Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [725,2,Mod(1,725)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(725, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("725.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 725 = 5^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 725.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: | \(5.78915414654\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.337383424.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 13x^{4} + 41x^{2} - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 145) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.156785\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 725.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.156785 | −0.110864 | −0.0554318 | − | 0.998462i | \(-0.517654\pi\) | ||||
−0.0554318 | + | 0.998462i | \(0.517654\pi\) | |||||||
\(3\) | 2.56387 | 1.48025 | 0.740126 | − | 0.672468i | \(-0.234766\pi\) | ||||
0.740126 | + | 0.672468i | \(0.234766\pi\) | |||||||
\(4\) | −1.97542 | −0.987709 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.401976 | −0.164106 | ||||||||
\(7\) | 1.09364 | 0.413357 | 0.206678 | − | 0.978409i | \(-0.433735\pi\) | ||||
0.206678 | + | 0.978409i | \(0.433735\pi\) | |||||||
\(8\) | 0.623285 | 0.220365 | ||||||||
\(9\) | 3.57344 | 1.19115 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.40198 | −1.32725 | −0.663623 | − | 0.748067i | \(-0.730982\pi\) | ||||
−0.663623 | + | 0.748067i | \(0.730982\pi\) | |||||||
\(12\) | −5.06472 | −1.46206 | ||||||||
\(13\) | 3.97108 | 1.10138 | 0.550690 | − | 0.834710i | \(-0.314365\pi\) | ||||
0.550690 | + | 0.834710i | \(0.314365\pi\) | |||||||
\(14\) | −0.171466 | −0.0458262 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.85312 | 0.963279 | ||||||||
\(17\) | 6.22138 | 1.50891 | 0.754454 | − | 0.656353i | \(-0.227902\pi\) | ||||
0.754454 | + | 0.656353i | \(0.227902\pi\) | |||||||
\(18\) | −0.560261 | −0.132055 | ||||||||
\(19\) | 6.97542 | 1.60027 | 0.800135 | − | 0.599819i | \(-0.204761\pi\) | ||||
0.800135 | + | 0.599819i | \(0.204761\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.80395 | 0.611873 | ||||||||
\(22\) | 0.690163 | 0.147143 | ||||||||
\(23\) | −0.780070 | −0.162656 | −0.0813279 | − | 0.996687i | \(-0.525916\pi\) | ||||
−0.0813279 | + | 0.996687i | \(0.525916\pi\) | |||||||
\(24\) | 1.59802 | 0.326195 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.622605 | −0.122103 | ||||||||
\(27\) | 1.47023 | 0.282946 | ||||||||
\(28\) | −2.16040 | −0.408276 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.40198 | 1.14983 | 0.574914 | − | 0.818214i | \(-0.305035\pi\) | ||||
0.574914 | + | 0.818214i | \(0.305035\pi\) | |||||||
\(32\) | −1.85068 | −0.327157 | ||||||||
\(33\) | −11.2861 | −1.96466 | ||||||||
\(34\) | −0.975419 | −0.167283 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −7.05904 | −1.17651 | ||||||||
\(37\) | −1.09364 | −0.179793 | −0.0898966 | − | 0.995951i | \(-0.528654\pi\) | ||||
−0.0898966 | + | 0.995951i | \(0.528654\pi\) | |||||||
\(38\) | −1.09364 | −0.177412 | ||||||||
\(39\) | 10.1813 | 1.63032 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | −0.439617 | −0.0678344 | ||||||||
\(43\) | −0.376593 | −0.0574299 | −0.0287150 | − | 0.999588i | \(-0.509142\pi\) | ||||
−0.0287150 | + | 0.999588i | \(0.509142\pi\) | |||||||
\(44\) | 8.69575 | 1.31093 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.122303 | 0.0180326 | ||||||||
\(47\) | −4.75115 | −0.693027 | −0.346513 | − | 0.938045i | \(-0.612634\pi\) | ||||
−0.346513 | + | 0.938045i | \(0.612634\pi\) | |||||||
\(48\) | 9.87890 | 1.42590 | ||||||||
\(49\) | −5.80395 | −0.829136 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 15.9508 | 2.23356 | ||||||||
\(52\) | −7.84455 | −1.08784 | ||||||||
\(53\) | −11.2861 | −1.55027 | −0.775133 | − | 0.631798i | \(-0.782317\pi\) | ||||
−0.775133 | + | 0.631798i | \(0.782317\pi\) | |||||||
\(54\) | −0.230510 | −0.0313685 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.681649 | 0.0910892 | ||||||||
\(57\) | 17.8841 | 2.36880 | ||||||||
\(58\) | 0.156785 | 0.0205869 | ||||||||
\(59\) | 10.0000 | 1.30189 | 0.650945 | − | 0.759125i | \(-0.274373\pi\) | ||||
0.650945 | + | 0.759125i | \(0.274373\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.14688 | −0.146844 | −0.0734218 | − | 0.997301i | \(-0.523392\pi\) | ||||
−0.0734218 | + | 0.997301i | \(0.523392\pi\) | |||||||
\(62\) | −1.00373 | −0.127474 | ||||||||
\(63\) | 3.90806 | 0.492369 | ||||||||
\(64\) | −7.41607 | −0.927009 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.76949 | 0.217809 | ||||||||
\(67\) | −5.90782 | −0.721754 | −0.360877 | − | 0.932613i | \(-0.617523\pi\) | ||||
−0.360877 | + | 0.932613i | \(0.617523\pi\) | |||||||
\(68\) | −12.2898 | −1.49036 | ||||||||
\(69\) | −2.00000 | −0.240772 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.00000 | 0.237356 | 0.118678 | − | 0.992933i | \(-0.462134\pi\) | ||||
0.118678 | + | 0.992933i | \(0.462134\pi\) | |||||||
\(72\) | 2.22727 | 0.262487 | ||||||||
\(73\) | 8.72223 | 1.02086 | 0.510430 | − | 0.859919i | \(-0.329486\pi\) | ||||
0.510430 | + | 0.859919i | \(0.329486\pi\) | |||||||
\(74\) | 0.171466 | 0.0199325 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −13.7794 | −1.58060 | ||||||||
\(77\) | −4.81418 | −0.548626 | ||||||||
\(78\) | −1.59628 | −0.180743 | ||||||||
\(79\) | −5.54886 | −0.624296 | −0.312148 | − | 0.950034i | \(-0.601048\pi\) | ||||
−0.312148 | + | 0.950034i | \(0.601048\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.95084 | −0.772315 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.22138 | 0.682886 | 0.341443 | − | 0.939903i | \(-0.389084\pi\) | ||||
0.341443 | + | 0.939903i | \(0.389084\pi\) | |||||||
\(84\) | −5.53898 | −0.604352 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.0590441 | 0.00636689 | ||||||||
\(87\) | −2.56387 | −0.274876 | ||||||||
\(88\) | −2.74369 | −0.292478 | ||||||||
\(89\) | −10.8040 | −1.14522 | −0.572608 | − | 0.819829i | \(-0.694068\pi\) | ||||
−0.572608 | + | 0.819829i | \(0.694068\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.34293 | 0.455263 | ||||||||
\(92\) | 1.54096 | 0.160657 | ||||||||
\(93\) | 16.4139 | 1.70204 | ||||||||
\(94\) | 0.744908 | 0.0768314 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.74491 | −0.484275 | ||||||||
\(97\) | −17.4176 | −1.76849 | −0.884244 | − | 0.467026i | \(-0.845326\pi\) | ||||
−0.884244 | + | 0.467026i | \(0.845326\pi\) | |||||||
\(98\) | 0.909972 | 0.0919210 | ||||||||
\(99\) | −15.7302 | −1.58095 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.7548 | −1.26915 | −0.634574 | − | 0.772862i | \(-0.718825\pi\) | ||||
−0.634574 | + | 0.772862i | \(0.718825\pi\) | |||||||
\(102\) | −2.50085 | −0.247621 | ||||||||
\(103\) | −5.15463 | −0.507901 | −0.253950 | − | 0.967217i | \(-0.581730\pi\) | ||||
−0.253950 | + | 0.967217i | \(0.581730\pi\) | |||||||
\(104\) | 2.47512 | 0.242705 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.76949 | 0.171868 | ||||||||
