Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [201,3,Mod(17,201)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(201, base_ring=CyclotomicField(66))
chi = DirichletCharacter(H, H._module([33, 64]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("201.17");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 201 = 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 201.o (of order \(66\), degree \(20\), 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: | \(5.47685331364\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\Q(\zeta_{33})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{19} + x^{17} - x^{16} + x^{14} - x^{13} + x^{11} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{66}]$ |
Embedding invariants
Embedding label | 167.1 | ||
Root | \(0.928368 + 0.371662i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 201.167 |
Dual form | 201.3.o.a.65.1 |
$q$-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 \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).
\(n\) | \(68\) | \(136\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{16}{33}\right)\) |
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 | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) | ||||
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(3\) | 2.87848 | − | 0.845198i | 0.959493 | − | 0.281733i | ||||
\(4\) | −3.98189 | + | 0.380224i | −0.995472 | + | 0.0950560i | ||||
\(5\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −11.9416 | − | 6.15630i | −1.70594 | − | 0.879472i | −0.981825 | − | 0.189789i | \(-0.939220\pi\) |
−0.724112 | − | 0.689682i | \(-0.757750\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.57128 | − | 4.86577i | 0.841254 | − | 0.540641i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.327068 | − | 0.945001i | \(-0.393939\pi\) | ||||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(12\) | −11.1404 | + | 4.45995i | −0.928368 | + | 0.371662i | ||||
\(13\) | −20.3617 | − | 16.0126i | −1.56629 | − | 1.23174i | −0.836283 | − | 0.548298i | \(-0.815276\pi\) |
−0.730003 | − | 0.683443i | \(-0.760482\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 15.7109 | − | 3.02802i | 0.981929 | − | 0.189251i | ||||
\(17\) | 0 | 0 | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) | ||||
0.995472 | + | 0.0950560i | \(0.0303030\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 15.2339 | − | 7.85364i | 0.801786 | − | 0.413350i | −0.00807751 | − | 0.999967i | \(-0.502571\pi\) |
0.809864 | + | 0.586618i | \(0.199541\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −39.5768 | − | 7.62781i | −1.88461 | − | 0.363229i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.55787 | + | 24.7455i | −0.142315 | + | 0.989821i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 17.6812 | − | 20.4052i | 0.654861 | − | 0.755750i | ||||
\(28\) | 49.8907 | + | 19.9732i | 1.78181 | + | 0.713330i | ||||
\(29\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −42.7047 | + | 33.5834i | −1.37757 | + | 1.08334i | −0.390933 | + | 0.920419i | \(0.627847\pi\) |
−0.986640 | + | 0.162916i | \(0.947910\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −28.2979 | + | 22.2537i | −0.786053 | + | 0.618159i | ||||
\(37\) | 36.1385 | − | 62.5937i | 0.976717 | − | 1.69172i | 0.302567 | − | 0.953128i | \(-0.402157\pi\) |
0.674150 | − | 0.738595i | \(-0.264510\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −72.1446 | − | 28.8824i | −1.84986 | − | 0.740573i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.580057 | − | 0.814576i | \(-0.303030\pi\) | ||||
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −21.3206 | − | 46.6855i | −0.495827 | − | 1.08571i | −0.977803 | − | 0.209526i | \(-0.932808\pi\) |
0.481976 | − | 0.876184i | \(-0.339919\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.723734 | − | 0.690079i | \(-0.757576\pi\) | ||||
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(48\) | 42.6641 | − | 21.9949i | 0.888835 | − | 0.458227i | ||||
\(49\) | 76.2780 | + | 107.117i | 1.55669 | + | 2.18607i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 87.1665 | + | 56.0185i | 1.67628 | + | 1.07728i | ||||
\(53\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 37.2127 | − | 35.4822i | 0.652854 | − | 0.622495i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.37545 | + | 12.6420i | 0.0717286 | + | 0.207246i | 0.975167 | − | 0.221473i | \(-0.0710863\pi\) |
−0.903438 | + | 0.428719i | \(0.858965\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −120.368 | + | 11.4938i | −1.91060 | + | 0.182441i | ||||
\(64\) | −61.4076 | + | 18.0309i | −0.959493 | + | 0.281733i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 46.3306 | − | 48.3991i | 0.691502 | − | 0.722375i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 23.3501 | + | 67.4656i | 0.319864 | + | 0.924187i | 0.984248 | + | 0.176795i | \(0.0565729\pi\) |
