Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4008,2,Mod(1,4008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4008 = 2^{3} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4008.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: | \(32.0040411301\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} - 31 x^{10} + 131 x^{9} + 309 x^{8} - 1453 x^{7} - 1072 x^{6} + 6350 x^{5} + \cdots + 3008 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(1.53322\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4008.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.53322 | 0.685678 | 0.342839 | − | 0.939394i | \(-0.388611\pi\) | ||||
0.342839 | + | 0.939394i | \(0.388611\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.915565 | −0.346051 | −0.173025 | − | 0.984917i | \(-0.555354\pi\) | ||||
−0.173025 | + | 0.984917i | \(0.555354\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.09767 | 0.933984 | 0.466992 | − | 0.884262i | \(-0.345338\pi\) | ||||
0.466992 | + | 0.884262i | \(0.345338\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.39795 | 0.387721 | 0.193861 | − | 0.981029i | \(-0.437899\pi\) | ||||
0.193861 | + | 0.981029i | \(0.437899\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.53322 | 0.395877 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.50046 | −0.363914 | −0.181957 | − | 0.983306i | \(-0.558243\pi\) | ||||
−0.181957 | + | 0.983306i | \(0.558243\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.21086 | −0.966038 | −0.483019 | − | 0.875610i | \(-0.660460\pi\) | ||||
−0.483019 | + | 0.875610i | \(0.660460\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.915565 | −0.199793 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.95660 | 1.03352 | 0.516761 | − | 0.856129i | \(-0.327137\pi\) | ||||
0.516761 | + | 0.856129i | \(0.327137\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.64923 | −0.529845 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.76793 | 0.328297 | 0.164148 | − | 0.986436i | \(-0.447512\pi\) | ||||
0.164148 | + | 0.986436i | \(0.447512\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.79993 | 0.682487 | 0.341244 | − | 0.939975i | \(-0.389152\pi\) | ||||
0.341244 | + | 0.939975i | \(0.389152\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.09767 | 0.539236 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.40377 | −0.237280 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.15442 | 0.682982 | 0.341491 | − | 0.939885i | \(-0.389068\pi\) | ||||
0.341491 | + | 0.939885i | \(0.389068\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.39795 | 0.223851 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.32859 | 1.30071 | 0.650354 | − | 0.759631i | \(-0.274621\pi\) | ||||
0.650354 | + | 0.759631i | \(0.274621\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.45697 | 1.28968 | 0.644838 | − | 0.764319i | \(-0.276925\pi\) | ||||
0.644838 | + | 0.764319i | \(0.276925\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.53322 | 0.228559 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.81577 | −0.994182 | −0.497091 | − | 0.867699i | \(-0.665598\pi\) | ||||
−0.497091 | + | 0.867699i | \(0.665598\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.16174 | −0.880249 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.50046 | −0.210106 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.43276 | 0.196804 | 0.0984021 | − | 0.995147i | \(-0.468627\pi\) | ||||
0.0984021 | + | 0.995147i | \(0.468627\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.74943 | 0.640413 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.21086 | −0.557742 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.9348 | 1.68397 | 0.841987 | − | 0.539499i | \(-0.181386\pi\) | ||||
0.841987 | + | 0.539499i | \(0.181386\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.76679 | −0.482288 | −0.241144 | − | 0.970489i | \(-0.577523\pi\) | ||||
−0.241144 | + | 0.970489i | \(0.577523\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.915565 | −0.115350 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.14337 | 0.265852 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.30009 | 0.891848 | 0.445924 | − | 0.895071i | \(-0.352875\pi\) | ||||
0.445924 | + | 0.895071i | \(0.352875\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.95660 | 0.596705 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.883952 | 0.104906 | 0.0524529 | − | 0.998623i | \(-0.483296\pi\) | ||||
0.0524529 | + | 0.998623i | \(0.483296\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.891880 | −0.104387 | −0.0521933 | − | 0.998637i | \(-0.516621\pi\) | ||||
−0.0521933 | + | 0.998637i | \(0.516621\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.64923 | −0.305906 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.83612 | −0.323206 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.12995 | −0.127129 | −0.0635645 | − | 0.997978i | \(-0.520247\pi\) | ||||
−0.0635645 | + | 0.997978i | \(0.520247\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.26402 | 0.468037 | 0.234018 | − | 0.972232i | \(-0.424812\pi\) | ||||
0.234018 | + | 0.972232i | \(0.424812\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.30053 | −0.249528 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.76793 | 0.189542 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 17.6794 | 1.87401 | 0.937007 | − | 0.349311i | \(-0.113584\pi\) | ||||
0.937007 | + | 0.349311i | \(0.113584\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.27991 | −0.134171 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.79993 | 0.394034 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.45620 | −0.662392 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.28751 | −0.435331 | −0.217666 | − | 0.976023i | \(-0.569844\pi\) | ||||
−0.217666 | + | 0.976023i | \(0.569844\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.09767 | 0.311328 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.5844 | −1.55071 | −0.775355 | − | 0.631526i | \(-0.782429\pi\) | ||||
−0.775355 | + | 0.631526i | \(0.782429\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.71458 | −0.563075 | −0.281537 | − | 0.959550i | \(-0.590844\pi\) | ||||
−0.281537 | + | 0.959550i | \(0.590844\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.40377 | −0.136993 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.17924 | −0.307349 | −0.153675 | − | 0.988122i | \(-0.549111\pi\) | ||||
