Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2166,2,Mod(1,2166)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2166, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2166.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2166 = 2 \cdot 3 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2166.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: | \(17.2955970778\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{20})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} + 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.17557\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2166.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.17557 | 1.42016 | 0.710079 | − | 0.704122i | \(-0.248659\pi\) | ||||
0.710079 | + | 0.704122i | \(0.248659\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0.381966 | 0.144370 | 0.0721848 | − | 0.997391i | \(-0.477003\pi\) | ||||
0.0721848 | + | 0.997391i | \(0.477003\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.17557 | −1.00420 | ||||||||
\(11\) | 2.66605 | 0.803843 | 0.401921 | − | 0.915674i | \(-0.368342\pi\) | ||||
0.401921 | + | 0.915674i | \(0.368342\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 7.04029 | 1.95263 | 0.976313 | − | 0.216362i | \(-0.0694193\pi\) | ||||
0.976313 | + | 0.216362i | \(0.0694193\pi\) | |||||||
\(14\) | −0.381966 | −0.102085 | ||||||||
\(15\) | 3.17557 | 0.819929 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.68915 | 1.13729 | 0.568643 | − | 0.822584i | \(-0.307468\pi\) | ||||
0.568643 | + | 0.822584i | \(0.307468\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 3.17557 | 0.710079 | ||||||||
\(21\) | 0.381966 | 0.0833518 | ||||||||
\(22\) | −2.66605 | −0.568403 | ||||||||
\(23\) | 1.43184 | 0.298560 | 0.149280 | − | 0.988795i | \(-0.452304\pi\) | ||||
0.149280 | + | 0.988795i | \(0.452304\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 5.08425 | 1.01685 | ||||||||
\(26\) | −7.04029 | −1.38072 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.381966 | 0.0721848 | ||||||||
\(29\) | −8.20524 | −1.52368 | −0.761838 | − | 0.647768i | \(-0.775703\pi\) | ||||
−0.761838 | + | 0.647768i | \(0.775703\pi\) | |||||||
\(30\) | −3.17557 | −0.579777 | ||||||||
\(31\) | −8.62750 | −1.54955 | −0.774773 | − | 0.632240i | \(-0.782136\pi\) | ||||
−0.774773 | + | 0.632240i | \(0.782136\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 2.66605 | 0.464099 | ||||||||
\(34\) | −4.68915 | −0.804183 | ||||||||
\(35\) | 1.21296 | 0.205028 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 2.70228 | 0.444252 | 0.222126 | − | 0.975018i | \(-0.428700\pi\) | ||||
0.222126 | + | 0.975018i | \(0.428700\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.04029 | 1.12735 | ||||||||
\(40\) | −3.17557 | −0.502102 | ||||||||
\(41\) | −3.25731 | −0.508707 | −0.254353 | − | 0.967111i | \(-0.581863\pi\) | ||||
−0.254353 | + | 0.967111i | \(0.581863\pi\) | |||||||
\(42\) | −0.381966 | −0.0589386 | ||||||||
\(43\) | −8.72353 | −1.33033 | −0.665163 | − | 0.746699i | \(-0.731638\pi\) | ||||
−0.665163 | + | 0.746699i | \(0.731638\pi\) | |||||||
\(44\) | 2.66605 | 0.401921 | ||||||||
\(45\) | 3.17557 | 0.473386 | ||||||||
\(46\) | −1.43184 | −0.211114 | ||||||||
\(47\) | 5.35706 | 0.781408 | 0.390704 | − | 0.920516i | \(-0.372232\pi\) | ||||
0.390704 | + | 0.920516i | \(0.372232\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −6.85410 | −0.979157 | ||||||||
\(50\) | −5.08425 | −0.719021 | ||||||||
\(51\) | 4.68915 | 0.656613 | ||||||||
\(52\) | 7.04029 | 0.976313 | ||||||||
\(53\) | 8.20524 | 1.12708 | 0.563538 | − | 0.826090i | \(-0.309440\pi\) | ||||
0.563538 | + | 0.826090i | \(0.309440\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 8.46621 | 1.14158 | ||||||||
\(56\) | −0.381966 | −0.0510424 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 8.20524 | 1.07740 | ||||||||
\(59\) | −11.8137 | −1.53801 | −0.769006 | − | 0.639241i | \(-0.779248\pi\) | ||||
−0.769006 | + | 0.639241i | \(0.779248\pi\) | |||||||
\(60\) | 3.17557 | 0.409964 | ||||||||
\(61\) | −5.27044 | −0.674811 | −0.337405 | − | 0.941359i | \(-0.609549\pi\) | ||||
−0.337405 | + | 0.941359i | \(0.609549\pi\) | |||||||
\(62\) | 8.62750 | 1.09569 | ||||||||
\(63\) | 0.381966 | 0.0481232 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 22.3570 | 2.77304 | ||||||||
\(66\) | −2.66605 | −0.328167 | ||||||||
\(67\) | 12.2147 | 1.49226 | 0.746132 | − | 0.665798i | \(-0.231909\pi\) | ||||
0.746132 | + | 0.665798i | \(0.231909\pi\) | |||||||
\(68\) | 4.68915 | 0.568643 | ||||||||
\(69\) | 1.43184 | 0.172374 | ||||||||
\(70\) | −1.21296 | −0.144976 | ||||||||
\(71\) | −15.0996 | −1.79200 | −0.895999 | − | 0.444057i | \(-0.853539\pi\) | ||||
−0.895999 | + | 0.444057i | \(0.853539\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −3.84818 | −0.450395 | −0.225198 | − | 0.974313i | \(-0.572303\pi\) | ||||
−0.225198 | + | 0.974313i | \(0.572303\pi\) | |||||||
\(74\) | −2.70228 | −0.314134 | ||||||||
\(75\) | 5.08425 | 0.587078 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.01834 | 0.116050 | ||||||||
\(78\) | −7.04029 | −0.797156 | ||||||||
\(79\) | −1.39560 | −0.157018 | −0.0785089 | − | 0.996913i | \(-0.525016\pi\) | ||||
−0.0785089 | + | 0.996913i | \(0.525016\pi\) | |||||||
\(80\) | 3.17557 | 0.355040 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.25731 | 0.359710 | ||||||||
\(83\) | −4.31562 | −0.473700 | −0.236850 | − | 0.971546i | \(-0.576115\pi\) | ||||
−0.236850 | + | 0.971546i | \(0.576115\pi\) | |||||||
\(84\) | 0.381966 | 0.0416759 | ||||||||
\(85\) | 14.8907 | 1.61513 | ||||||||
\(86\) | 8.72353 | 0.940682 | ||||||||
\(87\) | −8.20524 | −0.879694 | ||||||||
\(88\) | −2.66605 | −0.284201 | ||||||||
\(89\) | 7.80423 | 0.827246 | 0.413623 | − | 0.910448i | \(-0.364263\pi\) | ||||
0.413623 | + | 0.910448i | \(0.364263\pi\) | |||||||
\(90\) | −3.17557 | −0.334735 | ||||||||
\(91\) | 2.68915 | 0.281900 | ||||||||
\(92\) | 1.43184 | 0.149280 | ||||||||
\(93\) | −8.62750 | −0.894630 | ||||||||
\(94\) | −5.35706 | −0.552539 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −12.7448 | −1.29404 | −0.647018 | − | 0.762475i | \(-0.723984\pi\) | ||||
−0.647018 | + | 0.762475i | \(0.723984\pi\) | |||||||
\(98\) | 6.85410 | 0.692369 | ||||||||
\(99\) | 2.66605 | 0.267948 | ||||||||
\(100\) | 5.08425 | 0.508425 | ||||||||
\(101\) | 3.56597 | 0.354827 | 0.177413 | − | 0.984136i | \(-0.443227\pi\) | ||||
0.177413 | + | 0.984136i | \(0.443227\pi\) | |||||||
\(102\) | −4.68915 | −0.464295 | ||||||||
\(103\) | −7.04216 | −0.693885 | −0.346942 | − | 0.937886i | \(-0.612780\pi\) | ||||
−0.346942 | + | 0.937886i | \(0.612780\pi\) | |||||||
\(104\) | −7.04029 | −0.690358 | ||||||||
\(105\) | 1.21296 | 0.118373 | ||||||||
\(106\) | −8.20524 | −0.796964 | ||||||||
\(107\) | −3.63116 | −0.351038 | −0.175519 | − | 0.984476i | \(-0.556160\pi\) | ||||
−0.175519 | + | 0.984476i | \(0.556160\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −3.46621 | −0.332003 | −0.166002 | − | 0.986125i | \(-0.553086\pi\) | ||||
−0.166002 | + | 0.986125i | \(0.553086\pi\) | |||||||
