Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2898,2,Mod(1,2898)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2898, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2898.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2898 = 2 \cdot 3^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2898.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: | \(23.1406465058\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.568.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.12489\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2898.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.484862 | −0.216837 | −0.108418 | − | 0.994105i | \(-0.534579\pi\) | ||||
−0.108418 | + | 0.994105i | \(0.534579\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.484862 | 0.153327 | ||||||||
\(11\) | −6.24977 | −1.88438 | −0.942188 | − | 0.335084i | \(-0.891235\pi\) | ||||
−0.942188 | + | 0.335084i | \(0.891235\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.12489 | −0.311987 | −0.155994 | − | 0.987758i | \(-0.549858\pi\) | ||||
−0.155994 | + | 0.987758i | \(0.549858\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.60975 | −0.875492 | −0.437746 | − | 0.899099i | \(-0.644223\pi\) | ||||
−0.437746 | + | 0.899099i | \(0.644223\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.64002 | 1.06449 | 0.532247 | − | 0.846589i | \(-0.321348\pi\) | ||||
0.532247 | + | 0.846589i | \(0.321348\pi\) | |||||||
\(20\) | −0.484862 | −0.108418 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.24977 | 1.33246 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.76491 | −0.952982 | ||||||||
\(26\) | 1.12489 | 0.220608 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 1.76491 | 0.327735 | 0.163868 | − | 0.986482i | \(-0.447603\pi\) | ||||
0.163868 | + | 0.986482i | \(0.447603\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.60975 | −0.289119 | −0.144560 | − | 0.989496i | \(-0.546177\pi\) | ||||
−0.144560 | + | 0.989496i | \(0.546177\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.60975 | 0.619067 | ||||||||
\(35\) | 0.484862 | 0.0819566 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.76491 | −0.618947 | −0.309474 | − | 0.950908i | \(-0.600153\pi\) | ||||
−0.309474 | + | 0.950908i | \(0.600153\pi\) | |||||||
\(38\) | −4.64002 | −0.752711 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.484862 | 0.0766634 | ||||||||
\(41\) | 2.73463 | 0.427078 | 0.213539 | − | 0.976935i | \(-0.431501\pi\) | ||||
0.213539 | + | 0.976935i | \(0.431501\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.79518 | 1.03626 | 0.518128 | − | 0.855303i | \(-0.326629\pi\) | ||||
0.518128 | + | 0.855303i | \(0.326629\pi\) | |||||||
\(44\) | −6.24977 | −0.942188 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −6.15516 | −0.897823 | −0.448911 | − | 0.893576i | \(-0.648188\pi\) | ||||
−0.448911 | + | 0.893576i | \(0.648188\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 4.76491 | 0.673860 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.12489 | −0.155994 | ||||||||
\(53\) | 11.5298 | 1.58374 | 0.791871 | − | 0.610688i | \(-0.209107\pi\) | ||||
0.791871 | + | 0.610688i | \(0.209107\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.03028 | 0.408602 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.76491 | −0.231744 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.21949 | 1.18044 | 0.590218 | − | 0.807244i | \(-0.299042\pi\) | ||||
0.590218 | + | 0.807244i | \(0.299042\pi\) | |||||||
\(62\) | 1.60975 | 0.204438 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.545414 | 0.0676503 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.4995 | 1.52706 | 0.763531 | − | 0.645771i | \(-0.223464\pi\) | ||||
0.763531 | + | 0.645771i | \(0.223464\pi\) | |||||||
\(68\) | −3.60975 | −0.437746 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.484862 | −0.0579521 | ||||||||
\(71\) | 8.31032 | 0.986254 | 0.493127 | − | 0.869957i | \(-0.335854\pi\) | ||||
0.493127 | + | 0.869957i | \(0.335854\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.2800 | 1.32023 | 0.660115 | − | 0.751165i | \(-0.270508\pi\) | ||||
0.660115 | + | 0.751165i | \(0.270508\pi\) | |||||||
\(74\) | 3.76491 | 0.437662 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.64002 | 0.532247 | ||||||||
\(77\) | 6.24977 | 0.712227 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.24977 | −0.478137 | −0.239068 | − | 0.971003i | \(-0.576842\pi\) | ||||
−0.239068 | + | 0.971003i | \(0.576842\pi\) | |||||||
\(80\) | −0.484862 | −0.0542092 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.73463 | −0.301990 | ||||||||
\(83\) | −3.67030 | −0.402868 | −0.201434 | − | 0.979502i | \(-0.564560\pi\) | ||||
−0.201434 | + | 0.979502i | \(0.564560\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.75023 | 0.189839 | ||||||||
\(86\) | −6.79518 | −0.732744 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.24977 | 0.666228 | ||||||||
\(89\) | −13.2001 | −1.39921 | −0.699605 | − | 0.714530i | \(-0.746641\pi\) | ||||
−0.699605 | + | 0.714530i | \(0.746641\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.12489 | 0.117920 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.15516 | 0.634856 | ||||||||
\(95\) | −2.24977 | −0.230822 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.12489 | 0.520353 | 0.260177 | − | 0.965561i | \(-0.416219\pi\) | ||||
0.260177 | + | 0.965561i | \(0.416219\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.76491 | −0.476491 | ||||||||
\(101\) | −18.1698 | −1.80797 | −0.903983 | − | 0.427568i | \(-0.859371\pi\) | ||||
−0.903983 | + | 0.427568i | \(0.859371\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.4546 | 1.12865 | 0.564327 | − | 0.825551i | \(-0.309136\pi\) | ||||
0.564327 | + | 0.825551i | \(0.309136\pi\) | |||||||
\(104\) | 1.12489 | 0.110304 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11.5298 | −1.11987 | ||||||||
\(107\) | 1.75023 | 0.169201 | 0.0846005 | − | 0.996415i | \(-0.473039\pi\) | ||||
0.0846005 | + | 0.996415i | \(0.473039\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.73463 | −0.645061 | −0.322530 | − | 0.946559i | \(-0.604533\pi\) | ||||
−0.322530 | + | 0.946559i | \(0.604533\pi\) | |||||||
\(110\) | −3.03028 | −0.288925 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 0.484862 | 0.0456120 | 0.0228060 | − | 0.999740i | \(-0.492740\pi\) | ||||
0.0228060 | + | 0.999740i | \(0.492740\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.484862 | −0.0452136 | ||||||||
