Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8008,2,Mod(1,8008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("8008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.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: | \(63.9442019386\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 3x^{8} - 15x^{7} + 45x^{6} + 64x^{5} - 201x^{4} - 63x^{3} + 282x^{2} + 3x - 116 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.21838\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8008.1 |
$q$-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 | ||||||||
\(3\) | −1.21838 | −0.703430 | −0.351715 | − | 0.936107i | \(-0.614401\pi\) | ||||
−0.351715 | + | 0.936107i | \(0.614401\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.90030 | 1.29705 | 0.648526 | − | 0.761193i | \(-0.275386\pi\) | ||||
0.648526 | + | 0.761193i | \(0.275386\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.51556 | −0.505186 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.53365 | −0.912385 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.20996 | 0.778529 | 0.389265 | − | 0.921126i | \(-0.372729\pi\) | ||||
0.389265 | + | 0.921126i | \(0.372729\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.338048 | −0.0775536 | −0.0387768 | − | 0.999248i | \(-0.512346\pi\) | ||||
−0.0387768 | + | 0.999248i | \(0.512346\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.21838 | 0.265872 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.17564 | 1.49622 | 0.748112 | − | 0.663573i | \(-0.230961\pi\) | ||||
0.748112 | + | 0.663573i | \(0.230961\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.41172 | 0.682344 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.50165 | 1.05879 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.5557 | 1.96015 | 0.980075 | − | 0.198626i | \(-0.0636479\pi\) | ||||
0.980075 | + | 0.198626i | \(0.0636479\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.34712 | 0.241950 | 0.120975 | − | 0.992656i | \(-0.461398\pi\) | ||||
0.120975 | + | 0.992656i | \(0.461398\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.21838 | −0.212092 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.90030 | −0.490240 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.97901 | 0.489746 | 0.244873 | − | 0.969555i | \(-0.421254\pi\) | ||||
0.244873 | + | 0.969555i | \(0.421254\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.21838 | 0.195096 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.83082 | −0.598273 | −0.299137 | − | 0.954210i | \(-0.596699\pi\) | ||||
−0.299137 | + | 0.954210i | \(0.596699\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.40992 | −0.367510 | −0.183755 | − | 0.982972i | \(-0.558825\pi\) | ||||
−0.183755 | + | 0.982972i | \(0.558825\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.39557 | −0.655253 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.1040 | −1.76555 | −0.882777 | − | 0.469793i | \(-0.844329\pi\) | ||||
−0.882777 | + | 0.469793i | \(0.844329\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.91094 | −0.547641 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.77133 | 0.243311 | 0.121656 | − | 0.992572i | \(-0.461180\pi\) | ||||
0.121656 | + | 0.992572i | \(0.461180\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.90030 | 0.391076 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.411870 | 0.0545535 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.34524 | −0.826080 | −0.413040 | − | 0.910713i | \(-0.635533\pi\) | ||||
−0.413040 | + | 0.910713i | \(0.635533\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.55153 | −0.838837 | −0.419419 | − | 0.907793i | \(-0.637766\pi\) | ||||
−0.419419 | + | 0.907793i | \(0.637766\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.51556 | 0.190942 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.90030 | −0.359737 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.479975 | −0.0586383 | −0.0293192 | − | 0.999570i | \(-0.509334\pi\) | ||||
−0.0293192 | + | 0.999570i | \(0.509334\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.74263 | −1.05249 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.64425 | −0.907205 | −0.453603 | − | 0.891204i | \(-0.649861\pi\) | ||||
−0.453603 | + | 0.891204i | \(0.649861\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.07758 | −0.594286 | −0.297143 | − | 0.954833i | \(-0.596034\pi\) | ||||
−0.297143 | + | 0.954833i | \(0.596034\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.15676 | −0.479981 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.11643 | 0.125608 | 0.0628038 | − | 0.998026i | \(-0.479996\pi\) | ||||
0.0628038 | + | 0.998026i | \(0.479996\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.15641 | −0.239601 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.65360 | 0.840092 | 0.420046 | − | 0.907503i | \(-0.362014\pi\) | ||||
0.420046 | + | 0.907503i | \(0.362014\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.30983 | 1.00979 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −12.8609 | −1.37883 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.7332 | 1.66771 | 0.833856 | − | 0.551983i | \(-0.186129\pi\) | ||||
0.833856 | + | 0.551983i | \(0.186129\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.64130 | −0.170195 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.980440 | −0.100591 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.9715 | 1.72320 | 0.861598 | − | 0.507591i | \(-0.169464\pi\) | ||||
0.861598 | + | 0.507591i | \(0.169464\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.51556 | −0.152319 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.90578 | 0.886159 | 0.443079 | − | 0.896482i | \(-0.353886\pi\) | ||||
0.443079 | + | 0.896482i | \(0.353886\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.8118 | −1.26238 | −0.631191 | − | 0.775628i | \(-0.717434\pi\) | ||||
−0.631191 | + | 0.775628i | \(0.717434\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.53365 | 0.344849 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.75077 | −0.942642 | −0.471321 | − | 0.881962i | \(-0.656223\pi\) | ||||
−0.471321 | + | 0.881962i | \(0.656223\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.90638 | 0.469946 | 0.234973 | − | 0.972002i | \(-0.424500\pi\) | ||||