\(110\) | −8.46621 | −0.807222 | ||||||||
\(111\) | 2.70228 | 0.256489 | ||||||||
\(112\) | 0.381966 | 0.0360924 | ||||||||
\(113\) | 10.2764 | 0.966719 | 0.483359 | − | 0.875422i | \(-0.339416\pi\) | ||||
0.483359 | + | 0.875422i | \(0.339416\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.54691 | 0.424002 | ||||||||
\(116\) | −8.20524 | −0.761838 | ||||||||
\(117\) | 7.04029 | 0.650875 | ||||||||
\(118\) | 11.8137 | 1.08754 | ||||||||
\(119\) | 1.79110 | 0.164190 | ||||||||
\(120\) | −3.17557 | −0.289889 | ||||||||
\(121\) | −3.89220 | −0.353837 | ||||||||
\(122\) | 5.27044 | 0.477163 | ||||||||
\(123\) | −3.25731 | −0.293702 | ||||||||
\(124\) | −8.62750 | −0.774773 | ||||||||
\(125\) | 0.267536 | 0.0239291 | ||||||||
\(126\) | −0.381966 | −0.0340282 | ||||||||
\(127\) | −21.2723 | −1.88761 | −0.943806 | − | 0.330500i | \(-0.892783\pi\) | ||||
−0.943806 | + | 0.330500i | \(0.892783\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −8.72353 | −0.768064 | ||||||||
\(130\) | −22.3570 | −1.96083 | ||||||||
\(131\) | 2.93731 | 0.256634 | 0.128317 | − | 0.991733i | \(-0.459043\pi\) | ||||
0.128317 | + | 0.991733i | \(0.459043\pi\) | |||||||
\(132\) | 2.66605 | 0.232049 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −12.2147 | −1.05519 | ||||||||
\(135\) | 3.17557 | 0.273310 | ||||||||
\(136\) | −4.68915 | −0.402092 | ||||||||
\(137\) | 7.61218 | 0.650353 | 0.325176 | − | 0.945653i | \(-0.394576\pi\) | ||||
0.325176 | + | 0.945653i | \(0.394576\pi\) | |||||||
\(138\) | −1.43184 | −0.121886 | ||||||||
\(139\) | 0.434034 | 0.0368143 | 0.0184071 | − | 0.999831i | \(-0.494140\pi\) | ||||
0.0184071 | + | 0.999831i | \(0.494140\pi\) | |||||||
\(140\) | 1.21296 | 0.102514 | ||||||||
\(141\) | 5.35706 | 0.451146 | ||||||||
\(142\) | 15.0996 | 1.26713 | ||||||||
\(143\) | 18.7697 | 1.56960 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −26.0563 | −2.16386 | ||||||||
\(146\) | 3.84818 | 0.318478 | ||||||||
\(147\) | −6.85410 | −0.565317 | ||||||||
\(148\) | 2.70228 | 0.222126 | ||||||||
\(149\) | 17.1352 | 1.40377 | 0.701884 | − | 0.712292i | \(-0.252343\pi\) | ||||
0.701884 | + | 0.712292i | \(0.252343\pi\) | |||||||
\(150\) | −5.08425 | −0.415127 | ||||||||
\(151\) | 9.31852 | 0.758330 | 0.379165 | − | 0.925329i | \(-0.376211\pi\) | ||||
0.379165 | + | 0.925329i | \(0.376211\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.68915 | 0.379096 | ||||||||
\(154\) | −1.01834 | −0.0820601 | ||||||||
\(155\) | −27.3972 | −2.20060 | ||||||||
\(156\) | 7.04029 | 0.563675 | ||||||||
\(157\) | −17.6428 | −1.40805 | −0.704025 | − | 0.710175i | \(-0.748616\pi\) | ||||
−0.704025 | + | 0.710175i | \(0.748616\pi\) | |||||||
\(158\) | 1.39560 | 0.111028 | ||||||||
\(159\) | 8.20524 | 0.650718 | ||||||||
\(160\) | −3.17557 | −0.251051 | ||||||||
\(161\) | 0.546915 | 0.0431029 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −7.25731 | −0.568436 | −0.284218 | − | 0.958760i | \(-0.591734\pi\) | ||||
−0.284218 | + | 0.958760i | \(0.591734\pi\) | |||||||
\(164\) | −3.25731 | −0.254353 | ||||||||
\(165\) | 8.46621 | 0.659094 | ||||||||
\(166\) | 4.31562 | 0.334957 | ||||||||
\(167\) | 11.8386 | 0.916098 | 0.458049 | − | 0.888927i | \(-0.348548\pi\) | ||||
0.458049 | + | 0.888927i | \(0.348548\pi\) | |||||||
\(168\) | −0.381966 | −0.0294693 | ||||||||
\(169\) | 36.5657 | 2.81275 | ||||||||
\(170\) | −14.8907 | −1.14207 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −8.72353 | −0.665163 | ||||||||
\(173\) | 15.0711 | 1.14584 | 0.572918 | − | 0.819613i | \(-0.305811\pi\) | ||||
0.572918 | + | 0.819613i | \(0.305811\pi\) | |||||||
\(174\) | 8.20524 | 0.622038 | ||||||||
\(175\) | 1.94201 | 0.146802 | ||||||||
\(176\) | 2.66605 | 0.200961 | ||||||||
\(177\) | −11.8137 | −0.887972 | ||||||||
\(178\) | −7.80423 | −0.584951 | ||||||||
\(179\) | 0.0630049 | 0.00470921 | 0.00235460 | − | 0.999997i | \(-0.499251\pi\) | ||||
0.00235460 | + | 0.999997i | \(0.499251\pi\) | |||||||
\(180\) | 3.17557 | 0.236693 | ||||||||
\(181\) | 3.79110 | 0.281790 | 0.140895 | − | 0.990025i | \(-0.455002\pi\) | ||||
0.140895 | + | 0.990025i | \(0.455002\pi\) | |||||||
\(182\) | −2.68915 | −0.199333 | ||||||||
\(183\) | −5.27044 | −0.389602 | ||||||||
\(184\) | −1.43184 | −0.105557 | ||||||||
\(185\) | 8.58129 | 0.630909 | ||||||||
\(186\) | 8.62750 | 0.632599 | ||||||||
\(187\) | 12.5015 | 0.914200 | ||||||||
\(188\) | 5.35706 | 0.390704 | ||||||||
\(189\) | 0.381966 | 0.0277839 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 26.2572 | 1.89990 | 0.949952 | − | 0.312396i | \(-0.101131\pi\) | ||||
0.949952 | + | 0.312396i | \(0.101131\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −11.8897 | −0.855839 | −0.427920 | − | 0.903817i | \(-0.640753\pi\) | ||||
−0.427920 | + | 0.903817i | \(0.640753\pi\) | |||||||
\(194\) | 12.7448 | 0.915021 | ||||||||
\(195\) | 22.3570 | 1.60101 | ||||||||
\(196\) | −6.85410 | −0.489579 | ||||||||
\(197\) | −8.00186 | −0.570109 | −0.285055 | − | 0.958511i | \(-0.592012\pi\) | ||||
−0.285055 | + | 0.958511i | \(0.592012\pi\) | |||||||
\(198\) | −2.66605 | −0.189468 | ||||||||
\(199\) | −24.3452 | −1.72578 | −0.862892 | − | 0.505389i | \(-0.831349\pi\) | ||||
−0.862892 | + | 0.505389i | \(0.831349\pi\) | |||||||
\(200\) | −5.08425 | −0.359511 | ||||||||
\(201\) | 12.2147 | 0.861559 | ||||||||
\(202\) | −3.56597 | −0.250900 | ||||||||
\(203\) | −3.13412 | −0.219972 | ||||||||
\(204\) | 4.68915 | 0.328306 | ||||||||
\(205\) | −10.3438 | −0.722444 | ||||||||
\(206\) | 7.04216 | 0.490650 | ||||||||
\(207\) | 1.43184 | 0.0995199 | ||||||||
\(208\) | 7.04029 | 0.488157 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −1.21296 | −0.0837022 | ||||||||
\(211\) | 20.2016 | 1.39073 | 0.695367 | − | 0.718655i | \(-0.255242\pi\) | ||||
0.695367 | + | 0.718655i | \(0.255242\pi\) | |||||||
\(212\) | 8.20524 | 0.563538 | ||||||||
\(213\) | −15.0996 | −1.03461 | ||||||||
\(214\) | 3.63116 | 0.248221 | ||||||||
\(215\) | −27.7022 | −1.88927 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −3.29541 | −0.223707 | ||||||||
\(218\) | 3.46621 | 0.234762 | ||||||||
\(219\) | −3.84818 | −0.260036 | ||||||||
\(220\) | 8.46621 | 0.570792 | ||||||||
\(221\) | 33.0130 | 2.22070 | ||||||||
\(222\) | −2.70228 | −0.181365 | ||||||||
\(223\) | 18.3581 | 1.22935 | 0.614675 | − | 0.788781i | \(-0.289287\pi\) | ||||
0.614675 | + | 0.788781i | \(0.289287\pi\) | |||||||
\(224\) | −0.381966 | −0.0255212 | ||||||||
\(225\) | 5.08425 | 0.338950 | ||||||||
\(226\) | −10.2764 | −0.683573 | ||||||||
\(227\) | −1.53141 | −0.101643 | −0.0508217 | − | 0.998708i | \(-0.516184\pi\) | ||||
−0.0508217 | + | 0.998708i | \(0.516184\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.2381 | −1.40346 | −0.701728 | − | 0.712445i | \(-0.747588\pi\) | ||||
−0.701728 | + | 0.712445i | \(0.747588\pi\) | |||||||
\(230\) | −4.54691 | −0.299815 | ||||||||
\(231\) | 1.01834 | 0.0670018 | ||||||||
\(232\) | 8.20524 | 0.538701 | ||||||||
\(233\) | −10.9655 | −0.718375 | −0.359187 | − | 0.933265i | \(-0.616946\pi\) | ||||
−0.359187 | + | 0.933265i | \(0.616946\pi\) | |||||||
\(234\) | −7.04029 | −0.460238 | ||||||||