\(116\) | 1.76491 | 0.163868 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.60975 | 0.330905 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 28.0596 | 2.55088 | ||||||||
\(122\) | −9.21949 | −0.834694 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.60975 | −0.144560 | ||||||||
\(125\) | 4.73463 | 0.423478 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.51514 | 0.489389 | 0.244695 | − | 0.969600i | \(-0.421312\pi\) | ||||
0.244695 | + | 0.969600i | \(0.421312\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.545414 | −0.0478360 | ||||||||
\(131\) | 19.5298 | 1.70633 | 0.853164 | − | 0.521643i | \(-0.174681\pi\) | ||||
0.853164 | + | 0.521643i | \(0.174681\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.64002 | −0.402341 | ||||||||
\(134\) | −12.4995 | −1.07980 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.60975 | 0.309533 | ||||||||
\(137\) | −12.7952 | −1.09317 | −0.546583 | − | 0.837405i | \(-0.684072\pi\) | ||||
−0.546583 | + | 0.837405i | \(0.684072\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.5142 | −1.57036 | −0.785178 | − | 0.619270i | \(-0.787429\pi\) | ||||
−0.785178 | + | 0.619270i | \(0.787429\pi\) | |||||||
\(140\) | 0.484862 | 0.0409783 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −8.31032 | −0.697387 | ||||||||
\(143\) | 7.03028 | 0.587901 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.855737 | −0.0710651 | ||||||||
\(146\) | −11.2800 | −0.933543 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.76491 | −0.309474 | ||||||||
\(149\) | 4.90917 | 0.402175 | 0.201088 | − | 0.979573i | \(-0.435552\pi\) | ||||
0.201088 | + | 0.979573i | \(0.435552\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.54541 | −0.369901 | −0.184950 | − | 0.982748i | \(-0.559212\pi\) | ||||
−0.184950 | + | 0.982748i | \(0.559212\pi\) | |||||||
\(152\) | −4.64002 | −0.376356 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.24977 | −0.503621 | ||||||||
\(155\) | 0.780505 | 0.0626917 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.93945 | 0.314402 | 0.157201 | − | 0.987567i | \(-0.449753\pi\) | ||||
0.157201 | + | 0.987567i | \(0.449753\pi\) | |||||||
\(158\) | 4.24977 | 0.338094 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.484862 | 0.0383317 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.34060 | 0.731612 | 0.365806 | − | 0.930691i | \(-0.380793\pi\) | ||||
0.365806 | + | 0.930691i | \(0.380793\pi\) | |||||||
\(164\) | 2.73463 | 0.213539 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.67030 | 0.284870 | ||||||||
\(167\) | −2.39025 | −0.184963 | −0.0924817 | − | 0.995714i | \(-0.529480\pi\) | ||||
−0.0924817 | + | 0.995714i | \(0.529480\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.7346 | −0.902664 | ||||||||
\(170\) | −1.75023 | −0.134236 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.79518 | 0.518128 | ||||||||
\(173\) | 20.1093 | 1.52888 | 0.764440 | − | 0.644694i | \(-0.223015\pi\) | ||||
0.764440 | + | 0.644694i | \(0.223015\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.76491 | 0.360193 | ||||||||
\(176\) | −6.24977 | −0.471094 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 13.2001 | 0.989391 | ||||||||
\(179\) | 7.76491 | 0.580377 | 0.290188 | − | 0.956970i | \(-0.406282\pi\) | ||||
0.290188 | + | 0.956970i | \(0.406282\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.2195 | −0.982597 | −0.491299 | − | 0.870991i | \(-0.663478\pi\) | ||||
−0.491299 | + | 0.870991i | \(0.663478\pi\) | |||||||
\(182\) | −1.12489 | −0.0833821 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 1.82546 | 0.134211 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 22.5601 | 1.64976 | ||||||||
\(188\) | −6.15516 | −0.448911 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.24977 | 0.163216 | ||||||||
\(191\) | 18.1892 | 1.31613 | 0.658063 | − | 0.752963i | \(-0.271376\pi\) | ||||
0.658063 | + | 0.752963i | \(0.271376\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.3553 | −1.24926 | −0.624630 | − | 0.780921i | \(-0.714750\pi\) | ||||
−0.624630 | + | 0.780921i | \(0.714750\pi\) | |||||||
\(194\) | −5.12489 | −0.367945 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 1.57569 | 0.112263 | 0.0561316 | − | 0.998423i | \(-0.482123\pi\) | ||||
0.0561316 | + | 0.998423i | \(0.482123\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.57569 | −0.253474 | −0.126737 | − | 0.991936i | \(-0.540450\pi\) | ||||
−0.126737 | + | 0.991936i | \(0.540450\pi\) | |||||||
\(200\) | 4.76491 | 0.336930 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 18.1698 | 1.27843 | ||||||||
\(203\) | −1.76491 | −0.123872 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.32592 | −0.0926062 | ||||||||
\(206\) | −11.4546 | −0.798079 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.12489 | −0.0779968 | ||||||||
\(209\) | −28.9991 | −2.00591 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.18922 | 0.426083 | 0.213042 | − | 0.977043i | \(-0.431663\pi\) | ||||
0.213042 | + | 0.977043i | \(0.431663\pi\) | |||||||
\(212\) | 11.5298 | 0.791871 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.75023 | −0.119643 | ||||||||
\(215\) | −3.29473 | −0.224698 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.60975 | 0.109277 | ||||||||
\(218\) | 6.73463 | 0.456127 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.03028 | 0.204301 | ||||||||
\(221\) | 4.06055 | 0.273142 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.9503 | 1.13508 | 0.567540 | − | 0.823346i | \(-0.307895\pi\) | ||||
0.567540 | + | 0.823346i | \(0.307895\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.484862 | −0.0322525 | ||||||||
\(227\) | 11.1249 | 0.738385 | 0.369192 | − | 0.929353i | \(-0.379634\pi\) | ||||
0.369192 | + | 0.929353i | \(0.379634\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.3406 | 1.14590 | 0.572950 | − | 0.819591i | \(-0.305799\pi\) | ||||
0.572950 | + | 0.819591i | \(0.305799\pi\) | |||||||
\(230\) | 0.484862 | 0.0319709 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.76491 | −0.115872 | ||||||||
\(233\) | 10.0000 | 0.655122 | 0.327561 | − | 0.944830i | \(-0.393773\pi\) | ||||
0.327561 | + | 0.944830i | \(0.393773\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.98440 | 0.194681 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.60975 | −0.233985 | ||||||||
\(239\) | 8.31032 | 0.537550 | 0.268775 | − | 0.963203i | \(-0.413381\pi\) | ||||
0.268775 | + | 0.963203i | \(0.413381\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.6547 | 1.07282 | 0.536412 | − | 0.843956i | \(-0.319779\pi\) | ||||
