Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, 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("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.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: | \(64.1518129839\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - x^{14} - 48 x^{13} + 44 x^{12} + 872 x^{11} - 707 x^{10} - 7580 x^{9} + 5112 x^{8} + \cdots + 2048 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Root | \(-3.53778\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.53778 | 1.58214 | 0.791072 | − | 0.611723i | \(-0.209523\pi\) | ||||
0.791072 | + | 0.611723i | \(0.209523\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −4.09818 | −1.54897 | −0.774483 | − | 0.632594i | \(-0.781990\pi\) | ||||
−0.774483 | + | 0.632594i | \(0.781990\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.53778 | 1.11874 | ||||||||
\(11\) | −3.53153 | −1.06480 | −0.532398 | − | 0.846494i | \(-0.678709\pi\) | ||||
−0.532398 | + | 0.846494i | \(0.678709\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −4.09818 | −1.09528 | ||||||||
\(15\) | −3.53778 | −0.913451 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.18686 | −0.530391 | −0.265196 | − | 0.964195i | \(-0.585437\pi\) | ||||
−0.265196 | + | 0.964195i | \(0.585437\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −0.266722 | −0.0611903 | −0.0305952 | − | 0.999532i | \(-0.509740\pi\) | ||||
−0.0305952 | + | 0.999532i | \(0.509740\pi\) | |||||||
\(20\) | 3.53778 | 0.791072 | ||||||||
\(21\) | 4.09818 | 0.894296 | ||||||||
\(22\) | −3.53153 | −0.752925 | ||||||||
\(23\) | −9.08925 | −1.89524 | −0.947619 | − | 0.319402i | \(-0.896518\pi\) | ||||
−0.947619 | + | 0.319402i | \(0.896518\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 7.51589 | 1.50318 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −4.09818 | −0.774483 | ||||||||
\(29\) | 6.77872 | 1.25878 | 0.629389 | − | 0.777091i | \(-0.283305\pi\) | ||||
0.629389 | + | 0.777091i | \(0.283305\pi\) | |||||||
\(30\) | −3.53778 | −0.645907 | ||||||||
\(31\) | 6.69972 | 1.20331 | 0.601653 | − | 0.798758i | \(-0.294509\pi\) | ||||
0.601653 | + | 0.798758i | \(0.294509\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 3.53153 | 0.614761 | ||||||||
\(34\) | −2.18686 | −0.375043 | ||||||||
\(35\) | −14.4985 | −2.45069 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 10.3454 | 1.70078 | 0.850390 | − | 0.526153i | \(-0.176366\pi\) | ||||
0.850390 | + | 0.526153i | \(0.176366\pi\) | |||||||
\(38\) | −0.266722 | −0.0432681 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 3.53778 | 0.559372 | ||||||||
\(41\) | −5.22997 | −0.816784 | −0.408392 | − | 0.912807i | \(-0.633910\pi\) | ||||
−0.408392 | + | 0.912807i | \(0.633910\pi\) | |||||||
\(42\) | 4.09818 | 0.632363 | ||||||||
\(43\) | 6.71778 | 1.02445 | 0.512226 | − | 0.858851i | \(-0.328821\pi\) | ||||
0.512226 | + | 0.858851i | \(0.328821\pi\) | |||||||
\(44\) | −3.53153 | −0.532398 | ||||||||
\(45\) | 3.53778 | 0.527381 | ||||||||
\(46\) | −9.08925 | −1.34014 | ||||||||
\(47\) | −8.08805 | −1.17976 | −0.589882 | − | 0.807490i | \(-0.700826\pi\) | ||||
−0.589882 | + | 0.807490i | \(0.700826\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 9.79508 | 1.39930 | ||||||||
\(50\) | 7.51589 | 1.06291 | ||||||||
\(51\) | 2.18686 | 0.306222 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | 5.93846 | 0.815710 | 0.407855 | − | 0.913047i | \(-0.366277\pi\) | ||||
0.407855 | + | 0.913047i | \(0.366277\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −12.4938 | −1.68466 | ||||||||
\(56\) | −4.09818 | −0.547642 | ||||||||
\(57\) | 0.266722 | 0.0353283 | ||||||||
\(58\) | 6.77872 | 0.890090 | ||||||||
\(59\) | 1.22445 | 0.159410 | 0.0797048 | − | 0.996819i | \(-0.474602\pi\) | ||||
0.0797048 | + | 0.996819i | \(0.474602\pi\) | |||||||
\(60\) | −3.53778 | −0.456726 | ||||||||
\(61\) | −4.83351 | −0.618867 | −0.309434 | − | 0.950921i | \(-0.600139\pi\) | ||||
−0.309434 | + | 0.950921i | \(0.600139\pi\) | |||||||
\(62\) | 6.69972 | 0.850866 | ||||||||
\(63\) | −4.09818 | −0.516322 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.53778 | −0.438808 | ||||||||
\(66\) | 3.53153 | 0.434701 | ||||||||
\(67\) | 12.7005 | 1.55161 | 0.775806 | − | 0.630971i | \(-0.217343\pi\) | ||||
0.775806 | + | 0.630971i | \(0.217343\pi\) | |||||||
\(68\) | −2.18686 | −0.265196 | ||||||||
\(69\) | 9.08925 | 1.09422 | ||||||||
\(70\) | −14.4985 | −1.73290 | ||||||||
\(71\) | −8.30262 | −0.985340 | −0.492670 | − | 0.870216i | \(-0.663979\pi\) | ||||
−0.492670 | + | 0.870216i | \(0.663979\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 11.4874 | 1.34449 | 0.672247 | − | 0.740327i | \(-0.265329\pi\) | ||||
0.672247 | + | 0.740327i | \(0.265329\pi\) | |||||||
\(74\) | 10.3454 | 1.20263 | ||||||||
\(75\) | −7.51589 | −0.867860 | ||||||||
\(76\) | −0.266722 | −0.0305952 | ||||||||
\(77\) | 14.4729 | 1.64933 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | 16.9009 | 1.90150 | 0.950750 | − | 0.309960i | \(-0.100316\pi\) | ||||
0.950750 | + | 0.309960i | \(0.100316\pi\) | |||||||
\(80\) | 3.53778 | 0.395536 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.22997 | −0.577554 | ||||||||
\(83\) | 8.26872 | 0.907610 | 0.453805 | − | 0.891101i | \(-0.350066\pi\) | ||||
0.453805 | + | 0.891101i | \(0.350066\pi\) | |||||||
\(84\) | 4.09818 | 0.447148 | ||||||||
\(85\) | −7.73663 | −0.839155 | ||||||||
\(86\) | 6.71778 | 0.724396 | ||||||||
\(87\) | −6.77872 | −0.726755 | ||||||||
\(88\) | −3.53153 | −0.376462 | ||||||||
\(89\) | 11.1766 | 1.18472 | 0.592360 | − | 0.805673i | \(-0.298196\pi\) | ||||
0.592360 | + | 0.805673i | \(0.298196\pi\) | |||||||
\(90\) | 3.53778 | 0.372915 | ||||||||
\(91\) | 4.09818 | 0.429606 | ||||||||
\(92\) | −9.08925 | −0.947619 | ||||||||
\(93\) | −6.69972 | −0.694729 | ||||||||
\(94\) | −8.08805 | −0.834219 | ||||||||
\(95\) | −0.943606 | −0.0968119 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 8.23809 | 0.836451 | 0.418226 | − | 0.908343i | \(-0.362652\pi\) | ||||
0.418226 | + | 0.908343i | \(0.362652\pi\) | |||||||
\(98\) | 9.79508 | 0.989452 | ||||||||
\(99\) | −3.53153 | −0.354932 | ||||||||
\(100\) | 7.51589 | 0.751589 | ||||||||
\(101\) | −16.6091 | −1.65267 | −0.826334 | − | 0.563180i | \(-0.809578\pi\) | ||||
−0.826334 | + | 0.563180i | \(0.809578\pi\) | |||||||
\(102\) | 2.18686 | 0.216531 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 14.4985 | 1.41490 | ||||||||
\(106\) | 5.93846 | 0.576794 | ||||||||
\(107\) | 18.4079 | 1.77956 | 0.889778 | − | 0.456394i | \(-0.150859\pi\) | ||||
0.889778 | + | 0.456394i | \(0.150859\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 12.5219 | 1.19938 | 0.599689 | − | 0.800233i | \(-0.295291\pi\) | ||||
0.599689 | + | 0.800233i | \(0.295291\pi\) | |||||||
\(110\) | −12.4938 | −1.19124 | ||||||||
\(111\) | −10.3454 | −0.981945 | ||||||||
\(112\) | −4.09818 | −0.387242 | ||||||||
\(113\) | 12.1628 | 1.14418 | 0.572089 | − | 0.820191i | \(-0.306133\pi\) | ||||
0.572089 | + | 0.820191i | \(0.306133\pi\) | |||||||
\(114\) | 0.266722 | 0.0249808 | ||||||||