−0.153675 | + | 0.988122i | \(0.549111\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.5475 | −1.20184 | −0.600919 | − | 0.799310i | \(-0.705198\pi\) | ||||
−0.600919 | + | 0.799310i | \(0.705198\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.15442 | 0.394320 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.50783 | 0.235916 | 0.117958 | − | 0.993019i | \(-0.462365\pi\) | ||||
0.117958 | + | 0.993019i | \(0.462365\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.59958 | 0.708664 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.39795 | 0.129240 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.37376 | 0.125933 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.40441 | −0.127674 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.32859 | 0.750964 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.7280 | −1.04898 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.3437 | 1.53900 | 0.769501 | − | 0.638646i | \(-0.220505\pi\) | ||||
0.769501 | + | 0.638646i | \(0.220505\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.45697 | 0.744595 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.3850 | −1.43156 | −0.715782 | − | 0.698324i | \(-0.753929\pi\) | ||||
−0.715782 | + | 0.698324i | \(0.753929\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.85532 | 0.334298 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.53322 | 0.131959 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18.5673 | −1.58631 | −0.793154 | − | 0.609021i | \(-0.791563\pi\) | ||||
−0.793154 | + | 0.609021i | \(0.791563\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.0137 | 1.27345 | 0.636724 | − | 0.771092i | \(-0.280289\pi\) | ||||
0.636724 | + | 0.771092i | \(0.280289\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.81577 | −0.573991 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.33039 | 0.362125 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.71064 | 0.225106 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.16174 | −0.508212 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 22.6712 | 1.85729 | 0.928647 | − | 0.370965i | \(-0.120973\pi\) | ||||
0.928647 | + | 0.370965i | \(0.120973\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.2737 | 1.56847 | 0.784237 | − | 0.620462i | \(-0.213055\pi\) | ||||
0.784237 | + | 0.620462i | \(0.213055\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.50046 | −0.121305 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.82614 | 0.467967 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.3895 | 1.22821 | 0.614107 | − | 0.789222i | \(-0.289516\pi\) | ||||
0.614107 | + | 0.789222i | \(0.289516\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.43276 | 0.113625 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.53809 | −0.357651 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.65971 | −0.208325 | −0.104162 | − | 0.994560i | \(-0.533216\pi\) | ||||
−0.104162 | + | 0.994560i | \(0.533216\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.74943 | 0.369742 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0457 | −0.849672 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.21086 | −0.322013 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.5038 | 1.25476 | 0.627382 | − | 0.778712i | \(-0.284126\pi\) | ||||
0.627382 | + | 0.778712i | \(0.284126\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.42554 | 0.183353 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.9348 | 0.972242 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.202161 | 0.0151102 | 0.00755512 | − | 0.999971i | \(-0.497595\pi\) | ||||
0.00755512 | + | 0.999971i | \(0.497595\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.91030 | −0.216321 | −0.108160 | − | 0.994133i | \(-0.534496\pi\) | ||||
−0.108160 | + | 0.994133i | \(0.534496\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.76679 | −0.278449 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.36965 | 0.468306 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.64792 | −0.339890 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.915565 | −0.0665975 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.2680 | −1.10475 | −0.552377 | − | 0.833594i | \(-0.686279\pi\) | ||||
−0.552377 | + | 0.833594i | \(0.686279\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.99644 | 0.647578 | 0.323789 | − | 0.946129i | \(-0.395043\pi\) | ||||
0.323789 | + | 0.946129i | \(0.395043\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.14337 | 0.153490 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.6292 | 0.828547 | 0.414273 | − | 0.910152i | \(-0.364036\pi\) | ||||
0.414273 | + | 0.910152i | \(0.364036\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.6305 | 0.895350 | 0.447675 | − | 0.894196i | \(-0.352252\pi\) | ||||
0.447675 | + | 0.894196i | \(0.352252\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.30009 | 0.514909 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.61866 | −0.113607 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.7696 | 0.891867 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.95660 | 0.344508 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −13.0439 | −0.902264 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.2769 | −0.776331 | −0.388166 | − | 0.921590i | \(-0.626891\pi\) | ||||
−0.388166 | + | 0.921590i | \(0.626891\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.883952 | 0.0605674 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.9664 | 0.884303 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.47908 | −0.236175 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.891880 | −0.0602677 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.09756 | −0.141097 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.4567 | −0.767196 | −0.383598 | − | 0.923500i | \(-0.625315\pi\) | ||||
−0.383598 | + | 0.923500i | \(0.625315\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.64923 | −0.176615 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.99214 | 0.464085 | 0.232042 | − | 0.972706i | \(-0.425459\pi\) | ||||
0.232042 | + | 0.972706i | \(0.425459\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.84467 | 0.320145 | 0.160073 | − | 0.987105i | \(-0.448827\pi\) | ||||
0.160073 | + | 0.987105i | \(0.448827\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.83612 | −0.186603 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −26.4019 | −1.72965 | −0.864824 | − | 0.502075i | \(-0.832570\pi\) | ||||
