Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9,5,Mod(2,9)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9.2");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9 = 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 9.d (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: | \(0.930329667755\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 6.0.39400128.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 11x^{4} + 14x^{3} + 98x^{2} + 20x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 2.3 | ||
Root | \(-1.28901 + 2.23263i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9.2 |
Dual form | 9.5.d.a.5.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/9\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.86703 | + | 2.23263i | 0.966758 | + | 0.558158i | 0.898246 | − | 0.439492i | \(-0.144842\pi\) |
0.0685115 | + | 0.997650i | \(0.478175\pi\) | |||||||
\(3\) | −8.70335 | − | 2.29167i | −0.967039 | − | 0.254630i | ||||
\(4\) | 1.96929 | + | 3.41090i | 0.123080 | + | 0.213181i | ||||
\(5\) | 13.8760 | − | 8.01130i | 0.555039 | − | 0.320452i | −0.196113 | − | 0.980581i | \(-0.562832\pi\) |
0.751152 | + | 0.660129i | \(0.229499\pi\) | |||||||
\(6\) | −28.5397 | − | 28.2933i | −0.792768 | − | 0.785925i | ||||
\(7\) | −36.2418 | + | 62.7727i | −0.739630 | + | 1.28108i | 0.213033 | + | 0.977045i | \(0.431666\pi\) |
−0.952662 | + | 0.304031i | \(0.901667\pi\) | |||||||
\(8\) | − | 53.8574i | − | 0.841523i | ||||||
\(9\) | 70.4965 | + | 39.8904i | 0.870327 | + | 0.492474i | ||||
\(10\) | 71.5451 | 0.715451 | ||||||||
\(11\) | 83.2749 | + | 48.0788i | 0.688222 | + | 0.397345i | 0.802946 | − | 0.596052i | \(-0.203265\pi\) |
−0.114723 | + | 0.993397i | \(0.536598\pi\) | |||||||
\(12\) | −9.32272 | − | 34.1992i | −0.0647411 | − | 0.237495i | ||||
\(13\) | −76.9530 | − | 133.286i | −0.455343 | − | 0.788677i | 0.543365 | − | 0.839497i | \(-0.317150\pi\) |
−0.998708 | + | 0.0508193i | \(0.983817\pi\) | |||||||
\(14\) | −280.297 | + | 161.829i | −1.43009 | + | 0.825660i | ||||
\(15\) | −139.127 | + | 37.9260i | −0.618341 | + | 0.168560i | ||||
\(16\) | 151.752 | − | 262.843i | 0.592783 | − | 1.02673i | ||||
\(17\) | − | 72.7905i | − | 0.251870i | −0.992038 | − | 0.125935i | \(-0.959807\pi\) | ||
0.992038 | − | 0.125935i | \(-0.0401931\pi\) | |||||||
\(18\) | 183.552 | + | 311.650i | 0.566518 | + | 0.961883i | ||||
\(19\) | −190.660 | −0.528145 | −0.264072 | − | 0.964503i | \(-0.585066\pi\) | ||||
−0.264072 | + | 0.964503i | \(0.585066\pi\) | |||||||
\(20\) | 54.6515 | + | 31.5531i | 0.136629 | + | 0.0788827i | ||||
\(21\) | 459.280 | − | 463.279i | 1.04145 | − | 1.05052i | ||||
\(22\) | 214.684 | + | 371.844i | 0.443563 | + | 0.768273i | ||||
\(23\) | −12.5186 | + | 7.22762i | −0.0236647 | + | 0.0136628i | −0.511786 | − | 0.859113i | \(-0.671016\pi\) |
0.488121 | + | 0.872776i | \(0.337682\pi\) | |||||||
\(24\) | −123.423 | + | 468.740i | −0.214277 | + | 0.813785i | ||||
\(25\) | −184.138 | + | 318.937i | −0.294621 | + | 0.510298i | ||||
\(26\) | − | 687.231i | − | 1.01661i | ||||||
\(27\) | −522.140 | − | 508.734i | −0.716242 | − | 0.697852i | ||||
\(28\) | −285.482 | −0.364135 | ||||||||
\(29\) | 620.301 | + | 358.131i | 0.737575 | + | 0.425839i | 0.821187 | − | 0.570659i | \(-0.193312\pi\) |
−0.0836117 | + | 0.996498i | \(0.526646\pi\) | |||||||
\(30\) | −622.682 | − | 163.958i | −0.691869 | − | 0.182175i | ||||
\(31\) | 151.284 | + | 262.031i | 0.157423 | + | 0.272665i | 0.933939 | − | 0.357433i | \(-0.116348\pi\) |
−0.776515 | + | 0.630098i | \(0.783015\pi\) | |||||||
\(32\) | 427.392 | − | 246.755i | 0.417375 | − | 0.240971i | ||||
\(33\) | −614.590 | − | 609.285i | −0.564362 | − | 0.559490i | ||||
\(34\) | 162.514 | − | 281.483i | 0.140583 | − | 0.243498i | ||||
\(35\) | 1161.38i | 0.948063i | ||||||||
\(36\) | 2.76561 | + | 319.012i | 0.00213396 | + | 0.246151i | ||||
\(37\) | 826.277 | 0.603562 | 0.301781 | − | 0.953377i | \(-0.402419\pi\) | ||||
0.301781 | + | 0.953377i | \(0.402419\pi\) | |||||||
\(38\) | −737.289 | − | 425.674i | −0.510588 | − | 0.294788i | ||||
\(39\) | 364.300 | + | 1336.39i | 0.239514 | + | 0.878625i | ||||
\(40\) | −431.468 | − | 747.325i | −0.269668 | − | 0.467078i | ||||
\(41\) | 481.613 | − | 278.059i | 0.286504 | − | 0.165413i | −0.349860 | − | 0.936802i | \(-0.613771\pi\) |
0.636364 | + | 0.771389i | \(0.280438\pi\) | |||||||
\(42\) | 2810.38 | − | 766.110i | 1.59319 | − | 0.434303i | ||||
\(43\) | −446.340 | + | 773.084i | −0.241395 | + | 0.418109i | −0.961112 | − | 0.276159i | \(-0.910938\pi\) |
0.719717 | + | 0.694268i | \(0.244272\pi\) | |||||||
\(44\) | 378.723i | 0.195622i | ||||||||
\(45\) | 1297.78 | − | 11.2508i | 0.640880 | − | 0.00555597i | ||||
\(46\) | −64.5464 | −0.0305040 | ||||||||
\(47\) | −3425.50 | − | 1977.72i | −1.55070 | − | 0.895299i | −0.998085 | − | 0.0618654i | \(-0.980295\pi\) |
−0.552619 | − | 0.833434i | \(-0.686372\pi\) | |||||||
\(48\) | −1923.10 | + | 1939.85i | −0.834680 | + | 0.841947i | ||||
\(49\) | −1426.44 | − | 2470.67i | −0.594104 | − | 1.02902i | ||||
\(50\) | −1424.14 | + | 822.225i | −0.569654 | + | 0.328890i | ||||
\(51\) | −166.812 | + | 633.521i | −0.0641337 | + | 0.243568i | ||||
\(52\) | 303.085 | − | 524.958i | 0.112088 | − | 0.194141i | ||||
\(53\) | 1966.96i | 0.700234i | 0.936706 | + | 0.350117i | \(0.113858\pi\) | ||||
−0.936706 | + | 0.350117i | \(0.886142\pi\) | |||||||
\(54\) | −883.316 | − | 3133.04i | −0.302920 | − | 1.07443i | ||||
\(55\) | 1540.69 | 0.509320 | ||||||||
\(56\) | 3380.78 | + | 1951.89i | 1.07805 | + | 0.622415i | ||||
\(57\) | 1659.38 | + | 436.930i | 0.510736 | + | 0.134481i | ||||
\(58\) | 1599.15 | + | 2769.81i | 0.475371 | + | 0.823367i | ||||
\(59\) | 4689.48 | − | 2707.47i | 1.34716 | − | 0.777785i | 0.359316 | − | 0.933216i | \(-0.383010\pi\) |
0.987847 | + | 0.155431i | \(0.0496765\pi\) | |||||||
\(60\) | −403.342 | − | 399.861i | −0.112039 | − | 0.111072i | ||||
\(61\) | 856.210 | − | 1483.00i | 0.230102 | − | 0.398549i | −0.727736 | − | 0.685858i | \(-0.759427\pi\) |
0.957838 | + | 0.287309i | \(0.0927606\pi\) | |||||||
\(62\) | 1351.04i | 0.351468i | ||||||||
\(63\) | −5058.95 | + | 2979.56i | −1.27462 | + | 0.750707i | ||||
\(64\) | −2652.43 | −0.647565 | ||||||||
\(65\) | −2135.60 | − | 1232.99i | −0.505467 | − | 0.291831i | ||||
\(66\) | −1016.33 | − | 3728.28i | −0.233317 | − | 0.855894i | ||||
\(67\) | 2317.24 | + | 4013.58i | 0.516205 | + | 0.894093i | 0.999823 | + | 0.0188141i | \(0.00598907\pi\) |
−0.483618 | + | 0.875279i | \(0.660678\pi\) | |||||||
\(68\) | 248.281 | − | 143.345i | 0.0536941 | − | 0.0310003i | ||||
\(69\) | 125.517 | − | 34.2160i | 0.0263636 | − | 0.00718672i | ||||
\(70\) | −2592.93 | + | 4491.08i | −0.529169 | + | 0.916547i | ||||
\(71\) | − | 6697.12i | − | 1.32853i | −0.747497 | − | 0.664265i | \(-0.768744\pi\) | ||
0.747497 | − | 0.664265i | \(-0.231256\pi\) | |||||||
\(72\) | 2148.39 | − | 3796.76i | 0.414428 | − | 0.732400i | ||||
\(73\) | −4823.86 | −0.905208 | −0.452604 | − | 0.891712i | \(-0.649505\pi\) | ||||
−0.452604 | + | 0.891712i | \(0.649505\pi\) | |||||||
\(74\) | 3195.24 | + | 1844.77i | 0.583499 | + | 0.336883i | ||||
\(75\) | 2333.51 | − | 2353.83i | 0.414847 | − | 0.418459i | ||||
\(76\) | −375.464 | − | 650.324i | −0.0650042 | − | 0.112591i | ||||
\(77\) | −6036.07 | + | 3484.93i | −1.01806 | + | 0.587777i | ||||
\(78\) | −1574.90 | + | 5981.21i | −0.258860 | + | 0.983104i | ||||
\(79\) | 2864.40 | − | 4961.28i | 0.458964 | − | 0.794950i | −0.539942 | − | 0.841702i | \(-0.681554\pi\) |
0.998907 | + | 0.0467524i | \(0.0148872\pi\) | |||||||
\(80\) | − | 4862.94i | − | 0.759834i | ||||||
\(81\) | 3378.52 | + | 5624.26i | 0.514939 | + | 0.857227i | ||||
\(82\) | 2483.22 | 0.369307 | ||||||||
\(83\) | 2452.78 | + | 1416.12i | 0.356044 | + | 0.205562i | 0.667344 | − | 0.744750i | \(-0.267431\pi\) |
−0.311300 | + | 0.950312i | \(0.600765\pi\) | |||||||
\(84\) | 2484.65 | + | 654.230i | 0.352133 | + | 0.0927197i | ||||
\(85\) | −583.147 | − | 1010.04i | −0.0807124 | − | 0.139798i | ||||
\(86\) | −3452.02 | + | 1993.03i | −0.466742 | + | 0.269474i | ||||
\(87\) | −4577.98 | − | 4538.46i | −0.604832 | − | 0.599612i | ||||
\(88\) | 2589.40 | − | 4484.97i | 0.334375 | − | 0.579155i | ||||
\(89\) | 14277.7i | 1.80251i | 0.433290 | + | 0.901255i | \(0.357353\pi\) | ||||
−0.433290 | + | 0.901255i | \(0.642647\pi\) | |||||||
\(90\) | 5043.68 | + | 2853.96i | 0.622677 | + | 0.352341i | ||||
\(91\) | 11155.7 | 1.34714 | ||||||||
\(92\) | −49.3054 | − | 28.4665i | −0.00582531 | − | 0.00336324i | ||||
\(93\) | −716.187 | − | 2627.24i | −0.0828058 | − | 0.303763i | ||||
\(94\) | −8831.02 | − | 15295.8i | −0.999437 | − | 1.73107i | ||||
\(95\) | −2645.60 | + | 1527.44i | −0.293141 | + | 0.169245i | ||||
\(96\) | −4285.22 | + | 1168.15i | −0.464976 | + | 0.126753i | ||||
\(97\) | −3582.65 | + | 6205.34i | −0.380769 | + | 0.659511i | −0.991172 | − | 0.132580i | \(-0.957674\pi\) |
0.610403 | + | 0.792091i | \(0.291007\pi\) | |||||||
\(98\) | − | 12738.9i | − | 1.32641i | ||||||
\(99\) | 3952.71 | + | 6711.25i | 0.403297 | + | 0.684752i | ||||
\(100\) | −1450.48 | −0.145048 | ||||||||
\(101\) | −1696.72 | − | 979.600i | −0.166328 | − | 0.0960298i | 0.414525 | − | 0.910038i | \(-0.363948\pi\) |
−0.580853 | + | 0.814008i | \(0.697281\pi\) | |||||||
\(102\) | −2059.49 | + | 2077.42i | −0.197951 | + | 0.199675i | ||||
\(103\) | 2577.74 | + | 4464.77i | 0.242976 | + | 0.420848i | 0.961561 | − | 0.274592i | \(-0.0885429\pi\) |
−0.718584 | + | 0.695440i | \(0.755210\pi\) | |||||||
\(104\) | −7178.47 | + | 4144.49i | −0.663690 | + | 0.383182i | ||||
\(105\) | 2661.49 | − | 10107.9i | 0.241405 | − | 0.916814i | ||||
\(106\) | −4391.49 | + | 7606.29i | −0.390841 | + | 0.676957i | ||||
\(107\) | − | 9117.08i | − | 0.796321i | −0.917316 | − | 0.398161i | \(-0.869649\pi\) | ||
0.917316 | − | 0.398161i | \(-0.130351\pi\) | |||||||
\(108\) | 707.000 | − | 2782.81i | 0.0606139 | − | 0.238581i | ||||
\(109\) | −16161.1 | −1.36024 | −0.680122 | − | 0.733099i | \(-0.738073\pi\) | ||||