\(107\) | −1.09364 | −0.105726 | −0.0528631 | − | 0.998602i | \(-0.516835\pi\) | ||||
−0.0528631 | + | 0.998602i | \(0.516835\pi\) | |||||||
\(108\) | −2.90433 | −0.279469 | ||||||||
\(109\) | 15.3282 | 1.46818 | 0.734089 | − | 0.679053i | \(-0.237609\pi\) | ||||
0.734089 | + | 0.679053i | \(0.237609\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.80395 | −0.266139 | ||||||||
\(112\) | 4.21392 | 0.398178 | ||||||||
\(113\) | 7.28814 | 0.685611 | 0.342805 | − | 0.939406i | \(-0.388623\pi\) | ||||
0.342805 | + | 0.939406i | \(0.388623\pi\) | |||||||
\(114\) | −2.80395 | −0.262614 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.97542 | 0.183413 | ||||||||
\(117\) | 14.1904 | 1.31191 | ||||||||
\(118\) | −1.56785 | −0.144332 | ||||||||
\(119\) | 6.80395 | 0.623717 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.37739 | 0.761581 | ||||||||
\(122\) | 0.179814 | 0.0162796 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −12.6466 | −1.13570 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.612724 | −0.0545858 | ||||||||
\(127\) | 17.7312 | 1.57339 | 0.786693 | − | 0.617345i | \(-0.211792\pi\) | ||||
0.786693 | + | 0.617345i | \(0.211792\pi\) | |||||||
\(128\) | 4.86409 | 0.429929 | ||||||||
\(129\) | −0.965537 | −0.0850108 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.31835 | 0.639407 | 0.319704 | − | 0.947518i | \(-0.396417\pi\) | ||||
0.319704 | + | 0.947518i | \(0.396417\pi\) | |||||||
\(132\) | 22.2948 | 1.94051 | ||||||||
\(133\) | 7.62859 | 0.661483 | ||||||||
\(134\) | 0.926256 | 0.0800163 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.87770 | 0.332510 | ||||||||
\(137\) | 9.78899 | 0.836330 | 0.418165 | − | 0.908371i | \(-0.362673\pi\) | ||||
0.418165 | + | 0.908371i | \(0.362673\pi\) | |||||||
\(138\) | 0.313570 | 0.0266928 | ||||||||
\(139\) | −2.75479 | −0.233658 | −0.116829 | − | 0.993152i | \(-0.537273\pi\) | ||||
−0.116829 | + | 0.993152i | \(0.537273\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.1813 | −1.02585 | ||||||||
\(142\) | −0.313570 | −0.0263142 | ||||||||
\(143\) | −17.4806 | −1.46180 | ||||||||
\(144\) | 13.7689 | 1.14741 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.36751 | −0.113176 | ||||||||
\(147\) | −14.8806 | −1.22733 | ||||||||
\(148\) | 2.16040 | 0.177583 | ||||||||
\(149\) | −4.52428 | −0.370643 | −0.185322 | − | 0.982678i | \(-0.559333\pi\) | ||||
−0.185322 | + | 0.982678i | \(0.559333\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.80395 | 0.228182 | 0.114091 | − | 0.993470i | \(-0.463604\pi\) | ||||
0.114091 | + | 0.993470i | \(0.463604\pi\) | |||||||
\(152\) | 4.34768 | 0.352643 | ||||||||
\(153\) | 22.2318 | 1.79733 | ||||||||
\(154\) | 0.754790 | 0.0608227 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −20.1124 | −1.61028 | ||||||||
\(157\) | −4.97481 | −0.397033 | −0.198517 | − | 0.980098i | \(-0.563612\pi\) | ||||
−0.198517 | + | 0.980098i | \(0.563612\pi\) | |||||||
\(158\) | 0.869977 | 0.0692117 | ||||||||
\(159\) | −28.9361 | −2.29478 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.853115 | −0.0672349 | ||||||||
\(162\) | 1.08979 | 0.0856216 | ||||||||
\(163\) | −20.7615 | −1.62617 | −0.813084 | − | 0.582146i | \(-0.802213\pi\) | ||||
−0.813084 | + | 0.582146i | \(0.802213\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.975419 | −0.0757072 | ||||||||
\(167\) | −21.9182 | −1.69608 | −0.848040 | − | 0.529932i | \(-0.822217\pi\) | ||||
−0.848040 | + | 0.529932i | \(0.822217\pi\) | |||||||
\(168\) | 1.74766 | 0.134835 | ||||||||
\(169\) | 2.76949 | 0.213038 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 24.9263 | 1.90616 | ||||||||
\(172\) | 0.743929 | 0.0567241 | ||||||||
\(173\) | 3.25404 | 0.247400 | 0.123700 | − | 0.992320i | \(-0.460524\pi\) | ||||
0.123700 | + | 0.992320i | \(0.460524\pi\) | |||||||
\(174\) | 0.401976 | 0.0304737 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −16.9613 | −1.27851 | ||||||||
\(177\) | 25.6387 | 1.92712 | ||||||||
\(178\) | 1.69390 | 0.126963 | ||||||||
\(179\) | −7.19605 | −0.537858 | −0.268929 | − | 0.963160i | \(-0.586670\pi\) | ||||
−0.268929 | + | 0.963160i | \(0.586670\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.0345 | 0.968844 | 0.484422 | − | 0.874834i | \(-0.339030\pi\) | ||||
0.484422 | + | 0.874834i | \(0.339030\pi\) | |||||||
\(182\) | −0.680906 | −0.0504721 | ||||||||
\(183\) | −2.94047 | −0.217365 | ||||||||
\(184\) | −0.486206 | −0.0358436 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.57344 | −0.188694 | ||||||||
\(187\) | −27.3864 | −2.00269 | ||||||||
\(188\) | 9.38551 | 0.684509 | ||||||||
\(189\) | 1.60790 | 0.116958 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.1223 | −0.732424 | −0.366212 | − | 0.930531i | \(-0.619346\pi\) | ||||
−0.366212 | + | 0.930531i | \(0.619346\pi\) | |||||||
\(192\) | −19.0139 | −1.37221 | ||||||||
\(193\) | −22.8589 | −1.64542 | −0.822710 | − | 0.568462i | \(-0.807539\pi\) | ||||
−0.822710 | + | 0.568462i | \(0.807539\pi\) | |||||||
\(194\) | 2.73081 | 0.196061 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11.4652 | 0.818945 | ||||||||
\(197\) | −22.0711 | −1.57250 | −0.786251 | − | 0.617907i | \(-0.787981\pi\) | ||||
−0.786251 | + | 0.617907i | \(0.787981\pi\) | |||||||
\(198\) | 2.46626 | 0.175269 | ||||||||
\(199\) | 5.19605 | 0.368338 | 0.184169 | − | 0.982895i | \(-0.441041\pi\) | ||||
0.184169 | + | 0.982895i | \(0.441041\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.1469 | −1.06838 | ||||||||
\(202\) | 1.99976 | 0.140702 | ||||||||
\(203\) | −1.09364 | −0.0767585 | ||||||||
\(204\) | −31.5096 | −2.20611 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.808167 | 0.0563077 | ||||||||
\(207\) | −2.78754 | −0.193747 | ||||||||
\(208\) | 15.3010 | 1.06094 | ||||||||
\(209\) | −30.7056 | −2.12395 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.64719 | 0.113397 | 0.0566985 | − | 0.998391i | \(-0.481943\pi\) | ||||
0.0566985 | + | 0.998391i | \(0.481943\pi\) | |||||||
\(212\) | 22.2948 | 1.53121 | ||||||||
\(213\) | 5.12775 | 0.351347 | ||||||||
\(214\) | 0.171466 | 0.0117212 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.916374 | 0.0623514 | ||||||||
\(217\) | 7.00145 | 0.475290 | ||||||||
\(218\) | −2.40323 | −0.162768 | ||||||||
\(219\) | 22.3627 | 1.51113 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 24.7056 | 1.66188 | ||||||||
\(222\) | 0.439617 | 0.0295052 | ||||||||
\(223\) | −9.47542 | −0.634521 | −0.317261 | − | 0.948338i | \(-0.602763\pi\) | ||||
−0.317261 | + | 0.948338i | \(0.602763\pi\) | |||||||
\(224\) | −2.02398 | −0.135233 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.14267 | −0.0760093 | ||||||||
\(227\) | −5.72800 | −0.380181 | −0.190090 | − | 0.981767i | \(-0.560878\pi\) | ||||
−0.190090 | + | 0.981767i | \(0.560878\pi\) | |||||||
\(228\) | −35.3286 | −2.33969 | ||||||||
\(229\) | 15.1469 | 1.00093 | 0.500467 | − | 0.865756i | \(-0.333162\pi\) | ||||
0.500467 | + | 0.865756i | \(0.333162\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.3429 | −0.812105 | ||||||||