0.234973 | + | 0.972002i | \(0.424500\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.62955 | −0.344502 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.2893 | −1.25015 | −0.625077 | − | 0.780563i | \(-0.714933\pi\) | ||||
−0.625077 | + | 0.780563i | \(0.714933\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 20.8115 | 1.94068 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.51556 | 0.140113 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.20996 | −0.294256 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.66738 | 0.420844 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.60649 | −0.412017 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.66573 | 0.591488 | 0.295744 | − | 0.955267i | \(-0.404432\pi\) | ||||
0.295744 | + | 0.955267i | \(0.404432\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.93619 | 0.258517 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.77634 | 0.766792 | 0.383396 | − | 0.923584i | \(-0.374754\pi\) | ||||
0.383396 | + | 0.923584i | \(0.374754\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.338048 | 0.0293125 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 15.9564 | 1.37331 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.29231 | 0.793896 | 0.396948 | − | 0.917841i | \(-0.370069\pi\) | ||||
0.396948 | + | 0.917841i | \(0.370069\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.54313 | −0.470162 | −0.235081 | − | 0.971976i | \(-0.575536\pi\) | ||||
−0.235081 | + | 0.971976i | \(0.575536\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 14.7473 | 1.24194 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.00000 | −0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 30.6148 | 2.54242 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.21838 | −0.100490 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.44869 | −0.282528 | −0.141264 | − | 0.989972i | \(-0.545117\pi\) | ||||
−0.141264 | + | 0.989972i | \(0.545117\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.3094 | 1.65275 | 0.826377 | − | 0.563117i | \(-0.190398\pi\) | ||||
0.826377 | + | 0.563117i | \(0.190398\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.86488 | −0.393302 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.90704 | 0.313821 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.0052 | 1.11774 | 0.558869 | − | 0.829256i | \(-0.311236\pi\) | ||||
0.558869 | + | 0.829256i | \(0.311236\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.15815 | −0.171152 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.17564 | −0.565519 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 23.2055 | 1.81760 | 0.908799 | − | 0.417235i | \(-0.137001\pi\) | ||||
0.908799 | + | 0.417235i | \(0.137001\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.53365 | −0.275095 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.4507 | −1.50514 | −0.752569 | − | 0.658514i | \(-0.771185\pi\) | ||||
−0.752569 | + | 0.658514i | \(0.771185\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.512332 | 0.0391790 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.3217 | 1.01283 | 0.506416 | − | 0.862289i | \(-0.330970\pi\) | ||||
0.506416 | + | 0.862289i | \(0.330970\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.41172 | −0.257902 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.73090 | 0.581090 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.7801 | −1.17946 | −0.589731 | − | 0.807600i | \(-0.700766\pi\) | ||||
−0.589731 | + | 0.807600i | \(0.700766\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.04562 | −0.152050 | −0.0760251 | − | 0.997106i | \(-0.524223\pi\) | ||||
−0.0760251 | + | 0.997106i | \(0.524223\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.98223 | 0.590063 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.64000 | 0.635226 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.20996 | 0.234735 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.50165 | −0.400186 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.8934 | 1.43944 | 0.719718 | − | 0.694267i | \(-0.244271\pi\) | ||||
0.719718 | + | 0.694267i | \(0.244271\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.68351 | 0.193163 | 0.0965817 | − | 0.995325i | \(-0.469209\pi\) | ||||
0.0965817 | + | 0.995325i | \(0.469209\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.53365 | 0.253050 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.8597 | 0.844968 | 0.422484 | − | 0.906370i | \(-0.361158\pi\) | ||||
0.422484 | + | 0.906370i | \(0.361158\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.0890 | −1.14052 | −0.570261 | − | 0.821463i | \(-0.693158\pi\) | ||||
−0.570261 | + | 0.821463i | \(0.693158\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.584791 | 0.0412480 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.5557 | −0.740867 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.1105 | −0.775992 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −10.8751 | −0.755872 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.338048 | −0.0233833 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.95441 | −0.616447 | −0.308224 | − | 0.951314i | \(-0.599734\pi\) | ||||
−0.308224 | + | 0.951314i | \(0.599734\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.31357 | 0.638155 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.98949 | −0.476679 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.34712 | −0.0914483 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.18641 | 0.418039 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.20996 | −0.215925 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.41486 | 0.563501 | 0.281750 | − | 0.959488i | \(-0.409085\pi\) | ||||
0.281750 | + | 0.959488i | \(0.409085\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.17066 | −0.344711 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.9637 | 0.727687 | 0.363844 | − | 0.931460i | \(-0.381464\pi\) | ||||
0.363844 | + | 0.931460i | \(0.381464\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.4275 | 0.887315 | 0.443658 | − | 0.896196i | \(-0.353681\pi\) | ||||
0.443658 | + | 0.896196i | \(0.353681\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.21838 | 0.0801633 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.8452 | 1.23459 | 0.617294 | − | 0.786732i | \(-0.288229\pi\) | ||||
