Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [15,6,Mod(2,15)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(15, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("15.2");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 15 = 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 15.e (of order \(4\), 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: | \(2.40575729719\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 10768x^{12} + 16341006x^{8} + 4217167600x^{4} + 50906640625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{10}\cdot 5^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 2.3 | ||
Root | \(4.35647 + 4.35647i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 15.2 |
Dual form | 15.6.e.a.8.3 |
$q$-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 \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).
\(n\) | \(7\) | \(11\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.17835 | + | 3.17835i | −0.561858 | + | 0.561858i | −0.929835 | − | 0.367977i | \(-0.880051\pi\) |
0.367977 | + | 0.929835i | \(0.380051\pi\) | |||||||
\(3\) | 14.5679 | − | 5.54767i | 0.934530 | − | 0.355883i | ||||
\(4\) | 11.7962i | 0.368631i | ||||||||
\(5\) | 11.9990 | + | 54.5987i | 0.214645 | + | 0.976692i | ||||
\(6\) | −28.6694 | + | 63.9343i | −0.325117 | + | 0.725029i | ||||
\(7\) | 83.6967 | + | 83.6967i | 0.645600 | + | 0.645600i | 0.951926 | − | 0.306327i | \(-0.0991000\pi\) |
−0.306327 | + | 0.951926i | \(0.599100\pi\) | |||||||
\(8\) | −139.200 | − | 139.200i | −0.768976 | − | 0.768976i | ||||
\(9\) | 181.447 | − | 161.636i | 0.746694 | − | 0.665168i | ||||
\(10\) | −211.671 | − | 135.397i | −0.669362 | − | 0.428162i | ||||
\(11\) | − | 566.700i | − | 1.41212i | −0.708152 | − | 0.706060i | \(-0.750471\pi\) | ||
0.708152 | − | 0.706060i | \(-0.249529\pi\) | |||||||
\(12\) | 65.4414 | + | 171.846i | 0.131190 | + | 0.344497i | ||||
\(13\) | −208.475 | + | 208.475i | −0.342133 | + | 0.342133i | −0.857169 | − | 0.515036i | \(-0.827779\pi\) |
0.515036 | + | 0.857169i | \(0.327779\pi\) | |||||||
\(14\) | −532.035 | −0.725471 | ||||||||
\(15\) | 477.697 | + | 728.822i | 0.548181 | + | 0.836360i | ||||
\(16\) | 507.372 | 0.495480 | ||||||||
\(17\) | −155.680 | + | 155.680i | −0.130651 | + | 0.130651i | −0.769408 | − | 0.638757i | \(-0.779449\pi\) |
0.638757 | + | 0.769408i | \(0.279449\pi\) | |||||||
\(18\) | −62.9658 | + | 1090.44i | −0.0458061 | + | 0.793266i | ||||
\(19\) | − | 2305.83i | − | 1.46536i | −0.680574 | − | 0.732680i | \(-0.738269\pi\) | ||
0.680574 | − | 0.732680i | \(-0.261731\pi\) | |||||||
\(20\) | −644.057 | + | 141.543i | −0.360039 | + | 0.0791250i | ||||
\(21\) | 1683.61 | + | 754.962i | 0.833091 | + | 0.373574i | ||||
\(22\) | 1801.17 | + | 1801.17i | 0.793411 | + | 0.793411i | ||||
\(23\) | 1194.57 | + | 1194.57i | 0.470860 | + | 0.470860i | 0.902193 | − | 0.431333i | \(-0.141957\pi\) |
−0.431333 | + | 0.902193i | \(0.641957\pi\) | |||||||
\(24\) | −2800.08 | − | 1255.61i | −0.992298 | − | 0.444966i | ||||
\(25\) | −2837.05 | + | 1310.27i | −0.907855 | + | 0.419285i | ||||
\(26\) | − | 1325.21i | − | 0.384461i | ||||||
\(27\) | 1746.59 | − | 3361.30i | 0.461086 | − | 0.887355i | ||||
\(28\) | −987.303 | + | 987.303i | −0.237988 | + | 0.237988i | ||||
\(29\) | 1310.94 | 0.289460 | 0.144730 | − | 0.989471i | \(-0.453769\pi\) | ||||
0.144730 | + | 0.989471i | \(0.453769\pi\) | |||||||
\(30\) | −3834.74 | − | 798.162i | −0.777915 | − | 0.161915i | ||||
\(31\) | 303.760 | 0.0567709 | 0.0283855 | − | 0.999597i | \(-0.490963\pi\) | ||||
0.0283855 | + | 0.999597i | \(0.490963\pi\) | |||||||
\(32\) | 2841.78 | − | 2841.78i | 0.490587 | − | 0.490587i | ||||
\(33\) | −3143.87 | − | 8255.62i | −0.502550 | − | 1.31967i | ||||
\(34\) | − | 989.614i | − | 0.146814i | ||||||
\(35\) | −3565.45 | + | 5574.01i | −0.491977 | + | 0.769127i | ||||
\(36\) | 1906.69 | + | 2140.38i | 0.245202 | + | 0.275255i | ||||
\(37\) | 2750.09 | + | 2750.09i | 0.330250 | + | 0.330250i | 0.852681 | − | 0.522432i | \(-0.174975\pi\) |
−0.522432 | + | 0.852681i | \(0.674975\pi\) | |||||||
\(38\) | 7328.75 | + | 7328.75i | 0.823324 | + | 0.823324i | ||||
\(39\) | −1880.49 | + | 4193.59i | −0.197974 | + | 0.441493i | ||||
\(40\) | 5929.86 | − | 9270.38i | 0.585996 | − | 0.916110i | ||||
\(41\) | 84.6376i | 0.00786328i | 0.999992 | + | 0.00393164i | \(0.00125148\pi\) | ||||
−0.999992 | + | 0.00393164i | \(0.998749\pi\) | |||||||
\(42\) | −7750.62 | + | 2951.55i | −0.677974 | + | 0.258183i | ||||
\(43\) | −4683.92 | + | 4683.92i | −0.386312 | + | 0.386312i | −0.873370 | − | 0.487057i | \(-0.838070\pi\) |
0.487057 | + | 0.873370i | \(0.338070\pi\) | |||||||
\(44\) | 6684.90 | 0.520551 | ||||||||
\(45\) | 11002.3 | + | 7967.28i | 0.809938 | + | 0.586515i | ||||
\(46\) | −7593.51 | −0.529112 | ||||||||
\(47\) | −13211.3 | + | 13211.3i | −0.872369 | + | 0.872369i | −0.992730 | − | 0.120361i | \(-0.961595\pi\) |
0.120361 | + | 0.992730i | \(0.461595\pi\) | |||||||
\(48\) | 7391.33 | − | 2814.73i | 0.463041 | − | 0.176333i | ||||
\(49\) | − | 2796.73i | − | 0.166402i | ||||||
\(50\) | 4852.64 | − | 13181.6i | 0.274507 | − | 0.745664i | ||||
\(51\) | −1404.27 | + | 3131.60i | −0.0756006 | + | 0.168594i | ||||
\(52\) | −2459.21 | − | 2459.21i | −0.126121 | − | 0.126121i | ||||
\(53\) | −19545.6 | − | 19545.6i | −0.955782 | − | 0.955782i | 0.0432812 | − | 0.999063i | \(-0.486219\pi\) |
−0.999063 | + | 0.0432812i | \(0.986219\pi\) | |||||||
\(54\) | 5132.10 | + | 16234.7i | 0.239503 | + | 0.757633i | ||||
\(55\) | 30941.1 | − | 6799.85i | 1.37921 | − | 0.303105i | ||||
\(56\) | − | 23301.1i | − | 0.992902i | ||||||
\(57\) | −12792.0 | − | 33591.1i | −0.521497 | − | 1.36942i | ||||
\(58\) | −4166.63 | + | 4166.63i | −0.162636 | + | 0.162636i | ||||
\(59\) | 2080.36 | 0.0778051 | 0.0389026 | − | 0.999243i | \(-0.487614\pi\) | ||||
0.0389026 | + | 0.999243i | \(0.487614\pi\) | |||||||
\(60\) | −8597.32 | + | 5635.00i | −0.308308 | + | 0.202077i | ||||
\(61\) | −50807.1 | −1.74823 | −0.874117 | − | 0.485715i | \(-0.838559\pi\) | ||||
−0.874117 | + | 0.485715i | \(0.838559\pi\) | |||||||
\(62\) | −965.455 | + | 965.455i | −0.0318972 | + | 0.0318972i | ||||
\(63\) | 28714.9 | + | 1658.10i | 0.911497 | + | 0.0526332i | ||||
\(64\) | 34300.2i | 1.04676i | ||||||||
\(65\) | −13884.0 | − | 8880.97i | −0.407596 | − | 0.260721i | ||||
\(66\) | 36231.5 | + | 16246.9i | 1.02383 | + | 0.459105i | ||||
\(67\) | 30649.1 | + | 30649.1i | 0.834125 | + | 0.834125i | 0.988078 | − | 0.153953i | \(-0.0492004\pi\) |
−0.153953 | + | 0.988078i | \(0.549200\pi\) | |||||||
\(68\) | −1836.44 | − | 1836.44i | −0.0481619 | − | 0.0481619i | ||||
\(69\) | 24029.4 | + | 10775.3i | 0.607604 | + | 0.272461i | ||||
\(70\) | −6383.90 | − | 29048.4i | −0.155719 | − | 0.708561i | ||||
\(71\) | 75296.6i | 1.77268i | 0.463038 | + | 0.886339i | \(0.346759\pi\) | ||||
−0.463038 | + | 0.886339i | \(0.653241\pi\) | |||||||
\(72\) | −47756.9 | − | 2757.66i | −1.08569 | − | 0.0626917i | ||||
\(73\) | 19151.6 | − | 19151.6i | 0.420627 | − | 0.420627i | −0.464793 | − | 0.885420i | \(-0.653871\pi\) |
0.885420 | + | 0.464793i | \(0.153871\pi\) | |||||||
\(74\) | −17481.5 | −0.371107 | ||||||||
\(75\) | −34060.8 | + | 34826.8i | −0.699201 | + | 0.714925i | ||||
\(76\) | 27200.1 | 0.540177 | ||||||||
\(77\) | 47430.9 | − | 47430.9i | 0.911664 | − | 0.911664i | ||||
\(78\) | −7351.84 | − | 19305.5i | −0.136823 | − | 0.359290i | ||||
\(79\) | − | 56900.8i | − | 1.02577i | −0.858457 | − | 0.512886i | \(-0.828576\pi\) | ||
0.858457 | − | 0.512886i | \(-0.171424\pi\) | |||||||
\(80\) | 6087.97 | + | 27701.8i | 0.106352 | + | 0.483931i | ||||
\(81\) | 6796.76 | − | 58656.5i | 0.115104 | − | 0.993353i | ||||
\(82\) | −269.008 | − | 269.008i | −0.00441805 | − | 0.00441805i | ||||
\(83\) | 25593.9 | + | 25593.9i | 0.407794 | + | 0.407794i | 0.880969 | − | 0.473174i | \(-0.156892\pi\) |
−0.473174 | + | 0.880969i | \(0.656892\pi\) | |||||||
\(84\) | −8905.68 | + | 19860.1i | −0.137711 | + | 0.307103i | ||||
\(85\) | −10368.0 | − | 6631.94i | −0.155649 | − | 0.0995620i | ||||
\(86\) | − | 29774.3i | − | 0.434105i | ||||||
\(87\) | 19097.7 | − | 7272.68i | 0.270509 | − | 0.103014i | ||||
\(88\) | −78884.4 | + | 78884.4i | −1.08589 | + | 1.08589i | ||||
\(89\) | −42602.7 | −0.570114 | −0.285057 | − | 0.958511i | \(-0.592013\pi\) | ||||
−0.285057 | + | 0.958511i | \(0.592013\pi\) | |||||||
\(90\) | −60291.9 | + | 9646.33i | −0.784609 | + | 0.125532i | ||||
\(91\) | −34897.3 | −0.441762 | ||||||||
\(92\) | −14091.4 | + | 14091.4i | −0.173573 | + | 0.173573i | ||||
\(93\) | 4425.14 | − | 1685.16i | 0.0530542 | − | 0.0202038i | ||||
\(94\) | − | 83980.1i | − | 0.980295i | ||||||
\(95\) | 125896. | − | 27667.8i | 1.43121 | − | 0.314533i | ||||
\(96\) | 25633.5 | − | 57164.1i | 0.283877 | − | 0.633060i | ||||
\(97\) | 78017.6 | + | 78017.6i | 0.841906 | + | 0.841906i | 0.989107 | − | 0.147201i | \(-0.0470264\pi\) |
−0.147201 | + | 0.989107i | \(0.547026\pi\) | |||||||
\(98\) | 8888.97 | + | 8888.97i | 0.0934945 | + | 0.0934945i | ||||
\(99\) | −91599.0 | − | 102826.i | −0.939296 | − | 1.05442i | ||||
\(100\) | −15456.1 | − | 33466.4i | −0.154561 | − | 0.334664i | ||||
\(101\) | 7709.74i | 0.0752032i | 0.999293 | + | 0.0376016i | \(0.0119718\pi\) | ||||
−0.999293 | + | 0.0376016i | \(0.988028\pi\) | |||||||
\(102\) | −5490.05 | − | 14416.6i | −0.0522488 | − | 0.137202i | ||||
\(103\) | −14320.2 | + | 14320.2i | −0.133001 | + | 0.133001i | −0.770473 | − | 0.637472i | \(-0.779980\pi\) |
0.637472 | + | 0.770473i | \(0.279980\pi\) | |||||||
\(104\) | 58039.2 | 0.526185 | ||||||||
\(105\) | −21018.3 | + | 100982.i | −0.186048 | + | 0.893859i | ||||
\(106\) | 124245. | 1.07403 | ||||||||
\(107\) | −86698.6 | + | 86698.6i | −0.732070 | + | 0.732070i | −0.971030 | − | 0.238959i | \(-0.923194\pi\) |
0.238959 | + | 0.971030i | \(0.423194\pi\) | |||||||
\(108\) | 39650.5 | + | 20603.1i | 0.327107 | + | 0.169971i | ||||
\(109\) | − | 12001.3i | − | 0.0967527i | −0.998829 | − | 0.0483764i | \(-0.984595\pi\) | ||
0.998829 | − | 0.0483764i | \(-0.0154047\pi\) | |||||||
\(110\) | −76729.3 | + | 119954.i | −0.604616 | + | 0.945220i | ||||
