Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8048,2,Mod(1,8048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8048, 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("8048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8048 = 2^{4} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8048.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: | \(64.2636035467\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 9x^{8} + 14x^{7} + 27x^{6} - 27x^{5} - 34x^{4} + 14x^{3} + 17x^{2} + x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 503) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.208270\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8048.1 |
$q$-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 | 0 | ||||||||
\(3\) | 0.791730 | 0.457106 | 0.228553 | − | 0.973532i | \(-0.426601\pi\) | ||||
0.228553 | + | 0.973532i | \(0.426601\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.178789 | 0.0799568 | 0.0399784 | − | 0.999201i | \(-0.487271\pi\) | ||||
0.0399784 | + | 0.999201i | \(0.487271\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.0809018 | 0.0305780 | 0.0152890 | − | 0.999883i | \(-0.495133\pi\) | ||||
0.0152890 | + | 0.999883i | \(0.495133\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.37316 | −0.791054 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.30391 | 1.29768 | 0.648839 | − | 0.760926i | \(-0.275255\pi\) | ||||
0.648839 | + | 0.760926i | \(0.275255\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.10019 | 0.305139 | 0.152569 | − | 0.988293i | \(-0.451245\pi\) | ||||
0.152569 | + | 0.988293i | \(0.451245\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.141552 | 0.0365487 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.06504 | −0.743381 | −0.371690 | − | 0.928357i | \(-0.621222\pi\) | ||||
−0.371690 | + | 0.928357i | \(0.621222\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.15853 | 0.495200 | 0.247600 | − | 0.968862i | \(-0.420358\pi\) | ||||
0.247600 | + | 0.968862i | \(0.420358\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.0640524 | 0.0139774 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −9.15620 | −1.90920 | −0.954600 | − | 0.297892i | \(-0.903716\pi\) | ||||
−0.954600 | + | 0.297892i | \(0.903716\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.96803 | −0.993607 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.25410 | −0.818701 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.17849 | −1.14732 | −0.573658 | − | 0.819095i | \(-0.694476\pi\) | ||||
−0.573658 | + | 0.819095i | \(0.694476\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.82812 | 1.76518 | 0.882591 | − | 0.470141i | \(-0.155797\pi\) | ||||
0.882591 | + | 0.470141i | \(0.155797\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.40754 | 0.593176 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.0144643 | 0.00244492 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.08321 | 0.671275 | 0.335637 | − | 0.941991i | \(-0.391048\pi\) | ||||
0.335637 | + | 0.941991i | \(0.391048\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.871056 | 0.139481 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.58598 | 0.716210 | 0.358105 | − | 0.933681i | \(-0.383423\pi\) | ||||
0.358105 | + | 0.933681i | \(0.383423\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.03126 | −0.309764 | −0.154882 | − | 0.987933i | \(-0.549500\pi\) | ||||
−0.154882 | + | 0.987933i | \(0.549500\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.424295 | −0.0632501 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.12836 | 0.748049 | 0.374024 | − | 0.927419i | \(-0.377978\pi\) | ||||
0.374024 | + | 0.927419i | \(0.377978\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.99345 | −0.999065 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.42668 | −0.339804 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.69017 | 0.369523 | 0.184761 | − | 0.982783i | \(-0.440849\pi\) | ||||
0.184761 | + | 0.982783i | \(0.440849\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.769491 | 0.103758 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.70897 | 0.226359 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.21598 | −1.19982 | −0.599909 | − | 0.800068i | \(-0.704797\pi\) | ||||
−0.599909 | + | 0.800068i | \(0.704797\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.0554 | −1.79961 | −0.899805 | − | 0.436291i | \(-0.856292\pi\) | ||||
−0.899805 | + | 0.436291i | \(0.856292\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.191993 | −0.0241889 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.196702 | 0.0243979 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.62801 | −0.687570 | −0.343785 | − | 0.939048i | \(-0.611709\pi\) | ||||
−0.343785 | + | 0.939048i | \(0.611709\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.24924 | −0.872706 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.88191 | 0.579376 | 0.289688 | − | 0.957121i | \(-0.406448\pi\) | ||||
0.289688 | + | 0.957121i | \(0.406448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.9754 | 1.28457 | 0.642286 | − | 0.766465i | \(-0.277986\pi\) | ||||
0.642286 | + | 0.766465i | \(0.277986\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.93334 | −0.454183 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.348194 | 0.0396804 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −17.4356 | −1.96166 | −0.980828 | − | 0.194874i | \(-0.937570\pi\) | ||||
−0.980828 | + | 0.194874i | \(0.937570\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.75139 | 0.416822 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.48372 | 0.272624 | 0.136312 | − | 0.990666i | \(-0.456475\pi\) | ||||
0.136312 | + | 0.990666i | \(0.456475\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.547994 | −0.0594383 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.89170 | −0.524445 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.57230 | 0.590662 | 0.295331 | − | 0.955395i | \(-0.404570\pi\) | ||||
0.295331 | + | 0.955395i | \(0.404570\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0890076 | 0.00933053 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.78122 | 0.806875 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.385920 | 0.0395946 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.9731 | −1.41876 | −0.709379 | − | 0.704828i | \(-0.751024\pi\) | ||||
−0.709379 | + | 0.704828i | \(0.751024\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.2139 | −1.02653 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.98379 | −0.794417 | −0.397208 | − | 0.917728i | \(-0.630021\pi\) | ||||