−0.864824 | + | 0.502075i | \(0.832570\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.4501 | −0.681689 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.12995 | −0.0733979 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.9728 | 1.55067 | 0.775335 | − | 0.631550i | \(-0.217581\pi\) | ||||
0.775335 | + | 0.631550i | \(0.217581\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.33066 | 0.407794 | 0.203897 | − | 0.978992i | \(-0.434639\pi\) | ||||
0.203897 | + | 0.978992i | \(0.434639\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.44733 | −0.603568 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.88657 | −0.374553 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.26402 | 0.270221 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.5048 | 0.663059 | 0.331529 | − | 0.943445i | \(-0.392435\pi\) | ||||
0.331529 | + | 0.943445i | \(0.392435\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.3539 | 0.965294 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.30053 | −0.144065 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −25.5749 | −1.59532 | −0.797661 | − | 0.603107i | \(-0.793929\pi\) | ||||
−0.797661 | + | 0.603107i | \(0.793929\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.80364 | −0.236346 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.76793 | 0.109432 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −20.5255 | −1.26566 | −0.632828 | − | 0.774292i | \(-0.718106\pi\) | ||||
−0.632828 | + | 0.774292i | \(0.718106\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.19674 | 0.134944 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 17.6794 | 1.08196 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.2640 | 0.686781 | 0.343390 | − | 0.939193i | \(-0.388425\pi\) | ||||
0.343390 | + | 0.939193i | \(0.388425\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.25659 | −0.319315 | −0.159658 | − | 0.987172i | \(-0.551039\pi\) | ||||
−0.159658 | + | 0.987172i | \(0.551039\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.27991 | −0.0774638 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.20644 | −0.494867 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.4026 | −0.625034 | −0.312517 | − | 0.949912i | \(-0.601172\pi\) | ||||
−0.312517 | + | 0.949912i | \(0.601172\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.79993 | 0.227496 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.6130 | −1.28932 | −0.644661 | − | 0.764469i | \(-0.723001\pi\) | ||||
−0.644661 | + | 0.764469i | \(0.723001\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.2913 | 1.44397 | 0.721983 | − | 0.691911i | \(-0.243231\pi\) | ||||
0.721983 | + | 0.691911i | \(0.243231\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.45620 | −0.382432 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.62537 | −0.450111 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.7486 | −0.867567 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.28751 | −0.251339 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.1490 | 0.885014 | 0.442507 | − | 0.896765i | \(-0.354089\pi\) | ||||
0.442507 | + | 0.896765i | \(0.354089\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.8320 | 1.15466 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.09767 | 0.179745 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.92907 | 0.400718 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.74290 | −0.446293 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −15.5844 | −0.895303 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.77533 | −0.330694 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.37234 | 0.477835 | 0.238917 | − | 0.971040i | \(-0.423208\pi\) | ||||
0.238917 | + | 0.971040i | \(0.423208\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.71458 | −0.325091 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.65962 | 0.264223 | 0.132111 | − | 0.991235i | \(-0.457824\pi\) | ||||
0.132111 | + | 0.991235i | \(0.457824\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.10404 | −0.458067 | −0.229034 | − | 0.973419i | \(-0.573557\pi\) | ||||
−0.229034 | + | 0.973419i | \(0.573557\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.40377 | −0.0790932 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.1018 | −0.679706 | −0.339853 | − | 0.940479i | \(-0.610377\pi\) | ||||
−0.339853 | + | 0.940479i | \(0.610377\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.47648 | 0.306624 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.17924 | −0.177448 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.31822 | 0.351555 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.70348 | −0.205432 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −12.5475 | −0.693881 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.24027 | 0.344037 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.5342 | −0.633979 | −0.316989 | − | 0.948429i | \(-0.602672\pi\) | ||||
−0.316989 | + | 0.948429i | \(0.602672\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.15442 | 0.227661 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.1927 | 0.611521 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.87706 | 0.265670 | 0.132835 | − | 0.991138i | \(-0.457592\pi\) | ||||
0.132835 | + | 0.991138i | \(0.457592\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.50783 | 0.136206 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.7709 | 0.637432 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.0504 | 0.650662 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.59958 | 0.409148 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.41332 | −0.290602 | −0.145301 | − | 0.989387i | \(-0.546415\pi\) | ||||
−0.145301 | + | 0.989387i | \(0.546415\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.3896 | 0.877313 | 0.438656 | − | 0.898655i | \(-0.355455\pi\) | ||||
0.438656 | + | 0.898655i | \(0.355455\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.39795 | 0.0746169 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −33.9228 | −1.80553 | −0.902765 | − | 0.430133i | \(-0.858467\pi\) | ||||
−0.902765 | + | 0.430133i | \(0.858467\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.35530 | 0.0719316 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.37376 | 0.0727073 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 30.9733 | 1.63471 | 0.817354 | − | 0.576135i | \(-0.195440\pi\) | ||||