\(111\) | 55319.6 | + | 24806.4i | 0.426159 | + | 0.191098i | ||||
\(112\) | 42465.3 | + | 42465.3i | 0.319882 | + | 0.319882i | ||||
\(113\) | −77651.2 | − | 77651.2i | −0.572074 | − | 0.572074i | 0.360634 | − | 0.932707i | \(-0.382560\pi\) |
−0.932707 | + | 0.360634i | \(0.882560\pi\) | |||||||
\(114\) | 147422. | + | 66106.9i | 1.06243 | + | 0.476414i | ||||
\(115\) | −50888.3 | + | 79555.6i | −0.358817 | + | 0.560953i | ||||
\(116\) | 15464.1i | 0.106704i | ||||||||
\(117\) | −4130.06 | + | 71524.0i | −0.0278928 | + | 0.483045i | ||||
\(118\) | −6612.10 | + | 6612.10i | −0.0437154 | + | 0.0437154i | ||||
\(119\) | −26059.9 | −0.168696 | ||||||||
\(120\) | 34956.5 | − | 167947.i | 0.221602 | − | 1.06468i | ||||
\(121\) | −160098. | −0.994081 | ||||||||
\(122\) | 161483. | − | 161483.i | 0.982259 | − | 0.982259i | ||||
\(123\) | 469.542 | + | 1232.99i | 0.00279841 | + | 0.00734847i | ||||
\(124\) | 3583.21i | 0.0209275i | ||||||||
\(125\) | −105581. | − | 139177.i | −0.604379 | − | 0.796697i | ||||
\(126\) | −96535.9 | + | 85995.8i | −0.541704 | + | 0.482560i | ||||
\(127\) | −108319. | − | 108319.i | −0.595929 | − | 0.595929i | 0.343297 | − | 0.939227i | \(-0.388456\pi\) |
−0.939227 | + | 0.343297i | \(0.888456\pi\) | |||||||
\(128\) | −18081.1 | − | 18081.1i | −0.0975438 | − | 0.0975438i | ||||
\(129\) | −42250.0 | + | 94219.7i | −0.223538 | + | 0.498503i | ||||
\(130\) | 72354.9 | − | 15901.3i | 0.375500 | − | 0.0825227i | ||||
\(131\) | − | 228726.i | − | 1.16449i | −0.813012 | − | 0.582247i | \(-0.802174\pi\) | ||
0.813012 | − | 0.582247i | \(-0.197826\pi\) | |||||||
\(132\) | 97384.9 | − | 37085.7i | 0.486471 | − | 0.185256i | ||||
\(133\) | 192991. | − | 192991.i | 0.946035 | − | 0.946035i | ||||
\(134\) | −194827. | −0.937320 | ||||||||
\(135\) | 204480. | + | 55029.3i | 0.965643 | + | 0.259872i | ||||
\(136\) | 43341.3 | 0.200935 | ||||||||
\(137\) | −17998.3 | + | 17998.3i | −0.0819275 | + | 0.0819275i | −0.746883 | − | 0.664956i | \(-0.768450\pi\) |
0.664956 | + | 0.746883i | \(0.268450\pi\) | |||||||
\(138\) | −110621. | + | 42126.3i | −0.494472 | + | 0.188302i | ||||
\(139\) | 197969.i | 0.869082i | 0.900652 | + | 0.434541i | \(0.143089\pi\) | ||||
−0.900652 | + | 0.434541i | \(0.856911\pi\) | |||||||
\(140\) | −65752.2 | − | 42058.8i | −0.283524 | − | 0.181358i | ||||
\(141\) | −119169. | + | 265752.i | −0.504793 | + | 1.12572i | ||||
\(142\) | −239319. | − | 239319.i | −0.995993 | − | 0.995993i | ||||
\(143\) | 118143. | + | 118143.i | 0.483133 | + | 0.483133i | ||||
\(144\) | 92060.8 | − | 82009.4i | 0.369972 | − | 0.329577i | ||||
\(145\) | 15730.1 | + | 71575.8i | 0.0621313 | + | 0.282713i | ||||
\(146\) | 121741.i | 0.472665i | ||||||||
\(147\) | −15515.3 | − | 40742.4i | −0.0592199 | − | 0.155508i | ||||
\(148\) | −32440.6 | + | 32440.6i | −0.121740 | + | 0.121740i | ||||
\(149\) | 434636. | 1.60384 | 0.801919 | − | 0.597433i | \(-0.203813\pi\) | ||||
0.801919 | + | 0.597433i | \(0.203813\pi\) | |||||||
\(150\) | −2434.48 | − | 218949.i | −0.00883442 | − | 0.794538i | ||||
\(151\) | 238082. | 0.849738 | 0.424869 | − | 0.905255i | \(-0.360320\pi\) | ||||
0.424869 | + | 0.905255i | \(0.360320\pi\) | |||||||
\(152\) | −320971. | + | 320971.i | −1.12683 | + | 1.12683i | ||||
\(153\) | −3084.16 | + | 53411.2i | −0.0106515 | + | 0.184461i | ||||
\(154\) | 301504.i | 1.02445i | ||||||||
\(155\) | 3644.83 | + | 16584.9i | 0.0121856 | + | 0.0554477i | ||||
\(156\) | −49468.4 | − | 22182.6i | −0.162748 | − | 0.0729795i | ||||
\(157\) | −116365. | − | 116365.i | −0.376767 | − | 0.376767i | 0.493168 | − | 0.869934i | \(-0.335839\pi\) |
−0.869934 | + | 0.493168i | \(0.835839\pi\) | |||||||
\(158\) | 180851. | + | 180851.i | 0.576338 | + | 0.576338i | ||||
\(159\) | −393170. | − | 176305.i | −1.23335 | − | 0.553060i | ||||
\(160\) | 189256. | + | 121059.i | 0.584455 | + | 0.373850i | ||||
\(161\) | 199963.i | 0.607973i | ||||||||
\(162\) | 164828. | + | 208033.i | 0.493452 | + | 0.622796i | ||||
\(163\) | 89054.5 | − | 89054.5i | 0.262535 | − | 0.262535i | −0.563548 | − | 0.826083i | \(-0.690564\pi\) |
0.826083 | + | 0.563548i | \(0.190564\pi\) | |||||||
\(164\) | −998.402 | −0.00289865 | ||||||||
\(165\) | 413023. | − | 270711.i | 1.18104 | − | 0.774097i | ||||
\(166\) | −162693. | −0.458245 | ||||||||
\(167\) | 132460. | − | 132460.i | 0.367532 | − | 0.367532i | −0.499044 | − | 0.866576i | \(-0.666316\pi\) |
0.866576 | + | 0.499044i | \(0.166316\pi\) | |||||||
\(168\) | −129267. | − | 339448.i | −0.353357 | − | 0.927897i | ||||
\(169\) | 284369.i | 0.765890i | ||||||||
\(170\) | 54031.7 | − | 11874.4i | 0.143392 | − | 0.0315130i | ||||
\(171\) | −372705. | − | 418386.i | −0.974710 | − | 1.09418i | ||||
\(172\) | −55252.5 | − | 55252.5i | −0.142407 | − | 0.142407i | ||||
\(173\) | −152848. | − | 152848.i | −0.388280 | − | 0.388280i | 0.485794 | − | 0.874074i | \(-0.338531\pi\) |
−0.874074 | + | 0.485794i | \(0.838531\pi\) | |||||||
\(174\) | −37583.9 | + | 83814.2i | −0.0941085 | + | 0.209867i | ||||
\(175\) | −347116. | − | 127787.i | −0.856801 | − | 0.315421i | ||||
\(176\) | − | 287527.i | − | 0.699677i | ||||||
\(177\) | 30306.4 | − | 11541.1i | 0.0727112 | − | 0.0276895i | ||||
\(178\) | 135406. | − | 135406.i | 0.320323 | − | 0.320323i | ||||
\(179\) | 480813. | 1.12162 | 0.560808 | − | 0.827946i | \(-0.310491\pi\) | ||||
0.560808 | + | 0.827946i | \(0.310491\pi\) | |||||||
\(180\) | −93983.6 | + | 129785.i | −0.216208 | + | 0.298569i | ||||
\(181\) | 152370. | 0.345704 | 0.172852 | − | 0.984948i | \(-0.444702\pi\) | ||||
0.172852 | + | 0.984948i | \(0.444702\pi\) | |||||||
\(182\) | 110916. | − | 110916.i | 0.248208 | − | 0.248208i | ||||
\(183\) | −740152. | + | 281861.i | −1.63378 | + | 0.622168i | ||||
\(184\) | − | 332567.i | − | 0.724160i | ||||||
\(185\) | −117153. | + | 183150.i | −0.251666 | + | 0.393439i | ||||
\(186\) | −8708.61 | + | 19420.7i | −0.0184572 | + | 0.0411606i | ||||
\(187\) | 88224.1 | + | 88224.1i | 0.184494 | + | 0.184494i | ||||
\(188\) | −155843. | − | 155843.i | −0.321582 | − | 0.321582i | ||||
\(189\) | 427513. | − | 135146.i | 0.870553 | − | 0.275199i | ||||
\(190\) | −312203. | + | 488078.i | −0.627411 | + | 0.980857i | ||||
\(191\) | 121584.i | 0.241153i | 0.992704 | + | 0.120576i | \(0.0384743\pi\) | ||||
−0.992704 | + | 0.120576i | \(0.961526\pi\) | |||||||
\(192\) | 190287. | + | 499682.i | 0.372525 | + | 0.978229i | ||||
\(193\) | 110399. | − | 110399.i | 0.213340 | − | 0.213340i | −0.592344 | − | 0.805685i | \(-0.701798\pi\) |
0.805685 | + | 0.592344i | \(0.201798\pi\) | |||||||
\(194\) | −495935. | −0.946063 | ||||||||
\(195\) | −251529. | − | 52353.2i | −0.473697 | − | 0.0985954i | ||||
\(196\) | 32990.7 | 0.0613411 | ||||||||
\(197\) | −144403. | + | 144403.i | −0.265100 | + | 0.265100i | −0.827122 | − | 0.562022i | \(-0.810024\pi\) |
0.562022 | + | 0.827122i | \(0.310024\pi\) | |||||||
\(198\) | 617950. | + | 35682.7i | 1.12019 | + | 0.0646837i | ||||
\(199\) | − | 537929.i | − | 0.962924i | −0.876467 | − | 0.481462i | \(-0.840106\pi\) | ||
0.876467 | − | 0.481462i | \(-0.159894\pi\) | |||||||
\(200\) | 577304. | + | 212527.i | 1.02054 | + | 0.375699i | ||||
\(201\) | 616525. | + | 276462.i | 1.07637 | + | 0.482664i | ||||
\(202\) | −24504.2 | − | 24504.2i | −0.0422535 | − | 0.0422535i | ||||
\(203\) | 109722. | + | 109722.i | 0.186875 | + | 0.186875i | ||||
\(204\) | −36941.0 | − | 16565.1i | −0.0621488 | − | 0.0278687i | ||||
\(205\) | −4621.11 | + | 1015.57i | −0.00768000 | + | 0.00168782i | ||||
\(206\) | − | 91029.1i | − | 0.149456i | ||||||
\(207\) | 409835. | + | 23665.4i | 0.664789 | + | 0.0383874i | ||||
\(208\) | −105774. | + | 105774.i | −0.169520 | + | 0.169520i | ||||
\(209\) | −1.30672e6 | −2.06926 | ||||||||
\(210\) | −254151. | − | 387758.i | −0.397689 | − | 0.606754i | ||||
\(211\) | 727241. | 1.12453 | 0.562266 | − | 0.826956i | \(-0.309930\pi\) | ||||
0.562266 | + | 0.826956i | \(0.309930\pi\) | |||||||
\(212\) | 230563. | − | 230563.i | 0.352331 | − | 0.352331i | ||||
\(213\) | 417721. | + | 1.09691e6i | 0.630866 | + | 1.65662i | ||||
\(214\) | − | 551117.i | − | 0.822639i | ||||||
\(215\) | −311939. | − | 199534.i | −0.460228 | − | 0.294388i | ||||
\(216\) | −711016. | + | 224767.i | −1.03692 | + | 0.327791i | ||||
\(217\) | 25423.7 | + | 25423.7i | 0.0366513 | + | 0.0366513i | ||||
\(218\) | 38144.4 | + | 38144.4i | 0.0543613 | + | 0.0543613i | ||||
\(219\) | 172751. | − | 385245.i | 0.243395 | − | 0.542783i | ||||
\(220\) | 80212.4 | + | 364987.i | 0.111734 | + | 0.508418i | ||||
\(221\) | − | 64910.9i | − | 0.0893999i | ||||||
\(222\) | −254668. | + | 96981.5i | −0.346810 | + | 0.132071i | ||||
\(223\) | −682808. | + | 682808.i | −0.919468 | + | 0.919468i | −0.996991 | − | 0.0775229i | \(-0.975299\pi\) |
0.0775229 | + | 0.996991i | \(0.475299\pi\) | |||||||
\(224\) | 475696. | 0.633445 | ||||||||
\(225\) | −302987. | + | 696311.i | −0.398995 | + | 0.916953i | ||||
\(226\) | 493605. | 0.642848 | ||||||||
\(227\) | 354384. | − | 354384.i | 0.456467 | − | 0.456467i | −0.441027 | − | 0.897494i | \(-0.645386\pi\) |
0.897494 | + | 0.441027i | \(0.145386\pi\) | |||||||
\(228\) | 396248. | − | 150897.i | 0.504812 | − | 0.192240i | ||||
\(229\) | 1.01934e6i | 1.28449i | 0.766499 | + | 0.642246i | \(0.221997\pi\) | ||||
−0.766499 | + | 0.642246i | \(0.778003\pi\) | |||||||
\(230\) | −91114.8 | − | 414596.i | −0.113572 | − | 0.516780i | ||||
\(231\) | 427837. | − | 954099.i | 0.527531 | − | 1.17642i | ||||
\(232\) | −182483. | − | 182483.i | −0.222588 | − | 0.222588i | ||||
\(233\) | −483742. | − | 483742.i | −0.583746 | − | 0.583746i | 0.352185 | − | 0.935930i | \(-0.385439\pi\) |
−0.935930 | + | 0.352185i | \(0.885439\pi\) | |||||||
\(234\) | −214202. | − | 240455.i | −0.255731 | − | 0.287074i | ||||
\(235\) | −879842. | − | 562796.i | −1.03929 | − | 0.664786i | ||||
\(236\) | 24540.3i | 0.0286814i | ||||||||
\(237\) | −315667. | − | 828925.i | −0.365055 | − | 0.958615i | ||||
\(238\) | 82827.4 | − | 82827.4i | 0.0947833 | − | 0.0947833i | ||||
\(239\) | −445259. | −0.504218 | −0.252109 | − | 0.967699i | \(-0.581124\pi\) | ||||