−0.397208 | + | 0.917728i | \(0.630021\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.5314 | −1.03769 | −0.518846 | − | 0.854868i | \(-0.673638\pi\) | ||||
−0.518846 | + | 0.854868i | \(0.673638\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.0114518 | 0.00111759 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.31671 | 0.320638 | 0.160319 | − | 0.987065i | \(-0.448748\pi\) | ||||
0.160319 | + | 0.987065i | \(0.448748\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.7956 | −1.22559 | −0.612797 | − | 0.790240i | \(-0.709956\pi\) | ||||
−0.612797 | + | 0.790240i | \(0.709956\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.23280 | 0.306844 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.42086 | −0.415880 | −0.207940 | − | 0.978142i | \(-0.566676\pi\) | ||||
−0.207940 | + | 0.978142i | \(0.566676\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.63702 | −0.152653 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.61094 | −0.241381 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.247967 | −0.0227311 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.52364 | 0.683967 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.63086 | 0.327384 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.78217 | −0.159402 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.5071 | 1.55351 | 0.776753 | − | 0.629806i | \(-0.216865\pi\) | ||||
0.776753 | + | 0.629806i | \(0.216865\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.60821 | −0.141595 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.8336 | −1.03390 | −0.516952 | − | 0.856014i | \(-0.672934\pi\) | ||||
−0.516952 | + | 0.856014i | \(0.672934\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.174629 | 0.0151422 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.760584 | −0.0654607 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.19499 | −0.187530 | −0.0937651 | − | 0.995594i | \(-0.529890\pi\) | ||||
−0.0937651 | + | 0.995594i | \(0.529890\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.11773 | −0.518899 | −0.259450 | − | 0.965757i | \(-0.583541\pi\) | ||||
−0.259450 | + | 0.965757i | \(0.583541\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.06028 | 0.341937 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.73513 | 0.395972 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.10464 | −0.0917357 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.53693 | −0.456678 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.3950 | −1.42505 | −0.712526 | − | 0.701646i | \(-0.752449\pi\) | ||||
−0.712526 | + | 0.701646i | \(0.752449\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.9595 | 1.78704 | 0.893520 | − | 0.449024i | \(-0.148228\pi\) | ||||
0.893520 | + | 0.449024i | \(0.148228\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.27383 | 0.588055 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.75716 | 0.141138 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.5736 | −1.56214 | −0.781070 | − | 0.624444i | \(-0.785326\pi\) | ||||
−0.781070 | + | 0.624444i | \(0.785326\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.12989 | 0.168911 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.740753 | −0.0583795 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.2549 | 1.11653 | 0.558265 | − | 0.829663i | \(-0.311467\pi\) | ||||
0.558265 | + | 0.829663i | \(0.311467\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.609229 | 0.0474284 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.3555 | 1.49777 | 0.748886 | − | 0.662698i | \(-0.230589\pi\) | ||||
0.748886 | + | 0.662698i | \(0.230589\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.7896 | −0.906890 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.12254 | −0.391730 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 24.1751 | 1.83800 | 0.919000 | − | 0.394258i | \(-0.128998\pi\) | ||||
0.919000 | + | 0.394258i | \(0.128998\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.401923 | −0.0303825 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.29657 | −0.548444 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.7844 | −0.880807 | −0.440403 | − | 0.897800i | \(-0.645165\pi\) | ||||
−0.440403 | + | 0.897800i | \(0.645165\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.193747 | 0.0144011 | 0.00720054 | − | 0.999974i | \(-0.497708\pi\) | ||||
0.00720054 | + | 0.999974i | \(0.497708\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.1281 | −0.822612 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.730031 | 0.0536730 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.1916 | −0.964669 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.344164 | −0.0250342 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.0106 | 1.44791 | 0.723957 | − | 0.689845i | \(-0.242321\pi\) | ||||
0.723957 | + | 0.689845i | \(0.242321\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.4429 | −1.18358 | −0.591792 | − | 0.806091i | \(-0.701579\pi\) | ||||
−0.591792 | + | 0.806091i | \(0.701579\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.155735 | 0.0111524 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.3311 | 1.73352 | 0.866761 | − | 0.498723i | \(-0.166198\pi\) | ||||
0.866761 | + | 0.498723i | \(0.166198\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.2467 | 1.15170 | 0.575851 | − | 0.817555i | \(-0.304671\pi\) | ||||
0.575851 | + | 0.817555i | \(0.304671\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.45586 | −0.314292 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.499851 | −0.0350827 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.819922 | 0.0572659 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 21.7292 | 1.51028 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.29010 | 0.642610 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.5844 | −0.935189 | −0.467594 | − | 0.883943i | \(-0.654879\pi\) | ||||
−0.467594 | + | 0.883943i | \(0.654879\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.86515 | 0.264836 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.363166 | −0.0247677 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.795113 | 0.0539758 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.68955 | 0.587185 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.37213 | −0.226834 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.6725 | −1.65219 | −0.826096 | − | 0.563530i | \(-0.809443\pi\) | ||||
