Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(57,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.57");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.n (of order \(5\), degree \(4\), 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: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{5})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 365.2 | ||
Character | \(\chi\) | \(=\) | 1148.365 |
Dual form | 1148.2.n.e.953.2 |
$q$-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 \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).
\(n\) | \(493\) | \(575\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
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 | ||||||||
\(3\) | −0.660580 | −0.381386 | −0.190693 | − | 0.981650i | \(-0.561074\pi\) | ||||
−0.190693 | + | 0.981650i | \(0.561074\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.860652 | − | 2.64881i | 0.384895 | − | 1.18459i | −0.551661 | − | 0.834068i | \(-0.686006\pi\) |
0.936556 | − | 0.350517i | \(-0.113994\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.809017 | + | 0.587785i | 0.305780 | + | 0.222162i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.56363 | −0.854545 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.31434 | − | 4.04513i | −0.396290 | − | 1.21965i | −0.927953 | − | 0.372698i | \(-0.878433\pi\) |
0.531663 | − | 0.846956i | \(-0.321567\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.12587 | + | 1.54453i | −0.589609 | + | 0.428376i | −0.842176 | − | 0.539203i | \(-0.818725\pi\) |
0.252566 | + | 0.967580i | \(0.418725\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.568529 | + | 1.74975i | −0.146794 | + | 0.451784i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.363137 | + | 1.11762i | 0.0880736 | + | 0.271063i | 0.985387 | − | 0.170332i | \(-0.0544840\pi\) |
−0.897313 | + | 0.441394i | \(0.854484\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.50486 | − | 2.54643i | −0.804071 | − | 0.584192i | 0.108035 | − | 0.994147i | \(-0.465544\pi\) |
−0.912106 | + | 0.409955i | \(0.865544\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.534420 | − | 0.388279i | −0.116620 | − | 0.0847295i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.79186 | + | 4.93457i | −1.41620 | + | 1.02893i | −0.423816 | + | 0.905748i | \(0.639310\pi\) |
−0.992384 | + | 0.123182i | \(0.960690\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.23041 | − | 1.62048i | −0.446081 | − | 0.324097i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.67523 | 0.707297 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.24066 | − | 3.81836i | 0.230385 | − | 0.709052i | −0.767315 | − | 0.641270i | \(-0.778408\pi\) |
0.997700 | − | 0.0677821i | \(-0.0215923\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.90141 | + | 5.85195i | 0.341504 | + | 1.05104i | 0.963429 | + | 0.267964i | \(0.0863509\pi\) |
−0.621925 | + | 0.783077i | \(0.713649\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.868229 | + | 2.67214i | 0.151139 | + | 0.465159i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.25322 | − | 1.63706i | 0.380863 | − | 0.276713i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.16042 | + | 3.57141i | −0.190772 | + | 0.587136i | −1.00000 | 0.000358916i | \(-0.999886\pi\) | |
0.809228 | + | 0.587495i | \(0.199886\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.40431 | − | 1.02029i | 0.224869 | − | 0.163377i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.69701 | − | 6.17415i | −0.265028 | − | 0.964241i | ||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.641872 | + | 0.466348i | −0.0978846 | + | 0.0711173i | −0.635651 | − | 0.771977i | \(-0.719268\pi\) |
0.537766 | + | 0.843094i | \(0.319268\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.20640 | + | 6.79059i | −0.328910 | + | 1.01228i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.4153 | + | 7.56713i | −1.51922 | + | 1.10378i | −0.557349 | + | 0.830278i | \(0.688181\pi\) |
−0.961872 | + | 0.273500i | \(0.911819\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.309017 | + | 0.951057i | 0.0441453 | + | 0.135865i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.239881 | − | 0.738277i | −0.0335900 | − | 0.103379i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.26939 | − | 6.98447i | 0.311725 | − | 0.959390i | −0.665357 | − | 0.746525i | \(-0.731721\pi\) |
0.977082 | − | 0.212865i | \(-0.0682794\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11.8460 | −1.59731 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.31524 | + | 1.68212i | 0.306661 | + | 0.222803i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.15250 | − | 3.74351i | 0.670799 | − | 0.487364i | −0.199494 | − | 0.979899i | \(-0.563930\pi\) |
0.870293 | + | 0.492535i | \(0.163930\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.46506 | − | 1.79097i | −0.315619 | − | 0.229311i | 0.418685 | − | 0.908132i | \(-0.362491\pi\) |
−0.734304 | + | 0.678821i | \(0.762491\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.07402 | − | 1.50687i | −0.261302 | − | 0.189847i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.26155 | + | 6.96033i | 0.280511 | + | 0.863323i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.37463 | + | 7.30837i | −0.290108 | + | 0.892860i | 0.694713 | + | 0.719287i | \(0.255531\pi\) |
−0.984821 | + | 0.173573i | \(0.944469\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.48657 | − | 3.25968i | 0.540119 | − | 0.392420i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.999222 | − | 3.07529i | −0.118586 | − | 0.364970i | 0.874092 | − | 0.485760i | \(-0.161457\pi\) |
−0.992678 | + | 0.120790i | \(0.961457\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.45989 | −0.521991 | −0.260995 | − | 0.965340i | \(-0.584051\pi\) | ||||
−0.260995 | + | 0.965340i | \(0.584051\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.47336 | + | 1.07046i | 0.170129 | + | 0.123606i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.31434 | − | 4.04513i | 0.149783 | − | 0.460986i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.23436 | 0.251385 | 0.125693 | − | 0.992069i | \(-0.459885\pi\) | ||||
0.125693 | + | 0.992069i | \(0.459885\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.26312 | 0.584791 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.3979 | −1.36085 | −0.680423 | − | 0.732820i | \(-0.738204\pi\) | ||||
−0.680423 | + | 0.732820i | \(0.738204\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.27290 | 0.354996 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.819556 | + | 2.52233i | −0.0878657 | + | 0.270423i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.23269 | − | 1.62214i | −0.236664 | − | 0.171947i | 0.463132 | − | 0.886290i | \(-0.346726\pi\) |
−0.699796 | + | 0.714343i | \(0.746726\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.62772 | −0.275459 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.25604 | − | 3.86568i | −0.130245 | − | 0.400852i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.76149 | + | 7.09214i | −1.00151 | + | 0.727638i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.383518 | + | 1.18035i | −0.0389403 | + | 0.119846i | −0.968637 | − | 0.248480i | \(-0.920069\pi\) |
0.929697 | + | 0.368326i | \(0.120069\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.36950 | + | 10.3702i | 0.338647 | + | 1.04225i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.55569 | − | 4.76299i | −0.652316 | − | 0.473935i | 0.211743 | − | 0.977325i | \(-0.432086\pi\) |
−0.864059 | + | 0.503390i | \(0.832086\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.5968 | − | 10.6052i | −1.43827 | − | 1.04496i | −0.988401 | − | 0.151868i | \(-0.951471\pi\) |
−0.449868 | − | 0.893095i | \(-0.648529\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.48843 | + | 1.08141i | −0.145256 | + | 0.105535i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.18659 | − | 2.31519i | −0.308059 | − | 0.223818i | 0.423004 | − | 0.906128i | \(-0.360976\pi\) |