−0.252109 | + | 0.967699i | \(0.581124\pi\) | |||||||
\(240\) | 242370. | + | 369783.i | 0.271613 | + | 0.414399i | ||||
\(241\) | −616510. | −0.683750 | −0.341875 | − | 0.939745i | \(-0.611062\pi\) | ||||
−0.341875 | + | 0.939745i | \(0.611062\pi\) | |||||||
\(242\) | 508846. | − | 508846.i | 0.558532 | − | 0.558532i | ||||
\(243\) | −226393. | − | 892208.i | −0.245950 | − | 0.969282i | ||||
\(244\) | − | 599330.i | − | 0.644454i | ||||||
\(245\) | 152698. | − | 33558.0i | 0.162524 | − | 0.0357175i | ||||
\(246\) | −5411.24 | − | 2426.51i | −0.00570111 | − | 0.00255649i | ||||
\(247\) | 480709. | + | 480709.i | 0.501348 | + | 0.501348i | ||||
\(248\) | −42283.2 | − | 42283.2i | −0.0436555 | − | 0.0436555i | ||||
\(249\) | 514836. | + | 230862.i | 0.526223 | + | 0.235969i | ||||
\(250\) | 777926. | + | 106782.i | 0.787206 | + | 0.108055i | ||||
\(251\) | 1.07551e6i | 1.07754i | 0.842454 | + | 0.538768i | \(0.181110\pi\) | ||||
−0.842454 | + | 0.538768i | \(0.818890\pi\) | |||||||
\(252\) | −19559.3 | + | 338726.i | −0.0194023 | + | 0.336006i | ||||
\(253\) | 676962. | − | 676962.i | 0.664910 | − | 0.664910i | ||||
\(254\) | 688550. | 0.669655 | ||||||||
\(255\) | −187831. | − | 39095.2i | −0.180891 | − | 0.0376507i | ||||
\(256\) | −982672. | −0.937149 | ||||||||
\(257\) | −1.24679e6 | + | 1.24679e6i | −1.17750 | + | 1.17750i | −0.197118 | + | 0.980380i | \(0.563158\pi\) |
−0.980380 | + | 0.197118i | \(0.936842\pi\) | |||||||
\(258\) | −165178. | − | 433748.i | −0.154491 | − | 0.405685i | ||||
\(259\) | 460347.i | 0.426418i | ||||||||
\(260\) | 104762. | − | 163778.i | 0.0961101 | − | 0.150253i | ||||
\(261\) | 237866. | − | 211895.i | 0.216138 | − | 0.192540i | ||||
\(262\) | 726971. | + | 726971.i | 0.654280 | + | 0.654280i | ||||
\(263\) | 769745. | + | 769745.i | 0.686211 | + | 0.686211i | 0.961392 | − | 0.275181i | \(-0.0887379\pi\) |
−0.275181 | + | 0.961392i | \(0.588738\pi\) | |||||||
\(264\) | −711554. | + | 1.58680e6i | −0.628345 | + | 1.40124i | ||||
\(265\) | 832636. | − | 1.30169e6i | 0.728350 | − | 1.13866i | ||||
\(266\) | 1.22678e6i | 1.06308i | ||||||||
\(267\) | −620631. | + | 236346.i | −0.532789 | + | 0.202894i | ||||
\(268\) | −361543. | + | 361543.i | −0.307485 | + | 0.307485i | ||||
\(269\) | 2.10012e6 | 1.76955 | 0.884776 | − | 0.466017i | \(-0.154311\pi\) | ||||
0.884776 | + | 0.466017i | \(0.154311\pi\) | |||||||
\(270\) | −824812. | + | 475007.i | −0.688566 | + | 0.396543i | ||||
\(271\) | −982155. | −0.812376 | −0.406188 | − | 0.913790i | \(-0.633142\pi\) | ||||
−0.406188 | + | 0.913790i | \(0.633142\pi\) | |||||||
\(272\) | −78987.8 | + | 78987.8i | −0.0647348 | + | 0.0647348i | ||||
\(273\) | −508380. | + | 193599.i | −0.412840 | + | 0.157216i | ||||
\(274\) | − | 114410.i | − | 0.0920632i | ||||||
\(275\) | 742527. | + | 1.60775e6i | 0.592080 | + | 1.28200i | ||||
\(276\) | −127107. | + | 283456.i | −0.100438 | + | 0.223982i | ||||
\(277\) | −907548. | − | 907548.i | −0.710673 | − | 0.710673i | 0.256003 | − | 0.966676i | \(-0.417594\pi\) |
−0.966676 | + | 0.256003i | \(0.917594\pi\) | |||||||
\(278\) | −629215. | − | 629215.i | −0.488300 | − | 0.488300i | ||||
\(279\) | 55116.2 | − | 49098.5i | 0.0423905 | − | 0.0377622i | ||||
\(280\) | 1.27221e6 | − | 279591.i | 0.969759 | − | 0.213122i | ||||
\(281\) | − | 2.43616e6i | − | 1.84052i | −0.391308 | − | 0.920260i | \(-0.627977\pi\) | ||
0.391308 | − | 0.920260i | \(-0.372023\pi\) | |||||||
\(282\) | −465894. | − | 1.22341e6i | −0.348871 | − | 0.916115i | ||||
\(283\) | 828841. | − | 828841.i | 0.615184 | − | 0.615184i | −0.329108 | − | 0.944292i | \(-0.606748\pi\) |
0.944292 | + | 0.329108i | \(0.106748\pi\) | |||||||
\(284\) | −888214. | −0.653464 | ||||||||
\(285\) | 1.68054e6 | − | 1.10149e6i | 1.22557 | − | 0.803282i | ||||
\(286\) | −750997. | −0.542904 | ||||||||
\(287\) | −7083.89 | + | 7083.89i | −0.00507653 | + | 0.00507653i | ||||
\(288\) | 56298.2 | − | 974966.i | 0.0399957 | − | 0.692641i | ||||
\(289\) | 1.37138e6i | 0.965861i | ||||||||
\(290\) | −277489. | − | 177497.i | −0.193754 | − | 0.123936i | ||||
\(291\) | 1.56937e6 | + | 703736.i | 1.08641 | + | 0.487166i | ||||
\(292\) | 225916. | + | 225916.i | 0.155056 | + | 0.155056i | ||||
\(293\) | 284240. | + | 284240.i | 0.193426 | + | 0.193426i | 0.797175 | − | 0.603748i | \(-0.206327\pi\) |
−0.603748 | + | 0.797175i | \(0.706327\pi\) | |||||||
\(294\) | 178807. | + | 80180.4i | 0.120647 | + | 0.0541003i | ||||
\(295\) | 24962.3 | + | 113585.i | 0.0167005 | + | 0.0759916i | ||||
\(296\) | − | 765622.i | − | 0.507908i | ||||||
\(297\) | −1.90485e6 | − | 989793.i | −1.25305 | − | 0.651108i | ||||
\(298\) | −1.38143e6 | + | 1.38143e6i | −0.901129 | + | 0.901129i | ||||
\(299\) | −498075. | −0.322193 | ||||||||
\(300\) | −410824. | − | 401788.i | −0.263544 | − | 0.257747i | ||||
\(301\) | −784058. | −0.498806 | ||||||||
\(302\) | −756709. | + | 756709.i | −0.477432 | + | 0.477432i | ||||
\(303\) | 42771.1 | + | 112315.i | 0.0267636 | + | 0.0702797i | ||||
\(304\) | − | 1.16991e6i | − | 0.726056i | ||||||
\(305\) | −609636. | − | 2.77400e6i | −0.375250 | − | 1.70749i | ||||
\(306\) | −159957. | − | 179562.i | −0.0976562 | − | 0.109625i | ||||
\(307\) | 1.28579e6 | + | 1.28579e6i | 0.778617 | + | 0.778617i | 0.979596 | − | 0.200978i | \(-0.0644121\pi\) |
−0.200978 | + | 0.979596i | \(0.564412\pi\) | |||||||
\(308\) | 559504. | + | 559504.i | 0.336068 | + | 0.336068i | ||||
\(309\) | −129171. | + | 288059.i | −0.0769608 | + | 0.171627i | ||||
\(310\) | −64297.2 | − | 41128.1i | −0.0380003 | − | 0.0243072i | ||||
\(311\) | 361008.i | 0.211649i | 0.994385 | + | 0.105824i | \(0.0337482\pi\) | ||||
−0.994385 | + | 0.105824i | \(0.966252\pi\) | |||||||
\(312\) | 845509. | − | 321983.i | 0.491736 | − | 0.187260i | ||||
\(313\) | −1.01609e6 | + | 1.01609e6i | −0.586232 | + | 0.586232i | −0.936609 | − | 0.350377i | \(-0.886054\pi\) |
0.350377 | + | 0.936609i | \(0.386054\pi\) | |||||||
\(314\) | 739696. | 0.423379 | ||||||||
\(315\) | 254020. | + | 1.58769e6i | 0.144242 | + | 0.901550i | ||||
\(316\) | 671213. | 0.378131 | ||||||||
\(317\) | 1.40830e6 | − | 1.40830e6i | 0.787133 | − | 0.787133i | −0.193890 | − | 0.981023i | \(-0.562110\pi\) |
0.981023 | + | 0.193890i | \(0.0621104\pi\) | |||||||
\(318\) | 1.80999e6 | − | 689272.i | 1.00371 | − | 0.382229i | ||||
\(319\) | − | 742911.i | − | 0.408752i | ||||||
\(320\) | −1.87275e6 | + | 411570.i | −1.02236 | + | 0.224682i | ||||
\(321\) | −782040. | + | 1.74399e6i | −0.423610 | + | 0.944673i | ||||
\(322\) | −635552. | − | 635552.i | −0.341595 | − | 0.341595i | ||||
\(323\) | 358973. | + | 358973.i | 0.191450 | + | 0.191450i | ||||
\(324\) | 691924. | + | 80175.9i | 0.366181 | + | 0.0424308i | ||||
\(325\) | 318295. | − | 864610.i | 0.167156 | − | 0.454059i | ||||
\(326\) | 566092.i | 0.295015i | ||||||||
\(327\) | −66579.5 | − | 174834.i | −0.0344327 | − | 0.0904184i | ||||
\(328\) | 11781.5 | − | 11781.5i | 0.00604668 | − | 0.00604668i | ||||
\(329\) | −2.21148e6 | −1.12640 | ||||||||
\(330\) | −452319. | + | 2.17314e6i | −0.228644 | + | 1.09851i | ||||
\(331\) | 1.29322e6 | 0.648786 | 0.324393 | − | 0.945922i | \(-0.394840\pi\) | ||||
0.324393 | + | 0.945922i | \(0.394840\pi\) | |||||||
\(332\) | −301911. | + | 301911.i | −0.150326 | + | 0.150326i | ||||
\(333\) | 943507. | + | 54481.6i | 0.466267 | + | 0.0269240i | ||||
\(334\) | 842011.i | 0.413001i | ||||||||
\(335\) | −1.30564e6 | + | 2.04116e6i | −0.635642 | + | 0.993725i | ||||
\(336\) | 854214. | + | 383046.i | 0.412780 | + | 0.185099i | ||||
\(337\) | 1.56646e6 | + | 1.56646e6i | 0.751352 | + | 0.751352i | 0.974731 | − | 0.223380i | \(-0.0717090\pi\) |
−0.223380 | + | 0.974731i | \(0.571709\pi\) | |||||||
\(338\) | −903826. | − | 903826.i | −0.430321 | − | 0.430321i | ||||
\(339\) | −1.56200e6 | − | 700430.i | −0.738212 | − | 0.331029i | ||||
\(340\) | 78231.7 | − | 122303.i | 0.0367016 | − | 0.0573771i | ||||
\(341\) | − | 172141.i | − | 0.0801673i | ||||||
\(342\) | 2.51436e6 | + | 145189.i | 1.16242 | + | 0.0671224i | ||||
\(343\) | 1.64077e6 | − | 1.64077e6i | 0.753029 | − | 0.753029i | ||||
\(344\) | 1.30400e6 | 0.594130 | ||||||||
\(345\) | −299986. | + | 1.44127e6i | −0.135692 | + | 0.651924i | ||||
\(346\) | 971610. | 0.436316 | ||||||||
\(347\) | 629702. | − | 629702.i | 0.280745 | − | 0.280745i | −0.552661 | − | 0.833406i | \(-0.686388\pi\) |
0.833406 | + | 0.552661i | \(0.186388\pi\) | |||||||
\(348\) | 85790.0 | + | 225280.i | 0.0379742 | + | 0.0997181i | ||||
\(349\) | − | 2.65405e6i | − | 1.16639i | −0.812331 | − | 0.583197i | \(-0.801801\pi\) | ||
0.812331 | − | 0.583197i | \(-0.198199\pi\) | |||||||
\(350\) | 1.50941e6 | − | 697106.i | 0.658622 | − | 0.304179i | ||||
\(351\) | 336626. | + | 1.06487e6i | 0.145841 | + | 0.461347i | ||||
\(352\) | −1.61044e6 | − | 1.61044e6i | −0.692767 | − | 0.692767i | ||||
\(353\) | −749916. | − | 749916.i | −0.320314 | − | 0.320314i | 0.528574 | − | 0.848887i | \(-0.322727\pi\) |
−0.848887 | + | 0.528574i | \(0.822727\pi\) | |||||||
\(354\) | −59642.6 | + | 133006.i | −0.0252958 | + | 0.0564110i | ||||
\(355\) | −4.11110e6 | + | 903487.i | −1.73136 | + | 0.380497i | ||||
\(356\) | − | 502550.i | − | 0.210162i | ||||||
\(357\) | −379637. | + | 144572.i | −0.157652 | + | 0.0600362i | ||||
\(358\) | −1.52819e6 | + | 1.52819e6i | −0.630189 | + | 0.630189i | ||||
\(359\) | 403932. | 0.165414 | 0.0827069 | − | 0.996574i | \(-0.473643\pi\) | ||||
0.0827069 | + | 0.996574i | \(0.473643\pi\) | |||||||
\(360\) | −422472. | − | 2.64056e6i | −0.171807 | − | 1.07384i | ||||
\(361\) | −2.84078e6 | −1.14728 | ||||||||
\(362\) | −484286. | + | 484286.i | −0.194236 | + | 0.194236i | ||||
\(363\) | −2.33229e6 | + | 888170.i | −0.928999 | + | 0.353777i | ||||
\(364\) | − | 411655.i | − | 0.162847i | ||||||
\(365\) | 1.27545e6 | + | 815851.i | 0.501109 | + | 0.320537i | ||||
\(366\) | 1.45661e6 | − | 3.24831e6i | 0.568381 | − | 1.26752i | ||||
\(367\) | 2.79218e6 | + | 2.79218e6i | 1.08213 | + | 1.08213i | 0.996311 | + | 0.0858143i | \(0.0273492\pi\) |
0.0858143 | + | 0.996311i | \(0.472651\pi\) | |||||||
\(368\) | 606090. | + | 606090.i | 0.233302 | + | 0.233302i | ||||