\(235\) | 17.0117 | 1.10972 | ||||||||
\(236\) | −11.8137 | −0.769006 | ||||||||
\(237\) | −1.39560 | −0.0906543 | ||||||||
\(238\) | −1.79110 | −0.116100 | ||||||||
\(239\) | −6.85765 | −0.443584 | −0.221792 | − | 0.975094i | \(-0.571191\pi\) | ||||
−0.221792 | + | 0.975094i | \(0.571191\pi\) | |||||||
\(240\) | 3.17557 | 0.204982 | ||||||||
\(241\) | 19.1109 | 1.23104 | 0.615521 | − | 0.788121i | \(-0.288946\pi\) | ||||
0.615521 | + | 0.788121i | \(0.288946\pi\) | |||||||
\(242\) | 3.89220 | 0.250200 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −5.27044 | −0.337405 | ||||||||
\(245\) | −21.7657 | −1.39056 | ||||||||
\(246\) | 3.25731 | 0.207679 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 8.62750 | 0.547847 | ||||||||
\(249\) | −4.31562 | −0.273491 | ||||||||
\(250\) | −0.267536 | −0.0169204 | ||||||||
\(251\) | 10.5165 | 0.663795 | 0.331897 | − | 0.943315i | \(-0.392311\pi\) | ||||
0.331897 | + | 0.943315i | \(0.392311\pi\) | |||||||
\(252\) | 0.381966 | 0.0240616 | ||||||||
\(253\) | 3.81736 | 0.239995 | ||||||||
\(254\) | 21.2723 | 1.33474 | ||||||||
\(255\) | 14.8907 | 0.932494 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.60637 | 0.100203 | 0.0501014 | − | 0.998744i | \(-0.484046\pi\) | ||||
0.0501014 | + | 0.998744i | \(0.484046\pi\) | |||||||
\(258\) | 8.72353 | 0.543103 | ||||||||
\(259\) | 1.03218 | 0.0641365 | ||||||||
\(260\) | 22.3570 | 1.38652 | ||||||||
\(261\) | −8.20524 | −0.507892 | ||||||||
\(262\) | −2.93731 | −0.181468 | ||||||||
\(263\) | 13.4471 | 0.829181 | 0.414590 | − | 0.910008i | \(-0.363925\pi\) | ||||
0.414590 | + | 0.910008i | \(0.363925\pi\) | |||||||
\(264\) | −2.66605 | −0.164084 | ||||||||
\(265\) | 26.0563 | 1.60063 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.80423 | 0.477611 | ||||||||
\(268\) | 12.2147 | 0.746132 | ||||||||
\(269\) | 22.5492 | 1.37485 | 0.687424 | − | 0.726257i | \(-0.258742\pi\) | ||||
0.687424 | + | 0.726257i | \(0.258742\pi\) | |||||||
\(270\) | −3.17557 | −0.193259 | ||||||||
\(271\) | −5.02260 | −0.305101 | −0.152551 | − | 0.988296i | \(-0.548749\pi\) | ||||
−0.152551 | + | 0.988296i | \(0.548749\pi\) | |||||||
\(272\) | 4.68915 | 0.284322 | ||||||||
\(273\) | 2.68915 | 0.162755 | ||||||||
\(274\) | −7.61218 | −0.459869 | ||||||||
\(275\) | 13.5548 | 0.817387 | ||||||||
\(276\) | 1.43184 | 0.0861868 | ||||||||
\(277\) | 2.11288 | 0.126951 | 0.0634754 | − | 0.997983i | \(-0.479782\pi\) | ||||
0.0634754 | + | 0.997983i | \(0.479782\pi\) | |||||||
\(278\) | −0.434034 | −0.0260316 | ||||||||
\(279\) | −8.62750 | −0.516515 | ||||||||
\(280\) | −1.21296 | −0.0724882 | ||||||||
\(281\) | 18.7616 | 1.11922 | 0.559612 | − | 0.828754i | \(-0.310950\pi\) | ||||
0.559612 | + | 0.828754i | \(0.310950\pi\) | |||||||
\(282\) | −5.35706 | −0.319008 | ||||||||
\(283\) | −1.38434 | −0.0822905 | −0.0411453 | − | 0.999153i | \(-0.513101\pi\) | ||||
−0.0411453 | + | 0.999153i | \(0.513101\pi\) | |||||||
\(284\) | −15.0996 | −0.895999 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −18.7697 | −1.10988 | ||||||||
\(287\) | −1.24418 | −0.0734417 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 4.98816 | 0.293421 | ||||||||
\(290\) | 26.0563 | 1.53008 | ||||||||
\(291\) | −12.7448 | −0.747112 | ||||||||
\(292\) | −3.84818 | −0.225198 | ||||||||
\(293\) | 0.226599 | 0.0132381 | 0.00661903 | − | 0.999978i | \(-0.497893\pi\) | ||||
0.00661903 | + | 0.999978i | \(0.497893\pi\) | |||||||
\(294\) | 6.85410 | 0.399739 | ||||||||
\(295\) | −37.5152 | −2.18422 | ||||||||
\(296\) | −2.70228 | −0.157067 | ||||||||
\(297\) | 2.66605 | 0.154700 | ||||||||
\(298\) | −17.1352 | −0.992613 | ||||||||
\(299\) | 10.0806 | 0.582975 | ||||||||
\(300\) | 5.08425 | 0.293539 | ||||||||
\(301\) | −3.33209 | −0.192058 | ||||||||
\(302\) | −9.31852 | −0.536221 | ||||||||
\(303\) | 3.56597 | 0.204859 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −16.7367 | −0.958338 | ||||||||
\(306\) | −4.68915 | −0.268061 | ||||||||
\(307\) | −22.4853 | −1.28330 | −0.641651 | − | 0.766997i | \(-0.721750\pi\) | ||||
−0.641651 | + | 0.766997i | \(0.721750\pi\) | |||||||
\(308\) | 1.01834 | 0.0580252 | ||||||||
\(309\) | −7.04216 | −0.400614 | ||||||||
\(310\) | 27.3972 | 1.55606 | ||||||||
\(311\) | −4.22513 | −0.239585 | −0.119793 | − | 0.992799i | \(-0.538223\pi\) | ||||
−0.119793 | + | 0.992799i | \(0.538223\pi\) | |||||||
\(312\) | −7.04029 | −0.398578 | ||||||||
\(313\) | 2.09455 | 0.118391 | 0.0591956 | − | 0.998246i | \(-0.481146\pi\) | ||||
0.0591956 | + | 0.998246i | \(0.481146\pi\) | |||||||
\(314\) | 17.6428 | 0.995642 | ||||||||
\(315\) | 1.21296 | 0.0683426 | ||||||||
\(316\) | −1.39560 | −0.0785089 | ||||||||
\(317\) | 1.95616 | 0.109869 | 0.0549344 | − | 0.998490i | \(-0.482505\pi\) | ||||
0.0549344 | + | 0.998490i | \(0.482505\pi\) | |||||||
\(318\) | −8.20524 | −0.460127 | ||||||||
\(319\) | −21.8755 | −1.22480 | ||||||||
\(320\) | 3.17557 | 0.177520 | ||||||||
\(321\) | −3.63116 | −0.202672 | ||||||||
\(322\) | −0.546915 | −0.0304784 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 35.7946 | 1.98553 | ||||||||
\(326\) | 7.25731 | 0.401945 | ||||||||
\(327\) | −3.46621 | −0.191682 | ||||||||
\(328\) | 3.25731 | 0.179855 | ||||||||
\(329\) | 2.04622 | 0.112812 | ||||||||
\(330\) | −8.46621 | −0.466050 | ||||||||
\(331\) | −8.23015 | −0.452370 | −0.226185 | − | 0.974084i | \(-0.572625\pi\) | ||||
−0.226185 | + | 0.974084i | \(0.572625\pi\) | |||||||
\(332\) | −4.31562 | −0.236850 | ||||||||
\(333\) | 2.70228 | 0.148084 | ||||||||
\(334\) | −11.8386 | −0.647779 | ||||||||
\(335\) | 38.7887 | 2.11925 | ||||||||
\(336\) | 0.381966 | 0.0208380 | ||||||||
\(337\) | 7.56597 | 0.412144 | 0.206072 | − | 0.978537i | \(-0.433932\pi\) | ||||
0.206072 | + | 0.978537i | \(0.433932\pi\) | |||||||
\(338\) | −36.5657 | −1.98891 | ||||||||
\(339\) | 10.2764 | 0.558135 | ||||||||
\(340\) | 14.8907 | 0.807564 | ||||||||
\(341\) | −23.0013 | −1.24559 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.29180 | −0.285730 | ||||||||
\(344\) | 8.72353 | 0.470341 | ||||||||
\(345\) | 4.54691 | 0.244798 | ||||||||
\(346\) | −15.0711 | −0.810228 | ||||||||
\(347\) | −24.5084 | −1.31568 | −0.657839 | − | 0.753158i | \(-0.728529\pi\) | ||||
−0.657839 | + | 0.753158i | \(0.728529\pi\) | |||||||
\(348\) | −8.20524 | −0.439847 | ||||||||
\(349\) | −10.5278 | −0.563538 | −0.281769 | − | 0.959482i | \(-0.590921\pi\) | ||||
−0.281769 | + | 0.959482i | \(0.590921\pi\) | |||||||
\(350\) | −1.94201 | −0.103805 | ||||||||
\(351\) | 7.04029 | 0.375783 | ||||||||
\(352\) | −2.66605 | −0.142101 | ||||||||
\(353\) | 11.0249 | 0.586794 | 0.293397 | − | 0.955991i | \(-0.405214\pi\) | ||||
0.293397 | + | 0.955991i | \(0.405214\pi\) | |||||||
\(354\) | 11.8137 | 0.627891 | ||||||||
\(355\) | −47.9500 | −2.54492 | ||||||||
\(356\) | 7.80423 | 0.413623 | ||||||||
\(357\) | 1.79110 | 0.0947949 | ||||||||
\(358\) | −0.0630049 | −0.00332991 | ||||||||
\(359\) | −5.60034 | −0.295575 | −0.147787 | − | 0.989019i | \(-0.547215\pi\) | ||||
−0.147787 | + | 0.989019i | \(0.547215\pi\) | |||||||
