Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(161,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 5, 8]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.161");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.ba (of order \(10\), 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: | \(24.5232237924\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 161.8 | ||
Character | \(\chi\) | \(=\) | 900.161 |
Dual form | 900.3.ba.a.341.8 |
$q$-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 \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.42516 | − | 4.79259i | −0.285031 | − | 0.958518i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.71989 | −0.245698 | −0.122849 | − | 0.992425i | \(-0.539203\pi\) | ||||
−0.122849 | + | 0.992425i | \(0.539203\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 9.74736 | + | 13.4161i | 0.886123 | + | 1.21964i | 0.974687 | + | 0.223574i | \(0.0717724\pi\) |
−0.0885635 | + | 0.996071i | \(0.528228\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.00021 | + | 2.17978i | 0.230785 | + | 0.167675i | 0.697168 | − | 0.716908i | \(-0.254443\pi\) |
−0.466383 | + | 0.884583i | \(0.654443\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −8.79122 | + | 2.85644i | −0.517130 | + | 0.168026i | −0.555943 | − | 0.831221i | \(-0.687643\pi\) |
0.0388122 | + | 0.999247i | \(0.487643\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.50958 | + | 20.0344i | 0.342610 | + | 1.05444i | 0.962851 | + | 0.270033i | \(0.0870346\pi\) |
−0.620241 | + | 0.784411i | \(0.712965\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −24.2383 | − | 33.3611i | −1.05384 | − | 1.45048i | −0.885435 | − | 0.464764i | \(-0.846139\pi\) |
−0.168402 | − | 0.985718i | \(-0.553861\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −20.9379 | + | 13.6604i | −0.837514 | + | 0.546415i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 29.9693 | + | 9.73763i | 1.03343 | + | 0.335780i | 0.776144 | − | 0.630556i | \(-0.217173\pi\) |
0.257282 | + | 0.966336i | \(0.417173\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 15.2756 | + | 47.0134i | 0.492760 | + | 1.51656i | 0.820419 | + | 0.571763i | \(0.193740\pi\) |
−0.327658 | + | 0.944796i | \(0.606260\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.45111 | + | 8.24272i | 0.0700317 | + | 0.235506i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −22.7734 | − | 16.5458i | −0.615497 | − | 0.447185i | 0.235849 | − | 0.971790i | \(-0.424213\pi\) |
−0.851346 | + | 0.524605i | \(0.824213\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 37.7014 | − | 51.8915i | 0.919547 | − | 1.26565i | −0.0442532 | − | 0.999020i | \(-0.514091\pi\) |
0.963800 | − | 0.266627i | \(-0.0859092\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 53.4572 | 1.24319 | 0.621595 | − | 0.783339i | \(-0.286485\pi\) | ||||
0.621595 | + | 0.783339i | \(0.286485\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 68.8803 | + | 22.3806i | 1.46554 | + | 0.476182i | 0.929757 | − | 0.368174i | \(-0.120017\pi\) |
0.535782 | + | 0.844356i | \(0.320017\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −46.0420 | −0.939632 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 100.600 | + | 32.6868i | 1.89811 | + | 0.616732i | 0.969102 | + | 0.246660i | \(0.0793330\pi\) |
0.929003 | + | 0.370072i | \(0.120667\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 50.4063 | − | 65.8351i | 0.916478 | − | 1.19700i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.21215 | − | 3.04476i | 0.0374940 | − | 0.0516061i | −0.789858 | − | 0.613289i | \(-0.789846\pi\) |
0.827352 | + | 0.561683i | \(0.189846\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 47.8107 | − | 34.7365i | 0.783781 | − | 0.569451i | −0.122330 | − | 0.992489i | \(-0.539037\pi\) |
0.906112 | + | 0.423039i | \(0.139037\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.17102 | − | 17.4853i | 0.0949387 | − | 0.269004i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 17.3938 | + | 53.5326i | 0.259609 | + | 0.798995i | 0.992886 | + | 0.119065i | \(0.0379897\pi\) |
−0.733277 | + | 0.679930i | \(0.762010\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 24.2608 | + | 7.88282i | 0.341702 | + | 0.111026i | 0.474841 | − | 0.880072i | \(-0.342506\pi\) |
−0.133139 | + | 0.991097i | \(0.542506\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −74.9352 | + | 54.4436i | −1.02651 | + | 0.745803i | −0.967607 | − | 0.252460i | \(-0.918760\pi\) |
−0.0589030 | + | 0.998264i | \(0.518760\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −16.7644 | − | 23.0742i | −0.217719 | − | 0.299664i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −26.9769 | + | 83.0265i | −0.341480 | + | 1.05097i | 0.621961 | + | 0.783048i | \(0.286336\pi\) |
−0.963441 | + | 0.267920i | \(0.913664\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 78.7953 | − | 25.6021i | 0.949341 | − | 0.308460i | 0.206893 | − | 0.978364i | \(-0.433665\pi\) |
0.742448 | + | 0.669904i | \(0.233665\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 26.2186 | + | 38.0618i | 0.308454 | + | 0.447786i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −22.6909 | − | 31.2314i | −0.254954 | − | 0.350914i | 0.662285 | − | 0.749252i | \(-0.269587\pi\) |
−0.917239 | + | 0.398338i | \(0.869587\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.16002 | − | 3.74897i | −0.0567035 | − | 0.0411975i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 86.7397 | − | 59.7500i | 0.913049 | − | 0.628947i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −18.7062 | + | 57.5719i | −0.192848 | + | 0.593525i | 0.807147 | + | 0.590350i | \(0.201010\pi\) |
−0.999995 | + | 0.00317438i | \(0.998990\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 94.4170i | 0.934822i | 0.884040 | + | 0.467411i | \(0.154813\pi\) | ||||
−0.884040 | + | 0.467411i | \(0.845187\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 40.8757 | − | 125.803i | 0.396852 | − | 1.22138i | −0.530658 | − | 0.847586i | \(-0.678055\pi\) |