−0.826096 | + | 0.563530i | \(0.809443\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.7900 | 0.785997 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.9854 | −1.19373 | −0.596866 | − | 0.802341i | \(-0.703588\pi\) | ||||
−0.596866 | + | 0.802341i | \(0.703588\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.8558 | 1.04778 | 0.523891 | − | 0.851786i | \(-0.324480\pi\) | ||||
0.523891 | + | 0.851786i | \(0.324480\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.275676 | 0.0181381 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.33607 | 0.153041 | 0.0765205 | − | 0.997068i | \(-0.475619\pi\) | ||||
0.0765205 | + | 0.997068i | \(0.475619\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.916894 | 0.0598115 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.8043 | −0.896684 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.84852 | −0.313625 | −0.156812 | − | 0.987628i | \(-0.550122\pi\) | ||||
−0.156812 | + | 0.987628i | \(0.550122\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.42679 | −0.220739 | −0.110369 | − | 0.993891i | \(-0.535203\pi\) | ||||
−0.110369 | + | 0.993891i | \(0.535203\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.7324 | 1.00923 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.25035 | −0.0798820 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.37480 | 0.151105 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.96644 | 0.124618 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25.7166 | 1.62321 | 0.811607 | − | 0.584204i | \(-0.198593\pi\) | ||||
0.811607 | + | 0.584204i | \(0.198593\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −39.4074 | −2.47753 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.433864 | −0.0271696 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −24.1897 | −1.50891 | −0.754457 | − | 0.656350i | \(-0.772100\pi\) | ||||
−0.754457 | + | 0.656350i | \(0.772100\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.330339 | 0.0205262 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 14.6626 | 0.907590 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.1779 | −1.12089 | −0.560447 | − | 0.828190i | \(-0.689371\pi\) | ||||
−0.560447 | + | 0.828190i | \(0.689371\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.480972 | 0.0295458 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.41176 | 0.269995 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.69010 | −0.346931 | −0.173466 | − | 0.984840i | \(-0.555497\pi\) | ||||
−0.173466 | + | 0.984840i | \(0.555497\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.4138 | −0.997069 | −0.498535 | − | 0.866870i | \(-0.666128\pi\) | ||||
−0.498535 | + | 0.866870i | \(0.666128\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.0704700 | 0.00426504 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −21.3820 | −1.28938 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.4497 | −1.58921 | −0.794605 | − | 0.607127i | \(-0.792322\pi\) | ||||
−0.794605 | + | 0.607127i | \(0.792322\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −23.3237 | −1.39636 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.32607 | 0.198417 | 0.0992084 | − | 0.995067i | \(-0.468369\pi\) | ||||
0.0992084 | + | 0.995067i | \(0.468369\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.9817 | 1.30668 | 0.653339 | − | 0.757065i | \(-0.273367\pi\) | ||||
0.653339 | + | 0.757065i | \(0.273367\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.305545 | 0.0180989 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.371014 | 0.0219003 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.60555 | −0.447385 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.0630 | −0.648522 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.54118 | −0.382140 | −0.191070 | − | 0.981576i | \(-0.561196\pi\) | ||||
−0.191070 | + | 0.981576i | \(0.561196\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.64771 | −0.0959336 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −18.3092 | −1.06241 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.0736 | −0.582570 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.164333 | −0.00947197 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.32101 | −0.363132 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.51295 | −0.143891 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.6985 | −0.895959 | −0.447980 | − | 0.894044i | \(-0.647856\pi\) | ||||
−0.447980 | + | 0.894044i | \(0.647856\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.33804 | −0.474335 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −25.6166 | −1.45258 | −0.726292 | − | 0.687386i | \(-0.758758\pi\) | ||||
−0.726292 | + | 0.687386i | \(0.758758\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.69793 | 0.209019 | 0.104510 | − | 0.994524i | \(-0.466673\pi\) | ||||
0.104510 | + | 0.994524i | \(0.466673\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.0343262 | −0.00193406 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 19.0196 | 1.06825 | 0.534124 | − | 0.845406i | \(-0.320641\pi\) | ||||
0.534124 | + | 0.845406i | \(0.320641\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −26.5917 | −1.48885 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.62594 | 0.146566 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.61597 | −0.368122 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.46580 | −0.303188 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −10.1306 | −0.560226 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.414894 | 0.0228738 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.74934 | 0.261048 | 0.130524 | − | 0.991445i | \(-0.458334\pi\) | ||||
0.130524 | + | 0.991445i | \(0.458334\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.69011 | −0.531015 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.00622 | −0.0549759 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −29.8451 | −1.62576 | −0.812882 | − | 0.582428i | \(-0.802103\pi\) | ||||
−0.812882 | + | 0.582428i | \(0.802103\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.50013 | −0.190101 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 42.2993 | 2.29064 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.13210 | −0.0611274 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.29608 | −0.0697787 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.3781 | −0.825540 | −0.412770 | − | 0.910835i | \(-0.635439\pi\) | ||||
−0.412770 | + | 0.910835i | \(0.635439\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.64130 | 0.355501 | 0.177750 | − | 0.984076i | \(-0.443118\pi\) | ||||