\(232\) | −0.623285 | −0.0409207 | ||||||||
\(233\) | 0.717046 | 0.0469753 | 0.0234876 | − | 0.999724i | \(-0.492523\pi\) | ||||
0.0234876 | + | 0.999724i | \(0.492523\pi\) | |||||||
\(234\) | −2.22484 | −0.145443 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −19.7542 | −1.28589 | ||||||||
\(237\) | −14.2266 | −0.924115 | ||||||||
\(238\) | −1.06676 | −0.0691475 | ||||||||
\(239\) | −2.00000 | −0.129369 | −0.0646846 | − | 0.997906i | \(-0.520604\pi\) | ||||
−0.0646846 | + | 0.997906i | \(0.520604\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.3282 | 1.11621 | 0.558105 | − | 0.829770i | \(-0.311529\pi\) | ||||
0.558105 | + | 0.829770i | \(0.311529\pi\) | |||||||
\(242\) | −1.31345 | −0.0844316 | ||||||||
\(243\) | −22.2318 | −1.42617 | ||||||||
\(244\) | 2.26558 | 0.145039 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 27.7000 | 1.76251 | ||||||||
\(248\) | 3.99026 | 0.253382 | ||||||||
\(249\) | 15.9508 | 1.01084 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 26.0099 | 1.64173 | 0.820865 | − | 0.571123i | \(-0.193492\pi\) | ||||
0.820865 | + | 0.571123i | \(0.193492\pi\) | |||||||
\(252\) | −7.72005 | −0.486317 | ||||||||
\(253\) | 3.43385 | 0.215884 | ||||||||
\(254\) | −2.77998 | −0.174431 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 14.0695 | 0.879346 | ||||||||
\(257\) | −15.0335 | −0.937766 | −0.468883 | − | 0.883260i | \(-0.655343\pi\) | ||||
−0.468883 | + | 0.883260i | \(0.655343\pi\) | |||||||
\(258\) | 0.151382 | 0.00942461 | ||||||||
\(259\) | −1.19605 | −0.0743188 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.57344 | −0.221191 | ||||||||
\(262\) | −1.14741 | −0.0708870 | ||||||||
\(263\) | 12.0662 | 0.744032 | 0.372016 | − | 0.928226i | \(-0.378667\pi\) | ||||
0.372016 | + | 0.928226i | \(0.378667\pi\) | |||||||
\(264\) | −7.03446 | −0.432941 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.19605 | −0.0733344 | ||||||||
\(267\) | −27.7000 | −1.69521 | ||||||||
\(268\) | 11.6704 | 0.712884 | ||||||||
\(269\) | −10.8531 | −0.661726 | −0.330863 | − | 0.943679i | \(-0.607340\pi\) | ||||
−0.330863 | + | 0.943679i | \(0.607340\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.7449 | −0.774198 | −0.387099 | − | 0.922038i | \(-0.626523\pi\) | ||||
−0.387099 | + | 0.922038i | \(0.626523\pi\) | |||||||
\(272\) | 23.9717 | 1.45350 | ||||||||
\(273\) | 11.1347 | 0.673904 | ||||||||
\(274\) | −1.53476 | −0.0927185 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.95084 | 0.237812 | ||||||||
\(277\) | 20.0714 | 1.20597 | 0.602986 | − | 0.797752i | \(-0.293978\pi\) | ||||
0.602986 | + | 0.797752i | \(0.293978\pi\) | |||||||
\(278\) | 0.431909 | 0.0259042 | ||||||||
\(279\) | 22.8771 | 1.36962 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.9361 | −1.24895 | −0.624473 | − | 0.781047i | \(-0.714686\pi\) | ||||
−0.624473 | + | 0.781047i | \(0.714686\pi\) | |||||||
\(282\) | 1.90985 | 0.113730 | ||||||||
\(283\) | 16.9703 | 1.00878 | 0.504389 | − | 0.863477i | \(-0.331718\pi\) | ||||
0.504389 | + | 0.863477i | \(0.331718\pi\) | |||||||
\(284\) | −3.95084 | −0.234439 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.74069 | 0.162061 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −6.61330 | −0.389692 | ||||||||
\(289\) | 21.7056 | 1.27680 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −44.6565 | −2.61781 | ||||||||
\(292\) | −17.2301 | −1.00831 | ||||||||
\(293\) | −9.47542 | −0.553560 | −0.276780 | − | 0.960933i | \(-0.589267\pi\) | ||||
−0.276780 | + | 0.960933i | \(0.589267\pi\) | |||||||
\(294\) | 2.33305 | 0.136066 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.681649 | −0.0396201 | ||||||||
\(297\) | −6.47193 | −0.375539 | ||||||||
\(298\) | 0.709338 | 0.0410909 | ||||||||
\(299\) | −3.09772 | −0.179146 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.411857 | −0.0237391 | ||||||||
\(302\) | −0.439617 | −0.0252971 | ||||||||
\(303\) | −32.7017 | −1.87866 | ||||||||
\(304\) | 26.8771 | 1.54151 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.48560 | −0.199259 | ||||||||
\(307\) | 19.3812 | 1.10614 | 0.553072 | − | 0.833134i | \(-0.313456\pi\) | ||||
0.553072 | + | 0.833134i | \(0.313456\pi\) | |||||||
\(308\) | 9.51001 | 0.541883 | ||||||||
\(309\) | −13.2158 | −0.751821 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.26919 | −0.525607 | −0.262804 | − | 0.964849i | \(-0.584647\pi\) | ||||
−0.262804 | + | 0.964849i | \(0.584647\pi\) | |||||||
\(312\) | 6.34588 | 0.359265 | ||||||||
\(313\) | −14.5324 | −0.821422 | −0.410711 | − | 0.911766i | \(-0.634719\pi\) | ||||
−0.410711 | + | 0.911766i | \(0.634719\pi\) | |||||||
\(314\) | 0.779975 | 0.0440165 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.9613 | 0.616623 | ||||||||
\(317\) | −22.4116 | −1.25876 | −0.629380 | − | 0.777098i | \(-0.716691\pi\) | ||||
−0.629380 | + | 0.777098i | \(0.716691\pi\) | |||||||
\(318\) | 4.53675 | 0.254408 | ||||||||
\(319\) | 4.40198 | 0.246463 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.80395 | −0.156501 | ||||||||
\(322\) | 0.133756 | 0.00745390 | ||||||||
\(323\) | 43.3968 | 2.41466 | ||||||||
\(324\) | 13.7308 | 0.762823 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.25509 | 0.180283 | ||||||||
\(327\) | 39.2996 | 2.17327 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.19605 | −0.286467 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.89179 | 0.433772 | 0.216886 | − | 0.976197i | \(-0.430410\pi\) | ||||
0.216886 | + | 0.976197i | \(0.430410\pi\) | |||||||
\(332\) | −12.2898 | −0.674493 | ||||||||
\(333\) | −3.90806 | −0.214160 | ||||||||
\(334\) | 3.43644 | 0.188034 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 10.8040 | 0.589404 | ||||||||
\(337\) | 33.4280 | 1.82094 | 0.910468 | − | 0.413579i | \(-0.135721\pi\) | ||||
0.910468 | + | 0.413579i | \(0.135721\pi\) | |||||||
\(338\) | −0.434214 | −0.0236181 | ||||||||
\(339\) | 18.6859 | 1.01488 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −28.1813 | −1.52611 | ||||||||
\(342\) | −3.90806 | −0.211324 | ||||||||
\(343\) | −14.0029 | −0.756086 | ||||||||
\(344\) | −0.234725 | −0.0126555 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.510183 | −0.0274276 | ||||||||
\(347\) | 31.1069 | 1.66991 | 0.834954 | − | 0.550320i | \(-0.185494\pi\) | ||||
0.834954 | + | 0.550320i | \(0.185494\pi\) | |||||||
\(348\) | 5.06472 | 0.271498 | ||||||||
\(349\) | −5.76949 | −0.308834 | −0.154417 | − | 0.988006i | \(-0.549350\pi\) | ||||
−0.154417 | + | 0.988006i | \(0.549350\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.83842 | 0.311632 | ||||||||
\(352\) | 8.14665 | 0.434218 | ||||||||
\(353\) | −13.5095 | −0.719039 | −0.359520 | − | 0.933137i | \(-0.617059\pi\) | ||||
−0.359520 | + | 0.933137i | \(0.617059\pi\) | |||||||
\(354\) | −4.01976 | −0.213648 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 21.3423 | 1.13114 | ||||||||
\(357\) | 17.4445 | 0.923259 | ||||||||
\(358\) | 1.12823 | 0.0596289 | ||||||||
