Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,6,Mod(17,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 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("60.17");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.i (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: | \(9.62302918878\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{19} + 2 x^{18} - 382 x^{17} + 117610 x^{16} - 661518 x^{15} + 1160778 x^{14} + \cdots + 48\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{23}\cdot 3^{14}\cdot 5^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 53.3 | ||
Root | \(9.05032 + 16.3862i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 60.53 |
Dual form | 60.6.i.a.17.3 |
$q$-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 \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −12.0317 | + | 9.91146i | −0.771837 | + | 0.635821i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −26.7203 | + | 49.1022i | −0.477988 | + | 0.878366i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.70680 | − | 1.70680i | 0.0131655 | − | 0.0131655i | −0.700493 | − | 0.713659i | \(-0.747037\pi\) |
0.713659 | + | 0.700493i | \(0.247037\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 46.5259 | − | 238.504i | 0.191465 | − | 0.981500i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 159.189i | − | 0.396671i | −0.980134 | − | 0.198336i | \(-0.936446\pi\) | ||
0.980134 | − | 0.198336i | \(-0.0635536\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −348.051 | − | 348.051i | −0.571196 | − | 0.571196i | 0.361267 | − | 0.932462i | \(-0.382344\pi\) |
−0.932462 | + | 0.361267i | \(0.882344\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −165.182 | − | 855.623i | −0.189555 | − | 0.981870i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −286.676 | − | 286.676i | −0.240585 | − | 0.240585i | 0.576507 | − | 0.817092i | \(-0.304415\pi\) |
−0.817092 | + | 0.576507i | \(0.804415\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2120.89i | − | 1.34783i | −0.738811 | − | 0.673913i | \(-0.764612\pi\) | ||
0.738811 | − | 0.673913i | \(-0.235388\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.61890 | + | 37.4527i | −0.00179072 | + | 0.0185325i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −238.492 | + | 238.492i | −0.0940058 | + | 0.0940058i | −0.752546 | − | 0.658540i | \(-0.771174\pi\) |
0.658540 | + | 0.752546i | \(0.271174\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1697.05 | − | 2624.05i | −0.543055 | − | 0.839697i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1804.14 | + | 3330.76i | 0.476278 | + | 0.879295i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5308.79 | −1.17220 | −0.586098 | − | 0.810240i | \(-0.699337\pi\) | ||||
−0.586098 | + | 0.810240i | \(0.699337\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4749.30 | 0.887617 | 0.443809 | − | 0.896122i | \(-0.353627\pi\) | ||||
0.443809 | + | 0.896122i | \(0.353627\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1577.79 | + | 1915.32i | 0.252212 | + | 0.306166i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 38.2013 | + | 129.414i | 0.00527118 | + | 0.0178571i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7540.18 | + | 7540.18i | −0.905477 | + | 0.905477i | −0.995903 | − | 0.0904264i | \(-0.971177\pi\) |
0.0904264 | + | 0.995903i | \(0.471177\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7637.36 | + | 737.968i | 0.804048 | + | 0.0776920i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 15461.0i | − | 1.43641i | −0.695831 | − | 0.718205i | \(-0.744964\pi\) | ||
0.695831 | − | 0.718205i | \(-0.255036\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10753.2 | + | 10753.2i | 0.886884 | + | 0.886884i | 0.994223 | − | 0.107339i | \(-0.0342329\pi\) |
−0.107339 | + | 0.994223i | \(0.534233\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 10467.9 | + | 8657.44i | 0.770598 | + | 0.637321i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6192.52 | − | 6192.52i | −0.408905 | − | 0.408905i | 0.472451 | − | 0.881357i | \(-0.343369\pi\) |
−0.881357 | + | 0.472451i | \(0.843369\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16801.2i | 0.999653i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6290.58 | + | 607.835i | 0.338661 | + | 0.0327235i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −16971.1 | + | 16971.1i | −0.829889 | + | 0.829889i | −0.987501 | − | 0.157612i | \(-0.949620\pi\) |
0.157612 | + | 0.987501i | \(0.449620\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7816.52 | + | 4253.58i | 0.348423 | + | 0.189604i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 21021.1 | + | 25518.0i | 0.856975 | + | 1.04030i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −42879.1 | −1.60367 | −0.801836 | − | 0.597544i | \(-0.796143\pi\) | ||||
−0.801836 | + | 0.597544i | \(0.796143\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −24298.8 | −0.836105 | −0.418052 | − | 0.908423i | \(-0.637287\pi\) | ||||
−0.418052 | + | 0.908423i | \(0.637287\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −327.669 | − | 486.489i | −0.0104012 | − | 0.0154427i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 26390.1 | − | 7790.03i | 0.774743 | − | 0.228694i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 38389.1 | − | 38389.1i | 1.04477 | − | 1.04477i | 0.0458212 | − | 0.998950i | \(-0.485410\pi\) |
0.998950 | − | 0.0458212i | \(-0.0145904\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 505.672 | − | 5233.29i | 0.0127863 | − | 0.132328i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 72926.9i | − | 1.71689i | −0.512908 | − | 0.858444i | \(-0.671432\pi\) | ||
0.512908 | − | 0.858444i | \(-0.328568\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −57492.8 | − | 57492.8i | −1.26272 | − | 1.26272i | −0.949770 | − | 0.312948i | \(-0.898683\pi\) |
−0.312948 | − | 0.949770i | \(-0.601317\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 46426.6 | + | 14751.7i | 0.953047 | + | 0.302824i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −271.703 | − | 271.703i | −0.00522238 | − | 0.00522238i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 37982.7i | − | 0.684729i | −0.939567 | − | 0.342364i | \(-0.888772\pi\) | ||
0.939567 | − | 0.342364i | \(-0.111228\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −54719.7 | − | 22193.3i | −0.926683 | − | 0.375845i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −60200.5 | + | 60200.5i | −0.959190 | + | 0.959190i | −0.999199 | − | 0.0400092i | \(-0.987261\pi\) |
0.0400092 | + | 0.999199i | \(0.487261\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 21736.5 | − | 6416.33i | 0.326318 | − | 0.0963250i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 63874.0 | − | 52617.9i | 0.904745 | − | 0.745307i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −58847.5 | −0.787504 | −0.393752 | − | 0.919217i | \(-0.628823\pi\) | ||||
−0.393752 | + | 0.919217i | \(0.628823\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1188.11 | −0.0150401 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −57142.4 | + | 47072.5i | −0.685096 | + | 0.564365i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 104140. | + | 56670.9i | 1.18389 | + | 0.644245i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −46768.7 | + | 46768.7i | −0.504691 | + | 0.504691i | −0.912892 | − | 0.408201i | \(-0.866156\pi\) |
0.408201 | + | 0.912892i | \(0.366156\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −37967.2 | − | 7406.40i | −0.389333 | − | 0.0759485i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 99697.8i | − | 0.972483i | −0.873825 | − | 0.486241i | \(-0.838368\pi\) | ||
0.873825 | − | 0.486241i | \(-0.161632\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 61353.7 | + | 61353.7i | 0.569834 | + | 0.569834i | 0.932082 | − | 0.362248i | \(-0.117991\pi\) |
−0.362248 | + | 0.932082i | \(0.617991\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1742.31 | − | 1178.44i | −0.0154224 | − | 0.0104312i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 92648.6 | + | 92648.6i | 0.782311 | + | 0.782311i | 0.980220 | − | 0.197909i | \(-0.0634151\pi\) |