−0.680122 | + | 0.733099i | \(0.738073\pi\) | |||||||
\(110\) | 5957.91 | + | 3439.80i | 0.492389 | + | 0.284281i | ||||
\(111\) | −7191.38 | − | 1893.55i | −0.583668 | − | 0.153685i | ||||
\(112\) | 10999.6 | + | 19051.8i | 0.876879 | + | 1.51880i | ||||
\(113\) | 18272.5 | − | 10549.6i | 1.43100 | − | 0.826189i | 0.433804 | − | 0.901007i | \(-0.357171\pi\) |
0.997197 | + | 0.0748185i | \(0.0238377\pi\) | |||||||
\(114\) | 5441.38 | + | 5394.41i | 0.418696 | + | 0.415082i | ||||
\(115\) | −115.805 | + | 200.581i | −0.00875654 | + | 0.0151668i | ||||
\(116\) | 2821.05i | 0.209650i | ||||||||
\(117\) | −108.071 | − | 12465.9i | −0.00789470 | − | 0.910652i | ||||
\(118\) | 24179.1 | 1.73651 | ||||||||
\(119\) | 4569.26 | + | 2638.06i | 0.322665 | + | 0.186291i | ||||
\(120\) | 2042.60 | + | 7493.01i | 0.141847 | + | 0.520348i | ||||
\(121\) | −2697.36 | − | 4671.97i | −0.184233 | − | 0.319102i | ||||
\(122\) | 6621.98 | − | 3823.20i | 0.444906 | − | 0.256867i | ||||
\(123\) | −4828.87 | + | 1316.35i | −0.319180 | + | 0.0870084i | ||||
\(124\) | −595.842 | + | 1032.03i | −0.0387514 | + | 0.0671195i | ||||
\(125\) | 15914.9i | 1.01855i | ||||||||
\(126\) | −26215.4 | + | 227.269i | −1.65126 | + | 0.0143152i | ||||
\(127\) | −20660.9 | −1.28098 | −0.640489 | − | 0.767968i | \(-0.721268\pi\) | ||||
−0.640489 | + | 0.767968i | \(0.721268\pi\) | |||||||
\(128\) | −17095.3 | − | 9869.97i | −1.04341 | − | 0.602415i | ||||
\(129\) | 5656.31 | − | 5705.55i | 0.339902 | − | 0.342861i | ||||
\(130\) | −5505.61 | − | 9536.00i | −0.325776 | − | 0.564260i | ||||
\(131\) | 2772.53 | − | 1600.72i | 0.161560 | − | 0.0932768i | −0.417040 | − | 0.908888i | \(-0.636933\pi\) |
0.578600 | + | 0.815611i | \(0.303599\pi\) | |||||||
\(132\) | 867.908 | − | 3296.16i | 0.0498111 | − | 0.189174i | ||||
\(133\) | 6909.88 | − | 11968.3i | 0.390631 | − | 0.676594i | ||||
\(134\) | 20694.2i | 1.15250i | ||||||||
\(135\) | −11320.8 | − | 2876.17i | −0.621170 | − | 0.157814i | ||||
\(136\) | −3920.31 | −0.211955 | ||||||||
\(137\) | −3353.18 | − | 1935.96i | −0.178655 | − | 0.103147i | 0.408005 | − | 0.912980i | \(-0.366224\pi\) |
−0.586661 | + | 0.809833i | \(0.699558\pi\) | |||||||
\(138\) | 561.770 | + | 147.919i | 0.0294985 | + | 0.00776722i | ||||
\(139\) | 5839.62 | + | 10114.5i | 0.302242 | + | 0.523499i | 0.976644 | − | 0.214866i | \(-0.0689315\pi\) |
−0.674401 | + | 0.738365i | \(0.735598\pi\) | |||||||
\(140\) | −3961.35 | + | 2287.08i | −0.202109 | + | 0.116688i | ||||
\(141\) | 25281.1 | + | 25062.9i | 1.27162 | + | 1.26064i | ||||
\(142\) | 14952.2 | − | 25898.0i | 0.741530 | − | 1.28437i | ||||
\(143\) | − | 14799.2i | − | 0.723714i | ||||||
\(144\) | 21182.9 | − | 12476.0i | 1.02155 | − | 0.601661i | ||||
\(145\) | 11476.4 | 0.545844 | ||||||||
\(146\) | −18654.0 | − | 10769.9i | −0.875117 | − | 0.505249i | ||||
\(147\) | 6752.87 | + | 24772.1i | 0.312503 | + | 1.14638i | ||||
\(148\) | 1627.18 | + | 2818.35i | 0.0742867 | + | 0.128668i | ||||
\(149\) | −13069.8 | + | 7545.88i | −0.588705 | + | 0.339889i | −0.764585 | − | 0.644522i | \(-0.777056\pi\) |
0.175880 | + | 0.984412i | \(0.443723\pi\) | |||||||
\(150\) | 14279.0 | − | 3892.46i | 0.634623 | − | 0.172998i | ||||
\(151\) | −15127.7 | + | 26201.9i | −0.663465 | + | 1.14915i | 0.316234 | + | 0.948681i | \(0.397581\pi\) |
−0.979699 | + | 0.200474i | \(0.935752\pi\) | |||||||
\(152\) | 10268.5i | 0.444446i | ||||||||
\(153\) | 2903.64 | − | 5131.48i | 0.124040 | − | 0.219210i | ||||
\(154\) | −31122.2 | −1.31229 | ||||||||
\(155\) | 4198.42 | + | 2423.96i | 0.174752 | + | 0.100893i | ||||
\(156\) | −3840.88 | + | 3874.32i | −0.157827 | + | 0.159201i | ||||
\(157\) | −10311.4 | − | 17859.8i | −0.418328 | − | 0.724565i | 0.577443 | − | 0.816431i | \(-0.304050\pi\) |
−0.995771 | + | 0.0918653i | \(0.970717\pi\) | |||||||
\(158\) | 22153.4 | − | 12790.3i | 0.887415 | − | 0.512349i | ||||
\(159\) | 4507.61 | − | 17119.1i | 0.178300 | − | 0.677153i | ||||
\(160\) | 3953.65 | − | 6847.93i | 0.154440 | − | 0.267497i | ||||
\(161\) | − | 1047.77i | − | 0.0404216i | ||||||
\(162\) | 507.923 | + | 29292.2i | 0.0193539 | + | 1.11615i | ||||
\(163\) | 39790.7 | 1.49764 | 0.748818 | − | 0.662776i | \(-0.230622\pi\) | ||||
0.748818 | + | 0.662776i | \(0.230622\pi\) | |||||||
\(164\) | 1896.87 | + | 1095.16i | 0.0705260 | + | 0.0407182i | ||||
\(165\) | −13409.2 | − | 3530.76i | −0.492533 | − | 0.129688i | ||||
\(166\) | 6323.33 | + | 10952.3i | 0.229472 | + | 0.397457i | ||||
\(167\) | −23773.0 | + | 13725.3i | −0.852414 | + | 0.492141i | −0.861465 | − | 0.507818i | \(-0.830452\pi\) |
0.00905084 | + | 0.999959i | \(0.497119\pi\) | |||||||
\(168\) | −24951.0 | − | 24735.6i | −0.884035 | − | 0.876404i | ||||
\(169\) | 2436.98 | − | 4220.97i | 0.0853253 | − | 0.147788i | ||||
\(170\) | − | 5207.81i | − | 0.180201i | ||||||
\(171\) | −13440.9 | − | 7605.51i | −0.459659 | − | 0.260097i | ||||
\(172\) | −3515.89 | −0.118844 | ||||||||
\(173\) | 8729.26 | + | 5039.84i | 0.291666 | + | 0.168393i | 0.638693 | − | 0.769462i | \(-0.279475\pi\) |
−0.347027 | + | 0.937855i | \(0.612809\pi\) | |||||||
\(174\) | −7570.47 | − | 27771.3i | −0.250048 | − | 0.917271i | ||||
\(175\) | −13347.0 | − | 23117.7i | −0.435821 | − | 0.754864i | ||||
\(176\) | 25274.3 | − | 14592.1i | 0.815933 | − | 0.471079i | ||||
\(177\) | −47018.8 | + | 12817.3i | −1.50081 | + | 0.409120i | ||||
\(178\) | −31876.8 | + | 55212.2i | −1.00608 | + | 1.74259i | ||||
\(179\) | − | 1215.45i | − | 0.0379343i | −0.999820 | − | 0.0189672i | \(-0.993962\pi\) | ||
0.999820 | − | 0.0189672i | \(-0.00603779\pi\) | |||||||
\(180\) | 2594.08 | + | 4404.45i | 0.0800642 | + | 0.135940i | ||||
\(181\) | 28359.9 | 0.865661 | 0.432831 | − | 0.901475i | \(-0.357515\pi\) | ||||
0.432831 | + | 0.901475i | \(0.357515\pi\) | |||||||
\(182\) | 43139.3 | + | 24906.5i | 1.30236 | + | 0.751917i | ||||
\(183\) | −10850.4 | + | 10944.9i | −0.324000 | + | 0.326821i | ||||
\(184\) | 389.261 | + | 674.220i | 0.0114976 | + | 0.0199143i | ||||
\(185\) | 11465.4 | − | 6619.55i | 0.335001 | − | 0.193413i | ||||
\(186\) | 3096.15 | − | 11758.6i | 0.0894943 | − | 0.339883i | ||||
\(187\) | 3499.68 | − | 6061.62i | 0.100079 | − | 0.173343i | ||||
\(188\) | − | 15578.8i | − | 0.440775i | ||||||
\(189\) | 50858.0 | − | 14338.7i | 1.42376 | − | 0.401408i | ||||
\(190\) | −13640.8 | −0.377862 | ||||||||
\(191\) | −8445.34 | − | 4875.92i | −0.231500 | − | 0.133656i | 0.379764 | − | 0.925083i | \(-0.376005\pi\) |
−0.611264 | + | 0.791427i | \(0.709339\pi\) | |||||||
\(192\) | 23085.0 | + | 6078.48i | 0.626221 | + | 0.164889i | ||||
\(193\) | 26701.4 | + | 46248.2i | 0.716836 | + | 1.24160i | 0.962247 | + | 0.272177i | \(0.0877436\pi\) |
−0.245411 | + | 0.969419i | \(0.578923\pi\) | |||||||
\(194\) | −27708.5 | + | 15997.5i | −0.736223 | + | 0.425058i | ||||
\(195\) | 15761.2 | + | 15625.2i | 0.414497 | + | 0.410919i | ||||
\(196\) | 5618.15 | − | 9730.92i | 0.146245 | − | 0.253304i | ||||
\(197\) | − | 68537.7i | − | 1.76603i | −0.469349 | − | 0.883013i | \(-0.655511\pi\) | ||
0.469349 | − | 0.883013i | \(-0.344489\pi\) | |||||||
\(198\) | 301.497 | + | 34777.6i | 0.00769046 | + | 0.887092i | ||||
\(199\) | −8237.42 | −0.208010 | −0.104005 | − | 0.994577i | \(-0.533166\pi\) | ||||
−0.104005 | + | 0.994577i | \(0.533166\pi\) | |||||||
\(200\) | 17177.1 | + | 9917.21i | 0.429428 | + | 0.247930i | ||||
\(201\) | −10970.0 | − | 40242.0i | −0.271527 | − | 0.996064i | ||||
\(202\) | −4374.17 | − | 7576.28i | −0.107200 | − | 0.185675i | ||||
\(203\) | −44961.7 | + | 25958.7i | −1.09107 | + | 0.629927i | ||||
\(204\) | −2489.38 | + | 678.606i | −0.0598178 | + | 0.0163064i | ||||
\(205\) | 4455.24 | − | 7716.70i | 0.106014 | − | 0.183622i | ||||
\(206\) | 23020.6i | 0.542477i | ||||||||
\(207\) | −1170.83 | + | 10.1503i | −0.0273246 | + | 0.000236884i | ||||
\(208\) | −46711.2 | −1.07968 | ||||||||
\(209\) | −15877.2 | − | 9166.71i | −0.363481 | − | 0.209856i | ||||
\(210\) | 32859.2 | − | 33145.3i | 0.745107 | − | 0.751595i | ||||
\(211\) | −20393.7 | − | 35322.9i | −0.458069 | − | 0.793399i | 0.540790 | − | 0.841158i | \(-0.318125\pi\) |
−0.998859 | + | 0.0477587i | \(0.984792\pi\) | |||||||
\(212\) | −6709.10 | + | 3873.50i | −0.149277 | + | 0.0861851i | ||||
\(213\) | −15347.6 | + | 58287.4i | −0.338284 | + | 1.28474i | ||||
\(214\) | 20355.1 | − | 35256.0i | 0.444473 | − | 0.769850i | ||||
\(215\) | 14303.1i | 0.309423i | ||||||||
\(216\) | −27399.1 | + | 28121.1i | −0.587259 | + | 0.602734i | ||||
\(217\) | −21931.2 | −0.465740 | ||||||||
\(218\) | −62495.4 | − | 36081.7i | −1.31503 | − | 0.759231i | ||||
\(219\) | 41983.7 | + | 11054.7i | 0.875371 | + | 0.230493i | ||||
\(220\) | 3034.07 | + | 5255.16i | 0.0626873 | + | 0.108578i | ||||
\(221\) | −9701.99 | + | 5601.45i | −0.198644 | + | 0.114687i | ||||
\(222\) | −23581.7 | − | 23378.1i | −0.478485 | − | 0.474355i | ||||
\(223\) | 29959.8 | − | 51891.9i | 0.602461 | − | 1.04349i | −0.389986 | − | 0.920821i | \(-0.627520\pi\) |
0.992447 | − | 0.122672i | \(-0.0391464\pi\) | |||||||
\(224\) | 35771.4i | 0.712918i | ||||||||
\(225\) | −25703.6 | + | 15138.6i | −0.507725 | + | 0.299034i | ||||
\(226\) | 94213.5 | 1.84458 | ||||||||
\(227\) | 85572.3 | + | 49405.2i | 1.66066 | + | 0.958785i | 0.972399 | + | 0.233325i | \(0.0749607\pi\) |
0.688265 | + | 0.725459i | \(0.258373\pi\) | |||||||
\(228\) | 1777.47 | + | 6520.43i | 0.0341927 | + | 0.125432i | ||||
\(229\) | 2658.97 | + | 4605.47i | 0.0507040 | + | 0.0878220i | 0.890263 | − | 0.455446i | \(-0.150520\pi\) |
−0.839559 | + | 0.543268i | \(0.817187\pi\) | |||||||
\(230\) | −895.645 | + | 517.101i | −0.0169309 | + | 0.00977506i | ||||
\(231\) | 60520.3 | − | 16497.9i | 1.13417 | − | 0.309175i | ||||
\(232\) | 19288.0 | − | 33407.8i | 0.358353 | − | 0.620686i | ||||
\(233\) | 18467.8i | 0.340176i | 0.985429 | + | 0.170088i | \(0.0544052\pi\) | ||||
−0.985429 | + | 0.170088i | \(0.945595\pi\) | |||||||
\(234\) | 27413.9 | − | 48447.4i | 0.500655 | − | 0.884786i | ||||
\(235\) | −63376.3 | −1.14760 | ||||||||