\(115\) | −32.1558 | −2.99854 | ||||||||
\(116\) | 6.77872 | 0.629389 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 1.22445 | 0.112720 | ||||||||
\(119\) | 8.96214 | 0.821558 | ||||||||
\(120\) | −3.53778 | −0.322954 | ||||||||
\(121\) | 1.47171 | 0.133792 | ||||||||
\(122\) | −4.83351 | −0.437605 | ||||||||
\(123\) | 5.22997 | 0.471571 | ||||||||
\(124\) | 6.69972 | 0.601653 | ||||||||
\(125\) | 8.90067 | 0.796100 | ||||||||
\(126\) | −4.09818 | −0.365095 | ||||||||
\(127\) | −8.55557 | −0.759184 | −0.379592 | − | 0.925154i | \(-0.623936\pi\) | ||||
−0.379592 | + | 0.925154i | \(0.623936\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −6.71778 | −0.591467 | ||||||||
\(130\) | −3.53778 | −0.310284 | ||||||||
\(131\) | 6.96127 | 0.608209 | 0.304105 | − | 0.952639i | \(-0.401643\pi\) | ||||
0.304105 | + | 0.952639i | \(0.401643\pi\) | |||||||
\(132\) | 3.53153 | 0.307380 | ||||||||
\(133\) | 1.09308 | 0.0947818 | ||||||||
\(134\) | 12.7005 | 1.09716 | ||||||||
\(135\) | −3.53778 | −0.304484 | ||||||||
\(136\) | −2.18686 | −0.187522 | ||||||||
\(137\) | 12.7438 | 1.08878 | 0.544389 | − | 0.838833i | \(-0.316762\pi\) | ||||
0.544389 | + | 0.838833i | \(0.316762\pi\) | |||||||
\(138\) | 9.08925 | 0.773728 | ||||||||
\(139\) | 6.43994 | 0.546229 | 0.273114 | − | 0.961982i | \(-0.411946\pi\) | ||||
0.273114 | + | 0.961982i | \(0.411946\pi\) | |||||||
\(140\) | −14.4985 | −1.22534 | ||||||||
\(141\) | 8.08805 | 0.681137 | ||||||||
\(142\) | −8.30262 | −0.696740 | ||||||||
\(143\) | 3.53153 | 0.295321 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 23.9816 | 1.99157 | ||||||||
\(146\) | 11.4874 | 0.950701 | ||||||||
\(147\) | −9.79508 | −0.807885 | ||||||||
\(148\) | 10.3454 | 0.850390 | ||||||||
\(149\) | 1.99904 | 0.163767 | 0.0818837 | − | 0.996642i | \(-0.473906\pi\) | ||||
0.0818837 | + | 0.996642i | \(0.473906\pi\) | |||||||
\(150\) | −7.51589 | −0.613670 | ||||||||
\(151\) | 7.74370 | 0.630173 | 0.315087 | − | 0.949063i | \(-0.397966\pi\) | ||||
0.315087 | + | 0.949063i | \(0.397966\pi\) | |||||||
\(152\) | −0.266722 | −0.0216340 | ||||||||
\(153\) | −2.18686 | −0.176797 | ||||||||
\(154\) | 14.4729 | 1.16626 | ||||||||
\(155\) | 23.7022 | 1.90380 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | −6.61959 | −0.528300 | −0.264150 | − | 0.964482i | \(-0.585091\pi\) | ||||
−0.264150 | + | 0.964482i | \(0.585091\pi\) | |||||||
\(158\) | 16.9009 | 1.34456 | ||||||||
\(159\) | −5.93846 | −0.470950 | ||||||||
\(160\) | 3.53778 | 0.279686 | ||||||||
\(161\) | 37.2494 | 2.93566 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −9.98151 | −0.781812 | −0.390906 | − | 0.920431i | \(-0.627838\pi\) | ||||
−0.390906 | + | 0.920431i | \(0.627838\pi\) | |||||||
\(164\) | −5.22997 | −0.408392 | ||||||||
\(165\) | 12.4938 | 0.972640 | ||||||||
\(166\) | 8.26872 | 0.641777 | ||||||||
\(167\) | −23.0834 | −1.78625 | −0.893125 | − | 0.449809i | \(-0.851492\pi\) | ||||
−0.893125 | + | 0.449809i | \(0.851492\pi\) | |||||||
\(168\) | 4.09818 | 0.316181 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −7.73663 | −0.593372 | ||||||||
\(171\) | −0.266722 | −0.0203968 | ||||||||
\(172\) | 6.71778 | 0.512226 | ||||||||
\(173\) | 4.63859 | 0.352666 | 0.176333 | − | 0.984331i | \(-0.443576\pi\) | ||||
0.176333 | + | 0.984331i | \(0.443576\pi\) | |||||||
\(174\) | −6.77872 | −0.513894 | ||||||||
\(175\) | −30.8015 | −2.32837 | ||||||||
\(176\) | −3.53153 | −0.266199 | ||||||||
\(177\) | −1.22445 | −0.0920352 | ||||||||
\(178\) | 11.1766 | 0.837724 | ||||||||
\(179\) | −25.0381 | −1.87143 | −0.935717 | − | 0.352751i | \(-0.885246\pi\) | ||||
−0.935717 | + | 0.352751i | \(0.885246\pi\) | |||||||
\(180\) | 3.53778 | 0.263691 | ||||||||
\(181\) | −14.6223 | −1.08687 | −0.543435 | − | 0.839451i | \(-0.682877\pi\) | ||||
−0.543435 | + | 0.839451i | \(0.682877\pi\) | |||||||
\(182\) | 4.09818 | 0.303777 | ||||||||
\(183\) | 4.83351 | 0.357303 | ||||||||
\(184\) | −9.08925 | −0.670068 | ||||||||
\(185\) | 36.5999 | 2.69088 | ||||||||
\(186\) | −6.69972 | −0.491248 | ||||||||
\(187\) | 7.72296 | 0.564759 | ||||||||
\(188\) | −8.08805 | −0.589882 | ||||||||
\(189\) | 4.09818 | 0.298099 | ||||||||
\(190\) | −0.943606 | −0.0684563 | ||||||||
\(191\) | 24.7035 | 1.78748 | 0.893741 | − | 0.448584i | \(-0.148071\pi\) | ||||
0.893741 | + | 0.448584i | \(0.148071\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −13.9811 | −1.00638 | −0.503189 | − | 0.864176i | \(-0.667840\pi\) | ||||
−0.503189 | + | 0.864176i | \(0.667840\pi\) | |||||||
\(194\) | 8.23809 | 0.591460 | ||||||||
\(195\) | 3.53778 | 0.253346 | ||||||||
\(196\) | 9.79508 | 0.699649 | ||||||||
\(197\) | −24.1579 | −1.72118 | −0.860590 | − | 0.509299i | \(-0.829905\pi\) | ||||
−0.860590 | + | 0.509299i | \(0.829905\pi\) | |||||||
\(198\) | −3.53153 | −0.250975 | ||||||||
\(199\) | 13.8851 | 0.984288 | 0.492144 | − | 0.870514i | \(-0.336213\pi\) | ||||
0.492144 | + | 0.870514i | \(0.336213\pi\) | |||||||
\(200\) | 7.51589 | 0.531454 | ||||||||
\(201\) | −12.7005 | −0.895824 | ||||||||
\(202\) | −16.6091 | −1.16861 | ||||||||
\(203\) | −27.7804 | −1.94980 | ||||||||
\(204\) | 2.18686 | 0.153111 | ||||||||
\(205\) | −18.5025 | −1.29227 | ||||||||
\(206\) | −1.00000 | −0.0696733 | ||||||||
\(207\) | −9.08925 | −0.631746 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | 0.941939 | 0.0651553 | ||||||||
\(210\) | 14.4985 | 1.00049 | ||||||||
\(211\) | 13.7740 | 0.948244 | 0.474122 | − | 0.880459i | \(-0.342766\pi\) | ||||
0.474122 | + | 0.880459i | \(0.342766\pi\) | |||||||
\(212\) | 5.93846 | 0.407855 | ||||||||
\(213\) | 8.30262 | 0.568886 | ||||||||
\(214\) | 18.4079 | 1.25834 | ||||||||
\(215\) | 23.7660 | 1.62083 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −27.4567 | −1.86388 | ||||||||
\(218\) | 12.5219 | 0.848088 | ||||||||
\(219\) | −11.4874 | −0.776244 | ||||||||
\(220\) | −12.4938 | −0.842331 | ||||||||
\(221\) | 2.18686 | 0.147104 | ||||||||
\(222\) | −10.3454 | −0.694340 | ||||||||
\(223\) | 12.8558 | 0.860891 | 0.430445 | − | 0.902617i | \(-0.358357\pi\) | ||||
0.430445 | + | 0.902617i | \(0.358357\pi\) | |||||||
\(224\) | −4.09818 | −0.273821 | ||||||||
\(225\) | 7.51589 | 0.501059 | ||||||||
\(226\) | 12.1628 | 0.809057 | ||||||||
\(227\) | −12.2505 | −0.813097 | −0.406548 | − | 0.913629i | \(-0.633268\pi\) | ||||
−0.406548 | + | 0.913629i | \(0.633268\pi\) | |||||||
\(228\) | 0.266722 | 0.0176641 | ||||||||
\(229\) | −6.81988 | −0.450670 | −0.225335 | − | 0.974281i | \(-0.572348\pi\) | ||||
−0.225335 | + | 0.974281i | \(0.572348\pi\) | |||||||
\(230\) | −32.1558 | −2.12029 | ||||||||
\(231\) | −14.4729 | −0.952244 | ||||||||
\(232\) | 6.77872 | 0.445045 | ||||||||
\(233\) | 18.1244 | 1.18737 | 0.593685 | − | 0.804697i | \(-0.297672\pi\) | ||||
0.593685 | + | 0.804697i | \(0.297672\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | −28.6137 | −1.86655 | ||||||||
\(236\) | 1.22445 | 0.0797048 | ||||||||
\(237\) | −16.9009 | −1.09783 | ||||||||
\(238\) | 8.96214 | 0.580930 | ||||||||
\(239\) | 1.67370 | 0.108263 | 0.0541313 | − | 0.998534i | \(-0.482761\pi\) | ||||