0.817354 | + | 0.576135i | \(0.195440\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.26863 | −0.0667699 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.40441 | −0.0737126 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.36745 | −0.0715757 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.7551 | −1.03121 | −0.515603 | − | 0.856827i | \(-0.672432\pi\) | ||||
−0.515603 | + | 0.856827i | \(0.672432\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.32859 | 0.433569 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.31178 | −0.0681043 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.12807 | 0.472634 | 0.236317 | − | 0.971676i | \(-0.424060\pi\) | ||||
0.236317 | + | 0.971676i | \(0.424060\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.7280 | −0.605630 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.47148 | 0.127288 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.9800 | −0.718103 | −0.359052 | − | 0.933318i | \(-0.616900\pi\) | ||||
−0.359052 | + | 0.933318i | \(0.616900\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 17.3437 | 0.888543 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −34.7750 | −1.77692 | −0.888459 | − | 0.458956i | \(-0.848224\pi\) | ||||
−0.888459 | + | 0.458956i | \(0.848224\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.34841 | −0.221615 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.45697 | 0.429892 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.7127 | −0.847369 | −0.423684 | − | 0.905810i | \(-0.639263\pi\) | ||||
−0.423684 | + | 0.905810i | \(0.639263\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.43716 | −0.376113 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −16.3850 | −0.826513 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.73246 | −0.0871696 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.95221 | −0.198356 | −0.0991780 | − | 0.995070i | \(-0.531621\pi\) | ||||
−0.0991780 | + | 0.995070i | \(0.531621\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.85532 | 0.193007 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19.9460 | −0.996055 | −0.498028 | − | 0.867161i | \(-0.665942\pi\) | ||||
−0.498028 | + | 0.867161i | \(0.665942\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.31210 | 0.264615 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.53322 | 0.0761865 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.8690 | 0.637894 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.18390 | −0.206881 | −0.103440 | − | 0.994636i | \(-0.532985\pi\) | ||||
−0.103440 | + | 0.994636i | \(0.532985\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.5673 | −0.915856 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11.8427 | −0.582740 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.53769 | 0.320923 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 15.0137 | 0.735225 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −39.5510 | −1.93219 | −0.966097 | − | 0.258179i | \(-0.916877\pi\) | ||||
−0.966097 | + | 0.258179i | \(0.916877\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.4917 | −0.755019 | −0.377510 | − | 0.926006i | \(-0.623220\pi\) | ||||
−0.377510 | + | 0.926006i | \(0.623220\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.81577 | −0.331394 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.97505 | 0.192818 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.44874 | 0.166896 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.33039 | 0.209073 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.0476 | 0.772984 | 0.386492 | − | 0.922293i | \(-0.373687\pi\) | ||||
0.386492 | + | 0.922293i | \(0.373687\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.5403 | 1.03516 | 0.517580 | − | 0.855635i | \(-0.326833\pi\) | ||||
0.517580 | + | 0.855635i | \(0.326833\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.71064 | 0.129965 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −20.8716 | −0.998423 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.1392 | 0.961191 | 0.480595 | − | 0.876942i | \(-0.340421\pi\) | ||||
0.480595 | + | 0.876942i | \(0.340421\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.16174 | −0.293416 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.2013 | 0.817257 | 0.408629 | − | 0.912701i | \(-0.366007\pi\) | ||||
0.408629 | + | 0.912701i | \(0.366007\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 27.1065 | 1.28497 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 22.6712 | 1.07231 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28.7950 | −1.35892 | −0.679461 | − | 0.733712i | \(-0.737786\pi\) | ||||
−0.679461 | + | 0.733712i | \(0.737786\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 25.7993 | 1.21484 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 19.2737 | 0.905559 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.96239 | −0.0919983 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.8010 | 1.48759 | 0.743794 | − | 0.668409i | \(-0.233024\pi\) | ||||
0.743794 | + | 0.668409i | \(0.233024\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.50046 | −0.0700353 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.3828 | 1.08905 | 0.544524 | − | 0.838745i | \(-0.316710\pi\) | ||||
0.544524 | + | 0.838745i | \(0.316710\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 39.4475 | 1.83328 | 0.916640 | − | 0.399714i | \(-0.130891\pi\) | ||||
0.916640 | + | 0.399714i | \(0.130891\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.82614 | 0.270181 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −31.6227 | −1.46332 | −0.731661 | − | 0.681668i | \(-0.761255\pi\) | ||||
−0.731661 | + | 0.681668i | \(0.761255\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.68370 | −0.308625 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.3895 | 0.709110 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 26.1969 | 1.20454 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.1555 | 0.511851 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.43276 | 0.0656014 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13.4628 | −0.615129 | −0.307565 | − | 0.951527i | \(-0.599514\pi\) | ||||
−0.307565 | + | 0.951527i | \(0.599514\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.80766 | 0.264806 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.53809 | −0.206490 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.57372 | −0.298497 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.2506 | 1.55204 | 0.776022 | − | 0.630706i | \(-0.217235\pi\) | ||||
