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: | \( x^{20} - 2 x^{18} + 6 x^{16} - 24 x^{14} - 24 x^{12} + 1216 x^{10} - 384 x^{8} - 6144 x^{6} + \cdots + 1048576 \) |
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 | 353.3 | ||
Root | \(-1.85381 - 0.750590i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.353 |
Dual form | 384.3.i.d.161.3 |
$q$-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 | ||||||||
\(3\) | −1.50491 | − | 2.59524i | −0.501636 | − | 0.865079i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.59897 | − | 2.59897i | 0.519793 | − | 0.519793i | −0.397716 | − | 0.917509i | \(-0.630197\pi\) |
0.917509 | + | 0.397716i | \(0.130197\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.30027i | 1.04290i | 0.853283 | + | 0.521448i | \(0.174608\pi\) | ||||
−0.853283 | + | 0.521448i | \(0.825392\pi\) | |||||||
\(8\) | 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 | \(-0.937104\pi\) | ||
0.980542 | − | 0.196310i | \(-0.0628957\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −22.1936 | + | 22.1936i | −1.16809 | + | 1.16809i | −0.185428 | + | 0.982658i | \(0.559367\pi\) |
−0.982658 | + | 0.185428i | \(0.940633\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 18.9459 | − | 10.9862i | 0.902187 | − | 0.523154i | ||||
\(22\) | 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 | ||||||||
\(27\) | 26.9996 | − | 0.153096i | 0.999984 | − | 0.00567024i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.54272 | − | 1.54272i | −0.0531973 | − | 0.0531973i | 0.680008 | − | 0.733205i | \(-0.261976\pi\) |
−0.733205 | + | 0.680008i | \(0.761976\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −14.6082 | −0.471233 | −0.235616 | − | 0.971846i | \(-0.575711\pi\) | ||||
−0.235616 | + | 0.971846i | \(0.575711\pi\) | |||||||
\(32\) | 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 | \(-0.558846\pi\) | ||||
−0.183819 | + | 0.982960i | \(0.558846\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −26.3634 | − | 26.3634i | −0.613102 | − | 0.613102i | 0.330651 | − | 0.943753i | \(-0.392732\pi\) |
−0.943753 | + | 0.330651i | \(0.892732\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.68231 | + | 31.9197i | 0.192940 | + | 0.709326i | ||||
\(46\) | 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 | ||||||||
\(51\) | −17.3220 | + | 10.0445i | −0.339646 | + | 0.196952i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −50.9270 | + | 50.9270i | −0.960887 | + | 0.960887i | −0.999263 | − | 0.0383765i | \(-0.987781\pi\) |
0.0383765 | + | 0.999263i | \(0.487781\pi\) | |||||||
\(54\) | 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 | −0.670047 | − | 0.742318i | \(-0.733726\pi\) |
0.742318 | + | 0.670047i | \(0.233726\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −32.2636 | − | 55.6391i | −0.467589 | − | 0.806364i | ||||
\(70\) | 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 | ||||||||
\(75\) | 29.8212 | − | 17.2925i | 0.397616 | − | 0.230567i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −82.6105 | − | 82.6105i | −1.07286 | − | 1.07286i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 103.463 | 1.30966 | 0.654831 | − | 0.755775i | \(-0.272740\pi\) | ||||
0.654831 | + | 0.755775i | \(0.272740\pi\) | |||||||
\(80\) | 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 | \(-0.644903\pi\) | ||||
−0.439666 | + | 0.898162i | \(0.644903\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.44937 | + | 5.44937i | 0.0598832 | + | 0.0598832i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 21.9840 | + | 37.9118i | 0.236387 | + | 0.407653i | ||||
\(94\) | 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 | ||||||||
\(99\) | −37.8034 | − | 138.981i | −0.381853 | − | 1.40384i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 56.9675 | − | 56.9675i | 0.564034 | − | 0.564034i | −0.366417 | − | 0.930451i | \(-0.619415\pi\) |
0.930451 | + | 0.366417i | \(0.119415\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 153.944i | − | 1.49460i | −0.664485 | − | 0.747301i | \(-0.731349\pi\) | ||
0.664485 | − | 0.747301i | \(-0.268651\pi\) | |||||||
\(104\) | 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 | \(0.0543352\pi\) | ||||
