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: | \(1\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 3 x^{13} - 27 x^{12} + 78 x^{11} + 273 x^{10} - 750 x^{9} - 1306 x^{8} + 3378 x^{7} + \cdots - 128 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(-2.46105\) 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 | ||||||||
\(3\) | 2.46105 | 1.42089 | 0.710443 | − | 0.703754i | \(-0.248494\pi\) | ||||
0.710443 | + | 0.703754i | \(0.248494\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.12857 | −0.504713 | −0.252357 | − | 0.967634i | \(-0.581206\pi\) | ||||
−0.252357 | + | 0.967634i | \(0.581206\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.05676 | 1.01892 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.77747 | −0.717140 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.31528 | 1.53168 | 0.765840 | − | 0.643032i | \(-0.222324\pi\) | ||||
0.765840 | + | 0.643032i | \(0.222324\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.83477 | −0.420926 | −0.210463 | − | 0.977602i | \(-0.567497\pi\) | ||||
−0.210463 | + | 0.977602i | \(0.567497\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.46105 | 0.537045 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.30939 | −1.73263 | −0.866314 | − | 0.499500i | \(-0.833517\pi\) | ||||
−0.866314 | + | 0.499500i | \(0.833517\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.72632 | −0.745265 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.139682 | 0.0268819 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.64782 | −1.42016 | −0.710082 | − | 0.704119i | \(-0.751342\pi\) | ||||
−0.710082 | + | 0.704119i | \(0.751342\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.82327 | −1.04589 | −0.522945 | − | 0.852367i | \(-0.675167\pi\) | ||||
−0.522945 | + | 0.852367i | \(0.675167\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.46105 | −0.428413 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.12857 | −0.190764 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.38927 | 0.721592 | 0.360796 | − | 0.932645i | \(-0.382505\pi\) | ||||
0.360796 | + | 0.932645i | \(0.382505\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.46105 | −0.394083 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.61087 | −0.251576 | −0.125788 | − | 0.992057i | \(-0.540146\pi\) | ||||
−0.125788 | + | 0.992057i | \(0.540146\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.78285 | −1.49187 | −0.745936 | − | 0.666018i | \(-0.767997\pi\) | ||||
−0.745936 | + | 0.666018i | \(0.767997\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.44977 | −0.514262 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.50039 | 0.510584 | 0.255292 | − | 0.966864i | \(-0.417828\pi\) | ||||
0.255292 | + | 0.966864i | \(0.417828\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 15.5422 | 2.17634 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.6895 | 1.46832 | 0.734160 | − | 0.678976i | \(-0.237576\pi\) | ||||
0.734160 | + | 0.678976i | \(0.237576\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.12857 | 0.152177 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.51547 | −0.598088 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.5145 | −1.49906 | −0.749532 | − | 0.661968i | \(-0.769722\pi\) | ||||
−0.749532 | + | 0.661968i | \(0.769722\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.27639 | 0.931646 | 0.465823 | − | 0.884878i | \(-0.345758\pi\) | ||||
0.465823 | + | 0.884878i | \(0.345758\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.05676 | 0.385115 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.12857 | 0.139982 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.5388 | −1.28752 | −0.643762 | − | 0.765226i | \(-0.722627\pi\) | ||||
−0.643762 | + | 0.765226i | \(0.722627\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −20.4498 | −2.46187 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.2627 | 1.57399 | 0.786997 | − | 0.616957i | \(-0.211635\pi\) | ||||
0.786997 | + | 0.616957i | \(0.211635\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.6993 | −1.72042 | −0.860209 | − | 0.509942i | \(-0.829667\pi\) | ||||
−0.860209 | + | 0.509942i | \(0.829667\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −9.17066 | −1.05894 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.87583 | −0.998609 | −0.499304 | − | 0.866427i | \(-0.666411\pi\) | ||||
−0.499304 | + | 0.866427i | \(0.666411\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.82651 | −0.980723 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.7237 | −1.61614 | −0.808068 | − | 0.589089i | \(-0.799487\pi\) | ||||
−0.808068 | + | 0.589089i | \(0.799487\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.12725 | −0.773059 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −18.8216 | −2.01789 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.76039 | 0.610600 | 0.305300 | − | 0.952256i | \(-0.401243\pi\) | ||||
0.305300 | + | 0.952256i | \(0.401243\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −14.3313 | −1.48609 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.07068 | 0.212447 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.88319 | −0.800416 | −0.400208 | − | 0.916424i | \(-0.631062\pi\) | ||||
−0.400208 | + | 0.916424i | \(0.631062\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.05676 | −0.307216 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.6940 | 1.16359 | 0.581797 | − | 0.813334i | \(-0.302350\pi\) | ||||
0.581797 | + | 0.813334i | \(0.302350\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.2920 | 1.40824 | 0.704118 | − | 0.710083i | \(-0.251343\pi\) | ||||
0.704118 | + | 0.710083i | \(0.251343\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.77747 | −0.271053 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −17.6760 | −1.70881 | −0.854404 | − | 0.519610i | \(-0.826077\pi\) | ||||
−0.854404 | + | 0.519610i | \(0.826077\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.7778 | 1.31967 | 0.659837 | − | 0.751408i | \(-0.270625\pi\) | ||||
0.659837 | + | 0.751408i | \(0.270625\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.8022 | 1.02530 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.96334 | 0.466911 | 0.233456 | − | 0.972367i | \(-0.424997\pi\) | ||||