−0.664384 | + | 0.747392i | \(0.731306\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 10.6736 | + | 74.2366i | 0.142315 | + | 0.989821i | ||||
\(76\) | −57.6737 | + | 37.0646i | −0.758865 | + | 0.487693i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 63.8645 | − | 25.5675i | 0.808411 | − | 0.323639i | 0.0696203 | − | 0.997574i | \(-0.477821\pi\) |
0.738791 | + | 0.673934i | \(0.235397\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 33.6486 | − | 73.6802i | 0.415415 | − | 0.909632i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(84\) | 160.491 | + | 15.3250i | 1.91060 | + | 0.182441i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 144.572 | + | 316.569i | 1.58870 | + | 3.47878i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −94.5401 | + | 132.763i | −1.01656 | + | 1.42756i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 94.0250 | − | 162.856i | 0.969329 | − | 1.67893i | 0.271826 | − | 0.962346i | \(-0.412373\pi\) |
0.697504 | − | 0.716581i | \(-0.254294\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.75819 | − | 99.8867i | 0.0475819 | − | 0.998867i | ||||
\(101\) | 0 | 0 | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) | ||||
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −98.8434 | + | 77.7313i | −0.959645 | + | 0.754673i | −0.969453 | − | 0.245279i | \(-0.921120\pi\) |
0.00980773 | + | 0.999952i | \(0.496878\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(108\) | −62.6461 | + | 87.9742i | −0.580057 | + | 0.814576i | ||||
\(109\) | 28.7854 | − | 200.207i | 0.264086 | − | 1.83676i | −0.237177 | − | 0.971466i | \(-0.576222\pi\) |
0.501264 | − | 0.865295i | \(-0.332869\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 51.1199 | − | 210.719i | 0.460539 | − | 1.89837i | ||||
\(112\) | −206.254 | − | 60.5615i | −1.84155 | − | 0.540728i | ||||
\(113\) | 0 | 0 | −0.981929 | − | 0.189251i | \(-0.939394\pi\) | ||||
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −232.078 | − | 22.1608i | −1.98357 | − | 0.189408i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −95.1124 | − | 74.7972i | −0.786053 | − | 0.618159i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 157.276 | − | 149.963i | 1.26836 | − | 1.20938i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −51.8130 | − | 26.7115i | −0.407976 | − | 0.210326i | 0.242008 | − | 0.970274i | \(-0.422194\pi\) |
−0.649984 | + | 0.759948i | \(0.725224\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −100.829 | − | 116.363i | −0.781622 | − | 0.902040i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −230.266 | −1.73133 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −172.968 | − | 199.616i | −1.24437 | − | 1.43609i | −0.857925 | − | 0.513775i | \(-0.828247\pi\) |
−0.386450 | − | 0.922310i | \(-0.626299\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 104.218 | − | 99.3714i | 0.723734 | − | 0.690079i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 310.100 | + | 243.865i | 2.10952 | + | 1.65895i | ||||
\(148\) | −120.100 | + | 262.982i | −0.811485 | + | 1.77691i | ||||
\(149\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −184.363 | − | 17.6045i | −1.22095 | − | 0.116586i | −0.535390 | − | 0.844605i | \(-0.679835\pi\) |
−0.685557 | + | 0.728019i | \(0.740441\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 298.254 | + | 87.5752i | 1.91188 | + | 0.561379i | ||||
\(157\) | 13.6859 | − | 56.4139i | 0.0871710 | − | 0.359324i | −0.911474 | − | 0.411357i | \(-0.865055\pi\) |
0.998645 | + | 0.0520330i | \(0.0165701\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −139.627 | − | 241.841i | −0.856606 | − | 1.48369i | −0.875147 | − | 0.483857i | \(-0.839236\pi\) |
0.0185412 | − | 0.999828i | \(-0.494098\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) | ||||
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 118.352 | + | 487.854i | 0.700308 | + | 2.88671i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 77.1265 | − | 133.587i | 0.451032 | − | 0.781210i | ||||
\(172\) | 102.647 | + | 177.790i | 0.596785 | + | 1.03366i | ||||
\(173\) | 0 | 0 | −0.928368 | − | 0.371662i | \(-0.878788\pi\) | ||||
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 194.827 | − | 273.597i | 1.11330 | − | 1.56341i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 180.271 | + | 171.888i | 0.995970 | + | 0.949655i | 0.998732 | − | 0.0503410i | \(-0.0160308\pi\) |
−0.00276243 | + | 0.999996i | \(0.500879\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 23.2796 | + | 32.6917i | 0.127211 | + | 0.178643i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −336.762 | + | 134.819i | −1.78181 | + | 0.713330i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(192\) | −161.521 | + | 103.803i | −0.841254 | + | 0.540641i | ||||
\(193\) | 10.4657 | + | 72.7906i | 0.0542265 | + | 0.377153i | 0.998805 | + | 0.0488685i | \(0.0155615\pi\) |
−0.944579 | + | 0.328285i | \(0.893529\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −344.459 | − | 397.527i | −1.75744 | − | 2.02820i | ||||
