Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,6,Mod(35,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.35");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.h (of order \(6\), 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: | \(17.3214525398\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 35.16 | ||
Character | \(\chi\) | \(=\) | 108.35 |
Dual form | 108.6.h.a.71.16 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.64008 | + | 5.41389i | 0.289927 | + | 0.957049i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −26.6203 | + | 17.7584i | −0.831884 | + | 0.554949i | ||||
\(5\) | −38.3603 | + | 22.1474i | −0.686211 | + | 0.396184i | −0.802191 | − | 0.597068i | \(-0.796332\pi\) |
0.115980 | + | 0.993252i | \(0.462999\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 102.940 | + | 59.4323i | 0.794032 | + | 0.458435i | 0.841380 | − | 0.540444i | \(-0.181744\pi\) |
−0.0473481 | + | 0.998878i | \(0.515077\pi\) | |||||||
\(8\) | −139.801 | − | 114.994i | −0.772299 | − | 0.635259i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −182.817 | − | 171.355i | −0.578118 | − | 0.541873i | ||||
\(11\) | −349.253 | + | 604.924i | −0.870279 | + | 1.50737i | −0.00857110 | + | 0.999963i | \(0.502728\pi\) |
−0.861708 | + | 0.507404i | \(0.830605\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −271.774 | − | 470.726i | −0.446014 | − | 0.772520i | 0.552108 | − | 0.833773i | \(-0.313824\pi\) |
−0.998122 | + | 0.0612530i | \(0.980490\pi\) | |||||||
\(14\) | −152.931 | + | 654.777i | −0.208533 | + | 0.892840i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 393.281 | − | 945.466i | 0.384064 | − | 0.923307i | ||||
\(17\) | − | 1884.06i | − | 1.58114i | −0.612369 | − | 0.790572i | \(-0.709783\pi\) | ||
0.612369 | − | 0.790572i | \(-0.290217\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 961.023i | − | 0.610731i | −0.952235 | − | 0.305366i | \(-0.901221\pi\) | ||
0.952235 | − | 0.305366i | \(-0.0987786\pi\) | |||||||
\(20\) | 627.863 | − | 1270.79i | 0.350986 | − | 0.710391i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3847.79 | − | 898.695i | −1.69494 | − | 0.395873i | ||||
\(23\) | −566.279 | − | 980.824i | −0.223208 | − | 0.386608i | 0.732572 | − | 0.680690i | \(-0.238320\pi\) |
−0.955780 | + | 0.294081i | \(0.904986\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −581.490 | + | 1007.17i | −0.186077 | + | 0.322294i | ||||
\(26\) | 2102.73 | − | 2243.38i | 0.610027 | − | 0.650832i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3795.71 | + | 245.936i | −0.914951 | + | 0.0592825i | ||||
\(29\) | −173.063 | − | 99.9180i | −0.0382128 | − | 0.0220622i | 0.480772 | − | 0.876846i | \(-0.340357\pi\) |
−0.518985 | + | 0.854784i | \(0.673690\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −225.699 | + | 130.308i | −0.0421819 | + | 0.0243537i | −0.520943 | − | 0.853592i | \(-0.674419\pi\) |
0.478761 | + | 0.877945i | \(0.341086\pi\) | |||||||
\(32\) | 5763.66 | + | 578.543i | 0.995000 | + | 0.0998759i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 10200.1 | − | 3089.99i | 1.51323 | − | 0.458417i | ||||
\(35\) | −5265.07 | −0.726498 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11136.8 | −1.33738 | −0.668690 | − | 0.743541i | \(-0.733145\pi\) | ||||
−0.668690 | + | 0.743541i | \(0.733145\pi\) | |||||||
\(38\) | 5202.87 | − | 1576.15i | 0.584499 | − | 0.177068i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 7909.63 | + | 1314.99i | 0.781639 | + | 0.129949i | ||||
\(41\) | 8446.51 | − | 4876.59i | 0.784725 | − | 0.453061i | −0.0533772 | − | 0.998574i | \(-0.516999\pi\) |
0.838102 | + | 0.545513i | \(0.183665\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5303.93 | − | 3062.23i | −0.437448 | − | 0.252561i | 0.265066 | − | 0.964230i | \(-0.414606\pi\) |
−0.702515 | + | 0.711669i | \(0.747939\pi\) | |||||||
\(44\) | −1445.24 | − | 22305.4i | −0.112540 | − | 1.73692i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4381.33 | − | 4674.39i | 0.305289 | − | 0.325710i | ||||
\(47\) | −589.363 | + | 1020.81i | −0.0389169 | + | 0.0674061i | −0.884828 | − | 0.465918i | \(-0.845724\pi\) |
0.845911 | + | 0.533324i | \(0.179057\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1339.11 | − | 2319.40i | −0.0796755 | − | 0.138002i | ||||
\(50\) | −6406.39 | − | 1496.28i | −0.362400 | − | 0.0846426i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 15594.0 | + | 7704.61i | 0.799741 | + | 0.395132i | ||||
\(53\) | 34070.7i | 1.66606i | 0.553227 | + | 0.833031i | \(0.313396\pi\) | ||||
−0.553227 | + | 0.833031i | \(0.686604\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 30940.1i | − | 1.37916i | ||||||
\(56\) | −7556.71 | − | 20146.2i | −0.322005 | − | 0.858465i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 257.108 | − | 1100.82i | 0.0100357 | − | 0.0429680i | ||||
\(59\) | 5319.11 | + | 9212.96i | 0.198934 | + | 0.344564i | 0.948183 | − | 0.317725i | \(-0.102919\pi\) |
−0.749249 | + | 0.662288i | \(0.769585\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5470.51 | + | 9475.20i | −0.188236 | + | 0.326035i | −0.944662 | − | 0.328045i | \(-0.893610\pi\) |
0.756426 | + | 0.654079i | \(0.226944\pi\) | |||||||
\(62\) | −1075.63 | − | 1008.20i | −0.0355374 | − | 0.0333093i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6320.66 | + | 32152.6i | 0.192891 | + | 0.981220i | ||||
\(65\) | 20850.7 | + | 12038.1i | 0.612120 | + | 0.353408i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −49766.8 | + | 28732.9i | −1.35442 | + | 0.781974i | −0.988865 | − | 0.148816i | \(-0.952454\pi\) |
−0.365554 | + | 0.930790i | \(0.619121\pi\) | |||||||
\(68\) | 33457.8 | + | 50154.1i | 0.877454 | + | 1.31533i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −8635.12 | − | 28504.5i | −0.210631 | − | 0.695294i | ||||
\(71\) | −70902.1 | −1.66922 | −0.834610 | − | 0.550842i | \(-0.814307\pi\) | ||||
−0.834610 | + | 0.550842i | \(0.814307\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −18551.8 | −0.407454 | −0.203727 | − | 0.979028i | \(-0.565305\pi\) | ||||
−0.203727 | + | 0.979028i | \(0.565305\pi\) | |||||||
\(74\) | −18265.1 | − | 60293.2i | −0.387743 | − | 1.27994i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 17066.2 | + | 25582.7i | 0.338924 | + | 0.508058i | ||||
\(77\) | −71904.1 | + | 41513.8i | −1.38206 | + | 0.797932i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12856.7 | − | 7422.81i | −0.231772 | − | 0.133814i | 0.379617 | − | 0.925144i | \(-0.376056\pi\) |
−0.611389 | + | 0.791330i | \(0.709389\pi\) | |||||||
\(80\) | 5853.17 | + | 44978.5i | 0.102251 | + | 0.785743i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 40254.2 | + | 37730.4i | 0.661115 | + | 0.619665i | ||||
\(83\) | 1200.62 | − | 2079.54i | 0.0191298 | − | 0.0331338i | −0.856302 | − | 0.516475i | \(-0.827244\pi\) |
0.875432 | + | 0.483342i | \(0.160577\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 41726.9 | + | 72273.0i | 0.626424 | + | 1.08500i | ||||
\(86\) | 7879.69 | − | 33737.2i | 0.114885 | − | 0.491884i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 118389. | − | 44406.9i | 1.62968 | − | 0.611286i | ||||
\(89\) | 28779.3i | 0.385129i | 0.981284 | + | 0.192564i | \(0.0616804\pi\) | ||||
−0.981284 | + | 0.192564i | \(0.938320\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 64608.5i | − | 0.817874i | ||||||
\(92\) | 32492.3 | + | 16053.6i | 0.400232 | + | 0.197744i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6493.13 | − | 1516.54i | −0.0757940 | − | 0.0177025i | ||||
\(95\) | 21284.1 | + | 36865.2i | 0.241962 | + | 0.419090i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −78738.0 | + | 136378.i | −0.849680 | + | 1.47169i | 0.0318145 | + | 0.999494i | \(0.489871\pi\) |
−0.881494 | + | 0.472195i | \(0.843462\pi\) | |||||||
\(98\) | 10360.7 | − | 11053.8i | 0.108975 | − | 0.116264i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2406.25 | − | 37137.5i | −0.0240625 | − | 0.371375i | ||||
\(101\) | 48022.2 | + | 27725.6i | 0.468424 | + | 0.270444i | 0.715580 | − | 0.698531i | \(-0.246163\pi\) |
−0.247156 | + | 0.968976i | \(0.579496\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 99722.3 | − | 57574.7i | 0.926188 | − | 0.534735i | 0.0405841 | − | 0.999176i | \(-0.487078\pi\) |
0.885604 | + | 0.464441i | \(0.153745\pi\) | |||||||
\(104\) | −16136.5 | + | 97060.3i | −0.146294 | + | 0.879951i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −184455. | + | 55878.5i | −1.59450 | + | 0.483037i | ||||
\(107\) | −162431. | −1.37155 | −0.685773 | − | 0.727815i | \(-0.740536\pi\) | ||||
−0.685773 | + | 0.727815i | \(0.740536\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 174442. | 1.40632 | 0.703160 | − | 0.711032i | \(-0.251772\pi\) | ||||
0.703160 | + | 0.711032i | \(0.251772\pi\) | |||||||
\(110\) | 167506. | − | 50744.1i | 1.31993 | − | 0.399857i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 96675.5 | − | 73952.4i | 0.728234 | − | 0.557067i | ||||
