Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(165,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.i (of order \(3\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(9.16682615204\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 14 x^{14} - 8 x^{13} + 136 x^{12} - 87 x^{11} + 706 x^{10} - 568 x^{9} + 2685 x^{8} + \cdots + 121 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 165.2 | ||
Root | \(1.12452 - 1.94772i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1148.165 |
Dual form | 1148.2.i.d.821.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).
\(n\) | \(493\) | \(575\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.12452 | + | 1.94772i | −0.649241 | + | 1.12452i | 0.334063 | + | 0.942551i | \(0.391580\pi\) |
−0.983304 | + | 0.181968i | \(0.941753\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.735486 | + | 1.27390i | 0.328919 | + | 0.569705i | 0.982298 | − | 0.187326i | \(-0.0599822\pi\) |
−0.653378 | + | 0.757032i | \(0.726649\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.221110 | − | 2.63650i | 0.0835717 | − | 0.996502i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.02909 | − | 1.78243i | −0.343029 | − | 0.594144i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.247127 | − | 0.428036i | 0.0745114 | − | 0.129058i | −0.826362 | − | 0.563139i | \(-0.809594\pi\) |
0.900874 | + | 0.434081i | \(0.142927\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.52254 | 1.53168 | 0.765838 | − | 0.643033i | \(-0.222324\pi\) | ||||
0.765838 | + | 0.643033i | \(0.222324\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.30827 | −0.854193 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.12812 | − | 3.68601i | 0.516145 | − | 0.893989i | −0.483679 | − | 0.875245i | \(-0.660700\pi\) |
0.999824 | − | 0.0187440i | \(-0.00596676\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.480467 | + | 0.832194i | 0.110227 | + | 0.190918i | 0.915862 | − | 0.401494i | \(-0.131509\pi\) |
−0.805635 | + | 0.592412i | \(0.798176\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.88653 | + | 3.39545i | 1.06633 | + | 0.740948i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.15001 | + | 1.99187i | 0.239793 | + | 0.415333i | 0.960655 | − | 0.277746i | \(-0.0895872\pi\) |
−0.720862 | + | 0.693079i | \(0.756254\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.41812 | − | 2.45626i | 0.283624 | − | 0.491251i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.11820 | −0.407648 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.25851 | 0.233699 | 0.116850 | − | 0.993150i | \(-0.462720\pi\) | ||||
0.116850 | + | 0.993150i | \(0.462720\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.13238 | − | 7.15750i | 0.742198 | − | 1.28552i | −0.209294 | − | 0.977853i | \(-0.567117\pi\) |
0.951492 | − | 0.307672i | \(-0.0995500\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.555797 | + | 0.962669i | 0.0967518 | + | 0.167579i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.52125 | − | 1.65743i | 0.595201 | − | 0.280158i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.11309 | + | 7.12407i | 0.676187 | + | 1.17119i | 0.976120 | + | 0.217230i | \(0.0697022\pi\) |
−0.299933 | + | 0.953960i | \(0.596964\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.21020 | + | 10.7564i | −0.994428 | + | 1.72240i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.33579 | 0.813700 | 0.406850 | − | 0.913495i | \(-0.366627\pi\) | ||||
0.406850 | + | 0.913495i | \(0.366627\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.51376 | − | 2.62191i | 0.225658 | − | 0.390851i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.83383 | − | 3.17628i | −0.267491 | − | 0.463308i | 0.700722 | − | 0.713434i | \(-0.252861\pi\) |
−0.968213 | + | 0.250126i | \(0.919528\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.90222 | − | 1.16591i | −0.986032 | − | 0.166559i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.78622 | + | 8.28998i | 0.670205 | + | 1.16083i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.27318 | + | 7.40136i | −0.586966 | + | 1.01665i | 0.407661 | + | 0.913133i | \(0.366344\pi\) |
−0.994627 | + | 0.103521i | \(0.966989\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.727033 | 0.0980331 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.16118 | −0.286255 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.736223 | + | 1.27518i | −0.0958481 | + | 0.166014i | −0.909962 | − | 0.414691i | \(-0.863890\pi\) |
0.814114 | + | 0.580705i | \(0.197223\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.11685 | + | 5.39855i | 0.399072 | + | 0.691213i | 0.993612 | − | 0.112853i | \(-0.0359989\pi\) |
−0.594539 | + | 0.804066i | \(0.702666\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.92691 | + | 2.31907i | −0.620733 | + | 0.292175i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.06175 | + | 7.03516i | 0.503798 | + | 0.872604i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.95758 | + | 3.39063i | −0.239157 | + | 0.414232i | −0.960473 | − | 0.278375i | \(-0.910204\pi\) |
0.721316 | + | 0.692606i | \(0.243538\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.17281 | −0.622733 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.1617 | −1.20597 | −0.602987 | − | 0.797751i | \(-0.706023\pi\) | ||||
−0.602987 | + | 0.797751i | \(0.706023\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.387918 | + | 0.671894i | −0.0454024 | + | 0.0786392i | −0.887834 | − | 0.460165i | \(-0.847790\pi\) |
0.842431 | + | 0.538804i | \(0.181124\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.18941 | + | 5.52421i | 0.368281 | + | 0.637881i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.07387 | − | 0.746191i | −0.122379 | − | 0.0850364i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.99271 | + | 8.64763i | 0.561724 | + | 0.972935i | 0.997346 | + | 0.0728051i | \(0.0231951\pi\) |
−0.435622 | + | 0.900130i | \(0.643472\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.46922 | − | 9.47297i | 0.607691 | − | 1.05255i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.68368 | −0.843393 | −0.421697 | − | 0.906737i | \(-0.638565\pi\) | ||||
−0.421697 | + | 0.906737i | \(0.638565\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.26081 | 0.679080 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.41522 | + | 2.45123i | −0.151727 | + | 0.262799i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.41540 | + | 5.91564i | 0.362031 | + | 0.627057i | 0.988295 | − | 0.152555i | \(-0.0487500\pi\) |
−0.626264 | + | 0.779611i | \(0.715417\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.22109 | − | 14.5601i | 0.128005 | − | 1.52632i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.29389 | + | 16.0975i | 0.963732 | + | 1.66923i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.706754 | + | 1.22413i | −0.0725115 | + | 0.125594i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.83506 | −0.693995 | −0.346998 | − | 0.937866i | \(-0.612799\pi\) | ||||
−0.346998 | + | 0.937866i | \(0.612799\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.01726 | −0.102238 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.24772 | + | 2.16111i | −0.124152 | + | 0.215038i | −0.921401 | − | 0.388612i | \(-0.872955\pi\) |
0.797249 | + | 0.603651i | \(0.206288\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.13955 | + | 1.97377i | 0.112284 | + | 0.194481i | 0.916691 | − | 0.399598i | \(-0.130850\pi\) |
−0.804407 | + | 0.594079i | \(0.797517\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.731492 | + | 8.72225i | −0.0713863 | + | 0.851204i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.02994 | + | 5.24800i | 0.292915 | + | 0.507344i | 0.974498 | − | 0.224397i | \(-0.0720413\pi\) |