0.0541313 | + | 0.998534i | \(0.482761\pi\) | |||||||
\(240\) | −3.53778 | −0.228363 | ||||||||
\(241\) | −1.25519 | −0.0808540 | −0.0404270 | − | 0.999182i | \(-0.512872\pi\) | ||||
−0.0404270 | + | 0.999182i | \(0.512872\pi\) | |||||||
\(242\) | 1.47171 | 0.0946053 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −4.83351 | −0.309434 | ||||||||
\(245\) | 34.6528 | 2.21389 | ||||||||
\(246\) | 5.22997 | 0.333451 | ||||||||
\(247\) | 0.266722 | 0.0169711 | ||||||||
\(248\) | 6.69972 | 0.425433 | ||||||||
\(249\) | −8.26872 | −0.524009 | ||||||||
\(250\) | 8.90067 | 0.562928 | ||||||||
\(251\) | 3.37351 | 0.212934 | 0.106467 | − | 0.994316i | \(-0.466046\pi\) | ||||
0.106467 | + | 0.994316i | \(0.466046\pi\) | |||||||
\(252\) | −4.09818 | −0.258161 | ||||||||
\(253\) | 32.0990 | 2.01804 | ||||||||
\(254\) | −8.55557 | −0.536824 | ||||||||
\(255\) | 7.73663 | 0.484487 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 10.8138 | 0.674549 | 0.337274 | − | 0.941406i | \(-0.390495\pi\) | ||||
0.337274 | + | 0.941406i | \(0.390495\pi\) | |||||||
\(258\) | −6.71778 | −0.418230 | ||||||||
\(259\) | −42.3975 | −2.63445 | ||||||||
\(260\) | −3.53778 | −0.219404 | ||||||||
\(261\) | 6.77872 | 0.419592 | ||||||||
\(262\) | 6.96127 | 0.430069 | ||||||||
\(263\) | −10.1360 | −0.625012 | −0.312506 | − | 0.949916i | \(-0.601168\pi\) | ||||
−0.312506 | + | 0.949916i | \(0.601168\pi\) | |||||||
\(264\) | 3.53153 | 0.217351 | ||||||||
\(265\) | 21.0090 | 1.29057 | ||||||||
\(266\) | 1.09308 | 0.0670208 | ||||||||
\(267\) | −11.1766 | −0.683999 | ||||||||
\(268\) | 12.7005 | 0.775806 | ||||||||
\(269\) | −5.13298 | −0.312963 | −0.156482 | − | 0.987681i | \(-0.550015\pi\) | ||||
−0.156482 | + | 0.987681i | \(0.550015\pi\) | |||||||
\(270\) | −3.53778 | −0.215302 | ||||||||
\(271\) | −13.1844 | −0.800897 | −0.400449 | − | 0.916319i | \(-0.631146\pi\) | ||||
−0.400449 | + | 0.916319i | \(0.631146\pi\) | |||||||
\(272\) | −2.18686 | −0.132598 | ||||||||
\(273\) | −4.09818 | −0.248033 | ||||||||
\(274\) | 12.7438 | 0.769882 | ||||||||
\(275\) | −26.5426 | −1.60058 | ||||||||
\(276\) | 9.08925 | 0.547108 | ||||||||
\(277\) | 10.7211 | 0.644168 | 0.322084 | − | 0.946711i | \(-0.395617\pi\) | ||||
0.322084 | + | 0.946711i | \(0.395617\pi\) | |||||||
\(278\) | 6.43994 | 0.386242 | ||||||||
\(279\) | 6.69972 | 0.401102 | ||||||||
\(280\) | −14.4985 | −0.866449 | ||||||||
\(281\) | 18.2550 | 1.08900 | 0.544501 | − | 0.838760i | \(-0.316719\pi\) | ||||
0.544501 | + | 0.838760i | \(0.316719\pi\) | |||||||
\(282\) | 8.08805 | 0.481636 | ||||||||
\(283\) | 30.7561 | 1.82826 | 0.914131 | − | 0.405418i | \(-0.132874\pi\) | ||||
0.914131 | + | 0.405418i | \(0.132874\pi\) | |||||||
\(284\) | −8.30262 | −0.492670 | ||||||||
\(285\) | 0.943606 | 0.0558944 | ||||||||
\(286\) | 3.53153 | 0.208824 | ||||||||
\(287\) | 21.4334 | 1.26517 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −12.2176 | −0.718685 | ||||||||
\(290\) | 23.9816 | 1.40825 | ||||||||
\(291\) | −8.23809 | −0.482925 | ||||||||
\(292\) | 11.4874 | 0.672247 | ||||||||
\(293\) | −24.9096 | −1.45524 | −0.727619 | − | 0.685982i | \(-0.759373\pi\) | ||||
−0.727619 | + | 0.685982i | \(0.759373\pi\) | |||||||
\(294\) | −9.79508 | −0.571261 | ||||||||
\(295\) | 4.33183 | 0.252209 | ||||||||
\(296\) | 10.3454 | 0.601316 | ||||||||
\(297\) | 3.53153 | 0.204920 | ||||||||
\(298\) | 1.99904 | 0.115801 | ||||||||
\(299\) | 9.08925 | 0.525645 | ||||||||
\(300\) | −7.51589 | −0.433930 | ||||||||
\(301\) | −27.5307 | −1.58684 | ||||||||
\(302\) | 7.74370 | 0.445600 | ||||||||
\(303\) | 16.6091 | 0.954169 | ||||||||
\(304\) | −0.266722 | −0.0152976 | ||||||||
\(305\) | −17.0999 | −0.979136 | ||||||||
\(306\) | −2.18686 | −0.125014 | ||||||||
\(307\) | 21.8157 | 1.24509 | 0.622544 | − | 0.782585i | \(-0.286099\pi\) | ||||
0.622544 | + | 0.782585i | \(0.286099\pi\) | |||||||
\(308\) | 14.4729 | 0.824667 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | 23.7022 | 1.34619 | ||||||||
\(311\) | −31.2060 | −1.76953 | −0.884765 | − | 0.466037i | \(-0.845681\pi\) | ||||
−0.884765 | + | 0.466037i | \(0.845681\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | −19.1775 | −1.08398 | −0.541988 | − | 0.840386i | \(-0.682328\pi\) | ||||
−0.541988 | + | 0.840386i | \(0.682328\pi\) | |||||||
\(314\) | −6.61959 | −0.373565 | ||||||||
\(315\) | −14.4985 | −0.816896 | ||||||||
\(316\) | 16.9009 | 0.950750 | ||||||||
\(317\) | −31.2536 | −1.75538 | −0.877690 | − | 0.479230i | \(-0.840916\pi\) | ||||
−0.877690 | + | 0.479230i | \(0.840916\pi\) | |||||||
\(318\) | −5.93846 | −0.333012 | ||||||||
\(319\) | −23.9393 | −1.34034 | ||||||||
\(320\) | 3.53778 | 0.197768 | ||||||||
\(321\) | −18.4079 | −1.02743 | ||||||||
\(322\) | 37.2494 | 2.07583 | ||||||||
\(323\) | 0.583285 | 0.0324548 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −7.51589 | −0.416907 | ||||||||
\(326\) | −9.98151 | −0.552824 | ||||||||
\(327\) | −12.5219 | −0.692461 | ||||||||
\(328\) | −5.22997 | −0.288777 | ||||||||
\(329\) | 33.1463 | 1.82741 | ||||||||
\(330\) | 12.4938 | 0.687760 | ||||||||
\(331\) | −14.0854 | −0.774204 | −0.387102 | − | 0.922037i | \(-0.626524\pi\) | ||||
−0.387102 | + | 0.922037i | \(0.626524\pi\) | |||||||
\(332\) | 8.26872 | 0.453805 | ||||||||
\(333\) | 10.3454 | 0.566926 | ||||||||
\(334\) | −23.0834 | −1.26307 | ||||||||
\(335\) | 44.9316 | 2.45487 | ||||||||
\(336\) | 4.09818 | 0.223574 | ||||||||
\(337\) | 13.8956 | 0.756942 | 0.378471 | − | 0.925613i | \(-0.376450\pi\) | ||||
0.378471 | + | 0.925613i | \(0.376450\pi\) | |||||||
\(338\) | 1.00000 | 0.0543928 | ||||||||
\(339\) | −12.1628 | −0.660592 | ||||||||
\(340\) | −7.73663 | −0.419578 | ||||||||
\(341\) | −23.6603 | −1.28128 | ||||||||
\(342\) | −0.266722 | −0.0144227 | ||||||||
\(343\) | −11.4547 | −0.618498 | ||||||||
\(344\) | 6.71778 | 0.362198 | ||||||||
\(345\) | 32.1558 | 1.73121 | ||||||||
\(346\) | 4.63859 | 0.249372 | ||||||||
\(347\) | 0.0369366 | 0.00198286 | 0.000991429 | − | 1.00000i | \(-0.499684\pi\) | ||||
0.000991429 | 1.00000i | \(0.499684\pi\) | ||||||||
\(348\) | −6.77872 | −0.363378 | ||||||||
\(349\) | 15.1285 | 0.809810 | 0.404905 | − | 0.914359i | \(-0.367305\pi\) | ||||
0.404905 | + | 0.914359i | \(0.367305\pi\) | |||||||
\(350\) | −30.8015 | −1.64641 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | −3.53153 | −0.188231 | ||||||||
\(353\) | −3.79280 | −0.201871 | −0.100935 | − | 0.994893i | \(-0.532184\pi\) | ||||
−0.100935 | + | 0.994893i | \(0.532184\pi\) | |||||||
\(354\) | −1.22445 | −0.0650787 | ||||||||
\(355\) | −29.3728 | −1.55895 | ||||||||
\(356\) | 11.1766 | 0.592360 | ||||||||
\(357\) | −8.96214 | −0.474327 | ||||||||
\(358\) | −25.0381 | −1.32330 | ||||||||
\(359\) | 9.47254 | 0.499942 | 0.249971 | − | 0.968253i | \(-0.419579\pi\) | ||||
0.249971 | + | 0.968253i | \(0.419579\pi\) | |||||||
\(360\) | 3.53778 | 0.186457 | ||||||||
\(361\) | −18.9289 | −0.996256 | ||||||||
\(362\) | −14.6223 | −0.768534 | ||||||||
\(363\) | −1.47171 | −0.0772449 | ||||||||