\(113\) | 79120.9 | − | 45680.5i | 0.582901 | − | 0.336538i | −0.179384 | − | 0.983779i | \(-0.557411\pi\) |
0.762286 | + | 0.647241i | \(0.224077\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 43445.3 | + | 25083.2i | 0.306336 | + | 0.176863i | ||||
\(116\) | 6381.37 | − | 413.469i | 0.0440321 | − | 0.00285297i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −41154.2 | + | 43907.0i | −0.272088 | + | 0.290288i | ||||
\(119\) | 111974. | − | 193944.i | 0.724851 | − | 1.25548i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −163430. | − | 283069.i | −1.01477 | − | 1.75764i | ||||
\(122\) | −60269.7 | − | 14076.7i | −0.366606 | − | 0.0856249i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3694.14 | − | 7476.88i | 0.0215754 | − | 0.0436683i | ||||
\(125\) | − | 189935.i | − | 1.08725i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 188373.i | 1.03636i | 0.855273 | + | 0.518178i | \(0.173389\pi\) | ||||
−0.855273 | + | 0.518178i | \(0.826611\pi\) | |||||||
\(128\) | −163704. | + | 86952.1i | −0.883151 | + | 0.469089i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −30976.4 | + | 132627.i | −0.160758 | + | 0.688291i | ||||
\(131\) | 123193. | + | 213376.i | 0.627201 | + | 1.08634i | 0.988111 | + | 0.153743i | \(0.0491328\pi\) |
−0.360910 | + | 0.932601i | \(0.617534\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 57115.8 | − | 98927.5i | 0.279980 | − | 0.484940i | ||||
\(134\) | −237178. | − | 222308.i | −1.14107 | − | 1.06953i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −216656. | + | 263393.i | −1.00444 | + | 1.22112i | ||||
\(137\) | −88854.7 | − | 51300.3i | −0.404463 | − | 0.233517i | 0.283945 | − | 0.958841i | \(-0.408357\pi\) |
−0.688408 | + | 0.725324i | \(0.741690\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −194249. | + | 112150.i | −0.852750 | + | 0.492335i | −0.861578 | − | 0.507626i | \(-0.830523\pi\) |
0.00882796 | + | 0.999961i | \(0.497190\pi\) | |||||||
\(140\) | 140158. | − | 93499.0i | 0.604362 | − | 0.403169i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −116285. | − | 383856.i | −0.483952 | − | 1.59752i | ||||
\(143\) | 379671. | 1.55263 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8851.68 | 0.0349627 | ||||||||
\(146\) | −30426.3 | − | 100437.i | −0.118132 | − | 0.389953i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 296464. | − | 197771.i | 1.11255 | − | 0.742177i | ||||
\(149\) | 27795.8 | − | 16047.9i | 0.102568 | − | 0.0592179i | −0.447838 | − | 0.894115i | \(-0.647806\pi\) |
0.550407 | + | 0.834897i | \(0.314473\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 65816.4 | + | 37999.1i | 0.234905 | + | 0.135622i | 0.612833 | − | 0.790213i | \(-0.290030\pi\) |
−0.377928 | + | 0.925835i | \(0.623363\pi\) | |||||||
\(152\) | −110512. | + | 134352.i | −0.387973 | + | 0.471667i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −342679. | − | 321194.i | −1.16436 | − | 1.09136i | ||||
\(155\) | 5771.93 | − | 9997.28i | 0.0192971 | − | 0.0334236i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −255695. | − | 442876.i | −0.827890 | − | 1.43395i | −0.899690 | − | 0.436529i | \(-0.856208\pi\) |
0.0717997 | − | 0.997419i | \(-0.477126\pi\) | |||||||
\(158\) | 19100.3 | − | 81778.6i | 0.0608692 | − | 0.260614i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −233909. | + | 105457.i | −0.722349 | + | 0.325667i | ||||
\(161\) | − | 134621.i | − | 0.409306i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 206451.i | − | 0.608623i | −0.952573 | − | 0.304311i | \(-0.901574\pi\) | ||
0.952573 | − | 0.304311i | \(-0.0984263\pi\) | |||||||
\(164\) | −138248. | + | 279813.i | −0.401375 | + | 0.812377i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 13227.5 | + | 3089.43i | 0.0372569 | + | 0.00870178i | ||||
\(167\) | −160986. | − | 278836.i | −0.446681 | − | 0.773674i | 0.551487 | − | 0.834184i | \(-0.314061\pi\) |
−0.998168 | + | 0.0605096i | \(0.980727\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 37924.7 | − | 65687.4i | 0.102142 | − | 0.176915i | ||||
\(170\) | −322843. | + | 344438.i | −0.856779 | + | 0.914089i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 195572. | − | 12671.7i | 0.504065 | − | 0.0326599i | ||||
\(173\) | −474593. | − | 274007.i | −1.20561 | − | 0.696058i | −0.243812 | − | 0.969823i | \(-0.578398\pi\) |
−0.961797 | + | 0.273764i | \(0.911731\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −119717. | + | 69118.5i | −0.295502 | + | 0.170608i | ||||
\(176\) | 434581. | + | 568112.i | 1.05752 | + | 1.38246i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −155808. | + | 47200.3i | −0.368587 | + | 0.111659i | ||||
\(179\) | 169767. | 0.396024 | 0.198012 | − | 0.980200i | \(-0.436551\pi\) | ||||
0.198012 | + | 0.980200i | \(0.436551\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 652433. | 1.48027 | 0.740133 | − | 0.672461i | \(-0.234763\pi\) | ||||
0.740133 | + | 0.672461i | \(0.234763\pi\) | |||||||
\(182\) | 349783. | − | 105963.i | 0.782745 | − | 0.237124i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −33622.7 | + | 202239.i | −0.0732129 | + | 0.440373i | ||||
\(185\) | 427210. | − | 246650.i | 0.917724 | − | 0.529848i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.13971e6 | + | 658012.i | 2.38337 | + | 1.37604i | ||||
\(188\) | −2438.83 | − | 37640.3i | −0.00503254 | − | 0.0776710i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −164676. | + | 175692.i | −0.330938 | + | 0.353075i | ||||
\(191\) | −130899. | + | 226724.i | −0.259629 | + | 0.449690i | −0.966143 | − | 0.258009i | \(-0.916934\pi\) |
0.706514 | + | 0.707699i | \(0.250267\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 456035. | + | 789876.i | 0.881262 | + | 1.52639i | 0.849939 | + | 0.526882i | \(0.176639\pi\) |
0.0313238 | + | 0.999509i | \(0.490028\pi\) | |||||||
\(194\) | −867473. | − | 202608.i | −1.65482 | − | 0.386502i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 76836.1 | + | 37962.8i | 0.142865 | + | 0.0705859i | ||||
\(197\) | 141457.i | 0.259693i | 0.991534 | + | 0.129846i | \(0.0414484\pi\) | ||||
−0.991534 | + | 0.129846i | \(0.958552\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 568072.i | − | 1.01688i | −0.861097 | − | 0.508441i | \(-0.830222\pi\) | ||
0.861097 | − | 0.508441i | \(-0.169778\pi\) | |||||||
\(200\) | 197111. | − | 73935.4i | 0.348447 | − | 0.130701i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −71343.4 | + | 305459.i | −0.123020 | + | 0.526713i | ||||
\(203\) | −11876.7 | − | 20571.1i | −0.0202281 | − | 0.0350362i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −216007. | + | 374136.i | −0.358991 | + | 0.621791i | ||||
\(206\) | 475255. | + | 445458.i | 0.780294 | + | 0.731373i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −551939. | + | 71825.2i | −0.884571 | + | 0.115111i | ||||
\(209\) | 581346. | + | 335640.i | 0.920596 | + | 0.531506i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −395205. | + | 228172.i | −0.611106 | + | 0.352822i | −0.773398 | − | 0.633920i | \(-0.781445\pi\) |
0.162292 | + | 0.986743i | \(0.448111\pi\) | |||||||
\(212\) | −605039. | − | 906972.i | −0.924579 | − | 1.38597i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −266400. | − | 879385.i | −0.397649 | − | 1.31264i | ||||
\(215\) | 271281. | 0.400242 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −30977.9 | −0.0446584 | ||||||||
\(218\) | 286098. | + | 944408.i | 0.407730 | + | 1.34592i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 549446. | + | 823636.i | 0.765364 | + | 1.14730i | ||||
\(221\) | −886874. | + | 512037.i | −1.22147 | + | 0.705213i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −105529. | − | 60927.0i | −0.142105 | − | 0.0820441i | 0.427262 | − | 0.904128i | \(-0.359478\pi\) |
−0.569367 | + | 0.822084i | \(0.692812\pi\) | |||||||
\(224\) | 558925. | + | 402102.i | 0.744275 | + | 0.535447i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 377073. | + | 353432.i | 0.491082 | + | 0.460293i | ||||
\(227\) | 63879.8 | − | 110643.i | 0.0822809 | − | 0.142515i | −0.821948 | − | 0.569562i | \(-0.807113\pi\) |
0.904229 | + | 0.427047i | \(0.140446\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −194394. | − | 336700.i | −0.244959 | − | 0.424282i | 0.717161 | − | 0.696908i | \(-0.245441\pi\) |
−0.962120 | + | 0.272626i | \(0.912108\pi\) | |||||||
\(230\) | −64543.7 | + | 276346.i | −0.0804516 | + | 0.344456i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 12704.4 | + | 33869.9i | 0.0154965 | + | 0.0413137i | ||||
\(233\) | 147353.i | 0.177815i | 0.996040 | + | 0.0889077i | \(0.0283376\pi\) | ||||
−0.996040 | + | 0.0889077i | \(0.971662\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 52211.3i | − | 0.0616730i | ||||||
\(236\) | −305203. | − | 150793.i | −0.356705 | − | 0.176239i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.23364e6 | + | 288130.i | 1.41171 | + | 0.329720i | ||||
\(239\) | −186495. | − | 323018.i | −0.211189 | − | 0.365790i | 0.740898 | − | 0.671618i | \(-0.234400\pi\) |