−0.731063 | + | 0.682310i | \(0.760976\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.50586 | −0.240018 | −0.120009 | − | 0.992773i | \(-0.538292\pi\) | ||||
−0.120009 | + | 0.992773i | \(0.538292\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.766551 | − | 2.35920i | 0.0727578 | − | 0.223925i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.08326 | − | 18.7223i | −0.572265 | − | 1.76125i | −0.645310 | − | 0.763921i | \(-0.723272\pi\) |
0.0730454 | − | 0.997329i | \(-0.476728\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.22534 | + | 22.2373i | 0.673767 | + | 2.07364i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.44994 | − | 3.95962i | 0.503848 | − | 0.366067i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.363137 | + | 1.11762i | −0.0332887 | + | 0.102452i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.73643 | + | 4.16776i | −0.521493 | + | 0.378887i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.12101 | + | 4.07852i | 0.101078 | + | 0.367748i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.05411 | − | 3.67203i | 0.452054 | − | 0.328436i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.71971 | + | 11.4481i | −0.330071 | + | 1.01585i | 0.639029 | + | 0.769183i | \(0.279337\pi\) |
−0.969099 | + | 0.246671i | \(0.920663\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.424008 | − | 0.308060i | 0.0373318 | − | 0.0271232i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.917345 | − | 2.82330i | −0.0801488 | − | 0.246673i | 0.902951 | − | 0.429744i | \(-0.141396\pi\) |
−0.983100 | + | 0.183071i | \(0.941396\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.33874 | − | 4.12021i | −0.116083 | − | 0.357268i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.16309 | − | 9.73499i | 0.272235 | − | 0.837854i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.3089 | 0.966186 | 0.483093 | − | 0.875569i | \(-0.339513\pi\) | ||||
0.483093 | + | 0.875569i | \(0.339513\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.17717 | − | 4.48798i | −0.523941 | − | 0.380665i | 0.294146 | − | 0.955761i | \(-0.404965\pi\) |
−0.818086 | + | 0.575095i | \(0.804965\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.88011 | − | 4.99869i | 0.579410 | − | 0.420966i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.04196 | + | 6.56937i | 0.756127 | + | 0.549358i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.04636 | − | 6.57256i | −0.751259 | − | 0.545822i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.204130 | − | 0.628249i | −0.0168364 | − | 0.0518171i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.83270 | − | 21.0289i | 0.559757 | − | 1.72275i | −0.123281 | − | 0.992372i | \(-0.539342\pi\) |
0.683038 | − | 0.730383i | \(-0.260658\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.27106 | − | 5.28273i | 0.591710 | − | 0.429903i | −0.251217 | − | 0.967931i | \(-0.580831\pi\) |
0.842927 | + | 0.538028i | \(0.180831\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.930949 | − | 2.86517i | −0.0752628 | − | 0.231635i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 17.1372 | 1.37649 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.09331 | − | 2.97396i | −0.326682 | − | 0.237348i | 0.412340 | − | 0.911030i | \(-0.364712\pi\) |
−0.739021 | + | 0.673682i | \(0.764712\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.49911 | + | 4.61380i | −0.118887 | + | 0.365898i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.39520 | −0.661634 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.7170 | 0.839417 | 0.419709 | − | 0.907659i | \(-0.362132\pi\) | ||||
0.419709 | + | 0.907659i | \(0.362132\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.82523 | 0.609193 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.1405 | 1.48113 | 0.740566 | − | 0.671983i | \(-0.234557\pi\) | ||||
0.740566 | + | 0.671983i | \(0.234557\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.88349 | + | 5.79679i | −0.144884 | + | 0.445907i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.98519 | + | 6.52812i | 0.687115 | + | 0.499218i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.80401 | −0.137156 | −0.0685781 | − | 0.997646i | \(-0.521846\pi\) | ||||
−0.0685781 | + | 0.997646i | \(0.521846\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.851939 | − | 2.62200i | −0.0644006 | − | 0.198205i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.40364 | + | 2.47289i | −0.255833 | + | 0.185874i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.19241 | + | 9.82522i | −0.238612 | + | 0.734371i | 0.758010 | + | 0.652243i | \(0.226172\pi\) |
−0.996622 | + | 0.0821283i | \(0.973828\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.51210 | − | 4.65377i | −0.112394 | − | 0.345912i | 0.879001 | − | 0.476820i | \(-0.158211\pi\) |
−0.991395 | + | 0.130908i | \(0.958211\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.62837 | + | 1.18308i | 0.120373 | + | 0.0874559i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.46128 | + | 6.14748i | 0.622085 | + | 0.451971i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.04364 | − | 2.93787i | 0.295700 | − | 0.214839i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.97332 | + | 2.16024i | 0.216277 | + | 0.157135i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.35777 | 0.677105 | 0.338552 | − | 0.940948i | \(-0.390063\pi\) | ||||
0.338552 | + | 0.940948i | \(0.390063\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.67725 | − | 8.23972i | 0.192713 | − | 0.593108i | −0.807283 | − | 0.590164i | \(-0.799063\pi\) |
0.999996 | − | 0.00294386i | \(-0.000937061\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.49393 | − | 4.59785i | −0.106983 | − | 0.329259i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.81523 | + | 17.8975i | 0.414318 | + | 1.27514i | 0.912859 | + | 0.408274i | \(0.133869\pi\) |
−0.498541 | + | 0.866866i | \(0.666131\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.75316 | + | 5.63300i | −0.549607 | + | 0.399313i | −0.827641 | − | 0.561258i | \(-0.810317\pi\) |
0.278033 | + | 0.960571i | \(0.410317\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.56864 | − | 4.82777i | 0.110643 | − | 0.340524i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.24809 | − | 2.35988i | 0.227972 | − | 0.165631i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −17.8147 | − | 0.818738i | −1.24423 | − | 0.0571832i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 17.4118 | − | 12.6504i | 1.21021 | − | 0.879267i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.69407 | + | 17.5245i | −0.393867 | + | 1.21220i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.1667 | − | 10.2927i | 0.975278 | − | 0.708581i | 0.0186296 | − | 0.999826i | \(-0.494070\pi\) |
0.956648 | + | 0.291246i | \(0.0940697\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.660066 | + | 2.03147i | 0.0452270 | + | 0.139194i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.682839 | + | 2.10156i | 0.0465692 | + | 0.143325i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.90141 | + | 5.85195i | −0.129076 | + | 0.397256i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.94611 | 0.199080 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.49818 | − | 1.81503i | −0.168046 | − | 0.122092i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.19097 | − | 3.77146i | 0.347613 | − | 0.252556i | −0.400254 | − | 0.916404i | \(-0.631078\pi\) |
0.747867 | + | 0.663848i | \(0.231078\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.71794 | + | 4.15433i | 0.381196 | + | 0.276955i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.58368 | − | 3.33024i | −0.304229 | − | 0.221036i | 0.425187 | − | 0.905105i | \(-0.360208\pi\) |
−0.729416 | + | 0.684070i | \(0.760208\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.79574 | + | 14.7598i | 0.316912 | + | 0.975354i | 0.974960 | + | 0.222379i | \(0.0713821\pi\) |