0.177750 | + | 0.984076i | \(0.443118\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.68033 | −0.249817 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −33.7272 | −1.79512 | −0.897558 | − | 0.440896i | \(-0.854661\pi\) | ||||
−0.897558 | + | 0.440896i | \(0.854661\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.872830 | 0.0463250 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.196323 | −0.0103905 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 27.2110 | 1.43614 | 0.718071 | − | 0.695970i | \(-0.245025\pi\) | ||||
0.718071 | + | 0.695970i | \(0.245025\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.3408 | −0.754777 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.95669 | 0.312645 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.96228 | 0.102710 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.0523 | −0.733525 | −0.366763 | − | 0.930315i | \(-0.619534\pi\) | ||||
−0.366763 | + | 0.930315i | \(0.619534\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.8833 | −0.566561 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.217639 | 0.0112993 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.8673 | 1.02869 | 0.514345 | − | 0.857584i | \(-0.328035\pi\) | ||||
0.514345 | + | 0.857584i | \(0.328035\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.41100 | −0.0728637 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.79753 | −0.350091 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.4863 | 0.846844 | 0.423422 | − | 0.905933i | \(-0.360829\pi\) | ||||
0.423422 | + | 0.905933i | \(0.360829\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.8609 | 0.710116 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −22.2392 | −1.13637 | −0.568186 | − | 0.822900i | \(-0.692355\pi\) | ||||
−0.568186 | + | 0.822900i | \(0.692355\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.0622532 | 0.00317272 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.82051 | 0.245040 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.3650 | −0.525528 | −0.262764 | − | 0.964860i | \(-0.584634\pi\) | ||||
−0.262764 | + | 0.964860i | \(0.584634\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 28.0641 | 1.41926 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.36900 | −0.472604 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.11729 | −0.156848 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.54363 | −0.127661 | −0.0638306 | − | 0.997961i | \(-0.520332\pi\) | ||||
−0.0638306 | + | 0.997961i | \(0.520332\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.138259 | 0.00692160 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.4246 | 0.620455 | 0.310227 | − | 0.950662i | \(-0.399595\pi\) | ||||
0.310227 | + | 0.950662i | \(0.399595\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.8128 | 0.538625 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.670707 | 0.0333277 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 17.5738 | 0.871098 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.3575 | 0.709932 | 0.354966 | − | 0.934879i | \(-0.384492\pi\) | ||||
0.354966 | + | 0.934879i | \(0.384492\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.73784 | −0.0857211 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.745589 | −0.0366880 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.444061 | 0.0217981 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.84359 | −0.237192 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.6860 | −0.766309 | −0.383155 | − | 0.923684i | \(-0.625162\pi\) | ||||
−0.383155 | + | 0.923684i | \(0.625162\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.689920 | 0.0336247 | 0.0168123 | − | 0.999859i | \(-0.494648\pi\) | ||||
0.0168123 | + | 0.999859i | \(0.494648\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.1704 | −0.591747 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 15.2272 | 0.738628 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.13711 | −0.0550285 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.74895 | 0.181001 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −29.0858 | −1.40102 | −0.700508 | − | 0.713645i | \(-0.747043\pi\) | ||||
−0.700508 | + | 0.713645i | \(0.747043\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.1169 | 0.870643 | 0.435321 | − | 0.900275i | \(-0.356635\pi\) | ||||
0.435321 | + | 0.900275i | \(0.356635\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.874580 | −0.0419329 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −19.7639 | −0.945435 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.25712 | −0.155454 | −0.0777270 | − | 0.996975i | \(-0.524766\pi\) | ||||
−0.0777270 | + | 0.996975i | \(0.524766\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 16.5966 | 0.790315 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.5717 | 1.02490 | 0.512451 | − | 0.858717i | \(-0.328738\pi\) | ||||
0.512451 | + | 0.858717i | \(0.328738\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.996264 | 0.0472274 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −13.7721 | −0.651399 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.9612 | 0.894834 | 0.447417 | − | 0.894325i | \(-0.352344\pi\) | ||||
0.447417 | + | 0.894325i | \(0.352344\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.7377 | 0.929410 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 17.3860 | 0.816866 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.0159136 | 0.000746039 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.18789 | 0.195901 | 0.0979506 | − | 0.995191i | \(-0.468771\pi\) | ||||
0.0979506 | + | 0.995191i | \(0.468771\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 13.0390 | 0.608607 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.7101 | 0.638543 | 0.319271 | − | 0.947663i | \(-0.396562\pi\) | ||||
0.319271 | + | 0.947663i | \(0.396562\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.87808 | −0.226703 | −0.113352 | − | 0.993555i | \(-0.536159\pi\) | ||||
−0.113352 | + | 0.993555i | \(0.536159\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.39119 | 0.0645151 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.3373 | −0.570904 | −0.285452 | − | 0.958393i | \(-0.592144\pi\) | ||||
−0.285452 | + | 0.958393i | \(0.592144\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.455316 | −0.0210245 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15.4970 | −0.714063 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.74236 | −0.401974 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.7236 | −0.492034 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.38421 | −0.292313 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.56361 | 0.162826 | 0.0814128 | − | 0.996680i | \(-0.474057\pi\) | ||||
