Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3174,2,Mod(1,3174)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3174, 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("3174.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3174 = 2 \cdot 3 \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3174.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: | \(25.3445176016\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\Q(\zeta_{22})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 4x^{3} + 3x^{2} + 3x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 138) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.68251\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3174.1 |
$q$-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 | ||||||||
\(5\) | 2.59435 | 1.16023 | 0.580115 | − | 0.814535i | \(-0.303008\pi\) | ||||
0.580115 | + | 0.814535i | \(0.303008\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 1.23648 | 0.467345 | 0.233673 | − | 0.972315i | \(-0.424926\pi\) | ||||
0.233673 | + | 0.972315i | \(0.424926\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.59435 | 0.820406 | ||||||||
\(11\) | 0.622970 | 0.187832 | 0.0939162 | − | 0.995580i | \(-0.470061\pi\) | ||||
0.0939162 | + | 0.995580i | \(0.470061\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −1.32463 | −0.367388 | −0.183694 | − | 0.982984i | \(-0.558805\pi\) | ||||
−0.183694 | + | 0.982984i | \(0.558805\pi\) | |||||||
\(14\) | 1.23648 | 0.330463 | ||||||||
\(15\) | 2.59435 | 0.669859 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.70760 | 1.14176 | 0.570880 | − | 0.821033i | \(-0.306602\pi\) | ||||
0.570880 | + | 0.821033i | \(0.306602\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −3.79020 | −0.869530 | −0.434765 | − | 0.900544i | \(-0.643169\pi\) | ||||
−0.434765 | + | 0.900544i | \(0.643169\pi\) | |||||||
\(20\) | 2.59435 | 0.580115 | ||||||||
\(21\) | 1.23648 | 0.269822 | ||||||||
\(22\) | 0.622970 | 0.132818 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.73066 | 0.346132 | ||||||||
\(26\) | −1.32463 | −0.259782 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.23648 | 0.233673 | ||||||||
\(29\) | −1.11204 | −0.206501 | −0.103250 | − | 0.994655i | \(-0.532924\pi\) | ||||
−0.103250 | + | 0.994655i | \(0.532924\pi\) | |||||||
\(30\) | 2.59435 | 0.473662 | ||||||||
\(31\) | 9.45679 | 1.69849 | 0.849244 | − | 0.528000i | \(-0.177058\pi\) | ||||
0.849244 | + | 0.528000i | \(0.177058\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.622970 | 0.108445 | ||||||||
\(34\) | 4.70760 | 0.807347 | ||||||||
\(35\) | 3.20786 | 0.542227 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 1.62721 | 0.267512 | 0.133756 | − | 0.991014i | \(-0.457296\pi\) | ||||
0.133756 | + | 0.991014i | \(0.457296\pi\) | |||||||
\(38\) | −3.79020 | −0.614851 | ||||||||
\(39\) | −1.32463 | −0.212111 | ||||||||
\(40\) | 2.59435 | 0.410203 | ||||||||
\(41\) | −11.8497 | −1.85062 | −0.925309 | − | 0.379215i | \(-0.876194\pi\) | ||||
−0.925309 | + | 0.379215i | \(0.876194\pi\) | |||||||
\(42\) | 1.23648 | 0.190793 | ||||||||
\(43\) | 1.67879 | 0.256012 | 0.128006 | − | 0.991773i | \(-0.459142\pi\) | ||||
0.128006 | + | 0.991773i | \(0.459142\pi\) | |||||||
\(44\) | 0.622970 | 0.0939162 | ||||||||
\(45\) | 2.59435 | 0.386743 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.94494 | −1.01302 | −0.506512 | − | 0.862233i | \(-0.669065\pi\) | ||||
−0.506512 | + | 0.862233i | \(0.669065\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −5.47112 | −0.781589 | ||||||||
\(50\) | 1.73066 | 0.244752 | ||||||||
\(51\) | 4.70760 | 0.659196 | ||||||||
\(52\) | −1.32463 | −0.183694 | ||||||||
\(53\) | 11.2537 | 1.54581 | 0.772907 | − | 0.634520i | \(-0.218802\pi\) | ||||
0.772907 | + | 0.634520i | \(0.218802\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 1.61620 | 0.217929 | ||||||||
\(56\) | 1.23648 | 0.165231 | ||||||||
\(57\) | −3.79020 | −0.502024 | ||||||||
\(58\) | −1.11204 | −0.146018 | ||||||||
\(59\) | −9.74629 | −1.26886 | −0.634429 | − | 0.772981i | \(-0.718765\pi\) | ||||
−0.634429 | + | 0.772981i | \(0.718765\pi\) | |||||||
\(60\) | 2.59435 | 0.334929 | ||||||||
\(61\) | 14.3736 | 1.84035 | 0.920173 | − | 0.391512i | \(-0.128048\pi\) | ||||
0.920173 | + | 0.391512i | \(0.128048\pi\) | |||||||
\(62\) | 9.45679 | 1.20101 | ||||||||
\(63\) | 1.23648 | 0.155782 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.43657 | −0.426254 | ||||||||
\(66\) | 0.622970 | 0.0766823 | ||||||||
\(67\) | 6.12125 | 0.747830 | 0.373915 | − | 0.927463i | \(-0.378015\pi\) | ||||
0.373915 | + | 0.927463i | \(0.378015\pi\) | |||||||
\(68\) | 4.70760 | 0.570880 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.20786 | 0.383413 | ||||||||
\(71\) | 6.49255 | 0.770523 | 0.385262 | − | 0.922807i | \(-0.374111\pi\) | ||||
0.385262 | + | 0.922807i | \(0.374111\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −13.0900 | −1.53207 | −0.766035 | − | 0.642799i | \(-0.777773\pi\) | ||||
−0.766035 | + | 0.642799i | \(0.777773\pi\) | |||||||
\(74\) | 1.62721 | 0.189160 | ||||||||
\(75\) | 1.73066 | 0.199839 | ||||||||
\(76\) | −3.79020 | −0.434765 | ||||||||
\(77\) | 0.770289 | 0.0877826 | ||||||||
\(78\) | −1.32463 | −0.149985 | ||||||||
\(79\) | 12.0823 | 1.35937 | 0.679685 | − | 0.733504i | \(-0.262117\pi\) | ||||
0.679685 | + | 0.733504i | \(0.262117\pi\) | |||||||
\(80\) | 2.59435 | 0.290057 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −11.8497 | −1.30858 | ||||||||
\(83\) | −7.39068 | −0.811233 | −0.405617 | − | 0.914043i | \(-0.632943\pi\) | ||||
−0.405617 | + | 0.914043i | \(0.632943\pi\) | |||||||
\(84\) | 1.23648 | 0.134911 | ||||||||
\(85\) | 12.2132 | 1.32470 | ||||||||
\(86\) | 1.67879 | 0.181028 | ||||||||
\(87\) | −1.11204 | −0.119223 | ||||||||
\(88\) | 0.622970 | 0.0664088 | ||||||||
\(89\) | −3.38500 | −0.358809 | −0.179404 | − | 0.983775i | \(-0.557417\pi\) | ||||
−0.179404 | + | 0.983775i | \(0.557417\pi\) | |||||||
\(90\) | 2.59435 | 0.273469 | ||||||||
\(91\) | −1.63788 | −0.171697 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.45679 | 0.980623 | ||||||||
\(94\) | −6.94494 | −0.716316 | ||||||||
\(95\) | −9.83310 | −1.00885 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −11.4458 | −1.16214 | −0.581072 | − | 0.813852i | \(-0.697366\pi\) | ||||
−0.581072 | + | 0.813852i | \(0.697366\pi\) | |||||||
\(98\) | −5.47112 | −0.552667 | ||||||||
\(99\) | 0.622970 | 0.0626108 | ||||||||
\(100\) | 1.73066 | 0.173066 | ||||||||
\(101\) | −1.78374 | −0.177489 | −0.0887443 | − | 0.996054i | \(-0.528285\pi\) | ||||
−0.0887443 | + | 0.996054i | \(0.528285\pi\) | |||||||
\(102\) | 4.70760 | 0.466122 | ||||||||
\(103\) | −19.8505 | −1.95593 | −0.977963 | − | 0.208776i | \(-0.933052\pi\) | ||||
−0.977963 | + | 0.208776i | \(0.933052\pi\) | |||||||
\(104\) | −1.32463 | −0.129891 | ||||||||
\(105\) | 3.20786 | 0.313055 | ||||||||
\(106\) | 11.2537 | 1.09306 | ||||||||
\(107\) | 4.35922 | 0.421422 | 0.210711 | − | 0.977548i | \(-0.432422\pi\) | ||||
0.210711 | + | 0.977548i | \(0.432422\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −6.46538 | −0.619271 | −0.309636 | − | 0.950855i | \(-0.600207\pi\) | ||||