\(236\) | 18469.8 | + | 10663.6i | 0.331619 | + | 0.191460i | ||||
\(237\) | −36299.5 | + | 36615.5i | −0.646254 | + | 0.651881i | ||||
\(238\) | 11779.6 | + | 20402.9i | 0.207959 | + | 0.360196i | ||||
\(239\) | 22383.5 | − | 12923.1i | 0.391861 | − | 0.226241i | −0.291105 | − | 0.956691i | \(-0.594023\pi\) |
0.682966 | + | 0.730450i | \(0.260690\pi\) | |||||||
\(240\) | −11144.2 | + | 42323.8i | −0.193476 | + | 0.734789i | ||||
\(241\) | −41536.2 | + | 71942.7i | −0.715142 | + | 1.23866i | 0.247763 | + | 0.968821i | \(0.420305\pi\) |
−0.962905 | + | 0.269841i | \(0.913029\pi\) | |||||||
\(242\) | − | 24088.9i | − | 0.411325i | ||||||
\(243\) | −16515.5 | − | 56692.4i | −0.279691 | − | 0.960090i | ||||
\(244\) | 6744.49 | 0.113284 | ||||||||
\(245\) | −39586.6 | − | 22855.3i | −0.659502 | − | 0.380764i | ||||
\(246\) | −21612.3 | − | 5690.71i | −0.357134 | − | 0.0940365i | ||||
\(247\) | 14671.9 | + | 25412.4i | 0.240487 | + | 0.416536i | ||||
\(248\) | 14112.3 | − | 8147.76i | 0.229454 | − | 0.132475i | ||||
\(249\) | −18102.2 | − | 17945.9i | −0.291966 | − | 0.289446i | ||||
\(250\) | −35532.0 | + | 61543.3i | −0.568513 | + | 0.984693i | ||||
\(251\) | − | 49051.6i | − | 0.778585i | −0.921114 | − | 0.389292i | \(-0.872720\pi\) | ||
0.921114 | − | 0.389292i | \(-0.127280\pi\) | |||||||
\(252\) | −20125.5 | − | 11388.0i | −0.316917 | − | 0.179327i | ||||
\(253\) | −1389.98 | −0.0217154 | ||||||||
\(254\) | −79896.3 | − | 46128.1i | −1.23839 | − | 0.714988i | ||||
\(255\) | 2760.65 | + | 10127.1i | 0.0424553 | + | 0.155742i | ||||
\(256\) | −22852.6 | − | 39581.8i | −0.348703 | − | 0.603971i | ||||
\(257\) | 84096.0 | − | 48552.9i | 1.27324 | − | 0.735104i | 0.297641 | − | 0.954678i | \(-0.403800\pi\) |
0.975596 | + | 0.219574i | \(0.0704668\pi\) | |||||||
\(258\) | 34611.5 | − | 9435.11i | 0.519973 | − | 0.141745i | ||||
\(259\) | −29945.8 | + | 51867.7i | −0.446413 | + | 0.773209i | ||||
\(260\) | − | 9712.41i | − | 0.143675i | ||||||
\(261\) | 29443.1 | + | 49991.0i | 0.432217 | + | 0.733856i | ||||
\(262\) | 14295.3 | 0.208253 | ||||||||
\(263\) | 35921.0 | + | 20739.0i | 0.519323 | + | 0.299831i | 0.736658 | − | 0.676266i | \(-0.236403\pi\) |
−0.217335 | + | 0.976097i | \(0.569736\pi\) | |||||||
\(264\) | −32814.5 | + | 33100.2i | −0.470824 | + | 0.474923i | ||||
\(265\) | 15757.9 | + | 27293.5i | 0.224391 | + | 0.388657i | ||||
\(266\) | 53441.4 | − | 30854.4i | 0.755292 | − | 0.436068i | ||||
\(267\) | 32719.7 | − | 124264.i | 0.458973 | − | 1.74310i | ||||
\(268\) | −9126.63 | + | 15807.8i | −0.127069 | + | 0.220091i | ||||
\(269\) | 115737.i | 1.59944i | 0.600370 | + | 0.799722i | \(0.295020\pi\) | ||||
−0.600370 | + | 0.799722i | \(0.704980\pi\) | |||||||
\(270\) | −37356.6 | − | 36397.5i | −0.512436 | − | 0.499279i | ||||
\(271\) | −5077.71 | −0.0691400 | −0.0345700 | − | 0.999402i | \(-0.511006\pi\) | ||||
−0.0345700 | + | 0.999402i | \(0.511006\pi\) | |||||||
\(272\) | −19132.5 | − | 11046.1i | −0.258603 | − | 0.149304i | ||||
\(273\) | −97091.7 | − | 25565.1i | −1.30274 | − | 0.343022i | ||||
\(274\) | −8644.57 | − | 14972.8i | −0.115144 | − | 0.199436i | ||||
\(275\) | −30668.2 | + | 17706.3i | −0.405529 | + | 0.234133i | ||||
\(276\) | 363.886 | + | 360.745i | 0.00477692 | + | 0.00473568i | ||||
\(277\) | 21192.9 | − | 36707.2i | 0.276205 | − | 0.478401i | −0.694234 | − | 0.719750i | \(-0.744257\pi\) |
0.970438 | + | 0.241349i | \(0.0775899\pi\) | |||||||
\(278\) | 52150.9i | 0.674795i | ||||||||
\(279\) | 212.459 | + | 24507.1i | 0.00272939 | + | 0.314835i | ||||
\(280\) | 62548.8 | 0.797817 | ||||||||
\(281\) | −35902.5 | − | 20728.3i | −0.454687 | − | 0.262513i | 0.255121 | − | 0.966909i | \(-0.417885\pi\) |
−0.709807 | + | 0.704396i | \(0.751218\pi\) | |||||||
\(282\) | 41806.6 | + | 153362.i | 0.525711 | + | 1.92850i | ||||
\(283\) | −19194.0 | − | 33245.0i | −0.239658 | − | 0.415100i | 0.720958 | − | 0.692979i | \(-0.243702\pi\) |
−0.960616 | + | 0.277879i | \(0.910369\pi\) | |||||||
\(284\) | 22843.2 | − | 13188.5i | 0.283218 | − | 0.163516i | ||||
\(285\) | 26525.9 | − | 7230.98i | 0.326574 | − | 0.0890241i | ||||
\(286\) | 33041.2 | − | 57229.1i | 0.403946 | − | 0.699656i | ||||
\(287\) | 40309.6i | 0.489378i | ||||||||
\(288\) | 39972.8 | − | 346.535i | 0.481925 | − | 0.00417794i | ||||
\(289\) | 78222.5 | 0.936561 | ||||||||
\(290\) | 44379.5 | + | 25622.5i | 0.527699 | + | 0.304667i | ||||
\(291\) | 45401.7 | − | 45797.0i | 0.536149 | − | 0.540818i | ||||
\(292\) | −9499.55 | − | 16453.7i | −0.111413 | − | 0.192974i | ||||
\(293\) | −11239.5 | + | 6489.12i | −0.130922 | + | 0.0755876i | −0.564030 | − | 0.825754i | \(-0.690750\pi\) |
0.433109 | + | 0.901342i | \(0.357417\pi\) | |||||||
\(294\) | −29193.3 | + | 110871.i | −0.337745 | + | 1.28269i | ||||
\(295\) | 43380.7 | − | 75137.6i | 0.498486 | − | 0.863402i | ||||
\(296\) | − | 44501.2i | − | 0.507911i | ||||||
\(297\) | −19021.8 | − | 67468.7i | −0.215645 | − | 0.764873i | ||||
\(298\) | −67388.7 | −0.758847 | ||||||||
\(299\) | 1926.69 | + | 1112.37i | 0.0215511 | + | 0.0124425i | ||||
\(300\) | 12624.0 | + | 3324.02i | 0.140267 | + | 0.0369336i | ||||
\(301\) | −32352.4 | − | 56036.0i | −0.357086 | − | 0.618492i | ||||
\(302\) | −116998. | + | 67549.0i | −1.28282 | + | 0.740636i | ||||
\(303\) | 12522.2 | + | 12414.1i | 0.136394 | + | 0.135217i | ||||
\(304\) | −28933.2 | + | 50113.7i | −0.313075 | + | 0.542262i | ||||
\(305\) | − | 27437.4i | − | 0.294947i | ||||||
\(306\) | 22685.2 | − | 13360.8i | 0.242270 | − | 0.142689i | ||||
\(307\) | −126105. | −1.33799 | −0.668997 | − | 0.743265i | \(-0.733276\pi\) | ||||
−0.668997 | + | 0.743265i | \(0.733276\pi\) | |||||||
\(308\) | −23773.5 | − | 13725.6i | −0.250606 | − | 0.144688i | ||||
\(309\) | −12203.2 | − | 44765.8i | −0.127807 | − | 0.468845i | ||||
\(310\) | 10823.6 | + | 18747.1i | 0.112629 | + | 0.195079i | ||||
\(311\) | −86432.4 | + | 49901.7i | −0.893626 | + | 0.515935i | −0.875127 | − | 0.483894i | \(-0.839222\pi\) |
−0.0184989 | + | 0.999829i | \(0.505889\pi\) | |||||||
\(312\) | 71974.5 | − | 19620.3i | 0.739383 | − | 0.201556i | ||||
\(313\) | 1112.68 | − | 1927.21i | 0.0113574 | − | 0.0196716i | −0.860291 | − | 0.509804i | \(-0.829718\pi\) |
0.871648 | + | 0.490132i | \(0.163051\pi\) | |||||||
\(314\) | − | 92085.9i | − | 0.933972i | ||||||
\(315\) | −46327.8 | + | 81873.1i | −0.466896 | + | 0.825125i | ||||
\(316\) | 22563.3 | 0.225958 | ||||||||
\(317\) | −145552. | − | 84034.3i | −1.44843 | − | 0.836254i | −0.450046 | − | 0.893005i | \(-0.648592\pi\) |
−0.998388 | + | 0.0567515i | \(0.981926\pi\) | |||||||
\(318\) | 55651.8 | − | 56136.3i | 0.550332 | − | 0.555124i | ||||
\(319\) | 34437.0 | + | 59646.6i | 0.338410 | + | 0.586144i | ||||
\(320\) | −36805.0 | + | 21249.4i | −0.359424 | + | 0.207514i | ||||
\(321\) | −20893.3 | + | 79349.1i | −0.202767 | + | 0.770073i | ||||
\(322\) | 2339.28 | − | 4051.76i | 0.0225617 | − | 0.0390779i | ||||
\(323\) | 13878.3i | 0.133024i | ||||||||
\(324\) | −12530.6 | + | 22599.6i | −0.119366 | + | 0.215283i | ||||
\(325\) | 56679.9 | 0.536615 | ||||||||
\(326\) | 153872. | + | 88837.9i | 1.44785 | + | 0.835917i | ||||
\(327\) | 140655. | + | 37035.8i | 1.31541 | + | 0.346359i | ||||
\(328\) | −14975.6 | − | 25938.5i | −0.139199 | − | 0.241100i | ||||
\(329\) | 248293. | − | 143352.i | 2.29389 | − | 1.32438i | ||||
\(330\) | −43970.9 | − | 43591.4i | −0.403773 | − | 0.400288i | ||||
\(331\) | −3379.43 | + | 5853.34i | −0.0308452 | + | 0.0534254i | −0.881036 | − | 0.473049i | \(-0.843153\pi\) |
0.850191 | + | 0.526475i | \(0.176487\pi\) | |||||||
\(332\) | 11154.9i | 0.101202i | ||||||||
\(333\) | 58249.6 | + | 32960.5i | 0.525297 | + | 0.297239i | ||||
\(334\) | −122574. | −1.09877 | ||||||||
\(335\) | 64308.1 | + | 37128.3i | 0.573028 | + | 0.330838i | ||||
\(336\) | −52072.7 | − | 191022.i | −0.461245 | − | 1.69202i | ||||
\(337\) | 111046. | + | 192338.i | 0.977787 | + | 1.69358i | 0.670413 | + | 0.741988i | \(0.266117\pi\) |
0.307375 | + | 0.951589i | \(0.400550\pi\) | |||||||
\(338\) | 18847.7 | − | 10881.7i | 0.164978 | − | 0.0952500i | ||||
\(339\) | −183208. | + | 49942.5i | −1.59421 | + | 0.434581i | ||||
\(340\) | 2296.77 | − | 3978.11i | 0.0198682 | − | 0.0344128i | ||||
\(341\) | 29094.2i | 0.250206i | ||||||||
\(342\) | −34996.0 | − | 59419.3i | −0.299203 | − | 0.508013i | ||||
\(343\) | 32754.4 | 0.278408 | ||||||||
\(344\) | 41636.3 | + | 24038.7i | 0.351848 | + | 0.203140i | ||||
\(345\) | 1467.56 | − | 1480.34i | 0.0123298 | − | 0.0124372i | ||||
\(346\) | 22504.2 | + | 38978.4i | 0.187980 | + | 0.325591i | ||||
\(347\) | −140770. | + | 81273.8i | −1.16910 | + | 0.674981i | −0.953468 | − | 0.301494i | \(-0.902515\pi\) |
−0.215633 | + | 0.976475i | \(0.569181\pi\) | |||||||
\(348\) | 6464.91 | − | 24552.6i | 0.0533831 | − | 0.202739i | ||||
\(349\) | 36348.5 | − | 62957.4i | 0.298425 | − | 0.516887i | −0.677351 | − | 0.735660i | \(-0.736872\pi\) |
0.975776 | + | 0.218773i | \(0.0702054\pi\) | |||||||
\(350\) | − | 119196.i | − | 0.973027i | ||||||
\(351\) | −27627.2 | + | 108743.i | −0.224245 | + | 0.882646i | ||||
\(352\) | 47454.7 | 0.382995 | ||||||||
\(353\) | 111396. | + | 64314.6i | 0.893966 | + | 0.516131i | 0.875238 | − | 0.483693i | \(-0.160705\pi\) |
0.0187281 | + | 0.999825i | \(0.494038\pi\) | |||||||
\(354\) | −210439. | − | 55410.5i | −1.67927 | − | 0.442166i | ||||
\(355\) | −53652.7 | − | 92929.2i | −0.425730 | − | 0.737387i | ||||
\(356\) | −48699.8 | + | 28116.8i | −0.384261 | + | 0.221853i | ||||
\(357\) | −33722.3 | − | 33431.2i | −0.264594 | − | 0.262310i | ||||
\(358\) | 2713.66 | − | 4700.19i | 0.0211733 | − | 0.0366733i | ||||
\(359\) | − | 95302.8i | − | 0.739463i | −0.929139 | − | 0.369732i | \(-0.879450\pi\) | ||
0.929139 | − | 0.369732i | \(-0.120550\pi\) | |||||||
\(360\) | −605.942 | − | 69895.2i | −0.00467548 | − | 0.539315i | ||||
\(361\) | −93969.7 | −0.721063 | ||||||||
\(362\) | 109669. | + | 63317.3i | 0.836885 | + | 0.483176i | ||||
\(363\) | 12769.5 | + | 46843.2i | 0.0969081 | + | 0.355495i | ||||