0.0814128 | + | 0.996680i | \(0.474057\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.49231 | 0.204832 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.586476 | −0.0266856 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.49824 | −0.113439 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.09262 | 0.230769 | 0.115384 | − | 0.993321i | \(-0.463190\pi\) | ||||
0.115384 | + | 0.993321i | \(0.463190\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11.2860 | 0.510372 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −27.1049 | −1.22323 | −0.611614 | − | 0.791156i | \(-0.709479\pi\) | ||||
−0.611614 | + | 0.791156i | \(0.709479\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.9373 | 0.852893 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.82613 | −0.0820783 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.394955 | 0.0177162 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.49778 | 0.201348 | 0.100674 | − | 0.994919i | \(-0.467900\pi\) | ||||
0.100674 | + | 0.994919i | \(0.467900\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 15.3243 | 0.684640 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.00000 | 0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.42741 | −0.0635190 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.33416 | −0.414545 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.92656 | −0.439987 | −0.219993 | − | 0.975501i | \(-0.570604\pi\) | ||||
−0.219993 | + | 0.975501i | \(0.570604\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.887929 | 0.0392797 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9.18258 | −0.405421 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.88290 | −0.0829704 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.0720 | 0.970726 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19.1402 | 0.840160 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.65790 | −0.379309 | −0.189655 | − | 0.981851i | \(-0.560737\pi\) | ||||
−0.189655 | + | 0.981851i | \(0.560737\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.7111 | −0.774451 | −0.387226 | − | 0.921985i | \(-0.626567\pi\) | ||||
−0.387226 | + | 0.921985i | \(0.626567\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.318215 | −0.0138880 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −30.1236 | −1.31220 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 60.8360 | 2.64504 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 21.8710 | 0.949122 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.04547 | 0.218543 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.592990 | 0.0256372 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.33006 | −0.402622 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −30.0992 | −1.29646 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.8187 | −0.465131 | −0.232565 | − | 0.972581i | \(-0.574712\pi\) | ||||
−0.232565 | + | 0.972581i | \(0.574712\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.153395 | 0.00658282 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.28771 | −0.0979945 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.1188 | 1.41606 | 0.708028 | − | 0.706184i | \(-0.249585\pi\) | ||||
0.708028 | + | 0.706184i | \(0.249585\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 33.3558 | 1.42359 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.3364 | −0.568151 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.41057 | −0.0599835 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.577988 | 0.0245342 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12.3324 | 0.522541 | 0.261270 | − | 0.965266i | \(-0.415859\pi\) | ||||
0.261270 | + | 0.965266i | \(0.415859\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.23478 | −0.0945210 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.4442 | −0.440955 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −29.3356 | −1.23635 | −0.618174 | − | 0.786041i | \(-0.712127\pi\) | ||||
−0.618174 | + | 0.786041i | \(0.712127\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.790400 | −0.0332524 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.303495 | 0.0127456 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.339405 | 0.0142286 | 0.00711431 | − | 0.999975i | \(-0.497735\pi\) | ||||
0.00711431 | + | 0.999975i | \(0.497735\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.5993 | 0.694658 | 0.347329 | − | 0.937743i | \(-0.387089\pi\) | ||||
0.347329 | + | 0.937743i | \(0.387089\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.8430 | 0.661850 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 45.4883 | 1.89699 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.0207 | −0.791840 | −0.395920 | − | 0.918285i | \(-0.629574\pi\) | ||||
−0.395920 | + | 0.918285i | \(0.629574\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.0183 | −0.541023 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.200937 | 0.00833629 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.5782 | 0.479522 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.466806 | −0.0193001 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −29.3939 | −1.21322 | −0.606609 | − | 0.795000i | \(-0.707471\pi\) | ||||
−0.606609 | + | 0.795000i | \(0.707471\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21.2143 | 0.874118 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 19.2637 | 0.792403 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.6941 | −0.890871 | −0.445436 | − | 0.895314i | \(-0.646951\pi\) | ||||
−0.445436 | + | 0.895314i | \(0.646951\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.0443337 | −0.00181751 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.8630 | 0.526449 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.41054 | 0.302786 | 0.151393 | − | 0.988474i | \(-0.451624\pi\) | ||||
0.151393 | + | 0.988474i | \(0.451624\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.7208 | −0.722848 | −0.361424 | − | 0.932402i | \(-0.617709\pi\) | ||||
−0.361424 | + | 0.932402i | \(0.617709\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.3562 | 0.543906 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.34514 | 0.0546878 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −37.0318 | −1.50307 | −0.751536 | − | 0.659692i | \(-0.770687\pi\) | ||||
−0.751536 | + | 0.659692i | \(0.770687\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.395747 | −0.0160365 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.64219 | 0.228259 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 37.6348 | 1.52005 | 0.760027 | − | 0.649891i | \(-0.225185\pi\) | ||||