0.617294 | + | 0.786732i | \(0.288229\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −35.1053 | −2.29001 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.36023 | −0.0883562 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −26.9165 | −1.74109 | −0.870543 | − | 0.492093i | \(-0.836232\pi\) | ||||
−0.870543 | + | 0.492093i | \(0.836232\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.9783 | 1.15809 | 0.579043 | − | 0.815297i | \(-0.303426\pi\) | ||||
0.579043 | + | 0.815297i | \(0.303426\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.8776 | −0.890251 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.90030 | 0.185293 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.338048 | 0.0215095 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.32497 | −0.590946 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.4480 | 1.10131 | 0.550653 | − | 0.834734i | \(-0.314379\pi\) | ||||
0.550653 | + | 0.834734i | \(0.314379\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.17564 | 0.451128 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −11.3429 | −0.710318 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −16.0870 | −1.00348 | −0.501740 | − | 0.865019i | \(-0.667307\pi\) | ||||
−0.501740 | + | 0.865019i | \(0.667307\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.97901 | −0.185107 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −15.9978 | −0.990241 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.61980 | −0.531520 | −0.265760 | − | 0.964039i | \(-0.585623\pi\) | ||||
−0.265760 | + | 0.964039i | \(0.585623\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.13738 | 0.315587 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −19.1689 | −1.17312 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.93841 | 0.484013 | 0.242007 | − | 0.970275i | \(-0.422194\pi\) | ||||
0.242007 | + | 0.970275i | \(0.422194\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.9301 | 1.69663 | 0.848315 | − | 0.529492i | \(-0.177617\pi\) | ||||
0.848315 | + | 0.529492i | \(0.177617\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.21838 | −0.0737395 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.41172 | 0.205734 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.6275 | 1.11922 | 0.559609 | − | 0.828757i | \(-0.310951\pi\) | ||||
0.559609 | + | 0.828757i | \(0.310951\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.04164 | −0.122230 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.9773 | 0.953124 | 0.476562 | − | 0.879141i | \(-0.341883\pi\) | ||||
0.476562 | + | 0.879141i | \(0.341883\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 28.0250 | 1.66592 | 0.832958 | − | 0.553336i | \(-0.186646\pi\) | ||||
0.832958 | + | 0.553336i | \(0.186646\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.19454 | 0.0707587 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.83082 | 0.226126 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.69617 | −0.393893 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −20.6777 | −1.21215 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.21281 | 0.0708530 | 0.0354265 | − | 0.999372i | \(-0.488721\pi\) | ||||
0.0354265 | + | 0.999372i | \(0.488721\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −18.4031 | −1.07147 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.50165 | 0.319238 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.17564 | −0.414978 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.40992 | 0.138906 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.8506 | −0.623351 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −19.0014 | −1.08802 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.8553 | −0.904910 | −0.452455 | − | 0.891787i | \(-0.649452\pi\) | ||||
−0.452455 | + | 0.891787i | \(0.649452\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.6096 | 0.887997 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.4291 | −1.32854 | −0.664271 | − | 0.747492i | \(-0.731258\pi\) | ||||
−0.664271 | + | 0.747492i | \(0.731258\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −29.3280 | −1.65772 | −0.828859 | − | 0.559458i | \(-0.811009\pi\) | ||||
−0.828859 | + | 0.559458i | \(0.811009\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.39557 | 0.247662 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.88166 | −0.442678 | −0.221339 | − | 0.975197i | \(-0.571043\pi\) | ||||
−0.221339 | + | 0.975197i | \(0.571043\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.5557 | 0.591008 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.8801 | 0.663083 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.08512 | −0.0603777 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.41172 | −0.189248 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.97782 | −0.330574 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.1040 | 0.667316 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.0779 | 0.553930 | 0.276965 | − | 0.960880i | \(-0.410671\pi\) | ||||
0.276965 | + | 0.960880i | \(0.410671\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.51486 | −0.247413 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.39207 | −0.0760570 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.8753 | −1.02820 | −0.514102 | − | 0.857729i | \(-0.671875\pi\) | ||||
−0.514102 | + | 0.857729i | \(0.671875\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.1914 | 0.879396 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.34712 | 0.0729505 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −25.3562 | −1.36513 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.3631 | 0.985784 | 0.492892 | − | 0.870091i | \(-0.335940\pi\) | ||||
0.492892 | + | 0.870091i | \(0.335940\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.22415 | −0.119056 | −0.0595281 | − | 0.998227i | \(-0.518960\pi\) | ||||
−0.0595281 | + | 0.998227i | \(0.518960\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.50165 | −0.293656 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.40051 | 0.287440 | 0.143720 | − | 0.989618i | \(-0.454093\pi\) | ||||
0.143720 | + | 0.989618i | \(0.454093\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −22.1706 | −1.17669 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.91094 | 0.206989 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −24.5262 | −1.29444 | −0.647222 | − | 0.762302i | \(-0.724069\pi\) | ||||
