||||||
\(985\) | −29.0132 | −0.924436 | ||||||||
\(986\) | 41.7082 | 1.32826 | ||||||||
\(987\) | −6.47214 | −0.206010 | ||||||||
\(988\) | −12.7639 | −0.406075 | ||||||||
\(989\) | −14.9443 | −0.475200 | ||||||||
\(990\) | 2.03444 | 0.0646588 | ||||||||
\(991\) | 33.1033 | 1.05156 | 0.525781 | − | 0.850620i | \(-0.323773\pi\) | ||||
0.525781 | + | 0.850620i | \(0.323773\pi\) | |||||||
\(992\) | 7.38197 | 0.234378 | ||||||||
\(993\) | −45.3050 | −1.43771 | ||||||||
\(994\) | −9.52786 | −0.302205 | ||||||||
\(995\) | 11.7771 | 0.373359 | ||||||||
\(996\) | 23.4164 | 0.741977 | ||||||||
\(997\) | −17.7771 | −0.563006 | −0.281503 | − | 0.959560i | \(-0.590833\pi\) | ||||
−0.281503 | + | 0.959560i | \(0.590833\pi\) | |||||||
\(998\) | 10.2918 | 0.325781 | ||||||||
\(999\) | −5.47214 | −0.173131 |
(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 | 74.2.a.b.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 666.2.a.i.1.1 | 2 | |||
4.3 | odd | 2 | 592.2.a.g.1.2 | 2 | |||
5.2 | odd | 4 | 1850.2.b.j.149.4 | 4 | |||
5.3 | odd | 4 | 1850.2.b.j.149.1 | 4 | |||
5.4 | even | 2 | 1850.2.a.t.1.2 | 2 | |||
7.6 | odd | 2 | 3626.2.a.s.1.2 | 2 | |||
8.3 | odd | 2 | 2368.2.a.u.1.1 | 2 | |||
8.5 | even | 2 | 2368.2.a.y.1.2 | 2 | |||
11.10 | odd | 2 | 8954.2.a.j.1.1 | 2 | |||
12.11 | even | 2 | 5328.2.a.bc.1.1 | 2 | |||
37.36 | even | 2 | 2738.2.a.g.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.2.a.b.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
592.2.a.g.1.2 | 2 | 4.3 | odd | 2 | |||
666.2.a.i.1.1 | 2 | 3.2 | odd | 2 | |||
1850.2.a.t.1.2 | 2 | 5.4 | even | 2 | |||
1850.2.b.j.149.1 | 4 | 5.3 | odd | 4 | |||
1850.2.b.j.149.4 | 4 | 5.2 | odd | 4 | |||
2368.2.a.u.1.1 | 2 | 8.3 | odd | 2 | |||
2368.2.a.y.1.2 | 2 | 8.5 | even | 2 | |||
2738.2.a.g.1.1 | 2 | 37.36 | even | 2 | |||
3626.2.a.s.1.2 | 2 | 7.6 | odd | 2 | |||
5328.2.a.bc.1.1 | 2 | 12.11 | even | 2 | |||
8954.2.a.j.1.1 | 2 | 11.10 | odd | 2 |