Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,3,Mod(161,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.161");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.i (of order \(4\), degree \(2\), not 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: | \(10.4632421514\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{18} + 6 x^{16} - 24 x^{14} - 24 x^{12} + 1216 x^{10} - 384 x^{8} - 6144 x^{6} + 24576 x^{4} - 131072 x^{2} + 1048576 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{23} \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 353.2 | ||
Root | \(1.85381 + 0.750590i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.353 |
Dual form | 384.3.i.c.161.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.59524 | − | 1.50491i | −0.865079 | − | 0.501636i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.59897 | + | 2.59897i | −0.519793 | + | 0.519793i | −0.917509 | − | 0.397716i | \(-0.869803\pi\) |
0.397716 | + | 0.917509i | \(0.369803\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 7.30027i | − | 1.04290i | −0.853283 | − | 0.521448i | \(-0.825392\pi\) | ||
0.853283 | − | 0.521448i | \(-0.174608\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.47050 | + | 7.81118i | 0.496723 | + | 0.867909i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −11.3161 | + | 11.3161i | −1.02873 | + | 1.02873i | −0.0291601 | + | 0.999575i | \(0.509283\pi\) |
−0.999575 | + | 0.0291601i | \(0.990717\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.746462 | − | 0.746462i | 0.0574201 | − | 0.0574201i | −0.677814 | − | 0.735234i | \(-0.737072\pi\) |
0.735234 | + | 0.677814i | \(0.237072\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 10.6561 | − | 2.83373i | 0.710409 | − | 0.188915i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.67452i | 0.392619i | 0.980542 | + | 0.196310i | \(0.0628957\pi\) | ||||
−0.980542 | + | 0.196310i | \(0.937104\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 22.1936 | − | 22.1936i | 1.16809 | − | 1.16809i | 0.185428 | − | 0.982658i | \(-0.440633\pi\) |
0.982658 | − | 0.185428i | \(-0.0593670\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −10.9862 | + | 18.9459i | −0.523154 | + | 0.902187i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 21.4389 | 0.932128 | 0.466064 | − | 0.884751i | \(-0.345672\pi\) | ||||
0.466064 | + | 0.884751i | \(0.345672\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11.4908i | 0.459630i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.153096 | − | 26.9996i | 0.00567024 | − | 0.999984i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.54272 | + | 1.54272i | 0.0531973 | + | 0.0531973i | 0.733205 | − | 0.680008i | \(-0.238024\pi\) |
−0.680008 | + | 0.733205i | \(0.738024\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 14.6082 | 0.471233 | 0.235616 | − | 0.971846i | \(-0.424289\pi\) | ||||
0.235616 | + | 0.971846i | \(0.424289\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 46.3976 | − | 12.3382i | 1.40599 | − | 0.373886i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 18.9732 | + | 18.9732i | 0.542090 | + | 0.542090i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 50.1010 | + | 50.1010i | 1.35408 | + | 1.35408i | 0.881041 | + | 0.473039i | \(0.156843\pi\) |
0.473039 | + | 0.881041i | \(0.343157\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.06060 | + | 0.813888i | −0.0784769 | + | 0.0208689i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 15.0731 | 0.367637 | 0.183819 | − | 0.982960i | \(-0.441154\pi\) | ||||
0.183819 | + | 0.982960i | \(0.441154\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 26.3634 | + | 26.3634i | 0.613102 | + | 0.613102i | 0.943753 | − | 0.330651i | \(-0.107268\pi\) |
−0.330651 | + | 0.943753i | \(0.607268\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −31.9197 | − | 8.68231i | −0.709326 | − | 0.192940i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 36.6067i | 0.778866i | 0.921055 | + | 0.389433i | \(0.127329\pi\) | ||||
−0.921055 | + | 0.389433i | \(0.872671\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.29399 | −0.0876325 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.0445 | − | 17.3220i | 0.196952 | − | 0.339646i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 50.9270 | − | 50.9270i | 0.960887 | − | 0.960887i | −0.0383765 | − | 0.999263i | \(-0.512219\pi\) |
0.999263 | + | 0.0383765i | \(0.0122186\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 58.8202i | − | 1.06946i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −90.9971 | + | 24.1983i | −1.59644 | + | 0.424532i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.1683 | − | 12.1683i | 0.206242 | − | 0.206242i | −0.596426 | − | 0.802668i | \(-0.703413\pi\) |
0.802668 | + | 0.596426i | \(0.203413\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 27.5789 | − | 27.5789i | 0.452113 | − | 0.452113i | −0.443943 | − | 0.896055i | \(-0.646421\pi\) |
0.896055 | + | 0.443943i | \(0.146421\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 57.0238 | − | 32.6359i | 0.905139 | − | 0.518030i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.88006i | 0.0596932i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.84214 | + | 4.84214i | −0.0722707 | + | 0.0722707i | −0.742318 | − | 0.670047i | \(-0.766274\pi\) |
0.670047 | + | 0.742318i | \(0.266274\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −55.6391 | − | 32.2636i | −0.806364 | − | 0.467589i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −74.9072 | −1.05503 | −0.527515 | − | 0.849546i | \(-0.676876\pi\) | ||||
−0.527515 | + | 0.849546i | \(0.676876\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 3.47110i | − | 0.0475494i | −0.999717 | − | 0.0237747i | \(-0.992432\pi\) | ||
0.999717 | − | 0.0237747i | \(-0.00756843\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 17.2925 | − | 29.8212i | 0.230567 | − | 0.397616i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 82.6105 | + | 82.6105i | 1.07286 | + | 1.07286i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −103.463 | −1.30966 | −0.654831 | − | 0.755775i | \(-0.727260\pi\) | ||||
−0.654831 | + | 0.755775i | \(0.727260\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −41.0292 | + | 69.8399i | −0.506533 | + | 0.862221i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 31.7254 | + | 31.7254i | 0.382233 | + | 0.382233i | 0.871906 | − | 0.489673i | \(-0.162884\pi\) |
−0.489673 | + | 0.871906i | \(0.662884\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −17.3469 | − | 17.3469i | −0.204081 | − | 0.204081i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.68207 | − | 6.32538i | −0.0193342 | − | 0.0727056i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 78.2605 | 0.879331 | 0.439666 | − | 0.898162i | \(-0.355097\pi\) | ||||
0.439666 | + | 0.898162i | \(0.355097\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.44937 | − | 5.44937i | −0.0598832 | − | 0.0598832i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −37.9118 | − | 21.9840i | −0.407653 | − | 0.236387i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 115.361i | 1.21433i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −61.5651 | −0.634692 | −0.317346 | − | 0.948310i | \(-0.602792\pi\) | ||||
−0.317346 | + | 0.948310i | \(0.602792\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −138.981 | − | 37.8034i | −1.40384 | − | 0.381853i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −56.9675 | + | 56.9675i | −0.564034 | + | 0.564034i | −0.930451 | − | 0.366417i | \(-0.880585\pi\) |
0.366417 | + | 0.930451i | \(0.380585\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 153.944i | 1.49460i | 0.664485 | + | 0.747301i | \(0.268651\pi\) | ||||
−0.664485 | + | 0.747301i | \(0.731349\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −20.6870 | − | 77.7927i | −0.197019 | − | 0.740883i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −76.9344 | + | 76.9344i | −0.719013 | + | 0.719013i | −0.968403 | − | 0.249390i | \(-0.919770\pi\) |