0.233456 | + | 0.972367i | \(0.424997\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.37775 | 0.874480 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.05676 | −0.282597 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.31528 | 0.578920 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.96444 | −0.357461 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.84829 | 0.880858 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.9712 | −1.32848 | −0.664240 | − | 0.747519i | \(-0.731245\pi\) | ||||
−0.664240 | + | 0.747519i | \(0.731245\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −24.0761 | −2.11978 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.3791 | 1.34368 | 0.671838 | − | 0.740698i | \(-0.265505\pi\) | ||||
0.671838 | + | 0.740698i | \(0.265505\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.83477 | −0.159095 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.157642 | −0.0135676 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.0238 | −1.02726 | −0.513632 | − | 0.858010i | \(-0.671700\pi\) | ||||
−0.513632 | + | 0.858010i | \(0.671700\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.9661 | 1.77832 | 0.889162 | − | 0.457593i | \(-0.151288\pi\) | ||||
0.889162 | + | 0.457593i | \(0.151288\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.61462 | 0.725482 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.63112 | 0.716775 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.46105 | 0.202984 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.6526 | −1.20039 | −0.600195 | − | 0.799854i | \(-0.704910\pi\) | ||||
−0.600195 | + | 0.799854i | \(0.704910\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.0826 | 1.06465 | 0.532323 | − | 0.846542i | \(-0.321319\pi\) | ||||
0.532323 | + | 0.846542i | \(0.321319\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 19.3043 | 1.56066 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.57198 | 0.527874 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.44812 | −0.115572 | −0.0577862 | − | 0.998329i | \(-0.518404\pi\) | ||||
−0.0577862 | + | 0.998329i | \(0.518404\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 26.3075 | 2.08632 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.30939 | −0.654872 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.97261 | 0.546137 | 0.273069 | − | 0.961995i | \(-0.411961\pi\) | ||||
0.273069 | + | 0.961995i | \(0.411961\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.77747 | 0.216226 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.02380 | 0.388754 | 0.194377 | − | 0.980927i | \(-0.437732\pi\) | ||||
0.194377 | + | 0.980927i | \(0.437732\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.60846 | −0.428890 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.1426 | −0.923184 | −0.461592 | − | 0.887092i | \(-0.652722\pi\) | ||||
−0.461592 | + | 0.887092i | \(0.652722\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.72632 | −0.281684 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −28.3378 | −2.13000 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.10770 | −0.456511 | −0.228255 | − | 0.973601i | \(-0.573302\pi\) | ||||
−0.228255 | + | 0.973601i | \(0.573302\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.69721 | 0.720788 | 0.360394 | − | 0.932800i | \(-0.382642\pi\) | ||||
0.360394 | + | 0.932800i | \(0.382642\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 17.9075 | 1.32376 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.95361 | −0.364197 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.31528 | −0.461819 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.139682 | 0.0101604 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.52272 | −0.689040 | −0.344520 | − | 0.938779i | \(-0.611958\pi\) | ||||
−0.344520 | + | 0.938779i | \(0.611958\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.1215 | −0.728564 | −0.364282 | − | 0.931289i | \(-0.618686\pi\) | ||||
−0.364282 | + | 0.931289i | \(0.618686\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.77747 | 0.198899 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.40852 | −0.527835 | −0.263917 | − | 0.964545i | \(-0.585015\pi\) | ||||
−0.263917 | + | 0.964545i | \(0.585015\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.83670 | −0.271977 | −0.135988 | − | 0.990710i | \(-0.543421\pi\) | ||||
−0.135988 | + | 0.990710i | \(0.543421\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −25.9366 | −1.82943 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.64782 | −0.536771 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.81799 | 0.126974 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −25.3998 | −1.76541 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.83477 | 0.126914 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.48435 | −0.377558 | −0.188779 | − | 0.982020i | \(-0.560453\pi\) | ||||
−0.188779 | + | 0.982020i | \(0.560453\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 32.6402 | 2.23647 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.0407 | 0.752967 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.82327 | −0.395309 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −36.1756 | −2.44452 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.31528 | −0.424811 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.6506 | 0.713219 | 0.356610 | − | 0.934254i | \(-0.383933\pi\) | ||||
0.356610 | + | 0.934254i | \(0.383933\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.3905 | −0.759364 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −18.0320 | −1.19682 | −0.598412 | − | 0.801189i | \(-0.704201\pi\) | ||||
−0.598412 | + | 0.801189i | \(0.704201\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.70503 | 0.376999 | 0.188499 | − | 0.982073i | \(-0.439638\pi\) | ||||
0.188499 | + | 0.982073i | \(0.439638\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.46105 | −0.161925 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.49616 | 0.163529 | 0.0817645 | − | 0.996652i | \(-0.473944\pi\) | ||||
0.0817645 | + | 0.996652i | \(0.473944\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.95044 | −0.257698 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −21.8438 | −1.41891 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.30917 | −0.472791 | −0.236395 | − | 0.971657i | \(-0.575966\pi\) | ||||