−0.658049 | + | 0.752975i | \(0.728618\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.868229 | + | 2.67214i | −0.0571253 | + | 0.175814i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.26574 | + | 1.64616i | −0.148434 | + | 0.107843i | −0.659524 | − | 0.751684i | \(-0.729242\pi\) |
0.511090 | + | 0.859527i | \(0.329242\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.0800 | + | 34.1007i | 0.722779 | + | 2.22449i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.47597 | −0.0958748 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.7061 | + | 11.4111i | 1.01594 | + | 0.738125i | 0.965447 | − | 0.260599i | \(-0.0839200\pi\) |
0.0504954 | + | 0.998724i | \(0.483920\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.49040 | − | 23.0531i | 0.482499 | − | 1.48498i | −0.353072 | − | 0.935596i | \(-0.614863\pi\) |
0.835571 | − | 0.549383i | \(-0.185137\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.5024 | −0.930329 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.78513 | 0.177935 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.3839 | 0.724342 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.18980 | 0.519008 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.13619 | + | 9.65220i | −0.197955 | + | 0.609241i | 0.801975 | + | 0.597358i | \(0.203783\pi\) |
−0.999929 | + | 0.0118836i | \(0.996217\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 28.8879 | + | 20.9883i | 1.81616 | + | 1.31952i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.16201 | −0.135390 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.71537 | + | 11.4347i | 0.231758 | + | 0.713279i | 0.997535 | + | 0.0701721i | \(0.0223548\pi\) |
−0.765777 | + | 0.643107i | \(0.777645\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.03802 | + | 2.20725i | −0.188773 | + | 0.137152i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.18060 | + | 9.78889i | −0.196874 | + | 0.605917i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.34517 | + | 28.7615i | 0.576248 | + | 1.77351i | 0.631891 | + | 0.775057i | \(0.282279\pi\) |
−0.0556434 | + | 0.998451i | \(0.517721\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −16.5474 | − | 12.0224i | −1.01650 | − | 0.738529i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.47487 | + | 1.07155i | 0.0902605 | + | 0.0655781i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.4112 | − | 11.9234i | 1.00061 | − | 0.726984i | 0.0383892 | − | 0.999263i | \(-0.487777\pi\) |
0.962218 | + | 0.272279i | \(0.0877773\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.7796 | − | 14.3707i | −1.20152 | − | 0.872957i | −0.207089 | − | 0.978322i | \(-0.566399\pi\) |
−0.994434 | + | 0.105365i | \(0.966399\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.73582 | 0.105056 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.62356 | + | 11.1522i | −0.218509 | + | 0.672501i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.02910 | − | 21.6333i | −0.422338 | − | 1.29982i | −0.905521 | − | 0.424302i | \(-0.860519\pi\) |
0.483183 | − | 0.875519i | \(-0.339481\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.87453 | − | 15.0023i | −0.291830 | − | 0.898162i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.30938 | − | 0.951323i | 0.0781113 | − | 0.0567512i | −0.548044 | − | 0.836449i | \(-0.684627\pi\) |
0.626156 | + | 0.779698i | \(0.284627\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.12498 | − | 15.7731i | 0.304649 | − | 0.937612i | −0.675159 | − | 0.737672i | \(-0.735925\pi\) |
0.979808 | − | 0.199940i | \(-0.0640748\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.44825 | − | 4.68493i | 0.381961 | − | 0.277511i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.25617 | − | 5.99247i | 0.133177 | − | 0.353724i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.6361 | − | 9.18065i | 0.743299 | − | 0.540038i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.253344 | − | 0.779713i | 0.0148513 | − | 0.0457076i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.13257 | + | 6.63520i | −0.533530 | + | 0.387632i | −0.821677 | − | 0.569954i | \(-0.806961\pi\) |
0.288146 | + | 0.957586i | \(0.406961\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.48136 | − | 16.8699i | −0.319137 | − | 0.982202i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.83051 | − | 14.8668i | −0.280295 | − | 0.862658i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.81698 | − | 20.9805i | 0.394236 | − | 1.21333i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.793398 | −0.0457307 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.33056 | + | 3.14634i | 0.248784 | + | 0.180752i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.86551 | + | 4.98809i | −0.393118 | + | 0.285617i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.1972 | − | 11.7679i | −0.924423 | − | 0.671632i | 0.0201983 | − | 0.999796i | \(-0.493570\pi\) |
−0.944621 | + | 0.328164i | \(0.893570\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.64238 | + | 7.00560i | 0.548536 | + | 0.398535i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.06550 | − | 12.5123i | −0.230533 | − | 0.709508i | −0.997683 | − | 0.0680397i | \(-0.978326\pi\) |
0.767149 | − | 0.641468i | \(-0.221674\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.98338 | − | 6.10423i | 0.112108 | − | 0.345031i | −0.879225 | − | 0.476406i | \(-0.841939\pi\) |
0.991333 | + | 0.131375i | \(0.0419391\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.77642 | + | 4.19681i | −0.325464 | + | 0.236464i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.52911 | − | 13.9392i | −0.254380 | − | 0.782902i | −0.993951 | − | 0.109823i | \(-0.964971\pi\) |
0.739571 | − | 0.673079i | \(-0.235029\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −17.0765 | −0.956098 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.10500 | + | 1.52937i | 0.117490 | + | 0.0853612i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.57320 | − | 4.84181i | 0.0875351 | − | 0.269405i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.24444 | 0.401849 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.65532 | 0.0915396 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.8740 | −0.709765 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.84097 | −0.156154 | −0.0780769 | − | 0.996947i | \(-0.524878\pi\) | ||||
−0.0780769 | + | 0.996947i | \(0.524878\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.97489 | − | 9.15578i | 0.163023 | − | 0.501734i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 17.3148 | + | 12.5799i | 0.946008 | + | 0.687315i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.4878 | −0.734728 | −0.367364 | − | 0.930077i | \(-0.619740\pi\) | ||||
−0.367364 | + | 0.930077i | \(0.619740\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.01848 | + | 12.3676i | 0.218254 | + | 0.671716i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 21.1728 | − | 15.3829i | 1.14657 | − | 0.833033i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.309017 | + | 0.951057i | −0.0166853 | + | 0.0513522i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.77292 | − | 14.6895i | −0.256965 | − | 0.790858i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.7075 | + | 12.1387i | 0.896906 | + | 0.651640i | 0.937669 | − | 0.347529i | \(-0.112979\pi\) |
−0.0407636 | + | 0.999169i | \(0.512979\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.0772 | − | 11.6807i | −0.860591 | − | 0.625256i | 0.0674548 | − | 0.997722i | \(-0.478512\pi\) |
−0.928046 | + | 0.372466i | \(0.878512\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.81304 | + | 5.67651i | −0.417029 | + | 0.302989i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.5980 | + | 17.8715i | 1.30922 | + | 0.951203i | 1.00000 | 0.000212707i | \(6.77069e-5\pi\) | |
0.309219 | + | 0.950991i | \(0.399932\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.00585 | −0.477981 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.239881 | − | 0.738277i | 0.0126958 | − | 0.0390738i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.78981 | − | 14.7415i | −0.252796 | − | 0.778027i | −0.994256 | − | 0.107030i | \(-0.965866\pi\) |