\(369\) | 13680.5 | + | 15357.2i | 0.00523040 | + | 0.00587146i | ||||
\(370\) | −209761. | − | 954467.i | −0.0796563 | − | 0.362457i | ||||
\(371\) | − | 3.27180e6i | − | 1.23410i | ||||||
\(372\) | 19878.5 | + | 52199.8i | 0.00744776 | + | 0.0195574i | ||||
\(373\) | −244300. | + | 244300.i | −0.0909184 | + | 0.0909184i | −0.751103 | − | 0.660185i | \(-0.770478\pi\) |
0.660185 | + | 0.751103i | \(0.270478\pi\) | |||||||
\(374\) | −560814. | −0.207319 | ||||||||
\(375\) | −2.31020e6 | − | 1.44179e6i | −0.848342 | − | 0.529449i | ||||
\(376\) | 3.67801e6 | 1.34166 | ||||||||
\(377\) | −273299. | + | 273299.i | −0.0990339 | + | 0.0990339i | ||||
\(378\) | −929247. | + | 1.78833e6i | −0.334504 | + | 0.643750i | ||||
\(379\) | − | 2.36429e6i | − | 0.845480i | −0.906251 | − | 0.422740i | \(-0.861068\pi\) | ||
0.906251 | − | 0.422740i | \(-0.138932\pi\) | |||||||
\(380\) | 326375. | + | 1.48509e6i | 0.115947 | + | 0.527587i | ||||
\(381\) | −2.17889e6 | − | 977059.i | −0.768995 | − | 0.344833i | ||||
\(382\) | −386436. | − | 386436.i | −0.135494 | − | 0.135494i | ||||
\(383\) | 699669. | + | 699669.i | 0.243722 | + | 0.243722i | 0.818388 | − | 0.574666i | \(-0.194868\pi\) |
−0.574666 | + | 0.818388i | \(0.694868\pi\) | |||||||
\(384\) | −363711. | − | 163095.i | −0.125872 | − | 0.0564434i | ||||
\(385\) | 3.15879e6 | + | 2.02054e6i | 1.08610 | + | 0.694730i | ||||
\(386\) | 701775.i | 0.239734i | ||||||||
\(387\) | −92792.5 | + | 1.60697e6i | −0.0314946 | + | 0.545420i | ||||
\(388\) | −920311. | + | 920311.i | −0.310353 | + | 0.310353i | ||||
\(389\) | −1.08294e6 | −0.362852 | −0.181426 | − | 0.983405i | \(-0.558071\pi\) | ||||
−0.181426 | + | 0.983405i | \(0.558071\pi\) | |||||||
\(390\) | 965843. | − | 633049.i | 0.321547 | − | 0.210754i | ||||
\(391\) | −371942. | −0.123036 | ||||||||
\(392\) | −389303. | + | 389303.i | −0.127960 | + | 0.127960i | ||||
\(393\) | −1.26890e6 | − | 3.33205e6i | −0.414424 | − | 1.08825i | ||||
\(394\) | − | 917925.i | − | 0.297897i | ||||||
\(395\) | 3.10671e6 | − | 682755.i | 1.00186 | − | 0.220177i | ||||
\(396\) | 1.21295e6 | − | 1.08052e6i | 0.388692 | − | 0.346254i | ||||
\(397\) | −1.24433e6 | − | 1.24433e6i | −0.396242 | − | 0.396242i | 0.480663 | − | 0.876905i | \(-0.340396\pi\) |
−0.876905 | + | 0.480663i | \(0.840396\pi\) | |||||||
\(398\) | 1.70973e6 | + | 1.70973e6i | 0.541027 | + | 0.541027i | ||||
\(399\) | 1.74082e6 | − | 3.88212e6i | 0.547420 | − | 1.22078i | ||||
\(400\) | −1.43944e6 | + | 664791.i | −0.449824 | + | 0.207747i | ||||
\(401\) | 5.24320e6i | 1.62830i | 0.580652 | + | 0.814152i | \(0.302798\pi\) | ||||
−0.580652 | + | 0.814152i | \(0.697202\pi\) | |||||||
\(402\) | −2.83822e6 | + | 1.08084e6i | −0.875954 | + | 0.333577i | ||||
\(403\) | −63326.3 | + | 63326.3i | −0.0194232 | + | 0.0194232i | ||||
\(404\) | −90945.6 | −0.0277222 | ||||||||
\(405\) | 3.28413e6 | − | 332728.i | 0.994907 | − | 0.100798i | ||||
\(406\) | −697467. | −0.209995 | ||||||||
\(407\) | 1.55847e6 | − | 1.55847e6i | 0.466352 | − | 0.466352i | ||||
\(408\) | 631391. | − | 240444.i | 0.187780 | − | 0.0715093i | ||||
\(409\) | 6.02331e6i | 1.78044i | 0.455533 | + | 0.890219i | \(0.349449\pi\) | ||||
−0.455533 | + | 0.890219i | \(0.650551\pi\) | |||||||
\(410\) | 11459.7 | − | 17915.3i | 0.00336676 | − | 0.00526339i | ||||
\(411\) | −162348. | + | 362045.i | −0.0474071 | + | 0.105720i | ||||
\(412\) | −168924. | − | 168924.i | −0.0490284 | − | 0.0490284i | ||||
\(413\) | 174119. | + | 174119.i | 0.0502309 | + | 0.0502309i | ||||
\(414\) | −1.37782e6 | + | 1.22738e6i | −0.395085 | + | 0.351949i | ||||
\(415\) | −1.09029e6 | + | 1.70450e6i | −0.310758 | + | 0.485821i | ||||
\(416\) | 1.18488e6i | 0.335692i | ||||||||
\(417\) | 1.09827e6 | + | 2.88399e6i | 0.309292 | + | 0.812183i | ||||
\(418\) | 4.15320e6 | − | 4.15320e6i | 1.16263 | − | 1.16263i | ||||
\(419\) | 268063. | 0.0745937 | 0.0372969 | − | 0.999304i | \(-0.488125\pi\) | ||||
0.0372969 | + | 0.999304i | \(0.488125\pi\) | |||||||
\(420\) | −1.19120e6 | − | 247936.i | −0.329504 | − | 0.0685830i | ||||
\(421\) | 569052. | 0.156476 | 0.0782378 | − | 0.996935i | \(-0.475071\pi\) | ||||
0.0782378 | + | 0.996935i | \(0.475071\pi\) | |||||||
\(422\) | −2.31143e6 | + | 2.31143e6i | −0.631828 | + | 0.631828i | ||||
\(423\) | −261727. | + | 4.53256e6i | −0.0711209 | + | 1.23166i | ||||
\(424\) | 5.44147e6i | 1.46995i | ||||||||
\(425\) | 237690. | − | 645655.i | 0.0638320 | − | 0.173392i | ||||
\(426\) | −4.81403e6 | − | 2.15871e6i | −1.28524 | − | 0.576328i | ||||
\(427\) | −4.25238e6 | − | 4.25238e6i | −1.12866 | − | 1.12866i | ||||
\(428\) | −1.02271e6 | − | 1.02271e6i | −0.269864 | − | 0.269864i | ||||
\(429\) | 2.37651e6 | + | 1.06567e6i | 0.623441 | + | 0.279563i | ||||
\(430\) | 1.62564e6 | − | 357263.i | 0.423987 | − | 0.0931787i | ||||
\(431\) | 2.65898e6i | 0.689480i | 0.938698 | + | 0.344740i | \(0.112033\pi\) | ||||
−0.938698 | + | 0.344740i | \(0.887967\pi\) | |||||||
\(432\) | 886171. | − | 1.70543e6i | 0.228459 | − | 0.439667i | ||||
\(433\) | 3.76956e6 | − | 3.76956e6i | 0.966209 | − | 0.966209i | −0.0332380 | − | 0.999447i | \(-0.510582\pi\) |
0.999447 | + | 0.0332380i | \(0.0105819\pi\) | |||||||
\(434\) | −161611. | −0.0411857 | ||||||||
\(435\) | 626233. | + | 955443.i | 0.158677 | + | 0.242093i | ||||
\(436\) | 141570. | 0.0356661 | ||||||||
\(437\) | 2.75448e6 | − | 2.75448e6i | 0.689979 | − | 0.689979i | ||||
\(438\) | 675378. | + | 1.77351e6i | 0.168214 | + | 0.441720i | ||||
\(439\) | − | 2.74484e6i | − | 0.679760i | −0.940469 | − | 0.339880i | \(-0.889613\pi\) | ||
0.940469 | − | 0.339880i | \(-0.110387\pi\) | |||||||
\(440\) | −5.25353e6 | − | 3.36045e6i | −1.29366 | − | 0.827496i | ||||
\(441\) | −452051. | − | 507456.i | −0.110686 | − | 0.124252i | ||||
\(442\) | 206310. | + | 206310.i | 0.0502301 | + | 0.0502301i | ||||
\(443\) | −5.61400e6 | − | 5.61400e6i | −1.35914 | − | 1.35914i | −0.874982 | − | 0.484156i | \(-0.839127\pi\) |
−0.484156 | − | 0.874982i | \(-0.660873\pi\) | |||||||
\(444\) | −292621. | + | 652560.i | −0.0704446 | + | 0.157095i | ||||
\(445\) | −511191. | − | 2.32605e6i | −0.122372 | − | 0.556826i | ||||
\(446\) | − | 4.34040e6i | − | 1.03322i | ||||||
\(447\) | 6.33173e6 | − | 2.41122e6i | 1.49883 | − | 0.570779i | ||||
\(448\) | −2.87082e6 | + | 2.87082e6i | −0.675788 | + | 0.675788i | ||||
\(449\) | 4.10120e6 | 0.960054 | 0.480027 | − | 0.877254i | \(-0.340627\pi\) | ||||
0.480027 | + | 0.877254i | \(0.340627\pi\) | |||||||
\(450\) | −1.25012e6 | − | 3.17612e6i | −0.291019 | − | 0.739376i | ||||
\(451\) | 47964.1 | 0.0111039 | ||||||||
\(452\) | 915988. | − | 915988.i | 0.210884 | − | 0.210884i | ||||
\(453\) | 3.46836e6 | − | 1.32080e6i | 0.794106 | − | 0.302408i | ||||
\(454\) | 2.25271e6i | 0.512939i | ||||||||
\(455\) | −418734. | − | 1.90535e6i | −0.0948222 | − | 0.431466i | ||||
\(456\) | −2.89523e6 | + | 6.45652e6i | −0.652035 | + | 1.45407i | ||||
\(457\) | −6.11240e6 | − | 6.11240e6i | −1.36906 | − | 1.36906i | −0.861790 | − | 0.507266i | \(-0.830656\pi\) |
−0.507266 | − | 0.861790i | \(-0.669344\pi\) | |||||||
\(458\) | −3.23983e6 | − | 3.23983e6i | −0.721702 | − | 0.721702i | ||||
\(459\) | 251378. | + | 795199.i | 0.0556924 | + | 0.176175i | ||||
\(460\) | −938454. | − | 600288.i | −0.206785 | − | 0.132271i | ||||
\(461\) | 3.40793e6i | 0.746859i | 0.927659 | + | 0.373430i | \(0.121818\pi\) | ||||
−0.927659 | + | 0.373430i | \(0.878182\pi\) | |||||||
\(462\) | 1.67265e6 | + | 4.39228e6i | 0.364585 | + | 0.957381i | ||||
\(463\) | 565359. | − | 565359.i | 0.122566 | − | 0.122566i | −0.643163 | − | 0.765729i | \(-0.722378\pi\) |
0.765729 | + | 0.643163i | \(0.222378\pi\) | |||||||
\(464\) | 665135. | 0.143422 | ||||||||
\(465\) | 145105. | + | 221387.i | 0.0311208 | + | 0.0474809i | ||||
\(466\) | 3.07500e6 | 0.655964 | ||||||||
\(467\) | −2.53896e6 | + | 2.53896e6i | −0.538721 | + | 0.538721i | −0.923153 | − | 0.384432i | \(-0.874397\pi\) |
0.384432 | + | 0.923153i | \(0.374397\pi\) | |||||||
\(468\) | −843712. | − | 48719.0i | −0.178065 | − | 0.0102822i | ||||
\(469\) | 5.13046e6i | 1.07702i | ||||||||
\(470\) | 4.58521e6 | − | 1.00768e6i | 0.957446 | − | 0.210416i | ||||
\(471\) | −2.34074e6 | − | 1.04964e6i | −0.486185 | − | 0.218015i | ||||
\(472\) | −289585. | − | 289585.i | −0.0598303 | − | 0.0598303i | ||||
\(473\) | 2.65438e6 | + | 2.65438e6i | 0.545519 | + | 0.545519i | ||||
\(474\) | 3.63791e6 | + | 1.63131e6i | 0.743715 | + | 0.333496i | ||||
\(475\) | 3.02125e6 | + | 6.54176e6i | 0.614403 | + | 1.33033i | ||||
\(476\) | − | 307407.i | − | 0.0621866i | ||||||
\(477\) | −6.70574e6 | − | 387214.i | −1.34943 | − | 0.0779212i | ||||
\(478\) | 1.41519e6 | − | 1.41519e6i | 0.283299 | − | 0.283299i | ||||
\(479\) | −8.45014e6 | −1.68277 | −0.841385 | − | 0.540436i | \(-0.818259\pi\) | ||||
−0.841385 | + | 0.540436i | \(0.818259\pi\) | |||||||
\(480\) | 3.42866e6 | + | 713642.i | 0.679238 | + | 0.141377i | ||||
\(481\) | −1.14665e6 | −0.225979 | ||||||||
\(482\) | 1.95948e6 | − | 1.95948e6i | 0.384171 | − | 0.384171i | ||||
\(483\) | 1.10933e6 | + | 2.91304e6i | 0.216368 | + | 0.568170i | ||||
\(484\) | − | 1.88854e6i | − | 0.366449i | ||||||
\(485\) | −3.32353e6 | + | 5.19580e6i | −0.641571 | + | 1.00299i | ||||
\(486\) | 3.55530e6 | + | 2.11619e6i | 0.682788 | + | 0.406410i | ||||
\(487\) | 2.98007e6 | + | 2.98007e6i | 0.569383 | + | 0.569383i | 0.931955 | − | 0.362573i | \(-0.118102\pi\) |
−0.362573 | + | 0.931955i | \(0.618102\pi\) | |||||||
\(488\) | 7.07232e6 | + | 7.07232e6i | 1.34435 | + | 1.34435i | ||||
\(489\) | 803290. | − | 1.79138e6i | 0.151915 | − | 0.338778i | ||||
\(490\) | −378667. | + | 591986.i | −0.0712472 | + | 0.111384i | ||||
\(491\) | − | 8.65624e6i | − | 1.62041i | −0.586145 | − | 0.810206i | \(-0.699355\pi\) | ||
0.586145 | − | 0.810206i | \(-0.300645\pi\) | |||||||
\(492\) | −14544.6 | + | 5538.81i | −0.00270888 | + | 0.00103158i | ||||
\(493\) | −204088. | + | 204088.i | −0.0378182 | + | 0.0378182i | ||||
\(494\) | −3.05572e6 | −0.563373 | ||||||||
\(495\) | 4.51506e6 | − | 6.23500e6i | 0.828229 | − | 1.14373i | ||||