−0.681583 | + | 0.731741i | \(0.738708\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.77659 | − | 4.80919i | 0.265949 | − | 0.460637i | −0.701863 | − | 0.712312i | \(-0.747648\pi\) |
0.967812 | + | 0.251675i | \(0.0809814\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −18.5010 | −1.75603 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.60020 | 0.903111 | 0.451555 | − | 0.892243i | \(-0.350869\pi\) | ||||
0.451555 | + | 0.892243i | \(0.350869\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.69163 | + | 2.92998i | −0.157745 | + | 0.273222i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.68317 | − | 9.84354i | −0.525409 | − | 0.910036i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.24761 | − | 6.42579i | −0.847727 | − | 0.589052i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.37786 | + | 9.31472i | 0.488896 | + | 0.846793i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.12452 | + | 1.94772i | −0.101394 | + | 0.175620i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.5269 | 1.03100 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.29583 | 0.381193 | 0.190596 | − | 0.981668i | \(-0.438958\pi\) | ||||
0.190596 | + | 0.981668i | \(0.438958\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.00020 | + | 10.3927i | −0.528288 | + | 0.915022i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.43217 | − | 11.1408i | −0.561981 | − | 0.973379i | −0.997324 | − | 0.0731146i | \(-0.976706\pi\) |
0.435343 | − | 0.900265i | \(-0.356627\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.30031 | − | 1.08274i | 0.199462 | − | 0.0938858i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.55791 | − | 2.69838i | −0.134083 | − | 0.232239i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.91997 | − | 17.1819i | 0.847520 | − | 1.46795i | −0.0358948 | − | 0.999356i | \(-0.511428\pi\) |
0.883415 | − | 0.468592i | \(-0.155239\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.3831 | 0.880685 | 0.440342 | − | 0.897830i | \(-0.354857\pi\) | ||||
0.440342 | + | 0.897830i | \(0.354857\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.24869 | 0.694665 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.36477 | − | 2.36384i | 0.114127 | − | 0.197674i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.925615 | + | 1.60321i | 0.0768682 | + | 0.133140i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.0326 | − | 12.1325i | 0.827471 | − | 1.00067i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.19926 | + | 14.2015i | 0.671710 | + | 1.16344i | 0.977419 | + | 0.211310i | \(0.0677730\pi\) |
−0.305710 | + | 0.952125i | \(0.598894\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.44633 | − | 2.50512i | 0.117701 | − | 0.203864i | −0.801155 | − | 0.598456i | \(-0.795781\pi\) |
0.918856 | + | 0.394593i | \(0.129114\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.76008 | −0.708211 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.1572 | 0.976494 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.7590 | − | 18.6352i | 0.858665 | − | 1.48725i | −0.0145378 | − | 0.999894i | \(-0.504628\pi\) |
0.873203 | − | 0.487357i | \(-0.162039\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.61054 | − | 16.6459i | −0.762165 | − | 1.32011i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.50583 | − | 2.59156i | 0.433920 | − | 0.204244i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.01866 | − | 3.49643i | −0.158114 | − | 0.273861i | 0.776075 | − | 0.630641i | \(-0.217208\pi\) |
−0.934188 | + | 0.356780i | \(0.883875\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.817562 | + | 1.41606i | −0.0636471 | + | 0.110240i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.8080 | −1.22326 | −0.611630 | − | 0.791144i | \(-0.709486\pi\) | ||||
−0.611630 | + | 0.791144i | \(0.709486\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 17.4984 | 1.34603 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.988885 | − | 1.71280i | 0.0756220 | − | 0.130981i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.97356 | − | 12.0786i | −0.530190 | − | 0.918316i | −0.999380 | − | 0.0352188i | \(-0.988787\pi\) |
0.469189 | − | 0.883098i | \(-0.344546\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.16235 | − | 4.28197i | −0.465830 | − | 0.323687i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.65579 | − | 2.86792i | −0.124457 | − | 0.215566i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.22591 | + | 14.2477i | −0.614833 | + | 1.06492i | 0.375580 | + | 0.926790i | \(0.377443\pi\) |
−0.990414 | + | 0.138133i | \(0.955890\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.78054 | 0.132347 | 0.0661733 | − | 0.997808i | \(-0.478921\pi\) | ||||
0.0661733 | + | 0.997808i | \(0.478921\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.0198 | −1.03638 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.05024 | + | 10.4793i | −0.444822 | + | 0.770455i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.05183 | − | 1.82182i | −0.0769174 | − | 0.133225i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.468356 | + | 5.58463i | −0.0340679 | + | 0.406222i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.1268 | − | 19.2722i | −0.805107 | − | 1.39449i | −0.916219 | − | 0.400678i | \(-0.868775\pi\) |
0.111112 | − | 0.993808i | \(-0.464559\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.17412 | − | 3.76569i | 0.156497 | − | 0.271061i | −0.777106 | − | 0.629370i | \(-0.783313\pi\) |
0.933603 | + | 0.358309i | \(0.116647\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −18.2701 | −1.30835 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.5511 | −1.32171 | −0.660854 | − | 0.750514i | \(-0.729806\pi\) | ||||
−0.660854 | + | 0.750514i | \(0.729806\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.01494 | − | 5.22203i | 0.213724 | − | 0.370180i | −0.739153 | − | 0.673537i | \(-0.764774\pi\) |
0.952877 | + | 0.303357i | \(0.0981075\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.40268 | − | 7.62566i | −0.310541 | − | 0.537873i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.278269 | − | 3.31805i | 0.0195306 | − | 0.232882i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.735486 | + | 1.27390i | 0.0513686 | + | 0.0889730i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.36691 | − | 4.09961i | 0.164512 | − | 0.284943i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.474945 | 0.0328526 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.97038 | −0.548704 | −0.274352 | − | 0.961629i | \(-0.588463\pi\) | ||||
−0.274352 | + | 0.961629i | \(0.588463\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.4270 | − | 19.7922i | 0.782968 | − | 1.35614i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.92440 | + | 6.79726i | 0.267642 | + | 0.463569i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17.9570 | − | 12.4776i | −1.21900 | − | 0.847035i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.872443 | − | 1.51112i | −0.0589542 | − | 0.102112i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.7526 | − | 20.3561i | 0.790567 | − | 1.36930i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.1994 | −1.21872 | −0.609360 | − | 0.792894i | \(-0.708573\pi\) | ||||
−0.609360 | + | 0.792894i | \(0.708573\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.83748 | −0.389165 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.28970 | − | 2.23383i | 0.0856004 | − | 0.148264i | −0.820047 | − | 0.572297i | \(-0.806053\pi\) |
0.905647 | + | 0.424033i | \(0.139386\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.2766 | − | 19.5317i | −0.745180 | − | 1.29069i | −0.950111 | − | 0.311913i | \(-0.899030\pi\) |
0.204930 | − | 0.978777i | \(-0.434303\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.66096 | − | 1.25250i | 0.175079 | − | 0.0824085i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.774942 | + | 1.34224i | 0.0507682 | + | 0.0879330i | 0.890293 | − | 0.455389i | \(-0.150500\pi\) |