\(197\) | 0 | 0 | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.89425 | + | 144.728i | 0.0346445 | + | 0.727277i | 0.947646 | + | 0.319322i | \(0.103455\pi\) |
−0.913002 | + | 0.407955i | \(0.866242\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 92.4549 | − | 178.474i | 0.459975 | − | 0.887932i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −368.387 | − | 189.917i | −1.77109 | − | 0.913061i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −64.8282 | + | 61.8135i | −0.307243 | + | 0.292955i | −0.827975 | − | 0.560765i | \(-0.810507\pi\) |
0.520733 | + | 0.853720i | \(0.325659\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 716.711 | − | 138.135i | 3.30281 | − | 0.636565i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 124.235 | + | 174.463i | 0.567281 | + | 0.796635i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 194.869 | + | 57.2186i | 0.873851 | + | 0.256586i | 0.687753 | − | 0.725945i | \(-0.258597\pi\) |
0.186099 | + | 0.982531i | \(0.440416\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 93.4684 | + | 204.667i | 0.415415 | + | 0.909632i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.580057 | − | 0.814576i | \(-0.303030\pi\) | ||||
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(228\) | −134.686 | + | 155.435i | −0.590726 | + | 0.681734i | ||||
\(229\) | 243.439 | + | 97.4584i | 1.06305 | + | 0.425583i | 0.836245 | − | 0.548357i | \(-0.184746\pi\) |
0.226809 | + | 0.973939i | \(0.427171\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.235759 | − | 0.971812i | \(-0.575758\pi\) | ||||
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 162.223 | − | 127.574i | 0.684485 | − | 0.538285i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.83716 | − | 11.3527i | 0.0408181 | − | 0.0471066i | −0.734973 | − | 0.678096i | \(-0.762805\pi\) |
0.775792 | + | 0.630989i | \(0.217351\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 34.5825 | − | 240.527i | 0.142315 | − | 0.989821i | ||||
\(244\) | −22.2293 | − | 48.6755i | −0.0911038 | − | 0.199490i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −435.947 | − | 84.0219i | −1.76497 | − | 0.340170i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) | ||||
0.995472 | + | 0.0950560i | \(0.0303030\pi\) | |||||||
\(252\) | 474.922 | − | 91.5337i | 1.88461 | − | 0.363229i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 237.662 | − | 95.1456i | 0.928368 | − | 0.371662i | ||||
\(257\) | 0 | 0 | 0.327068 | − | 0.945001i | \(-0.393939\pi\) | ||||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −816.896 | + | 524.987i | −3.15404 | + | 2.02698i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −166.081 | + | 210.336i | −0.619705 | + | 0.784835i | ||||
\(269\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 453.754 | − | 133.234i | 1.67437 | − | 0.491639i | 0.699540 | − | 0.714594i | \(-0.253388\pi\) |
0.974829 | + | 0.222955i | \(0.0715702\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 683.711 | + | 789.044i | 2.50444 | + | 2.89027i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −58.9545 | + | 37.8877i | −0.212832 | + | 0.136779i | −0.642714 | − | 0.766106i | \(-0.722192\pi\) |
0.429882 | + | 0.902885i | \(0.358555\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −159.921 | + | 462.061i | −0.573193 | + | 1.65613i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
0.786053 | + | 0.618159i | \(0.212121\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −463.744 | − | 298.030i | −1.63867 | − | 1.05311i | −0.941942 | − | 0.335776i | \(-0.891001\pi\) |
−0.696730 | − | 0.717334i | \(-0.745362\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 283.777 | + | 54.6936i | 0.981929 | + | 0.189251i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 133.003 | − | 548.247i | 0.457056 | − | 1.88401i | ||||
\(292\) | −118.629 | − | 259.762i | −0.406265 | − | 0.889597i | ||||
\(293\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −70.7277 | − | 291.543i | −0.235759 | − | 0.971812i | ||||
\(301\) | −32.8094 | + | 688.754i | −0.109001 | + | 2.28822i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 215.557 | − | 169.516i | 0.709070 | − | 0.557619i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 184.444 | + | 73.8401i | 0.600793 | + | 0.240521i | 0.652065 | − | 0.758163i | \(-0.273903\pi\) |
−0.0512713 | + | 0.998685i | \(0.516327\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −218.820 | + | 307.290i | −0.708157 | + | 0.994467i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 430.886 | + | 126.520i | 1.37663 | + | 0.404216i | 0.884596 | − | 0.466358i | \(-0.154434\pi\) |
0.492037 | + | 0.870574i | \(0.336252\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −244.580 | + | 126.090i | −0.773987 | + | 0.399018i | ||||
\(317\) | 0 | 0 | −0.580057 | − | 0.814576i | \(-0.696970\pi\) | ||||