−0.985466 | + | 0.169871i | \(0.945665\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 55.7191 | − | 55.7191i | 0.484514 | − | 0.484514i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.49369 | + | 9.16781i | 0.0213136 | + | 0.0783573i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 48.7259 | 0.409461 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 135.108i | − | 1.11659i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 22.6837 | + | 39.1184i | 0.184420 | + | 0.318035i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 94.8382 | + | 94.8382i | 0.758706 | + | 0.758706i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −43.3417 | −0.341273 | −0.170636 | − | 0.985334i | \(-0.554582\pi\) | ||||
−0.170636 | + | 0.985334i | \(0.554582\pi\) | |||||||
\(128\) | 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 | \(-0.835522\pi\) | ||||
−0.869443 | + | 0.494033i | \(0.835522\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 26.5704 | + | 26.5704i | 0.191154 | + | 0.191154i | 0.796195 | − | 0.605041i | \(-0.206843\pi\) |
−0.605041 | + | 0.796195i | \(0.706843\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 95.0030 | − | 55.0897i | 0.673780 | − | 0.390707i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16.8940i | 0.118140i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.01896 | −0.0553032 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.46207 | + | 11.1439i | 0.0439596 | + | 0.0758090i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −133.254 | + | 133.254i | −0.894321 | + | 0.894321i | −0.994926 | − | 0.100605i | \(-0.967922\pi\) |
0.100605 | + | 0.994926i | \(0.467922\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 23.3716i | − | 0.154779i | −0.997001 | − | 0.0773895i | \(-0.975342\pi\) | ||
0.997001 | − | 0.0773895i | \(-0.0246585\pi\) | |||||||
\(152\) | 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 | −0.314896 | − | 0.949126i | \(-0.601970\pi\) |
0.949126 | + | 0.314896i | \(0.101970\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 152.652 | − | 88.5190i | 0.925166 | − | 0.536479i | ||||
\(166\) | 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 | ||||||||
\(171\) | −74.1418 | − | 272.575i | −0.433578 | − | 1.59401i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −144.265 | − | 144.265i | −0.833901 | − | 0.833901i | 0.154147 | − | 0.988048i | \(-0.450737\pi\) |
−0.988048 | + | 0.154147i | \(0.950737\pi\) | |||||||
\(174\) | 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 | ||||||||
\(189\) | 1.11765 | + | 197.104i | 0.00591347 | + | 1.04288i | ||||
\(190\) | 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 | ||||||||
\(195\) | −10.0697 | + | 5.83913i | −0.0516393 | + | 0.0299442i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −31.8524 | + | 31.8524i | −0.161688 | + | 0.161688i | −0.783314 | − | 0.621626i | \(-0.786472\pi\) |
0.621626 | + | 0.783314i | \(0.286472\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 128.347i | 0.644959i | 0.946576 | + | 0.322480i | \(0.104516\pi\) | ||||
−0.946576 | + | 0.322480i | \(0.895484\pi\) | |||||||
\(200\) | 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 | −0.868743 | − | 0.495262i | \(-0.835072\pi\) |
0.495262 | + | 0.868743i | \(0.335072\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 112.728 | + | 194.402i | 0.529241 | + | 0.912685i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −137.035 | −0.637372 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 106.644i | − | 0.491447i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.00834 | + | 5.22369i | −0.0411340 | + | 0.0238525i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.98228 | − | 4.98228i | −0.0225442 | − | 0.0225442i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −153.748 | −0.689455 | −0.344727 | − | 0.938703i | \(-0.612029\pi\) | ||||
−0.344727 | + | 0.938703i | \(0.612029\pi\) | |||||||
\(224\) | 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 | \(-0.522204\pi\) | ||||
−0.0696980 | + | 0.997568i | \(0.522204\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 95.1395 | + | 95.1395i | 0.404849 | + | 0.404849i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −155.703 | − | 268.512i | −0.656974 | − | 1.13296i | ||||
\(238\) | 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 | ||||||||
\(243\) | −119.506 | + | 211.583i | −0.491793 | + | 0.870712i | ||||
\(244\) | 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 | \(0.233236\pi\) | ||||
−0.743350 | + | 0.668903i | \(0.766764\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −365.751 | + | 365.751i | −1.41217 | + | 1.41217i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 18.9472 | − | 5.15374i | 0.0725948 | − | 0.0197461i | ||||
