Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,3,Mod(95,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.95");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.r (of order \(6\), degree \(2\), 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: | \(6.10355792167\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 28 x^{9} - 100 x^{8} + 140 x^{7} + 392 x^{6} + 1400 x^{5} + 8040 x^{4} + 11256 x^{3} + \cdots + 9604 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 191.1 | ||
Root | \(0.630651 + 2.35362i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 224.191 |
Dual form | 224.3.r.c.95.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −3.85030 | + | 2.22297i | −1.28343 | + | 0.740990i | −0.977474 | − | 0.211055i | \(-0.932310\pi\) |
−0.305958 | + | 0.952045i | \(0.598977\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.88318 | − | 4.99382i | 0.576637 | − | 0.998764i | −0.419225 | − | 0.907882i | \(-0.637698\pi\) |
0.995862 | − | 0.0908820i | \(-0.0289686\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.85985 | + | 3.82912i | −0.837121 | + | 0.547018i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.38318 | − | 9.32395i | 0.598132 | − | 1.03599i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 16.6383 | − | 9.60615i | 1.51258 | − | 0.873287i | 0.512685 | − | 0.858577i | \(-0.328651\pi\) |
0.999892 | − | 0.0147100i | \(-0.00468252\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.23363 | −0.402587 | −0.201293 | − | 0.979531i | \(-0.564514\pi\) | ||||
−0.201293 | + | 0.979531i | \(0.564514\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 25.6369i | 1.70913i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 14.5414 | + | 25.1865i | 0.855378 | + | 1.48156i | 0.876294 | + | 0.481777i | \(0.160009\pi\) |
−0.0209153 | + | 0.999781i | \(0.506658\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 9.49276 | + | 5.48065i | 0.499619 | + | 0.288455i | 0.728556 | − | 0.684986i | \(-0.240192\pi\) |
−0.228937 | + | 0.973441i | \(0.573525\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 14.0501 | − | 27.7695i | 0.669053 | − | 1.32236i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 11.3335 | + | 6.54340i | 0.492761 | + | 0.284496i | 0.725719 | − | 0.687991i | \(-0.241507\pi\) |
−0.232958 | + | 0.972487i | \(0.574841\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.12551 | − | 7.14559i | −0.165020 | − | 0.285824i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 7.85317i | 0.290858i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 46.5849 | 1.60638 | 0.803188 | − | 0.595726i | \(-0.203136\pi\) | ||||
0.803188 | + | 0.595726i | \(0.203136\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.8201 | − | 6.24702i | 0.349037 | − | 0.201517i | −0.315224 | − | 0.949017i | \(-0.602080\pi\) |
0.664261 | + | 0.747501i | \(0.268746\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −42.7084 | + | 73.9731i | −1.29419 | + | 2.24161i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.22694 | + | 40.3031i | 0.0636268 | + | 1.15152i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.90723 | − | 6.76752i | 0.105601 | − | 0.182906i | −0.808383 | − | 0.588657i | \(-0.799657\pi\) |
0.913984 | + | 0.405751i | \(0.132990\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 20.1510 | − | 11.6342i | 0.516693 | − | 0.298313i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 34.5154 | 0.841838 | 0.420919 | − | 0.907098i | \(-0.361708\pi\) | ||||
0.420919 | + | 0.907098i | \(0.361708\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 22.6330i | 0.526349i | 0.964748 | + | 0.263174i | \(0.0847694\pi\) | ||||
−0.964748 | + | 0.263174i | \(0.915231\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −31.0414 | − | 53.7653i | −0.689810 | − | 1.19479i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −32.2200 | − | 18.6022i | −0.685532 | − | 0.395792i | 0.116404 | − | 0.993202i | \(-0.462863\pi\) |
−0.801936 | + | 0.597410i | \(0.796196\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 19.6756 | − | 44.8762i | 0.401543 | − | 0.915840i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −111.978 | − | 64.6503i | −2.19564 | − | 1.26765i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −38.6002 | − | 66.8576i | −0.728307 | − | 1.26146i | −0.957598 | − | 0.288106i | \(-0.906974\pi\) |
0.229292 | − | 0.973358i | \(-0.426359\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 110.785i | − | 2.01428i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −48.7332 | −0.854969 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −34.2179 | + | 19.7557i | −0.579964 | + | 0.334843i | −0.761119 | − | 0.648612i | \(-0.775350\pi\) |
0.181155 | + | 0.983455i | \(0.442016\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −23.8418 | + | 41.2951i | −0.390848 | + | 0.676969i | −0.992562 | − | 0.121743i | \(-0.961152\pi\) |
0.601713 | + | 0.798712i | \(0.294485\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.15791 | + | 75.2498i | 0.0659985 | + | 1.19444i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −15.0895 | + | 26.1358i | −0.232147 | + | 0.402090i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 77.1378 | − | 44.5355i | 1.15131 | − | 0.664709i | 0.202104 | − | 0.979364i | \(-0.435222\pi\) |
0.949206 | + | 0.314655i | \(0.101889\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −58.1831 | −0.843233 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 92.5129i | − | 1.30300i | −0.758649 | − | 0.651499i | \(-0.774140\pi\) | ||
0.758649 | − | 0.651499i | \(-0.225860\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.4093 | + | 24.9576i | 0.197387 | + | 0.341885i | 0.947680 | − | 0.319221i | \(-0.103421\pi\) |
−0.750293 | + | 0.661105i | \(0.770088\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 31.7688 | + | 18.3418i | 0.423585 | + | 0.244557i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −60.7150 | + | 120.001i | −0.788507 | + | 1.55845i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 37.4277 | + | 21.6089i | 0.473768 | + | 0.273530i | 0.717816 | − | 0.696233i | \(-0.245142\pi\) |
−0.244048 | + | 0.969763i | \(0.578475\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 30.9913 | + | 53.6785i | 0.382609 | + | 0.662698i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 6.88400i | − | 0.0829398i | −0.999140 | − | 0.0414699i | \(-0.986796\pi\) | ||
0.999140 | − | 0.0414699i | \(-0.0132041\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 167.703 | 1.97297 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −179.366 | + | 103.557i | −2.06167 | + | 1.19031i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −57.2838 | + | 99.2184i | −0.643638 | + | 1.11481i | 0.340977 | + | 0.940072i | \(0.389242\pi\) |
−0.984614 | + | 0.174741i | \(0.944091\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 30.6683 | − | 20.0402i | 0.337014 | − | 0.220222i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −27.7738 | + | 48.1057i | −0.298644 | + | 0.517266i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 54.7387 | − | 31.6034i | 0.576197 | − | 0.332668i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −117.928 | −1.21575 | −0.607876 | − | 0.794032i | \(-0.707978\pi\) | ||||
−0.607876 | + | 0.794032i | \(0.707978\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 206.847i | − | 2.08936i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −48.9353 | − | 84.7585i | −0.484508 | − | 0.839193i | 0.515333 | − | 0.856990i | \(-0.327668\pi\) |
−0.999842 | + | 0.0177968i | \(0.994335\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 132.855 | + | 76.7037i | 1.28985 | + | 0.744696i | 0.978628 | − | 0.205641i | \(-0.0659279\pi\) |
0.311224 | + | 0.950337i | \(0.399261\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −98.1669 | − | 150.228i | −0.934923 | − | 1.43075i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 78.6271 | + | 45.3954i | 0.734832 | + | 0.424256i | 0.820187 | − | 0.572095i | \(-0.193869\pi\) |