\(359\) | −1.15677 | −0.0610518 | −0.0305259 | − | 0.999534i | \(-0.509718\pi\) | ||||
−0.0305259 | + | 0.999534i | \(0.509718\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 29.6565 | 1.56087 | ||||||||
\(362\) | −2.04361 | −0.107410 | ||||||||
\(363\) | 21.4786 | 1.12733 | ||||||||
\(364\) | −8.57911 | −0.449667 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.461020 | 0.0240979 | ||||||||
\(367\) | −10.5959 | −0.553104 | −0.276552 | − | 0.960999i | \(-0.589192\pi\) | ||||
−0.276552 | + | 0.960999i | \(0.589192\pi\) | |||||||
\(368\) | −3.00570 | −0.156683 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.3429 | −0.640813 | ||||||||
\(372\) | −32.4242 | −1.68112 | ||||||||
\(373\) | −7.09907 | −0.367576 | −0.183788 | − | 0.982966i | \(-0.558836\pi\) | ||||
−0.183788 | + | 0.982966i | \(0.558836\pi\) | |||||||
\(374\) | 4.29377 | 0.222026 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.96132 | −0.152719 | ||||||||
\(377\) | −3.97108 | −0.204521 | ||||||||
\(378\) | −0.252095 | −0.0129664 | ||||||||
\(379\) | 18.1223 | 0.930880 | 0.465440 | − | 0.885079i | \(-0.345896\pi\) | ||||
0.465440 | + | 0.885079i | \(0.345896\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 45.4604 | 2.32901 | ||||||||
\(382\) | 1.58702 | 0.0811992 | ||||||||
\(383\) | −3.28092 | −0.167647 | −0.0838236 | − | 0.996481i | \(-0.526713\pi\) | ||||
−0.0838236 | + | 0.996481i | \(0.526713\pi\) | |||||||
\(384\) | 12.4709 | 0.636403 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.58393 | 0.182417 | ||||||||
\(387\) | −1.34573 | −0.0684075 | ||||||||
\(388\) | 34.4070 | 1.74675 | ||||||||
\(389\) | −12.0000 | −0.608424 | −0.304212 | − | 0.952604i | \(-0.598393\pi\) | ||||
−0.304212 | + | 0.952604i | \(0.598393\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.85312 | −0.245433 | ||||||||
\(392\) | −3.61752 | −0.182712 | ||||||||
\(393\) | 18.7633 | 0.946484 | ||||||||
\(394\) | 3.46042 | 0.174333 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 31.0737 | 1.56151 | ||||||||
\(397\) | −36.3054 | −1.82212 | −0.911058 | − | 0.412278i | \(-0.864733\pi\) | ||||
−0.911058 | + | 0.412278i | \(0.864733\pi\) | |||||||
\(398\) | −0.814661 | −0.0408353 | ||||||||
\(399\) | 19.5587 | 0.979162 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.0830 | 1.30252 | 0.651262 | − | 0.758853i | \(-0.274240\pi\) | ||||
0.651262 | + | 0.758853i | \(0.274240\pi\) | |||||||
\(402\) | 2.37480 | 0.118444 | ||||||||
\(403\) | 25.4228 | 1.26640 | ||||||||
\(404\) | 25.1960 | 1.25355 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.171466 | 0.00850972 | ||||||||
\(407\) | 4.81418 | 0.238630 | ||||||||
\(408\) | 9.94192 | 0.492198 | ||||||||
\(409\) | 13.0486 | 0.645210 | 0.322605 | − | 0.946534i | \(-0.395442\pi\) | ||||
0.322605 | + | 0.946534i | \(0.395442\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 25.0977 | 1.23798 | ||||||||
\(412\) | 10.1825 | 0.501658 | ||||||||
\(413\) | 10.9364 | 0.538145 | ||||||||
\(414\) | 0.437043 | 0.0214795 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −7.34920 | −0.360324 | ||||||||
\(417\) | −7.06293 | −0.345873 | ||||||||
\(418\) | 4.81418 | 0.235469 | ||||||||
\(419\) | 35.8525 | 1.75151 | 0.875755 | − | 0.482756i | \(-0.160364\pi\) | ||||
0.875755 | + | 0.482756i | \(0.160364\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.7056 | 0.814182 | 0.407091 | − | 0.913388i | \(-0.366543\pi\) | ||||
0.407091 | + | 0.913388i | \(0.366543\pi\) | |||||||
\(422\) | −0.258254 | −0.0125716 | ||||||||
\(423\) | −16.9780 | −0.825497 | ||||||||
\(424\) | −7.03446 | −0.341624 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.803952 | −0.0389516 | ||||||||
\(427\) | −1.25428 | −0.0606988 | ||||||||
\(428\) | 2.16040 | 0.104427 | ||||||||
\(429\) | −44.8180 | −2.16384 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −26.3135 | −1.26748 | −0.633739 | − | 0.773547i | \(-0.718481\pi\) | ||||
−0.633739 | + | 0.773547i | \(0.718481\pi\) | |||||||
\(432\) | 5.66498 | 0.272556 | ||||||||
\(433\) | 10.7220 | 0.515266 | 0.257633 | − | 0.966243i | \(-0.417057\pi\) | ||||
0.257633 | + | 0.966243i | \(0.417057\pi\) | |||||||
\(434\) | −1.09772 | −0.0526923 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −30.2797 | −1.45013 | ||||||||
\(437\) | −5.44131 | −0.260293 | ||||||||
\(438\) | −3.50613 | −0.167529 | ||||||||
\(439\) | 29.5587 | 1.41076 | 0.705381 | − | 0.708828i | \(-0.250776\pi\) | ||||
0.705381 | + | 0.708828i | \(0.250776\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −20.7401 | −0.987623 | ||||||||
\(442\) | −3.87347 | −0.184242 | ||||||||
\(443\) | −3.40697 | −0.161870 | −0.0809349 | − | 0.996719i | \(-0.525791\pi\) | ||||
−0.0809349 | + | 0.996719i | \(0.525791\pi\) | |||||||
\(444\) | 5.53898 | 0.262868 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.48560 | 0.0703453 | ||||||||
\(447\) | −11.5997 | −0.548646 | ||||||||
\(448\) | −8.11051 | −0.383186 | ||||||||
\(449\) | 0.461020 | 0.0217569 | 0.0108784 | − | 0.999941i | \(-0.496537\pi\) | ||||
0.0108784 | + | 0.999941i | \(0.496537\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −14.3971 | −0.677184 | ||||||||
\(453\) | 7.18898 | 0.337768 | ||||||||
\(454\) | 0.898063 | 0.0421482 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 11.1469 | 0.522001 | ||||||||
\(457\) | 1.37262 | 0.0642084 | 0.0321042 | − | 0.999485i | \(-0.489779\pi\) | ||||
0.0321042 | + | 0.999485i | \(0.489779\pi\) | |||||||
\(458\) | −2.37480 | −0.110967 | ||||||||
\(459\) | 9.14688 | 0.426940 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.5875 | 0.679409 | 0.339705 | − | 0.940532i | \(-0.389673\pi\) | ||||
0.339705 | + | 0.940532i | \(0.389673\pi\) | |||||||
\(462\) | 1.93518 | 0.0900329 | ||||||||
\(463\) | −18.8517 | −0.876112 | −0.438056 | − | 0.898948i | \(-0.644333\pi\) | ||||
−0.438056 | + | 0.898948i | \(0.644333\pi\) | |||||||
\(464\) | −3.85312 | −0.178876 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.112422 | −0.00520785 | ||||||||
\(467\) | 29.9580 | 1.38629 | 0.693145 | − | 0.720798i | \(-0.256225\pi\) | ||||
0.693145 | + | 0.720798i | \(0.256225\pi\) | |||||||
\(468\) | −28.0320 | −1.29578 | ||||||||
\(469\) | −6.46102 | −0.298342 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.7548 | −0.587710 | ||||||||
\(472\) | 6.23285 | 0.286890 | ||||||||
\(473\) | 1.65776 | 0.0762237 | ||||||||
\(474\) | 2.23051 | 0.102451 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −13.4407 | −0.616051 | ||||||||
\(477\) | −40.3302 | −1.84660 | ||||||||
\(478\) | 0.313570 | 0.0143423 | ||||||||
\(479\) | −32.7647 | −1.49706 | −0.748528 | − | 0.663103i | \(-0.769239\pi\) | ||||
−0.748528 | + | 0.663103i | \(0.769239\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.34293 | −0.198021 | ||||||||
\(482\) | −2.71680 | −0.123747 | ||||||||
\(483\) | −2.18728 | −0.0995246 | ||||||||
\(484\) | −16.5489 | −0.752221 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 3.48560 | 0.158110 | ||||||||
\(487\) | −14.1098 | −0.639375 | −0.319688 | − | 0.947523i | \(-0.603578\pi\) | ||||