\(262\) | 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 | ||||||||
\(267\) | 117.775 | + | 203.104i | 0.441104 | + | 0.760691i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 102.194 | + | 102.194i | 0.379904 | + | 0.379904i | 0.871067 | − | 0.491164i | \(-0.163428\pi\) |
−0.491164 | + | 0.871067i | \(0.663428\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −38.5636 | −0.142301 | −0.0711505 | − | 0.997466i | \(-0.522667\pi\) | ||||
−0.0711505 | + | 0.997466i | \(0.522667\pi\) | |||||||
\(272\) | 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 | \(-0.196017\pi\) | ||||
0.816308 | + | 0.577617i | \(0.196017\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −276.746 | − | 276.746i | −0.977900 | − | 0.977900i | 0.0218614 | − | 0.999761i | \(-0.493041\pi\) |
−0.999761 | + | 0.0218614i | \(0.993041\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 299.389 | − | 173.608i | 1.05049 | − | 0.609149i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 110.038i | − | 0.383408i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 244.451 | 0.845850 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 92.6499 | + | 159.776i | 0.318384 | + | 0.549059i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 306.513 | − | 306.513i | 1.04612 | − | 1.04612i | 0.0472370 | − | 0.998884i | \(-0.484958\pi\) |
0.998884 | − | 0.0472370i | \(-0.0150416\pi\) | |||||||
\(294\) | 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 | \(-0.439211\pi\) |
0.981820 | − | 0.189814i | \(-0.0607886\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −399.521 | + | 231.672i | −1.29295 | + | 0.749746i | ||||
\(310\) | 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 | ||||||||
\(315\) | −233.022 | + | 63.3832i | −0.739754 | + | 0.201217i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 266.382 | + | 266.382i | 0.840322 | + | 0.840322i | 0.988901 | − | 0.148578i | \(-0.0474697\pi\) |
−0.148578 | + | 0.988901i | \(0.547470\pi\) | |||||||
\(318\) | 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 | 0.950995 | − | 0.309208i | \(-0.100064\pi\) |
−0.309208 | + | 0.950995i | \(0.600064\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −615.325 | + | 167.371i | −1.84782 | + | 0.502617i | ||||
\(334\) | 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 | ||||||||
\(339\) | 99.6335 | − | 57.7748i | 0.293904 | − | 0.170427i | ||||
\(340\) | 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 | \(0.136387\pi\) | ||||
−0.909601 | + | 0.415482i | \(0.863613\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −194.681 | + | 194.681i | −0.548398 | + | 0.548398i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −73.3279 | − | 126.455i | −0.205400 | − | 0.354216i | ||||
\(358\) | 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 | ||||||||
\(363\) | −350.636 | + | 203.324i | −0.965939 | + | 0.560122i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.02128 | − | 9.02128i | −0.0247158 | − | 0.0247158i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 221.149 | 0.602585 | 0.301292 | − | 0.953532i | \(-0.402582\pi\) | ||||
0.301292 | + | 0.953532i | \(0.402582\pi\) | |||||||
\(368\) | 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 | 0.193342 | − | 0.981131i | \(-0.438067\pi\) |
−0.981131 | + | 0.193342i | \(0.938067\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 65.2252 | + | 112.482i | 0.171195 | + | 0.295228i | ||||
\(382\) | 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 | ||||||||
\(387\) | 323.787 | − | 88.0716i | 0.836658 | − | 0.227575i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 314.075 | − | 314.075i | 0.807391 | − | 0.807391i | −0.176847 | − | 0.984238i | \(-0.556590\pi\) |
0.984238 | + | 0.176847i | \(0.0565899\pi\) | |||||||
\(390\) | 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 | \(0.108548\pi\) | ||||
−0.942416 | + | 0.334443i | \(0.891452\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.9045 | + | 10.9045i | −0.0270582 | + | 0.0270582i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −288.145 | − | 74.8780i | −0.711469 | − | 0.184884i | ||||
\(406\) | 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 | ||||||||
\(411\) | 358.510 | + | 618.257i | 0.872288 | + | 1.50427i | ||||
\(412\) | 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 | ||||||||
\(429\) | 43.8440 | − | 25.4240i | 0.102201 | − | 0.0592634i | ||||
\(430\) | 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 | ||||||||