0.249390 | + | 0.968403i | \(0.419770\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −74.1271 | + | 74.1271i | −0.680065 | + | 0.680065i | −0.960015 | − | 0.279949i | \(-0.909682\pi\) |
0.279949 | + | 0.960015i | \(0.409682\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −54.6265 | − | 205.421i | −0.492131 | − | 1.85064i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 38.3909i | − | 0.339742i | −0.985466 | − | 0.169871i | \(-0.945665\pi\) | ||
0.985466 | − | 0.169871i | \(-0.0543352\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −55.7191 | + | 55.7191i | −0.484514 | + | 0.484514i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.16781 | + | 2.49369i | 0.0783573 | + | 0.0213136i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 48.7259 | 0.409461 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 135.108i | − | 1.11659i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −39.1184 | − | 22.6837i | −0.318035 | − | 0.184420i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −94.8382 | − | 94.8382i | −0.758706 | − | 0.758706i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 43.3417 | 0.341273 | 0.170636 | − | 0.985334i | \(-0.445418\pi\) | ||||
0.170636 | + | 0.985334i | \(0.445418\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −28.7447 | − | 108.094i | −0.222827 | − | 0.837935i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.21414 | − | 1.21414i | −0.00926827 | − | 0.00926827i | 0.702457 | − | 0.711726i | \(-0.252086\pi\) |
−0.711726 | + | 0.702457i | \(0.752086\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −162.020 | − | 162.020i | −1.21819 | − | 1.21819i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 69.7730 | + | 70.5688i | 0.516837 | + | 0.522732i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 238.227 | 1.73889 | 0.869443 | − | 0.494033i | \(-0.164478\pi\) | ||||
0.869443 | + | 0.494033i | \(0.164478\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −26.5704 | − | 26.5704i | −0.191154 | − | 0.191154i | 0.605041 | − | 0.796195i | \(-0.293157\pi\) |
−0.796195 | + | 0.605041i | \(0.793157\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 55.0897 | − | 95.0030i | 0.390707 | − | 0.673780i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16.8940i | 0.118140i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.01896 | −0.0553032 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 11.1439 | + | 6.46207i | 0.0758090 | + | 0.0439596i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 133.254 | − | 133.254i | 0.894321 | − | 0.894321i | −0.100605 | − | 0.994926i | \(-0.532078\pi\) |
0.994926 | + | 0.100605i | \(0.0320779\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 23.3716i | 0.154779i | 0.997001 | + | 0.0773895i | \(0.0246585\pi\) | ||||
−0.997001 | + | 0.0773895i | \(0.975342\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −52.1359 | + | 29.8385i | −0.340758 | + | 0.195023i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −37.9662 | + | 37.9662i | −0.244943 | + | 0.244943i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 95.8780 | − | 95.8780i | 0.610688 | − | 0.610688i | −0.332438 | − | 0.943125i | \(-0.607871\pi\) |
0.943125 | + | 0.332438i | \(0.107871\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −208.808 | + | 55.5272i | −1.31326 | + | 0.349227i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 156.510i | − | 0.972113i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −103.379 | + | 103.379i | −0.634230 | + | 0.634230i | −0.949126 | − | 0.314896i | \(-0.898030\pi\) |
0.314896 | + | 0.949126i | \(0.398030\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −88.5190 | + | 152.652i | −0.536479 | + | 0.925166i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 113.980 | 0.682515 | 0.341258 | − | 0.939970i | \(-0.389147\pi\) | ||||
0.341258 | + | 0.939970i | \(0.389147\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 167.886i | 0.993406i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 272.575 | + | 74.1418i | 1.59401 | + | 0.433578i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 144.265 | + | 144.265i | 0.833901 | + | 0.833901i | 0.988048 | − | 0.154147i | \(-0.0492630\pi\) |
−0.154147 | + | 0.988048i | \(0.549263\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 83.8857 | 0.479347 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −49.8918 | + | 13.2674i | −0.281875 | + | 0.0749573i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.8240 | + | 16.8240i | 0.0939888 | + | 0.0939888i | 0.752538 | − | 0.658549i | \(-0.228829\pi\) |
−0.658549 | + | 0.752538i | \(0.728829\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −34.2037 | − | 34.2037i | −0.188971 | − | 0.188971i | 0.606280 | − | 0.795251i | \(-0.292661\pi\) |
−0.795251 | + | 0.606280i | \(0.792661\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −113.077 | + | 30.0700i | −0.617909 | + | 0.164317i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −260.421 | −1.40768 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −75.5295 | − | 75.5295i | −0.403901 | − | 0.403901i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −197.104 | − | 1.11765i | −1.04288 | − | 0.00591347i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 150.160i | − | 0.786177i | −0.919501 | − | 0.393088i | \(-0.871407\pi\) | ||
0.919501 | − | 0.393088i | \(-0.128593\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 117.637 | 0.609518 | 0.304759 | − | 0.952429i | \(-0.401424\pi\) | ||||
0.304759 | + | 0.952429i | \(0.401424\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.83913 | − | 10.0697i | 0.0299442 | − | 0.0516393i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 31.8524 | − | 31.8524i | 0.161688 | − | 0.161688i | −0.621626 | − | 0.783314i | \(-0.713528\pi\) |
0.783314 | + | 0.621626i | \(0.213528\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 128.347i | − | 0.644959i | −0.946576 | − | 0.322480i | \(-0.895484\pi\) | ||
0.946576 | − | 0.322480i | \(-0.104516\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 19.8535 | − | 5.27952i | 0.0987735 | − | 0.0262663i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 11.2623 | − | 11.2623i | 0.0554793 | − | 0.0554793i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −39.1746 | + | 39.1746i | −0.191095 | + | 0.191095i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 95.8429 | + | 167.464i | 0.463009 | + | 0.809003i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 502.290i | 2.40330i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 78.8045 | − | 78.8045i | 0.373481 | − | 0.373481i | −0.495262 | − | 0.868743i | \(-0.664928\pi\) |
0.868743 | + | 0.495262i | \(0.164928\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 194.402 | + | 112.728i | 0.912685 | + | 0.529241i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −137.035 | −0.637372 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 106.644i | − | 0.491447i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.22369 | + | 9.00834i | −0.0238525 | + | 0.0411340i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.98228 | + | 4.98228i | 0.0225442 | + | 0.0225442i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 153.748 | 0.689455 | 0.344727 | − | 0.938703i | \(-0.387971\pi\) | ||||
0.344727 | + | 0.938703i | \(0.387971\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −89.7564 | + | 51.3695i | −0.398917 | + | 0.228309i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 43.6518 | + | 43.6518i | 0.192299 | + | 0.192299i | 0.796689 | − | 0.604390i | \(-0.206583\pi\) |
−0.604390 | + | 0.796689i | \(0.706583\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 111.882 | + | 111.882i | 0.488566 | + | 0.488566i | 0.907853 | − | 0.419288i | \(-0.137720\pi\) |
−0.419288 | + | 0.907853i | \(0.637720\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −90.0726 | − | 338.715i | −0.389925 | − | 1.46630i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 32.4793 | 0.139396 | 0.0696980 | − | 0.997568i | \(-0.477796\pi\) | ||||