0.776022 | + | 0.630706i | \(0.217235\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.65971 | −0.120276 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.2041 | −0.731279 | −0.365639 | − | 0.930757i | \(-0.619150\pi\) | ||||
−0.365639 | + | 0.930757i | \(0.619150\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.65271 | −0.119472 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.74943 | 0.213471 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.809315 | −0.0363027 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.1460 | 0.857091 | 0.428545 | − | 0.903520i | \(-0.359026\pi\) | ||||
0.428545 | + | 0.903520i | \(0.359026\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.00000 | 0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.19733 | 0.365501 | 0.182750 | − | 0.983159i | \(-0.441500\pi\) | ||||
0.182750 | + | 0.983159i | \(0.441500\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23.8944 | −1.06329 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.0457 | −0.490559 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.4558 | 0.685065 | 0.342533 | − | 0.939506i | \(-0.388715\pi\) | ||||
0.342533 | + | 0.939506i | \(0.388715\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.816574 | 0.0361231 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.21086 | −0.185914 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.76173 | −0.386088 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −21.1130 | −0.928550 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.5038 | 0.724438 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.9773 | 1.00666 | 0.503328 | − | 0.864096i | \(-0.332109\pi\) | ||||
0.503328 | + | 0.864096i | \(0.332109\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.86529 | −0.0815636 | −0.0407818 | − | 0.999168i | \(-0.512985\pi\) | ||||
−0.0407818 | + | 0.999168i | \(0.512985\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.42554 | 0.105859 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.70163 | −0.248367 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.56789 | 0.0681692 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.9348 | 0.561324 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.6429 | 0.504312 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.87449 | −0.210743 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.202161 | 0.00872390 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −19.0871 | −0.822138 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −35.4871 | −1.52571 | −0.762854 | − | 0.646570i | \(-0.776203\pi\) | ||||
−0.762854 | + | 0.646570i | \(0.776203\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.91030 | −0.124893 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −19.2382 | −0.824074 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.16371 | 0.0497568 | 0.0248784 | − | 0.999690i | \(-0.492080\pi\) | ||||
0.0248784 | + | 0.999690i | \(0.492080\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.76679 | −0.160763 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.44452 | −0.317147 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.03454 | 0.0439931 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.36965 | 0.270377 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −27.6032 | −1.16958 | −0.584792 | − | 0.811183i | \(-0.698824\pi\) | ||||
−0.584792 | + | 0.811183i | \(0.698824\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.8224 | 0.500034 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.64792 | −0.196235 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 26.7132 | 1.12583 | 0.562913 | − | 0.826516i | \(-0.309681\pi\) | ||||
0.562913 | + | 0.826516i | \(0.309681\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.84506 | 0.161763 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.915565 | −0.0384501 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24.6239 | −1.03229 | −0.516143 | − | 0.856502i | \(-0.672633\pi\) | ||||
−0.516143 | + | 0.856502i | \(0.672633\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.6623 | −0.697294 | −0.348647 | − | 0.937254i | \(-0.613359\pi\) | ||||
−0.348647 | + | 0.937254i | \(0.613359\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.2680 | −0.637830 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.1312 | −0.547607 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.9442 | −0.455612 | −0.227806 | − | 0.973707i | \(-0.573155\pi\) | ||||
−0.227806 | + | 0.973707i | \(0.573155\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.99644 | 0.373879 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.90398 | −0.161965 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.43821 | 0.183812 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.14337 | 0.0886173 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.12881 | 0.0465908 | 0.0232954 | − | 0.999729i | \(-0.492584\pi\) | ||||
0.0232954 | + | 0.999729i | \(0.492584\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.0010 | −0.659309 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.6292 | 0.478362 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21.3857 | 0.878205 | 0.439102 | − | 0.898437i | \(-0.355297\pi\) | ||||
0.439102 | + | 0.898437i | \(0.355297\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.10629 | 0.0863494 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.6305 | 0.516930 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.0654 | −0.533837 | −0.266919 | − | 0.963719i | \(-0.586006\pi\) | ||||
−0.266919 | + | 0.963719i | \(0.586006\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.93394 | −0.323632 | −0.161816 | − | 0.986821i | \(-0.551735\pi\) | ||||
−0.161816 | + | 0.986821i | \(0.551735\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.30009 | 0.297283 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.15328 | −0.0875433 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 35.6021 | 1.44504 | 0.722522 | − | 0.691348i | \(-0.242983\pi\) | ||||
0.722522 | + | 0.691348i | \(0.242983\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.61866 | −0.0655913 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.52809 | −0.385465 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.26461 | 0.374194 | 0.187097 | − | 0.982341i | \(-0.440092\pi\) | ||||