0.760027 | + | 0.649891i | \(0.225185\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.649157 | 0.0261765 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.73601 | −0.351699 | −0.175849 | − | 0.984417i | \(-0.556267\pi\) | ||||
−0.175849 | + | 0.984417i | \(0.556267\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.0846 | −0.686687 | −0.343343 | − | 0.939210i | \(-0.611559\pi\) | ||||
−0.343343 | + | 0.939210i | \(0.611559\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 38.9513 | 1.56306 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.450809 | 0.0180613 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.5215 | 0.980862 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.35526 | 0.293741 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.5152 | −0.499013 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.0472 | 1.51464 | 0.757318 | − | 0.653046i | \(-0.226509\pi\) | ||||
0.757318 | + | 0.653046i | \(0.226509\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.7552 | −0.427480 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.13008 | 0.124213 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.69415 | −0.304853 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.5856 | −0.458318 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.5905 | 1.08976 | 0.544879 | − | 0.838514i | \(-0.316575\pi\) | ||||
0.544879 | + | 0.838514i | \(0.316575\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.89268 | −0.271821 | −0.135910 | − | 0.990721i | \(-0.543396\pi\) | ||||
−0.135910 | + | 0.990721i | \(0.543396\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.287530 | −0.0113215 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.60822 | −0.338424 | −0.169212 | − | 0.985580i | \(-0.554122\pi\) | ||||
−0.169212 | + | 0.985580i | \(0.554122\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −39.6647 | −1.55698 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.629515 | 0.0246726 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.73378 | 0.146114 | 0.0730571 | − | 0.997328i | \(-0.476724\pi\) | ||||
0.0730571 | + | 0.997328i | \(0.476724\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.11571 | −0.0826677 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −26.0464 | −1.01617 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.1373 | −0.394893 | −0.197447 | − | 0.980314i | \(-0.563265\pi\) | ||||
−0.197447 | + | 0.980314i | \(0.563265\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.0003 | −0.427863 | −0.213932 | − | 0.976849i | \(-0.568627\pi\) | ||||
−0.213932 | + | 0.976849i | \(0.568627\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.66982 | −0.103687 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.0312216 | 0.00121072 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 56.5715 | 2.19046 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −19.5339 | −0.755226 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −60.4932 | −2.33531 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −44.9940 | −1.73439 | −0.867196 | − | 0.497967i | \(-0.834080\pi\) | ||||
−0.867196 | + | 0.497967i | \(0.834080\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 21.1345 | 0.813467 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.4870 | 0.595213 | 0.297607 | − | 0.954689i | \(-0.403812\pi\) | ||||
0.297607 | + | 0.954689i | \(0.403812\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.13045 | −0.0433828 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.2396 | −0.545661 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.7255 | −1.29047 | −0.645235 | − | 0.763984i | \(-0.723241\pi\) | ||||
−0.645235 | + | 0.763984i | \(0.723241\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.392439 | −0.0149943 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.5535 | 0.478947 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.95970 | 0.112756 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.5728 | −0.516333 | −0.258166 | − | 0.966100i | \(-0.583118\pi\) | ||||
−0.258166 | + | 0.966100i | \(0.583118\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.826321 | −0.0313894 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.09378 | −0.0414895 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.0562 | −0.532417 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.84954 | 0.0699559 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −34.7789 | −1.31358 | −0.656790 | − | 0.754074i | \(-0.728086\pi\) | ||||
−0.656790 | + | 0.754074i | \(0.728086\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.81371 | 0.332415 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.725932 | 0.0273402 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.645903 | −0.0242917 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.1752 | −0.870362 | −0.435181 | − | 0.900343i | \(-0.643316\pi\) | ||||
−0.435181 | + | 0.900343i | \(0.643316\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 41.3775 | 1.55178 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −89.9882 | −3.37009 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.846588 | 0.0316606 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.83872 | −0.143360 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 39.5082 | 1.47341 | 0.736704 | − | 0.676215i | \(-0.236381\pi\) | ||||
0.736704 | + | 0.676215i | \(0.236381\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.852011 | −0.0317305 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.71309 | −0.100901 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 30.6950 | 1.13998 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.75881 | 0.213583 | 0.106791 | − | 0.994281i | \(-0.465942\pi\) | ||||
0.106791 | + | 0.994281i | \(0.465942\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.20162 | 0.0445043 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.22589 | 0.230273 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −41.9036 | −1.54774 | −0.773872 | − | 0.633343i | \(-0.781682\pi\) | ||||
−0.773872 | + | 0.633343i | \(0.781682\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.989941 | −0.0365145 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −24.2224 | −0.892245 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.5650 | 0.535780 | 0.267890 | − | 0.963449i | \(-0.413674\pi\) | ||||