−0.197909 | + | 0.980220i | \(0.563415\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 151720.i | 1.22314i | 0.791189 | + | 0.611572i | \(0.209463\pi\) | ||||
−0.791189 | + | 0.611572i | \(0.790537\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 15987.3 | − | 165456.i | 0.123160 | − | 1.27460i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8322.98 | − | 8322.98i | 0.0613172 | − | 0.0613172i | −0.675783 | − | 0.737100i | \(-0.736194\pi\) |
0.737100 | + | 0.675783i | \(0.236194\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5337.89 | − | 18083.1i | −0.0376379 | − | 0.127505i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −99205.1 | + | 66818.3i | −0.669992 | + | 0.451264i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −978.596 | −0.00633484 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 135710. | 0.842652 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 153241. | + | 186023.i | 0.913299 | + | 1.10867i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 174192. | − | 13213.1i | 0.997135 | − | 0.0756362i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −109942. | + | 109942.i | −0.604857 | + | 0.604857i | −0.941597 | − | 0.336741i | \(-0.890675\pi\) |
0.336741 | + | 0.941597i | \(0.390675\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −235960. | − | 22799.9i | −1.24843 | − | 0.120631i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9892.58i | 0.0503653i | 0.999683 | + | 0.0251826i | \(0.00801673\pi\) | ||||
−0.999683 | + | 0.0251826i | \(0.991983\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3619.93 | − | 3619.93i | −0.0177448 | − | 0.0177448i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −211755. | − | 411.993i | −0.999998 | − | 0.00194561i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 184071. | + | 184071.i | 0.837883 | + | 0.837883i | 0.988580 | − | 0.150697i | \(-0.0481517\pi\) |
−0.150697 | + | 0.988580i | \(0.548152\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1426.02i | 0.00626021i | 0.999995 | + | 0.00313011i | \(0.000996345\pi\) | ||||
−0.999995 | + | 0.00313011i | \(0.999004\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 135884. | + | 13129.9i | 0.575599 | + | 0.0556179i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −55405.9 | + | 55405.9i | −0.226577 | + | 0.226577i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 141853. | − | 260673.i | 0.560296 | − | 1.02962i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −166524. | − | 202147.i | −0.635600 | − | 0.771569i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 202862. | 0.748574 | 0.374287 | − | 0.927313i | \(-0.377887\pi\) | ||||
0.374287 | + | 0.927313i | \(0.377887\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −83433.4 | −0.297781 | −0.148891 | − | 0.988854i | \(-0.547570\pi\) | ||||
−0.148891 | + | 0.988854i | \(0.547570\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −81711.2 | + | 55035.6i | −0.282198 | + | 0.190071i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −126903. | + | 233201.i | −0.424270 | + | 0.779653i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10332.3 | + | 10332.3i | −0.0334541 | + | 0.0334541i | −0.723636 | − | 0.690182i | \(-0.757531\pi\) |
0.690182 | + | 0.723636i | \(0.257531\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 35983.6 | − | 372400.i | 0.112879 | − | 1.16820i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 814.117i | 0.00247527i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −286026. | − | 286026.i | −0.843212 | − | 0.843212i | 0.146063 | − | 0.989275i | \(-0.453340\pi\) |
−0.989275 | + | 0.146063i | \(0.953340\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −136206. | + | 26295.1i | −0.389480 | + | 0.0751909i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −108045. | − | 108045.i | −0.299789 | − | 0.299789i | 0.541142 | − | 0.840931i | \(-0.317992\pi\) |
−0.840931 | + | 0.541142i | \(0.817992\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 129014.i | − | 0.347471i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −505841. | − | 98676.2i | −1.32289 | − | 0.258061i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 190692. | − | 190692.i | 0.484416 | − | 0.484416i | −0.422123 | − | 0.906539i | \(-0.638715\pi\) |
0.906539 | + | 0.422123i | \(0.138715\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7375.25 | − | 1582.21i | −0.0182046 | − | 0.00390544i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 515911. | − | 424995.i | 1.23777 | − | 1.01965i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 225167. | 0.525257 | 0.262628 | − | 0.964897i | \(-0.415411\pi\) | ||||
0.262628 | + | 0.964897i | \(0.415411\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 247482. | 0.561496 | 0.280748 | − | 0.959782i | \(-0.409418\pi\) | ||||
0.280748 | + | 0.959782i | \(0.409418\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 292357. | − | 240837.i | 0.645336 | − | 0.531612i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −168763. | − | 571715.i | −0.362533 | − | 1.22815i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −45635.6 | + | 45635.6i | −0.0954332 | + | 0.0954332i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8764.25 | + | 2605.64i | 0.0178468 | + | 0.00530592i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 787664.i | 1.56228i | 0.624359 | + | 0.781138i | \(0.285360\pi\) | ||||
−0.624359 | + | 0.781138i | \(0.714640\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −483197. | − | 483197.i | −0.933751 | − | 0.933751i | 0.0641873 | − | 0.997938i | \(-0.479554\pi\) |
−0.997938 | + | 0.0641873i | \(0.979554\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −240309. | + | 355292.i | −0.452567 | + | 0.669113i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −264653. | − | 264653.i | −0.485860 | − | 0.485860i | 0.421137 | − | 0.906997i | \(-0.361631\pi\) |
−0.906997 | + | 0.421137i | \(0.861631\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 609515.i | 1.09107i | 0.838089 | + | 0.545534i | \(0.183673\pi\) | ||||
−0.838089 | + | 0.545534i | \(0.816327\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −81395.9 | + | 842380.i | −0.142106 | + | 1.47068i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9061.04 | + | 9061.04i | −0.0154326 | + | 0.0154326i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 759170. | + | 413124.i | 1.26169 | + | 0.686587i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 45785.4 | + | 67977.5i | 0.0742679 | + | 0.110265i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −337622. | −0.534644 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 48108.3 | 0.0743899 | 0.0371950 | − | 0.999308i | \(-0.488158\pi\) | ||||
0.0371950 | + | 0.999308i | \(0.488158\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 722812. | + | 877438.i | 1.09163 | + | 1.32516i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −815335. | + | 240676.i | −1.20293 | + | 0.355089i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8106.11 | − | 8106.11i | 0.0116859 | − | 0.0116859i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.26158e6 | + | 121901.i | 1.77748 | + | 0.171750i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 199556.i | 0.274842i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −209536. | − | 209536.i | −0.282161 | − | 0.282161i | 0.551809 | − | 0.833970i | \(-0.313938\pi\) |
−0.833970 | + | 0.551809i | \(0.813938\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −704805. | + | 282667.i | −0.928138 | + | 0.372236i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −738208. | − | 738208.i | −0.950855 | − | 0.950855i | 0.0479930 | − | 0.998848i | \(-0.484717\pi\) |
−0.998848 | + | 0.0479930i | \(0.984717\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.03498e6i | 1.30419i | 0.758136 | + | 0.652096i | \(0.226110\pi\) | ||||
−0.758136 | + | 0.652096i | \(0.773890\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5962.04 | + | 576.089i | 0.00735132 | + | 0.000710329i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.02815e6 | − | 1.02815e6i | 1.24070 | − | 1.24070i | 0.280984 | − | 0.959712i | \(-0.409339\pi\) |