0.0696980 | + | 0.997568i | \(0.477796\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −95.1395 | − | 95.1395i | −0.404849 | − | 0.404849i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 268.512 | + | 155.703i | 1.13296 | + | 0.656974i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 133.305i | 0.557762i | 0.960326 | + | 0.278881i | \(0.0899636\pi\) | ||||
−0.960326 | + | 0.278881i | \(0.910036\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 159.670 | 0.662532 | 0.331266 | − | 0.943537i | \(-0.392524\pi\) | ||||
0.331266 | + | 0.943537i | \(0.392524\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 211.583 | − | 119.506i | 0.870712 | − | 0.491793i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 11.1599 | − | 11.1599i | 0.0455508 | − | 0.0455508i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 33.1334i | − | 0.134143i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −34.5911 | − | 130.079i | −0.138920 | − | 0.522404i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 106.711 | − | 106.711i | 0.425141 | − | 0.425141i | −0.461828 | − | 0.886969i | \(-0.652806\pi\) |
0.886969 | + | 0.461828i | \(0.152806\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −242.605 | + | 242.605i | −0.958913 | + | 0.958913i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 18.9138 | + | 71.1246i | 0.0741717 | + | 0.278920i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 343.816i | − | 1.33781i | −0.743350 | − | 0.668903i | \(-0.766764\pi\) | ||
0.743350 | − | 0.668903i | \(-0.233236\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 365.751 | − | 365.751i | 1.41217 | − | 1.41217i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.15374 | + | 18.9472i | −0.0197461 | + | 0.0725948i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −266.255 | −1.01238 | −0.506188 | − | 0.862423i | \(-0.668946\pi\) | ||||
−0.506188 | + | 0.862423i | \(0.668946\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 264.715i | 0.998925i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −203.104 | − | 117.775i | −0.760691 | − | 0.441104i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −102.194 | − | 102.194i | −0.379904 | − | 0.379904i | 0.491164 | − | 0.871067i | \(-0.336572\pi\) |
−0.871067 | + | 0.491164i | \(0.836572\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 38.5636 | 0.142301 | 0.0711505 | − | 0.997466i | \(-0.477333\pi\) | ||||
0.0711505 | + | 0.997466i | \(0.477333\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.94161 | + | 22.3432i | 0.0217641 | + | 0.0818433i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −130.030 | − | 130.030i | −0.472838 | − | 0.472838i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 277.306 | + | 277.306i | 1.00111 | + | 1.00111i | 0.999999 | + | 0.00110593i | \(0.000352027\pi\) |
0.00110593 | + | 0.999999i | \(0.499648\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 65.3061 | + | 114.107i | 0.234072 | + | 0.408987i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −458.765 | −1.63262 | −0.816308 | − | 0.577617i | \(-0.803983\pi\) | ||||
−0.816308 | + | 0.577617i | \(0.803983\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 276.746 | + | 276.746i | 0.977900 | + | 0.977900i | 0.999761 | − | 0.0218614i | \(-0.00695927\pi\) |
−0.0218614 | + | 0.999761i | \(0.506959\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 173.608 | − | 299.389i | 0.609149 | − | 1.05049i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 110.038i | − | 0.383408i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 244.451 | 0.845850 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 159.776 | + | 92.6499i | 0.549059 | + | 0.318384i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −306.513 | + | 306.513i | −1.04612 | + | 1.04612i | −0.0472370 | + | 0.998884i | \(0.515042\pi\) |
−0.998884 | + | 0.0472370i | \(0.984958\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 63.2500i | 0.214407i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 303.797 | + | 307.262i | 1.02289 | + | 1.03455i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 16.0033 | − | 16.0033i | 0.0535229 | − | 0.0535229i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 192.460 | − | 192.460i | 0.639401 | − | 0.639401i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 233.575 | − | 62.1133i | 0.770874 | − | 0.204994i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 143.353i | 0.470010i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −359.692 | + | 359.692i | −1.17163 | + | 1.17163i | −0.189814 | + | 0.981820i | \(0.560789\pi\) |
−0.981820 | + | 0.189814i | \(0.939211\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 231.672 | − | 399.521i | 0.749746 | − | 1.29295i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 572.008 | 1.83925 | 0.919626 | − | 0.392794i | \(-0.128492\pi\) | ||||
0.919626 | + | 0.392794i | \(0.128492\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 333.314i | 1.06490i | 0.846461 | + | 0.532450i | \(0.178729\pi\) | ||||
−0.846461 | + | 0.532450i | \(0.821271\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −63.3832 | + | 233.022i | −0.201217 | + | 0.739754i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −266.382 | − | 266.382i | −0.840322 | − | 0.840322i | 0.148578 | − | 0.988901i | \(-0.452530\pi\) |
−0.988901 | + | 0.148578i | \(0.952530\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −34.9151 | −0.109452 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 315.442 | − | 83.8838i | 0.982686 | − | 0.261320i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 148.132 | + | 148.132i | 0.458613 | + | 0.458613i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.57741 | + | 8.57741i | 0.0263920 | + | 0.0263920i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 303.932 | − | 80.8229i | 0.929455 | − | 0.247165i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 267.239 | 0.812276 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −212.431 | − | 212.431i | −0.641787 | − | 0.641787i | 0.309208 | − | 0.950995i | \(-0.399936\pi\) |
−0.950995 | + | 0.309208i | \(0.899936\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −167.371 | + | 615.325i | −0.502617 | + | 1.84782i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 25.1691i | − | 0.0751317i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −207.477 | −0.615658 | −0.307829 | − | 0.951442i | \(-0.599602\pi\) | ||||
−0.307829 | + | 0.951442i | \(0.599602\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −57.7748 | + | 99.6335i | −0.170427 | + | 0.293904i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −165.308 | + | 165.308i | −0.484773 | + | 0.484773i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 326.366i | − | 0.951505i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 228.456 | − | 60.7521i | 0.662192 | − | 0.176093i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 98.4692 | − | 98.4692i | 0.283773 | − | 0.283773i | −0.550839 | − | 0.834612i | \(-0.685692\pi\) |
0.834612 | + | 0.550839i | \(0.185692\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 337.382 | − | 337.382i | 0.966711 | − | 0.966711i | −0.0327527 | − | 0.999463i | \(-0.510427\pi\) |
0.999463 | + | 0.0327527i | \(0.0104274\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −20.0399 | − | 20.2684i | −0.0570936 | − | 0.0577448i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 293.330i | − | 0.830964i | −0.909601 | − | 0.415482i | \(-0.863613\pi\) | ||
0.909601 | − | 0.415482i | \(-0.136387\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 194.681 | − | 194.681i | 0.548398 | − | 0.548398i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −126.455 | − | 73.3279i | −0.354216 | − | 0.205400i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 305.954 | 0.852239 | 0.426119 | − | 0.904667i | \(-0.359880\pi\) | ||||
0.426119 | + | 0.904667i | \(0.359880\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 624.114i | − | 1.72885i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −203.324 | + | 350.636i | −0.560122 | + | 0.965939i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.02128 | + | 9.02128i | 0.0247158 | + | 0.0247158i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −221.149 | −0.602585 | −0.301292 | − | 0.953532i | \(-0.597418\pi\) | ||||