−0.309636 | + | 0.950855i | \(0.600207\pi\) | |||||||
\(110\) | 1.61620 | 0.154099 | ||||||||
\(111\) | 1.62721 | 0.154448 | ||||||||
\(112\) | 1.23648 | 0.116836 | ||||||||
\(113\) | 1.36243 | 0.128166 | 0.0640832 | − | 0.997945i | \(-0.479588\pi\) | ||||
0.0640832 | + | 0.997945i | \(0.479588\pi\) | |||||||
\(114\) | −3.79020 | −0.354984 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.11204 | −0.103250 | ||||||||
\(117\) | −1.32463 | −0.122463 | ||||||||
\(118\) | −9.74629 | −0.897219 | ||||||||
\(119\) | 5.82085 | 0.533596 | ||||||||
\(120\) | 2.59435 | 0.236831 | ||||||||
\(121\) | −10.6119 | −0.964719 | ||||||||
\(122\) | 14.3736 | 1.30132 | ||||||||
\(123\) | −11.8497 | −1.06845 | ||||||||
\(124\) | 9.45679 | 0.849244 | ||||||||
\(125\) | −8.48182 | −0.758637 | ||||||||
\(126\) | 1.23648 | 0.110154 | ||||||||
\(127\) | 3.45519 | 0.306598 | 0.153299 | − | 0.988180i | \(-0.451010\pi\) | ||||
0.153299 | + | 0.988180i | \(0.451010\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 1.67879 | 0.147809 | ||||||||
\(130\) | −3.43657 | −0.301407 | ||||||||
\(131\) | 18.9474 | 1.65544 | 0.827721 | − | 0.561140i | \(-0.189637\pi\) | ||||
0.827721 | + | 0.561140i | \(0.189637\pi\) | |||||||
\(132\) | 0.622970 | 0.0542225 | ||||||||
\(133\) | −4.68650 | −0.406371 | ||||||||
\(134\) | 6.12125 | 0.528796 | ||||||||
\(135\) | 2.59435 | 0.223286 | ||||||||
\(136\) | 4.70760 | 0.403673 | ||||||||
\(137\) | 11.3960 | 0.973629 | 0.486815 | − | 0.873505i | \(-0.338159\pi\) | ||||
0.486815 | + | 0.873505i | \(0.338159\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.30267 | 0.449766 | 0.224883 | − | 0.974386i | \(-0.427800\pi\) | ||||
0.224883 | + | 0.974386i | \(0.427800\pi\) | |||||||
\(140\) | 3.20786 | 0.271114 | ||||||||
\(141\) | −6.94494 | −0.584870 | ||||||||
\(142\) | 6.49255 | 0.544842 | ||||||||
\(143\) | −0.825207 | −0.0690073 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −2.88502 | −0.239588 | ||||||||
\(146\) | −13.0900 | −1.08334 | ||||||||
\(147\) | −5.47112 | −0.451250 | ||||||||
\(148\) | 1.62721 | 0.133756 | ||||||||
\(149\) | −13.8186 | −1.13206 | −0.566030 | − | 0.824385i | \(-0.691521\pi\) | ||||
−0.566030 | + | 0.824385i | \(0.691521\pi\) | |||||||
\(150\) | 1.73066 | 0.141308 | ||||||||
\(151\) | −5.43503 | −0.442296 | −0.221148 | − | 0.975240i | \(-0.570980\pi\) | ||||
−0.221148 | + | 0.975240i | \(0.570980\pi\) | |||||||
\(152\) | −3.79020 | −0.307425 | ||||||||
\(153\) | 4.70760 | 0.380587 | ||||||||
\(154\) | 0.770289 | 0.0620716 | ||||||||
\(155\) | 24.5342 | 1.97064 | ||||||||
\(156\) | −1.32463 | −0.106056 | ||||||||
\(157\) | −5.28204 | −0.421553 | −0.210776 | − | 0.977534i | \(-0.567599\pi\) | ||||
−0.210776 | + | 0.977534i | \(0.567599\pi\) | |||||||
\(158\) | 12.0823 | 0.961219 | ||||||||
\(159\) | 11.2537 | 0.892476 | ||||||||
\(160\) | 2.59435 | 0.205101 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 9.09064 | 0.712034 | 0.356017 | − | 0.934480i | \(-0.384135\pi\) | ||||
0.356017 | + | 0.934480i | \(0.384135\pi\) | |||||||
\(164\) | −11.8497 | −0.925309 | ||||||||
\(165\) | 1.61620 | 0.125821 | ||||||||
\(166\) | −7.39068 | −0.573628 | ||||||||
\(167\) | 2.87790 | 0.222699 | 0.111349 | − | 0.993781i | \(-0.464483\pi\) | ||||
0.111349 | + | 0.993781i | \(0.464483\pi\) | |||||||
\(168\) | 1.23648 | 0.0953964 | ||||||||
\(169\) | −11.2453 | −0.865026 | ||||||||
\(170\) | 12.2132 | 0.936707 | ||||||||
\(171\) | −3.79020 | −0.289843 | ||||||||
\(172\) | 1.67879 | 0.128006 | ||||||||
\(173\) | 13.6627 | 1.03876 | 0.519378 | − | 0.854545i | \(-0.326164\pi\) | ||||
0.519378 | + | 0.854545i | \(0.326164\pi\) | |||||||
\(174\) | −1.11204 | −0.0843035 | ||||||||
\(175\) | 2.13992 | 0.161763 | ||||||||
\(176\) | 0.622970 | 0.0469581 | ||||||||
\(177\) | −9.74629 | −0.732576 | ||||||||
\(178\) | −3.38500 | −0.253716 | ||||||||
\(179\) | −20.3995 | −1.52473 | −0.762367 | − | 0.647145i | \(-0.775963\pi\) | ||||
−0.762367 | + | 0.647145i | \(0.775963\pi\) | |||||||
\(180\) | 2.59435 | 0.193372 | ||||||||
\(181\) | −9.53656 | −0.708847 | −0.354423 | − | 0.935085i | \(-0.615323\pi\) | ||||
−0.354423 | + | 0.935085i | \(0.615323\pi\) | |||||||
\(182\) | −1.63788 | −0.121408 | ||||||||
\(183\) | 14.3736 | 1.06252 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.22157 | 0.310376 | ||||||||
\(186\) | 9.45679 | 0.693405 | ||||||||
\(187\) | 2.93269 | 0.214460 | ||||||||
\(188\) | −6.94494 | −0.506512 | ||||||||
\(189\) | 1.23648 | 0.0899406 | ||||||||
\(190\) | −9.83310 | −0.713368 | ||||||||
\(191\) | −1.59304 | −0.115268 | −0.0576340 | − | 0.998338i | \(-0.518356\pi\) | ||||
−0.0576340 | + | 0.998338i | \(0.518356\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 17.5781 | 1.26530 | 0.632651 | − | 0.774437i | \(-0.281967\pi\) | ||||
0.632651 | + | 0.774437i | \(0.281967\pi\) | |||||||
\(194\) | −11.4458 | −0.821759 | ||||||||
\(195\) | −3.43657 | −0.246098 | ||||||||
\(196\) | −5.47112 | −0.390794 | ||||||||
\(197\) | 1.22161 | 0.0870358 | 0.0435179 | − | 0.999053i | \(-0.486143\pi\) | ||||
0.0435179 | + | 0.999053i | \(0.486143\pi\) | |||||||
\(198\) | 0.622970 | 0.0442725 | ||||||||
\(199\) | 0.100228 | 0.00710495 | 0.00355248 | − | 0.999994i | \(-0.498869\pi\) | ||||
0.00355248 | + | 0.999994i | \(0.498869\pi\) | |||||||
\(200\) | 1.73066 | 0.122376 | ||||||||
\(201\) | 6.12125 | 0.431760 | ||||||||
\(202\) | −1.78374 | −0.125503 | ||||||||
\(203\) | −1.37501 | −0.0965070 | ||||||||
\(204\) | 4.70760 | 0.329598 | ||||||||
\(205\) | −30.7424 | −2.14714 | ||||||||
\(206\) | −19.8505 | −1.38305 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.32463 | −0.0918469 | ||||||||
\(209\) | −2.36118 | −0.163326 | ||||||||
\(210\) | 3.20786 | 0.221363 | ||||||||
\(211\) | −16.6971 | −1.14948 | −0.574738 | − | 0.818337i | \(-0.694896\pi\) | ||||
−0.574738 | + | 0.818337i | \(0.694896\pi\) | |||||||
\(212\) | 11.2537 | 0.772907 | ||||||||
\(213\) | 6.49255 | 0.444862 | ||||||||
\(214\) | 4.35922 | 0.297990 | ||||||||
\(215\) | 4.35536 | 0.297033 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 11.6931 | 0.793780 | ||||||||
\(218\) | −6.46538 | −0.437891 | ||||||||
\(219\) | −13.0900 | −0.884541 | ||||||||
\(220\) | 1.61620 | 0.108964 | ||||||||
\(221\) | −6.23585 | −0.419469 | ||||||||
\(222\) | 1.62721 | 0.109211 | ||||||||
\(223\) | 18.2081 | 1.21931 | 0.609654 | − | 0.792668i | \(-0.291308\pi\) | ||||
0.609654 | + | 0.792668i | \(0.291308\pi\) | |||||||
\(224\) | 1.23648 | 0.0826157 | ||||||||
\(225\) | 1.73066 | 0.115377 | ||||||||
\(226\) | 1.36243 | 0.0906274 | ||||||||
\(227\) | −15.9853 | −1.06098 | −0.530490 | − | 0.847691i | \(-0.677992\pi\) | ||||
−0.530490 | + | 0.847691i | \(0.677992\pi\) | |||||||
\(228\) | −3.79020 | −0.251012 | ||||||||
\(229\) | 17.7317 | 1.17174 | 0.585872 | − | 0.810404i | \(-0.300752\pi\) | ||||
0.585872 | + | 0.810404i | \(0.300752\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.770289 | 0.0506813 | ||||||||
\(232\) | −1.11204 | −0.0730090 | ||||||||
\(233\) | −9.34447 | −0.612176 | −0.306088 | − | 0.952003i | \(-0.599020\pi\) | ||||
−0.306088 | + | 0.952003i | \(0.599020\pi\) | |||||||
\(234\) | −1.32463 | −0.0865941 | ||||||||
\(235\) | −18.0176 | −1.17534 | ||||||||