0.267890 | + | 0.963449i | \(0.413674\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.88020 | 0.0690708 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.9633 | 0.842440 | 0.421220 | − | 0.906958i | \(-0.361602\pi\) | ||||
0.421220 | + | 0.906958i | \(0.361602\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.11003 | −0.113943 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.89427 | −0.215660 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.268328 | 0.00980448 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.52609 | 0.311121 | 0.155561 | − | 0.987826i | \(-0.450282\pi\) | ||||
0.155561 | + | 0.987826i | \(0.450282\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 20.3606 | 0.741980 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.92611 | 0.142886 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.7364 | −0.717331 | −0.358665 | − | 0.933466i | \(-0.616768\pi\) | ||||
−0.358665 | + | 0.933466i | \(0.616768\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −31.2001 | −1.13249 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 44.7253 | 1.62129 | 0.810646 | − | 0.585537i | \(-0.199116\pi\) | ||||
0.810646 | + | 0.585537i | \(0.199116\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.03519 | −0.0374762 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.30048 | 0.0470189 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10.1394 | −0.366111 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.1170 | −1.01393 | −0.506963 | − | 0.861968i | \(-0.669232\pi\) | ||||
−0.506963 | + | 0.861968i | \(0.669232\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.1517 | −0.689733 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 34.5978 | 1.24440 | 0.622199 | − | 0.782859i | \(-0.286240\pi\) | ||||
0.622199 | + | 0.782859i | \(0.286240\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −48.8264 | −1.75390 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.261539 | 0.00938266 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.89897 | 0.354667 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.0113 | 0.751843 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 26.2839 | 0.939310 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.49953 | −0.124904 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 46.1869 | 1.64639 | 0.823193 | − | 0.567762i | \(-0.192190\pi\) | ||||
0.823193 | + | 0.567762i | \(0.192190\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14.3920 | −0.512367 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.357656 | −0.0127168 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.4637 | −0.549131 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.380800 | 0.0135056 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 31.0936 | 1.10139 | 0.550695 | − | 0.834707i | \(-0.314363\pi\) | ||||
0.550695 | + | 0.834707i | \(0.314363\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.7186 | −0.556085 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −13.2240 | −0.467246 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 47.2371 | 1.66696 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.132438 | −0.00466784 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.50502 | −0.158584 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −22.7451 | −0.799676 | −0.399838 | − | 0.916586i | \(-0.630934\pi\) | ||||
−0.399838 | + | 0.916586i | \(0.630934\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.2514 | 0.711121 | 0.355561 | − | 0.934653i | \(-0.384290\pi\) | ||||
0.355561 | + | 0.934653i | \(0.384290\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.9953 | −0.455766 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.54862 | 0.0892741 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.38453 | −0.153395 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.211230 | −0.00738096 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 47.0787 | 1.64306 | 0.821529 | − | 0.570167i | \(-0.193121\pi\) | ||||
0.821529 | + | 0.570167i | \(0.193121\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.97277 | 0.138482 | 0.0692411 | − | 0.997600i | \(-0.477942\pi\) | ||||
0.0692411 | + | 0.997600i | \(0.477942\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −16.9288 | −0.589384 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.1175 | 0.421366 | 0.210683 | − | 0.977554i | \(-0.432431\pi\) | ||||
0.210683 | + | 0.977554i | \(0.432431\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.0304 | 0.938804 | 0.469402 | − | 0.882985i | \(-0.344470\pi\) | ||||
0.469402 | + | 0.882985i | \(0.344470\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −20.9410 | −0.726437 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 21.4352 | 0.742686 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.46054 | 0.119757 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −41.8098 | −1.44516 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21.4624 | 0.740964 | 0.370482 | − | 0.928840i | \(-0.379193\pi\) | ||||
0.370482 | + | 0.928840i | \(0.379193\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.17374 | 0.316336 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.63335 | 0.0906974 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.10784 | −0.0725120 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.608676 | 0.0209144 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 17.4036 | 0.597290 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −37.3866 | −1.28160 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.5093 | −0.702226 | −0.351113 | − | 0.936333i | \(-0.614197\pi\) | ||||
−0.351113 | + | 0.936333i | \(0.614197\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.915852 | −0.0313215 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23.2772 | −0.795135 | −0.397567 | − | 0.917573i | \(-0.630146\pi\) | ||||
−0.397567 | + | 0.917573i | \(0.630146\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.80551 | 0.129842 | 0.0649212 | − | 0.997890i | \(-0.479320\pi\) | ||||
0.0649212 | + | 0.997890i | \(0.479320\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.293743 | 0.0100107 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 35.9633 | 1.22420 | 0.612102 | − | 0.790779i | \(-0.290324\pi\) | ||||
0.612102 | + | 0.790779i | \(0.290324\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.32224 | 0.146960 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.02154 | −0.204502 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −75.0412 | −2.54560 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.19189 | −0.209804 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 33.1605 | 1.12231 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.144181 | −0.00487421 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.2388 | 0.480810 | 0.240405 | − | 0.970673i | \(-0.422720\pi\) | ||||