−0.0853551 | + | 0.996351i | \(0.527202\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 19.0087 | + | 32.9240i | 0.174392 | + | 0.302055i | 0.939951 | − | 0.341311i | \(-0.110871\pi\) |
−0.765559 | + | 0.643366i | \(0.777537\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 34.7426i | 0.312997i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 118.024 | 1.04446 | 0.522231 | − | 0.852804i | \(-0.325100\pi\) | ||||
0.522231 | + | 0.852804i | \(0.325100\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 65.3532 | − | 37.7317i | 0.568288 | − | 0.328101i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −28.1736 | + | 48.7981i | −0.240800 | + | 0.417078i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −181.653 | − | 91.9081i | −1.52649 | − | 0.772337i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 124.056 | − | 214.872i | 1.02526 | − | 1.77580i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −132.894 | + | 76.7266i | −1.08044 | + | 0.623793i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 96.5808 | 0.772647 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.58246i | 0.0675785i | 0.999429 | + | 0.0337892i | \(0.0107575\pi\) | ||||
−0.999429 | + | 0.0337892i | \(0.989243\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −50.3124 | − | 87.1437i | −0.390019 | − | 0.675532i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −55.8213 | − | 32.2284i | −0.426116 | − | 0.246018i | 0.271574 | − | 0.962417i | \(-0.412456\pi\) |
−0.697691 | + | 0.716399i | \(0.745789\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −76.6122 | + | 4.23319i | −0.576031 | + | 0.0318285i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 39.2173 | + | 22.6421i | 0.290499 | + | 0.167720i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 49.0782 | + | 85.0060i | 0.358235 | + | 0.620482i | 0.987666 | − | 0.156575i | \(-0.0500452\pi\) |
−0.629431 | + | 0.777057i | \(0.716712\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 245.848i | 1.76869i | 0.466830 | + | 0.884347i | \(0.345396\pi\) | ||||
−0.466830 | + | 0.884347i | \(0.654604\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 165.409 | 1.17311 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −87.0790 | + | 50.2751i | −0.608944 | + | 0.351574i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 134.313 | − | 232.637i | 0.926296 | − | 1.60439i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 24.0013 | + | 216.525i | 0.163274 | + | 1.47296i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −79.0663 | + | 136.947i | −0.530646 | + | 0.919106i | 0.468714 | + | 0.883350i | \(0.344717\pi\) |
−0.999361 | + | 0.0357565i | \(0.988616\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.71809 | − | 0.991939i | 0.0113781 | − | 0.00656913i | −0.494300 | − | 0.869291i | \(-0.664576\pi\) |
0.505678 | + | 0.862722i | \(0.331242\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 313.117 | 2.04652 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 72.0452i | − | 0.464808i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −129.791 | − | 224.805i | −0.826696 | − | 1.43188i | −0.900616 | − | 0.434615i | \(-0.856884\pi\) |
0.0739206 | − | 0.997264i | \(-0.476449\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 297.245 | + | 171.614i | 1.86946 | + | 1.07934i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −91.4681 | + | 5.05404i | −0.568125 | + | 0.0313916i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −150.961 | − | 87.1575i | −0.926142 | − | 0.534709i | −0.0405529 | − | 0.999177i | \(-0.512912\pi\) |
−0.885589 | + | 0.464469i | \(0.846245\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 246.272 | + | 426.556i | 1.49256 | + | 2.58519i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 16.5232i | − | 0.0989415i | −0.998776 | − | 0.0494707i | \(-0.984247\pi\) | ||
0.998776 | − | 0.0494707i | \(-0.0157535\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −141.609 | −0.837924 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 102.203 | − | 59.0067i | 0.597676 | − | 0.345068i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.148738 | + | 0.257621i | −0.000859756 | + | 0.00148914i | −0.866455 | − | 0.499255i | \(-0.833607\pi\) |
0.865595 | + | 0.500744i | \(0.166940\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 51.5362 | + | 26.0750i | 0.294492 | + | 0.149000i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 87.8327 | − | 152.131i | 0.496230 | − | 0.859495i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −107.052 | + | 61.8065i | −0.598056 | + | 0.345288i | −0.768276 | − | 0.640118i | \(-0.778885\pi\) |
0.170220 | + | 0.985406i | \(0.445552\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 65.0497 | 0.359391 | 0.179695 | − | 0.983722i | \(-0.442489\pi\) | ||||
0.179695 | + | 0.983722i | \(0.442489\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 211.998i | − | 1.15846i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −22.5305 | − | 39.0240i | −0.121787 | − | 0.210941i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 483.891 | + | 279.374i | 2.58765 | + | 1.49398i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −30.0708 | − | 46.0184i | −0.159105 | − | 0.243483i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.2515 | − | 5.91871i | −0.0536728 | − | 0.0309880i | 0.472923 | − | 0.881104i | \(-0.343199\pi\) |
−0.526596 | + | 0.850115i | \(0.676532\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −29.4292 | − | 50.9730i | −0.152483 | − | 0.264109i | 0.779657 | − | 0.626207i | \(-0.215394\pi\) |
−0.932140 | + | 0.362099i | \(0.882060\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 134.174i | − | 0.688073i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −329.405 | −1.67211 | −0.836054 | − | 0.548647i | \(-0.815143\pi\) | ||||
−0.836054 | + | 0.548647i | \(0.815143\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.92070 | − | 4.57302i | 0.0398025 | − | 0.0229800i | −0.479967 | − | 0.877287i | \(-0.659351\pi\) |
0.519769 | + | 0.854307i | \(0.326018\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −198.002 | + | 342.950i | −0.985086 | + | 1.70622i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −272.980 | + | 178.379i | −1.34473 | + | 0.878716i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 99.5141 | − | 172.364i | 0.485435 | − | 0.840798i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 122.021 | − | 70.4487i | 0.589472 | − | 0.340332i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 210.592 | 1.00762 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 56.1119i | − | 0.265933i | −0.991121 | − | 0.132967i | \(-0.957550\pi\) | ||
0.991121 | − | 0.132967i | \(-0.0424503\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 205.653 | + | 356.202i | 0.965509 | + | 1.67231i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 113.025 | + | 65.2551i | 0.525698 | + | 0.303512i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −39.4838 | + | 78.0382i | −0.181953 | + | 0.359623i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −110.960 | − | 64.0627i | −0.506666 | − | 0.292524i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −76.1045 | − | 131.817i | −0.344364 | − | 0.596456i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 67.9891i | − | 0.304884i | −0.988312 | − | 0.152442i | \(-0.951286\pi\) | ||
0.988312 | − | 0.152442i | \(-0.0487137\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −88.8335 | −0.394815 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 214.074 | − | 123.596i | 0.943059 | − | 0.544475i | 0.0521408 | − | 0.998640i | \(-0.483396\pi\) |
0.890918 | + | 0.454165i | \(0.150062\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.8058 | + | 20.4482i | −0.0515536 | + | 0.0892934i | −0.890651 | − | 0.454688i | \(-0.849751\pi\) |
0.839097 | + | 0.543982i | \(0.183084\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −32.9874 | − | 597.007i | −0.142803 | − | 2.58444i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −69.4830 | + | 120.348i | −0.298210 | + | 0.516516i | −0.975727 | − | 0.218992i | \(-0.929723\pi\) |