\(435\) | 12.0678 | + | 20.8111i | 0.0277421 | + | 0.0478416i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −475.808 | + | 475.808i | −1.08881 | + | 1.08881i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 486.389i | − | 1.10795i | −0.832534 | − | 0.553973i | \(-0.813111\pi\) | ||
0.832534 | − | 0.553973i | \(-0.186889\pi\) | |||||||
\(440\) | 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 | \(-0.812878\pi\) | ||
0.832129 | − | 0.554582i | \(-0.187122\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 170.569 | − | 170.569i | 0.378201 | − | 0.378201i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −60.6549 | + | 35.1721i | −0.133896 | + | 0.0776427i | ||||
\(454\) | 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 | ||||||||
\(459\) | −1.02185 | − | 180.209i | −0.00222624 | − | 0.392613i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −389.251 | − | 389.251i | −0.844362 | − | 0.844362i | 0.145061 | − | 0.989423i | \(-0.453662\pi\) |
−0.989423 | + | 0.145061i | \(0.953662\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 500.857 | 1.08177 | 0.540883 | − | 0.841098i | \(-0.318090\pi\) | ||||
0.540883 | + | 0.841098i | \(0.318090\pi\) | |||||||
\(464\) | 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 | ||||||||
\(477\) | −170.131 | − | 625.470i | −0.356668 | − | 1.31126i | ||||
\(478\) | 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 | ||||||||
\(483\) | 406.181 | − | 235.533i | 0.840954 | − | 0.487647i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −160.006 | + | 160.006i | −0.329909 | + | 0.329909i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 196.238i | 0.402952i | 0.979493 | + | 0.201476i | \(0.0645739\pi\) | ||||
−0.979493 | + | 0.201476i | \(0.935426\pi\) | |||||||
\(488\) | 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 | −0.307582 | − | 0.951522i | \(-0.599520\pi\) |
0.951522 | + | 0.307582i | \(0.0995198\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −171.530 | − | 295.805i | −0.342374 | − | 0.590430i | ||||
\(502\) | 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 | ||||||||
\(507\) | 435.703 | − | 252.652i | 0.859374 | − | 0.498328i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 452.448 | + | 452.448i | 0.888897 | + | 0.888897i | 0.994417 | − | 0.105520i | \(-0.0336508\pi\) |
−0.105520 | + | 0.994417i | \(0.533651\pi\) | |||||||
\(510\) | 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 | \(-0.359553\pi\) | ||||
0.427050 | + | 0.904228i | \(0.359553\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −399.942 | − | 399.942i | −0.764707 | − | 0.764707i | 0.212462 | − | 0.977169i | \(-0.431852\pi\) |
−0.977169 | + | 0.212462i | \(0.931852\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 126.240 | + | 217.703i | 0.240458 | + | 0.414673i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 97.5029i | 0.185015i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −69.3715 | −0.131137 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 40.6504 | + | 149.447i | 0.0765544 | + | 0.281445i | ||||
\(532\) | 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 | −0.781084 | − | 0.624427i | \(-0.785333\pi\) |
0.624427 | + | 0.781084i | \(0.285333\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 92.1322 | + | 338.715i | 0.167818 | + | 0.616968i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 68.4772 | 0.124278 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 755.311i | 1.36584i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −391.910 | − | 675.855i | −0.706145 | − | 1.21776i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 104.194 | + | 104.194i | 0.187062 | + | 0.187062i | 0.794425 | − | 0.607363i | \(-0.207772\pi\) |
−0.607363 | + | 0.794425i | \(0.707772\pi\) | |||||||
\(558\) | 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 | \(-0.631401\pi\) | ||||
−0.401183 | + | 0.915998i | \(0.631401\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 475.108 | + | 475.108i | 0.832062 | + | 0.832062i | 0.987799 | − | 0.155736i | \(-0.0497750\pi\) |
−0.155736 | + | 0.987799i | \(0.549775\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −389.700 | + | 225.977i | −0.680105 | + | 0.394375i | ||||
\(574\) | 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 | ||||||||
\(579\) | −177.033 | − | 305.296i | −0.305756 | − | 0.527281i | ||||
\(580\) | 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 | \(0.262500\pi\) | ||||