−0.647222 | + | 0.762302i | \(0.724069\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8857 | −0.993985 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.21838 | −0.0639482 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.7265 | −0.770820 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 29.7524 | 1.55306 | 0.776532 | − | 0.630077i | \(-0.216977\pi\) | ||||
0.776532 | + | 0.630077i | \(0.216977\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.80583 | 0.302240 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.77133 | −0.0919629 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.3278 | 1.31142 | 0.655711 | − | 0.755012i | \(-0.272369\pi\) | ||||
0.655711 | + | 0.755012i | \(0.272369\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.61244 | 0.289825 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.5557 | −0.543648 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.3986 | −0.636872 | −0.318436 | − | 0.947944i | \(-0.603158\pi\) | ||||
−0.318436 | + | 0.947944i | \(0.603158\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.12137 | −0.416070 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 19.6711 | 1.00515 | 0.502574 | − | 0.864534i | \(-0.332387\pi\) | ||||
0.502574 | + | 0.864534i | \(0.332387\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.90030 | −0.147813 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.65238 | 0.185661 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.16212 | 0.464538 | 0.232269 | − | 0.972652i | \(-0.425385\pi\) | ||||
0.232269 | + | 0.972652i | \(0.425385\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 23.0335 | 1.16485 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.6929 | −0.539385 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.23796 | 0.162920 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.0924 | 0.556713 | 0.278357 | − | 0.960478i | \(-0.410210\pi\) | ||||
0.278357 | + | 0.960478i | \(0.410210\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.411870 | −0.0206193 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.1617 | 1.05676 | 0.528382 | − | 0.849006i | \(-0.322799\pi\) | ||||
0.528382 | + | 0.849006i | \(0.322799\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.34712 | −0.0671047 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.25422 | −0.310775 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.97901 | 0.147664 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 39.4751 | 1.95192 | 0.975959 | − | 0.217955i | \(-0.0699385\pi\) | ||||
0.975959 | + | 0.217955i | \(0.0699385\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.3215 | −0.558450 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.34524 | 0.312229 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 22.1977 | 1.08964 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.75362 | 0.330726 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.8391 | 1.36003 | 0.680016 | − | 0.733198i | \(-0.261973\pi\) | ||||
0.680016 | + | 0.733198i | \(0.261973\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.0248 | 0.927211 | 0.463606 | − | 0.886042i | \(-0.346555\pi\) | ||||
0.463606 | + | 0.886042i | \(0.346555\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 18.3444 | 0.891933 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10.9515 | 0.531224 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.55153 | 0.317051 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.21838 | 0.0588238 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.54985 | −0.267327 | −0.133664 | − | 0.991027i | \(-0.542674\pi\) | ||||
−0.133664 | + | 0.991027i | \(0.542674\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.7316 | 0.756010 | 0.378005 | − | 0.925803i | \(-0.376610\pi\) | ||||
0.378005 | + | 0.925803i | \(0.376610\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −37.3003 | −1.78841 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.42571 | −0.116037 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.98296 | 0.428733 | 0.214367 | − | 0.976753i | \(-0.431231\pi\) | ||||
0.214367 | + | 0.976753i | \(0.431231\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.51556 | −0.0721695 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.35431 | −0.206879 | −0.103440 | − | 0.994636i | \(-0.532985\pi\) | ||||
−0.103440 | + | 0.994636i | \(0.532985\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 45.6308 | 2.16311 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.20181 | 0.198739 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.4540 | 1.15406 | 0.577028 | − | 0.816724i | \(-0.304212\pi\) | ||||
0.577028 | + | 0.816724i | \(0.304212\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.83082 | −0.180386 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −24.7445 | −1.16260 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.90030 | 0.135968 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.9544 | 1.12054 | 0.560269 | − | 0.828311i | \(-0.310698\pi\) | ||||
0.560269 | + | 0.828311i | \(0.310698\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 17.6601 | 0.824301 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −40.4206 | −1.88257 | −0.941287 | − | 0.337608i | \(-0.890382\pi\) | ||||
−0.941287 | + | 0.337608i | \(0.890382\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.9033 | 0.646141 | 0.323071 | − | 0.946375i | \(-0.395285\pi\) | ||||
0.323071 | + | 0.946375i | \(0.395285\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.76025 | −0.220751 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.41389 | 0.157976 | 0.0789880 | − | 0.996876i | \(-0.474831\pi\) | ||||
0.0789880 | + | 0.996876i | \(0.474831\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.479975 | 0.0221632 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.0636 | −0.786250 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.40992 | −0.110808 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.15332 | −0.0529182 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.68456 | −0.122917 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 29.0810 | 1.32874 | 0.664371 | − | 0.747403i | \(-0.268699\pi\) | ||||
0.664371 | + | 0.747403i | \(0.268699\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.97901 | −0.135831 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.74263 | 0.397803 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 49.2224 | 2.23507 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −40.9117 | −1.85389 | −0.926944 | − | 0.375201i | \(-0.877574\pi\) | ||||