0.741459 | − | 0.670998i | \(-0.234134\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.0715713 | − | 0.220274i | −0.00376691 | − | 0.0115934i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.78937 | − | 2.75314i | 0.198890 | − | 0.144502i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.83841 | + | 11.8134i | −0.200912 | + | 0.618342i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.9526 | − | 10.1372i | 0.728321 | − | 0.529156i | −0.160711 | − | 0.987001i | \(-0.551379\pi\) |
0.889032 | + | 0.457846i | \(0.151379\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.35051 | + | 15.8283i | 0.226478 | + | 0.823987i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.94134 | − | 4.31664i | 0.308459 | − | 0.224109i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.38643 | + | 7.34469i | −0.123565 | + | 0.380294i | −0.993637 | − | 0.112631i | \(-0.964072\pi\) |
0.870072 | + | 0.492925i | \(0.164072\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.33865 | + | 2.42567i | −0.172407 | + | 0.125261i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.26011 | + | 10.0336i | 0.167904 | + | 0.516755i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.5989 | + | 32.6200i | 0.544428 | + | 1.67558i | 0.722346 | + | 0.691531i | \(0.243064\pi\) |
−0.177919 | + | 0.984045i | \(0.556936\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.45717 | − | 7.56238i | 0.125884 | − | 0.387432i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −24.2389 | −1.23855 | −0.619275 | − | 0.785174i | \(-0.712573\pi\) | ||||
−0.619275 | + | 0.785174i | \(0.712573\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.58361 | − | 6.96290i | −0.488426 | − | 0.354862i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.64553 | − | 1.19554i | 0.0836468 | − | 0.0607729i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.4570 | + | 7.59745i | 0.530191 | + | 0.385206i | 0.820429 | − | 0.571748i | \(-0.193735\pi\) |
−0.290238 | + | 0.956954i | \(0.593735\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.98135 | − | 5.79879i | −0.403634 | − | 0.293257i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.605980 | + | 1.86501i | 0.0305677 | + | 0.0940776i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.92301 | − | 5.91841i | 0.0967570 | − | 0.297787i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.4060 | − | 13.3728i | 0.923773 | − | 0.671160i | −0.0206872 | − | 0.999786i | \(-0.506585\pi\) |
0.944460 | + | 0.328626i | \(0.106585\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.884344 | + | 2.72173i | 0.0442726 | + | 0.136257i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −33.1881 | −1.65734 | −0.828669 | − | 0.559740i | \(-0.810901\pi\) | ||||
−0.828669 | + | 0.559740i | \(0.810901\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.0807 | − | 9.50367i | −0.651595 | − | 0.473412i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.52971 | − | 13.9410i | 0.225083 | − | 0.692735i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15.9720 | 0.791704 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.4102 | −0.712540 | −0.356270 | − | 0.934383i | \(-0.615952\pi\) | ||||
−0.356270 | + | 0.934383i | \(0.615952\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.47045 | −0.368490 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.36884 | 0.313390 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.6703 | + | 32.8397i | −0.523783 | + | 1.61204i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.08052 | + | 2.96467i | 0.199824 | + | 0.145180i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −25.5369 | −1.24756 | −0.623780 | − | 0.781600i | \(-0.714404\pi\) | ||||
−0.623780 | + | 0.781600i | \(0.714404\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.6382 | + | 32.7411i | 0.518475 | + | 1.59570i | 0.776869 | + | 0.629662i | \(0.216807\pi\) |
−0.258394 | + | 0.966040i | \(0.583193\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 26.7009 | − | 19.3993i | 1.29824 | − | 0.943228i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.00114 | − | 3.08120i | 0.0485626 | − | 0.149460i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.941570 | − | 2.89785i | −0.0455658 | − | 0.140237i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.97294 | − | 4.33960i | −0.288376 | − | 0.209518i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.3482 | − | 20.5962i | −1.36549 | − | 0.992083i | −0.998075 | − | 0.0620246i | \(-0.980244\pi\) |
−0.367411 | − | 0.930059i | \(-0.619756\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.99826 | + | 2.17836i | −0.144087 | + | 0.104685i | −0.657494 | − | 0.753460i | \(-0.728383\pi\) |
0.513407 | + | 0.858146i | \(0.328383\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.97584 | + | 4.34170i | 0.286520 | + | 0.208169i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 36.3701 | 1.73982 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.48593 | + | 19.9616i | −0.309556 | + | 0.952717i | 0.668381 | + | 0.743819i | \(0.266988\pi\) |
−0.977938 | + | 0.208898i | \(0.933012\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.792206 | − | 2.43816i | −0.0377241 | − | 0.116103i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.76868 | − | 17.7542i | −0.274078 | − | 0.843527i | −0.989462 | − | 0.144794i | \(-0.953748\pi\) |
0.715383 | − | 0.698732i | \(-0.246252\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.21831 | + | 4.51787i | −0.294776 | + | 0.214168i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.51355 | + | 13.8913i | −0.213483 | + | 0.657035i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.9388 | − | 14.4864i | 0.940970 | − | 0.683654i | −0.00768421 | − | 0.999970i | \(-0.502446\pi\) |
0.948654 | + | 0.316316i | \(0.102446\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.7448 | + | 14.9796i | −1.07101 | + | 0.705361i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.80312 | + | 3.48967i | −0.225670 | + | 0.163959i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.26155 | + | 6.96033i | −0.106023 | + | 0.326305i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.343361 | + | 0.249466i | −0.0160617 | + | 0.0116695i | −0.595787 | − | 0.803142i | \(-0.703160\pi\) |
0.579725 | + | 0.814812i | \(0.303160\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.33461 | + | 4.10750i | 0.0622942 | + | 0.191722i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.199643 | − | 0.614439i | −0.00929832 | − | 0.0286173i | 0.946300 | − | 0.323291i | \(-0.104789\pi\) |
−0.955598 | + | 0.294673i | \(0.904789\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.58609 | + | 17.1922i | −0.259608 | + | 0.798991i | 0.733279 | + | 0.679928i | \(0.237989\pi\) |
−0.992887 | + | 0.119063i | \(0.962011\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −11.3205 | −0.524975 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −21.5860 | − | 15.6832i | −0.998882 | − | 0.725730i | −0.0370339 | − | 0.999314i | \(-0.511791\pi\) |
−0.961848 | + | 0.273584i | \(0.911791\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.21687 | + | 4.51682i | −0.287069 | + | 0.208568i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.70396 | + | 1.96454i | 0.124592 | + | 0.0905213i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.73008 | + | 1.98352i | 0.125529 | + | 0.0912023i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.69081 | + | 11.3592i | 0.169346 | + | 0.521194i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.81789 | + | 17.9056i | −0.266383 | + | 0.819842i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.3854 | − | 13.3577i | 0.840048 | − | 0.610331i | −0.0823360 | − | 0.996605i | \(-0.526238\pi\) |