\(236\) | −9.74629 | −0.634429 | ||||||||
\(237\) | 12.0823 | 0.784832 | ||||||||
\(238\) | 5.82085 | 0.377309 | ||||||||
\(239\) | −5.00904 | −0.324008 | −0.162004 | − | 0.986790i | \(-0.551796\pi\) | ||||
−0.162004 | + | 0.986790i | \(0.551796\pi\) | |||||||
\(240\) | 2.59435 | 0.167465 | ||||||||
\(241\) | −14.5761 | −0.938932 | −0.469466 | − | 0.882951i | \(-0.655554\pi\) | ||||
−0.469466 | + | 0.882951i | \(0.655554\pi\) | |||||||
\(242\) | −10.6119 | −0.682159 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 14.3736 | 0.920173 | ||||||||
\(245\) | −14.1940 | −0.906822 | ||||||||
\(246\) | −11.8497 | −0.755511 | ||||||||
\(247\) | 5.02062 | 0.319455 | ||||||||
\(248\) | 9.45679 | 0.600506 | ||||||||
\(249\) | −7.39068 | −0.468366 | ||||||||
\(250\) | −8.48182 | −0.536437 | ||||||||
\(251\) | 18.7355 | 1.18258 | 0.591288 | − | 0.806460i | \(-0.298620\pi\) | ||||
0.591288 | + | 0.806460i | \(0.298620\pi\) | |||||||
\(252\) | 1.23648 | 0.0778908 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 3.45519 | 0.216798 | ||||||||
\(255\) | 12.2132 | 0.764818 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −1.74983 | −0.109151 | −0.0545756 | − | 0.998510i | \(-0.517381\pi\) | ||||
−0.0545756 | + | 0.998510i | \(0.517381\pi\) | |||||||
\(258\) | 1.67879 | 0.104517 | ||||||||
\(259\) | 2.01202 | 0.125021 | ||||||||
\(260\) | −3.43657 | −0.213127 | ||||||||
\(261\) | −1.11204 | −0.0688335 | ||||||||
\(262\) | 18.9474 | 1.17057 | ||||||||
\(263\) | 16.6550 | 1.02699 | 0.513494 | − | 0.858093i | \(-0.328351\pi\) | ||||
0.513494 | + | 0.858093i | \(0.328351\pi\) | |||||||
\(264\) | 0.622970 | 0.0383411 | ||||||||
\(265\) | 29.1960 | 1.79350 | ||||||||
\(266\) | −4.68650 | −0.287348 | ||||||||
\(267\) | −3.38500 | −0.207158 | ||||||||
\(268\) | 6.12125 | 0.373915 | ||||||||
\(269\) | −26.7029 | −1.62810 | −0.814051 | − | 0.580793i | \(-0.802743\pi\) | ||||
−0.814051 | + | 0.580793i | \(0.802743\pi\) | |||||||
\(270\) | 2.59435 | 0.157887 | ||||||||
\(271\) | 26.9079 | 1.63454 | 0.817269 | − | 0.576256i | \(-0.195487\pi\) | ||||
0.817269 | + | 0.576256i | \(0.195487\pi\) | |||||||
\(272\) | 4.70760 | 0.285440 | ||||||||
\(273\) | −1.63788 | −0.0991292 | ||||||||
\(274\) | 11.3960 | 0.688460 | ||||||||
\(275\) | 1.07815 | 0.0650147 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.13714 | −0.128408 | −0.0642042 | − | 0.997937i | \(-0.520451\pi\) | ||||
−0.0642042 | + | 0.997937i | \(0.520451\pi\) | |||||||
\(278\) | 5.30267 | 0.318033 | ||||||||
\(279\) | 9.45679 | 0.566163 | ||||||||
\(280\) | 3.20786 | 0.191706 | ||||||||
\(281\) | 27.7857 | 1.65756 | 0.828778 | − | 0.559578i | \(-0.189037\pi\) | ||||
0.828778 | + | 0.559578i | \(0.189037\pi\) | |||||||
\(282\) | −6.94494 | −0.413565 | ||||||||
\(283\) | −23.4814 | −1.39582 | −0.697911 | − | 0.716185i | \(-0.745887\pi\) | ||||
−0.697911 | + | 0.716185i | \(0.745887\pi\) | |||||||
\(284\) | 6.49255 | 0.385262 | ||||||||
\(285\) | −9.83310 | −0.582462 | ||||||||
\(286\) | −0.825207 | −0.0487955 | ||||||||
\(287\) | −14.6519 | −0.864877 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 5.16149 | 0.303617 | ||||||||
\(290\) | −2.88502 | −0.169414 | ||||||||
\(291\) | −11.4458 | −0.670964 | ||||||||
\(292\) | −13.0900 | −0.766035 | ||||||||
\(293\) | 18.9804 | 1.10884 | 0.554422 | − | 0.832236i | \(-0.312939\pi\) | ||||
0.554422 | + | 0.832236i | \(0.312939\pi\) | |||||||
\(294\) | −5.47112 | −0.319082 | ||||||||
\(295\) | −25.2853 | −1.47217 | ||||||||
\(296\) | 1.62721 | 0.0945799 | ||||||||
\(297\) | 0.622970 | 0.0361484 | ||||||||
\(298\) | −13.8186 | −0.800488 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.73066 | 0.0999196 | ||||||||
\(301\) | 2.07578 | 0.119646 | ||||||||
\(302\) | −5.43503 | −0.312751 | ||||||||
\(303\) | −1.78374 | −0.102473 | ||||||||
\(304\) | −3.79020 | −0.217383 | ||||||||
\(305\) | 37.2901 | 2.13522 | ||||||||
\(306\) | 4.70760 | 0.269116 | ||||||||
\(307\) | 14.9115 | 0.851043 | 0.425522 | − | 0.904948i | \(-0.360091\pi\) | ||||
0.425522 | + | 0.904948i | \(0.360091\pi\) | |||||||
\(308\) | 0.770289 | 0.0438913 | ||||||||
\(309\) | −19.8505 | −1.12925 | ||||||||
\(310\) | 24.5342 | 1.39345 | ||||||||
\(311\) | −5.28838 | −0.299876 | −0.149938 | − | 0.988695i | \(-0.547907\pi\) | ||||
−0.149938 | + | 0.988695i | \(0.547907\pi\) | |||||||
\(312\) | −1.32463 | −0.0749927 | ||||||||
\(313\) | 8.87040 | 0.501385 | 0.250692 | − | 0.968067i | \(-0.419342\pi\) | ||||
0.250692 | + | 0.968067i | \(0.419342\pi\) | |||||||
\(314\) | −5.28204 | −0.298083 | ||||||||
\(315\) | 3.20786 | 0.180742 | ||||||||
\(316\) | 12.0823 | 0.679685 | ||||||||
\(317\) | 3.03971 | 0.170727 | 0.0853636 | − | 0.996350i | \(-0.472795\pi\) | ||||
0.0853636 | + | 0.996350i | \(0.472795\pi\) | |||||||
\(318\) | 11.2537 | 0.631076 | ||||||||
\(319\) | −0.692767 | −0.0387875 | ||||||||
\(320\) | 2.59435 | 0.145029 | ||||||||
\(321\) | 4.35922 | 0.243308 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.8427 | −0.992795 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −2.29249 | −0.127164 | ||||||||
\(326\) | 9.09064 | 0.503484 | ||||||||
\(327\) | −6.46538 | −0.357536 | ||||||||
\(328\) | −11.8497 | −0.654292 | ||||||||
\(329\) | −8.58727 | −0.473432 | ||||||||
\(330\) | 1.61620 | 0.0889690 | ||||||||
\(331\) | 1.64126 | 0.0902119 | 0.0451059 | − | 0.998982i | \(-0.485637\pi\) | ||||
0.0451059 | + | 0.998982i | \(0.485637\pi\) | |||||||
\(332\) | −7.39068 | −0.405617 | ||||||||
\(333\) | 1.62721 | 0.0891708 | ||||||||
\(334\) | 2.87790 | 0.157472 | ||||||||
\(335\) | 15.8807 | 0.867654 | ||||||||
\(336\) | 1.23648 | 0.0674555 | ||||||||
\(337\) | −17.9706 | −0.978921 | −0.489461 | − | 0.872025i | \(-0.662806\pi\) | ||||
−0.489461 | + | 0.872025i | \(0.662806\pi\) | |||||||
\(338\) | −11.2453 | −0.611666 | ||||||||
\(339\) | 1.36243 | 0.0739969 | ||||||||
\(340\) | 12.2132 | 0.662352 | ||||||||
\(341\) | 5.89129 | 0.319031 | ||||||||
\(342\) | −3.79020 | −0.204950 | ||||||||
\(343\) | −15.4203 | −0.832617 | ||||||||
\(344\) | 1.67879 | 0.0905140 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 13.6627 | 0.734511 | ||||||||
\(347\) | 0.223203 | 0.0119822 | 0.00599109 | − | 0.999982i | \(-0.498093\pi\) | ||||
0.00599109 | + | 0.999982i | \(0.498093\pi\) | |||||||
\(348\) | −1.11204 | −0.0596116 | ||||||||
\(349\) | −20.2398 | −1.08341 | −0.541705 | − | 0.840568i | \(-0.682221\pi\) | ||||
−0.541705 | + | 0.840568i | \(0.682221\pi\) | |||||||
\(350\) | 2.13992 | 0.114384 | ||||||||
\(351\) | −1.32463 | −0.0707038 | ||||||||
\(352\) | 0.622970 | 0.0332044 | ||||||||
\(353\) | 19.0138 | 1.01200 | 0.506001 | − | 0.862533i | \(-0.331123\pi\) | ||||
0.506001 | + | 0.862533i | \(0.331123\pi\) | |||||||
\(354\) | −9.74629 | −0.518009 | ||||||||
\(355\) | 16.8439 | 0.893984 | ||||||||
\(356\) | −3.38500 | −0.179404 | ||||||||
\(357\) | 5.82085 | 0.308072 | ||||||||
\(358\) | −20.3995 | −1.07815 | ||||||||
\(359\) | −5.13597 | −0.271066 | −0.135533 | − | 0.990773i | \(-0.543275\pi\) | ||||
−0.135533 | + | 0.990773i | \(0.543275\pi\) | |||||||
\(360\) | 2.59435 | 0.136734 | ||||||||
\(361\) | −4.63442 | −0.243917 | ||||||||
\(362\) | −9.53656 | −0.501231 | ||||||||