−0.301292 | + | 0.953532i | \(0.597418\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 67.3845 | + | 117.739i | 0.182614 | + | 0.319076i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −371.781 | − | 371.781i | −1.00211 | − | 1.00211i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −147.216 | − | 147.216i | −0.394682 | − | 0.394682i | 0.481671 | − | 0.876352i | \(-0.340030\pi\) |
−0.876352 | + | 0.481671i | \(0.840030\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 103.405 | + | 388.850i | 0.275746 | + | 1.03693i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.30317 | 0.00610919 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 298.572 | + | 298.572i | 0.787790 | + | 0.787790i | 0.981131 | − | 0.193342i | \(-0.0619326\pi\) |
−0.193342 | + | 0.981131i | \(0.561933\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −112.482 | − | 65.2252i | −0.295228 | − | 0.171195i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 427.326i | − | 1.11573i | −0.829931 | − | 0.557866i | \(-0.811620\pi\) | ||
0.829931 | − | 0.557866i | \(-0.188380\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −429.404 | −1.11533 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −88.0716 | + | 323.787i | −0.227575 | + | 0.836658i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −314.075 | + | 314.075i | −0.807391 | + | 0.807391i | −0.984238 | − | 0.176847i | \(-0.943410\pi\) |
0.176847 | + | 0.984238i | \(0.443410\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 143.095i | 0.365971i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.32382 | + | 4.97816i | 0.00336849 | + | 0.0126671i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 268.898 | − | 268.898i | 0.680753 | − | 0.680753i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −189.839 | + | 189.839i | −0.478185 | + | 0.478185i | −0.904551 | − | 0.426366i | \(-0.859794\pi\) |
0.426366 | + | 0.904551i | \(0.359794\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 176.655 | + | 664.304i | 0.442743 | + | 1.66492i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 268.223i | − | 0.668886i | −0.942416 | − | 0.334443i | \(-0.891452\pi\) | ||
0.942416 | − | 0.334443i | \(-0.108548\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.9045 | − | 10.9045i | 0.0270582 | − | 0.0270582i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −74.8780 | − | 288.145i | −0.184884 | − | 0.711469i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1133.89 | −2.78598 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 25.8478i | − | 0.0631976i | −0.999501 | − | 0.0315988i | \(-0.989940\pi\) | ||
0.999501 | − | 0.0315988i | \(-0.0100599\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −618.257 | − | 358.510i | −1.50427 | − | 0.872288i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −88.8319 | − | 88.8319i | −0.215089 | − | 0.215089i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −164.906 | −0.397365 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 28.9705 | + | 108.942i | 0.0694735 | + | 0.261253i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −243.361 | − | 243.361i | −0.580813 | − | 0.580813i | 0.354313 | − | 0.935127i | \(-0.384715\pi\) |
−0.935127 | + | 0.354313i | \(0.884715\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −115.847 | − | 115.847i | −0.275171 | − | 0.275171i | 0.556007 | − | 0.831178i | \(-0.312333\pi\) |
−0.831178 | + | 0.556007i | \(0.812333\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −285.942 | + | 163.650i | −0.675985 | + | 0.386880i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −76.6953 | −0.180460 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −201.333 | − | 201.333i | −0.471507 | − | 0.471507i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 25.4240 | − | 43.8440i | 0.0592634 | − | 0.102201i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 568.037i | − | 1.31795i | −0.752165 | − | 0.658975i | \(-0.770990\pi\) | ||
0.752165 | − | 0.658975i | \(-0.229010\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −647.222 | −1.49474 | −0.747370 | − | 0.664408i | \(-0.768684\pi\) | ||||
−0.747370 | + | 0.664408i | \(0.768684\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 20.8111 | + | 12.0678i | 0.0478416 | + | 0.0277421i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 475.808 | − | 475.808i | 1.08881 | − | 1.08881i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 486.389i | 1.10795i | 0.832534 | + | 0.553973i | \(0.186889\pi\) | ||||
−0.832534 | + | 0.553973i | \(0.813111\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −19.1963 | − | 33.5412i | −0.0435291 | − | 0.0760571i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −258.469 | + | 258.469i | −0.583451 | + | 0.583451i | −0.935850 | − | 0.352399i | \(-0.885366\pi\) |
0.352399 | + | 0.935850i | \(0.385366\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −203.396 | + | 203.396i | −0.457070 | + | 0.457070i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −546.360 | + | 145.290i | −1.22228 | + | 0.325035i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 498.015i | 1.10916i | 0.832129 | + | 0.554582i | \(0.187122\pi\) | ||||
−0.832129 | + | 0.554582i | \(0.812878\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −170.569 | + | 170.569i | −0.378201 | + | 0.378201i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 35.1721 | − | 60.6549i | 0.0776427 | − | 0.133896i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 28.3255 | 0.0622538 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 466.468i | − | 1.02072i | −0.859961 | − | 0.510359i | \(-0.829513\pi\) | ||
0.859961 | − | 0.510359i | \(-0.170487\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 180.209 | + | 1.02185i | 0.392613 | + | 0.00222624i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 389.251 | + | 389.251i | 0.844362 | + | 0.844362i | 0.989423 | − | 0.145061i | \(-0.0463378\pi\) |
−0.145061 | + | 0.989423i | \(0.546338\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −500.857 | −1.08177 | −0.540883 | − | 0.841098i | \(-0.681910\pi\) | ||||
−0.540883 | + | 0.841098i | \(0.681910\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 155.667 | − | 41.3957i | 0.334768 | − | 0.0890229i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 188.836 | + | 188.836i | 0.404359 | + | 0.404359i | 0.879766 | − | 0.475407i | \(-0.157699\pi\) |
−0.475407 | + | 0.879766i | \(0.657699\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 35.3489 | + | 35.3489i | 0.0753709 | + | 0.0753709i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −393.113 | + | 104.538i | −0.834636 | + | 0.221950i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −596.660 | −1.26144 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 255.022 | + | 255.022i | 0.536888 | + | 0.536888i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 625.470 | + | 170.131i | 1.31126 | + | 0.356668i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 326.344i | 0.681303i | 0.940190 | + | 0.340652i | \(0.110648\pi\) | ||||
−0.940190 | + | 0.340652i | \(0.889352\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 74.7969 | 0.155503 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −235.533 | + | 406.181i | −0.487647 | + | 0.840954i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 160.006 | − | 160.006i | 0.329909 | − | 0.329909i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 196.238i | − | 0.402952i | −0.979493 | − | 0.201476i | \(-0.935426\pi\) | ||
0.979493 | − | 0.201476i | \(-0.0645739\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 423.871 | − | 112.718i | 0.866812 | − | 0.230506i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 349.172 | − | 349.172i | 0.711144 | − | 0.711144i | −0.255631 | − | 0.966774i | \(-0.582283\pi\) |