\(360\) | −3.17557 | −0.167367 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −3.79110 | −0.199256 | ||||||||
\(363\) | −3.89220 | −0.204288 | ||||||||
\(364\) | 2.68915 | 0.140950 | ||||||||
\(365\) | −12.2202 | −0.639633 | ||||||||
\(366\) | 5.27044 | 0.275490 | ||||||||
\(367\) | 37.3238 | 1.94828 | 0.974142 | − | 0.225937i | \(-0.0725443\pi\) | ||||
0.974142 | + | 0.225937i | \(0.0725443\pi\) | |||||||
\(368\) | 1.43184 | 0.0746399 | ||||||||
\(369\) | −3.25731 | −0.169569 | ||||||||
\(370\) | −8.58129 | −0.446120 | ||||||||
\(371\) | 3.13412 | 0.162716 | ||||||||
\(372\) | −8.62750 | −0.447315 | ||||||||
\(373\) | −29.4141 | −1.52300 | −0.761502 | − | 0.648162i | \(-0.775538\pi\) | ||||
−0.761502 | + | 0.648162i | \(0.775538\pi\) | |||||||
\(374\) | −12.5015 | −0.646437 | ||||||||
\(375\) | 0.267536 | 0.0138155 | ||||||||
\(376\) | −5.35706 | −0.276269 | ||||||||
\(377\) | −57.7673 | −2.97517 | ||||||||
\(378\) | −0.381966 | −0.0196462 | ||||||||
\(379\) | −28.2454 | −1.45087 | −0.725433 | − | 0.688293i | \(-0.758361\pi\) | ||||
−0.725433 | + | 0.688293i | \(0.758361\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −21.2723 | −1.08981 | ||||||||
\(382\) | −26.2572 | −1.34344 | ||||||||
\(383\) | 16.8254 | 0.859736 | 0.429868 | − | 0.902892i | \(-0.358560\pi\) | ||||
0.429868 | + | 0.902892i | \(0.358560\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 3.23381 | 0.164810 | ||||||||
\(386\) | 11.8897 | 0.605170 | ||||||||
\(387\) | −8.72353 | −0.443442 | ||||||||
\(388\) | −12.7448 | −0.647018 | ||||||||
\(389\) | 1.57035 | 0.0796199 | 0.0398100 | − | 0.999207i | \(-0.487325\pi\) | ||||
0.0398100 | + | 0.999207i | \(0.487325\pi\) | |||||||
\(390\) | −22.3570 | −1.13209 | ||||||||
\(391\) | 6.71413 | 0.339548 | ||||||||
\(392\) | 6.85410 | 0.346184 | ||||||||
\(393\) | 2.93731 | 0.148168 | ||||||||
\(394\) | 8.00186 | 0.403128 | ||||||||
\(395\) | −4.43184 | −0.222990 | ||||||||
\(396\) | 2.66605 | 0.133974 | ||||||||
\(397\) | 3.08780 | 0.154972 | 0.0774860 | − | 0.996993i | \(-0.475311\pi\) | ||||
0.0774860 | + | 0.996993i | \(0.475311\pi\) | |||||||
\(398\) | 24.3452 | 1.22031 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.08425 | 0.254212 | ||||||||
\(401\) | −3.92895 | −0.196202 | −0.0981012 | − | 0.995176i | \(-0.531277\pi\) | ||||
−0.0981012 | + | 0.995176i | \(0.531277\pi\) | |||||||
\(402\) | −12.2147 | −0.609214 | ||||||||
\(403\) | −60.7402 | −3.02568 | ||||||||
\(404\) | 3.56597 | 0.177413 | ||||||||
\(405\) | 3.17557 | 0.157795 | ||||||||
\(406\) | 3.13412 | 0.155544 | ||||||||
\(407\) | 7.20441 | 0.357109 | ||||||||
\(408\) | −4.68915 | −0.232148 | ||||||||
\(409\) | 28.7032 | 1.41928 | 0.709641 | − | 0.704563i | \(-0.248857\pi\) | ||||
0.709641 | + | 0.704563i | \(0.248857\pi\) | |||||||
\(410\) | 10.3438 | 0.510845 | ||||||||
\(411\) | 7.61218 | 0.375481 | ||||||||
\(412\) | −7.04216 | −0.346942 | ||||||||
\(413\) | −4.51243 | −0.222042 | ||||||||
\(414\) | −1.43184 | −0.0703712 | ||||||||
\(415\) | −13.7045 | −0.672730 | ||||||||
\(416\) | −7.04029 | −0.345179 | ||||||||
\(417\) | 0.434034 | 0.0212547 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.73663 | −0.182547 | −0.0912733 | − | 0.995826i | \(-0.529094\pi\) | ||||
−0.0912733 | + | 0.995826i | \(0.529094\pi\) | |||||||
\(420\) | 1.21296 | 0.0591864 | ||||||||
\(421\) | 21.6928 | 1.05724 | 0.528620 | − | 0.848858i | \(-0.322709\pi\) | ||||
0.528620 | + | 0.848858i | \(0.322709\pi\) | |||||||
\(422\) | −20.2016 | −0.983398 | ||||||||
\(423\) | 5.35706 | 0.260469 | ||||||||
\(424\) | −8.20524 | −0.398482 | ||||||||
\(425\) | 23.8408 | 1.15645 | ||||||||
\(426\) | 15.0996 | 0.731580 | ||||||||
\(427\) | −2.01313 | −0.0974221 | ||||||||
\(428\) | −3.63116 | −0.175519 | ||||||||
\(429\) | 18.7697 | 0.906212 | ||||||||
\(430\) | 27.7022 | 1.33592 | ||||||||
\(431\) | 5.09756 | 0.245541 | 0.122770 | − | 0.992435i | \(-0.460822\pi\) | ||||
0.122770 | + | 0.992435i | \(0.460822\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 18.1903 | 0.874171 | 0.437085 | − | 0.899420i | \(-0.356011\pi\) | ||||
0.437085 | + | 0.899420i | \(0.356011\pi\) | |||||||
\(434\) | 3.29541 | 0.158185 | ||||||||
\(435\) | −26.0563 | −1.24931 | ||||||||
\(436\) | −3.46621 | −0.166002 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 3.84818 | 0.183873 | ||||||||
\(439\) | 29.4760 | 1.40681 | 0.703406 | − | 0.710789i | \(-0.251662\pi\) | ||||
0.703406 | + | 0.710789i | \(0.251662\pi\) | |||||||
\(440\) | −8.46621 | −0.403611 | ||||||||
\(441\) | −6.85410 | −0.326386 | ||||||||
\(442\) | −33.0130 | −1.57027 | ||||||||
\(443\) | −20.6001 | −0.978740 | −0.489370 | − | 0.872076i | \(-0.662773\pi\) | ||||
−0.489370 | + | 0.872076i | \(0.662773\pi\) | |||||||
\(444\) | 2.70228 | 0.128245 | ||||||||
\(445\) | 24.7829 | 1.17482 | ||||||||
\(446\) | −18.3581 | −0.869281 | ||||||||
\(447\) | 17.1352 | 0.810465 | ||||||||
\(448\) | 0.381966 | 0.0180462 | ||||||||
\(449\) | 5.32606 | 0.251352 | 0.125676 | − | 0.992071i | \(-0.459890\pi\) | ||||
0.125676 | + | 0.992071i | \(0.459890\pi\) | |||||||
\(450\) | −5.08425 | −0.239674 | ||||||||
\(451\) | −8.68414 | −0.408920 | ||||||||
\(452\) | 10.2764 | 0.483359 | ||||||||
\(453\) | 9.31852 | 0.437822 | ||||||||
\(454\) | 1.53141 | 0.0718727 | ||||||||
\(455\) | 8.53960 | 0.400342 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.5527 | −0.680748 | −0.340374 | − | 0.940290i | \(-0.610554\pi\) | ||||
−0.340374 | + | 0.940290i | \(0.610554\pi\) | |||||||
\(458\) | 21.2381 | 0.992393 | ||||||||
\(459\) | 4.68915 | 0.218871 | ||||||||
\(460\) | 4.54691 | 0.212001 | ||||||||
\(461\) | −27.7283 | −1.29144 | −0.645718 | − | 0.763576i | \(-0.723442\pi\) | ||||
−0.645718 | + | 0.763576i | \(0.723442\pi\) | |||||||
\(462\) | −1.01834 | −0.0473774 | ||||||||
\(463\) | 3.33216 | 0.154859 | 0.0774293 | − | 0.996998i | \(-0.475329\pi\) | ||||
0.0774293 | + | 0.996998i | \(0.475329\pi\) | |||||||
\(464\) | −8.20524 | −0.380919 | ||||||||
\(465\) | −27.3972 | −1.27052 | ||||||||
\(466\) | 10.9655 | 0.507968 | ||||||||
\(467\) | 1.33094 | 0.0615884 | 0.0307942 | − | 0.999526i | \(-0.490196\pi\) | ||||
0.0307942 | + | 0.999526i | \(0.490196\pi\) | |||||||
\(468\) | 7.04029 | 0.325438 | ||||||||
\(469\) | 4.66560 | 0.215438 | ||||||||
\(470\) | −17.0117 | −0.784693 | ||||||||
\(471\) | −17.6428 | −0.812938 | ||||||||
\(472\) | 11.8137 | 0.543769 | ||||||||
\(473\) | −23.2573 | −1.06937 | ||||||||
\(474\) | 1.39560 | 0.0641023 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.79110 | 0.0820948 | ||||||||
\(477\) | 8.20524 | 0.375692 | ||||||||
\(478\) | 6.85765 | 0.313662 | ||||||||
\(479\) | −37.1883 | −1.69918 | −0.849589 | − | 0.527445i | \(-0.823150\pi\) | ||||
−0.849589 | + | 0.527445i | \(0.823150\pi\) | |||||||
\(480\) | −3.17557 | −0.144944 | ||||||||
\(481\) | 19.0249 | 0.867459 | ||||||||
\(482\) | −19.1109 | −0.870478 | ||||||||
\(483\) | 0.546915 | 0.0248855 | ||||||||
\(484\) | −3.89220 | −0.176918 | ||||||||
\(485\) | −40.4719 | −1.83773 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 25.6013 | 1.16010 | 0.580052 | − | 0.814579i | \(-0.303032\pi\) | ||||