0.677516 | + | 0.735508i | \(0.263056\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −185.792 | + | 107.267i | −0.790606 | + | 0.456456i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −192.143 | −0.810732 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 423.627i | 1.77250i | 0.463210 | + | 0.886248i | \(0.346697\pi\) | ||||
−0.463210 | + | 0.886248i | \(0.653303\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −122.283 | − | 211.800i | −0.507398 | − | 0.878839i | −0.999963 | − | 0.00856384i | \(-0.997274\pi\) |
0.492565 | − | 0.870276i | \(-0.336059\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −299.861 | − | 173.125i | −1.23400 | − | 0.712447i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −167.375 | − | 227.643i | −0.683164 | − | 0.929155i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −49.6816 | − | 28.6837i | −0.201140 | − | 0.116128i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.3029 | + | 26.5054i | 0.0614575 | + | 0.106448i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 176.193i | − | 0.701964i | −0.936382 | − | 0.350982i | \(-0.885848\pi\) | ||
0.936382 | − | 0.350982i | \(-0.114152\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 251.428 | 0.993785 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −645.704 | + | 372.798i | −2.53217 | + | 1.46195i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −25.5390 | + | 44.2348i | −0.0993735 | + | 0.172120i | −0.911426 | − | 0.411465i | \(-0.865017\pi\) |
0.812052 | + | 0.583585i | \(0.198351\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.01790 | + | 54.6179i | 0.0116521 | + | 0.210880i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 250.775 | − | 434.355i | 0.960824 | − | 1.66420i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −167.852 | + | 96.9095i | −0.638221 | + | 0.368477i | −0.783929 | − | 0.620851i | \(-0.786787\pi\) |
0.145708 | + | 0.989328i | \(0.453454\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −445.167 | −1.67987 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 509.360i | − | 1.90772i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.00342 | − | 5.20207i | −0.0111651 | − | 0.0193385i | 0.860389 | − | 0.509638i | \(-0.170221\pi\) |
−0.871554 | + | 0.490300i | \(0.836887\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −341.760 | − | 197.315i | −1.26111 | − | 0.728101i | −0.287819 | − | 0.957685i | \(-0.592930\pi\) |
−0.973289 | + | 0.229584i | \(0.926263\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −73.5332 | + | 145.335i | −0.269352 | + | 0.532364i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −137.283 | − | 79.2605i | −0.499212 | − | 0.288220i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −148.982 | − | 258.045i | −0.537842 | − | 0.931570i | −0.999020 | − | 0.0442619i | \(-0.985906\pi\) |
0.461178 | − | 0.887308i | \(-0.347427\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 134.515i | − | 0.482134i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 431.477 | 1.53551 | 0.767753 | − | 0.640746i | \(-0.221375\pi\) | ||||
0.767753 | + | 0.640746i | \(0.221375\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 383.084 | − | 221.174i | 1.35365 | − | 0.781532i | 0.364895 | − | 0.931049i | \(-0.381105\pi\) |
0.988759 | + | 0.149516i | \(0.0477717\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −140.507 | + | 243.365i | −0.493007 | + | 0.853913i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −202.255 | + | 132.164i | −0.704720 | + | 0.460500i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −278.406 | + | 482.214i | −0.963344 | + | 1.66856i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 454.058 | − | 262.150i | 1.56034 | − | 0.900860i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 66.8335 | 0.228101 | 0.114050 | − | 0.993475i | \(-0.463617\pi\) | ||||
0.114050 | + | 0.993475i | \(0.463617\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 227.837i | 0.772330i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 75.4388 | + | 130.664i | 0.254003 | + | 0.439945i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −59.3154 | − | 34.2457i | −0.198379 | − | 0.114534i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −86.6645 | − | 132.626i | −0.287922 | − | 0.440617i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 376.831 | + | 217.564i | 1.24367 | + | 0.718031i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 137.480 | + | 238.123i | 0.450755 | + | 0.780731i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 135.049i | 0.439900i | 0.975511 | + | 0.219950i | \(0.0705894\pi\) | ||||
−0.975511 | + | 0.219950i | \(0.929411\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −682.040 | −2.20725 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 269.408 | − | 155.543i | 0.866263 | − | 0.500137i | 0.000158189 | − | 1.00000i | \(-0.499950\pi\) |
0.866104 | + | 0.499863i | \(0.166616\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 64.6255 | − | 111.935i | 0.206471 | − | 0.357619i | −0.744129 | − | 0.668036i | \(-0.767135\pi\) |
0.950600 | + | 0.310417i | \(0.100469\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 387.772 | + | 196.195i | 1.23102 | + | 0.622842i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −177.441 | + | 307.337i | −0.559752 | + | 0.969519i | 0.437765 | + | 0.899089i | \(0.355770\pi\) |
−0.997517 | + | 0.0704293i | \(0.977563\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 775.096 | − | 447.502i | 2.42977 | − | 1.40283i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −403.650 | −1.25748 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 318.786i | 0.986953i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 21.5914 | + | 37.3974i | 0.0664350 | + | 0.115069i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −146.378 | − | 84.5115i | −0.447640 | − | 0.258445i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 260.034 | − | 14.3681i | 0.790378 | − | 0.0436721i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −219.277 | − | 126.599i | −0.662468 | − | 0.382476i | 0.130749 | − | 0.991416i | \(-0.458262\pi\) |
−0.793217 | + | 0.608940i | \(0.791595\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −42.0667 | − | 72.8616i | −0.126326 | − | 0.218804i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 513.617i | − | 1.53318i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 395.788 | 1.17444 | 0.587222 | − | 0.809426i | \(-0.300221\pi\) | ||||
0.587222 | + | 0.809426i | \(0.300221\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −454.428 | + | 262.364i | −1.34050 | + | 0.773936i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 120.020 | − | 207.880i | 0.351964 | − | 0.609619i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 56.5401 | + | 338.308i | 0.164840 | + | 0.986320i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −167.753 | + | 290.556i | −0.486240 | + | 0.842192i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −266.808 | + | 154.041i | −0.768898 | + | 0.443924i | −0.832481 | − | 0.554053i | \(-0.813081\pi\) |
0.0635832 | + | 0.997977i | \(0.479747\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 336.754 | 0.964911 | 0.482455 | − | 0.875921i | \(-0.339745\pi\) | ||||
0.482455 | + | 0.875921i | \(0.339745\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 41.1006i | − | 0.117096i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 86.4268 | + | 149.696i | 0.244835 | + | 0.424067i | 0.962085 | − | 0.272749i | \(-0.0879328\pi\) |
−0.717250 | + | 0.696816i | \(0.754599\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −461.993 | − | 266.732i | −1.30139 | − | 0.751357i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 903.726 | − | 49.9351i | 2.53144 | − | 0.139874i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 205.407 | + | 118.592i | 0.572163 | + | 0.330339i | 0.758013 | − | 0.652240i | \(-0.226170\pi\) |