−0.319688 | + | 0.947523i | \(0.603578\pi\) | |||||||
\(488\) | −0.714836 | −0.0323591 | ||||||||
\(489\) | −53.2299 | −2.40714 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.10821 | 0.185401 | 0.0927004 | − | 0.995694i | \(-0.470450\pi\) | ||||
0.0927004 | + | 0.995694i | \(0.470450\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.22138 | −0.280197 | ||||||||
\(494\) | −4.34293 | −0.195398 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 24.6676 | 1.10761 | ||||||||
\(497\) | 2.18728 | 0.0981129 | ||||||||
\(498\) | −2.50085 | −0.112066 | ||||||||
\(499\) | 30.0689 | 1.34607 | 0.673035 | − | 0.739611i | \(-0.264990\pi\) | ||||
0.673035 | + | 0.739611i | \(0.264990\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −56.1954 | −2.51063 | ||||||||
\(502\) | −4.07795 | −0.182008 | ||||||||
\(503\) | −14.8806 | −0.663493 | −0.331746 | − | 0.943369i | \(-0.607638\pi\) | ||||
−0.331746 | + | 0.943369i | \(0.607638\pi\) | |||||||
\(504\) | 2.43583 | 0.108501 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.538375 | −0.0239337 | ||||||||
\(507\) | 7.10062 | 0.315350 | ||||||||
\(508\) | −35.0264 | −1.55405 | ||||||||
\(509\) | 1.93674 | 0.0858445 | 0.0429223 | − | 0.999078i | \(-0.486333\pi\) | ||||
0.0429223 | + | 0.999078i | \(0.486333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.53898 | 0.421980 | ||||||||
\(512\) | −11.9341 | −0.527416 | ||||||||
\(513\) | 10.2555 | 0.452791 | ||||||||
\(514\) | 2.35703 | 0.103964 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.90734 | 0.0839660 | ||||||||
\(517\) | 20.9145 | 0.919817 | ||||||||
\(518\) | 0.187522 | 0.00823925 | ||||||||
\(519\) | 8.34293 | 0.366214 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.23051 | −0.185342 | −0.0926710 | − | 0.995697i | \(-0.529540\pi\) | ||||
−0.0926710 | + | 0.995697i | \(0.529540\pi\) | |||||||
\(522\) | 0.560261 | 0.0245220 | ||||||||
\(523\) | −4.40144 | −0.192462 | −0.0962308 | − | 0.995359i | \(-0.530679\pi\) | ||||
−0.0962308 | + | 0.995359i | \(0.530679\pi\) | |||||||
\(524\) | −14.4568 | −0.631548 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.89179 | −0.0824861 | ||||||||
\(527\) | 39.8292 | 1.73499 | ||||||||
\(528\) | −43.4867 | −1.89251 | ||||||||
\(529\) | −22.3915 | −0.973543 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 35.7344 | 1.55074 | ||||||||
\(532\) | −15.0697 | −0.653353 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 4.34293 | 0.187937 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.68225 | −0.159049 | ||||||||
\(537\) | −18.4497 | −0.796165 | ||||||||
\(538\) | 1.70160 | 0.0733613 | ||||||||
\(539\) | 25.5489 | 1.10047 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.4119 | −1.39349 | −0.696747 | − | 0.717317i | \(-0.745370\pi\) | ||||
−0.696747 | + | 0.717317i | \(0.745370\pi\) | |||||||
\(542\) | 1.99821 | 0.0858304 | ||||||||
\(543\) | 33.4187 | 1.43413 | ||||||||
\(544\) | −11.5138 | −0.493650 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.74576 | −0.0747114 | ||||||||
\(547\) | −12.9093 | −0.551961 | −0.275980 | − | 0.961163i | \(-0.589002\pi\) | ||||
−0.275980 | + | 0.961163i | \(0.589002\pi\) | |||||||
\(548\) | −19.3374 | −0.826051 | ||||||||
\(549\) | −4.09833 | −0.174912 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.97542 | −0.297163 | ||||||||
\(552\) | −1.24657 | −0.0530576 | ||||||||
\(553\) | −6.06845 | −0.258057 | ||||||||
\(554\) | −3.14688 | −0.133698 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.44186 | 0.230786 | ||||||||
\(557\) | 23.0195 | 0.975369 | 0.487685 | − | 0.873020i | \(-0.337842\pi\) | ||||
0.487685 | + | 0.873020i | \(0.337842\pi\) | |||||||
\(558\) | −3.58678 | −0.151841 | ||||||||
\(559\) | −1.49548 | −0.0632522 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −70.2152 | −2.96449 | ||||||||
\(562\) | 3.28247 | 0.138463 | ||||||||
\(563\) | −27.3234 | −1.15154 | −0.575771 | − | 0.817611i | \(-0.695298\pi\) | ||||
−0.575771 | + | 0.817611i | \(0.695298\pi\) | |||||||
\(564\) | 24.0633 | 1.01325 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.66068 | −0.111837 | ||||||||
\(567\) | −7.60171 | −0.319242 | ||||||||
\(568\) | 1.24657 | 0.0523049 | ||||||||
\(569\) | −0.803952 | −0.0337034 | −0.0168517 | − | 0.999858i | \(-0.505364\pi\) | ||||
−0.0168517 | + | 0.999858i | \(0.505364\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 43.4604 | 1.81876 | 0.909381 | − | 0.415964i | \(-0.136556\pi\) | ||||
0.909381 | + | 0.415964i | \(0.136556\pi\) | |||||||
\(572\) | 34.5315 | 1.44384 | ||||||||
\(573\) | −25.9523 | −1.08417 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −26.5009 | −1.10420 | ||||||||
\(577\) | −1.27345 | −0.0530146 | −0.0265073 | − | 0.999649i | \(-0.508439\pi\) | ||||
−0.0265073 | + | 0.999649i | \(0.508439\pi\) | |||||||
\(578\) | −3.40311 | −0.141551 | ||||||||
\(579\) | −58.6073 | −2.43564 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.80395 | 0.282276 | ||||||||
\(582\) | 7.00145 | 0.290220 | ||||||||
\(583\) | 49.6812 | 2.05758 | ||||||||
\(584\) | 5.43644 | 0.224961 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.48560 | 0.0613696 | ||||||||
\(587\) | 31.8678 | 1.31533 | 0.657663 | − | 0.753312i | \(-0.271545\pi\) | ||||
0.657663 | + | 0.753312i | \(0.271545\pi\) | |||||||
\(588\) | 29.3954 | 1.21225 | ||||||||
\(589\) | 44.6565 | 1.84004 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −56.5875 | −2.32770 | ||||||||
\(592\) | −4.21392 | −0.173191 | ||||||||
\(593\) | 1.21043 | 0.0497064 | 0.0248532 | − | 0.999691i | \(-0.492088\pi\) | ||||
0.0248532 | + | 0.999691i | \(0.492088\pi\) | |||||||
\(594\) | 1.01470 | 0.0416337 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.93735 | 0.366088 | ||||||||
\(597\) | 13.3220 | 0.545233 | ||||||||
\(598\) | 0.485676 | 0.0198608 | ||||||||
\(599\) | 24.2053 | 0.989003 | 0.494501 | − | 0.869177i | \(-0.335351\pi\) | ||||
0.494501 | + | 0.869177i | \(0.335351\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.68586 | 0.191140 | 0.0955702 | − | 0.995423i | \(-0.469533\pi\) | ||||
0.0955702 | + | 0.995423i | \(0.469533\pi\) | |||||||
\(602\) | 0.0645730 | 0.00263180 | ||||||||
\(603\) | −21.1112 | −0.859716 | ||||||||
\(604\) | −5.53898 | −0.225378 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5.12712 | 0.208275 | ||||||||
\(607\) | 0.502641 | 0.0204016 | 0.0102008 | − | 0.999948i | \(-0.496753\pi\) | ||||
0.0102008 | + | 0.999948i | \(0.496753\pi\) | |||||||
\(608\) | −12.9093 | −0.523540 | ||||||||
\(609\) | −2.80395 | −0.113622 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18.8672 | −0.763286 | ||||||||
\(612\) | −43.9170 | −1.77524 | ||||||||
\(613\) | −22.9142 | −0.925496 | −0.462748 | − | 0.886490i | \(-0.653137\pi\) | ||||
−0.462748 | + | 0.886490i | \(0.653137\pi\) | |||||||
\(614\) | −3.03868 | −0.122631 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.00060 | −0.120898 | ||||||||
\(617\) | 15.8574 | 0.638397 | 0.319198 | − | 0.947688i | \(-0.396586\pi\) | ||||
0.319198 | + | 0.947688i | \(0.396586\pi\) | |||||||