0.580052 | + | 0.814579i | \(0.303032\pi\) | |||||||
\(488\) | 5.27044 | 0.238582 | ||||||||
\(489\) | −7.25731 | −0.328187 | ||||||||
\(490\) | 21.7657 | 0.983273 | ||||||||
\(491\) | 25.3711 | 1.14498 | 0.572491 | − | 0.819911i | \(-0.305977\pi\) | ||||
0.572491 | + | 0.819911i | \(0.305977\pi\) | |||||||
\(492\) | −3.25731 | −0.146851 | ||||||||
\(493\) | −38.4756 | −1.73286 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.46621 | 0.380528 | ||||||||
\(496\) | −8.62750 | −0.387386 | ||||||||
\(497\) | −5.76755 | −0.258710 | ||||||||
\(498\) | 4.31562 | 0.193387 | ||||||||
\(499\) | 21.0996 | 0.944550 | 0.472275 | − | 0.881451i | \(-0.343433\pi\) | ||||
0.472275 | + | 0.881451i | \(0.343433\pi\) | |||||||
\(500\) | 0.267536 | 0.0119646 | ||||||||
\(501\) | 11.8386 | 0.528910 | ||||||||
\(502\) | −10.5165 | −0.469374 | ||||||||
\(503\) | −26.7154 | −1.19118 | −0.595591 | − | 0.803288i | \(-0.703082\pi\) | ||||
−0.595591 | + | 0.803288i | \(0.703082\pi\) | |||||||
\(504\) | −0.381966 | −0.0170141 | ||||||||
\(505\) | 11.3240 | 0.503910 | ||||||||
\(506\) | −3.81736 | −0.169702 | ||||||||
\(507\) | 36.5657 | 1.62394 | ||||||||
\(508\) | −21.2723 | −0.943806 | ||||||||
\(509\) | 4.44943 | 0.197217 | 0.0986087 | − | 0.995126i | \(-0.468561\pi\) | ||||
0.0986087 | + | 0.995126i | \(0.468561\pi\) | |||||||
\(510\) | −14.8907 | −0.659373 | ||||||||
\(511\) | −1.46987 | −0.0650234 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.60637 | −0.0708541 | ||||||||
\(515\) | −22.3629 | −0.985426 | ||||||||
\(516\) | −8.72353 | −0.384032 | ||||||||
\(517\) | 14.2822 | 0.628129 | ||||||||
\(518\) | −1.03218 | −0.0453514 | ||||||||
\(519\) | 15.0711 | 0.661549 | ||||||||
\(520\) | −22.3570 | −0.980417 | ||||||||
\(521\) | 4.52798 | 0.198374 | 0.0991871 | − | 0.995069i | \(-0.468376\pi\) | ||||
0.0991871 | + | 0.995069i | \(0.468376\pi\) | |||||||
\(522\) | 8.20524 | 0.359134 | ||||||||
\(523\) | 3.84233 | 0.168013 | 0.0840066 | − | 0.996465i | \(-0.473228\pi\) | ||||
0.0840066 | + | 0.996465i | \(0.473228\pi\) | |||||||
\(524\) | 2.93731 | 0.128317 | ||||||||
\(525\) | 1.94201 | 0.0847563 | ||||||||
\(526\) | −13.4471 | −0.586319 | ||||||||
\(527\) | −40.4557 | −1.76228 | ||||||||
\(528\) | 2.66605 | 0.116025 | ||||||||
\(529\) | −20.9498 | −0.910862 | ||||||||
\(530\) | −26.0563 | −1.13181 | ||||||||
\(531\) | −11.8137 | −0.512671 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −22.9324 | −0.993314 | ||||||||
\(534\) | −7.80423 | −0.337722 | ||||||||
\(535\) | −11.5310 | −0.498529 | ||||||||
\(536\) | −12.2147 | −0.527595 | ||||||||
\(537\) | 0.0630049 | 0.00271886 | ||||||||
\(538\) | −22.5492 | −0.972164 | ||||||||
\(539\) | −18.2733 | −0.787089 | ||||||||
\(540\) | 3.17557 | 0.136655 | ||||||||
\(541\) | −2.76766 | −0.118991 | −0.0594955 | − | 0.998229i | \(-0.518949\pi\) | ||||
−0.0594955 | + | 0.998229i | \(0.518949\pi\) | |||||||
\(542\) | 5.02260 | 0.215739 | ||||||||
\(543\) | 3.79110 | 0.162692 | ||||||||
\(544\) | −4.68915 | −0.201046 | ||||||||
\(545\) | −11.0072 | −0.471497 | ||||||||
\(546\) | −2.68915 | −0.115085 | ||||||||
\(547\) | 4.23955 | 0.181270 | 0.0906349 | − | 0.995884i | \(-0.471110\pi\) | ||||
0.0906349 | + | 0.995884i | \(0.471110\pi\) | |||||||
\(548\) | 7.61218 | 0.325176 | ||||||||
\(549\) | −5.27044 | −0.224937 | ||||||||
\(550\) | −13.5548 | −0.577980 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −1.43184 | −0.0609432 | ||||||||
\(553\) | −0.533074 | −0.0226686 | ||||||||
\(554\) | −2.11288 | −0.0897677 | ||||||||
\(555\) | 8.58129 | 0.364255 | ||||||||
\(556\) | 0.434034 | 0.0184071 | ||||||||
\(557\) | −17.5035 | −0.741646 | −0.370823 | − | 0.928704i | \(-0.620924\pi\) | ||||
−0.370823 | + | 0.928704i | \(0.620924\pi\) | |||||||
\(558\) | 8.62750 | 0.365231 | ||||||||
\(559\) | −61.4162 | −2.59763 | ||||||||
\(560\) | 1.21296 | 0.0512569 | ||||||||
\(561\) | 12.5015 | 0.527813 | ||||||||
\(562\) | −18.7616 | −0.791411 | ||||||||
\(563\) | −6.45162 | −0.271903 | −0.135952 | − | 0.990715i | \(-0.543409\pi\) | ||||
−0.135952 | + | 0.990715i | \(0.543409\pi\) | |||||||
\(564\) | 5.35706 | 0.225573 | ||||||||
\(565\) | 32.6333 | 1.37289 | ||||||||
\(566\) | 1.38434 | 0.0581882 | ||||||||
\(567\) | 0.381966 | 0.0160411 | ||||||||
\(568\) | 15.0996 | 0.633567 | ||||||||
\(569\) | 0.506508 | 0.0212339 | 0.0106170 | − | 0.999944i | \(-0.496620\pi\) | ||||
0.0106170 | + | 0.999944i | \(0.496620\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.08999 | 0.0874633 | 0.0437316 | − | 0.999043i | \(-0.486075\pi\) | ||||
0.0437316 | + | 0.999043i | \(0.486075\pi\) | |||||||
\(572\) | 18.7697 | 0.784802 | ||||||||
\(573\) | 26.2572 | 1.09691 | ||||||||
\(574\) | 1.24418 | 0.0519312 | ||||||||
\(575\) | 7.27984 | 0.303590 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 43.6345 | 1.81653 | 0.908264 | − | 0.418398i | \(-0.137408\pi\) | ||||
0.908264 | + | 0.418398i | \(0.137408\pi\) | |||||||
\(578\) | −4.98816 | −0.207480 | ||||||||
\(579\) | −11.8897 | −0.494119 | ||||||||
\(580\) | −26.0563 | −1.08193 | ||||||||
\(581\) | −1.64842 | −0.0683879 | ||||||||
\(582\) | 12.7448 | 0.528288 | ||||||||
\(583\) | 21.8755 | 0.905993 | ||||||||
\(584\) | 3.84818 | 0.159239 | ||||||||
\(585\) | 22.3570 | 0.924346 | ||||||||
\(586\) | −0.226599 | −0.00936072 | ||||||||
\(587\) | 44.2051 | 1.82454 | 0.912270 | − | 0.409590i | \(-0.134328\pi\) | ||||
0.912270 | + | 0.409590i | \(0.134328\pi\) | |||||||
\(588\) | −6.85410 | −0.282658 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 37.5152 | 1.54448 | ||||||||
\(591\) | −8.00186 | −0.329153 | ||||||||
\(592\) | 2.70228 | 0.111063 | ||||||||
\(593\) | 5.92278 | 0.243219 | 0.121610 | − | 0.992578i | \(-0.461194\pi\) | ||||
0.121610 | + | 0.992578i | \(0.461194\pi\) | |||||||
\(594\) | −2.66605 | −0.109389 | ||||||||
\(595\) | 5.68776 | 0.233175 | ||||||||
\(596\) | 17.1352 | 0.701884 | ||||||||
\(597\) | −24.3452 | −0.996382 | ||||||||
\(598\) | −10.0806 | −0.412226 | ||||||||
\(599\) | −26.3593 | −1.07701 | −0.538505 | − | 0.842622i | \(-0.681011\pi\) | ||||
−0.538505 | + | 0.842622i | \(0.681011\pi\) | |||||||
\(600\) | −5.08425 | −0.207564 | ||||||||
\(601\) | 2.85069 | 0.116282 | 0.0581410 | − | 0.998308i | \(-0.481483\pi\) | ||||
0.0581410 | + | 0.998308i | \(0.481483\pi\) | |||||||
\(602\) | 3.33209 | 0.135806 | ||||||||
\(603\) | 12.2147 | 0.497422 | ||||||||
\(604\) | 9.31852 | 0.379165 | ||||||||
\(605\) | −12.3600 | −0.502504 | ||||||||
\(606\) | −3.56597 | −0.144857 | ||||||||
\(607\) | −6.77821 | −0.275119 | −0.137560 | − | 0.990493i | \(-0.543926\pi\) | ||||
−0.137560 | + | 0.990493i | \(0.543926\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.13412 | −0.127001 | ||||||||
\(610\) | 16.7367 | 0.677647 | ||||||||
\(611\) | 37.7153 | 1.52580 | ||||||||
\(612\) | 4.68915 | 0.189548 | ||||||||
\(613\) | −20.2191 | −0.816642 | −0.408321 | − | 0.912838i | \(-0.633886\pi\) | ||||
−0.408321 | + | 0.912838i | \(0.633886\pi\) | |||||||
\(614\) | 22.4853 | 0.907431 | ||||||||
\(615\) | −10.3438 | −0.417103 | ||||||||
\(616\) | −1.01834 | −0.0410300 | ||||||||