\(364\) | 21968.7 | + | 38050.9i | 0.165807 | + | 0.287185i | ||||
\(365\) | −66935.7 | + | 38645.4i | −0.502426 | + | 0.290076i | ||||
\(366\) | −66394.9 | + | 18099.3i | −0.495647 | + | 0.135114i | ||||
\(367\) | −52073.0 | + | 90193.1i | −0.386616 | + | 0.669639i | −0.991992 | − | 0.126301i | \(-0.959690\pi\) |
0.605376 | + | 0.795940i | \(0.293023\pi\) | |||||||
\(368\) | 4387.23i | 0.0323963i | ||||||||
\(369\) | 45043.9 | − | 390.499i | 0.330814 | − | 0.00286792i | ||||
\(370\) | 59116.1 | 0.431820 | ||||||||
\(371\) | −123471. | − | 71286.2i | −0.897053 | − | 0.517914i | ||||
\(372\) | 7550.89 | − | 7616.63i | 0.0545648 | − | 0.0550399i | ||||
\(373\) | −122915. | − | 212896.i | −0.883463 | − | 1.53020i | −0.847465 | − | 0.530851i | \(-0.821872\pi\) |
−0.0359975 | − | 0.999352i | \(-0.511461\pi\) | |||||||
\(374\) | 27066.7 | − | 15627.0i | 0.193505 | − | 0.111720i | ||||
\(375\) | 36471.6 | − | 138513.i | 0.259354 | − | 0.984979i | ||||
\(376\) | −106515. | + | 184489.i | −0.753415 | + | 1.30495i | ||||
\(377\) | − | 110237.i | − | 0.775612i | ||||||
\(378\) | 228682. | + | 58098.9i | 1.60048 | + | 0.406616i | ||||
\(379\) | 200830. | 1.39814 | 0.699070 | − | 0.715053i | \(-0.253597\pi\) | ||||
0.699070 | + | 0.715053i | \(0.253597\pi\) | |||||||
\(380\) | −10419.9 | − | 6015.92i | −0.0721598 | − | 0.0416615i | ||||
\(381\) | 179819. | + | 47347.9i | 1.23875 | + | 0.326175i | ||||
\(382\) | −21772.3 | − | 37710.7i | −0.149203 | − | 0.258427i | ||||
\(383\) | 117206. | − | 67668.8i | 0.799008 | − | 0.461308i | −0.0441160 | − | 0.999026i | \(-0.514047\pi\) |
0.843124 | + | 0.537719i | \(0.180714\pi\) | |||||||
\(384\) | 126168. | + | 125078.i | 0.855628 | + | 0.848243i | ||||
\(385\) | −55837.6 | + | 96713.6i | −0.376708 | + | 0.652478i | ||||
\(386\) | 238458.i | 1.60043i | ||||||||
\(387\) | −62304.0 | + | 36695.0i | −0.416001 | + | 0.245011i | ||||
\(388\) | −28221.1 | −0.187461 | ||||||||
\(389\) | −175090. | − | 101088.i | −1.15708 | − | 0.668039i | −0.206475 | − | 0.978452i | \(-0.566199\pi\) |
−0.950602 | + | 0.310413i | \(0.899533\pi\) | |||||||
\(390\) | 26063.9 | + | 95612.1i | 0.171360 | + | 0.628614i | ||||
\(391\) | 526.102 | + | 911.236i | 0.00344125 | + | 0.00596043i | ||||
\(392\) | −133064. | + | 76824.6i | −0.865942 | + | 0.499952i | ||||
\(393\) | −27798.7 | + | 7577.92i | −0.179986 | + | 0.0490642i | ||||
\(394\) | 153019. | − | 265037.i | 0.985721 | − | 1.70732i | ||||
\(395\) | − | 91790.2i | − | 0.588304i | ||||||
\(396\) | −15107.4 | + | 26698.7i | −0.0963385 | + | 0.170255i | ||||
\(397\) | 102384. | 0.649608 | 0.324804 | − | 0.945781i | \(-0.394702\pi\) | ||||
0.324804 | + | 0.945781i | \(0.394702\pi\) | |||||||
\(398\) | −31854.4 | − | 18391.1i | −0.201096 | − | 0.116103i | ||||
\(399\) | −87566.4 | + | 88328.8i | −0.550037 | + | 0.554826i | ||||
\(400\) | 55886.8 | + | 96798.8i | 0.349292 | + | 0.604992i | ||||
\(401\) | −78026.4 | + | 45048.6i | −0.485236 | + | 0.280151i | −0.722596 | − | 0.691271i | \(-0.757051\pi\) |
0.237360 | + | 0.971422i | \(0.423718\pi\) | |||||||
\(402\) | 47424.3 | − | 180109.i | 0.293460 | − | 1.11451i | ||||
\(403\) | 23283.5 | − | 40328.2i | 0.143363 | − | 0.248313i | ||||
\(404\) | − | 7716.45i | − | 0.0472775i | ||||||
\(405\) | 91937.9 | + | 50975.9i | 0.560512 | + | 0.310781i | ||||
\(406\) | −231824. | −1.40639 | ||||||||
\(407\) | 68808.1 | + | 39726.4i | 0.415385 | + | 0.239823i | ||||
\(408\) | 34119.8 | + | 8984.05i | 0.204968 | + | 0.0539700i | ||||
\(409\) | −74861.0 | − | 129663.i | −0.447517 | − | 0.775122i | 0.550707 | − | 0.834699i | \(-0.314358\pi\) |
−0.998224 | + | 0.0595770i | \(0.981025\pi\) | |||||||
\(410\) | 34457.1 | − | 19893.8i | 0.204980 | − | 0.118345i | ||||
\(411\) | 24747.3 | + | 24533.7i | 0.146502 | + | 0.145238i | ||||
\(412\) | −10152.6 | + | 17584.8i | −0.0598113 | + | 0.103596i | ||||
\(413\) | 392495.i | 2.30109i | ||||||||
\(414\) | −4550.30 | − | 2574.78i | −0.0265485 | − | 0.0150224i | ||||
\(415\) | 45379.7 | 0.263491 | ||||||||
\(416\) | −65778.1 | − | 37977.0i | −0.380097 | − | 0.219449i | ||||
\(417\) | −27645.1 | − | 101413.i | −0.158981 | − | 0.583203i | ||||
\(418\) | −40931.8 | − | 70895.9i | −0.234265 | − | 0.405759i | ||||
\(419\) | 109423. | − | 63175.3i | 0.623276 | − | 0.359848i | −0.154868 | − | 0.987935i | \(-0.549495\pi\) |
0.778143 | + | 0.628087i | \(0.216162\pi\) | |||||||
\(420\) | 39718.2 | − | 10827.2i | 0.225160 | − | 0.0613787i | ||||
\(421\) | 107645. | − | 186446.i | 0.607335 | − | 1.05194i | −0.384342 | − | 0.923191i | \(-0.625572\pi\) |
0.991678 | − | 0.128745i | \(-0.0410949\pi\) | |||||||
\(422\) | − | 182126.i | − | 1.02270i | ||||||
\(423\) | −162594. | − | 276067.i | −0.908709 | − | 1.54288i | ||||
\(424\) | 105935. | 0.589263 | ||||||||
\(425\) | 23215.6 | + | 13403.5i | 0.128529 | + | 0.0742063i | ||||
\(426\) | −189484. | + | 191134.i | −1.04413 | + | 1.05322i | ||||
\(427\) | 62061.3 | + | 107493.i | 0.340381 | + | 0.589557i | ||||
\(428\) | 31097.5 | − | 17954.1i | 0.169761 | − | 0.0980115i | ||||
\(429\) | −33914.9 | + | 128803.i | −0.184279 | + | 0.699859i | ||||
\(430\) | −31933.5 | + | 55310.4i | −0.172707 | + | 0.299137i | ||||
\(431\) | 121972.i | 0.656607i | 0.944572 | + | 0.328304i | \(0.106477\pi\) | ||||
−0.944572 | + | 0.328304i | \(0.893523\pi\) | |||||||
\(432\) | −212953. | + | 60039.2i | −1.14108 | + | 0.321712i | ||||
\(433\) | −152419. | −0.812951 | −0.406475 | − | 0.913662i | \(-0.633242\pi\) | ||||
−0.406475 | + | 0.913662i | \(0.633242\pi\) | |||||||
\(434\) | −84808.7 | − | 48964.3i | −0.450258 | − | 0.259956i | ||||
\(435\) | −99882.9 | − | 26300.0i | −0.527853 | − | 0.138988i | ||||
\(436\) | −31825.8 | − | 55123.8i | −0.167419 | − | 0.289979i | ||||
\(437\) | 2386.80 | − | 1378.02i | 0.0124984 | − | 0.00721593i | ||||
\(438\) | 137671. | + | 136483.i | 0.717621 | + | 0.711426i | ||||
\(439\) | −115564. | + | 200162.i | −0.599643 | + | 1.03861i | 0.393230 | + | 0.919440i | \(0.371358\pi\) |
−0.992874 | + | 0.119173i | \(0.961976\pi\) | |||||||
\(440\) | − | 82977.9i | − | 0.428605i | ||||||
\(441\) | −2003.26 | − | 231075.i | −0.0103005 | − | 1.18816i | ||||
\(442\) | −50023.9 | −0.256055 | ||||||||
\(443\) | −17481.4 | − | 10092.9i | −0.0890774 | − | 0.0514289i | 0.454800 | − | 0.890594i | \(-0.349711\pi\) |
−0.543877 | + | 0.839165i | \(0.683044\pi\) | |||||||
\(444\) | −7703.15 | − | 28258.0i | −0.0390753 | − | 0.143343i | ||||
\(445\) | 114383. | + | 198117.i | 0.577618 | + | 1.00046i | ||||
\(446\) | 231711. | − | 133778.i | 1.16487 | − | 0.672537i | ||||
\(447\) | 131044. | − | 35722.7i | 0.655847 | − | 0.178784i | ||||
\(448\) | 96128.9 | − | 166500.i | 0.478958 | − | 0.829580i | ||||
\(449\) | 92962.8i | 0.461123i | 0.973058 | + | 0.230561i | \(0.0740562\pi\) | ||||
−0.973058 | + | 0.230561i | \(0.925944\pi\) | |||||||
\(450\) | −133195. | + | 1154.71i | −0.657755 | + | 0.00570227i | ||||
\(451\) | 53475.0 | 0.262905 | ||||||||
\(452\) | 71967.4 | + | 41550.4i | 0.352256 | + | 0.203375i | ||||
\(453\) | 191707. | − | 193376.i | 0.934205 | − | 0.942339i | ||||
\(454\) | 220607. | + | 382103.i | 1.07031 | + | 1.85383i | ||||
\(455\) | 154796. | − | 89371.5i | 0.747716 | − | 0.431694i | ||||
\(456\) | 23531.9 | − | 89370.1i | 0.113169 | − | 0.429796i | ||||
\(457\) | −110443. | + | 191293.i | −0.528819 | + | 0.915941i | 0.470616 | + | 0.882338i | \(0.344032\pi\) |
−0.999435 | + | 0.0336033i | \(0.989302\pi\) | |||||||
\(458\) | 23746.0i | 0.113203i | ||||||||
\(459\) | −37031.0 | + | 38006.9i | −0.175768 | + | 0.180400i | ||||
\(460\) | −912.215 | −0.00431103 | ||||||||
\(461\) | 91967.2 | + | 53097.3i | 0.432744 | + | 0.249845i | 0.700515 | − | 0.713638i | \(-0.252954\pi\) |
−0.267771 | + | 0.963483i | \(0.586287\pi\) | |||||||
\(462\) | 270868. | + | 71321.8i | 1.26903 | + | 0.334148i | ||||
\(463\) | 34090.0 | + | 59045.5i | 0.159025 | + | 0.275439i | 0.934517 | − | 0.355918i | \(-0.115832\pi\) |
−0.775493 | + | 0.631357i | \(0.782498\pi\) | |||||||
\(464\) | 188264. | − | 108694.i | 0.874444 | − | 0.504860i | ||||
\(465\) | −30985.4 | − | 30718.0i | −0.143302 | − | 0.142065i | ||||
\(466\) | −41231.8 | + | 71415.6i | −0.189872 | + | 0.328868i | ||||
\(467\) | − | 224350.i | − | 1.02871i | −0.857578 | − | 0.514353i | \(-0.828032\pi\) | ||
0.857578 | − | 0.514353i | \(-0.171968\pi\) | |||||||
\(468\) | 42307.2 | − | 24917.6i | 0.193162 | − | 0.113766i | ||||
\(469\) | −335925. | −1.52720 | ||||||||
\(470\) | −245078. | − | 141496.i | −1.10945 | − | 0.640543i | ||||
\(471\) | 48814.7 | + | 179070.i | 0.220043 | + | 0.807202i | ||||
\(472\) | −145817. | − | 252563.i | −0.654524 | − | 1.13367i | ||||
\(473\) | −74337.9 | + | 42919.0i | −0.332267 | + | 0.191835i | ||||
\(474\) | −222120. | + | 60550.0i | −0.988624 | + | 0.269499i | ||||
\(475\) | 35107.8 | − | 60808.5i | 0.155603 | − | 0.269511i | ||||
\(476\) | 20780.4i | 0.0917149i | ||||||||
\(477\) | −78462.7 | + | 138664.i | −0.344847 | + | 0.609433i | ||||
\(478\) | 115410. | 0.505113 | ||||||||
\(479\) | −94542.7 | − | 54584.3i | −0.412057 | − | 0.237901i | 0.279616 | − | 0.960112i | \(-0.409793\pi\) |
−0.691673 | + | 0.722211i | \(0.743126\pi\) | |||||||
\(480\) | −50103.2 | + | 50539.4i | −0.217462 | + | 0.219355i | ||||
\(481\) | −63584.5 | − | 110132.i | −0.274828 | − | 0.476016i | ||||
\(482\) | −321243. | + | 185470.i | −1.38274 | + | 0.798324i | ||||
\(483\) | −2401.14 | + | 9119.10i | −0.0102926 | + | 0.0390893i | ||||
\(484\) | 10623.8 | − | 18400.9i | 0.0453510 | − | 0.0785503i | ||||
\(485\) | 114807.i | 0.488073i | ||||||||
\(486\) | 62707.3 | − | 256104.i | 0.265489 | − | 1.08429i | ||||
\(487\) | 106309. | 0.448240 | 0.224120 | − | 0.974562i | \(-0.428049\pi\) | ||||
0.224120 | + | 0.974562i | \(0.428049\pi\) | |||||||
\(488\) | −79870.6 | − | 46113.3i | −0.335388 | − | 0.193636i | ||||
\(489\) | −346312. | − | 91187.0i | −1.44827 | − | 0.381343i | ||||
\(490\) | −102055. | − | 176765.i | −0.425052 | − | 0.736212i | ||||
\(491\) | −64472.7 | + | 37223.3i | −0.267432 | + | 0.154402i | −0.627720 | − | 0.778439i | \(-0.716012\pi\) |