−0.185850 | + | 0.982578i | \(0.559504\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −120.425 | − | 208.582i | −0.333587 | − | 0.577790i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1103.09i | 3.03883i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 166.178 | 0.455283 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −44.1618 | + | 25.4968i | −0.120332 | + | 0.0694736i | −0.558958 | − | 0.829196i | \(-0.688799\pi\) |
0.438626 | + | 0.898670i | \(0.355465\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 185.803 | − | 321.819i | 0.503530 | − | 0.872139i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 482.198 | + | 243.970i | 1.29972 | + | 0.657602i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 82.9591 | − | 143.689i | 0.222411 | − | 0.385226i | −0.733129 | − | 0.680090i | \(-0.761941\pi\) |
0.955539 | + | 0.294863i | \(0.0952741\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −371.865 | + | 214.696i | −0.991639 | + | 0.572523i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −243.808 | −0.646706 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 107.108i | − | 0.282608i | −0.989966 | − | 0.141304i | \(-0.954870\pi\) | ||
0.989966 | − | 0.141304i | \(-0.0451295\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −19.0786 | − | 33.0450i | −0.0500749 | − | 0.0867323i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.24980 | + | 1.29892i | 0.00587415 | + | 0.00339144i | 0.502934 | − | 0.864325i | \(-0.332254\pi\) |
−0.497060 | + | 0.867716i | \(0.665587\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 424.210 | + | 649.185i | 1.10185 | + | 1.68619i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 211.029 | + | 121.838i | 0.545294 | + | 0.314826i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −382.629 | − | 662.733i | −0.983622 | − | 1.70368i | −0.647907 | − | 0.761720i | \(-0.724355\pi\) |
−0.335715 | − | 0.941964i | \(-0.608978\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 380.602i | 0.973406i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 286.571 | 0.729189 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 215.822 | − | 124.605i | 0.546384 | − | 0.315455i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −58.4121 | + | 101.173i | −0.147134 | + | 0.254843i | −0.930167 | − | 0.367137i | \(-0.880338\pi\) |
0.783033 | + | 0.621980i | \(0.213671\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 285.569 | − | 186.606i | 0.715713 | − | 0.467683i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −161.192 | + | 279.192i | −0.401975 | + | 0.696240i | −0.993964 | − | 0.109705i | \(-0.965009\pi\) |
0.591990 | + | 0.805946i | \(0.298343\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −56.6287 | + | 32.6946i | −0.140518 | + | 0.0811280i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 357.415 | 0.882505 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 150.134i | − | 0.368879i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −150.890 | − | 261.350i | −0.368925 | − | 0.638997i | 0.620473 | − | 0.784228i | \(-0.286941\pi\) |
−0.989398 | + | 0.145231i | \(0.953607\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −377.931 | − | 218.199i | −0.919541 | − | 0.530897i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 124.865 | − | 246.790i | 0.302336 | − | 0.597554i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −34.3775 | − | 19.8478i | −0.0828373 | − | 0.0478261i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −546.514 | − | 946.589i | −1.31058 | − | 2.27000i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 384.000i | − | 0.916468i | −0.888832 | − | 0.458234i | \(-0.848482\pi\) | ||
0.888832 | − | 0.458234i | \(-0.151518\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 168.193 | 0.399509 | 0.199754 | − | 0.979846i | \(-0.435986\pi\) | ||||
0.199754 | + | 0.979846i | \(0.435986\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −346.892 | + | 200.278i | −0.820076 | + | 0.473471i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 119.982 | − | 207.814i | 0.282310 | − | 0.488975i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −18.4151 | − | 333.276i | −0.0431267 | − | 0.780506i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 223.520 | − | 387.148i | 0.521025 | − | 0.902442i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −32.9644 | + | 19.0320i | −0.0764836 | + | 0.0441578i | −0.537754 | − | 0.843102i | \(-0.680727\pi\) |
0.461270 | + | 0.887260i | \(0.347394\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 77.8536 | 0.179801 | 0.0899003 | − | 0.995951i | \(-0.471345\pi\) | ||||
0.0899003 | + | 0.995951i | \(0.471345\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1194.29i | 2.74550i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 71.7241 | + | 124.230i | 0.164128 | + | 0.284279i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 235.201 | + | 135.793i | 0.535765 | + | 0.309324i | 0.743361 | − | 0.668891i | \(-0.233231\pi\) |
−0.207596 | + | 0.978215i | \(0.566564\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −312.505 | − | 425.031i | −0.708629 | − | 0.963790i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −402.570 | − | 232.424i | −0.908735 | − | 0.524659i | −0.0287113 | − | 0.999588i | \(-0.509140\pi\) |
−0.880024 | + | 0.474929i | \(0.842474\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 330.319 | + | 572.130i | 0.742291 | + | 1.28568i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 703.048i | − | 1.57281i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 211.810 | 0.471736 | 0.235868 | − | 0.971785i | \(-0.424207\pi\) | ||||
0.235868 | + | 0.971785i | \(0.424207\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 574.278 | − | 331.560i | 1.27334 | − | 0.735166i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.41010 | + | 7.63851i | −0.00973532 | + | 0.0168621i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11.6550 | − | 210.932i | −0.0256153 | − | 0.463586i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 442.640 | − | 766.674i | 0.968577 | − | 1.67762i | 0.268896 | − | 0.963169i | \(-0.413341\pi\) |
0.699681 | − | 0.714455i | \(-0.253325\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −197.794 | + | 114.196i | −0.430923 | + | 0.248794i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −622.030 | −1.34931 | −0.674653 | − | 0.738135i | \(-0.735707\pi\) | ||||
−0.674653 | + | 0.738135i | \(0.735707\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 799.125i | 1.72597i | 0.505227 | + | 0.862986i | \(0.331409\pi\) | ||||
−0.505227 | + | 0.862986i | \(0.668591\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 160.154 | + | 277.395i | 0.344418 | + | 0.596549i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 139.052 | + | 80.2818i | 0.297756 | + | 0.171910i | 0.641435 | − | 0.767178i | \(-0.278340\pi\) |
−0.343678 | + | 0.939087i | \(0.611673\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −281.484 | + | 556.341i | −0.600178 | + | 1.18623i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 999.469 | + | 577.044i | 2.12202 | + | 1.22515i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 217.416 | + | 376.575i | 0.459653 | + | 0.796143i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 90.4418i | − | 0.190404i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −831.169 | −1.74249 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −244.409 | + | 141.109i | −0.510248 | + | 0.294592i | −0.732935 | − | 0.680298i | \(-0.761850\pi\) |
0.222688 | + | 0.974890i | \(0.428517\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.4490 | + | 35.4187i | −0.0425135 | + | 0.0736356i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 340.944 | − | 222.790i | 0.705889 | − | 0.461264i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −340.008 | + | 588.912i | −0.701048 | + | 1.21425i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −389.490 | + | 224.872i | −0.799773 | + | 0.461749i | −0.843392 | − | 0.537299i | \(-0.819445\pi\) |
0.0436185 | + | 0.999048i | \(0.486111\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 774.994 | 1.58485 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 253.137i | 0.515554i | 0.966204 | + | 0.257777i | \(0.0829901\pi\) | ||||