\(496\) | 154119. | 0.0281289 | ||||||||
\(497\) | −6.30208e6 | + | 6.30208e6i | −1.14444 | + | 1.14444i | ||||
\(498\) | −2.37009e6 | + | 902566.i | −0.428244 | + | 0.163082i | ||||
\(499\) | − | 583551.i | − | 0.104912i | −0.998623 | − | 0.0524562i | \(-0.983295\pi\) | ||
0.998623 | − | 0.0524562i | \(-0.0167050\pi\) | |||||||
\(500\) | 1.64176e6 | − | 1.24545e6i | 0.293687 | − | 0.222793i | ||||
\(501\) | 1.19482e6 | − | 2.66452e6i | 0.212671 | − | 0.474268i | ||||
\(502\) | −3.41836e6 | − | 3.41836e6i | −0.605422 | − | 0.605422i | ||||
\(503\) | −229863. | − | 229863.i | −0.0405088 | − | 0.0405088i | 0.686562 | − | 0.727071i | \(-0.259119\pi\) |
−0.727071 | + | 0.686562i | \(0.759119\pi\) | |||||||
\(504\) | −3.76629e6 | − | 4.22790e6i | −0.660446 | − | 0.741394i | ||||
\(505\) | −420942. | + | 92509.5i | −0.0734504 | + | 0.0161420i | ||||
\(506\) | 4.30324e6i | 0.747170i | ||||||||
\(507\) | 1.57759e6 | + | 4.14266e6i | 0.272567 | + | 0.715747i | ||||
\(508\) | 1.27775e6 | − | 1.27775e6i | 0.219678 | − | 0.219678i | ||||
\(509\) | 8.34113e6 | 1.42702 | 0.713511 | − | 0.700644i | \(-0.247104\pi\) | ||||
0.713511 | + | 0.700644i | \(0.247104\pi\) | |||||||
\(510\) | 721252. | − | 472735.i | 0.122790 | − | 0.0804808i | ||||
\(511\) | 3.20585e6 | 0.543113 | ||||||||
\(512\) | 3.70187e6 | − | 3.70187e6i | 0.624088 | − | 0.624088i | ||||
\(513\) | −7.75060e6 | − | 4.02735e6i | −1.30029 | − | 0.675657i | ||||
\(514\) | − | 7.92546e6i | − | 1.32317i | ||||||
\(515\) | −953693. | − | 610036.i | −0.158449 | − | 0.101353i | ||||
\(516\) | −1.11143e6 | − | 498389.i | −0.183764 | − | 0.0824032i | ||||
\(517\) | 7.48683e6 | + | 7.48683e6i | 1.23189 | + | 1.23189i | ||||
\(518\) | −1.46314e6 | − | 1.46314e6i | −0.239586 | − | 0.239586i | ||||
\(519\) | −3.07463e6 | − | 1.37872e6i | −0.501042 | − | 0.224677i | ||||
\(520\) | 696415. | + | 3.16887e6i | 0.112943 | + | 0.513920i | ||||
\(521\) | 1.63560e6i | 0.263986i | 0.991251 | + | 0.131993i | \(0.0421377\pi\) | ||||
−0.991251 | + | 0.131993i | \(0.957862\pi\) | |||||||
\(522\) | −82544.6 | + | 1.42950e6i | −0.0132590 | + | 0.229619i | ||||
\(523\) | −4.53453e6 | + | 4.53453e6i | −0.724901 | + | 0.724901i | −0.969599 | − | 0.244699i | \(-0.921311\pi\) |
0.244699 | + | 0.969599i | \(0.421311\pi\) | |||||||
\(524\) | 2.69810e6 | 0.429269 | ||||||||
\(525\) | −5.76567e6 | + | 64108.1i | −0.912959 | + | 0.0101511i | ||||
\(526\) | −4.89304e6 | −0.771106 | ||||||||
\(527\) | −47289.5 | + | 47289.5i | −0.00741717 | + | 0.00741717i | ||||
\(528\) | −1.59511e6 | − | 4.18867e6i | −0.249003 | − | 0.653869i | ||||
\(529\) | − | 3.58236e6i | − | 0.556582i | ||||||
\(530\) | 1.49082e6 | + | 6.78364e6i | 0.230535 | + | 1.04899i | ||||
\(531\) | 377474. | − | 336260.i | 0.0580966 | − | 0.0517534i | ||||
\(532\) | 2.27656e6 | + | 2.27656e6i | 0.348738 | + | 0.348738i | ||||
\(533\) | −17644.8 | − | 17644.8i | −0.00269029 | − | 0.00269029i | ||||
\(534\) | 1.22139e6 | − | 2.72377e6i | 0.185354 | − | 0.413350i | ||||
\(535\) | −5.77394e6 | − | 3.69334e6i | −0.872143 | − | 0.557872i | ||||
\(536\) | − | 8.53269e6i | − | 1.28285i | ||||||
\(537\) | 7.00443e6 | − | 2.66740e6i | 1.04818 | − | 0.399164i | ||||
\(538\) | −6.67491e6 | + | 6.67491e6i | −0.994237 | + | 0.994237i | ||||
\(539\) | −1.58490e6 | −0.234980 | ||||||||
\(540\) | −649137. | + | 2.41209e6i | −0.0957970 | + | 0.355966i | ||||
\(541\) | 4.13526e6 | 0.607449 | 0.303725 | − | 0.952760i | \(-0.401770\pi\) | ||||
0.303725 | + | 0.952760i | \(0.401770\pi\) | |||||||
\(542\) | 3.12163e6 | − | 3.12163e6i | 0.456440 | − | 0.456440i | ||||
\(543\) | 2.21972e6 | − | 845301.i | 0.323071 | − | 0.123030i | ||||
\(544\) | 884820.i | 0.128191i | ||||||||
\(545\) | 655258. | − | 144004.i | 0.0944976 | − | 0.0207675i | ||||
\(546\) | 1.00048e6 | − | 2.23113e6i | 0.143625 | − | 0.320290i | ||||
\(547\) | −6.14982e6 | − | 6.14982e6i | −0.878808 | − | 0.878808i | 0.114603 | − | 0.993411i | \(-0.463440\pi\) |
−0.993411 | + | 0.114603i | \(0.963440\pi\) | |||||||
\(548\) | −212311. | − | 212311.i | −0.0302010 | − | 0.0302010i | ||||
\(549\) | −9.21877e6 | + | 8.21224e6i | −1.30540 | + | 1.16287i | ||||
\(550\) | −7.47001e6 | − | 2.74999e6i | −1.05297 | − | 0.387637i | ||||
\(551\) | − | 3.02282e6i | − | 0.424163i | ||||||
\(552\) | −1.84497e6 | − | 4.84480e6i | −0.257716 | − | 0.676749i | ||||
\(553\) | 4.76241e6 | − | 4.76241e6i | 0.662238 | − | 0.662238i | ||||
\(554\) | 5.76901e6 | 0.798595 | ||||||||
\(555\) | −690615. | + | 3.31803e6i | −0.0951708 | + | 0.457244i | ||||
\(556\) | −2.33528e6 | −0.320371 | ||||||||
\(557\) | −3.86658e6 | + | 3.86658e6i | −0.528067 | + | 0.528067i | −0.919996 | − | 0.391929i | \(-0.871808\pi\) |
0.391929 | + | 0.919996i | \(0.371808\pi\) | |||||||
\(558\) | −19126.5 | + | 331231.i | −0.00260046 | + | 0.0450345i | ||||
\(559\) | − | 1.95296e6i | − | 0.264341i | ||||||
\(560\) | −1.80901e6 | + | 2.82810e6i | −0.243765 | + | 0.381087i | ||||
\(561\) | 1.77468e6 | + | 795800.i | 0.238074 | + | 0.106757i | ||||
\(562\) | 7.74298e6 | + | 7.74298e6i | 1.03411 | + | 1.03411i | ||||
\(563\) | 7.46303e6 | + | 7.46303e6i | 0.992303 | + | 0.992303i | 0.999971 | − | 0.00766747i | \(-0.00244065\pi\) |
−0.00766747 | + | 0.999971i | \(0.502441\pi\) | |||||||
\(564\) | −3.13487e6 | − | 1.40574e6i | −0.414974 | − | 0.186083i | ||||
\(565\) | 3.30792e6 | − | 5.17140e6i | 0.435947 | − | 0.681533i | ||||
\(566\) | 5.26869e6i | 0.691292i | ||||||||
\(567\) | 5.47822e6 | − | 4.34049e6i | 0.715619 | − | 0.566998i | ||||
\(568\) | 1.04813e7 | − | 1.04813e7i | 1.36315 | − | 1.36315i | ||||
\(569\) | 562233. | 0.0728008 | 0.0364004 | − | 0.999337i | \(-0.488411\pi\) | ||||
0.0364004 | + | 0.999337i | \(0.488411\pi\) | |||||||
\(570\) | −1.84043e6 | + | 8.84227e6i | −0.237264 | + | 1.13993i | ||||
\(571\) | 9.36133e6 | 1.20157 | 0.600783 | − | 0.799412i | \(-0.294856\pi\) | ||||
0.600783 | + | 0.799412i | \(0.294856\pi\) | |||||||
\(572\) | −1.39363e6 | + | 1.39363e6i | −0.178098 | + | 0.178098i | ||||
\(573\) | 674508. | + | 1.77122e6i | 0.0858223 | + | 0.225365i | ||||
\(574\) | − | 45030.1i | − | 0.00570458i | ||||||
\(575\) | −4.95425e6 | − | 1.82384e6i | −0.624896 | − | 0.230048i | ||||
\(576\) | 5.54415e6 | + | 6.22366e6i | 0.696271 | + | 0.781610i | ||||
\(577\) | 2.52643e6 | + | 2.52643e6i | 0.315913 | + | 0.315913i | 0.847195 | − | 0.531282i | \(-0.178289\pi\) |
−0.531282 | + | 0.847195i | \(0.678289\pi\) | |||||||
\(578\) | −4.35874e6 | − | 4.35874e6i | −0.542677 | − | 0.542677i | ||||
\(579\) | 995826. | − | 2.22074e6i | 0.123449 | − | 0.275297i | ||||
\(580\) | −844323. | + | 185555.i | −0.104217 | + | 0.0229035i | ||||
\(581\) | 4.28425e6i | 0.526544i | ||||||||
\(582\) | −7.22472e6 | + | 2.75128e6i | −0.884125 | + | 0.336688i | ||||
\(583\) | −1.10765e7 | + | 1.10765e7i | −1.34968 | + | 1.34968i | ||||
\(584\) | −5.33178e6 | −0.646904 | ||||||||
\(585\) | −3.95468e6 | + | 632723.i | −0.477773 | + | 0.0764406i | ||||
\(586\) | −1.80683e6 | −0.217356 | ||||||||
\(587\) | 1.64460e6 | − | 1.64460e6i | 0.196999 | − | 0.196999i | −0.601713 | − | 0.798712i | \(-0.705515\pi\) |
0.798712 | + | 0.601713i | \(0.205515\pi\) | |||||||
\(588\) | 480605. | − | 183022.i | 0.0573251 | − | 0.0218303i | ||||
\(589\) | − | 700420.i | − | 0.0831898i | ||||||
\(590\) | −440351. | − | 281674.i | −0.0520798 | − | 0.0333132i | ||||
\(591\) | −1.30254e6 | + | 2.90474e6i | −0.153399 | + | 0.342089i | ||||
\(592\) | 1.39532e6 | + | 1.39532e6i | 0.163632 | + | 0.163632i | ||||
\(593\) | 5.38412e6 | + | 5.38412e6i | 0.628750 | + | 0.628750i | 0.947754 | − | 0.319003i | \(-0.103348\pi\) |
−0.319003 | + | 0.947754i | \(0.603348\pi\) | |||||||
\(594\) | 9.20018e6 | − | 2.90836e6i | 1.06987 | − | 0.338207i | ||||
\(595\) | −312694. | − | 1.42284e6i | −0.0362098 | − | 0.164764i | ||||
\(596\) | 5.12705e6i | 0.591224i | ||||||||
\(597\) | −2.98425e6 | − | 7.83649e6i | −0.342689 | − | 0.899882i | ||||
\(598\) | 1.58306e6 | − | 1.58306e6i | 0.181027 | − | 0.181027i | ||||
\(599\) | −4.06152e6 | −0.462510 | −0.231255 | − | 0.972893i | \(-0.574283\pi\) | ||||
−0.231255 | + | 0.972893i | \(0.574283\pi\) | |||||||
\(600\) | 9.58913e6 | − | 106621.i | 1.08743 | − | 0.0120911i | ||||
\(601\) | −6.61384e6 | −0.746908 | −0.373454 | − | 0.927649i | \(-0.621827\pi\) | ||||
−0.373454 | + | 0.927649i | \(0.621827\pi\) | |||||||
\(602\) | 2.49201e6 | − | 2.49201e6i | 0.280258 | − | 0.280258i | ||||
\(603\) | 1.05152e7 | + | 607186.i | 1.17767 | + | 0.0680030i | ||||
\(604\) | 2.80847e6i | 0.313240i | ||||||||
\(605\) | −1.92102e6 | − | 8.74113e6i | −0.213375 | − | 0.970911i | ||||
\(606\) | −492917. | − | 221034.i | −0.0545245 | − | 0.0244499i | ||||
\(607\) | −707385. | − | 707385.i | −0.0779263 | − | 0.0779263i | 0.667069 | − | 0.744996i | \(-0.267548\pi\) |
−0.744996 | + | 0.667069i | \(0.767548\pi\) | |||||||
\(608\) | −6.55268e6 | − | 6.55268e6i | −0.718886 | − | 0.718886i | ||||
\(609\) | 2.20711e6 | + | 989712.i | 0.241147 | + | 0.108135i | ||||
\(610\) | 1.07544e7 | + | 6.87911e6i | 1.17020 | + | 0.748528i | ||||
\(611\) | − | 5.50844e6i | − | 0.596933i | ||||||
\(612\) | −630049. | − | 36381.4i | −0.0679980 | − | 0.00392646i | ||||
\(613\) | −1.14619e7 | + | 1.14619e7i | −1.23198 | + | 1.23198i | −0.268781 | + | 0.963201i | \(0.586621\pi\) |
−0.963201 | + | 0.268781i | \(0.913379\pi\) | |||||||
\(614\) | −8.17338e6 | −0.874945 | ||||||||
\(615\) | −61685.7 | + | 40431.1i | −0.00657653 | + | 0.00431050i | ||||
\(616\) | −1.32047e7 | −1.40210 | ||||||||
\(617\) | 9.62794e6 | − | 9.62794e6i | 1.01817 | − | 1.01817i | 0.0183386 | − | 0.999832i | \(-0.494162\pi\) |
0.999832 | − | 0.0183386i | \(-0.00583769\pi\) | |||||||
\(618\) | −505000. | − | 1.32610e6i | −0.0531888 | − | 0.139671i | ||||
\(619\) | − | 3.89290e6i | − | 0.408363i | −0.978933 | − | 0.204181i | \(-0.934547\pi\) | ||
0.978933 | − | 0.204181i | \(-0.0654532\pi\) | |||||||
\(620\) | −195639. | + | 42995.1i | −0.0204398 | + | 0.00449200i | ||||
\(621\) | 6.10172e6 | − | 1.92888e6i | 0.634927 | − | 0.200713i | ||||
\(622\) | −1.14741e6 | − | 1.14741e6i | −0.118917 | − | 0.118917i | ||||
\(623\) | −3.56570e6 | − | 3.56570e6i | −0.368066 | − | 0.368066i | ||||