0.360288 | + | 0.932841i | \(0.382678\pi\) | |||||||
\(492\) | −13999.4 | − | 13878.5i | −0.0578333 | − | 0.0573341i | ||||
\(493\) | 26068.5 | − | 45152.0i | 0.107256 | − | 0.185773i | ||||
\(494\) | 131028.i | 0.536919i | ||||||||
\(495\) | 108614. | + | 61458.9i | 0.443275 | + | 0.250827i | ||||
\(496\) | 91830.8 | 0.373271 | ||||||||
\(497\) | 420397. | + | 242716.i | 1.70195 | + | 0.982621i | ||||
\(498\) | −29935.0 | − | 109813.i | −0.120704 | − | 0.442787i | ||||
\(499\) | 55603.4 | + | 96308.0i | 0.223306 | + | 0.386777i | 0.955810 | − | 0.293985i | \(-0.0949817\pi\) |
−0.732504 | + | 0.680763i | \(0.761648\pi\) | |||||||
\(500\) | −54284.1 | + | 31340.9i | −0.217136 | + | 0.125364i | ||||
\(501\) | 238358. | − | 64976.6i | 0.949631 | − | 0.258870i | ||||
\(502\) | 109514. | − | 189684.i | 0.434573 | − | 0.752703i | ||||
\(503\) | − | 115897.i | − | 0.458077i | −0.973417 | − | 0.229038i | \(-0.926442\pi\) | ||
0.973417 | − | 0.229038i | \(-0.0735581\pi\) | |||||||
\(504\) | 160471. | + | 272462.i | 0.631737 | + | 1.07262i | ||||
\(505\) | −31391.5 | −0.123092 | ||||||||
\(506\) | −5375.10 | − | 3103.31i | −0.0209935 | − | 0.0121206i | ||||
\(507\) | −30882.9 | + | 31151.8i | −0.120144 | + | 0.121190i | ||||
\(508\) | −40687.2 | − | 70472.3i | −0.157663 | − | 0.273081i | ||||
\(509\) | −170299. | + | 98322.1i | −0.657319 | + | 0.379503i | −0.791255 | − | 0.611487i | \(-0.790572\pi\) |
0.133936 | + | 0.990990i | \(0.457238\pi\) | |||||||
\(510\) | −11934.6 | + | 45325.4i | −0.0458845 | + | 0.174261i | ||||
\(511\) | 174825. | − | 302807.i | 0.669519 | − | 1.15964i | ||||
\(512\) | 111753.i | 0.426305i | ||||||||
\(513\) | 99551.4 | + | 96995.4i | 0.378279 | + | 0.368567i | ||||
\(514\) | 433603. | 1.64122 | ||||||||
\(515\) | 71537.3 | + | 41302.1i | 0.269723 | + | 0.155725i | ||||
\(516\) | 30600.0 | + | 8057.24i | 0.114927 | + | 0.0302613i | ||||
\(517\) | −190172. | − | 329388.i | −0.711486 | − | 1.23233i | ||||
\(518\) | −231603. | + | 133716.i | −0.863146 | + | 0.498337i | ||||
\(519\) | −64424.2 | − | 63868.1i | −0.239174 | − | 0.237110i | ||||
\(520\) | −66405.5 | + | 115018.i | −0.245583 | + | 0.425362i | ||||
\(521\) | − | 299306.i | − | 1.10266i | −0.834289 | − | 0.551328i | \(-0.814121\pi\) | ||
0.834289 | − | 0.551328i | \(-0.185879\pi\) | |||||||
\(522\) | 2245.80 | + | 259052.i | 0.00824195 | + | 0.950707i | ||||
\(523\) | −162892. | −0.595520 | −0.297760 | − | 0.954641i | \(-0.596240\pi\) | ||||
−0.297760 | + | 0.954641i | \(0.596240\pi\) | |||||||
\(524\) | 10919.8 | + | 6304.56i | 0.0397698 | + | 0.0229611i | ||||
\(525\) | 63185.6 | + | 231788.i | 0.229245 | + | 0.840955i | ||||
\(526\) | 92605.2 | + | 160397.i | 0.334706 | + | 0.579728i | ||||
\(527\) | 19073.4 | − | 11012.0i | 0.0686763 | − | 0.0396503i | ||||
\(528\) | −253412. | + | 69080.1i | −0.908989 | + | 0.247791i | ||||
\(529\) | −139816. | + | 242168.i | −0.499627 | + | 0.865379i | ||||
\(530\) | 140726.i | 0.500983i | ||||||||
\(531\) | 438594. | − | 3802.29i | 1.55551 | − | 0.0134852i | ||||
\(532\) | 54430.1 | 0.192316 | ||||||||
\(533\) | −74123.1 | − | 42795.0i | −0.260915 | − | 0.150639i | ||||
\(534\) | 403963. | − | 407480.i | 1.41664 | − | 1.42897i | ||||
\(535\) | −73039.7 | − | 126508.i | −0.255183 | − | 0.441989i | ||||
\(536\) | 216161. | − | 124801.i | 0.752400 | − | 0.434398i | ||||
\(537\) | −2785.41 | + | 10578.5i | −0.00965920 | + | 0.0366839i | ||||
\(538\) | −258399. | + | 447560.i | −0.892742 | + | 1.54628i | ||||
\(539\) | − | 274327.i | − | 0.944257i | ||||||
\(540\) | −12483.6 | − | 44278.2i | −0.0428108 | − | 0.151846i | ||||
\(541\) | −62918.7 | −0.214974 | −0.107487 | − | 0.994207i | \(-0.534280\pi\) | ||||
−0.107487 | + | 0.994207i | \(0.534280\pi\) | |||||||
\(542\) | −19635.7 | − | 11336.7i | −0.0668416 | − | 0.0385910i | ||||
\(543\) | −246826. | − | 64991.5i | −0.837128 | − | 0.220423i | ||||
\(544\) | −17961.4 | − | 31110.1i | −0.0606936 | − | 0.105124i | ||||
\(545\) | −224251. | + | 129471.i | −0.754989 | + | 0.435893i | ||||
\(546\) | −318379. | − | 315631.i | −1.06797 | − | 1.05875i | ||||
\(547\) | 7403.57 | − | 12823.4i | 0.0247438 | − | 0.0428575i | −0.853388 | − | 0.521276i | \(-0.825456\pi\) |
0.878132 | + | 0.478418i | \(0.158790\pi\) | |||||||
\(548\) | − | 15249.8i | − | 0.0507813i | ||||||
\(549\) | 119517. | − | 70391.8i | 0.396539 | − | 0.233549i | ||||
\(550\) | −158126. | −0.522732 | ||||||||
\(551\) | −118267. | − | 68281.3i | −0.389547 | − | 0.224905i | ||||
\(552\) | −1842.79 | − | 6760.03i | −0.00604779 | − | 0.0221856i | ||||
\(553\) | 207622. | + | 359612.i | 0.678927 | + | 1.17594i | ||||
\(554\) | 163907. | − | 94631.9i | 0.534046 | − | 0.308332i | ||||
\(555\) | −114957. | + | 31337.4i | −0.373207 | + | 0.101736i | ||||
\(556\) | −22999.8 | + | 39836.8i | −0.0744002 | + | 0.128865i | ||||
\(557\) | − | 254392.i | − | 0.819962i | −0.912094 | − | 0.409981i | \(-0.865535\pi\) | ||
0.912094 | − | 0.409981i | \(-0.134465\pi\) | |||||||
\(558\) | −53893.7 | + | 95243.9i | −0.173089 | + | 0.305893i | ||||
\(559\) | 137389. | 0.439671 | ||||||||
\(560\) | 305260. | + | 176242.i | 0.973405 | + | 0.561996i | ||||
\(561\) | −44350.2 | + | 44736.3i | −0.140919 | + | 0.142146i | ||||
\(562\) | −92557.4 | − | 160314.i | −0.293048 | − | 0.507574i | ||||
\(563\) | 80806.7 | − | 46653.8i | 0.254936 | − | 0.147187i | −0.367087 | − | 0.930187i | \(-0.619645\pi\) |
0.622022 | + | 0.783000i | \(0.286311\pi\) | |||||||
\(564\) | −35701.3 | + | 135587.i | −0.112234 | + | 0.426246i | ||||
\(565\) | 169032. | − | 292772.i | 0.529508 | − | 0.917134i | ||||
\(566\) | − | 171412.i | − | 0.535068i | ||||||
\(567\) | −475494. | + | 8245.01i | −1.47904 | + | 0.0256463i | ||||
\(568\) | −360690. | −1.11799 | ||||||||
\(569\) | −136853. | − | 79012.1i | −0.422698 | − | 0.244045i | 0.273533 | − | 0.961863i | \(-0.411808\pi\) |
−0.696231 | + | 0.717818i | \(0.745141\pi\) | |||||||
\(570\) | 118721. | + | 31260.2i | 0.365407 | + | 0.0962149i | ||||
\(571\) | 219188. | + | 379644.i | 0.672270 | + | 1.16441i | 0.977259 | + | 0.212050i | \(0.0680141\pi\) |
−0.304988 | + | 0.952356i | \(0.598653\pi\) | |||||||
\(572\) | 50478.7 | − | 29143.9i | 0.154282 | − | 0.0890749i | ||||
\(573\) | 62328.8 | + | 61790.8i | 0.189836 | + | 0.188198i | ||||
\(574\) | −89996.4 | + | 155878.i | −0.273150 | + | 0.473110i | ||||
\(575\) | − | 5323.52i | − | 0.0161014i | ||||||
\(576\) | −186987. | − | 105806.i | −0.563594 | − | 0.318909i | ||||
\(577\) | 214770. | 0.645094 | 0.322547 | − | 0.946554i | \(-0.395461\pi\) | ||||
0.322547 | + | 0.946554i | \(0.395461\pi\) | |||||||
\(578\) | 302489. | + | 174642.i | 0.905428 | + | 0.522749i | ||||
\(579\) | −126406. | − | 463705.i | −0.377061 | − | 1.38320i | ||||
\(580\) | 22600.3 | + | 39144.8i | 0.0671827 | + | 0.116364i | ||||
\(581\) | −177787. | + | 102645.i | −0.526681 | + | 0.304079i | ||||
\(582\) | 277817. | − | 75733.1i | 0.820188 | − | 0.223584i | ||||
\(583\) | −94568.9 | + | 163798.i | −0.278235 | + | 0.481917i | ||||
\(584\) | 259801.i | 0.761753i | ||||||||
\(585\) | −101368. | − | 172111.i | −0.296202 | − | 0.502918i | ||||
\(586\) | −57951.3 | −0.168759 | ||||||||
\(587\) | 568470. | + | 328206.i | 1.64980 | + | 0.952512i | 0.977150 | + | 0.212550i | \(0.0681767\pi\) |
0.672649 | + | 0.739962i | \(0.265157\pi\) | |||||||
\(588\) | −71196.7 | + | 71816.6i | −0.205923 | + | 0.207716i | ||||
\(589\) | −28843.8 | − | 49959.0i | −0.0831423 | − | 0.144007i | ||||
\(590\) | 335509. | − | 193706.i | 0.963830 | − | 0.556467i | ||||
\(591\) | −157066. | + | 596507.i | −0.449683 | + | 1.70781i | ||||
\(592\) | 125390. | − | 217181.i | 0.357781 | − | 0.619696i | ||||
\(593\) | 118369.i | 0.336612i | 0.985735 | + | 0.168306i | \(0.0538296\pi\) | ||||
−0.985735 | + | 0.168306i | \(0.946170\pi\) | |||||||
\(594\) | 77074.6 | − | 303372.i | 0.218443 | − | 0.859811i | ||||
\(595\) | 84537.3 | 0.238789 | ||||||||
\(596\) | −51476.5 | − | 29720.0i | −0.144916 | − | 0.0836673i | ||||
\(597\) | 71693.1 | + | 18877.4i | 0.201154 | + | 0.0529656i | ||||
\(598\) | 4967.04 | + | 8603.17i | 0.0138898 | + | 0.0240578i | ||||
\(599\) | −306693. | + | 177069.i | −0.854772 | + | 0.493503i | −0.862258 | − | 0.506469i | \(-0.830950\pi\) |
0.00748620 | + | 0.999972i | \(0.497617\pi\) | |||||||
\(600\) | −126771. | − | 125677.i | −0.352143 | − | 0.349103i | ||||
\(601\) | 297820. | − | 515839.i | 0.824526 | − | 1.42812i | −0.0777554 | − | 0.996972i | \(-0.524775\pi\) |
0.902281 | − | 0.431148i | \(-0.141891\pi\) | |||||||
\(602\) | − | 288924.i | − | 0.797242i | ||||||
\(603\) | 3254.27 | + | 375379.i | 0.00894992 | + | 1.03237i | ||||
\(604\) | −119163. | −0.326638 | ||||||||
\(605\) | −74857.1 | − | 43218.8i | −0.204514 | − | 0.118076i | ||||
\(606\) | 20707.6 | + | 75963.2i | 0.0563877 | + | 0.206851i | ||||
\(607\) | −4860.81 | − | 8419.17i | −0.0131926 | − | 0.0228503i | 0.859354 | − | 0.511382i | \(-0.170866\pi\) |
−0.872546 | + | 0.488531i | \(0.837533\pi\) | |||||||
\(608\) | −81486.6 | + | 47046.3i | −0.220434 | + | 0.127268i | ||||
\(609\) | 450806. | − | 122890.i | 1.21550 | − | 0.331346i | ||||
\(610\) | 61257.7 | − | 106101.i | 0.164627 | − | 0.285142i | ||||
\(611\) | 608765.i | 1.63067i | ||||||||
\(612\) | 23221.1 | − | 201.310i | 0.0619982 | − | 0.000537480i | ||||
\(613\) | 194450. | 0.517473 | 0.258736 | − | 0.965948i | \(-0.416694\pi\) | ||||
0.258736 | + | 0.965948i | \(0.416694\pi\) | |||||||
\(614\) | −487650. | − | 281545.i | −1.29352 | − | 0.746811i | ||||
\(615\) | −56459.6 | + | 56951.2i | −0.149275 | + | 0.150575i | ||||
\(616\) | 187689. | + | 325087.i | 0.494627 | + | 0.856720i | ||||
\(617\) | 422308. | − | 243819.i | 1.10932 | − | 0.640469i | 0.170670 | − | 0.985328i | \(-0.445407\pi\) |
0.938654 | + | 0.344860i | \(0.112073\pi\) | |||||||
\(618\) | 52755.5 | − | 200356.i | 0.138131 | − | 0.524596i | ||||
\(619\) | −8628.23 | + | 14944.5i | −0.0225185 | + | 0.0390033i | −0.877065 | − | 0.480372i | \(-0.840502\pi\) |
0.854547 | + | 0.519375i | \(0.173835\pi\) | |||||||
\(620\) | 19093.9i | 0.0496719i | ||||||||