−0.926944 | + | 0.375201i | \(0.877574\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −28.2731 | −1.27855 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.8139 | 0.984447 | 0.492223 | − | 0.870469i | \(-0.336184\pi\) | ||||
0.492223 | + | 0.870469i | \(0.336184\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 33.8835 | 1.52603 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.39557 | −0.197566 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.64425 | 0.342891 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.60399 | 0.161337 | 0.0806684 | − | 0.996741i | \(-0.474295\pi\) | ||||
0.0806684 | + | 0.996741i | \(0.474295\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 23.6982 | 1.05876 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −40.9551 | −1.82610 | −0.913049 | − | 0.407850i | \(-0.866279\pi\) | ||||
−0.913049 | + | 0.407850i | \(0.866279\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 25.8294 | 1.14939 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.21838 | −0.0541100 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −25.9845 | −1.15174 | −0.575872 | − | 0.817540i | \(-0.695337\pi\) | ||||
−0.575872 | + | 0.817540i | \(0.695337\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.07758 | 0.224619 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.85982 | −0.0821132 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −37.1579 | −1.63737 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.1040 | −0.532334 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.2309 | −0.712456 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.37871 | 0.191835 | 0.0959173 | − | 0.995389i | \(-0.469422\pi\) | ||||
0.0959173 | + | 0.995389i | \(0.469422\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −39.8178 | −1.74111 | −0.870556 | − | 0.492070i | \(-0.836240\pi\) | ||||
−0.870556 | + | 0.492070i | \(0.836240\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.15676 | 0.181416 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.32419 | 0.188365 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 28.4898 | 1.23869 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.61659 | 0.417324 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.83082 | 0.165931 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −28.2801 | −1.22266 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 19.2261 | 0.829669 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.7361 | 0.461581 | 0.230790 | − | 0.973003i | \(-0.425869\pi\) | ||||
0.230790 | + | 0.973003i | \(0.425869\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.49234 | 0.106957 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.2299 | 0.609544 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.5328 | 1.39100 | 0.695500 | − | 0.718526i | \(-0.255183\pi\) | ||||
0.695500 | + | 0.718526i | \(0.255183\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.92923 | 0.423769 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.56835 | −0.152017 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.11643 | −0.0474752 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10.5268 | −0.446837 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.5348 | −0.615859 | −0.307930 | − | 0.951409i | \(-0.599636\pi\) | ||||
−0.307930 | + | 0.951409i | \(0.599636\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.40992 | 0.101929 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.91094 | −0.165120 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.6786 | 0.450050 | 0.225025 | − | 0.974353i | \(-0.427754\pi\) | ||||
0.225025 | + | 0.974353i | \(0.427754\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −38.5430 | −1.62152 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.15641 | 0.0905605 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.7695 | 0.451481 | 0.225740 | − | 0.974187i | \(-0.427520\pi\) | ||||
0.225740 | + | 0.974187i | \(0.427520\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.0492 | −0.755334 | −0.377667 | − | 0.925941i | \(-0.623274\pi\) | ||||
−0.377667 | + | 0.925941i | \(0.623274\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −24.2376 | −1.01254 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 24.4813 | 1.02094 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.9289 | −0.746388 | −0.373194 | − | 0.927753i | \(-0.621737\pi\) | ||||
−0.373194 | + | 0.927753i | \(0.621737\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.26953 | −0.135877 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.65360 | −0.317525 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.77133 | 0.0733610 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.39557 | 0.181734 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.0383 | −0.827069 | −0.413534 | − | 0.910488i | \(-0.635706\pi\) | ||||
−0.413534 | + | 0.910488i | \(0.635706\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.455391 | −0.0187640 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.4496 | −0.594376 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.5002 | −1.00610 | −0.503050 | − | 0.864257i | \(-0.667789\pi\) | ||||
−0.503050 | + | 0.864257i | \(0.667789\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.30983 | −0.381666 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 19.6025 | 0.802278 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.6370 | 0.516335 | 0.258168 | − | 0.966100i | \(-0.416881\pi\) | ||||
0.258168 | + | 0.966100i | \(0.416881\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.87669 | 0.0765517 | 0.0382759 | − | 0.999267i | \(-0.487813\pi\) | ||||
0.0382759 | + | 0.999267i | \(0.487813\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.727431 | 0.0296233 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.90030 | 0.117914 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.9699 | 1.05408 | 0.527042 | − | 0.849839i | \(-0.323301\pi\) | ||||
0.527042 | + | 0.849839i | \(0.323301\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 12.8609 | 0.521148 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.1040 | 0.489676 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.2858 | −0.940505 | −0.470252 | − | 0.882532i | \(-0.655837\pi\) | ||||