−0.236395 | + | 0.971657i | \(0.575966\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.84554 | −0.183297 | −0.0916486 | − | 0.995791i | \(-0.529214\pi\) | ||||
−0.0916486 | + | 0.995791i | \(0.529214\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −22.1415 | −1.42038 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.12857 | −0.0721019 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.83477 | 0.116744 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −36.2357 | −2.29635 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.21343 | −0.265949 | −0.132975 | − | 0.991119i | \(-0.542453\pi\) | ||||
−0.132975 | + | 0.991119i | \(0.542453\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.30939 | 0.522407 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −17.5405 | −1.09843 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.22890 | 0.450926 | 0.225463 | − | 0.974252i | \(-0.427610\pi\) | ||||
0.225463 | + | 0.974252i | \(0.427610\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.38927 | 0.272736 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −23.3775 | −1.44703 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 31.2574 | 1.92742 | 0.963708 | − | 0.266957i | \(-0.0860183\pi\) | ||||
0.963708 | + | 0.266957i | \(0.0860183\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.0639 | −0.741080 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.1766 | 0.867593 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.79410 | −0.414244 | −0.207122 | − | 0.978315i | \(-0.566410\pi\) | ||||
−0.207122 | + | 0.978315i | \(0.566410\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.25998 | 0.198029 | 0.0990147 | − | 0.995086i | \(-0.468431\pi\) | ||||
0.0990147 | + | 0.995086i | \(0.468431\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.46105 | −0.148949 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.72632 | 0.224706 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.94766 | −0.177108 | −0.0885539 | − | 0.996071i | \(-0.528225\pi\) | ||||
−0.0885539 | + | 0.996071i | \(0.528225\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −17.8003 | −1.06568 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.4355 | 0.622528 | 0.311264 | − | 0.950323i | \(-0.399248\pi\) | ||||
0.311264 | + | 0.950323i | \(0.399248\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.3817 | 1.27101 | 0.635505 | − | 0.772097i | \(-0.280792\pi\) | ||||
0.635505 | + | 0.772097i | \(0.280792\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.09603 | 0.301863 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.61087 | −0.0950868 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 22.8827 | 1.34604 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −19.4009 | −1.13730 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.12807 | 0.0659025 | 0.0329512 | − | 0.999457i | \(-0.489509\pi\) | ||||
0.0329512 | + | 0.999457i | \(0.489509\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.9950 | 0.756597 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.139682 | −0.00810520 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.30939 | 0.480545 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.78285 | −0.563874 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 28.7794 | 1.65333 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.21193 | −0.470214 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.8790 | 1.02041 | 0.510206 | − | 0.860052i | \(-0.329569\pi\) | ||||
0.510206 | + | 0.860052i | \(0.329569\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 35.1734 | 2.00094 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.2644 | −0.865563 | −0.432782 | − | 0.901499i | \(-0.642468\pi\) | ||||
−0.432782 | + | 0.901499i | \(0.642468\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.7555 | 0.664459 | 0.332230 | − | 0.943199i | \(-0.392199\pi\) | ||||
0.332230 | + | 0.943199i | \(0.392199\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.44977 | −0.194373 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −33.0135 | −1.85422 | −0.927110 | − | 0.374789i | \(-0.877715\pi\) | ||||
−0.927110 | + | 0.374789i | \(0.877715\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.64782 | 0.428195 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −43.5016 | −2.42802 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −11.5871 | −0.644724 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.72632 | 0.206699 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 33.9079 | 1.87511 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.50039 | 0.192982 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.1492 | −1.21743 | −0.608714 | − | 0.793390i | \(-0.708314\pi\) | ||||
−0.608714 | + | 0.793390i | \(0.708314\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 13.4169 | 0.735244 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.8938 | 0.649830 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.1041 | 1.36751 | 0.683755 | − | 0.729712i | \(-0.260346\pi\) | ||||
0.683755 | + | 0.729712i | \(0.260346\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.2150 | 0.663428 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.82327 | 0.315348 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 23.0791 | 1.24254 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −24.0730 | −1.29230 | −0.646152 | − | 0.763209i | \(-0.723623\pi\) | ||||
−0.646152 | + | 0.763209i | \(0.723623\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.3655 | −1.03661 | −0.518307 | − | 0.855195i | \(-0.673437\pi\) | ||||
−0.518307 | + | 0.855195i | \(0.673437\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.139682 | −0.00745570 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.02927 | −0.267681 | −0.133840 | − | 0.991003i | \(-0.542731\pi\) | ||||
−0.133840 | + | 0.991003i | \(0.542731\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.9679 | −0.794415 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 15.5422 | 0.822580 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.30526 | −0.332779 | −0.166389 | − | 0.986060i | \(-0.553211\pi\) | ||||
−0.166389 | + | 0.986060i | \(0.553211\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.6336 | −0.822821 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.46105 | 0.129172 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.5892 | 0.868317 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.60896 | −0.136187 | −0.0680933 | − | 0.997679i | \(-0.521692\pi\) | ||||