−0.839525 | + | 0.543322i | \(0.817166\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.69751 | − | 4.67222i | 0.175966 | − | 0.304782i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −22.4576 | −1.45878 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.3710 | 1.05895 | 0.529477 | − | 0.848324i | \(-0.322388\pi\) | ||||
0.529477 | + | 0.848324i | \(0.322388\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.88014 | + | 10.1847i | −0.378773 | + | 0.656054i | −0.990884 | − | 0.134718i | \(-0.956987\pi\) |
0.612111 | + | 0.790772i | \(0.290321\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.12318 | + | 15.8018i | 0.585253 | + | 1.01369i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.59124 | − | 9.65025i | −0.229436 | − | 0.616532i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.65340 | + | 4.59582i | 0.168832 | + | 0.292425i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.64044 | − | 14.9657i | 0.547566 | − | 0.948412i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.1858 | 0.958517 | 0.479259 | − | 0.877674i | \(-0.340906\pi\) | ||||
0.479259 | + | 0.877674i | \(0.340906\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.13679 | 0.0714692 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.04040 | + | 12.1943i | −0.440887 | + | 0.763639i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.0473438 | − | 0.0820019i | −0.00295323 | − | 0.00511514i | 0.864545 | − | 0.502555i | \(-0.167607\pi\) |
−0.867498 | + | 0.497440i | \(0.834273\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 19.6920 | − | 9.26893i | 1.22360 | − | 0.575943i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.29511 | − | 2.24320i | −0.0801656 | − | 0.138851i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.95875 | + | 15.5170i | −0.552420 | + | 0.956819i | 0.445679 | + | 0.895193i | \(0.352962\pi\) |
−0.998099 | + | 0.0616267i | \(0.980371\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.5714 | −0.772258 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −15.3627 | −0.940183 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.1780 | + | 28.0212i | −0.986393 | + | 1.70848i | −0.350817 | + | 0.936444i | \(0.614096\pi\) |
−0.635576 | + | 0.772038i | \(0.719237\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.49051 | + | 14.7060i | 0.515762 | + | 0.893325i | 0.999833 | + | 0.0182965i | \(0.00582429\pi\) |
−0.484071 | + | 0.875029i | \(0.660842\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 26.9860 | + | 18.7515i | 1.63327 | + | 1.13489i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.700910 | − | 1.21401i | −0.0422665 | − | 0.0732077i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.211304 | − | 0.365990i | 0.0126960 | − | 0.0219902i | −0.859608 | − | 0.510955i | \(-0.829292\pi\) |
0.872304 | + | 0.488965i | \(0.162625\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −17.0103 | −1.01838 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.4772 | −0.625016 | −0.312508 | − | 0.949915i | \(-0.601169\pi\) | ||||
−0.312508 | + | 0.949915i | \(0.601169\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.7671 | − | 23.8454i | 0.818372 | − | 1.41746i | −0.0885089 | − | 0.996075i | \(-0.528210\pi\) |
0.906881 | − | 0.421387i | \(-0.138456\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.58952 | − | 2.75313i | −0.0941549 | − | 0.163081i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.221110 | − | 2.63650i | 0.0130517 | − | 0.155627i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.557791 | − | 0.966123i | −0.0328113 | − | 0.0568308i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.68616 | − | 13.3128i | 0.450571 | − | 0.780411i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 22.6387 | 1.32257 | 0.661283 | − | 0.750137i | \(-0.270012\pi\) | ||||
0.661283 | + | 0.750137i | \(0.270012\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.16593 | −0.126105 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.523464 | + | 0.906666i | −0.0303745 | + | 0.0526101i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.35095 | + | 11.0002i | 0.367285 | + | 0.636156i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.17980 | − | 14.0678i | 0.0680023 | − | 0.810854i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.80616 | − | 4.86042i | −0.161210 | − | 0.279224i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.58481 | + | 7.94112i | −0.262525 | + | 0.454707i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.00706 | −0.514060 | −0.257030 | − | 0.966403i | \(-0.582744\pi\) | ||||
−0.257030 | + | 0.966403i | \(0.582744\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.12580 | −0.291597 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.9014 | − | 22.3459i | 0.731573 | − | 1.26712i | −0.224638 | − | 0.974442i | \(-0.572120\pi\) |
0.956211 | − | 0.292679i | \(-0.0945467\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.65320 | + | 4.59548i | 0.149968 | + | 0.259752i | 0.931215 | − | 0.364469i | \(-0.118750\pi\) |
−0.781247 | + | 0.624221i | \(0.785416\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.57794 | − | 4.57075i | −0.370625 | − | 0.257532i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.36857 | − | 2.37044i | −0.0768668 | − | 0.133137i | 0.825030 | − | 0.565089i | \(-0.191158\pi\) |
−0.901897 | + | 0.431952i | \(0.857825\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.311011 | − | 0.538686i | 0.0174133 | − | 0.0301606i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.6289 | −0.760690 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.08997 | 0.227572 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.83162 | − | 13.5648i | 0.434420 | − | 0.752438i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.24465 | + | 10.8161i | 0.345330 | + | 0.598129i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.77973 | + | 4.13257i | −0.484042 | + | 0.227836i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.77447 | + | 10.0017i | 0.317394 | + | 0.549742i | 0.979943 | − | 0.199276i | \(-0.0638590\pi\) |
−0.662550 | + | 0.749018i | \(0.730526\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.46545 | − | 14.6626i | 0.463904 | − | 0.803505i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.75910 | −0.314653 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −31.6744 | −1.72541 | −0.862706 | − | 0.505705i | \(-0.831232\pi\) | ||||
−0.862706 | + | 0.505705i | \(0.831232\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.7956 | + | 18.6985i | −0.586337 | + | 1.01557i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.04244 | − | 3.53762i | −0.110605 | − | 0.191573i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.60007 | + | 17.9399i | −0.248380 | + | 0.968663i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.80453 | − | 6.58964i | −0.204829 | − | 0.354774i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.07049 | − | 7.05030i | 0.218515 | − | 0.378480i | −0.735839 | − | 0.677157i | \(-0.763212\pi\) |
0.954354 | + | 0.298677i | \(0.0965453\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.07115 | 0.217924 | 0.108962 | − | 0.994046i | \(-0.465247\pi\) | ||||
0.108962 | + | 0.994046i | \(0.465247\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.6979 | −0.624385 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.2796 | + | 26.4651i | −0.813252 | + | 1.40859i | 0.0973245 | + | 0.995253i | \(0.468972\pi\) |
−0.910576 | + | 0.413341i | \(0.864362\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.47380 | − | 12.9450i | −0.396668 | − | 0.687050i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 22.9148 | − | 10.7859i | 1.21278 | − | 0.570848i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.5051 | + | 25.1236i | 0.765550 | + | 1.32597i | 0.939955 | + | 0.341297i | \(0.110866\pi\) |