−0.966204 | + | 0.257777i | \(0.917010\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 677.411 | + | 1173.31i | 1.37406 | + | 2.37994i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1032.96 | − | 596.378i | −2.08678 | − | 1.20480i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 354.243 | + | 542.112i | 0.712763 | + | 1.09077i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −261.296 | − | 150.859i | −0.523639 | − | 0.302323i | 0.214783 | − | 0.976662i | \(-0.431095\pi\) |
−0.738422 | + | 0.674339i | \(0.764429\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 36.7306 | + | 63.6193i | 0.0733146 | + | 0.126985i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 115.146i | 0.228918i | 0.993428 | + | 0.114459i | \(0.0365135\pi\) | ||||
−0.993428 | + | 0.114459i | \(0.963486\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −564.358 | −1.11754 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 545.237 | − | 314.793i | 1.07542 | − | 0.620893i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 217.015 | − | 375.880i | 0.426355 | − | 0.738468i | −0.570191 | − | 0.821512i | \(-0.693131\pi\) |
0.996546 | + | 0.0830438i | \(0.0264641\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −180.002 | − | 91.0727i | −0.352254 | − | 0.178225i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −43.0404 | + | 74.5482i | −0.0838995 | + | 0.145318i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 766.089 | − | 442.302i | 1.48755 | − | 0.858838i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −714.783 | −1.38256 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 1.32256i | − | 0.00254828i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −298.700 | − | 517.363i | −0.573320 | − | 0.993019i | −0.996222 | − | 0.0868439i | \(-0.972322\pi\) |
0.422902 | − | 0.906175i | \(-0.361011\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −134.862 | − | 77.8625i | −0.257862 | − | 0.148877i | 0.365497 | − | 0.930813i | \(-0.380899\pi\) |
−0.623359 | + | 0.781936i | \(0.714232\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −256.393 | + | 14.1670i | −0.488368 | + | 0.0269847i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 314.681 | + | 181.681i | 0.597117 | + | 0.344746i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −178.868 | − | 309.808i | −0.338124 | − | 0.585649i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 425.394i | 0.801120i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −180.641 | −0.338913 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 453.393 | − | 261.766i | 0.847463 | − | 0.489283i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 274.788 | − | 475.947i | 0.511710 | − | 0.886307i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −103.717 | − | 935.672i | −0.192425 | − | 1.73594i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −328.050 | + | 568.199i | −0.606377 | + | 1.05028i | 0.385456 | + | 0.922726i | \(0.374044\pi\) |
−0.991832 | + | 0.127549i | \(0.959289\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −250.461 | + | 144.604i | −0.461254 | + | 0.266305i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 219.222 | 0.402243 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 765.118i | − | 1.39875i | −0.714754 | − | 0.699376i | \(-0.753461\pi\) | ||
0.714754 | − | 0.699376i | \(-0.246539\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 256.689 | + | 444.599i | 0.467558 | + | 0.809834i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 442.219 | + | 255.315i | 0.802576 | + | 0.463367i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −302.064 | + | 16.6904i | −0.546227 | + | 0.0301816i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 173.498 | + | 100.169i | 0.312610 | + | 0.180485i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 294.325 | + | 509.786i | 0.528411 | + | 0.915236i | 0.999451 | + | 0.0331235i | \(0.0105455\pi\) |
−0.471040 | + | 0.882112i | \(0.656121\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 118.453i | − | 0.211901i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2484.16 | −4.42810 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −480.746 | + | 277.559i | −0.853901 | + | 0.493000i | −0.861965 | − | 0.506967i | \(-0.830766\pi\) |
0.00806399 | + | 0.999967i | \(0.497433\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 340.286 | − | 589.392i | 0.602275 | − | 1.04317i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −387.146 | − | 195.878i | −0.682797 | − | 0.345465i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −64.1433 | + | 111.099i | −0.112730 | + | 0.195254i | −0.916870 | − | 0.399186i | \(-0.869293\pi\) |
0.804140 | + | 0.594440i | \(0.202626\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −744.272 | + | 429.705i | −1.30345 | + | 0.752549i | −0.980995 | − | 0.194035i | \(-0.937843\pi\) |
−0.322458 | + | 0.946584i | \(0.604509\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 52.6284 | 0.0918472 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 107.979i | − | 0.187790i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 316.372 | + | 547.972i | 0.548305 | + | 0.949692i | 0.998391 | + | 0.0567065i | \(0.0180599\pi\) |
−0.450086 | + | 0.892985i | \(0.648607\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 226.623 | + | 130.841i | 0.391403 | + | 0.225977i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 26.3597 | + | 40.3392i | 0.0453695 | + | 0.0694306i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1284.49 | − | 741.600i | −2.20324 | − | 1.27204i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 162.459 | + | 281.388i | 0.277708 | + | 0.481005i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 647.488i | − | 1.10305i | −0.834160 | − | 0.551523i | \(-0.814047\pi\) | ||
0.834160 | − | 0.551523i | \(-0.185953\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 136.951 | 0.232514 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1268.31 | − | 732.258i | 2.14604 | − | 1.23902i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 339.014 | − | 587.190i | 0.571693 | − | 0.990202i | −0.424699 | − | 0.905335i | \(-0.639620\pi\) |
0.996392 | − | 0.0848672i | \(-0.0270466\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −982.711 | + | 642.154i | −1.65162 | + | 1.07925i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −20.3314 | + | 35.2149i | −0.0340559 | + | 0.0589865i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −93.3584 | + | 53.9005i | −0.155857 | + | 0.0899841i | −0.575900 | − | 0.817520i | \(-0.695348\pi\) |
0.420043 | + | 0.907504i | \(0.362015\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −690.543 | −1.14899 | −0.574495 | − | 0.818508i | \(-0.694802\pi\) | ||||
−0.574495 | + | 0.818508i | \(0.694802\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 958.972i | − | 1.59033i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −715.355 | − | 1239.03i | −1.18240 | − | 2.04799i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −552.137 | − | 318.776i | −0.909615 | − | 0.525167i | −0.0293080 | − | 0.999570i | \(-0.509330\pi\) |
−0.880307 | + | 0.474404i | \(0.842664\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 654.523 | − | 1293.64i | 1.07475 | − | 2.12420i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 168.627 | + | 97.3571i | 0.275986 | + | 0.159341i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −56.4517 | − | 97.7773i | −0.0920909 | − | 0.159506i | 0.816300 | − | 0.577628i | \(-0.196022\pi\) |
−0.908391 | + | 0.418122i | \(0.862688\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 884.867i | 1.43881i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.582311 | 0.000943779 | 0.000471889 | − | 1.00000i | \(-0.499850\pi\) | ||||
0.000471889 | 1.00000i | \(0.499850\pi\) | ||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 192.651 | − | 111.227i | 0.311230 | − | 0.179688i | −0.336247 | − | 0.941774i | \(-0.609158\pi\) |
