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: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 2 x^{12} - 49 x^{11} + 99 x^{10} + 901 x^{9} - 1879 x^{8} - 7582 x^{7} + 16968 x^{6} + \cdots + 12144 \) |
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 | 1.3 | ||
Root | \(-3.05600\) 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 | ||||||||
\(5\) | −3.05600 | −1.36668 | −0.683342 | − | 0.730098i | \(-0.739474\pi\) | ||||
−0.683342 | + | 0.730098i | \(0.739474\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.59989 | 0.982666 | 0.491333 | − | 0.870972i | \(-0.336510\pi\) | ||||
0.491333 | + | 0.870972i | \(0.336510\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.72064 | 1.42333 | 0.711663 | − | 0.702521i | \(-0.247942\pi\) | ||||
0.711663 | + | 0.702521i | \(0.247942\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.74051 | 1.86948 | 0.934740 | − | 0.355332i | \(-0.115632\pi\) | ||||
0.934740 | + | 0.355332i | \(0.115632\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.05600 | −0.789055 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.13623 | −0.760649 | −0.380324 | − | 0.924853i | \(-0.624188\pi\) | ||||
−0.380324 | + | 0.924853i | \(0.624188\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.68764 | 0.616587 | 0.308293 | − | 0.951291i | \(-0.400242\pi\) | ||||
0.308293 | + | 0.951291i | \(0.400242\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.59989 | 0.567342 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.99219 | 1.45797 | 0.728986 | − | 0.684528i | \(-0.239992\pi\) | ||||
0.728986 | + | 0.684528i | \(0.239992\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.33912 | 0.867825 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.69073 | −1.42813 | −0.714067 | − | 0.700078i | \(-0.753149\pi\) | ||||
−0.714067 | + | 0.700078i | \(0.753149\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.05540 | 0.728372 | 0.364186 | − | 0.931326i | \(-0.381347\pi\) | ||||
0.364186 | + | 0.931326i | \(0.381347\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.72064 | 0.821757 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.94526 | −1.34299 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.127532 | 0.0209662 | 0.0104831 | − | 0.999945i | \(-0.496663\pi\) | ||||
0.0104831 | + | 0.999945i | \(0.496663\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.74051 | 1.07935 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.00281 | −1.24983 | −0.624914 | − | 0.780693i | \(-0.714866\pi\) | ||||
−0.624914 | + | 0.780693i | \(0.714866\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.7440 | −1.63844 | −0.819221 | − | 0.573479i | \(-0.805594\pi\) | ||||
−0.819221 | + | 0.573479i | \(0.805594\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.05600 | −0.455561 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.96112 | 0.286059 | 0.143030 | − | 0.989718i | \(-0.454316\pi\) | ||||
0.143030 | + | 0.989718i | \(0.454316\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.240573 | −0.0343676 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.13623 | −0.439161 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.56814 | −1.03956 | −0.519782 | − | 0.854299i | \(-0.673987\pi\) | ||||
−0.519782 | + | 0.854299i | \(0.673987\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −14.4263 | −1.94524 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.68764 | 0.355986 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.2078 | 1.32895 | 0.664474 | − | 0.747311i | \(-0.268656\pi\) | ||||
0.664474 | + | 0.747311i | \(0.268656\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.45141 | 0.313871 | 0.156936 | − | 0.987609i | \(-0.449838\pi\) | ||||
0.156936 | + | 0.987609i | \(0.449838\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.59989 | 0.327555 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −20.5990 | −2.55499 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.1052 | 1.72323 | 0.861614 | − | 0.507564i | \(-0.169454\pi\) | ||||
0.861614 | + | 0.507564i | \(0.169454\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.99219 | 0.841761 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.69140 | −0.438088 | −0.219044 | − | 0.975715i | \(-0.570294\pi\) | ||||
−0.219044 | + | 0.975715i | \(0.570294\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.93617 | 0.577735 | 0.288867 | − | 0.957369i | \(-0.406721\pi\) | ||||
0.288867 | + | 0.957369i | \(0.406721\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.33912 | 0.501039 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.2731 | 1.39865 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.15118 | 1.02959 | 0.514794 | − | 0.857314i | \(-0.327868\pi\) | ||||
0.514794 | + | 0.857314i | \(0.327868\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.82320 | 0.858708 | 0.429354 | − | 0.903136i | \(-0.358741\pi\) | ||||
0.429354 | + | 0.903136i | \(0.358741\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.58433 | 1.03957 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.69073 | −0.824533 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.37710 | 0.569971 | 0.284986 | − | 0.958532i | \(-0.408011\pi\) | ||||
0.284986 | + | 0.958532i | \(0.408011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 17.5246 | 1.83707 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.05540 | 0.420526 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.21342 | −0.842679 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.3975 | −1.05571 | −0.527854 | − | 0.849335i | \(-0.677003\pi\) | ||||
−0.527854 | + | 0.849335i | \(0.677003\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.72064 | 0.474442 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.9764 | −1.09219 | −0.546094 | − | 0.837724i | \(-0.683886\pi\) | ||||
−0.546094 | + | 0.837724i | \(0.683886\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.67179 | −0.263260 | −0.131630 | − | 0.991299i | \(-0.542021\pi\) | ||||
−0.131630 | + | 0.991299i | \(0.542021\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.94526 | −0.775378 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.57525 | −0.345633 | −0.172816 | − | 0.984954i | \(-0.555287\pi\) | ||||
−0.172816 | + | 0.984954i | \(0.555287\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.87869 | −0.658859 | −0.329429 | − | 0.944180i | \(-0.606856\pi\) | ||||