0.536412 | + | 0.843956i | \(0.319779\pi\) | |||||||
\(242\) | −28.0596 | −1.80374 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 9.21949 | 0.590218 | ||||||||
\(245\) | −0.484862 | −0.0309767 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.21949 | −0.332108 | ||||||||
\(248\) | 1.60975 | 0.102219 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4.73463 | −0.299444 | ||||||||
\(251\) | 27.4646 | 1.73355 | 0.866774 | − | 0.498701i | \(-0.166189\pi\) | ||||
0.866774 | + | 0.498701i | \(0.166189\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.24977 | −0.392920 | ||||||||
\(254\) | −5.51514 | −0.346051 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 5.21949 | 0.325583 | 0.162792 | − | 0.986660i | \(-0.447950\pi\) | ||||
0.162792 | + | 0.986660i | \(0.447950\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.76491 | 0.233940 | ||||||||
\(260\) | 0.545414 | 0.0338251 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −19.5298 | −1.20656 | ||||||||
\(263\) | 1.20482 | 0.0742921 | 0.0371460 | − | 0.999310i | \(-0.488173\pi\) | ||||
0.0371460 | + | 0.999310i | \(0.488173\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.59037 | −0.343414 | ||||||||
\(266\) | 4.64002 | 0.284498 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 12.4995 | 0.763531 | ||||||||
\(269\) | 1.17076 | 0.0713824 | 0.0356912 | − | 0.999363i | \(-0.488637\pi\) | ||||
0.0356912 | + | 0.999363i | \(0.488637\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.3591 | −0.750759 | −0.375380 | − | 0.926871i | \(-0.622488\pi\) | ||||
−0.375380 | + | 0.926871i | \(0.622488\pi\) | |||||||
\(272\) | −3.60975 | −0.218873 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.7952 | 0.772985 | ||||||||
\(275\) | 29.7796 | 1.79578 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.9083 | −1.55668 | −0.778338 | − | 0.627845i | \(-0.783937\pi\) | ||||
−0.778338 | + | 0.627845i | \(0.783937\pi\) | |||||||
\(278\) | 18.5142 | 1.11041 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.484862 | −0.0289760 | ||||||||
\(281\) | 6.73463 | 0.401755 | 0.200877 | − | 0.979616i | \(-0.435621\pi\) | ||||
0.200877 | + | 0.979616i | \(0.435621\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −29.1689 | −1.73391 | −0.866956 | − | 0.498384i | \(-0.833927\pi\) | ||||
−0.866956 | + | 0.498384i | \(0.833927\pi\) | |||||||
\(284\) | 8.31032 | 0.493127 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.03028 | −0.415709 | ||||||||
\(287\) | −2.73463 | −0.161420 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.96972 | −0.233513 | ||||||||
\(290\) | 0.855737 | 0.0502506 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 11.2800 | 0.660115 | ||||||||
\(293\) | −11.7796 | −0.688171 | −0.344085 | − | 0.938938i | \(-0.611811\pi\) | ||||
−0.344085 | + | 0.938938i | \(0.611811\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.76491 | 0.218831 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.90917 | −0.284381 | ||||||||
\(299\) | −1.12489 | −0.0650538 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.79518 | −0.391668 | ||||||||
\(302\) | 4.54541 | 0.261559 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.64002 | 0.266124 | ||||||||
\(305\) | −4.47018 | −0.255962 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.0743 | 1.43107 | 0.715533 | − | 0.698579i | \(-0.246184\pi\) | ||||
0.715533 | + | 0.698579i | \(0.246184\pi\) | |||||||
\(308\) | 6.24977 | 0.356114 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.780505 | −0.0443297 | ||||||||
\(311\) | 24.1698 | 1.37055 | 0.685273 | − | 0.728286i | \(-0.259683\pi\) | ||||
0.685273 | + | 0.728286i | \(0.259683\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.6097 | 0.882315 | 0.441158 | − | 0.897430i | \(-0.354568\pi\) | ||||
0.441158 | + | 0.897430i | \(0.354568\pi\) | |||||||
\(314\) | −3.93945 | −0.222316 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.24977 | −0.239068 | ||||||||
\(317\) | −17.4839 | −0.981996 | −0.490998 | − | 0.871161i | \(-0.663368\pi\) | ||||
−0.490998 | + | 0.871161i | \(0.663368\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.0303 | −0.617577 | ||||||||
\(320\) | −0.484862 | −0.0271046 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.00000 | 0.0557278 | ||||||||
\(323\) | −16.7493 | −0.931957 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.35998 | 0.297318 | ||||||||
\(326\) | −9.34060 | −0.517328 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.73463 | −0.150995 | ||||||||
\(329\) | 6.15516 | 0.339345 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.47018 | −0.245703 | −0.122852 | − | 0.992425i | \(-0.539204\pi\) | ||||
−0.122852 | + | 0.992425i | \(0.539204\pi\) | |||||||
\(332\) | −3.67030 | −0.201434 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.39025 | 0.130789 | ||||||||
\(335\) | −6.06055 | −0.331123 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 34.2186 | 1.86400 | 0.932002 | − | 0.362452i | \(-0.118060\pi\) | ||||
0.932002 | + | 0.362452i | \(0.118060\pi\) | |||||||
\(338\) | 11.7346 | 0.638280 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.75023 | 0.0949195 | ||||||||
\(341\) | 10.0606 | 0.544809 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −6.79518 | −0.366372 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −20.1093 | −1.08108 | ||||||||
\(347\) | −13.4839 | −0.723856 | −0.361928 | − | 0.932206i | \(-0.617881\pi\) | ||||
−0.361928 | + | 0.932206i | \(0.617881\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.5104 | −1.36554 | −0.682771 | − | 0.730632i | \(-0.739225\pi\) | ||||
−0.682771 | + | 0.730632i | \(0.739225\pi\) | |||||||
\(350\) | −4.76491 | −0.254695 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.24977 | 0.333114 | ||||||||
\(353\) | 22.1433 | 1.17857 | 0.589286 | − | 0.807925i | \(-0.299409\pi\) | ||||
0.589286 | + | 0.807925i | \(0.299409\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.02936 | −0.213856 | ||||||||
\(356\) | −13.2001 | −0.699605 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7.76491 | −0.410388 | ||||||||
\(359\) | 8.48486 | 0.447814 | 0.223907 | − | 0.974611i | \(-0.428119\pi\) | ||||
0.223907 | + | 0.974611i | \(0.428119\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.52982 | 0.133148 | ||||||||
\(362\) | 13.2195 | 0.694801 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.12489 | 0.0589600 | ||||||||
\(365\) | −5.46927 | −0.286274 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.0147 | −0.522762 | −0.261381 | − | 0.965236i | \(-0.584178\pi\) | ||||