−0.0680933 | + | 0.997679i | \(0.521692\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.92405 | −0.256336 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.6895 | 0.554973 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.2717 | 0.531848 | 0.265924 | − | 0.963994i | \(-0.414323\pi\) | ||||
0.265924 | + | 0.963994i | \(0.414323\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 24.2371 | 1.25160 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.64782 | 0.393883 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.4041 | −1.30492 | −0.652460 | − | 0.757823i | \(-0.726263\pi\) | ||||
−0.652460 | + | 0.757823i | \(0.726263\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −36.8449 | −1.88762 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.2432 | −0.932183 | −0.466092 | − | 0.884736i | \(-0.654338\pi\) | ||||
−0.466092 | + | 0.884736i | \(0.654338\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.12857 | 0.0575174 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −29.9038 | −1.52010 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −34.2961 | −1.73888 | −0.869441 | − | 0.494038i | \(-0.835520\pi\) | ||||
−0.869441 | + | 0.494038i | \(0.835520\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −52.4761 | −2.65383 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 37.8487 | 1.90921 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.0170 | 0.504011 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.69756 | −0.235764 | −0.117882 | − | 0.993028i | \(-0.537610\pi\) | ||||
−0.117882 | + | 0.993028i | \(0.537610\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.51547 | −0.226056 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.7387 | −0.835889 | −0.417944 | − | 0.908473i | \(-0.637249\pi\) | ||||
−0.417944 | + | 0.908473i | \(0.637249\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.82327 | 0.290078 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.96135 | 0.494984 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.38927 | −0.217568 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −34.0983 | −1.68605 | −0.843027 | − | 0.537871i | \(-0.819229\pi\) | ||||
−0.843027 | + | 0.537871i | \(0.819229\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −29.5912 | −1.45963 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11.5145 | −0.566593 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16.6168 | 0.815685 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 51.5986 | 2.52680 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.3810 | −0.897971 | −0.448985 | − | 0.893539i | \(-0.648214\pi\) | ||||
−0.448985 | + | 0.893539i | \(0.648214\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.61356 | 0.322325 | 0.161163 | − | 0.986928i | \(-0.448476\pi\) | ||||
0.161163 | + | 0.986928i | \(0.448476\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.6998 | 0.520243 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −23.5328 | −1.14151 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.27639 | 0.352129 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.46105 | 0.118821 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 35.9318 | 1.73077 | 0.865386 | − | 0.501105i | \(-0.167073\pi\) | ||||
0.865386 | + | 0.501105i | \(0.167073\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.63283 | −0.174583 | −0.0872913 | − | 0.996183i | \(-0.527821\pi\) | ||||
−0.0872913 | + | 0.996183i | \(0.527821\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 21.2416 | 1.01846 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.2459 | 0.729308 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 39.0982 | 1.86606 | 0.933028 | − | 0.359804i | \(-0.117156\pi\) | ||||
0.933028 | + | 0.359804i | \(0.117156\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.05676 | 0.145560 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.86352 | −0.468630 | −0.234315 | − | 0.972161i | \(-0.575285\pi\) | ||||
−0.234315 | + | 0.972161i | \(0.575285\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.50102 | −0.308178 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −36.0608 | −1.70562 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.8132 | 1.40697 | 0.703487 | − | 0.710708i | \(-0.251625\pi\) | ||||
0.703487 | + | 0.710708i | \(0.251625\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.61087 | 0.0758531 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 32.1969 | 1.51274 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.12857 | 0.0529083 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.6736 | 0.733178 | 0.366589 | − | 0.930383i | \(-0.380526\pi\) | ||||
0.366589 | + | 0.930383i | \(0.380526\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.882133 | 0.0411745 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.65607 | 0.0771310 | 0.0385655 | − | 0.999256i | \(-0.487721\pi\) | ||||
0.0385655 | + | 0.999256i | \(0.487721\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −35.6461 | −1.65661 | −0.828306 | − | 0.560276i | \(-0.810695\pi\) | ||||
−0.828306 | + | 0.560276i | \(0.810695\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 16.1740 | 0.750049 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.2596 | 1.03005 | 0.515025 | − | 0.857175i | \(-0.327783\pi\) | ||||
0.515025 | + | 0.857175i | \(0.327783\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.5388 | −0.486638 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.56388 | −0.164215 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.78285 | 0.449816 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.83696 | 0.313701 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 32.6753 | 1.49610 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.2604 | −0.788647 | −0.394323 | − | 0.918972i | \(-0.629021\pi\) | ||||
−0.394323 | + | 0.918972i | \(0.629021\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.38927 | −0.200134 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −20.4498 | −0.930499 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.89675 | 0.403981 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.1130 | −0.956722 | −0.478361 | − | 0.878163i | \(-0.658769\pi\) | ||||