−0.329429 | + | 0.944180i | \(0.606856\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.127532 | 0.0121048 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.92908 | 0.839977 | 0.419989 | − | 0.907529i | \(-0.362034\pi\) | ||||
0.419989 | + | 0.907529i | \(0.362034\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −21.3681 | −1.99259 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.74051 | 0.623160 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.15386 | −0.747463 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.2844 | 1.02586 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.00281 | −0.721589 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.01963 | 0.180642 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.06592 | 0.272057 | 0.136028 | − | 0.990705i | \(-0.456566\pi\) | ||||
0.136028 | + | 0.990705i | \(0.456566\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.7440 | −0.945954 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.5982 | 1.45019 | 0.725097 | − | 0.688647i | \(-0.241795\pi\) | ||||
0.725097 | + | 0.688647i | \(0.241795\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.98756 | 0.605899 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.05600 | −0.263018 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.703806 | 0.0601302 | 0.0300651 | − | 0.999548i | \(-0.490429\pi\) | ||||
0.0300651 | + | 0.999548i | \(0.490429\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.7166 | 1.24825 | 0.624124 | − | 0.781326i | \(-0.285456\pi\) | ||||
0.624124 | + | 0.781326i | \(0.285456\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.96112 | 0.165156 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 31.8195 | 2.66088 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 23.5029 | 1.95181 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.240573 | −0.0198421 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.3086 | −0.844509 | −0.422255 | − | 0.906477i | \(-0.638761\pi\) | ||||
−0.422255 | + | 0.906477i | \(0.638761\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.20583 | 0.749160 | 0.374580 | − | 0.927195i | \(-0.377787\pi\) | ||||
0.374580 | + | 0.927195i | \(0.377787\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.13623 | −0.253550 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.3933 | −0.995454 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.9456 | −1.67164 | −0.835820 | − | 0.549004i | \(-0.815007\pi\) | ||||
−0.835820 | + | 0.549004i | \(0.815007\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.56814 | −0.600192 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 18.1789 | 1.43270 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.4063 | 1.28504 | 0.642521 | − | 0.766268i | \(-0.277889\pi\) | ||||
0.642521 | + | 0.766268i | \(0.277889\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −14.4263 | −1.12308 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 32.4344 | 2.49496 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.68764 | 0.205529 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.45025 | −0.338346 | −0.169173 | − | 0.985586i | \(-0.554110\pi\) | ||||
−0.169173 | + | 0.985586i | \(0.554110\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.2812 | 0.852782 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.2078 | 0.767269 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.7672 | 1.32798 | 0.663992 | − | 0.747740i | \(-0.268861\pi\) | ||||
0.663992 | + | 0.747740i | \(0.268861\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.0026 | −1.11514 | −0.557568 | − | 0.830132i | \(-0.688265\pi\) | ||||
−0.557568 | + | 0.830132i | \(0.688265\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.45141 | 0.181214 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.389739 | −0.0286542 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.8050 | −1.08265 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.59989 | 0.189114 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.2983 | −1.46873 | −0.734367 | − | 0.678753i | \(-0.762521\pi\) | ||||
−0.734367 | + | 0.678753i | \(0.762521\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.976343 | −0.0702787 | −0.0351394 | − | 0.999382i | \(-0.511188\pi\) | ||||
−0.0351394 | + | 0.999382i | \(0.511188\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −20.5990 | −1.47512 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.3449 | 1.59201 | 0.796003 | − | 0.605293i | \(-0.206944\pi\) | ||||
0.796003 | + | 0.605293i | \(0.206944\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.41395 | 0.667337 | 0.333669 | − | 0.942690i | \(-0.391713\pi\) | ||||
0.333669 | + | 0.942690i | \(0.391713\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.1052 | 0.994906 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −19.9951 | −1.40338 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 24.4566 | 1.70812 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.99219 | 0.485991 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.6874 | 0.877604 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.5125 | 1.27445 | 0.637227 | − | 0.770676i | \(-0.280081\pi\) | ||||
0.637227 | + | 0.770676i | \(0.280081\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.69140 | −0.252930 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 32.8336 | 2.23923 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.5436 | 0.715746 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.93617 | 0.333555 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −21.1398 | −1.42202 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.0821 | −1.34480 | −0.672400 | − | 0.740188i | \(-0.734736\pi\) | ||||
−0.672400 | + | 0.740188i | \(0.734736\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.33912 | 0.289275 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.07801 | 0.204295 | 0.102147 | − | 0.994769i | \(-0.467429\pi\) | ||||
0.102147 | + | 0.994769i | \(0.467429\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.3435 | 1.27825 | 0.639127 | − | 0.769101i | \(-0.279296\pi\) | ||||
0.639127 | + | 0.769101i | \(0.279296\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.2731 | 0.807513 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.27948 | −0.476895 | −0.238447 | − | 0.971155i | \(-0.576638\pi\) | ||||
−0.238447 | + | 0.971155i | \(0.576638\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.99319 | −0.390953 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.15118 | 0.594433 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.2464 | −1.05089 | −0.525446 | − | 0.850827i | \(-0.676102\pi\) | ||||