\(364\) | 4.09818 | 0.214803 | ||||||||
\(365\) | 40.6398 | 2.12718 | ||||||||
\(366\) | 4.83351 | 0.252651 | ||||||||
\(367\) | 7.47886 | 0.390393 | 0.195197 | − | 0.980764i | \(-0.437465\pi\) | ||||
0.195197 | + | 0.980764i | \(0.437465\pi\) | |||||||
\(368\) | −9.08925 | −0.473810 | ||||||||
\(369\) | −5.22997 | −0.272261 | ||||||||
\(370\) | 36.5999 | 1.90274 | ||||||||
\(371\) | −24.3369 | −1.26351 | ||||||||
\(372\) | −6.69972 | −0.347364 | ||||||||
\(373\) | −20.7493 | −1.07436 | −0.537179 | − | 0.843468i | \(-0.680510\pi\) | ||||
−0.537179 | + | 0.843468i | \(0.680510\pi\) | |||||||
\(374\) | 7.72296 | 0.399345 | ||||||||
\(375\) | −8.90067 | −0.459629 | ||||||||
\(376\) | −8.08805 | −0.417109 | ||||||||
\(377\) | −6.77872 | −0.349122 | ||||||||
\(378\) | 4.09818 | 0.210788 | ||||||||
\(379\) | −7.42769 | −0.381535 | −0.190767 | − | 0.981635i | \(-0.561098\pi\) | ||||
−0.190767 | + | 0.981635i | \(0.561098\pi\) | |||||||
\(380\) | −0.943606 | −0.0484059 | ||||||||
\(381\) | 8.55557 | 0.438315 | ||||||||
\(382\) | 24.7035 | 1.26394 | ||||||||
\(383\) | −11.2539 | −0.575049 | −0.287524 | − | 0.957773i | \(-0.592832\pi\) | ||||
−0.287524 | + | 0.957773i | \(0.592832\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 51.2018 | 2.60948 | ||||||||
\(386\) | −13.9811 | −0.711617 | ||||||||
\(387\) | 6.71778 | 0.341484 | ||||||||
\(388\) | 8.23809 | 0.418226 | ||||||||
\(389\) | 29.4974 | 1.49558 | 0.747788 | − | 0.663938i | \(-0.231116\pi\) | ||||
0.747788 | + | 0.663938i | \(0.231116\pi\) | |||||||
\(390\) | 3.53778 | 0.179142 | ||||||||
\(391\) | 19.8769 | 1.00522 | ||||||||
\(392\) | 9.79508 | 0.494726 | ||||||||
\(393\) | −6.96127 | −0.351150 | ||||||||
\(394\) | −24.1579 | −1.21706 | ||||||||
\(395\) | 59.7917 | 3.00844 | ||||||||
\(396\) | −3.53153 | −0.177466 | ||||||||
\(397\) | −7.73124 | −0.388020 | −0.194010 | − | 0.981000i | \(-0.562149\pi\) | ||||
−0.194010 | + | 0.981000i | \(0.562149\pi\) | |||||||
\(398\) | 13.8851 | 0.695996 | ||||||||
\(399\) | −1.09308 | −0.0547223 | ||||||||
\(400\) | 7.51589 | 0.375795 | ||||||||
\(401\) | −23.0488 | −1.15100 | −0.575501 | − | 0.817801i | \(-0.695193\pi\) | ||||
−0.575501 | + | 0.817801i | \(0.695193\pi\) | |||||||
\(402\) | −12.7005 | −0.633443 | ||||||||
\(403\) | −6.69972 | −0.333737 | ||||||||
\(404\) | −16.6091 | −0.826334 | ||||||||
\(405\) | 3.53778 | 0.175794 | ||||||||
\(406\) | −27.7804 | −1.37872 | ||||||||
\(407\) | −36.5352 | −1.81098 | ||||||||
\(408\) | 2.18686 | 0.108266 | ||||||||
\(409\) | −12.7459 | −0.630246 | −0.315123 | − | 0.949051i | \(-0.602046\pi\) | ||||
−0.315123 | + | 0.949051i | \(0.602046\pi\) | |||||||
\(410\) | −18.5025 | −0.913773 | ||||||||
\(411\) | −12.7438 | −0.628606 | ||||||||
\(412\) | −1.00000 | −0.0492665 | ||||||||
\(413\) | −5.01801 | −0.246920 | ||||||||
\(414\) | −9.08925 | −0.446712 | ||||||||
\(415\) | 29.2529 | 1.43597 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | −6.43994 | −0.315365 | ||||||||
\(418\) | 0.941939 | 0.0460717 | ||||||||
\(419\) | −8.38630 | −0.409697 | −0.204849 | − | 0.978794i | \(-0.565670\pi\) | ||||
−0.204849 | + | 0.978794i | \(0.565670\pi\) | |||||||
\(420\) | 14.4985 | 0.707452 | ||||||||
\(421\) | 24.5437 | 1.19619 | 0.598093 | − | 0.801426i | \(-0.295925\pi\) | ||||
0.598093 | + | 0.801426i | \(0.295925\pi\) | |||||||
\(422\) | 13.7740 | 0.670509 | ||||||||
\(423\) | −8.08805 | −0.393254 | ||||||||
\(424\) | 5.93846 | 0.288397 | ||||||||
\(425\) | −16.4362 | −0.797273 | ||||||||
\(426\) | 8.30262 | 0.402263 | ||||||||
\(427\) | 19.8086 | 0.958604 | ||||||||
\(428\) | 18.4079 | 0.889778 | ||||||||
\(429\) | −3.53153 | −0.170504 | ||||||||
\(430\) | 23.7660 | 1.14610 | ||||||||
\(431\) | 23.6338 | 1.13840 | 0.569200 | − | 0.822199i | \(-0.307253\pi\) | ||||
0.569200 | + | 0.822199i | \(0.307253\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −34.3781 | −1.65211 | −0.826053 | − | 0.563593i | \(-0.809419\pi\) | ||||
−0.826053 | + | 0.563593i | \(0.809419\pi\) | |||||||
\(434\) | −27.4567 | −1.31796 | ||||||||
\(435\) | −23.9816 | −1.14983 | ||||||||
\(436\) | 12.5219 | 0.599689 | ||||||||
\(437\) | 2.42431 | 0.115970 | ||||||||
\(438\) | −11.4874 | −0.548887 | ||||||||
\(439\) | 41.8211 | 1.99601 | 0.998007 | − | 0.0631002i | \(-0.0200988\pi\) | ||||
0.998007 | + | 0.0631002i | \(0.0200988\pi\) | |||||||
\(440\) | −12.4938 | −0.595618 | ||||||||
\(441\) | 9.79508 | 0.466432 | ||||||||
\(442\) | 2.18686 | 0.104018 | ||||||||
\(443\) | −6.44418 | −0.306172 | −0.153086 | − | 0.988213i | \(-0.548921\pi\) | ||||
−0.153086 | + | 0.988213i | \(0.548921\pi\) | |||||||
\(444\) | −10.3454 | −0.490973 | ||||||||
\(445\) | 39.5405 | 1.87440 | ||||||||
\(446\) | 12.8558 | 0.608742 | ||||||||
\(447\) | −1.99904 | −0.0945512 | ||||||||
\(448\) | −4.09818 | −0.193621 | ||||||||
\(449\) | 23.5623 | 1.11197 | 0.555986 | − | 0.831191i | \(-0.312341\pi\) | ||||
0.555986 | + | 0.831191i | \(0.312341\pi\) | |||||||
\(450\) | 7.51589 | 0.354303 | ||||||||
\(451\) | 18.4698 | 0.869709 | ||||||||
\(452\) | 12.1628 | 0.572089 | ||||||||
\(453\) | −7.74370 | −0.363831 | ||||||||
\(454\) | −12.2505 | −0.574946 | ||||||||
\(455\) | 14.4985 | 0.679698 | ||||||||
\(456\) | 0.266722 | 0.0124904 | ||||||||
\(457\) | −19.6464 | −0.919021 | −0.459511 | − | 0.888172i | \(-0.651975\pi\) | ||||
−0.459511 | + | 0.888172i | \(0.651975\pi\) | |||||||
\(458\) | −6.81988 | −0.318672 | ||||||||
\(459\) | 2.18686 | 0.102074 | ||||||||
\(460\) | −32.1558 | −1.49927 | ||||||||
\(461\) | −10.8812 | −0.506790 | −0.253395 | − | 0.967363i | \(-0.581547\pi\) | ||||
−0.253395 | + | 0.967363i | \(0.581547\pi\) | |||||||
\(462\) | −14.4729 | −0.673338 | ||||||||
\(463\) | −5.81015 | −0.270021 | −0.135010 | − | 0.990844i | \(-0.543107\pi\) | ||||
−0.135010 | + | 0.990844i | \(0.543107\pi\) | |||||||
\(464\) | 6.77872 | 0.314694 | ||||||||
\(465\) | −23.7022 | −1.09916 | ||||||||
\(466\) | 18.1244 | 0.839597 | ||||||||
\(467\) | −27.3350 | −1.26491 | −0.632456 | − | 0.774596i | \(-0.717953\pi\) | ||||
−0.632456 | + | 0.774596i | \(0.717953\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | −52.0489 | −2.40340 | ||||||||
\(470\) | −28.6137 | −1.31985 | ||||||||
\(471\) | 6.61959 | 0.305014 | ||||||||
\(472\) | 1.22445 | 0.0563598 | ||||||||
\(473\) | −23.7240 | −1.09083 | ||||||||
\(474\) | −16.9009 | −0.776284 | ||||||||
\(475\) | −2.00466 | −0.0919800 | ||||||||
\(476\) | 8.96214 | 0.410779 | ||||||||
\(477\) | 5.93846 | 0.271903 | ||||||||
\(478\) | 1.67370 | 0.0765532 | ||||||||
\(479\) | 35.2723 | 1.61163 | 0.805816 | − | 0.592166i | \(-0.201727\pi\) | ||||
0.805816 | + | 0.592166i | \(0.201727\pi\) | |||||||
\(480\) | −3.53778 | −0.161477 | ||||||||
\(481\) | −10.3454 | −0.471711 | ||||||||
\(482\) | −1.25519 | −0.0571724 | ||||||||
\(483\) | −37.2494 | −1.69490 | ||||||||
\(484\) | 1.47171 | 0.0668960 | ||||||||
\(485\) | 29.1446 | 1.32339 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 10.8224 | 0.490410 | 0.245205 | − | 0.969471i | \(-0.421145\pi\) | ||||
0.245205 | + | 0.969471i | \(0.421145\pi\) | |||||||