0.647477 | + | 0.762085i | \(0.275824\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −51.3864 | + | 89.0039i | −0.0827479 | + | 0.143324i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −44.2453 | − | 800.751i | −0.0710197 | − | 1.28531i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 381.598 | − | 660.947i | 0.610557 | − | 1.05752i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −810.840 | + | 468.139i | −1.29321 | + | 0.746633i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 227.267 | 0.361315 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 133.261i | 0.211190i | 0.994409 | + | 0.105595i | \(0.0336746\pi\) | ||||
−0.994409 | + | 0.105595i | \(0.966325\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 124.735 | + | 216.048i | 0.197054 | + | 0.341307i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 42.8593 | + | 24.7448i | 0.0674950 | + | 0.0389682i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −102.975 | + | 234.865i | −0.161656 | + | 0.368705i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −862.586 | − | 498.014i | −1.34990 | − | 0.779365i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 90.8335 | + | 157.328i | 0.141706 | + | 0.245442i | 0.928139 | − | 0.372233i | \(-0.121408\pi\) |
−0.786433 | + | 0.617675i | \(0.788075\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 872.108i | 1.35631i | 0.734919 | + | 0.678155i | \(0.237220\pi\) | ||||
−0.734919 | + | 0.678155i | \(0.762780\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −580.240 | −0.899597 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 491.471 | − | 283.751i | 0.759615 | − | 0.438564i | −0.0695427 | − | 0.997579i | \(-0.522154\pi\) |
0.829157 | + | 0.559015i | \(0.188821\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −379.553 | + | 657.405i | −0.584827 | + | 1.01295i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −21.4522 | − | 388.242i | −0.0329527 | − | 0.596377i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 77.1434 | − | 133.616i | 0.118137 | − | 0.204619i | −0.800892 | − | 0.598808i | \(-0.795641\pi\) |
0.919029 | + | 0.394189i | \(0.128975\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −321.886 | + | 185.841i | −0.491429 | + | 0.283727i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 310.271 | 0.472254 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 643.809i | 0.976948i | 0.872578 | + | 0.488474i | \(0.162446\pi\) | ||||
−0.872578 | + | 0.488474i | \(0.837554\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 73.7811 | + | 127.793i | 0.111620 | + | 0.193332i | 0.916424 | − | 0.400209i | \(-0.131063\pi\) |
−0.804803 | + | 0.593542i | \(0.797729\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 586.050 | + | 338.356i | 0.883936 | + | 0.510341i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −199.747 | + | 394.793i | −0.300372 | + | 0.593673i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 527.970 | + | 304.824i | 0.791559 | + | 0.457007i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 151.138 | + | 261.778i | 0.225916 | + | 0.391298i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 916.110i | 1.36529i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 200.134 | 0.297375 | 0.148688 | − | 0.988884i | \(-0.452495\pi\) | ||||
0.148688 | + | 0.988884i | \(0.452495\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 56.1155 | − | 32.3983i | 0.0831341 | − | 0.0479975i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 302.267 | − | 523.542i | 0.446480 | − | 0.773326i | −0.551674 | − | 0.834060i | \(-0.686011\pi\) |
0.998154 | + | 0.0607337i | \(0.0193440\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 691.040 | − | 451.561i | 1.01773 | − | 0.665038i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −549.500 | + | 951.761i | −0.806901 | + | 1.39759i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −282.520 | + | 163.113i | −0.413645 | + | 0.238818i | −0.692355 | − | 0.721557i | \(-0.743427\pi\) |
0.278710 | + | 0.960375i | \(0.410093\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 566.006 | 0.826287 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 104.975i | − | 0.152803i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 202.019 | + | 349.908i | 0.293207 | + | 0.507849i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 37.8620 | + | 21.8596i | 0.0547931 | + | 0.0316348i | 0.527146 | − | 0.849775i | \(-0.323262\pi\) |
−0.472353 | + | 0.881409i | \(0.656595\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 792.042 | + | 1212.09i | 1.14292 | + | 1.74905i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1227.72 | + | 708.826i | 1.76651 | + | 1.01989i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 501.903 | + | 869.321i | 0.720090 | + | 1.24723i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 617.835i | − | 0.883884i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 765.890 | 1.09257 | 0.546284 | − | 0.837600i | \(-0.316042\pi\) | ||||
0.546284 | + | 0.837600i | \(0.316042\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 74.1808 | − | 42.8283i | 0.105520 | − | 0.0609222i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 476.904 | − | 826.021i | 0.676459 | − | 1.17166i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 611.304 | + | 309.292i | 0.864645 | + | 0.437472i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −657.627 | + | 1139.04i | −0.927542 | + | 1.60655i | −0.140121 | + | 0.990134i | \(0.544749\pi\) |
−0.787421 | + | 0.616415i | \(0.788584\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 402.960 | − | 232.649i | 0.566751 | − | 0.327214i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 163.507 | 0.229322 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 579.809i | 0.810922i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −941.709 | − | 1631.09i | −1.31340 | − | 2.27488i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −154.245 | − | 89.0534i | −0.214527 | − | 0.123857i | 0.388886 | − | 0.921286i | \(-0.372860\pi\) |
−0.603414 | + | 0.797428i | \(0.706193\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1072.22 | + | 59.2450i | −1.48712 | + | 0.0821706i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 941.651 | + | 543.663i | 1.30242 | + | 0.751954i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −192.186 | − | 332.876i | −0.265085 | − | 0.459140i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 760.723i | − | 1.04639i | −0.852214 | − | 0.523193i | \(-0.824741\pi\) | ||
0.852214 | − | 0.523193i | \(-0.175259\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 981.560 | 1.34645 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −570.046 | + | 329.116i | −0.779816 | + | 0.450227i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −37.2538 | + | 64.5255i | −0.0508238 | + | 0.0880294i | −0.890318 | − | 0.455339i | \(-0.849518\pi\) |
0.839494 | + | 0.543369i | \(0.182851\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1150.49 | + | 504.423i | 1.56529 | + | 0.686289i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 855.630 | − | 1481.99i | 1.16096 | − | 2.01085i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −292.777 | + | 169.035i | −0.396180 | + | 0.228735i | −0.684835 | − | 0.728699i | \(-0.740126\pi\) |
0.288654 | + | 0.957433i | \(0.406792\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 255.052 | 0.344199 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 681.343i | 0.917016i | 0.888690 | + | 0.458508i | \(0.151616\pi\) | ||||
−0.888690 | + | 0.458508i | \(0.848384\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 455.925 | + | 789.686i | 0.611980 | + | 1.05998i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −64.1861 | − | 37.0578i | −0.0859251 | − | 0.0496089i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −634.567 | + | 35.0628i | −0.847219 | + | 0.0468129i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −386.501 | − | 223.147i | −0.514649 | − | 0.297133i | 0.220094 | − | 0.975479i | \(-0.429364\pi\) |