\(617\) | −10.9133 | −0.439351 | −0.219676 | − | 0.975573i | \(-0.570500\pi\) | ||||
−0.219676 | + | 0.975573i | \(0.570500\pi\) | |||||||
\(618\) | 7.04216 | 0.283277 | ||||||||
\(619\) | 13.8029 | 0.554787 | 0.277394 | − | 0.960756i | \(-0.410529\pi\) | ||||
0.277394 | + | 0.960756i | \(0.410529\pi\) | |||||||
\(620\) | −27.3972 | −1.10030 | ||||||||
\(621\) | 1.43184 | 0.0574578 | ||||||||
\(622\) | 4.22513 | 0.169412 | ||||||||
\(623\) | 2.98095 | 0.119429 | ||||||||
\(624\) | 7.04029 | 0.281837 | ||||||||
\(625\) | −24.5717 | −0.982866 | ||||||||
\(626\) | −2.09455 | −0.0837152 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −17.6428 | −0.704025 | ||||||||
\(629\) | 12.6714 | 0.505242 | ||||||||
\(630\) | −1.21296 | −0.0483255 | ||||||||
\(631\) | 28.2587 | 1.12496 | 0.562480 | − | 0.826811i | \(-0.309847\pi\) | ||||
0.562480 | + | 0.826811i | \(0.309847\pi\) | |||||||
\(632\) | 1.39560 | 0.0555142 | ||||||||
\(633\) | 20.2016 | 0.802941 | ||||||||
\(634\) | −1.95616 | −0.0776890 | ||||||||
\(635\) | −67.5517 | −2.68071 | ||||||||
\(636\) | 8.20524 | 0.325359 | ||||||||
\(637\) | −48.2549 | −1.91193 | ||||||||
\(638\) | 21.8755 | 0.866061 | ||||||||
\(639\) | −15.0996 | −0.597332 | ||||||||
\(640\) | −3.17557 | −0.125525 | ||||||||
\(641\) | −10.1379 | −0.400421 | −0.200211 | − | 0.979753i | \(-0.564163\pi\) | ||||
−0.200211 | + | 0.979753i | \(0.564163\pi\) | |||||||
\(642\) | 3.63116 | 0.143311 | ||||||||
\(643\) | −8.53379 | −0.336540 | −0.168270 | − | 0.985741i | \(-0.553818\pi\) | ||||
−0.168270 | + | 0.985741i | \(0.553818\pi\) | |||||||
\(644\) | 0.546915 | 0.0215515 | ||||||||
\(645\) | −27.7022 | −1.09077 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14.2383 | −0.559764 | −0.279882 | − | 0.960034i | \(-0.590295\pi\) | ||||
−0.279882 | + | 0.960034i | \(0.590295\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −31.4958 | −1.23632 | ||||||||
\(650\) | −35.7946 | −1.40398 | ||||||||
\(651\) | −3.29541 | −0.129157 | ||||||||
\(652\) | −7.25731 | −0.284218 | ||||||||
\(653\) | 28.5091 | 1.11565 | 0.557823 | − | 0.829960i | \(-0.311637\pi\) | ||||
0.557823 | + | 0.829960i | \(0.311637\pi\) | |||||||
\(654\) | 3.46621 | 0.135540 | ||||||||
\(655\) | 9.32764 | 0.364461 | ||||||||
\(656\) | −3.25731 | −0.127177 | ||||||||
\(657\) | −3.84818 | −0.150132 | ||||||||
\(658\) | −2.04622 | −0.0797698 | ||||||||
\(659\) | −40.5659 | −1.58022 | −0.790112 | − | 0.612963i | \(-0.789978\pi\) | ||||
−0.790112 | + | 0.612963i | \(0.789978\pi\) | |||||||
\(660\) | 8.46621 | 0.329547 | ||||||||
\(661\) | −4.47342 | −0.173996 | −0.0869980 | − | 0.996208i | \(-0.527727\pi\) | ||||
−0.0869980 | + | 0.996208i | \(0.527727\pi\) | |||||||
\(662\) | 8.23015 | 0.319874 | ||||||||
\(663\) | 33.0130 | 1.28212 | ||||||||
\(664\) | 4.31562 | 0.167478 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.70228 | −0.104711 | ||||||||
\(667\) | −11.7486 | −0.454908 | ||||||||
\(668\) | 11.8386 | 0.458049 | ||||||||
\(669\) | 18.3581 | 0.709765 | ||||||||
\(670\) | −38.7887 | −1.49854 | ||||||||
\(671\) | −14.0512 | −0.542442 | ||||||||
\(672\) | −0.381966 | −0.0147347 | ||||||||
\(673\) | −4.55272 | −0.175495 | −0.0877473 | − | 0.996143i | \(-0.527967\pi\) | ||||
−0.0877473 | + | 0.996143i | \(0.527967\pi\) | |||||||
\(674\) | −7.56597 | −0.291430 | ||||||||
\(675\) | 5.08425 | 0.195693 | ||||||||
\(676\) | 36.5657 | 1.40637 | ||||||||
\(677\) | −24.4472 | −0.939583 | −0.469792 | − | 0.882777i | \(-0.655671\pi\) | ||||
−0.469792 | + | 0.882777i | \(0.655671\pi\) | |||||||
\(678\) | −10.2764 | −0.394661 | ||||||||
\(679\) | −4.86807 | −0.186819 | ||||||||
\(680\) | −14.8907 | −0.571034 | ||||||||
\(681\) | −1.53141 | −0.0586838 | ||||||||
\(682\) | 23.0013 | 0.880766 | ||||||||
\(683\) | 25.3627 | 0.970476 | 0.485238 | − | 0.874382i | \(-0.338733\pi\) | ||||
0.485238 | + | 0.874382i | \(0.338733\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24.1730 | 0.923604 | ||||||||
\(686\) | 5.29180 | 0.202042 | ||||||||
\(687\) | −21.2381 | −0.810286 | ||||||||
\(688\) | −8.72353 | −0.332581 | ||||||||
\(689\) | 57.7673 | 2.20076 | ||||||||
\(690\) | −4.54691 | −0.173098 | ||||||||
\(691\) | −19.0686 | −0.725405 | −0.362702 | − | 0.931905i | \(-0.618146\pi\) | ||||
−0.362702 | + | 0.931905i | \(0.618146\pi\) | |||||||
\(692\) | 15.0711 | 0.572918 | ||||||||
\(693\) | 1.01834 | 0.0386835 | ||||||||
\(694\) | 24.5084 | 0.930325 | ||||||||
\(695\) | 1.37831 | 0.0522821 | ||||||||
\(696\) | 8.20524 | 0.311019 | ||||||||
\(697\) | −15.2740 | −0.578545 | ||||||||
\(698\) | 10.5278 | 0.398481 | ||||||||
\(699\) | −10.9655 | −0.414754 | ||||||||
\(700\) | 1.94201 | 0.0734011 | ||||||||
\(701\) | −16.5346 | −0.624504 | −0.312252 | − | 0.949999i | \(-0.601083\pi\) | ||||
−0.312252 | + | 0.949999i | \(0.601083\pi\) | |||||||
\(702\) | −7.04029 | −0.265719 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 2.66605 | 0.100480 | ||||||||
\(705\) | 17.0117 | 0.640699 | ||||||||
\(706\) | −11.0249 | −0.414926 | ||||||||
\(707\) | 1.36208 | 0.0512262 | ||||||||
\(708\) | −11.8137 | −0.443986 | ||||||||
\(709\) | 28.3262 | 1.06381 | 0.531906 | − | 0.846804i | \(-0.321476\pi\) | ||||
0.531906 | + | 0.846804i | \(0.321476\pi\) | |||||||
\(710\) | 47.9500 | 1.79953 | ||||||||
\(711\) | −1.39560 | −0.0523393 | ||||||||
\(712\) | −7.80423 | −0.292476 | ||||||||
\(713\) | −12.3532 | −0.462632 | ||||||||
\(714\) | −1.79110 | −0.0670301 | ||||||||
\(715\) | 59.6046 | 2.22909 | ||||||||
\(716\) | 0.0630049 | 0.00235460 | ||||||||
\(717\) | −6.85765 | −0.256104 | ||||||||
\(718\) | 5.60034 | 0.209003 | ||||||||
\(719\) | −20.6450 | −0.769929 | −0.384965 | − | 0.922931i | \(-0.625786\pi\) | ||||
−0.384965 | + | 0.922931i | \(0.625786\pi\) | |||||||
\(720\) | 3.17557 | 0.118347 | ||||||||
\(721\) | −2.68987 | −0.100176 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 19.1109 | 0.710742 | ||||||||
\(724\) | 3.79110 | 0.140895 | ||||||||
\(725\) | −41.7175 | −1.54935 | ||||||||
\(726\) | 3.89220 | 0.144453 | ||||||||
\(727\) | −18.2148 | −0.675549 | −0.337774 | − | 0.941227i | \(-0.609674\pi\) | ||||
−0.337774 | + | 0.941227i | \(0.609674\pi\) | |||||||
\(728\) | −2.68915 | −0.0996666 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 12.2202 | 0.452289 | ||||||||
\(731\) | −40.9059 | −1.51296 | ||||||||
\(732\) | −5.27044 | −0.194801 | ||||||||
\(733\) | −28.0081 | −1.03450 | −0.517252 | − | 0.855833i | \(-0.673045\pi\) | ||||
−0.517252 | + | 0.855833i | \(0.673045\pi\) | |||||||
\(734\) | −37.3238 | −1.37764 | ||||||||
\(735\) | −21.7657 | −0.802839 | ||||||||
\(736\) | −1.43184 | −0.0527784 | ||||||||
\(737\) | 32.5650 | 1.19955 | ||||||||
\(738\) | 3.25731 | 0.119903 | ||||||||
\(739\) | −46.2549 | −1.70151 | −0.850757 | − | 0.525559i | \(-0.823856\pi\) | ||||
−0.850757 | + | 0.525559i | \(0.823856\pi\) | |||||||
\(740\) | 8.58129 | 0.315454 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.13412 | −0.115057 | ||||||||
\(743\) | −30.8503 | −1.13179 | −0.565894 | − | 0.824478i | \(-0.691469\pi\) | ||||
−0.565894 | + | 0.824478i | \(0.691469\pi\) | |||||||
\(744\) | 8.62750 | 0.316300 | ||||||||
\(745\) | 54.4139 | 1.99357 | ||||||||