0.959712 | − | 0.280984i | \(-0.0906608\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 469533. | − | 138600.i | 0.554621 | − | 0.163717i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 376464. | + | 456999.i | 0.435365 | + | 0.528499i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 676145. | 0.765677 | 0.382838 | − | 0.923815i | \(-0.374947\pi\) | ||||
0.382838 | + | 0.923815i | \(0.374947\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 185935. | 0.206214 | 0.103107 | − | 0.994670i | \(-0.467122\pi\) | ||||
0.103107 | + | 0.994670i | \(0.467122\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 878341. | − | 275328.i | 0.954218 | − | 0.299113i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −824974. | − | 448933.i | −0.878062 | − | 0.477822i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −738178. | + | 738178.i | −0.769872 | + | 0.769872i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 127642. | − | 1.32099e6i | 0.130466 | − | 1.35021i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 559.689i | 0.000560741i | 1.00000 | 0.000280371i | \(8.92447e-5\pi\) | |||||
−1.00000 | 0.000280371i | \(0.999911\pi\) | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 37965.3 | + | 37965.3i | 0.0372894 | + | 0.0372894i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −197933. | + | 292640.i | −0.190619 | + | 0.281827i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −419945. | − | 419945.i | −0.396606 | − | 0.396606i | 0.480428 | − | 0.877034i | \(-0.340481\pi\) |
−0.877034 | + | 0.480428i | \(0.840481\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 25739.1i | 0.0238421i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −246996. | + | 1.26617e6i | −0.224434 | + | 1.15051i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.05942e6 | + | 1.05942e6i | −0.944449 | + | 0.944449i | −0.998536 | − | 0.0540873i | \(-0.982775\pi\) |
0.0540873 | + | 0.998536i | \(0.482775\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −379844. | − | 1.28679e6i | −0.332270 | − | 1.12562i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 708038. | − | 583265.i | 0.607825 | − | 0.500711i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −583920. | −0.492008 | −0.246004 | − | 0.969269i | \(-0.579118\pi\) | ||||
−0.246004 | + | 0.969269i | \(0.579118\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.33412e6 | 1.10350 | 0.551750 | − | 0.834010i | \(-0.313960\pi\) | ||||
0.551750 | + | 0.834010i | \(0.313960\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 14295.0 | − | 11775.9i | 0.0116085 | − | 0.00956284i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −417720. | + | 270151.i | −0.333084 | + | 0.215414i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −870629. | + | 870629.i | −0.681763 | + | 0.681763i | −0.960397 | − | 0.278634i | \(-0.910118\pi\) |
0.278634 | + | 0.960397i | \(0.410118\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 220966. | − | 1.13273e6i | 0.169947 | − | 0.871196i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.35673e6i | 1.02501i | 0.858684 | + | 0.512506i | \(0.171283\pi\) | ||||
−0.858684 | + | 0.512506i | \(0.828717\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.20786e6 | − | 1.20786e6i | −0.896504 | − | 0.896504i | 0.0986213 | − | 0.995125i | \(-0.468557\pi\) |
−0.995125 | + | 0.0986213i | \(0.968557\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.81468e6 | + | 350332.i | −1.32339 | + | 0.255487i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −26388.9 | − | 26388.9i | −0.0189111 | − | 0.0189111i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 1.25549e6i | − | 0.884238i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 99163.1 | − | 1.02626e6i | 0.0686463 | − | 0.710433i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.26013e6 | − | 1.26013e6i | 0.857527 | − | 0.857527i | −0.133519 | − | 0.991046i | \(-0.542628\pi\) |
0.991046 | + | 0.133519i | \(0.0426277\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.14574e6 | − | 2.10546e6i | 0.766536 | − | 1.40861i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 530220. | − | 287199.i | 0.348791 | − | 0.188926i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 166015. | 0.107391 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 36707.1 | 0.0233525 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 988150. | + | 1.19954e6i | 0.618325 | + | 0.750598i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 649273. | − | 1.19312e6i | 0.399648 | − | 0.734406i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −274503. | + | 274503.i | −0.166227 | + | 0.166227i | −0.785319 | − | 0.619092i | \(-0.787501\pi\) |
0.619092 | + | 0.785319i | \(0.287501\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.34630e6 | − | 130088.i | −0.802130 | − | 0.0775067i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 1.68608e6i | − | 0.988503i | −0.869319 | − | 0.494252i | \(-0.835442\pi\) | ||
0.869319 | − | 0.494252i | \(-0.164558\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.16841e6 | − | 1.16841e6i | −0.674116 | − | 0.674116i | 0.284546 | − | 0.958662i | \(-0.408157\pi\) |
−0.958662 | + | 0.284546i | \(0.908157\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 32643.1 | − | 3090.08i | 0.0185360 | − | 0.00175466i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.07096e6 | + | 2.07096e6i | 1.15751 | + | 1.15751i | 0.985010 | + | 0.172497i | \(0.0551836\pi\) |
0.172497 | + | 0.985010i | \(0.444816\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 845100.i | 0.464977i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.03301e6 | − | 196442.i | −1.10123 | − | 0.106407i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −608007. | + | 608007.i | −0.324267 | + | 0.324267i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −322646. | + | 1.50396e6i | −0.169441 | + | 0.789822i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.50377e6 | − | 1.82546e6i | −0.777700 | − | 0.944068i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −21138.8 | −0.0107669 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.19564e6 | 0.599833 | 0.299917 | − | 0.953965i | \(-0.403041\pi\) | ||||
0.299917 | + | 0.953965i | \(0.403041\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.44755e6 | + | 2.14918e6i | 0.715358 | + | 1.06209i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 859219. | + | 2.91076e6i | 0.418304 | + | 1.41708i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 303742. | − | 303742.i | 0.145690 | − | 0.145690i | −0.630499 | − | 0.776190i | \(-0.717150\pi\) |
0.776190 | + | 0.630499i | \(0.217150\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −17647.1 | + | 182633.i | −0.00834015 | + | 0.0863137i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 756036.i | − | 0.352092i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 57362.4 | + | 57362.4i | 0.0263264 | + | 0.0263264i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 243454. | + | 164665.i | 0.110121 | + | 0.0744823i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −315076. | − | 315076.i | −0.140473 | − | 0.140473i | 0.633373 | − | 0.773846i | \(-0.281670\pi\) |
−0.773846 | + | 0.633373i | \(0.781670\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.27223e6i | 1.87755i | 0.344531 | + | 0.938775i | \(0.388038\pi\) | ||||
−0.344531 | + | 0.938775i | \(0.611962\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 531344. | − | 1.78721e6i | 0.230201 | − | 0.774297i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.18140e6 | + | 2.18140e6i | −0.931747 | + | 0.931747i | −0.997815 | − | 0.0660681i | \(-0.978955\pi\) |
0.0660681 | + | 0.997815i | \(0.478955\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.58087e6 | + | 1.94863e6i | 1.50806 | + | 0.820651i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 11774.2 | − | 9699.31i | 0.00488947 | − | 0.00402782i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.07492e6 | 1.25921 | 0.629605 | − | 0.776915i | \(-0.283217\pi\) | ||||