−0.525446 | + | 0.850827i | \(0.676102\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.4511 | 1.57504 | 0.787518 | − | 0.616292i | \(-0.211366\pi\) | ||||
0.787518 | + | 0.616292i | \(0.211366\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.735191 | 0.0469697 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.1160 | 1.15270 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.82320 | 0.495775 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −28.1202 | −1.77493 | −0.887465 | − | 0.460874i | \(-0.847536\pi\) | ||||
−0.887465 | + | 0.460874i | \(0.847536\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 33.0076 | 2.07517 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.58433 | 0.600194 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.2270 | −1.13697 | −0.568485 | − | 0.822694i | \(-0.692470\pi\) | ||||
−0.568485 | + | 0.822694i | \(0.692470\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.331570 | 0.0206028 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.69073 | −0.476044 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.53367 | −0.341220 | −0.170610 | − | 0.985339i | \(-0.554574\pi\) | ||||
−0.170610 | + | 0.985339i | \(0.554574\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 23.1282 | 1.42076 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.37710 | 0.329073 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.1791 | −1.10840 | −0.554199 | − | 0.832385i | \(-0.686975\pi\) | ||||
−0.554199 | + | 0.832385i | \(0.686975\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −30.0438 | −1.82503 | −0.912516 | − | 0.409040i | \(-0.865864\pi\) | ||||
−0.912516 | + | 0.409040i | \(0.865864\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 17.5246 | 1.06064 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 20.4834 | 1.23520 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.0646 | −1.20557 | −0.602783 | − | 0.797905i | \(-0.705942\pi\) | ||||
−0.602783 | + | 0.797905i | \(0.705942\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.05540 | 0.242791 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.1320 | 1.20097 | 0.600486 | − | 0.799635i | \(-0.294974\pi\) | ||||
0.600486 | + | 0.799635i | \(0.294974\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.1003 | −1.49206 | −0.746028 | − | 0.665914i | \(-0.768042\pi\) | ||||
−0.746028 | + | 0.665914i | \(0.768042\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.21342 | −0.486521 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −20.8064 | −1.22816 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.16403 | −0.421414 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.3975 | −0.609513 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 29.6784 | 1.73383 | 0.866914 | − | 0.498457i | \(-0.166100\pi\) | ||||
0.866914 | + | 0.498457i | \(0.166100\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −31.1952 | −1.81625 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.72064 | 0.273919 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 47.1309 | 2.72565 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −27.9332 | −1.61004 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.9764 | −0.630575 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.49151 | −0.428963 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.0239 | 1.25697 | 0.628487 | − | 0.777820i | \(-0.283675\pi\) | ||||
0.628487 | + | 0.777820i | \(0.283675\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.67179 | −0.151993 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.7334 | −1.51591 | −0.757956 | − | 0.652305i | \(-0.773802\pi\) | ||||
−0.757956 | + | 0.652305i | \(0.773802\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.6867 | 1.39538 | 0.697688 | − | 0.716402i | \(-0.254212\pi\) | ||||
0.697688 | + | 0.716402i | \(0.254212\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7.94526 | −0.447665 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 29.6092 | 1.66302 | 0.831509 | − | 0.555511i | \(-0.187477\pi\) | ||||
0.831509 | + | 0.555511i | \(0.187477\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −36.3052 | −2.03270 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.57525 | −0.199551 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.42906 | −0.469006 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 29.2479 | 1.62238 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.87869 | −0.380392 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.09871 | 0.281101 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.19998 | −0.340781 | −0.170391 | − | 0.985377i | \(-0.554503\pi\) | ||||
−0.170391 | + | 0.985377i | \(0.554503\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.127532 | 0.00698874 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −43.1056 | −2.35511 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.1055 | −0.713904 | −0.356952 | − | 0.934123i | \(-0.616184\pi\) | ||||
−0.356952 | + | 0.934123i | \(0.616184\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.92908 | 0.484961 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 19.1441 | 1.03671 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.8247 | −1.01644 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −21.3681 | −1.15042 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −32.6932 | −1.75506 | −0.877530 | − | 0.479521i | \(-0.840810\pi\) | ||||
−0.877530 | + | 0.479521i | \(0.840810\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.07122 | −0.324985 | −0.162492 | − | 0.986710i | \(-0.551953\pi\) | ||||
−0.162492 | + | 0.986710i | \(0.551953\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.74051 | 0.359782 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.1820 | 1.07418 | 0.537091 | − | 0.843525i | \(-0.319523\pi\) | ||||
0.537091 | + | 0.843525i | \(0.319523\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.2809 | 0.598728 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.15386 | −0.431548 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 25.8863 | 1.36623 | 0.683113 | − | 0.730313i | \(-0.260626\pi\) | ||||