\(363\) | −10.6119 | −0.556981 | ||||||||
\(364\) | −1.63788 | −0.0858484 | ||||||||
\(365\) | −33.9601 | −1.77755 | ||||||||
\(366\) | 14.3736 | 0.751318 | ||||||||
\(367\) | −24.7772 | −1.29336 | −0.646679 | − | 0.762762i | \(-0.723843\pi\) | ||||
−0.646679 | + | 0.762762i | \(0.723843\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −11.8497 | −0.616872 | ||||||||
\(370\) | 4.22157 | 0.219469 | ||||||||
\(371\) | 13.9150 | 0.722428 | ||||||||
\(372\) | 9.45679 | 0.490311 | ||||||||
\(373\) | −37.1140 | −1.92169 | −0.960844 | − | 0.277090i | \(-0.910630\pi\) | ||||
−0.960844 | + | 0.277090i | \(0.910630\pi\) | |||||||
\(374\) | 2.93269 | 0.151646 | ||||||||
\(375\) | −8.48182 | −0.437999 | ||||||||
\(376\) | −6.94494 | −0.358158 | ||||||||
\(377\) | 1.47305 | 0.0758657 | ||||||||
\(378\) | 1.23648 | 0.0635976 | ||||||||
\(379\) | 31.1816 | 1.60169 | 0.800846 | − | 0.598870i | \(-0.204383\pi\) | ||||
0.800846 | + | 0.598870i | \(0.204383\pi\) | |||||||
\(380\) | −9.83310 | −0.504427 | ||||||||
\(381\) | 3.45519 | 0.177015 | ||||||||
\(382\) | −1.59304 | −0.0815068 | ||||||||
\(383\) | 11.5562 | 0.590494 | 0.295247 | − | 0.955421i | \(-0.404598\pi\) | ||||
0.295247 | + | 0.955421i | \(0.404598\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 1.99840 | 0.101848 | ||||||||
\(386\) | 17.5781 | 0.894704 | ||||||||
\(387\) | 1.67879 | 0.0853375 | ||||||||
\(388\) | −11.4458 | −0.581072 | ||||||||
\(389\) | −23.8039 | −1.20691 | −0.603453 | − | 0.797399i | \(-0.706209\pi\) | ||||
−0.603453 | + | 0.797399i | \(0.706209\pi\) | |||||||
\(390\) | −3.43657 | −0.174017 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −5.47112 | −0.276333 | ||||||||
\(393\) | 18.9474 | 0.955770 | ||||||||
\(394\) | 1.22161 | 0.0615436 | ||||||||
\(395\) | 31.3458 | 1.57718 | ||||||||
\(396\) | 0.622970 | 0.0313054 | ||||||||
\(397\) | −22.1253 | −1.11044 | −0.555220 | − | 0.831704i | \(-0.687366\pi\) | ||||
−0.555220 | + | 0.831704i | \(0.687366\pi\) | |||||||
\(398\) | 0.100228 | 0.00502396 | ||||||||
\(399\) | −4.68650 | −0.234618 | ||||||||
\(400\) | 1.73066 | 0.0865329 | ||||||||
\(401\) | 10.6876 | 0.533714 | 0.266857 | − | 0.963736i | \(-0.414015\pi\) | ||||
0.266857 | + | 0.963736i | \(0.414015\pi\) | |||||||
\(402\) | 6.12125 | 0.305300 | ||||||||
\(403\) | −12.5268 | −0.624004 | ||||||||
\(404\) | −1.78374 | −0.0887443 | ||||||||
\(405\) | 2.59435 | 0.128914 | ||||||||
\(406\) | −1.37501 | −0.0682408 | ||||||||
\(407\) | 1.01371 | 0.0502475 | ||||||||
\(408\) | 4.70760 | 0.233061 | ||||||||
\(409\) | −15.8801 | −0.785219 | −0.392610 | − | 0.919705i | \(-0.628428\pi\) | ||||
−0.392610 | + | 0.919705i | \(0.628428\pi\) | |||||||
\(410\) | −30.7424 | −1.51826 | ||||||||
\(411\) | 11.3960 | 0.562125 | ||||||||
\(412\) | −19.8505 | −0.977963 | ||||||||
\(413\) | −12.0511 | −0.592995 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −19.1740 | −0.941216 | ||||||||
\(416\) | −1.32463 | −0.0649456 | ||||||||
\(417\) | 5.30267 | 0.259673 | ||||||||
\(418\) | −2.36118 | −0.115489 | ||||||||
\(419\) | 4.63014 | 0.226197 | 0.113099 | − | 0.993584i | \(-0.463922\pi\) | ||||
0.113099 | + | 0.993584i | \(0.463922\pi\) | |||||||
\(420\) | 3.20786 | 0.156528 | ||||||||
\(421\) | 10.5088 | 0.512170 | 0.256085 | − | 0.966654i | \(-0.417567\pi\) | ||||
0.256085 | + | 0.966654i | \(0.417567\pi\) | |||||||
\(422\) | −16.6971 | −0.812803 | ||||||||
\(423\) | −6.94494 | −0.337675 | ||||||||
\(424\) | 11.2537 | 0.546528 | ||||||||
\(425\) | 8.14724 | 0.395199 | ||||||||
\(426\) | 6.49255 | 0.314565 | ||||||||
\(427\) | 17.7726 | 0.860077 | ||||||||
\(428\) | 4.35922 | 0.210711 | ||||||||
\(429\) | −0.825207 | −0.0398414 | ||||||||
\(430\) | 4.35536 | 0.210034 | ||||||||
\(431\) | −13.6284 | −0.656458 | −0.328229 | − | 0.944598i | \(-0.606452\pi\) | ||||
−0.328229 | + | 0.944598i | \(0.606452\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 8.61044 | 0.413791 | 0.206896 | − | 0.978363i | \(-0.433664\pi\) | ||||
0.206896 | + | 0.978363i | \(0.433664\pi\) | |||||||
\(434\) | 11.6931 | 0.561287 | ||||||||
\(435\) | −2.88502 | −0.138326 | ||||||||
\(436\) | −6.46538 | −0.309636 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −13.0900 | −0.625465 | ||||||||
\(439\) | −37.0323 | −1.76745 | −0.883727 | − | 0.468003i | \(-0.844974\pi\) | ||||
−0.883727 | + | 0.468003i | \(0.844974\pi\) | |||||||
\(440\) | 1.61620 | 0.0770494 | ||||||||
\(441\) | −5.47112 | −0.260530 | ||||||||
\(442\) | −6.23585 | −0.296609 | ||||||||
\(443\) | 14.4007 | 0.684196 | 0.342098 | − | 0.939664i | \(-0.388863\pi\) | ||||
0.342098 | + | 0.939664i | \(0.388863\pi\) | |||||||
\(444\) | 1.62721 | 0.0772242 | ||||||||
\(445\) | −8.78187 | −0.416301 | ||||||||
\(446\) | 18.2081 | 0.862181 | ||||||||
\(447\) | −13.8186 | −0.653595 | ||||||||
\(448\) | 1.23648 | 0.0584181 | ||||||||
\(449\) | 14.7629 | 0.696706 | 0.348353 | − | 0.937363i | \(-0.386741\pi\) | ||||
0.348353 | + | 0.937363i | \(0.386741\pi\) | |||||||
\(450\) | 1.73066 | 0.0815840 | ||||||||
\(451\) | −7.38202 | −0.347606 | ||||||||
\(452\) | 1.36243 | 0.0640832 | ||||||||
\(453\) | −5.43503 | −0.255360 | ||||||||
\(454\) | −15.9853 | −0.750226 | ||||||||
\(455\) | −4.24924 | −0.199208 | ||||||||
\(456\) | −3.79020 | −0.177492 | ||||||||
\(457\) | −6.62444 | −0.309878 | −0.154939 | − | 0.987924i | \(-0.549518\pi\) | ||||
−0.154939 | + | 0.987924i | \(0.549518\pi\) | |||||||
\(458\) | 17.7317 | 0.828548 | ||||||||
\(459\) | 4.70760 | 0.219732 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.35627 | 0.342616 | 0.171308 | − | 0.985218i | \(-0.445201\pi\) | ||||
0.171308 | + | 0.985218i | \(0.445201\pi\) | |||||||
\(462\) | 0.770289 | 0.0358371 | ||||||||
\(463\) | 34.6358 | 1.60966 | 0.804832 | − | 0.593503i | \(-0.202256\pi\) | ||||
0.804832 | + | 0.593503i | \(0.202256\pi\) | |||||||
\(464\) | −1.11204 | −0.0516251 | ||||||||
\(465\) | 24.5342 | 1.13775 | ||||||||
\(466\) | −9.34447 | −0.432874 | ||||||||
\(467\) | 14.1030 | 0.652608 | 0.326304 | − | 0.945265i | \(-0.394197\pi\) | ||||
0.326304 | + | 0.945265i | \(0.394197\pi\) | |||||||
\(468\) | −1.32463 | −0.0612313 | ||||||||
\(469\) | 7.56880 | 0.349495 | ||||||||
\(470\) | −18.0176 | −0.831091 | ||||||||
\(471\) | −5.28204 | −0.243384 | ||||||||
\(472\) | −9.74629 | −0.448609 | ||||||||
\(473\) | 1.04583 | 0.0480874 | ||||||||
\(474\) | 12.0823 | 0.554960 | ||||||||
\(475\) | −6.55953 | −0.300972 | ||||||||
\(476\) | 5.82085 | 0.266798 | ||||||||
\(477\) | 11.2537 | 0.515271 | ||||||||
\(478\) | −5.00904 | −0.229108 | ||||||||
\(479\) | 17.0476 | 0.778924 | 0.389462 | − | 0.921043i | \(-0.372661\pi\) | ||||
0.389462 | + | 0.921043i | \(0.372661\pi\) | |||||||
\(480\) | 2.59435 | 0.118415 | ||||||||
\(481\) | −2.15546 | −0.0982807 | ||||||||
\(482\) | −14.5761 | −0.663925 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.6119 | −0.482359 | ||||||||
\(485\) | −29.6944 | −1.34835 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −12.3279 | −0.558629 | −0.279314 | − | 0.960200i | \(-0.590107\pi\) | ||||
−0.279314 | + | 0.960200i | \(0.590107\pi\) | |||||||
\(488\) | 14.3736 | 0.650660 | ||||||||
\(489\) | 9.09064 | 0.411093 | ||||||||