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −105.970 | + | 306.180i | −0.327068 | + | 0.945001i | ||||
\(325\) | 468.686 | − | 446.891i | 1.44211 | − | 1.37505i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −86.3562 | − | 600.621i | −0.264086 | − | 1.83676i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −641.554 | + | 61.2610i | −1.93823 | + | 0.185079i | −0.990844 | − | 0.135014i | \(-0.956892\pi\) |
−0.947386 | + | 0.320093i | \(0.896286\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −30.9517 | − | 649.756i | −0.0929481 | − | 1.95122i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −644.883 | −1.91929 | ||||||||
\(337\) | 29.6231 | + | 621.865i | 0.0879023 | + | 1.84530i | 0.426647 | + | 0.904418i | \(0.359695\pi\) |
−0.338745 | + | 0.940878i | \(0.610002\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −157.742 | − | 1097.12i | −0.459890 | − | 3.19861i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.928368 | − | 0.371662i | \(-0.121212\pi\) | ||||
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 277.673 | − | 608.019i | 0.795625 | − | 1.74218i | 0.135827 | − | 0.990733i | \(-0.456631\pi\) |
0.659798 | − | 0.751443i | \(-0.270642\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −686.762 | + | 132.363i | −1.95659 | + | 0.377101i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.580057 | − | 0.814576i | \(-0.696970\pi\) | ||||
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −39.0073 | + | 54.7780i | −0.108053 | + | 0.151740i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −336.998 | − | 134.913i | −0.928368 | − | 0.371662i | ||||
\(364\) | −696.037 | − | 1205.57i | −1.91219 | − | 3.31201i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 138.009 | + | 568.881i | 0.376046 | + | 1.55008i | 0.774306 | + | 0.632811i | \(0.218099\pi\) |
−0.398260 | + | 0.917273i | \(0.630386\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 325.968 | − | 564.594i | 0.876259 | − | 1.51773i | ||||
\(373\) | 114.881 | + | 198.979i | 0.307991 | + | 0.533456i | 0.977923 | − | 0.208967i | \(-0.0670100\pi\) |
−0.669932 | + | 0.742423i | \(0.733677\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −79.5728 | + | 328.003i | −0.209955 | + | 0.865444i | 0.765177 | + | 0.643819i | \(0.222651\pi\) |
−0.975132 | + | 0.221625i | \(0.928864\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −171.719 | − | 33.0961i | −0.450706 | − | 0.0868665i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.888835 | − | 0.458227i | \(-0.151515\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −388.585 | − | 249.728i | −1.00410 | − | 0.645293i | ||||
\(388\) | −312.475 | + | 684.225i | −0.805348 | + | 1.76347i | ||||
\(389\) | 0 | 0 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
0.786053 | + | 0.618159i | \(0.212121\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 239.457 | + | 276.348i | 0.603167 | + | 0.696092i | 0.972420 | − | 0.233237i | \(-0.0749319\pi\) |
−0.369253 | + | 0.929329i | \(0.620386\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −662.817 | + | 194.621i | −1.66120 | + | 0.487771i | ||||
\(400\) | 19.0328 | + | 399.547i | 0.0475819 | + | 0.998867i | ||||
\(401\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1407.30 | 3.49206 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.6730 | + | 5.50231i | 0.0260953 | + | 0.0134531i | 0.471225 | − | 0.882013i | \(-0.343812\pi\) |
−0.445129 | + | 0.895466i | \(0.646842\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 364.028 | − | 347.100i | 0.883563 | − | 0.842476i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −666.600 | − | 428.398i | −1.59856 | − | 1.02733i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) | ||||
0.995472 | + | 0.0950560i | \(0.0303030\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 547.168 | − | 282.085i | 1.29969 | − | 0.670034i | 0.337217 | − | 0.941427i | \(-0.390514\pi\) |
0.962469 | + | 0.271393i | \(0.0874842\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 25.5784 | − | 177.902i | 0.0599027 | − | 0.416632i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(432\) | 216.000 | − | 374.123i | 0.500000 | − | 0.866025i | ||||
\(433\) | −161.115 | + | 126.703i | −0.372091 | + | 0.292616i | −0.786641 | − | 0.617411i | \(-0.788182\pi\) |
0.414550 | + | 0.910027i | \(0.363939\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −38.4968 | + | 808.146i | −0.0882953 | + | 1.85355i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.29742 | + | 9.17540i | −0.0120670 | + | 0.0209007i | −0.871996 | − | 0.489513i | \(-0.837174\pi\) |
0.859929 | + | 0.510414i | \(0.170508\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1098.73 | + | 439.865i | 2.49145 | + | 0.997427i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.580057 | − | 0.814576i | \(-0.303030\pi\) | ||||