0.927510 | − | 0.373798i | \(-0.121945\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 146.362i | − | 1.36787i | −0.729544 | − | 0.683934i | \(-0.760268\pi\) | ||
0.729544 | − | 0.683934i | \(-0.239732\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 159.767 | + | 116.078i | 1.46576 | + | 1.06493i | 0.981817 | + | 0.189832i | \(0.0607943\pi\) |
0.483939 | + | 0.875102i | \(0.339206\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −47.6991 | + | 65.6521i | −0.422116 | + | 0.580992i | −0.966121 | − | 0.258089i | \(-0.916907\pi\) |
0.544005 | + | 0.839082i | \(0.316907\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −125.343 | + | 163.709i | −1.08994 | + | 1.42355i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 15.1199 | − | 4.91276i | 0.127058 | − | 0.0412837i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −47.5894 | + | 146.465i | −0.393300 | + | 1.21045i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 95.3084 | + | 80.8784i | 0.762467 | + | 0.647027i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −42.7247 | + | 31.0413i | −0.336415 | + | 0.244420i | −0.743148 | − | 0.669128i | \(-0.766668\pi\) |
0.406733 | + | 0.913547i | \(0.366668\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −148.930 | + | 48.3904i | −1.13687 | + | 0.369393i | −0.816184 | − | 0.577792i | \(-0.803915\pi\) |
−0.320690 | + | 0.947184i | \(0.603915\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.1958 | − | 34.4570i | −0.0841786 | − | 0.259075i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.6043 | − | 22.8539i | 0.121199 | − | 0.166817i | −0.744106 | − | 0.668061i | \(-0.767124\pi\) |
0.865306 | + | 0.501245i | \(0.167124\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.7101 | − | 13.5937i | 0.134605 | − | 0.0977962i | −0.518445 | − | 0.855111i | \(-0.673489\pi\) |
0.653050 | + | 0.757315i | \(0.273489\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 61.4981i | 0.430057i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.95748 | − | 157.508i | 0.0272930 | − | 1.08626i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 136.554i | − | 0.916472i | −0.888831 | − | 0.458236i | \(-0.848481\pi\) | ||
0.888831 | − | 0.458236i | \(-0.151519\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 179.837 | 1.19098 | 0.595488 | − | 0.803364i | \(-0.296959\pi\) | ||||
0.595488 | + | 0.803364i | \(0.296959\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 203.546 | − | 140.211i | 1.31320 | − | 0.904586i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −63.0934 | −0.401869 | −0.200934 | − | 0.979605i | \(-0.564398\pi\) | ||||
−0.200934 | + | 0.979605i | \(0.564398\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 41.6871 | + | 57.3773i | 0.258926 | + | 0.356381i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 172.668 | + | 125.451i | 1.05931 | + | 0.769635i | 0.973961 | − | 0.226715i | \(-0.0727987\pi\) |
0.0853513 | + | 0.996351i | \(0.472799\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 136.050 | − | 44.2054i | 0.814672 | − | 0.264703i | 0.128097 | − | 0.991762i | \(-0.459113\pi\) |
0.686575 | + | 0.727059i | \(0.259113\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −47.9741 | − | 147.649i | −0.283870 | − | 0.873663i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 81.5907 | + | 112.300i | 0.471622 | + | 0.649133i | 0.976868 | − | 0.213843i | \(-0.0685981\pi\) |
−0.505246 | + | 0.862976i | \(0.668598\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 36.0108 | − | 23.4943i | 0.205776 | − | 0.134253i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −212.096 | − | 68.9143i | −1.18490 | − | 0.384996i | −0.350712 | − | 0.936483i | \(-0.614060\pi\) |
−0.834183 | + | 0.551487i | \(0.814060\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24.8085 | − | 76.3528i | −0.137064 | − | 0.421838i | 0.858842 | − | 0.512241i | \(-0.171185\pi\) |
−0.995905 | + | 0.0904027i | \(0.971185\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −46.8418 | + | 132.724i | −0.253199 | + | 0.717427i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −124.013 | − | 90.1010i | −0.663173 | − | 0.481824i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −70.1355 | + | 96.5332i | −0.367201 | + | 0.505409i | −0.952138 | − | 0.305670i | \(-0.901120\pi\) |
0.584936 | + | 0.811079i | \(0.301120\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −47.9079 | −0.248228 | −0.124114 | − | 0.992268i | \(-0.539609\pi\) | ||||
−0.124114 | + | 0.992268i | \(0.539609\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −175.908 | − | 57.1561i | −0.892936 | − | 0.290132i | −0.173617 | − | 0.984813i | \(-0.555546\pi\) |
−0.719318 | + | 0.694681i | \(0.755546\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −66.0335 | −0.331827 | −0.165913 | − | 0.986140i | \(-0.553057\pi\) | ||||
−0.165913 | + | 0.986140i | \(0.553057\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −51.5439 | − | 16.7476i | −0.253911 | − | 0.0825006i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −302.425 | − | 106.734i | −1.47525 | − | 0.520653i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −205.333 | + | 282.616i | −0.982452 | + | 1.35223i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 39.0231 | − | 28.3520i | 0.184944 | − | 0.134370i | −0.491461 | − | 0.870900i | \(-0.663537\pi\) |
0.676405 | + | 0.736530i | \(0.263537\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −76.1848 | − | 256.198i | −0.354348 | − | 1.19162i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −26.2723 | − | 80.8577i | −0.121070 | − | 0.372616i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −32.6019 | − | 10.5930i | −0.147520 | − | 0.0479321i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 105.372 | − | 76.5575i | 0.472522 | − | 0.343307i | −0.325901 | − | 0.945404i | \(-0.605668\pi\) |
0.798423 | + | 0.602096i | \(0.205668\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −130.958 | − | 180.248i | −0.576907 | − | 0.794044i | 0.416445 | − | 0.909161i | \(-0.363276\pi\) |
−0.993352 | + | 0.115117i | \(0.963276\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −125.407 | + | 385.963i | −0.547629 | + | 1.68543i | 0.167028 | + | 0.985952i | \(0.446583\pi\) |