\(488\) | −4.83351 | −0.218803 | ||||||||
\(489\) | 9.98151 | 0.451379 | ||||||||
\(490\) | 34.6528 | 1.56546 | ||||||||
\(491\) | 23.2696 | 1.05014 | 0.525070 | − | 0.851059i | \(-0.324039\pi\) | ||||
0.525070 | + | 0.851059i | \(0.324039\pi\) | |||||||
\(492\) | 5.22997 | 0.235785 | ||||||||
\(493\) | −14.8241 | −0.667645 | ||||||||
\(494\) | 0.266722 | 0.0120004 | ||||||||
\(495\) | −12.4938 | −0.561554 | ||||||||
\(496\) | 6.69972 | 0.300826 | ||||||||
\(497\) | 34.0256 | 1.52626 | ||||||||
\(498\) | −8.26872 | −0.370530 | ||||||||
\(499\) | 26.9387 | 1.20594 | 0.602971 | − | 0.797763i | \(-0.293983\pi\) | ||||
0.602971 | + | 0.797763i | \(0.293983\pi\) | |||||||
\(500\) | 8.90067 | 0.398050 | ||||||||
\(501\) | 23.0834 | 1.03129 | ||||||||
\(502\) | 3.37351 | 0.150567 | ||||||||
\(503\) | 30.5374 | 1.36160 | 0.680798 | − | 0.732472i | \(-0.261633\pi\) | ||||
0.680798 | + | 0.732472i | \(0.261633\pi\) | |||||||
\(504\) | −4.09818 | −0.182547 | ||||||||
\(505\) | −58.7594 | −2.61476 | ||||||||
\(506\) | 32.0990 | 1.42697 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −8.55557 | −0.379592 | ||||||||
\(509\) | 18.1183 | 0.803079 | 0.401540 | − | 0.915842i | \(-0.368475\pi\) | ||||
0.401540 | + | 0.915842i | \(0.368475\pi\) | |||||||
\(510\) | 7.73663 | 0.342584 | ||||||||
\(511\) | −47.0773 | −2.08258 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0.266722 | 0.0117761 | ||||||||
\(514\) | 10.8138 | 0.476978 | ||||||||
\(515\) | −3.53778 | −0.155893 | ||||||||
\(516\) | −6.71778 | −0.295734 | ||||||||
\(517\) | 28.5632 | 1.25621 | ||||||||
\(518\) | −42.3975 | −1.86284 | ||||||||
\(519\) | −4.63859 | −0.203612 | ||||||||
\(520\) | −3.53778 | −0.155142 | ||||||||
\(521\) | 5.68447 | 0.249041 | 0.124521 | − | 0.992217i | \(-0.460261\pi\) | ||||
0.124521 | + | 0.992217i | \(0.460261\pi\) | |||||||
\(522\) | 6.77872 | 0.296697 | ||||||||
\(523\) | 1.40621 | 0.0614891 | 0.0307446 | − | 0.999527i | \(-0.490212\pi\) | ||||
0.0307446 | + | 0.999527i | \(0.490212\pi\) | |||||||
\(524\) | 6.96127 | 0.304105 | ||||||||
\(525\) | 30.8015 | 1.34429 | ||||||||
\(526\) | −10.1360 | −0.441950 | ||||||||
\(527\) | −14.6514 | −0.638223 | ||||||||
\(528\) | 3.53153 | 0.153690 | ||||||||
\(529\) | 59.6144 | 2.59193 | ||||||||
\(530\) | 21.0090 | 0.912571 | ||||||||
\(531\) | 1.22445 | 0.0531365 | ||||||||
\(532\) | 1.09308 | 0.0473909 | ||||||||
\(533\) | 5.22997 | 0.226535 | ||||||||
\(534\) | −11.1766 | −0.483660 | ||||||||
\(535\) | 65.1230 | 2.81551 | ||||||||
\(536\) | 12.7005 | 0.548578 | ||||||||
\(537\) | 25.0381 | 1.08047 | ||||||||
\(538\) | −5.13298 | −0.221298 | ||||||||
\(539\) | −34.5916 | −1.48997 | ||||||||
\(540\) | −3.53778 | −0.152242 | ||||||||
\(541\) | −13.8989 | −0.597561 | −0.298781 | − | 0.954322i | \(-0.596580\pi\) | ||||
−0.298781 | + | 0.954322i | \(0.596580\pi\) | |||||||
\(542\) | −13.1844 | −0.566320 | ||||||||
\(543\) | 14.6223 | 0.627505 | ||||||||
\(544\) | −2.18686 | −0.0937608 | ||||||||
\(545\) | 44.2997 | 1.89759 | ||||||||
\(546\) | −4.09818 | −0.175386 | ||||||||
\(547\) | −5.45224 | −0.233121 | −0.116560 | − | 0.993184i | \(-0.537187\pi\) | ||||
−0.116560 | + | 0.993184i | \(0.537187\pi\) | |||||||
\(548\) | 12.7438 | 0.544389 | ||||||||
\(549\) | −4.83351 | −0.206289 | ||||||||
\(550\) | −26.5426 | −1.13178 | ||||||||
\(551\) | −1.80804 | −0.0770250 | ||||||||
\(552\) | 9.08925 | 0.386864 | ||||||||
\(553\) | −69.2629 | −2.94536 | ||||||||
\(554\) | 10.7211 | 0.455495 | ||||||||
\(555\) | −36.5999 | −1.55358 | ||||||||
\(556\) | 6.43994 | 0.273114 | ||||||||
\(557\) | 14.3364 | 0.607453 | 0.303727 | − | 0.952759i | \(-0.401769\pi\) | ||||
0.303727 | + | 0.952759i | \(0.401769\pi\) | |||||||
\(558\) | 6.69972 | 0.283622 | ||||||||
\(559\) | −6.71778 | −0.284132 | ||||||||
\(560\) | −14.4985 | −0.612672 | ||||||||
\(561\) | −7.72296 | −0.326064 | ||||||||
\(562\) | 18.2550 | 0.770040 | ||||||||
\(563\) | −20.0390 | −0.844543 | −0.422271 | − | 0.906470i | \(-0.638767\pi\) | ||||
−0.422271 | + | 0.906470i | \(0.638767\pi\) | |||||||
\(564\) | 8.08805 | 0.340568 | ||||||||
\(565\) | 43.0293 | 1.81026 | ||||||||
\(566\) | 30.7561 | 1.29278 | ||||||||
\(567\) | −4.09818 | −0.172107 | ||||||||
\(568\) | −8.30262 | −0.348370 | ||||||||
\(569\) | 38.1201 | 1.59808 | 0.799039 | − | 0.601279i | \(-0.205342\pi\) | ||||
0.799039 | + | 0.601279i | \(0.205342\pi\) | |||||||
\(570\) | 0.943606 | 0.0395233 | ||||||||
\(571\) | 24.6481 | 1.03149 | 0.515746 | − | 0.856742i | \(-0.327515\pi\) | ||||
0.515746 | + | 0.856742i | \(0.327515\pi\) | |||||||
\(572\) | 3.53153 | 0.147661 | ||||||||
\(573\) | −24.7035 | −1.03200 | ||||||||
\(574\) | 21.4334 | 0.894611 | ||||||||
\(575\) | −68.3138 | −2.84888 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 3.64245 | 0.151637 | 0.0758185 | − | 0.997122i | \(-0.475843\pi\) | ||||
0.0758185 | + | 0.997122i | \(0.475843\pi\) | |||||||
\(578\) | −12.2176 | −0.508187 | ||||||||
\(579\) | 13.9811 | 0.581033 | ||||||||
\(580\) | 23.9816 | 0.995783 | ||||||||
\(581\) | −33.8867 | −1.40586 | ||||||||
\(582\) | −8.23809 | −0.341480 | ||||||||
\(583\) | −20.9718 | −0.868565 | ||||||||
\(584\) | 11.4874 | 0.475350 | ||||||||
\(585\) | −3.53778 | −0.146269 | ||||||||
\(586\) | −24.9096 | −1.02901 | ||||||||
\(587\) | 15.7341 | 0.649417 | 0.324708 | − | 0.945814i | \(-0.394734\pi\) | ||||
0.324708 | + | 0.945814i | \(0.394734\pi\) | |||||||
\(588\) | −9.79508 | −0.403942 | ||||||||
\(589\) | −1.78697 | −0.0736307 | ||||||||
\(590\) | 4.33183 | 0.178339 | ||||||||
\(591\) | 24.1579 | 0.993723 | ||||||||
\(592\) | 10.3454 | 0.425195 | ||||||||
\(593\) | −12.5972 | −0.517307 | −0.258653 | − | 0.965970i | \(-0.583279\pi\) | ||||
−0.258653 | + | 0.965970i | \(0.583279\pi\) | |||||||
\(594\) | 3.53153 | 0.144900 | ||||||||
\(595\) | 31.7061 | 1.29982 | ||||||||
\(596\) | 1.99904 | 0.0818837 | ||||||||
\(597\) | −13.8851 | −0.568279 | ||||||||
\(598\) | 9.08925 | 0.371687 | ||||||||
\(599\) | 20.8720 | 0.852809 | 0.426404 | − | 0.904533i | \(-0.359780\pi\) | ||||
0.426404 | + | 0.904533i | \(0.359780\pi\) | |||||||
\(600\) | −7.51589 | −0.306835 | ||||||||
\(601\) | 8.13507 | 0.331836 | 0.165918 | − | 0.986140i | \(-0.446941\pi\) | ||||
0.165918 | + | 0.986140i | \(0.446941\pi\) | |||||||
\(602\) | −27.5307 | −1.12207 | ||||||||
\(603\) | 12.7005 | 0.517204 | ||||||||
\(604\) | 7.74370 | 0.315087 | ||||||||
\(605\) | 5.20660 | 0.211678 | ||||||||
\(606\) | 16.6091 | 0.674699 | ||||||||
\(607\) | −12.7719 | −0.518395 | −0.259197 | − | 0.965824i | \(-0.583458\pi\) | ||||
−0.259197 | + | 0.965824i | \(0.583458\pi\) | |||||||
\(608\) | −0.266722 | −0.0108170 | ||||||||
\(609\) | 27.7804 | 1.12572 | ||||||||
\(610\) | −17.0999 | −0.692354 | ||||||||
\(611\) | 8.08805 | 0.327207 | ||||||||
\(612\) | −2.18686 | −0.0883986 | ||||||||
\(613\) | 23.3889 | 0.944668 | 0.472334 | − | 0.881420i | \(-0.343412\pi\) | ||||
0.472334 | + | 0.881420i | \(0.343412\pi\) | |||||||
\(614\) | 21.8157 | 0.880410 | ||||||||
\(615\) | 18.5025 | 0.746093 | ||||||||
\(616\) | 14.4729 | 0.583128 | ||||||||