\(621\) | 10213.4 | + | 2594.81i | 0.0264842 | + | 0.00672857i | ||||
\(622\) | −445649. | −1.15189 | ||||||||
\(623\) | −896249. | − | 517449.i | −2.30915 | − | 1.33319i | ||||
\(624\) | 406544. | + | 107047.i | 1.04409 | + | 0.274918i | ||||
\(625\) | 12412.5 | + | 21499.1i | 0.0317760 | + | 0.0550376i | ||||
\(626\) | 8605.50 | − | 4968.39i | 0.0219598 | − | 0.0126785i | ||||
\(627\) | 117178. | + | 116166.i | 0.298065 | + | 0.295492i | ||||
\(628\) | 40612.1 | − | 70342.1i | 0.102976 | − | 0.178360i | ||||
\(629\) | − | 60145.1i | − | 0.152019i | ||||||
\(630\) | −361943. | + | 213173.i | −0.911926 | + | 0.537095i | ||||
\(631\) | −429836. | −1.07955 | −0.539777 | − | 0.841808i | \(-0.681491\pi\) | ||||
−0.539777 | + | 0.841808i | \(0.681491\pi\) | |||||||
\(632\) | −267202. | − | 154269.i | −0.668968 | − | 0.386229i | ||||
\(633\) | 96545.0 | + | 354163.i | 0.240948 | + | 0.883886i | ||||
\(634\) | −375235. | − | 649927.i | −0.933523 | − | 1.61691i | ||||
\(635\) | −286690. | + | 165521.i | −0.710993 | + | 0.410492i | ||||
\(636\) | 67268.4 | − | 18337.4i | 0.166302 | − | 0.0453339i | ||||
\(637\) | −219538. | + | 380251.i | −0.541042 | + | 0.937113i | ||||
\(638\) | 307540.i | 0.755546i | ||||||||
\(639\) | 267151. | − | 472124.i | 0.654266 | − | 1.15626i | ||||
\(640\) | −316285. | −0.772181 | ||||||||
\(641\) | −27979.5 | − | 16154.0i | −0.0680964 | − | 0.0393155i | 0.465565 | − | 0.885014i | \(-0.345851\pi\) |
−0.533662 | + | 0.845698i | \(0.679184\pi\) | |||||||
\(642\) | −257952. | + | 260198.i | −0.625849 | + | 0.631298i | ||||
\(643\) | −138524. | − | 239931.i | −0.335045 | − | 0.580315i | 0.648448 | − | 0.761259i | \(-0.275418\pi\) |
−0.983494 | + | 0.180943i | \(0.942085\pi\) | |||||||
\(644\) | 3573.84 | − | 2063.36i | 0.00861714 | − | 0.00497511i | ||||
\(645\) | 32777.9 | − | 124485.i | 0.0787882 | − | 0.299224i | ||||
\(646\) | −30985.0 | + | 53667.7i | −0.0742484 | + | 0.128602i | ||||
\(647\) | 125452.i | 0.299689i | 0.988710 | + | 0.149844i | \(0.0478773\pi\) | ||||
−0.988710 | + | 0.149844i | \(0.952123\pi\) | |||||||
\(648\) | 302908. | − | 181958.i | 0.721376 | − | 0.433333i | ||||
\(649\) | 520687. | 1.23620 | ||||||||
\(650\) | 219183. | + | 126545.i | 0.518776 | + | 0.299516i | ||||
\(651\) | 190875. | + | 50259.1i | 0.450388 | + | 0.118591i | ||||
\(652\) | 78359.2 | + | 135722.i | 0.184330 | + | 0.319268i | ||||
\(653\) | 245936. | − | 141991.i | 0.576760 | − | 0.332992i | −0.183085 | − | 0.983097i | \(-0.558608\pi\) |
0.759845 | + | 0.650105i | \(0.225275\pi\) | |||||||
\(654\) | 461231. | + | 457250.i | 1.07836 | + | 1.06905i | ||||
\(655\) | 25647.8 | − | 44423.2i | 0.0597815 | − | 0.103545i | ||||
\(656\) | − | 168785.i | − | 0.392216i | ||||||
\(657\) | −340065. | − | 192425.i | −0.787828 | − | 0.445791i | ||||
\(658\) | 1.28021e6 | 2.95685 | ||||||||
\(659\) | 311139. | + | 179636.i | 0.716446 | + | 0.413640i | 0.813443 | − | 0.581644i | \(-0.197590\pi\) |
−0.0969973 | + | 0.995285i | \(0.530924\pi\) | |||||||
\(660\) | −14363.5 | − | 52690.5i | −0.0329740 | − | 0.120961i | ||||
\(661\) | −98902.1 | − | 171303.i | −0.226362 | − | 0.392070i | 0.730366 | − | 0.683057i | \(-0.239350\pi\) |
−0.956727 | + | 0.290987i | \(0.906016\pi\) | |||||||
\(662\) | −26136.7 | + | 15090.0i | −0.0596396 | + | 0.0344330i | ||||
\(663\) | 97276.5 | − | 26517.6i | 0.221300 | − | 0.0603264i | ||||
\(664\) | 76268.4 | − | 132101.i | 0.172985 | − | 0.299619i | ||||
\(665\) | − | 221429.i | − | 0.500715i | ||||||
\(666\) | 151665. | + | 257509.i | 0.341929 | + | 0.580556i | ||||
\(667\) | −10353.7 | −0.0232726 | ||||||||
\(668\) | −93631.5 | − | 54058.2i | −0.209831 | − | 0.121146i | ||||
\(669\) | −379669. | + | 382975.i | −0.848307 | + | 0.855693i | ||||
\(670\) | 165788. | + | 287152.i | 0.369320 | + | 0.639680i | ||||
\(671\) | 142602. | − | 82331.1i | 0.316723 | − | 0.182860i | ||||
\(672\) | 81976.2 | − | 311331.i | 0.181530 | − | 0.689420i | ||||
\(673\) | −119036. | + | 206176.i | −0.262814 | + | 0.455207i | −0.966989 | − | 0.254820i | \(-0.917984\pi\) |
0.704175 | + | 0.710027i | \(0.251317\pi\) | |||||||
\(674\) | 991702.i | 2.18304i | ||||||||
\(675\) | 258400. | − | 72852.2i | 0.567133 | − | 0.159895i | ||||
\(676\) | 19196.4 | 0.0420075 | ||||||||
\(677\) | 216636. | + | 125075.i | 0.472666 | + | 0.272894i | 0.717355 | − | 0.696708i | \(-0.245353\pi\) |
−0.244689 | + | 0.969602i | \(0.578686\pi\) | |||||||
\(678\) | −819973. | − | 215906.i | −1.78378 | − | 0.469684i | ||||
\(679\) | −259684. | − | 449786.i | −0.563256 | − | 0.975588i | ||||
\(680\) | −54398.2 | + | 31406.8i | −0.117643 | + | 0.0679213i | ||||
\(681\) | −631545. | − | 626094.i | −1.36179 | − | 1.35004i | ||||
\(682\) | −64956.6 | + | 112508.i | −0.139654 | + | 0.241888i | ||||
\(683\) | − | 267358.i | − | 0.573129i | −0.958061 | − | 0.286564i | \(-0.907487\pi\) | ||
0.958061 | − | 0.286564i | \(-0.0925132\pi\) | |||||||
\(684\) | −527.292 | − | 60823.0i | −0.00112704 | − | 0.130004i | ||||
\(685\) | −62038.2 | −0.132214 | ||||||||
\(686\) | 126662. | + | 73128.5i | 0.269153 | + | 0.155396i | ||||
\(687\) | −12587.7 | − | 46176.5i | −0.0266707 | − | 0.0978380i | ||||
\(688\) | 135466. | + | 234635.i | 0.286190 | + | 0.495696i | ||||
\(689\) | 262169. | − | 151363.i | 0.552259 | − | 0.318847i | ||||
\(690\) | 8980.13 | − | 2447.99i | 0.0188619 | − | 0.00514175i | ||||
\(691\) | −168343. | + | 291579.i | −0.352565 | + | 0.610660i | −0.986698 | − | 0.162564i | \(-0.948024\pi\) |
0.634133 | + | 0.773224i | \(0.281357\pi\) | |||||||
\(692\) | 39699.5i | 0.0829036i | ||||||||
\(693\) | −564537. | + | 4894.13i | −1.17551 | + | 0.0101908i | ||||
\(694\) | −725817. | −1.50698 | ||||||||
\(695\) | 162061. | + | 93565.9i | 0.335513 | + | 0.193708i | ||||
\(696\) | −244430. | + | 246558.i | −0.504587 | + | 0.508980i | ||||
\(697\) | −20240.1 | − | 35056.9i | −0.0416627 | − | 0.0721618i | ||||
\(698\) | 281121. | − | 162305.i | 0.577009 | − | 0.333137i | ||||
\(699\) | 42322.1 | − | 160732.i | 0.0866189 | − | 0.328963i | ||||
\(700\) | 52568.2 | − | 91050.7i | 0.107282 | − | 0.185818i | ||||
\(701\) | − | 635795.i | − | 1.29384i | −0.762557 | − | 0.646921i | \(-0.776056\pi\) | ||
0.762557 | − | 0.646921i | \(-0.223944\pi\) | |||||||
\(702\) | −349618. | + | 358831.i | −0.709446 | + | 0.728141i | ||||
\(703\) | −157538. | −0.318768 | ||||||||
\(704\) | −220881. | − | 127525.i | −0.445669 | − | 0.257307i | ||||
\(705\) | 551586. | + | 145237.i | 1.10978 | + | 0.292214i | ||||
\(706\) | 287182. | + | 497413.i | 0.576165 | + | 0.997948i | ||||
\(707\) | 122984. | − | 71005.0i | 0.246043 | − | 0.142053i | ||||
\(708\) | −136312. | − | 135135.i | −0.271937 | − | 0.269589i | ||||
\(709\) | −215513. | + | 373280.i | −0.428728 | + | 0.742578i | −0.996760 | − | 0.0804279i | \(-0.974371\pi\) |
0.568033 | + | 0.823006i | \(0.307705\pi\) | |||||||
\(710\) | − | 479147.i | − | 0.950499i | ||||||
\(711\) | 399837. | − | 235491.i | 0.790941 | − | 0.465839i | ||||
\(712\) | 768959. | 1.51685 | ||||||||
\(713\) | −3787.73 | − | 2186.84i | −0.00745074 | − | 0.00430169i | ||||
\(714\) | −55765.6 | − | 204569.i | −0.109388 | − | 0.401276i | ||||
\(715\) | −118561. | − | 205354.i | −0.231916 | − | 0.401690i | ||||
\(716\) | 4145.79 | − | 2393.57i | 0.00808689 | − | 0.00466897i | ||||
\(717\) | −224427. | + | 61178.9i | −0.436553 | + | 0.119004i | ||||
\(718\) | 212776. | − | 368539.i | 0.412737 | − | 0.714882i | ||||
\(719\) | 798370.i | 1.54435i | 0.635409 | + | 0.772176i | \(0.280832\pi\) | ||||
−0.635409 | + | 0.772176i | \(0.719168\pi\) | |||||||
\(720\) | 193984. | − | 342820.i | 0.374198 | − | 0.661304i | ||||
\(721\) | −373688. | −0.718850 | ||||||||
\(722\) | −363384. | − | 209800.i | −0.697093 | − | 0.402467i | ||||
\(723\) | 526372. | − | 530956.i | 1.00697 | − | 1.01574i | ||||
\(724\) | 55848.8 | + | 96732.9i | 0.106546 | + | 0.184543i | ||||
\(725\) | −228442. | + | 131891.i | −0.434610 | + | 0.250922i | ||||
\(726\) | −55203.7 | + | 209654.i | −0.104736 | + | 0.397768i | ||||
\(727\) | −158557. | + | 274628.i | −0.299996 | + | 0.519609i | −0.976135 | − | 0.217166i | \(-0.930319\pi\) |
0.676139 | + | 0.736775i | \(0.263652\pi\) | |||||||
\(728\) | − | 600816.i | − | 1.13365i | ||||||
\(729\) | 13819.7 | + | 531261.i | 0.0260043 | + | 0.999662i | ||||
\(730\) | −345123. | −0.647632 | ||||||||
\(731\) | 56273.2 | + | 32489.3i | 0.105309 | + | 0.0608004i | ||||
\(732\) | −58699.6 | − | 15456.1i | −0.109550 | − | 0.0288455i | ||||
\(733\) | 488922. | + | 846837.i | 0.909979 | + | 1.57613i | 0.814091 | + | 0.580738i | \(0.197236\pi\) |
0.0958883 | + | 0.995392i | \(0.469431\pi\) | |||||||
\(734\) | −402736. | + | 232520.i | −0.747529 | + | 0.431586i | ||||
\(735\) | 292159. | + | 289637.i | 0.540810 | + | 0.536142i | ||||
\(736\) | −3566.90 | + | 6178.05i | −0.00658469 | + | 0.0114050i | ||||
\(737\) | 445641.i | 0.820446i | ||||||||
\(738\) | 175058. | + | 99056.5i | 0.321418 | + | 0.181874i | ||||
\(739\) | −392565. | −0.718825 | −0.359412 | − | 0.933179i | \(-0.617023\pi\) | ||||
−0.359412 | + | 0.933179i | \(0.617023\pi\) | |||||||
\(740\) | 45157.3 | + | 26071.6i | 0.0824640 | + | 0.0476106i | ||||
\(741\) | −69457.6 | − | 254796.i | −0.126498 | − | 0.464041i | ||||
\(742\) | −318312. | − | 551332.i | −0.578155 | − | 1.00139i | ||||
\(743\) | 899450. | − | 519298.i | 1.62929 | − | 0.940673i | 0.644990 | − | 0.764191i | \(-0.276861\pi\) |
0.984304 | − | 0.176482i | \(-0.0564719\pi\) | |||||||
\(744\) | −141497. | + | 38572.0i | −0.255623 | + | 0.0696829i | ||||
\(745\) | −120905. | + | 209413.i | −0.217836 | + | 0.377304i | ||||
\(746\) | − | 1.09770e6i | − | 1.97245i | ||||||
\(747\) | 116423. | + | 197674.i | 0.208641 | + | 0.354248i | ||||
\(748\) | 27567.5 | 0.0492713 | ||||||||
\(749\) | 572304. | + | 330420.i | 1.02015 | + | 0.588983i | ||||
\(750\) | 450284. | − | 454205.i | 0.800506 | − | 0.807476i | ||||
\(751\) | −159783. | − | 276752.i | −0.283302 | − | 0.490694i | 0.688894 | − | 0.724862i | \(-0.258097\pi\) |
−0.972196 | + | 0.234168i | \(0.924763\pi\) | |||||||