−0.478361 | + | 0.878163i | \(0.658769\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 17.1599 | 0.775999 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.9835 | 0.495678 | 0.247839 | − | 0.968801i | \(-0.420280\pi\) | ||||
0.247839 | + | 0.968801i | \(0.420280\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −48.2981 | −2.17524 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.44977 | 0.155056 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.2627 | 0.594914 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.7724 | 0.885132 | 0.442566 | − | 0.896736i | \(-0.354068\pi\) | ||||
0.442566 | + | 0.896736i | \(0.354068\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.3638 | 0.552375 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.2151 | 0.767582 | 0.383791 | − | 0.923420i | \(-0.374618\pi\) | ||||
0.383791 | + | 0.923420i | \(0.374618\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.1975 | −0.587281 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.46105 | 0.109299 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −32.2352 | −1.42880 | −0.714400 | − | 0.699738i | \(-0.753300\pi\) | ||||
−0.714400 | + | 0.699738i | \(0.753300\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.6993 | −0.650257 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.256286 | −0.0113153 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16.1296 | −0.710755 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.50039 | −0.153947 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −29.8835 | −1.31174 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.4244 | 0.544325 | 0.272162 | − | 0.962251i | \(-0.412261\pi\) | ||||
0.272162 | + | 0.962251i | \(0.412261\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.8783 | −0.650582 | −0.325291 | − | 0.945614i | \(-0.605462\pi\) | ||||
−0.325291 | + | 0.945614i | \(0.605462\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −9.17066 | −0.400240 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −36.7755 | −1.60197 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 46.0460 | 2.00200 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −35.1971 | −1.52743 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.61087 | 0.0697747 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19.9487 | 0.862457 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −15.0313 | −0.648650 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.0299 | 0.474212 | 0.237106 | − | 0.971484i | \(-0.423801\pi\) | ||||
0.237106 | + | 0.971484i | \(0.423801\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 23.8653 | 1.02416 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −15.5493 | −0.666057 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.1982 | −0.778101 | −0.389050 | − | 0.921217i | \(-0.627197\pi\) | ||||
−0.389050 | + | 0.921217i | \(0.627197\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 22.2422 | 0.949272 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.0320 | 0.597784 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.87583 | −0.377439 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −12.1911 | −0.517482 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.7801 | 0.880483 | 0.440241 | − | 0.897879i | \(-0.354893\pi\) | ||||
0.440241 | + | 0.897879i | \(0.354893\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.78285 | 0.413771 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15.5422 | −0.656192 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.41182 | −0.270226 | −0.135113 | − | 0.990830i | \(-0.543140\pi\) | ||||
−0.135113 | + | 0.990830i | \(0.543140\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.60149 | −0.235656 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.82651 | −0.370678 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 42.0250 | 1.76178 | 0.880889 | − | 0.473323i | \(-0.156946\pi\) | ||||
0.880889 | + | 0.473323i | \(0.156946\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.9071 | 0.916785 | 0.458393 | − | 0.888750i | \(-0.348425\pi\) | ||||
0.458393 | + | 0.888750i | \(0.348425\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −23.4359 | −0.979048 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 30.9635 | 1.29127 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.2586 | 0.968269 | 0.484134 | − | 0.874994i | \(-0.339135\pi\) | ||||
0.484134 | + | 0.874994i | \(0.339135\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −24.9096 | −1.03521 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.7237 | −0.610842 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.6895 | −0.442715 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.44977 | 0.142631 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −30.4207 | −1.25560 | −0.627799 | − | 0.778375i | \(-0.716044\pi\) | ||||
−0.627799 | + | 0.778375i | \(0.716044\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.6844 | 0.440242 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.2327 | −0.749994 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.5517 | 0.843957 | 0.421979 | − | 0.906606i | \(-0.361336\pi\) | ||||
0.421979 | + | 0.906606i | \(0.361336\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.12725 | −0.292189 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.44231 | −0.386448 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.38583 | −0.138341 | −0.0691707 | − | 0.997605i | \(-0.522035\pi\) | ||||
−0.0691707 | + | 0.997605i | \(0.522035\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 33.7434 | 1.37642 | 0.688211 | − | 0.725511i | \(-0.258396\pi\) | ||||
0.688211 | + | 0.725511i | \(0.258396\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −32.2147 | −1.31188 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.12857 | −0.0458830 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.2209 | 1.06427 | 0.532137 | − | 0.846658i | \(-0.321389\pi\) | ||||
0.532137 | + | 0.846658i | \(0.321389\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −18.8216 | −0.762691 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.50039 | −0.141610 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.1368 | 0.692149 | 0.346075 | − | 0.938207i | \(-0.387514\pi\) | ||||
0.346075 | + | 0.938207i | \(0.387514\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.47415 | 0.180415 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −28.7678 | −1.15815 | −0.579074 | − | 0.815275i | \(-0.696586\pi\) | ||||