\(617\) | 48.5879 | 1.95607 | 0.978037 | − | 0.208431i | \(-0.0668357\pi\) | ||||
0.978037 | + | 0.208431i | \(0.0668357\pi\) | |||||||
\(618\) | 1.00000 | 0.0402259 | ||||||||
\(619\) | −21.5137 | −0.864710 | −0.432355 | − | 0.901703i | \(-0.642317\pi\) | ||||
−0.432355 | + | 0.901703i | \(0.642317\pi\) | |||||||
\(620\) | 23.7022 | 0.951901 | ||||||||
\(621\) | 9.08925 | 0.364739 | ||||||||
\(622\) | −31.2060 | −1.25125 | ||||||||
\(623\) | −45.8038 | −1.83509 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | −6.09083 | −0.243633 | ||||||||
\(626\) | −19.1775 | −0.766487 | ||||||||
\(627\) | −0.941939 | −0.0376174 | ||||||||
\(628\) | −6.61959 | −0.264150 | ||||||||
\(629\) | −22.6240 | −0.902079 | ||||||||
\(630\) | −14.4985 | −0.577633 | ||||||||
\(631\) | −31.0257 | −1.23511 | −0.617556 | − | 0.786527i | \(-0.711877\pi\) | ||||
−0.617556 | + | 0.786527i | \(0.711877\pi\) | |||||||
\(632\) | 16.9009 | 0.672282 | ||||||||
\(633\) | −13.7740 | −0.547469 | ||||||||
\(634\) | −31.2536 | −1.24124 | ||||||||
\(635\) | −30.2677 | −1.20114 | ||||||||
\(636\) | −5.93846 | −0.235475 | ||||||||
\(637\) | −9.79508 | −0.388095 | ||||||||
\(638\) | −23.9393 | −0.947765 | ||||||||
\(639\) | −8.30262 | −0.328447 | ||||||||
\(640\) | 3.53778 | 0.139843 | ||||||||
\(641\) | −16.1406 | −0.637513 | −0.318757 | − | 0.947837i | \(-0.603265\pi\) | ||||
−0.318757 | + | 0.947837i | \(0.603265\pi\) | |||||||
\(642\) | −18.4079 | −0.726500 | ||||||||
\(643\) | −10.6907 | −0.421601 | −0.210801 | − | 0.977529i | \(-0.567607\pi\) | ||||
−0.210801 | + | 0.977529i | \(0.567607\pi\) | |||||||
\(644\) | 37.2494 | 1.46783 | ||||||||
\(645\) | −23.7660 | −0.935786 | ||||||||
\(646\) | 0.583285 | 0.0229490 | ||||||||
\(647\) | −17.9354 | −0.705114 | −0.352557 | − | 0.935790i | \(-0.614688\pi\) | ||||
−0.352557 | + | 0.935790i | \(0.614688\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −4.32418 | −0.169739 | ||||||||
\(650\) | −7.51589 | −0.294798 | ||||||||
\(651\) | 27.4567 | 1.07611 | ||||||||
\(652\) | −9.98151 | −0.390906 | ||||||||
\(653\) | −26.4130 | −1.03362 | −0.516810 | − | 0.856100i | \(-0.672881\pi\) | ||||
−0.516810 | + | 0.856100i | \(0.672881\pi\) | |||||||
\(654\) | −12.5219 | −0.489644 | ||||||||
\(655\) | 24.6275 | 0.962274 | ||||||||
\(656\) | −5.22997 | −0.204196 | ||||||||
\(657\) | 11.4874 | 0.448165 | ||||||||
\(658\) | 33.1463 | 1.29218 | ||||||||
\(659\) | −23.5594 | −0.917743 | −0.458872 | − | 0.888503i | \(-0.651746\pi\) | ||||
−0.458872 | + | 0.888503i | \(0.651746\pi\) | |||||||
\(660\) | 12.4938 | 0.486320 | ||||||||
\(661\) | 33.1998 | 1.29132 | 0.645662 | − | 0.763623i | \(-0.276581\pi\) | ||||
0.645662 | + | 0.763623i | \(0.276581\pi\) | |||||||
\(662\) | −14.0854 | −0.547445 | ||||||||
\(663\) | −2.18686 | −0.0849306 | ||||||||
\(664\) | 8.26872 | 0.320889 | ||||||||
\(665\) | 3.86707 | 0.149958 | ||||||||
\(666\) | 10.3454 | 0.400878 | ||||||||
\(667\) | −61.6135 | −2.38568 | ||||||||
\(668\) | −23.0834 | −0.893125 | ||||||||
\(669\) | −12.8558 | −0.497035 | ||||||||
\(670\) | 44.9316 | 1.73586 | ||||||||
\(671\) | 17.0697 | 0.658968 | ||||||||
\(672\) | 4.09818 | 0.158091 | ||||||||
\(673\) | −30.4630 | −1.17426 | −0.587132 | − | 0.809491i | \(-0.699743\pi\) | ||||
−0.587132 | + | 0.809491i | \(0.699743\pi\) | |||||||
\(674\) | 13.8956 | 0.535239 | ||||||||
\(675\) | −7.51589 | −0.289287 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −14.1077 | −0.542202 | −0.271101 | − | 0.962551i | \(-0.587388\pi\) | ||||
−0.271101 | + | 0.962551i | \(0.587388\pi\) | |||||||
\(678\) | −12.1628 | −0.467109 | ||||||||
\(679\) | −33.7612 | −1.29564 | ||||||||
\(680\) | −7.73663 | −0.296686 | ||||||||
\(681\) | 12.2505 | 0.469442 | ||||||||
\(682\) | −23.6603 | −0.905999 | ||||||||
\(683\) | −2.86939 | −0.109794 | −0.0548971 | − | 0.998492i | \(-0.517483\pi\) | ||||
−0.0548971 | + | 0.998492i | \(0.517483\pi\) | |||||||
\(684\) | −0.266722 | −0.0101984 | ||||||||
\(685\) | 45.0848 | 1.72260 | ||||||||
\(686\) | −11.4547 | −0.437344 | ||||||||
\(687\) | 6.81988 | 0.260195 | ||||||||
\(688\) | 6.71778 | 0.256113 | ||||||||
\(689\) | −5.93846 | −0.226237 | ||||||||
\(690\) | 32.1558 | 1.22415 | ||||||||
\(691\) | 6.46830 | 0.246066 | 0.123033 | − | 0.992403i | \(-0.460738\pi\) | ||||
0.123033 | + | 0.992403i | \(0.460738\pi\) | |||||||
\(692\) | 4.63859 | 0.176333 | ||||||||
\(693\) | 14.4729 | 0.549778 | ||||||||
\(694\) | 0.0369366 | 0.00140209 | ||||||||
\(695\) | 22.7831 | 0.864213 | ||||||||
\(696\) | −6.77872 | −0.256947 | ||||||||
\(697\) | 11.4372 | 0.433215 | ||||||||
\(698\) | 15.1285 | 0.572622 | ||||||||
\(699\) | −18.1244 | −0.685528 | ||||||||
\(700\) | −30.8015 | −1.16419 | ||||||||
\(701\) | 25.1756 | 0.950869 | 0.475434 | − | 0.879751i | \(-0.342291\pi\) | ||||
0.475434 | + | 0.879751i | \(0.342291\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | −2.75936 | −0.104071 | ||||||||
\(704\) | −3.53153 | −0.133100 | ||||||||
\(705\) | 28.6137 | 1.07766 | ||||||||
\(706\) | −3.79280 | −0.142744 | ||||||||
\(707\) | 68.0672 | 2.55993 | ||||||||
\(708\) | −1.22445 | −0.0460176 | ||||||||
\(709\) | 20.2006 | 0.758649 | 0.379324 | − | 0.925264i | \(-0.376156\pi\) | ||||
0.379324 | + | 0.925264i | \(0.376156\pi\) | |||||||
\(710\) | −29.3728 | −1.10234 | ||||||||
\(711\) | 16.9009 | 0.633833 | ||||||||
\(712\) | 11.1766 | 0.418862 | ||||||||
\(713\) | −60.8954 | −2.28055 | ||||||||
\(714\) | −8.96214 | −0.335400 | ||||||||
\(715\) | 12.4938 | 0.467241 | ||||||||
\(716\) | −25.0381 | −0.935717 | ||||||||
\(717\) | −1.67370 | −0.0625055 | ||||||||
\(718\) | 9.47254 | 0.353512 | ||||||||
\(719\) | 30.4655 | 1.13617 | 0.568085 | − | 0.822970i | \(-0.307684\pi\) | ||||
0.568085 | + | 0.822970i | \(0.307684\pi\) | |||||||
\(720\) | 3.53778 | 0.131845 | ||||||||
\(721\) | 4.09818 | 0.152624 | ||||||||
\(722\) | −18.9289 | −0.704459 | ||||||||
\(723\) | 1.25519 | 0.0466811 | ||||||||
\(724\) | −14.6223 | −0.543435 | ||||||||
\(725\) | 50.9481 | 1.89217 | ||||||||
\(726\) | −1.47171 | −0.0546204 | ||||||||
\(727\) | −9.45194 | −0.350553 | −0.175276 | − | 0.984519i | \(-0.556082\pi\) | ||||
−0.175276 | + | 0.984519i | \(0.556082\pi\) | |||||||
\(728\) | 4.09818 | 0.151889 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 40.6398 | 1.50415 | ||||||||
\(731\) | −14.6908 | −0.543360 | ||||||||
\(732\) | 4.83351 | 0.178652 | ||||||||
\(733\) | 39.4273 | 1.45628 | 0.728139 | − | 0.685429i | \(-0.240385\pi\) | ||||
0.728139 | + | 0.685429i | \(0.240385\pi\) | |||||||
\(734\) | 7.47886 | 0.276050 | ||||||||
\(735\) | −34.6528 | −1.27819 | ||||||||
\(736\) | −9.08925 | −0.335034 | ||||||||
\(737\) | −44.8522 | −1.65215 | ||||||||
\(738\) | −5.22997 | −0.192518 | ||||||||
\(739\) | 35.8088 | 1.31725 | 0.658624 | − | 0.752472i | \(-0.271139\pi\) | ||||
0.658624 | + | 0.752472i | \(0.271139\pi\) | |||||||
\(740\) | 36.5999 | 1.34544 | ||||||||
\(741\) | −0.266722 | −0.00979829 | ||||||||
\(742\) | −24.3369 | −0.893435 | ||||||||
\(743\) | −9.60364 | −0.352323 | −0.176162 | − | 0.984361i | \(-0.556368\pi\) | ||||