\(624\) | −954106. | + | 2.12771e6i | −0.0980923 | + | 0.218751i | ||||
\(625\) | 6.33204e6 | − | 7.43456e6i | 0.648401 | − | 0.761299i | ||||
\(626\) | − | 6.45895e6i | − | 0.658759i | ||||||
\(627\) | −1.90361e7 | + | 7.24924e6i | −1.93379 | + | 0.736416i | ||||
\(628\) | 1.37266e6 | − | 1.37266e6i | 0.138888 | − | 0.138888i | ||||
\(629\) | −856270. | −0.0862947 | ||||||||
\(630\) | −5.85360e6 | − | 4.23887e6i | −0.587587 | − | 0.425499i | ||||
\(631\) | 721341. | 0.0721219 | 0.0360610 | − | 0.999350i | \(-0.488519\pi\) | ||||
0.0360610 | + | 0.999350i | \(0.488519\pi\) | |||||||
\(632\) | −7.92057e6 | + | 7.92057e6i | −0.788794 | + | 0.788794i | ||||
\(633\) | 1.05944e7 | − | 4.03450e6i | 1.05091 | − | 0.400203i | ||||
\(634\) | 8.95217e6i | 0.884514i | ||||||||
\(635\) | 4.61435e6 | − | 7.21380e6i | 0.454126 | − | 0.709953i | ||||
\(636\) | 2.07973e6 | − | 4.63791e6i | 0.203875 | − | 0.454653i | ||||
\(637\) | 583047. | + | 583047.i | 0.0569318 | + | 0.0569318i | ||||
\(638\) | 2.36123e6 | + | 2.36123e6i | 0.229661 | + | 0.229661i | ||||
\(639\) | 1.21706e7 | + | 1.36623e7i | 1.17913 | + | 1.32365i | ||||
\(640\) | 770249. | − | 1.20416e6i | 0.0743329 | − | 0.116208i | ||||
\(641\) | − | 6.96826e6i | − | 0.669853i | −0.942244 | − | 0.334926i | \(-0.891289\pi\) | ||
0.942244 | − | 0.334926i | \(-0.108711\pi\) | |||||||
\(642\) | −3.05742e6 | − | 8.02861e6i | −0.292764 | − | 0.768781i | ||||
\(643\) | 9.45414e6 | − | 9.45414e6i | 0.901768 | − | 0.901768i | −0.0938213 | − | 0.995589i | \(-0.529908\pi\) |
0.995589 | + | 0.0938213i | \(0.0299082\pi\) | |||||||
\(644\) | −2.35880e6 | −0.224118 | ||||||||
\(645\) | −5.65124e6 | − | 1.17625e6i | −0.534865 | − | 0.111327i | ||||
\(646\) | −2.28189e6 | −0.215136 | ||||||||
\(647\) | −3.79202e6 | + | 3.79202e6i | −0.356131 | + | 0.356131i | −0.862385 | − | 0.506254i | \(-0.831030\pi\) |
0.506254 | + | 0.862385i | \(0.331030\pi\) | |||||||
\(648\) | −9.11107e6 | + | 7.21886e6i | −0.852377 | + | 0.675353i | ||||
\(649\) | − | 1.17894e6i | − | 0.109870i | ||||||
\(650\) | 1.73638e6 | + | 3.75969e6i | 0.161198 | + | 0.349034i | ||||
\(651\) | 511412. | + | 229327.i | 0.0472953 | + | 0.0212082i | ||||
\(652\) | 1.05050e6 | + | 1.05050e6i | 0.0967785 | + | 0.0967785i | ||||
\(653\) | −1.20802e7 | − | 1.20802e7i | −1.10864 | − | 1.10864i | −0.993330 | − | 0.115310i | \(-0.963214\pi\) |
−0.115310 | − | 0.993330i | \(-0.536786\pi\) | |||||||
\(654\) | 767296. | + | 344071.i | 0.0701486 | + | 0.0314560i | ||||
\(655\) | 1.24881e7 | − | 2.74449e6i | 1.13735 | − | 0.249953i | ||||
\(656\) | 42942.7i | 0.00389610i | ||||||||
\(657\) | 379409. | − | 6.57057e6i | 0.0342921 | − | 0.593867i | ||||
\(658\) | 7.02886e6 | − | 7.02886e6i | 0.632878 | − | 0.632878i | ||||
\(659\) | 2.17065e7 | 1.94705 | 0.973524 | − | 0.228585i | \(-0.0734098\pi\) | ||||
0.973524 | + | 0.228585i | \(0.0734098\pi\) | |||||||
\(660\) | 3.19336e6 | + | 4.87210e6i | 0.285356 | + | 0.435368i | ||||
\(661\) | −1.61371e7 | −1.43656 | −0.718278 | − | 0.695756i | \(-0.755069\pi\) | ||||
−0.718278 | + | 0.695756i | \(0.755069\pi\) | |||||||
\(662\) | −4.11029e6 | + | 4.11029e6i | −0.364525 | + | 0.364525i | ||||
\(663\) | −360105. | − | 945615.i | −0.0318159 | − | 0.0835469i | ||||
\(664\) | − | 7.12532e6i | − | 0.627168i | ||||||
\(665\) | 1.28528e7 | + | 8.22135e6i | 1.12705 | + | 0.720923i | ||||
\(666\) | −3.17196e6 | + | 2.82563e6i | −0.277103 | + | 0.246848i | ||||
\(667\) | 1.56601e6 | + | 1.56601e6i | 0.136295 | + | 0.136295i | ||||
\(668\) | 1.56253e6 | + | 1.56253e6i | 0.135484 | + | 0.135484i | ||||
\(669\) | −6.15907e6 | + | 1.37351e7i | −0.532047 | + | 1.18649i | ||||
\(670\) | −2.33774e6 | − | 1.06373e7i | −0.201191 | − | 0.915473i | ||||
\(671\) | 2.87924e7i | 2.46872i | ||||||||
\(672\) | 6.92988e6 | − | 2.63900e6i | 0.591974 | − | 0.225433i | ||||
\(673\) | −1.23106e7 | + | 1.23106e7i | −1.04771 | + | 1.04771i | −0.0489118 | + | 0.998803i | \(0.515575\pi\) |
−0.998803 | + | 0.0489118i | \(0.984425\pi\) | |||||||
\(674\) | −9.95748e6 | −0.844306 | ||||||||
\(675\) | −550968. | + | 1.18247e7i | −0.0465444 | + | 0.998916i | ||||
\(676\) | −3.35448e6 | −0.282331 | ||||||||
\(677\) | −4.28005e6 | + | 4.28005e6i | −0.358903 | + | 0.358903i | −0.863408 | − | 0.504505i | \(-0.831675\pi\) |
0.504505 | + | 0.863408i | \(0.331675\pi\) | |||||||
\(678\) | 7.19078e6 | − | 2.73836e6i | 0.600761 | − | 0.228779i | ||||
\(679\) | 1.30596e7i | 1.08707i | ||||||||
\(680\) | 520054. | + | 2.36638e6i | 0.0431297 | + | 0.196251i | ||||
\(681\) | 3.19662e6 | − | 7.12863e6i | 0.264133 | − | 0.589031i | ||||
\(682\) | 547123. | + | 547123.i | 0.0450427 | + | 0.0450427i | ||||
\(683\) | −2.81149e6 | − | 2.81149e6i | −0.230614 | − | 0.230614i | 0.582335 | − | 0.812949i | \(-0.302139\pi\) |
−0.812949 | + | 0.582335i | \(0.802139\pi\) | |||||||
\(684\) | 4.93536e6 | − | 4.39651e6i | 0.403347 | − | 0.359308i | ||||
\(685\) | −1.19865e6 | − | 766721.i | −0.0976032 | − | 0.0624325i | ||||
\(686\) | 1.04299e7i | 0.846191i | ||||||||
\(687\) | 5.65498e6 | + | 1.48497e7i | 0.457129 | + | 1.20040i | ||||
\(688\) | −2.37649e6 | + | 2.37649e6i | −0.191410 | + | 0.191410i | ||||
\(689\) | 8.14952e6 | 0.654009 | ||||||||
\(690\) | −3.62739e6 | − | 5.53431e6i | −0.290049 | − | 0.442528i | ||||
\(691\) | 1.44868e7 | 1.15419 | 0.577097 | − | 0.816676i | \(-0.304185\pi\) | ||||
0.577097 | + | 0.816676i | \(0.304185\pi\) | |||||||
\(692\) | 1.80303e6 | − | 1.80303e6i | 0.143132 | − | 0.143132i | ||||
\(693\) | 939647. | − | 1.62727e7i | 0.0743244 | − | 1.28714i | ||||
\(694\) | 4.00283e6i | 0.315477i | ||||||||
\(695\) | −1.08089e7 | + | 2.37544e6i | −0.848825 | + | 0.186544i | ||||
\(696\) | −3.67074e6 | − | 1.64603e6i | −0.287231 | − | 0.128800i | ||||
\(697\) | −13176.4 | − | 13176.4i | −0.00102734 | − | 0.00102734i | ||||
\(698\) | 8.43550e6 | + | 8.43550e6i | 0.655348 | + | 0.655348i | ||||
\(699\) | −9.73073e6 | − | 4.36345e6i | −0.753273 | − | 0.337783i | ||||
\(700\) | 1.50739e6 | − | 4.09465e6i | 0.116274 | − | 0.315843i | ||||
\(701\) | − | 1.46858e7i | − | 1.12876i | −0.825515 | − | 0.564381i | \(-0.809115\pi\) | ||
0.825515 | − | 0.564381i | \(-0.190885\pi\) | |||||||
\(702\) | −4.45443e6 | − | 2.31460e6i | −0.341153 | − | 0.177269i | ||||
\(703\) | 6.34125e6 | − | 6.34125e6i | 0.483934 | − | 0.483934i | ||||
\(704\) | 1.94379e7 | 1.47815 | ||||||||
\(705\) | −1.59396e7 | − | 3.31768e6i | −1.20783 | − | 0.251398i | ||||
\(706\) | 4.76699e6 | 0.359942 | ||||||||
\(707\) | −645280. | + | 645280.i | −0.0485512 | + | 0.0485512i | ||||
\(708\) | 136142. | + | 357500.i | 0.0102072 | + | 0.0268036i | ||||
\(709\) | − | 1.99808e7i | − | 1.49278i | −0.665506 | − | 0.746392i | \(-0.731784\pi\) | ||
0.665506 | − | 0.746392i | \(-0.268216\pi\) | |||||||
\(710\) | 1.01949e7 | − | 1.59381e7i | 0.758993 | − | 1.18656i | ||||
\(711\) | −9.19721e6 | − | 1.03245e7i | −0.682310 | − | 0.765938i | ||||
\(712\) | 5.93028e6 | + | 5.93028e6i | 0.438404 | + | 0.438404i | ||||
\(713\) | 362862. | + | 362862.i | 0.0267311 | + | 0.0267311i | ||||
\(714\) | 747121. | − | 1.66612e6i | 0.0548460 | − | 0.122310i | ||||
\(715\) | −5.03284e6 | + | 7.86804e6i | −0.368170 | + | 0.575574i | ||||
\(716\) | 5.67177e6i | 0.413462i | ||||||||
\(717\) | −6.48649e6 | + | 2.47015e6i | −0.471207 | + | 0.179443i | ||||
\(718\) | −1.28384e6 | + | 1.28384e6i | −0.0929391 | + | 0.0929391i | ||||
\(719\) | −1.26151e7 | −0.910058 | −0.455029 | − | 0.890477i | \(-0.650371\pi\) | ||||
−0.455029 | + | 0.890477i | \(0.650371\pi\) | |||||||
\(720\) | 5.58225e6 | + | 4.04237e6i | 0.401308 | + | 0.290606i | ||||
\(721\) | −2.39711e6 | −0.171731 | ||||||||
\(722\) | 9.02898e6 | − | 9.02898e6i | 0.644608 | − | 0.644608i | ||||
\(723\) | −8.98125e6 | + | 3.42020e6i | −0.638985 | + | 0.243335i | ||||
\(724\) | 1.79739e6i | 0.127437i | ||||||||
\(725\) | −3.71921e6 | + | 1.71768e6i | −0.262788 | + | 0.121366i | ||||
\(726\) | 4.58990e6 | − | 1.02357e7i | 0.323193 | − | 0.720738i | ||||
\(727\) | −1.72884e7 | − | 1.72884e7i | −1.21316 | − | 1.21316i | −0.969982 | − | 0.243177i | \(-0.921810\pi\) |
−0.243177 | − | 0.969982i | \(-0.578190\pi\) | |||||||
\(728\) | 4.85769e6 | + | 4.85769e6i | 0.339705 | + | 0.339705i | ||||
\(729\) | −8.24775e6 | − | 1.17416e7i | −0.574800 | − | 0.818294i | ||||
\(730\) | −6.64689e6 | + | 1.46077e6i | −0.461648 | + | 0.101455i | ||||
\(731\) | − | 1.45839e6i | − | 0.100944i | ||||||
\(732\) | −3.32489e6 | − | 8.73097e6i | −0.229350 | − | 0.602261i | ||||
\(733\) | −7.89945e6 | + | 7.89945e6i | −0.543046 | + | 0.543046i | −0.924421 | − | 0.381374i | \(-0.875451\pi\) |
0.381374 | + | 0.924421i | \(0.375451\pi\) | |||||||
\(734\) | −1.77490e7 | −1.21600 | ||||||||
\(735\) | 2.03831e6 | − | 1.33599e6i | 0.139172 | − | 0.0912187i | ||||
\(736\) | 6.78941e6 | 0.461995 | ||||||||
\(737\) | 1.73689e7 | − | 1.73689e7i | 1.17788 | − | 1.17788i | ||||
\(738\) | −92291.9 | − | 5329.28i | −0.00623767 | − | 0.000360186i | ||||
\(739\) | 1.57456e7i | 1.06059i | 0.847812 | + | 0.530296i | \(0.177919\pi\) | ||||
−0.847812 | + | 0.530296i | \(0.822081\pi\) | |||||||
\(740\) | −2.16047e6 | − | 1.38196e6i | −0.145034 | − | 0.0927718i | ||||
\(741\) | 9.66972e6 | + | 4.33609e6i | 0.646947 | + | 0.290104i | ||||
\(742\) | 1.03989e7 | + | 1.03989e7i | 0.693392 | + | 0.693392i | ||||
\(743\) | −835548. | − | 835548.i | −0.0555264 | − | 0.0555264i | 0.678798 | − | 0.734325i | \(-0.262501\pi\) |
−0.734325 | + | 0.678798i | \(0.762501\pi\) | |||||||
\(744\) | −850551. | − | 381404.i | −0.0563337 | − | 0.0252611i | ||||
\(745\) | 5.21522e6 | + | 2.37306e7i | 0.344256 | + | 1.56646i | ||||
\(746\) | − | 1.55294e6i | − | 0.102167i | ||||||
\(747\) | 8.78081e6 | + | 507037.i | 0.575749 | + | 0.0332459i | ||||
\(748\) | −1.04071e6 | + | 1.04071e6i | −0.0680104 | + | 0.0680104i | ||||
\(749\) | −1.45128e7 | −0.945248 | ||||||||
\(750\) | 1.19251e7 | − | 2.76010e6i | 0.774123 | − | 0.179172i | ||||
\(751\) | −1.08728e6 | −0.0703466 | −0.0351733 | − | 0.999381i | \(-0.511198\pi\) | ||||
−0.0351733 | + | 0.999381i | \(0.511198\pi\) | |||||||
\(752\) | −6.70302e6 | + | 6.70302e6i | −0.432241 | + | 0.432241i | ||||