\(752\) | −1.03966e6 | + | 600246.i | −1.83846 | + | 1.06144i | ||||
\(753\) | −112410. | + | 426913.i | −0.198251 | + | 0.752921i | ||||
\(754\) | 246118. | − | 426290.i | 0.432914 | − | 0.749829i | ||||
\(755\) | 484769.i | 0.850435i | ||||||||
\(756\) | 149062. | + | 145235.i | 0.260809 | + | 0.254113i | ||||
\(757\) | 500321. | 0.873085 | 0.436543 | − | 0.899684i | \(-0.356203\pi\) | ||||
0.436543 | + | 0.899684i | \(0.356203\pi\) | |||||||
\(758\) | 776617. | + | 448380.i | 1.35166 | + | 0.780383i | ||||
\(759\) | 12097.5 | + | 3185.37i | 0.0209996 | + | 0.00552939i | ||||
\(760\) | 82263.8 | + | 142485.i | 0.142424 | + | 0.246685i | ||||
\(761\) | −783645. | + | 452437.i | −1.35316 | + | 0.781249i | −0.988691 | − | 0.149966i | \(-0.952083\pi\) |
−0.364471 | + | 0.931215i | \(0.618750\pi\) | |||||||
\(762\) | 589655. | + | 584565.i | 1.01552 | + | 1.00675i | ||||
\(763\) | 585707. | − | 1.01447e6i | 1.00608 | − | 1.74258i | ||||
\(764\) | − | 38408.3i | − | 0.0658019i | ||||||
\(765\) | −818.955 | − | 94466.2i | −0.00139938 | − | 0.161419i | ||||
\(766\) | 604318. | 1.02993 | ||||||||
\(767\) | −721738. | − | 416696.i | −1.22684 | − | 0.708318i | ||||
\(768\) | 108186. | + | 396865.i | 0.183420 | + | 0.672853i | ||||
\(769\) | −71688.6 | − | 124168.i | −0.121227 | − | 0.209970i | 0.799025 | − | 0.601298i | \(-0.205349\pi\) |
−0.920252 | + | 0.391327i | \(0.872016\pi\) | |||||||
\(770\) | −431852. | + | 249330.i | −0.728372 | + | 0.420526i | ||||
\(771\) | −843184. | + | 229852.i | −1.41845 | + | 0.386670i | ||||
\(772\) | −105165. | + | 182152.i | −0.176457 | + | 0.305632i | ||||
\(773\) | − | 710063.i | − | 1.18833i | −0.804342 | − | 0.594166i | \(-0.797482\pi\) | ||
0.804342 | − | 0.594166i | \(-0.202518\pi\) | |||||||
\(774\) | −322858. | + | 2798.95i | −0.538927 | + | 0.00467211i | ||||
\(775\) | −111428. | −0.185521 | ||||||||
\(776\) | 334204. | + | 192953.i | 0.554993 | + | 0.320426i | ||||
\(777\) | 379492. | − | 382796.i | 0.628580 | − | 0.634053i | ||||
\(778\) | −451386. | − | 781823.i | −0.745742 | − | 1.29166i | ||||
\(779\) | −91824.5 | + | 53014.9i | −0.151316 | + | 0.0873621i | ||||
\(780\) | −22257.6 | + | 84530.5i | −0.0365839 | + | 0.138939i | ||||
\(781\) | 321990. | − | 557702.i | 0.527885 | − | 0.914324i | ||||
\(782\) | 4698.37i | 0.00768305i | ||||||||
\(783\) | −141691. | − | 502563.i | −0.231109 | − | 0.819723i | ||||
\(784\) | −865865. | −1.40870 | ||||||||
\(785\) | −286161. | − | 165215.i | −0.464377 | − | 0.268108i | ||||
\(786\) | −124417. | − | 32760.1i | −0.201388 | − | 0.0530274i | ||||
\(787\) | 300855. | + | 521097.i | 0.485745 | + | 0.841335i | 0.999866 | − | 0.0163827i | \(-0.00521501\pi\) |
−0.514121 | + | 0.857718i | \(0.671882\pi\) | |||||||
\(788\) | 233775. | − | 134970.i | 0.376484 | − | 0.217363i | ||||
\(789\) | −265106. | − | 262818.i | −0.425859 | − | 0.422183i | ||||
\(790\) | 204934. | − | 354956.i | 0.328367 | − | 0.568748i | ||||
\(791\) | 1.52935e6i | 2.44429i | ||||||||
\(792\) | 361451. | − | 212883.i | 0.576234 | − | 0.339383i | ||||
\(793\) | −263552. | −0.419102 | ||||||||
\(794\) | 395923. | + | 228586.i | 0.628014 | + | 0.362584i | ||||
\(795\) | −74598.8 | − | 273656.i | −0.118031 | − | 0.432983i | ||||
\(796\) | −16221.8 | − | 28097.0i | −0.0256020 | − | 0.0443439i | ||||
\(797\) | −372227. | + | 214905.i | −0.585991 | + | 0.338322i | −0.763511 | − | 0.645795i | \(-0.776526\pi\) |
0.177519 | + | 0.984117i | \(0.443193\pi\) | |||||||
\(798\) | −535828. | + | 146067.i | −0.841432 | + | 0.229375i | ||||
\(799\) | −143959. | + | 249344.i | −0.225499 | + | 0.390576i | ||||
\(800\) | 181748.i | 0.283981i | ||||||||
\(801\) | −569542. | + | 1.00653e6i | −0.887688 | + | 1.56877i | ||||
\(802\) | −402308. | −0.625474 | ||||||||
\(803\) | −401706. | − | 231925.i | −0.622984 | − | 0.359680i | ||||
\(804\) | 115658. | − | 116665.i | 0.178923 | − | 0.180480i | ||||
\(805\) | −8393.99 | − | 14538.8i | −0.0129532 | − | 0.0224356i | ||||
\(806\) | 180076. | − | 103967.i | 0.277195 | − | 0.160039i | ||||
\(807\) | 265232. | − | 1.00730e6i | 0.407266 | − | 1.54672i | ||||
\(808\) | −52758.7 | + | 91380.8i | −0.0808112 | + | 0.139969i | ||||
\(809\) | − | 629639.i | − | 0.962042i | −0.876709 | − | 0.481021i | \(-0.840266\pi\) | ||
0.876709 | − | 0.481021i | \(-0.159734\pi\) | |||||||
\(810\) | 241716. | + | 402389.i | 0.368414 | + | 0.613304i | ||||
\(811\) | 577760. | 0.878428 | 0.439214 | − | 0.898383i | \(-0.355257\pi\) | ||||
0.439214 | + | 0.898383i | \(0.355257\pi\) | |||||||
\(812\) | −177085. | − | 102240.i | −0.268577 | − | 0.155063i | ||||
\(813\) | 44193.1 | + | 11636.4i | 0.0668610 | + | 0.0176051i | ||||
\(814\) | 177389. | + | 307246.i | 0.267718 | + | 0.463701i | ||||
\(815\) | 552135. | − | 318775.i | 0.831246 | − | 0.479920i | ||||
\(816\) | 141202. | + | 139984.i | 0.212062 | + | 0.210231i | ||||
\(817\) | 85099.3 | − | 147396.i | 0.127492 | − | 0.220822i | ||||
\(818\) | − | 668548.i | − | 0.999140i | ||||||
\(819\) | 786436. | + | 445004.i | 1.17245 | + | 0.663431i | ||||
\(820\) | 35094.5 | 0.0521929 | ||||||||
\(821\) | 38728.3 | + | 22359.8i | 0.0574569 | + | 0.0331727i | 0.528453 | − | 0.848962i | \(-0.322772\pi\) |
−0.470996 | + | 0.882135i | \(0.656106\pi\) | |||||||
\(822\) | 40923.9 | + | 150124.i | 0.0605667 | + | 0.222181i | ||||
\(823\) | 146289. | + | 253380.i | 0.215979 | + | 0.374087i | 0.953575 | − | 0.301155i | \(-0.0973723\pi\) |
−0.737596 | + | 0.675242i | \(0.764039\pi\) | |||||||
\(824\) | 240461. | − | 138830.i | 0.354153 | − | 0.204470i | ||||
\(825\) | 307493. | − | 83822.6i | 0.451780 | − | 0.123155i | ||||
\(826\) | −876296. | + | 1.51779e6i | −1.28437 | + | 2.22460i | ||||
\(827\) | − | 806491.i | − | 1.17920i | −0.807694 | − | 0.589601i | \(-0.799285\pi\) | ||
0.807694 | − | 0.589601i | \(-0.200715\pi\) | |||||||
\(828\) | −2340.32 | − | 3973.60i | −0.00341362 | − | 0.00579593i | ||||
\(829\) | 204904. | 0.298154 | 0.149077 | − | 0.988826i | \(-0.452370\pi\) | ||||
0.149077 | + | 0.988826i | \(0.452370\pi\) | |||||||
\(830\) | 175485. | + | 101316.i | 0.254732 | + | 0.147069i | ||||
\(831\) | −268570. | + | 270908.i | −0.388916 | + | 0.392302i | ||||
\(832\) | 204112. | + | 353533.i | 0.294864 | + | 0.510720i | ||||
\(833\) | −179842. | + | 103832.i | −0.259179 | + | 0.149637i | ||||
\(834\) | 119513. | − | 453887.i | 0.171823 | − | 0.652553i | ||||
\(835\) | −219915. | + | 380905.i | −0.315415 | + | 0.546315i | ||||
\(836\) | − | 72207.5i | − | 0.103317i | ||||||
\(837\) | 54313.0 | − | 213780.i | 0.0775269 | − | 0.305152i | ||||
\(838\) | 564189. | 0.803409 | ||||||||
\(839\) | 667796. | + | 385552.i | 0.948681 | + | 0.547721i | 0.892671 | − | 0.450709i | \(-0.148829\pi\) |
0.0560100 | + | 0.998430i | \(0.482162\pi\) | |||||||
\(840\) | −544384. | − | 143341.i | −0.771520 | − | 0.203148i | ||||
\(841\) | −97125.1 | − | 168226.i | −0.137322 | − | 0.237848i | ||||
\(842\) | 832531. | − | 480662.i | 1.17429 | − | 0.677978i | ||||
\(843\) | 264970. | + | 262682.i | 0.372856 | + | 0.369637i | ||||
\(844\) | 80322.0 | − | 139122.i | 0.112759 | − | 0.195304i | ||||
\(845\) | − | 78093.4i | − | 0.109371i | ||||||
\(846\) | −12402.0 | − | 1.43057e6i | −0.0173281 | − | 1.99880i | ||||
\(847\) | 391030. | 0.545058 | ||||||||
\(848\) | 517001. | + | 298491.i | 0.718951 | + | 0.415087i | ||||
\(849\) | 90865.5 | + | 333329.i | 0.126062 | + | 0.462442i | ||||
\(850\) | 59850.2 | + | 103664.i | 0.0828376 | + | 0.143479i | ||||
\(851\) | −10343.8 | + | 5972.02i | −0.0142831 | + | 0.00824635i | ||||
\(852\) | −229036. | + | 62435.4i | −0.315519 | + | 0.0860106i | ||||
\(853\) | −541184. | + | 937358.i | −0.743784 | + | 1.28827i | 0.206977 | + | 0.978346i | \(0.433637\pi\) |
−0.950761 | + | 0.309925i | \(0.899696\pi\) | |||||||
\(854\) | 554240.i | 0.759945i | ||||||||
\(855\) | −247435. | + | 2145.09i | −0.338477 | + | 0.00293436i | ||||
\(856\) | −491023. | −0.670122 | ||||||||
\(857\) | −461890. | − | 266672.i | −0.628893 | − | 0.363092i | 0.151430 | − | 0.988468i | \(-0.451612\pi\) |
−0.780323 | + | 0.625376i | \(0.784945\pi\) | |||||||
\(858\) | −418719. | + | 422365.i | −0.568785 | + | 0.573737i | ||||
\(859\) | −565525. | − | 979517.i | −0.766417 | − | 1.32747i | −0.939494 | − | 0.342565i | \(-0.888704\pi\) |
0.173077 | − | 0.984908i | \(-0.444629\pi\) | |||||||
\(860\) | −48786.4 | + | 28166.8i | −0.0659632 | + | 0.0380839i | ||||
\(861\) | 92376.1 | − | 350828.i | 0.124610 | − | 0.473247i | ||||
\(862\) | −272319. | + | 471670.i | −0.366490 | + | 0.634780i | ||||
\(863\) | 110025.i | 0.147730i | 0.997268 | + | 0.0738649i | \(0.0235334\pi\) | ||||
−0.997268 | + | 0.0738649i | \(0.976467\pi\) | |||||||
\(864\) | −348691. | − | 88588.3i | −0.467104 | − | 0.118672i | ||||
\(865\) | 161503. | 0.215848 | ||||||||
\(866\) | −589410. | − | 340296.i | −0.785926 | − | 0.453755i | ||||
\(867\) | −680798. | − | 179260.i | −0.905691 | − | 0.238476i | ||||
\(868\) | −43188.8 | − | 74805.3i | −0.0573234 | − | 0.0992871i | ||||
\(869\) | 477065. | − | 275433.i | 0.631739 | − | 0.364735i | ||||
\(870\) | −327532. | − | 324705.i | −0.432728 | − | 0.428993i | ||||
\(871\) | 356638. | − | 617715.i | 0.470101 | − | 0.814238i | ||||
\(872\) | 870394.i | 1.14468i | ||||||||
\(873\) | −500098. | + | 294541.i | −0.656185 | + | 0.386472i | ||||
\(874\) | 12306.4 | 0.0161105 | ||||||||
\(875\) | −999020. | − | 576784.i | −1.30484 | − | 0.753351i | ||||
\(876\) | 44971.5 | + | 164972.i | 0.0586042 | + | 0.214982i | ||||
\(877\) | 204377. | + | 353991.i | 0.265725 | + | 0.460249i | 0.967753 | − | 0.251900i | \(-0.0810554\pi\) |
−0.702028 | + | 0.712149i | \(0.747722\pi\) | |||||||
\(878\) | −893778. | + | 516023.i | −1.15942 | + | 0.669391i | ||||
\(879\) | 112692. | − | 30719.9i | 0.145853 | − | 0.0397596i | ||||
\(880\) | 233804. | − | 404960.i | 0.301916 | − | 0.522935i | ||||
\(881\) | − | 235809.i | − | 0.303815i | −0.988395 | − | 0.151907i | \(-0.951458\pi\) | ||
0.988395 | − | 0.151907i | \(-0.0485416\pi\) | |||||||
\(882\) | 508159. | − | 898047.i | 0.653224 | − | 1.15442i | ||||