−0.952087 | + | 0.305827i | \(0.901067\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −292951. | + | 507405.i | −0.324902 | + | 0.562746i | −0.981492 | − | 0.191501i | \(-0.938665\pi\) |
0.656591 | + | 0.754247i | \(0.271998\pi\) | |||||||
\(242\) | 1.26447e6 | − | 1.34905e6i | 1.38793 | − | 1.48077i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −22637.4 | − | 349380.i | −0.0243418 | − | 0.375684i | ||||
\(245\) | 102737. | + | 59315.3i | 0.109348 | + | 0.0631323i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −452379. | + | 261181.i | −0.471802 | + | 0.272395i | ||||
\(248\) | 46537.6 | + | 7736.98i | 0.0480480 | + | 0.00798808i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.02829e6 | − | 311507.i | 1.04055 | − | 0.315223i | ||||
\(251\) | −713349. | −0.714691 | −0.357345 | − | 0.933972i | \(-0.616318\pi\) | ||||
−0.357345 | + | 0.933972i | \(0.616318\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 791098. | 0.777015 | ||||||||
\(254\) | −1.01983e6 | + | 308946.i | −0.991843 | + | 0.300468i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −739236. | − | 743668.i | −0.704990 | − | 0.709217i | ||||
\(257\) | −487256. | + | 281317.i | −0.460176 | + | 0.265683i | −0.712118 | − | 0.702059i | \(-0.752264\pi\) |
0.251942 | + | 0.967742i | \(0.418931\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.14642e6 | − | 661883.i | −1.06192 | − | 0.613101i | ||||
\(260\) | −768828. | + | 49814.8i | −0.705336 | + | 0.0457009i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −953148. | + | 1.01690e6i | −0.857841 | + | 0.915222i | ||||
\(263\) | −833666. | + | 1.44395e6i | −0.743195 | + | 1.28725i | 0.207838 | + | 0.978163i | \(0.433357\pi\) |
−0.951033 | + | 0.309088i | \(0.899976\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −754575. | − | 1.30696e6i | −0.660067 | − | 1.14327i | ||||
\(266\) | 629256. | + | 146970.i | 0.545285 | + | 0.127357i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 814559. | − | 1.64866e6i | 0.692765 | − | 1.40215i | ||||
\(269\) | 909140.i | 0.766038i | 0.923740 | + | 0.383019i | \(0.125116\pi\) | ||||
−0.923740 | + | 0.383019i | \(0.874884\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 1.38725e6i | − | 1.14744i | −0.819050 | − | 0.573722i | \(-0.805499\pi\) | ||
0.819050 | − | 0.573722i | \(-0.194501\pi\) | |||||||
\(272\) | −1.78131e6 | − | 740964.i | −1.45988 | − | 0.607260i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 132005. | − | 565185.i | 0.106222 | − | 0.454794i | ||||
\(275\) | −406174. | − | 703514.i | −0.323877 | − | 0.560972i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −540237. | + | 935718.i | −0.423044 | + | 0.732733i | −0.996235 | − | 0.0866882i | \(-0.972372\pi\) |
0.573192 | + | 0.819421i | \(0.305705\pi\) | |||||||
\(278\) | −925748. | − | 867707.i | −0.718424 | − | 0.673382i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 736063. | + | 605453.i | 0.561073 | + | 0.461514i | ||||
\(281\) | 340589. | + | 196639.i | 0.257315 | + | 0.148561i | 0.623109 | − | 0.782135i | \(-0.285869\pi\) |
−0.365794 | + | 0.930696i | \(0.619203\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −248928. | + | 143719.i | −0.184760 | + | 0.106671i | −0.589527 | − | 0.807749i | \(-0.700686\pi\) |
0.404767 | + | 0.914420i | \(0.367353\pi\) | |||||||
\(284\) | 1.88744e6 | − | 1.25911e6i | 1.38860 | − | 0.926331i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 622689. | + | 2.05550e6i | 0.450149 | + | 1.48594i | ||||
\(287\) | 1.15931e6 | 0.830796 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.12981e6 | −1.50002 | ||||||||
\(290\) | 14517.4 | + | 47922.0i | 0.0101366 | + | 0.0334610i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 493854. | − | 329449.i | 0.338954 | − | 0.226116i | ||||
\(293\) | 1.55571e6 | − | 898188.i | 1.05867 | − | 0.611221i | 0.133603 | − | 0.991035i | \(-0.457345\pi\) |
0.925063 | + | 0.379814i | \(0.124012\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −408086. | − | 235608.i | −0.273021 | − | 0.157629i | ||||
\(296\) | 1.55693e6 | + | 1.28066e6i | 1.03286 | + | 0.849583i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 132469. | + | 124164.i | 0.0864118 | + | 0.0809941i | ||||
\(299\) | −307799. | + | 533124.i | −0.199108 | + | 0.344866i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −363990. | − | 630450.i | −0.231565 | − | 0.401083i | ||||
\(302\) | −97779.0 | + | 418644.i | −0.0616919 | + | 0.264136i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −908615. | − | 377952.i | −0.563892 | − | 0.234560i | ||||
\(305\) | − | 484629.i | − | 0.298304i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.13601e6i | 0.687918i | 0.938985 | + | 0.343959i | \(0.111768\pi\) | ||||
−0.938985 | + | 0.343959i | \(0.888232\pi\) | |||||||
\(308\) | 1.17689e6 | − | 2.38201e6i | 0.706902 | − | 1.43076i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 63590.6 | + | 14852.3i | 0.0375827 | + | 0.00877787i | ||||
\(311\) | −176499. | − | 305706.i | −0.103477 | − | 0.179227i | 0.809638 | − | 0.586929i | \(-0.199663\pi\) |
−0.913115 | + | 0.407703i | \(0.866330\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 68385.0 | − | 118446.i | 0.0394548 | − | 0.0683377i | −0.845624 | − | 0.533780i | \(-0.820771\pi\) |
0.885078 | + | 0.465442i | \(0.154105\pi\) | |||||||
\(314\) | 1.97832e6 | − | 2.11065e6i | 1.13233 | − | 1.20807i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 474066. | − | 30716.2i | 0.267068 | − | 0.0173041i | ||||
\(317\) | 609932. | + | 352144.i | 0.340905 | + | 0.196822i | 0.660672 | − | 0.750675i | \(-0.270271\pi\) |
−0.319767 | + | 0.947496i | \(0.603605\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 120886. | − | 69793.3i | 0.0665117 | − | 0.0384005i | ||||
\(320\) | −954558. | − | 1.09340e6i | −0.521108 | − | 0.596903i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 728822. | − | 220789.i | 0.391726 | − | 0.118669i | ||||
\(323\) | −1.81062e6 | −0.965654 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 632134. | 0.331972 | ||||||||
\(326\) | 1.11770e6 | − | 338595.i | 0.582482 | − | 0.176456i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.74161e6 | − | 289547.i | −0.893854 | − | 0.148605i | ||||
\(329\) | −121338. | + | 70054.4i | −0.0618025 | + | 0.0356817i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.21122e6 | + | 699299.i | 0.607650 | + | 0.350827i | 0.772045 | − | 0.635567i | \(-0.219234\pi\) |
−0.164395 | + | 0.986395i | \(0.552567\pi\) | |||||||
\(332\) | 4968.27 | + | 76679.0i | 0.00247377 | + | 0.0381796i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.24556e6 | − | 1.32887e6i | 0.610939 | − | 0.651805i | ||||
\(335\) | 1.27272e6 | − | 2.20441e6i | 0.619611 | − | 1.07320i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 565468. | + | 979419.i | 0.271227 | + | 0.469779i | 0.969176 | − | 0.246368i | \(-0.0792372\pi\) |
−0.697949 | + | 0.716147i | \(0.745904\pi\) | |||||||
\(338\) | 417824. | + | 97587.4i | 0.198930 | + | 0.0464624i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.39423e6 | − | 1.18293e6i | −1.12323 | − | 0.554960i | ||||
\(341\) | − | 182041.i | − | 0.0847781i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 2.31610e6i | − | 1.06297i | ||||||
\(344\) | 389357. | + | 1.03802e6i | 0.177399 | + | 0.472946i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 705071. | − | 3.01878e6i | 0.316623 | − | 1.35563i | ||||
\(347\) | 669599. | + | 1.15978e6i | 0.298532 | + | 0.517073i | 0.975800 | − | 0.218663i | \(-0.0701697\pi\) |
−0.677268 | + | 0.735736i | \(0.736836\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −997138. | + | 1.72709e6i | −0.438220 | + | 0.759019i | −0.997552 | − | 0.0699247i | \(-0.977724\pi\) |
0.559333 | + | 0.828943i | \(0.311057\pi\) | |||||||
\(350\) | −570544. | − | 534773.i | −0.248954 | − | 0.233346i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.36295e6 | + | 3.28452e6i | −1.01648 | + | 1.41291i | ||||
\(353\) | −1.57369e6 | − | 908571.i | −0.672175 | − | 0.388081i | 0.124725 | − | 0.992191i | \(-0.460195\pi\) |
−0.796900 | + | 0.604111i | \(0.793528\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.71983e6 | − | 1.57029e6i | 1.14544 | − | 0.661318i | ||||
\(356\) | −511074. | − | 766115.i | −0.213727 | − | 0.320383i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 278431. | + | 919101.i | 0.114818 | + | 0.379014i | ||||
\(359\) | −1.16638e6 | −0.477644 | −0.238822 | − | 0.971063i | \(-0.576761\pi\) | ||||
−0.238822 | + | 0.971063i | \(0.576761\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.55253e6 | 0.627008 | ||||||||
\(362\) | 1.07004e6 | + | 3.53220e6i | 0.429169 | + | 1.41669i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.14734e6 | + | 1.71990e6i | 0.453878 | + | 0.680377i | ||||
\(365\) | 711652. | − | 410873.i | 0.279599 | − | 0.161427i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.42589e6 | − | 823237.i | −0.552612 | − | 0.319051i | 0.197563 | − | 0.980290i | \(-0.436697\pi\) |
−0.750175 | + | 0.661240i | \(0.770031\pi\) | |||||||