0.966774 | + | 0.255631i | \(0.0822831\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.2969 | + | 10.2969i | −0.0208863 | + | 0.0208863i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 459.456 | − | 262.956i | 0.928193 | − | 0.531224i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 546.843i | 1.10029i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −321.326 | + | 321.326i | −0.643940 | + | 0.643940i | −0.951522 | − | 0.307582i | \(-0.900480\pi\) |
0.307582 | + | 0.951522i | \(0.400480\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −295.805 | − | 171.530i | −0.590430 | − | 0.342374i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 623.698 | 1.23996 | 0.619978 | − | 0.784619i | \(-0.287142\pi\) | ||||
0.619978 | + | 0.784619i | \(0.287142\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 296.113i | − | 0.586362i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 252.652 | − | 435.703i | 0.498328 | − | 0.859374i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −452.448 | − | 452.448i | −0.888897 | − | 0.888897i | 0.105520 | − | 0.994417i | \(-0.466349\pi\) |
−0.994417 | + | 0.105520i | \(0.966349\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −25.3400 | −0.0495891 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −595.821 | − | 602.616i | −1.16144 | − | 1.17469i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −400.095 | − | 400.095i | −0.776884 | − | 0.776884i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −414.244 | − | 414.244i | −0.801247 | − | 0.801247i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −157.296 | − | 591.506i | −0.303075 | − | 1.13970i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −444.986 | −0.854100 | −0.427050 | − | 0.904228i | \(-0.640447\pi\) | ||||
−0.427050 | + | 0.904228i | \(0.640447\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 399.942 | + | 399.942i | 0.764707 | + | 0.764707i | 0.977169 | − | 0.212462i | \(-0.0681483\pi\) |
−0.212462 | + | 0.977169i | \(0.568148\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −217.703 | − | 126.240i | −0.414673 | − | 0.240458i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 97.5029i | 0.185015i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −69.3715 | −0.131137 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 149.447 | + | 40.6504i | 0.281445 | + | 0.0765544i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.2515 | − | 11.2515i | 0.0211098 | − | 0.0211098i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 399.900i | − | 0.747476i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −18.3437 | − | 68.9808i | −0.0341595 | − | 0.128456i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 48.5912 | − | 48.5912i | 0.0901506 | − | 0.0901506i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 116.940 | − | 116.940i | 0.216155 | − | 0.216155i | −0.590721 | − | 0.806876i | \(-0.701156\pi\) |
0.806876 | + | 0.590721i | \(0.201156\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 37.2932 | + | 140.240i | 0.0686800 | + | 0.258269i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 385.308i | − | 0.706987i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 85.6914 | − | 85.6914i | 0.156657 | − | 0.156657i | −0.624427 | − | 0.781084i | \(-0.714667\pi\) |
0.781084 | + | 0.624427i | \(0.214667\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 338.715 | + | 92.1322i | 0.616968 | + | 0.167818i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 68.4772 | 0.124278 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 755.311i | 1.36584i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 675.855 | + | 391.910i | 1.21776 | + | 0.706145i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −104.194 | − | 104.194i | −0.187062 | − | 0.187062i | 0.607363 | − | 0.794425i | \(-0.292228\pi\) |
−0.794425 | + | 0.607363i | \(0.792228\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 39.3585 | 0.0704087 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 82.3519 | + | 309.682i | 0.146795 | + | 0.552017i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 776.673 | + | 776.673i | 1.37953 | + | 1.37953i | 0.845414 | + | 0.534111i | \(0.179354\pi\) |
0.534111 | + | 0.845414i | \(0.320646\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 99.7766 | + | 99.7766i | 0.176596 | + | 0.176596i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 509.850 | + | 299.524i | 0.899207 | + | 0.528261i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 456.546 | 0.802366 | 0.401183 | − | 0.915998i | \(-0.368599\pi\) | ||||
0.401183 | + | 0.915998i | \(0.368599\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −475.108 | − | 475.108i | −0.832062 | − | 0.832062i | 0.155736 | − | 0.987799i | \(-0.450225\pi\) |
−0.987799 | + | 0.155736i | \(0.950225\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −225.977 | + | 389.700i | −0.394375 | + | 0.680105i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 246.350i | 0.428434i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1127.70 | 1.95443 | 0.977213 | − | 0.212262i | \(-0.0680832\pi\) | ||||
0.977213 | + | 0.212262i | \(0.0680832\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −305.296 | − | 177.033i | −0.527281 | − | 0.305756i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 231.604 | − | 231.604i | 0.398630 | − | 0.398630i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1152.59i | 1.97700i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −30.3078 | + | 17.3458i | −0.0518082 | + | 0.0296509i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −584.236 | + | 584.236i | −0.995292 | + | 0.995292i | −0.999989 | − | 0.00469688i | \(-0.998505\pi\) |
0.00469688 | + | 0.999989i | \(0.498505\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 324.209 | − | 324.209i | 0.550440 | − | 0.550440i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −130.600 | + | 34.7296i | −0.220981 | + | 0.0587642i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 870.906i | − | 1.46864i | −0.678801 | − | 0.734322i | \(-0.737500\pi\) | ||
0.678801 | − | 0.734322i | \(-0.262500\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −126.637 | + | 126.637i | −0.212835 | + | 0.212835i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −193.150 | + | 333.090i | −0.323535 | + | 0.557940i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −224.305 | −0.374466 | −0.187233 | − | 0.982316i | \(-0.559952\pi\) | ||||
−0.187233 | + | 0.982316i | \(0.559952\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 234.358i | 0.389946i | 0.980809 | + | 0.194973i | \(0.0624620\pi\) | ||||
−0.980809 | + | 0.194973i | \(0.937538\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −59.4697 | − | 16.1760i | −0.0986230 | − | 0.0268259i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 351.140 | + | 351.140i | 0.580396 | + | 0.580396i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 620.755 | 1.02266 | 0.511330 | − | 0.859384i | \(-0.329153\pi\) | ||||
0.511330 | + | 0.859384i | \(0.329153\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −46.1770 | + | 12.2796i | −0.0758244 | + | 0.0201635i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 27.3255 | + | 27.3255i | 0.0447226 | + | 0.0447226i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 645.945 | + | 645.945i | 1.05374 | + | 1.05374i | 0.998471 | + | 0.0552724i | \(0.0176027\pi\) |
0.0552724 | + | 0.998471i | \(0.482397\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 160.621 | − | 42.7131i | 0.261173 | − | 0.0694523i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 169.883 | 0.275337 | 0.137669 | − | 0.990478i | \(-0.456039\pi\) | ||||
0.137669 | + | 0.990478i | \(0.456039\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −647.603 | − | 647.603i | −1.04621 | − | 1.04621i | −0.998879 | − | 0.0473286i | \(-0.984929\pi\) |