0.683113 | + | 0.730313i | \(0.260626\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.7766 | −0.619821 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.2844 | 0.592278 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.0849 | −0.789581 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.18304 | −0.218353 | −0.109176 | − | 0.994022i | \(-0.534821\pi\) | ||||
−0.109176 | + | 0.994022i | \(0.534821\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.00281 | −0.416609 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19.6763 | −1.02154 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.51126 | 0.337140 | 0.168570 | − | 0.985690i | \(-0.446085\pi\) | ||||
0.168570 | + | 0.985690i | \(0.446085\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.01963 | 0.104293 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −51.8394 | −2.66987 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.9299 | 0.869631 | 0.434815 | − | 0.900520i | \(-0.356814\pi\) | ||||
0.434815 | + | 0.900520i | \(0.356814\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.06592 | 0.157072 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −26.0508 | −1.33113 | −0.665566 | − | 0.746339i | \(-0.731810\pi\) | ||||
−0.665566 | + | 0.746339i | \(0.731810\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −37.5067 | −1.91152 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.7440 | −0.546147 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 32.2295 | 1.63410 | 0.817049 | − | 0.576568i | \(-0.195608\pi\) | ||||
0.817049 | + | 0.576568i | \(0.195608\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.9292 | −1.10900 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16.5982 | 0.837270 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −27.9660 | −1.40712 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.5553 | −0.931263 | −0.465632 | − | 0.884979i | \(-0.654173\pi\) | ||||
−0.465632 | + | 0.884979i | \(0.654173\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.98756 | 0.349816 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.1254 | −0.505640 | −0.252820 | − | 0.967513i | \(-0.581358\pi\) | ||||
−0.252820 | + | 0.967513i | \(0.581358\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 27.3355 | 1.36168 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.05600 | −0.151854 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.602035 | 0.0298417 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −32.8568 | −1.62467 | −0.812333 | − | 0.583194i | \(-0.801803\pi\) | ||||
−0.812333 | + | 0.583194i | \(0.801803\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.703806 | 0.0347162 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 26.5393 | 1.30591 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −23.9077 | −1.17358 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.7166 | 0.720676 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.3416 | 1.23802 | 0.619010 | − | 0.785383i | \(-0.287534\pi\) | ||||
0.619010 | + | 0.785383i | \(0.287534\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.17825 | 0.0574242 | 0.0287121 | − | 0.999588i | \(-0.490859\pi\) | ||||
0.0287121 | + | 0.999588i | \(0.490859\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.96112 | 0.0953531 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −13.6085 | −0.660110 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.37340 | 0.308431 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 31.8195 | 1.53626 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.3794 | −0.885307 | −0.442653 | − | 0.896693i | \(-0.645963\pi\) | ||||
−0.442653 | + | 0.896693i | \(0.645963\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −24.5067 | −1.17772 | −0.588859 | − | 0.808236i | \(-0.700423\pi\) | ||||
−0.588859 | + | 0.808236i | \(0.700423\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 23.5029 | 1.12688 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18.7925 | 0.898967 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.5405 | 0.503070 | 0.251535 | − | 0.967848i | \(-0.419065\pi\) | ||||
0.251535 | + | 0.967848i | \(0.419065\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.240573 | −0.0114559 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.1918 | −0.626760 | −0.313380 | − | 0.949628i | \(-0.601461\pi\) | ||||
−0.313380 | + | 0.949628i | \(0.601461\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.4324 | −0.778970 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.3086 | −0.487578 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.6895 | 0.646046 | 0.323023 | − | 0.946391i | \(-0.395301\pi\) | ||||
0.323023 | + | 0.946391i | \(0.395301\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −37.7783 | −1.77891 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.20583 | 0.432528 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −53.5551 | −2.51070 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.7356 | 0.689303 | 0.344651 | − | 0.938731i | \(-0.387997\pi\) | ||||
0.344651 | + | 0.938731i | \(0.387997\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.13623 | −0.146387 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.8198 | −1.06283 | −0.531413 | − | 0.847113i | \(-0.678339\pi\) | ||||
−0.531413 | + | 0.847113i | \(0.678339\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.50925 | 0.395458 | 0.197729 | − | 0.980257i | \(-0.436643\pi\) | ||||
0.197729 | + | 0.980257i | \(0.436643\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −12.3933 | −0.574726 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.22222 | −0.287930 | −0.143965 | − | 0.989583i | \(-0.545985\pi\) | ||||
−0.143965 | + | 0.989583i | \(0.545985\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 36.6720 | 1.69336 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20.9456 | −0.965122 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −50.7184 | −2.33204 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.6620 | 0.535089 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.56814 | −0.346521 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 40.6592 | 1.85777 | 0.928884 | − | 0.370372i | \(-0.120770\pi\) | ||||
0.928884 | + | 0.370372i | \(0.120770\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.859634 | 0.0391959 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 18.1789 | 0.827170 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 31.7748 | 1.44282 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.3758 | −1.14989 | −0.574944 | − | 0.818193i | \(-0.694976\pi\) | ||||