\(368\) | −1.15004e6 | + | 149658.i | −0.442684 | + | 0.0576076i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.03599e6 | + | 1.90834e6i | 0.773164 | + | 0.724689i | ||||
\(371\) | −2.02490e6 | + | 3.50723e6i | −0.763780 | + | 1.32291i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 973750. | + | 1.68658e6i | 0.362389 | + | 0.627677i | 0.988354 | − | 0.152175i | \(-0.0486278\pi\) |
−0.625964 | + | 0.779852i | \(0.715294\pi\) | |||||||
\(374\) | −1.69319e6 | + | 7.24945e6i | −0.625932 | + | 2.67995i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 199780. | − | 74936.5i | 0.0728758 | − | 0.0273353i | ||||
\(377\) | 108620.i | 0.0393602i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.71999e6i | 1.68789i | 0.536432 | + | 0.843943i | \(0.319772\pi\) | ||||
−0.536432 | + | 0.843943i | \(0.680228\pi\) | |||||||
\(380\) | −1.22126e6 | − | 603391.i | −0.433858 | − | 0.214358i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.44214e6 | − | 336828.i | −0.505649 | − | 0.118100i | ||||
\(383\) | −252323. | − | 437037.i | −0.0878943 | − | 0.152237i | 0.818727 | − | 0.574184i | \(-0.194680\pi\) |
−0.906621 | + | 0.421946i | \(0.861347\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.83884e6 | − | 3.18497e6i | 0.632256 | − | 1.09510i | ||||
\(386\) | −3.52837e6 | + | 3.76438e6i | −1.20533 | + | 1.28595i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −325824. | − | 5.02869e6i | −0.109876 | − | 1.69580i | ||||
\(389\) | −1.60551e6 | − | 926943.i | −0.537947 | − | 0.310584i | 0.206299 | − | 0.978489i | \(-0.433858\pi\) |
−0.744247 | + | 0.667905i | \(0.767191\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.84793e6 | + | 1.06690e6i | −0.611284 | + | 0.352925i | ||||
\(392\) | −79509.1 | + | 478244.i | −0.0261337 | + | 0.157193i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −765834. | + | 232001.i | −0.248539 | + | 0.0752920i | ||||
\(395\) | 657583. | 0.212059 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.32765e6 | −0.741209 | −0.370605 | − | 0.928791i | \(-0.620850\pi\) | ||||
−0.370605 | + | 0.928791i | \(0.620850\pi\) | |||||||
\(398\) | 3.07548e6 | − | 931682.i | 0.973207 | − | 0.294822i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 723556. | + | 945879.i | 0.226111 | + | 0.295587i | ||||
\(401\) | −3.17463e6 | + | 1.83287e6i | −0.985897 | + | 0.569208i | −0.904045 | − | 0.427436i | \(-0.859417\pi\) |
−0.0818519 | + | 0.996645i | \(0.526083\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 122678. | + | 70828.3i | 0.0376275 | + | 0.0217242i | ||||
\(404\) | −1.77073e6 | + | 114731.i | −0.539757 | + | 0.0349725i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 91890.7 | − | 98037.2i | 0.0276666 | − | 0.0295173i | ||||
\(407\) | 3.88955e6 | − | 6.73690e6i | 1.16389 | − | 2.01592i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 699640. | + | 1.21181e6i | 0.206807 | + | 0.358201i | 0.950707 | − | 0.310090i | \(-0.100359\pi\) |
−0.743900 | + | 0.668291i | \(0.767026\pi\) | |||||||
\(410\) | −2.37980e6 | − | 555828.i | −0.699165 | − | 0.163298i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.63221e6 | + | 3.30356e6i | −0.473731 | + | 0.958825i | ||||
\(413\) | 1.26451e6i | 0.364793i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 106362.i | 0.0303157i | ||||||||
\(416\) | −1.29407e6 | − | 2.87033e6i | −0.366628 | − | 0.813203i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −863667. | + | 3.69782e6i | −0.241772 | + | 1.03515i | ||||
\(419\) | 1.83298e6 | + | 3.17481e6i | 0.510061 | + | 0.883452i | 0.999932 | + | 0.0116570i | \(0.00371063\pi\) |
−0.489871 | + | 0.871795i | \(0.662956\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.68932e6 | − | 4.65804e6i | 0.739498 | − | 1.28085i | −0.213224 | − | 0.977003i | \(-0.568396\pi\) |
0.952722 | − | 0.303845i | \(-0.0982704\pi\) | |||||||
\(422\) | −1.88346e6 | − | 1.76538e6i | −0.514844 | − | 0.482566i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.91793e6 | − | 4.76312e6i | 1.05838 | − | 1.28670i | ||||
\(425\) | 1.89756e6 | + | 1.09556e6i | 0.509594 | + | 0.294214i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.12627e6 | + | 650249.i | −0.298931 | + | 0.172588i | ||||
\(428\) | 4.32397e6 | − | 2.88452e6i | 1.14097 | − | 0.761138i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 444921. | + | 1.46868e6i | 0.116041 | + | 0.383051i | ||||
\(431\) | 7.43683e6 | 1.92839 | 0.964194 | − | 0.265198i | \(-0.0854372\pi\) | ||||
0.964194 | + | 0.265198i | \(0.0854372\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.75454e6 | 1.21868 | 0.609339 | − | 0.792910i | \(-0.291435\pi\) | ||||
0.609339 | + | 0.792910i | \(0.291435\pi\) | |||||||
\(434\) | −50806.1 | − | 167711.i | −0.0129477 | − | 0.0427402i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.64369e6 | + | 3.09780e6i | −1.16990 | + | 0.780436i | ||||
\(437\) | −942594. | + | 544207.i | −0.236114 | + | 0.136320i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.50776e6 | + | 870508.i | 0.373398 | + | 0.215582i | 0.674942 | − | 0.737871i | \(-0.264169\pi\) |
−0.301544 | + | 0.953452i | \(0.597502\pi\) | |||||||
\(440\) | −3.55794e6 | + | 4.32546e6i | −0.876126 | + | 1.06513i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.22665e6 | − | 3.96165e6i | −1.02906 | − | 0.964541i | ||||
\(443\) | 412027. | − | 713652.i | 0.0997509 | − | 0.172774i | −0.811831 | − | 0.583893i | \(-0.801529\pi\) |
0.911582 | + | 0.411119i | \(0.134862\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −637386. | − | 1.10399e6i | −0.152582 | − | 0.264279i | ||||
\(446\) | 156777. | − | 671245.i | 0.0373202 | − | 0.159788i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.26026e6 | + | 3.68543e6i | −0.296663 | + | 0.867548i | ||||
\(449\) | − | 3.08674e6i | − | 0.722577i | −0.932454 | − | 0.361289i | \(-0.882337\pi\) | ||
0.932454 | − | 0.361289i | \(-0.117663\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.81266e6i | 1.57716i | ||||||||
\(452\) | −1.29501e6 | + | 2.62109e6i | −0.298145 | + | 0.603441i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 703776. | + | 164375.i | 0.160249 | + | 0.0374279i | ||||
\(455\) | 1.43091e6 | + | 2.47840e6i | 0.324028 | + | 0.561234i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.12118e6 | − | 1.94195e6i | 0.251123 | − | 0.434958i | −0.712712 | − | 0.701456i | \(-0.752534\pi\) |
0.963835 | + | 0.266499i | \(0.0858668\pi\) | |||||||
\(458\) | 1.50404e6 | − | 1.60464e6i | 0.335038 | − | 0.357449i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.60196e6 | + | 103796.i | −0.352986 | + | 0.0228711i | ||||
\(461\) | 3.91078e6 | + | 2.25789e6i | 0.857059 | + | 0.494823i | 0.863026 | − | 0.505159i | \(-0.168566\pi\) |
−0.00596751 | + | 0.999982i | \(0.501900\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.40455e6 | − | 4.27502e6i | 1.60526 | − | 0.926799i | 0.614853 | − | 0.788642i | \(-0.289216\pi\) |
0.990410 | − | 0.138157i | \(-0.0441178\pi\) | |||||||
\(464\) | −162531. | + | 124329.i | −0.0350463 | + | 0.0268089i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −797752. | + | 241670.i | −0.170178 | + | 0.0515535i | ||||
\(467\) | −7.67458e6 | −1.62841 | −0.814203 | − | 0.580581i | \(-0.802826\pi\) | ||||
−0.814203 | + | 0.580581i | \(0.802826\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.83065e6 | −1.43394 | ||||||||
\(470\) | 282666. | − | 85630.5i | 0.0590241 | − | 0.0178807i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 315821. | − | 1.89965e6i | 0.0652508 | − | 0.392481i | ||||
\(473\) | 3.70483e6 | − | 2.13898e6i | 0.761404 | − | 0.439597i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 967913. | + | 558825.i | 0.196835 | + | 0.113643i | ||||
\(476\) | 463357. | + | 7.15133e6i | 0.0937342 | + | 1.44667i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.44292e6 | − | 1.53943e6i | 0.288850 | − | 0.308171i | ||||
\(479\) | 2.80988e6 | − | 4.86685e6i | 0.559562 | − | 0.969191i | −0.437970 | − | 0.898989i | \(-0.644303\pi\) |
0.997533 | − | 0.0702012i | \(-0.0223641\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.02668e6 | + | 5.24236e6i | 0.596491 | + | 1.03315i | ||||
\(482\) | −3.22750e6 | − | 753818.i | −0.632773 | − | 0.147791i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.37740e6 | + | 4.63313e6i | 1.81957 | + | 0.899004i | ||||
\(485\) | − | 6.97536e6i | − | 1.34652i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 4.64134e6i | − | 0.886790i | −0.896326 | − | 0.443395i | \(-0.853774\pi\) | ||
0.896326 | − | 0.443395i | \(-0.146226\pi\) | |||||||
\(488\) | 1.85438e6 | − | 695566.i | 0.352491 | − | 0.132217i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −152630. | + | 653488.i | −0.0287176 | + | 0.122955i | ||||
\(491\) | −32004.7 | − | 55433.7i | −0.00599115 | − | 0.0103770i | 0.863014 | − | 0.505180i | \(-0.168574\pi\) |
−0.869005 | + | 0.494803i | \(0.835240\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −188251. | + | 326060.i | −0.0348835 | + | 0.0604200i | ||||