−0.261381 | + | 0.965236i | \(0.584178\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.82546 | −0.0949012 | ||||||||
\(371\) | −11.5298 | −0.598598 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.59037 | −0.0823462 | −0.0411731 | − | 0.999152i | \(-0.513110\pi\) | ||||
−0.0411731 | + | 0.999152i | \(0.513110\pi\) | |||||||
\(374\) | −22.5601 | −1.16655 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.15516 | 0.317428 | ||||||||
\(377\) | −1.98532 | −0.102249 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.0752 | −0.620263 | −0.310132 | − | 0.950694i | \(-0.600373\pi\) | ||||
−0.310132 | + | 0.950694i | \(0.600373\pi\) | |||||||
\(380\) | −2.24977 | −0.115411 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −18.1892 | −0.930641 | ||||||||
\(383\) | 11.0303 | 0.563621 | 0.281810 | − | 0.959470i | \(-0.409065\pi\) | ||||
0.281810 | + | 0.959470i | \(0.409065\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.03028 | −0.154437 | ||||||||
\(386\) | 17.3553 | 0.883360 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.12489 | 0.260177 | ||||||||
\(389\) | 2.43899 | 0.123662 | 0.0618308 | − | 0.998087i | \(-0.480306\pi\) | ||||
0.0618308 | + | 0.998087i | \(0.480306\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.60975 | −0.182553 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.57569 | −0.0793821 | ||||||||
\(395\) | 2.06055 | 0.103678 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.8898 | 1.04843 | 0.524214 | − | 0.851586i | \(-0.324359\pi\) | ||||
0.524214 | + | 0.851586i | \(0.324359\pi\) | |||||||
\(398\) | 3.57569 | 0.179233 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.76491 | −0.238245 | ||||||||
\(401\) | 11.9394 | 0.596228 | 0.298114 | − | 0.954530i | \(-0.403643\pi\) | ||||
0.298114 | + | 0.954530i | \(0.403643\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.81078 | 0.0902014 | ||||||||
\(404\) | −18.1698 | −0.903983 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.76491 | 0.0875910 | ||||||||
\(407\) | 23.5298 | 1.16633 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.4390 | 0.812856 | 0.406428 | − | 0.913683i | \(-0.366774\pi\) | ||||
0.406428 | + | 0.913683i | \(0.366774\pi\) | |||||||
\(410\) | 1.32592 | 0.0654825 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 11.4546 | 0.564327 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.77959 | 0.0873566 | ||||||||
\(416\) | 1.12489 | 0.0551520 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 28.9991 | 1.41839 | ||||||||
\(419\) | −19.3893 | −0.947231 | −0.473616 | − | 0.880732i | \(-0.657051\pi\) | ||||
−0.473616 | + | 0.880732i | \(0.657051\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.88601 | 0.286867 | 0.143433 | − | 0.989660i | \(-0.454186\pi\) | ||||
0.143433 | + | 0.989660i | \(0.454186\pi\) | |||||||
\(422\) | −6.18922 | −0.301286 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −11.5298 | −0.559937 | ||||||||
\(425\) | 17.2001 | 0.834328 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.21949 | −0.446163 | ||||||||
\(428\) | 1.75023 | 0.0846005 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.29473 | 0.158886 | ||||||||
\(431\) | 24.2645 | 1.16878 | 0.584389 | − | 0.811474i | \(-0.301334\pi\) | ||||
0.584389 | + | 0.811474i | \(0.301334\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.4343 | 1.46258 | 0.731289 | − | 0.682067i | \(-0.238919\pi\) | ||||
0.731289 | + | 0.682067i | \(0.238919\pi\) | |||||||
\(434\) | −1.60975 | −0.0772703 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.73463 | −0.322530 | ||||||||
\(437\) | 4.64002 | 0.221962 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.2380 | 1.15681 | 0.578407 | − | 0.815748i | \(-0.303674\pi\) | ||||
0.578407 | + | 0.815748i | \(0.303674\pi\) | |||||||
\(440\) | −3.03028 | −0.144463 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.06055 | −0.193141 | ||||||||
\(443\) | −18.0752 | −0.858780 | −0.429390 | − | 0.903119i | \(-0.641271\pi\) | ||||
−0.429390 | + | 0.903119i | \(0.641271\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.40023 | 0.303400 | ||||||||
\(446\) | −16.9503 | −0.802622 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −40.4683 | −1.90982 | −0.954910 | − | 0.296896i | \(-0.904048\pi\) | ||||
−0.954910 | + | 0.296896i | \(0.904048\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17.0908 | −0.804776 | ||||||||
\(452\) | 0.484862 | 0.0228060 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −11.1249 | −0.522117 | ||||||||
\(455\) | −0.545414 | −0.0255694 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.3784 | −1.23393 | −0.616966 | − | 0.786990i | \(-0.711638\pi\) | ||||
−0.616966 | + | 0.786990i | \(0.711638\pi\) | |||||||
\(458\) | −17.3406 | −0.810273 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.484862 | −0.0226068 | ||||||||
\(461\) | −16.0799 | −0.748917 | −0.374458 | − | 0.927244i | \(-0.622171\pi\) | ||||
−0.374458 | + | 0.927244i | \(0.622171\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.7044 | 1.19458 | 0.597291 | − | 0.802024i | \(-0.296244\pi\) | ||||
0.597291 | + | 0.802024i | \(0.296244\pi\) | |||||||
\(464\) | 1.76491 | 0.0819338 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.0000 | −0.463241 | ||||||||
\(467\) | 16.0946 | 0.744770 | 0.372385 | − | 0.928078i | \(-0.378540\pi\) | ||||
0.372385 | + | 0.928078i | \(0.378540\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.4995 | −0.577175 | ||||||||
\(470\) | −2.98440 | −0.137660 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −42.4683 | −1.95270 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −22.1093 | −1.01444 | ||||||||
\(476\) | 3.60975 | 0.165452 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8.31032 | −0.380105 | ||||||||
\(479\) | 38.7787 | 1.77184 | 0.885921 | − | 0.463835i | \(-0.153527\pi\) | ||||
0.885921 | + | 0.463835i | \(0.153527\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.23509 | 0.193104 | ||||||||
\(482\) | −16.6547 | −0.758601 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 28.0596 | 1.27544 | ||||||||
\(485\) | −2.48486 | −0.112832 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.2956 | −0.647797 | −0.323899 | − | 0.946092i | \(-0.604994\pi\) | ||||
−0.323899 | + | 0.946092i | \(0.604994\pi\) | |||||||
\(488\) | −9.21949 | −0.417347 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.484862 | 0.0219038 | ||||||||
\(491\) | 10.0681 | 0.454368 | 0.227184 | − | 0.973852i | \(-0.427048\pi\) | ||||