\(490\) | −14.1940 | −0.641220 | ||||||||
\(491\) | −6.49393 | −0.293067 | −0.146534 | − | 0.989206i | \(-0.546812\pi\) | ||||
−0.146534 | + | 0.989206i | \(0.546812\pi\) | |||||||
\(492\) | −11.8497 | −0.534227 | ||||||||
\(493\) | −5.23504 | −0.235774 | ||||||||
\(494\) | 5.02062 | 0.225889 | ||||||||
\(495\) | 1.61620 | 0.0726429 | ||||||||
\(496\) | 9.45679 | 0.424622 | ||||||||
\(497\) | 8.02790 | 0.360100 | ||||||||
\(498\) | −7.39068 | −0.331184 | ||||||||
\(499\) | −13.6005 | −0.608841 | −0.304420 | − | 0.952538i | \(-0.598463\pi\) | ||||
−0.304420 | + | 0.952538i | \(0.598463\pi\) | |||||||
\(500\) | −8.48182 | −0.379319 | ||||||||
\(501\) | 2.87790 | 0.128575 | ||||||||
\(502\) | 18.7355 | 0.836208 | ||||||||
\(503\) | −3.01244 | −0.134318 | −0.0671590 | − | 0.997742i | \(-0.521393\pi\) | ||||
−0.0671590 | + | 0.997742i | \(0.521393\pi\) | |||||||
\(504\) | 1.23648 | 0.0550771 | ||||||||
\(505\) | −4.62764 | −0.205927 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.2453 | −0.499423 | ||||||||
\(508\) | 3.45519 | 0.153299 | ||||||||
\(509\) | 43.0295 | 1.90725 | 0.953625 | − | 0.300996i | \(-0.0973192\pi\) | ||||
0.953625 | + | 0.300996i | \(0.0973192\pi\) | |||||||
\(510\) | 12.2132 | 0.540808 | ||||||||
\(511\) | −16.1855 | −0.716005 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −3.79020 | −0.167341 | ||||||||
\(514\) | −1.74983 | −0.0771815 | ||||||||
\(515\) | −51.4991 | −2.26932 | ||||||||
\(516\) | 1.67879 | 0.0739044 | ||||||||
\(517\) | −4.32649 | −0.190279 | ||||||||
\(518\) | 2.01202 | 0.0884029 | ||||||||
\(519\) | 13.6627 | 0.599725 | ||||||||
\(520\) | −3.43657 | −0.150703 | ||||||||
\(521\) | 15.1561 | 0.664003 | 0.332001 | − | 0.943279i | \(-0.392276\pi\) | ||||
0.332001 | + | 0.943279i | \(0.392276\pi\) | |||||||
\(522\) | −1.11204 | −0.0486726 | ||||||||
\(523\) | −15.6900 | −0.686075 | −0.343037 | − | 0.939322i | \(-0.611456\pi\) | ||||
−0.343037 | + | 0.939322i | \(0.611456\pi\) | |||||||
\(524\) | 18.9474 | 0.827721 | ||||||||
\(525\) | 2.13992 | 0.0933938 | ||||||||
\(526\) | 16.6550 | 0.726191 | ||||||||
\(527\) | 44.5188 | 1.93927 | ||||||||
\(528\) | 0.622970 | 0.0271113 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | 29.1960 | 1.26819 | ||||||||
\(531\) | −9.74629 | −0.422953 | ||||||||
\(532\) | −4.68650 | −0.203185 | ||||||||
\(533\) | 15.6966 | 0.679894 | ||||||||
\(534\) | −3.38500 | −0.146483 | ||||||||
\(535\) | 11.3093 | 0.488946 | ||||||||
\(536\) | 6.12125 | 0.264398 | ||||||||
\(537\) | −20.3995 | −0.880305 | ||||||||
\(538\) | −26.7029 | −1.15124 | ||||||||
\(539\) | −3.40834 | −0.146808 | ||||||||
\(540\) | 2.59435 | 0.111643 | ||||||||
\(541\) | −21.7189 | −0.933769 | −0.466884 | − | 0.884318i | \(-0.654624\pi\) | ||||
−0.466884 | + | 0.884318i | \(0.654624\pi\) | |||||||
\(542\) | 26.9079 | 1.15579 | ||||||||
\(543\) | −9.53656 | −0.409253 | ||||||||
\(544\) | 4.70760 | 0.201837 | ||||||||
\(545\) | −16.7735 | −0.718496 | ||||||||
\(546\) | −1.63788 | −0.0700949 | ||||||||
\(547\) | 12.2110 | 0.522105 | 0.261053 | − | 0.965325i | \(-0.415930\pi\) | ||||
0.261053 | + | 0.965325i | \(0.415930\pi\) | |||||||
\(548\) | 11.3960 | 0.486815 | ||||||||
\(549\) | 14.3736 | 0.613449 | ||||||||
\(550\) | 1.07815 | 0.0459724 | ||||||||
\(551\) | 4.21485 | 0.179559 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.9396 | 0.635295 | ||||||||
\(554\) | −2.13714 | −0.0907984 | ||||||||
\(555\) | 4.22157 | 0.179195 | ||||||||
\(556\) | 5.30267 | 0.224883 | ||||||||
\(557\) | −16.2652 | −0.689180 | −0.344590 | − | 0.938753i | \(-0.611982\pi\) | ||||
−0.344590 | + | 0.938753i | \(0.611982\pi\) | |||||||
\(558\) | 9.45679 | 0.400338 | ||||||||
\(559\) | −2.22378 | −0.0940558 | ||||||||
\(560\) | 3.20786 | 0.135557 | ||||||||
\(561\) | 2.93269 | 0.123818 | ||||||||
\(562\) | 27.7857 | 1.17207 | ||||||||
\(563\) | −31.6637 | −1.33447 | −0.667233 | − | 0.744849i | \(-0.732522\pi\) | ||||
−0.667233 | + | 0.744849i | \(0.732522\pi\) | |||||||
\(564\) | −6.94494 | −0.292435 | ||||||||
\(565\) | 3.53462 | 0.148702 | ||||||||
\(566\) | −23.4814 | −0.986995 | ||||||||
\(567\) | 1.23648 | 0.0519272 | ||||||||
\(568\) | 6.49255 | 0.272421 | ||||||||
\(569\) | −36.8598 | −1.54524 | −0.772621 | − | 0.634868i | \(-0.781054\pi\) | ||||
−0.772621 | + | 0.634868i | \(0.781054\pi\) | |||||||
\(570\) | −9.83310 | −0.411863 | ||||||||
\(571\) | −30.8533 | −1.29117 | −0.645586 | − | 0.763688i | \(-0.723387\pi\) | ||||
−0.645586 | + | 0.763688i | \(0.723387\pi\) | |||||||
\(572\) | −0.825207 | −0.0345036 | ||||||||
\(573\) | −1.59304 | −0.0665501 | ||||||||
\(574\) | −14.6519 | −0.611560 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −45.6832 | −1.90182 | −0.950908 | − | 0.309474i | \(-0.899847\pi\) | ||||
−0.950908 | + | 0.309474i | \(0.899847\pi\) | |||||||
\(578\) | 5.16149 | 0.214690 | ||||||||
\(579\) | 17.5781 | 0.730523 | ||||||||
\(580\) | −2.88502 | −0.119794 | ||||||||
\(581\) | −9.13843 | −0.379126 | ||||||||
\(582\) | −11.4458 | −0.474443 | ||||||||
\(583\) | 7.01071 | 0.290354 | ||||||||
\(584\) | −13.0900 | −0.541668 | ||||||||
\(585\) | −3.43657 | −0.142085 | ||||||||
\(586\) | 18.9804 | 0.784071 | ||||||||
\(587\) | −30.4171 | −1.25545 | −0.627723 | − | 0.778437i | \(-0.716013\pi\) | ||||
−0.627723 | + | 0.778437i | \(0.716013\pi\) | |||||||
\(588\) | −5.47112 | −0.225625 | ||||||||
\(589\) | −35.8431 | −1.47689 | ||||||||
\(590\) | −25.2853 | −1.04098 | ||||||||
\(591\) | 1.22161 | 0.0502501 | ||||||||
\(592\) | 1.62721 | 0.0668781 | ||||||||
\(593\) | −27.8211 | −1.14248 | −0.571238 | − | 0.820784i | \(-0.693537\pi\) | ||||
−0.571238 | + | 0.820784i | \(0.693537\pi\) | |||||||
\(594\) | 0.622970 | 0.0255608 | ||||||||
\(595\) | 15.1013 | 0.619094 | ||||||||
\(596\) | −13.8186 | −0.566030 | ||||||||
\(597\) | 0.100228 | 0.00410205 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11.1914 | −0.457270 | −0.228635 | − | 0.973512i | \(-0.573426\pi\) | ||||
−0.228635 | + | 0.973512i | \(0.573426\pi\) | |||||||
\(600\) | 1.73066 | 0.0706538 | ||||||||
\(601\) | −41.0283 | −1.67358 | −0.836789 | − | 0.547525i | \(-0.815570\pi\) | ||||
−0.836789 | + | 0.547525i | \(0.815570\pi\) | |||||||
\(602\) | 2.07578 | 0.0846026 | ||||||||
\(603\) | 6.12125 | 0.249277 | ||||||||
\(604\) | −5.43503 | −0.221148 | ||||||||
\(605\) | −27.5310 | −1.11930 | ||||||||
\(606\) | −1.78374 | −0.0724594 | ||||||||
\(607\) | 36.6692 | 1.48836 | 0.744179 | − | 0.667981i | \(-0.232841\pi\) | ||||
0.744179 | + | 0.667981i | \(0.232841\pi\) | |||||||
\(608\) | −3.79020 | −0.153713 | ||||||||
\(609\) | −1.37501 | −0.0557184 | ||||||||
\(610\) | 37.2901 | 1.50983 | ||||||||
\(611\) | 9.19951 | 0.372172 | ||||||||
\(612\) | 4.70760 | 0.190293 | ||||||||
\(613\) | 0.233905 | 0.00944733 | 0.00472367 | − | 0.999989i | \(-0.498496\pi\) | ||||
0.00472367 | + | 0.999989i | \(0.498496\pi\) | |||||||
\(614\) | 14.9115 | 0.601778 | ||||||||
\(615\) | −30.7424 | −1.23965 | ||||||||
\(616\) | 0.770289 | 0.0310358 | ||||||||
\(617\) | 43.6491 | 1.75725 | 0.878623 | − | 0.477517i | \(-0.158463\pi\) | ||||
0.878623 | + | 0.477517i | \(0.158463\pi\) | |||||||
\(618\) | −19.8505 | −0.798504 | ||||||||
\(619\) | 1.18895 | 0.0477881 | 0.0238941 | − | 0.999714i | \(-0.492394\pi\) | ||||