−0.174405 | + | 0.984674i | \(0.555800\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.03830 | − | 15.6548i | 0.475700 | − | 0.823937i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −24.1900 | −1.26965 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.14123 | −0.0597349 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.22199 | + | 14.2409i | −0.429185 | + | 0.743369i | −0.996801 | − | 0.0799237i | \(-0.974532\pi\) |
0.567616 | + | 0.823293i | \(0.307866\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.02909 | − | 1.78243i | −0.0535721 | − | 0.0927896i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18.5688 | + | 12.9027i | 0.964044 | + | 0.669876i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.2182 | − | 22.8946i | −0.684413 | − | 1.18544i | −0.973621 | − | 0.228171i | \(-0.926725\pi\) |
0.289208 | − | 0.957266i | \(-0.406608\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.9622 | + | 22.4512i | −0.669366 | + | 1.15938i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.95016 | 0.357951 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.6085 | −0.801756 | −0.400878 | − | 0.916132i | \(-0.631295\pi\) | ||||
−0.400878 | + | 0.916132i | \(0.631295\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.83074 | + | 8.36709i | −0.247486 | + | 0.428659i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.68236 | + | 2.91393i | 0.0859645 | + | 0.148895i | 0.905802 | − | 0.423702i | \(-0.139270\pi\) |
−0.819837 | + | 0.572597i | \(0.805936\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.160754 | − | 1.91682i | 0.00819279 | − | 0.0976901i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.49099 | − | 9.51068i | −0.279123 | − | 0.483455i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.612558 | − | 1.06098i | 0.0310579 | − | 0.0537939i | −0.850079 | − | 0.526656i | \(-0.823446\pi\) |
0.881137 | + | 0.472862i | \(0.156779\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.78940 | 0.495071 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 28.9324 | 1.45945 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.34414 | + | 12.7204i | −0.369524 | + | 0.640034i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.2659 | − | 31.6375i | −0.916742 | − | 1.58784i | −0.804331 | − | 0.594181i | \(-0.797476\pi\) |
−0.112410 | − | 0.993662i | \(-0.535857\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.477858 | + | 5.69794i | −0.0239228 | + | 0.285254i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.9933 | + | 25.9691i | 0.748728 | + | 1.29684i | 0.948433 | + | 0.316979i | \(0.102668\pi\) |
−0.199704 | + | 0.979856i | \(0.563998\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 22.8212 | − | 39.5276i | 1.13681 | − | 1.96901i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 16.0901 | 0.799526 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.06581 | 0.201535 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.5125 | − | 32.0646i | 0.915386 | − | 1.58549i | 0.109050 | − | 0.994036i | \(-0.465219\pi\) |
0.806336 | − | 0.591458i | \(-0.201447\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 22.3104 | + | 38.6427i | 1.10049 | + | 1.90610i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.19921 | + | 2.22300i | 0.157423 | + | 0.109387i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.65124 | − | 9.78823i | −0.277408 | − | 0.480485i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.6760 | + | 20.2235i | −0.571777 | + | 0.990347i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.4042 | 1.19222 | 0.596112 | − | 0.802901i | \(-0.296711\pi\) | ||||
0.596112 | + | 0.802901i | \(0.296711\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.51451 | −0.122550 | −0.0612750 | − | 0.998121i | \(-0.519517\pi\) | ||||
−0.0612750 | + | 0.998121i | \(0.519517\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.77433 | + | 6.53734i | −0.183514 | + | 0.317856i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.03586 | − | 10.4544i | −0.292782 | − | 0.507114i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.9224 | − | 7.02390i | 0.722147 | − | 0.339910i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.06941 | + | 5.31637i | 0.148193 | + | 0.256677i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.91625 | + | 15.4434i | −0.429481 | + | 0.743882i | −0.996827 | − | 0.0795969i | \(-0.974637\pi\) |
0.567347 | + | 0.823479i | \(0.307970\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.2172 | −1.25992 | −0.629960 | − | 0.776628i | \(-0.716929\pi\) | ||||
−0.629960 | + | 0.776628i | \(0.716929\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.16349 | −0.199624 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.10508 | + | 1.91405i | −0.0528631 | + | 0.0915617i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.03303 | − | 10.4495i | −0.287941 | − | 0.498728i | 0.685377 | − | 0.728188i | \(-0.259637\pi\) |
−0.973318 | + | 0.229460i | \(0.926304\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.02483 | + | 13.5026i | 0.239278 | + | 0.642979i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.5949 | + | 27.0112i | 0.740937 | + | 1.28334i | 0.952069 | + | 0.305884i | \(0.0989519\pi\) |
−0.211131 | + | 0.977458i | \(0.567715\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.02395 | + | 8.70174i | −0.238158 | + | 0.412502i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −36.8809 | −1.74441 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.5606 | −0.592770 | −0.296385 | − | 0.955069i | \(-0.595781\pi\) | ||||
−0.296385 | + | 0.955069i | \(0.595781\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.247127 | − | 0.428036i | 0.0116367 | − | 0.0201554i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.25286 | + | 5.63411i | 0.152832 | + | 0.264714i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 19.4463 | − | 9.15325i | 0.911655 | − | 0.429111i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.104526 | + | 0.181044i | 0.00488950 | + | 0.00846887i | 0.868460 | − | 0.495760i | \(-0.165110\pi\) |
−0.863570 | + | 0.504228i | \(0.831777\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.50779 | + | 7.80772i | −0.210406 | + | 0.364433i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.3033 | −0.479873 | −0.239936 | − | 0.970789i | \(-0.577127\pi\) | ||||
−0.239936 | + | 0.970789i | \(0.577127\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.65140 | −0.402065 | −0.201032 | − | 0.979585i | \(-0.564430\pi\) | ||||
−0.201032 | + | 0.979585i | \(0.564430\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −13.6711 | + | 23.6790i | −0.633980 | + | 1.09809i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.3792 | − | 19.7093i | −0.526566 | − | 0.912040i | −0.999521 | − | 0.0309530i | \(-0.990146\pi\) |
0.472954 | − | 0.881087i | \(-0.343188\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.50655 | + | 5.91086i | 0.392796 | + | 0.272938i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 24.1975 | + | 41.9113i | 1.11496 | + | 1.93117i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.31862 | − | 2.28391i | 0.0606300 | − | 0.105014i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.72544 | 0.125052 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 17.5899 | 0.805385 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.884953 | + | 1.53278i | −0.0404345 | + | 0.0700347i | −0.885534 | − | 0.464574i | \(-0.846208\pi\) |
0.845100 | + | 0.534608i | \(0.179541\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22.7147 | + | 39.3430i | 1.03570 | + | 1.79388i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.14376 | + | 13.6381i | −0.0520429 | + | 0.620555i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.02709 | − | 8.70718i | −0.228269 | − | 0.395373i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.5661 | − | 23.4971i | 0.614738 | − | 1.06476i | −0.375692 | − | 0.926744i | \(-0.622595\pi\) |