\(494\) | −2.15594e6 | − | 2.02077e6i | −0.397483 | − | 0.372563i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 34438.1 | + | 264639.i | 0.00628543 | + | 0.0483002i | ||||
\(497\) | −7.29865e6 | − | 4.21388e6i | −1.32541 | − | 0.765228i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.98798e6 | + | 2.30246e6i | −0.716972 | + | 0.413944i | −0.813637 | − | 0.581373i | \(-0.802516\pi\) |
0.0966654 | + | 0.995317i | \(0.469182\pi\) | |||||||
\(500\) | 3.37293e6 | + | 5.05612e6i | 0.603368 | + | 0.904466i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.16995e6 | − | 3.86199e6i | −0.207208 | − | 0.683994i | ||||
\(503\) | −4.30022e6 | −0.757829 | −0.378914 | − | 0.925432i | \(-0.623703\pi\) | ||||
−0.378914 | + | 0.925432i | \(0.623703\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.45620e6 | −0.428583 | ||||||||
\(506\) | 1.29746e6 | + | 4.28292e6i | 0.225278 | + | 0.743641i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.34519e6 | − | 5.01454e6i | −0.575124 | − | 0.862128i | ||||
\(509\) | 6.05140e6 | − | 3.49378e6i | 1.03529 | − | 0.597724i | 0.116793 | − | 0.993156i | \(-0.462739\pi\) |
0.918495 | + | 0.395433i | \(0.129405\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.90971e6 | − | 1.10257e6i | −0.323531 | − | 0.186791i | ||||
\(512\) | 2.81373e6 | − | 5.22181e6i | 0.474359 | − | 0.880331i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.32216e6 | − | 2.17657e6i | −0.387689 | − | 0.363382i | ||||
\(515\) | −2.55025e6 | + | 4.41717e6i | −0.423707 | + | 0.733882i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −411674. | − | 713040.i | −0.0677372 | − | 0.117324i | ||||
\(518\) | 1.70315e6 | − | 7.29210e6i | 0.278888 | − | 1.19407i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.53063e6 | − | 4.08065e6i | −0.248234 | − | 0.661791i | ||||
\(521\) | 6.03385e6i | 0.973868i | 0.873439 | + | 0.486934i | \(0.161885\pi\) | ||||
−0.873439 | + | 0.486934i | \(0.838115\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 1.21106e6i | − | 0.193603i | −0.995304 | − | 0.0968013i | \(-0.969139\pi\) | ||
0.995304 | − | 0.0968013i | \(-0.0308612\pi\) | |||||||
\(524\) | −7.06863e6 | − | 3.49243e6i | −1.12462 | − | 0.555648i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.18467e6 | − | 2.14518e6i | −1.44743 | − | 0.338065i | ||||
\(527\) | 245507. | + | 425230.i | 0.0385067 | + | 0.0666956i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.57683e6 | − | 4.46320e6i | 0.400356 | − | 0.693437i | ||||
\(530\) | 5.83819e6 | − | 6.22870e6i | 0.902793 | − | 0.963181i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 236350. | + | 3.64776e6i | 0.0362057 | + | 0.558789i | ||||
\(533\) | −4.59108e6 | − | 2.65066e6i | −0.699997 | − | 0.404144i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.23092e6 | − | 3.59743e6i | 0.941170 | − | 0.543385i | ||||
\(536\) | 1.02616e7 | + | 1.70601e6i | 1.54277 | + | 0.256489i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.92198e6 | + | 1.49106e6i | −0.733136 | + | 0.222095i | ||||
\(539\) | 1.87075e6 | 0.277360 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.95265e6 | −0.727519 | −0.363760 | − | 0.931493i | \(-0.618507\pi\) | ||||
−0.363760 | + | 0.931493i | \(0.618507\pi\) | |||||||
\(542\) | 7.51041e6 | − | 2.27519e6i | 1.09816 | − | 0.332675i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.09001e6 | − | 1.08590e7i | 0.157918 | − | 1.57324i | ||||
\(545\) | −6.69165e6 | + | 3.86342e6i | −0.965032 | + | 0.557161i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −381241. | − | 220109.i | −0.0544792 | − | 0.0314536i | 0.472513 | − | 0.881324i | \(-0.343347\pi\) |
−0.526992 | + | 0.849870i | \(0.676680\pi\) | |||||||
\(548\) | 3.27635e6 | − | 212285.i | 0.466056 | − | 0.0301972i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.14259e6 | − | 3.35280e6i | 0.442977 | − | 0.472607i | ||||
\(551\) | −96023.5 | + | 166318.i | −0.0134741 | + | 0.0233378i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −882310. | − | 1.52821e6i | −0.122690 | − | 0.212505i | ||||
\(554\) | −5.95190e6 | − | 1.39013e6i | −0.823913 | − | 0.192434i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.17937e6 | − | 6.43500e6i | 0.436168 | − | 0.882799i | ||||
\(557\) | − | 2.77476e6i | − | 0.378955i | −0.981885 | − | 0.189477i | \(-0.939321\pi\) | ||
0.981885 | − | 0.189477i | \(-0.0606794\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.32893e6i | 0.450583i | ||||||||
\(560\) | −2.07065e6 | + | 4.97795e6i | −0.279021 | + | 0.670780i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −505991. | + | 2.16641e6i | −0.0675774 | + | 0.289335i | ||||
\(563\) | −1.99125e6 | − | 3.44895e6i | −0.264762 | − | 0.458581i | 0.702740 | − | 0.711447i | \(-0.251960\pi\) |
−0.967501 | + | 0.252867i | \(0.918627\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.02340e6 | + | 3.50464e6i | −0.266662 | + | 0.461872i | ||||
\(566\) | −1.18634e6 | − | 1.11196e6i | −0.155656 | − | 0.145897i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.91219e6 | + | 8.15334e6i | 1.28914 | + | 1.06039i | ||||
\(569\) | 6.64391e6 | + | 3.83587e6i | 0.860287 | + | 0.496687i | 0.864108 | − | 0.503306i | \(-0.167883\pi\) |
−0.00382141 | + | 0.999993i | \(0.501216\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.95051e6 | + | 2.85818e6i | −0.635418 | + | 0.366859i | −0.782847 | − | 0.622214i | \(-0.786234\pi\) |
0.147429 | + | 0.989073i | \(0.452900\pi\) | |||||||
\(572\) | −1.01070e7 | + | 6.74234e6i | −1.29161 | + | 0.861629i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.90135e6 | + | 6.27636e6i | 0.240870 | + | 0.795112i | ||||
\(575\) | 1.31714e6 | 0.166136 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.39744e6 | −1.17509 | −0.587544 | − | 0.809192i | \(-0.699905\pi\) | ||||
−0.587544 | + | 0.809192i | \(0.699905\pi\) | |||||||
\(578\) | −3.49305e6 | − | 1.15305e7i | −0.434896 | − | 1.43559i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −235634. | + | 157191.i | −0.0290850 | + | 0.0194025i | ||||
\(581\) | 247183. | − | 142711.i | 0.0303794 | − | 0.0175395i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.06102e7 | − | 1.18993e7i | −2.51137 | − | 1.44994i | ||||
\(584\) | 2.59356e6 | + | 2.13335e6i | 0.314676 | + | 0.258839i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.41416e6 | + | 6.94932e6i | 0.891904 | + | 0.835985i | ||||
\(587\) | −7.92251e6 | + | 1.37222e7i | −0.949002 | + | 1.64372i | −0.201471 | + | 0.979495i | \(0.564572\pi\) |
−0.747532 | + | 0.664226i | \(0.768761\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 125229. | + | 216902.i | 0.0148736 | + | 0.0257618i | ||||
\(590\) | 606265. | − | 2.59574e6i | 0.0717022 | − | 0.306995i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.37988e6 | + | 1.05294e7i | −0.513639 | + | 1.23481i | ||||
\(593\) | 945465.i | 0.110410i | 0.998475 | + | 0.0552050i | \(0.0175812\pi\) | ||||
−0.998475 | + | 0.0552050i | \(0.982419\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.91969e6i | 1.14870i | ||||||||
\(596\) | −454948. | + | 920809.i | −0.0524622 | + | 0.106183i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.39109e6 | − | 792026.i | −0.387780 | − | 0.0905705i | ||||
\(599\) | −3.63749e6 | − | 6.30031e6i | −0.414223 | − | 0.717455i | 0.581123 | − | 0.813815i | \(-0.302613\pi\) |
−0.995347 | + | 0.0963599i | \(0.969280\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.93990e6 | + | 5.09206e6i | −0.332007 | + | 0.575053i | −0.982905 | − | 0.184112i | \(-0.941059\pi\) |
0.650898 | + | 0.759165i | \(0.274392\pi\) | |||||||
\(602\) | 2.81621e6 | − | 3.00459e6i | 0.316719 | − | 0.337904i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.42686e6 | + | 157244.i | −0.270677 | + | 0.0175380i | ||||
\(605\) | 1.25385e7 | + | 7.23908e6i | 1.39269 | + | 0.804072i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.03686e6 | − | 1.75333e6i | 0.334544 | − | 0.193149i | −0.323313 | − | 0.946292i | \(-0.604797\pi\) |
0.657857 | + | 0.753143i | \(0.271463\pi\) | |||||||
\(608\) | 555994. | − | 5.53901e6i | 0.0609973 | − | 0.607677i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.62373e6 | − | 794828.i | 0.285492 | − | 0.0864866i | ||||
\(611\) | 640694. | 0.0694300 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.60744e7 | 1.72776 | 0.863880 | − | 0.503697i | \(-0.168027\pi\) | ||||
0.863880 | + | 0.503697i | \(0.168027\pi\) | |||||||
\(614\) | −6.15023e6 | + | 1.86314e6i | −0.658371 | + | 0.199446i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.48261e7 | + | 2.46487e6i | 1.57426 | + | 0.261724i | ||||
\(617\) | −5.66445e6 | + | 3.27037e6i | −0.599024 | + | 0.345847i | −0.768658 | − | 0.639660i | \(-0.779075\pi\) |
0.169633 | + | 0.985507i | \(0.445742\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.47481e6 | + | 5.47028e6i | 0.993903 | + | 0.573830i | 0.906439 | − | 0.422338i | \(-0.138790\pi\) |
0.0874641 | + | 0.996168i | \(0.472124\pi\) | |||||||
\(620\) | 23884.7 | + | 368631.i | 0.00249541 | + | 0.0385135i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.36558e6 | − | 1.45693e6i | 0.141528 | − | 0.150995i | ||||