0.0238941 | + | 0.999714i | \(0.492394\pi\) | |||||||
\(620\) | 24.5342 | 0.985318 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5.28838 | −0.212045 | ||||||||
\(623\) | −4.18548 | −0.167688 | ||||||||
\(624\) | −1.32463 | −0.0530278 | ||||||||
\(625\) | −30.6581 | −1.22632 | ||||||||
\(626\) | 8.87040 | 0.354533 | ||||||||
\(627\) | −2.36118 | −0.0942963 | ||||||||
\(628\) | −5.28204 | −0.210776 | ||||||||
\(629\) | 7.66027 | 0.305435 | ||||||||
\(630\) | 3.20786 | 0.127804 | ||||||||
\(631\) | −16.6637 | −0.663371 | −0.331686 | − | 0.943390i | \(-0.607617\pi\) | ||||
−0.331686 | + | 0.943390i | \(0.607617\pi\) | |||||||
\(632\) | 12.0823 | 0.480610 | ||||||||
\(633\) | −16.6971 | −0.663651 | ||||||||
\(634\) | 3.03971 | 0.120722 | ||||||||
\(635\) | 8.96397 | 0.355724 | ||||||||
\(636\) | 11.2537 | 0.446238 | ||||||||
\(637\) | 7.24724 | 0.287146 | ||||||||
\(638\) | −0.692767 | −0.0274269 | ||||||||
\(639\) | 6.49255 | 0.256841 | ||||||||
\(640\) | 2.59435 | 0.102551 | ||||||||
\(641\) | 29.8418 | 1.17868 | 0.589340 | − | 0.807885i | \(-0.299388\pi\) | ||||
0.589340 | + | 0.807885i | \(0.299388\pi\) | |||||||
\(642\) | 4.35922 | 0.172045 | ||||||||
\(643\) | 36.9937 | 1.45889 | 0.729445 | − | 0.684040i | \(-0.239779\pi\) | ||||
0.729445 | + | 0.684040i | \(0.239779\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.35536 | 0.171492 | ||||||||
\(646\) | −17.8427 | −0.702012 | ||||||||
\(647\) | 30.8934 | 1.21454 | 0.607272 | − | 0.794494i | \(-0.292264\pi\) | ||||
0.607272 | + | 0.794494i | \(0.292264\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −6.07164 | −0.238333 | ||||||||
\(650\) | −2.29249 | −0.0899188 | ||||||||
\(651\) | 11.6931 | 0.458289 | ||||||||
\(652\) | 9.09064 | 0.356017 | ||||||||
\(653\) | −25.9281 | −1.01465 | −0.507323 | − | 0.861756i | \(-0.669365\pi\) | ||||
−0.507323 | + | 0.861756i | \(0.669365\pi\) | |||||||
\(654\) | −6.46538 | −0.252816 | ||||||||
\(655\) | 49.1562 | 1.92069 | ||||||||
\(656\) | −11.8497 | −0.462654 | ||||||||
\(657\) | −13.0900 | −0.510690 | ||||||||
\(658\) | −8.58727 | −0.334767 | ||||||||
\(659\) | 20.3688 | 0.793455 | 0.396727 | − | 0.917937i | \(-0.370146\pi\) | ||||
0.396727 | + | 0.917937i | \(0.370146\pi\) | |||||||
\(660\) | 1.61620 | 0.0629106 | ||||||||
\(661\) | −42.0770 | −1.63661 | −0.818303 | − | 0.574787i | \(-0.805085\pi\) | ||||
−0.818303 | + | 0.574787i | \(0.805085\pi\) | |||||||
\(662\) | 1.64126 | 0.0637894 | ||||||||
\(663\) | −6.23585 | −0.242180 | ||||||||
\(664\) | −7.39068 | −0.286814 | ||||||||
\(665\) | −12.1584 | −0.471483 | ||||||||
\(666\) | 1.62721 | 0.0630533 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 2.87790 | 0.111349 | ||||||||
\(669\) | 18.2081 | 0.703968 | ||||||||
\(670\) | 15.8807 | 0.613524 | ||||||||
\(671\) | 8.95429 | 0.345677 | ||||||||
\(672\) | 1.23648 | 0.0476982 | ||||||||
\(673\) | 20.3437 | 0.784192 | 0.392096 | − | 0.919924i | \(-0.371750\pi\) | ||||
0.392096 | + | 0.919924i | \(0.371750\pi\) | |||||||
\(674\) | −17.9706 | −0.692202 | ||||||||
\(675\) | 1.73066 | 0.0666131 | ||||||||
\(676\) | −11.2453 | −0.432513 | ||||||||
\(677\) | −11.0440 | −0.424456 | −0.212228 | − | 0.977220i | \(-0.568072\pi\) | ||||
−0.212228 | + | 0.977220i | \(0.568072\pi\) | |||||||
\(678\) | 1.36243 | 0.0523237 | ||||||||
\(679\) | −14.1525 | −0.543122 | ||||||||
\(680\) | 12.2132 | 0.468353 | ||||||||
\(681\) | −15.9853 | −0.612557 | ||||||||
\(682\) | 5.89129 | 0.225589 | ||||||||
\(683\) | −10.7474 | −0.411239 | −0.205619 | − | 0.978632i | \(-0.565921\pi\) | ||||
−0.205619 | + | 0.978632i | \(0.565921\pi\) | |||||||
\(684\) | −3.79020 | −0.144922 | ||||||||
\(685\) | 29.5653 | 1.12963 | ||||||||
\(686\) | −15.4203 | −0.588749 | ||||||||
\(687\) | 17.7317 | 0.676507 | ||||||||
\(688\) | 1.67879 | 0.0640031 | ||||||||
\(689\) | −14.9070 | −0.567913 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.3444 | −0.811980 | −0.405990 | − | 0.913878i | \(-0.633073\pi\) | ||||
−0.405990 | + | 0.913878i | \(0.633073\pi\) | |||||||
\(692\) | 13.6627 | 0.519378 | ||||||||
\(693\) | 0.770289 | 0.0292609 | ||||||||
\(694\) | 0.223203 | 0.00847269 | ||||||||
\(695\) | 13.7570 | 0.521832 | ||||||||
\(696\) | −1.11204 | −0.0421517 | ||||||||
\(697\) | −55.7838 | −2.11296 | ||||||||
\(698\) | −20.2398 | −0.766087 | ||||||||
\(699\) | −9.34447 | −0.353440 | ||||||||
\(700\) | 2.13992 | 0.0808814 | ||||||||
\(701\) | 32.9410 | 1.24416 | 0.622082 | − | 0.782952i | \(-0.286287\pi\) | ||||
0.622082 | + | 0.782952i | \(0.286287\pi\) | |||||||
\(702\) | −1.32463 | −0.0499951 | ||||||||
\(703\) | −6.16746 | −0.232610 | ||||||||
\(704\) | 0.622970 | 0.0234791 | ||||||||
\(705\) | −18.0176 | −0.678583 | ||||||||
\(706\) | 19.0138 | 0.715593 | ||||||||
\(707\) | −2.20556 | −0.0829484 | ||||||||
\(708\) | −9.74629 | −0.366288 | ||||||||
\(709\) | 41.4933 | 1.55832 | 0.779158 | − | 0.626828i | \(-0.215647\pi\) | ||||
0.779158 | + | 0.626828i | \(0.215647\pi\) | |||||||
\(710\) | 16.8439 | 0.632142 | ||||||||
\(711\) | 12.0823 | 0.453123 | ||||||||
\(712\) | −3.38500 | −0.126858 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 5.82085 | 0.217840 | ||||||||
\(715\) | −2.14088 | −0.0800643 | ||||||||
\(716\) | −20.3995 | −0.762367 | ||||||||
\(717\) | −5.00904 | −0.187066 | ||||||||
\(718\) | −5.13597 | −0.191673 | ||||||||
\(719\) | −28.0271 | −1.04523 | −0.522617 | − | 0.852568i | \(-0.675044\pi\) | ||||
−0.522617 | + | 0.852568i | \(0.675044\pi\) | |||||||
\(720\) | 2.59435 | 0.0966858 | ||||||||
\(721\) | −24.5447 | −0.914093 | ||||||||
\(722\) | −4.63442 | −0.172475 | ||||||||
\(723\) | −14.5761 | −0.542093 | ||||||||
\(724\) | −9.53656 | −0.354423 | ||||||||
\(725\) | −1.92456 | −0.0714764 | ||||||||
\(726\) | −10.6119 | −0.393845 | ||||||||
\(727\) | −9.92976 | −0.368274 | −0.184137 | − | 0.982901i | \(-0.558949\pi\) | ||||
−0.184137 | + | 0.982901i | \(0.558949\pi\) | |||||||
\(728\) | −1.63788 | −0.0607040 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −33.9601 | −1.25692 | ||||||||
\(731\) | 7.90305 | 0.292305 | ||||||||
\(732\) | 14.3736 | 0.531262 | ||||||||
\(733\) | −17.8060 | −0.657678 | −0.328839 | − | 0.944386i | \(-0.606657\pi\) | ||||
−0.328839 | + | 0.944386i | \(0.606657\pi\) | |||||||
\(734\) | −24.7772 | −0.914543 | ||||||||
\(735\) | −14.1940 | −0.523554 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.81336 | 0.140467 | ||||||||
\(738\) | −11.8497 | −0.436195 | ||||||||
\(739\) | 21.7628 | 0.800557 | 0.400279 | − | 0.916393i | \(-0.368913\pi\) | ||||
0.400279 | + | 0.916393i | \(0.368913\pi\) | |||||||
\(740\) | 4.22157 | 0.155188 | ||||||||
\(741\) | 5.02062 | 0.184437 | ||||||||
\(742\) | 13.9150 | 0.510834 | ||||||||
\(743\) | 16.5987 | 0.608947 | 0.304474 | − | 0.952521i | \(-0.401519\pi\) | ||||
0.304474 | + | 0.952521i | \(0.401519\pi\) | |||||||
\(744\) | 9.45679 | 0.346703 | ||||||||
\(745\) | −35.8502 | −1.31345 | ||||||||
\(746\) | −37.1140 | −1.35884 | ||||||||
\(747\) | −7.39068 | −0.270411 | ||||||||
\(748\) | 2.93269 | 0.107230 | ||||||||
\(749\) | 5.39008 | 0.196949 | ||||||||
\(750\) | −8.48182 | −0.309712 | ||||||||