0.990430 | − | 0.138013i | \(-0.0440716\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.08010 | 0.410616 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.410698 | −0.0185345 | −0.00926727 | − | 0.999957i | \(-0.502950\pi\) | ||||
−0.00926727 | + | 0.999957i | \(0.502950\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.67826 | − | 4.63888i | 0.120623 | − | 0.208925i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.748180 | − | 1.29589i | −0.0336282 | − | 0.0582457i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.24686 | + | 26.7913i | −0.100785 | + | 1.20176i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.1026 | + | 17.4982i | 0.452255 | + | 0.783328i | 0.998526 | − | 0.0542805i | \(-0.0172865\pi\) |
−0.546271 | + | 0.837608i | \(0.683953\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.7764 | − | 30.7896i | 0.794191 | − | 1.37558i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −38.0193 | −1.69520 | −0.847599 | − | 0.530638i | \(-0.821952\pi\) | ||||
−0.847599 | + | 0.530638i | \(0.821952\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.67071 | −0.163345 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −19.6773 | + | 34.0821i | −0.873900 | + | 1.51364i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.6299 | − | 37.4642i | −0.958730 | − | 1.66057i | −0.725591 | − | 0.688126i | \(-0.758434\pi\) |
−0.233139 | − | 0.972443i | \(-0.574900\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.68567 | + | 1.17131i | 0.0745698 | + | 0.0518156i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.01773 | − | 1.76276i | −0.0449338 | − | 0.0778276i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.67625 | + | 2.90335i | −0.0738645 | + | 0.127937i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.81275 | −0.0797246 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 31.3676 | 1.37689 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.35210 | + | 4.07395i | −0.103047 | + | 0.178483i | −0.912939 | − | 0.408097i | \(-0.866193\pi\) |
0.809891 | + | 0.586580i | \(0.199526\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.59410 | − | 14.8854i | −0.375794 | − | 0.650894i | 0.614652 | − | 0.788799i | \(-0.289297\pi\) |
−0.990446 | + | 0.137905i | \(0.955963\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 15.2698 | − | 7.18740i | 0.666428 | − | 0.313684i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17.5884 | − | 30.4640i | −0.766164 | − | 1.32703i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.85498 | − | 15.3373i | 0.384999 | − | 0.666838i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.03055 | 0.131515 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.52254 | 0.239208 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.45695 | + | 7.71967i | −0.192691 | + | 0.333750i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −18.5004 | − | 32.0436i | −0.798351 | − | 1.38278i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.20477 | + | 2.66627i | −0.0949663 | + | 0.114844i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.71714 | + | 16.8306i | 0.417772 | + | 0.723603i | 0.995715 | − | 0.0924744i | \(-0.0294776\pi\) |
−0.577943 | + | 0.816077i | \(0.696144\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.00225 | + | 3.46800i | −0.0859249 | + | 0.148826i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.16857 | 0.349903 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.8699 | −1.06336 | −0.531681 | − | 0.846945i | \(-0.678439\pi\) | ||||
−0.531681 | + | 0.846945i | \(0.678439\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.41503 | − | 11.1112i | 0.273787 | − | 0.474213i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.604672 | + | 1.04732i | 0.0257599 | + | 0.0446175i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 23.9034 | − | 11.2512i | 1.01648 | − | 0.478449i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −13.6072 | − | 23.5684i | −0.577594 | − | 1.00042i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10.8840 | + | 18.8516i | −0.461169 | + | 0.798768i | −0.999020 | − | 0.0442721i | \(-0.985903\pi\) |
0.537851 | + | 0.843040i | \(0.319236\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 29.4671 | 1.24633 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.73121 | 0.199752 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17.3695 | + | 30.0848i | −0.732036 | + | 1.26792i | 0.223975 | + | 0.974595i | \(0.428097\pi\) |
−0.956011 | + | 0.293329i | \(0.905237\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.06082 | + | 12.2297i | 0.297051 | + | 0.514507i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −23.7661 | − | 16.5141i | −0.998084 | − | 0.693529i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.1067 | + | 33.0937i | 0.800993 | + | 1.38736i | 0.918963 | + | 0.394343i | \(0.129028\pi\) |
−0.117970 | + | 0.993017i | \(0.537639\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.8229 | − | 39.5304i | 0.955109 | − | 1.65430i | 0.220990 | − | 0.975276i | \(-0.429071\pi\) |
0.734119 | − | 0.679021i | \(-0.237595\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 50.0492 | 2.09083 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.52338 | 0.272044 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.59966 | − | 4.50274i | 0.108225 | − | 0.187452i | −0.806826 | − | 0.590789i | \(-0.798817\pi\) |
0.915051 | + | 0.403337i | \(0.132150\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.88969 | + | 8.46919i | 0.203209 | + | 0.351968i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.69894 | + | 20.2580i | −0.0704838 | + | 0.840443i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.11203 | + | 3.65814i | 0.0874713 | + | 0.151505i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.35979 | − | 14.4796i | 0.345635 | − | 0.598657i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.2599 | −0.506020 | −0.253010 | − | 0.967464i | \(-0.581421\pi\) | ||||
−0.253010 | + | 0.967464i | \(0.581421\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.94190 | 0.327240 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 20.8610 | − | 36.1324i | 0.858108 | − | 1.48629i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.23297 | − | 10.7958i | −0.255957 | − | 0.443331i | 0.709198 | − | 0.705010i | \(-0.249057\pi\) |
−0.965155 | + | 0.261679i | \(0.915724\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.38433 | − | 16.5066i | 0.0567519 | − | 0.676705i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.78072 | + | 11.7445i | 0.277516 | + | 0.480672i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.4454 | − | 37.1445i | 0.876235 | − | 1.51768i | 0.0207938 | − | 0.999784i | \(-0.493381\pi\) |
0.855441 | − | 0.517900i | \(-0.173286\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.40756 | 0.0982066 | 0.0491033 | − | 0.998794i | \(-0.484364\pi\) | ||||
0.0491033 | + | 0.998794i | \(0.484364\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.05809 | 0.328151 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.91068 | + | 13.7017i | −0.321615 | + | 0.557053i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.51826 | + | 6.09380i | 0.142802 | + | 0.247340i | 0.928551 | − | 0.371206i | \(-0.121056\pi\) |
−0.785749 | + | 0.618545i | \(0.787722\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.14973 | + | 4.27320i | 0.249200 | + | 0.173159i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.1274 | − | 17.5411i | −0.409710 | − | 0.709638i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.2736 | + | 26.4547i | −0.616897 | + | 1.06850i | 0.373152 | + | 0.927770i | \(0.378277\pi\) |
−0.990049 | + | 0.140726i | \(0.955056\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.30827 | −0.133402 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.2455 | −0.654018 | −0.327009 | − | 0.945021i | \(-0.606041\pi\) | ||||