\(618\) | 2.07204 | 0.0833496 | ||||||||
\(619\) | −35.4014 | −1.42290 | −0.711451 | − | 0.702736i | \(-0.751961\pi\) | ||||
−0.711451 | + | 0.702736i | \(0.751961\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.14688 | −0.0460229 | ||||||||
\(622\) | 1.45327 | 0.0582707 | ||||||||
\(623\) | −11.8156 | −0.473383 | ||||||||
\(624\) | 39.2299 | 1.57045 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.27846 | 0.0910658 | ||||||||
\(627\) | −78.7253 | −3.14399 | ||||||||
\(628\) | 9.82734 | 0.392154 | ||||||||
\(629\) | −6.80395 | −0.271291 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 44.7056 | 1.77970 | 0.889851 | − | 0.456250i | \(-0.150808\pi\) | ||||
0.889851 | + | 0.456250i | \(0.150808\pi\) | |||||||
\(632\) | −3.45852 | −0.137573 | ||||||||
\(633\) | 4.22318 | 0.167856 | ||||||||
\(634\) | 3.51379 | 0.139551 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 57.1610 | 2.26658 | ||||||||
\(637\) | −23.0480 | −0.913194 | ||||||||
\(638\) | −0.690163 | −0.0273238 | ||||||||
\(639\) | 7.14688 | 0.282726 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.0689 | 0.397699 | 0.198849 | − | 0.980030i | \(-0.436280\pi\) | ||||
0.198849 | + | 0.980030i | \(0.436280\pi\) | |||||||
\(642\) | 0.439617 | 0.0173503 | ||||||||
\(643\) | −13.9760 | −0.551161 | −0.275580 | − | 0.961278i | \(-0.588870\pi\) | ||||
−0.275580 | + | 0.961278i | \(0.588870\pi\) | |||||||
\(644\) | 1.68526 | 0.0664085 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.80395 | −0.267698 | ||||||||
\(647\) | −31.1607 | −1.22505 | −0.612527 | − | 0.790450i | \(-0.709847\pi\) | ||||
−0.612527 | + | 0.790450i | \(0.709847\pi\) | |||||||
\(648\) | −4.33235 | −0.170191 | ||||||||
\(649\) | −44.0198 | −1.72793 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 17.9508 | 0.703549 | ||||||||
\(652\) | 41.0127 | 1.60618 | ||||||||
\(653\) | 26.1129 | 1.02188 | 0.510939 | − | 0.859617i | \(-0.329298\pi\) | ||||
0.510939 | + | 0.859617i | \(0.329298\pi\) | |||||||
\(654\) | −6.16158 | −0.240937 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 31.1684 | 1.21600 | ||||||||
\(658\) | 0.814661 | 0.0317588 | ||||||||
\(659\) | −28.5974 | −1.11400 | −0.556999 | − | 0.830513i | \(-0.688047\pi\) | ||||
−0.556999 | + | 0.830513i | \(0.688047\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −38.9994 | −1.51690 | −0.758450 | − | 0.651731i | \(-0.774043\pi\) | ||||
−0.758450 | + | 0.651731i | \(0.774043\pi\) | |||||||
\(662\) | −1.23731 | −0.0480895 | ||||||||
\(663\) | 63.3421 | 2.46000 | ||||||||
\(664\) | 3.87770 | 0.150484 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.612724 | 0.0237426 | ||||||||
\(667\) | 0.780070 | 0.0302044 | ||||||||
\(668\) | 43.2976 | 1.67523 | ||||||||
\(669\) | −24.2938 | −0.939251 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.04856 | 0.194897 | ||||||||
\(672\) | −5.18922 | −0.200178 | ||||||||
\(673\) | 38.6725 | 1.49072 | 0.745358 | − | 0.666665i | \(-0.232279\pi\) | ||||
0.745358 | + | 0.666665i | \(0.232279\pi\) | |||||||
\(674\) | −5.24100 | −0.201876 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.47090 | −0.210419 | ||||||||
\(677\) | −28.4800 | −1.09458 | −0.547288 | − | 0.836944i | \(-0.684340\pi\) | ||||
−0.547288 | + | 0.836944i | \(0.684340\pi\) | |||||||
\(678\) | −2.92966 | −0.112513 | ||||||||
\(679\) | −19.0486 | −0.731017 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.6859 | −0.562764 | ||||||||
\(682\) | 4.41841 | 0.169190 | ||||||||
\(683\) | −12.4159 | −0.475081 | −0.237540 | − | 0.971378i | \(-0.576341\pi\) | ||||
−0.237540 | + | 0.971378i | \(0.576341\pi\) | |||||||
\(684\) | −49.2398 | −1.88273 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.19544 | 0.0838224 | ||||||||
\(687\) | 38.8347 | 1.48164 | ||||||||
\(688\) | −1.45106 | −0.0553211 | ||||||||
\(689\) | −44.8180 | −1.70743 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.8040 | 0.411002 | 0.205501 | − | 0.978657i | \(-0.434118\pi\) | ||||
0.205501 | + | 0.978657i | \(0.434118\pi\) | |||||||
\(692\) | −6.42808 | −0.244359 | ||||||||
\(693\) | −17.2032 | −0.653495 | ||||||||
\(694\) | −4.87709 | −0.185132 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.59802 | −0.0605729 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0.904568 | 0.0342384 | ||||||||
\(699\) | 1.83842 | 0.0695352 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.47512 | 0.320101 | 0.160050 | − | 0.987109i | \(-0.448834\pi\) | ||||
0.160050 | + | 0.987109i | \(0.448834\pi\) | |||||||
\(702\) | −0.915375 | −0.0345486 | ||||||||
\(703\) | −7.62859 | −0.287718 | ||||||||
\(704\) | 32.6454 | 1.23037 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.11809 | 0.0797153 | ||||||||
\(707\) | −13.9491 | −0.524612 | ||||||||
\(708\) | −50.6472 | −1.90344 | ||||||||
\(709\) | −32.8180 | −1.23251 | −0.616254 | − | 0.787548i | \(-0.711350\pi\) | ||||
−0.616254 | + | 0.787548i | \(0.711350\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −19.8285 | −0.743628 | ||||||||
\(712\) | −6.73394 | −0.252365 | ||||||||
\(713\) | −4.99399 | −0.187026 | ||||||||
\(714\) | −2.73503 | −0.102356 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 14.2152 | 0.531247 | ||||||||
\(717\) | −5.12775 | −0.191499 | ||||||||
\(718\) | 0.181363 | 0.00676842 | ||||||||
\(719\) | 39.7542 | 1.48258 | 0.741290 | − | 0.671184i | \(-0.234214\pi\) | ||||
0.741290 | + | 0.671184i | \(0.234214\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.63731 | −0.209944 | ||||||||
\(722\) | −4.64968 | −0.173043 | ||||||||
\(723\) | 44.4274 | 1.65227 | ||||||||
\(724\) | −25.7485 | −0.956936 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −3.36751 | −0.124980 | ||||||||
\(727\) | 49.4844 | 1.83527 | 0.917637 | − | 0.397419i | \(-0.130094\pi\) | ||||
0.917637 | + | 0.397419i | \(0.130094\pi\) | |||||||
\(728\) | 2.70689 | 0.100324 | ||||||||
\(729\) | −36.1469 | −1.33877 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.34293 | −0.0866565 | ||||||||
\(732\) | 5.80865 | 0.214694 | ||||||||
\(733\) | −46.2381 | −1.70784 | −0.853921 | − | 0.520403i | \(-0.825782\pi\) | ||||
−0.853921 | + | 0.520403i | \(0.825782\pi\) | |||||||
\(734\) | 1.66128 | 0.0613191 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.44366 | 0.0532140 | ||||||||
\(737\) | 26.0061 | 0.957946 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.7155 | 1.05632 | 0.528159 | − | 0.849146i | \(-0.322883\pi\) | ||||
0.528159 | + | 0.849146i | \(0.322883\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 71.0192 | 2.60895 | ||||||||
\(742\) | 1.93518 | 0.0710428 | ||||||||
\(743\) | 27.0536 | 0.992502 | 0.496251 | − | 0.868179i | \(-0.334710\pi\) | ||||
0.496251 | + | 0.868179i | \(0.334710\pi\) | |||||||
\(744\) | 10.2305 | 0.375069 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.11303 | 0.0407508 | ||||||||
\(747\) | 22.2318 | 0.813418 | ||||||||
\(748\) | 54.0996 | 1.97808 | ||||||||
\(749\) | −1.19605 | −0.0437026 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.8771 | −0.980759 | −0.490380 | − | 0.871509i | \(-0.663142\pi\) | ||||