−0.579074 | + | 0.815275i | \(0.696586\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.70624 | −0.189160 | −0.0945800 | − | 0.995517i | \(-0.530151\pi\) | ||||
−0.0945800 | + | 0.995517i | \(0.530151\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.16068 | −0.0465763 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.76039 | 0.230785 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.51711 | 0.300684 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.51547 | 0.180330 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 27.7195 | 1.10525 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.62586 | −0.383199 | −0.191600 | − | 0.981473i | \(-0.561368\pi\) | ||||
−0.191600 | + | 0.981473i | \(0.561368\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −13.4972 | −0.536467 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16.8961 | 0.670501 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 40.5409 | 1.60377 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.47126 | −0.137107 | −0.0685534 | − | 0.997647i | \(-0.521838\pi\) | ||||
−0.0685534 | + | 0.997647i | \(0.521838\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.9442 | 0.510470 | 0.255235 | − | 0.966879i | \(-0.417847\pi\) | ||||
0.255235 | + | 0.966879i | \(0.417847\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 27.1716 | 1.06988 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23.2745 | −0.915016 | −0.457508 | − | 0.889206i | \(-0.651258\pi\) | ||||
−0.457508 | + | 0.889206i | \(0.651258\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.5145 | 0.451985 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14.3313 | −0.561689 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17.5041 | 0.684987 | 0.342493 | − | 0.939520i | \(-0.388729\pi\) | ||||
0.342493 | + | 0.939520i | \(0.388729\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.3564 | −0.678171 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −44.9320 | −1.75297 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.94490 | −0.387398 | −0.193699 | − | 0.981061i | \(-0.562049\pi\) | ||||
−0.193699 | + | 0.981061i | \(0.562049\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.0326 | 0.506908 | 0.253454 | − | 0.967347i | \(-0.418433\pi\) | ||||
0.253454 | + | 0.967347i | \(0.418433\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −15.5422 | −0.603609 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.07068 | 0.0802974 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 63.5487 | 2.46062 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 26.2117 | 1.01340 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.27639 | −0.280902 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −34.6008 | −1.33376 | −0.666881 | − | 0.745165i | \(-0.732371\pi\) | ||||
−0.666881 | + | 0.745165i | \(0.732371\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.520502 | −0.0200341 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −31.3813 | −1.20608 | −0.603040 | − | 0.797711i | \(-0.706044\pi\) | ||||
−0.603040 | + | 0.797711i | \(0.706044\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.88319 | −0.302529 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −44.3775 | −1.70055 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.50776 | 0.325540 | 0.162770 | − | 0.986664i | \(-0.447957\pi\) | ||||
0.162770 | + | 0.986664i | \(0.447957\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.5698 | 0.518474 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.0403 | 0.535673 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.6895 | −0.407239 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.2712 | 1.26570 | 0.632848 | − | 0.774276i | \(-0.281886\pi\) | ||||
0.632848 | + | 0.774276i | \(0.281886\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.05676 | −0.116117 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −23.6618 | −0.897543 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.1731 | −0.385334 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.14317 | 0.232356 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 49.2054 | 1.85846 | 0.929231 | − | 0.369500i | \(-0.120471\pi\) | ||||
0.929231 | + | 0.369500i | \(0.120471\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.05332 | −0.303737 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.72222 | −0.366160 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.6940 | 0.439797 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.3934 | −0.953671 | −0.476835 | − | 0.878993i | \(-0.658216\pi\) | ||||
−0.476835 | + | 0.878993i | \(0.658216\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −27.1313 | −1.01750 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 48.3878 | 1.81214 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.12857 | −0.0422062 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −17.9882 | −0.671782 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.03613 | −0.150522 | −0.0752611 | − | 0.997164i | \(-0.523979\pi\) | ||||
−0.0752611 | + | 0.997164i | \(0.523979\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.2920 | 0.532263 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.00300 | −0.260444 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 28.4982 | 1.05840 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 36.8804 | 1.36782 | 0.683909 | − | 0.729567i | \(-0.260279\pi\) | ||||
0.683909 | + | 0.729567i | \(0.260279\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −28.0118 | −1.03747 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −61.7814 | −2.28507 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 46.0408 | 1.70056 | 0.850278 | − | 0.526334i | \(-0.176434\pi\) | ||||
0.850278 | + | 0.526334i | \(0.176434\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.77747 | −0.102449 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.5388 | 0.388203 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33.7700 | −1.24225 | −0.621124 | − | 0.783712i | \(-0.713324\pi\) | ||||
−0.621124 | + | 0.783712i | \(0.713324\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.51547 | 0.165880 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −32.8431 | −1.20490 | −0.602448 | − | 0.798158i | \(-0.705808\pi\) | ||||