0.227184 | + | 0.973852i | \(0.427048\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.37088 | −0.286930 | ||||||||
\(494\) | 5.21949 | 0.234836 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.60975 | −0.0722798 | ||||||||
\(497\) | −8.31032 | −0.372769 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −26.5677 | −1.18933 | −0.594666 | − | 0.803973i | \(-0.702716\pi\) | ||||
−0.594666 | + | 0.803973i | \(0.702716\pi\) | |||||||
\(500\) | 4.73463 | 0.211739 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −27.4646 | −1.22580 | ||||||||
\(503\) | −3.52982 | −0.157387 | −0.0786934 | − | 0.996899i | \(-0.525075\pi\) | ||||
−0.0786934 | + | 0.996899i | \(0.525075\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.80986 | 0.392034 | ||||||||
\(506\) | 6.24977 | 0.277836 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.51514 | 0.244695 | ||||||||
\(509\) | 3.79897 | 0.168386 | 0.0841931 | − | 0.996449i | \(-0.473169\pi\) | ||||
0.0841931 | + | 0.996449i | \(0.473169\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.2800 | −0.499000 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.21949 | −0.230222 | ||||||||
\(515\) | −5.55389 | −0.244734 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 38.4683 | 1.69184 | ||||||||
\(518\) | −3.76491 | −0.165421 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.545414 | −0.0239180 | ||||||||
\(521\) | 23.8283 | 1.04394 | 0.521969 | − | 0.852964i | \(-0.325198\pi\) | ||||
0.521969 | + | 0.852964i | \(0.325198\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.0790 | −1.18408 | −0.592041 | − | 0.805908i | \(-0.701678\pi\) | ||||
−0.592041 | + | 0.805908i | \(0.701678\pi\) | |||||||
\(524\) | 19.5298 | 0.853164 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.20482 | −0.0525324 | ||||||||
\(527\) | 5.81078 | 0.253122 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 5.59037 | 0.242830 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.64002 | −0.201171 | ||||||||
\(533\) | −3.07615 | −0.133243 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.848620 | −0.0366890 | ||||||||
\(536\) | −12.4995 | −0.539898 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.17076 | −0.0504750 | ||||||||
\(539\) | −6.24977 | −0.269197 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −36.5601 | −1.57184 | −0.785921 | − | 0.618327i | \(-0.787811\pi\) | ||||
−0.785921 | + | 0.618327i | \(0.787811\pi\) | |||||||
\(542\) | 12.3591 | 0.530867 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.60975 | 0.154767 | ||||||||
\(545\) | 3.26537 | 0.139873 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.969724 | 0.0414624 | 0.0207312 | − | 0.999785i | \(-0.493401\pi\) | ||||
0.0207312 | + | 0.999785i | \(0.493401\pi\) | |||||||
\(548\) | −12.7952 | −0.546583 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −29.7796 | −1.26981 | ||||||||
\(551\) | 8.18922 | 0.348872 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.24977 | 0.180719 | ||||||||
\(554\) | 25.9083 | 1.10074 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −18.5142 | −0.785178 | ||||||||
\(557\) | −33.1807 | −1.40591 | −0.702957 | − | 0.711233i | \(-0.748137\pi\) | ||||
−0.702957 | + | 0.711233i | \(0.748137\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.64380 | −0.323298 | ||||||||
\(560\) | 0.484862 | 0.0204892 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.73463 | −0.284083 | ||||||||
\(563\) | 27.1249 | 1.14318 | 0.571589 | − | 0.820540i | \(-0.306327\pi\) | ||||
0.571589 | + | 0.820540i | \(0.306327\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.235091 | −0.00989036 | ||||||||
\(566\) | 29.1689 | 1.22606 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.31032 | −0.348693 | ||||||||
\(569\) | 44.4755 | 1.86451 | 0.932254 | − | 0.361804i | \(-0.117839\pi\) | ||||
0.932254 | + | 0.361804i | \(0.117839\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.05964 | 0.295437 | 0.147718 | − | 0.989029i | \(-0.452807\pi\) | ||||
0.147718 | + | 0.989029i | \(0.452807\pi\) | |||||||
\(572\) | 7.03028 | 0.293951 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.73463 | 0.114141 | ||||||||
\(575\) | −4.76491 | −0.198710 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.749313 | 0.0311943 | 0.0155971 | − | 0.999878i | \(-0.495035\pi\) | ||||
0.0155971 | + | 0.999878i | \(0.495035\pi\) | |||||||
\(578\) | 3.96972 | 0.165119 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.855737 | −0.0355326 | ||||||||
\(581\) | 3.67030 | 0.152270 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −72.0587 | −2.98437 | ||||||||
\(584\) | −11.2800 | −0.466772 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.7796 | 0.486610 | ||||||||
\(587\) | −29.2800 | −1.20852 | −0.604258 | − | 0.796788i | \(-0.706531\pi\) | ||||
−0.604258 | + | 0.796788i | \(0.706531\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.46927 | −0.307766 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.76491 | −0.154737 | ||||||||
\(593\) | 8.95504 | 0.367740 | 0.183870 | − | 0.982951i | \(-0.441138\pi\) | ||||
0.183870 | + | 0.982951i | \(0.441138\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.75023 | −0.0717524 | ||||||||
\(596\) | 4.90917 | 0.201088 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.12489 | 0.0460000 | ||||||||
\(599\) | 0.378437 | 0.0154625 | 0.00773126 | − | 0.999970i | \(-0.497539\pi\) | ||||
0.00773126 | + | 0.999970i | \(0.497539\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.7181 | −1.25302 | −0.626509 | − | 0.779414i | \(-0.715517\pi\) | ||||
−0.626509 | + | 0.779414i | \(0.715517\pi\) | |||||||
\(602\) | 6.79518 | 0.276951 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.54541 | −0.184950 | ||||||||
\(605\) | −13.6050 | −0.553124 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.35998 | 0.136377 | 0.0681886 | − | 0.997672i | \(-0.478278\pi\) | ||||
0.0681886 | + | 0.997672i | \(0.478278\pi\) | |||||||
\(608\) | −4.64002 | −0.188178 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.47018 | 0.180992 | ||||||||
\(611\) | 6.92385 | 0.280109 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −44.3250 | −1.79027 | −0.895135 | − | 0.445795i | \(-0.852921\pi\) | ||||
−0.895135 | + | 0.445795i | \(0.852921\pi\) | |||||||
\(614\) | −25.0743 | −1.01192 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.24977 | −0.251810 | ||||||||
\(617\) | −6.62065 | −0.266537 | −0.133269 | − | 0.991080i | \(-0.542547\pi\) | ||||
−0.133269 | + | 0.991080i | \(0.542547\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.58039 | −0.224295 | −0.112147 | − | 0.993692i | \(-0.535773\pi\) | ||||