−0.0473286 | − | 0.998879i | \(-0.515071\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.28222 | − | 578.842i | 0.00528539 | − | 0.932113i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 571.323i | − | 0.917051i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 205.694 | 0.329110 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 755.900 | − | 1303.56i | 1.20558 | − | 2.07904i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −334.400 | + | 334.400i | −0.531638 | + | 0.531638i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 975.374i | − | 1.54576i | −0.634553 | − | 0.772880i | \(-0.718816\pi\) | ||
0.634553 | − | 0.772880i | \(-0.281184\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −323.110 | + | 85.9228i | −0.510442 | + | 0.135739i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −112.643 | + | 112.643i | −0.177391 | + | 0.177391i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.20530 | + | 3.20530i | −0.00503187 | + | 0.00503187i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −334.873 | − | 585.114i | −0.524058 | − | 0.915671i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 771.555i | 1.20367i | 0.798619 | + | 0.601837i | \(0.205564\pi\) | ||||
−0.798619 | + | 0.601837i | \(0.794436\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 319.214 | − | 319.214i | 0.496445 | − | 0.496445i | −0.413884 | − | 0.910330i | \(-0.635828\pi\) |
0.910330 | + | 0.413884i | \(0.135828\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 355.638 | + | 206.225i | 0.551377 | + | 0.319729i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 360.720 | 0.557527 | 0.278764 | − | 0.960360i | \(-0.410075\pi\) | ||||
0.278764 | + | 0.960360i | \(0.410075\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 275.395i | 0.424338i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −160.489 | + | 276.766i | −0.246527 | + | 0.425140i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −415.043 | − | 415.043i | −0.635595 | − | 0.635595i | 0.313871 | − | 0.949466i | \(-0.398374\pi\) |
−0.949466 | + | 0.313871i | \(0.898374\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.31104 | 0.00963517 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 27.1134 | − | 15.5176i | 0.0412685 | − | 0.0236189i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −363.535 | − | 363.535i | −0.551646 | − | 0.551646i | 0.375269 | − | 0.926916i | \(-0.377550\pi\) |
−0.926916 | + | 0.375269i | \(0.877550\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 151.997 | + | 151.997i | 0.229951 | + | 0.229951i | 0.812672 | − | 0.582721i | \(-0.198012\pi\) |
−0.582721 | + | 0.812672i | \(0.698012\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.43232 | − | 20.4280i | −0.00819354 | − | 0.0308115i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 842.166 | 1.26642 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 33.0743 | + | 33.0743i | 0.0495867 | + | 0.0495867i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −399.013 | − | 231.377i | −0.596433 | − | 0.345855i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 624.170i | 0.930208i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −271.149 | −0.402896 | −0.201448 | − | 0.979499i | \(-0.564565\pi\) | ||||
−0.201448 | + | 0.979499i | \(0.564565\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 310.245 | + | 1.75919i | 0.459623 | + | 0.00260621i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −639.750 | + | 639.750i | −0.944978 | + | 0.944978i | −0.998563 | − | 0.0535849i | \(-0.982935\pi\) |
0.0535849 | + | 0.998563i | \(0.482935\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 449.442i | 0.661918i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −47.5948 | − | 178.979i | −0.0698895 | − | 0.262817i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −93.1730 | + | 93.1730i | −0.136417 | + | 0.136417i | −0.772018 | − | 0.635601i | \(-0.780752\pi\) |
0.635601 | + | 0.772018i | \(0.280752\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −619.145 | + | 619.145i | −0.903861 | + | 0.903861i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −121.988 | − | 458.731i | −0.177566 | − | 0.667730i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 76.0301i | − | 0.110348i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 303.844 | − | 303.844i | 0.439716 | − | 0.439716i | −0.452200 | − | 0.891916i | \(-0.649361\pi\) |
0.891916 | + | 0.452200i | \(0.149361\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −275.975 | + | 1014.60i | −0.398233 | + | 1.46406i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 138.111 | 0.198721 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 100.606i | 0.144341i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −84.2914 | − | 48.8783i | −0.120589 | − | 0.0699261i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 797.170 | + | 797.170i | 1.13719 | + | 1.13719i | 0.988952 | + | 0.148238i | \(0.0473601\pi\) |
0.148238 | + | 0.988952i | \(0.452640\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2223.85 | 3.16336 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 103.733 | + | 390.086i | 0.147140 | + | 0.553313i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 415.878 | + | 415.878i | 0.588229 | + | 0.588229i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −592.848 | − | 592.848i | −0.836176 | − | 0.836176i | 0.152178 | − | 0.988353i | \(-0.451371\pi\) |
−0.988353 | + | 0.152178i | \(0.951371\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −462.533 | − | 808.171i | −0.650539 | − | 1.13667i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 313.185 | 0.439249 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −43.9070 | − | 43.9070i | −0.0614084 | − | 0.0614084i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 200.612 | − | 345.959i | 0.279794 | − | 0.482508i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1252.89i | 1.74255i | 0.490799 | + | 0.871273i | \(0.336705\pi\) | ||||
−0.490799 | + | 0.871273i | \(0.663295\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1123.83 | 1.55872 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −414.382 | − | 240.289i | −0.573142 | − | 0.332350i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −17.7270 | + | 17.7270i | −0.0244511 | + | 0.0244511i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1182.91i | − | 1.62711i | −0.581490 | − | 0.813553i | \(-0.697530\pi\) | ||
0.581490 | − | 0.813553i | \(-0.302470\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −728.953 | − | 8.26707i | −0.999936 | − | 0.0113403i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −175.963 | + | 175.963i | −0.240715 | + | 0.240715i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −679.023 | + | 679.023i | −0.926361 | + | 0.926361i | −0.997469 | − | 0.0711072i | \(-0.977347\pi\) |
0.0711072 | + | 0.997469i | \(0.477347\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −45.7574 | + | 12.1680i | −0.0622549 | + | 0.0165551i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 109.588i | − | 0.148695i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 408.587 | − | 408.587i | 0.552892 | − | 0.552892i | −0.374383 | − | 0.927274i | \(-0.622145\pi\) |
0.927274 | + | 0.374383i | \(0.122145\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −49.8627 | + | 85.9889i | −0.0672911 | + | 0.116044i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −228.202 | −0.307137 | −0.153568 | − | 0.988138i | \(-0.549077\pi\) | ||||
−0.153568 | + | 0.988138i | \(0.549077\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 692.644i | 0.929724i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −105.984 | + | 389.641i | −0.141880 | + | 0.521608i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 561.642 | + | 561.642i | 0.749856 | + | 0.749856i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −835.943 | −1.11311 | −0.556553 | − | 0.830812i | \(-0.687876\pi\) | ||||
−0.556553 | + | 0.830812i | \(0.687876\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −437.528 | + | 116.350i | −0.581047 | + | 0.154515i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −60.7421 | − | 60.7421i | −0.0804530 | − | 0.0804530i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −144.017 | − | 144.017i | −0.190247 | − | 0.190247i | 0.605556 | − | 0.795803i | \(-0.292951\pi\) |