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(444\) | −123.433 | + | 858.496i | −0.278003 | + | 1.93355i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 844.305 | + | 162.727i | 1.88461 | + | 0.363229i | ||||
\(449\) | 0 | 0 | −0.723734 | − | 0.690079i | \(-0.757576\pi\) | ||||
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −545.564 | + | 105.149i | −1.20434 | + | 0.232117i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 494.849 | − | 198.108i | 1.08282 | − | 0.433496i | 0.239494 | − | 0.970898i | \(-0.423018\pi\) |
0.843326 | + | 0.537402i | \(0.180594\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.96763 | + | 28.7996i | 0.0215284 | + | 0.0622021i | 0.955253 | − | 0.295790i | \(-0.0955828\pi\) |
−0.933725 | + | 0.357992i | \(0.883462\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) | ||||
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(468\) | 932.535 | 1.99260 | ||||||||
\(469\) | −851.219 | + | 292.735i | −1.81497 | + | 0.624169i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.28642 | − | 173.953i | −0.0175932 | − | 0.369328i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 140.142 | + | 404.914i | 0.295036 | + | 0.852451i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1738.13 | + | 695.844i | −3.61358 | + | 1.44666i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 407.167 | + | 261.670i | 0.841254 | + | 0.540641i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −563.892 | − | 791.876i | −1.15789 | − | 1.62603i | −0.629363 | − | 0.777111i | \(-0.716684\pi\) |
−0.528526 | − | 0.848917i | \(-0.677255\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −606.316 | − | 578.121i | −1.23991 | − | 1.18225i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −569.237 | + | 656.935i | −1.14766 | + | 1.32447i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 495.603 | − | 858.410i | 0.993193 | − | 1.72026i | 0.395722 | − | 0.918370i | \(-0.370494\pi\) |
0.597471 | − | 0.801891i | \(-0.296172\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) | ||||
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 753.007 | + | 1304.25i | 1.48522 | + | 2.57248i | ||||
\(508\) | 216.470 | + | 86.6615i | 0.426122 | + | 0.170593i | ||||
\(509\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 136.502 | − | 949.395i | 0.267128 | − | 1.85792i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 109.100 | − | 449.714i | 0.212670 | − | 0.876636i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 445.735 | + | 425.007i | 0.863828 | + | 0.823658i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 496.264 | + | 390.266i | 0.948879 | + | 0.746207i | 0.967303 | − | 0.253624i | \(-0.0816224\pi\) |
−0.0184240 | + | 0.999830i | \(0.505865\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 329.563 | − | 952.211i | 0.627740 | − | 1.81373i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −470.194 | − | 242.402i | −0.888835 | − | 0.458227i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 916.895 | − | 87.5529i | 1.72349 | − | 0.164573i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 654.221 | + | 755.012i | 1.20928 | + | 1.39559i | 0.894887 | + | 0.446294i | \(0.147256\pi\) |
0.314395 | + | 0.949292i | \(0.398198\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 664.184 | + | 342.411i | 1.22317 | + | 0.630590i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 194.902 | − | 563.134i | 0.356312 | − | 1.02950i | −0.614347 | − | 0.789036i | \(-0.710581\pi\) |
0.970659 | − | 0.240459i | \(-0.0772981\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 94.6409 | + | 74.4264i | 0.172388 | + | 0.135567i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −920.043 | − | 87.8534i | −1.66373 | − | 0.158867i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 764.638 | + | 729.081i | 1.37525 | + | 1.31130i | ||||
\(557\) | 0 | 0 | −0.981929 | − | 0.189251i | \(-0.939394\pi\) | ||||
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −313.435 | + | 1292.00i | −0.560706 | + | 2.31126i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −855.414 | + | 672.705i | −1.50867 | + | 1.18643i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) | ||||
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −268.401 | − | 1106.36i | −0.470053 | − | 1.93759i | −0.311560 | − | 0.950227i | \(-0.600851\pi\) |
−0.158494 | − | 0.987360i | \(-0.550664\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −377.200 | + | 435.312i | −0.654861 | + | 0.755750i | ||||
\(577\) | 617.902 | − | 867.721i | 1.07089 | − | 1.50385i | 0.222166 | − | 0.975009i | \(-0.428687\pi\) |
0.848721 | − | 0.528841i | \(-0.177373\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 91.6478 | + | 200.681i | 0.158286 | + | 0.346599i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(588\) | −1327.51 | − | 853.137i | −2.25766 | − | 1.45091i | ||||
\(589\) | −386.810 | + | 846.995i | −0.656723 | + | 1.43802i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 378.232 | − | 1092.83i | 0.638905 | − | 1.84600i | ||||