0.187097 | + | 0.982341i | \(0.440092\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.7696 | 0.514920 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.9004 | −0.760902 | −0.380451 | − | 0.924801i | \(-0.624231\pi\) | ||||
−0.380451 | + | 0.924801i | \(0.624231\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.98374 | −0.0797333 | −0.0398666 | − | 0.999205i | \(-0.512693\pi\) | ||||
−0.0398666 | + | 0.999205i | \(0.512693\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.95660 | 0.198902 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −16.1866 | −0.648504 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.73548 | −0.189419 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −13.0439 | −0.520923 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.23352 | −0.248547 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.1079 | −1.11896 | −0.559480 | − | 0.828844i | \(-0.688999\pi\) | ||||
−0.559480 | + | 0.828844i | \(0.688999\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11.2769 | −0.448215 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 26.5917 | 1.05526 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.61379 | −0.341291 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.883952 | 0.0349686 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.6872 | −0.540611 | −0.270306 | − | 0.962775i | \(-0.587125\pi\) | ||||
−0.270306 | + | 0.962775i | \(0.587125\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.8120 | 0.465820 | 0.232910 | − | 0.972498i | \(-0.425175\pi\) | ||||
0.232910 | + | 0.972498i | \(0.425175\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12.9664 | 0.510553 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.9647 | 0.509696 | 0.254848 | − | 0.966981i | \(-0.417975\pi\) | ||||
0.254848 | + | 0.966981i | \(0.417975\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 40.0679 | 1.57280 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.47908 | −0.136356 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −47.8071 | −1.87084 | −0.935419 | − | 0.353541i | \(-0.884978\pi\) | ||||
−0.935419 | + | 0.353541i | \(0.884978\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −25.1219 | −0.981592 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.891880 | −0.0347956 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.2125 | 0.631550 | 0.315775 | − | 0.948834i | \(-0.397735\pi\) | ||||
0.315775 | + | 0.948834i | \(0.397735\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −41.9378 | −1.63119 | −0.815595 | − | 0.578623i | \(-0.803590\pi\) | ||||
−0.815595 | + | 0.578623i | \(0.803590\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.09756 | −0.0814625 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.91106 | 0.229221 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.76294 | 0.339302 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.4567 | −0.442941 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.6683 | −0.450449 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.9537 | −0.692064 | −0.346032 | − | 0.938223i | \(-0.612471\pi\) | ||||
−0.346032 | + | 0.938223i | \(0.612471\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.64923 | −0.101969 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.80016 | −0.376651 | −0.188325 | − | 0.982107i | \(-0.560306\pi\) | ||||
−0.188325 | + | 0.982107i | \(0.560306\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.92550 | 0.150647 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.99214 | 0.267939 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −42.7950 | −1.63751 | −0.818753 | − | 0.574145i | \(-0.805334\pi\) | ||||
−0.818753 | + | 0.574145i | \(0.805334\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −28.4678 | −1.08770 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.84467 | 0.184836 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.00292 | 0.0763051 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 47.2115 | 1.79601 | 0.898005 | − | 0.439985i | \(-0.145016\pi\) | ||||
0.898005 | + | 0.439985i | \(0.145016\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.83612 | −0.107735 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 23.0194 | 0.873176 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.4967 | −0.473346 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −26.4019 | −0.998613 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.0922506 | −0.00348426 | −0.00174213 | − | 0.999998i | \(-0.500555\pi\) | ||||
−0.00174213 | + | 0.999998i | \(0.500555\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −17.4937 | −0.659787 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −10.4501 | −0.393573 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.2686 | 0.536624 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −33.0225 | −1.24019 | −0.620093 | − | 0.784528i | \(-0.712905\pi\) | ||||
−0.620093 | + | 0.784528i | \(0.712905\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.12995 | −0.0423763 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18.8347 | 0.705366 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.63945 | 0.248301 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 23.9728 | 0.895279 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.96188 | −0.110459 | −0.0552297 | − | 0.998474i | \(-0.517589\pi\) | ||||
−0.0552297 | + | 0.998474i | \(0.517589\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.23207 | 0.194852 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.33066 | 0.235440 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.68365 | −0.173946 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.9351 | 0.553914 | 0.276957 | − | 0.960882i | \(-0.410674\pi\) | ||||
0.276957 | + | 0.960882i | \(0.410674\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.6893 | −0.469331 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.0289 | −1.03527 | −0.517635 | − | 0.855602i | \(-0.673187\pi\) | ||||
−0.517635 | + | 0.855602i | \(0.673187\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9.44733 | −0.348470 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 22.6133 | 0.832971 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −34.2689 | −1.26060 | −0.630300 | − | 0.776351i | \(-0.717068\pi\) | ||||
−0.630300 | + | 0.776351i | \(0.717068\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.88657 | −0.216248 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −40.7965 | −1.49668 | −0.748340 | − | 0.663316i | \(-0.769149\pi\) | ||||