0.629605 | + | 0.776915i | \(0.283217\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.02207e6 | −0.816635 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.63283e6 | + | 1.34508e6i | −0.650390 | + | 0.535775i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.35925e6 | − | 1.28680e6i | 1.71269 | − | 0.505565i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −668839. | + | 668839.i | −0.259213 | + | 0.259213i | −0.824734 | − | 0.565521i | \(-0.808675\pi\) |
0.565521 | + | 0.824734i | \(0.308675\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.68752e6 | − | 719338.i | −1.40984 | − | 0.275022i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 57932.5i | 0.0218518i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 179707. | + | 179707.i | 0.0668794 | + | 0.0668794i | 0.739755 | − | 0.672876i | \(-0.234941\pi\) |
−0.672876 | + | 0.739755i | \(0.734941\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.96488e6 | + | 1.88548e6i | −0.721535 | + | 0.692378i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.84773e6 | + | 1.84773e6i | 0.669553 | + | 0.669553i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.12353e6i | 0.759383i | 0.925113 | + | 0.379691i | \(0.123970\pi\) | ||||
−0.925113 | + | 0.379691i | \(0.876030\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 233108. | − | 2.41247e6i | 0.0822705 | − | 0.851431i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 865082. | − | 865082.i | 0.301342 | − | 0.301342i | −0.540197 | − | 0.841539i | \(-0.681650\pi\) |
0.841539 | + | 0.540197i | \(0.181650\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 20601.2 | − | 6081.22i | 0.00708339 | − | 0.00209093i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.06499e6 | − | 2.06438e6i | 1.04028 | − | 0.700669i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.57596e6 | −1.86829 | −0.934147 | − | 0.356888i | \(-0.883838\pi\) | ||||
−0.934147 | + | 0.356888i | \(0.883838\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 136740. | 0.0452328 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −98049.9 | − | 119025.i | −0.0320233 | − | 0.0388738i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.86504e6 | + | 1.01491e6i | 0.601443 | + | 0.327292i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 918981. | − | 918981.i | 0.292638 | − | 0.292638i | −0.545484 | − | 0.838121i | \(-0.683654\pi\) |
0.838121 | + | 0.545484i | \(0.183654\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 79432.9 | + | 7675.29i | 0.0249786 | + | 0.00241359i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 2.31260e6i | − | 0.718189i | −0.933301 | − | 0.359095i | \(-0.883086\pi\) | ||
0.933301 | − | 0.359095i | \(-0.116914\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.65300e6 | − | 1.65300e6i | −0.507003 | − | 0.507003i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.55187e6 | − | 2.09384e6i | 0.773073 | − | 0.634318i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.20031e6 | + | 1.20031e6i | 0.359177 | + | 0.359177i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 2.08308e6i | − | 0.615742i | −0.951428 | − | 0.307871i | \(-0.900384\pi\) | ||
0.951428 | − | 0.307871i | \(-0.0996164\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.03911e6 | − | 390283.i | −1.17945 | − | 0.113966i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −73186.0 | + | 73186.0i | −0.0211132 | + | 0.0211132i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.34740e6 | − | 4.56455e6i | −0.384039 | − | 1.30100i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14134.0 | − | 17157.5i | −0.00398037 | − | 0.00483186i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.14299e6 | 0.318059 | 0.159029 | − | 0.987274i | \(-0.449164\pi\) | ||||
0.159029 | + | 0.987274i | \(0.449164\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 560751. | 0.154193 | 0.0770965 | − | 0.997024i | \(-0.475435\pi\) | ||||
0.0770965 | + | 0.997024i | \(0.475435\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.76506e6 | + | 1.18883e6i | −0.479631 | + | 0.323050i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −265750. | + | 1.23875e6i | −0.0713676 | + | 0.332669i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −41473.2 | + | 41473.2i | −0.0110077 | + | 0.0110077i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 117476. | − | 1.21578e6i | 0.0308182 | − | 0.318943i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 6.08563e6i | − | 1.57802i | −0.614381 | − | 0.789009i | \(-0.710594\pi\) | ||
0.614381 | − | 0.789009i | \(-0.289406\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.86084e6 | − | 1.86084e6i | −0.476969 | − | 0.476969i | 0.427192 | − | 0.904161i | \(-0.359503\pi\) |
−0.904161 | + | 0.427192i | \(0.859503\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 876916. | + | 4.54232e6i | 0.222195 | + | 1.15094i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 505816. | + | 505816.i | 0.126703 | + | 0.126703i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 4.65060e6i | − | 1.15172i | −0.817547 | − | 0.575861i | \(-0.804667\pi\) | ||
0.817547 | − | 0.575861i | \(-0.195333\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.00715e6 | + | 781690.i | 0.981159 | + | 0.191398i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.02519e6 | + | 5.02519e6i | −1.21659 | + | 1.21659i | −0.247767 | + | 0.968820i | \(0.579697\pi\) |
−0.968820 | + | 0.247767i | \(0.920303\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.57242e6 | − | 2.88954e6i | 0.376418 | − | 0.691717i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.44078e6 | + | 2.01066e6i | −0.577777 | + | 0.475959i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.01321e6 | −0.705364 | −0.352682 | − | 0.935743i | \(-0.614730\pi\) | ||||
−0.352682 | + | 0.935743i | \(0.614730\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.46122e6 | −0.569783 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.00385e6 | − | 826947.i | 0.229839 | − | 0.189336i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 31746.6 | − | 58338.6i | 0.00718901 | − | 0.0132108i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.48634e6 | − | 1.48634e6i | 0.332911 | − | 0.332911i | −0.520780 | − | 0.853691i | \(-0.674359\pi\) |
0.853691 | + | 0.520780i | \(0.174359\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 437646. | − | 1.47205e6i | 0.0969597 | − | 0.326130i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.60249e6i | 1.22780i | 0.789383 | + | 0.613901i | \(0.210401\pi\) | ||||
−0.789383 | + | 0.613901i | \(0.789599\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.95717e6 | + | 2.95717e6i | 0.641096 | + | 0.641096i | 0.950825 | − | 0.309729i | \(-0.100238\pi\) |
−0.309729 | + | 0.950825i | \(0.600238\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −784499. | − | 4.06361e6i | −0.168252 | − | 0.871525i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.14460e6 | − | 4.14460e6i | −0.879408 | − | 0.879408i | 0.114065 | − | 0.993473i | \(-0.463613\pi\) |
−0.993473 | + | 0.114065i | \(0.963613\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 131045.i | − | 0.0275099i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 21907.5 | − | 226724.i | 0.00455030 | − | 0.0470919i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.71179e6 | − | 1.71179e6i | 0.351802 | − | 0.351802i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.56533e6 | + | 3.59925e6i | −1.13177 | + | 0.731944i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.25808e6 | + | 4.83727e6i | 0.655641 | + | 0.973430i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.43812e6 | −0.286388 | −0.143194 | − | 0.989695i | \(-0.545737\pi\) | ||||
−0.143194 | + | 0.989695i | \(0.545737\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.24874e6 | 1.03441 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8069.09 | − | 9795.25i | −0.00157383 | − | 0.00191050i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.04677e6 | − | 3.54612e6i | −0.202068 | − | 0.684540i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.84038e6 | + | 5.84038e6i | −1.11588 | + | 1.11588i | −0.123544 | + | 0.992339i | \(0.539426\pi\) |