−0.112147 | + | 0.993692i | \(0.535773\pi\) | |||||||
\(620\) | 0.780505 | 0.0313458 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −24.1698 | −0.969122 | ||||||||
\(623\) | 13.2001 | 0.528852 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.5289 | 0.861156 | ||||||||
\(626\) | −15.6097 | −0.623891 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.93945 | 0.157201 | ||||||||
\(629\) | 13.5904 | 0.541884 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.09839 | 0.202964 | 0.101482 | − | 0.994837i | \(-0.467642\pi\) | ||||
0.101482 | + | 0.994837i | \(0.467642\pi\) | |||||||
\(632\) | 4.24977 | 0.169047 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 17.4839 | 0.694376 | ||||||||
\(635\) | −2.67408 | −0.106118 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.12489 | −0.0445696 | ||||||||
\(638\) | 11.0303 | 0.436693 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.484862 | 0.0191659 | ||||||||
\(641\) | −25.2654 | −0.997922 | −0.498961 | − | 0.866624i | \(-0.666285\pi\) | ||||
−0.498961 | + | 0.866624i | \(0.666285\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.518919 | −0.0204642 | −0.0102321 | − | 0.999948i | \(-0.503257\pi\) | ||||
−0.0102321 | + | 0.999948i | \(0.503257\pi\) | |||||||
\(644\) | −1.00000 | −0.0394055 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 16.7493 | 0.658993 | ||||||||
\(647\) | −20.0100 | −0.786674 | −0.393337 | − | 0.919394i | \(-0.628679\pi\) | ||||
−0.393337 | + | 0.919394i | \(0.628679\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −5.35998 | −0.210236 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.34060 | 0.365806 | ||||||||
\(653\) | 22.2645 | 0.871275 | 0.435638 | − | 0.900122i | \(-0.356523\pi\) | ||||
0.435638 | + | 0.900122i | \(0.356523\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.46927 | −0.369995 | ||||||||
\(656\) | 2.73463 | 0.106769 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6.15516 | −0.239953 | ||||||||
\(659\) | −4.12110 | −0.160535 | −0.0802677 | − | 0.996773i | \(-0.525578\pi\) | ||||
−0.0802677 | + | 0.996773i | \(0.525578\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27.7502 | −1.07936 | −0.539679 | − | 0.841871i | \(-0.681455\pi\) | ||||
−0.539679 | + | 0.841871i | \(0.681455\pi\) | |||||||
\(662\) | 4.47018 | 0.173739 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.67030 | 0.142435 | ||||||||
\(665\) | 2.24977 | 0.0872424 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.76491 | 0.0683375 | ||||||||
\(668\) | −2.39025 | −0.0924817 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.06055 | 0.234140 | ||||||||
\(671\) | −57.6197 | −2.22438 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.44702 | 0.0557787 | 0.0278893 | − | 0.999611i | \(-0.491121\pi\) | ||||
0.0278893 | + | 0.999611i | \(0.491121\pi\) | |||||||
\(674\) | −34.2186 | −1.31805 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.7346 | −0.451332 | ||||||||
\(677\) | 38.8392 | 1.49271 | 0.746356 | − | 0.665547i | \(-0.231802\pi\) | ||||
0.746356 | + | 0.665547i | \(0.231802\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.12489 | −0.196675 | ||||||||
\(680\) | −1.75023 | −0.0671182 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −10.0606 | −0.385238 | ||||||||
\(683\) | −0.249771 | −0.00955722 | −0.00477861 | − | 0.999989i | \(-0.501521\pi\) | ||||
−0.00477861 | + | 0.999989i | \(0.501521\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.20390 | 0.237039 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.79518 | 0.259064 | ||||||||
\(689\) | −12.9697 | −0.494107 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.1358 | 0.994252 | 0.497126 | − | 0.867678i | \(-0.334389\pi\) | ||||
0.497126 | + | 0.867678i | \(0.334389\pi\) | |||||||
\(692\) | 20.1093 | 0.764440 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 13.4839 | 0.511844 | ||||||||
\(695\) | 8.97684 | 0.340511 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.87133 | −0.373903 | ||||||||
\(698\) | 25.5104 | 0.965584 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.76491 | 0.180097 | ||||||||
\(701\) | −15.1202 | −0.571082 | −0.285541 | − | 0.958367i | \(-0.592173\pi\) | ||||
−0.285541 | + | 0.958367i | \(0.592173\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −17.4693 | −0.658866 | ||||||||
\(704\) | −6.24977 | −0.235547 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −22.1433 | −0.833376 | ||||||||
\(707\) | 18.1698 | 0.683347 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.2876 | −0.874585 | −0.437292 | − | 0.899319i | \(-0.644062\pi\) | ||||
−0.437292 | + | 0.899319i | \(0.644062\pi\) | |||||||
\(710\) | 4.02936 | 0.151219 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 13.2001 | 0.494695 | ||||||||
\(713\) | −1.60975 | −0.0602855 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.40871 | −0.127479 | ||||||||
\(716\) | 7.76491 | 0.290188 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −8.48486 | −0.316652 | ||||||||
\(719\) | −23.8136 | −0.888099 | −0.444050 | − | 0.896002i | \(-0.646459\pi\) | ||||
−0.444050 | + | 0.896002i | \(0.646459\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.4546 | −0.426591 | ||||||||
\(722\) | −2.52982 | −0.0941501 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −13.2195 | −0.491299 | ||||||||
\(725\) | −8.40963 | −0.312326 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.0984 | 0.559968 | 0.279984 | − | 0.960005i | \(-0.409671\pi\) | ||||
0.279984 | + | 0.960005i | \(0.409671\pi\) | |||||||
\(728\) | −1.12489 | −0.0416910 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 5.46927 | 0.202427 | ||||||||
\(731\) | −24.5289 | −0.907234 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.9688 | 1.32854 | 0.664269 | − | 0.747494i | \(-0.268743\pi\) | ||||
0.664269 | + | 0.747494i | \(0.268743\pi\) | |||||||
\(734\) | 10.0147 | 0.369649 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −78.1193 | −2.87756 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.90161 | −0.106737 | −0.0533687 | − | 0.998575i | \(-0.516996\pi\) | ||||
−0.0533687 | + | 0.998575i | \(0.516996\pi\) | |||||||
\(740\) | 1.82546 | 0.0671053 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 11.5298 | 0.423273 | ||||||||
\(743\) | 21.8108 | 0.800160 | 0.400080 | − | 0.916480i | \(-0.368982\pi\) | ||||
0.400080 | + | 0.916480i | \(0.368982\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.38027 | −0.0872064 | ||||||||