−0.748340 | + | 0.663316i | \(0.769149\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 34.7600 | 1.27351 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.26402 | 0.156012 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.91080 | 0.106358 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 41.0708 | 1.49869 | 0.749347 | − | 0.662177i | \(-0.230367\pi\) | ||||
0.749347 | + | 0.662177i | \(0.230367\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.5048 | 0.382817 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 29.5509 | 1.07547 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33.5015 | −1.21763 | −0.608817 | − | 0.793311i | \(-0.708356\pi\) | ||||
−0.608817 | + | 0.793311i | \(0.708356\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 15.3539 | 0.557313 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.9152 | −0.576926 | −0.288463 | − | 0.957491i | \(-0.593144\pi\) | ||||
−0.288463 | + | 0.957491i | \(0.593144\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.4881 | 0.415897 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.30053 | −0.0831760 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18.0822 | 0.652912 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.5047 | −0.883661 | −0.441830 | − | 0.897099i | \(-0.645671\pi\) | ||||
−0.441830 | + | 0.897099i | \(0.645671\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −25.5749 | −0.921059 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 28.0247 | 1.00798 | 0.503990 | − | 0.863710i | \(-0.331865\pi\) | ||||
0.503990 | + | 0.863710i | \(0.331865\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.0669 | −0.361612 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.80364 | −0.136455 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −35.0706 | −1.25653 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.73819 | 0.0979803 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.76793 | 0.0631808 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 23.5955 | 0.842160 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.5173 | −0.481840 | −0.240920 | − | 0.970545i | \(-0.577449\pi\) | ||||
−0.240920 | + | 0.970545i | \(0.577449\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −20.5255 | −0.730727 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.29608 | −0.0816391 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.26577 | −0.186993 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.19674 | 0.0779102 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.3513 | 0.437504 | 0.218752 | − | 0.975780i | \(-0.429801\pi\) | ||||
0.218752 | + | 0.975780i | \(0.429801\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.2268 | 0.361797 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 17.6794 | 0.624671 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.76275 | −0.0974955 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.95790 | −0.245234 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.2640 | 0.396513 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −49.9778 | −1.75713 | −0.878563 | − | 0.477626i | \(-0.841497\pi\) | ||||
−0.878563 | + | 0.477626i | \(0.841497\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −41.8896 | −1.47094 | −0.735472 | − | 0.677556i | \(-0.763039\pi\) | ||||
−0.735472 | + | 0.677556i | \(0.763039\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.25659 | −0.184357 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.07793 | −0.142844 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −35.6111 | −1.24588 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.27991 | −0.0447237 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20.6369 | −0.720232 | −0.360116 | − | 0.932908i | \(-0.617263\pi\) | ||||
−0.360116 | + | 0.932908i | \(0.617263\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 33.0136 | 1.15078 | 0.575390 | − | 0.817879i | \(-0.304850\pi\) | ||||
0.575390 | + | 0.817879i | \(0.304850\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −8.20644 | −0.285711 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.76225 | −0.165600 | −0.0827998 | − | 0.996566i | \(-0.526386\pi\) | ||||
−0.0827998 | + | 0.996566i | \(0.526386\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.3978 | 1.29888 | 0.649439 | − | 0.760414i | \(-0.275004\pi\) | ||||
0.649439 | + | 0.760414i | \(0.275004\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.4026 | −0.360863 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.24542 | 0.320335 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.53322 | 0.0530594 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.79993 | 0.131345 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −29.8684 | −1.03117 | −0.515585 | − | 0.856838i | \(-0.672425\pi\) | ||||
−0.515585 | + | 0.856838i | \(0.672425\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.8744 | −0.892221 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −21.6130 | −0.744390 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −16.9356 | −0.582602 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.28583 | 0.0441817 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 24.2913 | 0.833674 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20.5918 | 0.705877 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.5896 | 0.739214 | 0.369607 | − | 0.929188i | \(-0.379492\pi\) | ||||
0.369607 | + | 0.929188i | \(0.379492\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.45620 | −0.220797 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −30.7368 | −1.04995 | −0.524975 | − | 0.851118i | \(-0.675925\pi\) | ||||
−0.524975 | + | 0.851118i | \(0.675925\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.952468 | −0.0324978 | −0.0162489 | − | 0.999868i | \(-0.505172\pi\) | ||||
−0.0162489 | + | 0.999868i | \(0.505172\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.62537 | −0.259872 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −14.7115 | −0.500786 | −0.250393 | − | 0.968144i | \(-0.580560\pi\) | ||||
−0.250393 | + | 0.968144i | \(0.580560\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 25.3041 | 0.860365 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14.7486 | −0.500890 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.50021 | −0.118736 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.2051 | 0.345788 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.28751 | −0.145110 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.7377 | 0.363001 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.3949 | −0.654919 | −0.327459 | − | 0.944865i | \(-0.606192\pi\) | ||||