−0.992339 | + | 0.123544i | \(0.960574\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.27633e6 | + | 606457.i | 1.18695 | + | 0.114691i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 8.77431e6i | − | 1.64251i | −0.570558 | − | 0.821257i | \(-0.693273\pi\) | ||
0.570558 | − | 0.821257i | \(-0.306727\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.52190e6 | + | 1.52190e6i | 0.282013 | + | 0.282013i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.37817e6 | − | 1.66637e6i | 0.252807 | − | 0.305674i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −124472. | − | 124472.i | −0.0226037 | − | 0.0226037i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.68446e6i | 0.302837i | 0.988470 | + | 0.151418i | \(0.0483841\pi\) | ||||
−0.988470 | + | 0.151418i | \(0.951616\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.37086e6 | + | 229087.i | 0.422000 | + | 0.0407762i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.23036e6 | − | 4.23036e6i | 0.745516 | − | 0.745516i | −0.228117 | − | 0.973634i | \(-0.573257\pi\) |
0.973634 | + | 0.228117i | \(0.0732570\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.89538e6 | + | 2.66396e6i | 0.854196 | + | 0.464835i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.27871e6 | + | 1.55226e6i | 0.220929 | + | 0.268191i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.80043e6 | −0.308023 | −0.154011 | − | 0.988069i | \(-0.549219\pi\) | ||||
−0.154011 | + | 0.988069i | \(0.549219\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −196257. | −0.0332486 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.06418e6 | − | 3.82638e6i | 1.18514 | − | 0.641940i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.65199e6 | + | 1.37321e6i | −0.772896 | + | 0.228149i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −985780. | + | 985780.i | −0.162201 | + | 0.162201i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −404323. | + | 4.18440e6i | −0.0658885 | + | 0.681891i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.93499e6i | 0.796512i | 0.917274 | + | 0.398256i | \(0.130384\pi\) | ||||
−0.917274 | + | 0.398256i | \(0.869616\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.22362e6 | + | 4.22362e6i | 0.675197 | + | 0.675197i | 0.958909 | − | 0.283712i | \(-0.0915660\pi\) |
−0.283712 | + | 0.958909i | \(0.591566\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 104419. | − | 54062.7i | 0.0165342 | − | 0.00856051i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.36151e6 | − | 1.36151e6i | −0.213547 | − | 0.213547i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.32259e6i | 0.982326i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.99499e6 | + | 1.02269e7i | −0.307046 | + | 1.57400i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.38123e6 | + | 5.38123e6i | −0.820471 | + | 0.820471i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.02485e6 | + | 2.07365e6i | −1.06109 | + | 0.313220i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.70915e6 | + | 2.23173e6i | −0.405413 | + | 0.333969i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.67456e6 | 0.396534 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.71467e6 | 0.545666 | 0.272833 | − | 0.962061i | \(-0.412039\pi\) | ||||
0.272833 | + | 0.962061i | \(0.412039\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.97764e6 | + | 2.45290e6i | −0.433383 | + | 0.357011i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.44980e6 | − | 4.05402e6i | −1.07437 | − | 0.584648i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.16600e6 | − | 6.16600e6i | 0.881121 | − | 0.881121i | −0.112528 | − | 0.993649i | \(-0.535895\pi\) |
0.993649 | + | 0.112528i | \(0.0358948\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.13052e6 | + | 5.79538e6i | −0.160084 | + | 0.820636i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.12593e7i | 1.57992i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −64828.9 | − | 64828.9i | −0.00901480 | − | 0.00901480i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.69705e6 | + | 5.20605e6i | 1.06070 | + | 0.717423i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.71742e6 | − | 2.71742e6i | −0.371123 | − | 0.371123i | 0.496763 | − | 0.867886i | \(-0.334522\pi\) |
−0.867886 | + | 0.496763i | \(0.834522\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 7.48533e6i | − | 1.01317i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 96760.5 | − | 1.00139e6i | 0.0129805 | − | 0.134337i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.53542e6 | − | 8.53542e6i | 1.13489 | − | 1.13489i | 0.145537 | − | 0.989353i | \(-0.453509\pi\) |
0.989353 | − | 0.145537i | \(-0.0464911\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 186284. | + | 631069.i | 0.0245501 | + | 0.0831679i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −131275. | + | 55516.1i | −0.0171484 | + | 0.00725206i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.03664e6 | 0.134229 | 0.0671144 | − | 0.997745i | \(-0.478621\pi\) | ||||
0.0671144 | + | 0.997745i | \(0.478621\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.40785e6 | −1.20754 | −0.603768 | − | 0.797160i | \(-0.706335\pi\) | ||||
−0.603768 | + | 0.797160i | \(0.706335\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.80690e6 | − | 9.47697e6i | −0.993327 | − | 1.20582i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.03055e6 | + | 221084.i | 0.129987 | + | 0.0278861i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.93464e6 | − | 2.93464e6i | 0.366958 | − | 0.366958i | −0.499409 | − | 0.866366i | \(-0.666449\pi\) |
0.866366 | + | 0.499409i | \(0.166449\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.06029e7 | + | 1.02452e6i | 1.31440 | + | 0.127005i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 205500.i | 0.0252564i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.70161e6 | + | 2.70161e6i | 0.329193 | + | 0.329193i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −630131. | − | 6.65660e6i | −0.0761275 | − | 0.804197i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.11826e6 | − | 6.11826e6i | −0.732880 | − | 0.732880i | 0.238309 | − | 0.971189i | \(-0.423407\pi\) |
−0.971189 | + | 0.238309i | \(0.923407\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 1.00727e7i | − | 1.19635i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.80733e6 | + | 561140.i | 0.683924 | + | 0.0660849i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.00015e6 | − | 3.00015e6i | 0.350353 | − | 0.350353i | −0.509888 | − | 0.860241i | \(-0.670313\pi\) |
0.860241 | + | 0.509888i | \(0.170313\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 26148.4 | − | 48051.2i | 0.00302798 | − | 0.00556431i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.04118e6 | − | 7.33353e6i | −0.693723 | − | 0.842126i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.34031e7 | 1.52630 | 0.763150 | − | 0.646222i | \(-0.223652\pi\) | ||||
0.763150 | + | 0.646222i | \(0.223652\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.33813e7 | −1.51116 | −0.755580 | − | 0.655056i | \(-0.772645\pi\) | ||||
−0.755580 | + | 0.655056i | \(0.772645\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.36988e6 | − | 1.09421e7i | −0.825405 | − | 1.22548i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.62621e6 | + | 6.66365e6i | −0.402777 | + | 0.740157i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.90305e6 | − | 5.90305e6i | 0.650286 | − | 0.650286i | −0.302776 | − | 0.953062i | \(-0.597913\pi\) |
0.953062 | + | 0.302776i | \(0.0979133\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 19212.0 | − | 198828.i | 0.00209908 | − | 0.0217238i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.31063e6i | 0.467130i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.34586e6 | − | 6.34586e6i | −0.682086 | − | 0.682086i | 0.278384 | − | 0.960470i | \(-0.410201\pi\) |
−0.960470 | + | 0.278384i | \(0.910201\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.32288e7 | + | 2.55388e6i | −1.41037 | + | 0.272278i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.47580e6 | + | 1.47580e6i | 0.156068 | + | 0.156068i | 0.780822 | − | 0.624754i | \(-0.214801\pi\) |
−0.624754 | + | 0.780822i | \(0.714801\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 5.76985e6i | − | 0.605254i | −0.953109 | − | 0.302627i | \(-0.902136\pi\) | ||