\(593\) | 0 | 0 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 142.169 | + | 410.770i | 0.238139 | + | 0.688057i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 56.7840 | + | 1192.04i | 0.0944825 | + | 1.98343i | 0.166553 | + | 0.986032i | \(0.446736\pi\) |
−0.0720706 | + | 0.997400i | \(0.522961\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 115.284 | − | 591.877i | 0.191183 | − | 0.981554i | ||||
\(604\) | 740.807 | 1.22650 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 934.129 | − | 89.1985i | 1.53893 | − | 0.146950i | 0.709155 | − | 0.705052i | \(-0.249076\pi\) |
0.829772 | + | 0.558103i | \(0.188470\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −186.793 | + | 178.106i | −0.304719 | + | 0.290549i | −0.826974 | − | 0.562241i | \(-0.809939\pi\) |
0.522255 | + | 0.852789i | \(0.325091\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1062.75 | + | 204.828i | −1.71688 | + | 0.330901i | −0.950321 | − | 0.311272i | \(-0.899245\pi\) |
−0.766559 | + | 0.642174i | \(0.778033\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1220.91 | − | 235.311i | −1.95659 | − | 0.377101i | ||||
\(625\) | −599.683 | − | 176.083i | −0.959493 | − | 0.281733i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −33.0456 | + | 229.837i | −0.0526204 | + | 0.365983i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −879.435 | − | 352.072i | −1.39372 | − | 0.557960i | −0.451291 | − | 0.892377i | \(-0.649036\pi\) |
−0.942425 | + | 0.334418i | \(0.891460\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −134.362 | + | 232.722i | −0.212262 | + | 0.367649i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 162.081 | − | 3402.51i | 0.254445 | − | 5.34146i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −828.282 | + | 955.888i | −1.28815 | + | 1.48661i | −0.507483 | + | 0.861662i | \(0.669424\pi\) |
−0.780669 | + | 0.624945i | \(0.785122\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1946.29 | − | 1003.38i | 2.98969 | − | 1.54129i | ||||
\(652\) | 647.932 | + | 909.893i | 0.993760 | + | 1.39554i | ||||
\(653\) | 0 | 0 | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) | ||||
0.995472 | + | 0.0950560i | \(0.0303030\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 505.062 | + | 397.185i | 0.768740 | + | 0.604544i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.327068 | − | 0.945001i | \(-0.393939\pi\) | ||||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −207.432 | + | 133.309i | −0.313816 | + | 0.201677i | −0.688062 | − | 0.725652i | \(-0.741538\pi\) |
0.374245 | + | 0.927330i | \(0.377902\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 609.287 | 0.910743 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −266.048 | + | 78.1186i | −0.395316 | + | 0.116075i | −0.473348 | − | 0.880876i | \(-0.656955\pi\) |
0.0780319 | + | 0.996951i | \(0.475136\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 442.031 | + | 510.131i | 0.654861 | + | 0.755750i | ||||
\(676\) | −656.758 | − | 1897.58i | −0.971536 | − | 2.80707i | ||||
\(677\) | 0 | 0 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
0.888835 | + | 0.458227i | \(0.151515\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2125.40 | + | 1365.91i | −3.13018 | + | 2.01165i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
0.786053 | + | 0.618159i | \(0.212121\pi\) | |||||||
\(684\) | −256.316 | + | 561.254i | −0.374731 | + | 0.820546i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 783.107 | + | 74.7776i | 1.13989 | + | 0.108847i | ||||
\(688\) | −476.329 | − | 668.911i | −0.692339 | − | 0.972254i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −219.844 | − | 42.3715i | −0.318154 | − | 0.0613191i | 0.0276745 | − | 0.999617i | \(-0.491190\pi\) |
−0.345828 | + | 0.938298i | \(0.612402\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −671.753 | + | 1163.51i | −0.959647 | + | 1.66216i | ||||
\(701\) | 0 | 0 | 0.786053 | − | 0.618159i | \(-0.212121\pi\) | ||||
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 58.9431 | − | 1237.37i | 0.0838451 | − | 1.76013i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 552.912 | + | 221.352i | 0.779847 | + | 0.312204i | 0.727215 | − | 0.686410i | \(-0.240815\pi\) |
0.0526326 | + | 0.998614i | \(0.483239\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 359.131 | − | 504.328i | 0.505106 | − | 0.709323i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.580057 | − | 0.814576i | \(-0.696970\pi\) | ||||
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1658.88 | − | 319.723i | 2.30081 | − | 0.443444i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 18.7208 | − | 40.9928i | 0.0258932 | − | 0.0566982i | ||||
\(724\) | −783.173 | − | 615.894i | −1.08173 | − | 0.850682i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −606.370 | + | 578.172i | −0.834071 | + | 0.795285i | −0.981030 | − | 0.193857i | \(-0.937900\pi\) |