−0.795803 | + | 0.605556i | \(0.792951\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 994.715 | − | 264.519i | 1.31056 | − | 0.348510i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1238.49 | 1.62745 | 0.813727 | − | 0.581247i | \(-0.197435\pi\) | ||||
0.813727 | + | 0.581247i | \(0.197435\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 541.148 | + | 541.148i | 0.709238 | + | 0.709238i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 57.9503 | − | 213.049i | 0.0757520 | − | 0.278495i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 18.1663i | − | 0.0236849i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −906.729 | −1.17910 | −0.589551 | − | 0.807732i | \(-0.700695\pi\) | ||||
−0.589551 | + | 0.807732i | \(0.700695\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −517.411 | + | 892.284i | −0.671091 | + | 1.15731i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 989.152 | − | 989.152i | 1.27963 | − | 1.27963i | 0.338752 | − | 0.940876i | \(-0.389995\pi\) |
0.940876 | − | 0.338752i | \(-0.110005\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 167.859i | 0.216593i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1499.63 | + | 398.789i | −1.93003 | + | 0.513241i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 334.528 | − | 334.528i | 0.429432 | − | 0.429432i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 847.656 | − | 847.656i | 1.08535 | − | 1.08535i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 41.8890 | − | 41.4166i | 0.0534981 | − | 0.0528948i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 498.367i | 0.634862i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 100.012 | − | 100.012i | 0.127080 | − | 0.127080i | −0.640706 | − | 0.767786i | \(-0.721358\pi\) |
0.767786 | + | 0.640706i | \(0.221358\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 690.994 | + | 400.689i | 0.875785 | + | 0.507844i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −280.264 | −0.354316 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 41.1731i | − | 0.0519207i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 398.372 | − | 686.998i | 0.501097 | − | 0.864149i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −264.491 | − | 264.491i | −0.331858 | − | 0.331858i | 0.521433 | − | 0.853292i | \(-0.325397\pi\) |
−0.853292 | + | 0.521433i | \(0.825397\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −244.332 | −0.305798 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 349.864 | + | 611.307i | 0.436784 | + | 0.763180i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 39.2793 | + | 39.2793i | 0.0489157 | + | 0.0489157i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 406.765 | + | 406.765i | 0.505298 | + | 0.505298i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 111.425 | + | 419.011i | 0.138073 | + | 0.519220i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1041.53 | −1.28743 | −0.643717 | − | 0.765264i | \(-0.722609\pi\) | ||||
−0.643717 | + | 0.765264i | \(0.722609\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −442.482 | − | 442.482i | −0.545600 | − | 0.545600i | 0.379565 | − | 0.925165i | \(-0.376074\pi\) |
−0.925165 | + | 0.379565i | \(0.876074\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −100.082 | − | 58.0346i | −0.123102 | − | 0.0713833i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 537.359i | − | 0.659337i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1170.20 | 1.43231 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 18.2046 | − | 66.9275i | 0.0222279 | − | 0.0817186i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −104.027 | + | 104.027i | −0.126708 | + | 0.126708i | −0.767617 | − | 0.640909i | \(-0.778558\pi\) |
0.640909 | + | 0.767617i | \(0.278558\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 349.420i | 0.424568i | 0.977208 | + | 0.212284i | \(0.0680902\pi\) | ||||
−0.977208 | + | 0.212284i | \(0.931910\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 141.776 | + | 533.143i | 0.171850 | + | 0.646234i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 554.122 | − | 554.122i | 0.670038 | − | 0.670038i | −0.287686 | − | 0.957725i | \(-0.592886\pi\) |
0.957725 | + | 0.287686i | \(0.0928861\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 583.639 | − | 583.639i | 0.704027 | − | 0.704027i | −0.261245 | − | 0.965272i | \(-0.584133\pi\) |
0.965272 | + | 0.261245i | \(0.0841331\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −302.355 | − | 1137.00i | −0.363845 | − | 1.36823i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 28.6604i | − | 0.0344062i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −296.230 | + | 296.230i | −0.354767 | + | 0.354767i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.23646 | − | 394.415i | 0.00267200 | − | 0.471225i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1235.55 | −1.47264 | −0.736322 | − | 0.676632i | \(-0.763439\pi\) | ||||
−0.736322 | + | 0.676632i | \(0.763439\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 836.240i | − | 0.994340i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1190.60 | + | 690.399i | 1.41234 | + | 0.818979i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −436.329 | − | 436.329i | −0.516365 | − | 0.516365i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −986.322 | −1.16449 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −301.744 | − | 1134.70i | −0.355411 | − | 1.33651i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1074.11 | + | 1074.11i | 1.26218 | + | 1.26218i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −535.104 | − | 535.104i | −0.627320 | − | 0.627320i | 0.320073 | − | 0.947393i | \(-0.396293\pi\) |
−0.947393 | + | 0.320073i | \(0.896293\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −901.105 | + | 515.722i | −1.05392 | + | 0.603183i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −261.325 | −0.304929 | −0.152465 | − | 0.988309i | \(-0.548721\pi\) | ||||
−0.152465 | + | 0.988309i | \(0.548721\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −81.4524 | − | 81.4524i | −0.0948224 | − | 0.0948224i | 0.658104 | − | 0.752927i | \(-0.271359\pi\) |
−0.752927 | + | 0.658104i | \(0.771359\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −165.597 | + | 285.575i | −0.192331 | + | 0.331678i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1250.31i | 1.44879i | 0.689383 | + | 0.724397i | \(0.257882\pi\) | ||||
−0.689383 | + | 0.724397i | \(0.742118\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −749.878 | −0.866911 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −634.407 | − | 367.876i | −0.731727 | − | 0.424309i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1170.80 | − | 1170.80i | 1.34730 | − | 1.34730i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.22894i | 0.00829959i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −275.227 | − | 480.897i | −0.315266 | − | 0.550855i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −692.345 | + | 692.345i | −0.791251 | + | 0.791251i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −288.263 | + | 288.263i | −0.328692 | + | 0.328692i | −0.852089 | − | 0.523397i | \(-0.824664\pi\) |
0.523397 | + | 0.852089i | \(0.324664\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1256.75 | − | 334.200i | 1.42975 | − | 0.380205i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1682.63i | − | 1.90991i | −0.296744 | − | 0.954957i | \(-0.595901\pi\) | ||
0.296744 | − | 0.954957i | \(-0.404099\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −477.885 | + | 477.885i | −0.541206 | + | 0.541206i | −0.923882 | − | 0.382676i | \(-0.875002\pi\) |
0.382676 | + | 0.923882i | \(0.375002\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 95.1854 | − | 164.149i | 0.107554 | − | 0.185479i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1366.70 | 1.54081 | 0.770405 | − | 0.637555i | \(-0.220054\pi\) | ||||