−0.714656 | + | 0.699476i | \(0.753417\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 145.566 | − | 47.2973i | 0.624748 | − | 0.202993i | 0.0205007 | − | 0.999790i | \(-0.493474\pi\) |
0.604247 | + | 0.796797i | \(0.293474\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.09571 | − | 362.011i | 0.0387052 | − | 1.54047i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 97.3587 | + | 134.003i | 0.407358 | + | 0.560681i | 0.962572 | − | 0.271027i | \(-0.0873634\pi\) |
−0.555213 | + | 0.831708i | \(0.687363\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 366.395 | + | 266.202i | 1.52031 | + | 1.10457i | 0.961332 | + | 0.275392i | \(0.0888075\pi\) |
0.558981 | + | 0.829180i | \(0.311192\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 65.6170 | + | 220.660i | 0.267825 | + | 0.900655i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −24.1405 | + | 74.2969i | −0.0977349 | + | 0.300797i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 69.9103i | − | 0.278527i | −0.990255 | − | 0.139264i | \(-0.955526\pi\) | ||
0.990255 | − | 0.139264i | \(-0.0444735\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 211.316 | − | 650.365i | 0.835243 | − | 2.57061i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 88.8849i | 0.345856i | 0.984935 | + | 0.172928i | \(0.0553227\pi\) | ||||
−0.984935 | + | 0.172928i | \(0.944677\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 39.1677 | + | 28.4570i | 0.151227 | + | 0.109873i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −51.8933 | + | 71.4250i | −0.197313 | + | 0.271578i | −0.896196 | − | 0.443658i | \(-0.853681\pi\) |
0.698883 | + | 0.715236i | \(0.253681\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.2843 | − | 528.716i | 0.0501293 | − | 1.99516i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −265.111 | + | 86.1398i | −0.985543 | + | 0.320222i | −0.757074 | − | 0.653329i | \(-0.773372\pi\) |
−0.228469 | + | 0.973551i | \(0.573372\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 103.369 | − | 318.136i | 0.381434 | − | 1.17393i | −0.557600 | − | 0.830110i | \(-0.688278\pi\) |
0.939034 | − | 0.343824i | \(-0.111722\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −387.358 | − | 147.752i | −1.40857 | − | 0.537278i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −405.753 | + | 294.797i | −1.46481 | + | 1.06425i | −0.482735 | + | 0.875767i | \(0.660356\pi\) |
−0.982077 | + | 0.188481i | \(0.939644\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.6010 | − | 8.96810i | 0.0982241 | − | 0.0319150i | −0.259493 | − | 0.965745i | \(-0.583555\pi\) |
0.357717 | + | 0.933830i | \(0.383555\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −103.667 | − | 319.053i | −0.366313 | − | 1.12740i | −0.949155 | − | 0.314810i | \(-0.898059\pi\) |
0.582842 | − | 0.812585i | \(-0.301941\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −64.8422 | + | 89.2476i | −0.225931 | + | 0.310967i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −164.680 | + | 119.647i | −0.569826 | + | 0.414003i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 308.864i | 1.05414i | 0.849820 | + | 0.527072i | \(0.176710\pi\) | ||||
−0.849820 | + | 0.527072i | \(0.823290\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −17.7449 | − | 6.26266i | −0.0601523 | − | 0.0212293i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 152.924i | − | 0.511452i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −91.9403 | −0.305450 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −234.615 | − | 179.632i | −0.769231 | − | 0.588958i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −234.464 | −0.763727 | −0.381863 | − | 0.924219i | \(-0.624717\pi\) | ||||
−0.381863 | + | 0.924219i | \(0.624717\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.67272 | + | 10.5606i | 0.0246711 | + | 0.0339569i | 0.821174 | − | 0.570677i | \(-0.193319\pi\) |
−0.796503 | + | 0.604634i | \(0.793319\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 320.461 | + | 232.829i | 1.02384 | + | 0.743862i | 0.967066 | − | 0.254525i | \(-0.0819192\pi\) |
0.0567719 | + | 0.998387i | \(0.481919\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −412.283 | + | 133.959i | −1.30058 | + | 0.422583i | −0.875782 | − | 0.482706i | \(-0.839654\pi\) |
−0.424795 | + | 0.905289i | \(0.639654\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 161.481 | + | 496.987i | 0.506210 | + | 1.55795i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −114.454 | − | 157.533i | −0.354348 | − | 0.487718i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −92.5945 | − | 4.65591i | −0.284906 | − | 0.0143259i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −118.466 | − | 38.4921i | −0.360080 | − | 0.116997i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 122.732 | + | 377.731i | 0.370793 | + | 1.14118i | 0.946274 | + | 0.323367i | \(0.104815\pi\) |
−0.575481 | + | 0.817815i | \(0.695185\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 231.771 | − | 159.654i | 0.691854 | − | 0.476579i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −255.306 | − | 185.491i | −0.757585 | − | 0.550417i | 0.140584 | − | 0.990069i | \(-0.455102\pi\) |
−0.898169 | + | 0.439651i | \(0.855102\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −481.839 | + | 663.194i | −1.41302 | + | 1.94485i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 163.462 | 0.476564 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −394.043 | − | 128.032i | −1.13557 | − | 0.368969i | −0.319880 | − | 0.947458i | \(-0.603642\pi\) |
−0.815690 | + | 0.578489i | \(0.803642\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −208.117 | −0.596324 | −0.298162 | − | 0.954515i | \(-0.596374\pi\) | ||||
−0.298162 | + | 0.954515i | \(0.596374\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −126.510 | − | 41.1057i | −0.358386 | − | 0.116447i | 0.124289 | − | 0.992246i | \(-0.460335\pi\) |
−0.482675 | + | 0.875799i | \(0.660335\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.20367 | − | 127.507i | 0.00902441 | − | 0.359173i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 67.9510 | − | 93.5265i | 0.189279 | − | 0.260520i | −0.703822 | − | 0.710376i | \(-0.748525\pi\) |