\(746\) | 1.59037 | 0.0582276 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 22.5601 | 0.824879 | ||||||||
\(749\) | −1.75023 | −0.0639520 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32.6206 | −1.19034 | −0.595172 | − | 0.803598i | \(-0.702916\pi\) | ||||
−0.595172 | + | 0.803598i | \(0.702916\pi\) | |||||||
\(752\) | −6.15516 | −0.224456 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.98532 | 0.0723011 | ||||||||
\(755\) | 2.20390 | 0.0802081 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −48.4977 | −1.76268 | −0.881340 | − | 0.472483i | \(-0.843358\pi\) | ||||
−0.881340 | + | 0.472483i | \(0.843358\pi\) | |||||||
\(758\) | 12.0752 | 0.438592 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.24977 | 0.0816078 | ||||||||
\(761\) | −38.0975 | −1.38103 | −0.690516 | − | 0.723317i | \(-0.742617\pi\) | ||||
−0.690516 | + | 0.723317i | \(0.742617\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.73463 | 0.243810 | ||||||||
\(764\) | 18.1892 | 0.658063 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −11.0303 | −0.398540 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.9054 | 0.645685 | 0.322842 | − | 0.946453i | \(-0.395362\pi\) | ||||
0.322842 | + | 0.946453i | \(0.395362\pi\) | |||||||
\(770\) | 3.03028 | 0.109204 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −17.3553 | −0.624630 | ||||||||
\(773\) | 4.79518 | 0.172471 | 0.0862354 | − | 0.996275i | \(-0.472516\pi\) | ||||
0.0862354 | + | 0.996275i | \(0.472516\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.67030 | 0.275525 | ||||||||
\(776\) | −5.12489 | −0.183973 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.43899 | −0.0874420 | ||||||||
\(779\) | 12.6888 | 0.454622 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −51.9376 | −1.85847 | ||||||||
\(782\) | 3.60975 | 0.129084 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −1.91009 | −0.0681740 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.04965 | 0.251293 | 0.125647 | − | 0.992075i | \(-0.459899\pi\) | ||||
0.125647 | + | 0.992075i | \(0.459899\pi\) | |||||||
\(788\) | 1.57569 | 0.0561316 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.06055 | −0.0733112 | ||||||||
\(791\) | −0.484862 | −0.0172397 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.3709 | −0.368281 | ||||||||
\(794\) | −20.8898 | −0.741351 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.57569 | −0.126737 | ||||||||
\(797\) | −21.1443 | −0.748968 | −0.374484 | − | 0.927233i | \(-0.622180\pi\) | ||||
−0.374484 | + | 0.927233i | \(0.622180\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.2186 | 0.786037 | ||||||||
\(800\) | 4.76491 | 0.168465 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −11.9394 | −0.421597 | ||||||||
\(803\) | −70.4977 | −2.48781 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.484862 | 0.0170891 | ||||||||
\(806\) | −1.81078 | −0.0637821 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 18.1698 | 0.639213 | ||||||||
\(809\) | 13.5592 | 0.476715 | 0.238358 | − | 0.971177i | \(-0.423391\pi\) | ||||
0.238358 | + | 0.971177i | \(0.423391\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −50.3544 | −1.76818 | −0.884090 | − | 0.467316i | \(-0.845221\pi\) | ||||
−0.884090 | + | 0.467316i | \(0.845221\pi\) | |||||||
\(812\) | −1.76491 | −0.0619362 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −23.5298 | −0.824720 | ||||||||
\(815\) | −4.52890 | −0.158640 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 31.5298 | 1.10309 | ||||||||
\(818\) | −16.4390 | −0.574776 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.32592 | −0.0463031 | ||||||||
\(821\) | −40.7787 | −1.42319 | −0.711593 | − | 0.702592i | \(-0.752026\pi\) | ||||
−0.711593 | + | 0.702592i | \(0.752026\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.9532 | 1.00925 | 0.504623 | − | 0.863340i | \(-0.331632\pi\) | ||||
0.504623 | + | 0.863340i | \(0.331632\pi\) | |||||||
\(824\) | −11.4546 | −0.399039 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 41.8089 | 1.45384 | 0.726920 | − | 0.686722i | \(-0.240951\pi\) | ||||
0.726920 | + | 0.686722i | \(0.240951\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.04965 | −0.175382 | −0.0876909 | − | 0.996148i | \(-0.527949\pi\) | ||||
−0.0876909 | + | 0.996148i | \(0.527949\pi\) | |||||||
\(830\) | −1.77959 | −0.0617704 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.12489 | −0.0389984 | ||||||||
\(833\) | −3.60975 | −0.125070 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.15894 | 0.0401069 | ||||||||
\(836\) | −28.9991 | −1.00295 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 19.3893 | 0.669793 | ||||||||
\(839\) | −1.81834 | −0.0627762 | −0.0313881 | − | 0.999507i | \(-0.509993\pi\) | ||||
−0.0313881 | + | 0.999507i | \(0.509993\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.8851 | −0.892590 | ||||||||
\(842\) | −5.88601 | −0.202845 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6.18922 | 0.213042 | ||||||||
\(845\) | 5.68968 | 0.195731 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −28.0596 | −0.964140 | ||||||||
\(848\) | 11.5298 | 0.395936 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −17.2001 | −0.589959 | ||||||||
\(851\) | −3.76491 | −0.129059 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 52.6841 | 1.80387 | 0.901934 | − | 0.431874i | \(-0.142147\pi\) | ||||
0.901934 | + | 0.431874i | \(0.142147\pi\) | |||||||
\(854\) | 9.21949 | 0.315485 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.75023 | −0.0598216 | ||||||||
\(857\) | −44.2039 | −1.50998 | −0.754988 | − | 0.655738i | \(-0.772357\pi\) | ||||
−0.754988 | + | 0.655738i | \(0.772357\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −39.5133 | −1.34818 | −0.674088 | − | 0.738651i | \(-0.735463\pi\) | ||||
−0.674088 | + | 0.738651i | \(0.735463\pi\) | |||||||
\(860\) | −3.29473 | −0.112349 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −24.2645 | −0.826450 | ||||||||
\(863\) | 34.2791 | 1.16688 | 0.583438 | − | 0.812158i | \(-0.301707\pi\) | ||||
0.583438 | + | 0.812158i | \(0.301707\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.75023 | −0.331518 | ||||||||
\(866\) | −30.4343 | −1.03420 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.60975 | 0.0546384 | ||||||||
\(869\) | 26.5601 | 0.900989 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.0606 | −0.476424 | ||||||||
\(872\) | 6.73463 | 0.228063 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.64002 | −0.156951 | ||||||||