−0.602448 | + | 0.798158i | \(0.705808\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.5366 | 0.605853 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −45.0068 | −1.64671 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −17.6760 | −0.645868 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −44.4424 | −1.62172 | −0.810862 | − | 0.585237i | \(-0.801001\pi\) | ||||
−0.810862 | + | 0.585237i | \(0.801001\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −10.3694 | −0.377883 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −14.7646 | −0.537340 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.68206 | 0.0611357 | 0.0305678 | − | 0.999533i | \(-0.490268\pi\) | ||||
0.0305678 | + | 0.999533i | \(0.490268\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 20.4498 | 0.742281 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36.3394 | −1.31730 | −0.658651 | − | 0.752448i | \(-0.728873\pi\) | ||||
−0.658651 | + | 0.752448i | \(0.728873\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.7778 | 0.498790 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −21.7863 | −0.787684 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.5145 | 0.415766 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.81762 | −0.0655449 | −0.0327725 | − | 0.999463i | \(-0.510434\pi\) | ||||
−0.0327725 | + | 0.999463i | \(0.510434\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.7907 | 0.640715 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24.7208 | −0.889146 | −0.444573 | − | 0.895743i | \(-0.646645\pi\) | ||||
−0.444573 | + | 0.895743i | \(0.646645\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.6994 | 0.779465 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10.8022 | 0.387527 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.95559 | 0.105895 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.2627 | −0.474577 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.06827 | −0.0381767 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.63431 | 0.0583308 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.5597 | 1.08933 | 0.544667 | − | 0.838652i | \(-0.316656\pi\) | ||||
0.544667 | + | 0.838652i | \(0.316656\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 76.9261 | 2.73864 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.96334 | 0.176476 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.27639 | −0.258392 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −29.6899 | −1.05299 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 45.7590 | 1.62087 | 0.810433 | − | 0.585831i | \(-0.199232\pi\) | ||||
0.810433 | + | 0.585831i | \(0.199232\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.1059 | 0.782050 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 17.6081 | 0.622152 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14.6993 | 0.518725 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.37775 | 0.330522 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −16.7206 | −0.588593 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16.5329 | −0.581264 | −0.290632 | − | 0.956835i | \(-0.593866\pi\) | ||||
−0.290632 | + | 0.956835i | \(0.593866\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.39570 | −0.189469 | −0.0947343 | − | 0.995503i | \(-0.530200\pi\) | ||||
−0.0947343 | + | 0.995503i | \(0.530200\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.02296 | 0.281377 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.86910 | −0.275643 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 17.9493 | 0.627967 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.05676 | −0.106812 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.478489 | −0.0166994 | −0.00834969 | − | 0.999965i | \(-0.502658\pi\) | ||||
−0.00834969 | + | 0.999965i | \(0.502658\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.60949 | 0.230392 | 0.115196 | − | 0.993343i | \(-0.463250\pi\) | ||||
0.115196 | + | 0.993343i | \(0.463250\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9.17066 | 0.319281 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.3810 | 0.430530 | 0.215265 | − | 0.976556i | \(-0.430938\pi\) | ||||
0.215265 | + | 0.976556i | \(0.430938\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.0788 | −0.766830 | −0.383415 | − | 0.923576i | \(-0.625252\pi\) | ||||
−0.383415 | + | 0.923576i | \(0.625252\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.25434 | −0.251650 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.31528 | 0.218811 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.66973 | −0.196209 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.813408 | −0.0281155 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.8007 | 0.545500 | 0.272750 | − | 0.962085i | \(-0.412067\pi\) | ||||
0.272750 | + | 0.962085i | \(0.412067\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.4891 | 1.01687 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 25.6822 | 0.884542 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.12857 | −0.0388241 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 52.6214 | 1.80596 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −36.4722 | −1.25025 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −43.5280 | −1.49037 | −0.745185 | − | 0.666858i | \(-0.767639\pi\) | ||||
−0.745185 | + | 0.666858i | \(0.767639\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.32955 | 0.216466 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.61496 | −0.225963 | −0.112981 | − | 0.993597i | \(-0.536040\pi\) | ||||
−0.112981 | + | 0.993597i | \(0.536040\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.55129 | −0.189408 | −0.0947038 | − | 0.995505i | \(-0.530190\pi\) | ||||
−0.0947038 | + | 0.995505i | \(0.530190\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.96444 | −0.135108 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12.8522 | −0.437495 | −0.218748 | − | 0.975781i | \(-0.570197\pi\) | ||||
−0.218748 | + | 0.975781i | \(0.570197\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.7038 | 0.465943 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 56.3155 | 1.91257 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.87583 | 0.301092 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.5388 | 0.357095 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −24.0970 | −0.815560 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.84829 | 0.332933 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33.9578 | −1.14667 | −0.573337 | − | 0.819320i | \(-0.694351\pi\) | ||||