0.893101 | + | 0.449856i | \(0.148525\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −66.9488 | + | 48.6412i | −0.185454 | + | 0.134740i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 367.721 | + | 281.543i | 1.00745 | + | 0.771351i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −137.848 | − | 424.253i | −0.375608 | − | 1.15600i | −0.943068 | − | 0.332601i | \(-0.892074\pi\) |
0.567460 | − | 0.823401i | \(-0.307926\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −173.020 | − | 56.2176i | −0.466361 | − | 0.151530i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 275.067 | − | 199.848i | 0.737445 | − | 0.535785i | −0.154465 | − | 0.987998i | \(-0.549365\pi\) |
0.891910 | + | 0.452213i | \(0.149365\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 68.6883 | + | 94.5414i | 0.182197 | + | 0.250773i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.4865 | + | 72.2839i | −0.0619695 | + | 0.190723i | −0.977248 | − | 0.212098i | \(-0.931970\pi\) |
0.915279 | + | 0.402821i | \(0.131970\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 278.959 | − | 90.6394i | 0.728353 | − | 0.236656i | 0.0787121 | − | 0.996897i | \(-0.474919\pi\) |
0.649641 | + | 0.760241i | \(0.274919\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −86.6932 | + | 113.229i | −0.225177 | + | 0.294101i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −401.442 | − | 552.537i | −1.03198 | − | 1.42040i | −0.903447 | − | 0.428699i | \(-0.858972\pi\) |
−0.128536 | − | 0.991705i | \(-0.541028\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 308.378 | + | 224.050i | 0.788690 | + | 0.573017i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 436.358 | + | 10.9637i | 1.10470 | + | 0.0277563i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.0372 | − | 92.4450i | 0.0756604 | − | 0.232859i | −0.906073 | − | 0.423122i | \(-0.860934\pi\) |
0.981733 | + | 0.190263i | \(0.0609341\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 402.465i | 1.00365i | 0.864968 | + | 0.501827i | \(0.167338\pi\) | ||||
−0.864968 | + | 0.501827i | \(0.832662\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −56.6488 | + | 174.347i | −0.140568 | + | 0.432623i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 466.808i | − | 1.14695i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.9006 | + | 18.8179i | 0.0633266 | + | 0.0460094i | 0.618998 | − | 0.785392i | \(-0.287539\pi\) |
−0.555672 | + | 0.831402i | \(0.687539\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.80464 | + | 5.23664i | −0.00921221 | + | 0.0126795i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −234.996 | − | 341.147i | −0.566256 | − | 0.822040i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −652.348 | + | 211.961i | −1.55692 | + | 0.505873i | −0.955982 | − | 0.293426i | \(-0.905205\pi\) |
−0.600934 | + | 0.799299i | \(0.705205\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 63.4734 | − | 195.351i | 0.150768 | − | 0.464017i | −0.846939 | − | 0.531690i | \(-0.821557\pi\) |
0.997708 | + | 0.0676726i | \(0.0215573\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 145.049 | − | 179.899i | 0.341292 | − | 0.423292i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −82.2290 | + | 59.7429i | −0.192574 | + | 0.139913i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.8152 | + | 4.16390i | −0.0297335 | + | 0.00966101i | −0.323846 | − | 0.946110i | \(-0.604976\pi\) |
0.294112 | + | 0.955771i | \(0.404976\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −182.632 | − | 562.082i | −0.421782 | − | 1.29811i | −0.906042 | − | 0.423188i | \(-0.860911\pi\) |
0.484260 | − | 0.874924i | \(-0.339089\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 510.590 | − | 702.767i | 1.16840 | − | 1.60816i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 267.816 | − | 194.580i | 0.610059 | − | 0.443234i | −0.239376 | − | 0.970927i | \(-0.576943\pi\) |
0.849435 | + | 0.527693i | \(0.176943\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 407.657i | 0.920219i | 0.887862 | + | 0.460109i | \(0.152190\pi\) | ||||
−0.887862 | + | 0.460109i | \(0.847810\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −117.341 | + | 153.258i | −0.263688 | + | 0.344400i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 821.378i | 1.82935i | 0.404190 | + | 0.914675i | \(0.367553\pi\) | ||||
−0.404190 | + | 0.914675i | \(0.632447\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1063.67 | 2.35847 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10.6135 | + | 30.0727i | −0.0233263 | + | 0.0660939i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −757.886 | −1.65839 | −0.829197 | − | 0.558956i | \(-0.811202\pi\) | ||||
−0.829197 | + | 0.558956i | \(0.811202\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.9016 | + | 30.1450i | 0.0475090 | + | 0.0653905i | 0.832111 | − | 0.554610i | \(-0.187132\pi\) |
−0.784602 | + | 0.620000i | \(0.787132\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −244.571 | − | 177.692i | −0.528232 | − | 0.383783i | 0.291464 | − | 0.956582i | \(-0.405858\pi\) |
−0.819696 | + | 0.572799i | \(0.805858\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 842.339 | − | 273.693i | 1.80372 | − | 0.586065i | 0.803763 | − | 0.594949i | \(-0.202828\pi\) |
0.999961 | + | 0.00888392i | \(0.00282788\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −29.9154 | − | 92.0701i | −0.0637855 | − | 0.196312i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 521.066 | + | 717.186i | 1.10162 | + | 1.51625i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −409.975 | − | 330.555i | −0.863105 | − | 0.695905i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 90.6213 | + | 29.4447i | 0.189189 | + | 0.0614711i | 0.402079 | − | 0.915605i | \(-0.368288\pi\) |