0.922384 | + | 0.386274i | \(0.126238\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.04926 | − | 9.38465i | −0.139034 | − | 0.427903i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.54570 | 0.252338 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.79644 | + | 2.03173i | 0.126980 | + | 0.0922562i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.611173 | − | 1.88100i | 0.0276949 | − | 0.0852362i | −0.936254 | − | 0.351325i | \(-0.885731\pi\) |
0.963949 | + | 0.266088i | \(0.0857313\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.07941 | −0.320142 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.53842 | −0.340204 | −0.170102 | − | 0.985426i | \(-0.554410\pi\) | ||||
−0.170102 | + | 0.985426i | \(0.554410\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.71801 | 0.212488 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 30.3688 | 1.36498 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.999222 | − | 3.07529i | 0.0448212 | − | 0.137946i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.0927 | − | 13.1451i | −0.809940 | − | 0.588456i | 0.103873 | − | 0.994591i | \(-0.466876\pi\) |
−0.913813 | + | 0.406134i | \(0.866876\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.6438 | −0.564883 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.96962 | − | 9.13956i | −0.132409 | − | 0.407513i | 0.862769 | − | 0.505598i | \(-0.168728\pi\) |
−0.995178 | + | 0.0980854i | \(0.968728\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.2584 | + | 13.2655i | −0.812490 | + | 0.590308i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.24420 | − | 3.82925i | 0.0552567 | − | 0.170063i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.54112 | − | 17.0538i | −0.245606 | − | 0.755897i | −0.995536 | − | 0.0943804i | \(-0.969913\pi\) |
0.749930 | − | 0.661517i | \(-0.230087\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.60813 | − | 2.62146i | −0.159614 | − | 0.115966i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.8812 | − | 9.35871i | −0.568717 | − | 0.413197i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −40.6540 | + | 29.5369i | −1.79143 | + | 1.30155i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 44.2993 | + | 32.1853i | 1.94828 | + | 1.41551i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.19169 | 0.0523095 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.5708 | + | 38.6889i | −0.550736 | + | 1.69499i | 0.156212 | + | 0.987724i | \(0.450072\pi\) |
−0.706947 | + | 0.707266i | \(0.749928\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.1383 | − | 34.2802i | −0.487044 | − | 1.49897i | −0.828999 | − | 0.559251i | \(-0.811089\pi\) |
0.341955 | − | 0.939716i | \(-0.388911\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.562774 | + | 1.73204i | 0.0245615 | + | 0.0755924i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.84978 | + | 4.25011i | −0.254820 | + | 0.185138i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.6719 | − | 45.1556i | 0.637910 | − | 1.96329i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.2091 | + | 9.59700i | −0.573228 | + | 0.416474i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.1438 | + | 10.5043i | 0.569321 | + | 0.454994i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.87506 | + | 6.44811i | −0.383702 | + | 0.278776i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.10884 | − | 6.49034i | 0.0910031 | − | 0.280079i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.44100 | − | 2.50003i | 0.148214 | − | 0.107684i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.99007 | + | 21.5132i | 0.300527 | + | 0.924926i | 0.981309 | + | 0.192440i | \(0.0616400\pi\) |
−0.680782 | + | 0.732486i | \(0.738360\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.998865 | + | 3.07419i | 0.0428654 | + | 0.131926i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.15668 | + | 6.63757i | −0.0923819 | + | 0.284322i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.39316 | 0.187838 | 0.0939189 | − | 0.995580i | \(-0.470061\pi\) | ||||
0.0939189 | + | 0.995580i | \(0.470061\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.31952 | + | 4.59140i | 0.269710 | + | 0.195956i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14.0716 | + | 10.2236i | −0.599468 | + | 0.435539i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.80764 | + | 1.31332i | 0.0768685 | + | 0.0558482i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.58935 | − | 4.06090i | −0.237255 | − | 0.172376i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.7778 | + | 36.2485i | 0.499043 | + | 1.53590i | 0.810560 | + | 0.585656i | \(0.199163\pi\) |
−0.311517 | + | 0.950241i | \(0.600837\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.644246 | − | 1.98279i | 0.0272487 | − | 0.0838629i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.67114 | + | 1.94070i | −0.112776 | + | 0.0819364i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.39644 | + | 13.5308i | 0.185288 | + | 0.570257i | 0.999953 | − | 0.00967428i | \(-0.00307947\pi\) |
−0.814666 | + | 0.579931i | \(0.803079\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −54.8275 | −2.30661 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.25795 | + | 3.09359i | 0.178817 | + | 0.129918i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.9111 | − | 42.8140i | 0.583184 | − | 1.79486i | −0.0232591 | − | 0.999729i | \(-0.507404\pi\) |
0.606443 | − | 0.795127i | \(-0.292596\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.3157 | 1.01758 | 0.508790 | − | 0.860891i | \(-0.330093\pi\) | ||||
0.508790 | + | 0.860891i | \(0.330093\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.18156 | −0.258238 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 23.1450 | 0.965213 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −44.2583 | −1.84250 | −0.921249 | − | 0.388973i | \(-0.872830\pi\) | ||||
−0.921249 | + | 0.388973i | \(0.872830\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.76854 | + | 5.44300i | −0.0734979 | + | 0.226203i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.0301 | − | 7.28730i | −0.416119 | − | 0.302328i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −31.2359 | −1.29366 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.79778 | − | 17.8437i | −0.239709 | − | 0.737748i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.5201 | − | 9.09639i | 0.516760 | − | 0.375448i | −0.298622 | − | 0.954372i | \(-0.596527\pi\) |
0.815382 | + | 0.578923i | \(0.196527\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.23740 | − | 25.3521i | 0.339416 | − | 1.04462i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.84143 | − | 11.8227i | −0.158015 | − | 0.486321i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.18853 | + | 2.31661i | 0.130937 | + | 0.0951316i | 0.651326 | − | 0.758798i | \(-0.274213\pi\) |
−0.520389 | + | 0.853929i | \(0.674213\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.64783 | + | 1.92376i | 0.108551 | + | 0.0788666i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.12158 | − | 3.72105i | 0.209612 | − | 0.152292i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.33494 | − | 6.05569i | −0.340556 | − | 0.247429i | 0.404340 | − | 0.914609i | \(-0.367501\pi\) |
−0.744897 | + | 0.667180i | \(0.767501\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.5385 | −0.960154 | −0.480077 | − | 0.877226i | \(-0.659391\pi\) | ||||
−0.480077 | + | 0.877226i | \(0.659391\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.08769 | − | 18.7360i | 0.247910 | − | 0.762989i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.10255 | + | 18.7817i | 0.248104 | + | 0.763585i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.3029 | + | 31.7089i | 0.418180 | + | 1.28703i | 0.909375 | + | 0.415976i | \(0.136560\pi\) |
−0.491196 | + | 0.871049i | \(0.663440\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.14563 | + | 1.55889i | −0.0869452 | + | 0.0631694i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.4538 | − | 32.1734i | 0.422914 | − | 1.30160i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.17767 | + | 2.30871i | −0.128345 | + | 0.0932479i | −0.650106 | − | 0.759844i | \(-0.725275\pi\) |