\(746\) | 29.4141 | 1.07693 | ||||||||
\(747\) | −4.31562 | −0.157900 | ||||||||
\(748\) | 12.5015 | 0.457100 | ||||||||
\(749\) | −1.38698 | −0.0506792 | ||||||||
\(750\) | −0.267536 | −0.00976902 | ||||||||
\(751\) | 12.9512 | 0.472597 | 0.236299 | − | 0.971680i | \(-0.424066\pi\) | ||||
0.236299 | + | 0.971680i | \(0.424066\pi\) | |||||||
\(752\) | 5.35706 | 0.195352 | ||||||||
\(753\) | 10.5165 | 0.383242 | ||||||||
\(754\) | 57.7673 | 2.10376 | ||||||||
\(755\) | 29.5916 | 1.07695 | ||||||||
\(756\) | 0.381966 | 0.0138920 | ||||||||
\(757\) | 0.294101 | 0.0106893 | 0.00534464 | − | 0.999986i | \(-0.498299\pi\) | ||||
0.00534464 | + | 0.999986i | \(0.498299\pi\) | |||||||
\(758\) | 28.2454 | 1.02592 | ||||||||
\(759\) | 3.81736 | 0.138561 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.4993 | 0.561849 | 0.280925 | − | 0.959730i | \(-0.409359\pi\) | ||||
0.280925 | + | 0.959730i | \(0.409359\pi\) | |||||||
\(762\) | 21.2723 | 0.770614 | ||||||||
\(763\) | −1.32398 | −0.0479311 | ||||||||
\(764\) | 26.2572 | 0.949952 | ||||||||
\(765\) | 14.8907 | 0.538376 | ||||||||
\(766\) | −16.8254 | −0.607925 | ||||||||
\(767\) | −83.1719 | −3.00316 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −21.7968 | −0.786014 | −0.393007 | − | 0.919535i | \(-0.628565\pi\) | ||||
−0.393007 | + | 0.919535i | \(0.628565\pi\) | |||||||
\(770\) | −3.23381 | −0.116538 | ||||||||
\(771\) | 1.60637 | 0.0578521 | ||||||||
\(772\) | −11.8897 | −0.427920 | ||||||||
\(773\) | 7.46267 | 0.268413 | 0.134207 | − | 0.990953i | \(-0.457151\pi\) | ||||
0.134207 | + | 0.990953i | \(0.457151\pi\) | |||||||
\(774\) | 8.72353 | 0.313561 | ||||||||
\(775\) | −43.8644 | −1.57565 | ||||||||
\(776\) | 12.7448 | 0.457511 | ||||||||
\(777\) | 1.03218 | 0.0370292 | ||||||||
\(778\) | −1.57035 | −0.0562998 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 22.3570 | 0.800507 | ||||||||
\(781\) | −40.2563 | −1.44048 | ||||||||
\(782\) | −6.71413 | −0.240097 | ||||||||
\(783\) | −8.20524 | −0.293231 | ||||||||
\(784\) | −6.85410 | −0.244789 | ||||||||
\(785\) | −56.0260 | −1.99965 | ||||||||
\(786\) | −2.93731 | −0.104770 | ||||||||
\(787\) | 15.8788 | 0.566017 | 0.283009 | − | 0.959117i | \(-0.408667\pi\) | ||||
0.283009 | + | 0.959117i | \(0.408667\pi\) | |||||||
\(788\) | −8.00186 | −0.285055 | ||||||||
\(789\) | 13.4471 | 0.478728 | ||||||||
\(790\) | 4.43184 | 0.157678 | ||||||||
\(791\) | 3.92522 | 0.139565 | ||||||||
\(792\) | −2.66605 | −0.0947338 | ||||||||
\(793\) | −37.1054 | −1.31765 | ||||||||
\(794\) | −3.08780 | −0.109582 | ||||||||
\(795\) | 26.0563 | 0.924123 | ||||||||
\(796\) | −24.3452 | −0.862892 | ||||||||
\(797\) | 17.0673 | 0.604556 | 0.302278 | − | 0.953220i | \(-0.402253\pi\) | ||||
0.302278 | + | 0.953220i | \(0.402253\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.1201 | 0.888685 | ||||||||
\(800\) | −5.08425 | −0.179755 | ||||||||
\(801\) | 7.80423 | 0.275749 | ||||||||
\(802\) | 3.92895 | 0.138736 | ||||||||
\(803\) | −10.2594 | −0.362047 | ||||||||
\(804\) | 12.2147 | 0.430780 | ||||||||
\(805\) | 1.73677 | 0.0612130 | ||||||||
\(806\) | 60.7402 | 2.13948 | ||||||||
\(807\) | 22.5492 | 0.793769 | ||||||||
\(808\) | −3.56597 | −0.125450 | ||||||||
\(809\) | 33.6132 | 1.18178 | 0.590889 | − | 0.806753i | \(-0.298777\pi\) | ||||
0.590889 | + | 0.806753i | \(0.298777\pi\) | |||||||
\(810\) | −3.17557 | −0.111578 | ||||||||
\(811\) | 19.6047 | 0.688415 | 0.344207 | − | 0.938894i | \(-0.388148\pi\) | ||||
0.344207 | + | 0.938894i | \(0.388148\pi\) | |||||||
\(812\) | −3.13412 | −0.109986 | ||||||||
\(813\) | −5.02260 | −0.176150 | ||||||||
\(814\) | −7.20441 | −0.252514 | ||||||||
\(815\) | −23.0461 | −0.807270 | ||||||||
\(816\) | 4.68915 | 0.164153 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −28.7032 | −1.00358 | ||||||||
\(819\) | 2.68915 | 0.0939666 | ||||||||
\(820\) | −10.3438 | −0.361222 | ||||||||
\(821\) | 2.63979 | 0.0921292 | 0.0460646 | − | 0.998938i | \(-0.485332\pi\) | ||||
0.0460646 | + | 0.998938i | \(0.485332\pi\) | |||||||
\(822\) | −7.61218 | −0.265505 | ||||||||
\(823\) | −1.49912 | −0.0522560 | −0.0261280 | − | 0.999659i | \(-0.508318\pi\) | ||||
−0.0261280 | + | 0.999659i | \(0.508318\pi\) | |||||||
\(824\) | 7.04216 | 0.245325 | ||||||||
\(825\) | 13.5548 | 0.471919 | ||||||||
\(826\) | 4.51243 | 0.157008 | ||||||||
\(827\) | −31.6406 | −1.10025 | −0.550126 | − | 0.835082i | \(-0.685420\pi\) | ||||
−0.550126 | + | 0.835082i | \(0.685420\pi\) | |||||||
\(828\) | 1.43184 | 0.0497599 | ||||||||
\(829\) | −48.5942 | −1.68775 | −0.843873 | − | 0.536543i | \(-0.819730\pi\) | ||||
−0.843873 | + | 0.536543i | \(0.819730\pi\) | |||||||
\(830\) | 13.7045 | 0.475692 | ||||||||
\(831\) | 2.11288 | 0.0732950 | ||||||||
\(832\) | 7.04029 | 0.244078 | ||||||||
\(833\) | −32.1399 | −1.11358 | ||||||||
\(834\) | −0.434034 | −0.0150294 | ||||||||
\(835\) | 37.5943 | 1.30100 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.62750 | −0.298210 | ||||||||
\(838\) | 3.73663 | 0.129080 | ||||||||
\(839\) | 49.0971 | 1.69502 | 0.847510 | − | 0.530779i | \(-0.178101\pi\) | ||||
0.847510 | + | 0.530779i | \(0.178101\pi\) | |||||||
\(840\) | −1.21296 | −0.0418511 | ||||||||
\(841\) | 38.3260 | 1.32159 | ||||||||
\(842\) | −21.6928 | −0.747582 | ||||||||
\(843\) | 18.7616 | 0.646185 | ||||||||
\(844\) | 20.2016 | 0.695367 | ||||||||
\(845\) | 116.117 | 3.99455 | ||||||||
\(846\) | −5.35706 | −0.184180 | ||||||||
\(847\) | −1.48669 | −0.0510833 | ||||||||
\(848\) | 8.20524 | 0.281769 | ||||||||
\(849\) | −1.38434 | −0.0475105 | ||||||||
\(850\) | −23.8408 | −0.817733 | ||||||||
\(851\) | 3.86924 | 0.132636 | ||||||||
\(852\) | −15.0996 | −0.517305 | ||||||||
\(853\) | 9.55514 | 0.327162 | 0.163581 | − | 0.986530i | \(-0.447696\pi\) | ||||
0.163581 | + | 0.986530i | \(0.447696\pi\) | |||||||
\(854\) | 2.01313 | 0.0688879 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.63116 | 0.124111 | ||||||||
\(857\) | 2.77720 | 0.0948674 | 0.0474337 | − | 0.998874i | \(-0.484896\pi\) | ||||
0.0474337 | + | 0.998874i | \(0.484896\pi\) | |||||||
\(858\) | −18.7697 | −0.640788 | ||||||||
\(859\) | −38.1187 | −1.30059 | −0.650296 | − | 0.759681i | \(-0.725355\pi\) | ||||
−0.650296 | + | 0.759681i | \(0.725355\pi\) | |||||||
\(860\) | −27.7022 | −0.944636 | ||||||||
\(861\) | −1.24418 | −0.0424016 | ||||||||
\(862\) | −5.09756 | −0.173624 | ||||||||
\(863\) | 28.2441 | 0.961439 | 0.480720 | − | 0.876874i | \(-0.340375\pi\) | ||||
0.480720 | + | 0.876874i | \(0.340375\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 47.8594 | 1.62727 | ||||||||
\(866\) | −18.1903 | −0.618132 | ||||||||
\(867\) | 4.98816 | 0.169407 | ||||||||
\(868\) | −3.29541 | −0.111854 | ||||||||
\(869\) | −3.72075 | −0.126218 | ||||||||
\(870\) | 26.0563 | 0.883392 | ||||||||
\(871\) | 85.9952 | 2.91383 | ||||||||
\(872\) | 3.46621 | 0.117381 | ||||||||
\(873\) | −12.7448 | −0.431345 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.102189 | 0.00345464 | ||||||||
\(876\) | −3.84818 | −0.130018 | ||||||||
\(877\) | 22.1722 | 0.748703 | 0.374351 | − | 0.927287i | \(-0.377865\pi\) | ||||