−0.212890 | + | 0.977076i | \(0.568288\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −32.2586 | − | 99.2819i | −0.0670658 | − | 0.206407i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 302.578 | + | 7.60243i | 0.623872 | + | 0.0156751i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 325.516 | + | 236.501i | 0.668410 | + | 0.485628i | 0.869492 | − | 0.493946i | \(-0.164446\pi\) |
−0.201083 | + | 0.979574i | \(0.564446\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 79.8784 | − | 109.943i | 0.162685 | − | 0.223917i | −0.719890 | − | 0.694088i | \(-0.755808\pi\) |
0.882575 | + | 0.470171i | \(0.155808\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −291.282 | −0.590836 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −41.7259 | − | 13.5576i | −0.0839556 | − | 0.0272788i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 395.792 | 0.793170 | 0.396585 | − | 0.917998i | \(-0.370195\pi\) | ||||
0.396585 | + | 0.917998i | \(0.370195\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 455.484 | + | 147.996i | 0.905535 | + | 0.294226i | 0.724519 | − | 0.689254i | \(-0.242062\pi\) |
0.181015 | + | 0.983480i | \(0.442062\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 452.502 | − | 134.559i | 0.896044 | − | 0.266454i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 326.631 | − | 449.568i | 0.641710 | − | 0.883238i | −0.356995 | − | 0.934106i | \(-0.616199\pi\) |
0.998705 | + | 0.0508678i | \(0.0161987\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 128.880 | − | 93.6369i | 0.252212 | − | 0.183243i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −661.174 | − | 16.6123i | −1.28383 | − | 0.0322570i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 371.141 | + | 1142.26i | 0.717875 | + | 2.20939i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −130.243 | − | 42.3184i | −0.249986 | − | 0.0812253i | 0.181344 | − | 0.983420i | \(-0.441955\pi\) |
−0.431329 | + | 0.902195i | \(0.641955\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 664.497 | − | 482.785i | 1.27055 | − | 0.923108i | 0.271324 | − | 0.962488i | \(-0.412538\pi\) |
0.999224 | + | 0.0393804i | \(0.0125384\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −268.582 | − | 369.671i | −0.509643 | − | 0.701463i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −362.000 | + | 1114.12i | −0.684309 | + | 2.10609i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 226.224 | − | 73.5046i | 0.424435 | − | 0.137907i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −701.453 | + | 208.589i | −1.31113 | + | 0.389885i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −448.788 | − | 617.703i | −0.832630 | − | 1.14602i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −208.394 | − | 151.407i | −0.385201 | − | 0.279865i | 0.378285 | − | 0.925689i | \(-0.376514\pi\) |
−0.763486 | + | 0.645824i | \(0.776514\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 328.620 | − | 931.129i | 0.602972 | − | 1.70849i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −87.8866 | + | 270.487i | −0.160670 | + | 0.494492i | −0.998691 | − | 0.0511459i | \(-0.983713\pi\) |
0.838021 | + | 0.545638i | \(0.183713\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 663.807i | 1.20473i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 46.3973 | − | 142.796i | 0.0839011 | − | 0.258221i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 194.606i | − | 0.349382i | −0.984623 | − | 0.174691i | \(-0.944107\pi\) | ||
0.984623 | − | 0.174691i | \(-0.0558926\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 160.383 | + | 116.525i | 0.286910 | + | 0.208452i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 240.988 | − | 331.691i | 0.428042 | − | 0.589149i | −0.539461 | − | 0.842011i | \(-0.681372\pi\) |
0.967502 | + | 0.252862i | \(0.0813718\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 382.622 | + | 135.038i | 0.677208 | + | 0.239005i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −168.606 | + | 54.7833i | −0.296319 | + | 0.0962799i | −0.453404 | − | 0.891305i | \(-0.649790\pi\) |
0.157085 | + | 0.987585i | \(0.449790\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −252.479 | + | 777.052i | −0.442171 | + | 1.36086i | 0.443387 | + | 0.896331i | \(0.353777\pi\) |
−0.885557 | + | 0.464531i | \(0.846223\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 963.222 | + | 367.406i | 1.67517 | + | 0.638967i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 251.059 | − | 182.405i | 0.435112 | − | 0.316127i | −0.348578 | − | 0.937280i | \(-0.613335\pi\) |
0.783690 | + | 0.621153i | \(0.213335\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −135.519 | + | 44.0328i | −0.233251 | + | 0.0757880i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 542.051 | + | 1668.26i | 0.929762 | + | 2.86151i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −43.2182 | + | 59.4847i | −0.0736255 | + | 0.101337i | −0.844242 | − | 0.535963i | \(-0.819949\pi\) |
0.770616 | + | 0.637300i | \(0.219949\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −842.448 | + | 612.075i | −1.43030 | + | 1.03918i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 221.665i | 0.373802i | 0.982379 | + | 0.186901i | \(0.0598444\pi\) | ||||
−0.982379 | + | 0.186901i | \(0.940156\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −45.0931 | − | 65.4621i | −0.0757867 | − | 0.110020i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 163.866i | − | 0.273566i | −0.990601 | − | 0.136783i | \(-0.956324\pi\) | ||
0.990601 | − | 0.136783i | \(-0.0436763\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −167.070 | −0.277986 | −0.138993 | − | 0.990293i | \(-0.544387\pi\) | ||||
−0.138993 | + | 0.990293i | \(0.544387\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 769.769 | + | 19.3408i | 1.27235 | + | 0.0319683i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −393.046 | −0.647522 | −0.323761 | − | 0.946139i | \(-0.604947\pi\) | ||||
−0.323761 | + | 0.946139i | \(0.604947\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 157.871 | + | 217.290i | 0.258381 | + | 0.355630i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −637.094 | − | 462.876i | −1.03930 | − | 0.755099i | −0.0691547 | − | 0.997606i | \(-0.522030\pi\) |