\(623\) | −1.71042e6 | + | 2.96254e6i | −0.176556 | + | 0.305805i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.38940e6 | + | 4.13856e6i | 0.244674 | + | 0.423788i | ||||
\(626\) | 753411. | + | 175968.i | 0.0768415 | + | 0.0179472i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.46714e7 | + | 7.24878e6i | 1.48448 | + | 0.733443i | ||||
\(629\) | 2.09823e7i | 2.11459i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1.64472e7i | − | 1.64444i | −0.569168 | − | 0.822221i | \(-0.692735\pi\) | ||
0.569168 | − | 0.822221i | \(-0.307265\pi\) | |||||||
\(632\) | 943798. | + | 2.51616e6i | 0.0939910 | + | 0.250580i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −906135. | + | 3.87965e6i | −0.0895302 | + | 0.383327i | ||||
\(635\) | −4.17196e6 | − | 7.22604e6i | −0.410587 | − | 0.711158i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −727867. | + | 1.26070e6i | −0.0710728 | + | 0.123102i | ||||
\(638\) | 576115. | + | 539994.i | 0.0560347 | + | 0.0525216i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 4.35399e6 | − | 6.96113e6i | 0.420182 | − | 0.671784i | ||||
\(641\) | 6.01469e6 | + | 3.47258e6i | 0.578187 | + | 0.333816i | 0.760413 | − | 0.649440i | \(-0.224997\pi\) |
−0.182226 | + | 0.983257i | \(0.558330\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.22490e7 | − | 7.07195e6i | 1.16835 | − | 0.674546i | 0.215057 | − | 0.976601i | \(-0.431006\pi\) |
0.953290 | + | 0.302055i | \(0.0976728\pi\) | |||||||
\(644\) | 2.39065e6 | + | 3.58365e6i | 0.227144 | + | 0.340495i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.96956e6 | − | 9.80250e6i | −0.279969 | − | 0.924178i | ||||
\(647\) | 1.06848e7 | 1.00347 | 0.501736 | − | 0.865021i | \(-0.332695\pi\) | ||||
0.501736 | + | 0.865021i | \(0.332695\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.43086e6 | −0.692512 | ||||||||
\(650\) | 1.03675e6 | + | 3.42230e6i | 0.0962476 | + | 0.317713i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.66623e6 | + | 5.49579e6i | 0.337755 | + | 0.506304i | ||||
\(653\) | −7.15281e6 | + | 4.12968e6i | −0.656438 | + | 0.378995i | −0.790919 | − | 0.611921i | \(-0.790397\pi\) |
0.134480 | + | 0.990916i | \(0.457064\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.45143e6 | − | 5.45678e6i | −0.860784 | − | 0.496974i | ||||
\(656\) | −1.28880e6 | − | 9.90376e6i | −0.116930 | − | 0.898546i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −578270. | − | 542014.i | −0.0520674 | − | 0.0488030i | ||||
\(659\) | −1.13554e6 | + | 1.96681e6i | −0.101856 | + | 0.176420i | −0.912450 | − | 0.409189i | \(-0.865812\pi\) |
0.810593 | + | 0.585610i | \(0.199145\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.82941e6 | + | 1.18289e7i | 0.607967 | + | 1.05303i | 0.991575 | + | 0.129533i | \(0.0413480\pi\) |
−0.383608 | + | 0.923496i | \(0.625319\pi\) | |||||||
\(662\) | −1.79943e6 | + | 7.70432e6i | −0.159584 | + | 0.683265i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −406983. | + | 152657.i | −0.0358225 | + | 0.0134368i | ||||
\(665\) | 5.05986e6i | 0.443695i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 226326.i | 0.0196979i | ||||||||
\(668\) | 9.23718e6 | + | 4.56385e6i | 0.800936 | + | 0.395722i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.40218e7 | + | 3.27494e6i | 1.20674 | + | 0.281849i | ||||
\(671\) | −3.82118e6 | − | 6.61848e6i | −0.327636 | − | 0.567482i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.08153e6 | + | 8.80146e6i | −0.432471 | + | 0.749061i | −0.997085 | − | 0.0762934i | \(-0.975691\pi\) |
0.564615 | + | 0.825355i | \(0.309025\pi\) | |||||||
\(674\) | −4.37505e6 | + | 4.66770e6i | −0.370966 | + | 0.395779i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 156935. | + | 2.42210e6i | 0.0132085 | + | 0.203857i | ||||
\(677\) | −2.00175e7 | − | 1.15571e7i | −1.67856 | − | 0.969120i | −0.962578 | − | 0.271006i | \(-0.912644\pi\) |
−0.715987 | − | 0.698113i | \(-0.754023\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.62105e7 | + | 9.35916e6i | −1.34935 | + | 0.779045i | ||||
\(680\) | 2.47752e6 | − | 1.49022e7i | 0.205469 | − | 1.23588i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 985550. | − | 298561.i | 0.0811368 | − | 0.0245795i | ||||
\(683\) | −5.18871e6 | −0.425606 | −0.212803 | − | 0.977095i | \(-0.568259\pi\) | ||||
−0.212803 | + | 0.977095i | \(0.568259\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.54466e6 | 0.370062 | ||||||||
\(686\) | 1.25391e7 | − | 3.79858e6i | 1.01732 | − | 0.308185i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.98117e6 | + | 3.81037e6i | −0.401199 | + | 0.306900i | ||||
\(689\) | 1.60379e7 | − | 9.25951e6i | 1.28707 | − | 0.743088i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.57664e6 | + | 910275.i | 0.125614 | + | 0.0725233i | 0.561490 | − | 0.827483i | \(-0.310228\pi\) |
−0.435876 | + | 0.900007i | \(0.643562\pi\) | |||||||
\(692\) | 1.74997e7 | − | 1.13386e6i | 1.38920 | − | 0.0900108i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.18072e6 | + | 5.52726e6i | −0.408311 | + | 0.435623i | ||||
\(695\) | 4.96764e6 | − | 8.60420e6i | 0.390111 | − | 0.675691i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.18777e6 | − | 1.59137e7i | −0.716355 | − | 1.24076i | ||||
\(698\) | −1.09857e7 | − | 2.56583e6i | −0.853469 | − | 0.199337i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.95947e6 | − | 3.96593e6i | 0.151145 | − | 0.305914i | ||||
\(701\) | 1.38877e7i | 1.06742i | 0.845667 | + | 0.533711i | \(0.179203\pi\) | ||||
−0.845667 | + | 0.533711i | \(0.820797\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.07027e7i | 0.816779i | ||||||||
\(704\) | −2.16574e7 | − | 7.40588e6i | −1.64693 | − | 0.563177i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.33793e6 | − | 1.00099e7i | 0.176530 | − | 0.755820i | ||||
\(707\) | 3.29560e6 | + | 5.70814e6i | 0.247962 | + | 0.429483i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.24469e6 | + | 3.88792e6i | −0.167703 | + | 0.290470i | −0.937612 | − | 0.347684i | \(-0.886968\pi\) |
0.769909 | + | 0.638154i | \(0.220302\pi\) | |||||||
\(710\) | 1.29621e7 | + | 1.21494e7i | 0.965006 | + | 0.904504i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.30946e6 | − | 4.02338e6i | 0.244657 | − | 0.297434i | ||||
\(713\) | 255617. | + | 147581.i | 0.0188307 | + | 0.0108719i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.45643e7 | + | 8.40871e6i | −1.06543 | + | 0.615126i | ||||
\(716\) | −4.51926e6 | + | 3.01479e6i | −0.329446 | + | 0.219773i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.91295e6 | − | 6.31466e6i | −0.138482 | − | 0.457129i | ||||
\(719\) | −603305. | −0.0435226 | −0.0217613 | − | 0.999763i | \(-0.506927\pi\) | ||||
−0.0217613 | + | 0.999763i | \(0.506927\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.36872e7 | 0.980564 | ||||||||
\(722\) | 2.54627e6 | + | 8.40523e6i | 0.181787 | + | 0.600077i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.73680e7 | + | 1.15861e7i | −1.23141 | + | 0.821472i | ||||
\(725\) | 201269. | − | 116203.i | 0.0142210 | − | 0.00821052i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.84417e7 | + | 1.06473e7i | 1.29409 | + | 0.747144i | 0.979377 | − | 0.202043i | \(-0.0647579\pi\) |
0.314714 | + | 0.949186i | \(0.398091\pi\) | |||||||
\(728\) | −7.42961e6 | + | 9.03234e6i | −0.519562 | + | 0.631643i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.39158e6 | + | 3.17894e6i | 0.235556 | + | 0.220788i | ||||
\(731\) | −5.76941e6 | + | 9.99291e6i | −0.399335 | + | 0.691669i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.21399e6 | − | 7.29884e6i | −0.289690 | − | 0.501758i | 0.684046 | − | 0.729439i | \(-0.260219\pi\) |
−0.973736 | + | 0.227682i | \(0.926885\pi\) | |||||||
\(734\) | 2.11834e6 | − | 9.06976e6i | 0.145130 | − | 0.621378i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.69639e6 | − | 5.98075e6i | −0.183480 | − | 0.406968i | ||||
\(737\) | − | 4.01402e7i | − | 2.72214i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1.72623e7i | − | 1.16275i | −0.813635 | − | 0.581376i | \(-0.802514\pi\) | ||
0.813635 | − | 0.581376i | \(-0.197486\pi\) | |||||||
\(740\) | −6.99237e6 | + | 1.41524e7i | −0.469402 | + | 0.950063i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.23087e7 | − | 5.21045e6i | −1.48753 | − | 0.347428i | ||||
\(743\) | 8.79333e6 | + | 1.52305e7i | 0.584361 | + | 1.01214i | 0.994955 | + | 0.100324i | \(0.0319881\pi\) |
−0.410594 | + | 0.911818i | \(0.634679\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −710838. | + | 1.23121e6i | −0.0469224 | + | 0.0812719i | ||||
\(746\) | −7.53395e6 | + | 8.03789e6i | −0.495651 | + | 0.528805i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4.20247e7 | + | 2.72291e6i | −2.74632 | + | 0.177942i | ||||
\(749\) | −1.67206e7 | − | 9.65367e6i | −1.08905 | − | 0.628764i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.82336e7 | − | 1.05272e7i | 1.17970 | − | 0.681101i | 0.223756 | − | 0.974645i | \(-0.428168\pi\) |