0.953109 | − | 0.302627i | \(-0.0978636\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.22463e6 | − | 364088.i | −0.127432 | − | 0.0378859i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −100441. | + | 100441.i | −0.0103679 | + | 0.0103679i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.00569e6 | + | 8.90628e6i | −0.410182 | + | 0.912003i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.06218e6 | − | 3.34633e6i | 0.412658 | − | 0.339938i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.32317e6 | 0.435688 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.11410e7 | 1.11392 | 0.556958 | − | 0.830541i | \(-0.311969\pi\) | ||||
0.556958 | + | 0.830541i | \(0.311969\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −578827. | + | 476824.i | −0.0574169 | + | 0.0472987i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.46069e6 | − | 8.33604e6i | −0.242172 | − | 0.820400i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.84767e6 | − | 5.84767e6i | 0.570997 | − | 0.570997i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.73934e7 | − | 3.39299e6i | −1.68512 | − | 0.328723i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.02277e7i | 1.94448i | 0.233996 | + | 0.972238i | \(0.424820\pi\) | ||||
−0.233996 | + | 0.972238i | \(0.575180\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.55327e6 | + | 1.55327e6i | 0.148156 | + | 0.148156i | 0.777294 | − | 0.629138i | \(-0.216592\pi\) |
−0.629138 | + | 0.777294i | \(0.716592\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.42445e6 | − | 1.09769e7i | 0.702692 | − | 1.03892i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.43585e6 | + | 6.43585e6i | 0.604429 | + | 0.604429i | 0.941485 | − | 0.337056i | \(-0.109431\pi\) |
−0.337056 | + | 0.941485i | \(0.609431\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.82588e6i | 0.636131i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −17187.3 | + | 177874.i | −0.00158948 | + | 0.0164498i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.13970e6 | − | 4.13970e6i | 0.379915 | − | 0.379915i | −0.491157 | − | 0.871071i | \(-0.663426\pi\) |
0.871071 | + | 0.491157i | \(0.163426\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −485747. | − | 264333.i | −0.0442392 | − | 0.0240740i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.63872e7 | + | 1.10374e7i | −1.48112 | + | 0.997592i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.36670e6 | −0.391687 | −0.195844 | − | 0.980635i | \(-0.562745\pi\) | ||||
−0.195844 | + | 0.980635i | \(0.562745\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.79540e7 | −1.59830 | −0.799151 | − | 0.601131i | \(-0.794717\pi\) | ||||
−0.799151 | + | 0.601131i | \(0.794717\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.97789e6 | − | 2.40100e6i | −0.174750 | − | 0.212133i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 274472. | − | 81020.7i | 0.0240682 | − | 0.00710464i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.26611e6 | − | 1.26611e6i | 0.110193 | − | 0.110193i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.59789e6 | + | 444277.i | 0.397186 | + | 0.0383785i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.86810e6i | 0.331659i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.66735e6 | + | 9.66735e6i | 0.822754 | + | 0.822754i | 0.986502 | − | 0.163748i | \(-0.0523585\pi\) |
−0.163748 | + | 0.986502i | \(0.552359\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.67839e6 | − | 1.03866e7i | 0.479696 | − | 0.877435i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.44751e6 | + | 8.44751e6i | 0.708365 | + | 0.708365i | 0.966191 | − | 0.257826i | \(-0.0830062\pi\) |
−0.257826 | + | 0.966191i | \(0.583006\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 159650.i | 0.0132890i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.61987e7 | + | 1.56521e6i | 1.33848 | + | 0.129332i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.17200e6 | − | 3.17200e6i | 0.260185 | − | 0.260185i | −0.564944 | − | 0.825129i | \(-0.691102\pi\) |
0.825129 | + | 0.564944i | \(0.191102\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.39567e7 | + | 4.11984e6i | −1.13647 | + | 0.335470i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.02581e7 | − | 1.24526e7i | −0.829232 | − | 1.00662i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.18136e7 | 0.948057 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.82167e7 | 1.45136 | 0.725678 | − | 0.688034i | \(-0.241526\pi\) | ||||
0.725678 | + | 0.688034i | \(0.241526\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −77443.7 | + | 52161.2i | −0.00612566 | + | 0.00412586i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −70020.7 | − | 38103.8i | −0.00549876 | − | 0.00299231i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.43230e6 | + | 4.43230e6i | −0.345579 | + | 0.345579i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.17997e6 | + | 2.25609e7i | −0.168755 | + | 1.74648i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1.46631e7i | − | 1.12702i | −0.826111 | − | 0.563508i | \(-0.809451\pi\) | ||
0.826111 | − | 0.563508i | \(-0.190549\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.59919e7 | + | 1.59919e7i | 1.22043 | + | 1.22043i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.27557e6 | + | 6.32135e6i | −0.323982 | + | 0.479002i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −170164. | − | 170164.i | −0.0128032 | − | 0.0128032i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 1.49044e7i | − | 1.11352i | −0.830673 | − | 0.556760i | \(-0.812044\pi\) | ||
0.830673 | − | 0.556760i | \(-0.187956\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.05905e6 | − | 1.76718e6i | −0.672061 | − | 0.131101i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.13267e6 | + | 1.13267e6i | −0.0834412 | + | 0.0834412i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.24009e6 | − | 4.20101e6i | −0.0907165 | − | 0.307319i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.13521e6 | + | 6.70159e6i | −0.590977 | + | 0.486833i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.69566e6 | 0.483027 | 0.241514 | − | 0.970397i | \(-0.422356\pi\) | ||||
0.241514 | + | 0.970397i | \(0.422356\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 209437. | 0.0150043 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.23712e6 | + | 1.84289e6i | −0.159164 | + | 0.131115i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.00926e6 | + | 1.39305e7i | 0.636567 | + | 0.984290i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.68120e7 | + | 1.68120e7i | −1.17974 | + | 1.17974i | −0.199924 | + | 0.979811i | \(0.564069\pi\) |
−0.979811 | + | 0.199924i | \(0.935931\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.83907e6 | + | 1.20183e7i | −0.546318 | + | 0.837578i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 6.16536e6i | − | 0.426742i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.28485e6 | + | 6.28485e6i | 0.432051 | + | 0.432051i | 0.889326 | − | 0.457274i | \(-0.151174\pi\) |
−0.457274 | + | 0.889326i | \(0.651174\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.43755e7 | − | 2.77525e6i | 0.981530 | − | 0.189489i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.11112e6 | − | 6.11112e6i | −0.414431 | − | 0.414431i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1.03783e7i | − | 0.699061i | −0.936925 | − | 0.349530i | \(-0.886341\pi\) | ||
0.936925 | − | 0.349530i | \(-0.113659\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.56515e6 | − | 1.61980e7i | 0.104715 | − | 1.08372i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.14751e6 | + | 3.14751e6i | −0.209168 | + | 0.209168i | −0.803914 | − | 0.594746i | \(-0.797253\pi\) |
0.594746 | + | 0.803914i | \(0.297253\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.42054e6 | + | 9.96096e6i | −0.357810 | + | 0.657523i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.15572e7 | + | 1.71590e7i | 0.757794 | + | 1.12510i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 316265. | 0.0205990 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.31733e7 | 0.852304 | 0.426152 | − | 0.904652i | \(-0.359869\pi\) | ||||