−0.490380 | + | 0.871509i | \(0.663142\pi\) | |||||||
\(752\) | −18.3067 | −0.667578 | ||||||||
\(753\) | 66.6860 | 2.43017 | ||||||||
\(754\) | 0.622605 | 0.0226739 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.17629 | −0.115520 | ||||||||
\(757\) | −7.28814 | −0.264892 | −0.132446 | − | 0.991190i | \(-0.542283\pi\) | ||||
−0.132446 | + | 0.991190i | \(0.542283\pi\) | |||||||
\(758\) | −2.84130 | −0.103201 | ||||||||
\(759\) | 8.80395 | 0.319563 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.6079 | −1.14579 | −0.572893 | − | 0.819630i | \(-0.694179\pi\) | ||||
−0.572893 | + | 0.819630i | \(0.694179\pi\) | |||||||
\(762\) | −7.12750 | −0.258202 | ||||||||
\(763\) | 16.7636 | 0.606882 | ||||||||
\(764\) | 19.9958 | 0.723422 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.514398 | 0.0185860 | ||||||||
\(767\) | 39.7108 | 1.43387 | ||||||||
\(768\) | 36.0725 | 1.30165 | ||||||||
\(769\) | −0.293769 | −0.0105936 | −0.00529679 | − | 0.999986i | \(-0.501686\pi\) | ||||
−0.00529679 | + | 0.999986i | \(0.501686\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −38.5440 | −1.38813 | ||||||||
\(772\) | 45.1559 | 1.62520 | ||||||||
\(773\) | 28.4877 | 1.02463 | 0.512316 | − | 0.858797i | \(-0.328788\pi\) | ||||
0.512316 | + | 0.858797i | \(0.328788\pi\) | |||||||
\(774\) | 0.210991 | 0.00758391 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −10.8561 | −0.389712 | ||||||||
\(777\) | −3.06651 | −0.110011 | ||||||||
\(778\) | 1.88142 | 0.0674521 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.80395 | −0.315030 | ||||||||
\(782\) | 0.760895 | 0.0272095 | ||||||||
\(783\) | −1.47023 | −0.0525418 | ||||||||
\(784\) | −22.3633 | −0.798689 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −2.94180 | −0.104931 | ||||||||
\(787\) | −32.9883 | −1.17591 | −0.587954 | − | 0.808895i | \(-0.700066\pi\) | ||||
−0.587954 | + | 0.808895i | \(0.700066\pi\) | |||||||
\(788\) | 43.5997 | 1.55317 | ||||||||
\(789\) | 30.9361 | 1.10136 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.97060 | 0.283402 | ||||||||
\(792\) | −9.80441 | −0.348384 | ||||||||
\(793\) | −4.55437 | −0.161731 | ||||||||
\(794\) | 5.69213 | 0.202006 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.2644 | −0.363811 | ||||||||
\(797\) | −30.9194 | −1.09522 | −0.547611 | − | 0.836733i | \(-0.684463\pi\) | ||||
−0.547611 | + | 0.836733i | \(0.684463\pi\) | |||||||
\(798\) | −3.06651 | −0.108553 | ||||||||
\(799\) | −29.5587 | −1.04571 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −38.6073 | −1.36412 | ||||||||
\(802\) | −4.08942 | −0.144402 | ||||||||
\(803\) | −38.3951 | −1.35493 | ||||||||
\(804\) | 29.9214 | 1.05525 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.98590 | −0.140397 | ||||||||
\(807\) | −27.8260 | −0.979522 | ||||||||
\(808\) | −7.94987 | −0.279675 | ||||||||
\(809\) | 21.0977 | 0.741756 | 0.370878 | − | 0.928682i | \(-0.379057\pi\) | ||||
0.370878 | + | 0.928682i | \(0.379057\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.0000 | 0.983213 | 0.491606 | − | 0.870817i | \(-0.336410\pi\) | ||||
0.491606 | + | 0.870817i | \(0.336410\pi\) | |||||||
\(812\) | 2.16040 | 0.0758150 | ||||||||
\(813\) | −32.6763 | −1.14601 | ||||||||
\(814\) | −0.754790 | −0.0264554 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 61.4604 | 2.15154 | ||||||||
\(817\) | −2.62690 | −0.0919035 | ||||||||
\(818\) | −2.04582 | −0.0715303 | ||||||||
\(819\) | 15.5192 | 0.542285 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.2791 | −0.533243 | −0.266622 | − | 0.963801i | \(-0.585907\pi\) | ||||
−0.266622 | + | 0.963801i | \(0.585907\pi\) | |||||||
\(822\) | −3.93494 | −0.137247 | ||||||||
\(823\) | 7.78152 | 0.271247 | 0.135623 | − | 0.990760i | \(-0.456696\pi\) | ||||
0.135623 | + | 0.990760i | \(0.456696\pi\) | |||||||
\(824\) | −3.21280 | −0.111923 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.71466 | −0.0596607 | ||||||||
\(827\) | 0.376593 | 0.0130954 | 0.00654772 | − | 0.999979i | \(-0.497916\pi\) | ||||
0.00654772 | + | 0.999979i | \(0.497916\pi\) | |||||||
\(828\) | 5.50655 | 0.191366 | ||||||||
\(829\) | −49.8723 | −1.73214 | −0.866068 | − | 0.499927i | \(-0.833360\pi\) | ||||
−0.866068 | + | 0.499927i | \(0.833360\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 51.4604 | 1.78514 | ||||||||
\(832\) | −29.4498 | −1.02099 | ||||||||
\(833\) | −36.1086 | −1.25109 | ||||||||
\(834\) | 1.10736 | 0.0383447 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 60.6565 | 2.09785 | ||||||||
\(837\) | 9.41240 | 0.325340 | ||||||||
\(838\) | −5.62113 | −0.194179 | ||||||||
\(839\) | −0.0590441 | −0.00203843 | −0.00101921 | − | 0.999999i | \(-0.500324\pi\) | ||||
−0.00101921 | + | 0.999999i | \(0.500324\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −2.61919 | −0.0902632 | ||||||||
\(843\) | −53.6776 | −1.84875 | ||||||||
\(844\) | −3.25388 | −0.112003 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.66189 | 0.0915176 | ||||||||
\(847\) | 9.16185 | 0.314805 | ||||||||
\(848\) | −43.4867 | −1.49334 | ||||||||
\(849\) | 43.5096 | 1.49324 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.853115 | 0.0292444 | ||||||||
\(852\) | −10.1294 | −0.347029 | ||||||||
\(853\) | −2.77983 | −0.0951795 | −0.0475897 | − | 0.998867i | \(-0.515154\pi\) | ||||
−0.0475897 | + | 0.998867i | \(0.515154\pi\) | |||||||
\(854\) | 0.196652 | 0.00672929 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.681649 | −0.0232983 | ||||||||
\(857\) | −0.850802 | −0.0290628 | −0.0145314 | − | 0.999894i | \(-0.504626\pi\) | ||||
−0.0145314 | + | 0.999894i | \(0.504626\pi\) | |||||||
\(858\) | 7.02679 | 0.239891 | ||||||||
\(859\) | 7.35342 | 0.250895 | 0.125448 | − | 0.992100i | \(-0.459963\pi\) | ||||
0.125448 | + | 0.992100i | \(0.459963\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.12556 | 0.140517 | ||||||||
\(863\) | −42.6167 | −1.45069 | −0.725345 | − | 0.688386i | \(-0.758320\pi\) | ||||
−0.725345 | + | 0.688386i | \(0.758320\pi\) | |||||||
\(864\) | −2.72093 | −0.0925680 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.68105 | −0.0571242 | ||||||||
\(867\) | 55.6505 | 1.88999 | ||||||||
\(868\) | −13.8308 | −0.469448 | ||||||||
\(869\) | 24.4260 | 0.828594 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23.4604 | −0.794926 | ||||||||
\(872\) | 9.55386 | 0.323535 | ||||||||
\(873\) | −62.2407 | −2.10653 | ||||||||
\(874\) | 0.853115 | 0.0288571 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −44.1757 | −1.49256 | ||||||||
\(877\) | −13.4196 | −0.453148 | −0.226574 | − | 0.973994i | \(-0.572753\pi\) | ||||
−0.226574 | + | 0.973994i | \(0.572753\pi\) | |||||||
\(878\) | −4.63436 | −0.156402 | ||||||||
\(879\) | −24.2938 | −0.819408 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −38.3135 | −1.29082 | −0.645408 | − | 0.763838i | \(-0.723313\pi\) | ||||
−0.645408 | + | 0.763838i | \(0.723313\pi\) | |||||||
\(882\) | 3.25173 | 0.109491 | ||||||||
\(883\) | 31.5542 | 1.06188 | 0.530942 | − | 0.847408i | \(-0.321838\pi\) | ||||