\(753\) | 5.96660e6 | + | 1.56680e7i | 0.383477 | + | 1.00699i | ||||
\(754\) | − | 1.73728e6i | − | 0.111286i | ||||||
\(755\) | 2.85676e6 | + | 1.29990e7i | 0.182392 | + | 0.829932i | ||||
\(756\) | 1.59420e6 | + | 5.04303e6i | 0.101447 | + | 0.320913i | ||||
\(757\) | 3.23275e6 | + | 3.23275e6i | 0.205037 | + | 0.205037i | 0.802154 | − | 0.597117i | \(-0.203687\pi\) |
−0.597117 | + | 0.802154i | \(0.703687\pi\) | |||||||
\(758\) | 7.51455e6 | + | 7.51455e6i | 0.475040 | + | 0.475040i | ||||
\(759\) | 6.10634e6 | − | 1.36175e7i | 0.384748 | − | 0.858009i | ||||
\(760\) | −2.13760e7 | − | 1.36733e7i | −1.34243 | − | 0.858695i | ||||
\(761\) | 3.27238e6i | 0.204834i | 0.994742 | + | 0.102417i | \(0.0326577\pi\) | ||||
−0.994742 | + | 0.102417i | \(0.967342\pi\) | |||||||
\(762\) | 1.00307e7 | − | 3.81985e6i | 0.625813 | − | 0.238319i | ||||
\(763\) | 1.00447e6 | − | 1.00447e6i | 0.0624635 | − | 0.0624635i | ||||
\(764\) | −1.43423e6 | −0.0888965 | ||||||||
\(765\) | −2.95319e6 | + | 472492.i | −0.182448 | + | 0.0291905i | ||||
\(766\) | −4.44758e6 | −0.273875 | ||||||||
\(767\) | −433702. | + | 433702.i | −0.0266197 | + | 0.0266197i | ||||
\(768\) | −1.43155e7 | + | 5.45154e6i | −0.875794 | + | 0.333516i | ||||
\(769\) | − | 2.90881e7i | − | 1.77378i | −0.461979 | − | 0.886891i | \(-0.652860\pi\) | ||
0.461979 | − | 0.886891i | \(-0.347140\pi\) | |||||||
\(770\) | −1.64617e7 | + | 3.61776e6i | −1.00057 | + | 0.219894i | ||||
\(771\) | −1.12463e7 | + | 2.50799e7i | −0.681355 | + | 1.51946i | ||||
\(772\) | 1.30229e6 | + | 1.30229e6i | 0.0786439 | + | 0.0786439i | ||||
\(773\) | 8.11096e6 | + | 8.11096e6i | 0.488229 | + | 0.488229i | 0.907747 | − | 0.419518i | \(-0.137801\pi\) |
−0.419518 | + | 0.907747i | \(0.637801\pi\) | |||||||
\(774\) | −4.81259e6 | − | 5.40244e6i | −0.288753 | − | 0.324144i | ||||
\(775\) | −861781. | + | 398006.i | −0.0515398 | + | 0.0238032i | ||||
\(776\) | − | 2.17200e7i | − | 1.29481i | ||||||
\(777\) | 2.55385e6 | + | 6.70628e6i | 0.151755 | + | 0.398501i | ||||
\(778\) | 3.44195e6 | − | 3.44195e6i | 0.203871 | − | 0.203871i | ||||
\(779\) | 195160. | 0.0115225 | ||||||||
\(780\) | 617569. | − | 2.96708e6i | 0.0363453 | − | 0.174620i | ||||
\(781\) | 4.26706e7 | 2.50323 | ||||||||
\(782\) | 1.18216e6 | − | 1.18216e6i | 0.0691289 | − | 0.0691289i | ||||
\(783\) | 2.28968e6 | − | 4.40647e6i | 0.133466 | − | 0.256854i | ||||
\(784\) | − | 1.41898e6i | − | 0.0824491i | ||||||
\(785\) | 4.95711e6 | − | 7.74964e6i | 0.287114 | − | 0.448856i | ||||
\(786\) | 1.46234e7 | + | 6.55743e6i | 0.844292 | + | 0.378597i | ||||
\(787\) | 2.82266e6 | + | 2.82266e6i | 0.162451 | + | 0.162451i | 0.783652 | − | 0.621201i | \(-0.213355\pi\) |
−0.621201 | + | 0.783652i | \(0.713355\pi\) | |||||||
\(788\) | −1.70340e6 | − | 1.70340e6i | −0.0977242 | − | 0.0977242i | ||||
\(789\) | 1.54839e7 | + | 6.94327e6i | 0.885496 | + | 0.397074i | ||||
\(790\) | −7.70418e6 | + | 1.20443e7i | −0.439197 | + | 0.686613i | ||||
\(791\) | − | 1.29983e7i | − | 0.738661i | ||||||
\(792\) | −1.56277e6 | + | 2.70638e7i | −0.0885281 | + | 1.53312i | ||||
\(793\) | 1.05920e7 | − | 1.05920e7i | 0.598129 | − | 0.598129i | ||||
\(794\) | 7.90986e6 | 0.445264 | ||||||||
\(795\) | 4.90838e6 | − | 2.35821e7i | 0.275436 | − | 1.32332i | ||||
\(796\) | 6.34551e6 | 0.354964 | ||||||||
\(797\) | −2.40749e7 | + | 2.40749e7i | −1.34252 | + | 1.34252i | −0.448968 | + | 0.893548i | \(0.648208\pi\) |
−0.893548 | + | 0.448968i | \(0.851792\pi\) | |||||||
\(798\) | 6.80580e6 | + | 1.78716e7i | 0.378331 | + | 0.993476i | ||||
\(799\) | − | 4.11348e6i | − | 0.227951i | ||||||
\(800\) | −4.33878e6 | + | 1.17858e7i | −0.239686 | + | 0.651077i | ||||
\(801\) | −7.73011e6 | + | 6.88612e6i | −0.425701 | + | 0.379222i | ||||
\(802\) | −1.66647e7 | − | 1.66647e7i | −0.914876 | − | 0.914876i | ||||
\(803\) | −1.08532e7 | − | 1.08532e7i | −0.593976 | − | 0.593976i | ||||
\(804\) | −3.26120e6 | + | 7.27264e6i | −0.177925 | + | 0.396782i | ||||
\(805\) | −1.09177e7 | + | 2.39936e6i | −0.593803 | + | 0.130499i | ||||
\(806\) | − | 402546.i | − | 0.0218262i | ||||||
\(807\) | 3.05943e7 | − | 1.16508e7i | 1.65370 | − | 0.629754i | ||||
\(808\) | 1.07319e6 | − | 1.07319e6i | 0.0578295 | − | 0.0578295i | ||||
\(809\) | −2.33910e6 | −0.125654 | −0.0628271 | − | 0.998024i | \(-0.520012\pi\) | ||||
−0.0628271 | + | 0.998024i | \(0.520012\pi\) | |||||||
\(810\) | −9.38058e6 | + | 1.14956e7i | −0.502362 | + | 0.615631i | ||||
\(811\) | −2.56963e7 | −1.37189 | −0.685945 | − | 0.727654i | \(-0.740611\pi\) | ||||
−0.685945 | + | 0.727654i | \(0.740611\pi\) | |||||||
\(812\) | −1.29430e6 | + | 1.29430e6i | −0.0688881 | + | 0.0688881i | ||||
\(813\) | −1.43079e7 | + | 5.44868e6i | −0.759190 | + | 0.289111i | ||||
\(814\) | 9.90675e6i | 0.524047i | ||||||||
\(815\) | 5.93083e6 | + | 3.79370e6i | 0.312767 | + | 0.200064i | ||||
\(816\) | −712487. | + | 1.58888e6i | −0.0374586 | + | 0.0835347i | ||||
\(817\) | 1.08004e7 | + | 1.08004e7i | 0.566087 | + | 0.566087i | ||||
\(818\) | −1.91442e7 | − | 1.91442e7i | −1.00035 | − | 1.00035i | ||||
\(819\) | −6.33200e6 | + | 5.64065e6i | −0.329861 | + | 0.293846i | ||||
\(820\) | −11979.9 | − | 54511.5i | −0.000622182 | − | 0.00283109i | ||||
\(821\) | − | 5.06844e6i | − | 0.262432i | −0.991354 | − | 0.131216i | \(-0.958112\pi\) | ||
0.991354 | − | 0.131216i | \(-0.0418881\pi\) | |||||||
\(822\) | −634707. | − | 1.66671e6i | −0.0327638 | − | 0.0860358i | ||||
\(823\) | 1.27098e7 | − | 1.27098e7i | 0.654092 | − | 0.654092i | −0.299883 | − | 0.953976i | \(-0.596948\pi\) |
0.953976 | + | 0.299883i | \(0.0969478\pi\) | |||||||
\(824\) | 3.98673e6 | 0.204550 | ||||||||
\(825\) | 1.97363e7 | + | 1.93023e7i | 1.00956 | + | 0.987356i | ||||
\(826\) | −1.10682e6 | −0.0564453 | ||||||||
\(827\) | 2.01367e7 | − | 2.01367e7i | 1.02382 | − | 1.02382i | 0.0241111 | − | 0.999709i | \(-0.492324\pi\) |
0.999709 | − | 0.0241111i | \(-0.00767554\pi\) | |||||||
\(828\) | −279162. | + | 4.83450e6i | −0.0141508 | + | 0.245062i | ||||
\(829\) | 6.04072e6i | 0.305283i | 0.988282 | + | 0.152641i | \(0.0487779\pi\) | ||||
−0.988282 | + | 0.152641i | \(0.951222\pi\) | |||||||
\(830\) | −1.95216e6 | − | 8.88281e6i | −0.0983602 | − | 0.447564i | ||||
\(831\) | −1.82558e7 | − | 8.18627e6i | −0.917063 | − | 0.411229i | ||||
\(832\) | −7.15074e6 | − | 7.15074e6i | −0.358132 | − | 0.358132i | ||||
\(833\) | 435396. | + | 435396.i | 0.0217406 | + | 0.0217406i | ||||
\(834\) | −1.26570e7 | − | 5.67565e6i | −0.630110 | − | 0.282554i | ||||
\(835\) | 8.82157e6 | + | 5.64278e6i | 0.437854 | + | 0.280076i | ||||
\(836\) | − | 1.54143e7i | − | 0.762794i | ||||||
\(837\) | 530544. | − | 1.02103e6i | 0.0261763 | − | 0.0503760i | ||||
\(838\) | −851999. | + | 851999.i | −0.0419111 | + | 0.0419111i | ||||
\(839\) | 2.17575e7 | 1.06710 | 0.533548 | − | 0.845769i | \(-0.320858\pi\) | ||||
0.533548 | + | 0.845769i | \(0.320858\pi\) | |||||||
\(840\) | 1.69823e7 | − | 1.11309e7i | 0.830423 | − | 0.544290i | ||||
\(841\) | −1.87926e7 | −0.916213 | ||||||||
\(842\) | −1.80865e6 | + | 1.80865e6i | −0.0879171 | + | 0.0879171i | ||||
\(843\) | −1.35150e7 | − | 3.54897e7i | −0.655011 | − | 1.72002i | ||||
\(844\) | 8.57868e6i | 0.414538i | ||||||||
\(845\) | −1.55262e7 | + | 3.41216e6i | −0.748038 | + | 0.164395i | ||||
\(846\) | −1.35742e7 | − | 1.52379e7i | −0.652061 | − | 0.731980i | ||||
\(847\) | −1.33996e7 | − | 1.33996e7i | −0.641778 | − | 0.641778i | ||||
\(848\) | −9.91687e6 | − | 9.91687e6i | −0.473571 | − | 0.473571i | ||||
\(849\) | 7.47632e6 | − | 1.66726e7i | 0.355974 | − | 0.793842i | ||||
\(850\) | 1.29666e6 | + | 2.80758e6i | 0.0615570 | + | 0.133286i | ||||
\(851\) | 6.57034e6i | 0.311002i | ||||||||
\(852\) | −1.29394e7 | + | 4.92752e6i | −0.610682 | + | 0.232557i | ||||
\(853\) | −1.18523e7 | + | 1.18523e7i | −0.557737 | + | 0.557737i | −0.928662 | − | 0.370926i | \(-0.879040\pi\) |
0.370926 | + | 0.928662i | \(0.379040\pi\) | |||||||
\(854\) | 2.70311e7 | 1.26829 | ||||||||
\(855\) | 1.83712e7 | − | 2.53695e7i | 0.859455 | − | 1.18685i | ||||
\(856\) | 2.41368e7 | 1.12589 | ||||||||
\(857\) | −8.70826e6 | + | 8.70826e6i | −0.405023 | + | 0.405023i | −0.879999 | − | 0.474976i | \(-0.842457\pi\) |
0.474976 | + | 0.879999i | \(0.342457\pi\) | |||||||
\(858\) | −1.09404e7 | + | 4.16629e6i | −0.507360 | + | 0.193211i | ||||
\(859\) | 2.53846e7i | 1.17378i | 0.809665 | + | 0.586892i | \(0.199649\pi\) | ||||
−0.809665 | + | 0.586892i | \(0.800351\pi\) | |||||||
\(860\) | 2.35374e6 | − | 3.67969e6i | 0.108521 | − | 0.169655i | ||||
\(861\) | −63898.2 | + | 142496.i | −0.00293752 | + | 0.00655083i | ||||
\(862\) | −8.45116e6 | − | 8.45116e6i | −0.387390 | − | 0.387390i | ||||
\(863\) | 2.22012e7 | + | 2.22012e7i | 1.01473 | + | 1.01473i | 0.999890 | + | 0.0148363i | \(0.00472273\pi\) |
0.0148363 | + | 0.999890i | \(0.495277\pi\) | |||||||
\(864\) | −4.58865e6 | − | 1.45155e7i | −0.209122 | − | 0.661528i | ||||
\(865\) | 6.51129e6 | − | 1.01794e7i | 0.295888 | − | 0.462572i | ||||
\(866\) | 2.39620e7i | 1.08575i | ||||||||
\(867\) | 7.60799e6 | + | 1.99782e7i | 0.343734 | + | 0.902626i | ||||
\(868\) | −299903. | + | 299903.i | −0.0135108 | + | 0.0135108i | ||||
\(869\) | −3.22457e7 | −1.44851 | ||||||||
\(870\) | −5.02712e6 | − | 1.04635e6i | −0.225175 | − | 0.0468681i | ||||
\(871\) | −1.27791e7 | −0.570764 | ||||||||
\(872\) | −1.67058e6 | + | 1.67058e6i | −0.0744006 | + | 0.0744006i | ||||
\(873\) | 2.67665e7 | + | 1.54560e6i | 1.18865 | + | 0.0686373i | ||||
\(874\) | 1.75094e7i | 0.775340i | ||||||||
\(875\) | 2.81192e6 | − | 2.04854e7i | 0.124160 | − | 0.904534i | ||||
\(876\) | 4.54442e6 | + | 2.03781e6i | 0.200087 | + | 0.0897228i | ||||
\(877\) | 1.98709e6 | + | 1.98709e6i | 0.0872404 | + | 0.0872404i | 0.749380 | − | 0.662140i | \(-0.230352\pi\) |
−0.662140 | + | 0.749380i | \(0.730352\pi\) | |||||||
\(878\) | 8.72406e6 | + | 8.72406e6i | 0.381929 | + | 0.381929i | ||||
\(879\) | 5.71764e6 | + | 2.56390e6i | 0.249600 | + | 0.111926i | ||||
\(880\) | 1.56986e7 | − | 3.45005e6i | 0.683369 | − | 0.150182i | ||||