−0.678801 | + | 0.734322i | \(0.737500\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 126.637 | − | 126.637i | 0.212835 | − | 0.212835i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 333.090 | − | 193.150i | 0.557940 | − | 0.323535i | ||||
\(598\) | 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 | ||||||||
\(603\) | 16.1760 | + | 59.4697i | 0.0268259 | + | 0.0986230i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −351.140 | − | 351.140i | −0.580396 | − | 0.580396i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −620.755 | −1.02266 | −0.511330 | − | 0.859384i | \(-0.670847\pi\) | ||||
−0.511330 | + | 0.859384i | \(0.670847\pi\) | |||||||
\(608\) | 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 | \(-0.543961\pi\) | ||||
−0.137669 | + | 0.990478i | \(0.543961\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 647.603 | + | 647.603i | 1.04621 | + | 1.04621i | 0.998879 | + | 0.0473286i | \(0.0150708\pi\) |
0.0473286 | + | 0.998879i | \(0.484929\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 578.842 | − | 3.28222i | 0.932113 | − | 0.00528539i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 571.323i | − | 0.917051i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 205.694 | 0.329110 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1303.56 | + | 755.900i | −2.07904 | + | 1.20558i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 334.400 | − | 334.400i | 0.531638 | − | 0.531638i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 975.374i | 1.54576i | 0.634553 | + | 0.772880i | \(0.281184\pi\) | ||||
−0.634553 | + | 0.772880i | \(0.718816\pi\) | |||||||
\(632\) | 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 | \(-0.794436\pi\) | ||
0.798619 | − | 0.601837i | \(-0.205564\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −319.214 | + | 319.214i | −0.496445 | + | 0.496445i | −0.910330 | − | 0.413884i | \(-0.864172\pi\) |
0.413884 | + | 0.910330i | \(0.364172\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 206.225 | + | 355.638i | 0.319729 | + | 0.551377i | ||||
\(646\) | 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 | ||||||||
\(651\) | −276.766 | + | 160.489i | −0.425140 | + | 0.246527i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 415.043 | + | 415.043i | 0.635595 | + | 0.635595i | 0.949466 | − | 0.313871i | \(-0.101626\pi\) |
−0.313871 | + | 0.949466i | \(0.601626\pi\) | |||||||
\(654\) | 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 | ||||||||
\(669\) | 231.377 | + | 399.013i | 0.345855 | + | 0.596433i | ||||
\(670\) | 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 | ||||||||
\(675\) | 1.75919 | + | 310.245i | 0.00260621 | + | 0.459623i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 639.750 | − | 639.750i | 0.944978 | − | 0.944978i | −0.0535849 | − | 0.998563i | \(-0.517065\pi\) |
0.998563 | + | 0.0535849i | \(0.0170648\pi\) | |||||||
\(678\) | 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 | −0.891916 | − | 0.452200i | \(-0.850639\pi\) |
0.452200 | + | 0.891916i | \(0.350639\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1014.60 | − | 275.975i | 1.46406 | − | 0.398233i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 138.111 | 0.198721 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 100.606i | 0.144341i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 48.8783 | + | 84.2914i | 0.0699261 | + | 0.120589i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −797.170 | − | 797.170i | −1.13719 | − | 1.13719i | −0.988952 | − | 0.148238i | \(-0.952640\pi\) |
−0.148238 | − | 0.988952i | \(-0.547360\pi\) | |||||||
\(702\) | 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 | ||||||||
\(717\) | 345.959 | − | 200.612i | 0.482508 | − | 0.279794i | ||||
\(718\) | 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 | ||||||||
\(723\) | −240.289 | − | 414.382i | −0.332350 | − | 0.573142i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 17.7270 | − | 17.7270i | 0.0244511 | − | 0.0244511i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1182.91i | 1.62711i | 0.581490 | + | 0.813553i | \(0.302470\pi\) | ||||
−0.581490 | + | 0.813553i | \(0.697530\pi\) | |||||||
\(728\) | 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 | −0.927274 | − | 0.374383i | \(-0.877855\pi\) |
0.374383 | + | 0.927274i | \(0.377855\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 85.9889 | − | 49.8627i | 0.116044 | − | 0.0672911i | ||||