0.521761 | + | 0.853092i | \(0.325275\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11.7680 | + | 0.540842i | 0.474533 | + | 0.0218089i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.9094 | − | 8.65269i | 0.479454 | − | 0.348344i | −0.321660 | − | 0.946855i | \(-0.604241\pi\) |
0.801114 | + | 0.598511i | \(0.204241\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.19031 | + | 15.9741i | −0.208616 | + | 0.642055i | 0.790929 | + | 0.611908i | \(0.209598\pi\) |
−0.999545 | + | 0.0301471i | \(0.990402\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −24.9616 | + | 18.1357i | −1.00168 | + | 0.727760i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.852810 | − | 2.62468i | −0.0341671 | − | 0.105156i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.63638 | − | 29.6577i | −0.385455 | − | 1.18631i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.76139 | − | 11.5764i | 0.150215 | − | 0.462315i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.41287 | −0.175953 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.9180 | − | 22.4633i | −1.23083 | − | 0.894249i | −0.233876 | − | 0.972267i | \(-0.575141\pi\) |
−0.996952 | + | 0.0780179i | \(0.975141\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.35826 | + | 6.79917i | −0.371957 | + | 0.270243i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 27.1225 | + | 19.7056i | 1.07632 | + | 0.781994i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.12587 | − | 1.54453i | −0.0842299 | − | 0.0611966i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.56164 | + | 7.88391i | 0.101337 | + | 0.311883i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.19389 | − | 28.2959i | 0.363137 | − | 1.11762i | −0.588002 | − | 0.808859i | \(-0.700085\pi\) |
0.951139 | − | 0.308762i | \(-0.0999145\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.48194 | + | 4.70941i | −0.255623 | + | 0.185721i | −0.708215 | − | 0.705997i | \(-0.750499\pi\) |
0.452592 | + | 0.891718i | \(0.350499\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.451070 | − | 1.38825i | −0.0177609 | − | 0.0546623i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.7034 | −0.420795 | −0.210398 | − | 0.977616i | \(-0.567476\pi\) | ||||
−0.210398 | + | 0.977616i | \(0.567476\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −21.9152 | − | 15.9223i | −0.860246 | − | 0.625005i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.25604 | − | 3.86568i | 0.0492279 | − | 0.151508i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.3092 | 0.912159 | 0.456079 | − | 0.889939i | \(-0.349253\pi\) | ||||
0.456079 | + | 0.889939i | \(0.349253\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.26791 | −0.323054 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.4335 | 0.446064 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 42.2917 | 1.64745 | 0.823726 | − | 0.566988i | \(-0.191891\pi\) | ||||
0.823726 | + | 0.566988i | \(0.191891\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.85189 | + | 24.1656i | −0.305403 | + | 0.939934i | 0.674123 | + | 0.738619i | \(0.264522\pi\) |
−0.979526 | + | 0.201315i | \(0.935478\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.65025 | + | 1.19898i | 0.0640903 | + | 0.0465643i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.0659 | −0.467894 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.4156 | + | 32.0559i | 0.403294 | + | 1.24121i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.42905 | + | 2.49135i | −0.132575 | + | 0.0963213i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.00479 | + | 12.3255i | −0.154603 | + | 0.475819i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.79177 | + | 8.59218i | 0.107615 | + | 0.331204i | 0.990335 | − | 0.138694i | \(-0.0442905\pi\) |
−0.882720 | + | 0.469898i | \(0.844291\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −8.19724 | − | 5.95565i | −0.315512 | − | 0.229233i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 34.8330 | + | 25.3077i | 1.33874 | + | 0.972652i | 0.999489 | + | 0.0319568i | \(0.0101739\pi\) |
0.339252 | + | 0.940696i | \(0.389826\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.00406 | + | 0.729494i | −0.0385324 | + | 0.0279954i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.02789 | + | 2.19989i | 0.116029 | + | 0.0842999i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.09807 | −0.0420163 | −0.0210082 | − | 0.999779i | \(-0.506688\pi\) | ||||
−0.0210082 | + | 0.999779i | \(0.506688\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.73304 | − | 29.9552i | 0.371880 | − | 1.14453i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.16797 | − | 9.75002i | −0.120866 | − | 0.371986i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.96331 | + | 18.3532i | 0.227184 | + | 0.699201i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.75351 | + | 5.63325i | −0.294957 | + | 0.214299i | −0.725415 | − | 0.688312i | \(-0.758352\pi\) |
0.430458 | + | 0.902611i | \(0.358352\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.36950 | + | 10.3702i | −0.127997 | + | 0.393933i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −17.2042 | + | 12.4996i | −0.652593 | + | 0.474136i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.28411 | − | 4.13867i | 0.238028 | − | 0.156763i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.49671 | − | 1.08742i | 0.0566106 | − | 0.0411300i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.81022 | + | 27.1151i | −0.332757 | + | 1.02412i | 0.635059 | + | 0.772464i | \(0.280976\pi\) |
−0.967816 | + | 0.251658i | \(0.919024\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.1615 | − | 9.56237i | 0.496394 | − | 0.360651i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.31922 | − | 22.5263i | −0.275658 | − | 0.848388i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.50405 | − | 7.70668i | −0.0941746 | − | 0.289840i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.35984 | + | 13.4182i | −0.163737 | + | 0.503932i | −0.998941 | − | 0.0460090i | \(-0.985350\pi\) |
0.835204 | + | 0.549941i | \(0.185350\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.72808 | −0.214820 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −41.7910 | − | 30.3630i | −1.56509 | − | 1.13710i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 25.1830 | − | 18.2965i | 0.941791 | − | 0.684252i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −10.3751 | − | 7.53797i | −0.387466 | − | 0.281511i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.78742 | − | 4.93135i | −0.253128 | − | 0.183908i | 0.453984 | − | 0.891010i | \(-0.350002\pi\) |
−0.707112 | + | 0.707102i | \(0.750002\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.57549 | − | 17.1596i | −0.207642 | − | 0.639057i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.94801 | + | 15.2284i | −0.184018 | + | 0.566350i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.95478 | + | 6.50603i | −0.332572 | + | 0.241628i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.7364 | − | 48.4317i | −0.583631 | − | 1.79623i | −0.604699 | − | 0.796454i | \(-0.706707\pi\) |
0.0210681 | − | 0.999778i | \(-0.493293\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −6.20937 | −0.229977 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.754287 | − | 0.548021i | −0.0278983 | − | 0.0202693i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.54421 | + | 17.0633i | −0.204780 | + | 0.630248i | 0.794942 | + | 0.606685i | \(0.207501\pi\) |
−0.999722 | + | 0.0235631i | \(0.992499\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.83980 | −0.0678620 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 32.6844 | 1.20395 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36.5321 | −1.34386 | −0.671928 | − | 0.740617i | \(-0.734533\pi\) | ||||
−0.671928 | + | 0.740617i | \(0.734533\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.51999 | −0.276254 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.64444 | − | 8.13875i | 0.0970151 | − | 0.298582i | −0.890759 | − | 0.454477i | \(-0.849826\pi\) |