−0.470252 | + | 0.882532i | \(0.655837\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 13.5368 | 0.545856 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.2406 | 0.573306 | 0.286653 | − | 0.958034i | \(-0.407457\pi\) | ||||
0.286653 | + | 0.958034i | \(0.407457\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.9387 | 1.24353 | 0.621766 | − | 0.783203i | \(-0.286416\pi\) | ||||
0.621766 | + | 0.783203i | \(0.286416\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 39.4778 | 1.58419 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −15.7332 | −0.630336 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.4188 | −1.21675 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.411870 | 0.0164485 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.56249 | 0.381281 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.77785 | −0.110585 | −0.0552923 | − | 0.998470i | \(-0.517609\pi\) | ||||
−0.0552923 | + | 0.998470i | \(0.517609\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.9098 | 0.433627 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 19.3326 | 0.767191 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.5853 | 0.458308 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27.1749 | −1.07335 | −0.536673 | − | 0.843790i | \(-0.680319\pi\) | ||||
−0.536673 | + | 0.843790i | \(0.680319\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.95387 | 0.195362 | 0.0976808 | − | 0.995218i | \(-0.468858\pi\) | ||||
0.0976808 | + | 0.995218i | \(0.468858\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.51583 | 0.335311 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 32.6204 | 1.28244 | 0.641220 | − | 0.767357i | \(-0.278429\pi\) | ||||
0.641220 | + | 0.767357i | \(0.278429\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.34524 | −0.249073 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.64130 | 0.0643275 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.88950 | −0.113075 | −0.0565374 | − | 0.998400i | \(-0.518006\pi\) | ||||
−0.0565374 | + | 0.998400i | \(0.518006\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 25.4540 | 0.994569 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.69537 | 0.300225 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.94885 | −0.114871 | −0.0574355 | − | 0.998349i | \(-0.518292\pi\) | ||||
−0.0574355 | + | 0.998349i | \(0.518292\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.9628 | −1.12652 | −0.563261 | − | 0.826279i | \(-0.690454\pi\) | ||||
−0.563261 | + | 0.826279i | \(0.690454\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.91094 | 0.151888 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.980440 | 0.0380198 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 75.7441 | 2.93282 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −10.2525 | −0.396383 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.55153 | −0.252919 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.52456 | 0.174409 | 0.0872045 | − | 0.996190i | \(-0.472207\pi\) | ||||
0.0872045 | + | 0.996190i | \(0.472207\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 18.7701 | 0.722461 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.94320 | −0.382148 | −0.191074 | − | 0.981576i | \(-0.561197\pi\) | ||||
−0.191074 | + | 0.981576i | \(0.561197\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16.9715 | −0.651307 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −13.3579 | −0.511877 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.2544 | 1.38723 | 0.693617 | − | 0.720344i | \(-0.256016\pi\) | ||||
0.693617 | + | 0.720344i | \(0.256016\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 26.9504 | 1.02972 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.3598 | −0.624164 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.77133 | −0.0674823 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −45.4198 | −1.72785 | −0.863926 | − | 0.503619i | \(-0.832002\pi\) | ||||
−0.863926 | + | 0.503619i | \(0.832002\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.51556 | 0.0575713 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −16.0767 | −0.609825 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.2968 | −0.465773 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −22.9605 | −0.868447 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.0214 | −0.945045 | −0.472523 | − | 0.881319i | \(-0.656657\pi\) | ||||
−0.472523 | + | 0.881319i | \(0.656657\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.00705 | −0.0379815 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 42.7714 | 1.61086 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.90578 | −0.334936 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −49.3904 | −1.85490 | −0.927448 | − | 0.373952i | \(-0.878003\pi\) | ||||
−0.927448 | + | 0.373952i | \(0.878003\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.69201 | −0.0634552 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.66643 | 0.362011 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.90030 | −0.108465 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 32.7945 | 1.22473 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.951868 | 0.0354987 | 0.0177493 | − | 0.999842i | \(-0.494350\pi\) | ||||
0.0177493 | + | 0.999842i | \(0.494350\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.8118 | 0.477135 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −21.9044 | −0.814633 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 36.0132 | 1.33750 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.3584 | −0.829229 | −0.414614 | − | 0.909997i | \(-0.636083\pi\) | ||||
−0.414614 | + | 0.909997i | \(0.636083\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.3774 | 0.865830 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.73575 | −0.286117 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −33.9992 | −1.25579 | −0.627895 | − | 0.778298i | \(-0.716083\pi\) | ||||
−0.627895 | + | 0.778298i | \(0.716083\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.53365 | −0.130341 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.479975 | −0.0176801 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.6754 | 1.23877 | 0.619384 | − | 0.785088i | \(-0.287382\pi\) | ||||
0.619384 | + | 0.785088i | \(0.287382\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.411870 | −0.0151304 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.7180 | 0.796755 | 0.398378 | − | 0.917221i | \(-0.369573\pi\) | ||||