\(751\) | 4.09051 | 0.149265 | 0.0746324 | − | 0.997211i | \(-0.476222\pi\) | ||||
0.0746324 | + | 0.997211i | \(0.476222\pi\) | |||||||
\(752\) | −6.94494 | −0.253256 | ||||||||
\(753\) | 18.7355 | 0.682761 | ||||||||
\(754\) | 1.47305 | 0.0536452 | ||||||||
\(755\) | −14.1004 | −0.513165 | ||||||||
\(756\) | 1.23648 | 0.0449703 | ||||||||
\(757\) | −9.97094 | −0.362400 | −0.181200 | − | 0.983446i | \(-0.557998\pi\) | ||||
−0.181200 | + | 0.983446i | \(0.557998\pi\) | |||||||
\(758\) | 31.1816 | 1.13257 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −9.83310 | −0.356684 | ||||||||
\(761\) | 46.0080 | 1.66779 | 0.833894 | − | 0.551925i | \(-0.186107\pi\) | ||||
0.833894 | + | 0.551925i | \(0.186107\pi\) | |||||||
\(762\) | 3.45519 | 0.125168 | ||||||||
\(763\) | −7.99431 | −0.289413 | ||||||||
\(764\) | −1.59304 | −0.0576340 | ||||||||
\(765\) | 12.2132 | 0.441568 | ||||||||
\(766\) | 11.5562 | 0.417542 | ||||||||
\(767\) | 12.9103 | 0.466163 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −27.4543 | −0.990027 | −0.495013 | − | 0.868885i | \(-0.664837\pi\) | ||||
−0.495013 | + | 0.868885i | \(0.664837\pi\) | |||||||
\(770\) | 1.99840 | 0.0720173 | ||||||||
\(771\) | −1.74983 | −0.0630184 | ||||||||
\(772\) | 17.5781 | 0.632651 | ||||||||
\(773\) | −9.07298 | −0.326333 | −0.163166 | − | 0.986599i | \(-0.552171\pi\) | ||||
−0.163166 | + | 0.986599i | \(0.552171\pi\) | |||||||
\(774\) | 1.67879 | 0.0603427 | ||||||||
\(775\) | 16.3665 | 0.587901 | ||||||||
\(776\) | −11.4458 | −0.410880 | ||||||||
\(777\) | 2.01202 | 0.0721807 | ||||||||
\(778\) | −23.8039 | −0.853411 | ||||||||
\(779\) | 44.9128 | 1.60917 | ||||||||
\(780\) | −3.43657 | −0.123049 | ||||||||
\(781\) | 4.04466 | 0.144729 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.11204 | −0.0397411 | ||||||||
\(784\) | −5.47112 | −0.195397 | ||||||||
\(785\) | −13.7035 | −0.489098 | ||||||||
\(786\) | 18.9474 | 0.675832 | ||||||||
\(787\) | 52.0178 | 1.85424 | 0.927118 | − | 0.374770i | \(-0.122278\pi\) | ||||
0.927118 | + | 0.374770i | \(0.122278\pi\) | |||||||
\(788\) | 1.22161 | 0.0435179 | ||||||||
\(789\) | 16.6550 | 0.592932 | ||||||||
\(790\) | 31.3458 | 1.11523 | ||||||||
\(791\) | 1.68461 | 0.0598980 | ||||||||
\(792\) | 0.622970 | 0.0221363 | ||||||||
\(793\) | −19.0397 | −0.676120 | ||||||||
\(794\) | −22.1253 | −0.785199 | ||||||||
\(795\) | 29.1960 | 1.03548 | ||||||||
\(796\) | 0.100228 | 0.00355248 | ||||||||
\(797\) | −26.5148 | −0.939202 | −0.469601 | − | 0.882879i | \(-0.655602\pi\) | ||||
−0.469601 | + | 0.882879i | \(0.655602\pi\) | |||||||
\(798\) | −4.68650 | −0.165900 | ||||||||
\(799\) | −32.6940 | −1.15663 | ||||||||
\(800\) | 1.73066 | 0.0611880 | ||||||||
\(801\) | −3.38500 | −0.119603 | ||||||||
\(802\) | 10.6876 | 0.377393 | ||||||||
\(803\) | −8.15468 | −0.287772 | ||||||||
\(804\) | 6.12125 | 0.215880 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −12.5268 | −0.441237 | ||||||||
\(807\) | −26.7029 | −0.939985 | ||||||||
\(808\) | −1.78374 | −0.0627517 | ||||||||
\(809\) | −21.0758 | −0.740987 | −0.370493 | − | 0.928835i | \(-0.620811\pi\) | ||||
−0.370493 | + | 0.928835i | \(0.620811\pi\) | |||||||
\(810\) | 2.59435 | 0.0911562 | ||||||||
\(811\) | −35.3708 | −1.24204 | −0.621018 | − | 0.783796i | \(-0.713281\pi\) | ||||
−0.621018 | + | 0.783796i | \(0.713281\pi\) | |||||||
\(812\) | −1.37501 | −0.0482535 | ||||||||
\(813\) | 26.9079 | 0.943701 | ||||||||
\(814\) | 1.01371 | 0.0355303 | ||||||||
\(815\) | 23.5843 | 0.826122 | ||||||||
\(816\) | 4.70760 | 0.164799 | ||||||||
\(817\) | −6.36292 | −0.222611 | ||||||||
\(818\) | −15.8801 | −0.555234 | ||||||||
\(819\) | −1.63788 | −0.0572323 | ||||||||
\(820\) | −30.7424 | −1.07357 | ||||||||
\(821\) | −49.2971 | −1.72048 | −0.860241 | − | 0.509888i | \(-0.829687\pi\) | ||||
−0.860241 | + | 0.509888i | \(0.829687\pi\) | |||||||
\(822\) | 11.3960 | 0.397483 | ||||||||
\(823\) | −12.3852 | −0.431720 | −0.215860 | − | 0.976424i | \(-0.569255\pi\) | ||||
−0.215860 | + | 0.976424i | \(0.569255\pi\) | |||||||
\(824\) | −19.8505 | −0.691525 | ||||||||
\(825\) | 1.07815 | 0.0375363 | ||||||||
\(826\) | −12.0511 | −0.419311 | ||||||||
\(827\) | −30.0768 | −1.04587 | −0.522936 | − | 0.852372i | \(-0.675163\pi\) | ||||
−0.522936 | + | 0.852372i | \(0.675163\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 48.4553 | 1.68292 | 0.841462 | − | 0.540317i | \(-0.181696\pi\) | ||||
0.841462 | + | 0.540317i | \(0.181696\pi\) | |||||||
\(830\) | −19.1740 | −0.665540 | ||||||||
\(831\) | −2.13714 | −0.0741366 | ||||||||
\(832\) | −1.32463 | −0.0459234 | ||||||||
\(833\) | −25.7558 | −0.892387 | ||||||||
\(834\) | 5.30267 | 0.183616 | ||||||||
\(835\) | 7.46629 | 0.258381 | ||||||||
\(836\) | −2.36118 | −0.0816630 | ||||||||
\(837\) | 9.45679 | 0.326874 | ||||||||
\(838\) | 4.63014 | 0.159946 | ||||||||
\(839\) | 45.3388 | 1.56527 | 0.782635 | − | 0.622481i | \(-0.213875\pi\) | ||||
0.782635 | + | 0.622481i | \(0.213875\pi\) | |||||||
\(840\) | 3.20786 | 0.110682 | ||||||||
\(841\) | −27.7634 | −0.957358 | ||||||||
\(842\) | 10.5088 | 0.362159 | ||||||||
\(843\) | 27.7857 | 0.956990 | ||||||||
\(844\) | −16.6971 | −0.574738 | ||||||||
\(845\) | −29.1744 | −1.00363 | ||||||||
\(846\) | −6.94494 | −0.238772 | ||||||||
\(847\) | −13.1214 | −0.450857 | ||||||||
\(848\) | 11.2537 | 0.386453 | ||||||||
\(849\) | −23.4814 | −0.805878 | ||||||||
\(850\) | 8.14724 | 0.279448 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 6.49255 | 0.222431 | ||||||||
\(853\) | −14.5044 | −0.496621 | −0.248310 | − | 0.968681i | \(-0.579875\pi\) | ||||
−0.248310 | + | 0.968681i | \(0.579875\pi\) | |||||||
\(854\) | 17.7726 | 0.608166 | ||||||||
\(855\) | −9.83310 | −0.336285 | ||||||||
\(856\) | 4.35922 | 0.148995 | ||||||||
\(857\) | 49.9110 | 1.70493 | 0.852464 | − | 0.522785i | \(-0.175107\pi\) | ||||
0.852464 | + | 0.522785i | \(0.175107\pi\) | |||||||
\(858\) | −0.825207 | −0.0281721 | ||||||||
\(859\) | 55.0208 | 1.87729 | 0.938643 | − | 0.344890i | \(-0.112084\pi\) | ||||
0.938643 | + | 0.344890i | \(0.112084\pi\) | |||||||
\(860\) | 4.35536 | 0.148517 | ||||||||
\(861\) | −14.6519 | −0.499337 | ||||||||
\(862\) | −13.6284 | −0.464186 | ||||||||
\(863\) | 39.8912 | 1.35791 | 0.678955 | − | 0.734180i | \(-0.262433\pi\) | ||||
0.678955 | + | 0.734180i | \(0.262433\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 35.4458 | 1.20519 | ||||||||
\(866\) | 8.61044 | 0.292595 | ||||||||
\(867\) | 5.16149 | 0.175293 | ||||||||
\(868\) | 11.6931 | 0.396890 | ||||||||
\(869\) | 7.52693 | 0.255334 | ||||||||
\(870\) | −2.88502 | −0.0978114 | ||||||||
\(871\) | −8.10843 | −0.274744 | ||||||||
\(872\) | −6.46538 | −0.218945 | ||||||||
\(873\) | −11.4458 | −0.387381 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.4876 | −0.354545 | ||||||||
\(876\) | −13.0900 | −0.442270 | ||||||||
\(877\) | 3.81653 | 0.128875 | 0.0644375 | − | 0.997922i | \(-0.479475\pi\) | ||||
0.0644375 | + | 0.997922i | \(0.479475\pi\) | |||||||
\(878\) | −37.0323 | −1.24978 | ||||||||
\(879\) | 18.9804 | 0.640192 | ||||||||
\(880\) | 1.61620 | 0.0544822 | ||||||||
\(881\) | −20.7016 | −0.697455 | −0.348727 | − | 0.937224i | \(-0.613386\pi\) | ||||
−0.348727 | + | 0.937224i | \(0.613386\pi\) | |||||||