−0.327009 | + | 0.945021i | \(0.606041\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.1570 | + | 22.7886i | −0.528825 | + | 0.915952i | 0.470610 | + | 0.882342i | \(0.344034\pi\) |
−0.999435 | + | 0.0336109i | \(0.989299\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.43594 | − | 4.21918i | −0.0977511 | − | 0.169310i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.3517 | − | 7.69667i | 0.655119 | − | 0.308361i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.38727 | + | 2.40282i | 0.0554909 | + | 0.0961130i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.534085 | + | 0.925062i | −0.0213293 | + | 0.0369434i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 35.0126 | 1.39604 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.3206 | 1.32647 | 0.663237 | − | 0.748410i | \(-0.269182\pi\) | ||||
0.663237 | + | 0.748410i | \(0.269182\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.96285 | − | 15.5241i | 0.356241 | − | 0.617028i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.15952 | + | 5.47245i | 0.125382 | + | 0.217168i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −38.1178 | − | 6.43879i | −1.51028 | − | 0.255114i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.4573 | + | 18.1126i | 0.413684 | + | 0.716522i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.1231 | + | 29.6581i | −0.676322 | + | 1.17142i | 0.299758 | + | 0.954015i | \(0.403094\pi\) |
−0.976081 | + | 0.217409i | \(0.930239\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.7446 | 0.699777 | 0.349889 | − | 0.936791i | \(-0.386219\pi\) | ||||
0.349889 | + | 0.936791i | \(0.386219\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −17.6523 | −0.695057 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.17566 | + | 12.4286i | −0.282104 | + | 0.488619i | −0.971903 | − | 0.235382i | \(-0.924366\pi\) |
0.689799 | + | 0.724001i | \(0.257699\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.363881 | + | 0.630260i | 0.0142836 | + | 0.0247399i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 44.4959 | − | 20.9440i | 1.74393 | − | 0.820860i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.5483 | − | 26.9305i | −0.608452 | − | 1.05387i | −0.991496 | − | 0.130140i | \(-0.958457\pi\) |
0.383043 | − | 0.923730i | \(-0.374876\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.46154 | − | 16.3879i | 0.369693 | − | 0.640327i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.59681 | 0.0622973 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.5409 | −0.955980 | −0.477990 | − | 0.878365i | \(-0.658634\pi\) | ||||
−0.477990 | + | 0.878365i | \(0.658634\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.2992 | + | 23.0350i | −0.517281 | + | 0.895956i | 0.482518 | + | 0.875886i | \(0.339722\pi\) |
−0.999799 | + | 0.0200702i | \(0.993611\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 26.4321 | + | 45.7817i | 1.02654 | + | 1.77802i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.07115 | + | 2.13402i | 0.119094 | + | 0.0827539i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.44729 | + | 2.50678i | 0.0560393 | + | 0.0970630i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 20.4655 | − | 35.4473i | 0.791243 | − | 1.37047i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.08103 | 0.118942 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.9351 | −0.806988 | −0.403494 | − | 0.914982i | \(-0.632204\pi\) | ||||
−0.403494 | + | 0.914982i | \(0.632204\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.00387 | + | 5.20285i | −0.115619 | + | 0.200258i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.41343 | + | 2.44814i | 0.0543227 | + | 0.0940896i | 0.891908 | − | 0.452217i | \(-0.149367\pi\) |
−0.837585 | + | 0.546307i | \(0.816033\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.51130 | + | 18.0206i | −0.0579984 | + | 0.691568i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.90058 | + | 5.02396i | 0.111151 | + | 0.192519i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.35578 | + | 12.7406i | −0.281461 | + | 0.487505i | −0.971745 | − | 0.236034i | \(-0.924152\pi\) |
0.690284 | + | 0.723539i | \(0.257486\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 29.1840 | 1.11506 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 50.7231 | 1.93521 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −23.5988 | + | 40.8743i | −0.899042 | + | 1.55719i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.74185 | − | 8.21312i | −0.180388 | − | 0.312442i | 0.761624 | − | 0.648019i | \(-0.224402\pi\) |
−0.942013 | + | 0.335577i | \(0.891069\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.224926 | + | 2.68200i | −0.00854423 | + | 0.101881i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.63664 | + | 13.2271i | 0.289674 | + | 0.501731i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.12812 | − | 3.68601i | 0.0806083 | − | 0.139618i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.48575 | −0.131843 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.62883 | 0.250367 | 0.125184 | − | 0.992134i | \(-0.460048\pi\) | ||||
0.125184 | + | 0.992134i | \(0.460048\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.95241 | + | 6.84577i | −0.149068 | + | 0.258193i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.06680 | + | 10.5080i | 0.228489 | + | 0.395754i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.42187 | + | 3.76744i | 0.203910 | + | 0.141689i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.7298 | + | 25.5128i | 0.553191 | + | 0.958155i | 0.998042 | + | 0.0625502i | \(0.0199234\pi\) |
−0.444851 | + | 0.895605i | \(0.646743\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.2759 | − | 17.7983i | 0.385375 | − | 0.667490i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 19.0091 | 0.711895 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.01506 | 0.150155 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −18.4096 | + | 31.8863i | −0.687517 | + | 1.19081i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.02658 | − | 13.9024i | −0.299341 | − | 0.518473i | 0.676644 | − | 0.736310i | \(-0.263433\pi\) |
−0.975985 | + | 0.217836i | \(0.930100\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.45579 | − | 2.56801i | 0.203184 | − | 0.0956377i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13.2247 | − | 22.9058i | −0.491831 | − | 0.851875i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.78472 | − | 3.09122i | 0.0662827 | − | 0.114805i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 41.7494 | 1.54840 | 0.774199 | − | 0.632942i | \(-0.218153\pi\) | ||||
0.774199 | + | 0.632942i | \(0.218153\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.22146 | −0.304498 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.3552 | − | 19.6678i | 0.419987 | − | 0.727440i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.63490 | − | 13.2240i | −0.282002 | − | 0.488441i | 0.689876 | − | 0.723927i | \(-0.257665\pi\) |
−0.971878 | + | 0.235486i | \(0.924332\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 22.8344 | + | 3.85715i | 0.842261 | + | 0.142273i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.967541 | + | 1.67583i | 0.0356398 | + | 0.0617300i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.7304 | + | 44.5664i | −0.946508 | + | 1.63940i | −0.193805 | + | 0.981040i | \(0.562083\pi\) |
−0.752703 | + | 0.658360i | \(0.771250\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11.9352 | −0.438450 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.2055 | −0.521148 | −0.260574 | − | 0.965454i | \(-0.583912\pi\) | ||||