0.955945 | + | 0.293544i | \(0.0948349\pi\) | |||||||
\(752\) | 733353. | + | 958687.i | 0.0472899 | + | 0.0618205i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −588058. | + | 178146.i | −0.0376697 | + | 0.0114116i | ||||
\(755\) | −3.36632e6 | −0.214926 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.12325e6 | −0.451792 | −0.225896 | − | 0.974151i | \(-0.572531\pi\) | ||||
−0.225896 | + | 0.974151i | \(0.572531\pi\) | |||||||
\(758\) | −2.55535e7 | + | 7.74114e6i | −1.61539 | + | 0.489364i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.26374e6 | − | 7.60134e6i | 0.0793640 | − | 0.477371i | ||||
\(761\) | 4.12690e6 | − | 2.38267e6i | 0.258323 | − | 0.149143i | −0.365247 | − | 0.930911i | \(-0.619015\pi\) |
0.623569 | + | 0.781768i | \(0.285682\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.79570e7 | + | 1.03675e7i | 1.11666 | + | 0.644706i | ||||
\(764\) | −541671. | − | 8.36001e6i | −0.0335739 | − | 0.518171i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.95224e6 | − | 2.08282e6i | 0.120216 | − | 0.128257i | ||||
\(767\) | 2.89119e6 | − | 5.00768e6i | 0.177455 | − | 0.307361i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.98809e6 | − | 3.44347e6i | −0.121233 | − | 0.209981i | 0.799021 | − | 0.601303i | \(-0.205351\pi\) |
−0.920254 | + | 0.391321i | \(0.872018\pi\) | |||||||
\(770\) | 2.02589e7 | + | 4.73169e6i | 1.23137 | + | 0.287601i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.61667e7 | − | 1.29283e7i | −1.58018 | − | 0.780726i | ||||
\(773\) | − | 2.42703e7i | − | 1.46092i | −0.682957 | − | 0.730459i | \(-0.739306\pi\) | ||
0.682957 | − | 0.730459i | \(-0.260694\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 303090.i | − | 0.0181266i | ||||||
\(776\) | 2.66904e7 | − | 1.00114e7i | 1.59111 | − | 0.596817i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.38520e6 | − | 1.02123e7i | 0.141278 | − | 0.604888i | ||||
\(779\) | −4.68652e6 | − | 8.11729e6i | −0.276699 | − | 0.479256i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.47628e7 | − | 4.28904e7i | 1.45269 | − | 2.51613i | ||||
\(782\) | −8.80682e6 | − | 8.25466e6i | −0.514994 | − | 0.482706i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.71956e6 | + | 353903.i | −0.158019 | + | 0.0205634i | ||||
\(785\) | 1.96171e7 | + | 1.13259e7i | 1.13621 | + | 0.655994i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.72373e6 | − | 2.14990e6i | 0.214310 | − | 0.123732i | −0.389003 | − | 0.921236i | \(-0.627180\pi\) |
0.603313 | + | 0.797505i | \(0.293847\pi\) | |||||||
\(788\) | −2.51205e6 | − | 3.76564e6i | −0.144116 | − | 0.216034i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.07849e6 | + | 3.56008e6i | 0.0614818 | + | 0.202951i | ||||
\(791\) | 1.08596e7 | 0.617123 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.94696e6 | 0.335824 | ||||||||
\(794\) | −3.81752e6 | − | 1.26016e7i | −0.214897 | − | 0.709373i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.00880e7 | + | 1.51223e7i | 0.564318 | + | 0.845929i | ||||
\(797\) | −4.99939e6 | + | 2.88640e6i | −0.278786 | + | 0.160957i | −0.632874 | − | 0.774255i | \(-0.718125\pi\) |
0.354087 | + | 0.935212i | \(0.384792\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.92326e6 | + | 1.11039e6i | 0.106579 | + | 0.0615333i | ||||
\(800\) | −3.93420e6 | + | 5.46856e6i | −0.217336 | + | 0.302098i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.51296e7 | − | 1.41810e7i | −0.830598 | − | 0.778523i | ||||
\(803\) | 6.47926e6 | − | 1.12224e7i | 0.354598 | − | 0.614183i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.98150e6 | + | 5.16411e6i | 0.162160 | + | 0.280870i | ||||
\(806\) | −182255. | + | 780330.i | −0.00988192 | + | 0.0423098i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.52527e6 | − | 9.39835e6i | −0.189961 | − | 0.506434i | ||||
\(809\) | − | 1.31473e7i | − | 0.706260i | −0.935574 | − | 0.353130i | \(-0.885117\pi\) | ||
0.935574 | − | 0.353130i | \(-0.114883\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.56762e7i | 0.836930i | 0.908233 | + | 0.418465i | \(0.137432\pi\) | ||||
−0.908233 | + | 0.418465i | \(0.862568\pi\) | |||||||
\(812\) | 681470. | + | 336697.i | 0.0362708 | + | 0.0179205i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.28519e7 | + | 1.00086e7i | 2.26678 | + | 0.529432i | ||||
\(815\) | 4.57235e6 | + | 7.91954e6i | 0.241127 | + | 0.417643i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.94287e6 | + | 5.09720e6i | −0.154247 | + | 0.267163i | ||||
\(818\) | −5.41315e6 | + | 5.77523e6i | −0.282857 | + | 0.301777i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −893856. | − | 1.37955e7i | −0.0464230 | − | 0.716480i | ||||
\(821\) | 4.25997e6 | + | 2.45949e6i | 0.220571 | + | 0.127347i | 0.606215 | − | 0.795301i | \(-0.292687\pi\) |
−0.385644 | + | 0.922648i | \(0.626021\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.72278e7 | + | 1.57200e7i | −1.40124 | + | 0.809008i | −0.994520 | − | 0.104544i | \(-0.966662\pi\) |
−0.406722 | + | 0.913552i | \(0.633328\pi\) | |||||||
\(824\) | −2.05620e7 | − | 3.41848e6i | −1.05499 | − | 0.175394i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.84590e6 | + | 2.07389e6i | −0.349124 | + | 0.105763i | ||||
\(827\) | 7.97015e6 | 0.405231 | 0.202615 | − | 0.979258i | \(-0.435056\pi\) | ||||
0.202615 | + | 0.979258i | \(0.435056\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.91383e7 | −0.967204 | −0.483602 | − | 0.875288i | \(-0.660672\pi\) | ||||
−0.483602 | + | 0.875288i | \(0.660672\pi\) | |||||||
\(830\) | −575834. | + | 174442.i | −0.0290136 | + | 0.00878935i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.34173e7 | − | 1.17135e7i | 0.671980 | − | 0.586651i | ||||
\(833\) | −4.36988e6 | + | 2.52295e6i | −0.218201 | + | 0.125978i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.23510e7 | + | 7.13084e6i | 0.613034 | + | 0.353936i | ||||
\(836\) | −2.14360e7 | + | 1.38891e6i | −1.06079 | + | 0.0687318i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.41818e7 | + | 1.51305e7i | −0.697626 | + | 0.744290i | ||||
\(839\) | 9.33436e6 | − | 1.61676e7i | 0.457804 | − | 0.792940i | −0.541040 | − | 0.840997i | \(-0.681969\pi\) |
0.998845 | + | 0.0480564i | \(0.0153027\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.02356e7 | − | 1.77286e7i | −0.499027 | − | 0.864339i | ||||
\(842\) | 2.96288e7 | + | 6.92013e6i | 1.44023 | + | 0.336383i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6.46853e6 | − | 1.30922e7i | 0.312571 | − | 0.632640i | ||||
\(845\) | 3.35972e6i | 0.161868i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 3.88521e7i | − | 1.86083i | ||||||
\(848\) | 3.22127e7 | + | 1.33994e7i | 1.53829 | + | 0.639874i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.81908e6 | + | 1.20700e7i | −0.133832 | + | 0.573007i | ||||
\(851\) | 6.30651e6 | + | 1.09232e7i | 0.298515 | + | 0.517042i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.47087e7 | + | 2.54762e7i | −0.692151 | + | 1.19884i | 0.278980 | + | 0.960297i | \(0.410004\pi\) |
−0.971132 | + | 0.238545i | \(0.923330\pi\) | |||||||
\(854\) | −5.36754e6 | − | 5.03101e6i | −0.251843 | − | 0.236054i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.27081e7 | + | 1.86787e7i | 1.05924 | + | 0.871288i | ||||
\(857\) | −2.51109e6 | − | 1.44978e6i | −0.116791 | − | 0.0674295i | 0.440466 | − | 0.897769i | \(-0.354813\pi\) |
−0.557258 | + | 0.830340i | \(0.688146\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.24474e7 | + | 7.18653e6i | −0.575568 | + | 0.332305i | −0.759370 | − | 0.650659i | \(-0.774493\pi\) |
0.183802 | + | 0.982963i | \(0.441160\pi\) | |||||||
\(860\) | −7.22158e6 | + | 4.81750e6i | −0.332955 | + | 0.222114i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.21970e7 | + | 4.02621e7i | 0.559092 | + | 1.84556i | ||||
\(863\) | 1.28520e7 | 0.587415 | 0.293707 | − | 0.955895i | \(-0.405111\pi\) | ||||
0.293707 | + | 0.955895i | \(0.405111\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.42741e7 | 1.10307 | ||||||||
\(866\) | 7.79781e6 | + | 2.57405e7i | 0.353328 | + | 1.16633i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 824641. | − | 550117.i | 0.0371506 | − | 0.0247831i | ||||
\(869\) | 8.98048e6 | − | 5.18488e6i | 0.403413 | − | 0.232911i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.70506e7 | + | 1.56177e7i | 1.20818 | + | 0.697544i | ||||
\(872\) | −2.43871e7 | − | 2.00598e7i | −1.08610 | − | 0.893378i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.49220e6 | − | 4.21056e6i | −0.198921 | − | 0.186449i | ||||
\(875\) | 1.12883e7 | − | 1.95518e7i | 0.498433 | − | 0.863311i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.87712e6 | − | 1.36436e7i | −0.345834 | − | 0.599003i | 0.639671 | − | 0.768649i | \(-0.279071\pi\) |
−0.985505 | + | 0.169646i | \(0.945737\pi\) | |||||||
\(878\) | −2.23998e6 | + | 9.59056e6i | −0.0980638 | + | 0.419863i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.92528e7 | − | 1.21682e7i | −1.27339 | − | 0.529686i | ||||