−0.573337 | + | 0.819320i | \(0.694351\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.77623 | 0.0936399 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.7693 | 1.33986 | 0.669931 | − | 0.742423i | \(-0.266324\pi\) | ||||
0.669931 | + | 0.742423i | \(0.266324\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 50.8579 | 1.71150 | 0.855752 | − | 0.517387i | \(-0.173095\pi\) | ||||
0.855752 | + | 0.517387i | \(0.173095\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 31.9813 | 1.07504 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19.6392 | −0.659421 | −0.329711 | − | 0.944082i | \(-0.606951\pi\) | ||||
−0.329711 | + | 0.944082i | \(0.606951\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.9712 | −0.502118 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.82651 | 0.295699 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.42241 | −0.214918 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.89298 | 0.230407 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 20.4498 | 0.682799 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 44.5353 | 1.48533 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 67.5073 | 2.24900 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −24.0761 | −0.801202 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.9440 | −0.363791 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 39.9066 | 1.32508 | 0.662539 | − | 0.749028i | \(-0.269479\pi\) | ||||
0.662539 | + | 0.749028i | \(0.269479\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 35.7456 | 1.18561 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.32300 | −0.176359 | −0.0881794 | − | 0.996105i | \(-0.528105\pi\) | ||||
−0.0881794 | + | 0.996105i | \(0.528105\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.7237 | 0.487283 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −20.2100 | −0.668121 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15.3791 | 0.507862 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.7182 | 0.815379 | 0.407690 | − | 0.913121i | \(-0.366335\pi\) | ||||
0.407690 | + | 0.913121i | \(0.366335\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 44.0012 | 1.44989 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13.2627 | −0.436547 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.3558 | −0.537777 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 43.6873 | 1.43488 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −26.0883 | −0.855931 | −0.427965 | − | 0.903795i | \(-0.640769\pi\) | ||||
−0.427965 | + | 0.903795i | \(0.640769\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.83477 | −0.0601323 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −37.5663 | −1.22987 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.12725 | 0.233086 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.787111 | 0.0257138 | 0.0128569 | − | 0.999917i | \(-0.495907\pi\) | ||||
0.0128569 | + | 0.999917i | \(0.495907\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 28.9308 | 0.944122 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.09811 | 0.0683964 | 0.0341982 | − | 0.999415i | \(-0.489112\pi\) | ||||
0.0341982 | + | 0.999415i | \(0.489112\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.3854 | 0.435888 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.157642 | −0.00512809 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.80450 | −0.286108 | −0.143054 | − | 0.989715i | \(-0.545692\pi\) | ||||
−0.143054 | + | 0.989715i | \(0.545692\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.6993 | 0.477158 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −81.2477 | −2.63464 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42.1631 | 1.36580 | 0.682899 | − | 0.730513i | \(-0.260719\pi\) | ||||
0.682899 | + | 0.730513i | \(0.260719\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.7471 | 0.347767 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 18.8216 | 0.608417 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12.0238 | −0.388270 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.91044 | 0.0938850 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −54.0314 | −1.74114 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.4229 | 0.367716 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.8790 | 1.08947 | 0.544737 | − | 0.838607i | \(-0.316629\pi\) | ||||
0.544737 | + | 0.838607i | \(0.316629\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −28.5164 | −0.916079 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.12178 | −0.100183 | −0.0500913 | − | 0.998745i | \(-0.515951\pi\) | ||||
−0.0500913 | + | 0.998745i | \(0.515951\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.9661 | 0.672143 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9.17066 | 0.293696 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −47.2461 | −1.51154 | −0.755768 | − | 0.654840i | \(-0.772736\pi\) | ||||
−0.755768 | + | 0.654840i | \(0.772736\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.76039 | −0.184103 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 42.1154 | 1.34464 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.17996 | 0.197110 | 0.0985551 | − | 0.995132i | \(-0.468578\pi\) | ||||
0.0985551 | + | 0.995132i | \(0.468578\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.36105 | 0.266405 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.61462 | 0.274206 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 81.2896 | 2.58486 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34.3570 | −1.09139 | −0.545693 | − | 0.837985i | \(-0.683733\pi\) | ||||
−0.545693 | + | 0.837985i | \(0.683733\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −54.5102 | −1.72983 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.33000 | 0.137270 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.6230 | −0.558126 | −0.279063 | − | 0.960273i | \(-0.590024\pi\) | ||||
−0.279063 | + | 0.960273i | \(0.590024\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.613104 | 0.0193978 |
(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.y.1.13 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.y.1.13 | ✓ | 14 | 1.1 | even | 1 | trivial |