0.240405 | + | 0.970673i | \(0.422720\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.17885 | −0.174678 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.4845 | 0.925976 | 0.462988 | − | 0.886365i | \(-0.346777\pi\) | ||||
0.462988 | + | 0.886365i | \(0.346777\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.3360 | −0.818973 | −0.409487 | − | 0.912316i | \(-0.634292\pi\) | ||||
−0.409487 | + | 0.912316i | \(0.634292\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.30454 | −0.0438518 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26.2023 | 0.879787 | 0.439893 | − | 0.898050i | \(-0.355016\pi\) | ||||
0.439893 | + | 0.898050i | \(0.355016\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.41636 | 0.0475031 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 16.1457 | 0.540900 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.0697 | 0.370434 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.10692 | −0.0704265 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.97556 | −0.266296 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −60.7230 | −2.02522 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.24546 | −0.274696 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.130107 | −0.00432969 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.0346397 | 0.00115146 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −58.2340 | −1.93363 | −0.966814 | − | 0.255482i | \(-0.917766\pi\) | ||||
−0.966814 | + | 0.255482i | \(0.917766\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 18.9468 | 0.628427 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.4851 | 1.01002 | 0.505008 | − | 0.863114i | \(-0.331489\pi\) | ||||
0.505008 | + | 0.863114i | \(0.331489\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.6897 | 0.353778 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.98958 | −0.0657734 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.957358 | −0.0316148 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.94915 | 0.0972833 | 0.0486417 | − | 0.998816i | \(-0.484511\pi\) | ||||
0.0486417 | + | 0.998816i | \(0.484511\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.4290 | −0.409548 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.37104 | 0.176790 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.2855 | −0.666983 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 24.9928 | 0.820870 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 28.9881 | 0.951070 | 0.475535 | − | 0.879697i | \(-0.342255\pi\) | ||||
0.475535 | + | 0.879697i | \(0.342255\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.0956 | −0.494737 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −20.2814 | −0.663984 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.35852 | −0.0771318 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27.5952 | −0.901497 | −0.450748 | − | 0.892651i | \(-0.648843\pi\) | ||||
−0.450748 | + | 0.892651i | \(0.648843\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.92776 | 0.0955439 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.2064 | 0.626112 | 0.313056 | − | 0.949735i | \(-0.398647\pi\) | ||||
0.313056 | + | 0.949735i | \(0.398647\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −41.9902 | −1.36739 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.0615326 | −0.00200166 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 41.2922 | 1.34182 | 0.670908 | − | 0.741541i | \(-0.265905\pi\) | ||||
0.670908 | + | 0.741541i | \(0.265905\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.0750 | 0.391973 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15.0584 | 0.488302 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −24.0272 | −0.778317 | −0.389158 | − | 0.921171i | \(-0.627234\pi\) | ||||
−0.389158 | + | 0.921171i | \(0.627234\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.57767 | 0.115771 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −21.0534 | −0.680561 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.177578 | −0.00573430 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 65.5920 | 2.11587 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.87109 | −0.253642 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.93980 | −0.0946355 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.8553 | 0.349084 | 0.174542 | − | 0.984650i | \(-0.444155\pi\) | ||||
0.174542 | + | 0.984650i | \(0.444155\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.23806 | −0.168271 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17.1111 | 0.549122 | 0.274561 | − | 0.961570i | \(-0.411467\pi\) | ||||
0.274561 | + | 0.961570i | \(0.411467\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.494936 | −0.0158669 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.32744 | −0.138589 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.5277 | 0.720726 | 0.360363 | − | 0.932812i | \(-0.382653\pi\) | ||||
0.360363 | + | 0.932812i | \(0.382653\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23.9827 | 0.766489 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 30.3660 | 0.969512 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 27.0618 | 0.863138 | 0.431569 | − | 0.902080i | \(-0.357960\pi\) | ||||
0.431569 | + | 0.902080i | \(0.357960\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.35014 | 0.138607 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.328484 | 0.0104558 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18.5986 | 0.591401 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.8216 | 0.629655 | 0.314827 | − | 0.949149i | \(-0.398053\pi\) | ||||
0.314827 | + | 0.949149i | \(0.398053\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.76020 | 0.119326 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.90473 | 0.0920863 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −23.1120 | −0.731966 | −0.365983 | − | 0.930622i | \(-0.619267\pi\) | ||||
−0.365983 | + | 0.930622i | \(0.619267\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −17.3703 | −0.549573 |
(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 | 8048.2.a.p.1.5 | 10 | ||
4.3 | odd | 2 | 503.2.a.e.1.8 | ✓ | 10 | ||
12.11 | even | 2 | 4527.2.a.k.1.3 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
503.2.a.e.1.8 | ✓ | 10 | 4.3 | odd | 2 | ||
4527.2.a.k.1.3 | 10 | 12.11 | even | 2 | |||
8048.2.a.p.1.5 | 10 | 1.1 | even | 1 | trivial |