0.770405 | + | 0.637555i | \(0.220054\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 316.406i | − | 0.355912i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −326.024 | − | 1254.60i | −0.365908 | − | 1.40808i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 812.435 | + | 812.435i | 0.909782 | + | 0.909782i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −87.4499 | −0.0977094 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −65.6160 | + | 17.4489i | −0.0731506 | + | 0.0194525i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 22.5364 | + | 22.5364i | 0.0250683 | + | 0.0250683i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 339.914 | + | 339.914i | 0.377263 | + | 0.377263i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −789.113 | + | 209.844i | −0.873879 | + | 0.232386i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 177.788 | 0.196451 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 330.495 | + | 330.495i | 0.364383 | + | 0.364383i | 0.865424 | − | 0.501041i | \(-0.167049\pi\) |
−0.501041 | + | 0.865424i | \(0.667049\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −699.657 | − | 190.310i | −0.769699 | − | 0.209362i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1633.72i | 1.79332i | 0.442715 | + | 0.896662i | \(0.354015\pi\) | ||||
−0.442715 | + | 0.896662i | \(0.645985\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −718.014 | −0.786434 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 215.733 | − | 372.035i | 0.235774 | − | 0.406596i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.86358 | + | 8.86358i | −0.00966585 | + | 0.00966585i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 765.918i | 0.833426i | 0.909038 | + | 0.416713i | \(0.136818\pi\) | ||||
−0.909038 | + | 0.416713i | \(0.863182\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1474.79 | − | 392.182i | 1.60129 | − | 0.425822i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −55.9153 | + | 55.9153i | −0.0605800 | + | 0.0605800i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −575.698 | + | 575.698i | −0.622377 | + | 0.622377i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1202.49 | + | 688.208i | −1.29718 | + | 0.742403i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1283.88i | 1.38200i | 0.722855 | + | 0.691000i | \(0.242830\pi\) | ||||
−0.722855 | + | 0.691000i | \(0.757170\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −95.2993 | + | 95.2993i | −0.102362 | + | 0.102362i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1484.50 | − | 860.819i | −1.59110 | − | 0.922635i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 392.597 | 0.419890 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1617.33i | − | 1.72607i | −0.505141 | − | 0.863037i | \(-0.668560\pi\) | ||
0.505141 | − | 0.863037i | \(-0.331440\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 501.607 | − | 865.029i | 0.534193 | − | 0.921223i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −721.542 | − | 721.542i | −0.766782 | − | 0.766782i | 0.210757 | − | 0.977539i | \(-0.432407\pi\) |
−0.977539 | + | 0.210757i | \(0.932407\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 323.152 | 0.342685 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 515.172 | − | 509.362i | 0.545155 | − | 0.539008i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −442.411 | − | 442.411i | −0.467171 | − | 0.467171i | 0.433826 | − | 0.900997i | \(-0.357163\pi\) |
−0.900997 | + | 0.433826i | \(0.857163\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.59105 | − | 2.59105i | −0.00273029 | − | 0.00273029i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 290.444 | + | 1092.21i | 0.305409 | + | 1.14848i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 66.7031 | 0.0699928 | 0.0349964 | − | 0.999387i | \(-0.488858\pi\) | ||||
0.0349964 | + | 0.999387i | \(0.488858\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 390.260 | + | 390.260i | 0.408649 | + | 0.408649i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 90.6131 | + | 52.5441i | 0.0946845 | + | 0.0549050i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 1739.13i | − | 1.81348i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −747.600 | −0.777940 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −944.885 | − | 257.013i | −0.981189 | − | 0.266888i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −305.735 | + | 305.735i | −0.316823 | + | 0.316823i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 81.7617i | − | 0.0845519i | −0.999106 | − | 0.0422759i | \(-0.986539\pi\) | ||
0.999106 | − | 0.0422759i | \(-0.0134609\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −161.512 | − | 607.362i | −0.166679 | − | 0.626793i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −558.759 | + | 558.759i | −0.575447 | + | 0.575447i | −0.933646 | − | 0.358198i | \(-0.883391\pi\) |
0.358198 | + | 0.933646i | \(0.383391\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −193.971 | + | 193.971i | −0.199354 | + | 0.199354i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9.35219 | − | 35.1686i | −0.00959199 | − | 0.0360704i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 250.154i | 0.256043i | 0.991771 | + | 0.128021i | \(0.0408626\pi\) | ||||
−0.991771 | + | 0.128021i | \(0.959137\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −885.602 | + | 885.602i | −0.904599 | + | 0.904599i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −910.406 | − | 247.635i | −0.928039 | − | 0.252431i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1147.26 | −1.16710 | −0.583551 | − | 0.812077i | \(-0.698337\pi\) | ||||
−0.583551 | + | 0.812077i | \(0.698337\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 165.567i | 0.168088i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −693.548 | − | 402.170i | −0.702683 | − | 0.407467i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 565.203 | + | 565.203i | 0.571489 | + | 0.571489i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1364.34 | −1.37673 | −0.688364 | − | 0.725365i | \(-0.741671\pi\) | ||||
−0.688364 | + | 0.725365i | \(0.741671\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 231.620 | + | 871.000i | 0.233253 | + | 0.877140i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 333.569 | + | 333.569i | 0.335245 | + | 0.335245i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 328.128 | + | 328.128i | 0.329115 | + | 0.329115i | 0.852250 | − | 0.523135i | \(-0.175238\pi\) |
−0.523135 | + | 0.852250i | \(0.675238\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1360.38 | − | 1345.03i | 1.36174 | − | 1.34638i |
(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 | 384.3.i.c.353.2 | 20 | ||
3.2 | odd | 2 | inner | 384.3.i.c.353.8 | 20 | ||
4.3 | odd | 2 | 384.3.i.d.353.9 | 20 | |||
8.3 | odd | 2 | 48.3.i.b.5.9 | yes | 20 | ||
8.5 | even | 2 | 192.3.i.b.113.9 | 20 | |||
12.11 | even | 2 | 384.3.i.d.353.3 | 20 | |||
16.3 | odd | 4 | 384.3.i.d.161.3 | 20 | |||
16.5 | even | 4 | 192.3.i.b.17.3 | 20 | |||
16.11 | odd | 4 | 48.3.i.b.29.2 | yes | 20 | ||
16.13 | even | 4 | inner | 384.3.i.c.161.8 | 20 | ||
24.5 | odd | 2 | 192.3.i.b.113.3 | 20 | |||
24.11 | even | 2 | 48.3.i.b.5.2 | ✓ | 20 | ||
48.5 | odd | 4 | 192.3.i.b.17.9 | 20 | |||
48.11 | even | 4 | 48.3.i.b.29.9 | yes | 20 | ||
48.29 | odd | 4 | inner | 384.3.i.c.161.2 | 20 | ||
48.35 | even | 4 | 384.3.i.d.161.9 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.3.i.b.5.2 | ✓ | 20 | 24.11 | even | 2 | ||
48.3.i.b.5.9 | yes | 20 | 8.3 | odd | 2 | ||
48.3.i.b.29.2 | yes | 20 | 16.11 | odd | 4 | ||
48.3.i.b.29.9 | yes | 20 | 48.11 | even | 4 | ||
192.3.i.b.17.3 | 20 | 16.5 | even | 4 | |||
192.3.i.b.17.9 | 20 | 48.5 | odd | 4 | |||
192.3.i.b.113.3 | 20 | 24.5 | odd | 2 | |||
192.3.i.b.113.9 | 20 | 8.5 | even | 2 | |||
384.3.i.c.161.2 | 20 | 48.29 | odd | 4 | inner | ||
384.3.i.c.161.8 | 20 | 16.13 | even | 4 | inner | ||
384.3.i.c.353.2 | 20 | 1.1 | even | 1 | trivial | ||
384.3.i.c.353.8 | 20 | 3.2 | odd | 2 | inner | ||
384.3.i.d.161.3 | 20 | 16.3 | odd | 4 | |||
384.3.i.d.161.9 | 20 | 48.35 | even | 4 | |||
384.3.i.d.353.3 | 20 | 12.11 | even | 2 | |||
384.3.i.d.353.9 | 20 | 4.3 | odd | 2 |