0.398378 | + | 0.917221i | \(0.369573\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.0022 | −0.366453 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −11.5995 | −0.424403 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.75077 | 0.356285 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.64775 | 0.0601272 | 0.0300636 | − | 0.999548i | \(-0.490429\pi\) | ||||
0.0300636 | + | 0.999548i | \(0.490429\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −21.2582 | −0.774692 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 58.9033 | 2.14371 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.58858 | −0.275812 | −0.137906 | − | 0.990445i | \(-0.544037\pi\) | ||||
−0.137906 | + | 0.990445i | \(0.544037\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.74263 | −0.317337 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.206389 | −0.00748159 | −0.00374079 | − | 0.999993i | \(-0.501191\pi\) | ||||
−0.00374079 | + | 0.999993i | \(0.501191\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.90638 | −0.177623 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −14.1096 | −0.510133 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.34524 | 0.229113 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.1132 | 0.436812 | 0.218406 | − | 0.975858i | \(-0.429914\pi\) | ||||
0.218406 | + | 0.975858i | \(0.429914\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.6000 | 0.705878 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 44.7549 | 1.60972 | 0.804862 | − | 0.593462i | \(-0.202239\pi\) | ||||
0.804862 | + | 0.593462i | \(0.202239\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.59599 | 0.165093 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.62955 | 0.130209 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.29500 | 0.0463982 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.64425 | −0.273533 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 58.0740 | 2.07539 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 40.6193 | 1.44976 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.7427 | 0.988919 | 0.494460 | − | 0.869201i | \(-0.335366\pi\) | ||||
0.494460 | + | 0.869201i | \(0.335366\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.5022 | 0.373887 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.2893 | 0.472514 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.55153 | 0.232652 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.25927 | −0.221993 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −31.1866 | −1.10469 | −0.552343 | − | 0.833617i | \(-0.686266\pi\) | ||||
−0.552343 | + | 0.833617i | \(0.686266\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −38.8534 | −1.37453 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −23.8445 | −0.842505 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.07758 | −0.179184 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −20.8115 | −0.733508 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.67197 | −0.340469 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 47.8068 | 1.68080 | 0.840399 | − | 0.541969i | \(-0.182321\pi\) | ||||
0.840399 | + | 0.541969i | \(0.182321\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.5500 | −1.42390 | −0.711951 | − | 0.702229i | \(-0.752188\pi\) | ||||
−0.711951 | + | 0.702229i | \(0.752188\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −34.0293 | −1.19346 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 67.3029 | 2.35752 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.814670 | 0.0285017 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.51556 | −0.0529579 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.5251 | 0.716329 | 0.358165 | − | 0.933658i | \(-0.383403\pi\) | ||||
0.358165 | + | 0.933658i | \(0.383403\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −47.5837 | −1.65866 | −0.829332 | − | 0.558757i | \(-0.811279\pi\) | ||||
−0.829332 | + | 0.558757i | \(0.811279\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.15676 | −0.144720 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.2056 | 0.354882 | 0.177441 | − | 0.984131i | \(-0.443218\pi\) | ||||
0.177441 | + | 0.984131i | \(0.443218\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −36.1405 | −1.25521 | −0.627606 | − | 0.778531i | \(-0.715965\pi\) | ||||
−0.627606 | + | 0.778531i | \(0.715965\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −22.6953 | −0.787291 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.20996 | 0.111218 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −56.4127 | −1.95224 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.41137 | 0.256175 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.5312 | 0.363576 | 0.181788 | − | 0.983338i | \(-0.441812\pi\) | ||||
0.181788 | + | 0.983338i | \(0.441812\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 82.4235 | 2.84219 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −19.4663 | −0.670456 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.90030 | 0.0997732 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −34.1451 | −1.17186 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 21.3763 | 0.732769 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −33.2746 | −1.13930 | −0.569651 | − | 0.821887i | \(-0.692922\pi\) | ||||
−0.569651 | + | 0.821887i | \(0.692922\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.48591 | 0.0508172 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −32.9235 | −1.12465 | −0.562323 | − | 0.826917i | \(-0.690092\pi\) | ||||
−0.562323 | + | 0.826917i | \(0.690092\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.8803 | −1.15598 | −0.577991 | − | 0.816043i | \(-0.696163\pi\) | ||||
−0.577991 | + | 0.816043i | \(0.696163\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.66738 | −0.159064 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11.6252 | −0.395727 | −0.197864 | − | 0.980230i | \(-0.563400\pi\) | ||||
−0.197864 | + | 0.980230i | \(0.563400\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 38.6369 | 1.31370 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.15846 | 0.277076 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.11643 | 0.0378721 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.479975 | 0.0162633 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −25.7213 | −0.870535 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.60649 | 0.155728 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 50.0458 | 1.68993 | 0.844964 | − | 0.534823i | \(-0.179622\pi\) | ||||