\(742\) | 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 | ||||||||
\(747\) | −389.641 | + | 105.984i | −0.521608 | + | 0.141880i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −561.642 | − | 561.642i | −0.749856 | − | 0.749856i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 835.943 | 1.11311 | 0.556553 | − | 0.830812i | \(-0.312124\pi\) | ||||
0.556553 | + | 0.830812i | \(0.312124\pi\) | |||||||
\(752\) | 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 | \(-0.802565\pi\) | ||||
−0.813727 | + | 0.581247i | \(0.802565\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −541.148 | − | 541.148i | −0.709238 | − | 0.709238i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 213.049 | − | 57.9503i | 0.278495 | − | 0.0757520i | ||||
\(766\) | 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 | ||||||||
\(771\) | 892.284 | − | 517.411i | 1.15731 | − | 0.671091i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −989.152 | + | 989.152i | −1.27963 | + | 1.27963i | −0.338752 | + | 0.940876i | \(0.610005\pi\) |
−0.940876 | + | 0.338752i | \(0.889995\pi\) | |||||||
\(774\) | 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 | −0.767786 | − | 0.640706i | \(-0.778642\pi\) |
0.640706 | + | 0.767786i | \(0.278642\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 400.689 | + | 690.994i | 0.507844 | + | 0.875785i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −280.264 | −0.354316 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 41.1731i | − | 0.0519207i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 686.998 | − | 398.372i | 0.864149 | − | 0.501097i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 264.491 | + | 264.491i | 0.331858 | + | 0.331858i | 0.853292 | − | 0.521433i | \(-0.174603\pi\) |
−0.521433 | + | 0.853292i | \(0.674603\pi\) | |||||||
\(798\) | 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 | \(-0.277391\pi\) | ||||
0.643717 | + | 0.765264i | \(0.277391\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 442.482 | + | 442.482i | 0.545600 | + | 0.545600i | 0.925165 | − | 0.379565i | \(-0.123926\pi\) |
−0.379565 | + | 0.925165i | \(0.623926\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 58.0346 | + | 100.082i | 0.0713833 | + | 0.123102i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 537.359i | − | 0.659337i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1170.20 | 1.43231 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −66.9275 | + | 18.2046i | −0.0817186 | + | 0.0222279i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 104.027 | − | 104.027i | 0.126708 | − | 0.126708i | −0.640909 | − | 0.767617i | \(-0.721442\pi\) |
0.767617 | + | 0.640909i | \(0.221442\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 349.420i | − | 0.424568i | −0.977208 | − | 0.212284i | \(-0.931910\pi\) | ||
0.977208 | − | 0.212284i | \(-0.0680902\pi\) | |||||||
\(824\) | 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 | ||||||||
\(837\) | −394.415 | + | 2.23646i | −0.471225 | + | 0.00267200i | ||||
\(838\) | 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 | ||||||||
\(843\) | −690.399 | − | 1190.60i | −0.818979 | − | 1.41234i | ||||
\(844\) | 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 | \(-0.451279\pi\) | ||||
0.152465 | + | 0.988309i | \(0.451279\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 81.4524 | + | 81.4524i | 0.0948224 | + | 0.0948224i | 0.752927 | − | 0.658104i | \(-0.228641\pi\) |
−0.658104 | + | 0.752927i | \(0.728641\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −285.575 | + | 165.597i | −0.331678 | + | 0.192331i | ||||
\(862\) | 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 | ||||||||
\(867\) | −367.876 | − | 634.407i | −0.424309 | − | 0.731727i | ||||
\(868\) | 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 | \(0.404099\pi\) | ||||
−0.296744 | + | 0.954957i | \(0.595901\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 477.885 | − | 477.885i | 0.541206 | − | 0.541206i | −0.382676 | − | 0.923882i | \(-0.624998\pi\) |
0.923882 | + | 0.382676i | \(0.124998\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −164.149 | + | 95.1854i | −0.185479 | + | 0.107554i | ||||
\(886\) | 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 | ||||||||
\(891\) | 1254.60 | + | 326.024i | 1.40808 | + | 0.365908i | ||||
\(892\) | 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 | 0.501041 | − | 0.865424i | \(-0.332951\pi\) |