0.374351 | + | 0.927287i | \(0.377865\pi\) | |||||||
\(878\) | −29.4760 | −0.994766 | ||||||||
\(879\) | 0.226599 | 0.00764299 | ||||||||
\(880\) | 8.46621 | 0.285396 | ||||||||
\(881\) | 55.1257 | 1.85723 | 0.928616 | − | 0.371043i | \(-0.121000\pi\) | ||||
0.928616 | + | 0.371043i | \(0.121000\pi\) | |||||||
\(882\) | 6.85410 | 0.230790 | ||||||||
\(883\) | 20.5446 | 0.691381 | 0.345691 | − | 0.938349i | \(-0.387645\pi\) | ||||
0.345691 | + | 0.938349i | \(0.387645\pi\) | |||||||
\(884\) | 33.0130 | 1.11035 | ||||||||
\(885\) | −37.5152 | −1.26106 | ||||||||
\(886\) | 20.6001 | 0.692074 | ||||||||
\(887\) | −50.7843 | −1.70517 | −0.852585 | − | 0.522589i | \(-0.824966\pi\) | ||||
−0.852585 | + | 0.522589i | \(0.824966\pi\) | |||||||
\(888\) | −2.70228 | −0.0906826 | ||||||||
\(889\) | −8.12530 | −0.272514 | ||||||||
\(890\) | −24.7829 | −0.830724 | ||||||||
\(891\) | 2.66605 | 0.0893159 | ||||||||
\(892\) | 18.3581 | 0.614675 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −17.1352 | −0.573086 | ||||||||
\(895\) | 0.200076 | 0.00668782 | ||||||||
\(896\) | −0.381966 | −0.0127606 | ||||||||
\(897\) | 10.0806 | 0.336581 | ||||||||
\(898\) | −5.32606 | −0.177733 | ||||||||
\(899\) | 70.7908 | 2.36100 | ||||||||
\(900\) | 5.08425 | 0.169475 | ||||||||
\(901\) | 38.4756 | 1.28181 | ||||||||
\(902\) | 8.68414 | 0.289150 | ||||||||
\(903\) | −3.33209 | −0.110885 | ||||||||
\(904\) | −10.2764 | −0.341787 | ||||||||
\(905\) | 12.0389 | 0.400186 | ||||||||
\(906\) | −9.31852 | −0.309587 | ||||||||
\(907\) | 29.1553 | 0.968084 | 0.484042 | − | 0.875045i | \(-0.339168\pi\) | ||||
0.484042 | + | 0.875045i | \(0.339168\pi\) | |||||||
\(908\) | −1.53141 | −0.0508217 | ||||||||
\(909\) | 3.56597 | 0.118276 | ||||||||
\(910\) | −8.53960 | −0.283085 | ||||||||
\(911\) | 4.87180 | 0.161410 | 0.0807049 | − | 0.996738i | \(-0.474283\pi\) | ||||
0.0807049 | + | 0.996738i | \(0.474283\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.5056 | −0.380781 | ||||||||
\(914\) | 14.5527 | 0.481361 | ||||||||
\(915\) | −16.7367 | −0.553297 | ||||||||
\(916\) | −21.2381 | −0.701728 | ||||||||
\(917\) | 1.12195 | 0.0370501 | ||||||||
\(918\) | −4.68915 | −0.154765 | ||||||||
\(919\) | −13.1897 | −0.435088 | −0.217544 | − | 0.976051i | \(-0.569805\pi\) | ||||
−0.217544 | + | 0.976051i | \(0.569805\pi\) | |||||||
\(920\) | −4.54691 | −0.149907 | ||||||||
\(921\) | −22.4853 | −0.740915 | ||||||||
\(922\) | 27.7283 | 0.913183 | ||||||||
\(923\) | −106.306 | −3.49910 | ||||||||
\(924\) | 1.01834 | 0.0335009 | ||||||||
\(925\) | 13.7391 | 0.451738 | ||||||||
\(926\) | −3.33216 | −0.109502 | ||||||||
\(927\) | −7.04216 | −0.231295 | ||||||||
\(928\) | 8.20524 | 0.269350 | ||||||||
\(929\) | −16.0439 | −0.526384 | −0.263192 | − | 0.964744i | \(-0.584775\pi\) | ||||
−0.263192 | + | 0.964744i | \(0.584775\pi\) | |||||||
\(930\) | 27.3972 | 0.898391 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −10.9655 | −0.359187 | ||||||||
\(933\) | −4.22513 | −0.138325 | ||||||||
\(934\) | −1.33094 | −0.0435496 | ||||||||
\(935\) | 39.6994 | 1.29831 | ||||||||
\(936\) | −7.04029 | −0.230119 | ||||||||
\(937\) | −48.2717 | −1.57697 | −0.788484 | − | 0.615056i | \(-0.789133\pi\) | ||||
−0.788484 | + | 0.615056i | \(0.789133\pi\) | |||||||
\(938\) | −4.66560 | −0.152337 | ||||||||
\(939\) | 2.09455 | 0.0683532 | ||||||||
\(940\) | 17.0117 | 0.554861 | ||||||||
\(941\) | 11.1612 | 0.363845 | 0.181923 | − | 0.983313i | \(-0.441768\pi\) | ||||
0.181923 | + | 0.983313i | \(0.441768\pi\) | |||||||
\(942\) | 17.6428 | 0.574834 | ||||||||
\(943\) | −4.66395 | −0.151879 | ||||||||
\(944\) | −11.8137 | −0.384503 | ||||||||
\(945\) | 1.21296 | 0.0394576 | ||||||||
\(946\) | 23.2573 | 0.756160 | ||||||||
\(947\) | 0.116113 | 0.00377316 | 0.00188658 | − | 0.999998i | \(-0.499399\pi\) | ||||
0.00188658 | + | 0.999998i | \(0.499399\pi\) | |||||||
\(948\) | −1.39560 | −0.0453271 | ||||||||
\(949\) | −27.0923 | −0.879454 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.95616 | 0.0634328 | ||||||||
\(952\) | −1.79110 | −0.0580498 | ||||||||
\(953\) | −16.9191 | −0.548063 | −0.274031 | − | 0.961721i | \(-0.588357\pi\) | ||||
−0.274031 | + | 0.961721i | \(0.588357\pi\) | |||||||
\(954\) | −8.20524 | −0.265655 | ||||||||
\(955\) | 83.3816 | 2.69816 | ||||||||
\(956\) | −6.85765 | −0.221792 | ||||||||
\(957\) | −21.8755 | −0.707136 | ||||||||
\(958\) | 37.1883 | 1.20150 | ||||||||
\(959\) | 2.90759 | 0.0938911 | ||||||||
\(960\) | 3.17557 | 0.102491 | ||||||||
\(961\) | 43.4338 | 1.40109 | ||||||||
\(962\) | −19.0249 | −0.613386 | ||||||||
\(963\) | −3.63116 | −0.117013 | ||||||||
\(964\) | 19.1109 | 0.615521 | ||||||||
\(965\) | −37.7566 | −1.21543 | ||||||||
\(966\) | −0.546915 | −0.0175967 | ||||||||
\(967\) | 31.2513 | 1.00498 | 0.502488 | − | 0.864584i | \(-0.332418\pi\) | ||||
0.502488 | + | 0.864584i | \(0.332418\pi\) | |||||||
\(968\) | 3.89220 | 0.125100 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 40.4719 | 1.29947 | ||||||||
\(971\) | −21.1207 | −0.677796 | −0.338898 | − | 0.940823i | \(-0.610054\pi\) | ||||
−0.338898 | + | 0.940823i | \(0.610054\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 0.165786 | 0.00531486 | ||||||||
\(974\) | −25.6013 | −0.820317 | ||||||||
\(975\) | 35.7946 | 1.14634 | ||||||||
\(976\) | −5.27044 | −0.168703 | ||||||||
\(977\) | −46.4685 | −1.48666 | −0.743330 | − | 0.668925i | \(-0.766755\pi\) | ||||
−0.743330 | + | 0.668925i | \(0.766755\pi\) | |||||||
\(978\) | 7.25731 | 0.232063 | ||||||||
\(979\) | 20.8064 | 0.664976 | ||||||||
\(980\) | −21.7657 | −0.695279 | ||||||||
\(981\) | −3.46621 | −0.110668 | ||||||||
\(982\) | −25.3711 | −0.809625 | ||||||||
\(983\) | 8.96344 | 0.285889 | 0.142945 | − | 0.989731i | \(-0.454343\pi\) | ||||
0.142945 | + | 0.989731i | \(0.454343\pi\) | |||||||
\(984\) | 3.25731 | 0.103839 | ||||||||
\(985\) | −25.4105 | −0.809645 | ||||||||
\(986\) | 38.4756 | 1.22531 | ||||||||
\(987\) | 2.04622 | 0.0651318 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12.4907 | −0.397181 | ||||||||
\(990\) | −8.46621 | −0.269074 | ||||||||
\(991\) | −23.2216 | −0.737657 | −0.368829 | − | 0.929497i | \(-0.620241\pi\) | ||||
−0.368829 | + | 0.929497i | \(0.620241\pi\) | |||||||
\(992\) | 8.62750 | 0.273923 | ||||||||
\(993\) | −8.23015 | −0.261176 | ||||||||
\(994\) | 5.76755 | 0.182936 | ||||||||
\(995\) | −77.3098 | −2.45089 | ||||||||
\(996\) | −4.31562 | −0.136746 | ||||||||
\(997\) | 37.6024 | 1.19088 | 0.595440 | − | 0.803400i | \(-0.296978\pi\) | ||||
0.595440 | + | 0.803400i | \(0.296978\pi\) | |||||||
\(998\) | −21.0996 | −0.667897 | ||||||||
\(999\) | 2.70228 | 0.0854964 |
(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 | 2166.2.a.w.1.3 | ✓ | 4 | |
3.2 | odd | 2 | 6498.2.a.by.1.2 | 4 | |||
19.18 | odd | 2 | 2166.2.a.x.1.3 | yes | 4 | ||
57.56 | even | 2 | 6498.2.a.bv.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2166.2.a.w.1.3 | ✓ | 4 | 1.1 | even | 1 | trivial | |
2166.2.a.x.1.3 | yes | 4 | 19.18 | odd | 2 | ||
6498.2.a.bv.1.2 | 4 | 57.56 | even | 2 | |||
6498.2.a.by.1.2 | 4 | 3.2 | odd | 2 |