0.987774 | + | 0.155895i | \(0.0498262\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −49.8210 | − | 36.1971i | −1.82530 | − | 1.32616i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 31.7837 | 1.16290 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.21717 | − | 3.74606i | −0.0444744 | − | 0.136878i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.78998 | + | 2.75358i | −0.138298 | + | 0.100480i | −0.654783 | − | 0.755817i | \(-0.727240\pi\) |
0.516485 | + | 0.856296i | \(0.327240\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.07170 | − | 6.37605i | 0.0754971 | − | 0.232356i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.73513 | − | 23.8063i | −0.281510 | − | 0.866399i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.4584 | − | 14.1374i | −0.707229 | − | 0.513832i | 0.175050 | − | 0.984560i | \(-0.443991\pi\) |
−0.882278 | + | 0.470728i | \(0.843991\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −19.0827 | − | 13.8644i | −0.692660 | − | 0.503247i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.76788 | + | 7.09678i | −0.354085 | + | 0.257258i | −0.750581 | − | 0.660779i | \(-0.770226\pi\) |
0.396496 | + | 0.918037i | \(0.370226\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.02729 | − | 1.47291i | −0.0733927 | − | 0.0533229i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.39052 | −0.303360 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.17156 | + | 15.9164i | −0.186734 | + | 0.574709i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.55946 | + | 4.79954i | 0.0562357 | + | 0.173076i | 0.975229 | − | 0.221197i | \(-0.0709964\pi\) |
−0.918993 | + | 0.394273i | \(0.870996\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.45430 | − | 7.55355i | −0.0883894 | − | 0.272035i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −33.1362 | + | 24.0748i | −1.19183 | + | 0.865912i | −0.993456 | − | 0.114215i | \(-0.963565\pi\) |
−0.198370 | + | 0.980127i | \(0.563565\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.24207 | − | 16.1334i | 0.188301 | − | 0.579530i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.00686 | − | 1.45807i | 0.0719956 | − | 0.0523078i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.77428 | + | 25.9609i | −0.350200 | + | 0.930145i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.1266 | + | 8.08397i | −0.398142 | + | 0.289267i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.55971 | − | 14.0333i | 0.162951 | − | 0.501511i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11.4004 | + | 8.28287i | −0.406897 | + | 0.295628i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.67450 | + | 29.7750i | 0.344859 | + | 1.06137i | 0.961659 | + | 0.274246i | \(0.0884284\pi\) |
−0.616801 | + | 0.787119i | \(0.711572\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.17323 | − | 18.9993i | −0.219773 | − | 0.676391i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.08326 | − | 18.7223i | 0.216296 | − | 0.665690i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.00661 | 0.284323 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10.9309 | + | 7.94175i | 0.387678 | + | 0.281665i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.15538 | − | 3.74560i | 0.182613 | − | 0.132676i | −0.492723 | − | 0.870186i | \(-0.663999\pi\) |
0.675336 | + | 0.737510i | \(0.263999\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.2393 | − | 8.89239i | −0.432996 | − | 0.314590i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.72379 | + | 4.15858i | 0.202240 | + | 0.146936i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.86183 | + | 18.0409i | 0.206859 | + | 0.636648i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.22534 | + | 22.2373i | −0.254660 | + | 0.783762i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10.8409 | + | 7.87638i | −0.381618 | + | 0.277262i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.3192 | + | 44.0700i | 0.503437 | + | 1.54942i | 0.803383 | + | 0.595462i | \(0.203031\pi\) |
−0.299947 | + | 0.953956i | \(0.596969\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.7425 | 0.903942 | 0.451971 | − | 0.892033i | \(-0.350721\pi\) | ||||
0.451971 | + | 0.892033i | \(0.350721\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.0660 | + | 9.49299i | 0.458244 | + | 0.332934i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.22357 | − | 28.3872i | 0.323088 | − | 0.994361i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.43720 | 0.120252 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.73650 | 0.235392 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17.1090 | −0.597107 | −0.298554 | − | 0.954393i | \(-0.596504\pi\) | ||||
−0.298554 | + | 0.954393i | \(0.596504\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 50.8710 | 1.77325 | 0.886626 | − | 0.462487i | \(-0.153043\pi\) | ||||
0.886626 | + | 0.462487i | \(0.153043\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.39365 | − | 7.36690i | 0.0833362 | − | 0.256482i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.9860 | − | 18.1534i | −0.868848 | − | 0.631255i | 0.0614299 | − | 0.998111i | \(-0.480434\pi\) |
−0.930277 | + | 0.366857i | \(0.880434\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.7745 | 0.999381 | 0.499690 | − | 0.866204i | \(-0.333447\pi\) | ||||
0.499690 | + | 0.866204i | \(0.333447\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.64328 | + | 14.2906i | 0.161074 | + | 0.495734i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.950704 | + | 0.690727i | −0.0329399 | + | 0.0239323i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.4733 | − | 50.6995i | 0.570081 | − | 1.75453i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.98812 | + | 21.5072i | 0.241545 | + | 0.743399i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.8423 | + | 12.2367i | 0.581462 | + | 0.422457i | 0.839251 | − | 0.543744i | \(-0.182994\pi\) |
−0.257789 | + | 0.966201i | \(0.582994\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.4208 | + | 7.57118i | 0.359339 | + | 0.261075i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.864953 | + | 0.628425i | −0.0297906 | + | 0.0216441i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13.7336 | + | 9.97804i | 0.472450 | + | 0.343255i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.09061 | −0.243636 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.38546 | + | 10.4194i | −0.116189 | + | 0.357592i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.74197 | − | 29.9827i | −0.333950 | − | 1.02779i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.01337 | + | 21.5849i | 0.240133 | + | 0.739054i | 0.996399 | + | 0.0847891i | \(0.0270217\pi\) |
−0.756266 | + | 0.654264i | \(0.772978\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 25.0249 | − | 18.1816i | 0.855833 | − | 0.621799i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8.11365 | + | 24.9712i | −0.277157 | + | 0.853002i | 0.711484 | + | 0.702703i | \(0.248024\pi\) |
−0.988641 | + | 0.150299i | \(0.951976\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −43.2439 | + | 31.4185i | −1.47546 | + | 1.07199i | −0.496477 | + | 0.868050i | \(0.665373\pi\) |
−0.978984 | + | 0.203936i | \(0.934627\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.49038 | + | 3.95851i | −0.0507920 | + | 0.134906i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.3401 | + | 14.0514i | −0.658345 | + | 0.478316i | −0.866104 | − | 0.499864i | \(-0.833383\pi\) |
0.207759 | + | 0.978180i | \(0.433383\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.55262 | + | 4.77848i | −0.0527908 | + | 0.162473i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.34714 | + | 6.06456i | −0.283484 | + | 0.205963i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.93672 | − | 9.03829i | −0.0996214 | − | 0.306603i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.23987 | − | 19.2043i | −0.211430 | − | 0.650714i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.983199 | − | 3.02597i | 0.0332762 | − | 0.102414i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.24723 | 0.211195 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 37.4177 | + | 27.1856i | 1.26351 | + | 0.917991i | 0.998924 | − | 0.0463724i | \(-0.0147661\pi\) |