\(883\) | −273719. | −0.351061 | −0.175531 | − | 0.984474i | \(-0.556164\pi\) | ||||
−0.175531 | + | 0.984474i | \(0.556164\pi\) | |||||||
\(884\) | −38212.0 | − | 22061.7i | −0.0488985 | − | 0.0282315i | ||||
\(885\) | −549748. | + | 554534.i | −0.701903 | + | 0.708014i | ||||
\(886\) | −45067.3 | − | 78058.8i | −0.0574109 | − | 0.0994385i | ||||
\(887\) | 322071. | − | 185948.i | 0.409359 | − | 0.236344i | −0.281155 | − | 0.959662i | \(-0.590718\pi\) |
0.690514 | + | 0.723319i | \(0.257384\pi\) | |||||||
\(888\) | −101982. | + | 387309.i | −0.129329 | + | 0.491170i | ||||
\(889\) | 748789. | − | 1.29694e6i | 0.947449 | − | 1.64103i | ||||
\(890\) | 1.02150e6i | 1.28961i | ||||||||
\(891\) | 10937.9 | + | 630795.i | 0.0137778 | + | 0.794571i | ||||
\(892\) | 235997. | 0.296604 | ||||||||
\(893\) | 653108. | + | 377072.i | 0.818996 | + | 0.472848i | ||||
\(894\) | 586507. | + | 154432.i | 0.733835 | + | 0.193225i | ||||
\(895\) | −9737.36 | − | 16865.6i | −0.0121561 | − | 0.0210550i | ||||
\(896\) | 1.23913e6 | − | 715412.i | 1.54348 | − | 0.891128i | ||||
\(897\) | −14219.4 | − | 14096.7i | −0.0176725 | − | 0.0175199i | ||||
\(898\) | −207552. | + | 359490.i | −0.257379 | + | 0.445794i | ||||
\(899\) | 216718.i | 0.268148i | ||||||||
\(900\) | −102254. | − | 57860.3i | −0.126239 | − | 0.0714324i | ||||
\(901\) | 143176. | 0.176368 | ||||||||
\(902\) | 206790. | + | 119390.i | 0.254165 | + | 0.146742i | ||||
\(903\) | 153158. | + | 561842.i | 0.187830 | + | 0.689030i | ||||
\(904\) | −568175. | − | 984108.i | −0.695257 | − | 1.20422i | ||||
\(905\) | 393522. | − | 227200.i | 0.480476 | − | 0.277403i | ||||
\(906\) | 1.17308e6 | − | 319781.i | 1.42912 | − | 0.389580i | ||||
\(907\) | 71965.4 | − | 124648.i | 0.0874801 | − | 0.151520i | −0.818965 | − | 0.573843i | \(-0.805452\pi\) |
0.906445 | + | 0.422323i | \(0.138785\pi\) | |||||||
\(908\) | 389172.i | 0.472030i | ||||||||
\(909\) | −80536.0 | − | 136741.i | −0.0974680 | − | 0.165490i | ||||
\(910\) | 798134. | 0.963814 | ||||||||
\(911\) | −772201. | − | 445830.i | −0.930451 | − | 0.537196i | −0.0434969 | − | 0.999054i | \(-0.513850\pi\) |
−0.886954 | + | 0.461857i | \(0.847183\pi\) | |||||||
\(912\) | 366659. | − | 369852.i | 0.440832 | − | 0.444670i | ||||
\(913\) | 136170. | + | 235854.i | 0.163358 | + | 0.282944i | ||||
\(914\) | −854175. | + | 493158.i | −1.02248 | + | 0.590329i | ||||
\(915\) | −62877.5 | + | 238798.i | −0.0751023 | + | 0.285225i | ||||
\(916\) | −10472.5 | + | 18139.0i | −0.0124813 | + | 0.0216183i | ||||
\(917\) | 232053.i | 0.275961i | ||||||||
\(918\) | −228055. | + | 64297.0i | −0.270617 | + | 0.0762967i | ||||
\(919\) | −582156. | −0.689300 | −0.344650 | − | 0.938731i | \(-0.612002\pi\) | ||||
−0.344650 | + | 0.938731i | \(0.612002\pi\) | |||||||
\(920\) | 10802.8 | + | 6236.98i | 0.0127632 | + | 0.00736883i | ||||
\(921\) | 1.09753e6 | + | 288990.i | 1.29389 | + | 0.340693i | ||||
\(922\) | 237093. | + | 410658.i | 0.278906 | + | 0.483079i | ||||
\(923\) | −892636. | + | 515364.i | −1.04778 | + | 0.604937i | ||||
\(924\) | 175454. | + | 173940.i | 0.205504 | + | 0.203730i | ||||
\(925\) | −152149. | + | 263530.i | −0.177822 | + | 0.307997i | ||||
\(926\) | 304441.i | 0.355043i | ||||||||
\(927\) | 3620.10 | + | 417578.i | 0.00421271 | + | 0.485935i | ||||
\(928\) | 353482. | 0.410460 | ||||||||
\(929\) | −668027. | − | 385685.i | −0.774038 | − | 0.446891i | 0.0602751 | − | 0.998182i | \(-0.480802\pi\) |
−0.834313 | + | 0.551291i | \(0.814136\pi\) | |||||||
\(930\) | −51239.7 | − | 187966.i | −0.0592435 | − | 0.217327i | ||||
\(931\) | 271966. | + | 471059.i | 0.313773 | + | 0.543470i | ||||
\(932\) | −62991.9 | + | 36368.4i | −0.0725192 | + | 0.0418690i | ||||
\(933\) | 866609. | − | 236238.i | 0.995543 | − | 0.271385i | ||||
\(934\) | 500890. | − | 867567.i | 0.574181 | − | 0.994510i | ||||
\(935\) | − | 112148.i | − | 0.128283i | ||||||
\(936\) | −671382. | + | 5820.41i | −0.766334 | + | 0.00664357i | ||||
\(937\) | −1.46097e6 | −1.66403 | −0.832015 | − | 0.554753i | \(-0.812813\pi\) | ||||
−0.832015 | + | 0.554753i | \(0.812813\pi\) | |||||||
\(938\) | −1.29903e6 | − | 749996.i | −1.47643 | − | 0.852420i | ||||
\(939\) | −14100.5 | + | 14223.3i | −0.0159921 | + | 0.0161313i | ||||
\(940\) | −124806. | − | 216170.i | −0.141247 | − | 0.244647i | ||||
\(941\) | 146658. | − | 84673.2i | 0.165626 | − | 0.0956240i | −0.414896 | − | 0.909869i | \(-0.636182\pi\) |
0.580522 | + | 0.814245i | \(0.302849\pi\) | |||||||
\(942\) | −211030. | + | 801456.i | −0.237817 | + | 0.903187i | ||||
\(943\) | −4019.42 | + | 6961.83i | −0.00452001 | + | 0.00782889i | ||||
\(944\) | − | 1.64346e6i | − | 1.84423i | ||||||
\(945\) | 590833. | − | 606402.i | 0.661608 | − | 0.679042i | ||||
\(946\) | −383289. | −0.428296 | ||||||||
\(947\) | 514322. | + | 296944.i | 0.573503 | + | 0.331112i | 0.758547 | − | 0.651618i | \(-0.225910\pi\) |
−0.185044 | + | 0.982730i | \(0.559243\pi\) | |||||||
\(948\) | −196376. | − | 51707.5i | −0.218510 | − | 0.0575356i | ||||
\(949\) | 371210. | + | 642955.i | 0.412180 | + | 0.713917i | ||||
\(950\) | 271526. | − | 156766.i | 0.300860 | − | 0.173702i | ||||
\(951\) | 1.07421e6 | + | 1.06494e6i | 1.18776 | + | 1.17750i | ||||
\(952\) | 142079. | − | 246089.i | 0.156768 | − | 0.271530i | ||||
\(953\) | 1.25477e6i | 1.38159i | 0.723050 | + | 0.690796i | \(0.242740\pi\) | ||||
−0.723050 | + | 0.690796i | \(0.757260\pi\) | |||||||
\(954\) | −613002. | + | 361038.i | −0.673543 | + | 0.396695i | ||||
\(955\) | −156250. | −0.171322 | ||||||||
\(956\) | 88159.0 | + | 50898.6i | 0.0964608 | + | 0.0556917i | ||||
\(957\) | −163027. | − | 598043.i | −0.178006 | − | 0.652993i | ||||
\(958\) | −243733. | − | 422158.i | −0.265573 | − | 0.459985i | ||||
\(959\) | 243051. | − | 140326.i | 0.264278 | − | 0.152581i | ||||
\(960\) | 369024. | − | 100596.i | 0.400416 | − | 0.109154i | ||||
\(961\) | 415987. | − | 720510.i | 0.450436 | − | 0.780178i | ||||
\(962\) | − | 567843.i | − | 0.613590i | ||||||
\(963\) | 363684. | − | 642722.i | 0.392167 | − | 0.693060i | ||||
\(964\) | −327186. | −0.352080 | ||||||||
\(965\) | 741017. | + | 427826.i | 0.795744 | + | 0.459423i | ||||
\(966\) | −29644.9 | + | 29903.0i | −0.0317684 | + | 0.0320450i | ||||
\(967\) | 528928. | + | 916130.i | 0.565645 | + | 0.979725i | 0.996989 | + | 0.0775381i | \(0.0247059\pi\) |
−0.431345 | + | 0.902187i | \(0.641961\pi\) | |||||||
\(968\) | −251620. | + | 145273.i | −0.268531 | + | 0.155037i | ||||
\(969\) | 31804.4 | − | 120787.i | 0.0338719 | − | 0.128639i | ||||
\(970\) | −256321. | + | 443962.i | −0.272422 | + | 0.471848i | ||||
\(971\) | − | 775745.i | − | 0.822774i | −0.911461 | − | 0.411387i | \(-0.865044\pi\) | ||
0.911461 | − | 0.411387i | \(-0.134956\pi\) | |||||||
\(972\) | 160848. | − | 167976.i | 0.170249 | − | 0.177793i | ||||
\(973\) | −846555. | −0.894189 | ||||||||
\(974\) | 411099. | + | 237348.i | 0.433339 | + | 0.250189i | ||||
\(975\) | −493305. | − | 129892.i | −0.518927 | − | 0.136638i | ||||
\(976\) | −259864. | − | 450098.i | −0.272801 | − | 0.472506i | ||||
\(977\) | −429995. | + | 248258.i | −0.450479 | + | 0.260084i | −0.708032 | − | 0.706180i | \(-0.750417\pi\) |
0.257554 | + | 0.966264i | \(0.417084\pi\) | |||||||
\(978\) | −1.13561e6 | − | 1.12581e6i | −1.18728 | − | 1.17703i | ||||
\(979\) | −686453. | + | 1.18897e6i | −0.716218 | + | 1.24053i | ||||
\(980\) | − | 180035.i | − | 0.187458i | ||||||
\(981\) | −1.13930e6 | − | 644671.i | −1.18386 | − | 0.669885i | ||||
\(982\) | −332424. | −0.344722 | ||||||||
\(983\) | 260643. | + | 150482.i | 0.269736 | + | 0.155732i | 0.628768 | − | 0.777593i | \(-0.283560\pi\) |
−0.359032 | + | 0.933325i | \(0.616893\pi\) | |||||||
\(984\) | 70895.3 | + | 260070.i | 0.0732196 | + | 0.268597i | ||||
\(985\) | −549076. | − | 951028.i | −0.565927 | − | 0.980214i | ||||
\(986\) | 201616. | − | 116403.i | 0.207382 | − | 0.119732i | ||||
\(987\) | −2.48950e6 | + | 678638.i | −2.55551 | + | 0.696633i | ||||
\(988\) | −57786.2 | + | 100089.i | −0.0591985 | + | 0.102535i | ||||
\(989\) | − | 12903.9i | − | 0.0131925i | ||||||
\(990\) | 282797. | + | 480157.i | 0.288539 | + | 0.489907i | ||||
\(991\) | 1.70094e6 | 1.73197 | 0.865987 | − | 0.500067i | \(-0.166691\pi\) | ||||
0.865987 | + | 0.500067i | \(0.166691\pi\) | |||||||
\(992\) | 129315. | + | 74660.0i | 0.131409 | + | 0.0758691i | ||||
\(993\) | 42826.3 | − | 43199.1i | 0.0434322 | − | 0.0438103i | ||||
\(994\) | 1.08379e6 | + | 1.87718e6i | 1.09691 | + | 1.89991i | ||||
\(995\) | −114302. | + | 65992.4i | −0.115454 | + | 0.0666573i | ||||
\(996\) | 25563.4 | − | 97085.3i | 0.0257692 | − | 0.0978667i | ||||
\(997\) | 312919. | − | 541991.i | 0.314805 | − | 0.545258i | −0.664591 | − | 0.747207i | \(-0.731394\pi\) |
0.979396 | + | 0.201949i | \(0.0647276\pi\) | |||||||
\(998\) | 496568.i | 0.498560i | ||||||||
\(999\) | −431432. | − | 420355.i | −0.432297 | − | 0.421197i |
(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 | 9.5.d.a.2.3 | ✓ | 6 | |
3.2 | odd | 2 | 27.5.d.a.8.1 | 6 | |||
4.3 | odd | 2 | 144.5.q.a.65.3 | 6 | |||
9.2 | odd | 6 | 81.5.b.a.80.5 | 6 | |||
9.4 | even | 3 | 27.5.d.a.17.1 | 6 | |||
9.5 | odd | 6 | inner | 9.5.d.a.5.3 | yes | 6 | |
9.7 | even | 3 | 81.5.b.a.80.2 | 6 | |||
12.11 | even | 2 | 432.5.q.a.305.1 | 6 | |||
36.7 | odd | 6 | 1296.5.e.c.161.5 | 6 | |||
36.11 | even | 6 | 1296.5.e.c.161.2 | 6 | |||
36.23 | even | 6 | 144.5.q.a.113.3 | 6 | |||
36.31 | odd | 6 | 432.5.q.a.17.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9.5.d.a.2.3 | ✓ | 6 | 1.1 | even | 1 | trivial | |
9.5.d.a.5.3 | yes | 6 | 9.5 | odd | 6 | inner | |
27.5.d.a.8.1 | 6 | 3.2 | odd | 2 | |||
27.5.d.a.17.1 | 6 | 9.4 | even | 3 | |||
81.5.b.a.80.2 | 6 | 9.7 | even | 3 | |||
81.5.b.a.80.5 | 6 | 9.2 | odd | 6 | |||
144.5.q.a.65.3 | 6 | 4.3 | odd | 2 | |||
144.5.q.a.113.3 | 6 | 36.23 | even | 6 | |||
432.5.q.a.17.1 | 6 | 36.31 | odd | 6 | |||
432.5.q.a.305.1 | 6 | 12.11 | even | 2 | |||
1296.5.e.c.161.2 | 6 | 36.11 | even | 6 | |||
1296.5.e.c.161.5 | 6 | 36.7 | odd | 6 |