−0.970150 | + | 0.242507i | \(0.922030\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −501.571 | + | 162.970i | −0.812919 | + | 0.264133i | −0.685833 | − | 0.727759i | \(-0.740562\pi\) |
−0.127085 | + | 0.991892i | \(0.540562\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 121.698 | + | 374.548i | 0.196604 | + | 0.605086i | 0.999954 | + | 0.00957871i | \(0.00304904\pi\) |
−0.803350 | + | 0.595508i | \(0.796951\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 39.0258 | + | 53.7144i | 0.0626418 | + | 0.0862190i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 251.788 | − | 572.038i | 0.402861 | − | 0.915261i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 247.468 | + | 80.4073i | 0.393431 | + | 0.127833i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 306.092 | + | 942.055i | 0.485091 | + | 1.49296i | 0.831850 | + | 0.555001i | \(0.187282\pi\) |
−0.346759 | + | 0.937954i | \(0.612718\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 209.658 | + | 160.523i | 0.330169 | + | 0.252792i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −138.135 | − | 100.361i | −0.216853 | − | 0.157553i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 346.383 | − | 476.755i | 0.540379 | − | 0.743768i | −0.448289 | − | 0.893889i | \(-0.647966\pi\) |
0.988668 | + | 0.150121i | \(0.0479664\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 425.988 | 0.662500 | 0.331250 | − | 0.943543i | \(-0.392530\pi\) | ||||
0.331250 | + | 0.943543i | \(0.392530\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 232.024 | + | 75.3893i | 0.358616 | + | 0.116521i | 0.482783 | − | 0.875740i | \(-0.339626\pi\) |
−0.124167 | + | 0.992261i | \(0.539626\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 62.4113 | 0.0961654 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −444.663 | − | 144.480i | −0.680954 | − | 0.221255i | −0.0519408 | − | 0.998650i | \(-0.516541\pi\) |
−0.629013 | + | 0.777395i | \(0.716541\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 444.165 | + | 644.799i | 0.678114 | + | 0.984426i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 171.201 | − | 235.638i | 0.259790 | − | 0.357570i | −0.659120 | − | 0.752038i | \(-0.729071\pi\) |
0.918910 | + | 0.394468i | \(0.129071\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 480.379 | − | 349.016i | 0.726746 | − | 0.528012i | −0.161786 | − | 0.986826i | \(-0.551726\pi\) |
0.888532 | + | 0.458814i | \(0.151726\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −149.183 | + | 102.763i | −0.224335 | + | 0.154531i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −401.546 | − | 1235.83i | −0.602019 | − | 1.85282i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 932.055 | + | 302.843i | 1.38905 | + | 0.451331i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 826.218 | − | 600.283i | 1.22766 | − | 0.891950i | 0.230952 | − | 0.972965i | \(-0.425816\pi\) |
0.996713 | + | 0.0810149i | \(0.0258161\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 417.353 | + | 574.437i | 0.616474 | + | 0.848503i | 0.997090 | − | 0.0762298i | \(-0.0242883\pi\) |
−0.380617 | + | 0.924733i | \(0.624288\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 32.1726 | − | 99.0172i | 0.0473824 | − | 0.145828i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −93.8795 | + | 30.5033i | −0.137452 | + | 0.0446607i | −0.376935 | − | 0.926240i | \(-0.623022\pi\) |
0.239483 | + | 0.970900i | \(0.423022\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −133.193 | − | 47.0073i | −0.194442 | − | 0.0686238i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 230.570 | + | 317.352i | 0.334644 | + | 0.460598i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −62.3169 | − | 45.2759i | −0.0901837 | − | 0.0655223i | 0.541780 | − | 0.840521i | \(-0.317751\pi\) |
−0.631963 | + | 0.774998i | \(0.717751\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −91.8137 | − | 70.2966i | −0.132106 | − | 0.101146i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −183.216 | + | 563.882i | −0.262864 | + | 0.809012i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1285.29i | − | 1.83351i | −0.399448 | − | 0.916756i | \(-0.630798\pi\) | ||
0.399448 | − | 0.916756i | \(-0.369202\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 183.241 | − | 563.959i | 0.260656 | − | 0.802217i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 162.387i | − | 0.229684i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 454.529 | + | 330.234i | 0.641084 | + | 0.465775i | 0.860222 | − | 0.509919i | \(-0.170325\pi\) |
−0.219138 | + | 0.975694i | \(0.570325\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1198.16 | − | 1649.13i | 1.68045 | − | 2.31295i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 294.735 | − | 87.6444i | 0.412217 | − | 0.122580i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 224.085 | − | 72.8096i | 0.311662 | − | 0.101265i | −0.149010 | − | 0.988836i | \(-0.547609\pi\) |
0.460672 | + | 0.887571i | \(0.347609\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −70.3016 | + | 216.366i | −0.0975057 | + | 0.300092i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −760.513 | + | 205.508i | −1.04898 | + | 0.283459i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −993.758 | + | 722.007i | −1.36693 | + | 0.993133i | −0.368960 | + | 0.929445i | \(0.620286\pi\) |
−0.997970 | + | 0.0636872i | \(0.979714\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −469.954 | + | 152.697i | −0.642891 | + | 0.208888i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 272.330 | + | 838.145i | 0.371528 | + | 1.14345i | 0.945791 | + | 0.324775i | \(0.105289\pi\) |
−0.574263 | + | 0.818671i | \(0.694711\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −548.655 | + | 755.159i | −0.744444 | + | 1.02464i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 221.229 | − | 160.732i | 0.299363 | − | 0.217500i | −0.427956 | − | 0.903800i | \(-0.640766\pi\) |
0.727319 | + | 0.686300i | \(0.240766\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1045.27i | 1.40682i | 0.710784 | + | 0.703411i | \(0.248341\pi\) | ||||