\(881\) | 2.21764e7i | 0.962614i | 0.876552 | + | 0.481307i | \(0.159838\pi\) | ||||
−0.876552 | + | 0.481307i | \(0.840162\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.26849e7i | 0.547503i | 0.961800 | + | 0.273751i | \(0.0882646\pi\) | ||||
−0.961800 | + | 0.273751i | \(0.911735\pi\) | |||||||
\(884\) | 1.45159e7 | − | 2.93800e7i | 0.624761 | − | 1.26451i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.53939e6 | + | 1.06023e6i | 0.194273 | + | 0.0453747i | ||||
\(887\) | −8.63224e6 | − | 1.49515e7i | −0.368395 | − | 0.638080i | 0.620919 | − | 0.783874i | \(-0.286759\pi\) |
−0.989315 | + | 0.145795i | \(0.953426\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.11954e7 | + | 1.93910e7i | −0.475101 | + | 0.822899i | ||||
\(890\) | 4.93149e6 | − | 5.26136e6i | 0.208691 | − | 0.222650i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.89117e6 | − | 252121.i | 0.163745 | − | 0.0106095i | ||||
\(893\) | 981020. | + | 566392.i | 0.0411670 | + | 0.0237678i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.51233e6 | + | 3.75990e6i | −0.271756 | + | 0.156898i | ||||
\(896\) | −2.20194e7 | − | 778493.i | −0.916297 | − | 0.0323955i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.67113e7 | − | 5.06249e6i | 0.691541 | − | 0.209495i | ||||
\(899\) | 52080.3 | 0.00214919 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.41911e7 | 2.63428 | ||||||||
\(902\) | −3.68830e7 | + | 1.11733e7i | −1.50942 | + | 0.457261i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.63142e7 | − | 2.71227e6i | −0.663963 | − | 0.110385i | ||||
\(905\) | −2.50276e7 | + | 1.44497e7i | −1.01577 | + | 0.586457i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.58029e7 | − | 1.48973e7i | −1.04148 | − | 0.601299i | −0.121228 | − | 0.992625i | \(-0.538683\pi\) |
−0.920252 | + | 0.391326i | \(0.872016\pi\) | |||||||
\(908\) | 264340. | + | 4.07975e6i | 0.0106402 | + | 0.164217i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.10710e7 | + | 1.18115e7i | −0.443183 | + | 0.472828i | ||||
\(911\) | −8.63136e6 | + | 1.49500e7i | −0.344575 | + | 0.596821i | −0.985276 | − | 0.170969i | \(-0.945310\pi\) |
0.640702 | + | 0.767790i | \(0.278643\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 838642. | + | 1.45257e6i | 0.0332966 | + | 0.0576714i | ||||
\(914\) | 1.23523e7 | + | 2.88502e6i | 0.489083 | + | 0.114231i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.11541e7 | + | 5.51094e6i | 0.439233 | + | 0.217014i | ||||
\(917\) | 2.92865e7i | 1.15012i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.37259e7i | 0.536108i | 0.963404 | + | 0.268054i | \(0.0863806\pi\) | ||||
−0.963404 | + | 0.268054i | \(0.913619\pi\) | |||||||
\(920\) | −3.18928e6 | − | 8.50261e6i | −0.124229 | − | 0.331194i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5.80997e6 | + | 2.48756e7i | −0.225085 | + | 0.963710i | ||||
\(923\) | 1.92693e7 | + | 3.33755e7i | 0.744496 | + | 1.28951i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.47591e6 | − | 1.12166e7i | 0.248855 | − | 0.431030i | ||||
\(926\) | 3.52885e7 | + | 3.30760e7i | 1.35240 | + | 1.26761i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −939669. | − | 676017.i | −0.0358183 | − | 0.0257684i | ||||
\(929\) | −9.81951e6 | − | 5.66929e6i | −0.373293 | − | 0.215521i | 0.301603 | − | 0.953434i | \(-0.402478\pi\) |
−0.674896 | + | 0.737913i | \(0.735812\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.22900e6 | + | 1.28691e6i | −0.0842821 | + | 0.0486603i | ||||
\(932\) | −2.61675e6 | − | 3.92258e6i | −0.0986784 | − | 0.147922i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.25869e7 | − | 4.15493e7i | −0.472119 | − | 1.55846i | ||||
\(935\) | −5.82929e7 | −2.18065 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.83186e6 | −0.328627 | −0.164314 | − | 0.986408i | \(-0.552541\pi\) | ||||
−0.164314 | + | 0.986408i | \(0.552541\pi\) | |||||||
\(938\) | −1.12028e7 | − | 3.69803e7i | −0.415737 | − | 1.37235i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 927188. | + | 1.38988e6i | 0.0342254 | + | 0.0513048i | ||||
\(941\) | 4.30299e7 | − | 2.48433e7i | 1.58415 | − | 0.914609i | 0.589905 | − | 0.807472i | \(-0.299165\pi\) |
0.994244 | − | 0.107137i | \(-0.0341683\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.56616e6 | − | 5.52302e6i | −0.350315 | − | 0.202254i | ||||
\(944\) | 1.08024e7 | − | 1.40575e6i | 0.394541 | − | 0.0513426i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.76564e7 | + | 1.65494e7i | 0.641468 | + | 0.601250i | ||||
\(947\) | 1.37159e7 | − | 2.37566e7i | 0.496992 | − | 0.860816i | −0.503002 | − | 0.864285i | \(-0.667771\pi\) |
0.999994 | + | 0.00346974i | \(0.00110445\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.04188e6 | + | 8.73280e6i | 0.181730 | + | 0.314766i | ||||
\(950\) | −1.43796e6 | + | 6.15669e6i | −0.0516938 | + | 0.221329i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.79565e7 | + | 1.42373e7i | −1.35736 | + | 0.509137i | ||||
\(953\) | 1.18932e7i | 0.424195i | 0.977248 | + | 0.212098i | \(0.0680295\pi\) | ||||
−0.977248 | + | 0.212098i | \(0.931971\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 1.15963e7i | − | 0.411443i | ||||||
\(956\) | 1.07008e7 | + | 5.28700e6i | 0.378680 | + | 0.187096i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.09570e7 | + | 7.23035e6i | 1.08979 | + | 0.254534i | ||||
\(959\) | −6.09778e6 | − | 1.05617e7i | −0.214104 | − | 0.370840i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.42806e7 | + | 2.47348e7i | −0.498814 | + | 0.863971i | ||||
\(962\) | −2.34176e7 | + | 2.49840e7i | −0.815838 | + | 0.870410i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.21225e6 | − | 1.87096e7i | −0.0420147 | − | 0.648443i | ||||
\(965\) | −3.49873e7 | − | 2.02000e7i | −1.20946 | − | 0.698284i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.04136e7 | − | 2.33328e7i | 1.38983 | − | 0.802419i | 0.396534 | − | 0.918020i | \(-0.370213\pi\) |
0.993296 | + | 0.115602i | \(0.0368796\pi\) | |||||||
\(968\) | −9.70362e6 | + | 5.83668e7i | −0.332847 | + | 2.00206i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.77638e7 | − | 1.14401e7i | 1.28868 | − | 0.390392i | ||||
\(971\) | −4.47524e7 | −1.52324 | −0.761620 | − | 0.648024i | \(-0.775595\pi\) | ||||
−0.761620 | + | 0.648024i | \(0.775595\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.66612e7 | −0.902814 | ||||||||
\(974\) | 2.51277e7 | − | 7.61214e6i | 0.848701 | − | 0.257104i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.80703e6 | + | 8.89859e6i | 0.228735 | + | 0.299018i | ||||
\(977\) | −3.02324e7 | + | 1.74547e7i | −1.01330 | + | 0.585027i | −0.912155 | − | 0.409845i | \(-0.865583\pi\) |
−0.101141 | + | 0.994872i | \(0.532249\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.74093e7 | − | 1.00513e7i | −0.580531 | − | 0.335169i | ||||
\(980\) | −3.78824e6 | + | 245452.i | −0.126000 | + | 0.00816395i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 247622. | − | 264185.i | 0.00819427 | − | 0.00874238i | ||||
\(983\) | −2.11197e7 | + | 3.65804e7i | −0.697114 | + | 1.20744i | 0.272349 | + | 0.962199i | \(0.412199\pi\) |
−0.969463 | + | 0.245238i | \(0.921134\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.13290e6 | − | 5.42635e6i | −0.102886 | − | 0.178204i | ||||
\(986\) | −2.07400e6 | − | 484406.i | −0.0679386 | − | 0.0158678i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.40431e6 | − | 1.49862e7i | 0.241319 | − | 0.488427i | ||||
\(989\) | 6.93630e6i | 0.225495i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1.67399e7i | − | 0.541463i | −0.962655 | − | 0.270732i | \(-0.912734\pi\) | ||
0.962655 | − | 0.270732i | \(-0.0872656\pi\) | |||||||
\(992\) | −1.37624e6 | + | 620471.i | −0.0444033 | + | 0.0200190i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.08431e7 | − | 4.64251e7i | 0.348087 | − | 1.49035i | ||||
\(995\) | 1.25813e7 | + | 2.17914e7i | 0.402873 | + | 0.697796i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.66678e7 | + | 2.88695e7i | −0.531056 | + | 0.919816i | 0.468287 | + | 0.883576i | \(0.344871\pi\) |
−0.999343 | + | 0.0362393i | \(0.988462\pi\) | |||||||
\(998\) | −1.90059e7 | − | 1.78143e7i | −0.604034 | − | 0.566163i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 108.6.h.a.35.16 | 56 | ||
3.2 | odd | 2 | 36.6.h.a.11.13 | yes | 56 | ||
4.3 | odd | 2 | inner | 108.6.h.a.35.27 | 56 | ||
9.4 | even | 3 | 36.6.h.a.23.2 | yes | 56 | ||
9.5 | odd | 6 | inner | 108.6.h.a.71.27 | 56 | ||
12.11 | even | 2 | 36.6.h.a.11.2 | ✓ | 56 | ||
36.23 | even | 6 | inner | 108.6.h.a.71.16 | 56 | ||
36.31 | odd | 6 | 36.6.h.a.23.13 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.6.h.a.11.2 | ✓ | 56 | 12.11 | even | 2 | ||
36.6.h.a.11.13 | yes | 56 | 3.2 | odd | 2 | ||
36.6.h.a.23.2 | yes | 56 | 9.4 | even | 3 | ||
36.6.h.a.23.13 | yes | 56 | 36.31 | odd | 6 | ||
108.6.h.a.35.16 | 56 | 1.1 | even | 1 | trivial | ||
108.6.h.a.35.27 | 56 | 4.3 | odd | 2 | inner | ||
108.6.h.a.71.16 | 56 | 36.23 | even | 6 | inner | ||
108.6.h.a.71.27 | 56 | 9.5 | odd | 6 | inner |