−0.176162 | + | 0.984361i | \(0.556368\pi\) | |||||||
\(744\) | −6.69972 | −0.245624 | ||||||||
\(745\) | 7.07215 | 0.259104 | ||||||||
\(746\) | −20.7493 | −0.759685 | ||||||||
\(747\) | 8.26872 | 0.302537 | ||||||||
\(748\) | 7.72296 | 0.282379 | ||||||||
\(749\) | −75.4387 | −2.75647 | ||||||||
\(750\) | −8.90067 | −0.325007 | ||||||||
\(751\) | −9.79075 | −0.357269 | −0.178635 | − | 0.983915i | \(-0.557168\pi\) | ||||
−0.178635 | + | 0.983915i | \(0.557168\pi\) | |||||||
\(752\) | −8.08805 | −0.294941 | ||||||||
\(753\) | −3.37351 | −0.122937 | ||||||||
\(754\) | −6.77872 | −0.246867 | ||||||||
\(755\) | 27.3955 | 0.997025 | ||||||||
\(756\) | 4.09818 | 0.149049 | ||||||||
\(757\) | −43.7464 | −1.58999 | −0.794996 | − | 0.606615i | \(-0.792527\pi\) | ||||
−0.794996 | + | 0.606615i | \(0.792527\pi\) | |||||||
\(758\) | −7.42769 | −0.269786 | ||||||||
\(759\) | −32.0990 | −1.16512 | ||||||||
\(760\) | −0.943606 | −0.0342282 | ||||||||
\(761\) | 40.5064 | 1.46836 | 0.734178 | − | 0.678957i | \(-0.237568\pi\) | ||||
0.734178 | + | 0.678957i | \(0.237568\pi\) | |||||||
\(762\) | 8.55557 | 0.309935 | ||||||||
\(763\) | −51.3169 | −1.85780 | ||||||||
\(764\) | 24.7035 | 0.893741 | ||||||||
\(765\) | −7.73663 | −0.279718 | ||||||||
\(766\) | −11.2539 | −0.406621 | ||||||||
\(767\) | −1.22445 | −0.0442123 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 13.3773 | 0.482396 | 0.241198 | − | 0.970476i | \(-0.422460\pi\) | ||||
0.241198 | + | 0.970476i | \(0.422460\pi\) | |||||||
\(770\) | 51.2018 | 1.84518 | ||||||||
\(771\) | −10.8138 | −0.389451 | ||||||||
\(772\) | −13.9811 | −0.503189 | ||||||||
\(773\) | 9.24662 | 0.332578 | 0.166289 | − | 0.986077i | \(-0.446822\pi\) | ||||
0.166289 | + | 0.986077i | \(0.446822\pi\) | |||||||
\(774\) | 6.71778 | 0.241465 | ||||||||
\(775\) | 50.3544 | 1.80878 | ||||||||
\(776\) | 8.23809 | 0.295730 | ||||||||
\(777\) | 42.3975 | 1.52100 | ||||||||
\(778\) | 29.4974 | 1.05753 | ||||||||
\(779\) | 1.39495 | 0.0499793 | ||||||||
\(780\) | 3.53778 | 0.126673 | ||||||||
\(781\) | 29.3210 | 1.04919 | ||||||||
\(782\) | 19.8769 | 0.710797 | ||||||||
\(783\) | −6.77872 | −0.242252 | ||||||||
\(784\) | 9.79508 | 0.349824 | ||||||||
\(785\) | −23.4186 | −0.835847 | ||||||||
\(786\) | −6.96127 | −0.248300 | ||||||||
\(787\) | −14.5093 | −0.517199 | −0.258600 | − | 0.965985i | \(-0.583261\pi\) | ||||
−0.258600 | + | 0.965985i | \(0.583261\pi\) | |||||||
\(788\) | −24.1579 | −0.860590 | ||||||||
\(789\) | 10.1360 | 0.360851 | ||||||||
\(790\) | 59.7917 | 2.12729 | ||||||||
\(791\) | −49.8453 | −1.77229 | ||||||||
\(792\) | −3.53153 | −0.125487 | ||||||||
\(793\) | 4.83351 | 0.171643 | ||||||||
\(794\) | −7.73124 | −0.274371 | ||||||||
\(795\) | −21.0090 | −0.745111 | ||||||||
\(796\) | 13.8851 | 0.492144 | ||||||||
\(797\) | −17.5455 | −0.621493 | −0.310746 | − | 0.950493i | \(-0.600579\pi\) | ||||
−0.310746 | + | 0.950493i | \(0.600579\pi\) | |||||||
\(798\) | −1.09308 | −0.0386945 | ||||||||
\(799\) | 17.6874 | 0.625736 | ||||||||
\(800\) | 7.51589 | 0.265727 | ||||||||
\(801\) | 11.1766 | 0.394907 | ||||||||
\(802\) | −23.0488 | −0.813882 | ||||||||
\(803\) | −40.5680 | −1.43161 | ||||||||
\(804\) | −12.7005 | −0.447912 | ||||||||
\(805\) | 131.780 | 4.64464 | ||||||||
\(806\) | −6.69972 | −0.235988 | ||||||||
\(807\) | 5.13298 | 0.180689 | ||||||||
\(808\) | −16.6091 | −0.584307 | ||||||||
\(809\) | −17.3211 | −0.608978 | −0.304489 | − | 0.952516i | \(-0.598486\pi\) | ||||
−0.304489 | + | 0.952516i | \(0.598486\pi\) | |||||||
\(810\) | 3.53778 | 0.124305 | ||||||||
\(811\) | 55.5789 | 1.95164 | 0.975820 | − | 0.218574i | \(-0.0701406\pi\) | ||||
0.975820 | + | 0.218574i | \(0.0701406\pi\) | |||||||
\(812\) | −27.7804 | −0.974902 | ||||||||
\(813\) | 13.1844 | 0.462398 | ||||||||
\(814\) | −36.5352 | −1.28056 | ||||||||
\(815\) | −35.3124 | −1.23694 | ||||||||
\(816\) | 2.18686 | 0.0765554 | ||||||||
\(817\) | −1.79178 | −0.0626865 | ||||||||
\(818\) | −12.7459 | −0.445651 | ||||||||
\(819\) | 4.09818 | 0.143202 | ||||||||
\(820\) | −18.5025 | −0.646135 | ||||||||
\(821\) | −37.1176 | −1.29541 | −0.647706 | − | 0.761890i | \(-0.724272\pi\) | ||||
−0.647706 | + | 0.761890i | \(0.724272\pi\) | |||||||
\(822\) | −12.7438 | −0.444492 | ||||||||
\(823\) | 11.3125 | 0.394328 | 0.197164 | − | 0.980370i | \(-0.436827\pi\) | ||||
0.197164 | + | 0.980370i | \(0.436827\pi\) | |||||||
\(824\) | −1.00000 | −0.0348367 | ||||||||
\(825\) | 26.5426 | 0.924095 | ||||||||
\(826\) | −5.01801 | −0.174599 | ||||||||
\(827\) | 15.5065 | 0.539212 | 0.269606 | − | 0.962971i | \(-0.413106\pi\) | ||||
0.269606 | + | 0.962971i | \(0.413106\pi\) | |||||||
\(828\) | −9.08925 | −0.315873 | ||||||||
\(829\) | 50.2473 | 1.74516 | 0.872580 | − | 0.488472i | \(-0.162445\pi\) | ||||
0.872580 | + | 0.488472i | \(0.162445\pi\) | |||||||
\(830\) | 29.2529 | 1.01538 | ||||||||
\(831\) | −10.7211 | −0.371910 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | −21.4205 | −0.742175 | ||||||||
\(834\) | −6.43994 | −0.222997 | ||||||||
\(835\) | −81.6641 | −2.82610 | ||||||||
\(836\) | 0.941939 | 0.0325776 | ||||||||
\(837\) | −6.69972 | −0.231576 | ||||||||
\(838\) | −8.38630 | −0.289700 | ||||||||
\(839\) | 2.22509 | 0.0768187 | 0.0384094 | − | 0.999262i | \(-0.487771\pi\) | ||||
0.0384094 | + | 0.999262i | \(0.487771\pi\) | |||||||
\(840\) | 14.4985 | 0.500244 | ||||||||
\(841\) | 16.9511 | 0.584520 | ||||||||
\(842\) | 24.5437 | 0.845832 | ||||||||
\(843\) | −18.2550 | −0.628735 | ||||||||
\(844\) | 13.7740 | 0.474122 | ||||||||
\(845\) | 3.53778 | 0.121703 | ||||||||
\(846\) | −8.08805 | −0.278073 | ||||||||
\(847\) | −6.03134 | −0.207239 | ||||||||
\(848\) | 5.93846 | 0.203927 | ||||||||
\(849\) | −30.7561 | −1.05555 | ||||||||
\(850\) | −16.4362 | −0.563757 | ||||||||
\(851\) | −94.0322 | −3.22338 | ||||||||
\(852\) | 8.30262 | 0.284443 | ||||||||
\(853\) | 34.4691 | 1.18020 | 0.590100 | − | 0.807330i | \(-0.299088\pi\) | ||||
0.590100 | + | 0.807330i | \(0.299088\pi\) | |||||||
\(854\) | 19.8086 | 0.677836 | ||||||||
\(855\) | −0.943606 | −0.0322706 | ||||||||
\(856\) | 18.4079 | 0.629168 | ||||||||
\(857\) | −11.2493 | −0.384270 | −0.192135 | − | 0.981369i | \(-0.561541\pi\) | ||||
−0.192135 | + | 0.981369i | \(0.561541\pi\) | |||||||
\(858\) | −3.53153 | −0.120564 | ||||||||
\(859\) | 9.47184 | 0.323175 | 0.161588 | − | 0.986858i | \(-0.448339\pi\) | ||||
0.161588 | + | 0.986858i | \(0.448339\pi\) | |||||||
\(860\) | 23.7660 | 0.810414 | ||||||||
\(861\) | −21.4334 | −0.730447 | ||||||||
\(862\) | 23.6338 | 0.804971 | ||||||||
\(863\) | 34.9733 | 1.19051 | 0.595253 | − | 0.803539i | \(-0.297052\pi\) | ||||
0.595253 | + | 0.803539i | \(0.297052\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 16.4103 | 0.557968 | ||||||||
\(866\) | −34.3781 | −1.16822 | ||||||||
\(867\) | 12.2176 | 0.414933 | ||||||||
\(868\) | −27.4567 | −0.931940 | ||||||||
\(869\) | −59.6860 | −2.02471 | ||||||||
\(870\) | −23.9816 | −0.813053 | ||||||||
\(871\) | −12.7005 | −0.430340 | ||||||||
\(872\) | 12.5219 | 0.424044 | ||||||||
\(873\) | 8.23809 | 0.278817 | ||||||||