−0.710784 | + | 0.703411i | \(0.751659\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −654.449 | + | 194.611i | −0.878455 | + | 0.261223i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 251.726i | 0.336083i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −57.6771 | −0.0768005 | −0.0384002 | − | 0.999262i | \(-0.512226\pi\) | ||||
−0.0384002 | + | 0.999262i | \(0.512226\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −256.296 | − | 861.887i | −0.339465 | − | 1.14157i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 634.193 | 0.837771 | 0.418886 | − | 0.908039i | \(-0.362421\pi\) | ||||
0.418886 | + | 0.908039i | \(0.362421\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 331.220 | + | 455.885i | 0.435243 | + | 0.599060i | 0.969147 | − | 0.246485i | \(-0.0792756\pi\) |
−0.533904 | + | 0.845545i | \(0.679276\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −274.782 | − | 199.641i | −0.360134 | − | 0.261652i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13.2738 | − | 4.31291i | 0.0173061 | − | 0.00562310i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 184.662 | + | 568.330i | 0.240132 | + | 0.739050i | 0.996399 | + | 0.0847874i | \(0.0270211\pi\) |
−0.756267 | + | 0.654263i | \(0.772979\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 108.761 | + | 149.697i | 0.140700 | + | 0.193657i | 0.873552 | − | 0.486731i | \(-0.161811\pi\) |
−0.732851 | + | 0.680389i | \(0.761811\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −962.058 | − | 775.689i | −1.24137 | − | 1.00089i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1285.04 | + | 417.534i | 1.64960 | + | 0.535987i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 130.722 | + | 402.322i | 0.167378 | + | 0.515137i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 89.9180 | + | 302.381i | 0.114545 | + | 0.385199i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −876.085 | − | 636.513i | −1.11320 | − | 0.808784i | −0.130032 | − | 0.991510i | \(-0.541508\pi\) |
−0.983164 | + | 0.182726i | \(0.941508\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 82.0370 | − | 112.914i | 0.103713 | − | 0.142749i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 219.160 | 0.276368 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 626.023 | + | 203.407i | 0.785474 | + | 0.255216i | 0.674176 | − | 0.738571i | \(-0.264499\pi\) |
0.111299 | + | 0.993787i | \(0.464499\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −669.471 | −0.837886 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1460.84 | − | 474.656i | −1.81923 | − | 0.591104i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 215.576 | − | 281.561i | 0.267796 | − | 0.349765i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 268.159 | − | 369.090i | 0.331470 | − | 0.456230i | −0.610456 | − | 0.792050i | \(-0.709014\pi\) |
0.941926 | + | 0.335821i | \(0.109014\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 960.392 | − | 697.765i | 1.18421 | − | 0.860376i | 0.191567 | − | 0.981480i | \(-0.438643\pi\) |
0.992640 | + | 0.121103i | \(0.0386432\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 355.155 | − | 1006.31i | 0.435772 | − | 1.23474i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 347.984 | + | 1070.98i | 0.425929 | + | 1.31087i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −237.227 | − | 77.0797i | −0.288949 | − | 0.0938852i | 0.160956 | − | 0.986962i | \(-0.448542\pi\) |
−0.449905 | + | 0.893076i | \(0.648542\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −915.459 | + | 665.120i | −1.11234 | + | 0.808165i | −0.983031 | − | 0.183439i | \(-0.941277\pi\) |
−0.129312 | + | 0.991604i | \(0.541277\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −524.264 | − | 721.587i | −0.633935 | − | 0.872536i | 0.364339 | − | 0.931266i | \(-0.381295\pi\) |
−0.998274 | + | 0.0587302i | \(0.981295\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 389.605 | − | 1199.08i | 0.469970 | − | 1.44642i | −0.382654 | − | 0.923892i | \(-0.624990\pi\) |
0.852623 | − | 0.522526i | \(-0.175010\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 404.765 | − | 131.516i | 0.485913 | − | 0.157883i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −405.751 | − | 589.033i | −0.485930 | − | 0.705429i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 199.477 | + | 274.557i | 0.237756 | + | 0.327243i | 0.911176 | − | 0.412017i | \(-0.135175\pi\) |
−0.673420 | + | 0.739260i | \(0.735175\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 122.956 | + | 89.3331i | 0.146203 | + | 0.106222i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −639.251 | + | 440.343i | −0.756510 | + | 0.521116i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 81.8483 | − | 251.903i | 0.0966332 | − | 0.297407i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1160.79i | 1.36403i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 247.683 | − | 762.289i | 0.290367 | − | 0.893657i | −0.694372 | − | 0.719616i | \(-0.744318\pi\) |
0.984739 | − | 0.174040i | \(-0.0556823\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 513.557i | − | 0.599250i | −0.954057 | − | 0.299625i | \(-0.903138\pi\) | ||
0.954057 | − | 0.299625i | \(-0.0968615\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −204.560 | − | 148.622i | −0.238138 | − | 0.173017i | 0.462316 | − | 0.886715i | \(-0.347019\pi\) |
−0.700453 | + | 0.713698i | \(0.747019\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 333.599 | − | 459.160i | 0.386557 | − | 0.532051i | −0.570749 | − | 0.821124i | \(-0.693347\pi\) |
0.957307 | + | 0.289074i | \(0.0933472\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 421.928 | − | 551.076i | 0.487778 | − | 0.637082i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1376.84 | + | 447.364i | −1.58440 | + | 0.514803i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −64.5042 | + | 198.524i | −0.0740577 | + | 0.227926i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −163.920 | − | 139.102i | −0.187337 | − | 0.158973i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 843.349 | − | 612.729i | 0.961629 | − | 0.698664i | 0.00810044 | − | 0.999967i | \(-0.497422\pi\) |