−0.734743 | + | 0.678346i | \(0.762697\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 391.672 | + | 678.395i | 0.520148 | + | 0.900923i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 11.4398i | − | 0.0151520i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 455.207 | 0.601330 | 0.300665 | − | 0.953730i | \(-0.402791\pi\) | ||||
0.300665 | + | 0.953730i | \(0.402791\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −968.071 | + | 558.916i | −1.27546 | + | 0.736385i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −408.242 | + | 707.095i | −0.536454 | + | 0.929166i | 0.462637 | + | 0.886548i | \(0.346903\pi\) |
−0.999091 | + | 0.0426181i | \(0.986430\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −237.458 | − | 120.143i | −0.311216 | − | 0.157462i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 902.774 | − | 1563.65i | 1.18010 | − | 2.04399i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 179.084 | − | 103.394i | 0.233486 | − | 0.134803i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −203.680 | −0.264863 | −0.132431 | − | 0.991192i | \(-0.542278\pi\) | ||||
−0.132431 | + | 0.991192i | \(0.542278\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 227.090i | − | 0.294539i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −257.358 | − | 445.756i | −0.332934 | − | 0.576658i | 0.650152 | − | 0.759804i | \(-0.274705\pi\) |
−0.983086 | + | 0.183146i | \(0.941372\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −89.2772 | − | 51.5442i | −0.115196 | − | 0.0665087i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −133.034 | − | 203.586i | −0.171215 | − | 0.262016i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 327.646 | + | 189.166i | 0.420598 | + | 0.242832i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −888.693 | − | 1539.26i | −1.13789 | − | 1.97089i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 365.839i | 0.467227i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1496.85 | −1.90681 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 53.6099 | − | 30.9517i | 0.0681193 | − | 0.0393287i | −0.465554 | − | 0.885020i | \(-0.654145\pi\) |
0.533673 | + | 0.845691i | \(0.320811\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 430.854 | − | 746.260i | 0.546076 | − | 0.945831i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −691.604 | + | 451.929i | −0.874341 | + | 0.571339i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 124.779 | − | 216.123i | 0.157350 | − | 0.272539i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1714.02 | − | 989.592i | 2.15600 | − | 1.24477i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 674.547 | 0.846357 | 0.423179 | − | 0.906046i | \(-0.360914\pi\) | ||||
0.423179 | + | 0.906046i | \(0.360914\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1082.01i | − | 1.35421i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 616.738 | + | 1068.22i | 0.769960 | + | 1.33361i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 479.493 | + | 276.835i | 0.597127 | + | 0.344751i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −238.480 | + | 471.347i | −0.296249 | + | 0.585524i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 23.1281 | + | 13.3530i | 0.0286593 | + | 0.0165465i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −613.272 | − | 1062.22i | −0.758062 | − | 1.31300i | −0.943838 | − | 0.330409i | \(-0.892813\pi\) |
0.185776 | − | 0.982592i | \(-0.440520\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 920.398i | − | 1.13489i | −0.823410 | − | 0.567446i | \(-0.807931\pi\) | ||
0.823410 | − | 0.567446i | \(-0.192069\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1754.50 | 2.15806 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −870.498 | + | 502.582i | −1.06810 | + | 0.616665i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −124.043 | + | 214.849i | −0.151828 | + | 0.262974i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −21.7610 | − | 393.830i | −0.0265702 | − | 0.480867i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 85.1028 | − | 147.402i | 0.103657 | − | 0.179540i | −0.809531 | − | 0.587077i | \(-0.800279\pi\) |
0.913189 | + | 0.407537i | \(0.133612\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −974.415 | + | 562.579i | −1.18398 | + | 0.683571i | −0.956932 | − | 0.290313i | \(-0.906241\pi\) |
−0.227047 | + | 0.973884i | \(0.572907\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 704.775 | 0.854273 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 749.693i | 0.906521i | 0.891378 | + | 0.453261i | \(0.149739\pi\) | ||||
−0.891378 | + | 0.453261i | \(0.850261\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 397.023 | + | 687.664i | 0.478918 | + | 0.829510i | 0.999708 | − | 0.0241749i | \(-0.00769586\pi\) |
−0.520790 | + | 0.853685i | \(0.674363\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1147.25 | + | 662.366i | 1.38057 | + | 0.797071i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1416.39 | − | 157.003i | 1.70034 | − | 0.188479i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −82.5141 | − | 47.6395i | −0.0988193 | − | 0.0570533i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 49.0589 | + | 84.9725i | 0.0586128 | + | 0.101520i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1580.69i | 1.88402i | 0.335586 | + | 0.942010i | \(0.391066\pi\) | ||||
−0.335586 | + | 0.942010i | \(0.608934\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1329.15 | 1.58044 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1661.31 | + | 959.160i | −1.97072 | + | 1.13779i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −408.285 | + | 707.171i | −0.483178 | + | 0.836888i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 95.8197 | + | 1734.14i | 0.113128 | + | 2.04740i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −983.325 | + | 1703.17i | −1.15821 | + | 2.00609i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 88.5652 | − | 51.1332i | 0.104072 | − | 0.0600860i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1404.70 | −1.64678 | −0.823389 | − | 0.567477i | \(-0.807920\pi\) | ||||
−0.823389 | + | 0.567477i | \(0.807920\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 680.508i | − | 0.795916i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −630.820 | − | 1092.61i | −0.736079 | − | 1.27493i | −0.954248 | − | 0.299016i | \(-0.903342\pi\) |
0.218169 | − | 0.975911i | \(-0.429992\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −145.467 | − | 83.9852i | −0.169344 | − | 0.0977709i | 0.412932 | − | 0.910762i | \(-0.364505\pi\) |
−0.582277 | + | 0.812991i | \(0.697838\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 484.945 | − | 958.475i | 0.563235 | − | 1.11321i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1316.73 | − | 760.214i | −1.52576 | − | 0.880897i | −0.999533 | − | 0.0305517i | \(-0.990274\pi\) |
−0.526225 | − | 0.850345i | \(-0.676393\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.857677 | + | 1.48554i | 0.000991534 | + | 0.00171739i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 2475.56i | − | 2.85531i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 830.313 | 0.955481 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −403.711 | + | 233.082i | −0.463503 | + | 0.267603i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −634.828 | + | 1099.55i | −0.727180 | + | 1.25951i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −565.949 | + | 369.820i | −0.646799 | + | 0.422651i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.5472 | + | 33.8568i | −0.0222887 | + | 0.0386052i | −0.876955 | − | 0.480573i | \(-0.840429\pi\) |
0.854666 | + | 0.519178i | \(0.173762\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −257.329 | + | 148.569i | −0.292752 | + | 0.169020i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −915.577 | −1.03925 | −0.519624 | − | 0.854395i | \(-0.673928\pi\) | ||||
−0.519624 | + | 0.854395i | \(0.673928\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 331.093i | − | 0.374963i | −0.982268 | − | 0.187482i | \(-0.939967\pi\) | ||