0.146959 | + | 0.989143i | \(0.453052\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −103.748 | − | 721.580i | −0.142315 | − | 0.989821i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −105.127 | − | 121.323i | −0.143616 | − | 0.165742i | ||||
\(733\) | −306.611 | + | 29.2778i | −0.418296 | + | 0.0399424i | −0.302082 | − | 0.953282i | \(-0.597682\pi\) |
−0.116214 | + | 0.993224i | \(0.537076\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.50377 | − | 31.5680i | −0.00203487 | − | 0.0427172i | 0.997622 | − | 0.0689296i | \(-0.0219584\pi\) |
−0.999656 | + | 0.0262124i | \(0.991655\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1325.88 | + | 126.606i | −1.78931 | + | 0.170858i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.327068 | − | 0.945001i | \(-0.606061\pi\) | ||||
0.327068 | + | 0.945001i | \(0.393939\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 547.768 | − | 1199.44i | 0.729385 | − | 1.59713i | −0.0708817 | − | 0.997485i | \(-0.522581\pi\) |
0.800266 | − | 0.599645i | \(-0.204691\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1289.69 | − | 664.881i | 1.70594 | − | 0.879472i | ||||
\(757\) | −664.026 | − | 633.147i | −0.877181 | − | 0.836390i | 0.110338 | − | 0.993894i | \(-0.464807\pi\) |
−0.987518 | + | 0.157504i | \(0.949655\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1576.28 | + | 2213.57i | −2.06589 | + | 2.90114i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 603.689 | − | 474.746i | 0.786053 | − | 0.618159i | ||||
\(769\) | −326.035 | − | 1343.93i | −0.423973 | − | 1.74764i | −0.637259 | − | 0.770650i | \(-0.719932\pi\) |
0.213286 | − | 0.976990i | \(-0.431583\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −69.3500 | − | 285.865i | −0.0898317 | − | 0.370291i | ||||
\(773\) | 0 | 0 | 0.786053 | − | 0.618159i | \(-0.212121\pi\) | ||||
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −679.101 | − | 1176.24i | −0.876259 | − | 1.51773i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1907.70 | + | 2201.60i | −2.45521 | + | 2.83347i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1522.75 | + | 1451.94i | 1.94228 | + | 1.85196i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.1435 | + | 2.87836i | 0.0383018 | + | 0.00365738i | 0.114189 | − | 0.993459i | \(-0.463573\pi\) |
−0.0758876 | + | 0.997116i | \(0.524179\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 113.340 | − | 327.476i | 0.142926 | − | 0.412958i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −82.4813 | − | 573.670i | −0.103620 | − | 0.720691i | ||||
\(797\) | 0 | 0 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
0.888835 | + | 0.458227i | \(0.151515\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −300.285 | + | 745.818i | −0.373489 | + | 0.927635i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1377.55 | + | 710.175i | 1.69858 | + | 0.875678i | 0.984450 | + | 0.175663i | \(0.0562070\pi\) |
0.714128 | + | 0.700015i | \(0.246823\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1193.51 | − | 767.023i | 1.46803 | − | 0.943448i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −691.448 | − | 543.761i | −0.846325 | − | 0.665558i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2634.95 | + | 1693.38i | 3.21727 | + | 2.06762i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) | ||||
0.995472 | + | 0.0950560i | \(0.0303030\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1074.75 | − | 554.071i | 1.30589 | − | 0.673233i | 0.342041 | − | 0.939685i | \(-0.388882\pi\) |
0.963848 | + | 0.266452i | \(0.0858514\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 86.4416 | − | 601.214i | 0.104272 | − | 0.725228i | −0.868873 | − | 0.495035i | \(-0.835155\pi\) |
0.973145 | − | 0.230193i | \(-0.0739358\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −137.677 | + | 158.887i | −0.165676 | + | 0.191200i | ||||
\(832\) | 1539.09 | + | 616.157i | 1.84986 | + | 0.740573i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −69.7959 | + | 1465.20i | −0.0833882 | + | 1.75053i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.235759 | − | 0.971812i | \(-0.575758\pi\) | ||||
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −420.500 | + | 728.327i | −0.500000 | + | 0.866025i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 234.636 | − | 270.784i | 0.278004 | − | 0.320834i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 675.316 | + | 1478.74i | 0.797304 | + | 1.74585i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1586.77 | − | 465.918i | −1.86899 | − | 0.548785i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 806.213 | + | 1132.17i | 0.945151 | + | 1.32728i | 0.944928 | + | 0.327278i | \(0.106131\pi\) |
0.000222537 | 1.00000i | \(0.499929\pi\) | ||||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1556.80 | − | 623.248i | 1.81234 | − | 0.725551i | 0.825378 | − | 0.564580i | \(-0.190962\pi\) |