−0.574944 | + | 0.818193i | \(0.694976\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 16.4063 | 0.741919 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.83989 | 0.128162 | 0.0640812 | − | 0.997945i | \(-0.479588\pi\) | ||||
0.0640812 | + | 0.997945i | \(0.479588\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 24.1199 | 1.08631 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −14.4263 | −0.648412 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.59722 | −0.430494 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.3425 | 0.507759 | 0.253879 | − | 0.967236i | \(-0.418293\pi\) | ||||
0.253879 | + | 0.967236i | \(0.418293\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 23.7022 | 1.05683 | 0.528415 | − | 0.848986i | \(-0.322786\pi\) | ||||
0.528415 | + | 0.848986i | \(0.322786\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 33.5437 | 1.49268 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 32.4344 | 1.44046 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.62782 | 0.0721517 | 0.0360758 | − | 0.999349i | \(-0.488514\pi\) | ||||
0.0360758 | + | 0.999349i | \(0.488514\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.8335 | 0.567720 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.68764 | 0.118662 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.16500 | 0.359793 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.25775 | 0.407156 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.45025 | −0.195344 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.03728 | 0.220687 | 0.110344 | − | 0.993893i | \(-0.464805\pi\) | ||||
0.110344 | + | 0.993893i | \(0.464805\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.7066 | 1.08034 | 0.540172 | − | 0.841555i | \(-0.318359\pi\) | ||||
0.540172 | + | 0.841555i | \(0.318359\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 11.2812 | 0.492354 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.7187 | −0.554035 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25.8908 | 1.12568 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.2078 | 0.442983 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −53.9430 | −2.33653 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.9260 | 0.472370 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 17.7672 | 0.766712 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.13566 | −0.0489163 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.18767 | 0.0940552 | 0.0470276 | − | 0.998894i | \(-0.485025\pi\) | ||||
0.0470276 | + | 0.998894i | \(0.485025\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −15.0026 | −0.643824 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 21.0213 | 0.900451 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.8845 | 0.679172 | 0.339586 | − | 0.940575i | \(-0.389713\pi\) | ||||
0.339586 | + | 0.940575i | \(0.389713\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.45141 | 0.104624 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −20.6699 | −0.880568 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 23.7921 | 1.01174 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.389739 | −0.0165435 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.88069 | 0.0796873 | 0.0398436 | − | 0.999206i | \(-0.487314\pi\) | ||||
0.0398436 | + | 0.999206i | \(0.487314\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −72.4199 | −3.06303 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.8050 | −0.625069 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.8631 | 0.837131 | 0.418565 | − | 0.908187i | \(-0.362533\pi\) | ||||
0.418565 | + | 0.908187i | \(0.362533\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −27.2873 | −1.14798 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.59989 | 0.109185 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.6129 | −0.906058 | −0.453029 | − | 0.891496i | \(-0.649657\pi\) | ||||
−0.453029 | + | 0.891496i | \(0.649657\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.15758 | 0.341384 | 0.170692 | − | 0.985324i | \(-0.445400\pi\) | ||||
0.170692 | + | 0.985324i | \(0.445400\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −20.2983 | −0.847974 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 30.3400 | 1.26527 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.3812 | −0.598698 | −0.299349 | − | 0.954144i | \(-0.596769\pi\) | ||||
−0.299349 | + | 0.954144i | \(0.596769\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.976343 | −0.0405754 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 20.3395 | 0.843823 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −35.7264 | −1.47964 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −20.5990 | −0.851663 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.4163 | 0.677573 | 0.338786 | − | 0.940863i | \(-0.389984\pi\) | ||||
0.338786 | + | 0.940863i | \(0.389984\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.8995 | 0.449104 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 22.3449 | 0.919145 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −26.4055 | −1.08434 | −0.542171 | − | 0.840268i | \(-0.682398\pi\) | ||||
−0.542171 | + | 0.840268i | \(0.682398\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 24.9182 | 1.02155 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.41395 | 0.385287 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.34234 | −0.177423 | −0.0887116 | − | 0.996057i | \(-0.528275\pi\) | ||||
−0.0887116 | + | 0.996057i | \(0.528275\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.5387 | 0.878583 | 0.439292 | − | 0.898344i | \(-0.355229\pi\) | ||||
0.439292 | + | 0.898344i | \(0.355229\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.1052 | 0.574409 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −34.4852 | −1.40202 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.25626 | −0.253934 | −0.126967 | − | 0.991907i | \(-0.540524\pi\) | ||||
−0.126967 | + | 0.991907i | \(0.540524\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −19.9951 | −0.810241 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.2190 | 0.534782 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −32.0598 | −1.29488 | −0.647441 | − | 0.762116i | \(-0.724161\pi\) | ||||
−0.647441 | + | 0.762116i | \(0.724161\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 24.4566 | 0.986184 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −32.0392 | −1.28985 | −0.644925 | − | 0.764246i | \(-0.723111\pi\) | ||||