−0.327459 | + | 0.944865i | \(0.606192\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 15.1490 | 0.510963 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −40.8536 | −1.37639 | −0.688197 | − | 0.725524i | \(-0.741597\pi\) | ||||
−0.688197 | + | 0.725524i | \(0.741597\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −51.0635 | −1.71843 | −0.859213 | − | 0.511619i | \(-0.829046\pi\) | ||||
−0.859213 | + | 0.511619i | \(0.829046\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 19.8320 | 0.666646 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.844140 | −0.0283434 | −0.0141717 | − | 0.999900i | \(-0.504511\pi\) | ||||
−0.0141717 | + | 0.999900i | \(0.504511\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −15.8792 | −0.532573 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.09767 | 0.103776 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 28.7003 | 0.960418 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.309958 | 0.0103608 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.92907 | 0.231355 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.71802 | 0.224058 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.14979 | −0.0716198 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.74290 | −0.257668 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.46214 | −0.148326 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.2678 | 0.473754 | 0.236877 | − | 0.971540i | \(-0.423876\pi\) | ||||
0.236877 | + | 0.971540i | \(0.423876\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −15.5844 | −0.516903 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.15685 | 0.0714598 | 0.0357299 | − | 0.999361i | \(-0.488624\pi\) | ||||
0.0357299 | + | 0.999361i | \(0.488624\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.2085 | 0.437139 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.77533 | −0.190926 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15.0015 | 0.495394 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −50.7401 | −1.67376 | −0.836881 | − | 0.547386i | \(-0.815623\pi\) | ||||
−0.836881 | + | 0.547386i | \(0.815623\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.37234 | 0.275878 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.23572 | 0.0406742 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.0060 | −0.361874 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.71458 | −0.187692 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −20.0006 | −0.656199 | −0.328100 | − | 0.944643i | \(-0.606408\pi\) | ||||
−0.328100 | + | 0.944643i | \(0.606408\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 25.9463 | 0.850354 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.65962 | 0.152549 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.12631 | −0.233055 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.79635 | 0.287364 | 0.143682 | − | 0.989624i | \(-0.454106\pi\) | ||||
0.143682 | + | 0.989624i | \(0.454106\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.10404 | −0.264465 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.3968 | −0.501921 | −0.250961 | − | 0.967997i | \(-0.580746\pi\) | ||||
−0.250961 | + | 0.967997i | \(0.580746\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 41.2815 | 1.34431 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.40377 | −0.0456645 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −33.6342 | −1.09297 | −0.546483 | − | 0.837470i | \(-0.684034\pi\) | ||||
−0.546483 | + | 0.837470i | \(0.684034\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.24680 | −0.0404729 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.1018 | −0.392429 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.0383 | 0.616712 | 0.308356 | − | 0.951271i | \(-0.400221\pi\) | ||||
0.308356 | + | 0.951271i | \(0.400221\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −23.4093 | −0.757507 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.47648 | 0.177029 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16.9995 | 0.548943 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.5605 | −0.534211 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.17924 | −0.102450 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 13.7935 | 0.444030 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37.3295 | −1.20044 | −0.600218 | − | 0.799836i | \(-0.704920\pi\) | ||||
−0.600218 | + | 0.799836i | \(0.704920\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.31822 | 0.202970 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −52.8286 | −1.69535 | −0.847675 | − | 0.530516i | \(-0.821998\pi\) | ||||
−0.847675 | + | 0.530516i | \(0.821998\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13.7460 | −0.440678 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.70348 | −0.118606 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 31.0861 | 0.994532 | 0.497266 | − | 0.867598i | \(-0.334337\pi\) | ||||
0.497266 | + | 0.867598i | \(0.334337\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 54.7651 | 1.75030 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.5475 | −0.400612 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.74694 | −0.0876136 | −0.0438068 | − | 0.999040i | \(-0.513949\pi\) | ||||
−0.0438068 | + | 0.999040i | \(0.513949\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.8302 | 0.568117 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.24027 | 0.198630 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 41.9178 | 1.33291 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.1120 | 1.14713 | 0.573567 | − | 0.819158i | \(-0.305559\pi\) | ||||
0.573567 | + | 0.819158i | \(0.305559\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −11.5342 | −0.366028 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.3653 | 0.613922 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −52.4769 | −1.66196 | −0.830980 | − | 0.556302i | \(-0.812220\pi\) | ||||
−0.830980 | + | 0.556302i | \(0.812220\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.15442 | 0.131440 |
(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 | 4008.2.a.l.1.7 | ✓ | 12 | |
4.3 | odd | 2 | 8016.2.a.bf.1.7 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.l.1.7 | ✓ | 12 | 1.1 | even | 1 | trivial | |
8016.2.a.bf.1.7 | 12 | 4.3 | odd | 2 |