0.982268 | − | 0.187482i | \(-0.0600325\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −506.476 | − | 877.241i | −0.572289 | − | 0.991233i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1039.22 | − | 599.992i | −1.17161 | − | 0.676428i | −0.217550 | − | 0.976049i | \(-0.569807\pi\) |
−0.954058 | + | 0.299621i | \(0.903140\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −32.8633 | − | 50.2919i | −0.0369666 | − | 0.0565714i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1031.29 | + | 595.415i | 1.15745 | + | 0.668254i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −203.904 | − | 353.173i | −0.228336 | − | 0.395490i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 712.798i | 0.796423i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 304.509 | 0.339475 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 504.055 | − | 291.017i | 0.560685 | − | 0.323711i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1122.61 | − | 1944.41i | 1.24596 | − | 2.15806i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 628.507 | + | 317.996i | 0.696021 | + | 0.352155i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 187.550 | − | 324.847i | 0.207238 | − | 0.358947i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −263.969 | + | 152.402i | −0.291035 | + | 0.168029i | −0.638408 | − | 0.769698i | \(-0.720407\pi\) |
0.347374 | + | 0.937727i | \(0.387074\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1053.71 | −1.15920 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1743.29i | − | 1.91360i | −0.290753 | − | 0.956798i | \(-0.593906\pi\) | ||
0.290753 | − | 0.956798i | \(-0.406094\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −66.1288 | − | 114.538i | −0.0724302 | − | 0.125453i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1058.68 | − | 611.229i | −1.15703 | − | 0.668010i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 450.511 | − | 24.8928i | 0.491287 | − | 0.0271460i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1069.37 | − | 617.403i | −1.16363 | − | 0.671821i | −0.211457 | − | 0.977387i | \(-0.567821\pi\) |
−0.952171 | + | 0.305567i | \(0.901154\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −300.210 | − | 519.979i | −0.325961 | − | 0.564581i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 484.178i | 0.524570i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −64.4772 | −0.0697051 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1430.36 | − | 825.820i | 1.54300 | − | 0.890852i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −664.417 | + | 1150.80i | −0.715196 | + | 1.23876i | 0.247688 | + | 0.968840i | \(0.420329\pi\) |
−0.962884 | + | 0.269916i | \(0.913004\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 432.726 | − | 318.163i | 0.464797 | − | 0.341744i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −691.533 | + | 1197.77i | −0.741193 | + | 1.28378i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2790.29 | − | 1610.98i | 2.98427 | − | 1.72297i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −206.866 | −0.220775 | −0.110387 | − | 0.993889i | \(-0.535209\pi\) | ||||
−0.110387 | + | 0.993889i | \(0.535209\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 574.642i | 0.611972i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 500.890 | + | 867.566i | 0.532295 | + | 0.921962i | 0.999289 | + | 0.0377016i | \(0.0120036\pi\) |
−0.466994 | + | 0.884261i | \(0.654663\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 391.180 | + | 225.848i | 0.414825 | + | 0.239499i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −316.507 | + | 17.4885i | −0.334928 | + | 0.0185064i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −162.584 | − | 93.8677i | −0.171683 | − | 0.0991212i | 0.411696 | − | 0.911321i | \(-0.364936\pi\) |
−0.583379 | + | 0.812200i | \(0.698270\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −75.4128 | − | 130.619i | −0.0794655 | − | 0.137638i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 1577.79i | − | 1.65908i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −876.232 | −0.919446 | −0.459723 | − | 0.888062i | \(-0.652051\pi\) | ||||
−0.459723 | + | 0.888062i | \(0.652051\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −59.1140 | + | 34.1295i | −0.0618994 | + | 0.0357377i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1989.56 | + | 3446.03i | −2.07896 | + | 3.60086i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −613.089 | − | 310.196i | −0.639301 | − | 0.323457i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −402.450 | + | 697.063i | −0.418782 | + | 0.725352i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 846.528 | − | 488.743i | 0.879053 | − | 0.507521i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −339.400 | −0.351710 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 311.857i | 0.322499i | 0.986914 | + | 0.161250i | \(0.0515524\pi\) | ||||
−0.986914 | + | 0.161250i | \(0.948448\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −708.651 | − | 1227.42i | −0.731322 | − | 1.26669i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 346.856 | + | 200.257i | 0.357215 | + | 0.206238i | 0.667858 | − | 0.744288i | \(-0.267211\pi\) |
−0.310643 | + | 0.950527i | \(0.600544\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −941.384 | − | 1440.63i | −0.967507 | − | 1.48061i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −166.266 | − | 95.9940i | −0.170530 | − | 0.0984553i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 488.351 | + | 845.848i | 0.499847 | + | 0.865761i | 1.00000 | 0.000176296i | \(-5.61167e-5\pi\) | |
−0.500153 | + | 0.865937i | \(0.666723\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2201.11i | 2.24832i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 409.309 | 0.417237 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1388.31 | − | 801.539i | 1.41232 | − | 0.815401i | 0.416710 | − | 0.909040i | \(-0.363183\pi\) |
0.995606 | + | 0.0936386i | \(0.0298498\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −949.737 | + | 1644.99i | −0.964200 | + | 1.67004i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −969.269 | + | 633.370i | −0.982036 | + | 0.641712i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −148.097 | + | 256.511i | −0.149744 | + | 0.259364i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 796.867 | − | 460.071i | 0.804104 | − | 0.464250i | −0.0408003 | − | 0.999167i | \(-0.512991\pi\) |
0.844904 | + | 0.534918i | \(0.179657\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1125.71 | 1.13364 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 52.7394i | − | 0.0530044i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 193.081 | + | 334.427i | 0.193662 | + | 0.335433i | 0.946461 | − | 0.322818i | \(-0.104630\pi\) |
−0.752799 | + | 0.658251i | \(0.771297\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 53.1465 | + | 30.6841i | 0.0531997 | + | 0.0307149i |
(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 | 224.3.r.c.191.1 | yes | 12 | |
4.3 | odd | 2 | inner | 224.3.r.c.191.6 | yes | 12 | |
7.2 | even | 3 | 1568.3.d.j.1471.1 | 6 | |||
7.4 | even | 3 | inner | 224.3.r.c.95.6 | yes | 12 | |
7.5 | odd | 6 | 1568.3.d.k.1471.6 | 6 | |||
8.3 | odd | 2 | 448.3.r.g.191.1 | 12 | |||
8.5 | even | 2 | 448.3.r.g.191.6 | 12 | |||
28.11 | odd | 6 | inner | 224.3.r.c.95.1 | ✓ | 12 | |
28.19 | even | 6 | 1568.3.d.k.1471.1 | 6 | |||
28.23 | odd | 6 | 1568.3.d.j.1471.6 | 6 | |||
56.11 | odd | 6 | 448.3.r.g.319.6 | 12 | |||
56.53 | even | 6 | 448.3.r.g.319.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.3.r.c.95.1 | ✓ | 12 | 28.11 | odd | 6 | inner | |
224.3.r.c.95.6 | yes | 12 | 7.4 | even | 3 | inner | |
224.3.r.c.191.1 | yes | 12 | 1.1 | even | 1 | trivial | |
224.3.r.c.191.6 | yes | 12 | 4.3 | odd | 2 | inner | |
448.3.r.g.191.1 | 12 | 8.3 | odd | 2 | |||
448.3.r.g.191.6 | 12 | 8.5 | even | 2 | |||
448.3.r.g.319.1 | 12 | 56.53 | even | 6 | |||
448.3.r.g.319.6 | 12 | 56.11 | odd | 6 | |||
1568.3.d.j.1471.1 | 6 | 7.2 | even | 3 | |||
1568.3.d.j.1471.6 | 6 | 28.23 | odd | 6 | |||
1568.3.d.k.1471.1 | 6 | 28.19 | even | 6 | |||
1568.3.d.k.1471.6 | 6 | 7.5 | odd | 6 |