−0.644925 | + | 0.764246i | \(0.723111\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.7106 | 0.832428 | 0.416214 | − | 0.909267i | \(-0.363357\pi\) | ||||
0.416214 | + | 0.909267i | \(0.363357\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.99219 | 0.280587 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.9799 | 0.560091 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.8676 | −1.11470 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12.6874 | 0.506685 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.399972 | −0.0159479 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.6970 | 1.06279 | 0.531395 | − | 0.847124i | \(-0.321668\pi\) | ||||
0.531395 | + | 0.847124i | \(0.321668\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18.5125 | 0.735806 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.36946 | −0.371816 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.62159 | −0.0642496 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.69140 | −0.146029 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.0039 | 0.474125 | 0.237062 | − | 0.971494i | \(-0.423815\pi\) | ||||
0.237062 | + | 0.971494i | \(0.423815\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.8943 | 1.33666 | 0.668331 | − | 0.743864i | \(-0.267009\pi\) | ||||
0.668331 | + | 0.743864i | \(0.267009\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 32.8336 | 1.29282 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.6487 | 0.693842 | 0.346921 | − | 0.937894i | \(-0.387227\pi\) | ||||
0.346921 | + | 0.937894i | \(0.387227\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 48.1875 | 1.89153 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.5436 | 0.413236 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.4535 | −0.487344 | −0.243672 | − | 0.969858i | \(-0.578352\pi\) | ||||
−0.243672 | + | 0.969858i | \(0.578352\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −50.7242 | −1.98196 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.93617 | 0.192578 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23.0086 | −0.896290 | −0.448145 | − | 0.893961i | \(-0.647915\pi\) | ||||
−0.448145 | + | 0.893961i | \(0.647915\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.59936 | −0.139999 | −0.0699994 | − | 0.997547i | \(-0.522300\pi\) | ||||
−0.0699994 | + | 0.997547i | \(0.522300\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −21.1398 | −0.821002 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −21.3540 | −0.828072 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −53.7751 | −2.08218 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −20.0821 | −0.776420 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.5722 | 0.446741 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −38.0723 | −1.46758 | −0.733791 | − | 0.679376i | \(-0.762251\pi\) | ||||
−0.733791 | + | 0.679376i | \(0.762251\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.33912 | 0.167013 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.9008 | 1.07232 | 0.536158 | − | 0.844118i | \(-0.319875\pi\) | ||||
0.536158 | + | 0.844118i | \(0.319875\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −27.0324 | −1.03741 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.07801 | 0.117950 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.7556 | −0.564608 | −0.282304 | − | 0.959325i | \(-0.591099\pi\) | ||||
−0.282304 | + | 0.959325i | \(0.591099\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.15083 | −0.0821790 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19.3435 | 0.738000 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −51.0131 | −1.94344 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.6875 | −1.01524 | −0.507619 | − | 0.861581i | \(-0.669474\pi\) | ||||
−0.507619 | + | 0.861581i | \(0.669474\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 12.2731 | 0.466218 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −44.9739 | −1.70596 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 25.0987 | 0.950680 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.27948 | −0.275335 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.51451 | 0.283819 | 0.141910 | − | 0.989880i | \(-0.454676\pi\) | ||||
0.141910 | + | 0.989880i | \(0.454676\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.342761 | 0.0129275 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.99319 | −0.225717 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −28.5373 | −1.07326 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −42.9604 | −1.61341 | −0.806706 | − | 0.590953i | \(-0.798752\pi\) | ||||
−0.806706 | + | 0.590953i | \(0.798752\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.15118 | 0.343196 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 28.3561 | 1.06195 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −97.2403 | −3.63658 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −16.2464 | −0.606733 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.20012 | 0.0820506 | 0.0410253 | − | 0.999158i | \(-0.486938\pi\) | ||||
0.0410253 | + | 0.999158i | \(0.486938\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.94637 | −0.258696 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 24.4511 | 0.909347 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −33.3710 | −1.23937 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.7783 | −0.399746 | −0.199873 | − | 0.979822i | \(-0.564053\pi\) | ||||
−0.199873 | + | 0.979822i | \(0.564053\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 33.6956 | 1.24628 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 46.4940 | 1.71730 | 0.858648 | − | 0.512565i | \(-0.171305\pi\) | ||||
0.858648 | + | 0.512565i | \(0.171305\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.735191 | 0.0271179 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 66.5857 | 2.45271 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.9324 | −0.770011 | −0.385006 | − | 0.922914i | \(-0.625801\pi\) | ||||
−0.385006 | + | 0.922914i | \(0.625801\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 18.1160 | 0.665510 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23.1270 | −0.848446 | −0.424223 | − | 0.905558i | \(-0.639453\pi\) | ||||