0.844964 | + | 0.534823i | \(0.179622\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.47766 | −0.0498402 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.0109 | −0.943710 | −0.471855 | − | 0.881676i | \(-0.656415\pi\) | ||||
−0.471855 | + | 0.881676i | \(0.656415\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.6504 | 0.459373 | 0.229686 | − | 0.973265i | \(-0.426230\pi\) | ||||
0.229686 | + | 0.973265i | \(0.426230\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 22.4219 | 0.753704 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.9354 | −0.367173 | −0.183587 | − | 0.983004i | \(-0.558771\pi\) | ||||
−0.183587 | + | 0.983004i | \(0.558771\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.66573 | −0.223561 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.15641 | −0.0722423 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.09174 | 0.136925 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −45.7670 | −1.52982 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.74263 | 0.291908 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 14.2198 | 0.474258 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.68590 | 0.189425 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.93619 | −0.0977104 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.93292 | −0.197217 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.9696 | 0.862305 | 0.431152 | − | 0.902279i | \(-0.358107\pi\) | ||||
0.431152 | + | 0.902279i | \(0.358107\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.4972 | −0.447675 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.7039 | −0.752213 | −0.376106 | − | 0.926576i | \(-0.622737\pi\) | ||||
−0.376106 | + | 0.926576i | \(0.622737\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.65360 | 0.253297 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 23.1508 | 0.765343 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.77634 | −0.289820 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35.0952 | 1.15768 | 0.578841 | − | 0.815440i | \(-0.303505\pi\) | ||||
0.578841 | + | 0.815440i | \(0.303505\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19.3177 | 0.636541 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.64425 | 0.251613 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.1635 | 0.334175 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 19.4170 | 0.637738 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −49.6592 | −1.62927 | −0.814633 | − | 0.579977i | \(-0.803062\pi\) | ||||
−0.814633 | + | 0.579977i | \(0.803062\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.338048 | −0.0110791 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 28.5455 | 0.934537 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.30983 | 0.304464 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.6784 | −0.348847 | −0.174423 | − | 0.984671i | \(-0.555806\pi\) | ||||
−0.174423 | + | 0.984671i | \(0.555806\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 35.7326 | 1.16609 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 46.1623 | 1.50485 | 0.752424 | − | 0.658679i | \(-0.228885\pi\) | ||||
0.752424 | + | 0.658679i | \(0.228885\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −27.4886 | −0.895151 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −15.9564 | −0.519062 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.5959 | 0.506799 | 0.253400 | − | 0.967362i | \(-0.418451\pi\) | ||||
0.253400 | + | 0.967362i | \(0.418451\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.07758 | 0.164825 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.60283 | 0.311393 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13.3604 | −0.432786 | −0.216393 | − | 0.976306i | \(-0.569429\pi\) | ||||
−0.216393 | + | 0.976306i | \(0.569429\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 57.6967 | 1.86702 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.8609 | −0.415733 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.29231 | −0.300064 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.1853 | −0.941460 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 14.7779 | 0.476210 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.78298 | 0.250543 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.8066 | 0.765569 | 0.382785 | − | 0.923838i | \(-0.374965\pi\) | ||||
0.382785 | + | 0.923838i | \(0.374965\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.32208 | 0.0424715 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.72845 | −0.215926 | −0.107963 | − | 0.994155i | \(-0.534433\pi\) | ||||
−0.107963 | + | 0.994155i | \(0.534433\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.54313 | 0.177705 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.15676 | 0.133123 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 39.2128 | 1.25453 | 0.627265 | − | 0.778806i | \(-0.284174\pi\) | ||||
0.627265 | + | 0.778806i | \(0.284174\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.7332 | 0.502834 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.43590 | −0.237410 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.3795 | 0.586214 | 0.293107 | − | 0.956080i | \(-0.405311\pi\) | ||||
0.293107 | + | 0.956080i | \(0.405311\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 34.3966 | 1.09597 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −14.7473 | −0.469410 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −17.2927 | −0.549877 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.3735 | 0.869549 | 0.434775 | − | 0.900539i | \(-0.356828\pi\) | ||||
0.434775 | + | 0.900539i | \(0.356828\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −12.2787 | −0.389651 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −46.6630 | −1.47932 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 56.7976 | 1.79880 | 0.899399 | − | 0.437129i | \(-0.144005\pi\) | ||||
0.899399 | + | 0.437129i | \(0.144005\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 16.3895 | 0.518540 |
(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 | 8008.2.a.n.1.4 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.n.1.4 | ✓ | 9 | 1.1 | even | 1 | trivial |