−0.865424 | + | 0.501041i | \(0.832951\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 190.310 | + | 699.657i | 0.209362 | + | 0.769699i | ||||
\(910\) | 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 | ||||||||
\(915\) | −372.035 | + | 215.733i | −0.406596 | + | 0.235774i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.86358 | − | 8.86358i | 0.00966585 | − | 0.00966585i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 765.918i | − | 0.833426i | −0.909038 | − | 0.416713i | \(-0.863182\pi\) | ||
0.909038 | − | 0.416713i | \(-0.136818\pi\) | |||||||
\(920\) | 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 | \(-0.757170\pi\) | ||
0.722855 | − | 0.691000i | \(-0.242830\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 95.2993 | − | 95.2993i | 0.102362 | − | 0.102362i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −860.819 | − | 1484.50i | −0.922635 | − | 1.59110i | ||||
\(934\) | 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 | ||||||||
\(939\) | 865.029 | − | 501.607i | 0.921223 | − | 0.534193i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 721.542 | + | 721.542i | 0.766782 | + | 0.766782i | 0.977539 | − | 0.210757i | \(-0.0675928\pi\) |
−0.210757 | + | 0.977539i | \(0.567593\pi\) | |||||||
\(942\) | 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 | \(-0.511142\pi\) | ||||
−0.0349964 | + | 0.999387i | \(0.511142\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −390.260 | − | 390.260i | −0.408649 | − | 0.408649i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −52.5441 | − | 90.6131i | −0.0549050 | − | 0.0946845i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 1739.13i | − | 1.81348i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −747.600 | −0.777940 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −257.013 | − | 944.885i | −0.266888 | − | 0.981189i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 305.735 | − | 305.735i | 0.316823 | − | 0.316823i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 81.7617i | 0.0845519i | 0.999106 | + | 0.0422759i | \(0.0134609\pi\) | ||||
−0.999106 | + | 0.0422759i | \(0.986539\pi\) | |||||||
\(968\) | 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 | \(-0.959137\pi\) | ||
0.991771 | − | 0.128021i | \(-0.0408626\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 885.602 | − | 885.602i | 0.904599 | − | 0.904599i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −247.635 | − | 910.406i | −0.252431 | − | 0.928039i | ||||
\(982\) | 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 | ||||||||
\(987\) | 402.170 | + | 693.548i | 0.407467 | + | 0.702683i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −565.203 | − | 565.203i | −0.571489 | − | 0.571489i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1364.34 | 1.37673 | 0.688364 | − | 0.725365i | \(-0.258329\pi\) | ||||
0.688364 | + | 0.725365i | \(0.258329\pi\) | |||||||
\(992\) | 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.d.353.3 | 20 | ||
3.2 | odd | 2 | inner | 384.3.i.d.353.9 | 20 | ||
4.3 | odd | 2 | 384.3.i.c.353.8 | 20 | |||
8.3 | odd | 2 | 192.3.i.b.113.3 | 20 | |||
8.5 | even | 2 | 48.3.i.b.5.2 | ✓ | 20 | ||
12.11 | even | 2 | 384.3.i.c.353.2 | 20 | |||
16.3 | odd | 4 | 384.3.i.c.161.2 | 20 | |||
16.5 | even | 4 | 48.3.i.b.29.9 | yes | 20 | ||
16.11 | odd | 4 | 192.3.i.b.17.9 | 20 | |||
16.13 | even | 4 | inner | 384.3.i.d.161.9 | 20 | ||
24.5 | odd | 2 | 48.3.i.b.5.9 | yes | 20 | ||
24.11 | even | 2 | 192.3.i.b.113.9 | 20 | |||
48.5 | odd | 4 | 48.3.i.b.29.2 | yes | 20 | ||
48.11 | even | 4 | 192.3.i.b.17.3 | 20 | |||
48.29 | odd | 4 | inner | 384.3.i.d.161.3 | 20 | ||
48.35 | even | 4 | 384.3.i.c.161.8 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.3.i.b.5.2 | ✓ | 20 | 8.5 | even | 2 | ||
48.3.i.b.5.9 | yes | 20 | 24.5 | odd | 2 | ||
48.3.i.b.29.2 | yes | 20 | 48.5 | odd | 4 | ||
48.3.i.b.29.9 | yes | 20 | 16.5 | even | 4 | ||
192.3.i.b.17.3 | 20 | 48.11 | even | 4 | |||
192.3.i.b.17.9 | 20 | 16.11 | odd | 4 | |||
192.3.i.b.113.3 | 20 | 8.3 | odd | 2 | |||
192.3.i.b.113.9 | 20 | 24.11 | even | 2 | |||
384.3.i.c.161.2 | 20 | 16.3 | odd | 4 | |||
384.3.i.c.161.8 | 20 | 48.35 | even | 4 | |||
384.3.i.c.353.2 | 20 | 12.11 | even | 2 | |||
384.3.i.c.353.8 | 20 | 4.3 | odd | 2 | |||
384.3.i.d.161.3 | 20 | 48.29 | odd | 4 | inner | ||
384.3.i.d.161.9 | 20 | 16.13 | even | 4 | inner | ||
384.3.i.d.353.3 | 20 | 1.1 | even | 1 | trivial | ||
384.3.i.d.353.9 | 20 | 3.2 | odd | 2 | inner |