−0.424223 | + | 0.905558i | \(0.639453\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 31.5029 | 1.15418 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.82320 | 0.286236 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.29526 | −0.339641 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.0814 | −0.623311 | −0.311655 | − | 0.950195i | \(-0.600883\pi\) | ||||
−0.311655 | + | 0.950195i | \(0.600883\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −28.1202 | −1.02476 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −28.1330 | −1.02387 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.85466 | 0.358174 | 0.179087 | − | 0.983833i | \(-0.442686\pi\) | ||||
0.179087 | + | 0.983833i | \(0.442686\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 33.0076 | 1.19810 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.6740 | 1.03943 | 0.519716 | − | 0.854339i | \(-0.326038\pi\) | ||||
0.519716 | + | 0.854339i | \(0.326038\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −17.8838 | −0.647438 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.58433 | 0.346522 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 68.8061 | 2.48444 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.9620 | −1.26076 | −0.630381 | − | 0.776286i | \(-0.717101\pi\) | ||||
−0.630381 | + | 0.776286i | \(0.717101\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.2270 | −0.656430 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.10284 | −0.291439 | −0.145720 | − | 0.989326i | \(-0.546550\pi\) | ||||
−0.145720 | + | 0.989326i | \(0.546550\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17.5969 | 0.632099 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.331570 | 0.0118950 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −21.5086 | −0.770627 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.4257 | −0.623542 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.69073 | −0.274844 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 64.0097 | 2.28460 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 37.6200 | 1.34101 | 0.670504 | − | 0.741906i | \(-0.266078\pi\) | ||||
0.670504 | + | 0.741906i | \(0.266078\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.53367 | −0.197004 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 23.2146 | 0.825417 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.5238 | 0.586776 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 23.1282 | 0.820273 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −29.2219 | −1.03509 | −0.517546 | − | 0.855655i | \(-0.673154\pi\) | ||||
−0.517546 | + | 0.855655i | \(0.673154\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.15054 | −0.217591 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.37710 | 0.189990 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 23.3019 | 0.822304 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −55.5548 | −1.95805 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18.1791 | −0.639933 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27.9431 | −0.982427 | −0.491213 | − | 0.871039i | \(-0.663446\pi\) | ||||
−0.491213 | + | 0.871039i | \(0.663446\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −46.9869 | −1.64993 | −0.824967 | − | 0.565181i | \(-0.808806\pi\) | ||||
−0.824967 | + | 0.565181i | \(0.808806\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −30.0438 | −1.05368 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −50.1377 | −1.75625 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −28.8759 | −1.01024 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 17.5246 | 0.612358 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.11204 | −0.213312 | −0.106656 | − | 0.994296i | \(-0.534014\pi\) | ||||
−0.106656 | + | 0.994296i | \(0.534014\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.3315 | 0.813285 | 0.406643 | − | 0.913587i | \(-0.366699\pi\) | ||||
0.406643 | + | 0.913587i | \(0.366699\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 20.4834 | 0.713142 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 47.3352 | 1.64601 | 0.823003 | − | 0.568037i | \(-0.192297\pi\) | ||||
0.823003 | + | 0.568037i | \(0.192297\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.7216 | 1.31012 | 0.655062 | − | 0.755575i | \(-0.272642\pi\) | ||||
0.655062 | + | 0.755575i | \(0.272642\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −20.0646 | −0.696034 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.754494 | 0.0261417 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.05600 | 0.105757 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.05540 | 0.140175 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −38.0910 | −1.31505 | −0.657524 | − | 0.753434i | \(-0.728396\pi\) | ||||
−0.657524 | + | 0.753434i | \(0.728396\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 30.1474 | 1.03956 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 20.1320 | 0.693382 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −99.1196 | −3.40982 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 29.3382 | 1.00807 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −25.1003 | −0.861439 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.891732 | 0.0305682 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 51.7150 | 1.77069 | 0.885343 | − | 0.464938i | \(-0.153923\pi\) | ||||
0.885343 | + | 0.464938i | \(0.153923\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.21342 | −0.280893 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.25379 | −0.0428287 | −0.0214143 | − | 0.999771i | \(-0.506817\pi\) | ||||
−0.0214143 | + | 0.999771i | \(0.506817\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 48.8539 | 1.66687 | 0.833436 | − | 0.552616i | \(-0.186370\pi\) | ||||
0.833436 | + | 0.552616i | \(0.186370\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −20.8064 | −0.709081 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.6303 | 0.600143 | 0.300072 | − | 0.953917i | \(-0.402989\pi\) | ||||
0.300072 | + | 0.953917i | \(0.402989\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.5999 | 0.462412 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.16403 | −0.243303 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 43.1994 | 1.46544 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 95.0764 | 3.22154 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −10.3975 | −0.351903 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.25083 | 0.177510 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.77076 | −0.0597945 | −0.0298972 | − | 0.999553i | \(-0.509518\pi\) | ||||