0.953528 | + | 0.301303i | \(0.0974215\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 768.835 | − | 249.809i | 0.872684 | − | 0.283552i | 0.161768 | − | 0.986829i | \(-0.448280\pi\) |
0.710916 | + | 0.703277i | \(0.248280\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −38.1068 | − | 117.281i | −0.0431560 | − | 0.132821i | 0.927157 | − | 0.374673i | \(-0.122245\pi\) |
−0.970313 | + | 0.241852i | \(0.922245\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 292.819 | − | 403.031i | 0.330123 | − | 0.454376i | −0.611401 | − | 0.791321i | \(-0.709394\pi\) |
0.941524 | + | 0.336945i | \(0.109394\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 73.4816 | − | 53.3875i | 0.0826565 | − | 0.0600535i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1525.67i | 1.70847i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −28.0075 | + | 1114.70i | −0.0312933 | + | 1.24548i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1557.71i | 1.73271i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −977.761 | −1.08519 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −330.572 | + | 227.712i | −0.365272 | + | 0.251615i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1502.05 | 1.65607 | 0.828034 | − | 0.560677i | \(-0.189459\pi\) | ||||
0.828034 | + | 0.560677i | \(0.189459\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −639.996 | − | 880.879i | −0.702520 | − | 0.966936i | −0.999926 | − | 0.0121847i | \(-0.996121\pi\) |
0.297406 | − | 0.954751i | \(-0.403879\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1111.53 | + | 807.571i | 1.21744 | + | 0.884525i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 256.144 | − | 83.2261i | 0.279328 | − | 0.0907591i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −320.231 | − | 985.571i | −0.348456 | − | 1.07244i | −0.959707 | − | 0.281001i | \(-0.909333\pi\) |
0.611251 | − | 0.791437i | \(-0.290667\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 55.6047 | + | 76.5333i | 0.0602435 | + | 0.0829180i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 702.849 | + | 35.3412i | 0.759836 | + | 0.0382067i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −709.137 | − | 230.413i | −0.763334 | − | 0.248022i | −0.0986248 | − | 0.995125i | \(-0.531444\pi\) |
−0.664709 | + | 0.747103i | \(0.731444\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −299.714 | − | 922.425i | −0.321927 | − | 0.990790i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −255.079 | + | 722.754i | −0.272812 | + | 0.772998i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.2360 | + | 17.6085i | 0.0258656 | + | 0.0187924i | 0.600643 | − | 0.799517i | \(-0.294911\pi\) |
−0.574777 | + | 0.818310i | \(0.694911\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 166.570 | − | 229.264i | 0.177014 | − | 0.243638i | −0.711286 | − | 0.702903i | \(-0.751887\pi\) |
0.888300 | + | 0.459264i | \(0.151887\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2644.97 | −2.80485 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 637.644 | + | 207.183i | 0.673331 | + | 0.218778i | 0.625673 | − | 0.780085i | \(-0.284824\pi\) |
0.0476576 | + | 0.998864i | \(0.484824\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −343.496 | −0.361956 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1268.11 | − | 412.034i | −1.33065 | − | 0.432355i | −0.444511 | − | 0.895773i | \(-0.646623\pi\) |
−0.886139 | + | 0.463419i | \(0.846623\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 562.598 | + | 198.556i | 0.589108 | + | 0.207912i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −28.5576 | + | 39.3061i | −0.0297785 | + | 0.0409865i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1199.45 | + | 871.449i | −1.24812 | + | 0.906815i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 68.2763 | + | 229.603i | 0.0707526 | + | 0.237931i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −249.879 | − | 769.048i | −0.258406 | − | 0.795293i | −0.993139 | − | 0.116936i | \(-0.962693\pi\) |
0.734733 | − | 0.678356i | \(-0.237307\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1530.88 | − | 497.413i | −1.57660 | − | 0.512268i | −0.615422 | − | 0.788198i | \(-0.711014\pi\) |
−0.961178 | + | 0.275929i | \(0.911014\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −32.1792 | + | 23.3796i | −0.0330722 | + | 0.0240283i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −856.460 | − | 1178.82i | −0.876622 | − | 1.20657i | −0.977345 | − | 0.211652i | \(-0.932116\pi\) |
0.100723 | − | 0.994915i | \(-0.467884\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 197.826 | − | 608.846i | 0.202070 | − | 0.621906i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −31.8957 | + | 10.3635i | −0.0324473 | + | 0.0105428i | −0.325196 | − | 0.945647i | \(-0.605430\pi\) |
0.292748 | + | 0.956190i | \(0.405430\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −23.2289 | + | 924.513i | −0.0235826 | + | 0.938592i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1295.71 | − | 1783.39i | −1.31012 | − | 1.80323i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 63.1416 | + | 45.8751i | 0.0637151 | + | 0.0462917i | 0.619187 | − | 0.785244i | \(-0.287462\pi\) |
−0.555472 | + | 0.831535i | \(0.687462\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 94.1080 | + | 316.472i | 0.0945810 | + | 0.318062i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −59.8578 | + | 184.223i | −0.0600379 | + | 0.184778i | −0.976577 | − | 0.215167i | \(-0.930971\pi\) |
0.916539 | + | 0.399944i | \(0.130971\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 900.3.ba.a.161.8 | ✓ | 80 | |
3.2 | odd | 2 | inner | 900.3.ba.a.161.13 | yes | 80 | |
25.16 | even | 5 | inner | 900.3.ba.a.341.13 | yes | 80 | |
75.41 | odd | 10 | inner | 900.3.ba.a.341.8 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
900.3.ba.a.161.8 | ✓ | 80 | 1.1 | even | 1 | trivial | |
900.3.ba.a.161.13 | yes | 80 | 3.2 | odd | 2 | inner | |
900.3.ba.a.341.8 | yes | 80 | 75.41 | odd | 10 | inner | |
900.3.ba.a.341.13 | yes | 80 | 25.16 | even | 5 | inner |