\(882\) | −5.47112 | −0.184222 | ||||||||
\(883\) | 18.1201 | 0.609789 | 0.304894 | − | 0.952386i | \(-0.401379\pi\) | ||||
0.304894 | + | 0.952386i | \(0.401379\pi\) | |||||||
\(884\) | −6.23585 | −0.209734 | ||||||||
\(885\) | −25.2853 | −0.849956 | ||||||||
\(886\) | 14.4007 | 0.483800 | ||||||||
\(887\) | −28.1843 | −0.946336 | −0.473168 | − | 0.880972i | \(-0.656890\pi\) | ||||
−0.473168 | + | 0.880972i | \(0.656890\pi\) | |||||||
\(888\) | 1.62721 | 0.0546057 | ||||||||
\(889\) | 4.27227 | 0.143287 | ||||||||
\(890\) | −8.78187 | −0.294369 | ||||||||
\(891\) | 0.622970 | 0.0208703 | ||||||||
\(892\) | 18.2081 | 0.609654 | ||||||||
\(893\) | 26.3227 | 0.880855 | ||||||||
\(894\) | −13.8186 | −0.462162 | ||||||||
\(895\) | −52.9236 | −1.76904 | ||||||||
\(896\) | 1.23648 | 0.0413079 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 14.7629 | 0.492646 | ||||||||
\(899\) | −10.5163 | −0.350739 | ||||||||
\(900\) | 1.73066 | 0.0576886 | ||||||||
\(901\) | 52.9779 | 1.76495 | ||||||||
\(902\) | −7.38202 | −0.245794 | ||||||||
\(903\) | 2.07578 | 0.0690777 | ||||||||
\(904\) | 1.36243 | 0.0453137 | ||||||||
\(905\) | −24.7412 | −0.822425 | ||||||||
\(906\) | −5.43503 | −0.180567 | ||||||||
\(907\) | −24.8123 | −0.823880 | −0.411940 | − | 0.911211i | \(-0.635149\pi\) | ||||
−0.411940 | + | 0.911211i | \(0.635149\pi\) | |||||||
\(908\) | −15.9853 | −0.530490 | ||||||||
\(909\) | −1.78374 | −0.0591629 | ||||||||
\(910\) | −4.24924 | −0.140861 | ||||||||
\(911\) | 37.6655 | 1.24791 | 0.623957 | − | 0.781459i | \(-0.285524\pi\) | ||||
0.623957 | + | 0.781459i | \(0.285524\pi\) | |||||||
\(912\) | −3.79020 | −0.125506 | ||||||||
\(913\) | −4.60417 | −0.152376 | ||||||||
\(914\) | −6.62444 | −0.219117 | ||||||||
\(915\) | 37.2901 | 1.23277 | ||||||||
\(916\) | 17.7317 | 0.585872 | ||||||||
\(917\) | 23.4281 | 0.773663 | ||||||||
\(918\) | 4.70760 | 0.155374 | ||||||||
\(919\) | −51.5748 | −1.70129 | −0.850647 | − | 0.525737i | \(-0.823790\pi\) | ||||
−0.850647 | + | 0.525737i | \(0.823790\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.9115 | 0.491350 | ||||||||
\(922\) | 7.35627 | 0.242266 | ||||||||
\(923\) | −8.60025 | −0.283081 | ||||||||
\(924\) | 0.770289 | 0.0253406 | ||||||||
\(925\) | 2.81615 | 0.0925945 | ||||||||
\(926\) | 34.6358 | 1.13820 | ||||||||
\(927\) | −19.8505 | −0.651976 | ||||||||
\(928\) | −1.11204 | −0.0365045 | ||||||||
\(929\) | −13.5989 | −0.446165 | −0.223082 | − | 0.974800i | \(-0.571612\pi\) | ||||
−0.223082 | + | 0.974800i | \(0.571612\pi\) | |||||||
\(930\) | 24.5342 | 0.804509 | ||||||||
\(931\) | 20.7366 | 0.679615 | ||||||||
\(932\) | −9.34447 | −0.306088 | ||||||||
\(933\) | −5.28838 | −0.173134 | ||||||||
\(934\) | 14.1030 | 0.461463 | ||||||||
\(935\) | 7.60843 | 0.248822 | ||||||||
\(936\) | −1.32463 | −0.0432970 | ||||||||
\(937\) | 10.4764 | 0.342248 | 0.171124 | − | 0.985250i | \(-0.445260\pi\) | ||||
0.171124 | + | 0.985250i | \(0.445260\pi\) | |||||||
\(938\) | 7.56880 | 0.247130 | ||||||||
\(939\) | 8.87040 | 0.289475 | ||||||||
\(940\) | −18.0176 | −0.587670 | ||||||||
\(941\) | −14.3525 | −0.467877 | −0.233938 | − | 0.972251i | \(-0.575161\pi\) | ||||
−0.233938 | + | 0.972251i | \(0.575161\pi\) | |||||||
\(942\) | −5.28204 | −0.172098 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −9.74629 | −0.317215 | ||||||||
\(945\) | 3.20786 | 0.104352 | ||||||||
\(946\) | 1.04583 | 0.0340029 | ||||||||
\(947\) | −2.21149 | −0.0718639 | −0.0359319 | − | 0.999354i | \(-0.511440\pi\) | ||||
−0.0359319 | + | 0.999354i | \(0.511440\pi\) | |||||||
\(948\) | 12.0823 | 0.392416 | ||||||||
\(949\) | 17.3395 | 0.562863 | ||||||||
\(950\) | −6.55953 | −0.212819 | ||||||||
\(951\) | 3.03971 | 0.0985694 | ||||||||
\(952\) | 5.82085 | 0.188655 | ||||||||
\(953\) | −22.9994 | −0.745023 | −0.372511 | − | 0.928028i | \(-0.621503\pi\) | ||||
−0.372511 | + | 0.928028i | \(0.621503\pi\) | |||||||
\(954\) | 11.2537 | 0.364352 | ||||||||
\(955\) | −4.13290 | −0.133737 | ||||||||
\(956\) | −5.00904 | −0.162004 | ||||||||
\(957\) | −0.692767 | −0.0223940 | ||||||||
\(958\) | 17.0476 | 0.550782 | ||||||||
\(959\) | 14.0910 | 0.455021 | ||||||||
\(960\) | 2.59435 | 0.0837323 | ||||||||
\(961\) | 58.4308 | 1.88486 | ||||||||
\(962\) | −2.15546 | −0.0694950 | ||||||||
\(963\) | 4.35922 | 0.140474 | ||||||||
\(964\) | −14.5761 | −0.469466 | ||||||||
\(965\) | 45.6039 | 1.46804 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.31090 | −0.267261 | −0.133630 | − | 0.991031i | \(-0.542663\pi\) | ||||
−0.133630 | + | 0.991031i | \(0.542663\pi\) | |||||||
\(968\) | −10.6119 | −0.341080 | ||||||||
\(969\) | −17.8427 | −0.573191 | ||||||||
\(970\) | −29.6944 | −0.953429 | ||||||||
\(971\) | −14.9920 | −0.481115 | −0.240557 | − | 0.970635i | \(-0.577330\pi\) | ||||
−0.240557 | + | 0.970635i | \(0.577330\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 6.55664 | 0.210196 | ||||||||
\(974\) | −12.3279 | −0.395010 | ||||||||
\(975\) | −2.29249 | −0.0734184 | ||||||||
\(976\) | 14.3736 | 0.460086 | ||||||||
\(977\) | 52.3758 | 1.67565 | 0.837824 | − | 0.545940i | \(-0.183827\pi\) | ||||
0.837824 | + | 0.545940i | \(0.183827\pi\) | |||||||
\(978\) | 9.09064 | 0.290686 | ||||||||
\(979\) | −2.10875 | −0.0673959 | ||||||||
\(980\) | −14.1940 | −0.453411 | ||||||||
\(981\) | −6.46538 | −0.206424 | ||||||||
\(982\) | −6.49393 | −0.207230 | ||||||||
\(983\) | 30.1510 | 0.961666 | 0.480833 | − | 0.876812i | \(-0.340334\pi\) | ||||
0.480833 | + | 0.876812i | \(0.340334\pi\) | |||||||
\(984\) | −11.8497 | −0.377756 | ||||||||
\(985\) | 3.16927 | 0.100981 | ||||||||
\(986\) | −5.23504 | −0.166718 | ||||||||
\(987\) | −8.58727 | −0.273336 | ||||||||
\(988\) | 5.02062 | 0.159727 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 1.61620 | 0.0513663 | ||||||||
\(991\) | 2.70097 | 0.0857992 | 0.0428996 | − | 0.999079i | \(-0.486340\pi\) | ||||
0.0428996 | + | 0.999079i | \(0.486340\pi\) | |||||||
\(992\) | 9.45679 | 0.300253 | ||||||||
\(993\) | 1.64126 | 0.0520838 | ||||||||
\(994\) | 8.02790 | 0.254629 | ||||||||
\(995\) | 0.260026 | 0.00824337 | ||||||||
\(996\) | −7.39068 | −0.234183 | ||||||||
\(997\) | 9.07176 | 0.287305 | 0.143653 | − | 0.989628i | \(-0.454115\pi\) | ||||
0.143653 | + | 0.989628i | \(0.454115\pi\) | |||||||
\(998\) | −13.6005 | −0.430515 | ||||||||
\(999\) | 1.62721 | 0.0514828 |
(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 | 3174.2.a.bd.1.4 | 5 | ||
3.2 | odd | 2 | 9522.2.a.bq.1.2 | 5 | |||
23.7 | odd | 22 | 138.2.e.a.49.1 | yes | 10 | ||
23.10 | odd | 22 | 138.2.e.a.31.1 | ✓ | 10 | ||
23.22 | odd | 2 | 3174.2.a.bc.1.2 | 5 | |||
69.53 | even | 22 | 414.2.i.d.325.1 | 10 | |||
69.56 | even | 22 | 414.2.i.d.307.1 | 10 | |||
69.68 | even | 2 | 9522.2.a.bt.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
138.2.e.a.31.1 | ✓ | 10 | 23.10 | odd | 22 | ||
138.2.e.a.49.1 | yes | 10 | 23.7 | odd | 22 | ||
414.2.i.d.307.1 | 10 | 69.56 | even | 22 | |||
414.2.i.d.325.1 | 10 | 69.53 | even | 22 | |||
3174.2.a.bc.1.2 | 5 | 23.22 | odd | 2 | |||
3174.2.a.bd.1.4 | 5 | 1.1 | even | 1 | trivial | ||
9522.2.a.bq.1.2 | 5 | 3.2 | odd | 2 | |||
9522.2.a.bt.1.4 | 5 | 69.68 | even | 2 |