0.426152 | + | 0.904652i | \(0.359869\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5547.34 | − | 6734.04i | −0.000356531 | − | 0.000432801i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.22937e6 | − | 4.09676e6i | 0.142336 | − | 0.261561i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.69115e6 | − | 7.69115e6i | 0.487811 | − | 0.487811i | −0.419804 | − | 0.907615i | \(-0.637901\pi\) |
0.907615 | + | 0.419804i | \(0.137901\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −833081. | − | 80497.3i | −0.0524907 | − | 0.00507197i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 8.06267e6i | − | 0.504681i | −0.967638 | − | 0.252341i | \(-0.918800\pi\) | ||
0.967638 | − | 0.252341i | \(-0.0812003\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 258956. | + | 258956.i | 0.0161033 | + | 0.0161033i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −519014. | − | 5.48277e6i | −0.0320646 | − | 0.338724i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.49241e7 | + | 1.49241e7i | 0.916011 | + | 0.916011i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.04385e6i | 0.429531i | 0.976666 | + | 0.214765i | \(0.0688987\pi\) | ||||
−0.976666 | + | 0.214765i | \(0.931101\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.21494e6 | + | 890404.i | 0.558286 | + | 0.0539450i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.28966e7 | + | 1.28966e7i | −0.776295 | + | 0.776295i | −0.979199 | − | 0.202904i | \(-0.934962\pi\) |
0.202904 | + | 0.979199i | \(0.434962\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.05979e6 | − | 1.24624e7i | −0.482025 | − | 0.745329i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −255112. | − | 309687.i | −0.0151593 | − | 0.0184022i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.27911e7 | −1.93603 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.16091e7 | −0.681040 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.57779e6 | − | 1.76823e7i | −0.558292 | − | 1.03071i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −231256. | − | 783423.i | −0.0133943 | − | 0.0453756i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.29667e6 | − | 3.29667e6i | 0.189731 | − | 0.189731i | −0.605849 | − | 0.795580i | \(-0.707166\pi\) |
0.795580 | + | 0.605849i | \(0.207166\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.24627e6 | − | 2.32471e7i | 0.128461 | − | 1.32946i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 28411.3i | − | 0.00161454i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.45723e6 | + | 8.45723e6i | 0.477579 | + | 0.477579i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.73242e7 | + | 1.17175e7i | 0.972152 | + | 0.657534i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.05205e7 | − | 1.05205e7i | −0.586664 | − | 0.586664i | 0.350062 | − | 0.936726i | \(-0.386160\pi\) |
−0.936726 | + | 0.350062i | \(0.886160\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.55049e6i | 0.196753i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.73793e6 | + | 1.40354e7i | −0.150779 | + | 0.772935i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.15222e6 | + | 9.15222e6i | −0.500884 | + | 0.500884i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −39974.9 | − | 21753.5i | −0.00217419 | − | 0.00118315i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.02557e6 | − | 5.78750e6i | 0.379750 | − | 0.312829i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.87579e6 | −0.315642 | −0.157821 | − | 0.987468i | \(-0.550447\pi\) | ||||
−0.157821 | + | 0.987468i | \(0.550447\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.38892e7 | −1.80929 | −0.904646 | − | 0.426164i | \(-0.859865\pi\) | ||||
−0.904646 | + | 0.426164i | \(0.859865\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.60518e7 | + | 1.32231e7i | −0.851721 | + | 0.701627i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.16872e7 | − | 6.40179e6i | 1.14369 | − | 0.337604i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.28064e7 | − | 2.28064e7i | 1.19537 | − | 1.19537i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −55277.7 | + | 283369.i | −0.00287966 | + | 0.0147619i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 3.59758e7i | − | 1.86274i | −0.364072 | − | 0.931371i | \(-0.618614\pi\) | ||
0.364072 | − | 0.931371i | \(-0.381386\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.55143e7 | − | 1.55143e7i | −0.798424 | − | 0.798424i | 0.184423 | − | 0.982847i | \(-0.440958\pi\) |
−0.982847 | + | 0.184423i | \(0.940958\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.34831e6 | − | 7.39060e6i | 0.120122 | − | 0.378046i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.87490e6 | + | 2.87490e6i | 0.146170 | + | 0.146170i | 0.776405 | − | 0.630235i | \(-0.217041\pi\) |
−0.630235 | + | 0.776405i | \(0.717041\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 1.31575e7i | − | 0.664945i | −0.943113 | − | 0.332472i | \(-0.892117\pi\) | ||
0.943113 | − | 0.332472i | \(-0.107883\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.84598e6 | − | 1.91044e7i | 0.0927310 | − | 0.959689i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.81649e6 | − | 4.81649e6i | 0.240502 | − | 0.240502i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.19228e6 | − | 2.41826e6i | 0.406620 | − | 0.120029i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.56840e6 | + | 1.58188e7i | 0.422753 | + | 0.780477i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.80055e7 | −1.37353 | −0.686764 | − | 0.726880i | \(-0.740970\pi\) | ||||
−0.686764 | + | 0.726880i | \(0.740970\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.67209e6 | 0.374045 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.34472e7 | − | 1.63239e7i | −0.651724 | − | 0.791142i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.33485e6 | + | 3.44729e6i | 0.305207 | + | 0.166087i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 231630. | − | 231630.i | 0.0110939 | − | 0.0110939i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.65044e7 | + | 2.56102e6i | 1.26197 | + | 0.121939i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 3.59655e6i | − | 0.170240i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.35022e7 | − | 1.35022e7i | −0.635376 | − | 0.635376i | 0.314035 | − | 0.949411i | \(-0.398319\pi\) |
−0.949411 | + | 0.314035i | \(0.898319\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.83615e7 | − | 2.22012e7i | 0.858998 | − | 1.03863i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.61749e7 | − | 1.61749e7i | −0.752298 | − | 0.752298i | 0.222610 | − | 0.974908i | \(-0.428542\pi\) |
−0.974908 | + | 0.222610i | \(0.928542\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1.91209e6i | − | 0.0884149i | −0.999022 | − | 0.0442075i | \(-0.985924\pi\) | ||
0.999022 | − | 0.0442075i | \(-0.0140763\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 579056. | + | 55952.0i | 0.0266203 | + | 0.00257222i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.65774e6 | + | 4.65774e6i | −0.212887 | + | 0.212887i | −0.805493 | − | 0.592606i | \(-0.798099\pi\) |
0.592606 | + | 0.805493i | \(0.298099\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.26805e6 | + | 1.44588e7i | 0.193950 | + | 0.657039i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.24438e7 | + | 1.51058e7i | 0.562216 | + | 0.682487i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.04643e6 | −0.271612 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.67228e7 | −1.19354 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.97858e6 | + | 1.33305e7i | 0.398724 | + | 0.591985i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 274759. | − | 319864.i | 0.0121320 | − | 0.0141236i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.80145e7 | − | 2.80145e7i | 1.22994 | − | 1.22994i | 0.265952 | − | 0.963986i | \(-0.414314\pi\) |
0.963986 | − | 0.265952i | \(-0.0856862\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.67185e6 | + | 2.76514e7i | −0.116638 | + | 1.20710i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1.69086e7i | − | 0.733952i | −0.930230 | − | 0.366976i | \(-0.880393\pi\) | ||