−0.0298972 | + | 0.999553i | \(0.509518\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 29.6784 | 1.00103 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −43.8943 | −1.47884 | −0.739419 | − | 0.673246i | \(-0.764900\pi\) | ||||
−0.739419 | + | 0.673246i | \(0.764900\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.5616 | 0.590996 | 0.295498 | − | 0.955343i | \(-0.404514\pi\) | ||||
0.295498 | + | 0.955343i | \(0.404514\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −31.1952 | −1.04861 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.0970 | 0.473332 | 0.236666 | − | 0.971591i | \(-0.423945\pi\) | ||||
0.236666 | + | 0.971591i | \(0.423945\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.97106 | 0.267341 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.72064 | 0.158147 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.27079 | 0.176380 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −54.2966 | −1.81493 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 47.1309 | 1.57366 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −31.1890 | −1.04021 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.7355 | 0.790743 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −27.9332 | −0.929557 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 45.8479 | 1.52404 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.8504 | 0.426692 | 0.213346 | − | 0.976977i | \(-0.431564\pi\) | ||||
0.213346 | + | 0.976977i | \(0.431564\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.9764 | −0.364063 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.4133 | 0.610060 | 0.305030 | − | 0.952343i | \(-0.401333\pi\) | ||||
0.305030 | + | 0.952343i | \(0.401333\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 36.9305 | 1.22222 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.49151 | −0.247662 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 43.1536 | 1.42506 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −43.6473 | −1.43979 | −0.719895 | − | 0.694082i | \(-0.755810\pi\) | ||||
−0.719895 | + | 0.694082i | \(0.755810\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22.0239 | 0.725714 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −24.8819 | −0.818997 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.553379 | 0.0181950 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.67179 | −0.0877533 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.48680 | −0.212825 | −0.106412 | − | 0.994322i | \(-0.533936\pi\) | ||||
−0.106412 | + | 0.994322i | \(0.533936\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.646574 | −0.0211906 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −26.7334 | −0.875213 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 45.2441 | 1.47964 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.5535 | 0.508110 | 0.254055 | − | 0.967190i | \(-0.418236\pi\) | ||||
0.254055 | + | 0.967190i | \(0.418236\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 24.6867 | 0.805620 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 47.2420 | 1.54004 | 0.770022 | − | 0.638017i | \(-0.220245\pi\) | ||||
0.770022 | + | 0.638017i | \(0.220245\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −55.9572 | −1.82222 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.94526 | −0.258459 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −31.0655 | −1.00949 | −0.504747 | − | 0.863268i | \(-0.668414\pi\) | ||||
−0.504747 | + | 0.863268i | \(0.668414\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 33.2723 | 1.08006 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 29.6092 | 0.960144 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.77668 | −0.284304 | −0.142152 | − | 0.989845i | \(-0.545402\pi\) | ||||
−0.142152 | + | 0.989845i | \(0.545402\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 62.0316 | 2.00730 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −36.3052 | −1.17358 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.82982 | 0.0590879 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.5537 | −0.469475 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.57525 | −0.115211 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.98370 | 0.0960488 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −23.9661 | −0.770697 | −0.385348 | − | 0.922771i | \(-0.625919\pi\) | ||||
−0.385348 | + | 0.922771i | \(0.625919\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.42906 | −0.270781 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.9528 | −0.608223 | −0.304112 | − | 0.952636i | \(-0.598360\pi\) | ||||
−0.304112 | + | 0.952636i | \(0.598360\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 38.2616 | 1.22661 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 29.2479 | 0.936683 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −46.2775 | −1.48055 | −0.740274 | − | 0.672305i | \(-0.765304\pi\) | ||||
−0.740274 | + | 0.672305i | \(0.765304\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 25.3833 | 0.811254 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.87869 | −0.219620 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.63097 | −0.243390 | −0.121695 | − | 0.992568i | \(-0.538833\pi\) | ||||
−0.121695 | + | 0.992568i | \(0.538833\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −68.2859 | −2.17577 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.09871 | 0.162294 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −75.1239 | −2.38880 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.91696 | 0.187959 | 0.0939793 | − | 0.995574i | \(-0.470041\pi\) | ||||
0.0939793 | + | 0.995574i | \(0.470041\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.19998 | −0.196750 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −28.7690 | −0.912039 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.25299 | −0.103023 | −0.0515117 | − | 0.998672i | \(-0.516404\pi\) | ||||
−0.0515117 | + | 0.998672i | \(0.516404\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.127532 | 0.00403495 |
(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.m.1.3 | ✓ | 13 | |
4.3 | odd | 2 | 8016.2.a.bg.1.3 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.m.1.3 | ✓ | 13 | 1.1 | even | 1 | trivial | |
8016.2.a.bg.1.3 | 13 | 4.3 | odd | 2 |