−0.260574 | + | 0.965454i | \(0.583912\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.0609 | + | 20.8901i | −0.441877 | + | 0.765353i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.90717 | + | 13.6956i | 0.289308 | + | 0.501097i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.5063 | − | 6.82803i | 0.530048 | − | 0.249491i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.0768 | − | 41.7023i | −0.878576 | − | 1.52174i | −0.852904 | − | 0.522068i | \(-0.825161\pi\) |
−0.0256728 | − | 0.999670i | \(-0.508173\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −17.0767 | + | 29.5777i | −0.622309 | + | 1.07787i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.25503 | 0.154856 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.7677 | −0.754816 | −0.377408 | − | 0.926047i | \(-0.623185\pi\) | ||||
−0.377408 | + | 0.926047i | \(0.623185\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.27834 | + | 2.21415i | −0.0464008 | + | 0.0803685i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.90446 | + | 6.76273i | 0.141537 | + | 0.245149i | 0.928075 | − | 0.372392i | \(-0.121462\pi\) |
−0.786539 | + | 0.617541i | \(0.788129\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.0655 | − | 8.38382i | −0.436800 | − | 0.303515i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.44292 | − | 11.1595i | −0.232944 | − | 0.403471i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.06582 | + | 7.04221i | −0.146808 | + | 0.254279i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.74705 | −0.243305 | −0.121652 | − | 0.992573i | \(-0.538819\pi\) | ||||
−0.121652 | + | 0.992573i | \(0.538819\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.212956 | 0.00766943 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.0211 | − | 20.8212i | 0.432369 | − | 0.748885i | −0.564708 | − | 0.825291i | \(-0.691011\pi\) |
0.997077 | + | 0.0764061i | \(0.0243445\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.7204 | − | 20.3004i | −0.421010 | − | 0.729211i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.09075 | + | 48.7777i | −0.146755 | + | 1.74989i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.480467 | + | 0.832194i | 0.0172145 | + | 0.0298164i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.51123 | + | 4.34958i | −0.0898589 | + | 0.155640i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.66578 | −0.0952671 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 31.6525 | 1.12973 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.3714 | + | 28.3560i | −0.583576 | + | 1.01078i | 0.411476 | + | 0.911421i | \(0.365014\pi\) |
−0.995051 | + | 0.0993620i | \(0.968320\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −20.1486 | − | 34.8983i | −0.717308 | − | 1.24241i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.12270 | − | 25.3109i | 0.0754745 | − | 0.899952i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.2129 | + | 29.8137i | 0.611250 | + | 1.05872i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 14.1368 | − | 24.4857i | 0.501382 | − | 0.868419i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −50.3514 | −1.78354 | −0.891769 | − | 0.452491i | \(-0.850535\pi\) | ||||
−0.891769 | + | 0.452491i | \(0.850535\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.6104 | −0.552257 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.02948 | − | 12.1754i | 0.248374 | − | 0.430197i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.191730 | + | 0.332086i | 0.00676600 | + | 0.0117190i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.35085 | + | 5.10781i | 0.259083 | + | 0.180027i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −36.3850 | − | 63.0207i | −1.28081 | − | 2.21844i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20.1863 | + | 34.9637i | −0.709712 | + | 1.22926i | 0.255252 | + | 0.966875i | \(0.417842\pi\) |
−0.964964 | + | 0.262383i | \(0.915492\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 46.0779 | 1.61801 | 0.809007 | − | 0.587799i | \(-0.200006\pi\) | ||||
0.809007 | + | 0.587799i | \(0.200006\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −38.1910 | −1.33942 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.96940 | − | 5.14315i | 0.104013 | − | 0.180157i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.56367 | + | 4.44041i | 0.0896916 | + | 0.155350i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −27.2091 | + | 12.8072i | −0.950762 | + | 0.447518i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.08693 | − | 14.0070i | −0.282236 | − | 0.488847i | 0.689699 | − | 0.724096i | \(-0.257743\pi\) |
−0.971935 | + | 0.235249i | \(0.924409\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.81340 | + | 4.87295i | −0.0980689 | + | 0.169860i | −0.910885 | − | 0.412660i | \(-0.864600\pi\) |
0.812816 | + | 0.582520i | \(0.197933\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.15275 | 0.109765 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.75878 | −0.304573 | −0.152286 | − | 0.988336i | \(-0.548664\pi\) | ||||
−0.152286 | + | 0.988336i | \(0.548664\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.80296 | + | 16.9792i | −0.340471 | + | 0.589713i | −0.984520 | − | 0.175271i | \(-0.943920\pi\) |
0.644049 | + | 0.764984i | \(0.277253\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.475231 | + | 0.823125i | 0.0164856 | + | 0.0285539i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.9863 | + | 22.9605i | −0.657837 | + | 0.795533i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.6266 | − | 20.1378i | −0.402354 | − | 0.696898i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.75323 | + | 15.1610i | −0.302556 | + | 0.524042i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.03213 | 0.311824 | 0.155912 | − | 0.987771i | \(-0.450168\pi\) | ||||
0.155912 | + | 0.987771i | \(0.450168\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.4162 | −0.945385 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11.7818 | − | 20.4067i | 0.405786 | − | 0.702843i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.8698 | + | 22.2912i | 0.442736 | + | 0.766842i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 25.7473 | − | 12.1191i | 0.884688 | − | 0.416418i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 30.9628 | + | 53.6292i | 1.06264 | + | 1.84055i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.46014 | + | 16.3854i | −0.324289 | + | 0.561686i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23.1999 | −0.794348 | −0.397174 | − | 0.917743i | \(-0.630009\pi\) | ||||
−0.397174 | + | 0.917743i | \(0.630009\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.90925 | 0.0994941 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.78332 | + | 4.82085i | −0.0950763 | + | 0.164677i | −0.909640 | − | 0.415397i | \(-0.863643\pi\) |
0.814564 | + | 0.580073i | \(0.196976\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.3020 | + | 23.0398i | 0.453860 | + | 0.786108i | 0.998622 | − | 0.0524826i | \(-0.0167134\pi\) |
−0.544762 | + | 0.838591i | \(0.683380\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.88653 | + | 3.39545i | 0.166532 | + | 0.115717i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.63236 | + | 4.55938i | 0.0896066 | + | 0.155203i | 0.907345 | − | 0.420387i | \(-0.138106\pi\) |
−0.817738 | + | 0.575590i | \(0.804772\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.2579 | − | 17.7672i | 0.348780 | − | 0.604104i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.50899 | 0.0852097 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.93533 | 0.167420 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.8108 | + | 18.7249i | −0.366311 | + | 0.634469i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.03387 | + | 12.1830i | 0.238061 | + | 0.412333i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.54871 | − | 30.3906i | 0.0861621 | − | 1.02739i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.9460 | − | 25.8873i | −0.504691 | − | 0.874151i | −0.999985 | − | 0.00542540i | \(-0.998273\pi\) |