0.264582 | + | 0.964363i | \(0.414766\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.03279 | − | 4.38308i | 0.203481 | − | 0.147838i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.5635 | − | 17.8464i | −0.827564 | − | 0.601261i | 0.0913050 | − | 0.995823i | \(-0.470896\pi\) |
−0.918869 | + | 0.394562i | \(0.870896\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.4858 | − | 25.7819i | −1.19419 | − | 0.867631i | −0.200490 | − | 0.979696i | \(-0.564254\pi\) |
−0.993701 | + | 0.112065i | \(0.964254\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.62087 | + | 11.1439i | 0.121714 | + | 0.374598i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.99047 | − | 15.3591i | 0.167564 | − | 0.515708i | −0.831652 | − | 0.555297i | \(-0.812605\pi\) |
0.999216 | + | 0.0395887i | \(0.0126048\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.73833 | + | 7.07531i | −0.326613 | + | 0.237298i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.91755 | − | 21.2900i | −0.231747 | − | 0.713243i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 55.7732 | 1.86638 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23.2776 | + | 16.9122i | 0.778085 | + | 0.565312i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.50316 | + | 13.8593i | −0.150356 | + | 0.462748i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 24.7039 | 0.823921 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.63008 | 0.287510 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.524103 | 0.0174410 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −13.6284 | −0.453022 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.82801 | + | 17.9368i | −0.193516 | + | 0.595580i | 0.806475 | + | 0.591268i | \(0.201373\pi\) |
−0.999991 | + | 0.00431196i | \(0.998627\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16.8064 | + | 12.2106i | 0.557433 | + | 0.404999i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.37060 | −0.277330 | −0.138665 | − | 0.990339i | \(-0.544281\pi\) | ||||
−0.138665 | + | 0.990339i | \(0.544281\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.2951 | + | 50.1511i | 0.539289 | + | 1.65976i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.53522 | − | 3.29503i | 0.149930 | − | 0.108930i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.917345 | − | 2.82330i | 0.0302934 | − | 0.0932335i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.1680 | + | 43.6047i | 0.467360 | + | 1.43839i | 0.855990 | + | 0.516992i | \(0.172948\pi\) |
−0.388630 | + | 0.921394i | \(0.627052\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.6995 | + | 7.77367i | 0.352562 | + | 0.256151i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.87410 | + | 4.99432i | 0.226264 | + | 0.164390i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.37562 | − | 6.08525i | 0.275389 | − | 0.200082i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 37.4209 | + | 27.1879i | 1.22906 | + | 0.892968i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.86307 | −0.290788 | −0.145394 | − | 0.989374i | \(-0.546445\pi\) | ||||
−0.145394 | + | 0.989374i | \(0.546445\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.33874 | − | 4.12021i | 0.0438754 | − | 0.135035i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.68559 | + | 8.26538i | 0.0879221 | + | 0.270596i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.30172 | − | 13.2393i | −0.140681 | − | 0.432972i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.92458 | − | 1.39829i | 0.0628733 | − | 0.0456801i | −0.555905 | − | 0.831246i | \(-0.687628\pi\) |
0.618778 | + | 0.785566i | \(0.287628\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.31018 | + | 4.03233i | −0.0427562 | + | 0.131590i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.7710 | + | 15.0910i | −0.677114 | + | 0.491952i | −0.872399 | − | 0.488794i | \(-0.837437\pi\) |
0.195285 | + | 0.980747i | \(0.437437\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 41.9927 | + | 33.5600i | 1.36747 | + | 1.09286i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.28107 | − | 6.01655i | 0.269383 | − | 0.195718i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.6718 | − | 38.9999i | 0.411780 | − | 1.26733i | −0.503320 | − | 0.864100i | \(-0.667888\pi\) |
0.915100 | − | 0.403227i | \(-0.132112\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.48113 | − | 6.88845i | 0.307771 | − | 0.223608i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.99184 | + | 9.20794i | 0.0970171 | + | 0.298588i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.97703 | − | 12.2400i | −0.128829 | − | 0.396493i | 0.865751 | − | 0.500476i | \(-0.166842\pi\) |
−0.994579 | + | 0.103982i | \(0.966842\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.05378 | − | 24.7870i | 0.260614 | − | 0.802088i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11.2804 | 0.364642 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.14911 | + | 6.64722i | 0.295440 | + | 0.214650i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.55042 | + | 4.03261i | −0.179046 | + | 0.130084i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.16925 | + | 5.93531i | 0.263251 | + | 0.191263i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19.5213 | − | 14.1831i | −0.628413 | − | 0.456569i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.99742 | + | 18.4582i | 0.192864 | + | 0.593575i | 0.999995 | + | 0.00320201i | \(0.00101923\pi\) |
−0.807131 | + | 0.590373i | \(0.798981\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.03922 | + | 3.19840i | −0.0333847 | + | 0.102747i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 28.0327 | − | 20.3670i | 0.899613 | − | 0.653607i | −0.0387535 | − | 0.999249i | \(-0.512339\pi\) |
0.938367 | + | 0.345642i | \(0.112339\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.35947 | − | 7.26170i | −0.0756411 | − | 0.232799i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.78553 | −0.153260 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −24.8073 | − | 18.0235i | −0.793655 | − | 0.576624i | 0.115391 | − | 0.993320i | \(-0.463188\pi\) |
−0.909046 | + | 0.416696i | \(0.863188\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.62726 | + | 11.1636i | −0.115928 | + | 0.356789i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.42412 | 0.205106 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −12.1897 | −0.388791 | −0.194395 | − | 0.980923i | \(-0.562275\pi\) | ||||
−0.194395 | + | 0.980923i | \(0.562275\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 52.4119 | 1.66998 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.50428 | 0.270694 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.05828 | − | 6.33473i | 0.0654495 | − | 0.201433i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47.2625 | − | 34.3382i | −1.50134 | − | 1.09079i | −0.969843 | − | 0.243731i | \(-0.921628\pi\) |
−0.531500 | − | 0.847058i | \(-0.678372\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.87669 | 0.0595549 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.24800 | + | 25.3847i | 0.261479 | + | 0.804750i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.84567 | + | 1.34096i | −0.0584529 | + | 0.0424685i | −0.616628 | − | 0.787255i | \(-0.711502\pi\) |
0.558175 | + | 0.829723i | \(0.311502\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.26481 | + | 13.1257i | −0.134933 | + | 0.415280i |
(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.n.e.365.2 | ✓ | 24 | |
41.10 | even | 5 | inner | 1148.2.n.e.953.2 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.n.e.365.2 | ✓ | 24 | 1.1 | even | 1 | trivial | |
1148.2.n.e.953.2 | yes | 24 | 41.10 | even | 5 | inner |