\(874\) | 2.42431 | 0.0820034 | ||||||||
\(875\) | −36.4766 | −1.23313 | ||||||||
\(876\) | −11.4874 | −0.388122 | ||||||||
\(877\) | −54.9994 | −1.85720 | −0.928599 | − | 0.371085i | \(-0.878986\pi\) | ||||
−0.928599 | + | 0.371085i | \(0.878986\pi\) | |||||||
\(878\) | 41.8211 | 1.41140 | ||||||||
\(879\) | 24.9096 | 0.840181 | ||||||||
\(880\) | −12.4938 | −0.421165 | ||||||||
\(881\) | 27.7577 | 0.935180 | 0.467590 | − | 0.883946i | \(-0.345122\pi\) | ||||
0.467590 | + | 0.883946i | \(0.345122\pi\) | |||||||
\(882\) | 9.79508 | 0.329817 | ||||||||
\(883\) | −2.25682 | −0.0759481 | −0.0379741 | − | 0.999279i | \(-0.512090\pi\) | ||||
−0.0379741 | + | 0.999279i | \(0.512090\pi\) | |||||||
\(884\) | 2.18686 | 0.0735520 | ||||||||
\(885\) | −4.33183 | −0.145613 | ||||||||
\(886\) | −6.44418 | −0.216496 | ||||||||
\(887\) | −8.79693 | −0.295372 | −0.147686 | − | 0.989034i | \(-0.547183\pi\) | ||||
−0.147686 | + | 0.989034i | \(0.547183\pi\) | |||||||
\(888\) | −10.3454 | −0.347170 | ||||||||
\(889\) | 35.0623 | 1.17595 | ||||||||
\(890\) | 39.5405 | 1.32540 | ||||||||
\(891\) | −3.53153 | −0.118311 | ||||||||
\(892\) | 12.8558 | 0.430445 | ||||||||
\(893\) | 2.15726 | 0.0721901 | ||||||||
\(894\) | −1.99904 | −0.0668578 | ||||||||
\(895\) | −88.5793 | −2.96088 | ||||||||
\(896\) | −4.09818 | −0.136911 | ||||||||
\(897\) | −9.08925 | −0.303481 | ||||||||
\(898\) | 23.5623 | 0.786283 | ||||||||
\(899\) | 45.4156 | 1.51469 | ||||||||
\(900\) | 7.51589 | 0.250530 | ||||||||
\(901\) | −12.9866 | −0.432645 | ||||||||
\(902\) | 18.4698 | 0.614977 | ||||||||
\(903\) | 27.5307 | 0.916163 | ||||||||
\(904\) | 12.1628 | 0.404528 | ||||||||
\(905\) | −51.7307 | −1.71959 | ||||||||
\(906\) | −7.74370 | −0.257267 | ||||||||
\(907\) | 5.55253 | 0.184369 | 0.0921844 | − | 0.995742i | \(-0.470615\pi\) | ||||
0.0921844 | + | 0.995742i | \(0.470615\pi\) | |||||||
\(908\) | −12.2505 | −0.406548 | ||||||||
\(909\) | −16.6091 | −0.550890 | ||||||||
\(910\) | 14.4985 | 0.480619 | ||||||||
\(911\) | −26.5524 | −0.879720 | −0.439860 | − | 0.898066i | \(-0.644972\pi\) | ||||
−0.439860 | + | 0.898066i | \(0.644972\pi\) | |||||||
\(912\) | 0.266722 | 0.00883206 | ||||||||
\(913\) | −29.2012 | −0.966420 | ||||||||
\(914\) | −19.6464 | −0.649846 | ||||||||
\(915\) | 17.0999 | 0.565305 | ||||||||
\(916\) | −6.81988 | −0.225335 | ||||||||
\(917\) | −28.5285 | −0.942095 | ||||||||
\(918\) | 2.18686 | 0.0721771 | ||||||||
\(919\) | −21.4100 | −0.706252 | −0.353126 | − | 0.935576i | \(-0.614881\pi\) | ||||
−0.353126 | + | 0.935576i | \(0.614881\pi\) | |||||||
\(920\) | −32.1558 | −1.06014 | ||||||||
\(921\) | −21.8157 | −0.718852 | ||||||||
\(922\) | −10.8812 | −0.358355 | ||||||||
\(923\) | 8.30262 | 0.273284 | ||||||||
\(924\) | −14.4729 | −0.476122 | ||||||||
\(925\) | 77.7552 | 2.55657 | ||||||||
\(926\) | −5.81015 | −0.190933 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | 6.77872 | 0.222522 | ||||||||
\(929\) | 49.0695 | 1.60992 | 0.804960 | − | 0.593330i | \(-0.202187\pi\) | ||||
0.804960 | + | 0.593330i | \(0.202187\pi\) | |||||||
\(930\) | −23.7022 | −0.777224 | ||||||||
\(931\) | −2.61257 | −0.0856234 | ||||||||
\(932\) | 18.1244 | 0.593685 | ||||||||
\(933\) | 31.2060 | 1.02164 | ||||||||
\(934\) | −27.3350 | −0.894428 | ||||||||
\(935\) | 27.3221 | 0.893530 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | 6.02397 | 0.196795 | 0.0983973 | − | 0.995147i | \(-0.468628\pi\) | ||||
0.0983973 | + | 0.995147i | \(0.468628\pi\) | |||||||
\(938\) | −52.0489 | −1.69946 | ||||||||
\(939\) | 19.1775 | 0.625834 | ||||||||
\(940\) | −28.6137 | −0.933277 | ||||||||
\(941\) | 9.03028 | 0.294379 | 0.147189 | − | 0.989108i | \(-0.452977\pi\) | ||||
0.147189 | + | 0.989108i | \(0.452977\pi\) | |||||||
\(942\) | 6.61959 | 0.215678 | ||||||||
\(943\) | 47.5365 | 1.54800 | ||||||||
\(944\) | 1.22445 | 0.0398524 | ||||||||
\(945\) | 14.4985 | 0.471635 | ||||||||
\(946\) | −23.7240 | −0.771335 | ||||||||
\(947\) | −30.3063 | −0.984821 | −0.492411 | − | 0.870363i | \(-0.663884\pi\) | ||||
−0.492411 | + | 0.870363i | \(0.663884\pi\) | |||||||
\(948\) | −16.9009 | −0.548916 | ||||||||
\(949\) | −11.4874 | −0.372896 | ||||||||
\(950\) | −2.00466 | −0.0650397 | ||||||||
\(951\) | 31.2536 | 1.01347 | ||||||||
\(952\) | 8.96214 | 0.290465 | ||||||||
\(953\) | −32.8060 | −1.06269 | −0.531345 | − | 0.847156i | \(-0.678313\pi\) | ||||
−0.531345 | + | 0.847156i | \(0.678313\pi\) | |||||||
\(954\) | 5.93846 | 0.192265 | ||||||||
\(955\) | 87.3955 | 2.82805 | ||||||||
\(956\) | 1.67370 | 0.0541313 | ||||||||
\(957\) | 23.9393 | 0.773847 | ||||||||
\(958\) | 35.2723 | 1.13960 | ||||||||
\(959\) | −52.2265 | −1.68648 | ||||||||
\(960\) | −3.53778 | −0.114181 | ||||||||
\(961\) | 13.8863 | 0.447945 | ||||||||
\(962\) | −10.3454 | −0.333550 | ||||||||
\(963\) | 18.4079 | 0.593185 | ||||||||
\(964\) | −1.25519 | −0.0404270 | ||||||||
\(965\) | −49.4619 | −1.59223 | ||||||||
\(966\) | −37.2494 | −1.19848 | ||||||||
\(967\) | 29.5884 | 0.951500 | 0.475750 | − | 0.879581i | \(-0.342177\pi\) | ||||
0.475750 | + | 0.879581i | \(0.342177\pi\) | |||||||
\(968\) | 1.47171 | 0.0473026 | ||||||||
\(969\) | −0.583285 | −0.0187378 | ||||||||
\(970\) | 29.1446 | 0.935775 | ||||||||
\(971\) | 36.7491 | 1.17933 | 0.589667 | − | 0.807647i | \(-0.299259\pi\) | ||||
0.589667 | + | 0.807647i | \(0.299259\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −26.3921 | −0.846090 | ||||||||
\(974\) | 10.8224 | 0.346772 | ||||||||
\(975\) | 7.51589 | 0.240701 | ||||||||
\(976\) | −4.83351 | −0.154717 | ||||||||
\(977\) | −32.9434 | −1.05395 | −0.526977 | − | 0.849879i | \(-0.676675\pi\) | ||||
−0.526977 | + | 0.849879i | \(0.676675\pi\) | |||||||
\(978\) | 9.98151 | 0.319173 | ||||||||
\(979\) | −39.4706 | −1.26149 | ||||||||
\(980\) | 34.6528 | 1.10694 | ||||||||
\(981\) | 12.5219 | 0.399793 | ||||||||
\(982\) | 23.2696 | 0.742562 | ||||||||
\(983\) | −39.7184 | −1.26682 | −0.633410 | − | 0.773817i | \(-0.718345\pi\) | ||||
−0.633410 | + | 0.773817i | \(0.718345\pi\) | |||||||
\(984\) | 5.22997 | 0.166725 | ||||||||
\(985\) | −85.4654 | −2.72315 | ||||||||
\(986\) | −14.8241 | −0.472096 | ||||||||
\(987\) | −33.1463 | −1.05506 | ||||||||
\(988\) | 0.266722 | 0.00848557 | ||||||||
\(989\) | −61.0595 | −1.94158 | ||||||||
\(990\) | −12.4938 | −0.397078 | ||||||||
\(991\) | 60.6842 | 1.92770 | 0.963849 | − | 0.266450i | \(-0.0858506\pi\) | ||||
0.963849 | + | 0.266450i | \(0.0858506\pi\) | |||||||
\(992\) | 6.69972 | 0.212716 | ||||||||
\(993\) | 14.0854 | 0.446987 | ||||||||
\(994\) | 34.0256 | 1.07923 | ||||||||
\(995\) | 49.1224 | 1.55728 | ||||||||
\(996\) | −8.26872 | −0.262004 | ||||||||
\(997\) | 1.38146 | 0.0437513 | 0.0218757 | − | 0.999761i | \(-0.493036\pi\) | ||||
0.0218757 | + | 0.999761i | \(0.493036\pi\) | |||||||
\(998\) | 26.9387 | 0.852730 | ||||||||
\(999\) | −10.3454 | −0.327315 |
(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 | 8034.2.a.bc.1.14 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.bc.1.14 | ✓ | 15 | 1.1 | even | 1 | trivial |