0.495294 | − | 0.868725i | \(-0.335060\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −25.4576 | + | 44.0939i | −0.858665 | + | 1.48725i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.34231 | −0.213678 | −0.106839 | − | 0.994276i | \(-0.534073\pi\) | ||||
−0.106839 | + | 0.994276i | \(0.534073\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.9746 | −0.537587 | −0.268794 | − | 0.963198i | \(-0.586625\pi\) | ||||
−0.268794 | + | 0.963198i | \(0.586625\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.43563 | − | 4.21863i | 0.0818727 | − | 0.141808i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.77839 | + | 11.7405i | 0.227596 | + | 0.394208i | 0.957095 | − | 0.289774i | \(-0.0935801\pi\) |
−0.729499 | + | 0.683982i | \(0.760247\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.949850 | − | 11.3259i | 0.0318569 | − | 0.379859i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.70318 | − | 4.68204i | −0.0905599 | − | 0.156854i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.76219 | − | 3.05220i | 0.0589693 | − | 0.102138i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −24.2002 | −0.808923 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −28.5670 | −0.953826 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.20064 | − | 9.00777i | 0.173451 | − | 0.300426i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.1877 | + | 31.5020i | 0.605919 | + | 1.04948i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 26.0735 | + | 18.1174i | 0.867671 | + | 0.602910i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.30956 | + | 2.26823i | 0.0435314 | + | 0.0753985i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.2253 | + | 24.6390i | −0.472344 | + | 0.818123i | −0.999499 | − | 0.0316455i | \(-0.989925\pi\) |
0.527155 | + | 0.849769i | \(0.323259\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.13604 | 0.170352 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27.8892 | 0.924011 | 0.462006 | − | 0.886877i | \(-0.347130\pi\) | ||||
0.462006 | + | 0.886877i | \(0.347130\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.89884 | + | 3.28889i | −0.0628424 | + | 0.108846i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −10.3114 | − | 17.8599i | −0.340885 | − | 0.590429i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −30.7950 | + | 14.4950i | −1.01694 | + | 0.478668i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.6711 | − | 25.4111i | −0.483955 | − | 0.838234i | 0.515875 | − | 0.856664i | \(-0.327467\pi\) |
−0.999830 | + | 0.0184294i | \(0.994133\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.1286 | − | 17.5433i | 0.333749 | − | 0.578071i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −56.1185 | −1.84716 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 23.3314 | 0.767132 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.34540 | − | 4.06235i | 0.0770331 | − | 0.133425i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22.8697 | − | 39.6114i | −0.750329 | − | 1.29961i | −0.947663 | − | 0.319272i | \(-0.896562\pi\) |
0.197334 | − | 0.980336i | \(-0.436772\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.34603 | − | 6.30417i | −0.0768880 | − | 0.206611i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 29.0158 | + | 50.2568i | 0.949935 | + | 1.64534i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.54721 | − | 2.67985i | 0.0505993 | − | 0.0876405i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.24433 | 0.269331 | 0.134665 | − | 0.990891i | \(-0.457004\pi\) | ||||
0.134665 | + | 0.990891i | \(0.457004\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.9343 | −0.389462 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.11811 | − | 8.86482i | 0.166846 | − | 0.288985i | −0.770464 | − | 0.637484i | \(-0.779975\pi\) |
0.937309 | + | 0.348499i | \(0.113309\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.15001 | + | 1.99187i | 0.0374493 | + | 0.0648641i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.45873 | + | 3.51078i | −0.242633 | + | 0.114206i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.51873 | − | 9.55872i | −0.179335 | − | 0.310617i | 0.762318 | − | 0.647202i | \(-0.224061\pi\) |
−0.941653 | + | 0.336586i | \(0.890728\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.14229 | + | 3.71056i | −0.0695418 | + | 0.120450i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.15595 | 0.199620 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.620938 | 0.0201141 | 0.0100571 | − | 0.999949i | \(-0.496799\pi\) | ||||
0.0100571 | + | 0.999949i | \(0.496799\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.3672 | − | 28.3488i | 0.529630 | − | 0.917347i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.699475 | + | 1.21153i | 0.0226108 | + | 0.0391631i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −43.1066 | − | 29.9530i | −1.39198 | − | 0.967234i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18.6532 | − | 32.3083i | −0.601716 | − | 1.04220i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.23614 | − | 10.8013i | 0.200957 | − | 0.348067i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.39616 | 0.205900 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.9164 | 0.511836 | 0.255918 | − | 0.966698i | \(-0.417622\pi\) | ||||
0.255918 | + | 0.966698i | \(0.417622\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.59925 | + | 7.96613i | −0.147749 | + | 0.255909i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17.3535 | + | 30.0571i | 0.556899 | + | 0.964577i | 0.997753 | + | 0.0669986i | \(0.0213423\pi\) |
−0.440854 | + | 0.897579i | \(0.645324\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.29581 | − | 27.3751i | 0.0736003 | − | 0.877604i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 17.6136 | + | 30.5077i | 0.564087 | + | 0.977028i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.0728 | − | 20.9106i | 0.386242 | − | 0.668991i | −0.605699 | − | 0.795694i | \(-0.707106\pi\) |
0.991941 | + | 0.126703i | \(0.0404396\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.37614 | 0.107902 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.4294 | −0.364913 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.54460 | + | 6.13942i | −0.113055 | + | 0.195817i | −0.917001 | − | 0.398886i | \(-0.869397\pi\) |
0.803946 | + | 0.594703i | \(0.202730\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.6441 | − | 23.6322i | −0.434736 | − | 0.752984i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.82387 | − | 21.7476i | 0.0580543 | − | 0.692235i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.13619 | + | 10.6282i | 0.195119 | + | 0.337957i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.5531 | + | 42.5273i | −0.779956 | + | 1.35092i | 0.152010 | + | 0.988379i | \(0.451425\pi\) |
−0.931966 | + | 0.362545i | \(0.881908\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −25.9740 | −0.824260 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.86979 | 0.281191 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.9228 | − | 20.6509i | 0.377599 | − | 0.654021i | −0.613113 | − | 0.789995i | \(-0.710083\pi\) |
0.990712 | + | 0.135974i | \(0.0434164\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.71235 | − | 15.0902i | −0.275647 | − | 0.477434i |
(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 | 1148.2.i.d.165.2 | ✓ | 16 | |
7.2 | even | 3 | inner | 1148.2.i.d.821.2 | yes | 16 | |
7.3 | odd | 6 | 8036.2.a.n.1.2 | 8 | |||
7.4 | even | 3 | 8036.2.a.m.1.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.i.d.165.2 | ✓ | 16 | 1.1 | even | 1 | trivial | |
1148.2.i.d.821.2 | yes | 16 | 7.2 | even | 3 | inner | |
8036.2.a.m.1.7 | 8 | 7.4 | even | 3 | |||
8036.2.a.n.1.2 | 8 | 7.3 | odd | 6 |