\(875\) | −4.73463 | −0.160060 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.7493 | 0.970795 | 0.485398 | − | 0.874293i | \(-0.338675\pi\) | ||||
0.485398 | + | 0.874293i | \(0.338675\pi\) | |||||||
\(878\) | −24.2380 | −0.817991 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.03028 | 0.102151 | ||||||||
\(881\) | 22.5483 | 0.759671 | 0.379835 | − | 0.925054i | \(-0.375981\pi\) | ||||
0.379835 | + | 0.925054i | \(0.375981\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.8099 | −0.363781 | −0.181890 | − | 0.983319i | \(-0.558222\pi\) | ||||
−0.181890 | + | 0.983319i | \(0.558222\pi\) | |||||||
\(884\) | 4.06055 | 0.136571 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 18.0752 | 0.607249 | ||||||||
\(887\) | 25.1689 | 0.845090 | 0.422545 | − | 0.906342i | \(-0.361137\pi\) | ||||
0.422545 | + | 0.906342i | \(0.361137\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.51514 | −0.184972 | ||||||||
\(890\) | −6.40023 | −0.214536 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 16.9503 | 0.567540 | ||||||||
\(893\) | −28.5601 | −0.955727 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.76491 | −0.125847 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 40.4683 | 1.35045 | ||||||||
\(899\) | −2.84106 | −0.0947546 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −41.6197 | −1.38655 | ||||||||
\(902\) | 17.0908 | 0.569062 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.484862 | −0.0161263 | ||||||||
\(905\) | 6.40963 | 0.213063 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 51.4839 | 1.70950 | 0.854748 | − | 0.519043i | \(-0.173712\pi\) | ||||
0.854748 | + | 0.519043i | \(0.173712\pi\) | |||||||
\(908\) | 11.1249 | 0.369192 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.545414 | 0.0180803 | ||||||||
\(911\) | −32.0147 | −1.06069 | −0.530347 | − | 0.847781i | \(-0.677938\pi\) | ||||
−0.530347 | + | 0.847781i | \(0.677938\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22.9385 | 0.759155 | ||||||||
\(914\) | 26.3784 | 0.872521 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 17.3406 | 0.572950 | ||||||||
\(917\) | −19.5298 | −0.644931 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.4002 | 1.06879 | 0.534393 | − | 0.845236i | \(-0.320540\pi\) | ||||
0.534393 | + | 0.845236i | \(0.320540\pi\) | |||||||
\(920\) | 0.484862 | 0.0159854 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 16.0799 | 0.529564 | ||||||||
\(923\) | −9.34816 | −0.307698 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17.9394 | 0.589845 | ||||||||
\(926\) | −25.7044 | −0.844698 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.76491 | −0.0579360 | ||||||||
\(929\) | −36.2039 | −1.18781 | −0.593906 | − | 0.804535i | \(-0.702415\pi\) | ||||
−0.593906 | + | 0.804535i | \(0.702415\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.64002 | 0.152071 | ||||||||
\(932\) | 10.0000 | 0.327561 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −16.0946 | −0.526632 | ||||||||
\(935\) | −10.9385 | −0.357728 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −56.0928 | −1.83247 | −0.916236 | − | 0.400640i | \(-0.868788\pi\) | ||||
−0.916236 | + | 0.400640i | \(0.868788\pi\) | |||||||
\(938\) | 12.4995 | 0.408125 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.98440 | 0.0973405 | ||||||||
\(941\) | −19.4234 | −0.633185 | −0.316592 | − | 0.948562i | \(-0.602539\pi\) | ||||
−0.316592 | + | 0.948562i | \(0.602539\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.73463 | 0.0890519 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 42.4683 | 1.38077 | ||||||||
\(947\) | −34.4537 | −1.11959 | −0.559797 | − | 0.828630i | \(-0.689121\pi\) | ||||
−0.559797 | + | 0.828630i | \(0.689121\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.6888 | −0.411895 | ||||||||
\(950\) | 22.1093 | 0.717320 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.60975 | −0.116993 | ||||||||
\(953\) | 36.6576 | 1.18746 | 0.593728 | − | 0.804666i | \(-0.297656\pi\) | ||||
0.593728 | + | 0.804666i | \(0.297656\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.81926 | −0.285385 | ||||||||
\(956\) | 8.31032 | 0.268775 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −38.7787 | −1.25288 | ||||||||
\(959\) | 12.7952 | 0.413178 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.4087 | −0.916410 | ||||||||
\(962\) | −4.23509 | −0.136545 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 16.6547 | 0.536412 | ||||||||
\(965\) | 8.41491 | 0.270886 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52.8780 | 1.70044 | 0.850221 | − | 0.526427i | \(-0.176469\pi\) | ||||
0.850221 | + | 0.526427i | \(0.176469\pi\) | |||||||
\(968\) | −28.0596 | −0.901871 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.48486 | 0.0797841 | ||||||||
\(971\) | 42.4490 | 1.36225 | 0.681126 | − | 0.732166i | \(-0.261491\pi\) | ||||
0.681126 | + | 0.732166i | \(0.261491\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.5142 | 0.593539 | ||||||||
\(974\) | 14.2956 | 0.458062 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.21949 | 0.295109 | ||||||||
\(977\) | 41.8236 | 1.33806 | 0.669028 | − | 0.743237i | \(-0.266711\pi\) | ||||
0.669028 | + | 0.743237i | \(0.266711\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 82.4977 | 2.63664 | ||||||||
\(980\) | −0.484862 | −0.0154883 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −10.0681 | −0.321286 | ||||||||
\(983\) | 46.0606 | 1.46910 | 0.734552 | − | 0.678553i | \(-0.237392\pi\) | ||||
0.734552 | + | 0.678553i | \(0.237392\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.763992 | −0.0243428 | ||||||||
\(986\) | 6.37088 | 0.202890 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.21949 | −0.166054 | ||||||||
\(989\) | 6.79518 | 0.216074 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −43.0209 | −1.36660 | −0.683302 | − | 0.730136i | \(-0.739457\pi\) | ||||
−0.683302 | + | 0.730136i | \(0.739457\pi\) | |||||||
\(992\) | 1.60975 | 0.0511095 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8.31032 | 0.263587 | ||||||||
\(995\) | 1.73372 | 0.0549625 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.29095 | 0.199236 | 0.0996181 | − | 0.995026i | \(-0.468238\pi\) | ||||
0.0996181 | + | 0.995026i | \(0.468238\pi\) | |||||||
\(998\) | 26.5677 | 0.840984 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2898.2.a.bf.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 2898.2.a.bg.1.2 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2898.2.a.bf.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
2898.2.a.bg.1.2 | yes | 3 | 3.2 | odd | 2 |