0.530942 | + | 0.847408i | \(0.321838\pi\) | |||||||
\(884\) | −48.8040 | −1.64145 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.534161 | 0.0179455 | ||||||||
\(887\) | −23.3961 | −0.785565 | −0.392783 | − | 0.919631i | \(-0.628488\pi\) | ||||
−0.392783 | + | 0.919631i | \(0.628488\pi\) | |||||||
\(888\) | −1.74766 | −0.0586477 | ||||||||
\(889\) | 19.3915 | 0.650370 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 30.5974 | 1.02505 | ||||||||
\(892\) | 18.7179 | 0.626722 | ||||||||
\(893\) | −33.1413 | −1.10903 | ||||||||
\(894\) | 1.81865 | 0.0608248 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 5.31956 | 0.177714 | ||||||||
\(897\) | −7.94216 | −0.265181 | ||||||||
\(898\) | −0.0722810 | −0.00241205 | ||||||||
\(899\) | −6.40198 | −0.213518 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −70.2152 | −2.33921 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.05595 | −0.0351398 | ||||||||
\(904\) | 4.54259 | 0.151084 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.12712 | −0.0374461 | ||||||||
\(907\) | −32.4150 | −1.07632 | −0.538161 | − | 0.842842i | \(-0.680881\pi\) | ||||
−0.538161 | + | 0.842842i | \(0.680881\pi\) | |||||||
\(908\) | 11.3152 | 0.375508 | ||||||||
\(909\) | −45.5785 | −1.51174 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −45.2749 | −1.50002 | −0.750011 | − | 0.661425i | \(-0.769952\pi\) | ||||
−0.750011 | + | 0.661425i | \(0.769952\pi\) | |||||||
\(912\) | 68.9094 | 2.28182 | ||||||||
\(913\) | −27.3864 | −0.906357 | ||||||||
\(914\) | −0.215206 | −0.00711837 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −29.9214 | −0.988632 | ||||||||
\(917\) | 8.00364 | 0.264303 | ||||||||
\(918\) | −1.43409 | −0.0473321 | ||||||||
\(919\) | −5.90167 | −0.194678 | −0.0973391 | − | 0.995251i | \(-0.531033\pi\) | ||||
−0.0973391 | + | 0.995251i | \(0.531033\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 49.6909 | 1.63737 | ||||||||
\(922\) | −2.28710 | −0.0753218 | ||||||||
\(923\) | 7.94216 | 0.261419 | ||||||||
\(924\) | 24.3825 | 0.802124 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.95566 | 0.0971289 | ||||||||
\(927\) | −18.4198 | −0.604985 | ||||||||
\(928\) | 1.85068 | 0.0607516 | ||||||||
\(929\) | −6.00000 | −0.196854 | −0.0984268 | − | 0.995144i | \(-0.531381\pi\) | ||||
−0.0984268 | + | 0.995144i | \(0.531381\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −40.4850 | −1.32684 | ||||||||
\(932\) | −1.41647 | −0.0463979 | ||||||||
\(933\) | −23.7650 | −0.778032 | ||||||||
\(934\) | −4.69695 | −0.153689 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 8.84469 | 0.289098 | ||||||||
\(937\) | −43.0755 | −1.40721 | −0.703607 | − | 0.710589i | \(-0.748429\pi\) | ||||
−0.703607 | + | 0.710589i | \(0.748429\pi\) | |||||||
\(938\) | 1.01299 | 0.0330753 | ||||||||
\(939\) | −37.2593 | −1.21591 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.91637 | 0.0950711 | 0.0475355 | − | 0.998870i | \(-0.484863\pi\) | ||||
0.0475355 | + | 0.998870i | \(0.484863\pi\) | |||||||
\(942\) | 1.99976 | 0.0651556 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 38.5312 | 1.25408 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.259911 | −0.00845043 | ||||||||
\(947\) | −0.556407 | −0.0180808 | −0.00904041 | − | 0.999959i | \(-0.502878\pi\) | ||||
−0.00904041 | + | 0.999959i | \(0.502878\pi\) | |||||||
\(948\) | 28.1034 | 0.912757 | ||||||||
\(949\) | 34.6367 | 1.12435 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −57.4604 | −1.86328 | ||||||||
\(952\) | 4.24080 | 0.137445 | ||||||||
\(953\) | 37.1661 | 1.20393 | 0.601964 | − | 0.798523i | \(-0.294385\pi\) | ||||
0.601964 | + | 0.798523i | \(0.294385\pi\) | |||||||
\(954\) | 6.32317 | 0.204720 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.95084 | 0.127779 | ||||||||
\(957\) | 11.2861 | 0.364828 | ||||||||
\(958\) | 5.13700 | 0.165969 | ||||||||
\(959\) | 10.7056 | 0.345703 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.98530 | 0.322106 | ||||||||
\(962\) | 0.680906 | 0.0219533 | ||||||||
\(963\) | −3.90806 | −0.125935 | ||||||||
\(964\) | −34.2305 | −1.10249 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.342932 | 0.0110337 | ||||||||
\(967\) | 24.2754 | 0.780643 | 0.390322 | − | 0.920679i | \(-0.372364\pi\) | ||||
0.390322 | + | 0.920679i | \(0.372364\pi\) | |||||||
\(968\) | 5.22151 | 0.167826 | ||||||||
\(969\) | 111.264 | 3.57431 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.1709 | −0.551039 | −0.275520 | − | 0.961295i | \(-0.588850\pi\) | ||||
−0.275520 | + | 0.961295i | \(0.588850\pi\) | |||||||
\(972\) | 43.9170 | 1.40864 | ||||||||
\(973\) | −3.01275 | −0.0965842 | ||||||||
\(974\) | 2.21220 | 0.0708834 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.41908 | −0.141451 | ||||||||
\(977\) | 4.95785 | 0.158616 | 0.0793078 | − | 0.996850i | \(-0.474729\pi\) | ||||
0.0793078 | + | 0.996850i | \(0.474729\pi\) | |||||||
\(978\) | 8.34564 | 0.266864 | ||||||||
\(979\) | 47.5587 | 1.51998 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 54.7746 | 1.74882 | ||||||||
\(982\) | −0.644104 | −0.0205542 | ||||||||
\(983\) | 11.5651 | 0.368869 | 0.184434 | − | 0.982845i | \(-0.440955\pi\) | ||||
0.184434 | + | 0.982845i | \(0.440955\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.975419 | 0.0310637 | ||||||||
\(987\) | −13.3220 | −0.424044 | ||||||||
\(988\) | −54.7190 | −1.74084 | ||||||||
\(989\) | 0.293769 | 0.00934132 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.3429 | −0.582682 | −0.291341 | − | 0.956619i | \(-0.594102\pi\) | ||||
−0.291341 | + | 0.956619i | \(0.594102\pi\) | |||||||
\(992\) | −11.8480 | −0.376175 | ||||||||
\(993\) | 20.2336 | 0.642092 | ||||||||
\(994\) | −0.342932 | −0.0108771 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −31.5096 | −0.998419 | ||||||||
\(997\) | −32.2997 | −1.02294 | −0.511471 | − | 0.859300i | \(-0.670899\pi\) | ||||
−0.511471 | + | 0.859300i | \(0.670899\pi\) | |||||||
\(998\) | −4.71435 | −0.149230 | ||||||||
\(999\) | −1.60790 | −0.0508719 |
(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 | 725.2.a.l.1.3 | 6 | ||
3.2 | odd | 2 | 6525.2.a.bt.1.4 | 6 | |||
5.2 | odd | 4 | 145.2.b.c.59.3 | ✓ | 6 | ||
5.3 | odd | 4 | 145.2.b.c.59.4 | yes | 6 | ||
5.4 | even | 2 | inner | 725.2.a.l.1.4 | 6 | ||
15.2 | even | 4 | 1305.2.c.h.784.4 | 6 | |||
15.8 | even | 4 | 1305.2.c.h.784.3 | 6 | |||
15.14 | odd | 2 | 6525.2.a.bt.1.3 | 6 | |||
20.3 | even | 4 | 2320.2.d.g.929.2 | 6 | |||
20.7 | even | 4 | 2320.2.d.g.929.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
145.2.b.c.59.3 | ✓ | 6 | 5.2 | odd | 4 | ||
145.2.b.c.59.4 | yes | 6 | 5.3 | odd | 4 | ||
725.2.a.l.1.3 | 6 | 1.1 | even | 1 | trivial | ||
725.2.a.l.1.4 | 6 | 5.4 | even | 2 | inner | ||
1305.2.c.h.784.3 | 6 | 15.8 | even | 4 | |||
1305.2.c.h.784.4 | 6 | 15.2 | even | 4 | |||
2320.2.d.g.929.2 | 6 | 20.3 | even | 4 | |||
2320.2.d.g.929.5 | 6 | 20.7 | even | 4 | |||
6525.2.a.bt.1.3 | 6 | 15.14 | odd | 2 | |||
6525.2.a.bt.1.4 | 6 | 3.2 | odd | 2 |