0.930230 | − | 0.366976i | \(-0.119607\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.32751e6 | + | 6.32751e6i | 0.273106 | + | 0.273106i | 0.830349 | − | 0.557243i | \(-0.188141\pi\) |
−0.557243 | + | 0.830349i | \(0.688141\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.08285e6 | + | 3.66883e7i | 0.303984 | + | 1.57460i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.73038e6 | + | 7.73038e6i | 0.329907 | + | 0.329907i | 0.852551 | − | 0.522644i | \(-0.175054\pi\) |
−0.522644 | + | 0.852551i | \(0.675054\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 375296.i | 0.0159265i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.53292e6 | + | 8.71076e6i | −0.149087 | + | 0.367589i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.31336e7 | + | 1.31336e7i | −0.551133 | + | 0.551133i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.01653e6 | + | 1.10562e7i | −0.251066 | + | 0.461368i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.99745e6 | + | 1.64545e6i | −0.0828886 | + | 0.0682816i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.52130e7 | −1.04046 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.73039e6 | 0.399318 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −441651. | + | 363821.i | −0.0180244 | + | 0.0148480i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.61279e6 | + | 1.21519e7i | −0.268388 | + | 0.493199i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.25983e7 | + | 2.25983e7i | −0.912131 | + | 0.912131i | −0.996440 | − | 0.0843087i | \(-0.973132\pi\) |
0.0843087 | + | 0.996440i | \(0.473132\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.37784e7 | − | 4.63853e6i | −0.954491 | − | 0.186196i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33960.8i | 0.00135576i | 1.00000 | 0.000677880i | \(0.000215776\pi\) | |||||
−1.00000 | 0.000677880i | \(0.999784\pi\) | ||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.58324e6 | + | 9.58324e6i | 0.380483 | + | 0.380483i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.01373e6 | + | 2.07906e7i | 0.158487 | + | 0.820946i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16884.6 | + | 16884.6i | 0.000663084 | + | 0.000663084i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.29040e7i | 0.504007i | 0.967726 | + | 0.252004i | \(0.0810895\pi\) | ||||
−0.967726 | + | 0.252004i | \(0.918911\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 582026. | − | 6.02348e6i | 0.0226096 | − | 0.233991i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.53823e7 | + | 2.53823e7i | −0.980678 | + | 0.980678i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.25819e7 | + | 6.98979e6i | 1.25205 | + | 0.268602i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.74877e7 | − | 1.17786e7i | 0.668394 | − | 0.450188i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.22853e7 | 1.60750 | 0.803749 | − | 0.594969i | \(-0.202836\pi\) | ||||
0.803749 | + | 0.594969i | \(0.202836\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.56334e7 | 1.34736 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.67116e7 | + | 2.02865e7i | 0.628511 | + | 0.762963i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.02141e6 | − | 3.46020e6i | −0.0382094 | − | 0.129441i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.21532e7 | + | 2.21532e7i | −0.824305 | + | 0.824305i | −0.986722 | − | 0.162417i | \(-0.948071\pi\) |
0.162417 | + | 0.986722i | \(0.448071\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.56387e7 | + | 2.47737e6i | 0.948925 | + | 0.0916909i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 2.34896e7i | − | 0.864771i | −0.901689 | − | 0.432385i | \(-0.857672\pi\) | ||
0.901689 | − | 0.432385i | \(-0.142328\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.68734e6 | + | 3.68734e6i | 0.135031 | + | 0.135031i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −362126. | + | 360720.i | −0.0131911 | + | 0.0131399i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.36672e7 | − | 1.36672e7i | −0.495228 | − | 0.495228i | 0.414721 | − | 0.909949i | \(-0.363879\pi\) |
−0.909949 | + | 0.414721i | \(0.863879\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.00209e7i | 1.44252i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.54435e7 | − | 4.39103e6i | −1.62937 | − | 0.157440i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.45787e7 | − | 1.45787e7i | 0.519981 | − | 0.519981i | −0.397584 | − | 0.917566i | \(-0.630151\pi\) |
0.917566 | + | 0.397584i | \(0.130151\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.86760e7 | − | 2.10466e7i | −1.37225 | − | 0.746749i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.37617e6 | − | 1.01680e7i | −0.295642 | − | 0.358886i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 628344. | 0.0220623 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.07327e6 | −0.212136 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.64077e7 | − | 1.77865e7i | 0.917623 | − | 0.618053i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.66372e7 | − | 1.08148e7i | 1.26650 | − | 0.373854i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.59614e7 | + | 1.59614e7i | −0.548914 | + | 0.548914i | −0.926127 | − | 0.377213i | \(-0.876883\pi\) |
0.377213 | + | 0.926127i | \(0.376883\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.28915e6 | − | 1.33416e7i | 0.0441056 | − | 0.456456i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.08866e7i | 1.05129i | 0.850705 | + | 0.525644i | \(0.176175\pi\) | ||||
−0.850705 | + | 0.525644i | \(0.823825\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2433.93 | + | 2433.93i | 8.24188e−5 | + | 8.24188e-5i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.10245e7 | − | 2.12932e7i | −0.371404 | − | 0.717347i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.02775e6 | + | 2.02775e6i | 0.0679637 | + | 0.0679637i | 0.740272 | − | 0.672308i | \(-0.234697\pi\) |
−0.672308 | + | 0.740272i | \(0.734697\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.36786e6i | 0.312380i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.61860e7 | + | 7.05893e6i | 1.20052 | + | 0.234189i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.95587e7 | − | 3.95587e7i | 1.30574 | − | 1.30574i | 0.381286 | − | 0.924457i | \(-0.375481\pi\) |
0.924457 | − | 0.381286i | \(-0.124519\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.00666e7 | − | 5.92342e6i | 0.658998 | − | 0.194528i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 254337. | − | 209516.i | 0.00831028 | − | 0.00684581i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.12911e6 | −0.166744 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.23122e7 | 1.36862 | 0.684308 | − | 0.729193i | \(-0.260104\pi\) | ||||
0.684308 | + | 0.729193i | \(0.260104\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.43856e7 | + | 1.18505e7i | −0.462973 | + | 0.381386i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.99285e7 | − | 1.62864e7i | −0.958357 | − | 0.521517i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.76141e6 | + | 1.76141e6i | −0.0561208 | + | 0.0561208i | −0.734610 | − | 0.678489i | \(-0.762635\pi\) |
0.678489 | + | 0.734610i | \(0.262635\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.87181e7 | − | 1.15110e7i | −1.22744 | − | 0.364922i |
(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 | 60.6.i.a.53.3 | yes | 20 | |
3.2 | odd | 2 | inner | 60.6.i.a.53.8 | yes | 20 | |
5.2 | odd | 4 | inner | 60.6.i.a.17.8 | yes | 20 | |
5.3 | odd | 4 | 300.6.i.d.257.3 | 20 | |||
5.4 | even | 2 | 300.6.i.d.293.8 | 20 | |||
15.2 | even | 4 | inner | 60.6.i.a.17.3 | ✓ | 20 | |
15.8 | even | 4 | 300.6.i.d.257.8 | 20 | |||
15.14 | odd | 2 | 300.6.i.d.293.3 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.6.i.a.17.3 | ✓ | 20 | 15.2 | even | 4 | inner | |
60.6.i.a.17.8 | yes | 20 | 5.2 | odd | 4 | inner | |
60.6.i.a.53.3 | yes | 20 | 1.1 | even | 1 | trivial | |
60.6.i.a.53.8 | yes | 20 | 3.2 | odd | 2 | inner | |
300.6.i.d.257.3 | 20 | 5.3 | odd | 4 | |||
300.6.i.d.257.8 | 20 | 15.8 | even | 4 | |||
300.6.i.d.293.3 | 20 | 15.14 | odd | 2 | |||
300.6.i.d.293.8 | 20 | 5.4 | even | 2 |