0.986959 | − | 0.160971i | \(-0.0514624\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 863.074 | − | 82.4136i | 0.995472 | − | 0.0950560i | ||||
\(868\) | −2801.34 | + | 822.547i | −3.22735 | + | 0.947635i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1718.37 | + | 243.613i | −1.97287 | + | 0.279694i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −80.5300 | − | 1690.53i | −0.0922451 | − | 1.93646i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −561.023 | − | 647.455i | −0.640437 | − | 0.739104i | ||||
\(877\) | 73.2802 | + | 211.729i | 0.0835578 | + | 0.241424i | 0.979038 | − | 0.203676i | \(-0.0652891\pi\) |
−0.895480 | + | 0.445101i | \(0.853168\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1639.30 | − | 656.276i | 1.85651 | − | 0.743235i | 0.922473 | − | 0.386061i | \(-0.126164\pi\) |
0.934038 | − | 0.357174i | \(-0.116260\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 454.284 | + | 637.953i | 0.511006 | + | 0.717607i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −797.702 | − | 153.744i | −0.894284 | − | 0.172359i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −450.000 | − | 779.423i | −0.500000 | − | 0.866025i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 487.692 | + | 2010.29i | 0.540080 | + | 2.22624i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1180.26 | + | 928.164i | −1.30127 | + | 1.02333i | −0.303769 | + | 0.952746i | \(0.598245\pi\) |
−0.997506 | + | 0.0705881i | \(0.977512\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(912\) | 477.203 | − | 670.137i | 0.523248 | − | 0.734800i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1006.40 | − | 295.507i | −1.09869 | − | 0.322606i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −584.953 | + | 301.564i | −0.636510 | + | 0.328144i | −0.746101 | − | 0.665833i | \(-0.768076\pi\) |
0.109591 | + | 0.993977i | \(0.465046\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 593.326 | + | 56.6558i | 0.644220 | + | 0.0615155i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1420.34 | + | 1116.97i | 1.53550 | + | 1.20753i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −370.149 | + | 1069.47i | −0.399298 | + | 1.15369i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2003.28 | + | 1032.76i | 2.15175 | + | 1.10930i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 478.950 | 0.511152 | 0.255576 | − | 0.966789i | \(-0.417735\pi\) | ||||
0.255576 | + | 0.966789i | \(0.417735\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1347.23 | 1.43475 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(948\) | −597.447 | + | 569.665i | −0.630219 | + | 0.600912i | ||||
\(949\) | 604.855 | − | 1747.61i | 0.637360 | − | 1.84153i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 469.287 | − | 1934.43i | 0.488332 | − | 2.01293i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −34.8539 | + | 48.9454i | −0.0361555 | + | 0.0507733i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −391.470 | − | 678.046i | −0.404829 | − | 0.701185i | 0.589472 | − | 0.807789i | \(-0.299336\pi\) |
−0.994302 | + | 0.106604i | \(0.966002\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) | ||||
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(972\) | −46.2496 | + | 970.899i | −0.0475819 | + | 0.998867i | ||||
\(973\) | 836.614 | + | 3448.57i | 0.859829 | + | 3.54426i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 971.391 | − | 1682.50i | 0.996298 | − | 1.72564i | ||||
\(976\) | 107.022 | + | 185.368i | 0.109654 | + | 0.189926i | ||||
\(977\) | 0 | 0 | −0.928368 | − | 0.371662i | \(-0.878788\pi\) | ||||
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −756.218 | − | 1655.89i | −0.770864 | − | 1.68796i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1767.84 | + | 168.808i | 1.78931 | + | 0.170858i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −609.567 | + | 1334.77i | −0.615103 | + | 1.34689i | 0.303925 | + | 0.952696i | \(0.401703\pi\) |
−0.919028 | + | 0.394192i | \(0.871025\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1794.92 | + | 718.579i | −1.80758 | + | 0.723644i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −283.626 | − | 1972.67i | −0.284480 | − | 1.97860i | −0.174347 | − | 0.984684i | \(-0.555781\pi\) |
−0.110133 | − | 0.993917i | \(-0.535128\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −638.266 | − | 1844.15i | −0.638905 | − | 1.84600i |
(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 | 201.3.o.a.167.1 | yes | 20 | |
3.2 | odd | 2 | CM | 201.3.o.a.167.1 | yes | 20 | |
67.65 | even | 33 | inner | 201.3.o.a.65.1 | ✓ | 20 | |
201.65 | odd | 66 | inner | 201.3.o.a.65.1 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
201.3.o.a.65.1 | ✓ | 20 | 67.65 | even | 33 | inner | |
201.3.o.a.65.1 | ✓ | 20 | 201.65 | odd | 66 | inner | |
201.3.o.a.167.1 | yes | 20 | 1.1 | even | 1 | trivial | |
201.3.o.a.167.1 | yes | 20 | 3.2 | odd | 2 | CM |