\(881\) | 8.58185e6i | 0.372513i | 0.982501 | + | 0.186256i | \(0.0596355\pi\) | ||||
−0.982501 | + | 0.186256i | \(0.940364\pi\) | |||||||
\(882\) | 3.04965e6 | + | 176098.i | 0.132001 | + | 0.00762225i | ||||
\(883\) | 1.10673e7 | − | 1.10673e7i | 0.477685 | − | 0.477685i | −0.426706 | − | 0.904390i | \(-0.640326\pi\) |
0.904390 | + | 0.426706i | \(0.140326\pi\) | |||||||
\(884\) | 765702. | 0.0329556 | ||||||||
\(885\) | 993780. | + | 1.51621e6i | 0.0426513 | + | 0.0650730i | ||||
\(886\) | 3.56865e7 | 1.52728 | ||||||||
\(887\) | −2.07797e7 | + | 2.07797e7i | −0.886809 | + | 0.886809i | −0.994215 | − | 0.107406i | \(-0.965745\pi\) |
0.107406 | + | 0.994215i | \(0.465745\pi\) | |||||||
\(888\) | −4.24742e6 | − | 1.11535e7i | −0.180756 | − | 0.474656i | ||||
\(889\) | − | 1.81319e7i | − | 0.769463i | ||||||
\(890\) | 9.01775e6 | + | 5.76826e6i | 0.381613 | + | 0.244101i | ||||
\(891\) | −3.32406e7 | − | 3.85172e6i | −1.40273 | − | 0.162540i | ||||
\(892\) | −8.05454e6 | − | 8.05454e6i | −0.338944 | − | 0.338944i | ||||
\(893\) | 3.04630e7 | + | 3.04630e7i | 1.27833 | + | 1.27833i | ||||
\(894\) | −1.24608e7 | + | 2.77882e7i | −0.521435 | + | 1.16283i | ||||
\(895\) | 5.76930e6 | + | 2.62518e7i | 0.240750 | + | 1.09547i | ||||
\(896\) | − | 3.02666e6i | − | 0.125948i | ||||||
\(897\) | −7.25590e6 | + | 2.76316e6i | −0.301100 | + | 0.114663i | ||||
\(898\) | −1.30351e7 | + | 1.30351e7i | −0.539414 | + | 0.539414i | ||||
\(899\) | 398212. | 0.0164329 | ||||||||
\(900\) | −8.21382e6 | − | 3.57409e6i | −0.338017 | − | 0.147082i | ||||
\(901\) | 6.08573e6 | 0.249747 | ||||||||
\(902\) | −152447. | + | 152447.i | −0.00623881 | + | 0.00623881i | ||||
\(903\) | −1.14221e7 | + | 4.34970e6i | −0.466150 | + | 0.177517i | ||||
\(904\) | 2.16180e7i | 0.879822i | ||||||||
\(905\) | 1.82830e6 | + | 8.31923e6i | 0.0742037 | + | 0.337646i | ||||
\(906\) | −6.82567e6 | + | 1.52216e7i | −0.276264 | + | 0.616085i | ||||
\(907\) | −2.77720e7 | − | 2.77720e7i | −1.12096 | − | 1.12096i | −0.991598 | − | 0.129358i | \(-0.958708\pi\) |
−0.129358 | − | 0.991598i | \(-0.541292\pi\) | |||||||
\(908\) | 4.18038e6 | + | 4.18038e6i | 0.168268 | + | 0.168268i | ||||
\(909\) | 1.24617e6 | + | 1.39891e6i | 0.0500228 | + | 0.0561538i | ||||
\(910\) | 7.38675e6 | + | 4.72498e6i | 0.295699 | + | 0.189146i | ||||
\(911\) | 2.08056e7i | 0.830586i | 0.909688 | + | 0.415293i | \(0.136321\pi\) | ||||
−0.909688 | + | 0.415293i | \(0.863679\pi\) | |||||||
\(912\) | −6.49031e6 | − | 1.70432e7i | −0.258391 | − | 0.678522i | ||||
\(913\) | 1.45041e7 | − | 1.45041e7i | 0.575854 | − | 0.575854i | ||||
\(914\) | 3.88547e7 | 1.53843 | ||||||||
\(915\) | −2.42704e7 | − | 3.70293e7i | −0.958349 | − | 1.46215i | ||||
\(916\) | −1.20244e7 | −0.473504 | ||||||||
\(917\) | 1.91436e7 | − | 1.91436e7i | 0.751797 | − | 0.751797i | ||||
\(918\) | −3.32639e6 | − | 1.72845e6i | −0.130277 | − | 0.0676940i | ||||
\(919\) | 2.67083e6i | 0.104318i | 0.998639 | + | 0.0521588i | \(0.0166102\pi\) | ||||
−0.998639 | + | 0.0521588i | \(0.983390\pi\) | |||||||
\(920\) | 1.81577e7 | − | 3.99048e6i | 0.707281 | − | 0.155438i | ||||
\(921\) | 2.58644e7 | + | 1.15981e7i | 1.00474 | + | 0.450544i | ||||
\(922\) | −1.08316e7 | − | 1.08316e7i | −0.419629 | − | 0.419629i | ||||
\(923\) | −1.56974e7 | − | 1.56974e7i | −0.606492 | − | 0.606492i | ||||
\(924\) | 1.12547e7 | + | 5.04685e6i | 0.433666 | + | 0.194464i | ||||
\(925\) | −1.14055e7 | − | 4.19878e6i | −0.438287 | − | 0.161350i | ||||
\(926\) | 3.59382e6i | 0.137730i | ||||||||
\(927\) | −283695. | + | 4.91301e6i | −0.0108431 | + | 0.187779i | ||||
\(928\) | 3.72542e6 | − | 3.72542e6i | 0.142005 | − | 0.142005i | ||||
\(929\) | −3.48724e7 | −1.32569 | −0.662846 | − | 0.748756i | \(-0.730651\pi\) | ||||
−0.662846 | + | 0.748756i | \(0.730651\pi\) | |||||||
\(930\) | −1.16484e6 | − | 242450.i | −0.0441630 | − | 0.00919209i | ||||
\(931\) | −6.44879e6 | −0.243839 | ||||||||
\(932\) | 5.70631e6 | − | 5.70631e6i | 0.215187 | − | 0.215187i | ||||
\(933\) | 2.00276e6 | + | 5.25913e6i | 0.0753224 | + | 0.197792i | ||||
\(934\) | − | 1.61394e7i | − | 0.605369i | ||||||
\(935\) | −3.75832e6 | + | 5.87553e6i | −0.140593 | + | 0.219795i | ||||
\(936\) | 1.05310e7 | − | 9.38121e6i | 0.392899 | − | 0.350001i | ||||
\(937\) | 2.07137e7 | + | 2.07137e7i | 0.770742 | + | 0.770742i | 0.978236 | − | 0.207494i | \(-0.0665308\pi\) |
−0.207494 | + | 0.978236i | \(0.566531\pi\) | |||||||
\(938\) | −1.63064e7 | − | 1.63064e7i | −0.605133 | − | 0.605133i | ||||
\(939\) | −9.16531e6 | + | 2.04391e7i | −0.339221 | + | 0.756482i | ||||
\(940\) | 6.63886e6 | − | 1.03788e7i | 0.245061 | − | 0.383113i | ||||
\(941\) | − | 548205.i | − | 0.0201822i | −0.999949 | − | 0.0100911i | \(-0.996788\pi\) | ||
0.999949 | − | 0.0100911i | \(-0.00321215\pi\) | |||||||
\(942\) | 1.07758e7 | − | 4.10359e6i | 0.395660 | − | 0.150674i | ||||
\(943\) | −101105. | + | 101105.i | −0.00370250 | + | 0.00370250i | ||||
\(944\) | 1.05551e6 | 0.0385509 | ||||||||
\(945\) | 1.25085e7 | + | 2.17201e7i | 0.455645 | + | 0.791192i | ||||
\(946\) | −1.68731e7 | −0.613009 | ||||||||
\(947\) | 8.77113e6 | − | 8.77113e6i | 0.317820 | − | 0.317820i | −0.530110 | − | 0.847929i | \(-0.677849\pi\) |
0.847929 | + | 0.530110i | \(0.177849\pi\) | |||||||
\(948\) | 9.77816e6 | − | 3.72367e6i | 0.353375 | − | 0.134571i | ||||
\(949\) | 7.98524e6i | 0.287821i | ||||||||
\(950\) | −3.03946e7 | − | 1.11894e7i | −1.09267 | − | 0.402251i | ||||
\(951\) | 1.27032e7 | − | 2.83288e7i | 0.455472 | − | 1.01573i | ||||
\(952\) | 3.62753e6 | + | 3.62753e6i | 0.129723 | + | 0.129723i | ||||
\(953\) | −3.42460e7 | − | 3.42460e7i | −1.22145 | − | 1.22145i | −0.967115 | − | 0.254338i | \(-0.918142\pi\) |
−0.254338 | − | 0.967115i | \(-0.581858\pi\) | |||||||
\(954\) | 2.25439e7 | − | 2.00825e7i | 0.801970 | − | 0.714408i | ||||
\(955\) | −6.63833e6 | + | 1.45889e6i | −0.235532 | + | 0.0517624i | ||||
\(956\) | − | 5.25237e6i | − | 0.185870i | ||||||
\(957\) | −4.12143e6 | − | 1.08226e7i | −0.145468 | − | 0.381991i | ||||
\(958\) | 2.68575e7 | − | 2.68575e7i | 0.945478 | − | 0.945478i | ||||
\(959\) | −3.01279e6 | −0.105785 | ||||||||
\(960\) | −2.49988e7 | + | 1.63851e7i | −0.875468 | + | 0.573814i | ||||
\(961\) | −2.85369e7 | −0.996777 | ||||||||
\(962\) | 3.64445e6 | − | 3.64445e6i | 0.126968 | − | 0.126968i | ||||
\(963\) | −1.71757e6 | + | 2.97448e7i | −0.0596829 | + | 1.03358i | ||||
\(964\) | − | 7.27247e6i | − | 0.252052i | ||||||
\(965\) | 7.35235e6 | + | 4.70298e6i | 0.254160 | + | 0.162575i | ||||
\(966\) | −1.27845e7 | − | 5.73281e6i | −0.440799 | − | 0.197663i | ||||
\(967\) | −3.38352e6 | − | 3.38352e6i | −0.116360 | − | 0.116360i | 0.646529 | − | 0.762889i | \(-0.276220\pi\) |
−0.762889 | + | 0.646529i | \(0.776220\pi\) | |||||||
\(968\) | 2.22855e7 | + | 2.22855e7i | 0.764425 | + | 0.764425i | ||||
\(969\) | 7.22095e6 | + | 3.23802e6i | 0.247050 | + | 0.110782i | ||||
\(970\) | −5.95074e6 | − | 2.70774e7i | −0.203068 | − | 0.924012i | ||||
\(971\) | − | 7.86809e6i | − | 0.267807i | −0.990994 | − | 0.133903i | \(-0.957249\pi\) | ||
0.990994 | − | 0.133903i | \(-0.0427512\pi\) | |||||||
\(972\) | 1.05247e7 | − | 2.67058e6i | 0.357308 | − | 0.0906649i | ||||
\(973\) | −1.65694e7 | + | 1.65694e7i | −0.561079 | + | 0.561079i | ||||
\(974\) | −1.89434e7 | −0.639824 | ||||||||
\(975\) | −159683. | − | 1.43613e7i | −0.00537956 | − | 0.483820i | ||||
\(976\) | −2.57781e7 | −0.866215 | ||||||||
\(977\) | 2.25244e7 | − | 2.25244e7i | 0.754947 | − | 0.754947i | −0.220451 | − | 0.975398i | \(-0.570753\pi\) |
0.975398 | + | 0.220451i | \(0.0707530\pi\) | |||||||
\(978\) | 3.14050e6 | + | 8.24677e6i | 0.104991 | + | 0.275700i | ||||
\(979\) | 2.41429e7i | 0.805069i | ||||||||
\(980\) | 395857. | + | 1.80125e6i | 0.0131666 | + | 0.0599114i | ||||
\(981\) | −1.93984e6 | − | 2.17760e6i | −0.0643568 | − | 0.0722447i | ||||
\(982\) | 2.75126e7 | + | 2.75126e7i | 0.910442 | + | 0.910442i | ||||
\(983\) | −1.53567e7 | − | 1.53567e7i | −0.506891 | − | 0.506891i | 0.406680 | − | 0.913571i | \(-0.366686\pi\) |
−0.913571 | + | 0.406680i | \(0.866686\pi\) | |||||||
\(984\) | 106272. | − | 236992.i | 0.00349889 | − | 0.00780272i | ||||
\(985\) | −9.61691e6 | − | 6.15152e6i | −0.315824 | − | 0.202019i | ||||
\(986\) | − | 1.29733e6i | − | 0.0424969i | ||||||
\(987\) | −3.22166e7 | + | 1.22686e7i | −1.05266 | + | 0.400868i | ||||
\(988\) | −5.67053e6 | + | 5.67053e6i | −0.184813 | + | 0.184813i | ||||
\(989\) | −1.11905e7 | −0.363798 | ||||||||
\(990\) | 5.46657e6 | + | 3.41674e7i | 0.177267 | + | 1.10796i | ||||
\(991\) | 4.62484e7 | 1.49593 | 0.747967 | − | 0.663736i | \(-0.231030\pi\) | ||||
0.747967 | + | 0.663736i | \(0.231030\pi\) | |||||||
\(992\) | 863220. | − | 863220.i | 0.0278511 | − | 0.0278511i | ||||
\(993\) | 1.88394e7 | − | 7.17434e6i | 0.606310 | − | 0.230892i | ||||
\(994\) | − | 4.00604e7i | − | 1.28603i | ||||||
\(995\) | 2.93702e7 | − | 6.45463e6i | 0.940480 | − | 0.206687i | ||||
\(996\) | −2.72330e6 | + | 6.07310e6i | −0.0869855 | + | 0.193982i | ||||
\(997\) | 2.96424e7 | + | 2.96424e7i | 0.944443 | + | 0.944443i | 0.998536 | − | 0.0540925i | \(-0.0172266\pi\) |
−0.0540925 | + | 0.998536i | \(0.517227\pi\) | |||||||
\(998\) | 1.85473e6 | + | 1.85473e6i | 0.0589459 | + | 0.0589459i | ||||
\(999\) | 1.40471e7 | − | 4.44059e6i | 0.445322 | − | 0.140775i |
(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 | 15.6.e.a.2.3 | ✓ | 16 | |
3.2 | odd | 2 | inner | 15.6.e.a.2.6 | yes | 16 | |
5.2 | odd | 4 | 75.6.e.e.68.3 | 16 | |||
5.3 | odd | 4 | inner | 15.6.e.a.8.6 | yes | 16 | |
5.4 | even | 2 | 75.6.e.e.32.6 | 16 | |||
15.2 | even | 4 | 75.6.e.e.68.6 | 16 | |||
15.8 | even | 4 | inner | 15.6.e.a.8.3 | yes | 16 | |
15.14 | odd | 2 | 75.6.e.e.32.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.6.e.a.2.3 | ✓ | 16 | 1.1 | even | 1 | trivial | |
15.6.e.a.2.6 | yes | 16 | 3.2 | odd | 2 | inner | |
15.6.e.a.8.3 | yes | 16 | 15.8 | even | 4 | inner | |
15.6.e.a.8.6 | yes | 16 | 5.3 | odd | 4 | inner | |
75.6.e.e.32.3 | 16 | 15.14 | odd | 2 | |||
75.6.e.e.32.6 | 16 | 5.4 | even | 2 | |||
75.6.e.e.68.3 | 16 | 5.2 | odd | 4 | |||
75.6.e.e.68.6 | 16 | 15.2 | even | 4 |